LMFDB - Embedded newform 627.2.s.a.94.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [627,2,Mod(94,627)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("627.94"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(627, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 9, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.s (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			94.18
Character	$\chi$	$=$	627.94
Dual form			627.2.s.a.607.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.134089 - 0.412683i) q^{2} +(0.587785 - 0.809017i) q^{3} +(1.46571 - 1.06490i) q^{4} +(-0.0446214 + 0.137331i) q^{5} +(-0.412683 - 0.134089i) q^{6} +(2.66082 + 3.66230i) q^{7} +(-1.33810 - 0.972186i) q^{8} +(-0.309017 - 0.951057i) q^{9} +0.0626572 q^{10} +(2.63252 - 2.01739i) q^{11} -1.81171i q^{12} +(0.384319 + 1.18281i) q^{13} +(1.15458 - 1.58915i) q^{14} +(0.0848750 + 0.116820i) q^{15} +(0.897920 - 2.76351i) q^{16} +(-0.899421 - 0.292240i) q^{17} +(-0.351049 + 0.255052i) q^{18} +(0.285902 + 4.34951i) q^{19} +(0.0808412 + 0.248804i) q^{20} +4.52685 q^{21} +(-1.18553 - 0.815885i) q^{22} -1.47223 q^{23} +(-1.57303 + 0.511108i) q^{24} +(4.02822 + 2.92667i) q^{25} +(0.436594 - 0.317204i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(7.79995 + 2.53436i) q^{28} +(7.30304 - 5.30597i) q^{29} +(0.0368290 - 0.0506908i) q^{30} +(-8.99544 + 2.92279i) q^{31} -4.56882 q^{32} +(-0.0847493 - 3.31554i) q^{33} +0.410362i q^{34} +(-0.621675 + 0.201995i) q^{35} +(-1.46571 - 1.06490i) q^{36} +(-5.32323 - 7.32679i) q^{37} +(1.75663 - 0.701208i) q^{38} +(1.18281 + 0.384319i) q^{39} +(0.193219 - 0.140382i) q^{40} +(0.855911 + 0.621856i) q^{41} +(-0.607001 - 1.86816i) q^{42} -4.40172i q^{43} +(1.71018 - 5.76026i) q^{44} +0.144398 q^{45} +(0.197410 + 0.607566i) q^{46} +(-5.12668 - 3.72475i) q^{47} +(-1.70794 - 2.35078i) q^{48} +(-4.16938 + 12.8320i) q^{49} +(0.667648 - 2.05481i) q^{50} +(-0.765093 + 0.555873i) q^{51} +(1.82287 + 1.32439i) q^{52} +(-8.96506 + 2.91292i) q^{53} +0.433921i q^{54} +(0.159583 + 0.451544i) q^{55} -7.48733i q^{56} +(3.68688 + 2.32528i) q^{57} +(-3.16894 - 2.30237i) q^{58} +(-0.705083 - 0.970463i) q^{59} +(0.248804 + 0.0808412i) q^{60} +(0.348946 + 0.113379i) q^{61} +(2.41238 + 3.32035i) q^{62} +(2.66082 - 3.66230i) q^{63} +(-1.18321 - 3.64155i) q^{64} -0.179585 q^{65} +(-1.35690 + 0.479552i) q^{66} -11.1883i q^{67} +(-1.62949 + 0.529454i) q^{68} +(-0.865357 + 1.19106i) q^{69} +(0.166719 + 0.229470i) q^{70} +(14.3760 + 4.67106i) q^{71} +(-0.511108 + 1.57303i) q^{72} +(-0.292049 - 0.401971i) q^{73} +(-2.30986 + 3.17925i) q^{74} +(4.73545 - 1.53864i) q^{75} +(5.05084 + 6.07065i) q^{76} +(14.3929 + 4.27316i) q^{77} -0.539659i q^{78} +(1.47154 + 4.52893i) q^{79} +(0.339448 + 0.246624i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(0.141861 - 0.436604i) q^{82} +(-13.5685 - 4.40866i) q^{83} +(6.63504 - 4.82064i) q^{84} +(0.0802669 - 0.110478i) q^{85} +(-1.81652 + 0.590222i) q^{86} -9.02705i q^{87} +(-5.48384 + 0.140174i) q^{88} +11.3562i q^{89} +(-0.0193621 - 0.0595906i) q^{90} +(-3.30921 + 4.55474i) q^{91} +(-2.15786 + 1.56778i) q^{92} +(-2.92279 + 8.99544i) q^{93} +(-0.849710 + 2.61514i) q^{94} +(-0.610078 - 0.154818i) q^{95} +(-2.68548 + 3.69625i) q^{96} +(2.45500 - 0.797679i) q^{97} +5.85463 q^{98} +(-2.73214 - 1.88026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 40 q^{4} + 4 q^{5} - 10 q^{7} + 40 q^{9} + 10 q^{11} - 40 q^{16} - 50 q^{17} + 76 q^{20} + 16 q^{23} - 80 q^{25} - 68 q^{26} - 40 q^{35} + 40 q^{36} - 62 q^{38} + 8 q^{42} + 40 q^{44} - 4 q^{45}+ \cdots - 10 q^{99}+O(q^{100}) $ 160 * q - 40 * q^4 + 4 * q^5 - 10 * q^7 + 40 * q^9 + 10 * q^11 - 40 * q^16 - 50 * q^17 + 76 * q^20 + 16 * q^23 - 80 * q^25 - 68 * q^26 - 40 * q^35 + 40 * q^36 - 62 * q^38 + 8 * q^42 + 40 * q^44 - 4 * q^45 + 20 * q^47 + 110 * q^49 - 18 * q^55 - 20 * q^57 - 24 * q^58 + 10 * q^61 + 120 * q^62 - 10 * q^63 - 136 * q^64 - 12 * q^66 + 160 * q^68 + 20 * q^73 - 100 * q^74 + 90 * q^77 - 156 * q^80 - 40 * q^81 + 68 * q^82 - 200 * q^83 + 30 * q^85 - 84 * q^92 - 96 * q^93 - 60 * q^95 + 100 * q^96 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.134089	−	0.412683i	−0.0948151	−	0.291811i	0.892390	−	0.451264i	$-0.149027\pi$
$2$	−0.134089	−	0.412683i	−0.0948151	−	0.291811i	−0.987205	+	0.159453i	$0.949027\pi$
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$4$	1.46571	−	1.06490i	0.732853	−	0.532449i
$5$	−0.0446214	+	0.137331i	−0.0199553	+	0.0614161i	−0.960538	−	0.278148i	$-0.910279\pi$
$5$	−0.0446214	+	0.137331i	−0.0199553	+	0.0614161i	0.940583	+	0.339564i	$0.110279\pi$
$6$	−0.412683	−	0.134089i	−0.168477	−	0.0547415i
$7$	2.66082	+	3.66230i	1.00569	+	1.38422i	0.921765	+	0.387748i	$0.126747\pi$
$7$	2.66082	+	3.66230i	1.00569	+	1.38422i	0.0839289	+	0.996472i	$0.473253\pi$
$8$	−1.33810	−	0.972186i	−0.473089	−	0.343720i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$	0.0626572			0.0198140
$11$	2.63252	−	2.01739i	0.793733	−	0.608266i
$11$	2.63252	−	2.01739i	0.793733	−	0.608266i
$12$		−	1.81171i		−	0.522996i
$13$	0.384319	+	1.18281i	0.106591	+	0.328053i	0.990101	−	0.140360i	$-0.0448260\pi$
$13$	0.384319	+	1.18281i	0.106591	+	0.328053i	−0.883510	+	0.468413i	$0.844826\pi$
$14$	1.15458	−	1.58915i	0.308575	−	0.424718i
$15$	0.0848750	+	0.116820i	0.0219146	+	0.0301629i
$16$	0.897920	−	2.76351i	0.224480	−	0.690878i
$17$	−0.899421	−	0.292240i	−0.218142	−	0.0708785i	0.197907	−	0.980221i	$-0.436586\pi$
$17$	−0.899421	−	0.292240i	−0.218142	−	0.0708785i	−0.416049	+	0.909342i	$0.636586\pi$
$18$	−0.351049	+	0.255052i	−0.0827431	+	0.0601164i
$19$	0.285902	+	4.34951i	0.0655905	+	0.997847i
$19$	0.285902	+	4.34951i	0.0655905	+	0.997847i
$20$	0.0808412	+	0.248804i	0.0180766	+	0.0556342i
$21$	4.52685			0.987840
$22$	−1.18553	−	0.815885i	−0.252757	−	0.173947i
$23$	−1.47223			−0.306982			−0.153491	−	0.988150i	$-0.549052\pi$
$23$	−1.47223			−0.306982			−0.153491	+	0.988150i	$0.549052\pi$
$24$	−1.57303	+	0.511108i	−0.321093	+	0.104330i
$25$	4.02822	+	2.92667i	0.805643	+	0.585334i
$26$	0.436594	−	0.317204i	0.0856231	−	0.0622088i
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	7.79995	+	2.53436i	1.47405	+	0.478949i
$29$	7.30304	−	5.30597i	1.35614	−	0.985293i	0.357460	−	0.933929i	$-0.383643\pi$
$29$	7.30304	−	5.30597i	1.35614	−	0.985293i	0.998680	−	0.0513646i	$-0.0163570\pi$
$30$	0.0368290	−	0.0506908i	0.00672402	−	0.00925483i
$31$	−8.99544	+	2.92279i	−1.61563	+	0.524949i	−0.970905	−	0.239466i	$-0.923027\pi$
$31$	−8.99544	+	2.92279i	−1.61563	+	0.524949i	−0.644723	+	0.764416i	$0.723027\pi$
$32$	−4.56882			−0.807661
$33$	−0.0847493	−	3.31554i	−0.0147530	−	0.577162i
$34$			0.410362i			0.0703765i
$35$	−0.621675	+	0.201995i	−0.105082	+	0.0341433i
$36$	−1.46571	−	1.06490i	−0.244284	−	0.177483i
$37$	−5.32323	−	7.32679i	−0.875133	−	1.20452i	−0.977745	−	0.209796i	$-0.932720\pi$
$37$	−5.32323	−	7.32679i	−0.875133	−	1.20452i	0.102612	−	0.994721i	$-0.467280\pi$
$38$	1.75663	−	0.701208i	0.284964	−	0.113751i
$39$	1.18281	+	0.384319i	0.189402	+	0.0615403i
$40$	0.193219	−	0.140382i	0.0305505	−	0.0221963i
$41$	0.855911	+	0.621856i	0.133671	+	0.0971176i	0.652611	−	0.757693i	$-0.273673\pi$
$41$	0.855911	+	0.621856i	0.133671	+	0.0971176i	−0.518941	+	0.854810i	$0.673673\pi$
$42$	−0.607001	−	1.86816i	−0.0936622	−	0.288263i
$43$		−	4.40172i		−	0.671256i	−0.941995	−	0.335628i	$-0.891051\pi$
$43$		−	4.40172i		−	0.671256i	0.941995	−	0.335628i	$-0.108949\pi$
$44$	1.71018	−	5.76026i	0.257819	−	0.868392i
$45$	0.144398			0.0215256
$46$	0.197410	+	0.607566i	0.0291065	+	0.0895807i
$47$	−5.12668	−	3.72475i	−0.747803	−	0.543310i	0.147342	−	0.989086i	$-0.452928\pi$
$47$	−5.12668	−	3.72475i	−0.747803	−	0.543310i	−0.895145	+	0.445775i	$0.852928\pi$
$48$	−1.70794	−	2.35078i	−0.246521	−	0.339306i
$49$	−4.16938	+	12.8320i	−0.595626	+	1.83315i
$50$	0.667648	−	2.05481i	0.0944198	−	0.290594i
$51$	−0.765093	+	0.555873i	−0.107135	+	0.0778378i
$52$	1.82287	+	1.32439i	0.252787	+	0.183661i
$53$	−8.96506	+	2.91292i	−1.23145	+	0.400121i	−0.851238	−	0.524780i	$-0.824148\pi$
$53$	−8.96506	+	2.91292i	−1.23145	+	0.400121i	−0.380208	+	0.924901i	$0.624148\pi$
$54$			0.433921i			0.0590491i
$55$	0.159583	+	0.451544i	0.0215181	+	0.0608861i
$56$		−	7.48733i		−	1.00054i
$57$	3.68688	+	2.32528i	0.488339	+	0.307991i
$58$	−3.16894	−	2.30237i	−0.416102	−	0.302316i
$59$	−0.705083	−	0.970463i	−0.0917940	−	0.126344i	0.760650	−	0.649162i	$-0.224880\pi$
$59$	−0.705083	−	0.970463i	−0.0917940	−	0.126344i	−0.852444	+	0.522819i	$0.824880\pi$
$60$	0.248804	+	0.0808412i	0.0321204	+	0.0104365i
$61$	0.348946	+	0.113379i	0.0446779	+	0.0145167i	0.331271	−	0.943536i	$-0.392523\pi$
$61$	0.348946	+	0.113379i	0.0446779	+	0.0145167i	−0.286593	+	0.958052i	$0.592523\pi$
$62$	2.41238	+	3.32035i	0.306372	+	0.421685i
$63$	2.66082	−	3.66230i	0.335231	−	0.461407i
$64$	−1.18321	−	3.64155i	−0.147901	−	0.455194i
$65$	−0.179585			−0.0222748
$66$	−1.35690	+	0.479552i	−0.167023	+	0.0590288i
$67$		−	11.1883i		−	1.36686i	−0.730015	−	0.683431i	$-0.760487\pi$
$67$		−	11.1883i		−	1.36686i	0.730015	−	0.683431i	$-0.239513\pi$
$68$	−1.62949	+	0.529454i	−0.197605	+	0.0642058i
