LMFDB - Embedded newform 880.2.bo.j.801.3

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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 15 x^{10} - 22 x^{9} + 89 x^{8} - 118 x^{7} + 205 x^{6} - 68 x^{5} + 1061 x^{4} + \cdots + 400 $ x^12 - 2x^11 + 15x^10 - 22x^9 + 89x^8 - 118x^7 + 205x^6 - 68x^5 + 1061x^4 - 1490x^3 + 2760x^2 - 1600*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 440)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			801.3
Root			$1.65720 - 1.20403i$ of defining polynomial
Character	$\chi$	$=$	880.801
Dual form			880.2.bo.j.401.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.68141 - 1.94816i) q^{3} +(-0.309017 - 0.951057i) q^{5} +(0.150443 + 0.109303i) q^{7} +(2.46759 - 7.59446i) q^{9} +(3.31662 + 0.00161122i) q^{11} +(0.931229 - 2.86603i) q^{13} +(-2.68141 - 1.94816i) q^{15} +(1.58167 + 4.86789i) q^{17} +(-3.93381 + 2.85808i) q^{19} +0.616340 q^{21} -6.20391 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-5.10598 - 15.7146i) q^{27} +(0.154031 + 0.111910i) q^{29} +(-2.49095 + 7.66636i) q^{31} +(8.89637 - 6.45699i) q^{33} +(0.0574641 - 0.176856i) q^{35} +(2.07098 + 1.50466i) q^{37} +(-3.08647 - 9.49918i) q^{39} +(7.24600 - 5.26453i) q^{41} +7.83103 q^{43} -7.98529 q^{45} +(-4.28839 + 3.11570i) q^{47} +(-2.15243 - 6.62451i) q^{49} +(13.7245 + 9.97146i) q^{51} +(0.401996 - 1.23722i) q^{53} +(-1.02336 - 3.15480i) q^{55} +(-4.98017 + 15.3274i) q^{57} +(-0.480227 - 0.348906i) q^{59} +(-0.350728 - 1.07943i) q^{61} +(1.20133 - 0.872818i) q^{63} -3.01352 q^{65} +1.73474 q^{67} +(-16.6352 + 12.0862i) q^{69} +(-4.03917 - 12.4313i) q^{71} +(-0.723322 - 0.525524i) q^{73} +(-1.02421 + 3.15219i) q^{75} +(0.498787 + 0.362760i) q^{77} +(-4.11137 + 12.6535i) q^{79} +(-24.9250 - 18.1091i) q^{81} +(5.23780 + 16.1203i) q^{83} +(4.14087 - 3.00852i) q^{85} +0.631040 q^{87} -7.22907 q^{89} +(0.453363 - 0.329388i) q^{91} +(8.25603 + 25.4094i) q^{93} +(3.93381 + 2.85808i) q^{95} +(1.04923 - 3.22920i) q^{97} +(8.19631 - 25.1840i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{3} + 3 q^{5} + 8 q^{7} + 10 q^{9} + 4 q^{11} - 7 q^{13} - q^{15} + 7 q^{17} - 3 q^{19} + 4 q^{21} - 36 q^{23} - 3 q^{25} - 8 q^{27} + 13 q^{29} - 2 q^{31} - 19 q^{33} + 2 q^{35} - 22 q^{37}+ \cdots + 79 q^{99}+O(q^{100}) $ 12 * q + q^3 + 3 * q^5 + 8 * q^7 + 10 * q^9 + 4 * q^11 - 7 * q^13 - q^15 + 7 * q^17 - 3 * q^19 + 4 * q^21 - 36 * q^23 - 3 * q^25 - 8 * q^27 + 13 * q^29 - 2 * q^31 - 19 * q^33 + 2 * q^35 - 22 * q^37 + q^39 + 7 * q^41 - 6 * q^43 - 20 * q^45 + 2 * q^47 - 19 * q^49 + 33 * q^51 + 3 * q^53 - 4 * q^55 - 25 * q^57 - 19 * q^59 + 22 * q^61 + 2 * q^63 + 12 * q^65 - 22 * q^67 + 21 * q^69 - 44 * q^71 + 17 * q^73 + q^75 - 38 * q^77 + 43 * q^79 - 85 * q^81 + 15 * q^83 + 18 * q^85 - 50 * q^87 + 2 * q^89 - 59 * q^91 + 5 * q^93 + 3 * q^95 - 20 * q^97 + 79 * q^99

Character values

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

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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
$3$	2.68141	−	1.94816i	1.54811	−	1.12477i	0.603135	−	0.797639i	$-0.293918\pi$
$3$	2.68141	−	1.94816i	1.54811	−	1.12477i	0.944979	−	0.327131i	$-0.106082\pi$
$4$		0			0
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$		0			0
$7$	0.150443	+	0.109303i	0.0568621	+	0.0413128i	0.615853	−	0.787861i	$-0.288811\pi$
$7$	0.150443	+	0.109303i	0.0568621	+	0.0413128i	−0.558991	+	0.829174i	$0.688811\pi$
$8$		0			0
$9$	2.46759	−	7.59446i	0.822530	−	2.53149i
$10$		0			0
$11$	3.31662	+	0.00161122i	1.00000	+	0.000485801i
$11$	3.31662	+	0.00161122i	1.00000	+	0.000485801i
$12$		0			0
$13$	0.931229	−	2.86603i	0.258276	−	0.794893i	−0.734890	−	0.678186i	$-0.762766\pi$
$13$	0.931229	−	2.86603i	0.258276	−	0.794893i	0.993166	−	0.116707i	$-0.0372338\pi$
$14$		0			0
$15$	−2.68141	−	1.94816i	−0.692337	−	0.503013i
$16$		0			0
$17$	1.58167	+	4.86789i	0.383612	+	1.18064i	0.937482	+	0.348033i	$0.113150\pi$
$17$	1.58167	+	4.86789i	0.383612	+	1.18064i	−0.553870	+	0.832603i	$0.686850\pi$
$18$		0			0
$19$	−3.93381	+	2.85808i	−0.902478	+	0.655689i	−0.939101	−	0.343640i	$-0.888340\pi$
$19$	−3.93381	+	2.85808i	−0.902478	+	0.655689i	0.0366231	+	0.999329i	$0.488340\pi$
$20$		0			0
$21$	0.616340			0.134496
$22$		0			0
$23$	−6.20391			−1.29361			−0.646803	−	0.762657i	$-0.723894\pi$
$23$	−6.20391			−1.29361			−0.646803	+	0.762657i	$0.723894\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$		0			0
$27$	−5.10598	−	15.7146i	−0.982646	−	3.02427i
$28$		0			0
$29$	0.154031	+	0.111910i	0.0286029	+	0.0207812i	0.601995	−	0.798500i	$-0.294373\pi$
$29$	0.154031	+	0.111910i	0.0286029	+	0.0207812i	−0.573392	+	0.819281i	$0.694373\pi$
$30$		0			0
$31$	−2.49095	+	7.66636i	−0.447388	+	1.37692i	0.432455	+	0.901655i	$0.357647\pi$
$31$	−2.49095	+	7.66636i	−0.447388	+	1.37692i	−0.879843	+	0.475264i	$0.842353\pi$
$32$		0			0
$33$	8.89637	−	6.45699i	1.54866	−	1.12402i
$34$		0			0
$35$	0.0574641	−	0.176856i	0.00971321	−	0.0298942i
$36$		0			0
$37$	2.07098	+	1.50466i	0.340468	+	0.247364i	0.744859	−	0.667222i	$-0.232517\pi$
$37$	2.07098	+	1.50466i	0.340468	+	0.247364i	−0.404391	+	0.914586i	$0.632517\pi$
$38$		0			0
$39$	−3.08647	−	9.49918i	−0.494231	−	1.52109i
$40$		0			0
$41$	7.24600	−	5.26453i	1.13164	−	0.822181i	0.145703	−	0.989328i	$-0.453456\pi$
$41$	7.24600	−	5.26453i	1.13164	−	0.822181i	0.985932	+	0.167147i	$0.0534555\pi$
$42$		0			0
$43$	7.83103			1.19422			0.597111	−	0.802159i	$-0.296315\pi$
$43$	7.83103			1.19422			0.597111	+	0.802159i	$0.296315\pi$
$44$		0			0
$45$	−7.98529			−1.19038
$46$		0			0
$47$	−4.28839	+	3.11570i	−0.625526	+	0.454472i	−0.854848	−	0.518879i	$-0.826349\pi$
$47$	−4.28839	+	3.11570i	−0.625526	+	0.454472i	0.229321	+	0.973351i	$0.426349\pi$
$48$		0			0
$49$	−2.15243	−	6.62451i	−0.307490	−	0.946358i
$50$		0			0
$51$	13.7245	+	9.97146i	1.92182	+	1.39628i
$52$		0			0
$53$	0.401996	−	1.23722i	0.0552184	−	0.169945i	−0.919644	−	0.392754i	$-0.871523\pi$
$53$	0.401996	−	1.23722i	0.0552184	−	0.169945i	0.974862	+	0.222809i	$0.0715226\pi$
$54$		0			0
$55$	−1.02336	−	3.15480i	−0.137990	−	0.425392i
$56$		0			0
$57$	−4.98017	+	15.3274i	−0.659639	+	2.03016i
$58$		0			0
$59$	−0.480227	−	0.348906i	−0.0625203	−	0.0454236i	0.556086	−	0.831125i	$-0.312302\pi$
$59$	−0.480227	−	0.348906i	−0.0625203	−	0.0454236i	−0.618606	+	0.785701i	$0.712302\pi$
$60$		0			0
$61$	−0.350728	−	1.07943i	−0.0449061	−	0.138207i	0.926090	−	0.377304i	$-0.123149\pi$
$61$	−0.350728	−	1.07943i	−0.0449061	−	0.138207i	−0.970996	+	0.239097i	$0.923149\pi$
$62$		0			0
$63$	1.20133	−	0.872818i	0.151354	−	0.109965i
$64$		0			0
$65$	−3.01352			−0.373781
$66$		0			0
$67$	1.73474			0.211932			0.105966	−	0.994370i	$-0.466207\pi$
$67$	1.73474			0.211932			0.105966	+	0.994370i	$0.466207\pi$
