LMFDB - Embedded newform 605.2.j.g.444.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{14} + 25x^{12} - 57x^{10} + 194x^{8} - 303x^{6} + 235x^{4} - 33x^{2} + 121 $ x^16 - 7x^14 + 25x^12 - 57x^10 + 194x^8 - 303x^6 + 235x^4 - 33*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			444.3
Root			$0.471815 + 0.649397i$ of defining polynomial
Character	$\chi$	$=$	605.444
Dual form			605.2.j.g.124.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.471815 - 0.649397i) q^{2} +(1.67457 + 0.544099i) q^{3} +(0.418926 + 1.28932i) q^{4} +(2.07703 + 0.828231i) q^{5} +(1.14342 - 0.830744i) q^{6} +(-0.563124 + 0.182970i) q^{7} +(2.56176 + 0.832367i) q^{8} +(0.0810736 + 0.0589034i) q^{9} +O(q^{10})$	\(q+(0.471815 - 0.649397i) q^{2} +(1.67457 + 0.544099i) q^{3} +(0.418926 + 1.28932i) q^{4} +(2.07703 + 0.828231i) q^{5} +(1.14342 - 0.830744i) q^{6} +(-0.563124 + 0.182970i) q^{7} +(2.56176 + 0.832367i) q^{8} +(0.0810736 + 0.0589034i) q^{9} +(1.51782 - 0.958043i) q^{10} +2.38699i q^{12} +(1.05501 - 1.45210i) q^{13} +(-0.146870 + 0.452019i) q^{14} +(3.02747 + 2.51703i) q^{15} +(-0.444313 + 0.322812i) q^{16} +(-4.15982 - 5.72551i) q^{17} +(0.0765034 - 0.0248575i) q^{18} +(-0.706673 + 2.17492i) q^{19} +(-0.197736 + 3.02492i) q^{20} -1.04254 q^{21} +1.49081i q^{23} +(3.83695 + 2.78771i) q^{24} +(3.62807 + 3.44051i) q^{25} +(-0.445218 - 1.37024i) q^{26} +(-3.00110 - 4.13066i) q^{27} +(-0.471815 - 0.649397i) q^{28} +(1.10489 + 3.40050i) q^{29} +(3.06296 - 0.778460i) q^{30} +(-4.98940 - 3.62501i) q^{31} +5.82804i q^{32} -5.68079 q^{34} +(-1.32116 - 0.0863629i) q^{35} +(-0.0419817 + 0.129206i) q^{36} +(6.97831 - 2.26739i) q^{37} +(1.07897 + 1.48507i) q^{38} +(2.55677 - 1.85760i) q^{39} +(4.63145 + 3.85058i) q^{40} +(-2.59890 + 7.99858i) q^{41} +(-0.491886 + 0.677023i) q^{42} -9.51936i q^{43} +(0.119606 + 0.189492i) q^{45} +(0.968128 + 0.703386i) q^{46} +(-1.83711 - 0.596914i) q^{47} +(-0.919674 + 0.298820i) q^{48} +(-5.37949 + 3.90843i) q^{49} +(3.94603 - 0.732773i) q^{50} +(-3.85065 - 11.8511i) q^{51} +(2.31419 + 0.751927i) q^{52} +(1.40064 - 1.92781i) q^{53} -4.09840 q^{54} -1.59489 q^{56} +(-2.36674 + 3.25754i) q^{57} +(2.72957 + 0.886893i) q^{58} +(0.0118285 + 0.0364043i) q^{59} +(-1.97698 + 4.95784i) q^{60} +(-2.78430 + 2.02291i) q^{61} +(-4.70814 + 1.52977i) q^{62} +(-0.0564320 - 0.0183359i) q^{63} +(2.89608 + 2.10413i) q^{64} +(3.39395 - 2.14225i) q^{65} -6.79162i q^{67} +(5.63937 - 7.76192i) q^{68} +(-0.811149 + 2.49646i) q^{69} +(-0.679428 + 0.817212i) q^{70} +(9.54114 - 6.93205i) q^{71} +(0.158662 + 0.218380i) q^{72} +(6.48882 - 2.10835i) q^{73} +(1.82003 - 5.60148i) q^{74} +(4.20346 + 7.73539i) q^{75} -3.10021 q^{76} -2.53680i q^{78} +(-3.66165 - 2.66035i) q^{79} +(-1.19021 + 0.302496i) q^{80} +(-2.87095 - 8.83588i) q^{81} +(3.96806 + 5.46156i) q^{82} +(3.49299 + 4.80768i) q^{83} +(-0.436748 - 1.34417i) q^{84} +(-3.89802 - 15.3373i) q^{85} +(-6.18185 - 4.49137i) q^{86} +6.29552i q^{87} +6.21375 q^{89} +(0.179487 + 0.0117329i) q^{90} +(-0.328411 + 1.01074i) q^{91} +(-1.92214 + 0.624540i) q^{92} +(-6.38271 - 8.78504i) q^{93} +(-1.25441 + 0.911382i) q^{94} +(-3.26911 + 3.93207i) q^{95} +(-3.17103 + 9.75943i) q^{96} +(3.15976 - 4.34904i) q^{97} +5.33748i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4} - 2 q^{5} - 12 q^{6} + 2 q^{9}+O(q^{10}) $ 16 * q + 6 * q^4 - 2 * q^5 - 12 * q^6 + 2 * q^9	$ 16 q + 6 q^{4} - 2 q^{5} - 12 q^{6} + 2 q^{9} + 8 q^{14} + 24 q^{15} + 6 q^{16} - 6 q^{19} + 12 q^{20} - 8 q^{21} + 4 q^{24} + 24 q^{25} - 50 q^{26} - 22 q^{29} + 4 q^{30} - 22 q^{31} - 16 q^{34} + 8 q^{35} - 30 q^{36} - 12 q^{40} - 18 q^{41} + 12 q^{45} - 38 q^{46} - 20 q^{49} + 12 q^{50} + 12 q^{51} + 40 q^{54} - 20 q^{56} - 8 q^{59} - 2 q^{60} - 20 q^{61} + 22 q^{64} + 40 q^{65} + 6 q^{69} + 26 q^{70} + 6 q^{71} + 52 q^{74} + 40 q^{75} - 56 q^{76} + 22 q^{79} - 6 q^{80} - 32 q^{81} + 18 q^{84} + 62 q^{85} - 68 q^{86} + 24 q^{89} + 32 q^{90} + 56 q^{94} + 22 q^{95} - 94 q^{96}+O(q^{100}) $ 16 * q + 6 * q^4 - 2 * q^5 - 12 * q^6 + 2 * q^9 + 8 * q^14 + 24 * q^15 + 6 * q^16 - 6 * q^19 + 12 * q^20 - 8 * q^21 + 4 * q^24 + 24 * q^25 - 50 * q^26 - 22 * q^29 + 4 * q^30 - 22 * q^31 - 16 * q^34 + 8 * q^35 - 30 * q^36 - 12 * q^40 - 18 * q^41 + 12 * q^45 - 38 * q^46 - 20 * q^49 + 12 * q^50 + 12 * q^51 + 40 * q^54 - 20 * q^56 - 8 * q^59 - 2 * q^60 - 20 * q^61 + 22 * q^64 + 40 * q^65 + 6 * q^69 + 26 * q^70 + 6 * q^71 + 52 * q^74 + 40 * q^75 - 56 * q^76 + 22 * q^79 - 6 * q^80 - 32 * q^81 + 18 * q^84 + 62 * q^85 - 68 * q^86 + 24 * q^89 + 32 * q^90 + 56 * q^94 + 22 * q^95 - 94 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.471815	−	0.649397i	0.333623	−	0.459193i	−0.608942	−	0.793215i	$-0.708406\pi$
$2$	0.471815	−	0.649397i	0.333623	−	0.459193i	0.942565	+	0.334022i	$0.108406\pi$
$3$	1.67457	+	0.544099i	0.966811	+	0.314136i	0.749528	−	0.661973i	$-0.230281\pi$
$3$	1.67457	+	0.544099i	0.966811	+	0.314136i	0.217283	+	0.976109i	$0.430281\pi$
$4$	0.418926	+	1.28932i	0.209463	+	0.644661i
$5$	2.07703	+	0.828231i	0.928874	+	0.370396i
$5$	2.07703	+	0.828231i	0.928874	+	0.370396i
$6$	1.14342	−	0.830744i	0.466800	−	0.339150i
$7$	−0.563124	+	0.182970i	−0.212841	+	0.0691561i	−0.413497	−	0.910506i	$-0.635693\pi$
$7$	−0.563124	+	0.182970i	−0.212841	+	0.0691561i	0.200656	+	0.979662i	$0.435693\pi$
$8$	2.56176	+	0.832367i	0.905720	+	0.294286i
$9$	0.0810736	+	0.0589034i	0.0270245	+	0.0196345i
$10$	1.51782	−	0.958043i	0.479977	−	0.302960i
$11$		0			0
$11$		0			0
$12$			2.38699i			0.689065i
$13$	1.05501	−	1.45210i	0.292607	−	0.402739i	−0.637252	−	0.770656i	$-0.719929\pi$
$13$	1.05501	−	1.45210i	0.292607	−	0.402739i	0.929859	+	0.367917i	$0.119929\pi$
$14$	−0.146870	+	0.452019i	−0.0392526	+	0.120807i
$15$	3.02747	+	2.51703i	0.781691	+	0.649895i
$16$	−0.444313	+	0.322812i	−0.111078	+	0.0807031i
$17$	−4.15982	−	5.72551i	−1.00891	−	1.38864i	−0.919698	−	0.392626i	$-0.871567\pi$
$17$	−4.15982	−	5.72551i	−1.00891	−	1.38864i	−0.0892075	−	0.996013i	$-0.528433\pi$
$18$	0.0765034	−	0.0248575i	0.0180320	−	0.00585896i
$19$	−0.706673	+	2.17492i	−0.162122	+	0.498960i	−0.998813	−	0.0487157i	$-0.984487\pi$
$19$	−0.706673	+	2.17492i	−0.162122	+	0.498960i	0.836691	+	0.547676i	$0.184487\pi$
$20$	−0.197736	+	3.02492i	−0.0442151	+	0.676394i
$21$	−1.04254			−0.227501
$22$		0			0
$23$			1.49081i			0.310855i	0.987847	+	0.155428i	$0.0496756\pi$
$23$			1.49081i			0.310855i	−0.987847	+	0.155428i	$0.950324\pi$
$24$	3.83695	+	2.78771i	0.783214	+	0.569038i
$25$	3.62807	+	3.44051i	0.725614	+	0.688102i
$26$	−0.445218	−	1.37024i	−0.0873145	−	0.268726i
$27$	−3.00110	−	4.13066i	−0.577562	−	0.794946i
$28$	−0.471815	−	0.649397i	−0.0891646	−	0.122725i
$29$	1.10489	+	3.40050i	0.205173	+	0.631456i	0.999706	+	0.0242362i	$0.00771537\pi$
$29$	1.10489	+	3.40050i	0.205173	+	0.631456i	−0.794534	+	0.607220i	$0.792285\pi$
$30$	3.06296	−	0.778460i	0.559218	−	0.142127i
$31$	−4.98940	−	3.62501i	−0.896122	−	0.651071i	0.0413447	−	0.999145i	$-0.486836\pi$
$31$	−4.98940	−	3.62501i	−0.896122	−	0.651071i	−0.937467	+	0.348074i	$0.886836\pi$
$32$			5.82804i			1.03026i
$33$		0			0
$34$	−5.68079			−0.974248
$35$	−1.32116	−	0.0863629i	−0.223317	−	0.0145980i
$36$	−0.0419817	+	0.129206i	−0.00699694	+	0.0215344i
$37$	6.97831	−	2.26739i	1.14723	−	0.372757i	0.327129	−	0.944980i	$-0.393919\pi$
$37$	6.97831	−	2.26739i	1.14723	−	0.372757i	0.820098	+	0.572223i	$0.193919\pi$
$38$	1.07897	+	1.48507i	0.175031	+	0.240910i
$39$	2.55677	−	1.85760i	0.409410	−	0.297454i
$40$	4.63145	+	3.85058i	0.732297	+	0.608830i
$41$	−2.59890	+	7.99858i	−0.405879	+	1.24917i	0.514280	+	0.857623i	$0.328059\pi$
$41$	−2.59890	+	7.99858i	−0.405879	+	1.24917i	−0.920159	+	0.391545i	$0.871941\pi$
$42$	−0.491886	+	0.677023i	−0.0758997	+	0.104467i
$43$		−	9.51936i		−	1.45169i	−0.687859	−	0.725844i	$-0.741449\pi$
$43$		−	9.51936i		−	1.45169i	0.687859	−	0.725844i	$-0.258551\pi$
$44$		0			0
$45$	0.119606	+	0.189492i	0.0178299	+	0.0282477i
$46$	0.968128	+	0.703386i	0.142743	+	0.103709i
$47$	−1.83711	−	0.596914i	−0.267970	−	0.0870688i	0.171950	−	0.985106i	$-0.444993\pi$
$47$	−1.83711	−	0.596914i	−0.267970	−	0.0870688i	−0.439920	+	0.898037i	$0.644993\pi$
$48$	−0.919674	+	0.298820i	−0.132743	+	0.0431310i
$49$	−5.37949	+	3.90843i	−0.768498	+	0.558347i
$50$	3.94603	−	0.732773i	0.558054	−	0.103630i
$51$	−3.85065	−	11.8511i	−0.539199	−	1.65948i
$52$	2.31419	+	0.751927i	0.320921	+	0.104273i
$53$	1.40064	−	1.92781i	0.192392	−	0.264806i	−0.701913	−	0.712263i	$-0.747670\pi$
$53$	1.40064	−	1.92781i	0.192392	−	0.264806i	0.894305	+	0.447457i	$0.147670\pi$
$54$	−4.09840			−0.557722
$55$		0			0
$56$	−1.59489			−0.213126
$57$	−2.36674	+	3.25754i	−0.313482	+	0.431471i
$58$	2.72957	+	0.886893i	0.358411	+	0.116455i
$59$	0.0118285	+	0.0364043i	0.00153994	+	0.00473944i	0.951824	−	0.306646i	$-0.0992069\pi$
$59$	0.0118285	+	0.0364043i	0.00153994	+	0.00473944i	−0.950284	+	0.311386i	$0.899207\pi$
$60$	−1.97698	+	4.95784i	−0.255227	+	0.640055i
$61$	−2.78430	+	2.02291i	−0.356493	+	0.259007i	−0.751588	−	0.659633i	$-0.770712\pi$
$61$	−2.78430	+	2.02291i	−0.356493	+	0.259007i	0.395095	+	0.918640i	$0.370712\pi$
$62$	−4.70814	+	1.52977i	−0.597935	+	0.194281i
