LMFDB - Embedded newform 1638.2.p.i.991.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(919,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("1638.919");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.p (of order $3$, degree $2$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.1
Root			$1.19003 - 0.764088i$ of defining polynomial
Character	$\chi$	$=$	1638.991
Dual form			1638.2.p.i.919.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.05781 - 3.56422i) q^{5} +(1.65876 + 2.06119i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.05781 - 3.56422i) q^{5} +(1.65876 + 2.06119i) q^{7} -1.00000 q^{8} -4.11561 q^{10} -4.04474 q^{11} +(1.81454 - 3.11568i) q^{13} +(2.61442 - 0.405935i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.357690 + 0.619538i) q^{17} -3.84879 q^{19} +(-2.05781 + 3.56422i) q^{20} +(-2.02237 + 3.50284i) q^{22} +(-2.04891 + 3.54881i) q^{23} +(-5.96913 + 10.3388i) q^{25} +(-1.79099 - 3.12928i) q^{26} +(0.955663 - 2.46713i) q^{28} +(-4.50457 - 7.80214i) q^{29} +(1.82642 - 3.16346i) q^{31} +(0.500000 + 0.866025i) q^{32} +0.715381 q^{34} +(3.93314 - 10.1537i) q^{35} +(-3.59797 + 6.23187i) q^{37} +(-1.92440 + 3.33315i) q^{38} +(2.05781 + 3.56422i) q^{40} +(2.88423 + 4.99563i) q^{41} +(1.28209 - 2.22064i) q^{43} +(2.02237 + 3.50284i) q^{44} +(2.04891 + 3.54881i) q^{46} +(-1.28800 - 2.23088i) q^{47} +(-1.49702 + 6.83805i) q^{49} +(5.96913 + 10.3388i) q^{50} +(-3.60553 - 0.0135995i) q^{52} +(1.35888 - 2.35365i) q^{53} +(8.32328 + 14.4163i) q^{55} +(-1.65876 - 2.06119i) q^{56} -9.00914 q^{58} +(6.45133 + 11.1740i) q^{59} -9.43076 q^{61} +(-1.82642 - 3.16346i) q^{62} +1.00000 q^{64} +(-14.8389 - 0.0559702i) q^{65} -1.16632 q^{67} +(0.357690 - 0.619538i) q^{68} +(-6.82682 - 8.48306i) q^{70} +(-5.10254 + 8.83786i) q^{71} +(-1.25673 + 2.17673i) q^{73} +(3.59797 + 6.23187i) q^{74} +(1.92440 + 3.33315i) q^{76} +(-6.70925 - 8.33697i) q^{77} +(-6.70468 - 11.6129i) q^{79} +4.11561 q^{80} +5.76846 q^{82} +15.5024 q^{83} +(1.47212 - 2.54978i) q^{85} +(-1.28209 - 2.22064i) q^{86} +4.04474 q^{88} +(-5.45685 + 9.45154i) q^{89} +(9.43190 - 1.42805i) q^{91} +4.09781 q^{92} -2.57600 q^{94} +(7.92007 + 13.7180i) q^{95} +(-3.10135 + 5.37170i) q^{97} +(5.17342 + 4.71548i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8	$ 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8} - 4 q^{10} - 12 q^{11} - 11 q^{13} + 3 q^{14} - 4 q^{16} - 4 q^{17} - 12 q^{19} - 2 q^{20} - 6 q^{22} + 10 q^{23} - 18 q^{25} - 10 q^{26} - 2 q^{29} + 6 q^{31} + 4 q^{32} - 8 q^{34} - 18 q^{35} - 28 q^{37} - 6 q^{38} + 2 q^{40} - 6 q^{43} + 6 q^{44} - 10 q^{46} - q^{47} - 7 q^{49} + 18 q^{50} + q^{52} - 7 q^{53} + q^{55} - 3 q^{56} - 4 q^{58} - 2 q^{59} - 48 q^{61} - 6 q^{62} + 8 q^{64} - 19 q^{65} + 30 q^{67} - 4 q^{68} - 18 q^{70} - 6 q^{71} + q^{73} + 28 q^{74} + 6 q^{76} + 22 q^{77} - 12 q^{79} + 4 q^{80} + 32 q^{83} - 13 q^{85} + 6 q^{86} + 12 q^{88} - 25 q^{89} + 34 q^{91} - 20 q^{92} - 2 q^{94} + 8 q^{95} - q^{97} - 2 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8 - 4 * q^10 - 12 * q^11 - 11 * q^13 + 3 * q^14 - 4 * q^16 - 4 * q^17 - 12 * q^19 - 2 * q^20 - 6 * q^22 + 10 * q^23 - 18 * q^25 - 10 * q^26 - 2 * q^29 + 6 * q^31 + 4 * q^32 - 8 * q^34 - 18 * q^35 - 28 * q^37 - 6 * q^38 + 2 * q^40 - 6 * q^43 + 6 * q^44 - 10 * q^46 - q^47 - 7 * q^49 + 18 * q^50 + q^52 - 7 * q^53 + q^55 - 3 * q^56 - 4 * q^58 - 2 * q^59 - 48 * q^61 - 6 * q^62 + 8 * q^64 - 19 * q^65 + 30 * q^67 - 4 * q^68 - 18 * q^70 - 6 * q^71 + q^73 + 28 * q^74 + 6 * q^76 + 22 * q^77 - 12 * q^79 + 4 * q^80 + 32 * q^83 - 13 * q^85 + 6 * q^86 + 12 * q^88 - 25 * q^89 + 34 * q^91 - 20 * q^92 - 2 * q^94 + 8 * q^95 - q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.05781	−	3.56422i	−0.920279	−	1.59397i	−0.798983	−	0.601353i	$-0.794628\pi$
$5$	−2.05781	−	3.56422i	−0.920279	−	1.59397i	−0.121296	−	0.992616i	$-0.538705\pi$
$6$		0			0
$7$	1.65876	+	2.06119i	0.626953	+	0.779057i
$7$	1.65876	+	2.06119i	0.626953	+	0.779057i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−4.11561			−1.30147
$11$	−4.04474			−1.21953			−0.609767	−	0.792581i	$-0.708737\pi$
$11$	−4.04474			−1.21953			−0.609767	+	0.792581i	$0.708737\pi$
$12$		0			0
$13$	1.81454	−	3.11568i	0.503263	−	0.864133i
$13$	1.81454	−	3.11568i	0.503263	−	0.864133i
$14$	2.61442	−	0.405935i	0.698734	−	0.108491i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.357690	+	0.619538i	0.0867527	+	0.150260i	0.906137	−	0.422985i	$-0.139018\pi$
$17$	0.357690	+	0.619538i	0.0867527	+	0.150260i	−0.819384	+	0.573245i	$0.805684\pi$
$18$		0			0
$19$	−3.84879			−0.882973			−0.441487	−	0.897268i	$-0.645549\pi$
$19$	−3.84879			−0.882973			−0.441487	+	0.897268i	$0.645549\pi$
$20$	−2.05781	+	3.56422i	−0.460139	+	0.796985i
$21$		0			0
$22$	−2.02237	+	3.50284i	−0.431170	+	0.746809i
$23$	−2.04891	+	3.54881i	−0.427227	+	0.739978i	−0.996625	−	0.0820832i	$-0.973843\pi$
$23$	−2.04891	+	3.54881i	−0.427227	+	0.739978i	0.569399	+	0.822061i	$0.307176\pi$
$24$		0			0
$25$	−5.96913	+	10.3388i	−1.19383	+	2.06777i
$26$	−1.79099	−	3.12928i	−0.351241	−	0.613702i
$27$		0			0
$28$	0.955663	−	2.46713i	0.180603	−	0.466243i
$29$	−4.50457	−	7.80214i	−0.836478	−	1.44882i	−0.892822	−	0.450410i	$-0.851278\pi$
$29$	−4.50457	−	7.80214i	−0.836478	−	1.44882i	0.0563442	−	0.998411i	$-0.482056\pi$
$30$		0			0
$31$	1.82642	−	3.16346i	0.328035	−	0.568174i	−0.654087	−	0.756420i	$-0.726947\pi$
$31$	1.82642	−	3.16346i	0.328035	−	0.568174i	0.982122	+	0.188246i	$0.0602802\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	0.715381			0.122687
$35$	3.93314	−	10.1537i	0.664821	−	1.71629i
$36$		0			0
$37$	−3.59797	+	6.23187i	−0.591503	+	1.02451i	0.402527	+	0.915408i	$0.368132\pi$
$37$	−3.59797	+	6.23187i	−0.591503	+	1.02451i	−0.994030	+	0.109105i	$0.965201\pi$
$38$	−1.92440	+	3.33315i	−0.312178	+	0.540709i
$39$		0			0
$40$	2.05781	+	3.56422i	0.325368	+	0.563553i
$41$	2.88423	+	4.99563i	0.450441	+	0.780187i	0.998413	−	0.0563098i	$-0.0179334\pi$
$41$	2.88423	+	4.99563i	0.450441	+	0.780187i	−0.547972	+	0.836496i	$0.684600\pi$
$42$		0			0
$43$	1.28209	−	2.22064i	0.195516	−	0.338644i	−0.751553	−	0.659672i	$-0.770695\pi$
$43$	1.28209	−	2.22064i	0.195516	−	0.338644i	0.947070	+	0.321028i	$0.104028\pi$
$44$	2.02237	+	3.50284i	0.304883	+	0.528074i
$45$		0			0
$46$	2.04891	+	3.54881i	0.302095	+	0.523244i
$47$	−1.28800	−	2.23088i	−0.187874	−	0.325408i	0.756667	−	0.653800i	$-0.226826\pi$
$47$	−1.28800	−	2.23088i	−0.187874	−	0.325408i	−0.944541	+	0.328393i	$0.893493\pi$
$48$		0			0
$49$	−1.49702	+	6.83805i	−0.213859	+	0.976864i
$50$	5.96913	+	10.3388i	0.844163	+	1.46213i
$51$		0			0
$52$	−3.60553	−	0.0135995i	−0.499996	−	0.00188591i
$53$	1.35888	−	2.35365i	0.186656	−	0.323298i	−0.757477	−	0.652862i	$-0.773568\pi$
$53$	1.35888	−	2.35365i	0.186656	−	0.323298i	0.944133	+	0.329564i	$0.106902\pi$
$54$		0			0
$55$	8.32328	+	14.4163i	1.12231	+	1.94390i
$56$	−1.65876	−	2.06119i	−0.221661	−	0.275438i
$57$		0			0
$58$	−9.00914			−1.18296
$59$	6.45133	+	11.1740i	0.839892	+	1.45474i	0.889984	+	0.455991i	$0.150715\pi$
$59$	6.45133	+	11.1740i	0.839892	+	1.45474i	−0.0500924	+	0.998745i	$0.515952\pi$
$60$		0			0
$61$	−9.43076			−1.20749			−0.603743	−	0.797179i	$-0.706325\pi$
$61$	−9.43076			−1.20749			−0.603743	+	0.797179i	$0.706325\pi$
$62$	−1.82642	−	3.16346i	−0.231956	−	0.401760i
$63$		0			0
