LMFDB - Embedded newform 81.2.e.a.46.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(10,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, 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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			46.2
Root			$0.500000 + 0.258654i$ of defining polynomial
Character	$\chi$	$=$	81.46
Dual form			81.2.e.a.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62143 + 1.36054i) q^{2} +(0.430663 + 2.44241i) q^{4} +(-2.52129 - 0.917674i) q^{5} +(0.168844 - 0.957561i) q^{7} +(-0.508086 + 0.880031i) q^{8} +O(q^{10})$	\(q+(1.62143 + 1.36054i) q^{2} +(0.430663 + 2.44241i) q^{4} +(-2.52129 - 0.917674i) q^{5} +(0.168844 - 0.957561i) q^{7} +(-0.508086 + 0.880031i) q^{8} +(-2.83955 - 4.91825i) q^{10} +(-0.297791 + 0.108387i) q^{11} +(-1.15981 + 0.973200i) q^{13} +(1.57657 - 1.32290i) q^{14} +(2.63991 - 0.960847i) q^{16} +(0.587342 + 1.01731i) q^{17} +(-3.11040 + 5.38737i) q^{19} +(1.15551 - 6.55323i) q^{20} +(-0.630310 - 0.229414i) q^{22} +(-0.375556 - 2.12988i) q^{23} +(1.68454 + 1.41350i) q^{25} -3.20463 q^{26} +2.41147 q^{28} +(3.37436 + 2.83142i) q^{29} +(-1.50609 - 8.54146i) q^{31} +(7.49746 + 2.72885i) q^{32} +(-0.431752 + 2.44859i) q^{34} +(-1.30443 + 2.25934i) q^{35} +(2.23332 + 3.86823i) q^{37} +(-12.3730 + 4.50341i) q^{38} +(2.08861 - 1.75255i) q^{40} +(-4.47767 + 3.75721i) q^{41} +(-5.25381 + 1.91223i) q^{43} +(-0.392973 - 0.680649i) q^{44} +(2.28885 - 3.96441i) q^{46} +(0.429965 - 2.43845i) q^{47} +(5.68943 + 2.07078i) q^{49} +(0.808243 + 4.58377i) q^{50} +(-2.87645 - 2.41362i) q^{52} +10.8920 q^{53} +0.850279 q^{55} +(0.756896 + 0.635111i) q^{56} +(1.61901 + 9.18189i) q^{58} +(-1.62023 - 0.589715i) q^{59} +(0.176214 - 0.999361i) q^{61} +(9.17898 - 15.8985i) q^{62} +(5.63455 + 9.75933i) q^{64} +(3.81731 - 1.38939i) q^{65} +(0.656156 - 0.550580i) q^{67} +(-2.23174 + 1.87265i) q^{68} +(-5.18896 + 1.88863i) q^{70} +(-4.79788 - 8.31018i) q^{71} +(7.62091 - 13.1998i) q^{73} +(-1.64171 + 9.31057i) q^{74} +(-14.4977 - 5.27674i) q^{76} +(0.0535070 + 0.303453i) q^{77} +(-8.59024 - 7.20807i) q^{79} -7.53771 q^{80} -12.3721 q^{82} +(-3.58886 - 3.01141i) q^{83} +(-0.547303 - 3.10391i) q^{85} +(-11.1203 - 4.04747i) q^{86} +(0.0559194 - 0.317135i) q^{88} +(-7.74976 + 13.4230i) q^{89} +(0.736071 + 1.27491i) q^{91} +(5.04032 - 1.83453i) q^{92} +(4.01476 - 3.36879i) q^{94} +(12.7861 - 10.7288i) q^{95} +(5.21481 - 1.89804i) q^{97} +(6.40762 + 11.0983i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8	$ 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} - 6 q^{13} - 15 q^{14} - 9 q^{17} - 3 q^{19} + 3 q^{20} + 3 q^{22} + 12 q^{23} + 3 q^{25} + 30 q^{26} - 12 q^{28} + 6 q^{29} + 3 q^{31} + 9 q^{34} - 12 q^{35} - 3 q^{37} - 42 q^{38} + 21 q^{40} - 15 q^{41} + 3 q^{43} - 3 q^{44} - 3 q^{46} + 15 q^{47} + 12 q^{49} + 33 q^{50} + 9 q^{52} + 18 q^{53} - 12 q^{55} + 33 q^{56} + 21 q^{58} + 12 q^{59} + 12 q^{61} + 12 q^{62} + 12 q^{64} - 3 q^{65} - 15 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} - 33 q^{74} - 48 q^{76} - 15 q^{77} - 42 q^{79} - 42 q^{80} - 12 q^{82} - 39 q^{83} - 27 q^{85} - 51 q^{86} - 30 q^{88} - 9 q^{89} + 6 q^{91} + 39 q^{92} - 15 q^{94} + 33 q^{95} + 3 q^{97} + 45 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 - 6 * q^13 - 15 * q^14 - 9 * q^17 - 3 * q^19 + 3 * q^20 + 3 * q^22 + 12 * q^23 + 3 * q^25 + 30 * q^26 - 12 * q^28 + 6 * q^29 + 3 * q^31 + 9 * q^34 - 12 * q^35 - 3 * q^37 - 42 * q^38 + 21 * q^40 - 15 * q^41 + 3 * q^43 - 3 * q^44 - 3 * q^46 + 15 * q^47 + 12 * q^49 + 33 * q^50 + 9 * q^52 + 18 * q^53 - 12 * q^55 + 33 * q^56 + 21 * q^58 + 12 * q^59 + 12 * q^61 + 12 * q^62 + 12 * q^64 - 3 * q^65 - 15 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 - 33 * q^74 - 48 * q^76 - 15 * q^77 - 42 * q^79 - 42 * q^80 - 12 * q^82 - 39 * q^83 - 27 * q^85 - 51 * q^86 - 30 * q^88 - 9 * q^89 + 6 * q^91 + 39 * q^92 - 15 * q^94 + 33 * q^95 + 3 * q^97 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	1.62143	+	1.36054i	1.14652	+	0.962046i	0.999633	−	0.0271067i	$-0.00862938\pi$
$2$	1.62143	+	1.36054i	1.14652	+	0.962046i	0.146889	+	0.989153i	$0.453074\pi$
$3$		0			0
$3$		0			0
$4$	0.430663	+	2.44241i	0.215332	+	1.22121i
$5$	−2.52129	−	0.917674i	−1.12755	−	0.410396i	−0.290150	−	0.956981i	$-0.593705\pi$
$5$	−2.52129	−	0.917674i	−1.12755	−	0.410396i	−0.837404	+	0.546585i	$0.815928\pi$
$6$		0			0
$7$	0.168844	−	0.957561i	0.0638170	−	0.361924i	−0.936130	−	0.351653i	$-0.885620\pi$
$7$	0.168844	−	0.957561i	0.0638170	−	0.361924i	0.999947	−	0.0102706i	$-0.00326930\pi$
$8$	−0.508086	+	0.880031i	−0.179636	+	0.311138i
$9$		0			0
$10$	−2.83955	−	4.91825i	−0.897945	−	1.55529i
$11$	−0.297791	+	0.108387i	−0.0897872	+	0.0326799i	−0.386523	−	0.922280i	$-0.626324\pi$
$11$	−0.297791	+	0.108387i	−0.0897872	+	0.0326799i	0.296736	+	0.954960i	$0.404102\pi$
$12$		0			0
$13$	−1.15981	+	0.973200i	−0.321675	+	0.269917i	−0.789297	−	0.614011i	$-0.789555\pi$
$13$	−1.15981	+	0.973200i	−0.321675	+	0.269917i	0.467623	+	0.883928i	$0.345111\pi$
$14$	1.57657	−	1.32290i	0.421355	−	0.353559i
$15$		0			0
$16$	2.63991	−	0.960847i	0.659977	−	0.240212i
$17$	0.587342	+	1.01731i	0.142451	+	0.246733i	0.928419	−	0.371534i	$-0.121168\pi$
$17$	0.587342	+	1.01731i	0.142451	+	0.246733i	−0.785968	+	0.618267i	$0.787835\pi$
$18$		0			0
$19$	−3.11040	+	5.38737i	−0.713575	+	1.23595i	0.249931	+	0.968264i	$0.419592\pi$
$19$	−3.11040	+	5.38737i	−0.713575	+	1.23595i	−0.963507	+	0.267685i	$0.913741\pi$
$20$	1.15551	−	6.55323i	0.258380	−	1.46535i
$21$		0			0
$22$	−0.630310	−	0.229414i	−0.134383	−	0.0489113i
$23$	−0.375556	−	2.12988i	−0.0783089	−	0.444112i	−0.998601	−	0.0528796i	$-0.983160\pi$
$23$	−0.375556	−	2.12988i	−0.0783089	−	0.444112i	0.920292	−	0.391232i	$-0.127951\pi$
$24$		0			0
$25$	1.68454	+	1.41350i	0.336909	+	0.282700i
$26$	−3.20463			−0.628480
$27$		0			0
$28$	2.41147			0.455726
$29$	3.37436	+	2.83142i	0.626602	+	0.525782i	0.899871	−	0.436156i	$-0.143660\pi$
$29$	3.37436	+	2.83142i	0.626602	+	0.525782i	−0.273269	+	0.961938i	$0.588105\pi$
$30$		0			0
$31$	−1.50609	−	8.54146i	−0.270502	−	1.53409i	−0.752897	−	0.658138i	$-0.771344\pi$
$31$	−1.50609	−	8.54146i	−0.270502	−	1.53409i	0.482395	−	0.875954i	$-0.339767\pi$
$32$	7.49746	+	2.72885i	1.32538	+	0.482398i
$33$		0			0
$34$	−0.431752	+	2.44859i	−0.0740449	+	0.419930i
$35$	−1.30443	+	2.25934i	−0.220489	+	0.381899i
