LMFDB - Embedded newform 880.2.bo.a.801.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(81,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [4,0,-4,0,1,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			801.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	880.801
Dual form			880.2.bo.a.401.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 0.726543i) q^{3} +(-0.309017 - 0.951057i) q^{5} +(0.309017 + 0.224514i) q^{7} +(-0.454915 + 1.40008i) q^{9} +(-3.04508 - 1.31433i) q^{11} +(0.190983 - 0.587785i) q^{13} +(1.00000 + 0.726543i) q^{15} +(-0.236068 - 0.726543i) q^{17} +(5.73607 - 4.16750i) q^{19} -0.472136 q^{21} -6.85410 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-1.70820 - 5.25731i) q^{27} +(-2.61803 - 1.90211i) q^{29} +(0.854102 - 2.62866i) q^{31} +(4.00000 - 0.898056i) q^{33} +(0.118034 - 0.363271i) q^{35} +(-4.73607 - 3.44095i) q^{37} +(0.236068 + 0.726543i) q^{39} +(-3.92705 + 2.85317i) q^{41} +4.76393 q^{43} +1.47214 q^{45} +(-3.50000 + 2.54290i) q^{47} +(-2.11803 - 6.51864i) q^{49} +(0.763932 + 0.555029i) q^{51} +(3.73607 - 11.4984i) q^{53} +(-0.309017 + 3.30220i) q^{55} +(-2.70820 + 8.33499i) q^{57} +(3.73607 + 2.71441i) q^{59} +(-2.76393 - 8.50651i) q^{61} +(-0.454915 + 0.330515i) q^{63} -0.618034 q^{65} -5.23607 q^{67} +(6.85410 - 4.97980i) q^{69} +(-2.70820 - 8.33499i) q^{71} +(-9.47214 - 6.88191i) q^{73} +(0.381966 - 1.17557i) q^{75} +(-0.645898 - 1.08981i) q^{77} +(3.23607 - 9.95959i) q^{79} +(1.95492 + 1.42033i) q^{81} +(-0.708204 - 2.17963i) q^{83} +(-0.618034 + 0.449028i) q^{85} +4.00000 q^{87} +17.0344 q^{89} +(0.190983 - 0.138757i) q^{91} +(1.05573 + 3.24920i) q^{93} +(-5.73607 - 4.16750i) q^{95} +(-3.70820 + 11.4127i) q^{97} +(3.22542 - 3.66547i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + q^{5} - q^{7} - 13 q^{9} - q^{11} + 3 q^{13} + 4 q^{15} + 8 q^{17} + 14 q^{19} + 16 q^{21} - 14 q^{23} - q^{25} + 20 q^{27} - 6 q^{29} - 10 q^{31} + 16 q^{33} - 4 q^{35} - 10 q^{37}+ \cdots - 43 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + q^5 - q^7 - 13 * q^9 - q^11 + 3 * q^13 + 4 * q^15 + 8 * q^17 + 14 * q^19 + 16 * q^21 - 14 * q^23 - q^25 + 20 * q^27 - 6 * q^29 - 10 * q^31 + 16 * q^33 - 4 * q^35 - 10 * q^37 - 8 * q^39 - 9 * q^41 + 28 * q^43 - 12 * q^45 - 14 * q^47 - 4 * q^49 + 12 * q^51 + 6 * q^53 + q^55 + 16 * q^57 + 6 * q^59 - 20 * q^61 - 13 * q^63 + 2 * q^65 - 12 * q^67 + 14 * q^69 + 16 * q^71 - 20 * q^73 + 6 * q^75 - 16 * q^77 + 4 * q^79 + 19 * q^81 + 24 * q^83 + 2 * q^85 + 16 * q^87 + 10 * q^89 + 3 * q^91 + 40 * q^93 - 14 * q^95 + 12 * q^97 - 43 * 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
$3$	−1.00000	+	0.726543i	−0.577350	+	0.419470i	−0.837768	−	0.546027i	$-0.816140\pi$
$3$	−1.00000	+	0.726543i	−0.577350	+	0.419470i	0.260418	+	0.965496i	$0.416140\pi$
$4$		0			0
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$		0			0
$7$	0.309017	+	0.224514i	0.116797	+	0.0848583i	0.644651	−	0.764477i	$-0.277003\pi$
$7$	0.309017	+	0.224514i	0.116797	+	0.0848583i	−0.527853	+	0.849336i	$0.677003\pi$
$8$		0			0
$9$	−0.454915	+	1.40008i	−0.151638	+	0.466695i
$10$		0			0
$11$	−3.04508	−	1.31433i	−0.918128	−	0.396285i
$11$	−3.04508	−	1.31433i	−0.918128	−	0.396285i
$12$		0			0
$13$	0.190983	−	0.587785i	0.0529692	−	0.163022i	−0.921073	−	0.389391i	$-0.872685\pi$
$13$	0.190983	−	0.587785i	0.0529692	−	0.163022i	0.974042	+	0.226369i	$0.0726855\pi$
$14$		0			0
$15$	1.00000	+	0.726543i	0.258199	+	0.187592i
$16$		0			0
$17$	−0.236068	−	0.726543i	−0.0572549	−	0.176212i	0.918339	−	0.395794i	$-0.129531\pi$
$17$	−0.236068	−	0.726543i	−0.0572549	−	0.176212i	−0.975594	+	0.219582i	$0.929531\pi$
$18$		0			0
$19$	5.73607	−	4.16750i	1.31594	−	0.956089i	0.315971	−	0.948769i	$-0.397670\pi$
$19$	5.73607	−	4.16750i	1.31594	−	0.956089i	0.999973	−	0.00732062i	$-0.00233025\pi$
$20$		0			0
$21$	−0.472136			−0.103029
$22$		0			0
$23$	−6.85410			−1.42918			−0.714590	−	0.699544i	$-0.753386\pi$
$23$	−6.85410			−1.42918			−0.714590	+	0.699544i	$0.753386\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$		0			0
$27$	−1.70820	−	5.25731i	−0.328744	−	1.01177i
$28$		0			0
$29$	−2.61803	−	1.90211i	−0.486157	−	0.353214i	0.317548	−	0.948242i	$-0.397141\pi$
$29$	−2.61803	−	1.90211i	−0.486157	−	0.353214i	−0.803704	+	0.595029i	$0.797141\pi$
$30$		0			0
$31$	0.854102	−	2.62866i	0.153401	−	0.472120i	−0.844594	−	0.535407i	$-0.820158\pi$
$31$	0.854102	−	2.62866i	0.153401	−	0.472120i	0.997995	+	0.0632866i	$0.0201582\pi$
$32$		0			0
$33$	4.00000	−	0.898056i	0.696311	−	0.156331i
$34$		0			0
$35$	0.118034	−	0.363271i	0.0199514	−	0.0614041i
$36$		0			0
$37$	−4.73607	−	3.44095i	−0.778605	−	0.565689i	0.125955	−	0.992036i	$-0.459800\pi$
$37$	−4.73607	−	3.44095i	−0.778605	−	0.565689i	−0.904560	+	0.426346i	$0.859800\pi$
$38$		0			0
$39$	0.236068	+	0.726543i	0.0378011	+	0.116340i
$40$		0			0
$41$	−3.92705	+	2.85317i	−0.613302	+	0.445590i	−0.850576	−	0.525853i	$-0.823746\pi$
$41$	−3.92705	+	2.85317i	−0.613302	+	0.445590i	0.237273	+	0.971443i	$0.423746\pi$
$42$		0			0
$43$	4.76393			0.726493			0.363246	−	0.931693i	$-0.381668\pi$
$43$	4.76393			0.726493			0.363246	+	0.931693i	$0.381668\pi$
$44$		0			0
$45$	1.47214			0.219453
$46$		0			0
$47$	−3.50000	+	2.54290i	−0.510527	+	0.370920i	−0.813024	−	0.582231i	$-0.802180\pi$
$47$	−3.50000	+	2.54290i	−0.510527	+	0.370920i	0.302496	+	0.953151i	$0.402180\pi$
$48$		0			0
$49$	−2.11803	−	6.51864i	−0.302576	−	0.931234i
$50$		0			0
$51$	0.763932	+	0.555029i	0.106972	+	0.0777196i
$52$		0			0
$53$	3.73607	−	11.4984i	0.513188	−	1.57943i	−0.273366	−	0.961910i	$-0.588137\pi$
$53$	3.73607	−	11.4984i	0.513188	−	1.57943i	0.786554	−	0.617521i	$-0.211863\pi$
$54$		0			0
$55$	−0.309017	+	3.30220i	−0.0416678	+	0.445268i
$56$		0			0
$57$	−2.70820	+	8.33499i	−0.358710	+	1.10400i
$58$		0			0
$59$	3.73607	+	2.71441i	0.486395	+	0.353386i	0.803796	−	0.594905i	$-0.202810\pi$
$59$	3.73607	+	2.71441i	0.486395	+	0.353386i	−0.317401	+	0.948291i	$0.602810\pi$
$60$		0			0
$61$	−2.76393	−	8.50651i	−0.353885	−	1.08915i	−0.956653	−	0.291230i	$-0.905935\pi$
$61$	−2.76393	−	8.50651i	−0.353885	−	1.08915i	0.602768	−	0.797917i	$-0.294065\pi$
$62$		0			0
$63$	−0.454915	+	0.330515i	−0.0573139	+	0.0416410i
$64$		0			0
$65$	−0.618034			−0.0766577
$66$		0			0
$67$	−5.23607			−0.639688			−0.319844	−	0.947470i	$-0.603630\pi$
$67$	−5.23607			−0.639688			−0.319844	+	0.947470i	$0.603630\pi$
$68$		0			0
$69$	6.85410	−	4.97980i	0.825137	−	0.599497i
$70$		0			0
$71$	−2.70820	−	8.33499i	−0.321405	−	0.989182i	−0.973037	−	0.230647i	$-0.925916\pi$
$71$	−2.70820	−	8.33499i	−0.321405	−	0.989182i	0.651633	−	0.758535i	$-0.274084\pi$
$72$		0			0
$73$	−9.47214	−	6.88191i	−1.10863	−	0.805467i	−0.126182	−	0.992007i	$-0.540272\pi$
$73$	−9.47214	−	6.88191i	−1.10863	−	0.805467i	−0.982447	+	0.186540i	$0.940272\pi$