$63$	−0.0564320	−	0.0183359i	−0.00710977	−	0.00231010i
$64$	2.89608	+	2.10413i	0.362010	+	0.263016i
$65$	3.39395	−	2.14225i	0.420968	−	0.265713i
$66$		0			0
$67$		−	6.79162i		−	0.829728i	−0.909883	−	0.414864i	$-0.863829\pi$
$67$		−	6.79162i		−	0.829728i	0.909883	−	0.414864i	$-0.136171\pi$
$68$	5.63937	−	7.76192i	0.683874	−	0.941271i
$69$	−0.811149	+	2.49646i	−0.0976508	+	0.300538i
$70$	−0.679428	+	0.817212i	−0.0812072	+	0.0976756i
$71$	9.54114	−	6.93205i	1.13233	−	0.822683i	0.146294	−	0.989241i	$-0.453265\pi$
$71$	9.54114	−	6.93205i	1.13233	−	0.822683i	0.986032	+	0.166559i	$0.0532655\pi$
$72$	0.158662	+	0.218380i	0.0186985	+	0.0257363i
$73$	6.48882	−	2.10835i	0.759459	−	0.246763i	0.0964127	−	0.995341i	$-0.469263\pi$
$73$	6.48882	−	2.10835i	0.759459	−	0.246763i	0.663046	+	0.748578i	$0.269263\pi$
$74$	1.82003	−	5.60148i	0.211574	−	0.651159i
$75$	4.20346	+	7.73539i	0.485373	+	0.893206i
$76$	−3.10021			−0.355619
$77$		0			0
$78$		−	2.53680i		−	0.287236i
$79$	−3.66165	−	2.66035i	−0.411968	−	0.299313i	0.362430	−	0.932011i	$-0.381947\pi$
$79$	−3.66165	−	2.66035i	−0.411968	−	0.299313i	−0.774398	+	0.632699i	$0.781947\pi$
$80$	−1.19021	+	0.302496i	−0.133070	+	0.0338201i
$81$	−2.87095	−	8.83588i	−0.318995	−	0.981765i
$82$	3.96806	+	5.46156i	0.438198	+	0.603128i
$83$	3.49299	+	4.80768i	0.383405	+	0.527712i	0.956483	−	0.291789i	$-0.0942506\pi$
$83$	3.49299	+	4.80768i	0.383405	+	0.527712i	−0.573077	+	0.819501i	$0.694251\pi$
$84$	−0.436748	−	1.34417i	−0.0476531	−	0.146661i
$85$	−3.89802	−	15.3373i	−0.422800	−	1.66357i
$86$	−6.18185	−	4.49137i	−0.666606	−	0.484317i
$87$			6.29552i			0.674951i
$88$		0			0
$89$	6.21375			0.658656			0.329328	−	0.944216i	$-0.393178\pi$
$89$	6.21375			0.658656			0.329328	+	0.944216i	$0.393178\pi$
$90$	0.179487	+	0.0117329i	0.0189196	+	0.00123675i
$91$	−0.328411	+	1.01074i	−0.0344268	+	0.105955i
$92$	−1.92214	+	0.624540i	−0.200396	+	0.0651128i
$93$	−6.38271	−	8.78504i	−0.661856	−	0.910967i
$94$	−1.25441	+	0.911382i	−0.129383	+	0.0940019i
$95$	−3.26911	+	3.93207i	−0.335404	+	0.403422i
$96$	−3.17103	+	9.75943i	−0.323642	+	0.996067i
$97$	3.15976	−	4.34904i	0.320825	−	0.441578i	−0.617894	−	0.786262i	$-0.712014\pi$
$97$	3.15976	−	4.34904i	0.320825	−	0.441578i	0.938719	+	0.344684i	$0.112014\pi$
$98$			5.33748i			0.539167i
$99$		0			0
$100$	−2.91604	+	6.11907i	−0.291604	+	0.611907i
$101$	−8.03459	−	5.83747i	−0.799472	−	0.580850i	0.111287	−	0.993788i	$-0.464503\pi$
$101$	−8.03459	−	5.83747i	−0.799472	−	0.580850i	−0.910759	+	0.412938i	$0.864503\pi$
$102$	−9.51286	−	3.09092i	−0.941913	−	0.306046i
$103$	−12.8596	+	4.17833i	−1.26709	+	0.411703i	−0.864017	−	0.503463i	$-0.832059\pi$
$103$	−12.8596	+	4.17833i	−1.26709	+	0.411703i	−0.403076	+	0.915166i	$0.632059\pi$
$104$	3.91136	−	2.84177i	0.383541	−	0.278658i
$105$	−2.16538	−	0.863464i	−0.211320	−	0.0842655i
$106$	−0.591075	−	1.81914i	−0.0574103	−	0.176691i
$107$	−5.33010	−	1.73185i	−0.515280	−	0.167425i	0.0398221	−	0.999207i	$-0.487321\pi$
$107$	−5.33010	−	1.73185i	−0.515280	−	0.167425i	−0.555102	+	0.831782i	$0.687321\pi$
$108$	4.06852	−	5.59983i	0.391493	−	0.538844i
$109$	18.6001			1.78157			0.890784	−	0.454428i	$-0.150156\pi$
$109$	18.6001			1.78157			0.890784	+	0.454428i	$0.150156\pi$
$110$		0			0
$111$	12.9193			1.22625
$112$	0.191138	−	0.263079i	0.0180609	−	0.0248587i
$113$	−11.2238	−	3.64683i	−1.05584	−	0.343065i	−0.270885	−	0.962612i	$-0.587316\pi$
$113$	−11.2238	−	3.64683i	−1.05584	−	0.343065i	−0.784960	+	0.619547i	$0.787316\pi$
$114$	0.998773	+	3.07391i	0.0935437	+	0.287898i
$115$	−1.23473	+	3.09645i	−0.115140	+	0.288745i
$116$	−3.92147	+	2.84912i	−0.364099	+	0.264534i
$117$	0.171067	−	0.0555830i	0.0158151	−	0.00513865i
$118$	0.0292217	+	0.00949471i	0.00269008	+	0.000874059i
$119$	3.39009	+	2.46304i	0.310769	+	0.225787i
$120$	5.66057	+	8.96801i	0.516737	+	0.818664i
$121$		0			0
$122$			2.76255i			0.250110i
$123$	−8.70404	+	11.9801i	−0.784817	+	1.08021i
$124$	2.58362	−	7.95156i	0.232016	−	0.714071i
$125$	4.68605	+	10.1509i	0.419133	+	0.907925i
$126$	−0.0385327	+	0.0279957i	−0.00343277	+	0.00249405i
$127$	9.43784	+	12.9901i	0.837473	+	1.15268i	0.986486	+	0.163847i	$0.0523904\pi$
$127$	9.43784	+	12.9901i	0.837473	+	1.15268i	−0.149013	+	0.988835i	$0.547610\pi$
$128$	−8.35275	+	2.71397i	−0.738286	+	0.239884i
$129$	5.17948	−	15.9408i	0.456027	−	1.40351i
$130$	0.210146	−	3.21477i	0.0184310	−	0.281954i
$131$	−18.0296			−1.57525			−0.787625	−	0.616154i	$-0.788690\pi$
$131$	−18.0296			−1.57525			−0.787625	+	0.616154i	$0.788690\pi$
$132$		0			0
$133$		−	1.35405i		−	0.117411i
$134$	−4.41046	−	3.20438i	−0.381005	−	0.276817i
$135$	−2.81222	−	11.0651i	−0.242038	−	0.952331i
$136$	−5.89076	−	18.1299i	−0.505128	−	1.55463i
$137$	−2.36999	−	3.26202i	−0.202482	−	0.278693i	0.695685	−	0.718347i	$-0.255101\pi$
$137$	−2.36999	−	3.26202i	−0.202482	−	0.278693i	−0.898167	+	0.439654i	$0.855101\pi$
$138$	1.23848	+	1.70462i	0.105427	+	0.145107i
$139$	2.45203	+	7.54656i	0.207978	+	0.640091i	0.999578	+	0.0290509i	$0.00924848\pi$
$139$	2.45203	+	7.54656i	0.207978	+	0.640091i	−0.791600	+	0.611040i	$0.790752\pi$
$140$	−0.442120	−	1.73959i	−0.0373660	−	0.147022i
$141$	−2.75158	−	1.99914i	−0.231725	−	0.168358i
$142$		−	9.46663i		−	0.794422i
$143$		0			0
$144$	−0.0550368			−0.00458640
$145$	−0.521514	+	7.97802i	−0.0433094	+	0.662538i
$146$	1.69237	−	5.20857i	0.140061	−	0.431064i
$147$	−11.1349	+	3.61794i	−0.918389	+	0.298403i
$148$	5.84679	+	8.04742i	0.480604	+	0.661494i
$149$	−10.1134	+	7.34783i	−0.828524	+	0.601958i	−0.919141	−	0.393928i	$-0.871116\pi$
$149$	−10.1134	+	7.34783i	−0.828524	+	0.601958i	0.0906173	+	0.995886i	$0.471116\pi$
$150$	7.00659	+	0.919957i	0.572086	+	0.0751142i
$151$	−2.59651	+	7.99123i	−0.211301	+	0.650317i	0.788095	+	0.615554i	$0.211068\pi$
$151$	−2.59651	+	7.99123i	−0.211301	+	0.650317i	−0.999396	+	0.0347632i	$0.988932\pi$
$152$	−3.62066	+	4.98341i	−0.293674	+	0.404208i
$153$		−	0.709215i		−	0.0573367i
$154$		0			0
$155$	−7.36076	−	11.6616i	−0.591231	−	0.936683i
$156$	3.46614	+	2.51830i	0.277514	+	0.201625i
$157$	13.3109	+	4.32496i	1.06232	+	0.345170i	0.787493	−	0.616323i	$-0.211379\pi$
$157$	13.3109	+	4.32496i	1.06232	+	0.345170i	0.274830	+	0.961493i	$0.411379\pi$
$158$	−3.45524	+	1.12268i	−0.274885	+	0.0893154i
$159$	3.39438	−	2.46616i	0.269192	−	0.195579i
$160$	−4.82696	+	12.1050i	−0.381605	+	0.956983i
$161$	−0.272773	−	0.839510i	−0.0214976	−	0.0661627i
$162$	−7.09255	−	2.30451i	−0.557244	−	0.181059i
$163$	−6.96025	+	9.57996i	−0.545169	+	0.750360i	−0.989347	−	0.145578i	$-0.953496\pi$
$163$	−6.96025	+	9.57996i	−0.545169	+	0.750360i	0.444178	+	0.895939i	$0.353496\pi$
$164$	−11.4015			−0.890307
$165$		0			0
$166$	4.77014			0.370235
$167$	−5.12918	+	7.05971i	−0.396908	+	0.546297i	−0.959965	−	0.280121i	$-0.909625\pi$
$167$	−5.12918	+	7.05971i	−0.396908	+	0.546297i	0.563057	+	0.826418i	$0.309625\pi$
$168$	−2.67074	−	0.867777i	−0.206052	−	0.0669504i
$169$	3.02168	+	9.29978i	0.232437	+	0.715368i
$170$	−11.7992	−	4.70501i	−0.904954	−	0.360858i
$171$	−0.185402	+	0.134703i	−0.0141781	+	0.0103010i
$172$	12.2735	−	3.98791i	0.935848	−	0.304075i
$173$	−8.72938	−	2.83635i	−0.663682	−	0.215643i	−0.0422448	−	0.999107i	$-0.513451\pi$
$173$	−8.72938	−	2.83635i	−0.663682	−	0.215643i	−0.621437	+	0.783464i	$0.713451\pi$
$174$	4.08829	+	2.97032i	0.309933	+	0.225179i
$175$	−2.67256	−	1.27361i	−0.202027	−	0.0962755i
$176$		0			0
$177$			0.0673973i			0.00506589i
$178$	2.93174	−	4.03519i	0.219743	−	0.302450i
$179$	−0.447507	+	1.37729i	−0.0334483	+	0.102943i	−0.966387	−	0.257093i	$-0.917235\pi$
$179$	−0.447507	+	1.37729i	−0.0334483	+	0.102943i	0.932939	+	0.360036i	$0.117235\pi$
$180$	−0.194210	+	0.233594i	−0.0144755	+	0.0174111i
$181$	−0.641957	+	0.466409i	−0.0477163	+	0.0346679i	−0.611388	−	0.791331i	$-0.709388\pi$
$181$	−0.641957	+	0.466409i	−0.0477163	+	0.0346679i	0.563671	+	0.825999i	$0.309388\pi$
$182$	0.501426	+	0.690153i	0.0371681	+	0.0511576i
$183$	−5.76315	+	1.87256i	−0.426024	+	0.138424i
$184$	−1.24090	+	3.81910i	−0.0914804	+	0.281548i
$185$	16.3720	+	1.07022i	1.20370	+	0.0786843i
$186$	−8.71644			−0.639120
$187$		0			0
$188$		−	2.61869i		−	0.190988i
$189$	2.44578	+	1.77696i	0.177904	+	0.129255i
$190$	1.01106	+	3.97816i	0.0733500	+	0.288606i
$191$	−2.51858	−	7.75139i	−0.182238	−	0.560871i	0.817652	−	0.575713i	$-0.195275\pi$
$191$	−2.51858	−	7.75139i	−0.182238	−	0.560871i	−0.999890	+	0.0148421i	$0.995275\pi$
$192$	3.70483	+	5.09926i	0.267373	+	0.368007i
$193$	2.56766	+	3.53408i	0.184824	+	0.254389i	0.891368	−	0.453281i	$-0.149747\pi$
$193$	2.56766	+	3.53408i	0.184824	+	0.254389i	−0.706544	+	0.707670i	$0.749747\pi$
$194$	−1.33343	−	4.10388i	−0.0957348	−	0.294642i
$195$	6.84899	−	1.74069i	0.490466	−	0.124653i
$196$	−7.29283	−	5.29855i	−0.520917	−	0.378468i
$197$		−	15.6525i		−	1.11520i	−0.830111	−	0.557599i	$-0.811723\pi$
$197$		−	15.6525i		−	1.11520i	0.830111	−	0.557599i	$-0.188277\pi$
$198$		0			0
$199$	−1.43830			−0.101959			−0.0509793	−	0.998700i	$-0.516234\pi$
$199$	−1.43830			−0.101959			−0.0509793	+	0.998700i	$0.516234\pi$
$200$	6.43048	+	11.8337i	0.454704	+	0.836766i
$201$	3.69531	−	11.3730i	0.260647	−	0.802190i