$69$	−0.865357	+	1.19106i	−0.104177	+	0.143387i
$70$	0.166719	+	0.229470i	0.0199268	+	0.0274269i
$71$	14.3760	+	4.67106i	1.70612	+	0.554353i	0.989680	−	0.143294i	$-0.0457695\pi$
$71$	14.3760	+	4.67106i	1.70612	+	0.554353i	0.716442	+	0.697647i	$0.245769\pi$
$72$	−0.511108	+	1.57303i	−0.0602347	+	0.185383i
$73$	−0.292049	−	0.401971i	−0.0341818	−	0.0470472i	0.791584	−	0.611060i	$-0.209257\pi$
$73$	−0.292049	−	0.401971i	−0.0341818	−	0.0470472i	−0.825766	+	0.564013i	$0.809257\pi$
$74$	−2.30986	+	3.17925i	−0.268516	+	0.369580i
$75$	4.73545	−	1.53864i	0.546803	−	0.177667i
$76$	5.05084	+	6.07065i	0.579371	+	0.696352i
$77$	14.3929	+	4.27316i	1.64023	+	0.486971i
$78$		−	0.539659i		−	0.0611044i
$79$	1.47154	+	4.52893i	0.165561	+	0.509544i	0.999077	−	0.0429507i	$-0.0136758\pi$
$79$	1.47154	+	4.52893i	0.165561	+	0.509544i	−0.833516	+	0.552495i	$0.813676\pi$
$80$	0.339448	+	0.246624i	0.0379515	+	0.0275734i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	0.141861	−	0.436604i	0.0156660	−	0.0482148i
$83$	−13.5685	−	4.40866i	−1.48933	−	0.483913i	−0.552446	−	0.833549i	$-0.686305\pi$
$83$	−13.5685	−	4.40866i	−1.48933	−	0.483913i	−0.936886	+	0.349636i	$0.886305\pi$
$84$	6.63504	−	4.82064i	0.723942	−	0.525975i
$85$	0.0802669	−	0.110478i	0.00870617	−	0.0119830i
$86$	−1.81652	+	0.590222i	−0.195880	+	0.0636453i
$87$		−	9.02705i		−	0.967801i
$88$	−5.48384	+	0.140174i	−0.584580	+	0.0149426i
$89$			11.3562i			1.20376i	0.798588	+	0.601878i	$0.205581\pi$
$89$			11.3562i			1.20376i	−0.798588	+	0.601878i	$0.794419\pi$
$90$	−0.0193621	−	0.0595906i	−0.00204095	−	0.00628140i
$91$	−3.30921	+	4.55474i	−0.346900	+	0.477466i
$92$	−2.15786	+	1.56778i	−0.224973	+	0.163452i
$93$	−2.92279	+	8.99544i	−0.303080	+	0.932783i
$94$	−0.849710	+	2.61514i	−0.0876409	+	0.269731i
$95$	−0.610078	−	0.154818i	−0.0625927	−	0.0158840i
$96$	−2.68548	+	3.69625i	−0.274086	+	0.377247i
$97$	2.45500	−	0.797679i	0.249268	−	0.0809920i	−0.181718	−	0.983351i	$-0.558166\pi$
$97$	2.45500	−	0.797679i	0.249268	−	0.0809920i	0.430986	+	0.902359i	$0.358166\pi$
$98$	5.85463			0.591407
$99$	−2.73214	−	1.88026i	−0.274591	−	0.188974i
$100$	9.02079			0.902079
$101$	−10.4999	+	3.41161i	−1.04477	+	0.339468i	−0.780616	−	0.625011i	$-0.785094\pi$
$101$	−10.4999	+	3.41161i	−1.04477	+	0.339468i	−0.264159	+	0.964479i	$0.585094\pi$
$102$	0.331990	+	0.241205i	0.0328719	+	0.0238828i
$103$	8.23749	+	11.3379i	0.811664	+	1.11716i	0.991065	+	0.133383i	$0.0425841\pi$
$103$	8.23749	+	11.3379i	0.811664	+	1.11716i	−0.179401	+	0.983776i	$0.557416\pi$
$104$	0.635656	−	1.95635i	0.0623312	−	0.191836i
$105$	−0.201995	+	0.621675i	−0.0197126	+	0.0606693i
$106$	2.40423	+	3.30914i	0.233519	+	0.321412i
$107$	−10.5021	−	7.63023i	−1.01528	−	0.737642i	−0.0499678	−	0.998751i	$-0.515912\pi$
$107$	−10.5021	−	7.63023i	−1.01528	−	0.737642i	−0.965309	+	0.261109i	$0.915912\pi$
$108$	−1.72304	+	0.559850i	−0.165800	+	0.0538716i
$109$	11.3438			1.08654			0.543268	−	0.839559i	$-0.317187\pi$
$109$	11.3438			1.08654			0.543268	+	0.839559i	$0.317187\pi$
$110$	0.164946	−	0.126404i	0.0157270	−	0.0120522i
$111$	−9.05642			−0.859597
$112$	12.5100	−	4.06475i	1.18209	−	0.384083i
$113$	−9.15937	+	12.6068i	−0.861641	+	1.18595i	0.119535	+	0.992830i	$0.461860\pi$
$113$	−9.15937	+	12.6068i	−0.861641	+	1.18595i	−0.981176	+	0.193117i	$0.938140\pi$
$114$	0.465234	−	1.83331i	0.0435732	−	0.171705i
$115$	0.0656931	−	0.202183i	0.00612591	−	0.0188536i
$116$	5.05379	−	15.5540i	0.469233	−	1.44415i
$117$	1.00616	−	0.731018i	0.0930195	−	0.0675826i
$118$	−0.305950	+	0.421104i	−0.0281650	+	0.0387658i
$119$	−1.32293	−	4.07155i	−0.121272	−	0.373238i
$120$		−	0.238831i		−	0.0218022i
$121$	2.86027	−	10.6216i	0.260025	−	0.965602i
$122$		−	0.159207i		−	0.0144139i
$123$	1.00618	−	0.326929i	0.0907245	−	0.0294782i
$124$	−10.0722	+	13.8632i	−0.904509	+	1.24495i
$125$	−1.16577	+	0.846980i	−0.104269	+	0.0757562i
$126$	−1.86816	−	0.607001i	−0.166429	−	0.0540759i
$127$	−5.19177	+	15.9786i	−0.460695	+	1.41787i	0.403621	+	0.914926i	$0.367751\pi$
$127$	−5.19177	+	15.9786i	−0.460695	+	1.41787i	−0.864317	+	0.502948i	$0.832249\pi$
$128$	−8.73665	+	6.34755i	−0.772218	+	0.561050i
$129$	−3.56107	−	2.58727i	−0.313535	−	0.227796i
$130$	0.0240804	+	0.0741117i	0.00211199	+	0.00650003i
$131$			8.59246i			0.750727i	0.926878	+	0.375364i	$0.122482\pi$
$131$			8.59246i			0.750727i	−0.926878	+	0.375364i	$0.877518\pi$
$132$	−3.65493	−	4.76936i	−0.318121	−	0.415120i
$133$	−15.1685	+	12.6203i	−1.31527	+	1.09432i
$134$	−4.61720	+	1.50022i	−0.398866	+	0.129599i
$135$	0.0848750	−	0.116820i	0.00730487	−	0.0100543i
$136$	0.919403	+	1.26545i	0.0788382	+	0.108511i
$137$	4.88190	−	15.0250i	0.417089	−	1.28367i	−0.493280	−	0.869871i	$-0.664202\pi$
$137$	4.88190	−	15.0250i	0.417089	−	1.28367i	0.910369	−	0.413798i	$-0.135798\pi$
$138$	0.607566	+	0.197410i	0.0517194	+	0.0168047i
$139$	1.98724	+	2.73520i	0.168555	+	0.231997i	0.884936	−	0.465714i	$-0.154202\pi$
$139$	1.98724	+	2.73520i	0.168555	+	0.231997i	−0.716380	+	0.697710i	$0.754202\pi$
$140$	−0.696090	+	0.958085i	−0.0588303	+	0.0809730i
$141$	−6.02677	+	1.95822i	−0.507546	+	0.164912i
$142$		−	6.55909i		−	0.550426i
$143$	3.39792	+	2.33845i	0.284148	+	0.195551i
$144$	−2.90573			−0.242144
$145$	0.402800	+	1.23969i	0.0334507	+	0.102951i
$146$	−0.126726	+	0.174424i	−0.0104879	+	0.0144354i
$147$	7.93063	+	10.9156i	0.654107	+	0.900302i
$148$	−15.6046	−	5.07023i	−1.28269	−	0.416771i
$149$	−0.496544	−	0.161337i	−0.0406784	−	0.0132172i	0.288607	−	0.957448i	$-0.406808\pi$
$149$	−0.496544	−	0.161337i	−0.0406784	−	0.0132172i	−0.329286	+	0.944230i	$0.606808\pi$
$150$	−1.26994	−	1.74793i	−0.103690	−	0.142718i
$151$	2.70560	+	1.96574i	0.220179	+	0.159969i	0.692407	−	0.721507i	$-0.256550\pi$
$151$	2.70560	+	1.96574i	0.220179	+	0.159969i	−0.472228	+	0.881476i	$0.656550\pi$
$152$	3.84597	−	6.09803i	0.311949	−	0.494615i
$153$			0.945708i			0.0764559i
$154$	−0.166473	−	6.51270i	−0.0134147	−	0.524809i
$155$		−	1.36577i		−	0.109701i
$156$	2.14292	−	0.696276i	0.171571	−	0.0557467i
$157$	−12.0623	−	8.76378i	−0.962677	−	0.699426i	−0.00890640	−	0.999960i	$-0.502835\pi$
$157$	−12.0623	−	8.76378i	−0.962677	−	0.699426i	−0.953771	+	0.300534i	$0.902835\pi$
$158$	1.67170	−	1.21456i	0.132993	−	0.0966250i
$159$	−2.91292	+	8.96506i	−0.231010	+	0.710976i
$160$	0.203867	−	0.627438i	0.0161171	−	0.0496034i
$161$	−3.91734	−	5.39176i	−0.308730	−	0.424930i
$162$	0.351049	+	0.255052i	0.0275810	+	0.0200388i
$163$	3.62855	+	11.1675i	0.284210	+	0.874708i	0.986634	+	0.162949i	$0.0521008\pi$
$163$	3.62855	+	11.1675i	0.284210	+	0.874708i	−0.702425	+	0.711758i	$0.747899\pi$
$164$	1.91673			0.149671
$165$	0.459107	+	0.136305i	0.0357414	+	0.0106114i
$166$			6.19062i			0.480486i
$167$	2.00511	+	6.17111i	0.155160	+	0.477535i	0.998177	−	0.0603528i	$-0.0192226\pi$
$167$	2.00511	+	6.17111i	0.155160	+	0.477535i	−0.843017	+	0.537887i	$0.819223\pi$
$168$	−6.05738	−	4.40094i	−0.467337	−	0.339540i
$169$	9.26588	−	6.73205i	0.712760	−	0.517850i
$170$	−0.0563552	−	0.0183109i	−0.00432225	−	0.00140438i
$171$	4.04828	−	1.61598i	0.309580	−	0.123577i
$172$	−4.68738	−	6.45163i	−0.357410	−	0.491932i
$173$	−1.50380	−	1.09257i	−0.114332	−	0.0830669i	0.529150	−	0.848528i	$-0.322511\pi$
$173$	−1.50380	−	1.09257i	−0.114332	−	0.0830669i	−0.643482	+	0.765461i	$0.722511\pi$
$174$	−3.72531	+	1.21043i	−0.282415	+	0.0917622i
$175$			22.5399i			1.70385i
$176$	−3.21130	−	9.08644i	−0.242061	−	0.684916i
$177$	−1.19956			−0.0901644
$178$	4.68652	−	1.52274i	0.351270	−	0.114134i
$179$	−4.01165	+	5.52156i	−0.299845	+	0.412701i	−0.932181	−	0.361993i	$-0.882096\pi$
$179$	−4.01165	+	5.52156i	−0.299845	+	0.412701i	0.632336	+	0.774694i	$0.282096\pi$
$180$	0.211645	−	0.153769i	0.0157751	−	0.0114613i
$181$	3.98881	+	1.29604i	0.296486	+	0.0963341i	0.453483	−	0.891265i	$-0.350181\pi$
$181$	3.98881	+	1.29604i	0.296486	+	0.0963341i	−0.156997	+	0.987599i	$0.550181\pi$
$182$	2.32339	+	0.754916i	0.172221	+	0.0559581i
$183$	0.296831	−	0.215660i	0.0219424	−	0.0159421i
$184$	1.96999	+	1.43128i	0.145230	+	0.105516i
$185$	1.24372	−	0.404110i	0.0914403	−	0.0297108i
$186$	4.10418			0.300933
$187$	−2.95730	+	1.04516i	−0.216259	+	0.0764295i
$188$	−11.4807			−0.837315
$189$	−1.39887	−	4.30529i	−0.101753	−	0.313164i
$190$	0.0179138	+	0.272528i	0.00129961	+	0.0197713i
$191$	−16.4494	+	11.9512i	−1.19024	+	0.864757i	−0.993289	−	0.115657i	$-0.963103\pi$
$191$	−16.4494	+	11.9512i	−1.19024	+	0.864757i	−0.196947	+	0.980414i	$0.563103\pi$
$192$	−3.64155	−	1.18321i	−0.262806	−	0.0853910i
$193$	0.759763	−	2.33831i	0.0546889	−	0.168315i	−0.919981	−	0.391962i	$-0.871796\pi$
$193$	0.759763	−	2.33831i	0.0546889	−	0.168315i	0.974670	+	0.223647i	$0.0717963\pi$
$194$	−0.658377	−	0.906178i	−0.0472687	−	0.0650598i
$195$	−0.105557	+	0.145287i	−0.00755913	+	0.0104042i
$196$	7.55372	+	23.2480i	0.539551	+	1.66057i
$197$			24.4995i			1.74551i	0.488155	+	0.872757i	$0.337670\pi$
$197$			24.4995i			1.74551i	−0.488155	+	0.872757i	$0.662330\pi$
$198$	−0.409603	+	1.37963i	−0.0291092	+	0.0980462i
$199$	−6.68343			−0.473776			−0.236888	−	0.971537i	$-0.576127\pi$
$199$	−6.68343			−0.473776			−0.236888	+	0.971537i	$0.576127\pi$
