LMFDB - Embedded newform 198.2.f.b.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,2,Mod(37,198)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("198.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	198.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.58103796002$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	198.37
Dual form			198.2.f.b.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-1.11803 + 0.812299i) q^{5} +(0.881966 + 2.71441i) q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-1.11803 + 0.812299i) q^{5} +(0.881966 + 2.71441i) q^{7} +(0.309017 - 0.951057i) q^{8} +1.38197 q^{10} +(1.23607 + 3.07768i) q^{11} +(2.00000 + 1.45309i) q^{13} +(0.881966 - 2.71441i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-1.00000 + 0.726543i) q^{17} +(0.618034 - 1.90211i) q^{19} +(-1.11803 - 0.812299i) q^{20} +(0.809017 - 3.21644i) q^{22} +7.23607 q^{23} +(-0.954915 + 2.93893i) q^{25} +(-0.763932 - 2.35114i) q^{26} +(-2.30902 + 1.67760i) q^{28} +(0.809017 + 2.48990i) q^{29} +(-5.54508 - 4.02874i) q^{31} +1.00000 q^{32} +1.23607 q^{34} +(-3.19098 - 2.31838i) q^{35} +(-3.00000 - 9.23305i) q^{37} +(-1.61803 + 1.17557i) q^{38} +(0.427051 + 1.31433i) q^{40} +(-3.47214 + 10.6861i) q^{41} +(-2.54508 + 2.12663i) q^{44} +(-5.85410 - 4.25325i) q^{46} +(2.85410 - 8.78402i) q^{47} +(-0.927051 + 0.673542i) q^{49} +(2.50000 - 1.81636i) q^{50} +(-0.763932 + 2.35114i) q^{52} +(-9.39919 - 6.82891i) q^{53} +(-3.88197 - 2.43690i) q^{55} +2.85410 q^{56} +(0.809017 - 2.48990i) q^{58} +(-1.02786 - 3.16344i) q^{59} +(-5.85410 + 4.25325i) q^{61} +(2.11803 + 6.51864i) q^{62} +(-0.809017 - 0.587785i) q^{64} -3.41641 q^{65} +6.94427 q^{67} +(-1.00000 - 0.726543i) q^{68} +(1.21885 + 3.75123i) q^{70} +(4.23607 - 3.07768i) q^{71} +(-1.42705 - 4.39201i) q^{73} +(-3.00000 + 9.23305i) q^{74} +2.00000 q^{76} +(-7.26393 + 6.06961i) q^{77} +(11.2082 + 8.14324i) q^{79} +(0.427051 - 1.31433i) q^{80} +(9.09017 - 6.60440i) q^{82} +(13.5902 - 9.87384i) q^{83} +(0.527864 - 1.62460i) q^{85} +(3.30902 - 0.224514i) q^{88} +16.1803 q^{89} +(-2.18034 + 6.71040i) q^{91} +(2.23607 + 6.88191i) q^{92} +(-7.47214 + 5.42882i) q^{94} +(0.854102 + 2.62866i) q^{95} +(11.2082 + 8.14324i) q^{97} +1.14590 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - q^{4} + 8 q^{7} - q^{8}+O(q^{10}) $ 4 * q - q^2 - q^4 + 8 * q^7 - q^8	$ 4 q - q^{2} - q^{4} + 8 q^{7} - q^{8} + 10 q^{10} - 4 q^{11} + 8 q^{13} + 8 q^{14} - q^{16} - 4 q^{17} - 2 q^{19} + q^{22} + 20 q^{23} - 15 q^{25} - 12 q^{26} - 7 q^{28} + q^{29} - 11 q^{31} + 4 q^{32} - 4 q^{34} - 15 q^{35} - 12 q^{37} - 2 q^{38} - 5 q^{40} + 4 q^{41} + q^{44} - 10 q^{46} - 2 q^{47} + 3 q^{49} + 10 q^{50} - 12 q^{52} - 13 q^{53} - 20 q^{55} - 2 q^{56} + q^{58} - 22 q^{59} - 10 q^{61} + 4 q^{62} - q^{64} + 40 q^{65} - 8 q^{67} - 4 q^{68} + 25 q^{70} + 8 q^{71} + q^{73} - 12 q^{74} + 8 q^{76} - 38 q^{77} + 18 q^{79} - 5 q^{80} + 14 q^{82} + 32 q^{83} + 20 q^{85} + 11 q^{88} + 20 q^{89} + 36 q^{91} - 12 q^{94} - 10 q^{95} + 18 q^{97} + 18 q^{98}+O(q^{100}) $ 4 * q - q^2 - q^4 + 8 * q^7 - q^8 + 10 * q^10 - 4 * q^11 + 8 * q^13 + 8 * q^14 - q^16 - 4 * q^17 - 2 * q^19 + q^22 + 20 * q^23 - 15 * q^25 - 12 * q^26 - 7 * q^28 + q^29 - 11 * q^31 + 4 * q^32 - 4 * q^34 - 15 * q^35 - 12 * q^37 - 2 * q^38 - 5 * q^40 + 4 * q^41 + q^44 - 10 * q^46 - 2 * q^47 + 3 * q^49 + 10 * q^50 - 12 * q^52 - 13 * q^53 - 20 * q^55 - 2 * q^56 + q^58 - 22 * q^59 - 10 * q^61 + 4 * q^62 - q^64 + 40 * q^65 - 8 * q^67 - 4 * q^68 + 25 * q^70 + 8 * q^71 + q^73 - 12 * q^74 + 8 * q^76 - 38 * q^77 + 18 * q^79 - 5 * q^80 + 14 * q^82 + 32 * q^83 + 20 * q^85 + 11 * q^88 + 20 * q^89 + 36 * q^91 - 12 * q^94 - 10 * q^95 + 18 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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
$5$	−1.11803	+	0.812299i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$5$	−1.11803	+	0.812299i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$6$		0			0
$7$	0.881966	+	2.71441i	0.333352	+	1.02595i	0.967528	+	0.252763i	$0.0813393\pi$
$7$	0.881966	+	2.71441i	0.333352	+	1.02595i	−0.634176	+	0.773188i	$0.718661\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$		0			0
$10$	1.38197			0.437016
$11$	1.23607	+	3.07768i	0.372689	+	0.927957i
$11$	1.23607	+	3.07768i	0.372689	+	0.927957i
$12$		0			0
$13$	2.00000	+	1.45309i	0.554700	+	0.403013i	0.829515	−	0.558484i	$-0.188617\pi$
$13$	2.00000	+	1.45309i	0.554700	+	0.403013i	−0.274815	+	0.961497i	$0.588617\pi$
$14$	0.881966	−	2.71441i	0.235715	−	0.725457i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.00000	+	0.726543i	−0.242536	+	0.176212i	−0.702412	−	0.711770i	$-0.747894\pi$
$17$	−1.00000	+	0.726543i	−0.242536	+	0.176212i	0.459877	+	0.887983i	$0.347894\pi$
$18$		0			0
$19$	0.618034	−	1.90211i	0.141787	−	0.436375i	−0.854797	−	0.518962i	$-0.826318\pi$
$19$	0.618034	−	1.90211i	0.141787	−	0.436375i	0.996584	+	0.0825877i	$0.0263185\pi$
$20$	−1.11803	−	0.812299i	−0.250000	−	0.181636i
$21$		0			0
$22$	0.809017	−	3.21644i	0.172483	−	0.685747i
$23$	7.23607			1.50882			0.754412	−	0.656401i	$-0.227922\pi$
$23$	7.23607			1.50882			0.754412	+	0.656401i	$0.227922\pi$
$24$		0			0
$25$	−0.954915	+	2.93893i	−0.190983	+	0.587785i
$26$	−0.763932	−	2.35114i	−0.149819	−	0.461097i
$27$		0			0
$28$	−2.30902	+	1.67760i	−0.436363	+	0.317036i
$29$	0.809017	+	2.48990i	0.150231	+	0.462363i	0.997646	−	0.0685673i	$-0.0218428\pi$
$29$	0.809017	+	2.48990i	0.150231	+	0.462363i	−0.847416	+	0.530930i	$0.821843\pi$
$30$		0			0
$31$	−5.54508	−	4.02874i	−0.995927	−	0.723583i	−0.0347157	−	0.999397i	$-0.511053\pi$
$31$	−5.54508	−	4.02874i	−0.995927	−	0.723583i	−0.961211	+	0.275814i	$0.911053\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	1.23607			0.211984
$35$	−3.19098	−	2.31838i	−0.539375	−	0.391879i
$36$		0			0
$37$	−3.00000	−	9.23305i	−0.493197	−	1.51790i	−0.819748	−	0.572725i	$-0.805886\pi$
$37$	−3.00000	−	9.23305i	−0.493197	−	1.51790i	0.326551	−	0.945180i	$-0.394114\pi$
$38$	−1.61803	+	1.17557i	−0.262480	+	0.190703i
$39$		0			0
$40$	0.427051	+	1.31433i	0.0675227	+	0.207813i
$41$	−3.47214	+	10.6861i	−0.542257	+	1.66889i	0.185168	+	0.982707i	$0.440717\pi$
$41$	−3.47214	+	10.6861i	−0.542257	+	1.66889i	−0.727425	+	0.686187i	$0.759283\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	−2.54508	+	2.12663i	−0.383686	+	0.320601i
$45$		0			0
$46$	−5.85410	−	4.25325i	−0.863140	−	0.627108i
$47$	2.85410	−	8.78402i	0.416314	−	1.28128i	−0.494757	−	0.869031i	$-0.664743\pi$
$47$	2.85410	−	8.78402i	0.416314	−	1.28128i	0.911071	−	0.412250i	$-0.135257\pi$
$48$		0			0
$49$	−0.927051	+	0.673542i	−0.132436	+	0.0962203i
$50$	2.50000	−	1.81636i	0.353553	−	0.256872i
$51$		0			0
$52$	−0.763932	+	2.35114i	−0.105938	+	0.326045i
$53$	−9.39919	−	6.82891i	−1.29108	−	0.938023i	−0.291251	−	0.956647i	$-0.594071\pi$
$53$	−9.39919	−	6.82891i	−1.29108	−	0.938023i	−0.999827	+	0.0186239i	$0.994071\pi$
$54$		0			0
$55$	−3.88197	−	2.43690i	−0.523444	−	0.328591i
$56$	2.85410			0.381395
$57$		0			0
$58$	0.809017	−	2.48990i	0.106229	−	0.326940i
$59$	−1.02786	−	3.16344i	−0.133817	−	0.411845i	0.861588	−	0.507609i	$-0.169471\pi$
$59$	−1.02786	−	3.16344i	−0.133817	−	0.411845i	−0.995404	+	0.0957642i	$0.969471\pi$
$60$		0			0
$61$	−5.85410	+	4.25325i	−0.749541	+	0.544573i	−0.895685	−	0.444690i	$-0.853314\pi$
$61$	−5.85410	+	4.25325i	−0.749541	+	0.544573i	0.146144	+	0.989263i	$0.453314\pi$
$62$	2.11803	+	6.51864i	0.268991	+	0.827868i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−3.41641			−0.423753
