LMFDB - Embedded newform 572.2.bb.b.51.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(51,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7, 5]))

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

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

chi := DirichletCharacter("572.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bb (of order $10$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			51.4
Character	$\chi$	$=$	572.51
Dual form			572.2.bb.b.415.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39723 - 0.218517i) q^{2} +(-1.60576 - 0.521744i) q^{3} +(1.90450 + 0.610638i) q^{4} +(-2.10647 - 2.89931i) q^{5} +(2.12961 + 1.07988i) q^{6} +(-0.788330 + 0.256144i) q^{7} +(-2.52759 - 1.26937i) q^{8} +(-0.120789 - 0.0877584i) q^{9} +O(q^{10})$	\(q+(-1.39723 - 0.218517i) q^{2} +(-1.60576 - 0.521744i) q^{3} +(1.90450 + 0.610638i) q^{4} +(-2.10647 - 2.89931i) q^{5} +(2.12961 + 1.07988i) q^{6} +(-0.788330 + 0.256144i) q^{7} +(-2.52759 - 1.26937i) q^{8} +(-0.120789 - 0.0877584i) q^{9} +(2.30967 + 4.51130i) q^{10} +(2.24388 - 2.44234i) q^{11} +(-2.73958 - 1.97420i) q^{12} +(-3.47958 - 0.944724i) q^{13} +(1.15745 - 0.185628i) q^{14} +(1.86980 + 5.75464i) q^{15} +(3.25424 + 2.32592i) q^{16} +(-3.21575 - 4.42609i) q^{17} +(0.149593 + 0.149013i) q^{18} +(0.773861 + 0.251443i) q^{19} +(-2.24134 - 6.80802i) q^{20} +1.39951 q^{21} +(-3.66891 + 2.92218i) q^{22} +0.732905i q^{23} +(3.39643 + 3.35706i) q^{24} +(-2.42368 + 7.45932i) q^{25} +(4.65534 + 2.08035i) q^{26} +(3.12542 + 4.30177i) q^{27} +(-1.65779 + 0.00644191i) q^{28} +(5.90754 - 1.91948i) q^{29} +(-1.35504 - 8.44914i) q^{30} +(-1.25555 - 0.912211i) q^{31} +(-4.03867 - 3.96095i) q^{32} +(-4.87742 + 2.75109i) q^{33} +(3.52596 + 6.88697i) q^{34} +(2.40323 + 1.74605i) q^{35} +(-0.176454 - 0.240894i) q^{36} +(-4.27047 + 1.38756i) q^{37} +(-1.02632 - 0.520425i) q^{38} +(5.09449 + 3.33246i) q^{39} +(1.64400 + 10.0021i) q^{40} +(-0.714521 + 2.19907i) q^{41} +(-1.95544 - 0.305818i) q^{42} +1.39822 q^{43} +(5.76485 - 3.28123i) q^{44} +0.535065i q^{45} +(0.160152 - 1.02404i) q^{46} +(-2.14892 + 6.61369i) q^{47} +(-4.01201 - 5.43276i) q^{48} +(-5.10726 + 3.71064i) q^{49} +(5.01643 - 9.89276i) q^{50} +(2.85444 + 8.78506i) q^{51} +(-6.04998 - 3.92399i) q^{52} +(1.37028 + 0.995570i) q^{53} +(-3.42692 - 6.69353i) q^{54} +(-11.8077 - 1.36098i) q^{55} +(2.31771 + 0.353254i) q^{56} +(-1.11145 - 0.807515i) q^{57} +(-8.67363 + 1.39105i) q^{58} +(3.77526 + 11.6191i) q^{59} +(0.0470246 + 12.1015i) q^{60} +(-3.19409 - 4.39629i) q^{61} +(1.55496 + 1.54893i) q^{62} +(0.117700 + 0.0382432i) q^{63} +(4.77741 + 6.41688i) q^{64} +(4.59059 + 12.0784i) q^{65} +(7.41603 - 2.77810i) q^{66} +12.3062 q^{67} +(-3.42165 - 10.3932i) q^{68} +(0.382389 - 1.17687i) q^{69} +(-2.97632 - 2.96478i) q^{70} +(-10.0507 + 7.30225i) q^{71} +(0.193907 + 0.375143i) q^{72} +(4.15504 + 12.7879i) q^{73} +(6.27003 - 1.00557i) q^{74} +(7.78371 - 10.7134i) q^{75} +(1.32028 + 0.951422i) q^{76} +(-1.14333 + 2.50012i) q^{77} +(-6.38996 - 5.76944i) q^{78} +(-0.945887 - 0.687227i) q^{79} +(-0.111405 - 14.3345i) q^{80} +(-2.63585 - 8.11232i) q^{81} +(1.47889 - 2.91647i) q^{82} +(-7.62433 - 10.4940i) q^{83} +(2.66537 + 0.854596i) q^{84} +(-6.05873 + 18.6469i) q^{85} +(-1.95364 - 0.305536i) q^{86} -10.4876 q^{87} +(-8.77183 + 3.32492i) q^{88} -10.1938i q^{89} +(0.116921 - 0.747609i) q^{90} +(2.98504 - 0.146520i) q^{91} +(-0.447539 + 1.39582i) q^{92} +(1.54018 + 2.11987i) q^{93} +(4.44774 - 8.77127i) q^{94} +(-0.901105 - 2.77332i) q^{95} +(4.41855 + 8.46751i) q^{96} +(3.19230 - 4.39382i) q^{97} +(7.94686 - 4.06860i) q^{98} +(-0.485372 + 0.0980884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q - 14 q^{4} + 72 q^{9}+O(q^{10}) $ 304 * q - 14 * q^4 + 72 * q^9	$ 304 q - 14 q^{4} + 72 q^{9} - 20 q^{12} - 10 q^{13} + 2 q^{14} + 14 q^{16} + 20 q^{17} - 66 q^{22} + 72 q^{25} - 34 q^{26} - 100 q^{29} - 60 q^{30} + 62 q^{36} - 14 q^{38} - 10 q^{40} - 68 q^{42} + 4 q^{48} + 40 q^{49} - 30 q^{52} - 12 q^{53} - 132 q^{56} - 20 q^{61} + 130 q^{62} - 38 q^{64} + 86 q^{66} - 60 q^{68} + 56 q^{69} + 40 q^{74} + 68 q^{77} - 48 q^{78} - 48 q^{81} - 70 q^{82} - 102 q^{88} + 180 q^{90} - 2 q^{92} - 190 q^{94}+O(q^{100}) $ 304 * q - 14 * q^4 + 72 * q^9 - 20 * q^12 - 10 * q^13 + 2 * q^14 + 14 * q^16 + 20 * q^17 - 66 * q^22 + 72 * q^25 - 34 * q^26 - 100 * q^29 - 60 * q^30 + 62 * q^36 - 14 * q^38 - 10 * q^40 - 68 * q^42 + 4 * q^48 + 40 * q^49 - 30 * q^52 - 12 * q^53 - 132 * q^56 - 20 * q^61 + 130 * q^62 - 38 * q^64 + 86 * q^66 - 60 * q^68 + 56 * q^69 + 40 * q^74 + 68 * q^77 - 48 * q^78 - 48 * q^81 - 70 * q^82 - 102 * q^88 + 180 * q^90 - 2 * q^92 - 190 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	−1.39723	−	0.218517i	−0.987990	−	0.154515i
$2$	−1.39723	−	0.218517i	−0.987990	−	0.154515i
$3$	−1.60576	−	0.521744i	−0.927088	−	0.301229i	−0.193717	−	0.981057i	$-0.562054\pi$
$3$	−1.60576	−	0.521744i	−0.927088	−	0.301229i	−0.733371	+	0.679828i	$0.762054\pi$
$4$	1.90450	+	0.610638i	0.952250	+	0.305319i
$5$	−2.10647	−	2.89931i	−0.942042	−	1.29661i	−0.954973	−	0.296693i	$-0.904116\pi$
$5$	−2.10647	−	2.89931i	−0.942042	−	1.29661i	0.0129313	−	0.999916i	$-0.495884\pi$
$6$	2.12961	+	1.07988i	0.869410	+	0.440861i
$7$	−0.788330	+	0.256144i	−0.297961	+	0.0968133i	−0.454182	−	0.890909i	$-0.650069\pi$
$7$	−0.788330	+	0.256144i	−0.297961	+	0.0968133i	0.156222	+	0.987722i	$0.450069\pi$
$8$	−2.52759	−	1.26937i	−0.893638	−	0.448789i
$9$	−0.120789	−	0.0877584i	−0.0402630	−	0.0292528i
$10$	2.30967	+	4.51130i	0.730382	+	1.42660i
$11$	2.24388	−	2.44234i	0.676555	−	0.736392i
$11$	2.24388	−	2.44234i	0.676555	−	0.736392i
$12$	−2.73958	−	1.97420i	−0.790849	−	0.569903i
$13$	−3.47958	−	0.944724i	−0.965063	−	0.262019i
$13$	−3.47958	−	0.944724i	−0.965063	−	0.262019i
$14$	1.15745	−	0.185628i	0.309341	−	0.0496112i
$15$	1.86980	+	5.75464i	0.482779	+	1.48584i
$16$	3.25424	+	2.32592i	0.813561	+	0.581480i
$17$	−3.21575	−	4.42609i	−0.779933	−	1.07349i	−0.995289	−	0.0969501i	$-0.969091\pi$
$17$	−3.21575	−	4.42609i	−0.779933	−	1.07349i	0.215356	−	0.976536i	$-0.430909\pi$
$18$	0.149593	+	0.149013i	0.0352595	+	0.0351227i
$19$	0.773861	+	0.251443i	0.177536	+	0.0576849i	0.396436	−	0.918062i	$-0.370247\pi$
$19$	0.773861	+	0.251443i	0.177536	+	0.0576849i	−0.218900	+	0.975747i	$0.570247\pi$
$20$	−2.24134	−	6.80802i	−0.501180	−	1.52232i
$21$	1.39951			0.305399
$22$	−3.66891	+	2.92218i	−0.782213	+	0.623010i
$23$			0.732905i			0.152821i	0.997076	+	0.0764106i	$0.0243460\pi$
$23$			0.732905i			0.152821i	−0.997076	+	0.0764106i	$0.975654\pi$
$24$	3.39643	+	3.35706i	0.693293	+	0.685257i
$25$	−2.42368	+	7.45932i	−0.484736	+	1.49186i
$26$	4.65534	+	2.08035i	0.912987	+	0.407989i
$27$	3.12542	+	4.30177i	0.601488	+	0.827877i
$28$	−1.65779	+	0.00644191i	−0.313292	+	0.00121741i
$29$	5.90754	−	1.91948i	1.09700	−	0.356438i	0.296054	−	0.955171i	$-0.404329\pi$
$29$	5.90754	−	1.91948i	1.09700	−	0.356438i	0.800949	+	0.598733i	$0.204329\pi$
$30$	−1.35504	−	8.44914i	−0.247396	−	1.54259i
$31$	−1.25555	−	0.912211i	−0.225504	−	0.163838i	0.469297	−	0.883040i	$-0.344507\pi$
$31$	−1.25555	−	0.912211i	−0.225504	−	0.163838i	−0.694801	+	0.719202i	$0.744507\pi$
$32$	−4.03867	−	3.96095i	−0.713943	−	0.700204i
$33$	−4.87742	+	2.75109i	−0.849049	+	0.478903i
$34$	3.52596	+	6.88697i	0.604697	+	1.18111i
$35$	2.40323	+	1.74605i	0.406220	+	0.295136i
$36$	−0.176454	−	0.240894i	−0.0294090	−	0.0401491i
$37$	−4.27047	+	1.38756i	−0.702060	+	0.228113i	−0.638228	−	0.769847i	$-0.720332\pi$
$37$	−4.27047	+	1.38756i	−0.702060	+	0.228113i	−0.0638324	+	0.997961i	$0.520332\pi$
$38$	−1.02632	−	0.520425i	−0.166491	−	0.0844241i
$39$	5.09449	+	3.33246i	0.815771	+	0.533620i
$40$	1.64400	+	10.0021i	0.259939	+	1.58148i
$41$	−0.714521	+	2.19907i	−0.111589	+	0.343437i	−0.991220	−	0.132220i	$-0.957790\pi$
$41$	−0.714521	+	2.19907i	−0.111589	+	0.343437i	0.879631	+	0.475657i	$0.157790\pi$
$42$	−1.95544	−	0.305818i	−0.301731	−	0.0471888i
$43$	1.39822			0.213227			0.106614	−	0.994301i	$-0.465999\pi$
$43$	1.39822			0.213227			0.106614	+	0.994301i	$0.465999\pi$
$44$	5.76485	−	3.28123i	0.869084	−	0.494665i
$45$			0.535065i			0.0797628i
$46$	0.160152	−	1.02404i	0.0236132	−	0.150986i
$47$	−2.14892	+	6.61369i	−0.313452	+	0.964706i	0.662935	+	0.748677i	$0.269311\pi$
$47$	−2.14892	+	6.61369i	−0.313452	+	0.964706i	−0.976387	+	0.216029i	$0.930689\pi$
$48$	−4.01201	−	5.43276i	−0.579084	−	0.784152i
$49$	−5.10726	+	3.71064i	−0.729609	+	0.530092i
$50$	5.01643	−	9.89276i	0.709430	−	1.39905i
$51$	2.85444	+	8.78506i	0.399702	+	1.23015i
$52$	−6.04998	−	3.92399i	−0.838981	−	0.544160i
$53$	1.37028	+	0.995570i	0.188223	+	0.136752i	0.677906	−	0.735148i	$-0.262888\pi$
$53$	1.37028	+	0.995570i	0.188223	+	0.136752i	−0.489683	+	0.871900i	$0.662888\pi$
$54$	−3.42692	−	6.69353i	−0.466345	−	0.910873i
$55$	−11.8077	−	1.36098i	−1.59216	−	0.183515i
$56$	2.31771	+	0.353254i	0.309718	+	0.0472056i
$57$	−1.11145	−	0.807515i	−0.147215	−	0.106958i
$58$	−8.67363	+	1.39105i	−1.13890	+	0.182654i
$59$	3.77526	+	11.6191i	0.491497	+	1.51267i	0.822345	+	0.568989i	$0.192665\pi$
$59$	3.77526	+	11.6191i	0.491497	+	1.51267i	−0.330848	+	0.943684i	$0.607335\pi$
$60$	0.0470246	+	12.1015i	0.00607085	+	1.56229i
$61$	−3.19409	−	4.39629i	−0.408962	−	0.562887i	0.554003	−	0.832515i	$-0.313100\pi$
$61$	−3.19409	−	4.39629i	−0.408962	−	0.562887i	−0.962965	+	0.269627i	$0.913100\pi$
$62$	1.55496	+	1.54893i	0.197480	+	0.196714i
