LMFDB - Embedded newform 280.2.b.c.141.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(141,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("280.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.b (of order $2$, degree $1$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			141.2
Root			$0.500000 - 0.0297061i$ of defining polynomial
Character	$\chi$	$=$	280.141
Dual form			280.2.b.c.141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.874559 + 1.11137i) q^{2} -2.41421i q^{3} +(-0.470294 - 1.94392i) q^{4} -1.00000i q^{5} +(2.68309 + 2.11137i) q^{6} -1.00000 q^{7} +(2.57172 + 1.17740i) q^{8} -2.82843 q^{9} +O(q^{10})$	\(q+(-0.874559 + 1.11137i) q^{2} -2.41421i q^{3} +(-0.470294 - 1.94392i) q^{4} -1.00000i q^{5} +(2.68309 + 2.11137i) q^{6} -1.00000 q^{7} +(2.57172 + 1.17740i) q^{8} -2.82843 q^{9} +(1.11137 + 0.874559i) q^{10} -1.66981i q^{11} +(-4.69304 + 1.13539i) q^{12} +0.143434i q^{13} +(0.874559 - 1.11137i) q^{14} -2.41421 q^{15} +(-3.55765 + 1.82843i) q^{16} -6.03127 q^{17} +(2.47363 - 3.14343i) q^{18} -6.64167i q^{19} +(-1.94392 + 0.470294i) q^{20} +2.41421i q^{21} +(1.85578 + 1.46035i) q^{22} -5.30205 q^{23} +(2.84250 - 6.20867i) q^{24} -1.00000 q^{25} +(-0.159408 - 0.125441i) q^{26} -0.414214i q^{27} +(0.470294 + 1.94392i) q^{28} +3.67647i q^{29} +(2.11137 - 2.68309i) q^{30} +6.80029 q^{31} +(1.07931 - 5.55294i) q^{32} -4.03127 q^{33} +(5.27470 - 6.70299i) q^{34} +1.00000i q^{35} +(1.33019 + 5.49824i) q^{36} +4.35480i q^{37} +(7.38136 + 5.80853i) q^{38} +0.346280 q^{39} +(1.17740 - 2.57172i) q^{40} +8.64167 q^{41} +(-2.68309 - 2.11137i) q^{42} -8.80029i q^{43} +(-3.24597 + 0.785301i) q^{44} +2.82843i q^{45} +(4.63696 - 5.89255i) q^{46} +7.13048 q^{47} +(4.41421 + 8.58892i) q^{48} +1.00000 q^{49} +(0.874559 - 1.11137i) q^{50} +14.5608i q^{51} +(0.278824 - 0.0674560i) q^{52} +5.11529i q^{53} +(0.460345 + 0.362254i) q^{54} -1.66981 q^{55} +(-2.57172 - 1.17740i) q^{56} -16.0344 q^{57} +(-4.08593 - 3.21529i) q^{58} +8.40569i q^{59} +(1.13539 + 4.69304i) q^{60} -13.8664i q^{61} +(-5.94725 + 7.55765i) q^{62} +2.82843 q^{63} +(5.22746 + 6.05588i) q^{64} +0.143434 q^{65} +(3.52559 - 4.48024i) q^{66} -9.11529i q^{67} +(2.83647 + 11.7243i) q^{68} +12.8003i q^{69} +(-1.11137 - 0.874559i) q^{70} -3.89450 q^{71} +(-7.27391 - 3.33019i) q^{72} -1.89450 q^{73} +(-4.83980 - 3.80853i) q^{74} +2.41421i q^{75} +(-12.9109 + 3.12354i) q^{76} +1.66981i q^{77} +(-0.302842 + 0.384845i) q^{78} +11.8351 q^{79} +(1.82843 + 3.55765i) q^{80} -9.48528 q^{81} +(-7.55765 + 9.60411i) q^{82} -1.77568i q^{83} +(4.69304 - 1.13539i) q^{84} +6.03127i q^{85} +(9.78039 + 7.69637i) q^{86} +8.87579 q^{87} +(1.96603 - 4.29427i) q^{88} +7.13401 q^{89} +(-3.14343 - 2.47363i) q^{90} -0.143434i q^{91} +(2.49352 + 10.3068i) q^{92} -16.4173i q^{93} +(-6.23602 + 7.92461i) q^{94} -6.64167 q^{95} +(-13.4060 - 2.60568i) q^{96} +5.23322 q^{97} +(-0.874559 + 1.11137i) q^{98} +4.72293i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} - 8 q^{7} + 12 q^{8}+O(q^{10}) $ 8 * q - 4 * q^4 - 8 * q^7 + 12 * q^8	$ 8 q - 4 q^{4} - 8 q^{7} + 12 q^{8} - 4 q^{10} - 12 q^{12} - 8 q^{15} - 8 q^{17} + 8 q^{18} - 4 q^{20} - 4 q^{22} - 8 q^{23} + 20 q^{24} - 8 q^{25} - 20 q^{26} + 4 q^{28} + 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{36} + 16 q^{38} - 32 q^{39} + 4 q^{40} + 24 q^{41} + 20 q^{44} + 24 q^{48} + 8 q^{49} - 12 q^{52} + 8 q^{54} - 8 q^{55} - 12 q^{56} - 8 q^{57} - 32 q^{58} + 12 q^{60} - 24 q^{62} + 8 q^{64} - 16 q^{65} + 4 q^{66} - 20 q^{68} + 4 q^{70} + 16 q^{71} + 16 q^{72} + 32 q^{73} + 16 q^{74} + 8 q^{76} - 4 q^{78} + 48 q^{79} - 8 q^{80} - 8 q^{81} - 32 q^{82} + 12 q^{84} + 24 q^{86} - 32 q^{87} + 4 q^{88} + 56 q^{89} - 8 q^{90} - 8 q^{94} - 8 q^{95} - 48 q^{96} + 24 q^{97}+O(q^{100}) $ 8 * q - 4 * q^4 - 8 * q^7 + 12 * q^8 - 4 * q^10 - 12 * q^12 - 8 * q^15 - 8 * q^17 + 8 * q^18 - 4 * q^20 - 4 * q^22 - 8 * q^23 + 20 * q^24 - 8 * q^25 - 20 * q^26 + 4 * q^28 + 4 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^34 + 16 * q^36 + 16 * q^38 - 32 * q^39 + 4 * q^40 + 24 * q^41 + 20 * q^44 + 24 * q^48 + 8 * q^49 - 12 * q^52 + 8 * q^54 - 8 * q^55 - 12 * q^56 - 8 * q^57 - 32 * q^58 + 12 * q^60 - 24 * q^62 + 8 * q^64 - 16 * q^65 + 4 * q^66 - 20 * q^68 + 4 * q^70 + 16 * q^71 + 16 * q^72 + 32 * q^73 + 16 * q^74 + 8 * q^76 - 4 * q^78 + 48 * q^79 - 8 * q^80 - 8 * q^81 - 32 * q^82 + 12 * q^84 + 24 * q^86 - 32 * q^87 + 4 * q^88 + 56 * q^89 - 8 * q^90 - 8 * q^94 - 8 * q^95 - 48 * q^96 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	−0.874559	+	1.11137i	−0.618406	+	0.785858i
$2$	−0.874559	+	1.11137i	−0.618406	+	0.785858i
$3$		−	2.41421i		−	1.39385i	−0.717146	−	0.696923i	$-0.754552\pi$
$3$		−	2.41421i		−	1.39385i	0.717146	−	0.696923i	$-0.245448\pi$
$4$	−0.470294	−	1.94392i	−0.235147	−	0.971960i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	2.68309	+	2.11137i	1.09537	+	0.861964i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	2.57172	+	1.17740i	0.909239	+	0.416274i
$9$	−2.82843			−0.942809
$10$	1.11137	+	0.874559i	0.351447	+	0.276560i
$11$		−	1.66981i		−	0.503466i	−0.967797	−	0.251733i	$-0.919000\pi$
$11$		−	1.66981i		−	0.503466i	0.967797	−	0.251733i	$-0.0810005\pi$
$12$	−4.69304	+	1.13539i	−1.35476	+	0.327759i
$13$			0.143434i			0.0397814i	0.999802	+	0.0198907i	$0.00633182\pi$
$13$			0.143434i			0.0397814i	−0.999802	+	0.0198907i	$0.993668\pi$
$14$	0.874559	−	1.11137i	0.233736	−	0.297027i
$15$	−2.41421			−0.623347
$16$	−3.55765	+	1.82843i	−0.889412	+	0.457107i
$17$	−6.03127			−1.46280			−0.731399	−	0.681949i	$-0.761132\pi$
$17$	−6.03127			−1.46280			−0.731399	+	0.681949i	$0.761132\pi$
$18$	2.47363	−	3.14343i	0.583039	−	0.740914i
$19$		−	6.64167i		−	1.52370i	−0.647752	−	0.761852i	$-0.724291\pi$
$19$		−	6.64167i		−	1.52370i	0.647752	−	0.761852i	$-0.275709\pi$
$20$	−1.94392	+	0.470294i	−0.434674	+	0.105161i
$21$			2.41421i			0.526825i
$22$	1.85578	+	1.46035i	0.395653	+	0.311347i
$23$	−5.30205			−1.10555			−0.552777	−	0.833329i	$-0.686432\pi$
$23$	−5.30205			−1.10555			−0.552777	+	0.833329i	$0.686432\pi$
$24$	2.84250	−	6.20867i	0.580222	−	1.26734i
$25$	−1.00000			−0.200000
$26$	−0.159408	−	0.125441i	−0.0312625	−	0.0246010i
$27$		−	0.414214i		−	0.0797154i
$28$	0.470294	+	1.94392i	0.0888772	+	0.367366i
$29$			3.67647i			0.682704i	0.939936	+	0.341352i	$0.110885\pi$
$29$			3.67647i			0.682704i	−0.939936	+	0.341352i	$0.889115\pi$
$30$	2.11137	−	2.68309i	0.385482	−	0.489863i
$31$	6.80029			1.22137			0.610684	−	0.791874i	$-0.290895\pi$
$31$	6.80029			1.22137			0.610684	+	0.791874i	$0.290895\pi$
$32$	1.07931	−	5.55294i	0.190797	−	0.981630i
$33$	−4.03127			−0.701755
$34$	5.27470	−	6.70299i	0.904604	−	1.14955i
$35$			1.00000i			0.169031i
$36$	1.33019	+	5.49824i	0.221699	+	0.916373i
$37$			4.35480i			0.715925i	0.933736	+	0.357962i	$0.116528\pi$
$37$			4.35480i			0.715925i	−0.933736	+	0.357962i	$0.883472\pi$
$38$	7.38136	+	5.80853i	1.19742	+	0.942268i
$39$	0.346280			0.0554491
$40$	1.17740	−	2.57172i	0.186163	−	0.406624i
$41$	8.64167			1.34960			0.674801	−	0.738000i	$-0.264229\pi$
$41$	8.64167			1.34960			0.674801	+	0.738000i	$0.264229\pi$
$42$	−2.68309	−	2.11137i	−0.414010	−	0.325792i
$43$		−	8.80029i		−	1.34203i	−0.741443	−	0.671016i	$-0.765858\pi$
$43$		−	8.80029i		−	1.34203i	0.741443	−	0.671016i	$-0.234142\pi$
$44$	−3.24597	+	0.785301i	−0.489349	+	0.118389i
$45$			2.82843i			0.421637i
$46$	4.63696	−	5.89255i	0.683682	−	0.868809i
$47$	7.13048			1.04009			0.520044	−	0.854140i	$-0.325916\pi$
$47$	7.13048			1.04009			0.520044	+	0.854140i	$0.325916\pi$
$48$	4.41421	+	8.58892i	0.637137	+	1.23970i
$49$	1.00000			0.142857
$50$	0.874559	−	1.11137i	0.123681	−	0.157172i
$51$			14.5608i			2.03892i
$52$	0.278824	−	0.0674560i	0.0386659	−	0.00935447i
$53$			5.11529i			0.702640i	0.936255	+	0.351320i	$0.114267\pi$
$53$			5.11529i			0.702640i	−0.936255	+	0.351320i	$0.885733\pi$
$54$	0.460345	+	0.362254i	0.0626450	+	0.0492965i
$55$	−1.66981			−0.225157
$56$	−2.57172	−	1.17740i	−0.343660	−	0.157337i
$57$	−16.0344			−2.12381
$58$	−4.08593	−	3.21529i	−0.536508	−	0.422188i
