LMFDB - Embedded newform 1350.2.q.h.1007.1

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			1007.1
Root			$0.500000 + 1.33108i$ of defining polynomial
Character	$\chi$	$=$	1350.1007
Dual form			1350.2.q.h.1043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-3.75574 + 1.00635i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-3.75574 + 1.00635i) q^{7} +(0.707107 + 0.707107i) q^{8} +(3.44125 + 1.98681i) q^{11} +(-0.956351 - 0.256253i) q^{13} +(1.94411 + 3.36730i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.120239 + 0.120239i) q^{17} -1.88492i q^{19} +(1.02845 - 3.83821i) q^{22} +(1.36362 - 5.08911i) q^{23} +0.990087i q^{26} +(2.74939 - 2.74939i) q^{28} +(2.15618 - 3.73461i) q^{29} +(-4.70172 - 8.14362i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.147262 + 0.0850217i) q^{34} +(-3.26863 - 3.26863i) q^{37} +(-1.82070 + 0.487854i) q^{38} +(-7.15775 + 4.13253i) q^{41} +(-0.533983 - 1.99285i) q^{43} -3.97361 q^{44} -5.26863 q^{46} +(0.897060 + 3.34787i) q^{47} +(7.03067 - 4.05916i) q^{49} +(0.956351 - 0.256253i) q^{52} +(-3.66571 - 3.66571i) q^{53} +(-3.36730 - 1.94411i) q^{56} +(-4.16541 - 1.11612i) q^{58} +(-2.72877 - 4.72637i) q^{59} +(-4.35623 + 7.54520i) q^{61} +(-6.64923 + 6.64923i) q^{62} +1.00000i q^{64} +(2.10759 - 7.86563i) q^{67} +(0.0440105 - 0.164249i) q^{68} -6.94911i q^{71} +(8.27728 - 8.27728i) q^{73} +(-2.31127 + 4.00324i) q^{74} +(0.942462 + 1.63239i) q^{76} +(-14.9238 - 3.99883i) q^{77} +(-11.7529 - 6.78553i) q^{79} +(5.84428 + 5.84428i) q^{82} +(6.75913 - 1.81110i) q^{83} +(-1.78674 + 1.03157i) q^{86} +(1.02845 + 3.83821i) q^{88} -4.87832 q^{89} +3.84968 q^{91} +(1.36362 + 5.08911i) q^{92} +(3.00162 - 1.73299i) q^{94} +(-1.44518 + 0.387234i) q^{97} +(-5.74052 - 5.74052i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.258819	−	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			0
$5$		0			0
$6$		0			0
$7$	−3.75574	+	1.00635i	−1.41954	+	0.380364i	−0.885319	−	0.464984i	$-0.846060\pi$
$7$	−3.75574	+	1.00635i	−1.41954	+	0.380364i	−0.534217	+	0.845347i	$0.679394\pi$
$8$	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
$13$	−0.956351	−	0.256253i	−0.265244	−	0.0710719i	0.123746	−	0.992314i	$-0.460509\pi$
$13$	−0.956351	−	0.256253i	−0.265244	−	0.0710719i	−0.388990	+	0.921242i	$0.627176\pi$
$14$	1.94411	+	3.36730i	0.519586	+	0.899950i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.120239	+	0.120239i	−0.0291622	+	0.0291622i	−0.721538	−	0.692375i	$-0.756564\pi$
$17$	−0.120239	+	0.120239i	−0.0291622	+	0.0291622i	0.692375	+	0.721538i	$0.256564\pi$
$18$		0			0
$19$		−	1.88492i		−	0.432431i	−0.976346	−	0.216216i	$-0.930629\pi$
$19$		−	1.88492i		−	0.432431i	0.976346	−	0.216216i	$-0.0693714\pi$
$20$		0			0
$21$		0			0
$22$	1.02845	−	3.83821i	0.219265	−	0.818310i
$23$	1.36362	−	5.08911i	0.284335	−	1.06115i	−0.664989	−	0.746853i	$-0.731564\pi$
$23$	1.36362	−	5.08911i	0.284335	−	1.06115i	0.949324	−	0.314299i	$-0.101770\pi$
$24$		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	−0.593381	−	0.804922i	$-0.702207\pi$
$29$	2.15618	−	3.73461i	0.400392	−	0.693499i	0.993773	+	0.111422i	$0.0355406\pi$
$30$		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	$-0.486741\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$		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	0.385393	−	0.922753i	$-0.374066\pi$
$37$	−3.26863	−	3.26863i	−0.537360	−	0.537360i	−0.922753	+	0.385393i	$0.874066\pi$
$38$	−1.82070	+	0.487854i	−0.295356	+	0.0791404i
$39$		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
$43$	−0.533983	−	1.99285i	−0.0814316	−	0.303907i	0.913183	−	0.407550i	$-0.133617\pi$
$43$	−0.533983	−	1.99285i	−0.0814316	−	0.303907i	−0.994615	+	0.103643i	$0.966950\pi$
$44$	−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	$-0.00198773\pi$
$47$	0.897060	+	3.34787i	0.130850	+	0.488338i	−0.869131	+	0.494582i	$0.835321\pi$
$48$		0			0
$49$	7.03067	−	4.05916i	1.00438	−	0.579880i
$50$		0			0
$51$		0			0
$52$	0.956351	−	0.256253i	0.132622	−	0.0355359i
$53$	−3.66571	−	3.66571i	−0.503524	−	0.503524i	0.409007	−	0.912531i	$-0.365875\pi$
$53$	−3.66571	−	3.66571i	−0.503524	−	0.503524i	−0.912531	+	0.409007i	$0.865875\pi$
$54$		0			0
$55$		0			0
$56$	−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	0.631906	−	0.775045i	$-0.282273\pi$
$59$	−2.72877	−	4.72637i	−0.355255	−	0.615320i	−0.987162	+	0.159724i	$0.948939\pi$
$60$		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
