LMFDB - Embedded newform 1350.2.q.h.1043.1

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			1043.1
Root			$0.500000 - 1.33108i$ of defining polynomial
Character	$\chi$	$=$	1350.1043
Dual form			1350.2.q.h.1007.1

$q$-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 $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.75574	−	1.00635i	−1.41954	−	0.380364i	−0.534217	−	0.845347i	$-0.679394\pi$
$7$	−3.75574	−	1.00635i	−1.41954	−	0.380364i	−0.885319	+	0.464984i	$0.846060\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$		0			0
$11$	3.44125	−	1.98681i	1.03758	−	0.599044i	0.118430	−	0.992962i	$-0.462214\pi$
$11$	3.44125	−	1.98681i	1.03758	−	0.599044i	0.919145	+	0.393918i	$0.128881\pi$
$12$		0			0
$13$	−0.956351	+	0.256253i	−0.265244	+	0.0710719i	−0.388990	−	0.921242i	$-0.627176\pi$
$13$	−0.956351	+	0.256253i	−0.265244	+	0.0710719i	0.123746	+	0.992314i	$0.460509\pi$
$14$	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	0.692375	−	0.721538i	$-0.256564\pi$
$17$	−0.120239	−	0.120239i	−0.0291622	−	0.0291622i	−0.721538	+	0.692375i	$0.756564\pi$
$18$		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
$22$	1.02845	+	3.83821i	0.219265	+	0.818310i
$23$	1.36362	+	5.08911i	0.284335	+	1.06115i	0.949324	+	0.314299i	$0.101770\pi$
$23$	1.36362	+	5.08911i	0.284335	+	1.06115i	−0.664989	+	0.746853i	$0.731564\pi$
$24$		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	$-0.0355406\pi$
$29$	2.15618	+	3.73461i	0.400392	+	0.693499i	−0.593381	+	0.804922i	$0.702207\pi$
$30$		0			0
$31$	−4.70172	+	8.14362i	−0.844454	+	1.46264i	0.0416413	+	0.999133i	$0.486741\pi$
$31$	−4.70172	+	8.14362i	−0.844454	+	1.46264i	−0.886095	+	0.463504i	$0.846592\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$		0			0
$34$	0.147262	−	0.0850217i	0.0252552	−	0.0145811i
$35$		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	$0.374066\pi$
$38$	−1.82070	−	0.487854i	−0.295356	−	0.0791404i
$39$		0			0
$40$		0			0
$41$	−7.15775	−	4.13253i	−1.11785	−	0.645393i	−0.177001	−	0.984211i	$-0.556640\pi$
$41$	−7.15775	−	4.13253i	−1.11785	−	0.645393i	−0.940852	+	0.338818i	$0.889973\pi$
$42$		0			0
$43$	−0.533983	+	1.99285i	−0.0814316	+	0.303907i	−0.994615	−	0.103643i	$-0.966950\pi$
$43$	−0.533983	+	1.99285i	−0.0814316	+	0.303907i	0.913183	+	0.407550i	$0.133617\pi$
$44$	−3.97361			−0.599044
$45$		0			0
$46$	−5.26863			−0.776818
$47$	0.897060	−	3.34787i	0.130850	−	0.488338i	−0.869131	−	0.494582i	$-0.835321\pi$
$47$	0.897060	−	3.34787i	0.130850	−	0.488338i	0.999981	+	0.00624459i	$0.00198773\pi$
$48$		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	−0.912531	−	0.409007i	$-0.865875\pi$
$53$	−3.66571	+	3.66571i	−0.503524	+	0.503524i	0.409007	+	0.912531i	$0.365875\pi$
$54$		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	−0.987162	−	0.159724i	$-0.948939\pi$
$59$	−2.72877	+	4.72637i	−0.355255	+	0.615320i	0.631906	+	0.775045i	$0.282273\pi$
$60$		0			0
$61$	−4.35623	−	7.54520i	−0.557758	−	0.966064i	−0.997683	−	0.0680302i	$-0.978329\pi$
$61$	−4.35623	−	7.54520i	−0.557758	−	0.966064i	0.439926	−	0.898034i	$-0.355005\pi$
$62$	−6.64923	−	6.64923i	−0.844454	−	0.844454i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$		0			0
$67$	2.10759	+	7.86563i	0.257483	+	0.960940i	0.966692	+	0.255942i	$0.0823855\pi$
$67$	2.10759	+	7.86563i	0.257483	+	0.960940i	−0.709209	+	0.704998i	$0.750948\pi$
$68$	0.0440105	+	0.164249i	0.00533705	+	0.0199182i
$69$		0			0
$70$		0			0
$71$			6.94911i			0.824708i	0.911024	+	0.412354i	$0.135293\pi$
$71$			6.94911i			0.824708i	−0.911024	+	0.412354i	$0.864707\pi$
$72$		0			0
$73$	8.27728	+	8.27728i	0.968783	+	0.968783i	0.999527	−	0.0307446i	$-0.00978785\pi$
$73$	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
$77$	−14.9238	+	3.99883i	−1.70073	+	0.455709i
$78$		0			0
$79$	−11.7529	+	6.78553i	−1.32230	+	0.763431i	−0.984095	−	0.177641i	$-0.943153\pi$
$79$	−11.7529	+	6.78553i	−1.32230	+	0.763431i	−0.338206	+	0.941072i	$0.609820\pi$
$80$		0			0
$81$		0			0
$82$	5.84428	−	5.84428i	0.645393	−	0.645393i
$83$	6.75913	+	1.81110i	0.741911	+	0.198795i	0.609927	−	0.792457i	$-0.291199\pi$
$83$	6.75913	+	1.81110i	0.741911	+	0.198795i	0.131984	+	0.991252i	$0.457865\pi$