$63$	0.117700	+	0.0382432i	0.0148289	+	0.00481819i
$64$	4.77741	+	6.41688i	0.597176	+	0.802110i
$65$	4.59059	+	12.0784i	0.569393	+	1.49814i
$66$	7.41603	−	2.77810i	0.912850	−	0.341960i
$67$	12.3062			1.50344			0.751719	−	0.659483i	$-0.229225\pi$
$67$	12.3062			1.50344			0.751719	+	0.659483i	$0.229225\pi$
$68$	−3.42165	−	10.3932i	−0.414936	−	1.26036i
$69$	0.382389	−	1.17687i	0.0460342	−	0.141679i
$70$	−2.97632	−	2.96478i	−0.355739	−	0.354359i
$71$	−10.0507	+	7.30225i	−1.19280	+	0.866618i	−0.993557	−	0.113332i	$-0.963847\pi$
$71$	−10.0507	+	7.30225i	−1.19280	+	0.866618i	−0.199240	+	0.979951i	$0.563847\pi$
$72$	0.193907	+	0.375143i	0.0228522	+	0.0442110i
$73$	4.15504	+	12.7879i	0.486310	+	1.49671i	0.830074	+	0.557653i	$0.188298\pi$
$73$	4.15504	+	12.7879i	0.486310	+	1.49671i	−0.343764	+	0.939056i	$0.611702\pi$
$74$	6.27003	−	1.00557i	0.728876	−	0.116895i
$75$	7.78371	−	10.7134i	0.898786	−	1.23707i
$76$	1.32028	+	0.951422i	0.151446	+	0.109136i
$77$	−1.14333	+	2.50012i	−0.130294	+	0.284915i
$78$	−6.38996	−	5.76944i	−0.723521	−	0.653261i
$79$	−0.945887	−	0.687227i	−0.106421	−	0.0773191i	0.533302	−	0.845925i	$-0.320951\pi$
$79$	−0.945887	−	0.687227i	−0.106421	−	0.0773191i	−0.639723	+	0.768606i	$0.720951\pi$
$80$	−0.111405	−	14.3345i	−0.0124555	−	1.60265i
$81$	−2.63585	−	8.11232i	−0.292872	−	0.901369i
$82$	1.47889	−	2.91647i	0.163316	−	0.322070i
$83$	−7.62433	−	10.4940i	−0.836879	−	1.15186i	−0.986603	−	0.163137i	$-0.947839\pi$
$83$	−7.62433	−	10.4940i	−0.836879	−	1.15186i	0.149725	−	0.988728i	$-0.452161\pi$
$84$	2.66537	+	0.854596i	0.290816	+	0.0932441i
$85$	−6.05873	+	18.6469i	−0.657162	+	2.02254i
$86$	−1.95364	−	0.305536i	−0.210666	−	0.0329468i
$87$	−10.4876			−1.12439
$88$	−8.77183	+	3.32492i	−0.935080	+	0.354437i
$89$		−	10.1938i		−	1.08054i	−0.841492	−	0.540270i	$-0.818322\pi$
$89$		−	10.1938i		−	1.08054i	0.841492	−	0.540270i	$-0.181678\pi$
$90$	0.116921	−	0.747609i	0.0123246	−	0.0788049i
$91$	2.98504	−	0.146520i	0.312918	−	0.0153594i
$92$	−0.447539	+	1.39582i	−0.0466592	+	0.145524i
$93$	1.54018	+	2.11987i	0.159709	+	0.219821i
$94$	4.44774	−	8.77127i	0.458749	−	0.904688i
$95$	−0.901105	−	2.77332i	−0.0924514	−	0.284536i
$96$	4.41855	+	8.46751i	0.450966	+	0.864212i
$97$	3.19230	−	4.39382i	0.324129	−	0.446125i	−0.615594	−	0.788064i	$-0.711084\pi$
$97$	3.19230	−	4.39382i	0.324129	−	0.446125i	0.939722	+	0.341939i	$0.111084\pi$
$98$	7.94686	−	4.06860i	0.802754	−	0.410990i
$99$	−0.485372	+	0.0980884i	−0.0487817	+	0.00985826i
$100$	−9.17084	+	12.7263i	−0.917084	+	1.27263i
$101$	10.2720	−	14.1382i	1.02210	−	1.40680i	0.111382	−	0.993778i	$-0.464472\pi$
$101$	10.2720	−	14.1382i	1.02210	−	1.40680i	0.910720	−	0.413025i	$-0.135528\pi$
$102$	−2.06862	−	12.8985i	−0.204824	−	1.27714i
$103$	−9.12178	+	2.96385i	−0.898795	+	0.292036i	−0.721740	−	0.692164i	$-0.756657\pi$
$103$	−9.12178	+	2.96385i	−0.898795	+	0.292036i	−0.177056	+	0.984201i	$0.556657\pi$
$104$	7.59575	+	6.80475i	0.744825	+	0.667260i
$105$	−2.94803	−	4.05762i	−0.287699	−	0.395983i
$106$	−1.69705	−	1.69047i	−0.164832	−	0.164193i
$107$	1.33668	−	4.11388i	0.129222	−	0.397704i	−0.865425	−	0.501039i	$-0.832951\pi$
$107$	1.33668	−	4.11388i	0.129222	−	0.397704i	0.994647	+	0.103335i	$0.0329514\pi$
$108$	3.32554	+	10.1012i	0.320000	+	0.971992i
$109$	11.8736			1.13729			0.568643	−	0.822584i	$-0.307468\pi$
$109$	11.8736			1.13729			0.568643	+	0.822584i	$0.307468\pi$
$110$	16.2007	+	4.48180i	1.54468	+	0.427323i
$111$	7.58132			0.719587
$112$	−3.16119	−	1.00004i	−0.298704	−	0.0944948i
$113$	1.82354	−	5.61229i	0.171545	−	0.527960i	−0.827914	−	0.560855i	$-0.810473\pi$
$113$	1.82354	−	5.61229i	0.171545	−	0.527960i	0.999459	+	0.0328948i	$0.0104726\pi$
$114$	1.37649	+	1.37116i	0.128920	+	0.128420i
$115$	2.12492	−	1.54384i	0.198149	−	0.143964i
$116$	12.4230	−	0.0482740i	1.15345	−	0.00448213i
$117$	0.337388	+	0.419475i	0.0311915	+	0.0387805i
$118$	−2.73594	−	17.0595i	−0.251864	−	1.57045i
$119$	3.66879	+	2.66553i	0.336317	+	0.244349i
$120$	2.57868	−	16.9188i	0.235400	−	1.54447i
$121$	−0.930018	−	10.9606i	−0.0845470	−	0.996419i
$122$	3.50221	+	6.84059i	0.317075	+	0.619318i
$123$	2.29471	−	3.15839i	0.206907	−	0.284783i
$124$	−1.83417	−	2.50399i	−0.164713	−	0.224865i
$125$	9.69055	−	3.14865i	0.866749	−	0.281624i
$126$	−0.156098	−	0.0791541i	−0.0139063	−	0.00705161i
$127$	−2.56960	+	1.86692i	−0.228015	+	0.165662i	−0.695927	−	0.718113i	$-0.745006\pi$
$127$	−2.56960	+	1.86692i	−0.228015	+	0.165662i	0.467912	+	0.883775i	$0.345006\pi$
$128$	−5.27294	−	10.0098i	−0.466066	−	0.884750i
$129$	−2.24522	−	0.729516i	−0.197680	−	0.0642303i
$130$	−3.77476	−	17.8794i	−0.331069	−	1.56813i
$131$	−18.1584			−1.58651			−0.793254	−	0.608890i	$-0.791615\pi$
$131$	−18.1584			−1.58651			−0.793254	+	0.608890i	$0.791615\pi$
$132$	−10.9690	+	2.26111i	−0.954725	+	0.196804i
$133$	−0.674463			−0.0584834
$134$	−17.1946	−	2.68911i	−1.48538	−	0.232304i
$135$	5.88856	−	18.1231i	0.506806	−	1.55979i
$136$	2.50974	+	15.2693i	0.215208	+	1.30933i
$137$	1.44832	+	1.99345i	0.123739	+	0.170312i	0.866392	−	0.499364i	$-0.166433\pi$
$137$	1.44832	+	1.99345i	0.123739	+	0.170312i	−0.742654	+	0.669676i	$0.766433\pi$
$138$	−0.791452	+	1.56080i	−0.0673729	+	0.132864i
$139$	−4.24487	−	13.0644i	−0.360045	−	1.10810i	−0.953026	−	0.302888i	$-0.902049\pi$
$139$	−4.24487	−	13.0644i	−0.360045	−	1.10810i	0.592981	−	0.805216i	$-0.297951\pi$
$140$	3.51075	+	4.79286i	0.296713	+	0.405071i
$141$	6.90132	−	9.49885i	0.581196	−	0.799947i
$142$	15.6388	−	8.00667i	1.31238	−	0.671905i
$143$	−10.1151	+	6.37847i	−0.845867	+	0.533394i
$144$	−0.188958	−	0.566533i	−0.0157465	−	0.0472111i
$145$	−18.0092	−	13.0845i	−1.49558	−	1.08660i
$146$	−3.01116	−	18.7756i	−0.249206	−	1.55388i
$147$	10.1371	−	3.29373i	0.836092	−	0.271663i
$148$	−8.98040	+	0.0348965i	−0.738184	+	0.00286848i
$149$	−6.26781	+	4.55383i	−0.513479	+	0.373064i	−0.814142	−	0.580666i	$-0.802792\pi$
$149$	−6.26781	+	4.55383i	−0.513479	+	0.373064i	0.300663	+	0.953730i	$0.402792\pi$
$150$	−13.2167	+	13.2681i	−1.07914	+	1.08334i
$151$	−19.5439	−	6.35021i	−1.59046	−	0.516773i	−0.625739	−	0.780033i	$-0.715202\pi$
$151$	−19.5439	−	6.35021i	−1.59046	−	0.516773i	−0.964725	+	0.263260i	$0.915202\pi$
$152$	−1.63683	−	1.61786i	−0.132764	−	0.131226i
$153$			0.816833i			0.0660370i
$154$	2.14381	−	3.24341i	0.172753	−	0.261361i
$155$			5.56177i			0.446732i
$156$	7.66752	+	9.45755i	0.613893	+	0.757210i
$157$	2.56708	−	7.90067i	0.204876	−	0.630542i	−0.794843	−	0.606815i	$-0.792447\pi$
$157$	2.56708	−	7.90067i	0.204876	−	0.630542i	0.999718	−	0.0237269i	$-0.00755320\pi$
$158$	1.17145	+	1.16691i	0.0931956	+	0.0928341i
$159$	−1.68092	−	2.31359i	−0.133306	−	0.183480i
$160$	−2.97669	+	20.0530i	−0.235328	+	1.58533i
$161$	−0.187729	−	0.577771i	−0.0147951	−	0.0455347i
$162$	1.91021	+	11.9108i	0.150080	+	0.935797i
$163$	7.67019	+	5.57272i	0.600776	+	0.436489i	0.846154	−	0.532938i	$-0.178912\pi$
$163$	7.67019	+	5.57272i	0.600776	+	0.436489i	−0.245378	+	0.969427i	$0.578912\pi$
$164$	−2.70364	+	3.75182i	−0.211119	+	0.292968i
$165$	18.2504	+	8.34604i	1.42079	+	0.649739i
$166$	8.35982	+	16.3286i	0.648848	+	1.26734i
$167$	−3.79429	+	5.22239i	−0.293611	+	0.404121i	−0.930183	−	0.367097i	$-0.880352\pi$
$167$	−3.79429	+	5.22239i	−0.293611	+	0.404121i	0.636572	+	0.771217i	$0.280352\pi$
$168$	−3.53740	−	1.77650i	−0.272916	−	0.137060i
$169$	11.2150	+	6.57449i	0.862692	+	0.505730i
$170$	12.5401	−	24.7300i	0.961782	−	1.89671i
$171$	−0.0714078	−	0.0982844i	−0.00546069	−	0.00751599i
$172$	2.66292	+	0.853809i	0.203046	+	0.0651023i
$173$	−7.92050	−	2.57353i	−0.602184	−	0.195662i	−0.00796999	−	0.999968i	$-0.502537\pi$
$173$	−7.92050	−	2.57353i	−0.602184	−	0.195662i	−0.594214	+	0.804307i	$0.702537\pi$
$174$	14.6536	+	2.29172i	1.11088	+	0.173735i
$175$		−	6.50121i		−	0.491446i
$176$	12.9828	−	2.72887i	0.978616	−	0.205696i
$177$		−	20.6272i		−	1.55044i
$178$	−2.22752	+	14.2431i	−0.166960	+	1.06756i
$179$	10.2704	+	3.33706i	0.767646	+	0.249423i	0.666557	−	0.745454i	$-0.267767\pi$
$179$	10.2704	+	3.33706i	0.767646	+	0.249423i	0.101089	+	0.994877i	$0.467767\pi$
$180$	−0.326731	+	1.01903i	−0.0243531	+	0.0759541i
$181$	−5.95203	+	4.32440i	−0.442411	+	0.321430i	−0.786592	−	0.617473i	$-0.788157\pi$
$181$	−5.95203	+	4.32440i	−0.442411	+	0.321430i	0.344181	+	0.938903i	$0.388157\pi$
$182$	−4.20281	−	0.447563i	−0.311533	−	0.0331756i
$183$	2.83522	+	8.72591i	0.209585	+	0.645038i
$184$	0.930326	−	1.85248i	0.0685845	−	0.136567i
$185$	13.0186	+	9.45854i	0.957144	+	0.695406i
$186$	−1.68875	−	3.29850i	−0.123825	−	0.241858i
$187$	−18.0258	−	2.07768i	−1.31817	−	0.151935i
$188$	−8.13119	+	11.2836i	−0.593028	+	0.822939i
$189$	−3.56574	−	2.59066i	−0.259369	−	0.188443i
$190$	0.653032	+	4.07187i	0.0473760	+	0.295404i
$191$	16.8780	−	5.48401i	1.22125	−	0.396809i	0.373714	−	0.927544i	$-0.378084\pi$
$191$	16.8780	−	5.48401i	1.22125	−	0.396809i	0.847538	+	0.530735i	$0.178084\pi$
$192$	−4.32342	−	12.7966i	−0.312016	−	0.923514i
$193$	5.24605	−	3.81148i	0.377619	−	0.274356i	−0.382744	−	0.923854i	$-0.625021\pi$
$193$	5.24605	−	3.81148i	0.377619	−	0.274356i	0.760363	+	0.649498i	$0.225021\pi$
$194$	−5.42050	+	5.44160i	−0.389169	+	0.390684i
$195$	−1.06956	−	21.7902i	−0.0765929	−	1.56043i
$196$	−11.9926	+	3.94823i	−0.856618	+	0.282017i
$197$	−23.2715			−1.65803			−0.829014	−	0.559228i	$-0.811098\pi$
$197$	−23.2715			−1.65803			−0.829014	+	0.559228i	$0.811098\pi$
$198$	0.699610	−	0.0309898i	0.0497191	−	0.00220235i
