LMFDB - Embedded newform 720.2.cf.a.11.59

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(11,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2, 0]))

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

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

chi := DirichletCharacter("720.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cf (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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.59
Character	$\chi$	$=$	720.11
Dual form			720.2.cf.a.131.59

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.448012 + 1.34137i) q^{2} +(-1.72559 + 0.149511i) q^{3} +(-1.59857 + 1.20190i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-0.973634 - 2.24767i) q^{6} +(0.558968 - 0.968161i) q^{7} +(-2.32838 - 1.60581i) q^{8} +(2.95529 - 0.515989i) q^{9} +O(q^{10})$	\(q+(0.448012 + 1.34137i) q^{2} +(-1.72559 + 0.149511i) q^{3} +(-1.59857 + 1.20190i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-0.973634 - 2.24767i) q^{6} +(0.558968 - 0.968161i) q^{7} +(-2.32838 - 1.60581i) q^{8} +(2.95529 - 0.515989i) q^{9} +(0.0855734 + 1.41162i) q^{10} +(5.97725 - 1.60160i) q^{11} +(2.57877 - 2.31299i) q^{12} +(-2.19154 - 0.587222i) q^{13} +(1.54909 + 0.316037i) q^{14} +(-1.70548 - 0.302198i) q^{15} +(1.11085 - 3.84266i) q^{16} +6.56037i q^{17} +(2.01614 + 3.73298i) q^{18} +(3.18689 + 3.18689i) q^{19} +(-1.85518 + 0.747210i) q^{20} +(-0.819796 + 1.75422i) q^{21} +(4.82623 + 7.30020i) q^{22} +(5.38164 - 3.10709i) q^{23} +(4.25791 + 2.42285i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-0.194154 - 3.20276i) q^{26} +(-5.02246 + 1.33223i) q^{27} +(0.270087 + 2.21950i) q^{28} +(-6.75676 + 1.81047i) q^{29} +(-0.358718 - 2.42308i) q^{30} +(3.07203 - 1.77364i) q^{31} +(5.65212 - 0.231489i) q^{32} +(-10.0748 + 3.65737i) q^{33} +(-8.79991 + 2.93913i) q^{34} +(0.790500 - 0.790500i) q^{35} +(-4.10407 + 4.37682i) q^{36} +(-3.91661 - 3.91661i) q^{37} +(-2.84704 + 5.70257i) q^{38} +(3.86949 + 0.685642i) q^{39} +(-1.83343 - 2.15373i) q^{40} +(-0.657291 - 1.13846i) q^{41} +(-2.72034 - 0.313743i) q^{42} +(2.51014 + 9.36797i) q^{43} +(-7.63009 + 9.74436i) q^{44} +(2.98814 + 0.266479i) q^{45} +(6.57881 + 5.82678i) q^{46} +(-2.65100 + 4.59166i) q^{47} +(-1.34235 + 6.79692i) q^{48} +(2.87511 + 4.97984i) q^{49} +(-0.282697 + 1.38567i) q^{50} +(-0.980850 - 11.3205i) q^{51} +(4.20912 - 1.69531i) q^{52} +(2.17994 - 2.17994i) q^{53} +(-4.03715 - 6.14015i) q^{54} +6.18811 q^{55} +(-2.85618 + 1.35665i) q^{56} +(-5.97572 - 5.02277i) q^{57} +(-5.45562 - 8.25223i) q^{58} +(0.796288 - 2.97179i) q^{59} +(3.08955 - 1.56674i) q^{60} +(3.37076 + 12.5798i) q^{61} +(3.75542 + 3.32613i) q^{62} +(1.15235 - 3.14962i) q^{63} +(2.84273 + 7.47789i) q^{64} +(-1.96488 - 1.13443i) q^{65} +(-9.41953 - 11.8755i) q^{66} +(0.884660 - 3.30160i) q^{67} +(-7.88494 - 10.4872i) q^{68} +(-8.82193 + 6.16617i) q^{69} +(1.41451 + 0.706203i) q^{70} -4.77985i q^{71} +(-7.70963 - 3.54423i) q^{72} +3.66416i q^{73} +(3.49895 - 7.00832i) q^{74} +(-1.56916 - 0.733312i) q^{75} +(-8.92479 - 1.26413i) q^{76} +(1.79049 - 6.68219i) q^{77} +(0.813878 + 5.49761i) q^{78} +(13.1905 + 7.61552i) q^{79} +(2.06755 - 3.42421i) q^{80} +(8.46751 - 3.04980i) q^{81} +(1.23263 - 1.39172i) q^{82} +(-0.511272 - 1.90809i) q^{83} +(-0.797899 - 3.78955i) q^{84} +(-1.69795 + 6.33683i) q^{85} +(-11.4414 + 7.56401i) q^{86} +(11.3887 - 4.13433i) q^{87} +(-16.4892 - 5.86921i) q^{88} +12.2779 q^{89} +(0.981277 + 4.12760i) q^{90} +(-1.79353 + 1.79353i) q^{91} +(-4.86850 + 11.4351i) q^{92} +(-5.03587 + 3.51987i) q^{93} +(-7.34682 - 1.49886i) q^{94} +(2.25347 + 3.90312i) q^{95} +(-9.71860 + 1.24451i) q^{96} +(2.16946 - 3.75762i) q^{97} +(-5.39174 + 6.08763i) q^{98} +(16.8381 - 7.81740i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{6}+O(q^{10}) $ 384 * q - 12 * q^6	$ 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) $ 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.448012	+	1.34137i	0.316793	+	0.948495i
$2$	0.448012	+	1.34137i	0.316793	+	0.948495i
$3$	−1.72559	+	0.149511i	−0.996267	+	0.0863204i
$3$	−1.72559	+	0.149511i	−0.996267	+	0.0863204i
$4$	−1.59857	+	1.20190i	−0.799285	+	0.600952i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$6$	−0.973634	−	2.24767i	−0.397485	−	0.917609i
$7$	0.558968	−	0.968161i	0.211270	−	0.365930i	−0.740842	−	0.671679i	$-0.765573\pi$
$7$	0.558968	−	0.968161i	0.211270	−	0.365930i	0.952112	+	0.305749i	$0.0989067\pi$
$8$	−2.32838	−	1.60581i	−0.823208	−	0.567741i
$9$	2.95529	−	0.515989i	0.985098	−	0.171996i
$10$	0.0855734	+	1.41162i	0.0270607	+	0.446394i
$11$	5.97725	−	1.60160i	1.80221	−	0.482901i	0.807890	−	0.589333i	$-0.200610\pi$
$11$	5.97725	−	1.60160i	1.80221	−	0.482901i	0.994320	+	0.106433i	$0.0339429\pi$
$12$	2.57877	−	2.31299i	0.744427	−	0.667704i
$13$	−2.19154	−	0.587222i	−0.607825	−	0.162866i	−0.0582379	−	0.998303i	$-0.518548\pi$
$13$	−2.19154	−	0.587222i	−0.607825	−	0.162866i	−0.549587	+	0.835437i	$0.685215\pi$
$14$	1.54909	+	0.316037i	0.414012	+	0.0844645i
$15$	−1.70548	−	0.302198i	−0.440354	−	0.0780271i
$16$	1.11085	−	3.84266i	0.277713	−	0.960664i
$17$			6.56037i			1.59112i	0.605872	+	0.795562i	$0.292824\pi$
$17$			6.56037i			1.59112i	−0.605872	+	0.795562i	$0.707176\pi$
$18$	2.01614	+	3.73298i	0.475209	+	0.879873i
$19$	3.18689	+	3.18689i	0.731122	+	0.731122i	0.970842	−	0.239720i	$-0.0770557\pi$
$19$	3.18689	+	3.18689i	0.731122	+	0.731122i	−0.239720	+	0.970842i	$0.577056\pi$
$20$	−1.85518	+	0.747210i	−0.414830	+	0.167081i
$21$	−0.819796	+	1.75422i	−0.178894	+	0.382801i
$22$	4.82623	+	7.30020i	1.02896	+	1.55641i
$23$	5.38164	−	3.10709i	1.12215	−	0.647873i	0.180200	−	0.983630i	$-0.442325\pi$
$23$	5.38164	−	3.10709i	1.12215	−	0.647873i	0.941949	+	0.335757i	$0.108992\pi$
$24$	4.25791	+	2.42285i	0.869142	+	0.494562i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	−0.194154	−	3.20276i	−0.0380766	−	0.628114i
$27$	−5.02246	+	1.33223i	−0.966574	+	0.256389i
$28$	0.270087	+	2.21950i	0.0510417	+	0.419446i
$29$	−6.75676	+	1.81047i	−1.25470	+	0.336195i	−0.824150	−	0.566372i	$-0.808346\pi$
$29$	−6.75676	+	1.81047i	−1.25470	+	0.336195i	−0.430548	+	0.902567i	$0.641680\pi$
$30$	−0.358718	−	2.42308i	−0.0654926	−	0.442392i
$31$	3.07203	−	1.77364i	0.551753	−	0.318555i	−0.198076	−	0.980187i	$-0.563469\pi$
$31$	3.07203	−	1.77364i	0.551753	−	0.318555i	0.749829	+	0.661632i	$0.230136\pi$
$32$	5.65212	−	0.231489i	0.999162	−	0.0409219i
$33$	−10.0748	+	3.65737i	−1.75380	+	0.636666i
$34$	−8.79991	+	2.93913i	−1.50917	+	0.504056i
$35$	0.790500	−	0.790500i	0.133619	−	0.133619i
$36$	−4.10407	+	4.37682i	−0.684012	+	0.729471i
$37$	−3.91661	−	3.91661i	−0.643886	−	0.643886i	0.307622	−	0.951509i	$-0.400467\pi$
$37$	−3.91661	−	3.91661i	−0.643886	−	0.643886i	−0.951509	+	0.307622i	$0.900467\pi$
$38$	−2.84704	+	5.70257i	−0.461851	+	0.925079i
$39$	3.86949	+	0.685642i	0.619615	+	0.109791i
$40$	−1.83343	−	2.15373i	−0.289891	−	0.340534i
$41$	−0.657291	−	1.13846i	−0.102652	−	0.177798i	0.810125	−	0.586258i	$-0.199399\pi$
$41$	−0.657291	−	1.13846i	−0.102652	−	0.177798i	−0.912776	+	0.408460i	$0.866066\pi$
$42$	−2.72034	−	0.313743i	−0.419758	−	0.0484116i
$43$	2.51014	+	9.36797i	0.382793	+	1.42860i	0.841617	+	0.540075i	$0.181604\pi$
$43$	2.51014	+	9.36797i	0.382793	+	1.42860i	−0.458824	+	0.888527i	$0.651729\pi$
$44$	−7.63009	+	9.74436i	−1.15028	+	1.46902i
$45$	2.98814	+	0.266479i	0.445446	+	0.0397243i
$46$	6.57881	+	5.82678i	0.969993	+	0.859111i
$47$	−2.65100	+	4.59166i	−0.386688	+	0.669763i	−0.992002	−	0.126224i	$-0.959714\pi$
$47$	−2.65100	+	4.59166i	−0.386688	+	0.669763i	0.605314	+	0.795987i	$0.293048\pi$
$48$	−1.34235	+	6.79692i	−0.193751	+	0.981051i
$49$	2.87511	+	4.97984i	0.410730	+	0.711405i
$50$	−0.282697	+	1.38567i	−0.0399794	+	0.195963i
$51$	−0.980850	−	11.3205i	−0.137346	−	1.58518i
$52$	4.20912	−	1.69531i	0.583700	−	0.235097i
$53$	2.17994	−	2.17994i	0.299438	−	0.299438i	−0.541356	−	0.840794i	$-0.682089\pi$
$53$	2.17994	−	2.17994i	0.299438	−	0.299438i	0.840794	+	0.541356i	$0.182089\pi$
$54$	−4.03715	−	6.14015i	−0.549387	−	0.835568i
$55$	6.18811			0.834404
$56$	−2.85618	+	1.35665i	−0.381673	+	0.181290i
$57$	−5.97572	−	5.02277i	−0.791504	−	0.665282i
$58$	−5.45562	−	8.25223i	−0.716358	−	1.08357i
$59$	0.796288	−	2.97179i	0.103668	−	0.386894i	−0.894523	−	0.447022i	$-0.852484\pi$
$59$	0.796288	−	2.97179i	0.103668	−	0.386894i	0.998191	+	0.0601287i	$0.0191511\pi$
$60$	3.08955	−	1.56674i	0.398859	−	0.202266i
$61$	3.37076	+	12.5798i	0.431581	+	1.61068i	0.749117	+	0.662438i	$0.230478\pi$
$61$	3.37076	+	12.5798i	0.431581	+	1.61068i	−0.317536	+	0.948246i	$0.602855\pi$
$62$	3.75542	+	3.32613i	0.476939	+	0.422419i
$63$	1.15235	−	3.14962i	0.145183	−	0.396815i
$64$	2.84273	+	7.47789i	0.355341	+	0.934737i
$65$	−1.96488	−	1.13443i	−0.243714	−	0.140708i
$66$	−9.41953	−	11.8755i	−1.15946	−	1.46178i
$67$	0.884660	−	3.30160i	0.108078	−	0.403354i	−0.890598	−	0.454792i	$-0.849714\pi$
$67$	0.884660	−	3.30160i	0.108078	−	0.403354i	0.998676	+	0.0514376i	$0.0163803\pi$
$68$	−7.88494	−	10.4872i	−0.956189	−	1.27176i
$69$	−8.82193	+	6.16617i	−1.06204	+	0.742319i
$70$	1.41451	+	0.706203i	0.169066	+	0.0844074i
$71$		−	4.77985i		−	0.567263i	−0.958933	−	0.283632i	$-0.908461\pi$
$71$		−	4.77985i		−	0.567263i	0.958933	−	0.283632i	$-0.0915393\pi$