$68$		0			0
$69$	−16.6352	+	12.0862i	−2.00265	+	1.45501i
$70$		0			0
$71$	−4.03917	−	12.4313i	−0.479361	−	1.47532i	−0.839984	−	0.542611i	$-0.817436\pi$
$71$	−4.03917	−	12.4313i	−0.479361	−	1.47532i	0.360623	−	0.932712i	$-0.382564\pi$
$72$		0			0
$73$	−0.723322	−	0.525524i	−0.0846584	−	0.0615079i	0.544651	−	0.838663i	$-0.316662\pi$
$73$	−0.723322	−	0.525524i	−0.0846584	−	0.0615079i	−0.629309	+	0.777155i	$0.716662\pi$
$74$		0			0
$75$	−1.02421	+	3.15219i	−0.118265	+	0.363983i
$76$		0			0
$77$	0.498787	+	0.362760i	0.0568420	+	0.0413404i
$78$		0			0
$79$	−4.11137	+	12.6535i	−0.462565	+	1.42363i	0.399454	+	0.916753i	$0.369200\pi$
$79$	−4.11137	+	12.6535i	−0.462565	+	1.42363i	−0.862019	+	0.506876i	$0.830800\pi$
$80$		0			0
$81$	−24.9250	−	18.1091i	−2.76945	−	2.01212i
$82$		0			0
$83$	5.23780	+	16.1203i	0.574924	+	1.76943i	0.636439	+	0.771327i	$0.280407\pi$
$83$	5.23780	+	16.1203i	0.574924	+	1.76943i	−0.0615158	+	0.998106i	$0.519593\pi$
$84$		0			0
$85$	4.14087	−	3.00852i	0.449141	−	0.326320i
$86$		0			0
$87$	0.631040			0.0676546
$88$		0			0
$89$	−7.22907			−0.766280			−0.383140	−	0.923690i	$-0.625157\pi$
$89$	−7.22907			−0.766280			−0.383140	+	0.923690i	$0.625157\pi$
$90$		0			0
$91$	0.453363	−	0.329388i	0.0475254	−	0.0345292i
$92$		0			0
$93$	8.25603	+	25.4094i	0.856110	+	2.63484i
$94$		0			0
$95$	3.93381	+	2.85808i	0.403601	+	0.293233i
$96$		0			0
$97$	1.04923	−	3.22920i	0.106533	−	0.327875i	−0.883554	−	0.468329i	$-0.844856\pi$
$97$	1.04923	−	3.22920i	0.106533	−	0.327875i	0.990087	+	0.140454i	$0.0448562\pi$
$98$		0			0
$99$	8.19631	−	25.1840i	0.823760	−	2.53109i
$100$		0			0
$101$	−0.0893792	+	0.275081i	−0.00889356	+	0.0273716i	−0.955405	−	0.295299i	$-0.904581\pi$
$101$	−0.0893792	+	0.275081i	−0.00889356	+	0.0273716i	0.946511	+	0.322671i	$0.104581\pi$
$102$		0			0
$103$	14.0683	+	10.2212i	1.38619	+	1.00712i	0.996271	+	0.0862735i	$0.0274959\pi$
$103$	14.0683	+	10.2212i	1.38619	+	1.00712i	0.389916	+	0.920851i	$0.372504\pi$
$104$		0			0
$105$	−0.190459	−	0.586174i	−0.0185869	−	0.0572047i
$106$		0			0
$107$	−9.84949	+	7.15607i	−0.952186	+	0.691803i	−0.951323	−	0.308196i	$-0.900275\pi$
$107$	−9.84949	+	7.15607i	−0.952186	+	0.691803i	−0.000862886		1.00000i	$0.500275\pi$
$108$		0			0
$109$	14.0940			1.34996			0.674978	−	0.737838i	$-0.264153\pi$
$109$	14.0940			1.34996			0.674978	+	0.737838i	$0.264153\pi$
$110$		0			0
$111$	8.48448			0.805311
$112$		0			0
$113$	−8.47224	+	6.15545i	−0.797002	+	0.579056i	−0.910033	−	0.414536i	$-0.863944\pi$
$113$	−8.47224	+	6.15545i	−0.797002	+	0.579056i	0.113031	+	0.993591i	$0.463944\pi$
$114$		0			0
$115$	1.91711	+	5.90027i	0.178772	+	0.550203i
$116$		0			0
$117$	−19.4681	−	14.1444i	−1.79982	−	1.30765i
$118$		0			0
$119$	−0.294124	+	0.905222i	−0.0269623	+	0.0829815i
$120$		0			0
$121$	11.0000	+	0.0106876i	1.00000	+	0.000971603i
$122$		0			0
$123$	9.17337	−	28.2327i	0.827135	−	2.54566i
$124$		0			0
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$		0			0
$127$	−0.339507	−	1.04489i	−0.0301263	−	0.0927193i	0.934863	−	0.355009i	$-0.115522\pi$
$127$	−0.339507	−	1.04489i	−0.0301263	−	0.0927193i	−0.964989	+	0.262290i	$0.915522\pi$
$128$		0			0
$129$	20.9982	−	15.2561i	1.84879	−	1.34322i
$130$		0			0
$131$	−7.88959			−0.689317			−0.344659	−	0.938728i	$-0.612005\pi$
$131$	−7.88959			−0.689317			−0.344659	+	0.938728i	$0.612005\pi$
$132$		0			0
$133$	−0.904212			−0.0784051
$134$		0			0
$135$	−13.3676	+	9.71214i	−1.15050	+	0.835888i
$136$		0			0
$137$	1.56629	+	4.82053i	0.133817	+	0.411846i	0.995404	−	0.0957637i	$-0.0305293\pi$
$137$	1.56629	+	4.82053i	0.133817	+	0.411846i	−0.861587	+	0.507609i	$0.830529\pi$
$138$		0			0
$139$	−6.75959	−	4.91113i	−0.573341	−	0.416557i	0.262976	−	0.964802i	$-0.415296\pi$
$139$	−6.75959	−	4.91113i	−0.573341	−	0.416557i	−0.836317	+	0.548246i	$0.815296\pi$
$140$		0			0
$141$	−5.42907	+	16.7089i	−0.457210	+	1.40715i
$142$		0			0
$143$	3.09315	−	9.50404i	0.258663	−	0.794768i
$144$		0			0
$145$	0.0588347	−	0.181075i	0.00488596	−	0.0150374i
$146$		0			0
$147$	−18.6772	−	13.5697i	−1.54047	−	1.11921i
$148$		0			0
$149$	6.30025	+	19.3902i	0.516137	+	1.58850i	0.781205	+	0.624275i	$0.214606\pi$
$149$	6.30025	+	19.3902i	0.516137	+	1.58850i	−0.265068	+	0.964230i	$0.585394\pi$
$150$		0			0
$151$	10.6743	−	7.75534i	0.868663	−	0.631121i	−0.0615646	−	0.998103i	$-0.519609\pi$
$151$	10.6743	−	7.75534i	0.868663	−	0.631121i	0.930228	+	0.366982i	$0.119609\pi$
$152$		0			0
$153$	40.8719			3.30430
$154$		0			0
$155$	8.06089			0.647466
$156$		0			0
$157$	14.7798	−	10.7382i	1.17956	−	0.856999i	0.187436	−	0.982277i	$-0.439982\pi$
$157$	14.7798	−	10.7382i	1.17956	−	0.856999i	0.992122	+	0.125278i	$0.0399822\pi$
$158$		0			0
$159$	−1.33238	−	4.10064i	−0.105664	−	0.325202i
$160$		0			0
$161$	−0.933336	−	0.678108i	−0.0735572	−	0.0534424i
$162$		0			0
$163$	−4.17602	+	12.8525i	−0.327091	+	1.00668i	0.643397	+	0.765533i	$0.277525\pi$
$163$	−4.17602	+	12.8525i	−0.327091	+	1.00668i	−0.970488	+	0.241150i	$0.922475\pi$
$164$		0			0
$165$	−8.89010	−	6.46563i	−0.692093	−	0.503349i
$166$		0			0
$167$	1.15864	−	3.56593i	0.0896584	−	0.275940i	−0.896166	−	0.443718i	$-0.853659\pi$
$167$	1.15864	−	3.56593i	0.0896584	−	0.275940i	0.985825	+	0.167778i	$0.0536592\pi$
$168$		0			0
$169$	3.17029	+	2.30335i	0.243868	+	0.177181i
$170$		0			0
$171$	11.9986	+	36.9278i	0.917553	+	2.82394i
$172$		0			0
$173$	−7.83272	+	5.69080i	−0.595511	+	0.432664i	−0.844283	−	0.535898i	$-0.819973\pi$
$173$	−7.83272	+	5.69080i	−0.595511	+	0.432664i	0.248772	+	0.968562i	$0.419973\pi$
$174$		0			0
$175$	−0.185958			−0.0140571
$176$		0			0
$177$	−1.96741			−0.147880
$178$		0			0
$179$	8.82930	−	6.41486i	0.659933	−	0.479469i	−0.206707	−	0.978403i	$-0.566275\pi$
$179$	8.82930	−	6.41486i	0.659933	−	0.479469i	0.866640	+	0.498933i	$0.166275\pi$
$180$		0			0
$181$	−2.49160	−	7.66835i	−0.185199	−	0.569984i	0.814753	−	0.579809i	$-0.196873\pi$
$181$	−2.49160	−	7.66835i	−0.185199	−	0.569984i	−0.999952	+	0.00982450i	$0.996873\pi$
$182$		0			0
$183$	−3.04334	−	2.21112i	−0.224970	−	0.163451i
$184$		0			0
$185$	0.791046	−	2.43459i	0.0581588	−	0.178995i
$186$		0			0
$187$	5.23797	+	16.1475i	0.383038	+	1.18082i
$188$		0			0
$189$	0.949496	−	2.92225i	0.0690657	−	0.212562i
$190$		0			0
$191$	−10.3413	−	7.51343i	−0.748274	−	0.543653i	0.147018	−	0.989134i	$-0.453033\pi$
$191$	−10.3413	−	7.51343i	−0.748274	−	0.543653i	−0.895291	+	0.445481i	$0.853033\pi$
$192$		0			0
$193$	3.22597	+	9.92852i	0.232211	+	0.714671i	0.997479	+	0.0709595i	$0.0226061\pi$
$193$	3.22597	+	9.92852i	0.232211	+	0.714671i	−0.765269	+	0.643711i	$0.777394\pi$
$194$		0			0
$195$	−8.08049	+	5.87082i	−0.578656	+	0.420418i
$196$		0			0
$197$	−19.4651			−1.38683			−0.693417	−	0.720537i	$-0.743895\pi$