$59$			8.40569i			1.09433i	0.837025	+	0.547164i	$0.184293\pi$
$59$			8.40569i			1.09433i	−0.837025	+	0.547164i	$0.815707\pi$
$60$	1.13539	+	4.69304i	0.146578	+	0.605868i
$61$		−	13.8664i		−	1.77541i	−0.460417	−	0.887703i	$-0.652300\pi$
$61$		−	13.8664i		−	1.77541i	0.460417	−	0.887703i	$-0.347700\pi$
$62$	−5.94725	+	7.55765i	−0.755302	+	0.959822i
$63$	2.82843			0.356348
$64$	5.22746	+	6.05588i	0.653432	+	0.756985i
$65$	0.143434			0.0177908
$66$	3.52559	−	4.48024i	0.433970	−	0.551480i
$67$		−	9.11529i		−	1.11361i	−0.830643	−	0.556805i	$-0.812027\pi$
$67$		−	9.11529i		−	1.11361i	0.830643	−	0.556805i	$-0.187973\pi$
$68$	2.83647	+	11.7243i	0.343973	+	1.42178i
$69$			12.8003i			1.54097i
$70$	−1.11137	−	0.874559i	−0.132834	−	0.104530i
$71$	−3.89450			−0.462192			−0.231096	−	0.972931i	$-0.574231\pi$
$71$	−3.89450			−0.462192			−0.231096	+	0.972931i	$0.574231\pi$
$72$	−7.27391	−	3.33019i	−0.857239	−	0.392467i
$73$	−1.89450			−0.221735			−0.110867	−	0.993835i	$-0.535363\pi$
$73$	−1.89450			−0.221735			−0.110867	+	0.993835i	$0.535363\pi$
$74$	−4.83980	−	3.80853i	−0.562616	−	0.442733i
$75$			2.41421i			0.278769i
$76$	−12.9109	+	3.12354i	−1.48098	+	0.358294i
$77$			1.66981i			0.190292i
$78$	−0.302842	+	0.384845i	−0.0342901	+	0.0435752i
$79$	11.8351			1.33155			0.665776	−	0.746152i	$-0.268101\pi$
$79$	11.8351			1.33155			0.665776	+	0.746152i	$0.268101\pi$
$80$	1.82843	+	3.55765i	0.204424	+	0.397757i
$81$	−9.48528			−1.05392
$82$	−7.55765	+	9.60411i	−0.834603	+	1.06060i
$83$		−	1.77568i		−	0.194906i	−0.995240	−	0.0974530i	$-0.968930\pi$
$83$		−	1.77568i		−	0.194906i	0.995240	−	0.0974530i	$-0.0310696\pi$
$84$	4.69304	−	1.13539i	0.512052	−	0.123881i
$85$			6.03127i			0.654183i
$86$	9.78039	+	7.69637i	1.05465	+	0.829921i
$87$	8.87579			0.951584
$88$	1.96603	−	4.29427i	0.209580	−	0.457771i
$89$	7.13401			0.756204			0.378102	−	0.925764i	$-0.376577\pi$
$89$	7.13401			0.756204			0.378102	+	0.925764i	$0.376577\pi$
$90$	−3.14343	−	2.47363i	−0.331347	−	0.260743i
$91$		−	0.143434i		−	0.0150359i
$92$	2.49352	+	10.3068i	0.259968	+	1.07455i
$93$		−	16.4173i		−	1.70240i
$94$	−6.23602	+	7.92461i	−0.643197	+	0.817361i
$95$	−6.64167			−0.681421
$96$	−13.4060	−	2.60568i	−1.36824	−	0.265941i
$97$	5.23322			0.531353			0.265676	−	0.964062i	$-0.414405\pi$
$97$	5.23322			0.531353			0.265676	+	0.964062i	$0.414405\pi$
$98$	−0.874559	+	1.11137i	−0.0883438	+	0.112265i
$99$			4.72293i			0.474672i
$100$	0.470294	+	1.94392i	0.0470294	+	0.194392i
$101$		−	10.8628i		−	1.08089i	−0.841379	−	0.540446i	$-0.818255\pi$
$101$		−	10.8628i		−	1.08089i	0.841379	−	0.540446i	$-0.181745\pi$
$102$	−16.1824	−	12.7343i	−1.60230	−	1.26088i
$103$	12.1966			1.20176			0.600881	−	0.799338i	$-0.294816\pi$
$103$	12.1966			1.20176			0.600881	+	0.799338i	$0.294816\pi$
$104$	−0.168879	+	0.368871i	−0.0165599	+	0.0361708i
$105$	2.41421			0.235603
$106$	−5.68499	−	4.47363i	−0.552175	−	0.434517i
$107$			10.6533i			1.02990i	0.857221	+	0.514948i	$0.172189\pi$
$107$			10.6533i			1.02990i	−0.857221	+	0.514948i	$0.827811\pi$
$108$	−0.805198	+	0.194802i	−0.0774802	+	0.0187448i
$109$			0.927634i			0.0888512i	0.999013	+	0.0444256i	$0.0141458\pi$
$109$			0.927634i			0.0888512i	−0.999013	+	0.0444256i	$0.985854\pi$
$110$	1.46035	−	1.85578i	0.139238	−	0.176941i
$111$	10.5134			0.997890
$112$	3.55765	−	1.82843i	0.336166	−	0.172770i
$113$	8.96833			0.843670			0.421835	−	0.906673i	$-0.361386\pi$
$113$	8.96833			0.843670			0.421835	+	0.906673i	$0.361386\pi$
$114$	14.0230	−	17.8202i	1.31338	−	1.66901i
$115$			5.30205i			0.494419i
$116$	7.14677	−	1.72902i	0.663561	−	0.160536i
$117$		−	0.405692i		−	0.0375062i
$118$	−9.34185	−	7.35127i	−0.859987	−	0.676739i
$119$	6.03127			0.552886
$120$	−6.20867	−	2.84250i	−0.566772	−	0.259483i
$121$	8.21174			0.746522
$122$	15.4107	+	12.1270i	1.39522	+	1.09792i
$123$		−	20.8628i		−	1.88114i
$124$	−3.19813	−	13.2192i	−0.287201	−	1.18712i
$125$			1.00000i			0.0894427i
$126$	−2.47363	+	3.14343i	−0.220368	+	0.280039i
$127$	0.168043			0.0149114			0.00745571	−	0.999972i	$-0.497627\pi$
$127$	0.168043			0.0149114			0.00745571	+	0.999972i	$0.497627\pi$
$128$	−11.3021	+	0.513421i	−0.998970	+	0.0453804i
$129$	−21.2458			−1.87059
$130$	−0.125441	+	0.159408i	−0.0110019	+	0.0139810i
$131$		−	14.7909i		−	1.29228i	−0.763217	−	0.646142i	$-0.776381\pi$
$131$		−	14.7909i		−	1.29228i	0.763217	−	0.646142i	$-0.223619\pi$
$132$	1.89588	+	7.83647i	0.165015	+	0.682077i
$133$			6.64167i			0.575906i
$134$	10.1305	+	7.97186i	0.875140	+	0.688664i
$135$	−0.414214			−0.0356498
$136$	−15.5107	−	7.10123i	−1.33003	−	0.608925i
$137$	−5.85304			−0.500059			−0.250029	−	0.968238i	$-0.580440\pi$
$137$	−5.85304			−0.500059			−0.250029	+	0.968238i	$0.580440\pi$
$138$	−14.2259	−	11.1946i	−1.21099	−	0.952948i
$139$			7.41921i			0.629289i	0.949210	+	0.314644i	$0.101885\pi$
$139$			7.41921i			0.629289i	−0.949210	+	0.314644i	$0.898115\pi$
$140$	1.94392	−	0.470294i	0.164291	−	0.0397471i
$141$		−	17.2145i		−	1.44972i
$142$	3.40597	−	4.32824i	0.285823	−	0.363218i
$143$	0.239507			0.0200286
$144$	10.0625	−	5.17157i	0.838546	−	0.430964i
$145$	3.67647			0.305314
$146$	1.65685	−	2.10550i	0.137122	−	0.174252i
$147$		−	2.41421i		−	0.199121i
$148$	8.46538	−	2.04804i	0.695850	−	0.168348i
$149$		−	7.16451i		−	0.586940i	−0.955968	−	0.293470i	$-0.905190\pi$
$149$		−	7.16451i		−	0.586940i	0.955968	−	0.293470i	$-0.0948100\pi$
$150$	−2.68309	−	2.11137i	−0.219073	−	0.172393i
$151$	−19.8843			−1.61816			−0.809081	−	0.587697i	$-0.800035\pi$
$151$	−19.8843			−1.61816			−0.809081	+	0.587697i	$0.800035\pi$
$152$	7.81991	−	17.0805i	0.634278	−	1.38541i
$153$	17.0590			1.37914
$154$	−1.85578	−	1.46035i	−0.149543	−	0.117678i
$155$		−	6.80029i		−	0.546212i
$156$	−0.162853	−	0.673140i	−0.0130387	−	0.0538943i
$157$			4.77215i			0.380859i	0.981701	+	0.190429i	$0.0609880\pi$
$157$			4.77215i			0.380859i	−0.981701	+	0.190429i	$0.939012\pi$
$158$	−10.3505	+	13.1532i	−0.823440	+	1.04641i
$159$	12.3494			0.979372
$160$	−5.55294	−	1.07931i	−0.438998	−	0.0853269i
$161$	5.30205			0.417860
$162$	8.29544	−	10.5417i	0.651751	−	0.828232i
$163$		−	14.9043i		−	1.16739i	−0.811971	−	0.583697i	$-0.801605\pi$
$163$		−	14.9043i		−	1.16739i	0.811971	−	0.583697i	$-0.198395\pi$
$164$	−4.06412	−	16.7987i	−0.317355	−	1.31176i
$165$			4.03127i			0.313834i
$166$	1.97344	+	1.55294i	0.153169	+	0.120531i
$167$	−15.1930			−1.17567			−0.587836	−	0.808980i	$-0.700020\pi$
$167$	−15.1930			−1.17567			−0.587836	+	0.808980i	$0.700020\pi$
$168$	−2.84250	+	6.20867i	−0.219303	+	0.479010i
$169$	12.9794			0.998417
$170$	−6.70299	−	5.27470i	−0.514096	−	0.404551i
$171$			18.7855i			1.43656i
$172$	−17.1071	+	4.13872i	−1.30440	+	0.315575i
$173$			17.2328i			1.31019i	0.755548	+	0.655094i	$0.227371\pi$
$173$			17.2328i			1.31019i	−0.755548	+	0.655094i	$0.772629\pi$
$174$	−7.76240	+	9.86430i	−0.588466	+	0.747811i
$175$	1.00000			0.0755929
$176$	3.05312	+	5.94059i	0.230138	+	0.447789i
$177$	20.2931			1.52533
$178$	−6.23911	+	7.92854i	−0.467641	+	0.594269i
$179$			17.4325i			1.30297i	0.758662	+	0.651484i	$0.225853\pi$
$179$			17.4325i			1.30297i	−0.758662	+	0.651484i	$0.774147\pi$
$180$	5.49824	−	1.33019i	0.409814	−	0.0991467i
$181$			4.22432i			0.313991i	0.987599	+	0.156996i	$0.0501809\pi$
$181$			4.22432i			0.313991i	−0.987599	+	0.156996i	$0.949819\pi$
$182$	0.159408	+	0.125441i	0.0118161	+	0.00929832i
$183$	−33.4764			−2.47464
$184$	−13.6354	−	6.24264i	−1.00521	−	0.460214i
$185$	4.35480			0.320171
$186$	18.2458	+	14.3579i	1.33785	+	1.05277i
$187$			10.0711i			0.736469i
$188$	−3.35342	−	13.8611i	−0.244573	−	1.01092i
$189$			0.414214i			0.0301296i
$190$	5.80853	−	7.38136i	0.421395	−	0.535500i
$191$	−11.8976			−0.860883			−0.430441	−	0.902619i	$-0.641642\pi$
$191$	−11.8976			−0.860883			−0.430441	+	0.902619i	$0.641642\pi$
$192$	14.6202	−	12.6202i	1.05512	−	0.910784i
$193$	24.8495			1.78871			0.894353	−	0.447361i	$-0.147636\pi$
$193$	24.8495			1.78871			0.894353	+	0.447361i	$0.147636\pi$
$194$	−4.57676	+	5.81605i	−0.328592	+	0.417568i
$195$		−	0.346280i		−	0.0247976i
