LMFDB - Embedded newform 880.2.bo.a.81.1

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			81.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	880.81
Dual form			880.2.bo.a.641.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 3.07768i) q^{3} +(0.809017 - 0.587785i) q^{5} +(-0.809017 - 2.48990i) q^{7} +(-6.04508 - 4.39201i) q^{9} +(2.54508 - 2.12663i) q^{11} +(1.30902 + 0.951057i) q^{13} +(1.00000 + 3.07768i) q^{15} +(4.23607 - 3.07768i) q^{17} +(1.26393 - 3.88998i) q^{19} +8.47214 q^{21} -0.145898 q^{23} +(0.309017 - 0.951057i) q^{25} +(11.7082 - 8.50651i) q^{27} +(-0.381966 - 1.17557i) q^{29} +(-5.85410 - 4.25325i) q^{31} +(4.00000 + 9.95959i) q^{33} +(-2.11803 - 1.53884i) q^{35} +(-0.263932 - 0.812299i) q^{37} +(-4.23607 + 3.07768i) q^{39} +(-0.572949 + 1.76336i) q^{41} +9.23607 q^{43} -7.47214 q^{45} +(-3.50000 + 10.7719i) q^{47} +(0.118034 - 0.0857567i) q^{49} +(5.23607 + 16.1150i) q^{51} +(-0.736068 - 0.534785i) q^{53} +(0.809017 - 3.21644i) q^{55} +(10.7082 + 7.77997i) q^{57} +(-0.736068 - 2.26538i) q^{59} +(-7.23607 + 5.25731i) q^{61} +(-6.04508 + 18.6049i) q^{63} +1.61803 q^{65} -0.763932 q^{67} +(0.145898 - 0.449028i) q^{69} +(10.7082 - 7.77997i) q^{71} +(-0.527864 - 1.62460i) q^{73} +(2.61803 + 1.90211i) q^{75} +(-7.35410 - 4.61653i) q^{77} +(-1.23607 - 0.898056i) q^{79} +(7.54508 + 23.2214i) q^{81} +(12.7082 - 9.23305i) q^{83} +(1.61803 - 4.97980i) q^{85} +4.00000 q^{87} -12.0344 q^{89} +(1.30902 - 4.02874i) q^{91} +(18.9443 - 13.7638i) q^{93} +(-1.26393 - 3.88998i) q^{95} +(9.70820 + 7.05342i) q^{97} +(-24.7254 + 1.67760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

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

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	+	3.07768i	−0.577350	+	1.77690i	0.0506828	+	0.998715i	$0.483860\pi$
$3$	−1.00000	+	3.07768i	−0.577350	+	1.77690i	−0.628033	+	0.778187i	$0.716140\pi$
$4$		0			0
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$		0			0
$7$	−0.809017	−	2.48990i	−0.305780	−	0.941093i	−0.979385	−	0.202002i	$-0.935255\pi$
$7$	−0.809017	−	2.48990i	−0.305780	−	0.941093i	0.673605	−	0.739091i	$-0.264745\pi$
$8$		0			0
$9$	−6.04508	−	4.39201i	−2.01503	−	1.46400i
$10$		0			0
$11$	2.54508	−	2.12663i	0.767372	−	0.641202i
$11$	2.54508	−	2.12663i	0.767372	−	0.641202i
$12$		0			0
$13$	1.30902	+	0.951057i	0.363056	+	0.263776i	0.754326	−	0.656500i	$-0.227964\pi$
$13$	1.30902	+	0.951057i	0.363056	+	0.263776i	−0.391270	+	0.920276i	$0.627964\pi$
$14$		0			0
$15$	1.00000	+	3.07768i	0.258199	+	0.794654i
$16$		0			0
$17$	4.23607	−	3.07768i	1.02740	−	0.746448i	0.0596113	−	0.998222i	$-0.481014\pi$
$17$	4.23607	−	3.07768i	1.02740	−	0.746448i	0.967786	+	0.251774i	$0.0810139\pi$
$18$		0			0
$19$	1.26393	−	3.88998i	0.289966	−	0.892423i	−0.694900	−	0.719106i	$-0.744551\pi$
$19$	1.26393	−	3.88998i	0.289966	−	0.892423i	0.984866	−	0.173317i	$-0.0554485\pi$
$20$		0			0
$21$	8.47214			1.84877
$22$		0			0
$23$	−0.145898			−0.0304218			−0.0152109	−	0.999884i	$-0.504842\pi$
$23$	−0.145898			−0.0304218			−0.0152109	+	0.999884i	$0.504842\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$		0			0
$27$	11.7082	−	8.50651i	2.25324	−	1.63708i
$28$		0			0
$29$	−0.381966	−	1.17557i	−0.0709293	−	0.218298i	0.909308	−	0.416124i	$-0.136612\pi$
$29$	−0.381966	−	1.17557i	−0.0709293	−	0.218298i	−0.980237	+	0.197826i	$0.936612\pi$
$30$		0			0
$31$	−5.85410	−	4.25325i	−1.05143	−	0.763907i	−0.0789443	−	0.996879i	$-0.525155\pi$
$31$	−5.85410	−	4.25325i	−1.05143	−	0.763907i	−0.972483	+	0.232972i	$0.925155\pi$
$32$		0			0
$33$	4.00000	+	9.95959i	0.696311	+	1.73374i
$34$		0			0
$35$	−2.11803	−	1.53884i	−0.358013	−	0.260112i
$36$		0			0
$37$	−0.263932	−	0.812299i	−0.0433902	−	0.133541i	0.927015	−	0.375025i	$-0.122366\pi$
$37$	−0.263932	−	0.812299i	−0.0433902	−	0.133541i	−0.970405	+	0.241484i	$0.922366\pi$
$38$		0			0
$39$	−4.23607	+	3.07768i	−0.678314	+	0.492824i
$40$		0			0
$41$	−0.572949	+	1.76336i	−0.0894796	+	0.275390i	−0.985776	−	0.168066i	$-0.946248\pi$
$41$	−0.572949	+	1.76336i	−0.0894796	+	0.275390i	0.896296	+	0.443456i	$0.146248\pi$
$42$		0			0
$43$	9.23607			1.40849			0.704244	−	0.709958i	$-0.251286\pi$
$43$	9.23607			1.40849			0.704244	+	0.709958i	$0.251286\pi$
$44$		0			0
$45$	−7.47214			−1.11388
$46$		0			0
$47$	−3.50000	+	10.7719i	−0.510527	+	1.57124i	0.280748	+	0.959782i	$0.409418\pi$
$47$	−3.50000	+	10.7719i	−0.510527	+	1.57124i	−0.791275	+	0.611460i	$0.790582\pi$
$48$		0			0
$49$	0.118034	−	0.0857567i	0.0168620	−	0.0122510i
$50$		0			0
$51$	5.23607	+	16.1150i	0.733196	+	2.25655i
$52$		0			0
$53$	−0.736068	−	0.534785i	−0.101107	−	0.0734583i	0.536083	−	0.844165i	$-0.319903\pi$
$53$	−0.736068	−	0.534785i	−0.101107	−	0.0734583i	−0.637190	+	0.770707i	$0.719903\pi$
$54$		0			0
$55$	0.809017	−	3.21644i	0.109088	−	0.433705i
$56$		0			0
$57$	10.7082	+	7.77997i	1.41834	+	1.03048i
$58$		0			0
$59$	−0.736068	−	2.26538i	−0.0958279	−	0.294928i	0.891641	−	0.452744i	$-0.149555\pi$
$59$	−0.736068	−	2.26538i	−0.0958279	−	0.294928i	−0.987469	+	0.157816i	$0.949555\pi$
$60$		0			0
$61$	−7.23607	+	5.25731i	−0.926484	+	0.673130i	−0.945129	−	0.326696i	$-0.894065\pi$
$61$	−7.23607	+	5.25731i	−0.926484	+	0.673130i	0.0186458	+	0.999826i	$0.494065\pi$
$62$		0			0
$63$	−6.04508	+	18.6049i	−0.761609	+	2.34399i
$64$		0			0
$65$	1.61803			0.200692
$66$		0			0
$67$	−0.763932			−0.0933292			−0.0466646	−	0.998911i	$-0.514859\pi$
$67$	−0.763932			−0.0933292			−0.0466646	+	0.998911i	$0.514859\pi$
$68$		0			0
$69$	0.145898	−	0.449028i	0.0175641	−	0.0540566i
$70$		0			0
$71$	10.7082	−	7.77997i	1.27083	−	0.923312i	0.271595	−	0.962412i	$-0.412449\pi$
$71$	10.7082	−	7.77997i	1.27083	−	0.923312i	0.999235	+	0.0390997i	$0.0124490\pi$
$72$		0			0
$73$	−0.527864	−	1.62460i	−0.0617818	−	0.190145i	0.915402	−	0.402542i	$-0.131873\pi$
$73$	−0.527864	−	1.62460i	−0.0617818	−	0.190145i	−0.977184	+	0.212397i	$0.931873\pi$
$74$		0			0
$75$	2.61803	+	1.90211i	0.302305	+	0.219637i
$76$		0			0
$77$	−7.35410	−	4.61653i	−0.838078	−	0.526102i
$78$		0			0
$79$	−1.23607	−	0.898056i	−0.139069	−	0.101039i	0.516076	−	0.856543i	$-0.327392\pi$
$79$	−1.23607	−	0.898056i	−0.139069	−	0.101039i	−0.655144	+	0.755504i	$0.727392\pi$
$80$		0			0
$81$	7.54508	+	23.2214i	0.838343	+	2.58015i
$82$		0			0
$83$	12.7082	−	9.23305i	1.39491	−	1.01346i	0.399600	−	0.916690i	$-0.369149\pi$
$83$	12.7082	−	9.23305i	1.39491	−	1.01346i	0.995307	−	0.0967693i	$-0.0308509\pi$
$84$		0			0
$85$	1.61803	−	4.97980i	0.175500	−	0.540135i
$86$		0			0
$87$	4.00000			0.428845
$88$		0			0