$66$		0			0
$67$	6.94427			0.848378			0.424189	−	0.905574i	$-0.360559\pi$
$67$	6.94427			0.848378			0.424189	+	0.905574i	$0.360559\pi$
$68$	−1.00000	−	0.726543i	−0.121268	−	0.0881062i
$69$		0			0
$70$	1.21885	+	3.75123i	0.145680	+	0.448357i
$71$	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	$0.199435\pi$
$72$		0			0
$73$	−1.42705	−	4.39201i	−0.167024	−	0.514046i	0.832156	−	0.554542i	$-0.187106\pi$
$73$	−1.42705	−	4.39201i	−0.167024	−	0.514046i	−0.999180	+	0.0404955i	$0.987106\pi$
$74$	−3.00000	+	9.23305i	−0.348743	+	1.07332i
$75$		0			0
$76$	2.00000			0.229416
$77$	−7.26393	+	6.06961i	−0.827802	+	0.691696i
$78$		0			0
$79$	11.2082	+	8.14324i	1.26102	+	0.916186i	0.998807	−	0.0488240i	$-0.0155473\pi$
$79$	11.2082	+	8.14324i	1.26102	+	0.916186i	0.262214	+	0.965010i	$0.415547\pi$
$80$	0.427051	−	1.31433i	0.0477458	−	0.146946i
$81$		0			0
$82$	9.09017	−	6.60440i	1.00384	−	0.729333i
$83$	13.5902	−	9.87384i	1.49171	−	1.08379i	0.518176	−	0.855274i	$-0.326611\pi$
$83$	13.5902	−	9.87384i	1.49171	−	1.08379i	0.973539	−	0.228520i	$-0.0733887\pi$
$84$		0			0
$85$	0.527864	−	1.62460i	0.0572549	−	0.176212i
$86$		0			0
$87$		0			0
$88$	3.30902	−	0.224514i	0.352742	−	0.0239333i
$89$	16.1803			1.71511			0.857556	−	0.514390i	$-0.171982\pi$
$89$	16.1803			1.71511			0.857556	+	0.514390i	$0.171982\pi$
$90$		0			0
$91$	−2.18034	+	6.71040i	−0.228562	+	0.703441i
$92$	2.23607	+	6.88191i	0.233126	+	0.717489i
$93$		0			0
$94$	−7.47214	+	5.42882i	−0.770692	+	0.559940i
$95$	0.854102	+	2.62866i	0.0876290	+	0.269694i
$96$		0			0
$97$	11.2082	+	8.14324i	1.13802	+	0.826820i	0.986842	−	0.161686i	$-0.0516932\pi$
$97$	11.2082	+	8.14324i	1.13802	+	0.826820i	0.151178	+	0.988506i	$0.451693\pi$
$98$	1.14590			0.115753
$99$		0			0
$100$	−3.09017			−0.309017
$101$	−13.8262	−	10.0453i	−1.37576	−	0.999550i	−0.997262	−	0.0739484i	$-0.976440\pi$
$101$	−13.8262	−	10.0453i	−1.37576	−	0.999550i	−0.378500	−	0.925601i	$-0.623560\pi$
$102$		0			0
$103$	−0.354102	−	1.08981i	−0.0348907	−	0.107383i	0.932094	−	0.362215i	$-0.117980\pi$
$103$	−0.354102	−	1.08981i	−0.0348907	−	0.107383i	−0.966985	+	0.254833i	$0.917980\pi$
$104$	2.00000	−	1.45309i	0.196116	−	0.142487i
$105$		0			0
$106$	3.59017	+	11.0494i	0.348708	+	1.07321i
$107$	−2.20820	+	6.79615i	−0.213475	+	0.657009i	0.785783	+	0.618502i	$0.212260\pi$
$107$	−2.20820	+	6.79615i	−0.213475	+	0.657009i	−0.999258	+	0.0385069i	$0.987740\pi$
$108$		0			0
$109$	9.23607			0.884655			0.442327	−	0.896854i	$-0.354153\pi$
$109$	9.23607			0.884655			0.442327	+	0.896854i	$0.354153\pi$
$110$	1.70820	+	4.25325i	0.162871	+	0.405532i
$111$		0			0
$112$	−2.30902	−	1.67760i	−0.218182	−	0.158518i
$113$	1.14590	−	3.52671i	0.107797	−	0.331765i	−0.882580	−	0.470163i	$-0.844195\pi$
$113$	1.14590	−	3.52671i	0.107797	−	0.331765i	0.990377	+	0.138398i	$0.0441952\pi$
$114$		0			0
$115$	−8.09017	+	5.87785i	−0.754412	+	0.548113i
$116$	−2.11803	+	1.53884i	−0.196655	+	0.142878i
$117$		0			0
$118$	−1.02786	+	3.16344i	−0.0946226	+	0.291218i
$119$	−2.85410	−	2.07363i	−0.261635	−	0.190089i
$120$		0			0
$121$	−7.94427	+	7.60845i	−0.722207	+	0.691677i
$122$	7.23607			0.655123
$123$		0			0
$124$	2.11803	−	6.51864i	0.190205	−	0.585391i
$125$	−3.45492	−	10.6331i	−0.309017	−	0.951057i
$126$		0			0
$127$	13.7082	−	9.95959i	1.21641	−	0.883771i	0.220610	−	0.975362i	$-0.429195\pi$
$127$	13.7082	−	9.95959i	1.21641	−	0.883771i	0.995797	+	0.0915912i	$0.0291953\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$		0			0
$130$	2.76393	+	2.00811i	0.242413	+	0.176123i
$131$	0.0901699			0.00787818			0.00393909	−	0.999992i	$-0.498746\pi$
$131$	0.0901699			0.00787818			0.00393909	+	0.999992i	$0.498746\pi$
$132$		0			0
$133$	5.70820			0.494964
$134$	−5.61803	−	4.08174i	−0.485324	−	0.352609i
$135$		0			0
$136$	0.381966	+	1.17557i	0.0327533	+	0.100804i
$137$	−6.09017	+	4.42477i	−0.520318	+	0.378033i	−0.816724	−	0.577029i	$-0.804212\pi$
$137$	−6.09017	+	4.42477i	−0.520318	+	0.378033i	0.296405	+	0.955062i	$0.404212\pi$
$138$		0			0
$139$	−3.00000	−	9.23305i	−0.254457	−	0.783137i	−0.993936	−	0.109958i	$-0.964928\pi$
$139$	−3.00000	−	9.23305i	−0.254457	−	0.783137i	0.739480	−	0.673179i	$-0.235072\pi$
$140$	1.21885	−	3.75123i	0.103011	−	0.317036i
$141$		0			0
$142$	−5.23607			−0.439401
$143$	−2.00000	+	7.95148i	−0.167248	+	0.664936i
$144$		0			0
$145$	−2.92705	−	2.12663i	−0.243078	−	0.176607i
$146$	−1.42705	+	4.39201i	−0.118104	+	0.363485i
$147$		0			0
$148$	7.85410	−	5.70634i	0.645603	−	0.469058i
$149$	−6.78115	+	4.92680i	−0.555534	+	0.403619i	−0.829822	−	0.558029i	$-0.811558\pi$
$149$	−6.78115	+	4.92680i	−0.555534	+	0.403619i	0.274288	+	0.961648i	$0.411558\pi$
$150$		0			0
$151$	−1.89919	+	5.84510i	−0.154554	+	0.475667i	−0.998115	−	0.0613650i	$-0.980455\pi$
$151$	−1.89919	+	5.84510i	−0.154554	+	0.475667i	0.843562	+	0.537032i	$0.180455\pi$
$152$	−1.61803	−	1.17557i	−0.131240	−	0.0953514i
$153$		0			0
$154$	9.44427	−	0.640786i	0.761041	−	0.0516360i
$155$	9.47214			0.760820
$156$		0			0
$157$	0.708204	−	2.17963i	0.0565208	−	0.173953i	−0.918811	−	0.394699i	$-0.870849\pi$
$157$	0.708204	−	2.17963i	0.0565208	−	0.173953i	0.975331	+	0.220745i	$0.0708490\pi$
$158$	−4.28115	−	13.1760i	−0.340590	−	1.04823i
$159$		0			0
$160$	−1.11803	+	0.812299i	−0.0883883	+	0.0642179i
$161$	6.38197	+	19.6417i	0.502969	+	1.54798i
$162$		0			0
$163$	−11.2361	−	8.16348i	−0.880077	−	0.639413i	0.0531950	−	0.998584i	$-0.483060\pi$
$163$	−11.2361	−	8.16348i	−0.880077	−	0.639413i	−0.933272	+	0.359171i	$0.883060\pi$
$164$	−11.2361			−0.877390
$165$		0			0
$166$	−16.7984			−1.30381
$167$	−8.61803	−	6.26137i	−0.666883	−	0.484519i	0.202097	−	0.979366i	$-0.435224\pi$
$167$	−8.61803	−	6.26137i	−0.666883	−	0.484519i	−0.868981	+	0.494846i	$0.835224\pi$
$168$		0			0
$169$	−2.12868	−	6.55139i	−0.163744	−	0.503953i
$170$	−1.38197	+	1.00406i	−0.105992	+	0.0770077i
$171$		0			0
$172$		0			0
$173$	1.82624	−	5.62058i	0.138846	−	0.427325i	−0.857322	−	0.514780i	$-0.827874\pi$
$173$	1.82624	−	5.62058i	0.138846	−	0.427325i	0.996168	+	0.0874553i	$0.0278735\pi$
$174$		0			0
$175$	−8.81966			−0.666704
$176$	−2.80902	−	1.76336i	−0.211738	−	0.132918i
$177$		0			0
$178$	−13.0902	−	9.51057i	−0.981150	−	0.712847i
$179$	1.48278	−	4.56352i	0.110828	−	0.341094i	−0.880226	−	0.474555i	$-0.842609\pi$
$179$	1.48278	−	4.56352i	0.110828	−	0.341094i	0.991054	+	0.133461i	$0.0426091\pi$
$180$		0			0
$181$	−16.4721	+	11.9677i	−1.22436	+	0.889553i	−0.996455	−	0.0841297i	$-0.973189\pi$
$181$	−16.4721	+	11.9677i	−1.22436	+	0.889553i	−0.227909	+	0.973682i	$0.573189\pi$
$182$	5.70820	−	4.14725i	0.423120	−	0.307415i
$183$		0			0
$184$	2.23607	−	6.88191i	0.164845	−	0.507341i
$185$	10.8541	+	7.88597i	0.798009	+	0.579788i
$186$		0			0
$187$	−3.47214	−	2.17963i	−0.253908	−	0.159390i
$188$	9.23607			0.673609
$189$		0			0
$190$	0.854102	−	2.62866i	0.0619631	−	0.190703i
$191$	3.32624	+	10.2371i	0.240678	+	0.740731i	0.996317	+	0.0857430i	$0.0273264\pi$
$191$	3.32624	+	10.2371i	0.240678	+	0.740731i	−0.755639	+	0.654988i	$0.772674\pi$
$192$		0			0
$193$	10.3992	−	7.55545i	0.748550	−	0.543853i	−0.146827	−	0.989162i	$-0.546906\pi$
$193$	10.3992	−	7.55545i	0.748550	−	0.543853i	0.895377	+	0.445309i	$0.146906\pi$
$194$	−4.28115	−	13.1760i	−0.307369	−	0.945984i
$195$		0			0
$196$	−0.927051	−	0.673542i	−0.0662179	−	0.0481101i
$197$	2.61803			0.186527			0.0932636	−	0.995641i	$-0.470270\pi$
$197$	2.61803			0.186527			0.0932636	+	0.995641i	$0.470270\pi$
$198$		0			0
$199$	−14.7984			−1.04903			−0.524514	−	0.851402i	$-0.675753\pi$