$67$	2.10759	−	7.86563i	0.257483	−	0.960940i	−0.709209	−	0.704998i	$-0.750948\pi$
$67$	2.10759	−	7.86563i	0.257483	−	0.960940i	0.966692	−	0.255942i	$-0.0823855\pi$
$68$	0.0440105	−	0.164249i	0.00533705	−	0.0199182i
$69$		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	−0.0307446	−	0.999527i	$-0.509788\pi$
$73$	8.27728	−	8.27728i	0.968783	−	0.968783i	0.999527	+	0.0307446i	$0.00978785\pi$
$74$	−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	−0.338206	−	0.941072i	$-0.609820\pi$
$79$	−11.7529	−	6.78553i	−1.32230	−	0.763431i	−0.984095	+	0.177641i	$0.943153\pi$
$80$		0			0
$81$		0			0
$82$	5.84428	+	5.84428i	0.645393	+	0.645393i
$83$	6.75913	−	1.81110i	0.741911	−	0.198795i	0.131984	−	0.991252i	$-0.457865\pi$
$83$	6.75913	−	1.81110i	0.741911	−	0.198795i	0.609927	+	0.792457i	$0.291199\pi$
$84$		0			0
$85$		0			0
$86$	−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
$95$		0			0
$96$		0			0
$97$	−1.44518	+	0.387234i	−0.146736	+	0.0393177i	−0.331439	−	0.943477i	$-0.607534\pi$
$97$	−1.44518	+	0.387234i	−0.146736	+	0.0393177i	0.184704	+	0.982794i	$0.440868\pi$
$98$	−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
$103$	6.26326	+	1.67823i	0.617137	+	0.165361i	0.553826	−	0.832632i	$-0.313167\pi$
$103$	6.26326	+	1.67823i	0.617137	+	0.165361i	0.0633111	+	0.997994i	$0.479834\pi$
$104$	−0.495044	−	0.857441i	−0.0485430	−	0.0840790i
$105$		0			0
$106$	−2.59205	+	4.48956i	−0.251762	+	0.436065i
$107$	3.70057	−	3.70057i	0.357747	−	0.357747i	−0.505235	−	0.862982i	$-0.668594\pi$
$107$	3.70057	−	3.70057i	0.357747	−	0.357747i	0.862982	+	0.505235i	$0.168594\pi$
$108$		0			0
$109$			7.30160i			0.699367i	0.936868	+	0.349683i	$0.113711\pi$
$109$			7.30160i			0.699367i	−0.936868	+	0.349683i	$0.886289\pi$
$110$		0			0
$111$		0			0
$112$	−1.00635	+	3.75574i	−0.0950909	+	0.354884i
$113$	−1.09205	+	4.07557i	−0.102731	+	0.383397i	−0.998078	−	0.0619722i	$-0.980261\pi$
$113$	−1.09205	+	4.07557i	−0.102731	+	0.383397i	0.895347	+	0.445369i	$0.146928\pi$
$114$		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
$122$	8.41558	+	2.25495i	0.761911	+	0.204153i
$123$		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	−0.966411	−	0.257000i	$-0.917266\pi$
$127$	−13.7871	−	13.7871i	−1.22341	−	1.22341i	−0.257000	−	0.966411i	$-0.582734\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$		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
$133$	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	−0.954912	−	0.296888i	$-0.904051\pi$
$137$	−3.23492	−	12.0729i	−0.276378	−	1.03146i	0.678534	−	0.734569i	$-0.262616\pi$
$138$		0			0
$139$	3.60435	−	2.08097i	0.305717	−	0.176506i	−0.339291	−	0.940681i	$-0.610187\pi$
$139$	3.60435	−	2.08097i	0.305717	−	0.176506i	0.645008	+	0.764176i	$0.276854\pi$
$140$		0			0
$141$		0			0
$142$	−6.71233	+	1.79856i	−0.563286	+	0.150932i
$143$	−2.78191	−	2.78191i	−0.232635	−	0.232635i
$144$		0			0
$145$		0			0
$146$	−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	0.844016	−	0.536317i	$-0.180185\pi$
$149$	−0.518244	−	0.897625i	−0.0424562	−	0.0735363i	−0.886473	+	0.462781i	$0.846852\pi$
$150$		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
$157$	−2.36186	+	8.81460i	−0.188497	+	0.703481i	0.805357	+	0.592789i	$0.201973\pi$
$157$	−2.36186	+	8.81460i	−0.188497	+	0.703481i	−0.993855	+	0.110692i	$0.964693\pi$
$158$	−3.51245	+	13.1086i	−0.279435	+	1.04287i
$159$		0			0
$160$		0			0
$161$			20.4857i			1.61450i
$162$		0			0
$163$	−5.03848	+	5.03848i	−0.394644	+	0.394644i	−0.876339	−	0.481695i	$-0.840021\pi$
$163$	−5.03848	+	5.03848i	−0.394644	+	0.394644i	0.481695	+	0.876339i	$0.340021\pi$
$164$	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	$-0.554338\pi$
$167$	−10.4641	−	2.80384i	−0.809734	−	0.216968i	−0.639853	+	0.768497i	$0.721005\pi$
$168$		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
$173$	3.64139	−	0.975709i	0.276850	−	0.0741818i	−0.117722	−	0.993047i	$-0.537559\pi$
$173$	3.64139	−	0.975709i	0.276850	−	0.0741818i	0.394573	+	0.918865i	$0.370893\pi$
$174$		0			0
$175$		0			0
$176$	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
$185$		0			0
$186$		0			0
$187$	−0.652663	+	0.174880i	−0.0477274	+	0.0127885i
$188$	−2.45081	−	2.45081i	−0.178744	−	0.178744i
$189$		0			0
$190$		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
$193$	−15.6521	−	4.19397i	−1.12666	−	0.301889i	−0.353086	−	0.935591i	$-0.614868\pi$
$193$	−15.6521	−	4.19397i	−1.12666	−	0.301889i	−0.773577	+	0.633702i	$0.781534\pi$
$194$	0.748079	+	1.29571i	0.0537090	+	0.0930267i
