LMFDB - Embedded newform 360.2.br.e.77.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(77,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 10, 3]))

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

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

chi := DirichletCharacter("360.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.br (of order $12$, degree $4$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			77.15
Character	$\chi$	$=$	360.77
Dual form			360.2.br.e.173.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04120 - 0.957024i) q^{2} +(1.08549 + 1.34971i) q^{3} +(0.168211 + 1.99291i) q^{4} +(2.00950 + 0.980772i) q^{5} +(0.161481 - 2.44416i) q^{6} +(-0.563716 + 2.10382i) q^{7} +(1.73212 - 2.23601i) q^{8} +(-0.643411 + 2.93019i) q^{9} +O(q^{10})$	\(q+(-1.04120 - 0.957024i) q^{2} +(1.08549 + 1.34971i) q^{3} +(0.168211 + 1.99291i) q^{4} +(2.00950 + 0.980772i) q^{5} +(0.161481 - 2.44416i) q^{6} +(-0.563716 + 2.10382i) q^{7} +(1.73212 - 2.23601i) q^{8} +(-0.643411 + 2.93019i) q^{9} +(-1.15368 - 2.94432i) q^{10} +(-0.402987 - 0.697994i) q^{11} +(-2.50725 + 2.39033i) q^{12} +(1.13350 - 0.303720i) q^{13} +(2.60035 - 1.65101i) q^{14} +(0.857542 + 3.77685i) q^{15} +(-3.94341 + 0.670462i) q^{16} +(-0.676068 + 0.676068i) q^{17} +(3.47418 - 2.43517i) q^{18} -7.72926 q^{19} +(-1.61657 + 4.16973i) q^{20} +(-3.45145 + 1.52283i) q^{21} +(-0.248405 + 1.11242i) q^{22} +(4.67743 - 1.25331i) q^{23} +(4.89817 - 0.0893186i) q^{24} +(3.07617 + 3.94172i) q^{25} +(-1.47087 - 0.768550i) q^{26} +(-4.65331 + 2.31229i) q^{27} +(-4.28755 - 0.769552i) q^{28} +(3.67376 - 2.12105i) q^{29} +(2.72166 - 4.75316i) q^{30} +(-1.00188 + 1.73531i) q^{31} +(4.74754 + 3.07585i) q^{32} +(0.504647 - 1.30158i) q^{33} +(1.35094 - 0.0569116i) q^{34} +(-3.19615 + 3.67474i) q^{35} +(-5.94785 - 0.789370i) q^{36} +(0.914827 - 0.914827i) q^{37} +(8.04773 + 7.39708i) q^{38} +(1.64034 + 1.20020i) q^{39} +(5.67372 - 2.79444i) q^{40} +(2.89345 + 1.67053i) q^{41} +(5.05104 + 1.71754i) q^{42} +(2.07378 - 7.73945i) q^{43} +(1.32326 - 0.920529i) q^{44} +(-4.16678 + 5.25718i) q^{45} +(-6.06961 - 3.17146i) q^{46} +(9.60228 + 2.57292i) q^{47} +(-5.18547 - 4.59466i) q^{48} +(1.95390 + 1.12809i) q^{49} +(0.569400 - 7.04810i) q^{50} +(-1.64636 - 0.178626i) q^{51} +(0.795955 + 2.20787i) q^{52} +(7.07007 - 7.07007i) q^{53} +(7.05796 + 2.04577i) q^{54} +(-0.125229 - 1.79786i) q^{55} +(3.72774 + 4.90455i) q^{56} +(-8.39005 - 10.4322i) q^{57} +(-5.85503 - 1.30743i) q^{58} +(-9.15769 - 5.28719i) q^{59} +(-7.38269 + 2.34432i) q^{60} +(2.43200 - 1.40411i) q^{61} +(2.70389 - 0.847986i) q^{62} +(-5.80189 - 3.00542i) q^{63} +(-1.99950 - 7.74610i) q^{64} +(2.57564 + 0.501379i) q^{65} +(-1.77109 + 0.872253i) q^{66} +(2.47020 + 9.21891i) q^{67} +(-1.46107 - 1.23362i) q^{68} +(6.76893 + 4.95269i) q^{69} +(6.84466 - 0.767361i) q^{70} -2.99081i q^{71} +(5.43748 + 6.51413i) q^{72} +(0.0428672 - 0.0428672i) q^{73} +(-1.82803 + 0.0770105i) q^{74} +(-1.98100 + 8.43064i) q^{75} +(-1.30015 - 15.4037i) q^{76} +(1.69562 - 0.454341i) q^{77} +(-0.559302 - 2.81950i) q^{78} +(-9.44288 + 5.45185i) q^{79} +(-8.58185 - 2.52030i) q^{80} +(-8.17205 - 3.77063i) q^{81} +(-1.41393 - 4.50846i) q^{82} +(1.89938 + 0.508937i) q^{83} +(-3.61544 - 6.62228i) q^{84} +(-2.02163 + 0.695489i) q^{85} +(-9.56606 + 6.07369i) q^{86} +(6.85063 + 2.65612i) q^{87} +(-2.25875 - 0.307928i) q^{88} -17.0563 q^{89} +(9.36972 - 1.48608i) q^{90} +2.55589i q^{91} +(3.28455 + 9.11090i) q^{92} +(-3.42969 + 0.531420i) q^{93} +(-7.53558 - 11.8685i) q^{94} +(-15.5319 - 7.58064i) q^{95} +(1.00193 + 9.74660i) q^{96} +(3.41169 - 12.7326i) q^{97} +(-0.954806 - 3.04450i) q^{98} +(2.30454 - 0.731733i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 6 q^{2} - 8 q^{6}+O(q^{10}) $ 256 * q + 6 * q^2 - 8 * q^6	$ 256 q + 6 q^{2} - 8 q^{6} - 10 q^{12} + 28 q^{15} + 12 q^{16} - 28 q^{18} - 54 q^{20} + 14 q^{22} - 28 q^{25} - 32 q^{28} + 14 q^{30} - 32 q^{31} - 114 q^{32} + 4 q^{33} - 40 q^{36} - 30 q^{38} + 46 q^{40} + 24 q^{41} - 10 q^{42} - 16 q^{46} + 24 q^{47} - 2 q^{48} + 78 q^{50} + 38 q^{52} - 8 q^{55} - 96 q^{56} - 80 q^{57} - 18 q^{58} - 2 q^{60} - 144 q^{63} - 84 q^{65} - 4 q^{66} - 30 q^{68} - 30 q^{70} - 86 q^{72} + 64 q^{73} + 16 q^{76} - 82 q^{78} + 72 q^{81} - 64 q^{82} + 48 q^{86} - 4 q^{87} + 38 q^{88} + 78 q^{90} - 108 q^{92} - 24 q^{95} - 116 q^{96} + 36 q^{97}+O(q^{100}) $ 256 * q + 6 * q^2 - 8 * q^6 - 10 * q^12 + 28 * q^15 + 12 * q^16 - 28 * q^18 - 54 * q^20 + 14 * q^22 - 28 * q^25 - 32 * q^28 + 14 * q^30 - 32 * q^31 - 114 * q^32 + 4 * q^33 - 40 * q^36 - 30 * q^38 + 46 * q^40 + 24 * q^41 - 10 * q^42 - 16 * q^46 + 24 * q^47 - 2 * q^48 + 78 * q^50 + 38 * q^52 - 8 * q^55 - 96 * q^56 - 80 * q^57 - 18 * q^58 - 2 * q^60 - 144 * q^63 - 84 * q^65 - 4 * q^66 - 30 * q^68 - 30 * q^70 - 86 * q^72 + 64 * q^73 + 16 * q^76 - 82 * q^78 + 72 * q^81 - 64 * q^82 + 48 * q^86 - 4 * q^87 + 38 * q^88 + 78 * q^90 - 108 * q^92 - 24 * q^95 - 116 * q^96 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.04120	−	0.957024i	−0.736242	−	0.676718i
$2$	−1.04120	−	0.957024i	−0.736242	−	0.676718i
$3$	1.08549	+	1.34971i	0.626710	+	0.779253i
$3$	1.08549	+	1.34971i	0.626710	+	0.779253i
$4$	0.168211	+	1.99291i	0.0841057	+	0.996457i
$5$	2.00950	+	0.980772i	0.898675	+	0.438615i
$5$	2.00950	+	0.980772i	0.898675	+	0.438615i
$6$	0.161481	−	2.44416i	0.0659243	−	0.997825i
$7$	−0.563716	+	2.10382i	−0.213065	+	0.795169i	0.773774	+	0.633462i	$0.218367\pi$
$7$	−0.563716	+	2.10382i	−0.213065	+	0.795169i	−0.986839	+	0.161707i	$0.948300\pi$
$8$	1.73212	−	2.23601i	0.612398	−	0.790550i
$9$	−0.643411	+	2.93019i	−0.214470	+	0.976731i
$10$	−1.15368	−	2.94432i	−0.364824	−	0.931076i
$11$	−0.402987	−	0.697994i	−0.121505	−	0.210453i	0.798856	−	0.601522i	$-0.205439\pi$
$11$	−0.402987	−	0.697994i	−0.121505	−	0.210453i	−0.920361	+	0.391069i	$0.872105\pi$
$12$	−2.50725	+	2.39033i	−0.723782	+	0.690029i
$13$	1.13350	−	0.303720i	0.314376	−	0.0842367i	−0.0981812	−	0.995169i	$-0.531302\pi$
$13$	1.13350	−	0.303720i	0.314376	−	0.0842367i	0.412557	+	0.910932i	$0.364636\pi$
$14$	2.60035	−	1.65101i	0.694972	−	0.441252i
$15$	0.857542	+	3.77685i	0.221416	+	0.975179i
$16$	−3.94341	+	0.670462i	−0.985852	+	0.167615i
$17$	−0.676068	+	0.676068i	−0.163971	+	0.163971i	−0.784323	−	0.620353i	$-0.786990\pi$
$17$	−0.676068	+	0.676068i	−0.163971	+	0.163971i	0.620353	+	0.784323i	$0.286990\pi$
$18$	3.47418	−	2.43517i	0.818873	−	0.573975i
$19$	−7.72926			−1.77321			−0.886607	−	0.462524i	$-0.846944\pi$
$19$	−7.72926			−1.77321			−0.886607	+	0.462524i	$0.846944\pi$
$20$	−1.61657	+	4.16973i	−0.361477	+	0.932381i
$21$	−3.45145	+	1.52283i	−0.753167	+	0.332308i
$22$	−0.248405	+	1.11242i	−0.0529602	+	0.237169i
$23$	4.67743	−	1.25331i	0.975312	−	0.261334i	0.264243	−	0.964456i	$-0.414878\pi$
$23$	4.67743	−	1.25331i	0.975312	−	0.261334i	0.711069	+	0.703122i	$0.248211\pi$
$24$	4.89817	−	0.0893186i	0.999834	−	0.0182321i
$25$	3.07617	+	3.94172i	0.615234	+	0.788344i
$26$	−1.47087	−	0.768550i	−0.288461	−	0.150725i
$27$	−4.65331	+	2.31229i	−0.895531	+	0.445000i
$28$	−4.28755	−	0.769552i	−0.810271	−	0.145432i
$29$	3.67376	−	2.12105i	0.682201	−	0.393869i	−0.118483	−	0.992956i	$-0.537803\pi$
$29$	3.67376	−	2.12105i	0.682201	−	0.393869i	0.800684	+	0.599087i	$0.204470\pi$
$30$	2.72166	−	4.75316i	0.496905	−	0.867805i
$31$	−1.00188	+	1.73531i	−0.179943	+	0.311670i	−0.941861	−	0.336003i	$-0.890925\pi$
$31$	−1.00188	+	1.73531i	−0.179943	+	0.311670i	0.761918	+	0.647674i	$0.224258\pi$
$32$	4.74754	+	3.07585i	0.839255	+	0.543738i
$33$	0.504647	−	1.30158i	0.0878478	−	0.226576i
$34$	1.35094	−	0.0569116i	0.231684	−	0.00976026i
$35$	−3.19615	+	3.67474i	−0.540249	+	0.621145i
$36$	−5.94785	−	0.789370i	−0.991308	−	0.131562i
$37$	0.914827	−	0.914827i	0.150397	−	0.150397i	−0.627899	−	0.778295i	$-0.716085\pi$
$37$	0.914827	−	0.914827i	0.150397	−	0.150397i	0.778295	+	0.627899i	$0.216085\pi$
$38$	8.04773	+	7.39708i	1.30551	+	1.19997i
$39$	1.64034	+	1.20020i	0.262664	+	0.192186i
$40$	5.67372	−	2.79444i	0.897094	−	0.441841i
$41$	2.89345	+	1.67053i	0.451881	+	0.260893i	0.708624	−	0.705586i	$-0.249316\pi$
$41$	2.89345	+	1.67053i	0.451881	+	0.260893i	−0.256743	+	0.966480i	$0.582650\pi$
$42$	5.05104	+	1.71754i	0.779393	+	0.265022i
$43$	2.07378	−	7.73945i	0.316248	−	1.18025i	−0.606573	−	0.795028i	$-0.707456\pi$
$43$	2.07378	−	7.73945i	0.316248	−	1.18025i	0.922822	−	0.385227i	$-0.125877\pi$
$44$	1.32326	−	0.920529i	0.199488	−	0.138775i
$45$	−4.16678	+	5.25718i	−0.621148	+	0.783694i
$46$	−6.06961	−	3.17146i	−0.894916	−	0.467606i
$47$	9.60228	+	2.57292i	1.40064	+	0.375299i	0.878573	−	0.477608i	$-0.158496\pi$
$47$	9.60228	+	2.57292i	1.40064	+	0.375299i	0.522063	+	0.852907i	$0.325163\pi$
$48$	−5.18547	−	4.59466i	−0.748458	−	0.663182i
$49$	1.95390	+	1.12809i	0.279129	+	0.161155i
$50$	0.569400	−	7.04810i	0.0805253	−	0.996753i
$51$	−1.64636	−	0.178626i	−0.230536	−	0.0250126i
$52$	0.795955	+	2.20787i	0.110379	+	0.306177i
$53$	7.07007	−	7.07007i	0.971149	−	0.971149i	−0.0284460	−	0.999595i	$-0.509056\pi$
$53$	7.07007	−	7.07007i	0.971149	−	0.971149i	0.999595	+	0.0284460i	$0.00905586\pi$
$54$	7.05796	+	2.04577i	0.960467	+	0.278394i
$55$	−0.125229	−	1.79786i	−0.0168858	−	0.242423i
$56$	3.72774	+	4.90455i	0.498140	+	0.655398i
$57$	−8.39005	−	10.4322i	−1.11129	−	1.38178i
$58$	−5.85503	−	1.30743i	−0.768803	−	0.171675i
$59$	−9.15769	−	5.28719i	−1.19223	−	0.688334i	−0.233418	−	0.972377i	$-0.574991\pi$
$59$	−9.15769	−	5.28719i	−1.19223	−	0.688334i	−0.958812	+	0.284043i	$0.908324\pi$
$60$	−7.38269	+	2.34432i	−0.953102	+	0.302650i
