LMFDB - Embedded newform 384.2.v.a.13.4

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			13.4
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30780 - 0.538203i) q^{2} +(0.290285 + 0.956940i) q^{3} +(1.42068 + 1.40772i) q^{4} +(0.403677 + 4.09860i) q^{5} +(0.135394 - 1.40772i) q^{6} +(2.40587 - 3.60064i) q^{7} +(-1.10032 - 2.60563i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})$	\(q+(-1.30780 - 0.538203i) q^{2} +(0.290285 + 0.956940i) q^{3} +(1.42068 + 1.40772i) q^{4} +(0.403677 + 4.09860i) q^{5} +(0.135394 - 1.40772i) q^{6} +(2.40587 - 3.60064i) q^{7} +(-1.10032 - 2.60563i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(1.67795 - 5.57741i) q^{10} +(3.69226 - 1.97355i) q^{11} +(-0.934705 + 1.76814i) q^{12} +(2.07273 + 0.204146i) q^{13} +(-5.08427 + 3.41406i) q^{14} +(-3.80494 + 1.57606i) q^{15} +(0.0366390 + 3.99983i) q^{16} +(2.08349 + 0.863012i) q^{17} +(1.38640 - 0.279075i) q^{18} +(-0.762517 + 0.625782i) q^{19} +(-5.19620 + 6.39105i) q^{20} +(4.14398 + 1.25706i) q^{21} +(-5.89090 + 0.593827i) q^{22} +(-1.23231 + 6.19525i) q^{23} +(2.17403 - 1.80931i) q^{24} +(-11.7317 + 2.33357i) q^{25} +(-2.60084 - 1.38253i) q^{26} +(-0.773010 - 0.634393i) q^{27} +(8.48666 - 1.72854i) q^{28} +(-2.11203 + 3.95134i) q^{29} +(5.82433 - 0.0133375i) q^{30} +(-0.316443 + 0.316443i) q^{31} +(2.10480 - 5.25070i) q^{32} +(2.96038 + 2.96038i) q^{33} +(-2.26032 - 2.24999i) q^{34} +(15.7288 + 8.40721i) q^{35} +(-1.96334 - 0.381193i) q^{36} +(5.08749 - 6.19913i) q^{37} +(1.33402 - 0.408008i) q^{38} +(0.406326 + 2.04274i) q^{39} +(10.2353 - 5.56160i) q^{40} +(-10.8379 - 2.15579i) q^{41} +(-4.74294 - 3.87429i) q^{42} +(-0.851862 + 2.80821i) q^{43} +(8.02371 + 2.39389i) q^{44} +(-2.61271 - 3.18359i) q^{45} +(4.94591 - 7.43890i) q^{46} +(1.75384 - 4.23416i) q^{47} +(-3.81697 + 1.19615i) q^{48} +(-4.49760 - 10.8582i) q^{49} +(16.5986 + 3.26217i) q^{50} +(-0.221044 + 2.24430i) q^{51} +(2.65730 + 3.20785i) q^{52} +(0.570397 + 1.06714i) q^{53} +(0.669510 + 1.24570i) q^{54} +(9.57929 + 14.3364i) q^{55} +(-12.0291 - 2.30695i) q^{56} +(-0.820183 - 0.548029i) q^{57} +(4.88874 - 4.03085i) q^{58} +(3.98990 - 0.392970i) q^{59} +(-7.62423 - 3.11723i) q^{60} +(-0.499604 + 0.151553i) q^{61} +(0.584155 - 0.243534i) q^{62} +4.33045i q^{63} +(-5.57860 + 5.73404i) q^{64} +8.57771i q^{65} +(-2.27830 - 5.46486i) q^{66} +(-2.49792 + 0.757735i) q^{67} +(1.74509 + 4.15904i) q^{68} +(-6.28620 + 0.619137i) q^{69} +(-16.0453 - 19.4602i) q^{70} +(-4.03542 - 2.69638i) q^{71} +(2.36249 + 1.55520i) q^{72} +(3.48671 + 5.21823i) q^{73} +(-9.98981 + 5.36911i) q^{74} +(-5.63861 - 10.5491i) q^{75} +(-1.96422 - 0.184379i) q^{76} +(1.77704 - 18.0426i) q^{77} +(0.568015 - 2.89018i) q^{78} +(0.944047 + 2.27913i) q^{79} +(-16.3789 + 1.76481i) q^{80} +(0.382683 - 0.923880i) q^{81} +(13.0135 + 8.65232i) q^{82} +(-10.3791 - 12.6469i) q^{83} +(4.11766 + 7.61945i) q^{84} +(-2.69608 + 8.88780i) q^{85} +(2.62545 - 3.21410i) q^{86} +(-4.39429 - 0.874078i) q^{87} +(-9.20500 - 7.44911i) q^{88} +(-3.30001 - 16.5903i) q^{89} +(1.70348 + 5.56967i) q^{90} +(5.72177 - 6.97200i) q^{91} +(-10.4719 + 7.06668i) q^{92} +(-0.394676 - 0.210959i) q^{93} +(-4.57251 + 4.59350i) q^{94} +(-2.87264 - 2.87264i) q^{95} +(5.63559 + 0.489976i) q^{96} +(3.83195 - 3.83195i) q^{97} +(0.0380614 + 16.6209i) q^{98} +(-1.97355 + 3.69226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.30780	−	0.538203i	−0.924753	−	0.380567i
$2$	−1.30780	−	0.538203i	−0.924753	−	0.380567i
$3$	0.290285	+	0.956940i	0.167596	+	0.552490i
$3$	0.290285	+	0.956940i	0.167596	+	0.552490i
$4$	1.42068	+	1.40772i	0.710338	+	0.703861i
$5$	0.403677	+	4.09860i	0.180530	+	1.83295i	0.478163	+	0.878271i	$0.341303\pi$
$5$	0.403677	+	4.09860i	0.180530	+	1.83295i	−0.297633	+	0.954680i	$0.596197\pi$
$6$	0.135394	−	1.40772i	0.0552743	−	0.574698i
$7$	2.40587	−	3.60064i	0.909333	−	1.36091i	−0.0231625	−	0.999732i	$-0.507374\pi$
$7$	2.40587	−	3.60064i	0.909333	−	1.36091i	0.932496	−	0.361181i	$-0.117626\pi$
$8$	−1.10032	−	2.60563i	−0.389021	−	0.921229i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	1.67795	−	5.57741i	0.530615	−	1.76373i
$11$	3.69226	−	1.97355i	1.11326	−	0.595048i	0.190986	−	0.981593i	$-0.438831\pi$
$11$	3.69226	−	1.97355i	1.11326	−	0.595048i	0.922271	+	0.386544i	$0.126331\pi$
$12$	−0.934705	+	1.76814i	−0.269826	+	0.510419i
$13$	2.07273	+	0.204146i	0.574872	+	0.0566200i	0.381276	−	0.924461i	$-0.375485\pi$
$13$	2.07273	+	0.204146i	0.574872	+	0.0566200i	0.193596	+	0.981081i	$0.437985\pi$
$14$	−5.08427	+	3.41406i	−1.35883	+	0.912447i
$15$	−3.80494	+	1.57606i	−0.982431	+	0.406936i
$16$	0.0366390	+	3.99983i	0.00915974	+	0.999958i
$17$	2.08349	+	0.863012i	0.505322	+	0.209311i	0.620756	−	0.784004i	$-0.286826\pi$
$17$	2.08349	+	0.863012i	0.505322	+	0.209311i	−0.115434	+	0.993315i	$0.536826\pi$
$18$	1.38640	−	0.279075i	0.326779	−	0.0657786i
$19$	−0.762517	+	0.625782i	−0.174933	+	0.143564i	−0.717786	−	0.696264i	$-0.754844\pi$
$19$	−0.762517	+	0.625782i	−0.174933	+	0.143564i	0.542852	+	0.839828i	$0.317344\pi$
$20$	−5.19620	+	6.39105i	−1.16191	+	1.42908i
$21$	4.14398	+	1.25706i	0.904291	+	0.274314i
$22$	−5.89090	+	0.593827i	−1.25594	+	0.126604i
$23$	−1.23231	+	6.19525i	−0.256955	+	1.29180i	0.609597	+	0.792711i	$0.291331\pi$
$23$	−1.23231	+	6.19525i	−0.256955	+	1.29180i	−0.866552	+	0.499087i	$0.833669\pi$
$24$	2.17403	−	1.80931i	0.443771	−	0.369324i
$25$	−11.7317	+	2.33357i	−2.34633	+	0.466715i
$26$	−2.60084	−	1.38253i	−0.510067	−	0.271137i
$27$	−0.773010	−	0.634393i	−0.148766	−	0.122089i
$28$	8.48666	−	1.72854i	1.60383	−	0.326664i
$29$	−2.11203	+	3.95134i	−0.392195	+	0.733745i	−0.998089	−	0.0618007i	$-0.980316\pi$
$29$	−2.11203	+	3.95134i	−0.392195	+	0.733745i	0.605894	+	0.795546i	$0.292816\pi$
$30$	5.82433	−	0.0133375i	1.06337	−	0.00243509i
$31$	−0.316443	+	0.316443i	−0.0568349	+	0.0568349i	−0.734953	−	0.678118i	$-0.762796\pi$
$31$	−0.316443	+	0.316443i	−0.0568349	+	0.0568349i	0.678118	+	0.734953i	$0.262796\pi$
$32$	2.10480	−	5.25070i	0.372080	−	0.928201i
$33$	2.96038	+	2.96038i	0.515336	+	0.515336i
$34$	−2.26032	−	2.24999i	−0.387641	−	0.385870i
$35$	15.7288	+	8.40721i	2.65865	+	1.42108i
$36$	−1.96334	−	0.381193i	−0.327223	−	0.0635321i
$37$	5.08749	−	6.19913i	0.836379	−	1.01913i	−0.163092	−	0.986611i	$-0.552147\pi$
$37$	5.08749	−	6.19913i	0.836379	−	1.01913i	0.999471	−	0.0325198i	$-0.0103532\pi$
$38$	1.33402	−	0.408008i	0.216406	−	0.0661876i
$39$	0.406326	+	2.04274i	0.0650643	+	0.327100i
$40$	10.2353	−	5.56160i	1.61834	−	0.879366i
$41$	−10.8379	−	2.15579i	−1.69259	−	0.336678i	−0.747696	−	0.664041i	$-0.768840\pi$
$41$	−10.8379	−	2.15579i	−1.69259	−	0.336678i	−0.944899	+	0.327363i	$0.893840\pi$
$42$	−4.74294	−	3.87429i	−0.731852	−	0.597816i
$43$	−0.851862	+	2.80821i	−0.129908	+	0.428248i	−0.997630	−	0.0688002i	$-0.978083\pi$
$43$	−0.851862	+	2.80821i	−0.129908	+	0.428248i	0.867723	+	0.497049i	$0.165583\pi$
$44$	8.02371	+	2.39389i	1.20962	+	0.360893i
$45$	−2.61271	−	3.18359i	−0.389479	−	0.474582i
$46$	4.94591	−	7.43890i	0.729235	−	1.09681i
$47$	1.75384	−	4.23416i	0.255825	−	0.617615i	−0.742830	−	0.669481i	$-0.766517\pi$
$47$	1.75384	−	4.23416i	0.255825	−	0.617615i	0.998654	+	0.0518656i	$0.0165167\pi$
$48$	−3.81697	+	1.19615i	−0.550931	+	0.172650i
$49$	−4.49760	−	10.8582i	−0.642514	−	1.55117i
$50$	16.5986	+	3.26217i	2.34740	+	0.461341i
$51$	−0.221044	+	2.24430i	−0.0309524	+	0.314265i
$52$	2.65730	+	3.20785i	0.368501	+	0.444849i
$53$	0.570397	+	1.06714i	0.0783500	+	0.146583i	0.918046	−	0.396475i	$-0.129767\pi$
$53$	0.570397	+	1.06714i	0.0783500	+	0.146583i	−0.839696	+	0.543057i	$0.817267\pi$
$54$	0.669510	+	1.24570i	0.0911088	+	0.169518i
$55$	9.57929	+	14.3364i	1.29167	+	1.93312i
$56$	−12.0291	−	2.30695i	−1.60746	−	0.308280i
$57$	−0.820183	−	0.548029i	−0.108636	−	0.0725881i
$58$	4.88874	−	4.03085i	0.641923	−	0.529277i
$59$	3.98990	−	0.392970i	0.519440	−	0.0511604i	0.165100	−	0.986277i	$-0.447205\pi$
$59$	3.98990	−	0.392970i	0.519440	−	0.0511604i	0.354340	+	0.935116i	$0.384705\pi$
$60$	−7.62423	−	3.11723i	−0.984284	−	0.402432i
$61$	−0.499604	+	0.151553i	−0.0639677	+	0.0194044i	−0.322106	−	0.946703i	$-0.604391\pi$
$61$	−0.499604	+	0.151553i	−0.0639677	+	0.0194044i	0.258139	+	0.966108i	$0.416891\pi$
$62$	0.584155	−	0.243534i	0.0741877	−	0.0309288i
$63$			4.33045i			0.545585i
$64$	−5.57860	+	5.73404i	−0.697325	+	0.716755i
$65$			8.57771i			1.06393i
$66$	−2.27830	−	5.46486i	−0.280439	−	0.672678i
$67$	−2.49792	+	0.757735i	−0.305169	+	0.0925721i	−0.439155	−	0.898411i	$-0.644722\pi$
$67$	−2.49792	+	0.757735i	−0.305169	+	0.0925721i	0.133986	+	0.990983i	$0.457222\pi$
$68$	1.74509	+	4.15904i	0.211623	+	0.504358i
$69$	−6.28620	+	0.619137i	−0.756770	+	0.0745353i
$70$	−16.0453	−	19.4602i	−1.91778	−	2.32594i
$71$	−4.03542	−	2.69638i	−0.478916	−	0.320001i	0.292574	−	0.956243i	$-0.405488\pi$
$71$	−4.03542	−	2.69638i	−0.478916	−	0.320001i	−0.771490	+	0.636241i	$0.780488\pi$
$72$	2.36249	+	1.55520i	0.278422	+	0.183282i
$73$	3.48671	+	5.21823i	0.408089	+	0.610748i	0.977406	−	0.211370i	$-0.0677924\pi$
$73$	3.48671	+	5.21823i	0.408089	+	0.610748i	−0.569317	+	0.822118i	$0.692792\pi$
$74$	−9.98981	+	5.36911i	−1.16129	+	0.624147i
$75$	−5.63861	−	10.5491i	−0.651091	−	1.21811i
$76$	−1.96422	−	0.184379i	−0.225311	−	0.0211497i
