LMFDB - Embedded newform 529.2.c.n.255.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,2,Mod(118,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("529.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	529.c (of order $11$, degree $10$, 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:	$4.22408626693$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	20.0.54296067514572573056640625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 2 x^{18} - 3 x^{17} + 5 x^{16} - 8 x^{15} + 13 x^{14} - 21 x^{13} + 34 x^{12} + \cdots + 1 $ x^20 - x^19 + 2x^18 - 3x^17 + 5x^16 - 8x^15 + 13x^14 - 21x^13 + 34x^12 - 55x^11 + 89x^10 + 55x^9 + 34x^8 + 21x^7 + 13x^6 + 8x^5 + 5x^4 + 3x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			255.2
Root			$-0.404726 - 0.467079i$ of defining polynomial
Character	$\chi$	$=$	529.255
Dual form			529.2.c.n.334.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.519923 + 0.334134i) q^{2} +(0.318226 + 2.21331i) q^{3} +(-0.672156 - 1.47182i) q^{4} +(1.18600 + 0.348241i) q^{5} +(-0.574089 + 1.25708i) q^{6} +(2.11917 - 2.44566i) q^{7} +(0.318226 - 2.21331i) q^{8} +(-1.91899 + 0.563465i) q^{9} +(0.500269 + 0.577341i) q^{10} +(4.40486 - 2.83083i) q^{11} +(3.04368 - 1.95606i) q^{12} +(-1.96458 - 2.26725i) q^{13} +(1.91899 - 0.563465i) q^{14} +(-0.393349 + 2.73580i) q^{15} +(-1.21418 + 1.40124i) q^{16} +(-0.317349 + 0.694897i) q^{17} +(-1.18600 - 0.348241i) q^{18} +(0.830830 + 1.81926i) q^{19} +(-0.284630 - 1.97964i) q^{20} +(6.08737 + 3.91211i) q^{21} +3.23607 q^{22} +5.00000 q^{24} +(-2.92095 - 1.87718i) q^{25} +(-0.263866 - 1.83523i) q^{26} +(0.928896 + 2.03400i) q^{27} +(-5.02397 - 1.47517i) q^{28} +(-1.24625 + 2.72890i) q^{29} +(-1.11864 + 1.29097i) q^{30} +(-0.954677 + 6.63992i) q^{31} +(-5.39046 + 1.58278i) q^{32} +(7.66724 + 8.84847i) q^{33} +(-0.397186 + 0.255256i) q^{34} +(3.36501 - 2.16256i) q^{35} +(2.11917 + 2.44566i) q^{36} +(-1.18600 + 0.348241i) q^{37} +(-0.175911 + 1.22349i) q^{38} +(4.39294 - 5.06972i) q^{39} +(1.14818 - 2.51416i) q^{40} +(3.33149 + 0.978214i) q^{41} +(1.85779 + 4.06800i) q^{42} +(-7.12721 - 4.58038i) q^{44} -2.47214 q^{45} -2.23607 q^{47} +(-3.48775 - 2.24144i) q^{48} +(-0.494136 - 3.43679i) q^{49} +(-0.891438 - 1.95198i) q^{50} +(-1.63901 - 0.481257i) q^{51} +(-2.01647 + 4.41545i) q^{52} +(0.309183 - 0.356817i) q^{53} +(-0.196674 + 1.36790i) q^{54} +(6.20997 - 1.82341i) q^{55} +(-4.73862 - 5.46866i) q^{56} +(-3.76220 + 2.41782i) q^{57} +(-1.55977 + 1.00240i) q^{58} +(-4.23835 - 4.89131i) q^{59} +(4.29098 - 1.25995i) q^{60} +(-0.988273 + 6.87359i) q^{61} +(-2.71499 + 3.13326i) q^{62} +(-2.68862 + 5.88726i) q^{63} +(0.226506 + 0.0665080i) q^{64} +(-1.54044 - 3.37310i) q^{65} +(1.02980 + 7.16242i) q^{66} +(2.32517 + 1.49429i) q^{67} +1.23607 q^{68} +2.47214 q^{70} +(10.2936 + 6.61532i) q^{71} +(0.636451 + 4.42662i) q^{72} +(2.71177 + 5.93795i) q^{73} +(-0.732987 - 0.215225i) q^{74} +(3.22525 - 7.06232i) q^{75} +(2.11917 - 2.44566i) q^{76} +(2.41142 - 16.7718i) q^{77} +(3.97796 - 1.16803i) q^{78} +(-7.16697 - 8.27113i) q^{79} +(-1.92798 + 1.23904i) q^{80} +(-9.25379 + 5.94705i) q^{81} +(1.40526 + 1.62176i) q^{82} +(-8.40893 + 2.46908i) q^{83} +(1.66625 - 11.5890i) q^{84} +(-0.618367 + 0.713633i) q^{85} +(-6.43647 - 1.88992i) q^{87} +(-4.86376 - 10.6502i) q^{88} +(-1.49034 - 10.3655i) q^{89} +(-1.28532 - 0.826026i) q^{90} -9.70820 q^{91} -15.0000 q^{93} +(-1.16258 - 0.747147i) q^{94} +(0.351822 + 2.44697i) q^{95} +(-5.21857 - 11.4271i) q^{96} +(16.9909 + 4.98898i) q^{97} +(0.891438 - 1.95198i) q^{98} +(-6.85779 + 7.91431i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + q^{4} - 2 q^{5} + 5 q^{6} + 2 q^{7} - 4 q^{9} + 6 q^{10} - 6 q^{11} - 5 q^{12} - 6 q^{13} + 4 q^{14} - 10 q^{15} + 3 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 4 q^{20} - 10 q^{21} + 20 q^{22}+ \cdots - 12 q^{99}+O(q^{100}) $ 20 * q + q^2 + q^4 - 2 * q^5 + 5 * q^6 + 2 * q^7 - 4 * q^9 + 6 * q^10 - 6 * q^11 - 5 * q^12 - 6 * q^13 + 4 * q^14 - 10 * q^15 + 3 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 4 * q^20 - 10 * q^21 + 20 * q^22 + 100 * q^24 - 2 * q^25 + 3 * q^26 - 6 * q^28 + 6 * q^29 + 10 * q^30 - 9 * q^32 + 10 * q^33 - 8 * q^34 - 8 * q^35 + 2 * q^36 + 2 * q^37 + 2 * q^38 - 10 * q^40 - 2 * q^41 + 8 * q^44 + 40 * q^45 + 15 * q^48 + 2 * q^49 + 11 * q^50 + 10 * q^51 + 3 * q^52 - 8 * q^53 - 5 * q^54 + 4 * q^55 - 10 * q^56 - 3 * q^58 - 4 * q^59 + 4 * q^61 - 15 * q^62 + 4 * q^63 - 4 * q^64 - 6 * q^65 + 10 * q^66 - 10 * q^67 - 20 * q^68 - 40 * q^70 - 20 * q^71 - 22 * q^73 - 6 * q^74 - 20 * q^75 + 2 * q^76 + 16 * q^77 + 15 * q^78 - 4 * q^79 + 18 * q^80 + 22 * q^81 + 11 * q^82 - 22 * q^83 + 10 * q^84 + 16 * q^85 + 10 * q^88 - 12 * q^89 + 12 * q^90 - 60 * q^91 - 300 * q^93 + 5 * q^94 - 4 * q^95 + 5 * q^96 + 22 * q^97 - 11 * q^98 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/529\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{1}{11}\right)$

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 $

$2$	0.519923	+	0.334134i	0.367641	+	0.236269i	0.711397	−	0.702790i	$-0.248063\pi$
$2$	0.519923	+	0.334134i	0.367641	+	0.236269i	−0.343756	+	0.939059i	$0.611699\pi$
$3$	0.318226	+	2.21331i	0.183728	+	1.27785i	0.847852	+	0.530232i	$0.177895\pi$
$3$	0.318226	+	2.21331i	0.183728	+	1.27785i	−0.664125	+	0.747622i	$0.731196\pi$
$4$	−0.672156	−	1.47182i	−0.336078	−	0.735908i
$5$	1.18600	+	0.348241i	0.530395	+	0.155738i	0.535955	−	0.844247i	$-0.319952\pi$
$5$	1.18600	+	0.348241i	0.530395	+	0.155738i	−0.00556023	+	0.999985i	$0.501770\pi$
$6$	−0.574089	+	1.25708i	−0.234371	+	0.513201i
$7$	2.11917	−	2.44566i	0.800972	−	0.924371i	−0.197462	−	0.980311i	$-0.563270\pi$
$7$	2.11917	−	2.44566i	0.800972	−	0.924371i	0.998434	+	0.0559391i	$0.0178153\pi$
$8$	0.318226	−	2.21331i	0.112510	−	0.782523i
$9$	−1.91899	+	0.563465i	−0.639662	+	0.187822i
$10$	0.500269	+	0.577341i	0.158199	+	0.182571i
$11$	4.40486	−	2.83083i	1.32812	−	0.853528i	0.332147	−	0.943228i	$-0.392227\pi$
$11$	4.40486	−	2.83083i	1.32812	−	0.853528i	0.995969	+	0.0896998i	$0.0285908\pi$
$12$	3.04368	−	1.95606i	0.878636	−	0.564665i
$13$	−1.96458	−	2.26725i	−0.544877	−	0.628822i	0.414805	−	0.909910i	$-0.363850\pi$
$13$	−1.96458	−	2.26725i	−0.544877	−	0.628822i	−0.959682	+	0.281089i	$0.909304\pi$
$14$	1.91899	−	0.563465i	0.512871	−	0.150592i
$15$	−0.393349	+	2.73580i	−0.101562	+	0.706380i
$16$	−1.21418	+	1.40124i	−0.303545	+	0.350309i
$17$	−0.317349	+	0.694897i	−0.0769684	+	0.168537i	−0.944204	−	0.329360i	$-0.893167\pi$
$17$	−0.317349	+	0.694897i	−0.0769684	+	0.168537i	0.867236	+	0.497897i	$0.165894\pi$
$18$	−1.18600	−	0.348241i	−0.279543	−	0.0820811i
$19$	0.830830	+	1.81926i	0.190605	+	0.417368i	0.980674	−	0.195651i	$-0.0626821\pi$
$19$	0.830830	+	1.81926i	0.190605	+	0.417368i	−0.790068	+	0.613019i	$0.789955\pi$
$20$	−0.284630	−	1.97964i	−0.0636451	−	0.442662i
$21$	6.08737	+	3.91211i	1.32837	+	0.853693i
$22$	3.23607			0.689932
$23$		0			0
$23$		0			0
$24$	5.00000			1.02062
$25$	−2.92095	−	1.87718i	−0.584189	−	0.375436i
$26$	−0.263866	−	1.83523i	−0.0517484	−	0.359918i
$27$	0.928896	+	2.03400i	0.178766	+	0.391443i
$28$	−5.02397	−	1.47517i	−0.949441	−	0.278781i
$29$	−1.24625	+	2.72890i	−0.231422	+	0.506743i	−0.989343	−	0.145603i	$-0.953488\pi$
$29$	−1.24625	+	2.72890i	−0.231422	+	0.506743i	0.757921	+	0.652346i	$0.226215\pi$
$30$	−1.11864	+	1.29097i	−0.204234	+	0.235699i
$31$	−0.954677	+	6.63992i	−0.171465	+	1.19257i	0.704327	+	0.709876i	$0.251249\pi$
$31$	−0.954677	+	6.63992i	−0.171465	+	1.19257i	−0.875792	+	0.482689i	$0.839660\pi$
$32$	−5.39046	+	1.58278i	−0.952908	+	0.279799i
$33$	7.66724	+	8.84847i	1.33470	+	1.54032i
$34$	−0.397186	+	0.255256i	−0.0681168	+	0.0437760i
$35$	3.36501	−	2.16256i	0.568791	−	0.365540i
$36$	2.11917	+	2.44566i	0.353196	+	0.407609i
$37$	−1.18600	+	0.348241i	−0.194977	+	0.0572504i	−0.377763	−	0.925902i	$-0.623307\pi$
$37$	−1.18600	+	0.348241i	−0.194977	+	0.0572504i	0.182786	+	0.983153i	$0.441488\pi$
$38$	−0.175911	+	1.22349i	−0.0285365	+	0.198476i
$39$	4.39294	−	5.06972i	0.703433	−	0.811805i
$40$	1.14818	−	2.51416i	0.181543	−	0.397524i
$41$	3.33149	+	0.978214i	0.520291	+	0.152771i	0.531325	−	0.847168i	$-0.321694\pi$
$41$	3.33149	+	0.978214i	0.520291	+	0.152771i	−0.0110341	+	0.999939i	$0.503512\pi$
$42$	1.85779	+	4.06800i	0.286664	+	0.627706i
$43$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$43$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$44$	−7.12721	−	4.58038i	−1.07447	−	0.690519i
$45$	−2.47214			−0.368524
$46$		0			0
$47$	−2.23607			−0.326164			−0.163082	−	0.986613i	$-0.552144\pi$
$47$	−2.23607			−0.326164			−0.163082	+	0.986613i	$0.552144\pi$
$48$	−3.48775	−	2.24144i	−0.503414	−	0.323524i
$49$	−0.494136	−	3.43679i	−0.0705909	−	0.490971i
$50$	−0.891438	−	1.95198i	−0.126068	−	0.276051i
$51$	−1.63901	−	0.481257i	−0.229507	−	0.0673894i
$52$	−2.01647	+	4.41545i	−0.279634	+	0.612312i
$53$	0.309183	−	0.356817i	0.0424696	−	0.0490125i	−0.734117	−	0.679023i	$-0.762404\pi$
$53$	0.309183	−	0.356817i	0.0424696	−	0.0490125i	0.776587	+	0.630010i	$0.216949\pi$
$54$	−0.196674	+	1.36790i	−0.0267640	+	0.186148i
$55$	6.20997	−	1.82341i	0.837352	−	0.245869i
$56$	−4.73862	−	5.46866i	−0.633224	−	0.730780i
$57$	−3.76220	+	2.41782i	−0.498316	+	0.320248i
$58$	−1.55977	+	1.00240i	−0.204808	+	0.131622i
$59$	−4.23835	−	4.89131i	−0.551786	−	0.636795i	0.409512	−	0.912305i	$-0.365699\pi$