$199$	−14.7984			−1.04903			−0.524514	+	0.851402i	$0.675753\pi$
$200$	2.50000	+	1.81636i	0.176777	+	0.128436i
$201$		0			0
$202$	5.28115	+	16.2537i	0.371581	+	1.14361i
$203$	−6.04508	+	4.39201i	−0.424282	+	0.308259i
$204$		0			0
$205$	−4.79837	−	14.7679i	−0.335133	−	1.03143i
$206$	−0.354102	+	1.08981i	−0.0246715	+	0.0759309i
$207$		0			0
$208$	−2.47214			−0.171412
$209$	6.61803	−	0.449028i	0.457779	−	0.0310599i
$210$		0			0
$211$	8.85410	+	6.43288i	0.609542	+	0.442858i	0.849253	−	0.527986i	$-0.177053\pi$
$211$	8.85410	+	6.43288i	0.609542	+	0.442858i	−0.239711	+	0.970844i	$0.577053\pi$
$212$	3.59017	−	11.0494i	0.246574	−	0.758876i
$213$		0			0
$214$	5.78115	−	4.20025i	0.395191	−	0.287123i
$215$		0			0
$216$		0			0
$217$	6.04508	−	18.6049i	0.410367	−	1.26298i
$218$	−7.47214	−	5.42882i	−0.506077	−	0.367686i
$219$		0			0
$220$	1.11803	−	4.44501i	0.0753778	−	0.299683i
$221$	−3.05573			−0.205551
$222$		0			0
$223$	0.663119	−	2.04087i	0.0444057	−	0.136667i	−0.926396	−	0.376552i	$-0.877110\pi$
$223$	0.663119	−	2.04087i	0.0444057	−	0.136667i	0.970801	+	0.239885i	$0.0771097\pi$
$224$	0.881966	+	2.71441i	0.0589288	+	0.181364i
$225$		0			0
$226$	−3.00000	+	2.17963i	−0.199557	+	0.144987i
$227$	0.336881	+	1.03681i	0.0223596	+	0.0688157i	0.961614	−	0.274407i	$-0.0884815\pi$
$227$	0.336881	+	1.03681i	0.0223596	+	0.0688157i	−0.939254	+	0.343223i	$0.888481\pi$
$228$		0			0
$229$	3.47214	+	2.52265i	0.229445	+	0.166702i	0.696568	−	0.717491i	$-0.254709\pi$
$229$	3.47214	+	2.52265i	0.229445	+	0.166702i	−0.467123	+	0.884192i	$0.654709\pi$
$230$	10.0000			0.659380
$231$		0			0
$232$	2.61803			0.171882
$233$	17.7082	+	12.8658i	1.16010	+	0.842864i	0.989791	−	0.142526i	$-0.0455225\pi$
$233$	17.7082	+	12.8658i	1.16010	+	0.842864i	0.170312	+	0.985390i	$0.445522\pi$
$234$		0			0
$235$	3.94427	+	12.1392i	0.257296	+	0.791875i
$236$	2.69098	−	1.95511i	0.175168	−	0.127267i
$237$		0			0
$238$	1.09017	+	3.35520i	0.0706652	+	0.217485i
$239$	−4.14590	+	12.7598i	−0.268176	+	0.825360i	0.722769	+	0.691090i	$0.242869\pi$
$239$	−4.14590	+	12.7598i	−0.268176	+	0.825360i	−0.990945	+	0.134271i	$0.957131\pi$
$240$		0			0
$241$	−27.5066			−1.77185			−0.885927	−	0.463824i	$-0.846477\pi$
$241$	−27.5066			−1.77185			−0.885927	+	0.463824i	$0.846477\pi$
$242$	10.8992	−	1.48584i	0.700626	−	0.0955135i
$243$		0			0
$244$	−5.85410	−	4.25325i	−0.374770	−	0.272287i
$245$	0.489357	−	1.50609i	0.0312639	−	0.0962203i
$246$		0			0
$247$	4.00000	−	2.90617i	0.254514	−	0.184915i
$248$	−5.54508	+	4.02874i	−0.352113	+	0.255825i
$249$		0			0
$250$	−3.45492	+	10.6331i	−0.218508	+	0.672499i
$251$	−3.88197	−	2.82041i	−0.245028	−	0.178023i	0.458493	−	0.888698i	$-0.348390\pi$
$251$	−3.88197	−	2.82041i	−0.245028	−	0.178023i	−0.703520	+	0.710675i	$0.748390\pi$
$252$		0			0
$253$	8.94427	+	22.2703i	0.562322	+	1.40012i
$254$	−16.9443			−1.06318
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	0.909830	+	2.80017i	0.0567536	+	0.174670i	0.975415	−	0.220376i	$-0.0707286\pi$
$257$	0.909830	+	2.80017i	0.0567536	+	0.174670i	−0.918661	+	0.395046i	$0.870729\pi$
$258$		0			0
$259$	22.4164	−	16.2865i	1.39289	−	1.01199i
$260$	−1.05573	−	3.24920i	−0.0654735	−	0.201507i
$261$		0			0
$262$	−0.0729490	−	0.0530006i	−0.00450681	−	0.00327439i
$263$	−2.94427			−0.181552			−0.0907758	−	0.995871i	$-0.528935\pi$
$263$	−2.94427			−0.181552			−0.0907758	+	0.995871i	$0.528935\pi$
$264$		0			0
$265$	16.0557			0.986296
$266$	−4.61803	−	3.35520i	−0.283150	−	0.205720i
$267$		0			0
$268$	2.14590	+	6.60440i	0.131082	+	0.403428i
$269$	8.85410	−	6.43288i	0.539844	−	0.392220i	−0.284183	−	0.958770i	$-0.591722\pi$
$269$	8.85410	−	6.43288i	0.539844	−	0.392220i	0.824027	+	0.566550i	$0.191722\pi$
$270$		0			0
$271$	1.05573	+	3.24920i	0.0641309	+	0.197375i	0.977988	−	0.208662i	$-0.0669107\pi$
$271$	1.05573	+	3.24920i	0.0641309	+	0.197375i	−0.913857	+	0.406036i	$0.866911\pi$
$272$	0.381966	−	1.17557i	0.0231601	−	0.0712794i
$273$		0			0
$274$	7.52786			0.454775
$275$	−10.2254	+	0.693786i	−0.616616	+	0.0418369i
$276$		0			0
$277$	11.3262	+	8.22899i	0.680528	+	0.494432i	0.873533	−	0.486765i	$-0.161823\pi$
$277$	11.3262	+	8.22899i	0.680528	+	0.494432i	−0.193005	+	0.981198i	$0.561823\pi$
$278$	−3.00000	+	9.23305i	−0.179928	+	0.553762i
$279$		0			0
$280$	−3.19098	+	2.31838i	−0.190698	+	0.138550i
$281$	7.23607	−	5.25731i	0.431668	−	0.313625i	−0.350648	−	0.936507i	$-0.614039\pi$
$281$	7.23607	−	5.25731i	0.431668	−	0.313625i	0.782315	+	0.622883i	$0.214039\pi$
$282$		0			0
$283$	−4.41641	+	13.5923i	−0.262528	+	0.807979i	0.729724	+	0.683741i	$0.239648\pi$
$283$	−4.41641	+	13.5923i	−0.262528	+	0.807979i	−0.992253	+	0.124237i	$0.960352\pi$
$284$	4.23607	+	3.07768i	0.251364	+	0.182627i
$285$		0			0
$286$	6.29180	−	5.25731i	0.372042	−	0.310871i
$287$	−32.0689			−1.89297
$288$		0			0
$289$	−4.78115	+	14.7149i	−0.281244	+	0.865581i
$290$	1.11803	+	3.44095i	0.0656532	+	0.202060i
$291$		0			0
$292$	3.73607	−	2.71441i	0.218637	−	0.158849i
$293$	−8.40983	−	25.8828i	−0.491308	−	1.51209i	−0.822633	−	0.568573i	$-0.807496\pi$
$293$	−8.40983	−	25.8828i	−0.491308	−	1.51209i	0.331326	−	0.943516i	$-0.392504\pi$
$294$		0			0
$295$	3.71885	+	2.70190i	0.216520	+	0.157311i
$296$	−9.70820			−0.564278
$297$		0			0
$298$	8.38197			0.485554
$299$	14.4721	+	10.5146i	0.836945	+	0.608076i
$300$		0			0
$301$		0			0
$302$	4.97214	−	3.61247i	0.286114	−	0.207874i
$303$		0			0
$304$	0.618034	+	1.90211i	0.0354467	+	0.109094i
$305$	3.09017	−	9.51057i	0.176943	−	0.544573i
$306$		0			0
$307$	24.3607			1.39034			0.695169	−	0.718847i	$-0.255330\pi$
$307$	24.3607			1.39034			0.695169	+	0.718847i	$0.255330\pi$
$308$	−8.01722	−	5.03280i	−0.456824	−	0.286770i
$309$		0			0
$310$	−7.66312	−	5.56758i	−0.435236	−	0.316217i
$311$	−2.09017	+	6.43288i	−0.118523	+	0.364775i	−0.992665	−	0.120894i	$-0.961424\pi$
$311$	−2.09017	+	6.43288i	−0.118523	+	0.364775i	0.874143	+	0.485669i	$0.161424\pi$
$312$		0			0
$313$	−3.50000	+	2.54290i	−0.197832	+	0.143733i	−0.682291	−	0.731081i	$-0.739016\pi$
$313$	−3.50000	+	2.54290i	−0.197832	+	0.143733i	0.484459	+	0.874814i	$0.339016\pi$
$314$	−1.85410	+	1.34708i	−0.104633	+	0.0760203i
$315$		0			0
$316$	−4.28115	+	13.1760i	−0.240834	+	0.741210i
$317$	−16.8541	−	12.2452i	−0.946621	−	0.687760i	0.00338452	−	0.999994i	$-0.498923\pi$
$317$	−16.8541	−	12.2452i	−0.946621	−	0.687760i	−0.950005	+	0.312234i	$0.898923\pi$
$318$		0			0
$319$	−6.66312	+	5.56758i	−0.373063	+	0.311725i
$320$	1.38197			0.0772542
$321$		0			0
$322$	6.38197	−	19.6417i	0.355653	−	1.09459i
$323$	0.763932	+	2.35114i	0.0425063	+	0.130821i
$324$		0			0
$325$	−6.18034	+	4.49028i	−0.342824	+	0.249076i
$326$	4.29180	+	13.2088i	0.237701	+	0.731567i
$327$		0			0
$328$	9.09017	+	6.60440i	0.501921	+	0.364667i
$329$	26.3607			1.45331
$330$		0			0
$331$	−21.7082			−1.19319			−0.596595	−	0.802542i	$-0.703480\pi$
$331$	−21.7082			−1.19319			−0.596595	+	0.802542i	$0.703480\pi$
$332$	13.5902	+	9.87384i	0.745857	+	0.541897i
$333$		0			0
$334$	3.29180	+	10.1311i	0.180119	+	0.554349i
$335$	−7.76393	+	5.64083i	−0.424189	+	0.308191i
$336$		0			0
$337$	1.56231	+	4.80828i	0.0851042	+	0.261924i	0.984549	−	0.175111i	$-0.0560285\pi$
$337$	1.56231	+	4.80828i	0.0851042	+	0.261924i	−0.899444	+	0.437035i	$0.856029\pi$
$338$	−2.12868	+	6.55139i	−0.115785	+	0.356349i
$339$		0			0
$340$	1.70820			0.0926404
$341$	5.54508	−	22.0458i	0.300283	−	1.19385i
$342$		0			0
$343$	13.5172	+	9.82084i	0.729861	+	0.530275i
$344$		0			0
$345$		0			0