$196$	−0.470294	−	1.94392i	−0.0335924	−	0.138851i
$197$			4.39404i			0.313062i	0.987673	+	0.156531i	$0.0500311\pi$
$197$			4.39404i			0.313062i	−0.987673	+	0.156531i	$0.949969\pi$
$198$	−5.24893	−	4.13048i	−0.373025	−	0.293540i
$199$	−20.1118			−1.42569			−0.712843	−	0.701324i	$-0.752593\pi$
$199$	−20.1118			−1.42569			−0.712843	+	0.701324i	$0.752593\pi$
$200$	−2.57172	−	1.17740i	−0.181848	−	0.0832548i
$201$	−22.0063			−1.55220
$202$	12.0726	+	9.50019i	0.849428	+	0.668431i
$203$		−	3.67647i		−	0.258038i
$204$	28.3050	−	6.84785i	1.98175	−	0.479445i
$205$		−	8.64167i		−	0.603560i
$206$	−10.6666	+	13.5549i	−0.743178	+	0.944415i
$207$	14.9965			1.04233
$208$	−0.262258	−	0.510287i	−0.0181843	−	0.0353820i
$209$	−11.0903			−0.767133
$210$	−2.11137	+	2.68309i	−0.145698	+	0.185151i
$211$			6.49824i			0.447357i	0.974663	+	0.223678i	$0.0718066\pi$
$211$			6.49824i			0.447357i	−0.974663	+	0.223678i	$0.928193\pi$
$212$	9.94372	−	2.40569i	0.682938	−	0.165224i
$213$			9.40216i			0.644226i
$214$	−11.8398	−	9.31696i	−0.809352	−	0.636894i
$215$	−8.80029			−0.600175
$216$	0.487695	−	1.06524i	0.0331835	−	0.0724804i
$217$	−6.80029			−0.461634
$218$	−1.03095	−	0.811271i	−0.0698245	−	0.0549462i
$219$			4.57373i			0.309064i
$220$	0.785301	+	3.24597i	0.0529449	+	0.218843i
$221$		−	0.865088i		−	0.0581921i
$222$	−9.19460	+	11.6843i	−0.617101	+	0.784200i
$223$	10.1036			0.676590			0.338295	−	0.941040i	$-0.390150\pi$
$223$	10.1036			0.676590			0.338295	+	0.941040i	$0.390150\pi$
$224$	−1.07931	+	5.55294i	−0.0721144	+	0.371021i
$225$	2.82843			0.188562
$226$	−7.84333	+	9.96715i	−0.521731	+	0.663005i
$227$		−	10.2954i		−	0.683329i	−0.939822	−	0.341664i	$-0.889009\pi$
$227$		−	10.2954i		−	0.683329i	0.939822	−	0.341664i	$-0.110991\pi$
$228$	7.54088	+	31.1696i	0.499407	+	2.06426i
$229$			27.3740i			1.80893i	0.426552	+	0.904463i	$0.359728\pi$
$229$			27.3740i			1.80893i	−0.426552	+	0.904463i	$0.640272\pi$
$230$	−5.89255	−	4.63696i	−0.388543	−	0.305752i
$231$	4.03127			0.265238
$232$	−4.32868	+	9.45484i	−0.284192	+	0.620741i
$233$	11.2574			0.737499			0.368749	−	0.929529i	$-0.379786\pi$
$233$	11.2574			0.737499			0.368749	+	0.929529i	$0.379786\pi$
$234$	0.450874	+	0.354801i	0.0294746	+	0.0231941i
$235$		−	7.13048i		−	0.465141i
$236$	16.3400	−	3.95315i	1.06364	−	0.257328i
$237$		−	28.5724i		−	1.85598i
$238$	−5.27470	+	6.70299i	−0.341908	+	0.434490i
$239$	−28.7886			−1.86218			−0.931090	−	0.364789i	$-0.881141\pi$
$239$	−28.7886			−1.86218			−0.931090	+	0.364789i	$0.881141\pi$
$240$	8.58892	−	4.41421i	0.554412	−	0.284936i
$241$	−28.7275			−1.85050			−0.925251	−	0.379355i	$-0.876146\pi$
$241$	−28.7275			−1.85050			−0.925251	+	0.379355i	$0.876146\pi$
$242$	−7.18165	+	9.12630i	−0.461654	+	0.586661i
$243$			21.6569i			1.38929i
$244$	−26.9551	+	6.52127i	−1.72562	+	0.417481i
$245$		−	1.00000i		−	0.0638877i
$246$	23.1864	+	18.2458i	1.47831	+	1.16331i
$247$	0.952639			0.0606150
$248$	17.4884	+	8.00666i	1.11052	+	0.508424i
$249$	−4.28687			−0.271669
$250$	−1.11137	−	0.874559i	−0.0702893	−	0.0553120i
$251$			6.65332i			0.419954i	0.977706	+	0.209977i	$0.0673389\pi$
$251$			6.65332i			0.419954i	−0.977706	+	0.209977i	$0.932661\pi$
$252$	−1.33019	−	5.49824i	−0.0837942	−	0.346356i
$253$			8.85341i			0.556609i
$254$	−0.146964	+	0.186758i	−0.00922131	+	0.0117183i
$255$	14.5608			0.911831
$256$	9.31371	−	13.0098i	0.582107	−	0.813112i
$257$	19.5702			1.22076			0.610378	−	0.792110i	$-0.291018\pi$
$257$	19.5702			1.22076			0.610378	+	0.792110i	$0.291018\pi$
$258$	18.5807	−	23.6120i	1.15678	−	1.47002i
$259$		−	4.35480i		−	0.270594i
$260$	−0.0674560	−	0.278824i	−0.00418344	−	0.0172919i
$261$		−	10.3986i		−	0.643659i
$262$	16.4381	+	12.9355i	1.01555	+	0.799157i
$263$	5.22079			0.321928			0.160964	−	0.986960i	$-0.448540\pi$
$263$	5.22079			0.321928			0.160964	+	0.986960i	$0.448540\pi$
$264$	−10.3673	−	4.74642i	−0.638063	−	0.292122i
$265$	5.11529			0.314230
$266$	−7.38136	−	5.80853i	−0.452580	−	0.356144i
$267$		−	17.2230i		−	1.05403i
$268$	−17.7194	+	4.28687i	−1.08238	+	0.261862i
$269$		−	16.7721i		−	1.02262i	−0.859398	−	0.511308i	$-0.829161\pi$
$269$		−	16.7721i		−	1.02262i	0.859398	−	0.511308i	$-0.170839\pi$
$270$	0.362254	−	0.460345i	0.0220461	−	0.0280157i
$271$	8.30795			0.504672			0.252336	−	0.967640i	$-0.418801\pi$
$271$	8.30795			0.504672			0.252336	+	0.967640i	$0.418801\pi$
$272$	21.4571	−	11.0277i	1.30103	−	0.668655i
$273$	−0.346280			−0.0209578
$274$	5.11882	−	6.50490i	0.309239	−	0.392975i
$275$			1.66981i			0.100693i
$276$	24.8827	−	6.01990i	1.49776	−	0.362355i
$277$		−	5.88744i		−	0.353742i	−0.984234	−	0.176871i	$-0.943402\pi$
$277$		−	5.88744i		−	0.353742i	0.984234	−	0.176871i	$-0.0565976\pi$
$278$	−8.24549	−	6.48853i	−0.494532	−	0.389156i
$279$	−19.2341			−1.15152
$280$	−1.17740	+	2.57172i	−0.0703631	+	0.153689i
$281$	2.70607			0.161431			0.0807154	−	0.996737i	$-0.474280\pi$
$281$	2.70607			0.161431			0.0807154	+	0.996737i	$0.474280\pi$
$282$	19.1317	+	15.0551i	1.13928	+	0.896518i
$283$		−	22.5001i		−	1.33749i	−0.743492	−	0.668745i	$-0.766832\pi$
$283$		−	22.5001i		−	1.33749i	0.743492	−	0.668745i	$-0.233168\pi$
$284$	1.83156	+	7.57060i	0.108683	+	0.449233i
$285$			16.0344i			0.949796i
$286$	−0.209463	+	0.266181i	−0.0123858	+	0.0157396i
$287$	−8.64167			−0.510102
$288$	−3.05275	+	15.7061i	−0.179885	+	0.925489i
$289$	19.3763			1.13978
$290$	−3.21529	+	4.08593i	−0.188808	+	0.239934i
$291$		−	12.6341i		−	0.740624i
$292$	0.890973	+	3.68276i	0.0521403	+	0.215517i
$293$		−	9.41344i		−	0.549939i	−0.961453	−	0.274970i	$-0.911332\pi$
$293$		−	9.41344i		−	0.549939i	0.961453	−	0.274970i	$-0.0886678\pi$
$294$	2.68309	+	2.11137i	0.156481	+	0.123138i
$295$	8.40569			0.489398
$296$	−5.12735	+	11.1993i	−0.298021	+	0.650947i
$297$	−0.691657			−0.0401340
$298$	7.96244	+	6.26579i	0.461252	+	0.362967i
$299$		−	0.760493i		−	0.0439805i
$300$	4.69304	−	1.13539i	0.270953	−	0.0655518i
$301$			8.80029i			0.507240i
$302$	17.3900	−	22.0989i	1.00068	−	1.27165i
$303$	−26.2252			−1.50660
$304$	12.1438	+	23.6287i	0.696495	+	1.35520i
$305$	−13.8664			−0.793986
$306$	−14.9191	+	18.9589i	−0.852869	+	1.08381i
$307$			23.2185i			1.32515i	0.748995	+	0.662576i	$0.230537\pi$
$307$			23.2185i			1.32515i	−0.748995	+	0.662576i	$0.769463\pi$
$308$	3.24597	−	0.785301i	0.184956	−	0.0447466i
$309$		−	29.4451i		−	1.67507i
$310$	7.55765	+	5.94725i	0.429246	+	0.337781i
$311$	26.2517			1.48860			0.744298	−	0.667848i	$-0.232784\pi$
$311$	26.2517			1.48860			0.744298	+	0.667848i	$0.232784\pi$
$312$	0.890533	+	0.407710i	0.0504165	+	0.0230820i
$313$	−8.25559			−0.466634			−0.233317	−	0.972401i	$-0.574958\pi$
$313$	−8.25559			−0.466634			−0.233317	+	0.972401i	$0.574958\pi$
$314$	−5.30363	−	4.17352i	−0.299301	−	0.235526i
$315$		−	2.82843i		−	0.159364i
$316$	−5.56597	−	23.0065i	−0.313110	−	1.29421i
$317$		−	28.1610i		−	1.58168i	−0.612024	−	0.790839i	$-0.709644\pi$
$317$		−	28.1610i		−	1.58168i	0.612024	−	0.790839i	$-0.290356\pi$
$318$	−10.8003	+	13.7248i	−0.605650	+	0.769648i
$319$	6.13900			0.343718
$320$	6.05588	−	5.22746i	0.338534	−	0.292224i
$321$	25.7194			1.43552
$322$	−4.63696	+	5.89255i	−0.258408	+	0.328379i
$323$			40.0577i			2.22887i
$324$	4.46087	+	18.4386i	0.247826	+	1.02437i
$325$		−	0.143434i		−	0.00795627i
$326$	16.5642	+	13.0347i	0.917407	+	0.721925i
$327$	2.23951			0.123845
$328$	22.2239	+	10.1747i	1.22711	+	0.561804i
$329$	−7.13048			−0.393116
$330$	−4.48024	−	3.52559i	−0.246629	−	0.194077i
$331$			19.9670i			1.09749i	0.835991	+	0.548744i	$0.184894\pi$
$331$			19.9670i			1.09749i	−0.835991	+	0.548744i	$0.815106\pi$
$332$	−3.45178	+	0.835091i	−0.189441	+	0.0458316i
$333$		−	12.3172i		−	0.674981i
$334$	13.2872	−	16.8851i	0.727043	−	0.923911i
$335$	−9.11529			−0.498022
$336$	−4.41421	−	8.58892i	−0.240815	−	0.468564i
$337$	−33.2896			−1.81340			−0.906700	−	0.421776i	$-0.861407\pi$
$337$	−33.2896			−1.81340			−0.906700	+	0.421776i	$0.861407\pi$
$338$	−11.3513	+	14.4250i	−0.617428	+	0.784615i
$339$		−	21.6515i		−	1.17595i
$340$	11.7243	−	2.83647i	0.635840	−	0.153829i
$341$		−	11.3552i		−	0.614917i