$202$	−7.58168	+	2.46344i	−0.533445	+	0.173327i
$203$	−1.24438	−	1.71274i	−0.0873381	−	0.120211i
$204$	13.6667	−	9.92947i	0.956863	−	0.695202i
$205$	−12.0226	+	14.4608i	−0.839697	+	1.00998i
$206$	−3.35394	+	10.3224i	−0.233680	+	0.719194i
$207$	−0.0878138	+	0.120865i	−0.00610348	+	0.00840072i
$208$			0.985756i			0.0683499i
$209$		0			0
$210$	−1.58239	+	0.998799i	−0.109195	+	0.0689237i
$211$	7.02332	+	5.10274i	0.483505	+	0.351287i	0.802681	−	0.596408i	$-0.203406\pi$
$211$	7.02332	+	5.10274i	0.483505	+	0.351287i	−0.319176	+	0.947696i	$0.603406\pi$
$212$	3.07234	+	0.998263i	0.211009	+	0.0685610i
$213$	19.7490	−	6.41684i	1.35318	−	0.439674i
$214$	−3.63948	+	2.64424i	−0.248790	+	0.180756i
$215$	7.88422	−	19.7720i	0.537700	−	1.34844i
$216$	−4.24988	−	13.0798i	−0.289168	−	0.889967i
$217$	3.47292	+	1.12842i	0.235757	+	0.0766020i
$218$	8.77580	−	12.0789i	0.594372	−	0.818083i
$219$	12.0131			0.811770
$220$		0			0
$221$	−12.7026			−0.854472
$222$	6.09552	−	8.38977i	0.409105	−	0.563084i
$223$	5.99740	+	1.94867i	0.401616	+	0.130493i	0.502858	−	0.864369i	$-0.332282\pi$
$223$	5.99740	+	1.94867i	0.401616	+	0.130493i	−0.101243	+	0.994862i	$0.532282\pi$
$224$	−1.06636	−	3.28190i	−0.0712489	−	0.219281i
$225$	0.0914827	+	0.492640i	0.00609884	+	0.0328427i
$226$	−7.66379	+	5.56807i	−0.509787	+	0.370382i
$227$	−1.06215	+	0.345113i	−0.0704973	+	0.0229060i	−0.344053	−	0.938950i	$-0.611800\pi$
$227$	−1.06215	+	0.345113i	−0.0704973	+	0.0229060i	0.273556	+	0.961856i	$0.411800\pi$
$228$	−5.19151	−	1.68682i	−0.343816	−	0.111713i
$229$	−3.39477	−	2.46644i	−0.224332	−	0.162987i	0.469942	−	0.882697i	$-0.344275\pi$
$229$	−3.39477	−	2.46644i	−0.224332	−	0.162987i	−0.694275	+	0.719710i	$0.744275\pi$
$230$	1.42826	+	2.26278i	0.0941767	+	0.149204i
$231$		0			0
$232$			9.63094i			0.632302i
$233$	−3.98487	+	5.48471i	−0.261058	+	0.359315i	−0.919345	−	0.393451i	$-0.871281\pi$
$233$	−3.98487	+	5.48471i	−0.261058	+	0.359315i	0.658288	+	0.752766i	$0.271281\pi$
$234$	0.0446164	−	0.137315i	0.00291667	−	0.00897658i
$235$	−3.32135	−	2.76136i	−0.216661	−	0.180131i
$236$	−0.0419817	+	0.0305015i	−0.00273277	+	0.00198548i
$237$	−4.68419	−	6.44723i	−0.304271	−	0.418793i
$238$	3.19899	−	1.03941i	0.207360	−	0.0673752i
$239$	1.35908	−	4.18282i	0.0879117	−	0.270564i	−0.897430	−	0.441157i	$-0.854568\pi$
$239$	1.35908	−	4.18282i	0.0879117	−	0.270564i	0.985342	+	0.170593i	$0.0545682\pi$
$240$	−2.15768	−	0.141045i	−0.139277	−	0.00910441i
$241$	9.61218			0.619175			0.309587	−	0.950871i	$-0.399809\pi$
$241$	9.61218			0.619175			0.309587	+	0.950871i	$0.399809\pi$
$242$		0			0
$243$		−	1.04101i		−	0.0667807i
$244$	−3.77460	−	2.74241i	−0.241644	−	0.175565i
$245$	−14.4104	+	3.66245i	−0.920648	+	0.233985i
$246$	3.67314	+	11.3048i	0.234191	+	0.720765i
$247$	2.41264	+	3.32071i	0.153513	+	0.211292i
$248$	−9.76431	−	13.4394i	−0.620035	−	0.853404i
$249$	3.23338	+	9.95131i	0.204907	+	0.630639i
$250$	8.80292	+	1.74624i	0.556745	+	0.110442i
$251$	−10.8575	−	7.88843i	−0.685319	−	0.497913i	0.189799	−	0.981823i	$-0.439216\pi$
$251$	−10.8575	−	7.88843i	−0.685319	−	0.497913i	−0.875118	+	0.483910i	$0.839216\pi$
$252$		−	0.0804405i		−	0.00506727i
$253$		0			0
$254$	12.8886			0.808704
$255$	1.81753	−	27.8042i	0.113818	−	1.74117i
$256$	−4.39092	+	13.5138i	−0.274432	+	0.844616i
$257$	10.2879	−	3.34275i	0.641743	−	0.208515i	0.0299732	−	0.999551i	$-0.490458\pi$
$257$	10.2879	−	3.34275i	0.641743	−	0.208515i	0.611770	+	0.791036i	$0.290458\pi$
$258$	−7.90815	−	10.8846i	−0.492340	−	0.677648i
$259$	−3.51479	+	2.55364i	−0.218398	+	0.158676i
$260$	4.18387	+	3.47846i	0.259472	+	0.215725i
$261$	−0.110724	+	0.340772i	−0.00685362	+	0.0210933i
$262$	−8.50662	+	11.7084i	−0.525540	+	0.723344i
$263$			24.6351i			1.51906i	0.650471	+	0.759531i	$0.274572\pi$
$263$			24.6351i			1.51906i	−0.650471	+	0.759531i	$0.725428\pi$
$264$		0			0
$265$	4.50584	−	2.84407i	0.276791	−	0.174710i
$266$	−0.879314	−	0.638859i	−0.0539142	−	0.0391709i
$267$	10.4053	+	3.38089i	0.636795	+	0.206907i
$268$	8.75659	−	2.84519i	0.534894	−	0.173797i
$269$	−3.88410	+	2.82196i	−0.236818	+	0.172058i	−0.699864	−	0.714276i	$-0.746756\pi$
$269$	−3.88410	+	2.82196i	−0.236818	+	0.172058i	0.463047	+	0.886334i	$0.346756\pi$
$270$	−8.51249	−	3.39442i	−0.518053	−	0.206578i
$271$	−7.20947	−	22.1885i	−0.437944	−	1.34785i	−0.890039	−	0.455884i	$-0.849323\pi$
$271$	−7.20947	−	22.1885i	−0.437944	−	1.34785i	0.452095	−	0.891970i	$-0.350677\pi$
$272$	3.69653	+	1.20108i	0.224135	+	0.0728259i
$273$	−1.09989	+	1.51387i	−0.0665684	+	0.0916236i
$274$	−3.23654			−0.195527
$275$		0			0
$276$	−3.55855			−0.214200
$277$	12.8709	−	17.7153i	0.773337	−	1.06441i	−0.222649	−	0.974899i	$-0.571470\pi$
$277$	12.8709	−	17.7153i	0.773337	−	1.06441i	0.995986	−	0.0895089i	$-0.0285297\pi$
$278$	6.05761	+	1.96824i	0.363312	+	0.118047i
$279$	−0.190983	−	0.587785i	−0.0114339	−	0.0351898i
$280$	−3.31262	−	1.32093i	−0.197967	−	0.0789409i
$281$	12.7626	−	9.27257i	0.761353	−	0.553155i	−0.137972	−	0.990436i	$-0.544058\pi$
$281$	12.7626	−	9.27257i	0.761353	−	0.553155i	0.899325	+	0.437281i	$0.144058\pi$
$282$	−2.59647	+	0.843646i	−0.154618	+	0.0502384i
$283$	21.5026	+	6.98661i	1.27819	+	0.415311i	0.867944	−	0.496662i	$-0.165441\pi$
$283$	21.5026	+	6.98661i	1.27819	+	0.415311i	0.410251	+	0.911973i	$0.365441\pi$
$284$	12.9347	+	9.39760i	0.767532	+	0.557645i
$285$	−7.61377	+	4.80578i	−0.451001	+	0.284670i
$286$		0			0
$287$		−	4.97971i		−	0.293943i
$288$	−0.343291	+	0.472500i	−0.0202286	+	0.0278423i
$289$	−10.2240	+	31.4662i	−0.601412	+	1.85096i
$290$	4.93484	+	4.10282i	0.289784	+	0.240926i
$291$	7.65754	−	5.56353i	0.448893	−	0.326140i
$292$	5.43668	+	7.48294i	0.318157	+	0.437906i
$293$	12.6106	−	4.09744i	0.736721	−	0.239375i	0.0834635	−	0.996511i	$-0.473402\pi$
$293$	12.6106	−	4.09744i	0.736721	−	0.239375i	0.653258	+	0.757136i	$0.273402\pi$
$294$	−2.90412	+	8.93795i	−0.169372	+	0.521272i
$295$	−0.00558312	+	0.0854094i	−0.000325062	+	0.00497273i
$296$	19.7641			1.14876
$297$		0			0
$298$			10.0344i			0.581280i
$299$	2.16480	+	1.57282i	0.125194	+	0.0909585i
$300$	−8.21248	+	8.66017i	−0.474148	+	0.499995i
$301$	1.74176	+	5.36058i	0.100393	+	0.308978i
$302$	3.96441	+	5.45655i	0.228126	+	0.313989i
$303$	−10.2783	−	14.1468i	−0.590472	−	0.812715i
$304$	−0.388106	−	1.19447i	−0.0222594	−	0.0685074i
$305$	−7.45849	+	1.89560i	−0.427072	+	0.108542i
$306$	−0.460562	−	0.334618i	−0.0263286	−	0.0191288i
$307$		−	10.0161i		−	0.571650i	−0.958282	−	0.285825i	$-0.907732\pi$
$307$		−	10.0161i		−	0.571650i	0.958282	−	0.285825i	$-0.0922676\pi$
$308$		0			0
$309$	−23.8076			−1.35437
$310$	−11.0459	−	0.722060i	−0.627367	−	0.0410103i
$311$	−1.05321	+	3.24145i	−0.0597220	+	0.183806i	−0.976467	−	0.215668i	$-0.930807\pi$
$311$	−1.05321	+	3.24145i	−0.0597220	+	0.183806i	0.916745	+	0.399474i	$0.130807\pi$
$312$	8.09603	−	2.63056i	0.458348	−	0.148926i
$313$	14.4012	+	19.8216i	0.814005	+	1.12038i	0.990693	+	0.136115i	$0.0434616\pi$
$313$	14.4012	+	19.8216i	0.814005	+	1.12038i	−0.176688	+	0.984267i	$0.556538\pi$
$314$	9.08888	−	6.60346i	0.512915	−	0.372655i
$315$	−0.102024	−	0.0848228i	−0.00574842	−	0.00477922i
$316$	1.89608	−	5.83555i	0.106663	−	0.328275i
$317$	4.10774	−	5.65382i	0.230714	−	0.317550i	−0.677927	−	0.735129i	$-0.737121\pi$
$317$	4.10774	−	5.65382i	0.230714	−	0.317550i	0.908641	+	0.417579i	$0.137121\pi$
$318$		−	3.36787i		−	0.188861i
$319$		0			0
$320$	4.27254	+	6.76895i	0.238842	+	0.378396i
$321$	−7.98330	−	5.80020i	−0.445584	−	0.323736i
$322$	−0.673874	−	0.218955i	−0.0375535	−	0.0122019i
$323$	15.3921	−	5.00121i	0.856441	−	0.278275i
$324$	10.1896	−	7.40317i	0.566088	−	0.411287i
$325$	8.82360	−	1.63853i	0.489445	−	0.0908894i
$326$	2.93725	+	9.03993i	0.162679	+	0.500675i
$327$	31.1471	+	10.1203i	1.72244	+	0.559654i
$328$	−13.3155	+	18.3272i	−0.735226	+	1.01195i
$329$	1.14374			0.0630563
$330$		0			0
$331$	5.64321			0.310179			0.155089	−	0.987900i	$-0.450433\pi$
$331$	5.64321			0.310179			0.155089	+	0.987900i	$0.450433\pi$
$332$	−4.73535	+	6.51765i	−0.259886	+	0.357703i
$333$	0.699314	+	0.227221i	0.0383221	+	0.0124516i
$334$	2.16453	+	6.66175i	0.118438	+	0.364515i
$335$	5.62502	−	14.1064i	0.307328	−	0.770713i
$336$	0.463215	−	0.336545i	0.0252704	−	0.0183600i
$337$	21.5094	−	6.98884i	1.17169	−	0.380706i	0.342419	−	0.939547i	$-0.388754\pi$
$337$	21.5094	−	6.98884i	1.17169	−	0.380706i	0.829275	+	0.558841i	$0.188754\pi$
$338$	7.46493	+	2.42550i	0.406039	+	0.131930i
$339$	−16.8107	−	12.2137i	−0.913033	−	0.663357i
$340$	18.1418	−	11.4510i	0.983876	−	0.621018i
$341$		0			0
$342$			0.183955i			0.00994713i
$343$	4.75040	−	6.53836i	0.256497	−	0.353038i
$344$	7.92360	−	24.3863i	0.427212	−	1.31482i
$345$	−3.75242	+	4.51339i	−0.202023	+	0.242993i
$346$	−5.96056	+	4.33060i	−0.320442	+	0.232815i
$347$	−0.107209	−	0.147560i	−0.00575527	−	0.00792145i	0.806130	−	0.591739i	$-0.201558\pi$
$347$	−0.107209	−	0.147560i	−0.00575527	−	0.00792145i	−0.811885	+	0.583817i	$0.801558\pi$
$348$	−8.11696	+	2.63736i	−0.435115	+	0.141377i
$349$	−4.76729	+	14.6722i	−0.255187	+	0.785385i	0.738606	+	0.674138i	$0.235485\pi$
$349$	−4.76729	+	14.6722i	−0.255187	+	0.785385i	−0.993793	+	0.111248i	$0.964515\pi$
$350$	−2.08803	+	1.13465i	−0.111610	+	0.0606495i
