LMFDB - Embedded newform 1755.2.i.f.586.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1755,2,Mod(586,1755)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1755, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1755.586");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1755 = 3^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1755.i (of order $3$, degree $2$, not 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:	$14.0137455547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + \cdots + 268 $ x^16 - 5x^15 + 20x^14 - 44x^13 + 96x^12 - 107x^11 + 178x^10 - 19x^9 + 231x^8 + 326x^7 + 551x^6 + 859x^5 + 1118x^4 + 1215x^3 + 1103x^2 + 770*x + 268
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 585)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			586.7
Root			$-0.628312 + 0.590424i$ of defining polynomial
Character	$\chi$	$=$	1755.586
Dual form			1755.2.i.f.1171.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12831 - 1.95429i) q^{2} +(-1.54617 - 2.67805i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.353285 + 0.611908i) q^{7} -2.46502 q^{8} +O(q^{10})$	\(q+(1.12831 - 1.95429i) q^{2} +(-1.54617 - 2.67805i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.353285 + 0.611908i) q^{7} -2.46502 q^{8} -2.25662 q^{10} +(-1.16510 + 2.01802i) q^{11} +(0.500000 + 0.866025i) q^{13} +(0.797232 + 1.38085i) q^{14} +(0.311036 - 0.538731i) q^{16} -6.04736 q^{17} -7.91884 q^{19} +(-1.54617 + 2.67805i) q^{20} +(2.62920 + 4.55391i) q^{22} +(-4.47799 - 7.75611i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.25662 q^{26} +2.18496 q^{28} +(-1.20340 + 2.08435i) q^{29} +(1.53216 + 2.65378i) q^{31} +(-3.16691 - 5.48526i) q^{32} +(-6.82331 + 11.8183i) q^{34} +0.706571 q^{35} -2.38079 q^{37} +(-8.93492 + 15.4757i) q^{38} +(1.23251 + 2.13477i) q^{40} +(-4.72945 - 8.19164i) q^{41} +(-5.96795 + 10.3368i) q^{43} +7.20582 q^{44} -20.2103 q^{46} +(4.86433 - 8.42527i) q^{47} +(3.25038 + 5.62982i) q^{49} +(1.12831 + 1.95429i) q^{50} +(1.54617 - 2.67805i) q^{52} -5.90968 q^{53} +2.33021 q^{55} +(0.870856 - 1.50837i) q^{56} +(2.71562 + 4.70359i) q^{58} +(1.48719 + 2.57588i) q^{59} +(4.62078 - 8.00343i) q^{61} +6.91501 q^{62} -13.0489 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.847241 + 1.46746i) q^{67} +(9.35028 + 16.1952i) q^{68} +(0.797232 - 1.38085i) q^{70} +12.4439 q^{71} +4.88899 q^{73} +(-2.68628 + 4.65277i) q^{74} +(12.2439 + 21.2071i) q^{76} +(-0.823229 - 1.42587i) q^{77} +(5.51270 - 9.54827i) q^{79} -0.622073 q^{80} -21.3452 q^{82} +(-0.260845 + 0.451797i) q^{83} +(3.02368 + 5.23717i) q^{85} +(13.4674 + 23.3262i) q^{86} +(2.87201 - 4.97447i) q^{88} -10.7608 q^{89} -0.706571 q^{91} +(-13.8475 + 23.9846i) q^{92} +(-10.9770 - 19.0127i) q^{94} +(3.95942 + 6.85792i) q^{95} +(1.48153 - 2.56609i) q^{97} +14.6698 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8	$ 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8} - 6 q^{10} + 6 q^{11} + 8 q^{13} + 10 q^{14} - 11 q^{16} + 4 q^{17} - 20 q^{19} - 9 q^{20} - 3 q^{22} + 6 q^{23} - 8 q^{25} + 6 q^{26} - 68 q^{28} + 14 q^{29} + 31 q^{31} + q^{32} + 7 q^{34} - 22 q^{35} + 2 q^{37} + 9 q^{38} - 6 q^{40} - 12 q^{41} - 15 q^{43} - 32 q^{44} - 64 q^{46} - 18 q^{47} - 17 q^{49} + 3 q^{50} + 9 q^{52} - 4 q^{53} - 12 q^{55} + 16 q^{56} + 42 q^{58} + 24 q^{59} + 9 q^{61} + 40 q^{62} - 60 q^{64} + 8 q^{65} + 18 q^{67} - 14 q^{68} + 10 q^{70} - 20 q^{71} + 12 q^{73} - 37 q^{74} + 53 q^{76} - 34 q^{77} + 3 q^{79} + 22 q^{80} - 68 q^{82} - 10 q^{83} - 2 q^{85} + 60 q^{86} + 14 q^{88} + 26 q^{89} + 22 q^{91} + 5 q^{92} - 17 q^{94} + 10 q^{95} + 34 q^{97} + 60 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8 - 6 * q^10 + 6 * q^11 + 8 * q^13 + 10 * q^14 - 11 * q^16 + 4 * q^17 - 20 * q^19 - 9 * q^20 - 3 * q^22 + 6 * q^23 - 8 * q^25 + 6 * q^26 - 68 * q^28 + 14 * q^29 + 31 * q^31 + q^32 + 7 * q^34 - 22 * q^35 + 2 * q^37 + 9 * q^38 - 6 * q^40 - 12 * q^41 - 15 * q^43 - 32 * q^44 - 64 * q^46 - 18 * q^47 - 17 * q^49 + 3 * q^50 + 9 * q^52 - 4 * q^53 - 12 * q^55 + 16 * q^56 + 42 * q^58 + 24 * q^59 + 9 * q^61 + 40 * q^62 - 60 * q^64 + 8 * q^65 + 18 * q^67 - 14 * q^68 + 10 * q^70 - 20 * q^71 + 12 * q^73 - 37 * q^74 + 53 * q^76 - 34 * q^77 + 3 * q^79 + 22 * q^80 - 68 * q^82 - 10 * q^83 - 2 * q^85 + 60 * q^86 + 14 * q^88 + 26 * q^89 + 22 * q^91 + 5 * q^92 - 17 * q^94 + 10 * q^95 + 34 * q^97 + 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1755\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.12831	−	1.95429i	0.797837	−	1.38189i	−0.123185	−	0.992384i	$-0.539311\pi$
$2$	1.12831	−	1.95429i	0.797837	−	1.38189i	0.921022	−	0.389510i	$-0.127356\pi$
$3$		0			0
$3$		0			0
$4$	−1.54617	−	2.67805i	−0.773087	−	1.33903i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−0.353285	+	0.611908i	−0.133529	+	0.231280i	−0.925035	−	0.379883i	$-0.875964\pi$
$7$	−0.353285	+	0.611908i	−0.133529	+	0.231280i	0.791505	+	0.611162i	$0.209298\pi$
$8$	−2.46502			−0.871517
$9$		0			0
$10$	−2.25662			−0.713607
$11$	−1.16510	+	2.01802i	−0.351292	+	0.608456i	−0.986476	−	0.163905i	$-0.947591\pi$
$11$	−1.16510	+	2.01802i	−0.351292	+	0.608456i	0.635184	+	0.772361i	$0.280924\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	0.797232	+	1.38085i	0.213069	+	0.369047i
$15$		0			0
$16$	0.311036	−	0.538731i	0.0777591	−	0.134683i
$17$	−6.04736			−1.46670			−0.733351	−	0.679851i	$-0.762045\pi$
$17$	−6.04736			−1.46670			−0.733351	+	0.679851i	$0.762045\pi$
$18$		0			0
$19$	−7.91884			−1.81671			−0.908353	−	0.418204i	$-0.862660\pi$
$19$	−7.91884			−1.81671			−0.908353	+	0.418204i	$0.862660\pi$
$20$	−1.54617	+	2.67805i	−0.345735	+	0.598831i
$21$		0			0
$22$	2.62920	+	4.55391i	0.560548	+	0.970898i
$23$	−4.47799	−	7.75611i	−0.933726	−	1.61726i	−0.776890	−	0.629637i	$-0.783204\pi$
$23$	−4.47799	−	7.75611i	−0.933726	−	1.61726i	−0.156837	−	0.987625i	$-0.550130\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.25662			0.442560
$27$		0			0
$28$	2.18496			0.412919
$29$	−1.20340	+	2.08435i	−0.223465	+	0.387054i	−0.955858	−	0.293829i	$-0.905070\pi$
$29$	−1.20340	+	2.08435i	−0.223465	+	0.387054i	0.732392	+	0.680883i	$0.238404\pi$
$30$		0			0
$31$	1.53216	+	2.65378i	0.275184	+	0.476632i	0.970181	−	0.242380i	$-0.0779280\pi$
$31$	1.53216	+	2.65378i	0.275184	+	0.476632i	−0.694998	+	0.719012i	$0.744595\pi$
$32$	−3.16691	−	5.48526i	−0.559837	−	0.969665i
$33$		0			0
$34$	−6.82331	+	11.8183i	−1.17019	+	2.02683i
$35$	0.706571			0.119432
$36$		0			0
$37$	−2.38079			−0.391400			−0.195700	−	0.980664i	$-0.562698\pi$
$37$	−2.38079			−0.391400			−0.195700	+	0.980664i	$0.562698\pi$
$38$	−8.93492	+	15.4757i	−1.44944	+	2.51050i
$39$		0			0
$40$	1.23251	+	2.13477i	0.194877	+	0.337537i
$41$	−4.72945	−	8.19164i	−0.738616	−	1.27932i	−0.953119	−	0.302596i	$-0.902147\pi$
$41$	−4.72945	−	8.19164i	−0.738616	−	1.27932i	0.214503	−	0.976723i	$-0.431187\pi$
$42$		0			0
$43$	−5.96795	+	10.3368i	−0.910103	+	1.57635i	−0.0961869	+	0.995363i	$0.530665\pi$
$43$	−5.96795	+	10.3368i	−0.910103	+	1.57635i	−0.813916	+	0.580982i	$0.802669\pi$
$44$	7.20582			1.08632
$45$		0			0
$46$	−20.2103			−2.97985
$47$	4.86433	−	8.42527i	0.709536	−	1.22895i	−0.255493	−	0.966811i	$-0.582238\pi$
$47$	4.86433	−	8.42527i	0.709536	−	1.22895i	0.965029	−	0.262142i	$-0.0844288\pi$
$48$		0			0
$49$	3.25038	+	5.62982i	0.464340	+	0.804260i
