LMFDB - Embedded newform 675.2.l.c.76.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 0]))

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

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

chi := DirichletCharacter("675.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, 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:	$5.38990213644$
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			76.2
Root			$0.500000 - 0.258654i$ of defining polynomial
Character	$\chi$	$=$	675.76
Dual form			675.2.l.c.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62143 - 1.36054i) q^{2} +(0.986166 - 1.42389i) q^{3} +(0.430663 - 2.44241i) q^{4} +(-0.338267 - 3.65046i) q^{6} +(-0.168844 - 0.957561i) q^{7} +(-0.508086 - 0.880031i) q^{8} +(-1.05495 - 2.80839i) q^{9} +O(q^{10})$	\(q+(1.62143 - 1.36054i) q^{2} +(0.986166 - 1.42389i) q^{3} +(0.430663 - 2.44241i) q^{4} +(-0.338267 - 3.65046i) q^{6} +(-0.168844 - 0.957561i) q^{7} +(-0.508086 - 0.880031i) q^{8} +(-1.05495 - 2.80839i) q^{9} +(0.297791 + 0.108387i) q^{11} +(-3.05303 - 3.02185i) q^{12} +(1.15981 + 0.973200i) q^{13} +(-1.57657 - 1.32290i) q^{14} +(2.63991 + 0.960847i) q^{16} +(0.587342 - 1.01731i) q^{17} +(-5.53146 - 3.11830i) q^{18} +(-3.11040 - 5.38737i) q^{19} +(-1.52997 - 0.703898i) q^{21} +(0.630310 - 0.229414i) q^{22} +(-0.375556 + 2.12988i) q^{23} +(-1.75413 - 0.144396i) q^{24} +3.20463 q^{26} +(-5.03922 - 1.26740i) q^{27} -2.41147 q^{28} +(-3.37436 + 2.83142i) q^{29} +(-1.50609 + 8.54146i) q^{31} +(7.49746 - 2.72885i) q^{32} +(0.448003 - 0.317135i) q^{33} +(-0.431752 - 2.44859i) q^{34} +(-7.31359 + 1.36716i) q^{36} +(-2.23332 + 3.86823i) q^{37} +(-12.3730 - 4.50341i) q^{38} +(2.52950 - 0.691717i) q^{39} +(4.47767 + 3.75721i) q^{41} +(-3.43842 + 0.940269i) q^{42} +(5.25381 + 1.91223i) q^{43} +(0.392973 - 0.680649i) q^{44} +(2.28885 + 3.96441i) q^{46} +(0.429965 + 2.43845i) q^{47} +(3.97153 - 2.81139i) q^{48} +(5.68943 - 2.07078i) q^{49} +(-0.869320 - 1.83955i) q^{51} +(2.87645 - 2.41362i) q^{52} +10.8920 q^{53} +(-9.89507 + 4.80105i) q^{54} +(-0.756896 + 0.635111i) q^{56} +(-10.7384 - 0.883963i) q^{57} +(-1.61901 + 9.18189i) q^{58} +(1.62023 - 0.589715i) q^{59} +(0.176214 + 0.999361i) q^{61} +(9.17898 + 15.8985i) q^{62} +(-2.51109 + 1.48436i) q^{63} +(5.63455 - 9.75933i) q^{64} +(0.294929 - 1.12374i) q^{66} +(-0.656156 - 0.550580i) q^{67} +(-2.23174 - 1.87265i) q^{68} +(2.66237 + 2.63517i) q^{69} +(4.79788 - 8.31018i) q^{71} +(-1.93547 + 2.35530i) q^{72} +(-7.62091 - 13.1998i) q^{73} +(1.64171 + 9.31057i) q^{74} +(-14.4977 + 5.27674i) q^{76} +(0.0535070 - 0.303453i) q^{77} +(3.16030 - 4.56306i) q^{78} +(-8.59024 + 7.20807i) q^{79} +(-6.77415 + 5.92544i) q^{81} +12.3721 q^{82} +(-3.58886 + 3.01141i) q^{83} +(-2.37811 + 3.43369i) q^{84} +(11.1203 - 4.04747i) q^{86} +(0.703969 + 7.59698i) q^{87} +(-0.0559194 - 0.317135i) q^{88} +(7.74976 + 13.4230i) q^{89} +(0.736071 - 1.27491i) q^{91} +(5.04032 + 1.83453i) q^{92} +(10.6769 + 10.5678i) q^{93} +(4.01476 + 3.36879i) q^{94} +(3.50815 - 13.3667i) q^{96} +(-5.21481 - 1.89804i) q^{97} +(6.40762 - 11.0983i) q^{98} +(-0.00976156 - 0.950656i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 + 6 * q^7 - 6 * q^8	$ 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8} + 3 q^{11} - 12 q^{12} + 6 q^{13} + 15 q^{14} - 9 q^{17} - 9 q^{18} - 3 q^{19} - 12 q^{21} - 3 q^{22} + 12 q^{23} - 18 q^{24} - 30 q^{26} + 9 q^{27} + 12 q^{28} - 6 q^{29} + 3 q^{31} + 9 q^{34} + 18 q^{36} + 3 q^{37} - 42 q^{38} + 33 q^{39} + 15 q^{41} - 18 q^{42} - 3 q^{43} + 3 q^{44} - 3 q^{46} + 15 q^{47} + 15 q^{48} + 12 q^{49} - 18 q^{51} - 9 q^{52} + 18 q^{53} - 54 q^{54} - 33 q^{56} + 3 q^{57} - 21 q^{58} - 12 q^{59} + 12 q^{61} + 12 q^{62} - 9 q^{63} + 12 q^{64} - 9 q^{66} + 15 q^{67} - 9 q^{68} + 9 q^{69} + 27 q^{71} - 18 q^{72} - 6 q^{73} + 33 q^{74} - 48 q^{76} - 15 q^{77} - 18 q^{78} - 42 q^{79} + 36 q^{81} + 12 q^{82} - 39 q^{83} + 6 q^{84} + 51 q^{86} - 9 q^{87} + 30 q^{88} + 9 q^{89} + 6 q^{91} + 39 q^{92} + 39 q^{93} - 15 q^{94} - 3 q^{97} + 45 q^{98} - 27 q^{99}+O(q^{100}) $ 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 + 6 * q^7 - 6 * q^8 + 3 * q^11 - 12 * q^12 + 6 * q^13 + 15 * q^14 - 9 * q^17 - 9 * q^18 - 3 * q^19 - 12 * q^21 - 3 * q^22 + 12 * q^23 - 18 * q^24 - 30 * q^26 + 9 * q^27 + 12 * q^28 - 6 * q^29 + 3 * q^31 + 9 * q^34 + 18 * q^36 + 3 * q^37 - 42 * q^38 + 33 * q^39 + 15 * q^41 - 18 * q^42 - 3 * q^43 + 3 * q^44 - 3 * q^46 + 15 * q^47 + 15 * q^48 + 12 * q^49 - 18 * q^51 - 9 * q^52 + 18 * q^53 - 54 * q^54 - 33 * q^56 + 3 * q^57 - 21 * q^58 - 12 * q^59 + 12 * q^61 + 12 * q^62 - 9 * q^63 + 12 * q^64 - 9 * q^66 + 15 * q^67 - 9 * q^68 + 9 * q^69 + 27 * q^71 - 18 * q^72 - 6 * q^73 + 33 * q^74 - 48 * q^76 - 15 * q^77 - 18 * q^78 - 42 * q^79 + 36 * q^81 + 12 * q^82 - 39 * q^83 + 6 * q^84 + 51 * q^86 - 9 * q^87 + 30 * q^88 + 9 * q^89 + 6 * q^91 + 39 * q^92 + 39 * q^93 - 15 * q^94 - 3 * q^97 + 45 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	1.62143	−	1.36054i	1.14652	−	0.962046i	0.146889	−	0.989153i	$-0.453074\pi$
$2$	1.62143	−	1.36054i	1.14652	−	0.962046i	0.999633	+	0.0271067i	$0.00862938\pi$
$3$	0.986166	−	1.42389i	0.569363	−	0.822086i
$3$	0.986166	−	1.42389i	0.569363	−	0.822086i
$4$	0.430663	−	2.44241i	0.215332	−	1.22121i
$5$		0			0
$5$		0			0
$6$	−0.338267	−	3.65046i	−0.138097	−	1.49029i
$7$	−0.168844	−	0.957561i	−0.0638170	−	0.361924i	−0.999947	−	0.0102706i	$-0.996731\pi$
$7$	−0.168844	−	0.957561i	−0.0638170	−	0.361924i	0.936130	−	0.351653i	$-0.114380\pi$
$8$	−0.508086	−	0.880031i	−0.179636	−	0.311138i
$9$	−1.05495	−	2.80839i	−0.351651	−	0.936131i
$10$		0			0
$11$	0.297791	+	0.108387i	0.0897872	+	0.0326799i	0.386523	−	0.922280i	$-0.373676\pi$
$11$	0.297791	+	0.108387i	0.0897872	+	0.0326799i	−0.296736	+	0.954960i	$0.595898\pi$
$12$	−3.05303	−	3.02185i	−0.881335	−	0.872332i
$13$	1.15981	+	0.973200i	0.321675	+	0.269917i	0.789297	−	0.614011i	$-0.210445\pi$
$13$	1.15981	+	0.973200i	0.321675	+	0.269917i	−0.467623	+	0.883928i	$0.654889\pi$
$14$	−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	−0.785968	−	0.618267i	$-0.787835\pi$
$17$	0.587342	−	1.01731i	0.142451	−	0.246733i	0.928419	+	0.371534i	$0.121168\pi$
$18$	−5.53146	−	3.11830i	−1.30378	−	0.734991i
$19$	−3.11040	−	5.38737i	−0.713575	−	1.23595i	−0.963507	−	0.267685i	$-0.913741\pi$
$19$	−3.11040	−	5.38737i	−0.713575	−	1.23595i	0.249931	−	0.968264i	$-0.419592\pi$
$20$		0			0
$21$	−1.52997	−	0.703898i	−0.333868	−	0.153603i