$346$	−4.78115	+	3.47371i	−0.257036	+	0.186748i
$347$	−24.8713	+	18.0701i	−1.33516	+	0.970052i	−0.335556	+	0.942020i	$0.608924\pi$
$347$	−24.8713	+	18.0701i	−1.33516	+	0.970052i	−0.999607	+	0.0280320i	$0.991076\pi$
$348$		0			0
$349$	6.38197	−	19.6417i	0.341619	−	1.05139i	−0.621750	−	0.783216i	$-0.713578\pi$
$349$	6.38197	−	19.6417i	0.341619	−	1.05139i	0.963369	−	0.268179i	$-0.0864219\pi$
$350$	7.13525	+	5.18407i	0.381395	+	0.277100i
$351$		0			0
$352$	1.23607	+	3.07768i	0.0658826	+	0.164041i
$353$	−6.65248			−0.354076			−0.177038	−	0.984204i	$-0.556651\pi$
$353$	−6.65248			−0.354076			−0.177038	+	0.984204i	$0.556651\pi$
$354$		0			0
$355$	−2.23607	+	6.88191i	−0.118678	+	0.365254i
$356$	5.00000	+	15.3884i	0.264999	+	0.815585i
$357$		0			0
$358$	−3.88197	+	2.82041i	−0.205168	+	0.149063i
$359$	−4.14590	−	12.7598i	−0.218812	−	0.673434i	−0.998861	−	0.0477158i	$-0.984806\pi$
$359$	−4.14590	−	12.7598i	−0.218812	−	0.673434i	0.780049	−	0.625719i	$-0.215194\pi$
$360$		0			0
$361$	12.1353	+	8.81678i	0.638698	+	0.464041i
$362$	20.3607			1.07013
$363$		0			0
$364$	−7.05573			−0.369821
$365$	5.16312	+	3.75123i	0.270250	+	0.196348i
$366$		0			0
$367$	−7.89919	−	24.3112i	−0.412334	−	1.26903i	−0.914614	−	0.404329i	$-0.867505\pi$
$367$	−7.89919	−	24.3112i	−0.412334	−	1.26903i	0.502279	−	0.864705i	$-0.332495\pi$
$368$	−5.85410	+	4.25325i	−0.305166	+	0.221716i
$369$		0			0
$370$	−4.14590	−	12.7598i	−0.215535	−	0.663348i
$371$	10.2467	−	31.5361i	0.531983	−	1.63727i
$372$		0			0
$373$	−11.7082			−0.606228			−0.303114	−	0.952954i	$-0.598026\pi$
$373$	−11.7082			−0.606228			−0.303114	+	0.952954i	$0.598026\pi$
$374$	1.52786	+	3.80423i	0.0790040	+	0.196712i
$375$		0			0
$376$	−7.47214	−	5.42882i	−0.385346	−	0.279970i
$377$	−2.00000	+	6.15537i	−0.103005	+	0.317018i
$378$		0			0
$379$	20.0902	−	14.5964i	1.03196	−	0.749765i	0.0632621	−	0.997997i	$-0.479850\pi$
$379$	20.0902	−	14.5964i	1.03196	−	0.749765i	0.968701	+	0.248232i	$0.0798496\pi$
$380$	−2.23607	+	1.62460i	−0.114708	+	0.0833401i
$381$		0			0
$382$	3.32624	−	10.2371i	0.170185	−	0.523776i
$383$	22.9443	+	16.6700i	1.17240	+	0.851797i	0.991294	−	0.131667i	$-0.0420331\pi$
$383$	22.9443	+	16.6700i	1.17240	+	0.851797i	0.181104	+	0.983464i	$0.442033\pi$
$384$		0			0
$385$	3.19098	−	12.6865i	0.162628	−	0.646565i
$386$	−12.8541			−0.654257
$387$		0			0
$388$	−4.28115	+	13.1760i	−0.217343	+	0.668912i
$389$	0.145898	+	0.449028i	0.00739732	+	0.0227666i	0.954687	−	0.297612i	$-0.0961900\pi$
$389$	0.145898	+	0.449028i	0.00739732	+	0.0227666i	−0.947290	+	0.320378i	$0.896190\pi$
$390$		0			0
$391$	−7.23607	+	5.25731i	−0.365944	+	0.265874i
$392$	0.354102	+	1.08981i	0.0178849	+	0.0550439i
$393$		0			0
$394$	−2.11803	−	1.53884i	−0.106705	−	0.0775257i
$395$	−19.1459			−0.963335
$396$		0			0
$397$	−4.58359			−0.230044			−0.115022	−	0.993363i	$-0.536694\pi$
$397$	−4.58359			−0.230044			−0.115022	+	0.993363i	$0.536694\pi$
$398$	11.9721	+	8.69827i	0.600109	+	0.436005i
$399$		0			0
$400$	−0.954915	−	2.93893i	−0.0477458	−	0.146946i
$401$	25.0344	−	18.1886i	1.25016	−	0.908295i	0.251929	−	0.967746i	$-0.418935\pi$
$401$	25.0344	−	18.1886i	1.25016	−	0.908295i	0.998231	+	0.0594510i	$0.0189350\pi$
$402$		0			0
$403$	−5.23607	−	16.1150i	−0.260827	−	0.802743i
$404$	5.28115	−	16.2537i	0.262747	−	0.808653i
$405$		0			0
$406$	7.47214			0.370836
$407$	24.7082	−	20.6457i	1.22474	−	1.02337i
$408$		0			0
$409$	−20.2082	−	14.6821i	−0.999231	−	0.725984i	−0.0373081	−	0.999304i	$-0.511878\pi$
$409$	−20.2082	−	14.6821i	−0.999231	−	0.725984i	−0.961923	+	0.273320i	$0.911878\pi$
$410$	−4.79837	+	14.7679i	−0.236975	+	0.729333i
$411$		0			0
$412$	0.927051	−	0.673542i	0.0456725	−	0.0331830i
$413$	7.68034	−	5.58009i	0.377925	−	0.274578i
$414$		0			0
$415$	−7.17376	+	22.0786i	−0.352146	+	1.08379i
$416$	2.00000	+	1.45309i	0.0980581	+	0.0712434i
$417$		0			0
$418$	−5.61803	−	3.52671i	−0.274787	−	0.172497i
$419$	−19.8541			−0.969936			−0.484968	−	0.874532i	$-0.661169\pi$
$419$	−19.8541			−0.969936			−0.484968	+	0.874532i	$0.661169\pi$
$420$		0			0
$421$	7.14590	−	21.9928i	0.348270	−	1.07186i	−0.611540	−	0.791213i	$-0.709450\pi$
$421$	7.14590	−	21.9928i	0.348270	−	1.07186i	0.959810	−	0.280651i	$-0.0905503\pi$
$422$	−3.38197	−	10.4086i	−0.164632	−	0.506684i
$423$		0			0
$424$	−9.39919	+	6.82891i	−0.456465	+	0.331641i
$425$	−1.18034	−	3.63271i	−0.0572549	−	0.176212i
$426$		0			0
$427$	−16.7082	−	12.1392i	−0.808567	−	0.587458i
$428$	−7.14590			−0.345410
$429$		0			0
$430$		0			0
$431$	−7.56231	−	5.49434i	−0.364263	−	0.264653i	0.390565	−	0.920575i	$-0.372280\pi$
$431$	−7.56231	−	5.49434i	−0.364263	−	0.264653i	−0.754828	+	0.655923i	$0.772280\pi$
$432$		0			0
$433$	−3.20820	−	9.87384i	−0.154176	−	0.474506i	0.843900	−	0.536500i	$-0.180254\pi$
$433$	−3.20820	−	9.87384i	−0.154176	−	0.474506i	−0.998077	+	0.0619941i	$0.980254\pi$
$434$	−15.8262	+	11.4984i	−0.759684	+	0.551943i
$435$		0			0
$436$	2.85410	+	8.78402i	0.136687	+	0.420678i
$437$	4.47214	−	13.7638i	0.213931	−	0.658413i
$438$		0			0
$439$	−9.14590			−0.436510			−0.218255	−	0.975892i	$-0.570036\pi$
$439$	−9.14590			−0.436510			−0.218255	+	0.975892i	$0.570036\pi$
$440$	−3.51722	+	2.93893i	−0.167677	+	0.140108i
$441$		0			0
$442$	2.47214	+	1.79611i	0.117588	+	0.0854323i
$443$	−12.7918	+	39.3691i	−0.607757	+	1.87048i	−0.131158	+	0.991362i	$0.541869\pi$
$443$	−12.7918	+	39.3691i	−0.607757	+	1.87048i	−0.476599	+	0.879121i	$0.658131\pi$
$444$		0			0
$445$	−18.0902	+	13.1433i	−0.857556	+	0.623051i
$446$	−1.73607	+	1.26133i	−0.0822052	+	0.0597256i
$447$		0			0
$448$	0.881966	−	2.71441i	0.0416690	−	0.128244i
$449$	22.4164	+	16.2865i	1.05790	+	0.768606i	0.973698	−	0.227843i	$-0.0731672\pi$
$449$	22.4164	+	16.2865i	1.05790	+	0.768606i	0.0841978	+	0.996449i	$0.473167\pi$
$450$		0			0
$451$	−37.1803	+	2.52265i	−1.75075	+	0.118787i
$452$	3.70820			0.174419
$453$		0			0
$454$	0.336881	−	1.03681i	0.0158106	−	0.0486601i
$455$	−3.01316	−	9.27354i	−0.141259	−	0.434750i
$456$		0			0
$457$	−14.2082	+	10.3229i	−0.664632	+	0.482883i	−0.868224	−	0.496173i	$-0.834738\pi$
$457$	−14.2082	+	10.3229i	−0.664632	+	0.482883i	0.203592	+	0.979056i	$0.434738\pi$
$458$	−1.32624	−	4.08174i	−0.0619710	−	0.190727i
$459$		0			0
$460$	−8.09017	−	5.87785i	−0.377206	−	0.274056i
$461$	−23.5279			−1.09580			−0.547901	−	0.836543i	$-0.684573\pi$
$461$	−23.5279			−1.09580			−0.547901	+	0.836543i	$0.684573\pi$
$462$		0			0
$463$	18.2705			0.849103			0.424551	−	0.905404i	$-0.360432\pi$
$463$	18.2705			0.849103			0.424551	+	0.905404i	$0.360432\pi$
$464$	−2.11803	−	1.53884i	−0.0983273	−	0.0714389i
$465$		0			0
$466$	−6.76393	−	20.8172i	−0.313333	−	0.964340i
$467$	−10.2533	+	7.44945i	−0.474466	+	0.344719i	−0.799179	−	0.601093i	$-0.794732\pi$
$467$	−10.2533	+	7.44945i	−0.474466	+	0.344719i	0.324713	+	0.945812i	$0.394732\pi$
$468$		0			0
$469$	6.12461	+	18.8496i	0.282808	+	0.870394i
$470$	3.94427	−	12.1392i	0.181936	−	0.559940i
$471$		0			0
$472$	−3.32624			−0.153103
$473$		0			0
$474$		0			0
$475$	5.00000	+	3.63271i	0.229416	+	0.166680i
$476$	1.09017	−	3.35520i	0.0499679	−	0.153785i
$477$		0			0
$478$	10.8541	−	7.88597i	0.496455	−	0.360696i
$479$	−13.2361	+	9.61657i	−0.604771	+	0.439392i	−0.847569	−	0.530685i	$-0.821935\pi$
$479$	−13.2361	+	9.61657i	−0.604771	+	0.439392i	0.242798	+	0.970077i	$0.421935\pi$
$480$		0			0
$481$	7.41641	−	22.8254i	0.338159	−	1.04075i
$482$	22.2533	+	16.1680i	1.01361	+	0.736430i
$483$		0			0
$484$	−9.69098	−	5.20431i	−0.440499	−	0.236560i
$485$	−19.1459			−0.869370
$486$		0			0
