LMFDB - Embedded newform 880.2.bo.h.641.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(81,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("880.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bo (of order $5$, 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:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			641.2
Root			$-0.227943 - 0.701538i$ of defining polynomial
Character	$\chi$	$=$	880.641
Dual form			880.2.bo.h.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.868820 + 2.67395i) q^{3} +(0.809017 + 0.587785i) q^{5} +(-0.318714 + 0.980901i) q^{7} +(-3.96813 + 2.88301i) q^{9} +O(q^{10})$	\(q+(0.868820 + 2.67395i) q^{3} +(0.809017 + 0.587785i) q^{5} +(-0.318714 + 0.980901i) q^{7} +(-3.96813 + 2.88301i) q^{9} +(-1.93675 - 2.69240i) q^{11} +(-2.79029 + 2.02726i) q^{13} +(-0.868820 + 2.67395i) q^{15} +(-1.94020 - 1.40964i) q^{17} +(2.36979 + 7.29347i) q^{19} -2.89979 q^{21} -2.45589 q^{23} +(0.309017 + 0.951057i) q^{25} +(-4.33283 - 3.14799i) q^{27} +(-1.83998 + 5.66289i) q^{29} +(-2.98382 + 2.16787i) q^{31} +(5.51666 - 7.51798i) q^{33} +(-0.834404 + 0.606230i) q^{35} +(1.84130 - 5.66694i) q^{37} +(-7.84507 - 5.69978i) q^{39} +(1.21637 + 3.74360i) q^{41} +7.64941 q^{43} -4.90488 q^{45} +(-1.80557 - 5.55697i) q^{47} +(4.80253 + 3.48924i) q^{49} +(2.08362 - 6.41272i) q^{51} +(9.58526 - 6.96410i) q^{53} +(0.0156899 - 3.31659i) q^{55} +(-17.4435 + 12.6734i) q^{57} +(-0.910456 + 2.80210i) q^{59} +(-2.00666 - 1.45792i) q^{61} +(-1.56325 - 4.81120i) q^{63} -3.44899 q^{65} +6.14702 q^{67} +(-2.13372 - 6.56693i) q^{69} +(1.63676 + 1.18918i) q^{71} +(-0.255207 + 0.785446i) q^{73} +(-2.27460 + 1.65259i) q^{75} +(3.25824 - 1.04165i) q^{77} +(-9.77146 + 7.09938i) q^{79} +(0.106048 - 0.326382i) q^{81} +(1.30253 + 0.946345i) q^{83} +(-0.741089 - 2.28084i) q^{85} -16.7409 q^{87} +8.16116 q^{89} +(-1.09924 - 3.38312i) q^{91} +(-8.38919 - 6.09510i) q^{93} +(-2.36979 + 7.29347i) q^{95} +(-1.97625 + 1.43583i) q^{97} +(15.4475 + 5.10011i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{3} + 2 q^{5} + q^{7} - 5 q^{9}+O(q^{10}) $ 8 * q + 5 * q^3 + 2 * q^5 + q^7 - 5 * q^9	$ 8 q + 5 q^{3} + 2 q^{5} + q^{7} - 5 q^{9} - 3 q^{11} - 2 q^{13} - 5 q^{15} - 13 q^{17} - 15 q^{19} - 20 q^{21} - 10 q^{23} - 2 q^{25} - 10 q^{27} - 9 q^{29} + 10 q^{31} + 5 q^{33} + 4 q^{35} + 24 q^{37} - 21 q^{39} + 8 q^{41} + 38 q^{43} + q^{49} - q^{51} + 13 q^{53} - 7 q^{55} - 45 q^{57} + 27 q^{59} + 6 q^{61} - 25 q^{63} + 2 q^{65} + 38 q^{67} - q^{69} + 20 q^{71} + 13 q^{73} - 5 q^{75} + 34 q^{77} - 37 q^{79} + 8 q^{81} - 27 q^{83} - 12 q^{85} - 38 q^{87} - 16 q^{89} - 44 q^{91} - 35 q^{93} + 15 q^{95} + 24 q^{97} + 20 q^{99}+O(q^{100}) $ 8 * q + 5 * q^3 + 2 * q^5 + q^7 - 5 * q^9 - 3 * q^11 - 2 * q^13 - 5 * q^15 - 13 * q^17 - 15 * q^19 - 20 * q^21 - 10 * q^23 - 2 * q^25 - 10 * q^27 - 9 * q^29 + 10 * q^31 + 5 * q^33 + 4 * q^35 + 24 * q^37 - 21 * q^39 + 8 * q^41 + 38 * q^43 + q^49 - q^51 + 13 * q^53 - 7 * q^55 - 45 * q^57 + 27 * q^59 + 6 * q^61 - 25 * q^63 + 2 * q^65 + 38 * q^67 - q^69 + 20 * q^71 + 13 * q^73 - 5 * q^75 + 34 * q^77 - 37 * q^79 + 8 * q^81 - 27 * q^83 - 12 * q^85 - 38 * q^87 - 16 * q^89 - 44 * q^91 - 35 * q^93 + 15 * q^95 + 24 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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			0
$2$		0			0
$3$	0.868820	+	2.67395i	0.501614	+	1.54381i	0.806390	+	0.591384i	$0.201418\pi$
$3$	0.868820	+	2.67395i	0.501614	+	1.54381i	−0.304777	+	0.952424i	$0.598582\pi$
$4$		0			0
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$		0			0
$7$	−0.318714	+	0.980901i	−0.120463	+	0.370746i	−0.993047	−	0.117717i	$-0.962442\pi$
$7$	−0.318714	+	0.980901i	−0.120463	+	0.370746i	0.872585	+	0.488463i	$0.162442\pi$
$8$		0			0
$9$	−3.96813	+	2.88301i	−1.32271	+	0.961005i
$10$		0			0
$11$	−1.93675	−	2.69240i	−0.583951	−	0.811789i
$11$	−1.93675	−	2.69240i	−0.583951	−	0.811789i
$12$		0			0
$13$	−2.79029	+	2.02726i	−0.773887	+	0.562262i	−0.903138	−	0.429350i	$-0.858743\pi$
$13$	−2.79029	+	2.02726i	−0.773887	+	0.562262i	0.129251	+	0.991612i	$0.458743\pi$
$14$		0			0
$15$	−0.868820	+	2.67395i	−0.224328	+	0.690412i
$16$		0			0
$17$	−1.94020	−	1.40964i	−0.470567	−	0.341887i	0.327095	−	0.944991i	$-0.393930\pi$
$17$	−1.94020	−	1.40964i	−0.470567	−	0.341887i	−0.797662	+	0.603105i	$0.793930\pi$
$18$		0			0
$19$	2.36979	+	7.29347i	0.543668	+	1.67324i	0.724137	+	0.689656i	$0.242238\pi$
$19$	2.36979	+	7.29347i	0.543668	+	1.67324i	−0.180470	+	0.983581i	$0.557762\pi$
$20$		0			0
$21$	−2.89979			−0.632786
$22$		0			0
$23$	−2.45589			−0.512088			−0.256044	−	0.966665i	$-0.582419\pi$
$23$	−2.45589			−0.512088			−0.256044	+	0.966665i	$0.582419\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	−4.33283	−	3.14799i	−0.833854	−	0.605830i
$28$		0			0
$29$	−1.83998	+	5.66289i	−0.341677	+	1.05157i	0.621663	+	0.783285i	$0.286458\pi$
$29$	−1.83998	+	5.66289i	−0.341677	+	1.05157i	−0.963339	+	0.268287i	$0.913542\pi$
$30$		0			0
$31$	−2.98382	+	2.16787i	−0.535909	+	0.389361i	−0.822564	−	0.568673i	$-0.807457\pi$
$31$	−2.98382	+	2.16787i	−0.535909	+	0.389361i	0.286654	+	0.958034i	$0.407457\pi$
$32$		0			0
$33$	5.51666	−	7.51798i	0.960328	−	1.30871i
$34$		0			0
$35$	−0.834404	+	0.606230i	−0.141040	+	0.102472i
$36$		0			0
$37$	1.84130	−	5.66694i	0.302708	−	0.931640i	−0.677814	−	0.735233i	$-0.737073\pi$
$37$	1.84130	−	5.66694i	0.302708	−	0.931640i	0.980523	−	0.196407i	$-0.0629273\pi$
$38$		0			0
$39$	−7.84507	−	5.69978i	−1.25622	−	0.912695i
$40$		0			0
$41$	1.21637	+	3.74360i	0.189965	+	0.584652i	0.999999	−	0.00173135i	$-0.000551106\pi$
$41$	1.21637	+	3.74360i	0.189965	+	0.584652i	−0.810033	+	0.586384i	$0.800551\pi$
$42$		0			0
$43$	7.64941			1.16652			0.583262	−	0.812284i	$-0.301776\pi$
$43$	7.64941			1.16652			0.583262	+	0.812284i	$0.301776\pi$
$44$		0			0
$45$	−4.90488			−0.731176
$46$		0			0
$47$	−1.80557	−	5.55697i	−0.263369	−	0.810567i	−0.992065	−	0.125729i	$-0.959873\pi$
$47$	−1.80557	−	5.55697i	−0.263369	−	0.810567i	0.728695	−	0.684838i	$-0.240127\pi$
$48$		0			0
$49$	4.80253	+	3.48924i	0.686076	+	0.498463i
$50$		0			0
$51$	2.08362	−	6.41272i	0.291765	−	0.897960i
$52$		0			0
$53$	9.58526	−	6.96410i	1.31664	−	0.956592i	0.316669	−	0.948536i	$-0.397436\pi$
$53$	9.58526	−	6.96410i	1.31664	−	0.956592i	0.999968	−	0.00805607i	$-0.00256435\pi$
$54$		0			0
$55$	0.0156899	−	3.31659i	0.00211563	−	0.447209i
$56$		0			0
$57$	−17.4435	+	12.6734i	−2.31044	+	1.67864i
$58$		0			0
$59$	−0.910456	+	2.80210i	−0.118531	+	0.364802i	−0.992667	−	0.120880i	$-0.961428\pi$
$59$	−0.910456	+	2.80210i	−0.118531	+	0.364802i	0.874136	+	0.485681i	$0.161428\pi$
$60$		0			0
$61$	−2.00666	−	1.45792i	−0.256927	−	0.186668i	0.451864	−	0.892087i	$-0.350759\pi$
$61$	−2.00666	−	1.45792i	−0.256927	−	0.186668i	−0.708791	+	0.705419i	$0.750759\pi$
$62$		0			0
$63$	−1.56325	−	4.81120i	−0.196951	−	0.606154i
$64$		0			0
$65$	−3.44899			−0.427794
$66$		0			0
$67$	6.14702			0.750978			0.375489	−	0.926827i	$-0.377475\pi$