$89$	−12.0344			−1.27565			−0.637824	−	0.770182i	$-0.720165\pi$
$89$	−12.0344			−1.27565			−0.637824	+	0.770182i	$0.720165\pi$
$90$		0			0
$91$	1.30902	−	4.02874i	0.137222	−	0.422327i
$92$		0			0
$93$	18.9443	−	13.7638i	1.96443	−	1.42724i
$94$		0			0
$95$	−1.26393	−	3.88998i	−0.129677	−	0.399104i
$96$		0			0
$97$	9.70820	+	7.05342i	0.985719	+	0.716167i	0.958979	−	0.283476i	$-0.0914876\pi$
$97$	9.70820	+	7.05342i	0.985719	+	0.716167i	0.0267394	+	0.999642i	$0.491488\pi$
$98$		0			0
$99$	−24.7254	+	1.67760i	−2.48500	+	0.168605i
$100$		0			0
$101$	−3.00000	−	2.17963i	−0.298511	−	0.216881i	0.428440	−	0.903570i	$-0.359063\pi$
$101$	−3.00000	−	2.17963i	−0.298511	−	0.216881i	−0.726951	+	0.686689i	$0.759063\pi$
$102$		0			0
$103$	3.50000	+	10.7719i	0.344865	+	1.06139i	0.961656	+	0.274259i	$0.0884325\pi$
$103$	3.50000	+	10.7719i	0.344865	+	1.06139i	−0.616791	+	0.787127i	$0.711567\pi$
$104$		0			0
$105$	6.85410	−	4.97980i	0.668892	−	0.485978i
$106$		0			0
$107$	2.32624	−	7.15942i	0.224886	−	0.692128i	−0.773417	−	0.633897i	$-0.781454\pi$
$107$	2.32624	−	7.15942i	0.224886	−	0.692128i	0.998303	−	0.0582304i	$-0.0185458\pi$
$108$		0			0
$109$	7.52786			0.721039			0.360519	−	0.932752i	$-0.382599\pi$
$109$	7.52786			0.721039			0.360519	+	0.932752i	$0.382599\pi$
$110$		0			0
$111$	2.76393			0.262341
$112$		0			0
$113$	1.94427	−	5.98385i	0.182902	−	0.562914i	−0.817004	−	0.576632i	$-0.804367\pi$
$113$	1.94427	−	5.98385i	0.182902	−	0.562914i	0.999906	+	0.0137181i	$0.00436676\pi$
$114$		0			0
$115$	−0.118034	+	0.0857567i	−0.0110067	+	0.00799685i
$116$		0			0
$117$	−3.73607	−	11.4984i	−0.345400	−	1.06303i
$118$		0			0
$119$	−11.0902	−	8.05748i	−1.01663	−	0.738628i
$120$		0			0
$121$	1.95492	−	10.8249i	0.177720	−	0.984081i
$122$		0			0
$123$	−4.85410	−	3.52671i	−0.437680	−	0.317993i
$124$		0			0
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$		0			0
$127$	−1.92705	+	1.40008i	−0.170998	+	0.124237i	−0.669993	−	0.742368i	$-0.733703\pi$
$127$	−1.92705	+	1.40008i	−0.170998	+	0.124237i	0.498995	+	0.866605i	$0.333703\pi$
$128$		0			0
$129$	−9.23607	+	28.4257i	−0.813190	+	2.50274i
$130$		0			0
$131$	−11.4164			−0.997456			−0.498728	−	0.866758i	$-0.666199\pi$
$131$	−11.4164			−0.997456			−0.498728	+	0.866758i	$0.666199\pi$
$132$		0			0
$133$	−10.7082			−0.928519
$134$		0			0
$135$	4.47214	−	13.7638i	0.384900	−	1.18460i
$136$		0			0
$137$	4.23607	−	3.07768i	0.361912	−	0.262944i	−0.391937	−	0.919992i	$-0.628195\pi$
$137$	4.23607	−	3.07768i	0.361912	−	0.262944i	0.753849	+	0.657048i	$0.228195\pi$
$138$		0			0
$139$	2.51722	+	7.74721i	0.213508	+	0.657110i	0.999256	+	0.0385633i	$0.0122781\pi$
$139$	2.51722	+	7.74721i	0.213508	+	0.657110i	−0.785748	+	0.618546i	$0.787722\pi$
$140$		0			0
$141$	−29.6525	−	21.5438i	−2.49719	−	1.81431i
$142$		0			0
$143$	5.35410	−	0.363271i	0.447732	−	0.0303783i
$144$		0			0
$145$	−1.00000	−	0.726543i	−0.0830455	−	0.0603361i
$146$		0			0
$147$	0.145898	+	0.449028i	0.0120335	+	0.0370352i
$148$		0			0
$149$	3.23607	−	2.35114i	0.265109	−	0.192613i	−0.447287	−	0.894390i	$-0.647610\pi$
$149$	3.23607	−	2.35114i	0.265109	−	0.192613i	0.712396	+	0.701777i	$0.247610\pi$
$150$		0			0
$151$	−3.90983	+	12.0332i	−0.318177	+	0.979250i	0.656249	+	0.754544i	$0.272142\pi$
$151$	−3.90983	+	12.0332i	−0.318177	+	0.979250i	−0.974427	+	0.224705i	$0.927858\pi$
$152$		0			0
$153$	−39.1246			−3.16304
$154$		0			0
$155$	−7.23607			−0.581215
$156$		0			0
$157$	2.66312	−	8.19624i	0.212540	−	0.654131i	−0.786779	−	0.617235i	$-0.788253\pi$
$157$	2.66312	−	8.19624i	0.212540	−	0.654131i	0.999319	−	0.0368962i	$-0.0117471\pi$
$158$		0			0
$159$	2.38197	−	1.73060i	0.188902	−	0.137245i
$160$		0			0
$161$	0.118034	+	0.363271i	0.00930238	+	0.0286298i
$162$		0			0
$163$	−5.85410	−	4.25325i	−0.458529	−	0.333141i	0.334425	−	0.942422i	$-0.391458\pi$
$163$	−5.85410	−	4.25325i	−0.458529	−	0.333141i	−0.792954	+	0.609282i	$0.791458\pi$
$164$		0			0
$165$	9.09017	+	5.70634i	0.707669	+	0.444238i
$166$		0			0
$167$	6.39919	+	4.64928i	0.495184	+	0.359772i	0.807174	−	0.590313i	$-0.200996\pi$
$167$	6.39919	+	4.64928i	0.495184	+	0.359772i	−0.311990	+	0.950085i	$0.600996\pi$
$168$		0			0
$169$	−3.20820	−	9.87384i	−0.246785	−	0.759526i
$170$		0			0
$171$	−24.7254	+	17.9641i	−1.89080	+	1.37375i
$172$		0			0
$173$	−3.89919	+	12.0005i	−0.296450	+	0.912378i	0.686281	+	0.727337i	$0.259242\pi$
$173$	−3.89919	+	12.0005i	−0.296450	+	0.912378i	−0.982731	+	0.185042i	$0.940758\pi$
$174$		0			0
$175$	−2.61803			−0.197905
$176$		0			0
$177$	7.70820			0.579384
$178$		0			0
$179$	0.899187	−	2.76741i	0.0672084	−	0.206846i	−0.911812	−	0.410607i	$-0.865317\pi$
$179$	0.899187	−	2.76741i	0.0672084	−	0.206846i	0.979021	+	0.203761i	$0.0653167\pi$
$180$		0			0
$181$	16.5623	−	12.0332i	1.23107	−	0.894422i	0.234097	−	0.972213i	$-0.424787\pi$
$181$	16.5623	−	12.0332i	1.23107	−	0.894422i	0.996970	+	0.0777911i	$0.0247867\pi$
$182$		0			0
$183$	−8.94427	−	27.5276i	−0.661180	−	2.03490i
$184$		0			0
$185$	−0.690983	−	0.502029i	−0.0508021	−	0.0369099i
$186$		0			0
$187$	4.23607	−	16.8415i	0.309772	−	1.23157i
$188$		0			0
$189$	−30.6525	−	22.2703i	−2.22964	−	1.61993i
$190$		0			0
$191$	−7.85410	−	24.1724i	−0.568303	−	1.74906i	−0.657928	−	0.753081i	$-0.728567\pi$
$191$	−7.85410	−	24.1724i	−0.568303	−	1.74906i	0.0896251	−	0.995976i	$-0.471433\pi$
$192$		0			0
$193$	4.38197	−	3.18368i	0.315421	−	0.229167i	−0.418798	−	0.908079i	$-0.637549\pi$
$193$	4.38197	−	3.18368i	0.315421	−	0.229167i	0.734219	+	0.678913i	$0.237549\pi$
$194$		0			0
$195$	−1.61803	+	4.97980i	−0.115870	+	0.356611i
$196$		0			0
$197$	−4.90983			−0.349811			−0.174905	−	0.984585i	$-0.555962\pi$
$197$	−4.90983			−0.349811			−0.174905	+	0.984585i	$0.555962\pi$
$198$		0			0
$199$	−1.70820			−0.121091			−0.0605457	−	0.998165i	$-0.519284\pi$
$199$	−1.70820			−0.121091			−0.0605457	+	0.998165i	$0.519284\pi$
$200$		0			0
$201$	0.763932	−	2.35114i	0.0538836	−	0.165837i
$202$		0			0
$203$	−2.61803	+	1.90211i	−0.183750	+	0.133502i
$204$		0			0
$205$	0.572949	+	1.76336i	0.0400165	+	0.123158i
$206$		0			0
$207$	0.881966	+	0.640786i	0.0613009	+	0.0445377i
$208$		0			0
$209$	−5.05573	−	12.5882i	−0.349712	−	0.870747i
$210$		0			0
$211$	16.9443	+	12.3107i	1.16649	+	0.847506i	0.990585	−	0.136901i	$-0.0437142\pi$
$211$	16.9443	+	12.3107i	1.16649	+	0.847506i	0.175907	+	0.984407i	$0.443714\pi$
$212$		0			0
$213$	13.2361	+	40.7364i	0.906920	+	2.79121i
$214$		0			0
$215$	7.47214	−	5.42882i	0.509595	−	0.370243i
$216$		0			0
$217$	−5.85410	+	18.0171i	−0.397402	+	1.22308i
$218$		0			0
$219$	5.52786			0.373538
$220$		0			0
$221$	8.47214			0.569898