$36$		0			0
$37$	2.23332	+	3.86823i	0.367156	+	0.635933i	0.989120	−	0.147113i	$-0.0469982\pi$
$37$	2.23332	+	3.86823i	0.367156	+	0.635933i	−0.621964	+	0.783046i	$0.713665\pi$
$38$	−12.3730	+	4.50341i	−2.00717	+	0.730550i
$39$		0			0
$40$	2.08861	−	1.75255i	0.330239	−	0.277103i
$41$	−4.47767	+	3.75721i	−0.699295	+	0.586778i	−0.921573	−	0.388205i	$-0.873095\pi$
$41$	−4.47767	+	3.75721i	−0.699295	+	0.586778i	0.222278	+	0.974983i	$0.428651\pi$
$42$		0			0
$43$	−5.25381	+	1.91223i	−0.801199	+	0.291613i	−0.709983	−	0.704219i	$-0.751298\pi$
$43$	−5.25381	+	1.91223i	−0.801199	+	0.291613i	−0.0912158	+	0.995831i	$0.529075\pi$
$44$	−0.392973	−	0.680649i	−0.0592429	−	0.102612i
$45$		0			0
$46$	2.28885	−	3.96441i	0.337473	−	0.584521i
$47$	0.429965	−	2.43845i	0.0627168	−	0.355685i	−0.937258	−	0.348636i	$-0.886645\pi$
$47$	0.429965	−	2.43845i	0.0627168	−	0.355685i	0.999975	−	0.00704911i	$-0.00224382\pi$
$48$		0			0
$49$	5.68943	+	2.07078i	0.812776	+	0.295826i
$50$	0.808243	+	4.58377i	0.114303	+	0.648243i
$51$		0			0
$52$	−2.87645	−	2.41362i	−0.398891	−	0.334710i
$53$	10.8920			1.49613			0.748063	−	0.663628i	$-0.230984\pi$
$53$	10.8920			1.49613			0.748063	+	0.663628i	$0.230984\pi$
$54$		0			0
$55$	0.850279			0.114652
$56$	0.756896	+	0.635111i	0.101145	+	0.0848703i
$57$		0			0
$58$	1.61901	+	9.18189i	0.212587	+	1.20564i
$59$	−1.62023	−	0.589715i	−0.210936	−	0.0767743i	0.234391	−	0.972142i	$-0.424690\pi$
$59$	−1.62023	−	0.589715i	−0.210936	−	0.0767743i	−0.445327	+	0.895368i	$0.646913\pi$
$60$		0			0
$61$	0.176214	−	0.999361i	0.0225619	−	0.127955i	−0.971446	−	0.237259i	$-0.923751\pi$
$61$	0.176214	−	0.999361i	0.0225619	−	0.127955i	0.994008	+	0.109304i	$0.0348621\pi$
$62$	9.17898	−	15.8985i	1.16573	−	2.01911i
$63$		0			0
$64$	5.63455	+	9.75933i	0.704319	+	1.21992i
$65$	3.81731	−	1.38939i	0.473478	−	0.172332i
$66$		0			0
$67$	0.656156	−	0.550580i	0.0801622	−	0.0672641i	−0.601826	−	0.798627i	$-0.705560\pi$
$67$	0.656156	−	0.550580i	0.0801622	−	0.0672641i	0.681988	+	0.731363i	$0.261116\pi$
$68$	−2.23174	+	1.87265i	−0.270638	+	0.227092i
$69$		0			0
$70$	−5.18896	+	1.88863i	−0.620200	+	0.225734i
$71$	−4.79788	−	8.31018i	−0.569404	−	0.986237i	−0.996625	−	0.0820894i	$-0.973841\pi$
$71$	−4.79788	−	8.31018i	−0.569404	−	0.986237i	0.427221	−	0.904147i	$-0.359493\pi$
$72$		0			0
$73$	7.62091	−	13.1998i	0.891960	−	1.54492i	0.0544385	−	0.998517i	$-0.482663\pi$
$73$	7.62091	−	13.1998i	0.891960	−	1.54492i	0.837522	−	0.546404i	$-0.184004\pi$
$74$	−1.64171	+	9.31057i	−0.190844	+	1.08233i
$75$		0			0
$76$	−14.4977	−	5.27674i	−1.66300	−	0.605284i
$77$	0.0535070	+	0.303453i	0.00609768	+	0.0345817i
$78$		0			0
$79$	−8.59024	−	7.20807i	−0.966478	−	0.810971i	0.0155168	−	0.999880i	$-0.495061\pi$
$79$	−8.59024	−	7.20807i	−0.966478	−	0.810971i	−0.981995	+	0.188908i	$0.939505\pi$
$80$	−7.53771			−0.842741
$81$		0			0
$82$	−12.3721			−1.36626
$83$	−3.58886	−	3.01141i	−0.393929	−	0.330546i	0.424212	−	0.905563i	$-0.360551\pi$
$83$	−3.58886	−	3.01141i	−0.393929	−	0.330546i	−0.818141	+	0.575017i	$0.804995\pi$
$84$		0			0
$85$	−0.547303	−	3.10391i	−0.0593633	−	0.336666i
$86$	−11.1203	−	4.04747i	−1.19914	−	0.436450i
$87$		0			0
$88$	0.0559194	−	0.317135i	0.00596103	−	0.0338067i
$89$	−7.74976	+	13.4230i	−0.821473	+	1.42283i	0.0831130	+	0.996540i	$0.473514\pi$
$89$	−7.74976	+	13.4230i	−0.821473	+	1.42283i	−0.904586	+	0.426292i	$0.859820\pi$
$90$		0			0
$91$	0.736071	+	1.27491i	0.0771612	+	0.133647i
$92$	5.04032	−	1.83453i	0.525490	−	0.191263i
$93$		0			0
$94$	4.01476	−	3.36879i	0.414091	−	0.347464i
$95$	12.7861	−	10.7288i	1.31182	−	1.10075i
$96$		0			0
$97$	5.21481	−	1.89804i	0.529484	−	0.192716i	−0.0634241	−	0.997987i	$-0.520202\pi$
$97$	5.21481	−	1.89804i	0.529484	−	0.192716i	0.592908	+	0.805270i	$0.297980\pi$
$98$	6.40762	+	11.0983i	0.647267	+	1.12110i
$99$		0			0
$100$	−2.72688	+	4.72309i	−0.272688	+	0.472309i
$101$	1.76063	−	9.98501i	0.175189	−	0.993546i	−0.762737	−	0.646709i	$-0.776145\pi$
$101$	1.76063	−	9.98501i	0.175189	−	0.993546i	0.937926	−	0.346836i	$-0.112744\pi$
$102$		0			0
$103$	9.25906	+	3.37002i	0.912323	+	0.332058i	0.755180	−	0.655518i	$-0.227549\pi$
$103$	9.25906	+	3.37002i	0.912323	+	0.332058i	0.157143	+	0.987576i	$0.449772\pi$
$104$	−0.267160	−	1.51514i	−0.0261972	−	0.148572i
$105$		0			0
$106$	17.6605	+	14.8189i	1.71534	+	1.43934i
$107$	−5.17080			−0.499880			−0.249940	−	0.968261i	$-0.580411\pi$
$107$	−5.17080			−0.499880			−0.249940	+	0.968261i	$0.580411\pi$
$108$		0			0
$109$	−7.31065			−0.700234			−0.350117	−	0.936706i	$-0.613858\pi$
$109$	−7.31065			−0.700234			−0.350117	+	0.936706i	$0.613858\pi$
$110$	1.37867	+	1.15684i	0.131451	+	0.110300i
$111$		0			0
$112$	−0.474338	−	2.69010i	−0.0448207	−	0.254191i
$113$	9.74991	+	3.54868i	0.917195	+	0.333832i	0.757122	−	0.653274i	$-0.226605\pi$
$113$	9.74991	+	3.54868i	0.917195	+	0.333832i	0.160073	+	0.987105i	$0.448827\pi$
$114$		0			0
$115$	−1.00765	+	5.71469i	−0.0939642	+	0.532898i
$116$	−5.46229	+	9.46096i	−0.507161	+	0.878428i
$117$		0			0
$118$	−1.82475	−	3.16056i	−0.167982	−	0.290953i
$119$	1.07330	−	0.390650i	0.0983894	−	0.0358108i
$120$		0			0
$121$	−8.34956	+	7.00611i	−0.759051	+	0.636919i
$122$	1.64539	−	1.38064i	0.148966	−	0.124998i
$123$		0			0
$124$	20.2132	−	7.35699i	1.81520	−	0.660677i
$125$	3.75766	+	6.50846i	0.336095	+	0.582134i
$126$		0			0
$127$	−2.61372	+	4.52709i	−0.231930	+	0.401714i	−0.958376	−	0.285509i	$-0.907837\pi$
$127$	−2.61372	+	4.52709i	−0.231930	+	0.401714i	0.726446	+	0.687223i	$0.241171\pi$
$128$	−1.37098	+	7.77522i	−0.121179	+	0.687239i
$129$		0			0
$130$	8.07980	+	2.94081i	0.708645	+	0.257926i
$131$	1.25622	+	7.12440i	0.109757	+	0.622461i	0.989213	+	0.146482i	$0.0467951\pi$
$131$	1.25622	+	7.12440i	0.109757	+	0.622461i	−0.879457	+	0.475979i	$0.842094\pi$
$132$		0			0
$133$	4.63357	+	3.88802i	0.401781	+	0.337134i
$134$	1.81300			0.156619
$135$		0			0
$136$	−1.19368			−0.102357
$137$	−8.61748	−	7.23092i	−0.736241	−	0.617779i	0.195584	−	0.980687i	$-0.437340\pi$
$137$	−8.61748	−	7.23092i	−0.736241	−	0.617779i	−0.931825	+	0.362907i	$0.881784\pi$
$138$		0			0
$139$	1.62885	+	9.23766i	0.138157	+	0.783528i	0.972609	+	0.232447i	$0.0746733\pi$
$139$	1.62885	+	9.23766i	0.138157	+	0.783528i	−0.834452	+	0.551081i	$0.814216\pi$
$140$	−6.08002	−	2.21295i	−0.513855	−	0.187028i
$141$		0			0
$142$	3.52690	−	20.0021i	0.295971	−	1.67854i