$72$	−7.70963	−	3.54423i	−0.908589	−	0.417691i
$73$			3.66416i			0.428858i	0.976740	+	0.214429i	$0.0687890\pi$
$73$			3.66416i			0.428858i	−0.976740	+	0.214429i	$0.931211\pi$
$74$	3.49895	−	7.00832i	0.406744	−	0.814701i
$75$	−1.56916	−	0.733312i	−0.181191	−	0.0846756i
$76$	−8.92479	−	1.26413i	−1.02374	−	0.145005i
$77$	1.79049	−	6.68219i	0.204045	−	0.761506i
$78$	0.813878	+	5.49761i	0.0921535	+	0.622482i
$79$	13.1905	+	7.61552i	1.48404	+	0.856813i	0.999835	−	0.0181389i	$-0.00577412\pi$
$79$	13.1905	+	7.61552i	1.48404	+	0.856813i	0.484209	+	0.874952i	$0.339107\pi$
$80$	2.06755	−	3.42421i	0.231159	−	0.382838i
$81$	8.46751	−	3.04980i	0.940834	−	0.338867i
$82$	1.23263	−	1.39172i	0.136121	−	0.153690i
$83$	−0.511272	−	1.90809i	−0.0561194	−	0.209440i	0.932173	−	0.362014i	$-0.117911\pi$
$83$	−0.511272	−	1.90809i	−0.0561194	−	0.209440i	−0.988292	+	0.152573i	$0.951244\pi$
$84$	−0.797899	−	3.78955i	−0.0870579	−	0.413474i
$85$	−1.69795	+	6.33683i	−0.184168	+	0.687326i
$86$	−11.4414	+	7.56401i	−1.23376	+	0.815648i
$87$	11.3887	−	4.13433i	1.22099	−	0.443247i
$88$	−16.4892	−	5.86921i	−1.75776	−	0.625660i
$89$	12.2779			1.30145			0.650727	−	0.759312i	$-0.274464\pi$
$89$	12.2779			1.30145			0.650727	+	0.759312i	$0.274464\pi$
$90$	0.981277	+	4.12760i	0.103436	+	0.435087i
$91$	−1.79353	+	1.79353i	−0.188013	+	0.188013i
$92$	−4.86850	+	11.4351i	−0.507576	+	1.19219i
$93$	−5.03587	+	3.51987i	−0.522196	+	0.364993i
$94$	−7.34682	−	1.49886i	−0.757767	−	0.154596i
$95$	2.25347	+	3.90312i	0.231201	+	0.400452i
$96$	−9.71860	+	1.24451i	−0.991901	+	0.127017i
$97$	2.16946	−	3.75762i	0.220275	−	0.381528i	−0.734616	−	0.678483i	$-0.762638\pi$
$97$	2.16946	−	3.75762i	0.220275	−	0.381528i	0.954892	+	0.296955i	$0.0959711\pi$
$98$	−5.39174	+	6.08763i	−0.544648	+	0.614943i
$99$	16.8381	−	7.81740i	1.69230	−	0.785678i
$100$	−1.98535	+	0.241595i	−0.198535	+	0.0241595i
$101$	−3.13292	−	11.6922i	−0.311737	−	1.16342i	−0.926989	−	0.375088i	$-0.877612\pi$
$101$	−3.13292	−	11.6922i	−0.311737	−	1.16342i	0.615252	−	0.788330i	$-0.289054\pi$
$102$	14.7456	−	6.38740i	1.46003	−	0.632447i
$103$	1.35242	+	2.34246i	0.133258	+	0.230809i	0.924931	−	0.380136i	$-0.124123\pi$
$103$	1.35242	+	2.34246i	0.133258	+	0.230809i	−0.791673	+	0.610945i	$0.790789\pi$
$104$	4.15978	+	4.88649i	0.407900	+	0.479159i
$105$	−1.24589	+	1.48226i	−0.121586	+	0.144654i
$106$	3.90076	+	1.94748i	0.378875	+	0.189156i
$107$	−10.2790	−	10.2790i	−0.993707	−	0.993707i	0.00627345	−	0.999980i	$-0.498003\pi$
$107$	−10.2790	−	10.2790i	−0.993707	−	0.993707i	−0.999980	+	0.00627345i	$0.998003\pi$
$108$	6.42754	−	8.16619i	0.618491	−	0.785792i
$109$	−0.844282	+	0.844282i	−0.0808675	+	0.0808675i	−0.746384	−	0.665516i	$-0.768212\pi$
$109$	−0.844282	+	0.844282i	−0.0808675	+	0.0808675i	0.665516	+	0.746384i	$0.268212\pi$
$110$	2.77235	+	8.30057i	0.264333	+	0.791428i
$111$	7.34402	+	6.17286i	0.697063	+	0.585902i
$112$	−3.09938	−	3.22340i	−0.292864	−	0.304583i
$113$	8.13568	−	4.69714i	0.765341	−	0.441870i	−0.0658694	−	0.997828i	$-0.520982\pi$
$113$	8.13568	−	4.69714i	0.765341	−	0.441870i	0.831210	+	0.555959i	$0.187649\pi$
$114$	4.06022	−	10.2659i	0.380274	−	0.961494i
$115$	6.00244	−	1.60835i	0.559730	−	0.149979i
$116$	8.62514	−	11.0151i	0.800824	−	1.02273i
$117$	−6.77965	−	0.604601i	−0.626779	−	0.0558954i
$118$	4.34302	−	0.263277i	0.399808	−	0.0242366i
$119$	6.35149	+	3.66704i	0.582241	+	0.336157i
$120$	3.48575	+	3.44232i	0.318204	+	0.314239i
$121$	23.6362	−	13.6463i	2.14874	−	1.24058i
$122$	−15.3641	+	10.1574i	−1.39100	+	0.919605i
$123$	1.30442	+	1.86624i	0.117616	+	0.168273i
$124$	−2.77911	+	6.52757i	−0.249572	+	0.586193i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	4.74109	+	0.134668i	0.422370	+	0.0119972i
$127$		−	5.88983i		−	0.522638i	−0.965253	−	0.261319i	$-0.915843\pi$
$127$		−	5.88983i		−	0.522638i	0.965253	−	0.261319i	$-0.0841574\pi$
$128$	−8.75707	+	7.16335i	−0.774023	+	0.633157i
$129$	−5.73208	−	15.7899i	−0.504682	−	1.39023i
$130$	0.641398	−	3.14388i	0.0562543	−	0.275737i
$131$	−19.9370	−	5.34210i	−1.74190	−	0.466741i	−0.759034	−	0.651052i	$-0.774328\pi$
$131$	−19.9370	−	5.34210i	−1.74190	−	0.466741i	−0.982868	+	0.184310i	$0.940995\pi$
$132$	11.7095	−	17.9555i	1.01918	−	1.56283i
$133$	4.86679	−	1.30405i	0.422004	−	0.113076i
$134$	4.82502	−	0.292496i	0.416818	−	0.0252678i
$135$	−5.19614	−	0.0130705i	−0.447212	−	0.00112493i
$136$	10.5347	−	15.2751i	0.903346	−	1.30983i
$137$	−6.97425	+	12.0798i	−0.595850	+	1.03204i	0.397576	+	0.917569i	$0.369852\pi$
$137$	−6.97425	+	12.0798i	−0.595850	+	1.03204i	−0.993426	+	0.114474i	$0.963482\pi$
$138$	−12.2235	−	9.07099i	−1.04053	−	0.772174i
$139$	−14.9024	−	3.99310i	−1.26401	−	0.338690i	−0.436276	−	0.899813i	$-0.643703\pi$
$139$	−14.9024	−	3.99310i	−1.26401	−	0.338690i	−0.827732	+	0.561123i	$0.810369\pi$
$140$	−0.313564	+	2.21377i	−0.0265010	+	0.187098i
$141$	3.88802	−	8.31966i	0.327430	−	0.700642i
$142$	6.41156	−	2.14143i	0.538046	−	0.179705i
$143$	−14.0399			−1.17408
$144$	1.30012	−	11.9294i	0.108344	−	0.994114i
$145$	−6.99511			−0.580912
$146$	−4.91501	+	1.64159i	−0.406769	+	0.135859i
$147$	−5.70579	−	8.16327i	−0.470606	−	0.673295i
$148$	10.9684	+	1.55358i	0.901593	+	0.127704i
$149$	−10.6685	−	2.85862i	−0.873998	−	0.234187i	−0.206182	−	0.978514i	$-0.566104\pi$
$149$	−10.6685	−	2.85862i	−0.873998	−	0.234187i	−0.667816	+	0.744326i	$0.732771\pi$
$150$	0.280645	−	2.43336i	0.0229145	−	0.198683i
$151$	8.36341	−	14.4858i	0.680605	−	1.17884i	−0.294192	−	0.955746i	$-0.595051\pi$
$151$	8.36341	−	14.4858i	0.680605	−	1.17884i	0.974797	−	0.223095i	$-0.0716161\pi$
$152$	−2.30275	−	12.5378i	−0.186778	−	1.01695i
$153$	3.38508	+	19.3878i	0.273668	+	1.56741i
$154$	9.76547	−	0.591989i	0.786924	−	0.0477038i
$155$	3.42641	−	0.918102i	0.275215	−	0.0737438i
$156$	−7.00973	+	3.55471i	−0.561228	+	0.284605i
$157$	0.570739	+	0.152929i	0.0455499	+	0.0122051i	0.281522	−	0.959555i	$-0.409161\pi$
$157$	0.570739	+	0.152929i	0.0455499	+	0.0122051i	−0.235972	+	0.971760i	$0.575827\pi$
$158$	−4.30577	+	21.1052i	−0.342549	+	1.67904i
$159$	−3.43575	+	4.08760i	−0.272473	+	0.324168i
$160$	5.51944	+	1.23927i	0.436350	+	0.0979732i
$161$		−	6.94705i		−	0.547505i
$162$	7.88447	+	9.99175i	0.619463	+	0.785026i
$163$	9.86312	+	9.86312i	0.772539	+	0.772539i	0.978550	−	0.206010i	$-0.0660481\pi$
$163$	9.86312	+	9.86312i	0.772539	+	0.772539i	−0.206010	+	0.978550i	$0.566048\pi$
$164$	2.41905	+	1.02991i	0.188896	+	0.0804224i
$165$	−10.6781	+	0.925193i	−0.831290	+	0.0720261i
$166$	2.33041	−	1.54066i	0.180875	−	0.119578i
$167$	5.77396	−	3.33360i	0.446802	−	0.257961i	−0.259676	−	0.965696i	$-0.583616\pi$
$167$	5.77396	−	3.33360i	0.446802	−	0.257961i	0.706479	+	0.707734i	$0.250283\pi$
$168$	4.72574	−	2.76805i	0.364599	−	0.213560i
$169$	−6.80030	−	3.92615i	−0.523100	−	0.302012i
$170$	−9.26077	+	0.561393i	−0.710268	+	0.0430569i
$171$	11.0626	+	7.77378i	0.845977	+	0.594476i
$172$	−15.2720	−	11.9584i	−1.16448	−	0.911820i
$173$	7.75325	−	2.07748i	0.589469	−	0.157948i	0.0482583	−	0.998835i	$-0.484633\pi$
$173$	7.75325	−	2.07748i	0.589469	−	0.157948i	0.541210	+	0.840887i	$0.317966\pi$
$174$	10.6479	+	13.4242i	0.807219	+	1.01769i
$175$	0.968161	−	0.558968i	0.0731861	−	0.0422540i
$176$	0.485444	−	24.7477i	0.0365917	−	1.86543i
$177$	−0.929747	+	5.24713i	−0.0698841	+	0.394398i
$178$	5.50065	+	16.4693i	0.412291	+	1.23442i
$179$	3.14271	−	3.14271i	0.234897	−	0.234897i	−0.579836	−	0.814733i	$-0.696883\pi$
$179$	3.14271	−	3.14271i	0.234897	−	0.234897i	0.814733	+	0.579836i	$0.196883\pi$
$180$	−5.09703	+	3.16548i	−0.379911	+	0.235941i
$181$	0.846425	+	0.846425i	0.0629143	+	0.0629143i	0.737864	−	0.674950i	$-0.235835\pi$
$181$	0.846425	+	0.846425i	0.0629143	+	0.0629143i	−0.674950	+	0.737864i	$0.735835\pi$
$182$	−3.20932	−	1.60227i	−0.237890	−	0.118768i
$183$	−7.69736	−	21.2036i	−0.569005	−	1.56742i
$184$	−17.5199	−	1.40741i	−1.29159	−	0.103756i
$185$	−2.76946	−	4.79684i	−0.203615	−	0.352671i
$186$	−6.97759	−	5.17805i	−0.511622	−	0.379673i
$187$	10.5071	+	39.2130i	0.768355	+	2.86754i
$188$	−1.28093	−	10.5263i	−0.0934217	−	0.767712i
$189$	−1.51758	+	5.60723i	−0.110388	+	0.407866i
$190$	−4.22597	+	4.77139i	−0.306584	+	0.346153i
$191$	−1.05225	+	1.82255i	−0.0761380	+	0.131875i	−0.901581	−	0.432611i	$-0.857592\pi$
$191$	−1.05225	+	1.82255i	−0.0761380	+	0.131875i	0.825443	+	0.564486i	$0.190926\pi$
$192$	−6.02341	−	12.4787i	−0.434702	−	0.900574i
$193$	2.28332	+	3.95482i	0.164357	+	0.284674i	0.936427	−	0.350863i	$-0.114112\pi$
$193$	2.28332	+	3.95482i	0.164357	+	0.284674i	−0.772070	+	0.635537i	$0.780779\pi$
$194$	6.01231	+	1.22660i	0.431659	+	0.0880648i
$195$	3.56019	+	1.66378i	0.254950	+	0.119146i
$196$	−10.5814	−	4.50501i	−0.755811	−	0.321786i
$197$	−11.6891	+	11.6891i	−0.832815	+	0.832815i	−0.987901	−	0.155086i	$-0.950434\pi$
$197$	−11.6891	+	11.6891i	−0.832815	+	0.832815i	0.155086	+	0.987901i	$0.450434\pi$
$198$	18.0297	+	19.0839i	1.28132	+	1.35624i
$199$	−0.150713			−0.0106837			−0.00534187	−	0.999986i	$-0.501700\pi$
$199$	−0.150713			−0.0106837			−0.00534187	+	0.999986i	$0.501700\pi$
$200$	−1.21353	−	2.55487i	−0.0858097	−	0.180656i
$201$	−1.03293	+	5.82946i	−0.0728573	+	0.411178i
$202$	14.2800	−	9.44067i	1.00474	−	0.664243i
$203$	−2.02399	+	7.55362i	−0.142056	+	0.530160i