$197$	−19.4651			−1.38683			−0.693417	+	0.720537i	$0.743895\pi$
$198$		0			0
$199$	16.0219			1.13576			0.567882	−	0.823110i	$-0.307763\pi$
$199$	16.0219			1.13576			0.567882	+	0.823110i	$0.307763\pi$
$200$		0			0
$201$	4.65155	−	3.37955i	0.328095	−	0.238375i
$202$		0			0
$203$	0.0109408	+	0.0336722i	0.000767892	+	0.00236333i
$204$		0			0
$205$	−7.24600	−	5.26453i	−0.506083	−	0.367691i
$206$		0			0
$207$	−15.3087	+	47.1154i	−1.06403	+	3.27475i
$208$		0			0
$209$	−13.0516	+	9.47284i	−0.902797	+	0.655250i
$210$		0			0
$211$	−2.71353	+	8.35137i	−0.186807	+	0.574932i	−0.999975	−	0.00709686i	$-0.997741\pi$
$211$	−2.71353	+	8.35137i	−0.186807	+	0.574932i	0.813168	+	0.582029i	$0.197741\pi$
$212$		0			0
$213$	−35.0488	−	25.4644i	−2.40150	−	1.74479i
$214$		0			0
$215$	−2.41992	−	7.44776i	−0.165037	−	0.507933i
$216$		0			0
$217$	−1.21270	+	0.881082i	−0.0823238	+	0.0598117i
$218$		0			0
$219$	−2.96333			−0.200243
$220$		0			0
$221$	15.4244			1.03756
$222$		0			0
$223$	2.28835	−	1.66258i	0.153239	−	0.111335i	−0.508524	−	0.861048i	$-0.669809\pi$
$223$	2.28835	−	1.66258i	0.153239	−	0.111335i	0.661763	+	0.749713i	$0.269809\pi$
$224$		0			0
$225$	2.46759	+	7.59446i	0.164506	+	0.506298i
$226$		0			0
$227$	−13.9436	−	10.1306i	−0.925468	−	0.672392i	0.0194109	−	0.999812i	$-0.493821\pi$
$227$	−13.9436	−	10.1306i	−0.925468	−	0.672392i	−0.944879	+	0.327420i	$0.893821\pi$
$228$		0			0
$229$	−3.41153	+	10.4996i	−0.225440	+	0.693834i	0.772806	+	0.634642i	$0.218852\pi$
$229$	−3.41153	+	10.4996i	−0.225440	+	0.693834i	−0.998247	+	0.0591918i	$0.981148\pi$
$230$		0			0
$231$	2.04417		0.000993060i	0.134496		6.53385e-5i
$232$		0			0
$233$	7.34583	−	22.6081i	0.481241	−	1.48111i	−0.356110	−	0.934444i	$-0.615897\pi$
$233$	7.34583	−	22.6081i	0.481241	−	1.48111i	0.837351	−	0.546665i	$-0.184103\pi$
$234$		0			0
$235$	4.28839	+	3.11570i	0.279744	+	0.203246i
$236$		0			0
$237$	13.6267	+	41.9388i	0.885152	+	2.72422i
$238$		0			0
$239$	17.0979	−	12.4223i	1.10597	−	0.803534i	0.123946	−	0.992289i	$-0.460445\pi$
$239$	17.0979	−	12.4223i	1.10597	−	0.803534i	0.982024	+	0.188755i	$0.0604451\pi$
$240$		0			0
$241$	2.31116			0.148875			0.0744373	−	0.997226i	$-0.476284\pi$
$241$	2.31116			0.148875			0.0744373	+	0.997226i	$0.476284\pi$
$242$		0			0
$243$	−52.5437			−3.37068
$244$		0			0
$245$	−5.63514	+	4.09417i	−0.360016	+	0.261567i
$246$		0			0
$247$	4.52806	+	13.9359i	0.288114	+	0.886723i
$248$		0			0
$249$	45.4496	+	33.0211i	2.88025	+	2.09263i
$250$		0			0
$251$	−1.88507	+	5.80166i	−0.118985	+	0.366197i	−0.992757	−	0.120137i	$-0.961666\pi$
$251$	−1.88507	+	5.80166i	−0.118985	+	0.366197i	0.873773	+	0.486335i	$0.161666\pi$
$252$		0			0
$253$	−20.5761	−	0.00999588i	−1.29361	−	0.000628435i
$254$		0			0
$255$	5.24230	−	16.1342i	0.328286	−	1.01036i
$256$		0			0
$257$	−6.79279	−	4.93525i	−0.423722	−	0.307852i	0.355411	−	0.934710i	$-0.384341\pi$
$257$	−6.79279	−	4.93525i	−0.423722	−	0.307852i	−0.779134	+	0.626858i	$0.784341\pi$
$258$		0			0
$259$	0.147101	+	0.452731i	0.00914042	+	0.0281313i
$260$		0			0
$261$	1.22998	−	0.893636i	0.0761341	−	0.0553147i
$262$		0			0
$263$	−2.04759			−0.126260			−0.0631299	−	0.998005i	$-0.520108\pi$
$263$	−2.04759			−0.126260			−0.0631299	+	0.998005i	$0.520108\pi$
$264$		0			0
$265$	−1.30089			−0.0799128
$266$		0			0
$267$	−19.3841	+	14.0834i	−1.18629	+	0.861889i
$268$		0			0
$269$	−5.95340	−	18.3227i	−0.362985	−	1.11715i	−0.951233	−	0.308473i	$-0.900182\pi$
$269$	−5.95340	−	18.3227i	−0.362985	−	1.11715i	0.588248	−	0.808681i	$-0.299818\pi$
$270$		0			0
$271$	−15.6371	−	11.3610i	−0.949886	−	0.690133i	0.000893961	−	1.00000i	$-0.499715\pi$
$271$	−15.6371	−	11.3610i	−0.949886	−	0.690133i	−0.950780	+	0.309867i	$0.899715\pi$
$272$		0			0
$273$	0.573954	−	1.76645i	0.0347373	−	0.106910i
$274$		0			0
$275$	−2.68415	+	1.94816i	−0.161860	+	0.117478i
$276$		0			0
$277$	−8.11032	+	24.9610i	−0.487302	+	1.49976i	0.341317	+	0.939948i	$0.389127\pi$
$277$	−8.11032	+	24.9610i	−0.487302	+	1.49976i	−0.828619	+	0.559813i	$0.810873\pi$
$278$		0			0
$279$	52.0753	+	37.8349i	3.11766	+	2.26512i
$280$		0			0
$281$	1.24168	+	3.82150i	0.0740724	+	0.227971i	0.981237	−	0.192804i	$-0.0617581\pi$
$281$	1.24168	+	3.82150i	0.0740724	+	0.227971i	−0.907165	+	0.420775i	$0.861758\pi$
$282$		0			0
$283$	−5.40843	+	3.92946i	−0.321498	+	0.233582i	−0.736814	−	0.676095i	$-0.763671\pi$
$283$	−5.40843	+	3.92946i	−0.321498	+	0.233582i	0.415316	+	0.909677i	$0.363671\pi$
$284$		0			0
$285$	16.1162			0.954639
$286$		0			0
$287$	1.66554			0.0983137
$288$		0			0
$289$	−7.44134	+	5.40645i	−0.437726	+	0.318027i
$290$		0			0
$291$	−3.47757	−	10.7029i	−0.203859	−	0.627413i
$292$		0			0
$293$	6.78200	+	4.92741i	0.396209	+	0.287862i	0.767995	−	0.640456i	$-0.221255\pi$
$293$	6.78200	+	4.92741i	0.396209	+	0.287862i	−0.371786	+	0.928318i	$0.621255\pi$
$294$		0			0
$295$	−0.183431	+	0.564541i	−0.0106797	+	0.0328689i
$296$		0			0
$297$	−16.9093	−	52.1276i	−0.981176	−	3.02475i
$298$		0			0
$299$	−5.77727	+	17.7806i	−0.334108	+	1.02828i
$300$		0			0
$301$	1.17812	+	0.855957i	0.0679060	+	0.0493366i
$302$		0			0
$303$	0.296239	+	0.911730i	0.0170185	+	0.0523775i
$304$		0			0
$305$	−0.918217	+	0.667124i	−0.0525769	+	0.0381994i
$306$		0			0
$307$	−5.76000			−0.328741			−0.164370	−	0.986399i	$-0.552559\pi$
$307$	−5.76000			−0.328741			−0.164370	+	0.986399i	$0.552559\pi$
$308$		0			0
$309$	57.6353			3.27876
$310$		0			0
$311$	−0.833153	+	0.605321i	−0.0472437	+	0.0343246i	−0.611157	−	0.791510i	$-0.709295\pi$
$311$	−0.833153	+	0.605321i	−0.0472437	+	0.0343246i	0.563913	+	0.825834i	$0.309295\pi$
$312$		0			0
$313$	−2.45175	−	7.54570i	−0.138581	−	0.426508i	0.857549	−	0.514402i	$-0.171986\pi$
$313$	−2.45175	−	7.54570i	−0.138581	−	0.426508i	−0.996130	+	0.0878943i	$0.971986\pi$
$314$		0			0
$315$	−1.20133	−	0.872818i	−0.0676874	−	0.0491778i
$316$		0			0
$317$	−6.61185	+	20.3492i	−0.371359	+	1.14292i	0.574544	+	0.818474i	$0.305179\pi$
$317$	−6.61185	+	20.3492i	−0.371359	+	1.14292i	−0.945903	+	0.324451i	$0.894821\pi$
$318$		0			0
$319$	0.510684	+	0.371413i	0.0285928	+	0.0207951i
$320$		0			0
$321$	−12.4694	+	38.3767i	−0.695972	+	2.14198i
$322$		0			0
$323$	−20.1348	−	14.6288i	−1.12033	−	0.813968i
$324$		0			0
$325$	0.931229	+	2.86603i	0.0516553	+	0.158979i
$326$		0			0
$327$	37.7917	−	27.4573i	2.08988	−	1.51839i
$328$		0			0
$329$	−0.985715			−0.0543442
$330$		0			0
$331$	18.0669			0.993047			0.496523	−	0.868023i	$-0.334610\pi$
$331$	18.0669			0.993047			0.496523	+	0.868023i	$0.334610\pi$
$332$		0			0
$333$	16.5374	−	12.0151i	0.906245	−	0.658425i
$334$		0			0
$335$	−0.536064	−	1.64983i	−0.0292883	−	0.0901401i
$336$		0			0
$337$	−1.93249	−	1.40404i	−0.105269	−	0.0764827i	0.533905	−	0.845544i	$-0.320724\pi$
$337$	−1.93249	−	1.40404i	−0.105269	−	0.0764827i	−0.639175	+	0.769062i	$0.720724\pi$