$64$	1.00000			0.125000
$65$	−14.8389	−	0.0559702i	−1.84054	−	0.00694225i
$66$		0			0
$67$	−1.16632			−0.142488			−0.0712441	−	0.997459i	$-0.522697\pi$
$67$	−1.16632			−0.142488			−0.0712441	+	0.997459i	$0.522697\pi$
$68$	0.357690	−	0.619538i	0.0433763	−	0.0751300i
$69$		0			0
$70$	−6.82682	−	8.48306i	−0.815961	−	1.01392i
$71$	−5.10254	+	8.83786i	−0.605560	+	1.04886i	0.386402	+	0.922330i	$0.373718\pi$
$71$	−5.10254	+	8.83786i	−0.605560	+	1.04886i	−0.991963	+	0.126531i	$0.959616\pi$
$72$		0			0
$73$	−1.25673	+	2.17673i	−0.147090	+	0.254767i	−0.930151	−	0.367178i	$-0.880324\pi$
$73$	−1.25673	+	2.17673i	−0.147090	+	0.254767i	0.783061	+	0.621945i	$0.213657\pi$
$74$	3.59797	+	6.23187i	0.418256	+	0.724440i
$75$		0			0
$76$	1.92440	+	3.33315i	0.220743	+	0.382339i
$77$	−6.70925	−	8.33697i	−0.764590	−	0.950086i
$78$		0			0
$79$	−6.70468	−	11.6129i	−0.754336	−	1.30655i	−0.945704	−	0.325030i	$-0.894626\pi$
$79$	−6.70468	−	11.6129i	−0.754336	−	1.30655i	0.191368	−	0.981518i	$-0.438708\pi$
$80$	4.11561			0.460139
$81$		0			0
$82$	5.76846			0.637020
$83$	15.5024			1.70161			0.850807	−	0.525479i	$-0.176114\pi$
$83$	15.5024			1.70161			0.850807	+	0.525479i	$0.176114\pi$
$84$		0			0
$85$	1.47212	−	2.54978i	0.159673	−	0.276562i
$86$	−1.28209	−	2.22064i	−0.138251	−	0.239458i
$87$		0			0
$88$	4.04474			0.431170
$89$	−5.45685	+	9.45154i	−0.578425	+	1.00186i	0.417235	+	0.908798i	$0.362999\pi$
$89$	−5.45685	+	9.45154i	−0.578425	+	1.00186i	−0.995660	+	0.0930629i	$0.970334\pi$
$90$		0			0
$91$	9.43190	−	1.42805i	0.988731	−	0.149701i
$92$	4.09781			0.427227
$93$		0			0
$94$	−2.57600			−0.265694
$95$	7.92007	+	13.7180i	0.812582	+	1.40743i
$96$		0			0
$97$	−3.10135	+	5.37170i	−0.314895	+	0.545414i	−0.979415	−	0.201856i	$-0.935303\pi$
$97$	−3.10135	+	5.37170i	−0.314895	+	0.545414i	0.664520	+	0.747270i	$0.268636\pi$
$98$	5.17342	+	4.71548i	0.522594	+	0.476335i
$99$		0			0
$100$	11.9383			1.19383
$101$	−16.3065			−1.62256			−0.811278	−	0.584660i	$-0.801228\pi$
$101$	−16.3065			−1.62256			−0.811278	+	0.584660i	$0.801228\pi$
$102$		0			0
$103$	1.46023	+	2.52920i	0.143881	+	0.249209i	0.928955	−	0.370193i	$-0.120708\pi$
$103$	1.46023	+	2.52920i	0.143881	+	0.249209i	−0.785074	+	0.619402i	$0.787375\pi$
$104$	−1.81454	+	3.11568i	−0.177930	+	0.305517i
$105$		0			0
$106$	−1.35888	−	2.35365i	−0.131986	−	0.228606i
$107$	−2.01938	+	3.49768i	−0.195221	+	0.338133i	−0.946973	−	0.321313i	$-0.895876\pi$
$107$	−2.01938	+	3.49768i	−0.195221	+	0.338133i	0.751752	+	0.659446i	$0.229209\pi$
$108$		0			0
$109$	6.93314	−	12.0085i	0.664074	−	1.15021i	−0.315461	−	0.948938i	$-0.602159\pi$
$109$	6.93314	−	12.0085i	0.664074	−	1.15021i	0.979535	−	0.201272i	$-0.0645074\pi$
$110$	16.6466			1.58719
$111$		0			0
$112$	−2.61442	+	0.405935i	−0.247040	+	0.0383572i
$113$	7.30902	−	12.6596i	0.687575	−	1.19091i	−0.285045	−	0.958514i	$-0.592009\pi$
$113$	7.30902	−	12.6596i	0.687575	−	1.19091i	0.972620	−	0.232401i	$-0.0746581\pi$
$114$		0			0
$115$	16.8650			1.57267
$116$	−4.50457	+	7.80214i	−0.418239	+	0.724411i
$117$		0			0
$118$	12.9027			1.18779
$119$	−0.683663	+	1.76493i	−0.0626713	+	0.161791i
$120$		0			0
$121$	5.35989			0.487262
$122$	−4.71538	+	8.16728i	−0.426911	+	0.739431i
$123$		0			0
$124$	−3.65285			−0.328035
$125$	28.5552			2.55405
$126$		0			0
$127$	−1.26603	−	2.19283i	−0.112342	−	0.194582i	0.804372	−	0.594126i	$-0.202502\pi$
$127$	−1.26603	−	2.19283i	−0.112342	−	0.194582i	−0.916714	+	0.399544i	$0.869169\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−7.46794	+	12.8229i	−0.654982	+	1.12464i
$131$	−6.21657	−	10.7674i	−0.543144	−	0.940753i	−0.998721	−	0.0505568i	$-0.983900\pi$
$131$	−6.21657	−	10.7674i	−0.543144	−	0.940753i	0.455577	−	0.890196i	$-0.349433\pi$
$132$		0			0
$133$	−6.38423	−	7.93309i	−0.553583	−	0.687886i
$134$	−0.583158	+	1.01006i	−0.0503772	+	0.0872558i
$135$		0			0
$136$	−0.357690	−	0.619538i	−0.0306717	−	0.0531250i
$137$	−5.19240	−	8.99351i	−0.443617	−	0.768367i	0.554338	−	0.832292i	$-0.312972\pi$
$137$	−5.19240	−	8.99351i	−0.443617	−	0.768367i	−0.997955	+	0.0639247i	$0.979638\pi$
$138$		0			0
$139$	−0.636394	+	1.10227i	−0.0539783	+	0.0934931i	−0.891752	−	0.452525i	$-0.850524\pi$
$139$	−0.636394	+	1.10227i	−0.0539783	+	0.0934931i	0.837774	+	0.546018i	$0.183857\pi$
$140$	−10.7600	+	1.67067i	−0.909382	+	0.141197i
$141$		0			0
$142$	5.10254	+	8.83786i	0.428196	+	0.741657i
$143$	−7.33934	+	12.6021i	−0.613746	+	1.05384i
$144$		0			0
$145$	−18.5391	+	32.1106i	−1.53959	+	2.66664i
$146$	1.25673	+	2.17673i	0.104008	+	0.180147i
$147$		0			0
$148$	7.19594			0.591503
$149$	−23.3619			−1.91388			−0.956942	−	0.290278i	$-0.906252\pi$
$149$	−23.3619			−1.91388			−0.956942	+	0.290278i	$0.906252\pi$
$150$		0			0
$151$	1.19832	−	2.07555i	0.0975178	−	0.168906i	−0.813139	−	0.582070i	$-0.802243\pi$
$151$	1.19832	−	2.07555i	0.0975178	−	0.168906i	0.910657	+	0.413164i	$0.135576\pi$
$152$	3.84879			0.312178
$153$		0			0
$154$	−10.5747	+	1.64190i	−0.852130	+	0.132308i
$155$	−15.0337			−1.20754
$156$		0			0
$157$	5.79083	−	10.0300i	0.462158	−	0.800482i	−0.536910	−	0.843640i	$-0.680409\pi$
$157$	5.79083	−	10.0300i	0.462158	−	0.800482i	0.999068	+	0.0431579i	$0.0137419\pi$
$158$	−13.4094			−1.06679
$159$		0			0
$160$	2.05781	−	3.56422i	0.162684	−	0.281777i
$161$	−10.7134	+	1.66344i	−0.844336	+	0.131098i
$162$		0			0
$163$	17.9086			1.40271			0.701356	−	0.712811i	$-0.252578\pi$
$163$	17.9086			1.40271			0.701356	+	0.712811i	$0.252578\pi$
$164$	2.88423	−	4.99563i	0.225220	−	0.390093i
$165$		0			0
$166$	7.75122	−	13.4255i	0.601611	−	1.04202i
$167$	−3.15398	−	5.46286i	−0.244062	−	0.422728i	0.717805	−	0.696244i	$-0.245147\pi$
$167$	−3.15398	−	5.46286i	−0.244062	−	0.422728i	−0.961868	+	0.273516i	$0.911814\pi$
$168$		0			0
$169$	−6.41489	−	11.3070i	−0.493453	−	0.869773i
$170$	−1.47212	−	2.54978i	−0.112906	−	0.195559i
$171$		0			0
$172$	−2.56417			−0.195516
$173$	3.65127			0.277601			0.138800	−	0.990320i	$-0.455675\pi$
$173$	3.65127			0.277601			0.138800	+	0.990320i	$0.455675\pi$
$174$		0			0
$175$	−31.2117	+	4.84616i	−2.35938	+	0.366335i
$176$	2.02237	−	3.50284i	0.152442	−	0.264037i
$177$		0			0
$178$	5.45685	+	9.45154i	0.409008	+	0.708423i
$179$	−12.5191			−0.935723			−0.467861	−	0.883802i	$-0.654975\pi$
$179$	−12.5191			−0.935723			−0.467861	+	0.883802i	$0.654975\pi$
$180$		0			0
$181$	−18.1728			−1.35077			−0.675385	−	0.737465i	$-0.736023\pi$
$181$	−18.1728			−1.35077			−0.675385	+	0.737465i	$0.736023\pi$
$182$	3.47922	−	8.88229i	0.257897	−	0.658399i
$183$		0			0
$184$	2.04891	−	3.54881i	0.151047	−	0.261622i
$185$	29.6157			2.17739
$186$		0			0
$187$	−1.44676	−	2.50587i	−0.105798	−	0.183247i
$188$	−1.28800	+	2.23088i	−0.0939371	+	0.162704i
$189$		0			0
$190$	15.8401			1.14916
$191$	−4.46007			−0.322720			−0.161360	−	0.986896i	$-0.551588\pi$
$191$	−4.46007			−0.322720			−0.161360	+	0.986896i	$0.551588\pi$
$192$		0			0
$193$	−8.68485			−0.625149			−0.312575	−	0.949893i	$-0.601191\pi$
$193$	−8.68485			−0.625149			−0.312575	+	0.949893i	$0.601191\pi$
$194$	3.10135	+	5.37170i	0.222664	+	0.385666i
$195$		0			0
$196$	6.67043	−	2.12257i	0.476460	−	0.151612i
$197$	1.23397	+	2.13730i	0.0879166	+	0.152276i	0.906630	−	0.421926i	$-0.138646\pi$
$197$	1.23397	+	2.13730i	0.0879166	+	0.152276i	−0.818714	+	0.574202i	$0.805312\pi$
$198$		0			0
$199$	−10.2841	−	17.8125i	−0.729018	−	1.26270i	−0.957298	−	0.289101i	$-0.906644\pi$
