LMFDB - Embedded newform 1350.2.q.h.143.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(143,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("1350.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.q (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:	$10.7798042729$
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:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			143.2
Root			$0.500000 - 2.00333i$ of defining polynomial
Character	$\chi$	$=$	1350.143
Dual form			1350.2.q.h.557.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(1.00635 + 3.75574i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(1.00635 + 3.75574i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(3.44125 + 1.98681i) q^{11} +(0.256253 - 0.956351i) q^{13} +(-1.94411 - 3.36730i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.120239 + 0.120239i) q^{17} +1.88492i q^{19} +(-3.83821 - 1.02845i) q^{22} +(5.08911 + 1.36362i) q^{23} +0.990087i q^{26} +(2.74939 + 2.74939i) q^{28} +(-2.15618 + 3.73461i) q^{29} +(-4.70172 - 8.14362i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.147262 - 0.0850217i) q^{34} +(-3.26863 + 3.26863i) q^{37} +(-0.487854 - 1.82070i) q^{38} +(-7.15775 + 4.13253i) q^{41} +(1.99285 - 0.533983i) q^{43} +3.97361 q^{44} -5.26863 q^{46} +(3.34787 - 0.897060i) q^{47} +(-7.03067 + 4.05916i) q^{49} +(-0.256253 - 0.956351i) q^{52} +(3.66571 - 3.66571i) q^{53} +(-3.36730 - 1.94411i) q^{56} +(1.11612 - 4.16541i) q^{58} +(2.72877 + 4.72637i) q^{59} +(-4.35623 + 7.54520i) q^{61} +(6.64923 + 6.64923i) q^{62} -1.00000i q^{64} +(-7.86563 - 2.10759i) q^{67} +(0.164249 + 0.0440105i) q^{68} -6.94911i q^{71} +(8.27728 + 8.27728i) q^{73} +(2.31127 - 4.00324i) q^{74} +(0.942462 + 1.63239i) q^{76} +(-3.99883 + 14.9238i) q^{77} +(11.7529 + 6.78553i) q^{79} +(5.84428 - 5.84428i) q^{82} +(1.81110 + 6.75913i) q^{83} +(-1.78674 + 1.03157i) q^{86} +(-3.83821 + 1.02845i) q^{88} +4.87832 q^{89} +3.84968 q^{91} +(5.08911 - 1.36362i) q^{92} +(-3.00162 + 1.73299i) q^{94} +(0.387234 + 1.44518i) q^{97} +(5.74052 - 5.74052i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 8 q^{16} - 8 q^{22} - 24 q^{23} + 16 q^{28} - 8 q^{31} + 24 q^{38} - 24 q^{41} - 32 q^{46} + 48 q^{47} - 24 q^{56} - 16 q^{58} - 24 q^{61} + 16 q^{67} - 24 q^{68} - 16 q^{73} + 16 q^{76} - 72 q^{77} + 16 q^{82} + 48 q^{83} + 48 q^{86} - 8 q^{88} - 24 q^{92} + 48 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 8 * q^16 - 8 * q^22 - 24 * q^23 + 16 * q^28 - 8 * q^31 + 24 * q^38 - 24 * q^41 - 32 * q^46 + 48 * q^47 - 24 * q^56 - 16 * q^58 - 24 * q^61 + 16 * q^67 - 24 * q^68 - 16 * q^73 + 16 * q^76 - 72 * q^77 + 16 * q^82 + 48 * q^83 + 48 * q^86 - 8 * q^88 - 24 * q^92 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.965926	+	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
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.00635	+	3.75574i	0.380364	+	1.41954i	0.845347	+	0.534217i	$0.179394\pi$
$7$	1.00635	+	3.75574i	0.380364	+	1.41954i	−0.464984	+	0.885319i	$0.653940\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$		0			0
$11$	3.44125	+	1.98681i	1.03758	+	0.599044i	0.919145	−	0.393918i	$-0.128881\pi$
$11$	3.44125	+	1.98681i	1.03758	+	0.599044i	0.118430	+	0.992962i	$0.462214\pi$
$12$		0			0
$13$	0.256253	−	0.956351i	0.0710719	−	0.265244i	−0.921242	−	0.388990i	$-0.872824\pi$
$13$	0.256253	−	0.956351i	0.0710719	−	0.265244i	0.992314	+	0.123746i	$0.0394908\pi$
$14$	−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	$0.930629\pi$
$20$		0			0
$21$		0			0
$22$	−3.83821	−	1.02845i	−0.818310	−	0.219265i
$23$	5.08911	+	1.36362i	1.06115	+	0.284335i	0.746853	−	0.664989i	$-0.231564\pi$
$23$	5.08911	+	1.36362i	1.06115	+	0.284335i	0.314299	+	0.949324i	$0.398230\pi$
$24$		0			0
$25$		0			0
$26$			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	$-0.964459\pi$
$29$	−2.15618	+	3.73461i	−0.400392	+	0.693499i	0.593381	+	0.804922i	$0.297793\pi$
$30$		0			0
$31$	−4.70172	−	8.14362i	−0.844454	−	1.46264i	−0.886095	−	0.463504i	$-0.846592\pi$
$31$	−4.70172	−	8.14362i	−0.844454	−	1.46264i	0.0416413	−	0.999133i	$-0.486741\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$		0			0
$34$	−0.147262	−	0.0850217i	−0.0252552	−	0.0145811i
$35$		0			0
$36$		0			0
$37$	−3.26863	+	3.26863i	−0.537360	+	0.537360i	−0.922753	−	0.385393i	$-0.874066\pi$
$37$	−3.26863	+	3.26863i	−0.537360	+	0.537360i	0.385393	+	0.922753i	$0.374066\pi$
$38$	−0.487854	−	1.82070i	−0.0791404	−	0.295356i
$39$		0			0
$40$		0			0
$41$	−7.15775	+	4.13253i	−1.11785	+	0.645393i	−0.940852	−	0.338818i	$-0.889973\pi$
$41$	−7.15775	+	4.13253i	−1.11785	+	0.645393i	−0.177001	+	0.984211i	$0.556640\pi$
$42$		0			0
$43$	1.99285	−	0.533983i	0.303907	−	0.0814316i	−0.103643	−	0.994615i	$-0.533050\pi$
$43$	1.99285	−	0.533983i	0.303907	−	0.0814316i	0.407550	+	0.913183i	$0.366383\pi$
$44$	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	$-0.501988\pi$
$47$	3.34787	−	0.897060i	0.488338	−	0.130850i	0.494582	+	0.869131i	$0.335321\pi$
$48$		0			0
$49$	−7.03067	+	4.05916i	−1.00438	+	0.579880i
$50$		0			0
$51$		0			0
$52$	−0.256253	−	0.956351i	−0.0355359	−	0.132622i
$53$	3.66571	−	3.66571i	0.503524	−	0.503524i	−0.409007	−	0.912531i	$-0.634125\pi$
$53$	3.66571	−	3.66571i	0.503524	−	0.503524i	0.912531	+	0.409007i	$0.134125\pi$
