LMFDB - Embedded newform 555.2.bi.a.158.10

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			158.10
Character	$\chi$	$=$	555.158
Dual form			555.2.bi.a.137.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.16075 + 0.578972i) q^{2} +(1.71651 - 0.231467i) q^{3} +(2.60160 - 1.50203i) q^{4} +(0.335983 - 2.21068i) q^{5} +(-3.57495 + 1.49396i) q^{6} +(4.97795 + 1.33384i) q^{7} +(-1.58821 + 1.58821i) q^{8} +(2.89285 - 0.794631i) q^{9} +O(q^{10})$	\(q+(-2.16075 + 0.578972i) q^{2} +(1.71651 - 0.231467i) q^{3} +(2.60160 - 1.50203i) q^{4} +(0.335983 - 2.21068i) q^{5} +(-3.57495 + 1.49396i) q^{6} +(4.97795 + 1.33384i) q^{7} +(-1.58821 + 1.58821i) q^{8} +(2.89285 - 0.794631i) q^{9} +(0.553946 + 4.97126i) q^{10} +4.64526i q^{11} +(4.11801 - 3.18044i) q^{12} +(-0.473506 + 1.76715i) q^{13} -11.5284 q^{14} +(0.0650215 - 3.87244i) q^{15} +(-0.491864 + 0.851934i) q^{16} +(-1.35754 + 0.363752i) q^{17} +(-5.79066 + 3.39188i) q^{18} +(2.85167 - 1.64641i) q^{19} +(-2.44642 - 6.25596i) q^{20} +(8.85347 + 1.13732i) q^{21} +(-2.68947 - 10.0373i) q^{22} +(-2.68378 + 2.68378i) q^{23} +(-2.35857 + 3.09380i) q^{24} +(-4.77423 - 1.48550i) q^{25} -4.09252i q^{26} +(4.78168 - 2.03359i) q^{27} +(14.9541 - 4.00694i) q^{28} +6.85013 q^{29} +(2.10154 + 8.40503i) q^{30} -3.07108 q^{31} +(1.73220 - 6.46466i) q^{32} +(1.07522 + 7.97365i) q^{33} +(2.72271 - 1.57196i) q^{34} +(4.62120 - 10.5565i) q^{35} +(6.33245 - 6.41246i) q^{36} +(-5.96327 + 1.19974i) q^{37} +(-5.20853 + 5.20853i) q^{38} +(-0.403744 + 3.14294i) q^{39} +(2.97741 + 4.04464i) q^{40} +(-3.26251 + 1.88361i) q^{41} +(-19.7886 + 2.66844i) 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} +(11.1760 + 0.445663i) q^{50} +(-2.24604 + 0.938611i) q^{51} +(1.42244 + 5.30863i) q^{52} +(0.683368 + 2.55036i) q^{53} +(-9.15464 + 7.16256i) q^{54} +(10.2692 + 1.56073i) q^{55} +(-10.0244 + 5.78762i) q^{56} +(4.51385 - 3.48616i) q^{57} +(-14.8015 + 3.96604i) q^{58} +(-0.812581 + 1.40743i) q^{59} +(-5.64736 - 10.1722i) q^{60} +(1.47736 + 2.55885i) q^{61} +(6.63584 - 1.77807i) q^{62} +(15.4604 - 0.0970482i) q^{63} +13.0040i q^{64} +(3.74751 + 1.64050i) q^{65} +(-6.93981 - 16.6066i) q^{66} +(-3.01640 - 0.808241i) q^{67} +(-2.98540 + 2.98540i) q^{68} +(-3.98555 + 5.22796i) q^{69} +(-3.87335 + 25.4856i) q^{70} +(8.81440 - 5.08900i) q^{71} +(-3.33240 + 5.85649i) 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} +(-6.19602 + 23.1239i) q^{77} +(-0.947281 - 7.02487i) q^{78} +(-0.0724067 + 0.0418040i) q^{79} +(1.71810 + 1.37359i) q^{80} +(7.73712 - 4.59749i) q^{81} +(5.95893 - 5.95893i) q^{82} +(0.929013 + 3.46712i) q^{83} +(24.7414 - 10.3393i) q^{84} +(0.348029 + 3.12330i) q^{85} +(17.0457 + 9.84134i) q^{86} +(11.7584 - 1.58558i) q^{87} +(-7.37764 - 7.37764i) q^{88} +(4.94716 - 8.56874i) q^{89} +(5.55280 + 13.9409i) q^{90} +(-4.71418 + 8.16520i) q^{91} +(-2.95099 + 11.0133i) q^{92} +(-5.27155 + 0.710851i) q^{93} +(18.1525 + 10.4804i) q^{94} +(-2.68158 - 6.85731i) q^{95} +(1.47700 - 11.4976i) q^{96} +(2.90386 - 2.90386i) q^{97} +(-42.2625 - 11.3242i) q^{98} +(3.69127 + 13.4380i) 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 $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−2.16075	+	0.578972i	−1.52788	+	0.409395i	−0.922328	−	0.386408i	$-0.873716\pi$
$2$	−2.16075	+	0.578972i	−1.52788	+	0.409395i	−0.605555	+	0.795803i	$0.707049\pi$
$3$	1.71651	−	0.231467i	0.991030	−	0.133637i
$3$	1.71651	−	0.231467i	0.991030	−	0.133637i
$4$	2.60160	−	1.50203i	1.30080	−	0.751016i
$5$	0.335983	−	2.21068i	0.150256	−	0.988647i
$5$	0.335983	−	2.21068i	0.150256	−	0.988647i
$6$	−3.57495	+	1.49396i	−1.45947	+	0.609905i
$7$	4.97795	+	1.33384i	1.88149	+	0.504144i	0.999457	+	0.0329552i	$0.0104919\pi$
$7$	4.97795	+	1.33384i	1.88149	+	0.504144i	0.882033	+	0.471188i	$0.156175\pi$
$8$	−1.58821	+	1.58821i	−0.561517	+	0.561517i
$9$	2.89285	−	0.794631i	0.964282	−	0.264877i
$10$	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	$0.753050\pi$
$12$	4.11801	−	3.18044i	1.18877	−	0.918115i
$13$	−0.473506	+	1.76715i	−0.131327	+	0.490119i	−0.999986	−	0.00529159i	$-0.998316\pi$
$13$	−0.473506	+	1.76715i	−0.131327	+	0.490119i	0.868659	+	0.495410i	$0.164982\pi$
$14$	−11.5284			−3.08109
$15$	0.0650215	−	3.87244i	0.0167885	−	0.999859i
$16$	−0.491864	+	0.851934i	−0.122966	+	0.212984i
$17$	−1.35754	+	0.363752i	−0.329252	+	0.0882228i	−0.419658	−	0.907682i	$-0.637850\pi$
$17$	−1.35754	+	0.363752i	−0.329252	+	0.0882228i	0.0904064	+	0.995905i	$0.471183\pi$
$18$	−5.79066	+	3.39188i	−1.36487	+	0.799474i
$19$	2.85167	−	1.64641i	0.654218	−	0.377713i	−0.135852	−	0.990729i	$-0.543377\pi$
$19$	2.85167	−	1.64641i	0.654218	−	0.377713i	0.790071	+	0.613016i	$0.210044\pi$
$20$	−2.44642	−	6.25596i	−0.547037	−	1.39887i
$21$	8.85347	+	1.13732i	1.93199	+	0.248184i
$22$	−2.68947	−	10.0373i	−0.573398	−	2.13995i
$23$	−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	$0.379499\pi$
$24$	−2.35857	+	3.09380i	−0.481441	+	0.631520i
$25$	−4.77423	−	1.48550i	−0.954846	−	0.297101i
$26$		−	4.09252i		−	0.802609i
$27$	4.78168	−	2.03359i	0.920235	−	0.391365i
$28$	14.9541	−	4.00694i	2.82606	−	0.757240i
$29$	6.85013			1.27204			0.636019	−	0.771673i	$-0.280580\pi$
$29$	6.85013			1.27204			0.636019	+	0.771673i	$0.280580\pi$
$30$	2.10154	+	8.40503i	0.383687	+	1.53454i
$31$	−3.07108			−0.551582			−0.275791	−	0.961218i	$-0.588940\pi$
$31$	−3.07108			−0.551582			−0.275791	+	0.961218i	$0.588940\pi$
$32$	1.73220	−	6.46466i	0.306213	−	1.14280i
$33$	1.07522	+	7.97365i	0.187172	+	1.38803i
$34$	2.72271	−	1.57196i	0.466941	−	0.269588i
$35$	4.62120	−	10.5565i	0.781126	−	1.78438i
$36$	6.33245	−	6.41246i	1.05541	−	1.06874i
$37$	−5.96327	+	1.19974i	−0.980356	+	0.197236i
$37$	−5.96327	+	1.19974i	−0.980356	+	0.197236i
$38$	−5.20853	+	5.20853i	−0.844935	+	0.844935i
$39$	−0.403744	+	3.14294i	−0.0646508	+	0.503273i
$40$	2.97741	+	4.04464i	0.470770	+	0.639513i
$41$	−3.26251	+	1.88361i	−0.509519	+	0.294171i	−0.732636	−	0.680621i	$-0.761710\pi$
$41$	−3.26251	+	1.88361i	−0.509519	+	0.294171i	0.223117	+	0.974792i	$0.428377\pi$
$42$	−19.7886	+	2.66844i	−3.05345	+	0.411748i
$43$	−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
$50$	11.1760	+	0.445663i	1.58053	+	0.0630263i
$51$	−2.24604	+	0.938611i	−0.314509	+	0.131432i
$52$	1.42244	+	5.30863i	0.197257	+	0.736174i
$53$	0.683368	+	2.55036i	0.0938678	+	0.350319i	0.996845	−	0.0793683i	$-0.0252903\pi$
$53$	0.683368	+	2.55036i	0.0938678	+	0.350319i	−0.902978	+	0.429688i	$0.858624\pi$
$54$	−9.15464	+	7.16256i	−1.24579	+	0.974700i
$55$	10.2692	+	1.56073i	1.38470	+	0.210449i
$56$	−10.0244	+	5.78762i	−1.33957	+	0.773403i
$57$	4.51385	−	3.48616i	0.597874	−	0.461753i
$58$	−14.8015	+	3.96604i	−1.94353	+	0.520766i
$59$	−0.812581	+	1.40743i	−0.105789	+	0.183232i	−0.914060	−	0.405578i	$-0.867070\pi$
$59$	−0.812581	+	1.40743i	−0.105789	+	0.183232i	0.808271	+	0.588810i	$0.200403\pi$
$60$	−5.64736	−	10.1722i	−0.729072	−	1.31322i
$61$	1.47736	+	2.55885i	0.189156	+	0.327628i	0.944969	−	0.327160i	$-0.106092\pi$
$61$	1.47736	+	2.55885i	0.189156	+	0.327628i	−0.755813	+	0.654787i	$0.772758\pi$
$62$	6.63584	−	1.77807i	0.842752	−	0.225815i
$63$	15.4604	−	0.0970482i	1.94782	−	0.0122269i
$64$			13.0040i			1.62550i
$65$	3.74751	+	1.64050i	0.464822	+	0.203479i
$66$	−6.93981	−	16.6066i	−0.854231	−	2.04413i
$67$	−3.01640	−	0.808241i	−0.368512	−	0.0987424i	0.0698107	−	0.997560i	$-0.477760\pi$
$67$	−3.01640	−	0.808241i	−0.368512	−	0.0987424i	−0.438322	+	0.898818i	$0.644427\pi$
$68$	−2.98540	+	2.98540i	−0.362033	+	0.362033i
$69$	−3.98555	+	5.22796i	−0.479804	+	0.629373i
$70$	−3.87335	+	25.4856i	−0.462953	+	3.04611i
$71$	8.81440	−	5.08900i	1.04608	−	0.603953i	0.124529	−	0.992216i	$-0.460258\pi$
$71$	8.81440	−	5.08900i	1.04608	−	0.603953i	0.921549	+	0.388263i	$0.126925\pi$
$72$	−3.33240	+	5.85649i	−0.392728	+	0.690193i
$73$	−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
$77$	−6.19602	+	23.1239i	−0.706102	+	2.63521i
$78$	−0.947281	−	7.02487i	−0.107258	−	0.795410i
$79$	−0.0724067	+	0.0418040i	−0.00814639	+	0.00470332i	−0.504068	−	0.863664i	$-0.668164\pi$