$351$	−9.16431			−0.489155
$352$		0			0
$353$			23.9103i			1.27262i	0.771435	+	0.636308i	$0.219539\pi$
$353$			23.9103i			1.27262i	−0.771435	+	0.636308i	$0.780461\pi$
$354$	0.0437676	+	0.0317990i	0.00232622	+	0.00169010i
$355$	25.5585	−	6.49577i	1.35651	−	0.344760i
$356$	2.60310	+	8.01152i	0.137964	+	0.424610i
$357$	4.33679	+	5.96907i	0.229527	+	0.315917i
$358$	0.683265	+	0.940433i	0.0361117	+	0.0497035i
$359$	−2.70926	−	8.33824i	−0.142989	−	0.440075i	0.853758	−	0.520670i	$-0.174318\pi$
$359$	−2.70926	−	8.33824i	−0.142989	−	0.440075i	−0.996747	+	0.0805950i	$0.974318\pi$
$360$	0.148676	+	0.584989i	0.00783594	+	0.0308316i
$361$	11.1405	+	8.09401i	0.586340	+	0.426001i
$362$			0.636943i			0.0334770i
$363$		0			0
$364$	−1.44076			−0.0755161
$365$	15.2236	+	0.995152i	0.796842	+	0.0520887i
$366$	−1.50310	+	4.62608i	−0.0785685	+	0.241809i
$367$	−5.11889	+	1.66323i	−0.267204	+	0.0868198i	−0.439555	−	0.898216i	$-0.644864\pi$
$367$	−5.11889	+	1.66323i	−0.267204	+	0.0868198i	0.172351	+	0.985036i	$0.444864\pi$
$368$	−0.481252	−	0.662387i	−0.0250870	−	0.0345293i
$369$	−0.681845	+	0.495390i	−0.0354954	+	0.0257890i
$370$	8.41957	−	10.1270i	0.437713	−	0.526478i
$371$	−0.436001	+	1.34187i	−0.0226360	+	0.0696665i
$372$	8.65287	−	11.9097i	0.448631	−	0.617487i
$373$		−	3.22450i		−	0.166958i	−0.996510	−	0.0834792i	$-0.973397\pi$
$373$		−	3.22450i		−	0.166958i	0.996510	−	0.0834792i	$-0.0266032\pi$
$374$		0			0
$375$	2.32400	+	19.5480i	0.120011	+	1.00946i
$376$	−4.20939	−	3.05830i	−0.217083	−	0.157720i
$377$	6.10351	+	1.98315i	0.314347	+	0.102138i
$378$	2.30791	−	0.749884i	0.118706	−	0.0385699i
$379$	−15.9080	+	11.5578i	−0.817139	+	0.593687i	−0.915892	−	0.401425i	$-0.868515\pi$
$379$	−15.9080	+	11.5578i	−0.817139	+	0.593687i	0.0987522	+	0.995112i	$0.468515\pi$
$380$	−6.43922	−	2.56769i	−0.330325	−	0.131720i
$381$	8.73639	+	26.8878i	0.447579	+	1.37751i
$382$	−6.22203	−	2.02166i	−0.318347	−	0.103437i
$383$	−16.4434	+	22.6323i	−0.840216	+	1.15646i	0.145718	+	0.989326i	$0.453451\pi$
$383$	−16.4434	+	22.6323i	−0.840216	+	1.15646i	−0.985934	+	0.167132i	$0.946549\pi$
$384$	−15.4639			−0.789139
$385$		0			0
$386$	3.50648			0.178475
$387$	0.560723	−	0.771769i	0.0285031	−	0.0392312i
$388$	6.93103	+	2.25203i	0.351870	+	0.114329i
$389$	−4.02958	−	12.4018i	−0.204308	−	0.628795i	−0.999741	−	0.0227539i	$-0.992757\pi$
$389$	−4.02958	−	12.4018i	−0.204308	−	0.628795i	0.795433	−	0.606041i	$-0.207243\pi$
$390$	2.10106	−	5.26900i	0.106391	−	0.266806i
$391$	8.53564	−	6.20151i	0.431666	−	0.313624i
$392$	−17.0342	+	5.53475i	−0.860358	+	0.279547i
$393$	−30.1917	−	9.80987i	−1.52297	−	0.494843i
$394$	−10.1647	−	7.38510i	−0.512091	−	0.372056i
$395$	−5.40197	−	8.55830i	−0.271803	−	0.430615i
$396$		0			0
$397$		−	1.82243i		−	0.0914651i	−0.998954	−	0.0457325i	$-0.985438\pi$
$397$		−	1.82243i		−	0.0914651i	0.998954	−	0.0457325i	$-0.0145622\pi$
$398$	−0.678612	+	0.934030i	−0.0340158	+	0.0468187i
$399$	0.736735	−	2.26744i	0.0368829	−	0.113514i
$400$	−2.72264	−	0.357479i	−0.136132	−	0.0178740i
$401$	−4.35320	+	3.16278i	−0.217388	+	0.157942i	−0.691150	−	0.722711i	$-0.742896\pi$
$401$	−4.35320	+	3.16278i	−0.217388	+	0.157942i	0.473762	+	0.880653i	$0.342896\pi$
$402$	−5.64209	−	7.76568i	−0.281402	−	0.387317i
$403$	−10.5277	+	3.42067i	−0.524423	+	0.170395i
$404$	4.16048	−	12.8047i	0.206992	−	0.637055i
$405$	1.35511	−	20.7302i	0.0673358	−	1.03009i
$406$	−1.69936			−0.0843379
$407$		0			0
$408$		−	33.5648i		−	1.66171i
$409$	29.6764	+	21.5612i	1.46740	+	1.06613i	0.981356	+	0.192201i	$0.0615624\pi$
$409$	29.6764	+	21.5612i	1.46740	+	1.06613i	0.486049	+	0.873931i	$0.338438\pi$
$410$	3.71832	+	14.6303i	0.183635	+	0.722537i
$411$	−2.19385	−	6.75197i	−0.108215	−	0.333050i
$412$	−10.7744	−	14.8297i	−0.530819	−	0.730609i
$413$	−0.0133218	−	0.0183359i	−0.000655522	−	0.000902249i
$414$	0.0370578	+	0.114052i	0.00182129	+	0.00560535i
$415$	3.27315	+	12.8787i	0.160673	+	0.632190i
$416$	8.46287	+	6.14863i	0.414926	+	0.301462i
$417$			13.9713i			0.684180i
$418$		0			0
$419$	−2.86630			−0.140028			−0.0700141	−	0.997546i	$-0.522304\pi$
$419$	−2.86630			−0.140028			−0.0700141	+	0.997546i	$0.522304\pi$
$420$	0.206148	−	3.15361i	0.0100590	−	0.153880i
$421$	1.43994	−	4.43169i	0.0701785	−	0.215987i	−0.909816	−	0.415012i	$-0.863777\pi$
$421$	1.43994	−	4.43169i	0.0701785	−	0.215987i	0.979994	+	0.199025i	$0.0637774\pi$
$422$	6.62741	−	2.15338i	0.322617	−	0.104825i
$423$	−0.113781	−	0.156606i	−0.00553222	−	0.00761445i
$424$	5.19275	−	3.77275i	0.252182	−	0.183221i
$425$	4.60655	−	35.0845i	0.223450	−	1.70185i
$426$	5.15079	−	15.8525i	0.249556	−	0.768056i
$427$	1.19777	−	1.64859i	0.0579642	−	0.0797809i
$428$		−	7.59774i		−	0.367250i
$429$		0			0
$430$	−9.11996	−	14.4487i	−0.439803	−	0.696778i
$431$	16.8026	+	12.2078i	0.809351	+	0.588028i	0.913642	−	0.406519i	$-0.133257\pi$
$431$	16.8026	+	12.2078i	0.809351	+	0.588028i	−0.104291	+	0.994547i	$0.533257\pi$
$432$	2.66686	+	0.866515i	0.128309	+	0.0416902i
$433$	−12.1708	+	3.95454i	−0.584893	+	0.190043i	−0.586491	−	0.809955i	$-0.699491\pi$
$433$	−12.1708	+	3.95454i	−0.584893	+	0.190043i	0.00159840	+	0.999999i	$0.499491\pi$
$434$	2.37136	−	1.72290i	0.113829	−	0.0827017i
$435$	−5.21414	+	13.0760i	−0.249999	+	0.626944i
$436$	7.79208	+	23.9815i	0.373173	+	1.14851i
$437$	−3.24239	−	1.05352i	−0.155104	−	0.0503965i
$438$	5.66796	−	7.80128i	0.270826	−	0.372759i
$439$	−10.6208			−0.506905			−0.253452	−	0.967348i	$-0.581566\pi$
$439$	−10.6208			−0.506905			−0.253452	+	0.967348i	$0.581566\pi$
$440$		0			0
$441$	−0.666354			−0.0317312
$442$	−5.99329	+	8.24906i	−0.285072	+	0.392368i
$443$	−6.27596	−	2.03918i	−0.298180	−	0.0968846i	0.156106	−	0.987740i	$-0.450106\pi$
$443$	−6.27596	−	2.03918i	−0.298180	−	0.0968846i	−0.454286	+	0.890856i	$0.650106\pi$
$444$	5.41224	+	16.6572i	0.256854	+	0.790514i
$445$	12.9061	+	5.14641i	0.611808	+	0.243963i
$446$	4.09512	−	2.97528i	0.193910	−	0.140884i
$447$	−20.9335	+	6.80172i	−0.990122	+	0.321710i
$448$	−2.01585	−	0.654988i	−0.0952397	−	0.0309453i
$449$	11.0253	+	8.01037i	0.520317	+	0.378033i	0.816723	−	0.577029i	$-0.195788\pi$
$449$	11.0253	+	8.01037i	0.520317	+	0.378033i	−0.296406	+	0.955062i	$0.595788\pi$
$450$	0.363082	+	0.173026i	0.0171159	+	0.00815654i
$451$		0			0
$452$		−	15.9988i		−	0.752522i
$453$	−8.69605	+	11.9691i	−0.408576	+	0.562356i
$454$	−0.277022	+	0.852586i	−0.0130013	+	0.0400138i
$455$	−1.51925	+	1.82734i	−0.0712234	+	0.0856671i
$456$	−8.77449	+	6.37504i	−0.410903	+	0.298539i
$457$	−7.93503	−	10.9216i	−0.371185	−	0.510893i	0.582037	−	0.813162i	$-0.302256\pi$
$457$	−7.93503	−	10.9216i	−0.371185	−	0.510893i	−0.953223	+	0.302269i	$0.902256\pi$
$458$	−3.20340	+	1.04085i	−0.149685	+	0.0486356i
$459$	−11.1661	+	34.3656i	−0.521188	+	1.60405i
$460$	−4.50959	−	0.294787i	−0.210261	−	0.0137445i
$461$	−11.3217			−0.527303			−0.263652	−	0.964618i	$-0.584927\pi$
$461$	−11.3217			−0.527303			−0.263652	+	0.964618i	$0.584927\pi$
$462$		0			0
$463$			4.82990i			0.224464i	0.993682	+	0.112232i	$0.0358001\pi$
$463$			4.82990i			0.224464i	−0.993682	+	0.112232i	$0.964200\pi$
$464$	−1.58864	−	1.15421i	−0.0737507	−	0.0535830i
$465$	−5.98100	−	23.5331i	−0.277362	−	1.09132i
$466$	1.68163	+	5.17553i	0.0779001	+	0.239752i
$467$	−14.1170	−	19.4304i	−0.653257	−	0.899131i	0.345978	−	0.938243i	$-0.387547\pi$
$467$	−14.1170	−	19.4304i	−0.653257	−	0.899131i	−0.999235	+	0.0391117i	$0.987547\pi$
$468$	0.143329	+	0.197275i	0.00662538	+	0.00911905i
$469$	1.24266	+	3.82452i	0.0573808	+	0.176600i
$470$	−3.36028	+	0.854023i	−0.154998	+	0.0393932i
$471$	19.9367	+	14.4849i	0.918635	+	0.667427i
$472$			0.103105i			0.00474579i
$473$		0			0
$474$	−6.39688			−0.293818
$475$	−10.0467	+	5.45943i	−0.460973	+	0.250496i
$476$	−1.75546	+	5.40276i	−0.0804615	+	0.247635i
$477$	0.227110	−	0.0737924i	0.0103986	−	0.00337872i
$478$	−2.07508	−	2.85610i	−0.0949119	−	0.130635i
$479$	−34.9698	+	25.4070i	−1.59781	+	1.16088i	−0.706264	+	0.707949i	$0.749621\pi$
$479$	−34.9698	+	25.4070i	−1.59781	+	1.16088i	−0.891547	+	0.452929i	$0.850379\pi$
$480$	−14.6694	+	17.6442i	−0.669562	+	0.805345i
$481$	4.06971	−	12.5253i	0.185563	−	0.571104i
$482$	4.53517	−	6.24212i	0.206571	−	0.284321i
$483$		−	1.55423i		−	0.0707199i
$484$		0			0
$485$	10.1649	−	6.41606i	0.461565	−	0.291338i
$486$	−0.676027	−	0.491163i	−0.0306652	−	0.0222796i
$487$	−39.9072	−	12.9666i	−1.80837	−	0.587574i	−0.808367	−	0.588678i	$-0.799648\pi$
$487$	−39.9072	−	12.9666i	−1.80837	−	0.587574i	−0.999999	+	0.00110438i	$0.999648\pi$
$488$	−8.81651	+	2.86466i	−0.399105	+	0.129677i
$489$	−16.8678	+	12.2552i	−0.762790	+	0.554199i
$490$	−4.42066	+	11.0861i	−0.199705	+	0.500818i
$491$	2.79964	+	8.61641i	0.126346	+	0.388853i	0.994144	−	0.108064i	$-0.0344652\pi$
$491$	2.79964	+	8.61641i	0.126346	+	0.388853i	−0.867798	+	0.496917i	$0.834465\pi$
$492$	−19.0925	−	6.20354i	−0.860758	−	0.279677i
$493$	14.8734	−	20.4715i	0.669865	−	0.921990i
$494$	3.29478			0.148239
$495$		0			0
$496$	3.38705			0.152083
$497$	−4.10449	+	5.64934i	−0.184111	+	0.253408i
$498$	7.98791	+	2.59543i	0.357947	+	0.116304i
$499$	−9.35682	−	28.7973i	−0.418869	−	1.28915i	−0.908744	−	0.417353i	$-0.862958\pi$
