LMFDB - Embedded newform 675.2.q.a.557.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(143,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, 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("675.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.3
Root			$-0.186243 + 0.0499037i$ of defining polynomial
Character	$\chi$	$=$	675.557
Dual form			675.2.q.a.143.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.186243 + 0.0499037i) q^{2} +(-1.69985 - 0.981412i) q^{4} +(-0.632007 + 2.35868i) q^{7} +(-0.540289 - 0.540289i) q^{8} +O(q^{10})$	\(q+(0.186243 + 0.0499037i) q^{2} +(-1.69985 - 0.981412i) q^{4} +(-0.632007 + 2.35868i) q^{7} +(-0.540289 - 0.540289i) q^{8} +(2.14390 - 1.23778i) q^{11} +(0.422032 + 1.57505i) q^{13} +(-0.235414 + 0.407749i) q^{14} +(1.88916 + 3.27212i) q^{16} +(0.403949 - 0.403949i) q^{17} +4.28779i q^{19} +(0.461055 - 0.123539i) q^{22} +(6.82387 - 1.82845i) q^{23} +0.314402i q^{26} +(3.38916 - 3.38916i) q^{28} +(3.20524 + 5.55164i) q^{29} +(-1.97194 + 3.41550i) q^{31} +(0.584071 + 2.17978i) q^{32} +(0.0953913 - 0.0550742i) q^{34} +(0.171954 + 0.171954i) q^{37} +(-0.213977 + 0.798571i) q^{38} +(6.52359 + 3.76639i) q^{41} +(4.95226 + 1.32695i) q^{43} -4.85908 q^{44} +1.36214 q^{46} +(2.91430 + 0.780885i) q^{47} +(0.898221 + 0.518588i) q^{49} +(0.828375 - 3.09154i) q^{52} +(-6.12030 - 6.12030i) q^{53} +(1.61584 - 0.932904i) q^{56} +(0.319907 + 1.19391i) q^{58} +(2.27234 - 3.93581i) q^{59} +(-0.235795 - 0.408408i) q^{61} +(-0.537706 + 0.537706i) q^{62} -7.12153i q^{64} +(-1.65496 + 0.443446i) q^{67} +(-1.08310 + 0.290215i) q^{68} -3.50583i q^{71} +(-6.88847 + 6.88847i) q^{73} +(0.0234441 + 0.0406064i) q^{74} +(4.20809 - 7.28862i) q^{76} +(1.56457 + 5.83906i) q^{77} +(-6.50159 + 3.75369i) q^{79} +(1.02702 + 1.02702i) q^{82} +(-2.85794 + 10.6660i) q^{83} +(0.856104 + 0.494272i) q^{86} +(-1.82708 - 0.489565i) q^{88} -2.90124 q^{89} -3.98176 q^{91} +(-13.3941 - 3.58893i) q^{92} +(0.503800 + 0.290869i) q^{94} +(0.379633 - 1.41681i) q^{97} +(0.141408 + 0.141408i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} + 2 q^{7}+O(q^{10}) $ 16 * q - 6 * q^2 + 2 * q^7	$ 16 q - 6 q^{2} + 2 q^{7} + 2 q^{13} - 8 q^{16} + 10 q^{22} + 18 q^{23} + 16 q^{28} - 4 q^{31} + 30 q^{32} - 4 q^{37} - 30 q^{38} + 24 q^{41} + 2 q^{43} + 32 q^{46} - 12 q^{47} + 14 q^{52} - 36 q^{56} + 6 q^{58} + 8 q^{61} - 4 q^{67} + 42 q^{68} + 8 q^{73} + 24 q^{76} - 6 q^{77} - 32 q^{82} - 66 q^{83} + 48 q^{86} - 18 q^{88} - 40 q^{91} - 60 q^{92} - 28 q^{97}+O(q^{100}) $ 16 * q - 6 * q^2 + 2 * q^7 + 2 * q^13 - 8 * q^16 + 10 * q^22 + 18 * q^23 + 16 * q^28 - 4 * q^31 + 30 * q^32 - 4 * q^37 - 30 * q^38 + 24 * q^41 + 2 * q^43 + 32 * q^46 - 12 * q^47 + 14 * q^52 - 36 * q^56 + 6 * q^58 + 8 * q^61 - 4 * q^67 + 42 * q^68 + 8 * q^73 + 24 * q^76 - 6 * q^77 - 32 * q^82 - 66 * q^83 + 48 * q^86 - 18 * q^88 - 40 * q^91 - 60 * q^92 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.186243	+	0.0499037i	0.131694	+	0.0352872i	0.324064	−	0.946035i	$-0.394951\pi$
$2$	0.186243	+	0.0499037i	0.131694	+	0.0352872i	−0.192370	+	0.981322i	$0.561617\pi$
$3$		0			0
$3$		0			0
$4$	−1.69985	−	0.981412i	−0.849927	−	0.490706i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.632007	+	2.35868i	−0.238876	+	0.891499i	0.737487	+	0.675362i	$0.236012\pi$
$7$	−0.632007	+	2.35868i	−0.238876	+	0.891499i	−0.976363	+	0.216137i	$0.930654\pi$
$8$	−0.540289	−	0.540289i	−0.191021	−	0.191021i
$9$		0			0
$10$		0			0
$11$	2.14390	−	1.23778i	0.646409	−	0.373204i	−0.140670	−	0.990057i	$-0.544926\pi$
$11$	2.14390	−	1.23778i	0.646409	−	0.373204i	0.787079	+	0.616852i	$0.211592\pi$
$12$		0			0
$13$	0.422032	+	1.57505i	0.117051	+	0.436839i	0.999432	−	0.0336956i	$-0.0107277\pi$
$13$	0.422032	+	1.57505i	0.117051	+	0.436839i	−0.882381	+	0.470535i	$0.844061\pi$
$14$	−0.235414	+	0.407749i	−0.0629170	+	0.108975i
$15$		0			0
$16$	1.88916	+	3.27212i	0.472290	+	0.818031i
$17$	0.403949	−	0.403949i	0.0979721	−	0.0979721i	−0.656422	−	0.754394i	$-0.727931\pi$
$17$	0.403949	−	0.403949i	0.0979721	−	0.0979721i	0.754394	+	0.656422i	$0.227931\pi$
$18$		0			0
$19$			4.28779i			0.983687i	0.870684	+	0.491843i	$0.163677\pi$
$19$			4.28779i			0.983687i	−0.870684	+	0.491843i	$0.836323\pi$
$20$		0			0
$21$		0			0
$22$	0.461055	−	0.123539i	0.0982973	−	0.0263387i
$23$	6.82387	−	1.82845i	1.42288	−	0.381258i	0.536373	−	0.843981i	$-0.319794\pi$
$23$	6.82387	−	1.82845i	1.42288	−	0.381258i	0.886503	+	0.462723i	$0.153128\pi$
$24$		0			0
$25$		0			0
$26$			0.314402i			0.0616594i
$27$		0			0
$28$	3.38916	−	3.38916i	0.640491	−	0.640491i
$29$	3.20524	+	5.55164i	0.595199	+	1.03091i	0.993519	+	0.113668i	$0.0362600\pi$
$29$	3.20524	+	5.55164i	0.595199	+	1.03091i	−0.398320	+	0.917247i	$0.630407\pi$
$30$		0			0
$31$	−1.97194	+	3.41550i	−0.354171	+	0.613442i	−0.986976	−	0.160869i	$-0.948570\pi$
$31$	−1.97194	+	3.41550i	−0.354171	+	0.613442i	0.632805	+	0.774312i	$0.281904\pi$
$32$	0.584071	+	2.17978i	0.103250	+	0.385335i
$33$		0			0
$34$	0.0953913	−	0.0550742i	0.0163595	−	0.00944515i
$35$		0			0
$36$		0			0
$37$	0.171954	+	0.171954i	0.0282691	+	0.0282691i	0.721100	−	0.692831i	$-0.243637\pi$
$37$	0.171954	+	0.171954i	0.0282691	+	0.0282691i	−0.692831	+	0.721100i	$0.743637\pi$
$38$	−0.213977	+	0.798571i	−0.0347116	+	0.129545i
$39$		0			0
$40$		0			0
$41$	6.52359	+	3.76639i	1.01881	+	0.588212i	0.913760	−	0.406255i	$-0.133165\pi$
$41$	6.52359	+	3.76639i	1.01881	+	0.588212i	0.105053	+	0.994467i	$0.466499\pi$
$42$		0			0
$43$	4.95226	+	1.32695i	0.755213	+	0.202359i	0.615829	−	0.787880i	$-0.288821\pi$
$43$	4.95226	+	1.32695i	0.755213	+	0.202359i	0.139384	+	0.990238i	$0.455488\pi$
$44$	−4.85908			−0.732534
$45$		0			0
$46$	1.36214			0.200837
$47$	2.91430	+	0.780885i	0.425095	+	0.113904i	0.465023	−	0.885299i	$-0.346046\pi$
$47$	2.91430	+	0.780885i	0.425095	+	0.113904i	−0.0399279	+	0.999203i	$0.512713\pi$
$48$		0			0
$49$	0.898221	+	0.518588i	0.128317	+	0.0740841i
$50$		0			0
$51$		0			0
$52$	0.828375	−	3.09154i	0.114875	−	0.428719i
$53$	−6.12030	−	6.12030i	−0.840688	−	0.840688i	0.148260	−	0.988948i	$-0.452633\pi$
$53$	−6.12030	−	6.12030i	−0.840688	−	0.840688i	−0.988948	+	0.148260i	$0.952633\pi$
$54$		0			0
$55$		0			0
$56$	1.61584	−	0.932904i	0.215925	−	0.124665i
$57$		0			0
$58$	0.319907	+	1.19391i	0.0420058	+	0.156768i
$59$	2.27234	−	3.93581i	0.295833	−	0.512399i	−0.679345	−	0.733819i	$-0.737736\pi$
$59$	2.27234	−	3.93581i	0.295833	−	0.512399i	0.975178	+	0.221421i	$0.0710693\pi$
$60$		0			0
$61$	−0.235795	−	0.408408i	−0.0301904	−	0.0522913i	0.850535	−	0.525918i	$-0.176278\pi$
$61$	−0.235795	−	0.408408i	−0.0301904	−	0.0522913i	−0.880726	+	0.473626i	$0.842945\pi$
$62$	−0.537706	+	0.537706i	−0.0682888	+	0.0682888i
$63$		0			0
$64$		−	7.12153i		−	0.890191i
$65$		0			0
$66$		0			0
$67$	−1.65496	+	0.443446i	−0.202186	+	0.0541756i	−0.358491	−	0.933533i	$-0.616709\pi$
$67$	−1.65496	+	0.443446i	−0.202186	+	0.0541756i	0.156305	+	0.987709i	$0.450042\pi$
$68$	−1.08310	+	0.290215i	−0.131345	+	0.0351937i
$69$		0			0
$70$		0			0
$71$		−	3.50583i		−	0.416065i	−0.978122	−	0.208032i	$-0.933294\pi$
$71$		−	3.50583i		−	0.416065i	0.978122	−	0.208032i	$-0.0667060\pi$