$204$	15.1741	+	16.9177i	1.06240	+	1.18448i
$205$	−0.340239	−	1.26979i	−0.0237633	−	0.0886859i
$206$	−2.53621	+	2.86355i	−0.176706	+	0.199513i
$207$	14.3011	−	11.9592i	0.993994	−	0.831224i
$208$	−4.69097	+	7.76903i	−0.325261	+	0.538685i
$209$	24.1529	+	13.9447i	1.67069	+	0.964576i
$210$	−2.54644	−	1.00713i	−0.175721	−	0.0694984i
$211$	−1.73295	+	6.46746i	−0.119301	+	0.445238i	−0.999573	−	0.0292322i	$-0.990694\pi$
$211$	−1.73295	+	6.46746i	−0.119301	+	0.445238i	0.880271	+	0.474470i	$0.157360\pi$
$212$	−0.864707	+	6.10487i	−0.0593884	+	0.419284i
$213$	0.714641	+	8.24803i	0.0489664	+	0.565146i
$214$	9.18285	−	18.3931i	0.627727	−	1.25732i
$215$			9.69844i			0.661428i
$216$	13.8335	+	4.96319i	0.941253	+	0.337702i
$217$		−	3.96563i		−	0.269204i
$218$	−1.51075	−	0.754249i	−0.102321	−	0.0510842i
$219$	−0.547834	−	6.32283i	−0.0370192	−	0.427257i
$220$	−9.89212	+	7.43751i	−0.666927	+	0.501437i
$221$	3.85240	−	14.3773i	0.259140	−	0.967125i
$222$	−4.98991	+	12.6166i	−0.334901	+	0.846771i
$223$	−6.77748	−	3.91298i	−0.453854	−	0.262033i	0.255603	−	0.966782i	$-0.417726\pi$
$223$	−6.77748	−	3.91298i	−0.453854	−	0.262033i	−0.709456	+	0.704749i	$0.751059\pi$
$224$	2.93523	−	5.60155i	0.196118	−	0.374269i
$225$	2.81735	+	1.03079i	0.187824	+	0.0687191i
$226$	9.94551	+	8.80862i	0.661565	+	0.585941i
$227$	−2.93120	−	10.9394i	−0.194550	−	0.726072i	−0.992383	−	0.123193i	$-0.960687\pi$
$227$	−2.93120	−	10.9394i	−0.194550	−	0.726072i	0.797832	−	0.602879i	$-0.205980\pi$
$228$	15.5895	+	0.847004i	1.03244	+	0.0560942i
$229$	4.03420	−	15.0558i	0.266587	−	0.994917i	−0.694684	−	0.719315i	$-0.744456\pi$
$229$	4.03420	−	15.0558i	0.266587	−	0.994917i	0.961272	−	0.275602i	$-0.0888773\pi$
$230$	4.84656	+	7.33095i	0.319573	+	0.483389i
$231$	−2.09058	+	11.7984i	−0.137550	+	0.776277i
$232$	18.6396	+	6.63462i	1.22375	+	0.435584i
$233$	−13.8370			−0.906489			−0.453245	−	0.891386i	$-0.649734\pi$
$233$	−13.8370			−0.906489			−0.453245	+	0.891386i	$0.649734\pi$
$234$	−2.22637	−	9.36492i	−0.145543	−	0.612204i
$235$	−3.74908	+	3.74908i	−0.244563	+	0.244563i
$236$	2.29888	+	5.70767i	0.149644	+	0.371538i
$237$	−23.8999	−	11.1691i	−1.55247	−	0.725512i
$238$	−2.07332	+	10.1626i	−0.134393	+	0.658744i
$239$	−14.8872	−	25.7854i	−0.962973	−	1.66792i	−0.714966	−	0.699160i	$-0.753558\pi$
$239$	−14.8872	−	25.7854i	−0.962973	−	1.66792i	−0.248007	−	0.968758i	$-0.579776\pi$
$240$	−3.05578	+	6.21789i	−0.197250	+	0.401363i
$241$	−13.8436	+	23.9778i	−0.891745	+	1.54455i	−0.0539639	+	0.998543i	$0.517186\pi$
$241$	−13.8436	+	23.9778i	−0.891745	+	1.54455i	−0.837782	+	0.546006i	$0.816148\pi$
$242$	28.8941	+	25.5912i	1.85739	+	1.64507i
$243$	−14.1554	+	6.52868i	−0.908072	+	0.418815i
$244$	−20.5082	−	16.0584i	−1.31290	−	1.02804i
$245$	1.48827	+	5.55429i	0.0950818	+	0.354850i
$246$	−1.91893	+	2.58582i	−0.122346	+	0.164866i
$247$	−5.11279	−	8.85561i	−0.325319	−	0.563469i
$248$	−10.0010	−	0.803399i	−0.635064	−	0.0510159i
$249$	1.16753	+	3.21614i	0.0739889	+	0.203814i
$250$	−0.631702	+	1.26529i	−0.0399524	+	0.0800238i
$251$	15.7578	+	15.7578i	0.994622	+	0.994622i	0.999986	−	0.00536344i	$-0.00170724\pi$
$251$	15.7578	+	15.7578i	0.994622	+	0.994622i	−0.00536344	+	0.999986i	$0.501707\pi$
$252$	1.94342	+	6.41991i	0.122424	+	0.404416i
$253$	27.1911	−	27.1911i	1.70949	−	1.70949i
$254$	7.90046	−	2.63871i	0.495719	−	0.165568i
$255$	1.98253	−	11.1886i	0.124151	−	0.700658i
$256$	−13.5320	−	8.53724i	−0.845751	−	0.533578i
$257$	3.06377	−	1.76887i	0.191113	−	0.110339i	−0.401391	−	0.915907i	$-0.631473\pi$
$257$	3.06377	−	1.76887i	0.191113	−	0.110339i	0.592503	+	0.805568i	$0.298140\pi$
$258$	18.6122	−	14.7630i	1.15874	−	0.919102i
$259$	−5.98116	+	1.60265i	−0.371651	+	0.0995837i
$260$	4.50448	−	0.548143i	0.279356	−	0.0339944i
$261$	−19.0340	+	8.83687i	−1.17818	+	0.546989i
$262$	−1.76626	−	29.1363i	−0.109120	−	1.80004i
$263$	−5.70508	−	3.29383i	−0.351790	−	0.203106i	0.313683	−	0.949528i	$-0.398437\pi$
$263$	−5.70508	−	3.29383i	−0.351790	−	0.203106i	−0.665473	+	0.746422i	$0.731770\pi$
$264$	29.3310	+	7.66251i	1.80520	+	0.471595i
$265$	2.66987	−	1.54145i	0.164009	−	0.0946906i
$266$	3.92960	+	5.94395i	0.240939	+	0.364447i
$267$	−21.1866	+	1.83569i	−1.29660	+	0.112342i
$268$	2.55401	+	6.34111i	0.156011	+	0.387345i
$269$	15.1101	+	15.1101i	0.921280	+	0.921280i	0.997120	−	0.0758397i	$-0.0241637\pi$
$269$	15.1101	+	15.1101i	0.921280	+	0.921280i	−0.0758397	+	0.997120i	$0.524164\pi$
$270$	−2.31040	−	6.97582i	−0.140606	−	0.424535i
$271$		−	8.94506i		−	0.543374i	−0.962386	−	0.271687i	$-0.912418\pi$
$271$		−	8.94506i		−	0.543374i	0.962386	−	0.271687i	$-0.0875815\pi$
$272$	25.2093	+	7.28760i	1.52854	+	0.441876i
$273$	2.82673	−	3.36304i	0.171082	−	0.203540i
$274$	−19.3280	−	3.94320i	−1.16765	−	0.238218i
$275$	5.97725	+	1.60160i	0.360442	+	0.0965801i
$276$	6.69133	−	20.4602i	0.402771	−	1.23156i
$277$	−15.1743	+	4.06594i	−0.911735	+	0.244299i	−0.684049	−	0.729436i	$-0.739783\pi$
$277$	−15.1743	+	4.06594i	−0.911735	+	0.244299i	−0.227686	+	0.973735i	$0.573116\pi$
$278$	−1.32024	−	21.7787i	−0.0791827	−	1.30620i
$279$	8.16357	−	6.82675i	0.488740	−	0.408707i
$280$	−3.10998	+	0.571191i	−0.185857	+	0.0341352i
$281$	−2.01368	+	3.48779i	−0.120126	+	0.208064i	−0.919817	−	0.392347i	$-0.871663\pi$
$281$	−2.01368	+	3.48779i	−0.120126	+	0.208064i	0.799691	+	0.600411i	$0.204996\pi$
$282$	12.9017	+	1.48798i	0.768283	+	0.0886077i
$283$	−19.1360	−	5.12748i	−1.13752	−	0.304797i	−0.359565	−	0.933120i	$-0.617075\pi$
$283$	−19.1360	−	5.12748i	−1.13752	−	0.304797i	−0.777952	+	0.628323i	$0.783742\pi$
$284$	5.74492	+	7.64092i	0.340898	+	0.453405i
$285$	−4.47212	−	6.39825i	−0.264905	−	0.379000i
$286$	−6.29005	−	18.8328i	−0.371939	−	1.11361i
$287$	−1.46962			−0.0867488
$288$	16.5842	−	3.60055i	0.977234	−	0.212164i
$289$	−26.0385			−1.53168
$290$	−3.13389	−	9.38306i	−0.184029	−	0.550992i
$291$	−3.18178	+	6.80845i	−0.186519	+	0.399118i
$292$	−4.40397	−	5.85742i	−0.257723	−	0.342780i
$293$	−3.47148	−	0.930182i	−0.202806	−	0.0543418i	0.155986	−	0.987759i	$-0.450145\pi$
$293$	−3.47148	−	0.930182i	−0.202806	−	0.0543418i	−0.358792	+	0.933418i	$0.616811\pi$
$294$	8.39374	−	11.3108i	0.489533	−	0.659662i
$295$	1.53831	−	2.66443i	0.0895639	−	0.155129i
$296$	2.83002	+	15.4087i	0.164492	+	0.895612i
$297$	−27.8868	+	16.0071i	−1.61816	+	0.928825i
$298$	−0.945146	−	15.5912i	−0.0547508	−	0.903172i
$299$	−13.6186	+	3.64911i	−0.787587	+	0.211033i
$300$	3.38978	−	0.713725i	0.195709	−	0.0412070i
$301$	10.4728	+	2.80618i	0.603642	+	0.161745i
$302$	23.1779	+	4.72862i	1.33374	+	0.272102i
$303$	7.15424	+	19.7075i	0.411000	+	1.13217i
$304$	15.7863	−	8.70595i	0.905405	−	0.499321i
$305$			13.0236i			0.745730i
$306$	−24.4898	+	13.2266i	−1.39999	+	0.756117i
$307$	3.36252	+	3.36252i	0.191909	+	0.191909i	0.796521	−	0.604611i	$-0.206672\pi$
$307$	3.36252	+	3.36252i	0.191909	+	0.191909i	−0.604611	+	0.796521i	$0.706672\pi$
$308$	5.16913	+	12.8339i	0.294539	+	0.731281i
$309$	−2.68394	−	3.83991i	−0.152684	−	0.218445i
$310$	2.76659	+	4.18477i	0.157132	+	0.237679i
$311$	19.7186	−	11.3845i	1.11814	−	0.645557i	0.177213	−	0.984173i	$-0.443292\pi$
$311$	19.7186	−	11.3845i	1.11814	−	0.645557i	0.940925	+	0.338615i	$0.109959\pi$
$312$	−7.90865	−	7.81012i	−0.447739	−	0.442161i
$313$	10.5865	+	6.11211i	0.598384	+	0.345477i	0.768405	−	0.639963i	$-0.221050\pi$
$313$	10.5865	+	6.11211i	0.598384	+	0.345477i	−0.170022	+	0.985440i	$0.554384\pi$
$314$	0.0505630	+	0.834089i	0.00285344	+	0.0470704i
$315$	1.92827	−	2.74405i	0.108646	−	0.154610i
$316$	−30.2390	+	3.67974i	−1.70108	+	0.207002i
$317$	−31.4481	+	8.42648i	−1.76630	+	0.473278i	−0.987979	−	0.154589i	$-0.950595\pi$
$317$	−31.4481	+	8.42648i	−1.76630	+	0.473278i	−0.778320	+	0.627868i	$0.783928\pi$
$318$	−7.02226	−	2.77733i	−0.393789	−	0.155745i
$319$	−37.4872	+	21.6432i	−2.09888	+	1.21179i
$320$	0.810446	+	7.95884i	0.0453053	+	0.444913i
$321$	19.2741	+	16.2004i	1.07577	+	0.904221i
$322$	9.31860	−	3.11237i	0.519305	−	0.173445i
$323$	−20.9072	+	20.9072i	−1.16331	+	1.16331i
$324$	−9.87034	+	15.0525i	−0.548352	+	0.836247i
$325$	−1.60432	−	1.60432i	−0.0889917	−	0.0889917i
$326$	−8.81134	+	17.6489i	−0.488015	+	0.977484i
$327$	1.33065	−	1.58311i	0.0735852	−	0.0875462i
$328$	−0.297731	+	3.70626i	−0.0164394	+	0.204644i
$329$	2.96365	+	5.13319i	0.163391	+	0.283002i
$330$	−6.02495	−	13.9088i	−0.331663	−	0.765657i
$331$	1.29195	+	4.82163i	0.0710121	+	0.265021i	0.992300	−	0.123862i	$-0.0395279\pi$
$331$	1.29195	+	4.82163i	0.0710121	+	0.265021i	−0.921287	+	0.388882i	$0.872861\pi$
$332$	3.11065	+	2.43572i	0.170719	+	0.133677i
$333$	−13.5956	−	9.55379i	−0.745037	−	0.523545i
$334$	7.05840	+	6.25155i	0.386219	+	0.342069i
$335$	1.70903	−	2.96013i	0.0933744	−	0.161729i
$336$	5.83018	+	5.09887i	0.318062	+	0.278166i
$337$	−12.9922	−	22.5031i	−0.707728	−	1.22582i	−0.965698	−	0.259668i	$-0.916387\pi$
$337$	−12.9922	−	22.5031i	−0.707728	−	1.22582i	0.257970	−	0.966153i	$-0.416946\pi$
$338$	2.21982	−	10.8807i	0.120743	−	0.591832i
$339$	−13.3365	+	9.32169i	−0.724342	+	0.506285i
$340$	−4.90198	−	12.1706i	−0.265847	−	0.660046i
$341$	15.5216	−	15.5216i	0.840544	−	0.840544i
$342$	−5.47138	+	18.3218i	−0.295858	+	0.990730i
$343$	14.2539			0.769640
$344$	9.19864	−	25.8430i	0.495958	−	1.39336i
$345$	−10.1173	+	3.67277i	−0.544695	+	0.197736i