$77$	1.77704	−	18.0426i	0.202512	−	2.05614i
$78$	0.568015	−	2.89018i	0.0643151	−	0.327248i
$79$	0.944047	+	2.27913i	0.106214	+	0.256422i	0.968047	−	0.250769i	$-0.0806836\pi$
$79$	0.944047	+	2.27913i	0.106214	+	0.256422i	−0.861833	+	0.507192i	$0.830684\pi$
$80$	−16.3789	+	1.76481i	−1.83122	+	0.197312i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	13.0135	+	8.65232i	1.43710	+	0.955489i
$83$	−10.3791	−	12.6469i	−1.13925	−	1.38818i	−0.909896	−	0.414836i	$-0.863839\pi$
$83$	−10.3791	−	12.6469i	−1.13925	−	1.38818i	−0.229353	−	0.973343i	$-0.573661\pi$
$84$	4.11766	+	7.61945i	0.449274	+	0.831351i
$85$	−2.69608	+	8.88780i	−0.292431	+	0.964017i
$86$	2.62545	−	3.21410i	0.283110	−	0.346586i
$87$	−4.39429	−	0.874078i	−0.471117	−	0.0937110i
$88$	−9.20500	−	7.44911i	−0.981257	−	0.794078i
$89$	−3.30001	−	16.5903i	−0.349801	−	1.75857i	−0.609412	−	0.792854i	$-0.708595\pi$
$89$	−3.30001	−	16.5903i	−0.349801	−	1.75857i	0.259612	−	0.965713i	$-0.416405\pi$
$90$	1.70348	+	5.56967i	0.179562	+	0.587094i
$91$	5.72177	−	6.97200i	0.599805	−	0.730864i
$92$	−10.4719	+	7.06668i	−1.09177	+	0.736753i
$93$	−0.394676	−	0.210959i	−0.0409260	−	0.0218754i
$94$	−4.57251	+	4.59350i	−0.471618	+	0.473783i
$95$	−2.87264	−	2.87264i	−0.294727	−	0.294727i
$96$	5.63559	+	0.489976i	0.575180	+	0.0500079i
$97$	3.83195	−	3.83195i	0.389076	−	0.389076i	−0.485282	−	0.874358i	$-0.661283\pi$
$97$	3.83195	−	3.83195i	0.389076	−	0.389076i	0.874358	+	0.485282i	$0.161283\pi$
$98$	0.0380614	+	16.6209i	0.00384479	+	1.67897i
$99$	−1.97355	+	3.69226i	−0.198349	+	0.371086i
$100$	−19.9519	−	13.1997i	−1.99519	−	1.31997i
$101$	12.6817	+	10.4076i	1.26188	+	1.03560i	0.997463	+	0.0711881i	$0.0226791\pi$
$101$	12.6817	+	10.4076i	1.26188	+	1.03560i	0.264416	+	0.964409i	$0.414821\pi$
$102$	1.49697	−	2.81613i	0.148222	−	0.278838i
$103$	13.0794	−	2.60165i	1.28875	−	0.256348i	0.497298	−	0.867580i	$-0.334325\pi$
$103$	13.0794	−	2.60165i	1.28875	−	0.256348i	0.791452	+	0.611231i	$0.209325\pi$
$104$	−1.74873	−	5.62539i	−0.171478	−	0.551615i
$105$	−3.47937	+	17.4920i	−0.339552	+	1.70704i
$106$	−0.171628	−	1.70259i	−0.0166700	−	0.165370i
$107$	6.21814	+	1.88625i	0.601131	+	0.182351i	0.576160	−	0.817337i	$-0.304551\pi$
$107$	6.21814	+	1.88625i	0.601131	+	0.182351i	0.0249710	+	0.999688i	$0.492051\pi$
$108$	−0.205148	−	1.98945i	−0.0197404	−	0.191435i
$109$	−0.630276	+	0.517254i	−0.0603695	+	0.0495440i	−0.664094	−	0.747649i	$-0.731183\pi$
$109$	−0.630276	+	0.517254i	−0.0603695	+	0.0495440i	0.603725	+	0.797193i	$0.293683\pi$
$110$	−4.81188	−	23.9047i	−0.458795	−	2.27923i
$111$	7.40902	+	3.06892i	0.703233	+	0.291289i
$112$	14.4901	+	9.49115i	1.36919	+	0.896829i
$113$	−10.0526	+	4.16392i	−0.945668	+	0.391708i	−0.801601	−	0.597859i	$-0.796018\pi$
$113$	−10.0526	+	4.16392i	−0.945668	+	0.391708i	−0.144067	+	0.989568i	$0.546018\pi$
$114$	0.777683	+	1.15814i	0.0728367	+	0.108469i
$115$	−25.8893	−	2.54987i	−2.41419	−	0.237777i
$116$	−8.56290	+	2.64041i	−0.795045	+	0.245156i
$117$	−1.83683	+	0.981806i	−0.169815	+	0.0907680i
$118$	−5.42948	−	1.63345i	−0.499824	−	0.150371i
$119$	8.12001	−	5.42562i	0.744360	−	0.497365i
$120$	8.29326	+	8.18009i	0.757068	+	0.746737i
$121$	3.62658	−	5.42756i	0.329689	−	0.493414i
$122$	0.734947	+	0.0706870i	0.0665390	+	0.00639970i
$123$	−1.08311	−	10.9970i	−0.0976608	−	0.991567i
$124$	−0.895028	+	0.00409920i	−0.0803758	+	0.000368119i
$125$	−8.32261	−	27.4360i	−0.744397	−	2.45395i
$126$	2.33066	−	5.66336i	0.207632	−	0.504532i
$127$	19.2668			1.70966			0.854828	−	0.518912i	$-0.173663\pi$
$127$	19.2668			1.70966			0.854828	+	0.518912i	$0.173663\pi$
$128$	10.3818	−	4.49656i	0.917627	−	0.397443i
$129$	−2.93457			−0.258375
$130$	4.61655	−	11.2179i	0.404898	−	0.983877i
$131$	−5.36638	−	17.6906i	−0.468862	−	1.54563i	−0.798780	−	0.601623i	$-0.794521\pi$
$131$	−5.36638	−	17.6906i	−0.468862	−	1.54563i	0.329918	−	0.944010i	$-0.392979\pi$
$132$	0.0383486	+	8.37312i	0.00333782	+	0.728787i
$133$	0.418696	+	4.25110i	0.0363056	+	0.368617i
$134$	3.67459	+	0.353421i	0.317436	+	0.0305309i
$135$	2.28808	−	3.42435i	0.196927	−	0.294721i
$136$	−0.0438197	−	6.37840i	−0.00375751	−	0.546943i
$137$	−11.5968	+	7.74871i	−0.990778	+	0.662017i	−0.941586	−	0.336772i	$-0.890665\pi$
$137$	−11.5968	+	7.74871i	−0.990778	+	0.662017i	−0.0491922	+	0.998789i	$0.515665\pi$
$138$	8.55431	+	2.57354i	0.728191	+	0.219075i
$139$	−17.2078	+	9.19774i	−1.45954	+	0.780142i	−0.994459	−	0.105124i	$-0.966476\pi$
$139$	−17.2078	+	9.19774i	−1.45954	+	0.780142i	−0.465085	+	0.885266i	$0.653976\pi$
$140$	10.5105	+	34.0857i	0.888298	+	2.88076i
$141$	4.56095	+	0.449214i	0.384101	+	0.0378307i
$142$	3.82632	+	5.69819i	0.321097	+	0.478182i
$143$	8.05595	−	3.33688i	0.673672	−	0.279044i
$144$	−2.25265	−	3.30538i	−0.187721	−	0.275449i
$145$	−17.0475	−	7.06132i	−1.41572	−	0.586411i
$146$	−1.75145	−	8.70096i	−0.144951	−	0.720097i
$147$	9.08504	−	7.45590i	0.749321	−	0.614952i
$148$	15.9543	−	1.64518i	1.31144	−	0.135233i
$149$	1.24809	+	0.378604i	0.102247	+	0.0310164i	0.340994	−	0.940066i	$-0.389236\pi$
$149$	1.24809	+	0.378604i	0.102247	+	0.0310164i	−0.238746	+	0.971082i	$0.576736\pi$
$150$	1.69662	+	16.8308i	0.138528	+	1.37423i
$151$	1.78160	−	8.95670i	0.144984	−	0.728886i	−0.838069	−	0.545565i	$-0.816315\pi$
$151$	1.78160	−	8.95670i	0.144984	−	0.728886i	0.983053	−	0.183321i	$-0.0586848\pi$
$152$	2.46957	+	1.29828i	0.200308	+	0.105304i
$153$	−2.21183	+	0.439960i	−0.178816	+	0.0355686i
$154$	−12.0346	+	22.6397i	−0.969774	+	1.82436i
$155$	−1.42472	−	1.16923i	−0.114436	−	0.0939152i
$156$	−2.29835	+	3.47407i	−0.184015	+	0.278148i
$157$	−4.84861	+	9.07112i	−0.386961	+	0.723954i	−0.997693	−	0.0678836i	$-0.978375\pi$
$157$	−4.84861	+	9.07112i	−0.386961	+	0.723954i	0.610732	+	0.791837i	$0.290875\pi$
$158$	−0.00798910	−	3.48873i	−0.000635579	−	0.277549i
$159$	−0.855609	+	0.855609i	−0.0678542	+	0.0678542i
$160$	22.3702	+	6.50717i	1.76852	+	0.514437i
$161$	19.3421	+	19.3421i	1.52437	+	1.52437i
$162$	−0.997707	+	1.00229i	−0.0783873	+	0.0787471i
$163$	10.8632	+	5.80650i	0.850871	+	0.454800i	0.838357	−	0.545121i	$-0.183516\pi$
$163$	10.8632	+	5.80650i	0.850871	+	0.454800i	0.0125143	+	0.999922i	$0.496016\pi$
$164$	−12.3624	−	18.3194i	−0.965340	−	1.43051i
$165$	−10.9384	+	13.3284i	−0.851551	+	1.03762i
$166$	6.76711	+	22.1257i	0.525230	+	1.71728i
$167$	−1.16856	−	5.87472i	−0.0904255	−	0.454600i	−0.999296	−	0.0375210i	$-0.988054\pi$
$167$	−1.16856	−	5.87472i	−0.0904255	−	0.454600i	0.908870	−	0.417079i	$-0.136946\pi$
$168$	−1.28426	−	12.1808i	−0.0990828	−	0.939773i
$169$	−8.49567	−	1.68989i	−0.653513	−	0.129992i
$170$	8.30937	−	10.1724i	0.637300	−	0.780188i
$171$	0.286344	−	0.943950i	0.0218973	−	0.0721857i
$172$	−5.16340	+	2.79037i	−0.393706	+	0.212764i
$173$	9.66611	+	11.7782i	0.734901	+	0.895479i	0.997589	−	0.0694014i	$-0.0221089\pi$
$173$	9.66611	+	11.7782i	0.734901	+	0.895479i	−0.262688	+	0.964881i	$0.584609\pi$
$174$	5.27641	+	3.50813i	0.400004	+	0.265951i
$175$	−19.8225	+	47.8558i	−1.49844	+	3.61756i
$176$	8.02916	+	14.6961i	0.605221	+	1.10776i
$177$	1.53425	+	3.70402i	0.115322	+	0.278411i
$178$	−4.61318	+	23.4728i	−0.345773	+	1.75936i
$179$	1.49249	−	15.1535i	0.111554	−	1.13262i	−0.762565	−	0.646911i	$-0.776060\pi$
$179$	1.49249	−	15.1535i	0.111554	−	1.13262i	0.874119	−	0.485712i	$-0.161440\pi$
$180$	0.769803	−	8.20082i	0.0573778	−	0.611253i
$181$	−7.56082	−	14.1453i	−0.561991	−	1.05141i	−0.989105	−	0.147214i	$-0.952970\pi$
$181$	−7.56082	−	14.1453i	−0.561991	−	1.05141i	0.427113	−	0.904198i	$-0.359530\pi$
$182$	−11.2353	+	6.03850i	−0.832814	+	0.447604i
$183$	−0.290055	−	0.434097i	−0.0214414	−	0.0320894i
$184$	17.4984	−	3.60580i	1.29000	−	0.265823i
$185$	27.4615	+	18.3492i	2.01901	+	1.34906i
$186$	0.402618	+	0.488307i	0.0295214	+	0.0358044i
$187$	9.39600	−	0.925425i	0.687103	−	0.0676738i
$188$	8.45216	−	3.54644i	0.616437	−	0.258650i
$189$	−4.14398	+	1.25706i	−0.301430	+	0.0914379i
$190$	2.21077	+	5.30290i	0.160386	+	0.384713i
$191$		−	4.14071i		−	0.299611i	−0.988715	−	0.149806i	$-0.952135\pi$
$191$		−	4.14071i		−	0.299611i	0.988715	−	0.149806i	$-0.0478648\pi$
$192$	−7.10652	−	3.67388i	−0.512869	−	0.265140i
$193$		−	9.80073i		−	0.705472i	−0.935723	−	0.352736i	$-0.885251\pi$
$193$		−	9.80073i		−	0.705472i	0.935723	−	0.352736i	$-0.114749\pi$
$194$	−7.07379	+	2.94906i	−0.507869	+	0.211730i
$195$	−8.20836	+	2.48998i	−0.587813	+	0.178311i
$196$	8.89565	−	21.7573i	0.635404	−	1.55409i
$197$	12.3943	−	1.22074i	0.883060	−	0.0869738i	0.353688	−	0.935363i	$-0.384927\pi$
$197$	12.3943	−	1.22074i	0.883060	−	0.0869738i	0.529372	+	0.848390i	$0.322427\pi$
$198$	4.56819	−	3.76656i	0.324647	−	0.267678i
$199$	−6.90638	−	4.61470i	−0.489580	−	0.327127i	0.286157	−	0.958183i	$-0.407622\pi$
$199$	−6.90638	−	4.61470i	−0.489580	−	0.327127i	−0.775738	+	0.631055i	$0.782622\pi$
$200$	18.9890	+	28.0007i	1.34272	+	1.97995i
$201$	−1.45021	−	2.17040i	−0.102290	−	0.153088i
$202$	−10.9837	−	20.4364i	−0.772813	−	1.43790i
$203$	9.14606	+	17.1111i	0.641927	+	1.20096i
$204$	−3.47338	+	2.87725i	−0.243185	+	0.201448i
$205$	4.46072	−	45.2905i	0.311550	−	3.16322i
$206$	−18.5054	−	3.63692i	−1.28933	−	0.253396i
$207$	−2.41726	−	5.83579i	−0.168012	−	0.405616i
$208$	−0.740608	+	8.29805i	−0.0513519	+	0.575367i
$209$	−1.58040	+	3.81541i	−0.109318	+	0.263918i