$72$		0			0
$73$	−6.88847	+	6.88847i	−0.806234	+	0.806234i	−0.984062	−	0.177827i	$-0.943093\pi$
$73$	−6.88847	+	6.88847i	−0.806234	+	0.806234i	0.177827	+	0.984062i	$0.443093\pi$
$74$	0.0234441	+	0.0406064i	0.00272533	+	0.00472040i
$75$		0			0
$76$	4.20809	−	7.28862i	0.482701	−	0.836062i
$77$	1.56457	+	5.83906i	0.178299	+	0.665422i
$78$		0			0
$79$	−6.50159	+	3.75369i	−0.731485	+	0.422323i	−0.818965	−	0.573843i	$-0.805452\pi$
$79$	−6.50159	+	3.75369i	−0.731485	+	0.422323i	0.0874799	+	0.996166i	$0.472119\pi$
$80$		0			0
$81$		0			0
$82$	1.02702	+	1.02702i	0.113415	+	0.113415i
$83$	−2.85794	+	10.6660i	−0.313700	+	1.17074i	0.611493	+	0.791249i	$0.290569\pi$
$83$	−2.85794	+	10.6660i	−0.313700	+	1.17074i	−0.925194	+	0.379495i	$0.876098\pi$
$84$		0			0
$85$		0			0
$86$	0.856104	+	0.494272i	0.0923161	+	0.0532987i
$87$		0			0
$88$	−1.82708	−	0.489565i	−0.194767	−	0.0521878i
$89$	−2.90124			−0.307531			−0.153765	−	0.988107i	$-0.549140\pi$
$89$	−2.90124			−0.307531			−0.153765	+	0.988107i	$0.549140\pi$
$90$		0			0
$91$	−3.98176			−0.417402
$92$	−13.3941	−	3.58893i	−1.39643	−	0.374171i
$93$		0			0
$94$	0.503800	+	0.290869i	0.0519630	+	0.0300008i
$95$		0			0
$96$		0			0
$97$	0.379633	−	1.41681i	0.0385459	−	0.143855i	−0.943971	−	0.330028i	$-0.892942\pi$
$97$	0.379633	−	1.41681i	0.0385459	−	0.143855i	0.982517	+	0.186173i	$0.0596084\pi$
$98$	0.141408	+	0.141408i	0.0142844	+	0.0142844i
$99$		0			0
$100$		0			0
$101$	−15.3563	+	8.86596i	−1.52801	+	0.882196i	−0.528563	+	0.848894i	$0.677269\pi$
$101$	−15.3563	+	8.86596i	−1.52801	+	0.882196i	−0.999445	+	0.0333015i	$0.989398\pi$
$102$		0			0
$103$	−2.74330	−	10.2381i	−0.270305	−	1.00879i	−0.958922	−	0.283668i	$-0.908449\pi$
$103$	−2.74330	−	10.2381i	−0.270305	−	1.00879i	0.688617	−	0.725125i	$-0.258218\pi$
$104$	0.622960	−	1.07900i	0.0610863	−	0.105805i
$105$		0			0
$106$	−0.834438	−	1.44529i	−0.0810478	−	0.140379i
$107$	10.4591	−	10.4591i	1.01112	−	1.01112i	0.0111806	−	0.999937i	$-0.496441\pi$
$107$	10.4591	−	10.4591i	1.01112	−	1.01112i	0.999937	−	0.0111806i	$-0.00355898\pi$
$108$		0			0
$109$			0.343204i			0.0328730i	0.999865	+	0.0164365i	$0.00523214\pi$
$109$			0.343204i			0.0328730i	−0.999865	+	0.0164365i	$0.994768\pi$
$110$		0			0
$111$		0			0
$112$	−8.91187	+	2.38793i	−0.842092	+	0.225638i
$113$	5.19250	−	1.39133i	0.488469	−	0.130885i	−0.00617426	−	0.999981i	$-0.501965\pi$
$113$	5.19250	−	1.39133i	0.488469	−	0.130885i	0.494643	+	0.869096i	$0.335299\pi$
$114$		0			0
$115$		0			0
$116$		−	12.5827i		−	1.16827i
$117$		0			0
$118$	0.619619	−	0.619619i	0.0570405	−	0.0570405i
$119$	0.697490	+	1.20809i	0.0639388	+	0.110745i
$120$		0			0
$121$	−2.43581	+	4.21894i	−0.221437	+	0.383540i
$122$	−0.0235340	−	0.0878302i	−0.00213067	−	0.00795177i
$123$		0			0
$124$	6.70403	−	3.87057i	0.602039	−	0.347588i
$125$		0			0
$126$		0			0
$127$	3.59190	+	3.59190i	0.318729	+	0.318729i	0.848279	−	0.529550i	$-0.177639\pi$
$127$	3.59190	+	3.59190i	0.318729	+	0.318729i	−0.529550	+	0.848279i	$0.677639\pi$
$128$	1.52353	−	5.68590i	0.134662	−	0.502567i
$129$		0			0
$130$		0			0
$131$	−14.5188	−	8.38241i	−1.26851	−	0.732375i	−0.293804	−	0.955866i	$-0.594921\pi$
$131$	−14.5188	−	8.38241i	−1.26851	−	0.732375i	−0.974706	+	0.223491i	$0.928255\pi$
$132$		0			0
$133$	−10.1135	−	2.70992i	−0.876956	−	0.234980i
$134$	−0.330355			−0.0285383
$135$		0			0
$136$	−0.436499			−0.0374295
$137$	−6.17718	−	1.65517i	−0.527752	−	0.141411i	−0.0149021	−	0.999889i	$-0.504744\pi$
$137$	−6.17718	−	1.65517i	−0.527752	−	0.141411i	−0.512850	+	0.858478i	$0.671410\pi$
$138$		0			0
$139$	9.09433	+	5.25061i	0.771371	+	0.445351i	0.833364	−	0.552725i	$-0.186412\pi$
$139$	9.09433	+	5.25061i	0.771371	+	0.445351i	−0.0619924	+	0.998077i	$0.519745\pi$
$140$		0			0
$141$		0			0
$142$	0.174954	−	0.652936i	0.0146818	−	0.0547931i
$143$	2.85435	+	2.85435i	0.238693	+	0.238693i
$144$		0			0
$145$		0			0
$146$	−1.62669	+	0.939170i	−0.134626	+	0.0777262i
$147$		0			0
$148$	−0.123539	−	0.461055i	−0.0101549	−	0.0378985i
$149$	4.96581	−	8.60103i	0.406815	−	0.704624i	−0.587716	−	0.809067i	$-0.699973\pi$
$149$	4.96581	−	8.60103i	0.406815	−	0.704624i	0.994531	+	0.104443i	$0.0333061\pi$
$150$		0			0
$151$	−6.95939	−	12.0540i	−0.566347	−	0.980942i	−0.996923	−	0.0783879i	$-0.975023\pi$
$151$	−6.95939	−	12.0540i	−0.566347	−	0.980942i	0.430576	−	0.902555i	$-0.358311\pi$
$152$	2.31665	−	2.31665i	0.187905	−	0.187905i
$153$		0			0
$154$			1.16556i			0.0939236i
$155$		0			0
$156$		0			0
$157$	20.2365	−	5.42234i	1.61505	−	0.432750i	0.665504	−	0.746394i	$-0.268216\pi$
$157$	20.2365	−	5.42234i	1.61505	−	0.432750i	0.949541	+	0.313644i	$0.101550\pi$
$158$	−1.39820	+	0.374646i	−0.111235	+	0.0298052i
$159$		0			0
$160$		0			0
$161$			17.2510i			1.35957i
$162$		0			0
$163$	2.42872	−	2.42872i	0.190232	−	0.190232i	−0.605564	−	0.795796i	$-0.707052\pi$
$163$	2.42872	−	2.42872i	0.190232	−	0.190232i	0.795796	+	0.605564i	$0.207052\pi$
$164$	−7.39277	−	12.8046i	−0.577278	−	0.999875i
$165$		0			0
$166$	−1.06454	+	1.84385i	−0.0826247	+	0.143110i
$167$	−2.20590	−	8.23252i	−0.170697	−	0.637052i	−0.997245	−	0.0741841i	$-0.976365\pi$
$167$	−2.20590	−	8.23252i	−0.170697	−	0.637052i	0.826547	−	0.562868i	$-0.190302\pi$
$168$		0			0
$169$	8.95567	−	5.17056i	0.688898	−	0.397735i
$170$		0			0
$171$		0			0
$172$	−7.11584	−	7.11584i	−0.542577	−	0.542577i
$173$	−4.57458	+	17.0726i	−0.347799	+	1.29800i	0.541509	+	0.840695i	$0.317853\pi$
$173$	−4.57458	+	17.0726i	−0.347799	+	1.29800i	−0.889308	+	0.457308i	$0.848814\pi$
$174$		0			0
$175$		0			0
$176$	8.10033	+	4.67673i	0.610585	+	0.352521i
$177$		0			0
$178$	−0.540336	−	0.144783i	−0.0404999	−	0.0108519i
$179$	8.30788			0.620960			0.310480	−	0.950580i	$-0.399510\pi$
$179$	8.30788			0.620960			0.310480	+	0.950580i	$0.399510\pi$
$180$		0			0
$181$	−4.73429			−0.351897			−0.175948	−	0.984399i	$-0.556299\pi$
$181$	−4.73429			−0.351897			−0.175948	+	0.984399i	$0.556299\pi$
$182$	−0.741576	−	0.198705i	−0.0549693	−	0.0147290i
$183$		0			0
$184$	−4.67475	−	2.69897i	−0.344627	−	0.198971i
$185$		0			0
$186$		0			0
$187$	0.366025	−	1.36603i	0.0267664	−	0.0998937i
$188$	−4.18752	−	4.18752i	−0.305406	−	0.305406i
$189$		0			0
$190$		0			0
$191$	3.34902	−	1.93356i	0.242327	−	0.139907i	−0.373919	−	0.927461i	$-0.621986\pi$
$191$	3.34902	−	1.93356i	0.242327	−	0.139907i	0.616246	+	0.787554i	$0.288653\pi$
$192$		0			0
$193$	4.44530	+	16.5901i	0.319979	+	1.19418i	0.919263	+	0.393643i	$0.128785\pi$
$193$	4.44530	+	16.5901i	0.319979	+	1.19418i	−0.599284	+	0.800536i	$0.704548\pi$
$194$	0.141408	−	0.244926i	0.0101525	−	0.0175847i
$195$		0			0
$196$	−1.01790	−	1.76305i	−0.0727070	−	0.125932i
$197$	−11.0386	+	11.0386i	−0.786469	+	0.786469i	−0.980913	−	0.194445i	$-0.937709\pi$
$197$	−11.0386	+	11.0386i	−0.786469	+	0.786469i	0.194445	+	0.980913i	$0.437709\pi$
$198$		0			0
$199$		−	3.60138i		−	0.255295i	−0.991820	−	0.127648i	$-0.959257\pi$
$199$		−	3.60138i		−	0.255295i	0.991820	−	0.127648i	$-0.0407427\pi$
$200$		0			0
$201$		0			0
$202$	−3.30245	+	0.884888i	−0.232359	+	0.0622605i
$203$	−15.1203	+	4.05148i	−1.06124	+	0.284358i
$204$		0			0
$205$		0			0
$206$		−	2.04368i		−	0.142390i