$67$	6.14702			0.750978			0.375489	+	0.926827i	$0.377475\pi$
$68$		0			0
$69$	−2.13372	−	6.56693i	−0.256870	−	0.790565i
$70$		0			0
$71$	1.63676	+	1.18918i	0.194248	+	0.141129i	0.680658	−	0.732601i	$-0.261694\pi$
$71$	1.63676	+	1.18918i	0.194248	+	0.141129i	−0.486410	+	0.873731i	$0.661694\pi$
$72$		0			0
$73$	−0.255207	+	0.785446i	−0.0298697	+	0.0919295i	−0.964880	−	0.262691i	$-0.915390\pi$
$73$	−0.255207	+	0.785446i	−0.0298697	+	0.0919295i	0.935010	+	0.354621i	$0.115390\pi$
$74$		0			0
$75$	−2.27460	+	1.65259i	−0.262648	+	0.190825i
$76$		0			0
$77$	3.25824	−	1.04165i	0.371311	−	0.118707i
$78$		0			0
$79$	−9.77146	+	7.09938i	−1.09937	+	0.798742i	−0.980958	−	0.194221i	$-0.937782\pi$
$79$	−9.77146	+	7.09938i	−1.09937	+	0.798742i	−0.118417	+	0.992964i	$0.537782\pi$
$80$		0			0
$81$	0.106048	−	0.326382i	0.0117831	−	0.0362647i
$82$		0			0
$83$	1.30253	+	0.946345i	0.142971	+	0.103875i	0.656972	−	0.753915i	$-0.271837\pi$
$83$	1.30253	+	0.946345i	0.142971	+	0.103875i	−0.514000	+	0.857790i	$0.671837\pi$
$84$		0			0
$85$	−0.741089	−	2.28084i	−0.0803824	−	0.247392i
$86$		0			0
$87$	−16.7409			−1.79481
$88$		0			0
$89$	8.16116			0.865081			0.432541	−	0.901614i	$-0.357617\pi$
$89$	8.16116			0.865081			0.432541	+	0.901614i	$0.357617\pi$
$90$		0			0
$91$	−1.09924	−	3.38312i	−0.115232	−	0.354647i
$92$		0			0
$93$	−8.38919	−	6.09510i	−0.869918	−	0.632032i
$94$		0			0
$95$	−2.36979	+	7.29347i	−0.243136	+	0.748294i
$96$		0			0
$97$	−1.97625	+	1.43583i	−0.200658	+	0.145787i	−0.683577	−	0.729879i	$-0.739577\pi$
$97$	−1.97625	+	1.43583i	−0.200658	+	0.145787i	0.482919	+	0.875665i	$0.339577\pi$
$98$		0			0
$99$	15.4475	+	5.10011i	1.55253	+	0.512580i
$100$		0			0
$101$	6.08683	−	4.42234i	0.605662	−	0.440039i	−0.242222	−	0.970221i	$-0.577876\pi$
$101$	6.08683	−	4.42234i	0.605662	−	0.440039i	0.847884	+	0.530182i	$0.177876\pi$
$102$		0			0
$103$	2.93020	−	9.01821i	0.288721	−	0.888591i	−0.696538	−	0.717520i	$-0.745277\pi$
$103$	2.93020	−	9.01821i	0.288721	−	0.888591i	0.985259	−	0.171071i	$-0.0547228\pi$
$104$		0			0
$105$	−2.34598	−	1.70445i	−0.228944	−	0.166338i
$106$		0			0
$107$	1.43593	+	4.41935i	0.138817	+	0.427235i	0.996164	−	0.0875039i	$-0.0278890\pi$
$107$	1.43593	+	4.41935i	0.138817	+	0.427235i	−0.857347	+	0.514739i	$0.827889\pi$
$108$		0			0
$109$	−5.32826			−0.510355			−0.255178	−	0.966894i	$-0.582134\pi$
$109$	−5.32826			−0.510355			−0.255178	+	0.966894i	$0.582134\pi$
$110$		0			0
$111$	16.7529			1.59012
$112$		0			0
$113$	0.0942195	+	0.289978i	0.00886342	+	0.0272788i	0.955390	−	0.295346i	$-0.0954349\pi$
$113$	0.0942195	+	0.289978i	0.00886342	+	0.0272788i	−0.946527	+	0.322625i	$0.895435\pi$
$114$		0			0
$115$	−1.98685	−	1.44353i	−0.185275	−	0.134610i
$116$		0			0
$117$	5.22760	−	16.0889i	0.483292	−	1.48742i
$118$		0			0
$119$	2.00108	−	1.45387i	0.183439	−	0.133276i
$120$		0			0
$121$	−3.49802	+	10.4290i	−0.318001	+	0.948090i
$122$		0			0
$123$	−8.95341	+	6.50503i	−0.807302	+	0.586539i
$124$		0			0
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$		0			0
$127$	−9.63536	−	7.00050i	−0.855000	−	0.621194i	0.0715199	−	0.997439i	$-0.477215\pi$
$127$	−9.63536	−	7.00050i	−0.855000	−	0.621194i	−0.926520	+	0.376245i	$0.877215\pi$
$128$		0			0
$129$	6.64596	+	20.4542i	0.585145	+	1.80089i
$130$		0			0
$131$	11.1875			0.977452			0.488726	−	0.872437i	$-0.337462\pi$
$131$	11.1875			0.977452			0.488726	+	0.872437i	$0.337462\pi$
$132$		0			0
$133$	−7.90945			−0.685837
$134$		0			0
$135$	−1.65499	−	5.09355i	−0.142439	−	0.438383i
$136$		0			0
$137$	3.46360	+	2.51645i	0.295915	+	0.214995i	0.725829	−	0.687875i	$-0.241456\pi$
$137$	3.46360	+	2.51645i	0.295915	+	0.214995i	−0.429914	+	0.902870i	$0.641456\pi$
$138$		0			0
$139$	1.83964	−	5.66183i	0.156036	−	0.480230i	−0.842228	−	0.539121i	$-0.818757\pi$
$139$	1.83964	−	5.66183i	0.156036	−	0.480230i	0.998264	+	0.0588913i	$0.0187565\pi$
$140$		0			0
$141$	13.2904	−	9.65601i	1.11925	−	0.813183i
$142$		0			0
$143$	10.8623	+	3.58627i	0.908351	+	0.299899i
$144$		0			0
$145$	−4.81714	+	3.49986i	−0.400042	+	0.290647i
$146$		0			0
$147$	−5.15754	+	15.8733i	−0.425387	+	1.30921i
$148$		0			0
$149$	3.06168	+	2.22444i	0.250823	+	0.182233i	0.706091	−	0.708121i	$-0.250457\pi$
$149$	3.06168	+	2.22444i	0.250823	+	0.182233i	−0.455269	+	0.890354i	$0.650457\pi$
$150$		0			0
$151$	7.52661	+	23.1645i	0.612507	+	1.88510i	0.433159	+	0.901317i	$0.357399\pi$
$151$	7.52661	+	23.1645i	0.612507	+	1.88510i	0.179348	+	0.983786i	$0.442601\pi$
$152$		0			0
$153$	11.7629			0.950978
$154$		0			0
$155$	−3.68820			−0.296243
$156$		0			0
$157$	2.23484	+	6.87813i	0.178360	+	0.548935i	0.999771	−	0.0214015i	$-0.00681284\pi$
$157$	2.23484	+	6.87813i	0.178360	+	0.548935i	−0.821411	+	0.570336i	$0.806813\pi$
$158$		0			0
$159$	26.9495	+	19.5800i	2.13724	+	1.55279i
$160$		0			0
$161$	0.782725	−	2.40898i	0.0616874	−	0.189854i
$162$		0			0
$163$	15.1198	−	10.9852i	1.18428	−	0.860428i	0.191630	−	0.981467i	$-0.438623\pi$
$163$	15.1198	−	10.9852i	1.18428	−	0.860428i	0.992648	+	0.121039i	$0.0386226\pi$
$164$		0			0
$165$	8.88203	−	2.83956i	0.691465	−	0.221060i
$166$		0			0
$167$	6.35343	−	4.61604i	0.491644	−	0.357200i	−0.314172	−	0.949366i	$-0.601727\pi$
$167$	6.35343	−	4.61604i	0.491644	−	0.357200i	0.805816	+	0.592166i	$0.201727\pi$
$168$		0			0
$169$	−0.341302	+	1.05042i	−0.0262540	+	0.0808014i
$170$		0			0
$171$	−30.4308	−	22.1093i	−2.32710	−	1.69074i
$172$		0			0
$173$	3.46244	+	10.6563i	0.263244	+	0.810183i	0.992093	+	0.125508i	$0.0400560\pi$
$173$	3.46244	+	10.6563i	0.263244	+	0.810183i	−0.728848	+	0.684675i	$0.759944\pi$
$174$		0			0
$175$	−1.03138			−0.0779650
$176$		0			0
$177$	−8.28370			−0.622641
$178$		0			0
$179$	−0.452595	−	1.39295i	−0.0338286	−	0.104114i	0.932716	−	0.360611i	$-0.117432\pi$
$179$	−0.452595	−	1.39295i	−0.0338286	−	0.104114i	−0.966545	+	0.256497i	$0.917432\pi$
$180$		0			0
$181$	−7.51496	−	5.45994i	−0.558583	−	0.405834i	0.272357	−	0.962196i	$-0.412197\pi$
$181$	−7.51496	−	5.45994i	−0.558583	−	0.405834i	−0.830940	+	0.556362i	$0.812197\pi$
$182$		0			0
$183$	2.15499	−	6.63239i	0.159302	−	0.490280i
$184$		0			0
$185$	4.82059	−	3.50236i	0.354417	−	0.257499i
$186$		0			0
$187$	−0.0376278	+	7.95389i	−0.00275162	+	0.581646i
$188$		0			0
$189$	4.46880	−	3.24677i	0.325057	−	0.236168i
$190$		0			0
$191$	1.38222	−	4.25404i	0.100014	−	0.307811i	−0.888514	−	0.458850i	$-0.848262\pi$
$191$	1.38222	−	4.25404i	0.100014	−	0.307811i	0.988528	+	0.151038i	$0.0482617\pi$
$192$		0			0
$193$	18.3372	+	13.3227i	1.31994	+	0.958992i	0.999933	+	0.0115772i	$0.00368521\pi$
$193$	18.3372	+	13.3227i	1.31994	+	0.958992i	0.320007	+	0.947415i	$0.396315\pi$
$194$		0			0
$195$	−2.99655	−	9.22244i	−0.214587	−	0.660432i
$196$		0			0
$197$	−11.2080			−0.798535			−0.399267	−	0.916835i	$-0.630735\pi$
$197$	−11.2080			−0.798535			−0.399267	+	0.916835i	$0.630735\pi$
$198$		0			0
$199$	7.81979			0.554330			0.277165	−	0.960822i	$-0.410605\pi$
$199$	7.81979			0.554330			0.277165	+	0.960822i	$0.410605\pi$
