LMFDB - Embedded newform 270.2.m.b.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(17,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("270.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.m (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.4
Root			$0.500000 + 0.410882i$ of defining polynomial
Character	$\chi$	$=$	270.17
Dual form			270.2.m.b.143.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(1.51901 - 1.64092i) q^{5} +(-1.00635 + 3.75574i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(1.51901 - 1.64092i) q^{5} +(-1.00635 + 3.75574i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.89195 - 1.19185i) q^{10} +(3.44125 - 1.98681i) q^{11} +(-0.256253 - 0.956351i) q^{13} +(-1.94411 + 3.36730i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.120239 + 0.120239i) q^{17} -1.88492i q^{19} +(2.13596 - 0.661570i) q^{20} +(3.83821 - 1.02845i) q^{22} +(-5.08911 + 1.36362i) q^{23} +(-0.385214 - 4.98514i) q^{25} -0.990087i q^{26} +(-2.74939 + 2.74939i) q^{28} +(-2.15618 - 3.73461i) q^{29} +(-4.70172 + 8.14362i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-0.147262 + 0.0850217i) q^{34} +(4.63420 + 7.35634i) q^{35} +(3.26863 + 3.26863i) q^{37} +(0.487854 - 1.82070i) q^{38} +(2.23441 - 0.0862005i) q^{40} +(-7.15775 - 4.13253i) q^{41} +(-1.99285 - 0.533983i) q^{43} +3.97361 q^{44} -5.26863 q^{46} +(-3.34787 - 0.897060i) q^{47} +(-7.03067 - 4.05916i) q^{49} +(0.918161 - 4.91498i) q^{50} +(0.256253 - 0.956351i) q^{52} +(-3.66571 - 3.66571i) q^{53} +(1.96711 - 8.66478i) q^{55} +(-3.36730 + 1.94411i) q^{56} +(-1.11612 - 4.16541i) q^{58} +(2.72877 - 4.72637i) q^{59} +(-4.35623 - 7.54520i) q^{61} +(-6.64923 + 6.64923i) q^{62} +1.00000i q^{64} +(-1.95854 - 1.03222i) q^{65} +(7.86563 - 2.10759i) q^{67} +(-0.164249 + 0.0440105i) q^{68} +(2.57234 + 8.30510i) q^{70} +6.94911i q^{71} +(-8.27728 + 8.27728i) q^{73} +(2.31127 + 4.00324i) q^{74} +(0.942462 - 1.63239i) q^{76} +(3.99883 + 14.9238i) q^{77} +(11.7529 - 6.78553i) q^{79} +(2.18058 + 0.495044i) q^{80} +(-5.84428 - 5.84428i) q^{82} +(-1.81110 + 6.75913i) q^{83} +(0.0146578 + 0.379946i) q^{85} +(-1.78674 - 1.03157i) q^{86} +(3.83821 + 1.02845i) q^{88} +4.87832 q^{89} +3.84968 q^{91} +(-5.08911 - 1.36362i) q^{92} +(-3.00162 - 1.73299i) q^{94} +(-3.09300 - 2.86322i) q^{95} +(-0.387234 + 1.44518i) q^{97} +(-5.74052 - 5.74052i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) $ 16 * q + 12 * q^5 + 8 * q^7	$ 16 q + 12 q^{5} + 8 q^{7} - 8 q^{10} + 8 q^{16} + 12 q^{20} + 8 q^{22} + 24 q^{23} - 16 q^{25} - 16 q^{28} - 8 q^{31} - 24 q^{38} - 4 q^{40} - 24 q^{41} - 32 q^{46} - 48 q^{47} - 24 q^{50} + 24 q^{55} - 24 q^{56} + 16 q^{58} - 24 q^{61} - 16 q^{67} + 24 q^{68} + 16 q^{70} + 16 q^{73} + 16 q^{76} + 72 q^{77} - 16 q^{82} - 48 q^{83} - 4 q^{85} + 48 q^{86} + 8 q^{88} + 24 q^{92} - 84 q^{95} - 48 q^{97}+O(q^{100}) $ 16 * q + 12 * q^5 + 8 * q^7 - 8 * q^10 + 8 * q^16 + 12 * q^20 + 8 * q^22 + 24 * q^23 - 16 * q^25 - 16 * q^28 - 8 * q^31 - 24 * q^38 - 4 * q^40 - 24 * q^41 - 32 * q^46 - 48 * q^47 - 24 * q^50 + 24 * q^55 - 24 * q^56 + 16 * q^58 - 24 * q^61 - 16 * q^67 + 24 * q^68 + 16 * q^70 + 16 * q^73 + 16 * q^76 + 72 * q^77 - 16 * q^82 - 48 * q^83 - 4 * q^85 + 48 * q^86 + 8 * q^88 + 24 * q^92 - 84 * q^95 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	1.51901	−	1.64092i	0.679322	−	0.733840i
$5$	1.51901	−	1.64092i	0.679322	−	0.733840i
$6$		0			0
$7$	−1.00635	+	3.75574i	−0.380364	+	1.41954i	0.464984	+	0.885319i	$0.346060\pi$
$7$	−1.00635	+	3.75574i	−0.380364	+	1.41954i	−0.845347	+	0.534217i	$0.820606\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	1.89195	−	1.19185i	0.598288	−	0.376898i
$11$	3.44125	−	1.98681i	1.03758	−	0.599044i	0.118430	−	0.992962i	$-0.462214\pi$
$11$	3.44125	−	1.98681i	1.03758	−	0.599044i	0.919145	+	0.393918i	$0.128881\pi$
$12$		0			0
$13$	−0.256253	−	0.956351i	−0.0710719	−	0.265244i	0.921242	−	0.388990i	$-0.127176\pi$
$13$	−0.256253	−	0.956351i	−0.0710719	−	0.265244i	−0.992314	+	0.123746i	$0.960509\pi$
$14$	−1.94411	+	3.36730i	−0.519586	+	0.899950i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.120239	+	0.120239i	−0.0291622	+	0.0291622i	−0.721538	−	0.692375i	$-0.756564\pi$
$17$	−0.120239	+	0.120239i	−0.0291622	+	0.0291622i	0.692375	+	0.721538i	$0.256564\pi$
$18$		0			0
$19$		−	1.88492i		−	0.432431i	−0.976346	−	0.216216i	$-0.930629\pi$
$19$		−	1.88492i		−	0.432431i	0.976346	−	0.216216i	$-0.0693714\pi$
$20$	2.13596	−	0.661570i	0.477615	−	0.147932i
$21$		0			0
$22$	3.83821	−	1.02845i	0.818310	−	0.219265i
$23$	−5.08911	+	1.36362i	−1.06115	+	0.284335i	−0.746853	−	0.664989i	$-0.768436\pi$
$23$	−5.08911	+	1.36362i	−1.06115	+	0.284335i	−0.314299	+	0.949324i	$0.601770\pi$
$24$		0			0
$25$	−0.385214	−	4.98514i	−0.0770427	−	0.997028i
$26$		−	0.990087i		−	0.194172i
$27$		0			0
$28$	−2.74939	+	2.74939i	−0.519586	+	0.519586i
$29$	−2.15618	−	3.73461i	−0.400392	−	0.693499i	0.593381	−	0.804922i	$-0.297793\pi$
$29$	−2.15618	−	3.73461i	−0.400392	−	0.693499i	−0.993773	+	0.111422i	$0.964459\pi$
$30$		0			0
$31$	−4.70172	+	8.14362i	−0.844454	+	1.46264i	0.0416413	+	0.999133i	$0.486741\pi$
$31$	−4.70172	+	8.14362i	−0.844454	+	1.46264i	−0.886095	+	0.463504i	$0.846592\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$		0			0
$34$	−0.147262	+	0.0850217i	−0.0252552	+	0.0145811i
$35$	4.63420	+	7.35634i	0.783323	+	1.24345i
$36$		0			0
$37$	3.26863	+	3.26863i	0.537360	+	0.537360i	0.922753	−	0.385393i	$-0.125934\pi$
$37$	3.26863	+	3.26863i	0.537360	+	0.537360i	−0.385393	+	0.922753i	$0.625934\pi$
$38$	0.487854	−	1.82070i	0.0791404	−	0.295356i
$39$		0			0
$40$	2.23441	−	0.0862005i	0.353291	−	0.0136295i
$41$	−7.15775	−	4.13253i	−1.11785	−	0.645393i	−0.177001	−	0.984211i	$-0.556640\pi$
$41$	−7.15775	−	4.13253i	−1.11785	−	0.645393i	−0.940852	+	0.338818i	$0.889973\pi$
$42$		0			0
$43$	−1.99285	−	0.533983i	−0.303907	−	0.0814316i	0.103643	−	0.994615i	$-0.466950\pi$
$43$	−1.99285	−	0.533983i	−0.303907	−	0.0814316i	−0.407550	+	0.913183i	$0.633617\pi$
$44$	3.97361			0.599044
$45$		0			0
$46$	−5.26863			−0.776818
$47$	−3.34787	−	0.897060i	−0.488338	−	0.130850i	0.00624459	−	0.999981i	$-0.498012\pi$
$47$	−3.34787	−	0.897060i	−0.488338	−	0.130850i	−0.494582	+	0.869131i	$0.664679\pi$
$48$		0			0
$49$	−7.03067	−	4.05916i	−1.00438	−	0.579880i
$50$	0.918161	−	4.91498i	0.129848	−	0.695082i
$51$		0			0
$52$	0.256253	−	0.956351i	0.0355359	−	0.132622i
$53$	−3.66571	−	3.66571i	−0.503524	−	0.503524i	0.409007	−	0.912531i	$-0.365875\pi$
$53$	−3.66571	−	3.66571i	−0.503524	−	0.503524i	−0.912531	+	0.409007i	$0.865875\pi$
$54$		0			0
$55$	1.96711	−	8.66478i	0.265245	−	1.16836i
$56$	−3.36730	+	1.94411i	−0.449975	+	0.259793i
$57$		0			0
$58$	−1.11612	−	4.16541i	−0.146554	−	0.546946i
$59$	2.72877	−	4.72637i	0.355255	−	0.615320i	−0.631906	−	0.775045i	$-0.717727\pi$
$59$	2.72877	−	4.72637i	0.355255	−	0.615320i	0.987162	+	0.159724i	$0.0510606\pi$
$60$		0			0
$61$	−4.35623	−	7.54520i	−0.557758	−	0.966064i	−0.997683	−	0.0680302i	$-0.978329\pi$
$61$	−4.35623	−	7.54520i	−0.557758	−	0.966064i	0.439926	−	0.898034i	$-0.355005\pi$
$62$	−6.64923	+	6.64923i	−0.844454	+	0.844454i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−1.95854	−	1.03222i	−0.242927	−	0.128031i
$66$		0			0
$67$	7.86563	−	2.10759i	0.960940	−	0.257483i	0.255942	−	0.966692i	$-0.417615\pi$
$67$	7.86563	−	2.10759i	0.960940	−	0.257483i	0.704998	+	0.709209i	$0.250948\pi$
$68$	−0.164249	+	0.0440105i	−0.0199182	+	0.00533705i
$69$		0			0
$70$	2.57234	+	8.30510i	0.307453	+	0.992649i
$71$			6.94911i			0.824708i	0.911024	+	0.412354i	$0.135293\pi$
$71$			6.94911i			0.824708i	−0.911024	+	0.412354i	$0.864707\pi$
$72$		0			0
$73$	−8.27728	+	8.27728i	−0.968783	+	0.968783i	−0.999527	−	0.0307446i	$-0.990212\pi$