$84$		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	0.184704	−	0.982794i	$-0.440868\pi$
$97$	−1.44518	−	0.387234i	−0.146736	−	0.0393177i	−0.331439	+	0.943477i	$0.607534\pi$
$98$	−5.74052	+	5.74052i	−0.579880	+	0.579880i
$99$		0			0
$100$		0			0
$101$	8.91944	−	5.14964i	0.887517	−	0.512408i	0.0143875	−	0.999896i	$-0.495420\pi$
$101$	8.91944	−	5.14964i	0.887517	−	0.512408i	0.873130	+	0.487488i	$0.162087\pi$
$102$		0			0
$103$	6.26326	−	1.67823i	0.617137	−	0.165361i	0.0633111	−	0.997994i	$-0.479834\pi$
$103$	6.26326	−	1.67823i	0.617137	−	0.165361i	0.553826	+	0.832632i	$0.313167\pi$
$104$	−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	0.862982	−	0.505235i	$-0.168594\pi$
$107$	3.70057	+	3.70057i	0.357747	+	0.357747i	−0.505235	+	0.862982i	$0.668594\pi$
$108$		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
$112$	−1.00635	−	3.75574i	−0.0950909	−	0.354884i
$113$	−1.09205	−	4.07557i	−0.102731	−	0.383397i	0.895347	−	0.445369i	$-0.146928\pi$
$113$	−1.09205	−	4.07557i	−0.102731	−	0.383397i	−0.998078	+	0.0619722i	$0.980261\pi$
$114$		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	−0.257000	+	0.966411i	$0.582734\pi$
$127$	−13.7871	+	13.7871i	−1.22341	+	1.22341i	−0.966411	+	0.257000i	$0.917266\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$		0			0
$130$		0			0
$131$	3.88249	+	2.24156i	0.339215	+	0.195846i	0.659925	−	0.751332i	$-0.270588\pi$
$131$	3.88249	+	2.24156i	0.339215	+	0.195846i	−0.320710	+	0.947178i	$0.603921\pi$
$132$		0			0
$133$	1.89689	−	7.07929i	0.164481	−	0.613852i
$134$	−8.14310			−0.703457
$135$		0			0
$136$	−0.170043			−0.0145811
$137$	−3.23492	+	12.0729i	−0.276378	+	1.03146i	0.678534	+	0.734569i	$0.262616\pi$
$137$	−3.23492	+	12.0729i	−0.276378	+	1.03146i	−0.954912	+	0.296888i	$0.904051\pi$
$138$		0			0
$139$	3.60435	+	2.08097i	0.305717	+	0.176506i	0.645008	−	0.764176i	$-0.276854\pi$
$139$	3.60435	+	2.08097i	0.305717	+	0.176506i	−0.339291	+	0.940681i	$0.610187\pi$
$140$		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	−0.886473	−	0.462781i	$-0.846852\pi$
$149$	−0.518244	+	0.897625i	−0.0424562	+	0.0735363i	0.844016	+	0.536317i	$0.180185\pi$
$150$		0			0
$151$	−2.03451	−	3.52388i	−0.165566	−	0.286769i	0.771290	−	0.636484i	$-0.219612\pi$
$151$	−2.03451	−	3.52388i	−0.165566	−	0.286769i	−0.936856	+	0.349715i	$0.886278\pi$
$152$	1.33284	+	1.33284i	0.108108	+	0.108108i
$153$		0			0
$154$		−	15.4503i		−	1.24502i
$155$		0			0
$156$		0			0
$157$	−2.36186	−	8.81460i	−0.188497	−	0.703481i	−0.993855	−	0.110692i	$-0.964693\pi$
$157$	−2.36186	−	8.81460i	−0.188497	−	0.703481i	0.805357	−	0.592789i	$-0.201973\pi$
$158$	−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	0.481695	−	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
$167$	−10.4641	+	2.80384i	−0.809734	+	0.216968i	−0.639853	−	0.768497i	$-0.721005\pi$
$167$	−10.4641	+	2.80384i	−0.809734	+	0.216968i	−0.169881	+	0.985465i	$0.554338\pi$
$168$		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	0.394573	−	0.918865i	$-0.370893\pi$
$173$	3.64139	+	0.975709i	0.276850	+	0.0741818i	−0.117722	+	0.993047i	$0.537559\pi$
$174$		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	−0.862024	−	0.506868i	$-0.830803\pi$
$191$	−11.8036	+	6.81478i	−0.854075	+	0.493100i	0.00794868	+	0.999968i	$0.497470\pi$
$192$		0			0
$193$	−15.6521	+	4.19397i	−1.12666	+	0.301889i	−0.773577	−	0.633702i	$-0.781534\pi$
$193$	−15.6521	+	4.19397i	−1.12666	+	0.301889i	−0.353086	+	0.935591i	$0.614868\pi$
$194$	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	0.747250	−	0.664543i	$-0.231374\pi$
$197$	1.16085	+	1.16085i	0.0827072	+	0.0827072i	−0.664543	+	0.747250i	$0.731374\pi$
$198$		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
$202$	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	0.361048	+	0.932547i	$0.382419\pi$
$211$	−9.10894	+	15.7771i	−0.627085	+	1.08614i	−0.988134	+	0.153597i	$0.950914\pi$
$212$	5.00745	−	1.34174i	0.343913	−	0.0921513i
$213$		0			0
$214$	−4.53225	+	2.61670i	−0.309818	+	0.178874i
$215$		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	−0.994605	−	0.103734i	$-0.966921\pi$
$223$	−1.21534	+	4.53570i	−0.0813849	+	0.303733i	0.913220	+	0.407466i	$0.133588\pi$