$200$		0			0
$201$	5.34065	+	16.4368i	0.376701	+	1.15937i
$202$		0			0
$203$	−4.96830	−	3.60968i	−0.348707	−	0.253350i
$204$		0			0
$205$	−1.21637	+	3.74360i	−0.0849550	+	0.261464i
$206$		0			0
$207$	9.74527	−	7.08035i	0.677343	−	0.492119i
$208$		0			0
$209$	15.0472	−	20.5060i	1.04084	−	1.41843i
$210$		0			0
$211$	−18.4189	+	13.3821i	−1.26801	+	0.921262i	−0.999121	−	0.0419098i	$-0.986656\pi$
$211$	−18.4189	+	13.3821i	−1.26801	+	0.921262i	−0.268887	+	0.963172i	$0.586656\pi$
$212$		0			0
$213$	−1.75775	+	5.40980i	−0.120439	+	0.370673i
$214$		0			0
$215$	6.18851	+	4.49621i	0.422053	+	0.306639i
$216$		0			0
$217$	−1.17548	−	3.61776i	−0.0797969	−	0.245589i
$218$		0			0
$219$	−2.32197			−0.156905
$220$		0			0
$221$	8.27142			0.556396
$222$		0			0
$223$	4.95746	+	15.2575i	0.331976	+	1.02172i	0.968192	+	0.250207i	$0.0804985\pi$
$223$	4.95746	+	15.2575i	0.331976	+	1.02172i	−0.636216	+	0.771511i	$0.719501\pi$
$224$		0			0
$225$	−3.96813	−	2.88301i	−0.264542	−	0.192201i
$226$		0			0
$227$	7.46468	−	22.9739i	0.495448	−	1.52483i	−0.320809	−	0.947144i	$-0.603955\pi$
$227$	7.46468	−	22.9739i	0.495448	−	1.52483i	0.816257	−	0.577689i	$-0.196045\pi$
$228$		0			0
$229$	12.1468	−	8.82517i	0.802684	−	0.583184i	−0.109017	−	0.994040i	$-0.534770\pi$
$229$	12.1468	−	8.82517i	0.802684	−	0.583184i	0.911700	+	0.410856i	$0.134770\pi$
$230$		0			0
$231$	5.61616	+	7.80738i	0.369516	+	0.513688i
$232$		0			0
$233$	−9.24378	+	6.71600i	−0.605580	+	0.439980i	−0.847855	−	0.530228i	$-0.822106\pi$
$233$	−9.24378	+	6.71600i	−0.605580	+	0.439980i	0.242275	+	0.970208i	$0.422106\pi$
$234$		0			0
$235$	1.80557	−	5.55697i	0.117782	−	0.362497i
$236$		0			0
$237$	−27.4730	−	19.9603i	−1.78457	−	1.29656i
$238$		0			0
$239$	−8.46914	−	26.0653i	−0.547823	−	1.68603i	−0.714181	−	0.699961i	$-0.753201\pi$
$239$	−8.46914	−	26.0653i	−0.547823	−	1.68603i	0.166358	−	0.986065i	$-0.446799\pi$
$240$		0			0
$241$	10.9387			0.704624			0.352312	−	0.935883i	$-0.385396\pi$
$241$	10.9387			0.704624			0.352312	+	0.935883i	$0.385396\pi$
$242$		0			0
$243$	−15.1022			−0.968804
$244$		0			0
$245$	1.83440	+	5.64571i	0.117196	+	0.360691i
$246$		0			0
$247$	−21.3982	−	15.5467i	−1.36154	−	0.989213i
$248$		0			0
$249$	−1.39882	+	4.30511i	−0.0886463	+	0.272825i
$250$		0			0
$251$	13.9403	−	10.1282i	0.879902	−	0.639286i	−0.0533238	−	0.998577i	$-0.516982\pi$
$251$	13.9403	−	10.1282i	0.879902	−	0.639286i	0.933225	+	0.359291i	$0.116982\pi$
$252$		0			0
$253$	4.75643	+	6.61222i	0.299034	+	0.415707i
$254$		0			0
$255$	5.45498	−	3.96328i	0.341604	−	0.248190i
$256$		0			0
$257$	5.71540	−	17.5902i	0.356517	−	1.09725i	−0.598608	−	0.801042i	$-0.704279\pi$
$257$	5.71540	−	17.5902i	0.356517	−	1.09725i	0.955125	−	0.296204i	$-0.0957207\pi$
$258$		0			0
$259$	4.97186	+	3.61227i	0.308936	+	0.224455i
$260$		0			0
$261$	−9.02489	−	27.7758i	−0.558627	−	1.71928i
$262$		0			0
$263$	−3.69135			−0.227618			−0.113809	−	0.993503i	$-0.536305\pi$
$263$	−3.69135			−0.227618			−0.113809	+	0.993503i	$0.536305\pi$
$264$		0			0
$265$	11.8480			0.727819
$266$		0			0
$267$	7.09058	+	21.8226i	0.433937	+	1.33552i
$268$		0			0
$269$	8.04575	+	5.84558i	0.490558	+	0.356411i	0.805399	−	0.592733i	$-0.201951\pi$
$269$	8.04575	+	5.84558i	0.490558	+	0.356411i	−0.314841	+	0.949145i	$0.601951\pi$
$270$		0			0
$271$	−0.387400	+	1.19229i	−0.0235329	+	0.0724267i	−0.962133	−	0.272580i	$-0.912123\pi$
$271$	−0.387400	+	1.19229i	−0.0235329	+	0.0724267i	0.938600	+	0.345006i	$0.112123\pi$
$272$		0			0
$273$	8.09125	−	5.87864i	0.489705	−	0.355791i
$274$		0			0
$275$	1.96213	−	2.67395i	0.118321	−	0.161245i
$276$		0			0
$277$	6.54763	−	4.75713i	0.393409	−	0.285828i	−0.373442	−	0.927654i	$-0.621823\pi$
$277$	6.54763	−	4.75713i	0.393409	−	0.285828i	0.766851	+	0.641825i	$0.221823\pi$
$278$		0			0
$279$	5.59017	−	17.2048i	0.334675	−	1.03002i
$280$		0			0
$281$	−20.5250	−	14.9123i	−1.22442	−	0.889591i	−0.227958	−	0.973671i	$-0.573205\pi$
$281$	−20.5250	−	14.9123i	−1.22442	−	0.889591i	−0.996459	+	0.0840804i	$0.973205\pi$
$282$		0			0
$283$	6.31705	+	19.4419i	0.375510	+	1.15570i	0.943134	+	0.332412i	$0.107863\pi$
$283$	6.31705	+	19.4419i	0.375510	+	1.15570i	−0.567624	+	0.823288i	$0.692137\pi$
$284$		0			0
$285$	−21.5613			−1.27718
$286$		0			0
$287$	−4.05977			−0.239641
$288$		0			0
$289$	−3.47600	−	10.6980i	−0.204470	−	0.629295i
$290$		0			0
$291$	−5.55635	−	4.03693i	−0.325719	−	0.236649i
$292$		0			0
$293$	0.787705	−	2.42431i	0.0460182	−	0.141630i	−0.925407	−	0.378974i	$-0.876277\pi$
$293$	0.787705	−	2.42431i	0.0460182	−	0.141630i	0.971426	+	0.237344i	$0.0762770\pi$
$294$		0			0
$295$	−2.38361	+	1.73179i	−0.138779	+	0.100829i
$296$		0			0
$297$	−0.0840302	+	17.7626i	−0.00487593	+	1.03069i
$298$		0			0
$299$	6.85264	−	4.97873i	0.396298	−	0.287928i
$300$		0			0
$301$	−2.43797	+	7.50331i	−0.140523	+	0.432484i
$302$		0			0
$303$	17.1135	+	12.4337i	0.983144	+	0.714296i
$304$		0			0
$305$	−0.766476	−	2.35897i	−0.0438883	−	0.135074i
$306$		0			0
$307$	−8.99273			−0.513242			−0.256621	−	0.966512i	$-0.582609\pi$
$307$	−8.99273			−0.513242			−0.256621	+	0.966512i	$0.582609\pi$
$308$		0			0
$309$	26.6601			1.51664
$310$		0			0
$311$	6.21840	+	19.1383i	0.352613	+	1.08523i	0.957380	+	0.288830i	$0.0932662\pi$
$311$	6.21840	+	19.1383i	0.352613	+	1.08523i	−0.604767	+	0.796402i	$0.706734\pi$
$312$		0			0
$313$	−5.74792	−	4.17611i	−0.324892	−	0.236048i	0.413368	−	0.910564i	$-0.364352\pi$
$313$	−5.74792	−	4.17611i	−0.324892	−	0.236048i	−0.738260	+	0.674516i	$0.764352\pi$
$314$		0			0
$315$	1.56325	−	4.81120i	0.0880793	−	0.271080i
$316$		0			0
$317$	−1.85526	+	1.34793i	−0.104202	+	0.0757071i	−0.638666	−	0.769484i	$-0.720513\pi$
$317$	−1.85526	+	1.34793i	−0.104202	+	0.0757071i	0.534464	+	0.845191i	$0.320513\pi$
$318$		0			0
$319$	18.8103	−	6.01362i	1.05318	−	0.336698i
$320$		0			0
$321$	−10.5696	+	7.67924i	−0.589936	+	0.428613i
$322$		0			0
$323$	5.68327	−	17.4913i	0.316226	−	0.973242i
$324$		0			0
$325$	−2.79029	−	2.02726i	−0.154777	−	0.112452i
$326$		0			0
$327$	−4.62930	−	14.2475i	−0.256001	−	0.787890i
$328$		0			0
$329$	6.02629			0.332240
$330$		0			0
$331$	−15.3951			−0.846192			−0.423096	−	0.906085i	$-0.639057\pi$
$331$	−15.3951			−0.846192			−0.423096	+	0.906085i	$0.639057\pi$
$332$		0			0
$333$	9.03136	+	27.7957i	0.494915	+	1.52319i
$334$		0			0
$335$	4.97304	+	3.61313i	0.271706	+	0.197406i
$336$		0			0
$337$	−6.02485	+	18.5426i	−0.328195	+	1.01008i	0.641783	+	0.766886i	$0.278195\pi$
$337$	−6.02485	+	18.5426i	−0.328195	+	1.01008i	−0.969978	+	0.243193i	$0.921805\pi$
$338$		0			0
$339$	−0.693527	+	0.503877i	−0.0376672	+	0.0273668i
$340$		0			0
$341$	11.6157	+	3.83501i	0.629024	+	0.207677i
$342$		0			0
$343$	−10.7941	+	7.84234i	−0.582825	+	0.423447i
$344$		0			0
$345$	2.13372	−	6.56693i	0.114876	−	0.353551i
$346$		0			0
$347$	−1.75479	−	1.27493i	−0.0942023	−	0.0684420i	0.539687	−	0.841866i	$-0.318543\pi$
$347$	−1.75479	−	1.27493i	−0.0942023	−	0.0684420i	−0.633889	+	0.773424i	$0.718543\pi$
$348$		0			0