$22$	0.630310	−	0.229414i	0.134383	−	0.0489113i
$23$	−0.375556	+	2.12988i	−0.0783089	+	0.444112i	0.920292	+	0.391232i	$0.127951\pi$
$23$	−0.375556	+	2.12988i	−0.0783089	+	0.444112i	−0.998601	+	0.0528796i	$0.983160\pi$
$24$	−1.75413	−	0.144396i	−0.358060	−	0.0294747i
$25$		0			0
$26$	3.20463			0.628480
$27$	−5.03922	−	1.26740i	−0.969797	−	0.243912i
$28$	−2.41147			−0.455726
$29$	−3.37436	+	2.83142i	−0.626602	+	0.525782i	−0.899871	−	0.436156i	$-0.856340\pi$
$29$	−3.37436	+	2.83142i	−0.626602	+	0.525782i	0.273269	+	0.961938i	$0.411895\pi$
$30$		0			0
$31$	−1.50609	+	8.54146i	−0.270502	+	1.53409i	0.482395	+	0.875954i	$0.339767\pi$
$31$	−1.50609	+	8.54146i	−0.270502	+	1.53409i	−0.752897	+	0.658138i	$0.771344\pi$
$32$	7.49746	−	2.72885i	1.32538	−	0.482398i
$33$	0.448003	−	0.317135i	0.0779872	−	0.0552061i
$34$	−0.431752	−	2.44859i	−0.0740449	−	0.419930i
$35$		0			0
$36$	−7.31359	+	1.36716i	−1.21893	+	0.227859i
$37$	−2.23332	+	3.86823i	−0.367156	+	0.635933i	−0.989120	−	0.147113i	$-0.953002\pi$
$37$	−2.23332	+	3.86823i	−0.367156	+	0.635933i	0.621964	+	0.783046i	$0.286335\pi$
$38$	−12.3730	−	4.50341i	−2.00717	−	0.730550i
$39$	2.52950	−	0.691717i	0.405045	−	0.110763i
$40$		0			0
$41$	4.47767	+	3.75721i	0.699295	+	0.586778i	0.921573	−	0.388205i	$-0.126905\pi$
$41$	4.47767	+	3.75721i	0.699295	+	0.586778i	−0.222278	+	0.974983i	$0.571349\pi$
$42$	−3.43842	+	0.940269i	−0.530560	+	0.145087i
$43$	5.25381	+	1.91223i	0.801199	+	0.291613i	0.709983	−	0.704219i	$-0.248702\pi$
$43$	5.25381	+	1.91223i	0.801199	+	0.291613i	0.0912158	+	0.995831i	$0.470925\pi$
$44$	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	0.999975	+	0.00704911i	$0.00224382\pi$
$47$	0.429965	+	2.43845i	0.0627168	+	0.355685i	−0.937258	+	0.348636i	$0.886645\pi$
$48$	3.97153	−	2.81139i	0.573241	−	0.405790i
$49$	5.68943	−	2.07078i	0.812776	−	0.295826i
$50$		0			0
$51$	−0.869320	−	1.83955i	−0.121729	−	0.257588i
$52$	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	$0.230984\pi$
$54$	−9.89507	+	4.80105i	−1.34655	+	0.653340i
$55$		0			0
$56$	−0.756896	+	0.635111i	−0.101145	+	0.0848703i
$57$	−10.7384	−	0.883963i	−1.42234	−	0.117084i
$58$	−1.61901	+	9.18189i	−0.212587	+	1.20564i
$59$	1.62023	−	0.589715i	0.210936	−	0.0767743i	−0.234391	−	0.972142i	$-0.575310\pi$
$59$	1.62023	−	0.589715i	0.210936	−	0.0767743i	0.445327	+	0.895368i	$0.353087\pi$
$60$		0			0
$61$	0.176214	+	0.999361i	0.0225619	+	0.127955i	0.994008	−	0.109304i	$-0.0348621\pi$
$61$	0.176214	+	0.999361i	0.0225619	+	0.127955i	−0.971446	+	0.237259i	$0.923751\pi$
$62$	9.17898	+	15.8985i	1.16573	+	2.01911i
$63$	−2.51109	+	1.48436i	−0.316367	+	0.187012i
$64$	5.63455	−	9.75933i	0.704319	−	1.21992i
$65$		0			0
$66$	0.294929	−	1.12374i	0.0363033	−	0.138322i
$67$	−0.656156	−	0.550580i	−0.0801622	−	0.0672641i	0.601826	−	0.798627i	$-0.294440\pi$
$67$	−0.656156	−	0.550580i	−0.0801622	−	0.0672641i	−0.681988	+	0.731363i	$0.738884\pi$
$68$	−2.23174	−	1.87265i	−0.270638	−	0.227092i
$69$	2.66237	+	2.63517i	0.320512	+	0.317238i
$70$		0			0
$71$	4.79788	−	8.31018i	0.569404	−	0.986237i	−0.427221	−	0.904147i	$-0.640507\pi$
$71$	4.79788	−	8.31018i	0.569404	−	0.986237i	0.996625	−	0.0820894i	$-0.0261593\pi$
$72$	−1.93547	+	2.35530i	−0.228097	+	0.277574i
$73$	−7.62091	−	13.1998i	−0.891960	−	1.54492i	−0.837522	−	0.546404i	$-0.815996\pi$
$73$	−7.62091	−	13.1998i	−0.891960	−	1.54492i	−0.0544385	−	0.998517i	$-0.517337\pi$
$74$	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
$78$	3.16030	−	4.56306i	0.357833	−	0.516664i
$79$	−8.59024	+	7.20807i	−0.966478	+	0.810971i	−0.981995	−	0.188908i	$-0.939505\pi$
$79$	−8.59024	+	7.20807i	−0.966478	+	0.810971i	0.0155168	+	0.999880i	$0.495061\pi$
$80$		0			0
$81$	−6.77415	+	5.92544i	−0.752684	+	0.658382i
$82$	12.3721			1.36626
$83$	−3.58886	+	3.01141i	−0.393929	+	0.330546i	−0.818141	−	0.575017i	$-0.804995\pi$
$83$	−3.58886	+	3.01141i	−0.393929	+	0.330546i	0.424212	+	0.905563i	$0.360551\pi$
$84$	−2.37811	+	3.43369i	−0.259474	+	0.374646i
$85$		0			0
$86$	11.1203	−	4.04747i	1.19914	−	0.436450i
$87$	0.703969	+	7.59698i	0.0754734	+	0.814482i
$88$	−0.0559194	−	0.317135i	−0.00596103	−	0.0338067i
$89$	7.74976	+	13.4230i	0.821473	+	1.42283i	0.904586	+	0.426292i	$0.140180\pi$
$89$	7.74976	+	13.4230i	0.821473	+	1.42283i	−0.0831130	+	0.996540i	$0.526486\pi$
$90$		0			0
$91$	0.736071	−	1.27491i	0.0771612	−	0.133647i
$92$	5.04032	+	1.83453i	0.525490	+	0.191263i
$93$	10.6769	+	10.5678i	1.10714	+	1.09583i
$94$	4.01476	+	3.36879i	0.414091	+	0.347464i
$95$		0			0
$96$	3.50815	−	13.3667i	0.358049	−	1.36423i
$97$	−5.21481	−	1.89804i	−0.529484	−	0.192716i	0.0634241	−	0.997987i	$-0.479798\pi$
$97$	−5.21481	−	1.89804i	−0.529484	−	0.192716i	−0.592908	+	0.805270i	$0.702020\pi$
$98$	6.40762	−	11.0983i	0.647267	−	1.12110i
$99$	−0.00976156	−	0.950656i	−0.000981074	−	0.0955445i
$100$		0			0
$101$	−1.76063	−	9.98501i	−0.175189	−	0.993546i	−0.937926	−	0.346836i	$-0.887256\pi$
$101$	−1.76063	−	9.98501i	−0.175189	−	0.993546i	0.762737	−	0.646709i	$-0.223855\pi$
$102$	−3.91231	−	1.79995i	−0.387377	−	0.178221i
$103$	−9.25906	+	3.37002i	−0.912323	+	0.332058i	−0.755180	−	0.655518i	$-0.772451\pi$
$103$	−9.25906	+	3.37002i	−0.912323	+	0.332058i	−0.157143	+	0.987576i	$0.550228\pi$
$104$	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	$0.580411\pi$
$108$	−5.26573	+	11.7620i	−0.506695	+	1.13180i
$109$	−7.31065			−0.700234			−0.350117	−	0.936706i	$-0.613858\pi$
$109$	−7.31065			−0.700234			−0.350117	+	0.936706i	$0.613858\pi$
$110$		0			0
$111$	3.30552	+	6.99473i	0.313746	+	0.663911i
$112$	0.474338	−	2.69010i	0.0448207	−	0.254191i
$113$	9.74991	−	3.54868i	0.917195	−	0.333832i	0.160073	−	0.987105i	$-0.448827\pi$
$113$	9.74991	−	3.54868i	0.917195	−	0.333832i	0.757122	+	0.653274i	$0.226605\pi$
$114$	−18.6142	+	13.1768i	−1.74338	+	1.23412i
$115$		0			0
$116$	5.46229	+	9.46096i	0.507161	+	0.878428i
$117$	1.50958	−	4.28390i	0.139561	−	0.396046i
$118$	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
$123$	9.76560	−	2.67050i	0.880535	−	0.240790i
$124$	20.2132	+	7.35699i	1.81520	+	0.660677i
$125$		0			0
$126$	−2.05201	+	5.82321i	−0.182808	+	0.518773i
$127$	2.61372	+	4.52709i	0.231930	+	0.401714i	0.958376	−	0.285509i	$-0.0921627\pi$
$127$	2.61372	+	4.52709i	0.231930	+	0.401714i	−0.726446	+	0.687223i	$0.758829\pi$
$128$	−1.37098	−	7.77522i	−0.121179	−	0.687239i
$129$	7.90395	−	5.59510i	0.695904	−	0.492621i
$130$		0			0
$131$	−1.25622	+	7.12440i	−0.109757	+	0.622461i	0.879457	+	0.475979i	$0.157906\pi$
$131$	−1.25622	+	7.12440i	−0.109757	+	0.622461i	−0.989213	+	0.146482i	$0.953205\pi$