$338$		0			0
$339$	−10.7258	+	33.0106i	−0.582544	+	1.79289i
$340$		0			0
$341$	−8.27390	+	25.4224i	−0.448057	+	1.37670i
$342$		0			0
$343$	0.802511	−	2.46987i	0.0433315	−	0.133361i
$344$		0			0
$345$	16.6352	+	12.0862i	0.895611	+	0.650700i
$346$		0			0
$347$	−5.98128	−	18.4085i	−0.321092	−	0.988220i	−0.973174	−	0.230071i	$-0.926104\pi$
$347$	−5.98128	−	18.4085i	−0.321092	−	0.988220i	0.652082	−	0.758149i	$-0.273896\pi$
$348$		0			0
$349$	24.2979	−	17.6534i	1.30064	−	0.944967i	0.300674	−	0.953727i	$-0.402788\pi$
$349$	24.2979	−	17.6534i	1.30064	−	0.944967i	0.999962	+	0.00875972i	$0.00278834\pi$
$350$		0			0
$351$	−49.7933			−2.65777
$352$		0			0
$353$	−23.8329			−1.26850			−0.634249	−	0.773129i	$-0.718691\pi$
$353$	−23.8329			−1.26850			−0.634249	+	0.773129i	$0.718691\pi$
$354$		0			0
$355$	−10.5747	+	7.68296i	−0.561246	+	0.407769i
$356$		0			0
$357$	0.974848	+	3.00027i	0.0515944	+	0.158791i
$358$		0			0
$359$	−5.92429	−	4.30425i	−0.312672	−	0.227170i	0.420370	−	0.907353i	$-0.361900\pi$
$359$	−5.92429	−	4.30425i	−0.312672	−	0.227170i	−0.733042	+	0.680183i	$0.761900\pi$
$360$		0			0
$361$	1.43492	−	4.41623i	0.0755221	−	0.232433i
$362$		0			0
$363$	29.5163	−	21.4011i	1.54921	−	1.12327i
$364$		0			0
$365$	−0.276284	+	0.850316i	−0.0144614	+	0.0445076i
$366$		0			0
$367$	−27.2455	−	19.7950i	−1.42220	−	1.03329i	−0.991403	−	0.130842i	$-0.958232\pi$
$367$	−27.2455	−	19.7950i	−1.42220	−	1.03329i	−0.430798	−	0.902448i	$-0.641768\pi$
$368$		0			0
$369$	−22.1011	−	68.0202i	−1.15054	−	3.54099i
$370$		0			0
$371$	0.195709	−	0.142191i	0.0101607	−	0.00738219i
$372$		0			0
$373$	−28.3365			−1.46721			−0.733605	−	0.679576i	$-0.762164\pi$
$373$	−28.3365			−1.46721			−0.733605	+	0.679576i	$0.762164\pi$
$374$		0			0
$375$	3.31441			0.171155
$376$		0			0
$377$	0.464176	−	0.337244i	0.0239063	−	0.0173689i
$378$		0			0
$379$	4.45127	+	13.6996i	0.228646	+	0.703701i	0.997901	+	0.0647584i	$0.0206277\pi$
$379$	4.45127	+	13.6996i	0.228646	+	0.703701i	−0.769255	+	0.638942i	$0.779372\pi$
$380$		0			0
$381$	−2.94598	−	2.14038i	−0.150927	−	0.109655i
$382$		0			0
$383$	5.01401	−	15.4315i	0.256204	−	0.788515i	−0.737386	−	0.675471i	$-0.763940\pi$
$383$	5.01401	−	15.4315i	0.256204	−	0.788515i	0.993590	−	0.113043i	$-0.0360599\pi$
$384$		0			0
$385$	0.190872	−	0.586474i	0.00972773	−	0.0298895i
$386$		0			0
$387$	19.3238	−	59.4725i	0.982283	−	3.02316i
$388$		0			0
$389$	−26.1370	−	18.9896i	−1.32520	−	0.962812i	−0.999852	−	0.0172163i	$-0.994520\pi$
$389$	−26.1370	−	18.9896i	−1.32520	−	0.962812i	−0.325345	−	0.945595i	$-0.605480\pi$
$390$		0			0
$391$	−9.81256	−	30.1999i	−0.496242	−	1.52728i
$392$		0			0
$393$	−21.1552	+	15.3702i	−1.06714	+	0.775323i
$394$		0			0
$395$	13.3047			0.669430
$396$		0			0
$397$	−7.36161			−0.369469			−0.184734	−	0.982788i	$-0.559142\pi$
$397$	−7.36161			−0.369469			−0.184734	+	0.982788i	$0.559142\pi$
$398$		0			0
$399$	−2.42456	+	1.76155i	−0.121380	+	0.0881878i
$400$		0			0
$401$	−10.8913	−	33.5201i	−0.543888	−	1.67392i	−0.723619	−	0.690199i	$-0.757523\pi$
$401$	−10.8913	−	33.5201i	−0.543888	−	1.67392i	0.179731	−	0.983716i	$-0.442477\pi$
$402$		0			0
$403$	19.6524	+	14.2783i	0.978954	+	0.711252i
$404$		0			0
$405$	−9.52051	+	29.3011i	−0.473078	+	1.45598i
$406$		0			0
$407$	6.86625	+	4.99372i	0.340348	+	0.247530i
$408$		0			0
$409$	−4.42217	+	13.6100i	−0.218662	+	0.672972i	0.780211	+	0.625516i	$0.215112\pi$
$409$	−4.42217	+	13.6100i	−0.218662	+	0.672972i	−0.998873	+	0.0474564i	$0.984888\pi$
$410$		0			0
$411$	13.5910	+	9.87445i	0.670396	+	0.487071i
$412$		0			0
$413$	−0.0341103	−	0.104981i	−0.00167846	−	0.00516577i
$414$		0			0
$415$	13.7127	−	9.96289i	0.673132	−	0.489059i
$416$		0			0
$417$	−27.6929			−1.35613
$418$		0			0
$419$	−8.62183			−0.421204			−0.210602	−	0.977572i	$-0.567542\pi$
$419$	−8.62183			−0.421204			−0.210602	+	0.977572i	$0.567542\pi$
$420$		0			0
$421$	29.5863	−	21.4957i	1.44195	−	1.04764i	0.454319	−	0.890839i	$-0.349882\pi$
$421$	29.5863	−	21.4957i	1.44195	−	1.04764i	0.987631	−	0.156799i	$-0.0501175\pi$
$422$		0			0
$423$	13.0801	+	40.2563i	0.635975	+	1.95733i
$424$		0			0
$425$	−4.14087	−	3.00852i	−0.200862	−	0.145935i
$426$		0			0
$427$	0.0652205	−	0.200728i	0.00315624	−	0.00971392i
$428$		0			0
$429$	−10.2214	−	31.5102i	−0.493492	−	1.52133i
$430$		0			0
$431$	3.52368	−	10.8448i	0.169730	−	0.522375i	−0.829624	−	0.558323i	$-0.811445\pi$
$431$	3.52368	−	10.8448i	0.169730	−	0.522375i	0.999354	+	0.0359481i	$0.0114451\pi$
$432$		0			0
$433$	2.75983	+	2.00513i	0.132629	+	0.0963606i	0.652122	−	0.758114i	$-0.273879\pi$
$433$	2.75983	+	2.00513i	0.132629	+	0.0963606i	−0.519493	+	0.854475i	$0.673879\pi$
$434$		0			0
$435$	−0.195002	−	0.600155i	−0.00934964	−	0.0287752i
$436$		0			0
$437$	24.4050	−	17.7313i	1.16745	−	0.848203i
$438$		0			0
$439$	−2.90901			−0.138839			−0.0694196	−	0.997588i	$-0.522115\pi$
$439$	−2.90901			−0.138839			−0.0694196	+	0.997588i	$0.522115\pi$
$440$		0			0
$441$	−55.6209			−2.64861
$442$		0			0
$443$	12.1777	−	8.84759i	0.578578	−	0.420362i	−0.259633	−	0.965707i	$-0.583602\pi$
$443$	12.1777	−	8.84759i	0.578578	−	0.420362i	0.838211	+	0.545346i	$0.183602\pi$
$444$		0			0
$445$	2.23391	+	6.87526i	0.105897	+	0.325918i
$446$		0			0
$447$	54.6687	+	39.7191i	2.58574	+	1.87865i
$448$		0			0
$449$	0.804669	−	2.47652i	0.0379747	−	0.116874i	−0.930272	−	0.366870i	$-0.880429\pi$
$449$	0.804669	−	2.47652i	0.0379747	−	0.116874i	0.968247	+	0.249996i	$0.0804293\pi$
$450$		0			0
$451$	24.0407	−	17.4488i	1.13203	−	0.821631i
$452$		0			0
$453$	13.5136	−	41.5905i	0.634924	−	1.95409i
$454$		0			0
$455$	−0.453363	−	0.329388i	−0.0212540	−	0.0154419i
$456$		0			0
$457$	−1.58801	−	4.88739i	−0.0742839	−	0.228622i	0.907020	−	0.421088i	$-0.138352\pi$
$457$	−1.58801	−	4.88739i	−0.0742839	−	0.228622i	−0.981304	+	0.192466i	$0.938352\pi$
$458$		0			0
$459$	68.4208	−	49.7106i	3.19361	−	2.32029i
$460$		0			0
$461$	37.7325			1.75738			0.878688	−	0.477396i	$-0.158419\pi$
$461$	37.7325			1.75738			0.878688	+	0.477396i	$0.158419\pi$
$462$		0			0
$463$	14.7816			0.686961			0.343481	−	0.939160i	$-0.388394\pi$
$463$	14.7816			0.686961			0.343481	+	0.939160i	$0.388394\pi$
$464$		0			0
$465$	21.6146	−	15.7039i	1.00235	−	0.728251i
$466$		0			0
$467$	2.70669	+	8.33034i	0.125251	+	0.385482i	0.993947	−	0.109864i	$-0.0350414\pi$
$467$	2.70669	+	8.33034i	0.125251	+	0.385482i	−0.868696	+	0.495346i	$0.835041\pi$
$468$		0			0
$469$	0.260979	+	0.189613i	0.0120509	+	0.00875549i
$470$		0			0
$471$	18.7111	−	57.5869i	0.862163	−	2.65346i
$472$		0			0
$473$	25.9726	+	0.0126175i	1.19422	+	0.000580154i
$474$		0			0
$475$	1.50258	−	4.62447i	0.0689432	−	0.212185i
$476$		0			0
$477$	−8.40403	−	6.10589i	−0.384794	−	0.279569i
$478$		0			0