$210$	13.9646	−	21.0034i	0.963646	−	1.44937i
$211$	2.46336	+	3.00162i	0.169585	+	0.206640i	0.850867	−	0.525381i	$-0.176077\pi$
$211$	2.46336	+	3.00162i	0.169585	+	0.206640i	−0.681282	+	0.732021i	$0.738577\pi$
$212$	−0.691884	+	2.31902i	−0.0475188	+	0.159271i
$213$	1.40885	−	4.64437i	0.0965331	−	0.318227i
$214$	−7.11689	−	5.81346i	−0.486501	−	0.397400i
$215$	−11.8536	−	2.35783i	−0.808411	−	0.160803i
$216$	−0.802436	+	2.71221i	−0.0545988	+	0.184543i
$217$	0.378077	+	1.90072i	0.0256655	+	0.129029i
$218$	1.10266	−	0.337248i	0.0746817	−	0.0228413i
$219$	−3.98140	+	4.85135i	−0.269038	+	0.327824i
$220$	−6.57263	+	33.8524i	−0.443126	+	2.28233i
$221$	4.14234	+	2.21413i	0.278644	+	0.148938i
$222$	−8.03781	−	8.00108i	−0.539462	−	0.536997i
$223$	−8.46313	−	8.46313i	−0.566733	−	0.566733i	0.364479	−	0.931212i	$-0.381247\pi$
$223$	−8.46313	−	8.46313i	−0.566733	−	0.566733i	−0.931212	+	0.364479i	$0.881247\pi$
$224$	−13.8420	−	20.2111i	−0.924855	−	1.35041i
$225$	8.45806	−	8.45806i	0.563871	−	0.563871i
$226$	15.3878	−	0.0352376i	1.02358	−	0.00234397i
$227$	0.915977	−	1.71367i	0.0607955	−	0.113740i	−0.849688	−	0.527286i	$-0.823210\pi$
$227$	0.915977	−	1.71367i	0.0607955	−	0.113740i	0.910483	+	0.413545i	$0.135710\pi$
$228$	−0.393742	−	1.93316i	−0.0260762	−	0.128027i
$229$	−0.391555	−	0.321341i	−0.0258747	−	0.0212348i	0.621367	−	0.783520i	$-0.286578\pi$
$229$	−0.391555	−	0.321341i	−0.0258747	−	0.0212348i	−0.647242	+	0.762285i	$0.724078\pi$
$230$	32.4857	+	17.2684i	2.14204	+	1.13865i
$231$	17.7815	−	3.53697i	1.16994	−	0.232715i
$232$	12.6196	+	1.15545i	0.828519	+	0.0758587i
$233$	1.07635	−	5.41118i	0.0705141	−	0.354498i	−0.929379	−	0.369127i	$-0.879657\pi$
$233$	1.07635	−	5.41118i	0.0705141	−	0.354498i	0.999893	+	0.0146290i	$0.00465672\pi$
$234$	2.93061	−	0.295418i	0.191580	−	0.0193121i
$235$	18.0621	+	5.47908i	1.17824	+	0.357416i
$236$	6.22154	+	5.05838i	0.404988	+	0.329272i
$237$	−1.90695	+	1.56499i	−0.123870	+	0.101657i
$238$	−13.5394	+	2.72540i	−0.877630	+	0.176662i
$239$	13.7038	+	5.67630i	0.886425	+	0.367169i	0.778985	−	0.627043i	$-0.215735\pi$
$239$	13.7038	+	5.67630i	0.886425	+	0.367169i	0.107440	+	0.994212i	$0.465735\pi$
$240$	−6.44337	−	15.1614i	−0.415918	−	0.978662i
$241$	2.87476	−	1.19077i	0.185180	−	0.0767040i	−0.288167	−	0.957580i	$-0.593046\pi$
$241$	2.87476	−	1.19077i	0.185180	−	0.0767040i	0.473347	+	0.880876i	$0.343046\pi$
$242$	−7.66396	+	5.14632i	−0.492658	+	0.330818i
$243$	0.995185	+	0.0980171i	0.0638411	+	0.00628780i
$244$	−0.923119	−	0.487995i	−0.0590967	−	0.0312407i
$245$	42.6878	−	22.8171i	2.72722	−	1.45773i
$246$	−4.50213	+	14.9648i	−0.287045	+	0.954122i
$247$	−1.70824	+	1.14141i	−0.108693	+	0.0726263i
$248$	1.17272	+	0.476345i	0.0744679	+	0.0302480i
$249$	9.08946	−	13.6033i	0.576021	−	0.862077i
$250$	−3.88181	+	40.3600i	−0.245507	+	2.55259i
$251$	−1.63488	−	16.5992i	−0.103192	−	1.04773i	−0.897739	−	0.440528i	$-0.854791\pi$
$251$	−1.63488	−	16.5992i	−0.103192	−	1.04773i	0.794547	−	0.607203i	$-0.207709\pi$
$252$	−6.09607	+	6.15217i	−0.384016	+	0.387550i
$253$	7.67663	+	25.3065i	0.482626	+	1.59100i
$254$	−25.1972	−	10.3695i	−1.58101	−	0.650638i
$255$	−9.28772			−0.581620
$256$	−15.9973	+	0.293099i	−0.999832	+	0.0183187i
$257$	−30.3890			−1.89561			−0.947807	−	0.318843i	$-0.896706\pi$
$257$	−30.3890			−1.89561			−0.947807	+	0.318843i	$0.896706\pi$
$258$	3.83783	+	1.57940i	0.238933	+	0.0983289i
$259$	−10.0810	−	33.2325i	−0.626401	−	2.06497i
$260$	−12.0750	+	12.1861i	−0.748861	+	0.755753i
$261$	−0.439154	−	4.45880i	−0.0271829	−	0.275993i
$262$	−2.50297	+	26.0239i	−0.154634	+	1.60776i
$263$	1.10778	−	1.65791i	0.0683086	−	0.102231i	−0.795743	−	0.605635i	$-0.792919\pi$
$263$	1.10778	−	1.65791i	0.0683086	−	0.102231i	0.864051	+	0.503404i	$0.167919\pi$
$264$	4.45629	−	10.9710i	0.274265	−	0.675218i
$265$	−4.14352	+	2.76861i	−0.254534	+	0.170074i
$266$	1.74038	−	5.78492i	0.106710	−	0.354696i
$267$	14.9180	−	7.97382i	0.912965	−	0.487990i
$268$	−4.61541	−	2.43988i	−0.281931	−	0.149039i
$269$	−8.45877	−	0.833116i	−0.515740	−	0.0507960i	−0.163201	−	0.986593i	$-0.552182\pi$
$269$	−8.45877	−	0.833116i	−0.515740	−	0.0507960i	−0.352540	+	0.935797i	$0.614682\pi$
$270$	−4.83534	+	3.24691i	−0.294270	+	0.197601i
$271$	−24.7448	+	10.2496i	−1.50314	+	0.622620i	−0.974128	−	0.225995i	$-0.927437\pi$
$271$	−24.7448	+	10.2496i	−1.50314	+	0.622620i	−0.529010	+	0.848615i	$0.677437\pi$
$272$	−3.37557	+	8.36525i	−0.204674	+	0.507218i
$273$	8.33273	+	3.45153i	0.504320	+	0.208896i
$274$	19.3366	−	3.89234i	1.16817	−	0.235145i
$275$	−38.7109	+	31.7692i	−2.33436	+	1.91576i
$276$	−9.80223	−	7.96963i	−0.590025	−	0.479715i
$277$	2.24883	+	0.682174i	0.135119	+	0.0409879i	0.357120	−	0.934059i	$-0.383759\pi$
$277$	2.24883	+	0.682174i	0.135119	+	0.0409879i	−0.222001	+	0.975046i	$0.571259\pi$
$278$	27.4546	−	2.76753i	1.64661	−	0.165986i
$279$	0.0873065	−	0.438920i	0.00522690	−	0.0262774i
$280$	4.59939	−	50.2340i	0.274866	−	3.00205i
$281$	−10.7779	+	2.14386i	−0.642956	+	0.127892i	−0.505791	−	0.862656i	$-0.668799\pi$
$281$	−10.7779	+	2.14386i	−0.642956	+	0.127892i	−0.137165	+	0.990548i	$0.543799\pi$
$282$	−5.72303	−	3.04220i	−0.340802	−	0.181160i
$283$	11.5343	+	9.46599i	0.685645	+	0.562695i	0.911416	−	0.411486i	$-0.134990\pi$
$283$	11.5343	+	9.46599i	0.685645	+	0.562695i	−0.225771	+	0.974180i	$0.572490\pi$
$284$	−1.93727	−	9.51143i	−0.114956	−	0.564399i
$285$	1.91506	−	3.58283i	0.113439	−	0.212229i
$286$	−12.3315	+	0.0282387i	−0.729175	+	0.00166979i
$287$	−33.8368	+	33.8368i	−1.99732	+	1.99732i
$288$	1.16705	+	5.53516i	0.0687690	+	0.326162i
$289$	−8.42465	−	8.42465i	−0.495568	−	0.495568i
$290$	18.4943	+	18.4098i	1.08602	+	1.08106i
$291$	4.77931	+	2.55459i	0.280168	+	0.149753i
$292$	−2.39233	+	12.3217i	−0.140001	+	0.721075i
$293$	4.47488	−	5.45265i	0.261425	−	0.318547i	−0.625711	−	0.780055i	$-0.715191\pi$
$293$	4.47488	−	5.45265i	0.261425	−	0.318547i	0.887136	+	0.461507i	$0.152691\pi$
$294$	−15.8942	+	4.86122i	−0.926968	+	0.283512i
$295$	3.22126	+	16.1944i	0.187549	+	0.942873i
$296$	−21.7505	−	6.43510i	−1.26422	−	0.374033i
$297$	−4.10616	−	0.816766i	−0.238264	−	0.0473936i
$298$	−1.42848	−	1.16686i	−0.0827498	−	0.0675945i
$299$	−3.81898	+	12.5895i	−0.220858	+	0.728070i
$300$	6.83956	−	22.9245i	0.394882	−	1.32354i
$301$	8.06189	+	9.82344i	0.464679	+	0.566214i
$302$	−7.15049	+	10.7547i	−0.411464	+	0.618863i
$303$	−6.27816	+	15.1568i	−0.360671	+	0.870737i
$304$	−2.53096	−	3.02701i	−0.145160	−	0.173611i
$305$	−0.822835	−	1.98650i	−0.0471154	−	0.113747i
$306$	3.12941	+	0.615032i	0.178897	+	0.0351591i
$307$	1.40187	−	14.2335i	0.0800092	−	0.812347i	−0.868519	−	0.495655i	$-0.834928\pi$
$307$	1.40187	−	14.2335i	0.0800092	−	0.812347i	0.948529	−	0.316692i	$-0.102572\pi$
$308$	27.9235	−	23.1311i	1.59109	−	1.31802i
$309$	6.28637	+	11.7610i	0.357619	+	0.669058i
$310$	1.23396	+	2.29591i	0.0700841	+	0.130399i
$311$	−16.5216	−	24.7263i	−0.936854	−	1.40210i	−0.915495	−	0.402329i	$-0.868201\pi$
$311$	−16.5216	−	24.7263i	−0.936854	−	1.40210i	−0.0213592	−	0.999772i	$-0.506799\pi$
$312$	4.87553	−	3.30640i	0.276023	−	0.187188i
$313$	13.2628	+	8.86194i	0.749660	+	0.500907i	0.870745	−	0.491736i	$-0.163637\pi$
$313$	13.2628	+	8.86194i	0.749660	+	0.500907i	−0.121085	+	0.992642i	$0.538637\pi$
$314$	11.2231	−	9.25366i	0.633357	−	0.522214i
$315$	−17.7488	+	1.74810i	−1.00003	+	0.0984945i
$316$	−1.86720	+	4.56686i	−0.105038	+	0.256906i
$317$	10.9069	−	3.30856i	0.612590	−	0.185827i	0.0312817	−	0.999511i	$-0.490041\pi$
$317$	10.9069	−	3.30856i	0.612590	−	0.185827i	0.581308	+	0.813684i	$0.302541\pi$
$318$	1.57946	−	0.658474i	0.0885715	−	0.0369254i
$319$			18.7576i			1.05022i
$320$	−25.7535	−	20.5498i	−1.43967	−	1.14877i
$321$			6.49794i			0.362680i
$322$	−14.8856	−	35.7055i	−0.829540	−	1.98979i
$323$	−2.12876	+	0.645751i	−0.118447	+	0.0359306i
$324$	1.84423	−	0.773821i	0.102457	−	0.0429901i
$325$	−24.7930	+	2.44189i	−1.37527	+	0.135452i
$326$	−11.0818	−	13.4403i	−0.613764	−	0.744391i
$327$	−0.677941	−	0.452986i	−0.0374902	−	0.0250502i
$328$	6.30794	+	30.6116i	0.348298	+	1.69024i
$329$	−11.0261	−	16.5018i	−0.607891	−	0.909773i
$330$	21.4786	−	11.5439i	1.18236	−	0.635469i
$331$	8.17211	+	15.2889i	0.449180	+	0.840356i	0.999984	+	0.00572126i	$0.00182114\pi$
$331$	8.17211	+	15.2889i	0.449180	+	0.840356i	−0.550804	+	0.834635i	$0.685679\pi$
$332$	3.05807	−	32.5780i	0.167833	−	1.78795i
$333$	−0.786045	+	7.98085i	−0.0430750	+	0.437348i
$334$	−1.63356	+	8.31188i	−0.0893843	+	0.454806i
$335$	−4.11401	−	9.93209i	−0.224772	−	0.542648i
$336$	−4.87621	+	16.6213i	−0.266019	+	0.906766i
$337$	7.75748	−	18.7282i	0.422577	−	1.02019i	−0.559008	−	0.829162i	$-0.688818\pi$
$337$	7.75748	−	18.7282i	0.422577	−	1.02019i	0.981585	−	0.191028i	$-0.0611821\pi$
$338$	10.2011	+	6.78244i	0.554868	+	0.368916i
$339$	−6.90273	−	8.41101i	−0.374905	−	0.456823i
$340$	−16.3418	+	8.83134i	−0.886259	+	0.478947i
$341$	−0.543873	+	1.79291i	−0.0294524	+	0.0970914i
$342$	−0.882517	+	1.08039i	−0.0477211	+	0.0584206i
$343$	−20.1863	−	4.01530i	−1.08996	−	0.216806i
$344$	8.25448	−	0.870292i	0.445052	−	0.0469230i
$345$	−5.07519	−	25.5147i	−0.273239	−	1.37367i
$346$	−6.30228	−	20.6058i	−0.338812	−	1.10778i
$347$	−3.26437	+	3.97764i	−0.175240	+	0.213531i	−0.853222	−	0.521548i	$-0.825355\pi$
