LMFDB - Embedded newform 555.2.bi.a.248.63

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(47,555)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("555.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.bi (of order $12$, degree $4$, 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:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$72$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			248.63
Character	$\chi$	$=$	555.248
Dual form			555.2.bi.a.47.63

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.578972 - 2.16075i) q^{2} +(-1.05871 - 1.37081i) q^{3} +(-2.60160 - 1.50203i) q^{4} +(-2.08250 + 0.814371i) q^{5} +(-3.57495 + 1.49396i) q^{6} +(-1.33384 - 4.97795i) q^{7} +(-1.58821 + 1.58821i) q^{8} +(-0.758252 + 2.90259i) q^{9} +O(q^{10})$	\(q+(0.578972 - 2.16075i) q^{2} +(-1.05871 - 1.37081i) q^{3} +(-2.60160 - 1.50203i) q^{4} +(-2.08250 + 0.814371i) q^{5} +(-3.57495 + 1.49396i) q^{6} +(-1.33384 - 4.97795i) q^{7} +(-1.58821 + 1.58821i) q^{8} +(-0.758252 + 2.90259i) q^{9} +(0.553946 + 4.97126i) q^{10} +4.64526i q^{11} +(0.695340 + 5.15652i) q^{12} +(1.76715 - 0.473506i) q^{13} -11.5284 q^{14} +(3.32112 + 1.99253i) q^{15} +(-0.491864 - 0.851934i) q^{16} +(0.363752 - 1.35754i) q^{17} +(5.83278 + 3.31892i) q^{18} +(-2.85167 - 1.64641i) q^{19} +(6.64103 + 1.00932i) q^{20} +(-5.41169 + 7.09867i) q^{21} +(10.0373 + 2.68947i) q^{22} +(-2.68378 + 2.68378i) q^{23} +(3.85859 + 0.495678i) q^{24} +(3.67360 - 3.39185i) q^{25} -4.09252i q^{26} +(4.78168 - 2.03359i) q^{27} +(-4.00694 + 14.9541i) q^{28} +6.85013 q^{29} +(6.22820 - 6.02250i) q^{30} -3.07108 q^{31} +(-6.46466 + 1.73220i) q^{32} +(6.36777 - 4.91799i) q^{33} +(-2.72271 - 1.57196i) q^{34} +(6.83162 + 9.28034i) q^{35} +(6.33245 - 6.41246i) q^{36} +(-1.19974 + 5.96327i) q^{37} +(-5.20853 + 5.20853i) q^{38} +(-2.51999 - 1.92112i) q^{39} +(2.01405 - 4.60083i) q^{40} +(3.26251 + 1.88361i) q^{41} +(12.2053 + 15.8032i) q^{42} +(-6.22168 - 6.22168i) q^{43} +(6.97732 - 12.0851i) q^{44} +(-0.784729 - 6.66215i) q^{45} +(4.24516 + 7.35283i) q^{46} +(-6.62567 - 6.62567i) q^{47} +(-0.647098 + 1.57621i) q^{48} +(-16.9387 + 9.77957i) q^{49} +(-5.20204 - 9.90153i) q^{50} +(-2.24604 + 0.938611i) q^{51} +(-5.30863 - 1.42244i) q^{52} +(-2.55036 - 0.683368i) q^{53} +(-1.62563 - 11.5094i) q^{54} +(-3.78296 - 9.67374i) q^{55} +(10.0244 + 5.78762i) q^{56} +(0.762179 + 5.65219i) q^{57} +(3.96604 - 14.8015i) q^{58} +(-0.812581 - 1.40743i) q^{59} +(-5.64736 - 10.1722i) q^{60} +(1.47736 - 2.55885i) q^{61} +(-1.77807 + 6.63584i) q^{62} +(15.4604 - 0.0970482i) q^{63} +13.0040i q^{64} +(-3.29447 + 2.42519i) q^{65} +(-6.93981 - 16.6066i) q^{66} +(0.808241 + 3.01640i) q^{67} +(-2.98540 + 2.98540i) q^{68} +(6.52032 + 0.837606i) q^{69} +(24.0078 - 9.38838i) q^{70} +(-8.81440 - 5.08900i) q^{71} +(-3.40566 - 5.81419i) q^{72} +(-2.08180 - 2.08180i) q^{73} +(12.1905 + 6.04490i) q^{74} +(-8.53888 - 1.44482i) q^{75} +(4.94593 + 8.56660i) q^{76} +(23.1239 - 6.19602i) q^{77} +(-5.61007 + 4.33280i) q^{78} +(0.0724067 + 0.0418040i) q^{79} +(1.71810 + 1.37359i) q^{80} +(-7.85011 - 4.40180i) q^{81} +(5.95893 - 5.95893i) q^{82} +(-3.46712 - 0.929013i) q^{83} +(24.7414 - 10.3393i) q^{84} +(0.348029 + 3.12330i) q^{85} +(-17.0457 + 9.84134i) q^{86} +(-7.25233 - 9.39025i) q^{87} +(-7.37764 - 7.37764i) q^{88} +(4.94716 + 8.56874i) q^{89} +(-14.8496 - 2.16159i) q^{90} +(-4.71418 - 8.16520i) q^{91} +(11.0133 - 2.95099i) q^{92} +(3.25139 + 4.20987i) q^{93} +(-18.1525 + 10.4804i) q^{94} +(7.27939 + 1.10634i) q^{95} +(9.21875 + 7.02793i) q^{96} +(2.90386 - 2.90386i) q^{97} +(11.3242 + 42.2625i) q^{98} +(-13.4833 - 3.52228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 16 q^{6} - 4 q^{7}+O(q^{10}) $ 288 * q - 16 * q^6 - 4 * q^7	$ 288 q - 16 q^{6} - 4 q^{7} - 16 q^{10} - 18 q^{12} - 20 q^{13} + 6 q^{15} + 112 q^{16} + 20 q^{18} - 4 q^{21} - 12 q^{22} - 36 q^{25} + 48 q^{27} - 28 q^{28} - 16 q^{30} - 80 q^{31} + 2 q^{33} - 16 q^{36} - 36 q^{37} + 8 q^{40} - 32 q^{42} - 16 q^{43} + 76 q^{45} - 24 q^{46} + 112 q^{48} + 48 q^{55} + 2 q^{57} - 60 q^{58} - 56 q^{60} + 16 q^{61} - 36 q^{63} - 36 q^{70} - 58 q^{72} - 48 q^{73} - 88 q^{75} + 16 q^{76} + 20 q^{78} - 56 q^{81} - 136 q^{82} + 144 q^{85} + 16 q^{87} + 144 q^{88} - 42 q^{90} - 22 q^{93} - 80 q^{96} + 56 q^{97}+O(q^{100}) $ 288 * q - 16 * q^6 - 4 * q^7 - 16 * q^10 - 18 * q^12 - 20 * q^13 + 6 * q^15 + 112 * q^16 + 20 * q^18 - 4 * q^21 - 12 * q^22 - 36 * q^25 + 48 * q^27 - 28 * q^28 - 16 * q^30 - 80 * q^31 + 2 * q^33 - 16 * q^36 - 36 * q^37 + 8 * q^40 - 32 * q^42 - 16 * q^43 + 76 * q^45 - 24 * q^46 + 112 * q^48 + 48 * q^55 + 2 * q^57 - 60 * q^58 - 56 * q^60 + 16 * q^61 - 36 * q^63 - 36 * q^70 - 58 * q^72 - 48 * q^73 - 88 * q^75 + 16 * q^76 + 20 * q^78 - 56 * q^81 - 136 * q^82 + 144 * q^85 + 16 * q^87 + 144 * q^88 - 42 * q^90 - 22 * q^93 - 80 * q^96 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	0.578972	−	2.16075i	0.409395	−	1.52788i	−0.386408	−	0.922328i	$-0.626284\pi$
$2$	0.578972	−	2.16075i	0.409395	−	1.52788i	0.795803	−	0.605555i	$-0.207049\pi$
$3$	−1.05871	−	1.37081i	−0.611248	−	0.791439i
$3$	−1.05871	−	1.37081i	−0.611248	−	0.791439i
$4$	−2.60160	−	1.50203i	−1.30080	−	0.751016i
$5$	−2.08250	+	0.814371i	−0.931322	+	0.364198i
$5$	−2.08250	+	0.814371i	−0.931322	+	0.364198i
$6$	−3.57495	+	1.49396i	−1.45947	+	0.609905i
$7$	−1.33384	−	4.97795i	−0.504144	−	1.88149i	−0.471188	−	0.882033i	$-0.656175\pi$
$7$	−1.33384	−	4.97795i	−0.504144	−	1.88149i	−0.0329552	−	0.999457i	$-0.510492\pi$
$8$	−1.58821	+	1.58821i	−0.561517	+	0.561517i
$9$	−0.758252	+	2.90259i	−0.252751	+	0.967531i
$10$	0.553946	+	4.97126i	0.175173	+	1.57205i
$11$			4.64526i			1.40060i	0.713850	+	0.700299i	$0.246950\pi$
$11$			4.64526i			1.40060i	−0.713850	+	0.700299i	$0.753050\pi$
$12$	0.695340	+	5.15652i	0.200727	+	1.48856i
$13$	1.76715	−	0.473506i	0.490119	−	0.131327i	−0.00529159	−	0.999986i	$-0.501684\pi$
$13$	1.76715	−	0.473506i	0.490119	−	0.131327i	0.495410	+	0.868659i	$0.335018\pi$
$14$	−11.5284			−3.08109
$15$	3.32112	+	1.99253i	0.857509	+	0.514469i
$16$	−0.491864	−	0.851934i	−0.122966	−	0.212984i
$17$	0.363752	−	1.35754i	0.0882228	−	0.329252i	−0.907682	−	0.419658i	$-0.862150\pi$
$17$	0.363752	−	1.35754i	0.0882228	−	0.329252i	0.995905	+	0.0904064i	$0.0288166\pi$
$18$	5.83278	+	3.31892i	1.37480	+	0.782276i
$19$	−2.85167	−	1.64641i	−0.654218	−	0.377713i	0.135852	−	0.990729i	$-0.456623\pi$
$19$	−2.85167	−	1.64641i	−0.654218	−	0.377713i	−0.790071	+	0.613016i	$0.789956\pi$
$20$	6.64103	+	1.00932i	1.48498	+	0.225690i
$21$	−5.41169	+	7.09867i	−1.18093	+	1.54906i
$22$	10.0373	+	2.68947i	2.13995	+	0.573398i
$23$	−2.68378	+	2.68378i	−0.559608	+	0.559608i	−0.929196	−	0.369588i	$-0.879499\pi$
$23$	−2.68378	+	2.68378i	−0.559608	+	0.559608i	0.369588	+	0.929196i	$0.379499\pi$
$24$	3.85859	+	0.495678i	0.787632	+	0.101180i
$25$	3.67360	−	3.39185i	0.734720	−	0.678370i
$26$		−	4.09252i		−	0.802609i
$27$	4.78168	−	2.03359i	0.920235	−	0.391365i
$28$	−4.00694	+	14.9541i	−0.757240	+	2.82606i
$29$	6.85013			1.27204			0.636019	−	0.771673i	$-0.280580\pi$
$29$	6.85013			1.27204			0.636019	+	0.771673i	$0.280580\pi$
$30$	6.22820	−	6.02250i	1.13711	−	1.09955i
$31$	−3.07108			−0.551582			−0.275791	−	0.961218i	$-0.588940\pi$
$31$	−3.07108			−0.551582			−0.275791	+	0.961218i	$0.588940\pi$
$32$	−6.46466	+	1.73220i	−1.14280	+	0.306213i
$33$	6.36777	−	4.91799i	1.10849	−	0.856113i
$34$	−2.72271	−	1.57196i	−0.466941	−	0.269588i
$35$	6.83162	+	9.28034i	1.15475	+	1.56866i
$36$	6.33245	−	6.41246i	1.05541	−	1.06874i
$37$	−1.19974	+	5.96327i	−0.197236	+	0.980356i
$37$	−1.19974	+	5.96327i	−0.197236	+	0.980356i
$38$	−5.20853	+	5.20853i	−0.844935	+	0.844935i
$39$	−2.51999	−	1.92112i	−0.403522	−	0.307626i
$40$	2.01405	−	4.60083i	0.318450	−	0.727456i
$41$	3.26251	+	1.88361i	0.509519	+	0.294171i	0.732636	−	0.680621i	$-0.238290\pi$
$41$	3.26251	+	1.88361i	0.509519	+	0.294171i	−0.223117	+	0.974792i	$0.571623\pi$
$42$	12.2053	+	15.8032i	1.88331	+	2.43849i
$43$	−6.22168	−	6.22168i	−0.948798	−	0.948798i	0.0499535	−	0.998752i	$-0.484093\pi$
$43$	−6.22168	−	6.22168i	−0.948798	−	0.948798i	−0.998752	+	0.0499535i	$0.984093\pi$
$44$	6.97732	−	12.0851i	1.05187	−	1.82189i
$45$	−0.784729	−	6.66215i	−0.116981	−	0.993134i
$46$	4.24516	+	7.35283i	0.625915	+	1.08412i
$47$	−6.62567	−	6.62567i	−0.966454	−	0.966454i	0.0330015	−	0.999455i	$-0.489493\pi$
$47$	−6.62567	−	6.62567i	−0.966454	−	0.966454i	−0.999455	+	0.0330015i	$0.989493\pi$
$48$	−0.647098	+	1.57621i	−0.0934006	+	0.227506i
$49$	−16.9387	+	9.77957i	−2.41982	+	1.39708i
$50$	−5.20204	−	9.90153i	−0.735680	−	1.40029i
$51$	−2.24604	+	0.938611i	−0.314509	+	0.131432i
$52$	−5.30863	−	1.42244i	−0.736174	−	0.197257i
$53$	−2.55036	−	0.683368i	−0.350319	−	0.0938678i	0.0793683	−	0.996845i	$-0.474710\pi$
$53$	−2.55036	−	0.683368i	−0.350319	−	0.0938678i	−0.429688	+	0.902978i	$0.641376\pi$
$54$	−1.62563	−	11.5094i	−0.221221	−	1.56624i
$55$	−3.78296	−	9.67374i	−0.510094	−	1.30441i
$56$	10.0244	+	5.78762i	1.33957	+	0.773403i
$57$	0.762179	+	5.65219i	0.100953	+	0.748650i
$58$	3.96604	−	14.8015i	0.520766	−	1.94353i
$59$	−0.812581	−	1.40743i	−0.105789	−	0.183232i	0.808271	−	0.588810i	$-0.200403\pi$
$59$	−0.812581	−	1.40743i	−0.105789	−	0.183232i	−0.914060	+	0.405578i	$0.867070\pi$
$60$	−5.64736	−	10.1722i	−0.729072	−	1.31322i
$61$	1.47736	−	2.55885i	0.189156	−	0.327628i	−0.755813	−	0.654787i	$-0.772758\pi$
