LMFDB - Embedded newform 280.2.b.c.141.6

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			141.6
Root			$0.500000 - 1.44392i$ of defining polynomial
Character	$\chi$	$=$	280.141
Dual form			280.2.b.c.141.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.167452 + 1.40426i) q^{2} +2.41421i q^{3} +(-1.94392 + 0.470294i) q^{4} +1.00000i q^{5} +(-3.39020 + 0.404265i) q^{6} -1.00000 q^{7} +(-0.985930 - 2.65103i) q^{8} -2.82843 q^{9} +O(q^{10})$	\(q+(0.167452 + 1.40426i) q^{2} +2.41421i q^{3} +(-1.94392 + 0.470294i) q^{4} +1.00000i q^{5} +(-3.39020 + 0.404265i) q^{6} -1.00000 q^{7} +(-0.985930 - 2.65103i) q^{8} -2.82843 q^{9} +(-1.40426 + 0.167452i) q^{10} -2.49824i q^{11} +(-1.13539 - 4.69304i) q^{12} +6.97186i q^{13} +(-0.167452 - 1.40426i) q^{14} -2.41421 q^{15} +(3.55765 - 1.82843i) q^{16} +4.03127 q^{17} +(-0.473626 - 3.97186i) q^{18} -4.64167i q^{19} +(-0.470294 - 1.94392i) q^{20} -2.41421i q^{21} +(3.50818 - 0.418334i) q^{22} -2.35480 q^{23} +(6.40014 - 2.38025i) q^{24} -1.00000 q^{25} +(-9.79034 + 1.16745i) q^{26} +0.414214i q^{27} +(1.94392 - 0.470294i) q^{28} +9.33333i q^{29} +(-0.404265 - 3.39020i) q^{30} -0.315007 q^{31} +(3.16333 + 4.68971i) q^{32} +6.03127 q^{33} +(0.675045 + 5.66098i) q^{34} -1.00000i q^{35} +(5.49824 - 1.33019i) q^{36} -7.30205i q^{37} +(6.51813 - 0.777257i) q^{38} -16.8316 q^{39} +(2.65103 - 0.985930i) q^{40} -2.64167 q^{41} +(3.39020 - 0.404265i) q^{42} +1.68499i q^{43} +(1.17490 + 4.85637i) q^{44} -2.82843i q^{45} +(-0.394316 - 3.30676i) q^{46} +4.18323 q^{47} +(4.41421 + 8.58892i) q^{48} +1.00000 q^{49} +(-0.167452 - 1.40426i) q^{50} +9.73235i q^{51} +(-3.27882 - 13.5527i) q^{52} +9.11529i q^{53} +(-0.581666 + 0.0693609i) q^{54} +2.49824 q^{55} +(0.985930 + 2.65103i) q^{56} +11.2060 q^{57} +(-13.1065 + 1.56288i) q^{58} +11.7194i q^{59} +(4.69304 - 1.13539i) q^{60} -5.03794i q^{61} +(-0.0527485 - 0.442353i) q^{62} +2.82843 q^{63} +(-6.05588 + 5.22746i) q^{64} -6.97186 q^{65} +(1.00995 + 8.46950i) q^{66} -5.11529i q^{67} +(-7.83647 + 1.89588i) q^{68} -5.68499i q^{69} +(1.40426 - 0.167452i) q^{70} +7.89450 q^{71} +(2.78863 + 7.49824i) q^{72} +9.89450 q^{73} +(10.2540 - 1.22274i) q^{74} -2.41421i q^{75} +(2.18295 + 9.02303i) q^{76} +2.49824i q^{77} +(-2.81848 - 23.6360i) q^{78} +2.99334 q^{79} +(1.82843 + 3.55765i) q^{80} -9.48528 q^{81} +(-0.442353 - 3.70960i) q^{82} -4.11882i q^{83} +(1.13539 + 4.69304i) q^{84} +4.03127i q^{85} +(-2.36618 + 0.282156i) q^{86} -22.5326 q^{87} +(-6.62289 + 2.46309i) q^{88} +12.5228 q^{89} +(3.97186 - 0.473626i) q^{90} -6.97186i q^{91} +(4.57754 - 1.10745i) q^{92} -0.760493i q^{93} +(0.700490 + 5.87436i) q^{94} +4.64167 q^{95} +(-11.3220 + 7.63696i) q^{96} +17.7373 q^{97} +(0.167452 + 1.40426i) q^{98} +7.06608i 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 $

$2$	0.167452	+	1.40426i	0.118406	+	0.992965i
$2$	0.167452	+	1.40426i	0.118406	+	0.992965i
$3$			2.41421i			1.39385i	0.717146	+	0.696923i	$0.245448\pi$
$3$			2.41421i			1.39385i	−0.717146	+	0.696923i	$0.754552\pi$
$4$	−1.94392	+	0.470294i	−0.971960	+	0.235147i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−3.39020	+	0.404265i	−1.38404	+	0.165040i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−0.985930	−	2.65103i	−0.348579	−	0.937279i
$9$	−2.82843			−0.942809
$10$	−1.40426	+	0.167452i	−0.444068	+	0.0529530i
$11$		−	2.49824i		−	0.753246i	−0.926367	−	0.376623i	$-0.877085\pi$
$11$		−	2.49824i		−	0.753246i	0.926367	−	0.376623i	$-0.122915\pi$
$12$	−1.13539	−	4.69304i	−0.327759	−	1.35476i
$13$			6.97186i			1.93365i	0.255447	+	0.966823i	$0.417777\pi$
$13$			6.97186i			1.93365i	−0.255447	+	0.966823i	$0.582223\pi$
$14$	−0.167452	−	1.40426i	−0.0447534	−	0.375306i
$15$	−2.41421			−0.623347
$16$	3.55765	−	1.82843i	0.889412	−	0.457107i
$17$	4.03127			0.977727			0.488864	−	0.872360i	$-0.337412\pi$
$17$	4.03127			0.977727			0.488864	+	0.872360i	$0.337412\pi$
$18$	−0.473626	−	3.97186i	−0.111635	−	0.936177i
$19$		−	4.64167i		−	1.06487i	−0.846470	−	0.532436i	$-0.821277\pi$
$19$		−	4.64167i		−	1.06487i	0.846470	−	0.532436i	$-0.178723\pi$
$20$	−0.470294	−	1.94392i	−0.105161	−	0.434674i
$21$		−	2.41421i		−	0.526825i
$22$	3.50818	−	0.418334i	0.747947	−	0.0891892i
$23$	−2.35480			−0.491010			−0.245505	−	0.969395i	$-0.578954\pi$
$23$	−2.35480			−0.491010			−0.245505	+	0.969395i	$0.578954\pi$
$24$	6.40014	−	2.38025i	1.30642	−	0.485866i
$25$	−1.00000			−0.200000
$26$	−9.79034	+	1.16745i	−1.92004	+	0.228956i
$27$			0.414214i			0.0797154i
$28$	1.94392	−	0.470294i	0.367366	−	0.0888772i
$29$			9.33333i			1.73316i	0.499042	+	0.866578i	$0.333685\pi$
$29$			9.33333i			1.73316i	−0.499042	+	0.866578i	$0.666315\pi$
$30$	−0.404265	−	3.39020i	−0.0738083	−	0.618962i
$31$	−0.315007			−0.0565769			−0.0282884	−	0.999600i	$-0.509006\pi$
$31$	−0.315007			−0.0565769			−0.0282884	+	0.999600i	$0.509006\pi$
$32$	3.16333	+	4.68971i	0.559203	+	0.829031i
$33$	6.03127			1.04991
$34$	0.675045	+	5.66098i	0.115769	+	0.970849i
$35$		−	1.00000i		−	0.169031i
$36$	5.49824	−	1.33019i	0.916373	−	0.221699i
$37$		−	7.30205i		−	1.20045i	−0.799831	−	0.600225i	$-0.795078\pi$
$37$		−	7.30205i		−	1.20045i	0.799831	−	0.600225i	$-0.204922\pi$
$38$	6.51813	−	0.777257i	1.05738	−	0.126088i
$39$	−16.8316			−2.69521
$40$	2.65103	−	0.985930i	0.419164	−	0.155889i
$41$	−2.64167			−0.412559			−0.206280	−	0.978493i	$-0.566136\pi$
$41$	−2.64167			−0.412559			−0.206280	+	0.978493i	$0.566136\pi$
$42$	3.39020	−	0.404265i	0.523118	−	0.0623794i
$43$			1.68499i			0.256959i	0.991712	+	0.128480i	$0.0410097\pi$
$43$			1.68499i			0.256959i	−0.991712	+	0.128480i	$0.958990\pi$
$44$	1.17490	+	4.85637i	0.177124	+	0.732125i
$45$		−	2.82843i		−	0.421637i
$46$	−0.394316	−	3.30676i	−0.0581387	−	0.487556i
$47$	4.18323			0.610187			0.305093	−	0.952322i	$-0.401312\pi$
$47$	4.18323			0.610187			0.305093	+	0.952322i	$0.401312\pi$
$48$	4.41421	+	8.58892i	0.637137	+	1.23970i
$49$	1.00000			0.142857
$50$	−0.167452	−	1.40426i	−0.0236813	−	0.198593i
$51$			9.73235i			1.36280i
$52$	−3.27882	−	13.5527i	−0.454691	−	1.87943i
$53$			9.11529i			1.25208i	0.779790	+	0.626041i	$0.215326\pi$
$53$			9.11529i			1.25208i	−0.779790	+	0.626041i	$0.784674\pi$
$54$	−0.581666	+	0.0693609i	−0.0791547	+	0.00943882i
$55$	2.49824			0.336862
$56$	0.985930	+	2.65103i	0.131750	+	0.354258i
$57$	11.2060			1.48427
$58$	−13.1065	+	1.56288i	−1.72096	+	0.205217i
$59$			11.7194i			1.52574i	0.646554	+	0.762868i	$0.276209\pi$
$59$			11.7194i			1.52574i	−0.646554	+	0.762868i	$0.723791\pi$
$60$	4.69304	−	1.13539i	0.605868	−	0.146578i
$61$		−	5.03794i		−	0.645042i	−0.946562	−	0.322521i	$-0.895470\pi$
$61$		−	5.03794i		−	0.645042i	0.946562	−	0.322521i	$-0.104530\pi$
$62$	−0.0527485	−	0.442353i	−0.00669906	−	0.0561789i
$63$	2.82843			0.356348
$64$	−6.05588	+	5.22746i	−0.756985	+	0.653432i
$65$	−6.97186			−0.864753
$66$	1.00995	+	8.46950i	0.124316	+	1.04252i
$67$		−	5.11529i		−	0.624933i	−0.949929	−	0.312466i	$-0.898845\pi$
$67$		−	5.11529i		−	0.624933i	0.949929	−	0.312466i	$-0.101155\pi$
$68$	−7.83647	+	1.89588i	−0.950312	+	0.229910i
$69$		−	5.68499i		−	0.684393i
$70$	1.40426	−	0.167452i	0.167842	−	0.0200143i
$71$	7.89450			0.936905			0.468453	−	0.883489i	$-0.344812\pi$
$71$	7.89450			0.936905			0.468453	+	0.883489i	$0.344812\pi$
$72$	2.78863	+	7.49824i	0.328643	+	0.883675i
$73$	9.89450			1.15806			0.579032	−	0.815305i	$-0.303431\pi$
$73$	9.89450			1.15806			0.579032	+	0.815305i	$0.303431\pi$
$74$	10.2540	−	1.22274i	1.19201	−	0.142141i
$75$		−	2.41421i		−	0.278769i
$76$	2.18295	+	9.02303i	0.250401	+	1.03501i
$77$			2.49824i			0.284700i
$78$	−2.81848	−	23.6360i	−0.319130	−	2.67625i
$79$	2.99334			0.336777			0.168388	−	0.985721i	$-0.446144\pi$