$74$		0			0
$75$	0.381966	−	1.17557i	0.0441056	−	0.135743i
$76$		0			0
$77$	−0.645898	−	1.08981i	−0.0736069	−	0.124196i
$78$		0			0
$79$	3.23607	−	9.95959i	0.364086	−	1.12054i	−0.586465	−	0.809974i	$-0.699481\pi$
$79$	3.23607	−	9.95959i	0.364086	−	1.12054i	0.950551	−	0.310567i	$-0.100519\pi$
$80$		0			0
$81$	1.95492	+	1.42033i	0.217213	+	0.157814i
$82$		0			0
$83$	−0.708204	−	2.17963i	−0.0777355	−	0.239245i	0.904636	−	0.426185i	$-0.140143\pi$
$83$	−0.708204	−	2.17963i	−0.0777355	−	0.239245i	−0.982371	+	0.186940i	$0.940143\pi$
$84$		0			0
$85$	−0.618034	+	0.449028i	−0.0670352	+	0.0487039i
$86$		0			0
$87$	4.00000			0.428845
$88$		0			0
$89$	17.0344			1.80565			0.902824	−	0.430011i	$-0.141490\pi$
$89$	17.0344			1.80565			0.902824	+	0.430011i	$0.141490\pi$
$90$		0			0
$91$	0.190983	−	0.138757i	0.0200205	−	0.0145457i
$92$		0			0
$93$	1.05573	+	3.24920i	0.109474	+	0.336926i
$94$		0			0
$95$	−5.73607	−	4.16750i	−0.588508	−	0.427576i
$96$		0			0
$97$	−3.70820	+	11.4127i	−0.376511	+	1.15878i	0.565942	+	0.824445i	$0.308512\pi$
$97$	−3.70820	+	11.4127i	−0.376511	+	1.15878i	−0.942454	+	0.334337i	$0.891488\pi$
$98$		0			0
$99$	3.22542	−	3.66547i	0.324167	−	0.368393i
$100$		0			0
$101$	−3.00000	+	9.23305i	−0.298511	+	0.918723i	0.683508	+	0.729943i	$0.260453\pi$
$101$	−3.00000	+	9.23305i	−0.298511	+	0.918723i	−0.982019	+	0.188780i	$0.939547\pi$
$102$		0			0
$103$	3.50000	+	2.54290i	0.344865	+	0.250559i	0.746712	−	0.665148i	$-0.231631\pi$
$103$	3.50000	+	2.54290i	0.344865	+	0.250559i	−0.401847	+	0.915707i	$0.631631\pi$
$104$		0			0
$105$	0.145898	+	0.449028i	0.0142382	+	0.0438206i
$106$		0			0
$107$	−13.3262	+	9.68208i	−1.28830	+	0.936002i	−0.999769	−	0.0214700i	$-0.993165\pi$
$107$	−13.3262	+	9.68208i	−1.28830	+	0.936002i	−0.288527	+	0.957472i	$0.593165\pi$
$108$		0			0
$109$	16.4721			1.57774			0.788872	−	0.614557i	$-0.210665\pi$
$109$	16.4721			1.57774			0.788872	+	0.614557i	$0.210665\pi$
$110$		0			0
$111$	7.23607			0.686817
$112$		0			0
$113$	−15.9443	+	11.5842i	−1.49991	+	1.08975i	−0.529494	+	0.848314i	$0.677618\pi$
$113$	−15.9443	+	11.5842i	−1.49991	+	1.08975i	−0.970417	+	0.241435i	$0.922382\pi$
$114$		0			0
$115$	2.11803	+	6.51864i	0.197508	+	0.607866i
$116$		0			0
$117$	0.736068	+	0.534785i	0.0680495	+	0.0494409i
$118$		0			0
$119$	0.0901699	−	0.277515i	0.00826587	−	0.0254397i
$120$		0			0
$121$	7.54508	+	8.00448i	0.685917	+	0.727680i
$122$		0			0
$123$	1.85410	−	5.70634i	0.167179	−	0.514523i
$124$		0			0
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$		0			0
$127$	1.42705	+	4.39201i	0.126630	+	0.389728i	0.994195	−	0.107597i	$-0.0343156\pi$
$127$	1.42705	+	4.39201i	0.126630	+	0.389728i	−0.867564	+	0.497325i	$0.834316\pi$
$128$		0			0
$129$	−4.76393	+	3.46120i	−0.419441	+	0.304742i
$130$		0			0
$131$	15.4164			1.34694			0.673469	−	0.739216i	$-0.264804\pi$
$131$	15.4164			1.34694			0.673469	+	0.739216i	$0.264804\pi$
$132$		0			0
$133$	2.70820			0.234831
$134$		0			0
$135$	−4.47214	+	3.24920i	−0.384900	+	0.279646i
$136$		0			0
$137$	−0.236068	−	0.726543i	−0.0201686	−	0.0620727i	0.940466	−	0.339889i	$-0.110389\pi$
$137$	−0.236068	−	0.726543i	−0.0201686	−	0.0620727i	−0.960634	+	0.277816i	$0.910389\pi$
$138$		0			0
$139$	−12.0172	−	8.73102i	−1.01929	−	0.740556i	−0.0531507	−	0.998587i	$-0.516926\pi$
$139$	−12.0172	−	8.73102i	−1.01929	−	0.740556i	−0.966137	+	0.258031i	$0.916926\pi$
$140$		0			0
$141$	1.65248	−	5.08580i	0.139164	−	0.428301i
$142$		0			0
$143$	−1.35410	+	1.53884i	−0.113236	+	0.128684i
$144$		0			0
$145$	−1.00000	+	3.07768i	−0.0830455	+	0.255588i
$146$		0			0
$147$	6.85410	+	4.97980i	0.565317	+	0.410727i
$148$		0			0
$149$	−1.23607	−	3.80423i	−0.101263	−	0.311654i	0.887572	−	0.460668i	$-0.152390\pi$
$149$	−1.23607	−	3.80423i	−0.101263	−	0.311654i	−0.988835	+	0.149014i	$0.952390\pi$
$150$		0			0
$151$	−15.0902	+	10.9637i	−1.22802	+	0.892209i	−0.996740	−	0.0806779i	$-0.974291\pi$
$151$	−15.0902	+	10.9637i	−1.22802	+	0.892209i	−0.231280	+	0.972887i	$0.574291\pi$
$152$		0			0
$153$	1.12461			0.0909195
$154$		0			0
$155$	−2.76393			−0.222004
$156$		0			0
$157$	−5.16312	+	3.75123i	−0.412062	+	0.299380i	−0.774436	−	0.632652i	$-0.781966\pi$
$157$	−5.16312	+	3.75123i	−0.412062	+	0.299380i	0.362374	+	0.932033i	$0.381966\pi$
$158$		0			0
$159$	4.61803	+	14.2128i	0.366234	+	1.12715i
$160$		0			0
$161$	−2.11803	−	1.53884i	−0.166924	−	0.121278i
$162$		0			0
$163$	0.854102	−	2.62866i	0.0668984	−	0.205892i	−0.912019	−	0.410147i	$-0.865477\pi$
$163$	0.854102	−	2.62866i	0.0668984	−	0.205892i	0.978918	+	0.204255i	$0.0654772\pi$
$164$		0			0
$165$	−2.09017	−	3.52671i	−0.162720	−	0.274554i
$166$		0			0
$167$	−5.89919	+	18.1558i	−0.456493	+	1.40494i	0.412881	+	0.910785i	$0.364523\pi$
$167$	−5.89919	+	18.1558i	−0.456493	+	1.40494i	−0.869374	+	0.494155i	$0.835477\pi$
$168$		0			0
$169$	10.2082	+	7.41669i	0.785246	+	0.570515i
$170$		0			0
$171$	3.22542	+	9.92684i	0.246654	+	0.759124i
$172$		0			0
$173$	8.39919	−	6.10237i	0.638578	−	0.463954i	−0.220783	−	0.975323i	$-0.570861\pi$
$173$	8.39919	−	6.10237i	0.638578	−	0.463954i	0.859361	+	0.511369i	$0.170861\pi$
$174$		0			0
$175$	−0.381966			−0.0288739
$176$		0			0
$177$	−5.70820			−0.429055
$178$		0			0
$179$	−11.3992	+	8.28199i	−0.852015	+	0.619025i	−0.925701	−	0.378256i	$-0.876524\pi$
$179$	−11.3992	+	8.28199i	−0.852015	+	0.619025i	0.0736857	+	0.997282i	$0.476524\pi$
$180$		0			0
$181$	−3.56231	−	10.9637i	−0.264784	−	0.814922i	−0.991743	−	0.128241i	$-0.959067\pi$
$181$	−3.56231	−	10.9637i	−0.264784	−	0.814922i	0.726959	−	0.686681i	$-0.240933\pi$
$182$		0			0
$183$	8.94427	+	6.49839i	0.661180	+	0.480375i
$184$		0			0
$185$	−1.80902	+	5.56758i	−0.133002	+	0.409337i
$186$		0			0
$187$	−0.236068	+	2.52265i	−0.0172630	+	0.184475i
$188$		0			0
$189$	0.652476	−	2.00811i	0.0474606	−	0.146069i
$190$		0			0
$191$	−1.14590	−	0.832544i	−0.0829143	−	0.0602407i	0.545556	−	0.838074i	$-0.316319\pi$
$191$	−1.14590	−	0.832544i	−0.0829143	−	0.0602407i	−0.628470	+	0.777834i	$0.716319\pi$
$192$		0			0
$193$	6.61803	+	20.3682i	0.476377	+	1.46614i	0.844092	+	0.536198i	$0.180140\pi$
$193$	6.61803	+	20.3682i	0.476377	+	1.46614i	−0.367716	+	0.929938i	$0.619860\pi$
$194$		0			0
$195$	0.618034	−	0.449028i	0.0442583	−	0.0321556i
$196$		0			0
$197$	−16.0902			−1.14638			−0.573189	−	0.819423i	$-0.694294\pi$
$197$	−16.0902			−1.14638			−0.573189	+	0.819423i	$0.694294\pi$
$198$		0			0
$199$	11.7082			0.829973			0.414986	−	0.909828i	$-0.363786\pi$
$199$	11.7082			0.829973			0.414986	+	0.909828i	$0.363786\pi$
$200$		0			0
$201$	5.23607	−	3.80423i	0.369324	−	0.268329i
$202$		0			0
$203$	−0.381966	−	1.17557i	−0.0268088	−	0.0825089i
$204$		0			0
$205$	3.92705	+	2.85317i	0.274277	+	0.199274i
$206$		0			0
$207$	3.11803	−	9.59632i	0.216718	−	0.666990i
$208$		0			0
