LMFDB - Embedded newform 441.2.o.e.146.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(146,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("441.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			146.9
Character	$\chi$	$=$	441.146
Dual form			441.2.o.e.293.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.850109 - 0.490811i) q^{2} +(-0.900030 - 1.47985i) q^{3} +(-0.518210 - 0.897565i) q^{4} +(0.940599 + 1.62916i) q^{5} +(0.0387990 + 1.69978i) q^{6} +2.98061i q^{8} +(-1.37989 + 2.66381i) q^{9} +O(q^{10})$	\(q+(-0.850109 - 0.490811i) q^{2} +(-0.900030 - 1.47985i) q^{3} +(-0.518210 - 0.897565i) q^{4} +(0.940599 + 1.62916i) q^{5} +(0.0387990 + 1.69978i) q^{6} +2.98061i q^{8} +(-1.37989 + 2.66381i) q^{9} -1.84662i q^{10} +(3.54040 + 2.04405i) q^{11} +(-0.861855 + 1.57471i) q^{12} +(-3.51415 + 2.02890i) q^{13} +(1.56435 - 2.85824i) q^{15} +(0.426498 - 0.738716i) q^{16} -1.62145 q^{17} +(2.48049 - 1.58727i) q^{18} +8.12588i q^{19} +(0.974855 - 1.68850i) q^{20} +(-2.00648 - 3.47533i) q^{22} +(3.73318 - 2.15535i) q^{23} +(4.41085 - 2.68264i) q^{24} +(0.730548 - 1.26535i) q^{25} +3.98322 q^{26} +(5.18398 - 0.355482i) q^{27} +(-0.542317 - 0.313107i) q^{29} +(-2.73272 + 1.66202i) q^{30} +(-3.69833 + 2.13523i) q^{31} +(4.43744 - 2.56195i) q^{32} +(-0.161584 - 7.07895i) q^{33} +(1.37841 + 0.795827i) q^{34} +(3.10602 - 0.141870i) q^{36} +7.94153 q^{37} +(3.98827 - 6.90789i) q^{38} +(6.16530 + 3.37434i) q^{39} +(-4.85591 + 2.80356i) q^{40} +(-0.912023 - 1.57967i) q^{41} +(-3.53614 + 6.12477i) q^{43} -4.23698i q^{44} +(-5.63771 + 0.257507i) q^{45} -4.23148 q^{46} +(3.96868 - 6.87396i) q^{47} +(-1.47705 + 0.0337151i) q^{48} +(-1.24209 + 0.717122i) q^{50} +(1.45936 + 2.39950i) q^{51} +(3.64214 + 2.10279i) q^{52} +8.37133i q^{53} +(-4.58142 - 2.24215i) q^{54} +7.69052i q^{55} +(12.0251 - 7.31354i) q^{57} +(0.307352 + 0.532350i) q^{58} +(4.08715 + 7.07915i) q^{59} +(-3.37612 + 0.0770632i) q^{60} +(-3.24253 - 1.87208i) q^{61} +4.19198 q^{62} -6.73573 q^{64} +(-6.61081 - 3.81676i) q^{65} +(-3.33706 + 6.09718i) q^{66} +(-6.26559 - 10.8523i) q^{67} +(0.840253 + 1.45536i) q^{68} +(-6.54957 - 3.58466i) q^{69} +14.4969i q^{71} +(-7.93980 - 4.11293i) q^{72} +3.78935i q^{73} +(-6.75117 - 3.89779i) q^{74} +(-2.53004 + 0.0577505i) q^{75} +(7.29351 - 4.21091i) q^{76} +(-3.58501 - 5.89455i) q^{78} +(-4.18066 + 7.24112i) q^{79} +1.60465 q^{80} +(-5.19179 - 7.35155i) q^{81} +1.79052i q^{82} +(-4.38300 + 7.59159i) q^{83} +(-1.52514 - 2.64162i) q^{85} +(6.01221 - 3.47115i) q^{86} +(0.0247514 + 1.08435i) q^{87} +(-6.09252 + 10.5526i) q^{88} +9.80759 q^{89} +(4.91906 + 