LMFDB - Embedded newform 558.2.i.b.109.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(109,558)] 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("558.109"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.i (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1,0,-1,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.45565243279$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 186)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			109.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	558.109
Dual form			558.2.i.b.343.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +0.618034 q^{5} +(1.19098 - 3.66547i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.500000 + 0.363271i) q^{10} +(-0.427051 + 1.31433i) q^{11} +(-0.618034 - 0.449028i) q^{13} +(1.19098 + 3.66547i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-1.23607 - 3.80423i) q^{17} +(2.00000 - 1.45309i) q^{19} +(0.190983 - 0.587785i) q^{20} +(-0.427051 - 1.31433i) q^{22} +(-2.61803 - 8.05748i) q^{23} -4.61803 q^{25} +0.763932 q^{26} +(-3.11803 - 2.26538i) q^{28} +(-1.30902 + 0.951057i) q^{29} +(3.30902 + 4.47777i) q^{31} +1.00000 q^{32} +(3.23607 + 2.35114i) q^{34} +(0.736068 - 2.26538i) q^{35} +6.76393 q^{37} +(-0.763932 + 2.35114i) q^{38} +(0.190983 + 0.587785i) q^{40} +(6.47214 - 4.70228i) q^{41} +(5.85410 - 4.25325i) q^{43} +(1.11803 + 0.812299i) q^{44} +(6.85410 + 4.97980i) q^{46} +(-1.23607 - 0.898056i) q^{47} +(-6.35410 - 4.61653i) q^{49} +(3.73607 - 2.71441i) q^{50} +(-0.618034 + 0.449028i) q^{52} +(-0.736068 - 2.26538i) q^{53} +(-0.263932 + 0.812299i) q^{55} +3.85410 q^{56} +(0.500000 - 1.53884i) q^{58} +(6.54508 + 4.75528i) q^{59} -11.2361 q^{61} +(-5.30902 - 1.67760i) q^{62} +(-0.809017 + 0.587785i) q^{64} +(-0.381966 - 0.277515i) q^{65} +10.9443 q^{67} -4.00000 q^{68} +(0.736068 + 2.26538i) q^{70} +(0.618034 + 1.90211i) q^{71} +(-0.736068 + 2.26538i) q^{73} +(-5.47214 + 3.97574i) q^{74} +(-0.763932 - 2.35114i) q^{76} +(4.30902 + 3.13068i) q^{77} +(-3.50000 - 10.7719i) q^{79} +(-0.500000 - 0.363271i) q^{80} +(-2.47214 + 7.60845i) q^{82} +(5.23607 - 3.80423i) q^{83} +(-0.763932 - 2.35114i) q^{85} +(-2.23607 + 6.88191i) q^{86} -1.38197 q^{88} +(-0.909830 + 2.80017i) q^{89} +(-2.38197 + 1.73060i) q^{91} -8.47214 q^{92} +1.52786 q^{94} +(1.23607 - 0.898056i) q^{95} +(-2.14590 + 6.60440i) q^{97} +7.85410 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{4} - 2 q^{5} + 7 q^{7} - q^{8} - 2 q^{10} + 5 q^{11} + 2 q^{13} + 7 q^{14} - q^{16} + 4 q^{17} + 8 q^{19} + 3 q^{20} + 5 q^{22} - 6 q^{23} - 14 q^{25} + 12 q^{26} - 8 q^{28} - 3 q^{29}+ \cdots + 18 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^4 - 2 * q^5 + 7 * q^7 - q^8 - 2 * q^10 + 5 * q^11 + 2 * q^13 + 7 * q^14 - q^16 + 4 * q^17 + 8 * q^19 + 3 * q^20 + 5 * q^22 - 6 * q^23 - 14 * q^25 + 12 * q^26 - 8 * q^28 - 3 * q^29 + 11 * q^31 + 4 * q^32 + 4 * q^34 - 6 * q^35 + 36 * q^37 - 12 * q^38 + 3 * q^40 + 8 * q^41 + 10 * q^43 + 14 * q^46 + 4 * q^47 - 12 * q^49 + 6 * q^50 + 2 * q^52 + 6 * q^53 - 10 * q^55 + 2 * q^56 + 2 * q^58 + 15 * q^59 - 36 * q^61 - 19 * q^62 - q^64 - 6 * q^65 + 8 * q^67 - 16 * q^68 - 6 * q^70 - 2 * q^71 + 6 * q^73 - 4 * q^74 - 12 * q^76 + 15 * q^77 - 14 * q^79 - 2 * q^80 + 8 * q^82 + 12 * q^83 - 12 * q^85 - 10 * q^88 - 26 * q^89 - 14 * q^91 - 16 * q^92 + 24 * q^94 - 4 * q^95 - 22 * q^97 + 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.618034			0.276393			0.138197	−	0.990405i	$-0.455869\pi$
$5$	0.618034			0.276393			0.138197	+	0.990405i	$0.455869\pi$
$6$		0			0
$7$	1.19098	−	3.66547i	0.450149	−	1.38542i	−0.426587	−	0.904446i	$-0.640284\pi$
$7$	1.19098	−	3.66547i	0.450149	−	1.38542i	0.876737	−	0.480971i	$-0.159716\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$		0			0
$10$	−0.500000	+	0.363271i	−0.158114	+	0.114876i
$11$	−0.427051	+	1.31433i	−0.128761	+	0.396285i	−0.994567	−	0.104094i	$-0.966806\pi$
$11$	−0.427051	+	1.31433i	−0.128761	+	0.396285i	0.865807	+	0.500378i	$0.166806\pi$
$12$		0			0
$13$	−0.618034	−	0.449028i	−0.171412	−	0.124538i	0.498772	−	0.866733i	$-0.333785\pi$
$13$	−0.618034	−	0.449028i	−0.171412	−	0.124538i	−0.670184	+	0.742195i	$0.733785\pi$
$14$	1.19098	+	3.66547i	0.318304	+	0.979638i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.23607	−	3.80423i	−0.299791	−	0.922660i	−0.981570	−	0.191103i	$-0.938794\pi$
$17$	−1.23607	−	3.80423i	−0.299791	−	0.922660i	0.681780	−	0.731558i	$-0.261206\pi$
$18$		0			0
$19$	2.00000	−	1.45309i	0.458831	−	0.333361i	−0.334241	−	0.942488i	$-0.608480\pi$
$19$	2.00000	−	1.45309i	0.458831	−	0.333361i	0.793073	+	0.609127i	$0.208480\pi$
$20$	0.190983	−	0.587785i	0.0427051	−	0.131433i
$21$		0			0
$22$	−0.427051	−	1.31433i	−0.0910476	−	0.280216i
$23$	−2.61803	−	8.05748i	−0.545898	−	1.68010i	−0.718846	−	0.695170i	$-0.755329\pi$
$23$	−2.61803	−	8.05748i	−0.545898	−	1.68010i	0.172948	−	0.984931i	$-0.444671\pi$
$24$		0			0
$25$	−4.61803			−0.923607
$26$	0.763932			0.149819
$27$		0			0
$28$	−3.11803	−	2.26538i	−0.589253	−	0.428117i
$29$	−1.30902	+	0.951057i	−0.243078	+	0.176607i	−0.702654	−	0.711532i	$-0.748002\pi$
$29$	−1.30902	+	0.951057i	−0.243078	+	0.176607i	0.459575	+	0.888139i	$0.348002\pi$
$30$		0			0
$31$	3.30902	+	4.47777i	0.594317	+	0.804231i
$31$	3.30902	+	4.47777i	0.594317	+	0.804231i
$32$	1.00000			0.176777
$33$		0			0
$34$	3.23607	+	2.35114i	0.554981	+	0.403217i
$35$	0.736068	−	2.26538i	0.124418	−	0.382920i
$36$		0			0
$37$	6.76393			1.11198			0.555992	−	0.831188i	$-0.312339\pi$
$37$	6.76393			1.11198			0.555992	+	0.831188i	$0.312339\pi$
$38$	−0.763932	+	2.35114i	−0.123926	+	0.381405i
$39$		0			0
$40$	0.190983	+	0.587785i	0.0301971	+	0.0929370i
$41$	6.47214	−	4.70228i	1.01078	−	0.734373i	0.0464057	−	0.998923i	$-0.485223\pi$
$41$	6.47214	−	4.70228i	1.01078	−	0.734373i	0.964372	+	0.264550i	$0.0852233\pi$
$42$		0			0
$43$	5.85410	−	4.25325i	0.892742	−	0.648615i	−0.0438494	−	0.999038i	$-0.513962\pi$
$43$	5.85410	−	4.25325i	0.892742	−	0.648615i	0.936592	+	0.350423i	$0.113962\pi$
$44$	1.11803	+	0.812299i	0.168550	+	0.122459i
$45$		0			0
$46$	6.85410	+	4.97980i	1.01058	+	0.734231i
$47$	−1.23607	−	0.898056i	−0.180299	−	0.130995i	0.493975	−	0.869476i	$-0.335543\pi$
$47$	−1.23607	−	0.898056i	−0.180299	−	0.130995i	−0.674274	+	0.738481i	$0.735543\pi$
$48$		0			0
$49$	−6.35410	−	4.61653i	−0.907729	−	0.659504i
$50$	3.73607	−	2.71441i	0.528360	−	0.383876i
$51$		0			0
$52$	−0.618034	+	0.449028i	−0.0857059	+	0.0622690i
$53$	−0.736068	−	2.26538i	−0.101107	−	0.311174i	0.887690	−	0.460441i	$-0.152309\pi$
$53$	−0.736068	−	2.26538i	−0.101107	−	0.311174i	−0.988797	+	0.149267i	$0.952309\pi$
$54$		0			0
$55$	−0.263932	+	0.812299i	−0.0355886	+	0.109530i
$56$	3.85410			0.515026
$57$		0			0
$58$	0.500000	−	1.53884i	0.0656532	−	0.202060i
$59$	6.54508	+	4.75528i	0.852097	+	0.619085i	0.925724	−	0.378201i	$-0.123457\pi$
$59$	6.54508	+	4.75528i	0.852097	+	0.619085i	−0.0736261	+	0.997286i	$0.523457\pi$
$60$		0			0
$61$	−11.2361			−1.43863			−0.719316	−	0.694683i	$-0.755544\pi$
$61$	−11.2361			−1.43863			−0.719316	+	0.694683i	$0.755544\pi$
$62$	−5.30902	−	1.67760i	−0.674246	−	0.213055i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−0.381966	−	0.277515i	−0.0473771	−	0.0344214i
$66$		0			0
$67$	10.9443			1.33706			0.668528	−	0.743687i	$-0.266925\pi$
$67$	10.9443			1.33706			0.668528	+	0.743687i	$0.266925\pi$
$68$	−4.00000			−0.485071
$69$		0			0
$70$	0.736068	+	2.26538i	0.0879770	+	0.270765i