$499$	−9.35682	−	28.7973i	−0.418869	−	1.28915i	0.489875	−	0.871792i	$-0.337042\pi$
$500$	−11.1247	+	10.2943i	−0.497511	+	0.460376i
$501$	−12.4303	+	9.03116i	−0.555346	+	0.403483i
$502$	−10.2454	+	3.32895i	−0.457277	+	0.148578i
$503$	17.1797	+	5.58203i	0.766006	+	0.248890i	0.665854	−	0.746082i	$-0.268067\pi$
$503$	17.1797	+	5.58203i	0.766006	+	0.248890i	0.100152	+	0.994972i	$0.468067\pi$
$504$	−0.129303	−	0.0939443i	−0.00575962	−	0.00418461i
$505$	−11.8533	−	18.7791i	−0.527464	−	0.835658i
$506$		0			0
$507$			17.2172i			0.764642i
$508$	−12.7946	+	17.6103i	−0.567670	+	0.781331i
$509$	7.69937	−	23.6962i	0.341269	−	1.05032i	−0.622282	−	0.782793i	$-0.713794\pi$
$509$	7.69937	−	23.6962i	0.341269	−	1.05032i	0.963551	−	0.267524i	$-0.0862056\pi$
$510$	−17.1985	−	14.2988i	−0.761561	−	0.633159i
$511$	−3.26824	+	2.37452i	−0.144579	+	0.105043i
$512$	−3.62042	−	4.98307i	−0.160001	−	0.220223i
$513$	11.1046	−	3.60811i	0.490282	−	0.159302i
$514$	2.68322	−	8.25811i	0.118352	−	0.364249i
$515$	−30.1703	−	1.97220i	−1.32946	−	0.0869055i
$516$	22.7226			1.00031
$517$		0			0
$518$			3.48734i			0.153225i
$519$	−13.0747	−	9.49929i	−0.573914	−	0.416973i
$520$	10.4776	−	2.66292i	0.459475	−	0.116777i
$521$	11.2121	+	34.5073i	0.491211	+	1.51179i	0.822779	+	0.568362i	$0.192422\pi$
$521$	11.2121	+	34.5073i	0.491211	+	1.51179i	−0.331568	+	0.943431i	$0.607578\pi$
$522$	0.169055	+	0.232685i	0.00739936	+	0.0101843i
$523$	14.5224	+	19.9884i	0.635021	+	0.874032i	0.998338	−	0.0576339i	$-0.0183556\pi$
$523$	14.5224	+	19.9884i	0.635021	+	0.874032i	−0.363316	+	0.931666i	$0.618356\pi$
$524$	−7.55306	−	23.2459i	−0.329957	−	1.01550i
$525$	−3.78241	−	3.58687i	−0.165078	−	0.156544i
$526$	15.9979	+	11.6232i	0.697543	+	0.506795i
$527$			43.6462i			1.90126i
$528$		0			0
$529$	20.7775			0.903369
$530$	0.278991	−	4.26795i	0.0121186	−	0.185388i
$531$	−0.00118536	+	0.00364817i	−5.14403e−5	+	0.000158317i
$532$	1.74580	−	0.567246i	0.0756901	−	0.0245932i
$533$	8.87284	+	12.2124i	0.384325	+	0.528979i
$534$	7.10493	−	5.16203i	0.307460	−	0.223383i
$535$	−9.63638	−	8.01165i	−0.416617	−	0.346374i
$536$	5.65312	−	17.3985i	0.244177	−	0.751501i
$537$	−1.49876	+	2.06287i	−0.0646763	+	0.0890193i
$538$			3.85376i			0.166148i
$539$		0			0
$540$	13.0884	−	8.26132i	0.563233	−	0.355511i
$541$	−10.1467	−	7.37198i	−0.436239	−	0.316946i	0.347900	−	0.937532i	$-0.386895\pi$
$541$	−10.1467	−	7.37198i	−0.436239	−	0.316946i	−0.784139	+	0.620586i	$0.786895\pi$
$542$	−17.8107	−	5.78704i	−0.765034	−	0.248574i
$543$	−1.32877	+	0.431744i	−0.0570230	+	0.0185279i
$544$	33.3685	−	24.2436i	1.43066	−	1.03944i
$545$	38.6329	+	15.4052i	1.65485	+	0.659885i
$546$	0.464158	+	1.42853i	0.0198641	+	0.0611355i
$547$	−29.2361	−	9.49940i	−1.25005	−	0.406165i	−0.392110	−	0.919919i	$-0.628255\pi$
$547$	−29.2361	−	9.49940i	−1.25005	−	0.406165i	−0.857938	+	0.513754i	$0.828255\pi$
$548$	3.21294	−	4.42223i	0.137250	−	0.188908i
$549$	−0.344889			−0.0147195
$550$		0			0
$551$	−8.17659			−0.348334
$552$	−4.15594	+	5.72016i	−0.176889	+	0.243466i
$553$	2.54873	+	0.828132i	0.108383	+	0.0352157i
$554$	−5.43157	−	16.7167i	−0.230765	−	0.710222i
$555$	26.8337	+	10.7002i	1.13903	+	0.454197i
$556$	−8.70273	+	6.32290i	−0.369078	+	0.268151i
$557$	12.7721	−	4.14990i	0.541171	−	0.175837i	−0.0256608	−	0.999671i	$-0.508169\pi$
$557$	12.7721	−	4.14990i	0.541171	−	0.175837i	0.566832	+	0.823834i	$0.308169\pi$
$558$	−0.471815	−	0.153302i	−0.0199735	−	0.00648979i
$559$	−13.8230	−	10.0430i	−0.584652	−	0.424774i
$560$	0.614889	−	0.388116i	0.0259838	−	0.0164009i
$561$		0			0
$562$		−	12.6629i		−	0.534154i
$563$	17.9510	−	24.7075i	0.756546	−	1.04130i	−0.240948	−	0.970538i	$-0.577458\pi$
$563$	17.9510	−	24.7075i	0.756546	−	1.04130i	0.997494	−	0.0707576i	$-0.0225417\pi$
$564$	1.42483	−	4.38517i	0.0599961	−	0.184649i
$565$	−20.2917	−	16.8704i	−0.853677	−	0.709745i
$566$	14.6823	−	10.6673i	0.617143	−	0.448381i
$567$	3.23340	+	4.45039i	0.135790	+	0.186899i
$568$	30.2122	−	9.81652i	1.26767	−	0.411892i
$569$	7.94804	−	24.4616i	0.333199	−	1.02548i	−0.634403	−	0.773003i	$-0.718754\pi$
$569$	7.94804	−	24.4616i	0.333199	−	1.02548i	0.967602	−	0.252479i	$-0.0812460\pi$
$570$	−0.471427	+	7.21180i	−0.0197459	+	0.302069i
$571$	27.1115			1.13458			0.567291	−	0.823518i	$-0.307992\pi$
$571$	27.1115			1.13458			0.567291	+	0.823518i	$0.307992\pi$
$572$		0			0
$573$		−	14.3506i		−	0.599504i
$574$	−3.23381	−	2.34950i	−0.134977	−	0.0980662i
$575$	−5.12915	+	5.40876i	−0.213900	+	0.225561i
$576$	0.110856	+	0.341178i	0.00461898	+	0.0142158i
$577$	−1.68703	−	2.32200i	−0.0702321	−	0.0966662i	0.772456	−	0.635068i	$-0.219028\pi$
$577$	−1.68703	−	2.32200i	−0.0702321	−	0.0966662i	−0.842688	+	0.538402i	$0.819028\pi$
$578$	15.6103	+	21.4857i	0.649301	+	0.893686i
$579$	2.37682	+	7.31511i	0.0987773	+	0.304005i
$580$	−10.5047	+	2.66980i	−0.436185	+	0.110858i
$581$	−2.84664	−	2.06821i	−0.118099	−	0.0858037i
$582$		−	7.59774i		−	0.314936i
$583$		0			0
$584$	18.3777			0.760476
$585$	0.401346	+	0.0262355i	0.0165936	+	0.00108471i
$586$	3.28901	−	10.1225i	0.135868	−	0.418159i
$587$	−42.6416	+	13.8551i	−1.76001	+	0.571860i	−0.997201	−	0.0747690i	$-0.976178\pi$
$587$	−42.6416	+	13.8551i	−1.76001	+	0.571860i	−0.762804	+	0.646629i	$0.776178\pi$
$588$	−9.32939	−	12.8408i	−0.384737	−	0.529546i
$589$	11.4100	−	8.28982i	0.470139	−	0.341576i
$590$	0.0528304	+	0.0439231i	0.00217499	+	0.00180828i
$591$	8.51654	−	26.2112i	0.350324	−	1.07819i
$592$	−2.36861	+	3.26012i	−0.0973494	+	0.133990i
$593$		−	6.09322i		−	0.250219i	−0.992143	−	0.125109i	$-0.960072\pi$
$593$		−	6.09322i		−	0.250219i	0.992143	−	0.125109i	$-0.0399282\pi$
$594$		0			0
$595$	5.00133	+	7.92358i	0.205035	+	0.324835i
$596$	−13.7105	−	9.96127i	−0.561604	−	0.408029i
$597$	−2.40853	−	0.782579i	−0.0985746	−	0.0320288i
$598$	2.04277	−	0.663736i	0.0835350	−	0.0271422i
$599$	−10.4636	+	7.60225i	−0.427531	+	0.310619i	−0.780661	−	0.624955i	$-0.785117\pi$
$599$	−10.4636	+	7.60225i	−0.427531	+	0.310619i	0.353130	+	0.935574i	$0.385117\pi$
$600$	4.32958	+	23.3151i	0.176754	+	0.951833i
$601$	3.41374	+	10.5064i	0.139249	+	0.428566i	0.996227	−	0.0867885i	$-0.0276604\pi$
$601$	3.41374	+	10.5064i	0.139249	+	0.428566i	−0.856977	+	0.515354i	$0.827660\pi$
$602$	4.30293	+	1.39811i	0.175374	+	0.0569826i
$603$	0.400049	−	0.550621i	0.0162913	−	0.0224230i
$604$	−11.3910			−0.463494
$605$		0			0
$606$	−14.0364			−0.570188
$607$	−0.0681317	+	0.0937752i	−0.00276538	+	0.00380622i	−0.810397	−	0.585881i	$-0.800749\pi$
$607$	−0.0681317	+	0.0937752i	−0.00276538	+	0.00380622i	0.807632	+	0.589687i	$0.200749\pi$
$608$	−12.6755	−	4.11852i	−0.514059	−	0.167028i
$609$	−1.15189	−	3.54516i	−0.0466770	−	0.143657i
$610$	−2.28803	+	5.73789i	−0.0926397	+	0.232321i
$611$	−2.80495	+	2.03791i	−0.113476	+	0.0824451i
$612$	0.914408	−	0.297109i	0.0369627	−	0.0120099i
$613$	−18.1124	−	5.88509i	−0.731554	−	0.237696i	−0.0805288	−	0.996752i	$-0.525661\pi$
$613$	−18.1124	−	5.88509i	−0.731554	−	0.237696i	−0.651025	+	0.759056i	$0.725661\pi$
$614$	−6.50444	−	4.72575i	−0.262498	−	0.190716i
$615$	−28.0008	+	17.6740i	−1.12910	+	0.712684i
$616$		0			0
$617$			30.8894i			1.24356i	0.783192	+	0.621780i	$0.213590\pi$
$617$			30.8894i			1.24356i	−0.783192	+	0.621780i	$0.786410\pi$
$618$	−11.2328	+	15.4606i	−0.451849	+	0.621917i
$619$	−10.3736	+	31.9266i	−0.416950	+	1.28324i	0.493545	+	0.869720i	$0.335701\pi$
$619$	−10.3736	+	31.9266i	−0.416950	+	1.28324i	−0.910495	+	0.413520i	$0.864299\pi$
$620$	11.9520	−	14.3758i	0.480002	−	0.577344i
$621$	6.15803	−	4.47407i	0.247113	−	0.179538i
$622$	1.60807	+	2.21331i	0.0644776	+	0.0887458i
$623$	−3.49911	+	1.13693i	−0.140189	+	0.0455501i
$624$	−0.536349	+	1.65071i	−0.0214711	+	0.0660814i
$625$	1.32576	+	24.9648i	0.0530304	+	0.998593i
$626$	19.6668			0.786043
$627$		0			0
$628$			18.9738i			0.757139i
$629$	−42.0105	−	30.5224i	−1.67507	−	1.21701i
$630$	−0.103220	+	0.0262337i	−0.00411239	+	0.00104518i
$631$	7.61952	+	23.4505i	0.303328	+	0.933548i	0.980296	+	0.197535i	$0.0632937\pi$
$631$	7.61952	+	23.4505i	0.303328	+	0.933548i	−0.676968	+	0.736013i	$0.736706\pi$
$632$	−7.16590	−	9.86302i	−0.285044	−	0.392330i
$633$	8.98461	+	12.3663i	0.357106	+	0.491515i
$634$	−1.73348	−	5.33511i	−0.0688454	−	0.211884i
$635$	8.84386	+	34.7974i	0.350958	+	1.38089i
$636$	4.60168	+	3.34331i	0.182468	+	0.132571i
$637$			11.9350i			0.472880i
$638$		0			0
$639$	1.18186			0.0467535
$640$	−19.5967	−	1.28101i	−0.774627	−	0.0506365i
$641$	2.16821	−	6.67306i	0.0856390	−	0.263570i	−0.899062	−	0.437821i	$-0.855750\pi$
$641$	2.16821	−	6.67306i	0.0856390	−	0.263570i	0.984701	+	0.174251i	$0.0557504\pi$
$642$	−7.53327	+	2.44771i	−0.297315	+	0.0966034i
$643$	7.20185	+	9.91249i	0.284013	+	0.390910i	0.927058	−	0.374918i	$-0.122329\pi$
$643$	7.20185	+	9.91249i	0.284013	+	0.390910i	−0.643045	+	0.765828i	$0.722329\pi$
$644$	0.968128	−	0.703386i	0.0381496	−	0.0277173i
$645$	23.9606	−	28.8196i	0.943446	−	1.13477i
$646$	4.01446	−	12.3552i	0.157947	−	0.486111i
$647$	3.59733	−	4.95130i	0.141426	−	0.194656i	−0.732428	−	0.680844i	$-0.761613\pi$
$647$	3.59733	−	4.95130i	0.141426	−	0.194656i	0.873854	+	0.486188i	$0.161613\pi$
$648$		−	25.0251i		−	0.983079i
$649$		0			0