$61$	2.43200	−	1.40411i	0.311385	−	0.179778i	−0.336161	−	0.941805i	$-0.609129\pi$
$61$	2.43200	−	1.40411i	0.311385	−	0.179778i	0.647546	+	0.762026i	$0.275795\pi$
$62$	2.70389	−	0.847986i	0.343395	−	0.107694i
$63$	−5.80189	−	3.00542i	−0.730969	−	0.378647i
$64$	−1.99950	−	7.74610i	−0.249937	−	0.968262i
$65$	2.57564	+	0.501379i	0.319469	+	0.0621884i
$66$	−1.77109	+	0.872253i	−0.218006	+	0.107367i
$67$	2.47020	+	9.21891i	0.301783	+	1.12627i	0.935679	+	0.352851i	$0.114788\pi$
$67$	2.47020	+	9.21891i	0.301783	+	1.12627i	−0.633896	+	0.773418i	$0.718545\pi$
$68$	−1.46107	−	1.23362i	−0.177180	−	0.149599i
$69$	6.76893	+	4.95269i	0.814883	+	0.596234i
$70$	6.84466	−	0.767361i	0.818094	−	0.0917172i
$71$		−	2.99081i		−	0.354944i	−0.984126	−	0.177472i	$-0.943208\pi$
$71$		−	2.99081i		−	0.354944i	0.984126	−	0.177472i	$-0.0567919\pi$
$72$	5.43748	+	6.51413i	0.640813	+	0.767697i
$73$	0.0428672	−	0.0428672i	0.00501723	−	0.00501723i	−0.704594	−	0.709611i	$-0.748871\pi$
$73$	0.0428672	−	0.0428672i	0.00501723	−	0.00501723i	0.709611	+	0.704594i	$0.248871\pi$
$74$	−1.82803	+	0.0770105i	−0.212505	+	0.00895229i
$75$	−1.98100	+	8.43064i	−0.228747	+	0.973486i
$76$	−1.30015	−	15.4037i	−0.149137	−	1.76693i
$77$	1.69562	−	0.454341i	0.193234	−	0.0517770i
$78$	−0.559302	−	2.81950i	−0.0633285	−	0.319245i
$79$	−9.44288	+	5.45185i	−1.06241	+	0.613381i	−0.926097	−	0.377286i	$-0.876858\pi$
$79$	−9.44288	+	5.45185i	−1.06241	+	0.613381i	−0.136310	+	0.990666i	$0.543524\pi$
$80$	−8.58185	−	2.52030i	−0.959480	−	0.281778i
$81$	−8.17205	−	3.77063i	−0.908005	−	0.418959i
$82$	−1.41393	−	4.50846i	−0.156142	−	0.497877i
$83$	1.89938	+	0.508937i	0.208484	+	0.0558631i	0.361549	−	0.932353i	$-0.382248\pi$
$83$	1.89938	+	0.508937i	0.208484	+	0.0558631i	−0.153065	+	0.988216i	$0.548915\pi$
$84$	−3.61544	−	6.62228i	−0.394477	−	0.722550i
$85$	−2.02163	+	0.695489i	−0.219276	+	0.0754364i
$86$	−9.56606	+	6.07369i	−1.03154	+	0.654943i
$87$	6.85063	+	2.65612i	0.734465	+	0.284766i
$88$	−2.25875	−	0.307928i	−0.240783	−	0.0328252i
$89$	−17.0563			−1.80797			−0.903983	−	0.427569i	$-0.859370\pi$
$89$	−17.0563			−1.80797			−0.903983	+	0.427569i	$0.859370\pi$
$90$	9.36972	−	1.48608i	0.987655	−	0.156647i
$91$			2.55589i			0.267930i
$92$	3.28455	+	9.11090i	0.342438	+	0.949877i
$93$	−3.42969	+	0.531420i	−0.355642	+	0.0551057i
$94$	−7.53558	−	11.8685i	−0.777236	−	1.22415i
$95$	−15.5319	−	7.58064i	−1.59354	−	0.777758i
$96$	1.00193	+	9.74660i	0.102259	+	0.994758i
$97$	3.41169	−	12.7326i	0.346404	−	1.29280i	−0.544559	−	0.838723i	$-0.683303\pi$
$97$	3.41169	−	12.7326i	0.346404	−	1.29280i	0.890963	−	0.454076i	$-0.150031\pi$
$98$	−0.954806	−	3.04450i	−0.0964500	−	0.307541i
$99$	2.30454	−	0.731733i	0.231615	−	0.0735419i
$100$	−7.33806	+	6.79359i	−0.733806	+	0.679359i
$101$	−7.60004	−	13.1637i	−0.756233	−	1.30983i	−0.944759	−	0.327765i	$-0.893705\pi$
$101$	−7.60004	−	13.1637i	−0.756233	−	1.30983i	0.188527	−	0.982068i	$-0.439629\pi$
$102$	1.54325	+	1.76159i	0.152804	+	0.174424i
$103$	4.36560	+	16.2926i	0.430155	+	1.60536i	0.752401	+	0.658706i	$0.228896\pi$
$103$	4.36560	+	16.2926i	0.430155	+	1.60536i	−0.322245	+	0.946656i	$0.604438\pi$
$104$	1.28424	−	3.06059i	0.125930	−	0.300116i
$105$	−8.42922	−	0.324961i	−0.822608	−	0.0317129i
$106$	−14.1276	+	0.595161i	−1.37220	+	0.0578072i
$107$	−10.5824	−	10.5824i	−1.02304	−	1.02304i	−0.999728	−	0.0233136i	$-0.992578\pi$
$107$	−10.5824	−	10.5824i	−1.02304	−	1.02304i	−0.0233136	−	0.999728i	$-0.507422\pi$
$108$	−5.39093	−	8.88470i	−0.518742	−	0.854931i
$109$	13.0457			1.24955			0.624775	−	0.780805i	$-0.285191\pi$
$109$	13.0457			1.24955			0.624775	+	0.780805i	$0.285191\pi$
$110$	−1.59020	+	1.99178i	−0.151620	+	0.189909i
$111$	2.22779	+	0.241709i	0.211452	+	0.0229420i
$112$	0.812435	−	8.67417i	0.0767679	−	0.819632i
$113$	13.2094	−	3.53944i	1.24263	−	0.332963i	0.423147	−	0.906061i	$-0.360925\pi$
$113$	13.2094	−	3.53944i	1.24263	−	0.332963i	0.819486	+	0.573099i	$0.194259\pi$
$114$	−1.24813	+	18.8916i	−0.116898	+	1.76936i
$115$	10.6285	+	2.06896i	0.991114	+	0.192932i
$116$	4.84503	+	6.96471i	0.449850	+	0.646657i
$117$	0.160653	+	3.51678i	0.0148523	+	0.325127i
$118$	4.47505	+	14.2692i	0.411962	+	1.31358i
$119$	−1.04121	−	1.80343i	−0.0954479	−	0.165321i
$120$	9.93046	+	4.62450i	0.906523	+	0.422157i
$121$	5.17520	−	8.96371i	0.470473	−	0.814883i
$122$	−3.87598	−	0.865510i	−0.350915	−	0.0783596i
$123$	0.886089	+	5.71866i	0.0798960	+	0.515634i
$124$	−3.62685	−	1.70476i	−0.325700	−	0.153092i
$125$	2.31563	+	10.9379i	0.207116	+	0.978316i
$126$	3.16470	+	8.68180i	0.281934	+	0.773436i
$127$	−10.3744	−	10.3744i	−0.920576	−	0.920576i	0.0764937	−	0.997070i	$-0.475627\pi$
$127$	−10.3744	−	10.3744i	−0.920576	−	0.920576i	−0.997070	+	0.0764937i	$0.975627\pi$
$128$	−5.33131	+	9.97883i	−0.471226	+	0.882013i
$129$	12.6971	−	5.60212i	1.11791	−	0.493240i
$130$	−2.20194	−	2.98699i	−0.193123	−	0.261976i
$131$	5.70790	−	9.88638i	0.498702	−	0.863777i	−0.501297	−	0.865275i	$-0.667144\pi$
$131$	5.70790	−	9.88638i	0.498702	−	0.863777i	0.999999	+	0.00149841i	$0.000476960\pi$
$132$	2.67883	+	0.786777i	0.233162	+	0.0684802i
$133$	4.35711	−	16.2610i	0.377809	−	1.41000i
$134$	6.25073	−	11.9628i	0.539981	−	1.03343i
$135$	−11.6187	+	0.0826952i	−0.999975	+	0.00711727i
$136$	0.340663	+	2.68273i	0.0292116	+	0.230042i
$137$	6.67229	+	1.78783i	0.570052	+	0.152745i	0.532321	−	0.846543i	$-0.321320\pi$
$137$	6.67229	+	1.78783i	0.570052	+	0.152745i	0.0377317	+	0.999288i	$0.487987\pi$
$138$	−2.30799	−	11.6348i	−0.196469	−	0.990419i
$139$	2.98034	−	5.16211i	0.252790	−	0.437844i	−0.711503	−	0.702683i	$-0.751985\pi$
$139$	2.98034	−	5.16211i	0.252790	−	0.437844i	0.964293	+	0.264839i	$0.0853187\pi$
$140$	−7.86107	−	5.75153i	−0.664382	−	0.486093i
$141$	6.95051	+	15.7531i	0.585339	+	1.32665i
$142$	−2.86227	+	3.11404i	−0.240197	+	0.261325i
$143$	−0.668780	−	0.668780i	−0.0559262	−	0.0559262i
$144$	0.572651	−	11.9863i	0.0477209	−	0.998861i
$145$	9.46269	−	0.659118i	0.785833	−	0.0547368i
$146$	−0.0856584	+	0.00360858i	−0.00708914	+	0.000298648i
$147$	0.598363	+	3.86172i	0.0493521	+	0.318510i
$148$	1.97706	+	1.66929i	0.162513	+	0.137215i
$149$	5.61762	+	3.24333i	0.460213	+	0.265704i	0.712134	−	0.702044i	$-0.247729\pi$
$149$	5.61762	+	3.24333i	0.460213	+	0.265704i	−0.251921	+	0.967748i	$0.581062\pi$
$150$	10.1309	−	6.88214i	0.827188	−	0.561925i
$151$	9.16463	+	15.8736i	0.745807	+	1.29178i	0.949817	+	0.312807i	$0.101269\pi$
$151$	9.16463	+	15.8736i	0.745807	+	1.29178i	−0.204009	+	0.978969i	$0.565397\pi$
$152$	−13.3880	+	17.2827i	−1.08591	+	1.40181i
$153$	−1.54602	−	2.41600i	−0.124988	−	0.195322i
$154$	−2.20031	−	1.14969i	−0.177306	−	0.0926447i
$155$	−3.71522	+	2.50448i	−0.298414	+	0.201165i
$156$	−2.11598	+	3.47094i	−0.169414	+	0.277897i
$157$	−3.45834	−	12.9067i	−0.276006	−	1.03007i	−0.955164	−	0.296076i	$-0.904322\pi$
$157$	−3.45834	−	12.9067i	−0.276006	−	1.03007i	0.679159	−	0.733991i	$-0.262345\pi$
$158$	15.0495	+	3.36057i	1.19727	+	0.267353i
$159$	17.2170	+	1.86800i	1.36540	+	0.148142i
$160$	6.52347	+	10.8372i	0.515726	+	0.856754i
$161$			10.5470i			0.831219i
$162$	4.90018	+	11.7468i	0.384995	+	0.922919i
$163$	5.68536	+	5.68536i	0.445312	+	0.445312i	0.893793	−	0.448481i	$-0.148035\pi$
$163$	5.68536	+	5.68536i	0.445312	+	0.445312i	−0.448481	+	0.893793i	$0.648035\pi$
$164$	−2.84252	+	6.04740i	−0.221963	+	0.472222i
$165$	2.29064	−	2.12058i	0.178326	−	0.165087i
$166$	−1.49058	−	2.34766i	−0.115691	−	0.182214i
$167$	−2.14854	−	8.01848i	−0.166259	−	0.620488i	−0.997876	−	0.0651386i	$-0.979251\pi$
$167$	−2.14854	−	8.01848i	−0.166259	−	0.620488i	0.831617	−	0.555350i	$-0.187416\pi$
$168$	−2.57327	+	10.3552i	−0.198532	+	0.798921i
$169$	−10.0658	+	5.81147i	−0.774289	+	0.447036i
$170$	2.77053	+	1.21060i	0.212490	+	0.0928487i
$171$	4.97309	−	22.6482i	0.380302	−	1.73195i
$172$	15.7729	+	2.83100i	1.20267	+	0.215862i
$173$	−20.0324	−	5.36767i	−1.52304	−	0.408096i	−0.602296	−	0.798273i	$-0.705747\pi$
$173$	−20.0324	−	5.36767i	−1.52304	−	0.408096i	−0.920740	+	0.390177i	$0.872414\pi$
$174$	−4.59094	−	9.32178i	−0.348038	−	0.706682i
$175$	−10.0268	+	4.24969i	−0.757951	+	0.321246i
$176$	2.05712	+	2.48229i	0.155061	+	0.187110i
$177$	−2.80445	−	18.0994i	−0.210795	−	1.36043i
$178$	17.7591	+	16.3233i	1.33110	+	1.22348i
$179$			6.15468i			0.460023i	0.973188	+	0.230011i	$0.0738763\pi$
$179$			6.15468i			0.460023i	−0.973188	+	0.230011i	$0.926124\pi$
$180$	−11.1780	−	7.41972i	−0.833159	−	0.553034i
$181$			2.70230i			0.200860i	0.994944	+	0.100430i	$0.0320219\pi$
$181$			2.70230i			0.200860i	−0.994944	+	0.100430i	$0.967978\pi$
$182$	2.44604	−	2.66120i	0.181313	−	0.197261i
$183$	4.53506	+	1.75833i	0.335241	+	0.129979i
$184$	5.29946	−	12.6297i	0.390682	−	0.931073i
$185$	2.73558	−	0.941107i	0.201124	−	0.0691916i
$186$	4.07959	+	2.72898i	0.299130	+	0.200098i
$187$	0.744338	+	0.199445i	0.0544314	+	0.0145849i
$188$	−3.51240	+	19.5693i	−0.256168	+	1.42724i
$189$	−2.24148	−	11.0932i	−0.163044	−	0.806912i
$190$	8.91706	+	22.7574i	0.646911	+	1.65100i
$191$	3.83311	−	2.21305i	0.277354	−	0.160130i	−0.354871	−	0.934915i	$-0.615475\pi$
$191$	3.83311	−	2.21305i	0.277354	−	0.160130i	0.632225	+	0.774785i	$0.282142\pi$
$192$	8.28451	−	11.1071i	0.597883	−	0.801584i
$193$	5.30658	+	19.8044i	0.381976	+	1.42555i	0.842879	+	0.538103i	$0.180859\pi$
$193$	5.30658	+	19.8044i	0.381976	+	1.42555i	−0.460903	+	0.887451i	$0.652474\pi$
$194$	−15.7377	+	9.99216i	−1.12990	+	0.717395i
$195$	2.11913	+	4.02060i	0.151754	+	0.287921i
$196$	−1.91951	+	4.08372i	−0.137108	+	0.291694i
$197$	3.52669	+	3.52669i	0.251266	+	0.251266i	0.821490	−	0.570223i	$-0.193143\pi$
$197$	3.52669	+	3.52669i	0.251266	+	0.251266i	−0.570223	+	0.821490i	$0.693143\pi$
