LMFDB - Embedded newform 529.2.c.n.177.1

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			177.1
Root			$-0.592999 - 0.174120i$ of defining polynomial
Character	$\chi$	$=$	529.177
Dual form			529.2.c.n.266.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.404726 + 0.467079i) q^{2} +(-1.88110 + 1.20891i) q^{3} +(0.230270 + 1.60156i) q^{4} +(-0.513481 - 1.12437i) q^{5} +(0.196674 - 1.36790i) q^{6} +(3.10498 - 0.911706i) q^{7} +(-1.88110 - 1.20891i) q^{8} +(0.830830 - 1.81926i) q^{9} +O(q^{10})$	\(q+(-0.404726 + 0.467079i) q^{2} +(-1.88110 + 1.20891i) q^{3} +(0.230270 + 1.60156i) q^{4} +(-0.513481 - 1.12437i) q^{5} +(0.196674 - 1.36790i) q^{6} +(3.10498 - 0.911706i) q^{7} +(-1.88110 - 1.20891i) q^{8} +(0.830830 - 1.81926i) q^{9} +(0.732987 + 0.215225i) q^{10} +(-3.42890 - 3.95716i) q^{11} +(-2.36931 - 2.73433i) q^{12} +(-2.87848 - 0.845198i) q^{13} +(-0.830830 + 1.81926i) q^{14} +(2.32517 + 1.49429i) q^{15} +(-1.77900 + 0.522361i) q^{16} +(0.108719 - 0.756156i) q^{17} +(0.513481 + 1.12437i) q^{18} +(-0.284630 - 1.97964i) q^{19} +(1.68251 - 1.08128i) q^{20} +(-4.73862 + 5.46866i) q^{21} +3.23607 q^{22} +5.00000 q^{24} +(2.27377 - 2.62407i) q^{25} +(1.55977 - 1.00240i) q^{26} +(-0.318226 - 2.21331i) q^{27} +(2.17514 + 4.76289i) q^{28} +(0.426945 - 2.96946i) q^{29} +(-1.63901 + 0.481257i) q^{30} +(5.64330 + 3.62673i) q^{31} +(2.33382 - 5.11034i) q^{32} +(11.2339 + 3.29858i) q^{33} +(0.309183 + 0.356817i) q^{34} +(-2.61944 - 3.02300i) q^{35} +(3.10498 + 0.911706i) q^{36} +(0.513481 - 1.12437i) q^{37} +(1.03985 + 0.668269i) q^{38} +(6.43647 - 1.88992i) q^{39} +(-0.393349 + 2.73580i) q^{40} +(-1.44238 - 3.15837i) q^{41} +(-0.636451 - 4.42662i) q^{42} +(5.54807 - 6.40281i) q^{44} -2.47214 q^{45} -2.23607 q^{47} +(2.71499 - 3.13326i) q^{48} +(2.92095 - 1.87718i) q^{49} +(0.305393 + 2.12406i) q^{50} +(0.709614 + 1.55384i) q^{51} +(0.690811 - 4.80469i) q^{52} +(0.453011 - 0.133016i) q^{53} +(1.16258 + 0.747147i) q^{54} +(-2.68862 + 5.88726i) q^{55} +(-6.94296 - 2.03864i) q^{56} +(2.92863 + 3.37981i) q^{57} +(1.21418 + 1.40124i) q^{58} +(-6.20997 - 1.82341i) q^{59} +(-1.85779 + 4.06800i) q^{60} +(5.84189 + 3.75436i) q^{61} +(-3.97796 + 1.16803i) q^{62} +(0.921081 - 6.40626i) q^{63} +(-0.0980662 - 0.214735i) q^{64} +(0.527732 + 3.67046i) q^{65} +(-6.08737 + 3.91211i) q^{66} +(-1.80999 + 2.08884i) q^{67} +1.23607 q^{68} +2.47214 q^{70} +(-8.01292 + 9.24740i) q^{71} +(-3.76220 + 2.41782i) q^{72} +(-0.929012 - 6.46142i) q^{73} +(0.317349 + 0.694897i) q^{74} +(-1.10492 + 7.68491i) q^{75} +(3.10498 - 0.911706i) q^{76} +(-14.2544 - 9.16077i) q^{77} +(-1.72227 + 3.77124i) q^{78} +(-10.5010 - 3.08336i) q^{79} +(1.50081 + 1.73202i) q^{80} +(7.20347 + 8.31325i) q^{81} +(2.05897 + 0.604569i) q^{82} +(3.64067 - 7.97195i) q^{83} +(-9.84957 - 6.32993i) q^{84} +(-0.906022 + 0.266032i) q^{85} +(2.78669 + 6.10200i) q^{87} +(1.66625 + 11.5890i) q^{88} +(8.80972 - 5.66166i) q^{89} +(1.00054 - 1.15468i) q^{90} -9.70820 q^{91} -15.0000 q^{93} +(0.904995 - 1.04442i) q^{94} +(-2.07969 + 1.33654i) q^{95} +(1.78780 + 12.4344i) q^{96} +(-7.35625 - 16.1079i) q^{97} +(-0.305393 + 2.12406i) q^{98} +(-10.0479 + 2.95034i) 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}+O(q^{10}) $ 20 * q + q^2 + q^4 - 2 * q^5 + 5 * q^6 + 2 * q^7 - 4 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$
$\chi(n)$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−0.404726	+	0.467079i	−0.286185	+	0.330275i	−0.880579	−	0.473899i	$-0.842846\pi$
$2$	−0.404726	+	0.467079i	−0.286185	+	0.330275i	0.594395	+	0.804173i	$0.297392\pi$
$3$	−1.88110	+	1.20891i	−1.08605	+	0.697964i	−0.955948	−	0.293536i	$-0.905168\pi$
$3$	−1.88110	+	1.20891i	−1.08605	+	0.697964i	−0.130106	+	0.991500i	$0.541532\pi$
$4$	0.230270	+	1.60156i	0.115135	+	0.800782i
$5$	−0.513481	−	1.12437i	−0.229636	−	0.502832i	0.759379	−	0.650648i	$-0.225503\pi$
$5$	−0.513481	−	1.12437i	−0.229636	−	0.502832i	−0.989015	+	0.147816i	$0.952776\pi$
$6$	0.196674	−	1.36790i	0.0802919	−	0.558443i
$7$	3.10498	−	0.911706i	1.17357	−	0.344592i	0.363881	−	0.931446i	$-0.381452\pi$
$7$	3.10498	−	0.911706i	1.17357	−	0.344592i	0.809693	+	0.586853i	$0.199633\pi$
$8$	−1.88110	−	1.20891i	−0.665069	−	0.427414i
$9$	0.830830	−	1.81926i	0.276943	−	0.606421i
$10$	0.732987	+	0.215225i	0.231791	+	0.0680600i
$11$	−3.42890	−	3.95716i	−1.03385	−	1.19313i	−0.980896	−	0.194531i	$-0.937682\pi$
$11$	−3.42890	−	3.95716i	−1.03385	−	1.19313i	−0.0529544	−	0.998597i	$-0.516864\pi$
$12$	−2.36931	−	2.73433i	−0.683960	−	0.789332i
$13$	−2.87848	−	0.845198i	−0.798346	−	0.234416i	−0.142979	−	0.989726i	$-0.545668\pi$
$13$	−2.87848	−	0.845198i	−0.798346	−	0.234416i	−0.655368	+	0.755310i	$0.727486\pi$
$14$	−0.830830	+	1.81926i	−0.222049	+	0.486219i
$15$	2.32517	+	1.49429i	0.600356	+	0.385825i
$16$	−1.77900	+	0.522361i	−0.444749	+	0.130590i
$17$	0.108719	−	0.756156i	0.0263682	−	0.183395i	−0.972381	−	0.233400i	$-0.925015\pi$
$17$	0.108719	−	0.756156i	0.0263682	−	0.183395i	0.998749	+	0.0500054i	$0.0159239\pi$
$18$	0.513481	+	1.12437i	0.121029	+	0.265016i
$19$	−0.284630	−	1.97964i	−0.0652985	−	0.454161i	−0.996071	−	0.0885615i	$-0.971773\pi$
$19$	−0.284630	−	1.97964i	−0.0652985	−	0.454161i	0.930772	−	0.365600i	$-0.119136\pi$
$20$	1.68251	−	1.08128i	0.376220	−	0.241782i
$21$	−4.73862	+	5.46866i	−1.03405	+	1.19336i
$22$	3.23607			0.689932
$23$		0			0
$23$		0			0
$24$	5.00000			1.02062
$25$	2.27377	−	2.62407i	0.454753	−	0.524813i
$26$	1.55977	−	1.00240i	0.305896	−	0.196587i
$27$	−0.318226	−	2.21331i	−0.0612426	−	0.425951i
$28$	2.17514	+	4.76289i	0.411063	+	0.900103i
$29$	0.426945	−	2.96946i	0.0792816	−	0.551416i	−0.911007	−	0.412390i	$-0.864694\pi$
$29$	0.426945	−	2.96946i	0.0792816	−	0.551416i	0.990289	−	0.139025i	$-0.0443969\pi$
$30$	−1.63901	+	0.481257i	−0.299241	+	0.0878650i
$31$	5.64330	+	3.62673i	1.01357	+	0.651380i	0.938314	−	0.345785i	$-0.112387\pi$
$31$	5.64330	+	3.62673i	1.01357	+	0.651380i	0.0752528	+	0.997164i	$0.476024\pi$
$32$	2.33382	−	5.11034i	0.412564	−	0.903390i
$33$	11.2339	+	3.29858i	1.95558	+	0.574209i
$34$	0.309183	+	0.356817i	0.0530245	+	0.0611935i
$35$	−2.61944	−	3.02300i	−0.442767	−	0.510980i
$36$	3.10498	+	0.911706i	0.517497	+	0.151951i
$37$	0.513481	−	1.12437i	0.0844158	−	0.184845i	−0.862717	−	0.505688i	$-0.831239\pi$
$37$	0.513481	−	1.12437i	0.0844158	−	0.184845i	0.947132	+	0.320843i	$0.103966\pi$
$38$	1.03985	+	0.668269i	0.168685	+	0.108408i
$39$	6.43647	−	1.88992i	1.03066	−	0.302629i
$40$	−0.393349	+	2.73580i	−0.0621939	+	0.432568i
$41$	−1.44238	−	3.15837i	−0.225262	−	0.493254i	0.762929	−	0.646482i	$-0.223760\pi$
$41$	−1.44238	−	3.15837i	−0.225262	−	0.493254i	−0.988191	+	0.153228i	$0.951033\pi$
$42$	−0.636451	−	4.42662i	−0.0982066	−	0.683042i
$43$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$43$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$44$	5.54807	−	6.40281i	0.836403	−	0.965260i
$45$	−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	$0.552144\pi$
$48$	2.71499	−	3.13326i	0.391874	−	0.452247i
$49$	2.92095	−	1.87718i	0.417278	−	0.268168i
$50$	0.305393	+	2.12406i	0.0431891	+	0.300387i
$51$	0.709614	+	1.55384i	0.0993658	+	0.217581i
$52$	0.690811	−	4.80469i	0.0957982	−	0.666291i
$53$	0.453011	−	0.133016i	0.0622259	−	0.0182712i	−0.250471	−	0.968124i	$-0.580586\pi$
$53$	0.453011	−	0.133016i	0.0622259	−	0.0182712i	0.312697	+	0.949853i	$0.398767\pi$
$54$	1.16258	+	0.747147i	0.158208	+	0.101674i
$55$	−2.68862	+	5.88726i	−0.362534	+	0.793838i
$56$	−6.94296	−	2.03864i	−0.927792	−	0.272424i
$57$	2.92863	+	3.37981i	0.387906	+	0.447667i
$58$	1.21418	+	1.40124i	0.159429	+	0.183991i
$59$	−6.20997	−	1.82341i	−0.808469	−	0.237388i	−0.148725	−	0.988879i	$-0.547517\pi$
$59$	−6.20997	−	1.82341i	−0.808469	−	0.237388i	−0.659744	+	0.751491i	$0.729335\pi$
$60$	−1.85779	+	4.06800i	−0.239840	+	0.525176i
$61$	5.84189	+	3.75436i	0.747978	+	0.480696i	0.858267	−	0.513203i	$-0.171541\pi$
$61$	5.84189	+	3.75436i	0.747978	+	0.480696i	−0.110289	+	0.993900i	$0.535178\pi$
$62$	−3.97796	+	1.16803i	−0.505201	+	0.148341i
$63$	0.921081	−	6.40626i	0.116045	−	0.807113i
$64$	−0.0980662	−	0.214735i	−0.0122583	−	0.0268419i
$65$	0.527732	+	3.67046i	0.0654572	+	0.455265i
$66$	−6.08737	+	3.91211i	−0.749303	+	0.481548i
$67$	−1.80999	+	2.08884i	−0.221126	+	0.255192i	−0.855463	−	0.517864i	$-0.826727\pi$
$67$	−1.80999	+	2.08884i	−0.221126	+	0.255192i	0.634338	+	0.773056i	$0.281273\pi$
$68$	1.23607			0.149895
$69$		0			0
$70$	2.47214			0.295477
$71$	−8.01292	+	9.24740i	−0.950959	+	1.09746i	0.0441841	+	0.999023i	$0.485931\pi$
$71$	−8.01292	+	9.24740i	−0.950959	+	1.09746i	−0.995143	+	0.0984414i	$0.968614\pi$
$72$	−3.76220	+	2.41782i	−0.443380	+	0.284943i
$73$	−0.929012	−	6.46142i	−0.108733	−	0.756252i	−0.969116	−	0.246605i	$-0.920685\pi$
$73$	−0.929012	−	6.46142i	−0.108733	−	0.756252i	0.860384	−	0.509647i	$-0.170224\pi$
$74$	0.317349	+	0.694897i	0.0368911	+	0.0807801i
$75$	−1.10492	+	7.68491i	−0.127585	+	0.887377i
$76$	3.10498	−	0.911706i	0.356166	−	0.104580i
$77$	−14.2544	−	9.16077i	−1.62444	−	1.04397i
$78$	−1.72227	+	3.77124i	−0.195008	+	0.427009i