$487$	3.64590	−	11.2209i	0.165211	−	0.508468i	−0.833840	−	0.552006i	$-0.813863\pi$
$487$	3.64590	−	11.2209i	0.165211	−	0.508468i	0.999052	+	0.0435372i	$0.0138627\pi$
$488$	2.23607	+	6.88191i	0.101222	+	0.311529i
$489$		0			0
$490$	−1.28115	+	0.930812i	−0.0578766	+	0.0420498i
$491$	−7.41641	−	22.8254i	−0.334698	−	1.03009i	−0.966871	−	0.255267i	$-0.917837\pi$
$491$	−7.41641	−	22.8254i	−0.334698	−	1.03009i	0.632173	−	0.774827i	$-0.282163\pi$
$492$		0			0
$493$	−2.61803	−	1.90211i	−0.117910	−	0.0856669i
$494$	−4.94427			−0.222453
$495$		0			0
$496$	6.85410			0.307758
$497$	12.0902	+	8.78402i	0.542318	+	0.394017i
$498$		0			0
$499$	1.67376	+	5.15131i	0.0749279	+	0.230604i	0.981505	−	0.191435i	$-0.0613143\pi$
$499$	1.67376	+	5.15131i	0.0749279	+	0.230604i	−0.906577	+	0.422040i	$0.861314\pi$
$500$	9.04508	−	6.57164i	0.404508	−	0.293893i
$501$		0			0
$502$	1.48278	+	4.56352i	0.0661797	+	0.203680i
$503$	5.27051	−	16.2210i	0.235000	−	0.723257i	−0.762121	−	0.647435i	$-0.775842\pi$
$503$	5.27051	−	16.2210i	0.235000	−	0.723257i	0.997121	−	0.0758222i	$-0.0241581\pi$
$504$		0			0
$505$	23.6180			1.05099
$506$	5.85410	−	23.2744i	0.260247	−	1.03467i
$507$		0			0
$508$	13.7082	+	9.95959i	0.608203	+	0.441885i
$509$	−1.06231	+	3.26944i	−0.0470859	+	0.144915i	−0.971835	−	0.235661i	$-0.924274\pi$
$509$	−1.06231	+	3.26944i	−0.0470859	+	0.144915i	0.924749	+	0.380577i	$0.124274\pi$
$510$		0			0
$511$	10.6631	−	7.74721i	0.471709	−	0.342716i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$		0			0
$514$	0.909830	−	2.80017i	0.0401309	−	0.123510i
$515$	1.28115	+	0.930812i	0.0564543	+	0.0410165i
$516$		0			0
$517$	30.5623	−	2.07363i	1.34413	−	0.0911980i
$518$	−27.7082			−1.21743
$519$		0			0
$520$	−1.05573	+	3.24920i	−0.0462967	+	0.142487i
$521$	8.67376	+	26.6951i	0.380004	+	1.16953i	0.940040	+	0.341065i	$0.110788\pi$
$521$	8.67376	+	26.6951i	0.380004	+	1.16953i	−0.560035	+	0.828469i	$0.689212\pi$
$522$		0			0
$523$	−14.2361	+	10.3431i	−0.622500	+	0.452273i	−0.853794	−	0.520611i	$-0.825704\pi$
$523$	−14.2361	+	10.3431i	−0.622500	+	0.452273i	0.231294	+	0.972884i	$0.425704\pi$
$524$	0.0278640	+	0.0857567i	0.00121725	+	0.00374630i
$525$		0			0
$526$	2.38197	+	1.73060i	0.103859	+	0.0754577i
$527$	8.47214			0.369052
$528$		0			0
$529$	29.3607			1.27655
$530$	−12.9894	−	9.43732i	−0.564222	−	0.409931i
$531$		0			0
$532$	1.76393	+	5.42882i	0.0764762	+	0.235369i
$533$	−22.4721	+	16.3270i	−0.973376	+	0.707199i
$534$		0			0
$535$	−3.05166	−	9.39205i	−0.131935	−	0.406054i
$536$	2.14590	−	6.60440i	0.0926887	−	0.285266i
$537$		0			0
$538$	−10.9443			−0.471841
$539$	−3.21885	−	2.02063i	−0.138646	−	0.0870345i
$540$		0			0
$541$	−10.1803	−	7.39645i	−0.437687	−	0.317998i	0.347028	−	0.937855i	$-0.387191\pi$
$541$	−10.1803	−	7.39645i	−0.437687	−	0.317998i	−0.784715	+	0.619856i	$0.787191\pi$
$542$	1.05573	−	3.24920i	0.0453474	−	0.139565i
$543$		0			0
$544$	−1.00000	+	0.726543i	−0.0428746	+	0.0311503i
$545$	−10.3262	+	7.50245i	−0.442327	+	0.321370i
$546$		0			0
$547$	−11.8541	+	36.4832i	−0.506845	+	1.55991i	0.290802	+	0.956783i	$0.406078\pi$
$547$	−11.8541	+	36.4832i	−0.506845	+	1.55991i	−0.797647	+	0.603125i	$0.793922\pi$
$548$	−6.09017	−	4.42477i	−0.260159	−	0.189017i
$549$		0			0
$550$	8.68034	+	5.44907i	0.370131	+	0.232349i
$551$	5.23607			0.223064
$552$		0			0
$553$	−12.2188	+	37.6057i	−0.519598	+	1.59916i
$554$	−4.32624	−	13.3148i	−0.183804	−	0.565691i
$555$		0			0
$556$	7.85410	−	5.70634i	0.333088	−	0.242003i
$557$	−3.59017	−	11.0494i	−0.152120	−	0.468178i	0.845737	−	0.533599i	$-0.179161\pi$
$557$	−3.59017	−	11.0494i	−0.152120	−	0.468178i	−0.997858	+	0.0654210i	$0.979161\pi$
$558$		0			0
$559$		0			0
$560$	3.94427			0.166676
$561$		0			0
$562$	−8.94427			−0.377291
$563$	24.1803	+	17.5680i	1.01908	+	0.740405i	0.966094	−	0.258190i	$-0.0831262\pi$
$563$	24.1803	+	17.5680i	1.01908	+	0.740405i	0.0529858	+	0.998595i	$0.483126\pi$
$564$		0			0
$565$	1.58359	+	4.87380i	0.0666222	+	0.205042i
$566$	11.5623	−	8.40051i	0.486000	−	0.353100i
$567$		0			0
$568$	−1.61803	−	4.97980i	−0.0678912	−	0.208948i
$569$	4.52786	−	13.9353i	0.189818	−	0.584200i	−0.810180	−	0.586181i	$-0.800631\pi$
$569$	4.52786	−	13.9353i	0.189818	−	0.584200i	0.999998	+	0.00198150i	$0.000630731\pi$
$570$		0			0
$571$	37.2361			1.55828			0.779140	−	0.626849i	$-0.215656\pi$
$571$	37.2361			1.55828			0.779140	+	0.626849i	$0.215656\pi$
$572$	−8.18034	+	0.555029i	−0.342037	+	0.0232069i
$573$		0			0
$574$	25.9443	+	18.8496i	1.08289	+	0.786768i
$575$	−6.90983	+	21.2663i	−0.288160	+	0.886865i
$576$		0			0
$577$	−19.3435	+	14.0538i	−0.805279	+	0.585069i	−0.912458	−	0.409170i	$-0.865818\pi$
$577$	−19.3435	+	14.0538i	−0.805279	+	0.585069i	0.107179	+	0.994240i	$0.465818\pi$
$578$	12.5172	−	9.09429i	0.520648	−	0.378273i
$579$		0			0
$580$	1.11803	−	3.44095i	0.0464238	−	0.142878i
$581$	38.7877	+	28.1809i	1.60919	+	1.16914i
$582$		0			0
$583$	9.39919	−	37.3687i	0.389275	−	1.54765i
$584$	−4.61803			−0.191096
$585$		0			0
$586$	−8.40983	+	25.8828i	−0.347407	+	1.06921i
$587$	2.69756	+	8.30224i	0.111340	+	0.342670i	0.991166	−	0.132626i	$-0.0423409\pi$
$587$	2.69756	+	8.30224i	0.111340	+	0.342670i	−0.879826	+	0.475296i	$0.842341\pi$
$588$		0			0
$589$	−11.0902	+	8.05748i	−0.456962	+	0.332003i
$590$	−1.42047	−	4.37177i	−0.0584800	−	0.179983i
$591$		0			0
$592$	7.85410	+	5.70634i	0.322802	+	0.234529i
$593$	3.70820			0.152278			0.0761388	−	0.997097i	$-0.475741\pi$
$593$	3.70820			0.152278			0.0761388	+	0.997097i	$0.475741\pi$
$594$		0			0
$595$	4.87539			0.199871
$596$	−6.78115	−	4.92680i	−0.277767	−	0.201809i
$597$		0			0
$598$	−5.52786	−	17.0130i	−0.226051	−	0.695714i
$599$	36.2705	−	26.3521i	1.48197	−	1.07672i	0.505058	−	0.863085i	$-0.331471\pi$
$599$	36.2705	−	26.3521i	1.48197	−	1.07672i	0.976914	−	0.213631i	$-0.0685291\pi$
$600$		0			0
$601$	12.4443	+	38.2995i	0.507612	+	1.56227i	0.796334	+	0.604857i	$0.206770\pi$
$601$	12.4443	+	38.2995i	0.507612	+	1.56227i	−0.288721	+	0.957413i	$0.593230\pi$
$602$		0			0
$603$		0			0
$604$	−6.14590			−0.250073
$605$	2.70163	−	14.9596i	0.109837	−	0.608196i
$606$		0			0
$607$	12.0000	+	8.71851i	0.487065	+	0.353873i	0.804054	−	0.594556i	$-0.202672\pi$
$607$	12.0000	+	8.71851i	0.487065	+	0.353873i	−0.316990	+	0.948429i	$0.602672\pi$
$608$	0.618034	−	1.90211i	0.0250646	−	0.0771409i
$609$		0			0
$610$	−8.09017	+	5.87785i	−0.327561	+	0.237987i
$611$	18.4721	−	13.4208i	0.747303	−	0.542947i
$612$		0			0
$613$	10.0557	−	30.9483i	0.406147	−	1.24999i	−0.513787	−	0.857918i	$-0.671758\pi$
$613$	10.0557	−	30.9483i	0.406147	−	1.24999i	0.919934	−	0.392074i	$-0.128242\pi$
$614$	−19.7082	−	14.3188i	−0.795358	−	0.577862i
$615$		0			0
$616$	3.52786	+	8.78402i	0.142142	+	0.353918i
$617$	−26.0689			−1.04949			−0.524747	−	0.851258i	$-0.675840\pi$
$617$	−26.0689			−1.04949			−0.524747	+	0.851258i	$0.675840\pi$
$618$		0			0
$619$	−0.381966	+	1.17557i	−0.0153525	+	0.0472502i	−0.958439	−	0.285297i	$-0.907908\pi$
$619$	−0.381966	+	1.17557i	−0.0153525	+	0.0472502i	0.943087	+	0.332547i	$0.107908\pi$
$620$	2.92705	+	9.00854i	0.117553	+	0.361792i
$621$		0			0
$622$	5.47214	−	3.97574i	0.219413	−	0.159413i
$623$	14.2705	+	43.9201i	0.571736	+	1.75962i
$624$		0			0
$625$		0			0
$626$	4.32624			0.172911
$627$		0			0
$628$	2.29180			0.0914526
$629$	9.70820	+	7.05342i	0.387091	+	0.281238i
$630$		0			0
$631$	8.16970	+	25.1437i	0.325230	+	1.00096i	0.971336	+	0.237709i	$0.0763964\pi$
$631$	8.16970	+	25.1437i	0.325230	+	1.00096i	−0.646106	+	0.763248i	$0.723604\pi$
$632$	11.2082	−	8.14324i	0.445838	−	0.323921i