$71$	0.618034	+	1.90211i	0.0733471	+	0.225739i	0.981009	−	0.193963i	$-0.0621343\pi$
$71$	0.618034	+	1.90211i	0.0733471	+	0.225739i	−0.907662	+	0.419703i	$0.862134\pi$
$72$		0			0
$73$	−0.736068	+	2.26538i	−0.0861502	+	0.265143i	−0.984846	−	0.173428i	$-0.944515\pi$
$73$	−0.736068	+	2.26538i	−0.0861502	+	0.265143i	0.898696	+	0.438572i	$0.144515\pi$
$74$	−5.47214	+	3.97574i	−0.636123	+	0.462170i
$75$		0			0
$76$	−0.763932	−	2.35114i	−0.0876290	−	0.269694i
$77$	4.30902	+	3.13068i	0.491058	+	0.356775i
$78$		0			0
$79$	−3.50000	−	10.7719i	−0.393781	−	1.21193i	−0.929907	−	0.367795i	$-0.880113\pi$
$79$	−3.50000	−	10.7719i	−0.393781	−	1.21193i	0.536126	−	0.844138i	$-0.319887\pi$
$80$	−0.500000	−	0.363271i	−0.0559017	−	0.0406150i
$81$		0			0
$82$	−2.47214	+	7.60845i	−0.273002	+	0.840213i
$83$	5.23607	−	3.80423i	0.574733	−	0.417568i	−0.262088	−	0.965044i	$-0.584411\pi$
$83$	5.23607	−	3.80423i	0.574733	−	0.417568i	0.836822	+	0.547476i	$0.184411\pi$
$84$		0			0
$85$	−0.763932	−	2.35114i	−0.0828601	−	0.255017i
$86$	−2.23607	+	6.88191i	−0.241121	+	0.742095i
$87$		0			0
$88$	−1.38197			−0.147318
$89$	−0.909830	+	2.80017i	−0.0964418	+	0.296817i	−0.987627	−	0.156823i	$-0.949875\pi$
$89$	−0.909830	+	2.80017i	−0.0964418	+	0.296817i	0.891185	+	0.453640i	$0.149875\pi$
$90$		0			0
$91$	−2.38197	+	1.73060i	−0.249698	+	0.181416i
$92$	−8.47214			−0.883281
$93$		0			0
$94$	1.52786			0.157587
$95$	1.23607	−	0.898056i	0.126818	−	0.0921386i
$96$		0			0
$97$	−2.14590	+	6.60440i	−0.217883	+	0.670575i	0.781053	+	0.624464i	$0.214683\pi$
$97$	−2.14590	+	6.60440i	−0.217883	+	0.670575i	−0.998936	+	0.0461105i	$0.985317\pi$
$98$	7.85410			0.793384
$99$		0			0
$100$	−1.42705	+	4.39201i	−0.142705	+	0.439201i
$101$	−3.13525	−	9.64932i	−0.311970	−	0.960143i	−0.976984	−	0.213313i	$-0.931575\pi$
$101$	−3.13525	−	9.64932i	−0.311970	−	0.960143i	0.665014	−	0.746831i	$-0.268425\pi$
$102$		0			0
$103$	−7.23607	+	5.25731i	−0.712991	+	0.518018i	−0.884137	−	0.467227i	$-0.845253\pi$
$103$	−7.23607	+	5.25731i	−0.712991	+	0.518018i	0.171146	+	0.985246i	$0.445253\pi$
$104$	0.236068	−	0.726543i	0.0231484	−	0.0712434i
$105$		0			0
$106$	1.92705	+	1.40008i	0.187172	+	0.135988i
$107$	6.04508	+	18.6049i	0.584400	+	1.79860i	0.601665	+	0.798749i	$0.294504\pi$
$107$	6.04508	+	18.6049i	0.584400	+	1.79860i	−0.0172645	+	0.999851i	$0.505496\pi$
$108$		0			0
$109$	−3.23607	−	2.35114i	−0.309959	−	0.225198i	0.421920	−	0.906633i	$-0.361356\pi$
$109$	−3.23607	−	2.35114i	−0.309959	−	0.225198i	−0.731879	+	0.681435i	$0.761356\pi$
$110$	−0.263932	−	0.812299i	−0.0251649	−	0.0774497i
$111$		0			0
$112$	−3.11803	+	2.26538i	−0.294627	+	0.214059i
$113$	−3.76393	+	11.5842i	−0.354081	+	1.08975i	0.602460	+	0.798149i	$0.294187\pi$
$113$	−3.76393	+	11.5842i	−0.354081	+	1.08975i	−0.956540	+	0.291600i	$0.905813\pi$
$114$		0			0
$115$	−1.61803	−	4.97980i	−0.150882	−	0.464368i
$116$	0.500000	+	1.53884i	0.0464238	+	0.142878i
$117$		0			0
$118$	−8.09017			−0.744761
$119$	−15.4164			−1.41322
$120$		0			0
$121$	7.35410	+	5.34307i	0.668555	+	0.485733i
$122$	9.09017	−	6.60440i	0.822985	−	0.597934i
$123$		0			0
$124$	5.28115	−	1.76336i	0.474262	−	0.158354i
$125$	−5.94427			−0.531672
$126$		0			0
$127$	6.39919	+	4.64928i	0.567836	+	0.412557i	0.834318	−	0.551283i	$-0.185861\pi$
$127$	6.39919	+	4.64928i	0.567836	+	0.412557i	−0.266482	+	0.963840i	$0.585861\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$		0			0
$130$	0.472136			0.0414091
$131$	−5.26393	+	16.2007i	−0.459912	+	1.41546i	0.405359	+	0.914158i	$0.367147\pi$
$131$	−5.26393	+	16.2007i	−0.459912	+	1.41546i	−0.865270	+	0.501305i	$0.832853\pi$
$132$		0			0
$133$	−2.94427	−	9.06154i	−0.255301	−	0.785735i
$134$	−8.85410	+	6.43288i	−0.764878	+	0.555716i
$135$		0			0
$136$	3.23607	−	2.35114i	0.277491	−	0.201609i
$137$	−13.7082	−	9.95959i	−1.17117	−	0.850905i	−0.180022	−	0.983663i	$-0.557617\pi$
$137$	−13.7082	−	9.95959i	−1.17117	−	0.850905i	−0.991149	+	0.132757i	$0.957617\pi$
$138$		0			0
$139$	−3.85410	−	2.80017i	−0.326901	−	0.237507i	0.412214	−	0.911087i	$-0.364756\pi$
$139$	−3.85410	−	2.80017i	−0.326901	−	0.237507i	−0.739114	+	0.673580i	$0.764756\pi$
$140$	−1.92705	−	1.40008i	−0.162866	−	0.118329i
$141$		0			0
$142$	−1.61803	−	1.17557i	−0.135782	−	0.0986517i
$143$	0.854102	−	0.620541i	0.0714236	−	0.0518923i
$144$		0			0
$145$	−0.809017	+	0.587785i	−0.0671852	+	0.0488129i
$146$	−0.736068	−	2.26538i	−0.0609174	−	0.187485i
$147$		0			0
$148$	2.09017	−	6.43288i	0.171811	−	0.528780i
$149$	15.3262			1.25557			0.627787	−	0.778385i	$-0.283961\pi$
$149$	15.3262			1.25557			0.627787	+	0.778385i	$0.283961\pi$
$150$		0			0
$151$	−7.28115	+	22.4091i	−0.592532	+	1.82363i	−0.0258846	+	0.999665i	$0.508240\pi$
$151$	−7.28115	+	22.4091i	−0.592532	+	1.82363i	−0.566647	+	0.823961i	$0.691760\pi$
$152$	2.00000	+	1.45309i	0.162221	+	0.117861i
$153$		0			0
$154$	−5.32624			−0.429200
$155$	2.04508	+	2.76741i	0.164265	+	0.222284i
$156$		0			0
$157$	−18.7984	+	13.6578i	−1.50027	+	1.09001i	−0.530001	+	0.847997i	$0.677809\pi$
$157$	−18.7984	+	13.6578i	−1.50027	+	1.09001i	−0.970272	+	0.242016i	$0.922191\pi$
$158$	9.16312	+	6.65740i	0.728979	+	0.529634i
$159$		0			0
$160$	0.618034			0.0488599
$161$	−32.6525			−2.57338
$162$		0			0
$163$	3.56231	+	10.9637i	0.279021	+	0.858739i	0.988127	+	0.153637i	$0.0490988\pi$
$163$	3.56231	+	10.9637i	0.279021	+	0.858739i	−0.709106	+	0.705102i	$0.750901\pi$
$164$	−2.47214	−	7.60845i	−0.193041	−	0.594120i
$165$		0			0
$166$	−2.00000	+	6.15537i	−0.155230	+	0.477749i
$167$	16.1803	−	11.7557i	1.25207	−	0.909684i	0.253732	−	0.967275i	$-0.418342\pi$
$167$	16.1803	−	11.7557i	1.25207	−	0.909684i	0.998340	+	0.0575908i	$0.0183419\pi$
$168$		0			0
$169$	−3.83688	−	11.8087i	−0.295145	−	0.908362i
$170$	2.00000	+	1.45309i	0.153393	+	0.111447i
$171$		0			0
$172$	−2.23607	−	6.88191i	−0.170499	−	0.524741i
$173$	−6.69098	−	4.86128i	−0.508706	−	0.369597i	0.303626	−	0.952791i	$-0.401803\pi$
$173$	−6.69098	−	4.86128i	−0.508706	−	0.369597i	−0.812332	+	0.583195i	$0.801803\pi$
$174$		0			0
$175$	−5.50000	+	16.9273i	−0.415761	+	1.27958i
$176$	1.11803	−	0.812299i	0.0842750	−	0.0612294i
$177$		0			0
$178$	−0.909830	−	2.80017i	−0.0681946	−	0.209882i
$179$	1.79180	−	5.51458i	0.133925	−	0.412179i	−0.861496	−	0.507764i	$-0.830472\pi$
$179$	1.79180	−	5.51458i	0.133925	−	0.412179i	0.995421	+	0.0955849i	$0.0304722\pi$
$180$		0			0
$181$	6.94427			0.516164			0.258082	−	0.966123i	$-0.416910\pi$
$181$	6.94427			0.516164			0.258082	+	0.966123i	$0.416910\pi$
$182$	0.909830	−	2.80017i	0.0674411	−	0.207562i
$183$		0			0
$184$	6.85410	−	4.97980i	0.505291	−	0.367115i
$185$	4.18034			0.307345
$186$		0			0
$187$	5.52786			0.404237
$188$	−1.23607	+	0.898056i	−0.0901495	+	0.0654975i
$189$		0			0
$190$	−0.472136	+	1.45309i	−0.0342523	+	0.105418i
$191$	−8.29180			−0.599973			−0.299987	−	0.953943i	$-0.596982\pi$
$191$	−8.29180			−0.599973			−0.299987	+	0.953943i	$0.596982\pi$
$192$		0			0
$193$	−2.44427	+	7.52270i	−0.175943	+	0.541495i	−0.999675	−	0.0254829i	$-0.991888\pi$
$193$	−2.44427	+	7.52270i	−0.175943	+	0.541495i	0.823733	+	0.566978i	$0.191888\pi$
$194$	−2.14590	−	6.60440i	−0.154067	−	0.474168i
$195$		0			0
$196$	−6.35410	+	4.61653i	−0.453864	+	0.329752i
$197$	5.51722	−	16.9803i	0.393086	−	1.20979i	−0.537357	−	0.843355i	$-0.680577\pi$
$197$	5.51722	−	16.9803i	0.393086	−	1.20979i	0.930442	−	0.366438i	$-0.119423\pi$
$198$		0			0
$199$	3.30902	+	2.40414i	0.234570	+	0.170425i	0.698861	−	0.715258i	$-0.253691\pi$