$61$	1.47736	−	2.55885i	0.189156	−	0.327628i	0.944969	+	0.327160i	$0.106092\pi$
$62$	−1.77807	+	6.63584i	−0.225815	+	0.842752i
$63$	15.4604	−	0.0970482i	1.94782	−	0.0122269i
$64$			13.0040i			1.62550i
$65$	−3.29447	+	2.42519i	−0.408629	+	0.300808i
$66$	−6.93981	−	16.6066i	−0.854231	−	2.04413i
$67$	0.808241	+	3.01640i	0.0987424	+	0.368512i	0.997560	−	0.0698107i	$-0.0222395\pi$
$67$	0.808241	+	3.01640i	0.0987424	+	0.368512i	−0.898818	+	0.438322i	$0.855573\pi$
$68$	−2.98540	+	2.98540i	−0.362033	+	0.362033i
$69$	6.52032	+	0.837606i	0.784955	+	0.100836i
$70$	24.0078	−	9.38838i	2.86949	−	1.12213i
$71$	−8.81440	−	5.08900i	−1.04608	−	0.603953i	−0.124529	−	0.992216i	$-0.539742\pi$
$71$	−8.81440	−	5.08900i	−1.04608	−	0.603953i	−0.921549	+	0.388263i	$0.873075\pi$
$72$	−3.40566	−	5.81419i	−0.401361	−	0.685209i
$73$	−2.08180	−	2.08180i	−0.243657	−	0.243657i	0.574704	−	0.818361i	$-0.305117\pi$
$73$	−2.08180	−	2.08180i	−0.243657	−	0.243657i	−0.818361	+	0.574704i	$0.805117\pi$
$74$	12.1905	+	6.04490i	1.41712	+	0.702706i
$75$	−8.53888	−	1.44482i	−0.985985	−	0.166833i
$76$	4.94593	+	8.56660i	0.567337	+	0.982657i
$77$	23.1239	−	6.19602i	2.63521	−	0.706102i
$78$	−5.61007	+	4.33280i	−0.635216	+	0.490593i
$79$	0.0724067	+	0.0418040i	0.00814639	+	0.00470332i	0.504068	−	0.863664i	$-0.331836\pi$
$79$	0.0724067	+	0.0418040i	0.00814639	+	0.00470332i	−0.495921	+	0.868367i	$0.665170\pi$
$80$	1.71810	+	1.37359i	0.192089	+	0.153572i
$81$	−7.85011	−	4.40180i	−0.872234	−	0.489089i
$82$	5.95893	−	5.95893i	0.658054	−	0.658054i
$83$	−3.46712	−	0.929013i	−0.380566	−	0.101972i	0.0634642	−	0.997984i	$-0.479785\pi$
$83$	−3.46712	−	0.929013i	−0.380566	−	0.101972i	−0.444030	+	0.896012i	$0.646452\pi$
$84$	24.7414	−	10.3393i	2.69951	−	1.12811i
$85$	0.348029	+	3.12330i	0.0377490	+	0.338770i
$86$	−17.0457	+	9.84134i	−1.83809	+	1.06122i
$87$	−7.25233	−	9.39025i	−0.777531	−	1.00674i
$88$	−7.37764	−	7.37764i	−0.786459	−	0.786459i
$89$	4.94716	+	8.56874i	0.524398	+	0.908285i	0.999596	+	0.0284058i	$0.00904308\pi$
$89$	4.94716	+	8.56874i	0.524398	+	0.908285i	−0.475198	+	0.879879i	$0.657624\pi$
$90$	−14.8496	−	2.16159i	−1.56528	−	0.227852i
$91$	−4.71418	−	8.16520i	−0.494180	−	0.855946i
$92$	11.0133	−	2.95099i	1.14821	−	0.307662i
$93$	3.25139	+	4.20987i	0.337153	+	0.436543i
$94$	−18.1525	+	10.4804i	−1.87229	+	1.08097i
$95$	7.27939	+	1.10634i	0.746850	+	0.113508i
$96$	9.21875	+	7.02793i	0.940884	+	0.717286i
$97$	2.90386	−	2.90386i	0.294842	−	0.294842i	−0.544147	−	0.838990i	$-0.683147\pi$
$97$	2.90386	−	2.90386i	0.294842	−	0.294842i	0.838990	+	0.544147i	$0.183147\pi$
$98$	11.3242	+	42.2625i	1.14392	+	4.26916i
$99$	−13.4833	−	3.52228i	−1.35512	−	0.354002i
$100$	−14.6519	+	3.30636i	−1.46519	+	0.330636i
$101$		−	11.0072i		−	1.09525i	−0.836723	−	0.547627i	$-0.815531\pi$
$101$		−	11.0072i		−	1.09525i	0.836723	−	0.547627i	$-0.184469\pi$
$102$	0.727710	+	5.39657i	0.0720541	+	0.534340i
$103$	−10.8165	−	10.8165i	−1.06578	−	1.06578i	−0.997678	−	0.0681002i	$-0.978306\pi$
$103$	−10.8165	−	10.8165i	−1.06578	−	1.06578i	−0.0681002	−	0.997678i	$-0.521694\pi$
$104$	−2.05457	+	3.55863i	−0.201468	+	0.348952i
$105$	5.48888	−	19.1901i	0.535660	−	1.87276i
$106$	−2.95318	+	5.11506i	−0.286838	+	0.496818i
$107$	−12.6335	+	3.38514i	−1.22133	+	0.327254i	−0.811197	−	0.584772i	$-0.801184\pi$
$107$	−12.6335	+	3.38514i	−1.22133	+	0.327254i	−0.410131	+	0.912027i	$0.634517\pi$
$108$	−15.4945	−	1.89165i	−1.49096	−	0.182024i
$109$	8.78870	−	5.07416i	0.841805	−	0.486016i	−0.0160725	−	0.999871i	$-0.505116\pi$
$109$	8.78870	−	5.07416i	0.841805	−	0.486016i	0.857877	+	0.513855i	$0.171783\pi$
$110$	−23.0928	+	2.57322i	−2.20181	+	0.245347i
$111$	9.44471	−	4.66878i	0.896452	−	0.443141i
$112$	−3.58482	+	3.58482i	−0.338734	+	0.338734i
$113$	−18.1130	−	4.85336i	−1.70393	−	0.456566i	−0.730003	−	0.683443i	$-0.760482\pi$
$113$	−18.1130	−	4.85336i	−1.70393	−	0.456566i	−0.973923	+	0.226878i	$0.927148\pi$
$114$	12.6543	+	1.62558i	1.18518	+	0.152249i
$115$	3.40338	−	7.77457i	0.317367	−	0.724983i
$116$	−17.8213	−	10.2891i	−1.65466	−	0.955321i
$117$	0.0344516	+	5.48835i	0.00318505	+	0.507398i
$118$	−3.51157	+	0.940923i	−0.323267	+	0.0866190i
$119$	−7.24296			−0.663961
$120$	−8.43918	+	2.11008i	−0.770388	+	0.192623i
$121$	−10.5784			−0.961673
$122$	−4.67370	−	4.67370i	−0.423137	−	0.423137i
$123$	−0.871987	−	6.46650i	−0.0786244	−	0.583065i
$124$	7.98970	+	4.61285i	0.717496	+	0.414247i
$125$	−4.88804	+	10.0552i	−0.437200	+	0.899364i
$126$	8.74142	−	33.4622i	0.778748	−	2.98105i
$127$	14.7060	+	3.94046i	1.30495	+	0.349660i	0.843319	−	0.537414i	$-0.180599\pi$
$127$	14.7060	+	3.94046i	1.30495	+	0.349660i	0.461628	+	0.887073i	$0.347265\pi$
$128$	15.1691	+	4.06454i	1.34077	+	0.359258i
$129$	−1.94178	+	15.1157i	−0.170964	+	1.33087i
$130$	3.33283	+	8.52266i	0.292308	+	0.747487i
$131$	3.48392	−	2.01144i	0.304392	−	0.175741i	−0.340022	−	0.940417i	$-0.610435\pi$
$131$	3.48392	−	2.01144i	0.304392	−	0.175741i	0.644414	+	0.764677i	$0.277101\pi$
$132$	−23.9534	+	3.23003i	−2.08487	+	0.281138i
$133$	−4.39210	+	16.3915i	−0.380843	+	1.42133i
$134$	6.98564			0.603467
$135$	−8.30175	+	8.12902i	−0.714501	+	0.699635i
$136$	1.57834	+	2.73377i	0.135342	+	0.234419i
$137$	−0.292333	−	0.292333i	−0.0249757	−	0.0249757i	0.694509	−	0.719484i	$-0.255622\pi$
$137$	−0.292333	−	0.292333i	−0.0249757	−	0.0249757i	−0.719484	+	0.694509i	$0.755622\pi$
$138$	5.58495	−	13.6039i	0.475422	−	1.15804i
$139$	17.3866	−	10.0381i	1.47471	−	0.851425i	0.475117	−	0.879923i	$-0.342406\pi$
$139$	17.3866	−	10.0381i	1.47471	−	0.851425i	0.999594	+	0.0284980i	$0.00907243\pi$
$140$	−3.83374	−	34.4050i	−0.324010	−	2.90775i
$141$	−2.06787	+	16.0972i	−0.174146	+	1.35563i
$142$	−16.0994	+	16.0994i	−1.35103	+	1.35103i
$143$	2.19956	+	8.20886i	0.183936	+	0.686459i
$144$	2.84578	−	0.781702i	0.237148	−	0.0651418i
$145$	−14.2654	+	5.57855i	−1.18468	+	0.463273i
$146$	−5.70357	+	3.29296i	−0.472031	+	0.272527i
$147$	31.3392	+	12.8660i	2.58481	+	1.06117i
$148$	12.0783	−	13.7120i	0.992827	−	1.12712i
$149$	−2.47602			−0.202843			−0.101422	−	0.994844i	$-0.532339\pi$
$149$	−2.47602			−0.202843			−0.101422	+	0.994844i	$0.532339\pi$
$150$	−8.06567	+	17.6139i	−0.658559	+	1.43817i
$151$	7.90477	−	13.6915i	0.643281	−	1.11420i	−0.341414	−	0.939913i	$-0.610906\pi$
$151$	7.90477	−	13.6915i	0.643281	−	1.11420i	0.984696	−	0.174283i	$-0.0557607\pi$
$152$	7.14390	−	1.91420i	0.579447	−	0.155262i
$153$	3.66457	+	2.08518i	0.296263	+	0.168577i
$154$		−	53.5523i		−	4.31537i
$155$	6.39551	−	2.50100i	0.513700	−	0.200885i
$156$	3.67041	+	8.78309i	0.293868	+	0.703210i
$157$	13.3835	+	3.58611i	1.06812	+	0.286202i	0.749721	−	0.661754i	$-0.230188\pi$
$157$	13.3835	+	3.58611i	1.06812	+	0.286202i	0.318401	+	0.947956i	$0.396854\pi$
$158$	0.132250	−	0.132250i	0.0105212	−	0.0105212i
$159$	1.76334	+	4.21956i	0.139842	+	0.334633i
$160$	12.0520	−	8.87194i	0.952794	−	0.701388i
$161$	16.9395	+	9.78002i	1.33502	+	0.770774i
$162$	−14.0562	+	14.4136i	−1.10436	+	1.13244i
$163$	−2.41715	+	9.02093i	−0.189326	+	0.706574i	0.804337	+	0.594173i	$0.202521\pi$
$163$	−2.41715	+	9.02093i	−0.189326	+	0.706574i	−0.993663	+	0.112401i	$0.964146\pi$
$164$	−5.65850	−	9.80080i	−0.441854	−	0.765314i
$165$	−9.25581	+	15.4274i	−0.720564	+	1.20103i
$166$	−4.01473	+	6.95372i	−0.311604	+	0.539714i
$167$	2.21997	−	0.594840i	0.171787	−	0.0460301i	−0.171900	−	0.985114i	$-0.554991\pi$
$167$	2.21997	−	0.594840i	0.171787	−	0.0460301i	0.343687	+	0.939084i	$0.388324\pi$
$168$	−2.67928	−	19.8691i	−0.206711	−	1.53293i
$169$	−8.35973	+	4.82649i	−0.643056	+	0.371268i
$170$	6.95019	+	1.05630i	0.533055	+	0.0810147i
$171$	6.94116	−	7.02885i	0.530804	−	0.537510i
$172$	6.84114	+	25.5315i	0.521632	+	1.94676i
$173$	9.76916	+	2.61764i	0.742736	+	0.199015i	0.610294	−	0.792175i	$-0.291051\pi$
$173$	9.76916	+	2.61764i	0.742736	+	0.199015i	0.132442	+	0.991191i	$0.457718\pi$
$174$	−24.4889	+	10.2338i	−1.85650	+	0.775822i
$175$	−21.7845	−	13.7628i	−1.64675	−	1.04037i
$176$	3.95745	−	2.28484i	0.298304	−	0.172226i
$177$	−1.06903	+	2.60396i	−0.0803535	+	0.195726i
$178$	21.3792	−	5.72854i	1.60244	−	0.429372i
$179$	−4.39631			−0.328596			−0.164298	−	0.986411i	$-0.552536\pi$
$179$	−4.39631			−0.328596			−0.164298	+	0.986411i	$0.552536\pi$
$180$	−7.96521	+	18.5109i	−0.593692	+	1.37972i
$181$	6.28722	−	10.8898i	0.467325	−	0.809431i	−0.531978	−	0.846758i	$-0.678551\pi$
$181$	6.28722	−	10.8898i	0.467325	−	0.809431i	0.999303	+	0.0373271i	$0.0118843\pi$
$182$	−20.3724	+	5.45876i	−1.51010	+	0.404630i
$183$	−5.07180	+	0.683916i	−0.374919	+	0.0505566i
$184$		−	8.52482i		−	0.628458i
$185$	−2.35787	−	13.3955i	−0.173354	−	0.984860i
$186$	10.9790	−	4.58805i	0.805016	−	0.336412i
$187$	6.30612	+	1.68972i	0.461149	+	0.123565i
$188$	7.28535	+	27.1893i	0.531339	+	1.98298i
$189$	−16.5011	−	21.0905i	−1.20028	−	1.53411i
$190$	6.60508	−	15.0884i	0.479183	−	1.09463i
$191$			10.7222i			0.775831i	0.921695	+	0.387916i	$0.126805\pi$
$191$			10.7222i			0.775831i	−0.921695	+	0.387916i	$0.873195\pi$
$192$	17.8260	−	13.7675i	1.28648	−	0.993583i
$193$	−5.72710	−	5.72710i	−0.412246	−	0.412246i	0.470275	−	0.882520i	$-0.344155\pi$
$193$	−5.72710	−	5.72710i	−0.412246	−	0.412246i	−0.882520	+	0.470275i	$0.844155\pi$
$194$	−4.59327	−	7.95578i	−0.329778	−	0.571192i
$195$	6.81238	+	1.94852i	0.487845	+	0.139537i
$196$	58.7569			4.19692
$197$	6.61428	−	24.6848i	0.471248	−	1.75872i	−0.164047	−	0.986453i	$-0.552455\pi$