$222$		0			0
$223$	−2.98936	+	9.20029i	−0.200182	+	0.616097i	0.799695	+	0.600407i	$0.204995\pi$
$223$	−2.98936	+	9.20029i	−0.200182	+	0.616097i	−0.999877	+	0.0156905i	$0.995005\pi$
$224$		0			0
$225$	−6.04508	+	4.39201i	−0.403006	+	0.292801i
$226$		0			0
$227$	5.09017	+	15.6659i	0.337846	+	1.03978i	0.965303	+	0.261133i	$0.0840960\pi$
$227$	5.09017	+	15.6659i	0.337846	+	1.03978i	−0.627456	+	0.778652i	$0.715904\pi$
$228$		0			0
$229$	22.7984	+	16.5640i	1.50656	+	1.09458i	0.967675	+	0.252199i	$0.0811537\pi$
$229$	22.7984	+	16.5640i	1.50656	+	1.09458i	0.538884	+	0.842380i	$0.318846\pi$
$230$		0			0
$231$	21.5623	−	18.0171i	1.41870	−	1.18544i
$232$		0			0
$233$	−12.3262	−	8.95554i	−0.807519	−	0.586697i	0.105591	−	0.994410i	$-0.466326\pi$
$233$	−12.3262	−	8.95554i	−0.807519	−	0.586697i	−0.913110	+	0.407713i	$0.866326\pi$
$234$		0			0
$235$	3.50000	+	10.7719i	0.228315	+	0.702681i
$236$		0			0
$237$	4.00000	−	2.90617i	0.259828	−	0.188776i
$238$		0			0
$239$	−2.94427	+	9.06154i	−0.190449	+	0.586142i	−1.00000		0.000908170i	$-0.999711\pi$
$239$	−2.94427	+	9.06154i	−0.190449	+	0.586142i	0.809550	+	0.587050i	$0.199711\pi$
$240$		0			0
$241$	−1.85410			−0.119433			−0.0597166	−	0.998215i	$-0.519020\pi$
$241$	−1.85410			−0.119433			−0.0597166	+	0.998215i	$0.519020\pi$
$242$		0			0
$243$	−35.5967			−2.28353
$244$		0			0
$245$	0.0450850	−	0.138757i	0.00288037	−	0.00886488i
$246$		0			0
$247$	5.35410	−	3.88998i	0.340673	−	0.247514i
$248$		0			0
$249$	15.7082	+	48.3449i	0.995467	+	3.06373i
$250$		0			0
$251$	−8.11803	−	5.89810i	−0.512406	−	0.372285i	0.301330	−	0.953520i	$-0.402570\pi$
$251$	−8.11803	−	5.89810i	−0.512406	−	0.372285i	−0.813735	+	0.581235i	$0.802570\pi$
$252$		0			0
$253$	−0.371323	+	0.310271i	−0.0233449	+	0.0195066i
$254$		0			0
$255$	13.7082	+	9.95959i	0.858441	+	0.623694i
$256$		0			0
$257$	−3.70820	−	11.4127i	−0.231311	−	0.711903i	−0.997589	−	0.0693940i	$-0.977893\pi$
$257$	−3.70820	−	11.4127i	−0.231311	−	0.711903i	0.766278	−	0.642509i	$-0.222107\pi$
$258$		0			0
$259$	−1.80902	+	1.31433i	−0.112407	+	0.0816684i
$260$		0			0
$261$	−2.85410	+	8.78402i	−0.176664	+	0.543717i
$262$		0			0
$263$	−25.7984			−1.59080			−0.795398	−	0.606088i	$-0.792738\pi$
$263$	−25.7984			−1.59080			−0.795398	+	0.606088i	$0.792738\pi$
$264$		0			0
$265$	−0.909830			−0.0558904
$266$		0			0
$267$	12.0344	−	37.0382i	0.736496	−	2.26670i
$268$		0			0
$269$	−14.2361	+	10.3431i	−0.867988	+	0.630630i	−0.930046	−	0.367442i	$-0.880234\pi$
$269$	−14.2361	+	10.3431i	−0.867988	+	0.630630i	0.0620580	+	0.998073i	$0.480234\pi$
$270$		0			0
$271$	−4.14590	−	12.7598i	−0.251845	−	0.775100i	−0.994435	−	0.105353i	$-0.966403\pi$
$271$	−4.14590	−	12.7598i	−0.251845	−	0.775100i	0.742589	−	0.669747i	$-0.233597\pi$
$272$		0			0
$273$	11.0902	+	8.05748i	0.671208	+	0.487661i
$274$		0			0
$275$	−1.23607	−	3.07768i	−0.0745377	−	0.185591i
$276$		0			0
$277$	0.500000	+	0.363271i	0.0300421	+	0.0218269i	0.602705	−	0.797964i	$-0.294090\pi$
$277$	0.500000	+	0.363271i	0.0300421	+	0.0218269i	−0.572663	+	0.819791i	$0.694090\pi$
$278$		0			0
$279$	16.7082	+	51.4226i	1.00029	+	3.07859i
$280$		0			0
$281$	−14.5623	+	10.5801i	−0.868714	+	0.631158i	−0.930242	−	0.366947i	$-0.880403\pi$
$281$	−14.5623	+	10.5801i	−0.868714	+	0.631158i	0.0615273	+	0.998105i	$0.480403\pi$
$282$		0			0
$283$	−7.67376	+	23.6174i	−0.456158	+	1.40391i	0.413613	+	0.910453i	$0.364267\pi$
$283$	−7.67376	+	23.6174i	−0.456158	+	1.40391i	−0.869771	+	0.493456i	$0.835733\pi$
$284$		0			0
$285$	13.2361			0.784037
$286$		0			0
$287$	4.85410			0.286529
$288$		0			0
$289$	3.21885	−	9.90659i	0.189344	−	0.582741i
$290$		0			0
$291$	−31.4164	+	22.8254i	−1.84166	+	1.33805i
$292$		0			0
$293$	−7.33688	−	22.5806i	−0.428625	−	1.31917i	−0.899480	−	0.436962i	$-0.856054\pi$
$293$	−7.33688	−	22.5806i	−0.428625	−	1.31917i	0.470855	−	0.882211i	$-0.343946\pi$
$294$		0			0
$295$	−1.92705	−	1.40008i	−0.112197	−	0.0815161i
$296$		0			0
$297$	11.7082	−	46.5488i	0.679379	−	2.70103i
$298$		0			0
$299$	−0.190983	−	0.138757i	−0.0110448	−	0.00802454i
$300$		0			0
$301$	−7.47214	−	22.9969i	−0.430687	−	1.32552i
$302$		0			0
$303$	9.70820	−	7.05342i	0.557722	−	0.405209i
$304$		0			0
$305$	−2.76393	+	8.50651i	−0.158262	+	0.487081i
$306$		0			0
$307$	26.9443			1.53779			0.768895	−	0.639375i	$-0.220807\pi$
$307$	26.9443			1.53779			0.768895	+	0.639375i	$0.220807\pi$
$308$		0			0
$309$	−36.6525			−2.08509
$310$		0			0
$311$	0.763932	−	2.35114i	0.0433186	−	0.133321i	−0.927058	−	0.374917i	$-0.877671\pi$
$311$	0.763932	−	2.35114i	0.0433186	−	0.133321i	0.970377	+	0.241597i	$0.0776710\pi$
$312$		0			0
$313$	−22.1803	+	16.1150i	−1.25371	+	0.910871i	−0.998431	−	0.0559968i	$-0.982166\pi$
$313$	−22.1803	+	16.1150i	−1.25371	+	0.910871i	−0.255276	+	0.966868i	$0.582166\pi$
$314$		0			0
$315$	6.04508	+	18.6049i	0.340602	+	1.04827i
$316$		0			0
$317$	−5.01722	−	3.64522i	−0.281795	−	0.204736i	0.437905	−	0.899021i	$-0.355721\pi$
$317$	−5.01722	−	3.64522i	−0.281795	−	0.204736i	−0.719700	+	0.694285i	$0.755721\pi$
$318$		0			0
$319$	−3.47214	−	2.17963i	−0.194402	−	0.122036i
$320$		0			0
$321$	19.7082	+	14.3188i	1.10000	+	0.799200i
$322$		0			0
$323$	−6.61803	−	20.3682i	−0.368237	−	1.13332i
$324$		0			0
$325$	1.30902	−	0.951057i	0.0726112	−	0.0527551i
$326$		0			0
$327$	−7.52786	+	23.1684i	−0.416292	+	1.28121i
$328$		0			0
$329$	29.6525			1.63479
$330$		0			0
$331$	14.3820			0.790504			0.395252	−	0.918573i	$-0.370657\pi$
$331$	14.3820			0.790504			0.395252	+	0.918573i	$0.370657\pi$
$332$		0			0
$333$	−1.97214	+	6.06961i	−0.108072	+	0.332613i
$334$		0			0
$335$	−0.618034	+	0.449028i	−0.0337668	+	0.0245330i
$336$		0			0
$337$	10.9443	+	33.6830i	0.596172	+	1.83483i	0.548801	+	0.835953i	$0.315084\pi$
$337$	10.9443	+	33.6830i	0.596172	+	1.83483i	0.0473712	+	0.998877i	$0.484916\pi$
$338$		0			0
$339$	16.4721	+	11.9677i	0.894644	+	0.649997i
$340$		0			0
$341$	−23.9443	+	1.62460i	−1.29666	+	0.0879769i
$342$		0			0
$343$	−15.1353	−	10.9964i	−0.817227	−	0.593750i
$344$		0			0
$345$	−0.145898	−	0.449028i	−0.00785489	−	0.0241749i
$346$		0			0
$347$	−21.9443	+	15.9434i	−1.17803	+	0.855889i	−0.991948	−	0.126645i	$-0.959579\pi$
$347$	−21.9443	+	15.9434i	−1.17803	+	0.855889i	−0.186082	+	0.982534i	$0.559579\pi$
$348$		0			0
$349$	9.56231	−	29.4298i	0.511858	−	1.57534i	−0.277068	−	0.960850i	$-0.589363\pi$
$349$	9.56231	−	29.4298i	0.511858	−	1.57534i	0.788926	−	0.614488i	$-0.210637\pi$
$350$		0			0
$351$	23.4164			1.24988
$352$		0			0
$353$	11.7082			0.623165			0.311582	−	0.950219i	$-0.399141\pi$
$353$	11.7082			0.623165			0.311582	+	0.950219i	$0.399141\pi$