$73$	−8.27728	+	8.27728i	−0.968783	+	0.968783i	0.0307446	+	0.999527i	$0.490212\pi$
$74$	2.31127	+	4.00324i	0.268680	+	0.465368i
$75$		0			0
$76$	0.942462	−	1.63239i	0.108108	−	0.187248i
$77$	3.99883	+	14.9238i	0.455709	+	1.70073i
$78$		0			0
$79$	11.7529	−	6.78553i	1.32230	−	0.763431i	0.338206	−	0.941072i	$-0.390180\pi$
$79$	11.7529	−	6.78553i	1.32230	−	0.763431i	0.984095	+	0.177641i	$0.0568465\pi$
$80$	2.18058	+	0.495044i	0.243796	+	0.0553475i
$81$		0			0
$82$	−5.84428	−	5.84428i	−0.645393	−	0.645393i
$83$	−1.81110	+	6.75913i	−0.198795	+	0.741911i	0.792457	+	0.609927i	$0.208801\pi$
$83$	−1.81110	+	6.75913i	−0.198795	+	0.741911i	−0.991252	+	0.131984i	$0.957865\pi$
$84$		0			0
$85$	0.0146578	+	0.379946i	0.00158986	+	0.0412109i
$86$	−1.78674	−	1.03157i	−0.192669	−	0.111238i
$87$		0			0
$88$	3.83821	+	1.02845i	0.409155	+	0.109633i
$89$	4.87832			0.517100			0.258550	−	0.965998i	$-0.416755\pi$
$89$	4.87832			0.517100			0.258550	+	0.965998i	$0.416755\pi$
$90$		0			0
$91$	3.84968			0.403557
$92$	−5.08911	−	1.36362i	−0.530576	−	0.142168i
$93$		0			0
$94$	−3.00162	−	1.73299i	−0.309594	−	0.178744i
$95$	−3.09300	−	2.86322i	−0.317335	−	0.293760i
$96$		0			0
$97$	−0.387234	+	1.44518i	−0.0393177	+	0.146736i	−0.982794	−	0.184704i	$-0.940868\pi$
$97$	−0.387234	+	1.44518i	−0.0393177	+	0.146736i	0.943477	+	0.331439i	$0.107534\pi$
$98$	−5.74052	−	5.74052i	−0.579880	−	0.579880i
$99$		0			0
$100$	2.15896	−	4.50986i	0.215896	−	0.450986i
$101$	8.91944	−	5.14964i	0.887517	−	0.512408i	0.0143875	−	0.999896i	$-0.495420\pi$
$101$	8.91944	−	5.14964i	0.887517	−	0.512408i	0.873130	+	0.487488i	$0.162087\pi$
$102$		0			0
$103$	1.67823	+	6.26326i	0.165361	+	0.617137i	0.997994	+	0.0633111i	$0.0201660\pi$
$103$	1.67823	+	6.26326i	0.165361	+	0.617137i	−0.832632	+	0.553826i	$0.813167\pi$
$104$	0.495044	−	0.857441i	0.0485430	−	0.0840790i
$105$		0			0
$106$	−2.59205	−	4.48956i	−0.251762	−	0.436065i
$107$	3.70057	−	3.70057i	0.357747	−	0.357747i	−0.505235	−	0.862982i	$-0.668594\pi$
$107$	3.70057	−	3.70057i	0.357747	−	0.357747i	0.862982	+	0.505235i	$0.168594\pi$
$108$		0			0
$109$			7.30160i			0.699367i	0.936868	+	0.349683i	$0.113711\pi$
$109$			7.30160i			0.699367i	−0.936868	+	0.349683i	$0.886289\pi$
$110$	4.14269	−	7.86041i	0.394990	−	0.749460i
$111$		0			0
$112$	−3.75574	+	1.00635i	−0.354884	+	0.0950909i
$113$	4.07557	−	1.09205i	0.383397	−	0.102731i	−0.0619722	−	0.998078i	$-0.519739\pi$
$113$	4.07557	−	1.09205i	0.383397	−	0.102731i	0.445369	+	0.895347i	$0.353072\pi$
$114$		0			0
$115$	−5.49282	+	10.4222i	−0.512208	+	0.971872i
$116$		−	4.31235i		−	0.400392i
$117$		0			0
$118$	3.85906	−	3.85906i	0.355255	−	0.355255i
$119$	−0.330584	−	0.572588i	−0.0303046	−	0.0524891i
$120$		0			0
$121$	2.39479	−	4.14790i	0.217708	−	0.377081i
$122$	−2.25495	−	8.41558i	−0.204153	−	0.761911i
$123$		0			0
$124$	−8.14362	+	4.70172i	−0.731318	+	0.422227i
$125$	−8.76534	−	6.94038i	−0.783996	−	0.620766i
$126$		0			0
$127$	13.7871	+	13.7871i	1.22341	+	1.22341i	0.966411	+	0.257000i	$0.0827341\pi$
$127$	13.7871	+	13.7871i	1.22341	+	1.22341i	0.257000	+	0.966411i	$0.417266\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$		0			0
$130$	−1.62465	−	1.50395i	−0.142491	−	0.131905i
$131$	3.88249	+	2.24156i	0.339215	+	0.195846i	0.659925	−	0.751332i	$-0.270588\pi$
$131$	3.88249	+	2.24156i	0.339215	+	0.195846i	−0.320710	+	0.947178i	$0.603921\pi$
$132$		0			0
$133$	7.07929	+	1.89689i	0.613852	+	0.164481i
$134$	8.14310			0.703457
$135$		0			0
$136$	−0.170043			−0.0145811
$137$	12.0729	+	3.23492i	1.03146	+	0.276378i	0.734569	−	0.678534i	$-0.237384\pi$
$137$	12.0729	+	3.23492i	1.03146	+	0.276378i	0.296888	+	0.954912i	$0.404051\pi$
$138$		0			0
$139$	−3.60435	−	2.08097i	−0.305717	−	0.176506i	0.339291	−	0.940681i	$-0.389813\pi$
$139$	−3.60435	−	2.08097i	−0.305717	−	0.176506i	−0.645008	+	0.764176i	$0.723146\pi$
$140$	0.335167	+	8.68788i	0.0283268	+	0.734260i
$141$		0			0
$142$	−1.79856	+	6.71233i	−0.150932	+	0.563286i
$143$	−2.78191	−	2.78191i	−0.232635	−	0.232635i
$144$		0			0
$145$	−9.40344	−	2.13480i	−0.780913	−	0.177286i
$146$	−10.1376	+	5.85292i	−0.838990	+	0.484391i
$147$		0			0
$148$	1.19640	+	4.46504i	0.0983437	+	0.367024i
$149$	0.518244	−	0.897625i	0.0424562	−	0.0735363i	−0.844016	−	0.536317i	$-0.819815\pi$
$149$	0.518244	−	0.897625i	0.0424562	−	0.0735363i	0.886473	+	0.462781i	$0.153148\pi$
$150$		0			0
$151$	−2.03451	−	3.52388i	−0.165566	−	0.286769i	0.771290	−	0.636484i	$-0.219612\pi$
$151$	−2.03451	−	3.52388i	−0.165566	−	0.286769i	−0.936856	+	0.349715i	$0.886278\pi$
$152$	1.33284	−	1.33284i	0.108108	−	0.108108i
$153$		0			0
$154$			15.4503i			1.24502i
$155$	6.22103	+	20.0854i	0.499685	+	1.61330i
$156$		0			0
$157$	−8.81460	+	2.36186i	−0.703481	+	0.188497i	−0.592789	−	0.805357i	$-0.701973\pi$
$157$	−8.81460	+	2.36186i	−0.703481	+	0.188497i	−0.110692	+	0.993855i	$0.535307\pi$
$158$	13.1086	−	3.51245i	1.04287	−	0.279435i
$159$		0			0
$160$	1.97815	+	1.04255i	0.156387	+	0.0824209i
$161$		−	20.4857i		−	1.61450i
$162$		0			0
$163$	5.03848	−	5.03848i	0.394644	−	0.394644i	−0.481695	−	0.876339i	$-0.659979\pi$
$163$	5.03848	−	5.03848i	0.394644	−	0.394644i	0.876339	+	0.481695i	$0.159979\pi$
$164$	−4.13253	−	7.15775i	−0.322696	−	0.558926i
$165$		0			0
$166$	−3.49878	+	6.06007i	−0.271558	+	0.470353i
$167$	2.80384	+	10.4641i	0.216968	+	0.809734i	0.985465	+	0.169881i	$0.0543382\pi$
$167$	2.80384	+	10.4641i	0.216968	+	0.809734i	−0.768497	+	0.639853i	$0.778995\pi$
$168$		0			0
$169$	10.4094	−	6.00986i	0.800722	−	0.462297i
$170$	−0.0841789	+	0.370793i	−0.00645623	+	0.0284386i
$171$		0			0
$172$	−1.45887	−	1.45887i	−0.111238	−	0.111238i
$173$	−0.975709	+	3.64139i	−0.0741818	+	0.276850i	−0.993047	−	0.117722i	$-0.962441\pi$
$173$	−0.975709	+	3.64139i	−0.0741818	+	0.276850i	0.918865	+	0.394573i	$0.129107\pi$
$174$		0			0
$175$	19.1105	+	3.57002i	1.44462	+	0.269868i
$176$	3.44125	+	1.98681i	0.259394	+	0.149761i
$177$		0			0
$178$	4.71209	+	1.26260i	0.353186	+	0.0946359i
$179$	−12.8952			−0.963836			−0.481918	−	0.876216i	$-0.660060\pi$
$179$	−12.8952			−0.963836			−0.481918	+	0.876216i	$0.660060\pi$
$180$		0			0
$181$	24.3197			1.80767			0.903835	−	0.427881i	$-0.140740\pi$
$181$	24.3197			1.80767			0.903835	+	0.427881i	$0.140740\pi$
$182$	3.71851	+	0.996372i	0.275634	+	0.0738560i
$183$		0			0
$184$	−4.56277	−	2.63432i	−0.336372	−	0.194204i
$185$	10.3286	−	0.398466i	0.759377	−	0.0292958i
$186$		0			0
$187$	−0.174880	+	0.652663i	−0.0127885	+	0.0477274i
$188$	−2.45081	−	2.45081i	−0.178744	−	0.178744i
$189$		0			0
$190$	−2.24656	−	3.56619i	−0.162982	−	0.258718i
$191$	−11.8036	+	6.81478i	−0.854075	+	0.493100i	−0.862024	−	0.506868i	$-0.830803\pi$
$191$	−11.8036	+	6.81478i	−0.854075	+	0.493100i	0.00794868	+	0.999968i	$0.497470\pi$
$192$		0			0
$193$	−4.19397	−	15.6521i	−0.301889	−	1.12666i	−0.935591	−	0.353086i	$-0.885132\pi$
$193$	−4.19397	−	15.6521i	−0.301889	−	1.12666i	0.633702	−	0.773577i	$-0.281534\pi$
$194$	−0.748079	+	1.29571i	−0.0537090	+	0.0930267i
$195$		0			0
$196$	−4.05916	−	7.03067i	−0.289940	−	0.502191i
$197$	1.16085	−	1.16085i	0.0827072	−	0.0827072i	−0.664543	−	0.747250i	$-0.731374\pi$
$197$	1.16085	−	1.16085i	0.0827072	−	0.0827072i	0.747250	+	0.664543i	$0.231374\pi$
$198$		0			0
$199$		−	17.1733i		−	1.21738i	−0.793407	−	0.608691i	$-0.791695\pi$
$199$		−	17.1733i		−	1.21738i	0.793407	−	0.608691i	$-0.208305\pi$
$200$	3.25264	−	3.79741i	0.229996	−	0.268518i
$201$		0			0
$202$	9.94834	−	2.66565i	0.699963	−	0.187554i
$203$	16.1961	−	4.33973i	1.13674	−	0.304589i
$204$		0			0
$205$	−17.6538	+	5.46791i	−1.23300	+	0.381896i
$206$			6.48420i			0.451776i
$207$		0			0
$208$	0.700097	−	0.700097i	0.0485430	−	0.0485430i
$209$	−3.74498	−	6.48649i	−0.259046	−	0.448680i
$210$		0			0
$211$	−9.10894	+	15.7771i	−0.627085	+	1.08614i	0.361048	+	0.932547i	$0.382419\pi$
