LMFDB - Embedded newform 483.2.d.a.461.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(461,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("483.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.d (of order $2$, degree $1$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.4
Root			$1.61803i$ of defining polynomial
Character	$\chi$	$=$	483.461
Dual form			483.2.d.a.461.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.61803i q^{2} +(0.618034 + 1.61803i) q^{3} -0.618034 q^{4} -2.61803 q^{5} +(-2.61803 + 1.00000i) q^{6} +(2.61803 + 0.381966i) q^{7} +2.23607i q^{8} +(-2.23607 + 2.00000i) q^{9} -4.23607i q^{10} -2.23607i q^{11} +(-0.381966 - 1.00000i) q^{12} +6.85410i q^{13} +(-0.618034 + 4.23607i) q^{14} +(-1.61803 - 4.23607i) q^{15} -4.85410 q^{16} -1.47214 q^{17} +(-3.23607 - 3.61803i) q^{18} -5.47214i q^{19} +1.61803 q^{20} +(1.00000 + 4.47214i) q^{21} +3.61803 q^{22} -1.00000i q^{23} +(-3.61803 + 1.38197i) q^{24} +1.85410 q^{25} -11.0902 q^{26} +(-4.61803 - 2.38197i) q^{27} +(-1.61803 - 0.236068i) q^{28} +1.76393i q^{29} +(6.85410 - 2.61803i) q^{30} -0.527864i q^{31} -3.38197i q^{32} +(3.61803 - 1.38197i) q^{33} -2.38197i q^{34} +(-6.85410 - 1.00000i) q^{35} +(1.38197 - 1.23607i) q^{36} +5.76393 q^{37} +8.85410 q^{38} +(-11.0902 + 4.23607i) q^{39} -5.85410i q^{40} -0.236068 q^{41} +(-7.23607 + 1.61803i) q^{42} +7.61803 q^{43} +1.38197i q^{44} +(5.85410 - 5.23607i) q^{45} +1.61803 q^{46} +8.00000 q^{47} +(-3.00000 - 7.85410i) q^{48} +(6.70820 + 2.00000i) q^{49} +3.00000i q^{50} +(-0.909830 - 2.38197i) q^{51} -4.23607i q^{52} +13.5623i q^{53} +(3.85410 - 7.47214i) q^{54} +5.85410i q^{55} +(-0.854102 + 5.85410i) q^{56} +(8.85410 - 3.38197i) q^{57} -2.85410 q^{58} +7.56231 q^{59} +(1.00000 + 2.61803i) q^{60} -0.854102i q^{61} +0.854102 q^{62} +(-6.61803 + 4.38197i) q^{63} -4.23607 q^{64} -17.9443i q^{65} +(2.23607 + 5.85410i) q^{66} -10.6180 q^{67} +0.909830 q^{68} +(1.61803 - 0.618034i) q^{69} +(1.61803 - 11.0902i) q^{70} -5.32624i q^{71} +(-4.47214 - 5.00000i) q^{72} +8.23607i q^{73} +9.32624i q^{74} +(1.14590 + 3.00000i) q^{75} +3.38197i q^{76} +(0.854102 - 5.85410i) q^{77} +(-6.85410 - 17.9443i) q^{78} -7.76393 q^{79} +12.7082 q^{80} +(1.00000 - 8.94427i) q^{81} -0.381966i q^{82} +10.7082 q^{83} +(-0.618034 - 2.76393i) q^{84} +3.85410 q^{85} +12.3262i q^{86} +(-2.85410 + 1.09017i) q^{87} +5.00000 q^{88} -8.09017 q^{89} +(8.47214 + 9.47214i) q^{90} +(-2.61803 + 17.9443i) q^{91} +0.618034i q^{92} +(0.854102 - 0.326238i) q^{93} +12.9443i q^{94} +14.3262i q^{95} +(5.47214 - 2.09017i) q^{96} +1.94427i q^{97} +(-3.23607 + 10.8541i) q^{98} +(4.47214 + 5.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} - 6 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{12} + 2 q^{14} - 2 q^{15} - 6 q^{16} + 12 q^{17} - 4 q^{18} + 2 q^{20} + 4 q^{21} + 10 q^{22} - 10 q^{24} - 6 q^{25} - 22 q^{26} - 14 q^{27}+ \cdots - 4 q^{98}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 - 6 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^12 + 2 * q^14 - 2 * q^15 - 6 * q^16 + 12 * q^17 - 4 * q^18 + 2 * q^20 + 4 * q^21 + 10 * q^22 - 10 * q^24 - 6 * q^25 - 22 * q^26 - 14 * q^27 - 2 * q^28 + 14 * q^30 + 10 * q^33 - 14 * q^35 + 10 * q^36 + 32 * q^37 + 22 * q^38 - 22 * q^39 + 8 * q^41 - 20 * q^42 + 26 * q^43 + 10 * q^45 + 2 * q^46 + 32 * q^47 - 12 * q^48 - 26 * q^51 + 2 * q^54 + 10 * q^56 + 22 * q^57 + 2 * q^58 - 10 * q^59 + 4 * q^60 - 10 * q^62 - 22 * q^63 - 8 * q^64 - 38 * q^67 + 26 * q^68 + 2 * q^69 + 2 * q^70 + 18 * q^75 - 10 * q^77 - 14 * q^78 - 40 * q^79 + 24 * q^80 + 4 * q^81 + 16 * q^83 + 2 * q^84 + 2 * q^85 + 2 * q^87 + 20 * q^88 - 10 * q^89 + 16 * q^90 - 6 * q^91 - 10 * q^93 + 4 * q^96 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$			1.61803i			1.14412i	0.820211	+	0.572061i	$0.193856\pi$
$2$			1.61803i			1.14412i	−0.820211	+	0.572061i	$0.806144\pi$
$3$	0.618034	+	1.61803i	0.356822	+	0.934172i
$3$	0.618034	+	1.61803i	0.356822	+	0.934172i
$4$	−0.618034			−0.309017
$5$	−2.61803			−1.17082			−0.585410	−	0.810737i	$-0.699067\pi$
$5$	−2.61803			−1.17082			−0.585410	+	0.810737i	$0.699067\pi$
$6$	−2.61803	+	1.00000i	−1.06881	+	0.408248i
$7$	2.61803	+	0.381966i	0.989524	+	0.144370i
$7$	2.61803	+	0.381966i	0.989524	+	0.144370i
$8$			2.23607i			0.790569i
$9$	−2.23607	+	2.00000i	−0.745356	+	0.666667i
$10$		−	4.23607i		−	1.33956i
$11$		−	2.23607i		−	0.674200i	−0.941469	−	0.337100i	$-0.890554\pi$
$11$		−	2.23607i		−	0.674200i	0.941469	−	0.337100i	$-0.109446\pi$
$12$	−0.381966	−	1.00000i	−0.110264	−	0.288675i
$13$			6.85410i			1.90099i	0.310746	+	0.950493i	$0.399421\pi$
$13$			6.85410i			1.90099i	−0.310746	+	0.950493i	$0.600579\pi$
$14$	−0.618034	+	4.23607i	−0.165177	+	1.13214i
$15$	−1.61803	−	4.23607i	−0.417775	−	1.09375i
$16$	−4.85410			−1.21353
$17$	−1.47214			−0.357045			−0.178523	−	0.983936i	$-0.557132\pi$
$17$	−1.47214			−0.357045			−0.178523	+	0.983936i	$0.557132\pi$
$18$	−3.23607	−	3.61803i	−0.762749	−	0.852779i
$19$		−	5.47214i		−	1.25539i	−0.778458	−	0.627697i	$-0.783998\pi$
$19$		−	5.47214i		−	1.25539i	0.778458	−	0.627697i	$-0.216002\pi$
$20$	1.61803			0.361803
$21$	1.00000	+	4.47214i	0.218218	+	0.975900i
$22$	3.61803			0.771367
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	−3.61803	+	1.38197i	−0.738528	+	0.282093i
$25$	1.85410			0.370820
$26$	−11.0902			−2.17496
$27$	−4.61803	−	2.38197i	−0.888741	−	0.458410i
$28$	−1.61803	−	0.236068i	−0.305780	−	0.0446127i
$29$			1.76393i			0.327554i	0.986497	+	0.163777i	$0.0523677\pi$
$29$			1.76393i			0.327554i	−0.986497	+	0.163777i	$0.947632\pi$
$30$	6.85410	−	2.61803i	1.25138	−	0.477985i
$31$		−	0.527864i		−	0.0948072i	−0.998876	−	0.0474036i	$-0.984905\pi$
$31$		−	0.527864i		−	0.0948072i	0.998876	−	0.0474036i	$-0.0150947\pi$
$32$		−	3.38197i		−	0.597853i
$33$	3.61803	−	1.38197i	0.629819	−	0.240569i
$34$		−	2.38197i		−	0.408504i
$35$	−6.85410	−	1.00000i	−1.15855	−	0.169031i
$36$	1.38197	−	1.23607i	0.230328	−	0.206011i
$37$	5.76393			0.947585			0.473792	−	0.880637i	$-0.342885\pi$
$37$	5.76393			0.947585			0.473792	+	0.880637i	$0.342885\pi$
$38$	8.85410			1.43633
$39$	−11.0902	+	4.23607i	−1.77585	+	0.678314i
$40$		−	5.85410i		−	0.925615i
$41$	−0.236068			−0.0368676			−0.0184338	−	0.999830i	$-0.505868\pi$
$41$	−0.236068			−0.0368676			−0.0184338	+	0.999830i	$0.505868\pi$
$42$	−7.23607	+	1.61803i	−1.11655	+	0.249668i
$43$	7.61803			1.16174			0.580870	−	0.813997i	$-0.302713\pi$
$43$	7.61803			1.16174			0.580870	+	0.813997i	$0.302713\pi$
$44$			1.38197i			0.208339i
$45$	5.85410	−	5.23607i	0.872678	−	0.780547i
$46$	1.61803			0.238566
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$	−3.00000	−	7.85410i	−0.433013	−	1.13364i
$49$	6.70820	+	2.00000i	0.958315	+	0.285714i
$50$			3.00000i			0.424264i
$51$	−0.909830	−	2.38197i	−0.127402	−	0.333542i
$52$		−	4.23607i		−	0.587437i
$53$			13.5623i			1.86293i	0.363836	+	0.931463i	$0.381467\pi$
$53$			13.5623i			1.86293i	−0.363836	+	0.931463i	$0.618533\pi$
$54$	3.85410	−	7.47214i	0.524477	−	1.01683i
$55$			5.85410i			0.789367i
$56$	−0.854102	+	5.85410i	−0.114134	+	0.782287i
$57$	8.85410	−	3.38197i	1.17275	−	0.447952i
$58$	−2.85410			−0.374762
$59$	7.56231			0.984528			0.492264	−	0.870446i	$-0.336169\pi$
$59$	7.56231			0.984528			0.492264	+	0.870446i	$0.336169\pi$
$60$	1.00000	+	2.61803i	0.129099	+	0.337987i
$61$		−	0.854102i		−	0.109357i	−0.998504	−	0.0546783i	$-0.982587\pi$
$61$		−	0.854102i		−	0.109357i	0.998504	−	0.0546783i	$-0.0174133\pi$
$62$	0.854102			0.108471
$63$	−6.61803	+	4.38197i	−0.833794	+	0.552076i
$64$	−4.23607			−0.529508
$65$		−	17.9443i		−	2.22571i
$66$	2.23607	+	5.85410i	0.275241	+	0.720590i