$479$	−0.352897	−	1.08611i	−0.0161243	−	0.0496255i	0.942671	−	0.333725i	$-0.108306\pi$
$479$	−0.352897	−	1.08611i	−0.0161243	−	0.0496255i	−0.958795	+	0.284099i	$0.908306\pi$
$480$		0			0
$481$	6.24096	−	4.53432i	0.284563	−	0.206747i
$482$		0			0
$483$	−3.82372			−0.173985
$484$		0			0
$485$	−3.39538			−0.154176
$486$		0			0
$487$	1.13736	−	0.826341i	0.0515387	−	0.0374451i	−0.561718	−	0.827329i	$-0.689859\pi$
$487$	1.13736	−	0.826341i	0.0515387	−	0.0374451i	0.613256	+	0.789884i	$0.289859\pi$
$488$		0			0
$489$	13.8410	+	42.5983i	0.625913	+	1.92636i
$490$		0			0
$491$	−25.6495	−	18.6355i	−1.15755	−	0.841006i	−0.168080	−	0.985773i	$-0.553757\pi$
$491$	−25.6495	−	18.6355i	−1.15755	−	0.841006i	−0.989466	+	0.144767i	$0.953757\pi$
$492$		0			0
$493$	−0.301140	+	0.926812i	−0.0135626	+	0.0417415i
$494$		0			0
$495$	−26.4842	−	0.0128661i	−1.19038	−	0.000578287i
$496$		0			0
$497$	0.751115	−	2.31169i	0.0336921	−	0.103694i
$498$		0			0
$499$	−7.75906	−	5.63729i	−0.347343	−	0.252360i	0.400410	−	0.916336i	$-0.368868\pi$
$499$	−7.75906	−	5.63729i	−0.347343	−	0.252360i	−0.747754	+	0.663976i	$0.768868\pi$
$500$		0			0
$501$	−3.84021	−	11.8190i	−0.171568	−	0.528032i
$502$		0			0
$503$	−34.2828	+	24.9079i	−1.52860	+	1.11059i	−0.571584	+	0.820544i	$0.693671\pi$
$503$	−34.2828	+	24.9079i	−1.52860	+	1.11059i	−0.957012	+	0.290047i	$0.906329\pi$
$504$		0			0
$505$	0.289237			0.0128709
$506$		0			0
$507$	12.9881			0.576824
$508$		0			0
$509$	−26.0414	+	18.9202i	−1.15426	+	0.838621i	−0.989042	−	0.147635i	$-0.952834\pi$
$509$	−26.0414	+	18.9202i	−1.15426	+	0.838621i	−0.165221	+	0.986257i	$0.552834\pi$
$510$		0			0
$511$	−0.0513772	−	0.158123i	−0.00227280	−	0.00699495i
$512$		0			0
$513$	64.9995	+	47.2249i	2.86980	+	2.08503i
$514$		0			0
$515$	5.37360	−	16.5382i	0.236789	−	0.728762i
$516$		0			0
$517$	−14.2280	+	10.3267i	−0.625747	+	0.454168i
$518$		0			0
$519$	−9.91615	+	30.5188i	−0.435271	+	1.33963i
$520$		0			0
$521$	−13.7331	−	9.97771i	−0.601660	−	0.437131i	0.244808	−	0.969572i	$-0.421275\pi$
$521$	−13.7331	−	9.97771i	−0.601660	−	0.437131i	−0.846468	+	0.532440i	$0.821275\pi$
$522$		0			0
$523$	0.968181	+	2.97975i	0.0423356	+	0.130296i	0.969990	−	0.243143i	$-0.0781785\pi$
$523$	0.968181	+	2.97975i	0.0423356	+	0.130296i	−0.927655	+	0.373439i	$0.878179\pi$
$524$		0			0
$525$	−0.498629	+	0.362275i	−0.0217620	+	0.0158110i
$526$		0			0
$527$	−41.2588			−1.79726
$528$		0			0
$529$	15.4885			0.673415
$530$		0			0
$531$	−3.83476	+	2.78611i	−0.166414	+	0.120907i
$532$		0			0
$533$	−8.34060	−	25.6697i	−0.361271	−	1.11188i
$534$		0			0
$535$	9.84949	+	7.15607i	0.425830	+	0.309384i
$536$		0			0
$537$	11.1778	−	34.4018i	0.482358	−	1.48455i
$538$		0			0
$539$	−7.12814	−	21.9745i	−0.307031	−	0.946508i
$540$		0			0
$541$	6.47570	−	19.9302i	0.278412	−	0.856865i	−0.709884	−	0.704318i	$-0.751253\pi$
$541$	6.47570	−	19.9302i	0.278412	−	0.856865i	0.988296	−	0.152546i	$-0.0487473\pi$
$542$		0			0
$543$	−21.6202	−	15.7080i	−0.927811	−	0.674094i
$544$		0			0
$545$	−4.35527	−	13.4041i	−0.186559	−	0.574170i
$546$		0			0
$547$	−13.6974	+	9.95174i	−0.585659	+	0.425506i	−0.840760	−	0.541409i	$-0.817891\pi$
$547$	−13.6974	+	9.95174i	−0.585659	+	0.425506i	0.255101	+	0.966914i	$0.417891\pi$
$548$		0			0
$549$	−9.06313			−0.386805
$550$		0			0
$551$	−0.925779			−0.0394395
$552$		0			0
$553$	−2.00159	+	1.45424i	−0.0851165	+	0.0618407i
$554$		0			0
$555$	−2.62185	−	8.06922i	−0.111291	−	0.342519i
$556$		0			0
$557$	−0.123153	−	0.0894757i	−0.00521815	−	0.00379121i	0.585173	−	0.810908i	$-0.301027\pi$
$557$	−0.123153	−	0.0894757i	−0.00521815	−	0.00379121i	−0.590391	+	0.807117i	$0.701027\pi$
$558$		0			0
$559$	7.29249	−	22.4440i	0.308439	−	0.949279i
$560$		0			0
$561$	45.5031	+	33.0937i	1.92114	+	1.39722i
$562$		0			0
$563$	−10.9296	+	33.6378i	−0.460628	+	1.41767i	0.403771	+	0.914860i	$0.367699\pi$
$563$	−10.9296	+	33.6378i	−0.460628	+	1.41767i	−0.864399	+	0.502806i	$0.832301\pi$
$564$		0			0
$565$	8.47224	+	6.15545i	0.356430	+	0.258962i
$566$		0			0
$567$	−1.77041	−	5.44877i	−0.0743504	−	0.228827i
$568$		0			0
$569$	−22.0378	+	16.0114i	−0.923874	+	0.671234i	−0.944485	−	0.328554i	$-0.893439\pi$
$569$	−22.0378	+	16.0114i	−0.923874	+	0.671234i	0.0206111	+	0.999788i	$0.493439\pi$
$570$		0			0
$571$	−17.9295			−0.750325			−0.375162	−	0.926959i	$-0.622413\pi$
$571$	−17.9295			−0.750325			−0.375162	+	0.926959i	$0.622413\pi$
$572$		0			0
$573$	−42.3668			−1.76990
$574$		0			0
$575$	5.01907	−	3.64657i	0.209310	−	0.152072i
$576$		0			0
$577$	−2.66943	−	8.21568i	−0.111130	−	0.342023i	0.879990	−	0.474992i	$-0.157549\pi$
$577$	−2.66943	−	8.21568i	−0.111130	−	0.342023i	−0.991120	+	0.132969i	$0.957549\pi$
$578$		0			0
$579$	27.9925	+	20.3377i	1.16333	+	0.845208i
$580$		0			0
$581$	−0.974010	+	2.99770i	−0.0404088	+	0.124365i
$582$		0			0
$583$	1.33526	−	4.10273i	0.0553009	−	0.169918i
$584$		0			0
$585$	−7.43614	+	22.8861i	−0.307446	+	0.946223i
$586$		0			0
$587$	13.2919	+	9.65716i	0.548617	+	0.398594i	0.827275	−	0.561797i	$-0.189890\pi$
$587$	13.2919	+	9.65716i	0.548617	+	0.398594i	−0.278658	+	0.960390i	$0.589890\pi$
$588$		0			0
$589$	−12.1121	−	37.2774i	−0.499072	−	1.53599i
$590$		0			0
$591$	−52.1940	+	37.9212i	−2.14698	+	1.55987i
$592$		0			0
$593$	−9.98760			−0.410141			−0.205071	−	0.978747i	$-0.565742\pi$
$593$	−9.98760			−0.410141			−0.205071	+	0.978747i	$0.565742\pi$
$594$		0			0
$595$	0.951806			0.0390203
$596$		0			0
$597$	42.9614	−	31.2133i	1.75829	−	1.27747i
$598$		0			0
$599$	−6.32352	−	19.4618i	−0.258372	−	0.795188i	−0.993146	−	0.116876i	$-0.962712\pi$
$599$	−6.32352	−	19.4618i	−0.258372	−	0.795188i	0.734774	−	0.678312i	$-0.237288\pi$
$600$		0			0
$601$	18.6829	+	13.5739i	0.762092	+	0.553692i	0.899551	−	0.436815i	$-0.143894\pi$
$601$	18.6829	+	13.5739i	0.762092	+	0.553692i	−0.137459	+	0.990507i	$0.543894\pi$
$602$		0			0
$603$	4.28062	−	13.1744i	0.174321	−	0.536503i
$604$		0			0
$605$	−3.38902	−	10.4649i	−0.137783	−	0.425459i
$606$		0			0
$607$	−0.581319	+	1.78912i	−0.0235950	+	0.0726180i	−0.962161	−	0.272483i	$-0.912155\pi$
$607$	−0.581319	+	1.78912i	−0.0235950	+	0.0726180i	0.938566	+	0.345101i	$0.112155\pi$
$608$		0			0
$609$	0.0949356	+	0.0689748i	0.00384699	+	0.00279500i
$610$		0			0
$611$	4.93621	+	15.1921i	0.199698	+	0.614606i
$612$		0			0
$613$	13.9185	−	10.1124i	0.562162	−	0.408435i	−0.270087	−	0.962836i	$-0.587053\pi$
$613$	13.9185	−	10.1124i	0.562162	−	0.408435i	0.832250	+	0.554401i	$0.187053\pi$
$614$		0			0
$615$	−29.6856			−1.19704
$616$		0			0
$617$	−17.5502			−0.706546			−0.353273	−	0.935520i	$-0.614931\pi$
$617$	−17.5502			−0.706546			−0.353273	+	0.935520i	$0.614931\pi$
$618$		0			0
$619$	−27.3496	+	19.8707i	−1.09928	+	0.798670i	−0.980941	−	0.194304i	$-0.937755\pi$
$619$	−27.3496	+	19.8707i	−1.09928	+	0.798670i	−0.118334	+	0.992974i	$0.537755\pi$
