LMFDB - Embedded newform 507.2.j.i.361.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [507,2,Mod(316,507)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("507.316"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,6,22,0,0,0,0,-6,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.3
Root			$-0.385418 - 0.222521i$ of defining polynomial
Character	$\chi$	$=$	507.361
Dual form			507.2.j.i.316.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.77441 + 1.02446i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.09903 - 1.90358i) q^{4} +3.35690i q^{5} +(-1.77441 - 1.02446i) q^{6} +(1.94594 + 1.12349i) q^{7} +0.405813i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.43900 - 5.95652i) q^{10} +(-4.27730 + 2.46950i) q^{11} +2.19806 q^{12} -4.60388 q^{14} +(-2.90716 + 1.67845i) q^{15} +(1.78232 + 3.08707i) q^{16} +(0.455927 - 0.789689i) q^{17} -2.04892i q^{18} +(3.29257 + 1.90097i) q^{19} +(6.39011 + 3.68933i) q^{20} +2.24698i q^{21} +(5.05980 - 8.76383i) q^{22} +(1.01357 + 1.75556i) q^{23} +(-0.351445 + 0.202907i) q^{24} -6.26875 q^{25} -1.00000 q^{27} +(4.27730 - 2.46950i) q^{28} +(1.96950 + 3.41127i) q^{29} +(3.43900 - 5.95652i) q^{30} -8.82908i q^{31} +(-7.02805 - 4.05765i) q^{32} +(-4.27730 - 2.46950i) q^{33} +1.86831i q^{34} +(-3.77144 + 6.53232i) q^{35} +(1.09903 + 1.90358i) q^{36} +(-7.62270 + 4.40097i) q^{37} -7.78986 q^{38} -1.36227 q^{40} +(6.00935 - 3.46950i) q^{41} +(-2.30194 - 3.98707i) q^{42} +(-1.14310 + 1.97991i) q^{43} +10.8562i q^{44} +(-2.90716 - 1.67845i) q^{45} +(-3.59700 - 2.07673i) q^{46} -3.80194i q^{47} +(-1.78232 + 3.08707i) q^{48} +(-0.975541 - 1.68969i) q^{49} +(11.1234 - 6.42208i) q^{50} +0.911854 q^{51} +0.542877 q^{53} +(1.77441 - 1.02446i) q^{54} +(-8.28986 - 14.3585i) q^{55} +(-0.455927 + 0.789689i) q^{56} +3.80194i q^{57} +(-6.98942 - 4.03534i) q^{58} +(-4.08226 - 2.35690i) q^{59} +7.37867i q^{60} +(-1.83997 + 3.18692i) q^{61} +(9.04503 + 15.6665i) q^{62} +(-1.94594 + 1.12349i) q^{63} +9.49827 q^{64} +10.1196 q^{66} +(-1.31732 + 0.760553i) q^{67} +(-1.00216 - 1.73578i) q^{68} +(-1.01357 + 1.75556i) q^{69} -15.4547i q^{70} +(-2.05999 - 1.18933i) q^{71} +(-0.351445 - 0.202907i) q^{72} -7.41119i q^{73} +(9.01722 - 15.6183i) q^{74} +(-3.13437 - 5.42890i) q^{75} +(7.23728 - 4.17845i) q^{76} -11.0978 q^{77} -3.74094 q^{79} +(-10.3630 + 5.98307i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-7.10872 + 12.3127i) q^{82} +2.30798i q^{83} +(4.27730 + 2.46950i) q^{84} +(2.65090 + 1.53050i) q^{85} -4.68425i q^{86} +(-1.96950 + 3.41127i) q^{87} +(-1.00216 - 1.73578i) q^{88} +(8.71101 - 5.02930i) q^{89} +6.87800 q^{90} +4.45580 q^{92} +(7.64621 - 4.41454i) q^{93} +(3.89493 + 6.74621i) q^{94} +(-6.38135 + 11.0528i) q^{95} -8.11529i q^{96} +(13.9684 + 8.06465i) q^{97} +(3.46203 + 1.99880i) q^{98} -4.93900i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 22 q^{4} - 6 q^{9} - 2 q^{10} + 44 q^{12} - 20 q^{14} - 22 q^{16} - 2 q^{17} + 18 q^{22} - 44 q^{25} - 12 q^{27} + 4 q^{29} + 2 q^{30} - 8 q^{35} + 22 q^{36} + 12 q^{40} - 10 q^{42} - 30 q^{43}+ \cdots - 42 q^{95}+O(q^{100}) $ 12 * q + 6 * q^3 + 22 * q^4 - 6 * q^9 - 2 * q^10 + 44 * q^12 - 20 * q^14 - 22 * q^16 - 2 * q^17 + 18 * q^22 - 44 * q^25 - 12 * q^27 + 4 * q^29 + 2 * q^30 - 8 * q^35 + 22 * q^36 + 12 * q^40 - 10 * q^42 - 30 * q^43 + 22 * q^48 - 30 * q^49 - 4 * q^51 - 68 * q^53 - 6 * q^55 + 2 * q^56 + 26 * q^61 - 4 * q^62 + 36 * q^66 + 26 * q^68 - 30 * q^74 - 22 * q^75 - 60 * q^77 + 12 * q^79 - 6 * q^81 - 6 * q^82 - 4 * q^87 + 26 * q^88 + 4 * q^90 + 28 * q^92 - 42 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.77441	+	1.02446i	−1.25470	+	0.724402i	−0.972039	−	0.234818i	$-0.924551\pi$
$2$	−1.77441	+	1.02446i	−1.25470	+	0.724402i	−0.282661	+	0.959220i	$0.591217\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.09903	−	1.90358i	0.549516	−	0.951789i
$5$			3.35690i			1.50125i	0.660729	+	0.750625i	$0.270247\pi$
$5$			3.35690i			1.50125i	−0.660729	+	0.750625i	$0.729753\pi$
$6$	−1.77441	−	1.02446i	−0.724402	−	0.418234i
$7$	1.94594	+	1.12349i	0.735497	+	0.424639i	0.820430	−	0.571747i	$-0.193734\pi$
$7$	1.94594	+	1.12349i	0.735497	+	0.424639i	−0.0849330	+	0.996387i	$0.527068\pi$
$8$			0.405813i			0.143477i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−3.43900	−	5.95652i	−1.08751	−	1.88362i
$11$	−4.27730	+	2.46950i	−1.28965	+	0.744582i	−0.978593	−	0.205807i	$-0.934018\pi$
$11$	−4.27730	+	2.46950i	−1.28965	+	0.744582i	−0.311062	+	0.950390i	$0.600685\pi$
$12$	2.19806			0.634526
$13$		0			0
$13$		0			0
$14$	−4.60388			−1.23044
$15$	−2.90716	+	1.67845i	−0.750625	+	0.433373i
$16$	1.78232	+	3.08707i	0.445581	+	0.771769i
$17$	0.455927	−	0.789689i	0.110579	−	0.191528i	−0.805425	−	0.592698i	$-0.798063\pi$
$17$	0.455927	−	0.789689i	0.110579	−	0.191528i	0.916004	+	0.401170i	$0.131396\pi$
$18$		−	2.04892i		−	0.482934i
$19$	3.29257	+	1.90097i	0.755368	+	0.436112i	0.827630	−	0.561274i	$-0.189688\pi$
$19$	3.29257	+	1.90097i	0.755368	+	0.436112i	−0.0722619	+	0.997386i	$0.523022\pi$
$20$	6.39011	+	3.68933i	1.42887	+	0.824960i
$21$			2.24698i			0.490331i
$22$	5.05980	−	8.76383i	1.07875	−	1.86846i
$23$	1.01357	+	1.75556i	0.211345	+	0.366060i	0.952136	−	0.305676i	$-0.0988824\pi$
$23$	1.01357	+	1.75556i	0.211345	+	0.366060i	−0.740791	+	0.671736i	$0.765549\pi$
$24$	−0.351445	+	0.202907i	−0.0717383	+	0.0414181i
$25$	−6.26875			−1.25375
$26$		0			0
$27$	−1.00000			−0.192450
$28$	4.27730	−	2.46950i	0.808334	−	0.466692i
$29$	1.96950	+	3.41127i	0.365727	+	0.633458i	0.988893	−	0.148632i	$-0.0474870\pi$
$29$	1.96950	+	3.41127i	0.365727	+	0.633458i	−0.623165	+	0.782090i	$0.714154\pi$
$30$	3.43900	−	5.95652i	0.627873	−	1.08751i
$31$		−	8.82908i		−	1.58575i	−0.609384	−	0.792875i	$-0.708583\pi$
$31$		−	8.82908i		−	1.58575i	0.609384	−	0.792875i	$-0.291417\pi$
$32$	−7.02805	−	4.05765i	−1.24240	−	0.717297i
$33$	−4.27730	−	2.46950i	−0.744582	−	0.429885i
$34$			1.86831i			0.320413i
$35$	−3.77144	+	6.53232i	−0.637489	+	1.10416i
$36$	1.09903	+	1.90358i	0.183172	+	0.317263i
$37$	−7.62270	+	4.40097i	−1.25316	+	0.723515i	−0.971737	−	0.236068i	$-0.924141\pi$
$37$	−7.62270	+	4.40097i	−1.25316	+	0.723515i	−0.281428	+	0.959582i	$0.590808\pi$
$38$	−7.78986			−1.26368
$39$		0			0
$40$	−1.36227			−0.215394
$41$	6.00935	−	3.46950i	0.938503	−	0.541845i	0.0490123	−	0.998798i	$-0.484393\pi$
$41$	6.00935	−	3.46950i	0.938503	−	0.541845i	0.889491	+	0.456953i	$0.151059\pi$
$42$	−2.30194	−	3.98707i	−0.355197	−	0.615219i
$43$	−1.14310	+	1.97991i	−0.174322	+	0.301934i	−0.939926	−	0.341377i	$-0.889107\pi$
$43$	−1.14310	+	1.97991i	−0.174322	+	0.301934i	0.765605	+	0.643311i	$0.222440\pi$
$44$			10.8562i			1.63664i
$45$	−2.90716	−	1.67845i	−0.433373	−	0.250208i
$46$	−3.59700	−	2.07673i	−0.530349	−	0.306197i
$47$		−	3.80194i		−	0.554570i	−0.960788	−	0.277285i	$-0.910565\pi$
$47$		−	3.80194i		−	0.554570i	0.960788	−	0.277285i	$-0.0894346\pi$
$48$	−1.78232	+	3.08707i	−0.257256	+	0.445581i
$49$	−0.975541	−	1.68969i	−0.139363	−	0.241384i
$50$	11.1234	−	6.42208i	1.57308	−	0.908219i
$51$	0.911854			0.127685
$52$		0			0
$53$	0.542877			0.0745698			0.0372849	−	0.999305i	$-0.488129\pi$
$53$	0.542877			0.0745698			0.0372849	+	0.999305i	$0.488129\pi$
$54$	1.77441	−	1.02446i	0.241467	−	0.139411i
$55$	−8.28986	−	14.3585i	−1.11780	−	1.93609i
$56$	−0.455927	+	0.789689i	−0.0609258	+	0.105527i
$57$			3.80194i			0.503579i
$58$	−6.98942	−	4.03534i	−0.917756	−	0.529867i
$59$	−4.08226	−	2.35690i	−0.531465	−	0.306842i	0.210148	−	0.977670i	$-0.432606\pi$
$59$	−4.08226	−	2.35690i	−0.531465	−	0.306842i	−0.741613	+	0.670828i	$0.765939\pi$
$60$			7.37867i			0.952582i
$61$	−1.83997	+	3.18692i	−0.235584	+	0.408043i	−0.959442	−	0.281905i	$-0.909034\pi$
$61$	−1.83997	+	3.18692i	−0.235584	+	0.408043i	0.723858	+	0.689949i	$0.242367\pi$
$62$	9.04503	+	15.6665i	1.14872	+	1.98964i
$63$	−1.94594	+	1.12349i	−0.245166	+	0.141546i
$64$	9.49827			1.18728
$65$		0			0
$66$	10.1196			1.24564
$67$	−1.31732	+	0.760553i	−0.160936	+	0.0929164i	−0.578305	−	0.815821i	$-0.696286\pi$
$67$	−1.31732	+	0.760553i	−0.160936	+	0.0929164i	0.417369	+	0.908737i	$0.362952\pi$
$68$	−1.00216	−	1.73578i	−0.121529	−	0.210495i
$69$	−1.01357	+	1.75556i	−0.122020	+	0.211345i
$70$		−	15.4547i		−	1.84719i
$71$	−2.05999	−	1.18933i	−0.244475	−	0.141148i	0.372757	−	0.927929i	$-0.378413\pi$
