LMFDB - Embedded newform 1638.2.m.g.1621.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(289,1638)]

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, 2]))

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

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

chi := DirichletCharacter("1638.289");

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.m (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			1621.1
Root			$1.19003 - 0.764088i$ of defining polynomial
Character	$\chi$	$=$	1638.1621
Dual form			1638.2.m.g.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-2.05781 - 3.56422i) q^{5} +(-2.61442 + 0.405935i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-2.05781 - 3.56422i) q^{5} +(-2.61442 + 0.405935i) q^{7} -1.00000 q^{8} +(2.05781 + 3.56422i) q^{10} +(2.02237 + 3.50284i) q^{11} +(1.81454 + 3.11568i) q^{13} +(2.61442 - 0.405935i) q^{14} +1.00000 q^{16} -0.715381 q^{17} +(1.92440 - 3.33315i) q^{19} +(-2.05781 - 3.56422i) q^{20} +(-2.02237 - 3.50284i) q^{22} +4.09781 q^{23} +(-5.96913 + 10.3388i) q^{25} +(-1.81454 - 3.11568i) q^{26} +(-2.61442 + 0.405935i) q^{28} +(-4.50457 + 7.80214i) q^{29} +(1.82642 - 3.16346i) q^{31} -1.00000 q^{32} +0.715381 q^{34} +(6.82682 + 8.48306i) q^{35} +7.19594 q^{37} +(-1.92440 + 3.33315i) q^{38} +(2.05781 + 3.56422i) q^{40} +(2.88423 - 4.99563i) q^{41} +(1.28209 + 2.22064i) q^{43} +(2.02237 + 3.50284i) q^{44} -4.09781 q^{46} +(-1.28800 - 2.23088i) q^{47} +(6.67043 - 2.12257i) q^{49} +(5.96913 - 10.3388i) q^{50} +(1.81454 + 3.11568i) q^{52} +(1.35888 - 2.35365i) q^{53} +(8.32328 - 14.4163i) q^{55} +(2.61442 - 0.405935i) q^{56} +(4.50457 - 7.80214i) q^{58} -12.9027 q^{59} +(4.71538 - 8.16728i) q^{61} +(-1.82642 + 3.16346i) q^{62} +1.00000 q^{64} +(7.37100 - 12.8789i) q^{65} +(0.583158 + 1.01006i) q^{67} -0.715381 q^{68} +(-6.82682 - 8.48306i) q^{70} +(-5.10254 - 8.83786i) q^{71} +(-1.25673 + 2.17673i) q^{73} -7.19594 q^{74} +(1.92440 - 3.33315i) q^{76} +(-6.70925 - 8.33697i) q^{77} +(-6.70468 - 11.6129i) q^{79} +(-2.05781 - 3.56422i) q^{80} +(-2.88423 + 4.99563i) q^{82} +15.5024 q^{83} +(1.47212 + 2.54978i) q^{85} +(-1.28209 - 2.22064i) q^{86} +(-2.02237 - 3.50284i) q^{88} +10.9137 q^{89} +(-6.00874 - 7.40912i) q^{91} +4.09781 q^{92} +(1.28800 + 2.23088i) q^{94} -15.8401 q^{95} +(-3.10135 - 5.37170i) q^{97} +(-6.67043 + 2.12257i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8	$ 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8} + 2 q^{10} + 6 q^{11} - 11 q^{13} + 3 q^{14} + 8 q^{16} + 8 q^{17} + 6 q^{19} - 2 q^{20} - 6 q^{22} - 20 q^{23} - 18 q^{25} + 11 q^{26} - 3 q^{28} - 2 q^{29} + 6 q^{31} - 8 q^{32} - 8 q^{34} + 18 q^{35} + 56 q^{37} - 6 q^{38} + 2 q^{40} - 6 q^{43} + 6 q^{44} + 20 q^{46} - q^{47} + 5 q^{49} + 18 q^{50} - 11 q^{52} - 7 q^{53} + q^{55} + 3 q^{56} + 2 q^{58} + 4 q^{59} + 24 q^{61} - 6 q^{62} + 8 q^{64} - 22 q^{65} - 15 q^{67} + 8 q^{68} - 18 q^{70} - 6 q^{71} + q^{73} - 56 q^{74} + 6 q^{76} + 22 q^{77} - 12 q^{79} - 2 q^{80} + 32 q^{83} - 13 q^{85} + 6 q^{86} - 6 q^{88} + 50 q^{89} - 8 q^{91} - 20 q^{92} + q^{94} - 16 q^{95} - q^{97} - 5 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8 + 2 * q^10 + 6 * q^11 - 11 * q^13 + 3 * q^14 + 8 * q^16 + 8 * q^17 + 6 * q^19 - 2 * q^20 - 6 * q^22 - 20 * q^23 - 18 * q^25 + 11 * q^26 - 3 * q^28 - 2 * q^29 + 6 * q^31 - 8 * q^32 - 8 * q^34 + 18 * q^35 + 56 * q^37 - 6 * q^38 + 2 * q^40 - 6 * q^43 + 6 * q^44 + 20 * q^46 - q^47 + 5 * q^49 + 18 * q^50 - 11 * q^52 - 7 * q^53 + q^55 + 3 * q^56 + 2 * q^58 + 4 * q^59 + 24 * q^61 - 6 * q^62 + 8 * q^64 - 22 * q^65 - 15 * q^67 + 8 * q^68 - 18 * q^70 - 6 * q^71 + q^73 - 56 * q^74 + 6 * q^76 + 22 * q^77 - 12 * q^79 - 2 * q^80 + 32 * q^83 - 13 * q^85 + 6 * q^86 - 6 * q^88 + 50 * q^89 - 8 * q^91 - 20 * q^92 + q^94 - 16 * q^95 - q^97 - 5 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−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
$7$	−2.61442	+	0.405935i	−0.988160	+	0.153429i
$7$	−2.61442	+	0.405935i	−0.988160	+	0.153429i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	2.05781	+	3.56422i	0.650735	+	1.12711i
$11$	2.02237	+	3.50284i	0.609767	+	1.05615i	0.991279	+	0.131783i	$0.0420702\pi$
$11$	2.02237	+	3.50284i	0.609767	+	1.05615i	−0.381512	+	0.924364i	$0.624596\pi$
$12$		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
$16$	1.00000			0.250000
$17$	−0.715381			−0.173505			−0.0867527	−	0.996230i	$-0.527649\pi$
$17$	−0.715381			−0.173505			−0.0867527	+	0.996230i	$0.527649\pi$
$18$		0			0
$19$	1.92440	−	3.33315i	0.441487	−	0.764677i	−0.556313	−	0.830973i	$-0.687785\pi$
$19$	1.92440	−	3.33315i	0.441487	−	0.764677i	0.997800	+	0.0662953i	$0.0211179\pi$
$20$	−2.05781	−	3.56422i	−0.460139	−	0.796985i
$21$		0			0
$22$	−2.02237	−	3.50284i	−0.431170	−	0.746809i
$23$	4.09781			0.854453			0.427227	−	0.904145i	$-0.359491\pi$
$23$	4.09781			0.854453			0.427227	+	0.904145i	$0.359491\pi$
$24$		0			0
$25$	−5.96913	+	10.3388i	−1.19383	+	2.06777i
$26$	−1.81454	−	3.11568i	−0.355861	−	0.611035i
$27$		0			0
$28$	−2.61442	+	0.405935i	−0.494080	+	0.0767145i
$29$	−4.50457	+	7.80214i	−0.836478	+	1.44882i	0.0563442	+	0.998411i	$0.482056\pi$
$29$	−4.50457	+	7.80214i	−0.836478	+	1.44882i	−0.892822	+	0.450410i	$0.851278\pi$
$30$		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	$0.0602802\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	0.715381			0.122687
$35$	6.82682	+	8.48306i	1.15394	+	1.43390i
$36$		0			0
$37$	7.19594			1.18301			0.591503	−	0.806303i	$-0.298535\pi$
$37$	7.19594			1.18301			0.591503	+	0.806303i	$0.298535\pi$
$38$	−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	−0.547972	−	0.836496i	$-0.684600\pi$
$41$	2.88423	−	4.99563i	0.450441	−	0.780187i	0.998413	+	0.0563098i	$0.0179334\pi$
$42$		0			0
$43$	1.28209	+	2.22064i	0.195516	+	0.338644i	0.947070	−	0.321028i	$-0.104028\pi$
$43$	1.28209	+	2.22064i	0.195516	+	0.338644i	−0.751553	+	0.659672i	$0.770695\pi$
$44$	2.02237	+	3.50284i	0.304883	+	0.528074i
$45$		0			0
$46$	−4.09781			−0.604190
$47$	−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
$49$	6.67043	−	2.12257i	0.952919	−	0.303225i
$50$	5.96913	−	10.3388i	0.844163	−	1.46213i
$51$		0			0
$52$	1.81454	+	3.11568i	0.251631	+	0.432067i