$67$	−10.6180			−1.29720			−0.648600	−	0.761130i	$-0.724645\pi$
$67$	−10.6180			−1.29720			−0.648600	+	0.761130i	$0.724645\pi$
$68$	0.909830			0.110333
$69$	1.61803	−	0.618034i	0.194788	−	0.0744025i
$70$	1.61803	−	11.0902i	0.193392	−	1.32553i
$71$		−	5.32624i		−	0.632108i	−0.948741	−	0.316054i	$-0.897642\pi$
$71$		−	5.32624i		−	0.632108i	0.948741	−	0.316054i	$-0.102358\pi$
$72$	−4.47214	−	5.00000i	−0.527046	−	0.589256i
$73$			8.23607i			0.963959i	0.876183	+	0.481979i	$0.160082\pi$
$73$			8.23607i			0.963959i	−0.876183	+	0.481979i	$0.839918\pi$
$74$			9.32624i			1.08415i
$75$	1.14590	+	3.00000i	0.132317	+	0.346410i
$76$			3.38197i			0.387938i
$77$	0.854102	−	5.85410i	0.0973340	−	0.667137i
$78$	−6.85410	−	17.9443i	−0.776074	−	2.03179i
$79$	−7.76393			−0.873511			−0.436755	−	0.899580i	$-0.643872\pi$
$79$	−7.76393			−0.873511			−0.436755	+	0.899580i	$0.643872\pi$
$80$	12.7082			1.42082
$81$	1.00000	−	8.94427i	0.111111	−	0.993808i
$82$		−	0.381966i		−	0.0421811i
$83$	10.7082			1.17538			0.587689	−	0.809087i	$-0.300038\pi$
$83$	10.7082			1.17538			0.587689	+	0.809087i	$0.300038\pi$
$84$	−0.618034	−	2.76393i	−0.0674330	−	0.301570i
$85$	3.85410			0.418036
$86$			12.3262i			1.32917i
$87$	−2.85410	+	1.09017i	−0.305992	+	0.116878i
$88$	5.00000			0.533002
$89$	−8.09017			−0.857556			−0.428778	−	0.903410i	$-0.641056\pi$
$89$	−8.09017			−0.857556			−0.428778	+	0.903410i	$0.641056\pi$
$90$	8.47214	+	9.47214i	0.893042	+	0.998451i
$91$	−2.61803	+	17.9443i	−0.274445	+	1.88107i
$92$			0.618034i			0.0644345i
$93$	0.854102	−	0.326238i	0.0885662	−	0.0338293i
$94$			12.9443i			1.33510i
$95$			14.3262i			1.46984i
$96$	5.47214	−	2.09017i	0.558498	−	0.213327i
$97$			1.94427i			0.197411i	0.995117	+	0.0987055i	$0.0314702\pi$
$97$			1.94427i			0.197411i	−0.995117	+	0.0987055i	$0.968530\pi$
$98$	−3.23607	+	10.8541i	−0.326892	+	1.09643i
$99$	4.47214	+	5.00000i	0.449467	+	0.502519i
$100$	−1.14590			−0.114590
$101$	5.09017			0.506491			0.253245	−	0.967402i	$-0.418502\pi$
$101$	5.09017			0.506491			0.253245	+	0.967402i	$0.418502\pi$
$102$	3.85410	−	1.47214i	0.381613	−	0.145763i
$103$		−	10.1803i		−	1.00310i	−0.865129	−	0.501549i	$-0.832764\pi$
$103$		−	10.1803i		−	1.00310i	0.865129	−	0.501549i	$-0.167236\pi$
$104$	−15.3262			−1.50286
$105$	−2.61803	−	11.7082i	−0.255494	−	1.14260i
$106$	−21.9443			−2.13142
$107$			11.6180i			1.12316i	0.827423	+	0.561579i	$0.189806\pi$
$107$			11.6180i			1.12316i	−0.827423	+	0.561579i	$0.810194\pi$
$108$	2.85410	+	1.47214i	0.274636	+	0.141656i
$109$	3.09017			0.295985			0.147992	−	0.988989i	$-0.452719\pi$
$109$	3.09017			0.295985			0.147992	+	0.988989i	$0.452719\pi$
$110$	−9.47214			−0.903133
$111$	3.56231	+	9.32624i	0.338119	+	0.885207i
$112$	−12.7082	−	1.85410i	−1.20081	−	0.175196i
$113$			10.7984i			1.01583i	0.861409	+	0.507913i	$0.169583\pi$
$113$			10.7984i			1.01583i	−0.861409	+	0.507913i	$0.830417\pi$
$114$	5.47214	+	14.3262i	0.512512	+	1.34178i
$115$			2.61803i			0.244133i
$116$		−	1.09017i		−	0.101220i
$117$	−13.7082	−	15.3262i	−1.26732	−	1.41691i
$118$			12.2361i			1.12642i
$119$	−3.85410	−	0.562306i	−0.353305	−	0.0515465i
$120$	9.47214	−	3.61803i	0.864684	−	0.330280i
$121$	6.00000			0.545455
$122$	1.38197			0.125117
$123$	−0.145898	−	0.381966i	−0.0131552	−	0.0344407i
$124$			0.326238i			0.0292970i
$125$	8.23607			0.736656
$126$	−7.09017	−	10.7082i	−0.631643	−	0.953963i
$127$	7.79837			0.691994			0.345997	−	0.938236i	$-0.387541\pi$
$127$	7.79837			0.691994			0.345997	+	0.938236i	$0.387541\pi$
$128$		−	13.6180i		−	1.20368i
$129$	4.70820	+	12.3262i	0.414534	+	1.08526i
$130$	29.0344			2.54649
$131$	18.7082			1.63454			0.817272	−	0.576253i	$-0.195486\pi$
$131$	18.7082			1.63454			0.817272	+	0.576253i	$0.195486\pi$
$132$	−2.23607	+	0.854102i	−0.194625	+	0.0743400i
$133$	2.09017	−	14.3262i	0.181241	−	1.24224i
$134$		−	17.1803i		−	1.48416i
$135$	12.0902	+	6.23607i	1.04056	+	0.536715i
$136$		−	3.29180i		−	0.282269i
$137$		−	14.2361i		−	1.21627i	−0.793834	−	0.608135i	$-0.791918\pi$
$137$		−	14.2361i		−	1.21627i	0.793834	−	0.608135i	$-0.208082\pi$
$138$	1.00000	+	2.61803i	0.0851257	+	0.222862i
$139$			0.909830i			0.0771708i	0.999255	+	0.0385854i	$0.0122852\pi$
$139$			0.909830i			0.0771708i	−0.999255	+	0.0385854i	$0.987715\pi$
$140$	4.23607	+	0.618034i	0.358013	+	0.0522334i
$141$	4.94427	+	12.9443i	0.416383	+	1.09010i
$142$	8.61803			0.723209
$143$	15.3262			1.28164
$144$	10.8541	−	9.70820i	0.904508	−	0.809017i
$145$		−	4.61803i		−	0.383507i
$146$	−13.3262			−1.10289
$147$	0.909830	+	12.0902i	0.0750415	+	0.997180i
$148$	−3.56231			−0.292820
$149$		−	7.70820i		−	0.631481i	−0.948846	−	0.315740i	$-0.897747\pi$
$149$		−	7.70820i		−	0.631481i	0.948846	−	0.315740i	$-0.102253\pi$
$150$	−4.85410	+	1.85410i	−0.396336	+	0.151387i
$151$	−2.47214			−0.201180			−0.100590	−	0.994928i	$-0.532073\pi$
$151$	−2.47214			−0.201180			−0.100590	+	0.994928i	$0.532073\pi$
$152$	12.2361			0.992476
$153$	3.29180	−	2.94427i	0.266126	−	0.238030i
$154$	9.47214	+	1.38197i	0.763286	+	0.111362i
$155$			1.38197i			0.111002i
$156$	6.85410	−	2.61803i	0.548767	−	0.209610i
$157$		−	7.52786i		−	0.600789i	−0.953815	−	0.300394i	$-0.902882\pi$
$157$		−	7.52786i		−	0.600789i	0.953815	−	0.300394i	$-0.0971183\pi$
$158$		−	12.5623i		−	0.999403i
$159$	−21.9443	+	8.38197i	−1.74029	+	0.664733i
$160$			8.85410i			0.699978i
$161$	0.381966	−	2.61803i	0.0301031	−	0.206330i
$162$	14.4721	+	1.61803i	1.13704	+	0.127125i
$163$	−19.0902			−1.49526			−0.747629	−	0.664117i	$-0.768808\pi$
$163$	−19.0902			−1.49526			−0.747629	+	0.664117i	$0.768808\pi$
$164$	0.145898			0.0113927
$165$	−9.47214	+	3.61803i	−0.737405	+	0.281664i
$166$			17.3262i			1.34478i
$167$	19.1803			1.48422			0.742110	−	0.670279i	$-0.233825\pi$
$167$	19.1803			1.48422			0.742110	+	0.670279i	$0.233825\pi$
$168$	−10.0000	+	2.23607i	−0.771517	+	0.172516i
$169$	−33.9787			−2.61375
$170$			6.23607i			0.478285i
$171$	10.9443	+	12.2361i	0.836929	+	0.935716i
$172$	−4.70820			−0.358997
$173$	3.47214			0.263982			0.131991	−	0.991251i	$-0.457863\pi$
$173$	3.47214			0.263982			0.131991	+	0.991251i	$0.457863\pi$
$174$	−1.76393	−	4.61803i	−0.133723	−	0.350092i
$175$	4.85410	+	0.708204i	0.366936	+	0.0535352i
$176$			10.8541i			0.818159i
$177$	4.67376	+	12.2361i	0.351301	+	0.919719i
$178$		−	13.0902i		−	0.981150i
$179$		−	5.67376i		−	0.424077i	−0.977261	−	0.212038i	$-0.931990\pi$
$179$		−	5.67376i		−	0.424077i	0.977261	−	0.212038i	$-0.0680102\pi$
$180$	−3.61803	+	3.23607i	−0.269672	+	0.241202i
$181$			6.70820i			0.498617i	0.968424	+	0.249308i	$0.0802033\pi$
$181$			6.70820i			0.498617i	−0.968424	+	0.249308i	$0.919797\pi$
$182$	−29.0344	−	4.23607i	−2.15218	−	0.313998i
$183$	1.38197	−	0.527864i	0.102158	−	0.0390208i
$184$	2.23607			0.164845
$185$	−15.0902			−1.10945
$186$	0.527864	+	1.38197i	0.0387049	+	0.101331i
$187$			3.29180i			0.240720i
$188$	−4.94427			−0.360598
$189$	−11.1803	−	8.00000i	−0.813250	−	0.581914i
$190$	−23.1803			−1.68168
$191$		−	21.7082i		−	1.57075i	−0.619020	−	0.785375i	$-0.712470\pi$
$191$		−	21.7082i		−	1.57075i	0.619020	−	0.785375i	$-0.287530\pi$
$192$	−2.61803	−	6.85410i	−0.188940	−	0.494652i
$193$	15.7082			1.13070			0.565351	−	0.824851i	$-0.308741\pi$
$193$	15.7082			1.13070			0.565351	+	0.824851i	$0.308741\pi$
$194$	−3.14590			−0.225862
$195$	29.0344	−	11.0902i	2.07920	−	0.794184i
$196$	−4.14590	−	1.23607i	−0.296136	−	0.0882906i
$197$			26.0902i			1.85885i	0.369014	+	0.929424i	$0.379695\pi$
$197$			26.0902i			1.85885i	−0.369014	+	0.929424i	$0.620305\pi$
$198$	−8.09017	+	7.23607i	−0.574943	+	0.514245i
$199$		−	14.6180i		−	1.03624i	−0.855306	−	0.518122i	$-0.826631\pi$