$199$			25.0610i			1.77653i	0.459335	+	0.888263i	$0.348088\pi$
$199$			25.0610i			1.77653i	−0.459335	+	0.888263i	$0.651912\pi$
$200$	15.5947	−	15.7775i	1.10271	−	1.11564i
$201$	−19.7608	−	6.42068i	−1.39382	−	0.452880i
$202$	−17.4418	+	17.5097i	−1.22720	+	1.23198i
$203$	−4.16543	+	3.02636i	−0.292356	+	0.212409i
$204$	0.0717880	+	18.4742i	0.00502616	+	1.29345i
$205$	7.88090	−	2.56066i	0.550426	−	0.178844i
$206$	13.3929	−	2.14790i	0.933125	−	0.149652i
$207$	0.0643186	−	0.0885269i	0.00447045	−	0.00615304i
$208$	−9.12605	−	11.1676i	−0.632778	−	0.774333i
$209$	2.35056	−	1.32582i	0.162591	−	0.0917090i
$210$	3.23242	+	6.31362i	0.223058	+	0.435681i
$211$	19.7789	+	14.3702i	1.36163	+	0.989285i	0.998339	+	0.0576109i	$0.0183483\pi$
$211$	19.7789	+	14.3702i	1.36163	+	0.989285i	0.363295	+	0.931674i	$0.381652\pi$
$212$	2.00177	+	2.73281i	0.137482	+	0.187690i
$213$	19.9490	−	6.48181i	1.36688	−	0.444126i
$214$	−2.76661	+	5.45595i	−0.189121	+	0.372961i
$215$	−2.94532	−	4.05388i	−0.200869	−	0.276472i
$216$	−2.43925	−	14.8404i	−0.165970	−	1.00976i
$217$	1.22345	+	0.397522i	0.0830529	+	0.0269855i
$218$	−16.5902	−	2.59459i	−1.12363	−	0.175728i
$219$		−	22.7022i		−	1.53407i
$220$	−21.6568	−	9.80225i	−1.46010	−	0.660868i
$221$	7.00802	+	18.4390i	0.471410	+	1.24034i
$222$	−10.5928	−	1.65665i	−0.710945	−	0.111187i
$223$	4.16789	−	12.8274i	0.279102	−	0.858988i	−0.709002	−	0.705206i	$-0.750855\pi$
$223$	4.16789	−	12.8274i	0.279102	−	0.858988i	0.988105	−	0.153782i	$-0.0491455\pi$
$224$	4.19838	+	2.08806i	0.280516	+	0.139514i
$225$	0.947372	−	0.688306i	0.0631581	−	0.0458871i
$226$	−3.77429	+	7.44318i	−0.251062	+	0.495113i
$227$	7.53275	−	2.44754i	0.499966	−	0.162449i	−0.0481681	−	0.998839i	$-0.515338\pi$
$227$	7.53275	−	2.44754i	0.499966	−	0.162449i	0.548134	+	0.836390i	$0.315338\pi$
$228$	−1.62366	−	2.21661i	−0.107529	−	0.146798i
$229$	−2.90785	+	4.00232i	−0.192156	+	0.264480i	−0.894214	−	0.447639i	$-0.852265\pi$
$229$	−2.90785	+	4.00232i	−0.192156	+	0.264480i	0.702058	+	0.712120i	$0.252265\pi$
$230$	−3.30635	+	1.69277i	−0.218014	+	0.111618i
$231$	3.14034	−	3.41808i	0.206619	−	0.224893i
$232$	−17.3684	−	2.64720i	−1.14029	−	0.173797i
$233$	−14.0947	+	19.3997i	−0.923374	+	1.27092i	0.0390140	+	0.999239i	$0.487578\pi$
$233$	−14.0947	+	19.3997i	−0.923374	+	1.27092i	−0.962388	+	0.271677i	$0.912422\pi$
$234$	−0.379746	−	0.659828i	−0.0248248	−	0.0431343i
$235$	23.7018	−	7.70117i	1.54613	−	0.502369i
$236$	0.0949463	+	24.4338i	0.00618048	+	1.59051i
$237$	1.16031	+	1.59704i	0.0753706	+	0.103739i
$238$	−4.54367	−	4.52605i	−0.294522	−	0.293380i
$239$	−3.74334	−	1.21628i	−0.242136	−	0.0786748i	0.185435	−	0.982657i	$-0.440631\pi$
$239$	−3.74334	−	1.21628i	−0.242136	−	0.0786748i	−0.427571	+	0.903982i	$0.640631\pi$
$240$	−7.30007	+	23.0760i	−0.471217	+	1.48955i
$241$	7.47995			0.481826			0.240913	−	0.970547i	$-0.422553\pi$
$241$	7.47995			0.481826			0.240913	+	0.970547i	$0.422553\pi$
$242$	−1.09564	+	15.5177i	−0.0704303	+	0.997517i
$243$		−	1.55014i		−	0.0994417i
$244$	−3.39861	−	10.3232i	−0.217574	−	0.660873i
$245$	21.5166	+	6.99116i	1.37464	+	0.446649i
$246$	−3.89639	+	3.91156i	−0.248425	+	0.249392i
$247$	−2.45517	−	1.60600i	−0.156219	−	0.102187i
$248$	2.01558	+	3.89945i	0.127990	+	0.247615i
$249$	6.76770	+	20.8288i	0.428885	+	1.31997i
$250$	−14.2280	+	2.28183i	−0.899855	+	0.144316i
$251$	−5.00399	+	6.88740i	−0.315849	+	0.434729i	−0.937194	−	0.348808i	$-0.886586\pi$
$251$	−5.00399	+	6.88740i	−0.315849	+	0.434729i	0.621345	+	0.783537i	$0.286586\pi$
$252$	0.200808	+	0.144707i	0.0126497	+	0.00911566i
$253$	1.79000	+	1.64455i	0.112536	+	0.103392i
$254$	3.99827	−	2.04701i	0.250874	−	0.128441i
$255$	19.4578	−	26.7814i	1.21849	−	1.67711i
$256$	5.18019	+	15.1382i	0.323762	+	0.946139i
$257$	−6.50719	−	20.0271i	−0.405907	−	1.24925i	−0.920135	−	0.391600i	$-0.871922\pi$
$257$	−6.50719	−	20.0271i	−0.405907	−	1.24925i	0.514228	−	0.857653i	$-0.328078\pi$
$258$	2.97767	+	1.50992i	0.185382	+	0.0940035i
$259$	3.01112	−	2.18771i	0.187102	−	0.135938i
$260$	1.36724	+	25.8065i	0.0847928	+	1.60045i
$261$	−0.882017	−	0.286585i	−0.0545955	−	0.0177391i
$262$	25.3715	+	3.96793i	1.56746	+	0.245140i
$263$	−1.01125			−0.0623566			−0.0311783	−	0.999514i	$-0.509926\pi$
$263$	−1.01125			−0.0623566			−0.0311783	+	0.999514i	$0.509926\pi$
$264$	15.8202	−	0.762378i	0.973669	−	0.0469211i
$265$		−	6.07001i		−	0.372878i
$266$	0.942380	+	0.147382i	0.0577810	+	0.00903657i
$267$	−5.31856	+	16.3688i	−0.325490	+	1.00176i
$268$	23.4371	+	7.51462i	1.43165	+	0.459029i
$269$	−24.9656	+	18.1386i	−1.52218	+	1.10593i	−0.561786	+	0.827282i	$0.689886\pi$
$269$	−24.9656	+	18.1386i	−1.52218	+	1.10593i	−0.960394	+	0.278646i	$0.910114\pi$
$270$	−12.1879	+	24.0354i	−0.741731	+	1.46275i
$271$	−6.73036	+	2.18683i	−0.408840	+	0.132840i	−0.506215	−	0.862408i	$-0.668956\pi$
$271$	−6.73036	+	2.18683i	−0.408840	+	0.132840i	0.0973743	+	0.995248i	$0.468956\pi$
$272$	−0.170072	−	21.8832i	−0.0103121	−	1.32686i
$273$	−4.86972	−	1.32215i	−0.294729	−	0.0800204i
$274$	−1.58804	−	3.10179i	−0.0959368	−	0.187386i
$275$	12.7797	+	22.6572i	0.770646	+	1.36628i
$276$	1.44690	−	2.00785i	0.0870933	−	0.120858i
$277$	−8.41999	+	11.5891i	−0.505908	+	0.696322i	−0.983223	−	0.182410i	$-0.941610\pi$
$277$	−8.41999	+	11.5891i	−0.505908	+	0.696322i	0.477315	+	0.878732i	$0.341610\pi$
$278$	3.07626	+	19.1815i	0.184502	+	1.15043i
$279$	0.0716027	+	0.220370i	0.00428674	+	0.0131932i
$280$	−3.85800	−	7.46388i	−0.230560	−	0.446052i
$281$	−10.8301	+	7.86855i	−0.646072	+	0.469398i	−0.861931	−	0.507026i	$-0.830745\pi$
$281$	−10.8301	+	7.86855i	−0.646072	+	0.469398i	0.215859	+	0.976425i	$0.430745\pi$
$282$	−11.7184	+	11.7640i	−0.697820	+	0.700537i
$283$	−1.88182	+	5.79164i	−0.111862	+	0.344277i	−0.991280	−	0.131775i	$-0.957933\pi$
$283$	−1.88182	+	5.79164i	−0.111862	+	0.344277i	0.879417	+	0.476052i	$0.157933\pi$
$284$	−23.6006	+	7.76981i	−1.40044	+	0.461053i
$285$			4.92344i			0.291639i
$286$	15.5269	−	6.70186i	0.918126	−	0.396289i
$287$		−	1.91661i		−	0.113134i
$288$	0.140220	+	0.832867i	0.00826255	+	0.0490772i
$289$	−3.99600	+	12.2984i	−0.235059	+	0.723437i
$290$	22.3038	+	22.2173i	1.30972	+	1.30465i
$291$	−7.41853	+	5.38988i	−0.434882	+	0.315960i
$292$	0.104497	+	26.8918i	0.00611525	+	1.57372i
$293$	−8.81204	−	27.1207i	−0.514805	−	1.58441i	−0.783637	−	0.621219i	$-0.786638\pi$
$293$	−8.81204	−	27.1207i	−0.514805	−	1.58441i	0.268833	−	0.963187i	$-0.413362\pi$
$294$	−14.8836	+	2.38698i	−0.868026	+	0.139211i
$295$	25.7347	−	35.4208i	1.49833	−	2.06228i
$296$	12.5553	+	1.91362i	0.729762	+	0.111227i
$297$	17.5195	+	2.01933i	1.01658	+	0.117173i
$298$	9.75265	−	4.99312i	0.564956	−	0.289243i
$299$	0.692393	−	2.55020i	0.0400421	−	0.147482i
$300$	21.3661	−	15.6506i	1.23357	−	0.903586i
$301$	−1.10226	+	0.358147i	−0.0635333	+	0.0206432i
$302$	25.9197	+	13.1434i	1.49151	+	0.756318i
$303$	−23.8709	+	17.3432i	−1.37135	+	0.996343i
$304$	1.93350	+	2.61819i	0.110894	+	0.150164i
$305$	−6.01794	+	18.5213i	−0.344586	+	1.06053i
$306$	0.178492	−	1.14130i	0.0102037	−	0.0652439i
$307$			8.24937i			0.470817i	0.971897	+	0.235408i	$0.0756427\pi$
$307$			8.24937i			0.470817i	−0.971897	+	0.235408i	$0.924357\pi$
$308$	−3.70414	+	4.06333i	−0.211063	+	0.231529i
$309$	16.1938			0.921233
$310$	1.21534	−	7.77107i	0.0690269	−	0.441367i
$311$	−8.22187	−	2.67145i	−0.466220	−	0.151484i	0.0664811	−	0.997788i	$-0.478823\pi$
$311$	−8.22187	−	2.67145i	−0.466220	−	0.151484i	−0.532701	+	0.846304i	$0.678823\pi$
$312$	−8.64665	−	14.8899i	−0.489520	−	0.842972i
$313$	−19.0782	+	13.8612i	−1.07837	+	0.783479i	−0.977397	−	0.211411i	$-0.932194\pi$
$313$	−19.0782	+	13.8612i	−1.07837	+	0.783479i	−0.100969	+	0.994890i	$0.532194\pi$
$314$	−5.31324	+	10.4781i	−0.299843	+	0.591313i
$315$	−0.137054	−	0.421808i	−0.00772210	−	0.0237662i
$316$	−1.38180	−	1.88642i	−0.0777321	−	0.106119i
$317$	5.88521	−	8.10030i	0.330546	−	0.454958i	−0.611104	−	0.791550i	$-0.709274\pi$
$317$	5.88521	−	8.10030i	0.330546	−	0.454958i	0.941651	+	0.336592i	$0.109274\pi$
$318$	1.84307	+	3.59992i	0.103354	+	0.201874i
$319$	8.56780	−	18.7353i	0.479705	−	1.04897i
$320$	8.54103	−	27.3681i	0.477458	−	1.52993i
$321$	−4.29279	+	5.90852i	−0.239600	+	0.329781i
$322$	0.136048	+	0.848300i	0.00758164	+	0.0472739i
$323$	−1.37563	−	4.23376i	−0.0765422	−	0.235573i
$324$	−0.0662906	−	17.0595i	−0.00368281	−	0.947748i
$325$	15.4804	−	23.6656i	0.858697	−	1.31273i
$326$	−9.49929	−	9.46244i	−0.526117	−	0.524076i
$327$	−19.0662	−	6.19500i	−1.05437	−	0.342584i
$328$	4.59745	−	4.65135i	0.253851	−	0.256828i
$329$		−	5.76421i		−	0.317791i
$330$	−23.6762	−	15.6494i	−1.30333	−	0.861469i
$331$	−32.6788			−1.79619			−0.898095	−	0.439801i	$-0.855049\pi$
$331$	−32.6788			−1.79619			−0.898095	+	0.439801i	$0.855049\pi$
$332$	−8.11251	−	24.6415i	−0.445232	−	1.35238i
$333$	0.637596	+	0.207167i	0.0349400	+	0.0113527i
$334$	6.44268	−	6.46776i	0.352528	−	0.353900i
$335$	−25.9226	−	35.6794i	−1.41630	−	1.94937i
$336$	4.55436	+	3.25516i	0.248461	+	0.177583i
$337$	−1.76620	+	0.573873i	−0.0962110	+	0.0312609i	−0.356727	−	0.934209i	$-0.616107\pi$
$337$	−1.76620	+	0.573873i	−0.0962110	+	0.0312609i	0.260516	+	0.965470i	$0.416107\pi$
$338$	−14.2333	−	11.6367i	−0.774188	−	0.632956i
$339$	−5.85636	+	8.06059i	−0.318074	+	0.437791i
$340$	−22.9253	+	31.8133i	−1.24330	+	1.72532i
$341$	−5.04523	+	1.01959i	−0.273215	+	0.0552137i
$342$	0.0782962	+	0.152930i	0.00423377	+	0.00826949i
$343$	6.48625	−	8.92756i	0.350225	−	0.482043i