$50$	1.12831	+	1.95429i	0.159567	+	0.276379i
$51$		0			0
$52$	1.54617	−	2.67805i	0.214416	−	0.371379i
$53$	−5.90968			−0.811756			−0.405878	−	0.913927i	$-0.633034\pi$
$53$	−5.90968			−0.811756			−0.405878	+	0.913927i	$0.633034\pi$
$54$		0			0
$55$	2.33021			0.314205
$56$	0.870856	−	1.50837i	0.116373	−	0.201564i
$57$		0			0
$58$	2.71562	+	4.70359i	0.356578	+	0.617611i
$59$	1.48719	+	2.57588i	0.193615	+	0.335351i	0.946446	−	0.322863i	$-0.104645\pi$
$59$	1.48719	+	2.57588i	0.193615	+	0.335351i	−0.752831	+	0.658214i	$0.771312\pi$
$60$		0			0
$61$	4.62078	−	8.00343i	0.591630	−	1.02473i	−0.402383	−	0.915472i	$-0.631818\pi$
$61$	4.62078	−	8.00343i	0.591630	−	1.02473i	0.994013	−	0.109262i	$-0.0348488\pi$
$62$	6.91501			0.878207
$63$		0			0
$64$	−13.0489			−1.63111
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$		0			0
$67$	0.847241	+	1.46746i	0.103507	+	0.179279i	0.913127	−	0.407675i	$-0.133660\pi$
$67$	0.847241	+	1.46746i	0.103507	+	0.179279i	−0.809620	+	0.586954i	$0.800327\pi$
$68$	9.35028	+	16.1952i	1.13389	+	1.96395i
$69$		0			0
$70$	0.797232	−	1.38085i	0.0952875	−	0.165043i
$71$	12.4439			1.47682			0.738410	−	0.674352i	$-0.235577\pi$
$71$	12.4439			1.47682			0.738410	+	0.674352i	$0.235577\pi$
$72$		0			0
$73$	4.88899			0.572213			0.286106	−	0.958198i	$-0.407639\pi$
$73$	4.88899			0.572213			0.286106	+	0.958198i	$0.407639\pi$
$74$	−2.68628	+	4.65277i	−0.312273	+	0.540873i
$75$		0			0
$76$	12.2439	+	21.2071i	1.40447	+	2.43262i
$77$	−0.823229	−	1.42587i	−0.0938157	−	0.162493i
$78$		0			0
$79$	5.51270	−	9.54827i	0.620227	−	1.07426i	−0.369217	−	0.929343i	$-0.620374\pi$
$79$	5.51270	−	9.54827i	0.620227	−	1.07426i	0.989443	−	0.144921i	$-0.0462927\pi$
$80$	−0.622073			−0.0695499
$81$		0			0
$82$	−21.3452			−2.35718
$83$	−0.260845	+	0.451797i	−0.0286315	+	0.0495912i	−0.879986	−	0.474999i	$-0.842448\pi$
$83$	−0.260845	+	0.451797i	−0.0286315	+	0.0495912i	0.851355	+	0.524591i	$0.175782\pi$
$84$		0			0
$85$	3.02368	+	5.23717i	0.327964	+	0.568051i
$86$	13.4674	+	23.3262i	1.45223	+	2.51533i
$87$		0			0
$88$	2.87201	−	4.97447i	0.306157	−	0.530280i
$89$	−10.7608			−1.14065			−0.570323	−	0.821420i	$-0.693182\pi$
$89$	−10.7608			−1.14065			−0.570323	+	0.821420i	$0.693182\pi$
$90$		0			0
$91$	−0.706571			−0.0740687
$92$	−13.8475	+	23.9846i	−1.44370	+	2.50057i
$93$		0			0
$94$	−10.9770	−	19.0127i	−1.13219	−	1.96101i
$95$	3.95942	+	6.85792i	0.406228	+	0.703607i
$96$		0			0
$97$	1.48153	−	2.56609i	0.150427	−	0.260547i	−0.780958	−	0.624584i	$-0.785269\pi$
$97$	1.48153	−	2.56609i	0.150427	−	0.260547i	0.931384	+	0.364037i	$0.118602\pi$
$98$	14.6698			1.48187
$99$		0			0
$100$	3.09235			0.309235
$101$	6.83573	−	11.8398i	0.680181	−	1.17811i	−0.294745	−	0.955576i	$-0.595235\pi$
$101$	6.83573	−	11.8398i	0.680181	−	1.17811i	0.974925	−	0.222532i	$-0.0714321\pi$
$102$		0			0
$103$	3.56535	+	6.17537i	0.351305	+	0.608478i	0.986478	−	0.163892i	$-0.0524048\pi$
$103$	3.56535	+	6.17537i	0.351305	+	0.608478i	−0.635174	+	0.772369i	$0.719071\pi$
$104$	−1.23251	−	2.13477i	−0.120858	−	0.209332i
$105$		0			0
$106$	−6.66796	+	11.5492i	−0.647649	+	1.12176i
$107$	1.70776			0.165095			0.0825477	−	0.996587i	$-0.473694\pi$
$107$	1.70776			0.165095			0.0825477	+	0.996587i	$0.473694\pi$
$108$		0			0
$109$	−3.23628			−0.309979			−0.154989	−	0.987916i	$-0.549534\pi$
$109$	−3.23628			−0.309979			−0.154989	+	0.987916i	$0.549534\pi$
$110$	2.62920	−	4.55391i	0.250685	−	0.434199i
$111$		0			0
$112$	0.219769	+	0.380652i	0.0207662	+	0.0359682i
$113$	−0.339220	−	0.587547i	−0.0319112	−	0.0552717i	0.849629	−	0.527381i	$-0.176826\pi$
$113$	−0.339220	−	0.587547i	−0.0319112	−	0.0552717i	−0.881540	+	0.472109i	$0.843493\pi$
$114$		0			0
$115$	−4.47799	+	7.75611i	−0.417575	+	0.723261i
$116$	7.44266			0.691033
$117$		0			0
$118$	6.71204			0.617893
$119$	2.13645	−	3.70043i	0.195848	−	0.339218i
$120$		0			0
$121$	2.78506	+	4.82387i	0.253187	+	0.438533i
$122$	−10.4274	−	18.0607i	−0.944049	−	1.63514i
$123$		0			0
$124$	4.73797	−	8.20640i	0.425482	−	0.736957i
$125$	1.00000			0.0894427
$126$		0			0
$127$	14.6889			1.30343			0.651714	−	0.758465i	$-0.274050\pi$
$127$	14.6889			1.30343			0.651714	+	0.758465i	$0.274050\pi$
$128$	−8.38942	+	14.5309i	−0.741527	+	1.28436i
$129$		0			0
$130$	−1.12831	−	1.95429i	−0.0989595	−	0.171403i
$131$	−4.53194	−	7.84955i	−0.395957	−	0.685818i	0.597266	−	0.802044i	$-0.296254\pi$
$131$	−4.53194	−	7.84955i	−0.395957	−	0.685818i	−0.993223	+	0.116225i	$0.962921\pi$
$132$		0			0
$133$	2.79761	−	4.84560i	0.242584	−	0.420167i
$134$	3.82381			0.330327
$135$		0			0
$136$	14.9069			1.27825
$137$	−1.01492	+	1.75789i	−0.0867104	+	0.150187i	−0.906119	−	0.423023i	$-0.860969\pi$
$137$	−1.01492	+	1.75789i	−0.0867104	+	0.150187i	0.819408	+	0.573210i	$0.194302\pi$
$138$		0			0
$139$	1.42659	+	2.47092i	0.121002	+	0.209581i	0.920163	−	0.391536i	$-0.128056\pi$
$139$	1.42659	+	2.47092i	0.121002	+	0.209581i	−0.799161	+	0.601117i	$0.794723\pi$
$140$	−1.09248	−	1.89223i	−0.0923316	−	0.159923i
$141$		0			0
$142$	14.0406	−	24.3190i	1.17826	−	2.04081i
$143$	−2.33021			−0.194862
$144$		0			0
$145$	2.40680			0.199874
$146$	5.51630	−	9.55452i	0.456532	−	0.790737i
$147$		0			0
$148$	3.68112	+	6.37589i	0.302586	+	0.524095i
$149$	4.49112	+	7.77885i	0.367927	+	0.637269i	0.989241	−	0.146293i	$-0.0467342\pi$
$149$	4.49112	+	7.77885i	0.367927	+	0.637269i	−0.621314	+	0.783562i	$0.713401\pi$
$150$		0			0
$151$	1.37741	−	2.38575i	0.112092	−	0.194150i	−0.804521	−	0.593924i	$-0.797578\pi$
$151$	1.37741	−	2.38575i	0.112092	−	0.194150i	0.916614	+	0.399774i	$0.130911\pi$
$152$	19.5201			1.58329
$153$		0			0
$154$	−3.71544			−0.299398
$155$	1.53216	−	2.65378i	0.123066	−	0.213156i
$156$		0			0
$157$	−12.2493	−	21.2164i	−0.977601	−	1.69325i	−0.671071	−	0.741393i	$-0.734166\pi$
$157$	−12.2493	−	21.2164i	−0.977601	−	1.69325i	−0.306529	−	0.951861i	$-0.599168\pi$
$158$	−12.4401	−	21.5468i	−0.989679	−	1.71418i
$159$		0			0
$160$	−3.16691	+	5.48526i	−0.250367	+	0.433648i
$161$	6.32804			0.498719
$162$		0			0
$163$	−18.2489			−1.42937			−0.714684	−	0.699448i	$-0.753429\pi$
$163$	−18.2489			−1.42937			−0.714684	+	0.699448i	$0.753429\pi$
$164$	−14.6251	+	25.3314i	−1.14203	+	1.97805i
$165$		0			0
$166$	0.588630	+	1.01954i	0.0456865	+	0.0791314i
$167$	2.80066	+	4.85088i	0.216721	+	0.375372i	0.953804	−	0.300431i	$-0.0971304\pi$
$167$	2.80066	+	4.85088i	0.216721	+	0.375372i	−0.737082	+	0.675803i	$0.763797\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	13.6466			1.04665
$171$		0			0
$172$	36.9100			2.81436
$173$	−1.80130	+	3.11994i	−0.136950	+	0.237205i	−0.926341	−	0.376687i	$-0.877063\pi$
$173$	−1.80130	+	3.11994i	−0.136950	+	0.237205i	0.789391	+	0.613891i	$0.210397\pi$
$174$		0			0
$175$	−0.353285	−	0.611908i	−0.0267059	−	0.0462559i
$176$	0.724780	+	1.25536i	0.0546324	+	0.0946260i
$177$		0			0
$178$	−12.1416	+	21.0298i	−0.910050	+	1.57625i
$179$	−15.3123			−1.14449			−0.572246	−	0.820082i	$-0.693928\pi$
$179$	−15.3123			−1.14449			−0.572246	+	0.820082i	$0.693928\pi$
$180$		0			0
$181$	−7.23734			−0.537947			−0.268974	−	0.963148i	$-0.586684\pi$
$181$	−7.23734			−0.537947			−0.268974	+	0.963148i	$0.586684\pi$
$182$	−0.797232	+	1.38085i	−0.0590948	+	0.102355i
$183$		0			0
$184$	11.0384	+	19.1190i	0.813758	+	1.40947i
$185$	1.19040	+	2.06183i	0.0875197	+	0.151589i
$186$		0			0
$187$	7.04581	−	12.2037i	0.515241	−	0.892423i
$188$	−30.0844			−2.19413