$207$		0			0
$208$	−4.35646	+	4.35646i	−0.302066	+	0.302066i
$209$	5.30734	+	9.19258i	0.367116	+	0.635864i
$210$		0			0
$211$	9.56007	−	16.5585i	0.658142	−	1.13994i	−0.322954	−	0.946415i	$-0.604676\pi$
$211$	9.56007	−	16.5585i	0.658142	−	1.13994i	0.981096	−	0.193521i	$-0.0619909\pi$
$212$	4.39709	+	16.4102i	0.301993	+	1.12705i
$213$		0			0
$214$	2.46988	−	1.42599i	0.168837	−	0.0974783i
$215$		0			0
$216$		0			0
$217$	−6.80981	−	6.80981i	−0.462280	−	0.462280i
$218$	−0.0171272	+	0.0639194i	−0.00116000	+	0.00432917i
$219$		0			0
$220$		0			0
$221$	0.806719	+	0.465759i	0.0542658	+	0.0313304i
$222$		0			0
$223$	−4.03530	−	1.08126i	−0.270224	−	0.0724062i	0.121163	−	0.992633i	$-0.461338\pi$
$223$	−4.03530	−	1.08126i	−0.270224	−	0.0724062i	−0.391386	+	0.920226i	$0.628004\pi$
$224$	−5.51055			−0.368189
$225$		0			0
$226$	1.03650			0.0689469
$227$	13.2857	+	3.55990i	0.881803	+	0.236279i	0.671185	−	0.741290i	$-0.265786\pi$
$227$	13.2857	+	3.55990i	0.881803	+	0.236279i	0.210618	+	0.977568i	$0.432452\pi$
$228$		0			0
$229$	−13.2694	−	7.66109i	−0.876866	−	0.506259i	−0.00724242	−	0.999974i	$-0.502305\pi$
$229$	−13.2694	−	7.66109i	−0.876866	−	0.506259i	−0.869624	+	0.493715i	$0.835639\pi$
$230$		0			0
$231$		0			0
$232$	1.26773	−	4.73125i	0.0832308	−	0.310622i
$233$	−2.98562	−	2.98562i	−0.195595	−	0.195595i	0.602514	−	0.798108i	$-0.294166\pi$
$233$	−2.98562	−	2.98562i	−0.195595	−	0.195595i	−0.798108	+	0.602514i	$0.794166\pi$
$234$		0			0
$235$		0			0
$236$	−7.72529	+	4.46020i	−0.502874	+	0.290334i
$237$		0			0
$238$	0.0696146	+	0.259805i	0.00451245	+	0.0168407i
$239$	−2.59439	+	4.49362i	−0.167817	+	0.290668i	−0.937652	−	0.347575i	$-0.887005\pi$
$239$	−2.59439	+	4.49362i	−0.167817	+	0.290668i	0.769835	+	0.638243i	$0.220339\pi$
$240$		0			0
$241$	1.85872	+	3.21939i	0.119730	+	0.207379i	0.919661	−	0.392714i	$-0.128464\pi$
$241$	1.85872	+	3.21939i	0.119730	+	0.207379i	−0.799930	+	0.600093i	$0.795130\pi$
$242$	−0.664193	+	0.664193i	−0.0426959	+	0.0426959i
$243$		0			0
$244$			0.925646i			0.0592584i
$245$		0			0
$246$		0			0
$247$	−6.75347	+	1.80959i	−0.429713	+	0.115141i
$248$	2.91078	−	0.779940i	0.184834	−	0.0495262i
$249$		0			0
$250$		0			0
$251$		−	3.97271i		−	0.250755i	−0.992109	−	0.125378i	$-0.959986\pi$
$251$		−	3.97271i		−	0.250755i	0.992109	−	0.125378i	$-0.0400142\pi$
$252$		0			0
$253$	12.3665	−	12.3665i	0.777472	−	0.777472i
$254$	0.489717	+	0.848215i	0.0307276	+	0.0532217i
$255$		0			0
$256$	−6.55403	+	11.3519i	−0.409627	+	0.709495i
$257$	−4.42437	−	16.5120i	−0.275985	−	1.02999i	−0.955179	−	0.296030i	$-0.904337\pi$
$257$	−4.42437	−	16.5120i	−0.275985	−	1.02999i	0.679194	−	0.733959i	$-0.262329\pi$
$258$		0			0
$259$	−0.514262	+	0.296909i	−0.0319547	+	0.0184491i
$260$		0			0
$261$		0			0
$262$	−2.28571	−	2.28571i	−0.141211	−	0.141211i
$263$	2.77155	−	10.3436i	0.170901	−	0.637812i	−0.826312	−	0.563212i	$-0.809565\pi$
$263$	2.77155	−	10.3436i	0.170901	−	0.637812i	0.997214	−	0.0746001i	$-0.0237680\pi$
$264$		0			0
$265$		0			0
$266$	−1.74834	−	1.00941i	−0.107198	−	0.0618907i
$267$		0			0
$268$	3.24840	+	0.870407i	0.198428	+	0.0531685i
$269$	−15.8925			−0.968985			−0.484492	−	0.874796i	$-0.660996\pi$
$269$	−15.8925			−0.968985			−0.484492	+	0.874796i	$0.660996\pi$
$270$		0			0
$271$	0.974200			0.0591785			0.0295892	−	0.999562i	$-0.490580\pi$
$271$	0.974200			0.0591785			0.0295892	+	0.999562i	$0.490580\pi$
$272$	2.08490	+	0.558646i	0.126415	+	0.0338729i
$273$		0			0
$274$	−1.06786	−	0.616528i	−0.0645117	−	0.0372458i
$275$		0			0
$276$		0			0
$277$	−6.18395	+	23.0788i	−0.371557	+	1.38667i	0.486753	+	0.873540i	$0.338181\pi$
$277$	−6.18395	+	23.0788i	−0.371557	+	1.38667i	−0.858310	+	0.513131i	$0.828485\pi$
$278$	1.43173	+	1.43173i	0.0858695	+	0.0858695i
$279$		0			0
$280$		0			0
$281$	23.9241	−	13.8126i	1.42720	−	0.823991i	0.430296	−	0.902688i	$-0.358409\pi$
$281$	23.9241	−	13.8126i	1.42720	−	0.823991i	0.996899	+	0.0786961i	$0.0250757\pi$
$282$		0			0
$283$	−4.40870	−	16.4535i	−0.262070	−	0.978058i	−0.964020	−	0.265831i	$-0.914354\pi$
$283$	−4.40870	−	16.4535i	−0.262070	−	0.978058i	0.701950	−	0.712227i	$-0.252313\pi$
$284$	−3.44066	+	5.95939i	−0.204165	+	0.353625i
$285$		0			0
$286$	0.389161	+	0.674046i	0.0230115	+	0.0398572i
$287$	−13.0067	+	13.0067i	−0.767761	+	0.767761i
$288$		0			0
$289$			16.6736i			0.980803i
$290$		0			0
$291$		0			0
$292$	18.4698	−	4.94897i	1.08086	−	0.289617i
$293$	25.7566	−	6.90146i	1.50472	−	0.403188i	0.590041	−	0.807374i	$-0.299112\pi$
$293$	25.7566	−	6.90146i	1.50472	−	0.403188i	0.914677	+	0.404186i	$0.132445\pi$
$294$		0			0
$295$		0			0
$296$		−	0.185810i		−	0.0108000i
$297$		0			0
$298$	1.35407	−	1.35407i	0.0784392	−	0.0784392i
$299$	5.75979	+	9.97625i	0.333097	+	0.576941i
$300$		0			0
$301$	−6.25973	+	10.8422i	−0.360805	+	0.624933i
$302$	−0.694599	−	2.59228i	−0.0399697	−	0.149169i
$303$		0			0
$304$	−14.0302	+	8.10033i	−0.804686	+	0.464586i
$305$		0			0
$306$		0			0
$307$	12.3556	+	12.3556i	0.705171	+	0.705171i	0.965516	−	0.260345i	$-0.0838363\pi$
$307$	12.3556	+	12.3556i	0.705171	+	0.705171i	−0.260345	+	0.965516i	$0.583836\pi$
$308$	3.07098	−	11.4610i	0.174985	−	0.653053i
$309$		0			0
$310$		0			0
$311$	−7.49228	−	4.32567i	−0.424848	−	0.245286i	0.272301	−	0.962212i	$-0.412215\pi$
$311$	−7.49228	−	4.32567i	−0.424848	−	0.245286i	−0.697149	+	0.716926i	$0.745549\pi$
$312$		0			0
$313$	18.1094	+	4.85240i	1.02360	+	0.274274i	0.731303	−	0.682052i	$-0.238912\pi$
$313$	18.1094	+	4.85240i	1.02360	+	0.274274i	0.292301	+	0.956326i	$0.405579\pi$
$314$	4.03949			0.227962
$315$		0			0
$316$	14.7357			0.828946
$317$	18.7418	+	5.02186i	1.05265	+	0.282056i	0.743345	−	0.668908i	$-0.233238\pi$
$317$	18.7418	+	5.02186i	1.05265	+	0.282056i	0.309301	+	0.950964i	$0.399905\pi$
$318$		0			0
$319$	13.7434	+	7.93476i	0.769484	+	0.444262i
$320$		0			0
$321$		0			0
$322$	−0.860886	+	3.21287i	−0.0479753	+	0.179046i
$323$	1.73205	+	1.73205i	0.0963739	+	0.0963739i
$324$		0			0
$325$		0			0
$326$	0.573535	−	0.331131i	0.0317652	−	0.0183396i
$327$		0			0
$328$	−1.48968	−	5.55956i	−0.0822538	−	0.306975i
$329$	−3.68372	+	6.38039i	−0.203090	+	0.351763i
$330$		0			0
$331$	17.1969	+	29.7859i	0.945226	+	1.63718i	0.755298	+	0.655382i	$0.227492\pi$
$331$	17.1969	+	29.7859i	0.945226	+	1.63718i	0.189929	+	0.981798i	$0.439174\pi$
$332$	15.3258	−	15.3258i	0.841114	−	0.841114i
$333$		0			0
$334$		−	1.64333i		−	0.0899191i
$335$		0			0
$336$		0			0
$337$	−30.9291	+	8.28744i	−1.68482	+	0.451445i	−0.969044	−	0.246888i	$-0.920592\pi$
$337$	−30.9291	+	8.28744i	−1.68482	+	0.451445i	−0.715773	+	0.698333i	$0.753925\pi$
$338$	1.92596	−	0.516060i	0.104758	−	0.0280700i
$339$		0			0
$340$		0			0
$341$			9.76331i			0.528713i
$342$		0			0
$343$	−13.8776	+	13.8776i	−0.749320	+	0.749320i
$344$	−1.95871	−	3.39259i	−0.105607	−	0.182916i
$345$		0			0
$346$	−1.70397	+	2.95136i	−0.0916059	+	0.158666i
$347$	−4.15647	−	15.5122i	−0.223131	−	0.832737i	−0.983145	−	0.182829i	$-0.941474\pi$
$347$	−4.15647	−	15.5122i	−0.223131	−	0.832737i	0.760014	−	0.649907i	$-0.225192\pi$
$348$		0			0
$349$	−15.1664	+	8.75630i	−0.811837	+	0.468714i	−0.847593	−	0.530646i	$-0.821949\pi$