$79$	2.99334			0.336777			0.168388	+	0.985721i	$0.446144\pi$
$80$	1.82843	+	3.55765i	0.204424	+	0.397757i
$81$	−9.48528			−1.05392
$82$	−0.442353	−	3.70960i	−0.0488497	−	0.409657i
$83$		−	4.11882i		−	0.452100i	−0.974116	−	0.226050i	$-0.927419\pi$
$83$		−	4.11882i		−	0.452100i	0.974116	−	0.226050i	$-0.0725812\pi$
$84$	1.13539	+	4.69304i	0.123881	+	0.512052i
$85$			4.03127i			0.437253i
$86$	−2.36618	+	0.282156i	−0.255151	+	0.0304256i
$87$	−22.5326			−2.41575
$88$	−6.62289	+	2.46309i	−0.706002	+	0.262566i
$89$	12.5228			1.32742			0.663709	−	0.747991i	$-0.268981\pi$
$89$	12.5228			1.32742			0.663709	+	0.747991i	$0.268981\pi$
$90$	3.97186	−	0.473626i	0.418671	−	0.0499245i
$91$		−	6.97186i		−	0.730850i
$92$	4.57754	−	1.10745i	0.477242	−	0.115460i
$93$		−	0.760493i		−	0.0788595i
$94$	0.700490	+	5.87436i	0.0722500	+	0.605894i
$95$	4.64167			0.476225
$96$	−11.3220	+	7.63696i	−1.15554	+	0.779444i
$97$	17.7373			1.80095			0.900477	−	0.434903i	$-0.143217\pi$
$97$	17.7373			1.80095			0.900477	+	0.434903i	$0.143217\pi$
$98$	0.167452	+	1.40426i	0.0169152	+	0.141852i
$99$			7.06608i			0.710167i
$100$	1.94392	−	0.470294i	0.194392	−	0.0470294i
$101$		−	16.3776i		−	1.62963i	−0.579723	−	0.814814i	$-0.696839\pi$
$101$		−	16.3776i		−	1.62963i	0.579723	−	0.814814i	$-0.303161\pi$
$102$	−13.6668	+	1.62970i	−1.35322	+	0.161365i
$103$	−2.53970			−0.250244			−0.125122	−	0.992141i	$-0.539932\pi$
$103$	−2.53970			−0.250244			−0.125122	+	0.992141i	$0.539932\pi$
$104$	18.4826	−	6.87377i	1.81237	−	0.674029i
$105$	2.41421			0.235603
$106$	−12.8003	+	1.52637i	−1.24327	+	0.148255i
$107$		−	2.31724i		−	0.224016i	−0.993707	−	0.112008i	$-0.964272\pi$
$107$		−	2.31724i		−	0.224016i	0.993707	−	0.112008i	$-0.0357282\pi$
$108$	−0.194802	−	0.805198i	−0.0187448	−	0.0774802i
$109$		−	8.04293i		−	0.770373i	−0.922839	−	0.385186i	$-0.874137\pi$
$109$		−	8.04293i		−	0.770373i	0.922839	−	0.385186i	$-0.125863\pi$
$110$	0.418334	+	3.50818i	0.0398866	+	0.334492i
$111$	17.6287			1.67324
$112$	−3.55765	+	1.82843i	−0.336166	+	0.172770i
$113$	−6.48305			−0.609874			−0.304937	−	0.952373i	$-0.598635\pi$
$113$	−6.48305			−0.609874			−0.304937	+	0.952373i	$0.598635\pi$
$114$	1.87646	+	15.7362i	0.175747	+	1.47383i
$115$		−	2.35480i		−	0.219586i
$116$	−4.38941	−	18.1432i	−0.407546	−	1.68456i
$117$		−	19.7194i		−	1.82306i
$118$	−16.4571	+	1.96244i	−1.51500	+	0.180657i
$119$	−4.03127			−0.369546
$120$	2.38025	+	6.40014i	0.217286	+	0.584251i
$121$	4.75882			0.432620
$122$	7.07460	−	0.843613i	0.640504	−	0.0763771i
$123$		−	6.37755i		−	0.575045i
$124$	0.612348	−	0.148146i	0.0549904	−	0.0133039i
$125$		−	1.00000i		−	0.0894427i
$126$	0.473626	+	3.97186i	0.0421939	+	0.353841i
$127$	−8.16804			−0.724797			−0.362398	−	0.932023i	$-0.618042\pi$
$127$	−8.16804			−0.724797			−0.362398	+	0.932023i	$0.618042\pi$
$128$	−8.35480	−	7.62872i	−0.738467	−	0.674290i
$129$	−4.06793			−0.358162
$130$	−1.16745	−	9.79034i	−0.102392	−	0.858670i
$131$			20.1797i			1.76311i	0.472083	+	0.881554i	$0.343502\pi$
$131$			20.1797i			1.76311i	−0.472083	+	0.881554i	$0.656498\pi$
$132$	−11.7243	+	2.83647i	−1.02047	+	0.246883i
$133$			4.64167i			0.402484i
$134$	7.18323	−	0.856566i	0.620536	−	0.0739961i
$135$	−0.414214			−0.0356498
$136$	−3.97455	−	10.6870i	−0.340815	−	0.916404i
$137$	−4.63224			−0.395759			−0.197880	−	0.980226i	$-0.563406\pi$
$137$	−4.63224			−0.395759			−0.197880	+	0.980226i	$0.563406\pi$
$138$	7.98324	−	0.951963i	0.679578	−	0.0810365i
$139$		−	19.2082i		−	1.62922i	−0.580010	−	0.814610i	$-0.696951\pi$
$139$		−	19.2082i		−	1.62922i	0.580010	−	0.814610i	$-0.303049\pi$
$140$	0.470294	+	1.94392i	0.0397471	+	0.164291i
$141$			10.0992i			0.850507i
$142$	1.32195	+	11.0860i	0.110936	+	0.930314i
$143$	17.4173			1.45651
$144$	−10.0625	+	5.17157i	−0.838546	+	0.430964i
$145$	−9.33333			−0.775091
$146$	1.65685	+	13.8945i	0.137122	+	1.14992i
$147$			2.41421i			0.199121i
$148$	3.43411	+	14.1946i	0.282282	+	1.16679i
$149$		−	9.50766i		−	0.778898i	−0.921048	−	0.389449i	$-0.872665\pi$
$149$		−	9.50766i		−	0.778898i	0.921048	−	0.389449i	$-0.127335\pi$
$150$	3.39020	−	0.404265i	0.276808	−	0.0330081i
$151$	−8.60097			−0.699937			−0.349969	−	0.936761i	$-0.613808\pi$
$151$	−8.60097			−0.699937			−0.349969	+	0.936761i	$0.613808\pi$
$152$	−12.3052	+	4.57636i	−0.998082	+	0.371192i
$153$	−11.4022			−0.921810
$154$	−3.50818	+	0.418334i	−0.282698	+	0.0337104i
$155$		−	0.315007i		−	0.0253019i
$156$	32.7192	−	7.91578i	2.61963	−	0.633770i
$157$			9.45844i			0.754866i	0.926037	+	0.377433i	$0.123193\pi$
$157$			9.45844i			0.754866i	−0.926037	+	0.377433i	$0.876807\pi$
$158$	0.501240	+	4.20344i	0.0398765	+	0.334407i
$159$	−22.0063			−1.74521
$160$	−4.68971	+	3.16333i	−0.370754	+	0.250083i
$161$	2.35480			0.185584
$162$	−1.58833	−	13.3198i	−0.124791	−	1.04651i
$163$		−	22.9043i		−	1.79400i	−0.442027	−	0.897002i	$-0.645741\pi$
$163$		−	22.9043i		−	1.79400i	0.442027	−	0.897002i	$-0.354259\pi$
$164$	5.13519	−	1.24236i	0.400991	−	0.0970121i
$165$			6.03127i			0.469534i
$166$	5.78392	−	0.689705i	0.448919	−	0.0535315i
$167$	7.87932			0.609720			0.304860	−	0.952397i	$-0.401390\pi$
$167$	7.87932			0.609720			0.304860	+	0.952397i	$0.401390\pi$
$168$	−6.40014	+	2.38025i	−0.493782	+	0.183640i
$169$	−35.6068			−2.73899
$170$	−5.66098	+	0.675045i	−0.434177	+	0.0517736i
$171$			13.1286i			1.00397i
$172$	−0.792442	−	3.27549i	−0.0604231	−	0.249754i
$173$		−	4.22302i		−	0.321071i	−0.987030	−	0.160535i	$-0.948678\pi$
$173$		−	4.22302i		−	0.321071i	0.987030	−	0.160535i	$-0.0513220\pi$
$174$	−3.77314	−	31.6418i	−0.286041	−	2.39876i
$175$	1.00000			0.0755929
$176$	−4.56784	−	8.88784i	−0.344314	−	0.669946i
$177$	−28.2931			−2.12664
$178$	2.09698	+	17.5854i	0.157175	+	1.31808i
$179$		−	11.5380i		−	0.862393i	−0.902258	−	0.431196i	$-0.858092\pi$
$179$		−	11.5380i		−	0.862393i	0.902258	−	0.431196i	$-0.141908\pi$
$180$	1.33019	+	5.49824i	0.0991467	+	0.409814i
$181$		−	10.1188i		−	0.752126i	−0.926594	−	0.376063i	$-0.877278\pi$
$181$		−	10.1188i		−	0.752126i	0.926594	−	0.376063i	$-0.122722\pi$
$182$	9.79034	−	1.16745i	0.725708	−	0.0865373i
$183$	12.1627			0.899089
$184$	2.32167	+	6.24264i	0.171156	+	0.460214i
$185$	7.30205			0.536858
$186$	1.06793	−	0.127346i	0.0783047	−	0.00933747i
$187$		−	10.0711i		−	0.736469i
$188$	−8.13186	+	1.96735i	−0.593077	+	0.143484i
$189$		−	0.414214i		−	0.0301296i
$190$	0.777257	+	6.51813i	0.0563881	+	0.472875i
$191$	17.0692			1.23508			0.617542	−	0.786538i	$-0.288128\pi$
$191$	17.0692			1.23508			0.617542	+	0.786538i	$0.288128\pi$
$192$	−12.6202	−	14.6202i	−0.910784	−	1.05512i
$193$	15.2926			1.10079			0.550394	−	0.834905i	$-0.314478\pi$
$193$	15.2926			1.10079			0.550394	+	0.834905i	$0.314478\pi$
$194$	2.97015	+	24.9079i	0.213245	+	1.78829i
$195$		−	16.8316i		−	1.20533i
$196$	−1.94392	+	0.470294i	−0.138851	+	0.0335924i
$197$			18.6783i			1.33077i	0.746498	+	0.665387i	$0.231734\pi$
$197$			18.6783i			1.33077i	−0.746498	+	0.665387i	$0.768266\pi$
$198$	−9.92264	+	1.18323i	−0.705171	+	0.0840884i
$199$	2.45491			0.174024			0.0870120	−	0.996207i	$-0.472268\pi$
$199$	2.45491			0.174024			0.0870120	+	0.996207i	$0.472268\pi$
$200$	0.985930	+	2.65103i	0.0697158	+	0.187456i
$201$	12.3494			0.871060
$202$	22.9984	−	2.74245i	1.61816	−	0.192958i
$203$		−	9.33333i		−	0.655071i
$204$	−4.57707	−	18.9189i	−0.320459	−	1.32459i
$205$		−	2.64167i		−	0.184502i
$206$	−0.425278	−	3.56641i	−0.0296305	−	0.248484i
$207$	6.66038			0.462929
$208$	12.7475	+	24.8034i	0.883883	+	1.71981i
$209$	−11.5960			−0.802111
$210$	0.404265	+	3.39020i	0.0278969	+	0.233946i
$211$		−	2.33019i		−	0.160417i	−0.996778	−	0.0802085i	$-0.974441\pi$