$200$	−2.54488	−	7.83235i	−0.179950	−	0.553831i
$201$	−9.05149	−	6.57629i	−0.638443	−	0.463856i
$202$	2.81583	+	3.87565i	0.198121	+	0.272690i
$203$	38.8641	+	12.6277i	2.72772	+	0.886291i
$204$	−0.529454	+	1.62949i	−0.0370692	+	0.114087i
$205$	−0.123592	+	0.0897947i	−0.00863202	+	0.00627153i
$206$	3.57442	−	4.91976i	0.249041	−	0.342776i
$207$	0.454945	+	1.40018i	0.0316209	+	0.0973190i
$208$	3.61380			0.250572
$209$	9.52731	+	10.8734i	0.659018	+	0.752128i
$210$	0.283640			0.0195730
$211$	0.416710	+	1.28250i	0.0286875	+	0.0882911i	0.964375	−	0.264538i	$-0.0852196\pi$
$211$	0.416710	+	1.28250i	0.0286875	+	0.0882911i	−0.935688	+	0.352829i	$0.885220\pi$
$212$	−10.0382	+	13.8164i	−0.689425	+	0.948912i
$213$	12.2290	−	8.88488i	0.837917	−	0.608782i
$214$	−1.74065	+	5.35717i	−0.118988	+	0.366209i
$215$	0.604491	+	0.196411i	0.0412259	+	0.0133951i
$216$	0.972186	+	1.33810i	0.0661489	+	0.0910461i
$217$	−34.6394	−	25.1670i	−2.35147	−	1.70845i
$218$	−1.52107	−	4.68138i	−0.103020	−	0.317063i
$219$	−0.496864			−0.0335749
$220$	0.714749	+	0.491891i	0.0481884	+	0.0331633i
$221$		−	1.17616i		−	0.0791171i
$222$	1.21436	+	3.73743i	0.0815028	+	0.250840i
$223$	−2.71599	+	3.73824i	−0.181876	+	0.250331i	−0.890214	−	0.455542i	$-0.849445\pi$
$223$	−2.71599	+	3.73824i	−0.181876	+	0.250331i	0.708338	+	0.705874i	$0.249445\pi$
$224$	−12.1568	−	16.7324i	−0.812260	−	1.11798i
$225$	1.53864	−	4.73545i	0.102576	−	0.315697i
$226$	6.43078	+	2.08949i	0.427769	+	0.138991i
$227$	9.37602	−	6.81208i	0.622308	−	0.452134i	−0.231419	−	0.972854i	$-0.574337\pi$
$227$	9.37602	−	6.81208i	0.622308	−	0.452134i	0.853727	+	0.520721i	$0.174337\pi$
$228$	7.88007	−	0.517973i	0.521870	−	0.0343036i
$229$	−6.03883	−	18.5856i	−0.399057	−	1.22817i	−0.925756	−	0.378121i	$-0.876570\pi$
$229$	−6.03883	−	18.5856i	−0.399057	−	1.22817i	0.526699	−	0.850052i	$-0.323430\pi$
$230$	−0.0922461			−0.00608252
$231$	11.9170	−	9.13243i	0.784082	−	0.600870i
$232$	−14.9306			−0.980240
$233$	26.7443	−	8.68975i	1.75208	−	0.569284i	0.755746	−	0.654865i	$-0.227275\pi$
$233$	26.7443	−	8.68975i	1.75208	−	0.569284i	0.996331	+	0.0855806i	$0.0272745\pi$
$234$	−0.436594	−	0.317204i	−0.0285410	−	0.0207363i
$235$	0.740281	−	0.537846i	0.0482906	−	0.0350852i
$236$	−2.06689	−	0.671573i	−0.134543	−	0.0437157i
$237$	4.52893	+	1.47154i	0.294186	+	0.0955867i
$238$	−1.50287	+	1.09190i	−0.0974165	+	0.0707773i
$239$	7.69711	−	10.5942i	0.497884	−	0.685279i	−0.483933	−	0.875105i	$-0.660792\pi$
$239$	7.69711	−	10.5942i	0.497884	−	0.685279i	0.981818	+	0.189826i	$0.0607923\pi$
$240$	0.399045	−	0.129658i	0.0257583	−	0.00836937i
$241$	15.3226			0.987013			0.493507	−	0.869742i	$-0.335715\pi$
$241$	15.3226			0.987013			0.493507	+	0.869742i	$0.335715\pi$
$242$	−4.76689	+	0.243855i	−0.306428	+	0.0156756i
$243$			1.00000i			0.0641500i
$244$	0.632189	−	0.205411i	0.0404718	−	0.0131501i
$245$	−1.57619	−	1.14517i	−0.100699	−	0.0731620i
$246$	−0.269836	−	0.371397i	−0.0172041	−	0.0236794i
$247$	−5.03478	+	2.00977i	−0.320355	+	0.127879i
$248$	14.8783	+	4.83425i	0.944772	+	0.306975i
$249$	−11.5420	+	8.38577i	−0.731446	+	0.531426i
$250$	0.505851	+	0.367522i	0.0319928	+	0.0232441i
$251$	1.70479	+	5.24682i	0.107606	+	0.331176i	0.990333	−	0.138709i	$-0.0442953\pi$
$251$	1.70479	+	5.24682i	0.107606	+	0.331176i	−0.882728	+	0.469885i	$0.844295\pi$
$252$		−	8.20136i		−	0.516637i
$253$	−3.87568	+	2.97007i	−0.243662	+	0.186727i
$254$	7.29027			0.457432
$255$	−0.0421988	−	0.129875i	−0.00264259	−	0.00813306i
$256$	−2.40436	−	1.74687i	−0.150273	−	0.109179i
$257$	−8.77550	−	12.0784i	−0.547401	−	0.753433i	0.442256	−	0.896889i	$-0.354178\pi$
$257$	−8.77550	−	12.0784i	−0.547401	−	0.753433i	−0.989657	+	0.143456i	$0.954178\pi$
$258$	−0.590222	+	1.81652i	−0.0367456	+	0.113091i
$259$	12.6688	−	38.9905i	0.787200	−	2.42275i
$260$	−0.263219	+	0.191240i	−0.0163242	+	0.0118602i
$261$	−7.30304	−	5.30597i	−0.452047	−	0.328431i
$262$	3.54596	−	1.15215i	0.219070	−	0.0711803i
$263$			10.3076i			0.635592i	0.948159	+	0.317796i	$0.102943\pi$
$263$			10.3076i			0.635592i	−0.948159	+	0.317796i	$0.897057\pi$
$264$	−3.10992	+	4.51891i	−0.191402	+	0.278120i
$265$		−	1.36116i		−	0.0836151i
$266$	7.24212	+	4.56754i	0.444043	+	0.280054i
$267$	9.18738	+	6.67502i	0.562258	+	0.408505i
$268$	−11.9144	−	16.3987i	−0.727785	−	1.00171i
$269$	−23.0238	−	7.48090i	−1.40379	−	0.456119i	−0.493374	−	0.869817i	$-0.664237\pi$
$269$	−23.0238	−	7.48090i	−1.40379	−	0.456119i	−0.910414	+	0.413698i	$0.864237\pi$
$270$	−0.0595906	−	0.0193621i	−0.00362657	−	0.00117834i
$271$	−4.33794	−	5.97066i	−0.263511	−	0.362691i	0.656675	−	0.754174i	$-0.271962\pi$
$271$	−4.33794	−	5.97066i	−0.263511	−	0.362691i	−0.920186	+	0.391482i	$0.871962\pi$
$272$	−1.61522	+	2.22315i	−0.0979369	+	0.134799i
$273$	1.73976	+	5.35442i	0.105295	+	0.324064i
$274$	−6.85515			−0.414135
$275$	16.5086	−	0.421979i	0.995505	−	0.0254463i
$276$			2.66726i			0.160550i
$277$	−7.88927	+	2.56338i	−0.474021	+	0.154019i	−0.536278	−	0.844042i	$-0.680170\pi$
$277$	−7.88927	+	2.56338i	−0.474021	+	0.154019i	0.0622573	+	0.998060i	$0.480170\pi$
$278$	0.862304	−	1.18686i	0.0517176	−	0.0711831i
$279$	5.55949	+	7.65198i	0.332838	+	0.458112i
$280$	1.02824	+	0.334095i	0.0614490	+	0.0199660i
$281$	4.44483	−	13.6798i	0.265156	−	0.816066i	−0.726501	−	0.687165i	$-0.758855\pi$
$281$	4.44483	−	13.6798i	0.265156	−	0.816066i	0.991657	−	0.128901i	$-0.0411451\pi$
$282$	1.61625	+	2.22457i	0.0962460	+	0.132471i
$283$	12.0560	−	16.5937i	0.716656	−	0.986393i	−0.282972	−	0.959128i	$-0.591320\pi$
$283$	12.0560	−	16.5937i	0.716656	−	0.986393i	0.999628	−	0.0272648i	$-0.00867972\pi$
$284$	26.0453	−	8.46262i	1.54550	−	0.502164i
$285$	−0.483846	+	0.402564i	−0.0286605	+	0.0238458i
$286$	0.509415	−	1.71582i	0.0301224	−	0.101459i
$287$			4.78925i			0.282700i
$288$	1.41184	+	4.34520i	0.0831936	+	0.256044i
$289$	−13.0297	−	9.46666i	−0.766455	−	0.556862i
$290$	0.457588	−	0.332457i	0.0268705	−	0.0195226i
$291$	0.797679	−	2.45500i	0.0467608	−	0.143915i
$292$	−0.856117	−	0.278169i	−0.0501005	−	0.0162786i
$293$	−11.8198	+	8.58762i	−0.690523	+	0.501694i	−0.876832	−	0.480797i	$-0.840347\pi$
$293$	−11.8198	+	8.58762i	−0.690523	+	0.501694i	0.186309	+	0.982491i	$0.440347\pi$
$294$	3.44126	−	4.73649i	0.200699	−	0.276238i
$295$	0.164736	−	0.0535260i	0.00959130	−	0.00311640i
$296$			14.9791i			0.870645i
$297$	−3.12708	+	1.10516i	−0.181452	+	0.0641279i
$298$			0.226549i			0.0131236i
$299$	−0.565807	−	1.74138i	−0.0327215	−	0.100706i
$300$	5.30229	−	7.29797i	0.306128	−	0.421349i
$301$	16.1204	−	11.7122i	0.929166	−	0.675079i
$302$	0.448435	−	1.38014i	0.0258045	−	0.0794181i
$303$	−3.41161	+	10.4999i	−0.195992	+	0.603201i
$304$	12.2767	+	3.11542i	0.704114	+	0.178682i
$305$	−0.0311409	+	0.0428618i	−0.00178312	+	0.00245426i
$306$	0.390278	−	0.126809i	0.0223107	−	0.00724918i
$307$	27.4235			1.56514			0.782571	−	0.622562i	$-0.213908\pi$
$307$	27.4235			1.56514			0.782571	+	0.622562i	$0.213908\pi$
$308$	25.6463	−	9.06381i	1.46133	−	0.516459i
$309$	14.0144			0.797254
$310$	−0.563629	+	0.183134i	−0.0320120	+	0.0104013i
$311$	−15.1463	−	11.0044i	−0.858867	−	0.624004i	0.0687092	−	0.997637i	$-0.478112\pi$
$311$	−15.1463	−	11.0044i	−0.858867	−	0.624004i	−0.927577	+	0.373633i	$0.878112\pi$
$312$	−1.20909	−	1.66417i	−0.0684512	−	0.0942150i
$313$	−3.98734	+	12.2718i	−0.225378	+	0.693641i	0.772875	+	0.634558i	$0.218818\pi$
$313$	−3.98734	+	12.2718i	−0.225378	+	0.693641i	−0.998253	+	0.0590832i	$0.981182\pi$
$314$	−1.99924	+	6.15304i	−0.112824	+	0.347236i
$315$	0.384216	+	0.528829i	0.0216481	+	0.0297961i
$316$	6.97969	+	5.07104i	0.392638	+	0.285268i
$317$	7.59529	−	2.46786i	0.426594	−	0.138609i	−0.0878482	−	0.996134i	$-0.527999\pi$
$317$	7.59529	−	2.46786i	0.426594	−	0.138609i	0.514442	+	0.857525i	$0.327999\pi$
$318$	4.09032			0.229374
$319$	8.52115	−	28.7011i	0.477093	−	1.60695i
$320$	0.552893			0.0309076
$321$	−12.3460	+	4.01145i	−0.689085	+	0.223897i
$322$	−1.69982	+	2.33960i	−0.0947271	+	0.130381i
$323$	1.01395	−	3.99560i	0.0564179	−	0.222321i
$324$	−0.559850	+	1.72304i	−0.0311028	+	0.0957245i
$325$	−1.91358	+	5.88940i	−0.106146	+	0.326685i
$326$	4.12210	−	2.99488i	0.228302	−	0.165871i
$327$	6.66770	−	9.17730i	0.368725	−	0.507506i
$328$	−0.540734	−	1.66421i	−0.0298571	−	0.0918906i
$329$		−	28.6863i		−	1.58153i
$330$	−0.00531016	−	0.207743i	−0.000292314	−	0.0114359i
$331$		−	6.78794i		−	0.373099i	−0.982446	−	0.186550i	$-0.940270\pi$
$331$		−	6.78794i		−	0.373099i	0.982446	−	0.186550i	$-0.0597305\pi$
$332$	−24.5821	+	7.98722i	−1.34912	+	0.438356i
$333$	−5.32323	+	7.32679i	−0.291711	+	0.401506i
$334$	2.27785	−	1.65495i	0.124638	−	0.0905550i
$335$	1.53649	+	0.499236i	0.0839474	+	0.0272762i
$336$	4.06475	−	12.5100i	0.221750	−	0.682477i
$337$	−2.45360	+	1.78264i	−0.133656	+	0.0971068i	−0.652604	−	0.757699i	$-0.726324\pi$
$337$	−2.45360	+	1.78264i	−0.133656	+	0.0971068i	0.518948	+	0.854806i	$0.326324\pi$
$338$	−4.02066	−	2.92118i	−0.218695	−	0.158891i
$339$	4.81537	+	14.8202i	0.261535	+	0.804921i
$340$		−	0.247404i		−	0.0134174i
$341$	−17.7842	+	25.8416i	−0.963069	+	1.39940i
$342$	−1.20972	−	1.45397i	−0.0654141	−	0.0786219i
$343$	−27.9517	+	9.08205i	−1.50925	+	0.490384i