$199$	3.30902	+	2.40414i	0.234570	+	0.170425i	−0.464291	+	0.885683i	$0.653691\pi$
$200$	−1.42705	−	4.39201i	−0.100908	−	0.310562i
$201$		0			0
$202$	8.20820	+	5.96361i	0.577527	+	0.419598i
$203$	1.92705	+	5.93085i	0.135252	+	0.416264i
$204$		0			0
$205$	4.00000	−	2.90617i	0.279372	−	0.202976i
$206$	2.76393	−	8.50651i	0.192572	−	0.592677i
$207$		0			0
$208$	0.236068	+	0.726543i	0.0163684	+	0.0503767i
$209$	1.05573	+	3.24920i	0.0730262	+	0.224752i
$210$		0			0
$211$	−11.7082			−0.806026			−0.403013	−	0.915194i	$-0.632037\pi$
$211$	−11.7082			−0.806026			−0.403013	+	0.915194i	$0.632037\pi$
$212$	−2.38197			−0.163594
$213$		0			0
$214$	−15.8262	−	11.4984i	−1.08186	−	0.786017i
$215$	3.61803	−	2.62866i	0.246748	−	0.179273i
$216$		0			0
$217$	20.3541	−	6.79615i	1.38173	−	0.461353i
$218$	4.00000			0.270914
$219$		0			0
$220$	0.690983	+	0.502029i	0.0465861	+	0.0338468i
$221$	−0.944272	+	2.90617i	−0.0635186	+	0.195490i
$222$		0			0
$223$	28.2148			1.88940			0.944701	−	0.327934i	$-0.106352\pi$
$223$	28.2148			1.88940			0.944701	+	0.327934i	$0.106352\pi$
$224$	1.19098	−	3.66547i	0.0795759	−	0.244909i
$225$		0			0
$226$	−3.76393	−	11.5842i	−0.250373	−	0.770569i
$227$	9.11803	−	6.62464i	0.605185	−	0.439693i	−0.242530	−	0.970144i	$-0.577977\pi$
$227$	9.11803	−	6.62464i	0.605185	−	0.439693i	0.847716	+	0.530451i	$0.177977\pi$
$228$		0			0
$229$	12.4721	−	9.06154i	0.824182	−	0.598803i	−0.0937254	−	0.995598i	$-0.529878\pi$
$229$	12.4721	−	9.06154i	0.824182	−	0.598803i	0.917907	+	0.396795i	$0.129878\pi$
$230$	4.23607	+	3.07768i	0.279318	+	0.202936i
$231$		0			0
$232$	−1.30902	−	0.951057i	−0.0859412	−	0.0624399i
$233$	18.0902	+	13.1433i	1.18513	+	0.861045i	0.992741	−	0.120275i	$-0.0383775\pi$
$233$	18.0902	+	13.1433i	1.18513	+	0.861045i	0.192386	+	0.981319i	$0.438378\pi$
$234$		0			0
$235$	−0.763932	−	0.555029i	−0.0498334	−	0.0362061i
$236$	6.54508	−	4.75528i	0.426049	−	0.309543i
$237$		0			0
$238$	12.4721	−	9.06154i	0.808448	−	0.587372i
$239$	7.61803	+	23.4459i	0.492770	+	1.51659i	0.820404	+	0.571784i	$0.193749\pi$
$239$	7.61803	+	23.4459i	0.492770	+	1.51659i	−0.327634	+	0.944805i	$0.606251\pi$
$240$		0			0
$241$	−5.80902	+	17.8783i	−0.374192	+	1.15164i	0.569831	+	0.821762i	$0.307009\pi$
$241$	−5.80902	+	17.8783i	−0.374192	+	1.15164i	−0.944022	+	0.329881i	$0.892991\pi$
$242$	−9.09017			−0.584338
$243$		0			0
$244$	−3.47214	+	10.6861i	−0.222281	+	0.684110i
$245$	−3.92705	−	2.85317i	−0.250890	−	0.182282i
$246$		0			0
$247$	−1.88854			−0.120165
$248$	−3.23607	+	4.53077i	−0.205491	+	0.287704i
$249$		0			0
$250$	4.80902	−	3.49396i	0.304149	−	0.220977i
$251$	17.2984	+	12.5680i	1.09186	+	0.793285i	0.979713	−	0.200406i	$-0.0642261\pi$
$251$	17.2984	+	12.5680i	1.09186	+	0.793285i	0.112151	+	0.993691i	$0.464226\pi$
$252$		0			0
$253$	11.7082			0.736088
$254$	−7.90983			−0.496307
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−0.562306	−	1.73060i	−0.0350757	−	0.107952i	0.931986	−	0.362495i	$-0.118075\pi$
$257$	−0.562306	−	1.73060i	−0.0350757	−	0.107952i	−0.967061	+	0.254543i	$0.918075\pi$
$258$		0			0
$259$	8.05573	−	24.7930i	0.500559	−	1.54056i
$260$	−0.381966	+	0.277515i	−0.0236885	+	0.0172107i
$261$		0			0
$262$	−5.26393	−	16.2007i	−0.325207	−	1.00088i
$263$	4.70820	+	3.42071i	0.290320	+	0.210930i	0.723406	−	0.690423i	$-0.242575\pi$
$263$	4.70820	+	3.42071i	0.290320	+	0.210930i	−0.433086	+	0.901353i	$0.642575\pi$
$264$		0			0
$265$	−0.454915	−	1.40008i	−0.0279452	−	0.0860065i
$266$	7.70820	+	5.60034i	0.472620	+	0.343379i
$267$		0			0
$268$	3.38197	−	10.4086i	0.206586	−	0.635808i
$269$	−5.20820	+	3.78398i	−0.317550	+	0.230713i	−0.735129	−	0.677927i	$-0.762879\pi$
$269$	−5.20820	+	3.78398i	−0.317550	+	0.230713i	0.417579	+	0.908640i	$0.362879\pi$
$270$		0			0
$271$	−6.13525	−	18.8824i	−0.372690	−	1.14702i	−0.945024	−	0.327002i	$-0.893962\pi$
$271$	−6.13525	−	18.8824i	−0.372690	−	1.14702i	0.572334	−	0.820021i	$-0.306038\pi$
$272$	−1.23607	+	3.80423i	−0.0749476	+	0.230665i
$273$		0			0
$274$	16.9443			1.02364
$275$	1.97214	−	6.06961i	0.118924	−	0.366011i
$276$		0			0
$277$	−11.4721	+	8.33499i	−0.689294	+	0.500801i	−0.876428	−	0.481533i	$-0.840080\pi$
$277$	−11.4721	+	8.33499i	−0.689294	+	0.500801i	0.187134	+	0.982334i	$0.440080\pi$
$278$	4.76393			0.285722
$279$		0			0
$280$	2.38197			0.142350
$281$	−14.4721	+	10.5146i	−0.863335	+	0.627250i	−0.928790	−	0.370606i	$-0.879150\pi$
$281$	−14.4721	+	10.5146i	−0.863335	+	0.627250i	0.0654550	+	0.997856i	$0.479150\pi$
$282$		0			0
$283$	10.0000	−	30.7768i	0.594438	−	1.82949i	0.0369359	−	0.999318i	$-0.488240\pi$
$283$	10.0000	−	30.7768i	0.594438	−	1.82949i	0.557502	−	0.830175i	$-0.311760\pi$
$284$	2.00000			0.118678
$285$		0			0
$286$	−0.326238	+	1.00406i	−0.0192909	+	0.0593711i
$287$	−9.52786	−	29.3238i	−0.562412	−	1.73093i
$288$		0			0
$289$	0.809017	−	0.587785i	0.0475892	−	0.0345756i
$290$	0.309017	−	0.951057i	0.0181461	−	0.0558480i
$291$		0			0
$292$	1.92705	+	1.40008i	0.112772	+	0.0819337i
$293$	0.145898	+	0.449028i	0.00852345	+	0.0262325i	0.955228	−	0.295871i	$-0.0956100\pi$
$293$	0.145898	+	0.449028i	0.00852345	+	0.0262325i	−0.946704	+	0.322104i	$0.895610\pi$
$294$		0			0
$295$	4.04508	+	2.93893i	0.235514	+	0.171111i
$296$	2.09017	+	6.43288i	0.121489	+	0.373904i
$297$		0			0
$298$	−12.3992	+	9.00854i	−0.718266	+	0.521851i
$299$	−2.00000	+	6.15537i	−0.115663	+	0.355974i
$300$		0			0
$301$	−8.61803	−	26.5236i	−0.496735	−	1.52879i
$302$	−7.28115	−	22.4091i	−0.418983	−	1.28950i
$303$		0			0
$304$	−2.47214			−0.141787
$305$	−6.94427			−0.397628
$306$		0			0
$307$	−0.381966	−	0.277515i	−0.0218000	−	0.0158386i	0.576832	−	0.816863i	$-0.304289\pi$
$307$	−0.381966	−	0.277515i	−0.0218000	−	0.0158386i	−0.598632	+	0.801024i	$0.704289\pi$
$308$	4.30902	−	3.13068i	0.245529	−	0.178387i
$309$		0			0
$310$	−3.28115	−	1.03681i	−0.186357	−	0.0588870i
$311$	29.1246			1.65151			0.825753	−	0.564032i	$-0.190751\pi$
$311$	29.1246			1.65151			0.825753	+	0.564032i	$0.190751\pi$
$312$		0			0
$313$	−4.38197	−	3.18368i	−0.247683	−	0.179952i	0.457016	−	0.889458i	$-0.348918\pi$
$313$	−4.38197	−	3.18368i	−0.247683	−	0.179952i	−0.704699	+	0.709506i	$0.748918\pi$
$314$	7.18034	−	22.0988i	0.405210	−	1.24711i
$315$		0			0
$316$	−11.3262			−0.637151
$317$	−7.56231	+	23.2744i	−0.424741	+	1.30722i	0.478500	+	0.878087i	$0.341181\pi$
$317$	−7.56231	+	23.2744i	−0.424741	+	1.30722i	−0.903242	+	0.429132i	$0.858819\pi$
$318$		0			0
$319$	−0.690983	−	2.12663i	−0.0386876	−	0.119068i
$320$	−0.500000	+	0.363271i	−0.0279508	+	0.0203075i
$321$		0			0
$322$	26.4164	−	19.1926i	1.47213	−	1.06956i
$323$	−8.00000	−	5.81234i	−0.445132	−	0.323407i
$324$		0			0
$325$	2.85410	+	2.07363i	0.158317	+	0.115024i
$326$	−9.32624	−	6.77591i	−0.516533	−	0.375283i
$327$		0			0
$328$	6.47214	+	4.70228i	0.357364	+	0.259640i
$329$	−4.76393	+	3.46120i	−0.262644	+	0.190822i
$330$		0			0
$331$	−21.7082	+	15.7719i	−1.19319	+	0.866904i	−0.993598	−	0.112975i	$-0.963962\pi$
$331$	−21.7082	+	15.7719i	−1.19319	+	0.866904i	−0.199593	+	0.979879i	$0.563962\pi$
$332$	−2.00000	−	6.15537i	−0.109764	−	0.337820i
$333$		0			0
$334$	−6.18034	+	19.0211i	−0.338173	+	1.04079i
$335$	6.76393			0.369553
$336$		0			0
$337$	7.85410	−	24.1724i	0.427840	−	1.31676i	−0.472408	−	0.881380i	$-0.656615\pi$
$337$	7.85410	−	24.1724i	0.427840	−	1.31676i	0.900248	−	0.435377i	$-0.143385\pi$
$338$	10.0451	+	7.29818i	0.546381	+	0.396969i
$339$		0			0
$340$	−2.47214			−0.134070