$199$		−	14.6180i		−	1.03624i	0.855306	−	0.518122i	$-0.173369\pi$
$200$			4.14590i			0.293159i
$201$	−6.56231	−	17.1803i	−0.462869	−	1.21181i
$202$			8.23607i			0.579488i
$203$	−0.673762	+	4.61803i	−0.0472888	+	0.324122i
$204$	0.562306	+	1.47214i	0.0393693	+	0.103070i
$205$	0.618034			0.0431654
$206$	16.4721			1.14767
$207$	2.00000	+	2.23607i	0.139010	+	0.155417i
$208$		−	33.2705i		−	2.30689i
$209$	−12.2361			−0.846387
$210$	18.9443	−	4.23607i	1.30728	−	0.292316i
$211$	−3.00000			−0.206529			−0.103264	−	0.994654i	$-0.532929\pi$
$211$	−3.00000			−0.206529			−0.103264	+	0.994654i	$0.532929\pi$
$212$		−	8.38197i		−	0.575676i
$213$	8.61803	−	3.29180i	0.590498	−	0.225550i
$214$	−18.7984			−1.28503
$215$	−19.9443			−1.36019
$216$	5.32624	−	10.3262i	0.362405	−	0.702611i
$217$	0.201626	−	1.38197i	0.0136873	−	0.0938140i
$218$			5.00000i			0.338643i
$219$	−13.3262	+	5.09017i	−0.900504	+	0.343962i
$220$		−	3.61803i		−	0.243928i
$221$		−	10.0902i		−	0.678738i
$222$	−15.0902	+	5.76393i	−1.01279	+	0.386850i
$223$		−	17.0902i		−	1.14444i	−0.820099	−	0.572221i	$-0.806082\pi$
$223$		−	17.0902i		−	1.14444i	0.820099	−	0.572221i	$-0.193918\pi$
$224$	1.29180	−	8.85410i	0.0863118	−	0.591590i
$225$	−4.14590	+	3.70820i	−0.276393	+	0.247214i
$226$	−17.4721			−1.16223
$227$	−22.3262			−1.48184			−0.740922	−	0.671591i	$-0.765611\pi$
$227$	−22.3262			−1.48184			−0.740922	+	0.671591i	$0.765611\pi$
$228$	−5.47214	+	2.09017i	−0.362401	+	0.138425i
$229$			10.9098i			0.720942i	0.932770	+	0.360471i	$0.117384\pi$
$229$			10.9098i			0.720942i	−0.932770	+	0.360471i	$0.882616\pi$
$230$	−4.23607			−0.279318
$231$	10.0000	−	2.23607i	0.657952	−	0.147122i
$232$	−3.94427			−0.258954
$233$		−	13.6738i		−	0.895798i	−0.894084	−	0.447899i	$-0.852172\pi$
$233$		−	13.6738i		−	0.895798i	0.894084	−	0.447899i	$-0.147828\pi$
$234$	24.7984	−	22.1803i	1.62112	−	1.44997i
$235$	−20.9443			−1.36625
$236$	−4.67376			−0.304236
$237$	−4.79837	−	12.5623i	−0.311688	−	0.816009i
$238$	0.909830	−	6.23607i	0.0589755	−	0.404224i
$239$		−	5.67376i		−	0.367005i	−0.983019	−	0.183503i	$-0.941256\pi$
$239$		−	5.67376i		−	0.367005i	0.983019	−	0.183503i	$-0.0587436\pi$
$240$	7.85410	+	20.5623i	0.506980	+	1.32729i
$241$		−	0.527864i		−	0.0340027i	−0.999855	−	0.0170014i	$-0.994588\pi$
$241$		−	0.527864i		−	0.0340027i	0.999855	−	0.0170014i	$-0.00541196\pi$
$242$			9.70820i			0.624067i
$243$	15.0902	−	3.90983i	0.968035	−	0.250816i
$244$			0.527864i			0.0337930i
$245$	−17.5623	−	5.23607i	−1.12201	−	0.334520i
$246$	0.618034	−	0.236068i	0.0394044	−	0.0150511i
$247$	37.5066			2.38649
$248$	1.18034			0.0749517
$249$	6.61803	+	17.3262i	0.419401	+	1.09801i
$250$			13.3262i			0.842825i
$251$	6.47214			0.408518			0.204259	−	0.978917i	$-0.434522\pi$
$251$	6.47214			0.408518			0.204259	+	0.978917i	$0.434522\pi$
$252$	4.09017	−	2.70820i	0.257656	−	0.170601i
$253$	−2.23607			−0.140580
$254$			12.6180i			0.791726i
$255$	2.38197	+	6.23607i	0.149164	+	0.390518i
$256$	13.5623			0.847644
$257$	−30.9443			−1.93025			−0.965125	−	0.261788i	$-0.915688\pi$
$257$	−30.9443			−1.93025			−0.965125	+	0.261788i	$0.915688\pi$
$258$	−19.9443	+	7.61803i	−1.24168	+	0.474278i
$259$	15.0902	+	2.20163i	0.937658	+	0.136802i
$260$			11.0902i			0.687783i
$261$	−3.52786	−	3.94427i	−0.218369	−	0.244144i
$262$			30.2705i			1.87012i
$263$		−	17.9443i		−	1.10649i	−0.833018	−	0.553246i	$-0.813389\pi$
$263$		−	17.9443i		−	1.10649i	0.833018	−	0.553246i	$-0.186611\pi$
$264$	3.09017	+	8.09017i	0.190187	+	0.497916i
$265$		−	35.5066i		−	2.18115i
$266$	23.1803	+	3.38197i	1.42128	+	0.207362i
$267$	−5.00000	−	13.0902i	−0.305995	−	0.801105i
$268$	6.56231			0.400857
$269$	10.8541			0.661786			0.330893	−	0.943668i	$-0.392650\pi$
$269$	10.8541			0.661786			0.330893	+	0.943668i	$0.392650\pi$
$270$	−10.0902	+	19.5623i	−0.614068	+	1.19052i
$271$			2.23607i			0.135831i	0.997691	+	0.0679157i	$0.0216349\pi$
$271$			2.23607i			0.135831i	−0.997691	+	0.0679157i	$0.978365\pi$
$272$	7.14590			0.433284
$273$	−30.6525	+	6.85410i	−1.85517	+	0.414829i
$274$	23.0344			1.39156
$275$		−	4.14590i		−	0.250007i
$276$	−1.00000	+	0.381966i	−0.0601929	+	0.0229917i
$277$	7.14590			0.429355			0.214678	−	0.976685i	$-0.431130\pi$
$277$	7.14590			0.429355			0.214678	+	0.976685i	$0.431130\pi$
$278$	−1.47214			−0.0882928
$279$	1.05573	+	1.18034i	0.0632048	+	0.0706651i
$280$	2.23607	−	15.3262i	0.133631	−	0.915918i
$281$		−	1.05573i		−	0.0629795i	−0.999504	−	0.0314897i	$-0.989975\pi$
$281$		−	1.05573i		−	0.0629795i	0.999504	−	0.0314897i	$-0.0100251\pi$
$282$	−20.9443	+	8.00000i	−1.24721	+	0.476393i
$283$		−	8.79837i		−	0.523009i	−0.965202	−	0.261505i	$-0.915781\pi$
$283$		−	8.79837i		−	0.523009i	0.965202	−	0.261505i	$-0.0842186\pi$
$284$			3.29180i			0.195332i
$285$	−23.1803	+	8.85410i	−1.37308	+	0.524472i
$286$			24.7984i			1.46636i
$287$	−0.618034	−	0.0901699i	−0.0364814	−	0.00532256i
$288$	6.76393	+	7.56231i	0.398569	+	0.445613i
$289$	−14.8328			−0.872519
$290$	7.47214			0.438779
$291$	−3.14590	+	1.20163i	−0.184416	+	0.0704406i
$292$		−	5.09017i		−	0.297880i
$293$	−14.2918			−0.834936			−0.417468	−	0.908692i	$-0.637082\pi$
$293$	−14.2918			−0.834936			−0.417468	+	0.908692i	$0.637082\pi$
$294$	−19.5623	+	1.47214i	−1.14090	+	0.0858567i
$295$	−19.7984			−1.15271
$296$			12.8885i			0.749131i
$297$	−5.32624	+	10.3262i	−0.309060	+	0.599189i
$298$	12.4721			0.722491
$299$	6.85410			0.396383
$300$	−0.708204	−	1.85410i	−0.0408882	−	0.107047i
$301$	19.9443	+	2.90983i	1.14957	+	0.167720i
$302$		−	4.00000i		−	0.230174i
$303$	3.14590	+	8.23607i	0.180727	+	0.473150i
$304$			26.5623i			1.52345i
$305$			2.23607i			0.128037i
$306$	4.76393	+	5.32624i	0.272336	+	0.304481i
$307$		−	21.4721i		−	1.22548i	−0.790285	−	0.612740i	$-0.790067\pi$
$307$		−	21.4721i		−	1.22548i	0.790285	−	0.612740i	$-0.209933\pi$
$308$	−0.527864	+	3.61803i	−0.0300778	+	0.206157i
$309$	16.4721	−	6.29180i	0.937067	−	0.357928i
$310$	−2.23607			−0.127000
$311$	−23.3262			−1.32271			−0.661355	−	0.750073i	$-0.730018\pi$
$311$	−23.3262			−1.32271			−0.661355	+	0.750073i	$0.730018\pi$
$312$	−9.47214	−	24.7984i	−0.536254	−	1.40393i
$313$		−	10.1803i		−	0.575427i	−0.957717	−	0.287713i	$-0.907105\pi$
$313$		−	10.1803i		−	0.575427i	0.957717	−	0.287713i	$-0.0928951\pi$
$314$	12.1803			0.687376
$315$	17.3262	−	11.4721i	0.976223	−	0.646382i
$316$	4.79837			0.269930
$317$		−	0.618034i		−	0.0347122i	−0.999849	−	0.0173561i	$-0.994475\pi$
$317$		−	0.618034i		−	0.0347122i	0.999849	−	0.0173561i	$-0.00552490\pi$
$318$	−13.5623	−	35.5066i	−0.760536	−	1.99111i
$319$	3.94427			0.220837
$320$	11.0902			0.619959
$321$	−18.7984	+	7.18034i	−1.04922	+	0.400767i
$322$	4.23607	+	0.618034i	0.236067	+	0.0344417i
$323$			8.05573i			0.448233i
$324$	−0.618034	+	5.52786i	−0.0343352	+	0.307104i
$325$			12.7082i			0.704924i
$326$		−	30.8885i		−	1.71076i
$327$	1.90983	+	5.00000i	0.105614	+	0.276501i
$328$		−	0.527864i		−	0.0291464i
$329$	20.9443	+	3.05573i	1.15470	+	0.168468i
$330$	−5.85410	−	15.3262i	−0.322258	−	0.843682i
$331$	36.0689			1.98253			0.991263	−	0.131903i	$-0.0421089\pi$
$331$	36.0689			1.98253			0.991263	+	0.131903i	$0.0421089\pi$
$332$	−6.61803			−0.363212
$333$	−12.8885	+	11.5279i	−0.706288	+	0.631723i
$334$			31.0344i			1.69813i
$335$	27.7984			1.51879
$336$	−4.85410	−	21.7082i	−0.264813	−	1.18428i
$337$	−32.4508			−1.76771			−0.883855	−	0.467761i	$-0.845061\pi$
$337$	−32.4508			−1.76771			−0.883855	+	0.467761i	$0.845061\pi$
$338$		−	54.9787i		−	2.99045i
$339$	−17.4721	+	6.67376i	−0.948956	+	0.362469i
$340$	−2.38197			−0.129180
$341$	−1.18034			−0.0639190
$342$	−19.7984	+	17.7082i	−1.07057	+	0.957550i