$209$	−22.9443	+	5.15131i	−1.58709	+	0.356324i
$210$		0			0
$211$	−0.944272	+	2.90617i	−0.0650064	+	0.200069i	−0.978284	−	0.207268i	$-0.933543\pi$
$211$	−0.944272	+	2.90617i	−0.0650064	+	0.200069i	0.913278	+	0.407337i	$0.133543\pi$
$212$		0			0
$213$	8.76393	+	6.36737i	0.600495	+	0.436285i
$214$		0			0
$215$	−1.47214	−	4.53077i	−0.100399	−	0.308996i
$216$		0			0
$217$	0.854102	−	0.620541i	0.0579802	−	0.0421251i
$218$		0			0
$219$	14.4721			0.977936
$220$		0			0
$221$	−0.472136			−0.0317593
$222$		0			0
$223$	20.4894	−	14.8864i	1.37207	−	0.996866i	0.374496	−	0.927228i	$-0.377816\pi$
$223$	20.4894	−	14.8864i	1.37207	−	0.996866i	0.997572	−	0.0696380i	$-0.0221844\pi$
$224$		0			0
$225$	−0.454915	−	1.40008i	−0.0303277	−	0.0933390i
$226$		0			0
$227$	−6.09017	−	4.42477i	−0.404219	−	0.293682i	0.367038	−	0.930206i	$-0.380372\pi$
$227$	−6.09017	−	4.42477i	−0.404219	−	0.293682i	−0.771257	+	0.636524i	$0.780372\pi$
$228$		0			0
$229$	−1.79837	+	5.53483i	−0.118840	+	0.365752i	−0.992729	−	0.120375i	$-0.961590\pi$
$229$	−1.79837	+	5.53483i	−0.118840	+	0.365752i	0.873889	+	0.486126i	$0.161590\pi$
$230$		0			0
$231$	1.43769	+	0.620541i	0.0945933	+	0.0408286i
$232$		0			0
$233$	3.32624	−	10.2371i	0.217909	−	0.670655i	−0.781025	−	0.624500i	$-0.785303\pi$
$233$	3.32624	−	10.2371i	0.217909	−	0.670655i	0.998934	−	0.0461557i	$-0.0146970\pi$
$234$		0			0
$235$	3.50000	+	2.54290i	0.228315	+	0.165880i
$236$		0			0
$237$	4.00000	+	12.3107i	0.259828	+	0.799668i
$238$		0			0
$239$	14.9443	−	10.8576i	0.966665	−	0.702323i	0.0119756	−	0.999928i	$-0.496188\pi$
$239$	14.9443	−	10.8576i	0.966665	−	0.702323i	0.954689	+	0.297605i	$0.0961880\pi$
$240$		0			0
$241$	4.85410			0.312680			0.156340	−	0.987703i	$-0.450030\pi$
$241$	4.85410			0.312680			0.156340	+	0.987703i	$0.450030\pi$
$242$		0			0
$243$	13.5967			0.872232
$244$		0			0
$245$	−5.54508	+	4.02874i	−0.354262	+	0.257387i
$246$		0			0
$247$	−1.35410	−	4.16750i	−0.0861594	−	0.265172i
$248$		0			0
$249$	2.29180	+	1.66509i	0.145237	+	0.105521i
$250$		0			0
$251$	−5.88197	+	18.1028i	−0.371266	+	1.14264i	0.574697	+	0.818366i	$0.305120\pi$
$251$	−5.88197	+	18.1028i	−0.371266	+	1.14264i	−0.945963	+	0.324274i	$0.894880\pi$
$252$		0			0
$253$	20.8713	+	9.00854i	1.31217	+	0.566362i
$254$		0			0
$255$	0.291796	−	0.898056i	0.0182730	−	0.0562384i
$256$		0			0
$257$	9.70820	+	7.05342i	0.605581	+	0.439980i	0.847856	−	0.530227i	$-0.177893\pi$
$257$	9.70820	+	7.05342i	0.605581	+	0.439980i	−0.242274	+	0.970208i	$0.577893\pi$
$258$		0			0
$259$	−0.690983	−	2.12663i	−0.0429356	−	0.132142i
$260$		0			0
$261$	3.85410	−	2.80017i	0.238563	−	0.173326i
$262$		0			0
$263$	−1.20163			−0.0740954			−0.0370477	−	0.999313i	$-0.511795\pi$
$263$	−1.20163			−0.0740954			−0.0370477	+	0.999313i	$0.511795\pi$
$264$		0			0
$265$	−12.0902			−0.742693
$266$		0			0
$267$	−17.0344	+	12.3762i	−1.04249	+	0.757414i
$268$		0			0
$269$	−9.76393	−	30.0503i	−0.595317	−	1.83220i	−0.553140	−	0.833089i	$-0.686570\pi$
$269$	−9.76393	−	30.0503i	−0.595317	−	1.83220i	−0.0421778	−	0.999110i	$-0.513430\pi$
$270$		0			0
$271$	−10.8541	−	7.88597i	−0.659340	−	0.479038i	0.207100	−	0.978320i	$-0.433597\pi$
$271$	−10.8541	−	7.88597i	−0.659340	−	0.479038i	−0.866440	+	0.499281i	$0.833597\pi$
$272$		0			0
$273$	−0.0901699	+	0.277515i	−0.00545733	+	0.0167959i
$274$		0			0
$275$	3.23607	−	0.726543i	0.195142	−	0.0438122i
$276$		0			0
$277$	0.500000	−	1.53884i	0.0300421	−	0.0924600i	−0.934911	−	0.354882i	$-0.884521\pi$
$277$	0.500000	−	1.53884i	0.0300421	−	0.0924600i	0.964953	+	0.262422i	$0.0845211\pi$
$278$		0			0
$279$	3.29180	+	2.39163i	0.197075	+	0.143183i
$280$		0			0
$281$	5.56231	+	17.1190i	0.331819	+	1.02123i	0.968268	+	0.249916i	$0.0804029\pi$
$281$	5.56231	+	17.1190i	0.331819	+	1.02123i	−0.636448	+	0.771319i	$0.719597\pi$
$282$		0			0
$283$	−23.3262	+	16.9475i	−1.38660	+	1.00742i	−0.390372	+	0.920657i	$0.627654\pi$
$283$	−23.3262	+	16.9475i	−1.38660	+	1.00742i	−0.996229	+	0.0867675i	$0.972346\pi$
$284$		0			0
$285$	8.76393			0.519131
$286$		0			0
$287$	−1.85410			−0.109444
$288$		0			0
$289$	13.2812	−	9.64932i	0.781244	−	0.567607i
$290$		0			0
$291$	−4.58359	−	14.1068i	−0.268695	−	0.826958i
$292$		0			0
$293$	−15.1631	−	11.0167i	−0.885839	−	0.643600i	0.0489509	−	0.998801i	$-0.484412\pi$
$293$	−15.1631	−	11.0167i	−0.885839	−	0.643600i	−0.934790	+	0.355202i	$0.884412\pi$
$294$		0			0
$295$	1.42705	−	4.39201i	0.0830861	−	0.255713i
$296$		0			0
$297$	−1.70820	+	18.2541i	−0.0991200	+	1.05921i
$298$		0			0
$299$	−1.30902	+	4.02874i	−0.0757024	+	0.232988i
$300$		0			0
$301$	1.47214	+	1.06957i	0.0848525	+	0.0616490i
$302$		0			0
$303$	−3.70820	−	11.4127i	−0.213031	−	0.655641i
$304$		0			0
$305$	−7.23607	+	5.25731i	−0.414336	+	0.301033i
$306$		0			0
$307$	9.05573			0.516838			0.258419	−	0.966033i	$-0.416799\pi$
$307$	9.05573			0.516838			0.258419	+	0.966033i	$0.416799\pi$
$308$		0			0
$309$	−5.34752			−0.304210
$310$		0			0
$311$	5.23607	−	3.80423i	0.296910	−	0.215718i	−0.429349	−	0.903138i	$-0.641257\pi$
$311$	5.23607	−	3.80423i	0.296910	−	0.215718i	0.726260	+	0.687421i	$0.241257\pi$
$312$		0			0
$313$	0.180340	+	0.555029i	0.0101934	+	0.0313721i	0.956024	−	0.293289i	$-0.0947498\pi$
$313$	0.180340	+	0.555029i	0.0101934	+	0.0313721i	−0.945830	+	0.324661i	$0.894750\pi$
$314$		0			0
$315$	0.454915	+	0.330515i	0.0256316	+	0.0186224i
$316$		0			0
$317$	9.51722	−	29.2910i	0.534540	−	1.64515i	−0.210100	−	0.977680i	$-0.567379\pi$
$317$	9.51722	−	29.2910i	0.534540	−	1.64515i	0.744640	−	0.667466i	$-0.232621\pi$
$318$		0			0
$319$	5.47214	+	9.23305i	0.306381	+	0.516952i
$320$		0			0
$321$	6.29180	−	19.3642i	0.351174	−	1.08080i
$322$		0			0
$323$	−4.38197	−	3.18368i	−0.243819	−	0.177145i
$324$		0			0
$325$	0.190983	+	0.587785i	0.0105938	+	0.0326045i
$326$		0			0
$327$	−16.4721	+	11.9677i	−0.910911	+	0.661816i
$328$		0			0
$329$	−1.65248			−0.0911039
$330$		0			0
$331$	16.6180			0.913410			0.456705	−	0.889618i	$-0.349030\pi$
$331$	16.6180			0.913410			0.456705	+	0.889618i	$0.349030\pi$
$332$		0			0
$333$	6.97214	−	5.06555i	0.382071	−	0.277591i
$334$		0			0
$335$	1.61803	+	4.97980i	0.0884026	+	0.272075i
$336$		0			0
$337$	−6.94427	−	5.04531i	−0.378279	−	0.274835i	0.382357	−	0.924015i	$-0.375113\pi$
$337$	−6.94427	−	5.04531i	−0.378279	−	0.274835i	−0.760635	+	0.649179i	$0.775113\pi$
$338$		0			0
$339$	7.52786	−	23.1684i	0.408857	−	1.25833i
$340$		0			0
$341$	−6.05573	+	6.88191i	−0.327936	+	0.372676i
$342$		0			0
$343$	1.63525	−	5.03280i	0.0882955	−	0.271746i
$344$		0			0
$345$	−6.85410	−	4.97980i	−0.369012	−	0.268103i
$346$		0			0
$347$	−4.05573	−	12.4822i	−0.217723	−	0.670082i	−0.998949	−	0.0458341i	$-0.985405\pi$
$347$	−4.05573	−	12.4822i	−0.217723	−	0.670082i	0.781226	−	0.624248i	$-0.214595\pi$
$348$		0			0