$341$	−7.29837	+	2.43690i	−0.395229	+	0.131965i
$342$		0			0
$343$	−2.66312	+	1.93487i	−0.143795	+	0.104473i
$344$	5.85410	+	4.25325i	0.315632	+	0.229320i
$345$		0			0
$346$	8.27051			0.444625
$347$	15.5623			0.835428			0.417714	−	0.908578i	$-0.362831\pi$
$347$	15.5623			0.835428			0.417714	+	0.908578i	$0.362831\pi$
$348$		0			0
$349$	5.38197	+	16.5640i	0.288090	+	0.886650i	0.985455	+	0.169934i	$0.0543555\pi$
$349$	5.38197	+	16.5640i	0.288090	+	0.886650i	−0.697365	+	0.716716i	$0.745644\pi$
$350$	−5.50000	−	16.9273i	−0.293987	−	0.904800i
$351$		0			0
$352$	−0.427051	+	1.31433i	−0.0227619	+	0.0700539i
$353$	−1.23607	+	0.898056i	−0.0657893	+	0.0477987i	−0.620194	−	0.784449i	$-0.712946\pi$
$353$	−1.23607	+	0.898056i	−0.0657893	+	0.0477987i	0.554405	+	0.832247i	$0.312946\pi$
$354$		0			0
$355$	0.381966	+	1.17557i	0.0202727	+	0.0623928i
$356$	2.38197	+	1.73060i	0.126244	+	0.0917216i
$357$		0			0
$358$	1.79180	+	5.51458i	0.0946994	+	0.291455i
$359$	11.4721	+	8.33499i	0.605476	+	0.439904i	0.847818	−	0.530287i	$-0.177916\pi$
$359$	11.4721	+	8.33499i	0.605476	+	0.439904i	−0.242342	+	0.970191i	$0.577916\pi$
$360$		0			0
$361$	−3.98278	+	12.2577i	−0.209620	+	0.645144i
$362$	−5.61803	+	4.08174i	−0.295277	+	0.214532i
$363$		0			0
$364$	0.909830	+	2.80017i	0.0476881	+	0.146769i
$365$	−0.454915	+	1.40008i	−0.0238113	+	0.0732838i
$366$		0			0
$367$	−6.20163			−0.323722			−0.161861	−	0.986814i	$-0.551750\pi$
$367$	−6.20163			−0.323722			−0.161861	+	0.986814i	$0.551750\pi$
$368$	−2.61803	+	8.05748i	−0.136474	+	0.420025i
$369$		0			0
$370$	−3.38197	+	2.45714i	−0.175820	+	0.127741i
$371$	−9.18034			−0.476619
$372$		0			0
$373$	26.9443			1.39512			0.697561	−	0.716526i	$-0.254269\pi$
$373$	26.9443			1.39512			0.697561	+	0.716526i	$0.254269\pi$
$374$	−4.47214	+	3.24920i	−0.231249	+	0.168012i
$375$		0			0
$376$	0.472136	−	1.45309i	0.0243486	−	0.0749371i
$377$	1.23607			0.0636607
$378$		0			0
$379$	5.47214	−	16.8415i	0.281085	−	0.865090i	−0.706460	−	0.707753i	$-0.749709\pi$
$379$	5.47214	−	16.8415i	0.281085	−	0.865090i	0.987545	−	0.157337i	$-0.0502909\pi$
$380$	−0.472136	−	1.45309i	−0.0242201	−	0.0745417i
$381$		0			0
$382$	6.70820	−	4.87380i	0.343222	−	0.249365i
$383$	7.23607	−	22.2703i	0.369746	−	1.13796i	−0.577210	−	0.816596i	$-0.695858\pi$
$383$	7.23607	−	22.2703i	0.369746	−	1.13796i	0.946956	−	0.321365i	$-0.104142\pi$
$384$		0			0
$385$	2.66312	+	1.93487i	0.135725	+	0.0986101i
$386$	−2.44427	−	7.52270i	−0.124410	−	0.382895i
$387$		0			0
$388$	5.61803	+	4.08174i	0.285212	+	0.207219i
$389$	−10.2082	−	31.4176i	−0.517576	−	1.59294i	−0.778545	−	0.627589i	$-0.784042\pi$
$389$	−10.2082	−	31.4176i	−0.517576	−	1.59294i	0.260968	−	0.965347i	$-0.415958\pi$
$390$		0			0
$391$	−27.4164	+	19.9192i	−1.38651	+	1.00736i
$392$	2.42705	−	7.46969i	0.122585	−	0.377277i
$393$		0			0
$394$	5.51722	+	16.9803i	0.277954	+	0.855453i
$395$	−2.16312	−	6.65740i	−0.108838	−	0.334970i
$396$		0			0
$397$	−11.5967			−0.582024			−0.291012	−	0.956719i	$-0.593992\pi$
$397$	−11.5967			−0.582024			−0.291012	+	0.956719i	$0.593992\pi$
$398$	−4.09017			−0.205022
$399$		0			0
$400$	3.73607	+	2.71441i	0.186803	+	0.135721i
$401$	−20.0902	+	14.5964i	−1.00326	+	0.728908i	−0.962784	−	0.270273i	$-0.912886\pi$
$401$	−20.0902	+	14.5964i	−1.00326	+	0.728908i	−0.0404715	+	0.999181i	$0.512886\pi$
$402$		0			0
$403$	−0.0344419	−	4.25325i	−0.00171567	−	0.211870i
$404$	−10.1459			−0.504777
$405$		0			0
$406$	−5.04508	−	3.66547i	−0.250383	−	0.181914i
$407$	−2.88854	+	8.89002i	−0.143180	+	0.440662i
$408$		0			0
$409$	−37.0344			−1.83124			−0.915618	−	0.402050i	$-0.868298\pi$
$409$	−37.0344			−1.83124			−0.915618	+	0.402050i	$0.868298\pi$
$410$	−1.52786	+	4.70228i	−0.0754558	+	0.232229i
$411$		0			0
$412$	2.76393	+	8.50651i	0.136169	+	0.419086i
$413$	25.2254	−	18.3273i	1.24126	−	0.901830i
$414$		0			0
$415$	3.23607	−	2.35114i	0.158852	−	0.115413i
$416$	−0.618034	−	0.449028i	−0.0303016	−	0.0220154i
$417$		0			0
$418$	−2.76393	−	2.00811i	−0.135188	−	0.0982201i
$419$	21.8262	+	15.8577i	1.06628	+	0.774699i	0.975240	−	0.221148i	$-0.0709805\pi$
$419$	21.8262	+	15.8577i	1.06628	+	0.774699i	0.0910413	+	0.995847i	$0.470980\pi$
$420$		0			0
$421$	13.7082	+	9.95959i	0.668097	+	0.485401i	0.869388	−	0.494131i	$-0.164514\pi$
$421$	13.7082	+	9.95959i	0.668097	+	0.485401i	−0.201291	+	0.979532i	$0.564514\pi$
$422$	9.47214	−	6.88191i	0.461096	−	0.335006i
$423$		0			0
$424$	1.92705	−	1.40008i	0.0935859	−	0.0679941i
$425$	5.70820	+	17.5680i	0.276889	+	0.852175i
$426$		0			0
$427$	−13.3820	+	41.1855i	−0.647599	+	1.99310i
$428$	19.5623			0.945580
$429$		0			0
$430$	−1.38197	+	4.25325i	−0.0666443	+	0.205110i
$431$	−12.9443	−	9.40456i	−0.623504	−	0.453002i	0.230640	−	0.973039i	$-0.425918\pi$
$431$	−12.9443	−	9.40456i	−0.623504	−	0.453002i	−0.854144	+	0.520037i	$0.825918\pi$
$432$		0			0
$433$	20.6869			0.994150			0.497075	−	0.867708i	$-0.334407\pi$
$433$	20.6869			0.994150			0.497075	+	0.867708i	$0.334407\pi$
$434$	−12.4721	+	17.4620i	−0.598682	+	0.838205i
$435$		0			0
$436$	−3.23607	+	2.35114i	−0.154980	+	0.112599i
$437$	−16.9443	−	12.3107i	−0.810554	−	0.588902i
$438$		0			0
$439$	27.3262			1.30421			0.652105	−	0.758129i	$-0.273886\pi$
$439$	27.3262			1.30421			0.652105	+	0.758129i	$0.273886\pi$
$440$	−0.854102			−0.0407177
$441$		0			0
$442$	−0.944272	−	2.90617i	−0.0449144	−	0.138232i
$443$	−4.55573	−	14.0211i	−0.216449	−	0.666162i	−0.999048	−	0.0436351i	$-0.986106\pi$
$443$	−4.55573	−	14.0211i	−0.216449	−	0.666162i	0.782598	−	0.622527i	$-0.213894\pi$
$444$		0			0
$445$	−0.562306	+	1.73060i	−0.0266559	+	0.0820383i
$446$	−22.8262	+	16.5842i	−1.08085	+	0.785286i
$447$		0			0
$448$	1.19098	+	3.66547i	0.0562687	+	0.173177i
$449$	3.23607	+	2.35114i	0.152719	+	0.110957i	0.661521	−	0.749927i	$-0.269911\pi$
$449$	3.23607	+	2.35114i	0.152719	+	0.110957i	−0.508801	+	0.860884i	$0.669911\pi$
$450$		0			0
$451$	3.41641	+	10.5146i	0.160872	+	0.495114i
$452$	9.85410	+	7.15942i	0.463498	+	0.336751i
$453$		0			0
$454$	−3.48278	+	10.7189i	−0.163455	+	0.503063i
$455$	−1.47214	+	1.06957i	−0.0690148	+	0.0501422i
$456$		0			0
$457$	1.71885	+	5.29007i	0.0804043	+	0.247459i	0.983176	−	0.182661i	$-0.0584712\pi$
$457$	1.71885	+	5.29007i	0.0804043	+	0.247459i	−0.902772	+	0.430120i	$0.858471\pi$
$458$	−4.76393	+	14.6619i	−0.222604	+	0.685104i
$459$		0			0
$460$	−5.23607			−0.244133
$461$	−2.97214	+	9.14729i	−0.138426	+	0.426032i	−0.996107	−	0.0881502i	$-0.971904\pi$
$461$	−2.97214	+	9.14729i	−0.138426	+	0.426032i	0.857681	+	0.514182i	$0.171904\pi$
$462$		0			0
$463$	−13.7082	+	9.95959i	−0.637074	+	0.462862i	−0.858844	−	0.512238i	$-0.828817\pi$
$463$	−13.7082	+	9.95959i	−0.637074	+	0.462862i	0.221770	+	0.975099i	$0.428817\pi$
$464$	1.61803			0.0751153
$465$		0			0
$466$	−22.3607			−1.03584
$467$	−33.9615	+	24.6745i	−1.57155	+	1.14180i	−0.645898	+	0.763424i	$0.723517\pi$
$467$	−33.9615	+	24.6745i	−1.57155	+	1.14180i	−0.925653	+	0.378374i	$0.876483\pi$
$468$		0			0
$469$	13.0344	−	40.1159i	0.601875	−	1.85238i
$470$	0.944272			0.0435560
$471$		0			0
$472$	−2.50000	+	7.69421i	−0.115072	+	0.354155i
$473$	3.09017	+	9.51057i	0.142086	+	0.437296i
$474$		0			0
$475$	−9.23607	+	6.71040i	−0.423780	+	0.307894i
$476$	−4.76393	+	14.6619i	−0.218354	+	0.672026i
$477$		0			0
$478$	−19.9443	−	14.4904i	−0.912230	−	0.662774i
$479$	−1.76393	−	5.42882i	−0.0805961	−	0.248049i	0.902637	−	0.430403i	$-0.141628\pi$
$479$	−1.76393	−	5.42882i	−0.0805961	−	0.248049i	−0.983233	+	0.182353i	$0.941628\pi$