$79$	−10.5010	−	3.08336i	−1.18145	−	0.346905i	−0.368717	−	0.929542i	$-0.620203\pi$
$79$	−10.5010	−	3.08336i	−1.18145	−	0.346905i	−0.812733	+	0.582637i	$0.802021\pi$
$80$	1.50081	+	1.73202i	0.167795	+	0.193646i
$81$	7.20347	+	8.31325i	0.800385	+	0.923694i
$82$	2.05897	+	0.604569i	0.227376	+	0.0667635i
$83$	3.64067	−	7.97195i	0.399615	−	0.875036i	−0.597694	−	0.801724i	$-0.703916\pi$
$83$	3.64067	−	7.97195i	0.399615	−	0.875036i	0.997309	−	0.0733110i	$-0.0233566\pi$
$84$	−9.84957	−	6.32993i	−1.07468	−	0.690652i
$85$	−0.906022	+	0.266032i	−0.0982719	+	0.0288552i
$86$		0			0
$87$	2.78669	+	6.10200i	0.298764	+	0.654203i
$88$	1.66625	+	11.5890i	0.177623	+	1.23539i
$89$	8.80972	−	5.66166i	0.933829	−	0.600135i	0.0171900	−	0.999852i	$-0.494528\pi$
$89$	8.80972	−	5.66166i	0.933829	−	0.600135i	0.916639	+	0.399717i	$0.130892\pi$
$90$	1.00054	−	1.15468i	0.105466	−	0.121714i
$91$	−9.70820			−1.01770
$92$		0			0
$93$	−15.0000			−1.55543
$94$	0.904995	−	1.04442i	0.0933431	−	0.107724i
$95$	−2.07969	+	1.33654i	−0.213372	+	0.137126i
$96$	1.78780	+	12.4344i	0.182467	+	1.26908i
$97$	−7.35625	−	16.1079i	−0.746914	−	1.63551i	−0.771833	−	0.635825i	$-0.780660\pi$
$97$	−7.35625	−	16.1079i	−0.746914	−	1.63551i	0.0249189	−	0.999689i	$-0.492067\pi$
$98$	−0.305393	+	2.12406i	−0.0308494	+	0.214562i
$99$	−10.0479	+	2.95034i	−1.00986	+	0.296520i
$100$	4.72619	+	3.03734i	0.472619	+	0.303734i
$101$	1.85779	−	4.06800i	0.184857	−	0.404781i	−0.794402	−	0.607392i	$-0.792216\pi$
$101$	1.85779	−	4.06800i	0.184857	−	0.404781i	0.979259	+	0.202611i	$0.0649429\pi$
$102$	−1.01296	−	0.297433i	−0.100298	−	0.0294503i
$103$	−2.73754	−	3.15929i	−0.269738	−	0.311294i	0.604679	−	0.796469i	$-0.293301\pi$
$103$	−2.73754	−	3.15929i	−0.269738	−	0.311294i	−0.874417	+	0.485175i	$0.838756\pi$
$104$	4.39294	+	5.06972i	0.430763	+	0.497127i
$105$	8.58197	+	2.51989i	0.837514	+	0.245916i
$106$	−0.121216	+	0.265427i	−0.0117736	+	0.0257806i
$107$	−11.2866	−	7.25346i	−1.09112	−	0.701218i	−0.134018	−	0.990979i	$-0.542788\pi$
$107$	−11.2866	−	7.25346i	−1.09112	−	0.701218i	−0.957099	+	0.289761i	$0.906424\pi$
$108$	3.47148	−	1.01932i	0.334043	−	0.0980839i
$109$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$109$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$110$	−1.66166	−	3.63853i	−0.158433	−	0.346920i
$111$	0.393349	+	2.73580i	0.0373350	+	0.259671i
$112$	−5.04752	+	3.24384i	−0.476946	+	0.306515i
$113$	5.73915	−	6.62334i	0.539894	−	0.623071i	−0.418604	−	0.908169i	$-0.637481\pi$
$113$	5.73915	−	6.62334i	0.539894	−	0.623071i	0.958499	+	0.285098i	$0.0920260\pi$
$114$	−2.76393			−0.258866
$115$		0			0
$116$	4.85410			0.450692
$117$	−3.92916	+	4.53450i	−0.363251	+	0.419214i
$118$	3.36501	−	2.16256i	0.309775	−	0.199080i
$119$	−0.351822	−	2.44697i	−0.0322514	−	0.224314i
$120$	−2.56741	−	5.62183i	−0.234371	−	0.513201i
$121$	−2.33630	+	16.2493i	−0.212391	+	1.47721i
$122$	−4.11795	+	1.20914i	−0.372822	+	0.109470i
$123$	6.53144	+	4.19750i	0.588920	+	0.378476i
$124$	−4.50896	+	9.87324i	−0.404916	+	0.886643i
$125$	−10.0479	−	2.95034i	−0.898715	−	0.263887i
$126$	2.61944	+	3.02300i	0.233359	+	0.269310i
$127$	4.77511	+	5.51077i	0.423723	+	0.489002i	0.926967	−	0.375142i	$-0.122406\pi$
$127$	4.77511	+	5.51077i	0.423723	+	0.489002i	−0.503245	+	0.864144i	$0.667861\pi$
$128$	10.9209	+	3.20667i	0.965282	+	0.283432i
$129$		0			0
$130$	−1.92798	−	1.23904i	−0.169095	−	0.108671i
$131$	−17.9504	+	5.27071i	−1.56833	+	0.460504i	−0.946516	−	0.322658i	$-0.895424\pi$
$131$	−17.9504	+	5.27071i	−1.56833	+	0.460504i	−0.621817	+	0.783162i	$0.713605\pi$
$132$	−2.69605	+	18.7514i	−0.234661	+	1.63210i
$133$	−2.68862	−	5.88726i	−0.233133	−	0.510490i
$134$	−0.243103	−	1.69082i	−0.0210009	−	0.146064i
$135$	−2.32517	+	1.49429i	−0.200119	+	0.128608i
$136$	−1.11864	+	1.29097i	−0.0959222	+	0.110700i
$137$	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	$0.650049\pi$
$140$	4.23835	−	4.89131i	0.358206	−	0.413391i
$141$	4.20627	−	2.70320i	0.354232	−	0.227651i
$142$	−1.07623	−	7.48533i	−0.0903151	−	0.628155i
$143$	6.52542	+	14.2887i	0.545683	+	1.19488i
$144$	−0.527732	+	3.67046i	−0.0439777	+	0.305872i
$145$	−3.55800	+	1.04472i	−0.295475	+	0.0867594i
$146$	3.39399	+	2.18118i	0.280888	+	0.180516i
$147$	−3.22525	+	7.06232i	−0.266014	+	0.582490i
$148$	1.91899	+	0.563465i	0.157740	+	0.0463165i
$149$	15.6437	+	18.0538i	1.28158	+	1.47902i	0.796614	+	0.604488i	$0.206622\pi$
$149$	15.6437	+	18.0538i	1.28158	+	1.47902i	0.484965	+	0.874534i	$0.338832\pi$
$150$	−3.14227	−	3.62637i	−0.256565	−	0.296092i
$151$	−4.06448	−	1.19344i	−0.330762	−	0.0971206i	0.112135	−	0.993693i	$-0.464231\pi$
$151$	−4.06448	−	1.19344i	−0.330762	−	0.0971206i	−0.442897	+	0.896572i	$0.646049\pi$
$152$	−1.85779	+	4.06800i	−0.150687	+	0.329958i
$153$	−1.28532	−	0.826026i	−0.103912	−	0.0667802i
$154$	10.0479	−	2.95034i	0.809686	−	0.237745i
$155$	1.18005	−	8.20740i	0.0947835	−	0.659234i
$156$	4.50896	+	9.87324i	0.361005	+	0.790492i
$157$	−1.62472	−	11.3002i	−0.129667	−	0.901855i	−0.945975	−	0.324238i	$-0.894892\pi$
$157$	−1.62472	−	11.3002i	−0.129667	−	0.901855i	0.816308	−	0.577616i	$-0.196017\pi$
$158$	5.69018	−	3.65686i	0.452687	−	0.290924i
$159$	−0.691355	+	0.797866i	−0.0548280	+	0.0632749i
$160$	−6.94427			−0.548993
$161$		0			0
$162$	−6.79837			−0.534131
$163$	3.77457	−	4.35609i	0.295647	−	0.341195i	−0.588419	−	0.808556i	$-0.700250\pi$
$163$	3.77457	−	4.35609i	0.295647	−	0.341195i	0.884067	+	0.467361i	$0.154795\pi$
$164$	4.72619	−	3.03734i	0.369054	−	0.237176i
$165$	−2.05960	−	14.3248i	−0.160340	−	1.11519i
$166$	2.25006	+	4.92694i	0.174638	+	0.382405i
$167$	−0.217438	+	1.51231i	−0.0168258	+	0.117026i	−0.996503	−	0.0835528i	$-0.973373\pi$
$167$	−0.217438	+	1.51231i	−0.0168258	+	0.117026i	0.979678	+	0.200579i	$0.0642824\pi$
$168$	15.5249	−	4.55853i	1.19777	−	0.351698i
$169$	−3.36501	−	2.16256i	−0.258847	−	0.166351i
$170$	0.242433	−	0.530854i	0.0185938	−	0.0407146i
$171$	−3.83797	−	1.12693i	−0.293497	−	0.0861785i
$172$		0			0
$173$	−15.0253	−	17.3401i	−1.14235	−	1.31835i	−0.940837	−	0.338860i	$-0.889959\pi$
$173$	−15.0253	−	17.3401i	−1.14235	−	1.31835i	−0.201516	−	0.979485i	$-0.564587\pi$
$174$	−3.97796	−	1.16803i	−0.301568	−	0.0885485i
$175$	4.66763	−	10.2207i	0.352840	−	0.772611i
$176$	8.16706	+	5.24865i	0.615615	+	0.395632i
$177$	13.8859	−	4.07727i	1.04373	−	0.306467i
$178$	−0.921081	+	6.40626i	−0.0690379	+	0.480169i
$179$	0.294199	+	0.644205i	0.0219894	+	0.0481501i	0.920308	−	0.391194i	$-0.127938\pi$
$179$	0.294199	+	0.644205i	0.0219894	+	0.0481501i	−0.898319	+	0.439345i	$0.855211\pi$
$180$	−0.569259	−	3.95929i	−0.0424301	−	0.295108i
$181$	−14.0090	+	9.00301i	−1.04128	+	0.669188i	−0.945302	−	0.326195i	$-0.894233\pi$
$181$	−14.0090	+	9.00301i	−1.04128	+	0.669188i	−0.0959750	+	0.995384i	$0.530597\pi$
$182$	3.92916	−	4.53450i	0.291249	−	0.336119i
$183$	−15.5279			−1.14785
$184$		0			0
$185$	−1.52786			−0.112331
$186$	6.07089	−	7.00618i	0.445139	−	0.513718i
$187$	−3.36501	+	2.16256i	−0.246074	+	0.158142i
$188$	−0.514900	−	3.58121i	−0.0375529	−	0.261186i
$189$	−3.00597	−	6.58216i	−0.218652	−	0.478782i
$190$	0.217438	−	1.51231i	0.0157746	−	0.109715i
$191$	−25.1199	+	7.37585i	−1.81761	+	0.533698i	−0.999164	−	0.0408869i	$-0.986982\pi$
$191$	−25.1199	+	7.37585i	−1.81761	+	0.533698i	−0.818445	+	0.574585i	$0.805163\pi$
$192$	0.444067	+	0.285385i	0.0320478	+	0.0205959i
$193$	4.13100	−	9.04563i	0.297356	−	0.651119i	−0.700699	−	0.713457i	$-0.747128\pi$
$193$	4.13100	−	9.04563i	0.297356	−	0.651119i	0.998055	+	0.0623383i	$0.0198558\pi$
$194$	10.5010	+	3.08336i	0.753924	+	0.221372i
$195$	−5.42997	−	6.26652i	−0.388848	−	0.448755i
$196$	3.67903	+	4.24583i	0.262788	+	0.303273i
$197$	1.41250	+	0.414749i	0.100637	+	0.0295496i	0.331663	−	0.943398i	$-0.392390\pi$
$197$	1.41250	+	0.414749i	0.100637	+	0.0295496i	−0.231026	+	0.972947i	$0.574208\pi$
$198$	2.68862	−	5.88726i	0.191072	−	0.418389i
$199$	10.3405	+	6.64545i	0.733020	+	0.471083i	0.853144	−	0.521676i	$-0.174693\pi$
$199$	10.3405	+	6.64545i	0.733020	+	0.471083i	−0.120124	+	0.992759i	$0.538329\pi$
$200$	−7.44944	+	2.18735i	−0.526755	+	0.154669i
$201$	0.879554	−	6.11743i	0.0620390	−	0.431490i
$202$	1.14818	+	2.51416i	0.0807856	+	0.176896i
$203$	−1.38162	−	9.60939i	−0.0969708	−	0.674447i
$204$	−2.32517	+	1.49429i	−0.162794	+	0.104622i
$205$	−2.81053	+	3.24352i	−0.196296	+	0.226537i
$206$	2.58359			0.180007
$207$		0			0
$208$	5.56231			0.385677
$209$	−6.85779	+	7.91431i	−0.474363	+	0.547444i
$210$	−4.65034	+	2.98859i	−0.320904	+	0.206232i
$211$	3.33250	+	23.1781i	0.229419	+	1.59564i	0.700565	+	0.713588i	$0.252931\pi$
$211$	3.33250	+	23.1781i	0.229419	+	1.59564i	−0.471146	+	0.882055i	$0.656160\pi$
$212$	0.317349	+	0.694897i	0.0217956	+	0.0477257i
$213$	3.89383	−	27.0822i	0.266801	−	1.85564i
$214$	7.95592	−	2.33607i	0.543855	−	0.159690i
$215$		0			0
$216$	−2.07708	+	4.54816i	−0.141327	+	0.309463i
$217$	20.8289	+	6.11591i	1.41396	+	0.415175i
$218$		0			0
$219$	9.55884	+	11.0315i	0.645926	+	0.745439i
$220$	−10.0479	−	2.95034i	−0.677432	−	0.198912i