$53$	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
$56$	2.61442	−	0.405935i	0.349367	−	0.0542453i
$57$		0			0
$58$	4.50457	−	7.80214i	0.591479	−	1.02447i
$59$	−12.9027			−1.67978			−0.839892	−	0.542754i	$-0.817382\pi$
$59$	−12.9027			−1.67978			−0.839892	+	0.542754i	$0.817382\pi$
$60$		0			0
$61$	4.71538	−	8.16728i	0.603743	−	1.04571i	−0.388506	−	0.921446i	$-0.627009\pi$
$61$	4.71538	−	8.16728i	0.603743	−	1.04571i	0.992249	−	0.124267i	$-0.0396579\pi$
$62$	−1.82642	+	3.16346i	−0.231956	+	0.401760i
$63$		0			0
$64$	1.00000			0.125000
$65$	7.37100	−	12.8789i	0.914260	−	1.59743i
$66$		0			0
$67$	0.583158	+	1.01006i	0.0712441	+	0.123398i	0.899447	−	0.437030i	$-0.143970\pi$
$67$	0.583158	+	1.01006i	0.0712441	+	0.123398i	−0.828203	+	0.560429i	$0.810636\pi$
$68$	−0.715381			−0.0867527
$69$		0			0
$70$	−6.82682	−	8.48306i	−0.815961	−	1.01392i
$71$	−5.10254	−	8.83786i	−0.605560	−	1.04886i	−0.991963	−	0.126531i	$-0.959616\pi$
$71$	−5.10254	−	8.83786i	−0.605560	−	1.04886i	0.386402	−	0.922330i	$-0.373718\pi$
$72$		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	$0.213657\pi$
$74$	−7.19594			−0.836512
$75$		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	$-0.438708\pi$
$80$	−2.05781	−	3.56422i	−0.230070	−	0.398492i
$81$		0			0
$82$	−2.88423	+	4.99563i	−0.318510	+	0.551675i
$83$	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
$88$	−2.02237	−	3.50284i	−0.215585	−	0.373404i
$89$	10.9137			1.15685			0.578425	−	0.815736i	$-0.303668\pi$
$89$	10.9137			1.15685			0.578425	+	0.815736i	$0.303668\pi$
$90$		0			0
$91$	−6.00874	−	7.40912i	−0.629887	−	0.776687i
$92$	4.09781			0.427227
$93$		0			0
$94$	1.28800	+	2.23088i	0.132847	+	0.230098i
$95$	−15.8401			−1.62516
$96$		0			0
$97$	−3.10135	−	5.37170i	−0.314895	−	0.545414i	0.664520	−	0.747270i	$-0.268636\pi$
$97$	−3.10135	−	5.37170i	−0.314895	−	0.545414i	−0.979415	+	0.201856i	$0.935303\pi$
$98$	−6.67043	+	2.12257i	−0.673816	+	0.214412i
$99$		0			0
$100$	−5.96913	+	10.3388i	−0.596913	+	1.03388i
$101$	8.15325	+	14.1218i	0.811278	+	1.40518i	0.911970	+	0.410257i	$0.134561\pi$
$101$	8.15325	+	14.1218i	0.811278	+	1.40518i	−0.100692	+	0.994918i	$0.532106\pi$
$102$		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
$107$	4.03877			0.390442			0.195221	−	0.980759i	$-0.437458\pi$
$107$	4.03877			0.390442			0.195221	+	0.980759i	$0.437458\pi$
$108$		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	$-0.0645074\pi$
$110$	−8.32328	+	14.4163i	−0.793594	+	1.37454i
$111$		0			0
$112$	−2.61442	+	0.405935i	−0.247040	+	0.0383572i
$113$	7.30902	+	12.6596i	0.687575	+	1.19091i	0.972620	+	0.232401i	$0.0746581\pi$
$113$	7.30902	+	12.6596i	0.687575	+	1.19091i	−0.285045	+	0.958514i	$0.592009\pi$
$114$		0			0
$115$	−8.43251	−	14.6055i	−0.786335	−	1.36197i
$116$	−4.50457	+	7.80214i	−0.418239	+	0.724411i
$117$		0			0
$118$	12.9027			1.18779
$119$	1.87031	−	0.290398i	0.171451	−	0.0266207i
$120$		0			0
$121$	−2.67994	+	4.64180i	−0.243631	+	0.421982i
$122$	−4.71538	+	8.16728i	−0.426911	+	0.739431i
$123$		0			0
$124$	1.82642	−	3.16346i	0.164018	−	0.284087i
$125$	28.5552			2.55405
$126$		0			0
$127$	−1.26603	+	2.19283i	−0.112342	+	0.194582i	−0.916714	−	0.399544i	$-0.869169\pi$
$127$	−1.26603	+	2.19283i	−0.112342	+	0.194582i	0.804372	+	0.594126i	$0.202502\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−7.37100	+	12.8789i	−0.646480	+	1.12955i
$131$	−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
$133$	−3.67815	+	9.49545i	−0.318936	+	0.823360i
$134$	−0.583158	−	1.01006i	−0.0503772	−	0.0872558i
$135$		0			0
$136$	0.715381			0.0613434
$137$	10.3848			0.887234			0.443617	−	0.896216i	$-0.353695\pi$
$137$	10.3848			0.887234			0.443617	+	0.896216i	$0.353695\pi$
$138$		0			0
$139$	−0.636394	−	1.10227i	−0.0539783	−	0.0934931i	0.837774	−	0.546018i	$-0.183857\pi$
$139$	−0.636394	−	1.10227i	−0.0539783	−	0.0934931i	−0.891752	+	0.452525i	$0.850524\pi$
$140$	6.82682	+	8.48306i	0.576972	+	0.716950i
$141$		0			0
$142$	5.10254	+	8.83786i	0.428196	+	0.741657i
$143$	−7.24406	+	12.6571i	−0.605779	+	1.05844i
$144$		0			0
$145$	37.0781			3.07917
$146$	1.25673	−	2.17673i	0.104008	−	0.180147i
$147$		0			0
$148$	7.19594			0.591503
$149$	11.6810	−	20.2320i	0.956942	−	1.65747i	0.227083	−	0.973875i	$-0.427081\pi$
$149$	11.6810	−	20.2320i	0.956942	−	1.65747i	0.729859	−	0.683598i	$-0.239586\pi$
$150$		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	$0.135576\pi$
$152$	−1.92440	+	3.33315i	−0.156089	+	0.270354i
$153$		0			0
$154$	6.70925	+	8.33697i	0.540647	+	0.671812i
$155$	−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	$0.0137419\pi$
$158$	6.70468	+	11.6129i	0.533396	+	0.923869i
$159$		0			0
$160$	2.05781	+	3.56422i	0.162684	+	0.281777i
$161$	−10.7134	+	1.66344i	−0.844336	+	0.131098i
$162$		0			0
$163$	−8.95432	+	15.5093i	−0.701356	+	1.21478i	0.266634	+	0.963798i	$0.414088\pi$
$163$	−8.95432	+	15.5093i	−0.701356	+	1.21478i	−0.967990	+	0.250987i	$0.919245\pi$
$164$	2.88423	−	4.99563i	0.225220	−	0.390093i
$165$		0			0
$166$	−15.5024			−1.20322
$167$	−3.15398	+	5.46286i	−0.244062	+	0.422728i	−0.961868	−	0.273516i	$-0.911814\pi$
$167$	−3.15398	+	5.46286i	−0.244062	+	0.422728i	0.717805	+	0.696244i	$0.245147\pi$
$168$		0			0
$169$	−6.41489	+	11.3070i	−0.493453	+	0.869773i
$170$	−1.47212	−	2.54978i	−0.112906	−	0.195559i
$171$		0			0
$172$	1.28209	+	2.22064i	0.0977582	+	0.169322i
$173$	−1.82563	+	3.16209i	−0.138800	+	0.240409i	−0.927043	−	0.374956i	$-0.877658\pi$
$173$	−1.82563	+	3.16209i	−0.138800	+	0.240409i	0.788242	+	0.615365i	$0.210991\pi$
$174$		0			0
$175$	11.4090	−	29.4532i	0.862436	−	2.22645i
$176$	2.02237	+	3.50284i	0.152442	+	0.264037i
$177$		0			0
$178$	−10.9137			−0.818016
$179$	6.25956	+	10.8419i	0.467861	+	0.810360i	0.999326	−	0.0367210i	$-0.0116913\pi$
$179$	6.25956	+	10.8419i	0.467861	+	0.810360i	−0.531464	+	0.847081i	$0.678358\pi$
$180$		0			0
$181$	−18.1728			−1.35077			−0.675385	−	0.737465i	$-0.736023\pi$
$181$	−18.1728			−1.35077			−0.675385	+	0.737465i	$0.736023\pi$
$182$	6.00874	+	7.40912i	0.445397	+	0.549200i
$183$		0			0
$184$	−4.09781			−0.302095
$185$	−14.8079	−	25.6480i	−1.08870	−	1.88568i
$186$		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
$191$	2.23004	−	3.86254i	0.161360	−	0.279483i	−0.773997	−	0.633190i	$-0.781745\pi$
