LMFDB - Embedded newform 270.2.m.b.233.3

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			233.3
Root			$0.500000 + 1.74530i$ of defining polynomial
Character	$\chi$	$=$	270.233
Dual form			270.2.m.b.197.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.661570 + 2.13596i) q^{5} +(3.75574 + 1.00635i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.661570 + 2.13596i) q^{5} +(3.75574 + 1.00635i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.89195 + 1.19185i) q^{10} +(3.44125 - 1.98681i) q^{11} +(0.956351 - 0.256253i) q^{13} +(1.94411 - 3.36730i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.120239 + 0.120239i) q^{17} +1.88492i q^{19} +(1.64092 - 1.51901i) q^{20} +(-1.02845 - 3.83821i) q^{22} +(-1.36362 - 5.08911i) q^{23} +(-4.12465 - 2.82617i) q^{25} -0.990087i q^{26} +(-2.74939 - 2.74939i) q^{28} +(2.15618 + 3.73461i) q^{29} +(-4.70172 + 8.14362i) q^{31} +(0.965926 - 0.258819i) q^{32} +(0.147262 - 0.0850217i) q^{34} +(-4.63420 + 7.35634i) q^{35} +(3.26863 - 3.26863i) q^{37} +(1.82070 + 0.487854i) q^{38} +(-1.04255 - 1.97815i) q^{40} +(-7.15775 - 4.13253i) q^{41} +(0.533983 - 1.99285i) q^{43} -3.97361 q^{44} -5.26863 q^{46} +(-0.897060 + 3.34787i) q^{47} +(7.03067 + 4.05916i) q^{49} +(-3.79741 + 3.25264i) q^{50} +(-0.956351 - 0.256253i) q^{52} +(3.66571 - 3.66571i) q^{53} +(1.96711 + 8.66478i) q^{55} +(-3.36730 + 1.94411i) q^{56} +(4.16541 - 1.11612i) q^{58} +(-2.72877 + 4.72637i) q^{59} +(-4.35623 - 7.54520i) q^{61} +(6.64923 + 6.64923i) q^{62} -1.00000i q^{64} +(-0.0853460 + 2.21226i) q^{65} +(-2.10759 - 7.86563i) q^{67} +(-0.0440105 - 0.164249i) q^{68} +(5.90626 + 6.38026i) q^{70} +6.94911i q^{71} +(-8.27728 - 8.27728i) q^{73} +(-2.31127 - 4.00324i) q^{74} +(0.942462 - 1.63239i) q^{76} +(14.9238 - 3.99883i) q^{77} +(-11.7529 + 6.78553i) q^{79} +(-2.18058 + 0.495044i) q^{80} +(-5.84428 + 5.84428i) q^{82} +(-6.75913 - 1.81110i) q^{83} +(-0.336372 + 0.177279i) q^{85} +(-1.78674 - 1.03157i) q^{86} +(-1.02845 + 3.83821i) q^{88} -4.87832 q^{89} +3.84968 q^{91} +(-1.36362 + 5.08911i) q^{92} +(3.00162 + 1.73299i) q^{94} +(-4.02612 - 1.24701i) q^{95} +(1.44518 + 0.387234i) q^{97} +(5.74052 - 5.74052i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.661570	+	2.13596i	−0.295863	+	0.955230i
$5$	−0.661570	+	2.13596i	−0.295863	+	0.955230i
$6$		0			0
$7$	3.75574	+	1.00635i	1.41954	+	0.380364i	0.885319	−	0.464984i	$-0.153940\pi$
$7$	3.75574	+	1.00635i	1.41954	+	0.380364i	0.534217	+	0.845347i	$0.320606\pi$
$8$	−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
$13$	0.956351	−	0.256253i	0.265244	−	0.0710719i	−0.123746	−	0.992314i	$-0.539491\pi$
$13$	0.956351	−	0.256253i	0.265244	−	0.0710719i	0.388990	+	0.921242i	$0.372824\pi$
$14$	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	$-0.243436\pi$
$17$	0.120239	+	0.120239i	0.0291622	+	0.0291622i	−0.692375	+	0.721538i	$0.743436\pi$
$18$		0			0
$19$			1.88492i			0.432431i	0.976346	+	0.216216i	$0.0693714\pi$
$19$			1.88492i			0.432431i	−0.976346	+	0.216216i	$0.930629\pi$
$20$	1.64092	−	1.51901i	0.366920	−	0.339661i
$21$		0			0
$22$	−1.02845	−	3.83821i	−0.219265	−	0.818310i
$23$	−1.36362	−	5.08911i	−0.284335	−	1.06115i	−0.949324	−	0.314299i	$-0.898230\pi$
$23$	−1.36362	−	5.08911i	−0.284335	−	1.06115i	0.664989	−	0.746853i	$-0.268436\pi$
$24$		0			0
$25$	−4.12465	−	2.82617i	−0.824930	−	0.565235i
$26$		−	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	0.993773	−	0.111422i	$-0.0355406\pi$
$29$	2.15618	+	3.73461i	0.400392	+	0.693499i	−0.593381	+	0.804922i	$0.702207\pi$
$30$		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	$0.846592\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$		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	−0.385393	−	0.922753i	$-0.625934\pi$
$37$	3.26863	−	3.26863i	0.537360	−	0.537360i	0.922753	+	0.385393i	$0.125934\pi$
$38$	1.82070	+	0.487854i	0.295356	+	0.0791404i
$39$		0			0
$40$	−1.04255	−	1.97815i	−0.164842	−	0.312773i
$41$	−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
$43$	0.533983	−	1.99285i	0.0814316	−	0.303907i	−0.913183	−	0.407550i	$-0.866383\pi$
$43$	0.533983	−	1.99285i	0.0814316	−	0.303907i	0.994615	+	0.103643i	$0.0330500\pi$
$44$	−3.97361			−0.599044
$45$		0			0
$46$	−5.26863			−0.776818
$47$	−0.897060	+	3.34787i	−0.130850	+	0.488338i	−0.999981	−	0.00624459i	$-0.998012\pi$
$47$	−0.897060	+	3.34787i	−0.130850	+	0.488338i	0.869131	+	0.494582i	$0.164679\pi$
$48$		0			0
$49$	7.03067	+	4.05916i	1.00438	+	0.579880i
$50$	−3.79741	+	3.25264i	−0.537035	+	0.459993i
$51$		0			0
$52$	−0.956351	−	0.256253i	−0.132622	−	0.0355359i
$53$	3.66571	−	3.66571i	0.503524	−	0.503524i	−0.409007	−	0.912531i	$-0.634125\pi$
$53$	3.66571	−	3.66571i	0.503524	−	0.503524i	0.912531	+	0.409007i	$0.134125\pi$
$54$		0			0
$55$	1.96711	+	8.66478i	0.265245	+	1.16836i
$56$	−3.36730	+	1.94411i	−0.449975	+	0.259793i
$57$		0			0
$58$	4.16541	−	1.11612i	0.546946	−	0.146554i
$59$	−2.72877	+	4.72637i	−0.355255	+	0.615320i	−0.987162	−	0.159724i	$-0.948939\pi$
$59$	−2.72877	+	4.72637i	−0.355255	+	0.615320i	0.631906	+	0.775045i	$0.282273\pi$
$60$		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
$65$	−0.0853460	+	2.21226i	−0.0105859	+	0.274397i
$66$		0			0
$67$	−2.10759	−	7.86563i	−0.257483	−	0.960940i	−0.966692	−	0.255942i	$-0.917615\pi$
$67$	−2.10759	−	7.86563i	−0.257483	−	0.960940i	0.709209	−	0.704998i	$-0.249052\pi$
$68$	−0.0440105	−	0.164249i	−0.00533705	−	0.0199182i
$69$		0			0
$70$	5.90626	+	6.38026i	0.705933	+	0.762587i
$71$			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	0.0307446	−	0.999527i	$-0.490212\pi$
$73$	−8.27728	−	8.27728i	−0.968783	−	0.968783i	−0.999527	+	0.0307446i	$0.990212\pi$
$74$	−2.31127	−	4.00324i	−0.268680	−	0.465368i
$75$		0			0
$76$	0.942462	−	1.63239i	0.108108	−	0.187248i
$77$	14.9238	−	3.99883i	1.70073	−	0.455709i
$78$		0			0
$79$	−11.7529	+	6.78553i	−1.32230	+	0.763431i	−0.984095	−	0.177641i	$-0.943153\pi$
$79$	−11.7529	+	6.78553i	−1.32230	+	0.763431i	−0.338206	+	0.941072i	$0.609820\pi$
