LMFDB - Embedded newform 550.2.ba.c.499.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(49,550)] 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("550.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(550, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.ba (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,2,0,2,0,0,-14,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			499.1
Root			$-0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	550.499
Dual form			550.2.ba.c.399.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.587785 + 0.809017i) q^{2} +(0.363271 + 0.118034i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.309017 + 0.224514i) q^{6} +(-1.90211 + 0.618034i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-2.30902 - 1.67760i) q^{9} +(0.309017 - 3.30220i) q^{11} -0.381966i q^{12} +(0.726543 - 1.00000i) q^{13} +(0.618034 - 1.90211i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-0.363271 - 0.500000i) q^{17} +(2.71441 - 0.881966i) q^{18} +(1.80902 - 5.56758i) q^{19} -0.763932 q^{21} +(2.48990 + 2.19098i) q^{22} +1.23607i q^{23} +(0.309017 + 0.224514i) q^{24} +(0.381966 + 1.17557i) q^{26} +(-1.31433 - 1.80902i) q^{27} +(1.17557 + 1.61803i) q^{28} +(-1.38197 - 4.25325i) q^{29} +(-1.61803 - 1.17557i) q^{31} -1.00000i q^{32} +(0.502029 - 1.16312i) q^{33} +0.618034 q^{34} +(-0.881966 + 2.71441i) q^{36} +(-3.52671 + 1.14590i) q^{37} +(3.44095 + 4.73607i) q^{38} +(0.381966 - 0.277515i) q^{39} +(1.73607 - 5.34307i) q^{41} +(0.449028 - 0.618034i) q^{42} -8.56231i q^{43} +(-3.23607 + 0.726543i) q^{44} +(-1.00000 - 0.726543i) q^{46} +(6.15537 + 2.00000i) q^{47} +(-0.363271 + 0.118034i) q^{48} +(-2.42705 + 1.76336i) q^{49} +(-0.0729490 - 0.224514i) q^{51} +(-1.17557 - 0.381966i) q^{52} +(-0.898056 + 1.23607i) q^{53} +2.23607 q^{54} -2.00000 q^{56} +(1.31433 - 1.80902i) q^{57} +(4.25325 + 1.38197i) q^{58} +(2.66312 + 8.19624i) q^{59} +(2.00000 - 1.45309i) q^{61} +(1.90211 - 0.618034i) q^{62} +(5.42882 + 1.76393i) q^{63} +(0.809017 + 0.587785i) q^{64} +(0.645898 + 1.08981i) q^{66} -11.0902i q^{67} +(-0.363271 + 0.500000i) q^{68} +(-0.145898 + 0.449028i) q^{69} +(4.23607 - 3.07768i) q^{71} +(-1.67760 - 2.30902i) q^{72} +(-9.87384 + 3.20820i) q^{73} +(1.14590 - 3.52671i) q^{74} -5.85410 q^{76} +(1.45309 + 6.47214i) q^{77} +0.472136i q^{78} +(10.8541 + 7.88597i) q^{79} +(2.38197 + 7.33094i) q^{81} +(3.30220 + 4.54508i) q^{82} +(-5.48183 - 7.54508i) q^{83} +(0.236068 + 0.726543i) q^{84} +(6.92705 + 5.03280i) q^{86} -1.70820i q^{87} +(1.31433 - 3.04508i) q^{88} +8.09017 q^{89} +(-0.763932 + 2.35114i) q^{91} +(1.17557 - 0.381966i) q^{92} +(-0.449028 - 0.618034i) q^{93} +(-5.23607 + 3.80423i) q^{94} +(0.118034 - 0.363271i) q^{96} +(-4.20025 + 5.78115i) q^{97} -3.00000i q^{98} +(-6.25329 + 7.10642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 2 q^{6} - 14 q^{9} - 2 q^{11} - 4 q^{14} - 2 q^{16} + 10 q^{19} - 24 q^{21} - 2 q^{24} + 12 q^{26} - 20 q^{29} - 4 q^{31} - 4 q^{34} - 16 q^{36} + 12 q^{39} - 4 q^{41} - 8 q^{44} - 8 q^{46}+ \cdots + 26 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 + 2 * q^6 - 14 * q^9 - 2 * q^11 - 4 * q^14 - 2 * q^16 + 10 * q^19 - 24 * q^21 - 2 * q^24 + 12 * q^26 - 20 * q^29 - 4 * q^31 - 4 * q^34 - 16 * q^36 + 12 * q^39 - 4 * q^41 - 8 * q^44 - 8 * q^46 - 6 * q^49 - 14 * q^51 - 16 * q^56 - 10 * q^59 + 16 * q^61 + 2 * q^64 + 32 * q^66 - 28 * q^69 + 16 * q^71 + 36 * q^74 - 20 * q^76 + 60 * q^79 + 28 * q^81 - 16 * q^84 + 42 * q^86 + 20 * q^89 - 24 * q^91 - 24 * q^94 - 8 * q^96 + 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	0.363271	+	0.118034i	0.209735	+	0.0681470i	0.412000	−	0.911184i	$-0.364830\pi$
$3$	0.363271	+	0.118034i	0.209735	+	0.0681470i	−0.202265	+	0.979331i	$0.564830\pi$
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	−0.309017	+	0.224514i	−0.126156	+	0.0916575i
$7$	−1.90211	+	0.618034i	−0.718931	+	0.233595i	−0.645560	−	0.763710i	$-0.723376\pi$
$7$	−1.90211	+	0.618034i	−0.718931	+	0.233595i	−0.0733714	+	0.997305i	$0.523376\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	−2.30902	−	1.67760i	−0.769672	−	0.559200i
$10$		0			0
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$11$	0.309017	−	3.30220i	0.0931721	−	0.995650i
$12$		−	0.381966i		−	0.110264i
$13$	0.726543	−	1.00000i	0.201507	−	0.277350i	−0.696290	−	0.717761i	$-0.745167\pi$
$13$	0.726543	−	1.00000i	0.201507	−	0.277350i	0.897796	+	0.440411i	$0.145167\pi$
$14$	0.618034	−	1.90211i	0.165177	−	0.508361i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.363271	−	0.500000i	−0.0881062	−	0.121268i	0.762688	−	0.646766i	$-0.223879\pi$
$17$	−0.363271	−	0.500000i	−0.0881062	−	0.121268i	−0.850795	+	0.525498i	$0.823879\pi$
$18$	2.71441	−	0.881966i	0.639793	−	0.207881i
$19$	1.80902	−	5.56758i	0.415017	−	1.27729i	−0.497219	−	0.867625i	$-0.665645\pi$
$19$	1.80902	−	5.56758i	0.415017	−	1.27729i	0.912236	−	0.409666i	$-0.134355\pi$
$20$		0			0
$21$	−0.763932			−0.166704
$22$	2.48990	+	2.19098i	0.530848	+	0.467119i
$23$			1.23607i			0.257738i	0.991662	+	0.128869i	$0.0411347\pi$
$23$			1.23607i			0.257738i	−0.991662	+	0.128869i	$0.958865\pi$
$24$	0.309017	+	0.224514i	0.0630778	+	0.0458287i
$25$		0			0
$26$	0.381966	+	1.17557i	0.0749097	+	0.230548i
$27$	−1.31433	−	1.80902i	−0.252942	−	0.348145i
$28$	1.17557	+	1.61803i	0.222162	+	0.305780i
$29$	−1.38197	−	4.25325i	−0.256625	−	0.789809i	−0.993505	−	0.113787i	$-0.963702\pi$
$29$	−1.38197	−	4.25325i	−0.256625	−	0.789809i	0.736881	−	0.676023i	$-0.236298\pi$
$30$		0			0
$31$	−1.61803	−	1.17557i	−0.290607	−	0.211139i	0.432923	−	0.901431i	$-0.357482\pi$
$31$	−1.61803	−	1.17557i	−0.290607	−	0.211139i	−0.723531	+	0.690292i	$0.757482\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.502029	−	1.16312i	0.0873920	−	0.202473i
$34$	0.618034			0.105992
$35$		0			0
$36$	−0.881966	+	2.71441i	−0.146994	+	0.452402i
$37$	−3.52671	+	1.14590i	−0.579788	+	0.188384i	−0.584206	−	0.811606i	$-0.698594\pi$
$37$	−3.52671	+	1.14590i	−0.579788	+	0.188384i	0.00441771	+	0.999990i	$0.498594\pi$
$38$	3.44095	+	4.73607i	0.558197	+	0.768292i
$39$	0.381966	−	0.277515i	0.0611635	−	0.0444379i
$40$		0			0
$41$	1.73607	−	5.34307i	0.271128	−	0.834447i	−0.719090	−	0.694917i	$-0.755441\pi$
$41$	1.73607	−	5.34307i	0.271128	−	0.834447i	0.990218	−	0.139530i	$-0.0445591\pi$
$42$	0.449028	−	0.618034i	0.0692865	−	0.0953647i
$43$		−	8.56231i		−	1.30574i	−0.757470	−	0.652870i	$-0.773565\pi$
$43$		−	8.56231i		−	1.30574i	0.757470	−	0.652870i	$-0.226435\pi$
$44$	−3.23607	+	0.726543i	−0.487856	+	0.109530i
$45$		0			0
$46$	−1.00000	−	0.726543i	−0.147442	−	0.107123i
$47$	6.15537	+	2.00000i	0.897853	+	0.291730i	0.721350	−	0.692570i	$-0.243522\pi$
$47$	6.15537	+	2.00000i	0.897853	+	0.291730i	0.176502	+	0.984300i	$0.443522\pi$
$48$	−0.363271	+	0.118034i	−0.0524337	+	0.0170367i
$49$	−2.42705	+	1.76336i	−0.346722	+	0.251908i
$50$		0			0
$51$	−0.0729490	−	0.224514i	−0.0102149	−	0.0314382i
$52$	−1.17557	−	0.381966i	−0.163022	−	0.0529692i
$53$	−0.898056	+	1.23607i	−0.123357	+	0.169787i	−0.866229	−	0.499647i	$-0.833463\pi$
$53$	−0.898056	+	1.23607i	−0.123357	+	0.169787i	0.742872	+	0.669434i	$0.233463\pi$
$54$	2.23607			0.304290
$55$		0			0
$56$	−2.00000			−0.267261
$57$	1.31433	−	1.80902i	0.174087	−	0.239610i
$58$	4.25325	+	1.38197i	0.558480	+	0.181461i
$59$	2.66312	+	8.19624i	0.346709	+	1.06706i	0.960663	+	0.277718i	$0.0895779\pi$
$59$	2.66312	+	8.19624i	0.346709	+	1.06706i	−0.613954	+	0.789342i	$0.710422\pi$
$60$		0			0
$61$	2.00000	−	1.45309i	0.256074	−	0.186048i	−0.452341	−	0.891845i	$-0.649411\pi$
$61$	2.00000	−	1.45309i	0.256074	−	0.186048i	0.708414	+	0.705797i	$0.249411\pi$
$62$	1.90211	−	0.618034i	0.241569	−	0.0784904i
$63$	5.42882	+	1.76393i	0.683968	+	0.222235i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$		0			0
$66$	0.645898	+	1.08981i	0.0795046	+	0.134147i
$67$		−	11.0902i		−	1.35488i	−0.735578	−	0.677440i	$-0.763089\pi$
$67$		−	11.0902i		−	1.35488i	0.735578	−	0.677440i	$-0.236911\pi$
$68$	−0.363271	+	0.500000i	−0.0440531	+	0.0606339i
$69$	−0.145898	+	0.449028i	−0.0175641	+	0.0540566i
$70$		0			0
$71$	4.23607	−	3.07768i	0.502729	−	0.365254i	−0.307330	−	0.951603i	$-0.599435\pi$
$71$	4.23607	−	3.07768i	0.502729	−	0.365254i	0.810058	+	0.586349i	$0.199435\pi$
$72$	−1.67760	−	2.30902i	−0.197707	−	0.272120i