$349$	−10.5623	+	7.67396i	−0.565387	+	0.410778i	−0.833427	−	0.552630i	$-0.813624\pi$
$349$	−10.5623	+	7.67396i	−0.565387	+	0.410778i	0.268039	+	0.963408i	$0.413624\pi$
$350$		0			0
$351$	−3.41641			−0.182354
$352$		0			0
$353$	−1.70820			−0.0909185			−0.0454593	−	0.998966i	$-0.514475\pi$
$353$	−1.70820			−0.0909185			−0.0454593	+	0.998966i	$0.514475\pi$
$354$		0			0
$355$	−7.09017	+	5.15131i	−0.376307	+	0.273403i
$356$		0			0
$357$	0.111456	+	0.343027i	0.00589889	+	0.0181549i
$358$		0			0
$359$	−17.4164	−	12.6538i	−0.919203	−	0.667840i	0.0241226	−	0.999709i	$-0.492321\pi$
$359$	−17.4164	−	12.6538i	−0.919203	−	0.667840i	−0.943325	+	0.331869i	$0.892321\pi$
$360$		0			0
$361$	9.66312	−	29.7400i	0.508585	−	1.56526i
$362$		0			0
$363$	−13.3607	−	2.52265i	−0.701254	−	0.132405i
$364$		0			0
$365$	−3.61803	+	11.1352i	−0.189377	+	0.582841i
$366$		0			0
$367$	1.23607	+	0.898056i	0.0645222	+	0.0468781i	0.619579	−	0.784934i	$-0.287303\pi$
$367$	1.23607	+	0.898056i	0.0645222	+	0.0468781i	−0.555057	+	0.831813i	$0.687303\pi$
$368$		0			0
$369$	−2.20820	−	6.79615i	−0.114955	−	0.353794i
$370$		0			0
$371$	3.73607	−	2.71441i	0.193967	−	0.140925i
$372$		0			0
$373$	36.0344			1.86579			0.932896	−	0.360145i	$-0.117273\pi$
$373$	36.0344			1.86579			0.932896	+	0.360145i	$0.117273\pi$
$374$		0			0
$375$	−1.23607			−0.0638303
$376$		0			0
$377$	−1.61803	+	1.17557i	−0.0833330	+	0.0605450i
$378$		0			0
$379$	−1.64590	−	5.06555i	−0.0845441	−	0.260200i	0.899844	−	0.436212i	$-0.143680\pi$
$379$	−1.64590	−	5.06555i	−0.0845441	−	0.260200i	−0.984388	+	0.176012i	$0.943680\pi$
$380$		0			0
$381$	−4.61803	−	3.35520i	−0.236589	−	0.171892i
$382$		0			0
$383$	2.82624	−	8.69827i	0.144414	−	0.444461i	−0.852521	−	0.522693i	$-0.824928\pi$
$383$	2.82624	−	8.69827i	0.144414	−	0.444461i	0.996935	+	0.0782321i	$0.0249275\pi$
$384$		0			0
$385$	−0.836881	+	0.951057i	−0.0426514	+	0.0484703i
$386$		0			0
$387$	−2.16718	+	6.66991i	−0.110164	+	0.339050i
$388$		0			0
$389$	8.23607	+	5.98385i	0.417585	+	0.303393i	0.776665	−	0.629913i	$-0.216910\pi$
$389$	8.23607	+	5.98385i	0.417585	+	0.303393i	−0.359080	+	0.933307i	$0.616910\pi$
$390$		0			0
$391$	1.61803	+	4.97980i	0.0818275	+	0.251839i
$392$		0			0
$393$	−15.4164	+	11.2007i	−0.777655	+	0.564999i
$394$		0			0
$395$	−10.4721			−0.526910
$396$		0			0
$397$	−17.7984			−0.893275			−0.446637	−	0.894715i	$-0.647379\pi$
$397$	−17.7984			−0.893275			−0.446637	+	0.894715i	$0.647379\pi$
$398$		0			0
$399$	−2.70820	+	1.96763i	−0.135580	+	0.0985045i
$400$		0			0
$401$	9.80902	+	30.1891i	0.489839	+	1.50757i	0.824848	+	0.565354i	$0.191261\pi$
$401$	9.80902	+	30.1891i	0.489839	+	1.50757i	−0.335009	+	0.942215i	$0.608739\pi$
$402$		0			0
$403$	−1.38197	−	1.00406i	−0.0688406	−	0.0500156i
$404$		0			0
$405$	0.746711	−	2.29814i	0.0371044	−	0.114196i
$406$		0			0
$407$	9.89919	+	16.7027i	0.490684	+	0.827924i
$408$		0			0
$409$	−2.37132	+	7.29818i	−0.117254	+	0.360872i	−0.992411	−	0.122969i	$-0.960759\pi$
$409$	−2.37132	+	7.29818i	−0.117254	+	0.360872i	0.875156	+	0.483841i	$0.160759\pi$
$410$		0			0
$411$	0.763932	+	0.555029i	0.0376820	+	0.0273776i
$412$		0			0
$413$	0.545085	+	1.67760i	0.0268219	+	0.0825493i
$414$		0			0
$415$	−1.85410	+	1.34708i	−0.0910143	+	0.0661257i
$416$		0			0
$417$	18.3607			0.899126
$418$		0			0
$419$	−0.618034			−0.0301929			−0.0150965	−	0.999886i	$-0.504806\pi$
$419$	−0.618034			−0.0301929			−0.0150965	+	0.999886i	$0.504806\pi$
$420$		0			0
$421$	−10.2361	+	7.43694i	−0.498875	+	0.362454i	−0.808587	−	0.588376i	$-0.799767\pi$
$421$	−10.2361	+	7.43694i	−0.498875	+	0.362454i	0.309712	+	0.950830i	$0.399767\pi$
$422$		0			0
$423$	−1.96807	−	6.05710i	−0.0956909	−	0.294506i
$424$		0			0
$425$	0.618034	+	0.449028i	0.0299791	+	0.0217811i
$426$		0			0
$427$	1.05573	−	3.24920i	0.0510903	−	0.157240i
$428$		0			0
$429$	0.236068	−	2.52265i	0.0113975	−	0.121795i
$430$		0			0
$431$	1.18034	−	3.63271i	0.0568550	−	0.174982i	−0.918596	−	0.395197i	$-0.870676\pi$
$431$	1.18034	−	3.63271i	0.0568550	−	0.174982i	0.975451	+	0.220216i	$0.0706762\pi$
$432$		0			0
$433$	−14.9443	−	10.8576i	−0.718176	−	0.521785i	0.167625	−	0.985851i	$-0.446390\pi$
$433$	−14.9443	−	10.8576i	−0.718176	−	0.521785i	−0.885801	+	0.464066i	$0.846390\pi$
$434$		0			0
$435$	−1.23607	−	3.80423i	−0.0592649	−	0.182399i
$436$		0			0
$437$	−39.3156	+	28.5645i	−1.88072	+	1.36642i
$438$		0			0
$439$	−27.1246			−1.29459			−0.647294	−	0.762241i	$-0.724099\pi$
$439$	−27.1246			−1.29459			−0.647294	+	0.762241i	$0.724099\pi$
$440$		0			0
$441$	10.0902			0.480484
$442$		0			0
$443$	26.4164	−	19.1926i	1.25508	−	0.911870i	0.256576	−	0.966524i	$-0.417406\pi$
$443$	26.4164	−	19.1926i	1.25508	−	0.911870i	0.998505	+	0.0546540i	$0.0174056\pi$
$444$		0			0
$445$	−5.26393	−	16.2007i	−0.249534	−	0.767988i
$446$		0			0
$447$	4.00000	+	2.90617i	0.189194	+	0.137457i
$448$		0			0
$449$	3.04508	−	9.37181i	0.143706	−	0.442283i	−0.853136	−	0.521689i	$-0.825302\pi$
$449$	3.04508	−	9.37181i	0.143706	−	0.442283i	0.996842	+	0.0794057i	$0.0253023\pi$
$450$		0			0
$451$	15.7082	−	3.52671i	0.739670	−	0.166066i
$452$		0			0
$453$	7.12461	−	21.9273i	0.334743	−	1.03023i
$454$		0			0
$455$	−0.190983	−	0.138757i	−0.00895342	−	0.00650504i
$456$		0			0
$457$	−10.6738	−	32.8505i	−0.499298	−	1.53668i	−0.810151	−	0.586222i	$-0.800615\pi$
$457$	−10.6738	−	32.8505i	−0.499298	−	1.53668i	0.310853	−	0.950458i	$-0.399385\pi$
$458$		0			0
$459$	−3.41641	+	2.48217i	−0.159464	+	0.115858i
$460$		0			0
$461$	−38.5410			−1.79503			−0.897517	−	0.440980i	$-0.854631\pi$
$461$	−38.5410			−1.79503			−0.897517	+	0.440980i	$0.854631\pi$
$462$		0			0
$463$	22.5066			1.04597			0.522985	−	0.852342i	$-0.324818\pi$
$463$	22.5066			1.04597			0.522985	+	0.852342i	$0.324818\pi$
$464$		0			0
$465$	2.76393	−	2.00811i	0.128174	−	0.0931241i
$466$		0			0
$467$	−3.94427	−	12.1392i	−0.182519	−	0.561736i	0.817378	−	0.576102i	$-0.195427\pi$
$467$	−3.94427	−	12.1392i	−0.182519	−	0.561736i	−0.999897	+	0.0143661i	$0.995427\pi$
$468$		0			0
$469$	−1.61803	−	1.17557i	−0.0747139	−	0.0542828i
$470$		0			0
$471$	2.43769	−	7.50245i	0.112323	−	0.345695i
$472$		0			0
$473$	−14.5066	−	6.26137i	−0.667013	−	0.287898i
$474$		0			0
$475$	−2.19098	+	6.74315i	−0.100529	+	0.309397i
$476$		0			0
$477$	14.3992	+	10.4616i	0.659293	+	0.479005i
$478$		0			0
$479$	−6.05573	−	18.6376i	−0.276693	−	0.851574i	−0.988766	−	0.149469i	$-0.952244\pi$
$479$	−6.05573	−	18.6376i	−0.276693	−	0.851574i	0.712073	−	0.702105i	$-0.247756\pi$
$480$		0			0
$481$	−2.92705	+	2.12663i	−0.133462	+	0.0969658i
$482$		0			0
$483$	3.23607			0.147246
$484$		0			0
$485$	12.0000			0.544892
$486$		0			0
$487$	15.4164	−	11.2007i	0.698584	−	0.507551i	−0.180887	−	0.983504i	$-0.557897\pi$
$487$	15.4164	−	11.2007i	0.698584	−	0.507551i	0.879471	+	0.475953i	$0.157897\pi$
$488$		0			0