$80$	−2.18058	+	0.495044i	−0.243796	+	0.0553475i
$81$		0			0
$82$	−5.84428	+	5.84428i	−0.645393	+	0.645393i
$83$	−6.75913	−	1.81110i	−0.741911	−	0.198795i	−0.131984	−	0.991252i	$-0.542135\pi$
$83$	−6.75913	−	1.81110i	−0.741911	−	0.198795i	−0.609927	+	0.792457i	$0.708801\pi$
$84$		0			0
$85$	−0.336372	+	0.177279i	−0.0364847	+	0.0192286i
$86$	−1.78674	−	1.03157i	−0.192669	−	0.111238i
$87$		0			0
$88$	−1.02845	+	3.83821i	−0.109633	+	0.409155i
$89$	−4.87832			−0.517100			−0.258550	−	0.965998i	$-0.583245\pi$
$89$	−4.87832			−0.517100			−0.258550	+	0.965998i	$0.583245\pi$
$90$		0			0
$91$	3.84968			0.403557
$92$	−1.36362	+	5.08911i	−0.142168	+	0.530576i
$93$		0			0
$94$	3.00162	+	1.73299i	0.309594	+	0.178744i
$95$	−4.02612	−	1.24701i	−0.413072	−	0.127940i
$96$		0			0
$97$	1.44518	+	0.387234i	0.146736	+	0.0393177i	0.331439	−	0.943477i	$-0.392466\pi$
$97$	1.44518	+	0.387234i	0.146736	+	0.0393177i	−0.184704	+	0.982794i	$0.559132\pi$
$98$	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
$103$	−6.26326	+	1.67823i	−0.617137	+	0.165361i	−0.553826	−	0.832632i	$-0.686833\pi$
$103$	−6.26326	+	1.67823i	−0.617137	+	0.165361i	−0.0633111	+	0.997994i	$0.520166\pi$
$104$	−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	$-0.331406\pi$
$107$	−3.70057	−	3.70057i	−0.357747	−	0.357747i	−0.862982	+	0.505235i	$0.831406\pi$
$108$		0			0
$109$		−	7.30160i		−	0.699367i	−0.936868	−	0.349683i	$-0.886289\pi$
$109$		−	7.30160i		−	0.699367i	0.936868	−	0.349683i	$-0.113711\pi$
$110$	8.87866	+	0.342527i	0.846547	+	0.0326587i
$111$		0			0
$112$	1.00635	+	3.75574i	0.0950909	+	0.354884i
$113$	1.09205	+	4.07557i	0.102731	+	0.383397i	0.998078	−	0.0619722i	$-0.0197390\pi$
$113$	1.09205	+	4.07557i	0.102731	+	0.383397i	−0.895347	+	0.445369i	$0.853072\pi$
$114$		0			0
$115$	11.7723	+	0.454159i	1.09777	+	0.0423505i
$116$		−	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
$122$	−8.41558	+	2.25495i	−0.761911	+	0.204153i
$123$		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	0.257000	−	0.966411i	$-0.417266\pi$
$127$	13.7871	−	13.7871i	1.22341	−	1.22341i	0.966411	−	0.257000i	$-0.0827341\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$		0			0
$130$	2.11479	+	0.655012i	0.185479	+	0.0574483i
$131$	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
$133$	−1.89689	+	7.07929i	−0.164481	+	0.613852i
$134$	−8.14310			−0.703457
$135$		0			0
$136$	−0.170043			−0.0145811
$137$	3.23492	−	12.0729i	0.276378	−	1.03146i	−0.678534	−	0.734569i	$-0.737384\pi$
$137$	3.23492	−	12.0729i	0.276378	−	1.03146i	0.954912	−	0.296888i	$-0.0959489\pi$
$138$		0			0
$139$	3.60435	+	2.08097i	0.305717	+	0.176506i	0.645008	−	0.764176i	$-0.276854\pi$
$139$	3.60435	+	2.08097i	0.305717	+	0.176506i	−0.339291	+	0.940681i	$0.610187\pi$
$140$	7.69151	−	4.05368i	0.650051	−	0.342598i
$141$		0			0
$142$	6.71233	+	1.79856i	0.563286	+	0.150932i
$143$	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
$148$	−4.46504	+	1.19640i	−0.367024	+	0.0983437i
$149$	−0.518244	+	0.897625i	−0.0424562	+	0.0735363i	−0.886473	−	0.462781i	$-0.846852\pi$
$149$	−0.518244	+	0.897625i	−0.0424562	+	0.0735363i	0.844016	+	0.536317i	$0.180185\pi$
$150$		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
$155$	−14.2839	−	15.4303i	−1.14731	−	1.23939i
$156$		0			0
$157$	2.36186	+	8.81460i	0.188497	+	0.703481i	0.993855	+	0.110692i	$0.0353067\pi$
$157$	2.36186	+	8.81460i	0.188497	+	0.703481i	−0.805357	+	0.592789i	$0.798027\pi$
$158$	3.51245	+	13.1086i	0.279435	+	1.04287i
$159$		0			0
$160$	−0.0862005	+	2.23441i	−0.00681475	+	0.176645i
$161$		−	20.4857i		−	1.61450i
$162$		0			0
$163$	5.03848	+	5.03848i	0.394644	+	0.394644i	0.876339	−	0.481695i	$-0.159979\pi$
$163$	5.03848	+	5.03848i	0.394644	+	0.394644i	−0.481695	+	0.876339i	$0.659979\pi$
$164$	4.13253	+	7.15775i	0.322696	+	0.558926i
$165$		0			0
$166$	−3.49878	+	6.06007i	−0.271558	+	0.470353i
$167$	10.4641	−	2.80384i	0.809734	−	0.216968i	0.169881	−	0.985465i	$-0.445662\pi$
$167$	10.4641	−	2.80384i	0.809734	−	0.216968i	0.639853	+	0.768497i	$0.278995\pi$
$168$		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
$173$	−3.64139	−	0.975709i	−0.276850	−	0.0741818i	0.117722	−	0.993047i	$-0.462441\pi$
$173$	−3.64139	−	0.975709i	−0.276850	−	0.0741818i	−0.394573	+	0.918865i	$0.629107\pi$
$174$		0			0
$175$	−12.6470	−	14.7652i	−0.956023	−	1.11614i
$176$	3.44125	+	1.98681i	0.259394	+	0.149761i
$177$		0			0
$178$	−1.26260	+	4.71209i	−0.0946359	+	0.353186i
$179$	12.8952			0.963836			0.481918	−	0.876216i	$-0.339940\pi$
$179$	12.8952			0.963836			0.481918	+	0.876216i	$0.339940\pi$
$180$		0			0
$181$	24.3197			1.80767			0.903835	−	0.427881i	$-0.140740\pi$
$181$	24.3197			1.80767			0.903835	+	0.427881i	$0.140740\pi$
$182$	0.996372	−	3.71851i	0.0738560	−	0.275634i
$183$		0			0
$184$	4.56277	+	2.63432i	0.336372	+	0.194204i
$185$	4.81924	+	9.14410i	0.354318	+	0.672288i
$186$		0			0
$187$	0.652663	+	0.174880i	0.0477274	+	0.0127885i
$188$	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
$193$	15.6521	−	4.19397i	1.12666	−	0.301889i	0.353086	−	0.935591i	$-0.385132\pi$
$193$	15.6521	−	4.19397i	1.12666	−	0.301889i	0.773577	+	0.633702i	$0.218466\pi$
$194$	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	$-0.268626\pi$
$197$	−1.16085	−	1.16085i	−0.0827072	−	0.0827072i	−0.747250	+	0.664543i	$0.768626\pi$
$198$		0			0
$199$			17.1733i			1.21738i	0.793407	+	0.608691i	$0.208305\pi$
$199$			17.1733i			1.21738i	−0.793407	+	0.608691i	$0.791695\pi$
$200$	4.91498	−	0.918161i	0.347541	−	0.0649238i
$201$		0			0
$202$	−2.66565	−	9.94834i	−0.187554	−	0.699963i
$203$	4.33973	+	16.1961i	0.304589	+	1.13674i
$204$		0			0
$205$	13.5623	−	12.5547i	0.947230	−	0.876859i
$206$			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	$0.950914\pi$
$212$	−5.00745	+	1.34174i	−0.343913	+	0.0921513i
$213$		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
$218$	−7.05281	−	1.88979i	−0.477676	−	0.127993i
$219$		0			0
$220$	2.62882	−	8.48747i	0.177235	−	0.572225i
