LMFDB - Embedded newform 135.3.l.a.118.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,3,Mod(37,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.37"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			118.5
Character	$\chi$	$=$	135.118
Dual form			135.3.l.a.127.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.183646 + 0.0492077i) q^{2} +(-3.43280 - 1.98193i) q^{4} +(1.61810 + 4.73094i) q^{5} +(8.70492 + 2.33248i) q^{7} +(-1.07064 - 1.07064i) q^{8} +(0.0643587 + 0.948439i) q^{10} +(7.04110 + 12.1955i) q^{11} +(12.9444 - 3.46845i) q^{13} +(1.48385 + 0.856699i) q^{14} +(7.78377 + 13.4819i) q^{16} +(0.740694 - 0.740694i) q^{17} -7.09073i q^{19} +(3.82175 - 19.4473i) q^{20} +(0.692953 + 2.58614i) q^{22} +(-19.0499 + 5.10441i) q^{23} +(-19.7635 + 15.3103i) q^{25} +2.54786 q^{26} +(-25.2594 - 25.2594i) q^{28} +(-6.18301 + 3.56976i) q^{29} +(13.0783 - 22.6522i) q^{31} +(2.33357 + 8.70902i) q^{32} +(0.172473 - 0.0995774i) q^{34} +(3.05064 + 44.9566i) q^{35} +(-23.0151 + 23.0151i) q^{37} +(0.348919 - 1.30218i) q^{38} +(3.33274 - 6.79756i) q^{40} +(36.0387 - 62.4209i) q^{41} +(3.22835 - 12.0484i) q^{43} -55.8198i q^{44} -3.74961 q^{46} +(-51.8935 - 13.9048i) q^{47} +(27.9000 + 16.1081i) q^{49} +(-4.38286 + 1.83915i) q^{50} +(-51.3098 - 13.7484i) q^{52} +(-17.2907 - 17.2907i) q^{53} +(-46.3031 + 53.0446i) q^{55} +(-6.82262 - 11.8171i) q^{56} +(-1.31114 + 0.351320i) q^{58} +(-27.5407 - 15.9006i) q^{59} +(40.7317 + 70.5494i) q^{61} +(3.51643 - 3.51643i) q^{62} -60.5560i q^{64} +(37.3544 + 55.6269i) q^{65} +(-17.1864 - 64.1404i) q^{67} +(-4.01065 + 1.07465i) q^{68} +(-1.65197 + 8.40620i) q^{70} +36.3928 q^{71} +(2.90991 + 2.90991i) q^{73} +(-5.35915 + 3.09411i) q^{74} +(-14.0533 + 24.3410i) q^{76} +(32.8464 + 122.584i) q^{77} +(71.8823 - 41.5012i) q^{79} +(-51.1870 + 58.6396i) q^{80} +(9.68994 - 9.68994i) q^{82} +(13.7671 - 51.3796i) q^{83} +(4.70269 + 2.30566i) q^{85} +(1.18574 - 2.05377i) q^{86} +(5.51857 - 20.5956i) q^{88} +22.5436i q^{89} +120.770 q^{91} +(75.5111 + 20.2331i) q^{92} +(-8.84580 - 5.10712i) q^{94} +(33.5458 - 11.4735i) q^{95} +(33.7192 + 9.03502i) q^{97} +(4.33107 + 4.33107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + 2 q^{5} - 2 q^{7} + 24 q^{8} - 8 q^{10} - 8 q^{11} - 2 q^{13} + 28 q^{16} - 28 q^{17} + 114 q^{20} + 14 q^{22} - 82 q^{23} - 8 q^{25} + 112 q^{26} - 88 q^{28} - 4 q^{31} + 14 q^{32} - 352 q^{35}+ \cdots + 1876 q^{98}+O(q^{100}) $ 40 * q + 2 * q^2 + 2 * q^5 - 2 * q^7 + 24 * q^8 - 8 * q^10 - 8 * q^11 - 2 * q^13 + 28 * q^16 - 28 * q^17 + 114 * q^20 + 14 * q^22 - 82 * q^23 - 8 * q^25 + 112 * q^26 - 88 * q^28 - 4 * q^31 + 14 * q^32 - 352 * q^35 - 92 * q^37 - 330 * q^38 + 30 * q^40 + 28 * q^41 - 2 * q^43 - 136 * q^46 - 64 * q^47 + 458 * q^50 - 74 * q^52 + 608 * q^53 + 224 * q^55 + 192 * q^56 + 30 * q^58 + 92 * q^61 + 100 * q^62 + 326 * q^65 - 80 * q^67 - 626 * q^68 - 102 * q^70 - 248 * q^71 - 8 * q^73 - 96 * q^76 - 338 * q^77 - 1444 * q^80 + 104 * q^82 - 370 * q^83 - 98 * q^85 + 328 * q^86 - 210 * q^88 + 152 * q^91 - 388 * q^92 + 360 * q^95 + 292 * q^97 + 1876 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.183646	+	0.0492077i	0.0918228	+	0.0246039i	0.304438	−	0.952532i	$-0.401531\pi$
$2$	0.183646	+	0.0492077i	0.0918228	+	0.0246039i	−0.212615	+	0.977136i	$0.568198\pi$
$3$		0			0
$3$		0			0
$4$	−3.43280	−	1.98193i	−0.858199	−	0.495482i
$5$	1.61810	+	4.73094i	0.323620	+	0.946187i
$5$	1.61810	+	4.73094i	0.323620	+	0.946187i
$6$		0			0
$7$	8.70492	+	2.33248i	1.24356	+	0.333211i	0.819846	−	0.572585i	$-0.194059\pi$
$7$	8.70492	+	2.33248i	1.24356	+	0.333211i	0.423715	+	0.905796i	$0.360726\pi$
$8$	−1.07064	−	1.07064i	−0.133831	−	0.133831i
$9$		0			0
$10$	0.0643587	+	0.948439i	0.00643587	+	0.0948439i
$11$	7.04110	+	12.1955i	0.640100	+	1.10869i	0.985410	+	0.170197i	$0.0544405\pi$
$11$	7.04110	+	12.1955i	0.640100	+	1.10869i	−0.345310	+	0.938489i	$0.612226\pi$
$12$		0			0
$13$	12.9444	−	3.46845i	0.995725	−	0.266804i	0.276071	−	0.961137i	$-0.410967\pi$
$13$	12.9444	−	3.46845i	0.995725	−	0.266804i	0.719653	+	0.694333i	$0.244301\pi$
$14$	1.48385	+	0.856699i	0.105989	+	0.0611928i
$15$		0			0
$16$	7.78377	+	13.4819i	0.486486	+	0.842618i
$17$	0.740694	−	0.740694i	0.0435702	−	0.0435702i	−0.684986	−	0.728556i	$-0.740192\pi$
$17$	0.740694	−	0.740694i	0.0435702	−	0.0435702i	0.728556	+	0.684986i	$0.240192\pi$
$18$		0			0
$19$		−	7.09073i		−	0.373196i	−0.982436	−	0.186598i	$-0.940254\pi$
$19$		−	7.09073i		−	0.373196i	0.982436	−	0.186598i	$-0.0597463\pi$
$20$	3.82175	−	19.4473i	0.191088	−	0.972365i
$21$		0			0
$22$	0.692953	+	2.58614i	0.0314979	+	0.117552i
$23$	−19.0499	+	5.10441i	−0.828257	+	0.221931i	−0.647953	−	0.761680i	$-0.724375\pi$
$23$	−19.0499	+	5.10441i	−0.828257	+	0.221931i	−0.180304	+	0.983611i	$0.557708\pi$
$24$		0			0
$25$	−19.7635	+	15.3103i	−0.790540	+	0.612410i
$26$	2.54786			0.0979947
$27$		0			0
$28$	−25.2594	−	25.2594i	−0.902123	−	0.902123i
$29$	−6.18301	+	3.56976i	−0.213207	+	0.123095i	−0.602801	−	0.797892i	$-0.705949\pi$
$29$	−6.18301	+	3.56976i	−0.213207	+	0.123095i	0.389594	+	0.920987i	$0.372615\pi$
$30$		0			0
$31$	13.0783	−	22.6522i	0.421879	−	0.730716i	−0.574244	−	0.818684i	$-0.694704\pi$
$31$	13.0783	−	22.6522i	0.421879	−	0.730716i	0.996123	+	0.0879678i	$0.0280373\pi$
$32$	2.33357	+	8.70902i	0.0729242	+	0.272157i
$33$		0			0
$34$	0.172473	−	0.0995774i	0.00507274	−	0.00292875i
$35$	3.05064	+	44.9566i	0.0871612	+	1.28447i
$36$		0			0
$37$	−23.0151	+	23.0151i	−0.622031	+	0.622031i	−0.946050	−	0.324020i	$-0.894966\pi$
$37$	−23.0151	+	23.0151i	−0.622031	+	0.622031i	0.324020	+	0.946050i	$0.394966\pi$
$38$	0.348919	−	1.30218i	0.00918207	−	0.0342680i
$39$		0			0
$40$	3.33274	−	6.79756i	0.0833185	−	0.169939i
$41$	36.0387	−	62.4209i	0.878993	−	1.52246i	0.0265459	−	0.999648i	$-0.491549\pi$
$41$	36.0387	−	62.4209i	0.878993	−	1.52246i	0.852447	−	0.522813i	$-0.175117\pi$
$42$		0			0
$43$	3.22835	−	12.0484i	0.0750779	−	0.280195i	−0.918173	−	0.396180i	$-0.870336\pi$
$43$	3.22835	−	12.0484i	0.0750779	−	0.280195i	0.993251	+	0.115985i	$0.0370025\pi$
$44$		−	55.8198i		−	1.26863i
$45$		0			0
$46$	−3.74961			−0.0815133
$47$	−51.8935	−	13.9048i	−1.10412	−	0.295847i	−0.339677	−	0.940542i	$-0.610318\pi$
$47$	−51.8935	−	13.9048i	−1.10412	−	0.295847i	−0.764440	+	0.644695i	$0.776985\pi$
$48$		0			0
$49$	27.9000	+	16.1081i	0.569388	+	0.328736i
$50$	−4.38286	+	1.83915i	−0.0876573	+	0.0367829i
$51$		0			0
$52$	−51.3098	−	13.7484i	−0.986727	−	0.264393i
$53$	−17.2907	−	17.2907i	−0.326240	−	0.326240i	0.524915	−	0.851155i	$-0.324097\pi$
$53$	−17.2907	−	17.2907i	−0.326240	−	0.326240i	−0.851155	+	0.524915i	$0.824097\pi$
$54$		0			0
$55$	−46.3031	+	53.0446i	−0.841875	+	0.964447i
$56$	−6.82262	−	11.8171i	−0.121833	−	0.211020i
$57$		0			0
$58$	−1.31114	+	0.351320i	−0.0226059	+	0.00605724i
$59$	−27.5407	−	15.9006i	−0.466792	−	0.269502i	0.248104	−	0.968733i	$-0.420193\pi$
$59$	−27.5407	−	15.9006i	−0.466792	−	0.269502i	−0.714896	+	0.699231i	$0.753526\pi$
$60$		0			0
$61$	40.7317	+	70.5494i	0.667733	+	1.15655i	0.978537	+	0.206073i	$0.0660684\pi$
$61$	40.7317	+	70.5494i	0.667733	+	1.15655i	−0.310804	+	0.950474i	$0.600598\pi$
$62$	3.51643	−	3.51643i	0.0567166	−	0.0567166i
$63$		0			0
$64$		−	60.5560i		−	0.946187i
$65$	37.3544	+	55.6269i	0.574683	+	0.855799i
$66$		0			0
$67$	−17.1864	−	64.1404i	−0.256513	−	0.957319i	−0.967243	−	0.253854i	$-0.918302\pi$
$67$	−17.1864	−	64.1404i	−0.256513	−	0.957319i	0.710730	−	0.703465i	$-0.248365\pi$
$68$	−4.01065	+	1.07465i	−0.0589802	+	0.0158037i
$69$		0			0
$70$	−1.65197	+	8.40620i	−0.0235996	+	0.120089i
$71$	36.3928			0.512574			0.256287	−	0.966601i	$-0.417501\pi$