2.54814i) q^{90} +(-3.86914 - 2.23385i) q^{92} +(6.48843 + 3.55119i) q^{93} +(-6.74762 + 3.89574i) q^{94} +(-13.2384 + 7.64320i) q^{95} +(-7.78512 - 4.26089i) q^{96} +(-11.4579 - 6.61525i) q^{97} +(-10.3303 + 6.61038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4} + 16 q^{9}+O(q^{10}) $ 48 * q + 24 * q^4 + 16 * q^9	$ 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64} + 120 q^{65} + 56 q^{72} - 168 q^{74} - 88 q^{78} - 24 q^{79} - 96 q^{81} - 24 q^{85} + 24 q^{86} - 144 q^{92} - 32 q^{93} + 96 q^{95} - 72 q^{99}+O(q^{100}) $ 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.850109	−	0.490811i	−0.601118	−	0.347056i	0.168363	−	0.985725i	$-0.446152\pi$
$2$	−0.850109	−	0.490811i	−0.601118	−	0.347056i	−0.769481	+	0.638669i	$0.779485\pi$
$3$	−0.900030	−	1.47985i	−0.519633	−	0.854390i
$3$	−0.900030	−	1.47985i	−0.519633	−	0.854390i
$4$	−0.518210	−	0.897565i	−0.259105	−	0.448783i
$5$	0.940599	+	1.62916i	0.420648	+	0.728585i	0.996003	−	0.0893196i	$-0.0284692\pi$
$5$	0.940599	+	1.62916i	0.420648	+	0.728585i	−0.575355	+	0.817904i	$0.695136\pi$
$6$	0.0387990	+	1.69978i	0.0158396	+	0.693930i
$7$		0			0
$7$		0			0
$8$			2.98061i			1.05381i
$9$	−1.37989	+	2.66381i	−0.459964	+	0.887938i
$10$		−	1.84662i		−	0.583954i
$11$	3.54040	+	2.04405i	1.06747	+	0.616304i	0.927489	−	0.373850i	$-0.121963\pi$
$11$	3.54040	+	2.04405i	1.06747	+	0.616304i	0.139980	+	0.990154i	$0.455296\pi$
$12$	−0.861855	+	1.57471i	−0.248796	+	0.454579i
$13$	−3.51415	+	2.02890i	−0.974651	+	0.562715i	−0.900651	−	0.434544i	$-0.856910\pi$
$13$	−3.51415	+	2.02890i	−0.974651	+	0.562715i	−0.0739997	+	0.997258i	$0.523576\pi$
$14$		0			0
$15$	1.56435	−	2.85824i	0.403913	−	0.737994i
$16$	0.426498	−	0.738716i	0.106625	−	0.184679i
$17$	−1.62145			−0.393260			−0.196630	−	0.980478i	$-0.563000\pi$
$17$	−1.62145			−0.393260			−0.196630	+	0.980478i	$0.563000\pi$
$18$	2.48049	−	1.58727i	0.584656	−	0.374122i
$19$			8.12588i			1.86421i	0.362194	+	0.932103i	$0.382028\pi$
$19$			8.12588i			1.86421i	−0.362194	+	0.932103i	$0.617972\pi$
$20$	0.974855	−	1.68850i	0.217984	−	0.377560i
$21$		0			0
$22$	−2.00648	−	3.47533i	−0.427783	−	0.740943i
$23$	3.73318	−	2.15535i	0.778423	−	0.449423i	−0.0574484	−	0.998348i	$-0.518296\pi$
$23$	3.73318	−	2.15535i	0.778423	−	0.449423i	0.835871	+	0.548926i	$0.184963\pi$
$24$	4.41085	−	2.68264i	0.900361	−	0.547592i
$25$	0.730548	−	1.26535i	0.146110	−	0.253069i
$26$	3.98322			0.781173
$27$	5.18398	−	0.355482i	0.997657	−	0.0684126i
$28$		0			0
$29$	−0.542317	−	0.313107i	−0.100706	−	0.0581425i	0.448801	−	0.893632i	$-0.351851\pi$
$29$	−0.542317	−	0.313107i	−0.100706	−	0.0581425i	−0.549507	+	0.835489i	$0.685184\pi$