$346$	6.26022	+	9.46927i	0.336552	+	0.509071i
$347$	8.66607	−	32.3422i	0.465219	−	1.73622i	−0.190943	−	0.981601i	$-0.561155\pi$
$347$	8.66607	−	32.3422i	0.465219	−	1.73622i	0.656162	−	0.754620i	$-0.272179\pi$
$348$	−13.2365	+	20.2971i	−0.709552	+	1.08804i
$349$	−0.571399	−	2.13249i	−0.0305863	−	0.114150i	0.948945	−	0.315442i	$-0.102153\pi$
$349$	−0.571399	−	2.13249i	−0.0305863	−	0.114150i	−0.979531	+	0.201292i	$0.935486\pi$
$350$	1.18353	+	1.04824i	0.0632625	+	0.0560309i
$351$	11.7893	+	0.0296551i	0.629265	+	0.00158287i
$352$	33.4134	−	10.4361i	1.78094	−	0.556246i
$353$	3.37236	+	1.94703i	0.179492	+	0.103630i	0.587054	−	0.809548i	$-0.300288\pi$
$353$	3.37236	+	1.94703i	0.179492	+	0.103630i	−0.407562	+	0.913178i	$0.633621\pi$
$354$	−7.45490	+	1.10364i	−0.396223	+	0.0586577i
$355$	1.23712	−	4.61698i	0.0656593	−	0.245044i
$356$	−19.6271	+	14.7569i	−1.04023	+	0.782112i
$357$	−11.5083	−	5.37817i	−0.609085	−	0.284643i
$358$	5.62352	+	2.80757i	0.297212	+	0.148385i
$359$		−	2.99019i		−	0.157816i	−0.996882	−	0.0789081i	$-0.974857\pi$
$359$		−	2.99019i		−	0.157816i	0.996882	−	0.0789081i	$-0.0251434\pi$
$360$	−6.52962	−	5.41886i	−0.344141	−	0.285599i
$361$			1.31249i			0.0690786i
$362$	−0.756164	+	1.51458i	−0.0397431	+	0.0796046i
$363$	−38.7459	+	27.0818i	−2.03363	+	1.42143i
$364$	0.711431	−	5.02273i	0.0372891	−	0.263263i
$365$	−0.948355	+	3.53931i	−0.0496392	+	0.185256i
$366$	24.9935	−	19.8245i	1.30643	−	1.03624i
$367$	10.4311	+	6.02241i	0.544500	+	0.314367i	0.746901	−	0.664936i	$-0.231541\pi$
$367$	10.4311	+	6.02241i	0.544500	+	0.314367i	−0.202401	+	0.979303i	$0.564874\pi$
$368$	−5.96128	−	24.1313i	−0.310753	−	1.25793i
$369$	−2.52992	−	3.02533i	−0.131702	−	0.157492i
$370$	5.19361	−	5.86393i	0.270003	−	0.304851i
$371$	−0.892016	−	3.32905i	−0.0463112	−	0.172836i
$372$	3.81965	−	11.6794i	0.198040	−	0.605548i
$373$	3.16816	−	11.8237i	0.164041	−	0.612210i	−0.834119	−	0.551584i	$-0.814024\pi$
$373$	3.16816	−	11.8237i	0.164041	−	0.612210i	0.998161	−	0.0606262i	$-0.0193098\pi$
$374$	−47.8920	+	31.6619i	−2.47644	+	1.63720i
$375$	−1.32589	−	1.11445i	−0.0684689	−	0.0575501i
$376$	13.5459	−	6.43414i	0.698576	−	0.331816i
$377$	15.8709			0.817391
$378$	−8.20129	+	0.476465i	−0.421829	+	0.0245067i
$379$	−4.23729	+	4.23729i	−0.217655	+	0.217655i	−0.807510	−	0.589854i	$-0.799185\pi$
$379$	−4.23729	+	4.23729i	−0.217655	+	0.217655i	0.589854	+	0.807510i	$0.299185\pi$
$380$	−8.29351	−	3.53096i	−0.425448	−	0.181134i
$381$	0.880596	+	10.1634i	0.0451143	+	0.520687i
$382$	−2.91614	−	0.594935i	−0.149203	−	0.0304395i
$383$	−17.7006	−	30.6584i	−0.904459	−	1.56657i	−0.821642	−	0.570004i	$-0.806941\pi$
$383$	−17.7006	−	30.6584i	−0.904459	−	1.56657i	−0.0828175	−	0.996565i	$-0.526392\pi$
$384$	14.0401	−	13.6703i	0.716480	−	0.697608i
$385$	3.45895	−	5.99108i	0.176285	−	0.305334i
$386$	−4.28194	+	4.83459i	−0.217945	+	0.246074i
$387$	12.2520	+	26.3899i	0.622803	+	1.34147i
$388$	1.04826	+	8.61429i	0.0532173	+	0.437325i
$389$	−9.60064	−	35.8301i	−0.486772	−	1.81666i	−0.571947	−	0.820290i	$-0.693812\pi$
$389$	−9.60064	−	35.8301i	−0.486772	−	1.81666i	0.0851759	−	0.996366i	$-0.472855\pi$
$390$	−0.636741	+	5.52093i	−0.0322427	+	0.279563i
$391$	20.3837	+	35.3055i	1.03085	+	1.78548i
$392$	1.30233	−	16.2119i	0.0657776	−	0.818822i
$393$	35.2017	+	6.23744i	1.77569	+	0.314637i
$394$	−20.9163	−	10.4426i	−1.05375	−	0.526091i
$395$	10.7700	+	10.7700i	0.541896	+	0.541896i
$396$	−17.5212	+	32.7345i	−0.880471	+	1.64497i
$397$	3.28027	−	3.28027i	0.164632	−	0.164632i	−0.619983	−	0.784615i	$-0.712861\pi$
$397$	3.28027	−	3.28027i	0.164632	−	0.164632i	0.784615	+	0.619983i	$0.212861\pi$
$398$	−0.0675212	−	0.202162i	−0.00338453	−	0.0101335i
$399$	−8.20309	+	2.97789i	−0.410668	+	0.149081i
$400$	2.88335	−	2.77241i	0.144168	−	0.138621i
$401$	21.9105	−	12.6501i	1.09416	−	0.631714i	0.159480	−	0.987201i	$-0.449018\pi$
$401$	21.9105	−	12.6501i	1.09416	−	0.631714i	0.934681	+	0.355487i	$0.115685\pi$
$402$	−8.28225	+	1.22612i	−0.413081	+	0.0611533i
$403$	−7.77401	+	2.08304i	−0.387251	+	0.103764i
$404$	19.0611	+	14.9253i	0.948325	+	0.742564i
$405$	8.96833	−	0.754327i	0.445640	−	0.0374828i
$406$	−11.0390	+	0.669191i	−0.547856	+	0.0332114i
$407$	−29.6834	−	17.1377i	−1.47135	−	0.849485i
$408$	−15.8948	+	27.9335i	−0.786909	+	1.38291i
$409$	−30.2002	+	17.4361i	−1.49330	+	0.862159i	−0.999970	−	0.00768181i	$-0.997555\pi$
$409$	−30.2002	+	17.4361i	−1.49330	+	0.862159i	−0.493333	+	0.869841i	$0.664221\pi$
$410$	1.55083	−	1.02527i	0.0765901	−	0.0506344i
$411$	10.2286	−	21.8874i	0.504540	−	1.07963i
$412$	−4.97735	−	2.11911i	−0.245216	−	0.104401i
$413$	−2.43207	−	2.43207i	−0.119674	−	0.119674i
$414$	22.4489	+	13.8252i	1.10330	+	0.679473i
$415$		−	1.97540i		−	0.0969687i
$416$	−12.5228	−	2.81173i	−0.613980	−	0.137856i
$417$	26.3124	+	4.66235i	1.28853	+	0.228316i
$418$	−7.88426	+	38.6455i	−0.385632	+	1.89022i
$419$	−0.277976	−	0.0744833i	−0.0135800	−	0.00363875i	0.252023	−	0.967721i	$-0.418904\pi$
$419$	−0.277976	−	0.0744833i	−0.0135800	−	0.00363875i	−0.265603	+	0.964083i	$0.585571\pi$
$420$	0.210097	−	3.86694i	0.0102517	−	0.188687i
$421$	−15.8154	+	4.23772i	−0.770794	+	0.206534i	−0.622722	−	0.782443i	$-0.713973\pi$
$421$	−15.8154	+	4.23772i	−0.770794	+	0.206534i	−0.148072	+	0.988977i	$0.547307\pi$
$422$	−9.45167	+	0.572966i	−0.460100	+	0.0278916i
$423$	−5.46523	+	14.9376i	−0.265728	+	0.726291i
$424$	−8.57631	+	1.57516i	−0.416503	+	0.0764965i
$425$	−3.28019	+	5.68145i	−0.159112	+	0.275591i
$426$	−10.7435	+	4.65382i	−0.520526	+	0.225478i
$427$	14.0635	+	3.76829i	0.680578	+	0.182360i
$428$	28.7860	+	4.07732i	1.39143	+	0.197085i
$429$	24.2271	−	2.09913i	1.16969	−	0.101347i
$430$	−13.0092	+	4.34502i	−0.627361	+	0.209535i
$431$	−34.6723			−1.67011			−0.835054	−	0.550169i	$-0.814563\pi$
$431$	−34.6723			−1.67011			−0.835054	+	0.550169i	$0.814563\pi$
$432$	−0.459898	+	20.7795i	−0.0221269	+	0.999755i
$433$	−16.1784			−0.777482			−0.388741	−	0.921347i	$-0.627090\pi$
$433$	−16.1784			−0.777482			−0.388741	+	0.921347i	$0.627090\pi$
$434$	5.31939	−	1.77665i	0.255339	−	0.0852819i
$435$	12.0707	−	1.04585i	0.578744	−	0.0501446i
$436$	0.334898	−	2.36439i	0.0160387	−	0.113234i
$437$	27.0526	+	7.24873i	1.29410	+	0.346754i
$438$	8.23584	−	3.56755i	0.393524	−	0.170464i
$439$	−6.84948	+	11.8636i	−0.326908	+	0.566221i	−0.981897	−	0.189418i	$-0.939340\pi$
$439$	−6.84948	+	11.8636i	−0.326908	+	0.566221i	0.654989	+	0.755639i	$0.272673\pi$
$440$	−14.4083	−	9.93694i	−0.686888	−	0.473725i
$441$	11.0663	+	13.2333i	0.526968	+	0.630159i
$442$	21.0113	−	1.27372i	0.999406	−	0.0605846i
$443$	29.1243	−	7.80384i	1.38374	−	0.370772i	0.511261	−	0.859425i	$-0.329178\pi$
$443$	29.1243	−	7.80384i	1.38374	−	0.370772i	0.872478	+	0.488654i	$0.162512\pi$
$444$	−19.1591	−	1.04095i	−0.909252	−	0.0494012i
$445$	11.8595	+	3.17775i	0.562196	+	0.150640i
$446$	2.21238	−	10.8442i	0.104759	−	0.513488i
$447$	18.8368	+	3.33773i	0.890951	+	0.157869i
$448$	8.82880	+	1.42768i	0.417121	+	0.0674516i
$449$		−	21.6260i		−	1.02059i	−0.859999	−	0.510296i	$-0.829536\pi$
$449$		−	21.6260i		−	1.02059i	0.859999	−	0.510296i	$-0.170464\pi$
$450$	−0.120462	+	4.24093i	−0.00567861	+	0.199919i
$451$	−5.75215	−	5.75215i	−0.270858	−	0.270858i
$452$	−7.35995	+	17.2870i	−0.346183	+	0.813113i
$453$	−12.2660	+	26.2470i	−0.576306	+	1.23319i
$454$	13.3606	−	8.83281i	0.627044	−	0.414544i
$455$	−2.19661	+	1.26822i	−0.102979	+	0.0594549i
$456$	5.84814	+	21.2908i	0.273864	+	0.997034i
$457$	−19.5911	−	11.3109i	−0.916432	−	0.529102i	−0.0339369	−	0.999424i	$-0.510805\pi$
$457$	−19.5911	−	11.3109i	−0.916432	−	0.529102i	−0.882495	+	0.470322i	$0.844138\pi$
$458$	22.0029	−	1.33383i	1.02813	−	0.0623257i
$459$	−8.73995	−	32.9492i	−0.407946	−	1.53794i
$460$	−7.66223	+	9.78541i	−0.357254	+	0.456247i
$461$	4.66096	−	1.24890i	0.217082	−	0.0581671i	−0.148639	−	0.988892i	$-0.547489\pi$
$461$	4.66096	−	1.24890i	0.217082	−	0.0581671i	0.365721	+	0.930725i	$0.380822\pi$
$462$	−16.7627	+	2.48158i	−0.779869	+	0.115453i
$463$	10.9165	−	6.30265i	0.507333	−	0.292909i	−0.224403	−	0.974496i	$-0.572043\pi$
$463$	10.9165	−	6.30265i	0.507333	−	0.292909i	0.731737	+	0.681587i	$0.238710\pi$
$464$	−0.548752	+	27.9751i	−0.0254752	+	1.29871i
$465$	−5.77529	+	2.09655i	−0.267823	+	0.0972252i
$466$	−6.19913	−	18.5605i	−0.287169	−	0.859801i
$467$	4.83951	−	4.83951i	0.223946	−	0.223946i	−0.586212	−	0.810158i	$-0.699381\pi$
$467$	4.83951	−	4.83951i	0.223946	−	0.223946i	0.810158	+	0.586212i	$0.199381\pi$
$468$	11.5644	−	7.18200i	0.534566	−	0.331988i
$469$	−2.70198	−	2.70198i	−0.124766	−	0.124766i
$470$	−6.70855	−	3.34928i	−0.309442	−	0.154491i
$471$	−1.00772	−	0.178560i	−0.0464335	−	0.00822762i
$472$	−6.62620	+	5.64077i	−0.304995	+	0.259637i
$473$	30.0075	+	51.9745i	1.37975	+	2.38979i
$474$	4.27451	−	37.0626i	0.196335	−	1.70234i
$475$	1.16648	+	4.35337i	0.0535218	+	0.199746i
$476$	−14.5607	+	1.77187i	−0.667390	+	0.0812137i
$477$	5.31754	−	7.56719i	0.243473	−	0.346478i
$478$	27.9182	−	31.5215i	1.27695	−	1.44176i
$479$	−4.54963	+	7.88019i	−0.207878	+	0.360055i	−0.951046	−	0.309050i	$-0.899989\pi$
$479$	−4.54963	+	7.88019i	−0.207878	+	0.360055i	0.743168	+	0.669105i	$0.233322\pi$
$480$	−9.70955	−	1.31325i	−0.443178	−	0.0599416i
$481$	6.28350	+	10.8833i	0.286503	+	0.496237i