$195$		0			0
$196$	−4.05916	+	7.03067i	−0.289940	+	0.502191i
$197$	1.16085	−	1.16085i	0.0827072	−	0.0827072i	−0.664543	−	0.747250i	$-0.731374\pi$
$197$	1.16085	−	1.16085i	0.0827072	−	0.0827072i	0.747250	+	0.664543i	$0.231374\pi$
$198$		0			0
$199$		−	17.1733i		−	1.21738i	−0.793407	−	0.608691i	$-0.791695\pi$
$199$		−	17.1733i		−	1.21738i	0.793407	−	0.608691i	$-0.208305\pi$
$200$		0			0
$201$		0			0
$202$	2.66565	−	9.94834i	0.187554	−	0.699963i
$203$	−4.33973	+	16.1961i	−0.304589	+	1.13674i
$204$		0			0
$205$		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	$-0.382419\pi$
$212$	5.00745	+	1.34174i	0.343913	+	0.0921513i
$213$		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
$218$	7.05281	−	1.88979i	0.477676	−	0.127993i
$219$		0			0
$220$		0			0
$221$	0.145802	−	0.0841789i	0.00980771	−	0.00566249i
$222$		0			0
$223$	−1.21534	−	4.53570i	−0.0813849	−	0.303733i	0.913220	−	0.407466i	$-0.133588\pi$
$223$	−1.21534	−	4.53570i	−0.0813849	−	0.303733i	−0.994605	+	0.103734i	$0.966921\pi$
$224$	3.88823			0.259793
$225$		0			0
$226$	4.21934			0.280666
$227$	6.47859	+	24.1784i	0.429999	+	1.60478i	0.752758	+	0.658297i	$0.228723\pi$
$227$	6.47859	+	24.1784i	0.429999	+	1.60478i	−0.322759	+	0.946481i	$0.604610\pi$
$228$		0			0
$229$	−19.7350	+	11.3940i	−1.30412	+	0.752935i	−0.981108	−	0.193459i	$-0.938029\pi$
$229$	−19.7350	+	11.3940i	−1.30412	+	0.752935i	−0.323014	+	0.946394i	$0.604696\pi$
$230$		0			0
$231$		0			0
$232$	4.16541	−	1.11612i	0.273473	−	0.0732768i
$233$	20.6491	+	20.6491i	1.35277	+	1.35277i	0.882553	+	0.470214i	$0.155823\pi$
$233$	20.6491	+	20.6491i	1.35277	+	1.35277i	0.470214	+	0.882553i	$0.344177\pi$
$234$		0			0
$235$		0			0
$236$	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	0.975018	−	0.222127i	$-0.0713000\pi$
$239$	4.56277	+	7.90295i	0.295141	+	0.511199i	−0.679877	+	0.733327i	$0.737967\pi$
$240$		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
$247$	−0.483018	+	1.80265i	−0.0307337	+	0.114700i
$248$	2.43379	−	9.08302i	0.154546	−	0.576773i
$249$		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
$257$	28.0634	+	7.51956i	1.75055	+	0.469057i	0.984743	−	0.174018i	$-0.0556750\pi$
$257$	28.0634	+	7.51956i	1.75055	+	0.469057i	0.765803	+	0.643075i	$0.222342\pi$
$258$		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
$263$	−18.0249	+	4.82975i	−1.11146	+	0.297815i	−0.767424	−	0.641141i	$-0.778462\pi$
$263$	−18.0249	+	4.82975i	−1.11146	+	0.297815i	−0.344038	+	0.938956i	$0.611795\pi$
$264$		0			0
$265$		0			0
$266$	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
$275$		0			0
$276$		0			0
$277$	−3.99035	+	1.06921i	−0.239757	+	0.0642426i	−0.376696	−	0.926337i	$-0.622940\pi$
$277$	−3.99035	+	1.06921i	−0.239757	+	0.0642426i	0.136940	+	0.990579i	$0.456273\pi$
$278$	−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
$283$	−17.4857	−	4.68527i	−1.03941	−	0.278510i	−0.301544	−	0.953452i	$-0.597502\pi$
$283$	−17.4857	−	4.68527i	−1.03941	−	0.278510i	−0.737871	+	0.674942i	$0.764169\pi$
$284$	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
$292$	−3.02970	+	11.3070i	−0.177300	+	0.661691i
$293$	5.53752	−	20.6663i	0.323505	−	1.20734i	−0.592300	−	0.805717i	$-0.701780\pi$
$293$	5.53752	−	20.6663i	0.323505	−	1.20734i	0.915806	−	0.401621i	$-0.131553\pi$
$294$		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
$302$	3.93037	+	1.05314i	0.226168	+	0.0606014i
$303$		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	0.984838	+	0.173476i	$0.0555001\pi$
$307$	20.2953	+	20.2953i	1.15831	+	1.15831i	0.173476	+	0.984838i	$0.444500\pi$
$308$	14.9238	−	3.99883i	0.850365	−	0.227855i
$309$		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
$313$	4.79847	+	17.9081i	0.271226	+	1.01223i	0.958329	+	0.285668i	$0.0922154\pi$
$313$	4.79847	+	17.9081i	0.271226	+	1.01223i	−0.687103	+	0.726560i	$0.741118\pi$
$314$	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	$-0.0758184\pi$
$317$	0.217566	+	0.811966i	0.0122197	+	0.0456046i	−0.959547	+	0.281549i	$0.909152\pi$
$318$		0			0
$319$	14.8399	−	8.56781i	0.830874	−	0.479705i
$320$		0			0
$321$		0			0
$322$	19.7876	−	5.30208i	1.10272	−	0.295473i
$323$	0.226641	+	0.226641i	0.0126107	+	0.0126107i
$324$		0			0
$325$		0			0
$326$	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	−0.803114	−	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
$337$	0.840764	−	3.13777i	0.0457993	−	0.170925i	−0.939238	−	0.343267i	$-0.888467\pi$