$54$		0			0
$55$		0			0
$56$	−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	0.987162	−	0.159724i	$-0.0510606\pi$
$59$	2.72877	+	4.72637i	0.355255	+	0.615320i	−0.631906	+	0.775045i	$0.717727\pi$
$60$		0			0
$61$	−4.35623	+	7.54520i	−0.557758	+	0.966064i	0.439926	+	0.898034i	$0.355005\pi$
$61$	−4.35623	+	7.54520i	−0.557758	+	0.966064i	−0.997683	+	0.0680302i	$0.978329\pi$
$62$	6.64923	+	6.64923i	0.844454	+	0.844454i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$		0			0
$67$	−7.86563	−	2.10759i	−0.960940	−	0.257483i	−0.255942	−	0.966692i	$-0.582385\pi$
$67$	−7.86563	−	2.10759i	−0.960940	−	0.257483i	−0.704998	+	0.709209i	$0.749052\pi$
$68$	0.164249	+	0.0440105i	0.0199182	+	0.00533705i
$69$		0			0
$70$		0			0
$71$		−	6.94911i		−	0.824708i	−0.911024	−	0.412354i	$-0.864707\pi$
$71$		−	6.94911i		−	0.824708i	0.911024	−	0.412354i	$-0.135293\pi$
$72$		0			0
$73$	8.27728	+	8.27728i	0.968783	+	0.968783i	0.999527	−	0.0307446i	$-0.00978785\pi$
$73$	8.27728	+	8.27728i	0.968783	+	0.968783i	−0.0307446	+	0.999527i	$0.509788\pi$
$74$	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	0.984095	−	0.177641i	$-0.0568465\pi$
$79$	11.7529	+	6.78553i	1.32230	+	0.763431i	0.338206	+	0.941072i	$0.390180\pi$
$80$		0			0
$81$		0			0
$82$	5.84428	−	5.84428i	0.645393	−	0.645393i
$83$	1.81110	+	6.75913i	0.198795	+	0.741911i	0.991252	+	0.131984i	$0.0421347\pi$
$83$	1.81110	+	6.75913i	0.198795	+	0.741911i	−0.792457	+	0.609927i	$0.791199\pi$
$84$		0			0
$85$		0			0
$86$	−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
$95$		0			0
$96$		0			0
$97$	0.387234	+	1.44518i	0.0393177	+	0.146736i	0.982794	−	0.184704i	$-0.0591325\pi$
$97$	0.387234	+	1.44518i	0.0393177	+	0.146736i	−0.943477	+	0.331439i	$0.892466\pi$
$98$	5.74052	−	5.74052i	0.579880	−	0.579880i
$99$		0			0
$100$		0			0
$101$	8.91944	+	5.14964i	0.887517	+	0.512408i	0.873130	−	0.487488i	$-0.162087\pi$
$101$	8.91944	+	5.14964i	0.887517	+	0.512408i	0.0143875	+	0.999896i	$0.495420\pi$
$102$		0			0
$103$	−1.67823	+	6.26326i	−0.165361	+	0.617137i	0.832632	+	0.553826i	$0.186833\pi$
$103$	−1.67823	+	6.26326i	−0.165361	+	0.617137i	−0.997994	+	0.0633111i	$0.979834\pi$
$104$	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	$-0.113711\pi$
$110$		0			0
$111$		0			0
$112$	3.75574	+	1.00635i	0.354884	+	0.0950909i
$113$	−4.07557	−	1.09205i	−0.383397	−	0.102731i	0.0619722	−	0.998078i	$-0.480261\pi$
$113$	−4.07557	−	1.09205i	−0.383397	−	0.102731i	−0.445369	+	0.895347i	$0.646928\pi$
$114$		0			0
$115$		0			0
$116$			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
$125$		0			0
$126$		0			0
$127$	−13.7871	+	13.7871i	−1.22341	+	1.22341i	−0.257000	+	0.966411i	$0.582734\pi$
$127$	−13.7871	+	13.7871i	−1.22341	+	1.22341i	−0.966411	+	0.257000i	$0.917266\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$		0			0
$130$		0			0
$131$	3.88249	−	2.24156i	0.339215	−	0.195846i	−0.320710	−	0.947178i	$-0.603921\pi$
$131$	3.88249	−	2.24156i	0.339215	−	0.195846i	0.659925	+	0.751332i	$0.270588\pi$
$132$		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	$-0.762616\pi$
$137$	−12.0729	+	3.23492i	−1.03146	+	0.276378i	−0.296888	+	0.954912i	$0.595949\pi$
$138$		0			0
$139$	−3.60435	+	2.08097i	−0.305717	+	0.176506i	−0.645008	−	0.764176i	$-0.723146\pi$
$139$	−3.60435	+	2.08097i	−0.305717	+	0.176506i	0.339291	+	0.940681i	$0.389813\pi$
$140$		0			0
$141$		0			0
$142$	1.79856	+	6.71233i	0.150932	+	0.563286i
$143$	2.78191	−	2.78191i	0.232635	−	0.232635i
$144$		0			0
$145$		0			0
$146$	−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	0.886473	−	0.462781i	$-0.153148\pi$
$149$	0.518244	+	0.897625i	0.0424562	+	0.0735363i	−0.844016	+	0.536317i	$0.819815\pi$
$150$		0			0
$151$	−2.03451	+	3.52388i	−0.165566	+	0.286769i	−0.936856	−	0.349715i	$-0.886278\pi$
$151$	−2.03451	+	3.52388i	−0.165566	+	0.286769i	0.771290	+	0.636484i	$0.219612\pi$
$152$	−1.33284	−	1.33284i	−0.108108	−	0.108108i
$153$		0			0
$154$		−	15.4503i		−	1.24502i
$155$		0			0
$156$		0			0
$157$	8.81460	+	2.36186i	0.703481	+	0.188497i	0.592789	−	0.805357i	$-0.298027\pi$
$157$	8.81460	+	2.36186i	0.703481	+	0.188497i	0.110692	+	0.993855i	$0.464693\pi$
$158$	−13.1086	−	3.51245i	−1.04287	−	0.279435i
$159$		0			0
$160$		0			0
$161$			20.4857i			1.61450i
$162$		0			0
$163$	−5.03848	−	5.03848i	−0.394644	−	0.394644i	0.481695	−	0.876339i	$-0.340021\pi$
$163$	−5.03848	−	5.03848i	−0.394644	−	0.394644i	−0.876339	+	0.481695i	$0.840021\pi$
$164$	−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	0.768497	+	0.639853i	$0.221005\pi$
$167$	−2.80384	+	10.4641i	−0.216968	+	0.809734i	−0.985465	+	0.169881i	$0.945662\pi$
$168$		0			0
$169$	10.4094	+	6.00986i	0.800722	+	0.462297i
$170$		0			0
$171$		0			0
$172$	1.45887	−	1.45887i	0.111238	−	0.111238i
$173$	0.975709	+	3.64139i	0.0741818	+	0.276850i	0.993047	−	0.117722i	$-0.0375593\pi$
$173$	0.975709	+	3.64139i	0.0741818	+	0.276850i	−0.918865	+	0.394573i	$0.870893\pi$
$174$		0			0
$175$		0			0
$176$	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
$185$		0			0
$186$		0			0
$187$	0.174880	+	0.652663i	0.0127885	+	0.0477274i
$188$	2.45081	−	2.45081i	0.178744	−	0.178744i
$189$		0			0
$190$		0			0
$191$	−11.8036	−	6.81478i	−0.854075	−	0.493100i	0.00794868	−	0.999968i	$-0.497470\pi$