$620$		0			0
$621$	31.6770	+	97.4919i	1.27116	+	3.91221i
$622$		0			0
$623$	−1.08756	−	0.790161i	−0.0435723	−	0.0316571i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$		0			0
$627$	−16.5420	+	50.8271i	−0.660626	+	2.02984i
$628$		0			0
$629$	−4.04889	+	12.4612i	−0.161440	+	0.496860i
$630$		0			0
$631$	−24.5241	−	17.8178i	−0.976289	−	0.709315i	−0.0194127	−	0.999812i	$-0.506180\pi$
$631$	−24.5241	−	17.8178i	−0.976289	−	0.709315i	−0.956876	+	0.290496i	$0.906180\pi$
$632$		0			0
$633$	8.99373	+	27.6798i	0.357468	+	1.10017i
$634$		0			0
$635$	−0.888840	+	0.645780i	−0.0352725	+	0.0256270i
$636$		0			0
$637$	−20.9904			−0.831671
$638$		0			0
$639$	−104.376			−4.12905
$640$		0			0
$641$	2.98426	−	2.16819i	0.117871	−	0.0856385i	−0.527288	−	0.849687i	$-0.676791\pi$
$641$	2.98426	−	2.16819i	0.117871	−	0.0856385i	0.645159	+	0.764048i	$0.276791\pi$
$642$		0			0
$643$	1.47236	+	4.53147i	0.0580644	+	0.178704i	0.975882	−	0.218298i	$-0.0700506\pi$
$643$	1.47236	+	4.53147i	0.0580644	+	0.178704i	−0.917818	+	0.397002i	$0.870051\pi$
$644$		0			0
$645$	−20.9982	−	15.2561i	−0.826804	−	0.600708i
$646$		0			0
$647$	−10.7186	+	32.9885i	−0.421392	+	1.29691i	0.485016	+	0.874506i	$0.338814\pi$
$647$	−10.7186	+	32.9885i	−0.421392	+	1.29691i	−0.906407	+	0.422405i	$0.861186\pi$
$648$		0			0
$649$	−1.59217	−	1.15796i	−0.0624982	−	0.0454540i
$650$		0			0
$651$	−1.53527	+	4.72508i	−0.0601721	+	0.185191i
$652$		0			0
$653$	5.14301	+	3.73661i	0.201261	+	0.146225i	0.683851	−	0.729622i	$-0.260304\pi$
$653$	5.14301	+	3.73661i	0.201261	+	0.146225i	−0.482590	+	0.875847i	$0.660304\pi$
$654$		0			0
$655$	2.43802	+	7.50345i	0.0952613	+	0.293184i
$656$		0			0
$657$	−5.77594	+	4.19646i	−0.225341	+	0.163720i
$658$		0			0
$659$	−8.61834			−0.335723			−0.167861	−	0.985811i	$-0.553686\pi$
$659$	−8.61834			−0.335723			−0.167861	+	0.985811i	$0.553686\pi$
$660$		0			0
$661$	−17.5983			−0.684494			−0.342247	−	0.939610i	$-0.611188\pi$
$661$	−17.5983			−0.684494			−0.342247	+	0.939610i	$0.611188\pi$
$662$		0			0
$663$	41.3592	−	30.0492i	1.60626	−	1.16701i
$664$		0			0
$665$	0.279417	+	0.859957i	0.0108353	+	0.0333477i
$666$		0			0
$667$	−0.955597	−	0.694282i	−0.0370009	−	0.0268827i
$668$		0			0
$669$	2.89702	−	8.91612i	0.112005	−	0.344717i
$670$		0			0
$671$	−1.16149	−	3.58062i	−0.0448389	−	0.138228i
$672$		0			0
$673$	−15.7610	+	48.5073i	−0.607541	+	1.86982i	−0.129265	+	0.991610i	$0.541262\pi$
$673$	−15.7610	+	48.5073i	−0.607541	+	1.86982i	−0.478276	+	0.878209i	$0.658738\pi$
$674$		0			0
$675$	13.3676	+	9.71214i	0.514520	+	0.373821i
$676$		0			0
$677$	1.50360	+	4.62762i	0.0577882	+	0.177854i	0.975784	−	0.218736i	$-0.0701934\pi$
$677$	1.50360	+	4.62762i	0.0577882	+	0.177854i	−0.917996	+	0.396590i	$0.870193\pi$
$678$		0			0
$679$	0.510811	−	0.371126i	0.0196031	−	0.0142425i
$680$		0			0
$681$	−57.1245			−2.18902
$682$		0			0
$683$	9.50423			0.363669			0.181835	−	0.983329i	$-0.441796\pi$
$683$	9.50423			0.363669			0.181835	+	0.983329i	$0.441796\pi$
$684$		0			0
$685$	4.10059	−	2.97925i	0.156675	−	0.113831i
$686$		0			0
$687$	11.3072	+	34.8000i	0.431396	+	1.32770i
$688$		0			0
$689$	−3.17155	−	2.30426i	−0.120826	−	0.0877854i
$690$		0			0
$691$	8.28388	−	25.4952i	0.315134	−	0.969882i	−0.660566	−	0.750768i	$-0.729684\pi$
$691$	8.28388	−	25.4952i	0.315134	−	0.969882i	0.975699	−	0.219113i	$-0.0703165\pi$
$692$		0			0
$693$	3.98577	−	2.89288i	0.151407	−	0.109891i
$694$		0			0
$695$	−2.58193	+	7.94638i	−0.0979383	+	0.301423i
$696$		0			0
$697$	37.0879	+	26.9459i	1.40481	+	1.02065i
$698$		0			0
$699$	−24.3471	−	74.9326i	−0.920891	−	2.83421i
$700$		0			0
$701$	21.0714	−	15.3093i	0.795856	−	0.578223i	−0.113840	−	0.993499i	$-0.536315\pi$
$701$	21.0714	−	15.3093i	0.795856	−	0.578223i	0.909695	+	0.415276i	$0.136315\pi$
$702$		0			0
$703$	−12.4473			−0.469459
$704$		0			0
$705$	17.5688			0.661680
$706$		0			0
$707$	−0.0435137	+	0.0316146i	−0.00163650	+	0.00118899i
$708$		0			0
$709$	5.79825	+	17.8452i	0.217758	+	0.670190i	0.998946	+	0.0458945i	$0.0146138\pi$
$709$	5.79825	+	17.8452i	0.217758	+	0.670190i	−0.781188	+	0.624295i	$0.785386\pi$
$710$		0			0
$711$	85.9513	+	62.4473i	3.22343	+	2.34196i
$712$		0			0
$713$	15.4537	−	47.5614i	0.578744	−	1.78119i
$714$		0			0
$715$	−9.99472	−	0.00485545i	−0.373781	−	0.000181583i
$716$		0			0
$717$	21.6458	−	66.6188i	0.808376	−	2.48792i
$718$		0			0
$719$	24.8713	+	18.0701i	0.927543	+	0.673899i	0.945390	−	0.325941i	$-0.105681\pi$
$719$	24.8713	+	18.0701i	0.927543	+	0.673899i	−0.0178472	+	0.999841i	$0.505681\pi$
$720$		0			0
$721$	0.999263	+	3.07541i	0.0372145	+	0.114534i
$722$		0			0
$723$	6.19716	−	4.50250i	0.230475	−	0.167450i
$724$		0			0
$725$	−0.190393			−0.00707102
$726$		0			0
$727$	15.2620			0.566037			0.283019	−	0.959114i	$-0.408664\pi$
$727$	15.2620			0.566037			0.283019	+	0.959114i	$0.408664\pi$
$728$		0			0
$729$	−66.1163	+	48.0363i	−2.44875	+	1.77912i
$730$		0			0
$731$	12.3861	+	38.1206i	0.458117	+	1.40994i
$732$		0			0
$733$	6.31106	+	4.58525i	0.233104	+	0.169360i	0.698206	−	0.715897i	$-0.253982\pi$
$733$	6.31106	+	4.58525i	0.233104	+	0.169360i	−0.465101	+	0.885257i	$0.653982\pi$
$734$		0			0
$735$	−7.13404	+	21.9563i	−0.263143	+	0.809871i
$736$		0			0
$737$	5.75348	+	0.00279505i	0.211932	+	0.000102957i
$738$		0			0
$739$	−6.20972	+	19.1115i	−0.228428	+	0.703030i	0.769497	+	0.638650i	$0.220507\pi$
$739$	−6.20972	+	19.1115i	−0.228428	+	0.703030i	−0.997925	+	0.0643795i	$0.979493\pi$
$740$		0			0
$741$	39.2910	+	28.5466i	1.44339	+	1.04869i
$742$		0			0
$743$	−8.64656	−	26.6114i	−0.317212	−	0.976277i	−0.974835	−	0.222930i	$-0.928438\pi$
$743$	−8.64656	−	26.6114i	−0.317212	−	0.976277i	0.657623	−	0.753347i	$-0.271562\pi$
$744$		0			0
$745$	16.4943	−	11.9838i	0.604303	−	0.439052i
$746$		0			0
$747$	135.350			4.95219
$748$		0			0
$749$	−2.26397			−0.0827236
$750$		0			0
$751$	24.1759	−	17.5648i	0.882189	−	0.640948i	−0.0516405	−	0.998666i	$-0.516445\pi$
$751$	24.1759	−	17.5648i	0.882189	−	0.640948i	0.933830	+	0.357718i	$0.116445\pi$
$752$		0			0
$753$	6.24790	+	19.2291i	0.227686	+	0.700746i
$754$		0			0
$755$	−10.6743	−	7.75534i	−0.388478	−	0.282246i
$756$		0			0
$757$	2.13180	−	6.56101i	0.0774816	−	0.238464i	−0.904812	−	0.425811i	$-0.859989\pi$
$757$	2.13180	−	6.56101i	0.0774816	−	0.238464i	0.982294	+	0.187347i	$0.0599889\pi$
$758$		0			0
$759$	−55.1923	+	40.0586i	−2.00335	+	1.45404i
$760$		0			0
$761$	5.75913	−	17.7248i	0.208768	−	0.642522i	−0.790769	−	0.612114i	$-0.790319\pi$
$761$	5.75913	−	17.7248i	0.208768	−	0.642522i	0.999538	−	0.0304082i	$-0.00968072\pi$
$762$		0			0
$763$	2.12034	+	1.54051i	0.0767613	+	0.0557704i
$764$		0			0
$765$	−12.6301	−	38.8715i	−0.456643	−	1.40540i
$766$		0			0
$767$	−1.44717	+	1.05143i	−0.0522545	+	0.0379651i