$337$	0.840764	−	3.13777i	0.0457993	−	0.170925i	0.985037	+	0.172341i	$0.0551332\pi$
$338$	−3.11093	+	11.6102i	−0.169213	+	0.631510i
$339$		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
$347$	4.53334	+	1.21470i	0.243362	+	0.0652087i	0.378438	−	0.925627i	$-0.376461\pi$
$347$	4.53334	+	1.21470i	0.243362	+	0.0652087i	−0.135076	+	0.990835i	$0.543128\pi$
$348$		0			0
$349$	−8.42818	−	4.86601i	−0.451150	−	0.260472i	0.257166	−	0.966367i	$-0.417211\pi$
$349$	−8.42818	−	4.86601i	−0.451150	−	0.260472i	−0.708316	+	0.705896i	$0.750545\pi$
$350$		0			0
$351$		0			0
$352$	−2.80977	−	2.80977i	−0.149761	−	0.149761i
$353$	−4.92815	+	1.32049i	−0.262299	+	0.0702827i	−0.387572	−	0.921840i	$-0.626686\pi$
$353$	−4.92815	+	1.32049i	−0.262299	+	0.0702827i	0.125273	+	0.992122i	$0.460019\pi$
$354$		0			0
$355$		0			0
$356$	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
$365$		0			0
$366$		0			0
$367$	−9.74300	+	2.61063i	−0.508581	+	0.136274i	−0.503979	−	0.863716i	$-0.668131\pi$
$367$	−9.74300	+	2.61063i	−0.508581	+	0.136274i	−0.00460117	+	0.999989i	$0.501465\pi$
$368$	−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
$373$	−12.6656	−	3.39374i	−0.655801	−	0.175721i	−0.0844507	−	0.996428i	$-0.526914\pi$
$373$	−12.6656	−	3.39374i	−0.655801	−	0.175721i	−0.571350	+	0.820706i	$0.693580\pi$
$374$	0.337843	+	0.585162i	0.0174695	+	0.0302580i
$375$		0			0
$376$	−1.73299	+	3.00162i	−0.0893720	+	0.154797i
$377$	−3.01907	+	3.01907i	−0.155490	+	0.155490i
$378$		0			0
$379$			0.587648i			0.0301854i	0.999886	+	0.0150927i	$0.00480434\pi$
$379$			0.587648i			0.0301854i	−0.999886	+	0.0150927i	$0.995196\pi$
$380$		0			0
$381$		0			0
$382$	−3.52759	+	13.1652i	−0.180487	+	0.673588i
$383$	3.75319	−	14.0071i	0.191779	−	0.715729i	−0.801298	−	0.598265i	$-0.795857\pi$
$383$	3.75319	−	14.0071i	0.191779	−	0.715729i	0.993077	−	0.117464i	$-0.0374765\pi$
$384$		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	$0.343061\pi$
$389$	−10.3789	+	17.9767i	−0.526230	+	0.911456i	−0.999533	+	0.0305570i	$0.990272\pi$
$390$		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
$395$		0			0
$396$		0			0
$397$	−15.7430	−	15.7430i	−0.790118	−	0.790118i	0.191395	−	0.981513i	$-0.438699\pi$
$397$	−15.7430	−	15.7430i	−0.790118	−	0.790118i	−0.981513	+	0.191395i	$0.938699\pi$
$398$	−16.5881	+	4.44477i	−0.831487	+	0.222796i
$399$		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
$403$	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	0.302882	−	0.953028i	$-0.402051\pi$
$409$	25.8797	−	14.9417i	1.27967	−	0.738817i	0.976787	+	0.214211i	$0.0687180\pi$
$410$		0			0
$411$		0			0
$412$	−6.26326	+	1.67823i	−0.308568	+	0.0826807i
$413$	15.0049	+	15.0049i	0.738343	+	0.738343i
$414$		0			0
$415$		0			0
$416$	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	0.996934	−	0.0782412i	$-0.0249304\pi$
$419$	8.81638	+	15.2704i	0.430708	+	0.746009i	−0.566226	+	0.824250i	$0.691597\pi$
$420$		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
$427$	8.76775	−	32.7217i	0.424301	−	1.58351i
$428$	−1.35450	+	5.05507i	−0.0654723	+	0.244346i
$429$		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	−0.983609	−	0.180316i	$-0.942288\pi$
$433$	−16.7154	+	16.7154i	−0.803292	+	0.803292i	0.180316	+	0.983609i	$0.442288\pi$
$434$	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	0.999909	−	0.0134750i	$-0.00428934\pi$
$439$	31.1811	+	18.0024i	1.48819	+	0.859209i	0.488285	+	0.872684i	$0.337623\pi$
$440$		0			0
$441$		0			0
$442$	−0.119047	−	0.119047i	−0.00566249	−	0.00566249i
$443$	−25.9195	+	6.94511i	−1.23147	+	0.329972i	−0.815153	−	0.579246i	$-0.803347\pi$
$443$	−25.9195	+	6.94511i	−1.23147	+	0.329972i	−0.416320	+	0.909218i	$0.636680\pi$
$444$		0			0
$445$		0			0
$446$	−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
$455$		0			0
$456$		0			0
$457$	20.8557	−	5.58827i	0.975589	−	0.261408i	0.264403	−	0.964412i	$-0.414825\pi$
$457$	20.8557	−	5.58827i	0.975589	−	0.261408i	0.711186	+	0.703004i	$0.248158\pi$
$458$	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
$463$	21.3514	+	5.72110i	0.992286	+	0.265882i	0.718210	−	0.695826i	$-0.244962\pi$
$463$	21.3514	+	5.72110i	0.992286	+	0.265882i	0.274076	+	0.961708i	$0.411628\pi$
$464$	−2.15618	−	3.73461i	−0.100098	−	0.173375i
$465$		0			0
$466$	14.6011	−	25.2899i	0.676383	−	1.17153i
$467$	−3.48137	+	3.48137i	−0.161099	+	0.161099i	−0.783053	−	0.621955i	$-0.786339\pi$
$467$	−3.48137	+	3.48137i	−0.161099	+	0.161099i	0.621955	+	0.783053i	$0.286339\pi$
$468$		0			0
$469$			31.6622i			1.46203i