$354$		0			0
$355$	4.09017	−	12.5882i	0.217084	−	0.668115i
$356$		0			0
$357$	35.8885	−	26.0746i	1.89942	−	1.38001i
$358$		0			0
$359$	9.41641	+	28.9807i	0.496979	+	1.52954i	0.813850	+	0.581075i	$0.197368\pi$
$359$	9.41641	+	28.9807i	0.496979	+	1.52954i	−0.316871	+	0.948469i	$0.602632\pi$
$360$		0			0
$361$	1.83688	+	1.33457i	0.0966779	+	0.0702406i
$362$		0			0
$363$	31.3607	+	16.8415i	1.64601	+	0.883950i
$364$		0			0
$365$	−1.38197	−	1.00406i	−0.0723354	−	0.0525547i
$366$		0			0
$367$	−3.23607	−	9.95959i	−0.168921	−	0.519887i	0.830382	−	0.557194i	$-0.188122\pi$
$367$	−3.23607	−	9.95959i	−0.168921	−	0.519887i	−0.999304	+	0.0373073i	$0.988122\pi$
$368$		0			0
$369$	11.2082	−	8.14324i	0.583476	−	0.423920i
$370$		0			0
$371$	−0.736068	+	2.26538i	−0.0382147	+	0.117613i
$372$		0			0
$373$	6.96556			0.360663			0.180331	−	0.983606i	$-0.442283\pi$
$373$	6.96556			0.360663			0.180331	+	0.983606i	$0.442283\pi$
$374$		0			0
$375$	3.23607			0.167110
$376$		0			0
$377$	0.618034	−	1.90211i	0.0318304	−	0.0979638i
$378$		0			0
$379$	−8.35410	+	6.06961i	−0.429121	+	0.311775i	−0.781297	−	0.624159i	$-0.785442\pi$
$379$	−8.35410	+	6.06961i	−0.429121	+	0.311775i	0.352176	+	0.935934i	$0.385442\pi$
$380$		0			0
$381$	−2.38197	−	7.33094i	−0.122032	−	0.375575i
$382$		0			0
$383$	−12.8262	−	9.31881i	−0.655390	−	0.476169i	0.209713	−	0.977763i	$-0.432747\pi$
$383$	−12.8262	−	9.31881i	−0.655390	−	0.476169i	−0.865103	+	0.501594i	$0.832747\pi$
$384$		0			0
$385$	−8.66312	+	0.587785i	−0.441513	+	0.0299563i
$386$		0			0
$387$	−55.8328	−	40.5649i	−2.83814	−	2.06203i
$388$		0			0
$389$	3.76393	+	11.5842i	0.190839	+	0.587342i	1.00000		0.000245108i	$-7.80203e-5\pi$
$389$	3.76393	+	11.5842i	0.190839	+	0.587342i	−0.809161	+	0.587587i	$0.800078\pi$
$390$		0			0
$391$	−0.618034	+	0.449028i	−0.0312553	+	0.0227083i
$392$		0			0
$393$	11.4164	−	35.1361i	0.575882	−	1.77238i
$394$		0			0
$395$	−1.52786			−0.0768752
$396$		0			0
$397$	6.79837			0.341201			0.170600	−	0.985340i	$-0.445429\pi$
$397$	6.79837			0.341201			0.170600	+	0.985340i	$0.445429\pi$
$398$		0			0
$399$	10.7082	−	32.9565i	0.536081	−	1.64989i
$400$		0			0
$401$	8.69098	−	6.31437i	0.434007	−	0.315325i	−0.349242	−	0.937033i	$-0.613561\pi$
$401$	8.69098	−	6.31437i	0.434007	−	0.315325i	0.783249	+	0.621708i	$0.213561\pi$
$402$		0			0
$403$	−3.61803	−	11.1352i	−0.180227	−	0.554682i
$404$		0			0
$405$	19.7533	+	14.3516i	0.981549	+	0.713137i
$406$		0			0
$407$	−2.39919	−	1.50609i	−0.118923	−	0.0746539i
$408$		0			0
$409$	18.8713	+	13.7108i	0.933127	+	0.677956i	0.946756	−	0.321951i	$-0.104339\pi$
$409$	18.8713	+	13.7108i	0.933127	+	0.677956i	−0.0136296	+	0.999907i	$0.504339\pi$
$410$		0			0
$411$	5.23607	+	16.1150i	0.258276	+	0.794892i
$412$		0			0
$413$	−5.04508	+	3.66547i	−0.248252	+	0.180366i
$414$		0			0
$415$	4.85410	−	14.9394i	0.238278	−	0.733346i
$416$		0			0
$417$	−26.3607			−1.29089
$418$		0			0
$419$	1.61803			0.0790461			0.0395231	−	0.999219i	$-0.487416\pi$
$419$	1.61803			0.0790461			0.0395231	+	0.999219i	$0.487416\pi$
$420$		0			0
$421$	−5.76393	+	17.7396i	−0.280917	+	0.864573i	0.706676	+	0.707537i	$0.250194\pi$
$421$	−5.76393	+	17.7396i	−0.280917	+	0.864573i	−0.987593	+	0.157036i	$0.949806\pi$
$422$		0			0
$423$	68.4681	−	49.7450i	3.32903	−	2.41868i
$424$		0			0
$425$	−1.61803	−	4.97980i	−0.0784862	−	0.241556i
$426$		0			0
$427$	18.9443	+	13.7638i	0.916778	+	0.666078i
$428$		0			0
$429$	−4.23607	+	16.8415i	−0.204519	+	0.813115i
$430$		0			0
$431$	−21.1803	−	15.3884i	−1.02022	−	0.741234i	−0.0538929	−	0.998547i	$-0.517163\pi$
$431$	−21.1803	−	15.3884i	−1.02022	−	0.741234i	−0.966328	+	0.257313i	$0.917163\pi$
$432$		0			0
$433$	2.94427	+	9.06154i	0.141493	+	0.435470i	0.996543	−	0.0830748i	$-0.0264741\pi$
$433$	2.94427	+	9.06154i	0.141493	+	0.435470i	−0.855051	+	0.518545i	$0.826474\pi$
$434$		0			0
$435$	3.23607	−	2.35114i	0.155158	−	0.112729i
$436$		0			0
$437$	−0.184405	+	0.567541i	−0.00882130	+	0.0271492i
$438$		0			0
$439$	13.1246			0.626404			0.313202	−	0.949687i	$-0.398598\pi$
$439$	13.1246			0.626404			0.313202	+	0.949687i	$0.398598\pi$
$440$		0			0
$441$	−1.09017			−0.0519129
$442$		0			0
$443$	−0.416408	+	1.28157i	−0.0197841	+	0.0608893i	−0.960461	−	0.278414i	$-0.910191\pi$
$443$	−0.416408	+	1.28157i	−0.0197841	+	0.0608893i	0.940677	+	0.339303i	$0.110191\pi$
$444$		0			0
$445$	−9.73607	+	7.07367i	−0.461534	+	0.335324i
$446$		0			0
$447$	4.00000	+	12.3107i	0.189194	+	0.582278i
$448$		0			0
$449$	−2.54508	−	1.84911i	−0.120110	−	0.0872650i	0.526109	−	0.850417i	$-0.323651\pi$
$449$	−2.54508	−	1.84911i	−0.120110	−	0.0872650i	−0.646219	+	0.763152i	$0.723651\pi$
$450$		0			0
$451$	2.29180	+	5.70634i	0.107916	+	0.268701i
$452$		0			0
$453$	−33.1246	−	24.0664i	−1.55633	−	1.13074i
$454$		0			0
$455$	−1.30902	−	4.02874i	−0.0613677	−	0.188870i
$456$		0			0
$457$	−26.3262	+	19.1271i	−1.23149	+	0.894729i	−0.997001	−	0.0773894i	$-0.975342\pi$
$457$	−26.3262	+	19.1271i	−1.23149	+	0.894729i	−0.234489	+	0.972119i	$0.575342\pi$
$458$		0			0
$459$	23.4164	−	72.0683i	1.09298	−	3.36386i
$460$		0			0
$461$	28.5410			1.32929			0.664644	−	0.747160i	$-0.268583\pi$
$461$	28.5410			1.32929			0.664644	+	0.747160i	$0.268583\pi$
$462$		0			0
$463$	−15.5066			−0.720652			−0.360326	−	0.932826i	$-0.617335\pi$
$463$	−15.5066			−0.720652			−0.360326	+	0.932826i	$0.617335\pi$
$464$		0			0
$465$	7.23607	−	22.2703i	0.335565	−	1.03276i
$466$		0			0
$467$	13.9443	−	10.1311i	0.645264	−	0.468812i	−0.216391	−	0.976307i	$-0.569428\pi$
$467$	13.9443	−	10.1311i	0.645264	−	0.468812i	0.861655	+	0.507495i	$0.169428\pi$
$468$		0			0
$469$	0.618034	+	1.90211i	0.0285382	+	0.0878314i
$470$		0			0
$471$	22.5623	+	16.3925i	1.03962	+	0.755325i
$472$		0			0
$473$	23.5066	−	19.6417i	1.08083	−	0.903125i
$474$		0			0
$475$	−3.30902	−	2.40414i	−0.151828	−	0.110310i
$476$		0			0
$477$	2.10081	+	6.46564i	0.0961896	+	0.296041i
$478$		0			0
$479$	−23.9443	+	17.3965i	−1.09404	+	0.794868i	−0.980077	−	0.198617i	$-0.936355\pi$
$479$	−23.9443	+	17.3965i	−1.09404	+	0.794868i	−0.113965	+	0.993485i	$0.536355\pi$
$480$		0			0
$481$	0.427051	−	1.31433i	0.0194718	−	0.0599282i
$482$		0			0
$483$	−1.23607			−0.0562430
$484$		0			0
$485$	12.0000			0.544892
$486$		0			0
$487$	−11.4164	+	35.1361i	−0.517327	+	1.59217i	0.261681	+	0.965154i	$0.415723\pi$
$487$	−11.4164	+	35.1361i	−0.517327	+	1.59217i	−0.779008	+	0.627014i	$0.784277\pi$
$488$		0			0
$489$	18.9443	−	13.7638i	0.856690	−	0.622421i
$490$		0			0
$491$	−11.2639	−	34.6668i	−0.508334	−	1.56449i	−0.795092	−	0.606489i	$-0.792578\pi$