$489$	1.05573	+	3.24920i	0.0477417	+	0.146934i
$490$		0			0
$491$	−15.7361	−	11.4329i	−0.710159	−	0.515961i	0.173066	−	0.984910i	$-0.444633\pi$
$491$	−15.7361	−	11.4329i	−0.710159	−	0.515961i	−0.883225	+	0.468950i	$0.844633\pi$
$492$		0			0
$493$	−0.763932	+	2.35114i	−0.0344058	+	0.105890i
$494$		0			0
$495$	−4.48278	−	1.93487i	−0.201486	−	0.0869659i
$496$		0			0
$497$	1.03444	−	3.18368i	0.0464011	−	0.142808i
$498$		0			0
$499$	9.54508	+	6.93491i	0.427297	+	0.310449i	0.780567	−	0.625072i	$-0.214930\pi$
$499$	9.54508	+	6.93491i	0.427297	+	0.310449i	−0.353270	+	0.935521i	$0.614930\pi$
$500$		0			0
$501$	−7.29180	−	22.4418i	−0.325773	−	1.00263i
$502$		0			0
$503$	−24.6803	+	17.9313i	−1.10044	+	0.799518i	−0.981132	−	0.193339i	$-0.938068\pi$
$503$	−24.6803	+	17.9313i	−1.10044	+	0.799518i	−0.119310	+	0.992857i	$0.538068\pi$
$504$		0			0
$505$	9.70820			0.432009
$506$		0			0
$507$	−15.5967			−0.692676
$508$		0			0
$509$	−7.38197	+	5.36331i	−0.327200	+	0.237725i	−0.739242	−	0.673440i	$-0.764816\pi$
$509$	−7.38197	+	5.36331i	−0.327200	+	0.237725i	0.412042	+	0.911165i	$0.364816\pi$
$510$		0			0
$511$	−1.38197	−	4.25325i	−0.0611346	−	0.188153i
$512$		0			0
$513$	−31.7082	−	23.0374i	−1.39995	−	1.01712i
$514$		0			0
$515$	1.33688	−	4.11450i	0.0589100	−	0.181306i
$516$		0			0
$517$	14.0000	−	3.14320i	0.615719	−	0.138238i
$518$		0			0
$519$	−3.96556	+	12.2047i	−0.174069	+	0.535728i
$520$		0			0
$521$	5.16312	+	3.75123i	0.226200	+	0.164344i	0.695113	−	0.718900i	$-0.255354\pi$
$521$	5.16312	+	3.75123i	0.226200	+	0.164344i	−0.468913	+	0.883244i	$0.655354\pi$
$522$		0			0
$523$	11.9443	+	36.7607i	0.522287	+	1.60743i	0.769620	+	0.638502i	$0.220446\pi$
$523$	11.9443	+	36.7607i	0.522287	+	1.60743i	−0.247333	+	0.968930i	$0.579554\pi$
$524$		0			0
$525$	0.381966	−	0.277515i	0.0166704	−	0.0121117i
$526$		0			0
$527$	−2.11146			−0.0919765
$528$		0			0
$529$	23.9787			1.04255
$530$		0			0
$531$	−5.50000	+	3.99598i	−0.238680	+	0.173411i
$532$		0			0
$533$	0.927051	+	2.85317i	0.0401550	+	0.123584i
$534$		0			0
$535$	13.3262	+	9.68208i	0.576144	+	0.418593i
$536$		0			0
$537$	5.38197	−	16.5640i	0.232249	−	0.714789i
$538$		0			0
$539$	−2.11803	+	22.6336i	−0.0912302	+	0.974898i
$540$		0			0
$541$	−2.47214	+	7.60845i	−0.106285	+	0.327113i	−0.990030	−	0.140857i	$-0.955014\pi$
$541$	−2.47214	+	7.60845i	−0.106285	+	0.327113i	0.883745	+	0.467970i	$0.155014\pi$
$542$		0			0
$543$	11.5279	+	8.37548i	0.494708	+	0.359426i
$544$		0			0
$545$	−5.09017	−	15.6659i	−0.218039	−	0.671055i
$546$		0			0
$547$	27.1803	−	19.7477i	1.16215	−	0.844350i	0.172099	−	0.985080i	$-0.444945\pi$
$547$	27.1803	−	19.7477i	1.16215	−	0.844350i	0.990048	+	0.140730i	$0.0449450\pi$
$548$		0			0
$549$	13.1672			0.561962
$550$		0			0
$551$	−22.9443			−0.977459
$552$		0			0
$553$	3.23607	−	2.35114i	0.137612	−	0.0999807i
$554$		0			0
$555$	−2.23607	−	6.88191i	−0.0949158	−	0.292121i
$556$		0			0
$557$	14.7361	+	10.7064i	0.624387	+	0.453644i	0.854451	−	0.519532i	$-0.173894\pi$
$557$	14.7361	+	10.7064i	0.624387	+	0.453644i	−0.230064	+	0.973176i	$0.573894\pi$
$558$		0			0
$559$	0.909830	−	2.80017i	0.0384817	−	0.118435i
$560$		0			0
$561$	−1.59675	−	2.69417i	−0.0674147	−	0.113748i
$562$		0			0
$563$	3.67376	−	11.3067i	0.154831	−	0.476520i	−0.843313	−	0.537423i	$-0.819398\pi$
$563$	3.67376	−	11.3067i	0.154831	−	0.476520i	0.998144	+	0.0609030i	$0.0193980\pi$
$564$		0			0
$565$	15.9443	+	11.5842i	0.670781	+	0.487351i
$566$		0			0
$567$	0.285218	+	0.877812i	0.0119780	+	0.0368646i
$568$		0			0
$569$	5.92705	−	4.30625i	0.248475	−	0.180528i	−0.456576	−	0.889685i	$-0.650924\pi$
$569$	5.92705	−	4.30625i	0.248475	−	0.180528i	0.705051	+	0.709157i	$0.250924\pi$
$570$		0			0
$571$	17.9098			0.749503			0.374752	−	0.927125i	$-0.377728\pi$
$571$	17.9098			0.749503			0.374752	+	0.927125i	$0.377728\pi$
$572$		0			0
$573$	1.75078			0.0731397
$574$		0			0
$575$	5.54508	−	4.02874i	0.231246	−	0.168010i
$576$		0			0
$577$	−0.909830	−	2.80017i	−0.0378767	−	0.116573i	0.930330	−	0.366722i	$-0.119520\pi$
$577$	−0.909830	−	2.80017i	−0.0378767	−	0.116573i	−0.968207	+	0.250150i	$0.919520\pi$
$578$		0			0
$579$	−21.4164	−	15.5599i	−0.890036	−	0.646649i
$580$		0			0
$581$	0.270510	−	0.832544i	0.0112226	−	0.0345397i
$582$		0			0
$583$	−26.4894	+	30.1033i	−1.09708	+	1.24675i
$584$		0			0
$585$	0.281153	−	0.865300i	0.0116242	−	0.0357757i
$586$		0			0
$587$	−20.4164	−	14.8334i	−0.842675	−	0.612239i	0.0804414	−	0.996759i	$-0.474367\pi$
$587$	−20.4164	−	14.8334i	−0.842675	−	0.612239i	−0.923117	+	0.384520i	$0.874367\pi$
$588$		0			0
$589$	−6.05573	−	18.6376i	−0.249522	−	0.767950i
$590$		0			0
$591$	16.0902	−	11.6902i	0.661861	−	0.480870i
$592$		0			0
$593$	−6.29180			−0.258373			−0.129187	−	0.991620i	$-0.541237\pi$
$593$	−6.29180			−0.258373			−0.129187	+	0.991620i	$0.541237\pi$
$594$		0			0
$595$	−0.291796			−0.0119625
$596$		0			0
$597$	−11.7082	+	8.50651i	−0.479185	+	0.348148i
$598$		0			0
$599$	−2.32624	−	7.15942i	−0.0950475	−	0.292526i	0.892219	−	0.451604i	$-0.149148\pi$
$599$	−2.32624	−	7.15942i	−0.0950475	−	0.292526i	−0.987266	+	0.159078i	$0.949148\pi$
$600$		0			0
$601$	−1.97214	−	1.43284i	−0.0804451	−	0.0584468i	0.546836	−	0.837240i	$-0.315832\pi$
$601$	−1.97214	−	1.43284i	−0.0804451	−	0.0584468i	−0.627281	+	0.778793i	$0.715832\pi$
$602$		0			0
$603$	2.38197	−	7.33094i	0.0970012	−	0.298539i
$604$		0			0
$605$	5.28115	−	9.64932i	0.214709	−	0.392301i
$606$		0			0
$607$	3.81966	−	11.7557i	0.155035	−	0.477149i	−0.843129	−	0.537711i	$-0.819289\pi$
$607$	3.81966	−	11.7557i	0.155035	−	0.477149i	0.998164	+	0.0605616i	$0.0192892\pi$
$608$		0			0
$609$	1.23607	+	0.898056i	0.0500880	+	0.0363911i
$610$		0			0
$611$	0.826238	+	2.54290i	0.0334260	+	0.102875i
$612$		0			0
$613$	−16.5623	+	12.0332i	−0.668945	+	0.486017i	−0.869672	−	0.493630i	$-0.835670\pi$
$613$	−16.5623	+	12.0332i	−0.668945	+	0.486017i	0.200727	+	0.979647i	$0.435670\pi$
$614$		0			0
$615$	−6.00000			−0.241943
$616$		0			0
$617$	15.0557			0.606121			0.303060	−	0.952971i	$-0.401992\pi$
$617$	15.0557			0.606121			0.303060	+	0.952971i	$0.401992\pi$
$618$		0			0
$619$	−15.9721	+	11.6044i	−0.641974	+	0.466422i	−0.860528	−	0.509403i	$-0.829866\pi$
$619$	−15.9721	+	11.6044i	−0.641974	+	0.466422i	0.218554	+	0.975825i	$0.429866\pi$
$620$		0			0
$621$	11.7082	+	36.0341i	0.469834	+	1.44600i
$622$		0			0
$623$	5.26393	+	3.82447i	0.210895	+	0.153224i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$		0			0
$627$	19.2016	−	21.8213i	0.766839	−	0.871459i
$628$		0			0
$629$	−1.38197	+	4.25325i	−0.0551026	+	0.169588i
$630$		0			0
$631$	−15.7082	−	11.4127i	−0.625334	−	0.454332i	0.229447	−	0.973321i	$-0.426308\pi$
$631$	−15.7082	−	11.4127i	−0.625334	−	0.454332i	−0.854781	+	0.518990i	$0.826308\pi$
$632$		0			0
$633$	−1.16718	−	3.59222i	−0.0463914	−	0.142778i