$189$		0			0
$190$	17.8698			1.29641
$191$	−9.68393	+	16.7731i	−0.700705	+	1.21366i	0.267515	+	0.963554i	$0.413798\pi$
$191$	−9.68393	+	16.7731i	−0.700705	+	1.21366i	−0.968219	+	0.250102i	$0.919536\pi$
$192$		0			0
$193$	−2.52773	−	4.37816i	−0.181950	−	0.315147i	0.760595	−	0.649227i	$-0.224908\pi$
$193$	−2.52773	−	4.37816i	−0.181950	−	0.315147i	−0.942545	+	0.334081i	$0.891574\pi$
$194$	−3.34326	−	5.79069i	−0.240032	−	0.415747i
$195$		0			0
$196$	10.0513	−	17.4094i	0.717951	−	1.24353i
$197$	−6.35430			−0.452725			−0.226363	−	0.974043i	$-0.572683\pi$
$197$	−6.35430			−0.452725			−0.226363	+	0.974043i	$0.572683\pi$
$198$		0			0
$199$	−16.7816			−1.18961			−0.594807	−	0.803868i	$-0.702772\pi$
$199$	−16.7816			−1.18961			−0.594807	+	0.803868i	$0.702772\pi$
$200$	1.23251	−	2.13477i	0.0871517	−	0.150951i
$201$		0			0
$202$	−15.4257	−	26.7181i	−1.08535	−	1.87988i
$203$	−0.850286	−	1.47274i	−0.0596784	−	0.103366i
$204$		0			0
$205$	−4.72945	+	8.19164i	−0.330319	+	0.572129i
$206$	16.0913			1.12114
$207$		0			0
$208$	0.622073			0.0431330
$209$	9.22628	−	15.9804i	0.638195	−	1.10539i
$210$		0			0
$211$	5.68155	+	9.84073i	0.391134	+	0.677464i	0.992599	−	0.121435i	$-0.0387495\pi$
$211$	5.68155	+	9.84073i	0.391134	+	0.677464i	−0.601465	+	0.798899i	$0.705416\pi$
$212$	9.13739	+	15.8264i	0.627559	+	1.08696i
$213$		0			0
$214$	1.92689	−	3.33747i	0.131719	−	0.228144i
$215$	11.9359			0.814021
$216$		0			0
$217$	−2.16516			−0.146980
$218$	−3.65153	+	6.32463i	−0.247313	+	0.428358i
$219$		0			0
$220$	−3.60291	−	6.24043i	−0.242908	−	0.420729i
$221$	−3.02368	−	5.23717i	−0.203395	−	0.352290i
$222$		0			0
$223$	10.0428	−	17.3947i	0.672518	−	1.16484i	−0.304669	−	0.952458i	$-0.598546\pi$
$223$	10.0428	−	17.3947i	0.672518	−	1.16484i	0.977188	−	0.212378i	$-0.0681207\pi$
$224$	4.47530			0.299018
$225$		0			0
$226$	−1.53098			−0.101840
$227$	−5.67412	+	9.82787i	−0.376605	+	0.652299i	−0.990566	−	0.137038i	$-0.956242\pi$
$227$	−5.67412	+	9.82787i	−0.376605	+	0.652299i	0.613961	+	0.789336i	$0.289575\pi$
$228$		0			0
$229$	1.84068	+	3.18815i	0.121635	+	0.210679i	0.920413	−	0.390948i	$-0.127853\pi$
$229$	1.84068	+	3.18815i	0.121635	+	0.210679i	−0.798777	+	0.601627i	$0.794519\pi$
$230$	10.1051	+	17.5026i	0.666314	+	1.15409i
$231$		0			0
$232$	2.96640	−	5.13796i	0.194754	−	0.337324i
$233$	−12.5286			−0.820778			−0.410389	−	0.911911i	$-0.634607\pi$
$233$	−12.5286			−0.820778			−0.410389	+	0.911911i	$0.634607\pi$
$234$		0			0
$235$	−9.72867			−0.634628
$236$	4.59890	−	7.96552i	0.299363	−	0.518511i
$237$		0			0
$238$	−4.82115	−	8.35048i	−0.312509	−	0.541281i
$239$	1.66443	+	2.88288i	0.107663	+	0.186478i	0.914823	−	0.403855i	$-0.132330\pi$
$239$	1.66443	+	2.88288i	0.107663	+	0.186478i	−0.807160	+	0.590333i	$0.798996\pi$
$240$		0			0
$241$	13.3919	−	23.1955i	0.862649	−	1.49415i	−0.00671442	−	0.999977i	$-0.502137\pi$
$241$	13.3919	−	23.1955i	0.862649	−	1.49415i	0.869363	−	0.494174i	$-0.164529\pi$
$242$	12.5697			0.808009
$243$		0			0
$244$	−28.5781			−1.82953
$245$	3.25038	−	5.62982i	0.207659	−	0.359676i
$246$		0			0
$247$	−3.95942	−	6.85792i	−0.251932	−	0.436359i
$248$	−3.77680	−	6.54161i	−0.239827	−	0.415393i
$249$		0			0
$250$	1.12831	−	1.95429i	0.0713607	−	0.123600i
$251$	6.05718			0.382326			0.191163	−	0.981558i	$-0.438774\pi$
$251$	6.05718			0.382326			0.191163	+	0.981558i	$0.438774\pi$
$252$		0			0
$253$	20.8693			1.31204
$254$	16.5737	−	28.7064i	1.03992	−	1.80120i
$255$		0			0
$256$	5.88285	+	10.1894i	0.367678	+	0.636837i
$257$	−1.97635	−	3.42314i	−0.123281	−	0.213529i	0.797779	−	0.602951i	$-0.206008\pi$
$257$	−1.97635	−	3.42314i	−0.123281	−	0.213529i	−0.921060	+	0.389421i	$0.872675\pi$
$258$		0			0
$259$	0.841099	−	1.45683i	0.0522634	−	0.0905228i
$260$	−3.09235			−0.191779
$261$		0			0
$262$	−20.4538			−1.26364
$263$	5.65057	−	9.78708i	0.348429	−	0.603497i	−0.637541	−	0.770416i	$-0.720048\pi$
$263$	5.65057	−	9.78708i	0.348429	−	0.603497i	0.985971	+	0.166919i	$0.0533818\pi$
$264$		0			0
$265$	2.95484	+	5.11793i	0.181514	+	0.314392i
$266$	−6.31315	−	10.9347i	−0.387084	−	0.670450i
$267$		0			0
$268$	2.61997	−	4.53791i	0.160040	−	0.277197i
$269$	20.7773			1.26681			0.633407	−	0.773819i	$-0.281656\pi$
$269$	20.7773			1.26681			0.633407	+	0.773819i	$0.281656\pi$
$270$		0			0
$271$	−1.72567			−0.104827			−0.0524136	−	0.998625i	$-0.516691\pi$
$271$	−1.72567			−0.104827			−0.0524136	+	0.998625i	$0.516691\pi$
$272$	−1.88095	+	3.25790i	−0.114049	+	0.197539i
$273$		0			0
$274$	2.29029	+	3.96690i	0.138361	+	0.239649i
$275$	−1.16510	−	2.01802i	−0.0702585	−	0.121691i
$276$		0			0
$277$	1.73361	−	3.00270i	0.104163	−	0.180415i	−0.809233	−	0.587488i	$-0.800117\pi$
$277$	1.73361	−	3.00270i	0.104163	−	0.180415i	0.913396	+	0.407073i	$0.133450\pi$
$278$	6.43855			0.386158
$279$		0			0
$280$	−1.74171			−0.104087
$281$	0.586316	−	1.01553i	0.0349767	−	0.0605814i	−0.848007	−	0.529985i	$-0.822198\pi$
$281$	0.586316	−	1.01553i	0.0349767	−	0.0605814i	0.882984	+	0.469403i	$0.155531\pi$
$282$		0			0
$283$	−10.9061	−	18.8899i	−0.648301	−	1.12289i	−0.983529	−	0.180753i	$-0.942147\pi$
$283$	−10.9061	−	18.8899i	−0.648301	−	1.12289i	0.335228	−	0.942137i	$-0.391187\pi$
$284$	−19.2405	−	33.3255i	−1.14171	−	1.97750i
$285$		0			0
$286$	−2.62920	+	4.55391i	−0.155468	+	0.269279i
$287$	6.68338			0.394507
$288$		0			0
$289$	19.5706			1.15121
$290$	2.71562	−	4.70359i	0.159467	−	0.276204i
$291$		0			0
$292$	−7.55923	−	13.0930i	−0.442371	−	0.766208i
$293$	−13.9460	−	24.1551i	−0.814732	−	1.41116i	−0.909520	−	0.415659i	$-0.863551\pi$
$293$	−13.9460	−	24.1551i	−0.814732	−	1.41116i	0.0947888	−	0.995497i	$-0.469782\pi$
$294$		0			0
$295$	1.48719	−	2.57588i	0.0865873	−	0.149974i
$296$	5.86870			0.341112
$297$		0			0
$298$	20.2695			1.17418
$299$	4.47799	−	7.75611i	0.258969	−	0.448548i
$300$		0			0
$301$	−4.21678	−	7.30367i	−0.243051	−	0.420977i
$302$	−3.10831	−	5.38374i	−0.178863	−	0.309800i
$303$		0			0
$304$	−2.46305	+	4.26613i	−0.141266	+	0.244679i
$305$	−9.24156			−0.529170
$306$		0			0
$307$	−0.574330			−0.0327787			−0.0163894	−	0.999866i	$-0.505217\pi$
$307$	−0.574330			−0.0327787			−0.0163894	+	0.999866i	$0.505217\pi$
$308$	−2.54571	+	4.40930i	−0.145055	+	0.251243i
$309$		0			0
$310$	−3.45750	−	5.98857i	−0.196373	−	0.340128i
$311$	11.5536	+	20.0114i	0.655143	+	1.13474i	0.981858	+	0.189618i	$0.0607249\pi$
$311$	11.5536	+	20.0114i	0.655143	+	1.13474i	−0.326715	+	0.945123i	$0.605942\pi$
$312$		0			0
$313$	−12.7427	+	22.0710i	−0.720260	+	1.24753i	0.240635	+	0.970616i	$0.422644\pi$
$313$	−12.7427	+	22.0710i	−0.720260	+	1.24753i	−0.960895	+	0.276912i	$0.910689\pi$
$314$	−55.2841			−3.11986
$315$		0			0
$316$	−34.0944			−1.91796
$317$	16.1778	−	28.0208i	0.908638	−	1.57381i	0.0926799	−	0.995696i	$-0.470457\pi$
$317$	16.1778	−	28.0208i	0.908638	−	1.57381i	0.815958	−	0.578111i	$-0.196210\pi$
$318$		0			0
$319$	−2.80417	−	4.85697i	−0.157003	−	0.271938i
$320$	6.52446	+	11.3007i	0.364728	+	0.631728i
$321$		0			0
$322$	7.14000	−	12.3668i	0.397897	−	0.689177i
$323$	47.8881			2.66457
$324$		0			0
$325$	−1.00000			−0.0554700
$326$	−20.5905	+	35.6638i	−1.14040	+	1.97523i
$327$		0			0
$328$	11.6582	+	20.1926i	0.643716	+	1.11495i
$329$	3.43700	+	5.95305i	0.189488	+	0.328202i
$330$		0			0
$331$	−15.0848	+	26.1276i	−0.829135	+	1.43610i	0.0695818	+	0.997576i	$0.477834\pi$