$224$	3.88823			0.259793
$225$		0			0
$226$	4.21934			0.280666
$227$	6.47859	−	24.1784i	0.429999	−	1.60478i	−0.322759	−	0.946481i	$-0.604610\pi$
$227$	6.47859	−	24.1784i	0.429999	−	1.60478i	0.752758	−	0.658297i	$-0.228723\pi$
$228$		0			0
$229$	−19.7350	−	11.3940i	−1.30412	−	0.752935i	−0.323014	−	0.946394i	$-0.604696\pi$
$229$	−19.7350	−	11.3940i	−1.30412	−	0.752935i	−0.981108	+	0.193459i	$0.938029\pi$
$230$		0			0
$231$		0			0
$232$	4.16541	+	1.11612i	0.273473	+	0.0732768i
$233$	20.6491	−	20.6491i	1.35277	−	1.35277i	0.470214	−	0.882553i	$-0.344177\pi$
$233$	20.6491	−	20.6491i	1.35277	−	1.35277i	0.882553	−	0.470214i	$-0.155823\pi$
$234$		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	−0.679877	−	0.733327i	$-0.737967\pi$
$239$	4.56277	−	7.90295i	0.295141	−	0.511199i	0.975018	+	0.222127i	$0.0713000\pi$
$240$		0			0
$241$	0.869654	+	1.50629i	0.0560194	+	0.0970284i	0.892675	−	0.450701i	$-0.148826\pi$
$241$	0.869654	+	1.50629i	0.0560194	+	0.0970284i	−0.836656	+	0.547729i	$0.815492\pi$
$242$	3.38674	+	3.38674i	0.217708	+	0.217708i
$243$		0			0
$244$			8.71245i			0.557758i
$245$		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	$0.0623555\pi$
$251$			6.16751i			0.389290i	−0.980874	+	0.194645i	$0.937645\pi$
$252$		0			0
$253$	14.8036	+	14.8036i	0.930696	+	0.930696i
$254$	−9.74898	−	16.8857i	−0.611706	−	1.05951i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	28.0634	−	7.51956i	1.75055	−	0.469057i	0.765803	−	0.643075i	$-0.222342\pi$
$257$	28.0634	−	7.51956i	1.75055	−	0.469057i	0.984743	+	0.174018i	$0.0556750\pi$
$258$		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	−0.344038	−	0.938956i	$-0.611795\pi$
$263$	−18.0249	−	4.82975i	−1.11146	−	0.297815i	−0.767424	+	0.641141i	$0.778462\pi$
$264$		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	0.136940	−	0.990579i	$-0.456273\pi$
$277$	−3.99035	−	1.06921i	−0.239757	−	0.0642426i	−0.376696	+	0.926337i	$0.622940\pi$
$278$	−2.94294	+	2.94294i	−0.176506	+	0.176506i
$279$		0			0
$280$		0			0
$281$	−0.248640	+	0.143552i	−0.0148326	+	0.00856361i	−0.507398	−	0.861712i	$-0.669393\pi$
$281$	−0.248640	+	0.143552i	−0.0148326	+	0.00856361i	0.492565	+	0.870275i	$0.336059\pi$
$282$		0			0
$283$	−17.4857	+	4.68527i	−1.03941	+	0.278510i	−0.737871	−	0.674942i	$-0.764169\pi$
$283$	−17.4857	+	4.68527i	−1.03941	+	0.278510i	−0.301544	+	0.953452i	$0.597502\pi$
$284$	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	0.915806	+	0.401621i	$0.131553\pi$
$293$	5.53752	+	20.6663i	0.323505	+	1.20734i	−0.592300	+	0.805717i	$0.701780\pi$
$294$		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	0.173476	−	0.984838i	$-0.444500\pi$
$307$	20.2953	−	20.2953i	1.15831	−	1.15831i	0.984838	−	0.173476i	$-0.0555001\pi$
$308$	14.9238	+	3.99883i	0.850365	+	0.227855i
$309$		0			0
$310$		0			0
$311$	11.9868	+	6.92056i	0.679707	+	0.392429i	0.799745	−	0.600340i	$-0.204968\pi$
$311$	11.9868	+	6.92056i	0.679707	+	0.392429i	−0.120038	+	0.992769i	$0.538302\pi$
$312$		0			0
$313$	4.79847	−	17.9081i	0.271226	−	1.01223i	−0.687103	−	0.726560i	$-0.741118\pi$
$313$	4.79847	−	17.9081i	0.271226	−	1.01223i	0.958329	−	0.285668i	$-0.0922154\pi$
$314$	9.12554			0.514984
$315$		0			0
$316$	13.5711			0.763431
$317$	0.217566	−	0.811966i	0.0122197	−	0.0456046i	−0.959547	−	0.281549i	$-0.909152\pi$
$317$	0.217566	−	0.811966i	0.0122197	−	0.0456046i	0.971766	+	0.235945i	$0.0758184\pi$
$318$		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	0.917557	−	0.397604i	$-0.130158\pi$
$331$	2.08211	+	3.60631i	0.114443	+	0.198221i	−0.803114	+	0.595825i	$0.796825\pi$
$332$	−4.94803	−	4.94803i	−0.271558	−	0.271558i
$333$		0			0
$334$		−	10.8332i		−	0.592766i
$335$		0			0
$336$		0			0
$337$	0.840764	+	3.13777i	0.0457993	+	0.170925i	0.985037	−	0.172341i	$-0.0551332\pi$
$337$	0.840764	+	3.13777i	0.0457993	+	0.170925i	−0.939238	+	0.343267i	$0.888467\pi$
$338$	−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	−0.135076	−	0.990835i	$-0.543128\pi$
$347$	4.53334	−	1.21470i	0.243362	−	0.0652087i	0.378438	+	0.925627i	$0.376461\pi$
$348$		0			0
$349$	−8.42818	+	4.86601i	−0.451150	+	0.260472i	−0.708316	−	0.705896i	$-0.750545\pi$
