LMFDB - Embedded newform 855.2.k.i.676.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(406,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("855.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.k (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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 9x^{8} - 2x^{7} + 56x^{6} - 18x^{5} + 125x^{4} + x^{3} + 189x^{2} - 52x + 16 $ x^10 - x^9 + 9x^8 - 2x^7 + 56x^6 - 18x^5 + 125x^4 + x^3 + 189x^2 - 52*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 285)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			676.1
Root			$1.34580 + 2.33099i$ of defining polynomial
Character	$\chi$	$=$	855.676
Dual form			855.2.k.i.406.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34580 + 2.33099i) q^{2} +(-2.62233 - 4.54201i) q^{4} +(0.500000 - 0.866025i) q^{5} -0.797044 q^{7} +8.73329 q^{8} +O(q^{10})$	\(q+(-1.34580 + 2.33099i) q^{2} +(-2.62233 - 4.54201i) q^{4} +(0.500000 - 0.866025i) q^{5} -0.797044 q^{7} +8.73329 q^{8} +(1.34580 + 2.33099i) q^{10} -2.59225 q^{11} +(1.39852 + 2.42231i) q^{13} +(1.07266 - 1.85790i) q^{14} +(-6.50857 + 11.2732i) q^{16} +(-2.88624 + 4.99911i) q^{17} +(2.45159 - 3.60412i) q^{19} -5.24466 q^{20} +(3.48863 - 6.04249i) q^{22} +(-1.55307 - 2.68999i) q^{23} +(-0.500000 - 0.866025i) q^{25} -7.52850 q^{26} +(2.09011 + 3.62018i) q^{28} +(-2.39547 - 4.14907i) q^{29} -9.48932 q^{31} +(-8.78510 - 15.2162i) q^{32} +(-7.76857 - 13.4556i) q^{34} +(-0.398522 + 0.690261i) q^{35} +7.69227 q^{37} +(5.10182 + 10.5650i) q^{38} +(4.36665 - 7.56325i) q^{40} +(3.69159 - 6.39402i) q^{41} +(1.39852 - 2.42231i) q^{43} +(6.79773 + 11.7740i) q^{44} +8.36045 q^{46} +(-5.53865 - 9.59322i) q^{47} -6.36472 q^{49} +2.69159 q^{50} +(7.33477 - 12.7042i) q^{52} +(-4.43931 - 7.68910i) q^{53} +(-1.29612 + 2.24495i) q^{55} -6.96082 q^{56} +12.8952 q^{58} +(0.540099 - 0.935479i) q^{59} +(-2.03612 - 3.52667i) q^{61} +(12.7707 - 22.1195i) q^{62} +21.2575 q^{64} +2.79704 q^{65} +(-6.88784 - 11.9301i) q^{67} +30.2747 q^{68} +(-1.07266 - 1.85790i) q^{70} +(-5.98771 + 10.3710i) q^{71} +(-4.25389 + 7.36795i) q^{73} +(-10.3522 + 17.9306i) q^{74} +(-22.7988 - 1.68395i) q^{76} +2.06614 q^{77} +(-3.24092 + 5.61344i) q^{79} +(6.50857 + 11.2732i) q^{80} +(9.93625 + 17.2101i) q^{82} +2.79520 q^{83} +(2.88624 + 4.99911i) q^{85} +(3.76425 + 6.51987i) q^{86} -22.6389 q^{88} +(-6.67930 - 11.5689i) q^{89} +(-1.11468 - 1.93069i) q^{91} +(-8.14532 + 14.1081i) q^{92} +29.8155 q^{94} +(-1.89547 - 3.92520i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(8.56561 - 14.8361i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 7 q^{4} + 5 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) $ 10 * q - q^2 - 7 * q^4 + 5 * q^5 + 4 * q^7 + 12 * q^8	$ 10 q - q^{2} - 7 q^{4} + 5 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} - 10 q^{11} + 8 q^{13} - 4 q^{14} - 7 q^{16} + 10 q^{17} + 5 q^{19} - 14 q^{20} - 2 q^{22} - 2 q^{23} - 5 q^{25} + 4 q^{26} - 10 q^{28} - 7 q^{29} - 18 q^{31} - 23 q^{32} - 25 q^{34} + 2 q^{35} + 12 q^{37} + 37 q^{38} + 6 q^{40} + 12 q^{41} + 8 q^{43} + 16 q^{44} - 40 q^{46} + 6 q^{47} + 30 q^{49} + 2 q^{50} + 4 q^{52} + 8 q^{53} - 5 q^{55} - 72 q^{56} + 76 q^{58} - q^{59} - 7 q^{61} + 15 q^{62} + 28 q^{64} + 16 q^{65} + 14 q^{67} + 2 q^{68} + 4 q^{70} - 27 q^{71} - 26 q^{73} - 18 q^{74} - 56 q^{76} - 28 q^{77} - 23 q^{79} + 7 q^{80} + 36 q^{82} + 24 q^{83} - 10 q^{85} - 2 q^{86} - 9 q^{89} - 46 q^{91} - 52 q^{92} + 90 q^{94} - 2 q^{95} - 10 q^{97} + 21 q^{98}+O(q^{100}) $ 10 * q - q^2 - 7 * q^4 + 5 * q^5 + 4 * q^7 + 12 * q^8 + q^10 - 10 * q^11 + 8 * q^13 - 4 * q^14 - 7 * q^16 + 10 * q^17 + 5 * q^19 - 14 * q^20 - 2 * q^22 - 2 * q^23 - 5 * q^25 + 4 * q^26 - 10 * q^28 - 7 * q^29 - 18 * q^31 - 23 * q^32 - 25 * q^34 + 2 * q^35 + 12 * q^37 + 37 * q^38 + 6 * q^40 + 12 * q^41 + 8 * q^43 + 16 * q^44 - 40 * q^46 + 6 * q^47 + 30 * q^49 + 2 * q^50 + 4 * q^52 + 8 * q^53 - 5 * q^55 - 72 * q^56 + 76 * q^58 - q^59 - 7 * q^61 + 15 * q^62 + 28 * q^64 + 16 * q^65 + 14 * q^67 + 2 * q^68 + 4 * q^70 - 27 * q^71 - 26 * q^73 - 18 * q^74 - 56 * q^76 - 28 * q^77 - 23 * q^79 + 7 * q^80 + 36 * q^82 + 24 * q^83 - 10 * q^85 - 2 * q^86 - 9 * q^89 - 46 * q^91 - 52 * q^92 + 90 * q^94 - 2 * q^95 - 10 * q^97 + 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.34580	+	2.33099i	−0.951621	+	1.64826i	−0.209703	+	0.977765i	$0.567250\pi$
$2$	−1.34580	+	2.33099i	−0.951621	+	1.64826i	−0.741918	+	0.670491i	$0.766084\pi$
$3$		0			0
$3$		0			0
$4$	−2.62233	−	4.54201i	−1.31116	−	2.27100i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−0.797044			−0.301254			−0.150627	−	0.988591i	$-0.548129\pi$
$7$	−0.797044			−0.301254			−0.150627	+	0.988591i	$0.548129\pi$
$8$	8.73329			3.08769
$9$		0			0
$10$	1.34580	+	2.33099i	0.425578	+	0.737122i
$11$	−2.59225			−0.781592			−0.390796	−	0.920477i	$-0.627800\pi$
$11$	−2.59225			−0.781592			−0.390796	+	0.920477i	$0.627800\pi$
$12$		0			0
$13$	1.39852	+	2.42231i	0.387880	+	0.671828i	0.992164	−	0.124941i	$-0.0398741\pi$
$13$	1.39852	+	2.42231i	0.387880	+	0.671828i	−0.604284	+	0.796769i	$0.706541\pi$
$14$	1.07266	−	1.85790i	0.286680	−	0.496544i
$15$		0			0
$16$	−6.50857	+	11.2732i	−1.62714	+	2.81829i
$17$	−2.88624	+	4.99911i	−0.700015	+	1.21246i	0.268445	+	0.963295i	$0.413490\pi$
$17$	−2.88624	+	4.99911i	−0.700015	+	1.21246i	−0.968461	+	0.249167i	$0.919843\pi$
$18$		0			0
$19$	2.45159	−	3.60412i	0.562434	−	0.826843i
$19$	2.45159	−	3.60412i	0.562434	−	0.826843i
$20$	−5.24466			−1.17274
$21$		0			0
$22$	3.48863	−	6.04249i	0.743779	−	1.28826i
$23$	−1.55307	−	2.68999i	−0.323837	−	0.560903i	0.657439	−	0.753508i	$-0.271640\pi$
$23$	−1.55307	−	2.68999i	−0.323837	−	0.560903i	−0.981276	+	0.192605i	$0.938306\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−7.52850			−1.47646
$27$		0			0
$28$	2.09011	+	3.62018i	0.394994	+	0.684150i
$29$	−2.39547	−	4.14907i	−0.444827	−	0.770463i	0.553213	−	0.833040i	$-0.313401\pi$
$29$	−2.39547	−	4.14907i	−0.444827	−	0.770463i	−0.998040	+	0.0625768i	$0.980068\pi$
$30$		0			0
$31$	−9.48932			−1.70433			−0.852166	−	0.523272i	$-0.824711\pi$
$31$	−9.48932			−1.70433			−0.852166	+	0.523272i	$0.824711\pi$
$32$	−8.78510	−	15.2162i	−1.55300	−	2.68988i
$33$		0			0
$34$	−7.76857	−	13.4556i	−1.33230	−	2.30761i
$35$	−0.398522	+	0.690261i	−0.0673625	+	0.116675i
$36$		0			0
$37$	7.69227			1.26460			0.632301	−	0.774723i	$-0.282111\pi$
$37$	7.69227			1.26460			0.632301	+	0.774723i	$0.282111\pi$
$38$	5.10182	+	10.5650i	0.827624	+	1.71387i
$39$		0			0
$40$	4.36665	−	7.56325i	0.690428	−	1.19586i
$41$	3.69159	−	6.39402i	0.576530	−	0.998579i	−0.419344	−	0.907827i	$-0.637740\pi$
$41$	3.69159	−	6.39402i	0.576530	−	0.998579i	0.995874	−	0.0907511i	$-0.0289268\pi$
$42$		0			0
$43$	1.39852	−	2.42231i	0.213273	−	0.369399i	−0.739464	−	0.673196i	$-0.764921\pi$
$43$	1.39852	−	2.42231i	0.213273	−	0.369399i	0.952737	+	0.303797i	$0.0982544\pi$
$44$	6.79773	+	11.7740i	1.02480	+	1.77500i
$45$		0			0
$46$	8.36045			1.23268
$47$	−5.53865	−	9.59322i	−0.807895	−	1.39931i	−0.914319	−	0.404994i	$-0.867274\pi$
$47$	−5.53865	−	9.59322i	−0.807895	−	1.39931i	0.106424	−	0.994321i	$-0.466060\pi$
$48$		0			0
$49$	−6.36472			−0.909246
$50$	2.69159			0.380648
$51$		0			0
$52$	7.33477	−	12.7042i	1.01715	−	1.76176i
$53$	−4.43931	−	7.68910i	−0.609785	−	1.05618i	−0.991275	−	0.131806i	$-0.957922\pi$