$132$	−0.581636	−	1.23079i	−0.0506249	−	0.107126i
$133$	−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	−0.931825	−	0.362907i	$-0.881784\pi$
$137$	−8.61748	+	7.23092i	−0.736241	+	0.617779i	0.195584	+	0.980687i	$0.437340\pi$
$138$	7.90210	+	0.650482i	0.672671	+	0.0553727i
$139$	1.62885	−	9.23766i	0.138157	−	0.783528i	−0.834452	−	0.551081i	$-0.814216\pi$
$139$	1.62885	−	9.23766i	0.138157	−	0.783528i	0.972609	−	0.232447i	$-0.0746733\pi$
$140$		0			0
$141$	3.89612	+	1.79249i	0.328112	+	0.150955i
$142$	−3.52690	−	20.0021i	−0.295971	−	1.67854i
$143$	0.239900	+	0.415518i	0.0200614	+	0.0347474i
$144$	−0.0865360	−	8.42754i	−0.00721133	−	0.702295i
$145$		0			0
$146$	−30.3156	−	11.0340i	−2.50894	−	0.913179i
$147$	2.66215	−	10.1433i	0.219570	−	0.836605i
$148$	8.48600	+	7.12060i	0.697545	+	0.585310i
$149$	14.5941	+	12.2459i	1.19560	+	1.00322i	0.999745	+	0.0225899i	$0.00719121\pi$
$149$	14.5941	+	12.2459i	1.19560	+	1.00322i	0.195851	+	0.980634i	$0.437253\pi$
$150$		0			0
$151$	−3.77193	−	1.37287i	−0.306955	−	0.111723i	0.183950	−	0.982936i	$-0.441112\pi$
$151$	−3.77193	−	1.37287i	−0.306955	−	0.111723i	−0.490905	+	0.871213i	$0.663334\pi$
$152$	−3.16070	+	5.47450i	−0.256367	+	0.444041i
$153$	−3.47661	−	0.576279i	−0.281068	−	0.0465894i
$154$	−0.326102	−	0.564825i	−0.0262780	−	0.0455149i
$155$		0			0
$156$	−0.600093	−	6.47599i	−0.0480459	−	0.518494i
$157$	6.83713	−	2.48851i	0.545662	−	0.198605i	−0.0544560	−	0.998516i	$-0.517342\pi$
$157$	6.83713	−	2.48851i	0.545662	−	0.198605i	0.600118	+	0.799911i	$0.295120\pi$
$158$	−4.12159	+	23.3747i	−0.327896	+	1.85959i
$159$	10.7413	−	15.5090i	0.851839	−	1.22994i
$160$		0			0
$161$	2.10290			0.165732
$162$	−2.92200	+	18.8242i	−0.229574	+	1.47897i
$163$	−12.4492			−0.975094			−0.487547	−	0.873097i	$-0.662108\pi$
$163$	−12.4492			−0.975094			−0.487547	+	0.873097i	$0.662108\pi$
$164$	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	−0.425408	−	0.905002i	$-0.639869\pi$
$167$	−2.19126	+	0.797553i	−0.169565	+	0.0617165i	0.255843	+	0.966718i	$0.417647\pi$
$168$	0.157906	+	1.70407i	0.0121827	+	0.131472i
$169$	−1.85937	−	10.5450i	−0.143029	−	0.811157i
$170$		0			0
$171$	−11.8485	+	14.4187i	−0.906081	+	1.10262i
$172$	6.93308	−	12.0085i	0.528643	−	0.915636i
$173$	−3.36623	−	1.22521i	−0.255930	−	0.0931509i	0.210869	−	0.977514i	$-0.432371\pi$
$173$	−3.36623	−	1.22521i	−0.255930	−	0.0931509i	−0.466799	+	0.884363i	$0.654593\pi$
$174$	11.4774	+	11.3602i	0.870101	+	0.861213i
$175$		0			0
$176$	0.681996	+	0.572262i	0.0514074	+	0.0431359i
$177$	0.758123	−	2.88859i	0.0569840	−	0.217120i
$178$	30.8281	+	11.2205i	2.31067	+	0.841014i
$179$	9.99785	−	17.3168i	0.747275	−	1.29432i	−0.201850	−	0.979416i	$-0.564695\pi$
$179$	9.99785	−	17.3168i	0.747275	−	1.29432i	0.949124	−	0.314901i	$-0.101971\pi$
$180$		0			0
$181$	−4.86616	−	8.42844i	−0.361699	−	0.626481i	0.626542	−	0.779388i	$-0.284470\pi$
$181$	−4.86616	−	8.42844i	−0.361699	−	0.626481i	−0.988241	+	0.152907i	$0.951136\pi$
$182$	−0.541082	−	3.06863i	−0.0401077	−	0.227462i
$183$	1.59676	+	0.734626i	0.118036	+	0.0543051i
$184$	2.06518	−	0.751664i	0.152247	−	0.0554134i
$185$		0			0
$186$	31.6897	+	2.60862i	2.32360	+	0.191274i
$187$	0.285168	−	0.239284i	0.0208535	−	0.0174982i
$188$	6.14088			0.447869
$189$	−0.362776	+	5.03935i	−0.0263881	+	0.366559i
$190$		0			0
$191$	−13.6023	+	11.4137i	−0.984227	+	0.825864i	−0.984722	−	0.174135i	$-0.944287\pi$
$191$	−13.6023	+	11.4137i	−0.984227	+	0.825864i	0.000494763		1.00000i	$0.499843\pi$
$192$	−8.33965	−	17.6473i	−0.601862	−	1.27359i
$193$	−1.83795	+	10.4235i	−0.132299	+	0.750303i	0.844404	+	0.535706i	$0.179955\pi$
$193$	−1.83795	+	10.4235i	−0.132299	+	0.750303i	−0.976703	+	0.214596i	$0.931156\pi$
$194$	−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	0.999987	+	0.00507615i	$0.00161579\pi$
$197$	7.07945	+	12.2620i	0.504390	+	0.873628i	−0.495597	+	0.868552i	$0.665051\pi$
$198$	−1.30923	−	1.52814i	−0.0930431	−	0.108600i
$199$	−3.77010	+	6.53000i	−0.267255	+	0.462899i	−0.968152	−	0.250363i	$-0.919450\pi$
$199$	−3.77010	+	6.53000i	−0.267255	+	0.462899i	0.700897	+	0.713263i	$0.252783\pi$
$200$		0			0
$201$	−1.43105	+	0.391333i	−0.100938	+	0.0276025i
$202$	−16.4397	−	13.7946i	−1.15669	−	0.970582i
$203$	3.28100	+	2.75308i	0.230281	+	0.193229i
$204$	−4.86732	+	1.33101i	−0.340780	+	0.0931896i
$205$		0			0
$206$	−10.4278	+	18.0616i	−0.726543	+	1.25841i
$207$	6.37775	−	1.19222i	0.443284	−	0.0828648i
$208$	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	−0.505106	−	0.863058i	$-0.668546\pi$
$211$	−4.89922	+	1.78317i	−0.337276	+	0.122758i	0.167829	+	0.985816i	$0.446324\pi$
$212$	4.69077	−	26.6027i	0.322163	−	1.82708i
$213$	−7.10131	−	15.0269i	−0.486573	−	1.02963i
$214$	−8.38408	+	7.03508i	−0.573124	+	0.480908i
$215$		0			0
$216$	1.44500	+	5.07862i	0.0983199	+	0.345556i
$217$	8.43326			0.572487
$218$	−11.8537	+	9.94643i	−0.802833	+	0.673657i
$219$	−26.3106	−	2.16583i	−1.77791	−	0.146353i
$220$		0			0
$221$	1.67125	−	0.608285i	0.112420	−	0.0409177i
$222$	14.8763	+	6.84416i	0.998430	+	0.459350i
$223$	−3.07250	−	17.4250i	−0.205750	−	1.16686i	−0.896256	−	0.443537i	$-0.853723\pi$
$223$	−3.07250	−	17.4250i	−0.205750	−	1.16686i	0.690506	−	0.723326i	$-0.257388\pi$
$224$	−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	−0.200418	−	0.979711i	$-0.564230\pi$
$227$	−14.8208	−	5.39434i	−0.983692	−	0.358035i	−0.783275	+	0.621676i	$0.786452\pi$
$228$	−6.78365	+	25.8470i	−0.449258	+	1.71176i
$229$	−1.35350	−	1.13572i	−0.0894415	−	0.0750504i	0.596971	−	0.802263i	$-0.296371\pi$
$229$	−1.35350	−	1.13572i	−0.0894415	−	0.0750504i	−0.686412	+	0.727213i	$0.740815\pi$
$230$		0			0
$231$	−0.379318	−	0.375443i	−0.0249573	−	0.0247024i
$232$	4.20620	+	1.53093i	0.276151	+	0.100511i
$233$	−6.94920	+	12.0364i	−0.455257	+	0.788529i	−0.998703	−	0.0509157i	$-0.983786\pi$
$233$	−6.94920	+	12.0364i	−0.455257	+	0.788529i	0.543446	+	0.839444i	$0.317119\pi$
$234$	−3.38073	−	8.99987i	−0.221005	−	0.588340i
$235$		0			0
$236$	−0.742554	−	4.21123i	−0.0483362	−	0.274128i
$237$	1.79212	+	19.3400i	0.116411	+	1.25627i
$238$	−2.27177	+	0.826858i	−0.147257	+	0.0535973i
$239$	−3.44391	+	19.5314i	−0.222768	+	1.26338i	0.644138	+	0.764909i	$0.277216\pi$
$239$	−3.44391	+	19.5314i	−0.222768	+	1.26338i	−0.866906	+	0.498471i	$0.833895\pi$
$240$		0			0
$241$	14.8419	−	12.4538i	0.956050	−	0.802221i	−0.0242563	−	0.999706i	$-0.507722\pi$
$241$	14.8419	−	12.4538i	0.956050	−	0.802221i	0.980306	+	0.197485i	$0.0632773\pi$