$482$	−38.3654	−	7.82710i	−1.74749	−	0.356515i
$483$	1.03866	+	11.9877i	0.0472608	+	0.545461i
$484$	−21.3825	+	50.2230i	−0.971930	+	2.28287i
$485$	3.06808	−	3.06808i	0.139314	−	0.139314i
$486$	−15.0992	−	16.0628i	−0.684914	−	0.728624i
$487$	29.8785			1.35393			0.676963	−	0.736017i	$-0.263296\pi$
$487$	29.8785			1.35393			0.676963	+	0.736017i	$0.263296\pi$
$488$	12.3525	−	34.7035i	0.559169	−	1.57095i
$489$	−18.4943	−	15.5450i	−0.836342	−	0.702970i
$490$	−6.78361	+	4.48471i	−0.306452	+	0.202599i
$491$	2.32942	−	8.69351i	0.105125	−	0.392332i	−0.893234	−	0.449592i	$-0.851569\pi$
$491$	2.32942	−	8.69351i	0.105125	−	0.392332i	0.998359	+	0.0572593i	$0.0182362\pi$
$492$	−4.32826	−	1.41552i	−0.195133	−	0.0638166i
$493$	−11.8773	−	44.3268i	−0.534928	−	1.99638i
$494$	9.58810	−	10.8256i	0.431389	−	0.487066i
$495$	18.2877	−	3.19300i	0.821970	−	0.143515i
$496$	−3.40291	−	13.7750i	−0.152795	−	0.618516i
$497$	−4.62766	−	2.67178i	−0.207579	−	0.119846i
$498$	−3.79098	+	3.00696i	−0.169878	+	0.134745i
$499$	−6.52855	+	24.3649i	−0.292258	+	1.09072i	0.651112	+	0.758981i	$0.274303\pi$
$499$	−6.52855	+	24.3649i	−0.292258	+	1.09072i	−0.943371	+	0.331741i	$0.892364\pi$
$500$	−1.98023	−	0.280485i	−0.0885588	−	0.0125437i
$501$	−9.46505	+	6.61568i	−0.422867	+	0.295567i
$502$	−14.0774	+	28.1968i	−0.628305	+	1.25848i
$503$			15.5473i			0.693219i	0.938010	+	0.346609i	$0.112667\pi$
$503$			15.5473i			0.693219i	−0.938010	+	0.346609i	$0.887333\pi$
$504$	−7.74082	+	5.48306i	−0.344803	+	0.244235i
$505$		−	12.1047i		−	0.538651i
$506$	48.6554	+	24.2915i	2.16300	+	1.07989i
$507$	12.3215	+	5.75819i	0.547217	+	0.255730i
$508$	7.07901	+	9.41530i	0.314080	+	0.417736i
$509$	−8.16241	+	30.4625i	−0.361792	+	1.35023i	0.509925	+	0.860219i	$0.329673\pi$
$509$	−8.16241	+	30.4625i	−0.361792	+	1.35023i	−0.871717	+	0.490009i	$0.836993\pi$
$510$	15.8963	−	2.35332i	0.703901	−	0.104207i
$511$	3.54750	+	2.04815i	0.156932	+	0.0906048i
$512$	5.38913	−	21.9763i	0.238168	−	0.971224i
$513$	−20.2517	−	11.7603i	−0.894135	−	0.519232i
$514$	3.74532	+	3.31718i	0.165199	+	0.146315i
$515$	0.700064	+	2.61267i	0.0308485	+	0.115128i
$516$	28.1411	+	18.3519i	1.23884	+	0.807898i
$517$	−8.49168	+	31.6914i	−0.373464	+	1.39379i
$518$	−4.82938	−	7.30497i	−0.212191	−	0.320962i
$519$	−13.0683	+	4.74406i	−0.573634	+	0.208241i
$520$	2.75333	+	5.79662i	0.120741	+	0.254198i
$521$	16.5801			0.726386			0.363193	−	0.931714i	$-0.381686\pi$
$521$	16.5801			0.726386			0.363193	+	0.931714i	$0.381686\pi$
$522$	−20.3810	−	21.5727i	−0.892053	−	0.944211i
$523$	6.03065	−	6.03065i	0.263702	−	0.263702i	−0.562854	−	0.826556i	$-0.690297\pi$
$523$	6.03065	−	6.03065i	0.263702	−	0.263702i	0.826556	+	0.562854i	$0.190297\pi$
$524$	38.2913	−	15.4226i	1.67276	−	0.673740i
$525$	−1.58707	+	1.10930i	−0.0692655	+	0.0484137i
$526$	1.86231	−	9.12832i	0.0812006	−	0.398014i
$527$	11.6357	+	20.1537i	0.506860	+	0.877907i
$528$	2.86238	+	42.7768i	0.124569	+	1.86162i
$529$	7.80801	−	13.5239i	0.339479	−	0.587995i
$530$	3.26380	+	2.89071i	0.141770	+	0.125564i
$531$	0.819853	−	9.19338i	0.0355786	−	0.398958i
$532$	−6.21255	+	7.93403i	−0.269348	+	0.343984i
$533$	0.771952	+	2.88096i	0.0334369	+	0.124788i
$534$	−11.9542	−	27.5967i	−0.517308	−	1.19423i
$535$	−7.26834	−	12.5891i	−0.314238	−	0.544276i
$536$	−7.36157	+	6.26678i	−0.317972	+	0.270684i
$537$	−4.95314	+	5.89288i	−0.213744	+	0.254297i
$538$	−13.4988	+	27.0378i	−0.581975	+	1.16568i
$539$	25.1610	+	25.1610i	1.08376	+	1.08376i
$540$	8.32210	−	6.22436i	0.358126	−	0.267854i
$541$	−5.88862	+	5.88862i	−0.253172	+	0.253172i	−0.822270	−	0.569098i	$-0.807293\pi$
$541$	−5.88862	+	5.88862i	−0.253172	+	0.253172i	0.569098	+	0.822270i	$0.307293\pi$
$542$	11.9987	−	4.00750i	0.515387	−	0.172137i
$543$	−1.58713	−	1.33403i	−0.0681102	−	0.0572487i
$544$	1.51865	+	37.0800i	0.0651118	+	1.58979i
$545$	−1.03403	+	0.596997i	−0.0442930	+	0.0255726i
$546$	5.77751	+	2.28503i	0.247254	+	0.0977901i
$547$	21.9627	−	5.88488i	0.939056	−	0.251619i	0.243344	−	0.969940i	$-0.421756\pi$
$547$	21.9627	−	5.88488i	0.939056	−	0.251619i	0.695712	+	0.718321i	$0.255089\pi$
$548$	−3.36988	−	27.6927i	−0.143954	−	1.18297i
$549$	16.4526	+	35.4378i	0.702182	+	1.51245i
$550$	0.529538	+	8.73527i	0.0225796	+	0.372473i
$551$	−27.3028	−	15.7633i	−1.16314	−	0.671537i
$552$	30.4425	−	0.190823i	1.29572	−	0.00812195i
$553$	14.7461	−	8.51367i	0.627068	−	0.362038i
$554$	−12.2522	−	18.5328i	−0.520547	−	0.787384i
$555$	5.49612	+	7.86330i	0.233297	+	0.333779i
$556$	28.6219	−	11.5281i	1.21384	−	0.488899i
$557$	2.16687	+	2.16687i	0.0918134	+	0.0918134i	0.751522	−	0.659708i	$-0.229320\pi$
$557$	2.16687	+	2.16687i	0.0918134	+	0.0918134i	−0.659708	+	0.751522i	$0.729320\pi$
$558$	12.8146	+	7.89194i	0.542486	+	0.334092i
$559$		−	22.0043i		−	0.930684i
$560$	−2.15949	−	3.91575i	−0.0912552	−	0.165471i
$561$	−23.9937	−	66.0945i	−1.01301	−	2.79051i
$562$	−5.58058	−	1.13852i	−0.235403	−	0.0480256i
$563$	−12.7980	−	3.42922i	−0.539372	−	0.144524i	−0.0211592	−	0.999776i	$-0.506736\pi$
$563$	−12.7980	−	3.42922i	−0.539372	−	0.144524i	−0.518212	+	0.855252i	$0.673402\pi$
$564$	3.78417	+	17.9726i	0.159342	+	0.756783i
$565$	9.07417	−	2.43142i	0.381753	−	0.102291i
$566$	−1.69530	−	27.9657i	−0.0712588	−	1.17549i
$567$	1.78037	−	9.90265i	0.0747685	−	0.415872i
$568$	−7.67554	+	11.1293i	−0.322058	+	0.466975i
$569$	0.0323664	−	0.0560602i	0.00135687	−	0.00235017i	−0.865346	−	0.501175i	$-0.832901\pi$
$569$	0.0323664	−	0.0560602i	0.00135687	−	0.00235017i	0.866703	+	0.498824i	$0.166235\pi$
$570$	6.57889	−	8.86528i	0.275559	−	0.371326i
$571$	−7.68965	−	2.06044i	−0.321802	−	0.0862266i	0.0943019	−	0.995544i	$-0.469938\pi$
$571$	−7.68965	−	2.06044i	−0.321802	−	0.0862266i	−0.416104	+	0.909317i	$0.636605\pi$
$572$	22.4438	−	16.8746i	0.938421	−	0.705564i
$573$	1.54325	−	3.30228i	0.0644703	−	0.137955i
$574$	−0.658407	−	1.97131i	−0.0274814	−	0.0822808i
$575$	6.21418			0.259149
$576$	12.2596	+	20.6325i	0.510817	+	0.859689i
$577$	1.89687			0.0789678			0.0394839	−	0.999220i	$-0.487429\pi$
$577$	1.89687			0.0789678			0.0394839	+	0.999220i	$0.487429\pi$
$578$	−11.6656	−	34.9273i	−0.485223	−	1.45279i
$579$	−4.53135	−	6.48300i	−0.188316	−	0.269424i
$580$	11.1822	−	8.40745i	0.464314	−	0.349100i
$581$	−2.13313	−	0.571569i	−0.0884969	−	0.0237127i
$582$	−10.5582	−	1.21769i	−0.437650	−	0.0504751i
$583$	9.53866	−	16.5215i	0.395051	−	0.684249i
$584$	5.88396	−	8.53157i	0.243480	−	0.353039i
$585$	−6.39216	−	2.33870i	−0.264283	−	0.0966935i
$586$	−0.307546	−	5.07329i	−0.0127046	−	0.209576i
$587$	23.1772	−	6.21032i	0.956626	−	0.256327i	0.253455	−	0.967347i	$-0.418433\pi$
$587$	23.1772	−	6.21032i	0.956626	−	0.256327i	0.703172	+	0.711020i	$0.251767\pi$
$588$	18.9326	+	6.19175i	0.780766	+	0.255343i
$589$	15.4426	+	4.13783i	0.636301	+	0.170496i
$590$	4.26318	+	0.869752i	0.175512	+	0.0358071i
$591$	18.4229	−	21.9182i	0.757817	−	0.901595i
$592$	−19.4009	+	10.6994i	−0.797374	+	0.439743i
$593$			27.6248i			1.13442i	0.823575	+	0.567208i	$0.191976\pi$
$593$			27.6248i			1.13442i	−0.823575	+	0.567208i	$0.808024\pi$
$594$	−33.9651	−	30.2353i	−1.39361	−	1.24057i
$595$	5.18597	+	5.18597i	0.212604	+	0.212604i
$596$	20.4901	−	8.25283i	0.839309	−	0.338049i
$597$	0.260068	−	0.0225333i	0.0106439	−	0.000922226i
$598$	−10.9961	−	16.6329i	−0.449665	−	0.680168i
$599$	−13.1727	+	7.60525i	−0.538221	+	0.310742i	−0.744358	−	0.667781i	$-0.767244\pi$
$599$	−13.1727	+	7.60525i	−0.538221	+	0.310742i	0.206137	+	0.978523i	$0.433911\pi$
$600$	2.47604	+	4.22720i	0.101084	+	0.172575i
$601$	8.57974	+	4.95352i	0.349975	+	0.202058i	0.664674	−	0.747133i	$-0.268570\pi$
$601$	8.57974	+	4.95352i	0.349975	+	0.202058i	−0.314699	+	0.949191i	$0.601904\pi$
$602$	0.927807	+	15.3051i	0.0378146	+	0.623791i
$603$	0.910841	−	10.2137i	0.0370923	−	0.415932i
$604$	4.04111	+	33.2087i	0.164430	+	1.35124i
$605$	26.3627	−	7.06387i	1.07180	−	0.287187i
$606$	−23.2300	+	18.4257i	−0.943652	+	0.748493i
$607$	−23.0205	+	13.2909i	−0.934372	+	0.539460i	−0.888192	−	0.459473i	$-0.848038\pi$
$607$	−23.0205	+	13.2909i	−0.934372	+	0.539460i	−0.0461803	+	0.998933i	$0.514705\pi$
$608$	18.7504	+	17.2749i	0.760428	+	0.700591i
$609$	2.36321	−	13.3370i	0.0957621	−	0.540444i
$610$	−17.4695	+	5.83474i	−0.707321	+	0.236242i
$611$	8.50611	−	8.50611i	0.344120	−	0.344120i
$612$	−28.7136	−	26.9242i	−1.16068	−	1.08835i
$613$	1.04218	+	1.04218i	0.0420934	+	0.0420934i	0.727840	−	0.685747i	$-0.240524\pi$
$613$	1.04218	+	1.04218i	0.0420934	+	0.0420934i	−0.685747	+	0.727840i	$0.740524\pi$
$614$	−3.00395	+	6.01686i	−0.121230	+	0.242821i
$615$	0.776959	+	2.14026i	0.0313300	+	0.0863036i
$616$	−14.8993	+	12.6835i	−0.600309	+	0.511033i
$617$	11.4641	+	19.8564i	0.461528	+	0.799390i	0.999037	−	0.0438678i	$-0.0139680\pi$
$617$	11.4641	+	19.8564i	0.461528	+	0.799390i	−0.537509	+	0.843258i	$0.680635\pi$
$618$	3.94832	−	5.32050i	0.158825	−	0.214022i
$619$	1.45172	+	5.41790i	0.0583496	+	0.217764i	0.988944	−	0.148288i	$-0.0473761\pi$
$619$	1.45172	+	5.41790i	0.0583496	+	0.217764i	−0.930595	+	0.366051i	$0.880709\pi$
$620$	−4.37388	+	5.58586i	−0.175659	+	0.224334i
$621$	−22.8897	+	22.7748i	−0.918533	+	0.913923i
$622$	24.1051	+	21.3496i	0.966525	+	0.856040i
$623$	6.86295	−	11.8870i	0.274958	−	0.476242i