$344$	−3.53413	−	1.77486i	−0.190548	−	0.0956941i
$345$	−4.21760	+	1.37038i	−0.227068	+	0.0737789i
$346$	10.5044	+	5.32657i	0.564720	+	0.286358i
$347$	10.9334	−	7.94357i	0.586935	−	0.426433i	−0.254283	−	0.967130i	$-0.581839\pi$
$347$	10.9334	−	7.94357i	0.586935	−	0.426433i	0.841218	+	0.540697i	$0.181839\pi$
$348$	−19.9736	−	6.40413i	−1.07070	−	0.343297i
$349$	2.85385	−	8.78326i	0.152763	−	0.470157i	−0.845164	−	0.534507i	$-0.820497\pi$
$349$	2.85385	−	8.78326i	0.152763	−	0.470157i	0.997927	+	0.0643499i	$0.0204974\pi$
$350$	−1.42063	+	9.08369i	−0.0759358	+	0.485543i
$351$	−6.81117	−	17.9210i	−0.363554	−	0.956555i
$352$	−18.7363	+	0.975891i	−0.998646	+	0.0520152i
$353$			8.33524i			0.443640i	0.975088	+	0.221820i	$0.0711997\pi$
$353$			8.33524i			0.443640i	−0.975088	+	0.221820i	$0.928800\pi$
$354$	−4.50740	+	28.8209i	−0.239566	+	1.53182i
$355$	42.3429	+	13.7581i	2.24733	+	0.730202i
$356$	6.22472	−	19.4141i	0.329909	−	1.02894i
$357$	−4.50048	−	6.19438i	−0.238191	−	0.327841i
$358$	−13.6209	−	6.90690i	−0.719887	−	0.365041i
$359$	−15.2004	+	4.93891i	−0.802247	+	0.260666i	−0.681311	−	0.731994i	$-0.738590\pi$
$359$	−15.2004	+	4.93891i	−0.802247	+	0.260666i	−0.120936	+	0.992660i	$0.538590\pi$
$360$	0.679194	−	1.35242i	0.0357967	−	0.0712790i
$361$	−14.8357	−	10.7788i	−0.780826	−	0.567303i
$362$	9.26131	−	4.74156i	0.486764	−	0.249211i
$363$	−4.22525	+	18.0854i	−0.221768	+	0.949237i
$364$	5.77449	+	1.54374i	0.302665	+	0.0809137i
$365$	28.3235	−	38.9840i	1.48252	−	2.04052i
$366$	−2.05469	−	12.8116i	−0.107400	−	0.669675i
$367$	−24.8799	+	8.08398i	−1.29872	+	0.421980i	−0.875137	−	0.483876i	$-0.839229\pi$
$367$	−24.8799	+	8.08398i	−1.29872	+	0.421980i	−0.423586	+	0.905856i	$0.639229\pi$
$368$	−1.70468	+	2.38505i	−0.0888625	+	0.124329i
$369$	0.279293	−	0.202918i	0.0145394	−	0.0105635i
$370$	−16.1231	−	16.0605i	−0.838198	−	0.834948i
$371$	−1.33525	−	0.433847i	−0.0693225	−	0.0225242i
$372$	1.63879	+	4.97779i	0.0849675	+	0.258086i
$373$			8.22058i			0.425645i	0.977091	+	0.212823i	$0.0682657\pi$
$373$			8.22058i			0.425645i	−0.977091	+	0.212823i	$0.931734\pi$
$374$	24.7321	+	6.84195i	1.27887	+	0.353789i
$375$	−17.2035			−0.888387
$376$	13.8268	−	13.9889i	0.713062	−	0.721424i
$377$	−22.3692	+	1.09798i	−1.15207	+	0.0565488i
$378$	4.41605	+	4.39892i	0.227137	+	0.226256i
$379$	−3.58420	+	2.60407i	−0.184108	+	0.133762i	−0.676022	−	0.736882i	$-0.736298\pi$
$379$	−3.58420	+	2.60407i	−0.184108	+	0.133762i	0.491914	+	0.870644i	$0.336298\pi$
$380$	−0.0226624	−	5.83203i	−0.00116256	−	0.299177i
$381$	5.10022	−	1.65716i	0.261292	−	0.0848990i
$382$	−24.7808	+	3.97427i	−1.26790	+	0.203341i
$383$	24.8771	+	18.0742i	1.27116	+	0.923551i	0.999248	−	0.0387718i	$-0.0123446\pi$
$383$	24.8771	+	18.0742i	1.27116	+	0.923551i	0.271910	+	0.962323i	$0.412345\pi$
$384$	3.24454	+	18.8245i	0.165572	+	0.960634i
$385$	9.65701	−	1.95158i	0.492167	−	0.0994616i
$386$	−8.16281	+	4.17916i	−0.415476	+	0.212714i
$387$	−0.168890	−	0.122706i	−0.00858517	−	0.00623749i
$388$	8.76276	−	6.41869i	0.444862	−	0.325860i
$389$	6.29087	+	19.3613i	0.318960	+	0.981657i	0.974094	+	0.226144i	$0.0726121\pi$
$389$	6.29087	+	19.3613i	0.318960	+	0.981657i	−0.655134	+	0.755513i	$0.727388\pi$
$390$	−3.26711	+	30.6796i	−0.165437	+	1.55352i
$391$	3.24391	−	2.35684i	0.164051	−	0.119190i
$392$	17.6192	−	2.89599i	0.889906	−	0.146269i
$393$	29.1581	+	9.47406i	1.47083	+	0.477903i
$394$	32.5157	+	5.08524i	1.63812	+	0.256191i
$395$			4.19004i			0.210824i
$396$	−0.984287	−	0.109577i	−0.0494623	−	0.00550645i
$397$			3.40886i			0.171086i	0.996334	+	0.0855428i	$0.0272624\pi$
$397$			3.40886i			0.171086i	−0.996334	+	0.0855428i	$0.972738\pi$
$398$	5.47626	−	35.0160i	0.274500	−	1.75519i
$399$	1.08303	+	0.351897i	0.0542193	+	0.0176169i
$400$	−25.2370	+	18.6371i	−1.26185	+	0.931857i
$401$	7.83681	+	10.7864i	0.391351	+	0.538649i	0.958547	−	0.284934i	$-0.0919717\pi$
$401$	7.83681	+	10.7864i	0.391351	+	0.538649i	−0.567196	+	0.823583i	$0.691972\pi$
$402$	26.2074	+	13.2892i	1.30710	+	0.662807i
$403$	3.50701	+	4.36026i	0.174696	+	0.217200i
$404$	28.1963	−	20.6537i	1.40282	−	1.02756i
$405$	−17.9678	+	24.7305i	−0.892825	+	1.22887i
$406$	6.48137	−	3.31830i	0.321665	−	0.164685i
$407$	−6.19352	+	13.5434i	−0.307002	+	0.671323i
$408$	3.93663	−	25.8284i	0.194892	−	1.27869i
$409$	27.5944	+	20.0485i	1.36446	+	0.991335i	0.998147	+	0.0608414i	$0.0193784\pi$
$409$	27.5944	+	20.0485i	1.36446	+	0.991335i	0.366308	+	0.930494i	$0.380622\pi$
$410$	−11.5710	+	1.85571i	−0.571449	+	0.0916472i
$411$	−1.28560	−	3.95666i	−0.0634138	−	0.195168i
$412$	−19.1823	+	0.0745395i	−0.945042	+	0.00367230i
$413$	−5.95230	−	8.19264i	−0.292894	−	0.403134i
$414$	−0.109212	+	0.109638i	−0.00536750	+	0.00538840i
$415$	−14.3649	+	44.2105i	−0.705144	+	2.17021i
$416$	10.3109	+	17.5979i	0.505532	+	0.862808i
$417$			23.1930i			1.13577i
$418$	−3.57398	+	1.33884i	−0.174809	+	0.0654848i
$419$		−	30.9341i		−	1.51123i	−0.655015	−	0.755616i	$-0.727338\pi$
$419$		−	30.9341i		−	1.51123i	0.655015	−	0.755616i	$-0.272662\pi$
$420$	−3.13679	−	9.52792i	−0.153060	−	0.464915i
$421$	−20.0871	−	6.52670i	−0.978987	−	0.318092i	−0.224548	−	0.974463i	$-0.572091\pi$
$421$	−20.0871	−	6.52670i	−0.978987	−	0.318092i	−0.754438	+	0.656371i	$0.772091\pi$
$422$	−24.4955	−	24.4005i	−1.19242	−	1.18780i
$423$	0.839973	−	0.610276i	0.0408409	−	0.0296727i
$424$	−2.19977	−	4.25579i	−0.106830	−	0.206679i
$425$	40.8096	−	13.2598i	1.97956	−	0.643197i
$426$	−29.2897	+	4.69738i	−1.41909	+	0.227589i
$427$	3.64408	+	2.64758i	0.176349	+	0.128125i
$428$	5.05780	−	7.01866i	0.244478	−	0.339260i
$429$	19.5704	−	4.96482i	0.944867	−	0.239704i
$430$	3.22944	+	6.30780i	0.155737	+	0.304189i
$431$	−9.62778	+	13.2515i	−0.463754	+	0.638302i	−0.975282	−	0.220964i	$-0.929080\pi$
$431$	−9.62778	+	13.2515i	−0.463754	+	0.638302i	0.511528	+	0.859267i	$0.329080\pi$
$432$	0.165295	+	21.2685i	0.00795276	+	1.02328i
$433$	−7.88256	−	24.2600i	−0.378812	−	1.16586i	−0.940871	−	0.338765i	$-0.889991\pi$
$433$	−7.88256	−	24.2600i	−0.378812	−	1.16586i	0.562059	−	0.827097i	$-0.310009\pi$
$434$	−1.62257	−	0.822773i	−0.0778858	−	0.0394944i
$435$	22.0918	+	30.4068i	1.05922	+	1.45789i
$436$	22.6133	+	7.25048i	1.08298	+	0.347235i
$437$	−0.184283	+	0.567166i	−0.00881548	+	0.0271312i
$438$	−4.96083	+	31.7202i	−0.237037	+	1.51565i
$439$	23.2926			1.11170			0.555848	−	0.831284i	$-0.312394\pi$
$439$	23.2926			1.11170			0.555848	+	0.831284i	$0.312394\pi$
$440$	28.1175	+	18.4284i	1.34045	+	0.878539i
$441$	0.942542			0.0448830
$442$	−5.76257	−	27.2948i	−0.274098	−	1.29828i
$443$	−31.4566	−	10.2209i	−1.49455	−	0.485609i	−0.556127	−	0.831097i	$-0.687713\pi$
$443$	−31.4566	−	10.2209i	−1.49455	−	0.485609i	−0.938423	+	0.345489i	$0.887713\pi$
$444$	14.4386	+	4.62944i	0.685226	+	0.219703i
$445$	−29.5549	+	21.4729i	−1.40104	+	1.01791i
$446$	−8.62651	+	17.0121i	−0.408477	+	0.805547i
$447$	12.4406	−	4.04218i	0.588418	−	0.191189i
$448$	−5.40982	−	3.83491i	−0.255590	−	0.181183i
$449$	13.4429	−	18.5025i	0.634408	−	0.873187i	−0.363894	−	0.931440i	$-0.618553\pi$
$449$	13.4429	−	18.5025i	0.634408	−	0.873187i	0.998302	+	0.0582530i	$0.0185530\pi$
$450$	−1.47410	+	0.754704i	−0.0694899	+	0.0355771i
$451$	3.76757	+	6.67955i	0.177408	+	0.314528i
$452$	6.90002	−	9.57508i	0.324550	−	0.450374i
$453$	28.0698	+	20.3939i	1.31883	+	0.958189i
$454$	−11.0598	+	1.77374i	−0.519063	+	0.0832455i
$455$	−6.71271	−	8.34592i	−0.314697	−	0.391263i
$456$	1.78425	+	3.45191i	0.0835553	+	0.161650i
$457$	15.9045	−	11.5553i	0.743982	−	0.540535i	−0.149974	−	0.988690i	$-0.547919\pi$
$457$	15.9045	−	11.5553i	0.743982	−	0.540535i	0.893956	+	0.448155i	$0.147919\pi$
$458$	4.93751	−	4.95674i	0.230715	−	0.231613i
$459$	8.98950	−	27.6668i	0.419594	−	1.29138i
$460$	4.98963	−	1.64269i	0.232643	−	0.0765909i
$461$	−33.4890			−1.55974			−0.779869	−	0.625943i	$-0.784714\pi$
$461$	−33.4890			−1.55974			−0.779869	+	0.625943i	$0.784714\pi$
$462$	−5.13469	+	4.08963i	−0.238887	+	0.190267i
$463$	28.9036			1.34326			0.671632	−	0.740885i	$-0.265593\pi$
$463$	28.9036			1.34326			0.671632	+	0.740885i	$0.265593\pi$
$464$	23.6891	+	7.49403i	1.09974	+	0.347902i
$465$	2.90182	−	8.93090i	0.134569	−	0.414160i
$466$	23.9327	−	24.0259i	1.10866	−	1.11298i
$467$	17.2705	+	23.7708i	0.799184	+	1.09998i	0.992903	+	0.118926i	$0.0379451\pi$
$467$	17.2705	+	23.7708i	0.799184	+	1.09998i	−0.193719	+	0.981057i	$0.562055\pi$
$468$	0.386408	+	1.00491i	0.0178617	+	0.0464521i
$469$	−9.70133	+	3.15215i	−0.447966	+	0.145553i
$470$	−34.7996	+	5.58105i	−1.60519	+	0.257435i
$471$	−8.24426	+	11.3473i	−0.379876	+	0.522854i
$472$	5.20656	−	34.1604i	0.239651	−	1.57236i
$473$	3.13744	−	3.41493i	0.144260	−	0.157019i
$474$	−1.27225	−	2.48498i	−0.0584362	−	0.114139i
$475$	−3.75118	+	5.16306i	−0.172116	+	0.236897i
$476$	5.35953	+	7.31680i	0.245654	+	0.335365i
$477$	−0.0781458	−	0.240508i	−0.00357805	−	0.0110121i
$478$	4.96452	+	2.51741i	0.227072	+	0.115144i
$479$	−9.92871	−	13.6657i	−0.453654	−	0.624401i	0.519524	−	0.854456i	$-0.326109\pi$
$479$	−9.92871	−	13.6657i	−0.453654	−	0.624401i	−0.973178	+	0.230055i	$0.926109\pi$
$480$	15.2424	−	30.6473i	0.695716	−	1.39885i
$481$	16.1703	−	0.793712i	0.737302	−	0.0361902i
$482$	−10.4512	−	1.63450i	−0.476040	−	0.0744494i
$483$			1.02571i			0.0466714i
$484$	4.92175	−	21.4424i	0.223716	−	0.974654i
$485$	−19.4635			−0.883792
$486$	−0.338733	+	2.16590i	−0.0153652	+	0.0982474i
$487$	5.51718	−	16.9801i	0.250007	−	0.769444i	−0.744765	−	0.667327i	$-0.767438\pi$
