LMFDB - Embedded newform 529.2.c.o.334.1

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			334.1
Root			$1.05959 - 1.22283i$ of defining polynomial
Character	$\chi$	$=$	529.334
Dual form			529.2.c.o.255.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36118 + 0.874775i) q^{2} +(-0.318226 + 2.21331i) q^{3} +(0.256741 - 0.562183i) q^{4} +(3.10498 - 0.911706i) q^{5} +(-1.50299 - 3.29108i) q^{6} +(0.809452 + 0.934158i) q^{7} +(-0.318226 - 2.21331i) q^{8} +(-1.91899 - 0.563465i) q^{9} +(-3.42890 + 3.95716i) q^{10} +(-0.642661 - 0.413013i) q^{11} +(1.16258 + 0.747147i) q^{12} +(-1.96458 + 2.26725i) q^{13} +(-1.91899 - 0.563465i) q^{14} +(1.02980 + 7.16242i) q^{15} +(3.17876 + 3.66849i) q^{16} +(2.17514 + 4.76289i) q^{17} +(3.10498 - 0.911706i) q^{18} +(-0.830830 + 1.81926i) q^{19} +(0.284630 - 1.97964i) q^{20} +(-2.32517 + 1.49429i) q^{21} +1.23607 q^{22} +5.00000 q^{24} +(4.60345 - 2.95846i) q^{25} +(0.690811 - 4.80469i) q^{26} +(-0.928896 + 2.03400i) q^{27} +(0.732987 - 0.215225i) q^{28} +(-1.24625 - 2.72890i) q^{29} +(-7.66724 - 8.84847i) q^{30} +(0.954677 + 6.63992i) q^{31} +(-3.24497 - 0.952810i) q^{32} +(1.11864 - 1.29097i) q^{33} +(-7.12721 - 4.58038i) q^{34} +(3.36501 + 2.16256i) q^{35} +(-0.809452 + 0.934158i) q^{36} +(-3.10498 - 0.911706i) q^{37} +(-0.460540 - 3.20313i) q^{38} +(-4.39294 - 5.06972i) q^{39} +(-3.00597 - 6.58216i) q^{40} +(-5.25048 + 1.54168i) q^{41} +(1.85779 - 4.06800i) q^{42} +(-0.397186 + 0.255256i) q^{44} -6.47214 q^{45} +2.23607 q^{47} +(-9.13105 + 5.86817i) q^{48} +(0.778766 - 5.41644i) q^{49} +(-3.67813 + 8.05397i) q^{50} +(-11.2339 + 3.29858i) q^{51} +(0.770222 + 1.68655i) q^{52} +(5.54807 + 6.40281i) q^{53} +(-0.514900 - 3.58121i) q^{54} +(-2.37200 - 0.696481i) q^{55} +(1.80999 - 2.08884i) q^{56} +(-3.76220 - 2.41782i) q^{57} +(4.08353 + 2.62433i) q^{58} +(1.61890 - 1.86832i) q^{59} +(4.29098 + 1.25995i) q^{60} +(-1.55753 - 10.8329i) q^{61} +(-7.10793 - 8.20298i) q^{62} +(-1.02696 - 2.24873i) q^{63} +(-4.06448 + 1.19344i) q^{64} +(-4.03293 + 8.83089i) q^{65} +(-0.393349 + 2.73580i) q^{66} +(-6.08737 + 3.91211i) q^{67} +3.23607 q^{68} -6.47214 q^{70} +(6.53144 - 4.19750i) q^{71} +(-0.636451 + 4.42662i) q^{72} +(6.42736 - 14.0739i) q^{73} +(5.02397 - 1.47517i) q^{74} +(5.08305 + 11.1303i) q^{75} +(0.809452 + 0.934158i) q^{76} +(-0.134384 - 0.934661i) q^{77} +(10.4144 + 3.05795i) q^{78} +(-4.54753 + 5.24813i) q^{79} +(13.2146 + 8.49250i) q^{80} +(-9.25379 - 5.94705i) q^{81} +(5.79820 - 6.69148i) q^{82} +(12.6999 + 3.72903i) q^{83} +(0.243103 + 1.69082i) q^{84} +(11.0961 + 12.8056i) q^{85} +(6.43647 - 1.88992i) q^{87} +(-0.709614 + 1.55384i) q^{88} +(0.217438 - 1.51231i) q^{89} +(8.80972 - 5.66166i) q^{90} -3.70820 q^{91} -15.0000 q^{93} +(-3.04368 + 1.95606i) q^{94} +(-0.921081 + 6.40626i) q^{95} +(3.14150 - 6.87892i) q^{96} +(-4.11795 + 1.20914i) q^{97} +(3.67813 + 8.05397i) q^{98} +(1.00054 + 1.15468i) 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 $\left(\mathbb{Z}/529\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{10}{11}\right)$

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 $

$2$	−1.36118	+	0.874775i	−0.962497	+	0.618559i	−0.924688	−	0.380725i	$-0.875674\pi$
$2$	−1.36118	+	0.874775i	−0.962497	+	0.618559i	−0.0378092	+	0.999285i	$0.512038\pi$
$3$	−0.318226	+	2.21331i	−0.183728	+	1.27785i	0.664125	+	0.747622i	$0.268804\pi$
$3$	−0.318226	+	2.21331i	−0.183728	+	1.27785i	−0.847852	+	0.530232i	$0.822105\pi$
$4$	0.256741	−	0.562183i	0.128370	−	0.281092i
$5$	3.10498	−	0.911706i	1.38859	−	0.407727i	0.499840	−	0.866118i	$-0.333392\pi$
$5$	3.10498	−	0.911706i	1.38859	−	0.407727i	0.888751	+	0.458390i	$0.151574\pi$
$6$	−1.50299	−	3.29108i	−0.613591	−	1.34358i
$7$	0.809452	+	0.934158i	0.305944	+	0.353078i	0.887813	−	0.460204i	$-0.152224\pi$
$7$	0.809452	+	0.934158i	0.305944	+	0.353078i	−0.581869	+	0.813283i	$0.697678\pi$
$8$	−0.318226	−	2.21331i	−0.112510	−	0.782523i
$9$	−1.91899	−	0.563465i	−0.639662	−	0.187822i
$10$	−3.42890	+	3.95716i	−1.08431	+	1.25136i
$11$	−0.642661	−	0.413013i	−0.193769	−	0.124528i	0.440159	−	0.897920i	$-0.354922\pi$
$11$	−0.642661	−	0.413013i	−0.193769	−	0.124528i	−0.633928	+	0.773392i	$0.718559\pi$
$12$	1.16258	+	0.747147i	0.335609	+	0.215683i
$13$	−1.96458	+	2.26725i	−0.544877	+	0.628822i	−0.959682	−	0.281089i	$-0.909304\pi$
$13$	−1.96458	+	2.26725i	−0.544877	+	0.628822i	0.414805	+	0.909910i	$0.363850\pi$
$14$	−1.91899	−	0.563465i	−0.512871	−	0.150592i
$15$	1.02980	+	7.16242i	0.265893	+	1.84933i
$16$	3.17876	+	3.66849i	0.794690	+	0.917121i
$17$	2.17514	+	4.76289i	0.527549	+	1.15517i	0.966501	+	0.256661i	$0.0826225\pi$
$17$	2.17514	+	4.76289i	0.527549	+	1.15517i	−0.438952	+	0.898510i	$0.644650\pi$
$18$	3.10498	−	0.911706i	0.731852	−	0.214891i
$19$	−0.830830	+	1.81926i	−0.190605	+	0.417368i	−0.980674	−	0.195651i	$-0.937318\pi$
$19$	−0.830830	+	1.81926i	−0.190605	+	0.417368i	0.790068	+	0.613019i	$0.210045\pi$
$20$	0.284630	−	1.97964i	0.0636451	−	0.442662i
$21$	−2.32517	+	1.49429i	−0.507393	+	0.326082i
$22$	1.23607			0.263531
$23$		0			0
$23$		0			0
$24$	5.00000			1.02062
$25$	4.60345	−	2.95846i	0.920691	−	0.591692i
$26$	0.690811	−	4.80469i	0.135479	−	0.942278i
$27$	−0.928896	+	2.03400i	−0.178766	+	0.391443i
$28$	0.732987	−	0.215225i	0.138522	−	0.0406736i
$29$	−1.24625	−	2.72890i	−0.231422	−	0.506743i	0.757921	−	0.652346i	$-0.226215\pi$
$29$	−1.24625	−	2.72890i	−0.231422	−	0.506743i	−0.989343	+	0.145603i	$0.953488\pi$
$30$	−7.66724	−	8.84847i	−1.39984	−	1.61550i
$31$	0.954677	+	6.63992i	0.171465	+	1.19257i	0.875792	+	0.482689i	$0.160340\pi$
$31$	0.954677	+	6.63992i	0.171465	+	1.19257i	−0.704327	+	0.709876i	$0.748751\pi$
$32$	−3.24497	−	0.952810i	−0.573636	−	0.168435i
$33$	1.11864	−	1.29097i	0.194729	−	0.224730i
$34$	−7.12721	−	4.58038i	−1.22231	−	0.785529i
$35$	3.36501	+	2.16256i	0.568791	+	0.365540i
$36$	−0.809452	+	0.934158i	−0.134909	+	0.155693i
$37$	−3.10498	−	0.911706i	−0.510456	−	0.149883i	0.0163542	−	0.999866i	$-0.494794\pi$
$37$	−3.10498	−	0.911706i	−0.510456	−	0.149883i	−0.526810	+	0.849983i	$0.676612\pi$
$38$	−0.460540	−	3.20313i	−0.0747095	−	0.519616i
$39$	−4.39294	−	5.06972i	−0.703433	−	0.811805i
$40$	−3.00597	−	6.58216i	−0.475286	−	1.04073i
$41$	−5.25048	+	1.54168i	−0.819987	+	0.240770i	−0.664710	−	0.747101i	$-0.731445\pi$
$41$	−5.25048	+	1.54168i	−0.819987	+	0.240770i	−0.155276	+	0.987871i	$0.549627\pi$
$42$	1.85779	−	4.06800i	0.286664	−	0.627706i
$43$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$43$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$44$	−0.397186	+	0.255256i	−0.0598780	+	0.0384813i
$45$	−6.47214			−0.964809
$46$		0			0
$47$	2.23607			0.326164			0.163082	−	0.986613i	$-0.447856\pi$
$47$	2.23607			0.326164			0.163082	+	0.986613i	$0.447856\pi$
$48$	−9.13105	+	5.86817i	−1.31795	+	0.846997i
$49$	0.778766	−	5.41644i	0.111252	−	0.773777i
$50$	−3.67813	+	8.05397i	−0.520166	+	1.13900i
$51$	−11.2339	+	3.29858i	−1.57307	+	0.461894i
$52$	0.770222	+	1.68655i	0.106811	+	0.233882i
$53$	5.54807	+	6.40281i	0.762086	+	0.879494i	0.995681	−	0.0928399i	$-0.0295945\pi$
$53$	5.54807	+	6.40281i	0.762086	+	0.879494i	−0.233595	+	0.972334i	$0.575049\pi$
$54$	−0.514900	−	3.58121i	−0.0700690	−	0.487341i
$55$	−2.37200	−	0.696481i	−0.319840	−	0.0939135i
$56$	1.80999	−	2.08884i	0.241870	−	0.279133i
$57$	−3.76220	−	2.41782i	−0.498316	−	0.320248i
$58$	4.08353	+	2.62433i	0.536194	+	0.344591i
$59$	1.61890	−	1.86832i	0.210763	−	0.243234i	−0.640518	−	0.767943i	$-0.721280\pi$
$59$	1.61890	−	1.86832i	0.210763	−	0.243234i	0.851282	+	0.524709i	$0.175826\pi$
$60$	4.29098	+	1.25995i	0.553964	+	0.162658i
$61$	−1.55753	−	10.8329i	−0.199422	−	1.38701i	−0.805968	−	0.591959i	$-0.798355\pi$
$61$	−1.55753	−	10.8329i	−0.199422	−	1.38701i	0.606546	−	0.795048i	$-0.292554\pi$
$62$	−7.10793	−	8.20298i	−0.902707	−	1.04178i
$63$	−1.02696	−	2.24873i	−0.129385	−	0.283314i
$64$	−4.06448	+	1.19344i	−0.508060	+	0.149180i
$65$	−4.03293	+	8.83089i	−0.500224	+	1.09534i
$66$	−0.393349	+	2.73580i	−0.0484179	+	0.336754i
$67$	−6.08737	+	3.91211i	−0.743690	+	0.477941i	−0.856805	−	0.515641i	$-0.827554\pi$
$67$	−6.08737	+	3.91211i	−0.743690	+	0.477941i	0.113114	+	0.993582i	$0.463917\pi$
$68$	3.23607			0.392431
$69$		0			0
$70$	−6.47214			−0.773568
$71$	6.53144	−	4.19750i	0.775139	−	0.498151i	−0.0922783	−	0.995733i	$-0.529415\pi$
$71$	6.53144	−	4.19750i	0.775139	−	0.498151i	0.867417	+	0.497582i	$0.165779\pi$
$72$	−0.636451	+	4.42662i	−0.0750065	+	0.521682i
$73$	6.42736	−	14.0739i	0.752265	−	1.64723i	−0.00998608	−	0.999950i	$-0.503179\pi$
$73$	6.42736	−	14.0739i	0.752265	−	1.64723i	0.762251	−	0.647281i	$-0.224094\pi$
$74$	5.02397	−	1.47517i	0.584025	−	0.171485i
$75$	5.08305	+	11.1303i	0.586940	+	1.28522i
$76$	0.809452	+	0.934158i	0.0928506	+	0.107155i
$77$	−0.134384	−	0.934661i	−0.0153145	−	0.106514i
$78$	10.4144	+	3.05795i	1.17920	+	0.346245i
$79$	−4.54753	+	5.24813i	−0.511637	+	0.590461i	−0.951517	−	0.307596i	$-0.900476\pi$