$349$	−8.42818	+	4.86601i	−0.451150	+	0.260472i	0.257166	+	0.966367i	$0.417211\pi$
$350$		0			0
$351$		0			0
$352$	−2.80977	+	2.80977i	−0.149761	+	0.149761i
$353$	−4.92815	−	1.32049i	−0.262299	−	0.0702827i	0.125273	−	0.992122i	$-0.460019\pi$
$353$	−4.92815	−	1.32049i	−0.262299	−	0.0702827i	−0.387572	+	0.921840i	$0.626686\pi$
$354$		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	−0.00460117	−	0.999989i	$-0.501465\pi$
$367$	−9.74300	−	2.61063i	−0.508581	−	0.136274i	−0.503979	+	0.863716i	$0.668131\pi$
$368$	−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	−0.571350	−	0.820706i	$-0.693580\pi$
$373$	−12.6656	+	3.39374i	−0.655801	+	0.175721i	−0.0844507	+	0.996428i	$0.526914\pi$
$374$	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
$382$	−3.52759	−	13.1652i	−0.180487	−	0.673588i
$383$	3.75319	+	14.0071i	0.191779	+	0.715729i	0.993077	+	0.117464i	$0.0374765\pi$
$383$	3.75319	+	14.0071i	0.191779	+	0.715729i	−0.801298	+	0.598265i	$0.795857\pi$
$384$		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	−0.999533	−	0.0305570i	$-0.990272\pi$
$389$	−10.3789	−	17.9767i	−0.526230	−	0.911456i	0.473303	−	0.880899i	$-0.343061\pi$
$390$		0			0
$391$	0.447948	−	0.775869i	0.0226537	−	0.0392374i
$392$	7.84169	−	2.10118i	0.396065	−	0.106125i
$393$		0			0
$394$	−1.42175	+	0.820845i	−0.0716265	+	0.0413536i
$395$		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	$0.438699\pi$
$398$	−16.5881	−	4.44477i	−0.831487	−	0.222796i
$399$		0			0
$400$		0			0
$401$	−4.11737	−	2.37716i	−0.205612	−	0.118710i	0.393659	−	0.919257i	$-0.371209\pi$
$401$	−4.11737	−	2.37716i	−0.205612	−	0.118710i	−0.599270	+	0.800547i	$0.704543\pi$
$402$		0			0
$403$	2.40966	−	8.99298i	0.120034	−	0.447972i
$404$	−10.2993			−0.512408
$405$		0			0
$406$	16.7674			0.832153
$407$	−4.75404	+	17.7423i	−0.235649	+	0.879454i
$408$		0			0
$409$	25.8797	+	14.9417i	1.27967	+	0.738817i	0.976787	−	0.214211i	$-0.0687180\pi$
$409$	25.8797	+	14.9417i	1.27967	+	0.738817i	0.302882	+	0.953028i	$0.402051\pi$
$410$		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	−0.566226	−	0.824250i	$-0.691597\pi$
$419$	8.81638	−	15.2704i	0.430708	−	0.746009i	0.996934	+	0.0782412i	$0.0249304\pi$
$420$		0			0
$421$	13.9462	+	24.1555i	0.679696	+	1.17727i	0.975072	+	0.221887i	$0.0712215\pi$
$421$	13.9462	+	24.1555i	0.679696	+	1.17727i	−0.295377	+	0.955381i	$0.595445\pi$
$422$	−12.8820	−	12.8820i	−0.627085	−	0.627085i
$423$		0			0
$424$			5.18410i			0.251762i
$425$		0			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	$0.153805\pi$
$431$			19.2910i			0.929215i	−0.885517	+	0.464608i	$0.846195\pi$
$432$		0			0
$433$	−16.7154	−	16.7154i	−0.803292	−	0.803292i	0.180316	−	0.983609i	$-0.442288\pi$
$433$	−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
$437$	−9.59259	+	2.57033i	−0.458876	+	0.122955i
$438$		0			0
$439$	31.1811	−	18.0024i	1.48819	−	0.859209i	0.488285	−	0.872684i	$-0.337623\pi$
$439$	31.1811	−	18.0024i	1.48819	−	0.859209i	0.999909	+	0.0134750i	$0.00428934\pi$
$440$		0			0
$441$		0			0
$442$	−0.119047	+	0.119047i	−0.00566249	+	0.00566249i
$443$	−25.9195	−	6.94511i	−1.23147	−	0.329972i	−0.416320	−	0.909218i	$-0.636680\pi$
$443$	−25.9195	−	6.94511i	−1.23147	−	0.329972i	−0.815153	+	0.579246i	$0.803347\pi$
$444$		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	0.711186	−	0.703004i	$-0.248158\pi$
$457$	20.8557	+	5.58827i	0.975589	+	0.261408i	0.264403	+	0.964412i	$0.414825\pi$
$458$	16.1135	−	16.1135i	0.752935	−	0.752935i
$459$		0			0
$460$		0			0
$461$	10.8706	−	6.27615i	0.506295	−	0.292309i	−0.225015	−	0.974355i	$-0.572243\pi$
$461$	10.8706	−	6.27615i	0.506295	−	0.292309i	0.731309	+	0.682046i	$0.238910\pi$
$462$		0			0
$463$	21.3514	−	5.72110i	0.992286	−	0.265882i	0.274076	−	0.961708i	$-0.411628\pi$
$463$	21.3514	−	5.72110i	0.992286	−	0.265882i	0.718210	+	0.695826i	$0.244962\pi$
$464$	−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	0.621955	−	0.783053i	$-0.286339\pi$
$467$	−3.48137	−	3.48137i	−0.161099	−	0.161099i	−0.783053	+	0.621955i	$0.786339\pi$
$468$		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	0.833364	−	0.552724i	$-0.186412\pi$