$191$	−11.8036	−	6.81478i	−0.854075	−	0.493100i	−0.862024	+	0.506868i	$0.830803\pi$
$192$		0			0
$193$	4.19397	−	15.6521i	0.301889	−	1.12666i	−0.633702	−	0.773577i	$-0.718466\pi$
$193$	4.19397	−	15.6521i	0.301889	−	1.12666i	0.935591	−	0.353086i	$-0.114868\pi$
$194$	−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	$0.791695\pi$
$200$		0			0
$201$		0			0
$202$	−9.94834	−	2.66565i	−0.699963	−	0.187554i
$203$	−16.1961	−	4.33973i	−1.13674	−	0.304589i
$204$		0			0
$205$		0			0
$206$		−	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	−0.988134	−	0.153597i	$-0.950914\pi$
$211$	−9.10894	−	15.7771i	−0.627085	−	1.08614i	0.361048	−	0.932547i	$-0.382419\pi$
$212$	1.34174	−	5.00745i	0.0921513	−	0.343913i
$213$		0			0
$214$	4.53225	+	2.61670i	0.309818	+	0.178874i
$215$		0			0
$216$		0			0
$217$	25.8537	−	25.8537i	1.75507	−	1.75507i
$218$	1.88979	+	7.05281i	0.127993	+	0.477676i
$219$		0			0
$220$		0			0
$221$	0.145802	−	0.0841789i	0.00980771	−	0.00566249i
$222$		0			0
$223$	4.53570	−	1.21534i	0.303733	−	0.0813849i	−0.103734	−	0.994605i	$-0.533079\pi$
$223$	4.53570	−	1.21534i	0.303733	−	0.0813849i	0.407466	+	0.913220i	$0.366412\pi$
$224$	−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	$-0.271277\pi$
$227$	24.1784	−	6.47859i	1.60478	−	0.429999i	0.946481	+	0.322759i	$0.104610\pi$
$228$		0			0
$229$	19.7350	−	11.3940i	1.30412	−	0.752935i	0.323014	−	0.946394i	$-0.395304\pi$
$229$	19.7350	−	11.3940i	1.30412	−	0.752935i	0.981108	+	0.193459i	$0.0619706\pi$
$230$		0			0
$231$		0			0
$232$	−1.11612	−	4.16541i	−0.0732768	−	0.273473i
$233$	−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
$235$		0			0
$236$	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	0.679877	−	0.733327i	$-0.262033\pi$
$239$	−4.56277	−	7.90295i	−0.295141	−	0.511199i	−0.975018	+	0.222127i	$0.928700\pi$
$240$		0			0
$241$	0.869654	−	1.50629i	0.0560194	−	0.0970284i	−0.836656	−	0.547729i	$-0.815492\pi$
$241$	0.869654	−	1.50629i	0.0560194	−	0.0970284i	0.892675	+	0.450701i	$0.148826\pi$
$242$	−3.38674	−	3.38674i	−0.217708	−	0.217708i
$243$		0			0
$244$			8.71245i			0.557758i
$245$		0			0
$246$		0			0
$247$	1.80265	+	0.483018i	0.114700	+	0.0307337i
$248$	9.08302	+	2.43379i	0.576773	+	0.154546i
$249$		0			0
$250$		0			0
$251$		−	6.16751i		−	0.389290i	−0.980874	−	0.194645i	$-0.937645\pi$
$251$		−	6.16751i		−	0.389290i	0.980874	−	0.194645i	$-0.0623555\pi$
$252$		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	−0.174018	−	0.984743i	$-0.555675\pi$
$257$	7.51956	−	28.0634i	0.469057	−	1.75055i	0.643075	−	0.765803i	$-0.277658\pi$
$258$		0			0
$259$	−15.5655	−	8.98676i	−0.967194	−	0.558410i
$260$		0			0
$261$		0			0
$262$	−3.17004	+	3.17004i	−0.195846	+	0.195846i
$263$	−4.82975	−	18.0249i	−0.297815	−	1.11146i	−0.938956	−	0.344038i	$-0.888205\pi$
$263$	−4.82975	−	18.0249i	−0.297815	−	1.11146i	0.641141	−	0.767424i	$-0.278462\pi$
$264$		0			0
$265$		0			0
$266$	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
$275$		0			0
$276$		0			0
$277$	1.06921	+	3.99035i	0.0642426	+	0.239757i	0.990579	−	0.136940i	$-0.0437267\pi$
$277$	1.06921	+	3.99035i	0.0642426	+	0.239757i	−0.926337	+	0.376696i	$0.877060\pi$
$278$	2.94294	−	2.94294i	0.176506	−	0.176506i
$279$		0			0
$280$		0			0
$281$	−0.248640	−	0.143552i	−0.0148326	−	0.00856361i	0.492565	−	0.870275i	$-0.336059\pi$
$281$	−0.248640	−	0.143552i	−0.0148326	−	0.00856361i	−0.507398	+	0.861712i	$0.669393\pi$
$282$		0			0
$283$	4.68527	−	17.4857i	0.278510	−	1.03941i	−0.674942	−	0.737871i	$-0.735831\pi$
$283$	4.68527	−	17.4857i	0.278510	−	1.03941i	0.953452	−	0.301544i	$-0.0975019\pi$
$284$	−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			0
$291$		0			0
$292$	11.3070	+	3.02970i	0.661691	+	0.177300i
$293$	20.6663	+	5.53752i	1.20734	+	0.323505i	0.805717	−	0.592300i	$-0.201780\pi$
$293$	20.6663	+	5.53752i	1.20734	+	0.323505i	0.401621	+	0.915806i	$0.368447\pi$
$294$		0			0
$295$		0			0
$296$		−	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
$305$		0			0
$306$		0			0
$307$	20.2953	−	20.2953i	1.15831	−	1.15831i	0.173476	−	0.984838i	$-0.444500\pi$
$307$	20.2953	−	20.2953i	1.15831	−	1.15831i	0.984838	−	0.173476i	$-0.0555001\pi$
$308$	3.99883	+	14.9238i	0.227855	+	0.850365i
$309$		0			0
$310$		0			0
$311$	11.9868	−	6.92056i	0.679707	−	0.392429i	−0.120038	−	0.992769i	$-0.538302\pi$
$311$	11.9868	−	6.92056i	0.679707	−	0.392429i	0.799745	+	0.600340i	$0.204968\pi$
$312$		0			0
$313$	−17.9081	+	4.79847i	−1.01223	+	0.271226i	−0.726560	−	0.687103i	$-0.758882\pi$
$313$	−17.9081	+	4.79847i	−1.01223	+	0.271226i	−0.285668	+	0.958329i	$0.592215\pi$
$314$	−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	$-0.575818\pi$
$317$	0.811966	−	0.217566i	0.0456046	−	0.0122197i	0.281549	+	0.959547i	$0.409152\pi$
$318$		0			0
$319$	−14.8399	+	8.56781i	−0.830874	+	0.479705i
$320$		0			0
$321$		0			0
$322$	−5.30208	−	19.7876i	−0.295473	−	1.10272i
$323$	−0.226641	+	0.226641i	−0.0126107	+	0.0126107i
$324$		0			0
$325$		0			0
$326$	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	−0.803114	−	0.595825i	$-0.796825\pi$
$331$	2.08211	−	3.60631i	0.114443	−	0.198221i	0.917557	+	0.397604i	$0.130158\pi$
$332$	4.94803	+	4.94803i	0.271558	+	0.271558i
$333$		0			0
$334$		−	10.8332i		−	0.592766i
$335$		0			0
$336$		0			0