$211$		−	2.33019i		−	0.160417i	0.996778	−	0.0802085i	$-0.0255586\pi$
$212$	−4.28687	−	17.7194i	−0.294423	−	1.21697i
$213$			19.0590i			1.30590i
$214$	3.25402	−	0.388026i	0.222440	−	0.0265249i
$215$	−1.68499			−0.114916
$216$	1.09809	−	0.408386i	0.0747156	−	0.0277871i
$217$	0.315007			0.0213840
$218$	11.2944	−	1.34680i	0.764953	−	0.0912171i
$219$			23.8874i			1.61416i
$220$	−4.85637	+	1.17490i	−0.327416	+	0.0792121i
$221$			28.1055i			1.89058i
$222$	2.95196	+	24.7554i	0.198123	+	1.66147i
$223$	−7.07420			−0.473724			−0.236862	−	0.971543i	$-0.576119\pi$
$223$	−7.07420			−0.473724			−0.236862	+	0.971543i	$0.576119\pi$
$224$	−3.16333	−	4.68971i	−0.211359	−	0.313344i
$225$	2.82843			0.188562
$226$	−1.08560	−	9.10392i	−0.0722130	−	0.605584i
$227$			16.1899i			1.07456i	0.843404	+	0.537280i	$0.180548\pi$
$227$			16.1899i			1.07456i	−0.843404	+	0.537280i	$0.819452\pi$
$228$	−21.7835	+	5.27010i	−1.44265	+	0.349021i
$229$			8.20245i			0.542033i	0.962575	+	0.271017i	$0.0873598\pi$
$229$			8.20245i			0.542033i	−0.962575	+	0.271017i	$0.912640\pi$
$230$	3.30676	−	0.394316i	0.218042	−	0.0260004i
$231$	−6.03127			−0.396829
$232$	24.7429	−	9.20201i	1.62445	−	0.604142i
$233$	−2.97316			−0.194778			−0.0973891	−	0.995246i	$-0.531049\pi$
$233$	−2.97316			−0.194778			−0.0973891	+	0.995246i	$0.531049\pi$
$234$	27.6913	−	3.30205i	1.81023	−	0.215862i
$235$			4.18323i			0.272884i
$236$	−5.51156	−	22.7816i	−0.358772	−	1.48295i
$237$			7.22655i			0.469415i
$238$	−0.675045	−	5.66098i	−0.0437566	−	0.366947i
$239$	20.3033			1.31331			0.656657	−	0.754190i	$-0.271970\pi$
$239$	20.3033			1.31331			0.656657	+	0.754190i	$0.271970\pi$
$240$	−8.58892	+	4.41421i	−0.554412	+	0.284936i
$241$	−3.21360			−0.207006			−0.103503	−	0.994629i	$-0.533005\pi$
$241$	−3.21360			−0.207006			−0.103503	+	0.994629i	$0.533005\pi$
$242$	0.796874	+	6.68265i	0.0512250	+	0.429577i
$243$		−	21.6569i		−	1.38929i
$244$	2.36931	+	9.79334i	0.151680	+	0.626955i
$245$			1.00000i			0.0638877i
$246$	8.95577	−	1.06793i	0.570999	−	0.0680890i
$247$	32.3611			2.05909
$248$	0.310575	+	0.835091i	0.0197215	+	0.0530283i
$249$	9.94372			0.630158
$250$	1.40426	−	0.167452i	0.0888135	−	0.0105906i
$251$			1.68276i			0.106215i	0.998589	+	0.0531075i	$0.0169126\pi$
$251$			1.68276i			0.106215i	−0.998589	+	0.0531075i	$0.983087\pi$
$252$	−5.49824	+	1.33019i	−0.346356	+	0.0837942i
$253$			5.88285i			0.369851i
$254$	−1.36776	−	11.4701i	−0.0858206	−	0.719698i
$255$	−9.73235			−0.609464
$256$	9.31371	−	13.0098i	0.582107	−	0.813112i
$257$	−17.2271			−1.07459			−0.537297	−	0.843393i	$-0.680555\pi$
$257$	−17.2271			−1.07459			−0.537297	+	0.843393i	$0.680555\pi$
$258$	−0.681184	−	5.71246i	−0.0424086	−	0.355642i
$259$			7.30205i			0.453727i
$260$	13.5527	−	3.27882i	0.840505	−	0.203344i
$261$		−	26.3986i		−	1.63403i
$262$	−28.3376	+	3.37913i	−1.75071	+	0.208763i
$263$	2.77921			0.171373			0.0856867	−	0.996322i	$-0.472692\pi$
$263$	2.77921			0.171373			0.0856867	+	0.996322i	$0.472692\pi$
$264$	−5.94642	−	15.9891i	−0.365977	−	0.984059i
$265$	−9.11529			−0.559948
$266$	−6.51813	+	0.777257i	−0.399652	+	0.0476567i
$267$			30.2328i			1.85022i
$268$	2.40569	+	9.94372i	0.146951	+	0.607409i
$269$			2.54156i			0.154962i	0.996994	+	0.0774808i	$0.0246877\pi$
$269$			2.54156i			0.154962i	−0.996994	+	0.0774808i	$0.975312\pi$
$270$	−0.0693609	−	0.581666i	−0.00422117	−	0.0353990i
$271$	−15.4795			−0.940314			−0.470157	−	0.882583i	$-0.655803\pi$
$271$	−15.4795			−0.940314			−0.470157	+	0.882583i	$0.655803\pi$
$272$	14.3418	−	7.37089i	0.869602	−	0.446926i
$273$	16.8316			1.01869
$274$	−0.775679	−	6.50490i	−0.0468605	−	0.392975i
$275$			2.49824i			0.150649i
$276$	2.67362	+	11.0512i	0.160933	+	0.665202i
$277$		−	22.5737i		−	1.35632i	−0.734912	−	0.678162i	$-0.762777\pi$
$277$		−	22.5737i		−	1.35632i	0.734912	−	0.678162i	$-0.237223\pi$
$278$	26.9734	−	3.21645i	1.61776	−	0.192910i
$279$	0.890973			0.0533412
$280$	−2.65103	+	0.985930i	−0.158429	+	0.0589206i
$281$	0.264490			0.0157781			0.00788907	−	0.999969i	$-0.497489\pi$
$281$	0.264490			0.0157781			0.00788907	+	0.999969i	$0.497489\pi$
$282$	−14.1820	+	1.69113i	−0.844524	+	0.100705i
$283$			8.26948i			0.491570i	0.969324	+	0.245785i	$0.0790457\pi$
$283$			8.26948i			0.491570i	−0.969324	+	0.245785i	$0.920954\pi$
$284$	−15.3463	+	3.71274i	−0.910634	+	0.220310i
$285$			11.2060i			0.663785i
$286$	2.91657	+	24.4586i	0.172460	+	1.44627i
$287$	2.64167			0.155933
$288$	−8.94725	−	13.2645i	−0.527222	−	0.781618i
$289$	−0.748838			−0.0440493
$290$	−1.56288	−	13.1065i	−0.0917757	−	0.769638i
$291$			42.8217i			2.51025i
$292$	−19.2341	+	4.65332i	−1.12559	+	0.272315i
$293$		−	2.58502i		−	0.151018i	−0.997145	−	0.0755091i	$-0.975942\pi$
$293$		−	2.58502i		−	0.151018i	0.997145	−	0.0755091i	$-0.0240582\pi$
$294$	−3.39020	+	0.404265i	−0.197720	+	0.0235772i
$295$	−11.7194			−0.682330
$296$	−19.3579	+	7.19932i	−1.12516	+	0.418452i
$297$	1.03480			0.0600454
$298$	13.3513	−	1.59208i	0.773418	−	0.0922265i
$299$		−	16.4173i		−	0.949440i
$300$	1.13539	+	4.69304i	0.0655518	+	0.270953i
$301$		−	1.68499i		−	0.0971214i
$302$	−1.44025	−	12.0780i	−0.0828771	−	0.695013i
$303$	39.5389			2.27145
$304$	−8.48695	−	16.5134i	−0.486760	−	0.947110i
$305$	5.03794			0.288471
$306$	−1.90931	−	16.0117i	−0.109148	−	0.915325i
$307$			33.7038i			1.92358i	0.273791	+	0.961789i	$0.411722\pi$
$307$			33.7038i			1.92358i	−0.273791	+	0.961789i	$0.588278\pi$
$308$	−1.17490	−	4.85637i	−0.0669464	−	0.276717i
$309$		−	6.13138i		−	0.348802i
$310$	0.442353	−	0.0527485i	0.0251239	−	0.00299591i
$311$	−11.7664			−0.667211			−0.333605	−	0.942713i	$-0.608265\pi$
$311$	−11.7664			−0.667211			−0.333605	+	0.942713i	$0.608265\pi$
$312$	16.5947	+	44.6209i	0.939493	+	2.52616i
$313$	−4.08755			−0.231042			−0.115521	−	0.993305i	$-0.536854\pi$
$313$	−4.08755			−0.231042			−0.115521	+	0.993305i	$0.536854\pi$
$314$	−13.2822	+	1.58383i	−0.749555	+	0.0893810i
$315$			2.82843i			0.159364i
$316$	−5.81881	+	1.40775i	−0.327333	+	0.0791920i
$317$			3.15273i			0.177075i	0.996073	+	0.0885373i	$0.0282193\pi$
$317$			3.15273i			0.177075i	−0.996073	+	0.0885373i	$0.971781\pi$
$318$	−3.68499	−	30.9026i	−0.206644	−	1.73293i
$319$	23.3168			1.30549
$320$	−5.22746	−	6.05588i	−0.292224	−	0.338534i
$321$	5.59431			0.312244
$322$	0.394316	+	3.30676i	0.0219744	+	0.184279i
$323$		−	18.7118i		−	1.04115i
$324$	18.4386	−	4.46087i	1.02437	−	0.247826i
$325$		−	6.97186i		−	0.386729i
$326$	32.1637	−	3.83537i	1.78138	−	0.212422i
$327$	19.4173			1.07378
$328$	2.60450	+	7.00313i	0.143810	+	0.386683i
$329$	−4.18323			−0.230629
$330$	−8.46950	+	1.00995i	−0.466231	+	0.0555958i
$331$		−	11.6309i		−	0.639295i	−0.947537	−	0.319647i	$-0.896436\pi$
$331$		−	11.6309i		−	0.639295i	0.947537	−	0.319647i	$-0.103564\pi$
$332$	1.93706	+	8.00666i	0.106310	+	0.439423i
$333$			20.6533i			1.13180i
$334$	1.31941	+	11.0646i	0.0721948	+	0.605431i
$335$	5.11529			0.279478
$336$	−4.41421	−	8.58892i	−0.240815	−	0.468564i
$337$	23.6328			1.28736			0.643679	−	0.765296i	$-0.277407\pi$
$337$	23.6328			1.28736			0.643679	+	0.765296i	$0.277407\pi$
$338$	−5.96244	−	50.0014i	−0.324314	−	2.71972i
$339$		−	15.6515i		−	0.850071i
$340$	−1.89588	−	7.83647i	−0.102819	−	0.424992i
$341$			0.786961i			0.0426163i
$342$	−18.4361	+	2.19841i	−0.996908	+	0.118877i
$343$	−1.00000			−0.0539949
$344$	4.46696	−	1.66129i	0.240842	−	0.0895706i
$345$	5.68499			0.306070
$346$	5.93024	−	0.707154i	0.318812	−	0.0380168i
$347$			11.9289i			0.640377i	0.947354	+	0.320189i	$0.103746\pi$
$347$			11.9289i			0.640377i	−0.947354	+	0.320189i	$0.896254\pi$
$348$	43.8016	−	10.5970i	2.34801	−	0.568057i
$349$		−	14.3516i		−	0.768226i	−0.923286	−	0.384113i	$-0.874507\pi$