$342$	−20.8776	−	16.4290i	−1.12893	−	0.888379i
$343$	−1.00000			−0.0539949
$344$	10.3615	−	22.6318i	0.558653	−	1.22023i
$345$	12.8003			0.689144
$346$	−19.1521	−	15.0711i	−1.02962	−	0.810228i
$347$			27.1005i			1.45483i	0.686198	+	0.727415i	$0.259278\pi$
$347$			27.1005i			1.45483i	−0.686198	+	0.727415i	$0.740722\pi$
$348$	−4.17423	−	17.2538i	−0.223762	−	0.924902i
$349$		−	4.55266i		−	0.243698i	−0.992549	−	0.121849i	$-0.961118\pi$
$349$		−	4.55266i		−	0.243698i	0.992549	−	0.121849i	$-0.0388824\pi$
$350$	−0.874559	+	1.11137i	−0.0467471	+	0.0594053i
$351$	0.0594122			0.00317119
$352$	−9.27234	−	1.80224i	−0.494217	−	0.0960597i
$353$	8.85970			0.471554			0.235777	−	0.971807i	$-0.424236\pi$
$353$	8.85970			0.471554			0.235777	+	0.971807i	$0.424236\pi$
$354$	−17.7475	+	22.5532i	−0.943271	+	1.19869i
$355$			3.89450i			0.206699i
$356$	−3.35508	−	13.8679i	−0.177819	−	0.734999i
$357$		−	14.5608i		−	0.770638i
$358$	−19.3740	−	15.2458i	−1.02395	−	0.805764i
$359$	−21.9804			−1.16008			−0.580040	−	0.814588i	$-0.696963\pi$
$359$	−21.9804			−1.16008			−0.580040	+	0.814588i	$0.696963\pi$
$360$	−3.33019	+	7.27391i	−0.175517	+	0.383369i
$361$	−25.1118			−1.32167
$362$	−4.69479	−	3.69442i	−0.246753	−	0.194174i
$363$		−	19.8249i		−	1.04054i
$364$	−0.278824	+	0.0674560i	−0.0146143	+	0.00353566i
$365$			1.89450i			0.0991628i
$366$	29.2770	−	37.2047i	1.53034	−	1.94472i
$367$	−5.77754			−0.301585			−0.150792	−	0.988565i	$-0.548183\pi$
$367$	−5.77754			−0.301585			−0.150792	+	0.988565i	$0.548183\pi$
$368$	18.8628	−	9.69442i	0.983293	−	0.505356i
$369$	−24.4423			−1.27242
$370$	−3.80853	+	4.83980i	−0.197996	+	0.251609i
$371$		−	5.11529i		−	0.265573i
$372$	−31.9140	+	7.72098i	−1.65466	+	0.400314i
$373$			18.9285i			0.980082i	0.871699	+	0.490041i	$0.163018\pi$
$373$			18.9285i			0.980082i	−0.871699	+	0.490041i	$0.836982\pi$
$374$	−11.1927	−	8.80774i	−0.578761	−	0.455437i
$375$	2.41421			0.124669
$376$	18.3376	+	8.39543i	0.945688	+	0.432961i
$377$	−0.527330			−0.0271589
$378$	−0.460345	−	0.362254i	−0.0236776	−	0.0186323i
$379$			5.11529i			0.262755i	0.991332	+	0.131378i	$0.0419400\pi$
$379$			5.11529i			0.262755i	−0.991332	+	0.131378i	$0.958060\pi$
$380$	3.12354	+	12.9109i	0.160234	+	0.662314i
$381$		−	0.405692i		−	0.0207842i
$382$	10.4052	−	13.2227i	0.532375	−	0.676532i
$383$	−19.6927			−1.00625			−0.503126	−	0.864213i	$-0.667817\pi$
$383$	−19.6927			−1.00625			−0.503126	+	0.864213i	$0.667817\pi$
$384$	1.23951	+	27.2856i	0.0632533	+	1.39241i
$385$	1.66981			0.0851013
$386$	−21.7324	+	27.6170i	−1.10615	+	1.40567i
$387$			24.8910i			1.26528i
$388$	−2.46115	−	10.1730i	−0.124946	−	0.516453i
$389$			9.25745i			0.469371i	0.972071	+	0.234686i	$0.0754061\pi$
$389$			9.25745i			0.469371i	−0.972071	+	0.234686i	$0.924594\pi$
$390$	0.384845	+	0.302842i	0.0194874	+	0.0153350i
$391$	31.9781			1.61720
$392$	2.57172	+	1.17740i	0.129891	+	0.0594677i
$393$	−35.7083			−1.80125
$394$	−4.88341	−	3.84284i	−0.246023	−	0.193600i
$395$		−	11.8351i		−	0.595488i
$396$	9.18100	−	2.22117i	0.461362	−	0.111618i
$397$		−	16.1871i		−	0.812409i	−0.913782	−	0.406204i	$-0.866852\pi$
$397$		−	16.1871i		−	0.812409i	0.913782	−	0.406204i	$-0.133148\pi$
$398$	17.5889	−	22.3516i	0.881653	−	1.12039i
$399$	16.0344			0.802724
$400$	3.55765	−	1.82843i	0.177882	−	0.0914214i
$401$	−29.1914			−1.45775			−0.728873	−	0.684649i	$-0.759956\pi$
$401$	−29.1914			−1.45775			−0.728873	+	0.684649i	$0.759956\pi$
$402$	19.2458	−	24.4571i	0.959892	−	1.21981i
$403$			0.975391i			0.0485877i
$404$	−21.1165	+	5.10872i	−1.05058	+	0.254169i
$405$			9.48528i			0.471327i
$406$	4.08593	+	3.21529i	0.202781	+	0.159572i
$407$	7.27168			0.360444
$408$	−17.1439	+	37.4462i	−0.848748	+	1.85386i
$409$	16.5908			0.820361			0.410181	−	0.912004i	$-0.365466\pi$
$409$	16.5908			0.820361			0.410181	+	0.912004i	$0.365466\pi$
$410$	9.60411	+	7.55765i	0.474313	+	0.373246i
$411$			14.1305i			0.697005i
$412$	−5.73597	−	23.7091i	−0.282591	−	1.16806i
$413$		−	8.40569i		−	0.413617i
$414$	−13.1153	+	16.6667i	−0.644582	+	0.819121i
$415$	−1.77568			−0.0871646
$416$	0.796478	+	0.154809i	0.0390506	+	0.00759016i
$417$	17.9115			0.877132
$418$	9.69913	−	12.3255i	0.474400	−	0.602858i
$419$			8.11176i			0.396286i	0.980173	+	0.198143i	$0.0634910\pi$
$419$			8.11176i			0.396286i	−0.980173	+	0.198143i	$0.936509\pi$
$420$	−1.13539	−	4.69304i	−0.0554014	−	0.228997i
$421$			33.1886i			1.61751i	0.588144	+	0.808757i	$0.299859\pi$
$421$			33.1886i			1.61751i	−0.588144	+	0.808757i	$0.700141\pi$
$422$	−7.22195	−	5.68309i	−0.351559	−	0.276648i
$423$	−20.1680			−0.980604
$424$	−6.02275	+	13.1551i	−0.292491	+	0.638868i
$425$	6.03127			0.292560
$426$	−10.4493	−	8.22274i	−0.506270	−	0.398393i
$427$			13.8664i			0.671040i
$428$	20.7092	−	5.01019i	1.00102	−	0.242177i
$429$		−	0.578221i		−	0.0279168i
$430$	7.69637	−	9.78039i	0.371152	−	0.471652i
$431$	14.5277			0.699772			0.349886	−	0.936792i	$-0.386220\pi$
$431$	14.5277			0.699772			0.349886	+	0.936792i	$0.386220\pi$
$432$	0.757359	+	1.47363i	0.0364385	+	0.0708999i
$433$	10.7488			0.516556			0.258278	−	0.966071i	$-0.416845\pi$
$433$	10.7488			0.516556			0.258278	+	0.966071i	$0.416845\pi$
$434$	5.94725	−	7.55765i	0.285477	−	0.362779i
$435$		−	8.87579i		−	0.425561i
$436$	1.80325	−	0.436261i	0.0863598	−	0.0208931i
$437$			35.2145i			1.68454i
$438$	−5.08312	−	4.00000i	−0.242881	−	0.191127i
$439$	23.1386			1.10435			0.552173	−	0.833730i	$-0.313799\pi$
$439$	23.1386			1.10435			0.552173	+	0.833730i	$0.313799\pi$
$440$	−4.29427	−	1.96603i	−0.204721	−	0.0937269i
$441$	−2.82843			−0.134687
$442$	0.961434	+	0.756570i	0.0457308	+	0.0359864i
$443$		−	19.6983i		−	0.935895i	−0.883756	−	0.467948i	$-0.844994\pi$
$443$		−	19.6983i		−	0.935895i	0.883756	−	0.467948i	$-0.155006\pi$
$444$	−4.94440	−	20.4372i	−0.234651	−	0.969909i
$445$		−	7.13401i		−	0.338184i
$446$	−8.83623	+	11.2289i	−0.418407	+	0.531704i
$447$	−17.2967			−0.818104
$448$	−5.22746	−	6.05588i	−0.246974	−	0.286114i
$449$	32.9500			1.55501			0.777503	−	0.628879i	$-0.216486\pi$
$449$	32.9500			1.55501			0.777503	+	0.628879i	$0.216486\pi$
$450$	−2.47363	+	3.14343i	−0.116608	+	0.148183i
$451$		−	14.4299i		−	0.679479i
$452$	−4.21775	−	17.4337i	−0.198386	−	0.820013i
$453$			48.0050i			2.25547i
$454$	11.4420	+	9.00392i	0.537000	+	0.422575i
$455$	−0.143434			−0.00672428
$456$	−41.2360	−	18.8789i	−1.93105	−	0.884087i
$457$	33.7538			1.57894			0.789468	−	0.613791i	$-0.210356\pi$
$457$	33.7538			1.57894			0.789468	+	0.613791i	$0.210356\pi$
$458$	−30.4227	−	23.9402i	−1.42156	−	1.11865i
$459$			2.49824i			0.116608i
$460$	10.3068	−	2.49352i	0.480555	−	0.116261i
$461$		−	23.9626i		−	1.11605i	−0.829825	−	0.558024i	$-0.811560\pi$
$461$		−	23.9626i		−	1.11605i	0.829825	−	0.558024i	$-0.188440\pi$
$462$	−3.52559	+	4.48024i	−0.164025	+	0.208440i
$463$	2.77382			0.128910			0.0644552	−	0.997921i	$-0.479469\pi$
$463$	2.77382			0.128910			0.0644552	+	0.997921i	$0.479469\pi$
$464$	−6.72216	−	13.0796i	−0.312068	−	0.607205i
$465$	−16.4173			−0.761336
$466$	−9.84528	+	12.5112i	−0.456074	+	0.579570i
$467$		−	25.1301i		−	1.16288i	−0.813589	−	0.581441i	$-0.802489\pi$
$467$		−	25.1301i		−	1.16288i	0.813589	−	0.581441i	$-0.197511\pi$
$468$	−0.788632	+	0.190794i	−0.0364545	+	0.00881947i
$469$			9.11529i			0.420905i
$470$	7.92461	+	6.23602i	0.365535	+	0.287646i
$471$	11.5210			0.530859
$472$	−9.89687	+	21.6171i	−0.455540	+	0.995006i
$473$	−14.6948			−0.675667
$474$	31.7546	+	24.9883i	1.45854	+	1.14775i
$475$			6.64167i			0.304741i
$476$	−2.83647	−	11.7243i	−0.130009	−	0.537383i
$477$		−	14.4682i		−	0.662455i
$478$	25.1773	−	31.9948i	1.15158	−	1.46341i
$479$	−17.0568			−0.779344			−0.389672	−	0.920954i	$-0.627412\pi$
$479$	−17.0568			−0.779344			−0.389672	+	0.920954i	$0.627412\pi$
$480$	−2.60568	+	13.4060i	−0.118933	+	0.611896i
$481$	−0.624625			−0.0284805
$482$	25.1239	−	31.9270i	1.14436	−	1.45423i
$483$		−	12.8003i		−	0.582433i
$484$	−3.86193	−	15.9630i	−0.175542	−	0.725589i
$485$		−	5.23322i		−	0.237628i
$486$	−24.0688	−	18.9402i	−1.09178	−	0.859145i
$487$	40.3790			1.82975			0.914873	−	0.403741i	$-0.132290\pi$