$633$		0			0
$634$	6.43769	+	19.8132i	0.255673	+	0.786882i
$635$	−7.23607	+	22.2703i	−0.287155	+	0.883771i
$636$		0			0
$637$	−2.83282			−0.112240
$638$	8.66312	−	0.587785i	0.342976	−	0.0232706i
$639$		0			0
$640$	−1.11803	−	0.812299i	−0.0441942	−	0.0321089i
$641$	−12.7639	+	39.2833i	−0.504145	+	1.55160i	0.298058	+	0.954548i	$0.403661\pi$
$641$	−12.7639	+	39.2833i	−0.504145	+	1.55160i	−0.802203	+	0.597051i	$0.796339\pi$
$642$		0			0
$643$	30.2705	−	21.9928i	1.19375	−	0.867312i	0.200097	−	0.979776i	$-0.435874\pi$
$643$	30.2705	−	21.9928i	1.19375	−	0.867312i	0.993656	+	0.112464i	$0.0358744\pi$
$644$	−16.7082	+	12.1392i	−0.658395	+	0.478352i
$645$		0			0
$646$	0.763932	−	2.35114i	0.0300565	−	0.0925044i
$647$	−25.7984	−	18.7436i	−1.01424	−	0.736888i	−0.0491448	−	0.998792i	$-0.515650\pi$
$647$	−25.7984	−	18.7436i	−1.01424	−	0.736888i	−0.965094	+	0.261904i	$0.915650\pi$
$648$		0			0
$649$	8.46556	−	7.07367i	0.332302	−	0.277666i
$650$	7.63932			0.299639
$651$		0			0
$652$	4.29180	−	13.2088i	0.168080	−	0.517296i
$653$	−2.04508	−	6.29412i	−0.0800304	−	0.246308i	0.903034	−	0.429569i	$-0.141335\pi$
$653$	−2.04508	−	6.29412i	−0.0800304	−	0.246308i	−0.983064	+	0.183261i	$0.941335\pi$
$654$		0			0
$655$	−0.100813	+	0.0732450i	−0.00393909	+	0.00286192i
$656$	−3.47214	−	10.6861i	−0.135564	−	0.417224i
$657$		0			0
$658$	−21.3262	−	15.4944i	−0.831383	−	0.604035i
$659$	28.7984			1.12183			0.560913	−	0.827875i	$-0.310450\pi$
$659$	28.7984			1.12183			0.560913	+	0.827875i	$0.310450\pi$
$660$		0			0
$661$	6.18034			0.240387			0.120194	−	0.992750i	$-0.461648\pi$
$661$	6.18034			0.240387			0.120194	+	0.992750i	$0.461648\pi$
$662$	17.5623	+	12.7598i	0.682578	+	0.495922i
$663$		0			0
$664$	−5.19098	−	15.9762i	−0.201449	−	0.619997i
$665$	−6.38197	+	4.63677i	−0.247482	+	0.179806i
$666$		0			0
$667$	5.85410	+	18.0171i	0.226672	+	0.697624i
$668$	3.29180	−	10.1311i	0.127363	−	0.391984i
$669$		0			0
$670$	9.59675			0.370755
$671$	−20.3262	−	12.7598i	−0.784686	−	0.492585i
$672$		0			0
$673$	−19.9721	−	14.5106i	−0.769869	−	0.559343i	0.132052	−	0.991243i	$-0.457843\pi$
$673$	−19.9721	−	14.5106i	−0.769869	−	0.559343i	−0.901922	+	0.431900i	$0.857843\pi$
$674$	1.56231	−	4.80828i	0.0601778	−	0.185208i
$675$		0			0
$676$	5.57295	−	4.04898i	0.214344	−	0.155730i
$677$	−8.01722	+	5.82485i	−0.308127	+	0.223867i	−0.731092	−	0.682279i	$-0.760989\pi$
$677$	−8.01722	+	5.82485i	−0.308127	+	0.223867i	0.422965	+	0.906146i	$0.360989\pi$
$678$		0			0
$679$	−12.2188	+	37.6057i	−0.468916	+	1.44318i
$680$	−1.38197	−	1.00406i	−0.0529960	−	0.0385038i
$681$		0			0
$682$	−17.4443	+	14.5761i	−0.667976	+	0.558148i
$683$	−0.673762			−0.0257808			−0.0128904	−	0.999917i	$-0.504103\pi$
$683$	−0.673762			−0.0257808			−0.0128904	+	0.999917i	$0.504103\pi$
$684$		0			0
$685$	3.21478	−	9.89408i	0.122830	−	0.378033i
$686$	−5.16312	−	15.8904i	−0.197129	−	0.606700i
$687$		0			0
$688$		0			0
$689$	−8.87539	−	27.3156i	−0.338125	−	1.04064i
$690$		0			0
$691$	−14.7082	−	10.6861i	−0.559526	−	0.406520i	0.271759	−	0.962365i	$-0.412395\pi$
$691$	−14.7082	−	10.6861i	−0.559526	−	0.406520i	−0.831286	+	0.555846i	$0.812395\pi$
$692$	5.90983			0.224658
$693$		0			0
$694$	30.7426			1.16697
$695$	10.8541	+	7.88597i	0.411720	+	0.299132i
$696$		0			0
$697$	−4.29180	−	13.2088i	−0.162563	−	0.500319i
$698$	−16.7082	+	12.1392i	−0.632415	+	0.459476i
$699$		0			0
$700$	−2.72542	−	8.38800i	−0.103011	−	0.317036i
$701$	−5.56231	+	17.1190i	−0.210085	+	0.646576i	0.789381	+	0.613904i	$0.210402\pi$
$701$	−5.56231	+	17.1190i	−0.210085	+	0.646576i	−0.999466	+	0.0326724i	$0.989598\pi$
$702$		0			0
$703$	−19.4164			−0.732304
$704$	0.809017	−	3.21644i	0.0304910	−	0.121224i
$705$		0			0
$706$	5.38197	+	3.91023i	0.202553	+	0.147163i
$707$	15.0729	−	46.3898i	0.566877	−	1.74467i
$708$		0			0
$709$	−19.0902	+	13.8698i	−0.716946	+	0.520892i	−0.885407	−	0.464816i	$-0.846120\pi$
$709$	−19.0902	+	13.8698i	−0.716946	+	0.520892i	0.168461	+	0.985708i	$0.446120\pi$
$710$	5.85410	−	4.25325i	0.219701	−	0.159622i
$711$		0			0
$712$	5.00000	−	15.3884i	0.187383	−	0.576705i
$713$	−40.1246	−	29.1522i	−1.50268	−	1.09176i
$714$		0			0
$715$	−4.22291	−	10.5146i	−0.157928	−	0.393225i
$716$	4.79837			0.179324
$717$		0			0
$718$	−4.14590	+	12.7598i	−0.154724	+	0.476190i
$719$	6.00000	+	18.4661i	0.223762	+	0.688669i	0.998415	+	0.0562824i	$0.0179247\pi$
$719$	6.00000	+	18.4661i	0.223762	+	0.688669i	−0.774653	+	0.632387i	$0.782075\pi$
$720$		0			0
$721$	2.64590	−	1.92236i	0.0985384	−	0.0715923i
$722$	−4.63525	−	14.2658i	−0.172506	−	0.530920i
$723$		0			0
$724$	−16.4721	−	11.9677i	−0.612182	−	0.444776i
$725$	−8.09017			−0.300461
$726$		0			0
$727$	−28.0000			−1.03846			−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000			−1.03846			−0.519231	+	0.854634i	$0.673782\pi$
$728$	5.70820	+	4.14725i	0.211560	+	0.153707i
$729$		0			0
$730$	−1.97214	−	6.06961i	−0.0729920	−	0.224646i
$731$		0			0
$732$		0			0
$733$	−8.90983	−	27.4216i	−0.329092	−	1.01284i	−0.969559	−	0.244856i	$-0.921259\pi$
$733$	−8.90983	−	27.4216i	−0.329092	−	1.01284i	0.640467	−	0.767985i	$-0.278741\pi$
$734$	−7.89919	+	24.3112i	−0.291564	+	0.897343i
$735$		0			0
$736$	7.23607			0.266725
$737$	8.58359	+	21.3723i	0.316181	+	0.787258i
$738$		0			0
$739$	−19.6525	−	14.2784i	−0.722928	−	0.525238i	0.164390	−	0.986395i	$-0.447434\pi$
$739$	−19.6525	−	14.2784i	−0.722928	−	0.525238i	−0.887318	+	0.461157i	$0.847434\pi$
$740$	−4.14590	+	12.7598i	−0.152406	+	0.469058i
$741$		0			0
$742$	−26.8262	+	19.4904i	−0.984822	+	0.715515i
$743$	−9.32624	+	6.77591i	−0.342146	+	0.248584i	−0.745567	−	0.666431i	$-0.767821\pi$
$743$	−9.32624	+	6.77591i	−0.342146	+	0.248584i	0.403420	+	0.915015i	$0.367821\pi$
$744$		0			0
$745$	3.57953	−	11.0167i	0.131144	−	0.403619i
$746$	9.47214	+	6.88191i	0.346800	+	0.251965i
$747$		0			0
$748$	1.00000	−	3.97574i	0.0365636	−	0.145367i
$749$	−20.3951			−0.745222
$750$		0			0
$751$	10.2918	−	31.6749i	0.375553	−	1.15583i	−0.567552	−	0.823338i	$-0.692109\pi$
$751$	10.2918	−	31.6749i	0.375553	−	1.15583i	0.943105	−	0.332496i	$-0.107891\pi$
$752$	2.85410	+	8.78402i	0.104078	+	0.320320i
$753$		0			0
$754$	5.23607	−	3.80423i	0.190686	−	0.138542i
$755$	−2.62461	−	8.07772i	−0.0955194	−	0.293978i
$756$		0			0
$757$	−4.56231	−	3.31471i	−0.165820	−	0.120475i	0.501781	−	0.864995i	$-0.332678\pi$
$757$	−4.56231	−	3.31471i	−0.165820	−	0.120475i	−0.667600	+	0.744520i	$0.732678\pi$
$758$	−24.8328			−0.901968
$759$		0			0
$760$	2.76393			0.100258
$761$	−32.0344	−	23.2744i	−1.16125	−	0.843696i	−0.171312	−	0.985217i	$-0.554801\pi$
$761$	−32.0344	−	23.2744i	−1.16125	−	0.843696i	−0.989935	+	0.141521i	$0.954801\pi$
$762$		0			0
$763$	8.14590	+	25.0705i	0.294901	+	0.907613i
$764$	−8.70820	+	6.32688i	−0.315052	+	0.228899i
$765$		0			0
$766$	−8.76393	−	26.9726i	−0.316654	−	0.974560i
$767$	2.54102	−	7.82045i	0.0917509	−	0.282380i
$768$		0			0
$769$	−24.9787			−0.900755			−0.450378	−	0.892838i	$-0.648711\pi$
$769$	−24.9787			−0.900755			−0.450378	+	0.892838i	$0.648711\pi$
$770$	−10.0385	+	8.38800i	−0.361763	+	0.302282i
$771$		0			0
$772$	10.3992	+	7.55545i	0.374275	+	0.271927i
$773$	8.80902	−	27.1114i	0.316838	−	0.975128i	−0.658153	−	0.752884i	$-0.728662\pi$
$773$	8.80902	−	27.1114i	0.316838	−	0.975128i	0.974991	−	0.222244i	$-0.0713381\pi$
$774$		0			0
$775$	17.1353	−	12.4495i	0.615517	−	0.447199i
$776$	11.2082	−	8.14324i	0.402351	−	0.292325i
$777$		0			0
$778$	0.145898	−	0.449028i	0.00523070	−	0.0160984i
$779$	18.1803	+	13.2088i	0.651378	+	0.473254i