$768$		0			0
$769$	−23.0644			−0.831723			−0.415861	−	0.909428i	$-0.636520\pi$
$769$	−23.0644			−0.831723			−0.415861	+	0.909428i	$0.636520\pi$
$770$		0			0
$771$	−27.8289			−1.00223
$772$		0			0
$773$	1.28280	−	0.932007i	0.0461390	−	0.0335219i	−0.564477	−	0.825449i	$-0.690922\pi$
$773$	1.28280	−	0.932007i	0.0461390	−	0.0335219i	0.610616	+	0.791927i	$0.290922\pi$
$774$		0			0
$775$	−2.49095	−	7.66636i	−0.0894776	−	0.275384i
$776$		0			0
$777$	1.27643	+	0.927381i	0.0457917	+	0.0332696i
$778$		0			0
$779$	−13.4580	+	41.4193i	−0.482181	+	1.48400i
$780$		0			0
$781$	−13.3764	−	41.2364i	−0.478644	−	1.47555i
$782$		0			0
$783$	0.972143	−	2.99195i	0.0347415	−	0.106923i
$784$		0			0
$785$	−14.7798	−	10.7382i	−0.527514	−	0.383262i
$786$		0			0
$787$	−6.44376	−	19.8318i	−0.229695	−	0.706929i	−0.997781	−	0.0665820i	$-0.978791\pi$
$787$	−6.44376	−	19.8318i	−0.229695	−	0.706929i	0.768086	−	0.640347i	$-0.221209\pi$
$788$		0			0
$789$	−5.49043	+	3.98903i	−0.195465	+	0.142013i
$790$		0			0
$791$	−1.94740			−0.0692416
$792$		0			0
$793$	−3.42028			−0.121458
$794$		0			0
$795$	−3.48821	+	2.53433i	−0.123714	+	0.0898835i
$796$		0			0
$797$	3.72551	+	11.4659i	0.131964	+	0.406144i	0.995105	−	0.0988185i	$-0.0315063\pi$
$797$	3.72551	+	11.4659i	0.131964	+	0.406144i	−0.863141	+	0.504962i	$0.831506\pi$
$798$		0			0
$799$	−21.9497	−	15.9474i	−0.776525	−	0.564178i
$800$		0			0
$801$	−17.8384	+	54.9009i	−0.630289	+	1.93983i
$802$		0			0
$803$	−2.39814	−	1.74413i	−0.0846285	−	0.0615491i
$804$		0			0
$805$	−0.356502	+	1.09720i	−0.0125651	+	0.0386713i
$806$		0			0
$807$	−51.6590	−	37.5325i	−1.81848	−	1.32121i
$808$		0			0
$809$	−16.2614	−	50.0475i	−0.571721	−	1.75958i	−0.647082	−	0.762421i	$-0.724011\pi$
$809$	−16.2614	−	50.0475i	−0.571721	−	1.75958i	0.0753606	−	0.997156i	$-0.475989\pi$
$810$		0			0
$811$	38.9517	−	28.3001i	1.36778	−	0.993750i	0.369873	−	0.929083i	$-0.379401\pi$
$811$	38.9517	−	28.3001i	1.36778	−	0.993750i	0.997907	−	0.0646674i	$-0.0205986\pi$
$812$		0			0
$813$	−64.0626			−2.24677
$814$		0			0
$815$	13.5139			0.473371
$816$		0			0
$817$	−30.8058	+	22.3817i	−1.07776	+	0.783038i
$818$		0			0
$819$	−1.38281	−	4.25584i	−0.0483192	−	0.148711i
$820$		0			0
$821$	13.1488	+	9.55315i	0.458896	+	0.333407i	0.793098	−	0.609094i	$-0.208467\pi$
$821$	13.1488	+	9.55315i	0.458896	+	0.333407i	−0.334202	+	0.942501i	$0.608467\pi$
$822$		0			0
$823$	−7.13954	+	21.9732i	−0.248869	+	0.765939i	0.746107	+	0.665826i	$0.231921\pi$
$823$	−7.13954	+	21.9732i	−0.248869	+	0.765939i	−0.994976	+	0.100113i	$0.968079\pi$
$824$		0			0
$825$	−3.40199	+	10.4530i	−0.118442	+	0.363926i
$826$		0			0
$827$	−14.5902	+	44.9040i	−0.507351	+	1.56146i	0.289432	+	0.957199i	$0.406534\pi$
$827$	−14.5902	+	44.9040i	−0.507351	+	1.56146i	−0.796783	+	0.604266i	$0.793466\pi$
$828$		0			0
$829$	33.0065	+	23.9806i	1.14636	+	0.832881i	0.987993	−	0.154499i	$-0.0493762\pi$
$829$	33.0065	+	23.9806i	1.14636	+	0.832881i	0.158370	+	0.987380i	$0.449376\pi$
$830$		0			0
$831$	26.8809	+	82.7309i	0.932488	+	2.86990i
$832$		0			0
$833$	28.8429	−	20.9556i	0.999348	−	0.726068i
$834$		0			0
$835$	−3.74944			−0.129755
$836$		0			0
$837$	133.192			4.60380
$838$		0			0
$839$	35.4167	−	25.7317i	1.22272	−	0.888358i	0.226397	−	0.974035i	$-0.427305\pi$
$839$	35.4167	−	25.7317i	1.22272	−	0.888358i	0.996323	+	0.0856767i	$0.0273052\pi$
$840$		0			0
$841$	−8.95029	−	27.5462i	−0.308631	−	0.949868i
$842$		0			0
$843$	10.7743	+	7.82802i	0.371088	+	0.269611i
$844$		0			0
$845$	1.21094	−	3.72690i	0.0416577	−	0.128209i
$846$		0			0
$847$	1.65370	+	1.20394i	0.0568220	+	0.0413680i
$848$		0			0
$849$	−6.84702	+	21.0730i	−0.234989	+	0.723223i
$850$		0			0
$851$	−12.8482	−	9.33477i	−0.440431	−	0.319992i
$852$		0			0
$853$	16.5071	+	50.8038i	0.565194	+	1.73949i	0.667375	+	0.744722i	$0.267418\pi$
$853$	16.5071	+	50.8038i	0.565194	+	1.73949i	−0.102181	+	0.994766i	$0.532582\pi$
$854$		0			0
$855$	31.4126	−	22.8226i	1.07429	−	0.780517i
$856$		0			0
$857$	−21.6966			−0.741143			−0.370572	−	0.928804i	$-0.620838\pi$
$857$	−21.6966			−0.741143			−0.370572	+	0.928804i	$0.620838\pi$
$858$		0			0
$859$	−18.9254			−0.645725			−0.322863	−	0.946446i	$-0.604645\pi$
$859$	−18.9254			−0.645725			−0.322863	+	0.946446i	$0.604645\pi$
$860$		0			0
$861$	4.46600	−	3.24474i	0.152201	−	0.110580i
$862$		0			0
$863$	−7.74851	−	23.8475i	−0.263762	−	0.811777i	−0.991976	−	0.126427i	$-0.959649\pi$
$863$	−7.74851	−	23.8475i	−0.263762	−	0.811777i	0.728214	−	0.685350i	$-0.240351\pi$
$864$		0			0
$865$	7.83272	+	5.69080i	0.266320	+	0.193493i
$866$		0			0
$867$	−9.42067	+	28.9938i	−0.319943	+	0.984682i
$868$		0			0
$869$	−13.6563	+	41.9602i	−0.463257	+	1.42340i
$870$		0			0
$871$	1.61544	−	4.97181i	0.0547371	−	0.168463i
$872$		0			0
$873$	−21.9349	−	15.9367i	−0.742385	−	0.539374i
$874$		0			0
$875$	0.0574641	+	0.176856i	0.00194264	+	0.00597884i
$876$		0			0
$877$	2.76596	−	2.00959i	0.0933997	−	0.0678589i	−0.540105	−	0.841597i	$-0.681616\pi$
$877$	2.76596	−	2.00959i	0.0933997	−	0.0678589i	0.633505	+	0.773739i	$0.281616\pi$
$878$		0			0
$879$	27.7847			0.937155
$880$		0			0
$881$	1.37318			0.0462636			0.0231318	−	0.999732i	$-0.492636\pi$
$881$	1.37318			0.0462636			0.0231318	+	0.999732i	$0.492636\pi$
$882$		0			0
$883$	37.3931	−	27.1677i	1.25838	−	0.914265i	0.259701	−	0.965689i	$-0.416376\pi$
$883$	37.3931	−	27.1677i	1.25838	−	0.914265i	0.998677	+	0.0514240i	$0.0163760\pi$
$884$		0			0
$885$	0.607963	+	1.87112i	0.0204365	+	0.0628970i
$886$		0			0
$887$	−26.2701	−	19.0863i	−0.882063	−	0.640857i	0.0517331	−	0.998661i	$-0.483525\pi$
$887$	−26.2701	−	19.0863i	−0.882063	−	0.640857i	−0.933797	+	0.357804i	$0.883525\pi$
$888$		0			0
$889$	0.0631339	−	0.194306i	0.00211744	−	0.00651682i
$890$		0			0
$891$	−82.6377	−	60.1012i	−2.76847	−	2.01347i
$892$		0			0
$893$	7.96481	−	24.5132i	0.266532	−	0.820301i
$894$		0			0
$895$	−8.82930	−	6.41486i	−0.295131	−	0.214425i
$896$		0			0
$897$	19.1482	+	58.9321i	0.639340	+	1.96769i
$898$		0			0
$899$	−1.24163	+	0.902096i	−0.0414107	+	0.0300866i
$900$		0			0
$901$	6.65845			0.221825
$902$		0			0
$903$	4.82658			0.160618
$904$		0			0
$905$	−6.52309	+	4.73930i	−0.216835	+	0.157540i
$906$		0			0
$907$	−11.0047	−	33.8690i	−0.365405	−	1.12460i	−0.949727	−	0.313079i	$-0.898639\pi$
$907$	−11.0047	−	33.8690i	−0.365405	−	1.12460i	0.584322	−	0.811522i	$-0.301361\pi$
$908$		0			0
$909$	1.86854	+	1.35757i	0.0619756	+	0.0450279i
$910$		0			0
$911$	1.67043	−	5.14105i	0.0553438	−	0.170331i	−0.919564	−	0.392941i	$-0.871458\pi$
$911$	1.67043	−	5.14105i	0.0553438	−	0.170331i	0.974908	+	0.222610i	$0.0714577\pi$
$912$		0			0
$913$	17.3459	+	53.4734i	0.574064	+	1.76971i
$914$		0			0
$915$	−1.16245	+	3.57767i	−0.0384295	+	0.118274i
$916$		0			0