$71$	36.3928			0.512574			0.256287	+	0.966601i	$0.417501\pi$
$72$		0			0
$73$	2.90991	+	2.90991i	0.0398617	+	0.0398617i	0.726757	−	0.686895i	$-0.241027\pi$
$73$	2.90991	+	2.90991i	0.0398617	+	0.0398617i	−0.686895	+	0.726757i	$0.741027\pi$
$74$	−5.35915	+	3.09411i	−0.0724210	+	0.0418123i
$75$		0			0
$76$	−14.0533	+	24.3410i	−0.184912	+	0.320277i
$77$	32.8464	+	122.584i	0.426577	+	1.59201i
$78$		0			0
$79$	71.8823	−	41.5012i	0.909902	−	0.525332i	0.0295025	−	0.999565i	$-0.490608\pi$
$79$	71.8823	−	41.5012i	0.909902	−	0.525332i	0.880400	+	0.474232i	$0.157274\pi$
$80$	−51.1870	+	58.6396i	−0.639838	+	0.732995i
$81$		0			0
$82$	9.68994	−	9.68994i	0.118170	−	0.118170i
$83$	13.7671	−	51.3796i	0.165869	−	0.619031i	−0.832059	−	0.554687i	$-0.812838\pi$
$83$	13.7671	−	51.3796i	0.165869	−	0.619031i	0.997928	−	0.0643438i	$-0.0204954\pi$
$84$		0			0
$85$	4.70269	+	2.30566i	0.0553258	+	0.0271254i
$86$	1.18574	−	2.05377i	0.0137877	−	0.0238811i
$87$		0			0
$88$	5.51857	−	20.5956i	0.0627111	−	0.234041i
$89$			22.5436i			0.253299i	0.991948	+	0.126650i	$0.0404224\pi$
$89$			22.5436i			0.253299i	−0.991948	+	0.126650i	$0.959578\pi$
$90$		0			0
$91$	120.770			1.32715
$92$	75.5111	+	20.2331i	0.820773	+	0.219925i
$93$		0			0
$94$	−8.84580	−	5.10712i	−0.0941042	−	0.0543311i
$95$	33.5458	−	11.4735i	0.353114	−	0.120774i
$96$		0			0
$97$	33.7192	+	9.03502i	0.347620	+	0.0931446i	0.428405	−	0.903587i	$-0.359076\pi$
$97$	33.7192	+	9.03502i	0.347620	+	0.0931446i	−0.0807843	+	0.996732i	$0.525742\pi$
$98$	4.33107	+	4.33107i	0.0441946	+	0.0441946i
$99$		0			0
$100$	98.1879	−	13.3872i	0.981879	−	0.133872i
$101$	29.7283	+	51.4909i	0.294340	+	0.509811i	0.974831	−	0.222945i	$-0.0715670\pi$
$101$	29.7283	+	51.4909i	0.294340	+	0.509811i	−0.680491	+	0.732756i	$0.738234\pi$
$102$		0			0
$103$	−76.0184	+	20.3691i	−0.738043	+	0.197758i	−0.608208	−	0.793778i	$-0.708111\pi$
$103$	−76.0184	+	20.3691i	−0.738043	+	0.197758i	−0.129835	+	0.991536i	$0.541445\pi$
$104$	−17.5723	−	10.1454i	−0.168965	−	0.0975519i
$105$		0			0
$106$	−2.32453	−	4.02620i	−0.0219295	−	0.0379830i
$107$	50.6865	−	50.6865i	0.473706	−	0.473706i	−0.429406	−	0.903112i	$-0.641277\pi$
$107$	50.6865	−	50.6865i	0.473706	−	0.473706i	0.903112	+	0.429406i	$0.141277\pi$
$108$		0			0
$109$			47.8364i			0.438866i	0.975628	+	0.219433i	$0.0704208\pi$
$109$			47.8364i			0.438866i	−0.975628	+	0.219433i	$0.929579\pi$
$110$	−11.1136	+	7.46294i	−0.101032	+	0.0678449i
$111$		0			0
$112$	36.3109	+	135.514i	0.324205	+	1.20995i
$113$	−168.318	+	45.1005i	−1.48954	+	0.399120i	−0.909580	−	0.415529i	$-0.863597\pi$
$113$	−168.318	+	45.1005i	−1.48954	+	0.399120i	−0.579955	+	0.814648i	$0.696930\pi$
$114$		0			0
$115$	−54.9733	−	81.8645i	−0.478029	−	0.711865i
$116$	28.3000			0.243966
$117$		0			0
$118$	−4.27530	−	4.27530i	−0.0362313	−	0.0362313i
$119$	8.17534	−	4.72003i	0.0687003	−	0.0396641i
$120$		0			0
$121$	−38.6542	+	66.9510i	−0.319456	+	0.553314i
$122$	4.00863	+	14.9604i	0.0328576	+	0.122626i
$123$		0			0
$124$	−89.7900	+	51.8403i	−0.724113	+	0.418067i
$125$	−104.411	−	68.7263i	−0.835289	−	0.549810i
$126$		0			0
$127$	16.3333	−	16.3333i	0.128608	−	0.128608i	−0.639873	−	0.768481i	$-0.721013\pi$
$127$	16.3333	−	16.3333i	0.128608	−	0.128608i	0.768481	+	0.639873i	$0.221013\pi$
$128$	12.3141	−	45.9569i	0.0962041	−	0.359038i
$129$		0			0
$130$	4.12270	+	12.0538i	0.0317130	+	0.0927213i
$131$	27.6049	−	47.8130i	0.210724	−	0.364985i	−0.741217	−	0.671265i	$-0.765751\pi$
$131$	27.6049	−	47.8130i	0.210724	−	0.364985i	0.951941	+	0.306280i	$0.0990845\pi$
$132$		0			0
$133$	16.5390	−	61.7243i	0.124353	−	0.464092i
$134$		−	12.6248i		−	0.0942150i
$135$		0			0
$136$	−1.58604			−0.0116621
$137$	−189.371	−	50.7417i	−1.38227	−	0.370377i	−0.510323	−	0.859983i	$-0.670474\pi$
$137$	−189.371	−	50.7417i	−1.38227	−	0.370377i	−0.871944	+	0.489606i	$0.837141\pi$
$138$		0			0
$139$	−82.5364	−	47.6524i	−0.593787	−	0.342823i	0.172806	−	0.984956i	$-0.444717\pi$
$139$	−82.5364	−	47.6524i	−0.593787	−	0.342823i	−0.766594	+	0.642133i	$0.778050\pi$
$140$	78.6285	−	160.373i	0.561632	−	1.14552i
$141$		0			0
$142$	6.68338	+	1.79081i	0.0470660	+	0.0126113i
$143$	133.443	+	133.443i	0.933165	+	0.933165i
$144$		0			0
$145$	−26.8931	−	23.4752i	−0.185469	−	0.161898i
$146$	0.391202	+	0.677581i	0.00267946	+	0.00464097i
$147$		0			0
$148$	124.621	−	33.3920i	0.842031	−	0.225622i
$149$	225.341	+	130.101i	1.51235	+	0.873158i	0.999896	+	0.0144460i	$0.00459846\pi$
$149$	225.341	+	130.101i	1.51235	+	0.873158i	0.512458	+	0.858712i	$0.328735\pi$
$150$		0			0
$151$	−128.914	−	223.285i	−0.853735	−	1.47871i	−0.877814	−	0.479002i	$-0.840999\pi$
$151$	−128.914	−	223.285i	−0.853735	−	1.47871i	0.0240792	−	0.999710i	$-0.492335\pi$
$152$	−7.59165	+	7.59165i	−0.0499451	+	0.0499451i
$153$		0			0
$154$			24.1284i			0.156678i
$155$	128.328	+	25.2188i	0.827923	+	0.162702i
$156$		0			0
$157$	−12.0301	−	44.8971i	−0.0766251	−	0.285969i	0.916972	−	0.398952i	$-0.130626\pi$
$157$	−12.0301	−	44.8971i	−0.0766251	−	0.285969i	−0.993597	+	0.112983i	$0.963959\pi$
$158$	15.2431	−	4.08436i	0.0964750	−	0.0258504i
$159$		0			0
$160$	−37.4259	+	25.1321i	−0.233912	+	0.157075i
$161$	−177.734			−1.10394
$162$		0			0
$163$	76.8331	+	76.8331i	0.471369	+	0.471369i	0.902357	−	0.430989i	$-0.141835\pi$
$163$	76.8331	+	76.8331i	0.471369	+	0.471369i	−0.430989	+	0.902357i	$0.641835\pi$
$164$	−247.427	+	142.852i	−1.50870	+	0.871050i
$165$		0			0
$166$	5.05654	−	8.75819i	0.0304611	−	0.0527602i
$167$	−80.7212	−	301.256i	−0.483360	−	1.80393i	−0.587333	−	0.809346i	$-0.699822\pi$
$167$	−80.7212	−	301.256i	−0.483360	−	1.80393i	0.103972	−	0.994580i	$-0.466845\pi$
$168$		0			0
$169$	9.16964	−	5.29409i	0.0542582	−	0.0313260i
$170$	0.750173	+	0.654833i	0.00441278	+	0.00385196i
$171$		0			0
$172$	−34.9612	+	34.9612i	−0.203263	+	0.203263i
$173$	51.6158	−	192.633i	0.298357	−	1.11348i	−0.640157	−	0.768244i	$-0.721131\pi$
$173$	51.6158	−	192.633i	0.298357	−	1.11348i	0.938514	−	0.345240i	$-0.112203\pi$
$174$		0			0
$175$	−207.751	+	87.1767i	−1.18715	+	0.498153i
$176$	−109.613	+	189.855i	−0.622799	+	1.07872i
$177$		0			0
$178$	−1.10932	+	4.14004i	−0.00623214	+	0.0232587i
$179$		−	254.120i		−	1.41967i	−0.704370	−	0.709833i	$-0.748770\pi$
$179$		−	254.120i		−	1.41967i	0.704370	−	0.709833i	$-0.251230\pi$
$180$		0			0
$181$	−236.998			−1.30938			−0.654691	−	0.755896i	$-0.727201\pi$
$181$	−236.998			−1.30938			−0.654691	+	0.755896i	$0.727201\pi$
$182$	22.1789	+	5.94283i	0.121862	+	0.0326529i
$183$		0			0
$184$	25.8607	+	14.9307i	0.140547	+	0.0811450i
$185$	−146.124	−	71.6423i	−0.789859	−	0.387256i
$186$		0			0
$187$	14.2485	+	3.81787i	0.0761950	+	0.0204164i
$188$	150.582	+	150.582i	0.800966	+	0.800966i
$189$		0			0
$190$	6.72513	−	0.456350i	0.0353954	−	0.00240184i
$191$	−27.2962	−	47.2784i	−0.142912	−	0.247531i	0.785680	−	0.618633i	$-0.212313\pi$
$191$	−27.2962	−	47.2784i	−0.142912	−	0.247531i	−0.928592	+	0.371102i	$0.878980\pi$
$192$		0			0
$193$	−193.408	+	51.8234i	−1.00211	+	0.268515i	−0.722330	−	0.691548i	$-0.756929\pi$
$193$	−193.408	+	51.8234i	−1.00211	+	0.268515i	−0.279782	+	0.960063i	$0.590262\pi$
$194$	5.74779	+	3.31849i	0.0296278	+	0.0171056i
$195$		0			0
$196$	−63.8500	−	110.591i	−0.325765	−	0.564242i
$197$	−18.5367	+	18.5367i	−0.0940948	+	0.0940948i	−0.752587	−	0.658492i	$-0.771194\pi$
$197$	−18.5367	+	18.5367i	−0.0940948	+	0.0940948i	0.658492	+	0.752587i	$0.271194\pi$
$198$		0			0
$199$			206.081i			1.03558i	0.855507	+	0.517792i	$0.173246\pi$
$199$			206.081i			1.03558i	−0.855507	+	0.517792i	$0.826754\pi$
$200$	37.5515	+	4.76784i	0.187758	+	0.0238392i
$201$		0			0
$202$	2.92572	+	10.9190i	0.0144838	+	0.0540542i
$203$	−62.1490	+	16.6528i	−0.306153	+	0.0820334i
$204$		0			0