$479$	−1.35673	−	2.34993i	−0.0619906	−	0.107371i	−0.895355	+	0.445353i	$0.853078\pi$
$480$		0			0
$481$	2.28836	−	3.96356i	0.104340	−	0.180723i
$482$	−1.68004	+	0.450166i	−0.0765239	+	0.0205045i
$483$		0			0
$484$	−4.14790	+	2.39479i	−0.188541	+	0.108854i
$485$		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	$0.165288\pi$
$488$	−8.41558	−	2.25495i	−0.380955	−	0.102077i
$489$		0			0
$490$		0			0
$491$	−4.28058	−	2.47139i	−0.193180	−	0.111532i	0.400290	−	0.916388i	$-0.368909\pi$
$491$	−4.28058	−	2.47139i	−0.193180	−	0.111532i	−0.593470	+	0.804856i	$0.702243\pi$
$492$		0			0
$493$	0.189789	−	0.708301i	0.00854766	−	0.0319003i
$494$	1.86624			0.0839661
$495$		0			0
$496$	−9.40344			−0.422227
$497$	6.99322	−	26.0991i	0.313689	−	1.17070i
$498$		0			0
$499$	−28.1148	−	16.2321i	−1.25859	−	0.726649i	−0.285791	−	0.958292i	$-0.592256\pi$
$499$	−28.1148	−	16.2321i	−1.25859	−	0.726649i	−0.972801	+	0.231643i	$0.925590\pi$
$500$		0			0
$501$		0			0
$502$	−5.95736	−	1.59627i	−0.265890	−	0.0712450i
$503$	−19.6817	+	19.6817i	−0.877565	+	0.877565i	−0.993282	−	0.115717i	$-0.963083\pi$
$503$	−19.6817	+	19.6817i	−0.877565	+	0.877565i	0.115717	+	0.993282i	$0.463083\pi$
$504$		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	−0.958611	−	0.284718i	$-0.908100\pi$
$509$	−5.25069	+	9.09446i	−0.232733	+	0.403105i	0.725879	+	0.687823i	$0.241433\pi$
$510$		0			0
$511$	−22.7575	−	39.4171i	−1.00673	−	1.74371i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			29.0534i			1.28149i
$515$		0			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	$-0.787568\pi$
$521$		−	28.2545i		−	1.23785i	0.785450	−	0.618925i	$-0.212432\pi$
$522$		0			0
$523$	−13.6590	−	13.6590i	−0.597266	−	0.597266i	0.342318	−	0.939584i	$-0.388788\pi$
$523$	−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
$527$	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	0.263823	−	0.964571i	$-0.415016\pi$
$547$	0.234244	+	0.0627654i	0.0100155	+	0.00268365i	−0.253808	+	0.967255i	$0.581683\pi$
$548$	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	−0.901746	−	0.432266i	$-0.857714\pi$
$557$	−31.4838	−	31.4838i	−1.33401	−	1.33401i	−0.432266	−	0.901746i	$-0.642286\pi$
$558$		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	0.884127	+	0.467247i	$0.154754\pi$
$563$	8.35388	+	31.1771i	0.352074	+	1.31396i	−0.532053	+	0.846711i	$0.678579\pi$
$564$		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	−0.975811	−	0.218615i	$-0.929846\pi$
$569$	−16.1545	−	27.9804i	−0.677232	−	1.17300i	0.298580	−	0.954385i	$-0.403487\pi$
$570$		0			0
$571$	12.9565	−	22.4413i	0.542213	−	0.939141i	−0.456563	−	0.889691i	$-0.650920\pi$
$571$	12.9565	−	22.4413i	0.542213	−	0.939141i	0.998777	−	0.0494501i	$-0.0157469\pi$
$572$	3.80016	−	1.01825i	0.158893	−	0.0425752i
$573$		0			0
$574$	−27.8310	+	16.0682i	−1.16164	+	0.670674i
$575$		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	$0.307539\pi$
$578$	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	−0.955066	−	0.296392i	$-0.904216\pi$
$587$	0.490414	−	1.83025i	0.0202415	−	0.0755424i	0.975308	+	0.220850i	$0.0708831\pi$
$588$		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	−0.443996	−	0.896029i	$-0.646439\pi$
$593$	11.0077	−	11.0077i	0.452033	−	0.452033i	0.896029	+	0.443996i	$0.146439\pi$
$594$		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	0.470607	+	0.882343i	$0.344035\pi$
$599$	−12.9428	+	22.4176i	−0.528828	+	0.915957i	−0.999435	+	0.0336142i	$0.989298\pi$
$600$		0			0
$601$	−9.79604	−	16.9672i	−0.399589	−	0.692108i	0.594086	−	0.804401i	$-0.297514\pi$
$601$	−9.79604	−	16.9672i	−0.399589	−	0.692108i	−0.993675	+	0.112293i	$0.964180\pi$
$602$	5.67241	+	5.67241i	0.231190	+	0.231190i
$603$		0			0
$604$			4.06902i			0.165566i
$605$		0			0
$606$		0			0
$607$	−7.70972	−	28.7731i	−0.312928	−	1.16786i	−0.925903	−	0.377761i	$-0.876694\pi$
$607$	−7.70972	−	28.7731i	−0.312928	−	1.16786i	0.612975	−	0.790102i	$-0.289973\pi$
$608$	−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	0.912982	−	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
$617$	−7.14621	+	1.91482i	−0.287695	+	0.0770878i	−0.399781	−	0.916611i	$-0.630914\pi$
$617$	−7.14621	+	1.91482i	−0.287695	+	0.0770878i	0.112085	+	0.993699i	$0.464247\pi$