$198$	−3.09979	−	1.44362i	−0.220292	−	0.102594i
$199$		−	21.5542i		−	1.52794i	−0.645254	−	0.763968i	$-0.723248\pi$
$199$		−	21.5542i		−	1.52794i	0.645254	−	0.763968i	$-0.276752\pi$
$200$	14.1420	−	0.0508069i	0.999994	−	0.00359259i
$201$	−9.76143	+	13.3411i	−0.688518	+	0.941009i
$202$	−4.68474	+	20.9795i	−0.329617	+	1.47611i
$203$	2.39134	+	8.92460i	0.167839	+	0.626384i
$204$	0.0790493	−	3.31110i	0.00553456	−	0.231823i
$205$	4.17597	+	6.19475i	0.291662	+	0.432660i
$206$	11.0470	−	21.1420i	0.769679	−	1.47303i
$207$	0.662941	+	14.5122i	0.0460776	+	1.00867i
$208$	−4.26621	+	1.95766i	−0.295809	+	0.135739i
$209$	3.11479	+	5.39498i	0.215455	+	0.373178i
$210$	8.46555	+	8.40532i	0.584178	+	0.580022i
$211$	10.8872	+	6.28575i	0.749509	+	0.432729i	0.825516	−	0.564378i	$-0.190884\pi$
$211$	10.8872	+	6.28575i	0.749509	+	0.432729i	−0.0760078	+	0.997107i	$0.524217\pi$
$212$	15.2793	+	12.9008i	1.04939	+	0.886029i
$213$	4.03671	−	3.24650i	0.276591	−	0.222447i
$214$	0.890832	+	21.1461i	0.0608960	+	1.44552i
$215$	11.7579	−	13.5185i	0.801882	−	0.921955i
$216$	−2.88981	+	14.4100i	−0.196627	+	0.980478i
$217$	−3.08600	−	3.08600i	−0.209491	−	0.209491i
$218$	−13.5832	−	12.4850i	−0.919971	−	0.845592i
$219$	0.104390	+	0.0113261i	0.00705403	+	0.000765345i
$220$	3.56191	−	0.551990i	0.240144	−	0.0372152i
$221$	−0.560986	+	0.971657i	−0.0377360	+	0.0653607i
$222$	−2.08826	−	2.38371i	−0.140155	−	0.159984i
$223$	−10.9588	−	2.93641i	−0.733857	−	0.196636i	−0.127511	−	0.991837i	$-0.540699\pi$
$223$	−10.9588	−	2.93641i	−0.733857	−	0.196636i	−0.606346	+	0.795201i	$0.707365\pi$
$224$	−9.14729	+	8.25406i	−0.611179	+	0.551497i
$225$	−13.5292	+	6.47762i	−0.901949	+	0.431842i
$226$	−17.1410	−	8.95640i	−1.14020	−	0.595771i
$227$	0.0617427	−	0.230427i	0.00409801	−	0.0152940i	−0.963847	−	0.266458i	$-0.914147\pi$
$227$	0.0617427	−	0.230427i	0.00409801	−	0.0152940i	0.967945	+	0.251164i	$0.0808133\pi$
$228$	19.3792	−	18.4755i	1.28342	−	1.22357i
$229$	−7.07268	+	12.2502i	−0.467376	+	0.809519i	−0.999305	−	0.0372699i	$-0.988134\pi$
$229$	−7.07268	+	12.2502i	−0.467376	+	0.809519i	0.531929	+	0.846789i	$0.321467\pi$
$230$	−9.08640	−	12.3260i	−0.599140	−	0.812749i
$231$	2.45381	+	1.79541i	0.161449	+	0.118129i
$232$	1.62072	−	11.8885i	0.106406	−	0.780518i
$233$	−2.41398	−	2.41398i	−0.158145	−	0.158145i	0.623599	−	0.781744i	$-0.285670\pi$
$233$	−2.41398	−	2.41398i	−0.158145	−	0.158145i	−0.781744	+	0.623599i	$0.785670\pi$
$234$	3.19837	−	3.81544i	0.209084	−	0.249423i
$235$	16.7723	+	14.5879i	1.09410	+	0.951612i
$236$	8.99649	−	19.1398i	0.585622	−	1.24590i
$237$	−17.6086	−	6.82716i	−1.14380	−	0.443472i
$238$	−0.641814	+	2.87421i	−0.0416026	+	0.186307i
$239$	10.7897	−	18.6884i	0.697929	−	1.20885i	−0.271254	−	0.962508i	$-0.587438\pi$
$239$	10.7897	−	18.6884i	0.697929	−	1.20885i	0.969183	−	0.246341i	$-0.0792284\pi$
$240$	−5.91388	−	14.3187i	−0.381739	−	0.924270i
$241$	−6.13608	−	10.6280i	−0.395260	−	0.684610i	0.597874	−	0.801590i	$-0.296012\pi$
$241$	−6.13608	−	10.6280i	−0.395260	−	0.684610i	−0.993134	+	0.116980i	$0.962679\pi$
$242$	−13.9669	+	4.38026i	−0.897828	+	0.281574i
$243$	−3.78145	−	15.1229i	−0.242580	−	0.970131i
$244$	3.20737	+	4.61057i	0.205331	+	0.295162i
$245$	2.81997	+	4.18322i	0.180161	+	0.267256i
$246$	4.55029	−	6.80230i	0.290116	−	0.433699i
$247$	−8.76110	+	2.34753i	−0.557455	+	0.149370i
$248$	2.14479	+	5.24598i	0.136194	+	0.333120i
$249$	1.37485	+	3.11605i	0.0871274	+	0.197472i
$250$	8.05680	−	13.6047i	0.509557	−	0.860437i
$251$	−14.5004			−0.915256			−0.457628	−	0.889144i	$-0.651301\pi$
$251$	−14.5004			−0.915256			−0.457628	+	0.889144i	$0.651301\pi$
$252$	5.01359	−	12.0682i	0.315827	−	0.760226i
$253$	−2.75975	−	2.75975i	−0.173504	−	0.173504i
$254$	0.873318	+	20.7304i	0.0547968	+	1.30074i
$255$	−3.13317	−	1.97365i	−0.196206	−	0.123595i
$256$	15.1010	−	5.28781i	0.943810	−	0.330488i
$257$	4.64245	+	17.3258i	0.289588	+	1.08076i	0.945421	+	0.325851i	$0.105651\pi$
$257$	4.64245	+	17.3258i	0.289588	+	1.08076i	−0.655833	+	0.754906i	$0.727683\pi$
$258$	−18.5816	−	6.31842i	−1.15684	−	0.393368i
$259$	1.40893	+	2.44033i	0.0875465	+	0.151635i
$260$	−0.565952	+	5.21737i	−0.0350989	+	0.323568i
$261$	3.85134	+	12.1295i	0.238392	+	0.750799i
$262$	−15.4046	+	4.83114i	−0.951699	+	0.298469i
$263$	4.74486	−	17.7081i	0.292581	−	1.09193i	−0.650539	−	0.759473i	$-0.725457\pi$
$263$	4.74486	−	17.7081i	0.292581	−	1.09193i	0.943120	−	0.332453i	$-0.107876\pi$
$264$	−2.03624	−	3.38290i	−0.125322	−	0.208203i
$265$	21.1414	−	7.27317i	1.29871	−	0.446787i
$266$	−20.0988	+	12.7611i	−1.23233	+	0.782434i
$267$	−18.5145	−	23.0210i	−1.13307	−	1.40886i
$268$	−17.9570	+	6.47362i	−1.09690	+	0.395439i
$269$			6.12668i			0.373550i	0.982403	+	0.186775i	$0.0598036\pi$
$269$			6.12668i			0.373550i	−0.982403	+	0.186775i	$0.940196\pi$
$270$	12.1765	+	11.0332i	0.741040	+	0.671461i
$271$	21.1208			1.28299			0.641497	−	0.767125i	$-0.278314\pi$
$271$	21.1208			1.28299			0.641497	+	0.767125i	$0.278314\pi$
$272$	2.21274	−	3.11929i	0.134167	−	0.189135i
$273$	−3.44969	+	2.77440i	−0.208785	+	0.167914i
$274$	−5.23621	−	8.24704i	−0.316331	−	0.498222i
$275$	1.51164	−	3.73561i	0.0911555	−	0.225266i
$276$	−8.73168	+	14.3230i	−0.525585	+	0.862142i
$277$	−29.4895	−	7.90170i	−1.77186	−	0.474767i	−0.782795	−	0.622280i	$-0.786207\pi$
$277$	−29.4895	−	7.90170i	−1.77186	−	0.474767i	−0.989060	+	0.147513i	$0.952873\pi$
$278$	−8.04341	+	2.52255i	−0.482411	+	0.151292i
$279$	−4.44016	−	4.05222i	−0.265826	−	0.242600i
$280$	2.68064	+	13.5117i	0.160199	+	0.807481i
$281$	−27.9899	+	16.1599i	−1.66973	+	0.964022i	−0.701956	+	0.712221i	$0.747690\pi$
$281$	−27.9899	+	16.1599i	−1.66973	+	0.964022i	−0.967779	+	0.251801i	$0.918977\pi$
$282$	7.83922	−	23.0540i	0.466819	−	1.37285i
$283$	−25.8390	+	6.92355i	−1.53597	+	0.411562i	−0.924961	−	0.380061i	$-0.875903\pi$
$283$	−25.8390	+	6.92355i	−1.53597	+	0.411562i	−0.611009	+	0.791623i	$0.709236\pi$
$284$	5.96042	−	0.503088i	0.353686	−	0.0298528i
$285$	−6.62817	−	29.1923i	−0.392619	−	1.72920i
$286$	0.0562981	+	1.33637i	0.00332898	+	0.0790215i
$287$	−5.14558	+	5.14558i	−0.303734	+	0.303734i
$288$	−12.0674	+	11.9322i	−0.711081	+	0.703110i
$289$			16.0859i			0.946227i
$290$	−10.4834	−	8.36974i	−0.615605	−	0.491488i
$291$	20.8886	−	9.21636i	1.22451	−	0.540273i
$292$	0.0926414	+	0.0782199i	0.00542143	+	0.00457747i
$293$	1.97897	+	7.38560i	0.115612	+	0.431471i	0.999332	−	0.0365454i	$-0.0116354\pi$
$293$	1.97897	+	7.38560i	0.115612	+	0.431471i	−0.883720	+	0.468017i	$0.844969\pi$
$294$	3.07274	−	4.59349i	0.179206	−	0.267898i
$295$	−13.2168	−	19.6062i	−0.769513	−	1.14152i
$296$	−0.460971	−	3.63016i	−0.0267934	−	0.210999i
$297$	3.48919	+	2.31616i	0.202463	+	0.134398i
$298$	−2.74514	−	8.75316i	−0.159022	−	0.507057i
$299$	4.92120	−	2.84126i	0.284601	−	0.164314i
$300$	−17.1348	−	2.52984i	−0.989276	−	0.146060i
$301$	15.1134	+	8.72571i	0.871120	+	0.502941i
$302$	5.64917	−	25.2984i	0.325073	−	1.45576i
$303$	9.51728	−	24.5469i	0.546753	−	1.41018i
$304$	30.4796	−	5.18217i	1.74813	−	0.297218i
$305$	6.26421	−	0.436330i	0.358688	−	0.0249842i
$306$	−0.702446	+	3.99512i	−0.0401562	+	0.228386i
$307$	8.51598	−	8.51598i	0.486032	−	0.486032i	−0.421019	−	0.907052i	$-0.638328\pi$
$307$	8.51598	−	8.51598i	0.486032	−	0.486032i	0.907052	+	0.421019i	$0.138328\pi$
$308$	1.19069	+	3.30281i	0.0678456	+	0.188195i
$309$	−17.2514	+	23.5778i	−0.981401	+	1.34130i
$310$	6.26515	+	0.947876i	0.355837	+	0.0538357i
$311$	−0.980136	−	0.565882i	−0.0555784	−	0.0320882i	0.471953	−	0.881624i	$-0.343549\pi$
$311$	−0.980136	−	0.565882i	−0.0555784	−	0.0320882i	−0.527532	+	0.849535i	$0.676882\pi$
$312$	5.52493	−	1.58891i	0.312788	−	0.0899544i
$313$	−12.7316	−	3.41141i	−0.719631	−	0.192824i	−0.119624	−	0.992819i	$-0.538169\pi$
$313$	−12.7316	−	3.41141i	−0.719631	−	0.192824i	−0.600007	+	0.799995i	$0.704836\pi$
$314$	−8.75118	+	16.7482i	−0.493858	+	0.945157i
$315$	−8.71126	−	11.7297i	−0.490824	−	0.660895i
$316$	−12.4535	−	17.9018i	−0.700562	−	1.00705i
$317$	−7.74130	+	28.8909i	−0.434795	+	1.62268i	0.306763	+	0.951786i	$0.400754\pi$
$317$	−7.74130	+	28.8909i	−0.434795	+	1.62268i	−0.741557	+	0.670889i	$0.765913\pi$
$318$	−16.1387	−	18.4221i	−0.905014	−	1.03306i
$319$	−2.96096	−	1.70951i	−0.165782	−	0.0957142i
$320$	3.57917	−	17.5268i	0.200081	−	0.979779i
$321$	2.79601	−	25.7703i	0.156058	−	1.43836i
$322$	10.0937	−	10.9816i	0.562501	−	0.611978i
$323$	5.22550	−	5.22550i	0.290755	−	0.290755i
$324$	6.13992	−	16.9204i	0.341106	−	0.940025i
$325$	4.68401	+	3.53364i	0.259822	+	0.196011i
$326$	−0.478596	−	11.3606i	−0.0265070	−	0.629208i
$327$	14.1610	+	17.6078i	0.783105	+	0.973715i
$328$	8.74714	−	3.57622i	0.482980	−	0.197464i
$329$	−10.8259	+	18.7510i	−0.596852	+	1.03378i
$330$	−4.41448	+	0.0157596i	−0.243009	+	0.000867539i
$331$	−12.2626	+	7.07982i	−0.674014	+	0.389142i	−0.797596	−	0.603192i	$-0.793895\pi$
$331$	−12.2626	+	7.07982i	−0.674014	+	0.389142i	0.123582	+	0.992334i	$0.460562\pi$
$332$	−0.694770	+	3.87091i	−0.0381305	+	0.212444i
$333$	2.09201	+	3.26923i	0.114641	+	0.179153i
$334$	−5.43680	+	10.4051i	−0.297488	+	0.569341i
$335$	−4.07779	+	20.9481i	−0.222794	+	1.14452i
$336$	12.5895	−	8.31920i	0.686812	−	0.453849i
$337$	−10.1635	+	2.72331i	−0.553642	+	0.148348i	−0.524784	−	0.851235i	$-0.675854\pi$
$337$	−10.1635	+	2.72331i	−0.553642	+	0.148348i	−0.0288585	+	0.999584i	$0.509187\pi$
$338$	16.0422	+	3.58225i	0.872582	+	0.194848i
$339$	19.1159	+	13.9867i	1.03823	+	0.759655i
$340$	−1.72611	−	3.91194i	−0.0936115	−	0.212155i
$341$	1.61498			0.0874561
$342$	−26.8529	+	18.8220i	−1.45204	+	1.01778i
$343$	−14.2554	+	14.2554i	−0.769722	+	0.769722i