$59$	−4.23835	−	4.89131i	−0.551786	−	0.636795i	−0.961298	+	0.275510i	$0.911153\pi$
$60$	4.29098	−	1.25995i	0.553964	−	0.162658i
$61$	−0.988273	+	6.87359i	−0.126535	+	0.880073i	0.823363	+	0.567515i	$0.192095\pi$
$61$	−0.988273	+	6.87359i	−0.126535	+	0.880073i	−0.949899	+	0.312558i	$0.898814\pi$
$62$	−2.71499	+	3.13326i	−0.344804	+	0.397925i
$63$	−2.68862	+	5.88726i	−0.338735	+	0.741725i
$64$	0.226506	+	0.0665080i	0.0283132	+	0.00831350i
$65$	−1.54044	−	3.37310i	−0.191069	−	0.418382i
$66$	1.02980	+	7.16242i	0.126760	+	0.881632i
$67$	2.32517	+	1.49429i	0.284064	+	0.182557i	0.674912	−	0.737898i	$-0.264182\pi$
$67$	2.32517	+	1.49429i	0.284064	+	0.182557i	−0.390847	+	0.920455i	$0.627818\pi$
$68$	1.23607			0.149895
$69$		0			0
$70$	2.47214			0.295477
$71$	10.2936	+	6.61532i	1.22163	+	0.785094i	0.982567	−	0.185910i	$-0.0595234\pi$
$71$	10.2936	+	6.61532i	1.22163	+	0.785094i	0.239063	+	0.971004i	$0.423160\pi$
$72$	0.636451	+	4.42662i	0.0750065	+	0.521682i
$73$	2.71177	+	5.93795i	0.317389	+	0.694985i	0.999337	−	0.0364160i	$-0.0115941\pi$
$73$	2.71177	+	5.93795i	0.317389	+	0.694985i	−0.681948	+	0.731401i	$0.738867\pi$
$74$	−0.732987	−	0.215225i	−0.0852081	−	0.0250193i
$75$	3.22525	−	7.06232i	0.372420	−	0.815487i
$76$	2.11917	−	2.44566i	0.243086	−	0.280536i
$77$	2.41142	−	16.7718i	0.274807	−	1.91132i
$78$	3.97796	−	1.16803i	0.450415	−	0.132254i
$79$	−7.16697	−	8.27113i	−0.806348	−	0.930575i	0.192364	−	0.981324i	$-0.438385\pi$
$79$	−7.16697	−	8.27113i	−0.806348	−	0.930575i	−0.998711	+	0.0507490i	$0.983839\pi$
$80$	−1.92798	+	1.23904i	−0.215555	+	0.138529i
$81$	−9.25379	+	5.94705i	−1.02820	+	0.660783i
$82$	1.40526	+	1.62176i	0.155185	+	0.179094i
$83$	−8.40893	+	2.46908i	−0.923000	+	0.271017i	−0.708503	−	0.705707i	$-0.750629\pi$
$83$	−8.40893	+	2.46908i	−0.923000	+	0.271017i	−0.214497	+	0.976725i	$0.568811\pi$
$84$	1.66625	−	11.5890i	0.181803	−	1.26447i
$85$	−0.618367	+	0.713633i	−0.0670713	+	0.0774044i
$86$		0			0
$87$	−6.43647	−	1.88992i	−0.690063	−	0.202621i
$88$	−4.86376	−	10.6502i	−0.518479	−	1.13531i
$89$	−1.49034	−	10.3655i	−0.157976	−	1.09875i	−0.902357	−	0.430990i	$-0.858164\pi$
$89$	−1.49034	−	10.3655i	−0.157976	−	1.09875i	0.744381	−	0.667755i	$-0.232745\pi$
$90$	−1.28532	−	0.826026i	−0.135485	−	0.0870708i
$91$	−9.70820			−1.01770
$92$		0			0
$93$	−15.0000			−1.55543
$94$	−1.16258	−	0.747147i	−0.119911	−	0.0770624i
$95$	0.351822	+	2.44697i	0.0360961	+	0.251054i
$96$	−5.21857	−	11.4271i	−0.532618	−	1.16627i
$97$	16.9909	+	4.98898i	1.72516	+	0.506554i	0.985968	−	0.166936i	$-0.0533873\pi$
$97$	16.9909	+	4.98898i	1.72516	+	0.506554i	0.739196	+	0.673490i	$0.235205\pi$
$98$	0.891438	−	1.95198i	0.0900489	−	0.197180i
$99$	−6.85779	+	7.91431i	−0.689234	+	0.795418i
$100$	−0.799530	+	5.56085i	−0.0799530	+	0.556085i
$101$	−4.29098	+	1.25995i	−0.426969	+	0.125369i	−0.488155	−	0.872757i	$-0.662330\pi$
$101$	−4.29098	+	1.25995i	−0.426969	+	0.125369i	0.0611861	+	0.998126i	$0.480512\pi$
$102$	−0.691355	−	0.797866i	−0.0684543	−	0.0790005i
$103$	3.51673	−	2.26006i	0.346513	−	0.222691i	−0.355794	−	0.934564i	$-0.615790\pi$
$103$	3.51673	−	2.26006i	0.346513	−	0.222691i	0.702307	+	0.711874i	$0.252153\pi$
$104$	−5.64330	+	3.62673i	−0.553371	+	0.355630i
$105$	5.85725	+	6.75963i	0.571609	+	0.659672i
$106$	0.279976	−	0.0822085i	0.0271937	−	0.00798479i
$107$	1.90935	−	13.2798i	0.184584	−	1.28381i	−0.661169	−	0.750237i	$-0.729939\pi$
$107$	1.90935	−	13.2798i	0.184584	−	1.28381i	0.845753	−	0.533574i	$-0.179152\pi$
$108$	2.36931	−	2.73433i	0.227987	−	0.263111i
$109$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$109$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$110$	3.83797	+	1.12693i	0.365936	+	0.107449i
$111$	−1.14818	−	2.51416i	−0.108980	−	0.238634i
$112$	0.853889	+	5.93893i	0.0806849	+	0.561176i
$113$	−7.37269	−	4.73814i	−0.693564	−	0.445727i	0.145787	−	0.989316i	$-0.453429\pi$
$113$	−7.37269	−	4.73814i	−0.693564	−	0.445727i	−0.839351	+	0.543589i	$0.817065\pi$
$114$	−2.76393			−0.258866
$115$		0			0
$116$	4.85410			0.450692
$117$	5.04752	+	3.24384i	0.466643	+	0.299894i
$118$	−0.569259	−	3.95929i	−0.0524046	−	0.364482i
$119$	1.02696	+	2.24873i	0.0941415	+	0.206141i
$120$	5.92999	+	1.74120i	0.541332	+	0.158949i
$121$	6.81962	−	14.9329i	0.619966	−	1.35754i
$122$	−2.81053	+	3.24352i	−0.254453	+	0.293655i
$123$	−1.10492	+	7.68491i	−0.0996275	+	0.692925i
$124$	10.4144	−	3.05795i	0.935244	−	0.274612i
$125$	−6.85779	−	7.91431i	−0.613379	−	0.707878i
$126$	−3.36501	+	2.16256i	−0.299779	+	0.192656i
$127$	−6.13425	+	3.94224i	−0.544327	+	0.349817i	−0.783729	−	0.621103i	$-0.786685\pi$
$127$	−6.13425	+	3.94224i	−0.544327	+	0.349817i	0.239402	+	0.970920i	$0.423048\pi$
$128$	7.45360	+	8.60192i	0.658812	+	0.760309i
$129$		0			0
$130$	0.326157	−	2.26847i	0.0286058	−	0.198958i
$131$	−12.2513	+	14.1387i	−1.07040	+	1.23531i	−0.0996965	+	0.995018i	$0.531787\pi$
$131$	−12.2513	+	14.1387i	−1.07040	+	1.23531i	−0.970702	+	0.240288i	$0.922758\pi$
$132$	7.86973	−	17.2323i	0.684973	−	1.49988i
$133$	6.20997	+	1.82341i	0.538473	+	0.158110i
$134$	0.709614	+	1.55384i	0.0613013	+	0.134231i
$135$	0.393349	+	2.73580i	0.0338541	+	0.235460i
$136$	1.43703	+	0.923525i	0.123225	+	0.0791916i
$137$	21.8885			1.87006			0.935032	−	0.354563i	$-0.115370\pi$
$137$	21.8885			1.87006			0.935032	+	0.354563i	$0.115370\pi$
$138$		0			0
$139$	−10.7082			−0.908258			−0.454129	−	0.890936i	$-0.650049\pi$
$139$	−10.7082			−0.908258			−0.454129	+	0.890936i	$0.650049\pi$
$140$	−5.44471	−	3.49910i	−0.460162	−	0.295728i
$141$	−0.711574	−	4.94911i	−0.0599254	−	0.416790i
$142$	3.14150	+	6.87892i	0.263628	+	0.577266i
$143$	−15.0719	−	4.42551i	−1.26038	−	0.370080i
$144$	1.54044	−	3.37310i	0.128370	−	0.281092i
$145$	−2.42836	+	2.80247i	−0.201664	+	0.232733i
$146$	−0.574161	+	3.99338i	−0.0475179	+	0.330494i
$147$	7.44944	−	2.18735i	0.614419	−	0.180410i
$148$	1.30972	+	1.51150i	0.107658	+	0.124244i
$149$	−20.0963	+	12.9151i	−1.64635	+	1.05805i	−0.711705	+	0.702478i	$0.752077\pi$
$149$	−20.0963	+	12.9151i	−1.64635	+	1.05805i	−0.934650	+	0.355570i	$0.884287\pi$
$150$	4.03665	−	2.59420i	0.329591	−	0.211815i
$151$	−2.77403	−	3.20141i	−0.225748	−	0.260527i	0.631565	−	0.775323i	$-0.282413\pi$
$151$	−2.77403	−	3.20141i	−0.225748	−	0.260527i	−0.857312	+	0.514796i	$0.827868\pi$
$152$	4.29098	−	1.25995i	0.348045	−	0.102195i
$153$	0.217438	−	1.51231i	0.0175788	−	0.122263i
$154$	6.85779	−	7.91431i	0.552617	−	0.637753i
$155$	−3.44454	+	7.54248i	−0.276672	+	0.605827i
$156$	−10.4144	−	3.05795i	−0.833822	−	0.244832i
$157$	4.74255	+	10.3847i	0.378496	+	0.828792i	0.999005	+	0.0445922i	$0.0141988\pi$
$157$	4.74255	+	10.3847i	0.378496	+	0.828792i	−0.620509	+	0.784199i	$0.713074\pi$
$158$	−0.962608	−	6.69508i	−0.0765810	−	0.532632i
$159$	0.888135	+	0.570770i	0.0704337	+	0.0452650i
$160$	−6.94427			−0.548993
$161$		0			0
$162$	−6.79837			−0.534131
$163$	−4.84893	−	3.11622i	−0.379797	−	0.244081i	0.336788	−	0.941581i	$-0.390660\pi$
$163$	−4.84893	−	3.11622i	−0.379797	−	0.244081i	−0.716585	+	0.697500i	$0.754296\pi$
$164$	−0.799530	−	5.56085i	−0.0624328	−	0.434229i
$165$	6.01194	+	13.1643i	0.468029	+	1.02484i
$166$	−5.19701	−	1.52598i	−0.403366	−	0.118439i
$167$	0.634698	−	1.38979i	0.0491144	−	0.107545i	−0.883484	−	0.468461i	$-0.844809\pi$
$167$	0.634698	−	1.38979i	0.0491144	−	0.107545i	0.932598	+	0.360916i	$0.117536\pi$
$168$	10.5959	−	12.2283i	0.817489	−	0.943433i
$169$	0.569259	−	3.95929i	0.0437892	−	0.304560i
$170$	−0.559953	+	0.164417i	−0.0429464	+	0.0126102i
$171$	−2.61944	−	3.02300i	−0.200314	−	0.231174i
$172$		0			0
$173$	19.3019	−	12.4046i	1.46750	−	0.943105i	0.469306	−	0.883036i	$-0.344504\pi$
$173$	19.3019	−	12.4046i	1.46750	−	0.943105i	0.998194	−	0.0600694i	$-0.0191322\pi$
$174$	−2.71499	−	3.13326i	−0.205823	−	0.237532i
$175$	−10.7809	+	3.16557i	−0.814962	+	0.239294i
$176$	−1.38162	+	9.60939i	−0.104144	+	0.724335i
$177$	9.47723	−	10.9373i	0.712352	−	0.822099i
$178$	2.68862	−	5.88726i	0.201521	−	0.441269i
$179$	−0.679517	−	0.199524i	−0.0507895	−	0.0149131i	0.256239	−	0.966613i	$-0.417517\pi$
$179$	−0.679517	−	0.199524i	−0.0507895	−	0.0149131i	−0.307029	+	0.951700i	$0.599335\pi$
$180$	1.66166	+	3.63853i	0.123853	+	0.271200i
$181$	2.36989	+	16.4830i	0.176153	+	1.22517i	0.865563	+	0.500799i	$0.166961\pi$
$181$	2.36989	+	16.4830i	0.176153	+	1.22517i	−0.689411	+	0.724371i	$0.742130\pi$
$182$	−5.04752	−	3.24384i	−0.374147	−	0.240450i
$183$	−15.5279			−1.14785
$184$		0			0
$185$	−1.52786			−0.112331
$186$	−7.79885	−	5.01202i	−0.571839	−	0.367499i
$187$	0.569259	+	3.95929i	0.0416284	+	0.289532i
$188$	1.50299	+	3.29108i	0.109616	+	0.240027i
$189$	6.94296	+	2.03864i	0.505026	+	0.148289i
$190$	−0.634698	+	1.38979i	−0.0460458	+	0.100826i
$191$	−17.1445	+	19.7858i	−1.24053	+	1.43165i	−0.377876	+	0.925856i	$0.623345\pi$
$191$	−17.1445	+	19.7858i	−1.24053	+	1.43165i	−0.862655	+	0.505792i	$0.831200\pi$
$192$	−0.0751229	+	0.522491i	−0.00542153	+	0.0377076i
$193$	−9.54146	+	2.80163i	−0.686809	+	0.201665i	−0.606475	−	0.795103i	$-0.707417\pi$
$193$	−9.54146	+	2.80163i	−0.686809	+	0.201665i	−0.0803343	+	0.996768i	$0.525599\pi$
$194$	7.16697	+	8.27113i	0.514559	+	0.593832i
$195$	6.97550	−	4.48288i	0.499526	−	0.321026i
$196$	−4.72619	+	3.03734i	−0.337585	+	0.216953i
$197$	0.964044	+	1.11257i	0.0686853	+	0.0792671i	0.789052	−	0.614326i	$-0.210572\pi$
$197$	0.964044	+	1.11257i	0.0686853	+	0.0792671i	−0.720367	+	0.693593i	$0.756027\pi$
$198$	−6.20997	+	1.82341i	−0.441323	+	0.129584i