$470$		0			0
$471$		0			0
$472$	1.41251	−	5.27158i	0.0650163	−	0.242644i
$473$	2.12184	−	7.91881i	0.0975622	−	0.364107i
$474$		0			0
$475$		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	−0.895355	−	0.445353i	$-0.853078\pi$
$479$	−1.35673	+	2.34993i	−0.0619906	+	0.107371i	0.833364	+	0.552724i	$0.186412\pi$
$480$		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
$485$		0			0
$486$		0			0
$487$	8.20799	+	8.20799i	0.371940	+	0.371940i	0.868183	−	0.496244i	$-0.165288\pi$
$487$	8.20799	+	8.20799i	0.371940	+	0.371940i	−0.496244	+	0.868183i	$0.665288\pi$
$488$	−8.41558	+	2.25495i	−0.380955	+	0.102077i
$489$		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
$493$	0.189789	+	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	−0.972801	−	0.231643i	$-0.925590\pi$
$499$	−28.1148	+	16.2321i	−1.25859	+	0.726649i	−0.285791	+	0.958292i	$0.592256\pi$
$500$		0			0
$501$		0			0
$502$	−5.95736	+	1.59627i	−0.265890	+	0.0712450i
$503$	−19.6817	−	19.6817i	−0.877565	−	0.877565i	0.115717	−	0.993282i	$-0.463083\pi$
$503$	−19.6817	−	19.6817i	−0.877565	−	0.877565i	−0.993282	+	0.115717i	$0.963083\pi$
$504$		0			0
$505$		0			0
$506$	−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	0.725879	−	0.687823i	$-0.241433\pi$
$509$	−5.25069	−	9.09446i	−0.232733	−	0.403105i	−0.958611	+	0.284718i	$0.908100\pi$
$510$		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
$517$	−3.56457	+	13.3031i	−0.156770	+	0.585072i
$518$	4.65189	−	17.3611i	0.204392	−	0.762802i
$519$		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	−0.939584	−	0.342318i	$-0.888788\pi$
$523$	−13.6590	+	13.6590i	−0.597266	+	0.597266i	0.342318	+	0.939584i	$0.388788\pi$
$524$	−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
$530$		0			0
$531$		0			0
$532$	−5.18240	−	5.18240i	−0.224685	−	0.224685i
$533$	7.90429	−	2.11795i	0.342373	−	0.0917385i
$534$		0			0
$535$		0			0
$536$	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
$545$		0			0
$546$		0			0
$547$	0.234244	−	0.0627654i	0.0100155	−	0.00268365i	−0.253808	−	0.967255i	$-0.581683\pi$
$547$	0.234244	−	0.0627654i	0.0100155	−	0.00268365i	0.263823	+	0.964571i	$0.415016\pi$
$548$	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
$553$	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	−0.432266	+	0.901746i	$0.642286\pi$
$557$	−31.4838	+	31.4838i	−1.33401	+	1.33401i	−0.901746	+	0.432266i	$0.857714\pi$
$558$		0			0
$559$			2.04270i			0.0863969i
$560$		0			0
$561$		0			0
$562$	−0.0743081	+	0.277322i	−0.00313450	+	0.0116981i
$563$	8.35388	−	31.1771i	0.352074	−	1.31396i	−0.532053	−	0.846711i	$-0.678579\pi$
$563$	8.35388	−	31.1771i	0.352074	−	1.31396i	0.884127	−	0.467247i	$-0.154754\pi$
$564$		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	$0.403487\pi$
$569$	−16.1545	+	27.9804i	−0.677232	+	1.17300i	−0.975811	+	0.218615i	$0.929846\pi$
$570$		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	$0.650920\pi$
$572$	3.80016	+	1.01825i	0.158893	+	0.0425752i
$573$		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	0.568462	−	0.822710i	$-0.307539\pi$
$577$	−6.10724	−	6.10724i	−0.254248	−	0.254248i	−0.822710	+	0.568462i	$0.807539\pi$
$578$	16.3928	−	4.39244i	0.681851	−	0.182701i
$579$		0			0
$580$		0			0
$581$	−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	$-0.0708831\pi$
$587$	0.490414	+	1.83025i	0.0202415	+	0.0755424i	−0.955066	+	0.296392i	$0.904216\pi$
$588$		0			0
$589$	−15.3501	+	8.86238i	−0.632490	+	0.365168i
$590$		0			0
$591$		0			0
$592$	−4.46504	+	1.19640i	−0.183512	+	0.0491719i
$593$	11.0077	+	11.0077i	0.452033	+	0.452033i	0.896029	−	0.443996i	$-0.146439\pi$
$593$	11.0077	+	11.0077i	0.452033	+	0.452033i	−0.443996	+	0.896029i	$0.646439\pi$
$594$		0			0
$595$		0			0
$596$	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	−0.999435	−	0.0336142i	$-0.989298\pi$
$599$	−12.9428	−	22.4176i	−0.528828	−	0.915957i	0.470607	−	0.882343i	$-0.344035\pi$
$600$		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
$607$	−7.70972	+	28.7731i	−0.312928	+	1.16786i	0.612975	+	0.790102i	$0.289973\pi$
$607$	−7.70972	+	28.7731i	−0.312928	+	1.16786i	−0.925903	+	0.377761i	$0.876694\pi$
$608$	−0.487854	+	1.82070i	−0.0197851	+	0.0738390i
$609$		0			0
$610$		0			0
$611$		−	3.43162i		−	0.138828i
$612$		0			0
$613$	12.5028	−	12.5028i	0.504982	−	0.504982i	−0.408000	−	0.912982i	$-0.633774\pi$
$613$	12.5028	−	12.5028i	0.504982	−	0.504982i	0.912982	+	0.408000i	$0.133774\pi$
$614$	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	$-0.464247\pi$