$331$	−15.0848	+	26.1276i	−0.829135	+	1.43610i	−0.898717	+	0.438529i	$0.855500\pi$
$332$	1.61325			0.0885386
$333$		0			0
$334$	12.6400			0.691633
$335$	0.847241	−	1.46746i	0.0462897	−	0.0801762i
$336$		0			0
$337$	−3.28919	−	5.69705i	−0.179174	−	0.310338i	0.762424	−	0.647078i	$-0.224009\pi$
$337$	−3.28919	−	5.69705i	−0.179174	−	0.310338i	−0.941598	+	0.336740i	$0.890676\pi$
$338$	1.12831	+	1.95429i	0.0613721	+	0.106300i
$339$		0			0
$340$	9.35028	−	16.1952i	0.507090	−	0.878306i
$341$	−7.14050			−0.386680
$342$		0			0
$343$	−9.53924			−0.515071
$344$	14.7111	−	25.4804i	0.793170	−	1.37381i
$345$		0			0
$346$	4.06485	+	7.04053i	0.218528	+	0.378501i
$347$	−1.00532	−	1.74126i	−0.0539682	−	0.0934756i	0.837779	−	0.546009i	$-0.183854\pi$
$347$	−1.00532	−	1.74126i	−0.0539682	−	0.0934756i	−0.891747	+	0.452534i	$0.850520\pi$
$348$		0			0
$349$	−7.00194	+	12.1277i	−0.374805	+	0.649182i	−0.990298	−	0.138961i	$-0.955624\pi$
$349$	−7.00194	+	12.1277i	−0.374805	+	0.649182i	0.615493	+	0.788143i	$0.288957\pi$
$350$	−1.59446			−0.0852277
$351$		0			0
$352$	14.7591			0.786665
$353$	17.2999	−	29.9643i	0.920780	−	1.59484i	0.122570	−	0.992460i	$-0.460886\pi$
$353$	17.2999	−	29.9643i	0.920780	−	1.59484i	0.798211	−	0.602379i	$-0.205780\pi$
$354$		0			0
$355$	−6.22195	−	10.7767i	−0.330227	−	0.571970i
$356$	16.6381	+	28.8181i	0.881820	+	1.52736i
$357$		0			0
$358$	−17.2770	+	29.9247i	−0.913118	+	1.58157i
$359$	−22.7679			−1.20164			−0.600822	−	0.799382i	$-0.705160\pi$
$359$	−22.7679			−1.20164			−0.600822	+	0.799382i	$0.705160\pi$
$360$		0			0
$361$	43.7080			2.30042
$362$	−8.16597	+	14.1439i	−0.429194	+	0.743386i
$363$		0			0
$364$	1.09248	+	1.89223i	0.0572616	+	0.0991800i
$365$	−2.44449	−	4.23399i	−0.127951	−	0.221617i
$366$		0			0
$367$	5.69696	−	9.86742i	0.297379	−	0.515075i	−0.678157	−	0.734917i	$-0.737221\pi$
$367$	5.69696	−	9.86742i	0.297379	−	0.515075i	0.975535	+	0.219842i	$0.0705543\pi$
$368$	−5.57128			−0.290423
$369$		0			0
$370$	5.37255			0.279306
$371$	2.08780	−	3.61618i	0.108393	−	0.187743i
$372$		0			0
$373$	−1.29760	−	2.24750i	−0.0671870	−	0.116371i	0.830475	−	0.557056i	$-0.188069\pi$
$373$	−1.29760	−	2.24750i	−0.0671870	−	0.116371i	−0.897662	+	0.440685i	$0.854736\pi$
$374$	−15.8997	−	27.5392i	−0.822156	−	1.42402i
$375$		0			0
$376$	−11.9907	+	20.7685i	−0.618373	+	1.07105i
$377$	−2.40680			−0.123956
$378$		0			0
$379$	2.38710			0.122617			0.0613084	−	0.998119i	$-0.480473\pi$
$379$	2.38710			0.122617			0.0613084	+	0.998119i	$0.480473\pi$
$380$	12.2439	−	21.2071i	0.628099	−	1.08790i
$381$		0			0
$382$	21.8530	+	37.8505i	1.11810	+	1.93660i
$383$	−16.1363	−	27.9488i	−0.824525	−	1.42812i	−0.902282	−	0.431147i	$-0.858109\pi$
$383$	−16.1363	−	27.9488i	−0.824525	−	1.42812i	0.0777565	−	0.996972i	$-0.475224\pi$
$384$		0			0
$385$	−0.823229	+	1.42587i	−0.0419556	+	0.0726693i
$386$	−11.4083			−0.580666
$387$		0			0
$388$	−9.16282			−0.465172
$389$	3.75052	−	6.49610i	0.190159	−	0.329365i	−0.755144	−	0.655559i	$-0.772433\pi$
$389$	3.75052	−	6.49610i	0.190159	−	0.329365i	0.945303	+	0.326194i	$0.105766\pi$
$390$		0			0
$391$	27.0801	+	46.9040i	1.36950	+	2.37204i
$392$	−8.01226	−	13.8776i	−0.404680	−	0.700926i
$393$		0			0
$394$	−7.16963	+	12.4182i	−0.361201	+	0.625618i
$395$	−11.0254			−0.554748
$396$		0			0
$397$	−22.5214			−1.13032			−0.565158	−	0.824983i	$-0.691185\pi$
$397$	−22.5214			−1.13032			−0.565158	+	0.824983i	$0.691185\pi$
$398$	−18.9349	+	32.7961i	−0.949119	+	1.64392i
$399$		0			0
$400$	0.311036	+	0.538731i	0.0155518	+	0.0269366i
$401$	1.26630	+	2.19330i	0.0632362	+	0.109528i	0.895910	−	0.444235i	$-0.146525\pi$
$401$	1.26630	+	2.19330i	0.0632362	+	0.109528i	−0.832674	+	0.553763i	$0.813191\pi$
$402$		0			0
$403$	−1.53216	+	2.65378i	−0.0763222	+	0.132194i
$404$	−42.2770			−2.10336
$405$		0			0
$406$	−3.83755			−0.190454
$407$	2.77387	−	4.80449i	0.137496	−	0.238150i
$408$		0			0
$409$	3.18542	+	5.51731i	0.157509	+	0.272814i	0.933970	−	0.357352i	$-0.116320\pi$
$409$	3.18542	+	5.51731i	0.157509	+	0.272814i	−0.776461	+	0.630166i	$0.782987\pi$
$410$	10.6726	+	18.4855i	0.527081	+	0.912931i
$411$		0			0
$412$	11.0253	−	19.0964i	0.543179	−	0.940813i
$413$	−2.10160			−0.103413
$414$		0			0
$415$	0.521691			0.0256088
$416$	3.16691	−	5.48526i	0.155271	−	0.268937i
$417$		0			0
$418$	−20.8202	−	36.0617i	−1.01835	−	1.76384i
$419$	15.4679	+	26.7912i	0.755657	+	1.30884i	0.945047	+	0.326934i	$0.106016\pi$
$419$	15.4679	+	26.7912i	0.755657	+	1.30884i	−0.189390	+	0.981902i	$0.560651\pi$
$420$		0			0
$421$	6.98221	−	12.0935i	0.340292	−	0.589403i	−0.644195	−	0.764861i	$-0.722807\pi$
$421$	6.98221	−	12.0935i	0.340292	−	0.589403i	0.984487	+	0.175459i	$0.0561408\pi$
$422$	25.6422			1.24824
$423$		0			0
$424$	14.5675			0.707459
$425$	3.02368	−	5.23717i	0.146670	−	0.254040i
$426$		0			0
$427$	3.26491	+	5.65499i	0.158000	+	0.273664i
$428$	−2.64050	−	4.57348i	−0.127633	−	0.221067i
$429$		0			0
$430$	13.4674	−	23.3262i	0.649456	−	1.12489i
$431$	−20.2027			−0.973131			−0.486566	−	0.873644i	$-0.661751\pi$
$431$	−20.2027			−0.973131			−0.486566	+	0.873644i	$0.661751\pi$
$432$		0			0
$433$	−13.7657			−0.661537			−0.330768	−	0.943712i	$-0.607308\pi$
$433$	−13.7657			−0.661537			−0.330768	+	0.943712i	$0.607308\pi$
$434$	−2.44297	+	4.23135i	−0.117266	+	0.203111i
$435$		0			0
$436$	5.00385	+	8.66692i	0.239641	+	0.415070i
$437$	35.4605	+	61.4194i	1.69631	+	2.93809i
$438$		0			0
$439$	−3.88378	+	6.72690i	−0.185363	+	0.321058i	−0.943699	−	0.330806i	$-0.892679\pi$
$439$	−3.88378	+	6.72690i	−0.185363	+	0.321058i	0.758336	+	0.651864i	$0.226013\pi$
$440$	−5.74402			−0.273835
$441$		0			0
$442$	−13.6466			−0.649104
$443$	8.21573	−	14.2301i	0.390341	−	0.676090i	−0.602153	−	0.798380i	$-0.705690\pi$
$443$	8.21573	−	14.2301i	0.390341	−	0.676090i	0.992494	+	0.122290i	$0.0390238\pi$
$444$		0			0
$445$	5.38042	+	9.31916i	0.255056	+	0.441771i
$446$	−22.6629	−	39.2533i	−1.07312	−	1.85870i
$447$		0			0
$448$	4.60999	−	7.98474i	0.217802	−	0.377244i
$449$	−9.97715			−0.470851			−0.235425	−	0.971892i	$-0.575648\pi$
$449$	−9.97715			−0.470851			−0.235425	+	0.971892i	$0.575648\pi$
$450$		0			0
$451$	22.0412			1.03788
$452$	−1.04899	+	1.81690i	−0.0493402	+	0.0854598i
$453$		0			0
$454$	12.8044	+	22.1778i	0.600938	+	1.04086i
$455$	0.353285	+	0.611908i	0.0165623	+	0.0286867i
$456$		0			0
$457$	8.67799	−	15.0307i	0.405939	−	0.703108i	−0.588491	−	0.808504i	$-0.700278\pi$
$457$	8.67799	−	15.0307i	0.405939	−	0.703108i	0.994430	+	0.105396i	$0.0336111\pi$
$458$	8.30743			0.388181
$459$		0			0
$460$	27.6950			1.29129
$461$	−5.29646	+	9.17373i	−0.246681	+	0.427263i	−0.962603	−	0.270917i	$-0.912673\pi$
$461$	−5.29646	+	9.17373i	−0.246681	+	0.427263i	0.715922	+	0.698180i	$0.246006\pi$
$462$		0			0
$463$	1.80372	+	3.12414i	0.0838260	+	0.145191i	0.904890	−	0.425645i	$-0.139953\pi$
$463$	1.80372	+	3.12414i	0.0838260	+	0.145191i	−0.821064	+	0.570836i	$0.806619\pi$
$464$	0.748602	+	1.29662i	0.0347530	+	0.0601939i
$465$		0			0
$466$	−14.1362	+	24.4846i	−0.654847	+	1.13423i
$467$	−6.96611			−0.322353			−0.161177	−	0.986926i	$-0.551529\pi$
$467$	−6.96611			−0.322353			−0.161177	+	0.986926i	$0.551529\pi$
$468$		0			0
$469$	−1.19727			−0.0552849
$470$	−10.9770	+	19.0127i	−0.506330	+	0.876989i
$471$		0			0
$472$	−3.66594	−	6.34960i	−0.168739	−	0.292264i
$473$	−13.9066	−	24.0869i	−0.639425	−	1.10752i
$474$		0			0
$475$	3.95942	−	6.85792i	0.181671	−	0.314663i