$487$	5.51718	−	16.9801i	0.250007	−	0.769444i	0.994772	−	0.102117i	$-0.0325616\pi$
$488$	2.49284	+	15.1665i	0.112846	+	0.686555i
$489$	−9.40899	−	12.9504i	−0.425489	−	0.585636i
$490$	−28.5359	−	14.4700i	−1.28912	−	0.653688i
$491$	−8.78518	−	27.0380i	−0.396469	−	1.22021i	−0.927811	−	0.373050i	$-0.878312\pi$
$491$	−8.78518	−	27.0380i	−0.396469	−	1.22021i	0.531342	−	0.847158i	$-0.321688\pi$
$492$	6.29890	−	4.61392i	0.283976	−	0.208012i
$493$	−27.4929	−	19.9748i	−1.23822	−	0.899619i
$494$	3.07950	+	2.78045i	0.138553	+	0.125098i
$495$	1.30681	+	1.20062i	0.0587367	+	0.0539639i
$496$	−1.96414	−	5.88887i	−0.0881923	−	0.264418i
$497$	6.05283	−	8.33101i	0.271507	−	0.373697i
$498$	−4.90456	−	30.5815i	−0.219779	−	1.37039i
$499$	9.82492	+	30.2380i	0.439824	+	1.35364i	0.888062	+	0.459725i	$0.152052\pi$
$499$	9.82492	+	30.2380i	0.439824	+	1.35364i	−0.448238	+	0.893915i	$0.647948\pi$
$500$	20.3783	−	0.0791873i	0.911347	−	0.00354136i
$501$	8.81749	−	6.40628i	0.393936	−	0.286211i
$502$	8.49674	−	8.52982i	0.379228	−	0.380704i
$503$	−3.00088	+	9.23576i	−0.133803	+	0.411802i	−0.995402	−	0.0957870i	$-0.969463\pi$
$503$	−3.00088	+	9.23576i	−0.133803	+	0.411802i	0.861599	+	0.507589i	$0.169463\pi$
$504$	−0.248954	−	0.246068i	−0.0110893	−	0.0109608i
$505$	−62.6286			−2.78694
$506$	−2.14168	−	2.68896i	−0.0952092	−	0.119539i
$507$	−14.5784	−	16.4084i	−0.647451	−	0.728725i
$508$	−6.03381	+	1.98646i	−0.267707	+	0.0881348i
$509$	1.35225	+	0.439374i	0.0599376	+	0.0194749i	0.338832	−	0.940847i	$-0.389968\pi$
$509$	1.35225	+	0.439374i	0.0599376	+	0.0194749i	−0.278895	+	0.960322i	$0.589968\pi$
$510$	−33.0392	+	33.1678i	−1.46300	+	1.46870i
$511$	−6.55108	−	9.01679i	−0.289803	−	0.398879i
$512$	−3.92994	−	22.2835i	−0.173681	−	0.984802i
$513$	1.33699	+	4.11484i	0.0590297	+	0.181675i
$514$	4.71577	+	29.4043i	0.208004	+	1.29697i
$515$	27.8078	+	20.2036i	1.22536	+	0.890276i
$516$	−3.83055	−	2.76038i	−0.168630	−	0.121519i
$517$	11.3310	+	20.0887i	0.498335	+	0.883500i
$518$	−4.68528	+	2.39875i	−0.205859	+	0.105395i
$519$	11.3757	+	8.26495i	0.499339	+	0.362791i
$520$	3.72882	−	36.3564i	0.163520	−	1.59433i
$521$	−5.81697	−	17.9028i	−0.254846	−	0.784335i	−0.993860	−	0.110645i	$-0.964708\pi$
$521$	−5.81697	−	17.9028i	−0.254846	−	0.784335i	0.739014	−	0.673690i	$-0.235292\pi$
$522$	1.16976	+	0.593161i	0.0511988	+	0.0259619i
$523$	15.8048	−	11.4829i	0.691096	−	0.502111i	−0.185924	−	0.982564i	$-0.559528\pi$
$523$	15.8048	−	11.4829i	0.691096	−	0.502111i	0.877020	+	0.480453i	$0.159528\pi$
$524$	−34.5827	−	11.0882i	−1.51075	−	0.484391i
$525$	−3.39197	+	10.4394i	−0.148038	+	0.455613i
$526$	1.41295	+	0.220977i	0.0616077	+	0.00963504i
$527$			8.49063i			0.369858i
$528$	−22.2711	−	2.39178i	−0.969225	−	0.104089i
$529$	22.4629			0.976646
$530$	−1.32640	+	8.48120i	−0.0576153	+	0.368400i
$531$	0.563660	−	1.73477i	0.0244608	−	0.0752825i
$532$	−1.28452	−	0.411853i	−0.0556908	−	0.0178561i
$533$	4.56375	−	6.97682i	0.197678	−	0.302200i
$534$	11.0081	−	21.7088i	0.476368	−	0.939432i
$535$	−14.7431	+	4.79032i	−0.637399	+	0.207103i
$536$	−31.1050	−	15.6211i	−1.34353	−	0.674727i
$537$	−14.7508	−	10.7171i	−0.636542	−	0.462475i
$538$	38.8463	−	19.8883i	1.67478	−	0.857447i
$539$	−2.39744	+	20.7999i	−0.103265	+	0.895915i
$540$	22.2814	−	30.9197i	0.958840	−	1.33057i
$541$	−23.1985	−	16.8547i	−0.997382	−	0.724640i	−0.0358565	−	0.999357i	$-0.511416\pi$
$541$	−23.1985	−	16.8547i	−0.997382	−	0.724640i	−0.961525	+	0.274717i	$0.911416\pi$
$542$	9.88172	−	1.58480i	0.424456	−	0.0680729i
$543$	11.8138	−	3.83853i	0.506978	−	0.164727i
$544$	−4.54422	+	30.6130i	−0.194832	+	1.31252i
$545$	−25.0114	−	34.4253i	−1.07137	−	1.47462i
$546$	6.51521	+	2.91147i	0.278825	+	0.124600i
$547$	−13.0030	+	40.0192i	−0.555969	+	1.71110i	0.137402	+	0.990515i	$0.456125\pi$
$547$	−13.0030	+	40.0192i	−0.555969	+	1.71110i	−0.693371	+	0.720581i	$0.743875\pi$
$548$	1.54106	+	4.68092i	0.0658307	+	0.199959i
$549$			0.811332i			0.0346268i
$550$	−12.9052	−	34.4500i	−0.550280	−	1.46895i
$551$	5.05425			0.215318
$552$	−2.46041	+	2.48926i	−0.104722	+	0.105950i
$553$	0.921700	+	0.299479i	0.0391947	+	0.0127351i
$554$	14.2971	−	14.3527i	0.607425	−	0.609789i
$555$	−15.9698	−	21.9806i	−0.677881	−	0.933023i
$556$	−0.106757	−	27.4732i	−0.00452749	−	1.16512i
$557$	−7.11827	−	21.9078i	−0.301611	−	0.928262i	−0.980920	−	0.194411i	$-0.937721\pi$
$557$	−7.11827	−	21.9078i	−0.301611	−	0.928262i	0.679309	−	0.733852i	$-0.262279\pi$
$558$	−0.0518906	−	0.323554i	−0.00219670	−	0.0136971i
$559$	−4.86524	−	1.32094i	−0.205778	−	0.0558696i
$560$	3.75953	+	11.2718i	0.158869	+	0.476320i
$561$	27.8611	+	12.7411i	1.17630	+	0.537930i
$562$	16.8516	−	8.62760i	0.710842	−	0.363933i
$563$	15.2367	+	11.0701i	0.642152	+	0.466551i	0.860589	−	0.509300i	$-0.170096\pi$
$563$	15.2367	+	11.0701i	0.642152	+	0.466551i	−0.218437	+	0.975851i	$0.570096\pi$
$564$	18.9439	−	13.8763i	0.797683	−	0.584300i
$565$	−20.1130	+	6.53511i	−0.846160	+	0.274934i
$566$	3.89491	−	7.68104i	0.163715	−	0.322858i
$567$	4.15584	+	5.72003i	0.174529	+	0.240219i
$568$	34.6733	−	5.69907i	1.45486	−	0.239128i
$569$	30.1427	+	9.79397i	1.26365	+	0.410584i	0.862793	−	0.505557i	$-0.168713\pi$
$569$	30.1427	+	9.79397i	1.26365	+	0.410584i	0.400856	+	0.916141i	$0.368713\pi$
$570$	1.07586	−	6.87917i	0.0450627	−	0.288137i
$571$	−4.38174			−0.183370			−0.0916851	−	0.995788i	$-0.529225\pi$
$571$	−4.38174			−0.183370			−0.0916851	+	0.995788i	$0.529225\pi$
$572$	−23.1591	+	5.97113i	−0.968332	+	0.249665i
$573$	−29.9634			−1.25174
$574$	−0.418813	+	2.67795i	−0.0174809	+	0.111775i
$575$	−5.46697	−	1.77633i	−0.227988	−	0.0740779i
$576$	−0.0139237	−	1.19435i	−0.000580156	−	0.0497645i
$577$	0.695282	+	0.956973i	0.0289450	+	0.0398393i	0.823244	−	0.567687i	$-0.192162\pi$
$577$	0.695282	+	0.956973i	0.0289450	+	0.0398393i	−0.794299	+	0.607527i	$0.792162\pi$
$578$	8.27076	−	16.3105i	0.344018	−	0.678429i
$579$	−10.4125	+	3.38324i	−0.432731	+	0.140603i
$580$	−26.3087	−	35.9165i	−1.09241	−	1.49135i
$581$	8.69846	+	6.31980i	0.360873	+	0.262189i
$582$	11.5432	−	5.90981i	0.478480	−	0.244970i
$583$	5.50627	−	1.11276i	0.228046	−	0.0460857i
$584$	5.73031	−	37.5968i	0.237122	−	1.55577i
$585$	0.505489	−	1.86180i	0.0208994	−	0.0769761i
$586$	6.38610	+	39.8194i	0.263807	+	1.64492i
$587$	3.73979	+	11.5099i	0.154358	+	0.475064i	0.998095	−	0.0616916i	$-0.0196495\pi$
$587$	3.73979	+	11.5099i	0.154358	+	0.475064i	−0.843737	+	0.536756i	$0.819650\pi$
$588$	21.3173	−	0.0828360i	0.879112	−	0.00341610i
$589$	−0.742253	−	1.02162i	−0.0305840	−	0.0420953i
$590$	−43.6974	+	43.8675i	−1.79899	+	1.80600i
$591$	37.3686	+	12.1418i	1.53714	+	0.499447i
$592$	−17.1245	−	5.41731i	−0.703812	−	0.222650i
$593$	−12.0475			−0.494732			−0.247366	−	0.968922i	$-0.579565\pi$
$593$	−12.0475			−0.494732			−0.247366	+	0.968922i	$0.579565\pi$
$594$	−24.0374	−	6.64977i	−0.986268	−	0.272843i
$595$		−	16.2518i		−	0.666258i
$596$	−14.7178	+	4.84540i	−0.602864	+	0.198476i
$597$	13.0754	−	40.2420i	0.535142	−	1.64700i
$598$	−1.52470	+	3.41192i	−0.0623494	+	0.139524i
$599$	−1.85250	−	2.54975i	−0.0756911	−	0.104180i	0.769493	−	0.638656i	$-0.220509\pi$
$599$	−1.85250	−	2.54975i	−0.0756911	−	0.104180i	−0.845184	+	0.534476i	$0.820509\pi$
$600$	−33.2732	+	17.1986i	−1.35837	+	0.702129i
$601$	20.5251	−	6.66900i	0.837235	−	0.272034i	0.141145	−	0.989989i	$-0.454922\pi$
$601$	20.5251	−	6.66900i	0.837235	−	0.272034i	0.696090	+	0.717955i	$0.254922\pi$
$602$	1.61837	−	0.259549i	0.0659600	−	0.0105784i
$603$	−1.48645	−	1.07997i	−0.0605330	−	0.0439798i
$604$	−33.3438	−	24.0283i	−1.35674	−	0.977696i
$605$	−29.8191	+	25.7846i	−1.21232	+	1.04829i
$606$	37.1430	−	19.0163i	1.50883	−	0.772483i
$607$	−29.0967	−	21.1400i	−1.18100	−	0.858044i	−0.188713	−	0.982032i	$-0.560432\pi$
$607$	−29.0967	−	21.1400i	−1.18100	−	0.858044i	−0.992284	+	0.123988i	$0.960432\pi$
$608$	−2.12942	−	4.08072i	−0.0863592	−	0.165495i
$609$	8.26769	−	2.68633i	0.335024	−	0.108856i
$610$	12.4557	−	24.5635i	0.504315	−	0.994546i
$611$	13.7255	−	20.9828i	0.555273	−	0.848871i
$612$	−0.498789	+	1.55566i	−0.0201624	+	0.0628838i
$613$	5.70087	−	17.5455i	0.230256	−	0.708655i	−0.767459	−	0.641098i	$-0.778479\pi$
$613$	5.70087	−	17.5455i	0.230256	−	0.708655i	0.997715	−	0.0675574i	$-0.0215206\pi$
$614$	1.80263	−	11.5263i	0.0727483	−	0.465162i
$615$	−13.9909			−0.564166
$616$	6.06344	−	4.86798i	0.244303	−	0.196137i
$617$			31.4202i			1.26493i	0.774589	+	0.632465i	$0.217957\pi$
$617$			31.4202i			1.26493i	−0.774589	+	0.632465i	$0.782043\pi$
$618$	−22.6264	−	3.53863i	−0.910169	−	0.142344i
$619$	8.50378	−	26.1719i	0.341796	−	1.05194i	−0.621481	−	0.783429i	$-0.713469\pi$
$619$	8.50378	−	26.1719i	0.341796	−	1.05194i	0.963277	−	0.268510i	$-0.0865311\pi$
$620$	−3.39623	+	10.5924i	−0.136396	+	0.425401i
$621$	−3.15279	+	2.29064i	−0.126517	+	0.0919201i
$622$	10.9041	+	5.52925i	0.437214	+	0.221703i
$623$	2.61108	+	8.03607i	0.104611	+	0.321959i
$624$	8.82766	+	22.6940i	0.353389	+	0.908487i
$625$	2.18461	+	1.58721i	0.0873844	+	0.0634885i
$626$	29.6856	−	15.1983i	1.18647	−	0.607446i
$627$	−4.46618	+	0.902568i	−0.178362	+	0.0360451i
$628$	9.71346	−	13.4793i	0.387609	−	0.537881i
$629$	19.8742	+	14.4395i	0.792436	+	0.575739i
$630$	0.0993230	+	0.619311i	0.00395712	+	0.0246739i
$631$	−9.50571	−	29.2556i	−0.378416	−	1.16465i	−0.941145	−	0.338004i	$-0.890248\pi$
$631$	−9.50571	−	29.2556i	−0.378416	−	1.16465i	0.562728	−	0.826642i	$-0.309752\pi$
$632$	1.51847	+	2.93771i	0.0604015	+	0.116856i
$633$	−24.2626	−	33.3947i	−0.964354	−	1.32732i