$199$	−1.74930	+	12.1667i	−0.124005	+	0.862473i	0.828942	+	0.559335i	$0.188943\pi$
$199$	−1.74930	+	12.1667i	−0.124005	+	0.862473i	−0.952947	+	0.303138i	$0.901966\pi$
$200$	−5.08429	+	5.86759i	−0.359514	+	0.414901i
$201$	−2.56741	+	5.62183i	−0.181091	+	0.396534i
$202$	−2.65197	−	0.778690i	−0.186592	−	0.0547884i
$203$	4.03293	+	8.83089i	0.283056	+	0.619807i
$204$	0.393349	+	2.73580i	0.0275399	+	0.191544i
$205$	3.61049	+	2.32032i	0.252167	+	0.162058i
$206$	2.58359			0.180007
$207$		0			0
$208$	5.56231			0.385677
$209$	8.80972	+	5.66166i	0.609381	+	0.391625i
$210$	0.786697	+	5.47160i	0.0542873	+	0.377576i
$211$	−9.72753	−	21.3003i	−0.669671	−	1.46637i	−0.873228	−	0.487311i	$-0.837978\pi$
$211$	−9.72753	−	21.3003i	−0.669671	−	1.46637i	0.203558	−	0.979063i	$-0.434750\pi$
$212$	−0.732987	−	0.215225i	−0.0503418	−	0.0147817i
$213$	−11.3660	+	24.8881i	−0.778788	+	1.70531i
$214$	5.42997	−	6.26652i	0.371185	−	0.428371i
$215$		0			0
$216$	4.79746	−	1.40866i	0.326426	−	0.0958474i
$217$	14.2159	+	16.4060i	0.965035	+	1.11371i
$218$		0			0
$219$	−12.2796	+	7.89160i	−0.829776	+	0.533265i
$220$	−6.85779	−	7.91431i	−0.462352	−	0.533583i
$221$	2.19896	−	0.645674i	0.147918	−	0.0434327i
$222$	0.243103	−	1.69082i	0.0163160	−	0.113480i
$223$	−2.61944	+	3.02300i	−0.175411	+	0.202435i	−0.836646	−	0.547743i	$-0.815487\pi$
$223$	−2.61944	+	3.02300i	−0.175411	+	0.202435i	0.661235	+	0.750178i	$0.270032\pi$
$224$	−7.55239	+	16.5374i	−0.504615	+	1.10495i
$225$	6.66298	+	1.95643i	0.444199	+	0.130428i
$226$	−2.25006	−	4.92694i	−0.149672	−	0.327735i
$227$	−1.73344	−	12.0564i	−0.115053	−	0.800209i	−0.962879	−	0.269934i	$-0.912998\pi$
$227$	−1.73344	−	12.0564i	−0.115053	−	0.800209i	0.847826	−	0.530274i	$-0.177911\pi$
$228$	6.08737	+	3.91211i	0.403146	+	0.259086i
$229$	12.0000			0.792982			0.396491	−	0.918039i	$-0.370228\pi$
$229$	12.0000			0.792982			0.396491	+	0.918039i	$0.370228\pi$
$230$		0			0
$231$	37.8885			2.49288
$232$	5.64330	+	3.62673i	0.370501	+	0.238106i
$233$	0.929012	+	6.46142i	0.0608616	+	0.423302i	0.997359	+	0.0726275i	$0.0231384\pi$
$233$	0.929012	+	6.46142i	0.0608616	+	0.423302i	−0.936498	+	0.350674i	$0.885952\pi$
$234$	1.54044	+	3.37310i	0.100702	+	0.220507i
$235$	−2.65197	−	0.778690i	−0.172996	−	0.0507961i
$236$	−4.35028	+	9.52579i	−0.283179	+	0.620076i
$237$	16.0258	−	18.4948i	1.04099	−	1.20137i
$238$	−0.217438	+	1.51231i	−0.0140944	+	0.0980287i
$239$	−13.2064	+	3.87775i	−0.854251	+	0.250831i	−0.679403	−	0.733765i	$-0.737761\pi$
$239$	−13.2064	+	3.87775i	−0.854251	+	0.250831i	−0.174847	+	0.984596i	$0.555943\pi$
$240$	−3.35591	−	3.87292i	−0.216623	−	0.249996i
$241$	19.4537	−	12.5021i	1.25312	−	0.805332i	0.265793	−	0.964030i	$-0.414366\pi$
$241$	19.4537	−	12.5021i	1.25312	−	0.805332i	0.987327	+	0.158698i	$0.0507297\pi$
$242$	8.53527	−	5.48529i	0.548668	−	0.352608i
$243$	−11.7145	−	13.5193i	−0.751486	−	0.867261i
$244$	10.7809	−	3.16557i	0.690178	−	0.202655i
$245$	0.610786	−	4.24811i	0.0390217	−	0.271402i
$246$	−3.14227	+	3.62637i	−0.200344	+	0.231209i
$247$	2.49249	−	5.45779i	0.158593	−	0.347271i
$248$	14.3924	+	4.22599i	0.913918	+	0.268351i
$249$	−8.14078	−	17.8258i	−0.515901	−	1.12967i
$250$	−0.921081	−	6.40626i	−0.0582543	−	0.405167i
$251$	−1.92798	−	1.23904i	−0.121693	−	0.0782074i	0.478378	−	0.878154i	$-0.341225\pi$
$251$	−1.92798	−	1.23904i	−0.121693	−	0.0782074i	−0.600071	+	0.799946i	$0.704861\pi$
$252$	10.4721			0.659683
$253$		0			0
$254$	−4.50658			−0.282768
$255$	−1.77627	−	1.14154i	−0.111234	−	0.0714860i
$256$	0.933914	+	6.49551i	0.0583696	+	0.405969i
$257$	−3.10404	−	6.79689i	−0.193625	−	0.423979i	0.787773	−	0.615966i	$-0.211234\pi$
$257$	−3.10404	−	6.79689i	−0.193625	−	0.423979i	−0.981397	+	0.191987i	$0.938507\pi$
$258$		0			0
$259$	−1.66166	+	3.63853i	−0.103251	+	0.226087i
$260$	−3.92916	+	4.53450i	−0.243676	+	0.281218i
$261$	0.853889	−	5.93893i	0.0528544	−	0.367610i
$262$	−11.0940	+	3.25748i	−0.685387	+	0.201248i
$263$	1.92809	+	2.22513i	0.118891	+	0.137208i	0.812075	−	0.583553i	$-0.198338\pi$
$263$	1.92809	+	2.22513i	0.118891	+	0.137208i	−0.693184	+	0.720761i	$0.743793\pi$
$264$	22.0243	−	14.1542i	1.35550	−	0.871128i
$265$	0.490949	−	0.315514i	0.0301588	−	0.0193819i
$266$	2.61944	+	3.02300i	0.160608	+	0.185352i
$267$	22.4679	−	6.59716i	1.37501	−	0.403740i
$268$	0.636451	−	4.42662i	0.0388775	−	0.270399i
$269$	5.20239	−	6.00388i	0.317195	−	0.366063i	−0.574653	−	0.818397i	$-0.694863\pi$
$269$	5.20239	−	6.00388i	0.317195	−	0.366063i	0.891849	+	0.452334i	$0.149409\pi$
$270$	−0.709614	+	1.55384i	−0.0431857	+	0.0945635i
$271$	−7.67594	−	2.25386i	−0.466280	−	0.136912i	0.0401490	−	0.999194i	$-0.487217\pi$
$271$	−7.67594	−	2.25386i	−0.466280	−	0.136912i	−0.506429	+	0.862281i	$0.669035\pi$
$272$	−0.588397	−	1.28841i	−0.0356768	−	0.0781213i
$273$	−3.08940	−	21.4872i	−0.186979	−	1.30047i
$274$	11.3804	+	7.31372i	0.687513	+	0.441838i
$275$	−18.1803			−1.09632
$276$		0			0
$277$	15.4721			0.929631			0.464815	−	0.885408i	$-0.346121\pi$
$277$	15.4721			0.929631			0.464815	+	0.885408i	$0.346121\pi$
$278$	−5.56744	−	3.57798i	−0.333913	−	0.214593i
$279$	−1.90935	−	13.2798i	−0.114310	−	0.795044i
$280$	−3.71558	−	8.13600i	−0.222049	−	0.486219i
$281$	−8.40893	−	2.46908i	−0.501635	−	0.147293i	0.0211190	−	0.999777i	$-0.493277\pi$
$281$	−8.40893	−	2.46908i	−0.501635	−	0.147293i	−0.522754	+	0.852484i	$0.675095\pi$
$282$	1.28370	−	2.81092i	0.0764434	−	0.167388i
$283$	18.1450	−	20.9405i	1.07861	−	1.24478i	0.110600	−	0.993865i	$-0.464723\pi$
$283$	18.1450	−	20.9405i	1.07861	−	1.24478i	0.968009	−	0.250916i	$-0.0807319\pi$
$284$	2.81760	−	19.5969i	0.167194	−	1.16286i
$285$	−5.30395	+	1.55738i	−0.314179	+	0.0922512i
$286$	−6.35752	−	7.33697i	−0.375928	−	0.433844i
$287$	9.45238	−	6.07468i	0.557956	−	0.358577i
$288$	9.45238	−	6.07468i	0.556987	−	0.357954i
$289$	10.7505	+	12.4067i	0.632380	+	0.729805i
$290$	−2.19896	+	0.645674i	−0.129128	+	0.0379153i
$291$	−5.63520	+	39.1937i	−0.330342	+	2.29758i
$292$	6.91684	−	7.98246i	0.404777	−	0.467138i
$293$	0.634698	−	1.38979i	0.0370794	−	0.0811926i	−0.890186	−	0.455597i	$-0.849426\pi$
$293$	0.634698	−	1.38979i	0.0370794	−	0.0811926i	0.927265	+	0.374405i	$0.122153\pi$
$294$	4.60401	+	1.35186i	0.268511	+	0.0788420i
$295$	−3.32332	−	7.27706i	−0.193491	−	0.423687i
$296$	0.393349	+	2.73580i	0.0228629	+	0.159015i
$297$	9.84957	+	6.32993i	0.571530	+	0.367300i
$298$	−14.7639			−0.855252
$299$		0			0
$300$	−12.5623			−0.725285
$301$		0			0
$302$	−0.372585	−	2.59139i	−0.0214399	−	0.149118i
$303$	−4.15415	−	9.09632i	−0.238650	−	0.522570i
$304$	−3.55800	−	1.04472i	−0.204065	−	0.0599189i
$305$	−3.56575	+	7.80791i	−0.204174	+	0.447080i
$306$	0.618367	−	0.713633i	0.0353497	−	0.0407957i
$307$	−1.35596	+	9.43088i	−0.0773885	+	0.538249i	0.913838	+	0.406078i	$0.133104\pi$
$307$	−1.35596	+	9.43088i	−0.0773885	+	0.538249i	−0.991227	+	0.132171i	$0.957805\pi$
$308$	−26.3059	+	7.72409i	−1.49891	+	0.440121i
$309$	6.12133	+	7.06439i	0.348230	+	0.401879i
$310$	−4.31110	+	2.77057i	−0.244854	+	0.157358i
$311$	11.0880	−	7.12583i	0.628743	−	0.404069i	−0.187101	−	0.982341i	$-0.559909\pi$
$311$	11.0880	−	7.12583i	0.628743	−	0.404069i	0.815844	+	0.578272i	$0.196273\pi$
$312$	−9.82291	−	11.3362i	−0.556113	−	0.641788i
$313$	23.3739	−	6.86320i	1.32117	−	0.387931i	0.456256	−	0.889849i	$-0.349190\pi$
$313$	23.3739	−	6.86320i	1.32117	−	0.387931i	0.864915	+	0.501918i	$0.167372\pi$
$314$	−1.00413	+	6.98391i	−0.0566666	+	0.394125i
$315$	−5.23889	+	6.04600i	−0.295178	+	0.340653i
$316$	−7.35625	+	16.1079i	−0.413822	+	0.906143i
$317$	−24.3869	−	7.16063i	−1.36970	−	0.402181i	−0.487530	−	0.873106i	$-0.662102\pi$
$317$	−24.3869	−	7.16063i	−1.36970	−	0.402181i	−0.882173	+	0.470925i	$0.843920\pi$
$318$	0.271048	+	0.593513i	0.0151996	+	0.0332826i
$319$	2.23551	+	15.5483i	0.125165	+	0.870539i
$320$	0.245474	+	0.157757i	0.0137224	+	0.00881888i
$321$	30.0000			1.67444
$322$		0			0
$323$	−1.52786			−0.0850126
$324$	14.9729	+	9.62253i	0.831830	+	0.534585i
$325$	1.48241	+	10.3104i	0.0822293	+	0.571917i
$326$	−1.47984	−	3.24039i	−0.0819605	−	0.179468i
$327$		0			0
$328$	3.22525	−	7.06232i	0.178085	−	0.389951i
$329$	−4.73862	+	5.46866i	−0.261248	+	0.301497i
$330$	−1.27290	+	8.85323i	−0.0700710	+	0.487354i
$331$	18.8564	−	5.53674i	1.03644	−	0.304327i	0.281115	−	0.959674i	$-0.409296\pi$
$331$	18.8564	−	5.53674i	1.03644	−	0.304327i	0.755328	+	0.655347i	$0.227478\pi$
$332$	9.28615	+	10.7168i	0.509644	+	0.588160i
$333$	2.07969	−	1.33654i	0.113966	−	0.0732418i
$334$	0.794372	−	0.510512i	0.0434661	−	0.0279340i
$335$	2.23727	+	2.58195i	0.122235	+	0.141067i
$336$	−12.8729	+	3.77984i	−0.702277	+	0.206207i
$337$	3.33250	−	23.1781i	0.181533	−	1.26259i	−0.671607	−	0.740908i	$-0.734396\pi$
$337$	3.33250	−	23.1781i	0.181533	−	1.26259i	0.853140	−	0.521682i	$-0.174695\pi$
$338$	1.61890	−	1.86832i	0.0880568	−	0.101623i
$339$	8.14078	−	17.8258i	0.442147	−	0.968166i
$340$	1.46597	+	0.430449i	0.0795036	+	0.0233444i
$341$	14.5913	+	31.9505i	0.790163	+	1.73021i
$342$	−0.351822	−	2.44697i	−0.0190243	−	0.132317i
$343$	9.60409	+	6.17218i	0.518572	+	0.333266i
$344$		0			0
$345$		0			0
$346$	14.1803			0.762340
$347$	−8.31877	−	5.34615i	−0.446575	−	0.286996i	0.297962	−	0.954578i	$-0.403693\pi$
$347$	−8.31877	−	5.34615i	−0.446575	−	0.286996i	−0.744537	+	0.667581i	$0.767330\pi$
$348$	1.54470	+	10.7436i	0.0828046	+	0.575919i
$349$	10.1429	+	22.2099i	0.542939	+	1.18887i	0.960002	+	0.279993i	$0.0903323\pi$