$624$	6.93312	−	14.1075i	0.277547	−	0.564751i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−3.45575	+	16.9387i	−0.138120	+	0.677008i
$627$	−43.7629	−	20.4517i	−1.74772	−	0.816760i
$628$	−1.09617	+	0.441506i	−0.0437421	+	0.0176180i
$629$	25.6944	−	25.6944i	1.02450	−	1.02450i
$630$	4.54468	+	1.35716i	0.181065	+	0.0540707i
$631$	−19.7505			−0.786255			−0.393128	−	0.919484i	$-0.628607\pi$
$631$	−19.7505			−0.786255			−0.393128	+	0.919484i	$0.628607\pi$
$632$	−18.4834	−	38.9133i	−0.735229	−	1.54789i
$633$	2.02340	−	11.4193i	0.0804228	−	0.453875i
$634$	−25.3922	−	38.4084i	−1.00845	−	1.52539i
$635$	1.52440	−	5.68914i	0.0604939	−	0.225766i
$636$	0.579380	−	10.6638i	0.0229739	−	0.422845i
$637$	−3.37666	−	12.6019i	−0.133788	−	0.499304i
$638$	−45.8264	−	40.5879i	−1.81429	−	1.60689i
$639$	−2.46635	−	14.1258i	−0.0975673	−	0.558810i
$640$	−10.3127	+	4.65277i	−0.407645	+	0.183917i
$641$	15.4700	+	8.93160i	0.611028	+	0.352777i	0.773368	−	0.633958i	$-0.218571\pi$
$641$	15.4700	+	8.93160i	0.611028	+	0.352777i	−0.162340	+	0.986735i	$0.551904\pi$
$642$	−13.0958	+	33.1118i	−0.516851	+	1.30682i
$643$	−2.52502	+	9.42348i	−0.0995769	+	0.371626i	−0.997674	−	0.0681721i	$-0.978283\pi$
$643$	−2.52502	+	9.42348i	−0.0995769	+	0.371626i	0.898097	+	0.439798i	$0.144950\pi$
$644$	8.34969	+	11.1054i	0.329024	+	0.437612i
$645$	−1.45003	−	16.7355i	−0.0570948	−	0.658959i
$646$	−37.4110	−	18.6777i	−1.47192	−	0.734863i
$647$			10.7342i			0.422005i	0.977485	+	0.211003i	$0.0676729\pi$
$647$			10.7342i			0.422005i	−0.977485	+	0.211003i	$0.932327\pi$
$648$	−24.6130	−	6.49614i	−0.966890	−	0.255192i
$649$		−	19.0385i		−	0.747325i
$650$	1.43324	−	2.87075i	0.0562163	−	0.112600i
$651$	0.592906	+	6.84303i	0.0232378	+	0.268199i
$652$	−27.6214	−	3.91236i	−1.08174	−	0.153220i
$653$	7.24759	−	27.0484i	0.283620	−	1.05849i	−0.666221	−	0.745754i	$-0.732089\pi$
$653$	7.24759	−	27.0484i	0.283620	−	1.05849i	0.949842	−	0.312731i	$-0.101244\pi$
$654$	2.71969	+	1.07565i	0.106348	+	0.0420612i
$655$	−17.8750	−	10.3201i	−0.698434	−	0.403241i
$656$	−5.10487	+	1.26108i	−0.199312	+	0.0492369i
$657$	1.89067	+	10.8287i	0.0737620	+	0.422467i
$658$	−5.55777	+	6.27509i	−0.216665	+	0.244628i
$659$	−3.76161	−	14.0385i	−0.146532	−	0.546864i	−0.999682	−	0.0251992i	$-0.991978\pi$
$659$	−3.76161	−	14.0385i	−0.146532	−	0.546864i	0.853151	−	0.521664i	$-0.174689\pi$
$660$	15.9577	−	14.3131i	0.621153	−	0.557135i
$661$	10.2770	−	38.3542i	0.399728	−	1.49181i	−0.413847	−	0.910346i	$-0.635815\pi$
$661$	10.2770	−	38.3542i	0.399728	−	1.49181i	0.813576	−	0.581459i	$-0.197518\pi$
$662$	−5.88880	+	3.89314i	−0.228875	+	0.151311i
$663$	−4.49807	+	25.3853i	−0.174690	+	0.985884i
$664$	−1.87360	+	5.26378i	−0.0727099	+	0.204274i
$665$	5.03847			0.195383
$666$	6.72419	−	22.5171i	0.260557	−	0.872519i
$667$	−30.7371	+	30.7371i	−1.19015	+	1.19015i
$668$	−5.22341	+	12.2687i	−0.202100	+	0.474691i
$669$	12.2802	+	5.73887i	0.474778	+	0.221878i
$670$	4.73631	+	0.966277i	0.182980	+	0.0373305i
$671$	40.2958	+	69.7943i	1.55560	+	2.69438i
$672$	−4.22750	+	10.1048i	−0.163079	+	0.389801i
$673$	−2.03678	+	3.52780i	−0.0785120	+	0.135987i	−0.902608	−	0.430463i	$-0.858350\pi$
$673$	−2.03678	+	3.52780i	−0.0785120	+	0.135987i	0.824096	+	0.566450i	$0.191684\pi$
$674$	24.3644	−	27.5090i	0.938482	−	1.05961i
$675$	−5.01570	−	1.35748i	−0.193054	−	0.0522496i
$676$	15.5896	−	1.89708i	0.599600	−	0.0729644i
$677$	−11.2546	−	42.0026i	−0.432548	−	1.61429i	−0.746868	−	0.664973i	$-0.768443\pi$
$677$	−11.2546	−	42.0026i	−0.432548	−	1.61429i	0.314320	−	0.949317i	$-0.398223\pi$
$678$	−18.4788	−	13.7131i	−0.709675	−	0.526647i
$679$	−2.42532	−	4.20077i	−0.0930751	−	0.161211i
$680$	14.1292	−	12.0280i	0.541832	−	0.461252i
$681$	6.69360	+	18.4386i	0.256499	+	0.706569i
$682$	27.7742	+	13.8665i	1.06353	+	0.530974i
$683$	1.42511	+	1.42511i	0.0545302	+	0.0545302i	0.733846	−	0.679316i	$-0.237723\pi$
$683$	1.42511	+	1.42511i	0.0545302	+	0.0545302i	−0.679316	+	0.733846i	$0.737723\pi$
$684$	−27.0277	+	0.869229i	−1.03343	+	0.0332358i
$685$	−9.86308	+	9.86308i	−0.376849	+	0.376849i
$686$	6.38593	+	19.1199i	0.243816	+	0.729999i
$687$	−4.71034	+	26.5833i	−0.179711	+	1.01422i
$688$	38.7863	+	0.760823i	1.47871	+	0.0290061i
$689$	−6.05754	+	3.49732i	−0.230774	+	0.133237i
$690$	−9.45922	−	11.9256i	−0.360106	−	0.453999i
$691$	−34.9827	+	9.37357i	−1.33080	+	0.356588i	−0.853014	−	0.521887i	$-0.825228\pi$
$691$	−34.9827	+	9.37357i	−1.33080	+	0.356588i	−0.477788	+	0.878475i	$0.658561\pi$
$692$	−9.89718	+	12.6397i	−0.376234	+	0.480488i
$693$	1.84347	−	20.6717i	0.0700278	−	0.785252i
$694$	47.2655	−	2.86527i	1.79417	−	0.108764i
$695$	−13.3612	−	7.71407i	−0.506818	−	0.292611i
$696$	−33.1562	−	8.66178i	−1.25678	−	0.328324i
$697$	7.46873	−	4.31207i	0.282898	−	0.163331i
$698$	2.60447	−	1.72184i	0.0985808	−	0.0651727i
$699$	23.8769	−	2.06878i	0.903106	−	0.0782486i
$700$	−0.875847	+	2.05719i	−0.0331039	+	0.0777543i
$701$	−9.71312	−	9.71312i	−0.366859	−	0.366859i	0.499471	−	0.866331i	$-0.333528\pi$
$701$	−9.71312	−	9.71312i	−0.366859	−	0.366859i	−0.866331	+	0.499471i	$0.833528\pi$
$702$	5.24196	+	15.8271i	0.197845	+	0.597356i
$703$		−	24.9636i		−	0.941519i
$704$	28.9683	+	40.1443i	1.09178	+	1.51300i
$705$	5.90883	−	7.02989i	0.222539	−	0.264761i
$706$	−1.10084	+	5.39588i	−0.0414306	+	0.203077i
$707$	−13.0711	−	3.50240i	−0.491591	−	0.131721i
$708$	−4.82028	−	9.50537i	−0.181157	−	0.357234i
$709$	46.3476	−	12.4188i	1.74062	−	0.466398i	0.758036	−	0.652212i	$-0.226159\pi$
$709$	46.3476	−	12.4188i	1.74062	−	0.466398i	0.982585	+	0.185814i	$0.0594923\pi$
$710$	6.74734	−	0.409028i	0.253223	−	0.0153505i
$711$	42.9112	+	15.7000i	1.60930	+	0.588794i
$712$	−28.5876	−	19.7160i	−1.07137	−	0.738889i
$713$	11.0217	−	19.0901i	0.412766	−	0.714932i
$714$	2.05827	−	17.8464i	0.0770288	−	0.667886i
$715$	−13.5615	−	3.63380i	−0.507172	−	0.135896i
$716$	−1.24660	+	8.80107i	−0.0465878	+	0.328911i
$717$	29.5443	+	42.2691i	1.10335	+	1.57857i
$718$	4.01096	−	1.33964i	0.149688	−	0.0499950i
$719$	−50.6244			−1.88797			−0.943985	−	0.329987i	$-0.892956\pi$
$719$	−50.6244			−1.88797			−0.943985	+	0.329987i	$0.892956\pi$
$720$	4.34337	−	11.1864i	0.161868	−	0.416892i
$721$	3.02384			0.112614
$722$	−1.76054	+	0.588013i	−0.0655207	+	0.0218836i
$723$	20.3034	−	43.4456i	0.755091	−	1.61576i
$724$	−2.37039	−	0.335748i	−0.0880949	−	0.0124780i
$725$	−6.75676	−	1.81047i	−0.250940	−	0.0672391i
$726$	−53.6855	−	39.8398i	−1.99246	−	1.47859i
$727$	−3.21242	+	5.56408i	−0.119142	+	0.206360i	−0.919428	−	0.393259i	$-0.871348\pi$
$727$	−3.21242	+	5.56408i	−0.119142	+	0.206360i	0.800286	+	0.599619i	$0.204681\pi$
$728$	7.05609	−	1.29595i	0.261516	−	0.0480311i
$729$	23.4503	−	13.3822i	0.868530	−	0.495637i
$730$	−5.17241	+	0.313555i	−0.191440	+	0.0116052i
$731$	−61.4574	+	16.4675i	−2.27308	+	0.609071i
$732$	37.7895	+	24.6440i	1.39674	+	0.910868i
$733$	22.9010	+	6.13632i	0.845869	+	0.226650i	0.655625	−	0.755087i	$-0.272405\pi$
$733$	22.9010	+	6.13632i	0.845869	+	0.226650i	0.190244	+	0.981737i	$0.439072\pi$
$734$	−3.40504	+	16.6902i	−0.125682	+	0.616045i
$735$	−3.39856	−	9.36188i	−0.125358	−	0.345318i
$736$	29.6984	−	18.8074i	1.09470	−	0.693251i
$737$		−	21.1514i		−	0.779120i
$738$	2.92467	−	4.74896i	0.107658	−	0.174812i
$739$	13.6168	+	13.6168i	0.500901	+	0.500901i	0.911718	−	0.410817i	$-0.134756\pi$
$739$	13.6168	+	13.6168i	0.500901	+	0.500901i	−0.410817	+	0.911718i	$0.634756\pi$
$740$	10.1925	+	4.33947i	0.374685	+	0.159522i
$741$	10.1466	+	14.5167i	0.372744	+	0.533284i
$742$	4.06587	−	2.68798i	0.149263	−	0.0986789i
$743$	25.2006	−	14.5496i	0.924521	−	0.533773i	0.0394465	−	0.999222i	$-0.487441\pi$
$743$	25.2006	−	14.5496i	0.924521	−	0.533773i	0.885075	+	0.465449i	$0.154107\pi$
$744$	17.3777	−	0.108928i	0.637097	−	0.00399351i
$745$	−9.56512	−	5.52243i	−0.350439	−	0.202326i
$746$	17.2794	−	1.04749i	0.632645	−	0.0383514i
$747$	−2.49551	−	5.37516i	−0.0913061	−	0.196667i
$748$	−63.9266	−	50.0562i	−2.33739	−	1.83024i
$749$	−15.6973	+	4.20609i	−0.573568	+	0.153687i
$750$	0.900882	−	2.27781i	0.0328955	−	0.0831738i
$751$	−13.2731	+	7.66322i	−0.484342	+	0.279635i	−0.722224	−	0.691659i	$-0.756880\pi$
$751$	−13.2731	+	7.66322i	−0.484342	+	0.279635i	0.237882	+	0.971294i	$0.423547\pi$
$752$	14.6993	+	15.2875i	0.536029	+	0.557479i
$753$	−29.5474	−	24.8354i	−1.07677	−	0.905053i
$754$	7.11035	+	21.2888i	0.258944	+	0.775292i
$755$	11.8276	−	11.8276i	0.430452	−	0.430452i
$756$	−4.31340	−	10.7875i	−0.156877	−	0.392339i
$757$	28.9390	+	28.9390i	1.05180	+	1.05180i	0.998583	+	0.0532221i	$0.0169491\pi$
$757$	28.9390	+	28.9390i	1.05180	+	1.05180i	0.0532221	+	0.998583i	$0.483051\pi$
$758$	−7.58216	−	3.78544i	−0.275396	−	0.137493i
$759$	−42.8552	+	50.9859i	−1.55554	+	1.85067i
$760$	1.02075	−	12.7066i	0.0370264	−	0.460917i
$761$	−13.3472	−	23.1181i	−0.483836	−	0.838029i	0.515991	−	0.856594i	$-0.327424\pi$
$761$	−13.3472	−	23.1181i	−0.483836	−	0.838029i	−0.999828	+	0.0185645i	$0.994090\pi$
$762$	−13.2384	+	5.73454i	−0.479577	+	0.207740i
$763$	0.345474	+	1.28933i	0.0125070	+	0.0466768i
$764$	−0.508435	−	4.17817i	−0.0183945	−	0.151161i
$765$	−1.74820	+	19.6033i	−0.0632062	+	0.708759i
$766$	33.1942	−	37.4785i	1.19936	−	1.35415i
$767$	−3.49020	+	6.04520i	−0.126024	+	0.218280i
$768$	24.6271	+	12.7086i	0.888653	+	0.458581i
$769$	−5.57015	−	9.64778i	−0.200865	−	0.347908i	0.747943	−	0.663763i	$-0.231042\pi$