$197$	6.61428	−	24.6848i	0.471248	−	1.75872i	0.635295	−	0.772270i	$-0.280879\pi$
$198$	−15.4172	+	27.0948i	−1.09565	+	1.92554i
$199$		−	7.60467i		−	0.539081i	−0.962989	−	0.269540i	$-0.913128\pi$
$199$		−	7.60467i		−	0.539081i	0.962989	−	0.269540i	$-0.0868718\pi$
$200$	−0.447474	+	11.2214i	−0.0316412	+	0.793474i
$201$	3.27922	−	4.30145i	0.231298	−	0.303401i
$202$	−23.7838	−	6.37284i	−1.67342	−	0.448391i
$203$	−9.13697	−	34.0996i	−0.641290	−	2.39333i
$204$	7.25312	+	0.931741i	0.507820	+	0.0652349i
$205$	−8.32814	−	1.26573i	−0.581663	−	0.0884021i
$206$	−29.6342	+	17.1093i	−2.06471	+	1.19206i
$207$	−5.75495	−	9.82492i	−0.399997	−	0.682879i
$208$	−1.27259	−	1.27259i	−0.0882385	−	0.0882385i
$209$	7.64801	−	13.2467i	0.529024	−	0.916297i
$210$	−38.2871	−	22.9706i	−2.64206	−	1.58512i
$211$	6.09168			0.419369			0.209684	−	0.977769i	$-0.432756\pi$
$211$	6.09168			0.419369			0.209684	+	0.977769i	$0.432756\pi$
$212$	5.60857	+	5.60857i	0.385199	+	0.385199i
$213$	2.35587	+	17.4707i	0.161421	+	1.19707i
$214$			29.2578i			2.00002i
$215$	18.0234	+	7.88989i	1.22919	+	0.538086i
$216$	−4.36454	+	10.8241i	−0.296969	+	0.736486i
$217$	4.09632	+	15.2877i	0.278076	+	1.03779i
$218$	−5.87559	−	21.9280i	−0.397945	−	1.48515i
$219$	−0.649728	+	5.05779i	−0.0439046	+	0.341774i
$220$	−4.68853	+	30.8493i	−0.316101	+	2.07986i
$221$		−	2.57121i		−	0.172959i
$222$	−4.61987	−	23.1108i	−0.310065	−	1.55109i
$223$	12.8009	+	12.8009i	0.857212	+	0.857212i	0.991009	−	0.133797i	$-0.0427170\pi$
$223$	12.8009	+	12.8009i	0.857212	+	0.857212i	−0.133797	+	0.991009i	$0.542717\pi$
$224$	17.2456	+	29.8703i	1.15227	+	1.99579i
$225$	7.05966	+	13.2348i	0.470644	+	0.882323i
$226$	−20.9738	+	36.3277i	−1.39516	+	2.41649i
$227$	1.98066	−	0.530716i	0.131461	−	0.0352248i	−0.192489	−	0.981299i	$-0.561656\pi$
$227$	1.98066	−	0.530716i	0.131461	−	0.0352248i	0.323950	+	0.946074i	$0.394989\pi$
$228$	6.50688	−	15.8495i	0.430929	−	1.04966i
$229$	−8.88036	−	5.12708i	−0.586830	−	0.338807i	0.177013	−	0.984209i	$-0.443357\pi$
$229$	−8.88036	−	5.12708i	−0.586830	−	0.338807i	−0.763843	+	0.645402i	$0.776690\pi$
$230$	−14.8285	−	11.8551i	−0.977761	−	0.781704i
$231$	−32.9751	−	25.1387i	−2.16960	−	1.65400i
$232$	−10.8794	+	10.8794i	−0.714271	+	0.714271i
$233$	5.97240	−	5.97240i	0.391265	−	0.391265i	−0.483873	−	0.875138i	$-0.660770\pi$
$233$	5.97240	−	5.97240i	0.391265	−	0.391265i	0.875138	+	0.483873i	$0.160770\pi$
$234$	11.8789	+	3.10316i	0.776549	+	0.202860i
$235$	19.1937	+	8.40220i	1.25206	+	0.548099i
$236$			4.88209i			0.317797i
$237$	−0.0193525	−	0.143514i	−0.00125708	−	0.00932227i
$238$	−4.19347	+	15.6502i	−0.271822	+	1.01445i
$239$	−0.917410	−	1.58900i	−0.0593423	−	0.102784i	0.834828	−	0.550511i	$-0.185567\pi$
$239$	−0.917410	−	1.58900i	−0.0593423	−	0.102784i	−0.894170	+	0.447727i	$0.852234\pi$
$240$	0.0639635	−	3.80943i	0.00412883	−	0.245898i
$241$	1.00505	−	1.74080i	0.0647411	−	0.112135i	−0.831838	−	0.555018i	$-0.812711\pi$
$241$	1.00505	−	1.74080i	0.0647411	−	0.112135i	0.896579	+	0.442884i	$0.146045\pi$
$242$	−6.12460	+	22.8573i	−0.393704	+	1.46932i
$243$	2.27698	+	15.4213i	0.146068	+	0.989275i
$244$	−7.68696	+	4.43807i	−0.492107	+	0.284118i
$245$	27.3106	−	34.1603i	1.74481	−	2.18242i
$246$	−14.4774	−	1.85978i	−0.923043	−	0.118575i
$247$	−5.81891	−	1.55917i	−0.370249	−	0.0992078i
$248$	4.87751	−	4.87751i	0.309722	−	0.309722i
$249$	2.39719	+	5.73633i	0.151916	+	0.363525i
$250$	18.8968	+	16.3835i	1.19514	+	1.03619i
$251$		−	5.85930i		−	0.369836i	−0.982754	−	0.184918i	$-0.940798\pi$
$251$		−	5.85930i		−	0.369836i	0.982754	−	0.184918i	$-0.0592019\pi$
$252$	−40.3674	−	22.9695i	−2.54291	−	1.44694i
$253$	−12.4669	−	12.4669i	−0.783785	−	0.783785i
$254$	17.0287	−	29.4946i	1.06848	−	1.85066i
$255$	3.91300	−	3.78377i	0.245042	−	0.236949i
$256$	4.56095	−	7.89981i	0.285060	−	0.493738i
$257$	0.234205	−	0.874065i	0.0146093	−	0.0545227i	−0.958236	−	0.285977i	$-0.907682\pi$
$257$	0.234205	−	0.874065i	0.0146093	−	0.0545227i	0.972846	+	0.231455i	$0.0743485\pi$
$258$	31.5372	+	12.9473i	1.96342	+	0.806064i
$259$	31.2852	−	1.98181i	1.94396	−	0.123144i
$260$	12.2136	−	1.36096i	0.757455	−	0.0844030i
$261$	−5.19413	+	19.8832i	−0.321509	+	1.23074i
$262$	−2.32914	−	8.69247i	−0.143895	−	0.537023i
$263$	5.15214	+	19.2280i	0.317695	+	1.18565i	0.921455	+	0.388486i	$0.127002\pi$
$263$	5.15214	+	19.2280i	0.317695	+	1.18565i	−0.603760	+	0.797166i	$0.706331\pi$
$264$	−2.30255	+	17.9242i	−0.141712	+	1.10316i
$265$	5.86764	−	0.653829i	0.360447	−	0.0401644i
$266$	32.8752	+	18.9805i	2.01571	+	1.16377i
$267$	6.50851	−	15.8535i	0.398314	−	0.970217i
$268$	2.42801	−	9.06145i	0.148314	−	0.553516i
$269$	−10.5111			−0.640876			−0.320438	−	0.947270i	$-0.603830\pi$
$269$	−10.5111			−0.640876			−0.320438	+	0.947270i	$0.603830\pi$
$270$	12.7583	+	22.6445i	0.776447	+	1.37810i
$271$	−12.5624	−	21.7588i	−0.763114	−	1.32175i	−0.941238	−	0.337745i	$-0.890336\pi$
$271$	−12.5624	−	21.7588i	−0.763114	−	1.32175i	0.178123	−	0.984008i	$-0.442997\pi$
$272$	−1.33545	+	0.357833i	−0.0809737	+	0.0216968i
$273$	−6.20199	+	15.1069i	−0.375362	+	0.914309i
$274$	−0.800912	+	0.462407i	−0.0483849	+	0.0279350i
$275$	15.7560	+	17.0648i	0.950124	+	1.02905i
$276$	−15.7051	−	11.9728i	−0.945338	−	0.720681i
$277$	−3.71851	−	13.8777i	−0.223424	−	0.833829i	−0.983030	−	0.183446i	$-0.941275\pi$
$277$	−3.71851	−	13.8777i	−0.223424	−	0.833829i	0.759606	−	0.650383i	$-0.225392\pi$
$278$	−11.6236	−	43.3799i	−0.697138	−	2.60176i
$279$	2.32865	−	8.91409i	0.139413	−	0.533673i
$280$	−25.5892	−	3.88909i	−1.52924	−	0.232417i
$281$	−6.68407	+	3.85905i	−0.398738	+	0.230212i	−0.685940	−	0.727659i	$-0.740609\pi$
$281$	−6.68407	+	3.85905i	−0.398738	+	0.230212i	0.287201	+	0.957870i	$0.407275\pi$
$282$	33.5849	+	13.7880i	1.99995	+	0.821063i
$283$	16.4366	−	4.40417i	0.977053	−	0.261801i	0.265250	−	0.964180i	$-0.414546\pi$
$283$	16.4366	−	4.40417i	0.977053	−	0.261801i	0.711803	+	0.702379i	$0.247879\pi$
$284$	15.2877	+	26.4790i	0.907157	+	1.57124i
$285$	−6.19021	−	11.1500i	−0.366677	−	0.660467i
$286$	19.0108			1.12413
$287$	5.02487	−	18.7531i	0.296609	−	1.10696i
$288$	−0.126033	−	20.0777i	−0.00742654	−	1.18309i
$289$	13.0118	+	7.51238i	0.765402	+	0.441905i
$290$	3.79461	+	34.0538i	0.222827	+	1.99971i
$291$	−7.05500	−	0.906291i	−0.413572	−	0.0531277i
$292$	2.28908	+	8.54295i	0.133958	+	0.499938i
$293$	−4.00232	−	14.9369i	−0.233818	−	0.872621i	−0.978678	−	0.205400i	$-0.934150\pi$
$293$	−4.00232	−	14.9369i	−0.233818	−	0.872621i	0.744860	−	0.667221i	$-0.232516\pi$
$294$	45.9448	−	60.2672i	2.67956	−	3.51485i
$295$	2.83837	+	2.26923i	0.165256	+	0.132120i
$296$	−7.56549	−	11.3764i	−0.439735	−	0.661237i
$297$	9.44656	+	22.2121i	0.548145	+	1.28888i
$298$	−1.43355	+	5.35007i	−0.0830431	+	0.309921i
$299$	−3.47186	+	6.01343i	−0.200783	+	0.347766i
$300$	20.0446	+	16.5845i	1.15727	+	0.957507i
$301$	−22.6725	+	39.2700i	−1.30682	+	2.26348i
$302$	−25.0072	−	25.0072i	−1.43900	−	1.43900i
$303$	−15.0887	+	11.6534i	−0.866826	+	0.669472i
$304$			3.23925i			0.185784i
$305$	−0.992733	+	6.53192i	−0.0568437	+	0.374017i
$306$	6.62725	−	6.71098i	0.378855	−	0.383641i
$307$	−7.51301	+	7.51301i	−0.428790	+	0.428790i	−0.888216	−	0.459426i	$-0.848055\pi$
$307$	−7.51301	+	7.51301i	−0.428790	+	0.428790i	0.459426	+	0.888216i	$0.348055\pi$
$308$	−69.4656	−	18.6132i	−3.95817	−	1.06059i
$309$	−3.37581	+	26.2789i	−0.192043	+	1.49495i
$310$	−1.70121	−	15.2671i	−0.0966223	−	0.867115i
$311$	17.4851	−	10.0950i	0.991488	−	0.572436i	0.0857694	−	0.996315i	$-0.472665\pi$
$311$	17.4851	−	10.0950i	0.991488	−	0.572436i	0.905719	+	0.423879i	$0.139332\pi$
$312$	7.05342	−	0.951130i	0.399321	−	0.0538472i
$313$	4.80126	−	17.9185i	0.271383	−	1.01282i	−0.686843	−	0.726806i	$-0.741004\pi$
$313$	4.80126	−	17.9185i	0.271383	−	1.01282i	0.958226	−	0.286011i	$-0.0923292\pi$
$314$	15.4974	−	26.8423i	0.874568	−	1.51480i
$315$	−32.1172	+	12.7926i	−1.80960	+	0.720780i
$316$	−0.125582	−	0.217514i	−0.00706454	−	0.0122361i
$317$	3.34715	−	12.4917i	0.187995	−	0.701606i	−0.805975	−	0.591950i	$-0.798358\pi$
$317$	3.34715	−	12.4917i	0.187995	−	0.701606i	0.993970	−	0.109656i	$-0.0349749\pi$
$318$	10.1384	−	1.36712i	0.568531	−	0.0766645i
$319$			31.8206i			1.78161i
$320$	−10.5901	−	27.0808i	−0.592003	−	1.51386i
$321$	18.0157	+	13.7343i	1.00554	+	0.766573i
$322$	30.9397	−	30.9397i	1.72420	−	1.72420i
$323$	−3.27237	+	3.27237i	−0.182080	+	0.182080i
$324$	13.8112	+	23.2428i	0.767287	+	1.29127i
$325$	4.88573	−	7.73338i	0.271012	−	0.428971i
$326$	18.0926	+	10.4457i	1.00205	+	0.578536i
$327$	−16.2604	−	6.67558i	−0.899204	−	0.369160i
$328$	−8.17313	+	2.18998i	−0.451285	+	0.120922i
$329$	−24.1447	+	41.8199i	−1.33114	+	2.30560i
$330$	27.9761	+	28.9316i	1.54003	+	1.59263i
$331$	−9.79893	−	16.9722i	−0.538598	−	0.932879i	−0.998980	−	0.0451577i	$-0.985621\pi$
$331$	−9.79893	−	16.9722i	−0.538598	−	0.932879i	0.460382	−	0.887721i	$-0.347712\pi$
$332$	7.62464	+	7.62464i	0.418457	+	0.418457i
$333$	−16.3993	−	8.00401i	−0.898674	−	0.438617i
$334$		−	5.14121i		−	0.281314i
$335$	−4.13963	−	5.62343i	−0.226172	−	0.307241i
$336$	8.70941	+	1.11882i	0.475137	+	0.0610366i
$337$	−1.01611	−	3.79217i	−0.0553510	−	0.206573i	0.932712	−	0.360622i	$-0.117435\pi$
$337$	−1.01611	−	3.79217i	−0.0553510	−	0.206573i	−0.988063	+	0.154049i	$0.950769\pi$
$338$	5.58881	+	20.8577i	0.303991	+	1.13451i
$339$	12.5234	+	29.9678i	0.680179	+	1.62763i
$340$	3.78587	−	8.64833i	0.205318	−	0.469021i
$341$		−	14.2659i		−	0.772544i