$73$	−9.87384	+	3.20820i	−1.15565	+	0.375492i	−0.823267	−	0.567654i	$-0.807851\pi$
$73$	−9.87384	+	3.20820i	−1.15565	+	0.375492i	−0.332378	+	0.943146i	$0.607851\pi$
$74$	1.14590	−	3.52671i	0.133208	−	0.409972i
$75$		0			0
$76$	−5.85410			−0.671512
$77$	1.45309	+	6.47214i	0.165594	+	0.737568i
$78$			0.472136i			0.0534589i
$79$	10.8541	+	7.88597i	1.22118	+	0.887241i	0.996198	−	0.0871218i	$-0.0277669\pi$
$79$	10.8541	+	7.88597i	1.22118	+	0.887241i	0.224984	+	0.974362i	$0.427767\pi$
$80$		0			0
$81$	2.38197	+	7.33094i	0.264663	+	0.814549i
$82$	3.30220	+	4.54508i	0.364667	+	0.501921i
$83$	−5.48183	−	7.54508i	−0.601708	−	0.828181i	0.394155	−	0.919044i	$-0.371037\pi$
$83$	−5.48183	−	7.54508i	−0.601708	−	0.828181i	−0.995863	+	0.0908634i	$0.971037\pi$
$84$	0.236068	+	0.726543i	0.0257571	+	0.0792723i
$85$		0			0
$86$	6.92705	+	5.03280i	0.746963	+	0.542700i
$87$		−	1.70820i		−	0.183139i
$88$	1.31433	−	3.04508i	0.140108	−	0.324607i
$89$	8.09017			0.857556			0.428778	−	0.903410i	$-0.358944\pi$
$89$	8.09017			0.857556			0.428778	+	0.903410i	$0.358944\pi$
$90$		0			0
$91$	−0.763932	+	2.35114i	−0.0800818	+	0.246467i
$92$	1.17557	−	0.381966i	0.122562	−	0.0398227i
$93$	−0.449028	−	0.618034i	−0.0465620	−	0.0640871i
$94$	−5.23607	+	3.80423i	−0.540059	+	0.392376i
$95$		0			0
$96$	0.118034	−	0.363271i	0.0120468	−	0.0370762i
$97$	−4.20025	+	5.78115i	−0.426471	+	0.586987i	−0.967139	−	0.254249i	$-0.918172\pi$
$97$	−4.20025	+	5.78115i	−0.426471	+	0.586987i	0.540668	+	0.841236i	$0.318172\pi$
$98$		−	3.00000i		−	0.303046i
$99$	−6.25329	+	7.10642i	−0.628479	+	0.714222i
$100$		0			0
$101$	3.38197	+	2.45714i	0.336518	+	0.244495i	0.743191	−	0.669079i	$-0.233311\pi$
$101$	3.38197	+	2.45714i	0.336518	+	0.244495i	−0.406673	+	0.913574i	$0.633311\pi$
$102$	0.224514	+	0.0729490i	0.0222302	+	0.00722303i
$103$	−14.9394	+	4.85410i	−1.47202	+	0.478289i	−0.931718	−	0.363181i	$-0.881691\pi$
$103$	−14.9394	+	4.85410i	−1.47202	+	0.478289i	−0.540303	+	0.841470i	$0.681691\pi$
$104$	1.00000	−	0.726543i	0.0980581	−	0.0712434i
$105$		0			0
$106$	−0.472136	−	1.45309i	−0.0458579	−	0.141136i
$107$	1.08981	+	0.354102i	0.105356	+	0.0342323i	0.361221	−	0.932480i	$-0.382360\pi$
$107$	1.08981	+	0.354102i	0.105356	+	0.0342323i	−0.255864	+	0.966713i	$0.582360\pi$
$108$	−1.31433	+	1.80902i	−0.126471	+	0.174073i
$109$	−18.9443			−1.81453			−0.907266	−	0.420557i	$-0.861835\pi$
$109$	−18.9443			−1.81453			−0.907266	+	0.420557i	$0.861835\pi$
$110$		0			0
$111$	−1.41641			−0.134439
$112$	1.17557	−	1.61803i	0.111081	−	0.152890i
$113$	−1.76336	−	0.572949i	−0.165883	−	0.0538985i	0.224898	−	0.974382i	$-0.427795\pi$
$113$	−1.76336	−	0.572949i	−0.165883	−	0.0538985i	−0.390781	+	0.920484i	$0.627795\pi$
$114$	0.690983	+	2.12663i	0.0647165	+	0.199177i
$115$		0			0
$116$	−3.61803	+	2.62866i	−0.335926	+	0.244065i
$117$	−3.35520	+	1.09017i	−0.310188	+	0.100786i
$118$	−8.19624	−	2.66312i	−0.754525	−	0.245160i
$119$	1.00000	+	0.726543i	0.0916698	+	0.0666020i
$120$		0			0
$121$	−10.8090	−	2.04087i	−0.982638	−	0.185534i
$122$			2.47214i			0.223817i
$123$	1.26133	−	1.73607i	0.113730	−	0.156536i
$124$	−0.618034	+	1.90211i	−0.0555011	+	0.170815i
$125$		0			0
$126$	−4.61803	+	3.35520i	−0.411407	+	0.298905i
$127$	−6.43288	−	8.85410i	−0.570826	−	0.785675i	0.421826	−	0.906677i	$-0.361389\pi$
$127$	−6.43288	−	8.85410i	−0.570826	−	0.785675i	−0.992652	+	0.121002i	$0.961389\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	1.01064	−	3.11044i	0.0889822	−	0.273859i
$130$		0			0
$131$	6.79837			0.593977			0.296988	−	0.954881i	$-0.404018\pi$
$131$	6.79837			0.593977			0.296988	+	0.954881i	$0.404018\pi$
$132$	−1.26133	−	0.118034i	−0.109784	−	0.0102735i
$133$			11.7082i			1.01523i
$134$	8.97214	+	6.51864i	0.775074	+	0.563125i
$135$		0			0
$136$	−0.190983	−	0.587785i	−0.0163767	−	0.0504022i
$137$	9.45756	+	13.0172i	0.808014	+	1.11214i	0.991627	+	0.129138i	$0.0412209\pi$
$137$	9.45756	+	13.0172i	0.808014	+	1.11214i	−0.183612	+	0.982999i	$0.558779\pi$
$138$	−0.277515	−	0.381966i	−0.0236236	−	0.0325151i
$139$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$139$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$140$		0			0
$141$	2.00000	+	1.45309i	0.168430	+	0.122372i
$142$			5.23607i			0.439401i
$143$	−3.07768	−	2.70820i	−0.257369	−	0.226471i
$144$	2.85410			0.237842
$145$		0			0
$146$	3.20820	−	9.87384i	0.265513	−	0.817165i
$147$	−1.08981	+	0.354102i	−0.0898863	+	0.0292058i
$148$	2.17963	+	3.00000i	0.179164	+	0.246598i
$149$	−5.00000	+	3.63271i	−0.409616	+	0.297603i	−0.773446	−	0.633862i	$-0.781469\pi$
$149$	−5.00000	+	3.63271i	−0.409616	+	0.297603i	0.363830	+	0.931465i	$0.381469\pi$
$150$		0			0
$151$	−2.47214	+	7.60845i	−0.201180	+	0.619167i	0.798669	+	0.601770i	$0.205538\pi$
$151$	−2.47214	+	7.60845i	−0.201180	+	0.619167i	−0.999849	+	0.0173966i	$0.994462\pi$
$152$	3.44095	−	4.73607i	0.279098	−	0.384146i
$153$			1.76393i			0.142605i
$154$	−6.09017	−	2.62866i	−0.490760	−	0.211823i
$155$		0			0
$156$	−0.381966	−	0.277515i	−0.0305818	−	0.0222189i
$157$	−9.23305	−	3.00000i	−0.736878	−	0.239426i	−0.0835524	−	0.996503i	$-0.526627\pi$
$157$	−9.23305	−	3.00000i	−0.736878	−	0.239426i	−0.653325	+	0.757077i	$0.726627\pi$
$158$	−12.7598	+	4.14590i	−1.01511	+	0.329830i
$159$	−0.472136	+	0.343027i	−0.0374428	+	0.0272038i
$160$		0			0
$161$	−0.763932	−	2.35114i	−0.0602063	−	0.185296i
$162$	−7.33094	−	2.38197i	−0.575973	−	0.187145i
$163$	0.534785	−	0.736068i	0.0418876	−	0.0576533i	−0.787559	−	0.616239i	$-0.788656\pi$
$163$	0.534785	−	0.736068i	0.0418876	−	0.0576533i	0.829447	+	0.558585i	$0.188656\pi$
$164$	−5.61803			−0.438695
$165$		0			0
$166$	9.32624			0.723856
$167$	8.67802	−	11.9443i	0.671525	−	0.924276i	−0.328268	−	0.944585i	$-0.606465\pi$
$167$	8.67802	−	11.9443i	0.671525	−	0.924276i	0.999794	+	0.0203090i	$0.00646501\pi$
$168$	−0.726543	−	0.236068i	−0.0560540	−	0.0182130i
$169$	3.54508	+	10.9106i	0.272699	+	0.839281i
$170$		0			0
$171$	−13.5172	+	9.82084i	−1.03369	+	0.751018i
$172$	−8.14324	+	2.64590i	−0.620916	+	0.201748i
$173$	20.8172	+	6.76393i	1.58271	+	0.514252i	0.962752	−	0.270386i	$-0.0871514\pi$
$173$	20.8172	+	6.76393i	1.58271	+	0.514252i	0.619954	+	0.784638i	$0.287151\pi$
$174$	1.38197	+	1.00406i	0.104767	+	0.0761174i
$175$		0			0
$176$	1.69098	+	2.85317i	0.127463	+	0.215066i
$177$			3.29180i			0.247427i
$178$	−4.75528	+	6.54508i	−0.356423	+	0.490575i
$179$	2.66312	−	8.19624i	0.199051	−	0.612616i	−0.800855	−	0.598859i	$-0.795621\pi$
$179$	2.66312	−	8.19624i	0.199051	−	0.612616i	0.999905	−	0.0137566i	$-0.00437900\pi$
$180$		0			0
$181$	3.38197	−	2.45714i	0.251380	−	0.182638i	−0.454958	−	0.890513i	$-0.650346\pi$
$181$	3.38197	−	2.45714i	0.251380	−	0.182638i	0.706338	+	0.707875i	$0.250346\pi$
$182$	−1.45309	−	2.00000i	−0.107710	−	0.148250i
$183$	0.898056	−	0.291796i	0.0663862	−	0.0215702i
$184$	−0.381966	+	1.17557i	−0.0281589	+	0.0866642i
$185$		0			0
$186$	0.763932			0.0560142
$187$	−1.76336	+	1.04508i	−0.128949	+	0.0764242i
$188$		−	6.47214i		−	0.472029i
$189$	3.61803	+	2.62866i	0.263173	+	0.191207i
$190$		0			0
$191$	1.47214	+	4.53077i	0.106520	+	0.327835i	0.990084	−	0.140475i	$-0.0448630\pi$
$191$	1.47214	+	4.53077i	0.106520	+	0.327835i	−0.883564	+	0.468310i	$0.844863\pi$
$192$	0.224514	+	0.309017i	0.0162029	+	0.0223014i
$193$	−10.2371	−	14.0902i	−0.736883	−	1.01423i	−0.998792	−	0.0491400i	$-0.984352\pi$
$193$	−10.2371	−	14.0902i	−0.736883	−	1.01423i	0.261909	−	0.965093i	$-0.415648\pi$
$194$	−2.20820	−	6.79615i	−0.158540	−	0.487935i
$195$		0			0
$196$	2.42705	+	1.76336i	0.173361	+	0.125954i
$197$			20.9443i			1.49222i	0.665824	+	0.746109i	$0.268080\pi$
$197$			20.9443i			1.49222i	−0.665824	+	0.746109i	$0.731920\pi$
$198$	−2.07363	−	9.23607i	−0.147366	−	0.656379i
$199$	18.9443			1.34292			0.671462	−	0.741039i	$-0.265667\pi$
$199$	18.9443			1.34292			0.671462	+	0.741039i	$0.265667\pi$
$200$		0			0
$201$	1.30902	−	4.02874i	0.0923309	−	0.284165i
$202$	−3.97574	+	1.29180i	−0.279732	+	0.0908905i
$203$	5.25731	+	7.23607i	0.368991	+	0.507872i
$204$	−0.190983	+	0.138757i	−0.0133715	+	0.00971495i
$205$		0			0
$206$	4.85410	−	14.9394i	0.338201	−	1.04088i
$207$	2.07363	−	2.85410i	0.144127	−	0.198374i
$208$			1.23607i			0.0857059i
$209$	−17.8262	−	7.69421i	−1.23307	−	0.532220i
$210$		0			0
$211$	4.92705	+	3.57971i	0.339192	+	0.246438i	0.744321	−	0.667822i	$-0.232773\pi$