$349$	−15.1664	+	8.75630i	−0.811837	+	0.468714i	0.0357566	+	0.999361i	$0.488616\pi$
$350$		0			0
$351$		0			0
$352$	3.95028	+	3.95028i	0.210550	+	0.210550i
$353$	4.95294	−	18.4846i	0.263618	−	0.983837i	−0.699472	−	0.714660i	$-0.746582\pi$
$353$	4.95294	−	18.4846i	0.263618	−	0.983837i	0.963091	−	0.269177i	$-0.0867517\pi$
$354$		0			0
$355$		0			0
$356$	4.93169	+	2.84731i	0.261379	+	0.150907i
$357$		0			0
$358$	1.54728	+	0.414594i	0.0817766	+	0.0219120i
$359$	23.0127			1.21457			0.607283	−	0.794486i	$-0.292259\pi$
$359$	23.0127			1.21457			0.607283	+	0.794486i	$0.292259\pi$
$360$		0			0
$361$	0.614846			0.0323603
$362$	−0.881728	−	0.236258i	−0.0463426	−	0.0124175i
$363$		0			0
$364$	6.76842	+	3.90775i	0.354762	+	0.204822i
$365$		0			0
$366$		0			0
$367$	7.01692	−	26.1875i	0.366280	−	1.36698i	−0.499397	−	0.866373i	$-0.666445\pi$
$367$	7.01692	−	26.1875i	0.366280	−	1.36698i	0.865677	−	0.500603i	$-0.166888\pi$
$368$	18.8743	+	18.8743i	0.983891	+	0.983891i
$369$		0			0
$370$		0			0
$371$	18.3039	−	10.5678i	0.950293	−	0.548652i
$372$		0			0
$373$	7.76440	+	28.9771i	0.402025	+	1.50038i	0.809477	+	0.587152i	$0.199751\pi$
$373$	7.76440	+	28.9771i	0.402025	+	1.50038i	−0.407451	+	0.913227i	$0.633582\pi$
$374$	0.136339	−	0.236147i	0.00704994	−	0.0122109i
$375$		0			0
$376$	−1.15266	−	1.99647i	−0.0594440	−	0.102960i
$377$	−7.39138	+	7.39138i	−0.380675	+	0.380675i
$378$		0			0
$379$		−	20.0943i		−	1.03218i	−0.856535	−	0.516089i	$-0.827388\pi$
$379$		−	20.0943i		−	1.03218i	0.856535	−	0.516089i	$-0.172612\pi$
$380$		0			0
$381$		0			0
$382$	0.720223	−	0.192983i	0.0368498	−	0.00987388i
$383$	−26.6536	+	7.14181i	−1.36194	+	0.364929i	−0.864527	−	0.502587i	$-0.832382\pi$
$383$	−26.6536	+	7.14181i	−1.36194	+	0.364929i	−0.497409	+	0.867516i	$0.665715\pi$
$384$		0			0
$385$		0			0
$386$			3.31162i			0.168557i
$387$		0			0
$388$	−2.03579	+	2.03579i	−0.103352	+	0.103352i
$389$	−6.71184	−	11.6253i	−0.340304	−	0.589424i	0.644185	−	0.764870i	$-0.277197\pi$
$389$	−6.71184	−	11.6253i	−0.340304	−	0.589424i	−0.984489	+	0.175446i	$0.943863\pi$
$390$		0			0
$391$	2.01790	−	3.49510i	0.102049	−	0.176755i
$392$	−0.205111	−	0.765487i	−0.0103597	−	0.0386629i
$393$		0			0
$394$	−2.60673	+	1.50500i	−0.131325	+	0.0758207i
$395$		0			0
$396$		0			0
$397$	12.8716	+	12.8716i	0.646008	+	0.646008i	0.952026	−	0.306018i	$-0.0989967\pi$
$397$	12.8716	+	12.8716i	0.646008	+	0.646008i	−0.306018	+	0.952026i	$0.598997\pi$
$398$	0.179722	−	0.670732i	0.00900866	−	0.0336208i
$399$		0			0
$400$		0			0
$401$	21.7606	+	12.5635i	1.08667	+	0.627391i	0.932689	−	0.360682i	$-0.117456\pi$
$401$	21.7606	+	12.5635i	1.08667	+	0.627391i	0.153985	+	0.988073i	$0.450789\pi$
$402$		0			0
$403$	−6.21180	−	1.66445i	−0.309432	−	0.0829120i
$404$	34.8046			1.73159
$405$		0			0
$406$	−3.01824			−0.149793
$407$	0.581494	+	0.155811i	0.0288236	+	0.00772325i
$408$		0			0
$409$	−9.81878	−	5.66888i	−0.485508	−	0.280308i	0.237201	−	0.971461i	$-0.423770\pi$
$409$	−9.81878	−	5.66888i	−0.485508	−	0.280308i	−0.722709	+	0.691153i	$0.757103\pi$
$410$		0			0
$411$		0			0
$412$	−5.38461	+	20.0957i	−0.265281	+	0.990042i
$413$	7.84719	+	7.84719i	0.386135	+	0.386135i
$414$		0			0
$415$		0			0
$416$	−3.18676	+	1.83988i	−0.156244	+	0.0902074i
$417$		0			0
$418$	0.529711	+	1.97691i	0.0259090	+	0.0966938i
$419$	−4.26264	+	7.38311i	−0.208244	+	0.360688i	−0.951161	−	0.308694i	$-0.900108\pi$
$419$	−4.26264	+	7.38311i	−0.208244	+	0.360688i	0.742918	+	0.669383i	$0.233441\pi$
$420$		0			0
$421$	1.10329	+	1.91095i	0.0537710	+	0.0931341i	0.891658	−	0.452710i	$-0.149543\pi$
$421$	1.10329	+	1.91095i	0.0537710	+	0.0931341i	−0.837887	+	0.545844i	$0.816209\pi$
$422$	2.60683	−	2.60683i	0.126898	−	0.126898i
$423$		0			0
$424$			6.61346i			0.321178i
$425$		0			0
$426$		0			0
$427$	1.11233	−	0.298048i	0.0538294	−	0.0144235i
$428$	−28.0436	+	7.51426i	−1.35554	+	0.363215i
$429$		0			0
$430$		0			0
$431$			1.95738i			0.0942838i	0.998888	+	0.0471419i	$0.0150113\pi$
$431$			1.95738i			0.0942838i	−0.998888	+	0.0471419i	$0.984989\pi$
$432$		0			0
$433$	9.71652	−	9.71652i	0.466946	−	0.466946i	−0.433978	−	0.900924i	$-0.642890\pi$
$433$	9.71652	−	9.71652i	0.466946	−	0.466946i	0.900924	+	0.433978i	$0.142890\pi$
$434$	−0.928445	−	1.60811i	−0.0445668	−	0.0771919i
$435$		0			0
$436$	0.336825	−	0.583398i	0.0161310	−	0.0279397i
$437$	7.84002	+	29.2593i	0.375039	+	1.39966i
$438$		0			0
$439$	−4.68008	+	2.70205i	−0.223368	+	0.128962i	−0.607509	−	0.794313i	$-0.707831\pi$
$439$	−4.68008	+	2.70205i	−0.223368	+	0.128962i	0.384141	+	0.923275i	$0.374498\pi$
$440$		0			0
$441$		0			0
$442$	0.127003	+	0.127003i	0.00604090	+	0.00604090i
$443$	6.98940	−	26.0848i	0.332077	−	1.23933i	−0.574927	−	0.818204i	$-0.694970\pi$
$443$	6.98940	−	26.0848i	0.332077	−	1.23933i	0.907004	−	0.421122i	$-0.138364\pi$
$444$		0			0
$445$		0			0
$446$	−0.697588	−	0.402752i	−0.0330317	−	0.0190709i
$447$		0			0
$448$	16.7974	+	4.50086i	0.793604	+	0.212646i
$449$	−23.8541			−1.12574			−0.562872	−	0.826544i	$-0.690304\pi$
$449$	−23.8541			−1.12574			−0.562872	+	0.826544i	$0.690304\pi$
$450$		0			0
$451$	18.6479			0.878093
$452$	−10.1920	−	2.73093i	−0.479389	−	0.128452i
$453$		0			0
$454$	2.29672	+	1.32601i	0.107790	+	0.0622328i
$455$		0			0
$456$		0			0
$457$	5.13035	−	19.1467i	0.239988	−	0.895647i	−0.735849	−	0.677146i	$-0.763217\pi$
$457$	5.13035	−	19.1467i	0.239988	−	0.895647i	0.975837	−	0.218501i	$-0.0701167\pi$
$458$	−2.08902	−	2.08902i	−0.0976133	−	0.0976133i
$459$		0			0
$460$		0			0
$461$	1.14371	−	0.660321i	0.0532679	−	0.0307542i	−0.473130	−	0.880993i	$-0.656876\pi$
$461$	1.14371	−	0.660321i	0.0532679	−	0.0307542i	0.526397	+	0.850239i	$0.323542\pi$
$462$		0			0
$463$	−3.98780	−	14.8827i	−0.185329	−	0.691656i	−0.994560	−	0.104166i	$-0.966783\pi$
$463$	−3.98780	−	14.8827i	−0.185329	−	0.691656i	0.809231	−	0.587490i	$-0.199884\pi$
$464$	−12.1104	+	20.9759i	−0.562213	+	0.973782i
$465$		0			0
$466$	−0.407058	−	0.705045i	−0.0188566	−	0.0326606i
$467$	−1.77645	+	1.77645i	−0.0822044	+	0.0822044i	−0.747013	−	0.664809i	$-0.768513\pi$
$467$	−1.77645	+	1.77645i	−0.0822044	+	0.0822044i	0.664809	+	0.747013i	$0.268513\pi$
$468$		0			0
$469$		−	4.18380i		−	0.193190i
$470$		0			0
$471$		0			0
$472$	−3.35419	+	0.898753i	−0.154389	+	0.0413685i
$473$	12.2596	−	3.28495i	0.563697	−	0.151042i
$474$		0			0
$475$		0			0
$476$		−	2.73810i		−	0.125501i
$477$		0			0
$478$	−0.707436	+	0.707436i	−0.0323574	+	0.0323574i
$479$	−18.9907	−	32.8928i	−0.867705	−	1.50291i	−0.864336	−	0.502915i	$-0.832261\pi$
$479$	−18.9907	−	32.8928i	−0.867705	−	1.50291i	−0.00336919	−	0.999994i	$-0.501072\pi$
$480$		0			0
$481$	−0.198266	+	0.343406i	−0.00904014	+	0.0156580i
$482$	0.185513	+	0.692346i	0.00844991	+	0.0315355i
$483$		0			0
$484$	8.28104	−	4.78106i	0.376411	−	0.217321i
$485$		0			0
$486$		0			0
$487$	−23.6900	−	23.6900i	−1.07350	−	1.07350i	−0.997076	−	0.0764213i	$-0.975651\pi$
$487$	−23.6900	−	23.6900i	−1.07350	−	1.07350i	−0.0764213	−	0.997076i	$-0.524349\pi$
$488$	−0.0932612	+	0.348056i	−0.00422174	+	0.0157557i
$489$		0			0
$490$		0			0
$491$	−18.9114	−	10.9185i	−0.853460	−	0.492746i	0.00835660	−	0.999965i	$-0.497340\pi$