$242$	−23.0703			−1.48301
$243$	1.75676	+	15.4892i	0.112696	+	0.993629i
$244$	2.51674			0.161118
$245$		0			0
$246$	12.2009	−	17.6165i	0.777901	−	1.12319i
$247$	1.63550	−	9.27540i	0.104065	−	0.590179i
$248$	8.28198	−	3.01439i	0.525906	−	0.191414i
$249$	0.748720	+	8.07992i	0.0474482	+	0.512044i
$250$		0			0
$251$	2.73786	+	4.74212i	0.172812	+	0.299320i	0.939402	−	0.342818i	$-0.111381\pi$
$251$	2.73786	+	4.74212i	0.172812	+	0.299320i	−0.766590	+	0.642137i	$0.778048\pi$
$252$	2.54399	+	6.77237i	0.160256	+	0.426619i
$253$	−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	0.875833	−	0.482615i	$-0.160313\pi$
$257$	8.85943	+	7.43395i	0.552636	+	0.463717i	−0.323196	+	0.946332i	$0.604757\pi$
$258$	5.20333	−	19.8257i	0.323945	−	1.23429i
$259$	4.08115	+	1.48542i	0.253590	+	0.0922993i
$260$		0			0
$261$	11.5115	+	6.48951i	0.712546	+	0.401691i
$262$	7.65614	+	13.2608i	0.472998	+	0.819257i
$263$	−1.12488	−	6.37952i	−0.0693632	−	0.393378i	−0.999648	−	0.0265395i	$-0.991551\pi$
$263$	−1.12488	−	6.37952i	−0.0693632	−	0.393378i	0.930285	−	0.366839i	$-0.119560\pi$
$264$	−0.506712	−	0.233124i	−0.0311860	−	0.0143478i
$265$		0			0
$266$	−2.22318	+	12.6083i	−0.136312	+	0.773064i
$267$	26.7554	+	2.20245i	1.63741	+	0.134788i
$268$	−1.62733	+	1.36549i	−0.0994048	+	0.0834106i
$269$	−13.8387			−0.843758			−0.421879	−	0.906652i	$-0.638629\pi$
$269$	−13.8387			−0.843758			−0.421879	+	0.906652i	$0.638629\pi$
$270$		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
$273$	−1.08945	−	2.30536i	−0.0659366	−	0.139527i
$274$	−4.13466	+	23.4488i	−0.249784	+	1.41660i
$275$		0			0
$276$	7.58277	−	5.36774i	0.456429	−	0.323100i
$277$	−2.16586	−	12.2832i	−0.130134	−	0.738026i	−0.978125	−	0.208016i	$-0.933299\pi$
$277$	−2.16586	−	12.2832i	−0.130134	−	0.738026i	0.847991	−	0.530010i	$-0.177812\pi$
$278$	−9.92713	−	17.1943i	−0.595390	−	1.03125i
$279$	25.5766	−	4.78114i	1.53123	−	0.286239i
$280$		0			0
$281$	−9.16752	−	3.33670i	−0.546888	−	0.199051i	0.0537751	−	0.998553i	$-0.482875\pi$
$281$	−9.16752	−	3.33670i	−0.546888	−	0.199051i	−0.600663	+	0.799502i	$0.705097\pi$
$282$	8.75602	−	2.39442i	0.521414	−	0.142585i
$283$	−20.3547	−	17.0797i	−1.20996	−	1.01528i	−0.999288	−	0.0377246i	$-0.987989\pi$
$283$	−20.3547	−	17.0797i	−1.20996	−	1.01528i	−0.210676	−	0.977556i	$-0.567567\pi$
$284$	−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
$288$	−15.5732	−	18.1770i	−0.917657	−	1.07109i
$289$	7.81006	+	13.5274i	0.459415	+	0.795730i
$290$		0			0
$291$	−7.84527	+	5.55356i	−0.459898	+	0.325556i
$292$	−35.5214	+	12.9287i	−2.07873	+	0.756598i
$293$	−2.12849	+	12.0712i	−0.124347	+	0.705210i	0.857346	+	0.514741i	$0.172112\pi$
$293$	−2.12849	+	12.0712i	−0.124347	+	0.705210i	−0.981693	+	0.190469i	$0.938999\pi$
$294$	−9.48386	−	20.0686i	−0.553110	−	1.17042i
$295$		0			0
$296$	4.53888			0.263817
$297$	−1.36326	−	0.923606i	−0.0791044	−	0.0535930i
$298$	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
$303$	−15.9539	−	7.33993i	−0.916526	−	0.421668i
$304$	−3.03473	−	17.2108i	−0.174053	−	0.987106i
$305$		0			0
$306$	−6.42113	+	3.79567i	−0.367071	+	0.216984i
$307$	−13.2370	+	22.9271i	−0.755475	+	1.30852i	0.189663	+	0.981849i	$0.439260\pi$
$307$	−13.2370	+	22.9271i	−0.755475	+	1.30852i	−0.945138	+	0.326671i	$0.894073\pi$
$308$	−0.718114	−	0.261372i	−0.0409184	−	0.0148931i
$309$	−4.33242	+	16.5073i	−0.246463	+	0.939070i
$310$		0			0
$311$	−13.5280	−	11.3513i	−0.767100	−	0.643673i	0.172865	−	0.984946i	$-0.444698\pi$
$311$	−13.5280	−	11.3513i	−0.767100	−	0.643673i	−0.939964	+	0.341272i	$0.889142\pi$
$312$	−1.89394	−	1.87459i	−0.107223	−	0.106128i
$313$	9.06541	+	3.29954i	0.512407	+	0.186501i	0.585266	−	0.810841i	$-0.300990\pi$
$313$	9.06541	+	3.29954i	0.512407	+	0.186501i	−0.0728589	+	0.997342i	$0.523212\pi$
$314$	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	0.997541	−	0.0700850i	$-0.0223270\pi$
$317$	0.644320	+	3.65412i	0.0361886	+	0.205236i	−0.961352	+	0.275321i	$0.911216\pi$
$318$	−3.68439	−	39.7606i	−0.206610	−	2.22967i
$319$	−1.31174	+	0.477435i	−0.0734434	+	0.0267312i
$320$		0			0
$321$	−5.09927	+	7.36268i	−0.284614	+	0.410945i
$322$	3.40971	−	2.86108i	0.190016	−	0.159442i
$323$	−7.30748			−0.406599
$324$	11.5550	+	19.0972i	0.641944	+	1.06095i
$325$		0			0
$326$	−20.1854	+	16.9376i	−1.11797	+	0.938085i
$327$	−7.20952	+	10.4096i	−0.398687	+	0.575652i
$328$	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	0.977323	−	0.211755i	$-0.0679177\pi$
$331$	−0.245329	−	1.39133i	−0.0134845	−	0.0764745i	−0.990807	+	0.135280i	$0.956807\pi$
$332$	5.80953	+	10.0624i	0.318839	+	0.552246i
$333$	13.2196	+	2.19126i	0.724427	+	0.120080i
$334$	−2.46786	+	4.27446i	−0.135035	+	0.233888i
$335$		0			0
$336$	−3.36265	−	3.32830i	−0.183447	−	0.181573i
$337$	9.95097	+	8.34986i	0.542064	+	0.454846i	0.872243	−	0.489073i	$-0.162665\pi$
$337$	9.95097	+	8.34986i	0.542064	+	0.454846i	−0.330179	+	0.943918i	$0.607109\pi$
$338$	−17.3618	−	14.5683i	−0.944356	−	0.792409i
$339$	4.56209	−	17.3824i	0.247779	−	0.944084i
$340$		0			0
$341$	−1.37428	+	2.38033i	−0.0744215	+	0.128902i
$342$	0.405587	+	39.4992i	0.0219316	+	2.13587i
$343$	−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	−0.954224	−	0.299094i	$-0.903316\pi$
$347$	0.833591	−	4.72753i	0.0447495	−	0.253787i	0.998973	+	0.0453070i	$0.0144266\pi$
$348$	18.8581	+	1.55236i	1.01090	+	0.0832152i
$349$	−17.2954	+	14.5126i	−0.925803	+	0.776841i	−0.975059	−	0.221946i	$-0.928759\pi$
$349$	−17.2954	+	14.5126i	−0.925803	+	0.776841i	0.0492565	+	0.998786i	$0.484315\pi$
$350$		0			0
$351$	−4.61112	−	6.37412i	−0.246123	−	0.340225i
$352$	2.52845			0.134767
$353$	22.7565	−	19.0950i	1.21121	−	1.01632i	0.211972	−	0.977276i	$-0.432012\pi$
$353$	22.7565	−	19.0950i	1.21121	−	1.01632i	0.999237	−	0.0390490i	$-0.0124328\pi$
$354$	−2.70080	−	5.71509i	−0.143546	−	0.303754i
$355$		0			0
$356$	36.1220	−	13.1473i	1.91446	−	0.696807i
$357$	−1.61470	+	1.14302i	−0.0854589	+	0.0604952i
$358$	−7.34937	−	41.6804i	−0.388427	−	2.20288i
$359$	−6.70991	−	11.6219i	−0.354136	−	0.613381i	0.632834	−	0.774288i	$-0.281892\pi$
$359$	−6.70991	−	11.6219i	−0.354136	−	0.613381i	−0.986970	+	0.160906i	$0.948558\pi$
$360$		0			0
$361$	−9.84920	+	17.0593i	−0.518379	+	0.897858i
$362$	−19.3573	−	7.04550i	−1.01740	−	0.370303i
$363$	−18.2100	+	4.97970i	−0.955778	+	0.261366i
$364$	−2.79686	−	2.34685i	−0.146595	−	0.123008i
$365$		0			0
$366$	3.58852	−	0.981314i	0.187575	−	0.0512941i
$367$	−7.47054	−	2.71905i	−0.389959	−	0.141933i	0.139597	−	0.990208i	$-0.455419\pi$