$349$		−	14.3516i		−	0.768226i	0.923286	−	0.384113i	$-0.125493\pi$
$350$	0.167452	+	1.40426i	0.00895069	+	0.0750611i
$351$	−2.88784			−0.154141
$352$	11.7160	−	7.90274i	0.624464	−	0.421218i
$353$	−1.20285			−0.0640210			−0.0320105	−	0.999488i	$-0.510191\pi$
$353$	−1.20285			−0.0640210			−0.0320105	+	0.999488i	$0.510191\pi$
$354$	−4.73774	−	39.7311i	−0.251808	−	2.11168i
$355$			7.89450i			0.418997i
$356$	−24.3434	+	5.88942i	−1.29020	+	0.312138i
$357$		−	9.73235i		−	0.515091i
$358$	16.2025	−	1.93207i	0.856326	−	0.102113i
$359$	4.03923			0.213183			0.106591	−	0.994303i	$-0.466006\pi$
$359$	4.03923			0.213183			0.106591	+	0.994303i	$0.466006\pi$
$360$	−7.49824	+	2.78863i	−0.395192	+	0.146974i
$361$	−2.54509			−0.133952
$362$	14.2095	−	1.69442i	0.746835	−	0.0890566i
$363$			11.4888i			0.603006i
$364$	3.27882	+	13.5527i	0.171857	+	0.710356i
$365$			9.89450i			0.517902i
$366$	2.03666	+	17.0796i	0.106458	+	0.892764i
$367$	−28.8499			−1.50595			−0.752976	−	0.658048i	$-0.771382\pi$
$367$	−28.8499			−1.50595			−0.752976	+	0.658048i	$0.771382\pi$
$368$	−8.37755	+	4.30558i	−0.436710	+	0.224444i
$369$	7.47177			0.388965
$370$	1.22274	+	10.2540i	0.0635674	+	0.533081i
$371$		−	9.11529i		−	0.473243i
$372$	0.357655	+	1.47834i	0.0185436	+	0.0766482i
$373$			6.58539i			0.340979i	0.985360	+	0.170489i	$0.0545348\pi$
$373$			6.58539i			0.340979i	−0.985360	+	0.170489i	$0.945465\pi$
$374$	14.1424	−	1.68642i	0.731289	−	0.0872027i
$375$	2.41421			0.124669
$376$	−4.12437	−	11.0898i	−0.212698	−	0.571915i
$377$	−65.0706			−3.35131
$378$	0.581666	−	0.0693609i	0.0299176	−	0.00356754i
$379$			9.11529i			0.468221i	0.972210	+	0.234111i	$0.0752178\pi$
$379$			9.11529i			0.468221i	−0.972210	+	0.234111i	$0.924782\pi$
$380$	−9.02303	+	2.18295i	−0.462872	+	0.111983i
$381$		−	19.7194i		−	1.01026i
$382$	2.85827	+	23.9697i	0.146242	+	1.22640i
$383$	−34.9347			−1.78508			−0.892539	−	0.450970i	$-0.851078\pi$
$383$	−34.9347			−1.78508			−0.892539	+	0.450970i	$0.851078\pi$
$384$	18.4173	−	20.1703i	0.939856	−	1.02931i
$385$	−2.49824			−0.127322
$386$	2.56078	+	21.4749i	0.130340	+	1.09304i
$387$		−	4.76588i		−	0.242263i
$388$	−34.4800	+	8.34177i	−1.75046	+	0.423489i
$389$		−	34.0563i		−	1.72672i	−0.504588	−	0.863360i	$-0.668356\pi$
$389$		−	34.0563i		−	1.72672i	0.504588	−	0.863360i	$-0.331644\pi$
$390$	23.6360	−	2.81848i	1.19685	−	0.142719i
$391$	−9.49285			−0.480074
$392$	−0.985930	−	2.65103i	−0.0497970	−	0.133897i
$393$	−48.7181			−2.45750
$394$	−26.2293	+	3.12772i	−1.32141	+	0.157572i
$395$			2.99334i			0.150611i
$396$	−3.32313	−	13.7359i	−0.166994	−	0.690254i
$397$			13.9550i			0.700382i	0.936678	+	0.350191i	$0.113883\pi$
$397$			13.9550i			0.700382i	−0.936678	+	0.350191i	$0.886117\pi$
$398$	0.411080	+	3.44734i	0.0206056	+	0.172800i
$399$	−11.2060			−0.561001
$400$	−3.55765	+	1.82843i	−0.177882	+	0.0914214i
$401$	−26.7498			−1.33582			−0.667910	−	0.744242i	$-0.732811\pi$
$401$	−26.7498			−1.33582			−0.667910	+	0.744242i	$0.732811\pi$
$402$	2.06793	+	17.3418i	0.103139	+	0.864933i
$403$		−	2.19618i		−	0.109400i
$404$	7.70226	+	31.8366i	0.383202	+	1.58393i
$405$		−	9.48528i		−	0.471327i
$406$	13.1065	−	1.56288i	0.650463	−	0.0775646i
$407$	−18.2422			−0.904235
$408$	25.8007	−	9.59542i	1.27733	−	0.475044i
$409$	28.3798			1.40329			0.701645	−	0.712527i	$-0.252449\pi$
$409$	28.3798			1.40329			0.701645	+	0.712527i	$0.252449\pi$
$410$	3.70960	−	0.442353i	0.183204	−	0.0218462i
$411$		−	11.1832i		−	0.551628i
$412$	4.93698	−	1.19441i	0.243227	−	0.0588442i
$413$		−	11.7194i		−	0.576674i
$414$	1.11529	+	9.35294i	0.0548137	+	0.459672i
$415$	4.11882			0.202185
$416$	−32.6960	+	22.0543i	−1.60305	+	1.08130i
$417$	46.3727			2.27088
$418$	−1.94177	−	16.2838i	−0.0949751	−	0.796468i
$419$			14.4549i			0.706169i	0.935592	+	0.353084i	$0.114867\pi$
$419$			14.4549i			0.706169i	−0.935592	+	0.353084i	$0.885133\pi$
$420$	−4.69304	+	1.13539i	−0.228997	+	0.0554014i
$421$		−	34.4094i		−	1.67701i	−0.544893	−	0.838505i	$-0.683430\pi$
$421$		−	34.4094i		−	1.67701i	0.544893	−	0.838505i	$-0.316570\pi$
$422$	3.27221	−	0.390195i	0.159289	−	0.0189944i
$423$	−11.8320			−0.575289
$424$	24.1649	−	8.98705i	1.17355	−	0.436450i
$425$	−4.03127			−0.195545
$426$	−26.7639	+	3.19147i	−1.29672	+	0.154627i
$427$			5.03794i			0.243803i
$428$	1.08978	+	4.50453i	0.0526767	+	0.217734i
$429$			42.0492i			2.03015i
$430$	−0.282156	−	2.36618i	−0.0136067	−	0.114107i
$431$	−28.6698			−1.38097			−0.690487	−	0.723344i	$-0.742604\pi$
$431$	−28.6698			−1.38097			−0.690487	+	0.723344i	$0.742604\pi$
$432$	0.757359	+	1.47363i	0.0364385	+	0.0708999i
$433$	−9.37625			−0.450594			−0.225297	−	0.974290i	$-0.572335\pi$
$433$	−9.37625			−0.450594			−0.225297	+	0.974290i	$0.572335\pi$
$434$	0.0527485	+	0.442353i	0.00253201	+	0.0212336i
$435$		−	22.5326i		−	1.08036i
$436$	3.78254	+	15.6348i	0.181151	+	0.748771i
$437$			10.9302i			0.522863i
$438$	−33.5443	+	4.00000i	−1.60281	+	0.191127i
$439$	14.8025			0.706486			0.353243	−	0.935532i	$-0.385079\pi$
$439$	14.8025			0.706486			0.353243	+	0.935532i	$0.385079\pi$
$440$	−2.46309	−	6.62289i	−0.117423	−	0.315734i
$441$	−2.82843			−0.134687
$442$	−39.4675	+	4.70632i	−1.87728	+	0.223857i
$443$			9.13011i			0.433784i	0.976196	+	0.216892i	$0.0695920\pi$
$443$			9.13011i			0.433784i	−0.976196	+	0.216892i	$0.930408\pi$
$444$	−34.2688	+	8.29068i	−1.62633	+	0.393458i
$445$			12.5228i			0.593640i
$446$	−1.18459	−	9.93405i	−0.0560919	−	0.470391i
$447$	22.9535			1.08566
$448$	6.05588	−	5.22746i	0.286114	−	0.246974i
$449$	−15.6363			−0.737922			−0.368961	−	0.929445i	$-0.620286\pi$
$449$	−15.6363			−0.737922			−0.368961	+	0.929445i	$0.620286\pi$
$450$	0.473626	+	3.97186i	0.0223269	+	0.187235i
$451$			6.59951i			0.310759i
$452$	12.6025	−	3.04894i	0.592773	−	0.143410i
$453$		−	20.7646i		−	0.975605i
$454$	−22.7349	+	2.71103i	−1.06700	+	0.127235i
$455$	6.97186			0.326846
$456$	−11.0483	−	29.7073i	−0.517385	−	1.39117i
$457$	−13.6117			−0.636727			−0.318364	−	0.947969i	$-0.603133\pi$
$457$	−13.6117			−0.636727			−0.318364	+	0.947969i	$0.603133\pi$
$458$	−11.5184	+	1.37352i	−0.538220	+	0.0641802i
$459$			1.66981i			0.0779400i
$460$	1.10745	+	4.57754i	0.0516351	+	0.213429i
$461$		−	15.2763i		−	0.711487i	−0.934584	−	0.355744i	$-0.884228\pi$
$461$		−	15.2763i		−	0.711487i	0.934584	−	0.355744i	$-0.115772\pi$
$462$	−1.00995	−	8.46950i	−0.0469871	−	0.394037i
$463$	−32.0875			−1.49123			−0.745617	−	0.666375i	$-0.767845\pi$
$463$	−32.0875			−1.49123			−0.745617	+	0.666375i	$0.767845\pi$
$464$	17.0653	+	33.2047i	0.792237	+	1.54149i
$465$	0.760493			0.0352670
$466$	−0.497861	−	4.17510i	−0.0230630	−	0.193408i
$467$		−	3.33109i		−	0.154145i	−0.997026	−	0.0770723i	$-0.975443\pi$
$467$		−	3.33109i		−	0.154145i	0.997026	−	0.0770723i	$-0.0245572\pi$
$468$	9.27391	+	38.3329i	0.428687	+	1.77194i
$469$			5.11529i			0.236202i
$470$	−5.87436	+	0.700490i	−0.270964	+	0.0323112i
$471$	−22.8347			−1.05217
$472$	31.0684	−	11.5545i	1.43004	−	0.531840i
$473$	4.20951			0.193553
$474$	−10.1480	+	1.21010i	−0.466113	+	0.0555818i
$475$			4.64167i			0.212974i
$476$	7.83647	−	1.89588i	0.359184	−	0.0868977i
$477$		−	25.7819i		−	1.18047i
$478$	3.39983	+	28.5113i	0.155505	+	1.30407i
$479$	26.8558			1.22707			0.613536	−	0.789667i	$-0.289747\pi$
$479$	26.8558			1.22707			0.613536	+	0.789667i	$0.289747\pi$
$480$	−7.63696	−	11.3220i	−0.348578	−	0.516774i
$481$	50.9089			2.32125
$482$	−0.538124	−	4.51274i	−0.0245109	−	0.205550i
$483$			5.68499i			0.258676i
$484$	−9.25077	+	2.23804i	−0.420489	+	0.101729i
$485$			17.7373i			0.805411i
$486$	30.4120	−	3.62648i	1.37951	−	0.164501i
$487$	−22.4379			−1.01676			−0.508378	−	0.861134i	$-0.669755\pi$
$487$	−22.4379			−1.01676			−0.508378	+	0.861134i	$0.669755\pi$