$634$		0			0
$635$	3.73607	−	2.71441i	0.148261	−	0.107718i
$636$		0			0
$637$	−4.23607			−0.167839
$638$		0			0
$639$	12.9017			0.510383
$640$		0			0
$641$	25.2082	−	18.3148i	0.995664	−	0.723392i	0.0345100	−	0.999404i	$-0.489013\pi$
$641$	25.2082	−	18.3148i	0.995664	−	0.723392i	0.961154	+	0.276012i	$0.0890129\pi$
$642$		0			0
$643$	−4.14590	−	12.7598i	−0.163498	−	0.503196i	0.835424	−	0.549606i	$-0.185222\pi$
$643$	−4.14590	−	12.7598i	−0.163498	−	0.503196i	−0.998922	+	0.0464097i	$0.985222\pi$
$644$		0			0
$645$	4.76393	+	3.46120i	0.187580	+	0.136285i
$646$		0			0
$647$	7.70820	−	23.7234i	0.303041	−	0.932664i	−0.677360	−	0.735651i	$-0.736876\pi$
$647$	7.70820	−	23.7234i	0.303041	−	0.932664i	0.980401	−	0.197012i	$-0.0631238\pi$
$648$		0			0
$649$	−7.80902	−	13.1760i	−0.306531	−	0.517205i
$650$		0			0
$651$	−0.403252	+	1.24108i	−0.0158047	+	0.0486419i
$652$		0			0
$653$	−0.972136	−	0.706298i	−0.0380426	−	0.0276396i	0.568601	−	0.822613i	$-0.307485\pi$
$653$	−0.972136	−	0.706298i	−0.0380426	−	0.0276396i	−0.606644	+	0.794974i	$0.707485\pi$
$654$		0			0
$655$	−4.76393	−	14.6619i	−0.186142	−	0.572887i
$656$		0			0
$657$	13.9443	−	10.1311i	0.544018	−	0.395252i
$658$		0			0
$659$	15.6180			0.608392			0.304196	−	0.952609i	$-0.401612\pi$
$659$	15.6180			0.608392			0.304196	+	0.952609i	$0.401612\pi$
$660$		0			0
$661$	−20.1803			−0.784924			−0.392462	−	0.919768i	$-0.628377\pi$
$661$	−20.1803			−0.784924			−0.392462	+	0.919768i	$0.628377\pi$
$662$		0			0
$663$	0.472136	−	0.343027i	0.0183362	−	0.0133221i
$664$		0			0
$665$	−0.836881	−	2.57565i	−0.0324529	−	0.0998796i
$666$		0			0
$667$	17.9443	+	13.0373i	0.694805	+	0.504805i
$668$		0			0
$669$	−9.67376	+	29.7728i	−0.374009	+	1.15108i
$670$		0			0
$671$	−2.76393	+	29.5358i	−0.106700	+	1.14022i
$672$		0			0
$673$	−1.23607	+	3.80423i	−0.0476469	+	0.146642i	−0.972049	−	0.234776i	$-0.924564\pi$
$673$	−1.23607	+	3.80423i	−0.0476469	+	0.146642i	0.924403	+	0.381418i	$0.124564\pi$
$674$		0			0
$675$	4.47214	+	3.24920i	0.172133	+	0.125062i
$676$		0			0
$677$	−3.09017	−	9.51057i	−0.118765	−	0.365521i	0.873949	−	0.486018i	$-0.161551\pi$
$677$	−3.09017	−	9.51057i	−0.118765	−	0.365521i	−0.992714	+	0.120497i	$0.961551\pi$
$678$		0			0
$679$	−3.70820	+	2.69417i	−0.142308	+	0.103393i
$680$		0			0
$681$	9.30495			0.356567
$682$		0			0
$683$	−29.0132			−1.11016			−0.555079	−	0.831798i	$-0.687312\pi$
$683$	−29.0132			−1.11016			−0.555079	+	0.831798i	$0.687312\pi$
$684$		0			0
$685$	−0.618034	+	0.449028i	−0.0236139	+	0.0171565i
$686$		0			0
$687$	−2.22291	−	6.84142i	−0.0848094	−	0.261016i
$688$		0			0
$689$	−6.04508	−	4.39201i	−0.230299	−	0.167322i
$690$		0			0
$691$	8.88197	−	27.3359i	0.337886	−	1.03991i	−0.627397	−	0.778700i	$-0.715880\pi$
$691$	8.88197	−	27.3359i	0.337886	−	1.03991i	0.965283	−	0.261206i	$-0.0841203\pi$
$692$		0			0
$693$	1.81966	−	0.408539i	0.0691232	−	0.0155191i
$694$		0			0
$695$	−4.59017	+	14.1271i	−0.174115	+	0.535871i
$696$		0			0
$697$	3.00000	+	2.17963i	0.113633	+	0.0825593i
$698$		0			0
$699$	4.11146	+	12.6538i	0.155510	+	0.478609i
$700$		0			0
$701$	−22.7984	+	16.5640i	−0.861083	+	0.625613i	−0.928179	−	0.372133i	$-0.878626\pi$
$701$	−22.7984	+	16.5640i	−0.861083	+	0.625613i	0.0670966	+	0.997746i	$0.478626\pi$
$702$		0			0
$703$	−41.5066			−1.56545
$704$		0			0
$705$	−5.34752			−0.201399
$706$		0			0
$707$	−3.00000	+	2.17963i	−0.112827	+	0.0819733i
$708$		0			0
$709$	15.7984	+	48.6224i	0.593320	+	1.82605i	0.562915	+	0.826515i	$0.309680\pi$
$709$	15.7984	+	48.6224i	0.593320	+	1.82605i	0.0304053	+	0.999538i	$0.490320\pi$
$710$		0			0
$711$	12.4721	+	9.06154i	0.467742	+	0.339834i
$712$		0			0
$713$	−5.85410	+	18.0171i	−0.219238	+	0.674745i
$714$		0			0
$715$	1.88197	+	0.812299i	0.0703815	+	0.0303783i
$716$		0			0
$717$	−7.05573	+	21.7153i	−0.263501	+	0.810973i
$718$		0			0
$719$	37.3607	+	27.1441i	1.39332	+	1.01230i	0.995492	+	0.0948441i	$0.0302353\pi$
$719$	37.3607	+	27.1441i	1.39332	+	1.01230i	0.397826	+	0.917461i	$0.369765\pi$
$720$		0			0
$721$	0.510643	+	1.57160i	0.0190173	+	0.0585294i
$722$		0			0
$723$	−4.85410	+	3.52671i	−0.180526	+	0.131160i
$724$		0			0
$725$	3.23607			0.120185
$726$		0			0
$727$	−15.7984			−0.585929			−0.292965	−	0.956123i	$-0.594642\pi$
$727$	−15.7984			−0.585929			−0.292965	+	0.956123i	$0.594642\pi$
$728$		0			0
$729$	−19.4615	+	14.1396i	−0.720796	+	0.523689i
$730$		0			0
$731$	−1.12461	−	3.46120i	−0.0415953	−	0.128017i
$732$		0			0
$733$	35.7984	+	26.0090i	1.32224	+	0.960666i	0.999901	+	0.0140425i	$0.00447000\pi$
$733$	35.7984	+	26.0090i	1.32224	+	0.960666i	0.322342	+	0.946623i	$0.395530\pi$
$734$		0			0
$735$	2.61803	−	8.05748i	0.0965676	−	0.297205i
$736$		0			0
$737$	15.9443	+	6.88191i	0.587315	+	0.253498i
$738$		0			0
$739$	7.77051	−	23.9152i	0.285843	−	0.879734i	−0.700302	−	0.713847i	$-0.746951\pi$
$739$	7.77051	−	23.9152i	0.285843	−	0.879734i	0.986145	−	0.165887i	$-0.0530487\pi$
$740$		0			0
$741$	4.38197	+	3.18368i	0.160976	+	0.116956i
$742$		0			0
$743$	−7.64590	−	23.5317i	−0.280501	−	0.863293i	−0.987711	−	0.156290i	$-0.950047\pi$
$743$	−7.64590	−	23.5317i	−0.280501	−	0.863293i	0.707210	−	0.707003i	$-0.249953\pi$
$744$		0			0
$745$	−3.23607	+	2.35114i	−0.118560	+	0.0861391i
$746$		0			0
$747$	3.37384			0.123442
$748$		0			0
$749$	−6.29180			−0.229897
$750$		0			0
$751$	5.61803	−	4.08174i	0.205005	−	0.148945i	−0.480546	−	0.876970i	$-0.659561\pi$
$751$	5.61803	−	4.08174i	0.205005	−	0.148945i	0.685551	+	0.728025i	$0.259561\pi$
$752$		0			0
$753$	−7.27051	−	22.3763i	−0.264952	−	0.815439i
$754$		0			0
$755$	15.0902	+	10.9637i	0.549188	+	0.399008i
$756$		0			0
$757$	14.4615	−	44.5079i	0.525612	−	1.61767i	−0.237491	−	0.971390i	$-0.576325\pi$
$757$	14.4615	−	44.5079i	0.525612	−	1.61767i	0.763103	−	0.646277i	$-0.223675\pi$
$758$		0			0
$759$	−27.4164	+	6.15537i	−0.995153	+	0.223426i
$760$		0			0
$761$	10.3262	−	31.7809i	0.374326	−	1.15206i	−0.569607	−	0.821918i	$-0.692904\pi$
$761$	10.3262	−	31.7809i	0.374326	−	1.15206i	0.943932	−	0.330139i	$-0.107096\pi$
$762$		0			0
$763$	5.09017	+	3.69822i	0.184277	+	0.133885i
$764$		0			0
$765$	−0.347524	−	1.06957i	−0.0125648	−	0.0386704i
$766$		0			0
$767$	2.30902	−	1.67760i	0.0833738	−	0.0605746i
$768$		0			0
$769$	−20.9098			−0.754028			−0.377014	−	0.926208i	$-0.623049\pi$
$769$	−20.9098			−0.754028			−0.377014	+	0.926208i	$0.623049\pi$
$770$		0			0
$771$	−14.8328			−0.534191
$772$		0			0
$773$	14.1074	−	10.2496i	0.507408	−	0.368653i	−0.304432	−	0.952534i	$-0.598467\pi$
$773$	14.1074	−	10.2496i	0.507408	−	0.368653i	0.811839	+	0.583881i	$0.198467\pi$
$774$		0			0
$775$	0.854102	+	2.62866i	0.0306802	+	0.0944241i
$776$		0			0
$777$	2.23607	+	1.62460i	0.0802185	+	0.0582821i
$778$		0			0
$779$	−10.6353	+	32.7319i	−0.381048	+	1.17274i
$780$		0			0
$781$	−2.70820	+	28.9402i	−0.0969072	+	1.03556i