$211$	4.92705	+	3.57971i	0.339192	+	0.246438i	−0.405129	+	0.914260i	$0.632773\pi$
$212$	1.45309	+	0.472136i	0.0997983	+	0.0324264i
$213$	1.90211	−	0.618034i	0.130331	−	0.0423470i
$214$	−0.927051	+	0.673542i	−0.0633719	+	0.0460424i
$215$		0			0
$216$	−0.690983	−	2.12663i	−0.0470154	−	0.144699i
$217$	3.80423	+	1.23607i	0.258248	+	0.0839098i
$218$	11.1352	−	15.3262i	0.754168	−	1.03802i
$219$	−3.96556			−0.267968
$220$		0			0
$221$	−0.763932			−0.0513876
$222$	0.832544	−	1.14590i	0.0558767	−	0.0769076i
$223$	24.4500	+	7.94427i	1.63729	+	0.531988i	0.975931	−	0.218081i	$-0.0699798\pi$
$223$	24.4500	+	7.94427i	1.63729	+	0.531988i	0.661359	+	0.750069i	$0.269980\pi$
$224$	0.618034	+	1.90211i	0.0412941	+	0.127090i
$225$		0			0
$226$	1.50000	−	1.08981i	0.0997785	−	0.0724933i
$227$	13.7966	−	4.48278i	0.915711	−	0.297532i	0.187005	−	0.982359i	$-0.440122\pi$
$227$	13.7966	−	4.48278i	0.915711	−	0.297532i	0.728706	+	0.684827i	$0.240122\pi$
$228$	−2.12663	−	0.690983i	−0.140839	−	0.0457615i
$229$	1.38197	+	1.00406i	0.0913229	+	0.0663500i	0.632510	−	0.774552i	$-0.282025\pi$
$229$	1.38197	+	1.00406i	0.0913229	+	0.0663500i	−0.541187	+	0.840902i	$0.682025\pi$
$230$		0			0
$231$	−0.236068	+	2.52265i	−0.0155321	+	0.165978i
$232$		−	4.47214i		−	0.293610i
$233$	−5.65334	+	7.78115i	−0.370363	+	0.509760i	−0.952999	−	0.302972i	$-0.902021\pi$
$233$	−5.65334	+	7.78115i	−0.370363	+	0.509760i	0.582637	+	0.812733i	$0.302021\pi$
$234$	1.09017	−	3.35520i	0.0712666	−	0.219336i
$235$		0			0
$236$	6.97214	−	5.06555i	0.453847	−	0.329739i
$237$	3.01217	+	4.14590i	0.195662	+	0.269305i
$238$	−1.17557	+	0.381966i	−0.0762009	+	0.0247592i
$239$	6.70820	−	20.6457i	0.433918	−	1.33546i	−0.460274	−	0.887777i	$-0.652249\pi$
$239$	6.70820	−	20.6457i	0.433918	−	1.33546i	0.894192	−	0.447684i	$-0.147751\pi$
$240$		0			0
$241$	−11.0902			−0.714381			−0.357190	−	0.934032i	$-0.616265\pi$
$241$	−11.0902			−0.714381			−0.357190	+	0.934032i	$0.616265\pi$
$242$	8.00448	−	7.54508i	0.514547	−	0.485016i
$243$			9.65248i			0.619207i
$244$	−2.00000	−	1.45309i	−0.128037	−	0.0930242i
$245$		0			0
$246$	0.663119	+	2.04087i	0.0422789	+	0.130121i
$247$	−4.25325	−	5.85410i	−0.270628	−	0.372488i
$248$	−1.17557	−	1.61803i	−0.0746488	−	0.102745i
$249$	−1.10081	−	3.38795i	−0.0697612	−	0.214703i
$250$		0			0
$251$	−16.9443	−	12.3107i	−1.06951	−	0.777047i	−0.0936883	−	0.995602i	$-0.529866\pi$
$251$	−16.9443	−	12.3107i	−1.06951	−	0.777047i	−0.975825	+	0.218555i	$0.929866\pi$
$252$		−	5.70820i		−	0.359583i
$253$	4.08174	+	0.381966i	0.256617	+	0.0240140i
$254$	10.9443			0.686705
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−5.34307	+	1.73607i	−0.333291	+	0.108293i	−0.470882	−	0.882196i	$-0.656064\pi$
$257$	−5.34307	+	1.73607i	−0.333291	+	0.108293i	0.137590	+	0.990489i	$0.456064\pi$
$258$	1.92236	+	2.64590i	0.119681	+	0.164726i
$259$	6.00000	−	4.35926i	0.372822	−	0.270871i
$260$		0			0
$261$	−3.94427	+	12.1392i	−0.244144	+	0.751399i
$262$	−3.99598	+	5.50000i	−0.246873	+	0.339791i
$263$		−	23.2361i		−	1.43280i	−0.697691	−	0.716399i	$-0.745789\pi$
$263$		−	23.2361i		−	1.43280i	0.697691	−	0.716399i	$-0.254211\pi$
$264$	0.836881	−	0.951057i	0.0515065	−	0.0585335i
$265$		0			0
$266$	−9.47214	−	6.88191i	−0.580774	−	0.421957i
$267$	2.93893	+	0.954915i	0.179859	+	0.0584399i
$268$	−10.5474	+	3.42705i	−0.644284	+	0.209340i
$269$	5.00000	−	3.63271i	0.304855	−	0.221490i	−0.424830	−	0.905273i	$-0.639666\pi$
$269$	5.00000	−	3.63271i	0.304855	−	0.221490i	0.729686	+	0.683783i	$0.239666\pi$
$270$		0			0
$271$	0.618034	+	1.90211i	0.0375429	+	0.115545i	0.968072	−	0.250674i	$-0.0806521\pi$
$271$	0.618034	+	1.90211i	0.0375429	+	0.115545i	−0.930529	+	0.366219i	$0.880652\pi$
$272$	0.587785	+	0.190983i	0.0356397	+	0.0115800i
$273$	−0.555029	+	0.763932i	−0.0335919	+	0.0462353i
$274$	−16.0902			−0.972043
$275$		0			0
$276$	0.472136			0.0284192
$277$	13.9353	−	19.1803i	0.837293	−	1.15243i	−0.149228	−	0.988803i	$-0.547679\pi$
$277$	13.9353	−	19.1803i	0.837293	−	1.15243i	0.986521	−	0.163632i	$-0.0523210\pi$
$278$		0			0
$279$	1.76393	+	5.42882i	0.105604	+	0.325015i
$280$		0			0
$281$	13.0172	−	9.45756i	0.776542	−	0.564191i	−0.127397	−	0.991852i	$-0.540662\pi$
$281$	13.0172	−	9.45756i	0.776542	−	0.564191i	0.903939	+	0.427661i	$0.140662\pi$
$282$	−2.35114	+	0.763932i	−0.140008	+	0.0454915i
$283$	22.8254	+	7.41641i	1.35683	+	0.440860i	0.894982	−	0.446101i	$-0.147188\pi$
$283$	22.8254	+	7.41641i	1.35683	+	0.440860i	0.461844	+	0.886961i	$0.347188\pi$
$284$	−4.23607	−	3.07768i	−0.251364	−	0.182627i
$285$		0			0
$286$	4.00000	−	0.898056i	0.236525	−	0.0531032i
$287$			11.2361i			0.663244i
$288$	−1.67760	+	2.30902i	−0.0988535	+	0.136060i
$289$	5.13525	−	15.8047i	0.302074	−	0.929688i
$290$		0			0
$291$	−2.20820	+	1.60435i	−0.129447	+	0.0940489i
$292$	6.10237	+	8.39919i	0.357114	+	0.491525i
$293$	26.9726	−	8.76393i	1.57576	−	0.511994i	0.614798	−	0.788685i	$-0.289238\pi$
$293$	26.9726	−	8.76393i	1.57576	−	0.511994i	0.960959	+	0.276691i	$0.0892377\pi$
$294$	0.354102	−	1.08981i	0.0206516	−	0.0635592i
$295$		0			0
$296$	−3.70820			−0.215535
$297$	−6.37988	+	3.78115i	−0.370198	+	0.219405i
$298$		−	6.18034i		−	0.358017i
$299$	1.23607	+	0.898056i	0.0714837	+	0.0519359i
$300$		0			0
$301$	5.29180	+	16.2865i	0.305014	+	0.938737i
$302$	−4.70228	−	6.47214i	−0.270586	−	0.372430i
$303$	0.938545	+	1.29180i	0.0539180	+	0.0742117i
$304$	1.80902	+	5.56758i	0.103754	+	0.319323i
$305$		0			0
$306$	−1.42705	−	1.03681i	−0.0815791	−	0.0592707i
$307$		−	27.7984i		−	1.58654i	−0.608872	−	0.793268i	$-0.708378\pi$
$307$		−	27.7984i		−	1.58654i	0.608872	−	0.793268i	$-0.291622\pi$
$308$	5.70634	−	3.38197i	0.325149	−	0.192705i
$309$	−6.00000			−0.341328
$310$		0			0
$311$	8.05573	−	24.7930i	0.456798	−	1.40588i	−0.412212	−	0.911088i	$-0.635244\pi$
$311$	8.05573	−	24.7930i	0.456798	−	1.40588i	0.869011	−	0.494793i	$-0.164756\pi$
$312$	0.449028	−	0.145898i	0.0254212	−	0.00825985i
$313$	−2.54290	−	3.50000i	−0.143733	−	0.197832i	0.731081	−	0.682291i	$-0.239016\pi$
$313$	−2.54290	−	3.50000i	−0.143733	−	0.197832i	−0.874814	+	0.484459i	$0.839016\pi$
$314$	7.85410	−	5.70634i	0.443233	−	0.322027i
$315$		0			0
$316$	4.14590	−	12.7598i	0.233225	−	0.717793i
$317$	2.17963	−	3.00000i	0.122420	−	0.168497i	−0.743408	−	0.668838i	$-0.766792\pi$
$317$	2.17963	−	3.00000i	0.122420	−	0.168497i	0.865828	+	0.500341i	$0.166792\pi$
$318$		−	0.583592i		−	0.0327262i
$319$	−14.4721	+	3.24920i	−0.810284	+	0.181920i
$320$		0			0
$321$	0.354102	+	0.257270i	0.0197640	+	0.0143594i
$322$	2.35114	+	0.763932i	0.131024	+	0.0425723i
$323$	−3.44095	+	1.11803i	−0.191460	+	0.0622091i
$324$	6.23607	−	4.53077i	0.346448	−	0.251709i
$325$		0			0
$326$	0.281153	+	0.865300i	0.0155716	+	0.0479245i
$327$	−6.88191	−	2.23607i	−0.380570	−	0.123655i
$328$	3.30220	−	4.54508i	0.182333	−	0.250960i
$329$	−12.9443			−0.713641
$330$		0			0
$331$	6.27051			0.344658			0.172329	−	0.985039i	$-0.444871\pi$
$331$	6.27051			0.344658			0.172329	+	0.985039i	$0.444871\pi$
$332$	−5.48183	+	7.54508i	−0.300854	+	0.414090i
$333$	10.0656	+	3.27051i	0.551591	+	0.179223i
$334$	4.56231	+	14.0413i	0.249638	+	0.768308i
$335$		0			0
$336$	0.618034	−	0.449028i	0.0337165	−	0.0244965i
$337$	−25.4868	+	8.28115i	−1.38835	+	0.451103i	−0.905406	−	0.424547i	$-0.860433\pi$
$337$	−25.4868	+	8.28115i	−1.38835	+	0.451103i	−0.482947	+	0.875650i	$0.660433\pi$
$338$	−10.9106	−	3.54508i	−0.593461	−	0.192827i
$339$	−0.572949	−	0.416272i	−0.0311183	−	0.0226088i
$340$		0			0
$341$	−4.38197	+	4.97980i	−0.237297	+	0.269671i
$342$		−	16.7082i		−	0.903476i
$343$	11.7557	−	16.1803i	0.634748	−	0.873656i
$344$	2.64590	−	8.14324i	0.142657	−	0.439054i
$345$		0			0
$346$	−17.7082	+	12.8658i	−0.951999	+	0.691668i
$347$	9.76784	+	13.4443i	0.524365	+	0.721726i	0.986259	−	0.165209i	$-0.0528299\pi$
$347$	9.76784	+	13.4443i	0.524365	+	0.721726i	−0.461894	+	0.886935i	$0.652830\pi$
$348$	−1.62460	+	0.527864i	−0.0870876	+	0.0282965i
$349$	6.05573	−	18.6376i	0.324156	−	0.997649i	−0.647665	−	0.761926i	$-0.724254\pi$
$349$	6.05573	−	18.6376i	0.324156	−	0.997649i	0.971820	−	0.235723i	$-0.0757458\pi$
$350$		0			0
$351$	−2.76393			−0.147528
$352$	−3.30220	−	0.309017i	−0.176008	−	0.0164707i
$353$			32.6180i			1.73608i	0.496492	+	0.868041i	$0.334621\pi$
$353$			32.6180i			1.73608i	−0.496492	+	0.868041i	$0.665379\pi$
$354$	−2.66312	−	1.93487i	−0.141543	−	0.102837i
$355$		0			0