$30$	−2.73272	+	1.66202i	−0.498924	+	0.303441i
$31$	−3.69833	+	2.13523i	−0.664240	+	0.383499i	−0.793891	−	0.608060i	$-0.791948\pi$
$31$	−3.69833	+	2.13523i	−0.664240	+	0.383499i	0.129650	+	0.991560i	$0.458615\pi$
$32$	4.43744	−	2.56195i	0.784435	−	0.452894i
$33$	−0.161584	−	7.07895i	−0.0281281	−	1.23229i
$34$	1.37841	+	0.795827i	0.236396	+	0.136483i
$35$		0			0
$36$	3.10602	−	0.141870i	0.517670	−	0.0236450i
$37$	7.94153			1.30558			0.652790	−	0.757539i	$-0.273599\pi$
$37$	7.94153			1.30558			0.652790	+	0.757539i	$0.273599\pi$
$38$	3.98827	−	6.90789i	0.646983	−	1.12061i
$39$	6.16530	+	3.37434i	0.987238	+	0.540327i
$40$	−4.85591	+	2.80356i	−0.767787	+	0.443282i
$41$	−0.912023	−	1.57967i	−0.142434	−	0.246703i	0.785979	−	0.618254i	$-0.212160\pi$
$41$	−0.912023	−	1.57967i	−0.142434	−	0.246703i	−0.928413	+	0.371551i	$0.878826\pi$
$42$		0			0
$43$	−3.53614	+	6.12477i	−0.539256	+	0.934019i	0.459688	+	0.888080i	$0.347961\pi$
$43$	−3.53614	+	6.12477i	−0.539256	+	0.934019i	−0.998944	+	0.0459387i	$0.985372\pi$
$44$		−	4.23698i		−	0.638749i
$45$	−5.63771	+	0.257507i	−0.840421	+	0.0383869i
$46$	−4.23148			−0.623898
$47$	3.96868	−	6.87396i	0.578891	−	1.00267i	−0.416715	−	0.909037i	$-0.636819\pi$
$47$	3.96868	−	6.87396i	0.578891	−	1.00267i	0.995607	−	0.0936324i	$-0.0298478\pi$
$48$	−1.47705	+	0.0337151i	−0.213194	+	0.00486635i
$49$		0			0
$50$	−1.24209	+	0.717122i	−0.175658	+	0.101416i
$51$	1.45936	+	2.39950i	0.204351	+	0.335998i
$52$	3.64214	+	2.10279i	0.505073	+	0.291604i
$53$			8.37133i			1.14989i	0.818192	+	0.574945i	$0.194977\pi$
$53$			8.37133i			1.14989i	−0.818192	+	0.574945i	$0.805023\pi$
$54$	−4.58142	−	2.24215i	−0.623453	−	0.305118i
$55$			7.69052i			1.03699i
$56$		0			0
$57$	12.0251	−	7.31354i	1.59276	−	0.968702i
$58$	0.307352	+	0.532350i	0.0403573	+	0.0699009i
$59$	4.08715	+	7.07915i	0.532101	+	0.921627i	0.999298	+	0.0374731i	$0.0119308\pi$
$59$	4.08715	+	7.07915i	0.532101	+	0.921627i	−0.467196	+	0.884154i	$0.654736\pi$
$60$	−3.37612	+	0.0770632i	−0.435855	+	0.00994881i
$61$	−3.24253	−	1.87208i	−0.415164	−	0.239695i	0.277842	−	0.960627i	$-0.410381\pi$
$61$	−3.24253	−	1.87208i	−0.415164	−	0.239695i	−0.693006	+	0.720932i	$0.743714\pi$
$62$	4.19198			0.532382
$63$		0			0
$64$	−6.73573			−0.841966
$65$	−6.61081	−	3.81676i	−0.819971	−	0.473410i
$66$	−3.33706	+	6.09718i	−0.410764	+	0.750512i
$67$	−6.26559	−	10.8523i	−0.765464	−	1.32582i	−0.940001	−	0.341171i	$-0.889176\pi$
$67$	−6.26559	−	10.8523i	−0.765464	−	1.32582i	0.174537	−	0.984651i	$-0.444157\pi$
$68$	0.840253	+	1.45536i	0.101896	+	0.176489i
$69$	−6.54957	−	3.58466i	−0.788476	−	0.431542i
$70$		0			0