$367$	−7.47054	−	2.71905i	−0.389959	−	0.141933i	−0.529556	+	0.848275i	$0.677641\pi$
$368$	−3.03793	+	5.26184i	−0.158363	+	0.274293i
$369$	5.82801	−	16.5387i	0.303394	−	0.860973i
$370$		0			0
$371$	−1.83904	−	10.4297i	−0.0954782	−	0.541484i
$372$	30.4091	−	21.5262i	1.57664	−	1.11608i
$373$	−10.7318	+	3.90604i	−0.555670	+	0.202247i	−0.604564	−	0.796557i	$-0.706653\pi$
$373$	−10.7318	+	3.90604i	−0.555670	+	0.202247i	0.0488939	+	0.998804i	$0.484430\pi$
$374$	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
$378$	6.26801	+	8.66451i	0.322392	+	0.445654i
$379$	−24.1705			−1.24155			−0.620777	−	0.783987i	$-0.713183\pi$
$379$	−24.1705			−1.24155			−0.620777	+	0.783987i	$0.713183\pi$
$380$		0			0
$381$	9.02366	+	0.742807i	0.462296	+	0.0380551i
$382$	−6.52637	+	37.0129i	−0.333918	+	1.89374i
$383$	8.87378	−	3.22979i	0.453429	−	0.165035i	−0.105202	−	0.994451i	$-0.533549\pi$
$383$	8.87378	−	3.22979i	0.453429	−	0.165035i	0.558631	+	0.829416i	$0.311327\pi$
$384$	−12.4231	−	5.71553i	−0.633964	−	0.291669i
$385$		0			0
$386$	11.2015	+	19.4016i	0.570143	+	0.987516i
$387$	−0.172220	−	16.7721i	−0.00875442	−	0.852573i
$388$	−6.88162	+	11.9193i	−0.349361	+	0.605111i
$389$	2.39406	+	0.871367i	0.121384	+	0.0441801i	0.401998	−	0.915641i	$-0.368316\pi$
$389$	2.39406	+	0.871367i	0.121384	+	0.0441801i	−0.280614	+	0.959821i	$0.590538\pi$
$390$		0			0
$391$	1.94617	+	1.63303i	0.0984218	+	0.0825857i
$392$	−4.71308	−	3.95474i	−0.238046	−	0.199745i
$393$	8.90554	+	8.81457i	0.449225	+	0.444636i
$394$	28.1617	+	10.2500i	1.41876	+	0.516388i
$395$		0			0
$396$	−2.32610	−	0.385571i	−0.116891	−	0.0193757i
$397$	1.83759	+	3.18279i	0.0922258	+	0.159740i	0.908447	−	0.417999i	$-0.137269\pi$
$397$	1.83759	+	3.18279i	0.0922258	+	0.159740i	−0.816222	+	0.577739i	$0.803935\pi$
$398$	2.77138	+	15.7173i	0.138917	+	0.787836i
$399$	0.966669	+	10.4319i	0.0483940	+	0.522251i
$400$		0			0
$401$	2.80420	−	15.9034i	0.140035	−	0.794177i	−0.831186	−	0.555995i	$-0.812337\pi$
$401$	2.80420	−	15.9034i	0.140035	−	0.794177i	0.971220	−	0.238182i	$-0.0765516\pi$
$402$	−1.78791	+	2.58151i	−0.0891731	+	0.128754i
$403$	−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
$408$	−1.17717	+	1.69968i	−0.0582785	+	0.0841465i
$409$	1.59443	−	9.04248i	0.0788396	−	0.447122i	−0.919677	−	0.392676i	$-0.871550\pi$
$409$	1.59443	−	9.04248i	0.0788396	−	0.447122i	0.998517	−	0.0544462i	$-0.0173393\pi$
$410$		0			0
$411$	1.79780	+	19.4013i	0.0886792	+	0.956994i
$412$	4.24345	+	24.0658i	0.209060	+	1.18564i
$413$	−0.838253	−	1.45190i	−0.0412477	−	0.0714432i
$414$	8.71900	−	10.6103i	0.428515	−	0.521466i
$415$		0			0
$416$	11.3514	+	4.13157i	0.556548	+	0.202567i
$417$	−11.5471	−	11.4292i	−0.565466	−	0.559689i
$418$	−3.19646	−	2.68215i	−0.156344	−	0.131188i
$419$	−5.34613	−	4.48594i	−0.261176	−	0.219152i	0.502791	−	0.864408i	$-0.332306\pi$
$419$	−5.34613	−	4.48594i	−0.261176	−	0.219152i	−0.763967	+	0.645256i	$0.776751\pi$
$420$		0			0
$421$	−28.9525	−	10.5379i	−1.41106	−	0.513584i	−0.479619	−	0.877477i	$-0.659225\pi$
$421$	−28.9525	−	10.5379i	−1.41106	−	0.513584i	−0.931441	+	0.363894i	$0.881447\pi$
$422$	−5.51765	+	9.55686i	−0.268595	+	0.465221i
$423$	6.39454	−	3.77996i	0.310913	−	0.183788i
$424$	−5.53405	−	9.58526i	−0.268757	−	0.465502i
$425$		0			0
$426$	−31.9589	−	14.7034i	−1.54842	−	0.712383i
$427$	0.927196	−	0.337472i	0.0448702	−	0.0163314i
$428$	−2.22687	+	12.6292i	−0.107640	+	0.610457i
$429$	0.828236	+	0.0681784i	0.0399876	+	0.00329169i
$430$		0			0
$431$	27.8971			1.34376			0.671879	−	0.740661i	$-0.265487\pi$
$431$	27.8971			1.34376			0.671879	+	0.740661i	$0.265487\pi$
$432$	−12.0853	−	8.18774i	−0.581453	−	0.393933i
$433$	−19.1706			−0.921278			−0.460639	−	0.887588i	$-0.652380\pi$
$433$	−19.1706			−0.921278			−0.460639	+	0.887588i	$0.652380\pi$
$434$	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
$438$	−45.6075	+	32.2849i	−2.17921	+	1.54263i
$439$	−4.12397	−	23.3882i	−0.196826	−	1.11626i	−0.909794	−	0.415060i	$-0.863761\pi$
$439$	−4.12397	−	23.3882i	−0.196826	−	1.11626i	0.712968	−	0.701197i	$-0.247351\pi$
$440$		0			0
$441$	−11.8177	−	13.7936i	−0.562746	−	0.656838i
$442$	1.88221	−	3.26009i	0.0895278	−	0.155067i
$443$	21.9496	+	7.98900i	1.04286	+	0.379569i	0.805962	−	0.591967i	$-0.201648\pi$
$443$	21.9496	+	7.98900i	1.04286	+	0.379569i	0.236894	+	0.971536i	$0.423871\pi$
$444$	18.5076	−	5.06108i	0.878332	−	0.240188i
$445$		0			0
$446$	−28.6892	−	24.0731i	−1.35847	−	1.13989i
$447$	31.8291	−	8.70396i	1.50546	−	0.411683i
$448$	−10.2965	−	3.74762i	−0.486464	−	0.177059i
$449$	−2.40953	+	4.17343i	−0.113713	+	0.196956i	−0.917264	−	0.398279i	$-0.869608\pi$
$449$	−2.40953	+	4.17343i	−0.113713	+	0.196956i	0.803552	+	0.595235i	$0.202941\pi$
$450$		0			0
$451$	0.926176	+	1.60418i	0.0436119	+	0.0755380i
$452$	−4.46841	−	25.3416i	−0.210176	−	1.19197i
$453$	−5.67457	+	4.01695i	−0.266615	+	0.188733i
$454$	−31.3701	+	11.4178i	−1.47227	+	0.535863i
$455$		0			0
$456$	4.67813	+	9.89928i	0.219074	+	0.463576i
$457$	3.74872	−	3.14555i	0.175358	−	0.147142i	−0.550885	−	0.834581i	$-0.685710\pi$
$457$	3.74872	−	3.14555i	0.175358	−	0.147142i	0.726242	+	0.687439i	$0.241265\pi$
$458$	−3.73978			−0.174749
$459$	−4.24908	+	4.38203i	−0.198330	+	0.204535i
$460$		0			0
$461$	21.4419	−	17.9919i	0.998650	−	0.837967i	0.0118535	−	0.999930i	$-0.496227\pi$
$461$	21.4419	−	17.9919i	0.998650	−	0.837967i	0.986797	+	0.161963i	$0.0517824\pi$
$462$	−1.12584	−	0.0926768i	−0.0523789	−	0.00431171i
$463$	4.77104	−	27.0579i	0.221729	−	1.25749i	−0.647111	−	0.762396i	$-0.724023\pi$
$463$	4.77104	−	27.0579i	0.221729	−	1.25749i	0.868840	−	0.495093i	$-0.164866\pi$
$464$	−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	0.508368	−	0.861140i	$-0.330249\pi$
$467$	−10.6232	−	18.4000i	−0.491585	−	0.851450i	−0.999953	+	0.00968963i	$0.996916\pi$
$468$	−9.81292	−	5.53194i	−0.453602	−	0.255714i
$469$	−0.416426	+	0.721272i	−0.0192288	+	0.0333052i
$470$		0			0
$471$	3.19917	−	12.1894i	0.147410	−	0.561659i
$472$	−1.34218	−	1.12623i	−0.0617790	−	0.0518387i
$473$	1.35728	+	1.13889i	0.0624076	+	0.0523662i
$474$	29.2186	+	28.9201i	1.34205	+	1.32834i
$475$		0			0
$476$	−1.41636	+	2.45321i	−0.0649188	+	0.112443i
$477$	−11.4905	−	30.5889i	−0.526113	−	1.40057i
$478$	20.9892	+	36.3543i	0.960022	+	1.66281i
$479$	−7.23745	−	41.0456i	−0.330688	−	1.87542i	−0.466248	−	0.884654i	$-0.654394\pi$
$479$	−7.23745	−	41.0456i	−0.330688	−	1.87542i	0.135560	−	0.990769i	$-0.456717\pi$
$480$		0			0
$481$	−6.35480	+	2.31296i	−0.289754	+	0.105462i
$482$	7.12113	−	40.3859i	0.324358	−	1.83953i