$349$	10.1429	+	22.2099i	0.542939	+	1.18887i	−0.417063	+	0.908878i	$0.636940\pi$
$350$	−6.66298	−	1.95643i	−0.356151	−	0.104575i
$351$	2.78669	−	6.10200i	0.148742	−	0.325701i
$352$	−19.2637	+	22.2314i	−1.02676	+	1.18494i
$353$	−1.33216	+	9.26540i	−0.0709039	+	0.493148i	0.923166	+	0.384402i	$0.125592\pi$
$353$	−1.33216	+	9.26540i	−0.0709039	+	0.493148i	−0.994070	+	0.108745i	$0.965317\pi$
$354$	8.58197	−	2.51989i	0.456126	−	0.133931i
$355$	9.90451	+	11.4304i	0.525677	+	0.606664i
$356$	−14.2544	+	9.16077i	−0.755483	+	0.485520i
$357$	−4.65034	+	2.98859i	−0.246122	+	0.158173i
$358$	−0.286629	−	0.330787i	−0.0151488	−	0.0174826i
$359$	−19.0829	+	5.60325i	−1.00716	+	0.295728i	−0.743390	−	0.668858i	$-0.766783\pi$
$359$	−19.0829	+	5.60325i	−1.00716	+	0.295728i	−0.263768	+	0.964586i	$0.584965\pi$
$360$	−0.786697	+	5.47160i	−0.0414626	+	0.288379i
$361$	9.82291	−	11.3362i	0.516995	−	0.596644i
$362$	−4.27537	+	9.36175i	−0.224708	+	0.492042i
$363$	35.2213	+	10.3419i	1.84864	+	0.542809i
$364$	6.52542	+	14.2887i	0.342025	+	0.748931i
$365$	1.14832	+	7.98675i	0.0601059	+	0.418046i
$366$	−8.07330	−	5.18839i	−0.421998	−	0.271202i
$367$	4.18034			0.218212			0.109106	−	0.994030i	$-0.465201\pi$
$367$	4.18034			0.218212			0.109106	+	0.994030i	$0.465201\pi$
$368$		0			0
$369$	−6.94427			−0.361504
$370$	−0.794372	−	0.510512i	−0.0412974	−	0.0265403i
$371$	−0.217438	−	1.51231i	−0.0112888	−	0.0785154i
$372$	10.0823	+	22.0772i	0.522745	+	1.14465i
$373$	7.39597	+	2.17165i	0.382949	+	0.112444i	0.467540	−	0.883972i	$-0.345140\pi$
$373$	7.39597	+	2.17165i	0.382949	+	0.112444i	−0.0845915	+	0.996416i	$0.526959\pi$
$374$	−1.02696	+	2.24873i	−0.0531030	+	0.116279i
$375$	15.3345	−	17.6969i	0.791869	−	0.913866i
$376$	−0.711574	+	4.94911i	−0.0366966	+	0.255231i
$377$	8.63544	−	2.53559i	0.444748	−	0.130590i
$378$	2.92863	+	3.37981i	0.150632	+	0.173839i
$379$	−20.4935	+	13.1704i	−1.05268	+	0.676517i	−0.948091	−	0.317999i	$-0.896989\pi$
$379$	−20.4935	+	13.1704i	−1.05268	+	0.676517i	−0.104590	+	0.994515i	$0.533353\pi$
$380$	3.36501	−	2.16256i	0.172622	−	0.110937i
$381$	−10.6775	−	12.3225i	−0.547023	−	0.631299i
$382$	−15.5249	+	4.55853i	−0.794324	+	0.233235i
$383$	1.00413	−	6.98391i	0.0513089	−	0.356861i	−0.947952	−	0.318414i	$-0.896850\pi$
$383$	1.00413	−	6.98391i	0.0513089	−	0.356861i	0.999261	−	0.0384472i	$-0.0122411\pi$
$384$	−16.6668	+	19.2345i	−0.850522	+	0.981555i
$385$	8.70056	−	19.0516i	0.443422	−	0.970958i
$386$	−5.89695	−	1.73150i	−0.300147	−	0.0881310i
$387$		0			0
$388$	−4.07767	−	28.3608i	−0.207012	−	1.43980i
$389$	−21.4754	−	13.8014i	−1.08885	−	0.699759i	−0.132262	−	0.991215i	$-0.542224\pi$
$389$	−21.4754	−	13.8014i	−1.08885	−	0.699759i	−0.956584	+	0.291456i	$0.905860\pi$
$390$	5.12461			0.259495
$391$		0			0
$392$	−7.76393			−0.392138
$393$	−35.1920	−	22.6165i	−1.77520	−	1.14085i
$394$	0.129482	+	0.900569i	0.00652322	+	0.0453700i
$395$	−5.61968	−	12.3054i	−0.282757	−	0.619151i
$396$	16.2579	+	4.77375i	0.816991	+	0.239890i
$397$	−10.1429	+	22.2099i	−0.509060	+	1.11469i	0.464358	+	0.885648i	$0.346285\pi$
$397$	−10.1429	+	22.2099i	−0.509060	+	1.11469i	−0.973418	+	0.229038i	$0.926442\pi$
$398$	−4.97481	+	5.74124i	−0.249365	+	0.287782i
$399$	−2.05960	+	14.3248i	−0.103109	+	0.717139i
$400$	6.17692	−	1.81371i	0.308846	−	0.0906854i
$401$	−9.28615	−	10.7168i	−0.463728	−	0.535171i	0.474928	−	0.880024i	$-0.342474\pi$
$401$	−9.28615	−	10.7168i	−0.463728	−	0.535171i	−0.938656	+	0.344854i	$0.887929\pi$
$402$	−3.21330	+	2.06506i	−0.160265	+	0.102996i
$403$	16.9299	−	10.8802i	0.843338	−	0.541981i
$404$	4.73862	+	5.46866i	0.235755	+	0.272076i
$405$	−13.0460	+	3.83065i	−0.648260	+	0.190346i
$406$	−0.853889	+	5.93893i	−0.0423778	+	0.294744i
$407$	−4.23835	+	4.89131i	−0.210087	+	0.242453i
$408$	−1.58674	+	3.47449i	−0.0785555	+	0.172013i
$409$	−20.4954	−	6.01800i	−1.01343	−	0.297571i	−0.267476	−	0.963565i	$-0.586190\pi$
$409$	−20.4954	−	6.01800i	−1.01343	−	0.297571i	−0.745957	+	0.665994i	$0.768008\pi$
$410$	1.10188	+	2.41278i	0.0544179	+	0.119159i
$411$	6.96550	+	48.4461i	0.343583	+	2.38967i
$412$	−5.69018	−	3.65686i	−0.280335	−	0.180160i
$413$	−20.9443			−1.03060
$414$		0			0
$415$	−10.8328			−0.531762
$416$	14.1786	+	9.11202i	0.695162	+	0.446753i
$417$	−3.40763	−	23.7006i	−0.166872	−	1.16062i
$418$	2.68862	+	5.88726i	0.131505	+	0.287955i
$419$	−4.39792	−	1.29135i	−0.214853	−	0.0630864i	0.172535	−	0.985003i	$-0.444804\pi$
$419$	−4.39792	−	1.29135i	−0.214853	−	0.0630864i	−0.387388	+	0.921917i	$0.626622\pi$
$420$	6.01194	−	13.1643i	0.293353	−	0.642353i
$421$	−6.73969	+	7.77802i	−0.328473	+	0.379078i	−0.895832	−	0.444393i	$-0.853420\pi$
$421$	−6.73969	+	7.77802i	−0.328473	+	0.379078i	0.567360	+	0.823470i	$0.307965\pi$
$422$	2.05960	−	14.3248i	0.100260	−	0.697322i
$423$	4.29098	−	1.25995i	0.208635	−	0.0612607i
$424$	−0.691355	−	0.797866i	−0.0335752	−	0.0387478i
$425$	2.23140	−	1.43404i	0.108239	−	0.0695610i
$426$	−14.2255	+	9.14214i	−0.689226	+	0.442938i
$427$	14.7161	+	16.9833i	0.712163	+	0.821880i
$428$	−20.8289	+	6.11591i	−1.00680	+	0.295624i
$429$	4.99875	−	34.7671i	0.241342	−	1.67857i
$430$		0			0
$431$	7.28134	−	15.9439i	0.350730	−	0.767991i	−0.649243	−	0.760581i	$-0.724914\pi$
$431$	7.28134	−	15.9439i	0.350730	−	0.767991i	0.999973	−	0.00740975i	$-0.00235862\pi$
$432$	−3.97796	−	1.16803i	−0.191390	−	0.0561971i
$433$	−7.40255	−	16.2093i	−0.355744	−	0.778971i	−0.999901	−	0.0140774i	$-0.995519\pi$
$433$	−7.40255	−	16.2093i	−0.355744	−	0.778971i	0.644157	−	0.764893i	$-0.277208\pi$
$434$	1.90935	+	13.2798i	0.0916519	+	0.637453i
$435$	−6.97550	−	4.48288i	−0.334450	−	0.214938i
$436$		0			0
$437$		0			0
$438$	−9.02129			−0.431054
$439$	−15.7383	−	10.1144i	−0.751150	−	0.482735i	0.108196	−	0.994130i	$-0.465493\pi$
$439$	−15.7383	−	10.1144i	−0.751150	−	0.482735i	−0.859346	+	0.511395i	$0.829129\pi$
$440$	−2.05960	−	14.3248i	−0.0981876	−	0.682909i
$441$	2.88475	+	6.31673i	0.137369	+	0.300797i
$442$	1.35903	+	0.399048i	0.0646426	+	0.0189808i
$443$	15.8375	−	34.6794i	0.752464	−	1.64767i	−0.00942222	−	0.999956i	$-0.502999\pi$
$443$	15.8375	−	34.6794i	0.752464	−	1.64767i	0.761886	−	0.647711i	$-0.224273\pi$
$444$	−2.92863	+	3.37981i	−0.138986	+	0.160399i
$445$	1.84216	−	12.8125i	0.0873269	−	0.607372i
$446$	−2.37200	+	0.696481i	−0.112317	+	0.0329793i
$447$	−34.9803	−	40.3694i	−1.65451	−	1.90941i
$448$	0.642661	−	0.413013i	0.0303629	−	0.0195130i
$449$	−12.5719	+	8.07948i	−0.593306	+	0.381294i	−0.802564	−	0.596566i	$-0.796531\pi$
$449$	−12.5719	+	8.07948i	−0.593306	+	0.381294i	0.209258	+	0.977860i	$0.432895\pi$
$450$	2.81053	+	3.24352i	0.132490	+	0.152901i
$451$	17.4439	−	5.12199i	0.821402	−	0.241185i
$452$	−2.01807	+	14.0360i	−0.0949222	+	0.660198i
$453$	6.20293	−	7.15856i	0.291439	−	0.336339i
$454$	3.12719	−	6.84759i	0.146766	−	0.321373i
$455$	−11.5139	−	3.38079i	−0.539781	−	0.158494i
$456$	4.15415	+	9.09632i	0.194536	+	0.425974i
$457$	−0.729308	−	5.07245i	−0.0341156	−	0.237279i	0.965628	−	0.259928i	$-0.0836990\pi$
$457$	−0.729308	−	5.07245i	−0.0341156	−	0.237279i	−0.999743	+	0.0226493i	$0.992790\pi$
$458$	6.23908	+	4.00961i	0.291533	+	0.187357i
$459$	−1.70820			−0.0797321
$460$		0			0
$461$	−1.47214			−0.0685642			−0.0342821	−	0.999412i	$-0.510914\pi$
$461$	−1.47214			−0.0685642			−0.0342821	+	0.999412i	$0.510914\pi$
$462$	19.6991	+	12.6599i	0.916487	+	0.588990i
$463$	2.84630	+	19.7964i	0.132279	+	0.920018i	0.942574	+	0.333997i	$0.108397\pi$
$463$	2.84630	+	19.7964i	0.132279	+	0.920018i	−0.810296	+	0.586021i	$0.800693\pi$
$464$	−2.31067	−	5.05965i	−0.107270	−	0.234888i
$465$	−17.7900	−	5.22361i	−0.824990	−	0.242239i
$466$	−1.67597	+	3.66986i	−0.0776377	+	0.170003i
$467$	−8.54968	+	9.86686i	−0.395632	+	0.456584i	−0.918261	−	0.395977i	$-0.870406\pi$
$467$	−8.54968	+	9.86686i	−0.395632	+	0.456584i	0.522628	+	0.852561i	$0.324952\pi$
$468$	1.38162	−	9.60939i	0.0638655	−	0.444194i
$469$	8.58197	−	2.51989i	0.396278	−	0.116358i
$470$	−1.11864	−	1.29097i	−0.0515988	−	0.0595482i
$471$	−21.4754	+	13.8014i	−0.989534	+	0.635935i
$472$	−12.1747	+	7.82423i	−0.560388	+	0.360139i
$473$		0			0
$474$	14.5120	−	4.26110i	0.666556	−	0.195719i
$475$	0.988273	−	6.87359i	0.0453451	−	0.315382i
$476$	2.61944	−	3.02300i	0.120062	−	0.138559i
$477$	−0.392265	+	0.858940i	−0.0179606	+	0.0393282i
$478$	−8.16200	−	2.39658i	−0.373321	−	0.109617i
$479$	−13.1258	−	28.7414i	−0.599731	−	1.31323i	−0.929380	−	0.369125i	$-0.879657\pi$
$479$	−13.1258	−	28.7414i	−0.599731	−	1.31323i	0.329648	−	0.944104i	$-0.393070\pi$
$480$	−2.20985	−	15.3698i	−0.100865	−	0.701533i
$481$	3.11954	+	2.00481i	0.142239	+	0.0914113i
$482$	14.2918			0.650973
$483$		0			0
$484$	−26.5623			−1.20738
$485$	18.4138	+	11.8338i	0.836128	+	0.537347i
$486$	−1.57339	−	10.9432i	−0.0713706	−	0.496393i
$487$	−6.11001	−	13.3791i	−0.276871	−	0.606263i	0.719202	−	0.694801i	$-0.244508\pi$
$487$	−6.11001	−	13.3791i	−0.276871	−	0.606263i	−0.996073	+	0.0885385i	$0.971780\pi$
$488$	14.8989	+	4.37470i	0.674440	+	0.198034i
$489$	5.35409	−	11.7238i	0.242121	−	0.530170i
$490$	1.73700	−	2.00461i	0.0784698	−	0.0905589i
$491$	−1.18798	+	8.26256i	−0.0536126	+	0.372884i	0.945298	+	0.326209i	$0.105771\pi$
$491$	−1.18798	+	8.26256i	−0.0536126	+	0.372884i	−0.998910	+	0.0466746i	$0.985138\pi$
$492$	12.0534	−	3.53921i	0.543411	−	0.159560i
$493$	−1.50081	−	1.73202i	−0.0675930	−	0.0780064i
$494$	3.11954	−	2.00481i	0.140355	−	0.0902005i
$495$	−10.8894	+	6.99820i	−0.489443	+	0.314546i