$71$	−2.05999	−	1.18933i	−0.244475	−	0.141148i	−0.617232	+	0.786781i	$0.711746\pi$
$72$	−0.351445	−	0.202907i	−0.0414181	−	0.0239128i
$73$		−	7.41119i		−	0.867414i	−0.901054	−	0.433707i	$-0.857205\pi$
$73$		−	7.41119i		−	0.867414i	0.901054	−	0.433707i	$-0.142795\pi$
$74$	9.01722	−	15.6183i	1.04823	−	1.81559i
$75$	−3.13437	−	5.42890i	−0.361926	−	0.626875i
$76$	7.23728	−	4.17845i	0.830173	−	0.479301i
$77$	−11.0978			−1.26472
$78$		0			0
$79$	−3.74094			−0.420888			−0.210444	−	0.977606i	$-0.567491\pi$
$79$	−3.74094			−0.420888			−0.210444	+	0.977606i	$0.567491\pi$
$80$	−10.3630	+	5.98307i	−1.15862	+	0.668928i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−7.10872	+	12.3127i	−0.785027	+	1.35971i
$83$			2.30798i			0.253334i	0.991945	+	0.126667i	$0.0404279\pi$
$83$			2.30798i			0.253334i	−0.991945	+	0.126667i	$0.959572\pi$
$84$	4.27730	+	2.46950i	0.466692	+	0.269445i
$85$	2.65090	+	1.53050i	0.287531	+	0.166006i
$86$		−	4.68425i		−	0.505116i
$87$	−1.96950	+	3.41127i	−0.211153	+	0.365727i
$88$	−1.00216	−	1.73578i	−0.106830	−	0.185035i
$89$	8.71101	−	5.02930i	0.923365	−	0.533105i	0.0386580	−	0.999253i	$-0.487692\pi$
$89$	8.71101	−	5.02930i	0.923365	−	0.533105i	0.884707	+	0.466147i	$0.154358\pi$
$90$	6.87800			0.725005
$91$		0			0
$92$	4.45580			0.464549
$93$	7.64621	−	4.41454i	0.792875	−	0.457767i
$94$	3.89493	+	6.74621i	0.401731	+	0.695819i
$95$	−6.38135	+	11.0528i	−0.654713	+	1.13400i
$96$		−	8.11529i		−	0.828264i
$97$	13.9684	+	8.06465i	1.41827	+	0.818841i	0.996147	−	0.0876961i	$-0.0279504\pi$
$97$	13.9684	+	8.06465i	1.41827	+	0.818841i	0.422127	+	0.906537i	$0.361284\pi$
$98$	3.46203	+	1.99880i	0.349718	+	0.201910i
$99$		−	4.93900i		−	0.496388i
$100$	−6.88955	+	11.9331i	−0.688955	+	1.19331i
$101$	−4.97434	−	8.61582i	−0.494966	−	0.857306i	0.505017	−	0.863109i	$-0.331486\pi$
$101$	−4.97434	−	8.61582i	−0.494966	−	0.857306i	−0.999983	+	0.00580325i	$0.998153\pi$
$102$	−1.61801	+	0.934157i	−0.160207	+	0.0924953i
$103$	10.9879			1.08267			0.541336	−	0.840806i	$-0.317919\pi$
$103$	10.9879			1.08267			0.541336	+	0.840806i	$0.317919\pi$
$104$		0			0
$105$	−7.54288			−0.736109
$106$	−0.963288	+	0.556155i	−0.0935628	+	0.0540185i
$107$	4.93631	+	8.54994i	0.477211	+	0.826554i	0.999659	−	0.0261171i	$-0.00831428\pi$
$107$	4.93631	+	8.54994i	0.477211	+	0.826554i	−0.522448	+	0.852671i	$0.674981\pi$
$108$	−1.09903	+	1.90358i	−0.105754	+	0.183172i
$109$			20.2446i			1.93908i	0.244934	+	0.969540i	$0.421234\pi$
$109$			20.2446i			1.93908i	−0.244934	+	0.969540i	$0.578766\pi$
$110$	29.4193	+	16.9852i	2.80502	+	1.61948i
$111$	−7.62270	−	4.40097i	−0.723515	−	0.417721i
$112$			8.00969i			0.756844i
$113$	−4.84601	+	8.39354i	−0.455874	+	0.789598i	−0.998738	−	0.0502233i	$-0.984007\pi$
$113$	−4.84601	+	8.39354i	−0.455874	+	0.789598i	0.542864	+	0.839821i	$0.317340\pi$
$114$	−3.89493	−	6.74621i	−0.364793	−	0.631841i
$115$	−5.89324	+	3.40246i	−0.549547	+	0.317281i
$116$	8.65817			0.803891
$117$		0			0
$118$	9.65817			0.889107
$119$	1.77441	−	1.02446i	0.162660	−	0.0939120i
$120$	−0.681136	−	1.17976i	−0.0621790	−	0.107697i
$121$	6.69687	−	11.5993i	0.608806	−	1.05448i
$122$		−	7.53989i		−	0.682630i
$123$	6.00935	+	3.46950i	0.541845	+	0.312834i
$124$	−16.8068	−	9.70344i	−1.50930	−	0.871395i
$125$		−	4.25906i		−	0.380942i
$126$	2.30194	−	3.98707i	0.205073	−	0.355197i
$127$	6.90581	+	11.9612i	0.612792	+	1.06139i	0.990768	+	0.135571i	$0.0432869\pi$
$127$	6.90581	+	11.9612i	0.612792	+	1.06139i	−0.377976	+	0.925815i	$0.623380\pi$
$128$	−2.79777	+	1.61529i	−0.247290	+	0.142773i
$129$	−2.28621			−0.201289
$130$		0			0
$131$	2.99462			0.261641			0.130821	−	0.991406i	$-0.458239\pi$
$131$	2.99462			0.261641			0.130821	+	0.991406i	$0.458239\pi$
$132$	−9.40177	+	5.42812i	−0.818319	+	0.472457i
$133$	4.27144	+	7.39835i	0.370381	+	0.641518i
$134$	1.55831	−	2.69907i	0.134618	−	0.233164i
$135$		−	3.35690i		−	0.288916i
$136$	0.320466	+	0.185021i	0.0274797	+	0.0158654i
$137$	19.9354	+	11.5097i	1.70319	+	0.983339i	0.942487	+	0.334243i	$0.108481\pi$
$137$	19.9354	+	11.5097i	1.70319	+	0.983339i	0.760706	+	0.649096i	$0.224853\pi$
$138$		−	4.15346i		−	0.353566i
$139$	−0.491271	+	0.850906i	−0.0416690	+	0.0721729i	−0.886108	−	0.463479i	$-0.846601\pi$
$139$	−0.491271	+	0.850906i	−0.0416690	+	0.0721729i	0.844439	+	0.535652i	$0.179934\pi$
$140$	8.28986	+	14.3585i	0.700621	+	1.21351i
$141$	3.29257	−	1.90097i	0.277285	−	0.160090i
$142$	4.87369			0.408991
$143$		0			0
$144$	−3.56465			−0.297054
$145$	−11.4513	+	6.61141i	−0.950978	+	0.549048i
$146$	7.59246	+	13.1505i	0.628356	+	1.08835i
$147$	0.975541	−	1.68969i	0.0804613	−	0.139363i
$148$			19.3472i			1.59033i
$149$	−8.88461	−	5.12953i	−0.727855	−	0.420228i	0.0897817	−	0.995961i	$-0.471383\pi$
$149$	−8.88461	−	5.12953i	−0.727855	−	0.420228i	−0.817637	+	0.575734i	$0.804716\pi$
$150$	11.1234	+	6.42208i	0.908219	+	0.524360i
$151$			20.1685i			1.64129i	0.571438	+	0.820646i	$0.306386\pi$
$151$			20.1685i			1.64129i	−0.571438	+	0.820646i	$0.693614\pi$
$152$	−0.771438	+	1.33617i	−0.0625719	+	0.108378i
$153$	0.455927	+	0.789689i	0.0368595	+	0.0638425i
$154$	19.6922	−	11.3693i	1.58684	−	0.916162i
$155$	29.6383			2.38061
$156$		0			0
$157$	10.4383			0.833070			0.416535	−	0.909120i	$-0.363244\pi$
$157$	10.4383			0.833070			0.416535	+	0.909120i	$0.363244\pi$
$158$	6.63798	−	3.83244i	0.528089	−	0.304892i
$159$	0.271438	+	0.470145i	0.0215265	+	0.0372849i
$160$	13.6211	−	23.5924i	1.07684	−	1.86515i
$161$			4.55496i			0.358981i
$162$	1.77441	+	1.02446i	0.139411	+	0.0804891i
$163$	−9.56657	−	5.52326i	−0.749312	−	0.432615i	0.0761335	−	0.997098i	$-0.475742\pi$
$163$	−9.56657	−	5.52326i	−0.749312	−	0.432615i	−0.825445	+	0.564482i	$0.809076\pi$
$164$		−	15.2524i		−	1.19101i
$165$	8.28986	−	14.3585i	0.645364	−	1.11780i
$166$	−2.36443	−	4.09531i	−0.183515	−	0.317858i
$167$	−7.02339	+	4.05496i	−0.543487	+	0.313782i	−0.746491	−	0.665396i	$-0.768263\pi$
$167$	−7.02339	+	4.05496i	−0.543487	+	0.313782i	0.203004	+	0.979178i	$0.434929\pi$
$168$	−0.911854			−0.0703511
$169$		0			0
$170$	−6.27173			−0.481020
$171$	−3.29257	+	1.90097i	−0.251789	+	0.145371i
$172$	2.51261	+	4.35198i	0.191585	+	0.331835i
$173$	−9.02811	+	15.6371i	−0.686394	+	1.18887i	0.286602	+	0.958050i	$0.407474\pi$
$173$	−9.02811	+	15.6371i	−0.686394	+	1.18887i	−0.972996	+	0.230820i	$0.925859\pi$
$174$		−	8.07069i		−	0.611837i
$175$	−12.1986	−	7.04288i	−0.922129	−	0.532391i
$176$	−15.2471	−	8.80290i	−1.14929	−	0.663543i
$177$		−	4.71379i		−	0.354310i
$178$	−10.3046	+	17.8481i	−0.772364	+	1.33777i
$179$	−9.93512	−	17.2081i	−0.742585	−	1.28620i	−0.951314	−	0.308222i	$-0.900266\pi$
$179$	−9.93512	−	17.2081i	−0.742585	−	1.28620i	0.208729	−	0.977974i	$-0.433067\pi$
$180$	−6.39011	+	3.68933i	−0.476291	+	0.274987i
$181$	10.0828			0.749446			0.374723	−	0.927137i	$-0.377738\pi$
$181$	10.0828			0.749446			0.374723	+	0.927137i	$0.377738\pi$
$182$		0			0
$183$	−3.67994			−0.272029
$184$	−0.712430	+	0.411322i	−0.0525210	+	0.0303230i
$185$	−14.7736	−	25.5886i	−1.08618	−	1.88131i
$186$	−9.04503	+	15.6665i	−0.663214	+	1.14872i
$187$			4.50365i			0.329339i
$188$	−7.23728	−	4.17845i	−0.527833	−	0.304745i
$189$	−1.94594	−	1.12349i	−0.141546	−	0.0817219i
$190$		−	26.1497i		−	1.89710i
$191$	3.29374	−	5.70493i	0.238327	−	0.412794i	−0.721908	−	0.691990i	$-0.756734\pi$
$191$	3.29374	−	5.70493i	0.238327	−	0.412794i	0.960234	+	0.279196i	$0.0900678\pi$
$192$	4.74914	+	8.22574i	0.342739	+	0.593642i
$193$	−9.41131	+	5.43362i	−0.677441	+	0.391121i	−0.798890	−	0.601477i	$-0.794579\pi$
$193$	−9.41131	+	5.43362i	−0.677441	+	0.391121i	0.121449	+	0.992598i	$0.461246\pi$
$194$	−33.0476			−2.37268
$195$		0			0
$196$	−4.28860			−0.306329
$197$	8.00346	−	4.62080i	0.570223	−	0.329218i	−0.187015	−	0.982357i	$-0.559881\pi$
$197$	8.00346	−	4.62080i	0.570223	−	0.329218i	0.757238	+	0.653139i	$0.226548\pi$
$198$	5.05980	+	8.76383i	0.359585	+	0.622819i
$199$	−0.782323	+	1.35502i	−0.0554574	+	0.0960551i	−0.892421	−	0.451203i	$-0.850995\pi$
$199$	−0.782323	+	1.35502i	−0.0554574	+	0.0960551i	0.836964	+	0.547258i	$0.184328\pi$
$200$		−	2.54394i		−	0.179884i
$201$	−1.31732	−	0.760553i	−0.0929164	−	0.0536453i
$202$	17.6531	+	10.1920i	1.24207	+	0.717108i
$203$			8.85086i			0.621208i
$204$	1.00216	−	1.73578i	0.0701649	−	0.121529i