$349$	−7.74150	−	23.8259i	−0.414393	−	1.27537i	−0.912793	−	0.408423i	$-0.866079\pi$
$349$	−7.74150	−	23.8259i	−0.414393	−	1.27537i	0.498400	−	0.866947i	$-0.333921\pi$
$350$		0			0
$351$	18.4717			0.985944
$352$		0			0
$353$	−23.2532			−1.23764			−0.618821	−	0.785532i	$-0.712389\pi$
$353$	−23.2532			−1.23764			−0.618821	+	0.785532i	$0.712389\pi$
$354$		0			0
$355$	0.625187	+	1.92413i	0.0331815	+	0.102122i
$356$		0			0
$357$	5.62616	+	4.08764i	0.297768	+	0.216341i
$358$		0			0
$359$	−3.12799	+	9.62695i	−0.165089	+	0.508091i	−0.999043	−	0.0437429i	$-0.986072\pi$
$359$	−3.12799	+	9.62695i	−0.165089	+	0.508091i	0.833954	+	0.551834i	$0.186072\pi$
$360$		0			0
$361$	−32.2075	+	23.4001i	−1.69513	+	1.23158i
$362$		0			0
$363$	−30.9258	−	0.292611i	−1.62318	−	0.0153581i
$364$		0			0
$365$	−0.668140	+	0.485432i	−0.0349721	+	0.0254087i
$366$		0			0
$367$	−1.14622	+	3.52770i	−0.0598322	+	0.184145i	−0.976505	−	0.215493i	$-0.930864\pi$
$367$	−1.14622	+	3.52770i	−0.0598322	+	0.184145i	0.916673	+	0.399638i	$0.130864\pi$
$368$		0			0
$369$	−15.6196	−	11.3483i	−0.813122	−	0.590768i
$370$		0			0
$371$	3.77613	+	11.6217i	0.196047	+	0.603371i
$372$		0			0
$373$	−9.34017			−0.483616			−0.241808	−	0.970324i	$-0.577740\pi$
$373$	−9.34017			−0.483616			−0.241808	+	0.970324i	$0.577740\pi$
$374$		0			0
$375$	−2.81156			−0.145188
$376$		0			0
$377$	−6.34609	−	19.5312i	−0.326840	−	1.00591i
$378$		0			0
$379$	−7.93783	−	5.76717i	−0.407739	−	0.296240i	0.364947	−	0.931028i	$-0.381087\pi$
$379$	−7.93783	−	5.76717i	−0.407739	−	0.296240i	−0.772686	+	0.634789i	$0.781087\pi$
$380$		0			0
$381$	10.3476	−	31.8467i	0.530124	−	1.63156i
$382$		0			0
$383$	−14.6002	+	10.6076i	−0.746034	+	0.542025i	−0.894595	−	0.446878i	$-0.852536\pi$
$383$	−14.6002	+	10.6076i	−0.746034	+	0.542025i	0.148561	+	0.988903i	$0.452536\pi$
$384$		0			0
$385$	3.24824	+	1.07243i	0.165546	+	0.0546562i
$386$		0			0
$387$	−30.3539	+	22.0534i	−1.54297	+	1.12104i
$388$		0			0
$389$	9.63871	−	29.6649i	0.488702	−	1.50407i	−0.337844	−	0.941202i	$-0.609698\pi$
$389$	9.63871	−	29.6649i	0.488702	−	1.50407i	0.826546	−	0.562869i	$-0.190302\pi$
$390$		0			0
$391$	4.76490	+	3.46191i	0.240972	+	0.175076i
$392$		0			0
$393$	9.71989	+	29.9147i	0.490303	+	1.50900i
$394$		0			0
$395$	−12.0782			−0.607719
$396$		0			0
$397$	−10.6212			−0.533062			−0.266531	−	0.963826i	$-0.585877\pi$
$397$	−10.6212			−0.533062			−0.266531	+	0.963826i	$0.585877\pi$
$398$		0			0
$399$	−6.87189	−	21.1495i	−0.344025	−	1.05880i
$400$		0			0
$401$	22.3029	+	16.2040i	1.11375	+	0.809190i	0.983251	−	0.182258i	$-0.0583407\pi$
$401$	22.3029	+	16.2040i	1.11375	+	0.809190i	0.130503	+	0.991448i	$0.458341\pi$
$402$		0			0
$403$	3.93087	−	12.0980i	0.195811	−	0.602643i
$404$		0			0
$405$	0.277637	−	0.201715i	0.0137959	−	0.0100233i
$406$		0			0
$407$	−18.8238	+	6.01792i	−0.933061	+	0.298297i
$408$		0			0
$409$	−11.6241	+	8.44540i	−0.574774	+	0.417598i	−0.836836	−	0.547453i	$-0.815598\pi$
$409$	−11.6241	+	8.44540i	−0.574774	+	0.417598i	0.262062	+	0.965051i	$0.415598\pi$
$410$		0			0
$411$	−3.71963	+	11.4478i	−0.183476	+	0.564681i
$412$		0			0
$413$	−2.45840	−	1.78613i	−0.120970	−	0.0878899i
$414$		0			0
$415$	0.497523	+	1.53122i	0.0244224	+	0.0751645i
$416$		0			0
$417$	16.7378			0.819652
$418$		0			0
$419$	31.4707			1.53744			0.768722	−	0.639584i	$-0.220893\pi$
$419$	31.4707			1.53744			0.768722	+	0.639584i	$0.220893\pi$
$420$		0			0
$421$	8.21095	+	25.2707i	0.400177	+	1.23162i	0.924856	+	0.380318i	$0.124185\pi$
$421$	8.21095	+	25.2707i	0.400177	+	1.23162i	−0.524679	+	0.851300i	$0.675815\pi$
$422$		0			0
$423$	23.1855	+	16.8453i	1.12732	+	0.819045i
$424$		0			0
$425$	0.741089	−	2.28084i	0.0359481	−	0.110637i
$426$		0			0
$427$	2.06963	−	1.50367i	0.100156	−	0.0727679i
$428$		0			0
$429$	−0.152146	+	32.1611i	−0.00734568	+	1.55275i
$430$		0			0
$431$	−3.12984	+	2.27397i	−0.150759	+	0.109533i	−0.660608	−	0.750731i	$-0.729701\pi$
$431$	−3.12984	+	2.27397i	−0.150759	+	0.109533i	0.509849	+	0.860264i	$0.329701\pi$
$432$		0			0
$433$	12.4036	−	38.1743i	0.596077	−	1.83454i	0.0467895	−	0.998905i	$-0.485101\pi$
$433$	12.4036	−	38.1743i	0.596077	−	1.83454i	0.549288	−	0.835633i	$-0.314899\pi$
$434$		0			0
$435$	−13.5437	−	9.84007i	−0.649370	−	0.471795i
$436$		0			0
$437$	−5.81994	−	17.9119i	−0.278406	−	0.856844i
$438$		0			0
$439$	−1.02336			−0.0488425			−0.0244212	−	0.999702i	$-0.507774\pi$
$439$	−1.02336			−0.0488425			−0.0244212	+	0.999702i	$0.507774\pi$
$440$		0			0
$441$	−29.1166			−1.38650
$442$		0			0
$443$	4.96678	+	15.2862i	0.235979	+	0.726268i	0.996990	+	0.0775295i	$0.0247032\pi$
$443$	4.96678	+	15.2862i	0.235979	+	0.726268i	−0.761011	+	0.648739i	$0.775297\pi$
$444$		0			0
$445$	6.60252	+	4.79701i	0.312989	+	0.227400i
$446$		0			0
$447$	−3.28800	+	10.1194i	−0.155517	+	0.478633i
$448$		0			0
$449$	−28.9969	+	21.0675i	−1.36845	+	0.994235i	−0.370590	+	0.928797i	$0.620844\pi$
$449$	−28.9969	+	21.0675i	−1.36845	+	0.994235i	−0.997857	+	0.0654379i	$0.979156\pi$
$450$		0			0
$451$	7.72346	−	10.5254i	0.363684	−	0.495620i
$452$		0			0
$453$	−55.4016	+	40.2516i	−2.60299	+	1.89119i
$454$		0			0
$455$	1.09924	−	3.38312i	0.0515332	−	0.158603i
$456$		0			0
$457$	20.3488	+	14.7842i	0.951875	+	0.691578i	0.951250	−	0.308422i	$-0.0998009\pi$
$457$	20.3488	+	14.7842i	0.951875	+	0.691578i	0.000625413		1.00000i	$0.499801\pi$
$458$		0			0
$459$	3.96903	+	12.2154i	0.185259	+	0.570167i
$460$		0			0
$461$	6.65631			0.310015			0.155008	−	0.987913i	$-0.450460\pi$
$461$	6.65631			0.310015			0.155008	+	0.987913i	$0.450460\pi$
$462$		0			0
$463$	−38.7730			−1.80194			−0.900968	−	0.433886i	$-0.857142\pi$
$463$	−38.7730			−1.80194			−0.900968	+	0.433886i	$0.857142\pi$
$464$		0			0
$465$	−3.20438	−	9.86208i	−0.148600	−	0.457343i
$466$		0			0
$467$	18.2429	+	13.2542i	0.844179	+	0.613332i	0.923535	−	0.383514i	$-0.125286\pi$
$467$	18.2429	+	13.2542i	0.844179	+	0.613332i	−0.0793559	+	0.996846i	$0.525286\pi$
$468$		0			0
$469$	−1.95914	+	6.02961i	−0.0904647	+	0.278422i
$470$		0			0
$471$	−16.4501	+	11.9517i	−0.757982	+	0.550706i
$472$		0			0
$473$	−14.8150	−	20.5953i	−0.681194	−	0.946971i
$474$		0			0
$475$	−6.20420	+	4.50761i	−0.284668	+	0.206823i
$476$		0			0
$477$	−17.9579	+	55.2689i	−0.822238	+	2.53059i
$478$		0			0
$479$	−1.32021	−	0.959186i	−0.0603218	−	0.0438263i	0.557216	−	0.830368i	$-0.311870\pi$
$479$	−1.32021	−	0.959186i	−0.0603218	−	0.0438263i	−0.617538	+	0.786541i	$0.711870\pi$
$480$		0			0
$481$	6.35063	+	19.5452i	0.289564	+	0.891186i
$482$		0			0
$483$	7.12155			0.324042
$484$		0			0
$485$	−2.44278			−0.110921
$486$		0			0
$487$	−0.324560	−	0.998894i	−0.0147072	−	0.0452642i	0.943434	−	0.331562i	$-0.107575\pi$
$487$	−0.324560	−	0.998894i	−0.0147072	−	0.0452642i	−0.958141	+	0.286297i	$0.907575\pi$
$488$		0			0
$489$	42.5104	+	30.8856i	1.92239	+	1.39669i
$490$		0			0
$491$	4.29969	−	13.2331i	0.194042	−	0.597201i	−0.805944	−	0.591992i	$-0.798342\pi$
$491$	4.29969	−	13.2331i	0.194042	−	0.597201i	0.999986	−	0.00520928i	$-0.00165817\pi$