$143$	0.239900	−	0.415518i	0.0200614	−	0.0347474i
$144$		0			0
$145$	−5.90940	−	10.2354i	−0.490749	−	0.850003i
$146$	30.3156	−	11.0340i	2.50894	−	0.913179i
$147$		0			0
$148$	−8.48600	+	7.12060i	−0.697545	+	0.585310i
$149$	−14.5941	+	12.2459i	−1.19560	+	1.00322i	−0.195851	+	0.980634i	$0.562747\pi$
$149$	−14.5941	+	12.2459i	−1.19560	+	1.00322i	−0.999745	+	0.0225899i	$0.992809\pi$
$150$		0			0
$151$	−3.77193	+	1.37287i	−0.306955	+	0.111723i	−0.490905	−	0.871213i	$-0.663334\pi$
$151$	−3.77193	+	1.37287i	−0.306955	+	0.111723i	0.183950	+	0.982936i	$0.441112\pi$
$152$	−3.16070	−	5.47450i	−0.256367	−	0.444041i
$153$		0			0
$154$	−0.326102	+	0.564825i	−0.0262780	+	0.0455149i
$155$	−4.04099	+	22.9176i	−0.324580	+	1.84078i
$156$		0			0
$157$	−6.83713	−	2.48851i	−0.545662	−	0.198605i	0.0544560	−	0.998516i	$-0.482658\pi$
$157$	−6.83713	−	2.48851i	−0.545662	−	0.198605i	−0.600118	+	0.799911i	$0.704880\pi$
$158$	−4.12159	−	23.3747i	−0.327896	−	1.85959i
$159$		0			0
$160$	−16.3991	−	13.7604i	−1.29646	−	1.08786i
$161$	−2.10290			−0.165732
$162$		0			0
$163$	12.4492			0.975094			0.487547	−	0.873097i	$-0.337892\pi$
$163$	12.4492			0.975094			0.487547	+	0.873097i	$0.337892\pi$
$164$	−11.1050	−	9.31823i	−0.867157	−	0.727632i
$165$		0			0
$166$	−1.72194	−	9.76558i	−0.133648	−	0.757956i
$167$	−2.19126	−	0.797553i	−0.169565	−	0.0617165i	0.255843	−	0.966718i	$-0.417647\pi$
$167$	−2.19126	−	0.797553i	−0.169565	−	0.0617165i	−0.425408	+	0.905002i	$0.639869\pi$
$168$		0			0
$169$	−1.85937	+	10.5450i	−0.143029	+	0.811157i
$170$	3.33558	−	5.77739i	0.255827	−	0.443106i
$171$		0			0
$172$	−6.93308	−	12.0085i	−0.528643	−	0.915636i
$173$	−3.36623	+	1.22521i	−0.255930	+	0.0931509i	−0.466799	−	0.884363i	$-0.654593\pi$
$173$	−3.36623	+	1.22521i	−0.255930	+	0.0931509i	0.210869	+	0.977514i	$0.432371\pi$
$174$		0			0
$175$	1.63794	−	1.37439i	0.123816	−	0.103894i
$176$	−0.681996	+	0.572262i	−0.0514074	+	0.0431359i
$177$		0			0
$178$	−30.8281	+	11.2205i	−2.31067	+	0.841014i
$179$	−9.99785	−	17.3168i	−0.747275	−	1.29432i	−0.949124	−	0.314901i	$-0.898029\pi$
$179$	−9.99785	−	17.3168i	−0.747275	−	1.29432i	0.201850	−	0.979416i	$-0.435305\pi$
$180$		0			0
$181$	−4.86616	+	8.42844i	−0.361699	+	0.626481i	−0.988241	−	0.152907i	$-0.951136\pi$
$181$	−4.86616	+	8.42844i	−0.361699	+	0.626481i	0.626542	+	0.779388i	$0.284470\pi$
$182$	−0.541082	+	3.06863i	−0.0401077	+	0.227462i
$183$		0			0
$184$	2.06518	+	0.751664i	0.152247	+	0.0554134i
$185$	−2.08108	−	11.8024i	−0.153004	−	0.867728i
$186$		0			0
$187$	−0.285168	−	0.239284i	−0.0208535	−	0.0174982i
$188$	6.14088			0.447869
$189$		0			0
$190$	35.3286			2.56301
$191$	13.6023	+	11.4137i	0.984227	+	0.825864i	0.984722	−	0.174135i	$-0.0557130\pi$
$191$	13.6023	+	11.4137i	0.984227	+	0.825864i	−0.000494763		1.00000i	$0.500157\pi$
$192$		0			0
$193$	1.83795	+	10.4235i	0.132299	+	0.750303i	0.976703	+	0.214596i	$0.0688435\pi$
$193$	1.83795	+	10.4235i	0.132299	+	0.750303i	−0.844404	+	0.535706i	$0.820045\pi$
$194$	11.0378	+	4.01743i	0.792467	+	0.288434i
$195$		0			0
$196$	−2.60748	+	14.7878i	−0.186249	+	1.05627i
$197$	7.07945	−	12.2620i	0.504390	−	0.873628i	−0.495597	−	0.868552i	$-0.665051\pi$
$197$	7.07945	−	12.2620i	0.504390	−	0.873628i	0.999987	−	0.00507615i	$-0.00161579\pi$
$198$		0			0
$199$	−3.77010	−	6.53000i	−0.267255	−	0.462899i	0.700897	−	0.713263i	$-0.252783\pi$
$199$	−3.77010	−	6.53000i	−0.267255	−	0.462899i	−0.968152	+	0.250363i	$0.919450\pi$
$200$	−2.09982	+	0.764271i	−0.148479	+	0.0540421i
$201$		0			0
$202$	16.4397	−	13.7946i	1.15669	−	0.970582i
$203$	3.28100	−	2.75308i	0.230281	−	0.193229i
$204$		0			0
$205$	14.7374	−	5.36397i	1.02930	−	0.374636i
$206$	10.4278	+	18.0616i	0.726543	+	1.25841i
$207$		0			0
$208$	−2.12670	+	3.68356i	−0.147460	+	0.255409i
$209$	0.342328	−	1.94144i	0.0236793	−	0.134292i
$210$		0			0
$211$	−4.89922	−	1.78317i	−0.337276	−	0.122758i	0.167829	−	0.985816i	$-0.446324\pi$
$211$	−4.89922	−	1.78317i	−0.337276	−	0.122758i	−0.505106	+	0.863058i	$0.668546\pi$
$212$	4.69077	+	26.6027i	0.322163	+	1.82708i
$213$		0			0
$214$	−8.38408	−	7.03508i	−0.573124	−	0.480908i
$215$	15.0012			1.02307
$216$		0			0
$217$	−8.43326			−0.572487
$218$	−11.8537	−	9.94643i	−0.802833	−	0.673657i
$219$		0			0
$220$	0.366184	+	2.07673i	0.0246881	+	0.140013i
$221$	−1.67125	−	0.608285i	−0.112420	−	0.0409177i
$222$		0			0
$223$	3.07250	−	17.4250i	0.205750	−	1.16686i	−0.690506	−	0.723326i	$-0.742612\pi$
$223$	3.07250	−	17.4250i	0.205750	−	1.16686i	0.896256	−	0.443537i	$-0.146277\pi$
$224$	3.87894	−	6.71853i	0.259173	−	0.448901i
$225$		0			0
$226$	10.9807	+	19.0191i	0.730423	+	1.26513i
$227$	−14.8208	+	5.39434i	−0.983692	+	0.358035i	−0.783275	−	0.621676i	$-0.786452\pi$
$227$	−14.8208	+	5.39434i	−0.983692	+	0.358035i	−0.200418	+	0.979711i	$0.564230\pi$
$228$		0			0
$229$	−1.35350	+	1.13572i	−0.0894415	+	0.0750504i	−0.686412	−	0.727213i	$-0.740815\pi$
$229$	−1.35350	+	1.13572i	−0.0894415	+	0.0750504i	0.596971	+	0.802263i	$0.296371\pi$
$230$	−9.40889	+	7.89500i	−0.620404	+	0.520581i
$231$		0			0
$232$	−4.20620	+	1.53093i	−0.276151	+	0.100511i
$233$	−6.94920	−	12.0364i	−0.455257	−	0.788529i	0.543446	−	0.839444i	$-0.317119\pi$
$233$	−6.94920	−	12.0364i	−0.455257	−	0.788529i	−0.998703	+	0.0509157i	$0.983786\pi$
$234$		0			0
$235$	−3.32177	+	5.75347i	−0.216688	+	0.375315i
$236$	0.742554	−	4.21123i	0.0483362	−	0.274128i
$237$		0			0
$238$	2.27177	+	0.826858i	0.147257	+	0.0535973i
$239$	3.44391	+	19.5314i	0.222768	+	1.26338i	0.866906	+	0.498471i	$0.166105\pi$
$239$	3.44391	+	19.5314i	0.222768	+	1.26338i	−0.644138	+	0.764909i	$0.722784\pi$
$240$		0			0
$241$	14.8419	+	12.4538i	0.956050	+	0.802221i	0.980306	−	0.197485i	$-0.0632773\pi$
$241$	14.8419	+	12.4538i	0.956050	+	0.802221i	−0.0242563	+	0.999706i	$0.507722\pi$
$242$	−23.0703			−1.48301
$243$		0			0
$244$	2.51674			0.161118
$245$	−12.4444	−	10.4421i	−0.795043	−	0.667120i
$246$		0			0
$247$	−1.63550	−	9.27540i	−0.104065	−	0.590179i
$248$	8.28198	+	3.01439i	0.525906	+	0.191414i
$249$		0			0
$250$	−2.76224	+	15.6654i	−0.174699	+	0.990769i
$251$	−2.73786	+	4.74212i	−0.172812	+	0.299320i	−0.939402	−	0.342818i	$-0.888619\pi$
$251$	−2.73786	+	4.74212i	−0.172812	+	0.299320i	0.766590	+	0.642137i	$0.221952\pi$
$252$		0			0
$253$	0.342689	+	0.593554i	0.0215447	+	0.0373164i
$254$	−10.3972	+	3.78428i	−0.652380	+	0.237447i
$255$		0			0