$221$	0.145802	+	0.0841789i	0.00980771	+	0.00566249i
$222$		0			0
$223$	1.21534	−	4.53570i	0.0813849	−	0.303733i	−0.913220	−	0.407466i	$-0.866412\pi$
$223$	1.21534	−	4.53570i	0.0813849	−	0.303733i	0.994605	+	0.103734i	$0.0330790\pi$
$224$	3.88823			0.259793
$225$		0			0
$226$	4.21934			0.280666
$227$	−6.47859	+	24.1784i	−0.429999	+	1.60478i	0.322759	+	0.946481i	$0.395390\pi$
$227$	−6.47859	+	24.1784i	−0.429999	+	1.60478i	−0.752758	+	0.658297i	$0.771277\pi$
$228$		0			0
$229$	−19.7350	−	11.3940i	−1.30412	−	0.752935i	−0.323014	−	0.946394i	$-0.604696\pi$
$229$	−19.7350	−	11.3940i	−1.30412	−	0.752935i	−0.981108	+	0.193459i	$0.938029\pi$
$230$	3.48557	−	11.2536i	0.229832	−	0.742040i
$231$		0			0
$232$	−4.16541	−	1.11612i	−0.273473	−	0.0732768i
$233$	−20.6491	+	20.6491i	−1.35277	+	1.35277i	−0.470214	+	0.882553i	$0.655823\pi$
$233$	−20.6491	+	20.6491i	−1.35277	+	1.35277i	−0.882553	+	0.470214i	$0.844177\pi$
$234$		0			0
$235$	−6.55746	−	4.13094i	−0.427761	−	0.269473i
$236$	4.72637	−	2.72877i	0.307660	−	0.177628i
$237$		0			0
$238$	0.638639	−	0.171123i	0.0413968	−	0.0110922i
$239$	4.56277	−	7.90295i	0.295141	−	0.511199i	−0.679877	−	0.733327i	$-0.737967\pi$
$239$	4.56277	−	7.90295i	0.295141	−	0.511199i	0.975018	+	0.222127i	$0.0713000\pi$
$240$		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
$245$	−13.3215	+	12.3318i	−0.851078	+	0.787851i
$246$		0			0
$247$	0.483018	+	1.80265i	0.0307337	+	0.114700i
$248$	−2.43379	−	9.08302i	−0.154546	−	0.576773i
$249$		0			0
$250$	−4.43525	−	10.2630i	−0.280510	−	0.649087i
$251$			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
$257$	−28.0634	+	7.51956i	−1.75055	+	0.469057i	−0.984743	−	0.174018i	$-0.944325\pi$
$257$	−28.0634	+	7.51956i	−1.75055	+	0.469057i	−0.765803	+	0.643075i	$0.777658\pi$
$258$		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
$263$	18.0249	+	4.82975i	1.11146	+	0.297815i	0.767424	−	0.641141i	$-0.221538\pi$
$263$	18.0249	+	4.82975i	1.11146	+	0.297815i	0.344038	+	0.938956i	$0.388205\pi$
$264$		0			0
$265$	5.40469	+	10.2549i	0.332007	+	0.629956i
$266$	6.34711	+	3.66451i	0.389167	+	0.224685i
$267$		0			0
$268$	−2.10759	+	7.86563i	−0.128742	+	0.480470i
$269$	15.5553			0.948425			0.474212	−	0.880411i	$-0.342733\pi$
$269$	15.5553			0.948425			0.474212	+	0.880411i	$0.342733\pi$
$270$		0			0
$271$	−1.87184			−0.113706			−0.0568532	−	0.998383i	$-0.518107\pi$
$271$	−1.87184			−0.113706			−0.0568532	+	0.998383i	$0.518107\pi$
$272$	−0.0440105	+	0.164249i	−0.00266853	+	0.00995908i
$273$		0			0
$274$	−10.8243	−	6.24939i	−0.653918	−	0.377540i
$275$	−19.8090	−	1.53069i	−1.19453	−	0.0923040i
$276$		0			0
$277$	3.99035	+	1.06921i	0.239757	+	0.0642426i	0.376696	−	0.926337i	$-0.377060\pi$
$277$	3.99035	+	1.06921i	0.239757	+	0.0642426i	−0.136940	+	0.990579i	$0.543727\pi$
$278$	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
$283$	17.4857	−	4.68527i	1.03941	−	0.278510i	0.301544	−	0.953452i	$-0.402498\pi$
$283$	17.4857	−	4.68527i	1.03941	−	0.278510i	0.737871	+	0.674942i	$0.235831\pi$
$284$	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
$290$	−0.371727	+	9.63555i	−0.0218286	+	0.565819i
$291$		0			0
$292$	3.02970	+	11.3070i	0.177300	+	0.661691i
$293$	−5.53752	−	20.6663i	−0.323505	−	1.20734i	−0.915806	−	0.401621i	$-0.868447\pi$
$293$	−5.53752	−	20.6663i	−0.323505	−	1.20734i	0.592300	−	0.805717i	$-0.298220\pi$
$294$		0			0
$295$	−8.29006	−	8.95536i	−0.482666	−	0.521401i
$296$			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
$302$	−3.93037	+	1.05314i	−0.226168	+	0.0606014i
$303$		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	−0.173476	+	0.984838i	$0.555500\pi$
$307$	−20.2953	+	20.2953i	−1.15831	+	1.15831i	−0.984838	+	0.173476i	$0.944500\pi$
$308$	−14.9238	−	3.99883i	−0.850365	−	0.227855i
$309$		0			0
$310$	−18.6014	+	9.80356i	−1.05649	+	0.556805i
$311$	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
$313$	−4.79847	+	17.9081i	−0.271226	+	1.01223i	0.687103	+	0.726560i	$0.258882\pi$
$313$	−4.79847	+	17.9081i	−0.271226	+	1.01223i	−0.958329	+	0.285668i	$0.907785\pi$
$314$	9.12554			0.514984
$315$		0			0
$316$	13.5711			0.763431
$317$	−0.217566	+	0.811966i	−0.0122197	+	0.0456046i	−0.971766	−	0.235945i	$-0.924182\pi$
$317$	−0.217566	+	0.811966i	−0.0122197	+	0.0456046i	0.959547	+	0.281549i	$0.0908483\pi$
$318$		0			0
$319$	14.8399	+	8.56781i	0.830874	+	0.479705i
$320$	2.13596	+	0.661570i	0.119404	+	0.0369829i
$321$		0			0
$322$	−19.7876	−	5.30208i	−1.10272	−	0.295473i
$323$	−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
$328$	7.98343	−	2.13915i	0.440811	−	0.118115i
$329$	−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
$335$	18.1950	+	0.701939i	0.994099	+	0.0383510i
$336$		0			0
$337$	−0.840764	−	3.13777i	−0.0457993	−	0.170925i	0.939238	−	0.343267i	$-0.111533\pi$
$337$	−0.840764	−	3.13777i	−0.0457993	−	0.170925i	−0.985037	+	0.172341i	$0.944867\pi$
$338$	3.11093	+	11.6102i	0.169213	+	0.631510i
$339$		0			0
$340$	0.379946	+	0.0146578i	0.0206055	+	0.000794932i
$341$			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
$347$	−4.53334	+	1.21470i	−0.243362	+	0.0652087i	−0.378438	−	0.925627i	$-0.623539\pi$
$347$	−4.53334	+	1.21470i	−0.243362	+	0.0652087i	0.135076	+	0.990835i	$0.456872\pi$
$348$		0			0
$349$	−8.42818	+	4.86601i	−0.451150	+	0.260472i	−0.708316	−	0.705896i	$-0.750545\pi$
$349$	−8.42818	+	4.86601i	−0.451150	+	0.260472i	0.257166	+	0.966367i	$0.417211\pi$
$350$	−17.5354	+	8.39455i	−0.937305	+	0.448707i
$351$		0			0
$352$	2.80977	−	2.80977i	0.149761	−	0.149761i
$353$	4.92815	+	1.32049i	0.262299	+	0.0702827i	0.387572	−	0.921840i	$-0.373314\pi$
$353$	4.92815	+	1.32049i	0.262299	+	0.0702827i	−0.125273	+	0.992122i	$0.539981\pi$
$354$		0			0
$355$	−14.8430	−	4.59732i	−0.787786	−	0.244001i
$356$	4.22474	+	2.43916i	0.223911	+	0.129275i
$357$		0			0
$358$	3.33754	−	12.4559i	0.176394	−	0.658312i
$359$	1.27697			0.0673957			0.0336978	−	0.999432i	$-0.489272\pi$
$359$	1.27697			0.0673957			0.0336978	+	0.999432i	$0.489272\pi$