$476$	−13.2133			−0.605629
$477$		0			0
$478$	7.51200			0.343591
$479$	−11.0303	+	19.1050i	−0.503987	+	0.872932i	0.496002	+	0.868321i	$0.334801\pi$
$479$	−11.0303	+	19.1050i	−0.503987	+	0.872932i	−0.999989	+	0.00461038i	$0.998532\pi$
$480$		0			0
$481$	−1.19040	−	2.06183i	−0.0542774	−	0.0940112i
$482$	−30.2205	−	52.3434i	−1.37651	−	2.38418i
$483$		0			0
$484$	8.61238	−	14.9171i	0.391472	−	0.678049i
$485$	−2.96306			−0.134546
$486$		0			0
$487$	−5.19759			−0.235525			−0.117763	−	0.993042i	$-0.537572\pi$
$487$	−5.19759			−0.235525			−0.117763	+	0.993042i	$0.537572\pi$
$488$	−11.3903	+	19.7286i	−0.515616	+	0.893073i
$489$		0			0
$490$	−7.33488	−	12.7044i	−0.331356	−	0.573926i
$491$	−1.11828	−	1.93692i	−0.0504675	−	0.0874122i	0.839688	−	0.543069i	$-0.182738\pi$
$491$	−1.11828	−	1.93692i	−0.0504675	−	0.0874122i	−0.890156	+	0.455657i	$0.849404\pi$
$492$		0			0
$493$	7.27739	−	12.6048i	0.327757	−	0.567692i
$494$	−17.8698			−0.804002
$495$		0			0
$496$	1.90623			0.0855922
$497$	−4.39625	+	7.61453i	−0.197199	+	0.341558i
$498$		0			0
$499$	10.6446	+	18.4370i	0.476519	+	0.825356i	0.999638	−	0.0269043i	$-0.00856493\pi$
$499$	10.6446	+	18.4370i	0.476519	+	0.825356i	−0.523119	+	0.852260i	$0.675232\pi$
$500$	−1.54617	−	2.67805i	−0.0691470	−	0.119766i
$501$		0			0
$502$	6.83439	−	11.8375i	0.305034	−	0.528334i
$503$	33.5371			1.49534			0.747672	−	0.664068i	$-0.231171\pi$
$503$	33.5371			1.49534			0.747672	+	0.664068i	$0.231171\pi$
$504$		0			0
$505$	−13.6715			−0.608372
$506$	23.5471	−	40.7848i	1.04680	−	1.81311i
$507$		0			0
$508$	−22.7116	−	39.3376i	−1.00766	−	1.74533i
$509$	−1.53741	−	2.66287i	−0.0681444	−	0.118030i	0.829940	−	0.557853i	$-0.188375\pi$
$509$	−1.53741	−	2.66287i	−0.0681444	−	0.118030i	−0.898085	+	0.439823i	$0.855041\pi$
$510$		0			0
$511$	−1.72721	+	2.99161i	−0.0764072	+	0.132341i
$512$	−7.00695			−0.309666
$513$		0			0
$514$	−8.91975			−0.393433
$515$	3.56535	−	6.17537i	0.157108	−	0.272119i
$516$		0			0
$517$	11.3349	+	19.6327i	0.498509	+	0.863443i
$518$	−1.89804	−	3.28751i	−0.0833953	−	0.144445i
$519$		0			0
$520$	−1.23251	+	2.13477i	−0.0540492	+	0.0936159i
$521$	−32.8855			−1.44074			−0.720371	−	0.693589i	$-0.756028\pi$
$521$	−32.8855			−1.44074			−0.720371	+	0.693589i	$0.756028\pi$
$522$		0			0
$523$	19.0090			0.831206			0.415603	−	0.909546i	$-0.363571\pi$
$523$	19.0090			0.831206			0.415603	+	0.909546i	$0.363571\pi$
$524$	−14.0143	+	24.2735i	−0.612219	+	1.06039i
$525$		0			0
$526$	−12.7512	−	22.0858i	−0.555979	−	0.962985i
$527$	−9.26552	−	16.0483i	−0.403612	−	0.699077i
$528$		0			0
$529$	−28.6049	+	49.5451i	−1.24369	+	2.15413i
$530$	13.3359			0.579275
$531$		0			0
$532$	−17.3024			−0.750153
$533$	4.72945	−	8.19164i	0.204855	−	0.354819i
$534$		0			0
$535$	−0.853881	−	1.47896i	−0.0369165	−	0.0639412i
$536$	−2.08847	−	3.61733i	−0.0902081	−	0.156245i
$537$		0			0
$538$	23.4433	−	40.6049i	1.01071	−	1.75060i
$539$	−15.1481			−0.652476
$540$		0			0
$541$	−13.4399			−0.577825			−0.288912	−	0.957356i	$-0.593294\pi$
$541$	−13.4399			−0.577825			−0.288912	+	0.957356i	$0.593294\pi$
$542$	−1.94710	+	3.37247i	−0.0836351	+	0.144860i
$543$		0			0
$544$	19.1515	+	33.1713i	0.821113	+	1.42221i
$545$	1.61814	+	2.80270i	0.0693134	+	0.120054i
$546$		0			0
$547$	−5.66269	+	9.80807i	−0.242119	+	0.419363i	−0.961318	−	0.275442i	$-0.911176\pi$
$547$	−5.66269	+	9.80807i	−0.242119	+	0.419363i	0.719198	+	0.694805i	$0.244509\pi$
$548$	6.27697			0.268139
$549$		0			0
$550$	−5.25841			−0.224219
$551$	9.52952	−	16.5056i	0.405971	−	0.703163i
$552$		0			0
$553$	3.89511	+	6.74653i	0.165637	+	0.286892i
$554$	−3.91210	−	6.77596i	−0.166209	−	0.287883i
$555$		0			0
$556$	4.41151	−	7.64096i	0.187090	−	0.324049i
$557$	−4.71355			−0.199720			−0.0998598	−	0.995002i	$-0.531839\pi$
$557$	−4.71355			−0.199720			−0.0998598	+	0.995002i	$0.531839\pi$
$558$		0			0
$559$	−11.9359			−0.504835
$560$	0.219769	−	0.380652i	0.00928695	−	0.0160855i
$561$		0			0
$562$	−1.32309	−	2.29167i	−0.0558114	−	0.0966681i
$563$	17.6579	+	30.5844i	0.744193	+	1.28898i	0.950571	+	0.310508i	$0.100499\pi$
$563$	17.6579	+	30.5844i	0.744193	+	1.28898i	−0.206377	+	0.978473i	$0.566167\pi$
$564$		0			0
$565$	−0.339220	+	0.587547i	−0.0142711	+	0.0247183i
$566$	−49.2220			−2.06895
$567$		0			0
$568$	−30.6745			−1.28707
$569$	−13.2680	+	22.9808i	−0.556222	+	0.963404i	0.441586	+	0.897219i	$0.354416\pi$
$569$	−13.2680	+	22.9808i	−0.556222	+	0.963404i	−0.997807	+	0.0661850i	$0.978917\pi$
$570$		0			0
$571$	16.8771	+	29.2320i	0.706284	+	1.22332i	0.966226	+	0.257696i	$0.0829632\pi$
$571$	16.8771	+	29.2320i	0.706284	+	1.22332i	−0.259942	+	0.965624i	$0.583703\pi$
$572$	3.60291	+	6.24043i	0.150645	+	0.260925i
$573$		0			0
$574$	7.54093	−	13.0613i	0.314752	−	0.545167i
$575$	8.95599			0.373491
$576$		0			0
$577$	−30.7531			−1.28027			−0.640133	−	0.768264i	$-0.721121\pi$
$577$	−30.7531			−1.28027			−0.640133	+	0.768264i	$0.721121\pi$
$578$	22.0817	−	38.2467i	0.918480	−	1.59085i
$579$		0			0
$580$	−3.72133	−	6.44553i	−0.154520	−	0.267636i
$581$	−0.184306	−	0.319227i	−0.00764629	−	0.0132438i
$582$		0			0
$583$	6.88539	−	11.9259i	0.285164	−	0.493918i
$584$	−12.0515			−0.498693
$585$		0			0
$586$	−62.9416			−2.60009
$587$	2.61862	−	4.53559i	0.108082	−	0.187204i	−0.806911	−	0.590673i	$-0.798862\pi$
$587$	2.61862	−	4.53559i	0.108082	−	0.187204i	0.914993	+	0.403469i	$0.132196\pi$
$588$		0			0
$589$	−12.1329	−	21.0148i	−0.499928	−	0.865901i
$590$	−3.35602	−	5.81279i	−0.138165	−	0.239309i
$591$		0			0
$592$	−0.740513	+	1.28261i	−0.0304349	+	0.0527148i
$593$	−15.8490			−0.650839			−0.325420	−	0.945570i	$-0.605506\pi$
$593$	−15.8490			−0.650839			−0.325420	+	0.945570i	$0.605506\pi$
$594$		0			0
$595$	−4.27289			−0.175171
$596$	13.8881	−	24.0549i	0.568880	−	0.985329i
$597$		0			0
$598$	−10.1051	−	17.5026i	−0.413230	−	0.715736i
$599$	13.1618	+	22.7969i	0.537775	+	0.931454i	0.999023	+	0.0441829i	$0.0140684\pi$
$599$	13.1618	+	22.7969i	0.537775	+	0.931454i	−0.461248	+	0.887271i	$0.652598\pi$
$600$		0			0
$601$	−0.901862	+	1.56207i	−0.0367877	+	0.0637182i	−0.883833	−	0.467802i	$-0.845046\pi$
$601$	−0.901862	+	1.56207i	−0.0367877	+	0.0637182i	0.847045	+	0.531521i	$0.178379\pi$
$602$	−19.0314			−0.775660
$603$		0			0
$604$	−8.51889			−0.346629
$605$	2.78506	−	4.82387i	0.113229	−	0.196118i
$606$		0			0
$607$	−6.26933	−	10.8588i	−0.254464	−	0.440745i	0.710286	−	0.703914i	$-0.248566\pi$
$607$	−6.26933	−	10.8588i	−0.254464	−	0.440745i	−0.964750	+	0.263168i	$0.915232\pi$
$608$	25.0783	+	43.4369i	1.01706	+	1.76160i
$609$		0			0
$610$	−10.4274	+	18.0607i	−0.422192	+	0.731257i
$611$	9.72867			0.393580
$612$		0			0
$613$	9.01785			0.364228			0.182114	−	0.983277i	$-0.441706\pi$
$613$	9.01785			0.364228			0.182114	+	0.983277i	$0.441706\pi$
$614$	−0.648023	+	1.12241i	−0.0261521	+	0.0452968i
$615$		0			0
$616$	2.02928	+	3.51481i	0.0817619	+	0.141616i
$617$	7.34095	+	12.7149i	0.295536	+	0.511883i	0.975109	−	0.221725i	$-0.0711686\pi$
$617$	7.34095	+	12.7149i	0.295536	+	0.511883i	−0.679574	+	0.733607i	$0.737835\pi$
$618$		0			0
$619$	20.8355	−	36.0881i	0.837448	−	1.45050i	−0.0545741	−	0.998510i	$-0.517380\pi$
$619$	20.8355	−	36.0881i	0.837448	−	1.45050i	0.892022	−	0.451992i	$-0.149287\pi$
$620$	−9.47594			−0.380563
$621$		0			0
$622$	52.1441			2.09079
$623$	3.80165	−	6.58465i	0.152310	−	0.263808i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	28.7555	+	49.8060i	1.14930	+	1.99065i