$356$	−2.50000	−	7.69421i	−0.132500	−	0.407792i
$357$	0.277515	+	0.381966i	0.0146876	+	0.0202158i
$358$	5.06555	+	6.97214i	0.267723	+	0.368489i
$359$	−1.58359	−	4.87380i	−0.0835788	−	0.257229i	0.900531	−	0.434793i	$-0.143178\pi$
$359$	−1.58359	−	4.87380i	−0.0835788	−	0.257229i	−0.984109	+	0.177564i	$0.943178\pi$
$360$		0			0
$361$	−12.3541	−	8.97578i	−0.650216	−	0.472409i
$362$			4.18034i			0.219714i
$363$	−3.68571	−	2.01722i	−0.193450	−	0.105877i
$364$	2.47214			0.129575
$365$		0			0
$366$	−0.291796	+	0.898056i	−0.0152524	+	0.0469421i
$367$	18.7436	−	6.09017i	0.978409	−	0.317904i	0.224203	−	0.974542i	$-0.428022\pi$
$367$	18.7436	−	6.09017i	0.978409	−	0.317904i	0.754206	+	0.656638i	$0.228022\pi$
$368$	−0.726543	−	1.00000i	−0.0378736	−	0.0521286i
$369$	−12.9721	+	9.42481i	−0.675302	+	0.490636i
$370$		0			0
$371$	0.944272	−	2.90617i	0.0490242	−	0.150881i
$372$	−0.449028	+	0.618034i	−0.0232810	+	0.0320436i
$373$		−	4.29180i		−	0.222221i	−0.993808	−	0.111110i	$-0.964559\pi$
$373$		−	4.29180i		−	0.222221i	0.993808	−	0.111110i	$-0.0354407\pi$
$374$	0.190983	−	2.04087i	0.00987550	−	0.105531i
$375$		0			0
$376$	5.23607	+	3.80423i	0.270030	+	0.196188i
$377$	−5.25731	−	1.70820i	−0.270765	−	0.0879770i
$378$	−4.25325	+	1.38197i	−0.218764	+	0.0710807i
$379$	11.5451	−	8.38800i	0.593031	−	0.430862i	−0.250367	−	0.968151i	$-0.580551\pi$
$379$	11.5451	−	8.38800i	0.593031	−	0.430862i	0.843398	+	0.537289i	$0.180551\pi$
$380$		0			0
$381$	−1.29180	−	3.97574i	−0.0661807	−	0.203683i
$382$	−4.53077	−	1.47214i	−0.231814	−	0.0753210i
$383$	−16.6700	+	22.9443i	−0.851797	+	1.17240i	0.131667	+	0.991294i	$0.457967\pi$
$383$	−16.6700	+	22.9443i	−0.851797	+	1.17240i	−0.983464	+	0.181104i	$0.942033\pi$
$384$	−0.381966			−0.0194921
$385$		0			0
$386$	17.4164			0.886472
$387$	−14.3641	+	19.7705i	−0.730169	+	1.00499i
$388$	6.79615	+	2.20820i	0.345022	+	0.112105i
$389$	3.29180	+	10.1311i	0.166901	+	0.513667i	0.999171	−	0.0407020i	$-0.0129594\pi$
$389$	3.29180	+	10.1311i	0.166901	+	0.513667i	−0.832271	+	0.554370i	$0.812959\pi$
$390$		0			0
$391$	0.618034	−	0.449028i	0.0312553	−	0.0227083i
$392$	−2.85317	+	0.927051i	−0.144107	+	0.0468231i
$393$	2.46965	+	0.802439i	0.124578	+	0.0404777i
$394$	−16.9443	−	12.3107i	−0.853640	−	0.620206i
$395$		0			0
$396$	8.69098	+	3.75123i	0.436738	+	0.188506i
$397$			17.1246i			0.859460i	0.902958	+	0.429730i	$0.141391\pi$
$397$			17.1246i			0.859460i	−0.902958	+	0.429730i	$0.858609\pi$
$398$	−11.1352	+	15.3262i	−0.558155	+	0.768235i
$399$	−1.38197	+	4.25325i	−0.0691848	+	0.212929i
$400$		0			0
$401$	14.3992	−	10.4616i	0.719061	−	0.522428i	−0.167023	−	0.985953i	$-0.553415\pi$
$401$	14.3992	−	10.4616i	0.719061	−	0.522428i	0.886084	+	0.463525i	$0.153415\pi$
$402$	2.48990	+	3.42705i	0.124185	+	0.170926i
$403$	−2.35114	+	0.763932i	−0.117119	+	0.0380542i
$404$	1.29180	−	3.97574i	0.0642693	−	0.197800i
$405$		0			0
$406$	−8.94427			−0.443897
$407$	2.69417	+	12.0000i	0.133545	+	0.594818i
$408$		−	0.236068i		−	0.0116871i
$409$	−10.8541	−	7.88597i	−0.536701	−	0.389936i	0.286157	−	0.958183i	$-0.407622\pi$
$409$	−10.8541	−	7.88597i	−0.536701	−	0.389936i	−0.822858	+	0.568247i	$0.807622\pi$
$410$		0			0
$411$	1.89919	+	5.84510i	0.0936800	+	0.288317i
$412$	9.23305	+	12.7082i	0.454880	+	0.626088i
$413$	−10.1311	−	13.9443i	−0.498519	−	0.686153i
$414$	1.09017	+	3.35520i	0.0535789	+	0.164899i
$415$		0			0
$416$	−1.00000	−	0.726543i	−0.0490290	−	0.0356217i
$417$		0			0
$418$	16.7027	−	9.89919i	0.816958	−	0.484185i
$419$	10.8541			0.530258			0.265129	−	0.964213i	$-0.414586\pi$
$419$	10.8541			0.530258			0.265129	+	0.964213i	$0.414586\pi$
$420$		0			0
$421$	−9.70820	+	29.8788i	−0.473149	+	1.45620i	0.375289	+	0.926908i	$0.377543\pi$
$421$	−9.70820	+	29.8788i	−0.473149	+	1.45620i	−0.848438	+	0.529295i	$0.822457\pi$
$422$	−5.79210	+	1.88197i	−0.281955	+	0.0916127i
$423$	−10.8576	−	14.9443i	−0.527917	−	0.726615i
$424$	−1.23607	+	0.898056i	−0.0600288	+	0.0436135i
$425$		0			0
$426$	−0.618034	+	1.90211i	−0.0299438	+	0.0921577i
$427$	−2.90617	+	4.00000i	−0.140639	+	0.193574i
$428$		−	1.14590i		−	0.0553891i
$429$	−0.798374	−	1.34708i	−0.0385459	−	0.0650378i
$430$		0			0
$431$	13.7082	+	9.95959i	0.660301	+	0.479737i	0.866765	−	0.498718i	$-0.166196\pi$
$431$	13.7082	+	9.95959i	0.660301	+	0.479737i	−0.206464	+	0.978454i	$0.566196\pi$
$432$	2.12663	+	0.690983i	0.102317	+	0.0332449i
$433$	−26.3848	+	8.57295i	−1.26797	+	0.411990i	−0.864329	−	0.502926i	$-0.832257\pi$
$433$	−26.3848	+	8.57295i	−1.26797	+	0.411990i	−0.403644	+	0.914916i	$0.632257\pi$
$434$	−3.23607	+	2.35114i	−0.155336	+	0.112858i
$435$		0			0
$436$	5.85410	+	18.0171i	0.280361	+	0.862861i
$437$	6.88191	+	2.23607i	0.329206	+	0.106966i
$438$	2.33090	−	3.20820i	0.111375	−	0.153294i
$439$	6.58359			0.314218			0.157109	−	0.987581i	$-0.449783\pi$
$439$	6.58359			0.314218			0.157109	+	0.987581i	$0.449783\pi$
$440$		0			0
$441$	8.56231			0.407729
$442$	0.449028	−	0.618034i	0.0213581	−	0.0293969i
$443$	−8.14324	−	2.64590i	−0.386897	−	0.125710i	0.109109	−	0.994030i	$-0.465200\pi$
$443$	−8.14324	−	2.64590i	−0.386897	−	0.125710i	−0.496005	+	0.868319i	$0.665200\pi$
$444$	0.437694	+	1.34708i	0.0207720	+	0.0639298i
$445$		0			0
$446$	−20.7984	+	15.1109i	−0.984832	+	0.715522i
$447$	−2.24514	+	0.729490i	−0.106191	+	0.0345037i
$448$	−1.90211	−	0.618034i	−0.0898664	−	0.0291994i
$449$	7.50000	+	5.44907i	0.353947	+	0.257157i	0.750523	−	0.660844i	$-0.229802\pi$
$449$	7.50000	+	5.44907i	0.353947	+	0.257157i	−0.396576	+	0.918002i	$0.629802\pi$
$450$		0			0
$451$	−17.1074	−	7.38394i	−0.805556	−	0.347696i
$452$			1.85410i			0.0872096i
$453$	−1.79611	+	2.47214i	−0.0843887	+	0.116151i
$454$	−4.48278	+	13.7966i	−0.210387	+	0.647505i
$455$		0			0
$456$	1.80902	−	1.31433i	0.0847150	−	0.0615490i
$457$	−5.54734	−	7.63525i	−0.259493	−	0.357162i	0.659314	−	0.751867i	$-0.270847\pi$
$457$	−5.54734	−	7.63525i	−0.259493	−	0.357162i	−0.918808	+	0.394705i	$0.870847\pi$
$458$	−1.62460	+	0.527864i	−0.0759125	+	0.0246655i
$459$	−0.427051	+	1.31433i	−0.0199330	+	0.0613476i
$460$		0			0
$461$	1.34752			0.0627605			0.0313802	−	0.999508i	$-0.490010\pi$
$461$	1.34752			0.0627605			0.0313802	+	0.999508i	$0.490010\pi$
$462$	−1.90211	−	1.67376i	−0.0884943	−	0.0778705i
$463$		−	19.4164i		−	0.902357i	−0.892434	−	0.451178i	$-0.851004\pi$
$463$		−	19.4164i		−	0.902357i	0.892434	−	0.451178i	$-0.148996\pi$
$464$	3.61803	+	2.62866i	0.167963	+	0.122032i
$465$		0			0
$466$	−2.97214	−	9.14729i	−0.137682	−	0.423740i
$467$	−19.5762	−	26.9443i	−0.905877	−	1.24683i	−0.968555	−	0.248798i	$-0.919964\pi$
$467$	−19.5762	−	26.9443i	−0.905877	−	1.24683i	0.0626787	−	0.998034i	$-0.480036\pi$
$468$	2.07363	+	2.85410i	0.0958534	+	0.131931i
$469$	6.85410	+	21.0948i	0.316493	+	0.974065i
$470$		0			0
$471$	−3.00000	−	2.17963i	−0.138233	−	0.100432i
$472$			8.61803i			0.396677i
$473$	−28.2744	−	2.64590i	−1.30006	−	0.121659i
$474$	−5.12461			−0.235381
$475$		0			0
$476$	0.381966	−	1.17557i	0.0175074	−	0.0538822i
$477$	4.14725	−	1.34752i	0.189890	−	0.0616989i
$478$	12.7598	+	17.5623i	0.583618	+	0.803281i
$479$	−27.8885	+	20.2622i	−1.27426	+	0.925804i	−0.999364	−	0.0356697i	$-0.988644\pi$
$479$	−27.8885	+	20.2622i	−1.27426	+	0.925804i	−0.274896	+	0.961474i	$0.588644\pi$
$480$		0			0
$481$	−1.41641	+	4.35926i	−0.0645826	+	0.198765i
$482$	6.51864	−	8.97214i	0.296916	−	0.408670i
$483$		−	0.944272i		−	0.0429659i
$484$	1.39919	+	10.9106i	0.0635994	+	0.495939i
$485$		0			0
$486$	−7.80902	−	5.67358i	−0.354224	−	0.257359i
$487$	1.28157	+	0.416408i	0.0580736	+	0.0188692i	0.337910	−	0.941179i	$-0.390280\pi$
$487$	1.28157	+	0.416408i	0.0580736	+	0.0188692i	−0.279836	+	0.960048i	$0.590280\pi$
$488$	2.35114	−	0.763932i	0.106431	−	0.0345816i
$489$	0.281153	−	0.204270i	0.0127142	−	0.00923739i
$490$		0			0
$491$	7.06231	+	21.7355i	0.318717	+	0.980911i	0.974197	+	0.225699i	$0.0724664\pi$
$491$	7.06231	+	21.7355i	0.318717	+	0.980911i	−0.655480	+	0.755213i	$0.727534\pi$
$492$	−2.04087	−	0.663119i	−0.0920095	−	0.0298957i
$493$	−1.62460	+	2.23607i	−0.0731682	+	0.100707i
$494$	7.23607			0.325566
$495$		0			0
$496$	2.00000			0.0898027
$497$	−6.15537	+	8.47214i	−0.276106	+	0.380027i
$498$	3.38795	+	1.10081i	0.151818	+	0.0493286i
$499$	9.53444	+	29.3440i	0.426820	+	1.31362i	0.901241	+	0.433319i	$0.142658\pi$
$499$	9.53444	+	29.3440i	0.426820	+	1.31362i	−0.474420	+	0.880298i	$0.657342\pi$