$205$	353.623	+	69.4936i	1.72499	+	0.338993i
$206$	−14.9628			−0.0726348
$207$		0			0
$208$	147.518	+	147.518i	0.709219	+	0.709219i
$209$	86.4753	−	49.9266i	0.413758	−	0.238883i
$210$		0			0
$211$	121.373	−	210.225i	0.575230	−	0.996327i	−0.420787	−	0.907159i	$-0.638246\pi$
$211$	121.373	−	210.225i	0.575230	−	0.996327i	0.996017	−	0.0891675i	$-0.0284206\pi$
$212$	25.0866	+	93.6244i	0.118333	+	0.441625i
$213$		0			0
$214$	11.8025	−	6.81419i	0.0551520	−	0.0318420i
$215$	62.2238	−	4.22235i	0.289413	−	0.0196389i
$216$		0			0
$217$	166.681	−	166.681i	0.768115	−	0.768115i
$218$	−2.35392	+	8.78496i	−0.0107978	+	0.0402980i
$219$		0			0
$220$	264.080	−	90.3220i	1.20036	−	0.410555i
$221$	7.01880	−	12.1569i	0.0317593	−	0.0550087i
$222$		0			0
$223$	−53.2572	+	198.758i	−0.238821	+	0.891293i	0.737568	+	0.675273i	$0.235974\pi$
$223$	−53.2572	+	198.758i	−0.238821	+	0.891293i	−0.976389	+	0.216020i	$0.930692\pi$
$224$			81.2544i			0.362743i
$225$		0			0
$226$	−33.1301			−0.146593
$227$	179.821	+	48.1829i	0.792163	+	0.212259i	0.632140	−	0.774854i	$-0.282177\pi$
$227$	179.821	+	48.1829i	0.792163	+	0.212259i	0.160022	+	0.987113i	$0.448843\pi$
$228$		0			0
$229$	156.704	+	90.4733i	0.684298	+	0.395080i	0.801473	−	0.598031i	$-0.204050\pi$
$229$	156.704	+	90.4733i	0.684298	+	0.395080i	−0.117174	+	0.993111i	$0.537384\pi$
$230$	−6.06725	−	17.7392i	−0.0263793	−	0.0771268i
$231$		0			0
$232$	10.4417	+	2.79786i	0.0450075	+	0.0120597i
$233$	120.230	+	120.230i	0.516010	+	0.516010i	0.916362	−	0.400351i	$-0.131112\pi$
$233$	120.230	+	120.230i	0.516010	+	0.516010i	−0.400351	+	0.916362i	$0.631112\pi$
$234$		0			0
$235$	−18.1861	−	268.004i	−0.0773877	−	1.14044i
$236$	63.0278	+	109.167i	0.267067	+	0.462573i
$237$		0			0
$238$	1.73363	−	0.464524i	0.00728415	−	0.00195178i
$239$	332.123	+	191.751i	1.38963	+	0.802306i	0.993274	−	0.115790i	$-0.0369398\pi$
$239$	332.123	+	191.751i	1.38963	+	0.802306i	0.396360	+	0.918095i	$0.370273\pi$
$240$		0			0
$241$	162.944	+	282.226i	0.676114	+	1.17106i	0.976142	+	0.217134i	$0.0696708\pi$
$241$	162.944	+	282.226i	0.676114	+	1.17106i	−0.300028	+	0.953931i	$0.596996\pi$
$242$	−10.3932	+	10.3932i	−0.0429470	+	0.0429470i
$243$		0			0
$244$		−	322.909i		−	1.32340i
$245$	−31.0612	+	158.058i	−0.126781	+	0.645133i
$246$		0			0
$247$	−24.5938	−	91.7854i	−0.0995702	−	0.371601i
$248$	−38.2546	+	10.2503i	−0.154252	+	0.0413318i
$249$		0			0
$250$	−15.7928	−	17.7591i	−0.0631712	−	0.0710365i
$251$	−428.941			−1.70893			−0.854465	−	0.519509i	$-0.826115\pi$
$251$	−428.941			−1.70893			−0.854465	+	0.519509i	$0.826115\pi$
$252$		0			0
$253$	−196.383	−	196.383i	−0.776219	−	0.776219i
$254$	3.80325	−	2.19581i	0.0149734	−	0.00864492i
$255$		0			0
$256$	−116.589	+	201.938i	−0.455426	+	0.788821i
$257$	95.3527	+	355.861i	0.371022	+	1.38467i	0.859070	+	0.511857i	$0.171042\pi$
$257$	95.3527	+	355.861i	0.371022	+	1.38467i	−0.488048	+	0.872817i	$0.662291\pi$
$258$		0			0
$259$	−254.027	+	146.663i	−0.980800	+	0.566265i
$260$	−17.9815	−	264.990i	−0.0691597	−	1.01919i
$261$		0			0
$262$	7.42228	−	7.42228i	0.0283293	−	0.0283293i
$263$	−17.0763	+	63.7296i	−0.0649289	+	0.242318i	−0.990761	−	0.135616i	$-0.956699\pi$
$263$	−17.0763	+	63.7296i	−0.0649289	+	0.242318i	0.925833	+	0.377934i	$0.123365\pi$
$264$		0			0
$265$	53.8231	−	109.779i	0.203106	−	0.414262i
$266$	6.07462	−	10.5216i	0.0228369	−	0.0395547i
$267$		0			0
$268$	−68.1242	+	254.243i	−0.254195	+	0.948668i
$269$			146.927i			0.546197i	0.961986	+	0.273099i	$0.0880485\pi$
$269$			146.927i			0.546197i	−0.961986	+	0.273099i	$0.911951\pi$
$270$		0			0
$271$	−45.0155			−0.166109			−0.0830544	−	0.996545i	$-0.526468\pi$
$271$	−45.0155			−0.166109			−0.0830544	+	0.996545i	$0.526468\pi$
$272$	15.7513	+	4.22056i	0.0579094	+	0.0155168i
$273$		0			0
$274$	−32.2802	−	18.6370i	−0.117811	−	0.0680182i
$275$	−325.874	−	133.226i	−1.18500	−	0.484457i
$276$		0			0
$277$	153.339	+	41.0870i	0.553570	+	0.148329i	0.524751	−	0.851256i	$-0.324159\pi$
$277$	153.339	+	41.0870i	0.553570	+	0.148329i	0.0288193	+	0.999585i	$0.490825\pi$
$278$	−12.8126	−	12.8126i	−0.0460885	−	0.0460885i
$279$		0			0
$280$	44.8664	−	51.3987i	0.160237	−	0.183567i
$281$	33.0937	+	57.3199i	0.117771	+	0.203986i	0.918884	−	0.394528i	$-0.129092\pi$
$281$	33.0937	+	57.3199i	0.117771	+	0.203986i	−0.801113	+	0.598513i	$0.795758\pi$
$282$		0			0
$283$	388.793	−	104.177i	1.37383	−	0.368116i	0.504952	−	0.863148i	$-0.331510\pi$
$283$	388.793	−	104.177i	1.37383	−	0.368116i	0.868875	+	0.495032i	$0.164844\pi$
$284$	−124.929	−	72.1278i	−0.439891	−	0.253971i
$285$		0			0
$286$	17.9397	+	31.0726i	0.0627264	+	0.108645i
$287$	459.310	−	459.310i	1.60038	−	1.60038i
$288$		0			0
$289$			287.903i			0.996203i
$290$	−3.78363	−	5.63446i	−0.0130470	−	0.0194292i
$291$		0			0
$292$	−4.22190	−	15.7563i	−0.0144586	−	0.0539600i
$293$	209.736	−	56.1985i	0.715821	−	0.191804i	0.117515	−	0.993071i	$-0.462507\pi$
$293$	209.736	−	56.1985i	0.715821	−	0.191804i	0.598306	+	0.801267i	$0.295841\pi$
$294$		0			0
$295$	30.6612	−	156.022i	0.103936	−	0.528889i
$296$	49.2820			0.166493
$297$		0			0
$298$	34.9809	+	34.9809i	0.117386	+	0.117386i
$299$	−228.886	+	132.147i	−0.765504	+	0.441964i
$300$		0			0
$301$	56.2051	−	97.3500i	0.186728	−	0.323422i
$302$	−12.6871	−	47.3490i	−0.0420103	−	0.156785i
$303$		0			0
$304$	95.5965	−	55.1926i	0.314462	−	0.181555i
$305$	−267.857	+	306.855i	−0.878218	+	1.00608i
$306$		0			0
$307$	−219.096	+	219.096i	−0.713666	+	0.713666i	−0.967300	−	0.253634i	$-0.918374\pi$
$307$	−219.096	+	219.096i	−0.713666	+	0.713666i	0.253634	+	0.967300i	$0.418374\pi$
$308$	130.198	−	485.907i	0.422722	−	1.57762i
$309$		0			0
$310$	22.3259	+	10.9461i	0.0720191	+	0.0353099i
$311$	68.8478	−	119.248i	0.221376	−	0.383434i	−0.733850	−	0.679311i	$-0.762279\pi$
$311$	68.8478	−	119.248i	0.221376	−	0.383434i	0.955226	+	0.295877i	$0.0956120\pi$
$312$		0			0
$313$	1.70804	−	6.37451i	0.00545701	−	0.0203658i	−0.963144	−	0.268988i	$-0.913311\pi$
$313$	1.70804	−	6.37451i	0.00545701	−	0.0203658i	0.968601	+	0.248622i	$0.0799776\pi$
$314$		−	8.83713i		−	0.0281437i
$315$		0			0
$316$	−329.010			−1.04117
$317$	−427.280	−	114.489i	−1.34789	−	0.361165i	−0.488532	−	0.872546i	$-0.662467\pi$
$317$	−427.280	−	114.489i	−1.34789	−	0.361165i	−0.859354	+	0.511381i	$0.829134\pi$
$318$		0			0
$319$	−87.0704	−	50.2701i	−0.272948	−	0.157587i
$320$	286.486	−	97.9856i	0.895270	−	0.306205i
$321$		0			0
$322$	−32.6401	−	8.74588i	−0.101367	−	0.0271611i
$323$	−5.25206	−	5.25206i	−0.0162603	−	0.0162603i
$324$		0			0
$325$	−202.724	+	266.731i	−0.623767	+	0.820711i
$326$	10.3293	+	17.8909i	0.0316849	+	0.0548799i
$327$		0			0
$328$	−105.415	+	28.2459i	−0.321388	+	0.0861156i
$329$	−419.296	−	242.081i	−1.27446	−	0.735808i
$330$		0			0
$331$	−130.851	−	226.641i	−0.395321	−	0.684716i	0.597821	−	0.801630i	$-0.296033\pi$
$331$	−130.851	−	226.641i	−0.395321	−	0.684716i	−0.993142	+	0.116913i	$0.962700\pi$
$332$	−149.090	+	149.090i	−0.449067	+	0.449067i
$333$		0			0
$334$		−	59.2964i		−	0.177534i
$335$	275.635	−	185.093i	0.822791	−	0.552517i
$336$		0			0
$337$	−37.7355	−	140.831i	−0.111975	−	0.417895i	0.887068	−	0.461639i	$-0.152738\pi$
$337$	−37.7355	−	140.831i	−0.111975	−	0.417895i	−0.999043	+	0.0437433i	$0.986072\pi$
$338$	1.94447	−	0.521020i	0.00575288	−	0.00154148i
$339$		0			0
$340$	−11.5737	−	17.2352i	−0.0340404	−	0.0506919i
$341$	368.341			1.08018
$342$		0			0
$343$	−106.954	−	106.954i	−0.311820	−	0.311820i
$344$	−16.3559	+	9.44310i	−0.0475463	+	0.0274509i
$345$		0			0
$346$	18.9580	−	32.8363i	0.0547920	−	0.0949025i
$347$	2.62052	+	9.77990i	0.00755192	+	0.0281842i	0.969599	−	0.244699i	$-0.0786893\pi$
$347$	2.62052	+	9.77990i	0.00755192	+	0.0281842i	−0.962047	+	0.272884i	$0.912023\pi$