$221$	−0.952046	+	2.08469i	−0.0640416	+	0.140231i
$222$	−1.43703	−	0.923525i	−0.0964473	−	0.0619829i
$223$	−3.83797	+	1.12693i	−0.257010	+	0.0754648i	−0.407699	−	0.913116i	$-0.633669\pi$
$223$	−3.83797	+	1.12693i	−0.257010	+	0.0754648i	0.150690	+	0.988581i	$0.451851\pi$
$224$	2.58733	−	17.9953i	0.172873	−	1.20236i
$225$	−2.88475	−	6.31673i	−0.192317	−	0.421115i
$226$	0.770835	+	5.36128i	0.0512752	+	0.356627i
$227$	10.2468	−	6.58519i	0.680101	−	0.437074i	−0.154453	−	0.988000i	$-0.549362\pi$
$227$	10.2468	−	6.58519i	0.680101	−	0.437074i	0.834554	+	0.550926i	$0.185725\pi$
$228$	−4.73862	+	5.46866i	−0.313823	+	0.362171i
$229$	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
$232$	−4.39294	+	5.06972i	−0.288411	+	0.332844i
$233$	−5.49159	+	3.52923i	−0.359766	+	0.231208i	−0.708020	−	0.706193i	$-0.750411\pi$
$233$	−5.49159	+	3.52923i	−0.359766	+	0.231208i	0.348254	+	0.937400i	$0.386775\pi$
$234$	−0.527732	−	3.67046i	−0.0344989	−	0.239945i
$235$	1.14818	+	2.51416i	0.0748989	+	0.164006i
$236$	1.49034	−	10.3655i	0.0970129	−	0.674739i
$237$	23.4808	−	6.89460i	1.52524	−	0.447852i
$238$	1.28532	+	0.826026i	0.0833150	+	0.0535433i
$239$	5.71774	−	12.5201i	0.369850	−	0.809859i	−0.629607	−	0.776914i	$-0.716784\pi$
$239$	5.71774	−	12.5201i	0.369850	−	0.809859i	0.999457	−	0.0329450i	$-0.0104886\pi$
$240$	−4.91703	−	1.44377i	−0.317393	−	0.0931950i
$241$	−15.1434	−	17.4764i	−0.975472	−	1.12575i	−0.992044	−	0.125892i	$-0.959821\pi$
$241$	−15.1434	−	17.4764i	−0.975472	−	1.12575i	0.0165718	−	0.999863i	$-0.494725\pi$
$242$	−6.64415	−	7.66776i	−0.427102	−	0.492902i
$243$	−17.1639	−	5.03979i	−1.10107	−	0.323302i
$244$	−4.66763	+	10.2207i	−0.298814	+	0.654312i
$245$	−3.61049	−	2.32032i	−0.230666	−	0.148240i
$246$	−4.60401	+	1.35186i	−0.293541	+	0.0861913i
$247$	−0.853889	+	5.93893i	−0.0543317	+	0.377885i
$248$	−6.23123	−	13.6445i	−0.395683	−	0.866425i
$249$	2.78891	+	19.3973i	0.176740	+	1.22925i
$250$	5.44471	−	3.49910i	0.344354	−	0.221303i
$251$	1.50081	−	1.73202i	0.0947301	−	0.109324i	−0.706405	−	0.707808i	$-0.749684\pi$
$251$	1.50081	−	1.73202i	0.0947301	−	0.109324i	0.801135	+	0.598483i	$0.204230\pi$
$252$	10.4721			0.659683
$253$		0			0
$254$	−4.50658			−0.282768
$255$	1.38271	−	1.59573i	0.0865886	−	0.0999286i
$256$	−5.52056	+	3.54785i	−0.345035	+	0.221741i
$257$	1.06340	+	7.39608i	0.0663328	+	0.461355i	0.995733	+	0.0922812i	$0.0294159\pi$
$257$	1.06340	+	7.39608i	0.0663328	+	0.461355i	−0.929400	+	0.369074i	$0.879675\pi$
$258$		0			0
$259$	0.569259	−	3.95929i	0.0353721	−	0.246018i
$260$	−5.75696	+	1.69040i	−0.357031	+	0.104834i
$261$	−5.04752	−	3.24384i	−0.312434	−	0.200789i
$262$	4.80316	−	10.5174i	0.296740	−	0.649770i
$263$	2.82501	+	0.829497i	0.174197	+	0.0511490i	0.367668	−	0.929957i	$-0.380156\pi$
$263$	2.82501	+	0.829497i	0.174197	+	0.0511490i	−0.193471	+	0.981106i	$0.561974\pi$
$264$	−17.1445	−	19.7858i	−1.05517	−	1.21773i
$265$	−0.382172	−	0.441050i	−0.0234766	−	0.0270935i
$266$	3.83797	+	1.12693i	0.235321	+	0.0690965i
$267$	−9.72753	+	21.3003i	−0.595315	+	1.30356i
$268$	−3.76220	−	2.41782i	−0.229813	−	0.147692i
$269$	7.62247	−	2.23816i	0.464750	−	0.136463i	−0.0409702	−	0.999160i	$-0.513045\pi$
$269$	7.62247	−	2.23816i	0.464750	−	0.136463i	0.505721	+	0.862697i	$0.331227\pi$
$270$	0.243103	−	1.69082i	0.0147948	−	0.102900i
$271$	3.32332	+	7.27706i	0.201877	+	0.442050i	0.983310	−	0.181940i	$-0.0582378\pi$
$271$	3.32332	+	7.27706i	0.201877	+	0.442050i	−0.781432	+	0.623990i	$0.785511\pi$
$272$	0.201576	+	1.40199i	0.0122223	+	0.0850082i
$273$	18.2621	−	11.7363i	1.10527	−	0.710316i
$274$	−8.85887	+	10.2237i	−0.535184	+	0.617635i
$275$	−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	$0.346121\pi$
$278$	4.33389	−	5.00158i	0.259929	−	0.299975i
$279$	11.2866	−	7.25346i	0.675711	−	0.434253i
$280$	1.27290	+	8.85323i	0.0760705	+	0.529082i
$281$	3.64067	+	7.97195i	0.217184	+	0.475567i	0.986595	−	0.163187i	$-0.0521774\pi$
$281$	3.64067	+	7.97195i	0.217184	+	0.475567i	−0.769411	+	0.638754i	$0.779450\pi$
$282$	−0.439777	+	3.05872i	−0.0261883	+	0.182144i
$283$	26.5858	−	7.80630i	1.58036	−	0.464037i	0.630367	−	0.776297i	$-0.282904\pi$
$283$	26.5858	−	7.80630i	1.58036	−	0.464037i	0.949996	+	0.312261i	$0.101086\pi$
$284$	−16.6555	−	10.7038i	−0.988319	−	0.635154i
$285$	2.29636	−	5.02832i	0.136024	−	0.297852i
$286$	−9.31495	−	2.73512i	−0.550805	−	0.161731i
$287$	−7.35806	−	8.49165i	−0.434333	−	0.501246i
$288$	−7.35806	−	8.49165i	−0.433578	−	0.500375i
$289$	15.7514	+	4.62504i	0.926555	+	0.272061i
$290$	0.952046	−	2.08469i	0.0559061	−	0.122417i
$291$	33.3109	+	21.4076i	1.95272	+	1.25494i
$292$	10.1345	−	2.97575i	0.593074	−	0.174142i
$293$	−0.217438	+	1.51231i	−0.0127028	+	0.0883502i	−0.995187	−	0.0979979i	$-0.968756\pi$
$293$	−0.217438	+	1.51231i	−0.0127028	+	0.0883502i	0.982484	+	0.186348i	$0.0596652\pi$
$294$	−1.99332	−	4.36475i	−0.116253	−	0.254558i
$295$	1.13852	+	7.91857i	0.0662871	+	0.461037i
$296$	−2.32517	+	1.49429i	−0.135148	+	0.0868541i
$297$	−7.66724	+	8.84847i	−0.444899	+	0.513440i
$298$	−14.7639			−0.855252
$299$		0			0
$300$	−12.5623			−0.725285
$301$		0			0
$302$	2.20243	−	1.41542i	0.126736	−	0.0814480i
$303$	1.42315	+	9.89821i	0.0817577	+	0.568638i
$304$	1.54044	+	3.37310i	0.0883505	+	0.193461i
$305$	1.22157	−	8.49622i	0.0699470	−	0.486492i
$306$	0.906022	−	0.266032i	0.0517938	−	0.0152080i
$307$	8.01535	+	5.15115i	0.457460	+	0.293992i	0.749004	−	0.662566i	$-0.230532\pi$
$307$	8.01535	+	5.15115i	0.457460	+	0.293992i	−0.291544	+	0.956558i	$0.594169\pi$
$308$	11.3892	−	24.9388i	0.648959	−	1.42102i
$309$	8.96888	+	2.63350i	0.510222	+	0.149815i
$310$	3.35591	+	3.87292i	0.190603	+	0.219967i
$311$	−8.63129	−	9.96104i	−0.489435	−	0.564839i	0.456279	−	0.889837i	$-0.349182\pi$
$311$	−8.63129	−	9.96104i	−0.489435	−	0.564839i	−0.945715	+	0.324998i	$0.894636\pi$
$312$	−14.3924	−	4.22599i	−0.814809	−	0.239249i
$313$	−10.1198	+	22.1593i	−0.572004	+	1.25252i	0.373719	+	0.927542i	$0.378083\pi$
$313$	−10.1198	+	22.1593i	−0.572004	+	1.25252i	−0.945723	+	0.324973i	$0.894645\pi$
$314$	5.93566	+	3.81461i	0.334968	+	0.215271i
$315$	−7.67594	+	2.25386i	−0.432490	+	0.126991i
$316$	2.52014	−	17.5280i	0.141769	−	0.986025i
$317$	10.5584	+	23.1196i	0.593016	+	1.29852i	0.933602	+	0.358311i	$0.116647\pi$
$317$	10.5584	+	23.1196i	0.593016	+	1.29852i	−0.340586	+	0.940213i	$0.610625\pi$
$318$	−0.0928570	−	0.645835i	−0.00520716	−	0.0362166i
$319$	−13.2146	+	8.49250i	−0.739875	+	0.475489i
$320$	−0.191086	+	0.220525i	−0.0106820	+	0.0123277i
$321$	30.0000			1.67444
$322$		0			0
$323$	−1.52786			−0.0850126
$324$	−11.6555	+	13.4511i	−0.647525	+	0.747284i
$325$	−8.76284	+	5.63154i	−0.486075	+	0.312381i
$326$	0.506969	+	3.52605i	0.0280784	+	0.195290i
$327$		0			0
$328$	−1.10492	+	7.68491i	−0.0610092	+	0.424328i
$329$	−6.94296	+	2.03864i	−0.382778	+	0.112394i
$330$	7.52440	+	4.83564i	0.414205	+	0.266193i
$331$	−8.16393	+	17.8765i	−0.448730	+	0.982582i	0.541183	+	0.840905i	$0.317977\pi$
$331$	−8.16393	+	17.8765i	−0.448730	+	0.982582i	−0.989913	+	0.141677i	$0.954750\pi$
$332$	13.6059	+	3.99506i	0.746723	+	0.219258i
$333$	−1.61890	−	1.86832i	−0.0887154	−	0.102383i
$334$	−0.618367	−	0.713633i	−0.0338355	−	0.0390483i
$335$	3.27802	+	0.962513i	0.179097	+	0.0525877i
$336$	5.57338	−	12.2040i	0.304053	−	0.665782i
$337$	−19.6991	−	12.6599i	−1.07308	−	0.689627i	−0.120131	−	0.992758i	$-0.538332\pi$
$337$	−19.6991	−	12.6599i	−1.07308	−	0.689627i	−0.952949	+	0.303131i	$0.901968\pi$
$338$	2.37200	−	0.696481i	0.129020	−	0.0378836i
$339$	−2.78891	+	19.3973i	−0.151473	+	1.05352i
$340$	−0.634698	−	1.38979i	−0.0344213	−	0.0753722i
$341$	−4.99875	−	34.7671i	−0.270698	−	1.88274i
$342$	2.07969	−	1.33654i	0.112457	−	0.0722717i
$343$	−7.47616	+	8.62795i	−0.403675	+	0.465865i
$344$		0			0
$345$		0			0
$346$	14.1803			0.762340
$347$	6.47562	−	7.47326i	0.347629	−	0.401186i	−0.554828	−	0.831965i	$-0.687216\pi$
$347$	6.47562	−	7.47326i	0.347629	−	0.401186i	0.902457	+	0.430779i	$0.141761\pi$
$348$	−9.13105	+	5.86817i	−0.489476	+	0.314567i
$349$	−3.47482	−	24.1679i	−0.186003	−	1.29368i	−0.842232	−	0.539116i	$-0.818759\pi$
$349$	−3.47482	−	24.1679i	−0.186003	−	1.29368i	0.656229	−	0.754562i	$-0.272150\pi$
$350$	2.88475	+	6.31673i	0.154197	+	0.337644i
$351$	−0.954677	+	6.63992i	−0.0509569	+	0.354413i
$352$	−28.2248	+	8.28756i	−1.50439	+	0.441728i
$353$	7.87470	+	5.06077i	0.419128	+	0.269357i	0.733161	−	0.680055i	$-0.238044\pi$
$353$	7.87470	+	5.06077i	0.419128	+	0.269357i	−0.314033	+	0.949412i	$0.601680\pi$
$354$	−3.71558	+	8.13600i	−0.197481	+	0.432423i
$355$	14.5120	+	4.26110i	0.770215	+	0.226155i
$356$	11.0961	+	12.8056i	0.588094	+	0.678697i
$357$	3.61998	+	4.17768i	0.191590	+	0.221106i
$358$	−0.419964	−	0.123313i	−0.0221958	−	0.00651728i
$359$	8.26200	−	18.0913i	0.436052	−	0.954820i	−0.556255	−	0.831012i	$-0.687762\pi$
$359$	8.26200	−	18.0913i	0.436052	−	0.954820i	0.992306	−	0.123808i	$-0.0395107\pi$
$360$	4.65034	+	2.98859i	0.245094	+	0.157512i
$361$	14.3924	−	4.22599i	0.757494	−	0.222420i
$362$	1.46468	−	10.1870i	0.0769816	−	0.535419i
$363$	−15.2491	−	33.3910i	−0.800372	−	1.75257i