$491$	−18.9114	−	10.9185i	−0.853460	−	0.492746i	−0.861817	+	0.507220i	$0.830673\pi$
$492$		0			0
$493$	3.53734	+	0.947827i	0.159314	+	0.0426880i
$494$	−1.34809			−0.0606535
$495$		0			0
$496$	−14.9013			−0.669086
$497$	8.26913	+	2.21571i	0.370921	+	0.0993881i
$498$		0			0
$499$	−2.74862	−	1.58691i	−0.123045	−	0.0710401i	0.437214	−	0.899357i	$-0.355965\pi$
$499$	−2.74862	−	1.58691i	−0.123045	−	0.0710401i	−0.560259	+	0.828317i	$0.689298\pi$
$500$		0			0
$501$		0			0
$502$	0.198253	−	0.739889i	0.00884845	−	0.0330229i
$503$	−7.00484	−	7.00484i	−0.312330	−	0.312330i	0.533481	−	0.845812i	$-0.320883\pi$
$503$	−7.00484	−	7.00484i	−0.312330	−	0.312330i	−0.845812	+	0.533481i	$0.820883\pi$
$504$		0			0
$505$		0			0
$506$	2.92030	−	1.68603i	0.129823	−	0.0749534i
$507$		0			0
$508$	−2.58058	−	9.63084i	−0.114495	−	0.427299i
$509$	−8.36206	+	14.4835i	−0.370642	+	0.641971i	−0.989664	−	0.143403i	$-0.954196\pi$
$509$	−8.36206	+	14.4835i	−0.370642	+	0.641971i	0.619023	+	0.785373i	$0.287529\pi$
$510$		0			0
$511$	−11.8942	−	20.6013i	−0.526167	−	0.911347i
$512$	−10.1119	+	10.1119i	−0.446886	+	0.446886i
$513$		0			0
$514$		−	3.29603i		−	0.145382i
$515$		0			0
$516$		0			0
$517$	7.21452	−	1.93313i	0.317294	−	0.0850188i
$518$	−0.110595	+	0.0296337i	−0.00485925	+	0.00130203i
$519$		0			0
$520$		0			0
$521$		−	1.34092i		−	0.0587466i	−0.999569	−	0.0293733i	$-0.990649\pi$
$521$		−	1.34092i		−	0.0587466i	0.999569	−	0.0293733i	$-0.00935116\pi$
$522$		0			0
$523$	9.19187	−	9.19187i	0.401933	−	0.401933i	−0.476981	−	0.878914i	$-0.658269\pi$
$523$	9.19187	−	9.19187i	0.401933	−	0.401933i	0.878914	+	0.476981i	$0.158269\pi$
$524$	16.4532	+	28.4978i	0.718761	+	1.24493i
$525$		0			0
$526$	1.03237	−	1.78811i	0.0450133	−	0.0779653i
$527$	0.583126	+	2.17625i	0.0254014	+	0.0947991i
$528$		0			0
$529$	23.3034	−	13.4542i	1.01319	−	0.584967i
$530$		0			0
$531$		0			0
$532$	14.5320	+	14.5320i	0.630043	+	0.630043i
$533$	−3.17908	+	11.8645i	−0.137701	+	0.513908i
$534$		0			0
$535$		0			0
$536$	1.13375	+	0.654569i	0.0489704	+	0.0282731i
$537$		0			0
$538$	−2.95987	−	0.793096i	−0.127609	−	0.0341928i
$539$	2.56759			0.110594
$540$		0			0
$541$	−34.0389			−1.46345			−0.731724	−	0.681601i	$-0.761284\pi$
$541$	−34.0389			−1.46345			−0.731724	+	0.681601i	$0.761284\pi$
$542$	0.181438	+	0.0486162i	0.00779343	+	0.00208824i
$543$		0			0
$544$	1.11646	+	0.644587i	0.0478677	+	0.0276364i
$545$		0			0
$546$		0			0
$547$	−2.44487	+	9.12437i	−0.104535	+	0.390130i	−0.998292	−	0.0584215i	$-0.981393\pi$
$547$	−2.44487	+	9.12437i	−0.104535	+	0.390130i	0.893757	+	0.448552i	$0.148060\pi$
$548$	8.87591	+	8.87591i	0.379160	+	0.379160i
$549$		0			0
$550$		0			0
$551$	−23.8043	+	13.7434i	−1.01410	+	0.585489i
$552$		0			0
$553$	−4.74472	−	17.7075i	−0.201766	−	0.753001i
$554$	−2.30343	+	3.98967i	−0.0978636	+	0.169505i
$555$		0			0
$556$	−10.3060	−	17.8506i	−0.437073	−	0.757033i
$557$	1.48579	−	1.48579i	0.0629551	−	0.0629551i	−0.674928	−	0.737883i	$-0.735825\pi$
$557$	1.48579	−	1.48579i	0.0629551	−	0.0629551i	0.737883	+	0.674928i	$0.235825\pi$
$558$		0			0
$559$			8.36006i			0.353593i
$560$		0			0
$561$		0			0
$562$	5.14501	−	1.37860i	0.217029	−	0.0581527i
$563$	−20.6371	+	5.52969i	−0.869750	+	0.233049i	−0.665979	−	0.745970i	$-0.731986\pi$
$563$	−20.6371	+	5.52969i	−0.869750	+	0.233049i	−0.203770	+	0.979019i	$0.565319\pi$
$564$		0			0
$565$		0			0
$566$		−	3.28436i		−	0.138052i
$567$		0			0
$568$	−1.89416	+	1.89416i	−0.0794771	+	0.0794771i
$569$	−5.82589	−	10.0907i	−0.244234	−	0.423026i	0.717682	−	0.696371i	$-0.245203\pi$
$569$	−5.82589	−	10.0907i	−0.244234	−	0.423026i	−0.961916	+	0.273345i	$0.911870\pi$
$570$		0			0
$571$	10.5623	−	18.2945i	0.442020	−	0.765601i	−0.555819	−	0.831303i	$-0.687595\pi$
$571$	10.5623	−	18.2945i	0.442020	−	0.765601i	0.997839	+	0.0657023i	$0.0209288\pi$
$572$	−2.05069	−	7.65328i	−0.0857436	−	0.320000i
$573$		0			0
$574$	−3.07149	+	1.77332i	−0.128201	+	0.0740171i
$575$		0			0
$576$		0			0
$577$	−30.1119	−	30.1119i	−1.25357	−	1.25357i	−0.954106	−	0.299469i	$-0.903191\pi$
$577$	−30.1119	−	30.1119i	−1.25357	−	1.25357i	−0.299469	−	0.954106i	$-0.596809\pi$
$578$	−0.832076	+	3.10535i	−0.0346098	+	0.129166i
$579$		0			0
$580$		0			0
$581$	−23.3515	−	13.4820i	−0.968782	−	0.559327i
$582$		0			0
$583$	−20.6969	−	5.54571i	−0.857177	−	0.229680i
$584$	7.44353			0.308015
$585$		0			0
$586$	5.14140			0.212389
$587$	−8.53262	−	2.28631i	−0.352179	−	0.0943661i	0.0783924	−	0.996923i	$-0.475021\pi$
$587$	−8.53262	−	2.28631i	−0.352179	−	0.0943661i	−0.430571	+	0.902556i	$0.641688\pi$
$588$		0			0
$589$	−14.6450	−	8.45527i	−0.603435	−	0.348393i
$590$		0			0
$591$		0			0
$592$	−0.237806	+	0.887505i	−0.00977377	+	0.0364762i
$593$	24.5829	+	24.5829i	1.00950	+	1.00950i	0.999954	+	0.00954475i	$0.00303823\pi$
$593$	24.5829	+	24.5829i	1.00950	+	1.00950i	0.00954475	+	0.999954i	$0.496962\pi$
$594$		0			0
$595$		0			0
$596$	−16.8823	+	9.74700i	−0.691526	+	0.399253i
$597$		0			0
$598$	0.574869	+	2.14544i	0.0235082	+	0.0877336i
$599$	18.8291	−	32.6129i	0.769335	−	1.33253i	−0.168590	−	0.985686i	$-0.553921\pi$
$599$	18.8291	−	32.6129i	0.769335	−	1.33253i	0.937924	−	0.346840i	$-0.112745\pi$
$600$		0			0
$601$	11.1158	+	19.2532i	0.453424	+	0.785354i	0.998596	−	0.0529703i	$-0.0168689\pi$
$601$	11.1158	+	19.2532i	0.453424	+	0.785354i	−0.545172	+	0.838324i	$0.683536\pi$
$602$	−1.70690	+	1.70690i	−0.0695679	+	0.0695679i
$603$		0			0
$604$			27.3201i			1.11164i
$605$		0			0
$606$		0			0
$607$	20.8988	−	5.59982i	0.848257	−	0.227290i	0.191594	−	0.981474i	$-0.438634\pi$
$607$	20.8988	−	5.59982i	0.848257	−	0.227290i	0.656663	+	0.754184i	$0.271968\pi$
$608$	−9.34645	+	2.50437i	−0.379049	+	0.101566i
$609$		0			0
$610$		0			0
$611$			4.91972i			0.199031i
$612$		0			0
$613$	−15.7726	+	15.7726i	−0.637051	+	0.637051i	−0.949827	−	0.312776i	$-0.898741\pi$
$613$	−15.7726	+	15.7726i	−0.637051	+	0.637051i	0.312776	+	0.949827i	$0.398741\pi$
$614$	1.68455	+	2.91773i	0.0679830	+	0.117750i
$615$		0			0
$616$	2.30946	−	4.00010i	0.0930507	−	0.161169i
$617$	−10.9568	−	40.8914i	−0.441104	−	1.64622i	−0.726021	−	0.687672i	$-0.758633\pi$
$617$	−10.9568	−	40.8914i	−0.441104	−	1.64622i	0.284917	−	0.958552i	$-0.408034\pi$
$618$		0			0
$619$	27.5855	−	15.9265i	1.10876	−	0.640141i	0.170250	−	0.985401i	$-0.445543\pi$
$619$	27.5855	−	15.9265i	1.10876	−	0.640141i	0.938507	+	0.345260i	$0.112209\pi$
$620$		0			0
$621$		0			0
$622$	−1.17952	−	1.17952i	−0.0472944	−	0.0472944i
$623$	1.83361	−	6.84311i	0.0734619	−	0.274163i
$624$		0			0
$625$		0			0
$626$	3.13060	+	1.80745i	0.125124	+	0.0722403i
$627$		0			0
$628$	−39.7206	−	10.6431i	−1.58502	−	0.424706i
$629$	0.138922			0.00553917
$630$		0			0
$631$	15.7931			0.628713			0.314356	−	0.949305i	$-0.398211\pi$
$631$	15.7931			0.628713			0.314356	+	0.949305i	$0.398211\pi$
$632$	5.54081	+	1.48466i	0.220402	+	0.0590564i
$633$		0			0
$634$	3.23993	+	1.87057i	0.128674	+	0.0742899i
$635$		0			0
$636$		0			0
$637$	−0.437722	+	1.63360i	−0.0173432	+	0.0647256i
$638$	2.16364	+	2.16364i	0.0856594	+	0.0856594i
$639$		0			0
$640$		0			0
$641$	8.57453	−	4.95051i	0.338673	−	0.195533i	−0.321012	−	0.947075i	$-0.604023\pi$