$617$	−7.14621	−	1.91482i	−0.287695	−	0.0770878i	−0.399781	+	0.916611i	$0.630914\pi$
$618$		0			0
$619$	−16.4624	−	9.50460i	−0.661682	−	0.382022i	0.131236	−	0.991351i	$-0.458105\pi$
$619$	−16.4624	−	9.50460i	−0.661682	−	0.382022i	−0.792917	+	0.609329i	$0.791439\pi$
$620$		0			0
$621$		0			0
$622$	−9.78715	−	9.78715i	−0.392429	−	0.392429i
$623$	18.3217	−	4.90928i	0.734043	−	0.196686i
$624$		0			0
$625$		0			0
$626$	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
$635$		0			0
$636$		0			0
$637$	−7.76396	+	2.08035i	−0.307619	+	0.0824263i
$638$	−12.1167	−	12.1167i	−0.479705	−	0.479705i
$639$		0			0
$640$		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
$643$	−29.4639	−	7.89483i	−1.16194	−	0.311342i	−0.374202	−	0.927347i	$-0.622083\pi$
$643$	−29.4639	−	7.89483i	−1.16194	−	0.311342i	−0.787742	+	0.616006i	$0.788750\pi$
$644$	−10.2428	−	17.7411i	−0.403624	−	0.699097i
$645$		0			0
$646$	0.160260	−	0.277578i	0.00630533	−	0.0109211i
$647$	4.02651	−	4.02651i	0.158298	−	0.158298i	−0.623514	−	0.781812i	$-0.714296\pi$
$647$	4.02651	−	4.02651i	0.158298	−	0.158298i	0.781812	+	0.623514i	$0.214296\pi$
$648$		0			0
$649$		−	21.6861i		−	0.851255i
$650$		0			0
$651$		0			0
$652$	1.84421	−	6.88270i	0.0722249	−	0.269547i
$653$	−8.44081	+	31.5015i	−0.330314	+	1.23275i	0.578546	+	0.815650i	$0.303620\pi$
$653$	−8.44081	+	31.5015i	−0.330314	+	1.23275i	−0.908861	+	0.417100i	$0.863046\pi$
$654$		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	−0.674484	−	0.738290i	$-0.735634\pi$
$659$	7.75612	−	13.4340i	0.302136	−	0.523314i	0.976619	+	0.214975i	$0.0689671\pi$
$660$		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	$0.690812\pi$
$662$	−4.02232	−	1.07778i	−0.156332	−	0.0418890i
$663$		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
$668$	10.4641	−	2.80384i	0.404867	−	0.108484i
$669$		0			0
$670$		0			0
$671$	−29.9817	+	17.3099i	−1.15743	+	0.668243i
$672$		0			0
$673$	−2.49905	−	9.32657i	−0.0963312	−	0.359513i	0.900887	−	0.434054i	$-0.142917\pi$
$673$	−2.49905	−	9.32657i	−0.0963312	−	0.359513i	−0.997218	+	0.0745413i	$0.976251\pi$
$674$	−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	$-0.0368777\pi$
$677$	1.95869	+	7.30994i	0.0752787	+	0.280944i	−0.918018	+	0.396539i	$0.870211\pi$
$678$		0			0
$679$	5.03802	−	2.90870i	0.193342	−	0.111626i
$680$		0			0
$681$		0			0
$682$	−36.0924	+	9.67093i	−1.38205	+	0.370319i
$683$	−7.48288	−	7.48288i	−0.286325	−	0.286325i	0.549300	−	0.835625i	$-0.314894\pi$
$683$	−7.48288	−	7.48288i	−0.286325	−	0.286325i	−0.835625	+	0.549300i	$0.814894\pi$
$684$		0			0
$685$		0			0
$686$	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	−0.101975	−	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
$697$	0.363749	−	1.35753i	0.0137780	−	0.0514201i
$698$	−2.51883	+	9.40041i	−0.0953392	+	0.355811i
$699$		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
$707$	−38.6814	−	10.3647i	−1.45476	−	0.389803i
$708$		0			0
$709$	0.356646	+	0.205910i	0.0133941	+	0.00773310i	0.506682	−	0.862133i	$-0.330872\pi$
$709$	0.356646	+	0.205910i	0.0133941	+	0.00773310i	−0.493288	+	0.869866i	$0.664205\pi$
$710$		0			0
$711$		0			0
$712$	−3.44949	−	3.44949i	−0.129275	−	0.129275i
$713$	−47.8551	+	12.8227i	−1.79219	+	0.480215i
$714$		0			0
$715$		0			0
$716$	−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
$725$		0			0
$726$		0			0
$727$	13.7902	−	3.69508i	0.511451	−	0.137043i	0.00614188	−	0.999981i	$-0.498045\pi$
$727$	13.7902	−	3.69508i	0.511451	−	0.137043i	0.505310	+	0.862938i	$0.331378\pi$
$728$	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
$733$	29.6676	+	7.94942i	1.09580	+	0.293618i	0.761053	−	0.648690i	$-0.224683\pi$
$733$	29.6676	+	7.94942i	1.09580	+	0.293618i	0.334746	+	0.942308i	$0.391349\pi$
$734$	5.04335	+	8.73534i	0.186153	+	0.322427i
$735$		0			0
$736$	−2.63432	+	4.56277i	−0.0971022	+	0.168186i
$737$	22.8802	−	22.8802i	0.842803	−	0.842803i
$738$		0			0
$739$		−	19.6312i		−	0.722144i	−0.932538	−	0.361072i	$-0.882411\pi$
$739$		−	19.6312i		−	0.722144i	0.932538	−	0.361072i	$-0.117589\pi$
$740$		0			0
$741$		0			0
$742$	5.21700	−	19.4701i	0.191522	−	0.714771i
$743$	−9.31585	+	34.7672i	−0.341765	+	1.27549i	0.554580	+	0.832130i	$0.312879\pi$
$743$	−9.31585	+	34.7672i	−0.341765	+	1.27549i	−0.896346	+	0.443356i	$0.853788\pi$
$744$		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	$-0.517673\pi$
$752$	3.34787	+	0.897060i	0.122084	+	0.0327124i