$199$	−10.2841	−	17.8125i	−0.729018	−	1.26270i	0.228280	−	0.973595i	$-0.426690\pi$
$200$	5.96913	−	10.3388i	0.422081	−	0.731066i
$201$		0			0
$202$	−8.15325	+	14.1218i	−0.573660	+	0.993609i
$203$	8.60970	−	22.2267i	0.604282	−	1.56001i
$204$		0			0
$205$	11.8704	−	20.5601i	0.829063	−	1.43598i
$206$	2.92046			0.203478
$207$		0			0
$208$	1.79099	+	3.12928i	0.124182	+	0.216976i
$209$	15.5673			1.07682
$210$		0			0
$211$	2.22726	+	3.85773i	0.153331	+	0.265577i	0.932450	−	0.361299i	$-0.117667\pi$
$211$	2.22726	+	3.85773i	0.153331	+	0.265577i	−0.779119	+	0.626876i	$0.784333\pi$
$212$	−2.71776			−0.186656
$213$		0			0
$214$	2.01938	+	3.49768i	0.138042	+	0.239096i
$215$	−10.5531			−0.719718
$216$		0			0
$217$	9.55009	−	1.48282i	0.648303	−	0.100660i
$218$	−6.93314	−	12.0085i	−0.469571	−	0.813321i
$219$		0			0
$220$	8.32328	−	14.4163i	0.561155	−	0.971950i
$221$	2.57932	+	0.00972881i	0.173504	+	0.000654431i
$222$		0			0
$223$	−2.49662	−	4.32427i	−0.167186	−	0.289574i	0.770243	−	0.637750i	$-0.220135\pi$
$223$	−2.49662	−	4.32427i	−0.167186	−	0.289574i	−0.937429	+	0.348175i	$0.886801\pi$
$224$	−0.955663	+	2.46713i	−0.0638529	+	0.164842i
$225$		0			0
$226$	−7.30902	−	12.6596i	−0.486189	−	0.842104i
$227$	−0.786363	−	1.36202i	−0.0521927	−	0.0904005i	0.838749	−	0.544519i	$-0.183288\pi$
$227$	−0.786363	−	1.36202i	−0.0521927	−	0.0904005i	−0.890941	+	0.454118i	$0.849954\pi$
$228$		0			0
$229$	0.828619	+	1.43521i	0.0547567	+	0.0948413i	0.892104	−	0.451829i	$-0.149228\pi$
$229$	0.828619	+	1.43521i	0.0547567	+	0.0948413i	−0.837348	+	0.546671i	$0.815895\pi$
$230$	8.43251	−	14.6055i	0.556023	−	0.963060i
$231$		0			0
$232$	4.50457	+	7.80214i	0.295739	+	0.512236i
$233$	3.86181	+	6.68885i	0.252996	+	0.438201i	0.964349	−	0.264633i	$-0.0852509\pi$
$233$	3.86181	+	6.68885i	0.252996	+	0.438201i	−0.711354	+	0.702834i	$0.751918\pi$
$234$		0			0
$235$	−5.30091	+	9.18145i	−0.345793	+	0.598932i
$236$	6.45133	−	11.1740i	0.419946	−	0.727368i
$237$		0			0
$238$	1.18665	+	1.47454i	0.0769189	+	0.0955800i
$239$	28.7630			1.86052			0.930261	−	0.366899i	$-0.119580\pi$
$239$	28.7630			1.86052			0.930261	+	0.366899i	$0.119580\pi$
$240$		0			0
$241$	−12.8102	−	22.1879i	−0.825178	−	1.42925i	−0.901783	−	0.432189i	$-0.857741\pi$
$241$	−12.8102	−	22.1879i	−0.825178	−	1.42925i	0.0766048	−	0.997062i	$-0.475592\pi$
$242$	2.67994	−	4.64180i	0.172273	−	0.298386i
$243$		0			0
$244$	4.71538	+	8.16728i	0.301871	+	0.522856i
$245$	27.4529	−	8.73568i	1.75390	−	0.558102i
$246$		0			0
$247$	−6.98379	+	11.9916i	−0.444368	+	0.763007i
$248$	−1.82642	+	3.16346i	−0.115978	+	0.200880i
$249$		0			0
$250$	14.2776	−	24.7295i	0.902995	−	1.56403i
$251$	−0.339652	+	0.588295i	−0.0214387	+	0.0371329i	−0.876546	−	0.481319i	$-0.840158\pi$
$251$	−0.339652	+	0.588295i	−0.0214387	+	0.0371329i	0.855107	+	0.518452i	$0.173491\pi$
$252$		0			0
$253$	8.28729	−	14.3540i	0.521017	−	0.902428i
$254$	−2.53206			−0.158876
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.22293	+	2.11818i	−0.0762846	+	0.132129i	−0.901644	−	0.432479i	$-0.857639\pi$
$257$	−1.22293	+	2.11818i	−0.0762846	+	0.132129i	0.825360	+	0.564607i	$0.190972\pi$
$258$		0			0
$259$	−18.8133	+	2.92108i	−1.16900	+	0.181507i
$260$	7.37100	+	12.8789i	0.457130	+	0.798715i
$261$		0			0
$262$	−12.4331			−0.768122
$263$	−25.3192			−1.56125			−0.780625	−	0.625000i	$-0.785099\pi$
$263$	−25.3192			−1.56125			−0.780625	+	0.625000i	$0.785099\pi$
$264$		0			0
$265$	−11.1852			−0.687103
$266$	−10.0624	+	1.56236i	−0.616964	+	0.0957943i
$267$		0			0
$268$	0.583158	+	1.01006i	0.0356220	+	0.0616992i
$269$	−6.78327	−	11.7490i	−0.413583	−	0.716348i	0.581695	−	0.813407i	$-0.302390\pi$
$269$	−6.78327	−	11.7490i	−0.413583	−	0.716348i	−0.995279	+	0.0970593i	$0.969056\pi$
$270$		0			0
$271$	2.42970	−	4.20837i	0.147594	−	0.255640i	−0.782744	−	0.622344i	$-0.786180\pi$
$271$	2.42970	−	4.20837i	0.147594	−	0.255640i	0.930338	+	0.366704i	$0.119514\pi$
$272$	−0.715381			−0.0433763
$273$		0			0
$274$	−10.3848			−0.627369
$275$	24.1436	−	41.8179i	1.45591	−	2.52171i
$276$		0			0
$277$	−6.03127	−	10.4465i	−0.362384	−	0.627667i	0.625969	−	0.779848i	$-0.284704\pi$
$277$	−6.03127	−	10.4465i	−0.362384	−	0.627667i	−0.988353	+	0.152181i	$0.951370\pi$
$278$	0.636394	+	1.10227i	0.0381684	+	0.0661096i
$279$		0			0
$280$	−3.93314	+	10.1537i	−0.235050	+	0.606802i
$281$	−18.3963			−1.09743			−0.548716	−	0.836009i	$-0.684883\pi$
$281$	−18.3963			−1.09743			−0.548716	+	0.836009i	$0.684883\pi$
$282$		0			0
$283$	−0.694306			−0.0412722			−0.0206361	−	0.999787i	$-0.506569\pi$
$283$	−0.694306			−0.0412722			−0.0206361	+	0.999787i	$0.506569\pi$
$284$	10.2051			0.605560
$285$		0			0
$286$	7.24406	+	12.6571i	0.428350	+	0.748430i
$287$	−5.51270	+	14.2315i	−0.325404	+	0.840060i
$288$		0			0
$289$	8.24412	−	14.2792i	0.484948	−	0.839954i
$290$	18.5391	+	32.1106i	1.08865	+	1.88560i
$291$		0			0
$292$	2.51347			0.147090
$293$	−5.44518	+	9.43133i	−0.318111	+	0.550984i	−0.980094	−	0.198535i	$-0.936382\pi$
$293$	−5.44518	+	9.43133i	−0.318111	+	0.550984i	0.661983	+	0.749519i	$0.269715\pi$
$294$		0			0
$295$	26.5512	−	45.9880i	1.54587	−	2.67752i
$296$	3.59797	−	6.23187i	0.209128	−	0.362220i
$297$		0			0
$298$	−11.6810	+	20.2320i	−0.676661	+	1.17201i
$299$	7.33912	+	12.8232i	0.424433	+	0.741584i
$300$		0			0
$301$	6.70384	−	1.04089i	0.386403	−	0.0599957i
$302$	−1.19832	−	2.07555i	−0.0689555	−	0.119434i
$303$		0			0
$304$	1.92440	−	3.33315i	0.110372	−	0.191169i
$305$	19.4067	+	33.6134i	1.11122	+	1.92470i
$306$		0			0
$307$	23.7724			1.35676			0.678382	−	0.734709i	$-0.262681\pi$
$307$	23.7724			1.35676			0.678382	+	0.734709i	$0.262681\pi$
$308$	−3.86540	+	9.97887i	−0.220252	+	0.568599i
$309$		0			0
$310$	−7.51685	+	13.0196i	−0.426928	+	0.739462i
$311$	10.9242	−	18.9212i	0.619454	−	1.07293i	−0.370132	−	0.928979i	$-0.620688\pi$
$311$	10.9242	−	18.9212i	0.619454	−	1.07293i	0.989586	−	0.143946i	$-0.0459792\pi$
$312$		0			0
$313$	16.0323	+	27.7688i	0.906199	+	1.56958i	0.819300	+	0.573365i	$0.194362\pi$
$313$	16.0323	+	27.7688i	0.906199	+	1.56958i	0.0868992	+	0.996217i	$0.472304\pi$
$314$	−5.79083	−	10.0300i	−0.326795	−	0.566026i
$315$		0			0
$316$	−6.70468	+	11.6129i	−0.377168	+	0.653274i
$317$	−10.3068	−	17.8520i	−0.578889	−	1.00267i	−0.995607	−	0.0936296i	$-0.970153\pi$
$317$	−10.3068	−	17.8520i	−0.578889	−	1.00267i	0.416718	−	0.909036i	$-0.363180\pi$
$318$		0			0
$319$	18.2198	+	31.5576i	1.02011	+	1.76689i
$320$	−2.05781	−	3.56422i	−0.115035	−	0.199246i
$321$		0			0
$322$	−3.91613	+	10.1098i	−0.218237	+	0.563398i
$323$	−1.37668	−	2.38447i	−0.0766003	−	0.132676i
$324$		0			0
$325$	21.3813	+	37.3581i	1.18602	+	2.07226i
$326$	8.95432	−	15.5093i	0.495934	−	0.858982i
$327$		0			0
$328$	−2.88423	−	4.99563i	−0.159255	−	0.275838i
$329$	2.46179	−	6.35532i	0.135723	−	0.350380i
$330$		0			0
$331$	11.9956			0.659338			0.329669	−	0.944097i	$-0.393063\pi$
$331$	11.9956			0.659338			0.329669	+	0.944097i	$0.393063\pi$
$332$	−7.75122	−	13.4255i	−0.425403	−	0.736820i
$333$		0			0
$334$	−6.30796			−0.345156
$335$	2.40005	+	4.15701i	0.131129	+	0.227122i
$336$		0			0
$337$	−17.6146			−0.959526			−0.479763	−	0.877398i	$-0.659277\pi$
$337$	−17.6146			−0.959526			−0.479763	+	0.877398i	$0.659277\pi$
$338$	−12.9996	−	0.0980666i	−0.707087	−	0.00533412i
$339$		0			0
$340$	−2.94423			−0.159673
$341$	−7.38740	+	12.7954i	−0.400050	+	0.692907i