$342$	−11.1689	−	19.0676i	−0.603944	−	1.03106i
$343$	45.7670	+	45.7670i	2.47118	+	2.47118i
$344$	19.7627			1.06553
$345$	−14.2607	+	3.56565i	−0.767770	+	0.191968i
$346$	11.3121	−	19.5932i	0.608145	−	1.05334i
$347$	20.0966	+	20.0966i	1.07884	+	1.07884i	0.996614	+	0.0822276i	$0.0262035\pi$
$347$	20.0966	+	20.0966i	1.07884	+	1.07884i	0.0822276	+	0.996614i	$0.473797\pi$
$348$	4.76317	+	35.3229i	0.255333	+	1.89350i
$349$	−1.73516	+	1.00180i	−0.0928811	+	0.0536249i	−0.545721	−	0.837967i	$-0.683744\pi$
$349$	−1.73516	+	1.00180i	−0.0928811	+	0.0536249i	0.452840	+	0.891592i	$0.350411\pi$
$350$	−42.3507	+	39.1026i	−2.26374	+	2.09012i
$351$	7.48702	−	5.85782i	0.399628	−	0.312667i
$352$	−8.04652	−	30.0300i	−0.428881	−	1.60061i
$353$	−18.2339	−	4.88576i	−0.970494	−	0.260043i	−0.261457	−	0.965215i	$-0.584203\pi$
$353$	−18.2339	−	4.88576i	−0.970494	−	0.260043i	−0.709036	+	0.705172i	$0.750870\pi$
$354$	5.00758	+	3.81754i	0.266150	+	0.202900i
$355$	22.5003	+	3.41964i	1.19419	+	0.181495i
$356$		−	29.7232i		−	1.57533i
$357$	7.66822	+	9.92874i	0.405845	+	0.525484i
$358$	−2.54534	+	9.49935i	−0.134526	+	0.502056i
$359$	11.1059			0.586145			0.293073	−	0.956090i	$-0.405322\pi$
$359$	11.1059			0.586145			0.293073	+	0.956090i	$0.405322\pi$
$360$	11.8272	+	9.33457i	0.623348	+	0.491975i
$361$	−4.07865	−	7.06442i	−0.214666	−	0.371812i
$362$	−19.8900	−	19.8900i	−1.04540	−	1.04540i
$363$	11.1995	+	14.5010i	0.587821	+	0.761105i
$364$			28.3234i			1.48455i
$365$	6.03071	+	2.63999i	0.315662	+	0.138184i
$366$	−1.45866	+	11.3549i	−0.0762453	+	0.593529i
$367$	−7.38604	−	27.5651i	−0.385548	−	1.43889i	−0.837301	−	0.546742i	$-0.815868\pi$
$367$	−7.38604	−	27.5651i	−0.385548	−	1.43889i	0.451753	−	0.892143i	$-0.350799\pi$
$368$	3.60647	+	0.966350i	0.188000	+	0.0503745i
$369$	−7.94117	+	8.04150i	−0.413401	+	0.418624i
$370$	−30.3096	−	2.66088i	−1.57572	−	0.138332i
$371$			13.6071i			0.706445i
$372$	−2.13544	−	15.8361i	−0.110718	−	0.821062i
$373$	−22.0904	+	5.91911i	−1.14380	+	0.306480i	−0.780477	−	0.625184i	$-0.785024\pi$
$373$	−22.0904	+	5.91911i	−1.14380	+	0.306480i	−0.363321	+	0.931664i	$0.618357\pi$
$374$	7.30214	−	12.6477i	0.377585	−	0.653996i
$375$	18.9588	−	3.94499i	0.979030	−	0.203718i
$376$	21.0459			1.08536
$377$	12.1052	−	3.24358i	0.623450	−	0.167053i
$378$	−55.1251	+	23.4441i	−2.83533	+	1.20583i
$379$	−5.72889	+	3.30758i	−0.294273	+	0.169899i	−0.639867	−	0.768485i	$-0.721011\pi$
$379$	−5.72889	+	3.30758i	−0.294273	+	0.169899i	0.345594	+	0.938384i	$0.387677\pi$
$380$	−17.2763	−	13.8121i	−0.886255	−	0.708547i
$381$	−10.1678	−	24.3310i	−0.520913	−	1.24651i
$382$	23.1680	+	6.20786i	1.18538	+	0.317622i
$383$	4.97918	+	18.5826i	0.254424	+	0.949524i	0.968410	+	0.249364i	$0.0802215\pi$
$383$	4.97918	+	18.5826i	0.254424	+	0.949524i	−0.713986	+	0.700160i	$0.753112\pi$
$384$	−10.4880	−	25.0971i	−0.535212	−	1.28073i
$385$	−43.1096	+	31.7346i	−2.19707	+	1.61735i
$386$	−15.6907	+	9.05902i	−0.798634	+	0.461092i
$387$	22.7766	−	13.3414i	1.15780	−	0.678183i
$388$	−11.9164	+	3.19298i	−0.604961	+	0.162099i
$389$	−7.79118	+	13.4947i	−0.395029	+	0.684210i	−0.993105	−	0.117230i	$-0.962599\pi$
$389$	−7.79118	+	13.4947i	−0.395029	+	0.684210i	0.598076	+	0.801439i	$0.295932\pi$
$390$	8.15446	−	13.5917i	0.412917	−	0.688244i
$391$	2.66711	+	4.61958i	0.134882	+	0.233622i
$392$	11.3702	−	42.4342i	0.574283	−	2.14325i
$393$	−6.44579	−	2.64626i	−0.325147	−	0.133486i
$394$	−49.5084	−	28.5837i	−2.49420	−	1.44002i
$395$	−0.184831	−	0.0280909i	−0.00929985	−	0.00141341i
$396$	29.7875	+	29.4159i	1.49688	+	1.47820i
$397$	5.66077	−	5.66077i	0.284106	−	0.284106i	−0.550638	−	0.834744i	$-0.685616\pi$
$397$	5.66077	−	5.66077i	0.284106	−	0.284106i	0.834744	+	0.550638i	$0.185616\pi$
$398$	−16.4318	−	4.40289i	−0.823653	−	0.220697i
$399$	27.1197	−	11.3332i	1.35768	−	0.567369i
$400$	−4.69655	−	1.46133i	−0.234827	−	0.0730667i
$401$			20.7039i			1.03390i	0.856015	+	0.516951i	$0.172933\pi$
$401$			20.7039i			1.03390i	−0.856015	+	0.516951i	$0.827067\pi$
$402$	−7.39579	−	9.57600i	−0.368868	−	0.477607i
$403$	−5.42705	+	1.45417i	−0.270340	+	0.0724375i
$404$	−16.5331	+	28.6362i	−0.822553	+	1.42470i
$405$	19.9325	+	2.77384i	0.990455	+	0.137833i
$406$	−78.9710			−3.91926
$407$	−27.7009	−	5.57309i	−1.37308	−	0.276248i
$408$	2.07647	−	5.05789i	0.102801	−	0.250403i
$409$	−15.8024	+	9.12355i	−0.781381	+	0.451130i	−0.836919	−	0.547326i	$-0.815646\pi$
$409$	−15.8024	+	9.12355i	−0.781381	+	0.451130i	0.0555386	+	0.998457i	$0.482312\pi$
$410$	−7.55668	+	17.2622i	−0.373198	+	0.852521i
$411$	−0.0912368	+	0.710231i	−0.00450038	+	0.0350331i
$412$	11.8934	+	44.3868i	0.585946	+	2.18678i
$413$	−5.92228	+	5.92228i	−0.291416	+	0.291416i
$414$	−24.5612	+	6.74668i	−1.20712	+	0.331581i
$415$	7.97684	−	0.888856i	0.391568	−	0.0436322i
$416$	−10.6038	+	6.12211i	−0.519895	+	0.300161i
$417$	−32.1678	−	13.2062i	−1.57527	−	0.646711i
$418$	−24.1950	−	24.1950i	−1.18341	−	1.18341i
$419$	−7.48610	−	12.9663i	−0.365720	−	0.633446i	0.623171	−	0.782085i	$-0.285844\pi$
$419$	−7.48610	−	12.9663i	−0.365720	−	0.633446i	−0.988891	+	0.148640i	$0.952511\pi$
$420$	−43.1040	+	41.6804i	−2.10326	+	2.03379i
$421$	8.41951			0.410342			0.205171	−	0.978726i	$-0.434225\pi$
$421$	8.41951			0.410342			0.205171	+	0.978726i	$0.434225\pi$
$422$	3.52691	−	13.1626i	0.171687	−	0.640746i
$423$	24.2556	−	14.2077i	1.17935	−	0.690802i
$424$	5.13584	−	2.96518i	0.249419	−	0.144002i
$425$	−3.26830	−	6.22085i	−0.158536	−	0.301756i
$426$	39.1138	+	5.02459i	1.89507	+	0.243442i
$427$	−14.7084	−	3.94111i	−0.711790	−	0.190723i
$428$	37.9519	+	10.1692i	1.83447	+	0.491546i
$429$	8.92410	−	11.7060i	0.430860	−	0.565171i
$430$	27.4832	−	34.3761i	1.32536	−	1.65776i
$431$	10.0688	+	5.81323i	0.484997	+	0.280013i	0.722497	−	0.691374i	$-0.242994\pi$
$431$	10.0688	+	5.81323i	0.484997	+	0.280013i	−0.237500	+	0.971388i	$0.576328\pi$
$432$	−4.08443	−	3.07343i	−0.196512	−	0.147870i
$433$	11.4297	+	11.4297i	0.549276	+	0.549276i	0.926231	−	0.376955i	$-0.123029\pi$
$433$	11.4297	+	11.4297i	0.549276	+	0.549276i	−0.376955	+	0.926231i	$0.623029\pi$
$434$	35.4045			1.69947
$435$	22.7501	+	13.6491i	1.09078	+	0.654424i
$436$	−30.4862			−1.46002
$437$	12.0719	−	3.23465i	0.577477	−	0.154734i
$438$	10.5525	+	4.33222i	0.504217	+	0.207002i
$439$	−28.1667	−	16.2621i	−1.34432	−	0.776146i	−0.356886	−	0.934148i	$-0.616162\pi$
$439$	−28.1667	−	16.2621i	−1.34432	−	0.776146i	−0.987439	+	0.158002i	$0.949495\pi$
$440$	21.3721	+	9.35579i	1.01887	+	0.446020i
$441$	−15.5423	−	56.5816i	−0.740110	−	2.69436i
$442$	−5.55576	−	1.48866i	−0.264261	−	0.0708084i
$443$	−13.4205	+	13.4205i	−0.637625	+	0.637625i	−0.949969	−	0.312344i	$-0.898886\pi$
$443$	−13.4205	+	13.4205i	−0.637625	+	0.637625i	0.312344	+	0.949969i	$0.398886\pi$
$444$	−31.5840	−	2.03996i	−1.49891	−	0.0968124i
$445$	−17.2806	−	13.8156i	−0.819179	−	0.654920i
$446$	35.0710	−	20.2482i	1.66066	−	0.958781i
$447$	2.62140	+	3.39416i	0.123988	+	0.160538i
$448$	64.7332	−	17.3452i	3.05836	−	0.819484i
$449$	6.90028	−	11.9516i	0.325644	−	0.564033i	−0.655998	−	0.754762i	$-0.727752\pi$
$449$	6.90028	−	11.9516i	0.325644	−	0.564033i	0.981643	+	0.190730i	$0.0610855\pi$
$450$	32.6846	−	7.59157i	1.54077	−	0.357870i
$451$	−8.74987	+	15.1552i	−0.412015	+	0.713631i
$452$	39.8328	+	39.8328i	1.87358	+	1.87358i
$453$	−27.1373	+	3.65938i	−1.27502	+	0.171933i
$454$		−	4.58698i		−	0.215278i
$455$	16.4668	+	13.1649i	0.771974	+	0.617181i
$456$	−10.1874	−	7.76635i	−0.477067	−	0.363693i
$457$	4.07635	+	15.2131i	0.190683	+	0.711640i	0.993342	+	0.115202i	$0.0367514\pi$
$457$	4.07635	+	15.2131i	0.190683	+	0.711640i	−0.802659	+	0.596439i	$0.796582\pi$
$458$	−16.2198	+	16.2198i	−0.757903	+	0.757903i
$459$	−1.02134	−	7.23105i	−0.0476721	−	0.337517i
$460$	−20.5319	+	15.1143i	−0.957304	+	0.704708i
$461$	−12.9850	+	7.49688i	−0.604770	+	0.349164i	−0.770916	−	0.636937i	$-0.780201\pi$
$461$	−12.9850	+	7.49688i	−0.604770	+	0.349164i	0.166146	+	0.986101i	$0.446868\pi$
$462$	−73.4101	+	56.6965i	−3.41535	+	2.63776i
$463$	−10.6491	+	2.85340i	−0.494903	+	0.132609i	−0.497634	−	0.867387i	$-0.665798\pi$
$463$	−10.6491	+	2.85340i	−0.494903	+	0.132609i	0.00273025	+	0.999996i	$0.499131\pi$
$464$	−3.36934	−	5.83586i	−0.156418	−	0.270923i
$465$	−10.1994	−	6.11921i	−0.472986	−	0.283771i
$466$	−9.44703	−	16.3627i	−0.437625	−	0.757989i
$467$	−22.3558	−	22.3558i	−1.03450	−	1.03450i	−0.999383	−	0.0351186i	$-0.988819\pi$
$467$	−22.3558	−	22.3558i	−1.03450	−	1.03450i	−0.0351186	−	0.999383i	$-0.511181\pi$
$468$	8.15405	−	14.3302i	0.376921	−	0.662415i
$469$	13.9374	−	8.04677i	0.643570	−	0.371565i
$470$	29.2677	−	36.6082i	1.35002	−	1.68861i
$471$	−9.25344	−	22.1430i	−0.426376	−	1.02029i
$472$	3.52584	+	0.944747i	0.162290	+	0.0434855i
$473$	28.9013	−	28.9013i	1.32888	−	1.32888i
$474$	−0.321304	−	0.0412750i	−0.0147580	−	0.00189582i
$475$	−16.0603	+	3.62419i	−0.736897	+	0.166289i
$476$	18.8432	+	10.8792i	0.863679	+	0.498645i
$477$	3.91736	−	6.88451i	0.179364	−	0.315220i
$478$	−3.96459	+	1.06231i	−0.181336	+	0.0485889i
$479$	2.64211	+	4.57626i	0.120721	+	0.209095i	0.920052	−	0.391796i	$-0.128146\pi$
$479$	2.64211	+	4.57626i	0.120721	+	0.209095i	−0.799331	+	0.600891i	$0.794813\pi$
$480$	−24.9214	−	7.12818i	−1.13750	−	0.325356i
$481$	0.703532	+	11.1061i	0.0320783	+	0.506393i
$482$	−3.17955	−	3.17955i	−0.144824	−	0.144824i
$483$	−4.52749	−	33.5751i	−0.206008	−	1.52772i
$484$	27.5207	+	15.8891i	1.25094	+	0.722232i
$485$	−3.68246	+	8.41210i	−0.167212	+	0.381974i