$344$	−13.7135	−	18.0427i	−0.739380	−	0.972796i
$345$	8.74468	+	16.5912i	0.470798	+	0.893241i
$346$	15.7208	+	24.7603i	0.845158	+	1.33112i
$347$	18.6735	−	5.00356i	1.00245	−	0.268605i	0.279977	−	0.960007i	$-0.409673\pi$
$347$	18.6735	−	5.00356i	1.00245	−	0.268605i	0.722470	+	0.691402i	$0.243007\pi$
$348$	−4.14106	+	14.0995i	−0.221984	+	0.755813i
$349$	2.90812	+	5.03701i	0.155668	+	0.269625i	0.933302	−	0.359092i	$-0.116914\pi$
$349$	2.90812	+	5.03701i	0.155668	+	0.269625i	−0.777634	+	0.628717i	$0.783580\pi$
$350$	14.5070	+	5.17105i	0.775429	+	0.276404i
$351$	−4.57223	+	4.03428i	−0.244048	+	0.215334i
$352$	0.233726	−	4.55329i	0.0124577	−	0.242691i
$353$	3.34361	−	12.4785i	0.177963	−	0.664165i	−0.818066	−	0.575125i	$-0.804953\pi$
$353$	3.34361	−	12.4785i	0.177963	−	0.664165i	0.996028	−	0.0890401i	$-0.0283799\pi$
$354$	−14.4015	+	21.5291i	−0.765433	+	1.14426i
$355$	2.93330	−	6.01003i	0.155684	−	0.318979i
$356$	−2.86907	−	33.9918i	−0.152060	−	1.80156i
$357$	1.30388	−	3.36295i	0.0690085	−	0.177986i
$358$	5.89018	−	6.40828i	0.311305	−	0.338688i
$359$	−6.93339			−0.365930			−0.182965	−	0.983119i	$-0.558570\pi$
$359$	−6.93339			−0.365930			−0.182965	+	0.983119i	$0.558570\pi$
$360$	4.53773	+	18.4231i	0.239159	+	0.970980i
$361$	40.7414			2.14429
$362$	2.58617	−	2.81365i	0.135926	−	0.147882i
$363$	17.7160	−	2.74505i	0.929850	−	0.144078i
$364$	−5.09366	+	0.429929i	−0.266980	+	0.0225344i
$365$	0.128185	−	0.0440986i	0.00670949	−	0.00230823i
$366$	−3.03916	−	6.17093i	−0.158860	−	0.322560i
$367$	1.33578	−	4.98519i	0.0697271	−	0.260225i	−0.922259	−	0.386573i	$-0.873659\pi$
$367$	1.33578	−	4.98519i	0.0697271	−	0.260225i	0.991986	+	0.126348i	$0.0403255\pi$
$368$	−17.6047	+	8.07837i	−0.917710	+	0.421114i
$369$	−6.75666	+	7.40352i	−0.351738	+	0.385412i
$370$	−3.74896	−	1.63813i	−0.194899	−	0.0851624i
$371$	10.8886	+	18.8597i	0.565310	+	0.979145i
$372$	−1.63599	−	6.74568i	−0.0848220	−	0.349747i
$373$	−13.9909	+	3.74885i	−0.724421	+	0.194108i	−0.602143	−	0.798388i	$-0.705686\pi$
$373$	−13.9909	+	3.74885i	−0.724421	+	0.194108i	−0.122278	+	0.992496i	$0.539020\pi$
$374$	−0.584135	−	0.920012i	−0.0302049	−	0.0475727i
$375$	−12.2494	+	14.9984i	−0.632554	+	0.774516i
$376$	22.3854	−	17.0142i	1.15444	−	0.877440i
$377$	3.52000	−	3.52000i	0.181289	−	0.181289i
$378$	−8.28262	+	13.6954i	−0.426012	+	0.704417i
$379$	−7.63742			−0.392308			−0.196154	−	0.980573i	$-0.562845\pi$
$379$	−7.63742			−0.392308			−0.196154	+	0.980573i	$0.562845\pi$
$380$	12.4949	−	32.2290i	0.640976	−	1.65331i
$381$	2.74104	−	25.2636i	0.140428	−	1.29430i
$382$	−6.10899	−	1.36414i	−0.312563	−	0.0697956i
$383$	−13.4665	+	3.60835i	−0.688108	+	0.184378i	−0.585898	−	0.810385i	$-0.699258\pi$
$383$	−13.4665	+	3.60835i	−0.688108	+	0.184378i	−0.102210	+	0.994763i	$0.532591\pi$
$384$	−19.2556	+	3.63625i	−0.982633	+	0.185562i
$385$	3.85296	+	0.750023i	0.196365	+	0.0382247i
$386$	13.4281	−	25.6990i	0.683471	−	1.30804i
$387$	21.3438	+	11.0562i	1.08497	+	0.562019i
$388$	25.9488	+	4.65743i	1.31735	+	0.236445i
$389$	17.0336	−	9.83433i	0.863636	−	0.498620i	−0.00159252	−	0.999999i	$-0.500507\pi$
$389$	17.0336	−	9.83433i	0.863636	−	0.498620i	0.865228	+	0.501379i	$0.167174\pi$
$390$	1.64137	−	6.21432i	0.0831139	−	0.314674i
$391$	−2.31494	+	4.00959i	−0.117071	+	0.202774i
$392$	5.90681	−	2.41497i	0.298339	−	0.121974i
$393$	19.5396	−	3.02760i	0.985642	−	0.152722i
$394$	−0.296878	−	7.04713i	−0.0149565	−	0.355029i
$395$	−24.3225	+	1.69417i	−1.22380	+	0.0852428i
$396$	1.84593	+	4.46967i	0.0927615	+	0.224609i
$397$	−0.385863	+	0.385863i	−0.0193659	+	0.0193659i	−0.716723	−	0.697358i	$-0.754359\pi$
$397$	−0.385863	+	0.385863i	−0.0193659	+	0.0193659i	0.697358	+	0.716723i	$0.254359\pi$
$398$	−20.6279	+	22.4423i	−1.03398	+	1.12493i
$399$	26.6771	−	11.7703i	1.33553	−	0.589254i
$400$	−14.7734	−	13.4814i	−0.738669	−	0.674069i
$401$	0.917054	+	0.529461i	0.0457955	+	0.0264400i	0.522723	−	0.852503i	$-0.324916\pi$
$401$	0.917054	+	0.529461i	0.0457955	+	0.0264400i	−0.476927	+	0.878943i	$0.658250\pi$
$402$	22.9314	−	4.54889i	1.14371	−	0.226878i
$403$	−0.608582	+	2.27126i	−0.0303156	+	0.113139i
$404$	24.9556	−	17.3605i	1.24159	−	0.863718i
$405$	−12.7236	−	15.5920i	−0.632240	−	0.774773i
$406$	6.05118	−	11.5809i	0.300315	−	0.574750i
$407$	−1.00721	−	0.269881i	−0.0499255	−	0.0133775i
$408$	−3.25111	+	3.37188i	−0.160954	+	0.166933i
$409$	9.08683	+	5.24628i	0.449315	+	0.259412i	0.707541	−	0.706673i	$-0.249805\pi$
$409$	9.08683	+	5.24628i	0.449315	+	0.259412i	−0.258226	+	0.966085i	$0.583138\pi$
$410$	1.58049	−	10.4465i	0.0780547	−	0.515916i
$411$	4.82967	+	10.9463i	0.238230	+	0.539942i
$412$	−31.7355	+	11.4409i	−1.56350	+	0.563652i
$413$	16.2856	−	16.2856i	0.801364	−	0.801364i
$414$	13.1982	−	15.7446i	0.648658	−	0.773804i
$415$	3.31765	+	2.88557i	0.162857	+	0.141647i
$416$	6.31552	+	2.04455i	0.309644	+	0.100242i
$417$	10.2025	−	1.58084i	0.499617	−	0.0774142i
$418$	1.91999	−	8.59820i	0.0939097	−	0.420552i
$419$	−5.58093	−	3.22215i	−0.272646	−	0.157413i	0.357443	−	0.933935i	$-0.383649\pi$
$419$	−5.58093	−	3.22215i	−0.272646	−	0.157413i	−0.630090	+	0.776522i	$0.716982\pi$
$420$	−0.770273	−	16.8534i	−0.0375855	−	0.822361i
$421$	−11.9422	+	6.89481i	−0.582025	+	0.336032i	−0.761938	−	0.647650i	$-0.775752\pi$
$421$	−11.9422	+	6.89481i	−0.582025	+	0.336032i	0.179913	+	0.983683i	$0.442419\pi$
$422$	−5.32023	−	16.9641i	−0.258985	−	0.825799i
$423$	−13.7174	+	26.4811i	−0.666961	+	1.28755i
$424$	−3.56253	−	28.0550i	−0.173012	−	1.36247i
$425$	−4.74457	−	0.585172i	−0.230146	−	0.0283850i
$426$	−7.31002	−	0.482958i	−0.354172	−	0.0233994i
$427$	1.58305	+	5.90801i	0.0766089	+	0.285908i
$428$	19.3098	−	22.8699i	0.933373	−	1.10546i
$429$	0.176700	−	1.62861i	0.00853117	−	0.0786301i
$430$	−25.1799	+	2.82294i	−1.21428	+	0.136134i
$431$			14.6685i			0.706558i	0.935518	+	0.353279i	$0.114933\pi$
$431$			14.6685i			0.706558i	−0.935518	+	0.353279i	$0.885067\pi$
$432$	16.7996	−	12.2382i	0.808272	−	0.588809i
$433$	−2.81186	+	2.81186i	−0.135129	+	0.135129i	−0.771436	−	0.636307i	$-0.780461\pi$
$433$	−2.81186	+	2.81186i	−0.135129	+	0.135129i	0.636307	+	0.771436i	$0.280461\pi$
$434$	0.259780	+	6.16652i	0.0124698	+	0.296003i
$435$	11.1613	+	12.0564i	0.535143	+	0.578059i
$436$	2.19443	+	25.9989i	0.105094	+	1.24512i
$437$	−36.1531	+	9.68719i	−1.72944	+	0.463401i
$438$	−0.0978521	−	0.111697i	−0.00467556	−	0.00533707i
$439$	1.30959	−	0.756093i	0.0625034	−	0.0360864i	−0.468423	−	0.883505i	$-0.655178\pi$
$439$	1.30959	−	0.756093i	0.0625034	−	0.0360864i	0.530926	+	0.847418i	$0.321844\pi$
$440$	−4.23694	−	2.83410i	−0.201988	−	0.135110i
$441$	−4.56267	+	4.99949i	−0.217270	+	0.238071i
$442$	1.51400	−	0.474816i	0.0720136	−	0.0225847i
$443$	27.9867	+	7.49902i	1.32969	+	0.356289i	0.852599	−	0.522565i	$-0.175025\pi$
$443$	27.9867	+	7.49902i	1.32969	+	0.356289i	0.477090	+	0.878854i	$0.341692\pi$
$444$	−0.106966	+	4.48044i	−0.00507640	+	0.212632i
$445$	−34.2746	−	16.7284i	−1.62477	−	0.793000i
$446$	8.60016	+	13.5452i	0.407229	+	0.641386i
$447$	1.72034	+	11.1027i	0.0813692	+	0.525142i
$448$	17.4235	+	0.160018i	0.823184	+	0.00756016i
$449$	−15.4060			−0.727053			−0.363527	−	0.931584i	$-0.618427\pi$
$449$	−15.4060			−0.727053			−0.363527	+	0.931584i	$0.618427\pi$
$450$	20.2859	+	6.20328i	0.956288	+	0.292425i
$451$		−	2.69281i		−	0.126800i
$452$	9.27577	+	25.7298i	0.436295	+	1.21023i
$453$	−11.4766	+	29.6002i	−0.539216	+	1.39074i
$454$	−0.284811	+	0.180832i	−0.0133668	+	0.00848688i
$455$	−2.50674	+	5.13605i	−0.117518	+	0.240782i
$456$	−37.8592	+	0.690366i	−1.77292	+	0.0323294i
$457$	−0.578576	+	2.15928i	−0.0270647	+	0.101007i	−0.978137	−	0.207962i	$-0.933317\pi$
$457$	−0.578576	+	2.15928i	−0.0270647	+	0.101007i	0.951072	+	0.308968i	$0.0999837\pi$
$458$	19.0879	−	5.98628i	0.891918	−	0.279720i
$459$	1.58269	−	4.70922i	0.0738738	−	0.219808i
$460$	−2.33543	+	21.5297i	−0.108890	+	1.00383i
$461$	−4.41381	−	7.64494i	−0.205572	−	0.356060i	0.744743	−	0.667351i	$-0.232572\pi$
$461$	−4.41381	−	7.64494i	−0.205572	−	0.356060i	−0.950315	+	0.311291i	$0.899239\pi$
$462$	−0.836672	−	4.21775i	−0.0389255	−	0.196227i
$463$	2.94944	+	11.0075i	0.137072	+	0.511561i	0.999981	+	0.00620041i	$0.00197366\pi$
$463$	2.94944	+	11.0075i	0.137072	+	0.511561i	−0.862909	+	0.505360i	$0.831360\pi$
$464$	−13.0651	+	10.8273i	−0.606531	+	0.502644i
$465$	−7.41316	−	2.29586i	−0.343777	−	0.106468i
$466$	0.203210	+	4.82368i	0.00941350	+	0.223453i
$467$	−1.06356	−	1.06356i	−0.0492158	−	0.0492158i	0.682071	−	0.731286i	$-0.261080\pi$
$467$	−1.06356	−	1.06356i	−0.0492158	−	0.0492158i	−0.731286	+	0.682071i	$0.761080\pi$
$468$	−6.98162	+	0.911730i	−0.322725	+	0.0421447i
$469$	−20.7874			−0.959873
$470$	−3.50240	−	31.2405i	−0.161554	−	1.44102i
$471$	13.6662	−	18.6779i	0.629707	−	0.860631i
$472$	−27.6845	+	11.3186i	−1.27428	+	0.520982i
$473$	−6.23780	+	1.67141i	−0.286814	+	0.0768517i
$474$	11.8003	+	23.9603i	0.542008	+	1.10053i
$475$	−23.7765	−	30.4666i	−1.09094	−	1.39790i
$476$	3.41895	−	2.37841i	0.156707	−	0.109014i
$477$	16.1677	+	25.2656i	0.740269	+	1.15683i
$478$	−29.1195	+	9.13237i	−1.33190	+	0.417705i
$479$	2.51594	+	4.35773i	0.114956	+	0.199110i	0.917762	−	0.397130i	$-0.129994\pi$
$479$	2.51594	+	4.35773i	0.114956	+	0.199110i	−0.802806	+	0.596240i	$0.796661\pi$
$480$	−7.54581	+	20.5684i	−0.344418	+	0.938817i
$481$	0.759104	−	1.31481i	0.0346121	−	0.0599500i
$482$	−3.78234	+	16.9383i	−0.172281	+	0.771519i
$483$	−14.2353	+	11.4487i	−0.647730	+	0.520933i
$484$	18.7344	+	8.80593i	0.851565	+	0.400270i
$485$	19.3436	−	22.2400i	0.878346	−	1.00987i
$486$	−10.5357	+	19.3649i	−0.477907	+	0.878410i