$344$	−4.27929	+	5.88994i	−0.230724	+	0.317564i
$345$	−0.124956	−	0.171987i	−0.00672739	−	0.00925946i
$346$	−0.249244	+	0.767095i	−0.0133995	+	0.0412393i
$347$	−5.42691	−	1.76331i	−0.291332	−	0.0946595i	0.159705	−	0.987165i	$-0.448946\pi$
$347$	−5.42691	−	1.76331i	−0.291332	−	0.0946595i	−0.451037	+	0.892505i	$0.648946\pi$
$348$	−9.61289	−	13.2310i	−0.515305	−	0.709256i
$349$	11.6311	−	16.0088i	0.622596	−	0.856930i	−0.374942	−	0.927048i	$-0.622338\pi$
$349$	11.6311	−	16.0088i	0.622596	−	0.856930i	0.997539	+	0.0701177i	$0.0223375\pi$
$350$	9.30183	−	3.02235i	0.497203	−	0.161551i
$351$		−	1.24368i		−	0.0663828i
$352$	−12.0275	+	9.21709i	−0.641067	+	0.491272i
$353$	−15.7749			−0.839611			−0.419805	−	0.907614i	$-0.637902\pi$
$353$	−15.7749			−0.839611			−0.419805	+	0.907614i	$0.637902\pi$
$354$	0.160847	+	0.495038i	0.00854895	+	0.0263110i
$355$	−1.28296	+	1.76584i	−0.0680923	+	0.0937211i
$356$	12.0932	+	16.6449i	0.640939	+	0.882177i
$357$	−4.07155	−	1.32293i	−0.215489	−	0.0700167i
$358$	2.81657	+	0.915160i	0.148860	+	0.0483677i
$359$	16.0391	+	22.0759i	0.846509	+	1.16512i	0.984621	+	0.174703i	$0.0558966\pi$
$359$	16.0391	+	22.0759i	0.846509	+	1.16512i	−0.138112	+	0.990417i	$0.544103\pi$
$360$	−0.193219	−	0.140382i	−0.0101835	−	0.00739876i
$361$	−18.8365	+	2.48707i	−0.991396	+	0.130898i
$362$		−	1.81990i		−	0.0956517i
$363$	−6.91185	−	8.55724i	−0.362778	−	0.449139i
$364$			10.1999i			0.534619i
$365$	0.0682346	−	0.0221708i	0.00357156	−	0.00116047i
$366$	−0.128801	−	0.0935795i	−0.00673254	−	0.00489148i
$367$	−2.93592	+	2.13307i	−0.153254	+	0.111345i	−0.661770	−	0.749707i	$-0.730194\pi$
$367$	−2.93592	+	2.13307i	−0.153254	+	0.111345i	0.508516	+	0.861053i	$0.330194\pi$
$368$	−1.32195	+	4.06854i	−0.0689113	+	0.212087i
$369$	0.326929	−	1.00618i	0.0170192	−	0.0523798i
$370$	−0.333539	−	0.459077i	−0.0173399	−	0.0238663i
$371$	−34.5224	−	25.0820i	−1.79231	−	1.30219i
$372$	5.29526	+	16.2971i	0.274547	+	0.844968i
$373$	−3.91064			−0.202485			−0.101243	−	0.994862i	$-0.532282\pi$
$373$	−3.91064			−0.202485			−0.101243	+	0.994862i	$0.532282\pi$
$374$	0.827860	+	1.08028i	0.0428076	+	0.0558602i
$375$			1.44097i			0.0744113i
$376$	3.23885	+	9.96816i	0.167031	+	0.514069i
$377$	9.08265	+	6.59894i	0.467781	+	0.339862i
$378$	−1.58915	+	1.15458i	−0.0817370	+	0.0593854i
$379$	23.2206	+	7.54482i	1.19276	+	0.387551i	0.837092	−	0.547061i	$-0.184254\pi$
$379$	23.2206	+	7.54482i	1.19276	+	0.387551i	0.355667	+	0.934613i	$0.384254\pi$
$380$	−1.05906	+	0.422753i	−0.0543287	+	0.0216868i
$381$	9.87534	+	13.5922i	0.505929	+	0.696351i
$382$	7.13773	+	5.18587i	0.365198	+	0.265332i
$383$	27.0529	−	8.79003i	1.38234	−	0.449150i	0.478902	−	0.877868i	$-0.341035\pi$
$383$	27.0529	−	8.79003i	1.38234	−	0.449150i	0.903438	+	0.428719i	$0.141035\pi$
$384$			10.7991i			0.551089i
$385$	−1.22907	+	1.78592i	−0.0626391	+	0.0910187i
$386$	−1.06686			−0.0543016
$387$	−4.18629	+	1.36021i	−0.212801	+	0.0691432i
$388$	2.74887	−	3.78349i	0.139553	−	0.192078i
$389$	18.9431	−	13.7630i	0.960455	−	0.697812i	0.00719878	−	0.999974i	$-0.497709\pi$
$389$	18.9431	−	13.7630i	0.960455	−	0.697812i	0.953256	+	0.302163i	$0.0977085\pi$
$390$	0.0741117	+	0.0240804i	0.00375279	+	0.00121936i
$391$	1.32416	+	0.430245i	0.0669655	+	0.0217584i
$392$	18.0542	−	13.1171i	0.911873	−	0.662514i
$393$	6.95145	+	5.05052i	0.350654	+	0.254765i
$394$	10.1105	−	3.28511i	0.509360	−	0.165501i
$395$	−0.687622			−0.0345980
$396$	−6.00681	+	0.153541i	−0.301854	+	0.00771574i
$397$	16.3494			0.820553			0.410277	−	0.911961i	$-0.365432\pi$
$397$	16.3494			0.820553			0.410277	+	0.911961i	$0.365432\pi$
$398$	0.896173	+	2.75814i	0.0449211	+	0.138253i
$399$	1.29424	+	19.6896i	0.0647929	+	0.985713i
$400$	11.7049	−	8.50411i	0.585245	−	0.425206i
$401$	−11.8691	−	3.85652i	−0.592716	−	0.192585i	−0.00272702	−	0.999996i	$-0.500868\pi$
$401$	−11.8691	−	3.85652i	−0.592716	−	0.192585i	−0.589989	+	0.807411i	$0.700868\pi$
$402$	−1.50022	+	4.61720i	−0.0748242	+	0.230285i
$403$	−6.91423	−	9.51663i	−0.344422	−	0.474057i
$404$	−11.7567	+	16.1817i	−0.584917	+	0.805069i
$405$	−0.0446214	−	0.137331i	−0.00221726	−	0.00682401i
$406$		−	17.7318i		−	0.880014i
$407$	−28.7945	−	8.54887i	−1.42729	−	0.423752i
$408$	1.56418			0.0774386
$409$	−10.3413	−	31.8272i	−0.511343	−	1.57375i	−0.789839	−	0.613315i	$-0.789836\pi$
$409$	−10.3413	−	31.8272i	−0.511343	−	1.57375i	0.278495	−	0.960438i	$-0.410164\pi$
$410$	0.0536290	+	0.0389638i	0.00264855	+	0.00192428i
$411$	−9.28593	−	12.7810i	−0.458041	−	0.630440i
$412$	24.1475	+	7.84599i	1.18966	+	0.386544i
$413$	1.67803	−	5.16445i	0.0825706	−	0.254126i
$414$	0.516826	−	0.375496i	0.0254006	−	0.0184546i
$415$	1.21089	−	1.66664i	0.0594401	−	0.0818123i
$416$	−1.75588	−	5.40405i	−0.0860893	−	0.264955i
$417$	3.38089			0.165563
$418$	3.20976	−	5.38976i	0.156994	−	0.263622i
$419$	28.9904			1.41627			0.708137	−	0.706075i	$-0.249536\pi$
$419$	28.9904			1.41627			0.708137	+	0.706075i	$0.249536\pi$
$420$	0.365956	+	1.12630i	0.0178568	+	0.0549577i
$421$	8.55194	−	11.7707i	0.416796	−	0.573671i	−0.548063	−	0.836437i	$-0.684635\pi$
$421$	8.55194	−	11.7707i	0.416796	−	0.573671i	0.964860	+	0.262766i	$0.0846347\pi$
$422$	0.473391	−	0.343939i	0.0230443	−	0.0167427i
$423$	−1.95822	+	6.02677i	−0.0952117	+	0.293032i
$424$	14.8280	+	4.81792i	0.720113	+	0.233979i
$425$	−2.76777	−	3.80951i	−0.134257	−	0.184789i
$426$	−5.30641	−	3.85533i	−0.257096	−	0.186792i
$427$	0.513252	+	1.57963i	0.0248380	+	0.0764435i
$428$	−23.5184			−1.13681
$429$	3.88909	−	1.37447i	0.187767	−	0.0663599i
$430$		−	0.275800i		−	0.0133002i
$431$	3.33562	+	10.2660i	0.160671	+	0.494495i	0.998691	−	0.0511443i	$-0.0162869\pi$
$431$	3.33562	+	10.2660i	0.160671	+	0.494495i	−0.838020	+	0.545639i	$0.816287\pi$
$432$	−1.70794	+	2.35078i	−0.0821735	+	0.113102i
$433$	−21.7014	−	29.8694i	−1.04290	−	1.43543i	−0.894805	−	0.446457i	$-0.852686\pi$
$433$	−21.7014	−	29.8694i	−1.04290	−	1.43543i	−0.148096	−	0.988973i	$-0.547314\pi$
$434$	−5.74123	+	17.6697i	−0.275588	+	0.848172i
$435$	1.23969	+	0.402800i	0.0594386	+	0.0193128i
$436$	16.6266	−	12.0800i	0.796272	−	0.578525i
$437$	−0.420915	−	6.40350i	−0.0201351	−	0.306321i
$438$	0.0666239	+	0.205047i	0.00318341	+	0.00979754i
$439$	−5.58074			−0.266354			−0.133177	−	0.991092i	$-0.542518\pi$
$439$	−5.58074			−0.266354			−0.133177	+	0.991092i	$0.542518\pi$
$440$	0.225447	−	0.759354i	0.0107477	−	0.0362008i
$441$	13.4924			0.642495
$442$	−0.485381	+	0.157710i	−0.0230872	+	0.00750150i
$443$	−5.99461	−	4.35534i	−0.284812	−	0.206928i	0.436201	−	0.899849i	$-0.356324\pi$
$443$	−5.99461	−	4.35534i	−0.284812	−	0.206928i	−0.721014	+	0.692921i	$0.756324\pi$
$444$	−13.2740	+	9.64416i	−0.629958	+	0.457692i
$445$	−1.55956	−	0.506730i	−0.0739300	−	0.0240213i
$446$	1.90689	+	0.619588i	0.0902941	+	0.0293383i
$447$	−0.422385	+	0.306881i	−0.0199781	+	0.0145150i
$448$	10.1881	−	14.0228i	0.481345	−	0.662514i
$449$	−13.7719	+	4.47475i	−0.649935	+	0.211177i	−0.615385	−	0.788226i	$-0.711000\pi$
$449$	−13.7719	+	4.47475i	−0.649935	+	0.211177i	−0.0345494	+	0.999403i	$0.511000\pi$
$450$	−2.16056			−0.101850
$451$	3.50772	−	0.0896617i	0.165172	−	0.00422201i
$452$			28.2317i			1.32791i
$453$	3.18063	−	1.03345i	0.149439	−	0.0485556i
$454$	−4.06845	−	2.95590i	−0.190942	−	0.138727i
$455$	−0.477843	−	0.657695i	−0.0224016	−	0.0308332i
$456$	−2.67280	−	6.69578i	−0.125166	−	0.313559i
$457$	−30.3221	−	9.85226i	−1.41841	−	0.460869i	−0.503313	−	0.864104i	$-0.667886\pi$
$457$	−30.3221	−	9.85226i	−1.41841	−	0.460869i	−0.915096	+	0.403235i	$0.867886\pi$
$458$	−6.86023	+	4.98425i	−0.320558	+	0.232899i
$459$	0.765093	+	0.555873i	0.0357115	+	0.0259459i
$460$	−0.119017	−	0.366297i	−0.00554920	−	0.0170787i
$461$			27.2037i			1.26700i	0.773741	+	0.633502i	$0.218383\pi$
$461$			27.2037i			1.26700i	−0.773741	+	0.633502i	$0.781617\pi$
$462$	−5.36674	−	3.69339i	−0.249683	−	0.171832i
$463$	−2.45000			−0.113861			−0.0569306	−	0.998378i	$-0.518131\pi$
$463$	−2.45000			−0.113861			−0.0569306	+	0.998378i	$0.518131\pi$
$464$	−8.10556	−	24.9464i	−0.376291	−	1.15811i
$465$	−1.10493	−	0.802778i	−0.0512399	−	0.0372279i
$466$	−7.17222	−	9.87172i	−0.332247	−	0.457299i
$467$	−5.08134	+	15.6388i	−0.235136	+	0.723675i	0.761967	+	0.647616i	$0.224234\pi$
$467$	−5.08134	+	15.6388i	−0.235136	+	0.723675i	−0.997103	+	0.0760595i	$0.975766\pi$
$468$	0.696276	−	2.14292i	0.0321853	−	0.0990563i
$469$	40.9748	−	29.7699i	1.89204	−	1.37465i
$470$	−0.321223	−	0.233382i	−0.0148169	−	0.0107651i
$471$	−14.1801	+	4.60739i	−0.653385	+	0.212297i
$472$			1.98405i			0.0913232i
$473$	−8.87999	−	11.5876i	−0.408302	−	0.532798i
$474$		−	2.06633i		−	0.0949097i
$475$	−11.5779	+	18.3575i	−0.531231	+	0.842301i
$476$	−6.27480	−	4.55891i	−0.287605	−	0.208957i
$477$	5.54071	+	7.62614i	0.253692	+	0.349177i
$478$	−5.40413	−	1.75591i	−0.247179	−	0.0803133i
$479$	37.0817	+	12.0486i	1.69431	+	0.550514i	0.987600	−	0.156992i	$-0.0501798\pi$
$479$	37.0817	+	12.0486i	1.69431	+	0.550514i	0.706707	+	0.707506i	$0.250180\pi$
$480$	−0.387778	−	0.533731i	−0.0176996	−	0.0243614i
$481$	6.62040	−	9.11220i	0.301864	−	0.415481i
$482$	−2.05459	−	6.32336i	−0.0935838	−	0.288021i
$483$	−6.66458			−0.303249