$79$	−0.0724067	+	0.0418040i	−0.00814639	+	0.00470332i	0.495921	+	0.868367i	$0.334830\pi$
$80$	1.71810	+	1.37359i	0.192089	+	0.153572i
$81$	7.73712	−	4.59749i	0.859680	−	0.510833i
$82$	5.95893	−	5.95893i	0.658054	−	0.658054i
$83$	0.929013	+	3.46712i	0.101972	+	0.380566i	0.997984	−	0.0634642i	$-0.0202149\pi$
$83$	0.929013	+	3.46712i	0.101972	+	0.380566i	−0.896012	+	0.444030i	$0.853548\pi$
$84$	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
$87$	11.7584	−	1.58558i	1.26063	−	0.169992i
$88$	−7.37764	−	7.37764i	−0.786459	−	0.786459i
$89$	4.94716	−	8.56874i	0.524398	−	0.908285i	−0.475198	−	0.879879i	$-0.657624\pi$
$89$	4.94716	−	8.56874i	0.524398	−	0.908285i	0.999596	−	0.0284058i	$-0.00904308\pi$
$90$	5.55280	+	13.9409i	0.585317	+	1.46950i
$91$	−4.71418	+	8.16520i	−0.494180	+	0.855946i
$92$	−2.95099	+	11.0133i	−0.307662	+	1.14821i
$93$	−5.27155	+	0.710851i	−0.546634	+	0.0737119i
$94$	18.1525	+	10.4804i	1.87229	+	1.08097i
$95$	−2.68158	−	6.85731i	−0.275125	−	0.703545i
$96$	1.47700	−	11.4976i	0.150745	−	1.17347i
$97$	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	$0.183147\pi$
$98$	−42.2625	−	11.3242i	−4.26916	−	1.14392i
$99$	3.69127	+	13.4380i	0.370986	+	1.35057i
$100$	−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	$-0.184469\pi$
$102$	4.30971	−	3.32850i	0.426725	−	0.329571i
$103$	−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
$107$	3.38514	−	12.6335i	0.327254	−	1.22133i	−0.584772	−	0.811197i	$-0.698816\pi$
$107$	3.38514	−	12.6335i	0.327254	−	1.22133i	0.912027	−	0.410131i	$-0.134517\pi$
$108$	9.38548	−	12.4728i	0.903119	−	1.20020i
$109$	−8.78870	−	5.07416i	−0.841805	−	0.486016i	0.0160725	−	0.999871i	$-0.494884\pi$
$109$	−8.78870	−	5.07416i	−0.841805	−	0.486016i	−0.857877	+	0.513855i	$0.828217\pi$
$110$	−23.0928	+	2.57322i	−2.20181	+	0.245347i
$111$	−9.95835	+	3.43966i	−0.945205	+	0.326479i
$112$	−3.58482	+	3.58482i	−0.338734	+	0.338734i
$113$	4.85336	+	18.1130i	0.456566	+	1.70393i	0.683443	+	0.730003i	$0.260482\pi$
$113$	4.85336	+	18.1130i	0.456566	+	1.70393i	−0.226878	+	0.973923i	$0.572852\pi$
$114$	−7.73492	+	10.1461i	−0.724442	+	0.950272i
$115$	5.03129	+	6.83470i	0.469170	+	0.637339i
$116$	17.8213	−	10.2891i	1.65466	−	0.955321i
$117$	0.0344516	+	5.48835i	0.00318505	+	0.507398i
$118$	0.940923	−	3.51157i	0.0866190	−	0.323267i
$119$	−7.24296			−0.663961
$120$	6.04697	+	6.25351i	0.552011	+	0.570865i
$121$	−10.5784			−0.961673
$122$	−4.67370	−	4.67370i	−0.423137	−	0.423137i
$123$	−5.16416	+	3.98841i	−0.465637	+	0.359623i
$124$	−7.98970	+	4.61285i	−0.717496	+	0.414247i
$125$	−4.88804	+	10.0552i	−0.437200	+	0.899364i
$126$	−33.3498	+	9.16082i	−2.97104	+	0.816110i
$127$	−3.94046	−	14.7060i	−0.349660	−	1.30495i	−0.887073	−	0.461628i	$-0.847265\pi$
$127$	−3.94046	−	14.7060i	−0.349660	−	1.30495i	0.537414	−	0.843319i	$-0.319401\pi$
$128$	−4.06454	−	15.1691i	−0.359258	−	1.34077i
$129$	−12.1197	−	9.23950i	−1.06708	−	0.813493i
$130$	−9.04726	−	1.37502i	−0.793497	−	0.120597i
$131$	−3.48392	−	2.01144i	−0.304392	−	0.175741i	0.340022	−	0.940417i	$-0.389565\pi$
$131$	−3.48392	−	2.01144i	−0.304392	−	0.175741i	−0.644414	+	0.764677i	$0.722899\pi$
$132$	14.7740	+	19.1292i	1.28591	+	1.66498i
$133$	16.3915	−	4.39210i	1.42133	−	0.380843i
$134$	6.98564			0.603467
$135$	−2.88906	−	11.2540i	−0.248651	−	0.968593i
$136$	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	$-0.657594\pi$
$139$	−17.3866	−	10.0381i	−1.47471	−	0.851425i	−0.999594	+	0.0284980i	$0.990928\pi$
$140$	−3.83374	−	34.4050i	−0.324010	−	2.90775i
$141$	−12.9067	−	9.83944i	−1.08694	−	0.828631i
$142$	−16.0994	+	16.0994i	−1.35103	+	1.35103i
$143$	−8.20886	−	2.19956i	−0.686459	−	0.183936i
$144$	−0.745915	+	2.85537i	−0.0621595	+	0.237947i
$145$	2.30153	−	15.1435i	0.191132	−	1.25760i
$146$	5.70357	+	3.29296i	0.472031	+	0.272527i
$147$	31.3392	+	12.8660i	2.58481	+	1.06117i
$148$	−13.7120	+	12.0783i	−1.12712	+	0.992827i
$149$	−2.47602			−0.202843			−0.101422	−	0.994844i	$-0.532339\pi$
$149$	−2.47602			−0.202843			−0.101422	+	0.994844i	$0.532339\pi$
$150$	19.2869	−	1.82188i	1.57477	−	0.148756i
$151$	7.90477	+	13.6915i	0.643281	+	1.11420i	0.984696	+	0.174283i	$0.0557607\pi$
$151$	7.90477	+	13.6915i	0.643281	+	1.11420i	−0.341414	+	0.939913i	$0.610906\pi$
$152$	−1.91420	+	7.14390i	−0.155262	+	0.579447i
$153$	−3.63811	+	2.13102i	−0.294124	+	0.172283i
$154$		−	53.5523i		−	4.31537i
$155$	−1.03183	+	6.78917i	−0.0828786	+	0.545320i
$156$	3.67041	+	8.78309i	0.293868	+	0.703210i
$157$	−3.58611	−	13.3835i	−0.286202	−	1.06812i	−0.947956	−	0.318401i	$-0.896854\pi$
$157$	−3.58611	−	13.3835i	−0.286202	−	1.06812i	0.661754	−	0.749721i	$-0.269812\pi$
$158$	0.132250	−	0.132250i	0.0105212	−	0.0105212i
$159$	1.76334	+	4.21956i	0.139842	+	0.334633i
$160$	−13.7093	−	6.00137i	−1.08382	−	0.474450i
$161$	−16.9395	+	9.78002i	−1.33502	+	0.770774i
$162$	−14.0562	+	14.4136i	−1.10436	+	1.13244i
$163$	9.02093	−	2.41715i	0.706574	−	0.189326i	0.112401	−	0.993663i	$-0.464146\pi$
$163$	9.02093	−	2.41715i	0.706574	−	0.189326i	0.594173	+	0.804337i	$0.297479\pi$
$164$	−5.65850	+	9.80080i	−0.441854	+	0.765314i
$165$	17.9885	+	0.302041i	1.40040	+	0.0235139i
$166$	−4.01473	−	6.95372i	−0.311604	−	0.539714i
$167$	−0.594840	+	2.21997i	−0.0460301	+	0.171787i	−0.985114	−	0.171900i	$-0.945009\pi$
$167$	−0.594840	+	2.21997i	−0.0460301	+	0.171787i	0.939084	+	0.343687i	$0.111676\pi$
$168$	−15.8675	+	12.2549i	−1.22420	+	0.945482i
$169$	8.35973	+	4.82649i	0.643056	+	0.371268i
$170$	−2.56031	−	6.54719i	−0.196367	−	0.502147i
$171$	6.94116	−	7.02885i	0.530804	−	0.537510i
$172$	−25.5315	−	6.84114i	−1.94676	−	0.521632i
$173$	−2.61764	−	9.76916i	−0.199015	−	0.742736i	−0.991191	−	0.132442i	$-0.957718\pi$
$173$	−2.61764	−	9.76916i	−0.199015	−	0.742736i	0.792175	−	0.610294i	$-0.208949\pi$
$174$	−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
$178$	−5.72854	+	21.3792i	−0.429372	+	1.60244i
$179$	−4.39631			−0.328596			−0.164298	−	0.986411i	$-0.552536\pi$
$179$	−4.39631			−0.328596			−0.164298	+	0.986411i	$0.552536\pi$
$180$	−12.0483	−	16.1535i	−0.898028	−	1.20401i
$181$	6.28722	+	10.8898i	0.467325	+	0.809431i	0.999303	−	0.0373271i	$-0.0118843\pi$
$181$	6.28722	+	10.8898i	0.467325	+	0.809431i	−0.531978	+	0.846758i	$0.678551\pi$
$182$	5.45876	−	20.3724i	0.404630	−	1.51010i
$183$	3.12819	+	4.05035i	0.231243	+	0.299411i
$184$		−	8.52482i		−	0.628458i
$185$	0.648676	+	13.5860i	0.0476916	+	0.998862i
$186$	10.9790	−	4.58805i	0.805016	−	0.336412i
$187$	−1.68972	−	6.30612i	−0.123565	−	0.461149i
$188$	−27.1893	−	7.28535i	−1.98298	−	0.531339i
$189$	26.5155	−	3.74514i	1.92872	−	0.272419i
$190$	9.76443	+	13.2644i	0.708386	+	0.962300i
$191$			10.7222i			0.775831i	0.921695	+	0.387916i	$0.126805\pi$
$191$			10.7222i			0.775831i	−0.921695	+	0.387916i	$0.873195\pi$
$192$	3.00999	+	22.3215i	0.217227	+	1.61092i
$193$	−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
$197$	−24.6848	+	6.61428i	−1.75872	+	0.471248i	−0.986453	−	0.164047i	$-0.947545\pi$
$197$	−24.6848	+	6.61428i	−1.75872	+	0.471248i	−0.772270	+	0.635295i	$0.780879\pi$
$198$	−15.7562	−	26.8991i	−1.11974	−	1.91164i
$199$		−	7.60467i		−	0.539081i	−0.962989	−	0.269540i	$-0.913128\pi$
$199$		−	7.60467i		−	0.539081i	0.962989	−	0.269540i	$-0.0868718\pi$
$200$	9.94177	−	5.22318i	0.702989	−	0.369335i
$201$	−5.36477	−	0.689163i	−0.378402	−	0.0486098i
$202$	6.37284	+	23.7838i	0.448391	+	1.67342i
$203$	34.0996	+	9.13697i	2.39333	+	0.641290i
$204$	−4.43347	+	5.81551i	−0.310405	+	0.407167i
$205$	3.06792	+	7.84525i	0.214273	+	0.547936i
$206$	29.6342	+	17.1093i	2.06471	+	1.19206i
$207$	−5.63116	+	9.89640i	−0.391393	+	0.687847i
$208$	−1.27259	−	1.27259i	−0.0882385	−	0.0882385i
$209$	7.64801	+	13.2467i	0.529024	+	0.916297i
$210$	−0.749593	+	44.6429i	−0.0517268	+	3.08066i
$211$	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
$213$	13.9521	−	10.7756i	0.955984	−	0.738331i
$214$			29.2578i			2.00002i
$215$	−15.8445	+	11.6638i	−1.08059	+	0.795463i
$216$	−4.36454	+	10.8241i	−0.296969	+	0.736486i