$486$	34.6399	+	4.00850i	1.57130	+	0.181829i
$487$	−24.0416	+	24.0416i	−1.08943	+	1.08943i	−0.0938440	+	0.995587i	$0.529915\pi$
$487$	−24.0416	+	24.0416i	−1.08943	+	1.08943i	−0.995587	+	0.0938440i	$0.970085\pi$
$488$	1.71765	+	6.41034i	0.0777542	+	0.290183i
$489$	14.9251	−	6.23712i	0.674935	−	0.282052i
$490$	−58.0000	−	78.7895i	−2.62017	−	3.55935i
$491$		−	20.8392i		−	0.940461i	−0.882544	−	0.470231i	$-0.844171\pi$
$491$		−	20.8392i		−	0.940461i	0.882544	−	0.470231i	$-0.155829\pi$
$492$	−7.44433	+	18.1330i	−0.335616	+	0.817498i
$493$	2.49175	−	9.29933i	0.112223	−	0.418821i
$494$	−6.73798	+	11.6705i	−0.303156	+	0.525081i
$495$	30.9474	−	3.64527i	1.39098	−	0.163843i
$496$	1.51055	+	2.61635i	0.0678258	+	0.117478i
$497$	−13.5758	+	50.6656i	−0.608958	+	2.27266i
$498$	13.7827	−	1.85855i	0.617618	−	0.0832838i
$499$	13.3179	+	7.68909i	0.596191	+	0.344211i	0.767541	−	0.640999i	$-0.221480\pi$
$499$	13.3179	+	7.68909i	0.596191	+	0.344211i	−0.171351	+	0.985210i	$0.554813\pi$
$500$	27.8199	−	18.8176i	1.24415	−	0.841547i
$501$	−3.16573	−	2.41340i	−0.141434	−	0.107823i
$502$	−12.6605	−	3.39237i	−0.565066	−	0.151409i
$503$	19.3248	+	5.17807i	0.861652	+	0.230879i	0.662474	−	0.749084i	$-0.269506\pi$
$503$	19.3248	+	5.17807i	0.861652	+	0.230879i	0.199177	+	0.979963i	$0.436173\pi$
$504$	−24.4002	+	24.7084i	−1.08687	+	1.10060i
$505$	8.96391	+	22.9224i	0.398889	+	1.02003i
$506$	−34.1558	+	19.7199i	−1.51841	+	0.876655i
$507$	15.4668	+	6.34974i	0.686903	+	0.282002i
$508$	−32.3404	−	32.3404i	−1.43487	−	1.43487i
$509$	22.0946	+	38.2689i	0.979325	+	1.69624i	0.664855	+	0.746972i	$0.268493\pi$
$509$	22.0946	+	38.2689i	0.979325	+	1.69624i	0.314470	+	0.949268i	$0.398173\pi$
$510$	−5.91027	−	10.6457i	−0.261711	−	0.471401i
$511$	−7.58633	+	13.1399i	−0.335599	+	0.581275i
$512$	7.78019	+	7.78019i	0.343839	+	0.343839i
$513$	−16.9839	−	2.07349i	−0.749859	−	0.0915466i
$514$	−1.75304	−	1.01212i	−0.0773233	−	0.0446426i
$515$	31.3339	+	13.7167i	1.38074	+	0.604429i
$516$	27.7561	−	36.4084i	1.22189	−	1.60279i
$517$	30.7779	−	30.7779i	1.35361	−	1.35361i
$518$	13.8310	−	68.7469i	0.607701	−	3.02057i
$519$	−6.75445	−	16.1630i	−0.296488	−	0.709478i
$520$	1.38061	−	9.08402i	0.0605436	−	0.398361i
$521$	−18.3700	−	10.6059i	−0.804804	−	0.464654i	0.0403444	−	0.999186i	$-0.487154\pi$
$521$	−18.3700	−	10.6059i	−0.804804	−	0.464654i	−0.845148	+	0.534532i	$0.820488\pi$
$522$	39.9553	+	22.7350i	1.74880	+	0.995085i
$523$	−9.53115	+	2.55386i	−0.416768	+	0.111673i	−0.461108	−	0.887344i	$-0.652548\pi$
$523$	−9.53115	+	2.55386i	−0.416768	+	0.111673i	0.0443404	+	0.999016i	$0.485881\pi$
$524$	−12.0850			−0.527936
$525$	4.19726	+	44.4333i	0.183184	+	1.93923i
$526$	44.5300			1.94160
$527$	−1.11711	+	4.16911i	−0.0486621	+	0.181609i
$528$	−7.32189	−	3.00594i	−0.318644	−	0.130817i
$529$			8.59460i			0.373678i
$530$	1.98444	−	13.0571i	0.0861985	−	0.567163i
$531$	4.70134	−	1.29140i	0.204021	−	0.0560422i
$532$	36.0471	−	36.0471i	1.56284	−	1.56284i
$533$	6.65725	+	1.78380i	0.288357	+	0.0772652i
$534$	−30.4872	−	23.2420i	−1.31931	−	1.00578i
$535$	23.5525	−	17.3379i	1.01826	−	0.749584i
$536$	−6.07432	−	3.50701i	−0.262371	−	0.151480i
$537$	4.65444	+	6.02652i	0.200854	+	0.260064i
$538$	−6.08566	+	22.7120i	−0.262371	+	0.979184i
$539$	−45.4286	−	78.6847i	−1.95675	−	3.38919i
$540$	33.8078	−	8.67893i	1.45486	−	0.373482i
$541$	40.1861			1.72773			0.863867	−	0.503720i	$-0.168036\pi$
$541$	40.1861			1.72773			0.863867	+	0.503720i	$0.168036\pi$
$542$	−54.2887	+	14.5466i	−2.33190	+	0.624831i
$543$	−21.5842	+	2.91056i	−0.926267	+	0.124904i
$544$			9.40613i			0.403285i
$545$	−14.1702	+	17.7242i	−0.606985	+	0.759221i
$546$	29.0514	+	22.1474i	1.24329	+	0.947822i
$547$	4.97802	−	4.97802i	0.212845	−	0.212845i	−0.592630	−	0.805475i	$-0.701910\pi$
$547$	4.97802	−	4.97802i	0.212845	−	0.212845i	0.805475	+	0.592630i	$0.201910\pi$
$548$	0.321439	+	1.19963i	0.0137312	+	0.0512455i
$549$	6.30711	+	6.22842i	0.269181	+	0.265822i
$550$	45.9951	−	24.1648i	1.96124	−	1.03039i
$551$	−19.5343	−	11.2782i	−0.832191	−	0.480465i
$552$	−11.6859	+	9.02534i	−0.497386	+	0.384144i
$553$	0.111520	−	0.416197i	0.00474230	−	0.0176985i
$554$	−32.1392			−1.36546
$555$	−15.8665	+	17.4142i	−0.673494	+	0.739193i
$556$	−60.3105			−2.55773
$557$	−9.35959	+	34.9305i	−0.396578	+	1.48005i	0.422496	+	0.906365i	$0.361154\pi$
$557$	−9.35959	+	34.9305i	−0.396578	+	1.48005i	−0.819075	+	0.573687i	$0.805513\pi$
$558$	−17.9129	−	10.1926i	−0.758314	−	0.431489i
$559$	−13.9406	−	8.04863i	−0.589626	−	0.340421i
$560$	4.54601	−	10.3848i	0.192104	−	0.438836i
$561$	−4.36009	−	10.4334i	−0.184083	−	0.440500i
$562$	4.46857	+	16.6769i	0.188495	+	0.703473i
$563$	9.28169	−	9.28169i	0.391177	−	0.391177i	−0.483930	−	0.875107i	$-0.660791\pi$
$563$	9.28169	−	9.28169i	0.391177	−	0.391177i	0.875107	+	0.483930i	$0.160791\pi$
$564$	29.5583	−	38.7725i	1.24463	−	1.63262i
$565$	41.6727	−	4.64358i	1.75318	−	0.195357i
$566$		−	38.0653i		−	1.60000i
$567$	−11.4412	+	44.9488i	−0.480484	+	1.88767i
$568$	22.0815	−	5.91672i	0.926519	−	0.248260i
$569$	−31.1450			−1.30567			−0.652833	−	0.757502i	$-0.726420\pi$
$569$	−31.1450			−1.30567			−0.652833	+	0.757502i	$0.726420\pi$
$570$	−27.6763	+	6.92000i	−1.15923	+	0.289847i
$571$	−0.745666	−	1.29153i	−0.0312052	−	0.0540489i	0.850001	−	0.526781i	$-0.176601\pi$
$571$	−0.745666	−	1.29153i	−0.0312052	−	0.0540489i	−0.881206	+	0.472732i	$0.843268\pi$
$572$	6.60761	−	24.6599i	0.276278	−	1.03108i
$573$	14.6981	−	11.3517i	0.614023	−	0.474226i
$574$	−37.6115	−	21.7150i	−1.56987	−	0.906367i
$575$	−0.756150	+	18.9622i	−0.0315336	+	0.790777i
$576$	−37.7453	−	9.86030i	−1.57272	−	0.410846i
$577$	−27.5159	−	7.37287i	−1.14550	−	0.306937i	−0.364342	−	0.931265i	$-0.618706\pi$
$577$	−27.5159	−	7.37287i	−1.14550	−	0.306937i	−0.781162	+	0.624329i	$0.785373\pi$
$578$	23.7659	−	23.7659i	0.988531	−	0.988531i
$579$	−1.78742	+	13.9141i	−0.0742827	+	0.578252i
$580$	45.4919	+	6.91395i	1.88895	+	0.287086i
$581$			18.4983i			0.767440i
$582$	−6.04292	+	14.7194i	−0.250487	+	0.610139i
$583$	3.17442	−	11.8471i	0.131471	−	0.490656i
$584$	6.61268			0.273635
$585$	−4.54130	−	11.4014i	−0.187760	−	0.471391i
$586$	−34.5921			−1.42899
$587$	11.3083	−	3.03004i	0.466743	−	0.125063i	−0.0177802	−	0.999842i	$-0.505660\pi$
$587$	11.3083	−	3.03004i	0.466743	−	0.125063i	0.484523	+	0.874779i	$0.338993\pi$
$588$	−62.2067	−	80.5447i	−2.56536	−	3.32161i
$589$	8.75770	+	5.05626i	0.360855	+	0.208340i
$590$	6.54659	−	4.81920i	0.269519	−	0.198403i
$591$	−40.8409	+	17.0672i	−1.67997	+	0.702052i
$592$	5.67042	−	1.91103i	0.233053	−	0.0785427i
$593$	−9.58272	+	9.58272i	−0.393515	+	0.393515i	−0.875938	−	0.482423i	$-0.839757\pi$
$593$	−9.58272	+	9.58272i	−0.393515	+	0.393515i	0.482423	+	0.875938i	$0.339757\pi$
$594$	53.4643	−	7.55148i	2.19367	−	0.309841i
$595$	15.0835	−	5.89846i	0.618361	−	0.241813i
$596$	6.44160	+	3.71906i	0.263858	+	0.152339i
$597$	−10.4246	+	8.05117i	−0.426650	+	0.329512i
$598$	10.9834	+	10.9834i	0.449146	+	0.449146i
$599$	1.62038	−	2.80658i	0.0662069	−	0.114674i	−0.831022	−	0.556240i	$-0.812244\pi$
$599$	1.62038	−	2.80658i	0.0662069	−	0.114674i	0.897229	+	0.441566i	$0.145577\pi$
$600$	15.8562	−	11.2669i	0.647327	−	0.459968i
$601$	12.0905	+	20.9414i	0.493182	+	0.854217i	0.999969	−	0.00785470i	$-0.00250025\pi$
$601$	12.0905	+	20.9414i	0.493182	+	0.854217i	−0.506787	+	0.862071i	$0.669167\pi$
$602$	71.7260	+	71.7260i	2.92333	+	2.92333i
$603$	−9.36823	+	0.0588065i	−0.381504	+	0.00239479i
$604$	−41.1300	+	23.7464i	−1.67356	+	0.966229i
$605$	22.0295	−	8.61474i	0.895627	−	0.350239i
$606$	16.4442	+	39.3501i	0.668001	+	1.59849i
$607$	5.23979	+	1.40400i	0.212676	+	0.0569865i	0.363584	−	0.931561i	$-0.381553\pi$
$607$	5.23979	+	1.40400i	0.212676	+	0.0569865i	−0.150908	+	0.988548i	$0.548220\pi$
$608$	21.2870	+	5.70384i	0.863303	+	0.231321i
$609$	−37.0708	+	48.6268i	−1.50218	+	1.97046i
$610$	13.5391	+	5.92685i	0.548183	+	0.239971i
$611$	−14.8458	−	8.57125i	−0.600599	−	0.346756i
$612$	−6.40173	−	10.9291i	−0.258775	−	0.441783i
$613$	1.97778	−	7.38116i	0.0798816	−	0.298122i	−0.914414	−	0.404780i	$-0.867348\pi$
$613$	1.97778	−	7.38116i	0.0798816	−	0.298122i	0.994296	+	0.106658i	$0.0340149\pi$
$614$	11.8839	+	20.5836i	0.479597	+	0.830686i
$615$	7.08204	+	12.7564i	0.285576	+	0.514386i
$616$	−26.8850	+	46.5661i	−1.08323	+	1.87620i
$617$	9.03792	−	33.7300i	0.363853	−	1.35792i	−0.505116	−	0.863051i	$-0.668550\pi$
$617$	9.03792	−	33.7300i	0.363853	−	1.35792i	0.868969	−	0.494866i	$-0.164783\pi$
$618$	54.8277	+	22.5090i	2.20549	+	0.905446i
$619$			11.9809i			0.481553i	0.970581	+	0.240777i	$0.0774021\pi$
$619$			11.9809i			0.481553i	−0.970581	+	0.240777i	$0.922598\pi$
$620$	−20.3951	−	3.09968i	−0.819087	−	0.124486i
$621$	−7.37528	+	18.2907i	−0.295960	+	0.733982i
$622$	−11.6895	−	43.6257i	−0.468705	−	1.74923i
$623$	36.0561	−	36.0561i	1.44456	−	1.44456i
$624$	−0.397175	+	3.09180i	−0.0158997	+	0.123771i
$625$	1.99067	−	24.9206i	0.0796270	−	0.996825i
$626$	−35.9378	−	20.7487i	−1.43636	−	0.829284i
$627$	−26.2559	+	3.54052i	−1.04856	+	0.141395i
$628$	−29.4321	−	29.4321i	−1.17447	−	1.17447i
$629$	7.65898	+	3.79784i	0.305383	+	0.151430i
$630$	9.04666	+	76.8038i	0.360428	+	3.05994i
$631$	−1.66068	−	2.87638i	−0.0661106	−	0.114507i	0.831076	−	0.556160i	$-0.187726\pi$
$631$	−1.66068	−	2.87638i	−0.0661106	−	0.114507i	−0.897186	+	0.441653i	$0.854392\pi$
$632$	−0.181391	+	0.0486034i	−0.00721533	+	0.00193334i