$780$		0			0
$781$	14.7082	+	9.23305i	0.526301	+	0.330385i
$782$	8.94427			0.319847
$783$		0			0
$784$	0.354102	−	1.08981i	0.0126465	−	0.0389219i
$785$	0.978714	+	3.01217i	0.0349318	+	0.107509i
$786$		0			0
$787$	−13.7082	+	9.95959i	−0.488645	+	0.355021i	−0.804663	−	0.593732i	$-0.797654\pi$
$787$	−13.7082	+	9.95959i	−0.488645	+	0.355021i	0.316018	+	0.948753i	$0.397654\pi$
$788$	0.809017	+	2.48990i	0.0288200	+	0.0886990i
$789$		0			0
$790$	15.4894	+	11.2537i	0.551087	+	0.400388i
$791$	10.5836			0.376309
$792$		0			0
$793$	−17.8885			−0.635241
$794$	3.70820	+	2.69417i	0.131599	+	0.0956124i
$795$		0			0
$796$	−4.57295	−	14.0741i	−0.162084	−	0.498843i
$797$	−4.01722	+	2.91868i	−0.142297	+	0.103385i	−0.656656	−	0.754190i	$-0.728030\pi$
$797$	−4.01722	+	2.91868i	−0.142297	+	0.103385i	0.514359	+	0.857575i	$0.328030\pi$
$798$		0			0
$799$	3.52786	+	10.8576i	0.124807	+	0.384116i
$800$	−0.954915	+	2.93893i	−0.0337613	+	0.103907i
$801$		0			0
$802$	−30.9443			−1.09268
$803$	11.7533	−	9.82084i	0.414765	−	0.346570i
$804$		0			0
$805$	−23.0902	−	16.7760i	−0.813822	−	0.591276i
$806$	−5.23607	+	16.1150i	−0.184433	+	0.567625i
$807$		0			0
$808$	−13.8262	+	10.0453i	−0.486405	+	0.353394i
$809$	3.09017	−	2.24514i	0.108645	−	0.0789349i	−0.532136	−	0.846659i	$-0.678611\pi$
$809$	3.09017	−	2.24514i	0.108645	−	0.0789349i	0.640781	+	0.767724i	$0.278611\pi$
$810$		0			0
$811$	15.2148	−	46.8263i	0.534263	−	1.64429i	−0.210972	−	0.977492i	$-0.567663\pi$
$811$	15.2148	−	46.8263i	0.534263	−	1.64429i	0.745236	−	0.666801i	$-0.232337\pi$
$812$	−6.04508	−	4.39201i	−0.212141	−	0.154129i
$813$		0			0
$814$	−32.1246	+	2.17963i	−1.12597	+	0.0763959i
$815$	19.1935			0.672319
$816$		0			0
$817$		0			0
$818$	7.71885	+	23.7562i	0.269883	+	0.830615i
$819$		0			0
$820$	12.5623	−	9.12705i	0.438695	−	0.318730i
$821$	14.6459	+	45.0754i	0.511145	+	1.57314i	0.790188	+	0.612865i	$0.209983\pi$
$821$	14.6459	+	45.0754i	0.511145	+	1.57314i	−0.279042	+	0.960279i	$0.590017\pi$
$822$		0			0
$823$	2.26393	+	1.64484i	0.0789157	+	0.0573356i	0.626544	−	0.779386i	$-0.284469\pi$
$823$	2.26393	+	1.64484i	0.0789157	+	0.0573356i	−0.547628	+	0.836722i	$0.684469\pi$
$824$	−1.14590			−0.0399192
$825$		0			0
$826$	−9.49342			−0.330318
$827$	0.836881	+	0.608030i	0.0291012	+	0.0211433i	0.602241	−	0.798315i	$-0.294275\pi$
$827$	0.836881	+	0.608030i	0.0291012	+	0.0211433i	−0.573140	+	0.819458i	$0.694275\pi$
$828$		0			0
$829$	−0.381966	−	1.17557i	−0.0132662	−	0.0408293i	0.944204	−	0.329360i	$-0.106833\pi$
$829$	−0.381966	−	1.17557i	−0.0132662	−	0.0408293i	−0.957471	+	0.288531i	$0.906833\pi$
$830$	18.7812	−	13.6453i	0.651903	−	0.473635i
$831$		0			0
$832$	−0.763932	−	2.35114i	−0.0264846	−	0.0815111i
$833$	0.437694	−	1.34708i	0.0151652	−	0.0466737i
$834$		0			0
$835$	14.7214			0.509454
$836$	2.47214	+	6.15537i	0.0855006	+	0.212888i
$837$		0			0
$838$	16.0623	+	11.6699i	0.554863	+	0.403132i
$839$	14.3262	−	44.0916i	0.494597	−	1.52221i	−0.322988	−	0.946403i	$-0.604687\pi$
$839$	14.3262	−	44.0916i	0.494597	−	1.52221i	0.817584	−	0.575809i	$-0.195313\pi$
$840$		0			0
$841$	17.9164	−	13.0170i	0.617807	−	0.448863i
$842$	−18.7082	+	13.5923i	−0.644727	+	0.468422i
$843$		0			0
$844$	−3.38197	+	10.4086i	−0.116412	+	0.358280i
$845$	7.70163	+	5.59556i	0.264944	+	0.192493i
$846$		0			0
$847$	−27.6591	−	14.8536i	−0.950376	−	0.510377i
$848$	11.6180			0.398965
$849$		0			0
$850$	−1.18034	+	3.63271i	−0.0404853	+	0.124601i
$851$	−21.7082	−	66.8110i	−0.744148	−	2.29025i
$852$		0			0
$853$	−26.8885	+	19.5357i	−0.920646	+	0.668889i	−0.943685	−	0.330846i	$-0.892666\pi$
$853$	−26.8885	+	19.5357i	−0.920646	+	0.668889i	0.0230386	+	0.999735i	$0.492666\pi$
$854$	6.38197	+	19.6417i	0.218386	+	0.672124i
$855$		0			0
$856$	5.78115	+	4.20025i	0.197596	+	0.143562i
$857$	−26.1803			−0.894303			−0.447152	−	0.894458i	$-0.647562\pi$
$857$	−26.1803			−0.894303			−0.447152	+	0.894458i	$0.647562\pi$
$858$		0			0
$859$	−48.7214			−1.66235			−0.831176	−	0.556010i	$-0.812332\pi$
$859$	−48.7214			−1.66235			−0.831176	+	0.556010i	$0.812332\pi$
$860$		0			0
$861$		0			0
$862$	2.88854	+	8.89002i	0.0983842	+	0.302795i
$863$	−10.7984	+	7.84548i	−0.367581	+	0.267063i	−0.756207	−	0.654332i	$-0.772950\pi$
$863$	−10.7984	+	7.84548i	−0.367581	+	0.267063i	0.388626	+	0.921396i	$0.372950\pi$
$864$		0			0
$865$	2.52380	+	7.76745i	0.0858117	+	0.264101i
$866$	−3.20820	+	9.87384i	−0.109019	+	0.335527i
$867$		0			0
$868$	19.5623			0.663988
$869$	−11.2082	+	44.5609i	−0.380212	+	1.51162i
$870$		0			0
$871$	13.8885	+	10.0906i	0.470595	+	0.341908i
$872$	2.85410	−	8.78402i	0.0966521	−	0.297465i
$873$		0			0
$874$	−11.7082	+	8.50651i	−0.396036	+	0.287737i
$875$	25.8156	−	18.7561i	0.872726	−	0.634073i
$876$		0			0
$877$	−2.70820	+	8.33499i	−0.0914495	+	0.281453i	−0.986312	−	0.164889i	$-0.947273\pi$
$877$	−2.70820	+	8.33499i	−0.0914495	+	0.281453i	0.894863	+	0.446342i	$0.147273\pi$
$878$	7.39919	+	5.37582i	0.249710	+	0.181425i
$879$		0			0
$880$	4.57295	−	0.310271i	0.154154	−	0.0104592i
$881$	21.8885			0.737444			0.368722	−	0.929540i	$-0.379795\pi$
$881$	21.8885			0.737444			0.368722	+	0.929540i	$0.379795\pi$
$882$		0			0
$883$	2.72949	−	8.40051i	0.0918547	−	0.282700i	−0.894567	−	0.446935i	$-0.852516\pi$
$883$	2.72949	−	8.40051i	0.0918547	−	0.282700i	0.986421	+	0.164235i	$0.0525156\pi$
$884$	−0.944272	−	2.90617i	−0.0317593	−	0.0977451i
$885$		0			0
$886$	33.4894	−	24.3314i	1.12510	−	0.817431i
$887$	−8.67376	−	26.6951i	−0.291236	−	0.896334i	−0.984460	−	0.175611i	$-0.943810\pi$
$887$	−8.67376	−	26.6951i	−0.291236	−	0.896334i	0.693223	−	0.720723i	$-0.256190\pi$
$888$		0			0
$889$	39.1246	+	28.4257i	1.31220	+	0.953367i
$890$	22.3607			0.749532
$891$		0			0
$892$	2.14590			0.0718500
$893$	−14.9443	−	10.8576i	−0.500091	−	0.363337i
$894$		0			0
$895$	2.04915	+	6.30664i	0.0684955	+	0.210808i
$896$	−2.30902	+	1.67760i	−0.0771388	+	0.0560447i
$897$		0			0
$898$	−8.56231	−	26.3521i	−0.285728	−	0.879380i
$899$	5.54508	−	17.0660i	0.184939	−	0.569184i
$900$		0			0
$901$	14.3607			0.478424
$902$	31.5623	+	19.8132i	1.05091	+	0.659707i
$903$		0			0
$904$	−3.00000	−	2.17963i	−0.0997785	−	0.0724933i
$905$	8.69505	−	26.7606i	0.289033	−	0.889553i
$906$		0			0
$907$	28.1803	−	20.4742i	0.935713	−	0.679835i	−0.0116720	−	0.999932i	$-0.503715\pi$
$907$	28.1803	−	20.4742i	0.935713	−	0.679835i	0.947385	+	0.320097i	$0.103715\pi$
$908$	−0.881966	+	0.640786i	−0.0292691	+	0.0212652i
$909$		0			0
$910$	−3.01316	+	9.27354i	−0.0998851	+	0.307415i
$911$	−9.41641	−	6.84142i	−0.311980	−	0.226666i	0.420766	−	0.907169i	$-0.361761\pi$
$911$	−9.41641	−	6.84142i	−0.311980	−	0.226666i	−0.732745	+	0.680503i	$0.761761\pi$
$912$		0			0
$913$	47.1869	+	29.6215i	1.56166	+	0.980329i
$914$	17.5623			0.580909
$915$		0			0
$916$	−1.32624	+	4.08174i	−0.0438201	+	0.134865i
$917$	0.0795268	+	0.244758i	0.00262621	+	0.00808263i
$918$		0			0
$919$	23.9164	−	17.3763i	0.788929	−	0.573191i	−0.118716	−	0.992928i	$-0.537878\pi$
$919$	23.9164	−	17.3763i	0.788929	−	0.573191i	0.907646	+	0.419737i	$0.137878\pi$
$920$	3.09017	+	9.51057i	0.101880	+	0.313554i
$921$		0			0
$922$	19.0344	+	13.8293i	0.626866	+	0.455445i
$923$	12.9443			0.426066
$924$		0			0
$925$	30.0000			0.986394
$926$	−14.7812	−	10.7391i	−0.485739	−	0.352910i
$927$		0			0
$928$	0.809017	+	2.48990i	0.0265573	+	0.0817349i
$929$	−41.7426	+	30.3278i	−1.36953	+	0.995023i	−0.371758	+	0.928330i	$0.621245\pi$
$929$	−41.7426	+	30.3278i	−1.36953	+	0.995023i	−0.997774	+	0.0666935i	$0.978755\pi$
$930$		0			0