$650$	3.09905	−	6.50310i	0.121555	−	0.255073i
$651$	5.20165	+	3.77922i	0.203869	+	0.148119i
$652$	−15.2675	−	4.96071i	−0.597921	−	0.194276i
$653$	−36.1702	+	11.7524i	−1.41545	+	0.459907i	−0.914153	−	0.405370i	$-0.867143\pi$
$653$	−36.1702	+	11.7524i	−1.41545	+	0.459907i	−0.501295	+	0.865277i	$0.667143\pi$
$654$	21.2678	−	15.4519i	0.831635	−	0.604218i
$655$	−37.4479	−	14.9326i	−1.46321	−	0.583467i
$656$	−1.42732	−	4.39283i	−0.0557274	−	0.171511i
$657$	0.650261	+	0.211283i	0.0253691	+	0.00824292i
$658$	0.539632	−	0.742740i	0.0210371	−	0.0289550i
$659$	15.7879			0.615011			0.307505	−	0.951546i	$-0.400506\pi$
$659$	15.7879			0.615011			0.307505	+	0.951546i	$0.400506\pi$
$660$		0			0
$661$	−24.5794			−0.956027			−0.478014	−	0.878352i	$-0.658643\pi$
$661$	−24.5794			−0.956027			−0.478014	+	0.878352i	$0.658643\pi$
$662$	2.66255	−	3.66468i	0.103483	−	0.142432i
$663$	−21.2714	−	6.91150i	−0.826113	−	0.268420i
$664$	4.94644	+	15.2236i	0.191959	+	0.590790i
$665$	1.12146	−	2.81239i	0.0434884	−	0.109060i
$666$	0.477503	−	0.346926i	0.0185029	−	0.0134431i
$667$	−5.06949	+	1.64718i	−0.196292	+	0.0637790i
$668$	−11.2510	−	3.65567i	−0.435314	−	0.141442i
$669$	8.98277	+	6.52636i	0.347294	+	0.252324i
$670$	−6.50666	−	10.3085i	−0.251374	−	0.398251i
$671$		0			0
$672$		−	6.07597i		−	0.234385i
$673$	17.6179	−	24.2489i	0.679119	−	0.934727i	−0.320804	−	0.947146i	$-0.603953\pi$
$673$	17.6179	−	24.2489i	0.679119	−	0.934727i	0.999923	+	0.0124187i	$0.00395310\pi$
$674$	5.60993	−	17.2656i	0.216087	−	0.665046i
$675$	3.32339	−	25.3116i	0.127917	−	0.974246i
$676$	−10.7246	+	7.79185i	−0.412483	+	0.299687i
$677$	2.20836	+	3.03955i	0.0848744	+	0.116820i	0.849343	−	0.527842i	$-0.176999\pi$
$677$	2.20836	+	3.03955i	0.0848744	+	0.116820i	−0.764469	+	0.644661i	$0.776999\pi$
$678$	−15.8631	+	5.15423i	−0.609218	+	0.197947i
$679$	−0.983593	+	3.02719i	−0.0377468	+	0.116173i
$680$	2.78047	−	42.5351i	0.106626	−	1.63115i
$681$	−1.96641			−0.0753531
$682$		0			0
$683$		−	21.0157i		−	0.804144i	−0.915608	−	0.402072i	$-0.868290\pi$
$683$		−	21.0157i		−	0.804144i	0.915608	−	0.402072i	$-0.131710\pi$
$684$	−0.251345	−	0.182613i	−0.00961043	−	0.00698239i
$685$	−2.22084	−	8.73819i	−0.0848538	−	0.333869i
$686$	−2.00469	−	6.16979i	−0.0765393	−	0.235564i
$687$	−4.34277	−	5.97731i	−0.165687	−	0.228049i
$688$	3.07297	+	4.22958i	0.117156	+	0.161251i
$689$	−1.32168	−	4.06772i	−0.0503521	−	0.154968i
$690$	1.16054	+	4.56629i	0.0441808	+	0.173836i
$691$	30.9712	+	22.5019i	1.17820	+	0.856012i	0.991967	−	0.126494i	$-0.0403723\pi$
$691$	30.9712	+	22.5019i	1.17820	+	0.856012i	0.186232	+	0.982506i	$0.440372\pi$
$692$		−	12.4432i		−	0.473020i
$693$		0			0
$694$	−0.146408			−0.00555757
$695$	−1.15737	+	17.7052i	−0.0439016	+	0.671598i
$696$	−5.24018	+	16.1276i	−0.198629	+	0.611316i
$697$	56.6069	−	18.3927i	2.14414	−	0.696672i
$698$	7.27881	+	10.0184i	0.275507	+	0.379203i
$699$	−9.65715	+	7.01633i	−0.365267	+	0.265382i
$700$	0.522483	−	3.97934i	0.0197480	−	0.150405i
$701$	10.5790	−	32.5589i	0.399564	−	1.22973i	−0.525785	−	0.850617i	$-0.676228\pi$
$701$	10.5790	−	32.5589i	0.399564	−	1.22973i	0.925350	−	0.379115i	$-0.123772\pi$
$702$	−4.32385	+	5.95127i	−0.163193	+	0.224616i
$703$			16.7795i			0.632852i
$704$		0			0
$705$	−4.05936	−	6.43121i	−0.152884	−	0.242214i
$706$	15.5273	+	11.2812i	0.584376	+	0.424574i
$707$	5.59255	+	1.81713i	0.210329	+	0.0683402i
$708$	−0.0868968	+	0.0282345i	−0.00326578	+	0.00106112i
$709$	−3.33701	+	2.42448i	−0.125324	+	0.0910533i	−0.648682	−	0.761060i	$-0.724679\pi$
$709$	−3.33701	+	2.42448i	−0.125324	+	0.0910533i	0.523357	+	0.852113i	$0.324679\pi$
$710$	7.84055	−	19.6624i	0.294251	−	0.737918i
$711$	−0.140160	−	0.431368i	−0.00525641	−	0.0161776i
$712$	15.9181	+	5.17212i	0.596558	+	0.193833i
$713$	5.40420	−	7.43824i	0.202389	−	0.278564i
$714$	5.92246			0.221642
$715$		0			0
$716$	−1.96324			−0.0733697
$717$	4.55174	−	6.26494i	0.169988	−	0.233968i
$718$	−6.69310	−	2.17472i	−0.249784	−	0.0811598i
$719$	−9.07260	−	27.9226i	−0.338351	−	1.04134i	−0.965048	−	0.262074i	$-0.915594\pi$
$719$	−9.07260	−	27.9226i	−0.338351	−	1.04134i	0.626697	−	0.779263i	$-0.284406\pi$
$720$	−0.114313	−	0.0455832i	−0.00426019	−	0.00169879i
$721$	6.47703	−	4.70584i	0.241217	−	0.175255i
$722$	10.5125	−	3.41570i	0.391233	−	0.127119i
$723$	16.0962	+	5.22998i	0.598625	+	0.194505i
$724$	−0.870284	−	0.632299i	−0.0323439	−	0.0234992i
$725$	−7.69084	+	16.1386i	−0.285630	+	0.599373i
$726$		0			0
$727$		−	44.0893i		−	1.63518i	−0.575799	−	0.817591i	$-0.695309\pi$
$727$		−	44.0893i		−	1.63518i	0.575799	−	0.817591i	$-0.304691\pi$
$728$	−1.68262	+	2.31593i	−0.0623621	+	0.0858340i
$729$	−8.04644	+	24.7644i	−0.298016	+	0.917200i
$730$	7.82899	−	9.41666i	0.289764	−	0.348526i
$731$	−54.5032	+	39.5989i	−2.01587	+	1.46462i
$732$	−4.82867	−	6.64610i	−0.178473	−	0.245647i
$733$	−46.5533	+	15.1261i	−1.71948	+	0.558694i	−0.991866	−	0.127287i	$-0.959373\pi$
$733$	−46.5533	+	15.1261i	−1.71948	+	0.558694i	−0.727619	+	0.685982i	$0.759373\pi$
$734$	−1.33507	+	4.10893i	−0.0492784	+	0.151663i
$735$	−26.1239	−	1.70769i	−0.963595	−	0.0629891i
$736$	−8.68849			−0.320262
$737$		0			0
$738$			0.676520i			0.0249031i
$739$	16.7161	+	12.1450i	0.614911	+	0.446759i	0.851140	−	0.524938i	$-0.175912\pi$
$739$	16.7161	+	12.1450i	0.614911	+	0.446759i	−0.236229	+	0.971697i	$0.575912\pi$
$740$	5.47882	+	21.5572i	0.201405	+	0.792458i
$741$	2.23332	+	6.87347i	0.0820432	+	0.252503i
$742$	0.665696	+	0.916252i	0.0244385	+	0.0336367i
$743$	−17.7294	−	24.4025i	−0.650429	−	0.895239i	0.348688	−	0.937239i	$-0.386627\pi$
$743$	−17.7294	−	24.4025i	−0.650429	−	0.895239i	−0.999118	+	0.0419994i	$0.986627\pi$
$744$	−9.03860	−	27.8179i	−0.331371	−	1.01986i
$745$	−27.0915	+	6.88539i	−0.992557	+	0.252261i
$746$	−2.09398	−	1.52137i	−0.0766661	−	0.0557012i
$747$			0.595525i			0.0217891i
$748$		0			0
$749$	3.31838			0.121251
$750$	13.7909	+	7.71385i	0.503574	+	0.281670i
$751$	3.73806	−	11.5046i	0.136404	−	0.419808i	−0.859402	−	0.511301i	$-0.829164\pi$
$751$	3.73806	−	11.5046i	0.136404	−	0.419808i	0.995806	+	0.0914930i	$0.0291639\pi$
$752$	1.00894	−	0.327826i	0.0367924	−	0.0119546i
$753$	−13.8895	−	19.1172i	−0.506161	−	0.696671i
$754$	4.16758	−	3.02792i	0.151774	−	0.110271i
$755$	−12.0116	+	14.4475i	−0.437147	+	0.525798i
$756$	−1.26648	+	3.89781i	−0.0460613	+	0.141762i
$757$	12.1143	−	16.6739i	0.440302	−	0.606023i	−0.529977	−	0.848012i	$-0.677800\pi$
$757$	12.1143	−	16.6739i	0.440302	−	0.606023i	0.970279	+	0.241988i	$0.0777996\pi$
$758$			15.7838i			0.573293i
$759$		0			0
$760$	−11.6476	+	7.35192i	−0.422503	+	0.266682i
$761$	16.8640	+	12.2524i	0.611319	+	0.444149i	0.849878	−	0.526979i	$-0.176675\pi$
$761$	16.8640	+	12.2524i	0.611319	+	0.444149i	−0.238560	+	0.971128i	$0.576675\pi$
$762$	21.5828	+	7.01269i	0.781864	+	0.254043i
$763$	−10.4742	+	3.40326i	−0.379190	+	0.123206i
$764$	8.93895	−	6.49452i	0.323400	−	0.234964i
$765$	0.587394	−	1.47306i	0.0212373	−	0.0532585i
$766$	6.93916	+	21.3565i	0.250722	+	0.771643i
$767$	0.0653417	+	0.0212308i	0.00235935	+	0.000766600i
$768$	−14.7057	+	20.2407i	−0.530648	+	0.730374i
$769$	10.7167			0.386455			0.193228	−	0.981154i	$-0.438104\pi$
$769$	10.7167			0.386455			0.193228	+	0.981154i	$0.438104\pi$
$770$		0			0
$771$	19.0466			0.685946
$772$	−3.48091	+	4.79106i	−0.125281	+	0.172434i
$773$	19.3600	+	6.29043i	0.696329	+	0.226251i	0.635731	−	0.771911i	$-0.280699\pi$
$773$	19.3600	+	6.29043i	0.696329	+	0.226251i	0.0605989	+	0.998162i	$0.480699\pi$
$774$	−0.236627	−	0.728264i	−0.00850539	−	0.0261769i
$775$	−5.62999	−	30.3179i	−0.202235	−	1.08905i
$776$	11.7146	−	8.51113i	0.420528	−	0.305532i
$777$	−7.27517	+	2.36385i	−0.260995	+	0.0848025i
$778$	−9.95490	−	3.23454i	−0.356900	−	0.115964i
$779$	−15.5597	−	11.3048i	−0.557483	−	0.405035i
$780$	5.11353	+	8.10134i	0.183094	+	0.290074i
$781$		0			0
$782$		−	8.46898i		−	0.302850i
$783$	10.7304	−	14.7691i	0.383474	−	0.527806i
$784$	1.12849	−	3.47313i	0.0403032	−	0.124040i
$785$	24.0649	+	20.0075i	0.858915	+	0.714099i
$786$	−20.6154	+	14.9780i	−0.735326	+	0.534246i
$787$	8.35961	+	11.5060i	0.297988	+	0.410145i	0.931588	−	0.363516i	$-0.118424\pi$
$787$	8.35961	+	11.5060i	0.297988	+	0.410145i	−0.633600	+	0.773661i	$0.718424\pi$
$788$	20.1812	−	6.55727i	0.718925	−	0.233593i
$789$	−13.4039	+	41.2530i	−0.477192	+	1.46865i
$790$	−8.10647	−	0.529911i	−0.288415	−	0.0188534i
$791$	6.98764			0.248452
$792$		0			0
$793$			6.17726i			0.219361i
$794$	−1.18348	−	0.859849i	−0.0420001	−	0.0305149i
$795$	9.09277	−	2.31095i	0.322487	−	0.0819610i
$796$	−0.602543	−	1.85444i	−0.0213566	−	0.0657288i
$797$	26.4729	+	36.4368i	0.937719	+	1.29066i	0.956772	+	0.290841i	$0.0939349\pi$
$797$	26.4729	+	36.4368i	0.937719	+	1.29066i	−0.0190529	+	0.999818i	$0.506065\pi$
$798$	−1.12487	−	1.54824i	−0.0398198	−	0.0548073i
$799$	4.22443	+	13.0015i	0.149450	+	0.459958i
$800$	−20.0514	+	21.1445i	−0.708925	+	0.747571i
$801$	0.503771	+	0.366011i	0.0177999	+	0.0129324i
$802$			4.31920i			0.152516i
$803$		0			0
$804$	16.2115			0.571737
$805$	0.128751	−	1.96960i	0.00453787	−	0.0694194i
$806$	−2.74576	+	8.45060i	−0.0967154	+	0.297660i
$807$	−8.03960	+	2.61223i	−0.283007	+	0.0919547i