$53$	−4.43931	−	7.68910i	−0.609785	−	1.05618i	0.381490	−	0.924373i	$-0.375411\pi$
$54$		0			0
$55$	−1.29612	+	2.24495i	−0.174769	+	0.302709i
$56$	−6.96082			−0.930179
$57$		0			0
$58$	12.8952			1.69323
$59$	0.540099	−	0.935479i	0.0703149	−	0.121789i	−0.828724	−	0.559657i	$-0.810933\pi$
$59$	0.540099	−	0.935479i	0.0703149	−	0.121789i	0.899039	+	0.437868i	$0.144266\pi$
$60$		0			0
$61$	−2.03612	−	3.52667i	−0.260699	−	0.451544i	0.705729	−	0.708482i	$-0.250620\pi$
$61$	−2.03612	−	3.52667i	−0.260699	−	0.451544i	−0.966428	+	0.256938i	$0.917286\pi$
$62$	12.7707	−	22.1195i	1.62188	−	2.80917i
$63$		0			0
$64$	21.2575			2.65719
$65$	2.79704			0.346931
$66$		0			0
$67$	−6.88784	−	11.9301i	−0.841484	−	1.45749i	−0.888640	−	0.458605i	$-0.848349\pi$
$67$	−6.88784	−	11.9301i	−0.841484	−	1.45749i	0.0471566	−	0.998888i	$-0.484984\pi$
$68$	30.2747			3.67134
$69$		0			0
$70$	−1.07266	−	1.85790i	−0.128207	−	0.222061i
$71$	−5.98771	+	10.3710i	−0.710611	+	1.23081i	0.254017	+	0.967200i	$0.418248\pi$
$71$	−5.98771	+	10.3710i	−0.710611	+	1.23081i	−0.964628	+	0.263615i	$0.915085\pi$
$72$		0			0
$73$	−4.25389	+	7.36795i	−0.497880	+	0.862354i	−0.999997	−	0.00244612i	$-0.999221\pi$
$73$	−4.25389	+	7.36795i	−0.497880	+	0.862354i	0.502117	+	0.864800i	$0.332555\pi$
$74$	−10.3522	+	17.9306i	−1.20342	+	2.08439i
$75$		0			0
$76$	−22.7988	−	1.68395i	−2.61521	−	0.193162i
$77$	2.06614			0.235458
$78$		0			0
$79$	−3.24092	+	5.61344i	−0.364632	+	0.631561i	−0.988717	−	0.149795i	$-0.952139\pi$
$79$	−3.24092	+	5.61344i	−0.364632	+	0.631561i	0.624085	+	0.781356i	$0.285472\pi$
$80$	6.50857	+	11.2732i	0.727680	+	1.26038i
$81$		0			0
$82$	9.93625	+	17.2101i	1.09728	+	1.90054i
$83$	2.79520			0.306813			0.153407	−	0.988163i	$-0.450976\pi$
$83$	2.79520			0.306813			0.153407	+	0.988163i	$0.450976\pi$
$84$		0			0
$85$	2.88624	+	4.99911i	0.313056	+	0.542229i
$86$	3.76425	+	6.51987i	0.405909	+	0.703056i
$87$		0			0
$88$	−22.6389			−2.41331
$89$	−6.67930	−	11.5689i	−0.708005	−	1.22630i	−0.965596	−	0.260046i	$-0.916262\pi$
$89$	−6.67930	−	11.5689i	−0.708005	−	1.22630i	0.257591	−	0.966254i	$-0.417071\pi$
$90$		0			0
$91$	−1.11468	−	1.93069i	−0.116851	−	0.202391i
$92$	−8.14532	+	14.1081i	−0.849208	+	1.47087i
$93$		0			0
$94$	29.8155			3.07524
$95$	−1.89547	−	3.92520i	−0.194471	−	0.402717i
$96$		0			0
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$	8.56561	−	14.8361i	0.865257	−	1.49867i
$99$		0			0
$100$	−2.62233	+	4.54201i	−0.262233	+	0.454201i
$101$	6.54078	+	11.3290i	0.650832	+	1.12727i	0.982921	+	0.184026i	$0.0589132\pi$
$101$	6.54078	+	11.3290i	0.650832	+	1.12727i	−0.332089	+	0.943248i	$0.607753\pi$
$102$		0			0
$103$	14.4586			1.42465			0.712326	−	0.701849i	$-0.247642\pi$
$103$	14.4586			1.42465			0.712326	+	0.701849i	$0.247642\pi$
$104$	12.2137	+	21.1548i	1.19765	+	2.07439i
$105$		0			0
$106$	23.8976			2.32114
$107$	−3.20480			−0.309819			−0.154910	−	0.987929i	$-0.549509\pi$
$107$	−3.20480			−0.309819			−0.154910	+	0.987929i	$0.549509\pi$
$108$		0			0
$109$	−3.89921	+	6.75362i	−0.373476	+	0.646880i	−0.990098	−	0.140380i	$-0.955168\pi$
$109$	−3.89921	+	6.75362i	−0.373476	+	0.646880i	0.616622	+	0.787260i	$0.288501\pi$
$110$	−3.48863	−	6.04249i	−0.332628	−	0.576129i
$111$		0			0
$112$	5.18761	−	8.98521i	0.490184	−	0.849023i
$113$	−8.26042			−0.777075			−0.388538	−	0.921433i	$-0.627020\pi$
$113$	−8.26042			−0.777075			−0.388538	+	0.921433i	$0.627020\pi$
$114$		0			0
$115$	−3.10614			−0.289649
$116$	−12.5634	+	21.7605i	−1.16648	+	2.02041i
$117$		0			0
$118$	1.45373	+	2.51793i	0.133826	+	0.231794i
$119$	2.30046	−	3.98451i	0.210883	−	0.365259i
$120$		0			0
$121$	−4.28025			−0.389114
$122$	10.9608			0.992346
$123$		0			0
$124$	24.8841	+	43.1006i	2.23466	+	3.87054i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−2.24466	−	3.88786i	−0.199181	−	0.344992i	0.749082	−	0.662477i	$-0.230495\pi$
$127$	−2.24466	−	3.88786i	−0.199181	−	0.344992i	−0.948263	+	0.317485i	$0.897162\pi$
$128$	−11.0381	+	19.1185i	−0.975637	+	1.68985i
$129$		0			0
$130$	−3.76425	+	6.51987i	−0.330146	+	0.571830i
$131$	9.73940	−	16.8691i	0.850936	−	1.47386i	−0.0294291	−	0.999567i	$-0.509369\pi$
$131$	9.73940	−	16.8691i	0.850936	−	1.47386i	0.880365	−	0.474297i	$-0.157298\pi$
$132$		0			0
$133$	−1.95403	+	2.87265i	−0.169436	+	0.249090i
$134$	37.0785			3.20309
$135$		0			0
$136$	−25.2064	+	43.6587i	−2.16143	+	3.74370i
$137$	2.11376	+	3.66115i	0.180591	+	0.312793i	0.942082	−	0.335383i	$-0.108866\pi$
$137$	2.11376	+	3.66115i	0.180591	+	0.312793i	−0.761491	+	0.648176i	$0.775532\pi$
$138$		0			0
$139$	−3.89547	−	6.74715i	−0.330409	−	0.572285i	0.652183	−	0.758062i	$-0.273853\pi$
$139$	−3.89547	−	6.74715i	−0.330409	−	0.572285i	−0.982592	+	0.185776i	$0.940520\pi$
$140$	4.18023			0.353294
$141$		0			0
$142$	−16.1165	−	27.9146i	−1.35246	−	2.34254i
$143$	−3.62532	−	6.27923i	−0.303164	−	0.525096i
$144$		0			0
$145$	−4.79093			−0.397865
$146$	−11.4497	−	19.8315i	−0.947586	−	1.64127i
$147$		0			0
$148$	−20.1717	−	34.9384i	−1.65810	−	2.87192i
$149$	−0.0453536	+	0.0785548i	−0.00371552	+	0.00643546i	−0.867877	−	0.496779i	$-0.834516\pi$
$149$	−0.0453536	+	0.0785548i	−0.00371552	+	0.00643546i	0.864162	+	0.503214i	$0.167849\pi$
$150$		0			0
$151$	−4.49727			−0.365983			−0.182991	−	0.983115i	$-0.558578\pi$
$151$	−4.49727			−0.365983			−0.182991	+	0.983115i	$0.558578\pi$
$152$	21.4105	−	31.4759i	1.73662	−	2.55303i
$153$		0			0
$154$	−2.78060	+	4.81613i	−0.224067	+	0.388095i
$155$	−4.74466	+	8.21799i	−0.381100	+	0.660085i
$156$		0			0
$157$	−8.82341	+	15.2826i	−0.704184	+	1.21968i	0.262801	+	0.964850i	$0.415354\pi$
$157$	−8.82341	+	15.2826i	−0.704184	+	1.21968i	−0.966985	+	0.254833i	$0.917979\pi$
$158$	−8.72323	−	15.1091i	−0.693983	−	1.20201i
$159$		0			0
$160$	−17.5702			−1.38905
$161$	1.23786	+	2.14404i	0.0975574	+	0.168974i
$162$		0			0
$163$	4.25858			0.333558			0.166779	−	0.985994i	$-0.446663\pi$
$163$	4.25858			0.333558			0.166779	+	0.985994i	$0.446663\pi$
$164$	−38.7223			−3.02370
$165$		0			0
$166$	−3.76177	+	6.51558i	−0.291970	+	0.505707i
$167$	1.98985	+	3.44652i	0.153979	+	0.266700i	0.932687	−	0.360687i	$-0.117458\pi$
$167$	1.98985	+	3.44652i	0.153979	+	0.266700i	−0.778708	+	0.627387i	$0.784124\pi$
$168$		0			0
$169$	2.58827	−	4.48302i	0.199098	−	0.344848i
$170$	−15.5371			−1.19164
$171$		0			0
$172$	−14.6695			−1.11854
$173$	5.58614	−	9.67547i	0.424706	−	0.735613i	−0.571687	−	0.820472i	$-0.693711\pi$
$173$	5.58614	−	9.67547i	0.424706	−	0.735613i	0.996393	+	0.0848594i	$0.0270441\pi$
$174$		0			0
$175$	0.398522	+	0.690261i	0.0301254	+	0.0521788i
$176$	16.8718	−	29.2228i	1.27176	−	2.20275i
$177$		0			0
$178$	35.9559			2.69501
$179$	−9.63565			−0.720203			−0.360101	−	0.932913i	$-0.617258\pi$
$179$	−9.63565			−0.720203			−0.360101	+	0.932913i	$0.617258\pi$
$180$		0			0
$181$	−2.05001	−	3.55073i	−0.152376	−	0.263923i	0.779724	−	0.626123i	$-0.215359\pi$
$181$	−2.05001	−	3.55073i	−0.152376	−	0.263923i	−0.932101	+	0.362200i	$0.882026\pi$
$182$	6.00055			0.444790
$183$		0			0
$184$	−13.5634	−	23.4925i	−0.999908	−	1.73189i
$185$	3.84614	−	6.66170i	0.282774	−	0.489778i
$186$		0			0
$187$	7.48184	−	12.9589i	0.547126	−	0.947651i
$188$	−29.0483	+	50.3132i	−2.11857	+	3.66946i
$189$		0			0
$190$	11.7005	+	0.864212i	0.848843	+	0.0626965i
$191$	22.6143			1.63631			0.818156	−	0.574996i	$-0.194996\pi$