$488$	−13.3557	+	4.96706i	−0.604584	+	0.224848i
$489$	55.2959			2.50057
$490$	−1.40426	+	0.167452i	−0.0634382	+	0.00756471i
$491$		−	4.85471i		−	0.219090i	−0.993982	−	0.109545i	$-0.965061\pi$
$491$		−	4.85471i		−	0.219090i	0.993982	−	0.109545i	$-0.0349394\pi$
$492$	2.99932	+	12.3975i	0.135220	+	0.558920i
$493$			37.6252i			1.69455i
$494$	5.41893	+	45.4435i	0.243809	+	2.04460i
$495$	−7.06608			−0.317596
$496$	−1.12068	+	0.575967i	−0.0503201	+	0.0258617i
$497$	−7.89450			−0.354117
$498$	1.66510	+	13.9636i	0.0746147	+	0.625725i
$499$		−	32.5116i		−	1.45542i	−0.685886	−	0.727709i	$-0.740585\pi$
$499$		−	32.5116i		−	1.45542i	0.685886	−	0.727709i	$-0.259415\pi$
$500$	0.470294	+	1.94392i	0.0210322	+	0.0869347i
$501$			19.0224i			0.849856i
$502$	−2.36304	+	0.281782i	−0.105468	+	0.0125765i
$503$	−15.6291			−0.696867			−0.348433	−	0.937334i	$-0.613286\pi$
$503$	−15.6291			−0.696867			−0.348433	+	0.937334i	$0.613286\pi$
$504$	−2.78863	−	7.49824i	−0.124216	−	0.333998i
$505$	16.3776			0.728792
$506$	−8.26108	+	0.985095i	−0.367250	+	0.0437928i
$507$		−	85.9625i		−	3.81773i
$508$	15.8780	−	3.84138i	0.704473	−	0.170434i
$509$			16.8284i			0.745907i	0.927850	+	0.372953i	$0.121655\pi$
$509$			16.8284i			0.745907i	−0.927850	+	0.372953i	$0.878345\pi$
$510$	−1.62970	−	13.6668i	−0.0721644	−	0.605176i
$511$	−9.89450			−0.437707
$512$	19.8288	+	10.9004i	0.876317	+	0.481734i
$513$	1.92264			0.0848867
$514$	−2.88471	−	24.1914i	−0.127239	−	1.06703i
$515$		−	2.53970i		−	0.111913i
$516$	7.90774	−	1.91312i	0.348119	−	0.0842206i
$517$		−	10.4507i		−	0.459621i
$518$	−10.2540	+	1.22274i	−0.450536	+	0.0537243i
$519$	10.1953			0.447523
$520$	6.87377	+	18.4826i	0.301435	+	0.810515i
$521$	32.1101			1.40677			0.703384	−	0.710810i	$-0.251671\pi$
$521$	32.1101			1.40677			0.703384	+	0.710810i	$0.251671\pi$
$522$	37.0707	−	4.42050i	1.62254	−	0.193480i
$523$			4.04370i			0.176819i	0.996084	+	0.0884093i	$0.0281783\pi$
$523$			4.04370i			0.176819i	−0.996084	+	0.0884093i	$0.971822\pi$
$524$	−9.49039	−	39.2277i	−0.414590	−	1.71367i
$525$			2.41421i			0.105365i
$526$	0.465384	+	3.90274i	0.0202917	+	0.170168i
$527$	−1.26988			−0.0553167
$528$	21.4571	−	11.0277i	0.933802	−	0.479921i
$529$	−17.4549			−0.758909
$530$	−1.52637	−	12.8003i	−0.0663015	−	0.556009i
$531$		−	33.1475i		−	1.43848i
$532$	−2.18295	−	9.02303i	−0.0946428	−	0.391198i
$533$		−	18.4173i		−	0.797744i
$534$	−42.4549	+	5.06255i	−1.83720	+	0.219078i
$535$	2.31724			0.100183
$536$	−13.5608	+	5.04332i	−0.585737	+	0.217838i
$537$	27.8553			1.20204
$538$	−3.56902	+	0.425589i	−0.153872	+	0.0183485i
$539$		−	2.49824i		−	0.107607i
$540$	0.805198	−	0.194802i	0.0346502	−	0.00838295i
$541$			2.55412i			0.109810i	0.998492	+	0.0549050i	$0.0174856\pi$
$541$			2.55412i			0.109810i	−0.998492	+	0.0549050i	$0.982514\pi$
$542$	−2.59208	−	21.7373i	−0.111339	−	0.933699i
$543$	24.4290			1.04835
$544$	12.7523	+	18.9055i	0.546748	+	0.810566i
$545$	8.04293			0.344521
$546$	2.81848	+	23.6360i	0.120620	+	1.01153i
$547$			9.47325i			0.405047i	0.979277	+	0.202524i	$0.0649143\pi$
$547$			9.47325i			0.405047i	−0.979277	+	0.202524i	$0.935086\pi$
$548$	9.00471	−	2.17852i	0.384662	−	0.0930616i
$549$			14.2494i			0.608151i
$550$	−3.50818	+	0.418334i	−0.149589	+	0.0178378i
$551$	43.3222			1.84559
$552$	−15.0711	+	5.60501i	−0.641467	+	0.238565i
$553$	−2.99334			−0.127290
$554$	31.6995	−	3.78002i	1.34678	−	0.160598i
$555$			17.6287i			0.748297i
$556$	9.03350	+	37.3392i	0.383106	+	1.58354i
$557$		−	27.6309i		−	1.17076i	−0.810759	−	0.585380i	$-0.800945\pi$
$557$		−	27.6309i		−	1.17076i	0.810759	−	0.585380i	$-0.199055\pi$
$558$	0.149195	+	1.25116i	0.00631594	+	0.0529659i
$559$	−11.7475			−0.496868
$560$	−1.82843	−	3.55765i	−0.0772651	−	0.150338i
$561$	24.3137			1.02653
$562$	0.0442893	+	0.371414i	0.00186823	+	0.0156671i
$563$		−	41.6068i		−	1.75352i	−0.480929	−	0.876760i	$-0.659700\pi$
$563$		−	41.6068i		−	1.75352i	0.480929	−	0.876760i	$-0.340300\pi$
$564$	−4.74960	−	19.6320i	−0.199994	−	0.826658i
$565$		−	6.48305i		−	0.272744i
$566$	−11.6125	+	1.38474i	−0.488112	+	0.0582050i
$567$	9.48528			0.398344
$568$	−7.78343	−	20.9285i	−0.326585	−	0.878142i
$569$	−5.34588			−0.224111			−0.112056	−	0.993702i	$-0.535743\pi$
$569$	−5.34588			−0.224111			−0.112056	+	0.993702i	$0.535743\pi$
$570$	−15.7362	+	1.87646i	−0.659115	+	0.0785964i
$571$		−	41.8249i		−	1.75032i	−0.483836	−	0.875159i	$-0.660757\pi$
$571$		−	41.8249i		−	1.75032i	0.483836	−	0.875159i	$-0.339243\pi$
$572$	−33.8579	+	8.19127i	−1.41567	+	0.342494i
$573$			41.2087i			1.72152i
$574$	0.442353	+	3.70960i	0.0184634	+	0.154836i
$575$	2.35480			0.0982020
$576$	17.1286	−	14.7855i	0.713693	−	0.616062i
$577$	−5.50676			−0.229249			−0.114625	−	0.993409i	$-0.536567\pi$
$577$	−5.50676			−0.229249			−0.114625	+	0.993409i	$0.536567\pi$
$578$	−0.125394	−	1.05157i	−0.00521572	−	0.0437394i
$579$			36.9197i			1.53433i
$580$	18.1432	−	4.38941i	0.753357	−	0.182260i
$581$			4.11882i			0.170878i
$582$	−60.1331	+	7.17059i	−2.49260	+	0.297230i
$583$	22.7721			0.943126
$584$	−9.75529	−	26.2306i	−0.403677	−	1.08543i
$585$	19.7194			0.815297
$586$	3.63005	−	0.432866i	0.149956	−	0.0178815i
$587$			4.03923i			0.166717i	0.996520	+	0.0833585i	$0.0265647\pi$
$587$			4.03923i			0.166717i	−0.996520	+	0.0833585i	$0.973435\pi$
$588$	−1.13539	−	4.69304i	−0.0468227	−	0.193538i
$589$			1.46216i			0.0602471i
$590$	−1.96244	−	16.4571i	−0.0807923	−	0.677530i
$591$	−45.0934			−1.85490
$592$	−13.3513	−	25.9781i	−0.548734	−	1.06769i
$593$	−18.4414			−0.757299			−0.378649	−	0.925540i	$-0.623611\pi$
$593$	−18.4414			−0.757299			−0.378649	+	0.925540i	$0.623611\pi$
$594$	0.173280	+	1.45314i	0.00710976	+	0.0596229i
$595$		−	4.03127i		−	0.165266i
$596$	4.47139	+	18.4821i	0.183155	+	0.757057i
$597$			5.92668i			0.242563i
$598$	23.0543	−	2.74912i	0.942761	−	0.112420i
$599$	26.8549			1.09726			0.548630	−	0.836065i	$-0.315150\pi$
$599$	26.8549			1.09726			0.548630	+	0.836065i	$0.315150\pi$
$600$	−6.40014	+	2.38025i	−0.261285	+	0.0971732i
$601$	−5.59431			−0.228197			−0.114098	−	0.993469i	$-0.536398\pi$
$601$	−5.59431			−0.228197			−0.114098	+	0.993469i	$0.536398\pi$
$602$	2.36618	−	0.282156i	0.0964382	−	0.0114998i
$603$			14.4682i			0.589192i
$604$	16.7196	−	4.04498i	0.680311	−	0.164588i
$605$			4.75882i			0.193474i
$606$	6.62087	+	55.5231i	0.268954	+	2.25547i
$607$	34.4638			1.39884			0.699421	−	0.714710i	$-0.253441\pi$
$607$	34.4638			1.39884			0.699421	+	0.714710i	$0.253441\pi$
$608$	21.7681	−	14.6831i	0.882811	−	0.595480i
$609$	22.5326			0.913069
$610$	0.843613	+	7.07460i	0.0341569	+	0.286442i
$611$			29.1649i			1.17989i
$612$	22.1649	−	5.36237i	0.895962	−	0.216761i
$613$		−	19.0590i		−	0.769786i	−0.922961	−	0.384893i	$-0.874238\pi$
$613$		−	19.0590i		−	0.769786i	0.922961	−	0.384893i	$-0.125762\pi$
$614$	−47.3291	+	5.64377i	−1.91005	+	0.227764i
$615$	6.37755			0.257168
$616$	6.62289	−	2.46309i	0.266844	−	0.0992406i
$617$	25.0520			1.00855			0.504277	−	0.863542i	$-0.331759\pi$
$617$	25.0520			1.00855			0.504277	+	0.863542i	$0.331759\pi$
$618$	8.61008	−	1.02671i	0.346348	−	0.0413004i
$619$		−	29.3834i		−	1.18102i	−0.807030	−	0.590510i	$-0.798927\pi$
$619$		−	29.3834i		−	1.18102i	0.807030	−	0.590510i	$-0.201073\pi$
$620$	0.148146	+	0.612348i	0.00594967	+	0.0245925i
$621$		−	0.975391i		−	0.0391411i
$622$	−1.97031	−	16.5231i	−0.0790020	−	0.662517i
$623$	−12.5228			−0.501717
$624$	−59.8808	+	30.7753i	−2.39715	+	1.23200i
$625$	1.00000			0.0400000
$626$	−0.684469	−	5.74000i	−0.0273569	−	0.229417i
$627$		−	27.9952i		−	1.11802i
$628$	−4.44825	−	18.3864i	−0.177504	−	0.733699i
$629$		−	29.4366i		−	1.17371i
$630$	−3.97186	+	0.473626i	−0.158243	+	0.0188697i