$492$		0			0
$493$	11.5525	−	8.39341i	0.520300	−	0.378020i
$494$		0			0
$495$	9.49951	+	13.2059i	0.426971	+	0.593560i
$496$		0			0
$497$	−1.68812	+	1.22649i	−0.0757226	+	0.0550157i
$498$		0			0
$499$	−5.36679	+	16.5173i	−0.240250	+	0.739415i	0.756131	+	0.654420i	$0.227087\pi$
$499$	−5.36679	+	16.5173i	−0.240250	+	0.739415i	−0.996381	+	0.0849943i	$0.972913\pi$
$500$		0			0
$501$	17.8631	+	12.9783i	0.798063	+	0.579827i
$502$		0			0
$503$	−11.0794	−	34.0988i	−0.494005	−	1.52039i	−0.818502	−	0.574503i	$-0.805195\pi$
$503$	−11.0794	−	34.0988i	−0.494005	−	1.52039i	0.324498	−	0.945887i	$-0.394805\pi$
$504$		0			0
$505$	7.52373			0.334802
$506$		0			0
$507$	−3.10530			−0.137911
$508$		0			0
$509$	0.660921	+	2.03410i	0.0292948	+	0.0901601i	0.964635	−	0.263590i	$-0.0849065\pi$
$509$	0.660921	+	2.03410i	0.0292948	+	0.0901601i	−0.935340	+	0.353750i	$0.884906\pi$
$510$		0			0
$511$	−0.689106	−	0.500665i	−0.0304843	−	0.0221481i
$512$		0			0
$513$	12.6918	−	39.0614i	0.560358	−	1.72461i
$514$		0			0
$515$	7.67135	−	5.57356i	0.338040	−	0.245601i
$516$		0			0
$517$	−11.4646	+	15.6238i	−0.504214	+	0.687132i
$518$		0			0
$519$	−25.4862	+	18.5168i	−1.11872	+	0.812797i
$520$		0			0
$521$	−3.93540	+	12.1119i	−0.172413	+	0.530633i	−0.999506	−	0.0314326i	$-0.989993\pi$
$521$	−3.93540	+	12.1119i	−0.172413	+	0.530633i	0.827093	+	0.562065i	$0.189993\pi$
$522$		0			0
$523$	19.3426	+	14.0532i	0.845793	+	0.614504i	0.923983	−	0.382434i	$-0.124914\pi$
$523$	19.3426	+	14.0532i	0.845793	+	0.614504i	−0.0781901	+	0.996938i	$0.524914\pi$
$524$		0			0
$525$	−0.896084	−	2.75786i	−0.0391083	−	0.120363i
$526$		0			0
$527$	8.84510			0.385299
$528$		0			0
$529$	−16.9686			−0.737766
$530$		0			0
$531$	−4.46567	−	13.7439i	−0.193794	−	0.596436i
$532$		0			0
$533$	−10.9833	−	7.97983i	−0.475739	−	0.345645i
$534$		0			0
$535$	−1.43593	+	4.41935i	−0.0620808	+	0.191065i
$536$		0			0
$537$	3.33145	−	2.42044i	0.143763	−	0.104450i
$538$		0			0
$539$	0.0931395	−	19.6881i	0.00401180	−	0.848027i
$540$		0			0
$541$	−1.06726	+	0.775410i	−0.0458851	+	0.0333375i	−0.610491	−	0.792023i	$-0.709028\pi$
$541$	−1.06726	+	0.775410i	−0.0458851	+	0.0333375i	0.564606	+	0.825360i	$0.309028\pi$
$542$		0			0
$543$	8.07047	−	24.8384i	0.346337	−	1.06592i
$544$		0			0
$545$	−4.31066	−	3.13188i	−0.184648	−	0.134155i
$546$		0			0
$547$	−2.88044	−	8.86507i	−0.123159	−	0.379043i	0.870403	−	0.492341i	$-0.163859\pi$
$547$	−2.88044	−	8.86507i	−0.123159	−	0.379043i	−0.993561	+	0.113298i	$0.963859\pi$
$548$		0			0
$549$	12.1659			0.519228
$550$		0			0
$551$	−45.6625			−1.94529
$552$		0			0
$553$	−3.84949	−	11.8475i	−0.163697	−	0.503807i
$554$		0			0
$555$	13.5534	+	9.84711i	0.575309	+	0.417987i
$556$		0			0
$557$	12.1497	−	37.3929i	0.514798	−	1.58439i	−0.268850	−	0.963182i	$-0.586644\pi$
$557$	12.1497	−	37.3929i	0.514798	−	1.58439i	0.783648	−	0.621205i	$-0.213356\pi$
$558$		0			0
$559$	−21.3441	+	15.5074i	−0.902759	+	0.655893i
$560$		0			0
$561$	−21.3010	+	6.80989i	−0.899330	+	0.287514i
$562$		0			0
$563$	16.1649	−	11.7445i	0.681271	−	0.494972i	−0.192508	−	0.981295i	$-0.561662\pi$
$563$	16.1649	−	11.7445i	0.681271	−	0.494972i	0.873779	+	0.486323i	$0.161662\pi$
$564$		0			0
$565$	−0.0942195	+	0.289978i	−0.00396384	+	0.0121995i
$566$		0			0
$567$	0.286349	+	0.208045i	0.0120255	+	0.00873707i
$568$		0			0
$569$	−10.6811	−	32.8730i	−0.447775	−	1.37811i	−0.879412	−	0.476061i	$-0.842064\pi$
$569$	−10.6811	−	32.8730i	−0.447775	−	1.37811i	0.431637	−	0.902047i	$-0.357936\pi$
$570$		0			0
$571$	−3.15090			−0.131861			−0.0659306	−	0.997824i	$-0.521002\pi$
$571$	−3.15090			−0.131861			−0.0659306	+	0.997824i	$0.521002\pi$
$572$		0			0
$573$	12.5760			0.525370
$574$		0			0
$575$	−0.758911	−	2.33569i	−0.0316488	−	0.0974049i
$576$		0			0
$577$	−22.1044	−	16.0598i	−0.920220	−	0.668579i	0.0233590	−	0.999727i	$-0.492564\pi$
$577$	−22.1044	−	16.0598i	−0.920220	−	0.668579i	−0.943579	+	0.331148i	$0.892564\pi$
$578$		0			0
$579$	−19.6927	+	60.6079i	−0.818400	+	2.51878i
$580$		0			0
$581$	−1.34340	+	0.976041i	−0.0557338	+	0.0404930i
$582$		0			0
$583$	−37.3143	−	12.3196i	−1.54540	−	0.510227i
$584$		0			0
$585$	13.6860	−	9.94348i	0.565848	−	0.411112i
$586$		0			0
$587$	14.2667	−	43.9082i	0.588848	−	1.81229i	0.00561158	−	0.999984i	$-0.498214\pi$
$587$	14.2667	−	43.9082i	0.588848	−	1.81229i	0.583236	−	0.812303i	$-0.301786\pi$
$588$		0			0
$589$	−22.8823	−	16.6250i	−0.942850	−	0.685020i
$590$		0			0
$591$	−9.73771	−	29.9696i	−0.400556	−	1.23278i
$592$		0			0
$593$	39.4265			1.61905			0.809525	−	0.587085i	$-0.199725\pi$
$593$	39.4265			1.61905			0.809525	+	0.587085i	$0.199725\pi$
$594$		0			0
$595$	2.47347			0.101402
$596$		0			0
$597$	6.79399	+	20.9098i	0.278060	+	0.855780i
$598$		0			0
$599$	0.848455	+	0.616438i	0.0346669	+	0.0251870i	0.604984	−	0.796238i	$-0.293180\pi$
$599$	0.848455	+	0.616438i	0.0346669	+	0.0251870i	−0.570317	+	0.821425i	$0.693180\pi$
$600$		0			0
$601$	8.42065	−	25.9161i	0.343485	−	1.05714i	−0.618904	−	0.785466i	$-0.712423\pi$
$601$	8.42065	−	25.9161i	0.343485	−	1.05714i	0.962390	−	0.271673i	$-0.0875768\pi$
$602$		0			0
$603$	−24.3921	+	17.7219i	−0.993325	+	0.721693i
$604$		0			0
$605$	−8.95996	+	6.38115i	−0.364274	+	0.259431i
$606$		0			0
$607$	17.7350	−	12.8852i	0.719842	−	0.522996i	−0.166492	−	0.986043i	$-0.553244\pi$
$607$	17.7350	−	12.8852i	0.719842	−	0.522996i	0.886334	+	0.463047i	$0.153244\pi$
$608$		0			0
$609$	5.33556	−	16.4212i	0.216208	−	0.665420i
$610$		0			0
$611$	16.3035	+	11.8452i	0.659569	+	0.479205i
$612$		0			0
$613$	3.27313	+	10.0736i	0.132200	+	0.406871i	0.995144	−	0.0984293i	$-0.0313818\pi$
$613$	3.27313	+	10.0736i	0.132200	+	0.406871i	−0.862944	+	0.505300i	$0.831382\pi$
$614$		0			0
$615$	−11.0670			−0.446265
$616$		0			0
$617$	4.60402			0.185351			0.0926755	−	0.995696i	$-0.470458\pi$
$617$	4.60402			0.185351			0.0926755	+	0.995696i	$0.470458\pi$
$618$		0			0
$619$	−11.4348	−	35.1926i	−0.459603	−	1.41451i	−0.865645	−	0.500657i	$-0.833092\pi$
$619$	−11.4348	−	35.1926i	−0.459603	−	1.41451i	0.406043	−	0.913854i	$-0.366908\pi$
$620$		0			0
$621$	10.6409	+	7.73110i	0.427006	+	0.310238i
$622$		0			0
$623$	−2.60108	+	8.00529i	−0.104210	+	0.320725i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	67.9055	+	22.4195i	2.71189	+	0.895350i
$628$		0			0
$629$	−11.5608	+	8.39942i	−0.460960	+	0.334907i
$630$		0			0
$631$	7.67617	−	23.6248i	0.305583	−	0.940489i	−0.673875	−	0.738845i	$-0.735372\pi$
$631$	7.67617	−	23.6248i	0.305583	−	0.940489i	0.979459	−	0.201644i	$-0.0646284\pi$
$632$		0			0
$633$	−51.7858	−	37.6246i	−2.05830	−	1.49544i
$634$		0			0
$635$	−3.68038	−	11.3270i	−0.146051	−	0.449500i
$636$		0			0
$637$	−20.4741			−0.811213
$638$		0			0
$639$	−9.92328			−0.392559
$640$		0			0
$641$	−13.7294	−	42.2547i	−0.542278	−	1.66896i	−0.727374	−	0.686241i	$-0.759260\pi$
$641$	−13.7294	−	42.2547i	−0.542278	−	1.66896i	0.185096	−	0.982720i	$-0.440740\pi$
$642$		0			0
$643$	20.9220	+	15.2007i	0.825082	+	0.599457i	0.918164	−	0.396201i	$-0.129672\pi$