$360$		0			0
$361$	15.4471			0.813003
$362$	6.29441	−	23.4910i	0.330827	−	1.23466i
$363$		0			0
$364$	−3.33392	−	1.92484i	−0.174745	−	0.100889i
$365$	23.1559	−	12.2039i	1.21204	−	0.638784i
$366$		0			0
$367$	9.74300	+	2.61063i	0.508581	+	0.136274i	0.503979	−	0.863716i	$-0.331869\pi$
$367$	9.74300	+	2.61063i	0.508581	+	0.136274i	0.00460117	+	0.999989i	$0.498535\pi$
$368$	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
$373$	12.6656	−	3.39374i	0.655801	−	0.175721i	0.0844507	−	0.996428i	$-0.473086\pi$
$373$	12.6656	−	3.39374i	0.655801	−	0.175721i	0.571350	+	0.820706i	$0.306420\pi$
$374$	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	$-0.995196\pi$
$379$		−	0.587648i		−	0.0301854i	0.999886	−	0.0150927i	$-0.00480434\pi$
$380$	2.86322	+	3.09300i	0.146880	+	0.158668i
$381$		0			0
$382$	3.52759	+	13.1652i	0.180487	+	0.673588i
$383$	−3.75319	−	14.0071i	−0.191779	−	0.715729i	−0.993077	−	0.117464i	$-0.962524\pi$
$383$	−3.75319	−	14.0071i	−0.191779	−	0.715729i	0.801298	−	0.598265i	$-0.204143\pi$
$384$		0			0
$385$	−1.33182	+	34.5222i	−0.0678760	+	1.75942i
$386$		−	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	$-0.990272\pi$
$389$	−10.3789	−	17.9767i	−0.526230	−	0.911456i	0.473303	−	0.880899i	$-0.343061\pi$
$390$		0			0
$391$	0.447948	−	0.775869i	0.0226537	−	0.0392374i
$392$	−7.84169	+	2.10118i	−0.396065	+	0.106125i
$393$		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	−0.191395	−	0.981513i	$-0.561301\pi$
$397$	15.7430	−	15.7430i	0.790118	−	0.790118i	0.981513	+	0.191395i	$0.0613012\pi$
$398$	16.5881	+	4.44477i	0.831487	+	0.222796i
$399$		0			0
$400$	0.385214	−	4.98514i	0.0192607	−	0.249257i
$401$	−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
$403$	−2.40966	+	8.99298i	−0.120034	+	0.447972i
$404$	−10.2993			−0.512408
$405$		0			0
$406$	16.7674			0.832153
$407$	4.75404	−	17.7423i	0.235649	−	0.879454i
$408$		0			0
$409$	25.8797	+	14.9417i	1.27967	+	0.738817i	0.976787	−	0.214211i	$-0.0687180\pi$
$409$	25.8797	+	14.9417i	1.27967	+	0.738817i	0.302882	+	0.953028i	$0.402051\pi$
$410$	−8.61674	−	16.3495i	−0.425551	−	0.807446i
$411$		0			0
$412$	6.26326	+	1.67823i	0.308568	+	0.0826807i
$413$	−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
$418$	7.23474	−	1.93854i	0.353863	−	0.0948172i
$419$	8.81638	−	15.2704i	0.430708	−	0.746009i	−0.566226	−	0.824250i	$-0.691597\pi$
$419$	8.81638	−	15.2704i	0.430708	−	0.746009i	0.996934	+	0.0782412i	$0.0249304\pi$
$420$		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
$425$	−0.156127	−	0.835759i	−0.00757328	−	0.0405403i
$426$		0			0
$427$	−8.76775	−	32.7217i	−0.424301	−	1.58351i
$428$	1.35450	+	5.05507i	0.0654723	+	0.244346i
$429$		0			0
$430$	3.38546	−	3.13395i	0.163261	−	0.151132i
$431$			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	0.983609	−	0.180316i	$-0.0577122\pi$
$433$	16.7154	+	16.7154i	0.803292	+	0.803292i	−0.180316	+	0.983609i	$0.557712\pi$
$434$	18.2814	+	31.6642i	0.877533	+	1.51993i
$435$		0			0
$436$	−3.65080	+	6.32337i	−0.174842	+	0.302835i
$437$	9.59259	−	2.57033i	0.458876	−	0.122955i
$438$		0			0
$439$	31.1811	−	18.0024i	1.48819	−	0.859209i	0.488285	−	0.872684i	$-0.337623\pi$
$439$	31.1811	−	18.0024i	1.48819	−	0.859209i	0.999909	+	0.0134750i	$0.00428934\pi$
$440$	−7.51788	−	4.73597i	−0.358401	−	0.225778i
$441$		0			0
$442$	0.119047	−	0.119047i	0.00566249	−	0.00566249i
$443$	25.9195	+	6.94511i	1.23147	+	0.329972i	0.815153	−	0.579246i	$-0.196653\pi$
$443$	25.9195	+	6.94511i	1.23147	+	0.329972i	0.416320	+	0.909218i	$0.363320\pi$
$444$		0			0
$445$	3.22735	−	10.4199i	0.152991	−	0.493950i
$446$	−4.06659	−	2.34785i	−0.192559	−	0.111174i
$447$		0			0
$448$	1.00635	−	3.75574i	0.0475455	−	0.177442i
$449$	−41.3392			−1.95092			−0.975459	−	0.220182i	$-0.929335\pi$
$449$	−41.3392			−1.95092			−0.975459	+	0.220182i	$0.929335\pi$
$450$		0			0
$451$	−32.8421			−1.54647
$452$	1.09205	−	4.07557i	0.0513655	−	0.191699i
$453$		0			0
$454$	21.6778	+	12.5157i	1.01739	+	0.587390i
$455$	−2.54684	+	8.22277i	−0.119398	+	0.385489i
$456$		0			0
$457$	−20.8557	−	5.58827i	−0.975589	−	0.261408i	−0.264403	−	0.964412i	$-0.585175\pi$
$457$	−20.8557	−	5.58827i	−0.975589	−	0.261408i	−0.711186	+	0.703004i	$0.751842\pi$
$458$	−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
$463$	−21.3514	+	5.72110i	−0.992286	+	0.265882i	−0.718210	−	0.695826i	$-0.755038\pi$
$463$	−21.3514	+	5.72110i	−0.992286	+	0.265882i	−0.274076	+	0.961708i	$0.588372\pi$
$464$	−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	$-0.213661\pi$
$467$	3.48137	+	3.48137i	0.161099	+	0.161099i	−0.621955	+	0.783053i	$0.713661\pi$
$468$		0			0
$469$		−	31.6622i		−	1.46203i
$470$	−5.68738	+	5.26485i	−0.262339	+	0.242850i
$471$		0			0
$472$	−1.41251	−	5.27158i	−0.0650163	−	0.242644i
$473$	−2.12184	−	7.91881i	−0.0975622	−	0.364107i
$474$		0			0
$475$	5.32713	−	7.77465i	0.244425	−	0.356726i
$476$		−	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	0.833364	−	0.552724i	$-0.186412\pi$
$479$	−1.35673	−	2.34993i	−0.0619906	−	0.107371i	−0.895355	+	0.445353i	$0.853078\pi$
$480$		0			0
$481$	2.28836	−	3.96356i	0.104340	−	0.180723i
$482$	1.68004	−	0.450166i	0.0765239	−	0.0205045i
$483$		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	−0.868183	−	0.496244i	$-0.834712\pi$
$487$	−8.20799	+	8.20799i	−0.371940	+	0.371940i	0.496244	+	0.868183i	$0.334712\pi$
$488$	8.41558	+	2.25495i	0.380955	+	0.102077i
$489$		0			0
$490$	8.46376	+	16.0593i	0.382354	+	0.725484i
$491$	−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
$493$	−0.189789	+	0.708301i	−0.00854766	+	0.0319003i
$494$	1.86624			0.0839661
$495$		0			0
$496$	−9.40344			−0.422227
$497$	−6.99322	+	26.0991i	−0.313689	+	1.17070i
$498$		0			0
$499$	−28.1148	−	16.2321i	−1.25859	−	0.726649i	−0.285791	−	0.958292i	$-0.592256\pi$
$499$	−28.1148	−	16.2321i	−1.25859	−	0.726649i	−0.972801	+	0.231643i	$0.925590\pi$
$500$	−11.0612	+	1.62787i	−0.494672	+	0.0728006i
$501$		0			0
$502$	5.95736	+	1.59627i	0.265890	+	0.0712450i