$191$	22.6143			1.63631			0.818156	+	0.574996i	$0.194996\pi$
$192$		0			0
$193$	−8.30170	+	14.3790i	−0.597570	+	1.03502i	0.395609	+	0.918419i	$0.370534\pi$
$193$	−8.30170	+	14.3790i	−0.597570	+	1.03502i	−0.993179	+	0.116602i	$0.962800\pi$
$194$	−2.69159	−	4.66197i	−0.193245	−	0.334710i
$195$		0			0
$196$	16.6904	+	28.9086i	1.19217	+	2.06490i
$197$	17.6450			1.25715			0.628576	−	0.777748i	$-0.283638\pi$
$197$	17.6450			1.25715			0.628576	+	0.777748i	$0.283638\pi$
$198$		0			0
$199$	−9.53155	−	16.5091i	−0.675674	−	1.17030i	−0.976271	−	0.216550i	$-0.930519\pi$
$199$	−9.53155	−	16.5091i	−0.675674	−	1.17030i	0.300598	−	0.953751i	$-0.402814\pi$
$200$	−4.36665	−	7.56325i	−0.308769	−	0.534803i
$201$		0			0
$202$	−35.2102			−2.47738
$203$	1.90929	+	3.30699i	0.134006	+	0.232105i
$204$		0			0
$205$	−3.69159	−	6.39402i	−0.257832	−	0.446578i
$206$	−19.4584	+	33.7029i	−1.35573	+	2.34819i
$207$		0			0
$208$	−36.4095			−2.52454
$209$	−6.35513	+	9.34278i	−0.439594	+	0.646254i
$210$		0			0
$211$	7.02170	−	12.1619i	0.483394	−	0.837263i	−0.516424	−	0.856333i	$-0.672737\pi$
$211$	7.02170	−	12.1619i	0.483394	−	0.837263i	0.999818	+	0.0190700i	$0.00607055\pi$
$212$	−23.2826	+	40.3267i	−1.59906	+	2.76965i
$213$		0			0
$214$	4.31300	−	7.47033i	0.294831	−	0.510662i
$215$	−1.39852	−	2.42231i	−0.0953784	−	0.165200i
$216$		0			0
$217$	7.56341			0.513437
$218$	−10.4951	−	18.1780i	−0.710816	−	1.23117i
$219$		0			0
$220$	13.5955			0.916605
$221$	−16.1459			−1.08609
$222$		0			0
$223$	12.0926	−	20.9451i	0.809783	−	1.40259i	−0.103231	−	0.994657i	$-0.532918\pi$
$223$	12.0926	−	20.9451i	0.809783	−	1.40259i	0.913014	−	0.407928i	$-0.133748\pi$
$224$	7.00211	+	12.1280i	0.467848	+	0.810337i
$225$		0			0
$226$	11.1168	−	19.2549i	0.739481	−	1.28082i
$227$	−3.38455			−0.224640			−0.112320	−	0.993672i	$-0.535828\pi$
$227$	−3.38455			−0.224640			−0.112320	+	0.993672i	$0.535828\pi$
$228$		0			0
$229$	−25.9664			−1.71591			−0.857955	−	0.513726i	$-0.828265\pi$
$229$	−25.9664			−1.71591			−0.857955	+	0.513726i	$0.828265\pi$
$230$	4.18023	−	7.24036i	0.275636	−	0.477415i
$231$		0			0
$232$	−20.9203	−	36.2350i	−1.37349	−	2.37895i
$233$	−3.35911	+	5.81814i	−0.220062	+	0.381159i	−0.954827	−	0.297163i	$-0.903959\pi$
$233$	−3.35911	+	5.81814i	−0.220062	+	0.381159i	0.734764	+	0.678323i	$0.237293\pi$
$234$		0			0
$235$	−11.0773			−0.722603
$236$	−5.66527			−0.368778
$237$		0			0
$238$	6.19189	+	10.7247i	0.401361	+	0.695177i
$239$	−25.7818			−1.66769			−0.833843	−	0.552002i	$-0.813864\pi$
$239$	−25.7818			−1.66769			−0.833843	+	0.552002i	$0.813864\pi$
$240$		0			0
$241$	3.88929	+	6.73645i	0.250531	+	0.433933i	0.963672	−	0.267088i	$-0.0860614\pi$
$241$	3.88929	+	6.73645i	0.250531	+	0.433933i	−0.713141	+	0.701021i	$0.752728\pi$
$242$	5.76034	−	9.97721i	0.370289	−	0.641359i
$243$		0			0
$244$	−10.6788	+	18.4962i	−0.683638	+	1.18410i
$245$	−3.18236	+	5.51201i	−0.203314	+	0.352149i
$246$		0			0
$247$	12.1589	+	0.898071i	0.773653	+	0.0571429i
$248$	−82.8730			−5.26244
$249$		0			0
$250$	1.34580	−	2.33099i	0.0851156	−	0.147424i
$251$	5.43717	+	9.41745i	0.343191	+	0.594424i	0.985023	−	0.172421i	$-0.0551588\pi$
$251$	5.43717	+	9.41745i	0.343191	+	0.594424i	−0.641832	+	0.766845i	$0.721825\pi$
$252$		0			0
$253$	4.02594	+	6.97313i	0.253109	+	0.438397i
$254$	12.0834			0.758180
$255$		0			0
$256$	−8.45244	−	14.6401i	−0.528278	−	0.915004i
$257$	5.62716	+	9.74652i	0.351012	+	0.607971i	0.986427	−	0.164200i	$-0.0525042\pi$
$257$	5.62716	+	9.74652i	0.351012	+	0.607971i	−0.635415	+	0.772171i	$0.719171\pi$
$258$		0			0
$259$	−6.13108			−0.380967
$260$	−7.33477	−	12.7042i	−0.454883	−	0.787881i
$261$		0			0
$262$	26.2145	+	45.4048i	1.61954	+	2.80512i
$263$	−6.66936	+	11.5517i	−0.411250	+	0.712306i	−0.995027	−	0.0996082i	$-0.968241\pi$
$263$	−6.66936	+	11.5517i	−0.411250	+	0.712306i	0.583777	+	0.811914i	$0.301574\pi$
$264$		0			0
$265$	−8.87861			−0.545409
$266$	−4.06638	−	8.42080i	−0.249325	−	0.516312i
$267$		0			0
$268$	−36.1244	+	62.5693i	−2.20665	+	3.82203i
$269$	−3.53399	+	6.12105i	−0.215471	+	0.373207i	−0.953418	−	0.301652i	$-0.902462\pi$
$269$	−3.53399	+	6.12105i	−0.215471	+	0.373207i	0.737947	+	0.674859i	$0.235795\pi$
$270$		0			0
$271$	11.5289	−	19.9686i	0.700330	−	1.21301i	−0.268021	−	0.963413i	$-0.586370\pi$
$271$	11.5289	−	19.9686i	0.700330	−	1.21301i	0.968351	−	0.249594i	$-0.0802971\pi$
$272$	−37.5705	−	65.0741i	−2.27805	−	3.94569i
$273$		0			0
$274$	−11.3788			−0.687417
$275$	1.29612	+	2.24495i	0.0781592	+	0.135376i
$276$		0			0
$277$	18.8461			1.13235			0.566176	−	0.824284i	$-0.308422\pi$
$277$	18.8461			1.13235			0.566176	+	0.824284i	$0.308422\pi$
$278$	20.9700			1.25770
$279$		0			0
$280$	−3.48041	+	6.02825i	−0.207994	+	0.360257i
$281$	8.32486	+	14.4191i	0.496619	+	0.860170i	0.999992	−	0.00389922i	$-0.00124116\pi$
$281$	8.32486	+	14.4191i	0.496619	+	0.860170i	−0.503373	+	0.864069i	$0.667908\pi$
$282$		0			0
$283$	−6.52597	+	11.3033i	−0.387929	+	0.671912i	−0.992171	−	0.124888i	$-0.960143\pi$
$283$	−6.52597	+	11.3033i	−0.387929	+	0.671912i	0.604242	+	0.796801i	$0.293476\pi$
$284$	62.8070			3.72691
$285$		0			0
$286$	19.5157			1.15399
$287$	−2.94236	+	5.09632i	−0.173682	+	0.300826i
$288$		0			0
$289$	−8.16072	−	14.1348i	−0.480042	−	0.831458i
$290$	6.44762	−	11.1676i	0.378617	−	0.655784i
$291$		0			0
$292$	44.6204			2.61121
$293$	3.07225			0.179483			0.0897413	−	0.995965i	$-0.471396\pi$
$293$	3.07225			0.179483			0.0897413	+	0.995965i	$0.471396\pi$
$294$		0			0
$295$	−0.540099	−	0.935479i	−0.0314458	−	0.0544657i
$296$	67.1789			3.90469
$297$		0			0
$298$	−0.122073	−	0.211437i	−0.00707152	−	0.0122482i
$299$	4.34400	−	7.52403i	0.251220	−	0.435126i
$300$		0			0
$301$	−1.11468	+	1.93069i	−0.0642493	+	0.111283i
$302$	6.05240	−	10.4831i	0.348277	−	0.603233i
$303$		0			0
$304$	24.6735	+	51.0949i	1.41512	+	2.93049i
$305$	−4.07225			−0.233176
$306$		0			0
$307$	−11.7308	+	20.3183i	−0.669510	+	1.15963i	0.308531	+	0.951214i	$0.400163\pi$
$307$	−11.7308	+	20.3183i	−0.669510	+	1.15963i	−0.978041	+	0.208412i	$0.933171\pi$
$308$	−5.41809	−	9.38441i	−0.308724	−	0.534726i
$309$		0			0
$310$	−12.7707	−	22.1195i	−0.725326	−	1.25630i
$311$	5.59041			0.317003			0.158501	−	0.987359i	$-0.449334\pi$
$311$	5.59041			0.317003			0.158501	+	0.987359i	$0.449334\pi$
$312$		0			0
$313$	14.2140	+	24.6193i	0.803421	+	1.39157i	0.917352	+	0.398078i	$0.130323\pi$
$313$	14.2140	+	24.6193i	0.803421	+	1.39157i	−0.113930	+	0.993489i	$0.536344\pi$
$314$	−23.7490	−	41.1345i	−1.34023	−	2.32135i
$315$		0			0
$316$	33.9950			1.91237
$317$	−5.25481	−	9.10160i	−0.295140	−	0.511197i	0.679878	−	0.733325i	$-0.262033\pi$
$317$	−5.25481	−	9.10160i	−0.295140	−	0.511197i	−0.975017	+	0.222129i	$0.928699\pi$
$318$		0			0
$319$	6.20964	+	10.7554i	0.347673	+	0.602188i
$320$	10.6288	−	18.4096i	0.594166	−	1.02913i
$321$		0			0
$322$	−6.66365			−0.371351
$323$	10.9415	+	22.6581i	0.608803	+	1.26073i
$324$		0			0
$325$	1.39852	−	2.42231i	0.0775760	−	0.134366i
$326$	−5.73118	+	9.92670i	−0.317421	+	0.549789i
$327$		0			0
$328$	32.2397	−	55.8409i	1.78014	−	3.08330i
$329$	4.41455	+	7.64622i	0.243382	+	0.421550i
$330$		0			0
$331$	−6.39618			−0.351566			−0.175783	−	0.984429i	$-0.556246\pi$
$331$	−6.39618			−0.351566			−0.175783	+	0.984429i	$0.556246\pi$
$332$	−7.32995	−	12.6958i	−0.402283	−	0.696775i