$217$	−15.2877	−	4.09632i	−1.03779	−	0.278076i
$218$	21.9280	+	5.87559i	1.48515	+	0.397945i
$219$	−4.05531	−	3.09158i	−0.274033	−	0.208910i
$220$	29.0605	−	11.3643i	1.95926	−	0.766178i
$221$		−	2.57121i		−	0.172959i
$222$	19.5261	−	13.1979i	1.31050	−	0.885783i
$223$	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
$225$	−14.9915	−	0.503583i	−0.999436	−	0.0335722i
$226$	−20.9738	−	36.3277i	−1.39516	−	2.41649i
$227$	−0.530716	+	1.98066i	−0.0352248	+	0.131461i	−0.981299	−	0.192489i	$-0.938344\pi$
$227$	−0.530716	+	1.98066i	−0.0352248	+	0.131461i	0.946074	+	0.323950i	$0.105011\pi$
$228$	6.50688	−	15.8495i	0.430929	−	1.04966i
$229$	8.88036	−	5.12708i	0.586830	−	0.338807i	−0.177013	−	0.984209i	$-0.556643\pi$
$229$	8.88036	−	5.12708i	0.586830	−	0.338807i	0.763843	+	0.645402i	$0.223310\pi$
$230$	−14.8285	−	11.8551i	−0.977761	−	0.781704i
$231$	−5.28316	+	41.1266i	−0.347607	+	2.70593i
$232$	−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	$0.160770\pi$
$234$	−3.25204	−	11.8390i	−0.212593	−	0.773941i
$235$	−16.8734	+	12.4211i	−1.10070	+	0.810266i
$236$			4.88209i			0.317797i
$237$	−0.114611	+	0.0885170i	−0.00744478	+	0.00574980i
$238$	15.6502	−	4.19347i	1.01445	−	0.271822i
$239$	−0.917410	+	1.58900i	−0.0593423	+	0.102784i	−0.894170	−	0.447727i	$-0.852234\pi$
$239$	−0.917410	+	1.58900i	−0.0593423	+	0.102784i	0.834828	+	0.550511i	$0.185567\pi$
$240$	3.26708	+	1.96011i	0.210889	+	0.126524i
$241$	1.00505	+	1.74080i	0.0647411	+	0.112135i	0.896579	−	0.442884i	$-0.146045\pi$
$241$	1.00505	+	1.74080i	0.0647411	+	0.112135i	−0.831838	+	0.555018i	$0.812711\pi$
$242$	22.8573	−	6.12460i	1.46932	−	0.393704i
$243$	12.2167	−	9.68255i	0.783703	−	0.621136i
$244$	7.68696	+	4.43807i	0.492107	+	0.284118i
$245$	27.3106	−	34.1603i	1.74481	−	2.18242i
$246$	8.84930	−	11.6079i	0.564211	−	0.740092i
$247$	1.55917	+	5.81891i	0.0992078	+	0.370249i
$248$	4.87751	−	4.87751i	0.309722	−	0.309722i
$249$	2.39719	+	5.73633i	0.151916	+	0.363525i
$250$	4.74017	−	24.5568i	0.299795	−	1.55311i
$251$		−	5.85930i		−	0.369836i	−0.982754	−	0.184918i	$-0.940798\pi$
$251$		−	5.85930i		−	0.369836i	0.982754	−	0.184918i	$-0.0592019\pi$
$252$	40.0758	−	23.4744i	2.52454	−	1.47875i
$253$	−12.4669	−	12.4669i	−0.783785	−	0.783785i
$254$	17.0287	+	29.4946i	1.06848	+	1.85066i
$255$	1.32034	+	5.28064i	0.0826827	+	0.330687i
$256$	4.56095	+	7.89981i	0.285060	+	0.493738i
$257$	−0.874065	+	0.234205i	−0.0545227	+	0.0146093i	−0.285977	−	0.958236i	$-0.592318\pi$
$257$	−0.874065	+	0.234205i	−0.0545227	+	0.0146093i	0.231455	+	0.972846i	$0.425652\pi$
$258$	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
$261$	19.8164	−	5.44333i	1.22660	−	0.336934i
$262$	8.69247	+	2.32914i	0.537023	+	0.143895i
$263$	−19.2280	−	5.15214i	−1.18565	−	0.317695i	−0.388486	−	0.921455i	$-0.627002\pi$
$263$	−19.2280	−	5.15214i	−1.18565	−	0.317695i	−0.797166	+	0.603760i	$0.793669\pi$
$264$	−14.3715	−	10.9561i	−0.884505	−	0.674304i
$265$	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
$268$	−9.06145	+	2.42801i	−0.553516	+	0.148314i
$269$	−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	0.178123	+	0.984008i	$0.442997\pi$
$271$	−12.5624	+	21.7588i	−0.763114	+	1.32175i	−0.941238	+	0.337745i	$0.890336\pi$
$272$	0.357833	−	1.33545i	0.0216968	−	0.0809737i
$273$	−6.20199	+	15.1069i	−0.375362	+	0.914309i
$274$	0.800912	+	0.462407i	0.0483849	+	0.0279350i
$275$	6.90055	−	22.1775i	0.416119	−	1.33735i
$276$	−2.51622	+	19.5875i	−0.151459	+	1.17903i
$277$	13.8777	+	3.71851i	0.833829	+	0.223424i	0.650383	−	0.759606i	$-0.274608\pi$
$277$	13.8777	+	3.71851i	0.833829	+	0.223424i	0.183446	+	0.983030i	$0.441275\pi$
$278$	43.3799	+	11.6236i	2.60176	+	0.697138i
$279$	−8.88415	+	2.44037i	−0.531880	+	0.146101i
$280$	9.42653	+	24.1054i	0.563343	+	1.44057i
$281$	6.68407	+	3.85905i	0.398738	+	0.230212i	0.685940	−	0.727659i	$-0.259391\pi$
$281$	6.68407	+	3.85905i	0.398738	+	0.230212i	−0.287201	+	0.957870i	$0.592725\pi$
$282$	33.5849	+	13.7880i	1.99995	+	0.821063i
$283$	−4.40417	+	16.4366i	−0.261801	+	0.977053i	0.702379	+	0.711803i	$0.252121\pi$
$283$	−4.40417	+	16.4366i	−0.261801	+	0.977053i	−0.964180	+	0.265250i	$0.914546\pi$
$284$	15.2877	−	26.4790i	0.907157	−	1.57124i
$285$	−6.19021	−	11.1500i	−0.366677	−	0.660467i
$286$	19.0108			1.12413
$287$	−18.7531	+	5.02487i	−1.10696	+	0.296609i
$288$	−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
$291$	4.31237	−	5.65667i	0.252796	−	0.331600i
$292$	−8.54295	−	2.28908i	−0.499938	−	0.133958i
$293$	14.9369	+	4.00232i	0.872621	+	0.233818i	0.667221	−	0.744860i	$-0.267484\pi$
$293$	14.9369	+	4.00232i	0.872621	+	0.233818i	0.205400	+	0.978678i	$0.434150\pi$
$294$	−75.1654	−	9.65580i	−4.38373	−	0.563138i
$295$	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
$298$	5.35007	−	1.43355i	0.309921	−	0.0830431i
$299$	−3.47186	−	6.01343i	−0.200783	−	0.347766i
$300$	−24.3849	+	9.06684i	−1.40786	+	0.523475i
$301$	−22.6725	−	39.2700i	−1.30682	−	2.26348i
$302$	−25.0072	−	25.0072i	−1.43900	−	1.43900i
$303$	−2.54779	−	18.8940i	−0.146367	−	1.08543i
$304$			3.23925i			0.185784i
$305$	6.15318	−	2.40623i	0.352330	−	0.137780i
$306$	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	$0.348055\pi$
$308$	18.6132	+	69.4656i	1.06059	+	3.95817i
$309$	−21.0703	−	16.0630i	−1.19865	−	0.913791i
$310$	−1.70121	−	15.2671i	−0.0966223	−	0.867115i
$311$	−17.4851	−	10.0950i	−0.991488	−	0.572436i	−0.0857694	−	0.996315i	$-0.527335\pi$
$311$	−17.4851	−	10.0950i	−0.991488	−	0.572436i	−0.905719	+	0.423879i	$0.860668\pi$
$312$	−4.35041	−	5.63287i	−0.246294	−	0.318899i
$313$	−17.9185	+	4.80126i	−1.01282	+	0.271383i	−0.726806	−	0.686843i	$-0.758996\pi$
$313$	−17.9185	+	4.80126i	−1.01282	+	0.271383i	−0.286011	+	0.958226i	$0.592329\pi$
$314$	15.4974	+	26.8423i	0.874568	+	1.51480i
$315$	4.97988	−	34.2106i	0.280585	−	1.92755i
$316$	−0.125582	+	0.217514i	−0.00706454	+	0.0122361i
$317$	−12.4917	+	3.34715i	−0.701606	+	0.187995i	−0.591950	−	0.805975i	$-0.701642\pi$
$317$	−12.4917	+	3.34715i	−0.701606	+	0.187995i	−0.109656	+	0.993970i	$0.534975\pi$
$318$	−6.25314	−	8.09651i	−0.350659	−	0.454030i
$319$			31.8206i			1.78161i
$320$	28.7477	+	4.36912i	1.60704	+	0.244241i
$321$	2.88641	−	22.4692i	0.161104	−	1.25411i
$322$	30.9397	−	30.9397i	1.72420	−	1.72420i
$323$	−3.27237	+	3.27237i	−0.182080	+	0.182080i
$324$	13.2233	−	23.5822i	0.734627	−	1.31012i
$325$	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
$328$	2.18998	−	8.17313i	0.120922	−	0.451285i
$329$	−24.1447	−	41.8199i	−1.33114	−	2.30560i
$330$	−39.0435	+	9.76218i	−2.14927	+	0.537390i
$331$	−9.79893	+	16.9722i	−0.538598	+	0.932879i	0.460382	+	0.887721i	$0.347712\pi$
$331$	−9.79893	+	16.9722i	−0.538598	+	0.932879i	−0.998980	+	0.0451577i	$0.985621\pi$
$332$	7.62464	+	7.62464i	0.418457	+	0.418457i
$333$	−16.2975	+	8.20926i	−0.893097	+	0.449865i
$334$		−	5.14121i		−	0.281314i
$335$	−2.80022	+	6.39674i	−0.152993	+	0.349491i
$336$	−5.32363	+	6.98316i	−0.290428	+	0.380963i
$337$	3.79217	+	1.01611i	0.206573	+	0.0553510i	0.360622	−	0.932712i	$-0.382565\pi$
$337$	3.79217	+	1.01611i	0.206573	+	0.0553510i	−0.154049	+	0.988063i	$0.549231\pi$
$338$	−20.8577	−	5.58881i	−1.13451	−	0.303991i
$339$	12.5234	+	29.9678i	0.680179	+	1.62763i
$340$	5.59673	+	7.60283i	0.303525	+	0.412321i
$341$		−	14.2659i		−	0.772544i
$342$	−10.9286	+	19.2063i	−0.590952	+	1.03856i
$343$	45.7670	+	45.7670i	2.47118	+	2.47118i
$344$	19.7627			1.06553
$345$	10.2183	+	10.5673i	0.550134	+	0.568924i
$346$	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	$0.473797\pi$
$348$	28.2089	−	21.7865i	1.51216	−	1.16788i
$349$	1.73516	+	1.00180i	0.0928811	+	0.0536249i	0.545721	−	0.837967i	$-0.316256\pi$
$349$	1.73516	+	1.00180i	0.0928811	+	0.0536249i	−0.452840	+	0.891592i	$0.649589\pi$
$350$	55.0392	+	17.1255i	2.94197	+	0.915395i
$351$	1.32951	+	9.41286i	0.0709638	+	0.502421i
$352$	30.0300	+	8.04652i	1.60061	+	0.428881i
$353$	4.88576	+	18.2339i	0.260043	+	0.970494i	0.965215	+	0.261457i	$0.0842031\pi$
$353$	4.88576	+	18.2339i	0.260043	+	0.970494i	−0.705172	+	0.709036i	$0.749130\pi$