$491$	−11.2639	−	34.6668i	−0.508334	−	1.56449i	0.286758	−	0.958003i	$-0.407422\pi$
$492$		0			0
$493$	−5.23607	−	3.80423i	−0.235821	−	0.171334i
$494$		0			0
$495$	−19.0172	+	15.8904i	−0.854761	+	0.714222i
$496$		0			0
$497$	−28.0344	−	20.3682i	−1.25752	−	0.913639i
$498$		0			0
$499$	3.95492	+	12.1720i	0.177046	+	0.544893i	0.999721	−	0.0236199i	$-0.00751914\pi$
$499$	3.95492	+	12.1720i	0.177046	+	0.544893i	−0.822675	+	0.568512i	$0.807519\pi$
$500$		0			0
$501$	−20.7082	+	15.0454i	−0.925174	+	0.672178i
$502$		0			0
$503$	−2.31966	+	7.13918i	−0.103429	+	0.318320i	−0.989358	−	0.145499i	$-0.953521\pi$
$503$	−2.31966	+	7.13918i	−0.103429	+	0.318320i	0.885930	+	0.463819i	$0.153521\pi$
$504$		0			0
$505$	−3.70820			−0.165013
$506$		0			0
$507$	33.5967			1.49208
$508$		0			0
$509$	−9.61803	+	29.6013i	−0.426312	+	1.31205i	0.475421	+	0.879759i	$0.342296\pi$
$509$	−9.61803	+	29.6013i	−0.426312	+	1.31205i	−0.901733	+	0.432294i	$0.857704\pi$
$510$		0			0
$511$	−3.61803	+	2.62866i	−0.160052	+	0.116285i
$512$		0			0
$513$	−18.2918	−	56.2964i	−0.807603	−	2.48554i
$514$		0			0
$515$	9.16312	+	6.65740i	0.403775	+	0.293360i
$516$		0			0
$517$	14.0000	+	34.8586i	0.615719	+	1.53308i
$518$		0			0
$519$	−33.0344	−	24.0009i	−1.45005	−	1.05352i
$520$		0			0
$521$	−2.66312	−	8.19624i	−0.116673	−	0.359084i	0.875619	−	0.483002i	$-0.160454\pi$
$521$	−2.66312	−	8.19624i	−0.116673	−	0.359084i	−0.992292	+	0.123919i	$0.960454\pi$
$522$		0			0
$523$	−5.94427	+	4.31877i	−0.259925	+	0.188846i	−0.710114	−	0.704087i	$-0.751357\pi$
$523$	−5.94427	+	4.31877i	−0.259925	+	0.188846i	0.450189	+	0.892933i	$0.351357\pi$
$524$		0			0
$525$	2.61803	−	8.05748i	0.114260	−	0.351657i
$526$		0			0
$527$	−37.8885			−1.65045
$528$		0			0
$529$	−22.9787			−0.999075
$530$		0			0
$531$	−5.50000	+	16.9273i	−0.238680	+	0.734580i
$532$		0			0
$533$	−2.42705	+	1.76336i	−0.105127	+	0.0763794i
$534$		0			0
$535$	−2.32624	−	7.15942i	−0.100572	−	0.309529i
$536$		0			0
$537$	7.61803	+	5.53483i	0.328742	+	0.238845i
$538$		0			0
$539$	0.118034	−	0.469272i	0.00508408	−	0.0202130i
$540$		0			0
$541$	6.47214	+	4.70228i	0.278259	+	0.202167i	0.718158	−	0.695880i	$-0.244986\pi$
$541$	6.47214	+	4.70228i	0.278259	+	0.202167i	−0.439899	+	0.898047i	$0.644986\pi$
$542$		0			0
$543$	20.4721	+	63.0068i	0.878543	+	2.70388i
$544$		0			0
$545$	6.09017	−	4.42477i	0.260874	−	0.189536i
$546$		0			0
$547$	4.81966	−	14.8334i	0.206074	−	0.634230i	−0.793594	−	0.608448i	$-0.791792\pi$
$547$	4.81966	−	14.8334i	0.206074	−	0.634230i	0.999668	−	0.0257820i	$-0.00820757\pi$
$548$		0			0
$549$	66.8328			2.85236
$550$		0			0
$551$	−5.05573			−0.215381
$552$		0			0
$553$	−1.23607	+	3.80423i	−0.0525630	+	0.161772i
$554$		0			0
$555$	2.23607	−	1.62460i	0.0949158	−	0.0689604i
$556$		0			0
$557$	10.2639	+	31.5891i	0.434897	+	1.33847i	0.893192	+	0.449675i	$0.148460\pi$
$557$	10.2639	+	31.5891i	0.434897	+	1.33847i	−0.458296	+	0.888800i	$0.651540\pi$
$558$		0			0
$559$	12.0902	+	8.78402i	0.511360	+	0.371525i
$560$		0			0
$561$	47.5967	+	29.8788i	2.00954	+	1.26148i
$562$		0			0
$563$	19.3262	+	14.0413i	0.814504	+	0.591772i	0.915133	−	0.403152i	$-0.132086\pi$
$563$	19.3262	+	14.0413i	0.814504	+	0.591772i	−0.100629	+	0.994924i	$0.532086\pi$
$564$		0			0
$565$	−1.94427	−	5.98385i	−0.0817961	−	0.251743i
$566$		0			0
$567$	51.7148	−	37.5730i	2.17182	−	1.57792i
$568$		0			0
$569$	2.57295	−	7.91872i	0.107864	−	0.331970i	−0.882528	−	0.470259i	$-0.844160\pi$
$569$	2.57295	−	7.91872i	0.107864	−	0.331970i	0.990392	+	0.138289i	$0.0441604\pi$
$570$		0			0
$571$	29.0902			1.21739			0.608693	−	0.793406i	$-0.291694\pi$
$571$	29.0902			1.21739			0.608693	+	0.793406i	$0.291694\pi$
$572$		0			0
$573$	82.2492			3.43601
$574$		0			0
$575$	−0.0450850	+	0.138757i	−0.00188017	+	0.00578658i
$576$		0			0
$577$	−12.0902	+	8.78402i	−0.503320	+	0.365684i	−0.810284	−	0.586038i	$-0.800687\pi$
$577$	−12.0902	+	8.78402i	−0.503320	+	0.365684i	0.306963	+	0.951721i	$0.400687\pi$
$578$		0			0
$579$	5.41641	+	16.6700i	0.225098	+	0.692781i
$580$		0			0
$581$	−33.2705	−	24.1724i	−1.38029	−	1.00284i
$582$		0			0
$583$	−3.01064	+	0.204270i	−0.124688	+	0.00845998i
$584$		0			0
$585$	−9.78115	−	7.10642i	−0.404401	−	0.293814i
$586$		0			0
$587$	6.41641	+	19.7477i	0.264833	+	0.815074i	0.991732	+	0.128328i	$0.0409612\pi$
$587$	6.41641	+	19.7477i	0.264833	+	0.815074i	−0.726898	+	0.686745i	$0.759039\pi$
$588$		0			0
$589$	−23.9443	+	17.3965i	−0.986607	+	0.716812i
$590$		0			0
$591$	4.90983	−	15.1109i	0.201963	−	0.621579i
$592$		0			0
$593$	−19.7082			−0.809319			−0.404659	−	0.914467i	$-0.632610\pi$
$593$	−19.7082			−0.809319			−0.404659	+	0.914467i	$0.632610\pi$
$594$		0			0
$595$	−13.7082			−0.561982
$596$		0			0
$597$	1.70820	−	5.25731i	0.0699121	−	0.215167i
$598$		0			0
$599$	13.3262	−	9.68208i	0.544495	−	0.395599i	−0.281257	−	0.959633i	$-0.590751\pi$
$599$	13.3262	−	9.68208i	0.544495	−	0.395599i	0.825752	+	0.564034i	$0.190751\pi$
$600$		0			0
$601$	6.97214	+	21.4580i	0.284399	+	0.875291i	0.986578	+	0.163290i	$0.0522108\pi$
$601$	6.97214	+	21.4580i	0.284399	+	0.875291i	−0.702179	+	0.712001i	$0.747789\pi$
$602$		0			0
$603$	4.61803	+	3.35520i	0.188061	+	0.136634i
$604$		0			0
$605$	−4.78115	−	9.90659i	−0.194382	−	0.402760i
$606$		0			0
$607$	26.1803	+	19.0211i	1.06263	+	0.772044i	0.974573	−	0.224072i	$-0.0719350\pi$
$607$	26.1803	+	19.0211i	1.06263	+	0.772044i	0.0880546	+	0.996116i	$0.471935\pi$
$608$		0			0
$609$	−3.23607	−	9.95959i	−0.131132	−	0.403583i
$610$		0			0
$611$	−14.8262	+	10.7719i	−0.599805	+	0.435784i
$612$		0			0
$613$	3.56231	−	10.9637i	0.143880	−	0.442818i	−0.852985	−	0.521935i	$-0.825210\pi$
$613$	3.56231	−	10.9637i	0.143880	−	0.442818i	0.996865	+	0.0791176i	$0.0252103\pi$
$614$		0			0
$615$	−6.00000			−0.241943
$616$		0			0
$617$	32.9443			1.32629			0.663143	−	0.748493i	$-0.269222\pi$
$617$	32.9443			1.32629			0.663143	+	0.748493i	$0.269222\pi$
$618$		0			0
$619$	−7.02786	+	21.6295i	−0.282474	+	0.869365i	0.704671	+	0.709534i	$0.251095\pi$
$619$	−7.02786	+	21.6295i	−0.282474	+	0.869365i	−0.987145	+	0.159830i	$0.948905\pi$
$620$		0			0
$621$	−1.70820	+	1.24108i	−0.0685479	+	0.0498029i
$622$		0			0
$623$	9.73607	+	29.9645i	0.390067	+	1.20050i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$		0			0
$627$	43.7984	−	2.97168i	1.74914	−	0.118678i
$628$		0			0
$629$	−3.61803	−	2.62866i	−0.144260	−	0.104811i
$630$		0			0
$631$	−2.29180	−	7.05342i	−0.0912350	−	0.280792i	0.895019	−	0.446028i	$-0.147162\pi$
$631$	−2.29180	−	7.05342i	−0.0912350	−	0.280792i	−0.986254	+	0.165235i	$0.947162\pi$
$632$		0			0