$769$	−5.57015	−	9.64778i	−0.200865	−	0.347908i	−0.948807	+	0.315856i	$0.897709\pi$
$770$	9.58594	+	1.95567i	0.345453	+	0.0704776i
$771$	−5.02233	+	3.51040i	−0.180875	+	0.126424i
$772$	−8.40335	−	3.57773i	−0.302443	−	0.128765i
$773$	15.1296	−	15.1296i	0.544175	−	0.544175i	−0.380575	−	0.924750i	$-0.624274\pi$
$773$	15.1296	−	15.1296i	0.544175	−	0.544175i	0.924750	+	0.380575i	$0.124274\pi$
$774$	−29.9097	+	28.2575i	−1.07508	+	1.01569i
$775$	3.54728			0.127422
$776$	−11.0854	+	5.26542i	−0.397941	+	0.189018i
$777$	10.0814	−	3.65976i	0.361668	−	0.131293i
$778$	43.7603	−	28.9304i	1.56888	−	1.03720i
$779$	1.53344	−	5.72286i	0.0549410	−	0.205043i
$780$	−7.69091	+	1.61934i	−0.275379	+	0.0579816i
$781$	−7.65540	−	28.5704i	−0.273932	−	1.02233i
$782$	−38.2258	+	43.1594i	−1.36695	+	1.54338i
$783$	31.5236	−	18.0946i	1.12656	−	0.646648i
$784$	22.3296	−	5.51620i	0.797486	−	0.197007i
$785$	0.511711	+	0.295436i	0.0182637	+	0.0105446i
$786$	7.40404	+	50.0131i	0.264093	+	1.78391i
$787$	10.7381	−	40.0751i	0.382772	−	1.42852i	−0.458877	−	0.888500i	$-0.651748\pi$
$787$	10.7381	−	40.0751i	0.382772	−	1.42852i	0.841649	−	0.540025i	$-0.181585\pi$
$788$	4.63667	−	32.7351i	0.165174	−	1.16614i
$789$	10.3371	+	4.83081i	0.368009	+	0.171981i
$790$	−9.62149	+	19.2717i	−0.342317	+	0.685655i
$791$		−	10.5022i		−	0.373415i
$792$	−51.7589	−	8.83699i	−1.83917	−	0.314009i
$793$		−	29.5487i		−	1.04930i
$794$	5.86968	+	2.93047i	0.208307	+	0.103999i
$795$	−4.37663	+	3.05908i	−0.155223	+	0.108494i
$796$	0.240925	−	0.181142i	0.00853936	−	0.00642042i
$797$	7.65102	−	28.5540i	0.271013	−	1.01143i	−0.687453	−	0.726229i	$-0.741271\pi$
$797$	7.65102	−	28.5540i	0.271013	−	1.01143i	0.958466	−	0.285206i	$-0.0920619\pi$
$798$	−7.66955	−	9.66928i	−0.271499	−	0.342289i
$799$	−30.1230	−	17.3915i	−1.06568	−	0.615268i
$800$	5.01062	+	2.62558i	0.177152	+	0.0928284i
$801$	36.2848	−	6.33526i	1.28206	−	0.223846i
$802$	26.7847	+	23.7229i	0.945799	+	0.837683i
$803$	5.86852	+	21.9016i	0.207096	+	0.772892i
$804$	−5.35524	−	10.5603i	−0.188865	−	0.372432i
$805$	1.79803	−	6.71034i	0.0633722	−	0.236508i
$806$	−6.27699	−	9.49463i	−0.221097	−	0.334434i
$807$	−28.3329	−	23.8147i	−0.997367	−	0.838316i
$808$	−11.4809	+	32.2548i	−0.403896	+	1.13472i
$809$	−33.3206			−1.17149			−0.585745	−	0.810495i	$-0.699198\pi$
$809$	−33.3206			−1.17149			−0.585745	+	0.810495i	$0.699198\pi$
$810$	5.02976	+	11.6919i	0.176728	+	0.410813i
$811$	−8.31819	+	8.31819i	−0.292091	+	0.292091i	−0.837906	−	0.545815i	$-0.816220\pi$
$811$	−8.31819	+	8.31819i	−0.292091	+	0.292091i	0.545815	+	0.837906i	$0.316220\pi$
$812$	−5.84324	−	14.5076i	−0.205058	−	0.509118i
$813$	1.33739	+	15.4355i	0.0469043	+	0.541346i
$814$	9.68957	−	47.4944i	0.339619	−	1.66468i
$815$	6.97428	+	12.0798i	0.244298	+	0.423137i
$816$	−44.5903	−	8.80631i	−1.56097	−	0.308283i
$817$	−21.8551	+	37.8542i	−0.764614	+	1.32435i
$818$	−36.9184	−	32.6982i	−1.29082	−	1.14326i
$819$	−4.37496	+	6.22584i	−0.152873	+	0.217549i
$820$	2.07006	+	1.62091i	0.0722896	+	0.0566047i
$821$	−5.31481	−	19.8351i	−0.185488	−	0.692251i	−0.994526	−	0.104494i	$-0.966678\pi$
$821$	−5.31481	−	19.8351i	−0.185488	−	0.692251i	0.809037	−	0.587757i	$-0.199989\pi$
$822$	33.9417	+	3.91457i	1.18385	+	0.136536i
$823$	−19.1322	−	33.1379i	−0.666906	−	1.15512i	−0.978765	−	0.204987i	$-0.934285\pi$
$823$	−19.1322	−	33.1379i	−0.666906	−	1.15512i	0.311858	−	0.950129i	$-0.399049\pi$
$824$	0.612601	−	7.62588i	0.0213410	−	0.265660i
$825$	−10.5537	−	1.87003i	−0.367433	−	0.0651061i
$826$	2.17272	−	4.35191i	0.0755985	−	0.151422i
$827$	21.8851	+	21.8851i	0.761018	+	0.761018i	0.976506	−	0.215488i	$-0.0691343\pi$
$827$	21.8851	+	21.8851i	0.761018	+	0.761018i	−0.215488	+	0.976506i	$0.569134\pi$
$828$	−8.48744	+	36.3062i	−0.294959	+	1.26173i
$829$	−39.3426	+	39.3426i	−1.36642	+	1.36642i	−0.500945	+	0.865479i	$0.667014\pi$
$829$	−39.3426	+	39.3426i	−1.36642	+	1.36642i	−0.865479	+	0.500945i	$0.832986\pi$
$830$	2.64975	−	0.885005i	0.0919743	−	0.0307190i
$831$	25.5766	−	9.28486i	0.887244	−	0.322088i
$832$	−1.83878	−	18.0574i	−0.0637483	−	0.626029i
$833$	−32.6696	+	18.8618i	−1.13193	+	0.653522i
$834$	5.53435	+	37.3836i	0.191639	+	1.29449i
$835$	6.44001	−	1.72560i	0.222866	−	0.0597167i
$836$	−55.3704	+	6.73794i	−1.91502	+	0.233036i
$837$	−13.0663	+	13.0007i	−0.451636	+	0.449370i
$838$	−0.0246265	−	0.406239i	−0.000850707	−	0.0140333i
$839$	11.9978	+	6.92691i	0.414208	+	0.239143i	0.692596	−	0.721325i	$-0.256467\pi$
$839$	11.9978	+	6.92691i	0.414208	+	0.239143i	−0.278388	+	0.960469i	$0.589800\pi$
$840$	5.28114	−	1.45062i	0.182217	−	0.0500511i
$841$	17.2612	−	9.96577i	0.595214	−	0.343647i
$842$	−12.7698	−	19.3158i	−0.440078	−	0.665666i
$843$	2.95331	−	6.31955i	0.101717	−	0.217657i
$844$	−5.00303	−	12.4215i	−0.172211	−	0.427567i
$845$	−5.55242	−	5.55242i	−0.191009	−	0.191009i
$846$	−22.4854	−	0.638687i	−0.773064	−	0.0219585i
$847$		−	30.5115i		−	1.04839i
$848$	−5.95517	−	10.7984i	−0.204501	−	0.370817i
$849$	33.7874	+	5.98685i	1.15958	+	0.205468i
$850$	−9.09051	−	1.85460i	−0.311802	−	0.0636122i
$851$	−33.2470	−	8.90851i	−1.13969	−	0.305380i
$852$	−11.0558	−	12.3261i	−0.378764	−	0.422286i
$853$	38.5662	−	10.3338i	1.32048	−	0.353822i	0.471323	−	0.881961i	$-0.343777\pi$
$853$	38.5662	−	10.3338i	1.32048	−	0.353822i	0.849158	+	0.528139i	$0.177110\pi$
$854$	1.24591	+	20.5526i	0.0426342	+	0.703295i
$855$	8.67363	+	10.3721i	0.296632	+	0.354719i
$856$	7.42728	+	40.4395i	0.253859	+	1.38219i
$857$	−14.3536	+	24.8612i	−0.490311	+	0.849243i	−0.999938	−	0.0111524i	$-0.996450\pi$
$857$	−14.3536	+	24.8612i	−0.490311	+	0.849243i	0.509627	+	0.860395i	$0.329783\pi$
$858$	13.6697	+	31.5571i	0.466677	+	1.07734i
$859$	−12.2339	−	3.27805i	−0.417414	−	0.111846i	0.0439984	−	0.999032i	$-0.485990\pi$
$859$	−12.2339	−	3.27805i	−0.417414	−	0.111846i	−0.461412	+	0.887186i	$0.652657\pi$
$860$	−11.6566	−	15.5036i	−0.397487	−	0.528670i
$861$	2.53595	−	0.219725i	0.0864250	−	0.00748819i
$862$	−15.5336	−	46.5086i	−0.529077	−	1.58409i
$863$	12.2328			0.416409			0.208204	−	0.978085i	$-0.433238\pi$
$863$	12.2328			0.416409			0.208204	+	0.978085i	$0.433238\pi$
$864$	−28.0792	+	8.69259i	−0.955272	+	0.295728i
$865$	8.02675			0.272918
$866$	−7.24810	−	21.7012i	−0.246301	−	0.737438i
$867$	44.9316	−	3.89305i	1.52596	−	0.132215i
$868$	4.76630	+	6.33933i	0.161779	+	0.215171i
$869$	91.0398	+	24.3941i	3.08832	+	0.827512i
$870$	6.81068	+	15.7227i	0.230904	+	0.533050i
$871$	−3.87754	+	6.71610i	−0.131386	+	0.227566i
$872$	3.32157	−	0.610053i	0.112483	−	0.0206590i
$873$	4.47250	−	12.2243i	0.151371	−	0.413729i
$874$	2.39665	+	39.5352i	0.0810678	+	1.33730i
$875$	1.07984	−	0.289343i	0.0365054	−	0.00978158i
$876$	8.47518	+	9.44903i	0.286350	+	0.319253i
$877$	−33.8301	−	9.06474i	−1.14236	−	0.306094i	−0.362461	−	0.931999i	$-0.618063\pi$
$877$	−33.8301	−	9.06474i	−1.14236	−	0.306094i	−0.779900	+	0.625905i	$0.784730\pi$
$878$	−18.9822	−	3.87266i	−0.640620	−	0.130696i
$879$	6.12942	+	1.08608i	0.206740	+	0.0366326i
$880$	6.87407	−	23.7788i	0.231725	−	0.801582i
$881$			30.0674i			1.01300i	0.862241	+	0.506499i	$0.169060\pi$
$881$			30.0674i			1.01300i	−0.862241	+	0.506499i	$0.830940\pi$
$882$	−12.7930	+	20.7728i	−0.430763	+	0.699456i
$883$	20.9528	+	20.9528i	0.705118	+	0.705118i	0.965504	−	0.260387i	$-0.0838500\pi$
$883$	20.9528	+	20.9528i	0.705118	+	0.705118i	−0.260387	+	0.965504i	$0.583850\pi$
$884$	11.1219	+	27.6134i	0.374069	+	0.928739i
$885$	−2.25612	+	4.82770i	−0.0758387	+	0.162281i
$886$	23.5159	+	35.5704i	0.790033	+	1.19501i
$887$	−20.1629	+	11.6411i	−0.677005	+	0.390869i	−0.798726	−	0.601695i	$-0.794492\pi$
$887$	−20.1629	+	11.6411i	−0.677005	+	0.390869i	0.121720	+	0.992564i	$0.461159\pi$
$888$	−7.18722	−	26.1659i	−0.241187	−	0.878070i
$889$	−5.70230	−	3.29222i	−0.191249	−	0.110418i
$890$	1.05066	+	17.3318i	0.0352183	+	0.580962i
$891$	45.7279	−	31.7910i	1.53194	−	1.06504i
$892$	15.5373	−	1.89071i	0.520227	−	0.0633057i
$893$	−23.0815	+	6.18468i	−0.772394	+	0.206962i
$894$	3.96199	+	26.7626i	0.132509	+	0.895074i
$895$	3.84901	−	2.22223i	0.128658	−	0.0742809i
$896$	2.04035	+	12.4823i	0.0681635	+	0.417006i
$897$	22.9546	−	8.33299i	0.766430	−	0.278230i
$898$	29.0085	−	9.68870i	0.968026	−	0.323316i
$899$	−17.5458	+	17.5458i	−0.585187	+	0.585187i
$900$	−5.74264	+	1.73840i	−0.191421	+	0.0579468i
$901$	14.3012	+	14.3012i	0.476443	+	0.476443i
$902$	5.13876	−	10.2928i	0.171102	−	0.342714i
$903$	−18.4913	−	3.27650i	−0.615351	−	0.109035i
$904$	−26.4857	−	2.12765i	−0.880901	−	0.0707645i
$905$	0.598513	+	1.03665i	0.0198952	+	0.0344596i
$906$	−40.7024	−	4.69429i	−1.35225	−	0.155957i
$907$	−0.317944	−	1.18658i	−0.0105572	−	0.0393999i	0.960446	−	0.278465i	$-0.0898257\pi$
$907$	−0.317944	−	1.18658i	−0.0105572	−	0.0393999i	−0.971004	+	0.239065i	$0.923159\pi$
$908$	17.8338	+	13.9643i	0.591836	+	0.463423i
$909$	−15.2917	−	32.9373i	−0.507195	−	1.09246i
$910$	−2.68526	−	2.37831i	−0.0890156	−	0.0788401i
$911$	4.93028	−	8.53949i	0.163347	−	0.282926i	−0.772720	−	0.634747i	$-0.781104\pi$
$911$	4.93028	−	8.53949i	0.163347	−	0.282926i	0.936067	+	0.351821i	$0.114438\pi$
$912$	−25.9389	+	17.3831i	−0.858924	+	0.575612i
$913$	−6.11200	−	10.5863i	−0.202278	−	0.350355i
$914$	6.39513	−	31.3464i	0.211532	−	1.03685i