$808$	−15.7238	−	21.6419i	−0.553161	−	0.761361i
$809$	−19.2346	+	13.9748i	−0.676254	+	0.491327i	−0.872113	−	0.489305i	$-0.837251\pi$
$809$	−19.2346	+	13.9748i	−0.676254	+	0.491327i	0.195859	+	0.980632i	$0.437251\pi$
$810$	−12.8227	−	10.6608i	−0.450545	−	0.374582i
$811$	2.53354	−	7.79742i	0.0889645	−	0.273804i	−0.896669	−	0.442701i	$-0.854020\pi$
$811$	2.53354	−	7.79742i	0.0889645	−	0.273804i	0.985634	+	0.168896i	$0.0540204\pi$
$812$	1.68697	−	2.32192i	0.0592010	−	0.0814832i
$813$		−	41.0787i		−	1.44069i
$814$		0			0
$815$	−22.3910	+	14.1331i	−0.784323	+	0.495062i
$816$	5.53658	+	4.02256i	0.193819	+	0.140818i
$817$	20.7038	+	6.72707i	0.724334	+	0.235351i
$818$	28.0035	−	9.09890i	0.979121	−	0.318136i
$819$	−0.0861618	+	0.0626002i	−0.00301074	+	0.00218743i
$820$	−23.6812	−	9.44307i	−0.826983	−	0.329766i
$821$	13.4229	+	41.3113i	0.468461	+	1.44177i	0.854577	+	0.519324i	$0.173816\pi$
$821$	13.4229	+	41.3113i	0.468461	+	1.44177i	−0.386116	+	0.922450i	$0.626184\pi$
$822$	−5.41980	−	1.76100i	−0.189037	−	0.0614219i
$823$	30.3768	−	41.8101i	1.05887	−	1.45741i	0.178009	−	0.984029i	$-0.443034\pi$
$823$	30.3768	−	41.8101i	1.05887	−	1.45741i	0.880859	−	0.473378i	$-0.156966\pi$
$824$	−36.4211			−1.26879
$825$		0			0
$826$	−0.0181927			−0.000633004
$827$	−14.8756	+	20.4745i	−0.517276	+	0.711969i	−0.985125	−	0.171839i	$-0.945029\pi$
$827$	−14.8756	+	20.4745i	−0.517276	+	0.711969i	0.467849	+	0.883808i	$0.345029\pi$
$828$	−0.192622	−	0.0625867i	−0.00669408	−	0.00217504i
$829$	12.9404	+	39.8264i	0.449439	+	1.38323i	0.877542	+	0.479500i	$0.159182\pi$
$829$	12.9404	+	39.8264i	0.449439	+	1.38323i	−0.428103	+	0.903730i	$0.640818\pi$
$830$	9.90770	+	3.95077i	0.343901	+	0.137133i
$831$	31.1920	−	22.6623i	1.08204	−	0.786148i
$832$	6.11079	−	1.98552i	0.211854	−	0.0688354i
$833$	44.7555	+	14.5419i	1.55068	+	0.503848i
$834$	9.07295	+	6.59189i	0.314171	+	0.228258i
$835$	−16.5005	+	10.4151i	−0.571024	+	0.360428i
$836$		0			0
$837$			31.4885i			1.08840i
$838$	−1.35236	+	1.86137i	−0.0467167	+	0.0643000i
$839$	4.44515	−	13.6808i	0.153464	−	0.472313i	−0.844538	−	0.535495i	$-0.820125\pi$
$839$	4.44515	−	13.6808i	0.153464	−	0.472313i	0.998002	+	0.0631825i	$0.0201250\pi$
$840$	−4.82848	−	4.01438i	−0.166598	−	0.138509i
$841$	13.1189	−	9.53144i	0.452376	−	0.328670i
$842$	−2.19854	−	3.02603i	−0.0757666	−	0.104284i
$843$	26.4170	−	8.58341i	0.909850	−	0.295628i
$844$	−3.63683	+	11.1930i	−0.125185	+	0.385279i
$845$	−1.42625	+	21.8185i	−0.0490646	+	0.750580i
$846$	−0.155383			−0.00534218
$847$		0			0
$848$			1.30870i			0.0449408i
$849$	32.2060	+	23.3991i	1.10531	+	0.803053i
$850$	−20.6103	−	19.5448i	−0.706928	−	0.670382i
$851$	3.38025	+	10.4033i	0.115873	+	0.356622i
$852$	16.5467	+	22.7746i	0.566882	+	0.780246i
$853$	−25.2756	−	34.7889i	−0.865420	−	1.19115i	−0.980250	−	0.197763i	$-0.936632\pi$
$853$	−25.2756	−	34.7889i	−0.865420	−	1.19115i	0.114830	−	0.993385i	$-0.463368\pi$
$854$	−0.505464	−	1.55566i	−0.0172966	−	0.0532336i
$855$	−0.496651	+	0.126225i	−0.0169851	+	0.00431681i
$856$	−12.2129	−	8.87320i	−0.417429	−	0.303280i
$857$		−	54.3052i		−	1.85503i	−0.373784	−	0.927516i	$-0.621940\pi$
$857$		−	54.3052i		−	1.85503i	0.373784	−	0.927516i	$-0.378060\pi$
$858$		0			0
$859$	−24.3361			−0.830336			−0.415168	−	0.909745i	$-0.636277\pi$
$859$	−24.3361			−0.830336			−0.415168	+	0.909745i	$0.636277\pi$
$860$	28.7953	+	1.88232i	0.981913	+	0.0641865i
$861$	2.70945	−	8.33884i	0.0923380	−	0.284187i
$862$	15.8554	−	5.15173i	0.540037	−	0.175469i
$863$	−23.0118	−	31.6731i	−0.783332	−	1.07816i	−0.994906	−	0.100802i	$-0.967859\pi$
$863$	−23.0118	−	31.6731i	−0.783332	−	1.07816i	0.211575	−	0.977362i	$-0.432141\pi$
$864$	24.0736	−	17.4905i	0.819002	−	0.595040i
$865$	−15.7820	−	13.1211i	−0.536604	−	0.446131i
$866$	−3.17431	+	9.76952i	−0.107867	+	0.331982i
$867$	−34.2415	+	47.1294i	−1.16290	+	1.60060i
$868$			4.95043i			0.168029i
$869$		0			0
$870$	6.03138	+	9.55548i	0.204483	+	0.323961i
$871$	−9.86208	−	7.16522i	−0.334164	−	0.242784i
$872$	47.6491	+	15.4821i	1.61360	+	0.524291i
$873$	0.512347	−	0.166472i	0.0173403	−	0.00563421i
$874$	−2.21395	+	1.60853i	−0.0748881	+	0.0544094i
$875$	−4.49614	−	4.85881i	−0.151997	−	0.164258i
$876$	5.03261	+	15.4888i	0.170036	+	0.523317i
$877$	40.9793	+	13.3150i	1.38377	+	0.449615i	0.903908	−	0.427727i	$-0.140686\pi$
$877$	40.9793	+	13.3150i	1.38377	+	0.449615i	0.479865	+	0.877342i	$0.340686\pi$
$878$	−5.01107	+	6.89714i	−0.169115	+	0.232767i
$879$	23.3468			0.787466
$880$		0			0
$881$	−38.1083			−1.28390			−0.641950	−	0.766746i	$-0.721874\pi$
$881$	−38.1083			−1.28390			−0.641950	+	0.766746i	$0.721874\pi$
$882$	−0.314396	+	0.432729i	−0.0105863	+	0.0145707i
$883$	27.6054	+	8.96955i	0.928997	+	0.301849i	0.734152	−	0.678985i	$-0.237580\pi$
$883$	27.6054	+	8.96955i	0.928997	+	0.301849i	0.194845	+	0.980834i	$0.437580\pi$
$884$	−5.32147	−	16.3778i	−0.178980	−	0.550845i
$885$	−0.0558205	+	0.139986i	−0.00187638	+	0.00470557i
$886$	−4.28533	+	3.11348i	−0.143969	+	0.104599i
$887$	−2.10349	+	0.683467i	−0.0706284	+	0.0229486i	−0.344118	−	0.938926i	$-0.611822\pi$
$887$	−2.10349	+	0.683467i	−0.0706284	+	0.0229486i	0.273490	+	0.961875i	$0.411822\pi$
$888$	33.0962	+	10.7536i	1.11064	+	0.360868i
$889$	−7.69146	−	5.58817i	−0.257963	−	0.187421i
$890$	9.43136	−	5.95304i	0.316140	−	0.199546i
$891$		0			0
$892$			8.54894i			0.286240i
$893$	2.59647	−	3.57374i	0.0868877	−	0.119591i
$894$	−5.45973	+	16.8033i	−0.182601	+	0.561987i
$895$	−2.07019	+	2.49002i	−0.0691990	+	0.0832321i
$896$	4.20706	−	3.05661i	0.140548	−	0.102114i
$897$	2.76933	+	3.81165i	0.0924652	+	0.127267i
$898$	10.4038	−	3.38041i	0.347180	−	0.112806i
$899$	6.81411	−	20.9717i	0.227263	−	0.699444i
$900$	−0.596848	+	0.324331i	−0.0198949	+	0.0108110i
$901$	−16.8641			−0.561825
$902$		0			0
$903$			9.92432i			0.330261i
$904$	−25.7172	−	18.6846i	−0.855340	−	0.621441i
$905$	−1.71965	+	0.437055i	−0.0571632	+	0.0145282i
$906$	3.66976	+	11.2944i	0.121920	+	0.375230i
$907$	15.6858	+	21.5897i	0.520840	+	0.716874i	0.985700	−	0.168510i	$-0.0538954\pi$
$907$	15.6858	+	21.5897i	0.520840	+	0.716874i	−0.464860	+	0.885384i	$0.653895\pi$
$908$	−0.889924	−	1.22488i	−0.0295332	−	0.0406489i
$909$	−0.307546	−	0.946530i	−0.0102007	−	0.0313944i
$910$	0.469868	+	1.84876i	0.0155760	+	0.0612858i
$911$	29.3460	+	21.3211i	0.972276	+	0.706400i	0.955969	−	0.293467i	$-0.0948092\pi$
$911$	29.3460	+	21.3211i	0.972276	+	0.706400i	0.0163067	+	0.999867i	$0.494809\pi$
$912$		−	2.21138i		−	0.0732261i
$913$		0			0
$914$	−10.8363			−0.358434
$915$	−13.5211	−	0.883861i	−0.446995	−	0.0292195i
$916$	1.75788	−	5.41021i	0.0580821	−	0.178758i
$917$	10.1529	−	3.29887i	0.335277	−	0.108938i
$918$	17.0486	+	23.4654i	0.562689	+	0.774475i
$919$	24.0050	−	17.4406i	0.791851	−	0.575313i	−0.116661	−	0.993172i	$-0.537219\pi$
$919$	24.0050	−	17.4406i	0.791851	−	0.575313i	0.908512	+	0.417859i	$0.137219\pi$
$920$	−5.74048	+	6.90462i	−0.189258	+	0.227638i
$921$	5.44976	−	16.7726i	0.179576	−	0.552677i
$922$	−5.34174	+	7.35227i	−0.175921	+	0.242134i
$923$		−	21.1680i		−	0.696754i
$924$		0			0
$925$	33.1188	+	15.7827i	1.08894	+	0.518932i
$926$	3.13652	+	2.27882i	0.103073	+	0.0748866i
$927$	−1.28869	−	0.418721i	−0.0423262	−	0.0137526i
$928$	−19.8182	+	6.43933i	−0.650565	+	0.211381i
$929$	22.4685	−	16.3243i	0.737168	−	0.535584i	−0.154655	−	0.987968i	$-0.549427\pi$
$929$	22.4685	−	16.3243i	0.737168	−	0.535584i	0.891823	+	0.452385i	$0.149427\pi$
$930$	−18.1043	−	7.21922i	−0.593662	−	0.236728i
$931$	−4.69896	−	14.4619i	−0.154002	−	0.473970i
$932$	−8.74093	−	2.84010i	−0.286319	−	0.0930305i
$933$	−3.52734	+	4.85496i	−0.115480	+	0.158944i
$934$	−19.2786			−0.630817
$935$		0			0
$936$	0.484498			0.0158363
$937$	17.7759	−	24.4664i	0.580712	−	0.799282i	−0.413061	−	0.910703i	$-0.635540\pi$
$937$	17.7759	−	24.4664i	0.580712	−	0.799282i	0.993773	+	0.111422i	$0.0355404\pi$
$938$	3.06994	+	0.997483i	0.100237	+	0.0325690i
$939$	13.3309	+	41.0282i	0.435037	+	1.33891i
$940$	2.16888	−	5.43909i	0.0707411	−	0.177404i
$941$	−4.85954	+	3.53066i	−0.158416	+	0.115096i	−0.664169	−	0.747582i	$-0.731215\pi$
$941$	−4.85954	+	3.53066i	−0.158416	+	0.115096i	0.505753	+	0.862678i	$0.331215\pi$
$942$	18.8129	−	6.11267i	0.612956	−	0.199162i
$943$	−11.9244	−	3.87446i	−0.388311	−	0.126170i
$944$	−0.0170073	−	0.0123565i	−0.000553541	−	0.000402171i
$945$	3.60821	+	5.71646i	0.117375	+	0.185956i
$946$		0			0
$947$			10.0218i			0.325665i	0.986654	+	0.162833i	$0.0520630\pi$
$947$			10.0218i			0.325665i	−0.986654	+	0.162833i	$0.947937\pi$
$948$	6.35023	−	8.74034i	0.206246	−	0.283873i
$949$	3.78425	−	11.6467i	0.122842	−	0.378068i
$950$	−1.19484	+	9.10012i	−0.0387656	+	0.295247i
$951$	9.95492	−	7.23267i	0.322810	−	0.234535i
$952$	6.63445	+	9.13154i	0.215024	+	0.295955i
$953$	9.30263	−	3.02261i	0.301342	−	0.0979118i	−0.154444	−	0.988002i	$-0.549359\pi$
$953$	9.30263	−	3.02261i	0.301342	−	0.0979118i	0.455785	+	0.890090i	$0.349359\pi$
$954$	0.0592331	−	0.182301i	0.00191774	−	0.00590220i
$955$	1.18879	−	18.1858i	0.0384682	−	0.588479i
$956$	5.96237			0.192837
$957$		0			0
$958$			34.6967i			1.12100i
$959$	1.93145	+	1.40328i	0.0623698	+	0.0453143i
$960$	3.47166	+	13.6597i	0.112047	+	0.440866i