$342$		0			0
$343$	−16.5777	+	8.25707i	−0.895113	+	0.445840i
$344$	−1.28209	+	2.22064i	−0.0691255	+	0.119729i
$345$		0			0
$346$	1.82563	−	3.16209i	0.0981467	−	0.169995i
$347$	−7.92519	−	13.7268i	−0.425447	−	0.736895i	0.571015	−	0.820939i	$-0.306550\pi$
$347$	−7.92519	−	13.7268i	−0.425447	−	0.736895i	−0.996462	+	0.0840442i	$0.973216\pi$
$348$		0			0
$349$	5.15206	+	8.92363i	0.275783	+	0.477671i	0.970332	−	0.241775i	$-0.0777294\pi$
$349$	5.15206	+	8.92363i	0.275783	+	0.477671i	−0.694549	+	0.719445i	$0.744396\pi$
$350$	−11.4090	+	29.4532i	−0.609834	+	1.57434i
$351$		0			0
$352$	−2.02237	−	3.50284i	−0.107793	−	0.186702i
$353$	16.0195			0.852632			0.426316	−	0.904574i	$-0.359811\pi$
$353$	16.0195			0.852632			0.426316	+	0.904574i	$0.359811\pi$
$354$		0			0
$355$	42.0002			2.22914
$356$	10.9137			0.578425
$357$		0			0
$358$	−6.25956	+	10.8419i	−0.330828	+	0.573011i
$359$	−4.55623	−	7.89162i	−0.240469	−	0.416504i	0.720379	−	0.693580i	$-0.243968\pi$
$359$	−4.55623	−	7.89162i	−0.240469	−	0.416504i	−0.960848	+	0.277077i	$0.910634\pi$
$360$		0			0
$361$	−4.18681			−0.220358
$362$	−9.08638	+	15.7381i	−0.477570	+	0.827175i
$363$		0			0
$364$	−5.95268	−	7.45423i	−0.312005	−	0.390708i
$365$	10.3445			0.541454
$366$		0			0
$367$	10.2238			0.533677			0.266839	−	0.963741i	$-0.414021\pi$
$367$	10.2238			0.533677			0.266839	+	0.963741i	$0.414021\pi$
$368$	−2.04891	−	3.54881i	−0.106807	−	0.184995i
$369$		0			0
$370$	14.8079	−	25.6480i	0.769824	−	1.33337i
$371$	7.10537	−	1.10323i	0.368892	−	0.0572769i
$372$		0			0
$373$	−28.1592			−1.45803			−0.729015	−	0.684497i	$-0.760022\pi$
$373$	−28.1592			−1.45803			−0.729015	+	0.684497i	$0.760022\pi$
$374$	−2.89353			−0.149621
$375$		0			0
$376$	1.28800	+	2.23088i	0.0664236	+	0.115049i
$377$	−32.4827	−	0.122520i	−1.67294	−	0.00631008i
$378$		0			0
$379$	−3.08112	−	5.33666i	−0.158267	−	0.274126i	0.775977	−	0.630761i	$-0.217257\pi$
$379$	−3.08112	−	5.33666i	−0.158267	−	0.274126i	−0.934244	+	0.356635i	$0.883924\pi$
$380$	7.92007	−	13.7180i	0.406291	−	0.703716i
$381$		0			0
$382$	−2.23004	+	3.86254i	−0.114099	+	0.197625i
$383$	18.9632			0.968973			0.484487	−	0.874799i	$-0.339006\pi$
$383$	18.9632			0.968973			0.484487	+	0.874799i	$0.339006\pi$
$384$		0			0
$385$	−15.9085	+	41.0692i	−0.810772	+	2.09308i
$386$	−4.34243	+	7.52130i	−0.221024	+	0.382824i
$387$		0			0
$388$	6.20271			0.314895
$389$	−1.08192	+	1.87394i	−0.0548554	+	0.0950123i	−0.892149	−	0.451741i	$-0.850803\pi$
$389$	−1.08192	+	1.87394i	−0.0548554	+	0.0950123i	0.837294	+	0.546753i	$0.184136\pi$
$390$		0			0
$391$	−2.93150			−0.148252
$392$	1.49702	−	6.83805i	0.0756107	−	0.345374i
$393$		0			0
$394$	2.46794			0.124333
$395$	−27.5939	+	47.7940i	−1.38840	+	2.40478i
$396$		0			0
$397$	20.7716			1.04250			0.521249	−	0.853405i	$-0.325466\pi$
$397$	20.7716			1.04250			0.521249	+	0.853405i	$0.325466\pi$
$398$	−20.5681			−1.03099
$399$		0			0
$400$	−5.96913	−	10.3388i	−0.298457	−	0.516942i
$401$	1.15403	−	1.99885i	0.0576297	−	0.0998176i	−0.835771	−	0.549078i	$-0.814979\pi$
$401$	1.15403	−	1.99885i	0.0576297	−	0.0998176i	0.893401	+	0.449260i	$0.148312\pi$
$402$		0			0
$403$	−6.54220	−	11.4308i	−0.325890	−	0.569407i
$404$	8.15325	+	14.1218i	0.405639	+	0.702588i
$405$		0			0
$406$	−14.9440	−	18.5696i	−0.741659	−	0.921592i
$407$	14.5528	−	25.2063i	0.721358	−	1.24943i
$408$		0			0
$409$	−8.01566	−	13.8835i	−0.396349	−	0.686497i	0.596923	−	0.802298i	$-0.296390\pi$
$409$	−8.01566	−	13.8835i	−0.396349	−	0.686497i	−0.993272	+	0.115802i	$0.963056\pi$
$410$	−11.8704	−	20.5601i	−0.586236	−	1.01539i
$411$		0			0
$412$	1.46023	−	2.52920i	0.0719405	−	0.124605i
$413$	−12.3306	+	31.8325i	−0.606749	+	1.56637i
$414$		0			0
$415$	−31.9010	−	55.2542i	−1.56596	−	2.71232i
$416$	3.60553	+	0.0135995i	0.176775	+	0.000666770i
$417$		0			0
$418$	7.78367	−	13.4817i	0.380712	−	0.659412i
$419$	−1.48519	−	2.57242i	−0.0725561	−	0.125671i	0.827465	−	0.561518i	$-0.189782\pi$
$419$	−1.48519	−	2.57242i	−0.0725561	−	0.125671i	−0.900021	+	0.435847i	$0.856449\pi$
$420$		0			0
$421$	34.3026			1.67181			0.835903	−	0.548878i	$-0.184945\pi$
$421$	34.3026			1.67181			0.835903	+	0.548878i	$0.184945\pi$
$422$	4.45453			0.216843
$423$		0			0
$424$	−1.35888	+	2.35365i	−0.0659929	+	0.114303i
$425$	−8.54041			−0.414271
$426$		0			0
$427$	−15.6434	−	19.4386i	−0.757037	−	0.940700i
$428$	4.03877			0.195221
$429$		0			0
$430$	−5.27657	+	9.13929i	−0.254459	+	0.440736i
$431$	23.4495			1.12952			0.564762	−	0.825254i	$-0.308968\pi$
$431$	23.4495			1.12952			0.564762	+	0.825254i	$0.308968\pi$
$432$		0			0
$433$	0.402426	−	0.697022i	0.0193394	−	0.0334968i	−0.856194	−	0.516655i	$-0.827177\pi$
$433$	0.402426	−	0.697022i	0.0193394	−	0.0334968i	0.875533	+	0.483158i	$0.160510\pi$
$434$	3.49089	−	9.01203i	0.167568	−	0.432591i
$435$		0			0
$436$	−13.8663			−0.664074
$437$	7.88581	−	13.6586i	0.377230	−	0.653381i
$438$		0			0
$439$	0.798877	−	1.38370i	0.0381283	−	0.0660402i	−0.846332	−	0.532657i	$-0.821194\pi$
$439$	0.798877	−	1.38370i	0.0381283	−	0.0660402i	0.884460	+	0.466616i	$0.154527\pi$
$440$	−8.32328	−	14.4163i	−0.396797	−	0.687272i
$441$		0			0
$442$	1.29809	−	2.22890i	0.0617437	−	0.106018i
$443$	3.27335	+	5.66960i	0.155521	+	0.269371i	0.933249	−	0.359231i	$-0.116961\pi$
$443$	3.27335	+	5.66960i	0.155521	+	0.269371i	−0.777727	+	0.628602i	$0.783628\pi$
$444$		0			0
$445$	44.9166			2.12925
$446$	−4.99324			−0.236437
$447$		0			0
$448$	1.65876	+	2.06119i	0.0783691	+	0.0973821i
$449$	6.34113	−	10.9832i	0.299257	−	0.518328i	−0.676710	−	0.736250i	$-0.736595\pi$
$449$	6.34113	−	10.9832i	0.299257	−	0.518328i	0.975966	+	0.217923i	$0.0699280\pi$
$450$		0			0
$451$	−11.6659	−	20.2060i	−0.549328	−	0.951464i
$452$	−14.6180			−0.687575
$453$		0			0
$454$	−1.57273			−0.0738117
$455$	−24.4989	−	30.6787i	−1.14853	−	1.43824i
$456$		0			0
$457$	5.37753	−	9.31415i	0.251550	−	0.435697i	−0.712403	−	0.701771i	$-0.752393\pi$
$457$	5.37753	−	9.31415i	0.251550	−	0.435697i	0.963953	+	0.266073i	$0.0857264\pi$
$458$	1.65724			0.0774376
$459$		0			0
$460$	−8.43251	−	14.6055i	−0.393168	−	0.680986i
$461$	−9.19640	+	15.9286i	−0.428319	+	0.741870i	−0.996724	−	0.0808788i	$-0.974227\pi$
$461$	−9.19640	+	15.9286i	−0.428319	+	0.741870i	0.568405	+	0.822749i	$0.307561\pi$
$462$		0			0
$463$	−34.6818			−1.61180			−0.805901	−	0.592050i	$-0.798319\pi$
$463$	−34.6818			−1.61180			−0.805901	+	0.592050i	$0.798319\pi$
$464$	9.00914			0.418239
$465$		0			0
$466$	7.72362			0.357790
$467$	−14.1236	−	24.4627i	−0.653561	−	1.13200i	−0.982253	−	0.187563i	$-0.939941\pi$
$467$	−14.1236	−	24.4627i	−0.653561	−	1.13200i	0.328692	−	0.944437i	$-0.393392\pi$
$468$		0			0
$469$	−1.93464	−	2.40400i	−0.0893334	−	0.111006i
$470$	5.30091	+	9.18145i	0.244513	+	0.423509i
$471$		0			0
$472$	−6.45133	−	11.1740i	−0.296947	−	0.514327i
$473$	−5.18570	+	8.98189i	−0.238439	+	0.412988i
$474$		0			0
$475$	22.9739	−	39.7920i	1.05412	−	1.82578i
$476$	1.87031	−	0.290398i	0.0857255	−	0.0133104i
$477$		0			0
$478$	14.3815	−	24.9095i	0.657794	−	1.13933i
$479$	12.4585			0.569243			0.284622	−	0.958640i	$-0.408132\pi$
$479$	12.4585			0.569243			0.284622	+	0.958640i	$0.408132\pi$
$480$		0			0
$481$	12.8878	+	22.5181i	0.587634	+	1.02674i
$482$	−25.6204			−1.16698
$483$		0			0
$484$	−2.67994	−	4.64180i	−0.121816	−	0.210991i
$485$	25.5279			1.15916
$486$		0			0