$191$	2.23004	−	3.86254i	0.161360	−	0.279483i	0.935357	+	0.353706i	$0.115079\pi$
$192$		0			0
$193$	4.34243	+	7.52130i	0.312575	+	0.541395i	0.978919	−	0.204249i	$-0.0654752\pi$
$193$	4.34243	+	7.52130i	0.312575	+	0.541395i	−0.666344	+	0.745644i	$0.732142\pi$
$194$	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	−0.818714	−	0.574202i	$-0.805312\pi$
$197$	1.23397	−	2.13730i	0.0879166	−	0.152276i	0.906630	+	0.421926i	$0.138646\pi$
$198$		0			0
$199$	20.5681			1.45804			0.729018	−	0.684494i	$-0.239977\pi$
$199$	20.5681			1.45804			0.729018	+	0.684494i	$0.239977\pi$
$200$	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
$205$	−23.7407			−1.65813
$206$	−1.46023	−	2.52920i	−0.101739	−	0.176217i
$207$		0			0
$208$	1.81454	+	3.11568i	0.125816	+	0.216033i
$209$	15.5673			1.07682
$210$		0			0
$211$	2.22726	−	3.85773i	0.153331	−	0.265577i	−0.779119	−	0.626876i	$-0.784333\pi$
$211$	2.22726	−	3.85773i	0.153331	−	0.265577i	0.932450	+	0.361299i	$0.117667\pi$
$212$	1.35888	−	2.35365i	0.0933281	−	0.161649i
$213$		0			0
$214$	−4.03877			−0.276084
$215$	5.27657	−	9.13929i	0.359859	−	0.623294i
$216$		0			0
$217$	−3.49089	+	9.01203i	−0.236977	+	0.611777i
$218$	−6.93314	+	12.0085i	−0.469571	+	0.813321i
$219$		0			0
$220$	8.32328	−	14.4163i	0.561155	−	0.971950i
$221$	−1.29809	−	2.22890i	−0.0873188	−	0.149932i
$222$		0			0
$223$	−2.49662	+	4.32427i	−0.167186	+	0.289574i	−0.937429	−	0.348175i	$-0.886801\pi$
$223$	−2.49662	+	4.32427i	−0.167186	+	0.289574i	0.770243	+	0.637750i	$0.220135\pi$
$224$	2.61442	−	0.405935i	0.174684	−	0.0271227i
$225$		0			0
$226$	−7.30902	−	12.6596i	−0.486189	−	0.842104i
$227$	1.57273			0.104385			0.0521927	−	0.998637i	$-0.483379\pi$
$227$	1.57273			0.104385			0.0521927	+	0.998637i	$0.483379\pi$
$228$		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
$236$	−12.9027			−0.839892
$237$		0			0
$238$	−1.87031	+	0.290398i	−0.121234	+	0.0188237i
$239$	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
$241$	25.6204			1.65036			0.825178	−	0.564872i	$-0.191075\pi$
$241$	25.6204			1.65036			0.825178	+	0.564872i	$0.191075\pi$
$242$	2.67994	−	4.64180i	0.172273	−	0.298386i
$243$		0			0
$244$	4.71538	−	8.16728i	0.301871	−	0.522856i
$245$	−21.2918	−	19.4071i	−1.36028	−	1.23987i
$246$		0			0
$247$	13.8769	−	0.0523416i	0.882967	−	0.00333042i
$248$	−1.82642	+	3.16346i	−0.115978	+	0.200880i
$249$		0			0
$250$	−28.5552			−1.80599
$251$	−0.339652	−	0.588295i	−0.0214387	−	0.0371329i	0.855107	−	0.518452i	$-0.173491\pi$
$251$	−0.339652	−	0.588295i	−0.0214387	−	0.0371329i	−0.876546	+	0.481319i	$0.840158\pi$
$252$		0			0
$253$	8.28729	+	14.3540i	0.521017	+	0.902428i
$254$	1.26603	−	2.19283i	0.0794379	−	0.137590i
$255$		0			0
$256$	1.00000			0.0625000
$257$	2.44587			0.152569			0.0762846	−	0.997086i	$-0.475694\pi$
$257$	2.44587			0.152569			0.0762846	+	0.997086i	$0.475694\pi$
$258$		0			0
$259$	−18.8133	+	2.92108i	−1.16900	+	0.181507i
$260$	7.37100	−	12.8789i	0.457130	−	0.798715i
$261$		0			0
$262$	6.21657	+	10.7674i	0.384061	+	0.665213i
$263$	12.6596	+	21.9271i	0.780625	+	1.35208i	0.931578	+	0.363541i	$0.118432\pi$
$263$	12.6596	+	21.9271i	0.780625	+	1.35208i	−0.150953	+	0.988541i	$0.548234\pi$
$264$		0			0
$265$	−11.1852			−0.687103
$266$	3.67815	−	9.49545i	0.225522	−	0.582204i
$267$		0			0
$268$	0.583158	+	1.01006i	0.0356220	+	0.0616992i
$269$	13.5665			0.827167			0.413583	−	0.910466i	$-0.364277\pi$
$269$	13.5665			0.827167			0.413583	+	0.910466i	$0.364277\pi$
$270$		0			0
$271$	−4.85940			−0.295188			−0.147594	−	0.989048i	$-0.547153\pi$
$271$	−4.85940			−0.295188			−0.147594	+	0.989048i	$0.547153\pi$
$272$	−0.715381			−0.0433763
$273$		0			0
$274$	−10.3848			−0.627369
$275$	−48.2871			−2.91182
$276$		0			0
$277$	12.0625			0.724767			0.362384	−	0.932029i	$-0.381963\pi$
$277$	12.0625			0.724767			0.362384	+	0.932029i	$0.381963\pi$
$278$	0.636394	+	1.10227i	0.0381684	+	0.0661096i
$279$		0			0
$280$	−6.82682	−	8.48306i	−0.407981	−	0.506960i
$281$	−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
$283$	0.347153	+	0.601286i	0.0206361	+	0.0357428i	0.876159	−	0.482022i	$-0.160098\pi$
$283$	0.347153	+	0.601286i	0.0206361	+	0.0357428i	−0.855523	+	0.517765i	$0.826764\pi$
$284$	−5.10254	−	8.83786i	−0.302780	−	0.524431i
$285$		0			0
$286$	7.24406	−	12.6571i	0.428350	−	0.748430i
$287$	−5.51270	+	14.2315i	−0.325404	+	0.840060i
$288$		0			0
$289$	−16.4882			−0.969896
$290$	−37.0781			−2.17730
$291$		0			0
$292$	−1.25673	+	2.17673i	−0.0735448	+	0.127383i
$293$	−5.44518	−	9.43133i	−0.318111	−	0.550984i	0.661983	−	0.749519i	$-0.269715\pi$
$293$	−5.44518	−	9.43133i	−0.318111	−	0.550984i	−0.980094	+	0.198535i	$0.936382\pi$
$294$		0			0
$295$	26.5512	+	45.9880i	1.54587	+	2.67752i
$296$	−7.19594			−0.418256
$297$		0			0
$298$	−11.6810	+	20.2320i	−0.676661	+	1.17201i
$299$	7.43565	+	12.7675i	0.430015	+	0.738362i
$300$		0			0
$301$	−4.25335	−	5.28525i	−0.245159	−	0.304637i
$302$	−1.19832	+	2.07555i	−0.0689555	+	0.119434i
$303$		0			0
$304$	1.92440	−	3.33315i	0.110372	−	0.191169i
$305$	−38.8134			−2.22245
$306$		0			0
$307$	23.7724			1.35676			0.678382	−	0.734709i	$-0.262681\pi$
$307$	23.7724			1.35676			0.678382	+	0.734709i	$0.262681\pi$
$308$	−6.70925	−	8.33697i	−0.382295	−	0.475043i
$309$		0			0
$310$	15.0337			0.853857
$311$	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
$319$	−36.4396			−2.04023
$320$	−2.05781	−	3.56422i	−0.115035	−	0.199246i
$321$		0			0
$322$	10.7134	−	1.66344i	0.597036	−	0.0927002i
$323$	−1.37668	+	2.38447i	−0.0766003	+	0.132676i
$324$		0			0
$325$	−43.0437	+	0.162354i	−2.38764	+	0.00900579i
$326$	8.95432	−	15.5093i	0.495934	−	0.858982i
$327$		0			0
$328$	−2.88423	+	4.99563i	−0.159255	+	0.275838i
$329$	4.27298	+	5.30963i	0.235577	+	0.292730i
$330$		0			0
$331$	−5.99781	+	10.3885i	−0.329669	+	0.571004i	−0.982446	−	0.186546i	$-0.940271\pi$
$331$	−5.99781	+	10.3885i	−0.329669	+	0.571004i	0.652777	+	0.757550i	$0.273604\pi$
$332$	15.5024			0.850807
$333$		0			0
$334$	3.15398	−	5.46286i	0.172578	−	0.298914i
$335$	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	$0.659277\pi$
$338$	6.41489	−	11.3070i	0.348924	−	0.615022i
$339$		0			0
$340$	1.47212	+	2.54978i	0.0798367	+	0.138281i
$341$	14.7748			0.800100
$342$		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