$337$	−3.13777	−	0.840764i	−0.170925	−	0.0457993i	0.172341	−	0.985037i	$-0.444867\pi$
$337$	−3.13777	−	0.840764i	−0.170925	−	0.0457993i	−0.343267	+	0.939238i	$0.611533\pi$
$338$	−11.6102	−	3.11093i	−0.631510	−	0.169213i
$339$		0			0
$340$		0			0
$341$		−	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	$-0.876461\pi$
$347$	1.21470	−	4.53334i	0.0652087	−	0.243362i	0.990835	+	0.135076i	$0.0431279\pi$
$348$		0			0
$349$	8.42818	+	4.86601i	0.451150	+	0.260472i	0.708316	−	0.705896i	$-0.249455\pi$
$349$	8.42818	+	4.86601i	0.451150	+	0.260472i	−0.257166	+	0.966367i	$0.582789\pi$
$350$		0			0
$351$		0			0
$352$	−2.80977	+	2.80977i	−0.149761	+	0.149761i
$353$	−1.32049	−	4.92815i	−0.0702827	−	0.262299i	0.921840	−	0.387572i	$-0.126686\pi$
$353$	−1.32049	−	4.92815i	−0.0702827	−	0.262299i	−0.992122	+	0.125273i	$0.960019\pi$
$354$		0			0
$355$		0			0
$356$	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
$365$		0			0
$366$		0			0
$367$	2.61063	+	9.74300i	0.136274	+	0.508581i	0.999989	+	0.00460117i	$0.00146460\pi$
$367$	2.61063	+	9.74300i	0.136274	+	0.508581i	−0.863716	+	0.503979i	$0.831869\pi$
$368$	3.72549	−	3.72549i	0.194204	−	0.194204i
$369$		0			0
$370$		0			0
$371$	17.4564	+	10.0785i	0.906293	+	0.523249i
$372$		0			0
$373$	3.39374	−	12.6656i	0.175721	−	0.655801i	−0.820706	−	0.571350i	$-0.806420\pi$
$373$	3.39374	−	12.6656i	0.175721	−	0.655801i	0.996428	−	0.0844507i	$-0.0269135\pi$
$374$	−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	$-0.00480434\pi$
$380$		0			0
$381$		0			0
$382$	13.1652	+	3.52759i	0.673588	+	0.180487i
$383$	14.0071	+	3.75319i	0.715729	+	0.191779i	0.598265	−	0.801298i	$-0.295857\pi$
$383$	14.0071	+	3.75319i	0.715729	+	0.191779i	0.117464	+	0.993077i	$0.462524\pi$
$384$		0			0
$385$		0			0
$386$			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	−0.473303	−	0.880899i	$-0.656939\pi$
$389$	10.3789	−	17.9767i	0.526230	−	0.911456i	0.999533	−	0.0305570i	$-0.00972810\pi$
$390$		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
$395$		0			0
$396$		0			0
$397$	−15.7430	+	15.7430i	−0.790118	+	0.790118i	−0.981513	−	0.191395i	$-0.938699\pi$
$397$	−15.7430	+	15.7430i	−0.790118	+	0.790118i	0.191395	+	0.981513i	$0.438699\pi$
$398$	−4.44477	−	16.5881i	−0.222796	−	0.831487i
$399$		0			0
$400$		0			0
$401$	−4.11737	+	2.37716i	−0.205612	+	0.118710i	−0.599270	−	0.800547i	$-0.704543\pi$
$401$	−4.11737	+	2.37716i	−0.205612	+	0.118710i	0.393659	+	0.919257i	$0.371209\pi$
$402$		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	−0.976787	−	0.214211i	$-0.931282\pi$
$409$	−25.8797	+	14.9417i	−1.27967	+	0.738817i	−0.302882	+	0.953028i	$0.597949\pi$
$410$		0			0
$411$		0			0
$412$	1.67823	+	6.26326i	0.0826807	+	0.308568i
$413$	−15.0049	+	15.0049i	−0.738343	+	0.738343i
$414$		0			0
$415$		0			0
$416$	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	0.566226	−	0.824250i	$-0.308403\pi$
$419$	−8.81638	−	15.2704i	−0.430708	−	0.746009i	−0.996934	+	0.0782412i	$0.975070\pi$
$420$		0			0
$421$	13.9462	−	24.1555i	0.679696	−	1.17727i	−0.295377	−	0.955381i	$-0.595445\pi$
$421$	13.9462	−	24.1555i	0.679696	−	1.17727i	0.975072	−	0.221887i	$-0.0712215\pi$
$422$	12.8820	+	12.8820i	0.627085	+	0.627085i
$423$		0			0
$424$			5.18410i			0.251762i
$425$		0			0
$426$		0			0
$427$	−32.7217	−	8.76775i	−1.58351	−	0.424301i
$428$	−5.05507	−	1.35450i	−0.244346	−	0.0654723i
$429$		0			0
$430$		0			0
$431$		−	19.2910i		−	0.929215i	−0.885517	−	0.464608i	$-0.846195\pi$
$431$		−	19.2910i		−	0.929215i	0.885517	−	0.464608i	$-0.153805\pi$
$432$		0			0
$433$	−16.7154	−	16.7154i	−0.803292	−	0.803292i	0.180316	−	0.983609i	$-0.442288\pi$
$433$	−16.7154	−	16.7154i	−0.803292	−	0.803292i	−0.983609	+	0.180316i	$0.942288\pi$
$434$	−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	−0.488285	−	0.872684i	$-0.662377\pi$
$439$	−31.1811	−	18.0024i	−1.48819	−	0.859209i	−0.999909	+	0.0134750i	$0.995711\pi$
$440$		0			0
$441$		0			0
$442$	−0.119047	+	0.119047i	−0.00566249	+	0.00566249i
$443$	−6.94511	−	25.9195i	−0.329972	−	1.23147i	−0.909218	−	0.416320i	$-0.863320\pi$
$443$	−6.94511	−	25.9195i	−0.329972	−	1.23147i	0.579246	−	0.815153i	$-0.303347\pi$
$444$		0			0
$445$		0			0
$446$	−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
$455$		0			0
$456$		0			0
$457$	−5.58827	−	20.8557i	−0.261408	−	0.975589i	−0.964412	−	0.264403i	$-0.914825\pi$
$457$	−5.58827	−	20.8557i	−0.261408	−	0.975589i	0.703004	−	0.711186i	$-0.251842\pi$
$458$	−16.1135	+	16.1135i	−0.752935	+	0.752935i
$459$		0			0
$460$		0			0
$461$	10.8706	+	6.27615i	0.506295	+	0.292309i	0.731309	−	0.682046i	$-0.238910\pi$
$461$	10.8706	+	6.27615i	0.506295	+	0.292309i	−0.225015	+	0.974355i	$0.572243\pi$
$462$		0			0
$463$	−5.72110	+	21.3514i	−0.265882	+	0.992286i	0.695826	+	0.718210i	$0.255038\pi$
$463$	−5.72110	+	21.3514i	−0.265882	+	0.992286i	−0.961708	+	0.274076i	$0.911628\pi$
$464$	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
$470$		0			0
$471$		0			0
$472$	−5.27158	−	1.41251i	−0.242644	−	0.0650163i
$473$	7.91881	+	2.12184i	0.364107	+	0.0975622i
$474$		0			0
$475$		0			0
$476$			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	$-0.813588\pi$
$479$	1.35673	−	2.34993i	0.0619906	−	0.107371i	0.895355	+	0.445353i	$0.146922\pi$
$480$		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
$485$		0			0
$486$		0			0