$348$		0			0
$349$	94.1070	−	54.3327i	0.269648	−	0.155681i	−0.359080	−	0.933307i	$-0.616909\pi$
$349$	94.1070	−	54.3327i	0.269648	−	0.155681i	0.628727	+	0.777626i	$0.283576\pi$
$350$	−42.4423	+	5.78670i	−0.121264	+	0.0165334i
$351$		0			0
$352$	−89.7803	+	89.7803i	−0.255058	+	0.255058i
$353$	−125.168	+	467.133i	−0.354583	+	1.32332i	0.526425	+	0.850221i	$0.323532\pi$
$353$	−125.168	+	467.133i	−0.354583	+	1.32332i	−0.881008	+	0.473101i	$0.843135\pi$
$354$		0			0
$355$	58.8872	+	172.172i	0.165879	+	0.484991i
$356$	44.6798	−	77.3877i	0.125505	−	0.217381i
$357$		0			0
$358$	12.5047	−	46.6681i	0.0349293	−	0.130358i
$359$			279.063i			0.777333i	0.921378	+	0.388667i	$0.127064\pi$
$359$			279.063i			0.777333i	−0.921378	+	0.388667i	$0.872936\pi$
$360$		0			0
$361$	310.722			0.860724
$362$	−43.5237	−	11.6621i	−0.120231	−	0.0322159i
$363$		0			0
$364$	−414.580	−	239.358i	−1.13896	−	0.657576i
$365$	−9.05805	+	18.4751i	−0.0248166	+	0.0506167i
$366$		0			0
$367$	−172.547	−	46.2339i	−0.470156	−	0.125978i	0.0159593	−	0.999873i	$-0.494920\pi$
$367$	−172.547	−	46.2339i	−0.470156	−	0.125978i	−0.486115	+	0.873895i	$0.661586\pi$
$368$	−217.097	−	217.097i	−0.589938	−	0.589938i
$369$		0			0
$370$	−23.3097	−	20.3472i	−0.0629991	−	0.0549925i
$371$	−110.184	−	190.844i	−0.296992	−	0.514406i
$372$		0			0
$373$	84.7938	−	22.7204i	0.227329	−	0.0609127i	−0.143356	−	0.989671i	$-0.545789\pi$
$373$	84.7938	−	22.7204i	0.227329	−	0.0609127i	0.370685	+	0.928758i	$0.379123\pi$
$374$	2.42880	+	1.40227i	0.00649412	+	0.00374938i
$375$		0			0
$376$	40.6724	+	70.4466i	0.108171	+	0.187358i
$377$	−67.6540	+	67.6540i	−0.179453	+	0.179453i
$378$		0			0
$379$		−	10.3793i		−	0.0273860i	−0.999906	−	0.0136930i	$-0.995641\pi$
$379$		−	10.3793i		−	0.0273860i	0.999906	−	0.0136930i	$-0.00435875\pi$
$380$	−137.896	−	27.0990i	−0.362883	−	0.0713133i
$381$		0			0
$382$	−2.68637	−	10.0257i	−0.00703238	−	0.0262452i
$383$	−124.435	+	33.3422i	−0.324895	+	0.0870554i	−0.417580	−	0.908640i	$-0.637122\pi$
$383$	−124.435	+	33.3422i	−0.324895	+	0.0870554i	0.0926850	+	0.995695i	$0.470455\pi$
$384$		0			0
$385$	−526.790	+	353.748i	−1.36829	+	0.918827i
$386$	−38.0686			−0.0986233
$387$		0			0
$388$	−97.8443	−	97.8443i	−0.252176	−	0.252176i
$389$	635.357	−	366.824i	1.63331	−	0.942991i	0.650245	−	0.759724i	$-0.274666\pi$
$389$	635.357	−	366.824i	1.63331	−	0.942991i	0.983063	−	0.183267i	$-0.0586673\pi$
$390$		0			0
$391$	−10.3294	+	17.8910i	−0.0264178	+	0.0457570i
$392$	−12.6250	−	47.1170i	−0.0322065	−	0.120196i
$393$		0			0
$394$	−4.31633	+	2.49203i	−0.0109552	+	0.00632496i
$395$	312.652	+	272.917i	0.791525	+	0.690930i
$396$		0			0
$397$	151.257	−	151.257i	0.381000	−	0.381000i	−0.490463	−	0.871462i	$-0.663172\pi$
$397$	151.257	−	151.257i	0.381000	−	0.381000i	0.871462	+	0.490463i	$0.163172\pi$
$398$	−10.1408	+	37.8459i	−0.0254794	+	0.0950903i
$399$		0			0
$400$	−360.246	−	147.278i	−0.900614	−	0.368194i
$401$	3.27254	−	5.66821i	0.00816096	−	0.0141352i	−0.861916	−	0.507051i	$-0.830736\pi$
$401$	3.27254	−	5.66821i	0.00816096	−	0.0141352i	0.870077	+	0.492916i	$0.164069\pi$
$402$		0			0
$403$	90.7225	−	338.581i	0.225118	−	0.840151i
$404$		−	235.677i		−	0.583360i
$405$		0			0
$406$	−12.2328			−0.0301302
$407$	−442.734	−	118.630i	−1.08780	−	0.291475i
$408$		0			0
$409$	639.259	+	369.076i	1.56298	+	0.902387i	0.996953	+	0.0779993i	$0.0248532\pi$
$409$	639.259	+	369.076i	1.56298	+	0.902387i	0.566026	+	0.824387i	$0.308480\pi$
$410$	61.5218	+	30.1632i	0.150053	+	0.0735688i
$411$		0			0
$412$	301.326	+	80.7400i	0.731373	+	0.195971i
$413$	−202.652	−	202.652i	−0.490683	−	0.490683i
$414$		0			0
$415$	265.350	−	18.0060i	0.639398	−	0.0433879i
$416$	60.4136	+	104.639i	0.145225	+	0.251537i
$417$		0			0
$418$	18.3376	−	4.91354i	0.0438698	−	0.0117549i
$419$	235.376	+	135.894i	0.561756	+	0.324330i	0.753850	−	0.657047i	$-0.228195\pi$
$419$	235.376	+	135.894i	0.561756	+	0.324330i	−0.192094	+	0.981377i	$0.561528\pi$
$420$		0			0
$421$	102.996	+	178.395i	0.244647	+	0.423741i	0.962032	−	0.272936i	$-0.0879947\pi$
$421$	102.996	+	178.395i	0.244647	+	0.423741i	−0.717386	+	0.696676i	$0.754661\pi$
$422$	32.6344	−	32.6344i	0.0773327	−	0.0773327i
$423$		0			0
$424$			37.0244i			0.0873217i
$425$	−3.29849	+	25.9789i	−0.00776115	+	0.0611269i
$426$		0			0
$427$	190.011	+	709.133i	0.444992	+	1.66073i
$428$	−274.453	+	73.5396i	−0.641246	+	0.171821i
$429$		0			0
$430$	11.6349	+	2.28648i	0.0270579	+	0.00531738i
$431$	238.470			0.553294			0.276647	−	0.960972i	$-0.410777\pi$
$431$	238.470			0.553294			0.276647	+	0.960972i	$0.410777\pi$
$432$		0			0
$433$	79.6977	+	79.6977i	0.184059	+	0.184059i	0.793122	−	0.609063i	$-0.208454\pi$
$433$	79.6977	+	79.6977i	0.184059	+	0.184059i	−0.609063	+	0.793122i	$0.708454\pi$
$434$	38.8122	−	22.4083i	0.0894291	−	0.0516319i
$435$		0			0
$436$	94.8083	−	164.213i	0.217450	−	0.376635i
$437$	36.1940	+	135.078i	0.0828238	+	0.309103i
$438$		0			0
$439$	280.123	−	161.729i	0.638094	−	0.368404i	−0.145786	−	0.989316i	$-0.546571\pi$
$439$	280.123	−	161.729i	0.638094	−	0.368404i	0.783880	+	0.620912i	$0.213238\pi$
$440$	106.366	−	7.21774i	0.241741	−	0.0164039i
$441$		0			0
$442$	1.88719	−	1.88719i	0.00426965	−	0.00426965i
$443$	−195.518	+	729.682i	−0.441349	+	1.64714i	0.284051	+	0.958809i	$0.408322\pi$
$443$	−195.518	+	729.682i	−0.441349	+	1.64714i	−0.725400	+	0.688328i	$0.758345\pi$
$444$		0			0
$445$	−106.653	+	36.4779i	−0.239669	+	0.0819728i
$446$	−19.5609	+	33.8805i	−0.0438585	+	0.0759652i
$447$		0			0
$448$	141.245	−	527.135i	0.315280	−	1.17664i
$449$		−	514.733i		−	1.14640i	−0.819416	−	0.573199i	$-0.805702\pi$
$449$		−	514.733i		−	1.14640i	0.819416	−	0.573199i	$-0.194298\pi$
$450$		0			0
$451$	1015.01			2.25057
$452$	667.186	+	178.772i	1.47607	+	0.395513i
$453$		0			0
$454$	30.6524	+	17.6972i	0.0675162	+	0.0389805i
$455$	195.418	+	571.356i	0.429491	+	1.25573i
$456$		0			0
$457$	−550.455	−	147.494i	−1.20450	−	0.322744i	−0.399897	−	0.916560i	$-0.630954\pi$
$457$	−550.455	−	147.494i	−1.20450	−	0.322744i	−0.804601	+	0.593816i	$0.797621\pi$
$458$	24.3261	+	24.3261i	0.0531137	+	0.0531137i
$459$		0			0
$460$	26.4629	+	389.977i	0.0575280	+	0.847777i
$461$	119.334	+	206.693i	0.258860	+	0.448358i	0.965937	−	0.258778i	$-0.0833199\pi$
$461$	119.334	+	206.693i	0.258860	+	0.448358i	−0.707077	+	0.707137i	$0.749987\pi$
$462$		0			0
$463$	−796.822	+	213.508i	−1.72100	+	0.461140i	−0.978078	−	0.208239i	$-0.933227\pi$
$463$	−796.822	+	213.508i	−1.72100	+	0.461140i	−0.742921	+	0.669380i	$0.766560\pi$
$464$	−96.2543	−	55.5724i	−0.207445	−	0.119768i
$465$		0			0
$466$	16.1635	+	27.9961i	0.0346857	+	0.0600774i
$467$	−489.265	+	489.265i	−1.04768	+	1.04768i	−0.0488707	+	0.998805i	$0.515562\pi$
$467$	−489.265	+	489.265i	−1.04768	+	1.04768i	−0.998805	+	0.0488707i	$0.984438\pi$
$468$		0			0
$469$		−	598.424i		−	1.27596i
$470$	9.84808	−	50.1127i	0.0209534	−	0.106623i
$471$		0			0
$472$	12.4624	+	46.5102i	0.0264033	+	0.0985386i
$473$	169.667	−	45.4623i	0.358705	−	0.0961147i
$474$		0			0
$475$	108.561	+	140.138i	0.228549	+	0.295027i
$476$	−37.4190			−0.0786114
$477$		0			0
$478$	51.5572	+	51.5572i	0.107860	+	0.107860i
$479$	−142.795	+	82.4426i	−0.298110	+	0.172114i	−0.641594	−	0.767045i	$-0.721726\pi$
$479$	−142.795	+	82.4426i	−0.298110	+	0.172114i	0.343483	+	0.939159i	$0.388393\pi$
$480$		0			0
$481$	−218.091	+	377.744i	−0.453411	+	0.785331i
$482$	16.0362	+	59.8478i	0.0332700	+	0.124165i
$483$		0			0
$484$	265.384	−	153.220i	0.548314	−	0.316569i
$485$	11.8169	+	174.143i	0.0243647	+	0.359057i
$486$		0			0
$487$	326.960	−	326.960i	0.671376	−	0.671376i	−0.286657	−	0.958033i	$-0.592544\pi$
$487$	326.960	−	326.960i	0.671376	−	0.671376i	0.958033	+	0.286657i	$0.0925441\pi$