$256$	4.46383	−	3.74560i	0.278989	−	0.234100i
$257$	8.85943	−	7.43395i	0.552636	−	0.463717i	−0.323196	−	0.946332i	$-0.604757\pi$
$257$	8.85943	−	7.43395i	0.552636	−	0.463717i	0.875833	+	0.482615i	$0.160313\pi$
$258$		0			0
$259$	4.08115	−	1.48542i	0.253590	−	0.0922993i
$260$	5.03743	+	8.72508i	0.312408	+	0.541107i
$261$		0			0
$262$	−7.65614	+	13.2608i	−0.472998	+	0.819257i
$263$	−1.12488	+	6.37952i	−0.0693632	+	0.393378i	0.930285	+	0.366839i	$0.119560\pi$
$263$	−1.12488	+	6.37952i	−0.0693632	+	0.393378i	−0.999648	+	0.0265395i	$0.991551\pi$
$264$		0			0
$265$	−27.4618	−	9.99526i	−1.68696	−	0.614004i
$266$	2.22318	+	12.6083i	0.136312	+	0.773064i
$267$		0			0
$268$	1.62733	+	1.36549i	0.0994048	+	0.0834106i
$269$	13.8387			0.843758			0.421879	−	0.906652i	$-0.361371\pi$
$269$	13.8387			0.843758			0.421879	+	0.906652i	$0.361371\pi$
$270$		0			0
$271$	1.94536			0.118172			0.0590860	−	0.998253i	$-0.481181\pi$
$271$	1.94536			0.118172			0.0590860	+	0.998253i	$0.481181\pi$
$272$	2.52800	+	2.12125i	0.153283	+	0.128619i
$273$		0			0
$274$	−4.13466	−	23.4488i	−0.249784	−	1.41660i
$275$	−0.654846	−	0.238344i	−0.0394887	−	0.0143727i
$276$		0			0
$277$	2.16586	−	12.2832i	0.130134	−	0.738026i	−0.847991	−	0.530010i	$-0.822188\pi$
$277$	2.16586	−	12.2832i	0.130134	−	0.738026i	0.978125	−	0.208016i	$-0.0667007\pi$
$278$	−9.92713	+	17.1943i	−0.595390	+	1.03125i
$279$		0			0
$280$	−1.32553	−	2.29588i	−0.0792154	−	0.137205i
$281$	9.16752	−	3.33670i	0.546888	−	0.199051i	−0.0537751	−	0.998553i	$-0.517125\pi$
$281$	9.16752	−	3.33670i	0.546888	−	0.199051i	0.600663	+	0.799502i	$0.294903\pi$
$282$		0			0
$283$	20.3547	−	17.0797i	1.20996	−	1.01528i	0.210676	−	0.977556i	$-0.432433\pi$
$283$	20.3547	−	17.0797i	1.20996	−	1.01528i	0.999288	−	0.0377246i	$-0.0120110\pi$
$284$	18.2306	−	15.2973i	1.08179	−	0.907728i
$285$		0			0
$286$	0.954309	−	0.347340i	0.0564295	−	0.0205386i
$287$	2.84173	+	4.92202i	0.167742	+	0.290538i
$288$		0			0
$289$	7.81006	−	13.5274i	0.459415	−	0.795730i
$290$	4.34397	−	24.6359i	0.255087	−	1.44667i
$291$		0			0
$292$	35.5214	+	12.9287i	2.07873	+	0.756598i
$293$	−2.12849	−	12.0712i	−0.124347	−	0.705210i	−0.981693	−	0.190469i	$-0.938999\pi$
$293$	−2.12849	−	12.0712i	−0.124347	−	0.705210i	0.857346	−	0.514741i	$-0.172112\pi$
$294$		0			0
$295$	3.54389	+	2.97368i	0.206334	+	0.173134i
$296$	−4.53888			−0.263817
$297$		0			0
$298$	−40.3243			−2.33592
$299$	2.50838	+	2.10478i	0.145063	+	0.121723i
$300$		0			0
$301$	0.944004	+	5.35371i	0.0544115	+	0.308583i
$302$	−7.98375	−	2.90585i	−0.459413	−	0.167213i
$303$		0			0
$304$	−3.03473	+	17.2108i	−0.174053	+	0.987106i
$305$	−1.36137	+	2.35797i	−0.0779521	+	0.135017i
$306$		0			0
$307$	13.2370	+	22.9271i	0.755475	+	1.30852i	0.945138	+	0.326671i	$0.105927\pi$
$307$	13.2370	+	22.9271i	0.755475	+	1.30852i	−0.189663	+	0.981849i	$0.560740\pi$
$308$	−0.718114	+	0.261372i	−0.0409184	+	0.0148931i
$309$		0			0
$310$	−37.7324	+	31.6613i	−2.14306	+	1.79824i
$311$	13.5280	−	11.3513i	0.767100	−	0.643673i	−0.172865	−	0.984946i	$-0.555302\pi$
$311$	13.5280	−	11.3513i	0.767100	−	0.643673i	0.939964	+	0.341272i	$0.110858\pi$
$312$		0			0
$313$	−9.06541	+	3.29954i	−0.512407	+	0.186501i	−0.585266	−	0.810841i	$-0.699010\pi$
$313$	−9.06541	+	3.29954i	−0.512407	+	0.186501i	0.0728589	+	0.997342i	$0.476788\pi$
$314$	−7.70019	−	13.3371i	−0.434547	−	0.752657i
$315$		0			0
$316$	13.9056	−	24.0852i	0.782250	−	1.35490i
$317$	0.644320	−	3.65412i	0.0361886	−	0.205236i	−0.961352	−	0.275321i	$-0.911216\pi$
$317$	0.644320	−	3.65412i	0.0361886	−	0.205236i	0.997541	+	0.0700850i	$0.0223270\pi$
$318$		0			0
$319$	−1.31174	−	0.477435i	−0.0734434	−	0.0267312i
$320$	−5.25044	−	29.7767i	−0.293509	−	1.66457i
$321$		0			0
$322$	−3.40971	−	2.86108i	−0.190016	−	0.159442i
$323$	−7.30748			−0.406599
$324$		0			0
$325$	−3.32937			−0.184680
$326$	20.1854	+	16.9376i	1.11797	+	0.938085i
$327$		0			0
$328$	−1.03142	−	5.84948i	−0.0569507	−	0.322983i
$329$	−2.26237	−	0.823435i	−0.124728	−	0.0453974i
$330$		0			0
$331$	−0.245329	+	1.39133i	−0.0134845	+	0.0764745i	−0.990807	−	0.135280i	$-0.956807\pi$
$331$	−0.245329	+	1.39133i	−0.0134845	+	0.0764745i	0.977323	+	0.211755i	$0.0679177\pi$
$332$	5.80953	−	10.0624i	0.318839	−	0.552246i
$333$		0			0
$334$	−2.46786	−	4.27446i	−0.135035	−	0.233888i
$335$	−2.15961	+	0.786034i	−0.117992	+	0.0429456i
$336$		0			0
$337$	−9.95097	+	8.34986i	−0.542064	+	0.454846i	−0.872243	−	0.489073i	$-0.837335\pi$
$337$	−9.95097	+	8.34986i	−0.542064	+	0.454846i	0.330179	+	0.943918i	$0.392891\pi$
$338$	−17.3618	+	14.5683i	−0.944356	+	0.792409i
$339$		0			0
$340$	7.34533	−	2.67348i	0.398356	−	0.144990i
$341$	1.37428	+	2.38033i	0.0744215	+	0.128902i
$342$		0			0
$343$	6.34669	−	10.9928i	0.342689	−	0.593555i
$344$	0.986567	−	5.59510i	0.0531921	−	0.301667i
$345$		0			0
$346$	−7.12504	−	2.59330i	−0.383045	−	0.139417i
$347$	0.833591	+	4.72753i	0.0447495	+	0.253787i	0.998973	−	0.0453070i	$-0.0144266\pi$
$347$	0.833591	+	4.72753i	0.0447495	+	0.253787i	−0.954224	+	0.299094i	$0.903316\pi$
$348$		0			0
$349$	−17.2954	−	14.5126i	−0.925803	−	0.776841i	0.0492565	−	0.998786i	$-0.484315\pi$
$349$	−17.2954	−	14.5126i	−0.925803	−	0.776841i	−0.975059	+	0.221946i	$0.928759\pi$
$350$	4.52571			0.241909
$351$		0			0
$352$	−2.52845			−0.134767
$353$	22.7565	+	19.0950i	1.21121	+	1.01632i	0.999237	+	0.0390490i	$0.0124328\pi$
$353$	22.7565	+	19.0950i	1.21121	+	1.01632i	0.211972	+	0.977276i	$0.432012\pi$
$354$		0			0
$355$	4.47081	+	25.3552i	0.237286	+	1.34572i
$356$	−36.1220	−	13.1473i	−1.91446	−	0.696807i
$357$		0			0
$358$	7.34937	−	41.6804i	0.388427	−	2.20288i
$359$	6.70991	−	11.6219i	0.354136	−	0.613381i	−0.632834	−	0.774288i	$-0.718108\pi$
$359$	6.70991	−	11.6219i	0.354136	−	0.613381i	0.986970	+	0.160906i	$0.0514418\pi$
$360$		0			0
$361$	−9.84920	−	17.0593i	−0.518379	−	0.897858i
$362$	−19.3573	+	7.04550i	−1.01740	+	0.370303i
$363$		0			0
$364$	−2.79686	+	2.34685i	−0.146595	+	0.123008i
$365$	−31.3276	+	26.2870i	−1.63976	+	1.37592i
$366$		0			0
$367$	7.47054	−	2.71905i	0.389959	−	0.141933i	−0.139597	−	0.990208i	$-0.544581\pi$
$367$	7.47054	−	2.71905i	0.389959	−	0.141933i	0.529556	+	0.848275i	$0.322359\pi$
$368$	−3.03793	−	5.26184i	−0.158363	−	0.274293i
$369$		0			0
$370$	12.6833	−	21.9681i	0.659372	−	1.14207i
$371$	1.83904	−	10.4297i	0.0954782	−	0.541484i
$372$		0			0