$354$	0.802297	−	6.24546i	0.0426416	−	0.331943i
$355$	−8.28866	−	21.1957i	−0.439917	−	1.12495i
$356$		−	29.7232i		−	1.57533i
$357$	−12.4326	+	1.67650i	−0.658005	+	0.0887299i
$358$	9.49935	−	2.54534i	0.502056	−	0.134526i
$359$	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
$363$	−18.1580	+	2.44855i	−0.953047	+	0.128515i
$364$			28.3234i			1.48455i
$365$	−5.30166	+	3.90275i	−0.277501	+	0.204279i
$366$	−9.10429	−	6.94068i	−0.475889	−	0.362795i
$367$	27.5651	+	7.38604i	1.43889	+	0.385548i	0.892143	−	0.451753i	$-0.149201\pi$
$367$	27.5651	+	7.38604i	1.43889	+	0.385548i	0.546742	+	0.837301i	$0.315868\pi$
$368$	−0.966350	−	3.60647i	−0.0503745	−	0.188000i
$369$	−7.94117	+	8.04150i	−0.413401	+	0.418624i
$370$	−9.26754	−	28.9804i	−0.481797	−	1.50662i
$371$			13.6071i			0.706445i
$372$	−12.6467	+	9.76738i	−0.655702	+	0.506415i
$373$	5.91911	−	22.0904i	0.306480	−	1.14380i	−0.625184	−	0.780477i	$-0.714976\pi$
$373$	5.91911	−	22.0904i	0.306480	−	1.14380i	0.931664	−	0.363321i	$-0.118357\pi$
$374$	7.30214	+	12.6477i	0.377585	+	0.653996i
$375$	−6.06295	+	18.3913i	−0.313089	+	0.949724i
$376$	21.0459			1.08536
$377$	−3.24358	+	12.1052i	−0.167053	+	0.623450i
$378$	−55.1251	+	23.4441i	−2.83533	+	1.20583i
$379$	5.72889	+	3.30758i	0.294273	+	0.169899i	0.639867	−	0.768485i	$-0.278989\pi$
$379$	5.72889	+	3.30758i	0.294273	+	0.169899i	−0.345594	+	0.938384i	$0.612323\pi$
$380$	−17.2763	−	13.8121i	−0.886255	−	0.708547i
$381$	−10.1678	−	24.3310i	−0.520913	−	1.24651i
$382$	−6.20786	−	23.1680i	−0.317622	−	1.18538i
$383$	−18.5826	−	4.97918i	−0.949524	−	0.254424i	−0.249364	−	0.968410i	$-0.580221\pi$
$383$	−18.5826	−	4.97918i	−0.949524	−	0.254424i	−0.700160	+	0.713986i	$0.746888\pi$
$384$	−10.4880	−	25.0971i	−0.535212	−	1.28073i
$385$	49.0378	+	21.4667i	2.49920	+	1.09404i
$386$	15.6907	+	9.05902i	0.798634	+	0.461092i
$387$	−22.9423	−	13.0544i	−1.16622	−	0.663594i
$388$	3.19298	−	11.9164i	0.162099	−	0.604961i
$389$	−7.79118	−	13.4947i	−0.395029	−	0.684210i	0.598076	−	0.801439i	$-0.295932\pi$
$389$	−7.79118	−	13.4947i	−0.395029	−	0.684210i	−0.993105	+	0.117230i	$0.962599\pi$
$390$	−15.8480	−	0.266102i	−0.802496	−	0.0134746i
$391$	2.66711	−	4.61958i	0.134882	−	0.233622i
$392$	−42.4342	+	11.3702i	−2.14325	+	0.574283i
$393$	−6.44579	−	2.64626i	−0.325147	−	0.133486i
$394$	49.5084	−	28.5837i	2.49420	−	1.44002i
$395$	0.0680880	+	0.174114i	0.00342588	+	0.00876061i
$396$	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	$0.185616\pi$
$398$	4.40289	+	16.4318i	0.220697	+	0.823653i
$399$	27.1197	−	11.3332i	1.35768	−	0.567369i
$400$	3.61383	−	3.33666i	0.180691	−	0.166833i
$401$			20.7039i			1.03390i	0.856015	+	0.516951i	$0.172933\pi$
$401$			20.7039i			1.03390i	−0.856015	+	0.516951i	$0.827067\pi$
$402$	11.9910	−	1.61694i	0.598054	−	0.0806457i
$403$	1.45417	−	5.42705i	0.0724375	−	0.270340i
$404$	−16.5331	−	28.6362i	−0.822553	−	1.42470i
$405$	−7.56405	−	18.6490i	−0.375861	−	0.926676i
$406$	−78.9710			−3.91926
$407$	−5.57309	−	27.7009i	−0.276248	−	1.37308i
$408$	2.07647	−	5.05789i	0.102801	−	0.250403i
$409$	15.8024	+	9.12355i	0.781381	+	0.451130i	0.836919	−	0.547326i	$-0.184354\pi$
$409$	15.8024	+	9.12355i	0.781381	+	0.451130i	−0.0555386	+	0.998457i	$0.517688\pi$
$410$	−11.1712	−	15.1754i	−0.551706	−	0.749460i
$411$	−0.569459	−	0.434129i	−0.0280894	−	0.0214140i
$412$	−44.3868	−	11.8934i	−2.18678	−	0.585946i
$413$	−5.92228	+	5.92228i	−0.291416	+	0.291416i
$414$	6.43780	−	24.6440i	0.316401	−	1.21118i
$415$	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	−0.988891	−	0.148640i	$-0.952511\pi$
$419$	−7.48610	+	12.9663i	−0.365720	+	0.633446i	0.623171	+	0.782085i	$0.285844\pi$
$420$	−14.5443	−	58.1693i	−0.709688	−	2.83837i
$421$	8.41951			0.410342			0.205171	−	0.978726i	$-0.434225\pi$
$421$	8.41951			0.410342			0.205171	+	0.978726i	$0.434225\pi$
$422$	−13.1626	+	3.52691i	−0.640746	+	0.171687i
$423$	−24.4320	−	13.9021i	−1.18793	−	0.675943i
$424$	−5.13584	−	2.96518i	−0.249419	−	0.144002i
$425$	7.02157	+	0.279998i	0.340596	+	0.0135819i
$426$	−23.9083	+	31.3613i	−1.15836	+	1.51946i
$427$	3.94111	+	14.7084i	0.190723	+	0.711790i
$428$	−10.1692	−	37.9519i	−0.491546	−	1.83447i
$429$	−14.5997	−	1.87550i	−0.704882	−	0.0905498i
$430$	27.4832	−	34.3761i	1.32536	−	1.65776i
$431$	−10.0688	+	5.81323i	−0.484997	+	0.280013i	−0.722497	−	0.691374i	$-0.757006\pi$
$431$	−10.0688	+	5.81323i	−0.484997	+	0.280013i	0.237500	+	0.971388i	$0.423672\pi$
$432$	−0.619452	+	5.07393i	−0.0298034	+	0.244120i
$433$	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
$435$	0.445406	−	26.5267i	0.0213556	−	1.27186i
$436$	−30.4862			−1.46002
$437$	−3.23465	+	12.0719i	−0.154734	+	0.577477i
$438$	10.5525	+	4.33222i	0.504217	+	0.207002i
$439$	28.1667	−	16.2621i	1.34432	−	0.776146i	0.356886	−	0.934148i	$-0.383838\pi$
$439$	28.1667	−	16.2621i	1.34432	−	0.776146i	0.987439	+	0.158002i	$0.0505051\pi$
$440$	−18.7884	+	13.8308i	−0.895701	+	0.659360i
$441$	56.7723	+	14.8308i	2.70344	+	0.706227i
$442$	1.48866	+	5.55576i	0.0708084	+	0.264261i
$443$	−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	$0.398886\pi$
$444$	−20.7411	+	23.9064i	−0.984329	+	1.13455i
$445$	−17.2806	−	13.8156i	−0.819179	−	0.654920i
$446$	−35.0710	−	20.2482i	−1.66066	−	0.958781i
$447$	−4.25013	+	0.573116i	−0.201024	+	0.0271074i
$448$	−17.3452	+	64.7332i	−0.819484	+	3.05836i
$449$	6.90028	+	11.9516i	0.325644	+	0.564033i	0.981643	−	0.190730i	$-0.0610855\pi$
$449$	6.90028	+	11.9516i	0.325644	+	0.564033i	−0.655998	+	0.754762i	$0.727752\pi$
$450$	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
$453$	16.7378	+	21.6719i	0.786409	+	1.01824i
$454$		−	4.58698i		−	0.215278i
$455$	16.4668	+	13.1649i	0.771974	+	0.617181i
$456$	−1.63218	+	12.7057i	−0.0764340	+	0.594998i
$457$	−15.2131	−	4.07635i	−0.711640	−	0.190683i	−0.115202	−	0.993342i	$-0.536751\pi$
$457$	−15.2131	−	4.07635i	−0.711640	−	0.190683i	−0.596439	+	0.802659i	$0.703418\pi$
$458$	−16.2198	+	16.2198i	−0.757903	+	0.757903i
$459$	−5.75160	+	4.50003i	−0.268462	+	0.210044i
$460$	23.3553	+	10.2240i	1.08895	+	0.476695i
$461$	12.9850	+	7.49688i	0.604770	+	0.349164i	0.770916	−	0.636937i	$-0.219799\pi$
$461$	12.9850	+	7.49688i	0.604770	+	0.349164i	−0.166146	+	0.986101i	$0.553132\pi$
$462$	−12.3956	−	91.9233i	−0.576694	−	4.27666i
$463$	2.85340	−	10.6491i	0.132609	−	0.494903i	−0.867387	−	0.497634i	$-0.834202\pi$
$463$	2.85340	−	10.6491i	0.132609	−	0.494903i	0.999996	+	0.00273025i	$0.000869068\pi$
$464$	−3.36934	+	5.83586i	−0.156418	+	0.270923i
$465$	−0.199686	+	11.8926i	−0.00926021	+	0.551504i
$466$	−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	$-0.511181\pi$
$468$	8.33331	+	14.2267i	0.385207	+	0.657630i
$469$	−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
$472$	−0.944747	−	3.52584i	−0.0434855	−	0.162290i
$473$	28.9013	−	28.9013i	1.32888	−	1.32888i
$474$	0.196397	−	0.257620i	0.00902082	−	0.0118329i
$475$	−16.0603	+	3.62419i	−0.736897	+	0.166289i
$476$	−18.8432	+	10.8792i	−0.863679	+	0.498645i
$477$	4.00348	+	6.83479i	0.183307	+	0.312943i
$478$	1.06231	−	3.96459i	0.0485889	−	0.181336i
$479$	2.64211	−	4.57626i	0.120721	−	0.209095i	−0.799331	−	0.600891i	$-0.794813\pi$
$479$	2.64211	−	4.57626i	0.120721	−	0.209095i	0.920052	+	0.391796i	$0.128146\pi$
$480$	−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
$483$	−26.8131	+	20.7085i	−1.22004	+	0.942268i
$484$	−27.5207	+	15.8891i	−1.25094	+	0.722232i
$485$	−5.44386	−	7.39516i	−0.247193	−	0.335797i
$486$	−20.7914	+	27.9947i	−0.943116	+	1.26987i
$487$	−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	$0.970085\pi$
$488$	−6.41034	−	1.71765i	−0.290183	−	0.0777542i
$489$	14.9251	−	6.23712i	0.674935	−	0.282052i
$490$	−39.2337	+	89.6242i	−1.77240	+	4.04881i
$491$		−	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
$493$	−9.29933	+	2.49175i	−0.418821	+	0.112223i
$494$	−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
$497$	50.6656	−	13.5758i	2.27266	−	0.608958i
$498$	−8.50091	−	11.0069i	−0.380935	−	0.493231i
$499$	−13.3179	+	7.68909i	−0.596191	+	0.344211i	−0.767541	−	0.640999i	$-0.778520\pi$