$782$		0			0
$783$	−5.52786	+	17.0130i	−0.197550	+	0.607996i
$784$		0			0
$785$	5.16312	+	3.75123i	0.184280	+	0.133887i
$786$		0			0
$787$	11.1246	+	34.2380i	0.396550	+	1.22045i	0.927748	+	0.373207i	$0.121742\pi$
$787$	11.1246	+	34.2380i	0.396550	+	1.22045i	−0.531199	+	0.847247i	$0.678258\pi$
$788$		0			0
$789$	1.20163	−	0.873032i	0.0427790	−	0.0310808i
$790$		0			0
$791$	−7.52786			−0.267660
$792$		0			0
$793$	−5.52786			−0.196300
$794$		0			0
$795$	12.0902	−	8.78402i	0.428794	−	0.311537i
$796$		0			0
$797$	2.46149	+	7.57570i	0.0871905	+	0.268345i	0.985140	−	0.171754i	$-0.0549434\pi$
$797$	2.46149	+	7.57570i	0.0871905	+	0.268345i	−0.897949	+	0.440099i	$0.854943\pi$
$798$		0			0
$799$	2.67376	+	1.94260i	0.0945909	+	0.0687243i
$800$		0			0
$801$	−7.74922	+	23.8497i	−0.273805	+	0.842686i
$802$		0			0
$803$	19.7984	+	33.4055i	0.698669	+	1.17885i
$804$		0			0
$805$	−0.809017	+	2.48990i	−0.0285141	+	0.0877574i
$806$		0			0
$807$	31.5967	+	22.9564i	1.11226	+	0.808103i
$808$		0			0
$809$	6.19098	+	19.0539i	0.217663	+	0.669899i	0.998954	+	0.0457313i	$0.0145618\pi$
$809$	6.19098	+	19.0539i	0.217663	+	0.669899i	−0.781290	+	0.624168i	$0.785438\pi$
$810$		0			0
$811$	−35.9058	+	26.0871i	−1.26082	+	0.916041i	−0.998798	−	0.0490206i	$-0.984390\pi$
$811$	−35.9058	+	26.0871i	−1.26082	+	0.916041i	−0.262024	+	0.965061i	$0.584390\pi$
$812$		0			0
$813$	16.5836			0.581612
$814$		0			0
$815$	−2.76393			−0.0968163
$816$		0			0
$817$	27.3262	−	19.8537i	0.956024	−	0.694592i
$818$		0			0
$819$	0.107391	+	0.330515i	0.00375254	+	0.0115491i
$820$		0			0
$821$	−16.4721	−	11.9677i	−0.574882	−	0.417676i	0.261994	−	0.965070i	$-0.415620\pi$
$821$	−16.4721	−	11.9677i	−0.574882	−	0.417676i	−0.836875	+	0.547394i	$0.815620\pi$
$822$		0			0
$823$	−3.71885	+	11.4454i	−0.129631	+	0.398963i	−0.994716	−	0.102662i	$-0.967264\pi$
$823$	−3.71885	+	11.4454i	−0.129631	+	0.398963i	0.865085	+	0.501624i	$0.167264\pi$
$824$		0			0
$825$	−2.70820	+	3.07768i	−0.0942876	+	0.107151i
$826$		0			0
$827$	−6.79837	+	20.9232i	−0.236403	+	0.727572i	0.760530	+	0.649303i	$0.224939\pi$
$827$	−6.79837	+	20.9232i	−0.236403	+	0.727572i	−0.996932	+	0.0782692i	$0.975061\pi$
$828$		0			0
$829$	−4.00000	−	2.90617i	−0.138926	−	0.100935i	0.516152	−	0.856497i	$-0.327364\pi$
$829$	−4.00000	−	2.90617i	−0.138926	−	0.100935i	−0.655078	+	0.755562i	$0.727364\pi$
$830$		0			0
$831$	0.618034	+	1.90211i	0.0214394	+	0.0659836i
$832$		0			0
$833$	−4.23607	+	3.07768i	−0.146771	+	0.106635i
$834$		0			0
$835$	19.0902			0.660643
$836$		0			0
$837$	−15.2786			−0.528107
$838$		0			0
$839$	11.7639	−	8.54700i	0.406136	−	0.295075i	−0.365900	−	0.930654i	$-0.619239\pi$
$839$	11.7639	−	8.54700i	0.406136	−	0.295075i	0.772036	+	0.635579i	$0.219239\pi$
$840$		0			0
$841$	−5.72542	−	17.6210i	−0.197428	−	0.607622i
$842$		0			0
$843$	−18.0000	−	13.0778i	−0.619953	−	0.450422i
$844$		0			0
$845$	3.89919	−	12.0005i	0.134136	−	0.412828i
$846$		0			0
$847$	0.534442	+	4.16750i	0.0183636	+	0.143197i
$848$		0			0
$849$	11.0132	−	33.8950i	0.377971	−	1.16327i
$850$		0			0
$851$	32.4615	+	23.5847i	1.11277	+	0.808472i
$852$		0			0
$853$	13.9164	+	42.8303i	0.476489	+	1.46648i	0.843939	+	0.536439i	$0.180231\pi$
$853$	13.9164	+	42.8303i	0.476489	+	1.46648i	−0.367451	+	0.930043i	$0.619769\pi$
$854$		0			0
$855$	8.44427	−	6.13512i	0.288788	−	0.209817i
$856$		0			0
$857$	22.0000			0.751506			0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000			0.751506			0.375753	+	0.926720i	$0.377384\pi$
$858$		0			0
$859$	42.0902			1.43610			0.718049	−	0.695993i	$-0.245035\pi$
$859$	42.0902			1.43610			0.718049	+	0.695993i	$0.245035\pi$
$860$		0			0
$861$	1.85410	−	1.34708i	0.0631876	−	0.0459085i
$862$		0			0
$863$	9.51722	+	29.2910i	0.323970	+	0.997077i	0.971903	+	0.235380i	$0.0756335\pi$
$863$	9.51722	+	29.2910i	0.323970	+	0.997077i	−0.647933	+	0.761697i	$0.724367\pi$
$864$		0			0
$865$	−8.39919	−	6.10237i	−0.285581	−	0.207487i
$866$		0			0
$867$	−6.27051	+	19.2986i	−0.212958	+	0.655416i
$868$		0			0
$869$	−22.9443	+	26.0746i	−0.778331	+	0.884519i
$870$		0			0
$871$	−1.00000	+	3.07768i	−0.0338837	+	0.104283i
$872$		0			0
$873$	−14.2918	−	10.3836i	−0.483704	−	0.351432i
$874$		0			0
$875$	0.118034	+	0.363271i	0.00399028	+	0.0122808i
$876$		0			0
$877$	−3.73607	+	2.71441i	−0.126158	+	0.0916592i	−0.649075	−	0.760725i	$-0.724844\pi$
$877$	−3.73607	+	2.71441i	−0.126158	+	0.0916592i	0.522917	+	0.852384i	$0.324844\pi$
$878$		0			0
$879$	23.1672			0.781410
$880$		0			0
$881$	28.4508			0.958533			0.479267	−	0.877669i	$-0.340903\pi$
$881$	28.4508			0.958533			0.479267	+	0.877669i	$0.340903\pi$
$882$		0			0
$883$	−0.527864	+	0.383516i	−0.0177640	+	0.0129063i	−0.596632	−	0.802515i	$-0.703495\pi$
$883$	−0.527864	+	0.383516i	−0.0177640	+	0.0129063i	0.578868	+	0.815421i	$0.303495\pi$
$884$		0			0
$885$	1.76393	+	5.42882i	0.0592939	+	0.182488i
$886$		0			0
$887$	11.1074	+	8.06999i	0.372950	+	0.270964i	0.758433	−	0.651751i	$-0.225965\pi$
$887$	11.1074	+	8.06999i	0.372950	+	0.270964i	−0.385483	+	0.922715i	$0.625965\pi$
$888$		0			0
$889$	−0.545085	+	1.67760i	−0.0182816	+	0.0562649i
$890$		0			0
$891$	−4.08610	−	6.89442i	−0.136890	−	0.230972i
$892$		0			0
$893$	−9.47871	+	29.1725i	−0.317193	+	0.976220i
$894$		0			0
$895$	11.3992	+	8.28199i	0.381033	+	0.276837i
$896$		0			0
$897$	−1.61803	−	4.97980i	−0.0540246	−	0.166271i
$898$		0			0
$899$	−7.23607	+	5.25731i	−0.241336	+	0.175341i
$900$		0			0
$901$	−9.23607			−0.307698
$902$		0			0
$903$	−2.24922			−0.0748495
$904$		0			0
$905$	−9.32624	+	6.77591i	−0.310015	+	0.225239i
$906$		0			0
$907$	−5.76393	−	17.7396i	−0.191388	−	0.589032i	−1.00000		0.000689472i	$-0.999781\pi$
$907$	−5.76393	−	17.7396i	−0.191388	−	0.589032i	0.808612	−	0.588343i	$-0.200219\pi$
$908$		0			0
$909$	−11.5623	−	8.40051i	−0.383497	−	0.278627i
$910$		0			0
$911$	0.944272	−	2.90617i	0.0312851	−	0.0962857i	−0.934195	−	0.356764i	$-0.883880\pi$
$911$	0.944272	−	2.90617i	0.0312851	−	0.0962857i	0.965480	+	0.260478i	$0.0838801\pi$
$912$		0			0
$913$	−0.708204	+	7.56796i	−0.0234381	+	0.250463i
$914$		0			0
$915$	3.41641	−	10.5146i	0.112943	−	0.347603i
$916$		0			0
$917$	4.76393	+	3.46120i	0.157319	+	0.114299i
$918$		0			0
$919$	3.70820	+	11.4127i	0.122322	+	0.376470i	0.993404	−	0.114669i	$-0.0365808\pi$
$919$	3.70820	+	11.4127i	0.122322	+	0.376470i	−0.871081	+	0.491139i	$0.836581\pi$
$920$		0			0
$921$	−9.05573	+	6.57937i	−0.298396	+	0.216798i
$922$		0			0
$923$	−5.41641			−0.178283
$924$		0			0
$925$	5.85410			0.192482
$926$		0			0
$927$	−5.15248	+	3.74349i	−0.169230	+	0.122952i
$928$		0			0
$929$	6.09675	+	18.7639i	0.200028	+	0.615622i	0.999881	+	0.0154266i	$0.00491063\pi$
$929$	6.09675	+	18.7639i	0.200028	+	0.615622i	−0.799853	+	0.600196i	$0.795089\pi$
$930$		0			0