$631$	28.0453			1.11647			0.558233	−	0.829684i	$-0.311480\pi$
$631$	28.0453			1.11647			0.558233	+	0.829684i	$0.311480\pi$
$632$	−2.95122	−	7.93541i	−0.117393	−	0.315654i
$633$	5.62558			0.223597
$634$	−4.42726	+	0.527930i	−0.175829	+	0.0209668i
$635$		−	8.16804i		−	0.324139i
$636$	42.7784	−	10.3494i	1.69627	−	0.410381i
$637$			6.97186i			0.276235i
$638$	3.90445	+	32.7430i	0.154579	+	1.29631i
$639$	−22.3290			−0.883323
$640$	7.62872	−	8.35480i	0.301551	−	0.330253i
$641$	10.7792			0.425753			0.212877	−	0.977079i	$-0.431717\pi$
$641$	10.7792			0.425753			0.212877	+	0.977079i	$0.431717\pi$
$642$	0.936778	+	7.85589i	0.0369717	+	0.310047i
$643$			16.6089i			0.654992i	0.944853	+	0.327496i	$0.106205\pi$
$643$			16.6089i			0.654992i	−0.944853	+	0.327496i	$0.893795\pi$
$644$	−4.57754	+	1.10745i	−0.180381	+	0.0436396i
$645$		−	4.06793i		−	0.160175i
$646$	26.2764	−	3.13333i	1.03383	−	0.123279i
$647$	25.3818			0.997861			0.498930	−	0.866642i	$-0.333726\pi$
$647$	25.3818			0.997861			0.498930	+	0.866642i	$0.333726\pi$
$648$	9.35183	+	25.1457i	0.367374	+	0.987818i
$649$	29.2778			1.14925
$650$	9.79034	−	1.16745i	0.384009	−	0.0457912i
$651$			0.760493i			0.0298061i
$652$	10.7718	+	44.5241i	0.421854	+	1.74370i
$653$			1.34129i			0.0524886i	0.999656	+	0.0262443i	$0.00835479\pi$
$653$			1.34129i			0.0524886i	−0.999656	+	0.0262443i	$0.991645\pi$
$654$	3.25147	+	27.2671i	0.127143	+	1.06623i
$655$	−20.1797			−0.788486
$656$	−9.39813	+	4.83010i	−0.366935	+	0.188584i
$657$	−27.9859			−1.09183
$658$	−0.700490	−	5.87436i	−0.0273079	−	0.229006i
$659$			46.3357i			1.80498i	0.430709	+	0.902491i	$0.358263\pi$
$659$			46.3357i			1.80498i	−0.430709	+	0.902491i	$0.641737\pi$
$660$	−2.83647	−	11.7243i	−0.110409	−	0.456368i
$661$		−	23.6076i		−	0.918231i	−0.888377	−	0.459115i	$-0.848166\pi$
$661$		−	23.6076i		−	0.918231i	0.888377	−	0.459115i	$-0.151834\pi$
$662$	16.3329	−	1.94763i	0.634797	−	0.0756966i
$663$	−67.8526			−2.63518
$664$	−10.9191	+	4.06087i	−0.423744	+	0.157592i
$665$	−4.64167			−0.179996
$666$	−29.0027	+	3.45844i	−1.12383	+	0.134012i
$667$		−	21.9781i		−	0.850997i
$668$	−15.3168	+	3.70560i	−0.592623	+	0.143374i
$669$		−	17.0786i		−	0.660298i
$670$	0.856566	+	7.18323i	0.0330920	+	0.277512i
$671$	−12.5860			−0.485875
$672$	11.3220	−	7.63696i	0.436754	−	0.294602i
$673$	27.5458			1.06181			0.530906	−	0.847431i	$-0.321852\pi$
$673$	27.5458			1.06181			0.530906	+	0.847431i	$0.321852\pi$
$674$	3.95735	+	33.1866i	0.152431	+	1.27830i
$675$		−	0.414214i		−	0.0159431i
$676$	69.2168	−	16.7457i	2.66219	−	0.644065i
$677$			19.6322i			0.754528i	0.926106	+	0.377264i	$0.123135\pi$
$677$			19.6322i			0.754528i	−0.926106	+	0.377264i	$0.876865\pi$
$678$	21.9788	−	2.62087i	0.844091	−	0.100654i
$679$	−17.7373			−0.680697
$680$	10.6870	−	3.97455i	0.409828	−	0.152417i
$681$	−39.0859			−1.49777
$682$	−1.10510	+	0.131778i	−0.0423165	+	0.00504604i
$683$			40.1695i			1.53704i	0.639824	+	0.768521i	$0.279007\pi$
$683$			40.1695i			1.53704i	−0.639824	+	0.768521i	$0.720993\pi$
$684$	−6.17431	−	25.5210i	−0.236081	−	0.975819i
$685$		−	4.63224i		−	0.176989i
$686$	−0.167452	−	1.40426i	−0.00639335	−	0.0536151i
$687$	−19.8025			−0.755511
$688$	3.08089	+	5.99461i	0.117458	+	0.228542i
$689$	−63.5506			−2.42108
$690$	0.951963	+	7.98324i	0.0362406	+	0.303917i
$691$			32.2610i			1.22726i	0.789592	+	0.613632i	$0.210292\pi$
$691$			32.2610i			1.22726i	−0.789592	+	0.613632i	$0.789708\pi$
$692$	1.98606	+	8.20922i	0.0754988	+	0.312068i
$693$		−	7.06608i		−	0.268418i
$694$	−16.7513	+	1.99752i	−0.635873	+	0.0758248i
$695$	19.2082			0.728609
$696$	22.2156	+	59.7346i	0.842081	+	2.26424i
$697$	−10.6493			−0.403371
$698$	20.1535	−	2.40321i	0.762822	−	0.0909629i
$699$		−	7.17784i		−	0.271491i
$700$	−1.94392	+	0.470294i	−0.0734733	+	0.0177754i
$701$			23.3129i			0.880518i	0.897871	+	0.440259i	$0.145113\pi$
$701$			23.3129i			0.880518i	−0.897871	+	0.440259i	$0.854887\pi$
$702$	−0.483574	−	4.05529i	−0.0182513	−	0.153057i
$703$	−33.8937			−1.27833
$704$	13.0594	+	15.1290i	0.492195	+	0.570196i
$705$	−10.0992			−0.380358
$706$	−0.201419	−	1.68911i	−0.00758050	−	0.0635707i
$707$			16.3776i			0.615941i
$708$	54.9996	−	13.3061i	2.06701	−	0.500073i
$709$			2.16881i			0.0814515i	0.999170	+	0.0407257i	$0.0129670\pi$
$709$			2.16881i			0.0814515i	−0.999170	+	0.0407257i	$0.987033\pi$
$710$	−11.0860	+	1.32195i	−0.416049	+	0.0496119i
$711$	−8.46643			−0.317516
$712$	−12.3467	−	33.1984i	−0.462710	−	1.24416i
$713$	0.741778			0.0277798
$714$	13.6668	−	1.62970i	0.511467	−	0.0609901i
$715$			17.4173i			0.651372i
$716$	5.42627	+	22.4290i	0.202789	+	0.838211i
$717$			49.0166i			1.83056i
$718$	0.676378	+	5.67216i	0.0252422	+	0.211683i
$719$	−27.1167			−1.01128			−0.505642	−	0.862744i	$-0.668744\pi$
$719$	−27.1167			−1.01128			−0.505642	+	0.862744i	$0.668744\pi$
$720$	−5.17157	−	10.0625i	−0.192733	−	0.375009i
$721$	2.53970			0.0945834
$722$	−0.426180	−	3.57398i	−0.0158608	−	0.133010i
$723$		−	7.75832i		−	0.288535i
$724$	4.75882	+	19.6702i	0.176860	+	0.731037i
$725$		−	9.33333i		−	0.346631i
$726$	−16.1333	+	1.92382i	−0.598764	+	0.0713998i
$727$	19.0331			0.705899			0.352949	−	0.935642i	$-0.385179\pi$
$727$	19.0331			0.705899			0.352949	+	0.935642i	$0.385179\pi$
$728$	−18.4826	+	6.87377i	−0.685010	+	0.254759i
$729$	23.8284			0.882534
$730$	−13.8945	+	1.65685i	−0.514259	+	0.0613229i
$731$			6.79267i			0.251236i
$732$	−23.6432	+	5.72002i	−0.873879	+	0.211418i
$733$			22.2630i			0.822303i	0.911567	+	0.411151i	$0.134873\pi$
$733$			22.2630i			0.822303i	−0.911567	+	0.411151i	$0.865127\pi$
$734$	−4.83097	−	40.5129i	−0.178314	−	1.49536i
$735$	−2.41421			−0.0890496
$736$	−7.44902	−	11.0433i	−0.274574	−	0.407062i
$737$	−12.7792			−0.470728
$738$	1.25116	+	10.4923i	0.0460559	+	0.386228i
$739$			16.4982i			0.606897i	0.952848	+	0.303449i	$0.0981381\pi$
$739$			16.4982i			0.606897i	−0.952848	+	0.303449i	$0.901862\pi$
$740$	−14.1946	+	3.43411i	−0.521804	+	0.126240i
$741$			78.1265i			2.87005i
$742$	12.8003	−	1.52637i	0.469913	−	0.0560350i
$743$	51.6864			1.89619			0.948096	−	0.317985i	$-0.103006\pi$
$743$	51.6864			1.89619			0.948096	+	0.317985i	$0.103006\pi$
$744$	−2.01609	+	0.749793i	−0.0739134	+	0.0274888i
$745$	9.50766			0.348334
$746$	−9.24763	+	1.10274i	−0.338580	+	0.0403741i
$747$			11.6498i			0.426244i
$748$	4.73636	+	19.5773i	0.173179	+	0.715819i
$749$			2.31724i			0.0846700i
$750$	0.404265	+	3.39020i	0.0147617	+	0.123792i
$751$	−33.6670			−1.22853			−0.614264	−	0.789101i	$-0.710547\pi$
$751$	−33.6670			−1.22853			−0.614264	+	0.789101i	$0.710547\pi$
$752$	14.8825	−	7.64873i	0.542707	−	0.278920i
$753$	−4.06255			−0.148047
$754$	−10.8962	−	91.3764i	−0.396817	−	3.32773i
$755$		−	8.60097i		−	0.313021i
$756$	0.194802	+	0.805198i	0.00708488	+	0.0292848i
$757$		−	42.2806i		−	1.53671i	−0.640022	−	0.768356i	$-0.721075\pi$
$757$		−	42.2806i		−	1.53671i	0.640022	−	0.768356i	$-0.278925\pi$
$758$	−12.8003	+	1.52637i	−0.464927	+	0.0554404i
$759$	−14.2025			−0.515516
$760$	−4.57636	−	12.3052i	−0.166002	−	0.446356i
$761$	17.8399			0.646696			0.323348	−	0.946280i	$-0.395192\pi$
$761$	17.8399			0.646696			0.323348	+	0.946280i	$0.395192\pi$
$762$	27.6913	−	3.30205i	1.00315	−	0.119621i
$763$			8.04293i			0.291174i
$764$	−33.1812	+	8.02755i	−1.20045	+	0.290426i
$765$		−	11.4022i		−	0.412246i
$766$	−5.84988	−	49.0575i	−0.211365	−	1.77252i
$767$	−81.7060			−2.95023
$768$	31.4084	+	22.4853i	1.13335	+	0.811368i
$769$	26.4557			0.954015			0.477008	−	0.878899i	$-0.341721\pi$
$769$	26.4557			0.954015			0.477008	+	0.878899i	$0.341721\pi$
$770$	−0.418334	−	3.50818i	−0.0150757	−	0.126426i
$771$		−	41.5898i		−	1.49782i