$79$	−4.54753	+	5.24813i	−0.511637	+	0.590461i	0.439880	+	0.898057i	$0.355021\pi$
$80$	13.2146	+	8.49250i	1.47744	+	0.949490i
$81$	−9.25379	−	5.94705i	−1.02820	−	0.660783i
$82$	5.79820	−	6.69148i	0.640304	−	0.738951i
$83$	12.6999	+	3.72903i	1.39400	+	0.409314i	0.890618	−	0.454752i	$-0.150272\pi$
$83$	12.6999	+	3.72903i	1.39400	+	0.409314i	0.503378	+	0.864066i	$0.332090\pi$
$84$	0.243103	+	1.69082i	0.0265247	+	0.184483i
$85$	11.0961	+	12.8056i	1.20355	+	1.38897i
$86$		0			0
$87$	6.43647	−	1.88992i	0.690063	−	0.202621i
$88$	−0.709614	+	1.55384i	−0.0756451	+	0.165640i
$89$	0.217438	−	1.51231i	0.0230484	−	0.160305i	−0.975047	−	0.222000i	$-0.928742\pi$
$89$	0.217438	−	1.51231i	0.0230484	−	0.160305i	0.998095	+	0.0616951i	$0.0196506\pi$
$90$	8.80972	−	5.66166i	0.928626	−	0.596792i
$91$	−3.70820			−0.388725
$92$		0			0
$93$	−15.0000			−1.55543
$94$	−3.04368	+	1.95606i	−0.313932	+	0.201752i
$95$	−0.921081	+	6.40626i	−0.0945009	+	0.657268i
$96$	3.14150	−	6.87892i	0.320628	−	0.702076i
$97$	−4.11795	+	1.20914i	−0.418114	+	0.122769i	−0.484021	−	0.875056i	$-0.660824\pi$
$97$	−4.11795	+	1.20914i	−0.418114	+	0.122769i	0.0659068	+	0.997826i	$0.479006\pi$
$98$	3.67813	+	8.05397i	0.371547	+	0.813574i
$99$	1.00054	+	1.15468i	0.100558	+	0.116050i
$100$	−0.481304	−	3.34754i	−0.0481304	−	0.334754i
$101$	4.29098	+	1.25995i	0.426969	+	0.125369i	0.488155	−	0.872757i	$-0.337670\pi$
$101$	4.29098	+	1.25995i	0.426969	+	0.125369i	−0.0611861	+	0.998126i	$0.519488\pi$
$102$	12.4059	−	14.3171i	1.22836	−	1.41761i
$103$	15.2943	+	9.82903i	1.50699	+	0.968483i	0.993916	+	0.110139i	$0.0351295\pi$
$103$	15.2943	+	9.82903i	1.50699	+	0.968483i	0.513073	+	0.858345i	$0.328507\pi$
$104$	5.64330	+	3.62673i	0.553371	+	0.355630i
$105$	−5.85725	+	6.75963i	−0.571609	+	0.659672i
$106$	−13.1529	−	3.86205i	−1.27753	−	0.375115i
$107$	1.90935	+	13.2798i	0.184584	+	1.28381i	0.845753	+	0.533574i	$0.179152\pi$
$107$	1.90935	+	13.2798i	0.184584	+	1.28381i	−0.661169	+	0.750237i	$0.729939\pi$
$108$	0.904995	+	1.04442i	0.0870832	+	0.100499i
$109$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$109$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$110$	3.83797	−	1.12693i	0.365936	−	0.107449i
$111$	3.00597	−	6.58216i	0.285314	−	0.624751i
$112$	−0.853889	+	5.93893i	−0.0806849	+	0.561176i
$113$	11.1349	−	7.15596i	1.04748	−	0.673176i	0.100656	−	0.994921i	$-0.467906\pi$
$113$	11.1349	−	7.15596i	1.04748	−	0.673176i	0.946826	+	0.321745i	$0.104269\pi$
$114$	7.23607			0.677720
$115$		0			0
$116$	−1.85410			−0.172149
$117$	5.04752	−	3.24384i	0.466643	−	0.299894i
$118$	−0.569259	+	3.95929i	−0.0524046	+	0.364482i
$119$	−2.68862	+	5.88726i	−0.246466	+	0.539684i
$120$	15.5249	−	4.55853i	1.41723	−	0.416135i
$121$	−4.32713	−	9.47510i	−0.393376	−	0.861373i
$122$	11.5964	+	13.3830i	1.04989	+	1.21164i
$123$	−1.74137	−	12.1115i	−0.157014	−	1.09206i
$124$	3.97796	+	1.16803i	0.357231	+	0.104893i
$125$	1.00054	−	1.15468i	0.0894909	−	0.103278i
$126$	3.36501	+	2.16256i	0.299779	+	0.192656i
$127$	−17.4208	−	11.1957i	−1.54585	−	0.993458i	−0.986357	−	0.164623i	$-0.947359\pi$
$127$	−17.4208	−	11.1957i	−1.54585	−	0.993458i	−0.559494	−	0.828834i	$-0.689004\pi$
$128$	8.91792	−	10.2918i	0.788240	−	0.909677i
$129$		0			0
$130$	−2.23551	−	15.5483i	−0.196067	−	1.36368i
$131$	−3.46539	−	3.99927i	−0.302772	−	0.349418i	0.583892	−	0.811831i	$-0.301529\pi$
$131$	−3.46539	−	3.99927i	−0.302772	−	0.349418i	−0.886665	+	0.462413i	$0.846984\pi$
$132$	−0.438565	−	0.960324i	−0.0381722	−	0.0835855i
$133$	−2.37200	+	0.696481i	−0.205678	+	0.0603926i
$134$	4.86376	−	10.6502i	0.420165	−	0.920033i
$135$	−1.02980	+	7.16242i	−0.0886311	+	0.616443i
$136$	9.84957	−	6.32993i	0.844593	−	0.542787i
$137$	13.8885			1.18658			0.593289	−	0.804989i	$-0.297829\pi$
$137$	13.8885			1.18658			0.593289	+	0.804989i	$0.297829\pi$
$138$		0			0
$139$	2.70820			0.229707			0.114853	−	0.993382i	$-0.463360\pi$
$139$	2.70820			0.229707			0.114853	+	0.993382i	$0.463360\pi$
$140$	2.07969	−	1.33654i	0.175766	−	0.112958i
$141$	−0.711574	+	4.94911i	−0.0599254	+	0.416790i
$142$	−5.21857	+	11.4271i	−0.437933	+	0.958939i
$143$	2.19896	−	0.645674i	0.183886	−	0.0539939i
$144$	−4.03293	−	8.83089i	−0.336078	−	0.735908i
$145$	−6.35752	−	7.33697i	−0.527963	−	0.609302i
$146$	3.56277	+	24.7796i	0.294857	+	2.05078i
$147$	11.7404	+	3.44730i	0.968334	+	0.284328i
$148$	−1.30972	+	1.51150i	−0.107658	+	0.124244i
$149$	−10.0013	−	6.42743i	−0.819337	−	0.526556i	0.0625363	−	0.998043i	$-0.480081\pi$
$149$	−10.0013	−	6.42743i	−0.819337	−	0.526556i	−0.881873	+	0.471487i	$0.843717\pi$
$150$	−16.6555	−	10.7038i	−1.35991	−	0.873962i
$151$	0.154592	−	0.178408i	0.0125805	−	0.0145187i	−0.749424	−	0.662090i	$-0.769670\pi$
$151$	0.154592	−	0.178408i	0.0125805	−	0.0145187i	0.762005	+	0.647571i	$0.224215\pi$
$152$	4.29098	+	1.25995i	0.348045	+	0.102195i
$153$	−1.49034	−	10.3655i	−0.120487	−	0.838005i
$154$	1.00054	+	1.15468i	0.0806257	+	0.0930470i
$155$	9.01791	+	19.7465i	0.724336	+	1.58608i
$156$	−3.97796	+	1.16803i	−0.318492	+	0.0935176i
$157$	6.40421	−	14.0233i	0.511111	−	1.11918i	−0.461585	−	0.887096i	$-0.652719\pi$
$157$	6.40421	−	14.0233i	0.511111	−	1.11918i	0.972696	−	0.232082i	$-0.0745537\pi$
$158$	1.59906	−	11.1217i	0.127214	−	0.884795i
$159$	−15.9369	+	10.2420i	−1.26388	+	0.812247i
$160$	−10.9443			−0.865221
$161$		0			0
$162$	17.7984			1.39837
$163$	−8.61113	+	5.53404i	−0.674476	+	0.433459i	−0.832536	−	0.553970i	$-0.813112\pi$
$163$	−8.61113	+	5.53404i	−0.674476	+	0.433459i	0.158061	+	0.987429i	$0.449476\pi$
$164$	−0.481304	+	3.34754i	−0.0375835	+	0.261399i
$165$	2.29636	−	5.02832i	0.178771	−	0.391454i
$166$	−20.5489	+	6.03370i	−1.59490	+	0.468306i
$167$	4.35028	+	9.52579i	0.336635	+	0.737128i	0.999937	−	0.0112240i	$-0.00357280\pi$
$167$	4.35028	+	9.52579i	0.336635	+	0.737128i	−0.663302	+	0.748352i	$0.730846\pi$
$168$	4.04726	+	4.67079i	0.312253	+	0.360359i
$169$	0.569259	+	3.95929i	0.0437892	+	0.304560i
$170$	−26.3059	−	7.72409i	−2.01757	−	0.592411i
$171$	2.61944	−	3.02300i	0.200314	−	0.231174i
$172$		0			0
$173$	4.25315	+	2.73333i	0.323361	+	0.207811i	0.692243	−	0.721665i	$-0.256623\pi$
$173$	4.25315	+	2.73333i	0.323361	+	0.207811i	−0.368882	+	0.929476i	$0.620259\pi$
$174$	−7.10793	+	8.20298i	−0.538850	+	0.621867i
$175$	6.48995	+	1.90562i	0.490594	+	0.144051i
$176$	−0.527732	−	3.67046i	−0.0397793	−	0.276671i
$177$	3.61998	+	4.17768i	0.272094	+	0.314014i
$178$	1.02696	+	2.24873i	0.0769741	+	0.168550i
$179$	12.1934	−	3.58031i	0.911380	−	0.267605i	0.207758	−	0.978180i	$-0.433383\pi$
$179$	12.1934	−	3.58031i	0.911380	−	0.267605i	0.703622	+	0.710575i	$0.251565\pi$
$180$	−1.66166	+	3.63853i	−0.123853	+	0.271200i
$181$	2.08526	−	14.5033i	0.154997	−	1.07802i	−0.752690	−	0.658375i	$-0.771244\pi$
$181$	2.08526	−	14.5033i	0.154997	−	1.07802i	0.907686	−	0.419649i	$-0.137847\pi$
$182$	5.04752	−	3.24384i	0.374147	−	0.240450i
$183$	24.4721			1.80903
$184$		0			0
$185$	−10.4721			−0.769927
$186$	20.4177	−	13.1216i	1.49709	−	0.962124i
$187$	0.569259	−	3.95929i	0.0416284	−	0.289532i
$188$	0.574089	−	1.25708i	0.0418698	−	0.0916820i
$189$	−2.65197	+	0.778690i	−0.192903	+	0.0566413i
$190$	−4.35028	−	9.52579i	−0.315603	−	0.691073i
$191$	2.50135	+	2.88671i	0.180991	+	0.208875i	0.838994	−	0.544140i	$-0.183144\pi$
$191$	2.50135	+	2.88671i	0.180991	+	0.208875i	−0.658003	+	0.753015i	$0.728599\pi$
$192$	−1.34803	−	9.37572i	−0.0972854	−	0.676635i
$193$	7.62247	+	2.23816i	0.548678	+	0.161106i	0.544310	−	0.838884i	$-0.316792\pi$
$193$	7.62247	+	2.23816i	0.548678	+	0.161106i	0.00436765	+	0.999990i	$0.498610\pi$
$194$	4.54753	−	5.24813i	0.326494	−	0.376794i
$195$	−18.2621	−	11.7363i	−1.30778	−	0.840457i
$196$	−2.84509	−	1.82843i	−0.203221	−	0.130602i
$197$	−4.89321	+	5.64706i	−0.348627	+	0.402337i	−0.902797	−	0.430067i	$-0.858490\pi$
$197$	−4.89321	+	5.64706i	−0.348627	+	0.402337i	0.554171	+	0.832403i	$0.313036\pi$
$198$	−2.37200	−	0.696481i	−0.168570	−	0.0494968i
$199$	3.65866	+	25.4465i	0.259355	+	1.80386i	0.537442	+	0.843301i	$0.319391\pi$
$199$	3.65866	+	25.4465i	0.259355	+	1.80386i	−0.278086	+	0.960556i	$0.589700\pi$
$200$	−8.01292	−	9.24740i	−0.566599	−	0.653890i
$201$	−6.72156	−	14.7182i	−0.474102	−	1.03814i
$202$	−6.94296	+	2.03864i	−0.488505	+	0.143438i
$203$	1.54044	−	3.37310i	0.108118	−	0.236745i
$204$	−1.02980	+	7.16242i	−0.0721004	+	0.501469i
$205$	−14.8971	+	9.57378i	−1.04046	+	0.668662i
$206$	−29.4164			−2.04954
$207$		0			0
$208$	−14.5623			−1.00971
$209$	1.28532	−	0.826026i	0.0889075	−	0.0571374i
$210$	2.05960	−	14.3248i	0.142126	−	0.988507i
$211$	1.41923	−	3.10767i	0.0977036	−	0.213941i	−0.854469	−	0.519503i	$-0.826117\pi$
$211$	1.41923	−	3.10767i	0.0977036	−	0.213941i	0.952172	+	0.305562i	$0.0988443\pi$
$212$	5.02397	−	1.47517i	0.345048	−	0.101315i
$213$	7.21189	+	15.7918i	0.494150	+	1.08204i
$214$	−14.2159	−	16.4060i	−0.971776	−	1.12149i
$215$		0			0
$216$	4.79746	+	1.40866i	0.326426	+	0.0958474i
$217$	−5.42997	+	6.26652i	−0.368610	+	0.425399i
$218$		0			0
$219$	29.1046	+	18.7044i	1.96671	+	1.26393i