$333$		0			0
$334$	−10.7117			−0.586119
$335$	−13.7757			−0.752646
$336$		0			0
$337$	9.13861	−	15.8285i	0.497812	−	0.862235i	−0.502185	−	0.864760i	$-0.667470\pi$
$337$	9.13861	−	15.8285i	0.497812	−	0.862235i	0.999997	+	0.00252482i	$0.000803675\pi$
$338$	6.96657	+	12.0664i	0.378931	+	0.656328i
$339$		0			0
$340$	15.1373	−	26.2186i	0.820937	−	1.42190i
$341$	24.5987			1.33209
$342$		0			0
$343$	10.6523			0.575169
$344$	12.2137	−	21.1548i	0.658519	−	1.14059i
$345$		0			0
$346$	15.0356	+	26.0424i	0.808318	+	1.40005i
$347$	−15.8293	+	27.4171i	−0.849760	+	1.47183i	0.0316618	+	0.999499i	$0.489920\pi$
$347$	−15.8293	+	27.4171i	−0.849760	+	1.47183i	−0.881422	+	0.472329i	$0.843413\pi$
$348$		0			0
$349$	12.0802			0.646638			0.323319	−	0.946290i	$-0.395201\pi$
$349$	12.0802			0.646638			0.323319	+	0.946290i	$0.395201\pi$
$350$	−2.14532			−0.114672
$351$		0			0
$352$	22.7732	+	39.4443i	1.21381	+	2.10239i
$353$	−3.63101			−0.193259			−0.0966296	−	0.995320i	$-0.530806\pi$
$353$	−3.63101			−0.193259			−0.0966296	+	0.995320i	$0.530806\pi$
$354$		0			0
$355$	5.98771	+	10.3710i	0.317795	+	0.550437i
$356$	−35.0307	+	60.6749i	−1.85662	+	3.21576i
$357$		0			0
$358$	12.9676	−	22.4606i	0.685360	−	1.18708i
$359$	−2.95898	+	5.12510i	−0.156169	+	0.270493i	−0.933484	−	0.358619i	$-0.883248\pi$
$359$	−2.95898	+	5.12510i	−0.156169	+	0.270493i	0.777315	+	0.629112i	$0.216581\pi$
$360$		0			0
$361$	−6.97940	−	17.6717i	−0.367337	−	0.930088i
$362$	11.0356			0.580018
$363$		0			0
$364$	−5.84614	+	10.1258i	−0.306421	+	0.530736i
$365$	4.25389	+	7.36795i	0.222659	+	0.385656i
$366$		0			0
$367$	−3.09080	−	5.35342i	−0.161338	−	0.279446i	0.774011	−	0.633173i	$-0.218248\pi$
$367$	−3.09080	−	5.35342i	−0.161338	−	0.279446i	−0.935349	+	0.353727i	$0.884914\pi$
$368$	40.4330			2.10772
$369$		0			0
$370$	10.3522	+	17.9306i	0.538187	+	0.932167i
$371$	3.53832	+	6.12855i	0.183701	+	0.318179i
$372$		0			0
$373$	−7.24346			−0.375052			−0.187526	−	0.982260i	$-0.560047\pi$
$373$	−7.24346			−0.375052			−0.187526	+	0.982260i	$0.560047\pi$
$374$	20.1380	+	34.8801i	1.04131	+	1.80361i
$375$		0			0
$376$	−48.3706	−	83.7804i	−2.49453	−	4.32064i
$377$	6.70023	−	11.6051i	0.345079	−	0.597695i
$378$		0			0
$379$	15.4483			0.793524			0.396762	−	0.917922i	$-0.370134\pi$
$379$	15.4483			0.793524			0.396762	+	0.917922i	$0.370134\pi$
$380$	−12.8578	+	18.9024i	−0.659589	+	0.969672i
$381$		0			0
$382$	−30.4342	+	52.7136i	−1.55715	+	2.69706i
$383$	−9.75805	+	16.9014i	−0.498613	+	0.863623i	−0.999999	−	0.00160064i	$-0.999491\pi$
$383$	−9.75805	+	16.9014i	−0.498613	+	0.863623i	0.501386	+	0.865224i	$0.332824\pi$
$384$		0			0
$385$	1.03307	−	1.78933i	0.0526500	−	0.0911925i
$386$	−22.3448	−	38.7023i	−1.13732	−	1.96990i
$387$		0			0
$388$	10.4893			0.532514
$389$	7.12876	+	12.3474i	0.361443	+	0.626037i	0.988198	−	0.153179i	$-0.0489510\pi$
$389$	7.12876	+	12.3474i	0.361443	+	0.626037i	−0.626756	+	0.779216i	$0.715618\pi$
$390$		0			0
$391$	17.9301			0.906764
$392$	−55.5850			−2.80747
$393$		0			0
$394$	−23.7465	+	41.1302i	−1.19633	+	2.07211i
$395$	3.24092	+	5.61344i	0.163068	+	0.282443i
$396$		0			0
$397$	−13.9540	+	24.1690i	−0.700330	+	1.21301i	0.268021	+	0.963413i	$0.413630\pi$
$397$	−13.9540	+	24.1690i	−0.700330	+	1.21301i	−0.968351	+	0.249594i	$0.919703\pi$
$398$	51.3101			2.57194
$399$		0			0
$400$	13.0171			0.650857
$401$	9.86205	−	17.0816i	0.492487	−	0.853013i	−0.507475	−	0.861666i	$-0.669421\pi$
$401$	9.86205	−	17.0816i	0.492487	−	0.853013i	0.999963	+	0.00865308i	$0.00275440\pi$
$402$		0			0
$403$	−13.2710	−	22.9861i	−0.661077	−	1.14502i
$404$	34.3042	−	59.4166i	1.70670	−	2.95609i
$405$		0			0
$406$	−10.2781			−0.510092
$407$	−19.9403			−0.988403
$408$		0			0
$409$	−9.61555	−	16.6546i	−0.475459	−	0.823518i	0.524146	−	0.851628i	$-0.324385\pi$
$409$	−9.61555	−	16.6546i	−0.475459	−	0.823518i	−0.999605	+	0.0281099i	$0.991051\pi$
$410$	19.8725			0.981433
$411$		0			0
$412$	−37.9153	−	65.6712i	−1.86795	−	3.23539i
$413$	−0.430483	+	0.745618i	−0.0211827	+	0.0366895i
$414$		0			0
$415$	1.39760	−	2.42072i	0.0686056	−	0.118828i
$416$	24.5723	−	42.5605i	1.20476	−	2.08670i
$417$		0			0
$418$	−13.2252	−	27.3872i	−0.646865	−	1.33955i
$419$	4.45253			0.217520			0.108760	−	0.994068i	$-0.465312\pi$
$419$	4.45253			0.217520			0.108760	+	0.994068i	$0.465312\pi$
$420$		0			0
$421$	−6.04467	+	10.4697i	−0.294599	+	0.510261i	−0.974892	−	0.222680i	$-0.928519\pi$
$421$	−6.04467	+	10.4697i	−0.294599	+	0.510261i	0.680292	+	0.732941i	$0.261853\pi$
$422$	18.8995	+	32.7350i	0.920016	+	1.59351i
$423$		0			0
$424$	−38.7698	−	67.1512i	−1.88283	−	3.26115i
$425$	5.77247			0.280006
$426$		0			0
$427$	1.62288	+	2.81091i	0.0785367	+	0.136030i
$428$	8.40403	+	14.5562i	0.406224	+	0.703601i
$429$		0			0
$430$	7.52850			0.363056
$431$	−10.2716	−	17.7909i	−0.494763	−	0.856955i	0.505219	−	0.862991i	$-0.331412\pi$
$431$	−10.2716	−	17.7909i	−0.494763	−	0.856955i	−0.999982	+	0.00603633i	$0.998079\pi$
$432$		0			0
$433$	9.68673	+	16.7779i	0.465514	+	0.806294i	0.999225	−	0.0393730i	$-0.0125360\pi$
$433$	9.68673	+	16.7779i	0.465514	+	0.806294i	−0.533710	+	0.845667i	$0.679203\pi$
$434$	−10.1788	+	17.6302i	−0.488598	+	0.846276i
$435$		0			0
$436$	40.9000			1.95876
$437$	−13.5026	−	0.997314i	−0.645915	−	0.0477080i
$438$		0			0
$439$	−8.61579	+	14.9230i	−0.411209	+	0.712235i	−0.995022	−	0.0996528i	$-0.968227\pi$
$439$	−8.61579	+	14.9230i	−0.411209	+	0.712235i	0.583813	+	0.811888i	$0.301560\pi$
$440$	−11.3194	+	19.6058i	−0.539633	+	0.934671i
$441$		0			0
$442$	21.7290	−	37.6358i	1.03354	−	1.79015i
$443$	8.32774	+	14.4241i	0.395663	+	0.685308i	0.993186	−	0.116544i	$-0.0371815\pi$
$443$	8.32774	+	14.4241i	0.395663	+	0.685308i	−0.597523	+	0.801852i	$0.703848\pi$
$444$		0			0
$445$	−13.3586			−0.633259
$446$	32.5484	+	56.3755i	1.54121	+	2.66946i
$447$		0			0
$448$	−16.9432			−0.800490
$449$	18.4698			0.871644			0.435822	−	0.900033i	$-0.356458\pi$
$449$	18.4698			0.871644			0.435822	+	0.900033i	$0.356458\pi$
$450$		0			0
$451$	−9.56952	+	16.5749i	−0.450611	+	0.780481i
$452$	21.6616	+	37.5189i	1.01887	+	1.76474i
$453$		0			0
$454$	4.55491	−	7.88933i	0.213772	−	0.370265i
$455$	−2.22937			−0.104514
$456$		0			0
$457$	3.40669			0.159358			0.0796791	−	0.996821i	$-0.474610\pi$
$457$	3.40669			0.159358			0.0796791	+	0.996821i	$0.474610\pi$
$458$	34.9455	−	60.5273i	1.63289	−	2.82826i
$459$		0			0
$460$	8.14532	+	14.1081i	0.379777	+	0.657794i
$461$	20.2028	−	34.9924i	0.940940	−	1.62976i	0.177258	−	0.984164i	$-0.443277\pi$
$461$	20.2028	−	34.9924i	0.940940	−	1.62976i	0.763682	−	0.645592i	$-0.223389\pi$
$462$		0			0
$463$	−22.9724			−1.06762			−0.533809	−	0.845605i	$-0.679240\pi$
$463$	−22.9724			−1.06762			−0.533809	+	0.845605i	$0.679240\pi$
$464$	62.3642			2.89519
$465$		0			0
$466$	−9.04134	−	15.6601i	−0.418832	−	0.725438i
$467$	−7.02174			−0.324927			−0.162464	−	0.986715i	$-0.551944\pi$
$467$	−7.02174			−0.324927			−0.162464	+	0.986715i	$0.551944\pi$
$468$		0			0
$469$	5.48991	+	9.50881i	0.253501	+	0.439076i
$470$	14.9078	−	25.8210i	0.687644	−	1.19103i
$471$		0			0
$472$	4.71685	−	8.16982i	0.217110	−	0.376046i
$473$	−3.62532	+	6.27923i	−0.166692	+	0.288719i
$474$		0			0
$475$	−4.34706	−	0.321078i	−0.199457	−	0.0147321i
$476$	−24.1302			−1.10601
$477$		0			0
$478$	34.6970	−	60.0970i	1.58700	−	2.74877i