$634$	−9.99305	+	10.0320i	−0.396875	+	0.398420i
$635$	10.8255	+	3.51743i	0.429599	+	0.139585i
$636$	−1.78855	−	5.43266i	−0.0709206	−	0.215419i
$637$	21.2767	−	8.08654i	0.843013	−	0.320400i
$638$	−16.0652	+	24.3053i	−0.636026	+	0.962255i
$639$	1.85485			0.0733767
$640$	−17.9142	+	36.3732i	−0.708121	+	1.43778i
$641$	−8.47516	+	26.0839i	−0.334749	+	1.03025i	0.632097	+	0.774889i	$0.282194\pi$
$641$	−8.47516	+	26.0839i	−0.334749	+	1.03025i	−0.966846	+	0.255361i	$0.917806\pi$
$642$	7.28913	−	7.31751i	0.287679	−	0.288799i
$643$	20.3554	−	14.7891i	0.802739	−	0.583224i	−0.108977	−	0.994044i	$-0.534758\pi$
$643$	20.3554	−	14.7891i	0.802739	−	0.583224i	0.911716	+	0.410820i	$0.134758\pi$
$644$	−0.00472131	−	1.21500i	−0.000186046	−	0.0478777i
$645$	2.61439	+	8.04628i	0.102942	+	0.316822i
$646$	0.996923	+	6.21613i	0.0392234	+	0.244570i
$647$	−29.3158	+	40.3498i	−1.15252	+	1.58631i	−0.416857	+	0.908972i	$0.636868\pi$
$647$	−29.3158	+	40.3498i	−1.15252	+	1.58631i	−0.735668	+	0.677342i	$0.763132\pi$
$648$	−3.63517	+	23.8505i	−0.142803	+	0.936935i
$649$	36.8489	+	16.8513i	1.44645	+	0.661472i
$650$	−26.8010	+	29.6835i	−1.05122	+	1.16428i
$651$	−1.75716	−	1.27665i	−0.0688686	−	0.0500359i
$652$	11.2050	+	15.2970i	0.438821	+	0.599075i
$653$	−10.2370	−	31.5061i	−0.400603	−	1.23293i	−0.924511	−	0.381155i	$-0.875526\pi$
$653$	−10.2370	−	31.5061i	−0.400603	−	1.23293i	0.523908	−	0.851775i	$-0.324474\pi$
$654$	25.2862	+	12.8221i	0.988768	+	0.501385i
$655$	38.2502	+	52.6468i	1.49456	+	2.05708i
$656$	−7.44009	+	5.49439i	−0.290487	+	0.214520i
$657$	0.620362	−	1.90928i	0.0242026	−	0.0744880i
$658$	−1.25958	+	8.05392i	−0.0491035	+	0.313974i
$659$	−18.4373			−0.718217			−0.359108	−	0.933296i	$-0.616919\pi$
$659$	−18.4373			−0.718217			−0.359108	+	0.933296i	$0.616919\pi$
$660$	29.6614	+	27.0394i	1.15457	+	1.05251i
$661$			0.878350i			0.0341639i	0.999854	+	0.0170819i	$0.00543761\pi$
$661$			0.878350i			0.0341639i	−0.999854	+	0.0170819i	$0.994562\pi$
$662$	45.6598	+	7.14089i	1.77462	+	0.277539i
$663$	−1.63280	−	33.2650i	−0.0634126	−	1.29191i
$664$	5.95043	+	36.2026i	0.230922	+	1.40493i
$665$	1.42074	+	1.95548i	0.0550938	+	0.0758301i
$666$	−0.845598	−	0.428786i	−0.0327663	−	0.0166151i
$667$	1.40679	+	4.32966i	0.0544713	+	0.167645i
$668$	−10.4152	+	7.62911i	−0.402977	+	0.295179i
$669$	−13.3853	+	18.4233i	−0.517505	+	0.712284i
$670$	28.4232	+	55.5168i	1.09809	+	2.14480i
$671$	−17.9044	−	2.06369i	−0.691191	−	0.0796680i
$672$	−5.65217	−	5.54341i	−0.218037	−	0.213842i
$673$	−5.58733	+	7.69029i	−0.215376	+	0.296439i	−0.903011	−	0.429617i	$-0.858649\pi$
$673$	−5.58733	+	7.69029i	−0.215376	+	0.296439i	0.687636	+	0.726056i	$0.258649\pi$
$674$	2.59319	−	0.415887i	0.0998859	−	0.0160194i
$675$	−39.6633	+	12.8874i	−1.52664	+	0.496036i
$676$	17.3443	+	19.3694i	0.667089	+	0.744978i
$677$	7.60341	+	10.4652i	0.292223	+	0.402210i	0.929735	−	0.368231i	$-0.120036\pi$
$677$	7.60341	+	10.4652i	0.292223	+	0.402210i	−0.637512	+	0.770441i	$0.720036\pi$
$678$	9.94406	−	9.98278i	0.381899	−	0.383386i
$679$	−1.39113	+	4.28147i	−0.0533868	+	0.164308i
$680$	38.9837	−	39.4408i	1.49496	−	1.51249i
$681$	−13.3728			−0.512447
$682$	7.27214	−	0.322126i	0.278465	−	0.0123348i
$683$	24.9342			0.954079			0.477040	−	0.878882i	$-0.341710\pi$
$683$	24.9342			0.954079			0.477040	+	0.878882i	$0.341710\pi$
$684$	−0.0759799	−	0.230787i	−0.00290517	−	0.00882436i
$685$	2.72876	−	8.39826i	0.104261	−	0.320881i
$686$	−11.0136	+	11.0565i	−0.420502	+	0.422139i
$687$	6.75751	−	4.90962i	0.257815	−	0.187314i
$688$	4.55016	+	3.25216i	0.173473	+	0.123987i
$689$	−3.82748	−	4.75871i	−0.145815	−	0.181292i
$690$	6.19241	−	0.993119i	0.235741	−	0.0378074i
$691$	−16.4324	−	11.9388i	−0.625118	−	0.454175i	0.229587	−	0.973288i	$-0.426262\pi$
$691$	−16.4324	−	11.9388i	−0.625118	−	0.454175i	−0.854706	+	0.519113i	$0.826262\pi$
$692$	−13.5131	−	9.73784i	−0.513691	−	0.370177i
$693$	0.357508	−	0.201651i	0.0135806	−	0.00766009i
$694$	−17.0123	+	8.70985i	−0.645776	+	0.330621i
$695$	−28.9359	+	39.8268i	−1.09760	+	1.51072i
$696$	26.5083	+	13.3126i	1.00480	+	0.504614i
$697$	12.0310	−	3.90911i	0.455707	−	0.148068i
$698$	−5.90678	+	11.6486i	−0.223575	+	0.440906i
$699$	32.7544	−	23.7975i	1.23889	−	0.900104i
$700$	3.96989	−	12.3816i	0.150048	−	0.467979i
$701$	−37.9158	−	12.3196i	−1.43206	−	0.465305i	−0.512648	−	0.858599i	$-0.671335\pi$
$701$	−37.9158	−	12.3196i	−1.43206	−	0.465305i	−0.919413	+	0.393294i	$0.871335\pi$
$702$	5.60071	+	26.5282i	0.211385	+	1.00124i
$703$	−3.65364			−0.137800
$704$	26.3921	+	2.73066i	0.994690	+	0.102916i
$705$	−42.0775			−1.58473
$706$	1.82139	−	11.6462i	0.0685491	−	0.438312i
$707$	−4.47631	+	13.7767i	−0.168349	+	0.518125i
$708$	12.5958	−	39.2845i	0.473377	−	1.47640i
$709$	0.808569	+	1.11290i	0.0303664	+	0.0417958i	0.823930	−	0.566691i	$-0.191777\pi$
$709$	0.808569	+	1.11290i	0.0303664	+	0.0417958i	−0.793564	+	0.608487i	$0.791777\pi$
$710$	−56.1564	−	28.4758i	−2.10751	−	1.06868i
$711$	0.0539429	+	0.166019i	0.00202302	+	0.00622620i
$712$	−12.9397	+	25.7657i	−0.484935	+	0.965611i
$713$	0.668564	−	0.920199i	0.0250379	−	0.0344617i
$714$	4.93462	+	9.63841i	0.184674	+	0.360708i
$715$	39.8003	+	15.8907i	1.48845	+	0.594279i
$716$	17.5223	+	12.6269i	0.654837	+	0.471890i
$717$	5.37633	+	3.90613i	0.200783	+	0.145877i
$718$	22.3177	−	3.57924i	0.832889	−	0.133576i
$719$	−47.8178	+	15.5369i	−1.78330	+	0.579430i	−0.999153	−	0.0411407i	$-0.986901\pi$
$719$	−47.8178	+	15.5369i	−1.78330	+	0.579430i	−0.784150	+	0.620571i	$0.786901\pi$
$720$	−1.24452	+	1.74123i	−0.0463805	+	0.0648919i
$721$	6.43180	−	4.67298i	0.239533	−	0.174031i
$722$	18.3735	+	18.3023i	0.683791	+	0.681139i
$723$	−12.0110	−	3.90262i	−0.446695	−	0.145140i
$724$	−13.9763	+	4.60129i	−0.519425	+	0.171006i
$725$			48.7184i			1.80936i
$726$	9.85562	−	24.3462i	0.365776	−	0.903571i
$727$		−	4.36694i		−	0.161961i	−0.996716	−	0.0809805i	$-0.974195\pi$
$727$		−	4.36694i		−	0.161961i	0.996716	−	0.0809805i	$-0.0258051\pi$
$728$	−7.73095	−	3.41878i	−0.286528	−	0.126708i
$729$	−8.71634	+	26.8261i	−0.322827	+	0.993560i
$730$	−48.0932	+	48.2804i	−1.78001	+	1.78694i
$731$	−4.49633	−	6.18867i	−0.166303	−	0.228896i
$732$	0.0713046	+	18.3498i	0.00263549	+	0.678228i
$733$	11.9157	+	36.6728i	0.440117	+	1.35454i	0.887751	+	0.460324i	$0.152267\pi$
$733$	11.9157	+	36.6728i	0.440117	+	1.35454i	−0.447634	+	0.894217i	$0.647733\pi$
$734$	36.5295	−	5.85848i	1.34833	−	0.216240i
$735$	−30.9030	−	22.4523i	−1.13987	−	0.828166i
$736$	2.90300	−	2.95996i	0.107006	−	0.109106i
$737$	27.6136	−	30.0558i	1.01716	−	1.10712i
$738$	−0.434578	+	0.222493i	−0.0159970	+	0.00819009i
$739$	−25.4552	+	35.0361i	−0.936385	+	1.28882i	0.0209316	+	0.999781i	$0.493337\pi$
$739$	−25.4552	+	35.0361i	−0.936385	+	1.28882i	−0.957316	+	0.289042i	$0.906663\pi$
$740$	19.0181	+	25.9634i	0.699120	+	0.954435i
$741$	3.10450	+	3.85983i	0.114047	+	0.141794i
$742$	1.77084	+	0.897959i	0.0650096	+	0.0329651i
$743$	5.04390	+	6.94233i	0.185043	+	0.254689i	0.891453	−	0.453113i	$-0.149687\pi$
$743$	5.04390	+	6.94233i	0.185043	+	0.254689i	−0.706410	+	0.707802i	$0.749687\pi$
$744$	−1.20204	−	7.31322i	−0.0440688	−	0.268116i
$745$	26.4059	+	8.57979i	0.967437	+	0.314339i
$746$	1.79634	−	11.4860i	0.0657687	−	0.420534i
$747$			1.93666i			0.0708586i
$748$	−33.0613	−	14.9642i	−1.20884	−	0.547144i
$749$			3.58548i			0.131011i
$750$	24.0373	+	3.75927i	0.877718	+	0.137269i
$751$	−10.6011	−	3.44450i	−0.386838	−	0.125691i	0.109140	−	0.994026i	$-0.465190\pi$
$751$	−10.6011	−	3.44450i	−0.386838	−	0.125691i	−0.495978	+	0.868335i	$0.665190\pi$
$752$	−22.3760	+	16.5243i	−0.815970	+	0.602581i
$753$	11.6287	−	8.44874i	0.423773	−	0.307889i
$754$	31.4948	+	3.35392i	1.14697	+	0.122143i
$755$	22.7575	+	70.0404i	0.828231	+	2.54903i
$756$	−5.20899	−	7.11129i	−0.189449	−	0.258635i
$757$	27.3619	+	19.8796i	0.994484	+	0.722535i	0.960898	−	0.276901i	$-0.0893074\pi$
$757$	27.3619	+	19.8796i	0.994484	+	0.722535i	0.0335854	+	0.999436i	$0.489307\pi$
$758$	5.57699	−	2.85528i	0.202565	−	0.103708i
$759$	−2.01628	−	3.57468i	−0.0731865	−	0.129753i
$760$	−1.24274	+	8.15364i	−0.0450788	+	0.295763i
$761$	−6.00505	−	4.36292i	−0.217683	−	0.158156i	0.473600	−	0.880740i	$-0.342954\pi$
$761$	−6.00505	−	4.36292i	−0.217683	−	0.158156i	−0.691283	+	0.722584i	$0.742954\pi$
$762$	−7.48830	+	1.20095i	−0.271272	+	0.0435058i
$763$	−9.36033	+	3.04136i	−0.338867	+	0.110104i
$764$	35.4930	−	0.137920i	1.28409	−	0.00498979i
$765$	2.36825	−	1.72063i	0.0856242	−	0.0622096i
$766$	−30.8094	−	30.6899i	−1.11319	−	1.10887i
$767$	−2.15953	−	43.9961i	−0.0779760	−	1.58861i
$768$	−0.419877	−	27.0111i	−0.0151510	−	0.974681i
$769$	−4.21029			−0.151827			−0.0759134	−	0.997114i	$-0.524187\pi$
$769$	−4.21029			−0.151827			−0.0759134	+	0.997114i	$0.524187\pi$
$770$	−13.9195	+	0.616577i	−0.501624	+	0.0222199i
$771$			35.5538i			1.28044i
$772$	12.3185	−	4.05553i	0.443354	−	0.145962i
$773$	−16.6238	−	5.40139i	−0.597915	−	0.194274i	−0.00560481	−	0.999984i	$-0.501784\pi$
$773$	−16.6238	−	5.40139i	−0.597915	−	0.194274i	−0.592310	+	0.805710i	$0.701784\pi$
$774$	0.209165	+	0.208354i	0.00751828	+	0.00748912i
$775$	9.84752	−	7.15465i	0.353734	−	0.257002i
$776$	−13.6462	+	7.05357i	−0.489870	+	0.253208i
$777$	−5.97658	+	1.94191i	−0.214409	+	0.0696656i
$778$	−4.55900	−	28.4268i	−0.163448	−	1.01915i
$779$	−1.10588	+	1.52211i	−0.0396223	+	0.0545354i
$780$	11.2689	−	42.1525i	0.403493	−	1.50930i
$781$	−4.71797	+	40.9325i	−0.168822	+	1.46468i