$633$	−6.44934	−	8.35055i	−0.256338	−	0.331905i
$634$	−25.0536	−	14.4647i	−0.995007	−	0.574468i
$635$	−33.8342	+	3.77014i	−1.34267	+	0.149613i
$636$	1.75043	−	13.6262i	0.0694091	−	0.540313i
$637$	−25.3025	+	25.3025i	−1.00252	+	1.00252i
$638$	68.7565	+	18.4233i	2.72210	+	0.729384i
$639$	21.4548	−	21.7259i	0.848740	−	0.859463i
$640$	−34.8996	+	3.88885i	−1.37953	+	0.153720i
$641$	−12.5508	+	7.24618i	−0.495725	+	0.286207i	−0.726946	−	0.686694i	$-0.759061\pi$
$641$	−12.5508	+	7.24618i	−0.495725	+	0.286207i	0.231221	+	0.972901i	$0.425728\pi$
$642$	40.1070	−	30.9757i	1.58290	−	1.22251i
$643$	−8.05928	−	8.05928i	−0.317827	−	0.317827i	0.530105	−	0.847932i	$-0.322152\pi$
$643$	−8.05928	−	8.05928i	−0.317827	−	0.317827i	−0.847932	+	0.530105i	$0.822152\pi$
$644$	−29.3798	−	50.8873i	−1.15773	−	2.00524i
$645$	−8.26607	−	33.0598i	−0.325476	−	1.30173i
$646$	5.17618	+	8.96541i	0.203654	+	0.352739i
$647$	42.6638	−	11.4317i	1.67729	−	0.449428i	0.710227	−	0.703973i	$-0.248592\pi$
$647$	42.6638	−	11.4317i	1.67729	−	0.449428i	0.967061	+	0.254545i	$0.0819256\pi$
$648$	19.4586	−	5.47664i	0.764405	−	0.215143i
$649$	6.53788	−	3.77465i	0.256634	−	0.148168i
$650$	−13.8812	−	15.0343i	−0.544466	−	0.589693i
$651$	16.6197	−	21.8005i	0.651377	−	0.854431i
$652$	19.8382	−	19.8382i	0.776923	−	0.776923i
$653$	1.00561	+	3.75299i	0.0393526	+	0.146866i	0.982807	−	0.184637i	$-0.0591110\pi$
$653$	1.00561	+	3.75299i	0.0393526	+	0.146866i	−0.943454	+	0.331503i	$0.892444\pi$
$654$	−23.8386	+	31.2698i	−0.932164	+	1.22275i
$655$	−5.61720	+	7.02604i	−0.219482	+	0.274530i
$656$		−	3.70593i		−	0.144692i
$657$	7.62116	−	4.46410i	0.297330	−	0.174161i
$658$	76.3833	+	76.3833i	2.97773	+	2.97773i
$659$	−4.94454	+	8.56419i	−0.192612	+	0.333613i	−0.946115	−	0.323831i	$-0.895029\pi$
$659$	−4.94454	+	8.56419i	−0.192612	+	0.333613i	0.753503	+	0.657444i	$0.228362\pi$
$660$	47.2524	−	26.2335i	1.83930	−	1.02114i
$661$	−1.47448	+	2.55387i	−0.0573505	+	0.0993340i	−0.893275	−	0.449510i	$-0.851599\pi$
$661$	−1.47448	+	2.55387i	−0.0573505	+	0.0993340i	0.835925	+	0.548844i	$0.184932\pi$
$662$	−42.3461	+	11.3466i	−1.64583	+	0.440999i
$663$	−3.52465	+	2.72218i	−0.136886	+	0.105721i
$664$	6.98198	−	4.03105i	0.270953	−	0.156435i
$665$	−4.20225	−	37.7122i	−0.162956	−	1.46241i
$666$	−26.7894	+	30.8007i	−1.03807	+	1.19350i
$667$	−18.3843	+	18.3843i	−0.711842	+	0.711842i
$668$	−6.66893	−	1.78694i	−0.258029	−	0.0691386i
$669$	3.99515	−	31.1001i	0.154461	−	1.20240i
$670$	−14.5476	+	5.68890i	−0.562022	+	0.219781i
$671$	11.8865	+	6.86269i	0.458874	+	0.264931i
$672$	22.6884	−	55.2646i	0.875224	−	2.13188i
$673$	36.8157	−	9.86473i	1.41914	−	0.380258i	0.533962	−	0.845509i	$-0.320703\pi$
$673$	36.8157	−	9.86473i	1.41914	−	0.380258i	0.885179	+	0.465251i	$0.154036\pi$
$674$	−8.78225			−0.338280
$675$	10.6683	−	23.6894i	0.410625	−	0.911804i
$676$	28.9982			1.11531
$677$	−19.7378	−	19.7378i	−0.758584	−	0.758584i	0.217481	−	0.976065i	$-0.430216\pi$
$677$	−19.7378	−	19.7378i	−0.758584	−	0.758584i	−0.976065	+	0.217481i	$0.930216\pi$
$678$	72.0038	−	9.70948i	2.76529	−	0.372890i
$679$	−18.3286	−	10.5820i	−0.703386	−	0.406100i
$680$	−5.51320	−	4.40772i	−0.211422	−	0.169028i
$681$	−2.82446	−	2.15323i	−0.108234	−	0.0825121i
$682$	−30.8252	−	8.25958i	−1.18036	−	0.316276i
$683$	−32.2794	−	8.64924i	−1.23514	−	0.330954i	−0.418559	−	0.908189i	$-0.637465\pi$
$683$	−32.2794	−	8.64924i	−1.23514	−	0.330954i	−0.816578	+	0.577236i	$0.804131\pi$
$684$	−28.6156	+	7.86039i	−1.09415	+	0.300549i
$685$	0.846851	+	0.370716i	0.0323565	+	0.0141643i
$686$	125.389	−	72.3933i	4.78737	−	2.76399i
$687$	2.37349	+	17.6014i	0.0905544	+	0.671535i
$688$	−2.24024	+	8.36069i	−0.0854084	+	0.318748i
$689$	−4.83045			−0.184025
$690$	−0.552053	+	32.8782i	−0.0210163	+	1.25165i
$691$	−8.66554	−	15.0092i	−0.329653	−	0.570975i	0.652790	−	0.757539i	$-0.273598\pi$
$691$	−8.66554	−	15.0092i	−0.329653	−	0.570975i	−0.982443	+	0.186563i	$0.940265\pi$
$692$	−21.4836	−	21.4836i	−0.816685	−	0.816685i
$693$	0.450814	+	71.8174i	0.0171250	+	2.72812i
$694$	55.0591	−	31.7884i	2.09002	−	1.20667i
$695$	−28.0328	+	35.0636i	−1.06334	+	1.33004i
$696$	26.4319	+	3.39546i	1.00190	+	0.128705i
$697$	3.74383	−	3.74383i	0.141808	−	0.141808i
$698$	1.16002	+	4.32927i	0.0439076	+	0.163865i
$699$	−14.5101	−	1.86398i	−0.548822	−	0.0705022i
$700$	36.0022	+	68.5263i	1.36075	+	2.59005i
$701$	9.58105	−	5.53162i	0.361871	−	0.208926i	−0.308030	−	0.951377i	$-0.599670\pi$
$701$	9.58105	−	5.53162i	0.361871	−	0.208926i	0.669901	+	0.742450i	$0.266336\pi$
$702$	−8.32252	−	19.5691i	−0.314113	−	0.738589i
$703$	13.2393	−	15.0300i	0.499329	−	0.566869i
$704$	−60.4068			−2.27667
$705$	−8.80280	−	35.2065i	−0.331533	−	1.32595i
$706$	−21.1139	+	36.5703i	−0.794631	+	1.37634i
$707$	−54.7931	+	14.6818i	−2.06071	+	0.552165i
$708$	6.69243	−	5.16873i	0.251517	−	0.194253i
$709$			33.1729i			1.24583i	0.782288	+	0.622917i	$0.214052\pi$
$709$			33.1729i			1.24583i	−0.782288	+	0.622917i	$0.785948\pi$
$710$	20.4160	−	46.6378i	0.766201	−	1.75028i
$711$	−0.176243	+	0.178469i	−0.00660962	+	0.00669312i
$712$	−21.4661	−	5.75182i	−0.804475	−	0.215559i
$713$	8.24211	−	8.24211i	0.308669	−	0.308669i
$714$	25.8932	−	10.8207i	0.969030	−	0.404953i
$715$	−11.2656	−	15.3037i	−0.421311	−	0.572325i
$716$	11.4374	+	6.60340i	0.427437	+	0.246781i
$717$	−1.20695	+	2.93989i	−0.0450743	+	0.109792i
$718$	6.42999	−	23.9970i	0.239965	−	0.895562i
$719$	−9.27779	−	16.0696i	−0.346003	−	0.599295i	0.639532	−	0.768764i	$-0.279128\pi$
$719$	−9.27779	−	16.0696i	−0.346003	−	0.599295i	−0.985535	+	0.169469i	$0.945795\pi$
$720$	−5.28973	+	3.94541i	−0.197137	+	0.147037i
$721$	−39.4165	+	68.2713i	−1.46795	+	2.54256i
$722$	−17.6259	+	4.72284i	−0.655968	+	0.175766i
$723$	−3.45037	+	0.465272i	−0.128321	+	0.0173036i
$724$	−32.7136	+	18.8872i	−1.21579	+	0.701938i
$725$	25.1647	−	23.2346i	0.934592	−	0.862913i
$726$	37.8173	−	15.8037i	1.40353	−	0.586529i
$727$	10.7761	+	40.2171i	0.399665	+	1.49157i	0.813688	+	0.581302i	$0.197457\pi$
$727$	10.7761	+	40.2171i	0.399665	+	1.49157i	−0.414023	+	0.910266i	$0.635877\pi$
$728$	20.4552	+	5.48094i	0.758118	+	0.203137i
$729$	18.7290	−	19.4480i	0.693666	−	0.720296i
$730$	9.19599	−	11.5024i	0.340359	−	0.425723i
$731$	−10.7093	+	6.18304i	−0.396099	+	0.228688i
$732$	14.2220	+	5.83874i	0.525662	+	0.215806i
$733$	17.7977	−	4.76888i	0.657373	−	0.176143i	0.0853131	−	0.996354i	$-0.472811\pi$
$733$	17.7977	−	4.76888i	0.657373	−	0.176143i	0.572060	+	0.820211i	$0.306144\pi$
$734$	−63.8376			−2.35629
$735$	−75.7416	−	1.27176i	−2.79377	−	0.0469097i
$736$	12.7009	−	21.9986i	0.468162	−	0.810880i
$737$	−14.0119	+	3.75449i	−0.516136	+	0.138298i
$738$	12.7780	+	21.8147i	0.470364	+	0.803011i
$739$		−	33.4071i		−	1.22890i	−0.788955	−	0.614451i	$-0.789378\pi$
$739$		−	33.4071i		−	1.22890i	0.788955	−	0.614451i	$-0.210622\pi$
$740$	−13.9863	+	38.3914i	−0.514147	+	1.41129i
$741$	4.02323	+	9.62736i	0.147797	+	0.353670i
$742$	29.4016	+	7.87813i	1.07937	+	0.289215i
$743$	−12.4725	−	46.5479i	−0.457571	−	1.70768i	−0.680418	−	0.732825i	$-0.738202\pi$
$743$	−12.4725	−	46.5479i	−0.457571	−	1.70768i	0.222847	−	0.974854i	$-0.428465\pi$
$744$	−11.8500	−	1.52227i	−0.434443	−	0.0558090i
$745$	5.15631	−	2.01640i	0.188913	−	0.0738751i
$746$			51.1589i			1.87306i
$747$	5.32550	−	9.35923i	0.194850	−	0.342436i
$748$	−13.8680	−	13.8680i	−0.507063	−	0.507063i
$749$	33.7022	+	58.3738i	1.23145	+	2.13293i
$750$	2.45248	−	43.2494i	0.0895520	−	1.57924i
$751$	29.7538			1.08573			0.542867	−	0.839819i	$-0.317339\pi$
$751$	29.7538			1.08573			0.542867	+	0.839819i	$0.317339\pi$
$752$	−2.38570	+	8.90357i	−0.0869977	+	0.324680i
$753$	−8.03200	+	6.20332i	−0.292702	+	0.226061i
$754$		−	28.0343i		−	1.02095i
$755$	−5.31174	+	34.9499i	−0.193314	+	1.27196i
$756$	11.2506	+	79.6542i	0.409182	+	2.89700i
$757$	49.7827	+	13.3392i	1.80938	+	0.484823i	0.995378	−	0.0960332i	$-0.0306155\pi$
$757$	49.7827	+	13.3392i	1.80938	+	0.484823i	0.814006	+	0.580856i	$0.197282\pi$
$758$	3.82999	+	14.2937i	0.139111	+	0.519171i
$759$	−3.89090	+	30.2886i	−0.141231	+	1.09941i
$760$	−13.3183	+	9.80411i	−0.483105	+	0.355632i
$761$	10.5346	−	6.08214i	0.381878	−	0.220477i	−0.296757	−	0.954953i	$-0.595905\pi$
$761$	10.5346	−	6.08214i	0.381878	−	0.220477i	0.678635	+	0.734476i	$0.262572\pi$
$762$	−58.4602	+	7.88317i	−2.11779	+	0.285577i
$763$	−36.9816	−	36.9816i	−1.33882	−	1.33882i
$764$	16.1051	−	27.8948i	0.582662	−	1.00920i
$765$	−9.32958	−	1.35807i	−0.337312	−	0.0491010i
$766$	43.0351			1.55492
$767$	−2.10238	−	2.10238i	−0.0759125	−	0.0759125i
$768$	−15.6579	+	2.11142i	−0.565006	+	0.0761892i
$769$			11.4788i			0.413936i	0.978348	+	0.206968i	$0.0663596\pi$
$769$			11.4788i			0.413936i	−0.978348	+	0.206968i	$0.933640\pi$
$770$	43.6114	+	111.523i	1.57165	+	4.01899i
$771$	−1.44613	+	0.604333i	−0.0520813	+	0.0217645i
$772$	6.29731	+	23.5019i	0.226645	+	0.845851i
$773$	−12.6949	−	47.3779i	−0.456603	−	1.70406i	−0.683333	−	0.730107i	$-0.739470\pi$
$773$	−12.6949	−	47.3779i	−0.456603	−	1.70406i	0.226730	−	0.973958i	$-0.427197\pi$
$774$	−15.6405	−	56.9390i	−0.562186	−	2.04663i
$775$	−11.2819	+	10.4166i	−0.405258	+	0.374177i
$776$			9.22387i			0.331118i
$777$	−35.8387	−	40.7879i	−1.28571	−	1.46326i
$778$	24.6479	+	24.6479i	0.883670	+	0.883670i
$779$	−6.20241	−	10.7429i	−0.222225	−	0.384904i
$780$	−14.7963	−	15.3017i	−0.529793	−	0.547888i
$781$	23.6397	−	40.9452i	0.845895	−	1.46513i
$782$	11.5260	−	3.08837i	0.412167	−	0.110440i