$633$	−54.8328	+	39.8384i	−2.17941	+	1.58343i
$634$		0			0
$635$	−0.736068	+	2.26538i	−0.0292100	+	0.0898990i
$636$		0			0
$637$	0.236068			0.00935335
$638$		0			0
$639$	−98.9017			−3.91249
$640$		0			0
$641$	11.7918	−	36.2914i	0.465748	−	1.43342i	−0.392291	−	0.919841i	$-0.628318\pi$
$641$	11.7918	−	36.2914i	0.465748	−	1.43342i	0.858039	−	0.513584i	$-0.171682\pi$
$642$		0			0
$643$	−10.8541	+	7.88597i	−0.428044	+	0.310992i	−0.780866	−	0.624698i	$-0.785222\pi$
$643$	−10.8541	+	7.88597i	−0.428044	+	0.310992i	0.352822	+	0.935690i	$0.385222\pi$
$644$		0			0
$645$	9.23607	+	28.4257i	0.363670	+	1.11926i
$646$		0			0
$647$	−5.70820	−	4.14725i	−0.224413	−	0.163045i	0.469898	−	0.882721i	$-0.344291\pi$
$647$	−5.70820	−	4.14725i	−0.224413	−	0.163045i	−0.694311	+	0.719675i	$0.744291\pi$
$648$		0			0
$649$	−6.69098	−	4.20025i	−0.262644	−	0.164874i
$650$		0			0
$651$	−49.5967	−	36.0341i	−1.94385	−	1.41229i
$652$		0			0
$653$	7.97214	+	24.5357i	0.311974	+	0.960157i	0.976982	+	0.213321i	$0.0684279\pi$
$653$	7.97214	+	24.5357i	0.311974	+	0.960157i	−0.665008	+	0.746836i	$0.731572\pi$
$654$		0			0
$655$	−9.23607	+	6.71040i	−0.360883	+	0.262197i
$656$		0			0
$657$	−3.94427	+	12.1392i	−0.153881	+	0.473596i
$658$		0			0
$659$	13.3820			0.521287			0.260644	−	0.965435i	$-0.416065\pi$
$659$	13.3820			0.521287			0.260644	+	0.965435i	$0.416065\pi$
$660$		0			0
$661$	2.18034			0.0848054			0.0424027	−	0.999101i	$-0.486499\pi$
$661$	2.18034			0.0848054			0.0424027	+	0.999101i	$0.486499\pi$
$662$		0			0
$663$	−8.47214	+	26.0746i	−0.329030	+	1.01265i
$664$		0			0
$665$	−8.66312	+	6.29412i	−0.335941	+	0.244076i
$666$		0			0
$667$	0.0557281	+	0.171513i	0.00215780	+	0.00664103i
$668$		0			0
$669$	−25.3262	−	18.4006i	−0.979169	−	0.711408i
$670$		0			0
$671$	−7.23607	+	28.7687i	−0.279345	+	1.11060i
$672$		0			0
$673$	3.23607	+	2.35114i	0.124741	+	0.0906298i	0.648407	−	0.761294i	$-0.275436\pi$
$673$	3.23607	+	2.35114i	0.124741	+	0.0906298i	−0.523665	+	0.851924i	$0.675436\pi$
$674$		0			0
$675$	−4.47214	−	13.7638i	−0.172133	−	0.529770i
$676$		0			0
$677$	8.09017	−	5.87785i	0.310930	−	0.225904i	−0.421365	−	0.906891i	$-0.638449\pi$
$677$	8.09017	−	5.87785i	0.310930	−	0.225904i	0.732296	+	0.680987i	$0.238449\pi$
$678$		0			0
$679$	9.70820	−	29.8788i	0.372567	−	1.14664i
$680$		0			0
$681$	−53.3050			−2.04265
$682$		0			0
$683$	47.0132			1.79891			0.899454	−	0.437015i	$-0.143964\pi$
$683$	47.0132			1.79891			0.899454	+	0.437015i	$0.143964\pi$
$684$		0			0
$685$	1.61803	−	4.97980i	0.0618219	−	0.190268i
$686$		0			0
$687$	−73.7771	+	53.6022i	−2.81477	+	2.04505i
$688$		0			0
$689$	−0.454915	−	1.40008i	−0.0173309	−	0.0533390i
$690$		0			0
$691$	11.1180	+	8.07772i	0.422950	+	0.307291i	0.778824	−	0.627243i	$-0.215817\pi$
$691$	11.1180	+	8.07772i	0.422950	+	0.307291i	−0.355874	+	0.934534i	$0.615817\pi$
$692$		0			0
$693$	24.1803	+	60.2066i	0.918535	+	2.28706i
$694$		0			0
$695$	6.59017	+	4.78804i	0.249979	+	0.181621i
$696$		0			0
$697$	3.00000	+	9.23305i	0.113633	+	0.349727i
$698$		0			0
$699$	39.8885	−	28.9807i	1.50872	−	1.09615i
$700$		0			0
$701$	1.79837	−	5.53483i	0.0679236	−	0.209047i	−0.911334	−	0.411669i	$-0.864946\pi$
$701$	1.79837	−	5.53483i	0.0679236	−	0.209047i	0.979257	+	0.202621i	$0.0649461\pi$
$702$		0			0
$703$	−3.49342			−0.131757
$704$		0			0
$705$	−36.6525			−1.38041
$706$		0			0
$707$	−3.00000	+	9.23305i	−0.112827	+	0.347245i
$708$		0			0
$709$	−8.79837	+	6.39239i	−0.330430	+	0.240071i	−0.740613	−	0.671932i	$-0.765465\pi$
$709$	−8.79837	+	6.39239i	−0.330430	+	0.240071i	0.410183	+	0.912003i	$0.365465\pi$
$710$		0			0
$711$	3.52786	+	10.8576i	0.132305	+	0.407194i
$712$		0			0
$713$	0.854102	+	0.620541i	0.0319864	+	0.0232395i
$714$		0			0
$715$	4.11803	−	3.44095i	0.154006	−	0.128684i
$716$		0			0
$717$	−24.9443	−	18.1231i	−0.931561	−	0.676819i
$718$		0			0
$719$	−7.36068	−	22.6538i	−0.274507	−	0.844846i	−0.989349	−	0.145560i	$-0.953502\pi$
$719$	−7.36068	−	22.6538i	−0.274507	−	0.844846i	0.714842	−	0.699286i	$-0.246498\pi$
$720$		0			0
$721$	23.9894	−	17.4293i	0.893410	−	0.649101i
$722$		0			0
$723$	1.85410	−	5.70634i	0.0689548	−	0.212221i
$724$		0			0
$725$	−1.23607			−0.0459064
$726$		0			0
$727$	8.79837			0.326314			0.163157	−	0.986600i	$-0.447832\pi$
$727$	8.79837			0.326314			0.163157	+	0.986600i	$0.447832\pi$
$728$		0			0
$729$	12.9615	−	39.8914i	0.480055	−	1.47746i
$730$		0			0
$731$	39.1246	−	28.4257i	1.44708	−	1.05136i
$732$		0			0
$733$	11.2016	+	34.4751i	0.413742	+	1.27337i	0.913372	+	0.407127i	$0.133469\pi$
$733$	11.2016	+	34.4751i	0.413742	+	1.27337i	−0.499630	+	0.866239i	$0.666531\pi$
$734$		0			0
$735$	0.381966	+	0.277515i	0.0140890	+	0.0102363i
$736$		0			0
$737$	−1.94427	+	1.62460i	−0.0716182	+	0.0598429i
$738$		0			0
$739$	−25.7705	−	18.7234i	−0.947984	−	0.688750i	0.00234556	−	0.999997i	$-0.499253\pi$
$739$	−25.7705	−	18.7234i	−0.947984	−	0.688750i	−0.950329	+	0.311247i	$0.899253\pi$
$740$		0			0
$741$	6.61803	+	20.3682i	0.243120	+	0.748245i
$742$		0			0
$743$	−14.3541	+	10.4289i	−0.526601	+	0.382598i	−0.819085	−	0.573672i	$-0.805518\pi$
$743$	−14.3541	+	10.4289i	−0.526601	+	0.382598i	0.292484	+	0.956270i	$0.405518\pi$
$744$		0			0
$745$	1.23607	−	3.80423i	0.0452860	−	0.139376i
$746$		0			0
$747$	−117.374			−4.29448
$748$		0			0
$749$	−19.7082			−0.720122
$750$		0			0
$751$	3.38197	−	10.4086i	0.123410	−	0.379816i	−0.870198	−	0.492702i	$-0.836009\pi$
$751$	3.38197	−	10.4086i	0.123410	−	0.379816i	0.993608	+	0.112886i	$0.0360094\pi$
$752$		0			0
$753$	26.2705	−	19.0866i	0.957351	−	0.695556i
$754$		0			0
$755$	3.90983	+	12.0332i	0.142293	+	0.437934i
$756$		0			0
$757$	−17.9615	−	13.0498i	−0.652822	−	0.474303i	0.211410	−	0.977398i	$-0.432195\pi$
$757$	−17.9615	−	13.0498i	−0.652822	−	0.474303i	−0.864231	+	0.503095i	$0.832195\pi$
$758$		0			0
$759$	−0.583592	−	1.45309i	−0.0211831	−	0.0527436i
$760$		0			0
$761$	−5.32624	−	3.86974i	−0.193076	−	0.140278i	0.487048	−	0.873375i	$-0.338074\pi$
$761$	−5.32624	−	3.86974i	−0.193076	−	0.140278i	−0.680123	+	0.733098i	$0.738074\pi$
$762$		0			0
$763$	−6.09017	−	18.7436i	−0.220479	−	0.678564i
$764$		0			0
$765$	−31.6525	+	22.9969i	−1.14440	+	0.831454i
$766$		0			0
$767$	1.19098	−	3.66547i	0.0430039	−	0.132352i
$768$		0			0
$769$	−32.0902			−1.15720			−0.578601	−	0.815611i	$-0.696401\pi$
$769$	−32.0902			−1.15720			−0.578601	+	0.815611i	$0.696401\pi$
$770$		0			0
$771$	38.8328			1.39853
$772$		0			0
$773$	−11.6074	+	35.7239i	−0.417489	+	1.28490i	0.492517	+	0.870303i	$0.336077\pi$
$773$	−11.6074	+	35.7239i	−0.417489	+	1.28490i	−0.910006	+	0.414596i	$0.863923\pi$