$220$	−1.00054	+	1.15468i	−0.0674563	+	0.0778487i
$221$	−15.0719	−	4.42551i	−1.01385	−	0.297692i
$222$	1.66625	+	11.5890i	0.111831	+	0.777805i
$223$	−2.61944	−	3.02300i	−0.175411	−	0.202435i	0.661235	−	0.750178i	$-0.270032\pi$
$223$	−2.61944	−	3.02300i	−0.175411	−	0.202435i	−0.836646	+	0.547743i	$0.815487\pi$
$224$	−1.73658	−	3.80257i	−0.116030	−	0.254070i
$225$	−10.5010	+	3.08336i	−0.700063	+	0.205557i
$226$	−8.89670	+	19.4810i	−0.591800	+	1.29586i
$227$	−1.44881	+	10.0767i	−0.0961611	+	0.668815i	0.883541	+	0.468355i	$0.155153\pi$
$227$	−1.44881	+	10.0767i	−0.0961611	+	0.668815i	−0.979702	+	0.200461i	$0.935756\pi$
$228$	−2.32517	+	1.49429i	−0.153988	+	0.0989621i
$229$	−12.0000			−0.792982			−0.396491	−	0.918039i	$-0.629772\pi$
$229$	−12.0000			−0.792982			−0.396491	+	0.918039i	$0.629772\pi$
$230$		0			0
$231$	2.11146			0.138924
$232$	−5.64330	+	3.62673i	−0.370501	+	0.238106i
$233$	2.20191	−	15.3147i	0.144252	−	1.00330i	−0.781159	−	0.624332i	$-0.785371\pi$
$233$	2.20191	−	15.3147i	0.144252	−	1.00330i	0.925411	−	0.378964i	$-0.123720\pi$
$234$	−4.03293	+	8.83089i	−0.263641	+	0.577294i
$235$	6.94296	−	2.03864i	0.452909	−	0.132986i
$236$	−0.634698	−	1.38979i	−0.0413153	−	0.0904679i
$237$	−10.1686	−	11.7352i	−0.660521	−	0.762282i
$238$	−1.49034	−	10.3655i	−0.0966044	−	0.671898i
$239$	−17.4974	−	5.13769i	−1.13181	−	0.332330i	−0.338392	−	0.941005i	$-0.609883\pi$
$239$	−17.4974	−	5.13769i	−1.13181	−	0.332330i	−0.793419	+	0.608675i	$0.791701\pi$
$240$	−23.0017	+	26.5454i	−1.48476	+	1.71350i
$241$	14.4061	+	9.25826i	0.927981	+	0.596377i	0.914963	−	0.403538i	$-0.132220\pi$
$241$	14.4061	+	9.25826i	0.927981	+	0.596377i	0.0130182	+	0.999915i	$0.495856\pi$
$242$	14.1786	+	9.11202i	0.911433	+	0.585743i
$243$	11.7145	−	13.5193i	0.751486	−	0.867261i
$244$	−6.48995	−	1.90562i	−0.415476	−	0.121995i
$245$	−2.52014	−	17.5280i	−0.161006	−	1.11982i
$246$	12.9652	+	14.9626i	0.826630	+	0.953981i
$247$	−2.49249	−	5.45779i	−0.158593	−	0.347271i
$248$	14.3924	−	4.22599i	0.913918	−	0.268351i
$249$	−12.2949	+	26.9221i	−0.779160	+	1.70612i
$250$	−0.351822	+	2.44697i	−0.0222512	+	0.154760i
$251$	13.2146	−	8.49250i	0.834097	−	0.536042i	−0.0524803	−	0.998622i	$-0.516713\pi$
$251$	13.2146	−	8.49250i	0.834097	−	0.536042i	0.886577	+	0.462580i	$0.153076\pi$
$252$	−1.52786			−0.0962464
$253$		0			0
$254$	33.5066			2.10239
$255$	−31.8739	+	20.4841i	−1.99602	+	1.28276i
$256$	−1.93012	+	13.4243i	−0.120632	+	0.839016i
$257$	0.611547	−	1.33910i	0.0381473	−	0.0835309i	−0.889599	−	0.456742i	$-0.849016\pi$
$257$	0.611547	−	1.33910i	0.0381473	−	0.0835309i	0.927746	+	0.373211i	$0.121743\pi$
$258$		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
$262$	8.21547	+	2.41228i	0.507554	+	0.149031i
$263$	9.78642	−	11.2941i	0.603456	−	0.696426i	−0.369022	−	0.929421i	$-0.620307\pi$
$263$	9.78642	−	11.2941i	0.603456	−	0.696426i	0.972478	+	0.232995i	$0.0748526\pi$
$264$	−3.21330	−	2.06506i	−0.197765	−	0.127096i
$265$	23.0641	+	14.8224i	1.41682	+	0.910535i
$266$	2.61944	−	3.02300i	0.160608	−	0.185352i
$267$	3.27802	+	0.962513i	0.200612	+	0.0589049i
$268$	0.636451	+	4.42662i	0.0388775	+	0.270399i
$269$	−6.51211	−	7.51538i	−0.397051	−	0.458221i	0.521659	−	0.853154i	$-0.325313\pi$
$269$	−6.51211	−	7.51538i	−0.397051	−	0.458221i	−0.918710	+	0.394933i	$0.870768\pi$
$270$	−4.86376	−	10.6502i	−0.295999	−	0.648148i
$271$	−7.67594	+	2.25386i	−0.466280	+	0.136912i	−0.506429	−	0.862281i	$-0.669035\pi$
$271$	−7.67594	+	2.25386i	−0.466280	+	0.136912i	0.0401490	+	0.999194i	$0.487217\pi$
$272$	−10.5584	+	23.1196i	−0.640194	+	1.40183i
$273$	1.18005	−	8.20740i	0.0714196	−	0.496734i
$274$	−18.9048	+	12.1494i	−1.14208	+	0.733969i
$275$	−4.18034			−0.252084
$276$		0			0
$277$	6.52786			0.392221			0.196111	−	0.980582i	$-0.437169\pi$
$277$	6.52786			0.392221			0.196111	+	0.980582i	$0.437169\pi$
$278$	−3.68634	+	2.36907i	−0.221092	+	0.142087i
$279$	1.90935	−	13.2798i	0.114310	−	0.795044i
$280$	3.71558	−	8.13600i	0.222049	−	0.486219i
$281$	12.6999	−	3.72903i	0.757613	−	0.222455i	0.119960	−	0.992779i	$-0.461723\pi$
$281$	12.6999	−	3.72903i	0.757613	−	0.222455i	0.637653	+	0.770323i	$0.279905\pi$
$282$	−3.36078	−	7.35908i	−0.200131	−	0.438227i
$283$	−9.35914	−	10.8010i	−0.556343	−	0.642054i	0.406006	−	0.913870i	$-0.366921\pi$
$283$	−9.35914	−	10.8010i	−0.556343	−	0.642054i	−0.962349	+	0.271816i	$0.912376\pi$
$284$	−0.682880	−	4.74953i	−0.0405215	−	0.281833i
$285$	−13.8859	−	4.07727i	−0.822530	−	0.241517i
$286$	−2.42836	+	2.80247i	−0.143592	+	0.165714i
$287$	−5.69018	−	3.65686i	−0.335881	−	0.215857i
$288$	5.69018	+	3.65686i	0.335297	+	0.215482i
$289$	−6.82130	+	7.87220i	−0.401253	+	0.463070i
$290$	15.0719	+	4.42551i	0.885053	+	0.259875i
$291$	−1.36576	−	9.49907i	−0.0800622	−	0.556845i
$292$	−6.26198	−	7.22671i	−0.366455	−	0.422911i
$293$	−4.35028	−	9.52579i	−0.254146	−	0.556503i	0.738956	−	0.673754i	$-0.235319\pi$
$293$	−4.35028	−	9.52579i	−0.254146	−	0.556503i	−0.993102	+	0.117251i	$0.962592\pi$
$294$	−18.9964	+	5.57785i	−1.10789	+	0.325307i
$295$	3.32332	−	7.27706i	0.193491	−	0.423687i
$296$	−1.02980	+	7.16242i	−0.0598559	+	0.416307i
$297$	1.43703	−	0.923525i	0.0833851	−	0.0535883i
$298$	19.2361			1.11432
$299$		0			0
$300$	7.56231			0.436610
$301$		0			0
$302$	−0.0543594	+	0.378078i	−0.00312803	+	0.0217560i
$303$	−4.15415	+	9.09632i	−0.238650	+	0.522570i
$304$	−9.31495	+	2.73512i	−0.534249	+	0.156870i
$305$	−14.7125	−	32.2159i	−0.842436	−	1.84468i
$306$	11.0961	+	12.8056i	0.634324	+	0.732049i
$307$	−2.62886	−	18.2841i	−0.150037	−	1.04353i	−0.916153	−	0.400828i	$-0.868723\pi$
$307$	−2.62886	−	18.2841i	−0.150037	−	1.04353i	0.766116	−	0.642702i	$-0.222187\pi$
$308$	−0.559953	−	0.164417i	−0.0319063	−	0.00936852i
$309$	−26.6217	+	30.7231i	−1.51446	+	1.74778i
$310$	−29.5487	−	18.9898i	−1.67825	−	1.07855i
$311$	−7.72299	−	4.96327i	−0.437931	−	0.281441i	0.303041	−	0.952978i	$-0.401998\pi$
$311$	−7.72299	−	4.96327i	−0.437931	−	0.281441i	−0.740971	+	0.671537i	$0.765635\pi$
$312$	−9.82291	+	11.3362i	−0.556113	+	0.641788i
$313$	19.5359	+	5.73627i	1.10424	+	0.324233i	0.782534	−	0.622608i	$-0.213927\pi$
$313$	19.5359	+	5.73627i	1.10424	+	0.324233i	0.321702	+	0.946841i	$0.395745\pi$
$314$	3.54994	+	24.6904i	0.200335	+	1.39336i
$315$	−5.23889	−	6.04600i	−0.295178	−	0.340653i
$316$	1.78288	+	3.90396i	0.100295	+	0.219615i
$317$	1.35903	−	0.399048i	0.0763309	−	0.0224128i	−0.243344	−	0.969940i	$-0.578244\pi$
$317$	1.35903	−	0.399048i	0.0763309	−	0.0224128i	0.319675	+	0.947527i	$0.396426\pi$
$318$	12.7335	−	27.8825i	0.714059	−	1.56357i
$319$	−0.326157	+	2.26847i	−0.0182613	+	0.127010i
$320$	−11.5321	+	7.41121i	−0.644663	+	0.414299i
$321$	−30.0000			−1.67444
$322$		0			0
$323$	−10.4721			−0.582685
$324$	−5.71916	+	3.67548i	−0.317731	+	0.204193i
$325$	−2.33630	+	16.2493i	−0.129595	+	0.901350i
$326$	6.88023	−	15.0656i	0.381061	−	0.834407i
$327$		0			0
$328$	5.08305	+	11.1303i	0.280664	+	0.614569i
$329$	1.80999	+	2.08884i	0.0997880	+	0.115162i
$330$	1.27290	+	8.85323i	0.0700710	+	0.487354i
$331$	−11.1805	−	3.28288i	−0.614534	−	0.180444i	−0.0403715	−	0.999185i	$-0.512854\pi$
$331$	−11.1805	−	3.28288i	−0.614534	−	0.180444i	−0.574163	+	0.818741i	$0.694672\pi$
$332$	5.35698	−	6.18229i	0.294003	−	0.339297i
$333$	5.44471	+	3.49910i	0.298368	+	0.191750i
$334$	−14.2544	−	9.16077i	−0.779968	−	0.501255i
$335$	−15.3345	+	17.6969i	−0.837812	+	0.966887i
$336$	−12.8729	−	3.77984i	−0.702277	−	0.206207i
$337$	0.486206	+	3.38163i	0.0264853	+	0.184209i	0.998770	−	0.0495927i	$-0.0157923\pi$
$337$	0.486206	+	3.38163i	0.0264853	+	0.184209i	−0.972284	+	0.233802i	$0.924883\pi$
$338$	−4.23835	−	4.89131i	−0.230536	−	0.266052i
$339$	12.2949	+	26.9221i	0.667769	+	1.46221i
$340$	10.0479	−	2.95034i	0.544926	−	0.160005i
$341$	2.12884	−	4.66151i	0.115283	−	0.252435i
$342$	−0.921081	+	6.40626i	−0.0498064	+	0.346411i
$343$	12.9691	−	8.33474i	0.700266	−	0.450034i
$344$		0			0
$345$		0			0
$346$	−8.18034			−0.439778
$347$	21.7788	−	13.9964i	1.16915	−	0.751366i	0.195788	−	0.980646i	$-0.437273\pi$
$347$	21.7788	−	13.9964i	1.16915	−	0.751366i	0.973361	+	0.229280i	$0.0736371\pi$
$348$	0.590023	−	4.10370i	0.0316285	−	0.219981i
$349$	−1.00381	+	2.19804i	−0.0537328	+	0.117658i	−0.934594	−	0.355716i	$-0.884237\pi$
$349$	−1.00381	+	2.19804i	−0.0537328	+	0.117658i	0.880861	+	0.473375i	$0.156964\pi$
$350$	−10.5010	+	3.08336i	−0.561299	+	0.164812i
$351$	−2.78669	−	6.10200i	−0.148742	−	0.325701i
$352$	1.69189	+	1.95255i	0.0901782	+	0.104071i
$353$	5.03235	+	35.0008i	0.267845	+	1.86290i	0.468803	+	0.883303i	$0.344685\pi$
$353$	5.03235	+	35.0008i	0.267845	+	1.86290i	−0.200958	+	0.979600i	$0.564406\pi$
$354$	−8.58197	−	2.51989i	−0.456126	−	0.133931i
$355$	16.4531	−	18.9879i	0.873241	−	1.00777i
$356$	−0.794372	−	0.510512i	−0.0421016	−	0.0270571i
$357$	−12.1747	−	7.82423i	−0.644355	−	0.414102i
$358$	−13.4654	+	15.5400i	−0.711671	+	0.821312i
$359$	−15.2449	−	4.47632i	−0.804597	−	0.236251i	−0.146526	−	0.989207i	$-0.546809\pi$