$347$	−3.26437	+	3.97764i	−0.175240	+	0.213531i	0.677982	+	0.735079i	$0.262855\pi$
$348$	−5.01240	−	7.42771i	−0.268693	−	0.398167i
$349$	2.28216	+	1.21984i	0.122161	+	0.0652965i	0.531345	−	0.847155i	$-0.321687\pi$
$349$	2.28216	+	1.21984i	0.122161	+	0.0652965i	−0.409184	+	0.912452i	$0.634187\pi$
$350$	51.6799	−	51.9172i	2.76241	−	2.77509i
$351$	−1.47273	−	1.47273i	−0.0786087	−	0.0786087i
$352$	−2.59104	−	23.5409i	−0.138103	−	1.25473i
$353$	1.64386	−	1.64386i	0.0874940	−	0.0874940i	−0.662005	−	0.749499i	$-0.730294\pi$
$353$	1.64386	−	1.64386i	0.0874940	−	0.0874940i	0.749499	+	0.662005i	$0.230294\pi$
$354$	−0.0129838	−	5.66985i	−0.000690081	−	0.301349i
$355$	9.42238	−	17.6280i	0.500088	−	0.935599i
$356$	18.6663	−	28.2149i	0.989310	−	1.49539i
$357$	7.54911	+	6.19539i	0.399541	+	0.327895i
$358$	−10.1075	+	19.0144i	−0.534198	+	1.00494i
$359$	−4.96390	+	0.987381i	−0.261985	+	0.0521120i	−0.324335	−	0.945942i	$-0.605140\pi$
$359$	−4.96390	+	0.987381i	−0.261985	+	0.0521120i	0.0623502	+	0.998054i	$0.480140\pi$
$360$	−5.42045	+	10.3107i	−0.285683	+	0.543422i
$361$	−3.51689	+	17.6806i	−0.185099	+	0.930557i
$362$	2.27499	+	22.5685i	0.119571	+	1.18617i
$363$	6.24659	+	1.89488i	0.327861	+	0.0994555i
$364$	17.9434	−	1.85029i	0.940491	−	0.0969815i
$365$	−19.9800	+	16.3971i	−1.04580	+	0.858265i
$366$	0.145701	+	0.723820i	0.00761590	+	0.0378347i
$367$	8.05638	+	3.33706i	0.420539	+	0.174193i	0.582910	−	0.812537i	$-0.301914\pi$
$367$	8.05638	+	3.33706i	0.420539	+	0.174193i	−0.162371	+	0.986730i	$0.551914\pi$
$368$	−24.8251	−	4.70205i	−1.29410	−	0.245111i
$369$	10.2091	−	4.22874i	0.531463	−	0.220139i
$370$	−26.0385	−	38.7769i	−1.35368	−	2.01591i
$371$	5.21467	+	0.513601i	0.270732	+	0.0266648i
$372$	−0.263735	−	0.855298i	−0.0136740	−	0.0443451i
$373$	−26.1966	+	14.0024i	−1.35641	+	0.725015i	−0.979540	−	0.201252i	$-0.935499\pi$
$373$	−26.1966	+	14.0024i	−1.35641	+	0.725015i	−0.376869	+	0.926267i	$0.622999\pi$
$374$	−12.7861	−	3.84668i	−0.661156	−	0.198907i
$375$	23.8387	−	15.9285i	1.23102	−	0.822543i
$376$	−12.9624	+	0.0890520i	−0.668486	+	0.00459250i
$377$	−5.18433	+	7.75889i	−0.267006	+	0.399603i
$378$	6.09605	+	0.586317i	0.313547	+	0.0301569i
$379$	1.25509	+	12.7432i	0.0644698	+	0.654573i	0.972063	+	0.234721i	$0.0754178\pi$
$379$	1.25509	+	12.7432i	0.0644698	+	0.654573i	−0.907593	+	0.419851i	$0.862082\pi$
$380$	−0.0372121	−	8.12497i	−0.00190894	−	0.416802i
$381$	5.59287	+	18.4372i	0.286531	+	0.944567i
$382$	−2.22854	+	5.41522i	−0.114022	+	0.277067i
$383$	−3.92191			−0.200400			−0.100200	−	0.994967i	$-0.531948\pi$
$383$	−3.92191			−0.200400			−0.100200	+	0.994967i	$0.531948\pi$
$384$	7.31660	+	8.62945i	0.373374	+	0.440370i
$385$	74.6668			3.80537
$386$	−5.27478	+	12.8174i	−0.268479	+	0.652387i
$387$	−0.851862	−	2.80821i	−0.0433026	−	0.142749i
$388$	10.8383	−	0.0496390i	0.550231	−	0.00252004i
$389$	3.60284	+	36.5803i	0.182671	+	1.85469i	0.452474	+	0.891778i	$0.350542\pi$
$389$	3.60284	+	36.5803i	0.182671	+	1.85469i	−0.269802	+	0.962916i	$0.586958\pi$
$390$	12.0750	+	1.16137i	0.611441	+	0.0588082i
$391$	−7.91408	+	11.8443i	−0.400232	+	0.598990i
$392$	−23.3436	+	23.6665i	−1.17903	+	1.19534i
$393$	15.3710	−	10.2706i	0.775367	−	0.518083i
$394$	−16.8663	−	5.07419i	−0.849712	−	0.255634i
$395$	−8.96017	+	4.78931i	−0.450835	+	0.240976i
$396$	−8.00145	+	2.46729i	−0.402088	+	0.123986i
$397$	−31.7781	−	3.12987i	−1.59490	−	0.157084i	−0.738809	−	0.673915i	$-0.764612\pi$
$397$	−31.7781	−	3.12987i	−1.59490	−	0.157084i	−0.856087	+	0.516831i	$0.827112\pi$
$398$	6.54852	+	9.75213i	0.328247	+	0.488830i
$399$	−3.94650	+	1.63470i	−0.197572	+	0.0818371i
$400$	−9.76374	−	46.8392i	−0.488187	−	2.34196i
$401$	26.9242	+	11.1524i	1.34453	+	0.556922i	0.934764	−	0.355269i	$-0.115611\pi$
$401$	26.9242	+	11.1524i	1.34453	+	0.556922i	0.409765	+	0.912191i	$0.365611\pi$
$402$	0.728474	+	3.61895i	0.0363330	+	0.180497i
$403$	−0.720502	+	0.591301i	−0.0358908	+	0.0294548i
$404$	3.36558	+	32.6382i	0.167444	+	1.62381i
$405$	3.94110	+	1.19552i	0.195835	+	0.0594058i
$406$	−2.75198	−	27.3003i	−0.136578	−	1.35489i
$407$	6.55003	−	32.9292i	0.324673	−	1.63224i
$408$	6.09103	−	1.89348i	0.301551	−	0.0937415i
$409$	20.5939	−	4.09637i	1.01830	−	0.202553i	0.342407	−	0.939552i	$-0.388758\pi$
$409$	20.5939	−	4.09637i	1.01830	−	0.202553i	0.675894	+	0.736999i	$0.263758\pi$
$410$	−30.2092	+	56.8301i	−1.49193	+	2.80664i
$411$	−10.7814	−	8.84808i	−0.531808	−	0.436444i
$412$	22.2440	+	14.7160i	1.09588	+	0.725007i
$413$	8.18422	−	15.3116i	0.402719	−	0.753435i
$414$	0.0204564	+	8.93302i	0.00100538	+	0.439034i
$415$	47.6449	−	47.6449i	2.33880	−	2.33880i
$416$	5.43460	−	10.4536i	0.266453	−	0.512529i
$417$	−13.7968	−	13.7968i	−0.675634	−	0.675634i
$418$	4.12031	−	4.13922i	0.201531	−	0.202456i
$419$	−6.77057	−	3.61894i	−0.330764	−	0.176797i	0.297652	−	0.954674i	$-0.403796\pi$
$419$	−6.77057	−	3.61894i	−0.330764	−	0.176797i	−0.628416	+	0.777877i	$0.716296\pi$
$420$	−29.5669	+	19.9525i	−1.44272	+	0.973580i
$421$	−3.49466	+	4.25826i	−0.170319	+	0.207535i	−0.851174	−	0.524884i	$-0.824109\pi$
$421$	−3.49466	+	4.25826i	−0.170319	+	0.207535i	0.680854	+	0.732419i	$0.261609\pi$
$422$	−1.60611	−	5.25130i	−0.0781840	−	0.255629i
$423$	0.894102	+	4.49496i	0.0434727	+	0.218552i
$424$	2.15295	−	2.66043i	0.104556	−	0.129202i
$425$	−26.4568	−	5.26258i	−1.28334	−	0.255273i
$426$	−4.34211	+	5.31565i	−0.210376	+	0.257544i
$427$	−0.656293	+	2.16351i	−0.0317603	+	0.104700i
$428$	6.17865	+	11.4332i	0.298656	+	0.552643i
$429$	5.53171	+	6.74041i	0.267074	+	0.325430i
$430$	14.2332	+	9.46322i	0.686384	+	0.456357i
$431$	−4.96123	+	11.9775i	−0.238974	+	0.576935i	−0.997177	−	0.0750838i	$-0.976078\pi$
$431$	−4.96123	+	11.9775i	−0.238974	+	0.576935i	0.758203	+	0.652019i	$0.226078\pi$
$432$	2.50914	−	3.11516i	0.120721	−	0.149878i
$433$	7.76377	+	18.7434i	0.373103	+	0.900750i	0.993221	+	0.116241i	$0.0370846\pi$
$433$	7.76377	+	18.7434i	0.373103	+	0.900750i	−0.620118	+	0.784508i	$0.712915\pi$
$434$	0.528524	−	2.68924i	0.0253700	−	0.129088i
$435$	1.80863	−	18.3633i	0.0867169	−	0.880452i
$436$	−1.62357	−	0.152403i	−0.0777548	−	0.00729878i
$437$	−2.93721	−	5.49514i	−0.140506	−	0.262868i
$438$	7.81788	−	4.20179i	0.373553	−	0.200769i
$439$	−0.913309	−	1.36686i	−0.0435898	−	0.0652368i	0.809035	−	0.587761i	$-0.199990\pi$
$439$	−0.913309	−	1.36686i	−0.0435898	−	0.0652368i	−0.852624	+	0.522524i	$0.824990\pi$
$440$	26.8151	−	40.7347i	1.27836	−	1.94195i
$441$	9.77210	+	6.52951i	0.465338	+	0.310929i
$442$	−4.22570	−	5.12505i	−0.200996	−	0.243774i
$443$	30.0403	−	2.95871i	1.42726	−	0.140572i	0.645311	−	0.763920i	$-0.276728\pi$
$443$	30.0403	−	2.95871i	1.42726	−	0.140572i	0.781945	+	0.623347i	$0.214228\pi$
$444$	6.20563	+	14.7898i	0.294506	+	0.701892i
$445$	66.6649	−	20.2226i	3.16022	−	0.958641i
$446$	6.51319	+	15.6229i	0.308408	+	0.739768i
$447$			1.30425i			0.0616889i
$448$	7.22483	+	33.8819i	0.341341	+	1.60077i
$449$		−	5.66430i		−	0.267315i	−0.991028	−	0.133657i	$-0.957328\pi$
$449$		−	5.66430i		−	0.267315i	0.991028	−	0.133657i	$-0.0426722\pi$
$450$	−15.6136	+	6.50929i	−0.736032	+	0.306851i
$451$	−44.2709	+	13.4294i	−2.08463	+	0.632367i
$452$	−20.1431	−	8.23567i	−0.947452	−	0.387373i
$453$	9.08819	−	0.895109i	0.427001	−	0.0420559i
$454$	−2.12022	+	1.74816i	−0.0995067	+	0.0820451i
$455$	30.8852	+	20.6368i	1.44792	+	0.967470i
$456$	−0.525497	+	2.74010i	−0.0246086	+	0.128317i
$457$	−9.06354	−	13.5645i	−0.423975	−	0.634523i	0.556574	−	0.830798i	$-0.312115\pi$
$457$	−9.06354	−	13.5645i	−0.423975	−	0.634523i	−0.980549	+	0.196275i	$0.937115\pi$
$458$	0.339129	+	0.630985i	0.0158464	+	0.0294840i
$459$	−1.06307	−	1.98887i	−0.0496201	−	0.0928326i
$460$	−33.1908	−	40.0675i	−1.54753	−	1.86816i
$461$	−2.99436	+	30.4022i	−0.139461	+	1.41597i	0.629660	+	0.776871i	$0.283194\pi$
$461$	−2.99436	+	30.4022i	−0.139461	+	1.41597i	−0.769121	+	0.639103i	$0.779306\pi$
$462$	−25.1583	−	4.94443i	−1.17047	−	0.230036i
$463$	−5.80437	−	14.0130i	−0.269752	−	0.651239i	0.729719	−	0.683747i	$-0.239651\pi$
$463$	−5.80437	−	14.0130i	−0.269752	−	0.651239i	−0.999471	+	0.0325077i	$0.989651\pi$
$464$	−15.8821	−	8.30301i	−0.737307	−	0.385457i
$465$	0.705314	−	1.70278i	0.0327082	−	0.0789645i
$466$	−4.31996	+	6.49744i	−0.200118	+	0.300988i
$467$	7.81987	+	9.52854i	0.361861	+	0.440928i	0.921836	−	0.387581i	$-0.126689\pi$
$467$	7.81987	+	9.52854i	0.361861	+	0.440928i	−0.559975	+	0.828510i	$0.689189\pi$
$468$	−3.99165	−	1.19092i	−0.184514	−	0.0550502i
$469$	−3.28133	+	10.8171i	−0.151518	+	0.499488i
$470$	−20.6727	−	16.8866i	−0.953563	−	0.778921i
$471$	−10.0880	−	2.00663i	−0.464830	−	0.0924605i
$472$	−5.41409	−	9.96379i	−0.249204	−	0.458621i
$473$	2.39686	+	12.0498i	0.110208	+	0.554052i
$474$	3.33619	−	1.02037i	0.153236	−	0.0468672i
$475$	7.48529	−	9.12085i	0.343449	−	0.418493i
$476$	19.1737	+	3.72267i	0.878823	+	0.170628i
$477$	−1.06714	−	0.570397i	−0.0488609	−	0.0261167i
$478$	−14.8668	−	14.7989i	−0.679992	−	0.676885i
$479$	10.4293	+	10.4293i	0.476528	+	0.476528i	0.904019	−	0.427491i	$-0.140603\pi$
$479$	10.4293	+	10.4293i	0.476528	+	0.476528i	−0.427491	+	0.904019i	$0.640603\pi$
$480$	0.266745	+	23.2959i	0.0121752	+	1.06331i
$481$	11.8105	−	11.8105i	0.538514	−	0.538514i
$482$	−4.40049	+	0.0100770i	−0.200437	+	0.000458994i
$483$	−12.8945	+	24.1239i	−0.586720	+	1.09768i