$496$	−8.14496	−	9.39978i	−0.365719	−	0.422063i
$497$	37.9928	−	11.1557i	1.70421	−	0.500401i
$498$	1.72364	−	11.9882i	0.0772382	−	0.537203i
$499$	−12.6334	+	14.5798i	−0.565550	+	0.652680i	−0.964435	−	0.264321i	$-0.914852\pi$
$499$	−12.6334	+	14.5798i	−0.565550	+	0.652680i	0.398884	+	0.917001i	$0.369398\pi$
$500$	−7.03890	+	15.4131i	−0.314789	+	0.689293i
$501$	3.27802	+	0.962513i	0.146451	+	0.0430019i
$502$	−0.588397	−	1.28841i	−0.0262614	−	0.0575045i
$503$	−3.83457	−	26.6700i	−0.170975	−	1.18916i	−0.876830	−	0.480801i	$-0.840346\pi$
$503$	−3.83457	−	26.6700i	−0.170975	−	1.18916i	0.705855	−	0.708357i	$-0.250563\pi$
$504$	12.1747	+	7.82423i	0.542306	+	0.348519i
$505$	−5.52786			−0.245987
$506$		0			0
$507$	8.94427			0.397229
$508$	9.92542	+	6.37868i	0.440369	+	0.283008i
$509$	4.02821	+	28.0168i	0.178547	+	1.24182i	0.860127	+	0.510081i	$0.170384\pi$
$509$	4.02821	+	28.0168i	0.178547	+	1.24182i	−0.681579	+	0.731744i	$0.738706\pi$
$510$	−0.542097	−	1.18703i	−0.0240044	−	0.0525624i
$511$	20.2689	+	5.95149i	0.896644	+	0.263278i
$512$	7.77167	−	17.0176i	0.343462	−	0.752078i
$513$	−2.92863	+	3.37981i	−0.129302	+	0.149222i
$514$	0.657215	−	4.57103i	0.0289885	−	0.201619i
$515$	4.95788	−	1.45576i	0.218470	−	0.0641486i
$516$		0			0
$517$	−9.84957	+	6.32993i	−0.433184	+	0.278390i
$518$	−2.07969	+	1.33654i	−0.0913765	+	0.0587241i
$519$	33.5976	+	38.7737i	1.47477	+	1.70198i
$520$	−7.95592	+	2.33607i	−0.348890	+	0.102443i
$521$	4.47102	−	31.0966i	0.195879	−	1.36237i	−0.620207	−	0.784438i	$-0.712951\pi$
$521$	4.47102	−	31.0966i	0.195879	−	1.36237i	0.816086	−	0.577930i	$-0.196139\pi$
$522$	2.42836	−	2.80247i	0.106286	−	0.122661i
$523$	−17.0838	+	37.4083i	−0.747022	+	1.63575i	0.0246243	+	0.999697i	$0.492161\pi$
$523$	−17.0838	+	37.4083i	−0.747022	+	1.63575i	−0.771646	+	0.636052i	$0.780566\pi$
$524$	29.0443	+	8.52819i	1.26881	+	0.372556i
$525$	−10.4371	−	22.8542i	−0.455514	−	0.997437i
$526$	0.258965	+	1.80114i	0.0112914	+	0.0785334i
$527$	−4.31110	−	2.77057i	−0.187794	−	0.120688i
$528$	−21.7082			−0.944728
$529$		0			0
$530$	0.360680			0.0156669
$531$	10.8894	+	6.99820i	0.472560	+	0.303696i
$532$	−1.49034	−	10.3655i	−0.0646144	−	0.449403i
$533$	−4.32713	−	9.47510i	−0.187429	−	0.410412i
$534$	13.8859	+	4.07727i	0.600902	+	0.176441i
$535$	6.88907	−	15.0850i	0.297841	−	0.652180i
$536$	4.04726	−	4.67079i	0.174815	−	0.201747i
$537$	0.225369	−	1.56747i	0.00972538	−	0.0676415i
$538$	4.71095	−	1.38326i	0.203103	−	0.0596365i
$539$	−11.9056	−	13.7398i	−0.512810	−	0.591814i
$540$	3.76220	−	2.41782i	0.161899	−	0.104046i
$541$	−28.9529	+	18.6069i	−1.24478	+	0.799974i	−0.986127	−	0.165995i	$-0.946916\pi$
$541$	−28.9529	+	18.6069i	−1.24478	+	0.799974i	−0.258657	+	0.965969i	$0.583280\pi$
$542$	−3.23781	−	3.73663i	−0.139076	−	0.160502i
$543$	−35.7277	+	10.4906i	−1.53322	+	0.450195i
$544$	0.610786	−	4.24811i	0.0261872	−	0.182136i
$545$		0			0
$546$	5.57338	−	12.2040i	0.238519	−	0.522283i
$547$	28.3444	+	8.32267i	1.21192	+	0.355852i	0.824399	−	0.566010i	$-0.191513\pi$
$547$	28.3444	+	8.32267i	1.21192	+	0.355852i	0.387520	+	0.921861i	$0.373332\pi$
$548$	−14.7125	−	32.2159i	−0.628487	−	1.37619i
$549$	−1.97655	−	13.7472i	−0.0843569	−	0.586715i
$550$	−9.45238	−	6.07468i	−0.403051	−	0.259025i
$551$	−6.00000			−0.255609
$552$		0			0
$553$	−35.4164			−1.50606
$554$	8.04432	+	5.16977i	0.341771	+	0.219643i
$555$	−0.486206	−	3.38163i	−0.0206383	−	0.143542i
$556$	7.19758	+	15.7605i	0.305245	+	0.668394i
$557$	−7.11599	−	2.08944i	−0.301514	−	0.0885326i	0.127476	−	0.991842i	$-0.459312\pi$
$557$	−7.11599	−	2.08944i	−0.301514	−	0.0885326i	−0.428990	+	0.903309i	$0.641131\pi$
$558$	3.44454	−	7.54248i	0.145819	−	0.319299i
$559$		0			0
$560$	−1.05546	+	7.34092i	−0.0446015	+	0.310210i
$561$	−8.58197	+	2.51989i	−0.362331	+	0.106390i
$562$	−3.54699	−	4.09345i	−0.149621	−	0.172672i
$563$	27.7145	−	17.8110i	1.16803	−	0.750645i	0.194879	−	0.980827i	$-0.437569\pi$
$563$	27.7145	−	17.8110i	1.16803	−	0.750645i	0.973147	+	0.230182i	$0.0739323\pi$
$564$	−6.80588	+	4.37388i	−0.286579	+	0.184173i
$565$	−7.09399	−	8.18690i	−0.298446	−	0.344425i
$566$	16.4309	−	4.82456i	0.690644	−	0.202791i
$567$	−5.06595	+	35.2344i	−0.212750	+	1.47971i
$568$	17.9174	−	20.6778i	0.751799	−	0.867622i
$569$	9.21405	−	20.1759i	0.386273	−	0.845820i	−0.612207	−	0.790698i	$-0.709718\pi$
$569$	9.21405	−	20.1759i	0.386273	−	0.845820i	0.998480	−	0.0551219i	$-0.0175548\pi$
$570$	−3.27802	−	0.962513i	−0.137301	−	0.0403152i
$571$	5.93703	+	13.0003i	0.248457	+	0.544045i	0.992234	−	0.124383i	$-0.0396951\pi$
$571$	5.93703	+	13.0003i	0.248457	+	0.544045i	−0.743777	+	0.668427i	$0.766968\pi$
$572$	3.61713	+	25.1577i	0.151240	+	1.05190i
$573$	−49.2478	−	31.6497i	−2.05736	−	1.32218i
$574$	6.94427			0.289848
$575$		0			0
$576$	−0.472136			−0.0196723
$577$	19.2551	+	12.3745i	0.801599	+	0.515156i	0.876137	−	0.482062i	$-0.160112\pi$
$577$	19.2551	+	12.3745i	0.801599	+	0.515156i	−0.0745382	+	0.997218i	$0.523748\pi$
$578$	1.44391	+	10.0426i	0.0600588	+	0.417718i
$579$	−9.23720	−	20.2266i	−0.383885	−	0.840590i
$580$	5.75696	+	1.69040i	0.239045	+	0.0701898i
$581$	−11.7815	+	25.7978i	−0.488777	+	1.07027i
$582$	−16.0258	+	18.4948i	−0.664292	+	0.766634i
$583$	0.351822	−	2.44697i	0.0145710	−	0.101343i
$584$	14.0055	−	4.11238i	0.579551	−	0.170171i
$585$	4.85671	+	5.60495i	0.200800	+	0.231736i
$586$	0.794372	−	0.510512i	0.0328152	−	0.0210891i
$587$	−20.7859	+	13.3583i	−0.857924	+	0.551355i	−0.894037	−	0.447993i	$-0.852139\pi$
$587$	−20.7859	+	13.3583i	−0.857924	+	0.551355i	0.0361126	+	0.999348i	$0.488503\pi$
$588$	−8.22656	−	9.49396i	−0.339258	−	0.391524i
$589$	−12.8729	+	3.77984i	−0.530421	+	0.155746i
$590$	0.703643	−	4.89395i	0.0289685	−	0.201481i
$591$	−2.15567	+	2.48777i	−0.0886723	+	0.102333i
$592$	0.952046	−	2.08469i	0.0391289	−	0.0856803i
$593$	2.82501	+	0.829497i	0.116009	+	0.0340634i	0.339222	−	0.940706i	$-0.389836\pi$
$593$	2.82501	+	0.829497i	0.116009	+	0.0340634i	−0.223213	+	0.974770i	$0.571654\pi$
$594$	3.00597	+	6.58216i	0.123336	+	0.270069i
$595$	0.434875	+	3.02463i	0.0178282	+	0.123998i
$596$	32.5165	+	20.8971i	1.33193	+	0.855979i
$597$	−27.4853			−1.12490
$598$		0			0
$599$	33.8885			1.38465			0.692324	−	0.721587i	$-0.256587\pi$
$599$	33.8885			1.38465			0.692324	+	0.721587i	$0.256587\pi$
$600$	−14.6047	−	9.38589i	−0.596236	−	0.383177i
$601$	−6.67294	−	46.4113i	−0.272195	−	1.89316i	−0.425470	−	0.904972i	$-0.639891\pi$
$601$	−6.67294	−	46.4113i	−0.272195	−	1.89316i	0.153276	−	0.988183i	$-0.451018\pi$
$602$		0			0
$603$	−5.30395	−	1.55738i	−0.215993	−	0.0634214i
$604$	−2.84730	+	6.23471i	−0.115855	+	0.253687i
$605$	13.2883	−	15.3355i	0.540246	−	0.623477i
$606$	0.879554	−	6.11743i	0.0357294	−	0.248504i
$607$	−25.3998	+	7.45806i	−1.03095	+	0.302713i	−0.753096	−	0.657911i	$-0.771440\pi$
$607$	−25.3998	+	7.45806i	−1.03095	+	0.302713i	−0.277851	+	0.960624i	$0.589622\pi$
$608$	−7.35806	−	8.49165i	−0.298409	−	0.344382i
$609$	−18.2621	+	11.7363i	−0.740018	+	0.475581i
$610$	−4.46281	+	2.86807i	−0.180694	+	0.116125i
$611$	4.39294	+	5.06972i	0.177719	+	0.205099i
$612$	−2.37200	+	0.696481i	−0.0958823	+	0.0281536i
$613$	0.812362	−	5.65010i	0.0328110	−	0.228205i	−0.966817	−	0.255469i	$-0.917770\pi$
$613$	0.812362	−	5.65010i	0.0328110	−	0.228205i	0.999628	+	0.0272633i	$0.00867927\pi$
$614$	−3.85618	+	4.45026i	−0.155623	+	0.179598i
$615$	−3.98663	+	8.72951i	−0.160757	+	0.352008i
$616$	−36.3538	−	10.6744i	−1.46474	−	0.430085i
$617$	3.12719	+	6.84759i	0.125896	+	0.275673i	0.962076	−	0.272781i	$-0.0879436\pi$
$617$	3.12719	+	6.84759i	0.125896	+	0.275673i	−0.836180	+	0.548455i	$0.815216\pi$
$618$	0.822165	+	5.71829i	0.0330723	+	0.230023i
$619$	−16.3341	−	10.4973i	−0.656524	−	0.421922i	0.169521	−	0.985527i	$-0.445778\pi$
$619$	−16.3341	−	10.4973i	−0.656524	−	0.421922i	−0.826045	+	0.563604i	$0.809414\pi$
$620$	13.4164			0.538816
$621$		0			0
$622$	8.14590			0.326621
$623$	−28.5089	−	18.3215i	−1.14218	−	0.734037i
$624$	1.77007	+	12.3111i	0.0708594	+	0.492838i
$625$	1.83464	+	4.01731i	0.0733857	+	0.160692i
$626$	14.4459	+	4.24169i	0.577373	+	0.169532i
$627$	−9.72753	+	21.3003i	−0.388480	+	0.850653i
$628$	12.0967	−	13.9603i	0.482710	−	0.557077i
$629$	0.134384	−	0.934661i	0.00535824	−	0.0372674i
$630$	−4.74399	+	1.39296i	−0.189005	+	0.0554969i
$631$	8.09452	+	9.34158i	0.322238	+	0.371882i	0.893637	−	0.448790i	$-0.148145\pi$
$631$	8.09452	+	9.34158i	0.322238	+	0.371882i	−0.571400	+	0.820672i	$0.693599\pi$
$632$	−20.5873	+	13.2306i	−0.818918	+	0.526286i
$633$	44.0486	−	28.3083i	1.75077	−	1.12515i
$634$	−10.2867	−	11.8715i	−0.408536	−	0.471476i
$635$	−8.64806	+	2.53930i	−0.343188	+	0.100769i
$636$	0.243103	−	1.69082i	0.00963965	−	0.0670453i
$637$	−6.82130	+	7.87220i	−0.270270	+	0.311908i
$638$	−4.03293	+	8.83089i	−0.159665	+	0.349618i
$639$	−23.4808	−	6.89460i	−0.928888	−	0.272746i
$640$	5.84443	+	12.7975i	0.231021	+	0.505866i
$641$	−2.46275	−	17.1288i	−0.0972728	−	0.676547i	−0.978861	−	0.204528i	$-0.934434\pi$
$641$	−2.46275	−	17.1288i	−0.0972728	−	0.676547i	0.881588	−	0.472020i	$-0.156475\pi$
$642$	15.5977	+	10.0240i	0.615592	+	0.395617i
$643$	29.5967			1.16718			0.583591	−	0.812048i	$-0.301647\pi$
$643$	29.5967			1.16718			0.583591	+	0.812048i	$0.301647\pi$
$644$		0			0
$645$		0			0
$646$	−0.794372	−	0.510512i	−0.0312542	−	0.0200858i
$647$	−0.954677	−	6.63992i	−0.0375322	−	0.261042i	0.962412	−	0.271593i	$-0.0875506\pi$
$647$	−0.954677	−	6.63992i	−0.0375322	−	0.261042i	−0.999944	+	0.0105510i	$0.996641\pi$