$643$	20.9220	+	15.2007i	0.825082	+	0.599457i	−0.0930818	+	0.995658i	$0.529672\pi$
$644$		0			0
$645$	−6.64596	+	20.4542i	−0.261685	+	0.805382i
$646$		0			0
$647$	15.7649	−	11.4539i	0.619782	−	0.450298i	−0.233063	−	0.972462i	$-0.574875\pi$
$647$	15.7649	−	11.4539i	0.619782	−	0.450298i	0.852845	+	0.522163i	$0.174875\pi$
$648$		0			0
$649$	9.30768	−	2.97564i	0.365358	−	0.116804i
$650$		0			0
$651$	8.65244	−	6.28636i	0.339116	−	0.246382i
$652$		0			0
$653$	−5.16979	+	15.9110i	−0.202310	+	0.622645i	0.797504	+	0.603314i	$0.206153\pi$
$653$	−5.16979	+	15.9110i	−0.202310	+	0.622645i	−0.999813	+	0.0193305i	$0.993847\pi$
$654$		0			0
$655$	9.05084	+	6.57582i	0.353646	+	0.256939i
$656$		0			0
$657$	−1.25176	−	3.85251i	−0.0488357	−	0.150301i
$658$		0			0
$659$	1.66127			0.0647137			0.0323569	−	0.999476i	$-0.489699\pi$
$659$	1.66127			0.0647137			0.0323569	+	0.999476i	$0.489699\pi$
$660$		0			0
$661$	−44.0130			−1.71191			−0.855953	−	0.517053i	$-0.827029\pi$
$661$	−44.0130			−1.71191			−0.855953	+	0.517053i	$0.827029\pi$
$662$		0			0
$663$	7.18637	+	22.1174i	0.279096	+	0.858968i
$664$		0			0
$665$	−6.39888	−	4.64906i	−0.248138	−	0.180283i
$666$		0			0
$667$	4.51879	−	13.9074i	0.174968	−	0.538497i
$668$		0			0
$669$	−36.4907	+	26.5120i	−1.41081	+	1.02501i
$670$		0			0
$671$	−0.0389168	+	8.22636i	−0.00150237	+	0.317575i
$672$		0			0
$673$	31.2239	−	22.6855i	1.20359	−	0.874462i	0.208961	−	0.977924i	$-0.432992\pi$
$673$	31.2239	−	22.6855i	1.20359	−	0.874462i	0.994633	+	0.103462i	$0.0329920\pi$
$674$		0			0
$675$	1.65499	−	5.09355i	0.0637008	−	0.196051i
$676$		0			0
$677$	31.2271	+	22.6878i	1.20016	+	0.871964i	0.994300	−	0.106619i	$-0.0340024\pi$
$677$	31.2271	+	22.6878i	1.20016	+	0.871964i	0.205855	+	0.978582i	$0.434002\pi$
$678$		0			0
$679$	−0.778549	−	2.39613i	−0.0298780	−	0.0919549i
$680$		0			0
$681$	67.9167			2.60257
$682$		0			0
$683$	0.748158			0.0286275			0.0143137	−	0.999898i	$-0.495444\pi$
$683$	0.748158			0.0286275			0.0143137	+	0.999898i	$0.495444\pi$
$684$		0			0
$685$	1.32298	+	4.07170i	0.0505484	+	0.155572i
$686$		0			0
$687$	34.1515	+	24.8125i	1.30296	+	0.946656i
$688$		0			0
$689$	−12.6276	+	38.8637i	−0.481073	+	1.48059i
$690$		0			0
$691$	4.22456	−	3.06932i	0.160710	−	0.116763i	−0.504524	−	0.863398i	$-0.668332\pi$
$691$	4.22456	−	3.06932i	0.160710	−	0.116763i	0.665234	+	0.746635i	$0.268332\pi$
$692$		0			0
$693$	−9.92603	+	13.5270i	−0.377059	+	0.513847i
$694$		0			0
$695$	4.81624	−	3.49920i	0.182690	−	0.132732i
$696$		0			0
$697$	2.91712	−	8.97796i	0.110494	−	0.340065i
$698$		0			0
$699$	−25.9895	−	18.8824i	−0.983011	−	0.714200i
$700$		0			0
$701$	−4.37506	−	13.4650i	−0.165244	−	0.508568i	0.833811	−	0.552051i	$-0.186155\pi$
$701$	−4.37506	−	13.4650i	−0.165244	−	0.508568i	−0.999054	+	0.0434831i	$0.986155\pi$
$702$		0			0
$703$	45.6952			1.72343
$704$		0			0
$705$	16.4278			0.618706
$706$		0			0
$707$	2.39792	+	7.38004i	0.0901830	+	0.277555i
$708$		0			0
$709$	13.9267	+	10.1183i	0.523028	+	0.380002i	0.817744	−	0.575583i	$-0.195225\pi$
$709$	13.9267	+	10.1183i	0.523028	+	0.380002i	−0.294715	+	0.955585i	$0.595225\pi$
$710$		0			0
$711$	18.3068	−	56.3425i	0.686558	−	2.11301i
$712$		0			0
$713$	7.32792	−	5.32404i	0.274433	−	0.199387i
$714$		0			0
$715$	6.67982	+	9.28605i	0.249811	+	0.347279i
$716$		0			0
$717$	62.3393	−	45.2922i	2.32811	−	1.69147i
$718$		0			0
$719$	8.20624	−	25.2562i	0.306041	−	0.941897i	−0.673246	−	0.739419i	$-0.735100\pi$
$719$	8.20624	−	25.2562i	0.306041	−	0.941897i	0.979287	−	0.202478i	$-0.0648996\pi$
$720$		0			0
$721$	7.91208	+	5.74846i	0.294661	+	0.214084i
$722$		0			0
$723$	9.50377	+	29.2496i	0.353449	+	1.08780i
$724$		0			0
$725$	−5.95431			−0.221138
$726$		0			0
$727$	−44.1917			−1.63898			−0.819490	−	0.573094i	$-0.805743\pi$
$727$	−44.1917			−1.63898			−0.819490	+	0.573094i	$0.805743\pi$
$728$		0			0
$729$	−13.4392	−	41.3616i	−0.497748	−	1.53191i
$730$		0			0
$731$	−14.8414	−	10.7829i	−0.548928	−	0.398819i
$732$		0			0
$733$	7.71320	−	23.7388i	0.284894	−	0.876812i	−0.701537	−	0.712633i	$-0.747502\pi$
$733$	7.71320	−	23.7388i	0.284894	−	0.876812i	0.986431	−	0.164179i	$-0.0524975\pi$
$734$		0			0
$735$	−13.5026	+	9.81022i	−0.498051	+	0.361855i
$736$		0			0
$737$	−11.9052	−	16.5502i	−0.438534	−	0.609635i
$738$		0			0
$739$	17.1789	−	12.4812i	0.631934	−	0.459127i	−0.225135	−	0.974327i	$-0.572282\pi$
$739$	17.1789	−	12.4812i	0.631934	−	0.459127i	0.857070	+	0.515200i	$0.172282\pi$
$740$		0			0
$741$	22.9800	−	70.7251i	0.844190	−	2.59815i
$742$		0			0
$743$	−24.7986	−	18.0172i	−0.909772	−	0.660988i	0.0311852	−	0.999514i	$-0.490072\pi$
$743$	−24.7986	−	18.0172i	−0.909772	−	0.660988i	−0.940957	+	0.338526i	$0.890072\pi$
$744$		0			0
$745$	1.16946	+	3.59922i	0.0428456	+	0.131865i
$746$		0			0
$747$	−7.89694			−0.288934
$748$		0			0
$749$	−4.79259			−0.175118
$750$		0			0
$751$	9.36548	+	28.8240i	0.341751	+	1.05180i	0.963300	+	0.268427i	$0.0865037\pi$
$751$	9.36548	+	28.8240i	0.341751	+	1.05180i	−0.621549	+	0.783375i	$0.713496\pi$
$752$		0			0
$753$	39.1939	+	28.4760i	1.42831	+	1.03772i
$754$		0			0
$755$	−7.52661	+	23.1645i	−0.273922	+	0.843044i
$756$		0			0
$757$	28.2099	−	20.4957i	1.02531	−	0.744929i	0.0579427	−	0.998320i	$-0.481546\pi$
$757$	28.2099	−	20.4957i	1.02531	−	0.744929i	0.967364	+	0.253391i	$0.0815459\pi$
$758$		0			0
$759$	−13.5483	+	18.4633i	−0.491772	+	0.670176i
$760$		0			0
$761$	2.17603	−	1.58098i	0.0788809	−	0.0573104i	−0.547646	−	0.836710i	$-0.684476\pi$
$761$	2.17603	−	1.58098i	0.0788809	−	0.0573104i	0.626527	+	0.779400i	$0.284476\pi$
$762$		0			0
$763$	1.69819	−	5.22650i	0.0614787	−	0.189212i
$764$		0			0
$765$	9.51642	+	6.91409i	0.344067	+	0.249979i
$766$		0			0
$767$	−3.14015	−	9.66440i	−0.113384	−	0.348961i
$768$		0			0
$769$	−32.5735			−1.17463			−0.587315	−	0.809359i	$-0.699815\pi$
$769$	−32.5735			−1.17463			−0.587315	+	0.809359i	$0.699815\pi$
$770$		0			0
$771$	52.0010			1.87277
$772$		0			0
$773$	12.8748	+	39.6246i	0.463074	+	1.42520i	0.861388	+	0.507947i	$0.169595\pi$
$773$	12.8748	+	39.6246i	0.463074	+	1.42520i	−0.398314	+	0.917249i	$0.630405\pi$
$774$		0			0
$775$	−2.98382	−	2.16787i	−0.107182	−	0.0778722i
$776$		0			0
$777$	−5.33938	+	16.4329i	−0.191549	+	0.589528i
$778$		0			0
$779$	−24.4213	+	17.7431i	−0.874984	+	0.635713i
$780$		0			0
$781$	0.0317431	−	6.70994i	0.00113586	−	0.240101i
$782$		0			0
$783$	25.7990	−	18.7441i	0.921983	−	0.669860i
$784$		0			0
$785$	−2.23484	+	6.87813i	−0.0797649	+	0.245491i
$786$		0			0
$787$	−29.0605	−	21.1137i	−1.03589	−	0.752622i	−0.0664148	−	0.997792i	$-0.521156\pi$
$787$	−29.0605	−	21.1137i	−1.03589	−	0.752622i	−0.969480	+	0.245170i	$0.921156\pi$
$788$		0			0
$789$	−3.20712	−	9.87049i	−0.114176	−	0.351399i
$790$		0			0
$791$	−0.314468			−0.0111812
$792$		0			0
$793$	8.55476			0.303789
$794$		0			0
$795$	10.2938	+	31.6811i	0.365084	+	1.12361i
$796$		0			0
$797$	25.6618	+	18.6444i	0.908987	+	0.660418i	0.940759	−	0.339077i	$-0.110115\pi$