$205$	11.6468	+	20.1728i	0.813444	+	1.40893i
$206$	−19.4971	+	11.2567i	−1.35843	+	0.784289i
$207$	−2.02715			−0.140896
$208$		0			0
$209$	−18.7778			−1.29889
$210$	13.3842	−	7.72737i	0.923597	−	0.533239i
$211$	−11.6223	−	20.1304i	−0.800112	−	1.38583i	−0.919542	−	0.392991i	$-0.871440\pi$
$211$	−11.6223	−	20.1304i	−0.800112	−	1.38583i	0.119430	−	0.992843i	$-0.461893\pi$
$212$	0.596638	−	1.03341i	0.0409773	−	0.0709747i
$213$		−	2.37867i		−	0.162984i
$214$	−17.5181	−	10.1141i	−1.19751	−	0.691385i
$215$	−6.64637	−	3.83728i	−0.453278	−	0.261700i
$216$		−	0.405813i		−	0.0276121i
$217$	9.91939	−	17.1809i	0.673372	−	1.16631i
$218$	−20.7397	−	35.9223i	−1.40467	−	2.43296i
$219$	6.41828	−	3.70560i	0.433707	−	0.250401i
$220$	−36.4432			−2.45700
$221$		0			0
$222$	18.0344			1.21039
$223$	9.29985	−	5.36927i	0.622764	−	0.359553i	−0.155180	−	0.987886i	$-0.549596\pi$
$223$	9.29985	−	5.36927i	0.622764	−	0.359553i	0.777944	+	0.628333i	$0.216262\pi$
$224$	−9.11745	−	15.7919i	−0.609185	−	1.05514i
$225$	3.13437	−	5.42890i	0.208958	−	0.361926i
$226$		−	19.8582i		−	1.32094i
$227$	6.04125	+	3.48792i	0.400972	+	0.231501i	0.686903	−	0.726749i	$-0.258970\pi$
$227$	6.04125	+	3.48792i	0.400972	+	0.231501i	−0.285931	+	0.958250i	$0.592303\pi$
$228$	7.23728	+	4.17845i	0.479301	+	0.276724i
$229$			16.8049i			1.11050i	0.831683	+	0.555250i	$0.187378\pi$
$229$			16.8049i			1.11050i	−0.831683	+	0.555250i	$0.812622\pi$
$230$	6.97136	−	12.0748i	0.459678	−	0.796186i
$231$	−5.54892	−	9.61101i	−0.365092	−	0.632358i
$232$	−1.38434	+	0.799249i	−0.0908864	+	0.0524733i
$233$	−8.69202			−0.569433			−0.284717	−	0.958612i	$-0.591900\pi$
$233$	−8.69202			−0.569433			−0.284717	+	0.958612i	$0.591900\pi$
$234$		0			0
$235$	12.7627			0.832547
$236$	−8.97307	+	5.18060i	−0.584097	+	0.337229i
$237$	−1.87047	−	3.23975i	−0.121500	−	0.210444i
$238$	−2.09903	+	3.63563i	−0.136060	+	0.235663i
$239$		−	22.9191i		−	1.48252i	−0.671220	−	0.741258i	$-0.734229\pi$
$239$		−	22.9191i		−	1.48252i	0.671220	−	0.741258i	$-0.265771\pi$
$240$	−10.3630	−	5.98307i	−0.668928	−	0.386206i
$241$	19.0354	+	10.9901i	1.22618	+	0.707933i	0.966228	−	0.257690i	$-0.0829612\pi$
$241$	19.0354	+	10.9901i	1.22618	+	0.707933i	0.259948	+	0.965623i	$0.416295\pi$
$242$			27.4426i			1.76408i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	4.04437	+	7.00505i	0.258914	+	0.448452i
$245$	5.67210	−	3.27479i	0.362377	−	0.209219i
$246$	−14.2174			−0.906471
$247$		0			0
$248$	3.58296			0.227518
$249$	−1.99877	+	1.15399i	−0.126667	+	0.0731311i
$250$	4.36323	+	7.55734i	0.275955	+	0.477968i
$251$	13.3218	−	23.0741i	0.840868	−	1.45643i	−0.0482946	−	0.998833i	$-0.515379\pi$
$251$	13.3218	−	23.0741i	0.840868	−	1.45643i	0.889162	−	0.457592i	$-0.151288\pi$
$252$			4.93900i			0.311128i
$253$	−8.67072	−	5.00604i	−0.545123	−	0.314727i
$254$	−24.5075	−	14.1494i	−1.53774	−	0.887815i
$255$			3.06100i			0.191687i
$256$	−6.18867	+	10.7191i	−0.386792	+	0.669943i
$257$	11.5722	+	20.0436i	0.721853	+	1.25029i	0.960256	+	0.279119i	$0.0900425\pi$
$257$	11.5722	+	20.0436i	0.721853	+	1.25029i	−0.238404	+	0.971166i	$0.576624\pi$
$258$	4.05668	−	2.34213i	0.252558	−	0.145814i
$259$	−19.7778			−1.22893
$260$		0			0
$261$	−3.93900			−0.243818
$262$	−5.31370	+	3.06787i	−0.328282	+	0.189533i
$263$	9.26420	+	16.0461i	0.571255	+	0.989443i	0.996437	+	0.0843352i	$0.0268766\pi$
$263$	9.26420	+	16.0461i	0.571255	+	0.989443i	−0.425182	+	0.905108i	$0.639790\pi$
$264$	1.00216	−	1.73578i	0.0616784	−	0.106830i
$265$			1.82238i			0.111948i
$266$	−15.1586	−	8.75182i	−0.929434	−	0.536609i
$267$	8.71101	+	5.02930i	0.533105	+	0.307788i
$268$			3.34349i			0.204236i
$269$	−4.87920	+	8.45102i	−0.297490	+	0.515268i	−0.975561	−	0.219729i	$-0.929483\pi$
$269$	−4.87920	+	8.45102i	−0.297490	+	0.515268i	0.678071	+	0.734996i	$0.262816\pi$
$270$	3.43900	+	5.95652i	0.209291	+	0.362503i
$271$	19.7471	−	11.4010i	1.19955	−	0.692560i	0.239094	−	0.970996i	$-0.423150\pi$
$271$	19.7471	−	11.4010i	1.19955	−	0.692560i	0.960455	+	0.278437i	$0.0898163\pi$
$272$	3.25044			0.197087
$273$		0			0
$274$	−47.1648			−2.84933
$275$	26.8133	−	15.4807i	1.61690	−	0.933520i
$276$	2.22790	+	3.85883i	0.134104	+	0.232274i
$277$	−11.9852	+	20.7590i	−0.720123	+	1.24729i	0.240828	+	0.970568i	$0.422581\pi$
$277$	−11.9852	+	20.7590i	−0.720123	+	1.24729i	−0.960950	+	0.276721i	$0.910752\pi$
$278$		−	2.01315i		−	0.120741i
$279$	7.64621	+	4.41454i	0.457767	+	0.264292i
$280$	−2.65090	−	1.53050i	−0.158422	−	0.0914648i
$281$			4.12498i			0.246076i	0.992402	+	0.123038i	$0.0392637\pi$
$281$			4.12498i			0.246076i	−0.992402	+	0.123038i	$0.960736\pi$
$282$	−3.89493	+	6.74621i	−0.231940	+	0.401731i
$283$	−7.82789	−	13.5583i	−0.465320	−	0.805957i	0.533896	−	0.845550i	$-0.320727\pi$
$283$	−7.82789	−	13.5583i	−0.465320	−	0.805957i	−0.999216	+	0.0395927i	$0.987394\pi$
$284$	−4.52798	+	2.61423i	−0.268686	+	0.155126i
$285$	−12.7627			−0.755998
$286$		0			0
$287$	15.5918			0.920354
$288$	7.02805	−	4.05765i	0.414132	−	0.239099i
$289$	8.08426	+	14.0024i	0.475545	+	0.823668i
$290$	13.5462	−	23.4628i	0.795462	−	1.37778i
$291$			16.1293i			0.945516i
$292$	−14.1078	−	8.14513i	−0.825595	−	0.476658i
$293$	19.5677	+	11.2974i	1.14315	+	0.660001i	0.947210	−	0.320614i	$-0.103889\pi$
$293$	19.5677	+	11.2974i	1.14315	+	0.660001i	0.195945	+	0.980615i	$0.437223\pi$
$294$			3.99761i			0.233145i
$295$	7.91185	−	13.7037i	0.460646	−	0.797862i
$296$	−1.78597	−	3.09339i	−0.103807	−	0.179800i
$297$	4.27730	−	2.46950i	0.248194	−	0.143295i
$298$	21.0200			1.21765
$299$		0			0
$300$	−13.7791			−0.795537
$301$	−4.44883	+	2.56853i	−0.256426	+	0.148048i
$302$	−20.6618	−	35.7873i	−1.18895	−	2.05933i
$303$	4.97434	−	8.61582i	0.285769	−	0.494966i
$304$			13.5526i			0.777293i
$305$	−10.6982	−	6.17659i	−0.612575	−	0.353670i
$306$	−1.61801	−	0.934157i	−0.0924953	−	0.0534022i
$307$			6.55496i			0.374111i	0.982349	+	0.187056i	$0.0598945\pi$
$307$			6.55496i			0.374111i	−0.982349	+	0.187056i	$0.940106\pi$
$308$	−12.1969	+	21.1256i	−0.694981	+	1.20374i
$309$	5.49396	+	9.51582i	0.312540	+	0.541336i
$310$	−52.5907	+	30.3632i	−2.98695	+	1.72452i
$311$	12.0392			0.682682			0.341341	−	0.939940i	$-0.389119\pi$
$311$	12.0392			0.682682			0.341341	+	0.939940i	$0.389119\pi$
$312$		0			0
$313$	−33.8950			−1.91586			−0.957929	−	0.287005i	$-0.907340\pi$
$313$	−33.8950			−1.91586			−0.957929	+	0.287005i	$0.907340\pi$
$314$	−18.5219	+	10.6936i	−1.04525	+	0.603477i
$315$	−3.77144	−	6.53232i	−0.212496	−	0.368055i
$316$	−4.11141	+	7.12117i	−0.231285	+	0.400597i
$317$		−	4.49827i		−	0.252648i	−0.991989	−	0.126324i	$-0.959682\pi$
$317$		−	4.49827i		−	0.252648i	0.991989	−	0.126324i	$-0.0403179\pi$
$318$	−0.963288	−	0.556155i	−0.0540185	−	0.0311876i
$319$	−16.8483	−	9.72737i	−0.943323	−	0.544628i
$320$			31.8847i			1.78241i
$321$	−4.93631	+	8.54994i	−0.275518	+	0.477211i
$322$	−4.66637	−	8.08238i	−0.260046	−	0.450414i
$323$	3.00235	−	1.73341i	0.167055	−	0.0964493i
$324$	−2.19806			−0.122115
$325$		0			0
$326$	22.6334			1.25355
$327$	−17.5323	+	10.1223i	−0.969540	+	0.559764i
$328$	1.40797	+	2.43867i	0.0777421	+	0.134653i
$329$	4.27144	−	7.39835i	0.235492	−	0.407884i
$330$			33.9705i			1.87001i
$331$	9.71085	+	5.60656i	0.533757	+	0.308165i	0.742545	−	0.669796i	$-0.233619\pi$
$331$	9.71085	+	5.60656i	0.533757	+	0.308165i	−0.208788	+	0.977961i	$0.566952\pi$
$332$	4.39342	+	2.53654i	0.241120	+	0.139211i
$333$		−	8.80194i		−	0.482343i
$334$	8.30827	−	14.3904i	0.454609	−	0.787405i
$335$	−2.55310	−	4.42209i	−0.139491	−	0.241605i
$336$	−6.93659	+	4.00484i	−0.378422	+	0.218482i
$337$	−7.04892			−0.383979			−0.191989	−	0.981397i	$-0.561494\pi$
$337$	−7.04892			−0.383979			−0.191989	+	0.981397i	$0.561494\pi$
$338$		0			0
$339$	−9.69202			−0.526398
$340$	5.82685	−	3.36413i	0.316005	−	0.182446i
$341$	21.8034	+	37.7646i	1.18072	+	2.04507i
$342$	3.89493	−	6.74621i	0.210614	−	0.364793i
$343$		−	20.1129i		−	1.08599i
$344$	−0.803475	−	0.463887i	−0.0433205	−	0.0250111i
$345$	−5.89324	−	3.40246i	−0.317281	−	0.183182i
$346$		−	36.9957i		−	1.98890i
$347$	1.35205	−	2.34182i	0.0725819	−	0.125716i	−0.827450	−	0.561539i	$-0.810209\pi$
$347$	1.35205	−	2.34182i	0.0725819	−	0.125716i	0.900032	+	0.435823i	$0.143543\pi$
$348$	4.32908	+	7.49819i	0.232063	+	0.401945i
$349$	0.359835	−	0.207751i	0.0192615	−	0.0111207i	−0.490338	−	0.871532i	$-0.663127\pi$