$343$	16.7984	+	7.79837i	0.907027	+	0.421073i
$344$			17.0344i			0.918436i
$345$	−4.23607	+	1.61803i	−0.228062	+	0.0871120i
$346$			5.61803i			0.302027i
$347$		−	23.1803i		−	1.24439i	−0.782864	−	0.622193i	$-0.786242\pi$
$347$		−	23.1803i		−	1.24439i	0.782864	−	0.622193i	$-0.213758\pi$
$348$	1.76393	−	0.673762i	0.0945567	−	0.0361174i
$349$		−	31.8541i		−	1.70511i	−0.522637	−	0.852555i	$-0.675052\pi$
$349$		−	31.8541i		−	1.70511i	0.522637	−	0.852555i	$-0.324948\pi$
$350$	−1.14590	+	7.85410i	−0.0612508	+	0.419819i
$351$	16.3262	−	31.6525i	0.871430	−	1.68948i
$352$	−7.56231			−0.403072
$353$	−26.5279			−1.41194			−0.705968	−	0.708244i	$-0.749488\pi$
$353$	−26.5279			−1.41194			−0.705968	+	0.708244i	$0.749488\pi$
$354$	−19.7984	+	7.56231i	−1.05227	+	0.401932i
$355$			13.9443i			0.740085i
$356$	5.00000			0.264999
$357$	−1.47214	−	6.58359i	−0.0779137	−	0.348441i
$358$	9.18034			0.485196
$359$		−	2.90983i		−	0.153575i	−0.997047	−	0.0767875i	$-0.975534\pi$
$359$		−	2.90983i		−	0.153575i	0.997047	−	0.0767875i	$-0.0244663\pi$
$360$	11.7082	+	13.0902i	0.617077	+	0.689913i
$361$	−10.9443			−0.576014
$362$	−10.8541			−0.570479
$363$	3.70820	+	9.70820i	0.194630	+	0.509549i
$364$	1.61803	−	11.0902i	0.0848080	−	0.581283i
$365$		−	21.5623i		−	1.12862i
$366$	0.854102	+	2.23607i	0.0446446	+	0.116881i
$367$			22.2705i			1.16251i	0.813721	+	0.581256i	$0.197438\pi$
$367$			22.2705i			1.16251i	−0.813721	+	0.581256i	$0.802562\pi$
$368$			4.85410i			0.253038i
$369$	0.527864	−	0.472136i	0.0274795	−	0.0245784i
$370$		−	24.4164i		−	1.26935i
$371$	−5.18034	+	35.5066i	−0.268950	+	1.84341i
$372$	−0.527864	+	0.201626i	−0.0273685	+	0.0104538i
$373$	−1.00000			−0.0517780			−0.0258890	−	0.999665i	$-0.508242\pi$
$373$	−1.00000			−0.0517780			−0.0258890	+	0.999665i	$0.508242\pi$
$374$	−5.32624			−0.275413
$375$	5.09017	+	13.3262i	0.262855	+	0.688164i
$376$			17.8885i			0.922531i
$377$	−12.0902			−0.622675
$378$	12.9443	−	18.0902i	0.665782	−	0.930458i
$379$	24.4721			1.25705			0.628525	−	0.777790i	$-0.283659\pi$
$379$	24.4721			1.25705			0.628525	+	0.777790i	$0.283659\pi$
$380$		−	8.85410i		−	0.454206i
$381$	4.81966	+	12.6180i	0.246919	+	0.646441i
$382$	35.1246			1.79713
$383$	−8.23607			−0.420843			−0.210422	−	0.977611i	$-0.567484\pi$
$383$	−8.23607			−0.420843			−0.210422	+	0.977611i	$0.567484\pi$
$384$	22.0344	−	8.41641i	1.12444	−	0.429498i
$385$	−2.23607	+	15.3262i	−0.113961	+	0.781097i
$386$			25.4164i			1.29366i
$387$	−17.0344	+	15.2361i	−0.865909	+	0.774493i
$388$		−	1.20163i		−	0.0610033i
$389$		−	32.7082i		−	1.65837i	−0.558973	−	0.829186i	$-0.688804\pi$
$389$		−	32.7082i		−	1.65837i	0.558973	−	0.829186i	$-0.311196\pi$
$390$	17.9443	+	46.9787i	0.908644	+	2.37886i
$391$			1.47214i			0.0744491i
$392$	−4.47214	+	15.0000i	−0.225877	+	0.757614i
$393$	11.5623	+	30.2705i	0.583241	+	1.52695i
$394$	−42.2148			−2.12675
$395$	20.3262			1.02272
$396$	−2.76393	−	3.09017i	−0.138893	−	0.155287i
$397$			15.2361i			0.764676i	0.924022	+	0.382338i	$0.124881\pi$
$397$			15.2361i			0.764676i	−0.924022	+	0.382338i	$0.875119\pi$
$398$	23.6525			1.18559
$399$	24.4721	−	5.47214i	1.22514	−	0.273949i
$400$	−9.00000			−0.450000
$401$		−	8.41641i		−	0.420295i	−0.977670	−	0.210148i	$-0.932606\pi$
$401$		−	8.41641i		−	0.420295i	0.977670	−	0.210148i	$-0.0673945\pi$
$402$	27.7984	−	10.6180i	1.38646	−	0.529579i
$403$	3.61803			0.180227
$404$	−3.14590			−0.156514
$405$	−2.61803	+	23.4164i	−0.130091	+	1.16357i
$406$	−7.47214	−	1.09017i	−0.370836	−	0.0541042i
$407$		−	12.8885i		−	0.638861i
$408$	5.32624	−	2.03444i	0.263688	−	0.100720i
$409$			33.4721i			1.65509i	0.561399	+	0.827545i	$0.310263\pi$
$409$			33.4721i			1.65509i	−0.561399	+	0.827545i	$0.689737\pi$
$410$			1.00000i			0.0493865i
$411$	23.0344	−	8.79837i	1.13621	−	0.433992i
$412$			6.29180i			0.309975i
$413$	19.7984	+	2.88854i	0.974214	+	0.142136i
$414$	−3.61803	+	3.23607i	−0.177817	+	0.159044i
$415$	−28.0344			−1.37616
$416$	23.1803			1.13651
$417$	−1.47214	+	0.562306i	−0.0720908	+	0.0275362i
$418$		−	19.7984i		−	0.968370i
$419$	−24.7984			−1.21148			−0.605740	−	0.795663i	$-0.707123\pi$
$419$	−24.7984			−1.21148			−0.605740	+	0.795663i	$0.707123\pi$
$420$	1.61803	+	7.23607i	0.0789520	+	0.353084i
$421$	39.6869			1.93422			0.967111	−	0.254355i	$-0.0818631\pi$
$421$	39.6869			1.93422			0.967111	+	0.254355i	$0.0818631\pi$
$422$		−	4.85410i		−	0.236294i
$423$	−17.8885	+	16.0000i	−0.869771	+	0.777947i
$424$	−30.3262			−1.47277
$425$	−2.72949			−0.132400
$426$	5.32624	+	13.9443i	0.258057	+	0.675602i
$427$	0.326238	−	2.23607i	0.0157878	−	0.108211i
$428$		−	7.18034i		−	0.347075i
$429$	9.47214	+	24.7984i	0.457319	+	1.19728i
$430$		−	32.2705i		−	1.55622i
$431$			21.9098i			1.05536i	0.849443	+	0.527680i	$0.176938\pi$
$431$			21.9098i			1.05536i	−0.849443	+	0.527680i	$0.823062\pi$
$432$	22.4164	+	11.5623i	1.07851	+	0.556292i
$433$			1.52786i			0.0734245i	0.999326	+	0.0367122i	$0.0116885\pi$
$433$			1.52786i			0.0734245i	−0.999326	+	0.0367122i	$0.988312\pi$
$434$	2.23607	+	0.326238i	0.107335	+	0.0156599i
$435$	7.47214	−	2.85410i	0.358261	−	0.136844i
$436$	−1.90983			−0.0914643
$437$	−5.47214			−0.261768
$438$	−8.23607	−	21.5623i	−0.393535	−	1.03029i
$439$		−	25.4721i		−	1.21572i	−0.794045	−	0.607859i	$-0.792028\pi$
$439$		−	25.4721i		−	1.21572i	0.794045	−	0.607859i	$-0.207972\pi$
$440$	−13.0902			−0.624049
$441$	−19.0000	+	8.94427i	−0.904762	+	0.425918i
$442$	16.3262			0.776560
$443$			22.1803i			1.05382i	0.849921	+	0.526910i	$0.176649\pi$
$443$			22.1803i			1.05382i	−0.849921	+	0.526910i	$0.823351\pi$
$444$	−2.20163	−	5.76393i	−0.104485	−	0.273544i
$445$	21.1803			1.00404
$446$	27.6525			1.30938
$447$	12.4721	−	4.76393i	0.589912	−	0.225326i
$448$	−11.0902	−	1.61803i	−0.523961	−	0.0764449i
$449$			10.9098i			0.514867i	0.966296	+	0.257433i	$0.0828768\pi$
$449$			10.9098i			0.514867i	−0.966296	+	0.257433i	$0.917123\pi$
$450$	−6.00000	−	6.70820i	−0.282843	−	0.316228i
$451$			0.527864i			0.0248561i
$452$		−	6.67376i		−	0.313907i
$453$	−1.52786	−	4.00000i	−0.0717853	−	0.187936i
$454$		−	36.1246i		−	1.69541i
$455$	6.85410	−	46.9787i	0.321325	−	2.20240i
$456$	7.56231	+	19.7984i	0.354137	+	0.927144i
$457$	15.5623			0.727974			0.363987	−	0.931404i	$-0.381415\pi$
$457$	15.5623			0.727974			0.363987	+	0.931404i	$0.381415\pi$
$458$	−17.6525			−0.824846
$459$	6.79837	+	3.50658i	0.317321	+	0.163673i
$460$		−	1.61803i		−	0.0754412i
$461$	24.6869			1.14978			0.574892	−	0.818229i	$-0.305044\pi$
$461$	24.6869			1.14978			0.574892	+	0.818229i	$0.305044\pi$
$462$	3.61803	+	16.1803i	0.168326	+	0.752778i
$463$	−16.5279			−0.768115			−0.384057	−	0.923309i	$-0.625474\pi$
$463$	−16.5279			−0.768115			−0.384057	+	0.923309i	$0.625474\pi$
$464$		−	8.56231i		−	0.397495i
$465$	−2.23607	+	0.854102i	−0.103695	+	0.0396080i
$466$	22.1246			1.02490
$467$	−33.8328			−1.56560			−0.782798	−	0.622276i	$-0.786208\pi$
$467$	−33.8328			−1.56560			−0.782798	+	0.622276i	$0.786208\pi$
$468$	8.47214	+	9.47214i	0.391625	+	0.437850i
$469$	−27.7984	−	4.05573i	−1.28361	−	0.187276i
$470$		−	33.8885i		−	1.56316i
$471$	12.1803	−	4.65248i	0.561240	−	0.214375i
$472$			16.9098i			0.778338i
$473$		−	17.0344i		−	0.783244i
$474$	20.3262	−	7.76393i	0.933615	−	0.356609i
$475$		−	10.1459i		−	0.465526i
$476$	2.38197	+	0.347524i	0.109177	+	0.0159287i
$477$	−27.1246	−	30.3262i	−1.24195	−	1.38854i
$478$	9.18034			0.419899
$479$	25.6525			1.17209			0.586046	−	0.810278i	$-0.300684\pi$
$479$	25.6525			1.17209			0.586046	+	0.810278i	$0.300684\pi$
$480$	−14.3262	+	5.47214i	−0.653900	+	0.249768i
$481$			39.5066i			1.80134i
$482$	0.854102			0.0389033
$483$	4.47214	−	1.00000i	0.203489	−	0.0455016i