$499$	−13.3179	+	7.68909i	−0.596191	+	0.344211i	0.171351	+	0.985210i	$0.445187\pi$
$500$	2.38653	+	33.5016i	0.106729	+	1.49824i
$501$	−0.507202	+	3.94830i	−0.0226601	+	0.176397i
$502$	3.39237	+	12.6605i	0.151409	+	0.565066i
$503$	−5.17807	−	19.3248i	−0.230879	−	0.861652i	−0.979963	−	0.199177i	$-0.936173\pi$
$503$	−5.17807	−	19.3248i	−0.230879	−	0.861652i	0.749084	−	0.662474i	$-0.230494\pi$
$504$	−24.4002	+	24.7084i	−1.08687	+	1.10060i
$505$	−24.3333	−	3.69822i	−1.08282	−	0.164569i
$506$	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	0.314470	−	0.949268i	$-0.398173\pi$
$509$	22.0946	−	38.2689i	0.979325	−	1.69624i	0.664855	−	0.746972i	$-0.268493\pi$
$510$	−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
$513$	10.2877	−	13.6718i	0.454211	−	0.603623i
$514$	1.75304	−	1.01212i	0.0773233	−	0.0446426i
$515$	−27.5459	+	20.2776i	−1.21382	+	0.893539i
$516$	−45.4087	−	5.83323i	−1.99900	−	0.256794i
$517$	30.7779	−	30.7779i	1.35361	−	1.35361i
$518$	68.7469	−	13.8310i	3.02057	−	0.607701i
$519$	−6.75445	−	16.1630i	−0.296488	−	0.709478i
$520$	−8.55730	+	3.34637i	−0.375262	+	0.146748i
$521$	18.3700	−	10.6059i	0.804804	−	0.464654i	−0.0403444	−	0.999186i	$-0.512846\pi$
$521$	18.3700	−	10.6059i	0.804804	−	0.464654i	0.845148	+	0.534532i	$0.179512\pi$
$522$	−39.6668	+	23.2348i	−1.73617	+	1.01696i
$523$	2.55386	−	9.53115i	0.111673	−	0.416768i	−0.887344	−	0.461108i	$-0.847452\pi$
$523$	2.55386	−	9.53115i	0.111673	−	0.416768i	0.999016	+	0.0443404i	$0.0141186\pi$
$524$	−12.0850			−0.527936
$525$	−40.5790	−	18.5817i	−1.77101	−	0.810973i
$526$	44.5300			1.94160
$527$	4.16911	−	1.11711i	0.181609	−	0.0486621i
$528$	−7.32189	−	3.00594i	−0.318644	−	0.130817i
$529$			8.59460i			0.373678i
$530$	−12.3000	+	4.80997i	−0.534277	+	0.208932i
$531$	−1.23228	+	4.71719i	−0.0534765	+	0.204708i
$532$	36.0471	−	36.0471i	1.56284	−	1.56284i
$533$	−1.78380	−	6.65725i	−0.0772652	−	0.288357i
$534$	−4.88455	+	38.0237i	−0.211375	+	1.64545i
$535$	−26.7913	−	11.7281i	−1.15829	−	0.507051i
$536$	6.07432	−	3.50701i	0.262371	−	0.151480i
$537$	−7.54634	+	1.01760i	−0.325649	+	0.0439127i
$538$	22.7120	−	6.08566i	0.979184	−	0.262371i
$539$	−45.4286	+	78.6847i	−1.95675	+	3.38919i
$540$	−24.4201	−	24.9390i	−1.05087	−	1.07320i
$541$	40.1861			1.72773			0.863867	−	0.503720i	$-0.168036\pi$
$541$	40.1861			1.72773			0.863867	+	0.503720i	$0.168036\pi$
$542$	14.5466	−	54.2887i	0.624831	−	2.33190i
$543$	13.3127	+	17.2372i	0.571304	+	0.739719i
$544$			9.40613i			0.403285i
$545$	−14.1702	+	17.7242i	−0.606985	+	0.759221i
$546$	4.65452	−	36.2330i	0.199195	−	1.55063i
$547$	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	$0.201910\pi$
$548$	−1.19963	−	0.321439i	−0.0512455	−	0.0137312i
$549$	6.30711	+	6.22842i	0.269181	+	0.265822i
$550$	−2.07022	+	51.9154i	−0.0882744	+	2.21368i
$551$	19.5343	−	11.2782i	0.832191	−	0.480465i
$552$	−1.97321	−	14.6330i	−0.0839854	−	0.622821i
$553$	−0.416197	+	0.111520i	−0.0176985	+	0.00474230i
$554$	−32.1392			−1.36546
$555$	4.25817	+	23.1704i	0.180749	+	0.983529i
$556$	−60.3105			−2.55773
$557$	34.9305	−	9.35959i	1.48005	−	0.396578i	0.573687	−	0.819075i	$-0.305513\pi$
$557$	34.9305	−	9.35959i	1.48005	−	0.396578i	0.906365	+	0.422496i	$0.138846\pi$
$558$	17.7836	−	10.4167i	0.752838	−	0.440975i
$559$	13.9406	−	8.04863i	0.589626	−	0.340421i
$560$	6.72046	+	9.12934i	0.283991	+	0.385785i
$561$	−4.36009	−	10.4334i	−0.184083	−	0.440500i
$562$	−16.6769	−	4.46857i	−0.703473	−	0.188495i
$563$	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	$0.160791\pi$
$564$	−48.3571	−	6.21200i	−2.03620	−	0.261572i
$565$	41.6727	−	4.64358i	1.75318	−	0.195357i
$566$		−	38.0653i		−	1.60000i
$567$	44.6473	−	12.5660i	1.87501	−	0.527724i
$568$	−5.91672	+	22.0815i	−0.248260	+	0.926519i
$569$	−31.1450			−1.30567			−0.652833	−	0.757502i	$-0.726420\pi$
$569$	−31.1450			−1.30567			−0.652833	+	0.757502i	$0.726420\pi$
$570$	19.8310	+	20.5084i	0.830631	+	0.859002i
$571$	−0.745666	+	1.29153i	−0.0312052	+	0.0540489i	−0.881206	−	0.472732i	$-0.843268\pi$
$571$	−0.745666	+	1.29153i	−0.0312052	+	0.0540489i	0.850001	+	0.526781i	$0.176601\pi$
$572$	−24.6599	+	6.60761i	−1.03108	+	0.276278i
$573$	2.48183	+	18.4048i	0.103680	+	0.768872i
$574$	37.6115	−	21.7150i	1.56987	−	0.906367i
$575$	16.7998	−	8.82623i	0.700599	−	0.368079i
$576$	10.3334	+	37.6185i	0.430557	+	1.56744i
$577$	7.37287	+	27.5159i	0.306937	+	1.14550i	0.931265	+	0.364342i	$0.118706\pi$
$577$	7.37287	+	27.5159i	0.306937	+	1.14550i	−0.624329	+	0.781162i	$0.714627\pi$
$578$	23.7659	−	23.7659i	0.988531	−	0.988531i
$579$	−11.1563	−	8.50502i	−0.463639	−	0.353456i
$580$	−16.7583	−	42.8542i	−0.695851	−	1.77942i
$581$			18.4983i			0.767440i
$582$	−6.04292	+	14.7194i	−0.250487	+	0.610139i
$583$	−11.8471	+	3.17442i	−0.490656	+	0.131471i
$584$	6.61268			0.273635
$585$	12.1446	+	1.76783i	0.502116	+	0.0730909i
$586$	−34.5921			−1.42899
$587$	−3.03004	+	11.3083i	−0.125063	+	0.466743i	−0.999842	−	0.0177802i	$-0.994340\pi$
$587$	−3.03004	+	11.3083i	−0.125063	+	0.466743i	0.874779	+	0.484523i	$0.161007\pi$
$588$	100.857	−	13.6003i	4.15928	−	0.560865i
$589$	−8.75770	+	5.05626i	−0.360855	+	0.208340i
$590$	−7.44684	−	3.25991i	−0.306581	−	0.134208i
$591$	−40.8409	+	17.0672i	−1.67997	+	0.702052i
$592$	1.91103	−	5.67042i	0.0785427	−	0.233053i
$593$	−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	$0.339757\pi$
$594$	−33.2719	−	42.5257i	−1.36516	−	1.74485i
$595$	−2.43351	+	16.0119i	−0.0997643	+	0.656423i
$596$	−6.44160	+	3.71906i	−0.263858	+	0.152339i
$597$	−1.76023	−	13.0535i	−0.0720413	−	0.534246i
$598$	10.9834	+	10.9834i	0.449146	+	0.449146i
$599$	1.62038	+	2.80658i	0.0662069	+	0.114674i	0.897229	−	0.441566i	$-0.145577\pi$
$599$	1.62038	+	2.80658i	0.0662069	+	0.114674i	−0.831022	+	0.556240i	$0.812244\pi$
$600$	15.8562	−	11.2669i	0.647327	−	0.459968i
$601$	12.0905	−	20.9414i	0.493182	−	0.854217i	−0.506787	−	0.862071i	$-0.669167\pi$
$601$	12.0905	−	20.9414i	0.493182	−	0.854217i	0.999969	+	0.00785470i	$0.00250025\pi$
$602$	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
$605$	−3.55417	+	23.3855i	−0.144497	+	0.950755i
$606$	16.4442	+	39.3501i	0.668001	+	1.59849i
$607$	−1.40400	−	5.23979i	−0.0569865	−	0.212676i	0.931561	−	0.363584i	$-0.118447\pi$
$607$	−1.40400	−	5.23979i	−0.0569865	−	0.212676i	−0.988548	+	0.150908i	$0.951780\pi$
$608$	−5.70384	−	21.2870i	−0.231321	−	0.863303i
$609$	60.6475	+	7.79082i	2.45756	+	0.315700i
$610$	−11.9024	+	8.76179i	−0.481913	+	0.354754i
$611$	14.8458	−	8.57125i	0.600599	−	0.346756i
$612$	−6.26402	+	11.0086i	−0.253208	+	0.444997i
$613$	−7.38116	+	1.97778i	−0.298122	+	0.0798816i	−0.404780	−	0.914414i	$-0.632652\pi$
$613$	−7.38116	+	1.97778i	−0.298122	+	0.0798816i	0.106658	+	0.994296i	$0.465985\pi$
$614$	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
$617$	−33.7300	+	9.03792i	−1.35792	+	0.363853i	−0.863051	−	0.505116i	$-0.831450\pi$
$617$	−33.7300	+	9.03792i	−1.35792	+	0.363853i	−0.494866	+	0.868969i	$0.664783\pi$
$618$	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	$0.922598\pi$
$620$	7.51315	+	19.2125i	0.301735	+	0.771594i
$621$	−7.37528	+	18.2907i	−0.295960	+	0.733982i
$622$	43.6257	+	11.6895i	1.74923	+	0.468705i
$623$	36.0561	−	36.0561i	1.44456	−	1.44456i
$624$	−2.47899	−	1.88986i	−0.0992389	−	0.0756550i
$625$	20.5866	+	14.1843i	0.823462	+	0.567371i
$626$	35.9378	−	20.7487i	1.43636	−	0.829284i
$627$	16.1941	+	20.9680i	0.646730	+	0.837380i
$628$	−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	−0.897186	−	0.441653i	$-0.854392\pi$
$631$	−1.66068	+	2.87638i	−0.0661106	+	0.114507i	0.831076	+	0.556160i	$0.187726\pi$
$632$	0.0486034	−	0.181391i	0.00193334	−	0.00721533i
$633$	10.4565	−	1.41002i	0.415607	−	0.0560433i
$634$	25.0536	−	14.4647i	0.995007	−	0.574468i
$635$	−33.8342	+	3.77014i	−1.34267	+	0.149613i
$636$	10.9254	+	8.32900i	0.433220	+	0.330267i
$637$	−25.3025	+	25.3025i	−1.00252	+	1.00252i
$638$	−18.4233	−	68.7565i	−0.729384	−	2.72210i
$639$	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	$-0.240939\pi$