$500$		0			0
$501$	4.56231	−	3.31471i	0.203829	−	0.148090i
$502$	19.9192	−	6.47214i	0.889037	−	0.288866i
$503$	−3.07768	−	1.00000i	−0.137227	−	0.0445878i	0.239598	−	0.970872i	$-0.422984\pi$
$503$	−3.07768	−	1.00000i	−0.137227	−	0.0445878i	−0.376825	+	0.926284i	$0.622984\pi$
$504$	4.61803	+	3.35520i	0.205704	+	0.149452i
$505$		0			0
$506$	−2.70820	+	3.07768i	−0.120394	+	0.136820i
$507$			4.38197i			0.194610i
$508$	−6.43288	+	8.85410i	−0.285413	+	0.392837i
$509$	2.56231	−	7.88597i	0.113572	−	0.349539i	−0.878074	−	0.478524i	$-0.841172\pi$
$509$	2.56231	−	7.88597i	0.113572	−	0.349539i	0.991647	+	0.128985i	$0.0411719\pi$
$510$		0			0
$511$	16.7984	−	12.2047i	0.743116	−	0.539906i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	−12.4495	+	4.04508i	−0.549658	+	0.178595i
$514$	1.73607	−	5.34307i	0.0765747	−	0.235673i
$515$		0			0
$516$	−3.27051			−0.143976
$517$	8.50651	−	19.7082i	0.374116	−	0.866766i
$518$			7.41641i			0.325858i
$519$	6.76393	+	4.91428i	0.296904	+	0.215713i
$520$		0			0
$521$	−6.19098	−	19.0539i	−0.271232	−	0.834766i	−0.990192	−	0.139714i	$-0.955382\pi$
$521$	−6.19098	−	19.0539i	−0.271232	−	0.834766i	0.718960	−	0.695052i	$-0.244618\pi$
$522$	−7.50245	−	10.3262i	−0.328373	−	0.451967i
$523$	−5.40858	−	7.44427i	−0.236501	−	0.325515i	0.674226	−	0.738525i	$-0.264477\pi$
$523$	−5.40858	−	7.44427i	−0.236501	−	0.325515i	−0.910726	+	0.413010i	$0.864477\pi$
$524$	−2.10081	−	6.46564i	−0.0917744	−	0.282453i
$525$		0			0
$526$	18.7984	+	13.6578i	0.819648	+	0.595509i
$527$			1.23607i			0.0538440i
$528$	0.277515	+	1.23607i	0.0120773	+	0.0537930i
$529$	21.4721			0.933571
$530$		0			0
$531$	7.60081	−	23.3929i	0.329847	−	1.01517i
$532$	11.1352	−	3.61803i	0.482771	−	0.156862i
$533$	−4.08174	−	5.61803i	−0.176800	−	0.243344i
$534$	−2.50000	+	1.81636i	−0.108186	+	0.0786014i
$535$		0			0
$536$	3.42705	−	10.5474i	0.148026	−	0.455577i
$537$	1.93487	−	2.66312i	0.0834958	−	0.114922i
$538$			6.18034i			0.266453i
$539$	5.07295	+	8.55951i	0.218507	+	0.368684i
$540$		0			0
$541$	2.52786	+	1.83660i	0.108681	+	0.0789616i	0.640798	−	0.767709i	$-0.278603\pi$
$541$	2.52786	+	1.83660i	0.108681	+	0.0789616i	−0.532117	+	0.846671i	$0.678603\pi$
$542$	−1.90211	−	0.618034i	−0.0817028	−	0.0265468i
$543$	1.51860	−	0.493422i	0.0651693	−	0.0211748i
$544$	−0.500000	+	0.363271i	−0.0214373	+	0.0155751i
$545$		0			0
$546$	−0.291796	−	0.898056i	−0.0124877	−	0.0384332i
$547$	−7.91872	−	2.57295i	−0.338580	−	0.110011i	0.134792	−	0.990874i	$-0.456963\pi$
$547$	−7.91872	−	2.57295i	−0.338580	−	0.110011i	−0.473372	+	0.880863i	$0.656963\pi$
$548$	9.45756	−	13.0172i	0.404007	−	0.556068i
$549$	−7.05573			−0.301131
$550$		0			0
$551$	−26.1803			−1.11532
$552$	−0.277515	+	0.381966i	−0.0118118	+	0.0162576i
$553$	−25.5195	−	8.29180i	−1.08520	−	0.352603i
$554$	7.32624	+	22.5478i	0.311262	+	0.957966i
$555$		0			0
$556$		0			0
$557$	33.5115	−	10.8885i	1.41993	−	0.461362i	0.504348	−	0.863500i	$-0.331733\pi$
$557$	33.5115	−	10.8885i	1.41993	−	0.461362i	0.915579	+	0.402138i	$0.131733\pi$
$558$	−5.42882	−	1.76393i	−0.229820	−	0.0746732i
$559$	−8.56231	−	6.22088i	−0.362147	−	0.263115i
$560$		0			0
$561$	−0.763932	+	0.171513i	−0.0322532	+	0.00724130i
$562$			16.0902i			0.678723i
$563$	0.224514	−	0.309017i	0.00946214	−	0.0130235i	−0.804260	−	0.594278i	$-0.797438\pi$
$563$	0.224514	−	0.309017i	0.00946214	−	0.0130235i	0.813722	+	0.581254i	$0.197438\pi$
$564$	0.763932	−	2.35114i	0.0321673	−	0.0990009i
$565$		0			0
$566$	−19.4164	+	14.1068i	−0.816132	+	0.592955i
$567$	−9.06154	−	12.4721i	−0.380549	−	0.523780i
$568$	4.97980	−	1.61803i	0.208948	−	0.0678912i
$569$	−11.8090	+	36.3444i	−0.495060	+	1.52364i	0.321804	+	0.946806i	$0.395711\pi$
$569$	−11.8090	+	36.3444i	−0.495060	+	1.52364i	−0.816864	+	0.576831i	$0.804289\pi$
$570$		0			0
$571$	−2.47214			−0.103456			−0.0517278	−	0.998661i	$-0.516473\pi$
$571$	−2.47214			−0.103456			−0.0517278	+	0.998661i	$0.516473\pi$
$572$	−1.62460	+	3.76393i	−0.0679279	+	0.157378i
$573$			1.81966i			0.0760174i
$574$	−9.09017	−	6.60440i	−0.379416	−	0.275662i
$575$		0			0
$576$	−0.881966	−	2.71441i	−0.0367486	−	0.113101i
$577$	−3.99598	−	5.50000i	−0.166355	−	0.228968i	0.717698	−	0.696354i	$-0.245196\pi$
$577$	−3.99598	−	5.50000i	−0.166355	−	0.228968i	−0.884053	+	0.467386i	$0.845196\pi$
$578$	9.76784	+	13.4443i	0.406288	+	0.559208i
$579$	−2.05573	−	6.32688i	−0.0854331	−	0.262936i
$580$		0			0
$581$	15.0902	+	10.9637i	0.626046	+	0.454849i
$582$		−	2.72949i		−	0.113141i
$583$	3.80423	+	3.34752i	0.157555	+	0.138640i
$584$	−10.3820			−0.429609
$585$		0			0
$586$	−8.76393	+	26.9726i	−0.362035	+	1.11423i
$587$	21.0620	−	6.84346i	0.869322	−	0.282460i	0.159805	−	0.987149i	$-0.448913\pi$
$587$	21.0620	−	6.84346i	0.869322	−	0.282460i	0.709517	+	0.704689i	$0.248913\pi$
$588$	0.673542	+	0.927051i	0.0277764	+	0.0382309i
$589$	−9.47214	+	6.88191i	−0.390293	+	0.283564i
$590$		0			0
$591$	−2.47214	+	7.60845i	−0.101690	+	0.312970i
$592$	2.17963	−	3.00000i	0.0895821	−	0.123299i
$593$		−	28.6869i		−	1.17803i	−0.808122	−	0.589015i	$-0.799516\pi$
$593$		−	28.6869i		−	1.17803i	0.808122	−	0.589015i	$-0.200484\pi$
$594$	0.690983	−	7.38394i	0.0283514	−	0.302967i
$595$		0			0
$596$	5.00000	+	3.63271i	0.204808	+	0.148802i
$597$	6.88191	+	2.23607i	0.281658	+	0.0915162i
$598$	−1.45309	+	0.472136i	−0.0594211	+	0.0193071i
$599$	−10.8541	+	7.88597i	−0.443487	+	0.322212i	−0.787019	−	0.616929i	$-0.788377\pi$
$599$	−10.8541	+	7.88597i	−0.443487	+	0.322212i	0.343532	+	0.939141i	$0.388377\pi$
$600$		0			0
$601$	−8.38854	−	25.8173i	−0.342176	−	1.05311i	−0.963078	−	0.269221i	$-0.913234\pi$
$601$	−8.38854	−	25.8173i	−0.342176	−	1.05311i	0.620903	−	0.783888i	$-0.286766\pi$
$602$	−16.2865	−	5.29180i	−0.663787	−	0.215678i
$603$	−18.6049	+	25.6074i	−0.757648	+	1.04281i
$604$	8.00000			0.325515
$605$		0			0
$606$	−1.59675			−0.0648634
$607$	−13.5923	+	18.7082i	−0.551695	+	0.759343i	−0.990241	−	0.139366i	$-0.955494\pi$
$607$	−13.5923	+	18.7082i	−0.551695	+	0.759343i	0.438546	+	0.898709i	$0.355494\pi$
$608$	−5.56758	−	1.80902i	−0.225795	−	0.0733653i
$609$	1.05573	+	3.24920i	0.0427803	+	0.131664i
$610$		0			0
$611$	6.47214	−	4.70228i	0.261835	−	0.190234i
$612$	1.67760	−	0.545085i	0.0678129	−	0.0220338i
$613$	33.9605	+	11.0344i	1.37165	+	0.445677i	0.899916	−	0.436063i	$-0.143627\pi$
$613$	33.9605	+	11.0344i	1.37165	+	0.445677i	0.471736	+	0.881740i	$0.343627\pi$
$614$	22.4894	+	16.3395i	0.907597	+	0.659408i
$615$		0			0
$616$	−0.618034	+	6.60440i	−0.0249013	+	0.266099i
$617$		−	23.4508i		−	0.944096i	−0.881573	−	0.472048i	$-0.843515\pi$
$617$		−	23.4508i		−	0.944096i	0.881573	−	0.472048i	$-0.156485\pi$
$618$	3.52671	−	4.85410i	0.141865	−	0.195261i
$619$	−1.60739	+	4.94704i	−0.0646065	+	0.198838i	−0.978149	−	0.207905i	$-0.933336\pi$
$619$	−1.60739	+	4.94704i	−0.0646065	+	0.198838i	0.913543	+	0.406743i	$0.133336\pi$
$620$		0			0
$621$	2.23607	−	1.62460i	0.0897303	−	0.0651929i
$622$	15.3229	+	21.0902i	0.614393	+	0.845639i
$623$	−15.3884	+	5.00000i	−0.616524	+	0.200321i
$624$	−0.145898	+	0.449028i	−0.00584060	+	0.0179755i
$625$		0			0
$626$	4.32624			0.172911
$627$	−5.56758	−	4.89919i	−0.222348	−	0.195655i
$628$			9.70820i			0.387400i
$629$	1.85410	+	1.34708i	0.0739279	+	0.0537118i
$630$		0			0
$631$	7.32624	+	22.5478i	0.291653	+	0.897615i	0.984325	+	0.176363i	$0.0564332\pi$
$631$	7.32624	+	22.5478i	0.291653	+	0.897615i	−0.692672	+	0.721252i	$0.743567\pi$
$632$	7.88597	+	10.8541i	0.313687	+	0.431753i
$633$	1.36733	+	1.88197i	0.0543464	+	0.0748014i
$634$	1.14590	+	3.52671i	0.0455094	+	0.140064i
$635$		0			0
$636$	0.472136	+	0.343027i	0.0187214	+	0.0136019i
$637$			3.70820i			0.146924i
$638$	5.87785	−	13.6180i	0.232706	−	0.539143i
$639$	−14.9443			−0.591186
$640$		0			0
$641$	5.15248	−	15.8577i	0.203511	−	0.626341i	−0.796261	−	0.604954i	$-0.793192\pi$
$641$	5.15248	−	15.8577i	0.203511	−	0.626341i	0.999771	−	0.0213875i	$-0.00680836\pi$
$642$	−0.416272	+	0.135255i	−0.0164289	+	0.00533809i
$643$	−23.4989	−	32.3435i	−0.926706	−	1.27550i	−0.961131	−	0.276094i	$-0.910960\pi$
$643$	−23.4989	−	32.3435i	−0.926706	−	1.27550i	0.0344245	−	0.999407i	$-0.489040\pi$
$644$	−2.00000	+	1.45309i	−0.0788110	+	0.0572596i
$645$		0			0
$646$	1.11803	−	3.44095i	0.0439885	−	0.135383i
$647$	−17.0785	+	23.5066i	−0.671426	+	0.924139i	−0.999792	−	0.0204118i	$-0.993502\pi$