$211$	−9.10894	+	15.7771i	−0.627085	+	1.08614i	−0.988134	+	0.153597i	$0.950914\pi$
$212$	−1.34174	−	5.00745i	−0.0921513	−	0.343913i
$213$		0			0
$214$	4.53225	−	2.61670i	0.309818	−	0.178874i
$215$	−3.90338	+	2.45898i	−0.266208	+	0.167701i
$216$		0			0
$217$	−25.8537	−	25.8537i	−1.75507	−	1.75507i
$218$	−1.88979	+	7.05281i	−0.127993	+	0.477676i
$219$		0			0
$220$	6.03596	−	6.52036i	0.406944	−	0.439603i
$221$	0.145802	+	0.0841789i	0.00980771	+	0.00566249i
$222$		0			0
$223$	−4.53570	−	1.21534i	−0.303733	−	0.0813849i	0.103734	−	0.994605i	$-0.466921\pi$
$223$	−4.53570	−	1.21534i	−0.303733	−	0.0813849i	−0.407466	+	0.913220i	$0.633588\pi$
$224$	−3.88823			−0.259793
$225$		0			0
$226$	4.21934			0.280666
$227$	−24.1784	−	6.47859i	−1.60478	−	0.429999i	−0.658297	−	0.752758i	$-0.728723\pi$
$227$	−24.1784	−	6.47859i	−1.60478	−	0.429999i	−0.946481	+	0.322759i	$0.895390\pi$
$228$		0			0
$229$	19.7350	+	11.3940i	1.30412	+	0.752935i	0.981108	−	0.193459i	$-0.0619706\pi$
$229$	19.7350	+	11.3940i	1.30412	+	0.752935i	0.323014	+	0.946394i	$0.395304\pi$
$230$	−8.00311	+	8.64539i	−0.527709	+	0.570060i
$231$		0			0
$232$	1.11612	−	4.16541i	0.0732768	−	0.273473i
$233$	20.6491	+	20.6491i	1.35277	+	1.35277i	0.882553	+	0.470214i	$0.155823\pi$
$233$	20.6491	+	20.6491i	1.35277	+	1.35277i	0.470214	+	0.882553i	$0.344177\pi$
$234$		0			0
$235$	−6.55746	+	4.13094i	−0.427761	+	0.269473i
$236$	4.72637	−	2.72877i	0.307660	−	0.177628i
$237$		0			0
$238$	−0.171123	−	0.638639i	−0.0110922	−	0.0413968i
$239$	−4.56277	+	7.90295i	−0.295141	+	0.511199i	−0.975018	−	0.222127i	$-0.928700\pi$
$239$	−4.56277	+	7.90295i	−0.295141	+	0.511199i	0.679877	+	0.733327i	$0.262033\pi$
$240$		0			0
$241$	0.869654	+	1.50629i	0.0560194	+	0.0970284i	0.892675	−	0.450701i	$-0.148826\pi$
$241$	0.869654	+	1.50629i	0.0560194	+	0.0970284i	−0.836656	+	0.547729i	$0.815492\pi$
$242$	3.38674	−	3.38674i	0.217708	−	0.217708i
$243$		0			0
$244$		−	8.71245i		−	0.557758i
$245$	−17.3404	+	5.37084i	−1.10784	+	0.343130i
$246$		0			0
$247$	−1.80265	+	0.483018i	−0.114700	+	0.0307337i
$248$	−9.08302	+	2.43379i	−0.576773	+	0.154546i
$249$		0			0
$250$	−6.67037	−	8.97252i	−0.421871	−	0.567472i
$251$			6.16751i			0.389290i	0.980874	+	0.194645i	$0.0623555\pi$
$251$			6.16751i			0.389290i	−0.980874	+	0.194645i	$0.937645\pi$
$252$		0			0
$253$	−14.8036	+	14.8036i	−0.930696	+	0.930696i
$254$	9.74898	+	16.8857i	0.611706	+	1.05951i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.51956	−	28.0634i	−0.469057	−	1.75055i	−0.643075	−	0.765803i	$-0.722342\pi$
$257$	−7.51956	−	28.0634i	−0.469057	−	1.75055i	0.174018	−	0.984743i	$-0.444325\pi$
$258$		0			0
$259$	−15.5655	+	8.98676i	−0.967194	+	0.558410i
$260$	−1.18004	−	1.87320i	−0.0731830	−	0.116171i
$261$		0			0
$262$	3.17004	+	3.17004i	0.195846	+	0.195846i
$263$	4.82975	−	18.0249i	0.297815	−	1.11146i	−0.641141	−	0.767424i	$-0.721538\pi$
$263$	4.82975	−	18.0249i	0.297815	−	1.11146i	0.938956	−	0.344038i	$-0.111795\pi$
$264$		0			0
$265$	−11.5834	+	0.446872i	−0.711561	+	0.0274511i
$266$	6.34711	+	3.66451i	0.389167	+	0.224685i
$267$		0			0
$268$	7.86563	+	2.10759i	0.480470	+	0.128742i
$269$	−15.5553			−0.948425			−0.474212	−	0.880411i	$-0.657267\pi$
$269$	−15.5553			−0.948425			−0.474212	+	0.880411i	$0.657267\pi$
$270$		0			0
$271$	−1.87184			−0.113706			−0.0568532	−	0.998383i	$-0.518107\pi$
$271$	−1.87184			−0.113706			−0.0568532	+	0.998383i	$0.518107\pi$
$272$	−0.164249	−	0.0440105i	−0.00995908	−	0.00266853i
$273$		0			0
$274$	10.8243	+	6.24939i	0.653918	+	0.377540i
$275$	−11.2301	−	16.3898i	−0.677201	−	0.988339i
$276$		0			0
$277$	−1.06921	+	3.99035i	−0.0642426	+	0.239757i	−0.990579	−	0.136940i	$-0.956273\pi$
$277$	−1.06921	+	3.99035i	−0.0642426	+	0.239757i	0.926337	+	0.376696i	$0.122940\pi$
$278$	−2.94294	−	2.94294i	−0.176506	−	0.176506i
$279$		0			0
$280$	−1.92484	+	8.47860i	−0.115031	+	0.506693i
$281$	−0.248640	+	0.143552i	−0.0148326	+	0.00856361i	−0.507398	−	0.861712i	$-0.669393\pi$
$281$	−0.248640	+	0.143552i	−0.0148326	+	0.00856361i	0.492565	+	0.870275i	$0.336059\pi$
$282$		0			0
$283$	−4.68527	−	17.4857i	−0.278510	−	1.03941i	−0.953452	−	0.301544i	$-0.902498\pi$
$283$	−4.68527	−	17.4857i	−0.278510	−	1.03941i	0.674942	−	0.737871i	$-0.264169\pi$
$284$	−3.47456	+	6.01811i	−0.206177	+	0.357109i
$285$		0			0
$286$	−1.96711	−	3.40713i	−0.116318	−	0.201468i
$287$	22.7239	−	22.7239i	1.34135	−	1.34135i
$288$		0			0
$289$			16.9711i			0.998299i
$290$	−8.53050	−	4.49585i	−0.500928	−	0.264005i
$291$		0			0
$292$	−11.3070	+	3.02970i	−0.661691	+	0.177300i
$293$	−20.6663	+	5.53752i	−1.20734	+	0.323505i	−0.805717	−	0.592300i	$-0.798220\pi$
$293$	−20.6663	+	5.53752i	−1.20734	+	0.323505i	−0.401621	+	0.915806i	$0.631553\pi$
$294$		0			0
$295$	−3.61054	−	11.6571i	−0.210214	−	0.678702i
$296$			4.62255i			0.268680i
$297$		0			0
$298$	0.732907	−	0.732907i	0.0424562	−	0.0424562i
$299$	2.60820	+	4.51754i	0.150836	+	0.261256i
$300$		0			0
$301$	4.01100	−	6.94725i	0.231190	−	0.400433i
$302$	−1.05314	−	3.93037i	−0.0606014	−	0.226168i
$303$		0			0
$304$	1.63239	−	0.942462i	0.0936241	−	0.0540539i
$305$	−18.9982	−	4.31304i	−1.08783	−	0.246964i
$306$		0			0
$307$	−20.2953	−	20.2953i	−1.15831	−	1.15831i	−0.984838	−	0.173476i	$-0.944500\pi$
$307$	−20.2953	−	20.2953i	−1.15831	−	1.15831i	−0.173476	−	0.984838i	$-0.555500\pi$
$308$	−3.99883	+	14.9238i	−0.227855	+	0.850365i
$309$		0			0
$310$	0.810581	+	21.0111i	0.0460379	+	1.19335i
$311$	11.9868	+	6.92056i	0.679707	+	0.392429i	0.799745	−	0.600340i	$-0.204968\pi$
$311$	11.9868	+	6.92056i	0.679707	+	0.392429i	−0.120038	+	0.992769i	$0.538302\pi$
$312$		0			0
$313$	17.9081	+	4.79847i	1.01223	+	0.271226i	0.726560	−	0.687103i	$-0.241118\pi$
$313$	17.9081	+	4.79847i	1.01223	+	0.271226i	0.285668	+	0.958329i	$0.407785\pi$
$314$	−9.12554			−0.514984
$315$		0			0
$316$	13.5711			0.763431
$317$	−0.811966	−	0.217566i	−0.0456046	−	0.0122197i	0.235945	−	0.971766i	$-0.424182\pi$
$317$	−0.811966	−	0.217566i	−0.0456046	−	0.0122197i	−0.281549	+	0.959547i	$0.590848\pi$
$318$		0			0
$319$	−14.8399	−	8.56781i	−0.830874	−	0.479705i
$320$	1.64092	+	1.51901i	0.0917300	+	0.0849153i
$321$		0			0
$322$	5.30208	−	19.7876i	0.295473	−	1.10272i
$323$	0.226641	+	0.226641i	0.0126107	+	0.0126107i
$324$		0			0
$325$	−4.66883	+	1.64586i	−0.258980	+	0.0912958i
$326$	6.17086	−	3.56275i	0.341772	−	0.197322i
$327$		0			0
$328$	−2.13915	−	7.98343i	−0.118115	−	0.440811i
$329$	6.73825	−	11.6710i	0.371492	−	0.643443i
$330$		0			0
$331$	2.08211	+	3.60631i	0.114443	+	0.198221i	0.917557	−	0.397604i	$-0.130158\pi$
$331$	2.08211	+	3.60631i	0.114443	+	0.198221i	−0.803114	+	0.595825i	$0.796825\pi$
$332$	−4.94803	+	4.94803i	−0.271558	+	0.271558i
$333$		0			0
$334$			10.8332i			0.592766i
$335$	8.48960	−	16.1083i	0.463836	−	0.880090i
$336$		0			0
$337$	3.13777	−	0.840764i	0.170925	−	0.0457993i	−0.172341	−	0.985037i	$-0.555133\pi$
$337$	3.13777	−	0.840764i	0.170925	−	0.0457993i	0.343267	+	0.939238i	$0.388467\pi$
$338$	11.6102	−	3.11093i	0.631510	−	0.169213i
$339$		0			0
$340$	−0.177279	+	0.336372i	−0.00961430	+	0.0182423i
$341$			37.3656i			2.02346i
$342$		0			0
$343$	3.07470	−	3.07470i	0.166018	−	0.166018i
$344$	−1.03157	−	1.78674i	−0.0556188	−	0.0963346i
$345$		0			0
$346$	−1.88492	+	3.26478i	−0.101334	+	0.175516i
$347$	−1.21470	−	4.53334i	−0.0652087	−	0.243362i	0.925627	−	0.378438i	$-0.123539\pi$
$347$	−1.21470	−	4.53334i	−0.0652087	−	0.243362i	−0.990835	+	0.135076i	$0.956872\pi$
$348$		0			0
$349$	8.42818	−	4.86601i	0.451150	−	0.260472i	−0.257166	−	0.966367i	$-0.582789\pi$
$349$	8.42818	−	4.86601i	0.451150	−	0.260472i	0.708316	+	0.705896i	$0.249455\pi$
$350$	17.5354	+	8.39455i	0.937305	+	0.448707i
$351$		0			0
$352$	2.80977	+	2.80977i	0.149761	+	0.149761i