$488$	31.9241	−	119.142i	0.0654183	−	0.244144i
$489$		0			0
$490$	−13.4819	+	27.4981i	−0.0275141	+	0.0561186i
$491$	182.011	−	315.253i	0.370695	−	0.642063i	−0.618977	−	0.785409i	$-0.712453\pi$
$491$	182.011	−	315.253i	0.370695	−	0.642063i	0.989673	+	0.143346i	$0.0457861\pi$
$492$		0			0
$493$	−1.93562	+	7.22382i	−0.00392620	+	0.0146528i
$494$		−	18.0662i		−	0.0365713i
$495$		0			0
$496$	407.193			0.820953
$497$	316.796	+	84.8853i	0.637417	+	0.170795i
$498$		0			0
$499$	−353.578	−	204.138i	−0.708573	−	0.409095i	0.101960	−	0.994789i	$-0.467489\pi$
$499$	−353.578	−	204.138i	−0.708573	−	0.409095i	−0.810532	+	0.585694i	$0.800822\pi$
$500$	222.212	+	442.859i	0.444424	+	0.885717i
$501$		0			0
$502$	−78.7732	−	21.1072i	−0.156919	−	0.0420463i
$503$	−555.921	−	555.921i	−1.10521	−	1.10521i	−0.993771	−	0.111440i	$-0.964454\pi$
$503$	−555.921	−	555.921i	−1.10521	−	1.10521i	−0.111440	−	0.993771i	$-0.535546\pi$
$504$		0			0
$505$	−195.497	+	223.960i	−0.387123	+	0.443486i
$506$	−26.4014	−	45.7286i	−0.0521767	−	0.0903726i
$507$		0			0
$508$	−88.4400	+	23.6974i	−0.174095	+	0.0466485i
$509$	−453.968	−	262.098i	−0.891882	−	0.514928i	−0.0173243	−	0.999850i	$-0.505515\pi$
$509$	−453.968	−	262.098i	−0.891882	−	0.514928i	−0.874558	+	0.484922i	$0.838848\pi$
$510$		0			0
$511$	18.5432	+	32.1178i	0.0362881	+	0.0628528i
$512$	−165.919	+	165.919i	−0.324061	+	0.324061i
$513$		0			0
$514$			70.0445i			0.136273i
$515$	−219.370	−	326.679i	−0.425961	−	0.634328i
$516$		0			0
$517$	−195.811	−	730.775i	−0.378744	−	1.41349i
$518$	−53.8679	+	14.4339i	−0.103992	+	0.0278646i
$519$		0			0
$520$	19.5634	−	99.5499i	0.0376219	−	0.191442i
$521$	694.042			1.33213			0.666067	−	0.745892i	$-0.267977\pi$
$521$	694.042			1.33213			0.666067	+	0.745892i	$0.267977\pi$
$522$		0			0
$523$	244.233	+	244.233i	0.466985	+	0.466985i	0.900936	−	0.433951i	$-0.142881\pi$
$523$	244.233	+	244.233i	0.466985	+	0.466985i	−0.433951	+	0.900936i	$0.642881\pi$
$524$	−189.524	+	109.422i	−0.361687	+	0.208820i
$525$		0			0
$526$	−6.27198	+	10.8634i	−0.0119239	+	0.0206528i
$527$	−7.09137	−	26.4653i	−0.0134561	−	0.0502189i
$528$		0			0
$529$	−121.283	+	70.0227i	−0.229268	+	0.132368i
$530$	15.2864	−	17.5120i	0.0288422	−	0.0330415i
$531$		0			0
$532$	−179.108	+	179.108i	−0.336669	+	0.336669i
$533$	249.997	−	933.001i	0.469037	−	1.75047i
$534$		0			0
$535$	321.810	+	157.779i	0.601515	+	0.294913i
$536$	−50.2711	+	87.0720i	−0.0937893	+	0.162448i
$537$		0			0
$538$	−7.22994	+	26.9825i	−0.0134386	+	0.0501534i
$539$			453.674i			0.841696i
$540$		0			0
$541$	−682.588			−1.26172			−0.630858	−	0.775899i	$-0.717297\pi$
$541$	−682.588			−1.26172			−0.630858	+	0.775899i	$0.717297\pi$
$542$	−8.26689	−	2.21511i	−0.0152526	−	0.00408691i
$543$		0			0
$544$	8.17918	+	4.72225i	0.0150353	+	0.00868061i
$545$	−226.311	+	77.4042i	−0.415250	+	0.142026i
$546$		0			0
$547$	62.4694	+	16.7386i	0.114204	+	0.0306008i	0.315468	−	0.948936i	$-0.397838\pi$
$547$	62.4694	+	16.7386i	0.114204	+	0.0306008i	−0.201265	+	0.979537i	$0.564505\pi$
$548$	549.504	+	549.504i	1.00275	+	1.00275i
$549$		0			0
$550$	−53.2896	−	40.5018i	−0.0968901	−	0.0736396i
$551$	25.3122	+	43.8421i	0.0459387	+	0.0795682i
$552$		0			0
$553$	722.530	−	193.601i	1.30656	−	0.350093i
$554$	26.1382	+	15.0909i	0.0471809	+	0.0272399i
$555$		0			0
$556$	188.887	+	327.162i	0.339725	+	0.588421i
$557$	66.9124	−	66.9124i	0.120130	−	0.120130i	−0.644486	−	0.764616i	$-0.722929\pi$
$557$	66.9124	−	66.9124i	0.120130	−	0.120130i	0.764616	+	0.644486i	$0.222929\pi$
$558$		0			0
$559$		−	167.156i		−	0.299028i
$560$	−582.354	+	391.060i	−1.03992	+	0.698322i
$561$		0			0
$562$	3.25693	+	12.1550i	0.00579525	+	0.0216282i
$563$	137.436	−	36.8258i	0.244113	−	0.0654099i	−0.134688	−	0.990888i	$-0.543003\pi$
$563$	137.436	−	36.8258i	0.244113	−	0.0654099i	0.378801	+	0.925478i	$0.376337\pi$
$564$		0			0
$565$	−485.722	−	723.322i	−0.859686	−	1.28022i
$566$	76.5264			0.135206
$567$		0			0
$568$	−38.9637	−	38.9637i	−0.0685981	−	0.0685981i
$569$	−276.828	+	159.827i	−0.486517	+	0.280891i	−0.723128	−	0.690714i	$-0.757297\pi$
$569$	−276.828	+	159.827i	−0.486517	+	0.280891i	0.236611	+	0.971604i	$0.423963\pi$
$570$		0			0
$571$	−324.309	+	561.720i	−0.567967	+	0.983748i	0.428800	+	0.903400i	$0.358937\pi$
$571$	−324.309	+	561.720i	−0.567967	+	0.983748i	−0.996767	+	0.0803483i	$0.974397\pi$
$572$	−193.608	−	722.555i	−0.338475	−	1.26321i
$573$		0			0
$574$	106.952	−	61.7486i	0.186327	−	0.107576i
$575$	298.343	−	392.540i	0.518858	−	0.682679i
$576$		0			0
$577$	−519.616	+	519.616i	−0.900548	+	0.900548i	−0.995483	−	0.0949353i	$-0.969736\pi$
$577$	−519.616	+	519.616i	−0.900548	+	0.900548i	0.0949353	+	0.995483i	$0.469736\pi$
$578$	−14.1670	+	52.8721i	−0.0245104	+	0.0914742i
$579$		0			0
$580$	45.7923	+	133.886i	0.0789522	+	0.230837i
$581$	239.683	−	415.144i	0.412536	−	0.714533i
$582$		0			0
$583$	89.1240	−	332.615i	0.152871	−	0.570523i
$584$		−	6.23095i		−	0.0106694i
$585$		0			0
$586$	41.2824			0.0704478
$587$	797.684	+	213.739i	1.35892	+	0.364120i	0.863418	−	0.504489i	$-0.168319\pi$
$587$	797.684	+	213.739i	1.35892	+	0.364120i	0.495498	+	0.868609i	$0.334986\pi$
$588$		0			0
$589$	−160.621	−	92.7344i	−0.272701	−	0.157444i
$590$	13.3083	−	27.1440i	0.0225564	−	0.0460068i
$591$		0			0
$592$	−489.432	−	131.143i	−0.826743	−	0.221525i
$593$	−329.014	−	329.014i	−0.554829	−	0.554829i	0.373002	−	0.927831i	$-0.378329\pi$
$593$	−329.014	−	329.014i	−0.554829	−	0.554829i	−0.927831	+	0.373002i	$0.878329\pi$
$594$		0			0
$595$	35.5587	+	31.0395i	0.0597625	+	0.0521672i
$596$	−515.699	−	893.218i	−0.865267	−	1.49869i
$597$		0			0
$598$	−48.5366	+	13.0053i	−0.0811648	+	0.0217480i
$599$	−445.587	−	257.260i	−0.743885	−	0.429482i	0.0795952	−	0.996827i	$-0.474637\pi$
$599$	−445.587	−	257.260i	−0.743885	−	0.429482i	−0.823480	+	0.567345i	$0.807971\pi$
$600$		0			0
$601$	−19.7478	−	34.2041i	−0.0328582	−	0.0569121i	0.849129	−	0.528186i	$-0.177128\pi$
$601$	−19.7478	−	34.2041i	−0.0328582	−	0.0569121i	−0.881987	+	0.471274i	$0.843794\pi$
$602$	15.1122	−	15.1122i	0.0251033	−	0.0251033i
$603$		0			0
$604$			1021.99i			1.69204i
$605$	−379.287	−	74.5370i	−0.626921	−	0.123202i
$606$		0			0
$607$	104.659	+	390.594i	0.172421	+	0.643483i	0.996977	+	0.0777026i	$0.0247585\pi$
$607$	104.659	+	390.594i	0.172421	+	0.643483i	−0.824556	+	0.565781i	$0.808575\pi$
$608$	61.7533	−	16.5468i	0.101568	−	0.0272151i
$609$		0			0
$610$	−64.2903	+	43.1720i	−0.105394	+	0.0707738i
$611$	−719.960			−1.17833
$612$		0			0
$613$	−559.593	−	559.593i	−0.912876	−	0.912876i	0.0836213	−	0.996498i	$-0.473351\pi$
$613$	−559.593	−	559.593i	−0.912876	−	0.912876i	−0.996498	+	0.0836213i	$0.973351\pi$
$614$	−51.0172	+	29.4548i	−0.0830898	+	0.0479719i
$615$		0			0
$616$	96.0775	−	166.411i	0.155970	−	0.270148i
$617$	−90.4285	−	337.484i	−0.146562	−	0.546976i	−0.999681	−	0.0252596i	$-0.991959\pi$
$617$	−90.4285	−	337.484i	−0.146562	−	0.546976i	0.853119	−	0.521716i	$-0.174708\pi$
$618$		0			0
$619$	−384.591	+	222.044i	−0.621311	+	0.358714i	−0.777379	−	0.629032i	$-0.783451\pi$
$619$	−384.591	+	222.044i	−0.621311	+	0.358714i	0.156068	+	0.987746i	$0.450118\pi$
$620$	−390.542	−	340.908i	−0.629907	−	0.549852i
$621$		0			0
$622$	18.5115	−	18.5115i	0.0297613	−	0.0297613i
$623$	−52.5825	+	196.241i	−0.0844021	+	0.314993i
$624$		0			0
$625$	156.192	−	605.169i	0.249907	−	0.968270i
$626$	0.627350	−	1.08660i	0.00100216	−	0.00173579i
$627$		0			0
$628$	−47.6857	+	177.965i	−0.0759326	+	0.283384i
$629$			34.0943i			0.0542040i
$630$		0			0
$631$	−181.428			−0.287524			−0.143762	−	0.989612i	$-0.545920\pi$
$631$	−181.428			−0.287524			−0.143762	+	0.989612i	$0.545920\pi$