$487$	11.8553	+	11.8553i	0.537216	+	0.537216i	0.922710	−	0.385494i	$-0.125969\pi$
$487$	11.8553	+	11.8553i	0.537216	+	0.537216i	−0.385494	+	0.922710i	$0.625969\pi$
$488$	1.07290	−	7.87008i	0.0485680	−	0.356262i
$489$	−1.50215	+	13.8450i	−0.0679294	+	0.626092i
$490$	1.06728	−	7.05436i	0.0482148	−	0.318684i
$491$	−7.84742	+	13.5921i	−0.354149	+	0.613404i	−0.986972	−	0.160892i	$-0.948563\pi$
$491$	−7.84742	+	13.5921i	−0.354149	+	0.613404i	0.632823	+	0.774297i	$0.281896\pi$
$492$	−11.2477	+	2.72784i	−0.507087	+	0.122981i
$493$	−1.04974	+	3.91769i	−0.0472779	+	0.176444i
$494$	11.3687	+	5.94032i	0.511503	+	0.267268i
$495$	5.34864	+	0.789817i	0.240404	+	0.0354996i
$496$	2.78737	−	7.51475i	0.125156	−	0.337422i
$497$	6.29212	+	1.68597i	0.282240	+	0.0756260i
$498$	1.55064	−	4.56021i	0.0694857	−	0.204348i
$499$	0.533380	−	0.923842i	0.0238774	−	0.0413568i	−0.853840	−	0.520536i	$-0.825732\pi$
$499$	0.533380	−	0.923842i	0.0238774	−	0.0413568i	0.877717	+	0.479179i	$0.159066\pi$
$500$	−21.4088	+	6.45473i	−0.957430	+	0.288664i
$501$	8.49036	−	11.6039i	0.379321	−	0.518424i
$502$	15.0979	+	13.8772i	0.673850	+	0.619370i
$503$	7.39374	+	7.39374i	0.329670	+	0.329670i	0.852461	−	0.522791i	$-0.175109\pi$
$503$	7.39374	+	7.39374i	0.329670	+	0.329670i	−0.522791	+	0.852461i	$0.675109\pi$
$504$	−16.7697	+	7.76734i	−0.746983	+	0.345985i
$505$	−2.36172	−	33.9063i	−0.105095	−	1.50881i
$506$	0.232317	+	5.51461i	0.0103277	+	0.245154i
$507$	−18.7701	−	7.27750i	−0.833609	−	0.323205i
$508$	18.9301	−	22.4203i	0.839889	−	0.994740i
$509$	−8.70886	−	5.02806i	−0.386014	−	0.222865i	0.294418	−	0.955677i	$-0.404874\pi$
$509$	−8.70886	−	5.02806i	−0.386014	−	0.222865i	−0.680431	+	0.732812i	$0.738208\pi$
$510$	1.37343	+	5.05349i	0.0608166	+	0.223772i
$511$	0.0660199	+	0.114350i	0.00292055	+	0.00505854i
$512$	−20.7837	−	8.94629i	−0.918520	−	0.395374i
$513$	35.9667	−	17.8723i	1.58797	−	0.789080i
$514$	11.7475	−	22.4827i	0.518160	−	0.991668i
$515$	−7.20671	+	37.0217i	−0.317565	+	1.63137i
$516$	13.3003	+	24.3618i	0.585515	+	1.07247i
$517$	−2.07371	−	7.73919i	−0.0912016	−	0.340369i
$518$	0.868476	−	3.88926i	0.0381587	−	0.170884i
$519$	−14.5003	−	32.8644i	−0.636491	−	1.44259i
$520$	5.58242	−	4.89072i	0.244805	−	0.214472i
$521$		−	11.5423i		−	0.505675i	−0.967509	−	0.252838i	$-0.918636\pi$
$521$		−	11.5423i		−	0.505675i	0.967509	−	0.252838i	$-0.0813639\pi$
$522$	7.59822	−	16.3151i	0.332565	−	0.714094i
$523$	−8.88496	−	8.88496i	−0.388512	−	0.388512i	0.485644	−	0.874156i	$-0.338585\pi$
$523$	−8.88496	−	8.88496i	−0.388512	−	0.388512i	−0.874156	+	0.485644i	$0.838585\pi$
$524$	20.6628	+	9.71236i	0.902660	+	0.424286i
$525$	−16.6198	−	8.92016i	−0.725348	−	0.389308i
$526$	−21.8874	+	13.8968i	−0.954336	+	0.605928i
$527$	−0.495847	−	1.85053i	−0.0215994	−	0.0806101i
$528$	−1.11737	+	5.47102i	−0.0486273	+	0.238095i
$529$	0.389000	−	0.224590i	0.0169131	−	0.00976476i
$530$	−28.9731	−	12.6600i	−1.25851	−	0.549915i
$531$	21.3846	−	23.4319i	0.928014	−	1.01686i
$532$	33.1396	+	5.94806i	1.43678	+	0.257881i
$533$	3.78709	+	1.01475i	0.164037	+	0.0439536i
$534$	−2.75427	+	41.6884i	−0.119189	+	1.80403i
$535$	−10.8864	−	31.6443i	−0.470661	−	1.36810i
$536$	24.8923	+	10.4449i	1.07518	+	0.451151i
$537$	−8.30701	+	6.68086i	−0.358474	+	0.288301i
$538$	5.86338	−	6.37912i	0.252788	−	0.275024i
$539$		−	1.81842i		−	0.0783248i
$540$	−2.11920	−	23.1411i	−0.0911957	−	0.995833i
$541$			2.38060i			0.102350i	0.998690	+	0.0511750i	$0.0162966\pi$
$541$			2.38060i			0.102350i	−0.998690	+	0.0511750i	$0.983703\pi$
$542$	−21.9910	−	20.2131i	−0.944595	−	0.868226i
$543$	−3.64731	+	2.93333i	−0.156521	+	0.125881i
$544$	−5.28914	+	1.13018i	−0.226770	+	0.0484560i
$545$	26.2153	+	12.7948i	1.12294	+	0.548071i
$546$	6.24700	+	0.412726i	0.267347	+	0.0176631i
$547$	27.8742	+	7.46886i	1.19181	+	0.319345i	0.799602	−	0.600530i	$-0.205044\pi$
$547$	27.8742	+	7.46886i	1.19181	+	0.319345i	0.392211	+	0.919875i	$0.371710\pi$
$548$	−2.44064	+	13.5980i	−0.104259	+	0.580879i
$549$	2.54955	+	8.02964i	0.108812	+	0.342697i
$550$	−5.14900	+	2.44286i	−0.219554	+	0.104164i
$551$	−28.3955	+	16.3941i	−1.20969	+	0.698413i
$552$	22.7989	−	6.55672i	0.970385	−	0.279073i
$553$	−6.14659	−	22.9394i	−0.261380	−	0.975482i
$554$	23.1425	+	36.4495i	0.983231	+	1.54859i
$555$	4.23967	+	2.67067i	0.179964	+	0.113363i
$556$	10.7890	+	5.07124i	0.457554	+	0.215069i
$557$	17.9019	+	17.9019i	0.758530	+	0.758530i	0.976055	−	0.217525i	$-0.0697984\pi$
$557$	17.9019	+	17.9019i	0.758530	+	0.758530i	−0.217525	+	0.976055i	$0.569798\pi$
$558$	0.745048	+	8.46853i	0.0315404	+	0.358501i
$559$		−	9.40250i		−	0.397683i
$560$	10.1400	−	16.6339i	0.428492	−	0.702911i
$561$	0.538782	+	1.22113i	0.0227474	+	0.0515563i
$562$	44.6086	+	9.96115i	1.88170	+	0.420186i
$563$	0.935882	+	3.49276i	0.0394427	+	0.147202i	0.982839	−	0.184465i	$-0.0590554\pi$
$563$	0.935882	+	3.49276i	0.0394427	+	0.147202i	−0.943396	+	0.331668i	$0.892389\pi$
$564$	−30.2255	+	16.5016i	−1.27272	+	0.694844i
$565$	30.0156	+	5.84289i	1.26277	+	0.245812i
$566$	33.5297	+	17.5197i	1.40936	+	0.736409i
$567$	12.5394	−	15.0669i	0.526607	−	0.632752i
$568$	−6.68748	−	5.18045i	−0.280601	−	0.217367i
$569$	−2.95838	−	5.12406i	−0.124022	−	0.214812i	0.797328	−	0.603546i	$-0.206246\pi$
$569$	−2.95838	−	5.12406i	−0.124022	−	0.214812i	−0.921350	+	0.388734i	$0.872913\pi$
$570$	−21.0364	+	36.7384i	−0.881119	+	1.53880i
$571$	−33.1487	−	19.1384i	−1.38723	−	0.800916i	−0.394226	−	0.919014i	$-0.628987\pi$
$571$	−33.1487	−	19.1384i	−1.38723	−	0.800916i	−0.993002	+	0.118097i	$0.962321\pi$
$572$	1.22032	−	1.44532i	0.0510243	−	0.0604317i
$573$	7.14777	+	2.77132i	0.298603	+	0.115774i
$574$	10.2820	−	0.433157i	0.429164	−	0.0180796i
$575$	19.3288	+	14.5817i	0.806067	+	0.608100i
$576$	23.9840	−	0.874994i	0.999335	−	0.0364581i
$577$	−21.4686	−	21.4686i	−0.893751	−	0.893751i	0.101123	−	0.994874i	$-0.467756\pi$
$577$	−21.4686	−	21.4686i	−0.893751	−	0.893751i	−0.994874	+	0.101123i	$0.967756\pi$
$578$	15.3946	−	16.7487i	0.640329	−	0.696653i
$579$	−20.9699	+	28.6599i	−0.871479	+	1.19106i
$580$	2.90530	+	18.7474i	0.120636	+	0.778445i
$581$	−2.14142	+	3.70905i	−0.0888412	+	0.153877i
$582$	−30.5696	−	10.3948i	−1.26715	−	0.430878i
$583$	−7.78402	−	2.08572i	−0.322381	−	0.0863818i
$584$	−0.0216003	−	0.170103i	−0.000893827	−	0.00703891i
$585$	−3.12633	+	7.22453i	−0.129258	+	0.298698i
$586$	5.00769	−	9.58383i	0.206866	−	0.395904i
$587$	1.85957	−	6.94002i	0.0767527	−	0.286445i	−0.916872	−	0.399181i	$-0.869295\pi$
$587$	1.85957	−	6.94002i	0.0767527	−	0.286445i	0.993625	+	0.112736i	$0.0359613\pi$
$588$	−7.59543	+	1.84207i	−0.313230	+	0.0759658i
$589$	7.74379	−	13.4126i	0.319077	−	0.552658i
$590$	−5.00220	+	33.0629i	−0.205937	+	1.36118i
$591$	−0.931797	+	8.58819i	−0.0383290	+	0.353271i
$592$	−2.99418	+	4.22090i	−0.123060	+	0.173478i
$593$	14.6743	+	14.6743i	0.602601	+	0.602601i	0.941002	−	0.338401i	$-0.109886\pi$
$593$	14.6743	+	14.6743i	0.602601	+	0.602601i	−0.338401	+	0.941002i	$0.609886\pi$
$594$	−1.41633	−	5.75084i	−0.0581129	−	0.235960i
$595$	−0.323558	−	4.64519i	−0.0132646	−	0.190434i
$596$	−5.51873	+	11.7410i	−0.226056	+	0.480930i
$597$	29.0918	−	23.3969i	1.19065	−	0.957572i
$598$	−7.84313	−	1.75138i	−0.320729	−	0.0716192i
$599$	−14.5185	+	25.1467i	−0.593208	+	1.02747i	0.400589	+	0.916258i	$0.368806\pi$
$599$	−14.5185	+	25.1467i	−0.593208	+	1.02747i	−0.993797	+	0.111209i	$0.964528\pi$
$600$	15.4197	+	19.0324i	0.629505	+	0.776996i
$601$	−6.04414	−	10.4688i	−0.246546	−	0.427029i	0.716019	−	0.698080i	$-0.245962\pi$
$601$	−6.04414	−	10.4688i	−0.246546	−	0.427029i	−0.962565	+	0.271051i	$0.912629\pi$
$602$	−7.38539	−	23.5491i	−0.301006	−	0.959790i
$603$	−28.6025	+	1.30661i	−1.16479	+	0.0532094i
$604$	−30.0931	+	20.9344i	−1.22447	+	0.851811i
$605$	19.1909	−	12.9369i	0.780222	−	0.525959i
$606$	−33.4014	+	16.4501i	−1.35684	+	0.668238i
$607$	6.55916	−	1.75752i	0.266228	−	0.0713356i	−0.123236	−	0.992377i	$-0.539327\pi$
$607$	6.55916	−	1.75752i	0.266228	−	0.0713356i	0.389464	+	0.921042i	$0.372660\pi$
$608$	−36.6950	−	23.7740i	−1.48818	−	0.964164i
$609$	−9.44980	+	12.9152i	−0.382925	+	0.523350i
$610$	−6.93990	−	5.54069i	−0.280988	−	0.224336i
$611$	11.6656			0.471940
$612$	4.55482	−	3.48748i	0.184118	−	0.140973i
$613$	3.21798	+	3.21798i	0.129973	+	0.129973i	0.769101	−	0.639128i	$-0.220704\pi$
$613$	3.21798	+	3.21798i	0.129973	+	0.129973i	−0.639128	+	0.769101i	$0.720704\pi$
$614$	−17.0169	+	0.716878i	−0.686745	+	0.0289308i
$615$	−3.82810	+	12.3607i	−0.154364	+	0.498431i
$616$	1.92112	−	4.57841i	0.0774040	−	0.184469i
$617$	−10.9680	−	40.9332i	−0.441556	−	1.64791i	−0.724873	−	0.688883i	$-0.758101\pi$
$617$	−10.9680	−	40.9332i	−0.441556	−	1.64791i	0.283317	−	0.959026i	$-0.408565\pi$
$618$	40.5268	−	8.03928i	1.63023	−	0.323387i
$619$	−9.64315	−	16.7024i	−0.387591	−	0.671327i	0.604534	−	0.796579i	$-0.293359\pi$
$619$	−9.64315	−	16.7024i	−0.387591	−	0.671327i	−0.992125	+	0.125252i	$0.960026\pi$
$620$	−5.61616	−	6.98283i	−0.225550	−	0.280437i
$621$	−18.8675	+	16.6476i	−0.757128	+	0.668046i
$622$	0.478959	+	1.52721i	0.0192045	+	0.0612356i
$623$	9.61492	−	35.8834i	0.385214	−	1.43764i
$624$	−7.27321	−	3.63311i	−0.291161	−	0.145441i
$625$	−6.07435	+	24.2508i	−0.242974	+	0.970033i
$626$	9.99136	+	15.7364i	0.399335	+	0.628953i
$627$	−3.90055	+	10.0603i	−0.155773	+	0.401768i
$628$	25.1402	−	9.06323i	1.00320	−	0.361662i
$629$			1.23697i			0.0493213i
$630$	−2.15541	+	20.5499i	−0.0858738	+	0.818728i
$631$	12.7634			0.508101			0.254051	−	0.967191i	$-0.418237\pi$
$631$	12.7634			0.508101			0.254051	+	0.967191i	$0.418237\pi$
$632$	−4.16583	+	30.5577i	−0.165708	+	1.21552i
$633$	3.33411	+	21.5177i	0.132519	+	0.855252i