$774$		0			0
$775$	−5.85410	+	4.25325i	−0.210286	+	0.152781i
$776$		0			0
$777$	−2.23607	−	6.88191i	−0.0802185	−	0.246887i
$778$		0			0
$779$	6.13525	+	4.45752i	0.219818	+	0.159707i
$780$		0			0
$781$	10.7082	−	42.5730i	0.383170	−	1.52338i
$782$		0			0
$783$	−14.4721	−	10.5146i	−0.517192	−	0.375762i
$784$		0			0
$785$	−2.66312	−	8.19624i	−0.0950508	−	0.292536i
$786$		0			0
$787$	−29.1246	+	21.1603i	−1.03818	+	0.754282i	−0.969929	−	0.243386i	$-0.921742\pi$
$787$	−29.1246	+	21.1603i	−1.03818	+	0.754282i	−0.0682508	+	0.997668i	$0.521742\pi$
$788$		0			0
$789$	25.7984	−	79.3992i	0.918446	−	2.82669i
$790$		0			0
$791$	−16.4721			−0.585682
$792$		0			0
$793$	−14.4721			−0.513921
$794$		0			0
$795$	0.909830	−	2.80017i	0.0322683	−	0.0993118i
$796$		0			0
$797$	−29.9615	+	21.7683i	−1.06129	+	0.771073i	−0.974327	−	0.225139i	$-0.927716\pi$
$797$	−29.9615	+	21.7683i	−1.06129	+	0.771073i	−0.0869638	+	0.996211i	$0.527716\pi$
$798$		0			0
$799$	18.3262	+	56.4024i	0.648336	+	1.99537i
$800$		0			0
$801$	72.7492	+	52.8554i	2.57047	+	1.86755i
$802$		0			0
$803$	−4.79837	−	3.01217i	−0.169331	−	0.106297i
$804$		0			0
$805$	0.309017	+	0.224514i	0.0108914	+	0.00791308i
$806$		0			0
$807$	−17.5967	−	54.1572i	−0.619435	−	1.90642i
$808$		0			0
$809$	7.30902	−	5.31031i	0.256971	−	0.186701i	−0.451839	−	0.892099i	$-0.649232\pi$
$809$	7.30902	−	5.31031i	0.256971	−	0.186701i	0.708811	+	0.705399i	$0.249232\pi$
$810$		0			0
$811$	14.4058	−	44.3364i	0.505855	−	1.55686i	−0.293474	−	0.955967i	$-0.594811\pi$
$811$	14.4058	−	44.3364i	0.505855	−	1.55686i	0.799329	−	0.600894i	$-0.205189\pi$
$812$		0			0
$813$	43.4164			1.52268
$814$		0			0
$815$	−7.23607			−0.253468
$816$		0			0
$817$	11.6738	−	35.9281i	0.408413	−	1.25697i
$818$		0			0
$819$	−25.6074	+	18.6049i	−0.894795	+	0.650106i
$820$		0			0
$821$	−7.52786	−	23.1684i	−0.262724	−	0.808582i	−0.992209	−	0.124585i	$-0.960240\pi$
$821$	−7.52786	−	23.1684i	−0.262724	−	0.808582i	0.729485	−	0.683997i	$-0.239760\pi$
$822$		0			0
$823$	−13.7812	−	10.0126i	−0.480381	−	0.349017i	0.321092	−	0.947048i	$-0.395950\pi$
$823$	−13.7812	−	10.0126i	−0.480381	−	0.349017i	−0.801473	+	0.598031i	$0.795950\pi$
$824$		0			0
$825$	10.7082	−	0.726543i	0.372812	−	0.0252950i
$826$		0			0
$827$	17.7984	+	12.9313i	0.618910	+	0.449665i	0.852541	−	0.522661i	$-0.175061\pi$
$827$	17.7984	+	12.9313i	0.618910	+	0.449665i	−0.233631	+	0.972325i	$0.575061\pi$
$828$		0			0
$829$	−4.00000	−	12.3107i	−0.138926	−	0.427569i	0.857254	−	0.514893i	$-0.172168\pi$
$829$	−4.00000	−	12.3107i	−0.138926	−	0.427569i	−0.996180	+	0.0873239i	$0.972168\pi$
$830$		0			0
$831$	−1.61803	+	1.17557i	−0.0561290	+	0.0407801i
$832$		0			0
$833$	0.236068	−	0.726543i	0.00817927	−	0.0251732i
$834$		0			0
$835$	7.90983			0.273731
$836$		0			0
$837$	−104.721			−3.61970
$838$		0			0
$839$	16.2361	−	49.9695i	0.560531	−	1.72514i	−0.120338	−	0.992733i	$-0.538398\pi$
$839$	16.2361	−	49.9695i	0.560531	−	1.72514i	0.680869	−	0.732405i	$-0.261602\pi$
$840$		0			0
$841$	22.2254	−	16.1477i	0.766394	−	0.556818i
$842$		0			0
$843$	−18.0000	−	55.3983i	−0.619953	−	1.90802i
$844$		0			0
$845$	−8.39919	−	6.10237i	−0.288941	−	0.209928i
$846$		0			0
$847$	−28.5344	+	3.88998i	−0.980455	+	0.133661i
$848$		0			0
$849$	−65.0132	−	47.2348i	−2.23125	−	1.62109i
$850$		0			0
$851$	0.0385072	+	0.118513i	0.00132001	+	0.00406257i
$852$		0			0
$853$	−12.9164	+	9.38432i	−0.442249	+	0.321313i	−0.786528	−	0.617555i	$-0.788123\pi$
$853$	−12.9164	+	9.38432i	−0.442249	+	0.321313i	0.344279	+	0.938867i	$0.388123\pi$
$854$		0			0
$855$	−9.44427	+	29.0665i	−0.322987	+	0.994053i
$856$		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
$859$	30.9098			1.05463			0.527315	−	0.849670i	$-0.323199\pi$
$859$	30.9098			1.05463			0.527315	+	0.849670i	$0.323199\pi$
$860$		0			0
$861$	−4.85410	+	14.9394i	−0.165427	+	0.509133i
$862$		0			0
$863$	−5.01722	+	3.64522i	−0.170788	+	0.124085i	−0.669896	−	0.742455i	$-0.733661\pi$
$863$	−5.01722	+	3.64522i	−0.170788	+	0.124085i	0.499108	+	0.866540i	$0.333661\pi$
$864$		0			0
$865$	3.89919	+	12.0005i	0.132576	+	0.408028i
$866$		0			0
$867$	27.2705	+	19.8132i	0.926155	+	0.672891i
$868$		0			0
$869$	−5.05573	+	0.343027i	−0.171504	+	0.0116364i
$870$		0			0
$871$	−1.00000	−	0.726543i	−0.0338837	−	0.0246180i
$872$		0			0
$873$	−27.7082	−	85.2771i	−0.937781	−	2.88619i
$874$		0			0
$875$	−2.11803	+	1.53884i	−0.0716026	+	0.0520223i
$876$		0			0
$877$	0.736068	−	2.26538i	0.0248552	−	0.0764966i	−0.937859	−	0.347015i	$-0.887195\pi$
$877$	0.736068	−	2.26538i	0.0248552	−	0.0764966i	0.962715	+	0.270519i	$0.0871952\pi$
$878$		0			0
$879$	76.8328			2.59151
$880$		0			0
$881$	−27.4508			−0.924843			−0.462421	−	0.886660i	$-0.653019\pi$
$881$	−27.4508			−0.924843			−0.462421	+	0.886660i	$0.653019\pi$
$882$		0			0
$883$	−9.47214	+	29.1522i	−0.318763	+	0.981051i	0.655415	+	0.755269i	$0.272494\pi$
$883$	−9.47214	+	29.1522i	−0.318763	+	0.981051i	−0.974178	+	0.225782i	$0.927506\pi$
$884$		0			0
$885$	6.23607	−	4.53077i	0.209623	−	0.152300i
$886$		0			0
$887$	−14.6074	−	44.9569i	−0.490468	−	1.50951i	−0.823902	−	0.566732i	$-0.808207\pi$
$887$	−14.6074	−	44.9569i	−0.490468	−	1.50951i	0.333434	−	0.942774i	$-0.391793\pi$
$888$		0			0
$889$	5.04508	+	3.66547i	0.169207	+	0.122936i
$890$		0			0
$891$	68.5861	+	43.0548i	2.29772	+	1.44239i
$892$		0			0
$893$	37.4787	+	27.2299i	1.25418	+	0.911213i
$894$		0			0
$895$	−0.899187	−	2.76741i	−0.0300565	−	0.0925044i
$896$		0			0
$897$	0.618034	−	0.449028i	0.0206356	−	0.0149926i
$898$		0			0
$899$	−2.76393	+	8.50651i	−0.0921823	+	0.283708i
$900$		0			0
$901$	−4.76393			−0.158710
$902$		0			0
$903$	78.2492			2.60397
$904$		0			0
$905$	6.32624	−	19.4702i	0.210291	−	0.647210i
$906$		0			0
$907$	−10.2361	+	7.43694i	−0.339883	+	0.246939i	−0.744612	−	0.667497i	$-0.767366\pi$
$907$	−10.2361	+	7.43694i	−0.339883	+	0.246939i	0.404729	+	0.914436i	$0.367366\pi$
$908$		0			0
$909$	8.56231	+	26.3521i	0.283994	+	0.874043i
$910$		0			0
$911$	−16.9443	−	12.3107i	−0.561389	−	0.407873i	0.270578	−	0.962698i	$-0.412785\pi$
$911$	−16.9443	−	12.3107i	−0.561389	−	0.407873i	−0.831967	+	0.554825i	$0.812785\pi$
$912$		0			0
$913$	12.7082	−	50.5245i	0.420580	−	1.67212i
$914$		0			0
$915$	−23.4164	−	17.0130i	−0.774123	−	0.562433i
$916$		0			0
$917$	9.23607	+	28.4257i	0.305002	+	0.938699i
$918$		0			0
$919$	−9.70820	+	7.05342i	−0.320244	+	0.232671i	−0.736280	−	0.676677i	$-0.763419\pi$
$919$	−9.70820	+	7.05342i	−0.320244	+	0.232671i	0.416036	+	0.909348i	$0.363419\pi$
$920$		0			0
$921$	−26.9443	+	82.9259i	−0.887844	+	2.73250i
$922$		0			0