$641$	12.5508	+	7.24618i	0.495725	+	0.286207i	−0.231221	+	0.972901i	$0.574272\pi$
$642$	6.77221	+	50.2215i	0.267278	+	1.98208i
$643$	−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
$645$	−24.4976	+	23.6885i	−0.964593	+	0.932735i
$646$	5.17618	−	8.96541i	0.203654	−	0.352739i
$647$	−11.4317	+	42.6638i	−0.449428	+	1.67729i	0.254545	+	0.967061i	$0.418074\pi$
$647$	−11.4317	+	42.6638i	−0.449428	+	1.67729i	−0.703973	+	0.710227i	$0.748592\pi$
$648$	−4.98639	+	19.5899i	−0.195884	+	0.769566i
$649$	−6.53788	−	3.77465i	−0.256634	−	0.148168i
$650$	−6.07946	+	19.5386i	−0.238456	+	0.766368i
$651$	−27.1897	−	3.49281i	−1.06565	−	0.136894i
$652$	19.8382	−	19.8382i	0.776923	−	0.776923i
$653$	−3.75299	−	1.00561i	−0.146866	−	0.0393526i	0.184637	−	0.982807i	$-0.440889\pi$
$653$	−3.75299	−	1.00561i	−0.146866	−	0.0393526i	−0.331503	+	0.943454i	$0.607556\pi$
$654$	38.9998	+	5.00994i	1.52501	+	0.195904i
$655$	−5.61720	+	7.02604i	−0.219482	+	0.274530i
$656$		−	3.70593i		−	0.144692i
$657$	−7.67660	−	4.36807i	−0.299493	−	0.170415i
$658$	76.3833	+	76.3833i	2.97773	+	2.97773i
$659$	−4.94454	−	8.56419i	−0.192612	−	0.333613i	0.753503	−	0.657444i	$-0.228362\pi$
$659$	−4.94454	−	8.56419i	−0.192612	−	0.333613i	−0.946115	+	0.323831i	$0.895029\pi$
$660$	47.2524	−	26.2335i	1.83930	−	1.02114i
$661$	−1.47448	−	2.55387i	−0.0573505	−	0.0993340i	0.835925	−	0.548844i	$-0.184932\pi$
$661$	−1.47448	−	2.55387i	−0.0573505	−	0.0993340i	−0.893275	+	0.449510i	$0.851599\pi$
$662$	11.3466	−	42.3461i	0.440999	−	1.64583i
$663$	−0.595150	−	4.41353i	−0.0231137	−	0.171407i
$664$	−6.98198	−	4.03105i	−0.270953	−	0.156435i
$665$	−4.20225	−	37.7122i	−0.162956	−	1.46241i
$666$	30.4619	−	27.1740i	1.18038	−	1.05297i
$667$	−18.3843	+	18.3843i	−0.711842	+	0.711842i
$668$	1.78694	+	6.66893i	0.0691386	+	0.258029i
$669$	24.9359	+	19.0100i	0.964078	+	0.734967i
$670$	2.34706	−	15.4430i	0.0906748	−	0.596616i
$671$	−11.8865	+	6.86269i	−0.458874	+	0.264931i
$672$	22.6884	−	55.2646i	0.875224	−	2.13188i
$673$	−9.86473	+	36.8157i	−0.380258	+	1.41914i	0.465251	+	0.885179i	$0.345964\pi$
$673$	−9.86473	+	36.8157i	−0.380258	+	1.41914i	−0.845509	+	0.533962i	$0.820703\pi$
$674$	−8.78225			−0.338280
$675$	−25.8498	+	2.60563i	−0.994958	+	0.100291i
$676$	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	$0.930216\pi$
$678$	−44.4106	−	57.5024i	−1.70558	−	2.20837i
$679$	18.3286	−	10.5820i	0.703386	−	0.406100i
$680$	−5.51320	−	4.40772i	−0.211422	−	0.169028i
$681$	−0.452525	+	3.52267i	−0.0173408	+	0.134989i
$682$	8.25958	+	30.8252i	0.316276	+	1.18036i
$683$	8.64924	+	32.2794i	0.330954	+	1.23514i	0.908189	+	0.418559i	$0.137465\pi$
$683$	8.64924	+	32.2794i	0.330954	+	1.23514i	−0.577236	+	0.816578i	$0.695869\pi$
$684$	7.50053	−	28.7121i	0.286790	−	1.09783i
$685$	−0.744475	+	0.548036i	−0.0284449	+	0.0209394i
$686$	−125.389	−	72.3933i	−4.78737	−	2.76399i
$687$	14.0565	−	10.8562i	0.536290	−	0.414190i
$688$	8.36069	−	2.24024i	0.318748	−	0.0854084i
$689$	−4.83045			−0.184025
$690$	−28.1974	−	16.9172i	−1.07346	−	0.644027i
$691$	−8.66554	+	15.0092i	−0.329653	+	0.570975i	−0.982443	−	0.186563i	$-0.940265\pi$
$691$	−8.66554	+	15.0092i	−0.329653	+	0.570975i	0.652790	+	0.757539i	$0.273598\pi$
$692$	−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
$696$	−16.1565	+	21.1930i	−0.612411	+	0.803317i
$697$	3.74383	−	3.74383i	0.141808	−	0.141808i
$698$	−4.32927	−	1.16002i	−0.163865	−	0.0439076i
$699$	8.86930	−	11.6341i	0.335468	−	0.440043i
$700$	−77.3466	−	3.08433i	−2.92343	−	0.116577i
$701$	−9.58105	−	5.53162i	−0.361871	−	0.208926i	0.308030	−	0.951377i	$-0.400330\pi$
$701$	−9.58105	−	5.53162i	−0.361871	−	0.208926i	−0.669901	+	0.742450i	$0.733664\pi$
$702$	−8.32252	−	19.5691i	−0.314113	−	0.738589i
$703$	−15.0300	+	13.2393i	−0.566869	+	0.499329i
$704$	−60.4068			−2.27667
$705$	−26.0883	+	25.2267i	−0.982543	+	0.950092i
$706$	−21.1139	−	36.5703i	−0.794631	−	1.37634i
$707$	14.6818	−	54.7931i	0.552165	−	2.06071i
$708$	1.13004	+	8.38018i	0.0424695	+	0.314946i
$709$			33.1729i			1.24583i	0.782288	+	0.622917i	$0.214052\pi$
$709$			33.1729i			1.24583i	−0.782288	+	0.622917i	$0.785948\pi$
$710$	30.1815	+	40.9997i	1.13269	+	1.53869i
$711$	−0.176243	+	0.178469i	−0.00660962	+	0.00669312i
$712$	5.75182	+	21.4661i	0.215559	+	0.804475i
$713$	8.24211	−	8.24211i	0.308669	−	0.308669i
$714$	25.8932	−	10.8207i	0.969030	−	0.404953i
$715$	−7.62056	+	17.4082i	−0.284993	+	0.651028i
$716$	−11.4374	+	6.60340i	−0.427437	+	0.246781i
$717$	−1.20695	+	2.93989i	−0.0450743	+	0.109792i
$718$	−23.9970	+	6.42999i	−0.895562	+	0.239965i
$719$	−9.27779	+	16.0696i	−0.346003	+	0.599295i	−0.985535	−	0.169469i	$-0.945795\pi$
$719$	−9.27779	+	16.0696i	−0.346003	+	0.599295i	0.639532	+	0.768764i	$0.279128\pi$
$720$	6.06169	+	2.60834i	0.225906	+	0.0972069i
$721$	−39.4165	−	68.2713i	−1.46795	−	2.54256i
$722$	4.72284	−	17.6259i	0.175766	−	0.655968i
$723$	2.12812	+	2.75548i	0.0791458	+	0.102477i
$724$	32.7136	+	18.8872i	1.21579	+	0.701938i
$725$	−32.7041	−	10.1759i	−1.21460	−	0.377924i
$726$	37.8173	−	15.8037i	1.40353	−	0.586529i
$727$	−40.2171	−	10.7761i	−1.49157	−	0.399665i	−0.581302	−	0.813688i	$-0.697457\pi$
$727$	−40.2171	−	10.7761i	−1.49157	−	0.399665i	−0.910266	+	0.414023i	$0.864123\pi$
$728$	−5.48094	−	20.4552i	−0.203137	−	0.758118i
$729$	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
$733$	−4.76888	+	17.7977i	−0.176143	+	0.657373i	0.820211	+	0.572060i	$0.193856\pi$
$733$	−4.76888	+	17.7977i	−0.176143	+	0.657373i	−0.996354	+	0.0853131i	$0.972811\pi$
$734$	−63.8376			−2.35629
$735$	38.9722	−	64.9582i	1.43751	−	2.39602i
$736$	12.7009	+	21.9986i	0.468162	+	0.810880i
$737$	3.75449	−	14.0119i	0.138298	−	0.516136i
$738$	12.5031	−	21.9734i	0.460246	−	0.808853i
$739$		−	33.4071i		−	1.22890i	−0.788955	−	0.614451i	$-0.789378\pi$
$739$		−	33.4071i		−	1.22890i	0.788955	−	0.614451i	$-0.210622\pi$
$740$	22.0942	+	34.3709i	0.812199	+	1.26350i
$741$	4.02323	+	9.62736i	0.147797	+	0.353670i
$742$	−7.87813	−	29.4016i	−0.289215	−	1.07937i
$743$	46.5479	+	12.4725i	1.70768	+	0.457571i	0.974854	−	0.222847i	$-0.0715349\pi$
$743$	46.5479	+	12.4725i	1.70768	+	0.457571i	0.732825	+	0.680418i	$0.238202\pi$
$744$	7.24334	−	9.50130i	0.265554	−	0.348335i
$745$	−0.831901	+	5.47369i	−0.0304785	+	0.200541i
$746$			51.1589i			1.87306i
$747$	5.44258	+	9.29163i	0.199133	+	0.339963i
$748$	−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	$0.317339\pi$
$752$	8.90357	−	2.38570i	0.324680	−	0.0869977i
$753$	−1.35623	−	10.0576i	−0.0494238	−	0.366518i
$754$		−	28.0343i		−	1.02095i
$755$	32.9234	−	12.8748i	1.19820	−	0.468563i
$756$	63.3572	−	49.5704i	2.30428	−	1.80286i
$757$	−13.3392	−	49.7827i	−0.484823	−	1.80938i	−0.580856	−	0.814006i	$-0.697282\pi$
$757$	−13.3392	−	49.7827i	−0.484823	−	1.80938i	0.0960332	−	0.995378i	$-0.469385\pi$
$758$	−14.2937	−	3.82999i	−0.519171	−	0.139111i
$759$	−24.2852	−	18.5139i	−0.881498	−	0.672012i
$760$	15.1498	+	6.63192i	0.549539	+	0.240565i
$761$	−10.5346	−	6.08214i	−0.381878	−	0.220477i	0.296757	−	0.954953i	$-0.404095\pi$
$761$	−10.5346	−	6.08214i	−0.381878	−	0.220477i	−0.678635	+	0.734476i	$0.737428\pi$
$762$	36.0571	+	46.6864i	1.30621	+	1.69127i
$763$	−36.9816	−	36.9816i	−1.33882	−	1.33882i
$764$	16.1051	+	27.8948i	0.582662	+	1.00920i
$765$	3.48867	+	8.75869i	0.126133	+	0.316671i
$766$	43.0351			1.55492
$767$	−2.10238	−	2.10238i	−0.0759125	−	0.0759125i
$768$	9.65749	+	12.5044i	0.348485	+	0.451215i
$769$			11.4788i			0.413936i	0.978348	+	0.206968i	$0.0663596\pi$
$769$			11.4788i			0.413936i	−0.978348	+	0.206968i	$0.933640\pi$
$770$	−118.387	−	17.9927i	−4.26637	−	0.648411i
$771$	−1.44613	+	0.604333i	−0.0520813	+	0.0217645i
$772$	−23.5019	−	6.29731i	−0.845851	−	0.226645i
$773$	47.3779	+	12.6949i	1.70406	+	0.456603i	0.973958	−	0.226730i	$-0.0728035\pi$
$773$	47.3779	+	12.6949i	1.70406	+	0.456603i	0.730107	+	0.683333i	$0.239470\pi$
$774$	57.1309	+	14.9244i	2.05353	+	0.536448i
$775$	14.6620	+	4.56210i	0.526675	+	0.163875i
$776$			9.22387i			0.331118i
$777$	−54.1602	+	3.83966i	−1.94298	+	0.137747i
$778$	24.6479	+	24.6479i	0.883670	+	0.883670i