$634$	35.7096	−	22.6727i	1.41821	−	0.900449i
$635$	−10.6724	−	31.0222i	−0.423521	−	1.23108i
$636$	−0.826669	+	34.6263i	−0.0327796	+	1.37302i
$637$	2.55737	+	0.685244i	0.101327	+	0.0271504i
$638$	1.44692	+	4.61366i	0.0572841	+	0.182656i
$639$	8.76364	+	1.92432i	0.346684	+	0.0761249i
$640$	−20.5002	+	14.8237i	−0.810343	+	0.585956i
$641$	−32.3641	+	18.6854i	−1.27830	+	0.738029i	−0.976536	−	0.215353i	$-0.930910\pi$
$641$	−32.3641	+	18.6854i	−1.27830	+	0.738029i	−0.301767	+	0.953382i	$0.597577\pi$
$642$	−27.5740	+	24.1563i	−1.08826	+	0.953373i
$643$	−12.6990	+	3.40269i	−0.500801	+	0.134189i	−0.500372	−	0.865811i	$-0.666803\pi$
$643$	−12.6990	+	3.40269i	−0.500801	+	0.134189i	−0.000429141		1.00000i	$0.500137\pi$
$644$	−21.0192	+	1.77412i	−0.828274	+	0.0699103i
$645$	31.0091	+	1.19545i	1.22098	+	0.0470710i
$646$	−10.4417	+	0.439885i	−0.410825	+	0.0173070i
$647$	2.84972	−	2.84972i	0.112034	−	0.112034i	−0.648867	−	0.760902i	$-0.724757\pi$
$647$	2.84972	−	2.84972i	0.112034	−	0.112034i	0.760902	+	0.648867i	$0.224757\pi$
$648$	−22.5862	+	11.7416i	−0.887269	+	0.461253i
$649$			8.52269i			0.334545i
$650$	−1.49524	−	8.16195i	−0.0586480	−	0.320138i
$651$	0.815360	−	7.51501i	0.0319565	−	0.294537i
$652$	−10.3741	+	12.2868i	−0.406281	+	0.481187i
$653$	11.1822	+	41.7324i	0.437592	+	1.63312i	0.734787	+	0.678298i	$0.237282\pi$
$653$	11.1822	+	41.7324i	0.437592	+	1.63312i	−0.297195	+	0.954817i	$0.596051\pi$
$654$	2.10663	−	31.8857i	0.0823756	−	1.24683i
$655$	21.1663	−	14.2685i	0.827036	−	0.557517i
$656$	−12.5301	−	4.64765i	−0.489218	−	0.181460i
$657$	0.0980279	+	0.153190i	0.00382443	+	0.00597653i
$658$	29.2172	−	9.16300i	1.13900	−	0.357211i
$659$	13.4973	−	7.79269i	0.525781	−	0.303560i	−0.213515	−	0.976940i	$-0.568491\pi$
$659$	13.4973	−	7.79269i	0.525781	−	0.303560i	0.739297	+	0.673380i	$0.235158\pi$
$660$	4.61145	+	4.20835i	0.179501	+	0.163810i
$661$	13.3791	+	7.72445i	0.520389	+	0.300446i	0.737094	−	0.675791i	$-0.236198\pi$
$661$	13.3791	+	7.72445i	0.520389	+	0.300446i	−0.216705	+	0.976237i	$0.569531\pi$
$662$	19.5434	+	4.36407i	0.759577	+	0.169614i
$663$	−1.92040	+	0.297560i	−0.0745821	+	0.0115563i
$664$	4.42795	−	3.36549i	0.171838	−	0.130606i
$665$	24.7039	−	28.4030i	0.957976	−	1.10142i
$666$	0.950521	−	5.40604i	0.0368319	−	0.209480i
$667$	14.5254	−	14.5254i	0.562427	−	0.562427i
$668$	15.6187	−	5.63066i	0.604307	−	0.217857i
$669$	−7.93244	−	17.9786i	−0.306686	−	0.695094i
$670$	24.2936	−	17.9087i	0.938545	−	0.691873i
$671$	−1.96013	−	1.13168i	−0.0756699	−	0.0436881i
$672$	−21.0699	−	3.38643i	−0.812788	−	0.130635i
$673$	−27.5672	−	7.38662i	−1.06264	−	0.284733i	−0.315173	−	0.949034i	$-0.602063\pi$
$673$	−27.5672	−	7.38662i	−1.06264	−	0.284733i	−0.747465	+	0.664301i	$0.768729\pi$
$674$	13.1886	+	6.89121i	0.508005	+	0.265440i
$675$	−23.4288	−	11.2291i	−0.901774	−	0.432208i
$676$	−13.2749	−	19.0826i	−0.510574	−	0.733947i
$677$	3.53348	−	13.1871i	0.135803	−	0.506822i	−0.864191	−	0.503165i	$-0.832169\pi$
$677$	3.53348	−	13.1871i	0.135803	−	0.506822i	0.999993	−	0.00365795i	$-0.00116436\pi$
$678$	−6.51790	−	32.8574i	−0.250319	−	1.26188i
$679$	24.8638	+	14.3551i	0.954186	+	0.550900i
$680$	−1.94658	+	5.72505i	−0.0746481	+	0.219546i
$681$	0.378030	−	0.166792i	0.0144861	−	0.00639150i
$682$	−1.68152	−	1.54557i	−0.0643889	−	0.0591831i
$683$	16.8609	−	16.8609i	0.645163	−	0.645163i	−0.306657	−	0.951820i	$-0.599211\pi$
$683$	16.8609	−	16.8609i	0.645163	−	0.645163i	0.951820	+	0.306657i	$0.0992106\pi$
$684$	45.9725	+	6.10125i	1.75780	+	0.233287i
$685$	11.6545	+	10.1366i	0.445296	+	0.387301i
$686$	28.4856	−	1.20003i	1.08759	−	0.0458173i
$687$	−24.2116	+	3.75151i	−0.923729	+	0.143129i
$688$	−2.98876	+	31.9102i	−0.113945	+	1.21657i
$689$	5.86659	−	10.1612i	0.223499	−	0.387112i
$690$	6.77318	−	25.6437i	0.257851	−	0.976239i
$691$	−9.94647	+	5.74260i	−0.378381	+	0.218459i	−0.677114	−	0.735878i	$-0.736770\pi$
$691$	−9.94647	+	5.74260i	−0.378381	+	0.218459i	0.298732	+	0.954337i	$0.403436\pi$
$692$	7.32762	−	40.8258i	0.278554	−	1.55196i
$693$	0.240324	+	5.26083i	0.00912914	+	0.199842i
$694$	−24.2315	−	12.6613i	−0.919814	−	0.480616i
$695$	11.0519	−	7.45021i	0.419221	−	0.282603i
$696$	17.8052	−	10.7174i	0.674906	−	0.406241i
$697$	−3.08556	+	0.826774i	−0.116874	+	0.0313163i
$698$	1.79259	−	8.02769i	0.0678506	−	0.303853i
$699$	0.637804	−	5.87852i	0.0241240	−	0.222346i
$700$	−10.1559	−	19.2676i	−0.383856	−	0.728247i
$701$	10.3201			0.389786			0.194893	−	0.980825i	$-0.437564\pi$
$701$	10.3201			0.389786			0.194893	+	0.980825i	$0.437564\pi$
$702$	8.62153	+	0.175232i	0.325398	+	0.00661371i
$703$	−7.07094	+	7.07094i	−0.266685	+	0.266685i
$704$	−4.60096	+	4.51722i	−0.173405	+	0.170249i
$705$	−1.48319	+	38.4728i	−0.0558602	+	1.44897i
$706$	−15.4236	+	9.79278i	−0.580476	+	0.368556i
$707$	31.9782	−	8.56854i	1.20266	−	0.322253i
$708$	35.5988	−	8.63355i	1.33788	−	0.324469i
$709$	2.47357	+	4.28435i	0.0928970	+	0.160902i	0.908729	−	0.417387i	$-0.137054\pi$
$709$	2.47357	+	4.28435i	0.0928970	+	0.160902i	−0.815832	+	0.578289i	$0.803721\pi$
$710$	−8.80590	+	3.45042i	−0.330480	+	0.129492i
$711$	−9.89931	−	31.1772i	−0.371253	−	1.16924i
$712$	−29.5436	+	38.1381i	−1.10719	+	1.42929i
$713$	−2.51134	+	9.37246i	−0.0940505	+	0.351001i
$714$	−4.57602	+	2.25367i	−0.171253	+	0.0843416i
$715$	−0.687991	−	1.99983i	−0.0257294	−	0.0747895i
$716$	−12.2657	+	1.03529i	−0.458393	+	0.0386905i
$717$	36.9360	−	5.72312i	1.37940	−	0.213734i
$718$	7.21907	+	6.63542i	0.269413	+	0.247632i
$719$	0.960473			0.0358196			0.0179098	−	0.999840i	$-0.494299\pi$
$719$	0.960473			0.0358196			0.0179098	+	0.999840i	$0.494299\pi$
$720$	12.9066	−	23.5249i	0.481001	−	0.876720i
$721$	−36.7377			−1.36818
$722$	−42.4201	−	38.9905i	−1.57871	−	1.45108i
$723$	7.68401	−	19.8185i	0.285771	−	0.737059i
$724$	−5.38545	+	0.454558i	−0.200149	+	0.0168935i
$725$	19.6617	+	7.95625i	0.730217	+	0.295488i
$726$	−21.0731	−	14.0965i	−0.782095	−	0.523170i
$727$	3.60361	−	13.4488i	0.133650	−	0.498790i	−0.866349	−	0.499438i	$-0.833540\pi$
$727$	3.60361	−	13.4488i	0.133650	−	0.498790i	1.00000		0.000648487i	$0.000206420\pi$
$728$	5.71499	+	4.42711i	0.211812	+	0.164080i
$729$	16.3067	−	21.5196i	0.603950	−	0.797022i
$730$	−0.175670	−	0.0767600i	−0.00650183	−	0.00284102i
$731$	3.83038	+	6.63441i	0.141672	+	0.245382i
$732$	−2.74134	+	9.33375i	−0.101323	+	0.344985i
$733$	11.8211	−	3.16746i	0.436623	−	0.116993i	−0.0338105	−	0.999428i	$-0.510764\pi$
$733$	11.8211	−	3.16746i	0.436623	−	0.116993i	0.470433	+	0.882436i	$0.344098\pi$
$734$	−6.16177	+	3.91223i	−0.227435	+	0.144403i
$735$	−2.58506	+	8.34699i	−0.0953515	+	0.307883i
$736$	26.0613	+	8.43692i	0.960633	+	0.310989i
$737$	5.43929	−	5.43929i	0.200359	−	0.200359i
$738$	14.1204	−	1.24229i	0.519779	−	0.0457294i
$739$	−28.4989			−1.04835			−0.524174	−	0.851611i	$-0.675626\pi$
$739$	−28.4989			−1.04835			−0.524174	+	0.851611i	$0.675626\pi$
$740$	2.33570	+	5.29347i	0.0858621	+	0.194592i
$741$	−12.6786	−	9.27668i	−0.465759	−	0.340787i
$742$	6.71186	−	30.0574i	0.246400	−	1.10344i
$743$	−19.7005	+	5.27873i	−0.722741	+	0.193658i	−0.601394	−	0.798952i	$-0.705388\pi$
$743$	−19.7005	+	5.27873i	−0.722741	+	0.193658i	−0.121347	+	0.992610i	$0.538721\pi$
$744$	−4.75238	+	8.58931i	−0.174231	+	0.314899i
$745$	8.10762	+	12.0271i	0.297040	+	0.440638i
$746$	18.1551	+	9.48630i	0.664706	+	0.347318i
$747$	−2.71336	+	5.23809i	−0.0992768	+	0.191652i
$748$	−0.272270	+	1.51695i	−0.00995518	+	0.0554652i
$749$	28.2290	−	16.2980i	1.03146	−	0.595517i
$750$	27.1079	−	3.89351i	0.989842	−	0.142171i
$751$	15.4375	−	26.7385i	0.563321	−	0.975700i	−0.433883	−	0.900969i	$-0.642857\pi$
$751$	15.4375	−	26.7385i	0.563321	−	0.975700i	0.997204	−	0.0747309i	$-0.0238098\pi$
$752$	−39.5908	−	3.70813i	−1.44373	−	0.135221i
$753$	−15.7401	−	19.5713i	−0.573600	−	0.713216i
$754$	−7.03376	+	0.296315i	−0.256154	+	0.0107911i
$755$	2.84792	+	40.8864i	0.103646	+	1.48801i
$756$	21.7307	−	6.33308i	0.790340	−	0.230332i
$757$	29.3088	−	29.3088i	1.06525	−	1.06525i	0.0675289	−	0.997717i	$-0.478489\pi$
$757$	29.3088	−	29.3088i	1.06525	−	1.06525i	0.997717	−	0.0675289i	$-0.0215115\pi$
$758$	7.95211	+	7.30919i	0.288834	+	0.265482i
$759$	0.729162	−	6.72054i	0.0264669	−	0.243940i
$760$	−43.8536	+	21.5990i	−1.59074	+	0.783478i
$761$	−34.9305	−	20.1671i	−1.26623	−	0.731057i	−0.291956	−	0.956432i	$-0.594306\pi$
$761$	−34.9305	−	20.1671i	−1.26623	−	0.731057i	−0.974272	+	0.225375i	$0.927639\pi$
$762$	−27.0319	+	23.6814i	−0.979262	+	0.857885i
$763$	−7.35406	+	27.4457i	−0.266235	+	0.993602i
$764$	5.05518	+	7.26680i	0.182890	+	0.262903i
$765$	−0.737179	−	6.37124i	−0.0266528	−	0.230353i
$766$	17.4747	+	9.13077i	0.631386	+	0.329908i
$767$	−11.9860	−	3.21165i	−0.432791	−	0.115966i
$768$	23.5290	+	14.6420i	0.849029	+	0.528347i
$769$	−5.23950	−	3.02503i	−0.188941	−	0.109085i	0.402546	−	0.915400i	$-0.368126\pi$
$769$	−5.23950	−	3.02503i	−0.188941	−	0.109085i	−0.591487	+	0.806315i	$0.701459\pi$
$770$	−3.29393	−	4.46830i	−0.118705	−	0.161026i
$771$	−18.3454	+	25.0730i	−0.660695	+	0.902983i
$772$	−38.5759	+	13.9069i	−1.38838	+	0.500520i
$773$	−3.55922	+	3.55922i	−0.128016	+	0.128016i	−0.768212	−	0.640196i	$-0.778853\pi$
$773$	−3.55922	+	3.55922i	−0.128016	+	0.128016i	0.640196	+	0.768212i	$0.278853\pi$
$774$	−11.6422	−	31.9383i	−0.418469	−	1.14800i
$775$	−9.92206	+	1.38897i	−0.356411	+	0.0498932i
$776$	−22.5608	−	29.6830i	−0.809884	−	1.06556i
$777$	−1.76435	+	4.55060i	−0.0632958	+	0.163252i
$778$	−27.1471	−	6.06197i	−0.973270	−	0.217332i
$779$	−22.3642	−	12.9120i	−0.801281	−	0.462620i
$780$	−7.65625	+	4.89955i	−0.274138	+	0.175432i
$781$	−2.08757	+	1.20526i	−0.0746990	+	0.0431275i