$487$	8.20799	−	8.20799i	0.371940	−	0.371940i	−0.496244	−	0.868183i	$-0.665288\pi$
$487$	8.20799	−	8.20799i	0.371940	−	0.371940i	0.868183	+	0.496244i	$0.165288\pi$
$488$	−2.25495	−	8.41558i	−0.102077	−	0.380955i
$489$		0			0
$490$		0			0
$491$	−4.28058	+	2.47139i	−0.193180	+	0.111532i	−0.593470	−	0.804856i	$-0.702243\pi$
$491$	−4.28058	+	2.47139i	−0.193180	+	0.111532i	0.400290	+	0.916388i	$0.368909\pi$
$492$		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	0.285791	−	0.958292i	$-0.407744\pi$
$499$	28.1148	−	16.2321i	1.25859	−	0.726649i	0.972801	+	0.231643i	$0.0744102\pi$
$500$		0			0
$501$		0			0
$502$	1.59627	+	5.95736i	0.0712450	+	0.265890i
$503$	19.6817	−	19.6817i	0.877565	−	0.877565i	−0.115717	−	0.993282i	$-0.536917\pi$
$503$	19.6817	−	19.6817i	0.877565	−	0.877565i	0.993282	+	0.115717i	$0.0369166\pi$
$504$		0			0
$505$		0			0
$506$	−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	0.958611	−	0.284718i	$-0.0918999\pi$
$509$	5.25069	+	9.09446i	0.232733	+	0.403105i	−0.725879	+	0.687823i	$0.758567\pi$
$510$		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			0
$516$		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			0
$521$			28.2545i			1.23785i	0.785450	+	0.618925i	$0.212432\pi$
$521$			28.2545i			1.23785i	−0.785450	+	0.618925i	$0.787568\pi$
$522$		0			0
$523$	−13.6590	−	13.6590i	−0.597266	−	0.597266i	0.342318	−	0.939584i	$-0.388788\pi$
$523$	−13.6590	−	13.6590i	−0.597266	−	0.597266i	−0.939584	+	0.342318i	$0.888788\pi$
$524$	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
$530$		0			0
$531$		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			0
$536$	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
$545$		0			0
$546$		0			0
$547$	−0.0627654	−	0.234244i	−0.00268365	−	0.0100155i	0.964571	−	0.263823i	$-0.0849836\pi$
$547$	−0.0627654	−	0.234244i	−0.00268365	−	0.0100155i	−0.967255	+	0.253808i	$0.918317\pi$
$548$	−8.83798	+	8.83798i	−0.377540	+	0.377540i
$549$		0			0
$550$		0			0
$551$	−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	0.901746	+	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
$560$		0			0
$561$		0			0
$562$	0.277322	+	0.0743081i	0.0116981	+	0.00313450i
$563$	31.1771	+	8.35388i	1.31396	+	0.352074i	0.846711	−	0.532053i	$-0.178579\pi$
$563$	31.1771	+	8.35388i	1.31396	+	0.352074i	0.467247	+	0.884127i	$0.345246\pi$
$564$		0			0
$565$		0			0
$566$			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	−0.298580	−	0.954385i	$-0.596513\pi$
$569$	16.1545	−	27.9804i	0.677232	−	1.17300i	0.975811	−	0.218615i	$-0.0701538\pi$
$570$		0			0
$571$	12.9565	+	22.4413i	0.542213	+	0.939141i	0.998777	+	0.0494501i	$0.0157469\pi$
$571$	12.9565	+	22.4413i	0.542213	+	0.939141i	−0.456563	+	0.889691i	$0.650920\pi$
$572$	1.01825	−	3.80016i	0.0425752	−	0.158893i
$573$		0			0
$574$	27.8310	+	16.0682i	1.16164	+	0.670674i
$575$		0			0
$576$		0			0
$577$	−6.10724	+	6.10724i	−0.254248	+	0.254248i	−0.822710	−	0.568462i	$-0.807539\pi$
$577$	−6.10724	+	6.10724i	−0.254248	+	0.254248i	0.568462	+	0.822710i	$0.307539\pi$
$578$	4.39244	+	16.3928i	0.182701	+	0.681851i
$579$		0			0
$580$		0			0
$581$	−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	$-0.570883\pi$
$587$	1.83025	−	0.490414i	0.0755424	−	0.0202415i	0.296392	+	0.955066i	$0.404216\pi$
$588$		0			0
$589$	15.3501	−	8.86238i	0.632490	−	0.365168i
$590$		0			0
$591$		0			0
$592$	1.19640	+	4.46504i	0.0491719	+	0.183512i
$593$	−11.0077	+	11.0077i	−0.452033	+	0.452033i	−0.896029	−	0.443996i	$-0.853561\pi$
$593$	−11.0077	+	11.0077i	−0.452033	+	0.452033i	0.443996	+	0.896029i	$0.353561\pi$
$594$		0			0
$595$		0			0
$596$	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	0.999435	+	0.0336142i	$0.0107018\pi$
$599$	12.9428	+	22.4176i	0.528828	+	0.915957i	−0.470607	+	0.882343i	$0.655965\pi$
$600$		0			0
$601$	−9.79604	+	16.9672i	−0.399589	+	0.692108i	−0.993675	−	0.112293i	$-0.964180\pi$
$601$	−9.79604	+	16.9672i	−0.399589	+	0.692108i	0.594086	+	0.804401i	$0.297514\pi$
$602$	−5.67241	−	5.67241i	−0.231190	−	0.231190i
$603$		0			0
$604$			4.06902i			0.165566i
$605$		0			0
$606$		0			0
$607$	28.7731	+	7.70972i	1.16786	+	0.312928i	0.790102	−	0.612975i	$-0.210027\pi$
$607$	28.7731	+	7.70972i	1.16786	+	0.312928i	0.377761	+	0.925903i	$0.376694\pi$
$608$	−1.82070	−	0.487854i	−0.0738390	−	0.0197851i
$609$		0			0
$610$		0			0
$611$		−	3.43162i		−	0.138828i
$612$		0			0
$613$	12.5028	+	12.5028i	0.504982	+	0.504982i	0.912982	−	0.408000i	$-0.133774\pi$
$613$	12.5028	+	12.5028i	0.504982	+	0.504982i	−0.408000	+	0.912982i	$0.633774\pi$
$614$	−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	$-0.964247\pi$
$617$	−1.91482	+	7.14621i	−0.0770878	+	0.287695i	0.916611	+	0.399781i	$0.130914\pi$
$618$		0			0
$619$	16.4624	+	9.50460i	0.661682	+	0.382022i	0.792917	−	0.609329i	$-0.208561\pi$
$619$	16.4624	+	9.50460i	0.661682	+	0.382022i	−0.131236	+	0.991351i	$0.541895\pi$
$620$		0			0
$621$		0			0
$622$	−9.78715	+	9.78715i	−0.392429	+	0.392429i
$623$	4.90928	+	18.3217i	0.196686	+	0.734043i
$624$		0			0
$625$		0			0
$626$	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
$635$		0			0
$636$		0			0
$637$	2.08035	+	7.76396i	0.0824263	+	0.307619i
$638$	12.1167	−	12.1167i	0.479705	−	0.479705i
$639$		0			0
$640$		0			0