$484$	−7.11862	−	18.6141i	−0.323574	−	0.846094i
$485$			0.372741i			0.0169253i
$486$	0.412683	−	0.134089i	0.0187197	−	0.00608239i
$487$	0.179486	−	0.247042i	0.00813330	−	0.0111945i	−0.804931	−	0.593368i	$-0.797798\pi$
$487$	0.179486	−	0.247042i	0.00813330	−	0.0111945i	0.813064	+	0.582174i	$0.197798\pi$
$488$	−0.356698	−	0.490953i	−0.0161470	−	0.0222244i
$489$	11.1675	+	3.62855i	0.505013	+	0.164089i
$490$	−0.261242	+	0.804020i	−0.0118017	+	0.0363219i
$491$	−19.5713	−	26.9376i	−0.883242	−	1.21568i	−0.975512	−	0.219945i	$-0.929412\pi$
$491$	−19.5713	−	26.9376i	−0.883242	−	1.21568i	0.0922702	−	0.995734i	$-0.470588\pi$
$492$	1.12662	−	1.55066i	0.0507921	−	0.0699094i
$493$	−8.11912	+	2.63806i	−0.365667	+	0.118812i
$494$	1.50451	+	1.80828i	0.0676909	+	0.0813584i
$495$	0.380130	−	0.291307i	0.0170856	−	0.0130933i
$496$			27.4834i			1.23404i
$497$	21.1452	+	65.0782i	0.948492	+	2.91916i
$498$	5.00832	+	3.63876i	0.224428	+	0.163057i
$499$	14.8577	−	10.7947i	0.665120	−	0.483238i	−0.203268	−	0.979123i	$-0.565156\pi$
$499$	14.8577	−	10.7947i	0.665120	−	0.483238i	0.868388	+	0.495885i	$0.165156\pi$
$500$	−0.806726	+	2.48285i	−0.0360779	+	0.111036i
$501$	6.17111	+	2.00511i	0.275705	+	0.0895819i
$502$	1.93668	−	1.40708i	0.0864382	−	0.0628010i
$503$	−13.6986	+	18.8545i	−0.610791	+	0.840682i	−0.996642	−	0.0818789i	$-0.973908\pi$
$503$	−13.6986	+	18.8545i	−0.610791	+	0.840682i	0.385851	+	0.922561i	$0.373908\pi$
$504$	−7.12087	+	2.31371i	−0.317189	+	0.103061i
$505$		−	1.59418i		−	0.0709401i
$506$	1.74538	+	1.20117i	0.0775917	+	0.0533987i
$507$		−	11.4533i		−	0.508657i
$508$	9.40600	+	28.9487i	0.417324	+	1.28439i
$509$	17.8037	−	24.5047i	0.789136	−	1.08615i	−0.205079	−	0.978745i	$-0.565745\pi$
$509$	17.8037	−	24.5047i	0.789136	−	1.08615i	0.994215	−	0.107407i	$-0.0342547\pi$
$510$	−0.0479386	+	0.0348295i	−0.00212276	+	0.00154227i
$511$	0.695050	−	2.13914i	0.0307472	−	0.0946302i
$512$	−7.07272	+	21.7676i	−0.312573	+	0.962000i
$513$	1.07216	−	4.22498i	0.0473372	−	0.186537i
$514$	−3.80787	+	5.24109i	−0.167958	+	0.231174i
$515$	−1.92461	+	0.625344i	−0.0848085	+	0.0275560i
$516$	−7.97466			−0.351065
$517$	−21.0103	+	0.537049i	−0.924033	+	0.0236194i
$518$	−17.7895			−0.781625
$519$	−1.76782	+	0.574401i	−0.0775988	+	0.0252134i
$520$	0.240303	+	0.174590i	0.0105380	+	0.00765628i
$521$	−21.4066	−	29.4637i	−0.937842	−	1.29083i	−0.956721	−	0.291006i	$-0.906010\pi$
$521$	−21.4066	−	29.4637i	−0.937842	−	1.29083i	0.0188795	−	0.999822i	$-0.493990\pi$
$522$	−1.21043	+	3.72531i	−0.0529789	+	0.163052i
$523$	2.79000	−	8.58675i	0.121998	−	0.375472i	−0.871344	−	0.490673i	$-0.836751\pi$
$523$	2.79000	−	8.58675i	0.121998	−	0.375472i	0.993342	+	0.115200i	$0.0367510\pi$
$524$	9.15010	+	12.5940i	0.399724	+	0.550173i
$525$	18.2351	+	13.2486i	0.795847	+	0.578217i
$526$	4.25376	−	1.38213i	0.185473	−	0.0602637i
$527$	8.94484			0.389644
$528$	−9.23864	−	2.74288i	−0.402060	−	0.119369i
$529$	−20.8325			−0.905762
$530$	−0.561726	+	0.182516i	−0.0243998	+	0.00792798i
$531$	−0.705083	+	0.970463i	−0.0305980	+	0.0421145i
$532$	−8.79320	+	34.6506i	−0.381234	+	1.50229i
$533$	−0.406596	+	1.25137i	−0.0176116	+	0.0542030i
$534$	1.52274	−	4.68652i	0.0658955	−	0.202806i
$535$	1.51648	−	1.10179i	0.0655633	−	0.0476345i
$536$	−10.8771	+	14.9710i	−0.469817	+	0.646648i
$537$	2.10905	+	6.49098i	0.0910122	+	0.280107i
$538$			10.5047i			0.452888i
$539$	14.9113	+	42.1918i	0.642273	+	1.81733i
$540$		−	0.261608i		−	0.0112578i
$541$	−20.5122	+	6.66481i	−0.881887	+	0.286542i	−0.714741	−	0.699390i	$-0.753455\pi$
$541$	−20.5122	+	6.66481i	−0.881887	+	0.286542i	−0.167146	+	0.985932i	$0.553455\pi$
$542$	−1.88232	+	2.59079i	−0.0808526	+	0.111284i
$543$	3.39308	−	2.46522i	0.145611	−	0.105793i
$544$	4.10929	+	1.33519i	0.176184	+	0.0572458i
$545$	−0.506175	+	1.55785i	−0.0216822	+	0.0667308i
$546$	1.97640	−	1.43594i	0.0845819	−	0.0614523i
$547$	5.97315	+	4.33975i	0.255394	+	0.185554i	0.708114	−	0.706098i	$-0.249546\pi$
$547$	5.97315	+	4.33975i	0.255394	+	0.185554i	−0.452720	+	0.891653i	$0.649546\pi$
$548$	−8.84461	−	27.2209i	−0.377823	−	1.16282i
$549$		−	0.366903i		−	0.0156590i
$550$	−2.38776	−	6.75623i	−0.101814	−	0.288087i
$551$	25.1663	+	30.2477i	1.07212	+	1.28859i
$552$	2.31587	−	0.752471i	0.0985698	−	0.0320273i
$553$	−12.6708	+	17.4399i	−0.538818	+	0.741619i
$554$	2.11573	+	2.91205i	0.0898887	+	0.123721i
$555$	0.404110	−	1.24372i	0.0171535	−	0.0527931i
$556$	5.82542	+	1.89279i	0.247053	+	0.0802723i
$557$	16.0039	+	22.0275i	0.678106	+	0.933333i	0.999909	−	0.0134734i	$-0.00428886\pi$
$557$	16.0039	+	22.0275i	0.678106	+	0.933333i	−0.321803	+	0.946807i	$0.604289\pi$
$558$	2.41238	−	3.32035i	0.102124	−	0.140562i
$559$	5.20641	−	1.69166i	0.220208	−	0.0715498i
$560$			1.89938i			0.0802635i
$561$	−0.892708	+	3.00684i	−0.0376901	+	0.126949i
$562$	−6.24141			−0.263278
$563$	11.8858	+	36.5808i	0.500928	+	1.54170i	0.807510	+	0.589853i	$0.200815\pi$
$563$	11.8858	+	36.5808i	0.500928	+	1.54170i	−0.306582	+	0.951844i	$0.599185\pi$
$564$	−6.74817	+	9.28806i	−0.284149	+	0.391098i
$565$	−1.32259	−	1.82039i	−0.0556419	−	0.0765846i
$566$	−8.46452	−	2.75029i	−0.355790	−	0.115603i
$567$	−4.30529	−	1.39887i	−0.180805	−	0.0587472i
$568$	−14.6954	−	20.2265i	−0.616606	−	0.848686i
$569$	−7.22244	−	5.24741i	−0.302780	−	0.219983i	0.426012	−	0.904717i	$-0.359918\pi$
$569$	−7.22244	−	5.24741i	−0.302780	−	0.219983i	−0.728793	+	0.684735i	$0.759918\pi$
$570$	0.231010	+	0.145696i	0.00967593	+	0.00610252i
$571$			14.6247i			0.612023i	0.952028	+	0.306011i	$0.0989946\pi$
$571$			14.6247i			0.612023i	−0.952028	+	0.306011i	$0.901005\pi$
$572$	7.47056	−	0.190957i	0.312360	−	0.00798430i
$573$			20.3326i			0.849405i
$574$	1.97644	−	0.642185i	0.0824951	−	0.0268043i
$575$	−5.93047	−	4.30874i	−0.247318	−	0.179687i
$576$	−3.09769	+	2.25060i	−0.129070	+	0.0937751i
$577$	−3.83967	+	11.8173i	−0.159848	+	0.491961i	−0.998620	−	0.0525221i	$-0.983274\pi$
$577$	−3.83967	+	11.8173i	−0.159848	+	0.491961i	0.838772	+	0.544483i	$0.183274\pi$
$578$	−2.15959	+	6.64652i	−0.0898270	+	0.276459i
$579$	−1.44515	−	1.98908i	−0.0600586	−	0.0826635i
$580$	1.91053	+	1.38808i	0.0793304	+	0.0576369i
$581$	−19.9573	−	61.4224i	−0.827970	−	2.54823i
$582$	−1.12010			−0.0464296
$583$	−17.7242	+	25.7543i	−0.734059	+	1.06664i
$584$			0.821803i			0.0340065i
$585$	0.0554948	+	0.170796i	0.00229443	+	0.00706153i
$586$	5.12887	+	3.72634i	0.211872	+	0.153934i
$587$	−0.994023	+	0.722200i	−0.0410277	+	0.0298084i	−0.608110	−	0.793853i	$-0.708072\pi$
$587$	−0.994023	+	0.722200i	−0.0410277	+	0.0298084i	0.567082	+	0.823661i	$0.308072\pi$
$588$	23.2480	+	7.55372i	0.958729	+	0.311510i
$589$	−15.2845	−	38.2901i	−0.629789	−	1.57772i
$590$	−0.0441785	−	0.0608066i	−0.00181880	−	0.00250337i
$591$	19.8205	+	14.4004i	0.815306	+	0.592354i
$592$	−25.0275	+	8.13193i	−1.02862	+	0.334220i
$593$		−	18.2521i		−	0.749523i	−0.927121	−	0.374762i	$-0.877725\pi$
$593$		−	18.2521i		−	0.749523i	0.927121	−	0.374762i	$-0.122275\pi$
$594$	0.875387	+	1.14230i	0.0359176	+	0.0468693i
$595$	0.618179			0.0253429
$596$	−0.899595	+	0.292296i	−0.0368488	+	0.0119729i
$597$	−3.92842	+	5.40701i	−0.160780	+	0.221294i
$598$	−0.642768	+	0.466998i	−0.0262847	+	0.0190970i
$599$	36.2014	+	11.7625i	1.47915	+	0.480605i	0.933859	−	0.357642i	$-0.116419\pi$
$599$	36.2014	+	11.7625i	1.47915	+	0.480605i	0.545291	+	0.838247i	$0.316419\pi$
$600$	−7.83235	−	2.54488i	−0.319754	−	0.103894i
$601$	−25.4576	+	18.4960i	−1.03844	+	0.754469i	−0.969980	−	0.243185i	$-0.921808\pi$
$601$	−25.4576	+	18.4960i	−1.03844	+	0.754469i	−0.0684577	+	0.997654i	$0.521808\pi$
$602$	−6.99499	−	5.08216i	−0.285094	−	0.207133i
$603$	−10.6407	+	3.45736i	−0.433321	+	0.140795i
$604$	6.05893			0.246534
$605$	1.33104	+	0.866755i	0.0541146	+	0.0352386i
$606$	4.79057			0.194604
$607$	−7.43379	−	22.8788i	−0.301728	−	0.928624i	−0.980878	−	0.194624i	$-0.937651\pi$
$607$	−7.43379	−	22.8788i	−0.301728	−	0.928624i	0.679150	−	0.734000i	$-0.262349\pi$
$608$	−1.30624	−	19.8721i	−0.0529748	−	0.805921i
$609$	33.0598	−	24.0193i	1.33965	−	0.973312i
$610$	0.0218640	+	0.00710404i	0.000885246	+	0.000287634i
$611$	2.43540	−	7.49539i	0.0985257	−	0.303231i
$612$	1.00708	+	1.38613i	0.0407089	+	0.0560310i
$613$	1.57645	−	2.16980i	0.0636723	−	0.0876374i	−0.775993	−	0.630741i	$-0.782751\pi$
$613$	1.57645	−	2.16980i	0.0636723	−	0.0876374i	0.839666	+	0.543104i	$0.182751\pi$
$614$	−3.67719	−	11.3172i	−0.148399	−	0.456726i
$615$			0.152768i			0.00616019i
$616$	−15.1049	−	19.7105i	−0.608592	−	0.794159i
$617$	15.9146			0.640698			0.320349	−	0.947300i	$-0.396200\pi$
$617$	15.9146			0.640698			0.320349	+	0.947300i	$0.396200\pi$
$618$	−1.87918	−	5.78353i	−0.0755918	−	0.232648i
$619$	1.73661	+	1.26172i	0.0698001	+	0.0507127i	0.622138	−	0.782908i	$-0.286264\pi$
$619$	1.73661	+	1.26172i	0.0698001	+	0.0507127i	−0.552338	+	0.833620i	$0.686264\pi$
$620$	−1.45440	−	2.00181i	−0.0584102	−	0.0803948i
$621$	1.40018	+	0.454945i	0.0561872	+	0.0182563i
$622$	−2.51039	+	7.72619i	−0.100658	+	0.309792i
$623$	−41.5899	+	30.2168i	−1.66626	+	1.21061i
$624$	2.12414	−	2.92363i	0.0850337	−	0.117039i
$625$	7.62891	+	23.4794i	0.305156	+	0.939175i
$626$	5.59901			0.223781