$359$	−15.2449	−	4.47632i	−0.804597	−	0.236251i	−0.658071	+	0.752956i	$0.728627\pi$
$360$	2.05960	+	14.3248i	0.108550	+	0.754985i
$361$	9.82291	+	11.3362i	0.516995	+	0.596644i
$362$	9.84874	+	21.5657i	0.517638	+	1.13347i
$363$	22.3483	−	6.56206i	1.17298	−	0.344419i
$364$	−0.952046	+	2.08469i	−0.0499008	+	0.109267i
$365$	7.12555	−	49.5593i	0.372968	−	2.59405i
$366$	−33.3109	+	21.4076i	−1.74119	+	1.11899i
$367$	18.1803			0.949006			0.474503	−	0.880254i	$-0.342628\pi$
$367$	18.1803			0.949006			0.474503	+	0.880254i	$0.342628\pi$
$368$		0			0
$369$	10.9443			0.569736
$370$	14.2544	−	9.16077i	0.741052	−	0.476245i
$371$	−1.49034	+	10.3655i	−0.0773746	+	0.538152i
$372$	−3.85111	+	8.43275i	−0.199671	+	0.437218i
$373$	5.47698	−	1.60819i	0.283587	−	0.0832688i	−0.136846	−	0.990592i	$-0.543696\pi$
$373$	5.47698	−	1.60819i	0.283587	−	0.0832688i	0.420433	+	0.907324i	$0.361878\pi$
$374$	2.68862	+	5.88726i	0.139025	+	0.304423i
$375$	2.23727	+	2.58195i	0.115532	+	0.133331i
$376$	−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
$379$	−17.1285	−	11.0078i	−0.879832	−	0.565433i	0.0209136	−	0.999781i	$-0.493343\pi$
$379$	−17.1285	−	11.0078i	−0.879832	−	0.565433i	−0.900745	+	0.434348i	$0.856979\pi$
$380$	3.36501	+	2.16256i	0.172622	+	0.110937i
$381$	30.3233	−	34.9949i	1.55351	−	1.79285i
$382$	−5.92999	−	1.74120i	−0.303405	−	0.0890877i
$383$	−3.54994	−	24.6904i	−0.181393	−	1.26162i	−0.853472	−	0.521139i	$-0.825507\pi$
$383$	−3.54994	−	24.6904i	−0.181393	−	1.26162i	0.672078	−	0.740480i	$-0.265402\pi$
$384$	19.9411	+	23.0132i	1.01761	+	1.17439i
$385$	−1.26940	−	2.77959i	−0.0646944	−	0.141661i
$386$	−12.3334	+	3.62142i	−0.627755	+	0.184325i
$387$		0			0
$388$	−0.377487	+	2.62548i	−0.0191640	+	0.133288i
$389$	28.9998	−	18.6370i	1.47035	−	0.944936i	0.472369	−	0.881401i	$-0.343399\pi$
$389$	28.9998	−	18.6370i	1.47035	−	0.944936i	0.997980	−	0.0635347i	$-0.0202374\pi$
$390$	35.1246			1.77860
$391$		0			0
$392$	−12.2361			−0.618015
$393$	9.95440	−	6.39730i	0.502133	−	0.322701i
$394$	1.72061	−	11.9671i	0.0866831	−	0.602894i
$395$	−9.33526	+	20.4414i	−0.469708	+	1.02852i
$396$	0.906022	−	0.266032i	0.0455293	−	0.0133686i
$397$	1.00381	+	2.19804i	0.0503799	+	0.110317i	0.933148	−	0.359492i	$-0.117050\pi$
$397$	1.00381	+	2.19804i	0.0503799	+	0.110317i	−0.882768	+	0.469809i	$0.844323\pi$
$398$	−27.2401	−	31.4367i	−1.36542	−	1.57578i
$399$	−0.786697	−	5.47160i	−0.0393841	−	0.273923i
$400$	25.4863	+	7.48347i	1.27432	+	0.374173i
$401$	−5.35698	+	6.18229i	−0.267515	+	0.308729i	−0.873574	−	0.486691i	$-0.838204\pi$
$401$	−5.35698	+	6.18229i	−0.267515	+	0.308729i	0.606059	+	0.795419i	$0.292749\pi$
$402$	22.0243	+	14.1542i	1.09847	+	0.705945i
$403$	−16.9299	−	10.8802i	−0.843338	−	0.541981i
$404$	1.80999	−	2.08884i	0.0900504	−	0.103924i
$405$	−34.1548	−	10.0288i	−1.69717	−	0.498333i
$406$	0.853889	+	5.93893i	0.0423778	+	0.294744i
$407$	1.61890	+	1.86832i	0.0802461	+	0.0926090i
$408$	10.8757	+	23.8145i	0.538428	+	1.17899i
$409$	22.4144	−	6.58146i	1.10832	−	0.325432i	0.324168	−	0.946000i	$-0.394916\pi$
$409$	22.4144	−	6.58146i	1.10832	−	0.325432i	0.784153	+	0.620567i	$0.213098\pi$
$410$	11.9027	−	26.0632i	0.587831	−	1.28717i
$411$	−4.41969	+	30.7396i	−0.218007	+	1.51627i
$412$	9.45238	−	6.07468i	0.465685	−	0.299278i
$413$	3.05573			0.150363
$414$		0			0
$415$	42.8328			2.10258
$416$	8.53527	−	5.48529i	0.418476	−	0.268938i
$417$	−0.861820	+	5.99409i	−0.0422035	+	0.293532i
$418$	−1.02696	+	2.24873i	−0.0502304	+	0.109989i
$419$	30.1438	−	8.85102i	1.47262	−	0.432401i	0.555672	−	0.831402i	$-0.312461\pi$
$419$	30.1438	−	8.85102i	1.47262	−	0.432401i	0.916950	+	0.399001i	$0.130643\pi$
$420$	2.29636	+	5.02832i	0.112051	+	0.245357i
$421$	15.5256	+	17.9175i	0.756670	+	0.873244i	0.995197	−	0.0978921i	$-0.0312100\pi$
$421$	15.5256	+	17.9175i	0.756670	+	0.873244i	−0.238527	+	0.971136i	$0.576665\pi$
$422$	0.786697	+	5.47160i	0.0382958	+	0.266353i
$423$	−4.29098	−	1.25995i	−0.208635	−	0.0612607i
$424$	12.4059	−	14.3171i	0.602482	−	0.695301i
$425$	24.1040	+	15.4907i	1.16922	+	0.751409i
$426$	−23.6310	−	15.1867i	−1.14492	−	0.735798i
$427$	8.85887	−	10.2237i	0.428711	−	0.494758i
$428$	7.95592	+	2.33607i	0.384564	+	0.112918i
$429$	0.729308	+	5.07245i	0.0352113	+	0.244900i
$430$		0			0
$431$	−10.9969	−	24.0799i	−0.529703	−	1.15989i	−0.965633	−	0.259908i	$-0.916308\pi$
$431$	−10.9969	−	24.0799i	−0.529703	−	1.15989i	0.435930	−	0.899980i	$-0.356419\pi$
$432$	−10.4144	+	3.05795i	−0.501065	+	0.147126i
$433$	16.6915	−	36.5493i	0.802143	−	1.75645i	0.164106	−	0.986443i	$-0.447526\pi$
$433$	16.6915	−	36.5493i	0.802143	−	1.75645i	0.638037	−	0.770006i	$-0.279747\pi$
$434$	1.90935	−	13.2798i	0.0916519	−	0.637453i
$435$	18.2621	−	11.7363i	0.875601	−	0.562714i
$436$		0			0
$437$		0			0
$438$	−55.9787			−2.67477
$439$	−4.45174	+	2.86096i	−0.212470	+	0.136546i	−0.642548	−	0.766246i	$-0.722123\pi$
$439$	−4.45174	+	2.86096i	−0.212470	+	0.136546i	0.430078	+	0.902792i	$0.358486\pi$
$440$	−0.786697	+	5.47160i	−0.0375043	+	0.260848i
$441$	−4.54641	+	9.95526i	−0.216496	+	0.474060i
$442$	24.3869	−	7.16063i	1.15996	−	0.340596i
$443$	−0.882596	−	1.93261i	−0.0419334	−	0.0918213i	0.887506	−	0.460796i	$-0.152436\pi$
$443$	−0.882596	−	1.93261i	−0.0419334	−	0.0918213i	−0.929439	+	0.368975i	$0.879709\pi$
$444$	−2.92863	−	3.37981i	−0.138986	−	0.160399i
$445$	−0.703643	−	4.89395i	−0.0333559	−	0.231995i
$446$	6.20997	+	1.82341i	0.294051	+	0.0863410i
$447$	17.4086	−	20.0905i	0.823396	−	0.950250i
$448$	−4.40486	−	2.83083i	−0.208110	−	0.133744i
$449$	2.47688	+	1.59179i	0.116891	+	0.0751214i	0.597780	−	0.801660i	$-0.296050\pi$
$449$	2.47688	+	1.59179i	0.116891	+	0.0751214i	−0.480889	+	0.876782i	$0.659686\pi$
$450$	11.5964	−	13.3830i	0.546660	−	0.630879i
$451$	4.01101	+	1.17774i	0.188871	+	0.0554575i
$452$	−1.16418	−	8.09708i	−0.0547586	−	0.380854i
$453$	0.345677	+	0.398933i	0.0162413	+	0.0187435i
$454$	−6.84277	−	14.9836i	−0.321147	−	0.703214i
$455$	−11.5139	+	3.38079i	−0.539781	+	0.158494i
$456$	−4.15415	+	9.09632i	−0.194536	+	0.425974i
$457$	−4.99875	+	34.7671i	−0.233832	+	1.62634i	0.447446	+	0.894311i	$0.352334\pi$
$457$	−4.99875	+	34.7671i	−0.233832	+	1.62634i	−0.681278	+	0.732025i	$0.738575\pi$
$458$	16.3341	−	10.4973i	0.763243	−	0.490507i
$459$	−11.7082			−0.546492
$460$		0			0
$461$	7.47214			0.348012			0.174006	−	0.984745i	$-0.444329\pi$
$461$	7.47214			0.348012			0.174006	+	0.984745i	$0.444329\pi$
$462$	−2.87407	+	1.84705i	−0.133714	+	0.0859325i
$463$	2.84630	−	19.7964i	0.132279	−	0.920018i	−0.810296	−	0.586021i	$-0.800693\pi$
$463$	2.84630	−	19.7964i	0.132279	−	0.920018i	0.942574	−	0.333997i	$-0.108397\pi$
$464$	6.04940	−	13.2463i	0.280836	−	0.614946i
$465$	−46.5748	+	13.6756i	−2.15985	+	0.634190i
$466$	10.3997	+	22.7721i	0.481756	+	1.05490i
$467$	20.2642	+	23.3861i	0.937715	+	1.08218i	0.996473	+	0.0839084i	$0.0267403\pi$
$467$	20.2642	+	23.3861i	0.937715	+	1.08218i	−0.0587587	+	0.998272i	$0.518714\pi$
$468$	−0.527732	−	3.67046i	−0.0243944	−	0.169667i
$469$	−8.58197	−	2.51989i	−0.396278	−	0.116358i
$470$	−7.66724	+	8.84847i	−0.353664	+	0.408149i
$471$	28.9998	+	18.6370i	1.33624	+	0.858750i
$472$	−4.65034	−	2.98859i	−0.214049	−	0.137561i
$473$		0			0
$474$	24.1069	+	7.07842i	1.10727	+	0.325123i
$475$	1.55753	+	10.8329i	0.0714645	+	0.497046i
$476$	2.61944	+	3.02300i	0.120062	+	0.138559i
$477$	−7.03890	−	15.4131i	−0.322289	−	0.705715i
$478$	28.3114	−	8.31296i	1.29493	−	0.380226i
$479$	−7.30995	+	16.0066i	−0.334000	+	0.731359i	−0.999892	−	0.0146897i	$-0.995324\pi$
$479$	−7.30995	+	16.0066i	−0.334000	+	0.731359i	0.665892	+	0.746048i	$0.268051\pi$
$480$	3.48275	−	24.2230i	0.158965	−	1.10563i
$481$	8.16706	−	5.24865i	0.372386	−	0.239318i
$482$	−27.7082			−1.26207
$483$		0			0
$484$	−6.43769			−0.292622
$485$	−11.6838	+	7.50871i	−0.530533	+	0.340953i
$486$	−4.11920	+	28.6497i	−0.186851	+	1.29958i
$487$	−0.536631	+	1.17506i	−0.0243171	+	0.0532470i	−0.921401	−	0.388614i	$-0.872954\pi$
$487$	−0.536631	+	1.17506i	−0.0243171	+	0.0532470i	0.897084	+	0.441861i	$0.145681\pi$
$488$	−23.4808	+	6.89460i	−1.06293	+	0.312104i
$489$	−9.50824	−	20.8202i	−0.429978	−	0.941520i
$490$	18.7634	+	21.6541i	0.847643	+	0.978232i
$491$	−5.64314	−	39.2489i	−0.254671	−	1.77128i	−0.569366	−	0.822084i	$-0.692811\pi$
$491$	−5.64314	−	39.2489i	−0.254671	−	1.77128i	0.314695	−	0.949193i	$-0.398098\pi$
$492$	−7.25598	−	2.13055i	−0.327125	−	0.0960525i
$493$	10.2867	−	11.8715i	0.463289	−	0.534664i
$494$	8.16706	+	5.24865i	0.367453	+	0.236148i
$495$	4.15939	+	2.67308i	0.186951	+	0.120146i
$496$	−21.3238	+	24.6089i	−0.957466	+	1.10497i
$497$	9.20801	+	2.70372i	0.413036	+	0.121278i
$498$	−6.81525	−	47.4011i	−0.305399	−	2.12409i
$499$	−21.4193	−	24.7192i	−0.958860	−	1.10658i	−0.994236	−	0.107210i	$-0.965808\pi$
$499$	−21.4193	−	24.7192i	−0.958860	−	1.10658i	0.0353760	−	0.999374i	$-0.488737\pi$
$500$	−0.392265	−	0.858940i	−0.0175426	−	0.0384130i
$501$	−22.4679	+	6.59716i	−1.00379	+	0.294740i
$502$	−10.5584	+	23.1196i	−0.471243	+	1.03188i