$487$	40.3790			1.82975			0.914873	+	0.403741i	$0.132290\pi$
$488$	16.3263	−	35.6604i	0.739055	−	1.61427i
$489$	−35.9822			−1.62717
$490$	1.11137	+	0.874559i	0.0502067	+	0.0395085i
$491$		−	16.9968i		−	0.767057i	−0.923529	−	0.383528i	$-0.874709\pi$
$491$		−	16.9968i		−	0.767057i	0.923529	−	0.383528i	$-0.125291\pi$
$492$	−40.5557	+	9.81166i	−1.82839	+	0.442344i
$493$		−	22.1738i		−	0.998658i
$494$	−0.833139	+	1.05874i	−0.0374847	+	0.0476348i
$495$	4.72293			0.212280
$496$	−24.1930	+	12.4338i	−1.08630	+	0.558295i
$497$	3.89450			0.174692
$498$	3.74912	−	4.76430i	0.168002	−	0.213494i
$499$			10.6600i			0.477208i	0.971117	+	0.238604i	$0.0766897\pi$
$499$			10.6600i			0.477208i	−0.971117	+	0.238604i	$0.923310\pi$
$500$	1.94392	−	0.470294i	0.0869347	−	0.0210322i
$501$			36.6792i			1.63871i
$502$	−7.39432	−	5.81872i	−0.330024	−	0.259702i
$503$	5.00167			0.223014			0.111507	−	0.993764i	$-0.464432\pi$
$503$	5.00167			0.223014			0.111507	+	0.993764i	$0.464432\pi$
$504$	7.27391	+	3.33019i	0.324006	+	0.148339i
$505$	−10.8628			−0.483390
$506$	−9.83943	−	7.74283i	−0.437416	−	0.344211i
$507$		−	31.3351i		−	1.39164i
$508$	−0.0790296	−	0.326662i	−0.00350637	−	0.0144933i
$509$		−	16.8284i		−	0.745907i	−0.927850	−	0.372953i	$-0.878345\pi$
$509$		−	16.8284i		−	0.745907i	0.927850	−	0.372953i	$-0.121655\pi$
$510$	−12.7343	+	16.1824i	−0.563882	+	0.716570i
$511$	1.89450			0.0838079
$512$	6.31333	+	21.7288i	0.279013	+	0.960287i
$513$	−2.75107			−0.121463
$514$	−17.1153	+	21.7498i	−0.754923	+	0.959341i
$515$		−	12.1966i		−	0.537444i
$516$	9.99176	+	41.3001i	0.439863	+	1.81813i
$517$		−	11.9065i		−	0.523649i
$518$	4.83980	+	3.80853i	0.212649	+	0.167337i
$519$	41.6037			1.82620
$520$	0.368871	+	0.168879i	0.0161761	+	0.00740583i
$521$	30.1742			1.32195			0.660977	−	0.750406i	$-0.270142\pi$
$521$	30.1742			1.32195			0.660977	+	0.750406i	$0.270142\pi$
$522$	11.5567	+	9.09422i	0.505825	+	0.398043i
$523$		−	8.92686i		−	0.390345i	−0.980769	−	0.195172i	$-0.937473\pi$
$523$		−	8.92686i		−	0.390345i	0.980769	−	0.195172i	$-0.0625266\pi$
$524$	−28.7523	+	6.95605i	−1.25605	+	0.303877i
$525$		−	2.41421i		−	0.105365i
$526$	−4.56589	+	5.80224i	−0.199082	+	0.252990i
$527$	−41.0144			−1.78662
$528$	14.3418	−	7.37089i	0.624149	−	0.320777i
$529$	5.11176			0.222251
$530$	−4.47363	+	5.68499i	−0.194322	+	0.246940i
$531$		−	23.7749i		−	1.03174i
$532$	12.9109	−	3.12354i	0.559757	−	0.135422i
$533$			1.23951i			0.0536890i
$534$	19.1412	+	15.0625i	0.828320	+	0.651820i
$535$	10.6533			0.460583
$536$	10.7324	−	23.4420i	0.463567	−	1.01254i
$537$	42.0859			1.81614
$538$	18.6401	+	14.6682i	0.803631	+	0.632392i
$539$		−	1.66981i		−	0.0719237i
$540$	0.194802	+	0.805198i	0.00838295	+	0.0346502i
$541$			12.8973i			0.554497i	0.960798	+	0.277248i	$0.0894225\pi$
$541$			12.8973i			0.554497i	−0.960798	+	0.277248i	$0.910578\pi$
$542$	−7.26579	+	9.23322i	−0.312092	+	0.396601i
$543$	10.1984			0.437656
$544$	−6.50961	+	33.4913i	−0.279097	+	1.43593i
$545$	0.927634			0.0397355
$546$	0.302842	−	0.384845i	0.0129604	−	0.0164699i
$547$		−	20.0415i		−	0.856911i	−0.903563	−	0.428456i	$-0.859058\pi$
$547$		−	20.0415i		−	0.856911i	0.903563	−	0.428456i	$-0.140942\pi$
$548$	2.75265	+	11.3778i	0.117587	+	0.486037i
$549$			39.2200i			1.67387i
$550$	−1.85578	−	1.46035i	−0.0791306	−	0.0622693i
$551$	24.4179			1.04024
$552$	−15.0711	+	32.9187i	−0.641467	+	1.40111i
$553$	−11.8351			−0.503279
$554$	6.54314	+	5.14892i	0.277991	+	0.218756i
$555$		−	10.5134i		−	0.446270i
$556$	14.4223	−	3.48921i	0.611643	−	0.147975i
$557$			35.9670i			1.52397i	0.647593	+	0.761986i	$0.275776\pi$
$557$			35.9670i			1.52397i	−0.647593	+	0.761986i	$0.724224\pi$
$558$	16.8214	−	21.3763i	0.712105	−	0.904929i
$559$	1.26226			0.0533878
$560$	−1.82843	−	3.55765i	−0.0772651	−	0.150338i
$561$	24.3137			1.02653
$562$	−2.36662	+	3.00745i	−0.0998298	+	0.126862i
$563$		−	6.97943i		−	0.294148i	−0.989126	−	0.147074i	$-0.953014\pi$
$563$		−	6.97943i		−	0.294148i	0.989126	−	0.147074i	$-0.0469855\pi$
$564$	−33.4636	+	8.09588i	−1.40907	+	0.340898i
$565$		−	8.96833i		−	0.377301i
$566$	25.0059	+	19.6776i	1.05108	+	0.827113i
$567$	9.48528			0.398344
$568$	−10.0156	−	4.58539i	−0.420244	−	0.192399i
$569$	37.3459			1.56562			0.782810	−	0.622260i	$-0.213785\pi$
$569$	37.3459			1.56562			0.782810	+	0.622260i	$0.213785\pi$
$570$	−17.8202	−	14.0230i	−0.746405	−	0.587360i
$571$			33.4888i			1.40146i	0.713425	+	0.700732i	$0.247143\pi$
$571$			33.4888i			1.40146i	−0.713425	+	0.700732i	$0.752857\pi$
$572$	−0.112639	−	0.465582i	−0.00470966	−	0.0194670i
$573$			28.7234i			1.19994i
$574$	7.55765	−	9.60411i	0.315450	−	0.400868i
$575$	5.30205			0.221111
$576$	−14.7855	−	17.1286i	−0.616062	−	0.713693i
$577$	−21.4638			−0.893550			−0.446775	−	0.894646i	$-0.647428\pi$
$577$	−21.4638			−0.893550			−0.446775	+	0.894646i	$0.647428\pi$
$578$	−16.9457	+	21.5342i	−0.704847	+	0.895705i
$579$		−	59.9920i		−	2.49318i
$580$	−1.72902	−	7.14677i	−0.0717937	−	0.296753i
$581$			1.77568i			0.0736676i
$582$	14.0412	+	11.0493i	0.582026	+	0.458007i
$583$	8.54156			0.353755
$584$	−4.87213	−	2.23059i	−0.201610	−	0.0923024i
$585$	−0.405692			−0.0167733
$586$	10.4618	+	8.23261i	0.432174	+	0.340086i
$587$			21.9804i			0.907227i	0.891199	+	0.453613i	$0.149865\pi$
$587$			21.9804i			0.907227i	−0.891199	+	0.453613i	$0.850135\pi$
$588$	−4.69304	+	1.13539i	−0.193538	+	0.0468227i
$589$		−	45.1653i		−	1.86100i
$590$	−7.35127	+	9.34185i	−0.302647	+	0.384598i
$591$	10.6081			0.436361
$592$	−7.96244	−	15.4928i	−0.327254	−	0.636752i
$593$	−19.1566			−0.786665			−0.393333	−	0.919396i	$-0.628678\pi$
$593$	−19.1566			−0.786665			−0.393333	+	0.919396i	$0.628678\pi$
$594$	0.604895	−	0.768688i	0.0248191	−	0.0315397i
$595$		−	6.03127i		−	0.247258i
$596$	−13.9272	+	3.36943i	−0.570482	+	0.138017i
$597$			48.5541i			1.98719i
$598$	0.845191	+	0.665096i	0.0345624	+	0.0271978i
$599$	15.5715			0.636236			0.318118	−	0.948051i	$-0.396949\pi$
$599$	15.5715			0.636236			0.318118	+	0.948051i	$0.396949\pi$
$600$	−2.84250	+	6.20867i	−0.116044	+	0.253468i
$601$	−25.7194			−1.04912			−0.524558	−	0.851375i	$-0.675769\pi$
$601$	−25.7194			−1.04912			−0.524558	+	0.851375i	$0.675769\pi$
$602$	−9.78039	−	7.69637i	−0.398619	−	0.313681i
$603$			25.7819i			1.04992i
$604$	9.35147	+	38.6535i	0.380506	+	1.57279i
$605$		−	8.21174i		−	0.333855i
$606$	22.9355	−	29.1459i	0.931690	−	1.18397i
$607$	−20.5227			−0.832989			−0.416495	−	0.909138i	$-0.636741\pi$
$607$	−20.5227			−0.832989			−0.416495	+	0.909138i	$0.636741\pi$
$608$	−36.8808	−	7.16842i	−1.49571	−	0.290718i
$609$	−8.87579			−0.359665
$610$	12.1270	−	15.4107i	0.491006	−	0.623960i
$611$			1.02275i			0.0413761i
$612$	−8.02275	−	33.1614i	−0.324301	−	1.34047i
$613$		−	9.40216i		−	0.379750i	−0.981808	−	0.189875i	$-0.939192\pi$
$613$		−	9.40216i		−	0.379750i	0.981808	−	0.189875i	$-0.0608082\pi$
$614$	−25.8044	−	20.3060i	−1.04138	−	0.819482i
$615$	−20.8628			−0.841271
$616$	−1.96603	+	4.29427i	−0.0792137	+	0.173021i
$617$	−20.0814			−0.808446			−0.404223	−	0.914660i	$-0.632458\pi$
$617$	−20.0814			−0.808446			−0.404223	+	0.914660i	$0.632458\pi$
$618$	32.7244	+	25.7515i	1.31637	+	1.03588i
$619$		−	18.6972i		−	0.751502i	−0.926721	−	0.375751i	$-0.877385\pi$
$619$		−	18.6972i		−	0.751502i	0.926721	−	0.375751i	$-0.122615\pi$
$620$	−13.2192	+	3.19813i	−0.530896	+	0.128440i
$621$			2.19618i			0.0881298i
$622$	−22.9586	+	29.1754i	−0.920557	+	1.16983i
$623$	−7.13401			−0.285818
$624$	−1.23194	+	0.633147i	−0.0493171	+	0.0253462i
$625$	1.00000			0.0400000
$626$	7.22000	−	9.17503i	0.288569	−	0.366708i
$627$			26.7744i			1.06927i
$628$	9.27667	−	2.24431i	0.370180	−	0.0895578i
$629$		−	26.2650i		−	1.04725i
$630$	3.14343	+	2.47363i	0.125237	+	0.0985516i
$631$	−8.24630			−0.328280			−0.164140	−	0.986437i	$-0.552485\pi$
$631$	−8.24630			−0.328280			−0.164140	+	0.986437i	$0.552485\pi$
$632$	30.4365	+	13.9346i	1.21070	+	0.554290i
$633$	15.6881			0.623547
$634$	31.2973	+	24.6284i	1.24298	+	0.978120i
$635$		−	0.168043i		−	0.00666859i
$636$	−5.80785	−	24.0063i	−0.230296	−	0.951910i