$347$	15.8504			0.850893			0.425447	−	0.904984i	$-0.360117\pi$
$347$	15.8504			0.850893			0.425447	+	0.904984i	$0.360117\pi$
$348$		0			0
$349$	5.15206	−	8.92363i	0.275783	−	0.477671i	−0.694549	−	0.719445i	$-0.744396\pi$
$349$	5.15206	−	8.92363i	0.275783	−	0.477671i	0.970332	+	0.241775i	$0.0777294\pi$
$350$	−11.4090	+	29.4532i	−0.609834	+	1.57434i
$351$		0			0
$352$	−2.02237	−	3.50284i	−0.107793	−	0.186702i
$353$	−8.00975	−	13.8733i	−0.426316	−	0.738401i	0.570226	−	0.821488i	$-0.306855\pi$
$353$	−8.00975	−	13.8733i	−0.426316	−	0.738401i	−0.996542	+	0.0830868i	$0.973522\pi$
$354$		0			0
$355$	−21.0001	+	36.3732i	−1.11457	+	1.93049i
$356$	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
$361$	2.09340	+	3.62588i	0.110179	+	0.190836i
$362$	18.1728			0.955139
$363$		0			0
$364$	−6.00874	−	7.40912i	−0.314944	−	0.388343i
$365$	10.3445			0.541454
$366$		0			0
$367$	−5.11189	−	8.85406i	−0.266839	−	0.462178i	0.701205	−	0.712960i	$-0.252646\pi$
$367$	−5.11189	−	8.85406i	−0.266839	−	0.462178i	−0.968044	+	0.250782i	$0.919312\pi$
$368$	4.09781			0.213613
$369$		0			0
$370$	14.8079	+	25.6480i	0.769824	+	1.33337i
$371$	−2.59726	+	6.70504i	−0.134843	+	0.348109i
$372$		0			0
$373$	14.0796	−	24.3866i	0.729015	−	1.26269i	−0.228284	−	0.973594i	$-0.573312\pi$
$373$	14.0796	−	24.3866i	0.729015	−	1.26269i	0.957300	−	0.289097i	$-0.0933550\pi$
$374$	1.44676	+	2.50587i	0.0748104	+	0.129575i
$375$		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	−0.934244	−	0.356635i	$-0.883924\pi$
$379$	−3.08112	+	5.33666i	−0.158267	+	0.274126i	0.775977	+	0.630761i	$0.217257\pi$
$380$	−15.8401			−0.812582
$381$		0			0
$382$	−2.23004	+	3.86254i	−0.114099	+	0.197625i
$383$	−9.48159	+	16.4226i	−0.484487	+	0.839156i	−0.999841	−	0.0178215i	$-0.994327\pi$
$383$	−9.48159	+	16.4226i	−0.484487	+	0.839156i	0.515354	+	0.856977i	$0.327660\pi$
$384$		0			0
$385$	−15.9085	+	41.0692i	−0.810772	+	2.09308i
$386$	−4.34243	−	7.52130i	−0.221024	−	0.382824i
$387$		0			0
$388$	−3.10135	−	5.37170i	−0.157447	−	0.272707i
$389$	−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
$392$	−6.67043	+	2.12257i	−0.336908	+	0.107206i
$393$		0			0
$394$	−1.23397	+	2.13730i	−0.0621664	+	0.107675i
$395$	−27.5939	+	47.7940i	−1.38840	+	2.40478i
$396$		0			0
$397$	−10.3858	+	17.9888i	−0.521249	+	0.902830i	0.478445	+	0.878117i	$0.341200\pi$
$397$	−10.3858	+	17.9888i	−0.521249	+	0.902830i	−0.999695	+	0.0247127i	$0.992133\pi$
$398$	−20.5681			−1.03099
$399$		0			0
$400$	−5.96913	+	10.3388i	−0.298457	+	0.516942i
$401$	−2.30807			−0.115259			−0.0576297	−	0.998338i	$-0.518354\pi$
$401$	−2.30807			−0.115259			−0.0576297	+	0.998338i	$0.518354\pi$
$402$		0			0
$403$	13.1704	−	0.0496768i	0.656066	−	0.00247458i
$404$	8.15325	+	14.1218i	0.405639	+	0.702588i
$405$		0			0
$406$	−8.60970	+	22.2267i	−0.427292	+	1.10309i
$407$	14.5528	+	25.2063i	0.721358	+	1.24943i
$408$		0			0
$409$	16.0313			0.792698			0.396349	−	0.918100i	$-0.370277\pi$
$409$	16.0313			0.792698			0.396349	+	0.918100i	$0.370277\pi$
$410$	23.7407			1.17247
$411$		0			0
$412$	1.46023	+	2.52920i	0.0719405	+	0.124605i
$413$	33.7330	−	5.23764i	1.65989	−	0.257727i
$414$		0			0
$415$	−31.9010	−	55.2542i	−1.56596	−	2.71232i
$416$	−1.81454	−	3.11568i	−0.0889652	−	0.152759i
$417$		0			0
$418$	−15.5673			−0.761424
$419$	−1.48519	+	2.57242i	−0.0725561	+	0.125671i	−0.900021	−	0.435847i	$-0.856449\pi$
$419$	−1.48519	+	2.57242i	−0.0725561	+	0.125671i	0.827465	+	0.561518i	$0.189782\pi$
$420$		0			0
$421$	34.3026			1.67181			0.835903	−	0.548878i	$-0.184945\pi$
$421$	34.3026			1.67181			0.835903	+	0.548878i	$0.184945\pi$
$422$	−2.22726	+	3.85773i	−0.108422	+	0.187792i
$423$		0			0
$424$	−1.35888	+	2.35365i	−0.0659929	+	0.114303i
$425$	4.27020	−	7.39621i	0.207135	−	0.358769i
$426$		0			0
$427$	−9.01263	+	23.2669i	−0.436152	+	1.12596i
$428$	4.03877			0.195221
$429$		0			0
$430$	−5.27657	+	9.13929i	−0.254459	+	0.440736i
$431$	−11.7248	−	20.3079i	−0.564762	−	0.978196i	−0.997072	−	0.0764711i	$-0.975635\pi$
$431$	−11.7248	−	20.3079i	−0.564762	−	0.978196i	0.432310	−	0.901725i	$-0.357699\pi$
$432$		0			0
$433$	0.402426	+	0.697022i	0.0193394	+	0.0334968i	0.875533	−	0.483158i	$-0.160510\pi$
$433$	0.402426	+	0.697022i	0.0193394	+	0.0334968i	−0.856194	+	0.516655i	$0.827177\pi$
$434$	3.49089	−	9.01203i	0.167568	−	0.432591i
$435$		0			0
$436$	6.93314	−	12.0085i	0.332037	−	0.575105i
$437$	7.88581	−	13.6586i	0.377230	−	0.653381i
$438$		0			0
$439$	−1.59775			−0.0762566			−0.0381283	−	0.999273i	$-0.512140\pi$
$439$	−1.59775			−0.0762566			−0.0381283	+	0.999273i	$0.512140\pi$
$440$	−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
$445$	−22.4583	−	38.8989i	−1.06462	−	1.84398i
$446$	2.49662	−	4.32427i	0.118218	−	0.204760i
$447$		0			0
$448$	−2.61442	+	0.405935i	−0.123520	+	0.0191786i
$449$	6.34113	+	10.9832i	0.299257	+	0.518328i	0.975966	−	0.217923i	$-0.0699280\pi$
$449$	6.34113	+	10.9832i	0.299257	+	0.518328i	−0.676710	+	0.736250i	$0.736595\pi$
$450$		0			0
$451$	23.3319			1.09866
$452$	7.30902	+	12.6596i	0.343788	+	0.595457i
$453$		0			0
$454$	−1.57273			−0.0738117
$455$	−14.0429	+	36.6630i	−0.658343	+	1.71879i
$456$		0			0
$457$	−10.7551			−0.503100			−0.251550	−	0.967844i	$-0.580940\pi$
$457$	−10.7551			−0.503100			−0.251550	+	0.967844i	$0.580940\pi$
$458$	−0.828619	−	1.43521i	−0.0387188	−	0.0670629i
$459$		0			0
$460$	−8.43251	−	14.6055i	−0.393168	−	0.680986i
$461$	−9.19640	−	15.9286i	−0.428319	−	0.741870i	0.568405	−	0.822749i	$-0.307561\pi$
$461$	−9.19640	−	15.9286i	−0.428319	−	0.741870i	−0.996724	+	0.0808788i	$0.974227\pi$
$462$		0			0
$463$	−34.6818			−1.61180			−0.805901	−	0.592050i	$-0.798319\pi$
$463$	−34.6818			−1.61180			−0.805901	+	0.592050i	$0.798319\pi$
$464$	−4.50457	+	7.80214i	−0.209119	+	0.362205i
$465$		0			0
$466$	−3.86181	−	6.68885i	−0.178895	−	0.309855i
$467$	−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
$472$	12.9027			0.593893
$473$	−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
$478$	−28.7630			−1.31559
$479$	−6.22925	−	10.7894i	−0.284622	−	0.492979i	0.687896	−	0.725810i	$-0.258535\pi$
$479$	−6.22925	−	10.7894i	−0.284622	−	0.492979i	−0.972517	+	0.232830i	$0.925201\pi$
$480$		0			0
$481$	13.0573	+	22.4202i	0.595363	+	1.02227i
$482$	−25.6204			−1.16698
$483$		0			0