$487$	−4.17049	−	7.22350i	−0.188983	−	0.327328i	0.755929	−	0.654654i	$-0.227186\pi$
$487$	−4.17049	−	7.22350i	−0.188983	−	0.327328i	−0.944911	+	0.327326i	$0.893852\pi$
$488$	9.43076			0.426911
$489$		0			0
$490$	6.16114	−	28.1428i	0.278332	−	1.27136i
$491$	−8.82502	−	15.2854i	−0.398268	−	0.689820i	0.595245	−	0.803545i	$-0.297055\pi$
$491$	−8.82502	−	15.2854i	−0.398268	−	0.689820i	−0.993512	+	0.113725i	$0.963722\pi$
$492$		0			0
$493$	3.22248	−	5.58150i	0.145133	−	0.251378i
$494$	6.89313	+	12.0439i	0.310137	+	0.541882i
$495$		0			0
$496$	1.82642	+	3.16346i	0.0820088	+	0.142043i
$497$	−26.6804	+	4.14260i	−1.19678	+	0.185821i
$498$		0			0
$499$	−18.9853	−	32.8834i	−0.849897	−	1.47207i	−0.881299	−	0.472558i	$-0.843331\pi$
$499$	−18.9853	−	32.8834i	−0.849897	−	1.47207i	0.0314021	−	0.999507i	$-0.490003\pi$
$500$	−14.2776	−	24.7295i	−0.638514	−	1.10594i
$501$		0			0
$502$	0.339652	+	0.588295i	0.0151594	+	0.0262569i
$503$	10.4517	−	18.1029i	0.466019	−	0.807169i	−0.533228	−	0.845972i	$-0.679021\pi$
$503$	10.4517	−	18.1029i	0.466019	−	0.807169i	0.999247	+	0.0388027i	$0.0123544\pi$
$504$		0			0
$505$	33.5556	+	58.1200i	1.49320	+	2.58631i
$506$	−8.28729	−	14.3540i	−0.368415	−	0.638113i
$507$		0			0
$508$	−1.26603	+	2.19283i	−0.0561711	+	0.0972911i
$509$	−7.51054	+	13.0086i	−0.332899	+	0.576598i	−0.983079	−	0.183183i	$-0.941360\pi$
$509$	−7.51054	+	13.0086i	−0.332899	+	0.576598i	0.650180	+	0.759780i	$0.274693\pi$
$510$		0			0
$511$	−6.57127	+	1.02030i	−0.290696	+	0.0451356i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	1.22293	+	2.11818i	0.0539413	+	0.0934291i
$515$	6.00975	−	10.4092i	0.264821	−	0.458684i
$516$		0			0
$517$	5.20962	+	9.02333i	0.229119	+	0.396846i
$518$	−6.87689	+	17.7533i	−0.302153	+	0.780035i
$519$		0			0
$520$	14.8389	+	0.0559702i	0.650731	+	0.00245446i
$521$	−10.4549	+	18.1084i	−0.458037	+	0.793344i	−0.998857	−	0.0477946i	$-0.984781\pi$
$521$	−10.4549	+	18.1084i	−0.458037	+	0.793344i	0.540820	+	0.841138i	$0.318114\pi$
$522$		0			0
$523$	6.18390	−	10.7108i	0.270403	−	0.468352i	−0.698562	−	0.715550i	$-0.746176\pi$
$523$	6.18390	−	10.7108i	0.270403	−	0.468352i	0.968965	+	0.247198i	$0.0795097\pi$
$524$	−6.21657	+	10.7674i	−0.271572	+	0.470377i
$525$		0			0
$526$	−12.6596	+	21.9271i	−0.551985	+	0.956067i
$527$	2.61318			0.113832
$528$		0			0
$529$	3.10396	+	5.37622i	0.134955	+	0.233749i
$530$	−5.59261	+	9.68669i	−0.242928	+	0.420763i
$531$		0			0
$532$	−3.67815	+	9.49545i	−0.159468	+	0.411680i
$533$	20.7983	+	0.0784481i	0.900876	+	0.00339796i
$534$		0			0
$535$	16.6220			0.718632
$536$	1.16632			0.0503772
$537$		0			0
$538$	−13.5665			−0.584895
$539$	6.05503	−	27.6581i	0.260809	−	1.19132i
$540$		0			0
$541$	2.37409	+	4.11204i	0.102070	+	0.176791i	0.912537	−	0.408993i	$-0.134120\pi$
$541$	2.37409	+	4.11204i	0.102070	+	0.176791i	−0.810467	+	0.585784i	$0.800787\pi$
$542$	−2.42970	−	4.20837i	−0.104365	−	0.180765i
$543$		0			0
$544$	−0.357690	+	0.619538i	−0.0153359	+	0.0265625i
$545$	−57.0682			−2.44453
$546$		0			0
$547$	2.85148			0.121921			0.0609603	−	0.998140i	$-0.480584\pi$
$547$	2.85148			0.121921			0.0609603	+	0.998140i	$0.480584\pi$
$548$	−5.19240	+	8.99351i	−0.221808	+	0.384184i
$549$		0			0
$550$	−24.1436	−	41.8179i	−1.02948	−	1.78312i
$551$	17.3371	+	30.0288i	0.738587	+	1.27927i
$552$		0			0
$553$	12.8148	−	33.0826i	0.544942	−	1.40682i
$554$	−12.0625			−0.512488
$555$		0			0
$556$	1.27279			0.0539783
$557$	−14.0997			−0.597424			−0.298712	−	0.954343i	$-0.596557\pi$
$557$	−14.0997			−0.597424			−0.298712	+	0.954343i	$0.596557\pi$
$558$		0			0
$559$	−4.59239	−	8.02400i	−0.194238	−	0.339379i
$560$	6.82682	+	8.48306i	0.288486	+	0.358475i
$561$		0			0
$562$	−9.19816	+	15.9317i	−0.388001	+	0.672037i
$563$	−0.457406	−	0.792251i	−0.0192774	−	0.0333894i	0.856226	−	0.516602i	$-0.172803\pi$
$563$	−0.457406	−	0.792251i	−0.0192774	−	0.0333894i	−0.875503	+	0.483212i	$0.839470\pi$
$564$		0			0
$565$	−60.1622			−2.53104
$566$	−0.347153	+	0.601286i	−0.0145919	+	0.0252740i
$567$		0			0
$568$	5.10254	−	8.83786i	0.214098	−	0.370828i
$569$	−11.0384	+	19.1191i	−0.462755	+	0.801515i	−0.999097	−	0.0424858i	$-0.986472\pi$
$569$	−11.0384	+	19.1191i	−0.462755	+	0.801515i	0.536342	+	0.844001i	$0.319806\pi$
$570$		0			0
$571$	−1.38518	+	2.39921i	−0.0579682	+	0.100404i	−0.893553	−	0.448957i	$-0.851796\pi$
$571$	−1.38518	+	2.39921i	−0.0579682	+	0.100404i	0.835585	+	0.549361i	$0.185129\pi$
$572$	14.5834	+	0.0550063i	0.609762	+	0.00229993i
$573$		0			0
$574$	9.56850	+	11.8899i	0.399382	+	0.496275i
$575$	−24.4604	−	42.3666i	−1.02007	−	1.76681i
$576$		0			0
$577$	−13.6418	+	23.6282i	−0.567914	+	0.983656i	0.428858	+	0.903372i	$0.358916\pi$
$577$	−13.6418	+	23.6282i	−0.567914	+	0.983656i	−0.996772	+	0.0802839i	$0.974417\pi$
$578$	−8.24412	−	14.2792i	−0.342910	−	0.593938i
$579$		0			0
$580$	37.0781			1.53959
$581$	25.7149	+	31.9535i	1.06683	+	1.32565i
$582$		0			0
$583$	−5.49630	+	9.51987i	−0.227634	+	0.394273i
$584$	1.25673	−	2.17673i	0.0520040	−	0.0900736i
$585$		0			0
$586$	5.44518	+	9.43133i	0.224938	+	0.389604i
$587$	15.1737	+	26.2816i	0.626286	+	1.08476i	0.988291	+	0.152583i	$0.0487591\pi$
$587$	15.1737	+	26.2816i	0.626286	+	1.08476i	−0.362005	+	0.932176i	$0.617908\pi$
$588$		0			0
$589$	−7.02952	+	12.1755i	−0.289646	+	0.501682i
$590$	−26.5512	−	45.9880i	−1.09309	−	1.89330i
$591$		0			0
$592$	−3.59797	−	6.23187i	−0.147876	−	0.256128i
$593$	21.2192	+	36.7527i	0.871367	+	1.50925i	0.860583	+	0.509311i	$0.170100\pi$
$593$	21.2192	+	36.7527i	0.871367	+	1.50925i	0.0107847	+	0.999942i	$0.496567\pi$
$594$		0			0
$595$	7.69747	−	1.19517i	0.315565	−	0.0489970i
$596$	11.6810	+	20.2320i	0.478471	+	0.828736i
$597$		0			0
$598$	14.7748	+	0.0557282i	0.604185	+	0.00227889i
$599$	−15.1759	+	26.2854i	−0.620071	+	1.07399i	0.369401	+	0.929270i	$0.379563\pi$
$599$	−15.1759	+	26.2854i	−0.620071	+	1.07399i	−0.989472	+	0.144724i	$0.953771\pi$
$600$		0			0
$601$	−2.44125	−	4.22836i	−0.0995805	−	0.172479i	0.811931	−	0.583754i	$-0.198417\pi$
$601$	−2.44125	−	4.22836i	−0.0995805	−	0.172479i	−0.911511	+	0.411275i	$0.865083\pi$
$602$	2.45048	−	6.32614i	0.0998743	−	0.257834i
$603$		0			0
$604$	−2.39664			−0.0975178
$605$	−11.0296	−	19.1038i	−0.448417	−	0.776681i
$606$		0			0
$607$	−12.7969			−0.519409			−0.259704	−	0.965688i	$-0.583625\pi$
$607$	−12.7969			−0.519409			−0.259704	+	0.965688i	$0.583625\pi$
$608$	−1.92440	−	3.33315i	−0.0780445	−	0.135177i
$609$		0			0
$610$	38.8134			1.57151
$611$	−9.28784	−	0.0350323i	−0.375746	−	0.00141726i
$612$		0			0
$613$	4.04991			0.163574			0.0817871	−	0.996650i	$-0.473937\pi$
$613$	4.04991			0.163574			0.0817871	+	0.996650i	$0.473937\pi$
$614$	11.8862	−	20.5875i	0.479689	−	0.830845i
$615$		0			0
$616$	6.70925	+	8.33697i	0.270324	+	0.335906i
$617$	7.16474	−	12.4097i	0.288441	−	0.499595i	−0.684996	−	0.728546i	$-0.740196\pi$
$617$	7.16474	−	12.4097i	0.288441	−	0.499595i	0.973438	+	0.228951i	$0.0735296\pi$
$618$		0			0
$619$	−18.3950	+	31.8611i	−0.739358	+	1.28061i	0.213427	+	0.976959i	$0.431537\pi$
$619$	−18.3950	+	31.8611i	−0.739358	+	1.28061i	−0.952785	+	0.303646i	$0.901796\pi$
$620$	7.51685	+	13.0196i	0.301884	+	0.522878i
$621$		0			0
$622$	−10.9242	−	18.9212i	−0.438020	−	0.758673i
$623$	−28.5330	+	4.43025i	−1.14315	+	0.177494i
$624$		0			0
$625$	−28.9154	−	50.0829i	−1.15662	−	2.00332i
$626$	32.0646			1.28156
$627$		0			0
$628$	−11.5817			−0.462158
$629$	−5.14784			−0.205258