$637$			0.143434i			0.00568305i
$638$	−5.36892	+	6.82271i	−0.212557	+	0.270114i
$639$	11.0153			0.435759
$640$	0.513421	+	11.3021i	0.0202947	+	0.446753i
$641$	13.2208			0.522190			0.261095	−	0.965313i	$-0.415916\pi$
$641$	13.2208			0.522190			0.261095	+	0.965313i	$0.415916\pi$
$642$	−22.4931	+	28.5838i	−0.887733	+	1.12811i
$643$			27.0942i			1.06849i	0.845329	+	0.534245i	$0.179404\pi$
$643$			27.0942i			1.06849i	−0.845329	+	0.534245i	$0.820596\pi$
$644$	−2.49352	−	10.3068i	−0.0982586	−	0.406143i
$645$			21.2458i			0.836552i
$646$	−44.5190	−	35.0328i	−1.75158	−	1.37835i
$647$	−2.06807			−0.0813041			−0.0406520	−	0.999173i	$-0.512944\pi$
$647$	−2.06807			−0.0813041			−0.0406520	+	0.999173i	$0.512944\pi$
$648$	−24.3935	−	11.1680i	−0.958266	−	0.438720i
$649$	14.0359			0.550957
$650$	0.159408	+	0.125441i	0.00625250	+	0.00492021i
$651$			16.4173i			0.643447i
$652$	−28.9728	+	7.00940i	−1.13466	+	0.274509i
$653$			27.6256i			1.08107i	0.841321	+	0.540536i	$0.181778\pi$
$653$			27.6256i			1.08107i	−0.841321	+	0.540536i	$0.818222\pi$
$654$	−1.95858	+	2.48892i	−0.0765866	+	0.0973246i
$655$	−14.7909			−0.577927
$656$	−30.7440	+	15.8007i	−1.20035	+	0.616912i
$657$	5.35846			0.209054
$658$	6.23602	−	7.92461i	0.243106	−	0.308934i
$659$			34.8798i			1.35873i	0.733803	+	0.679363i	$0.237744\pi$
$659$			34.8798i			1.35873i	−0.733803	+	0.679363i	$0.762256\pi$
$660$	7.83647	−	1.89588i	0.305034	−	0.0737972i
$661$			26.0492i			1.01320i	0.862182	+	0.506599i	$0.169097\pi$
$661$			26.0492i			1.01320i	−0.862182	+	0.506599i	$0.830903\pi$
$662$	−22.1908	−	17.4623i	−0.862470	−	0.678693i
$663$	−2.08851			−0.0811109
$664$	2.09069	−	4.56654i	0.0811343	−	0.177216i
$665$	6.64167			0.257553
$666$	13.6890	+	10.7721i	0.530439	+	0.417412i
$667$		−	19.4928i		−	0.754766i
$668$	7.14519	+	29.5340i	0.276456	+	1.14271i
$669$		−	24.3923i		−	0.943062i
$670$	7.97186	−	10.1305i	0.307980	−	0.391375i
$671$	−23.1542			−0.893857
$672$	13.4060	+	2.60568i	0.517147	+	0.100516i
$673$	41.5669			1.60229			0.801143	−	0.598472i	$-0.204225\pi$
$673$	41.5669			1.60229			0.801143	+	0.598472i	$0.204225\pi$
$674$	29.1137	−	36.9971i	1.12142	−	1.42508i
$675$			0.414214i			0.0159431i
$676$	−6.10415	−	25.2310i	−0.234775	−	0.970422i
$677$		−	20.8530i		−	0.801447i	−0.916199	−	0.400724i	$-0.868759\pi$
$677$		−	20.8530i		−	0.801447i	0.916199	−	0.400724i	$-0.131241\pi$
$678$	24.0628	+	18.9355i	0.924127	+	0.727213i
$679$	−5.23322			−0.200832
$680$	−7.10123	+	15.5107i	−0.272320	+	0.594809i
$681$	−24.8553			−0.952456
$682$	12.6198	+	9.93077i	0.483238	+	0.380269i
$683$			3.74308i			0.143225i	0.997433	+	0.0716124i	$0.0228145\pi$
$683$			3.74308i			0.143225i	−0.997433	+	0.0716124i	$0.977186\pi$
$684$	36.5175	−	8.83469i	1.39628	−	0.337803i
$685$			5.85304i			0.223633i
$686$	0.874559	−	1.11137i	0.0333908	−	0.0424324i
$687$	66.0867			2.52137
$688$	16.0907	+	31.3083i	0.613452	+	1.19362i
$689$	−0.733706			−0.0279520
$690$	−11.1946	+	14.2259i	−0.426171	+	0.541570i
$691$		−	26.3665i		−	1.00303i	−0.865150	−	0.501514i	$-0.832777\pi$
$691$		−	26.3665i		−	1.00303i	0.865150	−	0.501514i	$-0.167223\pi$
$692$	33.4992	−	8.10449i	1.27345	−	0.308087i
$693$		−	4.72293i		−	0.179409i
$694$	−30.1187	−	23.7010i	−1.14329	−	0.899676i
$695$	7.41921			0.281427
$696$	22.8260	+	10.4504i	0.865218	+	0.396120i
$697$	−52.1203			−1.97420
$698$	5.05969	+	3.98156i	0.191512	+	0.150704i
$699$		−	27.1778i		−	1.02796i
$700$	−0.470294	−	1.94392i	−0.0177754	−	0.0734733i
$701$		−	11.3145i		−	0.427342i	−0.976906	−	0.213671i	$-0.931458\pi$
$701$		−	11.3145i		−	0.427342i	0.976906	−	0.213671i	$-0.0685420\pi$
$702$	−0.0519595	+	0.0660290i	−0.00196108	+	0.00249211i
$703$	28.9231			1.09086
$704$	10.1122	−	8.72885i	0.381116	−	0.328981i
$705$	−17.2145			−0.648336
$706$	−7.74833	+	9.84642i	−0.291612	+	0.370575i
$707$			10.8628i			0.408539i
$708$	−9.54374	−	39.4482i	−0.358676	−	1.48256i
$709$		−	5.83119i		−	0.218995i	−0.993987	−	0.109497i	$-0.965076\pi$
$709$		−	5.83119i		−	0.218995i	0.993987	−	0.109497i	$-0.0349241\pi$
$710$	−4.32824	−	3.40597i	−0.162436	−	0.127824i
$711$	−33.4747			−1.25540
$712$	18.3467	+	8.39959i	0.687570	+	0.314788i
$713$	−36.0555			−1.35029
$714$	16.1824	+	12.7343i	0.605613	+	0.476568i
$715$		−	0.239507i		−	0.00895705i
$716$	33.8874	−	8.19841i	1.26643	−	0.306389i
$717$			69.5019i			2.59559i
$718$	19.2231	−	24.4283i	0.717400	−	0.911658i
$719$	22.6903			0.846206			0.423103	−	0.906081i	$-0.360941\pi$
$719$	22.6903			0.846206			0.423103	+	0.906081i	$0.360941\pi$
$720$	−5.17157	−	10.0625i	−0.192733	−	0.375009i
$721$	−12.1966			−0.454223
$722$	21.9617	−	27.9085i	0.817330	−	1.03865i
$723$			69.3544i			2.57932i
$724$	8.21174	−	1.98667i	0.305187	−	0.0738341i
$725$		−	3.67647i		−	0.136541i
$726$	22.0328	+	17.3380i	0.817715	+	0.643475i
$727$	−1.09198			−0.0404994			−0.0202497	−	0.999795i	$-0.506446\pi$
$727$	−1.09198			−0.0404994			−0.0202497	+	0.999795i	$0.506446\pi$
$728$	0.168879	−	0.368871i	0.00625907	−	0.0136713i
$729$	23.8284			0.882534
$730$	−2.10550	−	1.65685i	−0.0779279	−	0.0613229i
$731$			53.0769i			1.96312i
$732$	15.7437	+	65.0754i	0.581905	+	2.40525i
$733$			17.7777i			0.656635i	0.944567	+	0.328318i	$0.106482\pi$
$733$			17.7777i			0.656635i	−0.944567	+	0.328318i	$0.893518\pi$
$734$	5.05280	−	6.42099i	0.186502	−	0.237003i
$735$	−2.41421			−0.0890496
$736$	−5.72256	+	29.4420i	−0.210936	+	1.08524i
$737$	−15.2208			−0.560665
$738$	21.3763	−	27.1645i	0.786871	−	0.999940i
$739$		−	12.3302i		−	0.453573i	−0.973944	−	0.226787i	$-0.927178\pi$
$739$		−	12.3302i		−	0.453573i	0.973944	−	0.226787i	$-0.0728220\pi$
$740$	−2.04804	−	8.46538i	−0.0752873	−	0.311194i
$741$		−	2.29987i		−	0.0844880i
$742$	5.68499	+	4.47363i	0.208703	+	0.164232i
$743$	23.2253			0.852052			0.426026	−	0.904711i	$-0.359913\pi$
$743$	23.2253			0.852052			0.426026	+	0.904711i	$0.359913\pi$
$744$	19.3298	−	42.2208i	0.708665	−	1.54789i
$745$	−7.16451			−0.262487
$746$	−21.0366	−	16.5541i	−0.770206	−	0.606089i
$747$			5.02238i			0.183759i
$748$	19.5773	−	4.73636i	0.715819	−	0.173179i
$749$		−	10.6533i		−	0.389264i
$750$	−2.11137	+	2.68309i	−0.0770964	+	0.0979725i
$751$	−33.1614			−1.21008			−0.605038	−	0.796197i	$-0.706842\pi$
$751$	−33.1614			−1.21008			−0.605038	+	0.796197i	$0.706842\pi$
$752$	−25.3677	+	13.0376i	−0.925066	+	0.475431i
$753$	16.0625			0.585352
$754$	0.461181	−	0.586060i	0.0167952	−	0.0213430i
$755$			19.8843i			0.723664i
$756$	0.805198	−	0.194802i	0.0292848	−	0.00708488i
$757$		−	15.6531i		−	0.568923i	−0.958687	−	0.284461i	$-0.908185\pi$
$757$		−	15.6531i		−	0.568923i	0.958687	−	0.284461i	$-0.0918148\pi$
$758$	−5.68499	−	4.47363i	−0.206488	−	0.162489i
$759$	21.3740			0.775828
$760$	−17.0805	−	7.81991i	−0.619575	−	0.283658i
$761$	−28.8105			−1.04438			−0.522189	−	0.852830i	$-0.674885\pi$
$761$	−28.8105			−1.04438			−0.522189	+	0.852830i	$0.674885\pi$
$762$	0.450874	+	0.354801i	0.0163335	+	0.0128531i
$763$		−	0.927634i		−	0.0335826i
$764$	5.59539	+	23.1281i	0.202434	+	0.836743i
$765$		−	17.0590i		−	0.616770i
$766$	17.2225	−	21.8860i	0.622273	−	0.790772i
$767$	−1.20566			−0.0435338
$768$	−31.4084	−	22.4853i	−1.13335	−	0.811368i
$769$	−23.1419			−0.834520			−0.417260	−	0.908787i	$-0.637010\pi$
$769$	−23.1419			−0.834520			−0.417260	+	0.908787i	$0.637010\pi$
$770$	−1.46035	+	1.85578i	−0.0526272	+	0.0668776i
$771$		−	47.2467i		−	1.70155i
$772$	−11.6866	−	48.3054i	−0.420609	−	1.73855i
$773$		−	4.49285i		−	0.161596i	−0.996730	−	0.0807982i	$-0.974253\pi$
$773$		−	4.49285i		−	0.161596i	0.996730	−	0.0807982i	$-0.0257469\pi$
$774$	−27.6631	−	21.7686i	−0.994330	−	0.782457i
$775$	−6.80029			−0.244274
$776$	13.4584	+	6.16159i	0.483127	+	0.221188i
$777$	−10.5134			−0.377167
$778$	−10.2885	−	8.09619i	−0.368860	−	0.290262i
$779$		−	57.3951i		−	2.05639i
$780$	−0.673140	+	0.162853i	−0.0241023	+	0.00583108i
$781$			6.50307i			0.232698i
$782$	−27.9668	+	35.5396i	−1.00009	+	1.27089i
$783$	1.52284			0.0544220
$784$	−3.55765	+	1.82843i	−0.127059	+	0.0653010i
$785$	4.77215			0.170325
$786$	31.2290	−	39.6852i	1.11390	−	1.41552i