$641$	−37.8297	−	21.8410i	−1.49418	−	0.862666i	−0.494204	−	0.869346i	$-0.664540\pi$
$641$	−37.8297	−	21.8410i	−1.49418	−	0.862666i	−0.999978	+	0.00667968i	$0.997874\pi$
$642$		0			0
$643$	7.89483	−	29.4639i	0.311342	−	1.16194i	−0.616006	−	0.787742i	$-0.711250\pi$
$643$	7.89483	−	29.4639i	0.311342	−	1.16194i	0.927347	−	0.374202i	$-0.122083\pi$
$644$	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
$650$		0			0
$651$		0			0
$652$	−6.88270	−	1.84421i	−0.269547	−	0.0722249i
$653$	−31.5015	−	8.44081i	−1.23275	−	0.330314i	−0.417100	−	0.908861i	$-0.636954\pi$
$653$	−31.5015	−	8.44081i	−1.23275	−	0.330314i	−0.815650	+	0.578546i	$0.803620\pi$
$654$		0			0
$655$		0			0
$656$			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	$-0.931033\pi$
$659$	−7.75612	+	13.4340i	−0.302136	+	0.523314i	0.674484	+	0.738290i	$0.264366\pi$
$660$		0			0
$661$	11.1307	+	19.2789i	0.432933	+	0.749862i	0.997124	−	0.0757821i	$-0.0241453\pi$
$661$	11.1307	+	19.2789i	0.432933	+	0.749862i	−0.564191	+	0.825644i	$0.690812\pi$
$662$	−1.07778	+	4.02232i	−0.0418890	+	0.156332i
$663$		0			0
$664$	−6.06007	−	3.49878i	−0.235176	−	0.135779i
$665$		0			0
$666$		0			0
$667$	−16.0656	+	16.0656i	−0.622063	+	0.622063i
$668$	2.80384	+	10.4641i	0.108484	+	0.404867i
$669$		0			0
$670$		0			0
$671$	−29.9817	+	17.3099i	−1.15743	+	0.668243i
$672$		0			0
$673$	9.32657	−	2.49905i	0.359513	−	0.0963312i	−0.0745413	−	0.997218i	$-0.523749\pi$
$673$	9.32657	−	2.49905i	0.359513	−	0.0963312i	0.434054	+	0.900887i	$0.357083\pi$
$674$	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	$-0.536878\pi$
$677$	7.30994	−	1.95869i	0.280944	−	0.0752787i	0.396539	+	0.918018i	$0.370211\pi$
$678$		0			0
$679$	−5.03802	+	2.90870i	−0.193342	+	0.111626i
$680$		0			0
$681$		0			0
$682$	9.67093	+	36.0924i	0.370319	+	1.38205i
$683$	7.48288	−	7.48288i	0.286325	−	0.286325i	−0.549300	−	0.835625i	$-0.685106\pi$
$683$	7.48288	−	7.48288i	0.286325	−	0.286325i	0.835625	+	0.549300i	$0.185106\pi$
$684$		0			0
$685$		0			0
$686$	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	−0.101975	−	0.994787i	$-0.532516\pi$
$691$	21.3061	−	36.9033i	0.810523	−	1.40387i	0.912498	−	0.409080i	$-0.134150\pi$
$692$	2.66569	+	2.66569i	0.101334	+	0.101334i
$693$		0			0
$694$			4.69326i			0.178154i
$695$		0			0
$696$		0			0
$697$	−1.35753	−	0.363749i	−0.0514201	−	0.0137780i
$698$	−9.40041	−	2.51883i	−0.355811	−	0.0953392i
$699$		0			0
$700$		0			0
$701$			36.3602i			1.37331i	0.726985	+	0.686653i	$0.240921\pi$
$701$			36.3602i			1.37331i	−0.726985	+	0.686653i	$0.759079\pi$
$702$		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	0.493288	−	0.869866i	$-0.335795\pi$
$709$	−0.356646	−	0.205910i	−0.0133941	−	0.00773310i	−0.506682	+	0.862133i	$0.669128\pi$
$710$		0			0
$711$		0			0
$712$	−3.44949	+	3.44949i	−0.129275	+	0.129275i
$713$	−12.8227	−	47.8551i	−0.480215	−	1.79219i
$714$		0			0
$715$		0			0
$716$	−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
$725$		0			0
$726$		0			0
$727$	−3.69508	−	13.7902i	−0.137043	−	0.511451i	−0.999981	−	0.00614188i	$-0.998045\pi$
$727$	−3.69508	−	13.7902i	−0.137043	−	0.511451i	0.862938	−	0.505310i	$-0.168622\pi$
$728$	−2.72214	+	2.72214i	−0.100889	+	0.100889i
$729$		0			0
$730$		0			0
$731$	0.303823	+	0.175413i	0.0112373	+	0.00648787i
$732$		0			0
$733$	−7.94942	+	29.6676i	−0.293618	+	1.09580i	0.648690	+	0.761053i	$0.275317\pi$
$733$	−7.94942	+	29.6676i	−0.293618	+	1.09580i	−0.942308	+	0.334746i	$0.891349\pi$
$734$	−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			0
$741$		0			0
$742$	−19.4701	−	5.21700i	−0.714771	−	0.191522i
$743$	−34.7672	−	9.31585i	−1.27549	−	0.341765i	−0.443356	−	0.896346i	$-0.646212\pi$
$743$	−34.7672	−	9.31585i	−1.27549	−	0.341765i	−0.832130	+	0.554580i	$0.812879\pi$
$744$		0			0
$745$		0			0
$746$			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	−0.836944	−	0.547289i	$-0.815660\pi$
$751$	−24.4567	−	42.3603i	−0.892438	−	1.54575i	−0.0554938	−	0.998459i	$-0.517673\pi$
$752$	0.897060	−	3.34787i	0.0327124	−	0.122084i
$753$		0			0
$754$	−3.69759	−	2.13480i	−0.134658	−	0.0777449i
$755$		0			0
$756$		0			0
$757$	−22.9129	+	22.9129i	−0.832783	+	0.832783i	−0.987897	−	0.155114i	$-0.950426\pi$
$757$	−22.9129	+	22.9129i	−0.832783	+	0.832783i	0.155114	+	0.987897i	$0.450426\pi$
$758$	0.152094	+	0.567624i	0.00552432	+	0.0206170i
$759$		0			0
$760$		0			0
$761$	9.19124	−	5.30657i	0.333182	−	0.192363i	−0.324071	−	0.946033i	$-0.605052\pi$
$761$	9.19124	−	5.30657i	0.333182	−	0.192363i	0.657253	+	0.753670i	$0.271718\pi$
$762$		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	−0.558633	−	0.829415i	$-0.688674\pi$
$769$	−3.31814	+	1.91573i	−0.119655	+	0.0690830i	0.438978	+	0.898498i	$0.355341\pi$
$770$		0			0
$771$		0			0
$772$	−4.19397	−	15.6521i	−0.150944	−	0.563332i
$773$	19.8976	−	19.8976i	0.715668	−	0.715668i	−0.252047	−	0.967715i	$-0.581104\pi$
$773$	19.8976	−	19.8976i	0.715668	−	0.715668i	0.967715	+	0.252047i	$0.0811037\pi$
$774$		0			0
$775$		0			0
$776$	−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
$785$		0			0
$786$		0			0
$787$	−6.98473	−	1.87155i	−0.248979	−	0.0667137i	0.132171	−	0.991227i	$-0.457805\pi$
$787$	−6.98473	−	1.87155i	−0.248979	−	0.0667137i	−0.381150	+	0.924513i	$0.624472\pi$
$788$	−1.58575	−	0.424901i	−0.0564901	−	0.0151365i
$789$		0			0
$790$		0			0