$483$	2.07381	−	2.99431i	0.0943618	−	0.136246i
$484$	−20.7077	+	17.3758i	−0.941258	+	0.789809i
$485$		0			0
$486$	23.9220	+	22.7244i	1.08513	+	1.03080i
$487$	−4.02801			−0.182527			−0.0912634	−	0.995827i	$-0.529091\pi$
$487$	−4.02801			−0.182527			−0.0912634	+	0.995827i	$0.529091\pi$
$488$	0.789937	−	0.662836i	0.0357588	−	0.0300052i
$489$	−12.2769	+	17.7263i	−0.555183	+	0.801611i
$490$		0			0
$491$	36.2922	−	13.2093i	1.63784	−	0.596126i	0.651184	−	0.758920i	$-0.274273\pi$
$491$	36.2922	−	13.2093i	1.63784	−	0.596126i	0.986660	+	0.162793i	$0.0520504\pi$
$492$	−2.31677	−	25.0017i	−0.104448	−	1.12716i
$493$	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
$498$	12.2070	+	12.0823i	0.547011	+	0.541423i
$499$	−3.11922	−	2.61734i	−0.139636	−	0.117168i	0.570295	−	0.821440i	$-0.306829\pi$
$499$	−3.11922	−	2.61734i	−0.139636	−	0.117168i	−0.709930	+	0.704272i	$0.751274\pi$
$500$		0			0
$501$	−1.02531	+	3.90664i	−0.0458076	+	0.174536i
$502$	10.8911	+	3.96403i	0.486093	+	0.176923i
$503$	−1.71297	+	2.96695i	−0.0763775	+	0.132290i	−0.901684	−	0.432395i	$-0.857669\pi$
$503$	−1.71297	+	2.96695i	−0.0763775	+	0.132290i	0.825307	+	0.564684i	$0.191002\pi$
$504$	2.58213	+	1.45565i	0.115017	+	0.0648398i
$505$		0			0
$506$	0.251909	+	1.42865i	0.0111987	+	0.0635111i
$507$	−16.8487	−	7.75161i	−0.748276	−	0.344261i
$508$	12.1827	−	4.43412i	0.540518	−	0.196732i
$509$	−2.12952	+	12.0771i	−0.0943893	+	0.535308i	0.900543	+	0.434766i	$0.143169\pi$
$509$	−2.12952	+	12.0771i	−0.0943893	+	0.535308i	−0.994933	+	0.100542i	$0.967942\pi$
$510$		0			0
$511$	−11.3529	+	9.52619i	−0.502222	+	0.421414i
$512$	28.1241			1.24292
$513$	8.84601	+	31.0903i	0.390561	+	1.37267i
$514$	24.4791			1.07973
$515$		0			0
$516$	−10.2616	−	21.7143i	−0.451742	−	0.955920i
$517$	−0.136257	+	0.772750i	−0.00599257	+	0.0339855i
$518$	8.63825	−	3.14407i	0.379543	−	0.138142i
$519$	−5.06423	+	3.58490i	−0.222295	+	0.157360i
$520$		0			0
$521$	−7.04117	−	12.1957i	−0.308479	−	0.534302i	0.669551	−	0.742766i	$-0.266487\pi$
$521$	−7.04117	−	12.1957i	−0.308479	−	0.534302i	−0.978030	+	0.208465i	$0.933153\pi$
$522$	27.4943	−	5.13962i	1.20339	−	0.224955i
$523$	4.88956	−	8.46897i	0.213806	−	0.370322i	−0.739097	−	0.673599i	$-0.764747\pi$
$523$	4.88956	−	8.46897i	0.213806	−	0.370322i	0.952902	+	0.303277i	$0.0980808\pi$
$524$	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
$528$	1.48740	−	0.406744i	0.0647309	−	0.0177013i
$529$	17.2176	+	6.26668i	0.748590	+	0.272464i
$530$		0			0
$531$	−3.36541	−	3.92812i	−0.146047	−	0.170466i
$532$	7.50065	+	12.9915i	0.325195	+	0.563254i
$533$	1.53675	+	8.71534i	0.0665640	+	0.377503i
$534$	46.3785	−	32.8307i	2.00699	−	1.42072i
$535$		0			0
$536$	−0.151144	+	0.857180i	−0.00652843	+	0.0370245i
$537$	−14.7977	−	31.3131i	−0.638569	−	1.35126i
$538$	−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
$543$	−16.8001	−	1.38294i	−0.720959	−	0.0593477i
$544$	1.62750	−	9.22999i	0.0697783	−	0.395732i
$545$		0			0
$546$	−4.90300	−	2.25573i	−0.209829	−	0.0965365i
$547$	−0.192798	−	1.09341i	−0.00824343	−	0.0467508i	0.980409	−	0.196975i	$-0.0631117\pi$
$547$	−0.192798	−	1.09341i	−0.00824343	−	0.0467508i	−0.988652	+	0.150224i	$0.952001\pi$
$548$	13.9497	+	24.1615i	0.595900	+	1.03213i
$549$	2.62070	−	1.54916i	0.111849	−	0.0661164i
$550$		0			0
$551$	25.7495	+	9.37206i	1.09697	+	0.399263i
$552$	0.966321	−	3.68186i	0.0411293	−	0.156711i
$553$	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	−0.209070	−	0.977901i	$-0.567044\pi$
$557$	17.5201	−	30.3458i	0.742352	−	1.28579i	0.951422	−	0.307890i	$-0.0996230\pi$
$558$	34.9657	−	42.5503i	1.48022	−	1.80130i
$559$	4.23247	+	7.33084i	0.179014	+	0.310062i
$560$		0			0
$561$	−0.0594925	−	0.642022i	−0.00251178	−	0.0271062i
$562$	−19.4042	+	7.06254i	−0.818516	+	0.297915i
$563$	6.73255	−	38.1822i	0.283743	−	1.60919i	−0.425998	−	0.904724i	$-0.640077\pi$
$563$	6.73255	−	38.1822i	0.283743	−	1.60919i	0.709741	−	0.704463i	$-0.248812\pi$
$564$	6.05593	−	8.74396i	0.255001	−	0.368187i
$565$		0			0
$566$	−56.2413			−2.36400
$567$	6.81774	+	5.48619i	0.286318	+	0.230398i
$568$	−9.75095			−0.409141
$569$	−26.0213	+	21.8344i	−1.09087	+	0.915347i	−0.996777	−	0.0802169i	$-0.974439\pi$
$569$	−26.0213	+	21.8344i	−1.09087	+	0.915347i	−0.0940904	+	0.995564i	$0.529994\pi$
$570$		0			0
$571$	1.75191	−	9.93559i	0.0733153	−	0.415792i	−0.925956	−	0.377631i	$-0.876739\pi$
$571$	1.75191	−	9.93559i	0.0733153	−	0.415792i	0.999272	−	0.0381610i	$-0.0121500\pi$
$572$	1.11818	−	0.406986i	0.0467536	−	0.0170169i
$573$	2.83775	+	30.6240i	0.118549	+	1.27934i
$574$	−2.08894	−	11.8470i	−0.0871908	−	0.494484i
$575$		0			0
$576$	−33.3522	−	5.52842i	−1.38968	−	0.230351i
$577$	−6.06615	+	10.5069i	−0.252537	+	0.437407i	−0.964224	−	0.265090i	$-0.914598\pi$
$577$	−6.06615	+	10.5069i	−0.252537	+	0.437407i	0.711687	+	0.702497i	$0.247932\pi$
$578$	31.0680	+	11.3078i	1.29226	+	0.470344i
$579$	13.0295	+	12.8964i	0.541487	+	0.535956i
$580$		0			0
$581$	3.48957	+	2.92810i	0.144772	+	0.121478i
$582$	−5.16470	+	19.6785i	−0.214084	+	0.815700i
$583$	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	−0.857743	−	0.514079i	$-0.828134\pi$
$587$	−5.51319	−	31.2669i	−0.227554	−	1.29052i	0.630189	−	0.776442i	$-0.282977\pi$
$588$	−23.6276	−	10.8704i	−0.974387	−	0.448288i
$589$	50.7006	−	18.4535i	2.08908	−	0.760363i
$590$		0			0
$591$	24.4412	+	2.01195i	1.00538	+	0.0827605i
$592$	−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	$0.589339\pi$
$594$	−3.46703	+	0.357210i	−0.142254	+	0.0146565i
$595$		0			0
$596$	36.1947	−	30.3710i	1.48259	−	1.24404i
$597$	5.58009	+	11.8079i	0.228378	+	0.483265i
$598$	−1.20352	+	6.82550i	−0.0492156	+	0.279115i
$599$	39.8715	−	14.5120i	1.62911	−	0.592946i	0.644020	−	0.765009i	$-0.277265\pi$
$599$	39.8715	−	14.5120i	1.62911	−	0.592946i	0.985086	+	0.172063i	$0.0550432\pi$
$600$		0			0
$601$	−3.43906	−	19.5039i	−0.140282	−	0.795579i	−0.971035	−	0.238938i	$-0.923201\pi$
$601$	−3.43906	−	19.5039i	−0.140282	−	0.795579i	0.830753	−	0.556641i	$-0.187910\pi$
$602$	−5.75330	−	9.96501i	−0.234487	−	0.406144i
$603$	−0.854034	+	2.42358i	−0.0347789	+	0.0986958i
$604$	−4.97755	+	8.62136i	−0.202533	+	0.350798i
$605$		0			0
$606$	−35.8543	+	9.80470i	−1.45648	+	0.398289i
$607$	27.5769	+	23.1397i	1.11931	+	0.939213i	0.998569	−	0.0534715i	$-0.0170286\pi$
$607$	27.5769	+	23.1397i	1.11931	+	0.939213i	0.120741	+	0.992684i	$0.461473\pi$
$608$	−38.0215	−	31.9038i	−1.54197	−	1.29387i
$609$	7.15571	−	1.95680i	0.289964	−	0.0792934i
$610$		0			0
$611$	−1.87442	+	3.24659i	−0.0758310	+	0.131343i