$961$	2.17387	+	6.69048i	0.0701248	+	0.215822i
$962$	−6.21374	−	8.55248i	−0.200339	−	0.275743i
$963$	−0.330118	−	0.454369i	−0.0106379	−	0.0146418i
$964$	4.02679	+	12.3932i	0.129694	+	0.399158i
$965$	2.40606	+	9.46698i	0.0774538	+	0.304753i
$966$	−1.00931	−	0.733309i	−0.0324741	−	0.0235938i
$967$			1.22635i			0.0394367i	0.999806	+	0.0197184i	$0.00627695\pi$
$967$			1.22635i			0.0394367i	−0.999806	+	0.0197184i	$0.993723\pi$
$968$		0			0
$969$	28.4963			0.915432
$970$	0.629388	−	9.62826i	0.0202084	−	0.309145i
$971$	−13.7966	+	42.4615i	−0.442753	+	1.36265i	0.442176	+	0.896928i	$0.354207\pi$
$971$	−13.7966	+	42.4615i	−0.442753	+	1.36265i	−0.884929	+	0.465726i	$0.845793\pi$
$972$	1.34220	−	0.436106i	0.0430509	−	0.0139881i
$973$	−2.76159	−	3.80100i	−0.0885324	−	0.121854i
$974$	−27.2493	+	19.7978i	−0.873123	+	0.634361i
$975$	15.6672	+	2.05709i	0.501753	+	0.0658795i
$976$	0.584080	−	1.79761i	0.0186959	−	0.0575402i
$977$	−27.7700	+	38.2221i	−0.888441	+	1.22283i	0.0855696	+	0.996332i	$0.472729\pi$
$977$	−27.7700	+	38.2221i	−0.888441	+	1.22283i	−0.974011	+	0.226502i	$0.927271\pi$
$978$			16.7361i			0.535162i
$979$		0			0
$980$	−10.7590	−	17.0454i	−0.343683	−	0.544495i
$981$	1.50798	+	1.09561i	0.0481460	+	0.0349801i
$982$	6.91639	+	2.24727i	0.220711	+	0.0717133i
$983$	13.2530	−	4.30617i	0.422706	−	0.137345i	−0.0899369	−	0.995947i	$-0.528667\pi$
$983$	13.2530	−	4.30617i	0.422706	−	0.137345i	0.512643	+	0.858602i	$0.328667\pi$
$984$	−32.2695	+	23.4452i	−1.02871	+	0.747405i
$985$	12.9639	−	32.5107i	0.413065	−	1.03588i
$986$	−6.27664	−	19.3175i	−0.199889	−	0.615195i
$987$	1.91526	+	0.622307i	0.0609635	+	0.0198082i
$988$	−3.27075	+	4.50181i	−0.104057	+	0.143222i
$989$	14.1916			0.451265
$990$		0			0
$991$	36.5755			1.16186			0.580930	−	0.813953i	$-0.302689\pi$
$991$	36.5755			1.16186			0.580930	+	0.813953i	$0.302689\pi$
$992$	21.1267	−	29.0784i	0.670773	−	0.923240i
$993$	9.44992	+	3.07046i	0.299884	+	0.0974382i
$994$	1.73211	+	5.33088i	0.0549392	+	0.169085i
$995$	−2.98739	−	1.19125i	−0.0947067	−	0.0377650i
$996$	−11.4759	+	8.33773i	−0.363628	+	0.264191i
$997$	18.3949	−	5.97686i	0.582572	−	0.189289i	−0.00288064	−	0.999996i	$-0.500917\pi$
$997$	18.3949	−	5.97686i	0.582572	−	0.189289i	0.585452	+	0.810707i	$0.300917\pi$
$998$	−23.1156	−	7.51071i	−0.731711	−	0.237747i
$999$	−30.3084	−	22.0204i	−0.958916	−	0.696693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.g.444.3		16
5.4	even	2	inner	605.2.j.g.444.2		16
11.2	odd	10		55.2.j.a.49.3	yes	16
11.3	even	5	inner	605.2.j.g.124.2		16
11.4	even	5		605.2.j.d.9.3		16
11.5	even	5		605.2.b.f.364.5		8
11.6	odd	10		605.2.b.g.364.4		8
11.7	odd	10		55.2.j.a.9.2	✓	16
11.8	odd	10		605.2.j.h.124.3		16
11.9	even	5		605.2.j.d.269.2		16
11.10	odd	2		605.2.j.h.444.2		16
33.2	even	10		495.2.ba.a.379.2		16
33.29	even	10		495.2.ba.a.64.3		16
44.7	even	10		880.2.cd.c.449.3		16
44.35	even	10		880.2.cd.c.49.2		16
55.2	even	20		275.2.h.d.126.3		16
55.4	even	10		605.2.j.d.9.2		16
55.7	even	20		275.2.h.d.251.3		16
55.9	even	10		605.2.j.d.269.3		16
55.13	even	20		275.2.h.d.126.2		16
55.14	even	10	inner	605.2.j.g.124.3		16
55.17	even	20		3025.2.a.bl.1.5		8
55.18	even	20		275.2.h.d.251.2		16
55.19	odd	10		605.2.j.h.124.2		16
55.24	odd	10		55.2.j.a.49.2	yes	16
55.27	odd	20		3025.2.a.bk.1.4		8
55.28	even	20		3025.2.a.bl.1.4		8
55.29	odd	10		55.2.j.a.9.3	yes	16
55.38	odd	20		3025.2.a.bk.1.5		8
55.39	odd	10		605.2.b.g.364.5		8
55.49	even	10		605.2.b.f.364.4		8
55.54	odd	2		605.2.j.h.444.3		16
165.29	even	10		495.2.ba.a.64.2		16
165.134	even	10		495.2.ba.a.379.3		16
220.79	even	10		880.2.cd.c.49.3		16
220.139	even	10		880.2.cd.c.449.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.9.2	✓	16	11.7	odd	10
55.2.j.a.9.3	yes	16	55.29	odd	10
55.2.j.a.49.2	yes	16	55.24	odd	10
55.2.j.a.49.3	yes	16	11.2	odd	10
275.2.h.d.126.2		16	55.13	even	20
275.2.h.d.126.3		16	55.2	even	20
275.2.h.d.251.2		16	55.18	even	20
275.2.h.d.251.3		16	55.7	even	20
495.2.ba.a.64.2		16	165.29	even	10
495.2.ba.a.64.3		16	33.29	even	10
495.2.ba.a.379.2		16	33.2	even	10
495.2.ba.a.379.3		16	165.134	even	10
605.2.b.f.364.4		8	55.49	even	10
605.2.b.f.364.5		8	11.5	even	5
605.2.b.g.364.4		8	11.6	odd	10
605.2.b.g.364.5		8	55.39	odd	10
605.2.j.d.9.2		16	55.4	even	10
605.2.j.d.9.3		16	11.4	even	5
605.2.j.d.269.2		16	11.9	even	5
605.2.j.d.269.3		16	55.9	even	10
605.2.j.g.124.2		16	11.3	even	5	inner
605.2.j.g.124.3		16	55.14	even	10	inner
605.2.j.g.444.2		16	5.4	even	2	inner
605.2.j.g.444.3		16	1.1	even	1	trivial
605.2.j.h.124.2		16	55.19	odd	10
605.2.j.h.124.3		16	11.8	odd	10
605.2.j.h.444.2		16	11.10	odd	2
605.2.j.h.444.3		16	55.54	odd	2
880.2.cd.c.49.2		16	44.35	even	10
880.2.cd.c.49.3		16	220.79	even	10
880.2.cd.c.449.2		16	220.139	even	10
880.2.cd.c.449.3		16	44.7	even	10
3025.2.a.bk.1.4		8	55.27	odd	20
3025.2.a.bk.1.5		8	55.38	odd	20
3025.2.a.bl.1.4		8	55.28	even	20
3025.2.a.bl.1.5		8	55.17	even	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.471815 - 0.649397i) q^{2} +(1.67457 + 0.544099i) q^{3} +(0.418926 + 1.28932i) q^{4} +(2.07703 + 0.828231i) q^{5} +(1.14342 - 0.830744i) q^{6} +(-0.563124 + 0.182970i) q^{7} +(2.56176 + 0.832367i) q^{8} +(0.0810736 + 0.0589034i) q^{9} +O(q^{10})\)	\(q+(0.471815 - 0.649397i) q^{2} +(1.67457 + 0.544099i) q^{3} +(0.418926 + 1.28932i) q^{4} +(2.07703 + 0.828231i) q^{5} +(1.14342 - 0.830744i) q^{6} +(-0.563124 + 0.182970i) q^{7} +(2.56176 + 0.832367i) q^{8} +(0.0810736 + 0.0589034i) q^{9} +(1.51782 - 0.958043i) q^{10} +2.38699i q^{12} +(1.05501 - 1.45210i) q^{13} +(-0.146870 + 0.452019i) q^{14} +(3.02747 + 2.51703i) q^{15} +(-0.444313 + 0.322812i) q^{16} +(-4.15982 - 5.72551i) q^{17} +(0.0765034 - 0.0248575i) q^{18} +(-0.706673 + 2.17492i) q^{19} +(-0.197736 + 3.02492i) q^{20} -1.04254 q^{21} +1.49081i q^{23} +(3.83695 + 2.78771i) q^{24} +(3.62807 + 3.44051i) q^{25} +(-0.445218 - 1.37024i) q^{26} +(-3.00110 - 4.13066i) q^{27} +(-0.471815 - 0.649397i) q^{28} +(1.10489 + 3.40050i) q^{29} +(3.06296 - 0.778460i) q^{30} +(-4.98940 - 3.62501i) q^{31} +5.82804i q^{32} -5.68079 q^{34} +(-1.32116 - 0.0863629i) q^{35} +(-0.0419817 + 0.129206i) q^{36} +(6.97831 - 2.26739i) q^{37} +(1.07897 + 1.48507i) q^{38} +(2.55677 - 1.85760i) q^{39} +(4.63145 + 3.85058i) q^{40} +(-2.59890 + 7.99858i) q^{41} +(-0.491886 + 0.677023i) q^{42} -9.51936i q^{43} +(0.119606 + 0.189492i) q^{45} +(0.968128 + 0.703386i) q^{46} +(-1.83711 - 0.596914i) q^{47} +(-0.919674 + 0.298820i) q^{48} +(-5.37949 + 3.90843i) q^{49} +(3.94603 - 0.732773i) q^{50} +(-3.85065 - 11.8511i) q^{51} +(2.31419 + 0.751927i) q^{52} +(1.40064 - 1.92781i) q^{53} -4.09840 q^{54} -1.59489 q^{56} +(-2.36674 + 3.25754i) q^{57} +(2.72957 + 0.886893i) q^{58} +(0.0118285 + 0.0364043i) q^{59} +(-1.97698 + 4.95784i) q^{60} +(-2.78430 + 2.02291i) q^{61} +(-4.70814 + 1.52977i) q^{62} +(-0.0564320 - 0.0183359i) q^{63} +(2.89608 + 2.10413i) q^{64} +(3.39395 - 2.14225i) q^{65} -6.79162i q^{67} +(5.63937 - 7.76192i) q^{68} +(-0.811149 + 2.49646i) q^{69} +(-0.679428 + 0.817212i) q^{70} +(9.54114 - 6.93205i) q^{71} +(0.158662 + 0.218380i) q^{72} +(6.48882 - 2.10835i) q^{73} +(1.82003 - 5.60148i) q^{74} +(4.20346 + 7.73539i) q^{75} -3.10021 q^{76} -2.53680i q^{78} +(-3.66165 - 2.66035i) q^{79} +(-1.19021 + 0.302496i) q^{80} +(-2.87095 - 8.83588i) q^{81} +(3.96806 + 5.46156i) q^{82} +(3.49299 + 4.80768i) q^{83} +(-0.436748 - 1.34417i) q^{84} +(-3.89802 - 15.3373i) q^{85} +(-6.18185 - 4.49137i) q^{86} +6.29552i q^{87} +6.21375 q^{89} +(0.179487 + 0.0117329i) q^{90} +(-0.328411 + 1.01074i) q^{91} +(-1.92214 + 0.624540i) q^{92} +(-6.38271 - 8.78504i) q^{93} +(-1.25441 + 0.911382i) q^{94} +(-3.26911 + 3.93207i) q^{95} +(-3.17103 + 9.75943i) q^{96} +(3.15976 - 4.34904i) q^{97} +5.33748i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4} - 2 q^{5} - 12 q^{6} + 2 q^{9}+O(q^{10}) \) 16 * q + 6 * q^4 - 2 * q^5 - 12 * q^6 + 2 * q^9	\( 16 q + 6 q^{4} - 2 q^{5} - 12 q^{6} + 2 q^{9} + 8 q^{14} + 24 q^{15} + 6 q^{16} - 6 q^{19} + 12 q^{20} - 8 q^{21} + 4 q^{24} + 24 q^{25} - 50 q^{26} - 22 q^{29} + 4 q^{30} - 22 q^{31} - 16 q^{34} + 8 q^{35} - 30 q^{36} - 12 q^{40} - 18 q^{41} + 12 q^{45} - 38 q^{46} - 20 q^{49} + 12 q^{50} + 12 q^{51} + 40 q^{54} - 20 q^{56} - 8 q^{59} - 2 q^{60} - 20 q^{61} + 22 q^{64} + 40 q^{65} + 6 q^{69} + 26 q^{70} + 6 q^{71} + 52 q^{74} + 40 q^{75} - 56 q^{76} + 22 q^{79} - 6 q^{80} - 32 q^{81} + 18 q^{84} + 62 q^{85} - 68 q^{86} + 24 q^{89} + 32 q^{90} + 56 q^{94} + 22 q^{95} - 94 q^{96}+O(q^{100}) \) 16 * q + 6 * q^4 - 2 * q^5 - 12 * q^6 + 2 * q^9 + 8 * q^14 + 24 * q^15 + 6 * q^16 - 6 * q^19 + 12 * q^20 - 8 * q^21 + 4 * q^24 + 24 * q^25 - 50 * q^26 - 22 * q^29 + 4 * q^30 - 22 * q^31 - 16 * q^34 + 8 * q^35 - 30 * q^36 - 12 * q^40 - 18 * q^41 + 12 * q^45 - 38 * q^46 - 20 * q^49 + 12 * q^50 + 12 * q^51 + 40 * q^54 - 20 * q^56 - 8 * q^59 - 2 * q^60 - 20 * q^61 + 22 * q^64 + 40 * q^65 + 6 * q^69 + 26 * q^70 + 6 * q^71 + 52 * q^74 + 40 * q^75 - 56 * q^76 + 22 * q^79 - 6 * q^80 - 32 * q^81 + 18 * q^84 + 62 * q^85 - 68 * q^86 + 24 * q^89 + 32 * q^90 + 56 * q^94 + 22 * q^95 - 94 * q^96

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