$484$	12.7927	−	2.60559i	0.581486	−	0.118436i
$485$	17.2525	+	14.1588i	0.783397	+	0.642917i
$486$	−1.24875	−	0.663798i	−0.0566444	−	0.0301105i
$487$	−24.6840	+	4.90996i	−1.11854	+	0.222492i	−0.719535	−	0.694456i	$-0.755645\pi$
$487$	−24.6840	+	4.90996i	−1.11854	+	0.222492i	−0.399006	+	0.916948i	$0.630645\pi$
$488$	0.944614	+	1.13502i	0.0427607	+	0.0513802i
$489$	−2.40305	+	12.0810i	−0.108670	+	0.546320i
$490$	−68.1072	+	6.86549i	−3.07677	+	0.310151i
$491$	25.5693	+	7.75636i	1.15393	+	0.350040i	0.808552	−	0.588425i	$-0.200252\pi$
$491$	25.5693	+	7.75636i	1.15393	+	0.350040i	0.345375	+	0.938465i	$0.387752\pi$
$492$	13.9420	−	17.1479i	0.628553	−	0.773087i
$493$	−7.81046	+	6.40988i	−0.351766	+	0.288687i
$494$	2.84835	−	0.573356i	0.128153	−	0.0257965i
$495$	−15.9298	−	6.59833i	−0.715990	−	0.296573i
$496$	−1.27731	−	1.25413i	−0.0573531	−	0.0563119i
$497$	−19.4174	+	8.04294i	−0.870988	+	0.360775i
$498$	−19.2085	+	12.8985i	−0.860755	+	0.577994i
$499$	−2.51403	−	0.247610i	−0.112543	−	0.0110846i	0.0415886	−	0.999135i	$-0.486758\pi$
$499$	−2.51403	−	0.247610i	−0.112543	−	0.0110846i	−0.154132	+	0.988050i	$0.549258\pi$
$500$	26.7985	−	50.6935i	1.19846	−	2.26708i
$501$	5.28255	−	2.82358i	0.236007	−	0.126148i
$502$	−6.79563	+	22.5883i	−0.303304	+	1.00816i
$503$	21.5818	−	14.4205i	0.962285	−	0.642978i	0.0280386	−	0.999607i	$-0.491074\pi$
$503$	21.5818	−	14.4205i	0.962285	−	0.642978i	0.934246	+	0.356629i	$0.116074\pi$
$504$	11.2835	−	4.76487i	0.502609	−	0.212244i
$505$	−37.5374	+	56.1787i	−1.67039	+	2.49992i
$506$	3.58052	−	37.2274i	0.159173	−	1.65496i
$507$	−0.849036	−	8.62040i	−0.0377070	−	0.382846i
$508$	27.3719	+	27.1224i	1.21443	+	1.20336i
$509$	−6.41845	−	21.1588i	−0.284493	−	0.937846i	−0.976420	−	0.215879i	$-0.930738\pi$
$509$	−6.41845	−	21.1588i	−0.284493	−	0.937846i	0.691927	−	0.721967i	$-0.256762\pi$
$510$	12.1465	+	4.99868i	0.537855	+	0.221345i
$511$	27.1775			1.20226
$512$	21.0790	+	8.22648i	0.931570	+	0.363563i
$513$	0.986425			0.0435517
$514$	39.7427	+	16.3555i	1.75298	+	0.721408i
$515$	15.9430	+	52.5570i	0.702532	+	2.31594i
$516$	−4.16908	−	4.13106i	−0.183533	−	0.181860i
$517$	−1.88068	−	19.0949i	−0.0827123	−	0.839792i
$518$	−4.70194	+	48.8871i	−0.206592	+	2.14797i
$519$	−8.46510	+	12.6689i	−0.371577	+	0.556104i
$520$	22.3503	−	9.43821i	0.980126	−	0.413893i
$521$	−26.5985	+	17.7725i	−1.16530	+	0.778629i	−0.978999	−	0.203863i	$-0.934650\pi$
$521$	−26.5985	+	17.7725i	−1.16530	+	0.778629i	−0.186302	+	0.982493i	$0.559650\pi$
$522$	−1.82541	+	6.06757i	−0.0798962	+	0.265570i
$523$	26.8265	−	14.3391i	1.17304	−	0.627005i	0.234483	−	0.972120i	$-0.424660\pi$
$523$	26.8265	−	14.3391i	1.17304	−	0.627005i	0.938560	+	0.345116i	$0.112160\pi$
$524$	17.2795	−	32.6869i	0.754859	−	1.42794i
$525$	−51.5493	−	5.07716i	−2.24979	−	0.221585i
$526$	−2.34104	+	1.57200i	−0.102074	+	0.0685425i
$527$	−0.932402	+	0.386214i	−0.0406161	+	0.0168237i
$528$	−11.7325	+	11.9495i	−0.510594	+	0.520034i
$529$	−15.6132	−	6.46722i	−0.678837	−	0.281183i
$530$	6.90896	−	1.39073i	0.300106	−	0.0604095i
$531$	−3.09915	+	2.54341i	−0.134492	+	0.110375i
$532$	−5.38953	+	6.62884i	−0.233666	+	0.287397i
$533$	−22.0239	−	6.68089i	−0.953963	−	0.289381i
$534$	−23.8012	+	2.39926i	−1.02998	+	0.103826i
$535$	−5.22088	+	26.2471i	−0.225718	+	1.13476i
$536$	4.72288	+	5.67489i	0.203997	+	0.245118i
$537$	14.9342	−	2.97060i	0.644459	−	0.128191i
$538$	10.6140	+	5.64208i	0.457601	+	0.243247i
$539$	−38.0355	−	31.2149i	−1.63830	−	1.34452i
$540$	8.07116	−	1.64392i	0.347327	−	0.0707429i
$541$	3.08515	−	5.77192i	0.132641	−	0.248154i	−0.806829	−	0.590785i	$-0.798818\pi$
$541$	3.08515	−	5.77192i	0.132641	−	0.248154i	0.939470	+	0.342631i	$0.111318\pi$
$542$	37.8776	−	0.0867386i	1.62698	−	0.00372574i
$543$	11.3414	−	11.3414i	0.486707	−	0.486707i
$544$	8.91676	−	9.12333i	0.382303	−	0.391159i
$545$	−2.37445	−	2.37445i	−0.101710	−	0.101710i
$546$	−9.03992	−	8.99861i	−0.386873	−	0.385105i
$547$	3.01786	+	1.61308i	0.129034	+	0.0689704i	0.534651	−	0.845073i	$-0.320443\pi$
$547$	3.01786	+	1.61308i	0.129034	+	0.0689704i	−0.405616	+	0.914043i	$0.632943\pi$
$548$	−27.3833	−	5.31661i	−1.16976	−	0.227114i
$549$	0.331207	−	0.403577i	0.0141356	−	0.0172242i
$550$	67.7243	−	20.7134i	2.88778	−	0.883224i
$551$	−0.862212	−	4.33463i	−0.0367315	−	0.184662i
$552$	8.53006	+	15.6983i	0.363064	+	0.668162i
$553$	10.4776	+	2.08412i	0.445552	+	0.0886258i
$554$	−2.57387	−	2.10247i	−0.109353	−	0.0893255i
$555$	−9.58742	+	31.6055i	−0.406963	+	1.34158i
$556$	−37.3945	−	11.1567i	−1.58588	−	0.473151i
$557$	−7.16254	−	8.72759i	−0.303487	−	0.369800i	0.598828	−	0.800878i	$-0.295633\pi$
$557$	−7.16254	−	8.72759i	−0.303487	−	0.369800i	−0.902315	+	0.431078i	$0.858133\pi$
$558$	−0.350407	+	0.527030i	−0.0148339	+	0.0223110i
$559$	−2.33897	+	5.64676i	−0.0989277	+	0.238833i
$560$	−33.0511	+	63.2205i	−1.39667	+	2.67155i
$561$	3.61309	+	8.72277i	0.152545	+	0.368276i
$562$	15.2492	+	2.99696i	0.643247	+	0.126419i
$563$	−0.482771	+	4.90165i	−0.0203464	+	0.206580i	0.979637	+	0.200778i	$0.0643469\pi$
$563$	−0.482771	+	4.90165i	−0.0203464	+	0.206580i	−0.999983	+	0.00580227i	$0.998153\pi$
$564$	5.84726	+	7.05873i	0.246214	+	0.297226i
$565$	−21.1243	−	39.5207i	−0.888704	−	1.66265i
$566$	−9.98998	−	18.5874i	−0.419910	−	0.781288i
$567$	−2.40587	−	3.60064i	−0.101037	−	0.151213i
$568$	−2.58552	+	13.4817i	−0.108486	+	0.565678i
$569$	14.4927	+	9.68371i	0.607566	+	0.405962i	0.820945	−	0.571007i	$-0.193447\pi$
$569$	14.4927	+	9.68371i	0.607566	+	0.405962i	−0.213380	+	0.976969i	$0.568447\pi$
$570$	−4.43281	+	3.65493i	−0.185670	+	0.153088i
$571$	−10.7873	+	1.06245i	−0.451433	+	0.0444623i	−0.321179	−	0.947018i	$-0.604079\pi$
$571$	−10.7873	+	1.06245i	−0.451433	+	0.0444623i	−0.130254	+	0.991481i	$0.541579\pi$
$572$	16.1423	+	6.59990i	0.674943	+	0.275956i
$573$	3.96241	−	1.20198i	0.165532	−	0.0502136i
$574$	62.4627	−	26.0407i	2.60714	−	1.08692i
$575$		−	75.5563i		−	3.15091i
$576$	1.45277	−	7.86698i	0.0605322	−	0.327791i
$577$			40.8833i			1.70200i	0.525169	+	0.850998i	$0.324002\pi$
$577$			40.8833i			1.70200i	−0.525169	+	0.850998i	$0.675998\pi$
$578$	6.48358	+	15.5519i	0.269681	+	0.646875i
$579$	9.37871	−	2.84500i	0.389766	−	0.118234i
$580$	−14.2787	−	34.0301i	−0.592889	−	1.41302i
$581$	−70.5076	+	6.94439i	−2.92515	+	0.288102i
$582$	−4.87548	−	5.91313i	−0.202095	−	0.245107i
$583$	4.21210	+	2.81444i	0.174447	+	0.116562i
$584$	9.76029	−	14.8268i	0.403883	−	0.613537i
$585$	−4.76552	−	7.13210i	−0.197030	−	0.294876i
$586$	−8.78687	+	4.72258i	−0.362982	+	0.195088i
$587$	5.09972	+	9.54091i	0.210488	+	0.393795i	0.964905	−	0.262601i	$-0.0845801\pi$
$587$	5.09972	+	9.54091i	0.210488	+	0.393795i	−0.754417	+	0.656396i	$0.772080\pi$
$588$	23.4027	+	2.19679i	0.965112	+	0.0905942i
$589$	0.0432690	−	0.439318i	0.00178287	−	0.0181018i
$590$	4.50309	−	22.9127i	0.185389	−	0.943300i
$591$	4.76606	+	11.5063i	0.196049	+	0.473305i
$592$	24.9819	+	20.1220i	1.02675	+	0.827009i
$593$	15.4872	−	37.3894i	0.635982	−	1.53540i	−0.196006	−	0.980603i	$-0.562797\pi$
$593$	15.4872	−	37.3894i	0.635982	−	1.53540i	0.831988	−	0.554794i	$-0.187203\pi$
$594$	4.93045	+	3.27811i	0.202299	+	0.134503i
$595$	25.5153	+	31.0905i	1.04603	+	1.27459i
$596$	1.24016	+	2.29483i	0.0507990	+	0.0940001i
$597$	2.41117	−	7.94857i	0.0986827	−	0.325313i
$598$	11.7702	−	14.4091i	0.481318	−	0.589234i
$599$	−3.60759	−	0.717595i	−0.147402	−	0.0293201i	0.120838	−	0.992672i	$-0.461442\pi$
$599$	−3.60759	−	0.717595i	−0.147402	−	0.0293201i	−0.268240	+	0.963352i	$0.586442\pi$
$600$	−21.2828	+	26.2995i	−0.868866	+	1.07367i
$601$	−5.11374	−	25.7085i	−0.208594	−	1.04867i	−0.933159	−	0.359465i	$-0.882959\pi$
$601$	−5.11374	−	25.7085i	−0.208594	−	1.04867i	0.724565	−	0.689206i	$-0.242041\pi$
$602$	−5.25633	−	17.1860i	−0.214232	−	0.700449i
$603$	1.65597	−	2.01780i	0.0674362	−	0.0821713i
$604$	15.1396	−	10.2166i	0.616022	−	0.415706i
$605$	23.7094	+	12.6729i	0.963923	+	0.515228i
$606$	16.3680	−	16.4432i	0.664905	−	0.667957i
$607$	−26.3292	−	26.3292i	−1.06867	−	1.06867i	−0.997461	−	0.0712099i	$-0.977314\pi$
$607$	−26.3292	−	26.3292i	−1.06867	−	1.06867i	−0.0712099	−	0.997461i	$-0.522686\pi$
$608$	1.68084	+	5.32089i	0.0681670	+	0.215791i
$609$	−13.7193	+	13.7193i	−0.555935	+	0.555935i
$610$	0.00696333	+	3.04079i	0.000281937	+	0.123118i
$611$	4.49963	−	8.41822i	0.182036	−	0.340565i
$612$	−3.76163	−	2.48860i	−0.152055	−	0.100596i
$613$	30.4058	+	24.9534i	1.22808	+	1.00786i	0.999410	+	0.0343560i	$0.0109380\pi$
$613$	30.4058	+	24.9534i	1.22808	+	1.00786i	0.228671	+	0.973504i	$0.426562\pi$
$614$	−9.49386	+	17.8600i	−0.383141	+	0.720772i
$615$	44.6352	−	8.87848i	1.79986	−	0.358015i
$616$	−48.9676	+	15.2223i	−1.97296	+	0.613323i
$617$	−5.23814	+	26.3339i	−0.210880	+	1.06016i	0.719759	+	0.694224i	$0.244252\pi$
$617$	−5.23814	+	26.3339i	−0.210880	+	1.06016i	−0.930639	+	0.365940i	$0.880748\pi$
$618$	−1.89152	−	18.7643i	−0.0760881	−	0.754812i
$619$	−37.1753	−	11.2770i	−1.49420	−	0.453261i	−0.565708	−	0.824606i	$-0.691397\pi$
$619$	−37.1753	−	11.2770i	−1.49420	−	0.453261i	−0.928495	+	0.371345i	$0.878897\pi$
$620$	−0.378103	−	3.66671i	−0.0151850	−	0.147259i
$621$	4.88281	−	4.00722i	0.195940	−	0.160804i
$622$	8.29916	+	41.2290i	0.332766	+	1.65313i
$623$	−67.6750	−	28.0319i	−2.71134	−	1.12307i
$624$	−8.15573	+	1.70008i	−0.326490	+	0.0680577i