$779$	−6.20241	+	10.7429i	−0.222225	+	0.384904i
$780$	20.6498	−	5.16314i	0.739382	−	0.184870i
$781$	23.6397	+	40.9452i	0.845895	+	1.46513i
$782$	−3.08837	+	11.5260i	−0.110440	+	0.412167i
$783$	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
$786$	15.4599	+	1.98599i	0.551435	+	0.0708379i
$787$	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
$789$	−34.1978	−	4.39308i	−1.21747	−	0.156398i
$790$	−0.247928	−	0.336796i	−0.00882089	−	0.0119827i
$791$			96.6392i			3.43609i
$792$	−27.2049	−	15.4799i	−0.966683	−	0.550053i
$793$	−5.22141	+	1.39907i	−0.185418	+	0.0496825i
$794$	−8.95410	+	15.5090i	−0.317769	+	0.550392i
$795$	9.92056	−	2.48047i	0.351846	−	0.0879733i
$796$	−11.4225	−	19.7843i	−0.404858	−	0.701235i
$797$	17.7174	−	4.74737i	0.627583	−	0.168160i	0.0690104	−	0.997616i	$-0.478016\pi$
$797$	17.7174	−	4.74737i	0.627583	−	0.168160i	0.558573	+	0.829456i	$0.311349\pi$
$798$	−52.0374	+	40.1898i	−1.84210	+	1.42270i
$799$	11.4047	+	6.58452i	0.403470	+	0.232944i
$800$	−17.8732	+	28.2906i	−0.631914	+	1.00022i
$801$	7.50240	−	28.7192i	0.265084	−	1.01474i
$802$	−11.9870	−	44.7359i	−0.423274	−	1.57968i
$803$	9.67051	−	9.67051i	0.341265	−	0.341265i
$804$	−14.9921	+	6.26513i	−0.528731	+	0.220954i
$805$	15.9291	+	40.7338i	0.561428	+	1.43568i
$806$			12.5684i			0.442704i
$807$	−18.0425	+	2.43298i	−0.635127	+	0.0856449i
$808$	17.4817	+	17.4817i	0.615003	+	0.615003i
$809$	4.87626	+	8.44593i	0.171440	+	0.296943i	0.938924	−	0.344126i	$-0.111825\pi$
$809$	4.87626	+	8.44593i	0.171440	+	0.296943i	−0.767483	+	0.641069i	$0.778491\pi$
$810$	27.1413	+	35.9165i	0.953648	+	1.26198i
$811$	−11.1202	−	19.2607i	−0.390482	−	0.676335i	0.602031	−	0.798473i	$-0.294358\pi$
$811$	−11.1202	−	19.2607i	−0.390482	−	0.676335i	−0.992513	+	0.122138i	$0.961025\pi$
$812$	102.438	−	27.4480i	3.59485	−	0.963238i
$813$	−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
$816$	0.305114	−	2.37515i	0.0106811	−	0.0831468i
$817$	−27.9857	−	7.49874i	−0.979095	−	0.262348i
$818$	−39.4275	−	10.5646i	−1.37855	−	0.369381i
$819$	−7.14908	+	27.3667i	−0.249809	+	0.956270i
$820$	19.7653	+	15.8020i	0.690234	+	0.551831i
$821$	4.58715	−	2.64839i	0.160093	−	0.0924296i	−0.417813	−	0.908533i	$-0.637203\pi$
$821$	4.58715	−	2.64839i	0.160093	−	0.0924296i	0.577906	+	0.816103i	$0.303870\pi$
$822$	1.48181	+	0.608344i	0.0516841	+	0.0212184i
$823$	32.1408	−	8.61210i	1.12036	−	0.300199i	0.349329	−	0.937000i	$-0.386409\pi$
$823$	32.1408	−	8.61210i	1.12036	−	0.300199i	0.771028	+	0.636801i	$0.219743\pi$
$824$	34.3576			1.19691
$825$	6.71154	−	39.6653i	0.233666	−	1.38097i
$826$	9.36774	−	16.2254i	0.325946	−	0.564554i
$827$	−9.90290	+	36.9581i	−0.344357	+	1.28516i	0.549004	+	0.835820i	$0.315007\pi$
$827$	−9.90290	+	36.9581i	−0.344357	+	1.28516i	−0.893361	+	0.449339i	$0.851659\pi$
$828$	0.214710	+	34.2046i	0.00746169	+	1.18869i
$829$	−17.6908	−	10.2138i	−0.614427	−	0.354740i	0.160269	−	0.987073i	$-0.448764\pi$
$829$	−17.6908	−	10.2138i	−0.614427	−	0.354740i	−0.774696	+	0.632334i	$0.782097\pi$
$830$	−16.7214	+	6.53897i	−0.580407	+	0.226971i
$831$	24.6820	+	3.17066i	0.856207	+	0.109989i
$832$	−22.9800	−	6.15746i	−0.796687	−	0.213472i
$833$	−26.5523	−	7.11467i	−0.919984	−	0.246509i
$834$	77.1528	+	9.91111i	2.67158	+	0.343194i
$835$	4.70779	+	2.06087i	0.162920	+	0.0713195i
$836$	39.7941	+	22.9751i	1.37631	+	0.794611i
$837$	−14.6849	+	6.24532i	−0.507585	+	0.215870i
$838$	8.66849	−	32.3512i	0.299448	−	1.11755i
$839$	19.8997	−	34.4673i	0.687014	−	1.18994i	−0.285785	−	0.958294i	$-0.592254\pi$
$839$	19.8997	−	34.4673i	0.687014	−	1.18994i	0.972799	−	0.231650i	$-0.0744124\pi$
$840$	21.7604	+	39.1954i	0.750804	+	1.35237i
$841$	17.9243			0.618081
$842$	−18.1925	+	4.87466i	−0.626955	+	0.167992i
$843$	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
$846$	60.8405	+	15.8935i	2.09174	+	0.546430i
$847$	−52.6588	−	14.1099i	−1.80938	−	0.484821i
$848$	−2.50887	−	0.672249i	−0.0861548	−	0.0230851i
$849$	−3.75530	+	29.2330i	−0.128882	+	1.00328i
$850$	−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
$853$	43.9131	−	11.7665i	1.50356	−	0.402877i	0.589268	−	0.807938i	$-0.299416\pi$
$853$	43.9131	−	11.7665i	1.50356	−	0.402877i	0.914290	+	0.405061i	$0.132750\pi$
$854$	−17.0315	−	29.4995i	−0.582806	−	1.00945i
$855$	−13.2064	−	17.7063i	−0.451651	−	0.605542i
$856$	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	$0.653497\pi$
$858$	32.6323	−	4.40036i	1.11405	−	0.150226i
$859$			15.8602i			0.541144i	0.962700	+	0.270572i	$0.0872127\pi$
$859$			15.8602i			0.541144i	−0.962700	+	0.270572i	$0.912787\pi$
$860$	−23.7017	+	54.1435i	−0.808222	+	1.84628i
$861$	−31.0269	+	12.9660i	−1.05739	+	0.441879i
$862$	18.3905	−	18.3905i	0.626383	−	0.626383i
$863$	−0.885156	−	3.30345i	−0.0301310	−	0.112451i	0.949223	−	0.314606i	$-0.101872\pi$
$863$	−0.885156	−	3.30345i	−0.0301310	−	0.112451i	−0.979354	+	0.202155i	$0.935206\pi$
$864$	−4.86366	−	34.4346i	−0.165465	−	1.17149i
$865$	−22.4760	+	2.50449i	−0.764207	+	0.0851553i
$866$	−31.3142	−	18.0793i	−1.06410	−	0.614359i
$867$	−20.5961	+	15.9069i	−0.699481	+	0.540227i
$868$	−45.9251	+	12.3056i	−1.55880	+	0.417679i
$869$	−0.194190	−	0.336348i	−0.00658746	−	0.0114098i
$870$	14.3958	+	57.5756i	0.488064	+	1.95199i
$871$	2.85656	−	4.94771i	0.0967910	−	0.167647i
$872$	22.0171	−	5.89947i	0.745594	−	0.199781i
$873$	6.09292	−	10.7079i	0.206214	−	0.362408i
$874$		−	27.9572i		−	0.945665i
$875$	−37.7445	+	43.5345i	−1.27600	+	1.47173i
$876$	−15.1939	−	1.95183i	−0.513356	−	0.0659461i
$877$	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
$879$	26.5657	+	3.41266i	0.896040	+	0.115106i
$880$	−6.38068	+	7.98100i	−0.215093	+	0.269040i
$881$	47.8677	−	27.6364i	1.61270	−	0.931095i	0.623964	−	0.781453i	$-0.285521\pi$
$881$	47.8677	−	27.6364i	1.61270	−	0.931095i	0.988740	−	0.149643i	$-0.0478123\pi$
$882$	−131.257	+	0.823933i	−4.41967	+	0.0277433i
$883$	−11.1762	+	41.7101i	−0.376109	+	1.40366i	0.475608	+	0.879657i	$0.342228\pi$
$883$	−11.1762	+	41.7101i	−0.376109	+	1.40366i	−0.851718	+	0.524001i	$0.824439\pi$
$884$	−3.86205	−	6.68926i	−0.129895	−	0.224984i
$885$	5.39736	+	3.23818i	0.181430	+	0.108850i
$886$	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	$-0.548320\pi$
$888$	10.3530	−	21.2788i	0.347425	−	0.714071i
$889$		−	78.4618i		−	2.63152i
$890$	45.3379	+	19.8470i	1.51973	+	0.665274i
$891$	21.3565	+	35.9409i	0.715471	+	1.20407i
$892$	52.5301	+	14.0754i	1.75884	+	0.471279i
$893$	−29.8028	−	7.98565i	−0.997314	−	0.267230i
$894$	8.85165	−	3.69907i	0.296044	−	0.123715i
$895$	−1.47709	+	9.71885i	−0.0493736	+	0.324865i
$896$		−	80.9324i		−	2.70376i
$897$	−7.35140	−	9.51853i	−0.245456	−	0.317814i
$898$	−21.8295	−	21.8295i	−0.728459	−	0.728459i
$899$	−21.0373			−0.701633
$900$	−39.7583	+	21.2077i	−1.32528	+	0.706922i
$901$	−1.85540	−	3.21365i	−0.0618123	−	0.107062i
$902$	27.6808	+	27.6808i	0.921668	+	0.921668i
$903$	−48.0074	−	62.1596i	−1.59759	−	2.06854i
$904$	−36.4754	−	21.0591i	−1.21315	−	0.700414i
$905$	26.1863	−	10.2403i	0.870460	−	0.340398i
$906$	−48.7136	−	37.1370i	−1.61840	−	1.23379i
$907$	26.1315	+	7.00192i	0.867683	+	0.232495i	0.665086	−	0.746767i	$-0.268395\pi$
$907$	26.1315	+	7.00192i	0.867683	+	0.232495i	0.202597	+	0.979262i	$0.435062\pi$
$908$	1.59430	+	5.95002i	0.0529088	+	0.197458i
$909$	−8.74664	−	31.8420i	−0.290108	−	1.05613i
$910$	−43.2028	−	18.9124i	−1.43216	−	0.626938i
$911$			57.9138i			1.91877i	0.282100	+	0.959385i	$0.408969\pi$
$911$			57.9138i			1.91877i	−0.282100	+	0.959385i	$0.591031\pi$
$912$	0.749778	+	5.56022i	0.0248276	+	0.184117i
$913$	−16.1057	+	4.31550i	−0.533020	+	0.142822i
$914$	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
$918$	9.82241	−	13.0535i	0.324188	−	0.430829i
$919$		−	30.8933i		−	1.01908i	−0.860448	−	0.509538i	$-0.829816\pi$
$919$		−	30.8933i		−	1.01908i	0.860448	−	0.509538i	$-0.170184\pi$
$920$	−18.8457	−	2.86420i	−0.621323	−	0.0944298i
$921$	−11.1572	+	14.6352i	−0.367642	+	0.482246i
$922$	−32.3978	−	8.68096i	−1.06696	−	0.285892i
$923$	4.81934	+	17.9860i	0.158631	+	0.592017i
$924$	48.0289	+	114.930i	1.58003	+	3.78093i