$612$	−2.90476	+	8.24315i	−0.117418	+	0.333209i
$613$	13.2314	+	22.9175i	0.534411	+	0.925627i	0.999192	+	0.0402013i	$0.0127999\pi$
$613$	13.2314	+	22.9175i	0.534411	+	0.925627i	−0.464780	+	0.885426i	$0.653867\pi$
$614$	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	−0.0239406	+	0.999713i	$0.507621\pi$
$617$	−8.52903	+	48.3705i	−0.343366	+	1.94732i	−0.319425	+	0.947611i	$0.603490\pi$
$618$	15.4342	+	32.6599i	0.620853	+	1.31377i
$619$	−18.5430	+	15.5595i	−0.745307	+	0.625387i	−0.934257	−	0.356600i	$-0.883936\pi$
$619$	−18.5430	+	15.5595i	−0.745307	+	0.625387i	0.188950	+	0.981987i	$0.439492\pi$
$620$		0			0
$621$	4.59193	−	10.2570i	0.184268	−	0.411598i
$622$	−37.3785			−1.49874
$623$	11.5448	−	9.68725i	0.462533	−	0.388111i
$624$	7.34229	+	0.604400i	0.293927	+	0.0241954i
$625$		0			0
$626$	19.1881	−	6.98388i	0.766909	−	0.279132i
$627$	−3.10199	−	1.42714i	−0.123882	−	0.0569945i
$628$	−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	−0.986643	−	0.162895i	$-0.947917\pi$
$631$	−8.84842	+	15.3259i	−0.352250	+	0.610115i	0.634393	+	0.773010i	$0.281250\pi$
$632$	10.7079	+	3.89736i	0.425938	+	0.155029i
$633$	−2.29240	+	8.73447i	−0.0911147	+	0.347164i
$634$	6.01629	+	5.04827i	0.238937	+	0.200492i
$635$		0			0
$636$	−33.2535	−	32.9138i	−1.31859	−	1.30512i
$637$	8.61398	+	3.13523i	0.341298	+	0.124222i
$638$	−1.47732	+	2.55880i	−0.0584878	+	0.101304i
$639$	−28.3998	−	4.70751i	−1.12348	−	0.186226i
$640$		0			0
$641$	6.60738	+	37.4723i	0.260976	+	1.48007i	0.780254	+	0.625463i	$0.215090\pi$
$641$	6.60738	+	37.4723i	0.260976	+	1.48007i	−0.519278	+	0.854605i	$0.673799\pi$
$642$	1.74911	+	18.8758i	0.0690319	+	0.744968i
$643$	44.1115	−	16.0553i	1.73959	−	0.633158i	0.740352	−	0.672220i	$-0.234659\pi$
$643$	44.1115	−	16.0553i	1.73959	−	0.633158i	0.999237	+	0.0390615i	$0.0124368\pi$
$644$	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	$0.312725\pi$
$648$	8.65643	+	2.95083i	0.340057	+	0.115920i
$649$	0.546406			0.0214483
$650$		0			0
$651$	8.31660	−	12.0081i	0.325953	−	0.470634i
$652$	−5.36140	+	30.4060i	−0.209969	+	1.19079i
$653$	33.1779	−	12.0758i	1.29835	−	0.472562i	0.401893	−	0.915687i	$-0.368353\pi$
$653$	33.1779	−	12.0758i	1.29835	−	0.472562i	0.896460	+	0.443125i	$0.146130\pi$
$654$	2.47295	+	26.6872i	0.0967001	+	1.04355i
$655$		0			0
$656$	8.21052	+	14.2210i	0.320567	+	0.555239i
$657$	−29.0306	+	35.3277i	−1.13259	+	1.37826i
$658$	2.54795	−	4.41318i	0.0993295	−	0.172044i
$659$	−39.1793	−	14.2601i	−1.52621	−	0.555494i	−0.563519	−	0.826103i	$-0.690553\pi$
$659$	−39.1793	−	14.2601i	−1.52621	−	0.555494i	−0.962689	+	0.270609i	$0.912775\pi$
$660$		0			0
$661$	0.975874	+	0.818856i	0.0379571	+	0.0318498i	0.661569	−	0.749884i	$-0.269891\pi$
$661$	0.975874	+	0.818856i	0.0379571	+	0.0318498i	−0.623612	+	0.781734i	$0.714335\pi$
$662$	−2.29075	−	1.92216i	−0.0890324	−	0.0747070i
$663$	0.781997	−	2.97956i	0.0303702	−	0.115716i
$664$	4.47359	+	1.62825i	0.173609	+	0.0631885i
$665$		0			0
$666$	24.4158	−	14.4328i	0.946095	−	0.559258i
$667$	−4.76334	−	8.25035i	−0.184437	−	0.319455i
$668$	1.00426	+	5.69543i	0.0388559	+	0.220363i
$669$	−27.8413	−	12.8090i	−1.07641	−	0.495226i
$670$		0			0
$671$	−0.0558427	+	0.316700i	−0.00215578	+	0.0122261i
$672$	−13.3918	−	1.10238i	−0.516598	−	0.0425252i
$673$	−27.2963	+	22.9043i	−1.05219	+	0.882896i	−0.993323	−	0.115370i	$-0.963195\pi$
$673$	−27.2963	+	22.9043i	−1.05219	+	0.882896i	−0.0588715	+	0.998266i	$0.518750\pi$
$674$	27.4951			1.05907
$675$		0			0
$676$	−26.5561			−1.02139
$677$	−13.7902	+	11.5714i	−0.530002	+	0.444725i	−0.868102	−	0.496386i	$-0.834660\pi$
$677$	−13.7902	+	11.5714i	−0.530002	+	0.444725i	0.338100	+	0.941110i	$0.390216\pi$
$678$	−16.2524	−	34.3913i	−0.624169	−	1.32079i
$679$	−0.936996	+	5.31397i	−0.0359586	+	0.203931i
$680$		0			0
$681$	−22.2968	+	15.7836i	−0.854414	+	0.604828i
$682$	1.01023	+	5.72929i	0.0386836	+	0.219386i
$683$	19.8807	+	34.4344i	0.760715	+	1.31760i	0.942483	+	0.334255i	$0.108485\pi$
$683$	19.8807	+	34.4344i	0.760715	+	1.31760i	−0.181768	+	0.983341i	$0.558182\pi$
$684$	30.1136	+	35.1486i	1.15142	+	1.34394i
$685$		0			0
$686$	−25.2468	−	9.18909i	−0.963928	−	0.350841i
$687$	−2.95192	+	0.807229i	−0.112623	+	0.0307977i
$688$	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	0.625006	−	0.780620i	$-0.285097\pi$
$691$	15.8251	+	5.75986i	0.602015	+	0.219115i	−0.0229909	+	0.999736i	$0.507319\pi$
$692$	−4.44218	+	7.69408i	−0.168866	+	0.292485i
$693$	−0.908663	+	0.169860i	−0.0345173	+	0.00645244i
$694$	−5.08038	−	8.79948i	−0.192849	−	0.334024i
$695$		0			0
$696$	6.32790	−	4.47944i	0.239859	−	0.169793i
$697$	6.45216	−	2.34839i	0.244393	−	0.0889518i
$698$	−8.29833	+	47.0622i	−0.314097	+	1.78133i
$699$	10.2854	+	21.7648i	0.389031	+	0.823220i
$700$		0			0
$701$	−8.96921			−0.338762			−0.169381	−	0.985551i	$-0.554177\pi$
$701$	−8.96921			−0.338762			−0.169381	+	0.985551i	$0.554177\pi$
$702$	−16.1488	−	4.06156i	−0.609498	−	0.153294i
$703$	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
$708$	−6.72864	−	3.09566i	−0.252878	−	0.116342i
$709$	3.15026	+	17.8660i	0.118311	+	0.670973i	0.985058	+	0.172225i	$0.0550955\pi$
$709$	3.15026	+	17.8660i	0.118311	+	0.670973i	−0.866747	+	0.498748i	$0.833793\pi$
$710$		0			0
$711$	29.3054	+	16.5206i	1.09904	+	0.619572i
$712$	7.87509	−	13.6401i	0.295131	−	0.511183i
$713$	−17.6267	−	6.41560i	−0.660125	−	0.240266i
$714$	−1.06299	+	4.05019i	−0.0397814	+	0.151574i
$715$		0			0
$716$	−37.9890	−	31.8766i	−1.41972	−	1.19128i
$717$	24.4144	+	24.1650i	0.911771	+	0.902457i
$718$	−26.6917	−	9.71498i	−0.996125	−	0.362560i
$719$	−15.7860	+	27.3421i	−0.588718	+	1.01969i	0.405683	+	0.914014i	$0.367034\pi$
$719$	−15.7860	+	27.3421i	−0.588718	+	1.01969i	−0.994401	+	0.105675i	$0.966300\pi$
$720$		0			0
$721$	4.79034	+	8.29711i	0.178402	+	0.309001i
$722$	7.24010	+	41.0606i	0.269449	+	1.52812i
$723$	−3.09636	−	33.4148i	−0.115155	−	1.24271i
$724$	−22.6814	+	8.25536i	−0.842948	+	0.306808i
$725$		0			0
$726$	−22.7511	+	32.8497i	−0.844374	+	1.21916i
$727$	−29.4232	+	24.6890i	−1.09125	+	0.915664i	−0.996806	−	0.0798662i	$-0.974551\pi$
$727$	−29.4232	+	24.6890i	−1.09125	+	0.915664i	−0.0944407	+	0.995530i	$0.530106\pi$
$728$	−1.49595			−0.0554436
$729$	23.7874	+	12.7734i	0.881014	+	0.473090i
$730$		0			0
$731$	5.03111	−	4.22160i	0.186082	−	0.156142i
$732$	2.48193	−	3.58358i	0.0917346	−	0.132453i
$733$	5.26680	−	29.8695i	0.194534	−	1.10326i	−0.718547	−	0.695478i	$-0.755193\pi$
$733$	5.26680	−	29.8695i	0.194534	−	1.10326i	0.913081	−	0.407778i	$-0.133696\pi$