$503$	19.6817	−	19.6817i	0.877565	−	0.877565i	−0.115717	−	0.993282i	$-0.536917\pi$
$503$	19.6817	−	19.6817i	0.877565	−	0.877565i	0.993282	+	0.115717i	$0.0369166\pi$
$504$		0			0
$505$	5.09859	+	22.4584i	0.226884	+	0.999386i
$506$	−18.1307	+	10.4677i	−0.806007	+	0.465348i
$507$		0			0
$508$	−18.8336	+	5.04645i	−0.835606	+	0.223900i
$509$	−5.25069	+	9.09446i	−0.232733	+	0.403105i	−0.958611	−	0.284718i	$-0.908100\pi$
$509$	−5.25069	+	9.09446i	−0.232733	+	0.403105i	0.725879	+	0.687823i	$0.241433\pi$
$510$		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
$515$	0.558941	−	14.4883i	0.0246299	−	0.638432i
$516$		0			0
$517$	3.56457	+	13.3031i	0.156770	+	0.585072i
$518$	−4.65189	−	17.3611i	−0.204392	−	0.762802i
$519$		0			0
$520$	−1.50395	−	1.62465i	−0.0659527	−	0.0712456i
$521$		−	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	0.939584	−	0.342318i	$-0.111212\pi$
$523$	13.6590	+	13.6590i	0.597266	+	0.597266i	−0.342318	+	0.939584i	$0.611212\pi$
$524$	−2.24156	−	3.88249i	−0.0979230	−	0.169608i
$525$		0			0
$526$	9.33036	−	16.1607i	0.406823	−	0.704638i
$527$	−1.54451	+	0.413850i	−0.0672798	+	0.0180276i
$528$		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
$533$	−7.90429	−	2.11795i	−0.342373	−	0.0917385i
$534$		0			0
$535$	10.3525	−	5.45608i	0.447575	−	0.235887i
$536$	7.05213	+	4.07155i	0.304606	+	0.175864i
$537$		0			0
$538$	4.02601	−	15.0253i	0.173574	−	0.647786i
$539$	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	$0.694775\pi$
$542$	−0.484468	+	1.80806i	−0.0208097	+	0.0776628i
$543$		0			0
$544$	0.147262	+	0.0850217i	0.00631380	+	0.00364528i
$545$	15.5959	+	4.83052i	0.668056	+	0.206917i
$546$		0			0
$547$	−0.234244	−	0.0627654i	−0.0100155	−	0.00268365i	0.253808	−	0.967255i	$-0.418317\pi$
$547$	−0.234244	−	0.0627654i	−0.0100155	−	0.00268365i	−0.263823	+	0.964571i	$0.584984\pi$
$548$	−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
$553$	−50.9693	+	13.6572i	−2.16744	+	0.580763i
$554$	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	0.901746	+	0.432266i	$0.142286\pi$
$557$	31.4838	+	31.4838i	1.33401	+	1.33401i	0.432266	+	0.901746i	$0.357714\pi$
$558$		0			0
$559$		−	2.04270i		−	0.0863969i
$560$	−8.68788	−	0.335167i	−0.367130	−	0.0141634i
$561$		0			0
$562$	0.0743081	+	0.277322i	0.00313450	+	0.0116981i
$563$	−8.35388	−	31.1771i	−0.352074	−	1.31396i	−0.884127	−	0.467247i	$-0.845246\pi$
$563$	−8.35388	−	31.1771i	−0.352074	−	1.31396i	0.532053	−	0.846711i	$-0.321421\pi$
$564$		0			0
$565$	−9.42772	−	0.363709i	−0.396627	−	0.0153014i
$566$		−	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	$-0.929846\pi$
$569$	−16.1545	−	27.9804i	−0.677232	−	1.17300i	0.298580	−	0.954385i	$-0.403487\pi$
$570$		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	$-0.0157469\pi$
$572$	−3.80016	+	1.01825i	−0.158893	+	0.0425752i
$573$		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	−0.568462	−	0.822710i	$-0.692461\pi$
$577$	6.10724	−	6.10724i	0.254248	−	0.254248i	0.822710	+	0.568462i	$0.192461\pi$
$578$	−16.3928	−	4.39244i	−0.681851	−	0.182701i
$579$		0			0
$580$	9.21102	+	2.85292i	0.382467	+	0.118461i
$581$	−23.5629	−	13.6041i	−0.977556	−	0.564392i
$582$		0			0
$583$	5.33157	−	19.8977i	0.220811	−	0.824077i
$584$	11.7058			0.484391
$585$		0			0
$586$	−21.3953			−0.883833
$587$	−0.490414	+	1.83025i	−0.0202415	+	0.0755424i	−0.975308	−	0.220850i	$-0.929117\pi$
$587$	−0.490414	+	1.83025i	−0.0202415	+	0.0755424i	0.955066	+	0.296392i	$0.0957836\pi$
$588$		0			0
$589$	−15.3501	−	8.86238i	−0.632490	−	0.365168i
$590$	−10.7958	+	5.68976i	−0.444458	+	0.234244i
$591$		0			0
$592$	4.46504	+	1.19640i	0.183512	+	0.0491719i
$593$	−11.0077	+	11.0077i	−0.452033	+	0.452033i	−0.896029	−	0.443996i	$-0.853561\pi$
$593$	−11.0077	+	11.0077i	−0.452033	+	0.452033i	0.443996	+	0.896029i	$0.353561\pi$
$594$		0			0
$595$	−1.44173	+	0.327307i	−0.0591051	+	0.0134183i
$596$	0.897625	−	0.518244i	0.0367681	−	0.0212281i
$597$		0			0
$598$	−5.03866	+	1.35011i	−0.206046	+	0.0552099i
$599$	−12.9428	+	22.4176i	−0.528828	+	0.915957i	0.470607	+	0.882343i	$0.344035\pi$
$599$	−12.9428	+	22.4176i	−0.528828	+	0.915957i	−0.999435	+	0.0336142i	$0.989298\pi$
$600$		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
$605$	7.27542	+	7.85930i	0.295788	+	0.319526i
$606$		0			0
$607$	7.70972	+	28.7731i	0.312928	+	1.16786i	0.925903	+	0.377761i	$0.123306\pi$
$607$	7.70972	+	28.7731i	0.312928	+	1.16786i	−0.612975	+	0.790102i	$0.710027\pi$
$608$	0.487854	+	1.82070i	0.0197851	+	0.0738390i
$609$		0			0
$610$	0.751018	−	19.4672i	0.0304078	−	0.788202i
$611$			3.43162i			0.138828i
$612$		0			0
$613$	−12.5028	−	12.5028i	−0.504982	−	0.504982i	0.408000	−	0.912982i	$-0.366226\pi$
$613$	−12.5028	−	12.5028i	−0.504982	−	0.504982i	−0.912982	+	0.408000i	$0.866226\pi$
$614$	14.3510	+	24.8566i	0.579157	+	1.00313i
$615$		0			0
$616$	−7.72515	+	13.3804i	−0.311255	+	0.539110i
$617$	7.14621	−	1.91482i	0.287695	−	0.0770878i	−0.112085	−	0.993699i	$-0.535753\pi$
$617$	7.14621	−	1.91482i	0.287695	−	0.0770878i	0.399781	+	0.916611i	$0.369086\pi$
$618$		0			0
$619$	−16.4624	+	9.50460i	−0.661682	+	0.382022i	−0.792917	−	0.609329i	$-0.791439\pi$
$619$	−16.4624	+	9.50460i	−0.661682	+	0.382022i	0.131236	+	0.991351i	$0.458105\pi$
$620$	4.65511	+	20.5050i	0.186954	+	0.823499i
$621$		0			0
$622$	9.78715	−	9.78715i	0.392429	−	0.392429i
$623$	−18.3217	−	4.90928i	−0.734043	−	0.196686i
$624$		0			0
$625$	9.02548	+	23.3140i	0.361019	+	0.932558i
$626$	16.0560	+	9.26994i	0.641727	+	0.370501i
$627$		0			0
$628$	2.36186	−	8.81460i	0.0942486	−	0.351741i
$629$	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	$0.514124\pi$
$632$	3.51245	−	13.1086i	0.139718	−	0.521433i
$633$		0			0
$634$	0.727989	+	0.420305i	0.0289121	+	0.0166924i
$635$	20.3276	+	38.5700i	0.806677	+	1.53060i
$636$		0			0
$637$	7.76396	+	2.08035i	0.307619	+	0.0824263i
$638$	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
$643$	29.4639	−	7.89483i	1.16194	−	0.311342i	0.374202	−	0.927347i	$-0.377917\pi$