$647$	−17.0785	+	23.5066i	−0.671426	+	0.924139i	0.328365	+	0.944551i	$0.393502\pi$
$648$			7.70820i			0.302807i
$649$	27.8885	−	6.26137i	1.09472	−	0.245780i
$650$		0			0
$651$	1.23607	+	0.898056i	0.0484453	+	0.0351976i
$652$	−0.865300	−	0.281153i	−0.0338878	−	0.0110108i
$653$	14.5964	−	4.74265i	0.571200	−	0.185594i	−0.00915459	−	0.999958i	$-0.502914\pi$
$653$	14.5964	−	4.74265i	0.571200	−	0.185594i	0.580354	+	0.814364i	$0.302914\pi$
$654$	5.85410	−	4.25325i	0.228914	−	0.166315i
$655$		0			0
$656$	1.73607	+	5.34307i	0.0677821	+	0.208612i
$657$	28.1809	+	9.15654i	1.09944	+	0.357231i
$658$	7.60845	−	10.4721i	0.296608	−	0.408246i
$659$	16.9098			0.658713			0.329357	−	0.944206i	$-0.393168\pi$
$659$	16.9098			0.658713			0.329357	+	0.944206i	$0.393168\pi$
$660$		0			0
$661$	−3.52786			−0.137218			−0.0686090	−	0.997644i	$-0.521856\pi$
$661$	−3.52786			−0.137218			−0.0686090	+	0.997644i	$0.521856\pi$
$662$	−3.68571	+	5.07295i	−0.143249	+	0.197166i
$663$	−0.277515	−	0.0901699i	−0.0107778	−	0.00350191i
$664$	−2.88197	−	8.86978i	−0.111842	−	0.344214i
$665$		0			0
$666$	−8.56231	+	6.22088i	−0.331783	+	0.241054i
$667$	5.25731	−	1.70820i	0.203564	−	0.0661419i
$668$	−14.0413	−	4.56231i	−0.543276	−	0.176521i
$669$	7.94427	+	5.77185i	0.307143	+	0.223153i
$670$		0			0
$671$	−4.18034	−	7.05342i	−0.161380	−	0.272294i
$672$			0.763932i			0.0294693i
$673$	5.79210	−	7.97214i	0.223269	−	0.307303i	−0.682657	−	0.730738i	$-0.739176\pi$
$673$	5.79210	−	7.97214i	0.223269	−	0.307303i	0.905926	+	0.423435i	$0.139176\pi$
$674$	8.28115	−	25.4868i	0.318978	−	0.981714i
$675$		0			0
$676$	9.28115	−	6.74315i	0.356967	−	0.259352i
$677$	−8.44100	−	11.6180i	−0.324414	−	0.446517i	0.615395	−	0.788219i	$-0.288997\pi$
$677$	−8.44100	−	11.6180i	−0.324414	−	0.446517i	−0.939808	+	0.341702i	$0.888997\pi$
$678$	0.673542	−	0.218847i	0.0258672	−	0.00840477i
$679$	4.41641	−	13.5923i	0.169486	−	0.521625i
$680$		0			0
$681$	5.54102			0.212332
$682$	−1.45309	−	6.47214i	−0.0556415	−	0.247831i
$683$			18.4721i			0.706817i	0.935469	+	0.353408i	$0.114977\pi$
$683$			18.4721i			0.706817i	−0.935469	+	0.353408i	$0.885023\pi$
$684$	13.5172	+	9.82084i	0.516844	+	0.375509i
$685$		0			0
$686$	6.18034	+	19.0211i	0.235966	+	0.726230i
$687$	0.383516	+	0.527864i	0.0146320	+	0.0201393i
$688$	5.03280	+	6.92705i	0.191874	+	0.264091i
$689$	0.583592	+	1.79611i	0.0222331	+	0.0684264i
$690$		0			0
$691$	21.2082	+	15.4087i	0.806798	+	0.586173i	0.912901	−	0.408182i	$-0.133837\pi$
$691$	21.2082	+	15.4087i	0.806798	+	0.586173i	−0.106102	+	0.994355i	$0.533837\pi$
$692$		−	21.8885i		−	0.832078i
$693$	7.50245	−	17.3820i	0.284995	−	0.660286i
$694$	−16.6180			−0.630812
$695$		0			0
$696$	0.527864	−	1.62460i	0.0200086	−	0.0615802i
$697$	−3.30220	+	1.07295i	−0.125080	+	0.0406408i
$698$	11.5187	+	15.8541i	0.435988	+	0.600087i
$699$	−2.97214	+	2.15938i	−0.112417	+	0.0816754i
$700$		0			0
$701$	−4.58359	+	14.1068i	−0.173120	+	0.532808i	−0.999543	−	0.0302419i	$-0.990372\pi$
$701$	−4.58359	+	14.1068i	−0.173120	+	0.532808i	0.826423	+	0.563050i	$0.190372\pi$
$702$	1.62460	−	2.23607i	0.0613165	−	0.0843949i
$703$			21.7082i			0.818740i
$704$	2.19098	−	2.48990i	0.0825758	−	0.0938416i
$705$		0			0
$706$	−26.3885	−	19.1724i	−0.993146	−	0.721563i
$707$	−7.95148	−	2.58359i	−0.299046	−	0.0971660i
$708$	3.13068	−	1.01722i	0.117658	−	0.0382295i
$709$	19.7984	−	14.3844i	0.743544	−	0.540216i	−0.150275	−	0.988644i	$-0.548016\pi$
$709$	19.7984	−	14.3844i	0.743544	−	0.540216i	0.893819	+	0.448428i	$0.148016\pi$
$710$		0			0
$711$	−11.8328	−	36.4177i	−0.443765	−	1.36577i
$712$	7.69421	+	2.50000i	0.288353	+	0.0936915i
$713$	1.45309	−	2.00000i	0.0544185	−	0.0749006i
$714$	−0.472136			−0.0176692
$715$		0			0
$716$	−8.61803			−0.322071
$717$	4.87380	−	6.70820i	0.182015	−	0.250522i
$718$	4.87380	+	1.58359i	0.181888	+	0.0590991i
$719$	−8.29180	−	25.5195i	−0.309232	−	0.951718i	−0.978064	−	0.208304i	$-0.933206\pi$
$719$	−8.29180	−	25.5195i	−0.309232	−	0.951718i	0.668832	−	0.743413i	$-0.266794\pi$
$720$		0			0
$721$	25.4164	−	18.4661i	0.946556	−	0.687714i
$722$	14.5231	−	4.71885i	0.540494	−	0.175617i
$723$	−4.02874	−	1.30902i	−0.149830	−	0.0486829i
$724$	−3.38197	−	2.45714i	−0.125690	−	0.0913190i
$725$		0			0
$726$	3.79837	−	1.79611i	0.140971	−	0.0666600i
$727$		−	2.87539i		−	0.106642i	−0.998577	−	0.0533211i	$-0.983019\pi$
$727$		−	2.87539i		−	0.106642i	0.998577	−	0.0533211i	$-0.0169807\pi$
$728$	−1.45309	+	2.00000i	−0.0538549	+	0.0741249i
$729$	6.00658	−	18.4863i	0.222466	−	0.684679i
$730$		0			0
$731$	−4.28115	+	3.11044i	−0.158344	+	0.115044i
$732$	−0.555029	−	0.763932i	−0.0205145	−	0.0282357i
$733$	8.95554	−	2.90983i	0.330780	−	0.107477i	−0.138918	−	0.990304i	$-0.544363\pi$
$733$	8.95554	−	2.90983i	0.330780	−	0.107477i	0.469699	+	0.882827i	$0.344363\pi$
$734$	−6.09017	+	18.7436i	−0.224792	+	0.691839i
$735$		0			0
$736$	1.23607			0.0455621
$737$	−36.6219	−	3.42705i	−1.34899	−	0.126237i
$738$		−	16.0344i		−	0.590236i
$739$	−30.3885	−	22.0786i	−1.11786	−	0.812173i	−0.133977	−	0.990984i	$-0.542775\pi$
$739$	−30.3885	−	22.0786i	−1.11786	−	0.812173i	−0.983883	+	0.178811i	$0.942775\pi$
$740$		0			0
$741$	−0.854102	−	2.62866i	−0.0313762	−	0.0965661i
$742$	1.79611	+	2.47214i	0.0659373	+	0.0907550i
$743$	5.15131	+	7.09017i	0.188983	+	0.260113i	0.892986	−	0.450084i	$-0.148606\pi$
$743$	5.15131	+	7.09017i	0.188983	+	0.260113i	−0.704003	+	0.710197i	$0.748606\pi$
$744$	−0.236068	−	0.726543i	−0.00865467	−	0.0266363i
$745$		0			0
$746$	3.47214	+	2.52265i	0.127124	+	0.0923609i
$747$			26.6180i			0.973903i
$748$	1.53884	+	1.35410i	0.0562656	+	0.0495109i
$749$	−2.29180			−0.0837404
$750$		0			0
$751$	−10.4377	+	32.1239i	−0.380877	+	1.17222i	0.558551	+	0.829470i	$0.311358\pi$
$751$	−10.4377	+	32.1239i	−0.380877	+	1.17222i	−0.939427	+	0.342748i	$0.888642\pi$
$752$	−6.15537	+	2.00000i	−0.224463	+	0.0729325i
$753$	−4.70228	−	6.47214i	−0.171361	−	0.235858i
$754$	4.47214	−	3.24920i	0.162866	−	0.118329i
$755$		0			0
$756$	1.38197	−	4.25325i	0.0502616	−	0.154689i
$757$	1.55909	−	2.14590i	0.0566660	−	0.0779940i	−0.779744	−	0.626099i	$-0.784651\pi$
$757$	1.55909	−	2.14590i	0.0566660	−	0.0779940i	0.836410	+	0.548105i	$0.184651\pi$
$758$			14.2705i			0.518328i
$759$	1.43769	+	0.620541i	0.0521850	+	0.0225242i
$760$		0			0
$761$	3.44427	+	2.50241i	0.124855	+	0.0907123i	0.648460	−	0.761249i	$-0.275413\pi$
$761$	3.44427	+	2.50241i	0.124855	+	0.0907123i	−0.523605	+	0.851961i	$0.675413\pi$
$762$	3.97574	+	1.29180i	0.144026	+	0.0467968i
$763$	36.0341	−	11.7082i	1.30452	−	0.423865i
$764$	3.85410	−	2.80017i	0.139437	−	0.101307i
$765$		0			0
$766$	−8.76393	−	26.9726i	−0.316654	−	0.974560i
$767$	10.1311	+	3.29180i	0.365813	+	0.118860i
$768$	0.224514	−	0.309017i	0.00810145	−	0.0111507i
$769$	−13.4164			−0.483808			−0.241904	−	0.970300i	$-0.577772\pi$
$769$	−13.4164			−0.483808			−0.241904	+	0.970300i	$0.577772\pi$
$770$		0			0
$771$	−2.14590			−0.0772826
$772$	−10.2371	+	14.0902i	−0.368442	+	0.507116i
$773$	−3.69822	−	1.20163i	−0.133016	−	0.0432195i	0.241753	−	0.970338i	$-0.422278\pi$
$773$	−3.69822	−	1.20163i	−0.133016	−	0.0432195i	−0.374768	+	0.927118i	$0.622278\pi$
$774$	−7.55166	−	23.2416i	−0.271439	−	0.835403i
$775$		0			0
$776$	−5.78115	+	4.20025i	−0.207531	+	0.150780i
$777$	2.69417	−	0.875388i	0.0966527	−	0.0314044i
$778$	−10.1311	−	3.29180i	−0.363218	−	0.118017i
$779$	−26.6074	−	19.3314i	−0.953309	−	0.692619i
$780$		0			0
$781$	−8.85410	−	14.9394i	−0.316825	−	0.534573i
$782$			0.763932i			0.0273182i
$783$	−5.87785	+	8.09017i	−0.210057	+	0.289119i
$784$	0.927051	−	2.85317i	0.0331090	−	0.101899i
$785$		0			0
$786$	−2.10081	+	1.52633i	−0.0749335	+	0.0544424i
$787$	15.4087	+	21.2082i	0.549259	+	0.755991i	0.989911	−	0.141687i	$-0.0452527\pi$
$787$	15.4087	+	21.2082i	0.549259	+	0.755991i	−0.440652	+	0.897678i	$0.645253\pi$
$788$	19.9192	−	6.47214i	0.709592	−	0.230560i
$789$	2.74265	−	8.44100i	0.0976408	−	0.300507i
$790$		0			0
$791$	3.70820			0.131849
$792$	−8.14324	+	4.82624i	−0.289357	+	0.171493i
$793$		−	3.05573i		−	0.108512i
$794$	−13.8541	−	10.0656i	−0.491664	−	0.357215i
$795$		0			0
$796$	−5.85410	−	18.0171i	−0.207493	−	0.638598i
$797$	−14.5559	−	20.0344i	−0.515596	−	0.709656i	0.469255	−	0.883063i	$-0.344523\pi$
$797$	−14.5559	−	20.0344i	−0.515596	−	0.709656i	−0.984850	+	0.173406i	$0.944523\pi$
$798$	−2.62866	−	3.61803i	−0.0930534	−	0.128077i