$782$	−5.04749	+	2.58419i	−0.180498	+	0.0924104i
$783$	26.7207	+	19.4137i	0.954921	+	0.693790i
$784$	−25.2509	+	0.196246i	−0.901819	+	0.00700878i
$785$	−28.3139	+	9.19976i	−1.01057	+	0.328353i
$786$	−38.6704	−	19.6090i	−1.37933	−	0.699430i
$787$	−23.9976	−	33.0298i	−0.855420	−	1.17739i	−0.982642	−	0.185511i	$-0.940606\pi$
$787$	−23.9976	−	33.0298i	−0.855420	−	1.17739i	0.127222	−	0.991874i	$-0.459394\pi$
$788$	−44.3206	−	14.2105i	−1.57886	−	0.506228i
$789$	1.62383	+	0.527616i	0.0578101	+	0.0187836i
$790$	0.915597	−	5.85445i	0.0325755	−	0.208292i
$791$			4.89143i			0.173919i
$792$	1.35133	+	0.368188i	0.0480174	+	0.0130830i
$793$	6.96083	+	18.3148i	0.247186	+	0.650377i
$794$	0.744894	−	4.76295i	0.0264353	−	0.169031i
$795$	−3.16699	+	9.74701i	−0.112322	+	0.345691i
$796$	−15.3032	+	47.7287i	−0.542407	+	1.69170i
$797$	−7.42571	+	5.39509i	−0.263032	+	0.191104i	−0.711483	−	0.702704i	$-0.751976\pi$
$797$	−7.42571	+	5.39509i	−0.263032	+	0.191104i	0.448451	+	0.893808i	$0.351976\pi$
$798$	−1.43634	−	0.728342i	−0.0508460	−	0.0257830i
$799$	36.1832	−	11.7566i	1.28007	−	0.415920i
$800$	39.3344	−	20.5256i	1.39068	−	0.725691i
$801$	−0.894591	+	1.23130i	−0.0316088	+	0.0435058i
$802$	−8.59279	−	16.7836i	−0.303422	−	0.592650i
$803$	40.5557	+	18.5465i	1.43118	+	0.654491i
$804$	−33.7138	−	24.2949i	−1.18899	−	0.856815i
$805$	−1.27969	+	1.76134i	−0.0451031	+	0.0620791i
$806$	−3.94730	−	6.85863i	−0.139038	−	0.241585i
$807$	49.5526	−	16.1006i	1.74433	−	0.566768i
$808$	−43.9099	+	22.6966i	−1.54475	+	0.798463i
$809$	0.0264059	+	0.0363445i	0.000928381	+	0.00127781i	0.809481	−	0.587146i	$-0.199749\pi$
$809$	0.0264059	+	0.0363445i	0.000928381	+	0.00127781i	−0.808553	+	0.588424i	$0.799749\pi$
$810$	30.5091	−	30.6279i	1.07198	−	1.07616i
$811$	−20.8622	−	6.77856i	−0.732573	−	0.238027i	−0.0811070	−	0.996705i	$-0.525846\pi$
$811$	−20.8622	−	6.77856i	−0.732573	−	0.238027i	−0.651466	+	0.758678i	$0.725846\pi$
$812$	−9.78107	+	3.22014i	−0.343248	+	0.113005i
$813$	11.9483			0.419047
$814$	11.6133	−	17.5699i	0.407044	−	0.615824i
$815$		−	33.9770i		−	1.19016i
$816$	−11.1443	+	35.2279i	−0.390129	+	1.23322i
$817$	1.08203	+	0.351573i	0.0378555	+	0.0123000i
$818$	−34.1748	−	34.0422i	−1.19489	−	1.19026i
$819$	−0.373419	−	0.244265i	−0.0130483	−	0.00853530i
$820$	16.5728	−	0.0643995i	0.578747	−	0.00224893i
$821$	−10.2926	−	31.6772i	−0.359213	−	1.10554i	−0.953526	−	0.301309i	$-0.902576\pi$
$821$	−10.2926	−	31.6772i	−0.359213	−	1.10554i	0.594314	−	0.804233i	$-0.297424\pi$
$822$	0.931674	+	5.80929i	0.0324959	+	0.202622i
$823$	−15.8527	+	21.8193i	−0.552589	+	0.760574i	−0.990361	−	0.138512i	$-0.955768\pi$
$823$	−15.8527	+	21.8193i	−0.552589	+	0.760574i	0.437771	+	0.899086i	$0.355768\pi$
$824$	26.8183	+	4.08751i	0.934260	+	0.142395i
$825$	−8.69993	−	43.0499i	−0.302893	−	1.49881i
$826$	6.52650	+	12.7477i	0.227086	+	0.443549i
$827$	2.45647	−	3.38104i	0.0854198	−	0.117570i	−0.764169	−	0.645017i	$-0.776850\pi$
$827$	2.45647	−	3.38104i	0.0854198	−	0.117570i	0.849588	+	0.527446i	$0.176850\pi$
$828$	0.176553	−	0.129324i	0.00613563	−	0.00449432i
$829$	1.93743	+	5.96281i	0.0672899	+	0.207097i	0.979048	−	0.203632i	$-0.0652744\pi$
$829$	1.93743	+	5.96281i	0.0672899	+	0.207097i	−0.911758	+	0.410728i	$0.865274\pi$
$830$	29.7318	−	58.6333i	1.03201	−	2.03519i
$831$	19.5671	−	14.2163i	0.678774	−	0.493158i
$832$	−10.5612	−	26.8414i	−0.366144	−	0.930558i
$833$	32.8473	+	10.6727i	1.13809	+	0.369789i
$834$	5.06808	−	32.4060i	0.175493	−	1.12213i
$835$	23.1339			0.800580
$836$	5.28624	−	1.08969i	0.182828	−	0.0376877i
$837$		−	8.25214i		−	0.285236i
$838$	−6.75965	+	43.2221i	−0.233508	+	1.49308i
$839$	−16.7651	+	51.5977i	−0.578796	+	1.78135i	0.0440774	+	0.999028i	$0.485965\pi$
$839$	−16.7651	+	51.5977i	−0.578796	+	1.78135i	−0.622873	+	0.782323i	$0.714035\pi$
$840$	2.30080	+	13.9981i	0.0793852	+	0.482981i
$841$	7.75316	−	5.63300i	0.267350	−	0.194241i
$842$	26.6401	+	13.5087i	0.918080	+	0.465540i
$843$	21.4960	−	6.98448i	0.740362	−	0.240558i
$844$	28.8939	+	39.4458i	0.994569	+	1.35778i
$845$	−4.56257	−	46.3647i	−0.156957	−	1.59499i
$846$	−1.30699	+	0.669147i	−0.0449353	+	0.0230058i
$847$	3.54066	+	8.40236i	0.121658	+	0.288709i
$848$	2.14362	+	6.42700i	0.0736122	+	0.220704i
$849$	6.04351	−	8.31818i	0.207413	−	0.285479i
$850$	−59.9178	+	9.60943i	−2.05517	+	0.329601i
$851$	−1.01695	−	3.12985i	−0.0348605	−	0.107290i
$852$	41.9508	−	0.163015i	1.43721	−	0.00558479i
$853$	15.5878	−	11.3252i	0.533716	−	0.387767i	−0.288030	−	0.957621i	$-0.593000\pi$
$853$	15.5878	−	11.3252i	0.533716	−	0.387767i	0.821746	+	0.569854i	$0.193000\pi$
$854$	−4.51308	−	4.49557i	−0.154434	−	0.153835i
$855$	−0.134538	+	0.414066i	−0.00460111	+	0.0141608i
$856$	−8.60061	+	8.70146i	−0.293963	+	0.297410i
$857$			18.0677i			0.617180i	0.951195	+	0.308590i	$0.0998572\pi$
$857$			18.0677i			0.617180i	−0.951195	+	0.308590i	$0.900143\pi$
$858$	−28.4292	+	2.66052i	−0.970558	+	0.0908286i
$859$			17.8183i			0.607952i	0.952680	+	0.303976i	$0.0983143\pi$
$859$			17.8183i			0.607952i	−0.952680	+	0.303976i	$0.901686\pi$
$860$	−3.13390	−	9.51914i	−0.106865	−	0.324600i
$861$	−0.999982	+	3.07763i	−0.0340793	+	0.104885i
$862$	16.3479	−	16.4115i	0.556812	−	0.558980i
$863$	−13.1022	+	9.51933i	−0.446005	+	0.324042i	−0.788016	−	0.615654i	$-0.788892\pi$
$863$	−13.1022	+	9.51933i	−0.446005	+	0.324042i	0.342011	+	0.939696i	$0.388892\pi$
$864$	4.41658	−	29.7531i	0.150255	−	1.01222i
$865$	9.22285	+	28.3850i	0.313586	+	0.965119i
$866$	5.71251	+	35.6193i	0.194119	+	1.21039i
$867$	12.8333	−	17.6635i	0.435841	−	0.599884i
$868$	2.08731	+	1.50416i	0.0708480	+	0.0510546i
$869$	−3.80090	+	0.768120i	−0.128937	+	0.0260567i
$870$	−24.2229	−	47.3127i	−0.821233	−	1.60405i
$871$	−42.8204	−	11.6259i	−1.45091	−	0.393930i
$872$	−30.0116	−	15.0720i	−1.01632	−	0.510402i
$873$	−0.771189	+	0.250575i	−0.0261008	+	0.00848066i
$874$	0.381422	−	0.752192i	0.0129018	−	0.0254433i
$875$	−6.83285	+	4.96435i	−0.230992	+	0.167826i
$876$	13.8628	−	43.2363i	0.468382	−	1.46082i
$877$	8.98643	−	27.6574i	0.303450	−	0.933923i	−0.676801	−	0.736166i	$-0.736634\pi$
$877$	8.98643	−	27.6574i	0.303450	−	0.933923i	0.980251	−	0.197757i	$-0.0633657\pi$
$878$	−32.5451	−	5.08984i	−1.09834	−	0.171774i
$879$			48.1470i			1.62396i
$880$	−35.2597	−	31.8928i	−1.18860	−	1.07511i
$881$	−41.1283			−1.38565			−0.692823	−	0.721108i	$-0.743633\pi$
$881$	−41.1283			−1.38565			−0.692823	+	0.721108i	$0.743633\pi$
$882$	−1.31695	−	0.205962i	−0.0443439	−	0.00693510i
$883$	−0.574024	−	0.186512i	−0.0193174	−	0.00627662i	0.299342	−	0.954146i	$-0.403233\pi$
$883$	−0.574024	−	0.186512i	−0.0193174	−	0.00627662i	−0.318660	+	0.947869i	$0.603233\pi$
$884$	2.08724	+	39.3964i	0.0702014	+	1.32504i
$885$	−59.8046	+	43.4506i	−2.01031	+	1.46057i
$886$	41.7187	+	21.1547i	1.40157	+	0.710707i
$887$	−5.95561	−	18.3295i	−0.199970	−	0.615444i	−0.999883	−	0.0153276i	$-0.995121\pi$
$887$	−5.95561	−	18.3295i	−0.199970	−	0.615444i	0.799913	−	0.600116i	$-0.204879\pi$
$888$	−19.1624	−	9.62348i	−0.643050	−	0.322943i
$889$	1.54749	−	2.12994i	0.0519011	−	0.0714357i
$890$	45.9872	−	23.5443i	1.54150	−	0.789208i
$891$	−25.7275	−	11.7654i	−0.861905	−	0.394156i
$892$	15.7707	−	21.8848i	0.528041	−	0.732757i
$893$	−3.32593	+	4.57775i	−0.111298	+	0.153189i
$894$	−18.2656	+	2.92938i	−0.610893	+	0.0979730i
$895$	−11.9591	−	36.8065i	−0.399750	−	1.23030i
$896$	6.72076	+	6.54040i	0.224525	+	0.218499i
$897$	−2.44237	+	3.73377i	−0.0815485	+	0.124667i
$898$	−22.8259	+	22.9147i	−0.761709	+	0.764675i
$899$	−9.16819	−	2.97892i	−0.305776	−	0.0993527i
$900$	2.22458	−	0.732378i	0.0741525	−	0.0244126i
$901$		−	9.26651i		−	0.308712i
$902$	−3.80456	−	10.1561i	−0.126678	−	0.338163i
$903$	1.95683			0.0651193
$904$	−11.7332	+	11.8708i	−0.390241	+	0.394817i
$905$	25.0755	+	8.14753i	0.833539	+	0.270833i
$906$	−34.7635	−	34.6287i	−1.15494	−	1.15046i
$907$	−15.6972	−	21.6053i	−0.521216	−	0.717392i	0.464544	−	0.885550i	$-0.346218\pi$
$907$	−15.6972	−	21.6053i	−0.521216	−	0.717392i	−0.985760	+	0.168158i	$0.946218\pi$
$908$	15.8407	−	0.0615546i	0.525691	−	0.00204276i
$909$	−2.48149	+	0.806285i	−0.0823058	+	0.0267428i
$910$	7.55547	+	13.1280i	0.250461	+	0.435189i
$911$	14.7332	−	20.2785i	0.488132	−	0.671857i	−0.491910	−	0.870646i	$-0.663701\pi$
$911$	14.7332	−	20.2785i	0.488132	−	0.671857i	0.980042	+	0.198790i	$0.0637010\pi$
$912$	−1.73871	−	5.21299i	−0.0575744	−	0.172619i
$913$	−42.7379	−	4.92606i	−1.41442	−	0.163029i
$914$	−24.7473	+	12.6700i	−0.818568	+	0.419086i
$915$	19.3268	−	26.6010i	0.638923	−	0.879403i
$916$	−7.98197	+	5.84677i	−0.263732	+	0.193183i
$917$	14.3148	−	4.65117i	0.472717	−	0.153595i
$918$	−18.6061	+	36.6925i	−0.614092	+	1.21103i
$919$	38.4143	−	27.9097i	1.26717	−	0.920655i	0.268086	−	0.963395i	$-0.413609\pi$
$919$	38.4143	−	27.9097i	1.26717	−	0.920655i	0.999086	+	0.0427404i	$0.0136088\pi$
$920$	−7.33061	+	1.20490i	−0.241683	+	0.0397243i
$921$	4.30407	−	13.2466i	0.141824	−	0.436489i
$922$	46.7918	+	7.31793i	1.54101	+	0.241003i
$923$	41.8708	−	15.9137i	1.37820	−	0.523805i
$924$	8.06799	−	4.59213i	0.265417	−	0.151070i
$925$		−	35.2178i		−	1.15795i
$926$	−40.3850	−	6.31594i	−1.32713	−	0.207555i
$927$	1.36191	+	0.442513i	0.0447311	+	0.0145340i
$928$	−31.4616	−	15.6474i	−1.03278	−	0.513650i
$929$	−12.9636	−	17.8428i	−0.425320	−	0.585403i	0.541551	−	0.840668i	$-0.317837\pi$
$929$	−12.9636	−	17.8428i	−0.425320	−	0.585403i	−0.966871	+	0.255265i	$0.917837\pi$
$930$	−6.00607	+	11.8444i	−0.196947	+	0.388394i