$641$	8.57453	−	4.95051i	0.338673	−	0.195533i	0.659685	+	0.751542i	$0.270690\pi$
$642$		0			0
$643$	12.2247	+	45.6232i	0.482095	+	1.79920i	0.592801	+	0.805349i	$0.298022\pi$
$643$	12.2247	+	45.6232i	0.482095	+	1.79920i	−0.110706	+	0.993853i	$0.535311\pi$
$644$	16.9303	−	29.3241i	0.667147	−	1.15553i
$645$		0			0
$646$	0.236147	+	0.409018i	0.00929107	+	0.0160926i
$647$	−9.75824	+	9.75824i	−0.383636	+	0.383636i	−0.872410	−	0.488774i	$-0.837444\pi$
$647$	−9.75824	+	9.75824i	−0.383636	+	0.383636i	0.488774	+	0.872410i	$0.337444\pi$
$648$		0			0
$649$		−	11.2506i		−	0.441625i
$650$		0			0
$651$		0			0
$652$	−6.51206	+	1.74490i	−0.255032	+	0.0683356i
$653$	−2.99335	+	0.802065i	−0.117139	+	0.0313872i	−0.316912	−	0.948455i	$-0.602646\pi$
$653$	−2.99335	+	0.802065i	−0.117139	+	0.0313872i	0.199773	+	0.979842i	$0.435979\pi$
$654$		0			0
$655$		0			0
$656$			28.4613i			1.11123i
$657$		0			0
$658$	−1.00447	+	1.00447i	−0.0391584	+	0.0391584i
$659$	−13.5644	−	23.4942i	−0.528393	−	0.915204i	−0.999452	−	0.0331023i	$-0.989461\pi$
$659$	−13.5644	−	23.4942i	−0.528393	−	0.915204i	0.471059	−	0.882102i	$-0.343872\pi$
$660$		0			0
$661$	−9.54526	+	16.5329i	−0.371268	+	0.643055i	−0.989761	−	0.142736i	$-0.954410\pi$
$661$	−9.54526	+	16.5329i	−0.371268	+	0.643055i	0.618493	+	0.785790i	$0.287743\pi$
$662$	1.71638	+	6.40560i	0.0667088	+	0.248961i
$663$		0			0
$664$	7.30683	−	4.21860i	0.283560	−	0.163713i
$665$		0			0
$666$		0			0
$667$	32.0231	+	32.0231i	1.23994	+	1.23994i
$668$	−4.32979	+	16.1590i	−0.167524	+	0.625210i
$669$		0			0
$670$		0			0
$671$	−1.01104	−	0.583723i	−0.0390307	−	0.0225344i
$672$		0			0
$673$	0.134287	+	0.0359820i	0.00517638	+	0.00138701i	0.261406	−	0.965229i	$-0.415814\pi$
$673$	0.134287	+	0.0359820i	0.00517638	+	0.00138701i	−0.256230	+	0.966616i	$0.582480\pi$
$674$	−6.17391			−0.237810
$675$		0			0
$676$	−20.2978			−0.780684
$677$	−7.80401	−	2.09108i	−0.299933	−	0.0803667i	0.105714	−	0.994397i	$-0.466287\pi$
$677$	−7.80401	−	2.09108i	−0.299933	−	0.0803667i	−0.405647	+	0.914030i	$0.632954\pi$
$678$		0			0
$679$	3.10188	+	1.79087i	0.119039	+	0.0687272i
$680$		0			0
$681$		0			0
$682$	−0.487225	+	1.81835i	−0.0186568	+	0.0696281i
$683$	−35.0271	−	35.0271i	−1.34027	−	1.34027i	−0.895784	−	0.444490i	$-0.853385\pi$
$683$	−35.0271	−	35.0271i	−1.34027	−	1.34027i	−0.444490	−	0.895784i	$-0.646615\pi$
$684$		0			0
$685$		0			0
$686$	−3.27715	+	1.89206i	−0.125122	+	0.0722393i
$687$		0			0
$688$	5.01366	+	18.7112i	0.191144	+	0.713359i
$689$	7.05680	−	12.2227i	0.268843	−	0.465649i
$690$		0			0
$691$	−20.5195	−	35.5408i	−0.780597	−	1.35203i	−0.931594	−	0.363500i	$-0.881582\pi$
$691$	−20.5195	−	35.5408i	−0.780597	−	1.35203i	0.150997	−	0.988534i	$-0.451752\pi$
$692$	24.5313	−	24.5313i	0.932541	−	0.932541i
$693$		0			0
$694$		−	3.09646i		−	0.117540i
$695$		0			0
$696$		0			0
$697$	4.15663	−	1.11377i	0.157444	−	0.0421869i
$698$	−3.26160	+	0.873943i	−0.123453	+	0.0330792i
$699$		0			0
$700$		0			0
$701$		−	37.2173i		−	1.40568i	−0.711348	−	0.702840i	$-0.751915\pi$
$701$		−	37.2173i		−	1.40568i	0.711348	−	0.702840i	$-0.248085\pi$
$702$		0			0
$703$	−0.737304	+	0.737304i	−0.0278080	+	0.0278080i
$704$	−8.81487	−	15.2678i	−0.332223	−	0.575427i
$705$		0			0
$706$	1.84490	−	3.19546i	0.0694337	−	0.120263i
$707$	−11.2067	−	41.8240i	−0.421471	−	1.57295i
$708$		0			0
$709$	−13.3449	+	7.70466i	−0.501177	+	0.289355i	−0.729199	−	0.684301i	$-0.760107\pi$
$709$	−13.3449	+	7.70466i	−0.501177	+	0.289355i	0.228023	+	0.973656i	$0.426774\pi$
$710$		0			0
$711$		0			0
$712$	1.56751	+	1.56751i	0.0587448	+	0.0587448i
$713$	−7.21120	+	26.9125i	−0.270061	+	1.00788i
$714$		0			0
$715$		0			0
$716$	−14.1222	−	8.15345i	−0.527771	−	0.304709i
$717$		0			0
$718$	4.28596	+	1.14842i	0.159951	+	0.0428587i
$719$	11.9324			0.445002			0.222501	−	0.974932i	$-0.428578\pi$
$719$	11.9324			0.445002			0.222501	+	0.974932i	$0.428578\pi$
$720$		0			0
$721$	25.8823			0.963908
$722$	0.114511	+	0.0306831i	0.00426165	+	0.00114191i
$723$		0			0
$724$	8.04760	+	4.64628i	0.299087	+	0.172678i
$725$		0			0
$726$		0			0
$727$	−1.12575	+	4.20134i	−0.0417516	+	0.155819i	−0.983654	−	0.180066i	$-0.942369\pi$
$727$	−1.12575	+	4.20134i	−0.0417516	+	0.155819i	0.941903	+	0.335885i	$0.109035\pi$
$728$	2.15130	+	2.15130i	0.0797326	+	0.0797326i
$729$		0			0
$730$		0			0
$731$	2.53649	−	1.46444i	0.0938153	−	0.0541643i
$732$		0			0
$733$	−12.7796	−	47.6943i	−0.472027	−	1.76163i	−0.632473	−	0.774583i	$-0.717960\pi$
$733$	−12.7796	−	47.6943i	−0.472027	−	1.76163i	0.160446	−	0.987045i	$-0.448707\pi$
$734$	2.61370	−	4.52707i	0.0964736	−	0.167097i
$735$		0			0
$736$	7.97125	+	13.8066i	0.293824	+	0.508918i
$737$	−2.99918	+	2.99918i	−0.110476	+	0.110476i
$738$		0			0
$739$		−	16.1890i		−	0.595523i	−0.954640	−	0.297761i	$-0.903760\pi$
$739$		−	16.1890i		−	0.595523i	0.954640	−	0.297761i	$-0.0962400\pi$
$740$		0			0
$741$		0			0
$742$	3.93635	−	1.05474i	0.144508	−	0.0387208i
$743$	19.2021	−	5.14520i	0.704458	−	0.188759i	0.111232	−	0.993795i	$-0.464520\pi$
$743$	19.2021	−	5.14520i	0.704458	−	0.188759i	0.593227	+	0.805035i	$0.297854\pi$
$744$		0			0
$745$		0			0
$746$			5.78426i			0.211777i
$747$		0			0
$748$	−1.96282	+	1.96282i	−0.0717679	+	0.0717679i
$749$	18.0595	+	31.2799i	0.659878	+	1.14294i
$750$		0			0
$751$	7.95061	−	13.7709i	0.290122	−	0.502506i	−0.683716	−	0.729748i	$-0.739637\pi$
$751$	7.95061	−	13.7709i	0.290122	−	0.502506i	0.973838	+	0.227242i	$0.0729708\pi$
$752$	2.95043	+	11.0112i	0.107591	+	0.401536i
$753$		0			0
$754$	−1.74545	+	1.00774i	−0.0635655	+	0.0366996i
$755$		0			0
$756$		0			0
$757$	−21.3482	−	21.3482i	−0.775914	−	0.775914i	0.203219	−	0.979133i	$-0.434860\pi$
$757$	−21.3482	−	21.3482i	−0.775914	−	0.775914i	−0.979133	+	0.203219i	$0.934860\pi$
$758$	1.00278	−	3.74243i	0.0364227	−	0.135931i
$759$		0			0
$760$		0			0
$761$	−4.74778	−	2.74113i	−0.172107	−	0.0993659i	0.411472	−	0.911422i	$-0.365015\pi$
$761$	−4.74778	−	2.74113i	−0.172107	−	0.0993659i	−0.583579	+	0.812056i	$0.698348\pi$
$762$		0			0
$763$	−0.809511	−	0.216908i	−0.0293063	−	0.00785259i
$764$	−7.59046			−0.274613
$765$		0			0
$766$	−5.32045			−0.192236
$767$	7.15808	+	1.91800i	0.258463	+	0.0692550i
$768$		0			0
$769$	−7.13004	−	4.11653i	−0.257116	−	0.148446i	0.365902	−	0.930653i	$-0.380760\pi$
$769$	−7.13004	−	4.11653i	−0.257116	−	0.148446i	−0.623018	+	0.782207i	$0.714094\pi$
$770$		0			0
$771$		0			0
$772$	8.72533	−	32.5634i	0.314031	−	1.17198i
$773$	−14.0889	−	14.0889i	−0.506743	−	0.506743i	0.406782	−	0.913525i	$-0.366651\pi$
$773$	−14.0889	−	14.0889i	−0.506743	−	0.506743i	−0.913525	+	0.406782i	$0.866651\pi$
$774$		0			0
$775$		0			0
$776$	−0.970598	+	0.560375i	−0.0348424	+	0.0201163i
$777$		0			0
$778$	−0.669891	−	2.50007i	−0.0240168	−	0.0896318i
$779$	−16.1495	+	27.9718i	−0.578616	+	1.00219i
$780$		0			0
$781$	−4.33944	−	7.51612i	−0.155277	−	0.268948i
$782$	0.550238	−	0.550238i	0.0196765	−	0.0196765i
$783$		0			0
$784$			3.91879i			0.139957i
$785$		0			0
$786$		0			0
$787$	−19.4505	+	5.21175i	−0.693336	+	0.185779i	−0.588244	−	0.808684i	$-0.700180\pi$
$787$	−19.4505	+	5.21175i	−0.693336	+	0.185779i	−0.105092	+	0.994462i	$0.533514\pi$