$364$	−2.23551	−	15.5483i	−0.117173	−	0.814953i
$365$	−6.78798	+	4.36237i	−0.355299	+	0.228337i
$366$	6.28453	−	7.25274i	0.328498	−	0.379107i
$367$	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
$370$	0.618367	−	0.713633i	0.0321473	−	0.0371000i
$371$	1.28532	−	0.826026i	0.0667305	−	0.0428851i
$372$	−3.45405	−	24.0235i	−0.179084	−	1.24556i
$373$	−3.20210	−	7.01163i	−0.165799	−	0.363048i	0.808436	−	0.588584i	$-0.200314\pi$
$373$	−3.20210	−	7.01163i	−0.165799	−	0.363048i	−0.974235	+	0.225535i	$0.927587\pi$
$374$	0.351822	−	2.44697i	0.0181923	−	0.126530i
$375$	22.4679	−	6.59716i	1.16024	−	0.340676i
$376$	4.20627	+	2.70320i	0.216922	+	0.139407i
$377$	−3.73874	+	8.18669i	−0.192555	+	0.421636i
$378$	4.29098	+	1.25995i	0.220704	+	0.0648046i
$379$	15.9529	+	18.4106i	0.819443	+	0.945688i	0.999277	−	0.0380093i	$-0.0121016\pi$
$379$	15.9529	+	18.4106i	0.819443	+	0.945688i	−0.179834	+	0.983697i	$0.557556\pi$
$380$	−2.61944	−	3.02300i	−0.134375	−	0.155077i
$381$	−15.6445	−	4.59364i	−0.801491	−	0.235339i
$382$	6.72156	−	14.7182i	0.343905	−	0.753046i
$383$	−5.93566	−	3.81461i	−0.303298	−	0.194918i	0.380135	−	0.924931i	$-0.375877\pi$
$383$	−5.93566	−	3.81461i	−0.303298	−	0.194918i	−0.683433	+	0.730013i	$0.739514\pi$
$384$	−24.4199	+	7.17033i	−1.24617	+	0.365910i
$385$	−2.98068	+	20.7311i	−0.151910	+	1.05655i
$386$	2.55310	+	5.59051i	0.129949	+	0.284549i
$387$		0			0
$388$	24.1040	−	15.4907i	1.22370	−	0.786421i
$389$	16.7172	−	19.2927i	0.847595	−	0.978177i	−0.152353	−	0.988326i	$-0.548685\pi$
$389$	16.7172	−	19.2927i	0.847595	−	0.978177i	0.999948	+	0.0101488i	$0.00323052\pi$
$390$	5.12461			0.259495
$391$		0			0
$392$	−7.76393			−0.392138
$393$	27.3947	−	31.6151i	1.38188	−	1.59477i
$394$	−0.765398	+	0.491891i	−0.0385602	+	0.0247811i
$395$	1.92522	+	13.3902i	0.0968681	+	0.673733i
$396$	−7.03890	−	15.4131i	−0.353718	−	0.774535i
$397$	3.47482	−	24.1679i	0.174396	−	1.21295i	−0.695064	−	0.718948i	$-0.744624\pi$
$397$	3.47482	−	24.1679i	0.174396	−	1.21295i	0.869460	−	0.494003i	$-0.164467\pi$
$398$	−7.28903	+	2.14025i	−0.365366	+	0.107281i
$399$	12.1747	+	7.82423i	0.609499	+	0.391701i
$400$	−2.67431	+	5.85593i	−0.133716	+	0.292797i
$401$	−13.6059	−	3.99506i	−0.679448	−	0.199504i	−0.0762420	−	0.997089i	$-0.524292\pi$
$401$	−13.6059	−	3.99506i	−0.679448	−	0.199504i	−0.603206	+	0.797585i	$0.706110\pi$
$402$	2.50135	+	2.88671i	0.124756	+	0.143976i
$403$	−13.1788	−	15.2092i	−0.656484	−	0.757623i
$404$	6.94296	+	2.03864i	0.345425	+	0.101426i
$405$	5.64829	−	12.3680i	0.280666	−	0.614573i
$406$	5.04752	+	3.24384i	0.250504	+	0.160989i
$407$	−6.20997	+	1.82341i	−0.307817	+	0.0903831i
$408$	0.543594	−	3.78078i	0.0269119	−	0.187177i
$409$	8.87355	+	19.4304i	0.438769	+	0.960769i	0.991823	+	0.127624i	$0.0407351\pi$
$409$	8.87355	+	19.4304i	0.438769	+	0.960769i	−0.553054	+	0.833145i	$0.686538\pi$
$410$	−0.377487	−	2.62548i	−0.0186427	−	0.129663i
$411$	−41.1745	+	26.4613i	−2.03099	+	1.30524i
$412$	4.42943	−	5.11184i	0.218223	−	0.251842i
$413$	−20.9443			−1.03060
$414$		0			0
$415$	−10.8328			−0.531762
$416$	−11.0371	+	12.7375i	−0.541138	+	0.624506i
$417$	20.1432	−	12.9453i	0.986417	−	0.633932i
$418$	−0.921081	−	6.40626i	−0.0450515	−	0.313340i
$419$	1.90409	+	4.16938i	0.0930210	+	0.203688i	0.950423	−	0.310959i	$-0.100650\pi$
$419$	1.90409	+	4.16938i	0.0930210	+	0.203688i	−0.857402	+	0.514647i	$0.827923\pi$
$420$	−2.05960	+	14.3248i	−0.100498	+	0.698980i
$421$	−9.87491	+	2.89953i	−0.481273	+	0.141315i	−0.513365	−	0.858170i	$-0.671601\pi$
$421$	−9.87491	+	2.89953i	−0.481273	+	0.141315i	0.0320917	+	0.999485i	$0.489783\pi$
$422$	−12.1747	−	7.82423i	−0.592657	−	0.380877i
$423$	−1.85779	+	4.06800i	−0.0903290	+	0.197793i
$424$	−1.01296	−	0.297433i	−0.0491939	−	0.0144446i
$425$	−1.73700	−	2.00461i	−0.0842570	−	0.0972377i
$426$	11.0736	+	12.7796i	0.536517	+	0.619173i
$427$	21.5619	+	6.33113i	1.04345	+	0.306385i
$428$	9.01791	−	19.7465i	0.435897	−	0.954482i
$429$	−29.5487	−	18.9898i	−1.42662	−	0.916836i
$430$		0			0
$431$	−2.49448	+	17.3495i	−0.120155	+	0.835694i	0.837224	+	0.546859i	$0.184177\pi$
$431$	−2.49448	+	17.3495i	−0.120155	+	0.835694i	−0.957379	+	0.288834i	$0.906732\pi$
$432$	1.72227	+	3.77124i	0.0828627	+	0.181444i
$433$	2.53600	+	17.6383i	0.121872	+	0.847642i	0.955432	+	0.295212i	$0.0953902\pi$
$433$	2.53600	+	17.6383i	0.121872	+	0.847642i	−0.833559	+	0.552430i	$0.813701\pi$
$434$	−11.2866	+	7.25346i	−0.541774	+	0.348177i
$435$	5.42997	−	6.26652i	0.260347	−	0.300457i
$436$		0			0
$437$		0			0
$438$	−9.02129			−0.431054
$439$	12.2513	−	14.1387i	0.584721	−	0.674804i	−0.383892	−	0.923378i	$-0.625416\pi$
$439$	12.2513	−	14.1387i	0.584721	−	0.674804i	0.968613	+	0.248574i	$0.0799619\pi$
$440$	12.1747	−	7.82423i	0.580408	−	0.373005i
$441$	−0.988273	−	6.87359i	−0.0470606	−	0.327314i
$442$	−0.588397	−	1.28841i	−0.0279872	−	0.0612834i
$443$	−5.42570	+	37.7366i	−0.257783	+	1.79292i	0.290761	+	0.956796i	$0.406092\pi$
$443$	−5.42570	+	37.7366i	−0.257783	+	1.79292i	−0.548543	+	0.836122i	$0.684817\pi$
$444$	−4.29098	+	1.25995i	−0.203641	+	0.0597944i
$445$	−10.8894	−	6.99820i	−0.516208	−	0.331747i
$446$	1.02696	−	2.24873i	0.0486281	−	0.106481i
$447$	−51.2527	−	15.0491i	−2.42417	−	0.711800i
$448$	−0.500269	−	0.577341i	−0.0236355	−	0.0272768i
$449$	9.78642	+	11.2941i	0.461850	+	0.533003i	0.938127	−	0.346292i	$-0.112560\pi$
$449$	9.78642	+	11.2941i	0.461850	+	0.533003i	−0.476277	+	0.879295i	$0.658014\pi$
$450$	4.11795	+	1.20914i	0.194122	+	0.0569993i
$451$	−7.55239	+	16.5374i	−0.355628	+	0.778717i
$452$	11.9293	+	7.66647i	0.561105	+	0.360600i
$453$	9.08845	−	2.66861i	0.427013	−	0.125382i
$454$	−1.07133	+	7.45124i	−0.0502799	+	0.349704i
$455$	4.98498	+	10.9156i	0.233699	+	0.511730i
$456$	−1.42315	−	9.89821i	−0.0666450	−	0.463526i
$457$	4.31110	−	2.77057i	0.201665	−	0.129602i	−0.435911	−	0.899990i	$-0.643574\pi$
$457$	4.31110	−	2.77057i	0.201665	−	0.129602i	0.637576	+	0.770388i	$0.279937\pi$
$458$	−4.85671	+	5.60495i	−0.226939	+	0.261902i
$459$	−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	$0.510914\pi$
$462$	−15.3345	+	17.6969i	−0.713425	+	0.823336i
$463$	−16.8251	+	10.8128i	−0.781927	+	0.502514i	−0.869673	−	0.493629i	$-0.835670\pi$
$463$	−16.8251	+	10.8128i	−0.781927	+	0.502514i	0.0877454	+	0.996143i	$0.472034\pi$
$464$	0.791599	+	5.50569i	0.0367490	+	0.255595i
$465$	7.70222	+	16.8655i	0.357182	+	0.782119i
$466$	0.574161	−	3.99338i	0.0265975	−	0.184990i
$467$	−12.5269	+	3.67822i	−0.579675	+	0.170208i	−0.558409	−	0.829566i	$-0.688588\pi$
$467$	−12.5269	+	3.67822i	−0.579675	+	0.170208i	−0.0212661	+	0.999774i	$0.506770\pi$
$468$	−8.16706	−	5.24865i	−0.377523	−	0.242619i
$469$	−3.71558	+	8.13600i	−0.171570	+	0.375685i
$470$	−1.63901	−	0.481257i	−0.0756019	−	0.0221987i
$471$	16.7172	+	19.2927i	0.770288	+	0.888959i
$472$	9.47723	+	10.9373i	0.436225	+	0.503431i
$473$		0			0
$474$	−6.28299	+	13.7578i	−0.288587	+	0.631918i
$475$	−5.84189	−	3.75436i	−0.268044	−	0.172262i
$476$	3.83797	−	1.12693i	0.175913	−	0.0516528i
$477$	0.134384	−	0.934661i	0.00615302	−	0.0427952i
$478$	3.53376	+	7.73786i	0.161630	+	0.353921i
$479$	4.49669	+	31.2751i	0.205459	+	1.42900i	0.787739	+	0.616009i	$0.211252\pi$
$479$	4.49669	+	31.2751i	0.205459	+	1.42900i	−0.582280	+	0.812988i	$0.697839\pi$
$480$	13.0629	−	8.39500i	0.596236	−	0.383177i
$481$	−2.42836	+	2.80247i	−0.110724	+	0.127782i
$482$	14.2918			0.650973
$483$		0			0
$484$	−26.5623			−1.20738
$485$	−14.3339	+	16.5423i	−0.650871	+	0.751145i
$486$	9.30067	−	5.97718i	0.421887	−	0.271130i
$487$	2.09320	+	14.5585i	0.0948517	+	0.659708i	0.980669	+	0.195674i	$0.0626895\pi$
$487$	2.09320	+	14.5585i	0.0948517	+	0.659708i	−0.885817	+	0.464034i	$0.846401\pi$
$488$	−6.45051	−	14.1246i	−0.292001	−	0.639392i
$489$	−1.83423	+	12.7574i	−0.0829468	+	0.576908i
$490$	2.54503	−	0.747289i	0.114973	−	0.0337591i
$491$	7.02238	+	4.51301i	0.316916	+	0.203669i	0.689421	−	0.724361i	$-0.257865\pi$
$491$	7.02238	+	4.51301i	0.316916	+	0.203669i	−0.372506	+	0.928030i	$0.621501\pi$
$492$	−5.21857	+	11.4271i	−0.235271	+	0.515172i
$493$	−2.19896	−	0.645674i	−0.0990363	−	0.0290797i
$494$	−2.42836	−	2.80247i	−0.109257	−	0.126089i
$495$	8.47670	+	9.78263i	0.380999	+	0.439696i
$496$	−11.9339	−	3.50410i	−0.535847	−	0.157339i
$497$	−16.4491	+	36.0185i	−0.737842	+	1.61565i
$498$	−10.1888	−	6.54795i	−0.456571	−	0.293421i
$499$	−18.5103	+	5.43513i	−0.828637	+	0.243310i	−0.668431	−	0.743774i	$-0.733034\pi$
$499$	−18.5103	+	5.43513i	−0.828637	+	0.243310i	−0.160206	+	0.987084i	$0.551216\pi$
$500$	2.41142	−	16.7718i	0.107842	−	0.750058i
$501$	−1.41923	−	3.10767i	−0.0634064	−	0.138841i
$502$	0.201576	+	1.40199i	0.00899677	+	0.0625739i
$503$	22.6670	−	14.5672i	1.01067	−	0.649518i	0.0731035	−	0.997324i	$-0.476710\pi$
$503$	22.6670	−	14.5672i	1.01067	−	0.649518i	0.937566	+	0.347806i	$0.113073\pi$
$504$	−9.47723	+	10.9373i	−0.422150	+	0.487187i
$505$	−5.52786			−0.245987
$506$		0			0
$507$	8.94427			0.397229
$508$	−7.72629	+	8.91662i	−0.342799	+	0.395611i
$509$	−23.8116	+	15.3028i	−1.05543	+	0.678285i	−0.948756	−	0.316009i	$-0.897657\pi$