$797$	25.6618	+	18.6444i	0.908987	+	0.660418i	−0.0317713	+	0.999495i	$0.510115\pi$
$798$		0			0
$799$	−4.33014	+	13.3268i	−0.153189	+	0.471468i
$800$		0			0
$801$	−32.3845	+	23.5287i	−1.14425	+	0.831347i
$802$		0			0
$803$	2.60900	−	0.834092i	0.0920698	−	0.0294345i
$804$		0			0
$805$	2.04920	−	1.48883i	0.0722249	−	0.0524744i
$806$		0			0
$807$	−8.64050	+	26.5927i	−0.304160	+	0.936108i
$808$		0			0
$809$	6.88936	+	5.00541i	0.242217	+	0.175981i	0.702270	−	0.711910i	$-0.252170\pi$
$809$	6.88936	+	5.00541i	0.242217	+	0.175981i	−0.460053	+	0.887891i	$0.652170\pi$
$810$		0			0
$811$	−2.79052	−	8.58832i	−0.0979882	−	0.301577i	0.890033	−	0.455897i	$-0.150681\pi$
$811$	−2.79052	−	8.58832i	−0.0979882	−	0.301577i	−0.988021	+	0.154320i	$0.950681\pi$
$812$		0			0
$813$	−3.52472			−0.123617
$814$		0			0
$815$	18.6892			0.654653
$816$		0			0
$817$	18.1275	+	55.7908i	0.634202	+	1.95187i
$818$		0			0
$819$	14.1155	+	10.2555i	0.493235	+	0.358356i
$820$		0			0
$821$	−16.7866	+	51.6638i	−0.585856	+	1.80308i	0.00994979	+	0.999950i	$0.496833\pi$
$821$	−16.7866	+	51.6638i	−0.585856	+	1.80308i	−0.595806	+	0.803129i	$0.703167\pi$
$822$		0			0
$823$	14.4486	−	10.4975i	0.503646	−	0.365920i	−0.306762	−	0.951786i	$-0.599245\pi$
$823$	14.4486	−	10.4975i	0.503646	−	0.365920i	0.810408	+	0.585866i	$0.199245\pi$
$824$		0			0
$825$	8.85477	+	2.92347i	0.308284	+	0.101782i
$826$		0			0
$827$	−42.0280	+	30.5351i	−1.46146	+	1.06181i	−0.478474	+	0.878102i	$0.658810\pi$
$827$	−42.0280	+	30.5351i	−1.46146	+	1.06181i	−0.982981	+	0.183708i	$0.941190\pi$
$828$		0			0
$829$	−6.10185	+	18.7796i	−0.211926	+	0.652241i	0.787431	+	0.616402i	$0.211410\pi$
$829$	−6.10185	+	18.7796i	−0.211926	+	0.652241i	−0.999358	+	0.0358392i	$0.988590\pi$
$830$		0			0
$831$	18.4091	+	13.3750i	0.638603	+	0.463972i
$832$		0			0
$833$	−4.39930	−	13.5396i	−0.152427	−	0.469121i
$834$		0			0
$835$	7.85328			0.271774
$836$		0			0
$837$	19.7528			0.682757
$838$		0			0
$839$	1.27207	+	3.91502i	0.0439166	+	0.135162i	0.970611	−	0.240655i	$-0.0773623\pi$
$839$	1.27207	+	3.91502i	0.0439166	+	0.135162i	−0.926694	+	0.375817i	$0.877362\pi$
$840$		0			0
$841$	−5.22128	−	3.79348i	−0.180044	−	0.130810i
$842$		0			0
$843$	22.0422	−	67.8389i	0.759173	−	2.33649i
$844$		0			0
$845$	−0.893540	+	0.649194i	−0.0307387	+	0.0223330i
$846$		0			0
$847$	−9.11494	−	6.75507i	−0.313193	−	0.232107i
$848$		0			0
$849$	−46.4983	+	33.7830i	−1.59582	+	1.15943i
$850$		0			0
$851$	−4.52203	+	13.9174i	−0.155013	+	0.477081i
$852$		0			0
$853$	−4.45190	−	3.23449i	−0.152430	−	0.110747i	0.508956	−	0.860792i	$-0.330032\pi$
$853$	−4.45190	−	3.23449i	−0.152430	−	0.110747i	−0.661386	+	0.750046i	$0.730032\pi$
$854$		0			0
$855$	−11.6235	−	35.7736i	−0.397516	−	1.22343i
$856$		0			0
$857$	−26.9281			−0.919847			−0.459924	−	0.887959i	$-0.652123\pi$
$857$	−26.9281			−0.919847			−0.459924	+	0.887959i	$0.652123\pi$
$858$		0			0
$859$	−19.1519			−0.653456			−0.326728	−	0.945118i	$-0.605946\pi$
$859$	−19.1519			−0.653456			−0.326728	+	0.945118i	$0.605946\pi$
$860$		0			0
$861$	−3.52721	−	10.8556i	−0.120207	−	0.369960i
$862$		0			0
$863$	4.01394	+	2.91630i	0.136636	+	0.0992720i	0.654004	−	0.756491i	$-0.273088\pi$
$863$	4.01394	+	2.91630i	0.136636	+	0.0992720i	−0.517368	+	0.855763i	$0.673088\pi$
$864$		0			0
$865$	−3.46244	+	10.6563i	−0.117726	+	0.362325i
$866$		0			0
$867$	25.5860	−	18.5893i	0.868946	−	0.631326i
$868$		0			0
$869$	38.0392	+	12.5589i	1.29039	+	0.426033i
$870$		0			0
$871$	−17.1520	+	12.4616i	−0.581172	+	0.422246i
$872$		0			0
$873$	3.70250	−	11.3951i	0.125311	−	0.385667i
$874$		0			0
$875$	−0.834404	−	0.606230i	−0.0282080	−	0.0204943i
$876$		0			0
$877$	−8.40691	−	25.8738i	−0.283881	−	0.873696i	−0.986732	−	0.162359i	$-0.948090\pi$
$877$	−8.40691	−	25.8738i	−0.283881	−	0.873696i	0.702851	−	0.711338i	$-0.251910\pi$
$878$		0			0
$879$	7.16686			0.241732
$880$		0			0
$881$	10.3570			0.348935			0.174467	−	0.984663i	$-0.444180\pi$
$881$	10.3570			0.348935			0.174467	+	0.984663i	$0.444180\pi$
$882$		0			0
$883$	−2.28515	−	7.03296i	−0.0769014	−	0.236678i	0.905215	−	0.424954i	$-0.139710\pi$
$883$	−2.28515	−	7.03296i	−0.0769014	−	0.236678i	−0.982116	+	0.188276i	$0.939710\pi$
$884$		0			0
$885$	−6.70165	−	4.86903i	−0.225274	−	0.163671i
$886$		0			0
$887$	5.58054	−	17.1752i	0.187376	−	0.576685i	−0.812605	−	0.582815i	$-0.801951\pi$
$887$	5.58054	−	17.1752i	0.187376	−	0.576685i	0.999981	+	0.00612989i	$0.00195122\pi$
$888$		0			0
$889$	9.93772	−	7.22018i	0.333300	−	0.242157i
$890$		0			0
$891$	−1.08414	+	0.346596i	−0.0363200	+	0.0116114i
$892$		0			0
$893$	36.2507	−	26.3377i	1.21309	−	0.881358i
$894$		0			0
$895$	0.452595	−	1.39295i	0.0151286	−	0.0465610i
$896$		0			0
$897$	19.2666	+	13.9980i	0.643293	+	0.467380i
$898$		0			0
$899$	−6.78623	−	20.8859i	−0.226334	−	0.696583i
$900$		0			0
$901$	−28.4141			−0.946612
$902$		0			0
$903$	−22.1817			−0.738160
$904$		0			0
$905$	−2.87046	−	8.83437i	−0.0954173	−	0.293664i
$906$		0			0
$907$	21.2748	+	15.4570i	0.706417	+	0.513242i	0.882016	−	0.471220i	$-0.156186\pi$
$907$	21.2748	+	15.4570i	0.706417	+	0.513242i	−0.175599	+	0.984462i	$0.556186\pi$
$908$		0			0
$909$	−11.4036	+	35.0968i	−0.378235	+	1.16409i
$910$		0			0
$911$	23.1774	−	16.8394i	0.767902	−	0.557913i	−0.133422	−	0.991059i	$-0.542597\pi$
$911$	23.1774	−	16.8394i	0.767902	−	0.557913i	0.901324	+	0.433146i	$0.142597\pi$
$912$		0			0
$913$	0.0252611	−	5.33976i	0.000836020	−	0.176720i
$914$		0			0
$915$	5.64185	−	4.09904i	0.186514	−	0.135510i
$916$		0			0
$917$	−3.56560	+	10.9738i	−0.117746	+	0.362386i
$918$		0			0
$919$	31.4358	+	22.8394i	1.03697	+	0.753404i	0.969692	−	0.244330i	$-0.0785681\pi$
$919$	31.4358	+	22.8394i	1.03697	+	0.753404i	0.0672794	+	0.997734i	$0.478568\pi$
$920$		0			0
$921$	−7.81306	−	24.0461i	−0.257449	−	0.792347i
$922$		0			0
$923$	−6.97781			−0.229677
$924$		0			0
$925$	5.95858			0.195917
$926$		0			0
$927$	14.3722	+	44.2332i	0.472046	+	1.45281i
$928$		0			0
$929$	−6.00397	−	4.36214i	−0.196984	−	0.143117i	0.484921	−	0.874558i	$-0.338848\pi$
$929$	−6.00397	−	4.36214i	−0.196984	−	0.143117i	−0.681905	+	0.731441i	$0.738848\pi$
$930$		0			0
$931$	−14.0677	+	43.2959i	−0.461050	+	1.41897i
$932$		0			0
$933$	−45.7722	+	33.2554i	−1.49851	+	1.08873i
$934$		0			0
$935$	−4.70562	+	6.41272i	−0.153890	+	0.209718i
$936$		0			0
$937$	12.0834	−	8.77914i	0.394749	−	0.286802i	−0.372650	−	0.927972i	$-0.621551\pi$
$937$	12.0834	−	8.77914i	0.394749	−	0.286802i	0.767399	+	0.641170i	$0.221551\pi$
$938$		0			0
$939$	6.17282	−	18.9980i	0.201442	−	0.619975i
$940$		0			0
$941$	42.3447	+	30.7652i	1.38040	+	1.00292i	0.996843	+	0.0793986i	$0.0253000\pi$
$941$	42.3447	+	30.7652i	1.38040	+	1.00292i	0.383554	+	0.923518i	$0.374700\pi$
$942$		0			0
$943$	−2.98727	−	9.19386i	−0.0972788	−	0.299393i
$944$		0			0
$945$	5.52373			0.179687
$946$		0			0
$947$	3.69553			0.120088			0.0600442	−	0.998196i	$-0.480876\pi$
$947$	3.69553			0.120088			0.0600442	+	0.998196i	$0.480876\pi$
$948$		0			0
$949$	−0.880206	−	2.70899i	−0.0285727	−	0.0879377i