$630$		0			0
$631$	−18.8504	+	32.6498i	−0.750422	+	1.29977i	0.197197	+	0.980364i	$0.436816\pi$
$631$	−18.8504	+	32.6498i	−0.750422	+	1.29977i	−0.947618	+	0.319405i	$0.896517\pi$
$632$	6.70468	+	11.6129i	0.266698	+	0.461935i
$633$		0			0
$634$	−20.6137			−0.818673
$635$	−5.21049	+	9.02484i	−0.206772	+	0.358140i
$636$		0			0
$637$	18.5888	+	17.0721i	0.736514	+	0.676423i
$638$	36.4396			1.44266
$639$		0			0
$640$	−4.11561			−0.162684
$641$	−0.594040	−	1.02891i	−0.0234632	−	0.0406394i	0.854055	−	0.520182i	$-0.174136\pi$
$641$	−0.594040	−	1.02891i	−0.0234632	−	0.0406394i	−0.877519	+	0.479543i	$0.840803\pi$
$642$		0			0
$643$	−14.9781	+	25.9429i	−0.590679	+	1.02309i	0.403462	+	0.914996i	$0.367807\pi$
$643$	−14.9781	+	25.9429i	−0.590679	+	1.02309i	−0.994141	+	0.108090i	$0.965527\pi$
$644$	6.79730	+	8.44638i	0.267851	+	0.332834i
$645$		0			0
$646$	−2.75335			−0.108329
$647$	30.4218			1.19600			0.598002	−	0.801495i	$-0.295962\pi$
$647$	30.4218			1.19600			0.598002	+	0.801495i	$0.295962\pi$
$648$		0			0
$649$	−26.0939	−	45.1960i	−1.02428	−	1.77410i
$650$	43.0437	+	0.162354i	1.68831	+	0.00636806i
$651$		0			0
$652$	−8.95432	−	15.5093i	−0.350678	−	0.607392i
$653$	−6.14648	+	10.6460i	−0.240530	+	0.416611i	−0.960865	−	0.277015i	$-0.910655\pi$
$653$	−6.14648	+	10.6460i	−0.240530	+	0.416611i	0.720335	+	0.693626i	$0.243988\pi$
$654$		0			0
$655$	−25.5850	+	44.3145i	−0.999688	+	1.73151i
$656$	−5.76846			−0.225220
$657$		0			0
$658$	−4.27298	−	5.30963i	−0.166578	−	0.206991i
$659$	−17.0038	+	29.4514i	−0.662374	+	1.14727i	0.317616	+	0.948219i	$0.397118\pi$
$659$	−17.0038	+	29.4514i	−0.662374	+	1.14727i	−0.979990	+	0.199046i	$0.936216\pi$
$660$		0			0
$661$	13.8167			0.537407			0.268703	−	0.963223i	$-0.413405\pi$
$661$	13.8167			0.537407			0.268703	+	0.963223i	$0.413405\pi$
$662$	5.99781	−	10.3885i	0.233111	−	0.403761i
$663$		0			0
$664$	−15.5024			−0.601611
$665$	−15.1378	+	39.0796i	−0.587020	+	1.51544i
$666$		0			0
$667$	36.9178			1.42946
$668$	−3.15398	+	5.46286i	−0.122031	+	0.211364i
$669$		0			0
$670$	4.80010			0.185444
$671$	38.1449			1.47257
$672$		0			0
$673$	19.8004	+	34.2952i	0.763248	+	1.32198i	0.941168	+	0.337939i	$0.109730\pi$
$673$	19.8004	+	34.2952i	0.763248	+	1.32198i	−0.177920	+	0.984045i	$0.556937\pi$
$674$	−8.80728	+	15.2547i	−0.339244	+	0.587587i
$675$		0			0
$676$	−6.58474	+	11.2090i	−0.253259	+	0.431114i
$677$	−16.8735	−	29.2258i	−0.648503	−	1.12324i	−0.983481	−	0.181013i	$-0.942062\pi$
$677$	−16.8735	−	29.2258i	−0.648503	−	1.12324i	0.334978	−	0.942226i	$-0.391271\pi$
$678$		0			0
$679$	−16.2165	+	2.51789i	−0.622333	+	0.0966279i
$680$	−1.47212	+	2.54978i	−0.0564530	+	0.0977795i
$681$		0			0
$682$	7.38740	+	12.7954i	0.282878	+	0.489959i
$683$	8.39495	+	14.5405i	0.321224	+	0.556376i	0.980741	−	0.195313i	$-0.0625724\pi$
$683$	8.39495	+	14.5405i	0.321224	+	0.556376i	−0.659517	+	0.751690i	$0.729239\pi$
$684$		0			0
$685$	−21.3699	+	37.0138i	−0.816503	+	1.41422i
$686$	−1.13803	+	18.4853i	−0.0434503	+	0.705771i
$687$		0			0
$688$	1.28209	+	2.22064i	0.0488791	+	0.0846610i
$689$	−4.86746	−	8.50461i	−0.185435	−	0.324000i
$690$		0			0
$691$	1.67963	−	2.90920i	0.0638960	−	0.110671i	−0.832308	−	0.554314i	$-0.812981\pi$
$691$	1.67963	−	2.90920i	0.0638960	−	0.110671i	0.896204	+	0.443643i	$0.146314\pi$
$692$	−1.82563	−	3.16209i	−0.0694002	−	0.120205i
$693$		0			0
$694$	−15.8504			−0.601672
$695$	5.23831			0.198700
$696$		0			0
$697$	−2.06332	+	3.57378i	−0.0781539	+	0.135367i
$698$	10.3041			0.390017
$699$		0			0
$700$	19.8027	+	24.6070i	0.748473	+	0.930059i
$701$	51.6652			1.95137			0.975683	−	0.219186i	$-0.0703403\pi$
$701$	51.6652			1.95137			0.975683	+	0.219186i	$0.0703403\pi$
$702$		0			0
$703$	13.8478	−	23.9852i	0.522281	−	0.904618i
$704$	−4.04474			−0.152442
$705$		0			0
$706$	8.00975	−	13.8733i	0.301451	−	0.522128i
$707$	−27.0486	−	33.6108i	−1.01727	−	1.26406i
$708$		0			0
$709$	−19.3061			−0.725055			−0.362527	−	0.931973i	$-0.618086\pi$
$709$	−19.3061			−0.725055			−0.362527	+	0.931973i	$0.618086\pi$
$710$	21.0001	−	36.3732i	0.788119	−	1.36506i
$711$		0			0
$712$	5.45685	−	9.45154i	0.204504	−	0.354211i
$713$	7.48434	+	12.9633i	0.280291	+	0.485478i
$714$		0			0
$715$	60.0196	+	0.226385i	2.24461	+	0.00846631i
$716$	6.25956	+	10.8419i	0.233931	+	0.405180i
$717$		0			0
$718$	−9.11246			−0.340074
$719$	8.55314			0.318978			0.159489	−	0.987200i	$-0.449015\pi$
$719$	8.55314			0.318978			0.159489	+	0.987200i	$0.449015\pi$
$720$		0			0
$721$	−2.79098	+	7.20515i	−0.103941	+	0.268334i
$722$	−2.09340	+	3.62588i	−0.0779084	+	0.134941i
$723$		0			0
$724$	9.08638	+	15.7381i	0.337693	+	0.584901i
$725$	107.553			3.99444
$726$		0			0
$727$	37.0524			1.37420			0.687100	−	0.726563i	$-0.258884\pi$
$727$	37.0524			1.37420			0.687100	+	0.726563i	$0.258884\pi$
$728$	−9.43190	+	1.42805i	−0.349569	+	0.0529272i
$729$		0			0
$730$	5.17223	−	8.95857i	0.191433	−	0.331571i
$731$	1.83436			0.0678463
$732$		0			0
$733$	7.89197	+	13.6693i	0.291497	+	0.504887i	0.974164	−	0.225843i	$-0.0725135\pi$
$733$	7.89197	+	13.6693i	0.291497	+	0.504887i	−0.682667	+	0.730729i	$0.739180\pi$
$734$	5.11189	−	8.85406i	0.188683	−	0.326809i
$735$		0			0
$736$	−4.09781			−0.151047
$737$	4.71744			0.173769
$738$		0			0
$739$	−36.3450			−1.33697			−0.668487	−	0.743724i	$-0.733058\pi$
$739$	−36.3450			−1.33697			−0.668487	+	0.743724i	$0.733058\pi$
$740$	−14.8079	−	25.6480i	−0.544348	−	0.942838i
$741$		0			0
$742$	2.59726	−	6.70504i	0.0953483	−	0.246150i
$743$	15.1149	+	26.1797i	0.554511	+	0.960441i	0.997941	+	0.0641324i	$0.0204280\pi$
$743$	15.1149	+	26.1797i	0.554511	+	0.960441i	−0.443430	+	0.896309i	$0.646239\pi$
$744$		0			0
$745$	48.0743	+	83.2672i	1.76131	+	3.05067i
$746$	−14.0796	+	24.3866i	−0.515492	+	0.892858i
$747$		0			0
$748$	−1.44676	+	2.50587i	−0.0528989	+	0.0916236i
$749$	−10.5591	+	1.63948i	−0.385819	+	0.0599052i
$750$		0			0
$751$	−15.3619	+	26.6076i	−0.560563	+	0.970924i	0.436884	+	0.899518i	$0.356082\pi$
$751$	−15.3619	+	26.6076i	−0.560563	+	0.970924i	−0.997447	+	0.0714063i	$0.977251\pi$
$752$	2.57600			0.0939371
$753$		0			0
$754$	−16.3474	+	28.0696i	−0.595339	+	1.02223i
$755$	−9.86363			−0.358974
$756$		0			0
$757$	−7.78491	−	13.4839i	−0.282947	−	0.490079i	0.689162	−	0.724607i	$-0.257979\pi$
$757$	−7.78491	−	13.4839i	−0.282947	−	0.490079i	−0.972109	+	0.234528i	$0.924646\pi$
$758$	−6.16224			−0.223823
$759$		0			0
$760$	−7.92007	−	13.7180i	−0.287291	−	0.497603i
$761$	−23.8556			−0.864765			−0.432382	−	0.901690i	$-0.642327\pi$
$761$	−23.8556			−0.864765			−0.432382	+	0.901690i	$0.642327\pi$
$762$		0			0
$763$	36.2523	−	5.62880i	1.31242	−	0.203776i
$764$	2.23004	+	3.86254i	0.0806799	+	0.139742i
$765$		0			0
$766$	9.48159	−	16.4226i	0.342584	−	0.593373i
$767$	46.5209	+	0.175470i	1.67977	+	0.00633584i
$768$		0			0
$769$	−23.2870	−	40.3342i	−0.839750	−	1.45449i	−0.890104	−	0.455758i	$-0.849368\pi$
$769$	−23.2870	−	40.3342i	−0.839750	−	1.45449i	0.0503539	−	0.998731i	$-0.483965\pi$
$770$	27.6127	+	34.3117i	0.995092	+	1.23651i
$771$		0			0
$772$	4.34243	+	7.52130i	0.156287	+	0.270698i
$773$	3.75330	+	6.50090i	0.134997	+	0.233821i	0.925596	−	0.378512i	$-0.123564\pi$
$773$	3.75330	+	6.50090i	0.134997	+	0.233821i	−0.790599	+	0.612334i	$0.790231\pi$
$774$		0			0
$775$	21.8043	+	37.7662i	0.783234	+	1.35660i
$776$	3.10135	−	5.37170i	0.111332	−	0.192833i
$777$		0			0