$627$	14.3968	−	1.31654i	0.574951	−	0.0525775i
$628$	−27.0123			−1.07791
$629$	2.64664	+	8.14553i	0.105529	+	0.324784i
$630$	0.166719	−	0.229470i	0.00664226	−	0.00914229i
$631$	−5.72355	+	4.15840i	−0.227851	+	0.165543i	−0.695854	−	0.718184i	$-0.744974\pi$
$631$	−5.72355	+	4.15840i	−0.227851	+	0.165543i	0.468003	+	0.883727i	$0.344974\pi$
$632$	2.43390	−	7.49076i	0.0968152	−	0.297967i
$633$	1.28250	+	0.416710i	0.0509749	+	0.0165627i
$634$	−2.03689	−	2.80353i	−0.0808951	−	0.111343i
$635$	−1.96269	−	1.42598i	−0.0778870	−	0.0565882i
$636$	5.27738	+	16.2421i	0.209262	+	0.644042i
$637$	−16.7803			−0.664858
$638$	−12.9871	+	0.331965i	−0.514162	+	0.0131426i
$639$		−	15.1159i		−	0.597974i
$640$	−0.481871	−	1.48305i	−0.0190476	−	0.0586225i
$641$	−7.33080	+	10.0900i	−0.289549	+	0.398530i	−0.928868	−	0.370412i	$-0.879217\pi$
$641$	−7.33080	+	10.0900i	−0.289549	+	0.398530i	0.639318	+	0.768942i	$0.279217\pi$
$642$	3.31091	+	4.55708i	0.130671	+	0.179854i
$643$	1.82955	−	5.63079i	0.0721506	−	0.222057i	−0.908478	−	0.417932i	$-0.862755\pi$
$643$	1.82955	−	5.63079i	0.0721506	−	0.222057i	0.980629	+	0.195876i	$0.0627549\pi$
$644$	−11.4834	−	3.73117i	−0.452507	−	0.147029i
$645$	0.514211	−	0.373596i	0.0202470	−	0.0147103i
$646$	−1.78487	+	0.117323i	−0.0702250	+	0.00461603i
$647$	−6.27373	−	19.3086i	−0.246646	−	0.759098i	−0.995361	−	0.0962063i	$-0.969329\pi$
$647$	−6.27373	−	19.3086i	−0.246646	−	0.759098i	0.748716	−	0.662891i	$-0.230671\pi$
$648$	1.65398			0.0649745
$649$	−3.81394	−	1.13233i	−0.149710	−	0.0444479i
$650$	2.68704			0.105395
$651$	−40.7210	+	13.2311i	−1.59598	+	0.518566i
$652$	17.2107	+	12.5043i	0.674021	+	0.489705i
$653$	13.9451	−	10.1317i	0.545715	−	0.396485i	−0.280488	−	0.959857i	$-0.590496\pi$
$653$	13.9451	−	10.1317i	0.545715	−	0.396485i	0.826203	+	0.563372i	$0.190496\pi$
$654$	−4.68138	−	1.52107i	−0.183057	−	0.0594787i
$655$	−1.18001	−	0.383408i	−0.0461067	−	0.0149810i
$656$	2.48705	−	1.80694i	0.0971028	−	0.0705493i
$657$	−0.292049	+	0.401971i	−0.0113939	+	0.0156824i
$658$	−11.8384	+	3.84651i	−0.461507	+	0.149953i
$659$	4.43838			0.172895			0.0864474	−	0.996256i	$-0.472449\pi$
$659$	4.43838			0.172895			0.0864474	+	0.996256i	$0.472449\pi$
$660$	0.818067	−	0.289118i	0.0318432	−	0.0112539i
$661$			0.0498566i			0.00193920i	1.00000		0.000969599i	$0.000308633\pi$
$661$			0.0498566i			0.00193920i	−1.00000		0.000969599i	$0.999691\pi$
$662$	−2.80127	+	0.910188i	−0.108874	+	0.0353754i
$663$	−0.951533	−	0.691329i	−0.0369545	−	0.0268490i
$664$	13.8699	+	19.0903i	0.538257	+	0.740847i
$665$	−1.05632	−	2.64623i	−0.0409622	−	0.102617i
$666$	3.73743	+	1.21436i	0.144822	+	0.0470557i
$667$	−10.7518	+	7.81162i	−0.416310	+	0.302467i
$668$	9.51051	+	6.90979i	0.367973	+	0.267348i
$669$	1.42788	+	4.39457i	0.0552051	+	0.169904i
$670$		−	0.701025i		−	0.0270830i
$671$	1.14734	−	0.405487i	0.0442924	−	0.0156536i
$672$	−20.6824			−0.797840
$673$	−12.3156	−	37.9035i	−0.474731	−	1.46107i	−0.846321	−	0.532674i	$-0.821187\pi$
$673$	−12.3156	−	37.9035i	−0.474731	−	1.46107i	0.371590	−	0.928397i	$-0.378813\pi$
$674$	1.06467	+	0.773526i	0.0410094	+	0.0297951i
$675$	−2.92667	−	4.02822i	−0.112648	−	0.155046i
$676$	6.41211	−	19.7344i	0.246619	−	0.759017i
$677$	−1.24360	+	3.82741i	−0.0477954	+	0.147099i	−0.972106	−	0.234542i	$-0.924641\pi$
$677$	−1.24360	+	3.82741i	−0.0477954	+	0.147099i	0.924311	+	0.381641i	$0.124641\pi$
$678$	5.47035	−	3.97444i	0.210087	−	0.152637i
$679$	9.45365	+	6.86848i	0.362798	+	0.263588i
$680$	−0.214810	+	0.0697960i	−0.00823759	+	0.00267655i
$681$		−	11.5894i		−	0.444107i
$682$	13.0491	+	3.87417i	0.499674	+	0.148350i
$683$		−	21.3964i		−	0.818710i	−0.912375	−	0.409355i	$-0.865754\pi$
$683$		−	21.3964i		−	0.818710i	0.912375	−	0.409355i	$-0.134246\pi$
$684$	4.21274	−	6.67957i	0.161078	−	0.255400i
$685$	1.84555	+	1.34087i	0.0705148	+	0.0512320i
$686$	7.49601	+	10.3174i	0.286199	+	0.393919i
$687$	−18.5856	−	6.03883i	−0.709086	−	0.230396i
$688$	−12.1642	−	3.95239i	−0.463756	−	0.150684i
$689$	−6.89089	−	9.48449i	−0.262522	−	0.361330i
$690$	−0.0542209	+	0.0746286i	−0.00206415	+	0.00284106i
$691$	−3.27636	−	10.0836i	−0.124638	−	0.383598i	0.869197	−	0.494467i	$-0.164637\pi$
$691$	−3.27636	−	10.0836i	−0.124638	−	0.383598i	−0.993835	+	0.110869i	$0.964637\pi$
$692$	−3.36761			−0.128017
$693$	−0.383648	−	15.0090i	−0.0145736	−	0.570144i
$694$			2.47604i			0.0939890i
$695$	−0.464300	+	0.150860i	−0.0176119	+	0.00572245i
$696$	−8.77597	+	12.0791i	−0.332652	+	0.457856i
$697$	−0.588094	−	0.809441i	−0.0222756	−	0.0306598i
$698$	−8.16615	−	2.65334i	−0.309093	−	0.100430i
$699$	8.68975	−	26.7443i	0.328676	−	1.01156i
$700$	24.0027	+	33.0368i	0.907216	+	1.24868i
$701$	−4.69460	+	6.46157i	−0.177313	+	0.244050i	−0.888418	−	0.459036i	$-0.848195\pi$
$701$	−4.69460	+	6.46157i	−0.177313	+	0.244050i	0.711105	+	0.703086i	$0.248195\pi$
$702$	−0.513247	+	0.166764i	−0.0193712	+	0.00629410i
$703$	30.3461	−	25.2482i	1.14452	−	0.952254i
$704$	−10.4613	−	7.19944i	−0.394273	−	0.271339i
$705$		−	0.915038i		−	0.0344623i
$706$	2.11523	+	6.51002i	0.0796078	+	0.245008i
$707$	−40.4325	−	29.3760i	−1.52062	−	1.10480i
$708$	−1.75820	+	1.27741i	−0.0660772	+	0.0480079i
$709$	4.50298	−	13.8587i	0.169113	−	0.520476i	−0.830203	−	0.557461i	$-0.811776\pi$
$709$	4.50298	−	13.8587i	0.169113	−	0.520476i	0.999316	+	0.0369855i	$0.0117755\pi$
$710$	0.900763	+	0.292676i	0.0338050	+	0.0109839i
$711$	3.85254	−	2.79903i	0.144481	−	0.104972i
$712$	11.0404	−	15.1957i	0.413755	−	0.569485i
$713$	13.2434	−	4.30304i	0.495969	−	0.161150i
$714$			1.85765i			0.0695208i
$715$	−0.472760	+	0.362293i	−0.0176802	+	0.0135490i
$716$			12.3650i			0.462101i
$717$	−4.04661	−	12.4542i	−0.151123	−	0.465110i
$718$	6.95968	−	9.57918i	0.259733	−	0.357492i
$719$	−30.2572	+	21.9831i	−1.12840	+	0.819833i	−0.985462	−	0.169898i	$-0.945656\pi$
$719$	−30.2572	+	21.9831i	−1.12840	+	0.819833i	−0.142941	+	0.989731i	$0.545656\pi$
$720$	0.129658	−	0.399045i	0.00483206	−	0.0148715i
$721$	−19.6045	+	60.3363i	−0.730108	+	2.24704i
$722$	3.55214	+	7.44002i	0.132197	+	0.276889i
$723$	9.00638	−	12.3962i	0.334951	−	0.461020i
$724$	7.22658	−	2.34806i	0.268574	−	0.0872648i
$725$	44.9470			1.66929
$726$	−2.60463	+	3.99983i	−0.0966668	+	0.148448i
$727$	38.2520			1.41869			0.709344	−	0.704862i	$-0.248991\pi$
$727$	38.2520			1.41869			0.709344	+	0.704862i	$0.248991\pi$
$728$	8.85610	−	2.87752i	0.328229	−	0.106648i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−0.0182990	−	0.0251864i	−0.000677276	−	0.000932191i
$731$	−1.28636	+	3.95900i	−0.0475777	+	0.146429i
$732$	0.205411	−	0.632189i	0.00759220	−	0.0233664i
$733$	12.9796	+	17.8648i	0.479411	+	0.659853i	0.978392	−	0.206760i	$-0.0662920\pi$
$733$	12.9796	+	17.8648i	0.479411	+	0.659853i	−0.498980	+	0.866613i	$0.666292\pi$
$734$	1.27396	+	0.925583i	0.0470226	+	0.0341639i
$735$	−1.85292	+	0.602050i	−0.0683459	+	0.0222069i
$736$	6.72637			0.247937
$737$	−22.5711	−	29.4533i	−0.831416	−	1.08492i
$738$	−0.459073			−0.0168987
$739$	−8.70206	+	2.82747i	−0.320110	+	0.104010i	−0.464665	−	0.885487i	$-0.653825\pi$
$739$	−8.70206	+	2.82747i	−0.320110	+	0.104010i	0.144554	+	0.989497i	$0.453825\pi$
$740$	1.39260	−	1.91674i	0.0511929	−	0.0704609i
$741$	−1.33343	+	5.25453i	−0.0489848	+	0.193030i
$742$	−5.72184	+	17.6100i	−0.210056	+	0.646484i
$743$	4.85514	−	14.9426i	0.178118	−	0.548190i	−0.821644	−	0.570001i	$-0.806943\pi$
$743$	4.85514	−	14.9426i	0.178118	−	0.548190i	0.999762	+	0.0218103i	$0.00694299\pi$
$744$	12.6562	−	9.19528i	0.464000	−	0.337115i
$745$	0.0443129	−	0.0609915i	0.00162350	−	0.00223456i
$746$	0.524373	+	1.61385i	0.0191986	+	0.0590874i
$747$			14.2667i			0.521992i
$748$	−3.22155	+	4.68112i	−0.117792	+	0.171159i
$749$		−	58.7645i		−	2.14721i
$750$	0.594663	−	0.193218i	0.0217140	−	0.00705532i
$751$	−13.7801	+	18.9667i	−0.502843	+	0.692103i	−0.982692	−	0.185248i	$-0.940691\pi$
$751$	−13.7801	+	18.9667i	−0.502843	+	0.692103i	0.479849	+	0.877351i	$0.340691\pi$
$752$	−14.8967	+	10.8231i	−0.543228	+	0.394678i
$753$	5.24682	+	1.70479i	0.191205	+	0.0621262i
$754$	1.50539	−	4.63310i	0.0548229	−	0.168728i
$755$	−0.390683	+	0.283848i	−0.0142184	+	0.0103303i
$756$	−6.63504	−	4.82064i	−0.241314	−	0.175325i
$757$	12.3229	+	37.9260i	0.447883	+	1.37844i	0.879290	+	0.476286i	$0.158017\pi$
$757$	12.3229	+	37.9260i	0.447883	+	1.37844i	−0.431407	+	0.902157i	$0.641983\pi$
$758$		−	10.5944i		−	0.384806i
$759$	0.124771	+	4.88125i	0.00452889	+	0.177178i
$760$	0.665833	+	0.800272i	0.0241523	+	0.0290289i
$761$	46.7612	−	15.1936i	1.69509	−	0.550769i	0.707351	−	0.706862i	$-0.249890\pi$
$761$	46.7612	−	15.1936i	1.69509	−	0.550769i	0.987742	+	0.156093i	$0.0498899\pi$
$762$	4.28511	−	5.89795i	0.155233	−	0.213660i
$763$	30.1837	+	41.5443i	1.09272	+	1.50400i
$764$	−11.3832	+	35.0339i	−0.411829	+	1.26748i
$765$	−0.129875	−	0.0421988i	−0.00469562	−	0.00152570i
$766$	−7.25499	−	9.98564i	−0.262134	−	0.360796i
$767$	0.876899	−	1.20695i	0.0316630	−	0.0435804i
$768$	−2.82650	+	0.918385i	−0.101992	+	0.0331394i
$769$			48.3347i			1.74300i	0.490399	+	0.871498i	$0.336851\pi$
$769$			48.3347i			1.74300i	−0.490399	+	0.871498i	$0.663149\pi$
$770$	0.901821	+	0.267744i	0.0324994	+	0.00964883i