$643$	29.4639	−	7.89483i	1.16194	−	0.311342i	0.787742	+	0.616006i	$0.211250\pi$
$644$	−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	$-0.285704\pi$
$647$	−4.02651	−	4.02651i	−0.158298	−	0.158298i	−0.781812	+	0.623514i	$0.785704\pi$
$648$		0			0
$649$			21.6861i			0.851255i
$650$	−2.79816	+	4.08376i	−0.109753	+	0.160178i
$651$		0			0
$652$	−1.84421	−	6.88270i	−0.0722249	−	0.269547i
$653$	8.44081	+	31.5015i	0.330314	+	1.23275i	0.908861	+	0.417100i	$0.136954\pi$
$653$	8.44081	+	31.5015i	0.330314	+	1.23275i	−0.578546	+	0.815650i	$0.696380\pi$
$654$		0			0
$655$	−7.35642	+	6.80990i	−0.287439	+	0.266085i
$656$		−	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	0.976619	−	0.214975i	$-0.0689671\pi$
$659$	7.75612	+	13.4340i	0.302136	+	0.523314i	−0.674484	+	0.738290i	$0.735634\pi$
$660$		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	$0.0241453\pi$
$662$	4.02232	−	1.07778i	0.156332	−	0.0418890i
$663$		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
$668$	−10.4641	−	2.80384i	−0.404867	−	0.108484i
$669$		0			0
$670$	5.38723	−	17.3933i	0.208127	−	0.671963i
$671$	−29.9817	−	17.3099i	−1.15743	−	0.668243i
$672$		0			0
$673$	2.49905	−	9.32657i	0.0963312	−	0.359513i	−0.900887	−	0.434054i	$-0.857083\pi$
$673$	2.49905	−	9.32657i	0.0963312	−	0.359513i	0.997218	+	0.0745413i	$0.0237493\pi$
$674$	−3.24846			−0.125126
$675$		0			0
$676$	12.0197			0.462297
$677$	−1.95869	+	7.30994i	−0.0752787	+	0.280944i	−0.993296	−	0.115596i	$-0.963122\pi$
$677$	−1.95869	+	7.30994i	−0.0752787	+	0.280944i	0.918018	+	0.396539i	$0.129789\pi$
$678$		0			0
$679$	5.03802	+	2.90870i	0.193342	+	0.111626i
$680$	0.112496	−	0.363206i	0.00431401	−	0.0139283i
$681$		0			0
$682$	36.0924	+	9.67093i	1.38205	+	0.370319i
$683$	7.48288	−	7.48288i	0.286325	−	0.286325i	−0.549300	−	0.835625i	$-0.685106\pi$
$683$	7.48288	−	7.48288i	0.286325	−	0.286325i	0.835625	+	0.549300i	$0.185106\pi$
$684$		0			0
$685$	23.6471	+	14.8967i	0.903509	+	0.569175i
$686$	3.76572	−	2.17414i	0.143776	−	0.0830090i
$687$		0			0
$688$	1.99285	−	0.533983i	0.0759767	−	0.0203579i
$689$	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
$695$	−6.82940	+	6.32203i	−0.259054	+	0.239808i
$696$		0			0
$697$	−0.363749	−	1.35753i	−0.0137780	−	0.0514201i
$698$	2.51883	+	9.40041i	0.0953392	+	0.355811i
$699$		0			0
$700$	3.57002	+	19.1105i	0.134934	+	0.722311i
$701$		−	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
$707$	38.6814	−	10.3647i	1.45476	−	0.389803i
$708$		0			0
$709$	0.356646	−	0.205910i	0.0133941	−	0.00773310i	−0.493288	−	0.869866i	$-0.664205\pi$
$709$	0.356646	−	0.205910i	0.0133941	−	0.00773310i	0.506682	+	0.862133i	$0.330872\pi$
$710$	−8.28233	+	13.1474i	−0.310830	+	0.493413i
$711$		0			0
$712$	3.44949	−	3.44949i	0.129275	−	0.129275i
$713$	47.8551	+	12.8227i	1.79219	+	0.480215i
$714$		0			0
$715$	4.10163	+	7.78249i	0.153392	+	0.291048i
$716$	−11.1676	−	6.44762i	−0.417353	−	0.240959i
$717$		0			0
$718$	0.330503	−	1.23345i	0.0123343	−	0.0460321i
$719$	−34.4664			−1.28538			−0.642690	−	0.766126i	$-0.722182\pi$
$719$	−34.4664			−1.28538			−0.642690	+	0.766126i	$0.722182\pi$
$720$		0			0
$721$	−25.2120			−0.938946
$722$	3.99799	−	14.9207i	0.148790	−	0.555291i
$723$		0			0
$724$	−21.0615	−	12.1599i	−0.782744	−	0.451918i
$725$	1.66118	−	21.4977i	0.0616946	−	0.798404i
$726$		0			0
$727$	−13.7902	−	3.69508i	−0.511451	−	0.137043i	−0.00614188	−	0.999981i	$-0.501955\pi$
$727$	−13.7902	−	3.69508i	−0.511451	−	0.137043i	−0.505310	+	0.862938i	$0.668622\pi$
$728$	−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
$733$	−29.6676	+	7.94942i	−1.09580	+	0.293618i	−0.761053	−	0.648690i	$-0.775317\pi$
$733$	−29.6676	+	7.94942i	−1.09580	+	0.293618i	−0.334746	+	0.942308i	$0.608651\pi$
$734$	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	$0.117589\pi$
$739$			19.6312i			0.722144i	−0.932538	+	0.361072i	$0.882411\pi$
$740$	0.398466	−	10.3286i	0.0146479	−	0.379689i
$741$		0			0
$742$	−5.21700	−	19.4701i	−0.191522	−	0.714771i
$743$	9.31585	+	34.7672i	0.341765	+	1.27549i	0.896346	+	0.443356i	$0.146212\pi$
$743$	9.31585	+	34.7672i	0.341765	+	1.27549i	−0.554580	+	0.832130i	$0.687121\pi$
$744$		0			0
$745$	−1.57444	−	1.70079i	−0.0576829	−	0.0623121i
$746$		−	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	$0.815660\pi$
$752$	−3.34787	+	0.897060i	−0.122084	+	0.0327124i
$753$		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	−0.155114	−	0.987897i	$-0.549574\pi$
$757$	22.9129	−	22.9129i	0.832783	−	0.832783i	0.987897	+	0.155114i	$0.0495745\pi$
$758$	−0.567624	−	0.152094i	−0.0206170	−	0.00552432i
$759$		0			0
$760$	3.72867	−	1.96513i	0.135253	−	0.0712828i
$761$	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
$763$	7.34795	−	27.4229i	0.266014	−	0.992777i
$764$	13.6296			0.493100
$765$		0			0
$766$	−14.5012			−0.523950
$767$	−1.39851	+	5.21932i	−0.0504974	+	0.188459i
$768$		0			0
$769$	3.31814	+	1.91573i	0.119655	+	0.0690830i	0.558633	−	0.829415i	$-0.311326\pi$
$769$	3.31814	+	1.91573i	0.119655	+	0.0690830i	−0.438978	+	0.898498i	$0.644659\pi$
$770$	33.0012	+	10.2215i	1.18928	+	0.368356i
$771$		0			0
$772$	−15.6521	−	4.19397i	−0.563332	−	0.150944i
$773$	19.8976	−	19.8976i	0.715668	−	0.715668i	−0.252047	−	0.967715i	$-0.581104\pi$
$773$	19.8976	−	19.8976i	0.715668	−	0.715668i	0.967715	+	0.252047i	$0.0811037\pi$
$774$		0			0
$775$	42.4082	−	20.3017i	1.52335	−	0.729258i
$776$	−1.29571	+	0.748079i	−0.0465133	+	0.0268545i
$777$		0			0
$778$	−20.0504	+	5.37250i	−0.718843	+	0.192613i
$779$	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
$785$	−20.3902	−	0.786626i	−0.727756	−	0.0280759i
$786$		0			0
$787$	−1.87155	−	6.98473i	−0.0667137	−	0.248979i	0.924513	−	0.381150i	$-0.124472\pi$
$787$	−1.87155	−	6.98473i	−0.0667137	−	0.248979i	−0.991227	+	0.132171i	$0.957805\pi$
$788$	0.424901	+	1.58575i	0.0151365	+	0.0564901i
$789$		0			0
$790$	−30.3232	−	1.16983i	−1.07885	−	0.0416207i
$791$			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
$797$	33.4396	−	8.96012i	1.18449	−	0.317384i	0.387786	−	0.921750i	$-0.373240\pi$