$782$	6.24759	−	1.95935i	0.223413	−	0.0700662i
$783$	−12.1907	+	18.3647i	−0.435660	+	0.656301i
$784$	−8.46138	−	3.13849i	−0.302192	−	0.112089i
$785$	5.70901	−	29.3278i	0.203763	−	1.04676i
$786$	−23.2422	−	15.5475i	−0.829021	−	0.554561i
$787$	12.0820	+	45.0906i	0.430677	+	1.60731i	0.751206	+	0.660068i	$0.229473\pi$
$787$	12.0820	+	45.0906i	0.430677	+	1.60731i	−0.320529	+	0.947239i	$0.603861\pi$
$788$	−6.43516	+	7.62162i	−0.229243	+	0.271509i
$789$	29.0512	−	12.8178i	1.03425	−	0.456326i
$790$	26.9460	+	21.5132i	0.958696	+	0.765405i
$791$			29.7854i			1.05905i
$792$	2.35559	−	6.42044i	0.0837022	−	0.228140i
$793$	2.33021	−	2.33021i	0.0827481	−	0.0827481i
$794$	0.771041	−	0.0324820i	0.0273632	−	0.00115274i
$795$	32.7655	+	20.6397i	1.16207	+	0.732016i
$796$	42.9556	−	3.62566i	1.52252	−	0.128508i
$797$	−10.8961	+	2.91961i	−0.385960	+	0.103418i	−0.446581	−	0.894743i	$-0.647359\pi$
$797$	−10.8961	+	2.91961i	−0.385960	+	0.103418i	0.0606208	+	0.998161i	$0.480692\pi$
$798$	−39.0408	−	13.2753i	−1.38203	−	0.469941i
$799$	−8.23126	+	4.75232i	−0.291201	+	0.168125i
$800$	2.48011	+	28.1753i	0.0876850	+	0.996148i
$801$	10.9742	−	49.9783i	0.387755	−	1.76590i
$802$	−0.448133	−	1.42892i	−0.0158241	−	0.0504569i
$803$	−0.0471960	−	0.0126461i	−0.00166551	−	0.000446272i
$804$	−28.2297	−	17.2096i	−0.995583	−	0.606935i
$805$	−10.3442	+	21.1942i	−0.364585	+	0.746996i
$806$	2.80731	−	1.78242i	0.0988831	−	0.0627829i
$807$	−8.26921	+	6.65047i	−0.291090	+	0.234107i
$808$	−42.5983	−	5.80729i	−1.49860	−	0.204300i
$809$	23.7479			0.834933			0.417467	−	0.908692i	$-0.362918\pi$
$809$	23.7479			0.834933			0.417467	+	0.908692i	$0.362918\pi$
$810$	−1.67407	+	28.4112i	−0.0588208	+	0.998269i
$811$			28.1683i			0.989124i	0.869142	+	0.494562i	$0.164671\pi$
$811$			28.1683i			0.989124i	−0.869142	+	0.494562i	$0.835329\pi$
$812$	−17.3837	+	6.26695i	−0.610048	+	0.219927i
$813$	22.9264	+	28.5068i	0.804065	+	0.999778i
$814$	0.790427	+	1.24492i	0.0277045	+	0.0436345i
$815$	5.84868	+	17.0008i	0.204870	+	0.595511i
$816$	6.61203	−	0.399426i	0.231467	−	0.0139827i
$817$	−16.0288	+	59.8202i	−0.560776	+	2.09284i
$818$	−4.44042	−	14.1588i	−0.155256	−	0.495049i
$819$	−7.48923	−	1.64448i	−0.261695	−	0.0574629i
$820$	−11.6432	+	9.36437i	−0.406597	+	0.327018i
$821$	−24.5653	−	42.5483i	−0.857334	−	1.48495i	−0.874463	−	0.485093i	$-0.838786\pi$
$821$	−24.5653	−	42.5483i	−0.857334	−	1.48495i	0.0171287	−	0.999853i	$-0.494548\pi$
$822$	5.44720	−	16.0195i	0.189993	−	0.558743i
$823$	−4.86264	−	18.1476i	−0.169501	−	0.632587i	−0.997423	−	0.0717434i	$-0.977144\pi$
$823$	−4.86264	−	18.1476i	−0.169501	−	0.632587i	0.827922	−	0.560843i	$-0.189523\pi$
$824$	43.9923	+	18.4593i	1.53254	+	0.643061i
$825$	6.68286	−	2.01471i	0.232667	−	0.0701432i
$826$	−32.5424	+	1.37093i	−1.13229	+	0.0477007i
$827$	8.79755	+	8.79755i	0.305921	+	0.305921i	0.843325	−	0.537404i	$-0.180595\pi$
$827$	8.79755	+	8.79755i	0.305921	+	0.305921i	−0.537404	+	0.843325i	$0.680595\pi$
$828$	−28.8100	+	3.76230i	−1.00122	+	0.130749i
$829$	−45.1878			−1.56944			−0.784719	−	0.619851i	$-0.787193\pi$
$829$	−45.1878			−1.56944			−0.784719	+	0.619851i	$0.787193\pi$
$830$	−0.692793	−	6.17953i	−0.0240472	−	0.214495i
$831$	−21.3457	−	48.3794i	−0.740475	−	1.67826i
$832$	−4.61907	−	8.17290i	−0.160137	−	0.283344i
$833$	−2.08363	+	0.558308i	−0.0721936	+	0.0193442i
$834$	−12.1358	−	8.11802i	−0.420227	−	0.281104i
$835$	3.54680	−	18.2204i	0.122742	−	0.630541i
$836$	−10.2278	+	7.11501i	−0.353735	+	0.246078i
$837$	0.649535	−	10.3916i	0.0224512	−	0.359185i
$838$	2.72721	+	8.69601i	0.0942100	+	0.300399i
$839$	−8.52147	−	14.7596i	−0.294194	−	0.509558i	0.680603	−	0.732652i	$-0.261718\pi$
$839$	−8.52147	−	14.7596i	−0.294194	−	0.509558i	−0.974797	+	0.223094i	$0.928384\pi$
$840$	−15.3271	+	18.2850i	−0.528834	+	0.630892i
$841$	−5.50231	+	9.53028i	−0.189735	+	0.328630i
$842$	19.0327	+	4.25003i	0.655911	+	0.146466i
$843$	−52.1940	−	20.2366i	−1.79766	−	0.696984i
$844$	−10.6956	+	22.7547i	−0.368158	+	0.783248i
$845$	−25.9269	+	1.80592i	−0.891911	+	0.0621255i
$846$	39.6256	−	14.4443i	1.36236	−	0.496607i
$847$	15.9407	+	15.9407i	0.547728	+	0.547728i
$848$	−23.1400	+	32.6204i	−0.794630	+	1.12019i
$849$	−37.3928	−	27.3596i	−1.28332	−	0.938980i
$850$	4.38004	+	5.14995i	0.150234	+	0.176642i
$851$	3.13248	−	5.42561i	0.107380	−	0.185988i
$852$	7.14902	+	7.49872i	0.244921	+	0.256902i
$853$	8.94360	−	33.3780i	0.306223	−	1.14284i	−0.625664	−	0.780092i	$-0.715172\pi$
$853$	8.94360	−	33.3780i	0.306223	−	1.14284i	0.931887	−	0.362748i	$-0.118161\pi$
$854$	4.00583	−	7.66645i	0.137077	−	0.262341i
$855$	32.2062	−	40.6341i	1.10143	−	1.38966i
$856$	−41.9925	+	5.33237i	−1.43527	+	0.182257i
$857$	13.2382	+	3.54715i	0.452207	+	0.121168i	0.477732	−	0.878506i	$-0.341459\pi$
$857$	13.2382	+	3.54715i	0.452207	+	0.121168i	−0.0255249	+	0.999674i	$0.508126\pi$
$858$	−1.74260	+	1.52661i	−0.0594914	+	0.0521176i
$859$	20.4481	−	35.4172i	0.697681	−	1.20842i	−0.271587	−	0.962414i	$-0.587549\pi$
$859$	20.4481	−	35.4172i	0.697681	−	1.20842i	0.969268	−	0.246005i	$-0.0791181\pi$
$860$	28.9190	+	21.1585i	0.986131	+	0.721499i
$861$	−12.5305	−	1.35953i	−0.427039	−	0.0463326i
$862$	14.0381	−	15.2729i	0.478140	−	0.520198i
$863$	−10.7525	−	10.7525i	−0.366018	−	0.366018i	0.500005	−	0.866023i	$-0.333332\pi$
$863$	−10.7525	−	10.7525i	−0.366018	−	0.366018i	−0.866023	+	0.500005i	$0.833332\pi$
$864$	−29.2040	−	3.33521i	−0.993542	−	0.113466i
$865$	−34.9906	−	30.4336i	−1.18972	−	1.03477i
$866$	5.61873	−	0.236703i	0.190932	−	0.00804349i
$867$	−21.7112	+	17.4611i	−0.737350	+	0.593010i
$868$	5.63102	−	6.66922i	0.191129	−	0.226368i
$869$	7.61072	+	4.39405i	0.258176	+	0.149058i
$870$	−0.0829479	−	23.2348i	−0.00281220	−	0.787732i
$871$	5.59993	+	9.69937i	0.189746	+	0.328651i
$872$	22.5967	−	29.1703i	0.765222	−	0.987831i
$873$	35.1138	+	18.1892i	1.18842	+	0.615611i
$874$	46.9136	+	24.5130i	1.58688	+	0.829165i
$875$	−24.3167	−	1.29422i	−0.822056	−	0.0437525i
$876$	−0.00501225	+	0.209946i	−0.000169348	+	0.00709341i
$877$	3.26343	+	12.1793i	0.110198	+	0.411265i	0.998883	−	0.0472536i	$-0.0150469\pi$
$877$	3.26343	+	12.1793i	0.110198	+	0.411265i	−0.888685	+	0.458519i	$0.848380\pi$
$878$	−2.08715	−	0.466063i	−0.0704380	−	0.0157289i
$879$	−7.82023	+	10.6880i	−0.263770	+	0.360498i
$880$	1.69922	+	7.00573i	0.0572808	+	0.236163i
$881$		−	28.3078i		−	0.953713i	−0.878981	−	0.476857i	$-0.841776\pi$
$881$		−	28.3078i		−	0.953713i	0.878981	−	0.476857i	$-0.158224\pi$
$882$	9.53530	−	0.838901i	0.321070	−	0.0282473i
$883$	1.78770	+	1.78770i	0.0601609	+	0.0601609i	0.736547	−	0.676386i	$-0.236455\pi$
$883$	1.78770	+	1.78770i	0.0601609	+	0.0601609i	−0.676386	+	0.736547i	$0.736455\pi$
$884$	−2.03079	−	0.954554i	−0.0683029	−	0.0321051i
$885$	12.1158	−	39.1212i	0.407270	−	1.31505i
$886$	−21.9632	−	34.5920i	−0.737867	−	1.16214i
$887$	3.21917	+	12.0141i	0.108089	+	0.403395i	0.998677	−	0.0514163i	$-0.0163735\pi$
$887$	3.21917	+	12.0141i	0.108089	+	0.403395i	−0.890588	+	0.454811i	$0.849707\pi$
$888$	4.39926	−	4.56269i	0.147630	−	0.153114i
$889$	27.6740	−	15.9776i	0.928156	−	0.535871i
$890$	19.6775	+	50.2193i	0.659590	+	1.68335i
$891$	0.661349	+	7.22356i	0.0221560	+	0.241998i
$892$	4.00861	−	22.3339i	0.134218	−	0.747795i
$893$	−74.2185	−	19.8868i	−2.48363	−	0.665486i
$894$	8.83436	−	13.2066i	0.295465	−	0.441696i
$895$	−6.03634	+	12.3678i	−0.201773	+	0.413411i
$896$	−17.9883	−	16.8413i	−0.600947	−	0.562630i
$897$	9.17679	+	3.55801i	0.306404	+	0.118799i
$898$	16.0408	+	14.7439i	0.535287	+	0.492010i
$899$			8.50015i			0.283496i
$900$	−15.1851	−	25.8730i	−0.506171	−	0.862433i
$901$			9.55970i			0.318480i
$902$	−2.57709	+	2.80377i	−0.0858076	+	0.0933553i
$903$	4.62832	+	29.8703i	0.154021	+	0.994021i
$904$	14.9660	−	35.6671i	0.497763	−	1.18627i
$905$	−2.65034	+	5.43027i	−0.0881003	+	0.180508i
$906$	40.2776	−	19.8366i	1.33813	−	0.659025i
$907$	3.72679	+	0.998590i	0.123746	+	0.0331576i	0.320161	−	0.947363i	$-0.396263\pi$
$907$	3.72679	+	0.998590i	0.123746	+	0.0331576i	−0.196415	+	0.980521i	$0.562930\pi$
$908$	0.469607	+	0.0842875i	0.0155845	+	0.00279718i
$909$	43.4620	−	13.7999i	1.44154	−	0.457715i
$910$	7.52535	−	2.94866i	0.249463	−	0.0977472i
$911$	48.7236	−	28.1306i	1.61428	−	0.932007i	0.625922	−	0.779886i	$-0.284723\pi$
$911$	48.7236	−	28.1306i	1.61428	−	0.932007i	0.988362	−	0.152122i	$-0.0486106\pi$
$912$	40.0798	+	35.5133i	1.32718	+	1.17596i
$913$	−0.410190	−	1.53085i	−0.0135753	−	0.0506638i
$914$	2.66889	−	1.69454i	0.0882792	−	0.0560502i
$915$	7.38868	+	7.98121i	0.244262	+	0.263851i
$916$	−25.6034	−	12.0346i	−0.845960	−	0.397635i
$917$	17.5815	+	17.5815i	0.580592	+	0.580592i
$918$	−6.15474	+	3.38858i	−0.203137	+	0.111840i
$919$			23.6388i			0.779773i	0.920863	+	0.389887i	$0.127486\pi$
$919$			23.6388i			0.779773i	−0.920863	+	0.389887i	$0.872514\pi$
$920$	23.0361	−	20.1818i	0.759478	−	0.665374i
$921$	20.7381	+	2.25003i	0.683343	+	0.0741410i
$922$	−2.72071	+	12.1841i	−0.0896019	+	0.401261i
$923$	−0.908368	−	3.39007i	−0.0298993	−	0.111586i
$924$	−3.16534	+	5.19225i	−0.104132	+	0.170812i
$925$	6.42016	+	0.791830i	0.211094	+	0.0260352i
$926$	7.46344	−	14.2837i	0.245264	−	0.469392i
$927$	−50.5494	+	2.30918i	−1.66026	+	0.0758436i
$928$	23.9654	+	1.23018i	0.786702	+	0.0403825i
$929$	−11.4135	−	19.7687i	−0.374463	−	0.648590i	0.615783	−	0.787916i	$-0.288840\pi$
$929$	−11.4135	−	19.7687i	−0.374463	−	0.648590i	−0.990247	+	0.139326i	$0.955506\pi$
$930$	5.52142	+	9.48502i	0.181055	+	0.311026i
$931$	−15.1022	−	8.71927i	−0.494955	−	0.285763i
$932$	4.40479	−	5.21691i	0.144284	−	0.170886i
$933$	−0.300157	−	1.93716i	−0.00982669	−	0.0634197i
$934$	0.0895309	+	2.12524i	0.00292954	+	0.0695399i