$373$	10.7318	+	3.90604i	0.555670	+	0.202247i	0.604564	−	0.796557i	$-0.293347\pi$
$373$	10.7318	+	3.90604i	0.555670	+	0.202247i	−0.0488939	+	0.998804i	$0.515570\pi$
$374$	−0.136823	−	0.775963i	−0.00707496	−	0.0401241i
$375$		0			0
$376$	1.92745	+	1.61733i	0.0994009	+	0.0834072i
$377$	−6.66917			−0.343480
$378$		0			0
$379$	−24.1705			−1.24155			−0.620777	−	0.783987i	$-0.713183\pi$
$379$	−24.1705			−1.24155			−0.620777	+	0.783987i	$0.713183\pi$
$380$	31.7106	+	26.6084i	1.62672	+	1.36498i
$381$		0			0
$382$	6.52637	+	37.0129i	0.333918	+	1.89374i
$383$	8.87378	+	3.22979i	0.453429	+	0.165035i	0.558631	−	0.829416i	$-0.311327\pi$
$383$	8.87378	+	3.22979i	0.453429	+	0.165035i	−0.105202	+	0.994451i	$0.533549\pi$
$384$		0			0
$385$	0.143564	−	0.814194i	0.00731672	−	0.0414952i
$386$	−11.2015	+	19.4016i	−0.570143	+	0.987516i
$387$		0			0
$388$	6.88162	+	11.9193i	0.349361	+	0.605111i
$389$	−2.39406	+	0.871367i	−0.121384	+	0.0441801i	−0.401998	−	0.915641i	$-0.631684\pi$
$389$	−2.39406	+	0.871367i	−0.121384	+	0.0441801i	0.280614	+	0.959821i	$0.409462\pi$
$390$		0			0
$391$	1.94617	−	1.63303i	0.0984218	−	0.0825857i
$392$	−4.71308	+	3.95474i	−0.238046	+	0.199745i
$393$		0			0
$394$	28.1617	−	10.2500i	1.41876	−	0.516388i
$395$	15.0438	+	26.0567i	0.756937	+	1.31105i
$396$		0			0
$397$	−1.83759	+	3.18279i	−0.0922258	+	0.159740i	−0.908447	−	0.417999i	$-0.862731\pi$
$397$	−1.83759	+	3.18279i	−0.0922258	+	0.159740i	0.816222	+	0.577739i	$0.196065\pi$
$398$	2.77138	−	15.7173i	0.138917	−	0.787836i
$399$		0			0
$400$	5.80519	+	2.11292i	0.290260	+	0.105646i
$401$	−2.80420	−	15.9034i	−0.140035	−	0.794177i	−0.971220	−	0.238182i	$-0.923448\pi$
$401$	−2.80420	−	15.9034i	−0.140035	−	0.794177i	0.831186	−	0.555995i	$-0.187663\pi$
$402$		0			0
$403$	10.0593	+	8.44078i	0.501091	+	0.420465i
$404$	25.1458			1.25105
$405$		0			0
$406$	9.06558			0.449917
$407$	−1.08433	−	0.909859i	−0.0537481	−	0.0451000i
$408$		0			0
$409$	1.59443	+	9.04248i	0.0788396	+	0.447122i	0.998517	+	0.0544462i	$0.0173393\pi$
$409$	1.59443	+	9.04248i	0.0788396	+	0.447122i	−0.919677	+	0.392676i	$0.871550\pi$
$410$	31.1935	+	11.3535i	1.54054	+	0.560710i
$411$		0			0
$412$	−4.24345	+	24.0658i	−0.209060	+	1.18564i
$413$	−0.838253	+	1.45190i	−0.0412477	+	0.0714432i
$414$		0			0
$415$	6.28506	+	10.8860i	0.308522	+	0.534375i
$416$	−11.3514	+	4.13157i	−0.556548	+	0.202567i
$417$		0			0
$418$	3.19646	−	2.68215i	0.156344	−	0.131188i
$419$	5.34613	−	4.48594i	0.261176	−	0.219152i	−0.502791	−	0.864408i	$-0.667694\pi$
$419$	5.34613	−	4.48594i	0.261176	−	0.219152i	0.763967	+	0.645256i	$0.223249\pi$
$420$		0			0
$421$	−28.9525	+	10.5379i	−1.41106	+	0.513584i	−0.931441	−	0.363894i	$-0.881447\pi$
$421$	−28.9525	+	10.5379i	−1.41106	+	0.513584i	−0.479619	+	0.877477i	$0.659225\pi$
$422$	−5.51765	−	9.55686i	−0.268595	−	0.465221i
$423$		0			0
$424$	−5.53405	+	9.58526i	−0.268757	+	0.465502i
$425$	−0.448559	+	2.54390i	−0.0217583	+	0.123397i
$426$		0			0
$427$	−0.927196	−	0.337472i	−0.0448702	−	0.0163314i
$428$	−2.22687	−	12.6292i	−0.107640	−	0.610457i
$429$		0			0
$430$	24.3233	+	20.4097i	1.17297	+	0.984242i
$431$	−27.8971			−1.34376			−0.671879	−	0.740661i	$-0.734513\pi$
$431$	−27.8971			−1.34376			−0.671879	+	0.740661i	$0.734513\pi$
$432$		0			0
$433$	19.1706			0.921278			0.460639	−	0.887588i	$-0.347620\pi$
$433$	19.1706			0.921278			0.460639	+	0.887588i	$0.347620\pi$
$434$	−13.6739	−	11.4738i	−0.656369	−	0.550759i
$435$		0			0
$436$	−3.14843	−	17.8556i	−0.150782	−	0.855130i
$437$	12.6426	+	4.60154i	0.604778	+	0.220121i
$438$		0			0
$439$	−4.12397	+	23.3882i	−0.196826	+	1.11626i	0.712968	+	0.701197i	$0.247351\pi$
$439$	−4.12397	+	23.3882i	−0.196826	+	1.11626i	−0.909794	+	0.415060i	$0.863761\pi$
$440$	−0.432015	+	0.748272i	−0.0205955	+	0.0356725i
$441$		0			0
$442$	−1.88221	−	3.26009i	−0.0895278	−	0.155067i
$443$	21.9496	−	7.98900i	1.04286	−	0.379569i	0.236894	−	0.971536i	$-0.423871\pi$
$443$	21.9496	−	7.98900i	1.04286	−	0.379569i	0.805962	+	0.591967i	$0.201648\pi$
$444$		0			0
$445$	31.8573	−	26.7314i	1.51018	−	1.26719i
$446$	28.6892	−	24.0731i	1.35847	−	1.13989i
$447$		0			0
$448$	10.2965	−	3.74762i	0.486464	−	0.177059i
$449$	2.40953	+	4.17343i	0.113713	+	0.196956i	0.917264	−	0.398279i	$-0.130392\pi$
$449$	2.40953	+	4.17343i	0.113713	+	0.196956i	−0.803552	+	0.595235i	$0.797059\pi$
$450$		0			0
$451$	0.926176	−	1.60418i	0.0436119	−	0.0755380i
$452$	−4.46841	+	25.3416i	−0.210176	+	1.19197i
$453$		0			0
$454$	−31.3701	−	11.4178i	−1.47227	−	0.535863i
$455$	−0.685893	−	3.88989i	−0.0321552	−	0.182361i
$456$		0			0
$457$	−3.74872	−	3.14555i	−0.175358	−	0.147142i	0.550885	−	0.834581i	$-0.314290\pi$
$457$	−3.74872	−	3.14555i	−0.175358	−	0.147142i	−0.726242	+	0.687439i	$0.758735\pi$
$458$	−3.73978			−0.174749
$459$		0			0
$460$	−14.3916			−0.671012
$461$	−21.4419	−	17.9919i	−0.998650	−	0.837967i	−0.0118535	−	0.999930i	$-0.503773\pi$
$461$	−21.4419	−	17.9919i	−0.998650	−	0.837967i	−0.986797	+	0.161963i	$0.948218\pi$
$462$		0			0
$463$	−4.77104	−	27.0579i	−0.221729	−	1.25749i	−0.868840	−	0.495093i	$-0.835134\pi$
$463$	−4.77104	−	27.0579i	−0.221729	−	1.25749i	0.647111	−	0.762396i	$-0.275977\pi$
$464$	11.6285	+	4.23245i	0.539842	+	0.196486i
$465$		0			0
$466$	5.10832	−	28.9707i	0.236639	−	1.34204i
$467$	−10.6232	+	18.4000i	−0.491585	+	0.851450i	−0.999953	−	0.00968963i	$-0.996916\pi$
$467$	−10.6232	+	18.4000i	−0.491585	+	0.851450i	0.508368	+	0.861140i	$0.330249\pi$
$468$		0			0
$469$	−0.416426	−	0.721272i	−0.0192288	−	0.0333052i
$470$	−13.2138	+	4.80944i	−0.609508	+	0.221843i
$471$		0			0
$472$	1.34218	−	1.12623i	0.0617790	−	0.0518387i
$473$	1.35728	−	1.13889i	0.0624076	−	0.0523662i
$474$		0			0
$475$	−12.8547	+	4.67871i	−0.589812	+	0.214674i
$476$	1.41636	+	2.45321i	0.0649188	+	0.112443i
$477$		0			0
$478$	−20.9892	+	36.3543i	−0.960022	+	1.66281i
$479$	7.23745	−	41.0456i	0.330688	−	1.87542i	−0.135560	−	0.990769i	$-0.543283\pi$
$479$	7.23745	−	41.0456i	0.330688	−	1.87542i	0.466248	−	0.884654i	$-0.345606\pi$
$480$		0			0
$481$	−6.35480	−	2.31296i	−0.289754	−	0.105462i
$482$	7.12113	+	40.3859i	0.324358	+	1.83953i
$483$		0			0
$484$	−20.7077	−	17.3758i	−0.941258	−	0.789809i
$485$	−14.8898			−0.676112
$486$		0			0
$487$	4.02801			0.182527			0.0912634	−	0.995827i	$-0.470909\pi$
$487$	4.02801			0.182527			0.0912634	+	0.995827i	$0.470909\pi$
$488$	0.789937	+	0.662836i	0.0357588	+	0.0300052i
$489$		0			0