$625$	53.8345	−	22.2990i	2.15338	−	0.891960i
$626$	−12.5756	−	18.7277i	−0.502622	−	0.748511i
$627$	−4.10989	−	0.404789i	−0.164133	−	0.0161657i
$628$	−19.6579	+	6.06162i	−0.784436	+	0.241885i
$629$	15.9497	−	8.52529i	0.635956	−	0.339925i
$630$	24.1527	+	7.26628i	0.962266	+	0.289496i
$631$	−16.9202	+	11.3057i	−0.673584	+	0.450074i	−0.844745	−	0.535169i	$-0.820248\pi$
$631$	−16.9202	+	11.3057i	−0.673584	+	0.450074i	0.171161	+	0.985243i	$0.445248\pi$
$632$	4.89982	−	4.96761i	0.194904	−	0.197601i
$633$	−2.15729	+	3.22861i	−0.0857446	+	0.128326i
$634$	−16.0446	−	1.54317i	−0.637214	−	0.0612871i
$635$	7.77759	+	78.9672i	0.308644	+	3.13372i
$636$	−2.42000	+	0.0110835i	−0.0959594	+	0.000439491i
$637$	−7.10566	−	23.4242i	−0.281537	−	0.928102i
$638$	10.0954	−	24.5311i	0.399680	−	0.971196i
$639$	4.85335			0.191996
$640$	22.6205	+	40.7356i	0.894153	+	1.61021i
$641$	8.21883			0.324624			0.162312	−	0.986739i	$-0.448105\pi$
$641$	8.21883			0.324624			0.162312	+	0.986739i	$0.448105\pi$
$642$	3.49721	−	8.49800i	0.138024	−	0.335389i
$643$	−4.03994	−	13.3179i	−0.159319	−	0.525206i	0.840544	−	0.541744i	$-0.182236\pi$
$643$	−4.03994	−	13.3179i	−0.159319	−	0.525206i	−0.999863	+	0.0165377i	$0.994736\pi$
$644$	0.250556	+	54.7070i	0.00987330	+	2.15576i
$645$	−1.18462	−	12.0277i	−0.0466444	−	0.473588i
$646$	3.13153	+	0.301190i	0.123208	+	0.0118502i
$647$	−12.7105	+	19.0227i	−0.499703	+	0.747859i	−0.992495	−	0.122289i	$-0.960977\pi$
$647$	−12.7105	+	19.0227i	−0.499703	+	0.747859i	0.492791	+	0.870148i	$0.335977\pi$
$648$	−2.82836	+	0.0194309i	−0.111108	+	0.000763316i
$649$	13.9562	−	9.32522i	0.547828	−	0.366047i
$650$	33.7385	+	10.1501i	1.32333	+	0.398121i
$651$	−1.70912	+	0.913546i	−0.0669859	+	0.0358047i
$652$	7.25915	+	23.5415i	0.284290	+	0.921957i
$653$	−3.78770	−	0.373055i	−0.148224	−	0.0145988i	0.0236330	−	0.999721i	$-0.492477\pi$
$653$	−3.78770	−	0.373055i	−0.148224	−	0.0145988i	−0.171857	+	0.985122i	$0.554977\pi$
$654$	0.642813	+	0.957284i	0.0251360	+	0.0374328i
$655$	70.3404	−	29.1359i	2.74843	−	1.13843i
$656$	8.22571	−	43.4287i	0.321160	−	1.69561i
$657$	−5.79819	−	2.40169i	−0.226209	−	0.0936988i
$658$	5.53867	+	27.5153i	0.215920	+	1.07266i
$659$	−32.7720	+	26.8953i	−1.27662	+	1.04769i	−0.280482	+	0.959859i	$0.590494\pi$
$659$	−32.7720	+	26.8953i	−1.27662	+	1.04769i	−0.996135	+	0.0878335i	$0.972006\pi$
$660$	−34.3026	+	3.53722i	−1.33523	+	0.137686i
$661$	8.43353	+	2.55828i	0.328026	+	0.0995057i	0.450002	−	0.893027i	$-0.351423\pi$
$661$	8.43353	+	2.55828i	0.328026	+	0.0995057i	−0.121976	+	0.992533i	$0.538923\pi$
$662$	−2.45892	−	24.3931i	−0.0955688	−	0.948065i
$663$	−0.916330	+	4.60670i	−0.0355873	+	0.178909i
$664$	−21.5329	+	40.9596i	−0.835638	+	1.58954i
$665$	−17.2545	+	3.43214i	−0.669102	+	0.133093i
$666$	5.32330	−	10.0143i	0.206274	−	0.388046i
$667$	−21.8768	−	17.9538i	−0.847074	−	0.695176i
$668$	6.60984	−	9.99108i	0.255742	−	0.386566i
$669$	5.64199	−	10.5554i	0.218132	−	0.408096i
$670$	0.0348152	+	15.2033i	0.00134503	+	0.587357i
$671$	−1.54557	+	1.54557i	−0.0596659	+	0.0596659i
$672$	15.3227	−	19.1129i	0.591087	−	0.737297i
$673$	−7.07020	−	7.07020i	−0.272536	−	0.272536i	0.557584	−	0.830120i	$-0.311728\pi$
$673$	−7.07020	−	7.07020i	−0.272536	−	0.272536i	−0.830120	+	0.557584i	$0.811728\pi$
$674$	−20.2248	+	20.3176i	−0.779030	+	0.782606i
$675$	10.5491	+	5.63861i	0.406035	+	0.217030i
$676$	−9.69069	−	14.3603i	−0.372719	−	0.552321i
$677$	−11.7917	+	14.3682i	−0.453191	+	0.552215i	−0.948613	−	0.316437i	$-0.897513\pi$
$677$	−11.7917	+	14.3682i	−0.453191	+	0.552215i	0.495422	+	0.868652i	$0.335013\pi$
$678$	4.50056	+	14.7150i	0.172843	+	0.565125i
$679$	−4.57830	−	23.0166i	−0.175699	−	0.883298i
$680$	26.1248	−	2.75441i	1.00184	−	0.105627i
$681$	1.90578	+	0.379082i	0.0730295	+	0.0145265i
$682$	1.67622	−	2.05205i	0.0641859	−	0.0785770i
$683$	5.17134	−	17.0476i	0.197876	−	0.652310i	−0.800705	−	0.599059i	$-0.795542\pi$
$683$	5.17134	−	17.0476i	0.197876	−	0.652310i	0.998581	−	0.0532510i	$-0.0169583\pi$
$684$	1.73562	−	0.937954i	0.0663631	−	0.0358636i
$685$	−36.4402	−	44.4026i	−1.39231	−	1.69653i
$686$	24.2386	+	16.1155i	0.925432	+	0.615293i
$687$	0.193842	−	0.467975i	0.00739552	−	0.0178544i
$688$	−11.2636	−	3.30441i	−0.429420	−	0.125980i
$689$	0.964427	+	2.32833i	0.0367417	+	0.0887024i
$690$	−7.09476	+	36.0996i	−0.270093	+	1.37429i
$691$	−0.972475	+	9.87370i	−0.0369947	+	0.375613i	0.958806	+	0.284063i	$0.0916823\pi$
$691$	−0.972475	+	9.87370i	−0.0369947	+	0.375613i	−0.995800	+	0.0915507i	$0.970818\pi$
$692$	−2.84801	+	30.3402i	−0.108265	+	1.15336i
$693$	8.54637	+	15.9891i	0.324650	+	0.607377i
$694$	6.40991	−	3.44507i	0.243317	−	0.130773i
$695$	−44.6443	−	66.8149i	−1.69345	−	2.53443i
$696$	2.55759	+	12.4116i	0.0969453	+	0.470462i
$697$	−20.7202	−	13.8448i	−0.784834	−	0.524410i
$698$	−2.32808	−	2.82357i	−0.0881193	−	0.106874i
$699$	5.49062	−	0.540779i	0.207674	−	0.0204541i
$700$	−95.5289	+	40.0829i	−3.61065	+	1.51499i
$701$	−37.6642	+	11.4253i	−1.42256	+	0.431528i	−0.905472	−	0.424407i	$-0.860483\pi$
$701$	−37.6642	+	11.4253i	−1.42256	+	0.431528i	−0.517084	+	0.855934i	$0.672983\pi$
$702$	1.13341	+	2.71867i	0.0427778	+	0.102610i
$703$			7.91060i			0.298354i
$704$	−9.28119	+	32.1812i	−0.349798	+	1.21288i
$705$			18.8749i			0.710868i
$706$	−3.03457	+	1.26511i	−0.114208	+	0.0476131i
$707$	67.9846	−	20.6229i	2.55683	−	0.775605i
$708$	−3.03455	+	7.42201i	−0.114045	+	0.278936i
$709$	32.6689	−	3.21760i	1.22691	−	0.120840i	0.536272	−	0.844045i	$-0.319832\pi$
$709$	32.6689	−	3.21760i	1.22691	−	0.120840i	0.690633	+	0.723205i	$0.257332\pi$
$710$	−21.8100	+	17.9828i	−0.818516	+	0.674882i
$711$	−2.05116	−	1.37054i	−0.0769247	−	0.0513994i
$712$	−39.5971	+	26.8532i	−1.48396	+	1.00637i
$713$	−1.57049	−	2.35040i	−0.0588152	−	0.0880232i
$714$	−6.53834	−	12.1653i	−0.244691	−	0.455274i
$715$	16.9286	+	31.6711i	0.633092	+	1.18443i
$716$	23.4522	−	19.4272i	0.876450	−	0.726027i
$717$	−1.45388	+	14.7615i	−0.0542960	+	0.551277i
$718$	7.02319	+	1.38029i	0.262103	+	0.0515119i
$719$	13.5867	+	32.8013i	0.506700	+	1.22328i	0.945772	+	0.324831i	$0.105307\pi$
$719$	13.5867	+	32.8013i	0.506700	+	1.22328i	−0.439072	+	0.898452i	$0.644693\pi$
$720$	12.6381	−	10.5670i	0.470995	−	0.393810i
$721$	22.0997	−	53.3534i	0.823035	−	1.98698i
$722$	14.1151	−	21.2298i	0.525310	−	0.790093i
$723$	1.97399	+	2.40532i	0.0734135	+	0.0894547i
$724$	9.17117	−	30.7394i	0.340844	−	1.14242i
$725$	15.5569	−	51.2844i	0.577770	−	1.90465i
$726$	−7.14945	−	5.84006i	−0.265341	−	0.216745i
$727$	20.9306	+	4.16335i	0.776272	+	0.154410i	0.567300	−	0.823511i	$-0.307988\pi$
$727$	20.9306	+	4.16335i	0.776272	+	0.154410i	0.208973	+	0.977921i	$0.432988\pi$
$728$	−24.4622	−	7.23740i	−0.906630	−	0.268236i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	34.9548	−	10.6909i	1.29373	−	0.395687i
$731$	−4.19837	+	5.11573i	−0.155282	+	0.189212i
$732$	0.199015	−	1.02503i	0.00735580	−	0.0378861i
$733$	12.9606	+	6.92760i	0.478712	+	0.255877i	0.693059	−	0.720881i	$-0.256263\pi$
$733$	12.9606	+	6.92760i	0.478712	+	0.255877i	−0.214348	+	0.976757i	$0.568763\pi$
$734$	−8.74011	−	8.70017i	−0.322603	−	0.321129i
$735$	34.2262	+	34.2262i	1.26245	+	1.26245i
$736$	29.9356	+	19.5103i	1.10344	+	0.719158i
$737$	−7.72752	+	7.72752i	−0.284647	+	0.284647i
$738$	−15.6273	+	0.0357861i	−0.575250	+	0.00131731i
$739$	12.1020	−	22.6412i	0.445178	−	0.832870i	−0.554821	−	0.831969i	$-0.687213\pi$
$739$	12.1020	−	22.6412i	0.445178	−	0.832870i	1.00000		0.000900240i	$-0.000286555\pi$
$740$	13.1833	+	64.7263i	0.484629	+	2.37939i
$741$	−1.58814	−	1.30335i	−0.0583418	−	0.0478798i
$742$	−6.54332	−	3.47824i	−0.240213	−	0.127690i
$743$	15.4970	−	3.08254i	0.568529	−	0.113088i	0.0975482	−	0.995231i	$-0.468900\pi$
$743$	15.4970	−	3.08254i	0.568529	−	0.113088i	0.470981	+	0.882143i	$0.343900\pi$
$744$	−0.115411	+	1.26050i	−0.00423116	+	0.0462122i
$745$	−1.04792	+	5.26826i	−0.0383929	+	0.193014i
$746$	41.7960	−	4.21321i	1.53026	−	0.154256i
$747$	15.6561	+	4.74923i	0.572827	+	0.173765i
$748$	14.6514	+	11.9122i	0.535708	+	0.435554i
$749$	21.7518	−	17.8512i	0.794792	−	0.652269i
$750$	−39.7489	+	8.00122i	−1.45143	+	0.292163i
$751$	−19.1001	−	7.91154i	−0.696974	−	0.288696i	0.00592843	−	0.999982i	$-0.498113\pi$
$751$	−19.1001	−	7.91154i	−0.696974	−	0.288696i	−0.702902	+	0.711286i	$0.748113\pi$
$752$	17.0002	+	6.85995i	0.619932	+	0.250157i
$753$	15.4098	−	6.38296i	0.561566	−	0.232608i
$754$	10.9559	−	7.35685i	0.398991	−	0.267921i
$755$	37.4291	+	3.68645i	1.36219	+	0.134164i
$756$	−7.65685	−	4.04769i	−0.278477	−	0.147213i
$757$	−17.6161	+	9.41601i	−0.640269	+	0.342231i	−0.759377	−	0.650651i	$-0.774496\pi$
$757$	−17.6161	+	9.41601i	−0.640269	+	0.342231i	0.119109	+	0.992881i	$0.461996\pi$
$758$	5.21700	−	17.3410i	0.189490	−	0.629854i
$759$	−21.9884	+	14.6922i	−0.798127	+	0.533292i
$760$	−4.32422	+	10.6459i	−0.156856	+	0.386166i
$761$	10.4636	−	15.6599i	0.379306	−	0.567671i	−0.591871	−	0.806033i	$-0.701610\pi$
$761$	10.4636	−	15.6599i	0.379306	−	0.567671i	0.971176	+	0.238362i	$0.0766103\pi$
$762$	2.60861	−	27.1223i	0.0945001	−	0.982536i
$763$	0.346083	+	3.51384i	0.0125291	+	0.127210i
$764$	5.82897	−	5.88261i	0.210885	−	0.212825i
$765$	−2.69608	−	8.88780i	−0.0974771	−	0.321339i
$766$	5.12907	+	2.11078i	0.185321	+	0.0762657i
$767$	8.35020			0.301508