$648$	10.2179	+	22.3740i	0.401395	+	0.878933i
$649$	−32.5158	−	9.54751i	−1.27636	−	0.374772i
$650$	−2.67431	+	5.85593i	−0.104895	+	0.229689i
$651$	−31.7876	+	36.6849i	−1.24585	+	1.43779i
$652$	−1.32726	+	9.23131i	−0.0519796	+	0.361526i
$653$	36.7533	−	10.7918i	1.43827	−	0.422314i	0.532625	−	0.846352i	$-0.321206\pi$
$653$	36.7533	−	10.7918i	1.43827	−	0.422314i	0.905645	+	0.424038i	$0.139388\pi$
$654$		0			0
$655$	−19.4537	+	12.5021i	−0.760117	+	0.488498i
$656$	−5.41573	+	3.48048i	−0.211449	+	0.135890i
$657$	−8.54968	−	9.86686i	−0.333555	−	0.384943i
$658$	−4.29098	+	1.25995i	−0.167280	+	0.0491178i
$659$	−1.51601	+	10.5440i	−0.0590552	+	0.410738i	0.938754	+	0.344587i	$0.111981\pi$
$659$	−1.51601	+	10.5440i	−0.0590552	+	0.410738i	−0.997810	+	0.0661510i	$0.978928\pi$
$660$	15.3345	−	17.6969i	0.596894	−	0.688852i
$661$	9.53140	−	20.8708i	0.370728	−	0.811782i	−0.628689	−	0.777657i	$-0.716408\pi$
$661$	9.53140	−	20.8708i	0.370728	−	0.811782i	0.999418	−	0.0341251i	$-0.0108645\pi$
$662$	11.6539	+	3.42189i	0.452942	+	0.132996i
$663$	2.12884	+	4.66151i	0.0826773	+	0.181038i
$664$	2.78891	+	19.3973i	0.108231	+	0.752760i
$665$	6.73003	+	4.32513i	0.260979	+	0.167721i
$666$	1.52786			0.0592035
$667$		0			0
$668$	−2.47214			−0.0956498
$669$	−7.52440	−	4.83564i	−0.290910	−	0.186957i
$670$	0.300492	+	2.08996i	0.0116090	+	0.0807424i
$671$	15.1048	+	33.0748i	0.583113	+	1.27684i
$672$	−39.0058	−	11.4531i	−1.50468	−	0.441814i
$673$	1.24625	−	2.72890i	0.0480392	−	0.105191i	−0.884091	−	0.467316i	$-0.845221\pi$
$673$	1.24625	−	2.72890i	0.0480392	−	0.105191i	0.932130	+	0.362124i	$0.117948\pi$
$674$	9.47723	−	10.9373i	0.365049	−	0.421289i
$675$	1.10492	−	7.68491i	0.0425285	−	0.295792i
$676$	−6.20997	+	1.82341i	−0.238845	+	0.0701312i
$677$	11.7875	+	13.6035i	0.453030	+	0.522825i	0.935614	−	0.353025i	$-0.114847\pi$
$677$	11.7875	+	13.6035i	0.453030	+	0.522825i	−0.482584	+	0.875850i	$0.660302\pi$
$678$	10.1888	−	6.54795i	0.391299	−	0.251472i
$679$	48.2080	−	30.9814i	1.85005	−	1.18896i
$680$	1.38271	+	1.59573i	0.0530245	+	0.0611935i
$681$	26.1328	−	7.67329i	1.00141	−	0.294041i
$682$	−3.08940	+	21.4872i	−0.118299	+	0.822789i
$683$	−17.4172	+	20.1005i	−0.666449	+	0.769124i	−0.983816	−	0.179179i	$-0.942656\pi$
$683$	−17.4172	+	20.1005i	−0.666449	+	0.769124i	0.317367	+	0.948303i	$0.397201\pi$
$684$	−2.68862	+	5.88726i	−0.102802	+	0.225105i
$685$	25.9598	+	7.62248i	0.991872	+	0.291240i
$686$	2.93106	+	6.41812i	0.111908	+	0.245045i
$687$	3.81871	+	26.5597i	0.145693	+	1.01332i
$688$		0			0
$689$	−1.41641			−0.0539608
$690$		0			0
$691$	7.05573			0.268413			0.134206	−	0.990953i	$-0.457152\pi$
$691$	7.05573			0.268413			0.134206	+	0.990953i	$0.457152\pi$
$692$	−31.2312	−	20.0711i	−1.18723	−	0.762988i
$693$	4.82284	+	33.5436i	0.183205	+	1.27422i
$694$	−2.53879	−	5.55918i	−0.0963712	−	0.211023i
$695$	−12.6999	−	3.72903i	−0.481735	−	0.141450i
$696$	−6.23123	+	13.6445i	−0.236194	+	0.517193i
$697$	−1.73700	+	2.00461i	−0.0657937	+	0.0759299i
$698$	−2.14756	+	14.9366i	−0.0812862	+	0.565358i
$699$	−14.0055	+	4.11238i	−0.529736	+	0.155544i
$700$	11.9056	+	13.7398i	0.449989	+	0.519315i
$701$	3.21330	−	2.06506i	0.121365	−	0.0779964i	−0.478550	−	0.878060i	$-0.658837\pi$
$701$	3.21330	−	2.06506i	0.121365	−	0.0779964i	0.599915	+	0.800064i	$0.295201\pi$
$702$	3.48775	−	2.24144i	0.131637	−	0.0845978i
$703$	−1.61890	−	1.86832i	−0.0610581	−	0.0704649i
$704$	1.18600	−	0.348241i	0.0446990	−	0.0131248i
$705$	0.879554	−	6.11743i	0.0331259	−	0.230396i
$706$	−3.78851	+	4.37218i	−0.142583	+	0.164549i
$707$	−6.01194	+	13.1643i	−0.226102	+	0.495095i
$708$	−22.4679	−	6.59716i	−0.844395	−	0.247937i
$709$	17.4760	+	38.2672i	0.656327	+	1.43715i	0.885906	+	0.463865i	$0.153538\pi$
$709$	17.4760	+	38.2672i	0.656327	+	1.43715i	−0.229579	+	0.973290i	$0.573735\pi$
$710$	1.33029	+	9.25238i	0.0499249	+	0.347236i
$711$	18.4138	+	11.8338i	0.690572	+	0.443804i
$712$	−23.4164			−0.877567
$713$		0			0
$714$	−3.41641			−0.127856
$715$	−16.3341	−	10.4973i	−0.610862	−	0.392577i
$716$	0.163078	+	1.13423i	0.00609452	+	0.0423883i
$717$	−12.7853	−	27.9958i	−0.477474	−	1.04552i
$718$	−11.7939	−	3.46300i	−0.440144	−	0.129238i
$719$	−1.26940	+	2.77959i	−0.0473405	+	0.103661i	−0.931824	−	0.362910i	$-0.881783\pi$
$719$	−1.26940	+	2.77959i	−0.0473405	+	0.103661i	0.884484	+	0.466571i	$0.154511\pi$
$720$	3.00161	−	3.46405i	0.111864	−	0.129097i
$721$	1.92522	−	13.3902i	0.0716988	−	0.498676i
$722$	8.89499	−	2.61180i	0.331037	−	0.0972013i
$723$	33.8617	+	39.0785i	1.25933	+	1.45334i
$724$	22.6670	−	14.5672i	0.842411	−	0.541385i
$725$	8.76284	−	5.63154i	0.325444	−	0.209150i
$726$	14.8568	+	17.1456i	0.551387	+	0.636334i
$727$	−26.5858	+	7.80630i	−0.986014	+	0.289520i	−0.734705	−	0.678387i	$-0.762679\pi$
$727$	−26.5858	+	7.80630i	−0.986014	+	0.289520i	−0.251309	+	0.967907i	$0.580861\pi$
$728$	−3.08940	+	21.4872i	−0.114501	+	0.796370i
$729$	4.58403	−	5.29025i	0.169779	−	0.195935i
$730$	−2.07161	+	4.53619i	−0.0766737	+	0.167892i
$731$		0			0
$732$	10.4371	+	22.8542i	0.385768	+	0.844714i
$733$	−4.44536	−	30.9181i	−0.164193	−	1.14199i	−0.890622	−	0.454745i	$-0.849730\pi$
$733$	−4.44536	−	30.9181i	−0.164193	−	1.14199i	0.726429	−	0.687242i	$-0.241179\pi$
$734$	2.17346	+	1.39680i	0.0802237	+	0.0515567i
$735$	9.59675			0.353981
$736$		0			0
$737$	14.4721			0.533088
$738$	−3.61049	−	2.32032i	−0.132904	−	0.0854122i
$739$	−3.81684	−	26.5467i	−0.140405	−	0.976535i	−0.931214	−	0.364473i	$-0.881249\pi$
$739$	−3.81684	−	26.5467i	−0.140405	−	0.976535i	0.790809	−	0.612062i	$-0.209660\pi$
$740$	1.02696	+	2.24873i	0.0377519	+	0.0826651i
$741$	12.8729	+	3.77984i	0.472900	+	0.138856i
$742$	0.392265	−	0.858940i	0.0144005	−	0.0315327i
$743$	26.9309	−	31.0799i	0.987999	−	1.14021i	−0.00212264	−	0.999998i	$-0.500676\pi$
$743$	26.9309	−	31.0799i	0.987999	−	1.14021i	0.990121	−	0.140213i	$-0.0447789\pi$
$744$	−4.77338	+	33.1996i	−0.175001	+	1.21716i
$745$	−28.3318	+	8.31896i	−1.03800	+	0.304783i
$746$	3.11971	+	3.60034i	0.114221	+	0.131818i
$747$	14.7454	−	9.47628i	0.539505	−	0.346719i
$748$	5.44471	−	3.49910i	0.199078	−	0.127940i
$749$	−28.4317	−	32.8119i	−1.03887	−	1.19892i
$750$	13.8859	−	4.07727i	0.507042	−	0.148881i
$751$	0.0513301	−	0.357009i	0.00187306	−	0.0130274i	−0.988863	−	0.148825i	$-0.952451\pi$
$751$	0.0513301	−	0.357009i	0.00187306	−	0.0130274i	0.990737	+	0.135798i	$0.0433598\pi$
$752$	2.71499	−	3.13326i	0.0990053	−	0.114258i
$753$	2.12884	−	4.66151i	0.0775793	−	0.169875i
$754$	5.33699	+	1.56708i	0.194362	+	0.0570698i
$755$	−2.17514	−	4.76289i	−0.0791615	−	0.173339i
$756$	−1.66625	−	11.5890i	−0.0606010	−	0.421489i
$757$	−1.34327	−	0.863267i	−0.0488220	−	0.0313760i	0.516002	−	0.856587i	$-0.327420\pi$
$757$	−1.34327	−	0.863267i	−0.0488220	−	0.0313760i	−0.564824	+	0.825211i	$0.691056\pi$
$758$	−15.0557			−0.546849
$759$		0			0
$760$	5.52786			0.200517
$761$	38.9542	+	25.0343i	1.41209	+	0.907494i	0.999993	−	0.00364631i	$-0.00116066\pi$
$761$	38.9542	+	25.0343i	1.41209	+	0.907494i	0.412095	+	0.911141i	$0.364797\pi$
$762$	−1.43411	−	9.97444i	−0.0519523	−	0.361336i
$763$		0			0
$764$	40.6448	+	11.9344i	1.47048	+	0.431771i
$765$	0.784529	−	1.71788i	0.0283647	−	0.0621101i
$766$	2.85564	−	3.29558i	0.103178	−	0.119074i
$767$	−2.76324	+	19.2188i	−0.0997749	+	0.693950i
$768$	−14.0794	+	4.13408i	−0.508046	+	0.149176i
$769$	−15.1434	−	17.4764i	−0.546085	−	0.630216i	0.413881	−	0.910331i	$-0.364173\pi$
$769$	−15.1434	−	17.4764i	−0.546085	−	0.630216i	−0.959966	+	0.280115i	$0.909627\pi$
$770$	10.8894	−	6.99820i	0.392427	−	0.252198i
$771$	14.0558	−	9.03314i	0.506209	−	0.325320i
$772$	10.5368	+	12.1601i	0.379228	+	0.437653i
$773$	−5.30395	+	1.55738i	−0.190770	+	0.0560150i	−0.375722	−	0.926732i	$-0.622605\pi$
$773$	−5.30395	+	1.55738i	−0.190770	+	0.0560150i	0.184952	+	0.982748i	$0.440787\pi$
$774$		0			0
$775$	15.2529	−	17.6028i	0.547900	−	0.632310i
$776$	16.4491	−	36.0185i	0.590488	−	1.29299i
$777$	−8.58197	−	2.51989i	−0.307876	−	0.0904006i
$778$	−6.55404	−	14.3513i	−0.234974	−	0.514521i
$779$	0.988273	+	6.87359i	0.0354086	+	0.246272i
$780$	−11.2866	−	7.25346i	−0.404125	−	0.259715i
$781$	64.0689			2.29256
$782$		0			0
$783$	−6.70820			−0.239732
$784$	5.41573	+	3.48048i	0.193419	+	0.124303i
$785$	2.00827	+	13.9678i	0.0716782	+	0.498533i
$786$	−10.7402	−	23.5177i	−0.383090	−	0.838849i
$787$	23.5878	+	6.92600i	0.840814	+	0.246885i	0.673656	−	0.739045i	$-0.264723\pi$
$787$	23.5878	+	6.92600i	0.840814	+	0.246885i	0.167158	+	0.985930i	$0.446541\pi$
$788$	0.989504	−	2.16671i	0.0352496	−	0.0771859i
$789$	−4.31134	+	4.97555i	−0.153488	+	0.177134i
$790$	1.18985	−	8.27558i	0.0423329	−	0.294432i
$791$	−27.2119	+	7.99013i	−0.967543	+	0.284096i
$792$	15.3345	+	17.6969i	0.544887	+	0.628833i
$793$	17.5257	−	11.2631i	0.622355	−	0.399963i
$794$	−12.6947	+	8.15836i	−0.450517	+	0.289529i
$795$	0.854562	+	0.986217i	0.0303082	+	0.0349775i
$796$	19.0829	−	5.60325i	0.676376	−	0.198602i
$797$	−4.89003	+	34.0109i	−0.173214	+	1.20473i	0.698825	+	0.715293i	$0.253707\pi$
$797$	−4.89003	+	34.0109i	−0.173214	+	1.20473i	−0.872039	+	0.489437i	$0.837202\pi$
$798$	−5.85725	+	6.75963i	−0.207344	+	0.239288i
$799$	0.709614	−	1.55384i	0.0251043	−	0.0549708i
$800$	18.7164	+	5.49564i	0.661726	+	0.194300i
$801$	8.70056	+	19.0516i	0.307419	+	0.673154i
$802$	−1.24724	−	8.67473i	−0.0440415	−	0.306315i
$803$	28.7543	+	18.4793i	1.01472	+	0.652120i
$804$	10.0000			0.352673
$805$		0			0