$632$	−121.393	−	32.5273i	−0.192078	−	0.0514672i
$633$		0			0
$634$	−72.8343	−	42.0509i	−0.114881	−	0.0663264i
$635$	103.700	+	50.8427i	0.163308	+	0.0800673i
$636$		0			0
$637$	417.019	+	111.740i	0.654661	+	0.175416i
$638$	−13.5164	−	13.5164i	−0.0211856	−	0.0211856i
$639$		0			0
$640$	237.345	−	16.1056i	0.370851	−	0.0251650i
$641$	−44.3645	−	76.8416i	−0.0692114	−	0.119878i	0.829343	−	0.558740i	$-0.188715\pi$
$641$	−44.3645	−	76.8416i	−0.0692114	−	0.119878i	−0.898554	+	0.438862i	$0.855382\pi$
$642$		0			0
$643$	−414.879	+	111.166i	−0.645224	+	0.172887i	−0.566568	−	0.824015i	$-0.691729\pi$
$643$	−414.879	+	111.166i	−0.645224	+	0.172887i	−0.0786553	+	0.996902i	$0.525063\pi$
$644$	610.125	+	352.256i	0.947399	+	0.546981i
$645$		0			0
$646$	−0.706077	−	1.22296i	−0.00109300	−	0.00189313i
$647$	−237.290	+	237.290i	−0.366755	+	0.366755i	−0.866292	−	0.499537i	$-0.833503\pi$
$647$	−237.290	+	237.290i	−0.366755	+	0.366755i	0.499537	+	0.866292i	$0.333503\pi$
$648$		0			0
$649$		−	447.832i		−	0.690034i
$650$	−50.3547	+	39.0084i	−0.0774687	+	0.0600130i
$651$		0			0
$652$	−111.475	−	416.030i	−0.170974	−	0.638083i
$653$	777.291	−	208.275i	1.19034	−	0.318950i	0.391319	−	0.920255i	$-0.372019\pi$
$653$	777.291	−	208.275i	1.19034	−	0.318950i	0.799020	+	0.601305i	$0.205352\pi$
$654$		0			0
$655$	270.868	+	53.2305i	0.413539	+	0.0812680i
$656$	1122.07			1.71047
$657$		0			0
$658$	−65.0897	−	65.0897i	−0.0989206	−	0.0989206i
$659$	407.245	−	235.123i	0.617974	−	0.356787i	−0.158106	−	0.987422i	$-0.550539\pi$
$659$	407.245	−	235.123i	0.617974	−	0.356787i	0.776080	+	0.630635i	$0.217205\pi$
$660$		0			0
$661$	379.580	−	657.451i	0.574251	−	0.994631i	−0.421872	−	0.906655i	$-0.638627\pi$
$661$	379.580	−	657.451i	0.574251	−	0.994631i	0.996123	−	0.0879760i	$-0.0280399\pi$
$662$	−12.8778	−	48.0606i	−0.0194528	−	0.0725990i
$663$		0			0
$664$	−69.7489	+	40.2696i	−0.105044	+	0.0606469i
$665$	318.775	−	21.6313i	0.479361	−	0.0325283i
$666$		0			0
$667$	99.5643	−	99.5643i	0.149272	−	0.149272i
$668$	−319.967	+	1194.13i	−0.478992	+	1.78762i
$669$		0			0
$670$	59.7272	−	20.4282i	0.0891450	−	0.0304899i
$671$	−573.592	+	993.490i	−0.854832	+	1.48061i
$672$		0			0
$673$	−326.337	+	1217.91i	−0.484899	+	1.80967i	0.0956152	+	0.995418i	$0.469518\pi$
$673$	−326.337	+	1217.91i	−0.484899	+	1.80967i	−0.580514	+	0.814250i	$0.697148\pi$
$674$		−	27.7198i		−	0.0411273i
$675$		0			0
$676$	−41.9700			−0.0620858
$677$	96.3967	+	25.8294i	0.142388	+	0.0381528i	0.329309	−	0.944222i	$-0.393184\pi$
$677$	96.3967	+	25.8294i	0.142388	+	0.0381528i	−0.186921	+	0.982375i	$0.559851\pi$
$678$		0			0
$679$	272.449	+	157.298i	0.401250	+	0.231662i
$680$	−2.56637	−	7.50345i	−0.00377408	−	0.0110345i
$681$		0			0
$682$	67.6443	+	18.1252i	0.0991852	+	0.0265766i
$683$	−366.381	−	366.381i	−0.536430	−	0.536430i	0.386049	−	0.922478i	$-0.373840\pi$
$683$	−366.381	−	366.381i	−0.536430	−	0.536430i	−0.922478	+	0.386049i	$0.873840\pi$
$684$		0			0
$685$	−66.3650	−	978.005i	−0.0968832	−	1.42774i
$686$	−14.3787	−	24.9047i	−0.0209602	−	0.0363042i
$687$		0			0
$688$	187.563	−	50.2575i	0.272621	−	0.0730486i
$689$	−283.790	−	163.846i	−0.411887	−	0.237803i
$690$		0			0
$691$	−298.133	−	516.381i	−0.431451	−	0.747296i	0.565547	−	0.824716i	$-0.308665\pi$
$691$	−298.133	−	516.381i	−0.431451	−	0.747296i	−0.996999	+	0.0774204i	$0.975332\pi$
$692$	−558.971	+	558.971i	−0.807761	+	0.807761i
$693$		0			0
$694$			1.92499i			0.00277376i
$695$	91.8883	−	467.581i	0.132213	−	0.672778i
$696$		0			0
$697$	−19.5411	−	72.9284i	−0.0280360	−	0.104632i
$698$	19.9559	−	5.34718i	0.0285902	−	0.00766071i
$699$		0			0
$700$	885.943	+	112.486i	1.26563	+	0.160695i
$701$	−147.235			−0.210036			−0.105018	−	0.994470i	$-0.533490\pi$
$701$	−147.235			−0.210036			−0.105018	+	0.994470i	$0.533490\pi$
$702$		0			0
$703$	163.194	+	163.194i	0.232140	+	0.232140i
$704$	738.513	−	426.381i	1.04902	−	0.605654i
$705$		0			0
$706$	−45.9731	+	79.6277i	−0.0651177	+	0.112787i
$707$	138.681	+	517.565i	0.196154	+	0.732058i
$708$		0			0
$709$	−123.232	+	71.1480i	−0.173811	+	0.100350i	−0.584382	−	0.811479i	$-0.698663\pi$
$709$	−123.232	+	71.1480i	−0.173811	+	0.100350i	0.410571	+	0.911829i	$0.365330\pi$
$710$	2.34219	+	34.5163i	0.00329886	+	0.0486145i
$711$		0			0
$712$	24.1362	−	24.1362i	0.0338992	−	0.0338992i
$713$	−133.514	+	498.280i	−0.187256	+	0.698849i
$714$		0			0
$715$	−415.385	+	847.232i	−0.580958	+	1.18494i
$716$	−503.648	+	872.343i	−0.703418	+	1.21836i
$717$		0			0
$718$	−13.7320	+	51.2486i	−0.0191254	+	0.0713769i
$719$			1075.81i			1.49626i	0.663555	+	0.748128i	$0.269047\pi$
$719$			1075.81i			1.49626i	−0.663555	+	0.748128i	$0.730953\pi$
$720$		0			0
$721$	−709.245			−0.983696
$722$	57.0627	+	15.2899i	0.0790342	+	0.0211771i
$723$		0			0
$724$	813.567	+	469.713i	1.12371	+	0.648775i
$725$	67.5439	−	165.215i	0.0931640	−	0.227882i
$726$		0			0
$727$	696.238	+	186.556i	0.957687	+	0.256611i	0.703621	−	0.710576i	$-0.251565\pi$
$727$	696.238	+	186.556i	0.957687	+	0.256611i	0.254066	+	0.967187i	$0.418232\pi$
$728$	−129.302	−	129.302i	−0.177613	−	0.177613i
$729$		0			0
$730$	−2.57259	+	2.94715i	−0.00352410	+	0.00403718i
$731$	−6.53293	−	11.3154i	−0.00893698	−	0.0154793i
$732$		0			0
$733$	1179.49	−	316.043i	1.60913	−	0.431164i	0.661345	−	0.750082i	$-0.269986\pi$
$733$	1179.49	−	316.043i	1.60913	−	0.431164i	0.947782	+	0.318918i	$0.103319\pi$
$734$	−29.4125	−	16.9813i	−0.0400715	−	0.0231353i
$735$		0			0
$736$	−88.9088	−	153.995i	−0.120800	−	0.209232i
$737$	661.216	−	661.216i	0.897173	−	0.897173i
$738$		0			0
$739$		−	683.603i		−	0.925038i	−0.886609	−	0.462519i	$-0.846946\pi$
$739$		−	683.603i		−	0.925038i	0.886609	−	0.462519i	$-0.153054\pi$
$740$	359.624	+	535.540i	0.485978	+	0.723703i
$741$		0			0
$742$	−10.8438	−	40.4697i	−0.0146143	−	0.0545413i
$743$	763.713	−	204.636i	1.02788	−	0.275419i	0.294797	−	0.955560i	$-0.404748\pi$
$743$	763.713	−	204.636i	1.02788	−	0.275419i	0.733081	+	0.680141i	$0.238081\pi$
$744$		0			0
$745$	−250.873	+	1276.59i	−0.336743	+	1.71354i
$746$	16.6900			0.0223727
$747$		0			0
$748$	−41.3454	−	41.3454i	−0.0552746	−	0.0552746i
$749$	559.447	−	322.997i	0.746925	−	0.431238i
$750$		0			0
$751$	326.862	−	566.142i	0.435236	−	0.753851i	−0.562079	−	0.827084i	$-0.689998\pi$
$751$	326.862	−	566.142i	0.435236	−	0.753851i	0.997315	+	0.0732329i	$0.0233317\pi$
$752$	−216.464	−	807.855i	−0.287851	−	1.07427i
$753$		0			0
$754$	−15.7535	+	9.09526i	−0.0208932	+	0.0120627i
$755$	847.754	−	971.182i	1.12285	−	1.28633i
$756$		0			0
$757$	668.868	−	668.868i	0.883577	−	0.883577i	−0.110319	−	0.993896i	$-0.535187\pi$
$757$	668.868	−	668.868i	0.883577	−	0.883577i	0.993896	+	0.110319i	$0.0351874\pi$
$758$	0.510741	−	1.90611i	0.000673800	−	0.00251466i
$759$		0			0
$760$	−48.1997	−	23.6316i	−0.0634206	−	0.0310942i
$761$	−478.705	+	829.141i	−0.629047	+	1.08954i	0.358696	+	0.933454i	$0.383221\pi$
$761$	−478.705	+	829.141i	−0.629047	+	1.08954i	−0.987743	+	0.156087i	$0.950112\pi$
$762$		0			0
$763$	−111.577	+	416.413i	−0.146235	+	0.545757i
$764$			216.396i			0.283241i
$765$		0			0
$766$	−24.4926			−0.0319747
$767$	−411.649	−	110.301i	−0.536700	−	0.143808i
$768$		0			0
$769$	−435.970	−	251.708i	−0.566932	−	0.327318i	0.188991	−	0.981979i	$-0.439478\pi$
$769$	−435.970	−	251.708i	−0.566932	−	0.327318i	−0.755923	+	0.654661i	$0.772812\pi$
$770$	−114.150	+	39.0422i	−0.148247	+	0.0507041i
$771$		0			0
$772$	766.640	+	205.421i	0.993057	+	0.266089i
$773$	362.267	+	362.267i	0.468651	+	0.468651i	0.901477	−	0.432827i	$-0.142484\pi$
$773$	362.267	+	362.267i	0.468651	+	0.468651i	−0.432827	+	0.901477i	$0.642484\pi$
$774$		0			0
$775$	88.3390	+	647.918i	0.113986	+	0.836024i
$776$	−26.4279	−	45.7745i	−0.0340566	−	0.0589878i