$923$	21.4164			0.704930
$924$		0			0
$925$	−0.854102			−0.0280827
$926$		0			0
$927$	26.1525	−	80.4890i	0.858960	−	2.64361i
$928$		0			0
$929$	−43.0967	+	31.3116i	−1.41396	+	1.02730i	−0.421226	+	0.906956i	$0.638400\pi$
$929$	−43.0967	+	31.3116i	−1.41396	+	1.02730i	−0.992732	+	0.120345i	$0.961600\pi$
$930$		0			0
$931$	−0.184405	−	0.567541i	−0.00604364	−	0.0186004i
$932$		0			0
$933$	6.47214	+	4.70228i	0.211888	+	0.153946i
$934$		0			0
$935$	−6.47214	−	16.1150i	−0.211661	−	0.527016i
$936$		0			0
$937$	38.9787	+	28.3197i	1.27338	+	0.925164i	0.999332	−	0.0365522i	$-0.0116375\pi$
$937$	38.9787	+	28.3197i	1.27338	+	0.925164i	0.274047	+	0.961716i	$0.411638\pi$
$938$		0			0
$939$	−27.4164	−	84.3790i	−0.894701	−	2.75361i
$940$		0			0
$941$	−45.3607	+	32.9565i	−1.47872	+	1.07435i	−0.500748	+	0.865593i	$0.666942\pi$
$941$	−45.3607	+	32.9565i	−1.47872	+	1.07435i	−0.977968	+	0.208757i	$0.933058\pi$
$942$		0			0
$943$	0.0835921	−	0.257270i	0.00272213	−	0.00837787i
$944$		0			0
$945$	−37.8885			−1.23251
$946$		0			0
$947$	−49.9574			−1.62340			−0.811699	−	0.584076i	$-0.801457\pi$
$947$	−49.9574			−1.62340			−0.811699	+	0.584076i	$0.801457\pi$
$948$		0			0
$949$	0.854102	−	2.62866i	0.0277253	−	0.0853298i
$950$		0			0
$951$	16.2361	−	11.7962i	0.526491	−	0.382518i
$952$		0			0
$953$	4.85410	+	14.9394i	0.157240	+	0.483934i	0.998381	−	0.0568813i	$-0.0181157\pi$
$953$	4.85410	+	14.9394i	0.157240	+	0.483934i	−0.841141	+	0.540816i	$0.818116\pi$
$954$		0			0
$955$	−20.5623	−	14.9394i	−0.665381	−	0.483427i
$956$		0			0
$957$	10.1803	−	8.50651i	0.329084	−	0.274976i
$958$		0			0
$959$	−11.0902	−	8.05748i	−0.358120	−	0.260190i
$960$		0			0
$961$	6.60081	+	20.3152i	0.212929	+	0.655329i
$962$		0			0
$963$	−45.5066	+	33.0625i	−1.46643	+	1.06542i
$964$		0			0
$965$	1.67376	−	5.15131i	0.0538803	−	0.165827i
$966$		0			0
$967$	−3.90983			−0.125732			−0.0628658	−	0.998022i	$-0.520024\pi$
$967$	−3.90983			−0.125732			−0.0628658	+	0.998022i	$0.520024\pi$
$968$		0			0
$969$	69.3050			2.22640
$970$		0			0
$971$	−12.1565	+	37.4140i	−0.390122	+	1.20067i	0.542574	+	0.840008i	$0.317450\pi$
$971$	−12.1565	+	37.4140i	−0.390122	+	1.20067i	−0.932696	+	0.360664i	$0.882550\pi$
$972$		0			0
$973$	17.2533	−	12.5352i	0.553115	−	0.401862i
$974$		0			0
$975$	1.61803	+	4.97980i	0.0518186	+	0.159481i
$976$		0			0
$977$	3.38197	+	2.45714i	0.108199	+	0.0786109i	0.640569	−	0.767901i	$-0.278699\pi$
$977$	3.38197	+	2.45714i	0.108199	+	0.0786109i	−0.532370	+	0.846512i	$0.678699\pi$
$978$		0			0
$979$	−30.6287	+	25.5928i	−0.978897	+	0.817948i
$980$		0			0
$981$	−45.5066	−	33.0625i	−1.45291	−	1.05560i
$982$		0			0
$983$	−3.10081	−	9.54332i	−0.0989006	−	0.304385i	0.889350	−	0.457227i	$-0.151157\pi$
$983$	−3.10081	−	9.54332i	−0.0989006	−	0.304385i	−0.988251	+	0.152842i	$0.951157\pi$
$984$		0			0
$985$	−3.97214	+	2.88593i	−0.126563	+	0.0919532i
$986$		0			0
$987$	−29.6525	+	91.2609i	−0.943849	+	2.90487i
$988$		0			0
$989$	−1.34752			−0.0428488
$990$		0			0
$991$	−54.7214			−1.73828			−0.869141	−	0.494565i	$-0.835327\pi$
$991$	−54.7214			−1.73828			−0.869141	+	0.494565i	$0.835327\pi$
$992$		0			0
$993$	−14.3820	+	44.2631i	−0.456398	+	1.40465i
$994$		0			0
$995$	−1.38197	+	1.00406i	−0.0438113	+	0.0318307i
$996$		0			0
$997$	−16.2148	−	49.9040i	−0.513527	−	1.58047i	−0.785946	−	0.618296i	$-0.787823\pi$
$997$	−16.2148	−	49.9040i	−0.513527	−	1.58047i	0.272418	−	0.962179i	$-0.412177\pi$
$998$		0			0
$999$	−10.0000	−	7.26543i	−0.316386	−	0.229868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bo.a.81.1		4
4.3	odd	2		110.2.g.a.81.1	✓	4
11.3	even	5	inner	880.2.bo.a.641.1		4
11.5	even	5		9680.2.a.bh.1.1		2
11.6	odd	10		9680.2.a.bi.1.1		2
12.11	even	2		990.2.n.f.631.1		4
20.3	even	4		550.2.ba.a.499.1		8
20.7	even	4		550.2.ba.a.499.2		8
20.19	odd	2		550.2.h.f.301.1		4
44.3	odd	10		110.2.g.a.91.1	yes	4
44.27	odd	10		1210.2.a.t.1.2		2
44.39	even	10		1210.2.a.p.1.2		2
132.47	even	10		990.2.n.f.91.1		4
220.3	even	20		550.2.ba.a.399.2		8
220.39	even	10		6050.2.a.cm.1.1		2
220.47	even	20		550.2.ba.a.399.1		8
220.159	odd	10		6050.2.a.bu.1.1		2
220.179	odd	10		550.2.h.f.201.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.a.81.1	✓	4	4.3	odd	2
110.2.g.a.91.1	yes	4	44.3	odd	10
550.2.h.f.201.1		4	220.179	odd	10
550.2.h.f.301.1		4	20.19	odd	2
550.2.ba.a.399.1		8	220.47	even	20
550.2.ba.a.399.2		8	220.3	even	20
550.2.ba.a.499.1		8	20.3	even	4
550.2.ba.a.499.2		8	20.7	even	4
880.2.bo.a.81.1		4	1.1	even	1	trivial
880.2.bo.a.641.1		4	11.3	even	5	inner
990.2.n.f.91.1		4	132.47	even	10
990.2.n.f.631.1		4	12.11	even	2
1210.2.a.p.1.2		2	44.39	even	10
1210.2.a.t.1.2		2	44.27	odd	10
6050.2.a.bu.1.1		2	220.159	odd	10
6050.2.a.cm.1.1		2	220.39	even	10
9680.2.a.bh.1.1		2	11.5	even	5
9680.2.a.bi.1.1		2	11.6	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 3.07768i) q^{3} +(0.809017 - 0.587785i) q^{5} +(-0.809017 - 2.48990i) q^{7} +(-6.04508 - 4.39201i) q^{9} +(2.54508 - 2.12663i) q^{11} +(1.30902 + 0.951057i) q^{13} +(1.00000 + 3.07768i) q^{15} +(4.23607 - 3.07768i) q^{17} +(1.26393 - 3.88998i) q^{19} +8.47214 q^{21} -0.145898 q^{23} +(0.309017 - 0.951057i) q^{25} +(11.7082 - 8.50651i) q^{27} +(-0.381966 - 1.17557i) q^{29} +(-5.85410 - 4.25325i) q^{31} +(4.00000 + 9.95959i) q^{33} +(-2.11803 - 1.53884i) q^{35} +(-0.263932 - 0.812299i) q^{37} +(-4.23607 + 3.07768i) q^{39} +(-0.572949 + 1.76336i) q^{41} +9.23607 q^{43} -7.47214 q^{45} +(-3.50000 + 10.7719i) q^{47} +(0.118034 - 0.0857567i) q^{49} +(5.23607 + 16.1150i) q^{51} +(-0.736068 - 0.534785i) q^{53} +(0.809017 - 3.21644i) q^{55} +(10.7082 + 7.77997i) q^{57} +(-0.736068 - 2.26538i) q^{59} +(-7.23607 + 5.25731i) q^{61} +(-6.04508 + 18.6049i) q^{63} +1.61803 q^{65} -0.763932 q^{67} +(0.145898 - 0.449028i) q^{69} +(10.7082 - 7.77997i) q^{71} +(-0.527864 - 1.62460i) q^{73} +(2.61803 + 1.90211i) q^{75} +(-7.35410 - 4.61653i) q^{77} +(-1.23607 - 0.898056i) q^{79} +(7.54508 + 23.2214i) q^{81} +(12.7082 - 9.23305i) q^{83} +(1.61803 - 4.97980i) q^{85} +4.00000 q^{87} -12.0344 q^{89} +(1.30902 - 4.02874i) q^{91} +(18.9443 - 13.7638i) q^{93} +(-1.26393 - 3.88998i) q^{95} +(9.70820 + 7.05342i) q^{97} +(-24.7254 + 1.67760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + q^{5} - q^{7} - 13 q^{9} - q^{11} + 3 q^{13} + 4 q^{15} + 8 q^{17} + 14 q^{19} + 16 q^{21} - 14 q^{23} - q^{25} + 20 q^{27} - 6 q^{29} - 10 q^{31} + 16 q^{33} - 4 q^{35} - 10 q^{37}+ \cdots - 43 q^{99}+O(q^{100}) \) 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

L-functions

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