$349$	0.359835	−	0.207751i	0.0192615	−	0.0111207i	0.509600	+	0.860412i	$0.329793\pi$
$350$	28.8605			1.54266
$351$		0			0
$352$	40.0814			2.13635
$353$	−27.8576	+	16.0836i	−1.48271	+	0.856044i	−0.999807	−	0.0196301i	$-0.993751\pi$
$353$	−27.8576	+	16.0836i	−1.48271	+	0.856044i	−0.482904	+	0.875674i	$0.660418\pi$
$354$	4.82908	+	8.36422i	0.256663	+	0.444553i
$355$	3.99247	−	6.91516i	0.211898	−	0.367018i
$356$		−	22.1094i		−	1.17180i
$357$	1.77441	+	1.02446i	0.0939120	+	0.0542201i
$358$	35.2580	+	20.3562i	1.86344	+	1.07586i
$359$		−	22.3521i		−	1.17970i	−0.807513	−	0.589850i	$-0.799187\pi$
$359$		−	22.3521i		−	1.17970i	0.807513	−	0.589850i	$-0.200813\pi$
$360$	0.681136	−	1.17976i	0.0358990	−	0.0621790i
$361$	−2.27263	−	3.93632i	−0.119612	−	0.207175i
$362$	−17.8910	+	10.3294i	−0.940331	+	0.542900i
$363$	13.3937			0.702989
$364$		0			0
$365$	24.8786			1.30221
$366$	6.52974	−	3.76995i	0.341315	−	0.197058i
$367$	1.15130	+	1.99411i	0.0600974	+	0.104092i	0.894509	−	0.447050i	$-0.147526\pi$
$367$	1.15130	+	1.99411i	0.0600974	+	0.104092i	−0.834411	+	0.551142i	$0.814192\pi$
$368$	−3.61303	+	6.25795i	−0.188342	+	0.326218i
$369$			6.93900i			0.361230i
$370$	52.4290	+	30.2699i	2.72565	+	1.57366i
$371$	1.05641	+	0.609916i	0.0548459	+	0.0316653i
$372$		−	19.4069i		−	1.00620i
$373$	9.63802	−	16.6935i	0.499038	−	0.864359i	−0.500961	−	0.865470i	$-0.667020\pi$
$373$	9.63802	−	16.6935i	0.499038	−	0.864359i	0.999999	+	0.00111058i	$0.000353507\pi$
$374$	−4.61380	−	7.99134i	−0.238574	−	0.413222i
$375$	3.68846	−	2.12953i	0.190471	−	0.109968i
$376$	1.54288			0.0795678
$377$		0			0
$378$	4.60388			0.236798
$379$	−6.35614	+	3.66972i	−0.326493	+	0.188501i	−0.654283	−	0.756250i	$-0.727029\pi$
$379$	−6.35614	+	3.66972i	−0.326493	+	0.188501i	0.327790	+	0.944751i	$0.393696\pi$
$380$	14.0266	+	24.2948i	0.719550	+	1.24630i
$381$	−6.90581	+	11.9612i	−0.353796	+	0.612792i
$382$			13.4972i			0.690577i
$383$	−16.5325	−	9.54503i	−0.844770	−	0.487728i	0.0141126	−	0.999900i	$-0.495508\pi$
$383$	−16.5325	−	9.54503i	−0.844770	−	0.487728i	−0.858883	+	0.512172i	$0.828841\pi$
$384$	−2.79777	−	1.61529i	−0.142773	−	0.0824301i
$385$		−	37.2543i		−	1.89865i
$386$	11.1330	−	19.2830i	0.566657	−	0.981479i
$387$	−1.14310	−	1.97991i	−0.0581072	−	0.100645i
$388$	30.7034	−	17.7266i	1.55873	−	0.899932i
$389$	23.9879			1.21624			0.608118	−	0.793847i	$-0.291925\pi$
$389$	23.9879			1.21624			0.608118	+	0.793847i	$0.291925\pi$
$390$		0			0
$391$	1.84846			0.0934807
$392$	0.685697	−	0.395888i	0.0346329	−	0.0199953i
$393$	1.49731	+	2.59342i	0.0755294	+	0.130821i
$394$	−9.46764	+	16.3984i	−0.476973	+	0.826141i
$395$		−	12.5579i		−	0.631859i
$396$	−9.40177	−	5.42812i	−0.472457	−	0.272773i
$397$	−3.82601	−	2.20895i	−0.192022	−	0.110864i	0.400907	−	0.916119i	$-0.368695\pi$
$397$	−3.82601	−	2.20895i	−0.192022	−	0.110864i	−0.592929	+	0.805255i	$0.702028\pi$
$398$		−	3.20583i		−	0.160694i
$399$	−4.27144	+	7.39835i	−0.213839	+	0.370381i
$400$	−11.1729	−	19.3521i	−0.558647	−	0.967605i
$401$	17.6745	−	10.2044i	0.882624	−	0.509583i	0.0111015	−	0.999938i	$-0.496466\pi$
$401$	17.6745	−	10.2044i	0.882624	−	0.509583i	0.871523	+	0.490355i	$0.163133\pi$
$402$	3.11662			0.155443
$403$		0			0
$404$	−21.8678			−1.08797
$405$	2.90716	−	1.67845i	0.144458	−	0.0834027i
$406$	−9.06734	−	15.7051i	−0.450004	−	0.779430i
$407$	21.7364	−	37.6485i	1.07743	−	1.86617i
$408$			0.370042i			0.0183198i
$409$	19.1817	+	11.0746i	0.948475	+	0.547602i	0.892607	−	0.450836i	$-0.148874\pi$
$409$	19.1817	+	11.0746i	0.948475	+	0.547602i	0.0558682	+	0.998438i	$0.482207\pi$
$410$	−41.3323	−	23.8632i	−2.04126	−	1.17852i
$411$			23.0194i			1.13546i
$412$	12.0761	−	20.9164i	0.594945	−	1.03047i
$413$	−5.29590	−	9.17276i	−0.260594	−	0.451362i
$414$	3.59700	−	2.07673i	0.176783	−	0.102066i
$415$	−7.74764			−0.380317
$416$		0			0
$417$	−0.982542			−0.0481153
$418$	33.3196	−	19.2371i	1.62971	−	0.940915i
$419$	−7.37800	−	12.7791i	−0.360439	−	0.624299i	0.627594	−	0.778541i	$-0.284040\pi$
$419$	−7.37800	−	12.7791i	−0.360439	−	0.624299i	−0.988033	+	0.154242i	$0.950706\pi$
$420$	−8.28986	+	14.3585i	−0.404504	+	0.700621i
$421$			8.47219i			0.412909i	0.978456	+	0.206455i	$0.0661926\pi$
$421$			8.47219i			0.412909i	−0.978456	+	0.206455i	$0.933807\pi$
$422$	41.2455	+	23.8131i	2.00780	+	1.15920i
$423$	3.29257	+	1.90097i	0.160090	+	0.0924283i
$424$			0.220306i			0.0106990i
$425$	−2.85809	+	4.95036i	−0.138638	+	0.240128i
$426$	2.43685	+	4.22074i	0.118066	+	0.204496i
$427$	−7.16095	+	4.13437i	−0.346543	+	0.200076i
$428$	21.7006			1.04894
$429$		0			0
$430$	15.7245			0.758305
$431$	2.07137	−	1.19591i	0.0997744	−	0.0576048i	−0.449283	−	0.893390i	$-0.648320\pi$
$431$	2.07137	−	1.19591i	0.0997744	−	0.0576048i	0.549057	+	0.835785i	$0.314987\pi$
$432$	−1.78232	−	3.08707i	−0.0857521	−	0.148527i
$433$	−5.21432	+	9.03147i	−0.250584	+	0.434025i	−0.963687	−	0.267035i	$-0.913956\pi$
$433$	−5.21432	+	9.03147i	−0.250584	+	0.434025i	0.713102	+	0.701060i	$0.247289\pi$
$434$			40.6480i			1.95117i
$435$	−11.4513	−	6.61141i	−0.549048	−	0.316993i
$436$	38.5371	+	22.2494i	1.84559	+	1.06555i
$437$			7.70709i			0.368680i
$438$	−7.59246	+	13.1505i	−0.362782	+	0.628356i
$439$	−16.2751	−	28.1893i	−0.776767	−	1.34540i	−0.933796	−	0.357807i	$-0.883525\pi$
$439$	−16.2751	−	28.1893i	−0.776767	−	1.34540i	0.157028	−	0.987594i	$-0.449809\pi$
$440$	5.82685	−	3.36413i	0.277784	−	0.160379i
$441$	1.95108			0.0929087
$442$		0			0
$443$	9.58211			0.455260			0.227630	−	0.973748i	$-0.426902\pi$
$443$	9.58211			0.455260			0.227630	+	0.973748i	$0.426902\pi$
$444$	−16.7552	+	9.67360i	−0.795165	+	0.459089i
$445$	16.8828	+	29.2419i	0.800324	+	1.38620i
$446$	−11.0012	+	19.0546i	−0.520922	+	0.902263i
$447$		−	10.2591i		−	0.485237i
$448$	18.4831	+	10.6712i	0.873243	+	0.504167i
$449$	−24.5897	−	14.1969i	−1.16046	−	0.669992i	−0.209045	−	0.977906i	$-0.567036\pi$
$449$	−24.5897	−	14.1969i	−1.16046	−	0.669992i	−0.951414	+	0.307914i	$0.900369\pi$
$450$			12.8442i			0.605479i
$451$	−17.1359	+	29.6802i	−0.806896	+	1.39759i
$452$	10.6518	+	18.4495i	0.501020	+	0.867792i
$453$	−17.4665	+	10.0843i	−0.820646	+	0.473800i
$454$	−14.2929			−0.670800
$455$		0			0
$456$	−1.54288			−0.0722518
$457$	4.32639	−	2.49784i	0.202380	−	0.116844i	−0.395385	−	0.918515i	$-0.629389\pi$
$457$	4.32639	−	2.49784i	0.202380	−	0.116844i	0.597765	+	0.801671i	$0.296056\pi$
$458$	−17.2159	−	29.8189i	−0.804448	−	1.39335i
$459$	−0.455927	+	0.789689i	−0.0212808	+	0.0368595i
$460$			14.9576i			0.697404i
$461$	−1.17137	−	0.676292i	−0.0545562	−	0.0314981i	0.472474	−	0.881345i	$-0.343361\pi$
$461$	−1.17137	−	0.676292i	−0.0545562	−	0.0314981i	−0.527030	+	0.849847i	$0.676694\pi$
$462$	19.6922	+	11.3693i	0.916162	+	0.528946i
$463$			3.36467i			0.156369i	0.996939	+	0.0781846i	$0.0249124\pi$
$463$			3.36467i			0.156369i	−0.996939	+	0.0781846i	$0.975088\pi$
$464$	−7.02057	+	12.1600i	−0.325922	+	0.564513i
$465$	14.8192	+	25.6675i	0.687222	+	1.19030i
$466$	15.4232	−	8.90462i	0.714468	−	0.412498i
$467$	−6.91079			−0.319793			−0.159897	−	0.987134i	$-0.551116\pi$
$467$	−6.91079			−0.319793			−0.159897	+	0.987134i	$0.551116\pi$
$468$		0			0
$469$	−3.41789			−0.157824
$470$	−22.6463	+	13.0749i	−1.04460	+	0.603099i
$471$	5.21917	+	9.03987i	0.240487	+	0.416535i
$472$	0.956459	−	1.65664i	0.0440246	−	0.0762529i
$473$		−	11.2916i		−	0.519188i
$474$	6.63798	+	3.83244i	0.304892	+	0.176030i
$475$	−20.6403	−	11.9167i	−0.947043	−	0.546776i
$476$		−	4.50365i		−	0.206424i
$477$	−0.271438	+	0.470145i	−0.0124283	+	0.0215265i
$478$	23.4797	+	40.6681i	1.07394	+	1.86011i
$479$	−3.04471	+	1.75786i	−0.139116	+	0.0803189i	−0.567943	−	0.823068i	$-0.692261\pi$
$479$	−3.04471	+	1.75786i	−0.139116	+	0.0803189i	0.428826	+	0.903387i	$0.358927\pi$
$480$	27.2422			1.24343
$481$		0			0
$482$	−45.0355			−2.05131
$483$	−3.94471	+	2.27748i	−0.179490	+	0.103629i
$484$	−14.7201	−	25.4960i	−0.669097	−	1.15891i
$485$	−27.0722	+	46.8904i	−1.22928	+	2.12918i
$486$			2.04892i			0.0929408i
$487$	11.1266	+	6.42394i	0.504194	+	0.291096i	0.730444	−	0.682973i	$-0.239313\pi$
$487$	11.1266	+	6.42394i	0.504194	+	0.291096i	−0.226250	+	0.974069i	$0.572647\pi$
$488$	−1.29329	−	0.746684i	−0.0585447	−	0.0338008i
$489$		−	11.0465i		−	0.499541i
$490$	−6.70978	+	11.6217i	−0.303117	+	0.525014i