$618$		0			0
$619$	−16.4624	+	9.50460i	−0.661682	+	0.382022i	−0.792917	−	0.609329i	$-0.791439\pi$
$619$	−16.4624	+	9.50460i	−0.661682	+	0.382022i	0.131236	+	0.991351i	$0.458105\pi$
$620$		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	−0.999978	−	0.00667968i	$-0.997874\pi$
$641$	−37.8297	+	21.8410i	−1.49418	+	0.862666i	−0.494204	+	0.869346i	$0.664540\pi$
$642$		0			0
$643$	−29.4639	+	7.89483i	−1.16194	+	0.311342i	−0.787742	−	0.616006i	$-0.788750\pi$
$643$	−29.4639	+	7.89483i	−1.16194	+	0.311342i	−0.374202	+	0.927347i	$0.622083\pi$
$644$	−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	0.781812	−	0.623514i	$-0.214296\pi$
$647$	4.02651	+	4.02651i	0.158298	+	0.158298i	−0.623514	+	0.781812i	$0.714296\pi$
$648$		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	−0.908861	−	0.417100i	$-0.863046\pi$
$653$	−8.44081	−	31.5015i	−0.330314	−	1.23275i	0.578546	−	0.815650i	$-0.303620\pi$
$654$		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	$-0.0689671\pi$
$659$	7.75612	+	13.4340i	0.302136	+	0.523314i	−0.674484	+	0.738290i	$0.735634\pi$
$660$		0			0
$661$	11.1307	−	19.2789i	0.432933	−	0.749862i	−0.564191	−	0.825644i	$-0.690812\pi$
$661$	11.1307	−	19.2789i	0.432933	−	0.749862i	0.997124	+	0.0757821i	$0.0241453\pi$
$662$	−4.02232	+	1.07778i	−0.156332	+	0.0418890i
$663$		0			0
$664$	6.06007	−	3.49878i	0.235176	−	0.135779i
$665$		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	−0.997218	−	0.0745413i	$-0.976251\pi$
$673$	−2.49905	+	9.32657i	−0.0963312	+	0.359513i	0.900887	+	0.434054i	$0.142917\pi$
$674$	−3.24846			−0.125126
$675$		0			0
$676$	12.0197			0.462297
$677$	1.95869	−	7.30994i	0.0752787	−	0.280944i	−0.918018	−	0.396539i	$-0.870211\pi$
$677$	1.95869	−	7.30994i	0.0752787	−	0.280944i	0.993296	+	0.115596i	$0.0368777\pi$
$678$		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	−0.835625	−	0.549300i	$-0.814894\pi$
$683$	−7.48288	+	7.48288i	−0.286325	+	0.286325i	0.549300	+	0.835625i	$0.314894\pi$
$684$		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	0.912498	+	0.409080i	$0.134150\pi$
$691$	21.3061	+	36.9033i	0.810523	+	1.40387i	−0.101975	+	0.994787i	$0.532516\pi$
$692$	−2.66569	−	2.66569i	−0.101334	−	0.101334i
$693$		0			0
$694$			4.69326i			0.178154i
$695$		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	$-0.759079\pi$
$701$		−	36.3602i		−	1.37331i	0.726985	−	0.686653i	$-0.240921\pi$
$702$		0			0
$703$	−6.16113	−	6.16113i	−0.232371	−	0.232371i
$704$	−1.98681	−	3.44125i	−0.0748805	−	0.129697i
$705$		0			0
$706$	2.55100	−	4.41846i	0.0960080	−	0.166291i
$707$	−38.6814	+	10.3647i	−1.45476	+	0.389803i
$708$		0			0
$709$	0.356646	−	0.205910i	0.0133941	−	0.00773310i	−0.493288	−	0.869866i	$-0.664205\pi$
$709$	0.356646	−	0.205910i	0.0133941	−	0.00773310i	0.506682	+	0.862133i	$0.330872\pi$
$710$		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	0.505310	−	0.862938i	$-0.331378\pi$
$727$	13.7902	+	3.69508i	0.511451	+	0.137043i	0.00614188	+	0.999981i	$0.498045\pi$
$728$	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	0.334746	−	0.942308i	$-0.391349\pi$
$733$	29.6676	−	7.94942i	1.09580	−	0.293618i	0.761053	+	0.648690i	$0.224683\pi$
$734$	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
$742$	5.21700	+	19.4701i	0.191522	+	0.714771i
$743$	−9.31585	−	34.7672i	−0.341765	−	1.27549i	−0.896346	−	0.443356i	$-0.853788\pi$
$743$	−9.31585	−	34.7672i	−0.341765	−	1.27549i	0.554580	−	0.832130i	$-0.312879\pi$
$744$		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	−0.0554938	+	0.998459i	$0.517673\pi$
$751$	−24.4567	+	42.3603i	−0.892438	+	1.54575i	−0.836944	+	0.547289i	$0.815660\pi$
$752$	3.34787	−	0.897060i	0.122084	−	0.0327124i
$753$		0			0
$754$	3.69759	−	2.13480i	0.134658	−	0.0777449i
$755$		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	$0.450426\pi$
$758$	0.567624	+	0.152094i	0.0206170	+	0.00552432i
$759$		0			0
$760$		0			0
$761$	9.19124	+	5.30657i	0.333182	+	0.192363i	0.657253	−	0.753670i	$-0.271718\pi$
$761$	9.19124	+	5.30657i	0.333182	+	0.192363i	−0.324071	+	0.946033i	$0.605052\pi$
$762$		0			0
$763$	−7.34795	+	27.4229i	−0.266014	+	0.992777i
$764$	13.6296			0.493100