$490$	−5.97081	−	33.8622i	−0.269734	−	1.52974i
$491$	−36.2922	−	13.2093i	−1.63784	−	0.596126i	−0.651184	−	0.758920i	$-0.725727\pi$
$491$	−36.2922	−	13.2093i	−1.63784	−	0.596126i	−0.986660	+	0.162793i	$0.947950\pi$
$492$		0			0
$493$	−0.898521	+	5.09577i	−0.0404674	+	0.229502i
$494$	9.96769	−	17.2645i	0.448468	−	0.776769i
$495$		0			0
$496$	−12.1830	−	21.1015i	−0.547032	−	0.947487i
$497$	−8.76759	+	3.19114i	−0.393280	+	0.143142i
$498$		0			0
$499$	−3.11922	+	2.61734i	−0.139636	+	0.117168i	−0.709930	−	0.704272i	$-0.751274\pi$
$499$	−3.11922	+	2.61734i	−0.139636	+	0.117168i	0.570295	+	0.821440i	$0.306829\pi$
$500$	−14.2781	+	11.9807i	−0.638534	+	0.535794i
$501$		0			0
$502$	−10.8911	+	3.96403i	−0.486093	+	0.176923i
$503$	−1.71297	−	2.96695i	−0.0763775	−	0.132290i	0.825307	−	0.564684i	$-0.191002\pi$
$503$	−1.71297	−	2.96695i	−0.0763775	−	0.132290i	−0.901684	+	0.432395i	$0.857669\pi$
$504$		0			0
$505$	−13.6020	+	23.5594i	−0.605282	+	1.04838i
$506$	−0.251909	+	1.42865i	−0.0111987	+	0.0635111i
$507$		0			0
$508$	−12.1827	−	4.43412i	−0.540518	−	0.196732i
$509$	2.12952	+	12.0771i	0.0943893	+	0.535308i	0.994933	+	0.100542i	$0.0320578\pi$
$509$	2.12952	+	12.0771i	0.0943893	+	0.535308i	−0.900543	+	0.434766i	$0.856831\pi$
$510$		0			0
$511$	−11.3529	−	9.52619i	−0.502222	−	0.421414i
$512$	28.1241			1.24292
$513$		0			0
$514$	24.4791			1.07973
$515$	−20.2522	−	16.9936i	−0.892418	−	0.748827i
$516$		0			0
$517$	0.136257	+	0.772750i	0.00599257	+	0.0339855i
$518$	8.63825	+	3.14407i	0.379543	+	0.138142i
$519$		0			0
$520$	−0.716818	+	4.06528i	−0.0314345	+	0.178274i
$521$	7.04117	−	12.1957i	0.308479	−	0.534302i	−0.669551	−	0.742766i	$-0.733513\pi$
$521$	7.04117	−	12.1957i	0.308479	−	0.534302i	0.978030	+	0.208465i	$0.0668466\pi$
$522$		0			0
$523$	−4.88956	−	8.46897i	−0.213806	−	0.370322i	0.739097	−	0.673599i	$-0.235253\pi$
$523$	−4.88956	−	8.46897i	−0.213806	−	0.370322i	−0.952902	+	0.303277i	$0.901919\pi$
$524$	−16.8597	+	6.13643i	−0.736520	+	0.268071i
$525$		0			0
$526$	−10.5035	+	8.81348i	−0.457974	+	0.384286i
$527$	7.80469	−	6.54892i	0.339978	−	0.285275i
$528$		0			0
$529$	17.2176	−	6.26668i	0.748590	−	0.272464i
$530$	−30.9283	−	53.5694i	−1.34344	−	2.32691i
$531$		0			0
$532$	−7.50065	+	12.9915i	−0.325195	+	0.563254i
$533$	1.53675	−	8.71534i	0.0665640	−	0.377503i
$534$		0			0
$535$	13.0371	+	4.74511i	0.563642	+	0.205149i
$536$	0.151144	+	0.857180i	0.00652843	+	0.0370245i
$537$		0			0
$538$	22.4384	+	18.8280i	0.967387	+	0.811734i
$539$	−1.91871			−0.0826445
$540$		0			0
$541$	40.9454			1.76038			0.880189	−	0.474623i	$-0.157416\pi$
$541$	40.9454			1.76038			0.880189	+	0.474623i	$0.157416\pi$
$542$	3.15426	+	2.64674i	0.135487	+	0.113687i
$543$		0			0
$544$	1.62750	+	9.22999i	0.0697783	+	0.395732i
$545$	18.4323	+	6.70879i	0.789551	+	0.287373i
$546$		0			0
$547$	0.192798	−	1.09341i	0.00824343	−	0.0467508i	−0.980409	−	0.196975i	$-0.936888\pi$
$547$	0.192798	−	1.09341i	0.00824343	−	0.0467508i	0.988652	+	0.150224i	$0.0479994\pi$
$548$	13.9497	−	24.1615i	0.595900	−	1.03213i
$549$		0			0
$550$	−0.737508	−	1.27740i	−0.0314474	−	0.0544686i
$551$	−25.7495	+	9.37206i	−1.09697	+	0.399263i
$552$		0			0
$553$	−8.35257	+	7.00864i	−0.355188	+	0.298038i
$554$	20.2236	−	16.9696i	0.859216	−	0.720968i
$555$		0			0
$556$	−21.8607	+	7.95664i	−0.927100	+	0.337437i
$557$	17.5201	+	30.3458i	0.742352	+	1.28579i	0.951422	+	0.307890i	$0.0996230\pi$
$557$	17.5201	+	30.3458i	0.742352	+	1.28579i	−0.209070	+	0.977901i	$0.567044\pi$
$558$		0			0
$559$	4.23247	−	7.33084i	0.179014	−	0.310062i
$560$	−1.27269	+	7.21781i	−0.0537812	+	0.305008i
$561$		0			0
$562$	19.4042	+	7.06254i	0.818516	+	0.297915i
$563$	6.73255	+	38.1822i	0.283743	+	1.60919i	0.709741	+	0.704463i	$0.248812\pi$
$563$	6.73255	+	38.1822i	0.283743	+	1.60919i	−0.425998	+	0.904724i	$0.640077\pi$
$564$		0			0
$565$	−21.3258	−	17.8945i	−0.897183	−	0.752826i
$566$	56.2413			2.36400
$567$		0			0
$568$	9.75095			0.409141
$569$	26.0213	+	21.8344i	1.09087	+	0.915347i	0.996777	−	0.0802169i	$-0.0255613\pi$
$569$	26.0213	+	21.8344i	1.09087	+	0.915347i	0.0940904	+	0.995564i	$0.470006\pi$
$570$		0			0
$571$	1.75191	+	9.93559i	0.0733153	+	0.415792i	0.999272	+	0.0381610i	$0.0121500\pi$
$571$	1.75191	+	9.93559i	0.0733153	+	0.415792i	−0.925956	+	0.377631i	$0.876739\pi$
$572$	1.11818	+	0.406986i	0.0467536	+	0.0170169i
$573$		0			0
$574$	−2.08894	+	11.8470i	−0.0871908	+	0.494484i
$575$	2.37795	−	4.11873i	0.0991674	−	0.171763i
$576$		0			0
$577$	6.06615	+	10.5069i	0.252537	+	0.437407i	0.964224	−	0.265090i	$-0.0854017\pi$
$577$	6.06615	+	10.5069i	0.252537	+	0.437407i	−0.711687	+	0.702497i	$0.752068\pi$
$578$	31.0680	−	11.3078i	1.29226	−	0.470344i
$579$		0			0
$580$	22.4541	−	18.8412i	0.932355	−	0.782339i
$581$	−3.48957	+	2.92810i	−0.144772	+	0.121478i
$582$		0			0
$583$	−3.24352	+	1.18055i	−0.134333	+	0.0488932i
$584$	7.74416	+	13.4133i	0.320456	+	0.555046i
$585$		0			0
$586$	12.9722	−	22.4685i	0.535877	−	0.928167i
$587$	−5.51319	+	31.2669i	−0.227554	+	1.29052i	0.630189	+	0.776442i	$0.282977\pi$
$587$	−5.51319	+	31.2669i	−0.227554	+	1.29052i	−0.857743	+	0.514079i	$0.828134\pi$
$588$		0			0
$589$	50.7006	+	18.4535i	2.08908	+	0.760363i
$590$	1.70036	+	9.64321i	0.0700027	+	0.397005i
$591$		0			0
$592$	9.61254	+	8.06588i	0.395073	+	0.331506i
$593$	−13.4906			−0.553993			−0.276996	−	0.960871i	$-0.589339\pi$
$593$	−13.4906			−0.553993			−0.276996	+	0.960871i	$0.589339\pi$
$594$		0			0
$595$	−3.06459			−0.125636
$596$	−36.1947	−	30.3710i	−1.48259	−	1.24404i
$597$		0			0
$598$	1.20352	+	6.82550i	0.0492156	+	0.279115i
$599$	−39.8715	−	14.5120i	−1.62911	−	0.592946i	−0.644020	−	0.765009i	$-0.722735\pi$
$599$	−39.8715	−	14.5120i	−1.62911	−	0.592946i	−0.985086	+	0.172063i	$0.944957\pi$
$600$		0			0
$601$	−3.43906	+	19.5039i	−0.140282	+	0.795579i	0.830753	+	0.556641i	$0.187910\pi$
$601$	−3.43906	+	19.5039i	−0.140282	+	0.795579i	−0.971035	+	0.238938i	$0.923201\pi$
$602$	−5.75330	+	9.96501i	−0.234487	+	0.406144i
$603$		0			0
$604$	−4.97755	−	8.62136i	−0.202533	−	0.350798i
$605$	27.4810	−	10.0022i	1.11726	−	0.406649i
$606$		0			0
$607$	−27.5769	+	23.1397i	−1.11931	+	0.939213i	−0.998569	−	0.0534715i	$-0.982971\pi$
$607$	−27.5769	+	23.1397i	−1.11931	+	0.939213i	−0.120741	+	0.992684i	$0.538527\pi$
$608$	−38.0215	+	31.9038i	−1.54197	+	1.29387i
$609$		0			0
$610$	−5.41548	+	1.97107i	−0.219266	+	0.0798064i