$491$	14.3354	+	24.8297i	0.646948	+	1.12055i	0.983848	+	0.179007i	$0.0572885\pi$
$491$	14.3354	+	24.8297i	0.646948	+	1.12055i	−0.336899	+	0.941541i	$0.609378\pi$
$492$	13.2089	−	7.62618i	0.595504	−	0.343815i
$493$	3.59179			0.161766
$494$		0			0
$495$	16.5797			0.745203
$496$	27.2560	−	15.7363i	1.22383	−	0.706580i
$497$	−2.67241	−	4.62874i	−0.119874	−	0.207628i
$498$	2.36443	−	4.09531i	0.105953	−	0.183515i
$499$		−	33.5555i		−	1.50215i	−0.660215	−	0.751076i	$-0.729535\pi$
$499$		−	33.5555i		−	1.50215i	0.660215	−	0.751076i	$-0.270465\pi$
$500$	−8.10745	−	4.68084i	−0.362576	−	0.209334i
$501$	−7.02339	−	4.05496i	−0.313782	−	0.181162i
$502$			54.5907i			2.43650i
$503$	−10.7817	+	18.6744i	−0.480730	+	0.832650i	−0.999756	−	0.0221094i	$-0.992962\pi$
$503$	−10.7817	+	18.6744i	−0.480730	+	0.832650i	0.519025	+	0.854759i	$0.326295\pi$
$504$	−0.455927	−	0.789689i	−0.0203086	−	0.0351755i
$505$	28.9224	−	16.6984i	1.28703	−	0.743067i
$506$	20.5139			0.911955
$507$		0			0
$508$	30.3588			1.34695
$509$	−7.69904	+	4.44504i	−0.341254	+	0.197023i	−0.660826	−	0.750539i	$-0.729794\pi$
$509$	−7.69904	+	4.44504i	−0.341254	+	0.197023i	0.319572	+	0.947562i	$0.396461\pi$
$510$	−3.13587	−	5.43148i	−0.138859	−	0.240510i
$511$	8.32640	−	14.4217i	0.368338	−	0.637980i
$512$		−	31.8213i		−	1.40632i
$513$	−3.29257	−	1.90097i	−0.145371	−	0.0839298i
$514$	−41.0677	−	23.7104i	−1.81142	−	1.04582i
$515$			36.8853i			1.62536i
$516$	−2.51261	+	4.35198i	−0.110612	+	0.191585i
$517$	9.38889	+	16.2620i	0.412923	+	0.715203i
$518$	35.0940	−	20.2615i	1.54194	−	0.890240i
$519$	−18.0562			−0.792580
$520$		0			0
$521$	19.3478			0.847642			0.423821	−	0.905746i	$-0.360688\pi$
$521$	19.3478			0.847642			0.423821	+	0.905746i	$0.360688\pi$
$522$	6.98942	−	4.03534i	0.305919	−	0.176622i
$523$	6.29739	+	10.9074i	0.275366	+	0.476947i	0.970227	−	0.242196i	$-0.0778678\pi$
$523$	6.29739	+	10.9074i	0.275366	+	0.476947i	−0.694862	+	0.719143i	$0.744534\pi$
$524$	3.29118	−	5.70050i	0.143776	−	0.249027i
$525$		−	14.0858i		−	0.614753i
$526$	−32.8771	−	18.9816i	−1.43351	−	0.827636i
$527$	−6.97223	−	4.02542i	−0.303715	−	0.175350i
$528$		−	17.6058i		−	0.766194i
$529$	9.44534	−	16.3598i	0.410667	−	0.711296i
$530$	−1.86695	−	3.23366i	−0.0810953	−	0.140461i
$531$	4.08226	−	2.35690i	0.177155	−	0.102281i
$532$	18.7778			0.814120
$533$		0			0
$534$	−20.6093			−0.891850
$535$	−28.7013	+	16.5707i	−1.24086	+	0.716413i
$536$	−0.308643	−	0.534585i	−0.0133313	−	0.0230905i
$537$	9.93512	−	17.2081i	0.428732	−	0.742585i
$538$		−	19.9941i		−	0.862009i
$539$	8.34537	+	4.81820i	0.359460	+	0.207535i
$540$	−6.39011	−	3.68933i	−0.274987	−	0.158764i
$541$		−	29.0019i		−	1.24689i	−0.781867	−	0.623445i	$-0.785733\pi$
$541$		−	29.0019i		−	1.24689i	0.781867	−	0.623445i	$-0.214267\pi$
$542$	−23.3596	+	40.4601i	−1.00338	+	1.73791i
$543$	5.04138	+	8.73193i	0.216347	+	0.374723i
$544$	−6.40856	+	3.69998i	−0.274765	+	0.158635i
$545$	−67.9590			−2.91104
$546$		0			0
$547$	27.7006			1.18439			0.592197	−	0.805793i	$-0.298261\pi$
$547$	27.7006			1.18439			0.592197	+	0.805793i	$0.298261\pi$
$548$	43.8192	−	25.2990i	1.87186	−	1.08072i
$549$	−1.83997	−	3.18692i	−0.0785280	−	0.136014i
$550$	−31.7186	+	54.9383i	−1.35249	+	2.34258i
$551$			14.9758i			0.637992i
$552$	−0.712430	−	0.411322i	−0.0303230	−	0.0175070i
$553$	−7.27965	−	4.20291i	−0.309562	−	0.178726i
$554$		−	49.1135i		−	2.08663i
$555$	14.7736	−	25.5886i	0.627104	−	1.08618i
$556$	1.07984	+	1.87034i	0.0457956	+	0.0793203i
$557$	−5.89738	+	3.40485i	−0.249880	+	0.144268i	−0.619709	−	0.784831i	$-0.712749\pi$
$557$	−5.89738	+	3.40485i	−0.249880	+	0.144268i	0.369829	+	0.929100i	$0.379416\pi$
$558$	−18.0901			−0.765814
$559$		0			0
$560$	−26.8877			−1.13621
$561$	−3.90027	+	2.25182i	−0.164670	+	0.0950721i
$562$	−4.22587	−	7.31943i	−0.178258	−	0.308751i
$563$	−9.62618	+	16.6730i	−0.405695	+	0.702684i	−0.994402	−	0.105662i	$-0.966304\pi$
$563$	−9.62618	+	16.6730i	−0.405695	+	0.702684i	0.588707	+	0.808346i	$0.299637\pi$
$564$		−	8.35690i		−	0.351889i
$565$	−28.1762	−	16.2676i	−1.18538	−	0.684381i
$566$	27.7798	+	16.0387i	1.16767	+	0.674157i
$567$		−	2.24698i		−	0.0943643i
$568$	0.482647	−	0.835969i	0.0202514	−	0.0350765i
$569$	3.92423	+	6.79697i	0.164512	+	0.284944i	0.936482	−	0.350716i	$-0.114062\pi$
$569$	3.92423	+	6.79697i	0.164512	+	0.284944i	−0.771970	+	0.635659i	$0.780728\pi$
$570$	22.6463	−	13.0749i	0.948551	−	0.547646i
$571$	−29.8568			−1.24947			−0.624735	−	0.780837i	$-0.714793\pi$
$571$	−29.8568			−1.24947			−0.624735	+	0.780837i	$0.714793\pi$
$572$		0			0
$573$	6.58748			0.275196
$574$	−27.6663	+	15.9731i	−1.15477	+	0.666706i
$575$	−6.35384	−	11.0052i	−0.264973	−	0.458947i
$576$	−4.74914	+	8.22574i	−0.197881	+	0.342739i
$577$			8.97823i			0.373769i	0.982382	+	0.186884i	$0.0598389\pi$
$577$			8.97823i			0.373769i	−0.982382	+	0.186884i	$0.940161\pi$
$578$	−28.6897	−	16.5640i	−1.19333	−	0.688971i
$579$	−9.41131	−	5.43362i	−0.391121	−	0.225814i
$580$			29.0646i			1.20684i
$581$	−2.59299	+	4.49119i	−0.107575	+	0.186326i
$582$	−16.5238	−	28.6201i	−0.684933	−	1.18634i
$583$	−2.32205	+	1.34063i	−0.0961693	+	0.0555234i
$584$	3.00756			0.124454
$585$		0			0
$586$	−46.2948			−1.91242
$587$	20.6580	−	11.9269i	0.852648	−	0.492277i	−0.00889531	−	0.999960i	$-0.502832\pi$
$587$	20.6580	−	11.9269i	0.852648	−	0.492277i	0.861543	+	0.507684i	$0.169498\pi$
$588$	−2.14430	−	3.71404i	−0.0884295	−	0.153164i
$589$	16.7838	−	29.0704i	0.691565	−	1.19783i
$590$			32.4215i			1.33477i
$591$	8.00346	+	4.62080i	0.329218	+	0.190074i
$592$	−27.1722	−	15.6879i	−1.11677	−	0.644769i
$593$		−	11.9866i		−	0.492230i	−0.969241	−	0.246115i	$-0.920846\pi$
$593$		−	11.9866i		−	0.492230i	0.969241	−	0.246115i	$-0.0791541\pi$
$594$	−5.05980	+	8.76383i	−0.207606	+	0.359585i
$595$	3.43900	+	5.95652i	0.140985	+	0.244194i
$596$	−19.5289	+	11.2750i	−0.799936	+	0.461843i
$597$	−1.56465			−0.0640367
$598$		0			0
$599$	29.1142			1.18958			0.594788	−	0.803883i	$-0.297236\pi$
$599$	29.1142			1.18958			0.594788	+	0.803883i	$0.297236\pi$
$600$	2.20312	−	1.27197i	0.0899419	−	0.0519280i
$601$	−18.5683	−	32.1612i	−0.757417	−	1.31188i	−0.944164	−	0.329476i	$-0.893128\pi$
$601$	−18.5683	−	32.1612i	−0.757417	−	1.31188i	0.186747	−	0.982408i	$-0.440205\pi$
$602$	5.26271	−	9.11528i	0.214492	−	0.371511i
$603$		−	1.52111i		−	0.0619442i
$604$	38.3924	+	22.1658i	1.56216	+	0.901915i
$605$	38.9377	+	22.4807i	1.58304	+	0.913970i
$606$			20.3840i			0.828045i
$607$	7.11625	−	12.3257i	0.288840	−	0.500285i	−0.684693	−	0.728831i	$-0.740064\pi$
$607$	7.11625	−	12.3257i	0.288840	−	0.500285i	0.973533	+	0.228546i	$0.0733972\pi$
$608$	−15.4269	−	26.7202i	−0.625644	−	1.08365i
$609$	−7.66507	+	4.42543i	−0.310604	+	0.179327i
$610$	25.3106			1.02480
$611$		0			0
$612$	2.00431			0.0810195
$613$	26.2526	−	15.1570i	1.06033	−	0.612184i	0.134810	−	0.990872i	$-0.456958\pi$
$613$	26.2526	−	15.1570i	1.06033	−	0.612184i	0.925525	+	0.378687i	$0.123624\pi$
$614$	−6.71528	−	11.6312i	−0.271007	−	0.469398i
$615$	−11.6468	+	20.1728i	−0.469642	+	0.813444i
$616$		−	4.50365i		−	0.181457i
$617$	21.6192	+	12.4819i	0.870358	+	0.502501i	0.867467	−	0.497494i	$-0.165746\pi$
$617$	21.6192	+	12.4819i	0.870358	+	0.502501i	0.00289086	+	0.999996i	$0.499080\pi$
$618$	−19.4971	−	11.2567i	−0.784289	−	0.452810i
$619$		−	35.6122i		−	1.43138i	−0.698420	−	0.715688i	$-0.746113\pi$
$619$		−	35.6122i		−	1.43138i	0.698420	−	0.715688i	$-0.253887\pi$
$620$	32.5734	−	56.4188i	1.30818	−	2.26584i
$621$	−1.01357	−	1.75556i	−0.0406733	−	0.0704482i
$622$	−21.3626	+	12.3337i	−0.856561	+	0.494536i
$623$	22.6015			0.905509
$624$		0			0
$625$	−17.0465			−0.681861
$626$	60.1438	−	34.7240i	2.40383	−	1.38785i
$627$	−9.38889	−	16.2620i	−0.374956	−	0.649443i
$628$	11.4721	−	19.8702i	0.457785	−	0.792907i
$629$			8.02608i			0.320021i
$630$	13.3842	+	7.72737i	0.533239	+	0.307866i
$631$	20.6832	+	11.9415i	0.823385	+	0.475382i	0.851582	−	0.524221i	$-0.175643\pi$
$631$	20.6832	+	11.9415i	0.823385	+	0.475382i	−0.0281972	+	0.999602i	$0.508977\pi$
$632$		−	1.51812i		−	0.0603877i
$633$	11.6223	−	20.1304i	0.461945	−	0.800112i
$634$	4.60829	+	7.98180i	0.183019	+	0.316998i
$635$	−40.1526	+	23.1821i	−1.59341	+	0.919953i
$636$	1.19328			0.0473165
$637$		0			0
$638$	39.8611			1.57812
$639$	2.05999	−	1.18933i	0.0814918	−	0.0470493i