$925$	30.2523	+	3.13065i	0.994688	+	0.102935i
$926$			24.6620i			0.810444i
$927$	−39.8855	−	22.6953i	−1.31001	−	0.745411i
$928$	11.8658	−	44.2838i	0.389514	−	1.45369i
$929$	6.11253	+	10.5872i	0.200546	+	0.347355i	0.948704	−	0.316164i	$-0.102395\pi$
$929$	6.11253	+	10.5872i	0.200546	+	0.347355i	−0.748159	+	0.663520i	$0.769062\pi$
$930$	−6.45398	−	25.8125i	−0.211634	−	0.846425i
$931$	64.4049			2.11078
$932$	6.56703	−	24.5085i	0.215110	−	0.802803i
$933$	−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
$937$	2.20667	+	8.23539i	0.0720886	+	0.269038i	0.992557	−	0.121778i	$-0.0388595\pi$
$937$	2.20667	+	8.23539i	0.0720886	+	0.269038i	−0.920469	+	0.390816i	$0.872193\pi$
$938$	34.7742	+	9.31771i	1.13542	+	0.304234i
$939$	−29.6461	+	12.3890i	−0.967465	+	0.404299i
$940$	−25.2407	+	57.6591i	−0.823262	+	1.88063i
$941$	−32.3751	−	18.6918i	−1.05540	−	0.609335i	−0.131243	−	0.991350i	$-0.541897\pi$
$941$	−32.3751	−	18.6918i	−1.05540	−	0.609335i	−0.924156	+	0.382016i	$0.875230\pi$
$942$	32.8146	+	42.4880i	1.06916	+	1.38433i
$943$	3.70067	−	13.8111i	0.120511	−	0.449751i
$944$	−0.799359	−	1.38453i	−0.0260169	−	0.0450626i
$945$	0.629443	−	59.8756i	0.0204758	−	1.94775i
$946$	−45.7156	+	79.1817i	−1.48634	+	2.57442i
$947$	−17.9478	+	4.80911i	−0.583226	+	0.156275i	−0.538356	−	0.842718i	$-0.680954\pi$
$947$	−17.9478	+	4.80911i	−0.583226	+	0.156275i	−0.0448708	+	0.998993i	$0.514288\pi$
$948$	−0.165216	+	0.402435i	−0.00536597	+	0.0130705i
$949$	4.66460	−	2.69311i	0.151419	−	0.0874220i
$950$	32.6040	−	17.1294i	1.05781	−	0.555752i
$951$	−20.6675	+	8.63685i	−0.670189	+	0.280069i
$952$	11.5033	−	11.5033i	0.372825	−	0.372825i
$953$	4.61043	+	17.2064i	0.149347	+	0.557369i	0.999523	+	0.0308718i	$0.00982835\pi$
$953$	4.61043	+	17.2064i	0.149347	+	0.557369i	−0.850177	+	0.526497i	$0.823505\pi$
$954$	−12.6077	−	12.4504i	−0.408189	−	0.403096i
$955$	23.7034	+	3.60248i	0.767023	+	0.116574i
$956$			5.51192i			0.178268i
$957$	7.36541	+	54.6206i	0.238090	+	1.76563i
$958$	−3.05941	+	11.4179i	−0.0988451	+	0.368895i
$959$	−1.06530	−	1.84515i	−0.0344002	−	0.0595829i
$960$	50.3571	+	0.845538i	1.62527	+	0.0272896i
$961$	−21.5685			−0.695758
$962$	4.90995	+	24.4048i	0.158303	+	0.786843i
$963$	−0.246298	−	39.2368i	−0.00793685	−	1.26439i
$964$	5.22948	+	3.01924i	0.168430	+	0.0972432i
$965$	−14.5850	+	10.7366i	−0.469508	+	0.345623i
$966$	45.9470	−	60.2700i	1.47832	−	1.93915i
$967$	−4.87171	−	1.30537i	−0.156664	−	0.0419779i	0.179635	−	0.983733i	$-0.442508\pi$
$967$	−4.87171	−	1.30537i	−0.156664	−	0.0419779i	−0.336298	+	0.941755i	$0.609175\pi$
$968$	16.8007	−	16.8007i	0.539995	−	0.539995i
$969$	−4.85963	+	6.37452i	−0.156114	+	0.204779i
$970$	16.0444	+	12.8273i	0.515156	+	0.411859i
$971$	−35.9579	−	20.7603i	−1.15394	−	0.666229i	−0.204098	−	0.978950i	$-0.565426\pi$
$971$	−35.9579	−	20.7603i	−1.15394	−	0.666229i	−0.949845	+	0.312721i	$0.898759\pi$
$972$	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
$975$	6.59642	−	14.4053i	0.211254	−	0.461340i
$976$	−2.90663			−0.0930391
$977$	57.5097	−	15.4097i	1.83990	−	0.492999i	0.841048	−	0.540960i	$-0.181939\pi$
$977$	57.5097	−	15.4097i	1.83990	−	0.492999i	0.998849	+	0.0479614i	$0.0152724\pi$
$978$	−28.6383	+	22.1181i	−0.915752	+	0.707258i
$979$	39.8040	+	22.9808i	1.27214	+	0.734471i
$980$	19.7413	−	129.893i	0.630614	−	4.14927i
$981$	−29.4564	−	7.69498i	−0.940472	−	0.245682i
$982$	12.0653	+	45.0284i	0.385020	+	1.43691i
$983$	3.65868	+	13.6544i	0.116694	+	0.435508i	0.999408	−	0.0344028i	$-0.0109529\pi$
$983$	3.65868	+	13.6544i	0.116694	+	0.435508i	−0.882714	+	0.469910i	$0.844286\pi$
$984$	1.86733	−	14.5362i	0.0595284	−	0.463397i
$985$	6.32838	+	56.7926i	0.201639	+	1.80956i
$986$	18.6509	−	10.7681i	0.593966	−	0.342926i
$987$	−51.1247	−	66.1957i	−1.62732	−	2.10703i
$988$	12.7965	+	12.7965i	0.407112	+	0.407112i
$989$	33.3953			1.06191
$990$	−64.7591	+	25.7942i	−2.05818	+	0.819793i
$991$	45.4771			1.44463			0.722314	−	0.691565i	$-0.243079\pi$
$991$	45.4771			1.44463			0.722314	+	0.691565i	$0.243079\pi$
$992$	−5.31972	+	19.8535i	−0.168901	+	0.630348i
$993$	−12.8915	+	31.4012i	−0.409099	+	0.996488i
$994$	−101.616	+	58.6679i	−3.22306	+	1.86083i
$995$	−16.8115	−	2.55504i	−0.532961	−	0.0810003i
$996$	14.8527	+	11.3230i	0.470625	+	0.358782i
$997$	−8.61802	−	32.1629i	−0.272936	−	1.01861i	−0.957212	−	0.289387i	$-0.906549\pi$
$997$	−8.61802	−	32.1629i	−0.272936	−	1.01861i	0.684277	−	0.729222i	$-0.260118\pi$
$998$	24.3249	−	24.3249i	0.769991	−	0.769991i
$999$	−26.0747	+	17.8636i	−0.824967	+	0.565181i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.bi.a.47.10	✓	288	5.2	odd	4	inner
555.2.bi.a.47.63	yes	288	15.2	even	4	inner
555.2.bi.a.137.10	yes	288	555.137	even	12	inner
555.2.bi.a.137.63	yes	288	185.137	odd	12	inner
555.2.bi.a.158.10	yes	288	1.1	even	1	trivial
555.2.bi.a.158.63	yes	288	3.2	odd	2	inner
555.2.bi.a.248.10	yes	288	111.26	odd	6	inner
555.2.bi.a.248.63	yes	288	37.26	even	3	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:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.bi (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.16075 + 0.578972i) q^{2} +(1.71651 - 0.231467i) q^{3} +(2.60160 - 1.50203i) q^{4} +(0.335983 - 2.21068i) q^{5} +(-3.57495 + 1.49396i) q^{6} +(4.97795 + 1.33384i) q^{7} +(-1.58821 + 1.58821i) q^{8} +(2.89285 - 0.794631i) q^{9} +O(q^{10})\)	\(q+(-2.16075 + 0.578972i) q^{2} +(1.71651 - 0.231467i) q^{3} +(2.60160 - 1.50203i) q^{4} +(0.335983 - 2.21068i) q^{5} +(-3.57495 + 1.49396i) q^{6} +(4.97795 + 1.33384i) q^{7} +(-1.58821 + 1.58821i) q^{8} +(2.89285 - 0.794631i) q^{9} +(0.553946 + 4.97126i) q^{10} +4.64526i q^{11} +(4.11801 - 3.18044i) q^{12} +(-0.473506 + 1.76715i) q^{13} -11.5284 q^{14} +(0.0650215 - 3.87244i) q^{15} +(-0.491864 + 0.851934i) q^{16} +(-1.35754 + 0.363752i) q^{17} +(-5.79066 + 3.39188i) q^{18} +(2.85167 - 1.64641i) q^{19} +(-2.44642 - 6.25596i) q^{20} +(8.85347 + 1.13732i) q^{21} +(-2.68947 - 10.0373i) q^{22} +(-2.68378 + 2.68378i) q^{23} +(-2.35857 + 3.09380i) q^{24} +(-4.77423 - 1.48550i) q^{25} -4.09252i q^{26} +(4.78168 - 2.03359i) q^{27} +(14.9541 - 4.00694i) q^{28} +6.85013 q^{29} +(2.10154 + 8.40503i) q^{30} -3.07108 q^{31} +(1.73220 - 6.46466i) q^{32} +(1.07522 + 7.97365i) q^{33} +(2.72271 - 1.57196i) q^{34} +(4.62120 - 10.5565i) q^{35} +(6.33245 - 6.41246i) q^{36} +(-5.96327 + 1.19974i) q^{37} +(-5.20853 + 5.20853i) q^{38} +(-0.403744 + 3.14294i) q^{39} +(2.97741 + 4.04464i) q^{40} +(-3.26251 + 1.88361i) q^{41} +(-19.7886 + 2.66844i) 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} +(11.1760 + 0.445663i) q^{50} +(-2.24604 + 0.938611i) q^{51} +(1.42244 + 5.30863i) q^{52} +(0.683368 + 2.55036i) q^{53} +(-9.15464 + 7.16256i) q^{54} +(10.2692 + 1.56073i) q^{55} +(-10.0244 + 5.78762i) q^{56} +(4.51385 - 3.48616i) q^{57} +(-14.8015 + 3.96604i) q^{58} +(-0.812581 + 1.40743i) q^{59} +(-5.64736 - 10.1722i) q^{60} +(1.47736 + 2.55885i) q^{61} +(6.63584 - 1.77807i) q^{62} +(15.4604 - 0.0970482i) q^{63} +13.0040i q^{64} +(3.74751 + 1.64050i) q^{65} +(-6.93981 - 16.6066i) q^{66} +(-3.01640 - 0.808241i) q^{67} +(-2.98540 + 2.98540i) q^{68} +(-3.98555 + 5.22796i) q^{69} +(-3.87335 + 25.4856i) q^{70} +(8.81440 - 5.08900i) q^{71} +(-3.33240 + 5.85649i) 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} +(-6.19602 + 23.1239i) q^{77} +(-0.947281 - 7.02487i) q^{78} +(-0.0724067 + 0.0418040i) q^{79} +(1.71810 + 1.37359i) q^{80} +(7.73712 - 4.59749i) q^{81} +(5.95893 - 5.95893i) q^{82} +(0.929013 + 3.46712i) q^{83} +(24.7414 - 10.3393i) q^{84} +(0.348029 + 3.12330i) q^{85} +(17.0457 + 9.84134i) q^{86} +(11.7584 - 1.58558i) q^{87} +(-7.37764 - 7.37764i) q^{88} +(4.94716 - 8.56874i) q^{89} +(5.55280 + 13.9409i) q^{90} +(-4.71418 + 8.16520i) q^{91} +(-2.95099 + 11.0133i) q^{92} +(-5.27155 + 0.710851i) q^{93} +(18.1525 + 10.4804i) q^{94} +(-2.68158 - 6.85731i) q^{95} +(1.47700 - 11.4976i) q^{96} +(2.90386 - 2.90386i) q^{97} +(-42.2625 - 11.3242i) q^{98} +(3.69127 + 13.4380i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more