$915$	−1.94718	−	22.4734i	−0.0643717	−	0.742946i
$916$	11.6467	+	28.9165i	0.384818	+	0.955428i
$917$	−16.3161	+	16.3161i	−0.538806	+	0.538806i
$918$	40.2817	−	26.4852i	1.32949	−	0.874142i
$919$	−32.0717			−1.05795			−0.528974	−	0.848638i	$-0.677423\pi$
$919$	−32.0717			−1.05795			−0.528974	+	0.848638i	$0.677423\pi$
$920$	−16.5587	−	5.89394i	−0.545923	−	0.194317i
$921$	−6.30506	−	5.29959i	−0.207759	−	0.174627i
$922$	3.76341	+	5.69257i	0.123941	+	0.187475i
$923$	−2.80683	+	10.4752i	−0.0923880	+	0.344797i
$924$	−10.8386	−	21.3732i	−0.356564	−	0.703127i
$925$	−1.43358	−	5.35018i	−0.0471357	−	0.175913i
$926$	13.3449	+	11.8195i	0.438542	+	0.388412i
$927$	5.20548	+	6.22482i	0.170970	+	0.204450i
$928$	−37.7709	+	11.7971i	−1.23989	+	0.387258i
$929$	−0.536381	−	0.309679i	−0.0175981	−	0.0101603i	0.491175	−	0.871061i	$-0.336567\pi$
$929$	−0.536381	−	0.309679i	−0.0175981	−	0.0101603i	−0.508773	+	0.860901i	$0.669901\pi$
$930$	−5.39966	−	6.80754i	−0.177062	−	0.223228i
$931$	−6.70752	+	25.0328i	−0.219830	+	0.820418i
$932$	22.1193	−	16.6307i	0.724543	−	0.544757i
$933$	−32.3240	+	22.5931i	−1.05824	+	0.739666i
$934$	8.65975	+	4.32343i	0.283356	+	0.141467i
$935$			40.5963i			1.32764i
$936$	14.8148	+	12.2946i	0.484235	+	0.401861i
$937$		−	16.5637i		−	0.541113i	−0.962704	−	0.270557i	$-0.912792\pi$
$937$		−	16.5637i		−	0.541113i	0.962704	−	0.270557i	$-0.0872078\pi$
$938$	2.41385	−	4.83489i	0.0788149	−	0.157865i
$939$	−19.1817	−	8.96417i	−0.625972	−	0.292535i
$940$	1.48713	−	10.4992i	0.0485048	−	0.342446i
$941$	0.947459	−	3.53596i	0.0308863	−	0.115269i	−0.948762	−	0.315992i	$-0.897663\pi$
$941$	0.947459	−	3.53596i	0.0308863	−	0.115269i	0.979648	+	0.200723i	$0.0643292\pi$
$942$	−0.211957	−	1.43173i	−0.00690592	−	0.0466484i
$943$	−7.07460	−	4.08452i	−0.230381	−	0.133010i
$944$	−10.5350	−	6.36108i	−0.342885	−	0.207035i
$945$	−2.91713	+	5.02339i	−0.0948942	+	0.163411i
$946$	−56.2735	+	63.5365i	−1.82961	+	2.06575i
$947$	−0.552908	−	2.06348i	−0.0179671	−	0.0670541i	0.956360	−	0.292190i	$-0.0943840\pi$
$947$	−0.552908	−	2.06348i	−0.0179671	−	0.0670541i	−0.974327	+	0.225136i	$0.927717\pi$
$948$	51.6299	−	10.8708i	1.67686	−	0.353067i
$949$	2.15168	−	8.03017i	0.0698464	−	0.260670i
$950$	−5.31690	+	3.51505i	−0.172503	+	0.114043i
$951$	53.0065	−	19.2425i	1.71885	−	0.623979i
$952$	−8.90013	−	18.7376i	−0.288455	−	0.607288i
$953$	30.0188			0.972404			0.486202	−	0.873847i	$-0.338382\pi$
$953$	30.0188			0.972404			0.486202	+	0.873847i	$0.338382\pi$
$954$	12.5328	+	3.74261i	0.405763	+	0.121172i
$955$	−1.48810	+	1.48810i	−0.0481539	+	0.0481539i
$956$	54.7898	+	23.3268i	1.77203	+	0.754441i
$957$	61.4515	−	42.9520i	1.98644	−	1.38844i
$958$	−12.6086	−	2.57233i	−0.407364	−	0.0831083i
$959$	7.79677	+	13.5044i	0.251771	+	0.436080i
$960$	−2.58843	−	13.6125i	−0.0835413	−	0.439341i
$961$	−9.20842	+	15.9494i	−0.297046	+	0.514498i
$962$	−11.7835	+	13.3044i	−0.379917	+	0.428951i
$963$	−35.6813	−	25.0736i	−1.14981	−	0.807984i
$964$	−6.68909	−	54.9690i	−0.215441	−	1.77043i
$965$	1.18193	+	4.41103i	0.0380477	+	0.141996i
$966$	−15.6147	+	6.76389i	−0.502395	+	0.217625i
$967$	16.4017	+	28.4085i	0.527442	+	0.913557i	0.999488	+	0.0319828i	$0.0101822\pi$
$967$	16.4017	+	28.4085i	0.527442	+	0.913557i	−0.472046	+	0.881574i	$0.656484\pi$
$968$	−76.9475	−	6.18134i	−2.47319	−	0.198676i
$969$	32.9512	−	39.2030i	1.05855	−	1.25938i
$970$	5.48998	+	2.74091i	0.176273	+	0.0880052i
$971$	−20.5948	−	20.5948i	−0.660920	−	0.660920i	0.294677	−	0.955597i	$-0.404788\pi$
$971$	−20.5948	−	20.5948i	−0.660920	−	0.660920i	−0.955597	+	0.294677i	$0.904788\pi$
$972$	14.7816	−	27.4500i	0.474120	−	0.880460i
$973$	−12.1959	+	12.1959i	−0.390984	+	0.390984i
$974$	13.3860	+	40.0783i	0.428914	+	1.28419i
$975$	3.00826	+	2.52853i	0.0963414	+	0.0809778i
$976$	52.0844	+	1.02168i	1.66718	+	0.0327030i
$977$	−13.9653	+	8.06287i	−0.446790	+	0.257954i	−0.706473	−	0.707740i	$-0.749715\pi$
$977$	−13.9653	+	8.06287i	−0.446790	+	0.257954i	0.259684	+	0.965694i	$0.416382\pi$
$978$	12.5660	−	31.7722i	0.401817	−	1.01596i
$979$	73.3881	−	19.6643i	2.34549	−	0.628473i
$980$	−9.05482	−	7.09016i	−0.289246	−	0.226487i
$981$	−2.05946	+	2.93074i	−0.0657535	+	0.0935713i
$982$	12.7049	−	0.770176i	0.405428	−	0.0245773i
$983$	−8.40773	−	4.85421i	−0.268165	−	0.154825i	0.359888	−	0.932995i	$-0.382815\pi$
$983$	−8.40773	−	4.85421i	−0.268165	−	0.154825i	−0.628053	+	0.778170i	$0.716148\pi$
$984$	−0.0403677	−	6.43998i	−0.00128687	−	0.205299i
$985$	−14.3162	+	8.26545i	−0.456151	+	0.263359i
$986$	54.1377	−	35.7909i	1.72409	−	1.13982i
$987$	−5.88149	−	8.41465i	−0.187210	−	0.267841i
$988$	18.8168	+	8.01123i	0.598641	+	0.254871i
$989$	42.6158	+	42.6158i	1.35510	+	1.35510i
$990$	12.4761	+	23.1001i	0.396517	+	0.734170i
$991$			14.5981i			0.463723i	0.972749	+	0.231862i	$0.0744817\pi$
$991$			14.5981i			0.463723i	−0.972749	+	0.231862i	$0.925518\pi$
$992$	16.9529	−	10.7359i	0.538255	−	0.340867i
$993$	−2.95026	−	8.12698i	−0.0936238	−	0.257902i
$994$	1.51061	−	7.40441i	0.0479136	−	0.234854i
$995$	−0.145577	−	0.0390074i	−0.00461511	−	0.00123662i
$996$	−5.73186	−	3.73797i	−0.181621	−	0.118442i
$997$	−5.89486	+	1.57952i	−0.186692	+	0.0500240i	−0.350954	−	0.936393i	$-0.614143\pi$
$997$	−5.89486	+	1.57952i	−0.186692	+	0.0500240i	0.164262	+	0.986417i	$0.447476\pi$
$998$	−35.6073	+	2.15854i	−1.12713	+	0.0683273i
$999$	24.8889	+	14.4532i	0.787449	+	0.457279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cf.a.11.59	✓	384
9.5	odd	6	inner	720.2.cf.a.491.90	yes	384
16.3	odd	4	inner	720.2.cf.a.371.90	yes	384
144.131	even	12	inner	720.2.cf.a.131.59	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cf.a.11.59	✓	384	1.1	even	1	trivial
720.2.cf.a.131.59	yes	384	144.131	even	12	inner
720.2.cf.a.371.90	yes	384	16.3	odd	4	inner
720.2.cf.a.491.90	yes	384	9.5	odd	6	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.448012 + 1.34137i) q^{2} +(-1.72559 + 0.149511i) q^{3} +(-1.59857 + 1.20190i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-0.973634 - 2.24767i) q^{6} +(0.558968 - 0.968161i) q^{7} +(-2.32838 - 1.60581i) q^{8} +(2.95529 - 0.515989i) q^{9} +O(q^{10})\)	\(q+(0.448012 + 1.34137i) q^{2} +(-1.72559 + 0.149511i) q^{3} +(-1.59857 + 1.20190i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-0.973634 - 2.24767i) q^{6} +(0.558968 - 0.968161i) q^{7} +(-2.32838 - 1.60581i) q^{8} +(2.95529 - 0.515989i) q^{9} +(0.0855734 + 1.41162i) q^{10} +(5.97725 - 1.60160i) q^{11} +(2.57877 - 2.31299i) q^{12} +(-2.19154 - 0.587222i) q^{13} +(1.54909 + 0.316037i) q^{14} +(-1.70548 - 0.302198i) q^{15} +(1.11085 - 3.84266i) q^{16} +6.56037i q^{17} +(2.01614 + 3.73298i) q^{18} +(3.18689 + 3.18689i) q^{19} +(-1.85518 + 0.747210i) q^{20} +(-0.819796 + 1.75422i) q^{21} +(4.82623 + 7.30020i) q^{22} +(5.38164 - 3.10709i) q^{23} +(4.25791 + 2.42285i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-0.194154 - 3.20276i) q^{26} +(-5.02246 + 1.33223i) q^{27} +(0.270087 + 2.21950i) q^{28} +(-6.75676 + 1.81047i) q^{29} +(-0.358718 - 2.42308i) q^{30} +(3.07203 - 1.77364i) q^{31} +(5.65212 - 0.231489i) q^{32} +(-10.0748 + 3.65737i) q^{33} +(-8.79991 + 2.93913i) q^{34} +(0.790500 - 0.790500i) q^{35} +(-4.10407 + 4.37682i) q^{36} +(-3.91661 - 3.91661i) q^{37} +(-2.84704 + 5.70257i) q^{38} +(3.86949 + 0.685642i) q^{39} +(-1.83343 - 2.15373i) q^{40} +(-0.657291 - 1.13846i) q^{41} +(-2.72034 - 0.313743i) q^{42} +(2.51014 + 9.36797i) q^{43} +(-7.63009 + 9.74436i) q^{44} +(2.98814 + 0.266479i) q^{45} +(6.57881 + 5.82678i) q^{46} +(-2.65100 + 4.59166i) q^{47} +(-1.34235 + 6.79692i) q^{48} +(2.87511 + 4.97984i) q^{49} +(-0.282697 + 1.38567i) q^{50} +(-0.980850 - 11.3205i) q^{51} +(4.20912 - 1.69531i) q^{52} +(2.17994 - 2.17994i) q^{53} +(-4.03715 - 6.14015i) q^{54} +6.18811 q^{55} +(-2.85618 + 1.35665i) q^{56} +(-5.97572 - 5.02277i) q^{57} +(-5.45562 - 8.25223i) q^{58} +(0.796288 - 2.97179i) q^{59} +(3.08955 - 1.56674i) q^{60} +(3.37076 + 12.5798i) q^{61} +(3.75542 + 3.32613i) q^{62} +(1.15235 - 3.14962i) q^{63} +(2.84273 + 7.47789i) q^{64} +(-1.96488 - 1.13443i) q^{65} +(-9.41953 - 11.8755i) q^{66} +(0.884660 - 3.30160i) q^{67} +(-7.88494 - 10.4872i) q^{68} +(-8.82193 + 6.16617i) q^{69} +(1.41451 + 0.706203i) q^{70} -4.77985i q^{71} +(-7.70963 - 3.54423i) q^{72} +3.66416i q^{73} +(3.49895 - 7.00832i) q^{74} +(-1.56916 - 0.733312i) q^{75} +(-8.92479 - 1.26413i) q^{76} +(1.79049 - 6.68219i) q^{77} +(0.813878 + 5.49761i) q^{78} +(13.1905 + 7.61552i) q^{79} +(2.06755 - 3.42421i) q^{80} +(8.46751 - 3.04980i) q^{81} +(1.23263 - 1.39172i) q^{82} +(-0.511272 - 1.90809i) q^{83} +(-0.797899 - 3.78955i) q^{84} +(-1.69795 + 6.33683i) q^{85} +(-11.4414 + 7.56401i) q^{86} +(11.3887 - 4.13433i) q^{87} +(-16.4892 - 5.86921i) q^{88} +12.2779 q^{89} +(0.981277 + 4.12760i) q^{90} +(-1.79353 + 1.79353i) q^{91} +(-4.86850 + 11.4351i) q^{92} +(-5.03587 + 3.51987i) q^{93} +(-7.34682 - 1.49886i) q^{94} +(2.25347 + 3.90312i) q^{95} +(-9.71860 + 1.24451i) q^{96} +(2.16946 - 3.75762i) q^{97} +(-5.39174 + 6.08763i) q^{98} +(16.8381 - 7.81740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{6}+O(q^{10}) \) 384 * q - 12 * q^6	\( 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) \) 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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