$484$	−3.70820			−0.168555
$485$		−	5.09017i		−	0.231133i
$486$	6.32624	+	24.4164i	0.286964	+	1.10755i
$487$	14.7082			0.666492			0.333246	−	0.942840i	$-0.391856\pi$
$487$	14.7082			0.666492			0.333246	+	0.942840i	$0.391856\pi$
$488$	1.90983			0.0864539
$489$	−11.7984	−	30.8885i	−0.533541	−	1.39683i
$490$	8.47214	−	28.4164i	0.382732	−	1.28372i
$491$			21.9098i			0.988777i	0.869241	+	0.494388i	$0.164608\pi$
$491$			21.9098i			0.988777i	−0.869241	+	0.494388i	$0.835392\pi$
$492$	0.0901699	+	0.236068i	0.00406518	+	0.0106428i
$493$		−	2.59675i		−	0.116952i
$494$			60.6869i			2.73043i
$495$	−11.7082	−	13.0902i	−0.526245	−	0.588359i
$496$			2.56231i			0.115051i
$497$	2.03444	−	13.9443i	0.0912572	−	0.625486i
$498$	−28.0344	+	10.7082i	−1.25625	+	0.479846i
$499$	−17.5623			−0.786197			−0.393098	−	0.919496i	$-0.628597\pi$
$499$	−17.5623			−0.786197			−0.393098	+	0.919496i	$0.628597\pi$
$500$	−5.09017			−0.227639
$501$	11.8541	+	31.0344i	0.529602	+	1.38652i
$502$			10.4721i			0.467394i
$503$	0.257354			0.0114749			0.00573743	−	0.999984i	$-0.498174\pi$
$503$	0.257354			0.0114749			0.00573743	+	0.999984i	$0.498174\pi$
$504$	−9.79837	−	14.7984i	−0.436454	−	0.659172i
$505$	−13.3262			−0.593010
$506$		−	3.61803i		−	0.160841i
$507$	−21.0000	−	54.9787i	−0.932643	−	2.44169i
$508$	−4.81966			−0.213838
$509$	−20.0000			−0.886484			−0.443242	−	0.896402i	$-0.646172\pi$
$509$	−20.0000			−0.886484			−0.443242	+	0.896402i	$0.646172\pi$
$510$	−10.0902	+	3.85410i	−0.446800	+	0.170663i
$511$	−3.14590	+	21.5623i	−0.139166	+	0.953860i
$512$		−	5.29180i		−	0.233867i
$513$	−13.0344	+	25.2705i	−0.575485	+	1.11572i
$514$		−	50.0689i		−	2.20844i
$515$			26.6525i			1.17445i
$516$	−2.90983	−	7.61803i	−0.128098	−	0.335365i
$517$		−	17.8885i		−	0.786737i
$518$	−3.56231	+	24.4164i	−0.156519	+	1.07280i
$519$	2.14590	+	5.61803i	0.0941945	+	0.246604i
$520$	40.1246			1.75958
$521$	36.4721			1.59787			0.798937	−	0.601415i	$-0.205396\pi$
$521$	36.4721			1.59787			0.798937	+	0.601415i	$0.205396\pi$
$522$	6.38197	−	5.70820i	0.279331	−	0.249841i
$523$			25.5967i			1.11927i	0.828740	+	0.559634i	$0.189058\pi$
$523$			25.5967i			1.11927i	−0.828740	+	0.559634i	$0.810942\pi$
$524$	−11.5623			−0.505102
$525$	1.85410	+	8.29180i	0.0809196	+	0.361884i
$526$	29.0344			1.26596
$527$			0.777088i			0.0338505i
$528$	−17.5623	+	6.70820i	−0.764301	+	0.291937i
$529$	−1.00000			−0.0434783
$530$	57.4508			2.49551
$531$	−16.9098	+	15.1246i	−0.733824	+	0.656352i
$532$	−1.29180	+	8.85410i	−0.0560065	+	0.383874i
$533$		−	1.61803i		−	0.0700848i
$534$	21.1803	−	8.09017i	0.916563	−	0.350096i
$535$		−	30.4164i		−	1.31502i
$536$		−	23.7426i		−	1.02553i
$537$	9.18034	−	3.50658i	0.396161	−	0.151320i
$538$			17.5623i			0.757165i
$539$	4.47214	−	15.0000i	0.192629	−	0.646096i
$540$	−7.47214	−	3.85410i	−0.321550	−	0.165854i
$541$	−25.2361			−1.08498			−0.542492	−	0.840061i	$-0.682519\pi$
$541$	−25.2361			−1.08498			−0.542492	+	0.840061i	$0.682519\pi$
$542$	−3.61803			−0.155408
$543$	−10.8541	+	4.14590i	−0.465794	+	0.177918i
$544$			4.97871i			0.213461i
$545$	−8.09017			−0.346545
$546$	−11.0902	−	49.5967i	−0.474615	−	2.12254i
$547$	−20.2148			−0.864322			−0.432161	−	0.901797i	$-0.642249\pi$
$547$	−20.2148			−0.864322			−0.432161	+	0.901797i	$0.642249\pi$
$548$			8.79837i			0.375848i
$549$	1.70820	+	1.90983i	0.0729044	+	0.0815096i
$550$	6.70820			0.286039
$551$	9.65248			0.411209
$552$	1.38197	+	3.61803i	0.0588204	+	0.153994i
$553$	−20.3262	−	2.96556i	−0.864360	−	0.126108i
$554$			11.5623i			0.491235i
$555$	−9.32624	−	24.4164i	−0.395877	−	1.03642i
$556$		−	0.562306i		−	0.0238471i
$557$			32.0689i			1.35880i	0.733767	+	0.679401i	$0.237760\pi$
$557$			32.0689i			1.35880i	−0.733767	+	0.679401i	$0.762240\pi$
$558$	−1.90983	+	1.70820i	−0.0808496	+	0.0723140i
$559$			52.2148i			2.20845i
$560$	33.2705	+	4.85410i	1.40594	+	0.205123i
$561$	−5.32624	+	2.03444i	−0.224874	+	0.0858942i
$562$	1.70820			0.0720562
$563$	24.8541			1.04748			0.523738	−	0.851880i	$-0.324537\pi$
$563$	24.8541			1.04748			0.523738	+	0.851880i	$0.324537\pi$
$564$	−3.05573	−	8.00000i	−0.128669	−	0.336861i
$565$		−	28.2705i		−	1.18935i
$566$	14.2361			0.598387
$567$	6.03444	−	23.0344i	0.253423	−	0.967356i
$568$	11.9098			0.499725
$569$		−	35.5967i		−	1.49229i	−0.665782	−	0.746147i	$-0.731902\pi$
$569$		−	35.5967i		−	1.49229i	0.665782	−	0.746147i	$-0.268098\pi$
$570$	−14.3262	−	37.5066i	−0.600060	−	1.57098i
$571$	−16.4164			−0.687005			−0.343503	−	0.939152i	$-0.611613\pi$
$571$	−16.4164			−0.687005			−0.343503	+	0.939152i	$0.611613\pi$
$572$	−9.47214			−0.396050
$573$	35.1246	−	13.4164i	1.46735	−	0.560478i
$574$	0.145898	−	1.00000i	0.00608967	−	0.0417392i
$575$		−	1.85410i		−	0.0773214i
$576$	9.47214	−	8.47214i	0.394672	−	0.353006i
$577$		−	33.3050i		−	1.38650i	−0.720696	−	0.693252i	$-0.756177\pi$
$577$		−	33.3050i		−	1.38650i	0.720696	−	0.693252i	$-0.243823\pi$
$578$		−	24.0000i		−	0.998268i
$579$	9.70820	+	25.4164i	0.403459	+	1.05627i
$580$			2.85410i			0.118510i
$581$	28.0344	+	4.09017i	1.16306	+	0.169689i
$582$	−1.94427	−	5.09017i	−0.0805927	−	0.210994i
$583$	30.3262			1.25598
$584$	−18.4164			−0.762076
$585$	35.8885	+	40.1246i	1.48381	+	1.65895i
$586$		−	23.1246i		−	0.955269i
$587$	13.3262			0.550033			0.275016	−	0.961440i	$-0.411317\pi$
$587$	13.3262			0.550033			0.275016	+	0.961440i	$0.411317\pi$
$588$	−0.562306	−	7.47214i	−0.0231891	−	0.308146i
$589$	−2.88854			−0.119020
$590$		−	32.0344i		−	1.31884i
$591$	−42.2148	+	16.1246i	−1.73648	+	0.663278i
$592$	−27.9787			−1.14992
$593$	−31.1246			−1.27813			−0.639067	−	0.769151i	$-0.720679\pi$
$593$	−31.1246			−1.27813			−0.639067	+	0.769151i	$0.720679\pi$
$594$	−16.7082	−	8.61803i	−0.685546	−	0.353602i
$595$	10.0902	+	1.47214i	0.413657	+	0.0603517i
$596$			4.76393i			0.195138i
$597$	23.6525	−	9.03444i	0.968031	−	0.369755i
$598$			11.0902i			0.453511i
$599$			3.14590i			0.128538i	0.997933	+	0.0642690i	$0.0204716\pi$
$599$			3.14590i			0.128538i	−0.997933	+	0.0642690i	$0.979528\pi$
$600$	−6.70820	+	2.56231i	−0.273861	+	0.104606i
$601$			9.67376i			0.394601i	0.980343	+	0.197300i	$0.0632175\pi$
$601$			9.67376i			0.394601i	−0.980343	+	0.197300i	$0.936783\pi$
$602$	−4.70820	+	32.2705i	−0.191892	+	1.31525i
$603$	23.7426	−	21.2361i	0.966875	−	0.864800i
$604$	1.52786			0.0621679
$605$	−15.7082			−0.638629
$606$	−13.3262	+	5.09017i	−0.541341	+	0.206774i
$607$		−	34.5623i		−	1.40284i	−0.712748	−	0.701420i	$-0.752550\pi$
$607$		−	34.5623i		−	1.40284i	0.712748	−	0.701420i	$-0.247450\pi$
$608$	−18.5066			−0.750541
$609$	−7.88854	+	1.76393i	−0.319660	+	0.0714781i
$610$	−3.61803			−0.146490
$611$			54.8328i			2.21830i
$612$	−2.03444	+	1.81966i	−0.0822374	+	0.0735554i
$613$	−5.47214			−0.221017			−0.110509	−	0.993875i	$-0.535248\pi$
$613$	−5.47214			−0.221017			−0.110509	+	0.993875i	$0.535248\pi$
$614$	34.7426			1.40210
$615$	0.381966	+	1.00000i	0.0154024	+	0.0403239i
$616$	13.0902	+	1.90983i	0.527418	+	0.0769492i
$617$			9.90983i			0.398955i	0.979902	+	0.199477i	$0.0639244\pi$
$617$			9.90983i			0.398955i	−0.979902	+	0.199477i	$0.936076\pi$
$618$	10.1803	+	26.6525i	0.409513	+	1.07212i
$619$			39.9787i			1.60688i	0.595386	+	0.803440i	$0.296999\pi$
$619$			39.9787i			1.60688i	−0.595386	+	0.803440i	$0.703001\pi$
$620$		−	0.854102i		−	0.0343016i
$621$	−2.38197	+	4.61803i	−0.0955850	+	0.185315i
$622$		−	37.7426i		−	1.51334i
$623$	−21.1803	−	3.09017i	−0.848572	−	0.123805i
$624$	53.8328	−	20.5623i	2.15504	−	0.823151i
$625$	−30.8328			−1.23331
$626$	16.4721			0.658359
$627$	−7.56231	−	19.7984i	−0.302009	−	0.790671i
$628$			4.65248i			0.185654i
$629$	−8.48529			−0.338331
$630$	18.5623	+	28.0344i	0.739540	+	1.11692i