$797$	33.4396	−	8.96012i	1.18449	−	0.317384i	0.796707	+	0.604366i	$0.206573\pi$
$798$		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
$803$	−44.9295	−	12.0388i	−1.58553	−	0.424841i
$804$		0			0
$805$	43.7565	+	13.5527i	1.54222	+	0.477670i
$806$	8.06289	+	4.65511i	0.284003	+	0.163969i
$807$		0			0
$808$	−2.66565	+	9.94834i	−0.0937772	+	0.349981i
$809$	52.6028			1.84942			0.924709	−	0.380675i	$-0.124308\pi$
$809$	52.6028			1.84942			0.924709	+	0.380675i	$0.124308\pi$
$810$		0			0
$811$	−13.8979			−0.488021			−0.244011	−	0.969773i	$-0.578463\pi$
$811$	−13.8979			−0.488021			−0.244011	+	0.969773i	$0.578463\pi$
$812$	4.33973	−	16.1961i	0.152295	−	0.568371i
$813$		0			0
$814$	−15.9073	−	9.18410i	−0.557551	−	0.321902i
$815$	−14.0953	+	7.42869i	−0.493737	+	0.260216i
$816$		0			0
$817$	3.75637	+	1.00652i	0.131419	+	0.0352136i
$818$	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
$823$	29.1118	−	7.80049i	1.01477	−	0.271908i	0.287151	−	0.957885i	$-0.407292\pi$
$823$	29.1118	−	7.80049i	1.01477	−	0.271908i	0.727623	+	0.685977i	$0.240625\pi$
$824$	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	$-0.217866\pi$
$827$	4.09863	+	4.09863i	0.142523	+	0.142523i	−0.632245	+	0.774768i	$0.717866\pi$
$828$		0			0
$829$			37.6756i			1.30853i	0.756266	+	0.654264i	$0.227021\pi$
$829$			37.6756i			1.30853i	−0.756266	+	0.654264i	$0.772979\pi$
$830$	−10.6294	−	11.4824i	−0.368951	−	0.398561i
$831$		0			0
$832$	−0.256253	−	0.956351i	−0.00888399	−	0.0331555i
$833$	0.357291	+	1.33343i	0.0123794	+	0.0462006i
$834$		0			0
$835$	−0.933827	+	24.2058i	−0.0323164	+	0.837675i
$836$		−	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	$0.0271069\pi$
$839$	16.5639	+	28.6895i	0.571849	+	0.990471i	−0.424527	+	0.905415i	$0.639560\pi$
$840$		0			0
$841$	5.20180	−	9.00978i	0.179372	−	0.310682i
$842$	26.9420	−	7.21908i	0.928482	−	0.248786i
$843$		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
$848$	5.00745	+	1.34174i	0.171957	+	0.0460757i
$849$		0			0
$850$	−0.847690	−	0.0655031i	−0.0290755	−	0.00224674i
$851$	−21.0916	−	12.1773i	−0.723011	−	0.417431i
$852$		0			0
$853$	0.689663	−	2.57386i	0.0236136	−	0.0881273i	−0.953113	−	0.302613i	$-0.902141\pi$
$853$	0.689663	−	2.57386i	0.0236136	−	0.0881273i	0.976727	+	0.214486i	$0.0688076\pi$
$854$	−33.8760			−1.15921
$855$		0			0
$856$	5.23339			0.178874
$857$	−4.05364	+	15.1284i	−0.138470	+	0.516776i	0.861490	+	0.507775i	$0.169532\pi$
$857$	−4.05364	+	15.1284i	−0.138470	+	0.516776i	−0.999959	+	0.00900123i	$0.997135\pi$
$858$		0			0
$859$	−0.691191	−	0.399059i	−0.0235831	−	0.0136157i	0.488162	−	0.872753i	$-0.337667\pi$
$859$	−0.691191	−	0.399059i	−0.0235831	−	0.0136157i	−0.511745	+	0.859137i	$0.671001\pi$
$860$	−2.15094	−	4.08123i	−0.0733464	−	0.139169i
$861$		0			0
$862$	18.6337	+	4.99288i	0.634666	+	0.170058i
$863$	30.2854	−	30.2854i	1.03093	−	1.03093i	0.0314193	−	0.999506i	$-0.489997\pi$
$863$	30.2854	−	30.2854i	1.03093	−	1.03093i	0.999506	−	0.0314193i	$-0.0100027\pi$
$864$		0			0
$865$	4.49311	−	7.13237i	0.152770	−	0.242508i
$866$	20.4721	−	11.8196i	0.695671	−	0.401646i
$867$		0			0
$868$	35.3169	−	9.46313i	1.19873	−	0.321199i
$869$	−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
$875$	39.9048	−	17.2453i	1.34903	−	0.582996i
$876$		0			0
$877$	4.48641	+	16.7435i	0.151495	+	0.565388i	0.999380	+	0.0352074i	$0.0112092\pi$
$877$	4.48641	+	16.7435i	0.151495	+	0.565388i	−0.847885	+	0.530180i	$0.822124\pi$
$878$	−9.31875	−	34.7780i	−0.314492	−	1.17370i
$879$		0			0
$880$	−6.52036	+	6.03596i	−0.219801	+	0.203472i
$881$		−	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	0.373461	−	0.927646i	$-0.378171\pi$
$883$	−16.4678	−	16.4678i	−0.554185	−	0.554185i	−0.927646	+	0.373461i	$0.878171\pi$
$884$	−0.0841789	−	0.145802i	−0.00283124	−	0.00490386i
$885$		0			0
$886$	13.4169	−	23.2388i	0.450750	−	0.780723i
$887$	−26.4123	+	7.07714i	−0.886837	+	0.237627i	−0.673355	−	0.739320i	$-0.735147\pi$
$887$	−26.4123	+	7.07714i	−0.886837	+	0.237627i	−0.213482	+	0.976947i	$0.568481\pi$
$888$		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
$893$	−6.31049	−	1.69089i	−0.211173	−	0.0565835i
$894$		0			0
$895$	−8.53111	+	27.5437i	−0.285164	+	0.920686i
$896$	−3.36730	−	1.94411i	−0.112494	−	0.0649483i
$897$		0			0
$898$	−10.6994	+	39.9306i	−0.357043	+	1.33250i
$899$	−40.5510			−1.35245
$900$		0			0
$901$	0.881522			0.0293678
$902$	−8.50016	+	31.7230i	−0.283025	+	1.05626i
$903$		0			0
$904$	−3.65405	−	2.10967i	−0.121532	−	0.0701666i
$905$	−16.0892	+	51.9459i	−0.534823	+	1.72674i
$906$		0			0
$907$	−24.7295	−	6.62626i	−0.821130	−	0.220021i	−0.176290	−	0.984338i	$-0.556410\pi$
$907$	−24.7295	−	6.62626i	−0.821130	−	0.220021i	−0.644841	+	0.764317i	$0.723076\pi$
$908$	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
$913$	−26.8582	+	7.19662i	−0.888875	+	0.238173i
$914$	−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	$-0.842002\pi$
$919$		−	28.8740i		−	0.952464i	0.879320	−	0.476232i	$-0.157998\pi$
$920$	−8.64539	+	8.00311i	−0.285030	+	0.263855i
$921$		0			0
$922$	−3.24877	−	12.1246i	−0.106993	−	0.399302i
$923$	1.78073	+	6.64579i	0.0586135	+	0.218749i
$924$		0			0
$925$	−22.7197	+	4.24424i	−0.747019	+	0.139550i
$926$			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	$-0.858540\pi$
$929$	−25.1077	−	43.4879i	−0.823758	−	1.42679i	0.0791067	−	0.996866i	$-0.474793\pi$
$930$		0			0
$931$	−7.65121	+	13.2523i	−0.250758	+	0.434326i
$932$	28.2072	−	7.55809i	0.923956	−	0.247573i
$933$		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	−0.720968	−	0.692968i	$-0.756303\pi$
$937$	−0.857094	+	0.857094i	−0.0280000	+	0.0280000i	0.692968	+	0.720968i	$0.256303\pi$
$938$	−30.5834	−	8.19479i	−0.998582	−	0.267569i
$939$		0			0
$940$	3.61346	+	6.85623i	0.117858	+	0.223625i
$941$	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
$943$	−11.2704	+	42.0618i	−0.367015	+	1.36972i
$944$	−5.45754			−0.177628
$945$		0			0
$946$	−8.19815			−0.266545