$509$	−23.8116	+	15.3028i	−1.05543	+	0.678285i	−0.106676	+	0.994294i	$0.534021\pi$
$510$	0.185714	+	1.29167i	0.00822355	+	0.0571961i
$511$	−8.77548	−	19.2156i	−0.388204	−	0.850049i
$512$	−2.66246	+	18.5178i	−0.117665	+	0.818378i
$513$	−4.29098	+	1.25995i	−0.189452	+	0.0556280i
$514$	−3.88494	−	2.49670i	−0.171357	−	0.110125i
$515$	−2.14653	+	4.70024i	−0.0945872	+	0.207117i
$516$		0			0
$517$	7.66724	+	8.84847i	0.337205	+	0.389155i
$518$	1.61890	+	1.86832i	0.0711306	+	0.0820891i
$519$	49.2267	+	14.4543i	2.16081	+	0.634472i
$520$	3.44454	−	7.54248i	0.151053	−	0.330760i
$521$	−26.4292	−	16.9850i	−1.15788	−	0.744126i	−0.186689	−	0.982419i	$-0.559776\pi$
$521$	−26.4292	−	16.9850i	−1.15788	−	0.744126i	−0.971193	+	0.238293i	$0.923412\pi$
$522$	3.55800	−	1.04472i	0.155729	−	0.0457262i
$523$	5.85264	−	40.7060i	0.255918	−	1.77995i	−0.305274	−	0.952265i	$-0.598748\pi$
$523$	5.85264	−	40.7060i	0.255918	−	1.77995i	0.561192	−	0.827686i	$-0.310343\pi$
$524$	−12.5748	−	27.5350i	−0.549334	−	1.20287i
$525$	3.57561	+	24.8689i	0.156052	+	1.08537i
$526$	−1.53080	+	0.983783i	−0.0667459	+	0.0428950i
$527$	3.35591	−	3.87292i	0.146186	−	0.168707i
$528$	−21.7082			−0.944728
$529$		0			0
$530$	0.360680			0.0156669
$531$	−8.47670	+	9.78263i	−0.367857	+	0.424530i
$532$	8.80972	−	5.66166i	0.381950	−	0.245464i
$533$	1.48241	+	10.3104i	0.0642103	+	0.446592i
$534$	−6.01194	−	13.1643i	−0.260162	−	0.569676i
$535$	−2.36009	+	16.4148i	−0.102036	+	0.709673i
$536$	5.92999	−	1.74120i	0.256137	−	0.0752085i
$537$	−1.33220	−	0.856155i	−0.0574888	−	0.0369458i
$538$	−2.03962	+	4.46614i	−0.0879341	+	0.192549i
$539$	−17.4439	−	5.12199i	−0.751362	−	0.220620i
$540$	−2.92863	−	3.37981i	−0.126028	−	0.145444i
$541$	22.5380	+	26.0102i	0.968982	+	1.11827i	0.992948	+	0.118552i	$0.0378254\pi$
$541$	22.5380	+	26.0102i	0.968982	+	1.11827i	−0.0239655	+	0.999713i	$0.507629\pi$
$542$	−4.74399	−	1.39296i	−0.203772	−	0.0598329i
$543$	15.4684	−	33.8711i	0.663814	−	1.45355i
$544$	−3.61049	−	2.32032i	−0.154798	−	0.0994829i
$545$		0			0
$546$	−1.90935	+	13.2798i	−0.0817128	+	0.568325i
$547$	−12.2718	−	26.8715i	−0.524704	−	1.14894i	−0.967628	−	0.252381i	$-0.918786\pi$
$547$	−12.2718	−	26.8715i	−0.524704	−	1.14894i	0.442924	−	0.896559i	$-0.353941\pi$
$548$	5.04028	+	35.0559i	0.215310	+	1.49751i
$549$	11.6838	−	7.50871i	0.498652	−	0.320464i
$550$	7.35806	−	8.49165i	0.313749	−	0.362085i
$551$	−6.00000			−0.255609
$552$		0			0
$553$	−35.4164			−1.50606
$554$	−6.26198	+	7.22671i	−0.266046	+	0.307033i
$555$	2.87407	−	1.84705i	0.121997	−	0.0784029i
$556$	−2.46578	−	17.1499i	−0.104572	−	0.727317i
$557$	3.08089	+	6.74620i	0.130541	+	0.285846i	0.963604	−	0.267332i	$-0.0861422\pi$
$557$	3.08089	+	6.74620i	0.130541	+	0.285846i	−0.833063	+	0.553178i	$0.813415\pi$
$558$	−1.18005	+	8.20740i	−0.0499553	+	0.347447i
$559$		0			0
$560$	6.23908	+	4.00961i	0.263649	+	0.169437i
$561$	3.71558	−	8.13600i	0.156872	−	0.343502i
$562$	−5.19701	−	1.52598i	−0.219222	−	0.0643695i
$563$	−21.5739	−	24.8976i	−0.909232	−	1.04931i	−0.998578	−	0.0533089i	$-0.983023\pi$
$563$	−21.5739	−	24.8976i	−0.909232	−	1.04931i	0.0893462	−	0.996001i	$-0.471522\pi$
$564$	5.29793	+	6.11414i	0.223083	+	0.257452i
$565$	−10.3940	−	3.05196i	−0.437279	−	0.128397i
$566$	−7.11382	+	15.5771i	−0.299016	+	0.654754i
$567$	29.9459	+	19.2451i	1.25761	+	0.808216i
$568$	26.2524	−	7.70839i	1.10153	−	0.323437i
$569$	−3.15659	+	21.9546i	−0.132331	+	0.920384i	0.810173	+	0.586190i	$0.199373\pi$
$569$	−3.15659	+	21.9546i	−0.132331	+	0.920384i	−0.942505	+	0.334193i	$0.891536\pi$
$570$	1.41923	+	3.10767i	0.0594449	+	0.130166i
$571$	−2.03393	−	14.1463i	−0.0851175	−	0.592005i	−0.987085	−	0.160200i	$-0.948786\pi$
$571$	−2.03393	−	14.1463i	−0.0851175	−	0.592005i	0.901967	−	0.431805i	$-0.142123\pi$
$572$	−21.3816	+	13.7411i	−0.894011	+	0.574546i
$573$	38.3362	−	44.2424i	1.60152	−	1.84825i
$574$	6.94427			0.289848
$575$		0			0
$576$	−0.472136			−0.0196723
$577$	−14.9888	+	17.2980i	−0.623992	+	0.720125i	−0.976460	−	0.215698i	$-0.930797\pi$
$577$	−14.9888	+	17.2980i	−0.623992	+	0.720125i	0.352468	+	0.935824i	$0.385343\pi$
$578$	−8.53527	+	5.48529i	−0.355021	+	0.228158i
$579$	3.16452	+	22.0097i	0.131513	+	0.914693i
$580$	−2.49249	−	5.45779i	−0.103495	−	0.226622i
$581$	4.03615	−	28.0720i	0.167448	−	1.16462i
$582$	−23.4808	+	6.89460i	−0.973312	+	0.285790i
$583$	−2.07969	−	1.33654i	−0.0861321	−	0.0553537i
$584$	−6.06371	+	13.2777i	−0.250918	+	0.549434i
$585$	7.11599	+	2.08944i	0.294210	+	0.0863879i
$586$	−0.618367	−	0.713633i	−0.0255445	−	0.0294799i
$587$	16.1804	+	18.6732i	0.667838	+	0.770726i	0.984036	−	0.177967i	$-0.0569520\pi$
$587$	16.1804	+	18.6732i	0.667838	+	0.770726i	−0.316199	+	0.948693i	$0.602407\pi$
$588$	−12.0534	−	3.53921i	−0.497076	−	0.145955i
$589$	5.57338	−	12.2040i	0.229647	−	0.502857i
$590$	−4.15939	−	2.67308i	−0.171239	−	0.110049i
$591$	−3.15846	+	0.927406i	−0.129921	+	0.0381484i
$592$	−0.326157	+	2.26847i	−0.0134050	+	0.0932335i
$593$	−1.22309	−	2.67820i	−0.0502265	−	0.109981i	0.882855	−	0.469646i	$-0.155618\pi$
$593$	−1.22309	−	2.67820i	−0.0502265	−	0.109981i	−0.933082	+	0.359665i	$0.882891\pi$
$594$	−1.02980	−	7.16242i	−0.0422532	−	0.293877i
$595$	−2.57064	+	1.65205i	−0.105386	+	0.0677275i
$596$	−25.3120	+	29.2116i	−1.03682	+	1.19655i
$597$	−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	$0.256587\pi$
$600$	11.3688	−	13.1203i	0.464130	−	0.535635i
$601$	39.4452	−	25.3499i	1.60900	−	1.03404i	0.646445	−	0.762961i	$-0.276255\pi$
$601$	39.4452	−	25.3499i	1.60900	−	1.03404i	0.962556	−	0.271082i	$-0.0873814\pi$
$602$		0			0
$603$	2.29636	+	5.02832i	0.0935149	+	0.204769i
$604$	0.975440	−	6.78434i	0.0396901	−	0.276051i
$605$	19.4698	−	5.71686i	0.791561	−	0.232423i
$606$	−5.19923	−	3.34134i	−0.211204	−	0.135733i
$607$	10.9969	−	24.0799i	0.446351	−	0.977373i	−0.544037	−	0.839061i	$-0.683105\pi$
$607$	10.9969	−	24.0799i	0.446351	−	0.977373i	0.990389	−	0.138312i	$-0.0441677\pi$
$608$	−10.7809	−	3.16557i	−0.437224	−	0.128381i
$609$	14.2159	+	16.4060i	0.576055	+	0.664803i
$610$	3.47400	+	4.00921i	0.140658	+	0.162328i
$611$	6.43647	+	1.88992i	0.260392	+	0.0764580i
$612$	1.02696	−	2.24873i	0.0415125	−	0.0908997i
$613$	−4.80205	−	3.08609i	−0.193953	−	0.124646i	0.440060	−	0.897968i	$-0.354957\pi$
$613$	−4.80205	−	3.08609i	−0.193953	−	0.124646i	−0.634013	+	0.773322i	$0.718593\pi$
$614$	−5.65002	+	1.65899i	−0.228016	+	0.0669516i
$615$	1.36576	−	9.49907i	0.0550727	−	0.383039i
$616$	15.7395	+	34.4646i	0.634161	+	1.38862i
$617$	−1.07133	−	7.45124i	−0.0431300	−	0.299976i	−0.999957	−	0.00931636i	$-0.997034\pi$
$617$	−1.07133	−	7.45124i	−0.0431300	−	0.299976i	0.956827	−	0.290659i	$-0.0938746\pi$
$618$	−4.86000	+	3.12333i	−0.195498	+	0.125639i
$619$	12.7150	−	14.6739i	0.511061	−	0.589796i	−0.440309	−	0.897846i	$-0.645131\pi$
$619$	12.7150	−	14.6739i	0.511061	−	0.589796i	0.951370	+	0.308051i	$0.0996766\pi$
$620$	13.4164			0.538816
$621$		0			0
$622$	8.14590			0.326621
$623$	22.1923	−	25.6113i	0.889115	−	1.02609i
$624$	−10.4633	+	6.72433i	−0.418865	+	0.269188i
$625$	−0.628520	−	4.37146i	−0.0251408	−	0.174858i
$626$	−6.25438	−	13.6952i	−0.249975	−	0.547369i
$627$	3.33250	−	23.1781i	0.133087	−	0.925643i
$628$	17.7239	−	5.20420i	0.707260	−	0.207670i
$629$	−0.794372	−	0.510512i	−0.0316737	−	0.0203554i
$630$	2.05392	−	4.49747i	0.0818303	−	0.179183i
$631$	11.8600	+	3.48241i	0.472139	+	0.138632i	0.509142	−	0.860683i	$-0.329963\pi$
$631$	11.8600	+	3.48241i	0.472139	+	0.138632i	−0.0370031	+	0.999315i	$0.511781\pi$
$632$	16.0258	+	18.4948i	0.637474	+	0.735684i
$633$	−34.2890	−	39.5716i	−1.36286	−	1.57283i
$634$	−15.0719	−	4.42551i	−0.598582	−	0.175760i
$635$	3.74420	−	8.19865i	0.148584	−	0.325354i
$636$	−1.43703	−	0.923525i	−0.0569820	−	0.0366201i
$637$	−9.99447	+	2.93464i	−0.395995	+	0.116275i
$638$	1.38162	−	9.60939i	0.0546989	−	0.380439i
$639$	10.1661	+	22.2606i	0.402164	+	0.880617i
$640$	−2.00221	−	13.9257i	−0.0791443	−	0.550461i
$641$	14.5579	−	9.35576i	0.575001	−	0.369530i	−0.220589	−	0.975367i	$-0.570798\pi$
$641$	14.5579	−	9.35576i	0.575001	−	0.369530i	0.795589	+	0.605837i	$0.207161\pi$
$642$	−12.1418	+	14.0124i	−0.479198	+	0.553024i
$643$	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
$646$	0.618367	−	0.713633i	0.0243293	−	0.0280775i
$647$	5.64330	−	3.62673i	0.221861	−	0.142581i	−0.424989	−	0.905198i	$-0.639722\pi$
$647$	5.64330	−	3.62673i	0.221861	−	0.142581i	0.646850	+	0.762617i	$0.276086\pi$
$648$	−3.50048	−	24.3464i	−0.137512	−	0.956416i
$649$	14.0778	+	30.8261i	0.552602	+	1.21003i
$650$	0.916179	−	6.37217i	0.0359355	−	0.249937i
$651$	−46.5748	+	13.6756i	−1.82541	+	0.535988i
$652$	7.84573	+	5.04214i	0.307263	+	0.197466i
$653$	−15.9125	+	34.8434i	−0.622702	+	1.36353i	0.290835	+	0.956773i	$0.406067\pi$
$653$	−15.9125	+	34.8434i	−0.622702	+	1.36353i	−0.913537	+	0.406755i	$0.866660\pi$
$654$		0			0
$655$	15.1434	+	17.4764i	0.591702	+	0.682860i
$656$	4.21579	+	4.86528i	0.164599	+	0.189957i
$657$	−12.5269	−	3.67822i	−0.488720	−	0.143501i
$658$	1.85779	−	4.06800i	0.0724243	−	0.158587i
$659$	8.96143	+	5.75916i	0.349088	+	0.224345i	0.703420	−	0.710775i	$-0.251655\pi$