$640$	−5.42237	−	9.39182i	−0.214338	−	0.371244i
$641$	−12.3288	+	21.3542i	−0.486960	+	0.843440i	−0.999888	−	0.0149922i	$-0.995228\pi$
$641$	−12.3288	+	21.3542i	−0.486960	+	0.843440i	0.512927	+	0.858432i	$0.328561\pi$
$642$		−	20.2282i		−	0.798343i
$643$	−41.4103	−	23.9083i	−1.63306	−	0.942850i	−0.983141	−	0.182850i	$-0.941468\pi$
$643$	−41.4103	−	23.9083i	−1.63306	−	0.942850i	−0.649923	−	0.760000i	$-0.725199\pi$
$644$	8.67072	+	5.00604i	0.341674	+	0.197266i
$645$		−	7.67456i		−	0.302186i
$646$	−3.55161	+	6.15156i	−0.139736	+	0.242030i
$647$	−2.69471	−	4.66737i	−0.105940	−	0.183493i	0.808182	−	0.588933i	$-0.200452\pi$
$647$	−2.69471	−	4.66737i	−0.105940	−	0.183493i	−0.914122	+	0.405440i	$0.867118\pi$
$648$	0.351445	−	0.202907i	0.0138060	−	0.00797092i
$649$	23.2814			0.913876
$650$		0			0
$651$	19.8388			0.777543
$652$	−21.0279	+	12.1405i	−0.823517	+	0.475458i
$653$	2.51895	+	4.36295i	0.0985741	+	0.170735i	0.911095	−	0.412197i	$-0.135239\pi$
$653$	2.51895	+	4.36295i	0.0985741	+	0.170735i	−0.812521	+	0.582933i	$0.801905\pi$
$654$	20.7397	−	35.9223i	0.810988	−	1.40467i
$655$			10.0526i			0.392789i
$656$	21.4212	+	12.3675i	0.836358	+	0.482871i
$657$	6.41828	+	3.70560i	0.250401	+	0.144569i
$658$			17.5036i			0.682363i
$659$	21.9906	−	38.0888i	0.856632	−	1.48373i	−0.0184899	−	0.999829i	$-0.505886\pi$
$659$	21.9906	−	38.0888i	0.856632	−	1.48373i	0.875122	−	0.483902i	$-0.160781\pi$
$660$	−18.2216	−	31.5608i	−0.709276	−	1.22850i
$661$	33.0989	−	19.1097i	1.28740	−	0.743280i	0.309210	−	0.950994i	$-0.399936\pi$
$661$	33.0989	−	19.1097i	1.28740	−	0.743280i	0.978190	+	0.207714i	$0.0666022\pi$
$662$	−22.9748			−0.892940
$663$		0			0
$664$	−0.936608			−0.0363474
$665$	−24.8355	+	14.3388i	−0.963079	+	0.556034i
$666$	9.01722	+	15.6183i	0.349410	+	0.605196i
$667$	−3.99247	+	6.91516i	−0.154589	+	0.267756i
$668$			17.8261i			0.689713i
$669$	9.29985	+	5.36927i	0.359553	+	0.207588i
$670$	9.06051	+	5.23109i	0.350038	+	0.202094i
$671$		−	18.1752i		−	0.701647i
$672$	9.11745	−	15.7919i	0.351713	−	0.609185i
$673$	−3.33244	−	5.77195i	−0.128456	−	0.222492i	0.794623	−	0.607104i	$-0.207669\pi$
$673$	−3.33244	−	5.77195i	−0.128456	−	0.222492i	−0.923079	+	0.384611i	$0.874335\pi$
$674$	12.5077	−	7.22132i	0.481779	−	0.278155i
$675$	6.26875			0.241284
$676$		0			0
$677$	4.80194			0.184553			0.0922767	−	0.995733i	$-0.470586\pi$
$677$	4.80194			0.184553			0.0922767	+	0.995733i	$0.470586\pi$
$678$	17.1977	−	9.92908i	0.660472	−	0.381324i
$679$	18.1211	+	31.3867i	0.695424	+	1.20451i
$680$	−0.621097	+	1.07577i	−0.0238180	+	0.0412539i
$681$			6.97584i			0.267315i
$682$	−77.3766	−	44.6734i	−2.96290	−	1.71063i
$683$	9.75063	+	5.62953i	0.373098	+	0.215408i	0.674811	−	0.737991i	$-0.264225\pi$
$683$	9.75063	+	5.62953i	0.373098	+	0.215408i	−0.301713	+	0.953399i	$0.597559\pi$
$684$			8.35690i			0.319534i
$685$	−38.6368	+	66.9209i	−1.47624	+	2.55692i
$686$	20.6048	+	35.6886i	0.786696	+	1.36260i
$687$	−14.5535	+	8.40246i	−0.555250	+	0.320574i
$688$	−8.14952			−0.310698
$689$		0			0
$690$	13.9427			0.530790
$691$	−21.4033	+	12.3572i	−0.814219	+	0.470090i	−0.848419	−	0.529325i	$-0.822445\pi$
$691$	−21.4033	+	12.3572i	−0.814219	+	0.470090i	0.0341997	+	0.999415i	$0.489112\pi$
$692$	19.8443	+	34.3714i	0.754369	+	1.30660i
$693$	5.54892	−	9.61101i	0.210786	−	0.365092i
$694$			5.54048i			0.210314i
$695$	−2.85640	−	1.64914i	−0.108350	−	0.0625556i
$696$	−1.38434	−	0.799249i	−0.0524733	−	0.0302955i
$697$		−	6.32736i		−	0.239666i
$698$	−0.425665	+	0.737273i	−0.0161116	+	0.0279062i
$699$	−4.34601	−	7.52751i	−0.164381	−	0.284717i
$700$	−26.8133	+	15.4807i	−1.01345	+	0.585115i
$701$	−25.8920			−0.977927			−0.488964	−	0.872304i	$-0.662625\pi$
$701$	−25.8920			−0.977927			−0.488964	+	0.872304i	$0.662625\pi$
$702$		0			0
$703$	−33.4644			−1.26213
$704$	−40.6270	+	23.4560i	−1.53119	+	0.884031i
$705$	6.38135	+	11.0528i	0.240336	+	0.416274i
$706$	32.9540	−	57.0779i	1.24024	−	2.14816i
$707$		−	22.3545i		−	0.840728i
$708$	−8.97307	−	5.18060i	−0.337229	−	0.194699i
$709$	0.0737525	+	0.0425810i	0.00276983	+	0.00159916i	0.501384	−	0.865225i	$-0.332824\pi$
$709$	0.0737525	+	0.0425810i	0.00276983	+	0.00159916i	−0.498614	+	0.866824i	$0.666158\pi$
$710$			16.3605i			0.613998i
$711$	1.87047	−	3.23975i	0.0701481	−	0.121500i
$712$	2.04096	+	3.53504i	0.0764881	+	0.132481i
$713$	15.5000	−	8.94893i	0.580479	−	0.335140i
$714$	−4.19806			−0.157109
$715$		0			0
$716$	−43.6760			−1.63225
$717$	19.8486	−	11.4596i	0.741258	−	0.427966i
$718$	22.8988	+	39.6619i	0.854576	+	1.48017i
$719$	13.5254	−	23.4267i	0.504413	−	0.873669i	−0.495574	−	0.868566i	$-0.665042\pi$
$719$	13.5254	−	23.4267i	0.504413	−	0.873669i	0.999987	−	0.00510319i	$-0.00162440\pi$
$720$		−	11.9661i		−	0.445952i
$721$	21.3818	+	12.3448i	0.796302	+	0.459745i
$722$	8.06519	+	4.65644i	0.300155	+	0.173295i
$723$			21.9801i			0.817451i
$724$	11.0813	−	19.1933i	0.411832	−	0.713315i
$725$	−12.3463	−	21.3844i	−0.458530	−	0.794198i
$726$	−23.7660	+	13.7213i	−0.882040	+	0.509246i
$727$	47.1584			1.74901			0.874503	−	0.485019i	$-0.161187\pi$
$727$	47.1584			1.74901			0.874503	+	0.485019i	$0.161187\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−44.1449	+	25.4871i	−1.63388	+	0.943320i
$731$	1.04234	+	1.80539i	0.0385525	+	0.0667749i
$732$	−4.04437	+	7.00505i	−0.149484	+	0.258914i
$733$		−	9.68186i		−	0.357608i	−0.983885	−	0.178804i	$-0.942777\pi$
$733$		−	9.68186i		−	0.357608i	0.983885	−	0.178804i	$-0.0572227\pi$
$734$	−4.08577	−	2.35892i	−0.150809	−	0.0870693i
$735$	5.67210	+	3.27479i	0.209219	+	0.120792i
$736$		−	16.4509i		−	0.606388i
$737$	3.75637	−	6.50623i	0.138368	−	0.239660i
$738$	−7.10872	−	12.3127i	−0.261676	−	0.453235i
$739$	−31.4488	+	18.1570i	−1.15686	+	0.667915i	−0.950550	−	0.310571i	$-0.899480\pi$
$739$	−31.4488	+	18.1570i	−1.15686	+	0.667915i	−0.206313	+	0.978486i	$0.566146\pi$
$740$	−64.9466			−2.38748
$741$		0			0
$742$	−2.49934			−0.0917535
$743$	−36.1597	+	20.8768i	−1.32657	+	0.765896i	−0.984768	−	0.173876i	$-0.944371\pi$
$743$	−36.1597	+	20.8768i	−1.32657	+	0.765896i	−0.341803	+	0.939772i	$0.611037\pi$
$744$	1.79148	+	3.10293i	0.0656788	+	0.113759i
$745$	17.2193	−	29.8247i	0.630866	−	1.09269i
$746$			39.4950i			1.44602i
$747$	−1.99877	−	1.15399i	−0.0731311	−	0.0422223i
$748$	8.57304	+	4.94965i	0.313462	+	0.180977i
$749$			22.1836i			0.810571i
$750$	−4.36323	+	7.55734i	−0.159323	+	0.275955i
$751$	−11.0963	−	19.2194i	−0.404911	−	0.701327i	0.589400	−	0.807841i	$-0.299364\pi$
$751$	−11.0963	−	19.2194i	−0.404911	−	0.701327i	−0.994311	+	0.106515i	$0.966031\pi$
$752$	11.7369	−	6.77628i	0.427999	−	0.247106i
$753$	26.6437			0.970950
$754$		0			0
$755$	−67.7036			−2.46399
$756$	−4.27730	+	2.46950i	−0.155564	+	0.0898149i
$757$	−4.61865	−	7.99973i	−0.167868	−	0.290755i	0.769802	−	0.638282i	$-0.220355\pi$
$757$	−4.61865	−	7.99973i	−0.167868	−	0.290755i	−0.937670	+	0.347527i	$0.887021\pi$
$758$	7.51895	−	13.0232i	0.273101	−	0.473024i
$759$		−	10.0121i		−	0.363416i
$760$	−4.48538	−	2.58964i	−0.162702	−	0.0939360i
$761$	−6.49669	−	3.75086i	−0.235505	−	0.135969i	0.377604	−	0.925967i	$-0.376748\pi$
$761$	−6.49669	−	3.75086i	−0.235505	−	0.135969i	−0.613109	+	0.789998i	$0.710081\pi$
$762$		−	28.2989i		−	1.02516i
$763$	−22.7446	+	39.3948i	−0.823409	+	1.42619i
$764$	−7.23985	−	12.5398i	−0.261929	−	0.453673i
$765$	−2.65090	+	1.53050i	−0.0958436	+	0.0553353i
$766$	39.1140			1.41325
$767$		0			0
$768$	−12.3773			−0.446629
$769$	4.45141	−	2.57002i	0.160522	−	0.0926774i	−0.417587	−	0.908637i	$-0.637124\pi$
$769$	4.45141	−	2.57002i	0.160522	−	0.0926774i	0.578109	+	0.815959i	$0.303791\pi$
$770$	38.1655	+	66.1045i	1.37539	+	2.38224i
$771$	−11.5722	+	20.0436i	−0.416762	+	0.721853i
$772$			23.8869i			0.859708i
$773$	7.36271	+	4.25086i	0.264818	+	0.152893i	0.626531	−	0.779397i	$-0.284474\pi$
$773$	7.36271	+	4.25086i	0.264818	+	0.152893i	−0.361712	+	0.932290i	$0.617808\pi$
$774$	4.05668	+	2.34213i	0.145814	+	0.0841860i
$775$			55.3473i			1.98813i
$776$	−3.27274	+	5.66855i	−0.117485	+	0.203489i
$777$	−9.88889	−	17.1281i	−0.354762	−	0.614466i
$778$	−42.5645	+	24.5746i	−1.52601	+	0.881043i
$779$	26.3817			0.945221
$780$		0			0
$781$	11.7482			0.420385
$782$	−3.27994	+	1.89367i	−0.117290	+	0.0677176i
$783$	−1.96950	−	3.41127i	−0.0703842	−	0.121909i
$784$	3.47746	−	6.02314i	0.124195	−	0.215112i