$772$	−29.7276	+	7.19203i	−1.06992	+	0.258847i
$773$		−	36.9781i		−	1.33001i	−0.746839	−	0.665005i	$-0.768429\pi$
$773$		−	36.9781i		−	1.33001i	0.746839	−	0.665005i	$-0.231571\pi$
$774$	6.69256	−	0.798056i	0.240559	−	0.0286855i
$775$	0.315007			0.0113154
$776$	−17.4878	−	47.0222i	−0.627775	−	1.68800i
$777$	−17.6287			−0.632427
$778$	47.8240	−	5.70279i	1.71457	−	0.204455i
$779$			12.2618i			0.439323i
$780$	7.91578	+	32.7192i	0.283430	+	1.17154i
$781$		−	19.7223i		−	0.705720i
$782$	−1.58960	−	13.3305i	−0.0568438	−	0.476697i
$783$	−3.86599			−0.138159
$784$	3.55765	−	1.82843i	0.127059	−	0.0653010i
$785$	−9.45844			−0.337586
$786$	−8.15794	−	68.4131i	−0.290984	−	2.44022i
$787$			35.8138i			1.27662i	0.769778	+	0.638312i	$0.220367\pi$
$787$			35.8138i			1.27662i	−0.769778	+	0.638312i	$0.779633\pi$
$788$	−8.78429	−	36.3091i	−0.312928	−	1.29346i
$789$			6.70960i			0.238868i
$790$	−4.20344	+	0.501240i	−0.149552	+	0.0178333i
$791$	6.48305			0.230511
$792$	18.7324	−	6.96666i	0.665625	−	0.247549i
$793$	35.1238			1.24728
$794$	−19.5965	+	2.33679i	−0.695455	+	0.0829297i
$795$		−	22.0063i		−	0.780482i
$796$	−4.77215	+	1.15453i	−0.169144	+	0.0409212i
$797$		−	24.4162i		−	0.864866i	−0.901666	−	0.432433i	$-0.857655\pi$
$797$		−	24.4162i		−	0.864866i	0.901666	−	0.432433i	$-0.142345\pi$
$798$	−1.87646	−	15.7362i	−0.0664261	−	0.557054i
$799$	16.8637			0.596596
$800$	−3.16333	−	4.68971i	−0.111841	−	0.165806i
$801$	−35.4200			−1.25150
$802$	−4.47930	−	37.5638i	−0.158170	−	1.32642i
$803$		−	24.7188i		−	0.872307i
$804$	−24.0063	+	5.80785i	−0.846636	+	0.204827i
$805$			2.35480i			0.0829958i
$806$	3.08402	−	0.367755i	0.108630	−	0.0129536i
$807$	−6.13587			−0.215993
$808$	−43.4173	+	16.1471i	−1.52742	+	0.568054i
$809$	−2.63095			−0.0924992			−0.0462496	−	0.998930i	$-0.514727\pi$
$809$	−2.63095			−0.0924992			−0.0462496	+	0.998930i	$0.514727\pi$
$810$	13.3198	−	1.58833i	0.468012	−	0.0558082i
$811$			34.8580i			1.22403i	0.790846	+	0.612015i	$0.209641\pi$
$811$			34.8580i			1.22403i	−0.790846	+	0.612015i	$0.790359\pi$
$812$	4.38941	+	18.1432i	0.154038	+	0.636703i
$813$		−	37.3709i		−	1.31065i
$814$	−3.05470	−	25.6169i	−0.107067	−	0.897873i
$815$	22.9043			0.802303
$816$	17.7949	+	34.6243i	0.622946	+	1.21209i
$817$	7.82118			0.273628
$818$	4.75225	+	39.8527i	0.166159	+	1.39342i
$819$			19.7194i			0.689052i
$820$	1.24236	+	5.13519i	0.0433851	+	0.179329i
$821$			18.8525i			0.657957i	0.944337	+	0.328979i	$0.106704\pi$
$821$			18.8525i			0.657957i	−0.944337	+	0.328979i	$0.893296\pi$
$822$	15.7042	−	1.87265i	0.547747	−	0.0653163i
$823$	12.1868			0.424804			0.212402	−	0.977182i	$-0.431871\pi$
$823$	12.1868			0.424804			0.212402	+	0.977182i	$0.431871\pi$
$824$	2.50397	+	6.73282i	0.0872299	+	0.234549i
$825$	−6.03127			−0.209982
$826$	16.4571	−	1.96244i	0.572617	−	0.0682819i
$827$		−	27.7498i		−	0.964954i	−0.875909	−	0.482477i	$-0.839737\pi$
$827$		−	27.7498i		−	0.964954i	0.875909	−	0.482477i	$-0.160263\pi$
$828$	−12.9473	+	3.13234i	−0.449948	+	0.108856i
$829$			18.1299i			0.629678i	0.949145	+	0.314839i	$0.101951\pi$
$829$			18.1299i			0.629678i	−0.949145	+	0.314839i	$0.898049\pi$
$830$	0.689705	+	5.78392i	0.0239400	+	0.200763i
$831$	54.4978			1.89051
$832$	−36.4451	−	42.2208i	−1.26351	−	1.46374i
$833$	4.03127			0.139675
$834$	7.76521	+	65.1196i	0.268887	+	2.25491i
$835$			7.87932i			0.272675i
$836$	22.5417	−	5.45352i	0.779619	−	0.188614i
$837$		−	0.130480i		−	0.00451005i
$838$	−20.2985	+	2.42050i	−0.701201	+	0.0836149i
$839$	5.23635			0.180779			0.0903895	−	0.995906i	$-0.471189\pi$
$839$	5.23635			0.180779			0.0903895	+	0.995906i	$0.471189\pi$
$840$	−2.38025	−	6.40014i	−0.0821263	−	0.220826i
$841$	−58.1110			−2.00383
$842$	48.3199	−	5.76192i	1.66521	−	0.198569i
$843$			0.638535i			0.0219923i
$844$	1.09588	+	4.52971i	0.0377216	+	0.155919i
$845$		−	35.6068i		−	1.22491i
$846$	−1.98128	−	16.6152i	−0.0681180	−	0.571242i
$847$	−4.75882			−0.163515
$848$	16.6667	+	32.4290i	0.572335	+	1.11362i
$849$	−19.9643			−0.685173
$850$	−0.675045	−	5.66098i	−0.0231538	−	0.194170i
$851$			17.1949i			0.589433i
$852$	−8.96334	−	37.0492i	−0.307079	−	1.26928i
$853$		−	25.0949i		−	0.859233i	−0.903011	−	0.429617i	$-0.858649\pi$
$853$		−	25.0949i		−	0.859233i	0.903011	−	0.429617i	$-0.141351\pi$
$854$	−7.07460	+	0.843613i	−0.242088	+	0.0288678i
$855$	−13.1286			−0.448989
$856$	−6.14306	+	2.28464i	−0.209965	+	0.0780872i
$857$	45.3244			1.54825			0.774127	−	0.633031i	$-0.218189\pi$
$857$	45.3244			1.54825			0.774127	+	0.633031i	$0.218189\pi$
$858$	−59.0482	+	7.04122i	−2.01587	+	0.240383i
$859$			15.2574i			0.520577i	0.965531	+	0.260288i	$0.0838176\pi$
$859$			15.2574i			0.520577i	−0.965531	+	0.260288i	$0.916182\pi$
$860$	3.27549	−	0.792442i	0.111693	−	0.0270221i
$861$			6.37755i			0.217346i
$862$	−4.80081	−	40.2600i	−0.163516	−	1.37126i
$863$	−27.0895			−0.922138			−0.461069	−	0.887364i	$-0.652534\pi$
$863$	−27.0895			−0.922138			−0.461069	+	0.887364i	$0.652534\pi$
$864$	−1.94254	+	1.31029i	−0.0660865	+	0.0445771i
$865$	4.22302			0.143587
$866$	−1.57007	−	13.1667i	−0.0533532	−	0.447424i
$867$		−	1.80785i		−	0.0613979i
$868$	−0.612348	+	0.148146i	−0.0207844	+	0.00502839i
$869$		−	7.47806i		−	0.253676i
$870$	31.6418	−	3.77314i	1.07276	−	0.127921i
$871$	35.6631			1.20840
$872$	−21.3220	+	7.92977i	−0.722055	+	0.268536i
$873$	−50.1688			−1.69796
$874$	−15.3489	+	1.83029i	−0.519185	+	0.0619103i
$875$			1.00000i			0.0338062i
$876$	−11.2341	−	46.4353i	−0.379566	−	1.56890i
$877$		−	18.6479i		−	0.629696i	−0.949142	−	0.314848i	$-0.898046\pi$
$877$		−	18.6479i		−	0.629696i	0.949142	−	0.314848i	$-0.101954\pi$
$878$	2.47871	+	20.7867i	0.0836525	+	0.701516i
$879$	6.24078			0.210496
$880$	8.88784	−	4.56784i	0.299609	−	0.153982i
$881$	6.66485			0.224544			0.112272	−	0.993677i	$-0.464187\pi$
$881$	6.66485			0.224544			0.112272	+	0.993677i	$0.464187\pi$
$882$	−0.473626	−	3.97186i	−0.0159478	−	0.133740i
$883$		−	56.6181i		−	1.90535i	−0.303988	−	0.952676i	$-0.598318\pi$
$883$		−	56.6181i		−	1.90535i	0.303988	−	0.952676i	$-0.401682\pi$
$884$	−13.2178	−	54.6348i	−0.444564	−	1.83757i
$885$		−	28.2931i		−	0.951063i
$886$	−12.8211	+	1.52885i	−0.430733	+	0.0513629i
$887$	−46.2584			−1.55320			−0.776602	−	0.629992i	$-0.783058\pi$
$887$	−46.2584			−1.55320			−0.776602	+	0.629992i	$0.783058\pi$
$888$	−17.3807	−	46.7342i	−0.583258	−	1.56830i
$889$	8.16804			0.273947
$890$	−17.5854	+	2.09698i	−0.589464	+	0.0702908i
$891$			23.6965i			0.793861i
$892$	13.7517	−	3.32695i	0.460440	−	0.111395i
$893$		−	19.4172i		−	0.649771i
$894$	3.84361	+	32.2328i	0.128550	+	1.07803i
$895$	11.5380			0.385674
$896$	8.35480	+	7.62872i	0.279114	+	0.254857i
$897$	39.6350			1.32337
$898$	−2.61833	−	21.9575i	−0.0873747	−	0.732731i
$899$		−	2.94006i		−	0.0980565i
$900$	−5.49824	+	1.33019i	−0.183275	+	0.0443397i
$901$			36.7462i			1.22419i
$902$	−9.26746	+	1.10510i	−0.308573	+	0.0367958i
$903$	4.06793			0.135372
$904$	6.39184	+	17.1867i	0.212589	+	0.571622i
$905$	10.1188			0.336361
$906$	29.1590	−	3.47707i	0.968742	−	0.115518i
$907$			57.2685i			1.90157i	0.309851	+	0.950785i	$0.399721\pi$
$907$			57.2685i			1.90157i	−0.309851	+	0.950785i	$0.600279\pi$
$908$	−7.61401	−	31.4718i	−0.252680	−	1.04443i
$909$			46.3227i			1.53643i
$910$	1.16745	+	9.79034i	0.0387007	+	0.324547i
$911$	56.0618			1.85741			0.928704	−	0.370821i	$-0.120924\pi$
$911$	56.0618			1.85741			0.928704	+	0.370821i	$0.120924\pi$
$912$	39.8669	−	20.4893i	1.32013	−	0.678469i
$913$	−10.2898			−0.340542
$914$	−2.27930	−	19.1144i	−0.0753926	−	0.632248i
$915$			12.1627i			0.402085i
$916$	−3.85756	−	15.9449i	−0.127457	−	0.526834i
$917$		−	20.1797i		−	0.666392i
$918$	−2.34485	+	0.279613i	−0.0773917	+	0.00922859i