$479$	−1.46058	−	2.52981i	−0.0667358	−	0.115590i	0.830727	−	0.556680i	$-0.187925\pi$
$479$	−1.46058	−	2.52981i	−0.0667358	−	0.115590i	−0.897463	+	0.441090i	$0.854592\pi$
$480$		0			0
$481$	10.7578	+	18.6331i	0.490514	+	0.849595i
$482$	−20.9368			−0.953643
$483$		0			0
$484$	11.2242	+	19.4409i	0.510192	+	0.883679i
$485$	1.00000	+	1.73205i	0.0454077	+	0.0786484i
$486$		0			0
$487$	19.2038			0.870207			0.435104	−	0.900380i	$-0.356712\pi$
$487$	19.2038			0.870207			0.435104	+	0.900380i	$0.356712\pi$
$488$	−17.7821	−	30.7994i	−0.804956	−	1.39423i
$489$		0			0
$490$	−8.56561	−	14.8361i	−0.386955	−	0.670225i
$491$	5.21845	−	9.03862i	0.235505	−	0.407907i	−0.723914	−	0.689890i	$-0.757659\pi$
$491$	5.21845	−	9.03862i	0.235505	−	0.407907i	0.959419	+	0.281983i	$0.0909922\pi$
$492$		0			0
$493$	27.6555			1.24554
$494$	−18.4568	+	27.1336i	−0.830410	+	1.22080i
$495$		0			0
$496$	61.7619	−	106.975i	2.77319	−	4.80330i
$497$	4.77247	−	8.26617i	0.214075	−	0.370788i
$498$		0			0
$499$	−13.0850	+	22.6639i	−0.585766	+	1.01458i	0.409014	+	0.912528i	$0.365873\pi$
$499$	−13.0850	+	22.6639i	−0.585766	+	1.01458i	−0.994780	+	0.102048i	$0.967461\pi$
$500$	2.62233	+	4.54201i	0.117274	+	0.203125i
$501$		0			0
$502$	−29.2693			−1.30635
$503$	2.67547	+	4.63405i	0.119293	+	0.206622i	0.919488	−	0.393119i	$-0.128604\pi$
$503$	2.67547	+	4.63405i	0.119293	+	0.206622i	−0.800195	+	0.599740i	$0.795270\pi$
$504$		0			0
$505$	13.0816			0.582122
$506$	−21.6724			−0.963454
$507$		0			0
$508$	−11.7725	+	20.3905i	−0.522319	+	0.904683i
$509$	4.89455	+	8.47760i	0.216947	+	0.375763i	0.953873	−	0.300210i	$-0.0970568\pi$
$509$	4.89455	+	8.47760i	0.216947	+	0.375763i	−0.736926	+	0.675973i	$0.763723\pi$
$510$		0			0
$511$	3.39054	−	5.87258i	0.149989	−	0.259788i
$512$	1.34875			0.0596067
$513$		0			0
$514$	−30.2920			−1.33612
$515$	7.22932	−	12.5215i	0.318562	−	0.551765i
$516$		0			0
$517$	14.3575	+	24.8680i	0.631444	+	1.09369i
$518$	8.25118	−	14.2915i	0.362536	−	0.627931i
$519$		0			0
$520$	24.4274			1.07121
$521$	−26.4315			−1.15799			−0.578993	−	0.815333i	$-0.696554\pi$
$521$	−26.4315			−1.15799			−0.578993	+	0.815333i	$0.696554\pi$
$522$		0			0
$523$	−14.3312	−	24.8223i	−0.626659	−	1.08541i	−0.988218	−	0.153056i	$-0.951089\pi$
$523$	−14.3312	−	24.8223i	−0.626659	−	1.08541i	0.361559	−	0.932349i	$-0.382245\pi$
$524$	−102.160			−4.46287
$525$		0			0
$526$	−17.9512	−	31.0924i	−0.782709	−	1.35569i
$527$	27.3884	−	47.4381i	1.19306	−	2.06644i
$528$		0			0
$529$	6.67595	−	11.5631i	0.290259	−	0.502743i
$530$	11.9488	−	20.6959i	0.519022	−	0.898973i
$531$		0			0
$532$	18.1717	+	1.34218i	0.787842	+	0.0581909i
$533$	20.6511			0.894498
$534$		0			0
$535$	−1.60240	+	2.77544i	−0.0692777	+	0.119993i
$536$	−60.1535	−	104.189i	−2.59824	−	4.50028i
$537$		0			0
$538$	−9.51205	−	16.4754i	−0.410094	−	0.710303i
$539$	16.4989			0.710659
$540$		0			0
$541$	12.0973	+	20.9531i	0.520103	+	0.900846i	0.999727	+	0.0233711i	$0.00743993\pi$
$541$	12.0973	+	20.9531i	0.520103	+	0.900846i	−0.479623	+	0.877474i	$0.659227\pi$
$542$	31.0310	+	53.7473i	1.33290	+	2.30865i
$543$		0			0
$544$	101.424			4.34850
$545$	3.89921	+	6.75362i	0.167024	+	0.289293i
$546$		0			0
$547$	−15.4959	−	26.8396i	−0.662555	−	1.14758i	−0.979942	−	0.199283i	$-0.936139\pi$
$547$	−15.4959	−	26.8396i	−0.662555	−	1.14758i	0.317387	−	0.948296i	$-0.397195\pi$
$548$	11.0860	−	19.2015i	0.473569	−	0.820246i
$549$		0			0
$550$	−6.97727			−0.297512
$551$	−20.8265	−	1.53827i	−0.887237	−	0.0655323i
$552$		0			0
$553$	2.58316	−	4.47416i	0.109847	−	0.190261i
$554$	−25.3630	+	43.9300i	−1.07757	+	1.86641i
$555$		0			0
$556$	−20.4304	+	35.3865i	−0.866442	+	1.50072i
$557$	6.38318	+	11.0560i	0.270464	+	0.468457i	0.968981	−	0.247136i	$-0.0794895\pi$
$557$	6.38318	+	11.0560i	0.270464	+	0.468457i	−0.698517	+	0.715594i	$0.746156\pi$
$558$		0			0
$559$	7.82346			0.330897
$560$	−5.18761	−	8.98521i	−0.219217	−	0.379695i
$561$		0			0
$562$	−44.8142			−1.89037
$563$	8.11088			0.341833			0.170916	−	0.985286i	$-0.445327\pi$
$563$	8.11088			0.341833			0.170916	+	0.985286i	$0.445327\pi$
$564$		0			0
$565$	−4.13021	+	7.15374i	−0.173759	+	0.300960i
$566$	−17.5652	−	30.4239i	−0.738322	−	1.27881i
$567$		0			0
$568$	−52.2925	+	90.5732i	−2.19414	+	3.80037i
$569$	−21.0412			−0.882091			−0.441046	−	0.897485i	$-0.645392\pi$
$569$	−21.0412			−0.882091			−0.441046	+	0.897485i	$0.645392\pi$
$570$		0			0
$571$	−8.45300			−0.353747			−0.176873	−	0.984234i	$-0.556598\pi$
$571$	−8.45300			−0.353747			−0.176873	+	0.984234i	$0.556598\pi$
$572$	−19.0135	+	32.9324i	−0.794996	+	1.37697i
$573$		0			0
$574$	−7.91963	−	13.7172i	−0.330559	−	0.572545i
$575$	−1.55307	+	2.68999i	−0.0647674	+	0.112181i
$576$		0			0
$577$	23.4005			0.974174			0.487087	−	0.873354i	$-0.338060\pi$
$577$	23.4005			0.974174			0.487087	+	0.873354i	$0.338060\pi$
$578$	43.9306			1.82727
$579$		0			0
$580$	12.5634	+	21.7605i	0.521667	+	0.903554i
$581$	−2.22790			−0.0924289
$582$		0			0
$583$	11.5078	+	19.9321i	0.476604	+	0.825501i
$584$	−37.1505	+	64.3465i	−1.53730	+	2.66268i
$585$		0			0
$586$	−4.13462	+	7.16136i	−0.170799	+	0.295833i
$587$	15.0838	−	26.1258i	0.622574	−	1.07833i	−0.366431	−	0.930445i	$-0.619420\pi$
$587$	15.0838	−	26.1258i	0.622574	−	1.07833i	0.989005	−	0.147884i	$-0.0472462\pi$
$588$		0			0
$589$	−23.2639	+	34.2007i	−0.958573	+	1.40921i
$590$	2.90745			0.119698
$591$		0			0
$592$	−50.0657	+	86.7163i	−2.05769	+	3.56402i
$593$	11.3496	+	19.6581i	0.466073	+	0.807262i	0.999249	−	0.0387422i	$-0.0123351\pi$
$593$	11.3496	+	19.6581i	0.466073	+	0.807262i	−0.533176	+	0.846004i	$0.679002\pi$
$594$		0			0
$595$	−2.30046	−	3.98451i	−0.0943096	−	0.163349i
$596$	0.475729			0.0194866
$597$		0			0
$598$	11.6923	+	20.2516i	0.478133	+	0.828150i
$599$	−9.96335	−	17.2570i	−0.407091	−	0.705103i	0.587471	−	0.809245i	$-0.300124\pi$
$599$	−9.96335	−	17.2570i	−0.407091	−	0.705103i	−0.994562	+	0.104142i	$0.966790\pi$
$600$		0			0
$601$	24.8942			1.01545			0.507727	−	0.861518i	$-0.330486\pi$
$601$	24.8942			1.01545			0.507727	+	0.861518i	$0.330486\pi$
$602$	−3.00027	−	5.19662i	−0.122282	−	0.211799i
$603$		0			0
$604$	11.7933	+	20.4266i	0.479864	+	0.831148i
$605$	−2.14013	+	3.70681i	−0.0870085	+	0.150703i
$606$		0			0
$607$	−11.3318			−0.459945			−0.229972	−	0.973197i	$-0.573864\pi$
$607$	−11.3318			−0.459945			−0.229972	+	0.973197i	$0.573864\pi$
$608$	−76.3787	−	5.64141i	−3.09756	−	0.228790i
$609$		0			0
$610$	5.48041	−	9.49235i	0.221895	−	0.384334i
$611$	15.4918	−	26.8327i	0.626733	−	1.08553i
$612$		0			0
$613$	3.48427	−	6.03493i	0.140728	−	0.243749i	−0.787043	−	0.616898i	$-0.788389\pi$
$613$	3.48427	−	6.03493i	0.140728	−	0.243749i	0.927771	+	0.373150i	$0.121722\pi$
$614$	−31.5744	−	54.6885i	−1.27424	−	2.20705i
$615$		0			0
$616$	18.0442			0.727020
$617$	−2.46999	−	4.27814i	−0.0994380	−	0.172232i	0.812014	−	0.583638i	$-0.198371\pi$
$617$	−2.46999	−	4.27814i	−0.0994380	−	0.172232i	−0.911452	+	0.411406i	$0.865038\pi$
$618$		0			0
$619$	−17.7750			−0.714439			−0.357219	−	0.934021i	$-0.616275\pi$
$619$	−17.7750			−0.714439			−0.357219	+	0.934021i	$0.616275\pi$
$620$	49.7682			1.99874
$621$		0			0
$622$	−7.52354	+	13.0312i	−0.301667	+	0.522502i
$623$	5.32370	+	9.22092i	0.213290	+	0.369428i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−76.5164			−3.05821
$627$		0			0
$628$	92.5515			3.69321
$629$	−22.2017	+	38.4545i	−0.885241	+	1.53328i