$806$	12.4377			0.438099
$807$	14.9440	+	9.60391i	0.526053	+	0.338074i
$808$	1.42315	+	9.89821i	0.0500662	+	0.348218i
$809$	5.03128	+	11.0170i	0.176890	+	0.387336i	0.977221	−	0.212222i	$-0.0680702\pi$
$809$	5.03128	+	11.0170i	0.176890	+	0.387336i	−0.800331	+	0.599558i	$0.795343\pi$
$810$	−8.06286	−	2.36747i	−0.283300	−	0.0831844i
$811$	−10.1143	+	22.1473i	−0.355162	+	0.777696i	0.644749	+	0.764394i	$0.276962\pi$
$811$	−10.1143	+	22.1473i	−0.355162	+	0.777696i	−0.999912	+	0.0133025i	$0.995766\pi$
$812$	10.2867	−	11.8715i	0.360992	−	0.416607i
$813$	2.54581	−	17.7065i	0.0892853	−	0.620993i
$814$	−3.83797	+	1.12693i	−0.134521	+	0.0394989i
$815$	−4.66563	−	5.38442i	−0.163430	−	0.188608i
$816$	2.66440	−	1.71231i	0.0932728	−	0.0599428i
$817$		0			0
$818$	−8.64523	−	9.97712i	−0.302273	−	0.348842i
$819$	18.6299	−	5.47023i	0.650982	−	0.191145i
$820$	0.988273	−	6.87359i	0.0345120	−	0.240036i
$821$	25.5031	−	29.4321i	0.890063	−	1.02719i	−0.109386	−	0.993999i	$-0.534888\pi$
$821$	25.5031	−	29.4321i	0.890063	−	1.02719i	0.999449	−	0.0331886i	$-0.0105662\pi$
$822$	−12.5660	+	27.5157i	−0.438289	+	0.959719i
$823$	37.9393	+	11.1400i	1.32248	+	0.388316i	0.865388	−	0.501103i	$-0.167072\pi$
$823$	37.9393	+	11.1400i	1.32248	+	0.388316i	0.457094	+	0.889418i	$0.348890\pi$
$824$	−3.88310	−	8.50281i	−0.135274	−	0.296209i
$825$	−5.78545	−	40.2387i	−0.201424	−	1.40093i
$826$	−10.8894	−	6.99820i	−0.378891	−	0.243499i
$827$	−1.52786			−0.0531290			−0.0265645	−	0.999647i	$-0.508457\pi$
$827$	−1.52786			−0.0531290			−0.0265645	+	0.999647i	$0.508457\pi$
$828$		0			0
$829$	40.2492			1.39791			0.698957	−	0.715164i	$-0.253648\pi$
$829$	40.2492			1.39791			0.698957	+	0.715164i	$0.253648\pi$
$830$	−5.63223	−	3.61962i	−0.195498	−	0.125639i
$831$	4.92363	+	34.2446i	0.170799	+	1.18793i
$832$	−0.294199	−	0.644205i	−0.0101995	−	0.0223338i
$833$	2.54503	+	0.747289i	0.0881801	+	0.0258920i
$834$	6.14747	−	13.4611i	0.212869	−	0.466119i
$835$	1.23673	−	1.42727i	0.0427989	−	0.0493926i
$836$	2.41142	−	16.7718i	0.0834008	−	0.580065i
$837$	−14.3924	+	4.22599i	−0.497474	+	0.146072i
$838$	−1.85510	−	2.14090i	−0.0640834	−	0.0739561i
$839$	34.5962	−	22.2336i	1.19439	−	0.767591i	0.216417	−	0.976301i	$-0.430563\pi$
$839$	34.5962	−	22.2336i	1.19439	−	0.767591i	0.977977	+	0.208710i	$0.0669266\pi$
$840$	16.8251	−	10.8128i	0.580520	−	0.373078i
$841$	13.0972	+	15.1150i	0.451628	+	0.521207i
$842$	−6.10303	+	1.79201i	−0.210324	+	0.0617568i
$843$	2.78891	−	19.3973i	0.0960551	−	0.668078i
$844$	−24.8117	+	28.6343i	−0.854055	+	0.985632i
$845$	2.05392	−	4.49747i	0.0706572	−	0.154718i
$846$	2.65197	+	0.778690i	0.0911767	+	0.0267719i
$847$	−22.0688	−	48.3238i	−0.758292	−	1.66043i
$848$	0.124581	+	0.866478i	0.00427812	+	0.0297550i
$849$	52.1219	+	33.4967i	1.78882	+	1.14960i
$850$	1.63932			0.0562282
$851$		0			0
$852$	44.2705			1.51668
$853$	−8.90348	−	5.72192i	−0.304849	−	0.195915i	0.379268	−	0.925287i	$-0.376176\pi$
$853$	−8.90348	−	5.72192i	−0.304849	−	0.195915i	−0.684117	+	0.729372i	$0.739812\pi$
$854$	1.97655	+	13.7472i	0.0676360	+	0.470419i
$855$	−2.05392	−	4.49747i	−0.0702427	−	0.153810i
$856$	−28.7848	−	8.45198i	−0.983844	−	0.288883i
$857$	0.611547	−	1.33910i	0.0208901	−	0.0457429i	−0.898899	−	0.438155i	$-0.855632\pi$
$857$	0.611547	−	1.33910i	0.0208901	−	0.0457429i	0.919789	+	0.392412i	$0.128359\pi$
$858$	14.2159	−	16.4060i	0.485321	−	0.560090i
$859$	2.37783	−	16.5381i	0.0811304	−	0.564274i	−0.908195	−	0.418548i	$-0.862539\pi$
$859$	2.37783	−	16.5381i	0.0811304	−	0.564274i	0.989325	−	0.145726i	$-0.0465518\pi$
$860$		0			0
$861$	16.4531	+	18.9879i	0.560721	+	0.647106i
$862$	9.11314	−	5.85666i	0.310395	−	0.199479i
$863$	−18.1215	+	11.6460i	−0.616862	+	0.396433i	−0.811425	−	0.584457i	$-0.801308\pi$
$863$	−18.1215	+	11.6460i	−0.616862	+	0.396433i	0.194563	+	0.980890i	$0.437671\pi$
$864$	−8.22656	−	9.49396i	−0.279873	−	0.322991i
$865$	27.2119	−	7.99013i	0.925231	−	0.271672i
$866$	1.56734	−	10.9011i	0.0532602	−	0.370433i
$867$	−24.0388	+	27.7422i	−0.816399	+	0.942175i
$868$	14.5913	−	31.9505i	0.495261	−	1.08447i
$869$	−54.9837	−	16.1447i	−1.86519	−	0.547670i
$870$	−2.12884	−	4.66151i	−0.0721745	−	0.158040i
$871$	−1.18005	−	8.20740i	−0.0399843	−	0.278097i
$872$		0			0
$873$	−35.4164			−1.19866
$874$		0			0
$875$	−33.8885			−1.14564
$876$	19.8688	+	12.7689i	0.671303	+	0.431420i
$877$	5.19053	+	36.1009i	0.175272	+	1.21904i	0.867528	+	0.497389i	$0.165708\pi$
$877$	5.19053	+	36.1009i	0.175272	+	1.21904i	−0.692256	+	0.721652i	$0.743383\pi$
$878$	−4.80316	−	10.5174i	−0.162099	−	0.354947i
$879$	3.27802	+	0.962513i	0.110565	+	0.0324648i
$880$	−4.98498	+	10.9156i	−0.168044	+	0.367964i
$881$	28.9320	−	33.3893i	0.974743	−	1.12491i	−0.0174058	−	0.999849i	$-0.505541\pi$
$881$	28.9320	−	33.3893i	0.974743	−	1.12491i	0.992149	−	0.125065i	$-0.0399138\pi$
$882$	−0.610786	+	4.24811i	−0.0205662	+	0.143041i
$883$	−3.83797	+	1.12693i	−0.129158	+	0.0379242i	−0.345673	−	0.938355i	$-0.612349\pi$
$883$	−3.83797	+	1.12693i	−0.129158	+	0.0379242i	0.216515	+	0.976279i	$0.430531\pi$
$884$	−2.42836	−	2.80247i	−0.0816745	−	0.0942574i
$885$	15.0488	−	9.67128i	0.505860	−	0.325096i
$886$	19.8219	−	12.7387i	0.665929	−	0.427966i
$887$	−15.1069	−	17.4343i	−0.507240	−	0.585386i	0.443150	−	0.896448i	$-0.353861\pi$
$887$	−15.1069	−	17.4343i	−0.507240	−	0.585386i	−0.950390	+	0.311061i	$0.899316\pi$
$888$	−5.92999	+	1.74120i	−0.198998	+	0.0584309i
$889$	−3.35817	+	23.3566i	−0.112629	+	0.783354i
$890$	5.23889	−	6.04600i	0.175608	−	0.202662i
$891$	−23.9266	+	52.3918i	−0.801570	+	1.75519i
$892$	6.20997	+	1.82341i	0.207925	+	0.0610523i
$893$	−1.85779	−	4.06800i	−0.0621687	−	0.136130i
$894$	−4.69826	−	32.6771i	−0.157133	−	1.09289i
$895$	−0.736423	−	0.473271i	−0.0246159	−	0.0158197i
$896$	36.8328			1.23050
$897$		0			0
$898$	−9.23607			−0.308212
$899$	−16.9299	−	10.8802i	−0.564644	−	0.362875i
$900$	−1.59906	−	11.1217i	−0.0533020	−	0.370723i
$901$	0.149832	+	0.328086i	0.00499162	+	0.0109301i
$902$	10.7809	+	3.16557i	0.358966	+	0.105402i
$903$		0			0
$904$	−12.8331	+	14.8102i	−0.426824	+	0.492581i
$905$	−2.92935	+	20.3741i	−0.0973749	+	0.677257i
$906$	5.61697	−	1.64929i	0.186611	−	0.0547940i
$907$	−26.3576	−	30.4183i	−0.875191	−	1.01002i	−0.999841	−	0.0178234i	$-0.994326\pi$
$907$	−26.3576	−	30.4183i	−0.875191	−	1.01002i	0.124650	−	0.992201i	$-0.460219\pi$
$908$	−16.5796	+	10.6551i	−0.550213	+	0.353601i
$909$	7.52440	−	4.83564i	0.249569	−	0.160388i
$910$	−4.85671	−	5.60495i	−0.160999	−	0.185802i
$911$	30.0369	−	8.81962i	0.995166	−	0.292207i	0.256695	−	0.966492i	$-0.417366\pi$
$911$	30.0369	−	8.81962i	0.995166	−	0.292207i	0.738471	+	0.674285i	$0.235548\pi$
$912$	1.18005	−	8.20740i	0.0390752	−	0.271774i
$913$	−30.0506	+	34.6802i	−0.994530	+	1.14775i
$914$	1.31570	−	2.88097i	0.0435194	−	0.0952941i
$915$	−18.4160	−	5.40743i	−0.608815	−	0.178764i
$916$	−8.06587	−	17.6618i	−0.266504	−	0.583562i
$917$	8.61589	+	59.9248i	0.284522	+	1.97889i
$918$	−0.888135	−	0.570770i	−0.0293128	−	0.0188382i
$919$	−41.1246			−1.35658			−0.678288	−	0.734796i	$-0.737278\pi$
$919$	−41.1246			−1.35658			−0.678288	+	0.734796i	$0.737278\pi$
$920$		0			0
$921$	−21.3050			−0.702022
$922$	−0.765398	−	0.491891i	−0.0252070	−	0.0161996i
$923$	−5.22412	−	36.3346i	−0.171954	−	1.19597i
$924$	−25.4670	−	55.7649i	−0.837803	−	1.83453i
$925$	4.11795	+	1.20914i	0.135397	+	0.0397562i
$926$	−5.13481	+	11.2437i	−0.168740	+	0.369490i
$927$	−5.47508	+	6.31858i	−0.179825	+	0.207529i
$928$	2.39859	−	16.6826i	0.0787375	−	0.547632i
$929$	23.0813	−	6.77728i	0.757273	−	0.222355i	0.119768	−	0.992802i	$-0.461785\pi$
$929$	23.0813	−	6.77728i	0.757273	−	0.222355i	0.637505	+	0.770446i	$0.279967\pi$
$930$	−7.50404	−	8.66012i	−0.246067	−	0.283977i
$931$	5.84189	−	3.75436i	0.191460	−	0.123044i
$932$	8.88558	−	5.71041i	0.291057	−	0.187051i
$933$	19.3001	+	22.2736i	0.631858	+	0.729203i
$934$	−7.74204	+	2.27327i	−0.253327	+	0.0743836i
$935$	−0.703643	+	4.89395i	−0.0230116	+	0.160049i
$936$	8.78588	−	10.1394i	0.287175	−	0.331418i
$937$	−14.1990	+	31.0915i	−0.463862	+	1.01572i	0.522728	+	0.852499i	$0.324914\pi$
$937$	−14.1990	+	31.0915i	−0.463862	+	1.01572i	−0.986590	+	0.163217i	$0.947813\pi$
$938$	5.30395	+	1.55738i	0.173180	+	0.0508502i
$939$	22.6285	+	49.5496i	0.738455	+	1.61699i
$940$	0.636451	+	4.42662i	0.0207588	+	0.144380i
$941$	−5.59642	−	3.59660i	−0.182438	−	0.117246i	0.446234	−	0.894916i	$-0.352765\pi$
$941$	−5.59642	−	3.59660i	−0.182438	−	0.117246i	−0.628672	+	0.777670i	$0.716401\pi$
$942$	−15.7771			−0.514045
$943$		0			0
$944$	12.0000			0.390567
$945$	7.52440	+	4.83564i	0.244769	+	0.157303i
$946$		0			0
$947$	−4.49465	−	9.84191i	−0.146056	−	0.319819i	0.822438	−	0.568855i	$-0.192613\pi$
$947$	−4.49465	−	9.84191i	−0.146056	−	0.319819i	−0.968494	+	0.249036i	$0.919886\pi$
$948$	−37.9928	−	11.1557i	−1.23395	−	0.362320i
$949$	8.13532	−	17.8139i	0.264084	−	0.578262i
$950$	2.81053	−	3.24352i	0.0911856	−	0.105234i
$951$	8.08815	−	56.2543i	0.262276	−	1.82417i
$952$	5.30395	−	1.55738i	0.171902	−	0.0504750i
$953$	13.4064	+	15.4718i	0.434276	+	0.501181i	0.930133	−	0.367223i	$-0.119691\pi$
$953$	13.4064	+	15.4718i	0.434276	+	0.501181i	−0.495857	+	0.868404i	$0.665146\pi$
$954$	−0.490949	+	0.315514i	−0.0158951	+	0.0102151i
$955$	−27.2235	+	17.4955i	−0.880933	+	0.566141i
$956$	14.5841	+	16.8309i	0.471683	+	0.544351i
$957$	−33.7018	+	9.89575i	−1.08943	+	0.319884i
$958$	2.77910	−	19.3291i	0.0897888	−	0.624495i