$353$	1.32049	−	4.92815i	0.0702827	−	0.262299i	−0.921840	−	0.387572i	$-0.873314\pi$
$353$	1.32049	−	4.92815i	0.0702827	−	0.262299i	0.992122	+	0.125273i	$0.0399806\pi$
$354$		0			0
$355$	11.4029	+	10.5558i	0.605204	+	0.560242i
$356$	4.22474	+	2.43916i	0.223911	+	0.129275i
$357$		0			0
$358$	−12.4559	−	3.33754i	−0.658312	−	0.176394i
$359$	−1.27697			−0.0673957			−0.0336978	−	0.999432i	$-0.510728\pi$
$359$	−1.27697			−0.0673957			−0.0336978	+	0.999432i	$0.510728\pi$
$360$		0			0
$361$	15.4471			0.813003
$362$	23.4910	+	6.29441i	1.23466	+	0.330827i
$363$		0			0
$364$	3.33392	+	1.92484i	0.174745	+	0.100889i
$365$	1.00905	+	26.1556i	0.0528161	+	1.36905i
$366$		0			0
$367$	−2.61063	+	9.74300i	−0.136274	+	0.508581i	0.863716	+	0.503979i	$0.168131\pi$
$367$	−2.61063	+	9.74300i	−0.136274	+	0.508581i	−0.999989	+	0.00460117i	$0.998535\pi$
$368$	−3.72549	−	3.72549i	−0.194204	−	0.194204i
$369$		0			0
$370$	10.0798	+	2.28836i	0.524026	+	0.118966i
$371$	17.4564	−	10.0785i	0.906293	−	0.523249i
$372$		0			0
$373$	−3.39374	−	12.6656i	−0.175721	−	0.655801i	−0.996428	−	0.0844507i	$-0.973086\pi$
$373$	−3.39374	−	12.6656i	−0.175721	−	0.655801i	0.820706	−	0.571350i	$-0.193580\pi$
$374$	−0.337843	+	0.585162i	−0.0174695	+	0.0302580i
$375$		0			0
$376$	−1.73299	−	3.00162i	−0.0893720	−	0.154797i
$377$	−3.01907	+	3.01907i	−0.155490	+	0.155490i
$378$		0			0
$379$			0.587648i			0.0301854i	0.999886	+	0.0150927i	$0.00480434\pi$
$379$			0.587648i			0.0301854i	−0.999886	+	0.0150927i	$0.995196\pi$
$380$	−1.24701	−	4.02612i	−0.0639702	−	0.206536i
$381$		0			0
$382$	−13.1652	+	3.52759i	−0.673588	+	0.180487i
$383$	−14.0071	+	3.75319i	−0.715729	+	0.191779i	−0.598265	−	0.801298i	$-0.704143\pi$
$383$	−14.0071	+	3.75319i	−0.715729	+	0.191779i	−0.117464	+	0.993077i	$0.537476\pi$
$384$		0			0
$385$	30.5631	+	16.1077i	1.55764	+	0.820926i
$386$		−	16.2043i		−	0.824775i
$387$		0			0
$388$	−1.05794	+	1.05794i	−0.0537090	+	0.0537090i
$389$	10.3789	+	17.9767i	0.526230	+	0.911456i	0.999533	+	0.0305570i	$0.00972810\pi$
$389$	10.3789	+	17.9767i	0.526230	+	0.911456i	−0.473303	+	0.880899i	$0.656939\pi$
$390$		0			0
$391$	0.447948	−	0.775869i	0.0226537	−	0.0392374i
$392$	−2.10118	−	7.84169i	−0.106125	−	0.396065i
$393$		0			0
$394$	1.42175	−	0.820845i	0.0716265	−	0.0413536i
$395$	6.71826	−	29.5928i	0.338032	−	1.48897i
$396$		0			0
$397$	15.7430	+	15.7430i	0.790118	+	0.790118i	0.981513	−	0.191395i	$-0.0613012\pi$
$397$	15.7430	+	15.7430i	0.790118	+	0.790118i	−0.191395	+	0.981513i	$0.561301\pi$
$398$	4.44477	−	16.5881i	0.222796	−	0.831487i
$399$		0			0
$400$	4.12465	−	2.82617i	0.206233	−	0.141309i
$401$	−4.11737	−	2.37716i	−0.205612	−	0.118710i	0.393659	−	0.919257i	$-0.371209\pi$
$401$	−4.11737	−	2.37716i	−0.205612	−	0.118710i	−0.599270	+	0.800547i	$0.704543\pi$
$402$		0			0
$403$	8.99298	+	2.40966i	0.447972	+	0.120034i
$404$	10.2993			0.512408
$405$		0			0
$406$	16.7674			0.832153
$407$	17.7423	+	4.75404i	0.879454	+	0.235649i
$408$		0			0
$409$	−25.8797	−	14.9417i	−1.27967	−	0.738817i	−0.302882	−	0.953028i	$-0.597949\pi$
$409$	−25.8797	−	14.9417i	−1.27967	−	0.738817i	−0.976787	+	0.214211i	$0.931282\pi$
$410$	−18.4675	+	0.712452i	−0.912044	+	0.0351855i
$411$		0			0
$412$	−1.67823	+	6.26326i	−0.0826807	+	0.308568i
$413$	15.0049	+	15.0049i	0.738343	+	0.738343i
$414$		0			0
$415$	8.34009	+	13.2391i	0.409399	+	0.649880i
$416$	0.857441	−	0.495044i	0.0420395	−	0.0242715i
$417$		0			0
$418$	−1.93854	−	7.23474i	−0.0948172	−	0.353863i
$419$	−8.81638	+	15.2704i	−0.430708	+	0.746009i	−0.996934	−	0.0782412i	$-0.975070\pi$
$419$	−8.81638	+	15.2704i	−0.430708	+	0.746009i	0.566226	+	0.824250i	$0.308403\pi$
$420$		0			0
$421$	13.9462	+	24.1555i	0.679696	+	1.17727i	0.975072	+	0.221887i	$0.0712215\pi$
$421$	13.9462	+	24.1555i	0.679696	+	1.17727i	−0.295377	+	0.955381i	$0.595445\pi$
$422$	−12.8820	+	12.8820i	−0.627085	+	0.627085i
$423$		0			0
$424$		−	5.18410i		−	0.251762i
$425$	0.645725	+	0.553090i	0.0313223	+	0.0268288i
$426$		0			0
$427$	32.7217	−	8.76775i	1.58351	−	0.424301i
$428$	5.05507	−	1.35450i	0.244346	−	0.0654723i
$429$		0			0
$430$	−4.40681	+	1.36492i	−0.212515	+	0.0658222i
$431$			19.2910i			0.929215i	0.885517	+	0.464608i	$0.153805\pi$
$431$			19.2910i			0.929215i	−0.885517	+	0.464608i	$0.846195\pi$
$432$		0			0
$433$	16.7154	−	16.7154i	0.803292	−	0.803292i	−0.180316	−	0.983609i	$-0.557712\pi$
$433$	16.7154	−	16.7154i	0.803292	−	0.803292i	0.983609	+	0.180316i	$0.0577122\pi$
$434$	−18.2814	−	31.6642i	−0.877533	−	1.51993i
$435$		0			0
$436$	−3.65080	+	6.32337i	−0.174842	+	0.302835i
$437$	2.57033	+	9.59259i	0.122955	+	0.458876i
$438$		0			0
$439$	−31.1811	+	18.0024i	−1.48819	+	0.859209i	−0.999909	−	0.0134750i	$-0.995711\pi$
$439$	−31.1811	+	18.0024i	−1.48819	+	0.859209i	−0.488285	+	0.872684i	$0.662377\pi$
$440$	7.51788	−	4.73597i	0.358401	−	0.225778i
$441$		0			0
$442$	0.119047	+	0.119047i	0.00566249	+	0.00566249i
$443$	6.94511	−	25.9195i	0.329972	−	1.23147i	−0.579246	−	0.815153i	$-0.696653\pi$
$443$	6.94511	−	25.9195i	0.329972	−	1.23147i	0.909218	−	0.416320i	$-0.136680\pi$
$444$		0			0
$445$	7.41021	−	8.00491i	0.351278	−	0.379469i
$446$	−4.06659	−	2.34785i	−0.192559	−	0.111174i
$447$		0			0
$448$	−3.75574	−	1.00635i	−0.177442	−	0.0475455i
$449$	41.3392			1.95092			0.975459	−	0.220182i	$-0.0706652\pi$
$449$	41.3392			1.95092			0.975459	+	0.220182i	$0.0706652\pi$
$450$		0			0
$451$	−32.8421			−1.54647
$452$	4.07557	+	1.09205i	0.191699	+	0.0513655i
$453$		0			0
$454$	−21.6778	−	12.5157i	−1.01739	−	0.587390i
$455$	5.84771	−	6.31701i	0.274145	−	0.296146i
$456$		0			0
$457$	5.58827	−	20.8557i	0.261408	−	0.975589i	−0.703004	−	0.711186i	$-0.748158\pi$
$457$	5.58827	−	20.8557i	0.261408	−	0.975589i	0.964412	−	0.264403i	$-0.0851750\pi$
$458$	16.1135	+	16.1135i	0.752935	+	0.752935i
$459$		0			0
$460$	−9.96800	+	6.27945i	−0.464761	+	0.292781i
$461$	10.8706	−	6.27615i	0.506295	−	0.292309i	−0.225015	−	0.974355i	$-0.572243\pi$
$461$	10.8706	−	6.27615i	0.506295	−	0.292309i	0.731309	+	0.682046i	$0.238910\pi$
$462$		0			0
$463$	5.72110	+	21.3514i	0.265882	+	0.992286i	0.961708	+	0.274076i	$0.0883718\pi$
$463$	5.72110	+	21.3514i	0.265882	+	0.992286i	−0.695826	+	0.718210i	$0.744962\pi$
$464$	2.15618	−	3.73461i	0.100098	−	0.173375i
$465$		0			0
$466$	14.6011	+	25.2899i	0.676383	+	1.17153i
$467$	−3.48137	+	3.48137i	−0.161099	+	0.161099i	−0.783053	−	0.621955i	$-0.786339\pi$
$467$	−3.48137	+	3.48137i	−0.161099	+	0.161099i	0.621955	+	0.783053i	$0.286339\pi$
$468$		0			0
$469$			31.6622i			1.46203i
$470$	−7.40318	+	2.29299i	−0.341483	+	0.105768i
$471$		0			0
$472$	5.27158	−	1.41251i	0.242644	−	0.0650163i
$473$	−7.91881	+	2.12184i	−0.364107	+	0.0975622i
$474$		0			0
$475$	−9.39661	+	0.726099i	−0.431146	+	0.0333157i
$476$		−	0.661168i		−	0.0303046i
$477$		0			0
$478$	−6.45273	+	6.45273i	−0.295141	+	0.295141i
$479$	1.35673	+	2.34993i	0.0619906	+	0.107371i	0.895355	−	0.445353i	$-0.146922\pi$
$479$	1.35673	+	2.34993i	0.0619906	+	0.107371i	−0.833364	+	0.552724i	$0.813588\pi$
$480$		0			0
$481$	2.28836	−	3.96356i	0.104340	−	0.180723i
$482$	0.450166	+	1.68004i	0.0205045	+	0.0765239i
$483$		0			0
$484$	4.14790	−	2.39479i	0.188541	−	0.108854i
$485$	1.78320	+	2.83066i	0.0809711	+	0.128534i
$486$		0			0
$487$	−8.20799	−	8.20799i	−0.371940	−	0.371940i	0.496244	−	0.868183i	$-0.334712\pi$
$487$	−8.20799	−	8.20799i	−0.371940	−	0.371940i	−0.868183	+	0.496244i	$0.834712\pi$
$488$	2.25495	−	8.41558i	0.102077	−	0.380955i
$489$		0			0
$490$	−18.1396	+	0.699803i	−0.819464	+	0.0316139i
$491$	−4.28058	−	2.47139i	−0.193180	−	0.111532i	0.400290	−	0.916388i	$-0.368909\pi$
$491$	−4.28058	−	2.47139i	−0.193180	−	0.111532i	−0.593470	+	0.804856i	$0.702243\pi$
$492$		0			0
$493$	0.708301	+	0.189789i	0.0319003	+	0.00854766i
$494$	−1.86624			−0.0839661