$785$			35.0404i			1.25065i
$786$	−5.31370	−	3.06787i	−0.189533	−	0.109427i
$787$	−6.74248	−	3.89277i	−0.240343	−	0.138762i	0.374991	−	0.927028i	$-0.377646\pi$
$787$	−6.74248	−	3.89277i	−0.240343	−	0.138762i	−0.615335	+	0.788266i	$0.710979\pi$
$788$		−	20.3136i		−	0.723643i
$789$	−9.26420	+	16.0461i	−0.329814	+	0.571255i
$790$	12.8651	+	22.2830i	0.457719	+	0.792793i
$791$	−18.8601	+	10.8889i	−0.670588	+	0.387164i
$792$	2.00431			0.0712201
$793$		0			0
$794$	9.05190			0.321240
$795$	−1.57823	+	0.911190i	−0.0559740	+	0.0323166i
$796$	1.71960	+	2.97843i	0.0609494	+	0.105568i
$797$	10.6920	−	18.5191i	0.378731	−	0.655981i	−0.612147	−	0.790744i	$-0.709694\pi$
$797$	10.6920	−	18.5191i	0.378731	−	0.655981i	0.990878	+	0.134763i	$0.0430273\pi$
$798$		−	17.5036i		−	0.619622i
$799$	−3.00235	−	1.73341i	−0.106215	−	0.0613235i
$800$	44.0571	+	25.4364i	1.55765	+	0.899312i
$801$			10.0586i			0.355403i
$802$	−20.9080	+	36.2137i	−0.738286	+	1.27875i
$803$	18.3019	+	31.6999i	0.645861	+	1.11866i
$804$	−2.89554	+	1.67174i	−0.102118	+	0.0589578i
$805$	−15.2905			−0.538920
$806$		0			0
$807$	−9.75840			−0.343512
$808$	3.49641	−	2.01865i	0.123003	−	0.0710160i
$809$	−1.14310	−	1.97991i	−0.0401894	−	0.0696101i	0.845231	−	0.534401i	$-0.179463\pi$
$809$	−1.14310	−	1.97991i	−0.0401894	−	0.0696101i	−0.885420	+	0.464791i	$0.846129\pi$
$810$	−3.43900	+	5.95652i	−0.120834	+	0.209291i
$811$			17.8079i			0.625320i	0.949865	+	0.312660i	$0.101220\pi$
$811$			17.8079i			0.625320i	−0.949865	+	0.312660i	$0.898780\pi$
$812$	16.8483	+	9.72737i	0.591259	+	0.341364i
$813$	19.7471	+	11.4010i	0.692560	+	0.399849i
$814$			89.0721i			3.12198i
$815$	18.5410	−	32.1140i	0.649463	−	1.12490i
$816$	1.62522	+	2.81496i	0.0568940	+	0.0985434i
$817$	−7.52751	+	4.34601i	−0.263354	+	0.152048i
$818$	−45.3818			−1.58674
$819$		0			0
$820$	51.2006			1.78800
$821$	12.0424	−	6.95271i	0.420284	−	0.242651i	−0.274915	−	0.961469i	$-0.588650\pi$
$821$	12.0424	−	6.95271i	0.420284	−	0.242651i	0.695199	+	0.718817i	$0.255316\pi$
$822$	−23.5824	−	40.8459i	−0.822531	−	1.42466i
$823$	−3.62415	+	6.27722i	−0.126330	+	0.218810i	−0.922252	−	0.386589i	$-0.873653\pi$
$823$	−3.62415	+	6.27722i	−0.126330	+	0.218810i	0.795922	+	0.605399i	$0.206987\pi$
$824$			4.45904i			0.155338i
$825$	26.8133	+	15.4807i	0.933520	+	0.538968i
$826$	18.7942	+	10.8509i	0.653935	+	0.377550i
$827$		−	54.1191i		−	1.88191i	−0.338536	−	0.940953i	$-0.609932\pi$
$827$		−	54.1191i		−	1.88191i	0.338536	−	0.940953i	$-0.390068\pi$
$828$	−2.22790	+	3.85883i	−0.0774248	+	0.134104i
$829$	−2.89589	−	5.01582i	−0.100578	−	0.174207i	0.811345	−	0.584568i	$-0.198736\pi$
$829$	−2.89589	−	5.01582i	−0.100578	−	0.174207i	−0.911923	+	0.410361i	$0.865403\pi$
$830$	13.7475	−	7.93714i	0.477184	−	0.275502i
$831$	−23.9705			−0.831526
$832$		0			0
$833$	−1.77910			−0.0616422
$834$	1.74344	−	1.00657i	0.0603703	−	0.0348548i
$835$	−13.6121	−	23.5768i	−0.471065	−	0.815909i
$836$	−20.6374	+	35.7450i	−0.713758	+	1.23627i
$837$			8.82908i			0.305178i
$838$	26.1833	+	15.1169i	0.904486	+	0.522205i
$839$	−4.58431	−	2.64675i	−0.158268	−	0.0913760i	0.418774	−	0.908090i	$-0.362460\pi$
$839$	−4.58431	−	2.64675i	−0.158268	−	0.0913760i	−0.577042	+	0.816714i	$0.695793\pi$
$840$		−	3.06100i		−	0.105614i
$841$	6.74214	−	11.6777i	0.232487	−	0.402680i
$842$	−8.67941	−	15.0332i	−0.299112	−	0.518077i
$843$	−3.57234	+	2.06249i	−0.123038	+	0.0710360i
$844$	−51.0930			−1.75870
$845$		0			0
$846$	−7.78986			−0.267821
$847$	26.0634	−	15.0477i	0.895550	−	0.517046i
$848$	0.967582	+	1.67590i	0.0332269	+	0.0575507i
$849$	7.82789	−	13.5583i	0.268652	−	0.465320i
$850$		−	11.7120i		−	0.401718i
$851$	−15.4523	−	8.92141i	−0.529699	−	0.305822i
$852$	−4.52798	−	2.61423i	−0.155126	−	0.0895620i
$853$			13.5961i			0.465522i	0.972534	+	0.232761i	$0.0747760\pi$
$853$			13.5961i			0.465522i	−0.972534	+	0.232761i	$0.925224\pi$
$854$	8.47099	−	14.6722i	0.289871	−	0.502072i
$855$	−6.38135	−	11.0528i	−0.218238	−	0.377999i
$856$	−3.46968	+	2.00322i	−0.118591	+	0.0684687i
$857$	23.8323			0.814097			0.407048	−	0.913407i	$-0.366558\pi$
$857$	23.8323			0.814097			0.407048	+	0.913407i	$0.366558\pi$
$858$		0			0
$859$	−26.9861			−0.920754			−0.460377	−	0.887723i	$-0.652286\pi$
$859$	−26.9861			−0.920754			−0.460377	+	0.887723i	$0.652286\pi$
$860$	−14.6091	+	8.43458i	−0.498167	+	0.287617i
$861$	7.79590	+	13.5029i	0.265683	+	0.460177i
$862$	−2.45031	+	4.24407i	−0.0834580	+	0.144553i
$863$		−	27.0291i		−	0.920080i	−0.887898	−	0.460040i	$-0.847835\pi$
$863$		−	27.0291i		−	0.920080i	0.887898	−	0.460040i	$-0.152165\pi$
$864$	7.02805	+	4.05765i	0.239099	+	0.138044i
$865$	−52.4922	−	30.3064i	−1.78479	−	1.03045i
$866$		−	21.3674i		−	0.726095i
$867$	−8.08426	+	14.0024i	−0.274556	+	0.475545i
$868$	−21.8034	−	37.7646i	−0.740057	−	1.28182i
$869$	16.0011	−	9.23825i	0.542801	−	0.313386i
$870$	27.0925			0.918520
$871$		0			0
$872$	−8.21552			−0.278213
$873$	−13.9684	+	8.06465i	−0.472758	+	0.272947i
$874$	−7.89559	−	13.6756i	−0.267072	−	0.462583i
$875$	4.78501	−	8.28788i	0.161763	−	0.280182i
$876$		−	16.2903i		−	0.550397i
$877$	−35.4014	−	20.4390i	−1.19542	−	0.690176i	−0.235889	−	0.971780i	$-0.575800\pi$
$877$	−35.4014	−	20.4390i	−1.19542	−	0.690176i	−0.959531	+	0.281604i	$0.909134\pi$
$878$	57.7575	+	33.3463i	1.94922	+	1.12538i
$879$			22.5948i			0.762103i
$880$	29.5504	−	51.1828i	0.996144	−	1.72537i
$881$	−11.2482	−	19.4824i	−0.378961	−	0.656379i	0.611951	−	0.790896i	$-0.290385\pi$
$881$	−11.2482	−	19.4824i	−0.378961	−	0.656379i	−0.990911	+	0.134517i	$0.957052\pi$
$882$	−3.46203	+	1.99880i	−0.116573	+	0.0673032i
$883$	4.16315			0.140101			0.0700505	−	0.997543i	$-0.477684\pi$
$883$	4.16315			0.140101			0.0700505	+	0.997543i	$0.477684\pi$
$884$		0			0
$885$	15.8237			0.531908
$886$	−17.0026	+	9.81647i	−0.571214	+	0.329791i
$887$	13.1501	+	22.7766i	0.441537	+	0.764765i	0.997804	−	0.0662389i	$-0.0211000\pi$
$887$	13.1501	+	22.7766i	0.441537	+	0.764765i	−0.556266	+	0.831004i	$0.687767\pi$
$888$	1.78597	−	3.09339i	0.0599333	−	0.103807i
$889$			31.0344i			1.04086i
$890$	−59.9143	−	34.5916i	−2.00833	−	1.15951i
$891$	4.27730	+	2.46950i	0.143295	+	0.0827314i
$892$		−	23.6040i		−	0.790320i
$893$	7.22737	−	12.5182i	0.241855	−	0.418904i
$894$	10.5100	+	18.2038i	0.351506	+	0.608827i
$895$	57.7659	−	33.3512i	1.93090	−	1.11481i
$896$	−7.25906			−0.242508
$897$		0			0
$898$	58.1764			1.94137
$899$	30.1184	−	17.3889i	1.00451	−	0.579952i
$900$	−6.88955	−	11.9331i	−0.229652	−	0.397768i
$901$	0.247512	−	0.428703i	0.00824582	−	0.0142822i
$902$		−	70.2199i		−	2.33807i
$903$	−4.44883	−	2.56853i	−0.148048	−	0.0854754i
$904$	−3.40621	−	1.96658i	−0.113289	−	0.0654073i
$905$			33.8468i			1.12511i
$906$	20.6618	−	35.7873i	0.686443	−	1.18895i
$907$	−28.9557	−	50.1527i	−0.961458	−	1.66529i	−0.718845	−	0.695171i	$-0.755329\pi$
$907$	−28.9557	−	50.1527i	−0.961458	−	1.66529i	−0.242613	−	0.970123i	$-0.578005\pi$
$908$	13.2790	−	7.66666i	0.440681	−	0.254427i
$909$	9.94869			0.329977
$910$		0			0
$911$	−0.286799			−0.00950208			−0.00475104	−	0.999989i	$-0.501512\pi$
$911$	−0.286799			−0.00950208			−0.00475104	+	0.999989i	$0.501512\pi$
$912$	−11.7369	+	6.77628i	−0.388646	+	0.224385i
$913$	−5.69955	−	9.87192i	−0.188628	−	0.326713i
$914$	−5.11788	+	8.86442i	−0.169284	+	0.293209i
$915$		−	12.3532i		−	0.408383i
$916$	31.9895	+	18.4691i	1.05696	+	0.610237i
$917$	5.82736	+	3.36443i	0.192436	+	0.111103i
$918$		−	1.86831i		−	0.0616635i
$919$	15.5620	−	26.9541i	0.513342	−	0.889134i	−0.486539	−	0.873659i	$-0.661741\pi$
$919$	15.5620	−	26.9541i	0.513342	−	0.889134i	0.999880	−	0.0154747i	$-0.00492596\pi$
$920$	−1.38076	−	2.39155i	−0.0455224	−	0.0788472i
$921$	−5.67676	+	3.27748i	−0.187056	+	0.107997i
$922$	2.77133			0.0912690
$923$		0			0
$924$	−24.3937			−0.802495
$925$	47.7848	−	27.5886i	1.57115	−	0.907107i
$926$	−3.44696	−	5.97031i	−0.113274	−	0.196197i
$927$	−5.49396	+	9.51582i	−0.180445	+	0.312540i
$928$		−	31.9661i		−	1.04934i
$929$	−6.60493	−	3.81336i	−0.216701	−	0.125112i	0.387721	−	0.921777i	$-0.373262\pi$
$929$	−6.60493	−	3.81336i	−0.216701	−	0.125112i	−0.604422	+	0.796665i	$0.706596\pi$
$930$	−52.5907	−	30.3632i	−1.72452	−	0.995650i
$931$		−	7.41789i		−	0.243112i
$932$	−9.55280	+	16.5459i	−0.312912	+	0.541980i
$933$	6.01961	+	10.4263i	0.197073	+	0.341341i