$959$	46.3856	−	53.5319i	1.49787	−	1.72863i
$960$	−0.271048	+	0.593513i	−0.00874804	+	0.0191555i
$961$	−13.4329	−	3.94426i	−0.433319	−	0.127234i
$962$	0.952046	+	2.08469i	0.0306952	+	0.0672131i
$963$	3.81871	+	26.5597i	0.123056	+	0.855874i
$964$	−31.4767	−	20.2288i	−1.01380	−	0.651527i
$965$	−12.2918			−0.395687
$966$		0			0
$967$	27.5410			0.885659			0.442830	−	0.896606i	$-0.353975\pi$
$967$	27.5410			0.885659			0.442830	+	0.896606i	$0.353975\pi$
$968$	−30.8809	−	19.8460i	−0.992550	−	0.637873i
$969$	−0.486206	−	3.38163i	−0.0156192	−	0.108634i
$970$	5.61968	+	12.3054i	0.180437	+	0.395102i
$971$	15.8049	+	4.64074i	0.507203	+	0.148928i	0.525315	−	0.850908i	$-0.323947\pi$
$971$	15.8049	+	4.64074i	0.507203	+	0.148928i	−0.0181120	+	0.999836i	$0.505766\pi$
$972$	−12.0239	+	26.3286i	−0.385666	+	0.844491i
$973$	−22.6925	+	26.1886i	−0.727490	+	0.839568i
$974$	1.29367	−	8.99765i	0.0414517	−	0.288303i
$975$	−22.3483	+	6.56206i	−0.715719	+	0.210154i
$976$	−8.43159	−	9.73057i	−0.269888	−	0.311468i
$977$	19.6412	−	12.6226i	0.628377	−	0.403834i	−0.187331	−	0.982297i	$-0.559984\pi$
$977$	19.6412	−	12.6226i	0.628377	−	0.403834i	0.815708	+	0.578463i	$0.196347\pi$
$978$	6.70105	−	4.30651i	0.214276	−	0.137707i
$979$	−35.9079	−	41.4399i	−1.14762	−	1.32442i
$980$	−6.66298	+	1.95643i	−0.212841	+	0.0624958i
$981$		0			0
$982$	−3.37846	+	3.89895i	−0.107811	+	0.124421i
$983$	16.8127	−	36.8147i	0.536243	−	1.17421i	−0.426673	−	0.904406i	$-0.640314\pi$
$983$	16.8127	−	36.8147i	0.536243	−	1.17421i	0.962916	−	0.269802i	$-0.0869583\pi$
$984$	16.6575	+	4.89107i	0.531020	+	0.155922i
$985$	0.755914	+	1.65522i	0.0240854	+	0.0527397i
$986$	−0.201576	−	1.40199i	−0.00641948	−	0.0446485i
$987$	−13.6118	−	8.74775i	−0.433267	−	0.278444i
$988$	−9.70820			−0.308859
$989$		0			0
$990$	−8.00000			−0.254257
$991$	20.1901	+	12.9754i	0.641359	+	0.412177i	0.820500	−	0.571647i	$-0.193695\pi$
$991$	20.1901	+	12.9754i	0.641359	+	0.412177i	−0.179141	+	0.983824i	$0.557332\pi$
$992$	−5.36341	−	37.3033i	−0.170288	−	1.18438i
$993$	18.2551	+	39.9731i	0.579308	+	1.26851i
$994$	23.4808	+	6.89460i	0.744767	+	0.218683i
$995$	−6.31161	+	13.8205i	−0.200091	+	0.438139i
$996$	−20.7645	+	23.9635i	−0.657947	+	0.759311i
$997$	−2.39556	+	16.6615i	−0.0758681	+	0.527674i	0.916077	+	0.401003i	$0.131338\pi$
$997$	−2.39556	+	16.6615i	−0.0758681	+	0.527674i	−0.991945	+	0.126671i	$0.959571\pi$
$998$	−11.4400	+	3.35909i	−0.362128	+	0.106330i
$999$	−1.80999	−	2.08884i	−0.0572656	−	0.0660880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.2.c.n.255.2		20
23.2	even	11	inner	529.2.c.n.399.1		20
23.3	even	11	inner	529.2.c.n.501.1		20
23.4	even	11	inner	529.2.c.n.170.1		20
23.5	odd	22		529.2.c.o.487.2		20
23.6	even	11	inner	529.2.c.n.118.1		20
23.7	odd	22		529.2.c.o.466.2		20
23.8	even	11	inner	529.2.c.n.266.1		20
23.9	even	11		529.2.a.a.1.2		2
23.10	odd	22		529.2.c.o.177.1		20
23.11	odd	22		529.2.c.o.334.2		20
23.12	even	11	inner	529.2.c.n.334.2		20
23.13	even	11	inner	529.2.c.n.177.1		20
23.14	odd	22		23.2.a.a.1.2	✓	2
23.15	odd	22		529.2.c.o.266.1		20
23.16	even	11	inner	529.2.c.n.466.2		20
23.17	odd	22		529.2.c.o.118.1		20
23.18	even	11	inner	529.2.c.n.487.2		20
23.19	odd	22		529.2.c.o.170.1		20
23.20	odd	22		529.2.c.o.501.1		20
23.21	odd	22		529.2.c.o.399.1		20
23.22	odd	2		529.2.c.o.255.2		20
69.14	even	22		207.2.a.d.1.1		2
69.32	odd	22		4761.2.a.w.1.1		2
92.55	odd	22		8464.2.a.bb.1.2		2
92.83	even	22		368.2.a.h.1.2		2
115.14	odd	22		575.2.a.f.1.1		2
115.37	even	44		575.2.b.d.24.3		4
115.83	even	44		575.2.b.d.24.2		4
161.83	even	22		1127.2.a.c.1.2		2
184.37	odd	22		1472.2.a.t.1.2		2
184.83	even	22		1472.2.a.s.1.1		2
253.175	even	22		2783.2.a.c.1.1		2
276.83	odd	22		3312.2.a.ba.1.1		2
299.129	odd	22		3887.2.a.i.1.1		2
345.14	even	22		5175.2.a.be.1.2		2
391.152	odd	22		6647.2.a.b.1.2		2
437.37	even	22		8303.2.a.e.1.1		2
460.359	even	22		9200.2.a.bt.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.a.a.1.2	✓	2	23.14	odd	22
207.2.a.d.1.1		2	69.14	even	22
368.2.a.h.1.2		2	92.83	even	22
529.2.a.a.1.2		2	23.9	even	11
529.2.c.n.118.1		20	23.6	even	11	inner
529.2.c.n.170.1		20	23.4	even	11	inner
529.2.c.n.177.1		20	23.13	even	11	inner
529.2.c.n.255.2		20	1.1	even	1	trivial
529.2.c.n.266.1		20	23.8	even	11	inner
529.2.c.n.334.2		20	23.12	even	11	inner
529.2.c.n.399.1		20	23.2	even	11	inner
529.2.c.n.466.2		20	23.16	even	11	inner
529.2.c.n.487.2		20	23.18	even	11	inner
529.2.c.n.501.1		20	23.3	even	11	inner
529.2.c.o.118.1		20	23.17	odd	22
529.2.c.o.170.1		20	23.19	odd	22
529.2.c.o.177.1		20	23.10	odd	22
529.2.c.o.255.2		20	23.22	odd	2
529.2.c.o.266.1		20	23.15	odd	22
529.2.c.o.334.2		20	23.11	odd	22
529.2.c.o.399.1		20	23.21	odd	22
529.2.c.o.466.2		20	23.7	odd	22
529.2.c.o.487.2		20	23.5	odd	22
529.2.c.o.501.1		20	23.20	odd	22
575.2.a.f.1.1		2	115.14	odd	22
575.2.b.d.24.2		4	115.83	even	44
575.2.b.d.24.3		4	115.37	even	44
1127.2.a.c.1.2		2	161.83	even	22
1472.2.a.s.1.1		2	184.83	even	22
1472.2.a.t.1.2		2	184.37	odd	22
2783.2.a.c.1.1		2	253.175	even	22
3312.2.a.ba.1.1		2	276.83	odd	22
3887.2.a.i.1.1		2	299.129	odd	22
4761.2.a.w.1.1		2	69.32	odd	22
5175.2.a.be.1.2		2	345.14	even	22
6647.2.a.b.1.2		2	391.152	odd	22
8303.2.a.e.1.1		2	437.37	even	22
8464.2.a.bb.1.2		2	92.55	odd	22
9200.2.a.bt.1.1		2	460.359	even	22

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:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	529.c (of order \(11\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.519923 + 0.334134i) q^{2} +(0.318226 + 2.21331i) q^{3} +(-0.672156 - 1.47182i) q^{4} +(1.18600 + 0.348241i) q^{5} +(-0.574089 + 1.25708i) q^{6} +(2.11917 - 2.44566i) q^{7} +(0.318226 - 2.21331i) q^{8} +(-1.91899 + 0.563465i) q^{9} +(0.500269 + 0.577341i) q^{10} +(4.40486 - 2.83083i) q^{11} +(3.04368 - 1.95606i) q^{12} +(-1.96458 - 2.26725i) q^{13} +(1.91899 - 0.563465i) q^{14} +(-0.393349 + 2.73580i) q^{15} +(-1.21418 + 1.40124i) q^{16} +(-0.317349 + 0.694897i) q^{17} +(-1.18600 - 0.348241i) q^{18} +(0.830830 + 1.81926i) q^{19} +(-0.284630 - 1.97964i) q^{20} +(6.08737 + 3.91211i) q^{21} +3.23607 q^{22} +5.00000 q^{24} +(-2.92095 - 1.87718i) q^{25} +(-0.263866 - 1.83523i) q^{26} +(0.928896 + 2.03400i) q^{27} +(-5.02397 - 1.47517i) q^{28} +(-1.24625 + 2.72890i) q^{29} +(-1.11864 + 1.29097i) q^{30} +(-0.954677 + 6.63992i) q^{31} +(-5.39046 + 1.58278i) q^{32} +(7.66724 + 8.84847i) q^{33} +(-0.397186 + 0.255256i) q^{34} +(3.36501 - 2.16256i) q^{35} +(2.11917 + 2.44566i) q^{36} +(-1.18600 + 0.348241i) q^{37} +(-0.175911 + 1.22349i) q^{38} +(4.39294 - 5.06972i) q^{39} +(1.14818 - 2.51416i) q^{40} +(3.33149 + 0.978214i) q^{41} +(1.85779 + 4.06800i) q^{42} +(-7.12721 - 4.58038i) q^{44} -2.47214 q^{45} -2.23607 q^{47} +(-3.48775 - 2.24144i) q^{48} +(-0.494136 - 3.43679i) q^{49} +(-0.891438 - 1.95198i) q^{50} +(-1.63901 - 0.481257i) q^{51} +(-2.01647 + 4.41545i) q^{52} +(0.309183 - 0.356817i) q^{53} +(-0.196674 + 1.36790i) q^{54} +(6.20997 - 1.82341i) q^{55} +(-4.73862 - 5.46866i) q^{56} +(-3.76220 + 2.41782i) q^{57} +(-1.55977 + 1.00240i) q^{58} +(-4.23835 - 4.89131i) q^{59} +(4.29098 - 1.25995i) q^{60} +(-0.988273 + 6.87359i) q^{61} +(-2.71499 + 3.13326i) q^{62} +(-2.68862 + 5.88726i) q^{63} +(0.226506 + 0.0665080i) q^{64} +(-1.54044 - 3.37310i) q^{65} +(1.02980 + 7.16242i) q^{66} +(2.32517 + 1.49429i) q^{67} +1.23607 q^{68} +2.47214 q^{70} +(10.2936 + 6.61532i) q^{71} +(0.636451 + 4.42662i) q^{72} +(2.71177 + 5.93795i) q^{73} +(-0.732987 - 0.215225i) q^{74} +(3.22525 - 7.06232i) q^{75} +(2.11917 - 2.44566i) q^{76} +(2.41142 - 16.7718i) q^{77} +(3.97796 - 1.16803i) q^{78} +(-7.16697 - 8.27113i) q^{79} +(-1.92798 + 1.23904i) q^{80} +(-9.25379 + 5.94705i) q^{81} +(1.40526 + 1.62176i) q^{82} +(-8.40893 + 2.46908i) q^{83} +(1.66625 - 11.5890i) q^{84} +(-0.618367 + 0.713633i) q^{85} +(-6.43647 - 1.88992i) q^{87} +(-4.86376 - 10.6502i) q^{88} +(-1.49034 - 10.3655i) q^{89} +(-1.28532 - 0.826026i) q^{90} -9.70820 q^{91} -15.0000 q^{93} +(-1.16258 - 0.747147i) q^{94} +(0.351822 + 2.44697i) q^{95} +(-5.21857 - 11.4271i) q^{96} +(16.9909 + 4.98898i) q^{97} +(0.891438 - 1.95198i) q^{98} +(-6.85779 + 7.91431i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + q^{4} - 2 q^{5} + 5 q^{6} + 2 q^{7} - 4 q^{9} + 6 q^{10} - 6 q^{11} - 5 q^{12} - 6 q^{13} + 4 q^{14} - 10 q^{15} + 3 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 4 q^{20} - 10 q^{21} + 20 q^{22}+ \cdots - 12 q^{99}+O(q^{100}) \) 20 * q + q^2 + q^4 - 2 * q^5 + 5 * q^6 + 2 * q^7 - 4 * q^9 + 6 * q^10 - 6 * q^11 - 5 * q^12 - 6 * q^13 + 4 * q^14 - 10 * q^15 + 3 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 4 * q^20 - 10 * q^21 + 20 * q^22 + 100 * q^24 - 2 * q^25 + 3 * q^26 - 6 * q^28 + 6 * q^29 + 10 * q^30 - 9 * q^32 + 10 * q^33 - 8 * q^34 - 8 * q^35 + 2 * q^36 + 2 * q^37 + 2 * q^38 - 10 * q^40 - 2 * q^41 + 8 * q^44 + 40 * q^45 + 15 * q^48 + 2 * q^49 + 11 * q^50 + 10 * q^51 + 3 * q^52 - 8 * q^53 - 5 * q^54 + 4 * q^55 - 10 * q^56 - 3 * q^58 - 4 * q^59 + 4 * q^61 - 15 * q^62 + 4 * q^63 - 4 * q^64 - 6 * q^65 + 10 * q^66 - 10 * q^67 - 20 * q^68 - 40 * q^70 - 20 * q^71 - 22 * q^73 - 6 * q^74 - 20 * q^75 + 2 * q^76 + 16 * q^77 + 15 * q^78 - 4 * q^79 + 18 * q^80 + 22 * q^81 + 11 * q^82 - 22 * q^83 + 10 * q^84 + 16 * q^85 + 10 * q^88 - 12 * q^89 + 12 * q^90 - 60 * q^91 - 300 * q^93 + 5 * q^94 - 4 * q^95 + 5 * q^96 + 22 * q^97 - 11 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more