$71$			14.4969i			1.72047i	0.509898	+	0.860235i	$0.329683\pi$
$71$			14.4969i			1.72047i	−0.509898	+	0.860235i	$0.670317\pi$
$72$	−7.93980	−	4.11293i	−0.935714	−	0.484713i
$73$			3.78935i			0.443510i	0.975102	+	0.221755i	$0.0711785\pi$
$73$			3.78935i			0.443510i	−0.975102	+	0.221755i	$0.928821\pi$
$74$	−6.75117	−	3.89779i	−0.784807	−	0.453109i
$75$	−2.53004	+	0.0577505i	−0.292143	+	0.00666846i
$76$	7.29351	−	4.21091i	0.836623	−	0.483025i
$77$		0			0
$78$	−3.58501	−	5.89455i	−0.405923	−	0.667426i
$79$	−4.18066	+	7.24112i	−0.470361	+	0.814690i	−0.999426	−	0.0338919i	$-0.989210\pi$
$79$	−4.18066	+	7.24112i	−0.470361	+	0.814690i	0.529064	+	0.848582i	$0.322543\pi$
$80$	1.60465			0.179406
$81$	−5.19179	−	7.35155i	−0.576866	−	0.816839i
$82$			1.79052i			0.197730i
$83$	−4.38300	+	7.59159i	−0.481097	+	0.833285i	−0.999765	−	0.0216912i	$-0.993095\pi$
$83$	−4.38300	+	7.59159i	−0.481097	+	0.833285i	0.518668	+	0.854976i	$0.326428\pi$
$84$		0			0
$85$	−1.52514	−	2.64162i	−0.165424	−	0.286524i
$86$	6.01221	−	3.47115i	0.648313	−	0.374304i
$87$	0.0247514	+	1.08435i	0.00265363	+	0.116255i
$88$	−6.09252	+	10.5526i	−0.649465	+	1.12491i
$89$	9.80759			1.03960			0.519801	−	0.854287i	$-0.326006\pi$
$89$	9.80759			1.03960			0.519801	+	0.854287i	$0.326006\pi$
$90$	4.91906	+	2.54814i	0.518514	+	0.268598i
$91$		0			0
$92$	−3.86914	−	2.23385i	−0.403386	−	0.232895i
$93$	6.48843	+	3.55119i	0.672819	+	0.368242i
$94$	−6.74762	+	3.89574i	−0.695964	+	0.401815i
$95$	−13.2384	+	7.64320i	−1.35823	+	0.784175i
$96$	−7.78512	−	4.26089i	−0.794566	−	0.434875i
$97$	−11.4579	−	6.61525i	−1.16338	−	0.671677i	−0.211267	−	0.977428i	$-0.567759\pi$
$97$	−11.4579	−	6.61525i	−1.16338	−	0.671677i	−0.952111	+	0.305752i	$0.901092\pi$
$98$		0			0
$99$	−10.3303	+	6.61038i	−1.03824	+	0.664369i
$100$	−1.51431			−0.151431
$101$	0.524900	−	0.909154i	0.0522295	−	0.0904642i	−0.838729	−	0.544550i	$-0.816701\pi$
$101$	0.524900	−	0.909154i	0.0522295	−	0.0904642i	0.890958	+	0.454085i	$0.150034\pi$
$102$	−0.0629109	−	2.75611i	−0.00622910	−	0.272895i
$103$	1.41937	−	0.819472i	0.139854	−	0.0807449i	−0.428440	−	0.903570i	$-0.640937\pi$
$103$	1.41937	−	0.819472i	0.139854	−	0.0807449i	0.568295	+	0.822825i	$0.307603\pi$
$104$	−6.04736	−	10.4743i	−0.592992	−	1.02709i
$105$		0			0
$106$	4.10874	−	7.11654i	0.399076	−	0.691220i
$107$			3.43549i			0.332122i	0.986116	+	0.166061i	$0.0531048\pi$
$107$			3.43549i			0.332122i	−0.986116	+	0.166061i	$0.946895\pi$
$108$	−3.00546	−	4.46875i	−0.289200	−	0.430005i
$109$	3.69058			0.353494			0.176747	−	0.984256i	$-0.443443\pi$
$109$	3.69058			0.353494			0.176747	+	0.984256i	$0.443443\pi$