$503$	1.28876	−	8.96355i	0.0574632	−	0.399665i	−0.940708	−	0.339217i	$-0.889838\pi$
$503$	1.28876	−	8.96355i	0.0574632	−	0.399665i	0.998171	−	0.0604482i	$-0.0192530\pi$
$504$	−4.65034	+	2.98859i	−0.207142	+	0.133122i
$505$	14.4721			0.644002
$506$		0			0
$507$	−8.94427			−0.397229
$508$	−10.7667	+	6.91932i	−0.477694	+	0.306995i
$509$	−4.88210	+	33.9558i	−0.216395	+	1.50506i	0.534797	+	0.844980i	$0.320388\pi$
$509$	−4.88210	+	33.9558i	−0.216395	+	1.50506i	−0.751193	+	0.660083i	$0.770521\pi$
$510$	25.4670	−	55.7649i	1.12770	−	2.46931i
$511$	18.3499	−	5.38803i	0.811753	−	0.238352i
$512$	2.19829	+	4.81359i	0.0971517	+	0.212733i
$513$	−2.92863	−	3.37981i	−0.129302	−	0.149222i
$514$	0.338989	+	2.35772i	0.0149522	+	0.103995i
$515$	56.4497	+	16.5751i	2.48747	+	0.730387i
$516$		0			0
$517$	−1.43703	−	0.923525i	−0.0632006	−	0.0406166i
$518$	5.44471	+	3.49910i	0.239227	+	0.153742i
$519$	−7.40317	+	8.54371i	−0.324963	+	0.375027i
$520$	20.8289	+	6.11591i	0.913406	+	0.268200i
$521$	−0.652313	−	4.53694i	−0.0285784	−	0.198767i	0.970530	−	0.240979i	$-0.0774685\pi$
$521$	−0.652313	−	4.53694i	−0.0285784	−	0.198767i	−0.999109	+	0.0422122i	$0.986559\pi$
$522$	−6.35752	−	7.33697i	−0.278261	−	0.321130i
$523$	0.363649	+	0.796281i	0.0159013	+	0.0348189i	0.917416	−	0.397929i	$-0.130271\pi$
$523$	0.363649	+	0.796281i	0.0159013	+	0.0348189i	−0.901515	+	0.432748i	$0.857544\pi$
$524$	−3.13803	+	0.921409i	−0.137086	+	0.0402519i
$525$	−6.28299	+	13.7578i	−0.274212	+	0.600441i
$526$	−3.44122	+	23.9342i	−0.150044	+	1.04358i
$527$	−29.5487	+	18.9898i	−1.28716	+	0.827209i
$528$	8.29180			0.360854
$529$		0			0
$530$	−44.3607			−1.92690
$531$	−4.15939	+	2.67308i	−0.180502	+	0.116002i
$532$	−0.217438	+	1.51231i	−0.00942712	+	0.0655671i
$533$	6.81962	−	14.9329i	0.295391	−	0.646815i
$534$	−5.30395	+	1.55738i	−0.229524	+	0.0673944i
$535$	18.0358	+	39.4930i	0.779757	+	1.70743i
$536$	10.5959	+	12.2283i	0.457672	+	0.528181i
$537$	4.04408	+	28.1272i	0.174515	+	1.21378i
$538$	15.4384	+	4.53312i	0.665597	+	0.195437i
$539$	−2.73754	+	3.15929i	−0.117914	+	0.136080i
$540$	3.76220	+	2.41782i	0.161899	+	0.104046i
$541$	−6.37972	−	4.10000i	−0.274286	−	0.176273i	0.396265	−	0.918136i	$-0.370306\pi$
$541$	−6.37972	−	4.10000i	−0.274286	−	0.176273i	−0.670551	+	0.741863i	$0.733942\pi$
$542$	8.47670	−	9.78263i	0.364105	−	0.420200i
$543$	31.4368	+	9.23067i	1.34908	+	0.396126i
$544$	−2.52014	−	17.5280i	−0.108050	−	0.751505i
$545$		0			0
$546$	5.57338	+	12.2040i	0.238519	+	0.522283i
$547$	−36.0203	+	10.5765i	−1.54012	+	0.452220i	−0.938130	−	0.346285i	$-0.887443\pi$
$547$	−36.0203	+	10.5765i	−1.54012	+	0.452220i	−0.601989	+	0.798504i	$0.705625\pi$
$548$	3.56575	−	7.80791i	0.152321	−	0.333537i
$549$	−3.11506	+	21.6658i	−0.132948	+	0.924672i
$550$	5.69018	−	3.65686i	0.242630	−	0.155929i
$551$	6.00000			0.255609
$552$		0			0
$553$	−8.58359			−0.365011
$554$	−8.88558	+	5.71041i	−0.377512	+	0.242612i
$555$	3.33250	−	23.1781i	0.141457	−	0.983854i
$556$	0.695306	−	1.52251i	0.0294875	−	0.0645687i
$557$	−18.6299	+	5.47023i	−0.789374	+	0.231781i	−0.651480	−	0.758666i	$-0.725852\pi$
$557$	−18.6299	+	5.47023i	−0.789374	+	0.231781i	−0.137894	+	0.990447i	$0.544033\pi$
$558$	9.01791	+	19.7465i	0.381759	+	0.835935i
$559$		0			0
$560$	2.76324	+	19.2188i	0.116768	+	0.812142i
$561$	8.58197	+	2.51989i	0.362331	+	0.106390i
$562$	−14.0248	+	16.1854i	−0.591599	+	0.682742i
$563$	−12.6657	−	8.13974i	−0.533795	−	0.343049i	0.245813	−	0.969317i	$-0.420945\pi$
$563$	−12.6657	−	8.13974i	−0.533795	−	0.343049i	−0.779608	+	0.626268i	$0.784582\pi$
$564$	2.59962	+	1.67067i	0.109464	+	0.0703480i
$565$	28.0495	−	32.3709i	1.18005	−	1.36185i
$566$	22.1879	+	6.51496i	0.932627	+	0.273844i
$567$	−1.93502	−	13.4584i	−0.0812632	−	0.565198i
$568$	−11.3688	−	13.1203i	−0.477025	−	0.550517i
$569$	0.0749159	+	0.164043i	0.00314064	+	0.00687704i	0.911196	−	0.411974i	$-0.135160\pi$
$569$	0.0749159	+	0.164043i	0.00314064	+	0.00687704i	−0.908055	+	0.418851i	$0.862433\pi$
$570$	22.4679	−	6.59716i	0.941076	−	0.276325i
$571$	−11.5104	+	25.2043i	−0.481695	+	1.05477i	0.500298	+	0.865853i	$0.333224\pi$
$571$	−11.5104	+	25.2043i	−0.481695	+	1.05477i	−0.981994	+	0.188913i	$0.939504\pi$
$572$	0.201576	−	1.40199i	0.00842831	−	0.0586202i
$573$	−7.18516	+	4.61762i	−0.300164	+	0.192904i
$574$	10.9443			0.456805
$575$		0			0
$576$	8.47214			0.353006
$577$	−10.8425	+	6.96807i	−0.451381	+	0.290085i	−0.746512	−	0.665372i	$-0.768273\pi$
$577$	−10.8425	+	6.96807i	−0.451381	+	0.290085i	0.295131	+	0.955457i	$0.404637\pi$
$578$	2.39859	−	16.6826i	0.0997681	−	0.693903i
$579$	−7.37940	+	16.1586i	−0.306678	+	0.671530i
$580$	−5.75696	+	1.69040i	−0.239045	+	0.0701898i
$581$	6.79647	+	14.8822i	0.281965	+	0.617418i
$582$	10.1686	+	11.7352i	0.421502	+	0.486439i
$583$	−0.921081	−	6.40626i	−0.0381473	−	0.265320i
$584$	−33.1953	−	9.74703i	−1.37363	−	0.403335i
$585$	12.7150	−	14.6739i	0.525702	−	0.606693i
$586$	14.2544	+	9.16077i	0.588845	+	0.378428i
$587$	−9.49926	−	6.10481i	−0.392077	−	0.251972i	0.329718	−	0.944079i	$-0.393046\pi$
$587$	−9.49926	−	6.10481i	−0.392077	−	0.251972i	−0.721795	+	0.692107i	$0.756683\pi$
$588$	4.95226	−	5.71521i	0.204228	−	0.235691i
$589$	−12.8729	−	3.77984i	−0.530421	−	0.155746i
$590$	1.84216	+	12.8125i	0.0758406	+	0.527483i
$591$	−10.9415	−	12.6272i	−0.450075	−	0.519414i
$592$	−6.52542	−	14.2887i	−0.268193	−	0.587261i
$593$	−14.3389	+	4.21029i	−0.588829	+	0.172896i	−0.562556	−	0.826759i	$-0.690182\pi$
$593$	−14.3389	+	4.21029i	−0.588829	+	0.172896i	−0.0262728	+	0.999655i	$0.508364\pi$
$594$	−1.14818	+	2.51416i	−0.0471103	+	0.103157i
$595$	−2.98068	+	20.7311i	−0.122196	+	0.849892i
$596$	−6.18113	+	3.97237i	−0.253189	+	0.162715i
$597$	−57.4853			−2.35272
$598$		0			0
$599$	−1.88854			−0.0771638			−0.0385819	−	0.999255i	$-0.512284\pi$
$599$	−1.88854			−0.0771638			−0.0385819	+	0.999255i	$0.512284\pi$
$600$	23.0173	−	14.7923i	0.939676	−	0.603893i
$601$	−1.58133	+	10.9984i	−0.0645036	+	0.448632i	0.931817	+	0.362928i	$0.118223\pi$
$601$	−1.58133	+	10.9984i	−0.0645036	+	0.448632i	−0.996321	+	0.0857040i	$0.972686\pi$
$602$		0			0
$603$	13.8859	−	4.07727i	0.565478	−	0.166039i
$604$	−0.0606082	−	0.132714i	−0.00246611	−	0.00540004i
$605$	−22.0742	−	25.4750i	−0.897443	−	1.03570i
$606$	−2.30270	−	16.0156i	−0.0935409	−	0.650591i
$607$	−16.8179	−	4.93817i	−0.682616	−	0.200434i	−0.0780025	−	0.996953i	$-0.524854\pi$
$607$	−16.8179	−	4.93817i	−0.682616	−	0.200434i	−0.604613	+	0.796519i	$0.706672\pi$
$608$	4.42943	−	5.11184i	0.179637	−	0.207312i
$609$	6.97550	+	4.48288i	0.282662	+	0.181656i
$610$	48.2080	+	30.9814i	1.95188	+	1.25440i
$611$	−4.39294	+	5.06972i	−0.177719	+	0.205099i
$612$	−6.20997	−	1.82341i	−0.251023	−	0.0737070i
$613$	1.09699	+	7.62975i	0.0443071	+	0.308163i	0.999909	+	0.0135013i	$0.00429772\pi$
$613$	1.09699	+	7.62975i	0.0443071	+	0.308163i	−0.955602	+	0.294661i	$0.904793\pi$
$614$	19.5728	+	22.5883i	0.789895	+	0.911588i
$615$	−16.4491	−	36.0185i	−0.663291	−	1.45240i
$616$	−2.02593	+	0.594866i	−0.0816269	+	0.0239678i
$617$	−6.84277	+	14.9836i	−0.275480	+	0.603216i	−0.995914	−	0.0903069i	$-0.971215\pi$
$617$	−6.84277	+	14.9836i	−0.275480	+	0.603216i	0.720434	+	0.693523i	$0.243942\pi$
$618$	9.36106	−	65.1076i	0.376557	−	2.61901i
$619$	−6.23908	+	4.00961i	−0.250770	+	0.161160i	−0.659987	−	0.751277i	$-0.729438\pi$
$619$	−6.23908	+	4.00961i	−0.250770	+	0.161160i	0.409217	+	0.912437i	$0.365802\pi$
$620$	13.4164			0.538816
$621$		0			0
$622$	14.8541			0.595595
$623$	1.58874	−	1.02102i	0.0636517	−	0.0409065i
$624$	4.63410	−	32.2309i	0.185512	−	1.29027i
$625$	−9.31211	+	20.3907i	−0.372484	+	0.815627i
$626$	−31.6098	+	9.28147i	−1.26338	+	0.370962i
$627$	1.41923	+	3.10767i	0.0566785	+	0.124109i
$628$	−6.23942	−	7.20068i	−0.248980	−	0.287338i
$629$	−2.41142	−	16.7718i	−0.0961497	−	0.668736i
$630$	12.4199	+	3.64682i	0.494822	+	0.145293i
$631$	21.1917	−	24.4566i	0.843630	−	0.973601i	−0.156271	−	0.987714i	$-0.549947\pi$
$631$	21.1917	−	24.4566i	0.843630	−	0.973601i	0.999900	+	0.0141136i	$0.00449265\pi$
$632$	13.0629	+	8.39500i	0.519613	+	0.333935i
$633$	6.42661	+	4.13013i	0.255435	+	0.164158i
$634$	−1.50081	+	1.73202i	−0.0596047	+	0.0687875i
$635$	−64.2987	−	18.8798i	−2.55161	−	0.749222i
$636$	1.66625	+	11.5890i	0.0660712	+	0.459535i
$637$	10.7505	+	12.4067i	0.425949	+	0.491571i
$638$	−1.54044	−	3.37310i	−0.0609867	−	0.133542i
$639$	−14.8989	+	4.37470i	−0.589390	+	0.173061i
$640$	18.3069	−	40.0865i	0.723643	−	1.58456i
$641$	−6.44757	+	44.8438i	−0.254664	+	1.77122i	0.314752	+	0.949174i	$0.398079\pi$
$641$	−6.44757	+	44.8438i	−0.254664	+	1.77122i	−0.569415	+	0.822050i	$0.692830\pi$
$642$	40.8353	−	26.2433i	1.61164	−	1.03574i
$643$	19.5967			0.772820			0.386410	−	0.922327i	$-0.373715\pi$
$643$	19.5967			0.772820			0.386410	+	0.922327i	$0.373715\pi$
$644$		0			0
$645$		0			0
$646$	14.2544	−	9.16077i	0.560833	−	0.360425i
$647$	0.954677	−	6.63992i	0.0375322	−	0.261042i	−0.962412	−	0.271593i	$-0.912449\pi$