$627$		0			0
$628$	−37.8791	+	65.6086i	−1.51154	+	2.61807i
$629$	14.3975			0.574067
$630$		0			0
$631$	−19.8681			−0.790936			−0.395468	−	0.918480i	$-0.629418\pi$
$631$	−19.8681			−0.790936			−0.395468	+	0.918480i	$0.629418\pi$
$632$	−13.5889	+	23.5367i	−0.540538	+	0.936239i
$633$		0			0
$634$	−36.5073	−	63.2325i	−1.44989	−	2.51128i
$635$	−7.34445	−	12.7210i	−0.291456	−	0.504816i
$636$		0			0
$637$	−3.25038	+	5.62982i	−0.128785	+	0.223062i
$638$	−12.6559			−0.501053
$639$		0			0
$640$	16.7788			0.663242
$641$	11.1576	−	19.3256i	0.440700	−	0.763315i	−0.557041	−	0.830485i	$-0.688063\pi$
$641$	11.1576	−	19.3256i	0.440700	−	0.763315i	0.997742	+	0.0671694i	$0.0213968\pi$
$642$		0			0
$643$	−7.72222	−	13.3753i	−0.304535	−	0.527470i	0.672623	−	0.739985i	$-0.265168\pi$
$643$	−7.72222	−	13.3753i	−0.304535	−	0.527470i	−0.977158	+	0.212516i	$0.931834\pi$
$644$	−9.78426	−	16.9468i	−0.385554	−	0.667799i
$645$		0			0
$646$	54.0327	−	93.5874i	2.12589	−	3.68215i
$647$	25.0635			0.985349			0.492675	−	0.870214i	$-0.336019\pi$
$647$	25.0635			0.985349			0.492675	+	0.870214i	$0.336019\pi$
$648$		0			0
$649$	−6.93091			−0.272062
$650$	−1.12831	+	1.95429i	−0.0442560	+	0.0766537i
$651$		0			0
$652$	28.2161	+	48.8716i	1.10503	+	1.91396i
$653$	−1.49244	−	2.58498i	−0.0584036	−	0.101158i	0.835345	−	0.549726i	$-0.185268\pi$
$653$	−1.49244	−	2.58498i	−0.0584036	−	0.101158i	−0.893749	+	0.448568i	$0.851934\pi$
$654$		0			0
$655$	−4.53194	+	7.84955i	−0.177077	+	0.306707i
$656$	−5.88412			−0.229736
$657$		0			0
$658$	15.5120			0.604721
$659$	−18.7165	+	32.4180i	−0.729092	+	1.26282i	0.228175	+	0.973620i	$0.426724\pi$
$659$	−18.7165	+	32.4180i	−0.729092	+	1.26282i	−0.957267	+	0.289204i	$0.906609\pi$
$660$		0			0
$661$	−7.68631	−	13.3131i	−0.298963	−	0.517819i	0.676936	−	0.736042i	$-0.263307\pi$
$661$	−7.68631	−	13.3131i	−0.298963	−	0.517819i	−0.975899	+	0.218223i	$0.929974\pi$
$662$	34.0407	+	58.9602i	1.32303	+	2.29155i
$663$		0			0
$664$	0.642989	−	1.11369i	0.0249528	−	0.0432196i
$665$	−5.59522			−0.216973
$666$		0			0
$667$	21.5552			0.834622
$668$	8.66061	−	15.0006i	0.335089	−	0.580391i
$669$		0			0
$670$	−1.91190	−	3.31152i	−0.0738633	−	0.127935i
$671$	10.7674	+	18.6497i	0.415670	+	0.719962i
$672$		0			0
$673$	0.271779	−	0.470734i	0.0104763	−	0.0181455i	−0.860740	−	0.509045i	$-0.829999\pi$
$673$	0.271779	−	0.470734i	0.0104763	−	0.0181455i	0.871216	+	0.490900i	$0.163332\pi$
$674$	−14.8449			−0.571805
$675$		0			0
$676$	3.09235			0.118937
$677$	−10.0293	+	17.3713i	−0.385458	+	0.667633i	−0.991833	−	0.127546i	$-0.959290\pi$
$677$	−10.0293	+	17.3713i	−0.385458	+	0.667633i	0.606374	+	0.795179i	$0.292623\pi$
$678$		0			0
$679$	1.04681	+	1.81312i	0.0401727	+	0.0695812i
$680$	−7.45344	−	12.9097i	−0.285826	−	0.495066i
$681$		0			0
$682$	−8.05671	+	13.9546i	−0.308507	+	0.534350i
$683$	−35.5213			−1.35919			−0.679593	−	0.733589i	$-0.737844\pi$
$683$	−35.5213			−1.35919			−0.679593	+	0.733589i	$0.737844\pi$
$684$		0			0
$685$	2.02984			0.0775561
$686$	−10.7632	+	18.6425i	−0.410942	+	0.711773i
$687$		0			0
$688$	3.71250	+	6.43024i	0.141538	+	0.245150i
$689$	−2.95484	−	5.11793i	−0.112570	−	0.194978i
$690$		0			0
$691$	25.6756	−	44.4714i	0.976746	−	1.69177i	0.302697	−	0.953087i	$-0.402113\pi$
$691$	25.6756	−	44.4714i	0.976746	−	1.69177i	0.674049	−	0.738686i	$-0.264554\pi$
$692$	11.1405			0.423498
$693$		0			0
$694$	−4.53724			−0.172231
$695$	1.42659	−	2.47092i	0.0541136	−	0.0937275i
$696$		0			0
$697$	28.6007	+	49.5378i	1.08333	+	1.87638i
$698$	15.8007	+	27.3677i	0.598067	+	1.03588i
$699$		0			0
$700$	−1.09248	+	1.89223i	−0.0412919	+	0.0715197i
$701$	−26.2661			−0.992057			−0.496029	−	0.868306i	$-0.665209\pi$
$701$	−26.2661			−0.992057			−0.496029	+	0.868306i	$0.665209\pi$
$702$		0			0
$703$	18.8531			0.711059
$704$	15.2034	−	26.3330i	0.572998	−	0.992462i
$705$		0			0
$706$	−39.0393	−	67.6181i	−1.46927	−	2.54484i
$707$	4.82993	+	8.36568i	0.181648	+	0.314624i
$708$		0			0
$709$	12.8681	−	22.2882i	0.483273	−	0.837053i	−0.516543	−	0.856261i	$-0.672781\pi$
$709$	12.8681	−	22.2882i	0.483273	−	0.837053i	0.999815	+	0.0192087i	$0.00611468\pi$
$710$	−28.0812			−1.05387
$711$		0			0
$712$	26.5257			0.994093
$713$	13.7220	−	23.7672i	0.513892	−	0.890088i
$714$		0			0
$715$	1.16510	+	2.01802i	0.0435725	+	0.0754697i
$716$	23.6754	+	41.0071i	0.884793	+	1.53251i
$717$		0			0
$718$	−25.6893	+	44.4952i	−0.958717	+	1.66055i
$719$	21.6829			0.808634			0.404317	−	0.914619i	$-0.367509\pi$
$719$	21.6829			0.808634			0.404317	+	0.914619i	$0.367509\pi$
$720$		0			0
$721$	−5.03835			−0.187638
$722$	49.3163	−	85.4183i	1.83536	−	3.17894i
$723$		0			0
$724$	11.1902	+	19.3820i	0.415880	+	0.720326i
$725$	−1.20340	−	2.08435i	−0.0446931	−	0.0774107i
$726$		0			0
$727$	24.6644	−	42.7200i	0.914752	−	1.58440i	0.107488	−	0.994206i	$-0.465719\pi$
$727$	24.6644	−	42.7200i	0.914752	−	1.58440i	0.807264	−	0.590190i	$-0.200947\pi$
$728$	1.74171			0.0645522
$729$		0			0
$730$	−11.0326			−0.408335
$731$	36.0903	−	62.5103i	1.33485	−	2.31203i
$732$		0			0
$733$	−13.0583	−	22.6176i	−0.482318	−	0.835399i	0.517476	−	0.855698i	$-0.326872\pi$
$733$	−13.0583	−	22.6176i	−0.482318	−	0.835399i	−0.999794	+	0.0202985i	$0.993538\pi$
$734$	−12.8559	−	22.2671i	−0.474520	−	0.821892i
$735$		0			0
$736$	−28.3628	+	49.1259i	−1.04547	+	1.81080i
$737$	−3.94850			−0.145445
$738$		0			0
$739$	−20.3143			−0.747275			−0.373637	−	0.927575i	$-0.621890\pi$
$739$	−20.3143			−0.747275			−0.373637	+	0.927575i	$0.621890\pi$
$740$	3.68112	−	6.37589i	0.135321	−	0.234382i
$741$		0			0
$742$	−4.71138	−	8.16036i	−0.172960	−	0.299576i
$743$	4.73644	+	8.20375i	0.173763	+	0.300966i	0.939733	−	0.341911i	$-0.111074\pi$
$743$	4.73644	+	8.20375i	0.173763	+	0.300966i	−0.765969	+	0.642877i	$0.777741\pi$
$744$		0			0
$745$	4.49112	−	7.77885i	0.164542	−	0.284995i
$746$	−5.85637			−0.214417
$747$		0			0
$748$	−43.5762			−1.59330
$749$	−0.603327	+	1.04499i	−0.0220451	+	0.0381832i
$750$		0			0
$751$	3.02922	+	5.24676i	0.110538	+	0.191457i	0.915987	−	0.401207i	$-0.131409\pi$
$751$	3.02922	+	5.24676i	0.110538	+	0.191457i	−0.805449	+	0.592664i	$0.798076\pi$
$752$	−3.02597	−	5.24114i	−0.110346	−	0.191125i
$753$		0			0
$754$	−2.71562	+	4.70359i	−0.0988970	+	0.171295i
$755$	−2.75483			−0.100258
$756$		0			0
$757$	19.3009			0.701503			0.350752	−	0.936469i	$-0.385926\pi$
$757$	19.3009			0.701503			0.350752	+	0.936469i	$0.385926\pi$
$758$	2.69339	−	4.66509i	0.0978283	−	0.169444i
$759$		0			0
$760$	−9.76006	−	16.9049i	−0.354035	−	0.613206i
$761$	−15.7544	−	27.2873i	−0.571095	−	0.989165i	−0.996454	−	0.0841405i	$-0.973186\pi$
$761$	−15.7544	−	27.2873i	−0.571095	−	0.989165i	0.425359	−	0.905025i	$-0.360148\pi$
$762$		0			0
$763$	1.14333	−	1.98030i	0.0413913	−	0.0716918i
$764$	59.8922			2.16682
$765$		0			0
$766$	−72.8270			−2.63135
$767$	−1.48719	+	2.57588i	−0.0536992	+	0.0930097i
$768$		0			0
$769$	−4.65962	−	8.07070i	−0.168030	−	0.291037i	0.769697	−	0.638409i	$-0.220407\pi$
$769$	−4.65962	−	8.07070i	−0.168030	−	0.291037i	−0.937727	+	0.347373i	$0.887074\pi$
$770$	1.85772	+	3.21766i	0.0669475	+	0.115956i
$771$		0			0
$772$	−7.81662	+	13.5388i	−0.281326	+	0.487272i
$773$	−24.3144			−0.874529			−0.437265	−	0.899333i	$-0.644053\pi$
$773$	−24.3144			−0.874529			−0.437265	+	0.899333i	$0.644053\pi$
$774$		0			0