$484$	−2.67994	+	4.64180i	−0.121816	+	0.210991i
$485$	−12.7640	+	22.1078i	−0.579582	+	1.00387i
$486$		0			0
$487$	8.34097			0.377966			0.188983	−	0.981980i	$-0.439481\pi$
$487$	8.34097			0.377966			0.188983	+	0.981980i	$0.439481\pi$
$488$	−4.71538	+	8.16728i	−0.213455	+	0.369715i
$489$		0			0
$490$	21.2918	+	19.4071i	0.961865	+	0.876723i
$491$	−8.82502	+	15.2854i	−0.398268	+	0.689820i	−0.993512	−	0.113725i	$-0.963722\pi$
$491$	−8.82502	+	15.2854i	−0.398268	+	0.689820i	0.595245	+	0.803545i	$0.297055\pi$
$492$		0			0
$493$	3.22248	−	5.58150i	0.145133	−	0.251378i
$494$	−13.8769	+	0.0523416i	−0.624352	+	0.00235496i
$495$		0			0
$496$	1.82642	−	3.16346i	0.0820088	−	0.142043i
$497$	16.9278	+	21.0346i	0.759316	+	0.943532i
$498$		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	$-0.490003\pi$
$500$	28.5552			1.27703
$501$		0			0
$502$	0.339652	+	0.588295i	0.0151594	+	0.0262569i
$503$	10.4517	+	18.1029i	0.466019	+	0.807169i	0.999247	−	0.0388027i	$-0.0123544\pi$
$503$	10.4517	+	18.1029i	0.466019	+	0.807169i	−0.533228	+	0.845972i	$0.679021\pi$
$504$		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
$509$	15.0211			0.665797			0.332899	−	0.942963i	$-0.391973\pi$
$509$	15.0211			0.665797			0.332899	+	0.942963i	$0.391973\pi$
$510$		0			0
$511$	2.40203	−	6.20104i	0.106259	−	0.274318i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−2.44587			−0.107883
$515$	6.00975	−	10.4092i	0.264821	−	0.458684i
$516$		0			0
$517$	5.20962	−	9.02333i	0.229119	−	0.396846i
$518$	18.8133	−	2.92108i	0.826607	−	0.128345i
$519$		0			0
$520$	−7.37100	+	12.8789i	−0.323240	+	0.564777i
$521$	−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
$523$	−12.3678			−0.540806			−0.270403	−	0.962747i	$-0.587157\pi$
$523$	−12.3678			−0.540806			−0.270403	+	0.962747i	$0.587157\pi$
$524$	−6.21657	−	10.7674i	−0.271572	−	0.470377i
$525$		0			0
$526$	−12.6596	−	21.9271i	−0.551985	−	0.956067i
$527$	−1.30659	+	2.26308i	−0.0569159	+	0.0985812i
$528$		0			0
$529$	−6.20792			−0.269910
$530$	11.1852			0.485855
$531$		0			0
$532$	−3.67815	+	9.49545i	−0.159468	+	0.411680i
$533$	20.7983	−	0.0784481i	0.900876	−	0.00339796i
$534$		0			0
$535$	−8.31100	−	14.3951i	−0.359316	−	0.622353i
$536$	−0.583158	−	1.01006i	−0.0251886	−	0.0436279i
$537$		0			0
$538$	−13.5665			−0.584895
$539$	20.9251	+	19.0729i	0.901308	+	0.821527i
$540$		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	$0.800787\pi$
$542$	4.85940			0.208729
$543$		0			0
$544$	0.715381			0.0306717
$545$	−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	$0.480584\pi$
$548$	10.3848			0.443617
$549$		0			0
$550$	48.2871			2.05897
$551$	17.3371	+	30.0288i	0.738587	+	1.27927i
$552$		0			0
$553$	22.2430	+	27.6393i	0.945867	+	1.17534i
$554$	−12.0625			−0.512488
$555$		0			0
$556$	−0.636394	−	1.10227i	−0.0269891	−	0.0467466i
$557$	7.04985	+	12.2107i	0.298712	+	0.517384i	0.975842	−	0.218480i	$-0.0701097\pi$
$557$	7.04985	+	12.2107i	0.298712	+	0.517384i	−0.677130	+	0.735864i	$0.736776\pi$
$558$		0			0
$559$	−4.59239	+	8.02400i	−0.194238	+	0.339379i
$560$	6.82682	+	8.48306i	0.288486	+	0.358475i
$561$		0			0
$562$	18.3963			0.776002
$563$	0.914813			0.0385548			0.0192774	−	0.999814i	$-0.493863\pi$
$563$	0.914813			0.0385548			0.0192774	+	0.999814i	$0.493863\pi$
$564$		0			0
$565$	30.0811	−	52.1020i	1.26552	−	2.19195i
$566$	−0.347153	−	0.601286i	−0.0145919	−	0.0252740i
$567$		0			0
$568$	5.10254	+	8.83786i	0.214098	+	0.370828i
$569$	22.0768			0.925509			0.462755	−	0.886486i	$-0.346861\pi$
$569$	22.0768			0.925509			0.462755	+	0.886486i	$0.346861\pi$
$570$		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	$0.185129\pi$
$572$	−7.24406	+	12.6571i	−0.302889	+	0.529220i
$573$		0			0
$574$	5.51270	−	14.2315i	0.230096	−	0.594012i
$575$	−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	$0.974417\pi$
$578$	16.4882			0.685820
$579$		0			0
$580$	37.0781			1.53959
$581$	−40.5299	+	6.29298i	−1.68147	+	0.261077i
$582$		0			0
$583$	10.9926			0.455267
$584$	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	−0.362005	−	0.932176i	$-0.617908\pi$
$587$	15.1737	−	26.2816i	0.626286	−	1.08476i	0.988291	−	0.152583i	$-0.0487591\pi$
$588$		0			0
$589$	−7.02952	−	12.1755i	−0.289646	−	0.501682i
$590$	−26.5512	−	45.9880i	−1.09309	−	1.89330i
$591$		0			0
$592$	7.19594			0.295751
$593$	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
$595$	−4.88378	−	6.06862i	−0.200215	−	0.248789i
$596$	11.6810	−	20.2320i	0.478471	−	0.828736i
$597$		0			0
$598$	−7.43565	−	12.7675i	−0.304066	−	0.522100i
$599$	−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	−0.911511	−	0.411275i	$-0.865083\pi$
$601$	−2.44125	+	4.22836i	−0.0995805	+	0.172479i	0.811931	+	0.583754i	$0.198417\pi$
$602$	4.25335	+	5.28525i	0.173354	+	0.215411i
$603$		0			0
$604$	1.19832	−	2.07555i	0.0487589	−	0.0844529i
$605$	22.0592			0.896834
$606$		0			0
$607$	6.39843	−	11.0824i	0.259704	−	0.449821i	−0.706458	−	0.707755i	$-0.749708\pi$
$607$	6.39843	−	11.0824i	0.259704	−	0.449821i	0.966163	+	0.257933i	$0.0830415\pi$
$608$	−1.92440	+	3.33315i	−0.0780445	+	0.135177i
$609$		0			0
$610$	38.8134			1.57151
$611$	4.61358	−	8.06102i	0.186646	−	0.326114i
$612$		0			0
$613$	−2.02495	−	3.50732i	−0.0817871	−	0.141659i	0.822231	−	0.569155i	$-0.192729\pi$
$613$	−2.02495	−	3.50732i	−0.0817871	−	0.141659i	−0.904018	+	0.427495i	$0.859396\pi$
$614$	−23.7724			−0.959377
$615$		0			0
$616$	6.70925	+	8.33697i	0.270324	+	0.335906i
$617$	7.16474	+	12.4097i	0.288441	+	0.499595i	0.973438	−	0.228951i	$-0.0735296\pi$
$617$	7.16474	+	12.4097i	0.288441	+	0.499595i	−0.684996	+	0.728546i	$0.740196\pi$
$618$		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	$0.901796\pi$
$620$	−15.0337			−0.603768
$621$		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
$626$	−16.0323	−	27.7688i	−0.640779	−	1.10986i
$627$		0			0
$628$	5.79083	−	10.0300i	0.231079	−	0.400241i
$629$	−5.14784			−0.205258
$630$		0			0
$631$	−18.8504	−	32.6498i	−0.750422	−	1.29977i	−0.947618	−	0.319405i	$-0.896517\pi$
$631$	−18.8504	−	32.6498i	−0.750422	−	1.29977i	0.197197	−	0.980364i	$-0.436816\pi$
$632$	6.70468	+	11.6129i	0.266698	+	0.461935i
$633$		0			0
$634$	10.3068	+	17.8520i	0.409336	+	0.708992i
$635$	10.4210			0.413544
$636$		0			0
$637$	18.7170	+	16.9314i	0.741595	+	0.670848i