$630$		0			0
$631$	5.14920	+	8.91868i	0.204987	+	0.355047i	0.950128	−	0.311859i	$-0.100952\pi$
$631$	5.14920	+	8.91868i	0.204987	+	0.355047i	−0.745142	+	0.666906i	$0.767618\pi$
$632$	−28.3039	+	49.0238i	−1.12587	+	1.95006i
$633$		0			0
$634$	28.2876			1.12344
$635$	−4.48932			−0.178153
$636$		0			0
$637$	−8.90120	−	15.4173i	−0.352678	−	0.610857i
$638$	−33.4276			−1.32341
$639$		0			0
$640$	11.0381	+	19.1185i	0.436318	+	0.755725i
$641$	12.4745	−	21.6065i	0.492713	−	0.853405i	−0.507251	−	0.861798i	$-0.669338\pi$
$641$	12.4745	−	21.6065i	0.492713	−	0.853405i	0.999965	+	0.00839344i	$0.00267175\pi$
$642$		0			0
$643$	2.84614	−	4.92965i	0.112241	−	0.194407i	−0.804433	−	0.594044i	$-0.797531\pi$
$643$	2.84614	−	4.92965i	0.112241	−	0.194407i	0.916673	+	0.399637i	$0.130864\pi$
$644$	6.49218	−	11.2448i	0.255828	−	0.443106i
$645$		0			0
$646$	−67.5408	−	4.98864i	−2.65736	−	0.196275i
$647$	19.9379			0.783840			0.391920	−	0.919999i	$-0.371811\pi$
$647$	19.9379			0.783840			0.391920	+	0.919999i	$0.371811\pi$
$648$		0			0
$649$	−1.40007	+	2.42499i	−0.0549576	+	0.0951894i
$650$	3.76425	+	6.51987i	0.147646	+	0.255730i
$651$		0			0
$652$	−11.1674	−	19.3425i	−0.437349	−	0.757511i
$653$	−21.5636			−0.843848			−0.421924	−	0.906631i	$-0.638645\pi$
$653$	−21.5636			−0.843848			−0.421924	+	0.906631i	$0.638645\pi$
$654$		0			0
$655$	−9.73940	−	16.8691i	−0.380550	−	0.659132i
$656$	48.0539	+	83.2318i	1.87619	+	3.24966i
$657$		0			0
$658$	−23.7643			−0.926429
$659$	−20.3255	−	35.2049i	−0.791771	−	1.37139i	−0.924870	−	0.380284i	$-0.875826\pi$
$659$	−20.3255	−	35.2049i	−0.791771	−	1.37139i	0.133099	−	0.991103i	$-0.457507\pi$
$660$		0			0
$661$	19.7551	+	34.2168i	0.768384	+	1.33088i	0.938439	+	0.345445i	$0.112272\pi$
$661$	19.7551	+	34.2168i	0.768384	+	1.33088i	−0.170055	+	0.985435i	$0.554395\pi$
$662$	8.60795	−	14.9094i	0.334557	−	0.579471i
$663$		0			0
$664$	24.4113			0.947343
$665$	1.51077	+	3.12856i	0.0585852	+	0.121320i
$666$		0			0
$667$	−7.44065	+	12.8876i	−0.288103	+	0.499009i
$668$	10.4361	−	18.0758i	0.403784	−	0.699375i
$669$		0			0
$670$	18.5392	−	32.1109i	0.716234	−	1.24055i
$671$	5.27814	+	9.14200i	0.203760	+	0.352923i
$672$		0			0
$673$	6.47351			0.249536			0.124768	−	0.992186i	$-0.460181\pi$
$673$	6.47351			0.249536			0.124768	+	0.992186i	$0.460181\pi$
$674$	24.5974	+	42.6039i	0.947456	+	1.64104i
$675$		0			0
$676$	−27.1492			−1.04420
$677$	−45.8593			−1.76252			−0.881258	−	0.472636i	$-0.843303\pi$
$677$	−45.8593			−1.76252			−0.881258	+	0.472636i	$0.843303\pi$
$678$		0			0
$679$	0.797044	−	1.38052i	0.0305877	−	0.0529795i
$680$	25.2064	+	43.6587i	0.966619	+	1.67423i
$681$		0			0
$682$	−33.1048	+	57.3391i	−1.26765	+	2.19563i
$683$	7.04406			0.269533			0.134767	−	0.990877i	$-0.456972\pi$
$683$	7.04406			0.269533			0.134767	+	0.990877i	$0.456972\pi$
$684$		0			0
$685$	4.22753			0.161526
$686$	−14.3358	+	24.8303i	−0.547343	+	0.948025i
$687$		0			0
$688$	18.2047	+	31.5315i	0.694049	+	1.20213i
$689$	12.4169	−	21.5068i	0.473047	−	0.819342i
$690$		0			0
$691$	6.01990			0.229008			0.114504	−	0.993423i	$-0.463472\pi$
$691$	6.01990			0.229008			0.114504	+	0.993423i	$0.463472\pi$
$692$	−58.5948			−2.22744
$693$		0			0
$694$	−42.6059	−	73.7957i	−1.61730	−	2.80124i
$695$	−7.79093			−0.295527
$696$		0			0
$697$	21.3096	+	36.9093i	0.807159	+	1.39804i
$698$	−16.2575	+	28.1588i	−0.615354	+	1.06583i
$699$		0			0
$700$	2.09011	−	3.62018i	0.0789988	−	0.136830i
$701$	0.268547	−	0.465137i	0.0101429	−	0.0175680i	−0.860909	−	0.508758i	$-0.830105\pi$
$701$	0.268547	−	0.465137i	0.0101429	−	0.0175680i	0.871052	+	0.491190i	$0.163438\pi$
$702$		0			0
$703$	18.8583	−	27.7239i	0.711255	−	1.04563i
$704$	−55.1048			−2.07684
$705$		0			0
$706$	4.88659	−	8.46383i	0.183909	−	0.318540i
$707$	−5.21329	−	9.02969i	−0.196066	−	0.339596i
$708$		0			0
$709$	−11.3786	−	19.7083i	−0.427333	−	0.740162i	0.569302	−	0.822128i	$-0.307213\pi$
$709$	−11.3786	−	19.7083i	−0.427333	−	0.740162i	−0.996635	+	0.0819663i	$0.973880\pi$
$710$	−32.2329			−1.20968
$711$		0			0
$712$	−58.3323	−	101.035i	−2.18610	−	3.78643i
$713$	14.7376	+	25.5262i	0.551926	+	0.955964i
$714$		0			0
$715$	−7.25063			−0.271158
$716$	25.2679	+	43.7652i	0.944304	+	1.63558i
$717$		0			0
$718$	−7.96436	−	13.7947i	−0.297227	−	0.514813i
$719$	1.29796	−	2.24814i	0.0484059	−	0.0838415i	−0.840807	−	0.541335i	$-0.817919\pi$
$719$	1.29796	−	2.24814i	0.0484059	−	0.0838415i	0.889213	+	0.457493i	$0.151253\pi$
$720$		0			0
$721$	−11.5242			−0.429183
$722$	50.5853	+	7.51356i	1.88259	+	0.279626i
$723$		0			0
$724$	−10.7516	+	18.6224i	−0.399581	+	0.692094i
$725$	−2.39547	+	4.14907i	−0.0889654	+	0.154093i
$726$		0			0
$727$	−12.0755	+	20.9155i	−0.447857	+	0.775711i	−0.998246	−	0.0591969i	$-0.981146\pi$
$727$	−12.0755	+	20.9155i	−0.447857	+	0.775711i	0.550389	+	0.834908i	$0.314479\pi$
$728$	−9.73486	−	16.8613i	−0.360798	−	0.624920i
$729$		0			0
$730$	−22.8995			−0.847547
$731$	8.07293	+	13.9827i	0.298588	+	0.517170i
$732$		0			0
$733$	0.0870881			0.00321667			0.00160834	−	0.999999i	$-0.499488\pi$
$733$	0.0870881			0.00321667			0.00160834	+	0.999999i	$0.499488\pi$
$734$	16.6383			0.614131
$735$		0			0
$736$	−27.2877	+	47.2637i	−1.00584	+	1.74216i
$737$	17.8550	+	30.9257i	0.657697	+	1.13916i
$738$		0			0
$739$	10.6880	−	18.5122i	0.393166	−	0.680983i	−0.599699	−	0.800225i	$-0.704713\pi$
$739$	10.6880	−	18.5122i	0.393166	−	0.680983i	0.992865	+	0.119242i	$0.0380465\pi$
$740$	−40.3434			−1.48305
$741$		0			0
$742$	−19.0474			−0.699253
$743$	−10.3616	+	17.9469i	−0.380131	+	0.658407i	−0.991081	−	0.133263i	$-0.957455\pi$
$743$	−10.3616	+	17.9469i	−0.380131	+	0.658407i	0.610949	+	0.791670i	$0.290788\pi$
$744$		0			0
$745$	0.0453536	+	0.0785548i	0.00166163	+	0.00287803i
$746$	9.74821	−	16.8844i	0.356907	−	0.618182i
$747$		0			0
$748$	−78.4794			−2.86949
$749$	2.55436			0.0933344
$750$		0			0
$751$	−6.81691	−	11.8072i	−0.248752	−	0.430852i	0.714427	−	0.699709i	$-0.246687\pi$
$751$	−6.81691	−	11.8072i	−0.248752	−	0.430852i	−0.963180	+	0.268858i	$0.913354\pi$
$752$	144.195			5.25824
$753$		0			0
$754$	18.0343	+	31.2363i	0.656769	+	1.13756i
$755$	−2.24864	+	3.89475i	−0.0818362	+	0.141744i
$756$		0			0
$757$	4.40600	−	7.63142i	0.160139	−	0.277369i	−0.774780	−	0.632232i	$-0.782139\pi$
$757$	4.40600	−	7.63142i	0.160139	−	0.277369i	0.934918	+	0.354863i	$0.115472\pi$
$758$	−20.7902	+	36.0097i	−0.755134	+	1.30793i
$759$		0			0
$760$	−16.5537	−	34.2799i	−0.600465	−	1.24346i
$761$	−36.5972			−1.32665			−0.663323	−	0.748333i	$-0.730855\pi$
$761$	−36.5972			−1.32665			−0.663323	+	0.748333i	$0.730855\pi$
$762$		0			0
$763$	3.10784	−	5.38294i	0.112511	−	0.194875i
$764$	−59.3021	−	102.714i	−2.14548	−	3.71607i
$765$		0			0
$766$	−26.2647	−	45.4918i	−0.948981	−	1.64368i
$767$	3.02136			0.109095
$768$		0			0
$769$	−5.91386	−	10.2431i	−0.213259	−	0.369376i	0.739473	−	0.673186i	$-0.235075\pi$
$769$	−5.91386	−	10.2431i	−0.213259	−	0.369376i	−0.952733	+	0.303810i	$0.901741\pi$
$770$	2.78060	+	4.81613i	0.100206	+	0.173561i
$771$		0			0
$772$	87.0792			3.13405
$773$	−6.57819	−	11.3938i	−0.236601	−	0.409805i	0.723136	−	0.690706i	$-0.242700\pi$
$773$	−6.57819	−	11.3938i	−0.236601	−	0.409805i	−0.959737	+	0.280901i	$0.909367\pi$
$774$		0			0
$775$	4.74466	+	8.21799i	0.170433	+	0.295199i
$776$	−8.73329	+	15.1265i	−0.313507	+	0.543010i