$950$		0			0
$951$	−5.21618	−	3.78978i	−0.169146	−	0.122892i
$952$		0			0
$953$	13.3349	−	41.0406i	0.431959	−	1.32943i	−0.464211	−	0.885724i	$-0.653662\pi$
$953$	13.3349	−	41.0406i	0.431959	−	1.32943i	0.896171	−	0.443709i	$-0.146338\pi$
$954$		0			0
$955$	3.61870	−	2.62914i	0.117098	−	0.0850770i
$956$		0			0
$957$	32.4229	+	45.0732i	1.04808	+	1.45701i
$958$		0			0
$959$	−3.57229	+	2.59542i	−0.115355	+	0.0838104i
$960$		0			0
$961$	−5.37602	+	16.5457i	−0.173420	+	0.533732i
$962$		0			0
$963$	−18.4390	−	13.3967i	−0.594189	−	0.431704i
$964$		0			0
$965$	7.00418	+	21.5567i	0.225473	+	0.693933i
$966$		0			0
$967$	29.2144			0.939471			0.469736	−	0.882807i	$-0.344349\pi$
$967$	29.2144			0.939471			0.469736	+	0.882807i	$0.344349\pi$
$968$		0			0
$969$	51.7087			1.66112
$970$		0			0
$971$	8.15948	+	25.1123i	0.261850	+	0.805892i	0.992402	+	0.123035i	$0.0392628\pi$
$971$	8.15948	+	25.1123i	0.261850	+	0.805892i	−0.730552	+	0.682857i	$0.760737\pi$
$972$		0			0
$973$	4.96737	+	3.60901i	0.159247	+	0.115699i
$974$		0			0
$975$	2.99655	−	9.22244i	0.0959664	−	0.295354i
$976$		0			0
$977$	12.8176	−	9.31251i	0.410070	−	0.297934i	−0.363560	−	0.931571i	$-0.618439\pi$
$977$	12.8176	−	9.31251i	0.410070	−	0.297934i	0.773630	+	0.633637i	$0.218439\pi$
$978$		0			0
$979$	−15.8061	−	21.9731i	−0.505166	−	0.702263i
$980$		0			0
$981$	21.1432	−	15.3615i	0.675051	−	0.490454i
$982$		0			0
$983$	−10.8477	+	33.3858i	−0.345988	+	1.06484i	0.615064	+	0.788477i	$0.289130\pi$
$983$	−10.8477	+	33.3858i	−0.345988	+	1.06484i	−0.961053	+	0.276365i	$0.910870\pi$
$984$		0			0
$985$	−9.06744	−	6.58788i	−0.288913	−	0.209907i
$986$		0			0
$987$	5.23576	+	16.1140i	0.166656	+	0.512915i
$988$		0			0
$989$	−18.7861			−0.597363
$990$		0			0
$991$	−18.9700			−0.602600			−0.301300	−	0.953529i	$-0.597421\pi$
$991$	−18.9700			−0.602600			−0.301300	+	0.953529i	$0.597421\pi$
$992$		0			0
$993$	−13.3756	−	41.1658i	−0.424461	−	1.30636i
$994$		0			0
$995$	6.32635	+	4.59636i	0.200559	+	0.145714i
$996$		0			0
$997$	9.31213	−	28.6598i	0.294918	−	0.907665i	−0.688331	−	0.725397i	$-0.741656\pi$
$997$	9.31213	−	28.6598i	0.294918	−	0.907665i	0.983249	−	0.182268i	$-0.0583438\pi$
$998$		0			0
$999$	−25.8175	+	18.7575i	−0.816830	+	0.593462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bo.h.641.2		8
4.3	odd	2		55.2.g.b.36.2	yes	8
11.2	odd	10		9680.2.a.cm.1.4		4
11.4	even	5	inner	880.2.bo.h.81.2		8
11.9	even	5		9680.2.a.cn.1.4		4
12.11	even	2		495.2.n.e.91.1		8
20.3	even	4		275.2.z.a.124.2		16
20.7	even	4		275.2.z.a.124.3		16
20.19	odd	2		275.2.h.a.201.1		8
44.3	odd	10		605.2.g.m.511.1		8
44.7	even	10		605.2.g.k.81.1		8
44.15	odd	10		55.2.g.b.26.2	✓	8
44.19	even	10		605.2.g.e.511.2		8
44.27	odd	10		605.2.g.m.251.1		8
44.31	odd	10		605.2.a.j.1.2		4
44.35	even	10		605.2.a.k.1.3		4
44.39	even	10		605.2.g.e.251.2		8
44.43	even	2		605.2.g.k.366.1		8
132.35	odd	10		5445.2.a.bi.1.2		4
132.59	even	10		495.2.n.e.136.1		8
132.119	even	10		5445.2.a.bp.1.3		4
220.59	odd	10		275.2.h.a.26.1		8
220.79	even	10		3025.2.a.w.1.2		4
220.103	even	20		275.2.z.a.224.3		16
220.119	odd	10		3025.2.a.bd.1.3		4
220.147	even	20		275.2.z.a.224.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.26.2	✓	8	44.15	odd	10
55.2.g.b.36.2	yes	8	4.3	odd	2
275.2.h.a.26.1		8	220.59	odd	10
275.2.h.a.201.1		8	20.19	odd	2
275.2.z.a.124.2		16	20.3	even	4
275.2.z.a.124.3		16	20.7	even	4
275.2.z.a.224.2		16	220.147	even	20
275.2.z.a.224.3		16	220.103	even	20
495.2.n.e.91.1		8	12.11	even	2
495.2.n.e.136.1		8	132.59	even	10
605.2.a.j.1.2		4	44.31	odd	10
605.2.a.k.1.3		4	44.35	even	10
605.2.g.e.251.2		8	44.39	even	10
605.2.g.e.511.2		8	44.19	even	10
605.2.g.k.81.1		8	44.7	even	10
605.2.g.k.366.1		8	44.43	even	2
605.2.g.m.251.1		8	44.27	odd	10
605.2.g.m.511.1		8	44.3	odd	10
880.2.bo.h.81.2		8	11.4	even	5	inner
880.2.bo.h.641.2		8	1.1	even	1	trivial
3025.2.a.w.1.2		4	220.79	even	10
3025.2.a.bd.1.3		4	220.119	odd	10
5445.2.a.bi.1.2		4	132.35	odd	10
5445.2.a.bp.1.3		4	132.119	even	10
9680.2.a.cm.1.4		4	11.2	odd	10
9680.2.a.cn.1.4		4	11.9	even	5

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bo (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.868820 + 2.67395i) q^{3} +(0.809017 + 0.587785i) q^{5} +(-0.318714 + 0.980901i) q^{7} +(-3.96813 + 2.88301i) q^{9} +O(q^{10})\)	\(q+(0.868820 + 2.67395i) q^{3} +(0.809017 + 0.587785i) q^{5} +(-0.318714 + 0.980901i) q^{7} +(-3.96813 + 2.88301i) q^{9} +(-1.93675 - 2.69240i) q^{11} +(-2.79029 + 2.02726i) q^{13} +(-0.868820 + 2.67395i) q^{15} +(-1.94020 - 1.40964i) q^{17} +(2.36979 + 7.29347i) q^{19} -2.89979 q^{21} -2.45589 q^{23} +(0.309017 + 0.951057i) q^{25} +(-4.33283 - 3.14799i) q^{27} +(-1.83998 + 5.66289i) q^{29} +(-2.98382 + 2.16787i) q^{31} +(5.51666 - 7.51798i) q^{33} +(-0.834404 + 0.606230i) q^{35} +(1.84130 - 5.66694i) q^{37} +(-7.84507 - 5.69978i) q^{39} +(1.21637 + 3.74360i) q^{41} +7.64941 q^{43} -4.90488 q^{45} +(-1.80557 - 5.55697i) q^{47} +(4.80253 + 3.48924i) q^{49} +(2.08362 - 6.41272i) q^{51} +(9.58526 - 6.96410i) q^{53} +(0.0156899 - 3.31659i) q^{55} +(-17.4435 + 12.6734i) q^{57} +(-0.910456 + 2.80210i) q^{59} +(-2.00666 - 1.45792i) q^{61} +(-1.56325 - 4.81120i) q^{63} -3.44899 q^{65} +6.14702 q^{67} +(-2.13372 - 6.56693i) q^{69} +(1.63676 + 1.18918i) q^{71} +(-0.255207 + 0.785446i) q^{73} +(-2.27460 + 1.65259i) q^{75} +(3.25824 - 1.04165i) q^{77} +(-9.77146 + 7.09938i) q^{79} +(0.106048 - 0.326382i) q^{81} +(1.30253 + 0.946345i) q^{83} +(-0.741089 - 2.28084i) q^{85} -16.7409 q^{87} +8.16116 q^{89} +(-1.09924 - 3.38312i) q^{91} +(-8.38919 - 6.09510i) q^{93} +(-2.36979 + 7.29347i) q^{95} +(-1.97625 + 1.43583i) q^{97} +(15.4475 + 5.10011i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{3} + 2 q^{5} + q^{7} - 5 q^{9}+O(q^{10}) \) 8 * q + 5 * q^3 + 2 * q^5 + q^7 - 5 * q^9	\( 8 q + 5 q^{3} + 2 q^{5} + q^{7} - 5 q^{9} - 3 q^{11} - 2 q^{13} - 5 q^{15} - 13 q^{17} - 15 q^{19} - 20 q^{21} - 10 q^{23} - 2 q^{25} - 10 q^{27} - 9 q^{29} + 10 q^{31} + 5 q^{33} + 4 q^{35} + 24 q^{37} - 21 q^{39} + 8 q^{41} + 38 q^{43} + q^{49} - q^{51} + 13 q^{53} - 7 q^{55} - 45 q^{57} + 27 q^{59} + 6 q^{61} - 25 q^{63} + 2 q^{65} + 38 q^{67} - q^{69} + 20 q^{71} + 13 q^{73} - 5 q^{75} + 34 q^{77} - 37 q^{79} + 8 q^{81} - 27 q^{83} - 12 q^{85} - 38 q^{87} - 16 q^{89} - 44 q^{91} - 35 q^{93} + 15 q^{95} + 24 q^{97} + 20 q^{99}+O(q^{100}) \) 8 * q + 5 * q^3 + 2 * q^5 + q^7 - 5 * q^9 - 3 * q^11 - 2 * q^13 - 5 * q^15 - 13 * q^17 - 15 * q^19 - 20 * q^21 - 10 * q^23 - 2 * q^25 - 10 * q^27 - 9 * q^29 + 10 * q^31 + 5 * q^33 + 4 * q^35 + 24 * q^37 - 21 * q^39 + 8 * q^41 + 38 * q^43 + q^49 - q^51 + 13 * q^53 - 7 * q^55 - 45 * q^57 + 27 * q^59 + 6 * q^61 - 25 * q^63 + 2 * q^65 + 38 * q^67 - q^69 + 20 * q^71 + 13 * q^73 - 5 * q^75 + 34 * q^77 - 37 * q^79 + 8 * q^81 - 27 * q^83 - 12 * q^85 - 38 * q^87 - 16 * q^89 - 44 * q^91 - 35 * q^93 + 15 * q^95 + 24 * q^97 + 20 * q^99

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