$753$		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	0.155114	−	0.987897i	$-0.450426\pi$
$757$	−22.9129	−	22.9129i	−0.832783	−	0.832783i	−0.987897	+	0.155114i	$0.950426\pi$
$758$	0.567624	−	0.152094i	0.0206170	−	0.00552432i
$759$		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
$763$	−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	−0.438978	−	0.898498i	$-0.644659\pi$
$769$	3.31814	−	1.91573i	0.119655	−	0.0690830i	0.558633	+	0.829415i	$0.311326\pi$
$770$		0			0
$771$		0			0
$772$	15.6521	−	4.19397i	0.563332	−	0.150944i
$773$	−19.8976	−	19.8976i	−0.715668	−	0.715668i	0.252047	−	0.967715i	$-0.418896\pi$
$773$	−19.8976	−	19.8976i	−0.715668	−	0.715668i	−0.967715	+	0.252047i	$0.918896\pi$
$774$		0			0
$775$		0			0
$776$	−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
$785$		0			0
$786$		0			0
$787$	1.87155	−	6.98473i	0.0667137	−	0.248979i	−0.924513	−	0.381150i	$-0.875528\pi$
$787$	1.87155	−	6.98473i	0.0667137	−	0.248979i	0.991227	+	0.132171i	$0.0421948\pi$
$788$	−0.424901	+	1.58575i	−0.0151365	+	0.0564901i
$789$		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
$797$	−33.4396	−	8.96012i	−1.18449	−	0.317384i	−0.387786	−	0.921750i	$-0.626760\pi$
$797$	−33.4396	−	8.96012i	−1.18449	−	0.317384i	−0.796707	+	0.604366i	$0.793427\pi$
$798$		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
$803$	44.9295	−	12.0388i	1.58553	−	0.424841i
$804$		0			0
$805$		0			0
$806$	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
$815$		0			0
$816$		0			0
$817$	−3.75637	+	1.00652i	−0.131419	+	0.0352136i
$818$	−21.1307	−	21.1307i	−0.738817	−	0.738817i
$819$		0			0
$820$		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
$823$	−29.1118	−	7.80049i	−1.01477	−	0.271908i	−0.287151	−	0.957885i	$-0.592708\pi$
$823$	−29.1118	−	7.80049i	−1.01477	−	0.271908i	−0.727623	+	0.685977i	$0.759375\pi$
$824$	3.24210	+	5.61548i	0.112944	+	0.195625i
$825$		0			0
$826$	10.6101	−	18.3772i	0.369172	−	0.639424i
$827$	−4.09863	+	4.09863i	−0.142523	+	0.142523i	−0.774768	−	0.632245i	$-0.782134\pi$
$827$	−4.09863	+	4.09863i	−0.142523	+	0.142523i	0.632245	+	0.774768i	$0.282134\pi$
$828$		0			0
$829$		−	37.6756i		−	1.30853i	−0.756266	−	0.654264i	$-0.772979\pi$
$829$		−	37.6756i		−	1.30853i	0.756266	−	0.654264i	$-0.227021\pi$
$830$		0			0
$831$		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			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	$-0.639560\pi$
$839$	16.5639	−	28.6895i	0.571849	−	0.990471i	0.996376	−	0.0850559i	$-0.0271069\pi$
$840$		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
$845$		0			0
$846$		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			0
$851$	−21.0916	+	12.1773i	−0.723011	+	0.417431i
$852$		0			0
$853$	−0.689663	−	2.57386i	−0.0236136	−	0.0881273i	0.953113	−	0.302613i	$-0.0978590\pi$
$853$	−0.689663	−	2.57386i	−0.0236136	−	0.0881273i	−0.976727	+	0.214486i	$0.931192\pi$
$854$	−33.8760			−1.15921
$855$		0			0
$856$	5.23339			0.178874
$857$	4.05364	+	15.1284i	0.138470	+	0.516776i	0.999959	+	0.00900123i	$0.00286522\pi$
$857$	4.05364	+	15.1284i	0.138470	+	0.516776i	−0.861490	+	0.507775i	$0.830468\pi$
$858$		0			0
$859$	−0.691191	+	0.399059i	−0.0235831	+	0.0136157i	−0.511745	−	0.859137i	$-0.671001\pi$
$859$	−0.691191	+	0.399059i	−0.0235831	+	0.0136157i	0.488162	+	0.872753i	$0.337667\pi$
$860$		0			0
$861$		0			0
$862$	−18.6337	+	4.99288i	−0.634666	+	0.170058i
$863$	−30.2854	−	30.2854i	−1.03093	−	1.03093i	−0.999506	−	0.0314193i	$-0.989997\pi$
$863$	−30.2854	−	30.2854i	−1.03093	−	1.03093i	−0.0314193	−	0.999506i	$-0.510003\pi$
$864$		0			0
$865$		0			0
$866$	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
$875$		0			0
$876$		0			0
$877$	−4.48641	+	16.7435i	−0.151495	+	0.565388i	0.847885	+	0.530180i	$0.177876\pi$
$877$	−4.48641	+	16.7435i	−0.151495	+	0.565388i	−0.999380	+	0.0352074i	$0.988791\pi$
$878$	9.31875	−	34.7780i	0.314492	−	1.17370i
$879$		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	−0.373461	−	0.927646i	$-0.621829\pi$
$883$	16.4678	−	16.4678i	0.554185	−	0.554185i	0.927646	+	0.373461i	$0.121829\pi$
$884$	−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	$-0.264853\pi$
$887$	26.4123	+	7.07714i	0.886837	+	0.237627i	0.213482	+	0.976947i	$0.431519\pi$
$888$		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
$893$	6.31049	−	1.69089i	0.211173	−	0.0565835i
$894$		0			0
$895$		0			0
$896$	−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
$905$		0			0
$906$		0			0
$907$	24.7295	−	6.62626i	0.821130	−	0.220021i	0.176290	−	0.984338i	$-0.443590\pi$