$791$		−	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	0.604366	+	0.796707i	$0.293427\pi$
$797$	−8.96012	+	33.4396i	−0.317384	+	1.18449i	−0.921750	+	0.387786i	$0.873240\pi$
$798$		0			0
$799$	0.510406	+	0.294683i	0.0180569	+	0.0104251i
$800$		0			0
$801$		0			0
$802$	3.36182	−	3.36182i	0.118710	−	0.118710i
$803$	12.0388	+	44.9295i	0.424841	+	1.58553i
$804$		0			0
$805$		0			0
$806$	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			0
$816$		0			0
$817$	1.00652	+	3.75637i	0.0352136	+	0.131419i
$818$	21.1307	−	21.1307i	0.738817	−	0.738817i
$819$		0			0
$820$		0			0
$821$	23.9657	+	13.8366i	0.836408	+	0.482900i	0.856042	−	0.516907i	$-0.172917\pi$
$821$	23.9657	+	13.8366i	0.836408	+	0.482900i	−0.0196338	+	0.999807i	$0.506250\pi$
$822$		0			0
$823$	7.80049	−	29.1118i	0.271908	−	1.01477i	−0.685977	−	0.727623i	$-0.740625\pi$
$823$	7.80049	−	29.1118i	0.271908	−	1.01477i	0.957885	−	0.287151i	$-0.0927083\pi$
$824$	−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	$0.772979\pi$
$830$		0			0
$831$		0			0
$832$	−0.956351	−	0.256253i	−0.0331555	−	0.00888399i
$833$	−1.33343	−	0.357291i	−0.0462006	−	0.0123794i
$834$		0			0
$835$		0			0
$836$			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	0.424527	+	0.905415i	$0.360440\pi$
$839$	−16.5639	+	28.6895i	−0.571849	+	0.990471i	−0.996376	+	0.0850559i	$0.972893\pi$
$840$		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
$845$		0			0
$846$		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			0
$851$	−21.0916	+	12.1773i	−0.723011	+	0.417431i
$852$		0			0
$853$	2.57386	−	0.689663i	0.0881273	−	0.0236136i	−0.214486	−	0.976727i	$-0.568808\pi$
$853$	2.57386	−	0.689663i	0.0881273	−	0.0236136i	0.302613	+	0.953113i	$0.402141\pi$
$854$	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	$-0.497135\pi$
$857$	15.1284	−	4.05364i	0.516776	−	0.138470i	0.507775	+	0.861490i	$0.330468\pi$
$858$		0			0
$859$	0.691191	−	0.399059i	0.0235831	−	0.0136157i	−0.488162	−	0.872753i	$-0.662333\pi$
$859$	0.691191	−	0.399059i	0.0235831	−	0.0136157i	0.511745	+	0.859137i	$0.328999\pi$
$860$		0			0
$861$		0			0
$862$	4.99288	+	18.6337i	0.170058	+	0.634666i
$863$	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
$865$		0			0
$866$	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
$875$		0			0
$876$		0			0
$877$	16.7435	+	4.48641i	0.565388	+	0.151495i	0.530180	−	0.847885i	$-0.322124\pi$
$877$	16.7435	+	4.48641i	0.565388	+	0.151495i	0.0352074	+	0.999380i	$0.488791\pi$
$878$	34.7780	+	9.31875i	1.17370	+	0.314492i
$879$		0			0
$880$		0			0
$881$			15.1033i			0.508843i	0.967093	+	0.254421i	$0.0818850\pi$
$881$			15.1033i			0.508843i	−0.967093	+	0.254421i	$0.918115\pi$
$882$		0			0
$883$	16.4678	+	16.4678i	0.554185	+	0.554185i	0.927646	−	0.373461i	$-0.121829\pi$
$883$	16.4678	+	16.4678i	0.554185	+	0.554185i	−0.373461	+	0.927646i	$0.621829\pi$
$884$	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	−0.739320	−	0.673355i	$-0.764853\pi$
$887$	7.07714	−	26.4123i	0.237627	−	0.886837i	0.976947	−	0.213482i	$-0.0684806\pi$
$888$		0			0
$889$	−65.6556	−	37.9063i	−2.20202	−	1.27134i
$890$		0			0
$891$		0			0
$892$	3.32036	−	3.32036i	0.111174	−	0.111174i
$893$	1.69089	+	6.31049i	0.0565835	+	0.211173i
$894$		0			0
$895$		0			0
$896$	−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
$905$		0			0
$906$		0			0
$907$	−6.62626	−	24.7295i	−0.220021	−	0.821130i	−0.984338	−	0.176290i	$-0.943590\pi$
$907$	−6.62626	−	24.7295i	−0.220021	−	0.821130i	0.764317	−	0.644841i	$-0.223076\pi$
$908$	17.6998	−	17.6998i	0.587390	−	0.587390i
$909$		0			0
$910$		0			0
$911$	−3.55075	−	2.05003i	−0.117642	−	0.0679204i	0.440025	−	0.897986i	$-0.354970\pi$
$911$	−3.55075	−	2.05003i	−0.117642	−	0.0679204i	−0.557666	+	0.830065i	$0.688303\pi$
$912$		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	$-0.842002\pi$
$919$		−	28.8740i		−	0.952464i	0.879320	−	0.476232i	$-0.157998\pi$
$920$		0			0
$921$		0			0
$922$	−12.1246	−	3.24877i	−0.399302	−	0.106993i
$923$	−6.64579	−	1.78073i	−0.218749	−	0.0586135i
$924$		0			0
$925$		0			0
$926$		−	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	−0.0791067	−	0.996866i	$-0.525207\pi$
$929$	25.1077	−	43.4879i	0.823758	−	1.42679i	0.902865	−	0.429925i	$-0.141460\pi$
$930$		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			0
$936$		0			0
$937$	0.857094	−	0.857094i	0.0280000	−	0.0280000i	−0.692968	−	0.720968i	$-0.743697\pi$
$937$	0.857094	−	0.857094i	0.0280000	−	0.0280000i	0.720968	+	0.692968i	$0.243697\pi$
$938$	8.19479	+	30.5834i	0.267569	+	0.998582i
$939$		0			0
$940$		0			0
$941$	43.4478	−	25.0846i	1.41636	−	0.817735i	0.420382	−	0.907347i	$-0.361896\pi$
$941$	43.4478	−	25.0846i	1.41636	−	0.817735i	0.995977	+	0.0896119i	$0.0285627\pi$
$942$		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	$-0.569711\pi$
$947$	2.54334	−	0.681485i	0.0826473	−	0.0221453i	0.299906	+	0.953969i	$0.403045\pi$
$948$		0			0
$949$	10.0371	−	5.79490i	0.325817	−	0.188111i
$950$		0			0
$951$		0			0
$952$	−0.171123	−	0.638639i	−0.00554612	−	0.0206984i
$953$	−28.1499	+	28.1499i	−0.911864	+	0.911864i	−0.996419	−	0.0845545i	$-0.973053\pi$
$953$	−28.1499	+	28.1499i	−0.911864	+	0.911864i	0.0845545	+	0.996419i	$0.473053\pi$
$954$		0			0
$955$		0			0
$956$	−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