$659$	8.96143	+	5.75916i	0.349088	+	0.224345i	−0.354332	+	0.935120i	$0.615292\pi$
$660$	22.4679	−	6.59716i	0.874561	−	0.256794i
$661$	−3.26531	+	22.7107i	−0.127006	+	0.883345i	0.822314	+	0.569034i	$0.192683\pi$
$661$	−3.26531	+	22.7107i	−0.127006	+	0.883345i	−0.949320	+	0.314311i	$0.898226\pi$
$662$	−5.04559	−	11.0483i	−0.196102	−	0.429404i
$663$	−0.729308	−	5.07245i	−0.0283240	−	0.196998i
$664$	−16.4858	+	10.5948i	−0.639774	+	0.411158i
$665$	−5.23889	+	6.04600i	−0.203155	+	0.234454i
$666$	1.52786			0.0592035
$667$		0			0
$668$	−2.47214			−0.0956498
$669$	5.85725	−	6.75963i	0.226454	−	0.261342i
$670$	−1.77627	+	1.14154i	−0.0686233	+	0.0441015i
$671$	−5.17466	−	35.9906i	−0.199766	−	1.38940i
$672$	16.8876	+	36.9788i	0.651455	+	1.42649i
$673$	−0.426945	+	2.96946i	−0.0164575	+	0.114464i	−0.996394	−	0.0848445i	$-0.972961\pi$
$673$	−0.426945	+	2.96946i	−0.0164575	+	0.114464i	0.979937	+	0.199309i	$0.0638697\pi$
$674$	13.8859	−	4.07727i	0.534865	−	0.157051i
$675$	−6.53144	−	4.19750i	−0.251395	−	0.161562i
$676$	2.68862	−	5.88726i	0.103409	−	0.226433i
$677$	17.2709	+	5.07119i	0.663774	+	0.194902i	0.596229	−	0.802815i	$-0.296665\pi$
$677$	17.2709	+	5.07119i	0.663774	+	0.194902i	0.0675450	+	0.997716i	$0.478483\pi$
$678$	−7.93132	−	9.15323i	−0.304600	−	0.351528i
$679$	−37.5268	−	43.3082i	−1.44014	−	1.66202i
$680$	2.02593	+	0.594866i	0.0776908	+	0.0228121i
$681$	−11.3143	+	24.7748i	−0.433564	+	0.949372i
$682$	18.2621	+	11.7363i	0.699292	+	0.449408i
$683$	−25.5194	+	7.49317i	−0.976472	+	0.286718i	−0.730767	−	0.682626i	$-0.760838\pi$
$683$	−25.5194	+	7.49317i	−0.976472	+	0.286718i	−0.245705	+	0.969345i	$0.579019\pi$
$684$	0.921081	−	6.40626i	0.0352184	−	0.244949i
$685$	−11.2394	−	24.6108i	−0.429434	−	0.940329i
$686$	−1.00413	−	6.98391i	−0.0383380	−	0.266647i
$687$	−22.5732	+	14.5069i	−0.861221	+	0.553473i
$688$		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	$0.457152\pi$
$692$	24.3115	−	28.0569i	0.924183	−	1.06656i
$693$	−28.5089	+	18.3215i	−1.08296	+	0.695977i
$694$	0.869751	+	6.04925i	0.0330153	+	0.229626i
$695$	5.49846	+	12.0400i	0.208569	+	0.456701i
$696$	2.13472	−	14.8473i	0.0809165	−	0.562786i
$697$	−2.54503	+	0.747289i	−0.0964000	+	0.0283056i
$698$	12.6947	+	8.15836i	0.480500	+	0.308799i
$699$	6.06371	−	13.2777i	0.229351	−	0.502208i
$700$	17.4439	+	5.12199i	0.659318	+	0.193593i
$701$	−2.50135	−	2.88671i	−0.0944745	−	0.109029i	0.706544	−	0.707670i	$-0.250253\pi$
$701$	−2.50135	−	2.88671i	−0.0944745	−	0.109029i	−0.801018	+	0.598640i	$0.795708\pi$
$702$	−2.71499	−	3.13326i	−0.102471	−	0.118257i
$703$	−2.37200	−	0.696481i	−0.0894616	−	0.0262683i
$704$	−0.513481	+	1.12437i	−0.0193526	+	0.0423762i
$705$	−5.19923	−	3.34134i	−0.195814	−	0.125842i
$706$	−5.55088	+	1.62988i	−0.208910	+	0.0613415i
$707$	2.05960	−	14.3248i	0.0774592	−	0.538741i
$708$	9.72753	+	21.3003i	0.365583	+	0.800515i
$709$	−5.98703	−	41.6407i	−0.224847	−	1.56385i	−0.719335	−	0.694664i	$-0.755553\pi$
$709$	−5.98703	−	41.6407i	−0.224847	−	1.56385i	0.494487	−	0.869185i	$-0.335356\pi$
$710$	−7.86364	+	5.05365i	−0.295117	+	0.189660i
$711$	−14.3339	+	16.5423i	−0.537565	+	0.620383i
$712$	−23.4164			−0.877567
$713$		0			0
$714$	−3.41641			−0.127856
$715$	12.7150	−	14.6739i	0.475516	−	0.548774i
$716$	−0.963991	+	0.619519i	−0.0360260	+	0.0231525i
$717$	4.38004	+	30.4638i	0.163575	+	1.13769i
$718$	5.10620	+	11.1810i	0.190562	+	0.417272i
$719$	0.434875	−	3.02463i	0.0162181	−	0.112799i	−0.980104	−	0.198483i	$-0.936398\pi$
$719$	0.434875	−	3.02463i	0.0162181	−	0.112799i	0.996322	+	0.0856839i	$0.0273075\pi$
$720$	4.39792	−	1.29135i	0.163901	−	0.0481257i
$721$	−11.3804	−	7.31372i	−0.423827	−	0.272377i
$722$	−3.85111	+	8.43275i	−0.143323	+	0.313835i
$723$	49.6137	+	14.5679i	1.84515	+	0.541785i
$724$	−17.6447	−	20.3631i	−0.655762	−	0.756789i
$725$	−6.82130	−	7.87220i	−0.253337	−	0.292366i
$726$	21.7679	+	6.39164i	0.807884	+	0.237216i
$727$	11.5104	−	25.2043i	0.426897	−	0.934775i	−0.566923	−	0.823771i	$-0.691866\pi$
$727$	11.5104	−	25.2043i	0.426897	−	0.934775i	0.993820	−	0.111004i	$-0.0354065\pi$
$728$	18.2621	+	11.7363i	0.676839	+	0.434978i
$729$	6.71645	−	1.97213i	0.248757	−	0.0730418i
$730$	0.709702	−	4.93609i	0.0262672	−	0.182693i
$731$		0			0
$732$	−3.57561	−	24.8689i	−0.132158	−	0.919180i
$733$	26.2775	−	16.8875i	0.970580	−	0.623754i	0.0436732	−	0.999046i	$-0.486094\pi$
$733$	26.2775	−	16.8875i	0.970580	−	0.623754i	0.926907	+	0.375292i	$0.122458\pi$
$734$	−1.69189	+	1.95255i	−0.0624489	+	0.0720699i
$735$	9.59675			0.353981
$736$		0			0
$737$	14.4721			0.533088
$738$	2.81053	−	3.24352i	0.103457	−	0.119396i
$739$	22.5621	−	14.4998i	0.829962	−	0.533384i	−0.0553042	−	0.998470i	$-0.517613\pi$
$739$	22.5621	−	14.4998i	0.829962	−	0.533384i	0.885266	+	0.465086i	$0.153976\pi$
$740$	−0.351822	−	2.44697i	−0.0129332	−	0.0899525i
$741$	−5.57338	−	12.2040i	−0.204743	−	0.448325i
$742$	−0.134384	+	0.934661i	−0.00493339	+	0.0343125i
$743$	39.4588	−	11.5861i	1.44760	−	0.425054i	0.538854	−	0.842399i	$-0.318857\pi$
$743$	39.4588	−	11.5861i	1.44760	−	0.425054i	0.908748	+	0.417345i	$0.137039\pi$
$744$	28.2165	+	18.1336i	1.03447	+	0.664812i
$745$	12.2663	−	26.8595i	0.449403	−	0.984056i
$746$	4.57096	+	1.34215i	0.167355	+	0.0491398i
$747$	−11.4783	−	13.2467i	−0.419969	−	0.484671i
$748$	−4.23835	−	4.89131i	−0.154969	−	0.178844i
$749$	−41.6577	−	12.2318i	−1.52214	−	0.446941i
$750$	−6.01194	+	13.1643i	−0.219525	+	0.480693i
$751$	−0.303423	−	0.194998i	−0.0110721	−	0.00711559i	0.535093	−	0.844793i	$-0.320277\pi$
$751$	−0.303423	−	0.194998i	−0.0110721	−	0.00711559i	−0.546165	+	0.837678i	$0.683913\pi$
$752$	3.97796	−	1.16803i	0.145061	−	0.0425938i
$753$	−0.729308	+	5.07245i	−0.0265775	+	0.184850i
$754$	−2.31067	−	5.05965i	−0.0841495	−	0.184262i
$755$	0.745170	+	5.18277i	0.0271195	+	0.188620i
$756$	9.84957	−	6.32993i	0.358225	−	0.230217i
$757$	1.04565	−	1.20674i	0.0380047	−	0.0438598i	−0.736429	−	0.676515i	$-0.763489\pi$
$757$	1.04565	−	1.20674i	0.0380047	−	0.0438598i	0.774434	+	0.632655i	$0.218035\pi$
$758$	−15.0557			−0.546849
$759$		0			0
$760$	5.52786			0.200517
$761$	−30.3233	+	34.9949i	−1.09922	+	1.26857i	−0.138705	+	0.990334i	$0.544294\pi$
$761$	−30.3233	+	34.9949i	−1.09922	+	1.26857i	−0.960514	+	0.278232i	$0.910252\pi$
$762$	8.47732	−	5.44805i	0.307101	−	0.197362i
$763$		0			0
$764$	−17.5973	−	38.5326i	−0.636647	−	1.39406i
$765$	−0.268768	+	1.86932i	−0.00971732	+	0.0675854i
$766$	4.18404	−	1.22855i	0.151176	−	0.0443892i
$767$	16.3341	+	10.4973i	0.589791	+	0.379036i
$768$	6.09570	−	13.3477i	0.219960	−	0.481644i
$769$	−22.1879	−	6.51496i	−0.800116	−	0.234935i	−0.143983	−	0.989580i	$-0.545991\pi$
$769$	−22.1879	−	6.51496i	−0.800116	−	0.234935i	−0.656133	+	0.754645i	$0.727809\pi$
$770$	−8.47670	−	9.78263i	−0.305479	−	0.352541i
$771$	−10.9415	−	12.6272i	−0.394050	−	0.454758i
$772$	15.4384	+	4.53312i	0.555640	+	0.163151i
$773$	2.29636	−	5.02832i	0.0825942	−	0.180856i	−0.863829	−	0.503785i	$-0.831940\pi$
$773$	2.29636	−	5.02832i	0.0825942	−	0.180856i	0.946423	+	0.322929i	$0.104668\pi$
$774$		0			0
$775$	22.3483	−	6.56206i	0.802775	−	0.235716i
$776$	−5.63520	+	39.1937i	−0.202292	+	1.40697i
$777$	3.71558	+	8.13600i	0.133296	+	0.291877i
$778$	2.24531	+	15.6165i	0.0804984	+	0.559879i
$779$	−5.84189	+	3.75436i	−0.209308	+	0.134514i
$780$	8.78588	−	10.1394i	0.314585	−	0.363050i
$781$	64.0689			2.29256
$782$		0			0
$783$	−6.70820			−0.239732
$784$	−4.21579	+	4.86528i	−0.150564	+	0.173760i
$785$	−11.8713	+	7.62923i	−0.423705	+	0.272299i
$786$	3.67942	+	25.5909i	0.131241	+	0.912799i
$787$	−10.2124	−	22.3620i	−0.364033	−	0.797120i	−0.999684	−	0.0251437i	$-0.991996\pi$
$787$	−10.2124	−	22.3620i	−0.364033	−	0.797120i	0.635651	−	0.771976i	$-0.280732\pi$
$788$	−0.338989	+	2.35772i	−0.0120760	+	0.0839903i
$789$	−6.31691	+	1.85481i	−0.224888	+	0.0660331i
$790$	−7.03345	−	4.52012i	−0.250239	−	0.160819i
$791$	11.7815	−	25.7978i	0.418900	−	0.917264i
$792$	22.4679	+	6.59716i	0.798361	+	0.234420i
$793$	−13.6426	−	15.7444i	−0.484463	−	0.559100i
$794$	9.88196	+	11.4044i	0.350698	+	0.404727i
$795$	1.25209	+	0.367647i	0.0444071	+	0.0130391i
$796$	−8.26200	+	18.0913i	−0.292839	+	0.641228i
$797$	28.9060	+	18.5768i	1.02390	+	0.658024i	0.940956	−	0.338530i	$-0.109930\pi$
$797$	28.9060	+	18.5768i	1.02390	+	0.658024i	0.0829491	+	0.996554i	$0.473566\pi$
$798$	−8.58197	+	2.51989i	−0.303798	+	0.0892032i
$799$	−0.243103	+	1.69082i	−0.00860036	+	0.0598168i
$800$	−8.10333	−	17.7438i	−0.286496	−	0.627338i
$801$	−2.98068	−	20.7311i	−0.105317	−	0.732497i
$802$	7.37269	−	4.73814i	0.260339	−	0.167310i
$803$	−22.3834	+	25.8318i	−0.789892	+	0.911584i
$804$	10.0000			0.352673
$805$		0			0
$806$	12.4377			0.438099
$807$	−11.6329	+	13.4251i	−0.409498	+	0.472585i
$808$	−8.41254	+	5.40641i	−0.295952	+	0.190197i
$809$	−1.72364	−	11.9882i	−0.0606000	−	0.421482i	−0.997427	−	0.0716891i	$-0.977161\pi$
$809$	−1.72364	−	11.9882i	−0.0606000	−	0.421482i	0.936827	−	0.349793i	$-0.113748\pi$
$810$	3.49084	+	7.64387i	0.122656	+	0.268578i
$811$	3.46501	−	24.0997i	0.121673	−	0.846255i	−0.833987	−	0.551784i	$-0.813947\pi$