$480$		0			0
$481$	−4.18034	−	3.03719i	−0.190607	−	0.138484i
$482$	−5.80902	−	17.8783i	−0.264593	−	0.814335i
$483$		0			0
$484$	7.35410	−	5.34307i	0.334277	−	0.242867i
$485$	−1.32624	+	4.08174i	−0.0602214	+	0.185342i
$486$		0			0
$487$	−2.00000	−	6.15537i	−0.0906287	−	0.278926i	0.895461	−	0.445140i	$-0.146846\pi$
$487$	−2.00000	−	6.15537i	−0.0906287	−	0.278926i	−0.986090	+	0.166213i	$0.946846\pi$
$488$	−3.47214	−	10.6861i	−0.157176	−	0.483739i
$489$		0			0
$490$	4.85410			0.219286
$491$	−25.5279			−1.15206			−0.576028	−	0.817430i	$-0.695398\pi$
$491$	−25.5279			−1.15206			−0.576028	+	0.817430i	$0.695398\pi$
$492$		0			0
$493$	5.23607	+	3.80423i	0.235821	+	0.171334i
$494$	1.52786	−	1.11006i	0.0687419	−	0.0499439i
$495$		0			0
$496$	−0.0450850	−	5.56758i	−0.00202437	−	0.249992i
$497$	7.70820			0.345760
$498$		0			0
$499$	−7.61803	−	5.53483i	−0.341030	−	0.247773i	0.404066	−	0.914730i	$-0.367597\pi$
$499$	−7.61803	−	5.53483i	−0.341030	−	0.247773i	−0.745096	+	0.666957i	$0.767597\pi$
$500$	−1.83688	+	5.65334i	−0.0821478	+	0.252825i
$501$		0			0
$502$	−21.3820			−0.954324
$503$	8.52786	−	26.2461i	0.380239	−	1.17025i	−0.559637	−	0.828738i	$-0.689059\pi$
$503$	8.52786	−	26.2461i	0.380239	−	1.17025i	0.939876	−	0.341517i	$-0.110941\pi$
$504$		0			0
$505$	−1.93769	−	5.96361i	−0.0862263	−	0.265377i
$506$	−9.47214	+	6.88191i	−0.421088	+	0.305938i
$507$		0			0
$508$	6.39919	−	4.64928i	0.283918	−	0.206279i
$509$	−3.61803	−	2.62866i	−0.160367	−	0.116513i	0.504708	−	0.863290i	$-0.331600\pi$
$509$	−3.61803	−	2.62866i	−0.160367	−	0.116513i	−0.665074	+	0.746777i	$0.731600\pi$
$510$		0			0
$511$	7.42705	+	5.39607i	0.328553	+	0.238708i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$		0			0
$514$	1.47214	+	1.06957i	0.0649331	+	0.0471767i
$515$	−4.47214	+	3.24920i	−0.197066	+	0.143177i
$516$		0			0
$517$	1.70820	−	1.24108i	0.0751267	−	0.0545828i
$518$	8.05573	+	24.7930i	0.353948	+	1.08934i
$519$		0			0
$520$	0.145898	−	0.449028i	0.00639805	−	0.0196912i
$521$	−10.2918			−0.450892			−0.225446	−	0.974256i	$-0.572384\pi$
$521$	−10.2918			−0.450892			−0.225446	+	0.974256i	$0.572384\pi$
$522$		0			0
$523$	−2.56231	+	7.88597i	−0.112042	+	0.344829i	−0.991319	−	0.131482i	$-0.958026\pi$
$523$	−2.56231	+	7.88597i	−0.112042	+	0.344829i	0.879277	+	0.476311i	$0.158026\pi$
$524$	13.7812	+	10.0126i	0.602032	+	0.437402i
$525$		0			0
$526$	−5.81966			−0.253749
$527$	12.9443	−	18.1231i	0.563861	−	0.789454i
$528$		0			0
$529$	−39.4615	+	28.6705i	−1.71572	+	1.24654i
$530$	1.19098	+	0.865300i	0.0517330	+	0.0375862i
$531$		0			0
$532$	−9.52786			−0.413085
$533$	−6.11146			−0.264717
$534$		0			0
$535$	3.73607	+	11.4984i	0.161524	+	0.497121i
$536$	3.38197	+	10.4086i	0.146079	+	0.449584i
$537$		0			0
$538$	1.98936	−	6.12261i	0.0857673	−	0.263965i
$539$	8.78115	−	6.37988i	0.378231	−	0.274801i
$540$		0			0
$541$	−0.472136	−	1.45309i	−0.0202987	−	0.0624730i	0.940394	−	0.340087i	$-0.110456\pi$
$541$	−0.472136	−	1.45309i	−0.0202987	−	0.0624730i	−0.960693	+	0.277614i	$0.910456\pi$
$542$	16.0623	+	11.6699i	0.689935	+	0.501267i
$543$		0			0
$544$	−1.23607	−	3.80423i	−0.0529960	−	0.163105i
$545$	−2.00000	−	1.45309i	−0.0856706	−	0.0622433i
$546$		0			0
$547$	11.4721	−	35.3076i	0.490513	−	1.50964i	−0.333321	−	0.942813i	$-0.608169\pi$
$547$	11.4721	−	35.3076i	0.490513	−	1.50964i	0.823834	−	0.566831i	$-0.191831\pi$
$548$	−13.7082	+	9.95959i	−0.585585	+	0.425453i
$549$		0			0
$550$	1.97214	+	6.06961i	0.0840922	+	0.258809i
$551$	−1.23607	+	3.80423i	−0.0526583	+	0.162065i
$552$		0			0
$553$	−43.6525			−1.85629
$554$	4.38197	−	13.4863i	0.186172	−	0.572978i
$555$		0			0
$556$	−3.85410	+	2.80017i	−0.163450	+	0.118754i
$557$	30.5066			1.29261			0.646303	−	0.763081i	$-0.276314\pi$
$557$	30.5066			1.29261			0.646303	+	0.763081i	$0.276314\pi$
$558$		0			0
$559$	−5.52786			−0.233804
$560$	−1.92705	+	1.40008i	−0.0814328	+	0.0591644i
$561$		0			0
$562$	5.52786	−	17.0130i	0.233179	−	0.717651i
$563$	−6.32624			−0.266619			−0.133310	−	0.991074i	$-0.542560\pi$
$563$	−6.32624			−0.266619			−0.133310	+	0.991074i	$0.542560\pi$
$564$		0			0
$565$	−2.32624	+	7.15942i	−0.0978656	+	0.301199i
$566$	10.0000	+	30.7768i	0.420331	+	1.29365i
$567$		0			0
$568$	−1.61803	+	1.17557i	−0.0678912	+	0.0493258i
$569$	11.2361	−	34.5811i	0.471040	−	1.44971i	−0.380184	−	0.924911i	$-0.624139\pi$
$569$	11.2361	−	34.5811i	0.471040	−	1.44971i	0.851224	−	0.524802i	$-0.175861\pi$
$570$		0			0
$571$	−2.14590	−	1.55909i	−0.0898030	−	0.0652457i	0.541978	−	0.840393i	$-0.317676\pi$
$571$	−2.14590	−	1.55909i	−0.0898030	−	0.0652457i	−0.631781	+	0.775147i	$0.717676\pi$
$572$	−0.326238	−	1.00406i	−0.0136407	−	0.0419817i
$573$		0			0
$574$	24.9443	+	18.1231i	1.04115	+	0.756443i
$575$	12.0902	+	37.2097i	0.504195	+	1.55175i
$576$		0			0
$577$	21.2082	−	15.4087i	0.882909	−	0.641471i	−0.0511104	−	0.998693i	$-0.516276\pi$
$577$	21.2082	−	15.4087i	0.882909	−	0.641471i	0.934020	+	0.357222i	$0.116276\pi$
$578$	−0.309017	+	0.951057i	−0.0128534	+	0.0395587i
$579$		0			0
$580$	0.309017	+	0.951057i	0.0128312	+	0.0394905i
$581$	−7.70820	−	23.7234i	−0.319790	−	0.984213i
$582$		0			0
$583$	3.29180			0.136332
$584$	−2.38197			−0.0985665
$585$		0			0
$586$	−0.381966	−	0.277515i	−0.0157789	−	0.0114640i
$587$	1.40983	−	1.02430i	0.0581899	−	0.0422774i	−0.558310	−	0.829632i	$-0.688550\pi$
$587$	1.40983	−	1.02430i	0.0581899	−	0.0422774i	0.616500	+	0.787355i	$0.288550\pi$
$588$		0			0
$589$	13.1246	+	4.14725i	0.540790	+	0.170885i
$590$	−5.00000			−0.205847
$591$		0			0
$592$	−5.47214	−	3.97574i	−0.224903	−	0.163402i
$593$	−4.67376	+	14.3844i	−0.191928	+	0.590695i	0.808070	+	0.589086i	$0.200512\pi$
$593$	−4.67376	+	14.3844i	−0.191928	+	0.590695i	−0.999999	+	0.00160883i	$0.999488\pi$
$594$		0			0
$595$	−9.52786			−0.390604
$596$	4.73607	−	14.5761i	0.193997	−	0.597061i
$597$		0			0
$598$	−2.00000	−	6.15537i	−0.0817861	−	0.251712i
$599$	−15.4721	+	11.2412i	−0.632174	+	0.459302i	−0.857153	−	0.515062i	$-0.827769\pi$
$599$	−15.4721	+	11.2412i	−0.632174	+	0.459302i	0.224978	+	0.974364i	$0.427769\pi$
$600$		0			0
$601$	1.02786	−	0.746787i	0.0419274	−	0.0304621i	−0.566624	−	0.823976i	$-0.691751\pi$
$601$	1.02786	−	0.746787i	0.0419274	−	0.0304621i	0.608552	+	0.793514i	$0.291751\pi$
$602$	22.5623	+	16.3925i	0.919571	+	0.668107i
$603$		0			0
$604$	19.0623	+	13.8496i	0.775634	+	0.563531i
$605$	4.54508	+	3.30220i	0.184784	+	0.134253i
$606$		0			0
$607$	16.5451	+	12.0207i	0.671544	+	0.487905i	0.870542	−	0.492095i	$-0.163769\pi$
$607$	16.5451	+	12.0207i	0.671544	+	0.487905i	−0.198997	+	0.980000i	$0.563769\pi$
$608$	2.00000	−	1.45309i	0.0811107	−	0.0589304i
$609$		0			0
$610$	5.61803	−	4.08174i	0.227468	−	0.165265i
$611$	0.360680	+	1.11006i	0.0145915	+	0.0449081i
$612$		0			0
$613$	−8.61803	+	26.5236i	−0.348079	+	1.07128i	0.611836	+	0.790985i	$0.290431\pi$
$613$	−8.61803	+	26.5236i	−0.348079	+	1.07128i	−0.959915	+	0.280292i	$0.909569\pi$
$614$	0.472136			0.0190539
$615$		0			0
$616$	−1.64590	+	5.06555i	−0.0663151	+	0.204097i
$617$	2.94427	+	2.13914i	0.118532	+	0.0861185i	0.645472	−	0.763784i	$-0.276661\pi$
$617$	2.94427	+	2.13914i	0.118532	+	0.0861185i	−0.526940	+	0.849902i	$0.676661\pi$
$618$		0			0
$619$	8.18034			0.328796			0.164398	−	0.986394i	$-0.447432\pi$
$619$	8.18034			0.328796			0.164398	+	0.986394i	$0.447432\pi$
$620$	3.26393	−	1.08981i	0.131083	−	0.0437680i
$621$		0			0
$622$	−23.5623	+	17.1190i	−0.944762	+	0.686410i