$638$	36.4396			1.44266
$639$		0			0
$640$	2.05781	+	3.56422i	0.0813419	+	0.140888i
$641$	1.18808			0.0469264			0.0234632	−	0.999725i	$-0.492531\pi$
$641$	1.18808			0.0469264			0.0234632	+	0.999725i	$0.492531\pi$
$642$		0			0
$643$	−14.9781	−	25.9429i	−0.590679	−	1.02309i	−0.994141	−	0.108090i	$-0.965527\pi$
$643$	−14.9781	−	25.9429i	−0.590679	−	1.02309i	0.403462	−	0.914996i	$-0.367807\pi$
$644$	−10.7134	+	1.66344i	−0.422168	+	0.0655489i
$645$		0			0
$646$	1.37668	−	2.38447i	0.0541646	−	0.0938158i
$647$	−15.2109	−	26.3460i	−0.598002	−	1.03577i	−0.993116	−	0.117138i	$-0.962628\pi$
$647$	−15.2109	−	26.3460i	−0.598002	−	1.03577i	0.395114	−	0.918632i	$-0.370705\pi$
$648$		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
$653$	12.2930			0.481061			0.240530	−	0.970642i	$-0.422679\pi$
$653$	12.2930			0.481061			0.240530	+	0.970642i	$0.422679\pi$
$654$		0			0
$655$	−25.5850	+	44.3145i	−0.999688	+	1.73151i
$656$	2.88423	−	4.99563i	0.112610	−	0.195047i
$657$		0			0
$658$	−4.27298	−	5.30963i	−0.166578	−	0.206991i
$659$	−17.0038	−	29.4514i	−0.662374	−	1.14727i	−0.979990	−	0.199046i	$-0.936216\pi$
$659$	−17.0038	−	29.4514i	−0.662374	−	1.14727i	0.317616	−	0.948219i	$-0.397118\pi$
$660$		0			0
$661$	−6.90834	−	11.9656i	−0.268703	−	0.465408i	0.699824	−	0.714315i	$-0.253262\pi$
$661$	−6.90834	−	11.9656i	−0.268703	−	0.465408i	−0.968527	+	0.248908i	$0.919928\pi$
$662$	5.99781	−	10.3885i	0.233111	−	0.403761i
$663$		0			0
$664$	−15.5024			−0.601611
$665$	41.4128	−	6.43006i	1.60592	−	0.249347i
$666$		0			0
$667$	−18.4589	+	31.9717i	−0.714731	+	1.23795i
$668$	−3.15398	+	5.46286i	−0.122031	+	0.211364i
$669$		0			0
$670$	−2.40005	+	4.15701i	−0.0927221	+	0.160599i
$671$	38.1449			1.47257
$672$		0			0
$673$	19.8004	−	34.2952i	0.763248	−	1.32198i	−0.177920	−	0.984045i	$-0.556937\pi$
$673$	19.8004	−	34.2952i	0.763248	−	1.32198i	0.941168	−	0.337939i	$-0.109730\pi$
$674$	17.6146			0.678487
$675$		0			0
$676$	−6.41489	+	11.3070i	−0.246726	+	0.434886i
$677$	−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
$679$	10.2888	+	12.7850i	0.394849	+	0.490642i
$680$	−1.47212	−	2.54978i	−0.0564530	−	0.0977795i
$681$		0			0
$682$	−14.7748			−0.565756
$683$	−16.7899			−0.642448			−0.321224	−	0.947003i	$-0.604094\pi$
$683$	−16.7899			−0.642448			−0.321224	+	0.947003i	$0.604094\pi$
$684$		0			0
$685$	−21.3699	−	37.0138i	−0.816503	−	1.41422i
$686$	16.5777	−	8.25707i	0.632940	−	0.315256i
$687$		0			0
$688$	1.28209	+	2.22064i	0.0488791	+	0.0846610i
$689$	9.79894	−	0.0369601i	0.373310	−	0.00140807i
$690$		0			0
$691$	−3.35925			−0.127792			−0.0638960	−	0.997957i	$-0.520353\pi$
$691$	−3.35925			−0.127792			−0.0638960	+	0.997957i	$0.520353\pi$
$692$	−1.82563	+	3.16209i	−0.0694002	+	0.120205i
$693$		0			0
$694$	−15.8504			−0.601672
$695$	−2.61915	+	4.53651i	−0.0993501	+	0.172079i
$696$		0			0
$697$	−2.06332	+	3.57378i	−0.0781539	+	0.135367i
$698$	−5.15206	+	8.92363i	−0.195008	+	0.337764i
$699$		0			0
$700$	11.4090	−	29.4532i	0.431218	−	1.11323i
$701$	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
$704$	2.02237	+	3.50284i	0.0762209	+	0.132018i
$705$		0			0
$706$	8.00975	+	13.8733i	0.301451	+	0.522128i
$707$	−27.0486	−	33.6108i	−1.01727	−	1.26406i
$708$		0			0
$709$	9.65303	−	16.7195i	0.362527	−	0.627916i	−0.625849	−	0.779944i	$-0.715247\pi$
$709$	9.65303	−	16.7195i	0.362527	−	0.627916i	0.988376	+	0.152029i	$0.0485806\pi$
$710$	21.0001	−	36.3732i	0.788119	−	1.36506i
$711$		0			0
$712$	−10.9137			−0.409008
$713$	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
$718$	4.55623	+	7.89162i	0.170037	+	0.294513i
$719$	−4.27657	+	7.40724i	−0.159489	+	0.276243i	−0.934685	−	0.355478i	$-0.884318\pi$
$719$	−4.27657	+	7.40724i	−0.159489	+	0.276243i	0.775195	+	0.631721i	$0.217651\pi$
$720$		0			0
$721$	−4.84436	−	6.01963i	−0.180413	−	0.224183i
$722$	−2.09340	−	3.62588i	−0.0779084	−	0.134941i
$723$		0			0
$724$	−18.1728			−0.675385
$725$	−53.7767	−	93.1440i	−1.99722	−	3.45928i
$726$		0			0
$727$	37.0524			1.37420			0.687100	−	0.726563i	$-0.258884\pi$
$727$	37.0524			1.37420			0.687100	+	0.726563i	$0.258884\pi$
$728$	6.00874	+	7.40912i	0.222699	+	0.274600i
$729$		0			0
$730$	−10.3445			−0.382866
$731$	−0.917180	−	1.58860i	−0.0339231	−	0.0587566i
$732$		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
$737$	−2.35872	+	4.08542i	−0.0868845	+	0.150488i
$738$		0			0
$739$	18.1725	+	31.4757i	0.668487	+	1.15785i	0.978327	+	0.207065i	$0.0663911\pi$
$739$	18.1725	+	31.4757i	0.668487	+	1.15785i	−0.309840	+	0.950789i	$0.600276\pi$
$740$	−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	−0.443430	−	0.896309i	$-0.646239\pi$
$743$	15.1149	−	26.1797i	0.554511	−	0.960441i	0.997941	−	0.0641324i	$-0.0204280\pi$
$744$		0			0
$745$	−96.1487			−3.52262
$746$	−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
$751$	30.7238			1.12113			0.560563	−	0.828112i	$-0.310585\pi$
$751$	30.7238			1.12113			0.560563	+	0.828112i	$0.310585\pi$
$752$	−1.28800	−	2.23088i	−0.0469686	−	0.0813520i
$753$		0			0
$754$	32.4827	−	0.122520i	1.18295	−	0.00446190i
$755$	−9.86363			−0.358974
$756$		0			0
$757$	−7.78491	+	13.4839i	−0.282947	+	0.490079i	−0.972109	−	0.234528i	$-0.924646\pi$
$757$	−7.78491	+	13.4839i	−0.282947	+	0.490079i	0.689162	+	0.724607i	$0.257979\pi$
$758$	3.08112	−	5.33666i	0.111911	−	0.193836i
$759$		0			0
$760$	15.8401			0.574582
$761$	11.9278	−	20.6596i	0.432382	−	0.748908i	−0.564696	−	0.825299i	$-0.691006\pi$
$761$	11.9278	−	20.6596i	0.432382	−	0.748908i	0.997078	+	0.0763911i	$0.0243397\pi$
$762$		0			0
$763$	−13.2515	+	34.2098i	−0.479736	+	1.23848i
$764$	2.23004	−	3.86254i	0.0806799	−	0.139742i
$765$		0			0
$766$	9.48159	−	16.4226i	0.342584	−	0.593373i
$767$	−23.4124	−	40.2005i	−0.845373	−	1.45156i
$768$		0			0
$769$	−23.2870	+	40.3342i	−0.839750	+	1.45449i	0.0503539	+	0.998731i	$0.483965\pi$
$769$	−23.2870	+	40.3342i	−0.839750	+	1.45449i	−0.890104	+	0.455758i	$0.849368\pi$
$770$	15.9085	−	41.0692i	0.573302	−	1.48003i
$771$		0			0
$772$	4.34243	+	7.52130i	0.156287	+	0.270698i
$773$	−7.50660			−0.269994			−0.134997	−	0.990846i	$-0.543102\pi$
$773$	−7.50660			−0.269994			−0.134997	+	0.990846i	$0.543102\pi$
$774$		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
$782$	2.93150			0.104830
$783$		0			0