$778$	1.08192	+	1.87394i	0.0387886	+	0.0671839i
$779$	−11.1008	−	19.2271i	−0.397727	−	0.688884i
$780$		0			0
$781$	20.6384	−	35.7468i	0.738501	−	1.27912i
$782$	−1.46575	+	2.53875i	−0.0524151	+	0.0907856i
$783$		0			0
$784$	−5.17342	−	4.71548i	−0.184765	−	0.168410i
$785$	−47.6656			−1.70126
$786$		0			0
$787$	−21.2447	−	36.7970i	−0.757293	−	1.31167i	−0.944226	−	0.329298i	$-0.893188\pi$
$787$	−21.2447	−	36.7970i	−0.757293	−	1.31167i	0.186933	−	0.982373i	$-0.440145\pi$
$788$	1.23397	−	2.13730i	0.0439583	−	0.0761380i
$789$		0			0
$790$	27.5939	+	47.7940i	0.981746	+	1.70043i
$791$	38.2178	−	5.93397i	1.35887	−	0.210988i
$792$		0			0
$793$	−17.1125	+	29.3832i	−0.607683	+	1.04343i
$794$	10.3858	−	17.9888i	0.368579	−	0.638397i
$795$		0			0
$796$	−10.2841	+	17.8125i	−0.364509	+	0.631348i
$797$	9.27713	−	16.0685i	0.328613	−	0.569174i	−0.653624	−	0.756819i	$-0.726752\pi$
$797$	9.27713	−	16.0685i	0.328613	−	0.569174i	0.982237	+	0.187645i	$0.0600856\pi$
$798$		0			0
$799$	0.921412	−	1.59593i	0.0325972	−	0.0564600i
$800$	−11.9383			−0.422081
$801$		0			0
$802$	−1.15403	−	1.99885i	−0.0407504	−	0.0705817i
$803$	5.08316	−	8.80429i	0.179381	−	0.310697i
$804$		0			0
$805$	27.9750	+	34.7620i	0.985991	+	1.22520i
$806$	−13.1704	−	0.0496768i	−0.463909	−	0.00174979i
$807$		0			0
$808$	16.3065			0.573660
$809$	−37.3361			−1.31267			−0.656334	−	0.754470i	$-0.727894\pi$
$809$	−37.3361			−1.31267			−0.656334	+	0.754470i	$0.727894\pi$
$810$		0			0
$811$	19.9446			0.700350			0.350175	−	0.936684i	$-0.386122\pi$
$811$	19.9446			0.700350			0.350175	+	0.936684i	$0.386122\pi$
$812$	−23.5537	+	3.65712i	−0.826573	+	0.128340i
$813$		0			0
$814$	−14.5528	−	25.2063i	−0.510077	−	0.883479i
$815$	−36.8525	−	63.8304i	−1.29089	−	2.23588i
$816$		0			0
$817$	−4.93448	+	8.54677i	−0.172636	+	0.299014i
$818$	−16.0313			−0.560522
$819$		0			0
$820$	−23.7407			−0.829063
$821$	12.0631	−	20.8939i	0.421005	−	0.729203i	−0.575033	−	0.818130i	$-0.695011\pi$
$821$	12.0631	−	20.8939i	0.421005	−	0.729203i	0.996038	+	0.0889276i	$0.0283440\pi$
$822$		0			0
$823$	−1.63853	−	2.83802i	−0.0571155	−	0.0989270i	0.836054	−	0.548647i	$-0.184857\pi$
$823$	−1.63853	−	2.83802i	−0.0571155	−	0.0989270i	−0.893169	+	0.449720i	$0.851524\pi$
$824$	−1.46023	−	2.52920i	−0.0508696	−	0.0881087i
$825$		0			0
$826$	21.4025	+	26.5949i	0.744687	+	0.925353i
$827$	−49.4538			−1.71968			−0.859838	−	0.510566i	$-0.829436\pi$
$827$	−49.4538			−1.71968			−0.859838	+	0.510566i	$0.829436\pi$
$828$		0			0
$829$	36.5908			1.27085			0.635426	−	0.772161i	$-0.280824\pi$
$829$	36.5908			1.27085			0.635426	+	0.772161i	$0.280824\pi$
$830$	−63.8020			−2.21460
$831$		0			0
$832$	1.81454	−	3.11568i	0.0629079	−	0.108017i
$833$	−4.77190	+	1.51845i	−0.165337	+	0.0526111i
$834$		0			0
$835$	−12.9806	+	22.4830i	−0.449211	+	0.778056i
$836$	−7.78367	−	13.4817i	−0.269204	−	0.466275i
$837$		0			0
$838$	−2.97037			−0.102610
$839$	21.2148	−	36.7451i	0.732416	−	1.26858i	−0.223431	−	0.974720i	$-0.571726\pi$
$839$	21.2148	−	36.7451i	0.732416	−	1.26858i	0.955848	−	0.293862i	$-0.0949408\pi$
$840$		0			0
$841$	−26.0823	+	45.1759i	−0.899389	+	1.55779i
$842$	17.1513	−	29.7069i	0.591072	−	1.02377i
$843$		0			0
$844$	2.22726	−	3.85773i	0.0766656	−	0.132789i
$845$	−27.1002	+	46.1318i	−0.932277	+	1.58698i
$846$		0			0
$847$	8.89078	+	11.0477i	0.305491	+	0.379605i
$848$	1.35888	+	2.35365i	0.0466641	+	0.0808245i
$849$		0			0
$850$	−4.27020	+	7.39621i	−0.146467	+	0.253688i
$851$	−14.7438	−	25.5370i	−0.505412	−	0.875399i
$852$		0			0
$853$	31.5639			1.08073			0.540363	−	0.841432i	$-0.318287\pi$
$853$	31.5639			1.08073			0.540363	+	0.841432i	$0.318287\pi$
$854$	−24.6560	+	3.82827i	−0.843712	+	0.131001i
$855$		0			0
$856$	2.01938	−	3.49768i	0.0690211	−	0.119548i
$857$	13.0273	−	22.5639i	0.445004	−	0.770769i	−0.553049	−	0.833149i	$-0.686536\pi$
$857$	13.0273	−	22.5639i	0.445004	−	0.770769i	0.998052	+	0.0623801i	$0.0198691\pi$
$858$		0			0
$859$	19.9113	+	34.4875i	0.679366	+	1.17670i	0.975172	+	0.221449i	$0.0710786\pi$
$859$	19.9113	+	34.4875i	0.679366	+	1.17670i	−0.295806	+	0.955248i	$0.595588\pi$
$860$	5.27657	+	9.13929i	0.179930	+	0.311647i
$861$		0			0
$862$	11.7248	−	20.3079i	0.399347	−	0.691689i
$863$	−10.4795	−	18.1510i	−0.356725	−	0.617866i	0.630687	−	0.776038i	$-0.282773\pi$
$863$	−10.4795	−	18.1510i	−0.356725	−	0.617866i	−0.987412	+	0.158172i	$0.949440\pi$
$864$		0			0
$865$	−7.51360	−	13.0139i	−0.255470	−	0.442487i
$866$	−0.402426	−	0.697022i	−0.0136750	−	0.0236858i
$867$		0			0
$868$	−6.05920	−	7.52922i	−0.205663	−	0.255558i
$869$	27.1187	+	46.9709i	0.919938	+	1.59338i
$870$		0			0
$871$	−2.11633	+	3.63386i	−0.0717090	+	0.123129i
$872$	−6.93314	+	12.0085i	−0.234786	+	0.406661i
$873$		0			0
$874$	−7.88581	−	13.6586i	−0.266742	−	0.462010i
$875$	47.3663	+	58.8577i	1.60127	+	1.98975i
$876$		0			0
$877$	−14.4891			−0.489263			−0.244632	−	0.969616i	$-0.578667\pi$
$877$	−14.4891			−0.489263			−0.244632	+	0.969616i	$0.578667\pi$
$878$	−0.798877	−	1.38370i	−0.0269608	−	0.0466974i
$879$		0			0
$880$	−16.6466			−0.561155
$881$	22.1191	+	38.3114i	0.745211	+	1.29074i	0.950096	+	0.311957i	$0.100984\pi$
$881$	22.1191	+	38.3114i	0.745211	+	1.29074i	−0.204886	+	0.978786i	$0.565682\pi$
$882$		0			0
$883$	−51.8997			−1.74656			−0.873282	−	0.487216i	$-0.838012\pi$
$883$	−51.8997			−1.74656			−0.873282	+	0.487216i	$0.838012\pi$
$884$	−1.28124	−	2.23862i	−0.0430927	−	0.0752931i
$885$		0			0
$886$	6.54669			0.219940
$887$	14.3951	−	24.9331i	0.483340	−	0.837170i	−0.516477	−	0.856301i	$-0.672757\pi$
$887$	14.3951	−	24.9331i	0.483340	−	0.837170i	0.999817	+	0.0191313i	$0.00609004\pi$
$888$		0			0
$889$	2.41980	−	6.24692i	0.0811574	−	0.209515i
$890$	22.4583	−	38.8989i	0.752803	−	1.30389i
$891$		0			0
$892$	−2.49662	+	4.32427i	−0.0835929	+	0.144787i
$893$	4.95725	+	8.58621i	0.165888	+	0.287326i
$894$		0			0
$895$	25.7619	+	44.6210i	0.861126	+	1.49151i
$896$	2.61442	−	0.405935i	0.0873418	−	0.0135613i
$897$		0			0
$898$	−6.34113	−	10.9832i	−0.211606	−	0.366513i
$899$	−32.9090			−1.09758
$900$		0			0
$901$	1.94423			0.0647717
$902$	−23.3319			−0.776867
$903$		0			0
$904$	−7.30902	+	12.6596i	−0.243095	+	0.421052i
$905$	37.3960	+	64.7718i	1.24309	+	2.15309i
$906$		0			0
$907$	−33.1216			−1.09978			−0.549892	−	0.835236i	$-0.685331\pi$
$907$	−33.1216			−1.09978			−0.549892	+	0.835236i	$0.685331\pi$
$908$	−0.786363	+	1.36202i	−0.0260964	+	0.0452002i
$909$		0			0
$910$	−38.8180	+	5.87731i	−1.28680	+	0.194831i
$911$	20.6630			0.684597			0.342298	−	0.939591i	$-0.388795\pi$
$911$	20.6630			0.684597			0.342298	+	0.939591i	$0.388795\pi$
$912$		0			0
$913$	−62.7032			−2.07517
$914$	−5.37753	−	9.31415i	−0.177873	−	0.308085i
$915$		0			0
$916$	0.828619	−	1.43521i	0.0273783	−	0.0474207i
$917$	11.8819	−	30.6741i	0.392374	−	1.01295i
$918$		0			0
$919$	51.6174			1.70270			0.851350	−	0.524598i	$-0.175784\pi$
$919$	51.6174			1.70270			0.851350	+	0.524598i	$0.175784\pi$
$920$	−16.8650			−0.556023
$921$		0			0
$922$	9.19640	+	15.9286i	0.302867	+	0.524581i
$923$	18.2772	+	31.9345i	0.601600	+	1.05114i
$924$		0			0
$925$	−42.9535	−	74.3977i	−1.41230	−	2.44618i
$926$	−17.3409	+	30.0354i	−0.569858	+	0.987023i
$927$		0			0
$928$	4.50457	−	7.80214i	0.147870	−	0.256118i
$929$	34.5180			1.13250			0.566250	−	0.824234i	$-0.308394\pi$
$929$	34.5180			1.13250			0.566250	+	0.824234i	$0.308394\pi$
$930$		0			0