$931$	−4.88533	+	1.58734i	−0.160110	+	0.0520229i
$932$	−38.6895	+	28.3400i	−1.26732	+	0.928306i
$933$	11.8086	+	8.57943i	0.386595	+	0.280878i
$934$	−18.9365	−	36.9872i	−0.619622	−	1.21026i
$935$	31.9469	+	56.6388i	1.04477	+	1.85229i
$936$	−0.320310	−	1.48853i	−0.0104697	−	0.0486541i
$937$	19.6495	−	27.0452i	0.641920	−	0.883527i	−0.356796	−	0.934182i	$-0.616131\pi$
$937$	19.6495	−	27.0452i	0.641920	−	0.883527i	0.998716	+	0.0506551i	$0.0161309\pi$
$938$	14.2438	−	2.28437i	0.465076	−	0.0745874i
$939$	37.8671	−	12.3038i	1.23575	−	0.401519i
$940$	49.8426	−	0.193681i	1.62569	−	0.00631718i
$941$	−5.44803	+	3.95822i	−0.177601	+	0.129034i	−0.673034	−	0.739612i	$-0.735009\pi$
$941$	−5.44803	+	3.95822i	−0.177601	+	0.129034i	0.495433	+	0.868646i	$0.335009\pi$
$942$	13.9987	−	14.0532i	0.456102	−	0.457878i
$943$	−1.61171	−	0.523676i	−0.0524845	−	0.0170532i
$944$	−14.7394	+	46.5922i	−0.479727	+	1.51645i
$945$			15.7953i			0.513821i
$946$	−5.12995	+	4.08586i	−0.166789	+	0.132843i
$947$	−15.5825			−0.506363			−0.253181	−	0.967419i	$-0.581477\pi$
$947$	−15.5825			−0.506363			−0.253181	+	0.967419i	$0.581477\pi$
$948$	1.23461	+	3.75009i	0.0400982	+	0.121797i
$949$	−2.37677	−	48.4219i	−0.0771531	−	1.57184i
$950$	6.36948	−	6.39428i	0.206653	−	0.207458i
$951$	−13.6766	+	9.93660i	−0.443493	+	0.322216i
$952$	−5.88965	−	11.3944i	−0.190885	−	0.369295i
$953$	−37.7558	+	12.2676i	−1.22303	+	0.397387i	−0.848185	−	0.529700i	$-0.822304\pi$
$953$	−37.7558	+	12.2676i	−1.22303	+	0.397387i	−0.374846	+	0.927087i	$0.622304\pi$
$954$	0.0566324	+	0.353121i	0.00183354	+	0.0114327i
$955$	−51.4529	−	37.3827i	−1.66498	−	1.20968i
$956$	−6.38648	−	4.60224i	−0.206553	−	0.148847i
$957$	−23.5329	+	25.6142i	−0.760710	+	0.827991i
$958$	10.8865	+	21.2637i	0.351726	+	0.686999i
$959$	−1.65237	−	1.20051i	−0.0533577	−	0.0387666i
$960$	−27.9941	+	39.4905i	−0.903504	+	1.27455i
$961$	−8.83525	−	27.1921i	−0.285008	−	0.877164i
$962$	−22.7671	−	2.42450i	−0.734040	−	0.0781689i
$963$	−0.522484	+	0.379607i	−0.0168368	+	0.0122327i
$964$	14.2456	+	4.56754i	0.458819	+	0.147111i
$965$	−22.1013	−	7.18115i	−0.711466	−	0.231169i
$966$	0.224136	−	1.43315i	0.00721144	−	0.0461109i
$967$			14.8352i			0.477067i	0.971134	+	0.238534i	$0.0766667\pi$
$967$			14.8352i			0.477067i	−0.971134	+	0.238534i	$0.923333\pi$
$968$	−11.5624	+	28.8845i	−0.371628	+	0.928382i
$969$			7.51615i			0.241453i
$970$	27.1950	+	4.25311i	0.873178	+	0.136559i
$971$	−19.6773	−	6.39353i	−0.631474	−	0.205178i	−0.0242460	−	0.999706i	$-0.507718\pi$
$971$	−19.6773	−	6.39353i	−0.631474	−	0.205178i	−0.607228	+	0.794528i	$0.707718\pi$
$972$	0.946576	−	2.95225i	0.0303614	−	0.0946933i
$973$	6.69271	+	9.21173i	0.214559	+	0.295314i
$974$	−11.4192	+	22.5196i	−0.365896	+	0.721573i
$975$	−37.2053	+	29.9246i	−1.19152	+	0.958353i
$976$	−0.168927	−	21.7358i	−0.00540722	−	0.695746i
$977$	9.10347	−	12.5299i	0.291246	−	0.400866i	−0.638172	−	0.769893i	$-0.720309\pi$
$977$	9.10347	−	12.5299i	0.291246	−	0.400866i	0.929418	+	0.369028i	$0.120309\pi$
$978$	10.3166	+	20.1507i	0.329890	+	0.644347i
$979$	−24.8967	−	22.8736i	−0.795701	−	0.731045i
$980$	36.7093	+	26.4535i	1.17264	+	0.845027i
$981$	−1.43420	−	1.04201i	−0.0457906	−	0.0332688i
$982$	6.36663	+	39.6980i	0.203167	+	1.26681i
$983$	16.6582	+	51.2687i	0.531315	+	1.63522i	0.751480	+	0.659756i	$0.229340\pi$
$983$	16.6582	+	51.2687i	0.531315	+	1.63522i	−0.220166	+	0.975463i	$0.570660\pi$
$984$	−9.80923	+	5.07029i	−0.312707	+	0.161635i
$985$	49.0208	+	67.4713i	1.56193	+	2.14981i
$986$	34.0491	+	33.9171i	1.08434	+	1.08014i
$987$	−3.00744	+	9.25596i	−0.0957279	+	0.294620i
$988$	−3.69519	−	4.55785i	−0.117560	−	0.145004i
$989$			1.02476i			0.0325856i
$990$	−1.56356	−	1.96310i	−0.0496931	−	0.0623915i
$991$		−	13.1743i		−	0.418494i	−0.977863	−	0.209247i	$-0.932899\pi$
$991$		−	13.1743i		−	0.418494i	0.977863	−	0.209247i	$-0.0671013\pi$
$992$	1.45753	+	8.65730i	0.0462766	+	0.274870i
$993$	52.4745	+	17.0500i	1.66523	+	0.541065i
$994$	−10.2777	+	10.3177i	−0.325988	+	0.327257i
$995$	72.6595	−	52.7902i	2.30346	−	1.67356i
$996$	0.170205	+	43.8011i	0.00539314	+	1.38789i
$997$	22.8856	−	7.43599i	0.724795	−	0.235500i	0.0766942	−	0.997055i	$-0.475563\pi$
$997$	22.8856	−	7.43599i	0.724795	−	0.235500i	0.648101	+	0.761554i	$0.275563\pi$
$998$	−7.12014	−	44.3964i	−0.225384	−	1.40534i
$999$	−19.3160	−	14.0339i	−0.611131	−	0.444012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bb.b.51.4	✓	304
4.3	odd	2	inner	572.2.bb.b.51.26	yes	304
11.8	odd	10	inner	572.2.bb.b.415.51	yes	304
13.12	even	2	inner	572.2.bb.b.51.73	yes	304
44.19	even	10	inner	572.2.bb.b.415.73	yes	304
52.51	odd	2	inner	572.2.bb.b.51.51	yes	304
143.129	odd	10	inner	572.2.bb.b.415.26	yes	304
572.415	even	10	inner	572.2.bb.b.415.4	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bb.b.51.4	✓	304	1.1	even	1	trivial
572.2.bb.b.51.26	yes	304	4.3	odd	2	inner
572.2.bb.b.51.51	yes	304	52.51	odd	2	inner
572.2.bb.b.51.73	yes	304	13.12	even	2	inner
572.2.bb.b.415.4	yes	304	572.415	even	10	inner
572.2.bb.b.415.26	yes	304	143.129	odd	10	inner
572.2.bb.b.415.51	yes	304	11.8	odd	10	inner
572.2.bb.b.415.73	yes	304	44.19	even	10	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39723 - 0.218517i) q^{2} +(-1.60576 - 0.521744i) q^{3} +(1.90450 + 0.610638i) q^{4} +(-2.10647 - 2.89931i) q^{5} +(2.12961 + 1.07988i) q^{6} +(-0.788330 + 0.256144i) q^{7} +(-2.52759 - 1.26937i) q^{8} +(-0.120789 - 0.0877584i) q^{9} +O(q^{10})\)	\(q+(-1.39723 - 0.218517i) q^{2} +(-1.60576 - 0.521744i) q^{3} +(1.90450 + 0.610638i) q^{4} +(-2.10647 - 2.89931i) q^{5} +(2.12961 + 1.07988i) q^{6} +(-0.788330 + 0.256144i) q^{7} +(-2.52759 - 1.26937i) q^{8} +(-0.120789 - 0.0877584i) q^{9} +(2.30967 + 4.51130i) q^{10} +(2.24388 - 2.44234i) q^{11} +(-2.73958 - 1.97420i) q^{12} +(-3.47958 - 0.944724i) q^{13} +(1.15745 - 0.185628i) q^{14} +(1.86980 + 5.75464i) q^{15} +(3.25424 + 2.32592i) q^{16} +(-3.21575 - 4.42609i) q^{17} +(0.149593 + 0.149013i) q^{18} +(0.773861 + 0.251443i) q^{19} +(-2.24134 - 6.80802i) q^{20} +1.39951 q^{21} +(-3.66891 + 2.92218i) q^{22} +0.732905i q^{23} +(3.39643 + 3.35706i) q^{24} +(-2.42368 + 7.45932i) q^{25} +(4.65534 + 2.08035i) q^{26} +(3.12542 + 4.30177i) q^{27} +(-1.65779 + 0.00644191i) q^{28} +(5.90754 - 1.91948i) q^{29} +(-1.35504 - 8.44914i) q^{30} +(-1.25555 - 0.912211i) q^{31} +(-4.03867 - 3.96095i) q^{32} +(-4.87742 + 2.75109i) q^{33} +(3.52596 + 6.88697i) q^{34} +(2.40323 + 1.74605i) q^{35} +(-0.176454 - 0.240894i) q^{36} +(-4.27047 + 1.38756i) q^{37} +(-1.02632 - 0.520425i) q^{38} +(5.09449 + 3.33246i) q^{39} +(1.64400 + 10.0021i) q^{40} +(-0.714521 + 2.19907i) q^{41} +(-1.95544 - 0.305818i) q^{42} +1.39822 q^{43} +(5.76485 - 3.28123i) q^{44} +0.535065i q^{45} +(0.160152 - 1.02404i) q^{46} +(-2.14892 + 6.61369i) q^{47} +(-4.01201 - 5.43276i) q^{48} +(-5.10726 + 3.71064i) q^{49} +(5.01643 - 9.89276i) q^{50} +(2.85444 + 8.78506i) q^{51} +(-6.04998 - 3.92399i) q^{52} +(1.37028 + 0.995570i) q^{53} +(-3.42692 - 6.69353i) q^{54} +(-11.8077 - 1.36098i) q^{55} +(2.31771 + 0.353254i) q^{56} +(-1.11145 - 0.807515i) q^{57} +(-8.67363 + 1.39105i) q^{58} +(3.77526 + 11.6191i) q^{59} +(0.0470246 + 12.1015i) q^{60} +(-3.19409 - 4.39629i) q^{61} +(1.55496 + 1.54893i) q^{62} +(0.117700 + 0.0382432i) q^{63} +(4.77741 + 6.41688i) q^{64} +(4.59059 + 12.0784i) q^{65} +(7.41603 - 2.77810i) q^{66} +12.3062 q^{67} +(-3.42165 - 10.3932i) q^{68} +(0.382389 - 1.17687i) q^{69} +(-2.97632 - 2.96478i) q^{70} +(-10.0507 + 7.30225i) q^{71} +(0.193907 + 0.375143i) q^{72} +(4.15504 + 12.7879i) q^{73} +(6.27003 - 1.00557i) q^{74} +(7.78371 - 10.7134i) q^{75} +(1.32028 + 0.951422i) q^{76} +(-1.14333 + 2.50012i) q^{77} +(-6.38996 - 5.76944i) q^{78} +(-0.945887 - 0.687227i) q^{79} +(-0.111405 - 14.3345i) q^{80} +(-2.63585 - 8.11232i) q^{81} +(1.47889 - 2.91647i) q^{82} +(-7.62433 - 10.4940i) q^{83} +(2.66537 + 0.854596i) q^{84} +(-6.05873 + 18.6469i) q^{85} +(-1.95364 - 0.305536i) q^{86} -10.4876 q^{87} +(-8.77183 + 3.32492i) q^{88} -10.1938i q^{89} +(0.116921 - 0.747609i) q^{90} +(2.98504 - 0.146520i) q^{91} +(-0.447539 + 1.39582i) q^{92} +(1.54018 + 2.11987i) q^{93} +(4.44774 - 8.77127i) q^{94} +(-0.901105 - 2.77332i) q^{95} +(4.41855 + 8.46751i) q^{96} +(3.19230 - 4.39382i) q^{97} +(7.94686 - 4.06860i) q^{98} +(-0.485372 + 0.0980884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q - 14 q^{4} + 72 q^{9}+O(q^{10}) \) 304 * q - 14 * q^4 + 72 * q^9	\( 304 q - 14 q^{4} + 72 q^{9} - 20 q^{12} - 10 q^{13} + 2 q^{14} + 14 q^{16} + 20 q^{17} - 66 q^{22} + 72 q^{25} - 34 q^{26} - 100 q^{29} - 60 q^{30} + 62 q^{36} - 14 q^{38} - 10 q^{40} - 68 q^{42} + 4 q^{48} + 40 q^{49} - 30 q^{52} - 12 q^{53} - 132 q^{56} - 20 q^{61} + 130 q^{62} - 38 q^{64} + 86 q^{66} - 60 q^{68} + 56 q^{69} + 40 q^{74} + 68 q^{77} - 48 q^{78} - 48 q^{81} - 70 q^{82} - 102 q^{88} + 180 q^{90} - 2 q^{92} - 190 q^{94}+O(q^{100}) \) 304 * q - 14 * q^4 + 72 * q^9 - 20 * q^12 - 10 * q^13 + 2 * q^14 + 14 * q^16 + 20 * q^17 - 66 * q^22 + 72 * q^25 - 34 * q^26 - 100 * q^29 - 60 * q^30 + 62 * q^36 - 14 * q^38 - 10 * q^40 - 68 * q^42 + 4 * q^48 + 40 * q^49 - 30 * q^52 - 12 * q^53 - 132 * q^56 - 20 * q^61 + 130 * q^62 - 38 * q^64 + 86 * q^66 - 60 * q^68 + 56 * q^69 + 40 * q^74 + 68 * q^77 - 48 * q^78 - 48 * q^81 - 70 * q^82 - 102 * q^88 + 180 * q^90 - 2 * q^92 - 190 * q^94

Introduction

L-functions

Modular forms

Varieties

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