$777$		0			0
$778$	134.731	−	36.1011i	0.173176	−	0.0464024i
$779$	−442.610	−	255.541i	−0.568177	−	0.328037i
$780$		0			0
$781$	256.245	+	443.830i	0.328099	+	0.568284i
$782$	−2.77732	+	2.77732i	−0.00355155	+	0.00355155i
$783$		0			0
$784$			501.526i			0.639701i
$785$	192.939	−	129.562i	0.245782	−	0.165047i
$786$		0			0
$787$	134.565	+	502.205i	0.170985	+	0.638126i	0.997201	+	0.0747716i	$0.0238228\pi$
$787$	134.565	+	502.205i	0.170985	+	0.638126i	−0.826215	+	0.563354i	$0.809511\pi$
$788$	100.371	−	26.8943i	0.127374	−	0.0341299i
$789$		0			0
$790$	43.9876	+	65.5050i	0.0556806	+	0.0829177i
$791$	−1570.39			−1.98532
$792$		0			0
$793$	771.945	+	771.945i	0.973449	+	0.973449i
$794$	35.2207	−	20.3347i	0.0443585	−	0.0256104i
$795$		0			0
$796$	408.438	−	707.435i	0.513113	−	0.888737i
$797$	−72.1737	−	269.356i	−0.0905567	−	0.337962i	0.905752	−	0.423809i	$-0.139307\pi$
$797$	−72.1737	−	269.356i	−0.0905567	−	0.337962i	−0.996308	+	0.0858466i	$0.972640\pi$
$798$		0			0
$799$	−48.7365	+	28.1380i	−0.0609968	+	0.0352165i
$800$	−179.457	−	136.393i	−0.224321	−	0.170491i
$801$		0			0
$802$	0.879908	−	0.879908i	0.00109714	−	0.00109714i
$803$	−14.9989	+	55.9768i	−0.0186786	+	0.0697096i
$804$		0			0
$805$	−287.592	−	840.848i	−0.357257	−	1.04453i
$806$	33.3216	−	57.7147i	0.0413419	−	0.0716063i
$807$		0			0
$808$	23.3000	−	86.9569i	0.0288367	−	0.107620i
$809$			423.966i			0.524062i	0.965060	+	0.262031i	$0.0843922\pi$
$809$			423.966i			0.524062i	−0.965060	+	0.262031i	$0.915608\pi$
$810$		0			0
$811$	−1163.79			−1.43501			−0.717506	−	0.696552i	$-0.754716\pi$
$811$	−1163.79			−1.43501			−0.717506	+	0.696552i	$0.754716\pi$
$812$	246.350	+	66.0092i	0.303386	+	0.0812921i
$813$		0			0
$814$	−75.4686	−	43.5718i	−0.0927133	−	0.0535281i
$815$	−239.169	+	487.816i	−0.293459	+	0.598548i
$816$		0			0
$817$	−85.4317	−	22.8914i	−0.104568	−	0.0280188i
$818$	99.2357	+	99.2357i	0.121315	+	0.121315i
$819$		0			0
$820$	−1076.19	−	939.413i	−1.31242	−	1.14563i
$821$	382.915	+	663.228i	0.466400	+	0.807829i	0.999264	−	0.0383722i	$-0.0122172\pi$
$821$	382.915	+	663.228i	0.466400	+	0.807829i	−0.532863	+	0.846202i	$0.678884\pi$
$822$		0			0
$823$	−955.510	+	256.028i	−1.16101	+	0.311091i	−0.787369	−	0.616482i	$-0.788557\pi$
$823$	−955.510	+	256.028i	−1.16101	+	0.311091i	−0.373640	+	0.927574i	$0.621891\pi$
$824$	103.197	+	59.5806i	0.125239	+	0.0723066i
$825$		0			0
$826$	−27.2441	−	47.1882i	−0.0329832	−	0.0571286i
$827$	260.100	−	260.100i	0.314510	−	0.314510i	−0.532144	−	0.846654i	$-0.678613\pi$
$827$	260.100	−	260.100i	0.314510	−	0.314510i	0.846654	+	0.532144i	$0.178613\pi$
$828$		0			0
$829$			325.275i			0.392370i	0.980567	+	0.196185i	$0.0628553\pi$
$829$			325.275i			0.392370i	−0.980567	+	0.196185i	$0.937145\pi$
$830$	49.6164	+	9.75055i	0.0597788	+	0.0117476i
$831$		0			0
$832$	−210.035	−	783.862i	−0.252446	−	0.942142i
$833$	32.5965	−	8.73421i	0.0391315	−	0.0104852i
$834$		0			0
$835$	1294.61	−	869.349i	1.55043	−	1.04114i
$836$	−395.803			−0.473449
$837$		0			0
$838$	36.5387	+	36.5387i	0.0436022	+	0.0436022i
$839$	81.4767	−	47.0406i	0.0971116	−	0.0560674i	−0.450658	−	0.892697i	$-0.648810\pi$
$839$	81.4767	−	47.0406i	0.0971116	−	0.0560674i	0.547769	+	0.836629i	$0.315477\pi$
$840$		0			0
$841$	−395.014	+	684.184i	−0.469695	+	0.813536i
$842$	10.1364	+	37.8296i	0.0120385	+	0.0449283i
$843$		0			0
$844$	−833.301	+	481.107i	−0.987323	+	0.570031i
$845$	39.8834	+	34.8146i	0.0471993	+	0.0412007i
$846$		0			0
$847$	−492.644	+	492.644i	−0.581633	+	0.581633i
$848$	98.5244	−	367.698i	0.116184	−	0.433606i
$849$		0			0
$850$	−1.88412	+	4.60861i	−0.00221661	+	0.00542189i
$851$	320.958	−	555.915i	0.377154	−	0.653249i
$852$		0			0
$853$	263.924	−	984.979i	0.309407	−	1.15472i	−0.619678	−	0.784856i	$-0.712737\pi$
$853$	263.924	−	984.979i	0.309407	−	1.15472i	0.929085	−	0.369867i	$-0.120597\pi$
$854$			139.579i			0.163442i
$855$		0			0
$856$	−108.534			−0.126793
$857$	−1522.95	−	408.073i	−1.77707	−	0.476164i	−0.787026	−	0.616920i	$-0.788380\pi$
$857$	−1522.95	−	408.073i	−1.77707	−	0.476164i	−0.990044	+	0.140756i	$0.955047\pi$
$858$		0			0
$859$	−507.067	−	292.755i	−0.590299	−	0.340809i	0.174917	−	0.984583i	$-0.444034\pi$
$859$	−507.067	−	292.755i	−0.590299	−	0.340809i	−0.765216	+	0.643774i	$0.777368\pi$
$860$	−221.970	−	108.829i	−0.258105	−	0.126545i
$861$		0			0
$862$	43.7939	+	11.7345i	0.0508050	+	0.0136132i
$863$	550.423	+	550.423i	0.637802	+	0.637802i	0.950013	−	0.312211i	$-0.101070\pi$
$863$	550.423	+	550.423i	0.637802	+	0.637802i	−0.312211	+	0.950013i	$0.601070\pi$
$864$		0			0
$865$	994.853	−	67.5082i	1.15012	−	0.0780442i
$866$	10.7144	+	18.5579i	0.0123723	+	0.0214294i
$867$		0			0
$868$	−902.531	+	241.833i	−1.03978	+	0.278609i
$869$	1012.26	+	584.429i	1.16486	+	0.672530i
$870$		0			0
$871$	−444.935	−	770.650i	−0.510833	−	0.884788i
$872$	51.2158	−	51.2158i	0.0587337	−	0.0587337i
$873$		0			0
$874$			26.5875i			0.0304205i
$875$	−748.589	−	841.794i	−0.855530	−	0.962050i
$876$		0			0
$877$	236.500	+	882.630i	0.269669	+	1.00642i	0.959330	+	0.282287i	$0.0910930\pi$
$877$	236.500	+	882.630i	0.269669	+	1.00642i	−0.689661	+	0.724133i	$0.742240\pi$
$878$	59.4017	−	15.9166i	0.0676557	−	0.0181283i
$879$		0			0
$880$	−1075.55	−	211.366i	−1.22222	−	0.240189i
$881$	459.689			0.521781			0.260891	−	0.965368i	$-0.415984\pi$
$881$	459.689			0.521781			0.260891	+	0.965368i	$0.415984\pi$
$882$		0			0
$883$	107.163	+	107.163i	0.121362	+	0.121362i	0.765179	−	0.643817i	$-0.222650\pi$
$883$	107.163	+	107.163i	0.121362	+	0.121362i	−0.643817	+	0.765179i	$0.722650\pi$
$884$	−48.1882	+	27.8215i	−0.0545116	+	0.0314723i
$885$		0			0
$886$	−71.8119	+	124.382i	−0.0810519	+	0.140386i
$887$	172.159	+	642.507i	0.194092	+	0.724360i	0.992500	+	0.122244i	$0.0390090\pi$
$887$	172.159	+	642.507i	0.194092	+	0.724360i	−0.798408	+	0.602116i	$0.794324\pi$
$888$		0			0
$889$	180.277	−	104.083i	0.202786	−	0.117078i
$890$	−21.3813	+	1.45088i	−0.0240239	+	0.00163020i
$891$		0			0
$892$	576.746	−	576.746i	0.646576	−	0.646576i
$893$	−98.5954	+	367.963i	−0.110409	+	0.412053i
$894$		0			0
$895$	1202.23	−	411.192i	1.34327	−	0.459433i
$896$	214.387	−	371.329i	0.239271	−	0.414430i
$897$		0			0
$898$	25.3288	−	94.5284i	0.0282058	−	0.105266i
$899$			186.745i			0.207725i
$900$		0			0
$901$	−25.6142			−0.0284287
$902$	186.402	+	49.9463i	0.206654	+	0.0553728i
$903$		0			0
$904$	228.495	+	131.922i	0.252760	+	0.145931i
$905$	−383.487	−	1121.22i	−0.423743	−	1.23892i
$906$		0			0
$907$	−804.640	−	215.603i	−0.887144	−	0.237710i	−0.213657	−	0.976909i	$-0.568538\pi$
$907$	−804.640	−	215.603i	−0.887144	−	0.237710i	−0.673487	+	0.739199i	$0.735204\pi$
$908$	−521.794	−	521.794i	−0.574663	−	0.574663i
$909$		0			0
$910$	7.77262	+	114.543i	0.00854134	+	0.125872i
$911$	38.7954	+	67.1955i	0.0425855	+	0.0737602i	0.886533	−	0.462666i	$-0.153107\pi$
$911$	38.7954	+	67.1955i	0.0425855	+	0.0737602i	−0.843947	+	0.536427i	$0.819774\pi$
$912$		0			0
$913$	723.538	−	193.871i	0.792484	−	0.212345i
$914$	−93.8309	−	54.1733i	−0.102660	−	0.0592706i
$915$		0			0
$916$	−358.623	−	621.153i	−0.391510	−	0.678115i
$917$	351.821	−	351.821i	0.383665	−	0.383665i
$918$		0			0
$919$			1478.95i			1.60930i	0.593750	+	0.804650i	$0.297647\pi$
$919$			1478.95i			1.60930i	−0.593750	+	0.804650i	$0.702353\pi$
$920$	−28.7909	+	146.505i	−0.0312944	+	0.159244i
$921$		0			0
$922$	11.7443	+	43.8305i	0.0127379	+	0.0475385i
$923$	471.083	−	126.226i	0.510383	−	0.136757i
$924$		0			0
$925$	102.492	−	807.227i	0.110802	−	0.872678i
$926$	−156.839			−0.169373
$927$		0			0
$928$	−45.5177	−	45.5177i	−0.0490492	−	0.0490492i
$929$	−1381.56	+	797.643i	−1.48715	+	0.858604i	−0.999893	−	0.0146572i	$-0.995334\pi$