$623$	9.18034	+	6.66991i	0.367803	+	0.267224i
$624$		0			0
$625$	19.4164			0.776656
$626$	5.41641			0.216483
$627$		0			0
$628$	7.18034	+	22.0988i	0.286527	+	0.881839i
$629$	−8.36068	−	25.7315i	−0.333362	−	1.02598i
$630$		0			0
$631$	8.89919	−	27.3889i	0.354271	−	1.09033i	−0.602160	−	0.798376i	$-0.705693\pi$
$631$	8.89919	−	27.3889i	0.354271	−	1.09033i	0.956431	−	0.291959i	$-0.0943070\pi$
$632$	9.16312	−	6.65740i	0.364489	−	0.264817i
$633$		0			0
$634$	−7.56231	−	23.2744i	−0.300338	−	0.924344i
$635$	3.95492	+	2.87341i	0.156946	+	0.114028i
$636$		0			0
$637$	1.85410	+	5.70634i	0.0734622	+	0.226093i
$638$	1.80902	+	1.31433i	0.0716197	+	0.0520347i
$639$		0			0
$640$	0.190983	−	0.587785i	0.00754927	−	0.0232343i
$641$	−21.0902	+	15.3229i	−0.833012	+	0.605218i	−0.920410	−	0.390955i	$-0.872145\pi$
$641$	−21.0902	+	15.3229i	−0.833012	+	0.605218i	0.0873981	+	0.996173i	$0.472145\pi$
$642$		0			0
$643$	−3.18034	−	9.78808i	−0.125420	−	0.386004i	0.868557	−	0.495589i	$-0.165048\pi$
$643$	−3.18034	−	9.78808i	−0.125420	−	0.386004i	−0.993977	+	0.109585i	$0.965048\pi$
$644$	−10.0902	+	31.0543i	−0.397608	+	1.22371i
$645$		0			0
$646$	9.88854			0.389060
$647$	−5.50658	+	16.9475i	−0.216486	+	0.666275i	0.782559	+	0.622577i	$0.213914\pi$
$647$	−5.50658	+	16.9475i	−0.216486	+	0.666275i	−0.999045	+	0.0436985i	$0.986086\pi$
$648$		0			0
$649$	−9.04508	+	6.57164i	−0.355051	+	0.257959i
$650$	−3.52786			−0.138374
$651$		0			0
$652$	11.5279			0.451466
$653$	32.4336	−	23.5644i	1.26923	−	0.922147i	0.270054	−	0.962845i	$-0.412958\pi$
$653$	32.4336	−	23.5644i	1.26923	−	0.922147i	0.999171	+	0.0406984i	$0.0129583\pi$
$654$		0			0
$655$	−3.25329	+	10.0126i	−0.127117	+	0.391224i
$656$	−8.00000			−0.312348
$657$		0			0
$658$	1.81966	−	5.60034i	0.0709377	−	0.218324i
$659$	−5.31966	−	16.3722i	−0.207225	−	0.637772i	−0.999615	−	0.0277569i	$-0.991164\pi$
$659$	−5.31966	−	16.3722i	−0.207225	−	0.637772i	0.792390	−	0.610015i	$-0.208836\pi$
$660$		0			0
$661$	10.1803	−	7.39645i	0.395969	−	0.287689i	−0.371928	−	0.928262i	$-0.621303\pi$
$661$	10.1803	−	7.39645i	0.395969	−	0.287689i	0.767897	+	0.640573i	$0.221303\pi$
$662$	8.29180	−	25.5195i	0.322270	−	0.991844i
$663$		0			0
$664$	5.23607	+	3.80423i	0.203199	+	0.147633i
$665$	−1.81966	−	5.60034i	−0.0705634	−	0.217172i
$666$		0			0
$667$	11.0902	+	8.05748i	0.429413	+	0.311987i
$668$	−6.18034	−	19.0211i	−0.239125	−	0.735950i
$669$		0			0
$670$	−5.47214	+	3.97574i	−0.211407	+	0.153596i
$671$	4.79837	−	14.7679i	0.185239	−	0.570108i
$672$		0			0
$673$	3.62868	+	11.1679i	0.139875	+	0.430492i	0.996316	−	0.0857529i	$-0.0273296\pi$
$673$	3.62868	+	11.1679i	0.139875	+	0.430492i	−0.856441	+	0.516245i	$0.827330\pi$
$674$	7.85410	+	24.1724i	0.302529	+	0.931088i
$675$		0			0
$676$	−12.4164			−0.477554
$677$	18.1459			0.697404			0.348702	−	0.937234i	$-0.386623\pi$
$677$	18.1459			0.697404			0.348702	+	0.937234i	$0.386623\pi$
$678$		0			0
$679$	21.6525	+	15.7314i	0.830946	+	0.603717i
$680$	2.00000	−	1.45309i	0.0766965	−	0.0557233i
$681$		0			0
$682$	4.47214	−	6.26137i	0.171247	−	0.239760i
$683$	−22.8328			−0.873673			−0.436837	−	0.899541i	$-0.643901\pi$
$683$	−22.8328			−0.873673			−0.436837	+	0.899541i	$0.643901\pi$
$684$		0			0
$685$	−8.47214	−	6.15537i	−0.323704	−	0.235184i
$686$	1.01722	−	3.13068i	0.0388377	−	0.119530i
$687$		0			0
$688$	−7.23607			−0.275873
$689$	−0.562306	+	1.73060i	−0.0214221	+	0.0659306i
$690$		0			0
$691$	−6.67376	−	20.5397i	−0.253882	−	0.781368i	−0.994048	−	0.108944i	$-0.965253\pi$
$691$	−6.67376	−	20.5397i	−0.253882	−	0.781368i	0.740166	−	0.672424i	$-0.234747\pi$
$692$	−6.69098	+	4.86128i	−0.254353	+	0.184798i
$693$		0			0
$694$	−12.5902	+	9.14729i	−0.477916	+	0.347227i
$695$	−2.38197	−	1.73060i	−0.0903531	−	0.0656454i
$696$		0			0
$697$	−25.8885	−	18.8091i	−0.980599	−	0.712447i
$698$	−14.0902	−	10.2371i	−0.533321	−	0.387480i
$699$		0			0
$700$	14.3992	+	10.4616i	0.544238	+	0.395412i
$701$	12.5623	−	9.12705i	0.474472	−	0.344724i	−0.324710	−	0.945814i	$-0.605267\pi$
$701$	12.5623	−	9.12705i	0.474472	−	0.344724i	0.799181	+	0.601090i	$0.205267\pi$
$702$		0			0
$703$	13.5279	−	9.82857i	0.510213	−	0.370691i
$704$	−0.427051	−	1.31433i	−0.0160951	−	0.0495356i
$705$		0			0
$706$	0.472136	−	1.45309i	0.0177691	−	0.0546876i
$707$	−39.1033			−1.47063
$708$		0			0
$709$	3.34752	−	10.3026i	0.125719	−	0.386923i	−0.868312	−	0.496018i	$-0.834795\pi$
$709$	3.34752	−	10.3026i	0.125719	−	0.386923i	0.994031	+	0.109095i	$0.0347951\pi$
$710$	−1.00000	−	0.726543i	−0.0375293	−	0.0272667i
$711$		0			0
$712$	−2.94427			−0.110341
$713$	27.4164	−	38.3853i	1.02675	−	1.43754i
$714$		0			0
$715$	0.527864	−	0.383516i	0.0197410	−	0.0143427i
$716$	−4.69098	−	3.40820i	−0.175310	−	0.127370i
$717$		0			0
$718$	−14.1803			−0.529206
$719$	−18.6525			−0.695620			−0.347810	−	0.937565i	$-0.613075\pi$
$719$	−18.6525			−0.695620			−0.347810	+	0.937565i	$0.613075\pi$
$720$		0			0
$721$	10.6525	+	32.7849i	0.396719	+	1.22098i
$722$	−3.98278	−	12.2577i	−0.148224	−	0.456186i
$723$		0			0
$724$	2.14590	−	6.60440i	0.0797517	−	0.245450i
$725$	6.04508	−	4.39201i	0.224509	−	0.163115i
$726$		0			0
$727$	−10.0451	−	30.9156i	−0.372552	−	1.14660i	−0.945116	−	0.326736i	$-0.894051\pi$
$727$	−10.0451	−	30.9156i	−0.372552	−	1.14660i	0.572564	−	0.819860i	$-0.305949\pi$
$728$	−2.38197	−	1.73060i	−0.0882815	−	0.0641403i
$729$		0			0
$730$	−0.454915	−	1.40008i	−0.0168372	−	0.0518195i
$731$	−23.4164	−	17.0130i	−0.866087	−	0.629249i
$732$		0			0
$733$	7.23607	−	22.2703i	0.267270	−	0.822573i	−0.723891	−	0.689914i	$-0.757648\pi$
$733$	7.23607	−	22.2703i	0.267270	−	0.822573i	0.991162	−	0.132659i	$-0.0423516\pi$
$734$	5.01722	−	3.64522i	0.185189	−	0.134548i
$735$		0			0
$736$	−2.61803	−	8.05748i	−0.0965020	−	0.297003i
$737$	−4.67376	+	14.3844i	−0.172160	+	0.529855i
$738$		0			0
$739$	−31.1246			−1.14494			−0.572469	−	0.819927i	$-0.694014\pi$
$739$	−31.1246			−1.14494			−0.572469	+	0.819927i	$0.694014\pi$
$740$	1.29180	−	3.97574i	0.0474874	−	0.146151i
$741$		0			0
$742$	7.42705	−	5.39607i	0.272656	−	0.198096i
$743$	−34.6525			−1.27128			−0.635638	−	0.771987i	$-0.719263\pi$
$743$	−34.6525			−1.27128			−0.635638	+	0.771987i	$0.719263\pi$
$744$		0			0
$745$	9.47214			0.347032
$746$	−21.7984	+	15.8374i	−0.798095	+	0.579850i
$747$		0			0
$748$	1.70820	−	5.25731i	0.0624581	−	0.192226i
$749$	75.3951			2.75488
$750$		0			0
$751$	−10.7639	+	33.1280i	−0.392781	+	1.20886i	0.537894	+	0.843012i	$0.319220\pi$
$751$	−10.7639	+	33.1280i	−0.392781	+	1.20886i	−0.930676	+	0.365845i	$0.880780\pi$
$752$	0.472136	+	1.45309i	0.0172170	+	0.0529886i
$753$		0			0
$754$	−1.00000	+	0.726543i	−0.0364179	+	0.0264591i
$755$	−4.50000	+	13.8496i	−0.163772	+	0.504038i
$756$		0			0
$757$	−9.76393	−	7.09391i	−0.354876	−	0.257833i	0.396036	−	0.918235i	$-0.370386\pi$
$757$	−9.76393	−	7.09391i	−0.354876	−	0.257833i	−0.750912	+	0.660403i	$0.770386\pi$
$758$	5.47214	+	16.8415i	0.198757	+	0.611711i
$759$		0			0
$760$	1.23607	+	0.898056i	0.0448369	+	0.0325759i
$761$	6.96556	+	21.4378i	0.252501	+	0.777119i	0.994312	+	0.106509i	$0.0339674\pi$
$761$	6.96556	+	21.4378i	0.252501	+	0.777119i	−0.741810	+	0.670610i	$0.766033\pi$
$762$		0			0
$763$	−12.4721	+	9.06154i	−0.451522	+	0.328050i
$764$	−2.56231	+	7.88597i	−0.0927010	+	0.285304i
$765$		0			0
$766$	7.23607	+	22.2703i	0.261450	+	0.804660i
$767$	−1.90983	−	5.87785i	−0.0689600	−	0.212237i
$768$		0			0
$769$	24.4721			0.882488			0.441244	−	0.897387i	$-0.354537\pi$