$965$		0			0
$966$		0			0
$967$	−1.28319	−	0.343829i	−0.0412646	−	0.0110568i	0.238128	−	0.971234i	$-0.423466\pi$
$967$	−1.28319	−	0.343829i	−0.0412646	−	0.0110568i	−0.279392	+	0.960177i	$0.590133\pi$
$968$	−4.62638	−	1.23963i	−0.148697	−	0.0398433i
$969$		0			0
$970$		0			0
$971$		−	38.7906i		−	1.24485i	−0.782679	−	0.622425i	$-0.786147\pi$
$971$		−	38.7906i		−	1.24485i	0.782679	−	0.622425i	$-0.213853\pi$
$972$		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	−0.525548	−	0.850764i	$-0.676140\pi$
$977$	11.0953	−	41.4084i	0.354972	−	1.32477i	0.880520	−	0.474009i	$-0.157193\pi$
$978$		0			0
$979$	16.7875	+	9.69226i	0.536530	+	0.309766i
$980$		0			0
$981$		0			0
$982$	3.49508	−	3.49508i	0.111532	−	0.111532i
$983$	8.34182	+	31.1321i	0.266063	+	0.992960i	0.961597	+	0.274466i	$0.0885012\pi$
$983$	8.34182	+	31.1321i	0.266063	+	0.992960i	−0.695534	+	0.718493i	$0.744832\pi$
$984$		0			0
$985$		0			0
$986$	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
$995$		0			0
$996$		0			0
$997$	−0.763421	−	2.84912i	−0.0241778	−	0.0902327i	0.952783	−	0.303653i	$-0.0982063\pi$
$997$	−0.763421	−	2.84912i	−0.0241778	−	0.0902327i	−0.976960	+	0.213420i	$0.931540\pi$
$998$	−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	1350.2.q.h.143.2		16
3.2	odd	2		450.2.p.h.443.4		16
5.2	odd	4	inner	1350.2.q.h.1007.1		16
5.3	odd	4		270.2.m.b.197.3		16
5.4	even	2		270.2.m.b.143.4		16
9.4	even	3		450.2.p.h.293.4		16
9.5	odd	6	inner	1350.2.q.h.1043.1		16
15.2	even	4		450.2.p.h.407.4		16
15.8	even	4		90.2.l.b.47.1	yes	16
15.14	odd	2		90.2.l.b.83.1	yes	16
45.4	even	6		90.2.l.b.23.1	✓	16
45.13	odd	12		90.2.l.b.77.1	yes	16
45.14	odd	6		270.2.m.b.233.3		16
45.22	odd	12		450.2.p.h.257.4		16
45.23	even	12		270.2.m.b.17.4		16
45.29	odd	6		810.2.f.c.323.8		16
45.32	even	12	inner	1350.2.q.h.557.2		16
45.34	even	6		810.2.f.c.323.1		16
45.38	even	12		810.2.f.c.647.1		16
45.43	odd	12		810.2.f.c.647.8		16
60.23	odd	4		720.2.cu.b.497.3		16
60.59	even	2		720.2.cu.b.353.4		16
180.103	even	12		720.2.cu.b.257.4		16
180.139	odd	6		720.2.cu.b.113.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.1	✓	16	45.4	even	6
90.2.l.b.47.1	yes	16	15.8	even	4
90.2.l.b.77.1	yes	16	45.13	odd	12
90.2.l.b.83.1	yes	16	15.14	odd	2
270.2.m.b.17.4		16	45.23	even	12
270.2.m.b.143.4		16	5.4	even	2
270.2.m.b.197.3		16	5.3	odd	4
270.2.m.b.233.3		16	45.14	odd	6
450.2.p.h.257.4		16	45.22	odd	12
450.2.p.h.293.4		16	9.4	even	3
450.2.p.h.407.4		16	15.2	even	4
450.2.p.h.443.4		16	3.2	odd	2
720.2.cu.b.113.3		16	180.139	odd	6
720.2.cu.b.257.4		16	180.103	even	12
720.2.cu.b.353.4		16	60.59	even	2
720.2.cu.b.497.3		16	60.23	odd	4
810.2.f.c.323.1		16	45.34	even	6
810.2.f.c.323.8		16	45.29	odd	6
810.2.f.c.647.1		16	45.38	even	12
810.2.f.c.647.8		16	45.43	odd	12
1350.2.q.h.143.2		16	1.1	even	1	trivial
1350.2.q.h.557.2		16	45.32	even	12	inner
1350.2.q.h.1007.1		16	5.2	odd	4	inner
1350.2.q.h.1043.1		16	9.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.q (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(1.00635 + 3.75574i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(1.00635 + 3.75574i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(3.44125 + 1.98681i) q^{11} +(0.256253 - 0.956351i) q^{13} +(-1.94411 - 3.36730i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.120239 + 0.120239i) q^{17} +1.88492i q^{19} +(-3.83821 - 1.02845i) q^{22} +(5.08911 + 1.36362i) q^{23} +0.990087i q^{26} +(2.74939 + 2.74939i) q^{28} +(-2.15618 + 3.73461i) q^{29} +(-4.70172 - 8.14362i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.147262 - 0.0850217i) q^{34} +(-3.26863 + 3.26863i) q^{37} +(-0.487854 - 1.82070i) q^{38} +(-7.15775 + 4.13253i) q^{41} +(1.99285 - 0.533983i) q^{43} +3.97361 q^{44} -5.26863 q^{46} +(3.34787 - 0.897060i) q^{47} +(-7.03067 + 4.05916i) q^{49} +(-0.256253 - 0.956351i) q^{52} +(3.66571 - 3.66571i) q^{53} +(-3.36730 - 1.94411i) q^{56} +(1.11612 - 4.16541i) q^{58} +(2.72877 + 4.72637i) q^{59} +(-4.35623 + 7.54520i) q^{61} +(6.64923 + 6.64923i) q^{62} -1.00000i q^{64} +(-7.86563 - 2.10759i) q^{67} +(0.164249 + 0.0440105i) q^{68} -6.94911i q^{71} +(8.27728 + 8.27728i) q^{73} +(2.31127 - 4.00324i) q^{74} +(0.942462 + 1.63239i) q^{76} +(-3.99883 + 14.9238i) q^{77} +(11.7529 + 6.78553i) q^{79} +(5.84428 - 5.84428i) q^{82} +(1.81110 + 6.75913i) q^{83} +(-1.78674 + 1.03157i) q^{86} +(-3.83821 + 1.02845i) q^{88} +4.87832 q^{89} +3.84968 q^{91} +(5.08911 - 1.36362i) q^{92} +(-3.00162 + 1.73299i) q^{94} +(0.387234 + 1.44518i) q^{97} +(5.74052 - 5.74052i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 8 q^{16} - 8 q^{22} - 24 q^{23} + 16 q^{28} - 8 q^{31} + 24 q^{38} - 24 q^{41} - 32 q^{46} + 48 q^{47} - 24 q^{56} - 16 q^{58} - 24 q^{61} + 16 q^{67} - 24 q^{68} - 16 q^{73} + 16 q^{76} - 72 q^{77} + 16 q^{82} + 48 q^{83} + 48 q^{86} - 8 q^{88} - 24 q^{92} + 48 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 8 * q^16 - 8 * q^22 - 24 * q^23 + 16 * q^28 - 8 * q^31 + 24 * q^38 - 24 * q^41 - 32 * q^46 + 48 * q^47 - 24 * q^56 - 16 * q^58 - 24 * q^61 + 16 * q^67 - 24 * q^68 - 16 * q^73 + 16 * q^76 - 72 * q^77 + 16 * q^82 + 48 * q^83 + 48 * q^86 - 8 * q^88 - 24 * q^92 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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