$799$	−1.23607	−	3.80423i	−0.0437289	−	0.134584i
$800$		0			0
$801$	−18.6803	−	13.5721i	−0.660037	−	0.479545i
$802$			17.7984i			0.628482i
$803$	7.54294	+	33.5967i	0.266185	+	1.18560i
$804$	−4.23607			−0.149395
$805$		0			0
$806$	0.763932	−	2.35114i	0.0269084	−	0.0828154i
$807$	2.24514	−	0.729490i	0.0790327	−	0.0256793i
$808$	2.45714	+	3.38197i	0.0864420	+	0.118977i
$809$	13.6803	−	9.93935i	0.480975	−	0.349449i	−0.320728	−	0.947171i	$-0.603928\pi$
$809$	13.6803	−	9.93935i	0.480975	−	0.349449i	0.801703	+	0.597722i	$0.203928\pi$
$810$		0			0
$811$	2.59017	−	7.97172i	0.0909532	−	0.279925i	−0.895225	−	0.445615i	$-0.852985\pi$
$811$	2.59017	−	7.97172i	0.0909532	−	0.279925i	0.986178	+	0.165690i	$0.0529851\pi$
$812$	5.25731	−	7.23607i	0.184495	−	0.253936i
$813$			0.763932i			0.0267923i
$814$	−11.2918	−	4.87380i	−0.395777	−	0.170826i
$815$		0			0
$816$	0.190983	+	0.138757i	0.00668574	+	0.00485748i
$817$	−47.6713	−	15.4894i	−1.66781	−	0.541904i
$818$	12.7598	−	4.14590i	0.446135	−	0.144958i
$819$	5.70820	−	4.14725i	0.199461	−	0.144917i
$820$		0			0
$821$	9.43769	+	29.0462i	0.329378	+	1.01372i	0.969426	+	0.245386i	$0.0789145\pi$
$821$	9.43769	+	29.0462i	0.329378	+	1.01372i	−0.640048	+	0.768335i	$0.721085\pi$
$822$	−5.84510	−	1.89919i	−0.203871	−	0.0662418i
$823$	13.8698	−	19.0902i	0.483472	−	0.665441i	−0.495696	−	0.868496i	$-0.665087\pi$
$823$	13.8698	−	19.0902i	0.483472	−	0.665441i	0.979167	+	0.203055i	$0.0650869\pi$
$824$	−15.7082			−0.547221
$825$		0			0
$826$	17.2361			0.599720
$827$	−23.1481	+	31.8607i	−0.804940	+	1.10790i	0.187145	+	0.982332i	$0.440077\pi$
$827$	−23.1481	+	31.8607i	−0.804940	+	1.10790i	−0.992085	+	0.125572i	$0.959923\pi$
$828$	−3.35520	−	1.09017i	−0.116601	−	0.0378860i
$829$	−9.59675	−	29.5358i	−0.333309	−	1.02582i	−0.967549	−	0.252683i	$-0.918687\pi$
$829$	−9.59675	−	29.5358i	−0.333309	−	1.02582i	0.634240	−	0.773136i	$-0.281313\pi$
$830$		0			0
$831$	7.32624	−	5.32282i	0.254144	−	0.184647i
$832$	1.17557	−	0.381966i	0.0407556	−	0.0132423i
$833$	1.76336	+	0.572949i	0.0610967	+	0.0198515i
$834$		0			0
$835$		0			0
$836$	−1.80902	+	19.3314i	−0.0625662	+	0.668590i
$837$			4.47214i			0.154580i
$838$	−6.37988	+	8.78115i	−0.220389	+	0.303340i
$839$	−3.74265	+	11.5187i	−0.129210	+	0.397669i	−0.994645	−	0.103354i	$-0.967043\pi$
$839$	−3.74265	+	11.5187i	−0.129210	+	0.397669i	0.865434	+	0.501023i	$0.167043\pi$
$840$		0			0
$841$	7.28115	−	5.29007i	0.251074	−	0.182416i
$842$	−18.4661	−	25.4164i	−0.636384	−	0.875907i
$843$	5.84510	−	1.89919i	0.201316	−	0.0654115i
$844$	1.88197	−	5.79210i	0.0647799	−	0.199372i
$845$		0			0
$846$	18.4721			0.635085
$847$	21.8213	−	2.79837i	0.749789	−	0.0961533i
$848$		−	1.52786i		−	0.0524671i
$849$	7.41641	+	5.38834i	0.254530	+	0.184927i
$850$		0			0
$851$	−1.41641	−	4.35926i	−0.0485538	−	0.149433i
$852$	−1.17557	−	1.61803i	−0.0402744	−	0.0554329i
$853$	17.9111	+	24.6525i	0.613263	+	0.844085i	0.996841	−	0.0794240i	$-0.0253081\pi$
$853$	17.9111	+	24.6525i	0.613263	+	0.844085i	−0.383577	+	0.923509i	$0.625308\pi$
$854$	−1.52786	−	4.70228i	−0.0522824	−	0.160909i
$855$		0			0
$856$	0.927051	+	0.673542i	0.0316860	+	0.0230212i
$857$			10.7426i			0.366962i	0.983023	+	0.183481i	$0.0587365\pi$
$857$			10.7426i			0.366962i	−0.983023	+	0.183481i	$0.941263\pi$
$858$	1.55909	+	0.145898i	0.0532263	+	0.00498088i
$859$	−46.5066			−1.58678			−0.793392	−	0.608711i	$-0.791687\pi$
$859$	−46.5066			−1.58678			−0.793392	+	0.608711i	$0.791687\pi$
$860$		0			0
$861$	−1.32624	+	4.08174i	−0.0451981	+	0.139105i
$862$	−16.1150	+	5.23607i	−0.548878	+	0.178341i
$863$	19.5357	+	26.8885i	0.665002	+	0.915297i	0.999634	−	0.0270522i	$-0.00861203\pi$
$863$	19.5357	+	26.8885i	0.665002	+	0.915297i	−0.334632	+	0.942349i	$0.608612\pi$
$864$	−1.80902	+	1.31433i	−0.0615440	+	0.0447143i
$865$		0			0
$866$	8.57295	−	26.3848i	0.291321	−	0.896593i
$867$	3.73098	−	5.13525i	0.126711	−	0.174402i
$868$		−	4.00000i		−	0.135769i
$869$	29.3951	−	33.4055i	0.997161	−	1.13320i
$870$		0			0
$871$	−11.0902	−	8.05748i	−0.375776	−	0.273017i
$872$	−18.0171	−	5.85410i	−0.610135	−	0.198245i
$873$	19.3969	−	6.30244i	0.656486	−	0.213305i
$874$	−5.85410	+	4.25325i	−0.198018	+	0.143868i
$875$		0			0
$876$	1.22542	+	3.77147i	0.0414033	+	0.127426i
$877$	26.8011	+	8.70820i	0.905009	+	0.294055i	0.724303	−	0.689482i	$-0.242162\pi$
$877$	26.8011	+	8.70820i	0.905009	+	0.294055i	0.180706	+	0.983537i	$0.442162\pi$
$878$	−3.86974	+	5.32624i	−0.130597	+	0.179752i
$879$	10.8328			0.365382
$880$		0			0
$881$	−46.3394			−1.56121			−0.780607	−	0.625022i	$-0.785090\pi$
$881$	−46.3394			−1.56121			−0.780607	+	0.625022i	$0.785090\pi$
$882$	−5.03280	+	6.92705i	−0.169463	+	0.233246i
$883$	−3.26944	−	1.06231i	−0.110025	−	0.0357494i	0.253487	−	0.967339i	$-0.418423\pi$
$883$	−3.26944	−	1.06231i	−0.110025	−	0.0357494i	−0.363512	+	0.931589i	$0.618423\pi$
$884$	0.236068	+	0.726543i	0.00793983	+	0.0244363i
$885$		0			0
$886$	6.92705	−	5.03280i	0.232719	−	0.169080i
$887$	−35.9281	+	11.6738i	−1.20635	+	0.391967i	−0.842093	−	0.539332i	$-0.818677\pi$
$887$	−35.9281	+	11.6738i	−1.20635	+	0.391967i	−0.364256	+	0.931299i	$0.618677\pi$
$888$	−1.34708	−	0.437694i	−0.0452052	−	0.0146881i
$889$	17.7082	+	12.8658i	0.593914	+	0.431504i
$890$		0			0
$891$	24.9443	−	5.60034i	0.835665	−	0.187618i
$892$		−	25.7082i		−	0.860774i
$893$	22.2703	−	30.6525i	0.745248	−	1.02575i
$894$	0.729490	−	2.24514i	0.0243978	−	0.0750887i
$895$		0			0
$896$	1.61803	−	1.17557i	0.0540547	−	0.0392731i
$897$	0.343027	+	0.472136i	0.0114533	+	0.0157642i
$898$	−8.81678	+	2.86475i	−0.294220	+	0.0955978i
$899$	−2.76393	+	8.50651i	−0.0921823	+	0.283708i
$900$		0			0
$901$	0.944272			0.0314583
$902$	16.0292	−	9.50000i	0.533714	−	0.316315i
$903$			6.54102i			0.217672i
$904$	−1.50000	−	1.08981i	−0.0498893	−	0.0362467i
$905$		0			0
$906$	−0.944272	−	2.90617i	−0.0313713	−	0.0965510i
$907$	6.13512	+	8.44427i	0.203713	+	0.280387i	0.898634	−	0.438699i	$-0.144561\pi$
$907$	6.13512	+	8.44427i	0.203713	+	0.280387i	−0.694921	+	0.719086i	$0.744561\pi$
$908$	−8.52675	−	11.7361i	−0.282970	−	0.389475i
$909$	−3.68692	−	11.3472i	−0.122287	−	0.376362i
$910$		0			0
$911$	−14.7082	−	10.6861i	−0.487305	−	0.354047i	0.316842	−	0.948478i	$-0.397377\pi$
$911$	−14.7082	−	10.6861i	−0.487305	−	0.354047i	−0.804147	+	0.594431i	$0.797377\pi$
$912$			2.23607i			0.0740436i
$913$	−26.6093	+	15.7705i	−0.880641	+	0.521928i
$914$	9.43769			0.312171
$915$		0			0
$916$	0.527864	−	1.62460i	0.0174411	−	0.0536782i
$917$	−12.9313	+	4.20163i	−0.427028	+	0.138750i
$918$	−0.812299	−	1.11803i	−0.0268099	−	0.0369006i
$919$	35.1246	−	25.5195i	1.15865	−	0.841811i	0.169047	−	0.985608i	$-0.445931\pi$
$919$	35.1246	−	25.5195i	1.15865	−	0.841811i	0.989607	+	0.143797i	$0.0459311\pi$
$920$		0			0
$921$	3.28115	−	10.0984i	0.108118	−	0.332752i
$922$	−0.792055	+	1.09017i	−0.0260849	+	0.0359028i
$923$		−	6.47214i		−	0.213033i
$924$	2.47214	−	0.555029i	0.0813273	−	0.0182591i
$925$		0			0
$926$	15.7082	+	11.4127i	0.516204	+	0.375044i
$927$	42.6385	+	13.8541i	1.40043	+	0.455028i
$928$	−4.25325	+	1.38197i	−0.139620	+	0.0453653i
$929$	−13.1525	+	9.55583i	−0.431519	+	0.313517i	−0.782256	−	0.622957i	$-0.785931\pi$
$929$	−13.1525	+	9.55583i	−0.431519	+	0.313517i	0.350737	+	0.936474i	$0.385931\pi$
$930$		0			0
$931$	5.42705	+	16.7027i	0.177864	+	0.547410i
$932$	9.14729	+	2.97214i	0.299630	+	0.0973556i
$933$	5.85283	−	8.05573i	0.191613	−	0.263733i
$934$	33.3050			1.08977
$935$		0			0
$936$	−3.52786			−0.115312
$937$	22.2501	−	30.6246i	0.726879	−	1.00046i	−0.272389	−	0.962187i	$-0.587814\pi$
$937$	22.2501	−	30.6246i	0.726879	−	1.00046i	0.999267	−	0.0382752i	$-0.0121863\pi$
$938$	−21.0948	−	6.85410i	−0.688768	−	0.223794i
$939$	−0.510643	−	1.57160i	−0.0166642	−	0.0512872i
$940$		0			0
$941$	−38.9787	+	28.3197i	−1.27067	+	0.923196i	−0.999229	−	0.0392595i	$-0.987500\pi$
$941$	−38.9787	+	28.3197i	−1.27067	+	0.923196i	−0.271441	+	0.962455i	$0.587500\pi$
$942$	3.52671	−	1.14590i	0.114906	−	0.0373354i
$943$	6.60440	+	2.14590i	0.215069	+	0.0698801i
$944$	−6.97214	−	5.06555i	−0.226924	−	0.164870i
$945$		0			0
$946$	18.7599	−	21.3193i	0.609936	−	0.693149i
$947$			30.2148i			0.981848i	0.871202	+	0.490924i	$0.163341\pi$
$947$			30.2148i			0.981848i	−0.871202	+	0.490924i	$0.836659\pi$
$948$	3.01217	−	4.14590i	0.0978308	−	0.134653i