$907$	24.7295	−	6.62626i	0.821130	−	0.220021i	0.644841	+	0.764317i	$0.276924\pi$
$908$	−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
$913$	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	$0.157998\pi$
$919$			28.8740i			0.952464i	−0.879320	+	0.476232i	$0.842002\pi$
$920$		0			0
$921$		0			0
$922$	3.24877	−	12.1246i	0.106993	−	0.399302i
$923$	−1.78073	+	6.64579i	−0.0586135	+	0.218749i
$924$		0			0
$925$		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	$0.474793\pi$
$929$	−25.1077	+	43.4879i	−0.823758	+	1.42679i	−0.902865	+	0.429925i	$0.858540\pi$
$930$		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			0
$936$		0			0
$937$	0.857094	+	0.857094i	0.0280000	+	0.0280000i	0.720968	−	0.692968i	$-0.243697\pi$
$937$	0.857094	+	0.857094i	0.0280000	+	0.0280000i	−0.692968	+	0.720968i	$0.743697\pi$
$938$	30.5834	−	8.19479i	0.998582	−	0.267569i
$939$		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
$943$	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	$-0.0697114\pi$
$947$	0.681485	+	2.54334i	0.0221453	+	0.0826473i	−0.953969	+	0.299906i	$0.903045\pi$
$948$		0			0
$949$	−10.0371	+	5.79490i	−0.325817	+	0.188111i
$950$		0			0
$951$		0			0
$952$	0.638639	−	0.171123i	0.0206984	−	0.00554612i
$953$	28.1499	+	28.1499i	0.911864	+	0.911864i	0.996419	−	0.0845545i	$-0.0269467\pi$
$953$	28.1499	+	28.1499i	0.911864	+	0.911864i	−0.0845545	+	0.996419i	$0.526947\pi$
$954$		0			0
$955$		0			0
$956$	−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
$965$		0			0
$966$		0			0
$967$	0.343829	−	1.28319i	0.0110568	−	0.0412646i	−0.960177	−	0.279392i	$-0.909867\pi$
$967$	0.343829	−	1.28319i	0.0110568	−	0.0412646i	0.971234	+	0.238128i	$0.0765337\pi$
$968$	−1.23963	+	4.62638i	−0.0398433	+	0.148697i
$969$		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
$977$	41.4084	+	11.0953i	1.32477	+	0.354972i	0.850764	−	0.525548i	$-0.176140\pi$
$977$	41.4084	+	11.0953i	1.32477	+	0.354972i	0.474009	+	0.880520i	$0.342807\pi$
$978$		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
$983$	31.1321	−	8.34182i	0.992960	−	0.266063i	0.274466	−	0.961597i	$-0.411499\pi$
$983$	31.1321	−	8.34182i	0.992960	−	0.266063i	0.718493	+	0.695534i	$0.244832\pi$
$984$		0			0
$985$		0			0
$986$	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
$995$		0			0
$996$		0			0
$997$	2.84912	−	0.763421i	0.0902327	−	0.0241778i	−0.213420	−	0.976960i	$-0.568460\pi$
$997$	2.84912	−	0.763421i	0.0902327	−	0.0241778i	0.303653	+	0.952783i	$0.401794\pi$
$998$	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.1007.1		16
3.2	odd	2		450.2.p.h.407.4		16
5.2	odd	4		270.2.m.b.143.4		16
5.3	odd	4	inner	1350.2.q.h.143.2		16
5.4	even	2		270.2.m.b.197.3		16
9.4	even	3		450.2.p.h.257.4		16
9.5	odd	6	inner	1350.2.q.h.557.2		16
15.2	even	4		90.2.l.b.83.1	yes	16
15.8	even	4		450.2.p.h.443.4		16
15.14	odd	2		90.2.l.b.47.1	yes	16
45.2	even	12		810.2.f.c.323.8		16
45.4	even	6		90.2.l.b.77.1	yes	16
45.7	odd	12		810.2.f.c.323.1		16
45.13	odd	12		450.2.p.h.293.4		16
45.14	odd	6		270.2.m.b.17.4		16
45.22	odd	12		90.2.l.b.23.1	✓	16
45.23	even	12	inner	1350.2.q.h.1043.1		16
45.29	odd	6		810.2.f.c.647.1		16
45.32	even	12		270.2.m.b.233.3		16
45.34	even	6		810.2.f.c.647.8		16
60.47	odd	4		720.2.cu.b.353.4		16
60.59	even	2		720.2.cu.b.497.3		16
180.67	even	12		720.2.cu.b.113.3		16
180.139	odd	6		720.2.cu.b.257.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.1	✓	16	45.22	odd	12
90.2.l.b.47.1	yes	16	15.14	odd	2
90.2.l.b.77.1	yes	16	45.4	even	6
90.2.l.b.83.1	yes	16	15.2	even	4
270.2.m.b.17.4		16	45.14	odd	6
270.2.m.b.143.4		16	5.2	odd	4
270.2.m.b.197.3		16	5.4	even	2
270.2.m.b.233.3		16	45.32	even	12
450.2.p.h.257.4		16	9.4	even	3
450.2.p.h.293.4		16	45.13	odd	12
450.2.p.h.407.4		16	3.2	odd	2
450.2.p.h.443.4		16	15.8	even	4
720.2.cu.b.113.3		16	180.67	even	12
720.2.cu.b.257.4		16	180.139	odd	6
720.2.cu.b.353.4		16	60.47	odd	4
720.2.cu.b.497.3		16	60.59	even	2
810.2.f.c.323.1		16	45.7	odd	12
810.2.f.c.323.8		16	45.2	even	12
810.2.f.c.647.1		16	45.29	odd	6
810.2.f.c.647.8		16	45.34	even	6
1350.2.q.h.143.2		16	5.3	odd	4	inner
1350.2.q.h.557.2		16	9.5	odd	6	inner
1350.2.q.h.1007.1		16	1.1	even	1	trivial
1350.2.q.h.1043.1		16	45.23	even	12	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)

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

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Database

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