$647$	0.954677	−	6.63992i	0.0375322	−	0.261042i	0.999944	+	0.0105510i	$0.00335854\pi$
$648$	−10.2179	+	22.3740i	−0.401395	+	0.878933i
$649$	−1.81204	+	0.532064i	−0.0711290	+	0.0208853i
$650$	−11.0344	−	24.1619i	−0.432804	−	0.947709i
$651$	−12.1418	−	14.0124i	−0.475874	−	0.549188i
$652$	0.900318	+	6.26185i	0.0352592	+	0.245233i
$653$	−23.3204	−	6.84750i	−0.912599	−	0.267963i	−0.208465	−	0.978030i	$-0.566847\pi$
$653$	−23.3204	−	6.84750i	−0.912599	−	0.267963i	−0.704134	+	0.710067i	$0.748665\pi$
$654$		0			0
$655$	−14.4061	−	9.25826i	−0.562894	−	0.361750i
$656$	−22.3456	−	14.3607i	−0.872450	−	0.560690i
$657$	−20.2642	+	23.3861i	−0.790581	+	0.912379i
$658$	−4.29098	−	1.25995i	−0.167280	−	0.0491178i
$659$	−2.93915	−	20.4423i	−0.114493	−	0.796318i	−0.963456	−	0.267865i	$-0.913682\pi$
$659$	−2.93915	−	20.4423i	−0.114493	−	0.796318i	0.848963	−	0.528452i	$-0.177227\pi$
$660$	−2.23727	−	2.58195i	−0.0870857	−	0.100502i
$661$	−2.10023	−	4.59885i	−0.0816893	−	0.178875i	0.864380	−	0.502839i	$-0.167711\pi$
$661$	−2.10023	−	4.59885i	−0.0816893	−	0.178875i	−0.946069	+	0.323965i	$0.894984\pi$
$662$	18.0904	−	5.31181i	0.703103	−	0.206450i
$663$	14.5913	−	31.9505i	0.566679	−	1.24085i
$664$	4.21206	−	29.2955i	0.163459	−	1.13689i
$665$	−6.73003	+	4.32513i	−0.260979	+	0.167721i
$666$	−10.4721			−0.405787
$667$		0			0
$668$	6.47214			0.250414
$669$	7.52440	−	4.83564i	0.290910	−	0.186957i
$670$	5.39210	−	37.5029i	0.208315	−	1.44886i
$671$	−3.47315	+	7.60514i	−0.134080	+	0.293593i
$672$	8.96888	−	2.63350i	0.345982	−	0.101590i
$673$	1.24625	+	2.72890i	0.0480392	+	0.105191i	0.932130	−	0.362124i	$-0.117948\pi$
$673$	1.24625	+	2.72890i	0.0480392	+	0.105191i	−0.884091	+	0.467316i	$0.845221\pi$
$674$	−3.61998	−	4.17768i	−0.139436	−	0.160918i
$675$	1.74137	+	12.1115i	0.0670255	+	0.466173i
$676$	2.37200	+	0.696481i	0.0912307	+	0.0267877i
$677$	−11.7875	+	13.6035i	−0.453030	+	0.522825i	−0.935614	−	0.353025i	$-0.885153\pi$
$677$	−11.7875	+	13.6035i	−0.453030	+	0.522825i	0.482584	+	0.875850i	$0.339698\pi$
$678$	−40.2864	−	25.8905i	−1.54719	−	0.994319i
$679$	−4.46281	−	2.86807i	−0.171267	−	0.110067i
$680$	24.8117	−	28.6343i	0.951486	−	1.09807i
$681$	−21.8418	−	6.41334i	−0.836981	−	0.245760i
$682$	1.18005	+	8.20740i	0.0451863	+	0.314277i
$683$	14.7977	+	17.0775i	0.566219	+	0.653452i	0.964584	−	0.263775i	$-0.0849677\pi$
$683$	14.7977	+	17.0775i	0.566219	+	0.653452i	−0.398365	+	0.917227i	$0.630422\pi$
$684$	−1.02696	−	2.24873i	−0.0392669	−	0.0859825i
$685$	43.1237	−	12.6623i	1.64767	−	0.483800i
$686$	−10.3622	+	22.6901i	−0.395632	+	0.866312i
$687$	3.81871	−	26.5597i	0.145693	−	1.01332i
$688$		0			0
$689$	−25.4164			−0.968288
$690$		0			0
$691$	24.9443			0.948925			0.474462	−	0.880276i	$-0.342642\pi$
$691$	24.9443			0.948925			0.474462	+	0.880276i	$0.342642\pi$
$692$	2.62859	−	1.68929i	0.0999240	−	0.0642173i
$693$	−0.268768	+	1.86932i	−0.0102096	+	0.0710096i
$694$	−17.4011	+	38.1032i	−0.660538	+	1.44638i
$695$	8.40893	−	2.46908i	0.318969	−	0.0936577i
$696$	−6.23123	−	13.6445i	−0.236194	−	0.517193i
$697$	−18.7634	−	21.6541i	−0.710714	−	0.820207i
$698$	−0.556427	−	3.87003i	−0.0210611	−	0.146483i
$699$	33.1953	+	9.74703i	1.25556	+	0.368667i
$700$	2.73754	−	3.15929i	0.103469	−	0.119410i
$701$	−22.0243	−	14.1542i	−0.831846	−	0.534595i	0.0540177	−	0.998540i	$-0.482797\pi$
$701$	−22.0243	−	14.1542i	−0.831846	−	0.534595i	−0.885864	+	0.463945i	$0.846434\pi$
$702$	9.13105	+	5.86817i	0.344629	+	0.221480i
$703$	4.23835	−	4.89131i	0.159852	−	0.184479i
$704$	3.10498	+	0.911706i	0.117024	+	0.0343612i
$705$	2.30270	+	16.0156i	0.0867248	+	0.603184i
$706$	−37.4677	−	43.2400i	−1.41012	−	1.62736i
$707$	2.29636	+	5.02832i	0.0863634	+	0.189110i
$708$	3.27802	−	0.962513i	0.123196	−	0.0361735i
$709$	6.67526	−	14.6168i	0.250694	−	0.548944i	−0.741887	−	0.670525i	$-0.766069\pi$
$709$	6.67526	−	14.6168i	0.250694	−	0.548944i	0.992582	+	0.121580i	$0.0387963\pi$
$710$	−5.78545	+	40.2387i	−0.217124	+	1.51013i
$711$	11.6838	−	7.50871i	0.438176	−	0.281599i
$712$	−3.41641			−0.128035
$713$		0			0
$714$	23.4164			0.876337
$715$	6.23908	−	4.00961i	0.233328	−	0.149951i
$716$	1.11776	−	7.77416i	0.0417725	−	0.290534i
$717$	16.9394	−	37.0921i	0.632614	−	1.38523i
$718$	24.6668	−	7.24284i	0.920558	−	0.270300i
$719$	−8.70056	−	19.0516i	−0.324476	−	0.710504i	0.675154	−	0.737676i	$-0.264077\pi$
$719$	−8.70056	−	19.0516i	−0.324476	−	0.710504i	−0.999631	+	0.0271724i	$0.991350\pi$
$720$	−20.5734	−	23.7429i	−0.766724	−	0.884847i
$721$	3.19812	+	22.2434i	0.119104	+	0.828388i
$722$	−23.2874	−	6.83779i	−0.866667	−	0.254476i
$723$	−25.0758	+	28.9390i	−0.932579	+	1.07625i
$724$	−7.61816	−	4.89590i	−0.283127	−	0.181955i
$725$	−13.8104	−	8.87538i	−0.512904	−	0.329623i
$726$	−24.6797	+	28.4819i	−0.915949	+	1.05706i
$727$	13.7129	+	4.02646i	0.508582	+	0.149333i	0.525949	−	0.850516i	$-0.323710\pi$
$727$	13.7129	+	4.02646i	0.508582	+	0.149333i	−0.0173669	+	0.999849i	$0.505528\pi$
$728$	1.18005	+	8.20740i	0.0437354	+	0.304186i
$729$	4.58403	+	5.29025i	0.169779	+	0.195935i
$730$	33.6541	+	73.6922i	1.24559	+	2.72747i
$731$		0			0
$732$	6.28299	−	13.7578i	0.232226	−	0.508504i
$733$	3.80890	−	26.4915i	0.140685	−	0.978486i	−0.790115	−	0.612958i	$-0.789979\pi$
$733$	3.80890	−	26.4915i	0.140685	−	0.978486i	0.930800	−	0.365528i	$-0.119112\pi$
$734$	−24.7467	+	15.9037i	−0.913416	+	0.587017i
$735$	39.5967			1.46055
$736$		0			0
$737$	5.52786			0.203621
$738$	−14.8971	+	9.57378i	−0.548369	+	0.352416i
$739$	−6.99909	+	48.6798i	−0.257466	+	1.79071i	0.293265	+	0.956031i	$0.405258\pi$
$739$	−6.99909	+	48.6798i	−0.257466	+	1.79071i	−0.550731	+	0.834683i	$0.685651\pi$
$740$	−2.68862	+	5.88726i	−0.0988357	+	0.216420i
$741$	12.8729	−	3.77984i	0.472900	−	0.138856i
$742$	−7.03890	−	15.4131i	−0.258406	−	0.565831i
$743$	−0.573257	−	0.661574i	−0.0210308	−	0.0242708i	0.745137	−	0.666912i	$-0.232384\pi$
$743$	−0.573257	−	0.661574i	−0.0210308	−	0.0242708i	−0.766168	+	0.642641i	$0.777839\pi$
$744$	4.77338	+	33.1996i	0.175001	+	1.21716i
$745$	−36.9137	−	10.8389i	−1.35241	−	0.397105i
$746$	−6.04834	+	6.98015i	−0.221445	+	0.255562i
$747$	−22.2698	−	14.3119i	−0.814809	−	0.523646i
$748$	−2.07969	−	1.33654i	−0.0760411	−	0.0488687i
$749$	−10.8599	+	12.5330i	−0.396814	+	0.457947i
$750$	−5.30395	−	1.55738i	−0.193673	−	0.0568675i
$751$	6.31318	+	43.9092i	0.230371	+	1.60227i	0.696504	+	0.717553i	$0.254738\pi$
$751$	6.31318	+	43.9092i	0.230371	+	1.60227i	−0.466133	+	0.884715i	$0.654353\pi$
$752$	7.10793	+	8.20298i	0.259199	+	0.299132i
$753$	14.5913	+	31.9505i	0.531736	+	1.16434i
$754$	−13.9724	+	4.10268i	−0.508846	+	0.149411i
$755$	0.317349	−	0.694897i	0.0115495	−	0.0252899i
$756$	−0.243103	+	1.69082i	−0.00884156	+	0.0614944i
$757$	−40.0409	+	25.7327i	−1.45531	+	0.935273i	−0.456347	+	0.889802i	$0.650842\pi$
$757$	−40.0409	+	25.7327i	−1.45531	+	0.935273i	−0.998966	+	0.0454705i	$0.985521\pi$
$758$	32.9443			1.19659
$759$		0			0
$760$	14.4721			0.524960
$761$	−13.7166	+	8.81512i	−0.497226	+	0.319548i	−0.765106	−	0.643904i	$-0.777313\pi$
$761$	−13.7166	+	8.81512i	−0.497226	+	0.319548i	0.267880	+	0.963452i	$0.413677\pi$
$762$	−10.6627	+	74.1604i	−0.386267	+	2.68655i
$763$		0			0
$764$	2.26506	−	0.665080i	0.0819468	−	0.0240618i
$765$	−14.0778	−	30.8261i	−0.508984	−	1.11452i
$766$	26.4306	+	30.5026i	0.954977	+	1.10210i
$767$	1.05546	+	7.34092i	0.0381106	+	0.265065i
$768$	−29.0978	−	8.54389i	−1.04998	−	0.308301i
$769$	−11.2142	+	12.9419i	−0.404396	+	0.466698i	−0.921020	−	0.389514i	$-0.872643\pi$
$769$	−11.2142	+	12.9419i	−0.404396	+	0.466698i	0.516625	+	0.856212i	$0.327188\pi$
$770$	4.15939	+	2.67308i	0.149894	+	0.0963309i
$771$	2.76924	+	1.77968i	0.0997316	+	0.0640936i
$772$	3.21525	−	3.71060i	0.115720	−	0.133547i
$773$	13.8859	+	4.07727i	0.499442	+	0.146649i	0.521744	−	0.853102i	$-0.325282\pi$
$773$	13.8859	+	4.07727i	0.499442	+	0.146649i	−0.0223026	+	0.999751i	$0.507100\pi$
$774$		0			0
$775$	24.0388	+	27.7422i	0.863498	+	0.996530i
$776$	3.98663	+	8.72951i	0.143112	+	0.313371i
$777$	8.58197	−	2.51989i	0.307876	−	0.0904006i
$778$	−23.1706	+	50.7366i	−0.830708	+	1.81900i
$779$	1.55753	−	10.8329i	0.0558044	−	0.388128i
$780$	−11.2866	+	7.25346i	−0.404125	+	0.259715i
$781$	−5.93112			−0.212232
$782$		0			0
$783$	6.70820			0.239732
$784$	22.3456	−	14.3607i	0.798058	−	0.512881i
$785$	7.09988	−	49.3808i	0.253406	−	1.76247i
$786$	−7.95349	+	17.4157i	−0.283692	+	0.621198i
$787$	−49.3337	+	14.4857i	−1.75856	+	0.516359i	−0.992046	−	0.125874i	$-0.959826\pi$
$787$	−49.3337	+	14.4857i	−1.75856	+	0.516359i	−0.766510	+	0.642233i	$0.778008\pi$
$788$	1.91840	+	4.20071i	0.0683402	+	0.149644i
$789$	21.8831	+	25.2544i	0.779059	+	0.899082i
$790$	−5.17466	−	35.9906i	−0.184106	−	1.28049i
$791$	15.6980	+	4.60934i	0.558155	+	0.163889i
$792$	2.23727	−	2.58195i	0.0794980	−	0.0917456i
$793$	27.6207	+	17.7508i	0.980841	+	0.630348i
$794$	−3.28916	−	2.11381i	−0.116728	−	0.0750164i
$795$	−40.1462	+	46.3312i	−1.42384	+	1.64320i
$796$	15.2449	+	4.47632i	0.540343	+	0.158659i