$768$	−4.92425	−	15.2234i	−0.177689	−	0.549327i
$769$	−13.1396			−0.473826			−0.236913	−	0.971531i	$-0.576136\pi$
$769$	−13.1396			−0.473826			−0.236913	+	0.971531i	$0.576136\pi$
$770$	−97.6491	−	40.1859i	−3.51903	−	1.44820i
$771$	−8.82147	−	29.0805i	−0.317697	−	1.04731i
$772$	13.7967	−	13.9237i	0.496554	−	0.501123i
$773$	−2.20545	−	22.3923i	−0.0793246	−	0.805396i	−0.949732	−	0.313064i	$-0.898645\pi$
$773$	−2.20545	−	22.3923i	−0.0793246	−	0.805396i	0.870407	−	0.492332i	$-0.163855\pi$
$774$	−0.397323	+	4.13105i	−0.0142815	+	0.148488i
$775$	2.97396	−	4.45085i	0.106828	−	0.159879i
$776$	−14.2010	−	5.76828i	−0.509787	−	0.207069i
$777$	28.8752	−	19.2938i	1.03589	−	0.692161i
$778$	14.9758	−	49.7787i	0.536909	−	1.78465i
$779$	9.61313	−	5.13833i	0.344426	−	0.184100i
$780$	−15.1666	−	8.01763i	−0.543052	−	0.287077i
$781$	−20.2212	−	1.99162i	−0.723573	−	0.0712657i
$782$	16.7246	−	11.2305i	0.598072	−	0.401603i
$783$	4.13933	−	1.71457i	0.147927	−	0.0612736i
$784$	43.2661	−	18.3875i	1.54522	−	0.656696i
$785$	−39.1362	−	16.2107i	−1.39683	−	0.578586i
$786$	−25.6299	+	5.15915i	−0.914188	+	0.184021i
$787$	13.7582	−	11.2910i	0.490425	−	0.402482i	−0.356416	−	0.934327i	$-0.616001\pi$
$787$	13.7582	−	11.2910i	0.490425	−	0.402482i	0.846841	+	0.531846i	$0.178501\pi$
$788$	19.3268	+	15.7135i	0.688489	+	0.559771i
$789$	1.90809	+	0.578813i	0.0679298	+	0.0206063i
$790$	14.2957	−	1.44107i	0.508619	−	0.0512709i
$791$	−9.19245	+	46.2136i	−0.326846	+	1.64317i
$792$	11.7922	+	1.07969i	0.419017	+	0.0383650i
$793$	−1.06648	+	0.212137i	−0.0378719	+	0.00753319i
$794$	39.8749	+	21.1963i	1.41511	+	0.752228i
$795$	−3.85219	−	3.16141i	−0.136623	−	0.112124i
$796$	−3.31552	−	16.2783i	−0.117515	−	0.576967i
$797$	−9.11506	+	17.0531i	−0.322872	+	0.604051i	−0.990029	−	0.140867i	$-0.955011\pi$
$797$	−9.11506	+	17.0531i	−0.322872	+	0.604051i	0.667157	+	0.744917i	$0.267511\pi$
$798$	6.04103	−	0.0138338i	0.213850	−	0.000489711i
$799$	7.30825	−	7.30825i	0.258547	−	0.258547i
$800$	−12.4400	+	66.5111i	−0.439820	+	2.35152i
$801$	11.9609	+	11.9609i	0.422619	+	0.422619i
$802$	−29.2092	−	29.0757i	−1.03141	−	1.02670i
$803$	23.1723	+	12.3859i	0.817733	+	0.437087i
$804$	0.995034	−	5.12493i	0.0350921	−	0.180742i
$805$	−71.4675	+	87.0834i	−2.51890	+	3.06929i
$806$	1.26051	−	0.385527i	0.0443996	−	0.0135796i
$807$	−1.65821	−	8.33638i	−0.0583717	−	0.293455i
$808$	13.1645	−	44.4956i	0.463124	−	1.56535i
$809$	37.6645	+	7.49194i	1.32421	+	0.263403i	0.806034	−	0.591869i	$-0.201610\pi$
$809$	37.6645	+	7.49194i	1.32421	+	0.263403i	0.518180	+	0.855271i	$0.326610\pi$
$810$	−4.51073	−	3.68461i	−0.158491	−	0.129464i
$811$	−1.42275	+	4.69017i	−0.0499594	+	0.164694i	−0.978370	−	0.206861i	$-0.933675\pi$
$811$	−1.42275	+	4.69017i	−0.0499594	+	0.164694i	0.928411	+	0.371555i	$0.121175\pi$
$812$	−11.0940	+	37.1844i	−0.389325	+	1.30492i
$813$	−16.9913	−	20.7040i	−0.595911	−	0.726120i
$814$	−26.2887	+	39.5395i	−0.921419	+	1.38586i
$815$	−19.4133	+	46.8679i	−0.680019	+	1.64171i
$816$	−8.98492	−	0.801911i	−0.314535	−	0.0280725i
$817$	−1.10777	−	2.67439i	−0.0387559	−	0.0935650i
$818$	−29.1373	−	5.72644i	−1.01876	−	0.200220i
$819$	−0.884045	+	8.97586i	−0.0308910	+	0.313642i
$820$	70.0936	−	58.0636i	2.44778	−	2.02767i
$821$	17.3311	+	32.4242i	0.604859	+	1.13161i	0.978927	+	0.204210i	$0.0654626\pi$
$821$	17.3311	+	32.4242i	0.604859	+	1.13161i	−0.374068	+	0.927401i	$0.622037\pi$
$822$	9.33786	+	17.3741i	0.325695	+	0.605991i
$823$	−30.5404	−	45.7070i	−1.06457	−	1.59325i	−0.770475	−	0.637470i	$-0.779981\pi$
$823$	−30.5404	−	45.7070i	−1.06457	−	1.59325i	−0.294097	−	0.955776i	$-0.595019\pi$
$824$	−21.1704	−	31.2174i	−0.737507	−	1.08751i
$825$	−41.6384	−	27.8219i	−1.44966	−	0.968634i
$826$	−18.9441	+	15.6197i	−0.659148	+	0.543480i
$827$	17.3147	−	1.70535i	0.602092	−	0.0593009i	0.207621	−	0.978209i	$-0.433428\pi$
$827$	17.3147	−	1.70535i	0.602092	−	0.0593009i	0.394471	+	0.918908i	$0.370928\pi$
$828$	4.78102	−	11.6936i	0.166152	−	0.406381i
$829$	25.0969	−	7.61305i	0.871650	−	0.264412i	0.177394	−	0.984140i	$-0.443233\pi$
$829$	25.0969	−	7.61305i	0.871650	−	0.264412i	0.694256	+	0.719728i	$0.255733\pi$
$830$	−87.9525	+	36.6673i	−3.05288	+	1.27274i
$831$			2.35002i			0.0815212i
$832$	−12.7335	+	10.7463i	−0.441455	+	0.372560i
$833$		−	26.5044i		−	0.918324i
$834$	10.6180	+	25.4690i	0.367671	+	0.881919i
$835$	23.6064	−	7.16094i	0.816935	−	0.247814i
$836$	−7.61627	+	3.19571i	−0.263414	+	0.110526i
$837$	0.445364	−	0.0438645i	0.0153940	−	0.00151618i
$838$	6.90682	+	8.37679i	0.238592	+	0.289371i
$839$	4.24917	+	2.83921i	0.146698	+	0.0980203i	0.626753	−	0.779218i	$-0.284383\pi$
$839$	4.24917	+	2.83921i	0.146698	+	0.0980203i	−0.480055	+	0.877238i	$0.659383\pi$
$840$	49.4060	−	10.1808i	1.70467	−	0.351271i
$841$	4.95916	+	7.42190i	0.171005	+	0.255928i
$842$	6.86212	−	3.68811i	0.236484	−	0.127101i
$843$	−5.18021	−	9.69148i	−0.178416	−	0.333792i
$844$	−0.725801	+	7.73205i	−0.0249831	+	0.266148i
$845$	3.49670	−	35.5026i	0.120290	−	1.22133i
$846$	1.24989	−	6.35971i	0.0429721	−	0.218651i
$847$	−10.8176	−	26.1160i	−0.371697	−	0.897356i
$848$	−4.24747	+	2.32059i	−0.145859	+	0.0796894i
$849$	−5.71015	+	13.7855i	−0.195972	+	0.473117i
$850$	31.7678	+	21.1215i	1.08963	+	0.724461i
$851$	32.1358	+	39.1575i	1.10160	+	1.34230i
$852$	8.53951	−	4.61487i	0.292559	−	0.158103i
$853$	−2.76276	+	9.10758i	−0.0945949	+	0.311838i	−0.991450	−	0.130487i	$-0.958346\pi$
$853$	−2.76276	+	9.10758i	−0.0945949	+	0.311838i	0.896855	+	0.442324i	$0.145846\pi$
$854$	2.02271	−	2.47622i	0.0692156	−	0.0847343i
$855$	3.98447	+	0.792560i	0.136266	+	0.0271050i
$856$	−1.92706	−	18.2776i	−0.0658657	−	0.624717i
$857$	−7.63995	−	38.4086i	−0.260976	−	1.31201i	−0.859593	−	0.510979i	$-0.829283\pi$
$857$	−7.63995	−	38.4086i	−0.260976	−	1.31201i	0.598617	−	0.801035i	$-0.295717\pi$
$858$	−3.60666	−	11.7923i	−0.123129	−	0.402582i
$859$	13.9900	−	17.0469i	0.477332	−	0.581631i	−0.477554	−	0.878602i	$-0.658477\pi$
$859$	13.9900	−	17.0469i	0.477332	−	0.581631i	0.954886	+	0.296971i	$0.0959765\pi$
$860$	−13.5210	−	20.0363i	−0.461062	−	0.683233i
$861$	−42.2021	−	22.5575i	−1.43824	−	0.768757i
$862$	12.9346	−	12.9940i	0.440554	−	0.442577i
$863$	−34.5010	−	34.5010i	−1.17443	−	1.17443i	−0.981143	−	0.193284i	$-0.938086\pi$
$863$	−34.5010	−	34.5010i	−1.17443	−	1.17443i	−0.193284	−	0.981143i	$-0.561914\pi$
$864$	−4.95804	+	2.72357i	−0.168676	+	0.0926577i
$865$	−44.3722	+	44.3722i	−1.50870	+	1.50870i
$866$	−0.0657017	−	28.6911i	−0.00223263	−	0.974962i
$867$	5.61634	−	10.5074i	0.190741	−	0.356851i
$868$	−2.13856	+	3.23253i	−0.0725874	+	0.109719i
$869$	7.98365	+	6.55201i	0.270827	+	0.222262i
$870$	−12.2485	+	23.0421i	−0.415262	+	0.781199i
$871$	−5.33220	+	1.06064i	−0.180675	+	0.0359384i
$872$	2.04128	+	1.07312i	0.0691264	+	0.0363405i
$873$	−1.05723	+	5.31507i	−0.0357819	+	0.179888i
$874$	0.883785	+	8.76735i	0.0298945	+	0.296560i
$875$	−118.810	−	36.0406i	−4.01651	−	1.21840i
$876$	−12.4856	+	1.28749i	−0.421850	+	0.0435003i
$877$	−1.50921	+	1.23858i	−0.0509625	+	0.0418238i	−0.659530	−	0.751678i	$-0.729245\pi$
$877$	−1.50921	+	1.23858i	−0.0509625	+	0.0418238i	0.608567	+	0.793502i	$0.291745\pi$
$878$	0.458775	+	2.27913i	0.0154829	+	0.0769168i
$879$	6.51685	+	2.69937i	0.219808	+	0.0910474i
$880$	−56.9923	+	38.8408i	−1.92121	+	1.30932i
$881$	−37.0794	+	15.3588i	−1.24924	+	0.517451i	−0.906590	−	0.422013i	$-0.861324\pi$
$881$	−37.0794	+	15.3588i	−1.24924	+	0.517451i	−0.342647	+	0.939464i	$0.611324\pi$
$882$	−9.26574	−	13.7986i	−0.311994	−	0.464625i
$883$	−39.5998	−	3.90024i	−1.33264	−	0.131254i	−0.593516	−	0.804822i	$-0.702261\pi$
$883$	−39.5998	−	3.90024i	−1.33264	−	0.131254i	−0.739125	+	0.673569i	$0.764761\pi$
$884$	2.76805	+	8.97682i	0.0930996	+	0.301923i
$885$	−14.5620	+	7.78353i	−0.489495	+	0.261641i
$886$	−40.8790	−	12.2984i	−1.37336	−	0.413171i
$887$	36.2827	−	24.2434i	1.21826	−	0.814012i	0.230969	−	0.972961i	$-0.425811\pi$
$887$	36.2827	−	24.2434i	1.21826	−	0.814012i	0.987287	+	0.158949i	$0.0508105\pi$
$888$	−0.155825	−	22.6819i	−0.00522915	−	0.761156i
$889$	46.3535	−	69.3729i	1.55465	−	2.32669i
$890$	−98.0681	−	9.43216i	−3.28725	−	0.316167i
$891$	−0.410359	−	4.16645i	−0.0137475	−	0.139581i
$892$	−0.109631	−	23.9371i	−0.00367072	−	0.801473i
$893$	1.31232	+	4.32614i	0.0439151	+	0.144769i
$894$	0.701951	−	1.70570i	0.0234767	−	0.0570470i
$895$	62.7105			2.09618
$896$	8.78669	−	48.1991i	0.293543	−	1.61022i
$897$	−13.1560			−0.439266
$898$	−3.04854	+	7.40776i	−0.101731	+	0.247200i
$899$	−0.582035	−	1.91871i	−0.0194120	−	0.0639927i
$900$	23.9228	−	0.109565i	0.797425	−	0.00365218i
$901$	0.267467	+	2.71563i	0.00891060	+	0.0904709i
$902$	65.1251	+	6.26372i	2.16843	+	0.208559i
$903$	−7.06020	+	10.5663i	−0.234949	+	0.351626i
$904$	21.9107	+	21.6117i	0.728738	+	0.718794i
$905$	54.9238	−	36.6989i	1.82573	−	1.21991i
$906$	−12.3673	−	3.72067i	−0.410875	−	0.123611i
$907$	7.51951	−	4.01926i	0.249681	−	0.133457i	−0.341809	−	0.939769i	$-0.611040\pi$
$907$	7.51951	−	4.01926i	0.249681	−	0.133457i	0.591490	+	0.806312i	$0.298540\pi$
$908$	3.71368	−	1.14513i	0.123243	−	0.0380025i
$909$	−16.3266	−	1.60803i	−0.541520	−	0.0533351i
$910$	−29.2849	−	43.6114i	−0.970783	−	1.44570i
$911$	−2.71916	+	1.12631i	−0.0900899	+	0.0373164i	−0.427273	−	0.904123i	$-0.640526\pi$