$110$	3.77459	−	6.53778i	0.359893	−	0.623353i
$111$	−7.14761	−	11.7522i	−0.678421	−	1.11547i
$112$		0			0
$113$	15.0858	−	8.70977i	1.41915	−	0.819346i	0.422925	−	0.906165i	$-0.361003\pi$
$113$	15.0858	−	8.70977i	1.41915	−	0.819346i	0.996224	+	0.0868183i	$0.0276699\pi$
$114$	−13.8122	+	0.315276i	−1.29363	+	0.0295283i
$115$	7.02285	+	4.05465i	0.654885	+	0.378098i
$116$			0.649020i			0.0602600i
$117$	−0.555449	−	12.1607i	−0.0513513	−	1.12426i
$118$		−	8.02407i		−	0.738675i
$119$		0			0
$120$	8.51931	+	4.66271i	0.777703	+	0.425646i
$121$	2.85627	+	4.94720i	0.259661	+	0.449746i
$122$	1.83767	+	3.18294i	0.166375	+	0.288170i
$123$	−1.51682	+	2.77140i	−0.136767	+	0.249889i
$124$	3.83303	+	2.21300i	0.344216	+	0.198733i
$125$	12.1546			1.08714
$126$		0			0
$127$	−10.1288			−0.898783			−0.449391	−	0.893335i	$-0.648359\pi$
$127$	−10.1288			−0.898783			−0.449391	+	0.893335i	$0.648359\pi$
$128$	−3.14876	−	1.81794i	−0.278314	−	0.160685i
$129$	12.2464	−	0.279535i	1.07823	−	0.0246117i
$130$	3.74661	+	6.48932i	0.328599	+	0.569151i
$131$	2.48851	+	4.31022i	0.217422	+	0.376586i	0.954019	−	0.299746i	$-0.0969019\pi$
$131$	2.48851	+	4.31022i	0.217422	+	0.376586i	−0.736597	+	0.676332i	$0.763569\pi$
$132$	−6.27008	+	3.81341i	−0.545741	+	0.331915i
$133$		0			0
$134$			12.3009i			1.06263i
$135$	5.45518	+	8.11119i	0.469507	+	0.698100i
$136$		−	4.83293i		−	0.414420i
$137$	0.728035	+	0.420331i	0.0622003	+	0.0359113i	0.530778	−	0.847511i	$-0.321900\pi$
$137$	0.728035	+	0.420331i	0.0622003	+	0.0359113i	−0.468577	+	0.883422i	$0.655233\pi$
$138$	3.80846	+	6.26195i	0.324198	+	0.533052i
$139$	5.74392	−	3.31626i	0.487193	−	0.281281i	−0.236216	−	0.971701i	$-0.575907\pi$
$139$	5.74392	−	3.31626i	0.487193	−	0.281281i	0.723409	+	0.690419i	$0.242574\pi$
$140$		0			0
$141$	−13.7443	+	0.313728i	−1.15748	+	0.0264206i
$142$	7.11525	−	12.3240i	0.597098	−	1.03420i
$143$	−16.5887			−1.38721
$144$	1.37928	+	2.15546i	0.114940	+	0.179622i
$145$		−	1.17803i		−	0.0978301i
$146$	1.85985	−	3.22136i	0.153923	−	0.266602i
$147$		0			0
$148$	−4.11538	−	7.12804i	−0.338282	−	0.585921i
$149$	−14.7023	+	8.48838i	−1.20446	+	0.695395i	−0.961544	−	0.274652i	$-0.911437\pi$
$149$	−14.7023	+	8.48838i	−1.20446	+	0.695395i	−0.242916	+	0.970047i	$0.578104\pi$
$150$	2.17915	+	1.19267i	0.177927	+	0.0973814i
$151$	−0.975709	+	1.68998i	−0.0794021	+	0.137528i	−0.902992	−	0.429657i	$-0.858634\pi$
$151$	−0.975709	+	1.68998i	−0.0794021	+	0.137528i	0.823590	+	0.567186i	$0.191968\pi$
$152$	−24.2201			−1.96451
$153$	2.23743	−	4.31925i	0.180886	−	0.349191i
$154$		0			0
$155$	−6.95730	−	4.01680i	−0.558823	−	0.322637i
$156$	−0.166227	−	7.28237i	−0.0133088	−	0.583057i