$771$	−14.9298			−0.537683
$772$	−1.37647	−	4.23634i	−0.0495403	−	0.152469i
$773$	−5.10943	+	7.03253i	−0.183773	+	0.252943i	−0.890957	−	0.454087i	$-0.849965\pi$
$773$	−5.10943	+	7.03253i	−0.183773	+	0.252943i	0.707184	+	0.707030i	$0.249965\pi$
$774$	1.12267	+	1.54522i	0.0403535	+	0.0555418i
$775$	−44.7896	−	14.5530i	−1.60889	−	0.522760i
$776$	−4.06053	−	1.31935i	−0.145764	−	0.0473618i
$777$	−24.0975	−	33.1673i	−0.864492	−	1.18987i
$778$	−8.21982	−	5.97205i	−0.294695	−	0.214108i
$779$	−2.46006	+	3.90059i	−0.0881409	+	0.139753i
$780$			0.325357i			0.0116496i
$781$	47.2685	−	16.7054i	1.69140	−	0.597768i
$782$		−	0.604149i		−	0.0216043i
$783$	−8.58523	+	2.78951i	−0.306811	+	0.0996890i
$784$	31.7177	+	23.0443i	1.13278	+	0.823009i
$785$	1.74177	−	1.26547i	0.0621665	−	0.0451666i
$786$	1.15215	−	3.54596i	0.0410960	−	0.126480i
$787$	−7.28594	+	22.4238i	−0.259716	+	0.799322i	0.733148	+	0.680069i	$0.238050\pi$
$787$	−7.28594	+	22.4238i	−0.259716	+	0.799322i	−0.992864	+	0.119253i	$0.961950\pi$
$788$	26.0894	+	35.9090i	0.929397	+	1.27921i
$789$	8.33900	+	6.05864i	0.296876	+	0.215693i
$790$	0.0922025	+	0.283770i	0.00328042	+	0.0100961i
$791$	−70.5413			−2.50816
$792$	1.82791	+	5.17213i	0.0649521	+	0.183784i
$793$			0.456311i			0.0162041i
$794$	−2.19227	−	6.74712i	−0.0778009	−	0.239446i
$795$	−1.10120	−	0.800067i	−0.0390555	−	0.0283755i
$796$	−9.79594	+	7.11717i	−0.347208	+	0.252261i
$797$	23.7574	+	7.71923i	0.841529	+	0.273429i	0.697894	−	0.716201i	$-0.254121\pi$
$797$	23.7574	+	7.71923i	0.841529	+	0.273429i	0.143635	+	0.989631i	$0.454121\pi$
$798$	7.95202	−	3.17427i	0.281499	−	0.112368i
$799$	3.52252	+	4.84834i	0.124618	+	0.171522i
$800$	−18.4042	−	13.3714i	−0.650686	−	0.472751i
$801$	10.8004	−	3.50927i	0.381614	−	0.123994i
$802$			5.41531i			0.191221i
$803$	−1.57976	−	0.469018i	−0.0557484	−	0.0165513i
$804$	−20.2699			−0.714864
$805$	0.915251	−	0.297383i	0.0322584	−	0.0104814i
$806$	−3.00023	+	4.12946i	−0.105679	+	0.145454i
$807$	−19.5853	+	14.2295i	−0.689433	+	0.500903i
$808$	17.3666	+	5.64274i	0.610953	+	0.198511i
$809$	11.8068	+	3.83627i	0.415106	+	0.134876i	0.509122	−	0.860695i	$-0.329970\pi$
$809$	11.8068	+	3.83627i	0.415106	+	0.134876i	−0.0940154	+	0.995571i	$0.529970\pi$
$810$	−0.0506908	+	0.0368290i	−0.00178109	+	0.00129404i
$811$	31.8347	+	23.1293i	1.11787	+	0.812180i	0.983885	−	0.178804i	$-0.0572228\pi$
$811$	31.8347	+	23.1293i	1.11787	+	0.812180i	0.133985	+	0.990983i	$0.457223\pi$
$812$	70.4106	−	22.8778i	2.47093	−	0.802853i
$813$	−7.38014			−0.258833
$814$	0.333045	+	13.0293i	0.0116732	+	0.456677i
$815$	−1.69555			−0.0593926
$816$	0.849169	+	2.61347i	0.0297269	+	0.0914899i
$817$	19.1453	−	1.25846i	0.669811	−	0.0440280i
$818$	−11.7479	+	8.53534i	−0.410755	+	0.298431i
$819$	5.35442	+	1.73976i	0.187098	+	0.0607920i
$820$	−0.0855271	+	0.263225i	−0.00298673	+	0.00919222i
$821$	6.14826	+	8.46235i	0.214576	+	0.295338i	0.902714	−	0.430242i	$-0.141572\pi$
$821$	6.14826	+	8.46235i	0.214576	+	0.295338i	−0.688138	+	0.725580i	$0.741572\pi$
$822$	−4.02936	+	5.54593i	−0.140540	+	0.193437i
$823$	−11.3248	−	34.8540i	−0.394757	−	1.21494i	−0.929151	−	0.369701i	$-0.879460\pi$
$823$	−11.3248	−	34.8540i	−0.394757	−	1.21494i	0.534394	−	0.845235i	$-0.320540\pi$
$824$		−	23.1796i		−	0.807501i
$825$	9.36211	−	13.6038i	0.325947	−	0.473622i
$826$	−2.35629			−0.0819857
$827$	−14.0239	−	43.1612i	−0.487660	−	1.50086i	−0.828092	−	0.560593i	$-0.810573\pi$
$827$	−14.0239	−	43.1612i	−0.487660	−	1.50086i	0.340432	−	0.940269i	$-0.389427\pi$
$828$	2.15786	+	1.56778i	0.0749909	+	0.0544841i
$829$	−23.8742	−	32.8600i	−0.829184	−	1.14127i	−0.988074	−	0.153978i	$-0.950792\pi$
$829$	−23.8742	−	32.8600i	−0.829184	−	1.14127i	0.158890	−	0.987296i	$-0.449208\pi$
$830$	−0.850162	−	0.276234i	−0.0295096	−	0.00958823i
$831$	−2.56338	+	7.88927i	−0.0889227	+	0.273676i
$832$	3.85254	−	2.79903i	0.133563	−	0.0970390i
$833$	7.50006	−	10.3229i	0.259862	−	0.357669i
$834$	−0.453340	−	1.39524i	−0.0156979	−	0.0483131i
$835$	−0.936952			−0.0324246
$836$	25.5433	+	5.79158i	0.883433	+	0.200306i
$837$	9.45836			0.326929
$838$	−3.88729	−	11.9638i	−0.134284	−	0.413284i
$839$	18.4432	−	25.3849i	0.636731	−	0.876385i	−0.361705	−	0.932292i	$-0.617805\pi$
$839$	18.4432	−	25.3849i	0.636731	−	0.876385i	0.998436	+	0.0559079i	$0.0178053\pi$
$840$	0.874672	−	0.635487i	0.0301791	−	0.0219264i
$841$	16.2196	−	49.9187i	0.559295	−	1.72133i
$842$	−6.00431	−	1.95092i	−0.206922	−	0.0672331i
$843$	−8.45456	−	11.6367i	−0.291191	−	0.400789i
$844$	1.97651	+	1.43602i	0.0680343	+	0.0494298i
$845$	0.511060	+	1.57288i	0.0175810	+	0.0541088i
$846$	2.74972			0.0945373
$847$	46.5102	−	17.7870i	1.59811	−	0.611169i
$848$			27.3906i			0.940598i
$849$	−6.33823	−	19.5071i	−0.217527	−	0.669481i
$850$	−1.20099	+	1.65303i	−0.0411938	+	0.0566984i
$851$	7.83703	+	10.7868i	0.268650	+	0.369765i
$852$	8.46262	−	26.0453i	0.289924	−	0.892296i
$853$	22.4180	+	7.28407i	0.767579	+	0.249402i	0.666528	−	0.745480i	$-0.267779\pi$
$853$	22.4180	+	7.28407i	0.767579	+	0.249402i	0.101051	+	0.994881i	$0.467779\pi$
$854$	0.583064	−	0.423620i	0.0199520	−	0.0144960i
$855$	0.0412837	+	0.628060i	0.00141187	+	0.0214792i
$856$	6.63486	+	20.4200i	0.226775	+	0.697941i
$857$	39.9283			1.36393			0.681963	−	0.731387i	$-0.261126\pi$
$857$	39.9283			1.36393			0.681963	+	0.731387i	$0.261126\pi$
$858$	−1.08870	−	1.42066i	−0.0371677	−	0.0485006i
$859$	13.8210			0.471567			0.235784	−	0.971806i	$-0.424234\pi$
$859$	13.8210			0.471567			0.235784	+	0.971806i	$0.424234\pi$
$860$	1.09516	−	0.355840i	0.0373448	−	0.0121341i
$861$	3.87458	+	2.81505i	0.132045	+	0.0959366i
$862$	3.78933	−	2.75311i	0.129065	−	0.0937712i
$863$	−9.37987	−	3.04770i	−0.319294	−	0.103745i	0.144985	−	0.989434i	$-0.453687\pi$
$863$	−9.37987	−	3.04770i	−0.319294	−	0.103745i	−0.464279	+	0.885689i	$0.653687\pi$
$864$	4.34520	+	1.41184i	0.147827	+	0.0480319i
$865$	0.217146	−	0.157765i	0.00738317	−	0.00536419i
$866$	−9.41667	+	12.9609i	−0.319991	+	0.440430i
$867$	−15.3174	+	4.97692i	−0.520205	+	0.169025i
$868$	−77.5714			−2.63295
$869$	13.0105	+	8.95381i	0.441350	+	0.303737i
$870$		−	0.565610i		−	0.0191760i
$871$	13.2336	−	4.29986i	0.448404	−	0.145695i
$872$	−15.1791	−	11.0283i	−0.514029	−	0.373464i
$873$	−1.51728	−	2.08835i	−0.0513520	−	0.0706800i
$874$	−2.58617	+	1.03234i	−0.0874787	+	0.0349195i
$875$	−6.20379	−	2.01573i	−0.209726	−	0.0681442i
$876$	−0.728257	+	0.529109i	−0.0246055	+	0.0178769i
$877$	−10.1023	−	7.33975i	−0.341131	−	0.247846i	0.404008	−	0.914755i	$-0.367617\pi$
$877$	−10.1023	−	7.33975i	−0.341131	−	0.247846i	−0.745139	+	0.666910i	$0.767617\pi$
$878$	0.748315	+	2.30308i	0.0252544	+	0.0777251i
$879$			14.6101i			0.492787i
$880$	1.39114	−	0.0355592i	0.0468953	−	0.00119870i
$881$	0.616164			0.0207591			0.0103795	−	0.999946i	$-0.496696\pi$
$881$	0.616164			0.0207591			0.0103795	+	0.999946i	$0.496696\pi$
$882$	−1.80918	−	5.56808i	−0.0609183	−	0.187487i
$883$	−9.31845	−	6.77025i	−0.313591	−	0.227837i	0.419845	−	0.907596i	$-0.362084\pi$
$883$	−9.31845	−	6.77025i	−0.313591	−	0.227837i	−0.733436	+	0.679759i	$0.762084\pi$
$884$	−1.25249	−	1.72390i	−0.0421258	−	0.0579812i
$885$	0.0535260	−	0.164736i	0.00179926	−	0.00553754i
$886$	−0.993564	+	3.05788i	−0.0333794	+	0.102731i
$887$	−8.61609	+	6.25996i	−0.289300	+	0.210189i	−0.722964	−	0.690886i	$-0.757221\pi$
$887$	−8.61609	+	6.25996i	−0.289300	+	0.210189i	0.433664	+	0.901075i	$0.357221\pi$
$888$	12.1184	+	8.80452i	0.406666	+	0.295460i
$889$	−72.3329	+	23.5024i	−2.42597	+	0.788245i
$890$			0.711549i			0.0238512i
$891$	−0.943957	+	3.17946i	−0.0316238	+	0.106516i
$892$			8.37142i			0.280296i
$893$	14.7351	−	23.3635i	0.493092	−	0.781828i
$894$	0.183282	+	0.133162i	0.00612986	+	0.00445360i
$895$	−0.579274	−	0.797302i	−0.0193630	−	0.0266509i
$896$	−46.4933	−	15.1066i	−1.55323	−	0.504675i
$897$	−1.74138	−	0.565807i	−0.0581428	−	0.0188917i
$898$	3.69331	+	5.08340i	0.123247	+	0.169635i
$899$	−50.1857	+	69.0748i	−1.67379	+	2.30377i
$900$	−2.78758	−	8.57928i	−0.0929192	−	0.285976i
$901$	8.91464			0.296990
$902$	−0.507349	−	1.43556i	−0.0168929	−	0.0477988i
$903$		−	19.9259i		−	0.663094i
$904$	24.5123	−	7.96452i	0.815266	−	0.264896i
$905$	−0.355972	+	0.489954i	−0.0118329	+	0.0162866i
$906$	−0.852973	−	1.17402i	−0.0283381	−	0.0390041i
$907$	−5.44185	−	1.76816i	−0.180694	−	0.0587109i	0.217273	−	0.976111i	$-0.430284\pi$
$907$	−5.44185	−	1.76816i	−0.180694	−	0.0587109i	−0.397966	+	0.917400i	$0.630284\pi$
$908$	6.48833	−	19.9690i	0.215323	−	0.662695i
$909$	6.48927	+	8.93171i	0.215235	+	0.296246i
$910$	−0.207346	+	0.285387i	−0.00687345	+	0.00946050i
$911$	6.36452	−	2.06796i	0.210866	−	0.0685145i	−0.201679	−	0.979452i	$-0.564640\pi$
$911$	6.36452	−	2.06796i	0.210866	−	0.0685145i	0.412545	+	0.910937i	$0.364640\pi$
$912$	9.73646	−	8.10082i	0.322406	−	0.268245i
$913$	−44.6132	+	15.7670i	−1.47648	+	0.521812i
$914$			13.8345i			0.457605i
$915$	0.0163717	+	0.0503870i	0.000541233	+	0.00166574i
$916$	−28.6430	−	20.8103i	−0.946390	−	0.687592i
$917$	−31.4682	+	22.8630i	−1.03917	+	0.755002i
$918$	0.126809	−	0.390278i	0.00418532	−	0.0128811i
$919$	55.3161	+	17.9733i	1.82471	+	0.592884i	0.999611	+	0.0278949i	$0.00888037\pi$