$797$	−1.47448	−	10.2552i	−0.0522287	−	0.363259i	−0.999129	−	0.0417309i	$-0.986713\pi$
$797$	−1.47448	−	10.2552i	−0.0522287	−	0.363259i	0.946900	−	0.321528i	$-0.104196\pi$
$798$	5.85725	+	6.75963i	0.207344	+	0.239288i
$799$	4.86376	+	10.6502i	0.172068	+	0.376775i
$800$	−17.7569	+	5.21391i	−0.627802	+	0.184339i
$801$	−1.26940	+	2.77959i	−0.0448519	+	0.0982119i
$802$	1.88369	−	13.1013i	0.0665154	−	0.462625i
$803$	−9.94333	+	6.39019i	−0.350893	+	0.225505i
$804$	−10.0000			−0.352673
$805$		0			0
$806$	32.5623			1.14696
$807$	18.7062	−	12.0217i	0.658488	−	0.423185i
$808$	1.42315	−	9.89821i	0.0500662	−	0.348218i
$809$	19.8936	−	43.5610i	0.699422	−	1.53152i	−0.141248	−	0.989974i	$-0.545111\pi$
$809$	19.8936	−	43.5610i	0.699422	−	1.53152i	0.840670	−	0.541547i	$-0.182161\pi$
$810$	55.2637	−	16.2269i	1.94177	−	0.570154i
$811$	−23.1189	−	50.6233i	−0.811813	−	1.77762i	−0.599411	−	0.800441i	$-0.704599\pi$
$811$	−23.1189	−	50.6233i	−0.811813	−	1.77762i	−0.212402	−	0.977182i	$-0.568129\pi$
$812$	−1.50081	−	1.73202i	−0.0526680	−	0.0607821i
$813$	−2.54581	−	17.7065i	−0.0892853	−	0.620993i
$814$	−3.83797	−	1.12693i	−0.134521	−	0.0394989i
$815$	−21.6920	+	25.0339i	−0.759838	+	0.876900i
$816$	−47.8108	−	30.7261i	−1.67371	−	1.07563i
$817$		0			0
$818$	−24.7527	+	28.5661i	−0.865457	+	0.998790i
$819$	7.11599	+	2.08944i	0.248653	+	0.0730111i
$820$	1.55753	+	10.8329i	0.0543914	+	0.378300i
$821$	13.7886	+	15.9129i	0.481224	+	0.555363i	0.943499	−	0.331374i	$-0.107512\pi$
$821$	13.7886	+	15.9129i	0.481224	+	0.555363i	−0.462275	+	0.886737i	$0.652967\pi$
$822$	−20.8743	−	45.7083i	−0.728074	−	1.59426i
$823$	−26.4254	+	7.75920i	−0.921132	+	0.270469i	−0.707720	−	0.706493i	$-0.750276\pi$
$823$	−26.4254	+	7.75920i	−0.921132	+	0.270469i	−0.213412	+	0.976962i	$0.568458\pi$
$824$	16.8876	−	36.9788i	0.588309	−	1.28822i
$825$	1.33029	−	9.25238i	0.0463148	−	0.322127i
$826$	−4.15939	+	2.67308i	−0.144724	+	0.0930082i
$827$	10.4721			0.364152			0.182076	−	0.983284i	$-0.441718\pi$
$827$	10.4721			0.364152			0.182076	+	0.983284i	$0.441718\pi$
$828$		0			0
$829$	−40.2492			−1.39791			−0.698957	−	0.715164i	$-0.746352\pi$
$829$	−40.2492			−1.39791			−0.698957	+	0.715164i	$0.746352\pi$
$830$	−58.3030	+	37.4691i	−2.02373	+	1.30057i
$831$	−2.07733	+	14.4482i	−0.0720619	+	0.501202i
$832$	5.27918	−	11.5598i	0.183023	−	0.400764i
$833$	27.4918	−	8.07234i	0.952536	−	0.279690i
$834$	−4.07039	−	8.91291i	−0.140946	−	0.308629i
$835$	22.1923	+	25.6113i	0.767995	+	0.886314i
$836$	−0.134384	−	0.934661i	−0.00464776	−	0.0323259i
$837$	−14.3924	−	4.22599i	−0.497474	−	0.146072i
$838$	−33.2884	+	38.4169i	−1.14993	+	1.32709i
$839$	−0.736423	−	0.473271i	−0.0254242	−	0.0163391i	0.527867	−	0.849327i	$-0.322992\pi$
$839$	−0.736423	−	0.473271i	−0.0254242	−	0.0163391i	−0.553291	+	0.832988i	$0.686628\pi$
$840$	16.8251	+	10.8128i	0.580520	+	0.373078i
$841$	13.0972	−	15.1150i	0.451628	−	0.521207i
$842$	−36.8068	−	10.8075i	−1.26845	−	0.372449i
$843$	4.21206	+	29.2955i	0.145071	+	1.00899i
$844$	−1.38271	−	1.59573i	−0.0475948	−	0.0549274i
$845$	5.37724	+	11.7745i	0.184983	+	0.405056i
$846$	6.94296	−	2.03864i	0.238704	−	0.0700897i
$847$	5.34863	−	11.7119i	0.183781	−	0.402424i
$848$	−5.85264	+	40.7060i	−0.200981	+	1.39785i
$849$	26.8843	−	17.2775i	0.922667	−	0.592962i
$850$	−46.3607			−1.59016
$851$		0			0
$852$	10.7295			0.367586
$853$	−31.4767	+	20.2288i	−1.07774	+	0.692622i	−0.954035	−	0.299697i	$-0.903115\pi$
$853$	−31.4767	+	20.2288i	−1.07774	+	0.692622i	−0.123707	+	0.992319i	$0.539478\pi$
$854$	−3.11506	+	21.6658i	−0.106595	+	0.741387i
$855$	5.37724	−	11.7745i	0.183898	−	0.402680i
$856$	28.7848	−	8.45198i	0.983844	−	0.288883i
$857$	−3.10404	−	6.79689i	−0.106032	−	0.232177i	0.849178	−	0.528107i	$-0.177098\pi$
$857$	−3.10404	−	6.79689i	−0.106032	−	0.232177i	−0.955210	+	0.295929i	$0.904371\pi$
$858$	−5.42997	−	6.26652i	−0.185376	−	0.213936i
$859$	0.468471	+	3.25829i	0.0159840	+	0.111171i	0.996251	−	0.0865045i	$-0.0275697\pi$
$859$	0.468471	+	3.25829i	0.0159840	+	0.111171i	−0.980267	+	0.197676i	$0.936661\pi$
$860$		0			0
$861$	9.90451	−	11.4304i	0.337545	−	0.389548i
$862$	36.0333	+	23.1572i	1.22730	+	0.788736i
$863$	38.3115	+	24.6213i	1.30414	+	0.838120i	0.993656	−	0.112459i	$-0.0358726\pi$
$863$	38.3115	+	24.6213i	1.30414	+	0.838120i	0.310484	+	0.950579i	$0.399509\pi$
$864$	4.95226	−	5.71521i	0.168479	−	0.194435i
$865$	15.6980	+	4.60934i	0.533747	+	0.156722i
$866$	9.25234	+	64.3514i	0.314407	+	2.18675i
$867$	−15.2529	−	17.6028i	−0.518015	−	0.597821i
$868$	2.12884	+	4.66151i	0.0722576	+	0.158222i
$869$	5.09006	−	1.49458i	0.172669	−	0.0507001i
$870$	−14.5913	+	31.9505i	−0.494691	+	1.08322i
$871$	3.08940	−	21.4872i	0.104680	−	0.728068i
$872$		0			0
$873$	8.58359			0.290511
$874$		0			0
$875$	1.88854			0.0638444
$876$	17.9877	−	11.5600i	0.607747	−	0.390575i
$877$	3.91762	−	27.2477i	0.132289	−	0.920088i	−0.810272	−	0.586054i	$-0.800681\pi$
$877$	3.91762	−	27.2477i	0.132289	−	0.920088i	0.942561	−	0.334035i	$-0.108410\pi$
$878$	3.55691	−	7.78855i	0.120040	−	0.262851i
$879$	22.4679	−	6.59716i	0.757823	−	0.222517i
$880$	−4.98498	−	10.9156i	−0.168044	−	0.367964i
$881$	−14.2888	−	16.4902i	−0.481403	−	0.555569i	0.462145	−	0.886804i	$-0.347080\pi$
$881$	−14.2888	−	16.4902i	−0.481403	−	0.555569i	−0.943548	+	0.331236i	$0.892535\pi$
$882$	−2.52014	−	17.5280i	−0.0848575	−	0.590197i
$883$	−3.83797	−	1.12693i	−0.129158	−	0.0379242i	0.216515	−	0.976279i	$-0.430531\pi$
$883$	−3.83797	−	1.12693i	−0.129158	−	0.0379242i	−0.345673	+	0.938355i	$0.612349\pi$
$884$	−6.35752	+	7.33697i	−0.213827	+	0.246769i
$885$	15.0488	+	9.67128i	0.505860	+	0.325096i
$886$	2.89197	+	1.85856i	0.0971577	+	0.0624395i
$887$	22.9652	−	26.5033i	0.771097	−	0.889894i	−0.225336	−	0.974281i	$-0.572348\pi$
$887$	22.9652	−	26.5033i	0.771097	−	0.889894i	0.996433	+	0.0843876i	$0.0268934\pi$
$888$	−15.5249	−	4.55853i	−0.520982	−	0.152974i
$889$	−3.64280	−	25.3362i	−0.122175	−	0.849749i
$890$	5.23889	+	6.04600i	0.175608	+	0.202662i
$891$	3.49084	+	7.64387i	0.116947	+	0.256079i
$892$	−2.37200	+	0.696481i	−0.0794203	+	0.0233199i
$893$	−1.85779	+	4.06800i	−0.0621687	+	0.136130i
$894$	−6.12141	+	42.5753i	−0.204731	+	1.42393i
$895$	34.5962	−	22.2336i	1.15642	−	0.743189i
$896$	16.8328			0.562345
$897$		0			0
$898$	−4.76393			−0.158974
$899$	16.9299	−	10.8802i	0.564644	−	0.362875i
$900$	−0.962608	+	6.69508i	−0.0320869	+	0.223169i
$901$	−18.4281	+	40.3519i	−0.613929	+	1.34432i
$902$	−6.48995	+	1.90562i	−0.216092	+	0.0634502i
$903$		0			0
$904$	−19.3817	−	22.3677i	−0.644627	−	0.743940i
$905$	−6.74806	−	46.9338i	−0.224313	−	1.56013i
$906$	−0.819505	−	0.240628i	−0.0272262	−	0.00799434i
$907$	−26.3576	+	30.4183i	−0.875191	+	1.01002i	0.124650	+	0.992201i	$0.460219\pi$
$907$	−26.3576	+	30.4183i	−0.875191	+	1.01002i	−0.999841	+	0.0178234i	$0.994326\pi$
$908$	5.29300	+	3.40160i	0.175654	+	0.112886i
$909$	−7.52440	−	4.83564i	−0.249569	−	0.160388i
$910$	12.7150	−	14.6739i	0.421500	−	0.486436i
$911$	30.0369	+	8.81962i	0.995166	+	0.292207i	0.738471	−	0.674285i	$-0.235548\pi$
$911$	30.0369	+	8.81962i	0.995166	+	0.292207i	0.256695	+	0.966492i	$0.417366\pi$
$912$	−3.08940	−	21.4872i	−0.102300	−	0.711514i
$913$	−6.62160	−	7.64173i	−0.219143	−	0.252904i
$914$	−23.6092	−	51.6969i	−0.780923	−	1.70998i
$915$	75.9856	−	22.3114i	2.51201	−	0.737592i
$916$	−3.08089	+	6.74620i	−0.101795	+	0.222901i
$917$	0.930884	−	6.47444i	0.0307405	−	0.213805i
$918$	15.9369	−	10.2420i	0.525997	−	0.338038i
$919$	0.875388			0.0288764			0.0144382	−	0.999896i	$-0.495404\pi$
$919$	0.875388			0.0288764			0.0144382	+	0.999896i	$0.495404\pi$
$920$		0			0
$921$	41.3050			1.36104
$922$	−10.1709	+	6.53644i	−0.334961	+	0.215266i
$923$	−3.31477	+	23.0547i	−0.109107	+	0.758855i
$924$	0.542097	−	1.18703i	0.0178337	−	0.0390503i
$925$	−16.9909	+	4.98898i	−0.558657	+	0.164037i
$926$	13.4431	+	29.4363i	0.441768	+	0.967337i
$927$	−23.8112	−	27.4796i	−0.782062	−	0.902547i
$928$	1.44391	+	10.0426i	0.0473987	+	0.329665i
$929$	40.2452	+	11.8171i	1.32040	+	0.387705i	0.864638	−	0.502395i	$-0.167548\pi$
$929$	40.2452	+	11.8171i	1.32040	+	0.387705i	0.455765	+	0.890100i	$0.349366\pi$
$930$	51.4334	−	59.3573i	1.68657	−	1.94640i
$931$	9.20691	+	5.91692i	0.301744	+	0.193919i
$932$	−8.04432	−	5.16977i	−0.263501	−	0.169342i
$933$	13.4429	−	15.5139i	0.440101	−	0.507903i
$934$	−48.0407	−	14.1060i	−1.57194	−	0.461564i
$935$	−1.84216	−	12.8125i	−0.0602451	−	0.419014i
$936$	−8.78588	−	10.1394i	−0.287175	−	0.331418i
$937$	4.91006	+	10.7515i	0.160405	+	0.351238i	0.972720	−	0.231981i	$-0.0745206\pi$
$937$	4.91006	+	10.7515i	0.160405	+	0.351238i	−0.812316	+	0.583218i	$0.801793\pi$
$938$	13.8859	−	4.07727i	0.453391	−	0.133128i
$939$	−18.9130	+	41.4136i	−0.617201	+	1.35148i
$940$	0.636451	−	4.42662i	0.0207588	−	0.144380i
$941$	−20.7390	+	13.3281i	−0.676072	+	0.434485i	−0.833110	−	0.553108i	$-0.813442\pi$
$941$	−20.7390	+	13.3281i	−0.676072	+	0.434485i	0.157038	+	0.987593i	$0.449805\pi$
$942$	−55.7771			−1.81732
$943$		0			0
$944$	12.0000			0.390567