$611$	1.87442	+	3.24659i	0.0758310	+	0.131343i
$612$		0			0
$613$	−13.2314	+	22.9175i	−0.534411	+	0.925627i	0.464780	+	0.885426i	$0.346133\pi$
$613$	−13.2314	+	22.9175i	−0.534411	+	0.925627i	−0.999192	+	0.0402013i	$0.987200\pi$
$614$	−9.73045	+	55.1841i	−0.392689	+	2.22705i
$615$		0			0
$616$	−0.294234	−	0.107093i	−0.0118550	−	0.00431488i
$617$	−8.52903	−	48.3705i	−0.343366	−	1.94732i	−0.319425	−	0.947611i	$-0.603490\pi$
$617$	−8.52903	−	48.3705i	−0.343366	−	1.94732i	−0.0239406	−	0.999713i	$-0.507621\pi$
$618$		0			0
$619$	−18.5430	−	15.5595i	−0.745307	−	0.625387i	0.188950	−	0.981987i	$-0.439492\pi$
$619$	−18.5430	−	15.5595i	−0.745307	−	0.625387i	−0.934257	+	0.356600i	$0.883936\pi$
$620$	−57.7145			−2.31787
$621$		0			0
$622$	37.3785			1.49874
$623$	11.5448	+	9.68725i	0.462533	+	0.388111i
$624$		0			0
$625$	−5.41077	−	30.6860i	−0.216431	−	1.22744i
$626$	−19.1881	−	6.98388i	−0.766909	−	0.279132i
$627$		0			0
$628$	3.13347	−	17.7708i	0.125039	−	0.709132i
$629$	−2.62345	+	4.54395i	−0.104604	+	0.181179i
$630$		0			0
$631$	−8.84842	−	15.3259i	−0.352250	−	0.610115i	0.634393	−	0.773010i	$-0.281250\pi$
$631$	−8.84842	−	15.3259i	−0.352250	−	0.610115i	−0.986643	+	0.162895i	$0.947917\pi$
$632$	10.7079	−	3.89736i	0.425938	−	0.155029i
$633$		0			0
$634$	6.01629	−	5.04827i	0.238937	−	0.200492i
$635$	10.7443	−	9.01555i	0.426375	−	0.357771i
$636$		0			0
$637$	−8.61398	+	3.13523i	−0.341298	+	0.124222i
$638$	−1.47732	−	2.55880i	−0.0584878	−	0.101304i
$639$		0			0
$640$	10.5917	−	18.3454i	0.418676	−	0.725167i
$641$	−6.60738	+	37.4723i	−0.260976	+	1.48007i	0.519278	+	0.854605i	$0.326201\pi$
$641$	−6.60738	+	37.4723i	−0.260976	+	1.48007i	−0.780254	+	0.625463i	$0.784910\pi$
$642$		0			0
$643$	−44.1115	−	16.0553i	−1.73959	−	0.633158i	−0.740352	−	0.672220i	$-0.765341\pi$
$643$	−44.1115	−	16.0553i	−1.73959	−	0.633158i	−0.999237	+	0.0390615i	$0.987563\pi$
$644$	−0.905644	−	5.13616i	−0.0356874	−	0.202393i
$645$		0			0
$646$	−11.8485	−	9.94211i	−0.466175	−	0.391167i
$647$	28.2333			1.10997			0.554983	−	0.831862i	$-0.312725\pi$
$647$	28.2333			1.10997			0.554983	+	0.831862i	$0.312725\pi$
$648$		0			0
$649$	0.546406			0.0214483
$650$	−5.39834	−	4.52974i	−0.211740	−	0.177671i
$651$		0			0
$652$	5.36140	+	30.4060i	0.209969	+	1.19079i
$653$	33.1779	+	12.0758i	1.29835	+	0.472562i	0.896460	−	0.443125i	$-0.146130\pi$
$653$	33.1779	+	12.0758i	1.29835	+	0.472562i	0.401893	+	0.915687i	$0.368353\pi$
$654$		0			0
$655$	3.37057	−	19.1155i	0.131699	−	0.746902i
$656$	−8.21052	+	14.2210i	−0.320567	+	0.555239i
$657$		0			0
$658$	−2.54795	−	4.41318i	−0.0993295	−	0.172044i
$659$	39.1793	−	14.2601i	1.52621	−	0.555494i	0.563519	−	0.826103i	$-0.309447\pi$
$659$	39.1793	−	14.2601i	1.52621	−	0.555494i	0.962689	+	0.270609i	$0.0872250\pi$
$660$		0			0
$661$	0.975874	−	0.818856i	0.0379571	−	0.0318498i	−0.623612	−	0.781734i	$-0.714335\pi$
$661$	0.975874	−	0.818856i	0.0379571	−	0.0318498i	0.661569	+	0.749884i	$0.269891\pi$
$662$	−2.29075	+	1.92216i	−0.0890324	+	0.0747070i
$663$		0			0
$664$	4.47359	−	1.62825i	0.173609	−	0.0631885i
$665$	−8.11461	−	14.0549i	−0.314671	−	0.545027i
$666$		0			0
$667$	4.76334	−	8.25035i	0.184437	−	0.319455i
$668$	1.00426	−	5.69543i	0.0388559	−	0.220363i
$669$		0			0
$670$	−4.57108	−	1.66374i	−0.176596	−	0.0642758i
$671$	0.0558427	+	0.316700i	0.00215578	+	0.0122261i
$672$		0			0
$673$	27.2963	+	22.9043i	1.05219	+	0.882896i	0.993323	−	0.115370i	$-0.0368053\pi$
$673$	27.2963	+	22.9043i	1.05219	+	0.882896i	0.0588715	+	0.998266i	$0.481250\pi$
$674$	−27.4951			−1.05907
$675$		0			0
$676$	−26.5561			−1.02139
$677$	−13.7902	−	11.5714i	−0.530002	−	0.444725i	0.338100	−	0.941110i	$-0.390216\pi$
$677$	−13.7902	−	11.5714i	−0.530002	−	0.444725i	−0.868102	+	0.496386i	$0.834660\pi$
$678$		0			0
$679$	−0.936996	−	5.31397i	−0.0359586	−	0.203931i
$680$	3.00961	+	1.09541i	0.115413	+	0.0420071i
$681$		0			0
$682$	−1.01023	+	5.72929i	−0.0386836	+	0.219386i
$683$	19.8807	−	34.4344i	0.760715	−	1.31760i	−0.181768	−	0.983341i	$-0.558182\pi$
$683$	19.8807	−	34.4344i	0.760715	−	1.31760i	0.942483	−	0.334255i	$-0.108485\pi$
$684$		0			0
$685$	15.0915	+	26.1393i	0.576617	+	0.998730i
$686$	25.2468	−	9.18909i	0.963928	−	0.350841i
$687$		0			0
$688$	−12.0322	+	10.0962i	−0.458724	+	0.384915i
$689$	−12.6327	+	10.6001i	−0.481266	+	0.403830i
$690$		0			0
$691$	15.8251	−	5.75986i	0.602015	−	0.219115i	−0.0229909	−	0.999736i	$-0.507319\pi$
$691$	15.8251	−	5.75986i	0.602015	−	0.219115i	0.625006	+	0.780620i	$0.285097\pi$
$692$	−4.44218	−	7.69408i	−0.168866	−	0.292485i
$693$		0			0
$694$	−5.08038	+	8.79948i	−0.192849	+	0.334024i
$695$	4.37036	−	24.7855i	0.165777	−	0.940169i
$696$		0			0
$697$	−6.45216	−	2.34839i	−0.244393	−	0.0889518i
$698$	−8.29833	−	47.0622i	−0.314097	−	1.78133i
$699$		0			0
$700$	4.06223	+	3.40862i	0.153538	+	0.128834i
$701$	8.96921			0.338762			0.169381	−	0.985551i	$-0.445823\pi$
$701$	8.96921			0.338762			0.169381	+	0.985551i	$0.445823\pi$
$702$		0			0
$703$	−27.7861			−1.04797
$704$	−2.73570	−	2.29552i	−0.103106	−	0.0865158i
$705$		0			0
$706$	10.9186	+	61.9223i	0.410926	+	2.33048i
$707$	−9.26398	−	3.37181i	−0.348408	−	0.126810i
$708$		0			0
$709$	3.15026	−	17.8660i	0.118311	−	0.670973i	−0.866747	−	0.498748i	$-0.833793\pi$
$709$	3.15026	−	17.8660i	0.118311	−	0.670973i	0.985058	−	0.172225i	$-0.0550955\pi$
$710$	−27.2477	+	47.1944i	−1.02259	+	1.77117i
$711$		0			0
$712$	−7.87509	−	13.6401i	−0.295131	−	0.511183i
$713$	−17.6267	+	6.41560i	−0.660125	+	0.240266i
$714$		0			0
$715$	−0.986166	+	0.827492i	−0.0368805	+	0.0309464i
$716$	37.9890	−	31.8766i	1.41972	−	1.19128i
$717$		0			0
$718$	26.6917	−	9.71498i	0.996125	−	0.362560i
$719$	15.7860	+	27.3421i	0.588718	+	1.01969i	0.994401	+	0.105675i	$0.0337004\pi$
$719$	15.7860	+	27.3421i	0.588718	+	1.01969i	−0.405683	+	0.914014i	$0.632966\pi$
$720$		0			0
$721$	4.79034	−	8.29711i	0.178402	−	0.309001i
$722$	7.24010	−	41.0606i	0.269449	−	1.52812i
$723$		0			0
$724$	−22.6814	−	8.25536i	−0.842948	−	0.306808i
$725$	1.68204	+	9.53930i	0.0624693	+	0.354281i
$726$		0			0
$727$	29.4232	+	24.6890i	1.09125	+	0.915664i	0.996806	−	0.0798662i	$-0.0254493\pi$
$727$	29.4232	+	24.6890i	1.09125	+	0.915664i	0.0944407	+	0.995530i	$0.469894\pi$
$728$	−1.49595			−0.0554436
$729$		0			0
$730$	−86.5599			−3.20373
$731$	−5.03111	−	4.22160i	−0.186082	−	0.156142i
$732$		0			0