$947$	−0.681485	+	2.54334i	−0.0221453	+	0.0826473i	−0.976114	−	0.217258i	$-0.930289\pi$
$947$	−0.681485	+	2.54334i	−0.0221453	+	0.0826473i	0.953969	+	0.299906i	$0.0969552\pi$
$948$		0			0
$949$	−10.0371	−	5.79490i	−0.325817	−	0.188111i
$950$	−6.13098	−	7.15784i	−0.198915	−	0.232231i
$951$		0			0
$952$	−0.638639	−	0.171123i	−0.0206984	−	0.00554612i
$953$	−28.1499	+	28.1499i	−0.911864	+	0.911864i	−0.996419	−	0.0845545i	$-0.973053\pi$
$953$	−28.1499	+	28.1499i	−0.911864	+	0.911864i	0.0845545	+	0.996419i	$0.473053\pi$
$954$		0			0
$955$	−6.74723	−	29.7204i	−0.218335	−	0.961729i
$956$	−7.90295	+	4.56277i	−0.255600	+	0.147571i
$957$		0			0
$958$	−2.62100	+	0.702296i	−0.0846808	+	0.0226901i
$959$	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
$965$	−1.39681	+	36.2069i	−0.0449651	+	1.16554i
$966$		0			0
$967$	−0.343829	−	1.28319i	−0.0110568	−	0.0412646i	0.960177	−	0.279392i	$-0.0901330\pi$
$967$	−0.343829	−	1.28319i	−0.0110568	−	0.0412646i	−0.971234	+	0.238128i	$0.923466\pi$
$968$	1.23963	+	4.62638i	0.0398433	+	0.148697i
$969$		0			0
$970$	2.27268	+	2.45507i	0.0729714	+	0.0788276i
$971$			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
$977$	−41.4084	+	11.0953i	−1.32477	+	0.354972i	−0.850764	−	0.525548i	$-0.823860\pi$
$977$	−41.4084	+	11.0953i	−1.32477	+	0.354972i	−0.474009	+	0.880520i	$0.657193\pi$
$978$		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
$983$	−31.1321	−	8.34182i	−0.992960	−	0.266063i	−0.274466	−	0.961597i	$-0.588501\pi$
$983$	−31.1321	−	8.34182i	−0.992960	−	0.266063i	−0.718493	+	0.695534i	$0.755168\pi$
$984$		0			0
$985$	3.24751	−	1.71155i	0.103474	−	0.0545344i
$986$	0.635046	+	0.366644i	0.0202240	+	0.0116763i
$987$		0			0
$988$	0.483018	−	1.80265i	0.0153669	−	0.0573499i
$989$	−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	$0.396561\pi$
$992$	−2.43379	+	9.08302i	−0.0772729	+	0.288386i
$993$		0			0
$994$	23.3998	+	13.5099i	0.742196	+	0.428507i
$995$	−36.6815	−	11.3613i	−1.16288	−	0.360178i
$996$		0			0
$997$	−2.84912	−	0.763421i	−0.0902327	−	0.0241778i	0.213420	−	0.976960i	$-0.431540\pi$
$997$	−2.84912	−	0.763421i	−0.0902327	−	0.0241778i	−0.303653	+	0.952783i	$0.598206\pi$
$998$	−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.233.3		16
3.2	odd	2		90.2.l.b.23.1	✓	16
5.2	odd	4	inner	270.2.m.b.17.4		16
5.3	odd	4		1350.2.q.h.557.2		16
5.4	even	2		1350.2.q.h.1043.1		16
9.2	odd	6	inner	270.2.m.b.143.4		16
9.4	even	3		810.2.f.c.323.8		16
9.5	odd	6		810.2.f.c.323.1		16
9.7	even	3		90.2.l.b.83.1	yes	16
12.11	even	2		720.2.cu.b.113.3		16
15.2	even	4		90.2.l.b.77.1	yes	16
15.8	even	4		450.2.p.h.257.4		16
15.14	odd	2		450.2.p.h.293.4		16
36.7	odd	6		720.2.cu.b.353.4		16
45.2	even	12	inner	270.2.m.b.197.3		16
45.7	odd	12		90.2.l.b.47.1	yes	16
45.22	odd	12		810.2.f.c.647.1		16
45.29	odd	6		1350.2.q.h.143.2		16
45.32	even	12		810.2.f.c.647.8		16
45.34	even	6		450.2.p.h.443.4		16
45.38	even	12		1350.2.q.h.1007.1		16
45.43	odd	12		450.2.p.h.407.4		16
60.47	odd	4		720.2.cu.b.257.4		16
180.7	even	12		720.2.cu.b.497.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.1	✓	16	3.2	odd	2
90.2.l.b.47.1	yes	16	45.7	odd	12
90.2.l.b.77.1	yes	16	15.2	even	4
90.2.l.b.83.1	yes	16	9.7	even	3
270.2.m.b.17.4		16	5.2	odd	4	inner
270.2.m.b.143.4		16	9.2	odd	6	inner
270.2.m.b.197.3		16	45.2	even	12	inner
270.2.m.b.233.3		16	1.1	even	1	trivial
450.2.p.h.257.4		16	15.8	even	4
450.2.p.h.293.4		16	15.14	odd	2
450.2.p.h.407.4		16	45.43	odd	12
450.2.p.h.443.4		16	45.34	even	6
720.2.cu.b.113.3		16	12.11	even	2
720.2.cu.b.257.4		16	60.47	odd	4
720.2.cu.b.353.4		16	36.7	odd	6
720.2.cu.b.497.3		16	180.7	even	12
810.2.f.c.323.1		16	9.5	odd	6
810.2.f.c.323.8		16	9.4	even	3
810.2.f.c.647.1		16	45.22	odd	12
810.2.f.c.647.8		16	45.32	even	12
1350.2.q.h.143.2		16	45.29	odd	6
1350.2.q.h.557.2		16	5.3	odd	4
1350.2.q.h.1007.1		16	45.38	even	12
1350.2.q.h.1043.1		16	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.661570 + 2.13596i) q^{5} +(3.75574 + 1.00635i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.661570 + 2.13596i) q^{5} +(3.75574 + 1.00635i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.89195 + 1.19185i) q^{10} +(3.44125 - 1.98681i) q^{11} +(0.956351 - 0.256253i) q^{13} +(1.94411 - 3.36730i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.120239 + 0.120239i) q^{17} +1.88492i q^{19} +(1.64092 - 1.51901i) q^{20} +(-1.02845 - 3.83821i) q^{22} +(-1.36362 - 5.08911i) q^{23} +(-4.12465 - 2.82617i) q^{25} -0.990087i q^{26} +(-2.74939 - 2.74939i) q^{28} +(2.15618 + 3.73461i) q^{29} +(-4.70172 + 8.14362i) q^{31} +(0.965926 - 0.258819i) q^{32} +(0.147262 - 0.0850217i) q^{34} +(-4.63420 + 7.35634i) q^{35} +(3.26863 - 3.26863i) q^{37} +(1.82070 + 0.487854i) q^{38} +(-1.04255 - 1.97815i) q^{40} +(-7.15775 - 4.13253i) q^{41} +(0.533983 - 1.99285i) q^{43} -3.97361 q^{44} -5.26863 q^{46} +(-0.897060 + 3.34787i) q^{47} +(7.03067 + 4.05916i) q^{49} +(-3.79741 + 3.25264i) q^{50} +(-0.956351 - 0.256253i) q^{52} +(3.66571 - 3.66571i) q^{53} +(1.96711 + 8.66478i) q^{55} +(-3.36730 + 1.94411i) q^{56} +(4.16541 - 1.11612i) q^{58} +(-2.72877 + 4.72637i) q^{59} +(-4.35623 - 7.54520i) q^{61} +(6.64923 + 6.64923i) q^{62} -1.00000i q^{64} +(-0.0853460 + 2.21226i) q^{65} +(-2.10759 - 7.86563i) q^{67} +(-0.0440105 - 0.164249i) q^{68} +(5.90626 + 6.38026i) q^{70} +6.94911i q^{71} +(-8.27728 - 8.27728i) q^{73} +(-2.31127 - 4.00324i) q^{74} +(0.942462 - 1.63239i) q^{76} +(14.9238 - 3.99883i) q^{77} +(-11.7529 + 6.78553i) q^{79} +(-2.18058 + 0.495044i) q^{80} +(-5.84428 + 5.84428i) q^{82} +(-6.75913 - 1.81110i) q^{83} +(-0.336372 + 0.177279i) q^{85} +(-1.78674 - 1.03157i) q^{86} +(-1.02845 + 3.83821i) q^{88} -4.87832 q^{89} +3.84968 q^{91} +(-1.36362 + 5.08911i) q^{92} +(3.00162 + 1.73299i) q^{94} +(-4.02612 - 1.24701i) q^{95} +(1.44518 + 0.387234i) q^{97} +(5.74052 - 5.74052i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) \) 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

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