$783$	32.7552	−	13.9304i	1.17057	−	0.497832i
$784$	16.6631	+	9.62045i	0.595111	+	0.343587i
$785$	−30.7916	+	3.43110i	−1.09900	+	0.122461i
$786$	−9.44985	+	12.3956i	−0.337065	+	0.442138i
$787$	22.0720	−	22.0720i	0.786782	−	0.786782i	−0.194183	−	0.980965i	$-0.562206\pi$
$787$	22.0720	−	22.0720i	0.786782	−	0.786782i	0.980965	+	0.194183i	$0.0622055\pi$
$788$	−54.2851	+	54.2851i	−1.93383	+	1.93383i
$789$	20.9034	−	27.4196i	0.744181	−	0.976164i
$790$	−0.167709	+	0.383110i	−0.00596683	+	0.0136304i
$791$			96.6392i			3.43609i
$792$	27.0084	−	15.8202i	0.959702	−	0.562146i
$793$	1.39907	−	5.22141i	0.0496825	−	0.185418i
$794$	−8.95410	−	15.5090i	−0.317769	−	0.550392i
$795$	−7.10843	−	7.35122i	−0.252110	−	0.260721i
$796$	−11.4225	+	19.7843i	−0.404858	+	0.701235i
$797$	−4.74737	+	17.7174i	−0.168160	+	0.627583i	0.829456	+	0.558573i	$0.188651\pi$
$797$	−4.74737	+	17.7174i	−0.168160	+	0.627583i	−0.997616	+	0.0690104i	$0.978016\pi$
$798$	−8.78670	−	65.1606i	−0.311046	−	2.30666i
$799$	−11.4047	+	6.58452i	−0.403470	+	0.232944i
$800$	−17.8732	+	28.2906i	−0.631914	+	1.00022i
$801$	−28.6228	+	7.86235i	−1.01134	+	0.277802i
$802$	44.7359	+	11.9870i	1.57968	+	0.423274i
$803$	9.67051	−	9.67051i	0.341265	−	0.341265i
$804$	−14.9921	+	6.26513i	−0.528731	+	0.220954i
$805$	−43.2410	−	6.57185i	−1.52405	−	0.231627i
$806$			12.5684i			0.442704i
$807$	11.1283	+	14.4088i	0.391734	+	0.507214i
$808$	17.4817	+	17.4817i	0.615003	+	0.615003i
$809$	4.87626	−	8.44593i	0.171440	−	0.296943i	−0.767483	−	0.641069i	$-0.778491\pi$
$809$	4.87626	−	8.44593i	0.171440	−	0.296943i	0.938924	+	0.344126i	$0.111825\pi$
$810$	17.5340	−	41.4633i	0.616080	−	1.45687i
$811$	−11.1202	+	19.2607i	−0.390482	+	0.676335i	−0.992513	−	0.122138i	$-0.961025\pi$
$811$	−11.1202	+	19.2607i	−0.390482	+	0.676335i	0.602031	+	0.798473i	$0.294358\pi$
$812$	−27.4480	+	102.438i	−0.963238	+	3.59485i
$813$	−16.5272	+	40.2571i	−0.579634	+	1.41188i
$814$	−28.0801	+	56.6282i	−0.984208	+	1.98482i
$815$	−2.31267	−	20.7545i	−0.0810093	−	0.727000i
$816$	1.90438	+	1.45181i	0.0666667	+	0.0508235i
$817$	7.49874	+	27.9857i	0.262348	+	0.979095i
$818$	10.5646	+	39.4275i	0.369381	+	1.37855i
$819$	27.2748	−	7.49207i	0.953059	−	0.261794i
$820$	19.7653	+	15.8020i	0.690234	+	0.551831i
$821$	−4.58715	−	2.64839i	−0.160093	−	0.0924296i	0.417813	−	0.908533i	$-0.362797\pi$
$821$	−4.58715	−	2.64839i	−0.160093	−	0.0924296i	−0.577906	+	0.816103i	$0.696130\pi$
$822$	1.48181	+	0.608344i	0.0516841	+	0.0212184i
$823$	−8.61210	+	32.1408i	−0.300199	+	1.12036i	0.636801	+	0.771028i	$0.280257\pi$
$823$	−8.61210	+	32.1408i	−0.300199	+	1.12036i	−0.937000	+	0.349329i	$0.886409\pi$
$824$	34.3576			1.19691
$825$	6.71154	−	39.6653i	0.233666	−	1.38097i
$826$	9.36774	+	16.2254i	0.325946	+	0.564554i
$827$	36.9581	−	9.90290i	1.28516	−	0.344357i	0.449339	−	0.893361i	$-0.351659\pi$
$827$	36.9581	−	9.90290i	1.28516	−	0.344357i	0.835820	+	0.549004i	$0.184993\pi$
$828$	0.214710	+	34.2046i	0.00746169	+	1.18869i
$829$	17.6908	−	10.2138i	0.614427	−	0.354740i	−0.160269	−	0.987073i	$-0.551236\pi$
$829$	17.6908	−	10.2138i	0.614427	−	0.354740i	0.774696	+	0.632334i	$0.217903\pi$
$830$	2.69777	−	17.7506i	0.0936409	−	0.616133i
$831$	−15.0869	+	19.7899i	−0.523357	+	0.686503i
$832$	6.15746	+	22.9800i	0.213472	+	0.796687i
$833$	7.11467	+	26.5523i	0.246509	+	0.919984i
$834$	−47.1597	+	61.8607i	−1.63301	+	2.14206i
$835$	−4.13867	+	3.04663i	−0.143224	+	0.105433i
$836$	−39.7941	+	22.9751i	−1.37631	+	0.794611i
$837$	−14.6849	+	6.24532i	−0.507585	+	0.215870i
$838$	−32.3512	+	8.66849i	−1.11755	+	0.299448i
$839$	19.8997	+	34.4673i	0.687014	+	1.18994i	0.972799	+	0.231650i	$0.0744124\pi$
$839$	19.8997	+	34.4673i	0.687014	+	1.18994i	−0.285785	+	0.958294i	$0.592254\pi$
$840$	21.7604	+	39.1954i	0.750804	+	1.35237i
$841$	17.9243			0.618081
$842$	4.87466	−	18.1925i	0.167992	−	0.626955i
$843$	12.3666	+	5.07698i	0.425927	+	0.174861i
$844$	−15.8481	−	9.14990i	−0.545514	−	0.314952i
$845$	13.4786	−	16.8591i	0.463677	−	0.579970i
$846$	−16.6561	−	60.6362i	−0.572647	−	2.08471i
$847$	14.1099	+	52.6588i	0.484821	+	1.80938i
$848$	0.672249	+	2.50887i	0.0230851	+	0.0861548i
$849$	−23.4389	−	17.8687i	−0.804421	−	0.613252i
$850$	−15.3340	+	3.46029i	−0.525951	+	0.118687i
$851$	−12.7843	−	19.2240i	−0.438240	−	0.658990i
$852$	20.1125	−	48.9902i	0.689043	−	1.67838i
$853$	−11.7665	+	43.9131i	−0.402877	+	1.50356i	0.405061	+	0.914290i	$0.367250\pi$
$853$	−11.7665	+	43.9131i	−0.402877	+	1.50356i	−0.807938	+	0.589268i	$0.799416\pi$
$854$	−17.0315	+	29.4995i	−0.582806	+	1.00945i
$855$	−8.73086	+	20.2902i	−0.298589	+	0.693912i
$856$	14.6884	−	25.4410i	0.502038	−	0.869555i
$857$	12.3601	+	12.3601i	0.422213	+	0.422213i	0.885965	−	0.463752i	$-0.153497\pi$
$857$	12.3601	+	12.3601i	0.422213	+	0.422213i	−0.463752	+	0.885965i	$0.653497\pi$
$858$	−20.1270	−	26.0602i	−0.687124	−	0.889682i
$859$			15.8602i			0.541144i	0.962700	+	0.270572i	$0.0872127\pi$
$859$			15.8602i			0.541144i	−0.962700	+	0.270572i	$0.912787\pi$
$860$	−35.0388	−	47.5980i	−1.19481	−	1.62308i
$861$	−31.0269	+	12.9660i	−1.05739	+	0.441879i
$862$	18.3905	−	18.3905i	0.626383	−	0.626383i
$863$	3.30345	+	0.885156i	0.112451	+	0.0301310i	0.314606	−	0.949223i	$-0.398128\pi$
$863$	3.30345	+	0.885156i	0.112451	+	0.0301310i	−0.202155	+	0.979354i	$0.564794\pi$
$864$	−27.3894	+	21.4293i	−0.931806	+	0.729041i
$865$	−22.4760	+	2.50449i	−0.764207	+	0.0851553i
$866$	31.3142	−	18.0793i	1.06410	−	0.614359i
$867$	−3.47773	−	25.7902i	−0.118110	−	0.875882i
$868$	12.3056	−	45.9251i	0.417679	−	1.55880i
$869$	−0.194190	+	0.336348i	−0.00658746	+	0.0114098i
$870$	42.6640	−	41.2549i	1.44644	−	1.39867i
$871$	2.85656	+	4.94771i	0.0967910	+	0.167647i
$872$	−5.89947	+	22.0171i	−0.199781	+	0.745594i
$873$	6.22687	+	10.6306i	0.210748	+	0.359791i
$874$		−	27.9572i		−	0.945665i
$875$	56.5742	+	10.9204i	1.91256	+	0.369178i
$876$	9.28730	−	12.1824i	0.313789	−	0.411606i
$877$	35.4226	−	35.4226i	1.19614	−	1.19614i	0.220824	−	0.975314i	$-0.429125\pi$
$877$	35.4226	−	35.4226i	1.19614	−	1.19614i	0.975314	−	0.220824i	$-0.0708746\pi$
$878$	−51.4461	+	51.4461i	−1.73622	+	1.73622i
$879$	−16.2383	+	21.3003i	−0.547705	+	0.718441i
$880$	−6.38068	+	7.98100i	−0.215093	+	0.269040i
$881$	−47.8677	−	27.6364i	−1.61270	−	0.931095i	−0.988740	−	0.149643i	$-0.952188\pi$
$881$	−47.8677	−	27.6364i	−1.61270	−	0.931095i	−0.623964	−	0.781453i	$-0.714479\pi$
$882$	−131.257	+	0.823933i	−4.41967	+	0.0277433i
$883$	41.7101	−	11.1762i	1.40366	−	0.376109i	0.524001	−	0.851718i	$-0.324439\pi$
$883$	41.7101	−	11.1762i	1.40366	−	0.376109i	0.879657	+	0.475608i	$0.157772\pi$
$884$	−3.86205	+	6.68926i	−0.129895	+	0.224984i
$885$	0.105670	−	6.29334i	0.00355207	−	0.211548i
$886$	21.2282	+	36.7683i	0.713176	+	1.23526i
$887$	−33.9438	−	33.9438i	−1.13972	−	1.13972i	−0.988500	−	0.151220i	$-0.951680\pi$
$887$	−33.9438	−	33.9438i	−1.13972	−	1.13972i	−0.151220	−	0.988500i	$-0.548320\pi$
$888$	−7.58516	+	22.4152i	−0.254541	+	0.752204i
$889$		−	78.4618i		−	2.63152i
$890$	−39.8570	+	29.3403i	−1.33601	+	0.983488i
$891$	20.4475	−	36.4658i	0.685016	−	1.22165i
$892$	−14.0754	−	52.5301i	−0.471279	−	1.75884i
$893$	7.98565	+	29.8028i	0.267230	+	0.997314i
$894$	8.85165	−	3.69907i	0.296044	−	0.123715i
$895$	9.15532	−	3.58023i	0.306029	−	0.119674i
$896$		−	80.9324i		−	2.70376i
$897$	11.9190	−	1.60724i	0.397964	−	0.0536641i
$898$	−21.8295	−	21.8295i	−0.728459	−	0.728459i
$899$	−21.0373			−0.701633
$900$	1.51280	−	45.0356i	0.0504265	−	1.50119i
$901$	−1.85540	+	3.21365i	−0.0618123	+	0.107062i
$902$	27.6808	+	27.6808i	0.921668	+	0.921668i
$903$	77.8355	−	10.4959i	2.59020	−	0.349281i
$904$	36.4754	−	21.0591i	1.21315	−	0.700414i
$905$	−4.22480	+	27.7981i	−0.140437	+	0.924040i
$906$	−7.80473	+	60.7557i	−0.259295	+	2.01847i
$907$	−7.00192	−	26.1315i	−0.232495	−	0.867683i	−0.979262	−	0.202597i	$-0.935062\pi$
$907$	−7.00192	−	26.1315i	−0.232495	−	0.867683i	0.746767	−	0.665086i	$-0.231605\pi$
$908$	−5.95002	−	1.59430i	−0.197458	−	0.0529088i
$909$	31.9493	+	8.34620i	1.05969	+	0.276826i
$910$	37.9800	−	27.9585i	1.25902	−	0.926816i
$911$			57.9138i			1.91877i	0.282100	+	0.959385i	$0.408969\pi$
$911$			57.9138i			1.91877i	−0.282100	+	0.959385i	$0.591031\pi$
$912$	4.44040	−	3.42944i	0.147036	−	0.113560i
$913$	4.31550	−	16.1057i	0.142822	−	0.533020i
$914$	35.2319			1.16537
$915$	10.0051	−	5.55458i	0.330757	−	0.183629i
$916$	15.4021	+	26.6772i	0.508899	+	0.881438i
$917$	−14.6599	−	14.6599i	−0.484112	−	0.484112i
$918$	−16.2158	−	1.97971i	−0.535203	−	0.0653403i
$919$		−	30.8933i		−	1.01908i	−0.860448	−	0.509538i	$-0.829816\pi$
$919$		−	30.8933i		−	1.01908i	0.860448	−	0.509538i	$-0.170184\pi$
$920$	6.94237	+	17.7529i	0.228883	+	0.585297i
$921$	18.2530	+	2.34480i	0.601458	+	0.0772638i
$922$	8.68096	+	32.3978i	0.285892	+	1.06696i
$923$	−17.9860	−	4.81934i	−0.592017	−	0.158631i
$924$	48.0289	+	114.930i	1.58003	+	3.78093i
$925$	15.8192	+	25.9760i	0.520132	+	0.854086i
$926$			24.6620i			0.810444i
$927$	39.5974	−	23.1942i	1.30055	−	0.761798i
$928$	−44.2838	+	11.8658i	−1.45369	+	0.389514i
$929$	6.11253	−	10.5872i	0.200546	−	0.347355i	−0.748159	−	0.663520i	$-0.769062\pi$
$929$	6.11253	−	10.5872i	0.200546	−	0.347355i	0.948704	+	0.316164i	$0.102395\pi$
$930$	−19.1273	+	18.4956i	−0.627208	+	0.606493i
$931$	64.4049			2.11078
$932$	−24.5085	+	6.56703i	−0.802803	+	0.215110i
$933$	−32.3501	−	13.2810i	−1.05909	−	0.434802i
$934$	−61.2487	+	35.3619i	−2.00412	+	1.15708i
$935$	−14.5086	+	1.61668i	−0.474480	+	0.0528712i