$495$		0			0
$496$	−9.40344			−0.422227
$497$	−26.0991	−	6.99322i	−1.17070	−	0.313689i
$498$		0			0
$499$	28.1148	+	16.2321i	1.25859	+	0.726649i	0.972801	−	0.231643i	$-0.0744102\pi$
$499$	28.1148	+	16.2321i	1.25859	+	0.726649i	0.285791	+	0.958292i	$0.407744\pi$
$500$	−4.12082	−	10.3932i	−0.184289	−	0.464799i
$501$		0			0
$502$	−1.59627	+	5.95736i	−0.0712450	+	0.265890i
$503$	−19.6817	−	19.6817i	−0.877565	−	0.877565i	0.115717	−	0.993282i	$-0.463083\pi$
$503$	−19.6817	−	19.6817i	−0.877565	−	0.877565i	−0.993282	+	0.115717i	$0.963083\pi$
$504$		0			0
$505$	5.09859	−	22.4584i	0.226884	−	0.999386i
$506$	−18.1307	+	10.4677i	−0.806007	+	0.465348i
$507$		0			0
$508$	5.04645	+	18.8336i	0.223900	+	0.835606i
$509$	5.25069	−	9.09446i	0.232733	−	0.403105i	−0.725879	−	0.687823i	$-0.758567\pi$
$509$	5.25069	−	9.09446i	0.232733	−	0.403105i	0.958611	+	0.284718i	$0.0918999\pi$
$510$		0			0
$511$	−22.7575	−	39.4171i	−1.00673	−	1.74371i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	29.0534i		−	1.28149i
$515$	12.8267	+	6.76011i	0.565214	+	0.297886i
$516$		0			0
$517$	−13.3031	+	3.56457i	−0.585072	+	0.156770i
$518$	−17.3611	+	4.65189i	−0.762802	+	0.204392i
$519$		0			0
$520$	−0.655012	−	2.11479i	−0.0287242	−	0.0927395i
$521$		−	28.2545i		−	1.23785i	−0.785450	−	0.618925i	$-0.787568\pi$
$521$		−	28.2545i		−	1.23785i	0.785450	−	0.618925i	$-0.212432\pi$
$522$		0			0
$523$	13.6590	−	13.6590i	0.597266	−	0.597266i	−0.342318	−	0.939584i	$-0.611212\pi$
$523$	13.6590	−	13.6590i	0.597266	−	0.597266i	0.939584	+	0.342318i	$0.111212\pi$
$524$	2.24156	+	3.88249i	0.0979230	+	0.169608i
$525$		0			0
$526$	9.33036	−	16.1607i	0.406823	−	0.704638i
$527$	−0.413850	−	1.54451i	−0.0180276	−	0.0672798i
$528$		0			0
$529$	4.12099	−	2.37925i	0.179173	−	0.103446i
$530$	−11.3043	−	2.56635i	−0.491029	−	0.111475i
$531$		0			0
$532$	5.18240	+	5.18240i	0.224685	+	0.224685i
$533$	−2.11795	+	7.90429i	−0.0917385	+	0.342373i
$534$		0			0
$535$	−0.451121	−	11.6935i	−0.0195037	−	0.505555i
$536$	7.05213	+	4.07155i	0.304606	+	0.175864i
$537$		0			0
$538$	−15.0253	−	4.02601i	−0.647786	−	0.173574i
$539$	−32.2590			−1.38949
$540$		0			0
$541$	−26.7216			−1.14885			−0.574427	−	0.818556i	$-0.694775\pi$
$541$	−26.7216			−1.14885			−0.574427	+	0.818556i	$0.694775\pi$
$542$	−1.80806	−	0.484468i	−0.0776628	−	0.0208097i
$543$		0			0
$544$	−0.147262	−	0.0850217i	−0.00631380	−	0.00364528i
$545$	11.9813	+	11.0912i	0.513223	+	0.475095i
$546$		0			0
$547$	0.0627654	−	0.234244i	0.00268365	−	0.0100155i	−0.964571	−	0.263823i	$-0.915016\pi$
$547$	0.0627654	−	0.234244i	0.00268365	−	0.0100155i	0.967255	+	0.253808i	$0.0816831\pi$
$548$	8.83798	+	8.83798i	0.377540	+	0.377540i
$549$		0			0
$550$	−6.60548	−	18.7379i	−0.281659	−	0.798985i
$551$	−7.03946	+	4.06423i	−0.299891	+	0.173142i
$552$		0			0
$553$	13.6572	+	50.9693i	0.580763	+	2.16744i
$554$	−2.06556	+	3.57765i	−0.0877571	+	0.152000i
$555$		0			0
$556$	−2.08097	−	3.60435i	−0.0882528	−	0.152858i
$557$	−31.4838	+	31.4838i	−1.33401	+	1.33401i	−0.432266	+	0.901746i	$0.642286\pi$
$557$	−31.4838	+	31.4838i	−1.33401	+	1.33401i	−0.901746	+	0.432266i	$0.857714\pi$
$558$		0			0
$559$			2.04270i			0.0863969i
$560$	−4.05368	+	7.69151i	−0.171299	+	0.325026i
$561$		0			0
$562$	−0.277322	+	0.0743081i	−0.0116981	+	0.00313450i
$563$	−31.1771	+	8.35388i	−1.31396	+	0.352074i	−0.846711	−	0.532053i	$-0.821421\pi$
$563$	−31.1771	+	8.35388i	−1.31396	+	0.352074i	−0.467247	+	0.884127i	$0.654754\pi$
$564$		0			0
$565$	4.39888	−	8.34650i	0.185062	−	0.351140i
$566$		−	18.1025i		−	0.760904i
$567$		0			0
$568$	−4.91376	+	4.91376i	−0.206177	+	0.206177i
$569$	16.1545	+	27.9804i	0.677232	+	1.17300i	0.975811	+	0.218615i	$0.0701538\pi$
$569$	16.1545	+	27.9804i	0.677232	+	1.17300i	−0.298580	+	0.954385i	$0.596513\pi$
$570$		0			0
$571$	12.9565	−	22.4413i	0.542213	−	0.939141i	−0.456563	−	0.889691i	$-0.650920\pi$
$571$	12.9565	−	22.4413i	0.542213	−	0.939141i	0.998777	−	0.0494501i	$-0.0157469\pi$
$572$	−1.01825	−	3.80016i	−0.0425752	−	0.158893i
$573$		0			0
$574$	27.8310	−	16.0682i	1.16164	−	0.670674i
$575$	8.75824	+	24.8446i	0.365244	+	1.03609i
$576$		0			0
$577$	6.10724	+	6.10724i	0.254248	+	0.254248i	0.822710	−	0.568462i	$-0.192461\pi$
$577$	6.10724	+	6.10724i	0.254248	+	0.254248i	−0.568462	+	0.822710i	$0.692461\pi$
$578$	−4.39244	+	16.3928i	−0.182701	+	0.681851i
$579$		0			0
$580$	−7.07621	−	6.55051i	−0.293824	−	0.271995i
$581$	−23.5629	−	13.6041i	−0.977556	−	0.564392i
$582$		0			0
$583$	−19.8977	−	5.33157i	−0.824077	−	0.220811i
$584$	−11.7058			−0.484391
$585$		0			0
$586$	−21.3953			−0.883833
$587$	−1.83025	−	0.490414i	−0.0755424	−	0.0202415i	0.220850	−	0.975308i	$-0.429117\pi$
$587$	−1.83025	−	0.490414i	−0.0755424	−	0.0202415i	−0.296392	+	0.955066i	$0.595784\pi$
$588$		0			0
$589$	15.3501	+	8.86238i	0.632490	+	0.365168i
$590$	−0.470442	−	12.1944i	−0.0193678	−	0.502034i
$591$		0			0
$592$	−1.19640	+	4.46504i	−0.0491719	+	0.183512i
$593$	11.0077	+	11.0077i	0.452033	+	0.452033i	0.896029	−	0.443996i	$-0.146439\pi$
$593$	11.0077	+	11.0077i	0.452033	+	0.452033i	−0.443996	+	0.896029i	$0.646439\pi$
$594$		0			0
$595$	−1.44173	−	0.327307i	−0.0591051	−	0.0134183i
$596$	0.897625	−	0.518244i	0.0367681	−	0.0212281i
$597$		0			0
$598$	1.35011	+	5.03866i	0.0552099	+	0.206046i
$599$	12.9428	−	22.4176i	0.528828	−	0.915957i	−0.470607	−	0.882343i	$-0.655965\pi$
$599$	12.9428	−	22.4176i	0.528828	−	0.915957i	0.999435	−	0.0336142i	$-0.0107018\pi$
$600$		0			0
$601$	−9.79604	−	16.9672i	−0.399589	−	0.692108i	0.594086	−	0.804401i	$-0.297514\pi$
$601$	−9.79604	−	16.9672i	−0.399589	−	0.692108i	−0.993675	+	0.112293i	$0.964180\pi$
$602$	5.67241	−	5.67241i	0.231190	−	0.231190i
$603$		0			0
$604$		−	4.06902i		−	0.165566i
$605$	−3.16864	−	10.2303i	−0.128824	−	0.415923i
$606$		0			0
$607$	−28.7731	+	7.70972i	−1.16786	+	0.312928i	−0.790102	−	0.612975i	$-0.789973\pi$
$607$	−28.7731	+	7.70972i	−1.16786	+	0.312928i	−0.377761	+	0.925903i	$0.623306\pi$
$608$	1.82070	−	0.487854i	0.0738390	−	0.0197851i
$609$		0			0
$610$	−17.2346	−	9.08318i	−0.697807	−	0.367767i
$611$			3.43162i			0.138828i
$612$		0			0
$613$	−12.5028	+	12.5028i	−0.504982	+	0.504982i	−0.912982	−	0.408000i	$-0.866226\pi$
$613$	−12.5028	+	12.5028i	−0.504982	+	0.504982i	0.408000	+	0.912982i	$0.366226\pi$
$614$	−14.3510	−	24.8566i	−0.579157	−	1.00313i
$615$		0			0
$616$	−7.72515	+	13.3804i	−0.311255	+	0.539110i
$617$	1.91482	+	7.14621i	0.0770878	+	0.287695i	0.993699	−	0.112085i	$-0.0357530\pi$
$617$	1.91482	+	7.14621i	0.0770878	+	0.287695i	−0.916611	+	0.399781i	$0.869086\pi$
$618$		0			0
$619$	16.4624	−	9.50460i	0.661682	−	0.382022i	−0.131236	−	0.991351i	$-0.541895\pi$
$619$	16.4624	−	9.50460i	0.661682	−	0.382022i	0.792917	+	0.609329i	$0.208561\pi$
$620$	−4.65511	+	20.5050i	−0.186954	+	0.823499i
$621$		0			0
$622$	9.78715	+	9.78715i	0.392429	+	0.392429i
$623$	−4.90928	+	18.3217i	−0.196686	+	0.734043i
$624$		0			0
$625$	−24.7032	+	3.84069i	−0.988129	+	0.153628i
$626$	16.0560	+	9.26994i	0.641727	+	0.370501i
$627$		0			0
$628$	−8.81460	−	2.36186i	−0.351741	−	0.0942486i
$629$	−0.786034			−0.0313412
$630$		0			0
$631$	−2.22853			−0.0887165			−0.0443583	−	0.999016i	$-0.514124\pi$
$631$	−2.22853			−0.0887165			−0.0443583	+	0.999016i	$0.514124\pi$
$632$	13.1086	+	3.51245i	0.521433	+	0.139718i
$633$		0			0
$634$	−0.727989	−	0.420305i	−0.0289121	−	0.0166924i
$635$	43.5664	−	1.68073i	1.72888	−	0.0666979i
$636$		0			0
$637$	−2.08035	+	7.76396i	−0.0824263	+	0.307619i
$638$	−12.1167	−	12.1167i	−0.479705	−	0.479705i
$639$		0			0
$640$	1.19185	+	1.89195i	0.0471122	+	0.0747860i
$641$	−37.8297	+	21.8410i	−1.49418	+	0.862666i	−0.999978	−	0.00667968i	$-0.997874\pi$
$641$	−37.8297	+	21.8410i	−1.49418	+	0.862666i	−0.494204	+	0.869346i	$0.664540\pi$
$642$		0			0