$157$	8.24558	−	4.76059i	0.658069	−	0.379936i	−0.133472	−	0.991053i	$-0.542613\pi$
$157$	8.24558	−	4.76059i	0.658069	−	0.379936i	0.791541	+	0.611116i	$0.209279\pi$
$158$	7.10804	−	4.10383i	0.565485	−	0.326483i
$159$	12.3883	−	7.53445i	0.982455	−	0.597521i
$160$	8.34769	+	4.81954i	0.659943	+	0.381018i
$161$		0			0
$162$	0.805373	+	8.79781i	0.0632761	+	0.691221i
$163$	1.11021			0.0869585			0.0434793	−	0.999054i	$-0.486156\pi$
$163$	1.11021			0.0869585			0.0434793	+	0.999054i	$0.486156\pi$
$164$	−0.945238	+	1.63720i	−0.0738107	+	0.127844i
$165$	11.3808	−	6.92170i	0.885993	−	0.538853i
$166$	7.45206	−	4.30245i	0.578392	−	0.333935i
$167$	7.00830	+	12.1387i	0.542319	+	0.939324i	0.998770	+	0.0495754i	$0.0157868\pi$
$167$	7.00830	+	12.1387i	0.542319	+	0.939324i	−0.456452	+	0.889748i	$0.650880\pi$
$168$		0			0
$169$	1.73285	−	3.00138i	0.133296	−	0.230875i
$170$			2.99422i			0.229646i
$171$	−21.6458	−	11.2128i	−1.65530	−	0.857468i
$172$	7.32985			0.558896
$173$	−3.55884	+	6.16410i	−0.270574	+	0.468647i	−0.969009	−	0.247026i	$-0.920547\pi$
$173$	−3.55884	+	6.16410i	−0.270574	+	0.468647i	0.698435	+	0.715673i	$0.253880\pi$
$174$	0.511170	−	0.933965i	0.0387517	−	0.0708037i
$175$		0			0
$176$	3.01994	−	1.74357i	0.227637	−	0.131426i
$177$	6.79750	−	12.4198i	0.510931	−	0.933529i
$178$	−8.33752	−	4.81367i	−0.624924	−	0.360800i
$179$		−	6.00265i		−	0.448659i	−0.974513	−	0.224330i	$-0.927981\pi$
$179$		−	6.00265i		−	0.448659i	0.974513	−	0.224330i	$-0.0720192\pi$
$180$	3.15265	+	4.92677i	0.234984	+	0.367220i
$181$			1.30283i			0.0968385i	0.998827	+	0.0484192i	$0.0154184\pi$
$181$			1.30283i			0.0968385i	−0.998827	+	0.0484192i	$0.984582\pi$
$182$		0			0
$183$	0.147989	+	6.48337i	0.0109397	+	0.479265i
$184$	6.42428	+	11.1272i	0.473604	+	0.820307i
$185$	7.46979	+	12.9381i	0.549190	+	0.951225i
$186$	−3.77291	−	6.20349i	−0.276643	−	0.454862i
$187$	−5.74059	−	3.31433i	−0.419794	−	0.242368i
$188$	−8.22643			−0.599974
$189$		0			0
$190$	15.0054			1.08861
$191$	4.96482	+	2.86644i	0.359242	+	0.207408i	0.668748	−	0.743489i	$-0.266830\pi$
$191$	4.96482	+	2.86644i	0.359242	+	0.207408i	−0.309506	+	0.950897i	$0.600164\pi$
$192$	6.06236	+	9.96785i	0.437513	+	0.719368i
$193$	−0.779518	−	1.35016i	−0.0561109	−	0.0971869i	0.836606	−	0.547806i	$-0.184537\pi$
$193$	−0.779518	−	1.35016i	−0.0561109	−	0.0971869i	−0.892716	+	0.450619i	$0.851203\pi$
$194$	6.49367	+	11.2474i	0.466218	+	0.807514i
$195$	0.301718	+	13.2182i	0.0216065	+	0.946574i
$196$		0			0
$197$		−	19.5504i		−	1.39291i	−0.717602	−	0.696454i	$-0.754760\pi$
$197$		−	19.5504i		−	1.39291i	0.717602	−	0.696454i	$-0.245240\pi$