$775$	−3.06432			−0.110073
$776$	−3.65200	+	6.32546i	−0.131099	+	0.227071i
$777$		0			0
$778$	−8.46352	−	14.6592i	−0.303432	−	0.525560i
$779$	37.4517	+	64.8683i	1.34185	+	2.32415i
$780$		0			0
$781$	−14.4985	+	25.1121i	−0.518796	+	0.898580i
$782$	122.219			4.37054
$783$		0			0
$784$	4.04395			0.144427
$785$	−12.2493	+	21.2164i	−0.437196	+	0.757246i
$786$		0			0
$787$	21.4150	+	37.0919i	0.763362	+	1.32218i	0.941108	+	0.338106i	$0.109786\pi$
$787$	21.4150	+	37.0919i	0.763362	+	1.32218i	−0.177746	+	0.984076i	$0.556880\pi$
$788$	9.82486	+	17.0172i	0.349996	+	0.606211i
$789$		0			0
$790$	−12.4401	+	21.5468i	−0.442598	+	0.766602i
$791$	0.479366			0.0170443
$792$		0			0
$793$	9.24156			0.328177
$794$	−25.4112	+	44.0134i	−0.901808	+	1.56198i
$795$		0			0
$796$	25.9473	+	44.9420i	0.919676	+	1.59293i
$797$	−15.4198	−	26.7079i	−0.546199	−	0.946044i	−0.998530	−	0.0541940i	$-0.982741\pi$
$797$	−15.4198	−	26.7079i	−0.546199	−	0.946044i	0.452332	−	0.891850i	$-0.350592\pi$
$798$		0			0
$799$	−29.4164	+	50.9507i	−1.04068	+	1.80251i
$800$	6.33383			0.223935
$801$		0			0
$802$	5.71514			0.201809
$803$	−5.69618	+	9.86608i	−0.201014	+	0.348166i
$804$		0			0
$805$	−3.16402	−	5.48024i	−0.111517	−	0.193153i
$806$	3.45750	+	5.98857i	0.121785	+	0.210938i
$807$		0			0
$808$	−16.8502	+	29.1855i	−0.592789	+	1.02674i
$809$	14.4671			0.508636			0.254318	−	0.967121i	$-0.418149\pi$
$809$	14.4671			0.508636			0.254318	+	0.967121i	$0.418149\pi$
$810$		0			0
$811$	40.9902			1.43936			0.719681	−	0.694305i	$-0.244288\pi$
$811$	40.9902			1.43936			0.719681	+	0.694305i	$0.244288\pi$
$812$	−2.62938	+	4.55422i	−0.0922732	+	0.159822i
$813$		0			0
$814$	−6.25959	−	10.8419i	−0.219398	−	0.380009i
$815$	9.12447	+	15.8040i	0.319616	+	0.553592i
$816$		0			0
$817$	47.2592	−	81.8554i	1.65339	−	2.86376i
$818$	14.3766			0.502666
$819$		0			0
$820$	29.2502			1.02146
$821$	−23.6408	+	40.9470i	−0.825068	+	1.42906i	0.0767992	+	0.997047i	$0.475530\pi$
$821$	−23.6408	+	40.9470i	−0.825068	+	1.42906i	−0.901867	+	0.432013i	$0.857803\pi$
$822$		0			0
$823$	−14.9104	−	25.8256i	−0.519744	−	0.900223i	−0.999737	−	0.0229503i	$-0.992694\pi$
$823$	−14.9104	−	25.8256i	−0.519744	−	0.900223i	0.479993	−	0.877272i	$-0.340639\pi$
$824$	−8.78868	−	15.2224i	−0.306168	−	0.530299i
$825$		0			0
$826$	−2.37126	+	4.10715i	−0.0825068	+	0.142906i
$827$	−3.90807			−0.135897			−0.0679484	−	0.997689i	$-0.521645\pi$
$827$	−3.90807			−0.135897			−0.0679484	+	0.997689i	$0.521645\pi$
$828$		0			0
$829$	−7.76600			−0.269724			−0.134862	−	0.990864i	$-0.543059\pi$
$829$	−7.76600			−0.269724			−0.134862	+	0.990864i	$0.543059\pi$
$830$	0.588630	−	1.01954i	0.0204316	−	0.0353886i
$831$		0			0
$832$	−6.52446	−	11.3007i	−0.226195	−	0.391781i
$833$	−19.6562	−	34.0456i	−0.681048	−	1.17961i
$834$		0			0
$835$	2.80066	−	4.85088i	0.0969207	−	0.167872i
$836$	−57.0618			−1.97352
$837$		0			0
$838$	69.8105			2.41156
$839$	7.80495	−	13.5186i	0.269457	−	0.466713i	−0.699265	−	0.714863i	$-0.746489\pi$
$839$	7.80495	−	13.5186i	0.269457	−	0.466713i	0.968722	+	0.248150i	$0.0798225\pi$
$840$		0			0
$841$	11.6037	+	20.0981i	0.400126	+	0.693039i
$842$	−15.7562	−	27.2906i	−0.542995	−	0.940495i
$843$		0			0
$844$	17.5693	−	30.4310i	0.604762	−	1.04748i
$845$	1.00000			0.0344010
$846$		0			0
$847$	−3.93569			−0.135232
$848$	−1.83813	+	3.18373i	−0.0631215	+	0.109330i
$849$		0			0
$850$	−6.82331	−	11.8183i	−0.234038	−	0.405365i
$851$	10.6612	+	18.4657i	0.365460	+	0.632996i
$852$		0			0
$853$	6.17301	−	10.6920i	0.211360	−	0.366086i	−0.740781	−	0.671747i	$-0.765544\pi$
$853$	6.17301	−	10.6920i	0.211360	−	0.366086i	0.952140	+	0.305661i	$0.0988775\pi$
$854$	14.7353			0.504233
$855$		0			0
$856$	−4.20967			−0.143884
$857$	−18.4503	+	31.9569i	−0.630251	+	1.09163i	0.357250	+	0.934009i	$0.383714\pi$
$857$	−18.4503	+	31.9569i	−0.630251	+	1.09163i	−0.987500	+	0.157617i	$0.949619\pi$
$858$		0			0
$859$	14.1989	+	24.5932i	0.484460	+	0.839109i	0.999841	−	0.0178523i	$-0.00568287\pi$
$859$	14.1989	+	24.5932i	0.484460	+	0.839109i	−0.515381	+	0.856961i	$0.672350\pi$
$860$	−18.4550	−	31.9650i	−0.629310	−	1.09000i
$861$		0			0
$862$	−22.7950	+	39.4821i	−0.776400	+	1.34476i
$863$	26.6238			0.906283			0.453142	−	0.891438i	$-0.350303\pi$
$863$	26.6238			0.906283			0.453142	+	0.891438i	$0.350303\pi$
$864$		0			0
$865$	3.60260			0.122492
$866$	−15.5320	+	26.9022i	−0.527798	+	0.914173i
$867$		0			0
$868$	3.34771	+	5.79840i	0.113629	+	0.196811i
$869$	12.8457	+	22.2495i	0.435762	+	0.754762i
$870$		0			0
$871$	−0.847241	+	1.46746i	−0.0287077	+	0.0497231i
$872$	7.97749			0.270152
$873$		0			0
$874$	160.042			5.41350
$875$	−0.353285	+	0.611908i	−0.0119432	+	0.0206863i
$876$		0			0
$877$	25.6019	+	44.3439i	0.864516	+	1.49739i	0.867527	+	0.497390i	$0.165708\pi$
$877$	25.6019	+	44.3439i	0.864516	+	1.49739i	−0.00301066	+	0.999995i	$0.500958\pi$
$878$	8.76423	+	15.1801i	0.295778	+	0.512303i
$879$		0			0
$880$	0.724780	−	1.25536i	0.0244323	−	0.0423181i
$881$	29.0213			0.977751			0.488876	−	0.872354i	$-0.337407\pi$
$881$	29.0213			0.977751			0.488876	+	0.872354i	$0.337407\pi$
$882$		0			0
$883$	21.5185			0.724154			0.362077	−	0.932148i	$-0.382068\pi$
$883$	21.5185			0.724154			0.362077	+	0.932148i	$0.382068\pi$
$884$	−9.35028	+	16.1952i	−0.314484	+	0.544702i
$885$		0			0
$886$	−18.5398	−	32.1119i	−0.622857	−	1.07882i
$887$	9.60108	+	16.6296i	0.322373	+	0.558366i	0.980977	−	0.194124i	$-0.0621863\pi$
$887$	9.60108	+	16.6296i	0.322373	+	0.558366i	−0.658604	+	0.752489i	$0.728853\pi$
$888$		0			0
$889$	−5.18937	+	8.98826i	−0.174046	+	0.301456i
$890$	24.2832			0.813974
$891$		0			0
$892$	−62.1120			−2.07966
$893$	−38.5199	+	66.7184i	−1.28902	+	2.23265i
$894$		0			0
$895$	7.65613	+	13.2608i	0.255916	+	0.443260i
$896$	−5.92772	−	10.2671i	−0.198031	−	0.343000i
$897$		0			0
$898$	−11.2573	+	19.4983i	−0.375662	+	0.650666i
$899$	−7.37519			−0.245976
$900$		0			0
$901$	35.7380			1.19060
$902$	24.8694	−	43.0750i	0.828059	−	1.43424i
$903$		0			0
$904$	0.836185	+	1.44832i	0.0278111	+	0.0481702i
$905$	3.61867	+	6.26772i	0.120289	+	0.208346i
$906$		0			0
$907$	−23.7416	+	41.1216i	−0.788326	+	1.36542i	0.138666	+	0.990339i	$0.455719\pi$
$907$	−23.7416	+	41.1216i	−0.788326	+	1.36542i	−0.926992	+	0.375081i	$0.877615\pi$
$908$	35.0927			1.16459
$909$		0			0
$910$	1.59446			0.0528560
$911$	−7.00522	+	12.1334i	−0.232093	+	0.401997i	−0.958424	−	0.285348i	$-0.907891\pi$
$911$	−7.00522	+	12.1334i	−0.232093	+	0.401997i	0.726331	+	0.687345i	$0.241224\pi$
$912$		0			0
$913$	−0.607824	−	1.05278i	−0.0201160	−	0.0348420i
$914$	−19.5830	−	33.9187i	−0.647747	−	1.12193i
$915$		0			0
$916$	5.69202	−	9.85886i	0.188070	−	0.325746i
$917$	6.40427			0.211488
$918$		0			0
$919$	47.7699			1.57579			0.787893	−	0.615813i	$-0.211172\pi$
$919$	47.7699			1.57579			0.787893	+	0.615813i	$0.211172\pi$
$920$	11.0384	−	19.1190i	0.363924	−	0.630334i
$921$		0			0
$922$	11.9521	+	20.7017i	0.393622	+	0.681773i
$923$	6.22195	+	10.7767i	0.204798	+	0.354721i
$924$		0			0
$925$	1.19040	−	2.06183i	0.0391400	−	0.0677924i
$926$	8.14064			0.267518
$927$		0			0
$928$	15.2442			0.500417
$929$	18.1478	−	31.4329i	0.595409	−	1.03128i	−0.398080	−	0.917351i	$-0.630323\pi$
$929$	18.1478	−	31.4329i	0.595409	−	1.03128i	0.993489	−	0.113928i	$-0.0363434\pi$
$930$		0			0
$931$	−25.7392	−	44.5817i	−0.843569	−	1.46110i
$932$	19.3715	+	33.5524i	0.634533	+	1.09904i