$936$	−8.77137	−	8.66193i	−0.286701	−	0.283124i
$937$	−8.23539	−	2.20667i	−0.269038	−	0.0720886i	0.121778	−	0.992557i	$-0.461140\pi$
$937$	−8.23539	−	2.20667i	−0.269038	−	0.0720886i	−0.390816	+	0.920469i	$0.627807\pi$
$938$	−9.31771	−	34.7742i	−0.304234	−	1.13542i
$939$	−29.6461	+	12.3890i	−0.967465	+	0.404299i
$940$	−37.3139	−	50.6887i	−1.21705	−	1.65328i
$941$	32.3751	−	18.6918i	1.05540	−	0.609335i	0.131243	−	0.991350i	$-0.458103\pi$
$941$	32.3751	−	18.6918i	1.05540	−	0.609335i	0.924156	+	0.382016i	$0.124770\pi$
$942$	−53.2030	+	7.17425i	−1.73345	+	0.233750i
$943$	−13.8111	+	3.70067i	−0.449751	+	0.120511i
$944$	−0.799359	+	1.38453i	−0.0260169	+	0.0450626i
$945$	51.5391	+	30.4829i	1.67657	+	0.991609i
$946$	−45.7156	−	79.1817i	−1.48634	−	2.57442i
$947$	4.80911	−	17.9478i	0.156275	−	0.583226i	−0.842718	−	0.538356i	$-0.819046\pi$
$947$	4.80911	−	17.9478i	0.156275	−	0.583226i	0.998993	−	0.0448708i	$-0.0142876\pi$
$948$	−0.165216	+	0.402435i	−0.00536597	+	0.0130705i
$949$	−4.66460	−	2.69311i	−0.151419	−	0.0874220i
$950$	−1.46749	+	36.8006i	−0.0476117	+	1.19397i
$951$	−20.6675	+	8.63685i	−0.670189	+	0.280069i
$952$	11.5033	−	11.5033i	0.372825	−	0.372825i
$953$	−17.2064	−	4.61043i	−0.557369	−	0.149347i	−0.0308718	−	0.999523i	$-0.509828\pi$
$953$	−17.2064	−	4.61043i	−0.557369	−	0.149347i	−0.526497	+	0.850177i	$0.676495\pi$
$954$	−12.6077	−	12.4504i	−0.408189	−	0.403096i
$955$	−8.73185	−	22.3290i	−0.282556	−	0.722548i
$956$			5.51192i			0.178268i
$957$	43.6201	−	33.6889i	1.41004	−	1.08901i
$958$	11.4179	−	3.05941i	0.368895	−	0.0988451i
$959$	−1.06530	+	1.84515i	−0.0344002	+	0.0595829i
$960$	−25.9108	+	43.1878i	−0.836268	+	1.39388i
$961$	−21.5685			−0.695758
$962$	24.4048	+	4.90995i	0.786843	+	0.158303i
$963$	−0.246298	−	39.2368i	−0.00793685	−	1.26439i
$964$	−5.22948	+	3.01924i	−0.168430	+	0.0972432i
$965$	16.5907	+	7.26269i	0.534072	+	0.233794i
$966$	−75.1688	−	9.65625i	−2.41852	−	0.310685i
$967$	1.30537	+	4.87171i	0.0419779	+	0.156664i	0.983733	−	0.179635i	$-0.0574916\pi$
$967$	1.30537	+	4.87171i	0.0419779	+	0.156664i	−0.941755	+	0.336298i	$0.890825\pi$
$968$	16.8007	−	16.8007i	0.539995	−	0.539995i
$969$	7.95032	+	1.02130i	0.255401	+	0.0328090i
$970$	16.0444	+	12.8273i	0.515156	+	0.411859i
$971$	35.9579	−	20.7603i	1.15394	−	0.666229i	0.204098	−	0.978950i	$-0.434574\pi$
$971$	35.9579	−	20.7603i	1.15394	−	0.666229i	0.949845	+	0.312721i	$0.101241\pi$
$972$	17.2395	−	43.5400i	0.552956	−	1.39655i
$973$	−73.1603	−	73.1603i	−2.34541	−	2.34541i
$974$	38.0286	+	65.8675i	1.21852	+	2.11053i
$975$	−15.7736	+	1.49001i	−0.505159	+	0.0477184i
$976$	−2.90663			−0.0930391
$977$	−15.4097	+	57.5097i	−0.492999	+	1.83990i	0.0479614	+	0.998849i	$0.484728\pi$
$977$	−15.4097	+	57.5097i	−0.492999	+	1.83990i	−0.540960	+	0.841048i	$0.681939\pi$
$978$	−4.83568	−	35.8605i	−0.154628	−	1.14669i
$979$	−39.8040	+	22.9808i	−1.27214	+	0.734471i
$980$	−122.361	+	47.8499i	−3.90868	+	1.52851i
$981$	8.06417	+	29.3575i	0.257469	+	0.937314i
$982$	−45.0284	−	12.0653i	−1.43691	−	0.385020i
$983$	−13.6544	−	3.65868i	−0.435508	−	0.116694i	0.0344028	−	0.999408i	$-0.489047\pi$
$983$	−13.6544	−	3.65868i	−0.435508	−	0.116694i	−0.469910	+	0.882714i	$0.655714\pi$
$984$	11.6551	+	8.88526i	0.371550	+	0.283252i
$985$	6.32838	+	56.7926i	0.201639	+	1.80956i
$986$	−18.6509	−	10.7681i	−0.593966	−	0.342926i
$987$	82.8895	−	11.1774i	2.63840	−	0.355780i
$988$	12.7965	+	12.7965i	0.407112	+	0.407112i
$989$	33.3953			1.06191
$990$	10.0411	−	68.9802i	0.319128	−	2.19233i
$991$	45.4771			1.44463			0.722314	−	0.691565i	$-0.243079\pi$
$991$	45.4771			1.44463			0.722314	+	0.691565i	$0.243079\pi$
$992$	19.8535	−	5.31972i	0.630348	−	0.168901i
$993$	−12.8915	+	31.4012i	−0.409099	+	0.996488i
$994$	101.616	+	58.6679i	3.22306	+	1.86083i
$995$	6.19302	+	15.8367i	0.196332	+	0.502058i
$996$	2.37964	−	18.5243i	0.0754019	−	0.586964i
$997$	32.1629	+	8.61802i	1.01861	+	0.272936i	0.729222	−	0.684277i	$-0.239882\pi$
$997$	32.1629	+	8.61802i	1.01861	+	0.272936i	0.289387	+	0.957212i	$0.406549\pi$
$998$	24.3249	−	24.3249i	0.769991	−	0.769991i
$999$	6.39011	+	30.9543i	0.202174	+	0.979350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.bi.a.248.63	yes	288
3.2	odd	2	inner	555.2.bi.a.248.10	yes	288
5.2	odd	4	inner	555.2.bi.a.137.63	yes	288
15.2	even	4	inner	555.2.bi.a.137.10	yes	288
37.10	even	3	inner	555.2.bi.a.158.10	yes	288
111.47	odd	6	inner	555.2.bi.a.158.63	yes	288
185.47	odd	12	inner	555.2.bi.a.47.10	✓	288
555.47	even	12	inner	555.2.bi.a.47.63	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.bi.a.47.10	✓	288	185.47	odd	12	inner
555.2.bi.a.47.63	yes	288	555.47	even	12	inner
555.2.bi.a.137.10	yes	288	15.2	even	4	inner
555.2.bi.a.137.63	yes	288	5.2	odd	4	inner
555.2.bi.a.158.10	yes	288	37.10	even	3	inner
555.2.bi.a.158.63	yes	288	111.47	odd	6	inner
555.2.bi.a.248.10	yes	288	3.2	odd	2	inner
555.2.bi.a.248.63	yes	288	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.bi (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.578972 - 2.16075i) q^{2} +(-1.05871 - 1.37081i) q^{3} +(-2.60160 - 1.50203i) q^{4} +(-2.08250 + 0.814371i) q^{5} +(-3.57495 + 1.49396i) q^{6} +(-1.33384 - 4.97795i) q^{7} +(-1.58821 + 1.58821i) q^{8} +(-0.758252 + 2.90259i) q^{9} +O(q^{10})\)	\(q+(0.578972 - 2.16075i) q^{2} +(-1.05871 - 1.37081i) q^{3} +(-2.60160 - 1.50203i) q^{4} +(-2.08250 + 0.814371i) q^{5} +(-3.57495 + 1.49396i) q^{6} +(-1.33384 - 4.97795i) q^{7} +(-1.58821 + 1.58821i) q^{8} +(-0.758252 + 2.90259i) q^{9} +(0.553946 + 4.97126i) q^{10} +4.64526i q^{11} +(0.695340 + 5.15652i) q^{12} +(1.76715 - 0.473506i) q^{13} -11.5284 q^{14} +(3.32112 + 1.99253i) q^{15} +(-0.491864 - 0.851934i) q^{16} +(0.363752 - 1.35754i) q^{17} +(5.83278 + 3.31892i) q^{18} +(-2.85167 - 1.64641i) q^{19} +(6.64103 + 1.00932i) q^{20} +(-5.41169 + 7.09867i) q^{21} +(10.0373 + 2.68947i) q^{22} +(-2.68378 + 2.68378i) q^{23} +(3.85859 + 0.495678i) q^{24} +(3.67360 - 3.39185i) q^{25} -4.09252i q^{26} +(4.78168 - 2.03359i) q^{27} +(-4.00694 + 14.9541i) q^{28} +6.85013 q^{29} +(6.22820 - 6.02250i) q^{30} -3.07108 q^{31} +(-6.46466 + 1.73220i) q^{32} +(6.36777 - 4.91799i) q^{33} +(-2.72271 - 1.57196i) q^{34} +(6.83162 + 9.28034i) q^{35} +(6.33245 - 6.41246i) q^{36} +(-1.19974 + 5.96327i) q^{37} +(-5.20853 + 5.20853i) q^{38} +(-2.51999 - 1.92112i) q^{39} +(2.01405 - 4.60083i) q^{40} +(3.26251 + 1.88361i) q^{41} +(12.2053 + 15.8032i) q^{42} +(-6.22168 - 6.22168i) q^{43} +(6.97732 - 12.0851i) q^{44} +(-0.784729 - 6.66215i) q^{45} +(4.24516 + 7.35283i) q^{46} +(-6.62567 - 6.62567i) q^{47} +(-0.647098 + 1.57621i) q^{48} +(-16.9387 + 9.77957i) q^{49} +(-5.20204 - 9.90153i) q^{50} +(-2.24604 + 0.938611i) q^{51} +(-5.30863 - 1.42244i) q^{52} +(-2.55036 - 0.683368i) q^{53} +(-1.62563 - 11.5094i) q^{54} +(-3.78296 - 9.67374i) q^{55} +(10.0244 + 5.78762i) q^{56} +(0.762179 + 5.65219i) q^{57} +(3.96604 - 14.8015i) q^{58} +(-0.812581 - 1.40743i) q^{59} +(-5.64736 - 10.1722i) q^{60} +(1.47736 - 2.55885i) q^{61} +(-1.77807 + 6.63584i) q^{62} +(15.4604 - 0.0970482i) q^{63} +13.0040i q^{64} +(-3.29447 + 2.42519i) q^{65} +(-6.93981 - 16.6066i) q^{66} +(0.808241 + 3.01640i) q^{67} +(-2.98540 + 2.98540i) q^{68} +(6.52032 + 0.837606i) q^{69} +(24.0078 - 9.38838i) q^{70} +(-8.81440 - 5.08900i) q^{71} +(-3.40566 - 5.81419i) q^{72} +(-2.08180 - 2.08180i) q^{73} +(12.1905 + 6.04490i) q^{74} +(-8.53888 - 1.44482i) q^{75} +(4.94593 + 8.56660i) q^{76} +(23.1239 - 6.19602i) q^{77} +(-5.61007 + 4.33280i) q^{78} +(0.0724067 + 0.0418040i) q^{79} +(1.71810 + 1.37359i) q^{80} +(-7.85011 - 4.40180i) q^{81} +(5.95893 - 5.95893i) q^{82} +(-3.46712 - 0.929013i) q^{83} +(24.7414 - 10.3393i) q^{84} +(0.348029 + 3.12330i) q^{85} +(-17.0457 + 9.84134i) q^{86} +(-7.25233 - 9.39025i) q^{87} +(-7.37764 - 7.37764i) q^{88} +(4.94716 + 8.56874i) q^{89} +(-14.8496 - 2.16159i) q^{90} +(-4.71418 - 8.16520i) q^{91} +(11.0133 - 2.95099i) q^{92} +(3.25139 + 4.20987i) q^{93} +(-18.1525 + 10.4804i) q^{94} +(7.27939 + 1.10634i) q^{95} +(9.21875 + 7.02793i) q^{96} +(2.90386 - 2.90386i) q^{97} +(11.3242 + 42.2625i) q^{98} +(-13.4833 - 3.52228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 16 q^{6} - 4 q^{7}+O(q^{10}) \) 288 * q - 16 * q^6 - 4 * q^7	\( 288 q - 16 q^{6} - 4 q^{7} - 16 q^{10} - 18 q^{12} - 20 q^{13} + 6 q^{15} + 112 q^{16} + 20 q^{18} - 4 q^{21} - 12 q^{22} - 36 q^{25} + 48 q^{27} - 28 q^{28} - 16 q^{30} - 80 q^{31} + 2 q^{33} - 16 q^{36} - 36 q^{37} + 8 q^{40} - 32 q^{42} - 16 q^{43} + 76 q^{45} - 24 q^{46} + 112 q^{48} + 48 q^{55} + 2 q^{57} - 60 q^{58} - 56 q^{60} + 16 q^{61} - 36 q^{63} - 36 q^{70} - 58 q^{72} - 48 q^{73} - 88 q^{75} + 16 q^{76} + 20 q^{78} - 56 q^{81} - 136 q^{82} + 144 q^{85} + 16 q^{87} + 144 q^{88} - 42 q^{90} - 22 q^{93} - 80 q^{96} + 56 q^{97}+O(q^{100}) \) 288 * q - 16 * q^6 - 4 * q^7 - 16 * q^10 - 18 * q^12 - 20 * q^13 + 6 * q^15 + 112 * q^16 + 20 * q^18 - 4 * q^21 - 12 * q^22 - 36 * q^25 + 48 * q^27 - 28 * q^28 - 16 * q^30 - 80 * q^31 + 2 * q^33 - 16 * q^36 - 36 * q^37 + 8 * q^40 - 32 * q^42 - 16 * q^43 + 76 * q^45 - 24 * q^46 + 112 * q^48 + 48 * q^55 + 2 * q^57 - 60 * q^58 - 56 * q^60 + 16 * q^61 - 36 * q^63 - 36 * q^70 - 58 * q^72 - 48 * q^73 - 88 * q^75 + 16 * q^76 + 20 * q^78 - 56 * q^81 - 136 * q^82 + 144 * q^85 + 16 * q^87 + 144 * q^88 - 42 * q^90 - 22 * q^93 - 80 * q^96 + 56 * q^97

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