$198$	12.0264	−	0.549313i	0.854676	−	0.0390380i
$199$		−	0.976403i		−	0.0692154i	−0.999401	−	0.0346077i	$-0.988982\pi$
$199$		−	0.976403i		−	0.0692154i	0.999401	−	0.0346077i	$-0.0110182\pi$
$200$	3.77151	+	2.17748i	0.266686	+	0.153971i
$201$	−10.4206	+	19.0395i	−0.735009	+	1.34294i
$202$	−0.892445	+	0.515253i	−0.0627922	+	0.0362531i
$203$		0			0
$204$	1.39746	−	2.55332i	0.0978417	−	0.178768i
$205$	1.71570	−	2.97167i	0.119829	−	0.207551i
$206$	−1.60882			−0.112092
$207$	0.590070	+	12.9187i	0.0410127	+	0.897909i
$208$			3.46128i			0.239997i
$209$	−16.6097	+	28.7688i	−1.14892	+	1.98998i
$210$		0			0
$211$	11.9752	+	20.7417i	0.824408	+	1.42792i	0.902371	+	0.430961i	$0.141825\pi$
$211$	11.9752	+	20.7417i	0.824408	+	1.42792i	−0.0779625	+	0.996956i	$0.524841\pi$
$212$	7.51382	−	4.33810i	0.516051	−	0.297942i
$213$	21.4532	−	13.0477i	1.46995	−	0.894012i
$214$	1.68618	−	2.92054i	0.115265	−	0.199644i
$215$	−13.3044			−0.907349
$216$	1.05956	+	15.4514i	0.0720936	+	1.05134i
$217$		0			0
$218$	−3.13740	−	1.81138i	−0.212491	−	0.122682i
$219$	5.60766	−	3.41053i	0.378931	−	0.230462i
$220$	6.90274	−	3.98530i	0.465383	−	0.268689i
$221$	5.69804	−	3.28976i	0.383292	−	0.221293i
$222$	0.308124	+	13.4988i	0.0206799	+	0.905981i
$223$	2.68394	+	1.54957i	0.179730	+	0.103767i	0.587166	−	0.809467i	$-0.300244\pi$
$223$	2.68394	+	1.54957i	0.179730	+	0.103767i	−0.407436	+	0.913234i	$0.633577\pi$
$224$		0			0
$225$	2.36257	+	3.69209i	0.157505	+	0.246139i
$226$	−17.0994			−1.13743
$227$	10.8991	−	18.8779i	0.723401	−	1.25297i	−0.236228	−	0.971698i	$-0.575911\pi$
$227$	10.8991	−	18.8779i	0.723401	−	1.25297i	0.959629	−	0.281269i	$-0.0907554\pi$
$228$	−12.7959	−	7.00333i	−0.847428	−	0.463807i
$229$	11.1810	−	6.45536i	0.738862	−	0.426582i	−0.0827937	−	0.996567i	$-0.526384\pi$
$229$	11.1810	−	6.45536i	0.738862	−	0.426582i	0.821655	+	0.569985i	$0.193051\pi$
$230$	−3.98013	−	6.89378i	−0.262442	−	0.454563i
$231$		0			0
$232$	0.933250	−	1.61644i	0.0612709	−	0.106124i
$233$		−	0.808011i		−	0.0529345i	−0.999650	−	0.0264673i	$-0.991574\pi$
$233$		−	0.808011i		−	0.0529345i	0.999650	−	0.0264673i	$-0.00842578\pi$
$234$	−5.49641	+	10.6105i	−0.359312	+	0.693633i
$235$	14.9317			0.974039
$236$	4.23600	−	7.33697i	0.275740	−	0.477596i
$237$	14.4785	−	0.330485i	0.940478	−	0.0214673i
$238$		0			0
$239$	12.2032	−	7.04552i	0.789360	−	0.455737i	−0.0503775	−	0.998730i	$-0.516042\pi$
$239$	12.2032	−	7.04552i	0.789360	−	0.455737i	0.839737	+	0.542993i	$0.182709\pi$
$240$	−1.44424	−	2.37464i	−0.0932251	−	0.153282i
$241$	−16.0205	−	9.24943i	−1.03197	−	0.595808i	−0.114422	−	0.993432i	$-0.536502\pi$