$919$	55.3161	+	17.9733i	1.82471	+	0.592884i	0.825098	+	0.564989i	$0.191120\pi$
$920$	−0.284463	+	0.206674i	−0.00937846	+	0.00681385i
$921$	16.1191	−	22.1861i	0.531143	−	0.731056i
$922$	11.2265	−	3.64772i	0.369726	−	0.120131i
$923$			18.7993i			0.618787i
$924$	7.74173	−	26.0759i	0.254684	−	0.857833i
$925$		−	45.0932i		−	1.48266i
$926$	0.328518	+	1.01107i	0.0107958	+	0.0332260i
$927$	8.23749	−	11.3379i	0.270555	−	0.372386i
$928$	−33.3662	+	24.2420i	−1.09530	+	0.795782i
$929$	13.7234	−	42.2363i	0.450250	−	1.38573i	−0.426371	−	0.904548i	$-0.640208\pi$
$929$	13.7234	−	42.2363i	0.450250	−	1.38573i	0.876622	−	0.481180i	$-0.159792\pi$
$930$	−0.183134	+	0.563629i	−0.00600521	+	0.0184821i
$931$	−57.0051	−	14.4661i	−1.86827	−	0.474106i
$932$	29.9456	−	41.2166i	0.980900	−	1.35009i
$933$	−17.8055	+	5.78537i	−0.582927	+	0.189404i
$934$	7.13520			0.233471
$935$	−0.0115732	−	0.452764i	−0.000378484	−	0.0148070i
$936$	−2.05703			−0.0672360
$937$	33.6880	−	10.9459i	1.10054	−	0.357586i	0.298228	−	0.954495i	$-0.403604\pi$
$937$	33.6880	−	10.9459i	1.10054	−	0.357586i	0.802310	+	0.596908i	$0.203604\pi$
$938$	−17.7798	−	12.9178i	−0.580531	−	0.421780i
$939$	7.58437	+	10.4390i	0.247506	+	0.340663i
$940$	0.512284	−	1.57665i	0.0167089	−	0.0514246i
$941$	1.77914	−	5.47563i	0.0579983	−	0.178500i	−0.917860	−	0.396903i	$-0.870085\pi$
$941$	1.77914	−	5.47563i	0.0579983	−	0.178500i	0.975859	+	0.218403i	$0.0700848\pi$
$942$	3.80279	+	5.23409i	0.123901	+	0.170536i
$943$	−1.26010	−	0.915517i	−0.0410345	−	0.0298133i
$944$	−3.31500	+	1.07711i	−0.107894	+	0.0350569i
$945$	0.653668			0.0212638
$946$	−3.59130	+	5.21839i	−0.116763	+	0.169664i
$947$	41.0880			1.33518			0.667590	−	0.744529i	$-0.267326\pi$
$947$	41.0880			1.33518			0.667590	+	0.744529i	$0.267326\pi$
$948$	8.20512	−	2.66600i	0.266490	−	0.0865878i
$949$	0.363216	−	0.499924i	0.0117905	−	0.0162282i
$950$	9.12831	+	2.31647i	0.296161	+	0.0751562i
$951$	2.46786	−	7.59529i	0.0800258	−	0.246294i
$952$	−2.18809	+	6.73426i	−0.0709166	+	0.218259i
$953$	−19.4394	+	14.1236i	−0.629704	+	0.457507i	−0.856298	−	0.516483i	$-0.827241\pi$
$953$	−19.4394	+	14.1236i	−0.629704	+	0.457507i	0.226594	+	0.973989i	$0.427241\pi$
$954$	2.40423	−	3.30914i	0.0778398	−	0.107137i
$955$	−0.907268	−	2.79228i	−0.0293585	−	0.0903562i
$956$		−	23.7246i		−	0.767307i
$957$	−18.2111	−	23.7638i	−0.588681	−	0.768176i
$958$		−	16.9186i		−	0.546615i
$959$	68.0157	−	22.0997i	2.19634	−	0.713635i
$960$	0.324982	−	0.447300i	0.0104888	−	0.0144365i
$961$	47.2956	−	34.3623i	1.52567	−	1.10846i
$962$	−4.64817	−	1.51028i	−0.149863	−	0.0486935i
$963$	−4.01145	+	12.3460i	−0.129267	+	0.397843i
$964$	22.4584	−	16.3170i	0.723336	−	0.525534i
$965$	0.287220	+	0.208677i	0.00924593	+	0.00671756i
$966$	0.893646	+	2.75036i	0.0287526	+	0.0884914i
$967$			19.4089i			0.624148i	0.950058	+	0.312074i	$0.101024\pi$
$967$			19.4089i			0.624148i	−0.950058	+	0.312074i	$0.898976\pi$
$968$	−14.1535	+	11.4321i	−0.454911	+	0.367440i
$969$	−2.63652	−	3.16886i	−0.0846972	−	0.101798i
$970$	0.153824	−	0.0499804i	0.00493898	−	0.00160477i
$971$	10.3882	−	14.2982i	0.333375	−	0.458851i	−0.609117	−	0.793080i	$-0.708476\pi$
$971$	10.3882	−	14.2982i	0.333375	−	0.458851i	0.942492	+	0.334229i	$0.108476\pi$
$972$	1.06490	+	1.46571i	0.0341566	+	0.0470126i
$973$	−4.72945	+	14.5557i	−0.151619	+	0.466636i
$974$	−0.126017	−	0.0409454i	−0.00403785	−	0.00131198i
$975$	3.63985	+	5.00982i	0.116568	+	0.160443i
$976$	0.626650	−	0.862510i	0.0200586	−	0.0276083i
$977$	47.7734	−	15.5225i	1.52841	−	0.496609i	0.580257	−	0.814433i	$-0.302952\pi$
$977$	47.7734	−	15.5225i	1.52841	−	0.496609i	0.948150	+	0.317824i	$0.102952\pi$
$978$		−	5.09519i		−	0.162926i
$979$	22.9099	+	29.8954i	0.732204	+	0.955462i
$980$	−3.52971			−0.112753
$981$	−3.50542	−	10.7886i	−0.111919	−	0.344452i
$982$	−8.49241	+	11.6888i	−0.271004	+	0.373005i
$983$	0.588047	+	0.809377i	0.0187558	+	0.0258151i	0.818292	−	0.574803i	$-0.194921\pi$
$983$	0.588047	+	0.809377i	0.0187558	+	0.0258151i	−0.799536	+	0.600618i	$0.794921\pi$
$984$	−1.66421	−	0.540734i	−0.0530530	−	0.0172380i
$985$	−3.36452	−	1.09320i	−0.107203	−	0.0348323i
$986$	2.17737	+	2.99689i	0.0693415	+	0.0954404i
$987$	−23.2077	−	16.8614i	−0.738709	−	0.536704i
$988$	−5.23931	+	8.30726i	−0.166685	+	0.264289i
$989$			6.48036i			0.206063i
$990$	−0.171189	−	0.117812i	−0.00544073	−	0.00374431i
$991$		−	8.36893i		−	0.265848i	−0.991126	−	0.132924i	$-0.957563\pi$
$991$		−	8.36893i		−	0.265848i	0.991126	−	0.132924i	$-0.0424366\pi$
$992$	41.0985	−	13.3537i	1.30488	−	0.423981i
$993$	−5.49156	−	3.98985i	−0.174269	−	0.126614i
$994$	24.0213	−	17.4525i	0.761911	−	0.553561i
$995$	0.298224	−	0.917839i	0.00945433	−	0.0290974i
$996$	−7.98722	+	24.5821i	−0.253085	+	0.778915i
$997$	12.8863	+	17.7365i	0.408114	+	0.561721i	0.962757	−	0.270367i	$-0.0871451\pi$
$997$	12.8863	+	17.7365i	0.408114	+	0.561721i	−0.554643	+	0.832089i	$0.687145\pi$
$998$	−6.44705	−	4.68405i	−0.204078	−	0.148271i
$999$	2.79859	+	8.61316i	0.0885434	+	0.272508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.s.a.94.18	✓	160
11.2	odd	10	inner	627.2.s.a.607.23	yes	160
19.18	odd	2	inner	627.2.s.a.94.23	yes	160
209.189	even	10	inner	627.2.s.a.607.18	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.s.a.94.18	✓	160	1.1	even	1	trivial
627.2.s.a.94.23	yes	160	19.18	odd	2	inner
627.2.s.a.607.18	yes	160	209.189	even	10	inner
627.2.s.a.607.23	yes	160	11.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.134089 - 0.412683i) q^{2} +(0.587785 - 0.809017i) q^{3} +(1.46571 - 1.06490i) q^{4} +(-0.0446214 + 0.137331i) q^{5} +(-0.412683 - 0.134089i) q^{6} +(2.66082 + 3.66230i) q^{7} +(-1.33810 - 0.972186i) q^{8} +(-0.309017 - 0.951057i) q^{9} +0.0626572 q^{10} +(2.63252 - 2.01739i) q^{11} -1.81171i q^{12} +(0.384319 + 1.18281i) q^{13} +(1.15458 - 1.58915i) q^{14} +(0.0848750 + 0.116820i) q^{15} +(0.897920 - 2.76351i) q^{16} +(-0.899421 - 0.292240i) q^{17} +(-0.351049 + 0.255052i) q^{18} +(0.285902 + 4.34951i) q^{19} +(0.0808412 + 0.248804i) q^{20} +4.52685 q^{21} +(-1.18553 - 0.815885i) q^{22} -1.47223 q^{23} +(-1.57303 + 0.511108i) q^{24} +(4.02822 + 2.92667i) q^{25} +(0.436594 - 0.317204i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(7.79995 + 2.53436i) q^{28} +(7.30304 - 5.30597i) q^{29} +(0.0368290 - 0.0506908i) q^{30} +(-8.99544 + 2.92279i) q^{31} -4.56882 q^{32} +(-0.0847493 - 3.31554i) q^{33} +0.410362i q^{34} +(-0.621675 + 0.201995i) q^{35} +(-1.46571 - 1.06490i) q^{36} +(-5.32323 - 7.32679i) q^{37} +(1.75663 - 0.701208i) q^{38} +(1.18281 + 0.384319i) q^{39} +(0.193219 - 0.140382i) q^{40} +(0.855911 + 0.621856i) q^{41} +(-0.607001 - 1.86816i) q^{42} -4.40172i q^{43} +(1.71018 - 5.76026i) q^{44} +0.144398 q^{45} +(0.197410 + 0.607566i) q^{46} +(-5.12668 - 3.72475i) q^{47} +(-1.70794 - 2.35078i) q^{48} +(-4.16938 + 12.8320i) q^{49} +(0.667648 - 2.05481i) q^{50} +(-0.765093 + 0.555873i) q^{51} +(1.82287 + 1.32439i) q^{52} +(-8.96506 + 2.91292i) q^{53} +0.433921i q^{54} +(0.159583 + 0.451544i) q^{55} -7.48733i q^{56} +(3.68688 + 2.32528i) q^{57} +(-3.16894 - 2.30237i) q^{58} +(-0.705083 - 0.970463i) q^{59} +(0.248804 + 0.0808412i) q^{60} +(0.348946 + 0.113379i) q^{61} +(2.41238 + 3.32035i) q^{62} +(2.66082 - 3.66230i) q^{63} +(-1.18321 - 3.64155i) q^{64} -0.179585 q^{65} +(-1.35690 + 0.479552i) q^{66} -11.1883i q^{67} +(-1.62949 + 0.529454i) q^{68} +(-0.865357 + 1.19106i) q^{69} +(0.166719 + 0.229470i) q^{70} +(14.3760 + 4.67106i) q^{71} +(-0.511108 + 1.57303i) q^{72} +(-0.292049 - 0.401971i) q^{73} +(-2.30986 + 3.17925i) q^{74} +(4.73545 - 1.53864i) q^{75} +(5.05084 + 6.07065i) q^{76} +(14.3929 + 4.27316i) q^{77} -0.539659i q^{78} +(1.47154 + 4.52893i) q^{79} +(0.339448 + 0.246624i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(0.141861 - 0.436604i) q^{82} +(-13.5685 - 4.40866i) q^{83} +(6.63504 - 4.82064i) q^{84} +(0.0802669 - 0.110478i) q^{85} +(-1.81652 + 0.590222i) q^{86} -9.02705i q^{87} +(-5.48384 + 0.140174i) q^{88} +11.3562i q^{89} +(-0.0193621 - 0.0595906i) q^{90} +(-3.30921 + 4.55474i) q^{91} +(-2.15786 + 1.56778i) q^{92} +(-2.92279 + 8.99544i) q^{93} +(-0.849710 + 2.61514i) q^{94} +(-0.610078 - 0.154818i) q^{95} +(-2.68548 + 3.69625i) q^{96} +(2.45500 - 0.797679i) q^{97} +5.85463 q^{98} +(-2.73214 - 1.88026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 40 q^{4} + 4 q^{5} - 10 q^{7} + 40 q^{9} + 10 q^{11} - 40 q^{16} - 50 q^{17} + 76 q^{20} + 16 q^{23} - 80 q^{25} - 68 q^{26} - 40 q^{35} + 40 q^{36} - 62 q^{38} + 8 q^{42} + 40 q^{44} - 4 q^{45}+ \cdots - 10 q^{99}+O(q^{100}) \) 160 * q - 40 * q^4 + 4 * q^5 - 10 * q^7 + 40 * q^9 + 10 * q^11 - 40 * q^16 - 50 * q^17 + 76 * q^20 + 16 * q^23 - 80 * q^25 - 68 * q^26 - 40 * q^35 + 40 * q^36 - 62 * q^38 + 8 * q^42 + 40 * q^44 - 4 * q^45 + 20 * q^47 + 110 * q^49 - 18 * q^55 - 20 * q^57 - 24 * q^58 + 10 * q^61 + 120 * q^62 - 10 * q^63 - 136 * q^64 - 12 * q^66 + 160 * q^68 + 20 * q^73 - 100 * q^74 + 90 * q^77 - 156 * q^80 - 40 * q^81 + 68 * q^82 - 200 * q^83 + 30 * q^85 - 84 * q^92 - 96 * q^93 - 60 * q^95 + 100 * q^96 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more