$811$	3.46501	−	24.0997i	0.121673	−	0.846255i	0.955660	−	0.294471i	$-0.0951435\pi$
$812$	15.0719	−	4.42551i	0.528920	−	0.155305i
$813$	−15.0488	−	9.67128i	−0.527784	−	0.339186i
$814$	1.66166	−	3.63853i	0.0582412	−	0.127530i
$815$	−6.83601	−	2.00724i	−0.239455	−	0.0703104i
$816$	−2.07406	−	2.39360i	−0.0726068	−	0.0837927i
$817$		0			0
$818$	−12.6669	−	3.71933i	−0.442887	−	0.130043i
$819$	−8.06587	+	17.6618i	−0.281844	+	0.617153i
$820$	−5.84189	−	3.75436i	−0.204008	−	0.131108i
$821$	37.3668	−	10.9719i	1.30411	−	0.382921i	0.445376	−	0.895344i	$-0.353070\pi$
$821$	37.3668	−	10.9719i	1.30411	−	0.382921i	0.858733	+	0.512423i	$0.171252\pi$
$822$	4.30491	−	29.9413i	0.150151	−	1.04432i
$823$	−16.4259	−	35.9678i	−0.572572	−	1.25376i	−0.945417	−	0.325864i	$-0.894345\pi$
$823$	−16.4259	−	35.9678i	−0.572572	−	1.25376i	0.372845	−	0.927894i	$-0.378382\pi$
$824$	1.33029	+	9.25238i	0.0463429	+	0.322322i
$825$	34.1990	−	21.9784i	1.19066	−	0.765189i
$826$	8.47670	−	9.78263i	0.294942	−	0.340381i
$827$	−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	$0.253648\pi$
$830$	4.38432	−	5.05978i	0.152182	−	0.175628i
$831$	−29.1046	+	18.7044i	−1.00963	+	0.648849i
$832$	0.100788	+	0.700995i	0.00349419	+	0.0243026i
$833$	−1.10188	−	2.41278i	−0.0381778	−	0.0835978i
$834$	−2.10603	+	14.6477i	−0.0729258	+	0.507210i
$835$	1.81204	−	0.532064i	0.0627084	−	0.0184128i
$836$	−14.2544	−	9.16077i	−0.493000	−	0.316832i
$837$	6.23123	−	13.6445i	0.215383	−	0.471622i
$838$	−2.71807	−	0.798096i	−0.0938941	−	0.0275698i
$839$	−26.9309	−	31.0799i	−0.929758	−	1.07300i	−0.997163	−	0.0752719i	$-0.976018\pi$
$839$	−26.9309	−	31.0799i	−0.929758	−	1.07300i	0.0674054	−	0.997726i	$-0.478528\pi$
$840$	−13.0972	−	15.1150i	−0.451897	−	0.521517i
$841$	19.1899	+	5.63465i	0.661719	+	0.194298i
$842$	2.64232	−	5.78588i	0.0910604	−	0.199395i
$843$	−16.4858	−	10.5948i	−0.567802	−	0.364904i
$844$	−36.3538	+	10.6744i	−1.25135	+	0.367429i
$845$	−0.703643	+	4.89395i	−0.0242061	+	0.168357i
$846$	−1.14818	−	2.51416i	−0.0394752	−	0.0864386i
$847$	7.56042	+	52.5839i	0.259779	+	1.80680i
$848$	−0.736423	+	0.473271i	−0.0252889	+	0.0162522i
$849$	−40.5735	+	46.8243i	−1.39248	+	1.60701i
$850$	1.63932			0.0562282
$851$		0			0
$852$	44.2705			1.51668
$853$	6.93078	−	7.99855i	0.237305	−	0.273865i	−0.624588	−	0.780954i	$-0.714733\pi$
$853$	6.93078	−	7.99855i	0.237305	−	0.273865i	0.861893	+	0.507089i	$0.169279\pi$
$854$	−11.6838	+	7.50871i	−0.399811	+	0.256943i
$855$	0.703643	+	4.89395i	0.0240641	+	0.167369i
$856$	12.4625	+	27.2890i	0.425958	+	0.932717i
$857$	−0.209507	+	1.45715i	−0.00715662	+	0.0497754i	−0.993087	−	0.117382i	$-0.962550\pi$
$857$	−0.209507	+	1.45715i	−0.00715662	+	0.0497754i	0.985930	+	0.167158i	$0.0534588\pi$
$858$	20.8289	−	6.11591i	0.711086	−	0.208794i
$859$	−14.0558	−	9.03314i	−0.479579	−	0.308207i	0.278423	−	0.960458i	$-0.410188\pi$
$859$	−14.0558	−	9.03314i	−0.479579	−	0.308207i	−0.758002	+	0.652252i	$0.773824\pi$
$860$		0			0
$861$	24.1069	+	7.07842i	0.821561	+	0.241232i
$862$	−7.09399	−	8.18690i	−0.241622	−	0.278847i
$863$	14.1064	+	16.2796i	0.480186	+	0.554165i	0.943217	−	0.332178i	$-0.107783\pi$
$863$	14.1064	+	16.2796i	0.480186	+	0.554165i	−0.463030	+	0.886342i	$0.653238\pi$
$864$	−12.0534	−	3.53921i	−0.410067	−	0.120406i
$865$	−11.7815	+	25.7978i	−0.400581	+	0.877151i
$866$	−9.26486	−	5.95416i	−0.314833	−	0.202331i
$867$	−35.2213	+	10.3419i	−1.19618	+	0.351229i
$868$	−4.99875	+	34.7671i	−0.169669	+	1.18007i
$869$	23.8053	+	52.1264i	0.807541	+	1.76827i
$870$	0.729308	+	5.07245i	0.0247259	+	0.171972i
$871$	6.97550	−	4.48288i	0.236356	−	0.151897i
$872$		0			0
$873$	−35.4164			−1.19866
$874$		0			0
$875$	−33.8885			−1.14564
$876$	−15.4665	+	17.8493i	−0.522565	+	0.603073i
$877$	−30.6823	+	19.7183i	−1.03607	+	0.665841i	−0.944011	−	0.329913i	$-0.892981\pi$
$877$	−30.6823	+	19.7183i	−1.03607	+	0.665841i	−0.0920568	+	0.995754i	$0.529344\pi$
$878$	1.64549	+	11.4446i	0.0555325	+	0.386237i
$879$	−1.41923	−	3.10767i	−0.0478693	−	0.104819i
$880$	1.70778	−	11.8779i	0.0575692	−	0.400402i
$881$	42.3907	−	12.4470i	1.42818	−	0.419351i	0.525916	−	0.850536i	$-0.323723\pi$
$881$	42.3907	−	12.4470i	1.42818	−	0.419351i	0.902264	+	0.431185i	$0.141904\pi$
$882$	3.61049	+	2.32032i	0.121571	+	0.0781292i
$883$	1.66166	−	3.63853i	0.0559193	−	0.122446i	−0.879610	−	0.475696i	$-0.842196\pi$
$883$	1.66166	−	3.63853i	0.0559193	−	0.122446i	0.935529	+	0.353250i	$0.114923\pi$
$884$	−3.55800	−	1.04472i	−0.119668	−	0.0351378i
$885$	−11.7145	−	13.5193i	−0.393779	−	0.454445i
$886$	−15.4300	−	17.8072i	−0.518382	−	0.598245i
$887$	−22.1344	−	6.49926i	−0.743201	−	0.218224i	−0.111855	−	0.993725i	$-0.535679\pi$
$887$	−22.1344	−	6.49926i	−0.743201	−	0.218224i	−0.631346	+	0.775501i	$0.717497\pi$
$888$	2.56741	−	5.62183i	0.0861565	−	0.188656i
$889$	19.8508	+	12.7574i	0.665776	+	0.427868i
$890$	7.67594	−	2.25386i	0.257298	−	0.0755496i
$891$	8.19687	−	57.0105i	0.274606	−	1.90992i
$892$	−2.68862	−	5.88726i	−0.0900217	−	0.197120i
$893$	0.636451	+	4.42662i	0.0212980	+	0.148131i
$894$	27.7724	−	17.8483i	0.928849	−	0.596935i
$895$	0.573257	−	0.661574i	0.0191619	−	0.0221140i
$896$	36.8328			1.23050
$897$		0			0
$898$	−9.23607			−0.308212
$899$	13.1788	−	15.2092i	0.439538	−	0.507254i
$900$	9.45238	−	6.07468i	0.315079	−	0.202489i
$901$	−0.0513301	−	0.357009i	−0.00171005	−	0.0118937i
$902$	−4.66763	−	10.2207i	−0.155415	−	0.340312i
$903$		0			0
$904$	−18.8029	+	5.52104i	−0.625377	+	0.183627i
$905$	17.3160	+	11.1283i	0.575604	+	0.369918i
$906$	−2.43188	+	5.32508i	−0.0807939	+	0.176914i
$907$	−38.6188	−	11.3395i	−1.28232	−	0.376522i	−0.431562	−	0.902083i	$-0.642037\pi$
$907$	−38.6188	−	11.3395i	−1.28232	−	0.376522i	−0.850756	+	0.525561i	$0.823855\pi$
$908$	12.9061	+	14.8945i	0.428305	+	0.494290i
$909$	−5.85725	−	6.75963i	−0.194273	−	0.224203i
$910$	−7.11599	−	2.08944i	−0.235893	−	0.0692644i
$911$	−13.0045	+	28.4760i	−0.430860	+	0.943451i	0.562327	+	0.826915i	$0.309906\pi$
$911$	−13.0045	+	28.4760i	−0.430860	+	0.943451i	−0.993186	+	0.116536i	$0.962821\pi$
$912$	−6.97550	−	4.48288i	−0.230982	−	0.148443i
$913$	−44.0297	+	12.9283i	−1.45717	+	0.427864i
$914$	−0.450737	+	3.13495i	−0.0149091	+	0.103695i
$915$	7.97327	+	17.4590i	0.263588	+	0.577177i
$916$	2.76324	+	19.2188i	0.0913001	+	0.635006i
$917$	−50.9303	+	32.7309i	−1.68187	+	1.08087i
$918$	0.691355	−	0.797866i	0.0228181	−	0.0263335i
$919$	−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
$922$	0.595812	−	0.687604i	0.0196220	−	0.0226450i
$923$	30.8809	−	19.8460i	1.01646	−	0.653238i
$924$	8.72460	+	60.6810i	0.287018	+	1.99626i
$925$	−1.78288	−	3.90396i	−0.0586206	−	0.128361i
$926$	1.75911	−	12.2349i	0.0578079	−	0.402063i
$927$	−8.02201	+	2.35548i	−0.263477	+	0.0773640i
$928$	−14.1786	−	9.11202i	−0.465434	−	0.299117i
$929$	−9.99311	+	21.8819i	−0.327863	+	0.717921i	−0.999741	−	0.0227412i	$-0.992761\pi$
$929$	−9.99311	+	21.8819i	−0.327863	+	0.717921i	0.671878	+	0.740662i	$0.265488\pi$
$930$	−10.9948	−	3.22837i	−0.360534	−	0.105862i
$931$	−4.54753	−	5.24813i	−0.149039	−	0.172001i
$932$	−6.91684	−	7.98246i	−0.226569	−	0.261474i
$933$	28.2783	+	8.30326i	0.925790	+	0.271837i
$934$	3.35194	−	7.33971i	0.109679	−	0.240163i
$935$	4.15939	+	2.67308i	0.136026	+	0.0874189i
$936$	12.8729	−	3.77984i	0.420766	−	0.123548i
$937$	4.86437	−	33.8324i	0.158912	−	1.10526i	−0.741731	−	0.670698i	$-0.765995\pi$
$937$	4.86437	−	33.8324i	0.158912	−	1.10526i	0.900643	−	0.434560i	$-0.143096\pi$
$938$	−2.29636	−	5.02832i	−0.0749787	−	0.164181i
$939$	−7.75219	−	53.9177i	−0.252983	−	1.75954i
$940$	−3.76220	+	2.41782i	−0.122709	+	0.0788606i
$941$	4.35645	−	5.02761i	0.142016	−	0.163895i	−0.680286	−	0.732947i	$-0.738144\pi$
$941$	4.35645	−	5.02761i	0.142016	−	0.163895i	0.822302	+	0.569052i	$0.192690\pi$
$942$	−15.7771			−0.514045
$943$		0			0
$944$	12.0000			0.390567
$945$	−5.85725	+	6.75963i	−0.190536	+	0.219891i
$946$		0			0
$947$	1.53980	+	10.7095i	0.0500367	+	0.348013i	0.999425	+	0.0339080i	$0.0107953\pi$
$947$	1.53980	+	10.7095i	0.0500367	+	0.348013i	−0.949388	+	0.314105i	$0.898296\pi$
$948$	16.4491	+	36.0185i	0.534241	+	1.16983i
$949$	−2.78704	+	19.3843i	−0.0904710	+	0.629240i
$950$	4.11795	−	1.20914i	0.133604	−	0.0392296i
$951$	−47.8108	−	30.7261i	−1.55037	−	0.996363i
$952$	−2.29636	+	5.02832i	−0.0744254	+	0.162969i
$953$	19.6429	+	5.76767i	0.636295	+	0.186833i	0.583942	−	0.811796i	$-0.301510\pi$
$953$	19.6429	+	5.76767i	0.636295	+	0.186833i	0.0523532	+	0.998629i	$0.483328\pi$
$954$	0.382172	+	0.441050i	0.0123733	+	0.0142795i
$955$	21.1917	+	24.4566i	0.685749	+	0.791396i
$956$	21.3684	+	6.27433i	0.691103	+	0.202926i
$957$	14.5913	−	31.9505i	0.471669	−	1.03281i
$958$	−16.4279	−	10.5576i	−0.530761	−	0.341099i
$959$	67.9636	−	19.9559i	2.19466	−	0.644410i
$960$	0.0928570	−	0.645835i	0.00299695	−	0.0208442i
$961$	5.81581	+	12.7348i	0.187607	+	0.410802i
$962$	−0.326157	−	2.26847i	−0.0105157	−	0.0731384i
$963$	−22.5732	+	14.5069i	−0.727411	+	0.467479i
$964$	24.5025	−	28.2774i	0.789174	−	0.910755i
$965$	−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	$0.353975\pi$