$787$		−	21.5832i		−	0.769358i	−0.923050	−	0.384679i	$-0.874312\pi$
$787$		−	21.5832i		−	0.769358i	0.923050	−	0.384679i	$-0.125688\pi$
$788$	8.54165	−	2.06649i	0.304284	−	0.0736156i
$789$		−	12.6041i		−	0.448718i
$790$	13.1532	+	10.3505i	0.467969	+	0.368254i
$791$	−8.96833			−0.318877
$792$	−5.56078	+	12.1460i	−0.197594	+	0.431591i
$793$	1.98890			0.0706281
$794$	17.9899	+	14.1566i	0.638438	+	0.502399i
$795$		−	12.3494i		−	0.437989i
$796$	9.45844	+	39.0957i	0.335246	+	1.38571i
$797$		−	30.2740i		−	1.07236i	−0.844103	−	0.536181i	$-0.819866\pi$
$797$		−	30.2740i		−	1.07236i	0.844103	−	0.536181i	$-0.180134\pi$
$798$	−14.0230	+	17.8202i	−0.496410	+	0.630828i
$799$	−43.0059			−1.52144
$800$	−1.07931	+	5.55294i	−0.0381594	+	0.196326i
$801$	−20.1780			−0.712956
$802$	25.5296	−	32.4424i	0.901480	−	1.14558i
$803$			3.16346i			0.111636i
$804$	10.3494	+	42.7784i	0.364996	+	1.50868i
$805$		−	5.30205i		−	0.186873i
$806$	−1.08402	−	0.853036i	−0.0381830	−	0.0300469i
$807$	−40.4915			−1.42537
$808$	12.7899	−	27.9361i	0.449947	−	0.982790i
$809$	−10.9670			−0.385580			−0.192790	−	0.981240i	$-0.561754\pi$
$809$	−10.9670			−0.385580			−0.192790	+	0.981240i	$0.561754\pi$
$810$	−10.5417	−	8.29544i	−0.370397	−	0.291472i
$811$		−	6.39683i		−	0.224623i	−0.993673	−	0.112312i	$-0.964175\pi$
$811$		−	6.39683i		−	0.224623i	0.993673	−	0.112312i	$-0.0358254\pi$
$812$	−7.14677	+	1.72902i	−0.250802	+	0.0606768i
$813$		−	20.0572i		−	0.703435i
$814$	−6.35951	+	8.08154i	−0.222901	+	0.283258i
$815$	−14.9043			−0.522075
$816$	−26.6233	−	51.8021i	−0.932003	−	1.81344i
$817$	−58.4486			−2.04486
$818$	−14.5096	+	18.4385i	−0.507317	+	0.644688i
$819$			0.405692i			0.0141760i
$820$	−16.7987	+	4.06412i	−0.586636	+	0.141925i
$821$		−	36.7455i		−	1.28243i	−0.767363	−	0.641213i	$-0.778432\pi$
$821$		−	36.7455i		−	1.28243i	0.767363	−	0.641213i	$-0.221568\pi$
$822$	−15.7042	−	12.3579i	−0.547747	−	0.431032i
$823$	23.4701			0.818116			0.409058	−	0.912508i	$-0.365857\pi$
$823$	23.4701			0.818116			0.409058	+	0.912508i	$0.365857\pi$
$824$	31.3661	+	14.3602i	1.09269	+	0.500262i
$825$	4.03127			0.140351
$826$	9.34185	+	7.35127i	0.325044	+	0.255783i
$827$			30.1914i			1.04986i	0.851147	+	0.524928i	$0.175908\pi$
$827$			30.1914i			1.04986i	−0.851147	+	0.524928i	$0.824092\pi$
$828$	−7.05275	−	29.1519i	−0.245100	−	1.01310i
$829$			20.8995i			0.725869i	0.931815	+	0.362934i	$0.118225\pi$
$829$			20.8995i			0.725869i	−0.931815	+	0.362934i	$0.881775\pi$
$830$	1.55294	−	1.97344i	0.0539032	−	0.0684991i
$831$	−14.2135			−0.493062
$832$	−0.868618	+	0.749793i	−0.0301139	+	0.0259944i
$833$	−6.03127			−0.208971
$834$	−15.6647	+	19.9064i	−0.542424	+	0.689302i
$835$			15.1930i			0.525776i
$836$	5.21571	+	21.5587i	0.180389	+	0.745622i
$837$		−	2.81677i		−	0.0973619i
$838$	−9.01519	−	7.09422i	−0.311424	−	0.245066i
$839$	0.562639			0.0194245			0.00971223	−	0.999953i	$-0.496908\pi$
$839$	0.562639			0.0194245			0.00971223	+	0.999953i	$0.496908\pi$
$840$	6.20867	+	2.84250i	0.214220	+	0.0980755i
$841$	15.4836			0.533916
$842$	−36.8849	−	29.0254i	−1.27114	−	1.00028i
$843$		−	6.53304i		−	0.225010i
$844$	12.6320	−	3.05608i	0.434813	−	0.105195i
$845$		−	12.9794i		−	0.446506i
$846$	17.6381	−	22.4142i	0.606412	−	0.770616i
$847$	−8.21174			−0.282159
$848$	−9.35294	−	18.1984i	−0.321181	−	0.624936i
$849$	−54.3200			−1.86426
$850$	−5.27470	+	6.70299i	−0.180921	+	0.229911i
$851$		−	23.0894i		−	0.791494i
$852$	18.2770	−	4.42178i	0.626161	−	0.151488i
$853$			11.8757i			0.406615i	0.979115	+	0.203307i	$0.0651691\pi$
$853$			11.8757i			0.406615i	−0.979115	+	0.203307i	$0.934831\pi$
$854$	−15.4107	−	12.1270i	−0.527343	−	0.414976i
$855$	18.7855			0.642450
$856$	−12.5432	+	27.3973i	−0.428719	+	0.936422i
$857$	41.8715			1.43030			0.715152	−	0.698969i	$-0.246357\pi$
$857$	41.8715			1.43030			0.715152	+	0.698969i	$0.246357\pi$
$858$	0.642618	+	0.505688i	0.0219386	+	0.0172639i
$859$		−	1.02684i		−	0.0350354i	−0.999847	−	0.0175177i	$-0.994424\pi$
$859$		−	1.02684i		−	0.0350354i	0.999847	−	0.0175177i	$-0.00557634\pi$
$860$	4.13872	+	17.1071i	0.141129	+	0.583346i
$861$			20.8628i			0.711003i
$862$	−12.7053	+	16.1456i	−0.432744	+	0.549922i
$863$	23.4327			0.797657			0.398829	−	0.917025i	$-0.369417\pi$
$863$	23.4327			0.797657			0.398829	+	0.917025i	$0.369417\pi$
$864$	−2.30010	−	0.447065i	−0.0782510	−	0.0152094i
$865$	17.2328			0.585933
$866$	−9.40049	+	11.9460i	−0.319442	+	0.405940i
$867$		−	46.7784i		−	1.58868i
$868$	3.19813	+	13.2192i	0.108552	+	0.448689i
$869$		−	19.7623i		−	0.670391i
$870$	9.86430	+	7.76240i	0.334431	+	0.263170i
$871$	1.30744			0.0443009
$872$	−1.09220	+	2.38561i	−0.0369865	+	0.0807870i
$873$	−14.8018			−0.500964
$874$	−39.1364	−	30.7971i	−1.32381	−	1.04173i
$875$		−	1.00000i		−	0.0338062i
$876$	8.89097	−	2.15100i	0.300398	−	0.0726755i
$877$		−	26.9911i		−	0.911424i	−0.890127	−	0.455712i	$-0.849385\pi$
$877$		−	26.9911i		−	0.911424i	0.890127	−	0.455712i	$-0.150615\pi$
$878$	−20.2361	+	25.7156i	−0.682934	+	0.867859i
$879$	−22.7261			−0.766531
$880$	5.94059	−	3.05312i	0.200257	−	0.102921i
$881$	45.9037			1.54653			0.773267	−	0.634080i	$-0.218621\pi$
$881$	45.9037			1.54653			0.773267	+	0.634080i	$0.218621\pi$
$882$	2.47363	−	3.14343i	0.0832913	−	0.105845i
$883$			24.4946i			0.824308i	0.911114	+	0.412154i	$0.135223\pi$
$883$			24.4946i			0.824308i	−0.911114	+	0.412154i	$0.864777\pi$
$884$	−1.68166	+	0.406846i	−0.0565604	+	0.0136837i
$885$		−	20.2931i		−	0.682146i
$886$	21.8922	+	17.2273i	0.735481	+	0.578764i
$887$	−54.5944			−1.83310			−0.916551	−	0.399918i	$-0.869039\pi$
$887$	−54.5944			−1.83310			−0.916551	+	0.399918i	$0.869039\pi$
$888$	27.0375	+	12.3785i	0.907320	+	0.415396i
$889$	−0.168043			−0.00563598
$890$	7.92854	+	6.23911i	0.265765	+	0.209135i
$891$			15.8386i			0.530613i
$892$	−4.75168	−	19.6407i	−0.159098	−	0.657618i
$893$		−	47.3583i		−	1.58478i
$894$	15.1270	−	19.2230i	0.505921	−	0.642914i
$895$	17.4325			0.582705
$896$	11.3021	−	0.513421i	0.377575	−	0.0171522i
$897$	−1.83599			−0.0613020
$898$	−28.8167	+	36.6197i	−0.961626	+	1.22201i
$899$			25.0011i			0.833832i
$900$	−1.33019	−	5.49824i	−0.0443397	−	0.183275i
$901$		−	30.8517i		−	1.02782i
$902$	16.0370	+	12.6198i	0.533974	+	0.420194i
$903$	21.2458			0.707015
$904$	23.0640	+	10.5593i	0.767098	+	0.351198i
$905$	4.22432			0.140421
$906$	−53.3514	−	41.9832i	−1.77248	−	1.39480i
$907$		−	9.90305i		−	0.328825i	−0.986392	−	0.164413i	$-0.947427\pi$
$907$		−	9.90305i		−	0.328825i	0.986392	−	0.164413i	$-0.0525729\pi$
$908$	−20.0134	+	4.84186i	−0.664168	+	0.160683i
$909$			30.7247i			1.01908i
$910$	0.125441	−	0.159408i	0.00415834	−	0.00528433i
$911$	−15.0912			−0.499993			−0.249997	−	0.968247i	$-0.580430\pi$
$911$	−15.0912			−0.499993			−0.249997	+	0.968247i	$0.580430\pi$
$912$	57.0448	−	29.3177i	1.88894	−	0.970808i
$913$	−2.96504			−0.0981286
$914$	−29.5197	+	37.5130i	−0.976425	+	1.24082i
$915$			33.4764i			1.10669i
$916$	53.2129	−	12.8738i	1.75820	−	0.425364i
$917$			14.7909i			0.488437i
$918$	−2.77647	−	2.18485i	−0.0916371	−	0.0721109i
$919$	34.0961			1.12472			0.562362	−	0.826891i	$-0.309893\pi$
$919$	34.0961			1.12472			0.562362	+	0.826891i	$0.309893\pi$
$920$	−6.24264	+	13.6354i	−0.205814	+	0.449545i
$921$	56.0545			1.84706
$922$	26.6313	+	20.9567i	0.877056	+	0.690171i
$923$		−	0.558603i		−	0.0183866i
$924$	−1.89588	−	7.83647i	−0.0623700	−	0.257801i
$925$		−	4.35480i		−	0.143185i
$926$	−2.42587	+	3.08275i	−0.0797190	+	0.101305i
$927$	−34.4971			−1.13303
$928$	20.4152	+	3.96805i	0.670162	+	0.130258i
$929$	−24.7981			−0.813598			−0.406799	−	0.913518i	$-0.633355\pi$
$929$	−24.7981			−0.813598			−0.406799	+	0.913518i	$0.633355\pi$
$930$	14.3579	−	18.2458i	0.470815	−	0.598303i
$931$		−	6.64167i		−	0.217672i
$932$	−5.29430	−	21.8835i	−0.173421	−	0.716819i
$933$		−	63.3771i		−	2.07487i
$934$	27.9289	+	21.9777i	0.913860	+	0.719133i
$935$	10.0711			0.329359
$936$	0.477662	−	1.04332i	0.0156129	−	0.0341021i
$937$	−8.60501			−0.281113			−0.140557	−	0.990073i	$-0.544889\pi$
$937$	−8.60501			−0.281113			−0.140557	+	0.990073i	$0.544889\pi$
$938$	−10.1305	−	7.97186i	−0.330772	−	0.260290i