$769$	24.4721			0.882488			0.441244	+	0.897387i	$0.354537\pi$
$770$	−3.29180			−0.118628
$771$		0			0
$772$	6.39919	+	4.64928i	0.230312	+	0.167331i
$773$	14.6803	−	10.6659i	0.528015	−	0.383625i	−0.291600	−	0.956540i	$-0.594187\pi$
$773$	14.6803	−	10.6659i	0.528015	−	0.383625i	0.819615	+	0.572915i	$0.194187\pi$
$774$		0			0
$775$	−15.2812	−	20.6785i	−0.548915	−	0.742793i
$776$	−6.94427			−0.249285
$777$		0			0
$778$	26.7254	+	19.4172i	0.958153	+	0.696139i
$779$	6.11146	−	18.8091i	0.218966	−	0.673907i
$780$		0			0
$781$	−2.76393			−0.0989013
$782$	10.4721	−	32.2299i	0.374483	−	1.15254i
$783$		0			0
$784$	2.42705	+	7.46969i	0.0866804	+	0.266775i
$785$	−11.6180	+	8.44100i	−0.414665	+	0.301272i
$786$		0			0
$787$	8.61803	−	6.26137i	0.307200	−	0.223194i	−0.423494	−	0.905899i	$-0.639197\pi$
$787$	8.61803	−	6.26137i	0.307200	−	0.223194i	0.730694	+	0.682705i	$0.239197\pi$
$788$	−14.4443	−	10.4944i	−0.514556	−	0.373847i
$789$		0			0
$790$	5.66312	+	4.11450i	0.201485	+	0.146387i
$791$	37.9787	+	27.5932i	1.35037	+	0.981099i
$792$		0			0
$793$	6.94427	+	5.04531i	0.246598	+	0.179164i
$794$	9.38197	−	6.81640i	0.332954	−	0.241905i
$795$		0			0
$796$	3.30902	−	2.40414i	0.117285	−	0.0852125i
$797$	−6.97214	−	21.4580i	−0.246966	−	0.760082i	−0.995307	−	0.0967684i	$-0.969149\pi$
$797$	−6.97214	−	21.4580i	−0.246966	−	0.760082i	0.748341	−	0.663314i	$-0.230851\pi$
$798$		0			0
$799$	−1.88854	+	5.81234i	−0.0668119	+	0.205626i
$800$	−4.61803			−0.163272
$801$		0			0
$802$	7.67376	−	23.6174i	0.270970	−	0.833960i
$803$	−2.66312	−	1.93487i	−0.0939794	−	0.0682801i
$804$		0			0
$805$	−20.1803			−0.711264
$806$	2.52786	+	3.42071i	0.0890402	+	0.120489i
$807$		0			0
$808$	8.20820	−	5.96361i	0.288764	−	0.209799i
$809$	2.61803	+	1.90211i	0.0920452	+	0.0668747i	0.632856	−	0.774270i	$-0.281883\pi$
$809$	2.61803	+	1.90211i	0.0920452	+	0.0668747i	−0.540811	+	0.841144i	$0.681883\pi$
$810$		0			0
$811$	44.0689			1.54747			0.773734	−	0.633511i	$-0.218387\pi$
$811$	44.0689			1.54747			0.773734	+	0.633511i	$0.218387\pi$
$812$	6.23607			0.218843
$813$		0			0
$814$	−2.88854	−	8.89002i	−0.101243	−	0.311595i
$815$	2.20163	+	6.77591i	0.0771196	+	0.237350i
$816$		0			0
$817$	5.52786	−	17.0130i	0.193395	−	0.595210i
$818$	29.9615	−	21.7683i	1.04758	−	0.761111i
$819$		0			0
$820$	−1.52786	−	4.70228i	−0.0533553	−	0.164211i
$821$	22.3992	+	16.2740i	0.781737	+	0.567965i	0.905500	−	0.424347i	$-0.139496\pi$
$821$	22.3992	+	16.2740i	0.781737	+	0.567965i	−0.123763	+	0.992312i	$0.539496\pi$
$822$		0			0
$823$	−0.0278640	−	0.0857567i	−0.000971280	−	0.00298929i	0.950570	−	0.310511i	$-0.100500\pi$
$823$	−0.0278640	−	0.0857567i	−0.000971280	−	0.00298929i	−0.951541	+	0.307522i	$0.900500\pi$
$824$	−7.23607	−	5.25731i	−0.252080	−	0.183147i
$825$		0			0
$826$	−9.63525	+	29.6543i	−0.335253	+	1.03180i
$827$	14.1180	−	10.2574i	0.490932	−	0.356683i	−0.314611	−	0.949221i	$-0.601874\pi$
$827$	14.1180	−	10.2574i	0.490932	−	0.356683i	0.805543	+	0.592538i	$0.201874\pi$
$828$		0			0
$829$	−13.7984	−	42.4670i	−0.479237	−	1.47494i	−0.840157	−	0.542344i	$-0.817537\pi$
$829$	−13.7984	−	42.4670i	−0.479237	−	1.47494i	0.360919	−	0.932597i	$-0.382463\pi$
$830$	−1.23607	+	3.80423i	−0.0429045	+	0.132047i
$831$		0			0
$832$	0.763932			0.0264846
$833$	−9.70820	+	29.8788i	−0.336369	+	1.03524i
$834$		0			0
$835$	10.0000	−	7.26543i	0.346064	−	0.251430i
$836$	3.41641			0.118159
$837$		0			0
$838$	−26.9787			−0.931964
$839$	25.8885	−	18.8091i	0.893772	−	0.649363i	−0.0430869	−	0.999071i	$-0.513719\pi$
$839$	25.8885	−	18.8091i	0.893772	−	0.649363i	0.936859	+	0.349708i	$0.113719\pi$
$840$		0			0
$841$	−8.15248	+	25.0907i	−0.281120	+	0.865198i
$842$	−16.9443			−0.583938
$843$		0			0
$844$	−3.61803	+	11.1352i	−0.124538	+	0.383288i
$845$	−2.37132	−	7.29818i	−0.0815760	−	0.251065i
$846$		0			0
$847$	28.3435	−	20.5927i	0.973893	−	0.707575i
$848$	−0.736068	+	2.26538i	−0.0252767	+	0.0777936i
$849$		0			0
$850$	−14.9443	−	10.8576i	−0.512584	−	0.372414i
$851$	−17.7082	−	54.5002i	−0.607029	−	1.86824i
$852$		0			0
$853$	23.4721	+	17.0535i	0.803671	+	0.583901i	0.911989	−	0.410215i	$-0.134546\pi$
$853$	23.4721	+	17.0535i	0.803671	+	0.583901i	−0.108318	+	0.994116i	$0.534546\pi$
$854$	−13.3820	−	41.1855i	−0.457921	−	1.40934i
$855$		0			0
$856$	−15.8262	+	11.4984i	−0.540930	+	0.393008i
$857$	−14.4377	+	44.4347i	−0.493182	+	1.51786i	0.326588	+	0.945167i	$0.394101\pi$
$857$	−14.4377	+	44.4347i	−0.493182	+	1.51786i	−0.819771	+	0.572692i	$0.805899\pi$
$858$		0			0
$859$	−2.25735	−	6.94742i	−0.0770199	−	0.237043i	0.905133	−	0.425130i	$-0.139771\pi$
$859$	−2.25735	−	6.94742i	−0.0770199	−	0.237043i	−0.982152	+	0.188087i	$0.939771\pi$
$860$	−1.38197	−	4.25325i	−0.0471246	−	0.145035i
$861$		0			0
$862$	16.0000			0.544962
$863$	−45.7771			−1.55827			−0.779135	−	0.626856i	$-0.784341\pi$
$863$	−45.7771			−1.55827			−0.779135	+	0.626856i	$0.784341\pi$
$864$		0			0
$865$	−4.13525	−	3.00444i	−0.140603	−	0.102154i
$866$	−16.7361	+	12.1595i	−0.568715	+	0.413195i
$867$		0			0
$868$	−0.173762	−	21.4580i	−0.00589787	−	0.728333i
$869$	15.6525			0.530974
$870$		0			0
$871$	−6.76393	−	4.91428i	−0.229187	−	0.166514i
$872$	1.23607	−	3.80423i	0.0418585	−	0.128827i
$873$		0			0
$874$	20.9443			0.708451
$875$	−7.07953	+	21.7885i	−0.239332	+	0.736587i
$876$		0			0
$877$	−6.27051	−	19.2986i	−0.211740	−	0.651669i	−0.999369	−	0.0355191i	$-0.988692\pi$
$877$	−6.27051	−	19.2986i	−0.211740	−	0.651669i	0.787629	−	0.616150i	$-0.211308\pi$
$878$	−22.1074	+	16.0620i	−0.746088	+	0.542065i
$879$		0			0
$880$	0.690983	−	0.502029i	0.0232930	−	0.0169234i
$881$	9.32624	+	6.77591i	0.314209	+	0.228286i	0.733700	−	0.679473i	$-0.237792\pi$
$881$	9.32624	+	6.77591i	0.314209	+	0.228286i	−0.419491	+	0.907759i	$0.637792\pi$
$882$		0			0
$883$	27.0902	+	19.6822i	0.911657	+	0.662357i	0.941433	−	0.337199i	$-0.109480\pi$
$883$	27.0902	+	19.6822i	0.911657	+	0.662357i	−0.0297765	+	0.999557i	$0.509480\pi$
$884$	2.47214	+	1.79611i	0.0831469	+	0.0604098i
$885$		0			0
$886$	11.9271	+	8.66551i	0.400697	+	0.291123i
$887$	−40.0689	+	29.1117i	−1.34538	+	0.977477i	−0.346154	+	0.938178i	$0.612513\pi$
$887$	−40.0689	+	29.1117i	−1.34538	+	0.977477i	−0.999227	+	0.0392991i	$0.987487\pi$
$888$		0			0
$889$	24.6631	−	17.9188i	0.827174	−	0.600977i
$890$	−0.562306	−	1.73060i	−0.0188485	−	0.0580098i
$891$		0			0
$892$	8.71885	−	26.8339i	0.291929	−	0.898464i
$893$	−3.77709			−0.126395
$894$		0			0
$895$	1.10739	−	3.40820i	0.0370160	−	0.113924i
$896$	−3.11803	−	2.26538i	−0.104166	−	0.0756812i
$897$		0			0
$898$	−4.00000			−0.133482
$899$	−8.59017	−	2.71441i	−0.286498	−	0.0905307i
$900$		0			0
$901$	−7.70820	+	5.60034i	−0.256798	+	0.186574i
$902$	−8.94427	−	6.49839i	−0.297812	−	0.216373i
$903$		0			0
$904$	−12.1803			−0.405112
$905$	4.29180			0.142664
$906$		0			0
$907$	−9.41641	−	28.9807i	−0.312667	−	0.962289i	−0.976704	−	0.214590i	$-0.931159\pi$
$907$	−9.41641	−	28.9807i	−0.312667	−	0.962289i	0.664038	−	0.747699i	$-0.268841\pi$
$908$	−3.48278	−	10.7189i	−0.115580	−	0.355719i
$909$		0			0
$910$	0.562306	−	1.73060i	0.0186403	−	0.0573688i
$911$	18.4721	−	13.4208i	0.612009	−	0.444651i	−0.238112	−	0.971238i	$-0.576529\pi$
$911$	18.4721	−	13.4208i	0.612009	−	0.444651i	0.850121	+	0.526587i	$0.176529\pi$
$912$		0			0
$913$	2.76393	+	8.50651i	0.0914728	+	0.281524i
$914$	−4.50000	−	3.26944i	−0.148847	−	0.108144i
$915$		0			0
$916$	−4.76393	−	14.6619i	−0.157405	−	0.484442i
$917$	53.1140	+	38.5896i	1.75398	+	1.27434i
$918$		0			0