$788$	29.5975	−	7.93062i	1.05437	−	0.282516i
$789$		0			0
$790$		0			0
$791$			13.1268i			0.466735i
$792$		0			0
$793$	0.543749	−	0.543749i	0.0193091	−	0.0193091i
$794$	1.75491	+	3.03959i	0.0622793	+	0.107871i
$795$		0			0
$796$	−3.53444	+	6.12183i	−0.125275	+	0.216982i
$797$	11.4576	+	42.7605i	0.405850	+	1.51465i	0.802483	+	0.596676i	$0.203512\pi$
$797$	11.4576	+	42.7605i	0.405850	+	1.51465i	−0.396632	+	0.917978i	$0.629821\pi$
$798$		0			0
$799$	1.49267	−	0.861793i	0.0528068	−	0.0304880i
$800$		0			0
$801$		0			0
$802$	3.42580	+	3.42580i	0.120969	+	0.120969i
$803$	−6.24176	+	23.2946i	−0.220267	+	0.822047i
$804$		0			0
$805$		0			0
$806$	−1.07384	−	0.619983i	−0.0378245	−	0.0218380i
$807$		0			0
$808$	13.0870	+	3.50665i	0.460399	+	0.123364i
$809$	−35.4591			−1.24667			−0.623337	−	0.781953i	$-0.714223\pi$
$809$	−35.4591			−1.24667			−0.623337	+	0.781953i	$0.714223\pi$
$810$		0			0
$811$	−9.68119			−0.339952			−0.169976	−	0.985448i	$-0.554369\pi$
$811$	−9.68119			−0.339952			−0.169976	+	0.985448i	$0.554369\pi$
$812$	29.6785	+	7.95233i	1.04151	+	0.279072i
$813$		0			0
$814$	0.100524	+	0.0580373i	0.00352335	+	0.00203421i
$815$		0			0
$816$		0			0
$817$	−5.68970	+	21.2343i	−0.199058	+	0.742893i
$818$	−1.54578	−	1.54578i	−0.0540470	−	0.0540470i
$819$		0			0
$820$		0			0
$821$	−14.6602	+	8.46408i	−0.511645	+	0.295398i	−0.733510	−	0.679679i	$-0.762119\pi$
$821$	−14.6602	+	8.46408i	−0.511645	+	0.295398i	0.221865	+	0.975077i	$0.428786\pi$
$822$		0			0
$823$	−9.19340	−	34.3102i	−0.320462	−	1.19598i	−0.918796	−	0.394733i	$-0.870837\pi$
$823$	−9.19340	−	34.3102i	−0.320462	−	1.19598i	0.598334	−	0.801247i	$-0.295830\pi$
$824$	−4.04938	+	7.01372i	−0.141067	+	0.244335i
$825$		0			0
$826$	1.06988	+	1.85309i	0.0372259	+	0.0644772i
$827$	−31.4545	+	31.4545i	−1.09378	+	1.09378i	−0.0986577	+	0.995121i	$0.531455\pi$
$827$	−31.4545	+	31.4545i	−1.09378	+	1.09378i	−0.995121	+	0.0986577i	$0.968545\pi$
$828$		0			0
$829$		−	17.3376i		−	0.602161i	−0.953599	−	0.301081i	$-0.902653\pi$
$829$		−	17.3376i		−	0.602161i	0.953599	−	0.301081i	$-0.0973474\pi$
$830$		0			0
$831$		0			0
$832$	11.2167	−	3.00551i	0.388870	−	0.104197i
$833$	0.572320	−	0.153353i	0.0198297	−	0.00531335i
$834$		0			0
$835$		0			0
$836$		−	20.8347i		−	0.720584i
$837$		0			0
$838$	−1.16233	+	1.16233i	−0.0401521	+	0.0401521i
$839$	12.8988	+	22.3413i	0.445315	+	0.771308i	0.998074	−	0.0620331i	$-0.0197584\pi$
$839$	12.8988	+	22.3413i	0.445315	+	0.771308i	−0.552759	+	0.833341i	$0.686425\pi$
$840$		0			0
$841$	−6.04717	+	10.4740i	−0.208523	+	0.361173i
$842$	0.110116	+	0.410960i	0.00379486	+	0.0141626i
$843$		0			0
$844$	−32.5015	+	18.7647i	−1.11875	+	0.645909i
$845$		0			0
$846$		0			0
$847$	−8.41170	−	8.41170i	−0.289030	−	0.289030i
$848$	8.46415	−	31.5886i	0.290660	−	1.08476i
$849$		0			0
$850$		0			0
$851$	1.48780	+	0.858984i	0.0510013	+	0.0294456i
$852$		0			0
$853$	13.7160	+	3.67518i	0.469626	+	0.125836i	0.485868	−	0.874032i	$-0.338504\pi$
$853$	13.7160	+	3.67518i	0.469626	+	0.125836i	−0.0162423	+	0.999868i	$0.505170\pi$
$854$	0.222037			0.00759796
$855$		0			0
$856$	−11.3019			−0.386289
$857$	−48.2115	−	12.9182i	−1.64687	−	0.441278i	−0.688137	−	0.725581i	$-0.741571\pi$
$857$	−48.2115	−	12.9182i	−1.64687	−	0.441278i	−0.958735	+	0.284303i	$0.908238\pi$
$858$		0			0
$859$	35.6374	+	20.5752i	1.21593	+	0.702018i	0.964045	−	0.265739i	$-0.0856158\pi$
$859$	35.6374	+	20.5752i	1.21593	+	0.702018i	0.251886	+	0.967757i	$0.418949\pi$
$860$		0			0
$861$		0			0
$862$	−0.0976806	+	0.364549i	−0.00332701	+	0.0124166i
$863$	20.5637	+	20.5637i	0.699996	+	0.699996i	0.964410	−	0.264413i	$-0.0851783\pi$
$863$	20.5637	+	20.5637i	0.699996	+	0.699996i	−0.264413	+	0.964410i	$0.585178\pi$
$864$		0			0
$865$		0			0
$866$	2.29452	−	1.32474i	0.0779711	−	0.0450166i
$867$		0			0
$868$	4.89246	+	18.2589i	0.166061	+	0.619748i
$869$	−9.29248	+	16.0950i	−0.315226	+	0.545987i
$870$		0			0
$871$	−1.39690	−	2.41950i	−0.0473320	−	0.0819815i
$872$	0.185430	−	0.185430i	0.00627944	−	0.00627944i
$873$		0			0
$874$			5.84059i			0.197561i
$875$		0			0
$876$		0			0
$877$	−48.3556	+	12.9568i	−1.63285	+	0.437521i	−0.954741	−	0.297438i	$-0.903868\pi$
$877$	−48.3556	+	12.9568i	−1.63285	+	0.437521i	−0.678111	+	0.734959i	$0.737201\pi$
$878$	−1.00647	+	0.269684i	−0.0339669	+	0.00910140i
$879$		0			0
$880$		0			0
$881$			25.4215i			0.856471i	0.903667	+	0.428235i	$0.140865\pi$
$881$			25.4215i			0.856471i	−0.903667	+	0.428235i	$0.859135\pi$
$882$		0			0
$883$	27.7207	−	27.7207i	0.932874	−	0.932874i	−0.0650103	−	0.997885i	$-0.520708\pi$
$883$	27.7207	−	27.7207i	0.932874	−	0.932874i	0.997885	+	0.0650103i	$0.0207080\pi$
$884$	−0.914203	−	1.58345i	−0.0307480	−	0.0532571i
$885$		0			0
$886$	2.60346	−	4.50932i	0.0874648	−	0.151493i
$887$	5.34114	+	19.9334i	0.179338	+	0.669298i	0.995772	+	0.0918595i	$0.0292811\pi$
$887$	5.34114	+	19.9334i	0.179338	+	0.669298i	−0.816434	+	0.577439i	$0.804052\pi$
$888$		0			0
$889$	−10.7423	+	6.20205i	−0.360284	+	0.208010i
$890$		0			0
$891$		0			0
$892$	5.79827	+	5.79827i	0.194140	+	0.194140i
$893$	−3.34827	+	12.4959i	−0.112046	+	0.418160i
$894$		0			0
$895$		0			0
$896$	12.4484	+	7.18706i	0.415870	+	0.240103i
$897$		0			0
$898$	−4.44266	−	1.19041i	−0.148253	−	0.0397244i
$899$	−25.2822			−0.843209
$900$		0			0
$901$	−4.94459			−0.164728
$902$	3.47303	+	0.930596i	0.115639	+	0.0309855i
$903$		0			0
$904$	−3.55717	−	2.05373i	−0.118310	−	0.0683061i
$905$		0			0
$906$		0			0
$907$	10.1886	−	38.0242i	0.338305	−	1.26257i	−0.561935	−	0.827181i	$-0.689943\pi$
$907$	10.1886	−	38.0242i	0.338305	−	1.26257i	0.900241	−	0.435392i	$-0.143390\pi$
$908$	−19.0901	−	19.0901i	−0.633526	−	0.633526i
$909$		0			0
$910$		0			0
$911$	42.5747	−	24.5805i	1.41056	−	0.814389i	0.415122	−	0.909766i	$-0.363739\pi$
$911$	42.5747	−	24.5805i	1.41056	−	0.814389i	0.995441	+	0.0953768i	$0.0304056\pi$
$912$		0			0
$913$	7.07501	+	26.4043i	0.234149	+	0.873854i
$914$	1.91099	−	3.30992i	0.0632098	−	0.109483i
$915$		0			0
$916$	15.0374	+	26.0455i	0.496848	+	0.860567i
$917$	28.9474	−	28.9474i	0.955928	−	0.955928i
$918$		0			0
$919$			7.00522i			0.231081i	0.993303	+	0.115540i	$0.0368600\pi$
$919$			7.00522i			0.231081i	−0.993303	+	0.115540i	$0.963140\pi$
$920$		0			0
$921$		0			0
$922$	0.245960	−	0.0659049i	0.00810028	−	0.00217046i
$923$	5.52184	−	1.47957i	0.181753	−	0.0487007i
$924$		0			0
$925$		0			0
$926$		−	2.97080i		−	0.0976265i
$927$		0			0
$928$	−10.2293	+	10.2293i	−0.335793	+	0.335793i
$929$	1.96179	+	3.39791i	0.0643641	+	0.111482i	0.896412	−	0.443222i	$-0.146165\pi$
$929$	1.96179	+	3.39791i	0.0643641	+	0.111482i	−0.832048	+	0.554704i	$0.812831\pi$
$930$		0			0
$931$	−2.22360	+	3.85139i	−0.0728755	+	0.126224i
$932$	2.14500	+	8.00525i	0.0702618	+	0.262221i
$933$		0			0
$934$	−0.419503	+	0.242200i	−0.0137266	+	0.00792504i
$935$		0			0
$936$		0			0
$937$	28.6351	+	28.6351i	0.935468	+	0.935468i	0.998040	−	0.0625728i	$-0.0199305\pi$
$937$	28.6351	+	28.6351i	0.935468	+	0.935468i	−0.0625728	+	0.998040i	$0.519931\pi$
$938$	0.208787	−	0.779203i	0.00681713	−	0.0254419i
$939$		0			0
$940$		0			0
$941$	50.0184	+	28.8781i	1.63055	+	0.941400i	0.983922	+	0.178596i	$0.0571557\pi$