$765$		0			0
$766$	−14.5012			−0.523950
$767$	1.39851	−	5.21932i	0.0504974	−	0.188459i
$768$		0			0
$769$	3.31814	+	1.91573i	0.119655	+	0.0690830i	0.558633	−	0.829415i	$-0.311326\pi$
$769$	3.31814	+	1.91573i	0.119655	+	0.0690830i	−0.438978	+	0.898498i	$0.644659\pi$
$770$		0			0
$771$		0			0
$772$	15.6521	+	4.19397i	0.563332	+	0.150944i
$773$	−19.8976	+	19.8976i	−0.715668	+	0.715668i	−0.967715	−	0.252047i	$-0.918896\pi$
$773$	−19.8976	+	19.8976i	−0.715668	+	0.715668i	0.252047	+	0.967715i	$0.418896\pi$
$774$		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	0.991227	−	0.132171i	$-0.0421948\pi$
$787$	1.87155	+	6.98473i	0.0667137	+	0.248979i	−0.924513	+	0.381150i	$0.875528\pi$
$788$	−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	−0.796707	−	0.604366i	$-0.793427\pi$
$797$	−33.4396	+	8.96012i	−1.18449	+	0.317384i	−0.387786	+	0.921750i	$0.626760\pi$
$798$		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	−0.0196338	−	0.999807i	$-0.506250\pi$
$821$	23.9657	−	13.8366i	0.836408	−	0.482900i	0.856042	+	0.516907i	$0.172917\pi$
$822$		0			0
$823$	−29.1118	+	7.80049i	−1.01477	+	0.271908i	−0.727623	−	0.685977i	$-0.759375\pi$
$823$	−29.1118	+	7.80049i	−1.01477	+	0.271908i	−0.287151	+	0.957885i	$0.592708\pi$
$824$	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	0.632245	−	0.774768i	$-0.282134\pi$
$827$	−4.09863	−	4.09863i	−0.142523	−	0.142523i	−0.774768	+	0.632245i	$0.782134\pi$
$828$		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
$832$	0.256253	+	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	0.996376	+	0.0850559i	$0.0271069\pi$
$839$	16.5639	+	28.6895i	0.571849	+	0.990471i	−0.424527	+	0.905415i	$0.639560\pi$
$840$		0			0
$841$	5.20180	−	9.00978i	0.179372	−	0.310682i
$842$	−26.9420	+	7.21908i	−0.928482	+	0.248786i
$843$		0			0
$844$	15.7771	−	9.10894i	0.543072	−	0.313543i
$845$		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	−0.976727	−	0.214486i	$-0.931192\pi$
$853$	−0.689663	+	2.57386i	−0.0236136	+	0.0881273i	0.953113	+	0.302613i	$0.0978590\pi$
$854$	−33.8760			−1.15921
$855$		0			0
$856$	5.23339			0.178874
$857$	4.05364	−	15.1284i	0.138470	−	0.516776i	−0.861490	−	0.507775i	$-0.830468\pi$
$857$	4.05364	−	15.1284i	0.138470	−	0.516776i	0.999959	−	0.00900123i	$-0.00286522\pi$
$858$		0			0
$859$	−0.691191	−	0.399059i	−0.0235831	−	0.0136157i	0.488162	−	0.872753i	$-0.337667\pi$
$859$	−0.691191	−	0.399059i	−0.0235831	−	0.0136157i	−0.511745	+	0.859137i	$0.671001\pi$
$860$		0			0
$861$		0			0
$862$	−18.6337	−	4.99288i	−0.634666	−	0.170058i
$863$	−30.2854	+	30.2854i	−1.03093	+	1.03093i	−0.0314193	+	0.999506i	$0.510003\pi$
$863$	−30.2854	+	30.2854i	−1.03093	+	1.03093i	−0.999506	+	0.0314193i	$0.989997\pi$
$864$		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	−0.999380	−	0.0352074i	$-0.988791\pi$
$877$	−4.48641	−	16.7435i	−0.151495	−	0.565388i	0.847885	−	0.530180i	$-0.177876\pi$
$878$	9.31875	+	34.7780i	0.314492	+	1.17370i
$879$		0			0
$880$		0			0
$881$		−	15.1033i		−	0.508843i	−0.967093	−	0.254421i	$-0.918115\pi$
$881$		−	15.1033i		−	0.508843i	0.967093	−	0.254421i	$-0.0818850\pi$
$882$		0			0
$883$	16.4678	+	16.4678i	0.554185	+	0.554185i	0.927646	−	0.373461i	$-0.121829\pi$
$883$	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
$887$	26.4123	−	7.07714i	0.886837	−	0.237627i	0.213482	−	0.976947i	$-0.431519\pi$
$887$	26.4123	−	7.07714i	0.886837	−	0.237627i	0.673355	+	0.739320i	$0.264853\pi$
$888$		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	0.644841	−	0.764317i	$-0.276924\pi$
$907$	24.7295	+	6.62626i	0.821130	+	0.220021i	0.176290	+	0.984338i	$0.443590\pi$
$908$	−17.6998	+	17.6998i	−0.587390	+	0.587390i
$909$		0			0
$910$		0			0
$911$	−3.55075	+	2.05003i	−0.117642	+	0.0679204i	−0.557666	−	0.830065i	$-0.688303\pi$
$911$	−3.55075	+	2.05003i	−0.117642	+	0.0679204i	0.440025	+	0.897986i	$0.354970\pi$
$912$		0			0
$913$	26.8582	−	7.19662i	0.888875	−	0.238173i
$914$	−10.7957	+	18.6987i	−0.357090	+	0.618499i
$915$		0			0
$916$	11.3940	+	19.7350i	0.376468	+	0.652061i
$917$	−12.3259	−	12.3259i	−0.407035	−	0.407035i
$918$		0			0
$919$		−	28.8740i		−	0.952464i	−0.879320	−	0.476232i	$-0.842002\pi$