$777$		0			0
$778$	−38.3754			−1.37583
$779$	−13.9946	−	28.9805i	−0.501408	−	1.03833i
$780$		0			0
$781$	15.5216	−	26.8843i	0.555408	−	0.961995i
$782$	−24.1302	+	41.7948i	−0.862895	+	1.49458i
$783$		0			0
$784$	41.4252	−	71.7506i	1.47947	−	2.56252i
$785$	8.82341	+	15.2826i	0.314921	+	0.545459i
$786$		0			0
$787$	4.59331			0.163734			0.0818669	−	0.996643i	$-0.473912\pi$
$787$	4.59331			0.163734			0.0818669	+	0.996643i	$0.473912\pi$
$788$	−46.2709	−	80.1436i	−1.64833	−	2.85500i
$789$		0			0
$790$	−17.4465			−0.620717
$791$	6.58392			0.234097
$792$		0			0
$793$	5.69513	−	9.86425i	0.202240	−	0.350290i
$794$	−37.5584	−	65.0530i	−1.33290	−	2.30865i
$795$		0			0
$796$	−49.9897	+	86.5848i	−1.77184	+	3.06892i
$797$	−10.1848			−0.360764			−0.180382	−	0.983597i	$-0.557733\pi$
$797$	−10.1848			−0.360764			−0.180382	+	0.983597i	$0.557733\pi$
$798$		0			0
$799$	63.9434			2.26215
$800$	−8.78510	+	15.2162i	−0.310600	+	0.537975i
$801$		0			0
$802$	26.5446	+	45.9766i	0.937323	+	1.62349i
$803$	11.0271	−	19.0996i	0.389139	−	0.674009i
$804$		0			0
$805$	2.47573			0.0872580
$806$	71.4403			2.51638
$807$		0			0
$808$	57.1226	+	98.9392i	2.00957	+	3.48067i
$809$	−31.9669			−1.12390			−0.561948	−	0.827173i	$-0.689948\pi$
$809$	−31.9669			−1.12390			−0.561948	+	0.827173i	$0.689948\pi$
$810$		0			0
$811$	−11.1179	−	19.2568i	−0.390403	−	0.676198i	0.602099	−	0.798421i	$-0.294331\pi$
$811$	−11.1179	−	19.2568i	−0.390403	−	0.676198i	−0.992503	+	0.122223i	$0.960998\pi$
$812$	10.0136	−	17.3440i	0.351408	−	0.608657i
$813$		0			0
$814$	26.8355	−	46.4805i	0.940585	−	1.62914i
$815$	2.12929	−	3.68804i	0.0745858	−	0.129186i
$816$		0			0
$817$	−5.30170	−	10.9790i	−0.185483	−	0.384105i
$818$	51.7623			1.80983
$819$		0			0
$820$	−19.3611	+	33.5345i	−0.676120	+	1.17107i
$821$	25.5604	+	44.2720i	0.892065	+	1.54510i	0.837395	+	0.546598i	$0.184078\pi$
$821$	25.5604	+	44.2720i	0.892065	+	1.54510i	0.0546706	+	0.998504i	$0.482589\pi$
$822$		0			0
$823$	17.1145	+	29.6431i	0.596573	+	1.03329i	0.993323	+	0.115368i	$0.0368046\pi$
$823$	17.1145	+	29.6431i	0.596573	+	1.03329i	−0.396750	+	0.917927i	$0.629862\pi$
$824$	126.272			4.39888
$825$		0			0
$826$	−1.15868	−	2.00690i	−0.0403158	−	0.0698290i
$827$	4.28856	+	7.42801i	0.149128	+	0.258297i	0.930905	−	0.365260i	$-0.119020\pi$
$827$	4.28856	+	7.42801i	0.149128	+	0.258297i	−0.781777	+	0.623558i	$0.785687\pi$
$828$		0			0
$829$	−13.4230			−0.466199			−0.233099	−	0.972453i	$-0.574887\pi$
$829$	−13.4230			−0.466199			−0.233099	+	0.972453i	$0.574887\pi$
$830$	3.76177	+	6.51558i	0.130573	+	0.226159i
$831$		0			0
$832$	29.7291	+	51.4923i	1.03067	+	1.78518i
$833$	18.3701	−	31.8179i	0.636486	−	1.10243i
$834$		0			0
$835$	3.97970			0.137723
$836$	59.1002	+	4.36521i	2.04402	+	0.150974i
$837$		0			0
$838$	−5.99219	+	10.3788i	−0.206997	+	0.358529i
$839$	19.8194	−	34.3282i	0.684242	−	1.18514i	−0.289433	−	0.957198i	$-0.593467\pi$
$839$	19.8194	−	34.3282i	0.684242	−	1.18514i	0.973675	−	0.227943i	$-0.0731999\pi$
$840$		0			0
$841$	3.02348	−	5.23682i	0.104258	−	0.180580i
$842$	−16.2698	−	28.1801i	−0.560693	−	0.971150i
$843$		0			0
$844$	−73.6529			−2.53524
$845$	−2.58827	−	4.48302i	−0.0890393	−	0.154221i
$846$		0			0
$847$	3.41155			0.117222
$848$	115.574			3.96883
$849$		0			0
$850$	−7.76857	+	13.4556i	−0.266460	+	0.461522i
$851$	−11.9466	−	20.6922i	−0.409525	−	0.709319i
$852$		0			0
$853$	3.02452	−	5.23863i	0.103558	−	0.179367i	−0.809590	−	0.586995i	$-0.800311\pi$
$853$	3.02452	−	5.23863i	0.103558	−	0.179367i	0.913148	+	0.407628i	$0.133644\pi$
$854$	−8.73626			−0.298949
$855$		0			0
$856$	−27.9884			−0.956625
$857$	25.6680	−	44.4583i	0.876803	−	1.51867i	0.0219737	−	0.999759i	$-0.493005\pi$
$857$	25.6680	−	44.4583i	0.876803	−	1.51867i	0.854829	−	0.518909i	$-0.173662\pi$
$858$		0			0
$859$	−6.03713	−	10.4566i	−0.205984	−	0.356775i	0.744462	−	0.667665i	$-0.232706\pi$
$859$	−6.03713	−	10.4566i	−0.205984	−	0.356775i	−0.950446	+	0.310890i	$0.899373\pi$
$860$	−7.33477	+	12.7042i	−0.250114	+	0.433210i
$861$		0			0
$862$	55.2936			1.88331
$863$	12.8023			0.435797			0.217898	−	0.975971i	$-0.430080\pi$
$863$	12.8023			0.435797			0.217898	+	0.975971i	$0.430080\pi$
$864$		0			0
$865$	−5.58614	−	9.67547i	−0.189934	−	0.328976i
$866$	−52.1454			−1.77197
$867$		0			0
$868$	−19.8337	−	34.3531i	−0.673201	−	1.16602i
$869$	8.40127	−	14.5514i	0.284993	−	0.493623i
$870$		0			0
$871$	19.2656	−	33.3690i	0.652790	−	1.13067i
$872$	−34.0529	+	58.9814i	−1.15318	+	1.99736i
$873$		0			0
$874$	20.4964	−	30.1321i	0.693301	−	1.01923i
$875$	0.797044			0.0269450
$876$		0			0
$877$	15.2683	−	26.4455i	0.515575	−	0.893002i	−0.484262	−	0.874923i	$-0.660912\pi$
$877$	15.2683	−	26.4455i	0.515575	−	0.893002i	0.999837	−	0.0180785i	$-0.00575488\pi$
$878$	−23.1902	−	40.1666i	−0.782631	−	1.35556i
$879$		0			0
$880$	−16.8718	−	29.2228i	−0.568749	−	0.985102i
$881$	6.79947			0.229080			0.114540	−	0.993419i	$-0.463461\pi$
$881$	6.79947			0.229080			0.114540	+	0.993419i	$0.463461\pi$
$882$		0			0
$883$	−13.5370	−	23.4468i	−0.455558	−	0.789049i	0.543162	−	0.839628i	$-0.317227\pi$
$883$	−13.5370	−	23.4468i	−0.455558	−	0.789049i	−0.998720	+	0.0505785i	$0.983893\pi$
$884$	42.3398	+	73.3346i	1.42404	+	2.46651i
$885$		0			0
$886$	−44.8297			−1.50608
$887$	−5.62312	−	9.73952i	−0.188806	−	0.327021i	0.756047	−	0.654518i	$-0.227128\pi$
$887$	−5.62312	−	9.73952i	−0.188806	−	0.327021i	−0.944852	+	0.327497i	$0.893795\pi$
$888$		0			0
$889$	1.78909	+	3.09880i	0.0600042	+	0.103930i
$890$	17.9780	−	31.1387i	0.602622	−	1.04377i
$891$		0			0
$892$	−126.844			−4.24704
$893$	−48.1536	−	3.55668i	−1.61140	−	0.119020i
$894$		0			0
$895$	−4.81783	+	8.34472i	−0.161042	+	0.278933i
$896$	8.79783	−	15.2383i	0.293915	−	0.509075i
$897$		0			0
$898$	−24.8566	+	43.0528i	−0.829474	+	1.43669i
$899$	22.7313	+	39.3718i	0.758133	+	1.31312i
$900$		0			0
$901$	51.2515			1.70744
$902$	−25.7572	−	44.6128i	−0.857622	−	1.48544i
$903$		0			0
$904$	−72.1407			−2.39936
$905$	−4.10003			−0.136289
$906$		0			0
$907$	21.4377	−	37.1313i	0.711829	−	1.23292i	−0.252341	−	0.967638i	$-0.581201\pi$
$907$	21.4377	−	37.1313i	0.711829	−	1.23292i	0.964170	−	0.265285i	$-0.0854661\pi$
$908$	8.87540	+	15.3726i	0.294541	+	0.510159i
$909$		0			0
$910$	3.00027	−	5.19662i	0.0994581	−	0.172266i
$911$	−39.7951			−1.31847			−0.659235	−	0.751937i	$-0.729120\pi$
$911$	−39.7951			−1.31847			−0.659235	+	0.751937i	$0.729120\pi$
$912$		0			0
$913$	−7.24586			−0.239803
$914$	−4.58471	+	7.94095i	−0.151649	+	0.262663i
$915$		0			0
$916$	68.0925	+	117.940i	2.24984	+	3.89684i
$917$	−7.76274	+	13.4455i	−0.256348	+	0.444008i
$918$		0			0
$919$	−51.8927			−1.71178			−0.855891	−	0.517156i	$-0.826991\pi$
$919$	−51.8927			−1.71178			−0.855891	+	0.517156i	$0.826991\pi$
$920$	−27.1268			−0.894345
$921$		0			0
$922$	54.3778	+	94.1851i	1.79084	+	3.10182i
$923$	−33.4958			−1.10253
$924$		0			0
$925$	−3.84614	−	6.66170i	−0.126460	−	0.219036i
$926$	30.9161	−	53.5483i	1.01597	−	1.75971i
$927$		0			0
$928$	−42.0888	+	72.9000i	−1.38163	+	2.39306i
$929$	−13.0662	+	22.6313i	−0.428687	+	0.742508i	−0.996757	−	0.0804727i	$-0.974357\pi$
$929$	−13.0662	+	22.6313i	−0.428687	+	0.742508i	0.568070	+	0.822980i	$0.307690\pi$
$930$		0			0
$931$	−15.6037	+	22.9392i	−0.511390	+	0.751803i
$932$	35.2347			1.15415
$933$		0			0
$934$	9.44982	−	16.3676i	0.309208	−	0.535563i