$631$	−6.81966			−0.271486			−0.135743	−	0.990744i	$-0.543342\pi$
$631$	−6.81966			−0.271486			−0.135743	+	0.990744i	$0.543342\pi$
$632$		−	17.3607i		−	0.690571i
$633$	−1.85410	−	4.85410i	−0.0736939	−	0.192933i
$634$	1.00000			0.0397151
$635$	−20.4164			−0.810200
$636$	13.5623	−	5.18034i	0.537780	−	0.205414i
$637$	−13.7082	+	45.9787i	−0.543139	+	1.82174i
$638$			6.38197i			0.252664i
$639$	10.6525	+	11.9098i	0.421405	+	0.471146i
$640$			35.6525i			1.40929i
$641$		−	7.43769i		−	0.293771i	−0.989153	−	0.146886i	$-0.953075\pi$
$641$		−	7.43769i		−	0.293771i	0.989153	−	0.146886i	$-0.0469249\pi$
$642$	−11.6180	−	30.4164i	−0.458527	−	1.20044i
$643$			5.79837i			0.228666i	0.993443	+	0.114333i	$0.0364730\pi$
$643$			5.79837i			0.228666i	−0.993443	+	0.114333i	$0.963527\pi$
$644$	−0.236068	+	1.61803i	−0.00930238	+	0.0637595i
$645$	−12.3262	−	32.2705i	−0.485345	−	1.27065i
$646$	−13.0344			−0.512833
$647$	−34.0344			−1.33803			−0.669016	−	0.743248i	$-0.733284\pi$
$647$	−34.0344			−1.33803			−0.669016	+	0.743248i	$0.733284\pi$
$648$	20.0000	+	2.23607i	0.785674	+	0.0878410i
$649$		−	16.9098i		−	0.663769i
$650$	−20.5623			−0.806520
$651$	2.36068	−	0.527864i	0.0925223	−	0.0206886i
$652$	11.7984			0.462060
$653$			2.50658i			0.0980900i	0.998797	+	0.0490450i	$0.0156178\pi$
$653$			2.50658i			0.0980900i	−0.998797	+	0.0490450i	$0.984382\pi$
$654$	−8.09017	+	3.09017i	−0.316351	+	0.120835i
$655$	−48.9787			−1.91376
$656$	1.14590			0.0447398
$657$	−16.4721	−	18.4164i	−0.642639	−	0.718493i
$658$	−4.94427	+	33.8885i	−0.192748	+	1.32111i
$659$		−	4.41641i		−	0.172039i	−0.996293	−	0.0860194i	$-0.972585\pi$
$659$		−	4.41641i		−	0.172039i	0.996293	−	0.0860194i	$-0.0274147\pi$
$660$	5.85410	−	2.23607i	0.227871	−	0.0870388i
$661$		−	16.0557i		−	0.624495i	−0.950001	−	0.312248i	$-0.898918\pi$
$661$		−	16.0557i		−	0.624495i	0.950001	−	0.312248i	$-0.101082\pi$
$662$			58.3607i			2.26825i
$663$	16.3262	−	6.23607i	0.634059	−	0.242189i
$664$			23.9443i			0.929218i
$665$	−5.47214	+	37.5066i	−0.212200	+	1.45444i
$666$	−18.6525	−	20.8541i	−0.722769	−	0.808080i
$667$	1.76393			0.0682997
$668$	−11.8541			−0.458649
$669$	27.6525	−	10.5623i	1.06911	−	0.408362i
$670$			44.9787i			1.73768i
$671$	−1.90983			−0.0737282
$672$	15.1246	−	3.38197i	0.583445	−	0.130462i
$673$	6.23607			0.240383			0.120191	−	0.992751i	$-0.461649\pi$
$673$	6.23607			0.240383			0.120191	+	0.992751i	$0.461649\pi$
$674$		−	52.5066i		−	2.02248i
$675$	−8.56231	−	4.41641i	−0.329563	−	0.169988i
$676$	21.0000			0.807692
$677$	−13.5066			−0.519100			−0.259550	−	0.965730i	$-0.583574\pi$
$677$	−13.5066			−0.519100			−0.259550	+	0.965730i	$0.583574\pi$
$678$	−10.7984	−	28.2705i	−0.414709	−	1.08572i
$679$	−0.742646	+	5.09017i	−0.0285001	+	0.195343i
$680$			8.61803i			0.330487i
$681$	−13.7984	−	36.1246i	−0.528755	−	1.38430i
$682$		−	1.90983i		−	0.0731312i
$683$		−	28.5967i		−	1.09422i	−0.837059	−	0.547112i	$-0.815727\pi$
$683$		−	28.5967i		−	1.09422i	0.837059	−	0.547112i	$-0.184273\pi$
$684$	−6.76393	−	7.56231i	−0.258625	−	0.289152i
$685$			37.2705i			1.42403i
$686$	−12.6180	+	27.1803i	−0.481759	+	1.03775i
$687$	−17.6525	+	6.74265i	−0.673484	+	0.257248i
$688$	−36.9787			−1.40980
$689$	−92.9574			−3.54140
$690$	−2.61803	−	6.85410i	−0.0996669	−	0.260931i
$691$			8.09017i			0.307765i	0.988089	+	0.153882i	$0.0491777\pi$
$691$			8.09017i			0.307765i	−0.988089	+	0.153882i	$0.950822\pi$
$692$	−2.14590			−0.0815748
$693$	9.79837	+	14.7984i	0.372209	+	0.562144i
$694$	37.5066			1.42373
$695$		−	2.38197i		−	0.0903531i
$696$	−2.43769	−	6.38197i	−0.0924006	−	0.241908i
$697$	0.347524			0.0131634
$698$	51.5410			1.95086
$699$	22.1246	−	8.45085i	0.836830	−	0.319640i
$700$	−3.00000	−	0.437694i	−0.113389	−	0.0165433i
$701$		−	31.6312i		−	1.19469i	−0.801983	−	0.597347i	$-0.796222\pi$
$701$		−	31.6312i		−	1.19469i	0.801983	−	0.597347i	$-0.203778\pi$
$702$	51.2148	+	26.4164i	1.93298	+	0.997023i
$703$		−	31.5410i		−	1.18959i
$704$			9.47214i			0.356995i
$705$	−12.9443	−	33.8885i	−0.487509	−	1.27632i
$706$		−	42.9230i		−	1.61543i
$707$	13.3262	+	1.94427i	0.501185	+	0.0731219i
$708$	−2.88854	−	7.56231i	−0.108558	−	0.284209i
$709$	32.5623			1.22290			0.611452	−	0.791282i	$-0.290586\pi$
$709$	32.5623			1.22290			0.611452	+	0.791282i	$0.290586\pi$
$710$	−22.5623			−0.846748
$711$	17.3607	−	15.5279i	0.651076	−	0.582340i
$712$		−	18.0902i		−	0.677958i
$713$	−0.527864			−0.0197687
$714$	10.6525	−	2.38197i	0.398659	−	0.0891428i
$715$	−40.1246			−1.50058
$716$			3.50658i			0.131047i
$717$	9.18034	−	3.50658i	0.342846	−	0.130956i
$718$	4.70820			0.175709
$719$	17.7639			0.662483			0.331241	−	0.943546i	$-0.392533\pi$
$719$	17.7639			0.662483			0.331241	+	0.943546i	$0.392533\pi$
$720$	−28.4164	+	25.4164i	−1.05902	+	0.947214i
$721$	3.88854	−	26.6525i	0.144817	−	0.992590i
$722$		−	17.7082i		−	0.659031i
$723$	0.854102	−	0.326238i	0.0317644	−	0.0121329i
$724$		−	4.14590i		−	0.154081i
$725$			3.27051i			0.121464i
$726$	−15.7082	+	6.00000i	−0.582986	+	0.222681i
$727$		−	2.52786i		−	0.0937533i	−0.998901	−	0.0468766i	$-0.985073\pi$
$727$		−	2.52786i		−	0.0937533i	0.998901	−	0.0468766i	$-0.0149268\pi$
$728$	−40.1246	−	5.85410i	−1.48712	−	0.216967i
$729$	15.6525	+	22.0000i	0.579721	+	0.814815i
$730$	34.8885			1.29128
$731$	−11.2148			−0.414794
$732$	−0.854102	+	0.326238i	−0.0315685	+	0.0120581i
$733$			38.3607i			1.41688i	0.705769	+	0.708442i	$0.250602\pi$
$733$			38.3607i			1.41688i	−0.705769	+	0.708442i	$0.749398\pi$
$734$	−36.0344			−1.33006
$735$	−2.38197	−	31.6525i	−0.0878601	−	1.16752i
$736$	−3.38197			−0.124661
$737$			23.7426i			0.874572i
$738$	0.763932	+	0.854102i	0.0281207	+	0.0314399i
$739$	−28.4164			−1.04531			−0.522657	−	0.852543i	$-0.675059\pi$
$739$	−28.4164			−1.04531			−0.522657	+	0.852543i	$0.675059\pi$
$740$	9.32624			0.342839
$741$	23.1803	+	60.6869i	0.851551	+	2.22939i
$742$	−57.4508	−	8.38197i	−2.10909	−	0.307712i
$743$			11.8541i			0.434885i	0.976073	+	0.217442i	$0.0697714\pi$
$743$			11.8541i			0.434885i	−0.976073	+	0.217442i	$0.930229\pi$
$744$	0.729490	+	1.90983i	0.0267444	+	0.0700178i
$745$			20.1803i			0.739350i
$746$		−	1.61803i		−	0.0592404i
$747$	−23.9443	+	21.4164i	−0.876075	+	0.783585i
$748$		−	2.03444i		−	0.0743866i
$749$	−4.43769	+	30.4164i	−0.162150	+	1.11139i
$750$	−21.5623	+	8.23607i	−0.787344	+	0.300739i
$751$	44.0344			1.60684			0.803420	−	0.595413i	$-0.203012\pi$
$751$	44.0344			1.60684			0.803420	+	0.595413i	$0.203012\pi$
$752$	−38.8328			−1.41609
$753$	4.00000	+	10.4721i	0.145768	+	0.381626i
$754$		−	19.5623i		−	0.712417i
$755$	6.47214			0.235545
$756$	6.90983	+	4.94427i	0.251308	+	0.179821i
$757$	−17.0000			−0.617876			−0.308938	−	0.951082i	$-0.599973\pi$
$757$	−17.0000			−0.617876			−0.308938	+	0.951082i	$0.599973\pi$
$758$			39.5967i			1.43822i
$759$	−1.38197	−	3.61803i	−0.0501622	−	0.131326i
$760$	−32.0344			−1.16201
$761$	22.0000			0.797499			0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000			0.797499			0.398750	+	0.917060i	$0.369444\pi$
$762$	−20.4164	+	7.79837i	−0.739608	+	0.282505i
$763$	8.09017	+	1.18034i	0.292884	+	0.0427312i
$764$			13.4164i			0.485389i
$765$	−8.61803	+	7.70820i	−0.311586	+	0.278691i
$766$		−	13.3262i		−	0.481497i
$767$			51.8328i			1.87157i
$768$	8.38197	+	21.9443i	0.302458	+	0.791846i
$769$		−	22.1803i		−	0.799844i	−0.916549	−	0.399922i	$-0.869037\pi$
$769$		−	22.1803i		−	0.799844i	0.916549	−	0.399922i	$-0.130963\pi$
$770$	−24.7984	−	3.61803i	−0.893671	−	0.130385i
$771$	−19.1246	−	50.0689i	−0.688756	−	1.80319i
$772$	−9.70820			−0.349406
$773$	0.708204			0.0254723			0.0127362	−	0.999919i	$-0.495946\pi$