$919$		−	28.8740i		−	0.952464i	0.879320	−	0.476232i	$-0.157998\pi$
$920$		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	−0.902865	−	0.429925i	$-0.858540\pi$
$929$	−25.1077	−	43.4879i	−0.823758	−	1.42679i	0.0791067	−	0.996866i	$-0.474793\pi$
$930$		0			0
$931$	−7.65121	+	13.2523i	−0.250758	+	0.434326i
$932$	−28.2072	+	7.55809i	−0.923956	+	0.247573i
$933$		0			0
$934$	4.26380	−	2.46170i	0.139516	−	0.0805494i
$935$		0			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	$0.243697\pi$
$938$	30.5834	+	8.19479i	0.998582	+	0.267569i
$939$		0			0
$940$		0			0
$941$	43.4478	+	25.0846i	1.41636	+	0.817735i	0.995977	−	0.0896119i	$-0.0285627\pi$
$941$	43.4478	+	25.0846i	1.41636	+	0.817735i	0.420382	+	0.907347i	$0.361896\pi$
$942$		0			0
$943$	11.2704	−	42.0618i	0.367015	−	1.36972i
$944$	−5.45754			−0.177628
$945$		0			0
$946$	−8.19815			−0.266545
$947$	0.681485	−	2.54334i	0.0221453	−	0.0826473i	−0.953969	−	0.299906i	$-0.903045\pi$
$947$	0.681485	−	2.54334i	0.0221453	−	0.0826473i	0.976114	+	0.217258i	$0.0697114\pi$
$948$		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	−0.0845545	−	0.996419i	$-0.526947\pi$
$953$	28.1499	−	28.1499i	0.911864	−	0.911864i	0.996419	+	0.0845545i	$0.0269467\pi$
$954$		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	0.971234	−	0.238128i	$-0.0765337\pi$
$967$	0.343829	+	1.28319i	0.0110568	+	0.0412646i	−0.960177	+	0.279392i	$0.909867\pi$
$968$	−1.23963	−	4.62638i	−0.0398433	−	0.148697i
$969$		0			0
$970$		0			0
$971$			38.7906i			1.24485i	0.782679	+	0.622425i	$0.213853\pi$
$971$			38.7906i			1.24485i	−0.782679	+	0.622425i	$0.786147\pi$
$972$		0			0
$973$	−11.4428	−	11.4428i	−0.366840	−	0.366840i
$974$	5.80393	+	10.0527i	0.185970	+	0.322109i
$975$		0			0
$976$	4.35623	−	7.54520i	0.139439	−	0.241516i
$977$	41.4084	−	11.0953i	1.32477	−	0.354972i	0.474009	−	0.880520i	$-0.342807\pi$
$977$	41.4084	−	11.0953i	1.32477	−	0.354972i	0.850764	+	0.525548i	$0.176140\pi$
$978$		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	0.718493	−	0.695534i	$-0.244832\pi$
$983$	31.1321	+	8.34182i	0.992960	+	0.266063i	0.274466	+	0.961597i	$0.411499\pi$
$984$		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	0.303653	−	0.952783i	$-0.401794\pi$
$997$	2.84912	+	0.763421i	0.0902327	+	0.0241778i	−0.213420	+	0.976960i	$0.568460\pi$
$998$	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.1043.1		16
3.2	odd	2		450.2.p.h.293.4		16
5.2	odd	4	inner	1350.2.q.h.557.2		16
5.3	odd	4		270.2.m.b.17.4		16
5.4	even	2		270.2.m.b.233.3		16
9.2	odd	6	inner	1350.2.q.h.143.2		16
9.7	even	3		450.2.p.h.443.4		16
15.2	even	4		450.2.p.h.257.4		16
15.8	even	4		90.2.l.b.77.1	yes	16
15.14	odd	2		90.2.l.b.23.1	✓	16
45.2	even	12	inner	1350.2.q.h.1007.1		16
45.4	even	6		810.2.f.c.323.8		16
45.7	odd	12		450.2.p.h.407.4		16
45.13	odd	12		810.2.f.c.647.1		16
45.14	odd	6		810.2.f.c.323.1		16
45.23	even	12		810.2.f.c.647.8		16
45.29	odd	6		270.2.m.b.143.4		16
45.34	even	6		90.2.l.b.83.1	yes	16
45.38	even	12		270.2.m.b.197.3		16
45.43	odd	12		90.2.l.b.47.1	yes	16
60.23	odd	4		720.2.cu.b.257.4		16
60.59	even	2		720.2.cu.b.113.3		16
180.43	even	12		720.2.cu.b.497.3		16
180.79	odd	6		720.2.cu.b.353.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.1	✓	16	15.14	odd	2
90.2.l.b.47.1	yes	16	45.43	odd	12
90.2.l.b.77.1	yes	16	15.8	even	4
90.2.l.b.83.1	yes	16	45.34	even	6
270.2.m.b.17.4		16	5.3	odd	4
270.2.m.b.143.4		16	45.29	odd	6
270.2.m.b.197.3		16	45.38	even	12
270.2.m.b.233.3		16	5.4	even	2
450.2.p.h.257.4		16	15.2	even	4
450.2.p.h.293.4		16	3.2	odd	2
450.2.p.h.407.4		16	45.7	odd	12
450.2.p.h.443.4		16	9.7	even	3
720.2.cu.b.113.3		16	60.59	even	2
720.2.cu.b.257.4		16	60.23	odd	4
720.2.cu.b.353.4		16	180.79	odd	6
720.2.cu.b.497.3		16	180.43	even	12
810.2.f.c.323.1		16	45.14	odd	6
810.2.f.c.323.8		16	45.4	even	6
810.2.f.c.647.1		16	45.13	odd	12
810.2.f.c.647.8		16	45.23	even	12
1350.2.q.h.143.2		16	9.2	odd	6	inner
1350.2.q.h.557.2		16	5.2	odd	4	inner
1350.2.q.h.1007.1		16	45.2	even	12	inner
1350.2.q.h.1043.1		16	1.1	even	1	trivial

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

Groups

Database

Properties

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