$968$	24.0388	−	27.7422i	0.772635	−	0.891668i
$969$	2.87407	−	1.84705i	0.0923283	−	0.0593358i
$970$	−1.92522	−	13.3902i	−0.0618150	−	0.429932i
$971$	−6.84277	−	14.9836i	−0.219595	−	0.480846i	0.767486	−	0.641065i	$-0.221507\pi$
$971$	−6.84277	−	14.9836i	−0.219595	−	0.480846i	−0.987081	+	0.160219i	$0.948780\pi$
$972$	4.11920	−	28.6497i	0.132123	−	0.918938i
$973$	−33.2488	+	9.76273i	−1.06591	+	0.312979i
$974$	−7.64714	−	4.91452i	−0.245030	−	0.157471i
$975$	9.67576	−	21.1870i	0.309872	−	0.678526i
$976$	−12.3538	−	3.62742i	−0.395437	−	0.116111i
$977$	−15.2894	−	17.6449i	−0.489151	−	0.564510i	0.456488	−	0.889730i	$-0.349107\pi$
$977$	−15.2894	−	17.6449i	−0.489151	−	0.564510i	−0.945638	+	0.325220i	$0.894562\pi$
$978$	−5.21633	−	6.01997i	−0.166800	−	0.192497i
$979$	−52.6117	−	15.4482i	−1.68148	−	0.493726i
$980$	2.88475	−	6.31673i	0.0921501	−	0.201781i
$981$		0			0
$982$	−4.95008	+	1.45347i	−0.157963	+	0.0463822i
$983$	−5.75979	+	40.0602i	−0.183709	+	1.27772i	0.664190	+	0.747564i	$0.268776\pi$
$983$	−5.75979	+	40.0602i	−0.183709	+	1.27772i	−0.847899	+	0.530158i	$0.822133\pi$
$984$	−7.21189	−	15.7918i	−0.229907	−	0.503425i
$985$	−0.258965	−	1.80114i	−0.00825130	−	0.0573890i
$986$	1.19156	−	0.765768i	0.0379469	−	0.0243870i
$987$	10.5959	−	12.2283i	0.337270	−	0.389231i
$988$	−9.70820			−0.308859
$989$		0			0
$990$	−8.00000			−0.254257
$991$	−15.7167	+	18.1380i	−0.499256	+	0.576172i	−0.948315	−	0.317330i	$-0.897214\pi$
$991$	−15.7167	+	18.1380i	−0.499256	+	0.576172i	0.449059	+	0.893502i	$0.351759\pi$
$992$	31.7043	−	20.3751i	1.00661	−	0.646910i
$993$	−6.25392	−	43.4970i	−0.198462	−	1.38034i
$994$	−10.1661	−	22.2606i	−0.322449	−	0.706065i
$995$	2.16226	−	15.0388i	0.0685482	−	0.476764i
$996$	−30.4238	+	8.93323i	−0.964015	+	0.283060i
$997$	14.1607	+	9.10051i	0.448473	+	0.288216i	0.745317	−	0.666710i	$-0.232298\pi$
$997$	14.1607	+	9.10051i	0.448473	+	0.288216i	−0.296845	+	0.954926i	$0.595934\pi$
$998$	4.95299	−	10.8455i	0.156784	−	0.343309i
$999$	−2.65197	−	0.778690i	−0.0839047	−	0.0246366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.2.c.n.177.1		20
23.2	even	11	inner	529.2.c.n.501.1		20
23.3	even	11	inner	529.2.c.n.466.2		20
23.4	even	11	inner	529.2.c.n.118.1		20
23.5	odd	22		529.2.c.o.170.1		20
23.6	even	11		529.2.a.a.1.2		2
23.7	odd	22		529.2.c.o.255.2		20
23.8	even	11	inner	529.2.c.n.334.2		20
23.9	even	11	inner	529.2.c.n.399.1		20
23.10	odd	22		529.2.c.o.266.1		20
23.11	odd	22		529.2.c.o.487.2		20
23.12	even	11	inner	529.2.c.n.487.2		20
23.13	even	11	inner	529.2.c.n.266.1		20
23.14	odd	22		529.2.c.o.399.1		20
23.15	odd	22		529.2.c.o.334.2		20
23.16	even	11	inner	529.2.c.n.255.2		20
23.17	odd	22		23.2.a.a.1.2	✓	2
23.18	even	11	inner	529.2.c.n.170.1		20
23.19	odd	22		529.2.c.o.118.1		20
23.20	odd	22		529.2.c.o.466.2		20
23.21	odd	22		529.2.c.o.501.1		20
23.22	odd	2		529.2.c.o.177.1		20
69.17	even	22		207.2.a.d.1.1		2
69.29	odd	22		4761.2.a.w.1.1		2
92.63	even	22		368.2.a.h.1.2		2
92.75	odd	22		8464.2.a.bb.1.2		2
115.17	even	44		575.2.b.d.24.3		4
115.63	even	44		575.2.b.d.24.2		4
115.109	odd	22		575.2.a.f.1.1		2
161.132	even	22		1127.2.a.c.1.2		2
184.109	odd	22		1472.2.a.t.1.2		2
184.155	even	22		1472.2.a.s.1.1		2
253.109	even	22		2783.2.a.c.1.1		2
276.155	odd	22		3312.2.a.ba.1.1		2
299.155	odd	22		3887.2.a.i.1.1		2
345.224	even	22		5175.2.a.be.1.2		2
391.339	odd	22		6647.2.a.b.1.2		2
437.132	even	22		8303.2.a.e.1.1		2
460.339	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	23.17	odd	22
207.2.a.d.1.1		2	69.17	even	22
368.2.a.h.1.2		2	92.63	even	22
529.2.a.a.1.2		2	23.6	even	11
529.2.c.n.118.1		20	23.4	even	11	inner
529.2.c.n.170.1		20	23.18	even	11	inner
529.2.c.n.177.1		20	1.1	even	1	trivial
529.2.c.n.255.2		20	23.16	even	11	inner
529.2.c.n.266.1		20	23.13	even	11	inner
529.2.c.n.334.2		20	23.8	even	11	inner
529.2.c.n.399.1		20	23.9	even	11	inner
529.2.c.n.466.2		20	23.3	even	11	inner
529.2.c.n.487.2		20	23.12	even	11	inner
529.2.c.n.501.1		20	23.2	even	11	inner
529.2.c.o.118.1		20	23.19	odd	22
529.2.c.o.170.1		20	23.5	odd	22
529.2.c.o.177.1		20	23.22	odd	2
529.2.c.o.255.2		20	23.7	odd	22
529.2.c.o.266.1		20	23.10	odd	22
529.2.c.o.334.2		20	23.15	odd	22
529.2.c.o.399.1		20	23.14	odd	22
529.2.c.o.466.2		20	23.20	odd	22
529.2.c.o.487.2		20	23.11	odd	22
529.2.c.o.501.1		20	23.21	odd	22
575.2.a.f.1.1		2	115.109	odd	22
575.2.b.d.24.2		4	115.63	even	44
575.2.b.d.24.3		4	115.17	even	44
1127.2.a.c.1.2		2	161.132	even	22
1472.2.a.s.1.1		2	184.155	even	22
1472.2.a.t.1.2		2	184.109	odd	22
2783.2.a.c.1.1		2	253.109	even	22
3312.2.a.ba.1.1		2	276.155	odd	22
3887.2.a.i.1.1		2	299.155	odd	22
4761.2.a.w.1.1		2	69.29	odd	22
5175.2.a.be.1.2		2	345.224	even	22
6647.2.a.b.1.2		2	391.339	odd	22
8303.2.a.e.1.1		2	437.132	even	22
8464.2.a.bb.1.2		2	92.75	odd	22
9200.2.a.bt.1.1		2	460.339	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)

\(f(q)\)	\(=\)	\(q+(-0.404726 + 0.467079i) q^{2} +(-1.88110 + 1.20891i) q^{3} +(0.230270 + 1.60156i) q^{4} +(-0.513481 - 1.12437i) q^{5} +(0.196674 - 1.36790i) q^{6} +(3.10498 - 0.911706i) q^{7} +(-1.88110 - 1.20891i) q^{8} +(0.830830 - 1.81926i) q^{9} +O(q^{10})\)	\(q+(-0.404726 + 0.467079i) q^{2} +(-1.88110 + 1.20891i) q^{3} +(0.230270 + 1.60156i) q^{4} +(-0.513481 - 1.12437i) q^{5} +(0.196674 - 1.36790i) q^{6} +(3.10498 - 0.911706i) q^{7} +(-1.88110 - 1.20891i) q^{8} +(0.830830 - 1.81926i) q^{9} +(0.732987 + 0.215225i) q^{10} +(-3.42890 - 3.95716i) q^{11} +(-2.36931 - 2.73433i) q^{12} +(-2.87848 - 0.845198i) q^{13} +(-0.830830 + 1.81926i) q^{14} +(2.32517 + 1.49429i) q^{15} +(-1.77900 + 0.522361i) q^{16} +(0.108719 - 0.756156i) q^{17} +(0.513481 + 1.12437i) q^{18} +(-0.284630 - 1.97964i) q^{19} +(1.68251 - 1.08128i) q^{20} +(-4.73862 + 5.46866i) q^{21} +3.23607 q^{22} +5.00000 q^{24} +(2.27377 - 2.62407i) q^{25} +(1.55977 - 1.00240i) q^{26} +(-0.318226 - 2.21331i) q^{27} +(2.17514 + 4.76289i) q^{28} +(0.426945 - 2.96946i) q^{29} +(-1.63901 + 0.481257i) q^{30} +(5.64330 + 3.62673i) q^{31} +(2.33382 - 5.11034i) q^{32} +(11.2339 + 3.29858i) q^{33} +(0.309183 + 0.356817i) q^{34} +(-2.61944 - 3.02300i) q^{35} +(3.10498 + 0.911706i) q^{36} +(0.513481 - 1.12437i) q^{37} +(1.03985 + 0.668269i) q^{38} +(6.43647 - 1.88992i) q^{39} +(-0.393349 + 2.73580i) q^{40} +(-1.44238 - 3.15837i) q^{41} +(-0.636451 - 4.42662i) q^{42} +(5.54807 - 6.40281i) q^{44} -2.47214 q^{45} -2.23607 q^{47} +(2.71499 - 3.13326i) q^{48} +(2.92095 - 1.87718i) q^{49} +(0.305393 + 2.12406i) q^{50} +(0.709614 + 1.55384i) q^{51} +(0.690811 - 4.80469i) q^{52} +(0.453011 - 0.133016i) q^{53} +(1.16258 + 0.747147i) q^{54} +(-2.68862 + 5.88726i) q^{55} +(-6.94296 - 2.03864i) q^{56} +(2.92863 + 3.37981i) q^{57} +(1.21418 + 1.40124i) q^{58} +(-6.20997 - 1.82341i) q^{59} +(-1.85779 + 4.06800i) q^{60} +(5.84189 + 3.75436i) q^{61} +(-3.97796 + 1.16803i) q^{62} +(0.921081 - 6.40626i) q^{63} +(-0.0980662 - 0.214735i) q^{64} +(0.527732 + 3.67046i) q^{65} +(-6.08737 + 3.91211i) q^{66} +(-1.80999 + 2.08884i) q^{67} +1.23607 q^{68} +2.47214 q^{70} +(-8.01292 + 9.24740i) q^{71} +(-3.76220 + 2.41782i) q^{72} +(-0.929012 - 6.46142i) q^{73} +(0.317349 + 0.694897i) q^{74} +(-1.10492 + 7.68491i) q^{75} +(3.10498 - 0.911706i) q^{76} +(-14.2544 - 9.16077i) q^{77} +(-1.72227 + 3.77124i) q^{78} +(-10.5010 - 3.08336i) q^{79} +(1.50081 + 1.73202i) q^{80} +(7.20347 + 8.31325i) q^{81} +(2.05897 + 0.604569i) q^{82} +(3.64067 - 7.97195i) q^{83} +(-9.84957 - 6.32993i) q^{84} +(-0.906022 + 0.266032i) q^{85} +(2.78669 + 6.10200i) q^{87} +(1.66625 + 11.5890i) q^{88} +(8.80972 - 5.66166i) q^{89} +(1.00054 - 1.15468i) q^{90} -9.70820 q^{91} -15.0000 q^{93} +(0.904995 - 1.04442i) q^{94} +(-2.07969 + 1.33654i) q^{95} +(1.78780 + 12.4344i) q^{96} +(-7.35625 - 16.1079i) q^{97} +(-0.305393 + 2.12406i) q^{98} +(-10.0479 + 2.95034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + q^{4} - 2 q^{5} + 5 q^{6} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) 20 * q + q^2 + q^4 - 2 * q^5 + 5 * q^6 + 2 * q^7 - 4 * q^9	\( 20 q + q^{2} + q^{4} - 2 q^{5} + 5 q^{6} + 2 q^{7} - 4 q^{9} + 6 q^{10} - 6 q^{11} - 5 q^{12} - 6 q^{13} + 4 q^{14} - 10 q^{15} + 3 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 4 q^{20} - 10 q^{21} + 20 q^{22} + 100 q^{24} - 2 q^{25} + 3 q^{26} - 6 q^{28} + 6 q^{29} + 10 q^{30} - 9 q^{32} + 10 q^{33} - 8 q^{34} - 8 q^{35} + 2 q^{36} + 2 q^{37} + 2 q^{38} - 10 q^{40} - 2 q^{41} + 8 q^{44} + 40 q^{45} + 15 q^{48} + 2 q^{49} + 11 q^{50} + 10 q^{51} + 3 q^{52} - 8 q^{53} - 5 q^{54} + 4 q^{55} - 10 q^{56} - 3 q^{58} - 4 q^{59} + 4 q^{61} - 15 q^{62} + 4 q^{63} - 4 q^{64} - 6 q^{65} + 10 q^{66} - 10 q^{67} - 20 q^{68} - 40 q^{70} - 20 q^{71} - 22 q^{73} - 6 q^{74} - 20 q^{75} + 2 q^{76} + 16 q^{77} + 15 q^{78} - 4 q^{79} + 18 q^{80} + 22 q^{81} + 11 q^{82} - 22 q^{83} + 10 q^{84} + 16 q^{85} + 10 q^{88} - 12 q^{89} + 12 q^{90} - 60 q^{91} - 300 q^{93} + 5 q^{94} - 4 q^{95} + 5 q^{96} + 22 q^{97} - 11 q^{98} - 12 q^{99}+O(q^{100}) \) 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