$773$	0.708204			0.0254723			0.0127362	+	0.999919i	$0.495946\pi$
$774$	−24.6525	−	27.5623i	−0.886115	−	0.990707i
$775$		−	0.978714i		−	0.0351564i
$776$	−4.34752			−0.156067
$777$	5.76393	+	25.7771i	0.206780	+	0.924748i
$778$	52.9230			1.89738
$779$			1.29180i			0.0462834i
$780$	−17.9443	+	6.85410i	−0.642508	+	0.245416i
$781$	−11.9098			−0.426167
$782$	−2.38197			−0.0851789
$783$	4.20163	−	8.14590i	0.150154	−	0.291111i
$784$	−32.5623	−	9.70820i	−1.16294	−	0.346722i
$785$			19.7082i			0.703416i
$786$	−48.9787	+	18.7082i	−1.74701	+	0.667300i
$787$		−	18.5066i		−	0.659688i	−0.944035	−	0.329844i	$-0.893004\pi$
$787$		−	18.5066i		−	0.659688i	0.944035	−	0.329844i	$-0.106996\pi$
$788$		−	16.1246i		−	0.574416i
$789$	29.0344	−	11.0902i	1.03365	−	0.394821i
$790$			32.8885i			1.17012i
$791$	−4.12461	+	28.2705i	−0.146654	+	1.00518i
$792$	−11.1803	+	10.0000i	−0.397276	+	0.355335i
$793$	5.85410			0.207885
$794$	−24.6525			−0.874884
$795$	57.4508	−	21.9443i	2.03757	−	0.778283i
$796$			9.03444i			0.320217i
$797$	26.5410			0.940131			0.470066	−	0.882631i	$-0.344230\pi$
$797$	26.5410			0.940131			0.470066	+	0.882631i	$0.344230\pi$
$798$	8.85410	+	39.5967i	0.313432	+	1.40171i
$799$	−11.7771			−0.416643
$800$		−	6.27051i		−	0.221696i
$801$	18.0902	−	16.1803i	0.639185	−	0.571704i
$802$	13.6180			0.480869
$803$	18.4164			0.649901
$804$	4.05573	+	10.6180i	0.143035	+	0.374469i
$805$	−1.00000	+	6.85410i	−0.0352454	+	0.241575i
$806$			5.85410i			0.206202i
$807$	6.70820	+	17.5623i	0.236140	+	0.618222i
$808$			11.3820i			0.400416i
$809$		−	23.0344i		−	0.809848i	−0.914350	−	0.404924i	$-0.867298\pi$
$809$		−	23.0344i		−	0.809848i	0.914350	−	0.404924i	$-0.132702\pi$
$810$	−37.8885	−	4.23607i	−1.33127	−	0.148840i
$811$			49.0689i			1.72304i	0.507722	+	0.861521i	$0.330488\pi$
$811$			49.0689i			1.72304i	−0.507722	+	0.861521i	$0.669512\pi$
$812$	0.416408	−	2.85410i	0.0146131	−	0.100159i
$813$	−3.61803	+	1.38197i	−0.126890	+	0.0484677i
$814$	20.8541			0.730936
$815$	49.9787			1.75068
$816$	4.41641	+	11.5623i	0.154605	+	0.404762i
$817$		−	41.6869i		−	1.45844i
$818$	−54.1591			−1.89363
$819$	−30.0344	−	45.3607i	−1.04949	−	1.58503i
$820$	−0.381966			−0.0133388
$821$			26.1803i			0.913700i	0.889544	+	0.456850i	$0.151022\pi$
$821$			26.1803i			0.913700i	−0.889544	+	0.456850i	$0.848978\pi$
$822$	14.2361	+	37.2705i	0.496540	+	1.29996i
$823$	11.5623			0.403037			0.201518	−	0.979485i	$-0.435412\pi$
$823$	11.5623			0.403037			0.201518	+	0.979485i	$0.435412\pi$
$824$	22.7639			0.793019
$825$	6.70820	−	2.56231i	0.233550	−	0.0892080i
$826$	−4.67376	+	32.0344i	−0.162621	+	1.11462i
$827$			26.2148i			0.911577i	0.890088	+	0.455789i	$0.150643\pi$
$827$			26.2148i			0.911577i	−0.890088	+	0.455789i	$0.849357\pi$
$828$	−1.23607	−	1.38197i	−0.0429563	−	0.0480266i
$829$		−	1.00000i		−	0.0347314i	−0.999849	−	0.0173657i	$-0.994472\pi$
$829$		−	1.00000i		−	0.0347314i	0.999849	−	0.0173657i	$-0.00552796\pi$
$830$		−	45.3607i		−	1.57449i
$831$	4.41641	+	11.5623i	0.153203	+	0.401092i
$832$		−	29.0344i		−	1.00659i
$833$	−9.87539	−	2.94427i	−0.342162	−	0.102013i
$834$	−0.909830	−	2.38197i	−0.0315048	−	0.0824807i
$835$	−50.2148			−1.73775
$836$	7.56231			0.261548
$837$	−1.25735	+	2.43769i	−0.0434605	+	0.0842590i
$838$		−	40.1246i		−	1.38608i
$839$	10.8541			0.374725			0.187363	−	0.982291i	$-0.440006\pi$
$839$	10.8541			0.374725			0.187363	+	0.982291i	$0.440006\pi$
$840$	26.1803	−	5.85410i	0.903308	−	0.201986i
$841$	25.8885			0.892708
$842$			64.2148i			2.21299i
$843$	1.70820	−	0.652476i	0.0588337	−	0.0224725i
$844$	1.85410			0.0638208
$845$	88.9574			3.06023
$846$	−25.8885	−	28.9443i	−0.890066	−	0.995125i
$847$	15.7082	+	2.29180i	0.539740	+	0.0787470i
$848$		−	65.8328i		−	2.26071i
$849$	14.2361	−	5.43769i	0.488581	−	0.186621i
$850$		−	4.41641i		−	0.151482i
$851$		−	5.76393i		−	0.197585i
$852$	−5.32624	+	2.03444i	−0.182474	+	0.0696988i
$853$			5.34752i			0.183096i	0.995801	+	0.0915479i	$0.0291815\pi$
$853$			5.34752i			0.183096i	−0.995801	+	0.0915479i	$0.970819\pi$
$854$	3.61803	+	0.527864i	0.123807	+	0.0180631i
$855$	−28.6525	−	32.0344i	−0.979894	−	1.09555i
$856$	−25.9787			−0.887934
$857$	−26.4721			−0.904271			−0.452135	−	0.891949i	$-0.649338\pi$
$857$	−26.4721			−0.904271			−0.452135	+	0.891949i	$0.649338\pi$
$858$	−40.1246	+	15.3262i	−1.36983	+	0.523229i
$859$			38.4721i			1.31265i	0.754477	+	0.656326i	$0.227890\pi$
$859$			38.4721i			1.31265i	−0.754477	+	0.656326i	$0.772110\pi$
$860$	12.3262			0.420321
$861$	−0.236068	−	1.05573i	−0.00804518	−	0.0359791i
$862$	−35.4508			−1.20746
$863$		−	16.3607i		−	0.556924i	−0.960447	−	0.278462i	$-0.910175\pi$
$863$		−	16.3607i		−	0.556924i	0.960447	−	0.278462i	$-0.0898246\pi$
$864$	−8.05573	+	15.6180i	−0.274061	+	0.531336i
$865$	−9.09017			−0.309075
$866$	−2.47214			−0.0840066
$867$	−9.16718	−	24.0000i	−0.311334	−	0.815083i
$868$	−0.124612	+	0.854102i	−0.00422960	+	0.0289901i
$869$			17.3607i			0.588921i
$870$	4.61803	+	12.0902i	0.156566	+	0.409895i
$871$		−	72.7771i		−	2.46596i
$872$			6.90983i			0.233996i
$873$	−3.88854	−	4.34752i	−0.131607	−	0.147141i
$874$		−	8.85410i		−	0.299494i
$875$	21.5623	+	3.14590i	0.728939	+	0.106351i
$876$	8.23607	−	3.14590i	0.278271	−	0.106290i
$877$	9.70820			0.327823			0.163911	−	0.986475i	$-0.447589\pi$
$877$	9.70820			0.327823			0.163911	+	0.986475i	$0.447589\pi$
$878$	41.2148			1.39093
$879$	−8.83282	−	23.1246i	−0.297923	−	0.779974i
$880$		−	28.4164i		−	0.957917i
$881$	−25.8885			−0.872207			−0.436104	−	0.899896i	$-0.643642\pi$
$881$	−25.8885			−0.872207			−0.436104	+	0.899896i	$0.643642\pi$
$882$	−14.4721	−	30.7426i	−0.487302	−	1.03516i
$883$	56.1591			1.88990			0.944951	−	0.327211i	$-0.106109\pi$
$883$	56.1591			1.88990			0.944951	+	0.327211i	$0.106109\pi$
$884$			6.23607i			0.209742i
$885$	−12.2361	−	32.0344i	−0.411311	−	1.07683i
$886$	−35.8885			−1.20570
$887$	19.9098			0.668507			0.334253	−	0.942483i	$-0.391516\pi$
$887$	19.9098			0.668507			0.334253	+	0.942483i	$0.391516\pi$
$888$	−20.8541	+	7.96556i	−0.699818	+	0.267307i
$889$	20.4164	+	2.97871i	0.684744	+	0.0999029i
$890$			34.2705i			1.14875i
$891$	−20.0000	−	2.23607i	−0.670025	−	0.0749111i
$892$			10.5623i			0.353652i
$893$		−	43.7771i		−	1.46494i
$894$	7.70820	+	20.1803i	0.257801	+	0.674932i
$895$			14.8541i			0.496518i
$896$	5.20163	−	35.6525i	0.173774	−	1.19107i
$897$	4.23607	+	11.0902i	0.141438	+	0.370290i
$898$	−17.6525			−0.589071
$899$	0.931116			0.0310545
$900$	2.56231	−	2.29180i	0.0854102	−	0.0763932i
$901$		−	19.9656i		−	0.665149i
$902$	−0.854102			−0.0284385
$903$	7.61803	+	34.0689i	0.253512	+	1.13374i
$904$	−24.1459			−0.803081
$905$		−	17.5623i		−	0.583791i
$906$	6.47214	−	2.47214i	0.215022	−	0.0821312i
$907$	−4.03444			−0.133961			−0.0669807	−	0.997754i	$-0.521337\pi$
$907$	−4.03444			−0.133961			−0.0669807	+	0.997754i	$0.521337\pi$
$908$	13.7984			0.457915
$909$	−11.3820	+	10.1803i	−0.377516	+	0.337661i
$910$	76.0132	+	11.0902i	2.51981	+	0.367636i
$911$			15.1246i			0.501101i	0.968104	+	0.250550i	$0.0806116\pi$
$911$			15.1246i			0.501101i	−0.968104	+	0.250550i	$0.919388\pi$
$912$	−42.9787	+	16.4164i	−1.42317	+	0.543602i
$913$		−	23.9443i		−	0.792440i
$914$			25.1803i			0.832892i
$915$	−3.61803	+	1.38197i	−0.119609	+	0.0456864i
$916$		−	6.74265i		−	0.222783i
$917$	48.9787	+	7.14590i	1.61742	+	0.235978i
$918$	−5.67376	+	11.0000i	−0.187262	+	0.363054i
$919$	−14.3475			−0.473281			−0.236641	−	0.971597i	$-0.576046\pi$
$919$	−14.3475			−0.473281			−0.236641	+	0.971597i	$0.576046\pi$
$920$	−5.85410			−0.193004
$921$	34.7426	−	13.2705i	1.14481	−	0.437278i
$922$			39.9443i			1.31549i
$923$	36.5066			1.20163
$924$	−6.18034	+	1.38197i	−0.203318	+	0.0454633i