$931$	0.708204	+	2.17963i	0.0232104	+	0.0714344i
$932$	−6.76393	+	20.8172i	−0.221560	+	0.681891i
$933$		0			0
$934$	12.6738			0.414698
$935$	5.65248	−	0.383516i	0.184856	−	0.0125423i
$936$		0			0
$937$	−33.0517	−	24.0134i	−1.07975	−	0.784485i	−0.102111	−	0.994773i	$-0.532560\pi$
$937$	−33.0517	−	24.0134i	−1.07975	−	0.784485i	−0.977639	+	0.210288i	$0.932560\pi$
$938$	6.12461	−	18.8496i	0.199976	−	0.615462i
$939$		0			0
$940$	−10.3262	+	7.50245i	−0.336805	+	0.244703i
$941$	5.14590	−	3.73871i	0.167751	−	0.121879i	−0.500742	−	0.865597i	$-0.666939\pi$
$941$	5.14590	−	3.73871i	0.167751	−	0.121879i	0.668493	+	0.743718i	$0.266939\pi$
$942$		0			0
$943$	−25.1246	+	77.3256i	−0.818170	+	2.51807i
$944$	2.69098	+	1.95511i	0.0875840	+	0.0636335i
$945$		0			0
$946$		0			0
$947$	46.7426			1.51893			0.759466	−	0.650547i	$-0.225460\pi$
$947$	46.7426			1.51893			0.759466	+	0.650547i	$0.225460\pi$
$948$		0			0
$949$	3.52786	−	10.8576i	0.114519	−	0.352454i
$950$	−1.90983	−	5.87785i	−0.0619631	−	0.190703i
$951$		0			0
$952$	−2.85410	+	2.07363i	−0.0925020	+	0.0672066i
$953$	1.43769	+	4.42477i	0.0465715	+	0.143332i	0.971638	−	0.236472i	$-0.0759912\pi$
$953$	1.43769	+	4.42477i	0.0465715	+	0.143332i	−0.925067	+	0.379805i	$0.875991\pi$
$954$		0			0
$955$	−12.0344	−	8.74353i	−0.389425	−	0.282934i
$956$	−13.4164			−0.433918
$957$		0			0
$958$	16.3607			0.528590
$959$	−17.3820	−	12.6287i	−0.561293	−	0.407803i
$960$		0			0
$961$	4.93769	+	15.1967i	0.159280	+	0.490215i
$962$	−19.4164	+	14.1068i	−0.626010	+	0.454823i
$963$		0			0
$964$	−8.50000	−	26.1603i	−0.273767	−	0.842567i
$965$	−5.48936	+	16.8945i	−0.176709	+	0.543853i
$966$		0			0
$967$	−9.56231			−0.307503			−0.153752	−	0.988110i	$-0.549136\pi$
$967$	−9.56231			−0.307503			−0.153752	+	0.988110i	$0.549136\pi$
$968$	4.78115	+	9.90659i	0.153672	+	0.318410i
$969$		0			0
$970$	15.4894	+	11.2537i	0.497333	+	0.361334i
$971$	−10.0000	+	30.7768i	−0.320915	+	0.987676i	0.652336	+	0.757930i	$0.273789\pi$
$971$	−10.0000	+	30.7768i	−0.320915	+	0.987676i	−0.973251	+	0.229745i	$0.926211\pi$
$972$		0			0
$973$	22.4164	−	16.2865i	0.718637	−	0.522120i
$974$	−9.54508	+	6.93491i	−0.305844	+	0.222209i
$975$		0			0
$976$	2.23607	−	6.88191i	0.0715748	−	0.220285i
$977$	−15.0902	−	10.9637i	−0.482777	−	0.350758i	0.319623	−	0.947545i	$-0.396444\pi$
$977$	−15.0902	−	10.9637i	−0.482777	−	0.350758i	−0.802400	+	0.596787i	$0.796444\pi$
$978$		0			0
$979$	20.0000	+	49.7980i	0.639203	+	1.59155i
$980$	1.58359			0.0505860
$981$		0			0
$982$	−7.41641	+	22.8254i	−0.236667	+	0.728386i
$983$	4.41641	+	13.5923i	0.140862	+	0.433527i	0.996456	−	0.0841201i	$-0.0268079\pi$
$983$	4.41641	+	13.5923i	0.140862	+	0.433527i	−0.855594	+	0.517647i	$0.826808\pi$
$984$		0			0
$985$	−2.92705	+	2.12663i	−0.0932636	+	0.0677600i
$986$	1.00000	+	3.07768i	0.0318465	+	0.0980134i
$987$		0			0
$988$	4.00000	+	2.90617i	0.127257	+	0.0924576i
$989$		0			0
$990$		0			0
$991$	−18.4377			−0.585693			−0.292846	−	0.956160i	$-0.594602\pi$
$991$	−18.4377			−0.585693			−0.292846	+	0.956160i	$0.594602\pi$
$992$	−5.54508	−	4.02874i	−0.176057	−	0.127913i
$993$		0			0
$994$	−4.61803	−	14.2128i	−0.146475	−	0.450804i
$995$	16.5451	−	12.0207i	0.524514	−	0.381082i
$996$		0			0
$997$	8.94427	+	27.5276i	0.283268	+	0.871809i	0.986912	+	0.161257i	$0.0515548\pi$
$997$	8.94427	+	27.5276i	0.283268	+	0.871809i	−0.703645	+	0.710552i	$0.748445\pi$
$998$	1.67376	−	5.15131i	0.0529820	−	0.163062i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.2.f.b.37.1	✓	4
3.2	odd	2		198.2.f.d.37.1	yes	4
11.3	even	5	inner	198.2.f.b.91.1	yes	4
11.5	even	5		2178.2.a.bc.1.1		2
11.6	odd	10		2178.2.a.u.1.1		2
33.5	odd	10		2178.2.a.n.1.2		2
33.14	odd	10		198.2.f.d.91.1	yes	4
33.17	even	10		2178.2.a.w.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.2.f.b.37.1	✓	4	1.1	even	1	trivial
198.2.f.b.91.1	yes	4	11.3	even	5	inner
198.2.f.d.37.1	yes	4	3.2	odd	2
198.2.f.d.91.1	yes	4	33.14	odd	10
2178.2.a.n.1.2		2	33.5	odd	10
2178.2.a.u.1.1		2	11.6	odd	10
2178.2.a.w.1.2		2	33.17	even	10
2178.2.a.bc.1.1		2	11.5	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	198.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-1.11803 + 0.812299i) q^{5} +(0.881966 + 2.71441i) q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-1.11803 + 0.812299i) q^{5} +(0.881966 + 2.71441i) q^{7} +(0.309017 - 0.951057i) q^{8} +1.38197 q^{10} +(1.23607 + 3.07768i) q^{11} +(2.00000 + 1.45309i) q^{13} +(0.881966 - 2.71441i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-1.00000 + 0.726543i) q^{17} +(0.618034 - 1.90211i) q^{19} +(-1.11803 - 0.812299i) q^{20} +(0.809017 - 3.21644i) q^{22} +7.23607 q^{23} +(-0.954915 + 2.93893i) q^{25} +(-0.763932 - 2.35114i) q^{26} +(-2.30902 + 1.67760i) q^{28} +(0.809017 + 2.48990i) q^{29} +(-5.54508 - 4.02874i) q^{31} +1.00000 q^{32} +1.23607 q^{34} +(-3.19098 - 2.31838i) q^{35} +(-3.00000 - 9.23305i) q^{37} +(-1.61803 + 1.17557i) q^{38} +(0.427051 + 1.31433i) q^{40} +(-3.47214 + 10.6861i) q^{41} +(-2.54508 + 2.12663i) q^{44} +(-5.85410 - 4.25325i) q^{46} +(2.85410 - 8.78402i) q^{47} +(-0.927051 + 0.673542i) q^{49} +(2.50000 - 1.81636i) q^{50} +(-0.763932 + 2.35114i) q^{52} +(-9.39919 - 6.82891i) q^{53} +(-3.88197 - 2.43690i) q^{55} +2.85410 q^{56} +(0.809017 - 2.48990i) q^{58} +(-1.02786 - 3.16344i) q^{59} +(-5.85410 + 4.25325i) q^{61} +(2.11803 + 6.51864i) q^{62} +(-0.809017 - 0.587785i) q^{64} -3.41641 q^{65} +6.94427 q^{67} +(-1.00000 - 0.726543i) q^{68} +(1.21885 + 3.75123i) q^{70} +(4.23607 - 3.07768i) q^{71} +(-1.42705 - 4.39201i) q^{73} +(-3.00000 + 9.23305i) q^{74} +2.00000 q^{76} +(-7.26393 + 6.06961i) q^{77} +(11.2082 + 8.14324i) q^{79} +(0.427051 - 1.31433i) q^{80} +(9.09017 - 6.60440i) q^{82} +(13.5902 - 9.87384i) q^{83} +(0.527864 - 1.62460i) q^{85} +(3.30902 - 0.224514i) q^{88} +16.1803 q^{89} +(-2.18034 + 6.71040i) q^{91} +(2.23607 + 6.88191i) q^{92} +(-7.47214 + 5.42882i) q^{94} +(0.854102 + 2.62866i) q^{95} +(11.2082 + 8.14324i) q^{97} +1.14590 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - q^{4} + 8 q^{7} - q^{8}+O(q^{10}) \) 4 * q - q^2 - q^4 + 8 * q^7 - q^8	\( 4 q - q^{2} - q^{4} + 8 q^{7} - q^{8} + 10 q^{10} - 4 q^{11} + 8 q^{13} + 8 q^{14} - q^{16} - 4 q^{17} - 2 q^{19} + q^{22} + 20 q^{23} - 15 q^{25} - 12 q^{26} - 7 q^{28} + q^{29} - 11 q^{31} + 4 q^{32} - 4 q^{34} - 15 q^{35} - 12 q^{37} - 2 q^{38} - 5 q^{40} + 4 q^{41} + q^{44} - 10 q^{46} - 2 q^{47} + 3 q^{49} + 10 q^{50} - 12 q^{52} - 13 q^{53} - 20 q^{55} - 2 q^{56} + q^{58} - 22 q^{59} - 10 q^{61} + 4 q^{62} - q^{64} + 40 q^{65} - 8 q^{67} - 4 q^{68} + 25 q^{70} + 8 q^{71} + q^{73} - 12 q^{74} + 8 q^{76} - 38 q^{77} + 18 q^{79} - 5 q^{80} + 14 q^{82} + 32 q^{83} + 20 q^{85} + 11 q^{88} + 20 q^{89} + 36 q^{91} - 12 q^{94} - 10 q^{95} + 18 q^{97} + 18 q^{98}+O(q^{100}) \) 4 * q - q^2 - q^4 + 8 * q^7 - q^8 + 10 * q^10 - 4 * q^11 + 8 * q^13 + 8 * q^14 - q^16 - 4 * q^17 - 2 * q^19 + q^22 + 20 * q^23 - 15 * q^25 - 12 * q^26 - 7 * q^28 + q^29 - 11 * q^31 + 4 * q^32 - 4 * q^34 - 15 * q^35 - 12 * q^37 - 2 * q^38 - 5 * q^40 + 4 * q^41 + q^44 - 10 * q^46 - 2 * q^47 + 3 * q^49 + 10 * q^50 - 12 * q^52 - 13 * q^53 - 20 * q^55 - 2 * q^56 + q^58 - 22 * q^59 - 10 * q^61 + 4 * q^62 - q^64 + 40 * q^65 - 8 * q^67 - 4 * q^68 + 25 * q^70 + 8 * q^71 + q^73 - 12 * q^74 + 8 * q^76 - 38 * q^77 + 18 * q^79 - 5 * q^80 + 14 * q^82 + 32 * q^83 + 20 * q^85 + 11 * q^88 + 20 * q^89 + 36 * q^91 - 12 * q^94 - 10 * q^95 + 18 * q^97 + 18 * q^98

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