$917$	−1.18693	−	0.862358i	−0.0391960	−	0.0284776i
$918$		0			0
$919$	−14.3775	−	44.2495i	−0.474271	−	1.45966i	−0.846939	−	0.531691i	$-0.821557\pi$
$919$	−14.3775	−	44.2495i	−0.474271	−	1.45966i	0.372668	−	0.927965i	$-0.378443\pi$
$920$		0			0
$921$	−15.4449	+	11.2214i	−0.508928	+	0.369758i
$922$		0			0
$923$	−39.3898			−1.29653
$924$		0			0
$925$	−2.55988			−0.0841683
$926$		0			0
$927$	112.339	−	81.6192i	3.68970	−	2.68073i
$928$		0			0
$929$	−9.73567	−	29.9633i	−0.319417	−	0.983064i	−0.973898	−	0.226986i	$-0.927113\pi$
$929$	−9.73567	−	29.9633i	−0.319417	−	0.983064i	0.654481	−	0.756078i	$-0.272887\pi$
$930$		0			0
$931$	27.4006	+	19.9077i	0.898020	+	0.652450i
$932$		0			0
$933$	−1.05476	+	3.24623i	−0.0345314	+	0.106277i
$934$		0			0
$935$	13.7386	−	9.97146i	0.449299	−	0.326101i
$936$		0			0
$937$	13.4436	−	41.3751i	0.439182	−	1.35166i	−0.449557	−	0.893252i	$-0.648418\pi$
$937$	13.4436	−	41.3751i	0.439182	−	1.35166i	0.888739	−	0.458413i	$-0.151582\pi$
$938$		0			0
$939$	−21.2744	−	15.4567i	−0.694263	−	0.504411i
$940$		0			0
$941$	7.50754	+	23.1058i	0.244739	+	0.753229i	0.995679	+	0.0928587i	$0.0296005\pi$
$941$	7.50754	+	23.1058i	0.244739	+	0.753229i	−0.750941	+	0.660370i	$0.770400\pi$
$942$		0			0
$943$	−44.9536	+	32.6607i	−1.46389	+	1.06358i
$944$		0			0
$945$	−3.07263			−0.0999528
$946$		0			0
$947$	37.0312			1.20335			0.601676	−	0.798740i	$-0.294500\pi$
$947$	37.0312			1.20335			0.601676	+	0.798740i	$0.294500\pi$
$948$		0			0
$949$	−2.17975	+	1.58368i	−0.0707575	+	0.0514084i
$950$		0			0
$951$	21.9144	+	67.4455i	0.710622	+	2.18707i
$952$		0			0
$953$	−10.1932	−	7.40583i	−0.330192	−	0.239898i	0.410320	−	0.911941i	$-0.365417\pi$
$953$	−10.1932	−	7.40583i	−0.330192	−	0.239898i	−0.740512	+	0.672043i	$0.765417\pi$
$954$		0			0
$955$	−3.95004	+	12.1570i	−0.127820	+	0.393391i
$956$		0			0
$957$	2.09292	+	0.00101675i	0.0676546	+	3.28667e-5i
$958$		0			0
$959$	−0.291263	+	0.896415i	−0.00940537	+	0.0289468i
$960$		0			0
$961$	−27.4887	−	19.9717i	−0.886733	−	0.644249i
$962$		0			0
$963$	30.0420	+	92.4598i	0.968090	+	2.97948i
$964$		0			0
$965$	8.44570	−	6.13616i	0.271877	−	0.197530i
$966$		0			0
$967$	−18.4170			−0.592251			−0.296126	−	0.955149i	$-0.595695\pi$
$967$	−18.4170			−0.592251			−0.296126	+	0.955149i	$0.595695\pi$
$968$		0			0
$969$	−82.4890			−2.64993
$970$		0			0
$971$	−1.58519	+	1.15170i	−0.0508710	+	0.0369600i	−0.612930	−	0.790137i	$-0.710009\pi$
$971$	−1.58519	+	1.15170i	−0.0508710	+	0.0369600i	0.562059	+	0.827097i	$0.310009\pi$
$972$		0			0
$973$	−0.480131	−	1.47769i	−0.0153923	−	0.0473726i
$974$		0			0
$975$	8.08049	+	5.87082i	0.258783	+	0.188017i
$976$		0			0
$977$	−2.50113	+	7.69768i	−0.0800181	+	0.246271i	−0.983061	−	0.183281i	$-0.941328\pi$
$977$	−2.50113	+	7.69768i	−0.0800181	+	0.246271i	0.903042	+	0.429551i	$0.141328\pi$
$978$		0			0
$979$	−23.9761	−	0.0116476i	−0.766280	−	0.000372260i
$980$		0			0
$981$	34.7781	−	107.036i	1.11038	−	3.41740i
$982$		0			0
$983$	−7.63600	−	5.54788i	−0.243550	−	0.176950i	0.459313	−	0.888274i	$-0.348096\pi$
$983$	−7.63600	−	5.54788i	−0.243550	−	0.176950i	−0.702864	+	0.711325i	$0.748096\pi$
$984$		0			0
$985$	6.01506	+	18.5124i	0.191656	+	0.589855i
$986$		0			0
$987$	−2.64311	+	1.92033i	−0.0841310	+	0.0611248i
$988$		0			0
$989$	−48.5831			−1.54485
$990$		0			0
$991$	44.9960			1.42934			0.714672	−	0.699459i	$-0.246576\pi$
$991$	44.9960			1.42934			0.714672	+	0.699459i	$0.246576\pi$
$992$		0			0
$993$	48.4448	−	35.1972i	1.53735	−	1.11695i
$994$		0			0
$995$	−4.95105	−	15.2378i	−0.156959	−	0.483070i
$996$		0			0
$997$	−19.0915	−	13.8708i	−0.604634	−	0.439292i	0.242887	−	0.970055i	$-0.421906\pi$
$997$	−19.0915	−	13.8708i	−0.604634	−	0.439292i	−0.847521	+	0.530762i	$0.821906\pi$
$998$		0			0
$999$	13.0707	−	40.2274i	0.413538	−	1.27274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bo.j.801.3		12
4.3	odd	2		440.2.y.b.361.1	✓	12
11.4	even	5		9680.2.a.cx.1.1		6
11.5	even	5	inner	880.2.bo.j.401.3		12
11.7	odd	10		9680.2.a.cy.1.1		6
44.7	even	10		4840.2.a.be.1.6		6
44.15	odd	10		4840.2.a.bf.1.6		6
44.27	odd	10		440.2.y.b.401.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.b.361.1	✓	12	4.3	odd	2
440.2.y.b.401.1	yes	12	44.27	odd	10
880.2.bo.j.401.3		12	11.5	even	5	inner
880.2.bo.j.801.3		12	1.1	even	1	trivial
4840.2.a.be.1.6		6	44.7	even	10
4840.2.a.bf.1.6		6	44.15	odd	10
9680.2.a.cx.1.1		6	11.4	even	5
9680.2.a.cy.1.1		6	11.7	odd	10

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)

\(f(q)\)	\(=\)	\(q+(2.68141 - 1.94816i) q^{3} +(-0.309017 - 0.951057i) q^{5} +(0.150443 + 0.109303i) q^{7} +(2.46759 - 7.59446i) q^{9} +(3.31662 + 0.00161122i) q^{11} +(0.931229 - 2.86603i) q^{13} +(-2.68141 - 1.94816i) q^{15} +(1.58167 + 4.86789i) q^{17} +(-3.93381 + 2.85808i) q^{19} +0.616340 q^{21} -6.20391 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-5.10598 - 15.7146i) q^{27} +(0.154031 + 0.111910i) q^{29} +(-2.49095 + 7.66636i) q^{31} +(8.89637 - 6.45699i) q^{33} +(0.0574641 - 0.176856i) q^{35} +(2.07098 + 1.50466i) q^{37} +(-3.08647 - 9.49918i) q^{39} +(7.24600 - 5.26453i) q^{41} +7.83103 q^{43} -7.98529 q^{45} +(-4.28839 + 3.11570i) q^{47} +(-2.15243 - 6.62451i) q^{49} +(13.7245 + 9.97146i) q^{51} +(0.401996 - 1.23722i) q^{53} +(-1.02336 - 3.15480i) q^{55} +(-4.98017 + 15.3274i) q^{57} +(-0.480227 - 0.348906i) q^{59} +(-0.350728 - 1.07943i) q^{61} +(1.20133 - 0.872818i) q^{63} -3.01352 q^{65} +1.73474 q^{67} +(-16.6352 + 12.0862i) q^{69} +(-4.03917 - 12.4313i) q^{71} +(-0.723322 - 0.525524i) q^{73} +(-1.02421 + 3.15219i) q^{75} +(0.498787 + 0.362760i) q^{77} +(-4.11137 + 12.6535i) q^{79} +(-24.9250 - 18.1091i) q^{81} +(5.23780 + 16.1203i) q^{83} +(4.14087 - 3.00852i) q^{85} +0.631040 q^{87} -7.22907 q^{89} +(0.453363 - 0.329388i) q^{91} +(8.25603 + 25.4094i) q^{93} +(3.93381 + 2.85808i) q^{95} +(1.04923 - 3.22920i) q^{97} +(8.19631 - 25.1840i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{3} + 3 q^{5} + 8 q^{7} + 10 q^{9} + 4 q^{11} - 7 q^{13} - q^{15} + 7 q^{17} - 3 q^{19} + 4 q^{21} - 36 q^{23} - 3 q^{25} - 8 q^{27} + 13 q^{29} - 2 q^{31} - 19 q^{33} + 2 q^{35} - 22 q^{37}+ \cdots + 79 q^{99}+O(q^{100}) \) 12 * q + q^3 + 3 * q^5 + 8 * q^7 + 10 * q^9 + 4 * q^11 - 7 * q^13 - q^15 + 7 * q^17 - 3 * q^19 + 4 * q^21 - 36 * q^23 - 3 * q^25 - 8 * q^27 + 13 * q^29 - 2 * q^31 - 19 * q^33 + 2 * q^35 - 22 * q^37 + q^39 + 7 * q^41 - 6 * q^43 - 20 * q^45 + 2 * q^47 - 19 * q^49 + 33 * q^51 + 3 * q^53 - 4 * q^55 - 25 * q^57 - 19 * q^59 + 22 * q^61 + 2 * q^63 + 12 * q^65 - 22 * q^67 + 21 * q^69 - 44 * q^71 + 17 * q^73 + q^75 - 38 * q^77 + 43 * q^79 - 85 * q^81 + 15 * q^83 + 18 * q^85 - 50 * q^87 + 2 * q^89 - 59 * q^91 + 5 * q^93 + 3 * q^95 - 20 * q^97 + 79 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more