$935$	1.30014	+	1.13081i	0.0425190	+	0.0369815i
$936$	8.14184	+	5.73228i	0.266124	+	0.187365i
$937$	10.2962	+	10.2962i	0.336361	+	0.336361i	0.854996	−	0.518635i	$-0.173560\pi$
$937$	10.2962	+	10.2962i	0.336361	+	0.336361i	−0.518635	+	0.854996i	$0.673560\pi$
$938$	21.6439	+	19.8940i	0.706699	+	0.649563i
$939$	−9.21562	−	20.8869i	−0.300740	−	0.681619i
$940$	−26.2512	+	35.8796i	−0.856219	+	1.17026i
$941$	−18.1402	+	31.4197i	−0.591354	+	1.02425i	0.402697	+	0.915333i	$0.368073\pi$
$941$	−18.1402	+	31.4197i	−0.591354	+	1.02425i	−0.994050	+	0.108921i	$0.965260\pi$
$942$	−32.1045	+	6.36856i	−1.04602	+	0.207499i
$943$	15.6276	+	4.18741i	0.508905	+	0.136361i
$944$	39.6574	+	14.7097i	1.29074	+	0.478760i
$945$	6.37565	−	24.4902i	0.207400	−	0.796665i
$946$	8.09440	+	4.22944i	0.263172	+	0.137511i
$947$	6.60977	−	24.6680i	0.214789	−	0.801603i	−0.771452	−	0.636288i	$-0.780469\pi$
$947$	6.60977	−	24.6680i	0.214789	−	0.801603i	0.986241	−	0.165315i	$-0.0528641\pi$
$948$	10.6440	−	36.2408i	0.345701	−	1.17704i
$949$	0.0355703	−	0.0616095i	0.00115466	−	0.00199993i
$950$	−4.40104	+	54.4766i	−0.142789	+	1.76746i
$951$	−47.3974	+	20.9124i	−1.53696	+	0.678131i
$952$	−5.83601	−	0.795605i	−0.189146	−	0.0257857i
$953$	−26.6283	−	26.6283i	−0.862575	−	0.862575i	0.129062	−	0.991637i	$-0.458803\pi$
$953$	−26.6283	−	26.6283i	−0.862575	−	0.862575i	−0.991637	+	0.129062i	$0.958803\pi$
$954$	7.34592	−	41.7796i	0.237833	−	1.35266i
$955$	9.87312	−	0.687707i	0.319487	−	0.0222537i
$956$	39.0592	+	18.3594i	1.26327	+	0.593785i
$957$	−0.906764	−	5.85208i	−0.0293115	−	0.189171i
$958$	1.55085	−	6.94510i	0.0501056	−	0.224386i
$959$	−7.52256	+	13.0295i	−0.242916	+	0.420743i
$960$	27.5412	−	14.1944i	0.888889	−	0.458123i
$961$	13.4925	+	23.3696i	0.435241	+	0.753860i
$962$	−2.04868	+	0.642501i	−0.0660522	+	0.0207151i
$963$	37.8174	−	24.1997i	1.21865	−	0.779824i
$964$	20.1485	−	14.0164i	0.648941	−	0.451439i
$965$	−8.76007	+	45.0015i	−0.281997	+	1.44865i
$966$	25.7785	+	1.70314i	0.829411	+	0.0547975i
$967$	53.7410	−	14.3999i	1.72819	−	0.463068i	0.748429	−	0.663215i	$-0.230809\pi$
$967$	53.7410	−	14.3999i	1.72819	−	0.463068i	0.979766	+	0.200147i	$0.0641419\pi$
$968$	−11.0789	−	27.0981i	−0.356089	−	0.870965i
$969$	12.7251	+	1.38065i	0.408790	+	0.0443527i
$970$	−41.4248	+	4.64417i	−1.33007	+	0.149115i
$971$	−54.8491			−1.76019			−0.880096	−	0.474795i	$-0.842522\pi$
$971$	−54.8491			−1.76019			−0.880096	+	0.474795i	$0.842522\pi$
$972$	29.5025	−	10.0799i	0.946292	−	0.323314i
$973$	9.18007	+	9.18007i	0.294299	+	0.294299i
$974$	−0.997985	−	23.6896i	−0.0319775	−	0.759065i
$975$	0.315088	+	10.1578i	0.0100909	+	0.325309i
$976$	−8.64896	+	7.16756i	−0.276846	+	0.229428i
$977$	7.50824	+	28.0211i	0.240210	+	0.896475i	0.975731	+	0.218973i	$0.0702708\pi$
$977$	7.50824	+	28.0211i	0.240210	+	0.896475i	−0.735521	+	0.677502i	$0.763063\pi$
$978$	14.8140	−	12.9779i	0.473700	−	0.414986i
$979$	6.87348	+	11.9052i	0.219677	+	0.380492i
$980$	−7.86245	+	6.32362i	−0.251157	+	0.202001i
$981$	−8.39373	+	38.2263i	−0.267991	+	1.22047i
$982$	21.1787	−	6.64201i	0.675841	−	0.211955i
$983$	−2.51171	+	9.37382i	−0.0801110	+	0.298978i	−0.994344	−	0.106212i	$-0.966128\pi$
$983$	−2.51171	+	9.37382i	−0.0801110	+	0.298978i	0.914233	+	0.405190i	$0.132795\pi$
$984$	14.3218	+	7.92411i	0.456562	+	0.252611i
$985$	3.62800	+	10.5458i	0.115598	+	0.336016i
$986$	4.84231	−	3.07448i	0.154211	−	0.0979115i
$987$	−37.0598	+	5.74232i	−1.17963	+	0.182780i
$988$	−6.15214	−	17.0652i	−0.195726	−	0.542917i
$989$		−	38.7999i		−	1.23376i
$990$	−4.81315	−	5.94114i	−0.152972	−	0.188822i
$991$	−30.1613			−0.958104			−0.479052	−	0.877786i	$-0.659020\pi$
$991$	−30.1613			−0.958104			−0.479052	+	0.877786i	$0.659020\pi$
$992$	−10.0940	+	5.15681i	−0.320485	+	0.163729i
$993$	−22.8666	−	8.86582i	−0.725651	−	0.281348i
$994$	−4.93787	−	7.77714i	−0.156620	−	0.246676i
$995$	21.1398	−	43.3131i	0.670175	−	1.37312i
$996$	−5.97875	+	3.26411i	−0.189444	+	0.103427i
$997$	0.818508	+	0.219319i	0.0259224	+	0.00694589i	0.271757	−	0.962366i	$-0.412395\pi$
$997$	0.818508	+	0.219319i	0.0259224	+	0.00694589i	−0.245835	+	0.969312i	$0.579062\pi$
$998$	−1.43950	+	0.451450i	−0.0455664	+	0.0142904i
$999$	−2.14164	+	6.37232i	−0.0677584	+	0.201611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.br.e.77.15	yes	256
5.3	odd	4	inner	360.2.br.e.293.16	yes	256
8.5	even	2	inner	360.2.br.e.77.5	✓	256
9.2	odd	6	inner	360.2.br.e.317.38	yes	256
40.13	odd	4	inner	360.2.br.e.293.38	yes	256
45.38	even	12	inner	360.2.br.e.173.5	yes	256
72.29	odd	6	inner	360.2.br.e.317.16	yes	256
360.173	even	12	inner	360.2.br.e.173.15	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.br.e.77.5	✓	256	8.5	even	2	inner
360.2.br.e.77.15	yes	256	1.1	even	1	trivial
360.2.br.e.173.5	yes	256	45.38	even	12	inner
360.2.br.e.173.15	yes	256	360.173	even	12	inner
360.2.br.e.293.16	yes	256	5.3	odd	4	inner
360.2.br.e.293.38	yes	256	40.13	odd	4	inner
360.2.br.e.317.16	yes	256	72.29	odd	6	inner
360.2.br.e.317.38	yes	256	9.2	odd	6	inner

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04120 - 0.957024i) q^{2} +(1.08549 + 1.34971i) q^{3} +(0.168211 + 1.99291i) q^{4} +(2.00950 + 0.980772i) q^{5} +(0.161481 - 2.44416i) q^{6} +(-0.563716 + 2.10382i) q^{7} +(1.73212 - 2.23601i) q^{8} +(-0.643411 + 2.93019i) q^{9} +O(q^{10})\)	\(q+(-1.04120 - 0.957024i) q^{2} +(1.08549 + 1.34971i) q^{3} +(0.168211 + 1.99291i) q^{4} +(2.00950 + 0.980772i) q^{5} +(0.161481 - 2.44416i) q^{6} +(-0.563716 + 2.10382i) q^{7} +(1.73212 - 2.23601i) q^{8} +(-0.643411 + 2.93019i) q^{9} +(-1.15368 - 2.94432i) q^{10} +(-0.402987 - 0.697994i) q^{11} +(-2.50725 + 2.39033i) q^{12} +(1.13350 - 0.303720i) q^{13} +(2.60035 - 1.65101i) q^{14} +(0.857542 + 3.77685i) q^{15} +(-3.94341 + 0.670462i) q^{16} +(-0.676068 + 0.676068i) q^{17} +(3.47418 - 2.43517i) q^{18} -7.72926 q^{19} +(-1.61657 + 4.16973i) q^{20} +(-3.45145 + 1.52283i) q^{21} +(-0.248405 + 1.11242i) q^{22} +(4.67743 - 1.25331i) q^{23} +(4.89817 - 0.0893186i) q^{24} +(3.07617 + 3.94172i) q^{25} +(-1.47087 - 0.768550i) q^{26} +(-4.65331 + 2.31229i) q^{27} +(-4.28755 - 0.769552i) q^{28} +(3.67376 - 2.12105i) q^{29} +(2.72166 - 4.75316i) q^{30} +(-1.00188 + 1.73531i) q^{31} +(4.74754 + 3.07585i) q^{32} +(0.504647 - 1.30158i) q^{33} +(1.35094 - 0.0569116i) q^{34} +(-3.19615 + 3.67474i) q^{35} +(-5.94785 - 0.789370i) q^{36} +(0.914827 - 0.914827i) q^{37} +(8.04773 + 7.39708i) q^{38} +(1.64034 + 1.20020i) q^{39} +(5.67372 - 2.79444i) q^{40} +(2.89345 + 1.67053i) q^{41} +(5.05104 + 1.71754i) q^{42} +(2.07378 - 7.73945i) q^{43} +(1.32326 - 0.920529i) q^{44} +(-4.16678 + 5.25718i) q^{45} +(-6.06961 - 3.17146i) q^{46} +(9.60228 + 2.57292i) q^{47} +(-5.18547 - 4.59466i) q^{48} +(1.95390 + 1.12809i) q^{49} +(0.569400 - 7.04810i) q^{50} +(-1.64636 - 0.178626i) q^{51} +(0.795955 + 2.20787i) q^{52} +(7.07007 - 7.07007i) q^{53} +(7.05796 + 2.04577i) q^{54} +(-0.125229 - 1.79786i) q^{55} +(3.72774 + 4.90455i) q^{56} +(-8.39005 - 10.4322i) q^{57} +(-5.85503 - 1.30743i) q^{58} +(-9.15769 - 5.28719i) q^{59} +(-7.38269 + 2.34432i) q^{60} +(2.43200 - 1.40411i) q^{61} +(2.70389 - 0.847986i) q^{62} +(-5.80189 - 3.00542i) q^{63} +(-1.99950 - 7.74610i) q^{64} +(2.57564 + 0.501379i) q^{65} +(-1.77109 + 0.872253i) q^{66} +(2.47020 + 9.21891i) q^{67} +(-1.46107 - 1.23362i) q^{68} +(6.76893 + 4.95269i) q^{69} +(6.84466 - 0.767361i) q^{70} -2.99081i q^{71} +(5.43748 + 6.51413i) q^{72} +(0.0428672 - 0.0428672i) q^{73} +(-1.82803 + 0.0770105i) q^{74} +(-1.98100 + 8.43064i) q^{75} +(-1.30015 - 15.4037i) q^{76} +(1.69562 - 0.454341i) q^{77} +(-0.559302 - 2.81950i) q^{78} +(-9.44288 + 5.45185i) q^{79} +(-8.58185 - 2.52030i) q^{80} +(-8.17205 - 3.77063i) q^{81} +(-1.41393 - 4.50846i) q^{82} +(1.89938 + 0.508937i) q^{83} +(-3.61544 - 6.62228i) q^{84} +(-2.02163 + 0.695489i) q^{85} +(-9.56606 + 6.07369i) q^{86} +(6.85063 + 2.65612i) q^{87} +(-2.25875 - 0.307928i) q^{88} -17.0563 q^{89} +(9.36972 - 1.48608i) q^{90} +2.55589i q^{91} +(3.28455 + 9.11090i) q^{92} +(-3.42969 + 0.531420i) q^{93} +(-7.53558 - 11.8685i) q^{94} +(-15.5319 - 7.58064i) q^{95} +(1.00193 + 9.74660i) q^{96} +(3.41169 - 12.7326i) q^{97} +(-0.954806 - 3.04450i) q^{98} +(2.30454 - 0.731733i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 6 q^{2} - 8 q^{6}+O(q^{10}) \) 256 * q + 6 * q^2 - 8 * q^6	\( 256 q + 6 q^{2} - 8 q^{6} - 10 q^{12} + 28 q^{15} + 12 q^{16} - 28 q^{18} - 54 q^{20} + 14 q^{22} - 28 q^{25} - 32 q^{28} + 14 q^{30} - 32 q^{31} - 114 q^{32} + 4 q^{33} - 40 q^{36} - 30 q^{38} + 46 q^{40} + 24 q^{41} - 10 q^{42} - 16 q^{46} + 24 q^{47} - 2 q^{48} + 78 q^{50} + 38 q^{52} - 8 q^{55} - 96 q^{56} - 80 q^{57} - 18 q^{58} - 2 q^{60} - 144 q^{63} - 84 q^{65} - 4 q^{66} - 30 q^{68} - 30 q^{70} - 86 q^{72} + 64 q^{73} + 16 q^{76} - 82 q^{78} + 72 q^{81} - 64 q^{82} + 48 q^{86} - 4 q^{87} + 38 q^{88} + 78 q^{90} - 108 q^{92} - 24 q^{95} - 116 q^{96} + 36 q^{97}+O(q^{100}) \) 256 * q + 6 * q^2 - 8 * q^6 - 10 * q^12 + 28 * q^15 + 12 * q^16 - 28 * q^18 - 54 * q^20 + 14 * q^22 - 28 * q^25 - 32 * q^28 + 14 * q^30 - 32 * q^31 - 114 * q^32 + 4 * q^33 - 40 * q^36 - 30 * q^38 + 46 * q^40 + 24 * q^41 - 10 * q^42 - 16 * q^46 + 24 * q^47 - 2 * q^48 + 78 * q^50 + 38 * q^52 - 8 * q^55 - 96 * q^56 - 80 * q^57 - 18 * q^58 - 2 * q^60 - 144 * q^63 - 84 * q^65 - 4 * q^66 - 30 * q^68 - 30 * q^70 - 86 * q^72 + 64 * q^73 + 16 * q^76 - 82 * q^78 + 72 * q^81 - 64 * q^82 + 48 * q^86 - 4 * q^87 + 38 * q^88 + 78 * q^90 - 108 * q^92 - 24 * q^95 - 116 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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