$784$	6.67043	−	2.12257i	0.238230	−	0.0758061i
$785$	−47.6656			−1.70126
$786$		0			0
$787$	42.4895			1.51459			0.757293	−	0.653075i	$-0.226521\pi$
$787$	42.4895			1.51459			0.757293	+	0.653075i	$0.226521\pi$
$788$	1.23397	−	2.13730i	0.0439583	−	0.0761380i
$789$		0			0
$790$	27.5939	−	47.7940i	0.981746	−	1.70043i
$791$	−24.2479	−	30.1306i	−0.862155	−	1.07132i
$792$		0			0
$793$	34.0029	−	0.128254i	1.20748	−	0.00455442i
$794$	10.3858	−	17.9888i	0.368579	−	0.638397i
$795$		0			0
$796$	20.5681			0.729018
$797$	9.27713	+	16.0685i	0.328613	+	0.569174i	0.982237	−	0.187645i	$-0.0600856\pi$
$797$	9.27713	+	16.0685i	0.328613	+	0.569174i	−0.653624	+	0.756819i	$0.726752\pi$
$798$		0			0
$799$	0.921412	+	1.59593i	0.0325972	+	0.0564600i
$800$	5.96913	−	10.3388i	0.211041	−	0.365533i
$801$		0			0
$802$	2.30807			0.0815007
$803$	−10.1663			−0.358761
$804$		0			0
$805$	27.9750	+	34.7620i	0.985991	+	1.22520i
$806$	−13.1704	+	0.0496768i	−0.463909	+	0.00174979i
$807$		0			0
$808$	−8.15325	−	14.1218i	−0.286830	−	0.496804i
$809$	18.6681	+	32.3340i	0.656334	+	1.13680i	0.981558	+	0.191167i	$0.0612271\pi$
$809$	18.6681	+	32.3340i	0.656334	+	1.13680i	−0.325224	+	0.945637i	$0.605440\pi$
$810$		0			0
$811$	19.9446			0.700350			0.350175	−	0.936684i	$-0.386122\pi$
$811$	19.9446			0.700350			0.350175	+	0.936684i	$0.386122\pi$
$812$	8.60970	−	22.2267i	0.302141	−	0.780003i
$813$		0			0
$814$	−14.5528	−	25.2063i	−0.510077	−	0.883479i
$815$	73.7050			2.58177
$816$		0			0
$817$	9.86896			0.345271
$818$	−16.0313			−0.560522
$819$		0			0
$820$	−23.7407			−0.829063
$821$	−24.1262			−0.842011			−0.421005	−	0.907058i	$-0.638323\pi$
$821$	−24.1262			−0.842011			−0.421005	+	0.907058i	$0.638323\pi$
$822$		0			0
$823$	3.27706			0.114231			0.0571155	−	0.998368i	$-0.481810\pi$
$823$	3.27706			0.114231			0.0571155	+	0.998368i	$0.481810\pi$
$824$	−1.46023	−	2.52920i	−0.0508696	−	0.0881087i
$825$		0			0
$826$	−33.7330	+	5.23764i	−1.17372	+	0.182241i
$827$	−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
$829$	−18.2954	−	31.6886i	−0.635426	−	1.10059i	−0.986425	−	0.164215i	$-0.947491\pi$
$829$	−18.2954	−	31.6886i	−0.635426	−	1.10059i	0.350998	−	0.936376i	$-0.385842\pi$
$830$	31.9010	+	55.2542i	1.10730	+	1.91790i
$831$		0			0
$832$	1.81454	+	3.11568i	0.0629079	+	0.108017i
$833$	−4.77190	+	1.51845i	−0.165337	+	0.0526111i
$834$		0			0
$835$	25.9611			0.898422
$836$	15.5673			0.538408
$837$		0			0
$838$	1.48519	−	2.57242i	0.0513049	−	0.0888627i
$839$	21.2148	+	36.7451i	0.732416	+	1.26858i	0.955848	+	0.293862i	$0.0949408\pi$
$839$	21.2148	+	36.7451i	0.732416	+	1.26858i	−0.223431	+	0.974720i	$0.571726\pi$
$840$		0			0
$841$	−26.0823	−	45.1759i	−0.899389	−	1.55779i
$842$	−34.3026			−1.18214
$843$		0			0
$844$	2.22726	−	3.85773i	0.0766656	−	0.132789i
$845$	53.5014	−	0.403604i	1.84051	−	0.0138844i
$846$		0			0
$847$	5.12224	−	13.2235i	0.176002	−	0.454365i
$848$	1.35888	−	2.35365i	0.0466641	−	0.0808245i
$849$		0			0
$850$	−4.27020	+	7.39621i	−0.146467	+	0.253688i
$851$	29.4876			1.01082
$852$		0			0
$853$	31.5639			1.08073			0.540363	−	0.841432i	$-0.318287\pi$
$853$	31.5639			1.08073			0.540363	+	0.841432i	$0.318287\pi$
$854$	9.01263	−	23.2669i	0.308406	−	0.796176i
$855$		0			0
$856$	−4.03877			−0.138042
$857$	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
$865$	15.0272			0.510940
$866$	−0.402426	−	0.697022i	−0.0136750	−	0.0236858i
$867$		0			0
$868$	−3.49089	+	9.01203i	−0.118489	+	0.305888i
$869$	27.1187	−	46.9709i	0.919938	−	1.59338i
$870$		0			0
$871$	−2.08885	+	3.64972i	−0.0707781	+	0.123666i
$872$	−6.93314	+	12.0085i	−0.234786	+	0.406661i
$873$		0			0
$874$	−7.88581	+	13.6586i	−0.266742	+	0.462010i
$875$	−74.6554	+	11.5915i	−2.52381	+	0.391866i
$876$		0			0
$877$	7.24457	−	12.5480i	0.244632	−	0.423714i	−0.717396	−	0.696665i	$-0.754666\pi$
$877$	7.24457	−	12.5480i	0.244632	−	0.423714i	0.962028	+	0.272951i	$0.0879996\pi$
$878$	1.59775			0.0539216
$879$		0			0
$880$	8.32328	−	14.4163i	0.280578	−	0.485975i
$881$	22.1191	−	38.3114i	0.745211	−	1.29074i	−0.204886	−	0.978786i	$-0.565682\pi$
$881$	22.1191	−	38.3114i	0.745211	−	1.29074i	0.950096	−	0.311957i	$-0.100984\pi$
$882$		0			0
$883$	−51.8997			−1.74656			−0.873282	−	0.487216i	$-0.838012\pi$
$883$	−51.8997			−1.74656			−0.873282	+	0.487216i	$0.838012\pi$
$884$	−1.29809	−	2.22890i	−0.0436594	−	0.0749659i
$885$		0			0
$886$	−3.27335	−	5.66960i	−0.109970	−	0.190474i
$887$	−28.7902			−0.966681			−0.483340	−	0.875433i	$-0.660577\pi$
$887$	−28.7902			−0.966681			−0.483340	+	0.875433i	$0.660577\pi$
$888$		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
$893$	−9.91450			−0.331776
$894$		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
$899$	16.4545	+	28.5000i	0.548788	+	0.950529i
$900$		0			0
$901$	−0.972115	+	1.68375i	−0.0323859	+	0.0560939i
$902$	−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
$907$	16.5608	+	28.6841i	0.549892	+	0.952441i	0.998281	+	0.0586026i	$0.0186645\pi$
$907$	16.5608	+	28.6841i	0.549892	+	0.952441i	−0.448389	+	0.893838i	$0.648002\pi$
$908$	1.57273			0.0521927
$909$		0			0
$910$	14.0429	−	36.6630i	0.465519	−	1.21537i
$911$	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
$913$	31.3516	+	54.3026i	1.03759	+	1.79715i
$914$	10.7551			0.355745
$915$		0			0
$916$	0.828619	+	1.43521i	0.0273783	+	0.0474207i
$917$	20.6236	+	25.6271i	0.681052	+	0.846280i
$918$		0			0
$919$	−25.8087	+	44.7020i	−0.851350	+	1.47458i	0.0286403	+	0.999590i	$0.490882\pi$
$919$	−25.8087	+	44.7020i	−0.851350	+	1.47458i	−0.879990	+	0.474992i	$0.842451\pi$
$920$	8.43251	+	14.6055i	0.278011	+	0.481530i
$921$		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
$926$	34.6818			1.13972
$927$		0			0
$928$	4.50457	−	7.80214i	0.147870	−	0.256118i
$929$	−17.2590	+	29.8935i	−0.566250	+	0.980773i	0.430682	+	0.902504i	$0.358273\pi$
$929$	−17.2590	+	29.8935i	−0.566250	+	0.980773i	−0.996932	+	0.0782698i	$0.975060\pi$
$930$		0			0
$931$	5.76170	−	26.3182i	0.188832	−	0.862545i
$932$	3.86181	+	6.68885i	0.126498	+	0.219101i
$933$		0			0
$934$	14.1236	+	24.4627i	0.462137	+	0.800445i
$935$	−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	$0.424607\pi$
$938$	1.93464	+	2.40400i	0.0631683	+	0.0784934i
$939$		0			0
$940$	−5.30091	+	9.18145i	−0.172897	+	0.299466i