$941$	50.0184	+	28.8781i	1.63055	+	0.941400i	0.646630	+	0.762804i	$0.276178\pi$
$942$		0			0
$943$	51.4028	+	13.7733i	1.67390	+	0.448521i
$944$	17.1713			0.558877
$945$		0			0
$946$	2.44720			0.0795653
$947$	8.02351	+	2.14989i	0.260729	+	0.0698622i	0.386816	−	0.922157i	$-0.373575\pi$
$947$	8.02351	+	2.14989i	0.260729	+	0.0698622i	−0.126086	+	0.992019i	$0.540242\pi$
$948$		0			0
$949$	−13.7568	−	7.94250i	−0.446565	−	0.257824i
$950$		0			0
$951$		0			0
$952$	0.275870	−	1.02956i	0.00894101	−	0.0333683i
$953$	−27.2237	−	27.2237i	−0.881861	−	0.881861i	0.111862	−	0.993724i	$-0.464318\pi$
$953$	−27.2237	−	27.2237i	−0.881861	−	0.881861i	−0.993724	+	0.111862i	$0.964318\pi$
$954$		0			0
$955$		0			0
$956$	8.82018	−	5.09233i	0.285265	−	0.164698i
$957$		0			0
$958$	−1.89541	−	7.07375i	−0.0612378	−	0.228543i
$959$	7.80805	−	13.5239i	0.252135	−	0.436711i
$960$		0			0
$961$	7.72289	+	13.3764i	0.249126	+	0.431498i
$962$	−0.0540628	+	0.0540628i	−0.00174306	+	0.00174306i
$963$		0			0
$964$		−	7.29666i		−	0.235010i
$965$		0			0
$966$		0			0
$967$	45.5627	−	12.2085i	1.46520	−	0.392598i	0.563916	−	0.825832i	$-0.309294\pi$
$967$	45.5627	−	12.2085i	1.46520	−	0.392598i	0.901282	+	0.433234i	$0.142628\pi$
$968$	3.59549	−	0.963408i	0.115563	−	0.0309651i
$969$		0			0
$970$		0			0
$971$		−	20.4752i		−	0.657080i	−0.944490	−	0.328540i	$-0.893443\pi$
$971$		−	20.4752i		−	0.657080i	0.944490	−	0.328540i	$-0.106557\pi$
$972$		0			0
$973$	−18.1322	+	18.1322i	−0.581292	+	0.581292i
$974$	−3.22988	−	5.59432i	−0.103492	−	0.179254i
$975$		0			0
$976$	0.890908	−	1.54310i	0.0285173	−	0.0493934i
$977$	9.36214	+	34.9400i	0.299521	+	1.11783i	0.937560	+	0.347824i	$0.113079\pi$
$977$	9.36214	+	34.9400i	0.299521	+	1.11783i	−0.638038	+	0.770005i	$0.720254\pi$
$978$		0			0
$979$	−6.21996	+	3.59109i	−0.198791	+	0.114772i
$980$		0			0
$981$		0			0
$982$	−2.97725	−	2.97725i	−0.0950077	−	0.0950077i
$983$	5.10700	−	19.0596i	0.162888	−	0.607906i	−0.835412	−	0.549624i	$-0.814771\pi$
$983$	5.10700	−	19.0596i	0.162888	−	0.607906i	0.998300	−	0.0582820i	$-0.0185623\pi$
$984$		0			0
$985$		0			0
$986$	0.611505	+	0.353052i	0.0194743	+	0.0112435i
$987$		0			0
$988$	13.2559	+	3.55190i	0.421725	+	0.113001i
$989$	36.2199			1.15172
$990$		0			0
$991$	53.0916			1.68651			0.843255	−	0.537513i	$-0.180636\pi$
$991$	53.0916			1.68651			0.843255	+	0.537513i	$0.180636\pi$
$992$	−8.59681	−	2.30351i	−0.272949	−	0.0731364i
$993$		0			0
$994$	1.42950	+	0.825320i	0.0453409	+	0.0261776i
$995$		0			0
$996$		0			0
$997$	−9.82689	+	36.6745i	−0.311221	+	1.16149i	0.616236	+	0.787562i	$0.288657\pi$
$997$	−9.82689	+	36.6745i	−0.311221	+	1.16149i	−0.927457	+	0.373930i	$0.878010\pi$
$998$	−0.432718	−	0.432718i	−0.0136974	−	0.0136974i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.q.a.557.3		16
3.2	odd	2		225.2.p.b.32.2		16
5.2	odd	4		135.2.m.a.98.2		16
5.3	odd	4	inner	675.2.q.a.368.3		16
5.4	even	2		135.2.m.a.17.2		16
9.2	odd	6	inner	675.2.q.a.332.3		16
9.7	even	3		225.2.p.b.182.2		16
15.2	even	4		45.2.l.a.23.3	yes	16
15.8	even	4		225.2.p.b.68.2		16
15.14	odd	2		45.2.l.a.32.3	yes	16
45.2	even	12		135.2.m.a.8.2		16
45.4	even	6		405.2.f.a.242.5		16
45.7	odd	12		45.2.l.a.38.3	yes	16
45.14	odd	6		405.2.f.a.242.4		16
45.22	odd	12		405.2.f.a.323.4		16
45.29	odd	6		135.2.m.a.62.2		16
45.32	even	12		405.2.f.a.323.5		16
45.34	even	6		45.2.l.a.2.3	✓	16
45.38	even	12	inner	675.2.q.a.143.3		16
45.43	odd	12		225.2.p.b.218.2		16
60.47	odd	4		720.2.cu.c.113.2		16
60.59	even	2		720.2.cu.c.257.1		16
180.7	even	12		720.2.cu.c.353.1		16
180.79	odd	6		720.2.cu.c.497.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.3	✓	16	45.34	even	6
45.2.l.a.23.3	yes	16	15.2	even	4
45.2.l.a.32.3	yes	16	15.14	odd	2
45.2.l.a.38.3	yes	16	45.7	odd	12
135.2.m.a.8.2		16	45.2	even	12
135.2.m.a.17.2		16	5.4	even	2
135.2.m.a.62.2		16	45.29	odd	6
135.2.m.a.98.2		16	5.2	odd	4
225.2.p.b.32.2		16	3.2	odd	2
225.2.p.b.68.2		16	15.8	even	4
225.2.p.b.182.2		16	9.7	even	3
225.2.p.b.218.2		16	45.43	odd	12
405.2.f.a.242.4		16	45.14	odd	6
405.2.f.a.242.5		16	45.4	even	6
405.2.f.a.323.4		16	45.22	odd	12
405.2.f.a.323.5		16	45.32	even	12
675.2.q.a.143.3		16	45.38	even	12	inner
675.2.q.a.332.3		16	9.2	odd	6	inner
675.2.q.a.368.3		16	5.3	odd	4	inner
675.2.q.a.557.3		16	1.1	even	1	trivial
720.2.cu.c.113.2		16	60.47	odd	4
720.2.cu.c.257.1		16	60.59	even	2
720.2.cu.c.353.1		16	180.7	even	12
720.2.cu.c.497.2		16	180.79	odd	6

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.q (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.186243 + 0.0499037i) q^{2} +(-1.69985 - 0.981412i) q^{4} +(-0.632007 + 2.35868i) q^{7} +(-0.540289 - 0.540289i) q^{8} +O(q^{10})\)	\(q+(0.186243 + 0.0499037i) q^{2} +(-1.69985 - 0.981412i) q^{4} +(-0.632007 + 2.35868i) q^{7} +(-0.540289 - 0.540289i) q^{8} +(2.14390 - 1.23778i) q^{11} +(0.422032 + 1.57505i) q^{13} +(-0.235414 + 0.407749i) q^{14} +(1.88916 + 3.27212i) q^{16} +(0.403949 - 0.403949i) q^{17} +4.28779i q^{19} +(0.461055 - 0.123539i) q^{22} +(6.82387 - 1.82845i) q^{23} +0.314402i q^{26} +(3.38916 - 3.38916i) q^{28} +(3.20524 + 5.55164i) q^{29} +(-1.97194 + 3.41550i) q^{31} +(0.584071 + 2.17978i) q^{32} +(0.0953913 - 0.0550742i) q^{34} +(0.171954 + 0.171954i) q^{37} +(-0.213977 + 0.798571i) q^{38} +(6.52359 + 3.76639i) q^{41} +(4.95226 + 1.32695i) q^{43} -4.85908 q^{44} +1.36214 q^{46} +(2.91430 + 0.780885i) q^{47} +(0.898221 + 0.518588i) q^{49} +(0.828375 - 3.09154i) q^{52} +(-6.12030 - 6.12030i) q^{53} +(1.61584 - 0.932904i) q^{56} +(0.319907 + 1.19391i) q^{58} +(2.27234 - 3.93581i) q^{59} +(-0.235795 - 0.408408i) q^{61} +(-0.537706 + 0.537706i) q^{62} -7.12153i q^{64} +(-1.65496 + 0.443446i) q^{67} +(-1.08310 + 0.290215i) q^{68} -3.50583i q^{71} +(-6.88847 + 6.88847i) q^{73} +(0.0234441 + 0.0406064i) q^{74} +(4.20809 - 7.28862i) q^{76} +(1.56457 + 5.83906i) q^{77} +(-6.50159 + 3.75369i) q^{79} +(1.02702 + 1.02702i) q^{82} +(-2.85794 + 10.6660i) q^{83} +(0.856104 + 0.494272i) q^{86} +(-1.82708 - 0.489565i) q^{88} -2.90124 q^{89} -3.98176 q^{91} +(-13.3941 - 3.58893i) q^{92} +(0.503800 + 0.290869i) q^{94} +(0.379633 - 1.41681i) q^{97} +(0.141408 + 0.141408i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} + 2 q^{7}+O(q^{10}) \) 16 * q - 6 * q^2 + 2 * q^7	\( 16 q - 6 q^{2} + 2 q^{7} + 2 q^{13} - 8 q^{16} + 10 q^{22} + 18 q^{23} + 16 q^{28} - 4 q^{31} + 30 q^{32} - 4 q^{37} - 30 q^{38} + 24 q^{41} + 2 q^{43} + 32 q^{46} - 12 q^{47} + 14 q^{52} - 36 q^{56} + 6 q^{58} + 8 q^{61} - 4 q^{67} + 42 q^{68} + 8 q^{73} + 24 q^{76} - 6 q^{77} - 32 q^{82} - 66 q^{83} + 48 q^{86} - 18 q^{88} - 40 q^{91} - 60 q^{92} - 28 q^{97}+O(q^{100}) \) 16 * q - 6 * q^2 + 2 * q^7 + 2 * q^13 - 8 * q^16 + 10 * q^22 + 18 * q^23 + 16 * q^28 - 4 * q^31 + 30 * q^32 - 4 * q^37 - 30 * q^38 + 24 * q^41 + 2 * q^43 + 32 * q^46 - 12 * q^47 + 14 * q^52 - 36 * q^56 + 6 * q^58 + 8 * q^61 - 4 * q^67 + 42 * q^68 + 8 * q^73 + 24 * q^76 - 6 * q^77 - 32 * q^82 - 66 * q^83 + 48 * q^86 - 18 * q^88 - 40 * q^91 - 60 * q^92 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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