$945$	−7.52440	+	4.83564i	−0.244769	+	0.157303i
$946$		0			0
$947$	−13.7836	+	30.1819i	−0.447907	+	0.980780i	0.542172	+	0.840268i	$0.317602\pi$
$947$	−13.7836	+	30.1819i	−0.447907	+	0.980780i	−0.990079	+	0.140512i	$0.955125\pi$
$948$	−9.20801	+	2.70372i	−0.299062	+	0.0878126i
$949$	19.2821	+	42.2218i	0.625923	+	1.37058i
$950$	−11.5964	−	13.3830i	−0.376237	−	0.434201i
$951$	0.450737	+	3.13495i	0.0146162	+	0.101658i
$952$	13.8859	+	4.07727i	0.450045	+	0.132145i
$953$	−7.54915	+	8.71218i	−0.244541	+	0.282215i	−0.864730	−	0.502237i	$-0.832510\pi$
$953$	−7.54915	+	8.71218i	−0.244541	+	0.282215i	0.620189	+	0.784452i	$0.287056\pi$
$954$	23.0641	+	14.8224i	0.746729	+	0.479894i
$955$	10.3985	+	6.68269i	0.336486	+	0.216247i
$956$	−7.38061	+	8.51768i	−0.238706	+	0.275482i
$957$	−4.91703	−	1.44377i	−0.158945	−	0.0466705i
$958$	−4.05201	−	28.1823i	−0.130914	−	0.910530i
$959$	11.2421	+	12.9741i	0.363027	+	0.418955i
$960$	−12.7335	−	27.8825i	−0.410972	−	0.899903i
$961$	−13.4329	+	3.94426i	−0.433319	+	0.127234i
$962$	−6.52542	+	14.2887i	−0.210388	+	0.460686i
$963$	3.81871	−	26.5597i	0.123056	−	0.855874i
$964$	8.90348	−	5.72192i	0.286762	−	0.184291i
$965$	25.7082			0.827576
$966$		0			0
$967$	−39.5410			−1.27155			−0.635777	−	0.771873i	$-0.719320\pi$
$967$	−39.5410			−1.27155			−0.635777	+	0.771873i	$0.719320\pi$
$968$	−19.5943	+	12.5925i	−0.629785	+	0.404738i
$969$	3.33250	−	23.1781i	0.107055	−	0.744587i
$970$	9.33526	−	20.4414i	0.299737	−	0.656333i
$971$	−7.22293	+	2.12084i	−0.231795	+	0.0680611i	−0.395567	−	0.918437i	$-0.629452\pi$
$971$	−7.22293	+	2.12084i	−0.231795	+	0.0680611i	0.163772	+	0.986498i	$0.447634\pi$
$972$	−4.59272	−	10.0566i	−0.147311	−	0.322567i
$973$	2.19216	+	2.52989i	0.0702775	+	0.0811045i
$974$	−0.297462	−	2.06890i	−0.00953130	−	0.0662917i
$975$	−35.2213	−	10.3419i	−1.12798	−	0.331206i
$976$	34.7892	−	40.1489i	1.11358	−	1.28514i
$977$	−45.9766	−	29.5474i	−1.47092	−	0.945304i	−0.997935	−	0.0642341i	$-0.979540\pi$
$977$	−45.9766	−	29.5474i	−1.47092	−	0.945304i	−0.472987	−	0.881070i	$-0.656824\pi$
$978$	31.1554	+	20.0223i	0.996238	+	0.640244i
$979$	−0.764343	+	0.882099i	−0.0244285	+	0.0281920i
$980$	−10.5010	−	3.08336i	−0.335441	−	0.0984942i
$981$		0			0
$982$	42.0152	+	48.4882i	1.34076	+	1.54732i
$983$	−13.0971	−	28.6788i	−0.417734	−	0.914710i	−0.995160	−	0.0982671i	$-0.968670\pi$
$983$	−13.0971	−	28.6788i	−0.417734	−	0.914710i	0.577426	−	0.816443i	$-0.304057\pi$
$984$	−26.2524	+	7.70839i	−0.836895	+	0.245735i
$985$	−10.0449	+	21.9952i	−0.320056	+	0.700826i
$986$	−3.61713	+	25.1577i	−0.115193	+	0.801185i
$987$	−5.19923	+	3.34134i	−0.165493	+	0.106356i
$988$	−3.70820			−0.117974
$989$		0			0
$990$	−8.00000			−0.254257
$991$	20.1901	−	12.9754i	0.641359	−	0.412177i	−0.179141	−	0.983824i	$-0.557332\pi$
$991$	20.1901	−	12.9754i	0.641359	−	0.412177i	0.820500	+	0.571647i	$0.193695\pi$
$992$	3.22869	−	22.4560i	0.102511	−	0.712979i
$993$	10.8239	−	23.7011i	0.343487	−	0.752132i
$994$	−14.8989	+	4.37470i	−0.472564	+	0.138757i
$995$	34.5598	+	75.6755i	1.09562	+	2.39907i
$996$	11.9786	+	13.8240i	0.379556	+	0.438031i
$997$	5.24186	+	36.4579i	0.166011	+	1.15463i	0.887028	+	0.461716i	$0.152766\pi$
$997$	5.24186	+	36.4579i	0.166011	+	1.15463i	−0.721017	+	0.692918i	$0.756325\pi$
$998$	50.7792	+	14.9101i	1.60739	+	0.471972i
$999$	4.73862	−	5.46866i	0.149923	−	0.173021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.2.c.o.334.1		20
23.2	even	11	inner	529.2.c.o.255.1		20
23.3	even	11	inner	529.2.c.o.177.2		20
23.4	even	11	inner	529.2.c.o.399.2		20
23.5	odd	22		529.2.a.a.1.1		2
23.6	even	11	inner	529.2.c.o.501.2		20
23.7	odd	22		529.2.c.n.266.2		20
23.8	even	11	inner	529.2.c.o.170.2		20
23.9	even	11	inner	529.2.c.o.466.1		20
23.10	odd	22		529.2.c.n.487.1		20
23.11	odd	22		529.2.c.n.118.2		20
23.12	even	11	inner	529.2.c.o.118.2		20
23.13	even	11	inner	529.2.c.o.487.1		20
23.14	odd	22		529.2.c.n.466.1		20
23.15	odd	22		529.2.c.n.170.2		20
23.16	even	11	inner	529.2.c.o.266.2		20
23.17	odd	22		529.2.c.n.501.2		20
23.18	even	11		23.2.a.a.1.1	✓	2
23.19	odd	22		529.2.c.n.399.2		20
23.20	odd	22		529.2.c.n.177.2		20
23.21	odd	22		529.2.c.n.255.1		20
23.22	odd	2		529.2.c.n.334.1		20
69.5	even	22		4761.2.a.w.1.2		2
69.41	odd	22		207.2.a.d.1.2		2
92.51	even	22		8464.2.a.bb.1.1		2
92.87	odd	22		368.2.a.h.1.1		2
115.18	odd	44		575.2.b.d.24.4		4
115.64	even	22		575.2.a.f.1.2		2
115.87	odd	44		575.2.b.d.24.1		4
161.41	odd	22		1127.2.a.c.1.1		2
184.133	even	22		1472.2.a.t.1.1		2
184.179	odd	22		1472.2.a.s.1.2		2
253.87	odd	22		2783.2.a.c.1.2		2
276.179	even	22		3312.2.a.ba.1.2		2
299.64	even	22		3887.2.a.i.1.2		2
345.179	odd	22		5175.2.a.be.1.1		2
391.271	even	22		6647.2.a.b.1.1		2
437.18	odd	22		8303.2.a.e.1.2		2
460.179	odd	22		9200.2.a.bt.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.a.a.1.1	✓	2	23.18	even	11
207.2.a.d.1.2		2	69.41	odd	22
368.2.a.h.1.1		2	92.87	odd	22
529.2.a.a.1.1		2	23.5	odd	22
529.2.c.n.118.2		20	23.11	odd	22
529.2.c.n.170.2		20	23.15	odd	22
529.2.c.n.177.2		20	23.20	odd	22
529.2.c.n.255.1		20	23.21	odd	22
529.2.c.n.266.2		20	23.7	odd	22
529.2.c.n.334.1		20	23.22	odd	2
529.2.c.n.399.2		20	23.19	odd	22
529.2.c.n.466.1		20	23.14	odd	22
529.2.c.n.487.1		20	23.10	odd	22
529.2.c.n.501.2		20	23.17	odd	22
529.2.c.o.118.2		20	23.12	even	11	inner
529.2.c.o.170.2		20	23.8	even	11	inner
529.2.c.o.177.2		20	23.3	even	11	inner
529.2.c.o.255.1		20	23.2	even	11	inner
529.2.c.o.266.2		20	23.16	even	11	inner
529.2.c.o.334.1		20	1.1	even	1	trivial
529.2.c.o.399.2		20	23.4	even	11	inner
529.2.c.o.466.1		20	23.9	even	11	inner
529.2.c.o.487.1		20	23.13	even	11	inner
529.2.c.o.501.2		20	23.6	even	11	inner
575.2.a.f.1.2		2	115.64	even	22
575.2.b.d.24.1		4	115.87	odd	44
575.2.b.d.24.4		4	115.18	odd	44
1127.2.a.c.1.1		2	161.41	odd	22
1472.2.a.s.1.2		2	184.179	odd	22
1472.2.a.t.1.1		2	184.133	even	22
2783.2.a.c.1.2		2	253.87	odd	22
3312.2.a.ba.1.2		2	276.179	even	22
3887.2.a.i.1.2		2	299.64	even	22
4761.2.a.w.1.2		2	69.5	even	22
5175.2.a.be.1.1		2	345.179	odd	22
6647.2.a.b.1.1		2	391.271	even	22
8303.2.a.e.1.2		2	437.18	odd	22
8464.2.a.bb.1.1		2	92.51	even	22
9200.2.a.bt.1.2		2	460.179	odd	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+(-1.36118 + 0.874775i) q^{2} +(-0.318226 + 2.21331i) q^{3} +(0.256741 - 0.562183i) q^{4} +(3.10498 - 0.911706i) q^{5} +(-1.50299 - 3.29108i) q^{6} +(0.809452 + 0.934158i) q^{7} +(-0.318226 - 2.21331i) q^{8} +(-1.91899 - 0.563465i) q^{9} +(-3.42890 + 3.95716i) q^{10} +(-0.642661 - 0.413013i) q^{11} +(1.16258 + 0.747147i) q^{12} +(-1.96458 + 2.26725i) q^{13} +(-1.91899 - 0.563465i) q^{14} +(1.02980 + 7.16242i) q^{15} +(3.17876 + 3.66849i) q^{16} +(2.17514 + 4.76289i) q^{17} +(3.10498 - 0.911706i) q^{18} +(-0.830830 + 1.81926i) q^{19} +(0.284630 - 1.97964i) q^{20} +(-2.32517 + 1.49429i) q^{21} +1.23607 q^{22} +5.00000 q^{24} +(4.60345 - 2.95846i) q^{25} +(0.690811 - 4.80469i) q^{26} +(-0.928896 + 2.03400i) q^{27} +(0.732987 - 0.215225i) q^{28} +(-1.24625 - 2.72890i) q^{29} +(-7.66724 - 8.84847i) q^{30} +(0.954677 + 6.63992i) q^{31} +(-3.24497 - 0.952810i) q^{32} +(1.11864 - 1.29097i) q^{33} +(-7.12721 - 4.58038i) q^{34} +(3.36501 + 2.16256i) q^{35} +(-0.809452 + 0.934158i) q^{36} +(-3.10498 - 0.911706i) q^{37} +(-0.460540 - 3.20313i) q^{38} +(-4.39294 - 5.06972i) q^{39} +(-3.00597 - 6.58216i) q^{40} +(-5.25048 + 1.54168i) q^{41} +(1.85779 - 4.06800i) q^{42} +(-0.397186 + 0.255256i) q^{44} -6.47214 q^{45} +2.23607 q^{47} +(-9.13105 + 5.86817i) q^{48} +(0.778766 - 5.41644i) q^{49} +(-3.67813 + 8.05397i) q^{50} +(-11.2339 + 3.29858i) q^{51} +(0.770222 + 1.68655i) q^{52} +(5.54807 + 6.40281i) q^{53} +(-0.514900 - 3.58121i) q^{54} +(-2.37200 - 0.696481i) q^{55} +(1.80999 - 2.08884i) q^{56} +(-3.76220 - 2.41782i) q^{57} +(4.08353 + 2.62433i) q^{58} +(1.61890 - 1.86832i) q^{59} +(4.29098 + 1.25995i) q^{60} +(-1.55753 - 10.8329i) q^{61} +(-7.10793 - 8.20298i) q^{62} +(-1.02696 - 2.24873i) q^{63} +(-4.06448 + 1.19344i) q^{64} +(-4.03293 + 8.83089i) q^{65} +(-0.393349 + 2.73580i) q^{66} +(-6.08737 + 3.91211i) q^{67} +3.23607 q^{68} -6.47214 q^{70} +(6.53144 - 4.19750i) q^{71} +(-0.636451 + 4.42662i) q^{72} +(6.42736 - 14.0739i) q^{73} +(5.02397 - 1.47517i) q^{74} +(5.08305 + 11.1303i) q^{75} +(0.809452 + 0.934158i) q^{76} +(-0.134384 - 0.934661i) q^{77} +(10.4144 + 3.05795i) q^{78} +(-4.54753 + 5.24813i) q^{79} +(13.2146 + 8.49250i) q^{80} +(-9.25379 - 5.94705i) q^{81} +(5.79820 - 6.69148i) q^{82} +(12.6999 + 3.72903i) q^{83} +(0.243103 + 1.69082i) q^{84} +(11.0961 + 12.8056i) q^{85} +(6.43647 - 1.88992i) q^{87} +(-0.709614 + 1.55384i) q^{88} +(0.217438 - 1.51231i) q^{89} +(8.80972 - 5.66166i) q^{90} -3.70820 q^{91} -15.0000 q^{93} +(-3.04368 + 1.95606i) q^{94} +(-0.921081 + 6.40626i) q^{95} +(3.14150 - 6.87892i) q^{96} +(-4.11795 + 1.20914i) q^{97} +(3.67813 + 8.05397i) q^{98} +(1.00054 + 1.15468i) 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

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