$643$	−7.89483	−	29.4639i	−0.311342	−	1.16194i	−0.927347	−	0.374202i	$-0.877917\pi$
$643$	−7.89483	−	29.4639i	−0.311342	−	1.16194i	0.616006	−	0.787742i	$-0.288750\pi$
$644$	10.2428	−	17.7411i	0.403624	−	0.699097i
$645$		0			0
$646$	0.160260	+	0.277578i	0.00630533	+	0.0109211i
$647$	4.02651	−	4.02651i	0.158298	−	0.158298i	−0.623514	−	0.781812i	$-0.714296\pi$
$647$	4.02651	−	4.02651i	0.158298	−	0.158298i	0.781812	+	0.623514i	$0.214296\pi$
$648$		0			0
$649$		−	21.6861i		−	0.851255i
$650$	−4.93572	+	0.381395i	−0.193595	+	0.0149595i
$651$		0			0
$652$	6.88270	−	1.84421i	0.269547	−	0.0722249i
$653$	31.5015	−	8.44081i	1.23275	−	0.330314i	0.417100	−	0.908861i	$-0.363046\pi$
$653$	31.5015	−	8.44081i	1.23275	−	0.330314i	0.815650	+	0.578546i	$0.196380\pi$
$654$		0			0
$655$	9.57576	−	2.96590i	0.374156	−	0.115887i
$656$		−	8.26506i		−	0.322696i
$657$		0			0
$658$	9.52933	−	9.52933i	0.371492	−	0.371492i
$659$	−7.75612	−	13.4340i	−0.302136	−	0.523314i	0.674484	−	0.738290i	$-0.264366\pi$
$659$	−7.75612	−	13.4340i	−0.302136	−	0.523314i	−0.976619	+	0.214975i	$0.931033\pi$
$660$		0			0
$661$	11.1307	−	19.2789i	0.432933	−	0.749862i	−0.564191	−	0.825644i	$-0.690812\pi$
$661$	11.1307	−	19.2789i	0.432933	−	0.749862i	0.997124	+	0.0757821i	$0.0241453\pi$
$662$	1.07778	+	4.02232i	0.0418890	+	0.156332i
$663$		0			0
$664$	−6.06007	+	3.49878i	−0.235176	+	0.135779i
$665$	13.8661	−	8.73512i	0.537706	−	0.338734i
$666$		0			0
$667$	16.0656	+	16.0656i	0.622063	+	0.622063i
$668$	−2.80384	+	10.4641i	−0.108484	+	0.404867i
$669$		0			0
$670$	12.3695	−	13.3621i	0.477874	−	0.516225i
$671$	−29.9817	−	17.3099i	−1.15743	−	0.668243i
$672$		0			0
$673$	−9.32657	−	2.49905i	−0.359513	−	0.0963312i	0.0745413	−	0.997218i	$-0.476251\pi$
$673$	−9.32657	−	2.49905i	−0.359513	−	0.0963312i	−0.434054	+	0.900887i	$0.642917\pi$
$674$	3.24846			0.125126
$675$		0			0
$676$	12.0197			0.462297
$677$	−7.30994	−	1.95869i	−0.280944	−	0.0752787i	0.115596	−	0.993296i	$-0.463122\pi$
$677$	−7.30994	−	1.95869i	−0.280944	−	0.0752787i	−0.396539	+	0.918018i	$0.629789\pi$
$678$		0			0
$679$	−5.03802	−	2.90870i	−0.193342	−	0.111626i
$680$	−0.258298	+	0.279027i	−0.00990527	+	0.0107002i
$681$		0			0
$682$	−9.67093	+	36.0924i	−0.370319	+	1.38205i
$683$	−7.48288	−	7.48288i	−0.286325	−	0.286325i	0.549300	−	0.835625i	$-0.314894\pi$
$683$	−7.48288	−	7.48288i	−0.286325	−	0.286325i	−0.835625	+	0.549300i	$0.814894\pi$
$684$		0			0
$685$	23.6471	−	14.8967i	0.903509	−	0.569175i
$686$	3.76572	−	2.17414i	0.143776	−	0.0830090i
$687$		0			0
$688$	−0.533983	−	1.99285i	−0.0203579	−	0.0759767i
$689$	−2.56635	+	4.44506i	−0.0977703	+	0.169343i
$690$		0			0
$691$	21.3061	+	36.9033i	0.810523	+	1.40387i	0.912498	+	0.409080i	$0.134150\pi$
$691$	21.3061	+	36.9033i	0.810523	+	1.40387i	−0.101975	+	0.994787i	$0.532516\pi$
$692$	−2.66569	+	2.66569i	−0.101334	+	0.101334i
$693$		0			0
$694$		−	4.69326i		−	0.178154i
$695$	−8.88974	+	2.75342i	−0.337207	+	0.104443i
$696$		0			0
$697$	1.35753	−	0.363749i	0.0514201	−	0.0137780i
$698$	9.40041	−	2.51883i	0.355811	−	0.0953392i
$699$		0			0
$700$	14.7652	+	12.6470i	0.558072	+	0.478012i
$701$		−	36.3602i		−	1.37331i	−0.726985	−	0.686653i	$-0.759079\pi$
$701$		−	36.3602i		−	1.37331i	0.726985	−	0.686653i	$-0.240921\pi$
$702$		0			0
$703$	6.16113	−	6.16113i	0.232371	−	0.232371i
$704$	1.98681	+	3.44125i	0.0748805	+	0.129697i
$705$		0			0
$706$	2.55100	−	4.41846i	0.0960080	−	0.166291i
$707$	10.3647	+	38.6814i	0.389803	+	1.45476i
$708$		0			0
$709$	−0.356646	+	0.205910i	−0.0133941	+	0.00773310i	−0.506682	−	0.862133i	$-0.669128\pi$
$709$	−0.356646	+	0.205910i	−0.0133941	+	0.00773310i	0.493288	+	0.869866i	$0.335795\pi$
$710$	8.28233	+	13.1474i	0.310830	+	0.493413i
$711$		0			0
$712$	3.44949	+	3.44949i	0.129275	+	0.129275i
$713$	12.8227	−	47.8551i	0.480215	−	1.79219i
$714$		0			0
$715$	−8.79064	+	0.339132i	−0.328751	+	0.0126828i
$716$	−11.1676	−	6.44762i	−0.417353	−	0.240959i
$717$		0			0
$718$	−1.23345	−	0.330503i	−0.0460321	−	0.0123343i
$719$	34.4664			1.28538			0.642690	−	0.766126i	$-0.277818\pi$
$719$	34.4664			1.28538			0.642690	+	0.766126i	$0.277818\pi$
$720$		0			0
$721$	−25.2120			−0.938946
$722$	14.9207	+	3.99799i	0.555291	+	0.148790i
$723$		0			0
$724$	21.0615	+	12.1599i	0.782744	+	0.451918i
$725$	−17.7870	+	12.1875i	−0.660591	+	0.452631i
$726$		0			0
$727$	3.69508	−	13.7902i	0.137043	−	0.511451i	−0.862938	−	0.505310i	$-0.831378\pi$
$727$	3.69508	−	13.7902i	0.137043	−	0.511451i	0.999981	−	0.00614188i	$-0.00195503\pi$
$728$	2.72214	+	2.72214i	0.100889	+	0.100889i
$729$		0			0
$730$	−5.79490	+	25.5255i	−0.214479	+	0.944743i
$731$	0.303823	−	0.175413i	0.0112373	−	0.00648787i
$732$		0			0
$733$	7.94942	+	29.6676i	0.293618	+	1.09580i	0.942308	+	0.334746i	$0.108651\pi$
$733$	7.94942	+	29.6676i	0.293618	+	1.09580i	−0.648690	+	0.761053i	$0.724683\pi$
$734$	−5.04335	+	8.73534i	−0.186153	+	0.322427i
$735$		0			0
$736$	−2.63432	−	4.56277i	−0.0971022	−	0.168186i
$737$	22.8802	−	22.8802i	0.842803	−	0.842803i
$738$		0			0
$739$		−	19.6312i		−	0.722144i	−0.932538	−	0.361072i	$-0.882411\pi$
$739$		−	19.6312i		−	0.722144i	0.932538	−	0.361072i	$-0.117589\pi$
$740$	9.14410	+	4.81924i	0.336144	+	0.177159i
$741$		0			0
$742$	19.4701	−	5.21700i	0.714771	−	0.191522i
$743$	34.7672	−	9.31585i	1.27549	−	0.341765i	0.443356	−	0.896346i	$-0.353788\pi$
$743$	34.7672	−	9.31585i	1.27549	−	0.341765i	0.832130	+	0.554580i	$0.187121\pi$
$744$		0			0
$745$	−0.685709	−	2.21390i	−0.0251224	−	0.0811109i
$746$		−	13.1124i		−	0.480080i
$747$		0			0
$748$	−0.477782	+	0.477782i	−0.0174695	+	0.0174695i
$749$	10.1743	+	17.6224i	0.371761	+	0.643910i
$750$		0			0
$751$	−24.4567	+	42.3603i	−0.892438	+	1.54575i	−0.0554938	+	0.998459i	$0.517673\pi$
$751$	−24.4567	+	42.3603i	−0.892438	+	1.54575i	−0.836944	+	0.547289i	$0.815660\pi$
$752$	−0.897060	−	3.34787i	−0.0327124	−	0.122084i
$753$		0			0
$754$	−3.69759	+	2.13480i	−0.134658	+	0.0777449i
$755$	−8.87283	−	2.01434i	−0.322915	−	0.0733095i
$756$		0			0
$757$	22.9129	+	22.9129i	0.832783	+	0.832783i	0.987897	−	0.155114i	$-0.0495745\pi$
$757$	22.9129	+	22.9129i	0.832783	+	0.832783i	−0.155114	+	0.987897i	$0.549574\pi$
$758$	−0.152094	+	0.567624i	−0.00552432	+	0.0206170i
$759$		0			0
$760$	−0.162481	−	4.21169i	−0.00589382	−	0.152774i
$761$	9.19124	+	5.30657i	0.333182	+	0.192363i	0.657253	−	0.753670i	$-0.271718\pi$
$761$	9.19124	+	5.30657i	0.333182	+	0.192363i	−0.324071	+	0.946033i	$0.605052\pi$
$762$		0			0
$763$	−27.4229	−	7.34795i	−0.992777	−	0.266014i
$764$	−13.6296			−0.493100
$765$		0			0
$766$	−14.5012			−0.523950
$767$	−5.21932	−	1.39851i	−0.188459	−	0.0504974i
$768$		0			0
$769$	−3.31814	−	1.91573i	−0.119655	−	0.0690830i	0.438978	−	0.898498i	$-0.355341\pi$
$769$	−3.31814	−	1.91573i	−0.119655	−	0.0690830i	−0.558633	+	0.829415i	$0.688674\pi$
$770$	25.3527	+	23.4692i	0.913646	+	0.845770i
$771$		0			0
$772$	4.19397	−	15.6521i	0.150944	−	0.563332i
$773$	−19.8976	−	19.8976i	−0.715668	−	0.715668i	0.252047	−	0.967715i	$-0.418896\pi$
$773$	−19.8976	−	19.8976i	−0.715668	−	0.715668i	−0.967715	+	0.252047i	$0.918896\pi$
$774$		0			0
$775$	42.4082	+	20.3017i	1.52335	+	0.729258i
$776$	−1.29571	+	0.748079i	−0.0465133	+	0.0268545i
$777$		0			0
$778$	5.37250	+	20.0504i	0.192613	+	0.718843i
$779$	−7.78950	+	13.4918i	−0.279088	+	0.483395i
$780$		0			0
$781$	13.8065	+	23.9136i	0.494036	+	0.855696i
$782$	0.633495	−	0.633495i	0.0226537	−	0.0226537i
$783$		0			0
$784$		−	8.11832i		−	0.289940i
$785$	−9.51384	+	18.0517i	−0.339564	+	0.644293i
$786$		0			0
$787$	6.98473	−	1.87155i	0.248979	−	0.0667137i	−0.132171	−	0.991227i	$-0.542195\pi$
$787$	6.98473	−	1.87155i	0.248979	−	0.0667137i	0.381150	+	0.924513i	$0.375528\pi$
$788$	1.58575	−	0.424901i	0.0564901	−	0.0151365i
$789$		0			0
$790$	14.1485	−	26.8456i	0.503382	−	0.955124i