$939$			19.9308i			0.650416i
$940$	−13.8611	+	3.35342i	−0.452099	+	0.109377i
$941$		−	54.3509i		−	1.77179i	−0.463889	−	0.885894i	$-0.653546\pi$
$941$		−	54.3509i		−	1.77179i	0.463889	−	0.885894i	$-0.346454\pi$
$942$	−10.0758	+	12.8041i	−0.328287	+	0.417180i
$943$	−45.8186			−1.49206
$944$	−15.3692	−	29.9045i	−0.500225	−	0.973308i
$945$	0.414214			0.0134744
$946$	12.8515	−	16.3314i	0.417837	−	0.530979i
$947$		−	6.40713i		−	0.208204i	−0.994567	−	0.104102i	$-0.966803\pi$
$947$		−	6.40713i		−	0.208204i	0.994567	−	0.104102i	$-0.0331968\pi$
$948$	−55.5425	+	13.4374i	−1.80394	+	0.436428i
$949$		−	0.271736i		−	0.00882091i
$950$	−7.38136	−	5.80853i	−0.239483	−	0.188454i
$951$	−67.9866			−2.20462
$952$	15.5107	+	7.10123i	0.502706	+	0.230152i
$953$	7.99852			0.259097			0.129549	−	0.991573i	$-0.458647\pi$
$953$	7.99852			0.259097			0.129549	+	0.991573i	$0.458647\pi$
$954$	16.0796	+	12.6533i	0.520596	+	0.409667i
$955$			11.8976i			0.384998i
$956$	13.5391	+	55.9627i	0.437886	+	1.80996i
$957$		−	14.8209i		−	0.479090i
$958$	14.9172	−	18.9564i	0.481952	−	0.612454i
$959$	5.85304			0.189004
$960$	−12.6202	−	14.6202i	−0.407315	−	0.471865i
$961$	15.2439			0.491739
$962$	0.546272	−	0.694191i	0.0176125	−	0.0223816i
$963$		−	30.1322i		−	0.970995i
$964$	13.5104	+	55.8440i	0.435140	+	1.79861i
$965$		−	24.8495i		−	0.799934i
$966$	14.2259	+	11.1946i	0.457710	+	0.360180i
$967$	47.6749			1.53312			0.766561	−	0.642172i	$-0.221966\pi$
$967$	47.6749			1.53312			0.766561	+	0.642172i	$0.221966\pi$
$968$	21.1183	+	9.66851i	0.678767	+	0.310758i
$969$	96.7079			3.10670
$970$	5.81605	+	4.57676i	0.186742	+	0.146951i
$971$		−	34.8989i		−	1.11996i	−0.828506	−	0.559980i	$-0.810809\pi$
$971$		−	34.8989i		−	1.11996i	0.828506	−	0.559980i	$-0.189191\pi$
$972$	42.0992	−	10.1851i	1.35033	−	0.326687i
$973$		−	7.41921i		−	0.237849i
$974$	−35.3138	+	44.8761i	−1.13153	+	1.43792i
$975$	−0.346280			−0.0110898
$976$	25.3536	+	49.3316i	0.811550	+	1.57907i
$977$	−10.2946			−0.329354			−0.164677	−	0.986348i	$-0.552658\pi$
$977$	−10.2946			−0.329354			−0.164677	+	0.986348i	$0.552658\pi$
$978$	31.4685	−	39.9896i	1.00625	−	1.27873i
$979$		−	11.9124i		−	0.380723i
$980$	−1.94392	+	0.470294i	−0.0620962	+	0.0150230i
$981$		−	2.62375i		−	0.0837697i
$982$	18.8898	+	14.8647i	0.602798	+	0.474353i
$983$	−16.6648			−0.531524			−0.265762	−	0.964039i	$-0.585624\pi$
$983$	−16.6648			−0.531524			−0.265762	+	0.964039i	$0.585624\pi$
$984$	24.5639	−	53.6533i	0.783069	−	1.71040i
$985$	4.39404			0.140006
$986$	24.6433	+	19.3923i	0.784804	+	0.617576i
$987$			17.2145i			0.547944i
$988$	−0.448020	−	1.85185i	−0.0142534	−	0.0589153i
$989$			46.6596i			1.48369i
$990$	−4.13048	+	5.24893i	−0.131275	+	0.166822i
$991$	−19.1012			−0.606769			−0.303384	−	0.952868i	$-0.598117\pi$
$991$	−19.1012			−0.606769			−0.303384	+	0.952868i	$0.598117\pi$
$992$	7.33962	−	37.7616i	0.233033	−	1.19893i
$993$	48.2047			1.52973
$994$	−3.40597	+	4.32824i	−0.108031	+	0.137283i
$995$			20.1118i			0.637586i
$996$	2.01609	+	8.33333i	0.0638822	+	0.264052i
$997$		−	21.8103i		−	0.690738i	−0.938467	−	0.345369i	$-0.887754\pi$
$997$		−	21.8103i		−	0.690738i	0.938467	−	0.345369i	$-0.112246\pi$
$998$	−11.8472	−	9.32281i	−0.375018	−	0.295108i
$999$	1.80382			0.0570703

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.b.c.141.2	yes	8
4.3	odd	2		1120.2.b.c.561.8		8
8.3	odd	2		1120.2.b.c.561.1		8
8.5	even	2	inner	280.2.b.c.141.1	✓	8
16.3	odd	4		8960.2.a.bs.1.2		4
16.5	even	4		8960.2.a.bt.1.2		4
16.11	odd	4		8960.2.a.bv.1.3		4
16.13	even	4		8960.2.a.bu.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.b.c.141.1	✓	8	8.5	even	2	inner
280.2.b.c.141.2	yes	8	1.1	even	1	trivial
1120.2.b.c.561.1		8	8.3	odd	2
1120.2.b.c.561.8		8	4.3	odd	2
8960.2.a.bs.1.2		4	16.3	odd	4
8960.2.a.bt.1.2		4	16.5	even	4
8960.2.a.bu.1.3		4	16.13	even	4
8960.2.a.bv.1.3		4	16.11	odd	4

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.874559 + 1.11137i) q^{2} -2.41421i q^{3} +(-0.470294 - 1.94392i) q^{4} -1.00000i q^{5} +(2.68309 + 2.11137i) q^{6} -1.00000 q^{7} +(2.57172 + 1.17740i) q^{8} -2.82843 q^{9} +O(q^{10})\)	\(q+(-0.874559 + 1.11137i) q^{2} -2.41421i q^{3} +(-0.470294 - 1.94392i) q^{4} -1.00000i q^{5} +(2.68309 + 2.11137i) q^{6} -1.00000 q^{7} +(2.57172 + 1.17740i) q^{8} -2.82843 q^{9} +(1.11137 + 0.874559i) q^{10} -1.66981i q^{11} +(-4.69304 + 1.13539i) q^{12} +0.143434i q^{13} +(0.874559 - 1.11137i) q^{14} -2.41421 q^{15} +(-3.55765 + 1.82843i) q^{16} -6.03127 q^{17} +(2.47363 - 3.14343i) q^{18} -6.64167i q^{19} +(-1.94392 + 0.470294i) q^{20} +2.41421i q^{21} +(1.85578 + 1.46035i) q^{22} -5.30205 q^{23} +(2.84250 - 6.20867i) q^{24} -1.00000 q^{25} +(-0.159408 - 0.125441i) q^{26} -0.414214i q^{27} +(0.470294 + 1.94392i) q^{28} +3.67647i q^{29} +(2.11137 - 2.68309i) q^{30} +6.80029 q^{31} +(1.07931 - 5.55294i) q^{32} -4.03127 q^{33} +(5.27470 - 6.70299i) q^{34} +1.00000i q^{35} +(1.33019 + 5.49824i) q^{36} +4.35480i q^{37} +(7.38136 + 5.80853i) q^{38} +0.346280 q^{39} +(1.17740 - 2.57172i) q^{40} +8.64167 q^{41} +(-2.68309 - 2.11137i) q^{42} -8.80029i q^{43} +(-3.24597 + 0.785301i) q^{44} +2.82843i q^{45} +(4.63696 - 5.89255i) q^{46} +7.13048 q^{47} +(4.41421 + 8.58892i) q^{48} +1.00000 q^{49} +(0.874559 - 1.11137i) q^{50} +14.5608i q^{51} +(0.278824 - 0.0674560i) q^{52} +5.11529i q^{53} +(0.460345 + 0.362254i) q^{54} -1.66981 q^{55} +(-2.57172 - 1.17740i) q^{56} -16.0344 q^{57} +(-4.08593 - 3.21529i) q^{58} +8.40569i q^{59} +(1.13539 + 4.69304i) q^{60} -13.8664i q^{61} +(-5.94725 + 7.55765i) q^{62} +2.82843 q^{63} +(5.22746 + 6.05588i) q^{64} +0.143434 q^{65} +(3.52559 - 4.48024i) q^{66} -9.11529i q^{67} +(2.83647 + 11.7243i) q^{68} +12.8003i q^{69} +(-1.11137 - 0.874559i) q^{70} -3.89450 q^{71} +(-7.27391 - 3.33019i) q^{72} -1.89450 q^{73} +(-4.83980 - 3.80853i) q^{74} +2.41421i q^{75} +(-12.9109 + 3.12354i) q^{76} +1.66981i q^{77} +(-0.302842 + 0.384845i) q^{78} +11.8351 q^{79} +(1.82843 + 3.55765i) q^{80} -9.48528 q^{81} +(-7.55765 + 9.60411i) q^{82} -1.77568i q^{83} +(4.69304 - 1.13539i) q^{84} +6.03127i q^{85} +(9.78039 + 7.69637i) q^{86} +8.87579 q^{87} +(1.96603 - 4.29427i) q^{88} +7.13401 q^{89} +(-3.14343 - 2.47363i) q^{90} -0.143434i q^{91} +(2.49352 + 10.3068i) q^{92} -16.4173i q^{93} +(-6.23602 + 7.92461i) q^{94} -6.64167 q^{95} +(-13.4060 - 2.60568i) q^{96} +5.23322 q^{97} +(-0.874559 + 1.11137i) q^{98} +4.72293i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} - 8 q^{7} + 12 q^{8}+O(q^{10}) \) 8 * q - 4 * q^4 - 8 * q^7 + 12 * q^8	\( 8 q - 4 q^{4} - 8 q^{7} + 12 q^{8} - 4 q^{10} - 12 q^{12} - 8 q^{15} - 8 q^{17} + 8 q^{18} - 4 q^{20} - 4 q^{22} - 8 q^{23} + 20 q^{24} - 8 q^{25} - 20 q^{26} + 4 q^{28} + 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{36} + 16 q^{38} - 32 q^{39} + 4 q^{40} + 24 q^{41} + 20 q^{44} + 24 q^{48} + 8 q^{49} - 12 q^{52} + 8 q^{54} - 8 q^{55} - 12 q^{56} - 8 q^{57} - 32 q^{58} + 12 q^{60} - 24 q^{62} + 8 q^{64} - 16 q^{65} + 4 q^{66} - 20 q^{68} + 4 q^{70} + 16 q^{71} + 16 q^{72} + 32 q^{73} + 16 q^{74} + 8 q^{76} - 4 q^{78} + 48 q^{79} - 8 q^{80} - 8 q^{81} - 32 q^{82} + 12 q^{84} + 24 q^{86} - 32 q^{87} + 4 q^{88} + 56 q^{89} - 8 q^{90} - 8 q^{94} - 8 q^{95} - 48 q^{96} + 24 q^{97}+O(q^{100}) \) 8 * q - 4 * q^4 - 8 * q^7 + 12 * q^8 - 4 * q^10 - 12 * q^12 - 8 * q^15 - 8 * q^17 + 8 * q^18 - 4 * q^20 - 4 * q^22 - 8 * q^23 + 20 * q^24 - 8 * q^25 - 20 * q^26 + 4 * q^28 + 4 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^34 + 16 * q^36 + 16 * q^38 - 32 * q^39 + 4 * q^40 + 24 * q^41 + 20 * q^44 + 24 * q^48 + 8 * q^49 - 12 * q^52 + 8 * q^54 - 8 * q^55 - 12 * q^56 - 8 * q^57 - 32 * q^58 + 12 * q^60 - 24 * q^62 + 8 * q^64 - 16 * q^65 + 4 * q^66 - 20 * q^68 + 4 * q^70 + 16 * q^71 + 16 * q^72 + 32 * q^73 + 16 * q^74 + 8 * q^76 - 4 * q^78 + 48 * q^79 - 8 * q^80 - 8 * q^81 - 32 * q^82 + 12 * q^84 + 24 * q^86 - 32 * q^87 + 4 * q^88 + 56 * q^89 - 8 * q^90 - 8 * q^94 - 8 * q^95 - 48 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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