$925$	10.6869			0.351384
$926$		−	26.7426i		−	0.878818i
$927$	20.3607	+	22.7639i	0.668732	+	0.747666i
$928$	5.96556			0.195829
$929$	−34.3951			−1.12847			−0.564234	−	0.825615i	$-0.690828\pi$
$929$	−34.3951			−1.12847			−0.564234	+	0.825615i	$0.690828\pi$
$930$	−1.38197	−	3.61803i	−0.0453165	−	0.118640i
$931$	10.9443	−	36.7082i	0.358684	−	1.20306i
$932$			8.45085i			0.276817i
$933$	−14.4164	−	37.7426i	−0.471972	−	1.23564i
$934$		−	54.7426i		−	1.79123i
$935$		−	8.61803i		−	0.281840i
$936$	34.2705	−	30.6525i	1.12017	−	1.00191i
$937$		−	38.7082i		−	1.26454i	−0.774747	−	0.632271i	$-0.782123\pi$
$937$		−	38.7082i		−	1.26454i	0.774747	−	0.632271i	$-0.217877\pi$
$938$	6.56231	−	44.9787i	0.214267	−	1.46861i
$939$	16.4721	−	6.29180i	0.537548	−	0.205325i
$940$	12.9443			0.422196
$941$	26.4721			0.862967			0.431483	−	0.902121i	$-0.357990\pi$
$941$	26.4721			0.862967			0.431483	+	0.902121i	$0.357990\pi$
$942$	7.52786	+	19.7082i	0.245271	+	0.642128i
$943$			0.236068i			0.00768743i
$944$	−36.7082			−1.19475
$945$	29.2705	+	20.9443i	0.952170	+	0.681317i
$946$	27.5623			0.896128
$947$			4.83282i			0.157045i	0.996912	+	0.0785227i	$0.0250203\pi$
$947$			4.83282i			0.157045i	−0.996912	+	0.0785227i	$0.974980\pi$
$948$	2.96556	+	7.76393i	0.0963169	+	0.252161i
$949$	−56.4508			−1.83247
$950$	16.4164			0.532619
$951$	1.00000	−	0.381966i	0.0324272	−	0.0123861i
$952$	1.25735	−	8.61803i	0.0407511	−	0.279312i
$953$			3.03444i			0.0982952i	0.998792	+	0.0491476i	$0.0156505\pi$
$953$			3.03444i			0.0982952i	−0.998792	+	0.0491476i	$0.984350\pi$
$954$	49.0689	−	43.8885i	1.58866	−	1.42094i
$955$			56.8328i			1.83907i
$956$			3.50658i			0.113411i
$957$	2.43769	+	6.38197i	0.0787995	+	0.206300i
$958$			41.5066i			1.34102i
$959$	5.43769	−	37.2705i	0.175592	−	1.20353i
$960$	6.85410	+	17.9443i	0.221215	+	0.579149i
$961$	30.7214			0.991012
$962$	−63.9230			−2.06096
$963$	−23.2361	−	25.9787i	−0.748772	−	0.837152i
$964$			0.326238i			0.0105074i
$965$	−41.1246			−1.32385
$966$	1.61803	+	7.23607i	0.0520594	+	0.232817i
$967$	15.8885			0.510941			0.255471	−	0.966817i	$-0.417770\pi$
$967$	15.8885			0.510941			0.255471	+	0.966817i	$0.417770\pi$
$968$			13.4164i			0.431220i
$969$	−13.0344	+	4.97871i	−0.418727	+	0.159939i
$970$	8.23607			0.264444
$971$	−6.74265			−0.216382			−0.108191	−	0.994130i	$-0.534506\pi$
$971$	−6.74265			−0.216382			−0.108191	+	0.994130i	$0.534506\pi$
$972$	−9.32624	+	2.41641i	−0.299139	+	0.0775063i
$973$	−0.347524	+	2.38197i	−0.0111411	+	0.0763623i
$974$			23.7984i			0.762549i
$975$	−20.5623	+	7.85410i	−0.658521	+	0.251533i
$976$			4.14590i			0.132707i
$977$		−	7.97871i		−	0.255262i	−0.991822	−	0.127631i	$-0.959263\pi$
$977$		−	7.97871i		−	0.255262i	0.991822	−	0.127631i	$-0.0407373\pi$
$978$	49.9787	−	19.0902i	1.59814	−	0.610436i
$979$			18.0902i			0.578164i
$980$	10.8541	+	3.23607i	0.346722	+	0.103372i
$981$	−6.90983	+	6.18034i	−0.220614	+	0.197323i
$982$	−35.4508			−1.13128
$983$	2.81966			0.0899332			0.0449666	−	0.998988i	$-0.485682\pi$
$983$	2.81966			0.0899332			0.0449666	+	0.998988i	$0.485682\pi$
$984$	0.854102	−	0.326238i	0.0272278	−	0.0104001i
$985$		−	68.3050i		−	2.17638i
$986$	4.20163			0.133807
$987$	8.00000	+	35.7771i	0.254643	+	1.13880i
$988$	−23.1803			−0.737465
$989$		−	7.61803i		−	0.242239i
$990$	21.1803	−	18.9443i	0.673155	−	0.602088i
$991$	2.20163			0.0699370			0.0349685	−	0.999388i	$-0.488867\pi$
$991$	2.20163			0.0699370			0.0349685	+	0.999388i	$0.488867\pi$
$992$	−1.78522			−0.0566807
$993$	22.2918	+	58.3607i	0.707409	+	1.85202i
$994$	22.5623	+	3.29180i	0.715633	+	0.104409i
$995$			38.2705i			1.21326i
$996$	−4.09017	−	10.7082i	−0.129602	−	0.339302i
$997$		−	18.0557i		−	0.571831i	−0.958255	−	0.285915i	$-0.907702\pi$
$997$		−	18.0557i		−	0.571831i	0.958255	−	0.285915i	$-0.0922976\pi$
$998$		−	28.4164i		−	0.899506i
$999$	−26.6180	−	13.7295i	−0.842157	−	0.434382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.d.a.461.4	yes	4
3.2	odd	2		483.2.d.b.461.1	yes	4
7.6	odd	2		483.2.d.b.461.4	yes	4
21.20	even	2	inner	483.2.d.a.461.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.d.a.461.1	✓	4	21.20	even	2	inner
483.2.d.a.461.4	yes	4	1.1	even	1	trivial
483.2.d.b.461.1	yes	4	3.2	odd	2
483.2.d.b.461.4	yes	4	7.6	odd	2

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.61803i q^{2} +(0.618034 + 1.61803i) q^{3} -0.618034 q^{4} -2.61803 q^{5} +(-2.61803 + 1.00000i) q^{6} +(2.61803 + 0.381966i) q^{7} +2.23607i q^{8} +(-2.23607 + 2.00000i) q^{9} -4.23607i q^{10} -2.23607i q^{11} +(-0.381966 - 1.00000i) q^{12} +6.85410i q^{13} +(-0.618034 + 4.23607i) q^{14} +(-1.61803 - 4.23607i) q^{15} -4.85410 q^{16} -1.47214 q^{17} +(-3.23607 - 3.61803i) q^{18} -5.47214i q^{19} +1.61803 q^{20} +(1.00000 + 4.47214i) q^{21} +3.61803 q^{22} -1.00000i q^{23} +(-3.61803 + 1.38197i) q^{24} +1.85410 q^{25} -11.0902 q^{26} +(-4.61803 - 2.38197i) q^{27} +(-1.61803 - 0.236068i) q^{28} +1.76393i q^{29} +(6.85410 - 2.61803i) q^{30} -0.527864i q^{31} -3.38197i q^{32} +(3.61803 - 1.38197i) q^{33} -2.38197i q^{34} +(-6.85410 - 1.00000i) q^{35} +(1.38197 - 1.23607i) q^{36} +5.76393 q^{37} +8.85410 q^{38} +(-11.0902 + 4.23607i) q^{39} -5.85410i q^{40} -0.236068 q^{41} +(-7.23607 + 1.61803i) q^{42} +7.61803 q^{43} +1.38197i q^{44} +(5.85410 - 5.23607i) q^{45} +1.61803 q^{46} +8.00000 q^{47} +(-3.00000 - 7.85410i) q^{48} +(6.70820 + 2.00000i) q^{49} +3.00000i q^{50} +(-0.909830 - 2.38197i) q^{51} -4.23607i q^{52} +13.5623i q^{53} +(3.85410 - 7.47214i) q^{54} +5.85410i q^{55} +(-0.854102 + 5.85410i) q^{56} +(8.85410 - 3.38197i) q^{57} -2.85410 q^{58} +7.56231 q^{59} +(1.00000 + 2.61803i) q^{60} -0.854102i q^{61} +0.854102 q^{62} +(-6.61803 + 4.38197i) q^{63} -4.23607 q^{64} -17.9443i q^{65} +(2.23607 + 5.85410i) q^{66} -10.6180 q^{67} +0.909830 q^{68} +(1.61803 - 0.618034i) q^{69} +(1.61803 - 11.0902i) q^{70} -5.32624i q^{71} +(-4.47214 - 5.00000i) q^{72} +8.23607i q^{73} +9.32624i q^{74} +(1.14590 + 3.00000i) q^{75} +3.38197i q^{76} +(0.854102 - 5.85410i) q^{77} +(-6.85410 - 17.9443i) q^{78} -7.76393 q^{79} +12.7082 q^{80} +(1.00000 - 8.94427i) q^{81} -0.381966i q^{82} +10.7082 q^{83} +(-0.618034 - 2.76393i) q^{84} +3.85410 q^{85} +12.3262i q^{86} +(-2.85410 + 1.09017i) q^{87} +5.00000 q^{88} -8.09017 q^{89} +(8.47214 + 9.47214i) q^{90} +(-2.61803 + 17.9443i) q^{91} +0.618034i q^{92} +(0.854102 - 0.326238i) q^{93} +12.9443i q^{94} +14.3262i q^{95} +(5.47214 - 2.09017i) q^{96} +1.94427i q^{97} +(-3.23607 + 10.8541i) q^{98} +(4.47214 + 5.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} - 6 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{12} + 2 q^{14} - 2 q^{15} - 6 q^{16} + 12 q^{17} - 4 q^{18} + 2 q^{20} + 4 q^{21} + 10 q^{22} - 10 q^{24} - 6 q^{25} - 22 q^{26} - 14 q^{27}+ \cdots - 4 q^{98}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 - 6 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^12 + 2 * q^14 - 2 * q^15 - 6 * q^16 + 12 * q^17 - 4 * q^18 + 2 * q^20 + 4 * q^21 + 10 * q^22 - 10 * q^24 - 6 * q^25 - 22 * q^26 - 14 * q^27 - 2 * q^28 + 14 * q^30 + 10 * q^33 - 14 * q^35 + 10 * q^36 + 32 * q^37 + 22 * q^38 - 22 * q^39 + 8 * q^41 - 20 * q^42 + 26 * q^43 + 10 * q^45 + 2 * q^46 + 32 * q^47 - 12 * q^48 - 26 * q^51 + 2 * q^54 + 10 * q^56 + 22 * q^57 + 2 * q^58 - 10 * q^59 + 4 * q^60 - 10 * q^62 - 22 * q^63 - 8 * q^64 - 38 * q^67 + 26 * q^68 + 2 * q^69 + 2 * q^70 + 18 * q^75 - 10 * q^77 - 14 * q^78 - 40 * q^79 + 24 * q^80 + 4 * q^81 + 16 * q^83 + 2 * q^84 + 2 * q^85 + 2 * q^87 + 20 * q^88 - 10 * q^89 + 16 * q^90 - 6 * q^91 - 10 * q^93 + 4 * q^96 - 4 * q^98

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