$911$	−2.71916	+	1.12631i	−0.0900899	+	0.0373164i	0.337183	+	0.941439i	$0.390526\pi$
$912$	2.16197	−	3.30067i	0.0715900	−	0.109296i
$913$	−63.2815	−	26.2120i	−2.09431	−	0.867492i
$914$	4.55281	+	22.6177i	0.150594	+	0.748128i
$915$	1.66210	−	1.36405i	0.0549475	−	0.0450942i
$916$	−0.103914	−	1.00772i	−0.00343342	−	0.0332961i
$917$	−76.6081	−	23.2388i	−2.52982	−	0.767414i
$918$	0.319871	+	3.17319i	0.0105573	+	0.104731i
$919$	−0.916868	+	4.60941i	−0.0302447	+	0.152050i	−0.992957	−	0.118478i	$-0.962198\pi$
$919$	−0.916868	+	4.60941i	−0.0302447	+	0.152050i	0.962712	+	0.270528i	$0.0871984\pi$
$920$	21.8425	+	70.2636i	0.720125	+	2.31652i
$921$	14.0275	−	2.79025i	0.462223	−	0.0919418i
$922$	20.2786	−	38.1484i	0.667840	−	1.25635i
$923$	−7.81388	−	6.41268i	−0.257197	−	0.211076i
$924$	30.2408	+	20.0066i	0.994851	+	0.658168i
$925$	−45.2187	+	84.5982i	−1.48678	+	2.78157i
$926$	0.0491201	+	21.4501i	0.00161419	+	0.704894i
$927$	−9.42971	+	9.42971i	−0.309712	+	0.309712i
$928$	16.3019	+	19.4064i	0.535134	+	0.637048i
$929$	−6.38360	−	6.38360i	−0.209439	−	0.209439i	0.594590	−	0.804029i	$-0.297314\pi$
$929$	−6.38360	−	6.38360i	−0.209439	−	0.209439i	−0.804029	+	0.594590i	$0.797314\pi$
$930$	−1.83885	+	1.84729i	−0.0602983	+	0.0605751i
$931$	10.2243	+	5.46502i	0.335089	+	0.179109i
$932$	9.14658	−	6.17233i	0.299606	−	0.202181i
$933$	18.8657	−	22.9879i	0.617634	−	0.752589i
$934$	−5.09853	−	16.6701i	−0.166829	−	0.545462i
$935$	7.58590	+	38.1369i	0.248085	+	1.24721i
$936$	4.57932	+	3.70580i	0.149680	+	0.121128i
$937$	−31.7489	−	6.31525i	−1.03719	−	0.206310i	−0.353008	−	0.935620i	$-0.614841\pi$
$937$	−31.7489	−	6.31525i	−1.03719	−	0.206310i	−0.684183	+	0.729310i	$0.739841\pi$
$938$	10.1131	−	12.3806i	0.330205	−	0.404240i
$939$	−4.63035	+	15.2642i	−0.151106	+	0.498129i
$940$	17.9474	+	33.2104i	0.585379	+	1.08320i
$941$	29.0628	+	35.4131i	0.947420	+	1.15443i	0.987875	+	0.155253i	$0.0496193\pi$
$941$	29.0628	+	35.4131i	0.947420	+	1.15443i	−0.0404549	+	0.999181i	$0.512881\pi$
$942$	12.1131	+	8.05365i	0.394666	+	0.262402i
$943$	26.7113	−	64.4868i	0.869840	−	2.09998i
$944$	1.71800	+	15.9445i	0.0559162	+	0.518950i
$945$	−6.82504	−	16.4771i	−0.222018	−	0.536000i
$946$	3.35064	−	17.0488i	0.108939	−	0.554303i
$947$	−2.22791	+	22.6204i	−0.0723974	+	0.735063i	0.888633	+	0.458619i	$0.151656\pi$
$947$	−2.22791	+	22.6204i	−0.0723974	+	0.735063i	−0.961030	+	0.276443i	$0.910844\pi$
$948$	−4.91223	−	0.461107i	−0.159542	−	0.0149761i
$949$	6.16173	+	11.5278i	0.200018	+	0.374208i
$950$	−14.6981	+	7.89964i	−0.476870	+	0.256298i
$951$	6.33218	+	9.47678i	0.205335	+	0.307306i
$952$	−23.0717	−	15.1878i	−0.747759	−	0.492240i
$953$	17.9184	+	11.9727i	0.580434	+	0.387834i	0.810846	−	0.585259i	$-0.199007\pi$
$953$	17.9184	+	11.9727i	0.580434	+	0.387834i	−0.230412	+	0.973093i	$0.574007\pi$
$954$	1.08861	+	1.32030i	0.0352451	+	0.0427463i
$955$	16.9711	−	1.67151i	0.549173	−	0.0540888i
$956$	11.4780	+	27.3553i	0.371225	+	0.884734i
$957$	−17.9499	+	5.44503i	−0.580237	+	0.176013i
$958$	−8.02637	−	19.2525i	−0.259320	−	0.622022i
$959$			60.3981i			1.95036i
$960$	12.1890	−	30.6099i	0.393400	−	0.987929i
$961$			30.7997i			0.993540i
$962$	−21.8023	+	9.08934i	−0.702933	+	0.293052i
$963$	−6.21814	+	1.88625i	−0.200377	+	0.0607837i
$964$	5.76037	+	2.35517i	0.185529	+	0.0758551i
$965$	40.1693	−	3.95633i	1.29310	−	0.127359i
$966$	29.8469	−	24.6094i	0.960310	−	0.791793i
$967$	−16.9677	−	11.3375i	−0.545644	−	0.364588i	0.251989	−	0.967730i	$-0.418915\pi$
$967$	−16.9677	−	11.3375i	−0.545644	−	0.364588i	−0.797634	+	0.603142i	$0.793915\pi$
$968$	−18.1326	−	3.47747i	−0.582804	−	0.111770i
$969$	−1.23589	−	1.84964i	−0.0397025	−	0.0594191i
$970$	−14.9425	−	27.8022i	−0.479776	−	0.892675i
$971$	−3.40356	−	6.36762i	−0.109226	−	0.204347i	0.821370	−	0.570396i	$-0.193210\pi$
$971$	−3.40356	−	6.36762i	−0.109226	−	0.204347i	−0.930596	+	0.366049i	$0.880710\pi$
$972$	1.27585	+	1.54019i	0.0409230	+	0.0494017i
$973$	−8.28190	+	84.0875i	−0.265505	+	2.69572i
$974$	34.9243	+	6.86378i	1.11905	+	0.219930i
$975$	−9.53377	−	23.0166i	−0.305325	−	0.737120i
$976$	−0.624492	−	1.99278i	−0.0199895	−	0.0637873i
$977$	−10.8508	+	26.1961i	−0.347147	+	0.838087i	0.649807	+	0.760099i	$0.274850\pi$
$977$	−10.8508	+	26.1961i	−0.347147	+	0.838087i	−0.996954	+	0.0779880i	$0.975150\pi$
$978$	9.64472	−	14.5062i	0.308404	−	0.463856i
$979$	−44.9263	−	54.7428i	−1.43585	−	1.74959i
$980$	92.7656	+	27.6768i	2.96329	+	0.884103i
$981$	0.236684	−	0.780244i	0.00755675	−	0.0249113i
$982$	−29.2650	−	23.9052i	−0.933884	−	0.762846i
$983$	18.0699	+	3.59433i	0.576341	+	0.114641i	0.474650	−	0.880175i	$-0.342575\pi$
$983$	18.0699	+	3.59433i	0.576341	+	0.114641i	0.101691	+	0.994816i	$0.467575\pi$
$984$	−27.4624	+	14.9224i	−0.875468	+	0.475709i
$985$	10.0066	+	50.3067i	0.318838	+	1.60290i
$986$	13.6643	−	4.17922i	0.435161	−	0.133094i
$987$	12.5905	−	15.3416i	0.400760	−	0.488328i
$988$	−4.03365	−	0.783155i	−0.128327	−	0.0249155i
$989$	−16.3478	−	8.73808i	−0.519830	−	0.277855i
$990$	17.2817	+	17.2027i	0.549249	+	0.546739i
$991$	31.9097	+	31.9097i	1.01364	+	1.01364i	0.999906	+	0.0137385i	$0.00437325\pi$
$991$	31.9097	+	31.9097i	1.01364	+	1.01364i	0.0137385	+	0.999906i	$0.495627\pi$
$992$	0.995496	+	2.32760i	0.0316070	+	0.0739013i
$993$	−12.2584	+	12.2584i	−0.389007	+	0.389007i
$994$	29.7227	−	0.0680642i	0.942748	−	0.00215887i
$995$	16.1259	−	30.1694i	0.511224	−	0.956433i
$996$	32.0629	−	6.53050i	1.01595	−	0.206927i
$997$	−7.08530	−	5.81475i	−0.224394	−	0.184155i	0.515479	−	0.856902i	$-0.327614\pi$
$997$	−7.08530	−	5.81475i	−0.224394	−	0.184155i	−0.739872	+	0.672747i	$0.765114\pi$
$998$	3.15458	+	1.67688i	0.0998564	+	0.0530807i
$999$	−7.86537	+	1.56452i	−0.248849	+	0.0494992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.4	✓	512
128.69	even	32	inner	384.2.v.a.325.4	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.4	✓	512	1.1	even	1	trivial
384.2.v.a.325.4	yes	512	128.69	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.30780 - 0.538203i) q^{2} +(0.290285 + 0.956940i) q^{3} +(1.42068 + 1.40772i) q^{4} +(0.403677 + 4.09860i) q^{5} +(0.135394 - 1.40772i) q^{6} +(2.40587 - 3.60064i) q^{7} +(-1.10032 - 2.60563i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(q+(-1.30780 - 0.538203i) q^{2} +(0.290285 + 0.956940i) q^{3} +(1.42068 + 1.40772i) q^{4} +(0.403677 + 4.09860i) q^{5} +(0.135394 - 1.40772i) q^{6} +(2.40587 - 3.60064i) q^{7} +(-1.10032 - 2.60563i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(1.67795 - 5.57741i) q^{10} +(3.69226 - 1.97355i) q^{11} +(-0.934705 + 1.76814i) q^{12} +(2.07273 + 0.204146i) q^{13} +(-5.08427 + 3.41406i) q^{14} +(-3.80494 + 1.57606i) q^{15} +(0.0366390 + 3.99983i) q^{16} +(2.08349 + 0.863012i) q^{17} +(1.38640 - 0.279075i) q^{18} +(-0.762517 + 0.625782i) q^{19} +(-5.19620 + 6.39105i) q^{20} +(4.14398 + 1.25706i) q^{21} +(-5.89090 + 0.593827i) q^{22} +(-1.23231 + 6.19525i) q^{23} +(2.17403 - 1.80931i) q^{24} +(-11.7317 + 2.33357i) q^{25} +(-2.60084 - 1.38253i) q^{26} +(-0.773010 - 0.634393i) q^{27} +(8.48666 - 1.72854i) q^{28} +(-2.11203 + 3.95134i) q^{29} +(5.82433 - 0.0133375i) q^{30} +(-0.316443 + 0.316443i) q^{31} +(2.10480 - 5.25070i) q^{32} +(2.96038 + 2.96038i) q^{33} +(-2.26032 - 2.24999i) q^{34} +(15.7288 + 8.40721i) q^{35} +(-1.96334 - 0.381193i) q^{36} +(5.08749 - 6.19913i) q^{37} +(1.33402 - 0.408008i) q^{38} +(0.406326 + 2.04274i) q^{39} +(10.2353 - 5.56160i) q^{40} +(-10.8379 - 2.15579i) q^{41} +(-4.74294 - 3.87429i) q^{42} +(-0.851862 + 2.80821i) q^{43} +(8.02371 + 2.39389i) q^{44} +(-2.61271 - 3.18359i) q^{45} +(4.94591 - 7.43890i) q^{46} +(1.75384 - 4.23416i) q^{47} +(-3.81697 + 1.19615i) q^{48} +(-4.49760 - 10.8582i) q^{49} +(16.5986 + 3.26217i) q^{50} +(-0.221044 + 2.24430i) q^{51} +(2.65730 + 3.20785i) q^{52} +(0.570397 + 1.06714i) q^{53} +(0.669510 + 1.24570i) q^{54} +(9.57929 + 14.3364i) q^{55} +(-12.0291 - 2.30695i) q^{56} +(-0.820183 - 0.548029i) q^{57} +(4.88874 - 4.03085i) q^{58} +(3.98990 - 0.392970i) q^{59} +(-7.62423 - 3.11723i) q^{60} +(-0.499604 + 0.151553i) q^{61} +(0.584155 - 0.243534i) q^{62} +4.33045i q^{63} +(-5.57860 + 5.73404i) q^{64} +8.57771i q^{65} +(-2.27830 - 5.46486i) q^{66} +(-2.49792 + 0.757735i) q^{67} +(1.74509 + 4.15904i) q^{68} +(-6.28620 + 0.619137i) q^{69} +(-16.0453 - 19.4602i) q^{70} +(-4.03542 - 2.69638i) q^{71} +(2.36249 + 1.55520i) q^{72} +(3.48671 + 5.21823i) q^{73} +(-9.98981 + 5.36911i) q^{74} +(-5.63861 - 10.5491i) q^{75} +(-1.96422 - 0.184379i) q^{76} +(1.77704 - 18.0426i) q^{77} +(0.568015 - 2.89018i) q^{78} +(0.944047 + 2.27913i) q^{79} +(-16.3789 + 1.76481i) q^{80} +(0.382683 - 0.923880i) q^{81} +(13.0135 + 8.65232i) q^{82} +(-10.3791 - 12.6469i) q^{83} +(4.11766 + 7.61945i) q^{84} +(-2.69608 + 8.88780i) q^{85} +(2.62545 - 3.21410i) q^{86} +(-4.39429 - 0.874078i) q^{87} +(-9.20500 - 7.44911i) q^{88} +(-3.30001 - 16.5903i) q^{89} +(1.70348 + 5.56967i) q^{90} +(5.72177 - 6.97200i) q^{91} +(-10.4719 + 7.06668i) q^{92} +(-0.394676 - 0.210959i) q^{93} +(-4.57251 + 4.59350i) q^{94} +(-2.87264 - 2.87264i) q^{95} +(5.63559 + 0.489976i) q^{96} +(3.83195 - 3.83195i) q^{97} +(0.0380614 + 16.6209i) q^{98} +(-1.97355 + 3.69226i) 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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