$934$	12.2626	−	7.07982i	0.401245	−	0.231659i
$935$	−15.1183			−0.494421
$936$		0			0
$937$	−5.67324			−0.185337			−0.0926683	−	0.995697i	$-0.529540\pi$
$937$	−5.67324			−0.185337			−0.0926683	+	0.995697i	$0.529540\pi$
$938$	6.06476	−	3.50149i	0.198021	−	0.114328i
$939$	−16.9475	−	29.3539i	−0.553061	−	0.957929i
$940$	14.0266	−	24.2948i	0.457498	−	0.792409i
$941$			41.5394i			1.35415i	0.735916	+	0.677073i	$0.236752\pi$
$941$			41.5394i			1.35415i	−0.735916	+	0.677073i	$0.763248\pi$
$942$	−18.5219	−	10.6936i	−0.603477	−	0.348418i
$943$	12.1818	+	7.03319i	0.396695	+	0.229032i
$944$		−	16.8030i		−	0.546891i
$945$	3.77144	−	6.53232i	0.122685	−	0.212496i
$946$	11.5678	+	20.0360i	0.376100	+	0.651425i
$947$	40.9725	−	23.6555i	1.33143	−	0.768700i	0.345909	−	0.938268i	$-0.387571\pi$
$947$	40.9725	−	23.6555i	1.33143	−	0.768700i	0.985518	+	0.169568i	$0.0542373\pi$
$948$	−8.22282			−0.267065
$949$		0			0
$950$	48.8327			1.58434
$951$	3.89562	−	2.24914i	0.126324	−	0.0729332i
$952$	0.415739	+	0.720081i	0.0134742	+	0.0233380i
$953$	−17.1717	+	29.7423i	−0.556247	+	0.963449i	0.441558	+	0.897233i	$0.354426\pi$
$953$	−17.1717	+	29.7423i	−0.556247	+	0.963449i	−0.997805	+	0.0662159i	$0.978907\pi$
$954$		−	1.11231i		−	0.0360123i
$955$	19.1508	+	11.0567i	0.619707	+	0.357788i
$956$	−43.6284	−	25.1889i	−1.41104	−	0.814666i
$957$		−	19.4547i		−	0.628882i
$958$	3.60172	−	6.23836i	0.116366	−	0.201552i
$959$	25.8620	+	44.7944i	0.835129	+	1.44649i
$960$	−27.6130	+	15.9424i	−0.891205	+	0.514537i
$961$	−46.9527			−1.51460
$962$		0			0
$963$	−9.87263			−0.318141
$964$	41.8409	−	24.1569i	1.34761	−	0.778040i
$965$	−18.2401	−	31.5928i	−0.587170	−	1.01701i
$966$	4.66637	−	8.08238i	0.150138	−	0.260046i
$967$			48.5096i			1.55996i	0.625802	+	0.779982i	$0.284772\pi$
$967$			48.5096i			1.55996i	−0.625802	+	0.779982i	$0.715228\pi$
$968$	4.70715	+	2.71768i	0.151294	+	0.0873494i
$969$	3.00235	+	1.73341i	0.0964493	+	0.0556850i
$970$		−	110.937i		−	3.56198i
$971$	−20.7325	+	35.9098i	−0.665338	+	1.15240i	0.313856	+	0.949471i	$0.398379\pi$
$971$	−20.7325	+	35.9098i	−0.665338	+	1.15240i	−0.979194	+	0.202928i	$0.934954\pi$
$972$	−1.09903	−	1.90358i	−0.0352514	−	0.0610573i
$973$	−1.91197	+	1.10388i	−0.0612949	+	0.0353886i
$974$	−26.3242			−0.843483
$975$		0			0
$976$	−13.1177			−0.419887
$977$	−1.81586	+	1.04838i	−0.0580944	+	0.0335408i	−0.528766	−	0.848768i	$-0.677345\pi$
$977$	−1.81586	+	1.04838i	−0.0580944	+	0.0335408i	0.470671	+	0.882309i	$0.344012\pi$
$978$	11.3167	+	19.6011i	0.361868	+	0.626774i
$979$	−24.8397	+	43.0237i	−0.793881	+	1.37504i
$980$		−	14.3964i		−	0.459876i
$981$	−17.5323	−	10.1223i	−0.559764	−	0.323180i
$982$	−50.8740	−	29.3721i	−1.62345	−	0.937301i
$983$		−	25.2336i		−	0.804826i	−0.915458	−	0.402413i	$-0.868172\pi$
$983$		−	25.2336i		−	0.804826i	0.915458	−	0.402413i	$-0.131828\pi$
$984$	−1.40797	+	2.43867i	−0.0448844	+	0.0777421i
$985$	15.5115	+	26.8668i	0.494239	+	0.856047i
$986$	−6.37333	+	3.67964i	−0.202968	+	0.117184i
$987$	8.54288			0.271923
$988$		0			0
$989$	−4.63448			−0.147368
$990$	−29.4193	+	16.9852i	−0.935006	+	0.539826i
$991$	−6.02446	−	10.4347i	−0.191373	−	0.331468i	0.754332	−	0.656493i	$-0.227961\pi$
$991$	−6.02446	−	10.4347i	−0.191373	−	0.331468i	−0.945706	+	0.325025i	$0.894627\pi$
$992$	−35.8253	+	62.0512i	−1.13745	+	1.97013i
$993$			11.2131i			0.355838i
$994$	9.48392	+	5.47554i	0.300812	+	0.173674i
$995$	−4.54867	−	2.62618i	−0.144203	−	0.0832554i
$996$			5.07308i			0.160747i
$997$	0.717013	−	1.24190i	0.0227080	−	0.0393314i	−0.854448	−	0.519537i	$-0.826105\pi$
$997$	0.717013	−	1.24190i	0.0227080	−	0.0393314i	0.877156	+	0.480205i	$0.159438\pi$
$998$	34.3763	+	59.5415i	1.08816	+	1.88475i
$999$	7.62270	−	4.40097i	0.241172	−	0.139240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.j.i.361.3		12
13.2	odd	12		507.2.a.l.1.1	yes	3
13.3	even	3		507.2.b.f.337.3		6
13.4	even	6	inner	507.2.j.i.316.3		12
13.5	odd	4		507.2.e.i.484.3		6
13.6	odd	12		507.2.e.i.22.3		6
13.7	odd	12		507.2.e.l.22.1		6
13.8	odd	4		507.2.e.l.484.1		6
13.9	even	3	inner	507.2.j.i.316.4		12
13.10	even	6		507.2.b.f.337.4		6
13.11	odd	12		507.2.a.i.1.3	✓	3
13.12	even	2	inner	507.2.j.i.361.4		12
39.2	even	12		1521.2.a.n.1.3		3
39.11	even	12		1521.2.a.s.1.1		3
39.23	odd	6		1521.2.b.k.1351.3		6
39.29	odd	6		1521.2.b.k.1351.4		6
52.11	even	12		8112.2.a.cg.1.2		3
52.15	even	12		8112.2.a.cp.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.a.i.1.3	✓	3	13.11	odd	12
507.2.a.l.1.1	yes	3	13.2	odd	12
507.2.b.f.337.3		6	13.3	even	3
507.2.b.f.337.4		6	13.10	even	6
507.2.e.i.22.3		6	13.6	odd	12
507.2.e.i.484.3		6	13.5	odd	4
507.2.e.l.22.1		6	13.7	odd	12
507.2.e.l.484.1		6	13.8	odd	4
507.2.j.i.316.3		12	13.4	even	6	inner
507.2.j.i.316.4		12	13.9	even	3	inner
507.2.j.i.361.3		12	1.1	even	1	trivial
507.2.j.i.361.4		12	13.12	even	2	inner
1521.2.a.n.1.3		3	39.2	even	12
1521.2.a.s.1.1		3	39.11	even	12
1521.2.b.k.1351.3		6	39.23	odd	6
1521.2.b.k.1351.4		6	39.29	odd	6
8112.2.a.cg.1.2		3	52.11	even	12
8112.2.a.cp.1.2		3	52.15	even	12

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.77441 + 1.02446i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.09903 - 1.90358i) q^{4} +3.35690i q^{5} +(-1.77441 - 1.02446i) q^{6} +(1.94594 + 1.12349i) q^{7} +0.405813i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.43900 - 5.95652i) q^{10} +(-4.27730 + 2.46950i) q^{11} +2.19806 q^{12} -4.60388 q^{14} +(-2.90716 + 1.67845i) q^{15} +(1.78232 + 3.08707i) q^{16} +(0.455927 - 0.789689i) q^{17} -2.04892i q^{18} +(3.29257 + 1.90097i) q^{19} +(6.39011 + 3.68933i) q^{20} +2.24698i q^{21} +(5.05980 - 8.76383i) q^{22} +(1.01357 + 1.75556i) q^{23} +(-0.351445 + 0.202907i) q^{24} -6.26875 q^{25} -1.00000 q^{27} +(4.27730 - 2.46950i) q^{28} +(1.96950 + 3.41127i) q^{29} +(3.43900 - 5.95652i) q^{30} -8.82908i q^{31} +(-7.02805 - 4.05765i) q^{32} +(-4.27730 - 2.46950i) q^{33} +1.86831i q^{34} +(-3.77144 + 6.53232i) q^{35} +(1.09903 + 1.90358i) q^{36} +(-7.62270 + 4.40097i) q^{37} -7.78986 q^{38} -1.36227 q^{40} +(6.00935 - 3.46950i) q^{41} +(-2.30194 - 3.98707i) q^{42} +(-1.14310 + 1.97991i) q^{43} +10.8562i q^{44} +(-2.90716 - 1.67845i) q^{45} +(-3.59700 - 2.07673i) q^{46} -3.80194i q^{47} +(-1.78232 + 3.08707i) q^{48} +(-0.975541 - 1.68969i) q^{49} +(11.1234 - 6.42208i) q^{50} +0.911854 q^{51} +0.542877 q^{53} +(1.77441 - 1.02446i) q^{54} +(-8.28986 - 14.3585i) q^{55} +(-0.455927 + 0.789689i) q^{56} +3.80194i q^{57} +(-6.98942 - 4.03534i) q^{58} +(-4.08226 - 2.35690i) q^{59} +7.37867i q^{60} +(-1.83997 + 3.18692i) q^{61} +(9.04503 + 15.6665i) q^{62} +(-1.94594 + 1.12349i) q^{63} +9.49827 q^{64} +10.1196 q^{66} +(-1.31732 + 0.760553i) q^{67} +(-1.00216 - 1.73578i) q^{68} +(-1.01357 + 1.75556i) q^{69} -15.4547i q^{70} +(-2.05999 - 1.18933i) q^{71} +(-0.351445 - 0.202907i) q^{72} -7.41119i q^{73} +(9.01722 - 15.6183i) q^{74} +(-3.13437 - 5.42890i) q^{75} +(7.23728 - 4.17845i) q^{76} -11.0978 q^{77} -3.74094 q^{79} +(-10.3630 + 5.98307i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-7.10872 + 12.3127i) q^{82} +2.30798i q^{83} +(4.27730 + 2.46950i) q^{84} +(2.65090 + 1.53050i) q^{85} -4.68425i q^{86} +(-1.96950 + 3.41127i) q^{87} +(-1.00216 - 1.73578i) q^{88} +(8.71101 - 5.02930i) q^{89} +6.87800 q^{90} +4.45580 q^{92} +(7.64621 - 4.41454i) q^{93} +(3.89493 + 6.74621i) q^{94} +(-6.38135 + 11.0528i) q^{95} -8.11529i q^{96} +(13.9684 + 8.06465i) q^{97} +(3.46203 + 1.99880i) q^{98} -4.93900i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 22 q^{4} - 6 q^{9} - 2 q^{10} + 44 q^{12} - 20 q^{14} - 22 q^{16} - 2 q^{17} + 18 q^{22} - 44 q^{25} - 12 q^{27} + 4 q^{29} + 2 q^{30} - 8 q^{35} + 22 q^{36} + 12 q^{40} - 10 q^{42} - 30 q^{43}+ \cdots - 42 q^{95}+O(q^{100}) \) 12 * q + 6 * q^3 + 22 * q^4 - 6 * q^9 - 2 * q^10 + 44 * q^12 - 20 * q^14 - 22 * q^16 - 2 * q^17 + 18 * q^22 - 44 * q^25 - 12 * q^27 + 4 * q^29 + 2 * q^30 - 8 * q^35 + 22 * q^36 + 12 * q^40 - 10 * q^42 - 30 * q^43 + 22 * q^48 - 30 * q^49 - 4 * q^51 - 68 * q^53 - 6 * q^55 + 2 * q^56 + 26 * q^61 - 4 * q^62 + 36 * q^66 + 26 * q^68 - 30 * q^74 - 22 * q^75 - 60 * q^77 + 12 * q^79 - 6 * q^81 - 6 * q^82 - 4 * q^87 + 26 * q^88 + 4 * q^90 + 28 * q^92 - 42 * q^95

Introduction

L-functions

Modular forms

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