$931$	5.76170	−	26.3182i	0.188832	−	0.862545i
$932$	3.86181	−	6.68885i	0.126498	−	0.219101i
$933$		0			0
$934$	−28.2471			−0.924274
$935$	−5.95432	+	10.3132i	−0.194727	+	0.337277i
$936$		0			0
$937$	14.3652			0.469291			0.234646	−	0.972081i	$-0.424607\pi$
$937$	14.3652			0.469291			0.234646	+	0.972081i	$0.424607\pi$
$938$	−3.04924	+	0.473448i	−0.0995614	+	0.0154586i
$939$		0			0
$940$	10.6018			0.345793
$941$	−4.16447	+	7.21307i	−0.135758	+	0.235139i	−0.925887	−	0.377801i	$-0.876680\pi$
$941$	−4.16447	+	7.21307i	−0.135758	+	0.235139i	0.790129	+	0.612941i	$0.210014\pi$
$942$		0			0
$943$	−23.6381			−0.769762
$944$	−12.9027			−0.419946
$945$		0			0
$946$	5.18570	+	8.98189i	0.168602	+	0.292027i
$947$	−0.160717	+	0.278371i	−0.00522262	+	0.00904583i	−0.868625	−	0.495470i	$-0.834996\pi$
$947$	−0.160717	+	0.278371i	−0.00522262	+	0.00904583i	0.863402	+	0.504516i	$0.168329\pi$
$948$		0			0
$949$	4.50159	+	7.86534i	0.146128	+	0.255320i
$950$	−22.9739	−	39.7920i	−0.745373	−	1.29102i
$951$		0			0
$952$	0.683663	−	1.76493i	0.0221576	−	0.0572019i
$953$	9.79426	−	16.9642i	0.317267	−	0.549523i	−0.662650	−	0.748930i	$-0.730568\pi$
$953$	9.79426	−	16.9642i	0.317267	−	0.549523i	0.979917	+	0.199407i	$0.0639014\pi$
$954$		0			0
$955$	9.17797	+	15.8967i	0.296992	+	0.514405i
$956$	−14.3815	−	24.9095i	−0.465130	−	0.805630i
$957$		0			0
$958$	6.22925	−	10.7894i	0.201258	−	0.348589i
$959$	9.92437	−	25.6206i	0.320475	−	0.827333i
$960$		0			0
$961$	8.82835	+	15.2912i	0.284786	+	0.493263i
$962$	25.9452	+	0.0978611i	0.836506	+	0.00315517i
$963$		0			0
$964$	−12.8102	+	22.1879i	−0.412589	+	0.714625i
$965$	17.8717	+	30.9548i	0.575312	+	0.996469i
$966$		0			0
$967$	−21.5461			−0.692875			−0.346437	−	0.938073i	$-0.612609\pi$
$967$	−21.5461			−0.692875			−0.346437	+	0.938073i	$0.612609\pi$
$968$	−5.35989			−0.172273
$969$		0			0
$970$	12.7640	−	22.1078i	0.409826	−	0.709840i
$971$	17.0756			0.547983			0.273991	−	0.961732i	$-0.411656\pi$
$971$	17.0756			0.547983			0.273991	+	0.961732i	$0.411656\pi$
$972$		0			0
$973$	−3.32761	+	0.516669i	−0.106678	+	0.0165637i
$974$	−8.34097			−0.267262
$975$		0			0
$976$	4.71538	−	8.16728i	0.150936	−	0.261428i
$977$	−8.72087			−0.279005			−0.139503	−	0.990222i	$-0.544550\pi$
$977$	−8.72087			−0.279005			−0.139503	+	0.990222i	$0.544550\pi$
$978$		0			0
$979$	22.0715	−	38.2290i	0.705409	−	1.22180i
$980$	−21.2918	−	19.4071i	−0.680141	−	0.619937i
$981$		0			0
$982$	−17.6500			−0.563236
$983$	−11.0826	+	19.1956i	−0.353480	+	0.612245i	−0.986857	−	0.161598i	$-0.948335\pi$
$983$	−11.0826	+	19.1956i	−0.353480	+	0.612245i	0.633377	+	0.773844i	$0.281668\pi$
$984$		0			0
$985$	5.07854	−	8.79628i	0.161816	−	0.280273i
$986$	−3.22248	−	5.58150i	−0.102625	−	0.177751i
$987$		0			0
$988$	13.8769	+	0.0523416i	0.441484	+	0.00166521i
$989$	5.25375	+	9.09976i	0.167060	+	0.289356i
$990$		0			0
$991$	17.9521			0.570267			0.285134	−	0.958488i	$-0.407962\pi$
$991$	17.9521			0.570267			0.285134	+	0.958488i	$0.407962\pi$
$992$	3.65285			0.115978
$993$		0			0
$994$	−9.75262	+	25.1772i	−0.309334	+	0.798573i
$995$	−42.3252	+	73.3095i	−1.34180	+	2.32407i
$996$		0			0
$997$	−29.4747	−	51.0516i	−0.933472	−	1.61682i	−0.777336	−	0.629086i	$-0.783429\pi$
$997$	−29.4747	−	51.0516i	−0.933472	−	1.61682i	−0.156137	−	0.987735i	$-0.549904\pi$
$998$	−37.9705			−1.20194
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.p.i.991.1		8
3.2	odd	2		546.2.k.b.445.4	yes	8
7.2	even	3		1638.2.m.g.289.1		8
13.9	even	3		1638.2.m.g.1621.1		8
21.2	odd	6		546.2.j.d.289.4	✓	8
39.35	odd	6		546.2.j.d.529.4	yes	8
91.9	even	3	inner	1638.2.p.i.919.1		8
273.191	odd	6		546.2.k.b.373.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.d.289.4	✓	8	21.2	odd	6
546.2.j.d.529.4	yes	8	39.35	odd	6
546.2.k.b.373.4	yes	8	273.191	odd	6
546.2.k.b.445.4	yes	8	3.2	odd	2
1638.2.m.g.289.1		8	7.2	even	3
1638.2.m.g.1621.1		8	13.9	even	3
1638.2.p.i.919.1		8	91.9	even	3	inner
1638.2.p.i.991.1		8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.p (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.05781 - 3.56422i) q^{5} +(1.65876 + 2.06119i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.05781 - 3.56422i) q^{5} +(1.65876 + 2.06119i) q^{7} -1.00000 q^{8} -4.11561 q^{10} -4.04474 q^{11} +(1.81454 - 3.11568i) q^{13} +(2.61442 - 0.405935i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.357690 + 0.619538i) q^{17} -3.84879 q^{19} +(-2.05781 + 3.56422i) q^{20} +(-2.02237 + 3.50284i) q^{22} +(-2.04891 + 3.54881i) q^{23} +(-5.96913 + 10.3388i) q^{25} +(-1.79099 - 3.12928i) q^{26} +(0.955663 - 2.46713i) q^{28} +(-4.50457 - 7.80214i) q^{29} +(1.82642 - 3.16346i) q^{31} +(0.500000 + 0.866025i) q^{32} +0.715381 q^{34} +(3.93314 - 10.1537i) q^{35} +(-3.59797 + 6.23187i) q^{37} +(-1.92440 + 3.33315i) q^{38} +(2.05781 + 3.56422i) q^{40} +(2.88423 + 4.99563i) q^{41} +(1.28209 - 2.22064i) q^{43} +(2.02237 + 3.50284i) q^{44} +(2.04891 + 3.54881i) q^{46} +(-1.28800 - 2.23088i) q^{47} +(-1.49702 + 6.83805i) q^{49} +(5.96913 + 10.3388i) q^{50} +(-3.60553 - 0.0135995i) q^{52} +(1.35888 - 2.35365i) q^{53} +(8.32328 + 14.4163i) q^{55} +(-1.65876 - 2.06119i) q^{56} -9.00914 q^{58} +(6.45133 + 11.1740i) q^{59} -9.43076 q^{61} +(-1.82642 - 3.16346i) q^{62} +1.00000 q^{64} +(-14.8389 - 0.0559702i) q^{65} -1.16632 q^{67} +(0.357690 - 0.619538i) q^{68} +(-6.82682 - 8.48306i) q^{70} +(-5.10254 + 8.83786i) q^{71} +(-1.25673 + 2.17673i) q^{73} +(3.59797 + 6.23187i) q^{74} +(1.92440 + 3.33315i) q^{76} +(-6.70925 - 8.33697i) q^{77} +(-6.70468 - 11.6129i) q^{79} +4.11561 q^{80} +5.76846 q^{82} +15.5024 q^{83} +(1.47212 - 2.54978i) q^{85} +(-1.28209 - 2.22064i) q^{86} +4.04474 q^{88} +(-5.45685 + 9.45154i) q^{89} +(9.43190 - 1.42805i) q^{91} +4.09781 q^{92} -2.57600 q^{94} +(7.92007 + 13.7180i) q^{95} +(-3.10135 + 5.37170i) q^{97} +(5.17342 + 4.71548i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8	\( 8 q + 4 q^{2} - 4 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8} - 4 q^{10} - 12 q^{11} - 11 q^{13} + 3 q^{14} - 4 q^{16} - 4 q^{17} - 12 q^{19} - 2 q^{20} - 6 q^{22} + 10 q^{23} - 18 q^{25} - 10 q^{26} - 2 q^{29} + 6 q^{31} + 4 q^{32} - 8 q^{34} - 18 q^{35} - 28 q^{37} - 6 q^{38} + 2 q^{40} - 6 q^{43} + 6 q^{44} - 10 q^{46} - q^{47} - 7 q^{49} + 18 q^{50} + q^{52} - 7 q^{53} + q^{55} - 3 q^{56} - 4 q^{58} - 2 q^{59} - 48 q^{61} - 6 q^{62} + 8 q^{64} - 19 q^{65} + 30 q^{67} - 4 q^{68} - 18 q^{70} - 6 q^{71} + q^{73} + 28 q^{74} + 6 q^{76} + 22 q^{77} - 12 q^{79} + 4 q^{80} + 32 q^{83} - 13 q^{85} + 6 q^{86} + 12 q^{88} - 25 q^{89} + 34 q^{91} - 20 q^{92} - 2 q^{94} + 8 q^{95} - q^{97} - 2 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8 - 4 * q^10 - 12 * q^11 - 11 * q^13 + 3 * q^14 - 4 * q^16 - 4 * q^17 - 12 * q^19 - 2 * q^20 - 6 * q^22 + 10 * q^23 - 18 * q^25 - 10 * q^26 - 2 * q^29 + 6 * q^31 + 4 * q^32 - 8 * q^34 - 18 * q^35 - 28 * q^37 - 6 * q^38 + 2 * q^40 - 6 * q^43 + 6 * q^44 - 10 * q^46 - q^47 - 7 * q^49 + 18 * q^50 + q^52 - 7 * q^53 + q^55 - 3 * q^56 - 4 * q^58 - 2 * q^59 - 48 * q^61 - 6 * q^62 + 8 * q^64 - 19 * q^65 + 30 * q^67 - 4 * q^68 - 18 * q^70 - 6 * q^71 + q^73 + 28 * q^74 + 6 * q^76 + 22 * q^77 - 12 * q^79 + 4 * q^80 + 32 * q^83 - 13 * q^85 + 6 * q^86 + 12 * q^88 - 25 * q^89 + 34 * q^91 - 20 * q^92 - 2 * q^94 + 8 * q^95 - q^97 - 2 * q^98

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