$933$		0			0
$934$	−7.85995	+	13.6138i	−0.257185	+	0.445458i
$935$	−14.0916			−0.460845
$936$		0			0
$937$	−16.6768			−0.544808			−0.272404	−	0.962183i	$-0.587819\pi$
$937$	−16.6768			−0.544808			−0.272404	+	0.962183i	$0.587819\pi$
$938$	−1.35090	+	2.33982i	−0.0441083	+	0.0763978i
$939$		0			0
$940$	15.0422	+	26.0539i	0.490623	+	0.849784i
$941$	24.4145	+	42.2872i	0.795890	+	1.37852i	0.922273	+	0.386540i	$0.126330\pi$
$941$	24.4145	+	42.2872i	0.795890	+	1.37852i	−0.126383	+	0.991982i	$0.540337\pi$
$942$		0			0
$943$	−42.3569	+	73.3643i	−1.37933	+	2.38907i
$944$	1.85028			0.0602213
$945$		0			0
$946$	−62.7638			−2.04063
$947$	−5.03571	+	8.72210i	−0.163639	+	0.283430i	−0.936171	−	0.351545i	$-0.885656\pi$
$947$	−5.03571	+	8.72210i	−0.163639	+	0.283430i	0.772532	+	0.634975i	$0.218990\pi$
$948$		0			0
$949$	2.44449	+	4.23399i	0.0793516	+	0.137441i
$950$	−8.93492	−	15.4757i	−0.289887	−	0.502099i
$951$		0			0
$952$	−5.26638	+	9.12164i	−0.170684	+	0.295634i
$953$	−19.2233			−0.622703			−0.311351	−	0.950295i	$-0.600782\pi$
$953$	−19.2233			−0.622703			−0.311351	+	0.950295i	$0.600782\pi$
$954$		0			0
$955$	19.3679			0.626729
$956$	5.14701	−	8.91489i	0.166466	−	0.288328i
$957$		0			0
$958$	24.8912	+	43.1129i	0.804199	+	1.39291i
$959$	−0.717112	−	1.24207i	−0.0231568	−	0.0401087i
$960$		0			0
$961$	10.8050	−	18.7148i	0.348548	−	0.603703i
$962$	−5.37255			−0.173218
$963$		0			0
$964$	−82.8249			−2.66761
$965$	−2.52773	+	4.37816i	−0.0813705	+	0.140938i
$966$		0			0
$967$	11.9833	+	20.7558i	0.385358	+	0.667460i	0.991819	−	0.127653i	$-0.0407445\pi$
$967$	11.9833	+	20.7558i	0.385358	+	0.667460i	−0.606460	+	0.795114i	$0.707411\pi$
$968$	−6.86524	−	11.8909i	−0.220657	−	0.382189i
$969$		0			0
$970$	−3.34326	+	5.79069i	−0.107345	+	0.185928i
$971$	−22.5951			−0.725111			−0.362556	−	0.931962i	$-0.618096\pi$
$971$	−22.5951			−0.725111			−0.362556	+	0.931962i	$0.618096\pi$
$972$		0			0
$973$	−2.01597			−0.0646291
$974$	−5.86450	+	10.1576i	−0.187911	+	0.325471i
$975$		0			0
$976$	−2.87446	−	4.97872i	−0.0920093	−	0.159365i
$977$	−4.77325	−	8.26751i	−0.152710	−	0.264501i	0.779513	−	0.626386i	$-0.215467\pi$
$977$	−4.77325	−	8.26751i	−0.152710	−	0.264501i	−0.932223	+	0.361885i	$0.882133\pi$
$978$		0			0
$979$	12.5375	−	21.7156i	0.400701	−	0.694034i
$980$	−20.1026			−0.642155
$981$		0			0
$982$	−5.04709			−0.161059
$983$	14.9234	−	25.8480i	0.475981	−	0.824424i	−0.523640	−	0.851940i	$-0.675426\pi$
$983$	14.9234	−	25.8480i	0.475981	−	0.824424i	0.999621	+	0.0275157i	$0.00875963\pi$
$984$		0			0
$985$	3.17715	+	5.50299i	0.101232	+	0.175340i
$986$	−16.4223	−	28.4443i	−0.522993	−	0.905851i
$987$		0			0
$988$	−12.2439	+	21.2071i	−0.389531	+	0.674687i
$989$	106.898			3.39915
$990$		0			0
$991$	−24.1499			−0.767146			−0.383573	−	0.923511i	$-0.625307\pi$
$991$	−24.1499			−0.767146			−0.383573	+	0.923511i	$0.625307\pi$
$992$	9.70442	−	16.8086i	0.308116	−	0.533672i
$993$		0			0
$994$	9.92068	+	17.1831i	0.314665	+	0.545016i
$995$	8.39079	+	14.5333i	0.266006	+	0.460736i
$996$		0			0
$997$	−15.9893	+	27.6943i	−0.506387	+	0.877088i	0.493586	+	0.869697i	$0.335686\pi$
$997$	−15.9893	+	27.6943i	−0.506387	+	0.877088i	−0.999973	+	0.00739074i	$0.997647\pi$
$998$	48.0419			1.52074
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1755.2.i.f.586.7		16
3.2	odd	2		585.2.i.e.196.2	✓	16
9.2	odd	6		5265.2.a.bf.1.7		8
9.4	even	3	inner	1755.2.i.f.1171.7		16
9.5	odd	6		585.2.i.e.391.2	yes	16
9.7	even	3		5265.2.a.ba.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.e.196.2	✓	16	3.2	odd	2
585.2.i.e.391.2	yes	16	9.5	odd	6
1755.2.i.f.586.7		16	1.1	even	1	trivial
1755.2.i.f.1171.7		16	9.4	even	3	inner
5265.2.a.ba.1.2		8	9.7	even	3
5265.2.a.bf.1.7		8	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1755.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.12831 - 1.95429i) q^{2} +(-1.54617 - 2.67805i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.353285 + 0.611908i) q^{7} -2.46502 q^{8} +O(q^{10})\)	\(q+(1.12831 - 1.95429i) q^{2} +(-1.54617 - 2.67805i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.353285 + 0.611908i) q^{7} -2.46502 q^{8} -2.25662 q^{10} +(-1.16510 + 2.01802i) q^{11} +(0.500000 + 0.866025i) q^{13} +(0.797232 + 1.38085i) q^{14} +(0.311036 - 0.538731i) q^{16} -6.04736 q^{17} -7.91884 q^{19} +(-1.54617 + 2.67805i) q^{20} +(2.62920 + 4.55391i) q^{22} +(-4.47799 - 7.75611i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.25662 q^{26} +2.18496 q^{28} +(-1.20340 + 2.08435i) q^{29} +(1.53216 + 2.65378i) q^{31} +(-3.16691 - 5.48526i) q^{32} +(-6.82331 + 11.8183i) q^{34} +0.706571 q^{35} -2.38079 q^{37} +(-8.93492 + 15.4757i) q^{38} +(1.23251 + 2.13477i) q^{40} +(-4.72945 - 8.19164i) q^{41} +(-5.96795 + 10.3368i) q^{43} +7.20582 q^{44} -20.2103 q^{46} +(4.86433 - 8.42527i) q^{47} +(3.25038 + 5.62982i) q^{49} +(1.12831 + 1.95429i) q^{50} +(1.54617 - 2.67805i) q^{52} -5.90968 q^{53} +2.33021 q^{55} +(0.870856 - 1.50837i) q^{56} +(2.71562 + 4.70359i) q^{58} +(1.48719 + 2.57588i) q^{59} +(4.62078 - 8.00343i) q^{61} +6.91501 q^{62} -13.0489 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.847241 + 1.46746i) q^{67} +(9.35028 + 16.1952i) q^{68} +(0.797232 - 1.38085i) q^{70} +12.4439 q^{71} +4.88899 q^{73} +(-2.68628 + 4.65277i) q^{74} +(12.2439 + 21.2071i) q^{76} +(-0.823229 - 1.42587i) q^{77} +(5.51270 - 9.54827i) q^{79} -0.622073 q^{80} -21.3452 q^{82} +(-0.260845 + 0.451797i) q^{83} +(3.02368 + 5.23717i) q^{85} +(13.4674 + 23.3262i) q^{86} +(2.87201 - 4.97447i) q^{88} -10.7608 q^{89} -0.706571 q^{91} +(-13.8475 + 23.9846i) q^{92} +(-10.9770 - 19.0127i) q^{94} +(3.95942 + 6.85792i) q^{95} +(1.48153 - 2.56609i) q^{97} +14.6698 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8	\( 16 q + 3 q^{2} - 9 q^{4} - 8 q^{5} + 11 q^{7} + 12 q^{8} - 6 q^{10} + 6 q^{11} + 8 q^{13} + 10 q^{14} - 11 q^{16} + 4 q^{17} - 20 q^{19} - 9 q^{20} - 3 q^{22} + 6 q^{23} - 8 q^{25} + 6 q^{26} - 68 q^{28} + 14 q^{29} + 31 q^{31} + q^{32} + 7 q^{34} - 22 q^{35} + 2 q^{37} + 9 q^{38} - 6 q^{40} - 12 q^{41} - 15 q^{43} - 32 q^{44} - 64 q^{46} - 18 q^{47} - 17 q^{49} + 3 q^{50} + 9 q^{52} - 4 q^{53} - 12 q^{55} + 16 q^{56} + 42 q^{58} + 24 q^{59} + 9 q^{61} + 40 q^{62} - 60 q^{64} + 8 q^{65} + 18 q^{67} - 14 q^{68} + 10 q^{70} - 20 q^{71} + 12 q^{73} - 37 q^{74} + 53 q^{76} - 34 q^{77} + 3 q^{79} + 22 q^{80} - 68 q^{82} - 10 q^{83} - 2 q^{85} + 60 q^{86} + 14 q^{88} + 26 q^{89} + 22 q^{91} + 5 q^{92} - 17 q^{94} + 10 q^{95} + 34 q^{97} + 60 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 9 * q^4 - 8 * q^5 + 11 * q^7 + 12 * q^8 - 6 * q^10 + 6 * q^11 + 8 * q^13 + 10 * q^14 - 11 * q^16 + 4 * q^17 - 20 * q^19 - 9 * q^20 - 3 * q^22 + 6 * q^23 - 8 * q^25 + 6 * q^26 - 68 * q^28 + 14 * q^29 + 31 * q^31 + q^32 + 7 * q^34 - 22 * q^35 + 2 * q^37 + 9 * q^38 - 6 * q^40 - 12 * q^41 - 15 * q^43 - 32 * q^44 - 64 * q^46 - 18 * q^47 - 17 * q^49 + 3 * q^50 + 9 * q^52 - 4 * q^53 - 12 * q^55 + 16 * q^56 + 42 * q^58 + 24 * q^59 + 9 * q^61 + 40 * q^62 - 60 * q^64 + 8 * q^65 + 18 * q^67 - 14 * q^68 + 10 * q^70 - 20 * q^71 + 12 * q^73 - 37 * q^74 + 53 * q^76 - 34 * q^77 + 3 * q^79 + 22 * q^80 - 68 * q^82 - 10 * q^83 - 2 * q^85 + 60 * q^86 + 14 * q^88 + 26 * q^89 + 22 * q^91 + 5 * q^92 - 17 * q^94 + 10 * q^95 + 34 * q^97 + 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more