$733$	−5.26680	−	29.8695i	−0.194534	−	1.10326i	−0.913081	−	0.407778i	$-0.866304\pi$
$733$	−5.26680	−	29.8695i	−0.194534	−	1.10326i	0.718547	−	0.695478i	$-0.244807\pi$
$734$	15.8123	+	5.75521i	0.583643	+	0.212429i
$735$		0			0
$736$	2.99643	−	16.9936i	0.110450	−	0.626391i
$737$	−0.135721	+	0.235076i	−0.00499936	+	0.00865915i
$738$		0			0
$739$	−5.00127	−	8.66245i	−0.183975	−	0.318653i	0.759256	−	0.650792i	$-0.225563\pi$
$739$	−5.00127	−	8.66245i	−0.183975	−	0.318653i	−0.943230	+	0.332139i	$0.892230\pi$
$740$	27.9300	−	10.1657i	1.02673	−	0.373699i
$741$		0			0
$742$	17.1719	−	14.4089i	0.630400	−	0.528969i
$743$	−27.7873	+	23.3163i	−1.01942	+	0.855394i	−0.989554	−	0.144160i	$-0.953952\pi$
$743$	−27.7873	+	23.3163i	−1.01942	+	0.855394i	−0.0298642	+	0.999554i	$0.509507\pi$
$744$		0			0
$745$	48.0337	−	17.4828i	1.75982	−	0.640521i
$746$	12.0865	+	20.9344i	0.442517	+	0.766461i
$747$		0			0
$748$	0.461619	−	0.799548i	0.0168785	−	0.0292344i
$749$	−0.873058	+	4.95136i	−0.0319008	+	0.180919i
$750$		0			0
$751$	13.6766	+	4.97788i	0.499067	+	0.181646i	0.579274	−	0.815133i	$-0.303336\pi$
$751$	13.6766	+	4.97788i	0.499067	+	0.181646i	−0.0802073	+	0.996778i	$0.525558\pi$
$752$	−1.20791	−	6.85041i	−0.0440480	−	0.249809i
$753$		0			0
$754$	−10.8136	−	9.07366i	−0.393807	−	0.330443i
$755$	10.7700			0.391959
$756$		0			0
$757$	−45.5754			−1.65646			−0.828232	−	0.560385i	$-0.810653\pi$
$757$	−45.5754			−1.65646			−0.828232	+	0.560385i	$0.810653\pi$
$758$	−39.1907	−	32.8849i	−1.42347	−	1.19443i
$759$		0			0
$760$	2.94524	+	16.7033i	0.106835	+	0.605892i
$761$	20.9040	+	7.60843i	0.757769	+	0.275805i	0.691871	−	0.722021i	$-0.256787\pi$
$761$	20.9040	+	7.60843i	0.757769	+	0.275805i	0.0658978	+	0.997826i	$0.479009\pi$
$762$		0			0
$763$	−1.23436	+	7.00040i	−0.0446868	+	0.253431i
$764$	−22.0189	+	38.1379i	−0.796616	+	1.37978i
$765$		0			0
$766$	9.99393	+	17.3100i	0.361096	+	0.625436i
$767$	2.45307	−	0.892846i	0.0885754	−	0.0322388i
$768$		0			0
$769$	10.4679	−	8.78365i	0.377484	−	0.316747i	−0.434230	−	0.900802i	$-0.642979\pi$
$769$	10.4679	−	8.78365i	0.377484	−	0.316747i	0.811714	+	0.584056i	$0.198535\pi$
$770$	1.34052	−	1.12483i	0.0483091	−	0.0405361i
$771$		0			0
$772$	−24.6670	+	8.97807i	−0.887786	+	0.323128i
$773$	−10.3270	−	17.8869i	−0.371436	−	0.643345i	0.618351	−	0.785902i	$-0.287801\pi$
$773$	−10.3270	−	17.8869i	−0.371436	−	0.643345i	−0.989787	+	0.142557i	$0.954468\pi$
$774$		0			0
$775$	9.53628	−	16.5173i	0.342553	−	0.593319i
$776$	−0.979243	+	5.55356i	−0.0351528	+	0.199361i
$777$		0			0
$778$	−5.06732	−	1.84436i	−0.181672	−	0.0661233i
$779$	−6.31415	−	35.8093i	−0.226228	−	1.28300i
$780$		0			0
$781$	2.32948	+	1.95466i	0.0833553	+	0.0699434i

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.62143 + 1.36054i) q^{2} +(0.430663 + 2.44241i) q^{4} +(-2.52129 - 0.917674i) q^{5} +(0.168844 - 0.957561i) q^{7} +(-0.508086 + 0.880031i) q^{8} +O(q^{10})\)	\(q+(1.62143 + 1.36054i) q^{2} +(0.430663 + 2.44241i) q^{4} +(-2.52129 - 0.917674i) q^{5} +(0.168844 - 0.957561i) q^{7} +(-0.508086 + 0.880031i) q^{8} +(-2.83955 - 4.91825i) q^{10} +(-0.297791 + 0.108387i) q^{11} +(-1.15981 + 0.973200i) q^{13} +(1.57657 - 1.32290i) q^{14} +(2.63991 - 0.960847i) q^{16} +(0.587342 + 1.01731i) q^{17} +(-3.11040 + 5.38737i) q^{19} +(1.15551 - 6.55323i) q^{20} +(-0.630310 - 0.229414i) q^{22} +(-0.375556 - 2.12988i) q^{23} +(1.68454 + 1.41350i) q^{25} -3.20463 q^{26} +2.41147 q^{28} +(3.37436 + 2.83142i) q^{29} +(-1.50609 - 8.54146i) q^{31} +(7.49746 + 2.72885i) q^{32} +(-0.431752 + 2.44859i) q^{34} +(-1.30443 + 2.25934i) q^{35} +(2.23332 + 3.86823i) q^{37} +(-12.3730 + 4.50341i) q^{38} +(2.08861 - 1.75255i) q^{40} +(-4.47767 + 3.75721i) q^{41} +(-5.25381 + 1.91223i) q^{43} +(-0.392973 - 0.680649i) q^{44} +(2.28885 - 3.96441i) q^{46} +(0.429965 - 2.43845i) q^{47} +(5.68943 + 2.07078i) q^{49} +(0.808243 + 4.58377i) q^{50} +(-2.87645 - 2.41362i) q^{52} +10.8920 q^{53} +0.850279 q^{55} +(0.756896 + 0.635111i) q^{56} +(1.61901 + 9.18189i) q^{58} +(-1.62023 - 0.589715i) q^{59} +(0.176214 - 0.999361i) q^{61} +(9.17898 - 15.8985i) q^{62} +(5.63455 + 9.75933i) q^{64} +(3.81731 - 1.38939i) q^{65} +(0.656156 - 0.550580i) q^{67} +(-2.23174 + 1.87265i) q^{68} +(-5.18896 + 1.88863i) q^{70} +(-4.79788 - 8.31018i) q^{71} +(7.62091 - 13.1998i) q^{73} +(-1.64171 + 9.31057i) q^{74} +(-14.4977 - 5.27674i) q^{76} +(0.0535070 + 0.303453i) q^{77} +(-8.59024 - 7.20807i) q^{79} -7.53771 q^{80} -12.3721 q^{82} +(-3.58886 - 3.01141i) q^{83} +(-0.547303 - 3.10391i) q^{85} +(-11.1203 - 4.04747i) q^{86} +(0.0559194 - 0.317135i) q^{88} +(-7.74976 + 13.4230i) q^{89} +(0.736071 + 1.27491i) q^{91} +(5.04032 - 1.83453i) q^{92} +(4.01476 - 3.36879i) q^{94} +(12.7861 - 10.7288i) q^{95} +(5.21481 - 1.89804i) q^{97} +(6.40762 + 11.0983i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8	\( 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8} - 3 q^{10} - 3 q^{11} - 6 q^{13} - 15 q^{14} - 9 q^{17} - 3 q^{19} + 3 q^{20} + 3 q^{22} + 12 q^{23} + 3 q^{25} + 30 q^{26} - 12 q^{28} + 6 q^{29} + 3 q^{31} + 9 q^{34} - 12 q^{35} - 3 q^{37} - 42 q^{38} + 21 q^{40} - 15 q^{41} + 3 q^{43} - 3 q^{44} - 3 q^{46} + 15 q^{47} + 12 q^{49} + 33 q^{50} + 9 q^{52} + 18 q^{53} - 12 q^{55} + 33 q^{56} + 21 q^{58} + 12 q^{59} + 12 q^{61} + 12 q^{62} + 12 q^{64} - 3 q^{65} - 15 q^{67} - 9 q^{68} - 15 q^{70} - 27 q^{71} + 6 q^{73} - 33 q^{74} - 48 q^{76} - 15 q^{77} - 42 q^{79} - 42 q^{80} - 12 q^{82} - 39 q^{83} - 27 q^{85} - 51 q^{86} - 30 q^{88} - 9 q^{89} + 6 q^{91} + 39 q^{92} - 15 q^{94} + 33 q^{95} + 3 q^{97} + 45 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 6 * q^8 - 3 * q^10 - 3 * q^11 - 6 * q^13 - 15 * q^14 - 9 * q^17 - 3 * q^19 + 3 * q^20 + 3 * q^22 + 12 * q^23 + 3 * q^25 + 30 * q^26 - 12 * q^28 + 6 * q^29 + 3 * q^31 + 9 * q^34 - 12 * q^35 - 3 * q^37 - 42 * q^38 + 21 * q^40 - 15 * q^41 + 3 * q^43 - 3 * q^44 - 3 * q^46 + 15 * q^47 + 12 * q^49 + 33 * q^50 + 9 * q^52 + 18 * q^53 - 12 * q^55 + 33 * q^56 + 21 * q^58 + 12 * q^59 + 12 * q^61 + 12 * q^62 + 12 * q^64 - 3 * q^65 - 15 * q^67 - 9 * q^68 - 15 * q^70 - 27 * q^71 + 6 * q^73 - 33 * q^74 - 48 * q^76 - 15 * q^77 - 42 * q^79 - 42 * q^80 - 12 * q^82 - 39 * q^83 - 27 * q^85 - 51 * q^86 - 30 * q^88 - 9 * q^89 + 6 * q^91 + 39 * q^92 - 15 * q^94 + 33 * q^95 + 3 * q^97 + 45 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more