$919$	8.00000	−	24.6215i	0.263896	−	0.812187i	−0.728050	−	0.685524i	$-0.759573\pi$
$919$	8.00000	−	24.6215i	0.263896	−	0.812187i	0.991946	−	0.126663i	$-0.0404268\pi$
$920$	4.23607	−	3.07768i	0.139659	−	0.101468i
$921$		0			0
$922$	−2.97214	−	9.14729i	−0.0978821	−	0.301250i
$923$	0.472136	−	1.45309i	0.0155405	−	0.0478289i
$924$		0			0
$925$	−31.2361			−1.02704
$926$	5.23607	−	16.1150i	0.172068	−	0.529570i
$927$		0			0
$928$	−1.30902	+	0.951057i	−0.0429706	+	0.0312200i
$929$	−1.23607			−0.0405541			−0.0202770	−	0.999794i	$-0.506455\pi$
$929$	−1.23607			−0.0405541			−0.0202770	+	0.999794i	$0.506455\pi$
$930$		0			0
$931$	−19.4164			−0.636347
$932$	18.0902	−	13.1433i	0.592563	−	0.430522i
$933$		0			0
$934$	12.9721	−	39.9241i	0.424461	−	1.30636i
$935$	3.41641			0.111728
$936$		0			0
$937$	−4.38854	+	13.5065i	−0.143367	+	0.441240i	−0.996797	−	0.0799678i	$-0.974518\pi$
$937$	−4.38854	+	13.5065i	−0.143367	+	0.441240i	0.853430	+	0.521208i	$0.174518\pi$
$938$	13.0344	+	40.1159i	0.425590	+	1.30983i
$939$		0			0
$940$	−0.763932	+	0.555029i	−0.0249167	+	0.0181031i
$941$	−1.73607	+	5.34307i	−0.0565942	+	0.174179i	−0.975358	−	0.220629i	$-0.929189\pi$
$941$	−1.73607	+	5.34307i	−0.0565942	+	0.174179i	0.918764	+	0.394808i	$0.129189\pi$
$942$		0			0
$943$	−54.8328	−	39.8384i	−1.78560	−	1.29732i
$944$	−2.50000	−	7.69421i	−0.0813681	−	0.250425i
$945$		0			0
$946$	−8.09017	−	5.87785i	−0.263034	−	0.191105i
$947$	10.3885	+	31.9727i	0.337582	+	1.03897i	0.965436	+	0.260640i	$0.0839336\pi$
$947$	10.3885	+	31.9727i	0.337582	+	1.03897i	−0.627854	+	0.778331i	$0.716066\pi$
$948$		0			0
$949$	1.47214	−	1.06957i	0.0477876	−	0.0347197i
$950$	3.52786	−	10.8576i	0.114459	−	0.352269i
$951$		0			0
$952$	−4.76393	−	14.6619i	−0.154400	−	0.475194i
$953$	16.8328	+	51.8061i	0.545268	+	1.67816i	0.720351	+	0.693610i	$0.243981\pi$
$953$	16.8328	+	51.8061i	0.545268	+	1.67816i	−0.175083	+	0.984554i	$0.556019\pi$
$954$		0			0
$955$	−5.12461			−0.165829
$956$	24.6525			0.797318
$957$		0			0
$958$	4.61803	+	3.35520i	0.149202	+	0.108402i
$959$	−52.8328	+	38.3853i	−1.70606	+	1.23953i
$960$		0			0
$961$	−9.10081	+	29.6340i	−0.293575	+	0.955936i
$962$	5.16718			0.166597
$963$		0			0
$964$	15.2082	+	11.0494i	0.489823	+	0.355877i
$965$	−1.51064	+	4.64928i	−0.0486293	+	0.149666i
$966$		0			0
$967$	16.9443			0.544891			0.272446	−	0.962171i	$-0.412168\pi$
$967$	16.9443			0.544891			0.272446	+	0.962171i	$0.412168\pi$
$968$	−2.80902	+	8.64527i	−0.0902852	+	0.277869i
$969$		0			0
$970$	−1.32624	−	4.08174i	−0.0425829	−	0.131057i
$971$	28.7254	−	20.8702i	0.921843	−	0.669758i	−0.0221393	−	0.999755i	$-0.507048\pi$
$971$	28.7254	−	20.8702i	0.921843	−	0.669758i	0.943982	+	0.329997i	$0.107048\pi$
$972$		0			0
$973$	−14.8541	+	10.7921i	−0.476201	+	0.345980i
$974$	5.23607	+	3.80423i	0.167774	+	0.121895i
$975$		0			0
$976$	9.09017	+	6.60440i	0.290969	+	0.211402i
$977$	−23.3262	−	16.9475i	−0.746272	−	0.542199i	0.148397	−	0.988928i	$-0.452589\pi$
$977$	−23.3262	−	16.9475i	−0.746272	−	0.542199i	−0.894669	+	0.446729i	$0.852589\pi$
$978$		0			0
$979$	−3.29180	−	2.39163i	−0.105206	−	0.0764368i
$980$	−3.92705	+	2.85317i	−0.125445	+	0.0911412i
$981$		0			0
$982$	20.6525	−	15.0049i	0.659047	−	0.478826i
$983$	−6.23607	−	19.1926i	−0.198900	−	0.612150i	−0.999909	−	0.0134983i	$-0.995703\pi$
$983$	−6.23607	−	19.1926i	−0.198900	−	0.612150i	0.801009	−	0.598652i	$-0.204297\pi$
$984$		0			0
$985$	3.40983	−	10.4944i	0.108646	−	0.334379i
$986$	−6.47214			−0.206115
$987$		0			0
$988$	−0.583592	+	1.79611i	−0.0185665	+	0.0571419i
$989$	−49.5967	−	36.0341i	−1.57708	−	1.14582i
$990$		0			0
$991$	−22.5623			−0.716715			−0.358358	−	0.933584i	$-0.616663\pi$
$991$	−22.5623			−0.716715			−0.358358	+	0.933584i	$0.616663\pi$
$992$	3.30902	+	4.47777i	0.105061	+	0.142169i
$993$		0			0
$994$	−6.23607	+	4.53077i	−0.197796	+	0.143707i
$995$	2.04508	+	1.48584i	0.0648336	+	0.0471043i
$996$		0			0
$997$	44.8328			1.41987			0.709935	−	0.704267i	$-0.248724\pi$
$997$	44.8328			1.41987			0.709935	+	0.704267i	$0.248724\pi$
$998$	9.41641			0.298071
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.i.b.109.1		4
3.2	odd	2		186.2.f.a.109.1	✓	4
31.2	even	5	inner	558.2.i.b.343.1		4
93.2	odd	10		186.2.f.a.157.1	yes	4
93.8	odd	10		5766.2.a.q.1.1		2
93.23	even	10		5766.2.a.m.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.f.a.109.1	✓	4	3.2	odd	2
186.2.f.a.157.1	yes	4	93.2	odd	10
558.2.i.b.109.1		4	1.1	even	1	trivial
558.2.i.b.343.1		4	31.2	even	5	inner
5766.2.a.m.1.1		2	93.23	even	10
5766.2.a.q.1.1		2	93.8	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:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +0.618034 q^{5} +(1.19098 - 3.66547i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.500000 + 0.363271i) q^{10} +(-0.427051 + 1.31433i) q^{11} +(-0.618034 - 0.449028i) q^{13} +(1.19098 + 3.66547i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-1.23607 - 3.80423i) q^{17} +(2.00000 - 1.45309i) q^{19} +(0.190983 - 0.587785i) q^{20} +(-0.427051 - 1.31433i) q^{22} +(-2.61803 - 8.05748i) q^{23} -4.61803 q^{25} +0.763932 q^{26} +(-3.11803 - 2.26538i) q^{28} +(-1.30902 + 0.951057i) q^{29} +(3.30902 + 4.47777i) q^{31} +1.00000 q^{32} +(3.23607 + 2.35114i) q^{34} +(0.736068 - 2.26538i) q^{35} +6.76393 q^{37} +(-0.763932 + 2.35114i) q^{38} +(0.190983 + 0.587785i) q^{40} +(6.47214 - 4.70228i) q^{41} +(5.85410 - 4.25325i) q^{43} +(1.11803 + 0.812299i) q^{44} +(6.85410 + 4.97980i) q^{46} +(-1.23607 - 0.898056i) q^{47} +(-6.35410 - 4.61653i) q^{49} +(3.73607 - 2.71441i) q^{50} +(-0.618034 + 0.449028i) q^{52} +(-0.736068 - 2.26538i) q^{53} +(-0.263932 + 0.812299i) q^{55} +3.85410 q^{56} +(0.500000 - 1.53884i) q^{58} +(6.54508 + 4.75528i) q^{59} -11.2361 q^{61} +(-5.30902 - 1.67760i) q^{62} +(-0.809017 + 0.587785i) q^{64} +(-0.381966 - 0.277515i) q^{65} +10.9443 q^{67} -4.00000 q^{68} +(0.736068 + 2.26538i) q^{70} +(0.618034 + 1.90211i) q^{71} +(-0.736068 + 2.26538i) q^{73} +(-5.47214 + 3.97574i) q^{74} +(-0.763932 - 2.35114i) q^{76} +(4.30902 + 3.13068i) q^{77} +(-3.50000 - 10.7719i) q^{79} +(-0.500000 - 0.363271i) q^{80} +(-2.47214 + 7.60845i) q^{82} +(5.23607 - 3.80423i) q^{83} +(-0.763932 - 2.35114i) q^{85} +(-2.23607 + 6.88191i) q^{86} -1.38197 q^{88} +(-0.909830 + 2.80017i) q^{89} +(-2.38197 + 1.73060i) q^{91} -8.47214 q^{92} +1.52786 q^{94} +(1.23607 - 0.898056i) q^{95} +(-2.14590 + 6.60440i) q^{97} +7.85410 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{4} - 2 q^{5} + 7 q^{7} - q^{8} - 2 q^{10} + 5 q^{11} + 2 q^{13} + 7 q^{14} - q^{16} + 4 q^{17} + 8 q^{19} + 3 q^{20} + 5 q^{22} - 6 q^{23} - 14 q^{25} + 12 q^{26} - 8 q^{28} - 3 q^{29}+ \cdots + 18 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^4 - 2 * q^5 + 7 * q^7 - q^8 - 2 * q^10 + 5 * q^11 + 2 * q^13 + 7 * q^14 - q^16 + 4 * q^17 + 8 * q^19 + 3 * q^20 + 5 * q^22 - 6 * q^23 - 14 * q^25 + 12 * q^26 - 8 * q^28 - 3 * q^29 + 11 * q^31 + 4 * q^32 + 4 * q^34 - 6 * q^35 + 36 * q^37 - 12 * q^38 + 3 * q^40 + 8 * q^41 + 10 * q^43 + 14 * q^46 + 4 * q^47 - 12 * q^49 + 6 * q^50 + 2 * q^52 + 6 * q^53 - 10 * q^55 + 2 * q^56 + 2 * q^58 + 15 * q^59 - 36 * q^61 - 19 * q^62 - q^64 - 6 * q^65 + 8 * q^67 - 16 * q^68 - 6 * q^70 - 2 * q^71 + 6 * q^73 - 4 * q^74 - 12 * q^76 + 15 * q^77 - 14 * q^79 - 2 * q^80 + 8 * q^82 + 12 * q^83 - 12 * q^85 - 10 * q^88 - 26 * q^89 - 14 * q^91 - 16 * q^92 + 24 * q^94 - 4 * q^95 - 22 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more