$791$			16.4058i			0.583321i
$792$		0			0
$793$	−6.09956	+	6.09956i	−0.216602	+	0.216602i
$794$	11.1320	+	19.2811i	0.395059	+	0.684262i
$795$		0			0
$796$	8.58664	−	14.8725i	0.304345	−	0.527142i
$797$	8.96012	+	33.4396i	0.317384	+	1.18449i	0.921750	+	0.387786i	$0.126760\pi$
$797$	8.96012	+	33.4396i	0.317384	+	1.18449i	−0.604366	+	0.796707i	$0.706573\pi$
$798$		0			0
$799$	0.510406	−	0.294683i	0.0180569	−	0.0104251i
$800$	4.71557	−	1.66234i	0.166721	−	0.0587725i
$801$		0			0
$802$	−3.36182	−	3.36182i	−0.118710	−	0.118710i
$803$	−12.0388	+	44.9295i	−0.424841	+	1.58553i
$804$		0			0
$805$	−33.6152	−	31.1179i	−1.18478	−	1.09676i
$806$	8.06289	+	4.65511i	0.284003	+	0.163969i
$807$		0			0
$808$	9.94834	+	2.66565i	0.349981	+	0.0937772i
$809$	−52.6028			−1.84942			−0.924709	−	0.380675i	$-0.875692\pi$
$809$	−52.6028			−1.84942			−0.924709	+	0.380675i	$0.875692\pi$
$810$		0			0
$811$	−13.8979			−0.488021			−0.244011	−	0.969773i	$-0.578463\pi$
$811$	−13.8979			−0.488021			−0.244011	+	0.969773i	$0.578463\pi$
$812$	16.1961	+	4.33973i	0.568371	+	0.152295i
$813$		0			0
$814$	15.9073	+	9.18410i	0.557551	+	0.321902i
$815$	−0.614221	−	15.9212i	−0.0215152	−	0.557697i
$816$		0			0
$817$	−1.00652	+	3.75637i	−0.0352136	+	0.131419i
$818$	−21.1307	−	21.1307i	−0.738817	−	0.738817i
$819$		0			0
$820$	−18.0226	−	4.09156i	−0.629377	−	0.142884i
$821$	23.9657	−	13.8366i	0.836408	−	0.482900i	−0.0196338	−	0.999807i	$-0.506250\pi$
$821$	23.9657	−	13.8366i	0.836408	−	0.482900i	0.856042	+	0.516907i	$0.172917\pi$
$822$		0			0
$823$	−7.80049	−	29.1118i	−0.271908	−	1.01477i	−0.957885	−	0.287151i	$-0.907292\pi$
$823$	−7.80049	−	29.1118i	−0.271908	−	1.01477i	0.685977	−	0.727623i	$-0.259375\pi$
$824$	−3.24210	+	5.61548i	−0.112944	+	0.195625i
$825$		0			0
$826$	10.6101	+	18.3772i	0.369172	+	0.639424i
$827$	−4.09863	+	4.09863i	−0.142523	+	0.142523i	−0.774768	−	0.632245i	$-0.782134\pi$
$827$	−4.09863	+	4.09863i	−0.142523	+	0.142523i	0.632245	+	0.774768i	$0.282134\pi$
$828$		0			0
$829$		−	37.6756i		−	1.30853i	−0.756266	−	0.654264i	$-0.772979\pi$
$829$		−	37.6756i		−	1.30853i	0.756266	−	0.654264i	$-0.227021\pi$
$830$	4.62938	+	14.9465i	0.160688	+	0.518802i
$831$		0			0
$832$	0.956351	−	0.256253i	0.0331555	−	0.00888399i
$833$	1.33343	−	0.357291i	0.0462006	−	0.0123794i
$834$		0			0
$835$	21.4297	+	11.2942i	0.741606	+	0.390851i
$836$		−	7.48995i		−	0.259046i
$837$		0			0
$838$	−12.4682	+	12.4682i	−0.430708	+	0.430708i
$839$	−16.5639	−	28.6895i	−0.571849	−	0.990471i	−0.996376	−	0.0850559i	$-0.972893\pi$
$839$	−16.5639	−	28.6895i	−0.571849	−	0.990471i	0.424527	−	0.905415i	$-0.360440\pi$
$840$		0			0
$841$	5.20180	−	9.00978i	0.179372	−	0.310682i
$842$	7.21908	+	26.9420i	0.248786	+	0.928482i
$843$		0			0
$844$	−15.7771	+	9.10894i	−0.543072	+	0.313543i
$845$	5.95029	−	26.2100i	0.204696	−	0.901651i
$846$		0			0
$847$	13.1684	+	13.1684i	0.452472	+	0.452472i
$848$	1.34174	−	5.00745i	0.0460757	−	0.171957i
$849$		0			0
$850$	0.480572	+	0.701370i	0.0164835	+	0.0240568i
$851$	−21.0916	−	12.1773i	−0.723011	−	0.417431i
$852$		0			0
$853$	−2.57386	−	0.689663i	−0.0881273	−	0.0236136i	0.214486	−	0.976727i	$-0.431192\pi$
$853$	−2.57386	−	0.689663i	−0.0881273	−	0.0236136i	−0.302613	+	0.953113i	$0.597859\pi$
$854$	33.8760			1.15921
$855$		0			0
$856$	5.23339			0.178874
$857$	−15.1284	−	4.05364i	−0.516776	−	0.138470i	−0.00900123	−	0.999959i	$-0.502865\pi$
$857$	−15.1284	−	4.05364i	−0.516776	−	0.138470i	−0.507775	+	0.861490i	$0.669532\pi$
$858$		0			0
$859$	0.691191	+	0.399059i	0.0235831	+	0.0136157i	0.511745	−	0.859137i	$-0.328999\pi$
$859$	0.691191	+	0.399059i	0.0235831	+	0.0136157i	−0.488162	+	0.872753i	$0.662333\pi$
$860$	−4.60991	+	0.177845i	−0.157197	+	0.00606445i
$861$		0			0
$862$	−4.99288	+	18.6337i	−0.170058	+	0.634666i
$863$	−30.2854	−	30.2854i	−1.03093	−	1.03093i	−0.999506	−	0.0314193i	$-0.989997\pi$
$863$	−30.2854	−	30.2854i	−1.03093	−	1.03093i	−0.0314193	−	0.999506i	$-0.510003\pi$
$864$		0			0
$865$	4.49311	+	7.13237i	0.152770	+	0.242508i
$866$	20.4721	−	11.8196i	0.695671	−	0.401646i
$867$		0			0
$868$	−9.46313	−	35.3169i	−0.321199	−	1.19873i
$869$	26.9630	−	46.7013i	0.914658	−	1.58423i
$870$		0			0
$871$	−4.03119	−	6.98222i	−0.136592	−	0.236584i
$872$	−5.16301	+	5.16301i	−0.174842	+	0.174842i
$873$		0			0
$874$			9.93098i			0.335920i
$875$	34.8872	−	25.9359i	1.17940	−	0.876794i
$876$		0			0
$877$	−16.7435	+	4.48641i	−0.565388	+	0.151495i	−0.530180	−	0.847885i	$-0.677876\pi$
$877$	−16.7435	+	4.48641i	−0.565388	+	0.151495i	−0.0352074	+	0.999380i	$0.511209\pi$
$878$	−34.7780	+	9.31875i	−1.17370	+	0.314492i
$879$		0			0
$880$	8.48747	−	2.62882i	0.286113	−	0.0886176i
$881$		−	15.1033i		−	0.508843i	−0.967093	−	0.254421i	$-0.918115\pi$
$881$		−	15.1033i		−	0.508843i	0.967093	−	0.254421i	$-0.0818850\pi$
$882$		0			0
$883$	−16.4678	+	16.4678i	−0.554185	+	0.554185i	−0.927646	−	0.373461i	$-0.878171\pi$
$883$	−16.4678	+	16.4678i	−0.554185	+	0.554185i	0.373461	+	0.927646i	$0.378171\pi$
$884$	0.0841789	+	0.145802i	0.00283124	+	0.00490386i
$885$		0			0
$886$	13.4169	−	23.2388i	0.450750	−	0.780723i
$887$	−7.07714	−	26.4123i	−0.237627	−	0.886837i	−0.976947	−	0.213482i	$-0.931519\pi$
$887$	−7.07714	−	26.4123i	−0.237627	−	0.886837i	0.739320	−	0.673355i	$-0.235147\pi$
$888$		0			0
$889$	−65.6556	+	37.9063i	−2.20202	+	1.27134i
$890$	9.22954	−	5.81424i	0.309375	−	0.194894i
$891$		0			0
$892$	−3.32036	−	3.32036i	−0.111174	−	0.111174i
$893$	−1.69089	+	6.31049i	−0.0565835	+	0.211173i
$894$		0			0
$895$	−19.5880	+	21.1600i	−0.654755	+	0.707302i
$896$	−3.36730	−	1.94411i	−0.112494	−	0.0649483i
$897$		0			0
$898$	39.9306	+	10.6994i	1.33250	+	0.357043i
$899$	40.5510			1.35245
$900$		0			0
$901$	0.881522			0.0293678
$902$	−31.7230	−	8.50016i	−1.05626	−	0.283025i
$903$		0			0
$904$	3.65405	+	2.10967i	0.121532	+	0.0701666i
$905$	36.9419	−	39.9066i	1.22799	−	1.32654i
$906$		0			0
$907$	6.62626	−	24.7295i	0.220021	−	0.821130i	−0.764317	−	0.644841i	$-0.776924\pi$
$907$	6.62626	−	24.7295i	0.220021	−	0.821130i	0.984338	−	0.176290i	$-0.0564096\pi$
$908$	−17.6998	−	17.6998i	−0.587390	−	0.587390i
$909$		0			0
$910$	7.28342	−	4.58826i	0.241443	−	0.152099i
$911$	−3.55075	+	2.05003i	−0.117642	+	0.0679204i	−0.557666	−	0.830065i	$-0.688303\pi$
$911$	−3.55075	+	2.05003i	−0.117642	+	0.0679204i	0.440025	+	0.897986i	$0.354970\pi$
$912$		0			0
$913$	7.19662	+	26.8582i	0.238173	+	0.888875i
$914$	10.7957	−	18.6987i	0.357090	−	0.618499i
$915$		0			0
$916$	11.3940	+	19.7350i	0.376468	+	0.652061i
$917$	−12.3259	+	12.3259i	−0.407035	+	0.407035i
$918$		0			0
$919$			28.8740i			0.952464i	0.879320	+	0.476232i	$0.157998\pi$
$919$			28.8740i			0.952464i	−0.879320	+	0.476232i	$0.842002\pi$
$920$	−11.2536	+	3.48557i	−0.371020	+	0.114916i
$921$		0			0
$922$	12.1246	−	3.24877i	0.399302	−	0.106993i
$923$	6.64579	−	1.78073i	0.218749	−	0.0586135i
$924$		0			0
$925$	15.0355	−	17.5537i	0.494363	−	0.577163i
$926$			22.1046i			0.726404i
$927$		0			0
$928$	3.04930	−	3.04930i	0.100098	−	0.100098i
$929$	25.1077	+	43.4879i	0.823758	+	1.42679i	0.902865	+	0.429925i	$0.141460\pi$
$929$	25.1077	+	43.4879i	0.823758	+	1.42679i	−0.0791067	+	0.996866i	$0.525207\pi$
$930$		0			0
$931$	−7.65121	+	13.2523i	−0.250758	+	0.434326i
$932$	7.55809	+	28.2072i	0.247573	+	0.923956i
$933$		0			0
$934$	−4.26380	+	2.46170i	−0.139516	+	0.0805494i
$935$	0.805320	+	1.27837i	0.0263368	+	0.0418070i
$936$		0			0
$937$	−0.857094	−	0.857094i	−0.0280000	−	0.0280000i	0.692968	−	0.720968i	$-0.256303\pi$
$937$	−0.857094	−	0.857094i	−0.0280000	−	0.0280000i	−0.720968	+	0.692968i	$0.756303\pi$
$938$	−8.19479	+	30.5834i	−0.267569	+	0.998582i
$939$		0			0
$940$	−7.74439	+	0.298769i	−0.252594	+	0.00974476i
$941$	43.4478	+	25.0846i	1.41636	+	0.817735i	0.995977	−	0.0896119i	$-0.0285627\pi$