$949$	−3.96556	+	12.2047i	−0.128727	+	0.396182i
$950$		0			0
$951$	1.14590	−	0.832544i	0.0371583	−	0.0269971i
$952$	0.726543	+	1.00000i	0.0235474	+	0.0324102i
$953$	10.7719	−	3.50000i	0.348936	−	0.113376i	−0.129305	−	0.991605i	$-0.541275\pi$
$953$	10.7719	−	3.50000i	0.348936	−	0.113376i	0.478241	+	0.878229i	$0.341275\pi$
$954$	−1.34752	+	4.14725i	−0.0436277	+	0.134272i
$955$		0			0
$956$	−21.7082			−0.702093
$957$	−5.64083	−	0.527864i	−0.182342	−	0.0170634i
$958$		−	34.4721i		−	1.11374i
$959$	−26.0344	−	18.9151i	−0.840696	−	0.610801i
$960$		0			0
$961$	−8.34346	−	25.6785i	−0.269144	−	0.828340i
$962$	−2.69417	−	3.70820i	−0.0868635	−	0.119557i
$963$	−1.92236	−	2.64590i	−0.0619471	−	0.0852629i
$964$	3.42705	+	10.5474i	0.110378	+	0.339708i
$965$		0			0
$966$	0.763932	+	0.555029i	0.0245791	+	0.0178578i
$967$		−	38.0000i		−	1.22200i	−0.791632	−	0.610999i	$-0.790768\pi$
$967$		−	38.0000i		−	1.22200i	0.791632	−	0.610999i	$-0.209232\pi$
$968$	−9.64932	−	5.28115i	−0.310141	−	0.169743i
$969$	−1.38197			−0.0443951
$970$		0			0
$971$	−3.12461	+	9.61657i	−0.100274	+	0.308610i	−0.988592	−	0.150617i	$-0.951874\pi$
$971$	−3.12461	+	9.61657i	−0.100274	+	0.308610i	0.888319	+	0.459228i	$0.151874\pi$
$972$	9.18005	−	2.98278i	0.294450	−	0.0956727i
$973$		0			0
$974$	−1.09017	+	0.792055i	−0.0349313	+	0.0253791i
$975$		0			0
$976$	−0.763932	+	2.35114i	−0.0244529	+	0.0752582i
$977$	25.4540	−	35.0344i	0.814346	−	1.12085i	−0.176292	−	0.984338i	$-0.556410\pi$
$977$	25.4540	−	35.0344i	0.814346	−	1.12085i	0.990638	−	0.136513i	$-0.0435896\pi$
$978$			0.347524i			0.0111126i
$979$	2.50000	−	26.7153i	0.0799003	−	0.853826i
$980$		0			0
$981$	43.7426	+	31.7809i	1.39660	+	1.01469i
$982$	−21.7355	−	7.06231i	−0.693609	−	0.225367i
$983$	5.70634	−	1.85410i	0.182004	−	0.0591367i	−0.216597	−	0.976261i	$-0.569496\pi$
$983$	5.70634	−	1.85410i	0.182004	−	0.0591367i	0.398601	+	0.917124i	$0.369496\pi$
$984$	1.73607	−	1.26133i	0.0553438	−	0.0402096i
$985$		0			0
$986$	−0.854102	−	2.62866i	−0.0272001	−	0.0837134i
$987$	−4.70228	−	1.52786i	−0.149675	−	0.0486324i
$988$	−4.25325	+	5.85410i	−0.135314	+	0.186244i
$989$	10.5836			0.336539
$990$		0			0
$991$	30.5410			0.970167			0.485084	−	0.874468i	$-0.338789\pi$
$991$	30.5410			0.970167			0.485084	+	0.874468i	$0.338789\pi$
$992$	−1.17557	+	1.61803i	−0.0373244	+	0.0513726i
$993$	2.27790	+	0.740133i	0.0722868	+	0.0234874i
$994$	−3.23607	−	9.95959i	−0.102642	−	0.315899i
$995$		0			0
$996$	−2.88197	+	2.09387i	−0.0913186	+	0.0663468i
$997$	8.22899	−	2.67376i	0.260615	−	0.0846789i	−0.175795	−	0.984427i	$-0.556250\pi$
$997$	8.22899	−	2.67376i	0.260615	−	0.0846789i	0.436410	+	0.899748i	$0.356250\pi$
$998$	−29.3440	−	9.53444i	−0.928868	−	0.301807i
$999$	6.70820	+	4.87380i	0.212238	+	0.154200i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.ba.c.499.1		8
5.2	odd	4		22.2.c.a.15.1	yes	4
5.3	odd	4		550.2.h.h.301.1		4
5.4	even	2	inner	550.2.ba.c.499.2		8
11.3	even	5	inner	550.2.ba.c.399.2		8
15.2	even	4		198.2.f.e.37.1		4
20.7	even	4		176.2.m.c.81.1		4
40.27	even	4		704.2.m.a.257.1		4
40.37	odd	4		704.2.m.h.257.1		4
55.2	even	20		242.2.c.d.27.1		4
55.3	odd	20		550.2.h.h.201.1		4
55.7	even	20		242.2.c.d.9.1		4
55.14	even	10	inner	550.2.ba.c.399.1		8
55.17	even	20		242.2.a.d.1.1		2
55.27	odd	20		242.2.a.f.1.1		2
55.28	even	20		6050.2.a.ci.1.2		2
55.32	even	4		242.2.c.c.81.1		4
55.37	odd	20		242.2.c.a.9.1		4
55.38	odd	20		6050.2.a.bs.1.2		2
55.42	odd	20		242.2.c.a.27.1		4
55.47	odd	20		22.2.c.a.3.1	✓	4
55.52	even	20		242.2.c.c.3.1		4
165.17	odd	20		2178.2.a.x.1.1		2
165.47	even	20		198.2.f.e.91.1		4
165.137	even	20		2178.2.a.p.1.1		2
220.27	even	20		1936.2.a.o.1.2		2
220.47	even	20		176.2.m.c.113.1		4
220.127	odd	20		1936.2.a.n.1.2		2
440.27	even	20		7744.2.a.cz.1.1		2
440.157	odd	20		704.2.m.h.641.1		4
440.237	even	20		7744.2.a.bn.1.2		2
440.267	even	20		704.2.m.a.641.1		4
440.347	odd	20		7744.2.a.cy.1.1		2
440.357	odd	20		7744.2.a.bm.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.2.c.a.3.1	✓	4	55.47	odd	20
22.2.c.a.15.1	yes	4	5.2	odd	4
176.2.m.c.81.1		4	20.7	even	4
176.2.m.c.113.1		4	220.47	even	20
198.2.f.e.37.1		4	15.2	even	4
198.2.f.e.91.1		4	165.47	even	20
242.2.a.d.1.1		2	55.17	even	20
242.2.a.f.1.1		2	55.27	odd	20
242.2.c.a.9.1		4	55.37	odd	20
242.2.c.a.27.1		4	55.42	odd	20
242.2.c.c.3.1		4	55.52	even	20
242.2.c.c.81.1		4	55.32	even	4
242.2.c.d.9.1		4	55.7	even	20
242.2.c.d.27.1		4	55.2	even	20
550.2.h.h.201.1		4	55.3	odd	20
550.2.h.h.301.1		4	5.3	odd	4
550.2.ba.c.399.1		8	55.14	even	10	inner
550.2.ba.c.399.2		8	11.3	even	5	inner
550.2.ba.c.499.1		8	1.1	even	1	trivial
550.2.ba.c.499.2		8	5.4	even	2	inner
704.2.m.a.257.1		4	40.27	even	4
704.2.m.a.641.1		4	440.267	even	20
704.2.m.h.257.1		4	40.37	odd	4
704.2.m.h.641.1		4	440.157	odd	20
1936.2.a.n.1.2		2	220.127	odd	20
1936.2.a.o.1.2		2	220.27	even	20
2178.2.a.p.1.1		2	165.137	even	20
2178.2.a.x.1.1		2	165.17	odd	20
6050.2.a.bs.1.2		2	55.38	odd	20
6050.2.a.ci.1.2		2	55.28	even	20
7744.2.a.bm.1.2		2	440.357	odd	20
7744.2.a.bn.1.2		2	440.237	even	20
7744.2.a.cy.1.1		2	440.347	odd	20
7744.2.a.cz.1.1		2	440.27	even	20

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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.ba (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(0.363271 + 0.118034i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.309017 + 0.224514i) q^{6} +(-1.90211 + 0.618034i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-2.30902 - 1.67760i) q^{9} +(0.309017 - 3.30220i) q^{11} -0.381966i q^{12} +(0.726543 - 1.00000i) q^{13} +(0.618034 - 1.90211i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-0.363271 - 0.500000i) q^{17} +(2.71441 - 0.881966i) q^{18} +(1.80902 - 5.56758i) q^{19} -0.763932 q^{21} +(2.48990 + 2.19098i) q^{22} +1.23607i q^{23} +(0.309017 + 0.224514i) q^{24} +(0.381966 + 1.17557i) q^{26} +(-1.31433 - 1.80902i) q^{27} +(1.17557 + 1.61803i) q^{28} +(-1.38197 - 4.25325i) q^{29} +(-1.61803 - 1.17557i) q^{31} -1.00000i q^{32} +(0.502029 - 1.16312i) q^{33} +0.618034 q^{34} +(-0.881966 + 2.71441i) q^{36} +(-3.52671 + 1.14590i) q^{37} +(3.44095 + 4.73607i) q^{38} +(0.381966 - 0.277515i) q^{39} +(1.73607 - 5.34307i) q^{41} +(0.449028 - 0.618034i) q^{42} -8.56231i q^{43} +(-3.23607 + 0.726543i) q^{44} +(-1.00000 - 0.726543i) q^{46} +(6.15537 + 2.00000i) q^{47} +(-0.363271 + 0.118034i) q^{48} +(-2.42705 + 1.76336i) q^{49} +(-0.0729490 - 0.224514i) q^{51} +(-1.17557 - 0.381966i) q^{52} +(-0.898056 + 1.23607i) q^{53} +2.23607 q^{54} -2.00000 q^{56} +(1.31433 - 1.80902i) q^{57} +(4.25325 + 1.38197i) q^{58} +(2.66312 + 8.19624i) q^{59} +(2.00000 - 1.45309i) q^{61} +(1.90211 - 0.618034i) q^{62} +(5.42882 + 1.76393i) q^{63} +(0.809017 + 0.587785i) q^{64} +(0.645898 + 1.08981i) q^{66} -11.0902i q^{67} +(-0.363271 + 0.500000i) q^{68} +(-0.145898 + 0.449028i) q^{69} +(4.23607 - 3.07768i) q^{71} +(-1.67760 - 2.30902i) q^{72} +(-9.87384 + 3.20820i) q^{73} +(1.14590 - 3.52671i) q^{74} -5.85410 q^{76} +(1.45309 + 6.47214i) q^{77} +0.472136i q^{78} +(10.8541 + 7.88597i) q^{79} +(2.38197 + 7.33094i) q^{81} +(3.30220 + 4.54508i) q^{82} +(-5.48183 - 7.54508i) q^{83} +(0.236068 + 0.726543i) q^{84} +(6.92705 + 5.03280i) q^{86} -1.70820i q^{87} +(1.31433 - 3.04508i) q^{88} +8.09017 q^{89} +(-0.763932 + 2.35114i) q^{91} +(1.17557 - 0.381966i) q^{92} +(-0.449028 - 0.618034i) q^{93} +(-5.23607 + 3.80423i) q^{94} +(0.118034 - 0.363271i) q^{96} +(-4.20025 + 5.78115i) q^{97} -3.00000i q^{98} +(-6.25329 + 7.10642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 2 q^{6} - 14 q^{9} - 2 q^{11} - 4 q^{14} - 2 q^{16} + 10 q^{19} - 24 q^{21} - 2 q^{24} + 12 q^{26} - 20 q^{29} - 4 q^{31} - 4 q^{34} - 16 q^{36} + 12 q^{39} - 4 q^{41} - 8 q^{44} - 8 q^{46}+ \cdots + 26 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 + 2 * q^6 - 14 * q^9 - 2 * q^11 - 4 * q^14 - 2 * q^16 + 10 * q^19 - 24 * q^21 - 2 * q^24 + 12 * q^26 - 20 * q^29 - 4 * q^31 - 4 * q^34 - 16 * q^36 + 12 * q^39 - 4 * q^41 - 8 * q^44 - 8 * q^46 - 6 * q^49 - 14 * q^51 - 16 * q^56 - 10 * q^59 + 16 * q^61 + 2 * q^64 + 32 * q^66 - 28 * q^69 + 16 * q^71 + 36 * q^74 - 20 * q^76 + 60 * q^79 + 28 * q^81 - 16 * q^84 + 42 * q^86 + 20 * q^89 - 24 * q^91 - 24 * q^94 - 8 * q^96 + 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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