$734$	−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
$738$	−13.0519	−	34.7456i	−0.480448	−	1.27900i
$739$	−5.00127	+	8.66245i	−0.183975	+	0.318653i	−0.943230	−	0.332139i	$-0.892230\pi$
$739$	−5.00127	+	8.66245i	−0.183975	+	0.318653i	0.759256	+	0.650792i	$0.225563\pi$
$740$		0			0
$741$	−11.5943	−	11.4759i	−0.425928	−	0.421577i
$742$	−17.1719	−	14.4089i	−0.630400	−	0.528969i
$743$	−27.7873	−	23.3163i	−1.01942	−	0.855394i	−0.0298642	−	0.999554i	$-0.509507\pi$
$743$	−27.7873	−	23.3163i	−1.01942	−	0.855394i	−0.989554	+	0.144160i	$0.953952\pi$
$744$	3.87523	−	14.7654i	0.142073	−	0.541324i
$745$		0			0
$746$	−12.0865	+	20.9344i	−0.442517	+	0.766461i
$747$	12.2433	+	6.90205i	0.447960	+	0.252533i
$748$	−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	−0.0802073	−	0.996778i	$-0.525558\pi$
$751$	13.6766	−	4.97788i	0.499067	−	0.181646i	0.579274	+	0.815133i	$0.303336\pi$
$752$	−1.20791	+	6.85041i	−0.0440480	+	0.249809i
$753$	9.45226	+	0.778089i	0.344460	+	0.0283551i
$754$	−10.8136	+	9.07366i	−0.393807	+	0.330443i
$755$		0			0
$756$	12.1519	+	3.05631i	0.441962	+	0.111157i
$757$	45.5754			1.65646			0.828232	−	0.560385i	$-0.189347\pi$
$757$	45.5754			1.65646			0.828232	+	0.560385i	$0.189347\pi$
$758$	−39.1907	+	32.8849i	−1.42347	+	1.19443i
$759$	0.507211	+	1.07330i	0.0184106	+	0.0389582i
$760$		0			0
$761$	−20.9040	+	7.60843i	−0.757769	+	0.275805i	−0.691871	−	0.722021i	$-0.743213\pi$
$761$	−20.9040	+	7.60843i	−0.757769	+	0.275805i	−0.0658978	+	0.997826i	$0.520991\pi$
$762$	15.6418	−	11.0726i	0.566643	−	0.401119i
$763$	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
$768$	9.73542	−	2.66224i	0.351297	−	0.0960654i
$769$	10.4679	+	8.78365i	0.377484	+	0.316747i	0.811714	−	0.584056i	$-0.198535\pi$
$769$	10.4679	+	8.78365i	0.377484	+	0.316747i	−0.434230	+	0.900802i	$0.642979\pi$
$770$		0			0
$771$	19.3220	−	5.28379i	0.695866	−	0.190291i
$772$	24.6670	+	8.97807i	0.887786	+	0.323128i
$773$	−10.3270	+	17.8869i	−0.371436	+	0.643345i	−0.989787

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.62143 - 1.36054i) q^{2} +(0.986166 - 1.42389i) q^{3} +(0.430663 - 2.44241i) q^{4} +(-0.338267 - 3.65046i) q^{6} +(-0.168844 - 0.957561i) q^{7} +(-0.508086 - 0.880031i) q^{8} +(-1.05495 - 2.80839i) q^{9} +O(q^{10})\)	\(q+(1.62143 - 1.36054i) q^{2} +(0.986166 - 1.42389i) q^{3} +(0.430663 - 2.44241i) q^{4} +(-0.338267 - 3.65046i) q^{6} +(-0.168844 - 0.957561i) q^{7} +(-0.508086 - 0.880031i) q^{8} +(-1.05495 - 2.80839i) q^{9} +(0.297791 + 0.108387i) q^{11} +(-3.05303 - 3.02185i) q^{12} +(1.15981 + 0.973200i) q^{13} +(-1.57657 - 1.32290i) q^{14} +(2.63991 + 0.960847i) q^{16} +(0.587342 - 1.01731i) q^{17} +(-5.53146 - 3.11830i) q^{18} +(-3.11040 - 5.38737i) q^{19} +(-1.52997 - 0.703898i) q^{21} +(0.630310 - 0.229414i) q^{22} +(-0.375556 + 2.12988i) q^{23} +(-1.75413 - 0.144396i) q^{24} +3.20463 q^{26} +(-5.03922 - 1.26740i) q^{27} -2.41147 q^{28} +(-3.37436 + 2.83142i) q^{29} +(-1.50609 + 8.54146i) q^{31} +(7.49746 - 2.72885i) q^{32} +(0.448003 - 0.317135i) q^{33} +(-0.431752 - 2.44859i) q^{34} +(-7.31359 + 1.36716i) q^{36} +(-2.23332 + 3.86823i) q^{37} +(-12.3730 - 4.50341i) q^{38} +(2.52950 - 0.691717i) q^{39} +(4.47767 + 3.75721i) q^{41} +(-3.43842 + 0.940269i) q^{42} +(5.25381 + 1.91223i) q^{43} +(0.392973 - 0.680649i) q^{44} +(2.28885 + 3.96441i) q^{46} +(0.429965 + 2.43845i) q^{47} +(3.97153 - 2.81139i) q^{48} +(5.68943 - 2.07078i) q^{49} +(-0.869320 - 1.83955i) q^{51} +(2.87645 - 2.41362i) q^{52} +10.8920 q^{53} +(-9.89507 + 4.80105i) q^{54} +(-0.756896 + 0.635111i) q^{56} +(-10.7384 - 0.883963i) q^{57} +(-1.61901 + 9.18189i) q^{58} +(1.62023 - 0.589715i) q^{59} +(0.176214 + 0.999361i) q^{61} +(9.17898 + 15.8985i) q^{62} +(-2.51109 + 1.48436i) q^{63} +(5.63455 - 9.75933i) q^{64} +(0.294929 - 1.12374i) q^{66} +(-0.656156 - 0.550580i) q^{67} +(-2.23174 - 1.87265i) q^{68} +(2.66237 + 2.63517i) q^{69} +(4.79788 - 8.31018i) q^{71} +(-1.93547 + 2.35530i) q^{72} +(-7.62091 - 13.1998i) q^{73} +(1.64171 + 9.31057i) q^{74} +(-14.4977 + 5.27674i) q^{76} +(0.0535070 - 0.303453i) q^{77} +(3.16030 - 4.56306i) q^{78} +(-8.59024 + 7.20807i) q^{79} +(-6.77415 + 5.92544i) q^{81} +12.3721 q^{82} +(-3.58886 + 3.01141i) q^{83} +(-2.37811 + 3.43369i) q^{84} +(11.1203 - 4.04747i) q^{86} +(0.703969 + 7.59698i) q^{87} +(-0.0559194 - 0.317135i) q^{88} +(7.74976 + 13.4230i) q^{89} +(0.736071 - 1.27491i) q^{91} +(5.04032 + 1.83453i) q^{92} +(10.6769 + 10.5678i) q^{93} +(4.01476 + 3.36879i) q^{94} +(3.50815 - 13.3667i) q^{96} +(-5.21481 - 1.89804i) q^{97} +(6.40762 - 11.0983i) q^{98} +(-0.00976156 - 0.950656i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 + 6 * q^7 - 6 * q^8	\( 12 q + 6 q^{2} + 6 q^{3} - 6 q^{4} + 6 q^{7} - 6 q^{8} + 3 q^{11} - 12 q^{12} + 6 q^{13} + 15 q^{14} - 9 q^{17} - 9 q^{18} - 3 q^{19} - 12 q^{21} - 3 q^{22} + 12 q^{23} - 18 q^{24} - 30 q^{26} + 9 q^{27} + 12 q^{28} - 6 q^{29} + 3 q^{31} + 9 q^{34} + 18 q^{36} + 3 q^{37} - 42 q^{38} + 33 q^{39} + 15 q^{41} - 18 q^{42} - 3 q^{43} + 3 q^{44} - 3 q^{46} + 15 q^{47} + 15 q^{48} + 12 q^{49} - 18 q^{51} - 9 q^{52} + 18 q^{53} - 54 q^{54} - 33 q^{56} + 3 q^{57} - 21 q^{58} - 12 q^{59} + 12 q^{61} + 12 q^{62} - 9 q^{63} + 12 q^{64} - 9 q^{66} + 15 q^{67} - 9 q^{68} + 9 q^{69} + 27 q^{71} - 18 q^{72} - 6 q^{73} + 33 q^{74} - 48 q^{76} - 15 q^{77} - 18 q^{78} - 42 q^{79} + 36 q^{81} + 12 q^{82} - 39 q^{83} + 6 q^{84} + 51 q^{86} - 9 q^{87} + 30 q^{88} + 9 q^{89} + 6 q^{91} + 39 q^{92} + 39 q^{93} - 15 q^{94} - 3 q^{97} + 45 q^{98} - 27 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 6 * q^3 - 6 * q^4 + 6 * q^7 - 6 * q^8 + 3 * q^11 - 12 * q^12 + 6 * q^13 + 15 * q^14 - 9 * q^17 - 9 * q^18 - 3 * q^19 - 12 * q^21 - 3 * q^22 + 12 * q^23 - 18 * q^24 - 30 * q^26 + 9 * q^27 + 12 * q^28 - 6 * q^29 + 3 * q^31 + 9 * q^34 + 18 * q^36 + 3 * q^37 - 42 * q^38 + 33 * q^39 + 15 * q^41 - 18 * q^42 - 3 * q^43 + 3 * q^44 - 3 * q^46 + 15 * q^47 + 15 * q^48 + 12 * q^49 - 18 * q^51 - 9 * q^52 + 18 * q^53 - 54 * q^54 - 33 * q^56 + 3 * q^57 - 21 * q^58 - 12 * q^59 + 12 * q^61 + 12 * q^62 - 9 * q^63 + 12 * q^64 - 9 * q^66 + 15 * q^67 - 9 * q^68 + 9 * q^69 + 27 * q^71 - 18 * q^72 - 6 * q^73 + 33 * q^74 - 48 * q^76 - 15 * q^77 - 18 * q^78 - 42 * q^79 + 36 * q^81 + 12 * q^82 - 39 * q^83 + 6 * q^84 + 51 * q^86 - 9 * q^87 + 30 * q^88 + 9 * q^89 + 6 * q^91 + 39 * q^92 + 39 * q^93 - 15 * q^94 - 3 * q^97 + 45 * q^98 - 27 * q^99

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