$941$	43.4478	+	25.0846i	1.41636	+	0.817735i	0.420382	+	0.907347i	$0.361896\pi$
$942$		0			0
$943$	42.0618	+	11.2704i	1.36972	+	0.367015i
$944$	5.45754			0.177628
$945$		0			0
$946$	−8.19815			−0.266545
$947$	−2.54334	−	0.681485i	−0.0826473	−	0.0221453i	0.217258	−	0.976114i	$-0.430289\pi$
$947$	−2.54334	−	0.681485i	−0.0826473	−	0.0221453i	−0.299906	+	0.953969i	$0.596955\pi$
$948$		0			0
$949$	10.0371	+	5.79490i	0.325817	+	0.188111i
$950$	−9.26436	−	1.73066i	−0.300575	−	0.0561502i
$951$		0			0
$952$	0.171123	−	0.638639i	0.00554612	−	0.0206984i
$953$	28.1499	+	28.1499i	0.911864	+	0.911864i	0.996419	−	0.0845545i	$-0.0269467\pi$
$953$	28.1499	+	28.1499i	0.911864	+	0.911864i	−0.0845545	+	0.996419i	$0.526947\pi$
$954$		0			0
$955$	−6.74723	+	29.7204i	−0.218335	+	0.961729i
$956$	−7.90295	+	4.56277i	−0.255600	+	0.147571i
$957$		0			0
$958$	0.702296	+	2.62100i	0.0226901	+	0.0846808i
$959$	−24.2991	+	42.0872i	−0.784658	+	1.35907i
$960$		0			0
$961$	−28.7123	−	49.7312i	−0.926204	−	1.60423i
$962$	3.23623	−	3.23623i	0.104340	−	0.104340i
$963$		0			0
$964$			1.73931i			0.0560194i
$965$	−32.0545	−	16.8938i	−1.03187	−	0.543830i
$966$		0			0
$967$	1.28319	−	0.343829i	0.0412646	−	0.0110568i	−0.238128	−	0.971234i	$-0.576534\pi$
$967$	1.28319	−	0.343829i	0.0412646	−	0.0110568i	0.279392	+	0.960177i	$0.409867\pi$
$968$	4.62638	−	1.23963i	0.148697	−	0.0398433i
$969$		0			0
$970$	0.989814	+	3.19574i	0.0317810	+	0.102609i
$971$			38.7906i			1.24485i	0.782679	+	0.622425i	$0.213853\pi$
$971$			38.7906i			1.24485i	−0.782679	+	0.622425i	$0.786147\pi$
$972$		0			0
$973$	11.4428	−	11.4428i	0.366840	−	0.366840i
$974$	−5.80393	−	10.0527i	−0.185970	−	0.322109i
$975$		0			0
$976$	4.35623	−	7.54520i	0.139439	−	0.241516i
$977$	−11.0953	−	41.4084i	−0.354972	−	1.32477i	−0.880520	−	0.474009i	$-0.842807\pi$
$977$	−11.0953	−	41.4084i	−0.354972	−	1.32477i	0.525548	−	0.850764i	$-0.323860\pi$
$978$		0			0
$979$	16.7875	−	9.69226i	0.536530	−	0.309766i
$980$	−17.7026	−	4.01892i	−0.565490	−	0.128380i
$981$		0			0
$982$	−3.49508	−	3.49508i	−0.111532	−	0.111532i
$983$	−8.34182	+	31.1321i	−0.266063	+	0.992960i	0.695534	+	0.718493i	$0.255168\pi$
$983$	−8.34182	+	31.1321i	−0.266063	+	0.992960i	−0.961597	+	0.274466i	$0.911499\pi$
$984$		0			0
$985$	−0.141515	−	3.66820i	−0.00450903	−	0.116879i
$986$	0.635046	+	0.366644i	0.0202240	+	0.0116763i
$987$		0			0
$988$	−1.80265	−	0.483018i	−0.0573499	−	0.0153669i
$989$	10.8700			0.345645
$990$		0			0
$991$	20.1017			0.638551			0.319275	−	0.947662i	$-0.396561\pi$
$991$	20.1017			0.638551			0.319275	+	0.947662i	$0.396561\pi$
$992$	−9.08302	−	2.43379i	−0.288386	−	0.0772729i
$993$		0			0
$994$	−23.3998	−	13.5099i	−0.742196	−	0.428507i
$995$	−28.1799	−	26.0864i	−0.893364	−	0.826995i
$996$		0			0
$997$	0.763421	−	2.84912i	0.0241778	−	0.0902327i	−0.952783	−	0.303653i	$-0.901794\pi$
$997$	0.763421	−	2.84912i	0.0241778	−	0.0902327i	0.976960	+	0.213420i	$0.0684603\pi$
$998$	22.9557	+	22.9557i	0.726649	+	0.726649i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.m.b.17.4		16
3.2	odd	2		90.2.l.b.77.1	yes	16
5.2	odd	4		1350.2.q.h.1043.1		16
5.3	odd	4	inner	270.2.m.b.233.3		16
5.4	even	2		1350.2.q.h.557.2		16
9.2	odd	6	inner	270.2.m.b.197.3		16
9.4	even	3		810.2.f.c.647.1		16
9.5	odd	6		810.2.f.c.647.8		16
9.7	even	3		90.2.l.b.47.1	yes	16
12.11	even	2		720.2.cu.b.257.4		16
15.2	even	4		450.2.p.h.293.4		16
15.8	even	4		90.2.l.b.23.1	✓	16
15.14	odd	2		450.2.p.h.257.4		16
36.7	odd	6		720.2.cu.b.497.3		16
45.2	even	12		1350.2.q.h.143.2		16
45.7	odd	12		450.2.p.h.443.4		16
45.13	odd	12		810.2.f.c.323.8		16
45.23	even	12		810.2.f.c.323.1		16
45.29	odd	6		1350.2.q.h.1007.1		16
45.34	even	6		450.2.p.h.407.4		16
45.38	even	12	inner	270.2.m.b.143.4		16
45.43	odd	12		90.2.l.b.83.1	yes	16
60.23	odd	4		720.2.cu.b.113.3		16
180.43	even	12		720.2.cu.b.353.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.1	✓	16	15.8	even	4
90.2.l.b.47.1	yes	16	9.7	even	3
90.2.l.b.77.1	yes	16	3.2	odd	2
90.2.l.b.83.1	yes	16	45.43	odd	12
270.2.m.b.17.4		16	1.1	even	1	trivial
270.2.m.b.143.4		16	45.38	even	12	inner
270.2.m.b.197.3		16	9.2	odd	6	inner
270.2.m.b.233.3		16	5.3	odd	4	inner
450.2.p.h.257.4		16	15.14	odd	2
450.2.p.h.293.4		16	15.2	even	4
450.2.p.h.407.4		16	45.34	even	6
450.2.p.h.443.4		16	45.7	odd	12
720.2.cu.b.113.3		16	60.23	odd	4
720.2.cu.b.257.4		16	12.11	even	2
720.2.cu.b.353.4		16	180.43	even	12
720.2.cu.b.497.3		16	36.7	odd	6
810.2.f.c.323.1		16	45.23	even	12
810.2.f.c.323.8		16	45.13	odd	12
810.2.f.c.647.1		16	9.4	even	3
810.2.f.c.647.8		16	9.5	odd	6
1350.2.q.h.143.2		16	45.2	even	12
1350.2.q.h.557.2		16	5.4	even	2
1350.2.q.h.1007.1		16	45.29	odd	6
1350.2.q.h.1043.1		16	5.2	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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.m (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(1.51901 - 1.64092i) q^{5} +(-1.00635 + 3.75574i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(1.51901 - 1.64092i) q^{5} +(-1.00635 + 3.75574i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.89195 - 1.19185i) q^{10} +(3.44125 - 1.98681i) q^{11} +(-0.256253 - 0.956351i) q^{13} +(-1.94411 + 3.36730i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.120239 + 0.120239i) q^{17} -1.88492i q^{19} +(2.13596 - 0.661570i) q^{20} +(3.83821 - 1.02845i) q^{22} +(-5.08911 + 1.36362i) q^{23} +(-0.385214 - 4.98514i) q^{25} -0.990087i q^{26} +(-2.74939 + 2.74939i) q^{28} +(-2.15618 - 3.73461i) q^{29} +(-4.70172 + 8.14362i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-0.147262 + 0.0850217i) q^{34} +(4.63420 + 7.35634i) q^{35} +(3.26863 + 3.26863i) q^{37} +(0.487854 - 1.82070i) q^{38} +(2.23441 - 0.0862005i) q^{40} +(-7.15775 - 4.13253i) q^{41} +(-1.99285 - 0.533983i) q^{43} +3.97361 q^{44} -5.26863 q^{46} +(-3.34787 - 0.897060i) q^{47} +(-7.03067 - 4.05916i) q^{49} +(0.918161 - 4.91498i) q^{50} +(0.256253 - 0.956351i) q^{52} +(-3.66571 - 3.66571i) q^{53} +(1.96711 - 8.66478i) q^{55} +(-3.36730 + 1.94411i) q^{56} +(-1.11612 - 4.16541i) q^{58} +(2.72877 - 4.72637i) q^{59} +(-4.35623 - 7.54520i) q^{61} +(-6.64923 + 6.64923i) q^{62} +1.00000i q^{64} +(-1.95854 - 1.03222i) q^{65} +(7.86563 - 2.10759i) q^{67} +(-0.164249 + 0.0440105i) q^{68} +(2.57234 + 8.30510i) q^{70} +6.94911i q^{71} +(-8.27728 + 8.27728i) q^{73} +(2.31127 + 4.00324i) q^{74} +(0.942462 - 1.63239i) q^{76} +(3.99883 + 14.9238i) q^{77} +(11.7529 - 6.78553i) q^{79} +(2.18058 + 0.495044i) q^{80} +(-5.84428 - 5.84428i) q^{82} +(-1.81110 + 6.75913i) q^{83} +(0.0146578 + 0.379946i) q^{85} +(-1.78674 - 1.03157i) q^{86} +(3.83821 + 1.02845i) q^{88} +4.87832 q^{89} +3.84968 q^{91} +(-5.08911 - 1.36362i) q^{92} +(-3.00162 - 1.73299i) q^{94} +(-3.09300 - 2.86322i) q^{95} +(-0.387234 + 1.44518i) q^{97} +(-5.74052 - 5.74052i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) \) 16 * q + 12 * q^5 + 8 * q^7	\( 16 q + 12 q^{5} + 8 q^{7} - 8 q^{10} + 8 q^{16} + 12 q^{20} + 8 q^{22} + 24 q^{23} - 16 q^{25} - 16 q^{28} - 8 q^{31} - 24 q^{38} - 4 q^{40} - 24 q^{41} - 32 q^{46} - 48 q^{47} - 24 q^{50} + 24 q^{55} - 24 q^{56} + 16 q^{58} - 24 q^{61} - 16 q^{67} + 24 q^{68} + 16 q^{70} + 16 q^{73} + 16 q^{76} + 72 q^{77} - 16 q^{82} - 48 q^{83} - 4 q^{85} + 48 q^{86} + 8 q^{88} + 24 q^{92} - 84 q^{95} - 48 q^{97}+O(q^{100}) \) 16 * q + 12 * q^5 + 8 * q^7 - 8 * q^10 + 8 * q^16 + 12 * q^20 + 8 * q^22 + 24 * q^23 - 16 * q^25 - 16 * q^28 - 8 * q^31 - 24 * q^38 - 4 * q^40 - 24 * q^41 - 32 * q^46 - 48 * q^47 - 24 * q^50 + 24 * q^55 - 24 * q^56 + 16 * q^58 - 24 * q^61 - 16 * q^67 + 24 * q^68 + 16 * q^70 + 16 * q^73 + 16 * q^76 + 72 * q^77 - 16 * q^82 - 48 * q^83 - 4 * q^85 + 48 * q^86 + 8 * q^88 + 24 * q^92 - 84 * q^95 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more