$929$	−1381.56	+	797.643i	−1.48715	+	0.858604i	−0.487253	+	0.873261i	$0.662001\pi$
$930$		0			0
$931$	114.218	−	197.831i	0.122683	−	0.212493i
$932$	−174.439	−	651.014i	−0.187166	−	0.698513i
$933$		0			0
$934$	−113.927	+	65.7757i	−0.121977	+	0.0704237i
$935$	4.99338	+	73.5863i	0.00534051	+	0.0787019i
$936$		0			0
$937$	−921.265	+	921.265i	−0.983207	+	0.983207i	−0.999861	−	0.0166542i	$-0.994699\pi$
$937$	−921.265	+	921.265i	−0.983207	+	0.983207i	0.0166542	+	0.999861i	$0.494699\pi$
$938$	29.4471	−	109.898i	0.0313935	−	0.117162i
$939$		0			0
$940$	−468.736	+	956.048i	−0.498655	+	1.01707i
$941$	618.185	−	1070.73i	0.656945	−	1.13786i	−0.324458	−	0.945900i	$-0.605182\pi$
$941$	618.185	−	1070.73i	0.656945	−	1.13786i	0.981402	−	0.191961i	$-0.0614849\pi$
$942$		0			0
$943$	−367.913	+	1373.07i	−0.390152	+	1.45607i
$944$		−	495.068i		−	0.524436i
$945$		0			0
$946$	33.3958			0.0353021
$947$	1561.01	+	418.272i	1.64838	+	0.441681i	0.959158	−	0.282872i	$-0.0912871\pi$
$947$	1561.01	+	418.272i	1.64838	+	0.441681i	0.689219	+	0.724553i	$0.257954\pi$
$948$		0			0
$949$	47.7599	+	27.5742i	0.0503265	+	0.0290560i
$950$	13.0409	+	31.0777i	0.0137273	+	0.0327134i
$951$		0			0
$952$	−13.8064	−	3.69940i	−0.0145025	−	0.00388593i
$953$	−1074.57	−	1074.57i	−1.12756	−	1.12756i	−0.990573	−	0.136988i	$-0.956258\pi$
$953$	−1074.57	−	1074.57i	−1.12756	−	1.12756i	−0.136988	−	0.990573i	$-0.543742\pi$
$954$		0			0
$955$	179.503	−	205.638i	0.187961	−	0.215328i
$956$	−760.073	−	1316.48i	−0.795055	−	1.37708i
$957$		0			0
$958$	−30.2804	+	8.11362i	−0.0316080	+	0.00846933i
$959$	−1530.10	−	883.405i	−1.59552	−	0.921173i
$960$		0			0
$961$	138.418	+	239.748i	0.144036	+	0.249477i
$962$	−58.6394	+	58.6394i	−0.0609557	+	0.0609557i
$963$		0			0
$964$		−	1291.77i		−	1.34001i
$965$	−558.127	−	831.144i	−0.578370	−	0.861289i
$966$		0			0
$967$	−46.6332	−	174.037i	−0.0482246	−	0.179977i	0.937613	−	0.347682i	$-0.113031\pi$
$967$	−46.6332	−	174.037i	−0.0482246	−	0.179977i	−0.985837	+	0.167705i	$0.946364\pi$
$968$	113.066	−	30.2958i	0.116803	−	0.0312974i
$969$		0			0
$970$	−6.39905	+	32.5621i	−0.00659696	+	0.0335691i
$971$	40.8568			0.0420770			0.0210385	−	0.999779i	$-0.493303\pi$
$971$	40.8568			0.0420770			0.0210385	+	0.999779i	$0.493303\pi$
$972$		0			0
$973$	−607.325	−	607.325i	−0.624178	−	0.624178i
$974$	76.1338	−	43.9558i	0.0781661	−	0.0451292i
$975$		0			0
$976$	−634.092	+	1098.28i	−0.649685	+	1.12529i
$977$	202.074	+	754.152i	0.206832	+	0.771906i	0.988883	+	0.148693i	$0.0475065\pi$
$977$	202.074	+	754.152i	0.206832	+	0.771906i	−0.782052	+	0.623213i	$0.785827\pi$
$978$		0			0
$979$	−274.932	+	158.732i	−0.280829	+	0.162137i
$980$	419.885	−	481.018i	0.428454	−	0.490835i
$981$		0			0
$982$	48.9385	−	48.9385i	0.0498355	−	0.0498355i
$983$	−133.041	+	496.515i	−0.135341	+	0.505101i	0.864655	+	0.502367i	$0.167537\pi$
$983$	−133.041	+	496.515i	−0.135341	+	0.505101i	−0.999996	+	0.00273477i	$0.999129\pi$
$984$		0			0
$985$	−117.690	−	57.7016i	−0.119482	−	0.0585803i
$986$	−0.710935	+	1.23138i	−0.000721030	+	0.00124886i
$987$		0			0
$988$	−97.4863	+	363.824i	−0.0986704	+	0.368243i
$989$			245.999i			0.248735i
$990$		0			0
$991$	941.294			0.949843			0.474922	−	0.880028i	$-0.342476\pi$
$991$	941.294			0.949843			0.474922	+	0.880028i	$0.342476\pi$
$992$	227.798	+	61.0382i	0.229635	+	0.0615304i
$993$		0			0
$994$	54.0013	+	31.1776i	0.0543272	+	0.0313658i
$995$	−974.957	+	333.460i	−0.979856	+	0.335136i
$996$		0			0
$997$	−1287.52	−	344.990i	−1.29140	−	0.346029i	−0.453206	−	0.891406i	$-0.649720\pi$
$997$	−1287.52	−	344.990i	−1.29140	−	0.346029i	−0.838191	+	0.545377i	$0.816386\pi$
$998$	−54.8879	−	54.8879i	−0.0549979	−	0.0549979i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.l.a.118.5		40
3.2	odd	2		45.3.k.a.13.6	yes	40
5.2	odd	4	inner	135.3.l.a.37.6		40
9.2	odd	6		45.3.k.a.43.5	yes	40
9.4	even	3		405.3.g.g.163.6		20
9.5	odd	6		405.3.g.h.163.5		20
9.7	even	3	inner	135.3.l.a.73.6		40
15.2	even	4		45.3.k.a.22.5	yes	40
15.8	even	4		225.3.o.b.157.6		40
15.14	odd	2		225.3.o.b.193.5		40
45.2	even	12		45.3.k.a.7.6	✓	40
45.7	odd	12	inner	135.3.l.a.127.5		40
45.22	odd	12		405.3.g.g.82.6		20
45.29	odd	6		225.3.o.b.43.6		40
45.32	even	12		405.3.g.h.82.5		20
45.38	even	12		225.3.o.b.7.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.6	✓	40	45.2	even	12
45.3.k.a.13.6	yes	40	3.2	odd	2
45.3.k.a.22.5	yes	40	15.2	even	4
45.3.k.a.43.5	yes	40	9.2	odd	6
135.3.l.a.37.6		40	5.2	odd	4	inner
135.3.l.a.73.6		40	9.7	even	3	inner
135.3.l.a.118.5		40	1.1	even	1	trivial
135.3.l.a.127.5		40	45.7	odd	12	inner
225.3.o.b.7.5		40	45.38	even	12
225.3.o.b.43.6		40	45.29	odd	6
225.3.o.b.157.6		40	15.8	even	4
225.3.o.b.193.5		40	15.14	odd	2
405.3.g.g.82.6		20	45.22	odd	12
405.3.g.g.163.6		20	9.4	even	3
405.3.g.h.82.5		20	45.32	even	12
405.3.g.h.163.5		20	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.183646 + 0.0492077i) q^{2} +(-3.43280 - 1.98193i) q^{4} +(1.61810 + 4.73094i) q^{5} +(8.70492 + 2.33248i) q^{7} +(-1.07064 - 1.07064i) q^{8} +(0.0643587 + 0.948439i) q^{10} +(7.04110 + 12.1955i) q^{11} +(12.9444 - 3.46845i) q^{13} +(1.48385 + 0.856699i) q^{14} +(7.78377 + 13.4819i) q^{16} +(0.740694 - 0.740694i) q^{17} -7.09073i q^{19} +(3.82175 - 19.4473i) q^{20} +(0.692953 + 2.58614i) q^{22} +(-19.0499 + 5.10441i) q^{23} +(-19.7635 + 15.3103i) q^{25} +2.54786 q^{26} +(-25.2594 - 25.2594i) q^{28} +(-6.18301 + 3.56976i) q^{29} +(13.0783 - 22.6522i) q^{31} +(2.33357 + 8.70902i) q^{32} +(0.172473 - 0.0995774i) q^{34} +(3.05064 + 44.9566i) q^{35} +(-23.0151 + 23.0151i) q^{37} +(0.348919 - 1.30218i) q^{38} +(3.33274 - 6.79756i) q^{40} +(36.0387 - 62.4209i) q^{41} +(3.22835 - 12.0484i) q^{43} -55.8198i q^{44} -3.74961 q^{46} +(-51.8935 - 13.9048i) q^{47} +(27.9000 + 16.1081i) q^{49} +(-4.38286 + 1.83915i) q^{50} +(-51.3098 - 13.7484i) q^{52} +(-17.2907 - 17.2907i) q^{53} +(-46.3031 + 53.0446i) q^{55} +(-6.82262 - 11.8171i) q^{56} +(-1.31114 + 0.351320i) q^{58} +(-27.5407 - 15.9006i) q^{59} +(40.7317 + 70.5494i) q^{61} +(3.51643 - 3.51643i) q^{62} -60.5560i q^{64} +(37.3544 + 55.6269i) q^{65} +(-17.1864 - 64.1404i) q^{67} +(-4.01065 + 1.07465i) q^{68} +(-1.65197 + 8.40620i) q^{70} +36.3928 q^{71} +(2.90991 + 2.90991i) q^{73} +(-5.35915 + 3.09411i) q^{74} +(-14.0533 + 24.3410i) q^{76} +(32.8464 + 122.584i) q^{77} +(71.8823 - 41.5012i) q^{79} +(-51.1870 + 58.6396i) q^{80} +(9.68994 - 9.68994i) q^{82} +(13.7671 - 51.3796i) q^{83} +(4.70269 + 2.30566i) q^{85} +(1.18574 - 2.05377i) q^{86} +(5.51857 - 20.5956i) q^{88} +22.5436i q^{89} +120.770 q^{91} +(75.5111 + 20.2331i) q^{92} +(-8.84580 - 5.10712i) q^{94} +(33.5458 - 11.4735i) q^{95} +(33.7192 + 9.03502i) q^{97} +(4.33107 + 4.33107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 2 q^{5} - 2 q^{7} + 24 q^{8} - 8 q^{10} - 8 q^{11} - 2 q^{13} + 28 q^{16} - 28 q^{17} + 114 q^{20} + 14 q^{22} - 82 q^{23} - 8 q^{25} + 112 q^{26} - 88 q^{28} - 4 q^{31} + 14 q^{32} - 352 q^{35}+ \cdots + 1876 q^{98}+O(q^{100}) \) 40 * q + 2 * q^2 + 2 * q^5 - 2 * q^7 + 24 * q^8 - 8 * q^10 - 8 * q^11 - 2 * q^13 + 28 * q^16 - 28 * q^17 + 114 * q^20 + 14 * q^22 - 82 * q^23 - 8 * q^25 + 112 * q^26 - 88 * q^28 - 4 * q^31 + 14 * q^32 - 352 * q^35 - 92 * q^37 - 330 * q^38 + 30 * q^40 + 28 * q^41 - 2 * q^43 - 136 * q^46 - 64 * q^47 + 458 * q^50 - 74 * q^52 + 608 * q^53 + 224 * q^55 + 192 * q^56 + 30 * q^58 + 92 * q^61 + 100 * q^62 + 326 * q^65 - 80 * q^67 - 626 * q^68 - 102 * q^70 - 248 * q^71 - 8 * q^73 - 96 * q^76 - 338 * q^77 - 1444 * q^80 + 104 * q^82 - 370 * q^83 - 98 * q^85 + 328 * q^86 - 210 * q^88 + 152 * q^91 - 388 * q^92 + 360 * q^95 + 292 * q^97 + 1876 * q^98

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