$919$	19.3598			0.638621			0.319310	−	0.947650i	$-0.396549\pi$
$919$	19.3598			0.638621			0.319310	+	0.947650i	$0.396549\pi$
$920$	−6.24264	+	2.32167i	−0.205814	+	0.0765432i
$921$	−81.3682			−2.68117
$922$	21.4519	−	2.55804i	0.706482	−	0.0842447i
$923$			55.0394i			1.81164i
$924$	11.7243	−	2.83647i	0.385701	−	0.0933130i
$925$			7.30205i			0.240090i
$926$	−5.37312	−	45.0594i	−0.176572	−	1.48074i
$927$	7.18336			0.235933
$928$	−43.7705	+	29.5244i	−1.43684	+	0.969186i
$929$	−2.23138			−0.0732092			−0.0366046	−	0.999330i	$-0.511654\pi$
$929$	−2.23138			−0.0732092			−0.0366046	+	0.999330i	$0.511654\pi$
$930$	0.127346	+	1.06793i	0.00417584	+	0.0350189i
$931$		−	4.64167i		−	0.152125i
$932$	5.77958	−	1.39826i	0.189317	−	0.0458015i
$933$		−	28.4066i		−	0.929989i
$934$	4.67774	−	0.557798i	0.153060	−	0.0182517i
$935$	10.0711			0.329359
$936$	−52.2767	+	19.4420i	−1.70872	+	0.635480i
$937$	29.9187			0.977402			0.488701	−	0.872451i	$-0.337471\pi$
$937$	29.9187			0.977402			0.488701	+	0.872451i	$0.337471\pi$
$938$	−7.18323	+	0.856566i	−0.234541	+	0.0279679i
$939$		−	9.86822i		−	0.322037i
$940$	−1.96735	−	8.13186i	−0.0641678	−	0.265232i
$941$		−	15.5813i		−	0.507936i	−0.967213	−	0.253968i	$-0.918264\pi$
$941$		−	15.5813i		−	0.507936i	0.967213	−	0.253968i	$-0.0817358\pi$
$942$	−3.82372	−	32.0660i	−0.124583	−	1.04477i
$943$	6.22061			0.202571
$944$	21.4281	+	41.6935i	0.697424	+	1.35701i
$945$	0.414214			0.0134744
$946$	0.704891	+	5.91127i	0.0229180	+	0.192192i
$947$		−	49.2944i		−	1.60185i	−0.598762	−	0.800927i	$-0.704341\pi$
$947$		−	49.2944i		−	1.60185i	0.598762	−	0.800927i	$-0.295659\pi$
$948$	−3.39860	−	14.0478i	−0.110382	−	0.456253i
$949$			68.9831i			2.23929i
$950$	−6.51813	+	0.777257i	−0.211476	+	0.0252175i
$951$	−7.61135			−0.246815
$952$	3.97455	+	10.6870i	0.128816	+	0.346368i
$953$	−34.4838			−1.11704			−0.558520	−	0.829491i	$-0.688631\pi$
$953$	−34.4838			−1.11704			−0.558520	+	0.829491i	$0.688631\pi$
$954$	36.2047	−	4.31724i	1.17217	−	0.139776i
$955$			17.0692i			0.552347i
$956$	−39.4680	+	9.54853i	−1.27649	+	0.308822i
$957$			56.2918i			1.81966i
$958$	4.49705	+	37.7126i	0.145293	+	1.21844i
$959$	4.63224			0.149583
$960$	14.6202	−	12.6202i	0.471865	−	0.407315i
$961$	−30.9008			−0.996799
$962$	8.52480	+	71.4896i	0.274850	+	2.30492i
$963$			6.55414i			0.211204i
$964$	6.24698	−	1.51134i	0.201202	−	0.0486769i
$965$			15.2926i			0.492287i
$966$	−7.98324	+	0.951963i	−0.256856	+	0.0306289i
$967$	−28.3612			−0.912035			−0.456017	−	0.889971i	$-0.650725\pi$
$967$	−28.3612			−0.912035			−0.456017	+	0.889971i	$0.650725\pi$
$968$	−4.69187	−	12.6158i	−0.150802	−	0.405486i
$969$	45.1744			1.45121
$970$	−24.9079	+	2.97015i	−0.799745	+	0.0953659i
$971$		−	40.2126i		−	1.29048i	−0.763978	−	0.645242i	$-0.776756\pi$
$971$		−	40.2126i		−	1.29048i	0.763978	−	0.645242i	$-0.223244\pi$
$972$	10.1851	+	42.0992i	0.326687	+	1.35033i
$973$			19.2082i			0.615787i
$974$	−3.75727	−	31.5087i	−0.120391	−	1.00960i
$975$	16.8316			0.539041
$976$	−9.21150	−	17.9232i	−0.294853	−	0.573708i
$977$	−4.19066			−0.134071			−0.0670356	−	0.997751i	$-0.521354\pi$
$977$	−4.19066			−0.134071			−0.0670356	+	0.997751i	$0.521354\pi$
$978$	9.25940	+	77.6501i	0.296083	+	2.48297i
$979$		−	31.2850i		−	0.999873i
$980$	−0.470294	−	1.94392i	−0.0150230	−	0.0620962i
$981$			22.7488i			0.726314i
$982$	6.81730	−	0.812931i	0.217549	−	0.0259417i
$983$	38.3216			1.22227			0.611135	−	0.791526i	$-0.290713\pi$
$983$	38.3216			1.22227			0.611135	+	0.791526i	$0.290713\pi$
$984$	−16.9071	+	6.28782i	−0.538977	+	0.200448i
$985$	−18.6783			−0.595140
$986$	−52.8357	+	6.30041i	−1.68263	+	0.200646i
$987$		−	10.0992i		−	0.321461i
$988$	−62.9073	+	15.2192i	−2.00135	+	0.484188i
$989$		−	3.96782i		−	0.126169i
$990$	−1.18323	−	9.92264i	−0.0376055	−	0.315362i
$991$	28.4738			0.904499			0.452249	−	0.891892i	$-0.350622\pi$
$991$	28.4738			0.904499			0.452249	+	0.891892i	$0.350622\pi$
$992$	−0.996470	−	1.47729i	−0.0316380	−	0.0469039i
$993$	28.0796			0.891079
$994$	−1.32195	−	11.0860i	−0.0419297	−	0.351626i
$995$			2.45491i			0.0778259i
$996$	−19.3298	+	4.67647i	−0.612488	+	0.148180i
$997$			38.2730i			1.21212i	0.795420	+	0.606059i	$0.207250\pi$
$997$			38.2730i			1.21212i	−0.795420	+	0.606059i	$0.792750\pi$
$998$	45.6548	−	5.44413i	1.44518	−	0.172331i
$999$	3.02461			0.0956944

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.b.c.141.6	yes	8
4.3	odd	2		1120.2.b.c.561.2		8
8.3	odd	2		1120.2.b.c.561.7		8
8.5	even	2	inner	280.2.b.c.141.5	✓	8
16.3	odd	4		8960.2.a.bv.1.4		4
16.5	even	4		8960.2.a.bu.1.4		4
16.11	odd	4		8960.2.a.bs.1.1		4
16.13	even	4		8960.2.a.bt.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.b.c.141.5	✓	8	8.5	even	2	inner
280.2.b.c.141.6	yes	8	1.1	even	1	trivial
1120.2.b.c.561.2		8	4.3	odd	2
1120.2.b.c.561.7		8	8.3	odd	2
8960.2.a.bs.1.1		4	16.11	odd	4
8960.2.a.bt.1.1		4	16.13	even	4
8960.2.a.bu.1.4		4	16.5	even	4
8960.2.a.bv.1.4		4	16.3	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)

\(f(q)\)	\(=\)	\(q+(0.167452 + 1.40426i) q^{2} +2.41421i q^{3} +(-1.94392 + 0.470294i) q^{4} +1.00000i q^{5} +(-3.39020 + 0.404265i) q^{6} -1.00000 q^{7} +(-0.985930 - 2.65103i) q^{8} -2.82843 q^{9} +O(q^{10})\)	\(q+(0.167452 + 1.40426i) q^{2} +2.41421i q^{3} +(-1.94392 + 0.470294i) q^{4} +1.00000i q^{5} +(-3.39020 + 0.404265i) q^{6} -1.00000 q^{7} +(-0.985930 - 2.65103i) q^{8} -2.82843 q^{9} +(-1.40426 + 0.167452i) q^{10} -2.49824i q^{11} +(-1.13539 - 4.69304i) q^{12} +6.97186i q^{13} +(-0.167452 - 1.40426i) q^{14} -2.41421 q^{15} +(3.55765 - 1.82843i) q^{16} +4.03127 q^{17} +(-0.473626 - 3.97186i) q^{18} -4.64167i q^{19} +(-0.470294 - 1.94392i) q^{20} -2.41421i q^{21} +(3.50818 - 0.418334i) q^{22} -2.35480 q^{23} +(6.40014 - 2.38025i) q^{24} -1.00000 q^{25} +(-9.79034 + 1.16745i) q^{26} +0.414214i q^{27} +(1.94392 - 0.470294i) q^{28} +9.33333i q^{29} +(-0.404265 - 3.39020i) q^{30} -0.315007 q^{31} +(3.16333 + 4.68971i) q^{32} +6.03127 q^{33} +(0.675045 + 5.66098i) q^{34} -1.00000i q^{35} +(5.49824 - 1.33019i) q^{36} -7.30205i q^{37} +(6.51813 - 0.777257i) q^{38} -16.8316 q^{39} +(2.65103 - 0.985930i) q^{40} -2.64167 q^{41} +(3.39020 - 0.404265i) q^{42} +1.68499i q^{43} +(1.17490 + 4.85637i) q^{44} -2.82843i q^{45} +(-0.394316 - 3.30676i) q^{46} +4.18323 q^{47} +(4.41421 + 8.58892i) q^{48} +1.00000 q^{49} +(-0.167452 - 1.40426i) q^{50} +9.73235i q^{51} +(-3.27882 - 13.5527i) q^{52} +9.11529i q^{53} +(-0.581666 + 0.0693609i) q^{54} +2.49824 q^{55} +(0.985930 + 2.65103i) q^{56} +11.2060 q^{57} +(-13.1065 + 1.56288i) q^{58} +11.7194i q^{59} +(4.69304 - 1.13539i) q^{60} -5.03794i q^{61} +(-0.0527485 - 0.442353i) q^{62} +2.82843 q^{63} +(-6.05588 + 5.22746i) q^{64} -6.97186 q^{65} +(1.00995 + 8.46950i) q^{66} -5.11529i q^{67} +(-7.83647 + 1.89588i) q^{68} -5.68499i q^{69} +(1.40426 - 0.167452i) q^{70} +7.89450 q^{71} +(2.78863 + 7.49824i) q^{72} +9.89450 q^{73} +(10.2540 - 1.22274i) q^{74} -2.41421i q^{75} +(2.18295 + 9.02303i) q^{76} +2.49824i q^{77} +(-2.81848 - 23.6360i) q^{78} +2.99334 q^{79} +(1.82843 + 3.55765i) q^{80} -9.48528 q^{81} +(-0.442353 - 3.70960i) q^{82} -4.11882i q^{83} +(1.13539 + 4.69304i) q^{84} +4.03127i q^{85} +(-2.36618 + 0.282156i) q^{86} -22.5326 q^{87} +(-6.62289 + 2.46309i) q^{88} +12.5228 q^{89} +(3.97186 - 0.473626i) q^{90} -6.97186i q^{91} +(4.57754 - 1.10745i) q^{92} -0.760493i q^{93} +(0.700490 + 5.87436i) q^{94} +4.64167 q^{95} +(-11.3220 + 7.63696i) q^{96} +17.7373 q^{97} +(0.167452 + 1.40426i) q^{98} +7.06608i 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

Fields

Representations

Groups

Database

Properties

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