$935$	−7.48184	−	12.9589i	−0.244682	−	0.423802i
$936$		0			0
$937$	−16.1159	−	27.9135i	−0.526483	−	0.911895i	−0.999524	−	0.0308547i	$-0.990177\pi$
$937$	−16.1159	−	27.9135i	−0.526483	−	0.911895i	0.473041	−	0.881040i	$-0.343156\pi$
$938$	−29.5532			−0.964946
$939$		0			0
$940$	29.0483	+	50.3132i	0.947452	+	1.64103i
$941$	−16.9670	−	29.3878i	−0.553110	−	0.958014i	−0.998048	−	0.0624526i	$-0.980108\pi$
$941$	−16.9670	−	29.3878i	−0.553110	−	0.958014i	0.444938	−	0.895561i	$-0.353226\pi$
$942$		0			0
$943$	−22.9332			−0.746807
$944$	7.03054	+	12.1773i	0.228825	+	0.396336i
$945$		0			0
$946$	−9.75787	−	16.9011i	−0.317256	−	0.549503i
$947$	0.448299	−	0.776476i	0.0145678	−	0.0252321i	−0.858650	−	0.512563i	$-0.828696\pi$
$947$	0.448299	−	0.776476i	0.0145678	−	0.0252321i	0.873217	+	0.487331i	$0.162029\pi$
$948$		0			0
$949$	−23.7966			−0.772471
$950$	6.59868	−	9.70082i	0.214089	−	0.314736i
$951$		0			0
$952$	20.0906	−	34.7979i	0.651139	−	1.12781i
$953$	−15.3609	+	26.6059i	−0.497590	+	0.861851i	−0.999996	−	0.00278072i	$-0.999115\pi$
$953$	−15.3609	+	26.6059i	−0.497590	+	0.861851i	0.502406	+	0.864632i	$0.332448\pi$
$954$		0			0
$955$	11.3071	−	19.5845i	0.365891	−	0.633741i
$956$	67.6084	+	117.101i	2.18661	+	3.78732i
$957$		0			0
$958$	7.86259			0.254029
$959$	−1.68476	−	2.91810i	−0.0544038	−	0.0942302i
$960$		0			0
$961$	59.0472			1.90475
$962$	−57.9113			−1.86713
$963$		0			0
$964$	20.3980	−	35.3304i	0.656976	−	1.13792i
$965$	8.30170	+	14.3790i	0.267241	+	0.462876i
$966$		0			0
$967$	6.82768	−	11.8259i	0.219563	−	0.380295i	−0.735111	−	0.677947i	$-0.762870\pi$
$967$	6.82768	−	11.8259i	0.219563	−	0.380295i	0.954675	+	0.297652i	$0.0962034\pi$
$968$	−37.3807			−1.20146
$969$		0			0
$970$	−5.38318			−0.172844
$971$	19.1657	−	33.1959i	0.615055	−	1.06531i	−0.375320	−	0.926895i	$-0.622467\pi$
$971$	19.1657	−	33.1959i	0.615055	−	1.06531i	0.990375	−	0.138411i	$-0.0441996\pi$
$972$		0			0
$973$	3.10486	+	5.37777i	0.0995372	+	0.172404i
$974$	−25.8444	+	44.7638i	−0.828108	+	1.43432i
$975$		0			0
$976$	53.0090			1.69678
$977$	57.0555			1.82537			0.912684	−	0.408666i	$-0.134006\pi$
$977$	57.0555			1.82537			0.912684	+	0.408666i	$0.134006\pi$
$978$		0			0
$979$	17.3144	+	29.9894i	0.553371	+	0.958467i
$980$	33.3808			1.06631
$981$		0			0
$982$	14.0459	+	24.3283i	0.448224	+	0.776346i
$983$	−14.4625	+	25.0499i	−0.461284	+	0.798967i	−0.999025	−	0.0441430i	$-0.985944\pi$
$983$	−14.4625	+	25.0499i	−0.461284	+	0.798967i	0.537742	+	0.843110i	$0.319278\pi$
$984$		0			0
$985$	8.82249	−	15.2810i	0.281108	−	0.486893i
$986$	−37.2187	+	64.4646i	−1.18528	+	2.05297i
$987$		0			0
$988$	−27.8056	−	57.5809i	−0.884615	−	1.83189i
$989$	−8.68800			−0.276262
$990$		0			0
$991$	−4.07064	+	7.05056i	−0.129308	+	0.223968i	−0.923409	−	0.383818i	$-0.874609\pi$
$991$	−4.07064	+	7.05056i	−0.129308	+	0.223968i	0.794101	+	0.607786i	$0.207942\pi$
$992$	83.3646	+	144.392i	2.64683	+	4.58444i
$993$		0			0
$994$	12.8455	+	22.2491i	0.407436	+	0.705700i
$995$	−19.0631			−0.604341
$996$		0			0
$997$	−21.8847	−	37.9054i	−0.693095	−	1.20047i	−0.970819	−	0.239814i	$-0.922914\pi$
$997$	−21.8847	−	37.9054i	−0.693095	−	1.20047i	0.277724	−	0.960661i	$-0.410420\pi$
$998$	−35.2195	−	61.0019i	−1.11485	−	1.93098i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.k.i.676.1		10
3.2	odd	2		285.2.i.f.106.5	✓	10
19.7	even	3	inner	855.2.k.i.406.1		10
57.8	even	6		5415.2.a.z.1.5		5
57.11	odd	6		5415.2.a.y.1.1		5
57.26	odd	6		285.2.i.f.121.5	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.f.106.5	✓	10	3.2	odd	2
285.2.i.f.121.5	yes	10	57.26	odd	6
855.2.k.i.406.1		10	19.7	even	3	inner
855.2.k.i.676.1		10	1.1	even	1	trivial
5415.2.a.y.1.1		5	57.11	odd	6
5415.2.a.z.1.5		5	57.8	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34580 + 2.33099i) q^{2} +(-2.62233 - 4.54201i) q^{4} +(0.500000 - 0.866025i) q^{5} -0.797044 q^{7} +8.73329 q^{8} +O(q^{10})\)	\(q+(-1.34580 + 2.33099i) q^{2} +(-2.62233 - 4.54201i) q^{4} +(0.500000 - 0.866025i) q^{5} -0.797044 q^{7} +8.73329 q^{8} +(1.34580 + 2.33099i) q^{10} -2.59225 q^{11} +(1.39852 + 2.42231i) q^{13} +(1.07266 - 1.85790i) q^{14} +(-6.50857 + 11.2732i) q^{16} +(-2.88624 + 4.99911i) q^{17} +(2.45159 - 3.60412i) q^{19} -5.24466 q^{20} +(3.48863 - 6.04249i) q^{22} +(-1.55307 - 2.68999i) q^{23} +(-0.500000 - 0.866025i) q^{25} -7.52850 q^{26} +(2.09011 + 3.62018i) q^{28} +(-2.39547 - 4.14907i) q^{29} -9.48932 q^{31} +(-8.78510 - 15.2162i) q^{32} +(-7.76857 - 13.4556i) q^{34} +(-0.398522 + 0.690261i) q^{35} +7.69227 q^{37} +(5.10182 + 10.5650i) q^{38} +(4.36665 - 7.56325i) q^{40} +(3.69159 - 6.39402i) q^{41} +(1.39852 - 2.42231i) q^{43} +(6.79773 + 11.7740i) q^{44} +8.36045 q^{46} +(-5.53865 - 9.59322i) q^{47} -6.36472 q^{49} +2.69159 q^{50} +(7.33477 - 12.7042i) q^{52} +(-4.43931 - 7.68910i) q^{53} +(-1.29612 + 2.24495i) q^{55} -6.96082 q^{56} +12.8952 q^{58} +(0.540099 - 0.935479i) q^{59} +(-2.03612 - 3.52667i) q^{61} +(12.7707 - 22.1195i) q^{62} +21.2575 q^{64} +2.79704 q^{65} +(-6.88784 - 11.9301i) q^{67} +30.2747 q^{68} +(-1.07266 - 1.85790i) q^{70} +(-5.98771 + 10.3710i) q^{71} +(-4.25389 + 7.36795i) q^{73} +(-10.3522 + 17.9306i) q^{74} +(-22.7988 - 1.68395i) q^{76} +2.06614 q^{77} +(-3.24092 + 5.61344i) q^{79} +(6.50857 + 11.2732i) q^{80} +(9.93625 + 17.2101i) q^{82} +2.79520 q^{83} +(2.88624 + 4.99911i) q^{85} +(3.76425 + 6.51987i) q^{86} -22.6389 q^{88} +(-6.67930 - 11.5689i) q^{89} +(-1.11468 - 1.93069i) q^{91} +(-8.14532 + 14.1081i) q^{92} +29.8155 q^{94} +(-1.89547 - 3.92520i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(8.56561 - 14.8361i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 7 q^{4} + 5 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) 10 * q - q^2 - 7 * q^4 + 5 * q^5 + 4 * q^7 + 12 * q^8	\( 10 q - q^{2} - 7 q^{4} + 5 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} - 10 q^{11} + 8 q^{13} - 4 q^{14} - 7 q^{16} + 10 q^{17} + 5 q^{19} - 14 q^{20} - 2 q^{22} - 2 q^{23} - 5 q^{25} + 4 q^{26} - 10 q^{28} - 7 q^{29} - 18 q^{31} - 23 q^{32} - 25 q^{34} + 2 q^{35} + 12 q^{37} + 37 q^{38} + 6 q^{40} + 12 q^{41} + 8 q^{43} + 16 q^{44} - 40 q^{46} + 6 q^{47} + 30 q^{49} + 2 q^{50} + 4 q^{52} + 8 q^{53} - 5 q^{55} - 72 q^{56} + 76 q^{58} - q^{59} - 7 q^{61} + 15 q^{62} + 28 q^{64} + 16 q^{65} + 14 q^{67} + 2 q^{68} + 4 q^{70} - 27 q^{71} - 26 q^{73} - 18 q^{74} - 56 q^{76} - 28 q^{77} - 23 q^{79} + 7 q^{80} + 36 q^{82} + 24 q^{83} - 10 q^{85} - 2 q^{86} - 9 q^{89} - 46 q^{91} - 52 q^{92} + 90 q^{94} - 2 q^{95} - 10 q^{97} + 21 q^{98}+O(q^{100}) \) 10 * q - q^2 - 7 * q^4 + 5 * q^5 + 4 * q^7 + 12 * q^8 + q^10 - 10 * q^11 + 8 * q^13 - 4 * q^14 - 7 * q^16 + 10 * q^17 + 5 * q^19 - 14 * q^20 - 2 * q^22 - 2 * q^23 - 5 * q^25 + 4 * q^26 - 10 * q^28 - 7 * q^29 - 18 * q^31 - 23 * q^32 - 25 * q^34 + 2 * q^35 + 12 * q^37 + 37 * q^38 + 6 * q^40 + 12 * q^41 + 8 * q^43 + 16 * q^44 - 40 * q^46 + 6 * q^47 + 30 * q^49 + 2 * q^50 + 4 * q^52 + 8 * q^53 - 5 * q^55 - 72 * q^56 + 76 * q^58 - q^59 - 7 * q^61 + 15 * q^62 + 28 * q^64 + 16 * q^65 + 14 * q^67 + 2 * q^68 + 4 * q^70 - 27 * q^71 - 26 * q^73 - 18 * q^74 - 56 * q^76 - 28 * q^77 - 23 * q^79 + 7 * q^80 + 36 * q^82 + 24 * q^83 - 10 * q^85 - 2 * q^86 - 9 * q^89 - 46 * q^91 - 52 * q^92 + 90 * q^94 - 2 * q^95 - 10 * q^97 + 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more