$941$	−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
$943$	11.8190	−	20.4712i	0.384881	−	0.666633i
$944$	−12.9027			−0.419946
$945$		0			0
$946$	5.18570	−	8.98189i	0.168602	−	0.292027i
$947$	0.321435			0.0104452			0.00522262	−	0.999986i	$-0.498338\pi$
$947$	0.321435			0.0104452			0.00522262	+	0.999986i	$0.498338\pi$
$948$		0			0
$949$	−9.06238	+	0.0341819i	−0.294177	+	0.00110959i
$950$	−22.9739	−	39.7920i	−0.745373	−	1.29102i
$951$		0			0
$952$	−1.87031	+	0.290398i	−0.0606171	+	0.00941185i
$953$	9.79426	+	16.9642i	0.317267	+	0.549523i	0.979917	−	0.199407i	$-0.0639014\pi$
$953$	9.79426	+	16.9642i	0.317267	+	0.549523i	−0.662650	+	0.748930i	$0.730568\pi$
$954$		0			0
$955$	−18.3559			−0.593984
$956$	28.7630			0.930261
$957$		0			0
$958$	6.22925	+	10.7894i	0.201258	+	0.348589i
$959$	−27.1503	+	4.21555i	−0.876729	+	0.136127i
$960$		0			0
$961$	8.82835	+	15.2912i	0.284786	+	0.493263i
$962$	−13.0573	−	22.4202i	−0.420985	−	0.722857i
$963$		0			0
$964$	25.6204			0.825178
$965$	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	$0.612609\pi$
$968$	2.67994	−	4.64180i	0.0861366	−	0.149193i
$969$		0			0
$970$	12.7640	−	22.1078i	0.409826	−	0.709840i
$971$	−8.53781	+	14.7879i	−0.273991	+	0.474567i	−0.969880	−	0.243583i	$-0.921677\pi$
$971$	−8.53781	+	14.7879i	−0.273991	+	0.474567i	0.695889	+	0.718150i	$0.255011\pi$
$972$		0			0
$973$	2.11125	+	2.62346i	0.0676837	+	0.0841043i
$974$	−8.34097			−0.267262
$975$		0			0
$976$	4.71538	−	8.16728i	0.150936	−	0.261428i
$977$	4.36043	+	7.55249i	0.139503	+	0.241626i	0.927308	−	0.374298i	$-0.122116\pi$
$977$	4.36043	+	7.55249i	0.139503	+	0.241626i	−0.787806	+	0.615924i	$0.788783\pi$
$978$		0			0
$979$	22.0715	+	38.2290i	0.705409	+	1.22180i
$980$	−21.2918	−	19.4071i	−0.680141	−	0.619937i
$981$		0			0
$982$	8.82502	−	15.2854i	0.281618	−	0.487776i
$983$	−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
$985$	−10.1571			−0.323631
$986$	−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
$991$	−8.97605	−	15.5470i	−0.285134	−	0.493866i	0.687508	−	0.726177i	$-0.258705\pi$
$991$	−8.97605	−	15.5470i	−0.285134	−	0.493866i	−0.972642	+	0.232311i	$0.925371\pi$
$992$	−1.82642	+	3.16346i	−0.0579890	+	0.100440i
$993$		0			0
$994$	−16.9278	−	21.0346i	−0.536917	−	0.667178i
$995$	−42.3252	−	73.3095i	−1.34180	−	2.32407i
$996$		0			0
$997$	58.9494			1.86694			0.933472	−	0.358649i	$-0.116763\pi$
$997$	58.9494			1.86694			0.933472	+	0.358649i	$0.116763\pi$
$998$	18.9853	+	32.8834i	0.600968	+	1.04091i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.d.289.4	✓	8	273.107	odd	6
546.2.j.d.529.4	yes	8	3.2	odd	2
546.2.k.b.373.4	yes	8	21.2	odd	6
546.2.k.b.445.4	yes	8	39.29	odd	6
1638.2.m.g.289.1		8	91.16	even	3	inner
1638.2.m.g.1621.1		8	1.1	even	1	trivial
1638.2.p.i.919.1		8	7.2	even	3
1638.2.p.i.991.1		8	13.3	even	3

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.m (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-2.05781 - 3.56422i) q^{5} +(-2.61442 + 0.405935i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-2.05781 - 3.56422i) q^{5} +(-2.61442 + 0.405935i) q^{7} -1.00000 q^{8} +(2.05781 + 3.56422i) q^{10} +(2.02237 + 3.50284i) q^{11} +(1.81454 + 3.11568i) q^{13} +(2.61442 - 0.405935i) q^{14} +1.00000 q^{16} -0.715381 q^{17} +(1.92440 - 3.33315i) q^{19} +(-2.05781 - 3.56422i) q^{20} +(-2.02237 - 3.50284i) q^{22} +4.09781 q^{23} +(-5.96913 + 10.3388i) q^{25} +(-1.81454 - 3.11568i) q^{26} +(-2.61442 + 0.405935i) q^{28} +(-4.50457 + 7.80214i) q^{29} +(1.82642 - 3.16346i) q^{31} -1.00000 q^{32} +0.715381 q^{34} +(6.82682 + 8.48306i) q^{35} +7.19594 q^{37} +(-1.92440 + 3.33315i) q^{38} +(2.05781 + 3.56422i) q^{40} +(2.88423 - 4.99563i) q^{41} +(1.28209 + 2.22064i) q^{43} +(2.02237 + 3.50284i) q^{44} -4.09781 q^{46} +(-1.28800 - 2.23088i) q^{47} +(6.67043 - 2.12257i) q^{49} +(5.96913 - 10.3388i) q^{50} +(1.81454 + 3.11568i) q^{52} +(1.35888 - 2.35365i) q^{53} +(8.32328 - 14.4163i) q^{55} +(2.61442 - 0.405935i) q^{56} +(4.50457 - 7.80214i) q^{58} -12.9027 q^{59} +(4.71538 - 8.16728i) q^{61} +(-1.82642 + 3.16346i) q^{62} +1.00000 q^{64} +(7.37100 - 12.8789i) q^{65} +(0.583158 + 1.01006i) q^{67} -0.715381 q^{68} +(-6.82682 - 8.48306i) q^{70} +(-5.10254 - 8.83786i) q^{71} +(-1.25673 + 2.17673i) q^{73} -7.19594 q^{74} +(1.92440 - 3.33315i) q^{76} +(-6.70925 - 8.33697i) q^{77} +(-6.70468 - 11.6129i) q^{79} +(-2.05781 - 3.56422i) q^{80} +(-2.88423 + 4.99563i) q^{82} +15.5024 q^{83} +(1.47212 + 2.54978i) q^{85} +(-1.28209 - 2.22064i) q^{86} +(-2.02237 - 3.50284i) q^{88} +10.9137 q^{89} +(-6.00874 - 7.40912i) q^{91} +4.09781 q^{92} +(1.28800 + 2.23088i) q^{94} -15.8401 q^{95} +(-3.10135 - 5.37170i) q^{97} +(-6.67043 + 2.12257i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8	\( 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} - 3 q^{7} - 8 q^{8} + 2 q^{10} + 6 q^{11} - 11 q^{13} + 3 q^{14} + 8 q^{16} + 8 q^{17} + 6 q^{19} - 2 q^{20} - 6 q^{22} - 20 q^{23} - 18 q^{25} + 11 q^{26} - 3 q^{28} - 2 q^{29} + 6 q^{31} - 8 q^{32} - 8 q^{34} + 18 q^{35} + 56 q^{37} - 6 q^{38} + 2 q^{40} - 6 q^{43} + 6 q^{44} + 20 q^{46} - q^{47} + 5 q^{49} + 18 q^{50} - 11 q^{52} - 7 q^{53} + q^{55} + 3 q^{56} + 2 q^{58} + 4 q^{59} + 24 q^{61} - 6 q^{62} + 8 q^{64} - 22 q^{65} - 15 q^{67} + 8 q^{68} - 18 q^{70} - 6 q^{71} + q^{73} - 56 q^{74} + 6 q^{76} + 22 q^{77} - 12 q^{79} - 2 q^{80} + 32 q^{83} - 13 q^{85} + 6 q^{86} - 6 q^{88} + 50 q^{89} - 8 q^{91} - 20 q^{92} + q^{94} - 16 q^{95} - q^{97} - 5 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 - 3 * q^7 - 8 * q^8 + 2 * q^10 + 6 * q^11 - 11 * q^13 + 3 * q^14 + 8 * q^16 + 8 * q^17 + 6 * q^19 - 2 * q^20 - 6 * q^22 - 20 * q^23 - 18 * q^25 + 11 * q^26 - 3 * q^28 - 2 * q^29 + 6 * q^31 - 8 * q^32 - 8 * q^34 + 18 * q^35 + 56 * q^37 - 6 * q^38 + 2 * q^40 - 6 * q^43 + 6 * q^44 + 20 * q^46 - q^47 + 5 * q^49 + 18 * q^50 - 11 * q^52 - 7 * q^53 + q^55 + 3 * q^56 + 2 * q^58 + 4 * q^59 + 24 * q^61 - 6 * q^62 + 8 * q^64 - 22 * q^65 - 15 * q^67 + 8 * q^68 - 18 * q^70 - 6 * q^71 + q^73 - 56 * q^74 + 6 * q^76 + 22 * q^77 - 12 * q^79 - 2 * q^80 + 32 * q^83 - 13 * q^85 + 6 * q^86 - 6 * q^88 + 50 * q^89 - 8 * q^91 - 20 * q^92 + q^94 - 16 * q^95 - q^97 - 5 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more