$931$	−39.3156	−	28.5645i	−1.28852	−	0.936162i
$932$		0			0
$933$	−2.47214	+	7.60845i	−0.0809341	+	0.249090i
$934$		0			0
$935$	2.47214	−	0.555029i	0.0808475	−	0.0181514i
$936$		0			0
$937$	−7.97871	+	24.5560i	−0.260653	+	0.802208i	0.732010	+	0.681294i	$0.238583\pi$
$937$	−7.97871	+	24.5560i	−0.260653	+	0.802208i	−0.992663	+	0.120914i	$0.961417\pi$
$938$		0			0
$939$	−0.583592	−	0.424005i	−0.0190448	−	0.0138369i
$940$		0			0
$941$	−0.639320	−	1.96763i	−0.0208412	−	0.0641428i	0.940095	−	0.340913i	$-0.110736\pi$
$941$	−0.639320	−	1.96763i	−0.0208412	−	0.0641428i	−0.960936	+	0.276770i	$0.910736\pi$
$942$		0			0
$943$	26.9164	−	19.5559i	0.876519	−	0.636828i
$944$		0			0
$945$	−2.11146			−0.0686857
$946$		0			0
$947$	43.9574			1.42842			0.714212	−	0.699929i	$-0.246785\pi$
$947$	43.9574			1.42842			0.714212	+	0.699929i	$0.246785\pi$
$948$		0			0
$949$	−5.85410	+	4.25325i	−0.190032	+	0.138066i
$950$		0			0
$951$	11.7639	+	36.2057i	0.381472	+	1.17405i
$952$		0			0
$953$	−1.85410	−	1.34708i	−0.0600603	−	0.0436363i	0.557350	−	0.830278i	$-0.311818\pi$
$953$	−1.85410	−	1.34708i	−0.0600603	−	0.0436363i	−0.617410	+	0.786641i	$0.711818\pi$
$954$		0			0
$955$	−0.437694	+	1.34708i	−0.0141634	+	0.0435906i
$956$		0			0
$957$	−12.1803	−	5.25731i	−0.393734	−	0.169945i
$958$		0			0
$959$	0.0901699	−	0.277515i	0.00291174	−	0.00896141i
$960$		0			0
$961$	18.8992	+	13.7311i	0.609651	+	0.442938i
$962$		0			0
$963$	−7.49342	−	23.0624i	−0.241472	−	0.743175i
$964$		0			0
$965$	17.3262	−	12.5882i	0.557751	−	0.405230i
$966$		0			0
$967$	−15.0902			−0.485267			−0.242634	−	0.970118i	$-0.578011\pi$
$967$	−15.0902			−0.485267			−0.242634	+	0.970118i	$0.578011\pi$
$968$		0			0
$969$	6.69505			0.215076
$970$		0			0
$971$	−42.3435	+	30.7643i	−1.35887	+	0.987274i	−0.360350	+	0.932817i	$0.617343\pi$
$971$	−42.3435	+	30.7643i	−1.35887	+	0.987274i	−0.998516	+	0.0544570i	$0.982657\pi$
$972$		0			0
$973$	−1.75329	−	5.39607i	−0.0562079	−	0.172990i
$974$		0			0
$975$	−0.618034	−	0.449028i	−0.0197929	−	0.0143804i
$976$		0			0
$977$	5.61803	−	17.2905i	0.179737	−	0.553173i	−0.820081	−	0.572247i	$-0.806072\pi$
$977$	5.61803	−	17.2905i	0.179737	−	0.553173i	0.999818	+	0.0190740i	$0.00607182\pi$
$978$		0			0
$979$	−51.8713	−	22.3888i	−1.65781	−	0.715550i
$980$		0			0
$981$	−7.49342	+	23.0624i	−0.239247	+	0.736325i
$982$		0			0
$983$	−15.3992	−	11.1882i	−0.491158	−	0.356847i	0.314472	−	0.949267i	$-0.398173\pi$
$983$	−15.3992	−	11.1882i	−0.491158	−	0.356847i	−0.805629	+	0.592420i	$0.798173\pi$
$984$		0			0
$985$	4.97214	+	15.3027i	0.158425	+	0.487583i
$986$		0			0
$987$	1.65248	−	1.20059i	0.0525989	−	0.0382153i
$988$		0			0
$989$	−32.6525			−1.03829
$990$		0			0
$991$	34.7214			1.10296			0.551480	−	0.834188i	$-0.314063\pi$
$991$	34.7214			1.10296			0.551480	+	0.834188i	$0.314063\pi$
$992$		0			0
$993$	−16.6180	+	12.0737i	−0.527357	+	0.383148i
$994$		0			0
$995$	−3.61803	−	11.1352i	−0.114699	−	0.353008i
$996$		0			0
$997$	35.2148	+	25.5850i	1.11526	+	0.810286i	0.983484	−	0.180993i	$-0.0579311\pi$
$997$	35.2148	+	25.5850i	1.11526	+	0.810286i	0.131779	+	0.991279i	$0.457931\pi$
$998$		0			0
$999$	−10.0000	+	30.7768i	−0.316386	+	0.973736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bo.a.801.1		4
4.3	odd	2		110.2.g.a.31.1	✓	4
11.4	even	5		9680.2.a.bh.1.2		2
11.5	even	5	inner	880.2.bo.a.401.1		4
11.7	odd	10		9680.2.a.bi.1.2		2
12.11	even	2		990.2.n.f.361.1		4
20.3	even	4		550.2.ba.a.449.1		8
20.7	even	4		550.2.ba.a.449.2		8
20.19	odd	2		550.2.h.f.251.1		4
44.7	even	10		1210.2.a.p.1.1		2
44.15	odd	10		1210.2.a.t.1.1		2
44.27	odd	10		110.2.g.a.71.1	yes	4
132.71	even	10		990.2.n.f.181.1		4
220.27	even	20		550.2.ba.a.49.1		8
220.59	odd	10		6050.2.a.bu.1.2		2
220.139	even	10		6050.2.a.cm.1.2		2
220.159	odd	10		550.2.h.f.401.1		4
220.203	even	20		550.2.ba.a.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.a.31.1	✓	4	4.3	odd	2
110.2.g.a.71.1	yes	4	44.27	odd	10
550.2.h.f.251.1		4	20.19	odd	2
550.2.h.f.401.1		4	220.159	odd	10
550.2.ba.a.49.1		8	220.27	even	20
550.2.ba.a.49.2		8	220.203	even	20
550.2.ba.a.449.1		8	20.3	even	4
550.2.ba.a.449.2		8	20.7	even	4
880.2.bo.a.401.1		4	11.5	even	5	inner
880.2.bo.a.801.1		4	1.1	even	1	trivial
990.2.n.f.181.1		4	132.71	even	10
990.2.n.f.361.1		4	12.11	even	2
1210.2.a.p.1.1		2	44.7	even	10
1210.2.a.t.1.1		2	44.15	odd	10
6050.2.a.bu.1.2		2	220.59	odd	10
6050.2.a.cm.1.2		2	220.139	even	10
9680.2.a.bh.1.2		2	11.4	even	5
9680.2.a.bi.1.2		2	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.00000 + 0.726543i) q^{3} +(-0.309017 - 0.951057i) q^{5} +(0.309017 + 0.224514i) q^{7} +(-0.454915 + 1.40008i) q^{9} +(-3.04508 - 1.31433i) q^{11} +(0.190983 - 0.587785i) q^{13} +(1.00000 + 0.726543i) q^{15} +(-0.236068 - 0.726543i) q^{17} +(5.73607 - 4.16750i) q^{19} -0.472136 q^{21} -6.85410 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-1.70820 - 5.25731i) q^{27} +(-2.61803 - 1.90211i) q^{29} +(0.854102 - 2.62866i) q^{31} +(4.00000 - 0.898056i) q^{33} +(0.118034 - 0.363271i) q^{35} +(-4.73607 - 3.44095i) q^{37} +(0.236068 + 0.726543i) q^{39} +(-3.92705 + 2.85317i) q^{41} +4.76393 q^{43} +1.47214 q^{45} +(-3.50000 + 2.54290i) q^{47} +(-2.11803 - 6.51864i) q^{49} +(0.763932 + 0.555029i) q^{51} +(3.73607 - 11.4984i) q^{53} +(-0.309017 + 3.30220i) q^{55} +(-2.70820 + 8.33499i) q^{57} +(3.73607 + 2.71441i) q^{59} +(-2.76393 - 8.50651i) q^{61} +(-0.454915 + 0.330515i) q^{63} -0.618034 q^{65} -5.23607 q^{67} +(6.85410 - 4.97980i) q^{69} +(-2.70820 - 8.33499i) q^{71} +(-9.47214 - 6.88191i) q^{73} +(0.381966 - 1.17557i) q^{75} +(-0.645898 - 1.08981i) q^{77} +(3.23607 - 9.95959i) q^{79} +(1.95492 + 1.42033i) q^{81} +(-0.708204 - 2.17963i) q^{83} +(-0.618034 + 0.449028i) q^{85} +4.00000 q^{87} +17.0344 q^{89} +(0.190983 - 0.138757i) q^{91} +(1.05573 + 3.24920i) q^{93} +(-5.73607 - 4.16750i) q^{95} +(-3.70820 + 11.4127i) q^{97} +(3.22542 - 3.66547i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + q^{5} - q^{7} - 13 q^{9} - q^{11} + 3 q^{13} + 4 q^{15} + 8 q^{17} + 14 q^{19} + 16 q^{21} - 14 q^{23} - q^{25} + 20 q^{27} - 6 q^{29} - 10 q^{31} + 16 q^{33} - 4 q^{35} - 10 q^{37}+ \cdots - 43 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + q^5 - q^7 - 13 * q^9 - q^11 + 3 * q^13 + 4 * q^15 + 8 * q^17 + 14 * q^19 + 16 * q^21 - 14 * q^23 - q^25 + 20 * q^27 - 6 * q^29 - 10 * q^31 + 16 * q^33 - 4 * q^35 - 10 * q^37 - 8 * q^39 - 9 * q^41 + 28 * q^43 - 12 * q^45 - 14 * q^47 - 4 * q^49 + 12 * q^51 + 6 * q^53 + q^55 + 16 * q^57 + 6 * q^59 - 20 * q^61 - 13 * q^63 + 2 * q^65 - 12 * q^67 + 14 * q^69 + 16 * q^71 - 20 * q^73 + 6 * q^75 - 16 * q^77 + 4 * q^79 + 19 * q^81 + 24 * q^83 + 2 * q^85 + 16 * q^87 + 10 * q^89 + 3 * q^91 + 40 * q^93 - 14 * q^95 + 12 * q^97 - 43 * q^99

Introduction

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