$241$	−16.0205	−	9.24943i	−1.03197	−	0.595808i	−0.917549	+	0.397624i	$0.869835\pi$
$242$		−	5.60755i		−	0.360467i
$243$	−6.20639	+	14.2997i	−0.398140	+	0.917325i
$244$			3.88051i			0.248424i
$245$		0			0
$246$	2.64970	−	1.61152i	0.168939	−	0.102747i
$247$	−16.4866	−	28.5556i	−1.04902	−	1.81695i
$248$	−6.36431	−	11.0233i	−0.404134	−	0.699981i
$249$	15.1792	−	0.346481i	0.961944	−	0.0219573i
$250$	−10.3327	−	5.96561i	−0.653499	−	0.377298i
$251$	22.1733			1.39957			0.699783	−	0.714355i	$-0.253280\pi$
$251$	22.1733			1.39957			0.699783	+	0.714355i	$0.253280\pi$
$252$		0			0
$253$	17.6226			1.10792
$254$	8.61056	+	4.97131i	0.540274	+	0.311928i
$255$	−2.53652	+	4.63450i	−0.158843	+	0.290224i
$256$	8.52026	+	14.7575i	0.532516	+	0.922345i
$257$	2.02896	+	3.51427i	0.126563	+	0.219214i	0.922343	−	0.386372i	$-0.126272\pi$
$257$	2.02896	+	3.51427i	0.126563	+	0.219214i	−0.795780	+	0.605586i	$0.792939\pi$
$258$	−10.5479	−	5.77301i	−0.656686	−	0.359412i
$259$		0			0
$260$			7.91152i			0.490652i
$261$	1.58240	−	1.01258i	0.0979479	−	0.0626769i
$262$		−	4.88554i		−	0.301830i
$263$	−8.62617	−	4.98032i	−0.531913	−	0.307100i	0.209882	−	0.977727i	$-0.432692\pi$
$263$	−8.62617	−	4.98032i	−0.531913	−	0.307100i	−0.741795	+	0.670627i	$0.766025\pi$
$264$	21.0996	−	0.481619i	1.29859	−	0.0296416i
$265$	−13.6383	+	7.87406i	−0.837793	+	0.483700i
$266$		0			0
$267$	−8.82712	−	14.5137i	−0.540211	−	0.888226i
$268$	−6.49378	+	11.2476i	−0.396671	+	0.687054i
$269$	−9.96799			−0.607759			−0.303880	−	0.952710i	$-0.598282\pi$
$269$	−9.96799			−0.607759			−0.303880	+	0.952710i	$0.598282\pi$
$270$	−0.656442	−	9.57286i	−0.0399498	−	0.582586i
$271$		−	19.0320i		−	1.15611i	−0.815997	−	0.578057i	$-0.803811\pi$
$271$		−	19.0320i		−	1.15611i	0.815997	−	0.578057i	$-0.196189\pi$
$272$	−0.691547	+	1.19780i	−0.0419312	+	0.0726270i
$273$		0			0
$274$	−0.412606	−	0.714655i	−0.0249265	−	0.0431739i
$275$	5.17286	−	2.98655i	0.311935	−	0.180096i
$276$	0.176588	+	7.73627i	0.0106293	+	0.465669i
$277$	7.81184	−	13.5305i	0.469368	−	0.812969i	−0.530019	−	0.847986i	$-0.677815\pi$
$277$	7.81184	−	13.5305i	0.469368	−	0.812969i	0.999387	+	0.0350166i	$0.0111484\pi$
$278$	−6.51062			−0.390481
$279$	−0.584561	−	12.7981i	−0.0349968	−	0.766200i
$280$		0			0
$281$	−20.8780	−	12.0539i	−1.24547	−	0.719075i	−0.275271	−	0.961367i	$-0.588768\pi$
$281$	−20.8780	−	12.0539i	−1.24547	−	0.719075i	−0.970203	+	0.242292i	$0.922101\pi$
$282$	11.8382	+	6.47916i	0.704952	+	0.385828i
$283$	2.61349	−	1.50890i	0.155356	−	0.0896946i	−0.420307	−	0.907382i	$-0.638078\pi$
$283$	2.61349	−	1.50890i	0.155356	−	0.0896946i	0.575662	+	0.817687i	$0.304744\pi$
$284$	13.0119	−	7.51245i	0.772117	−	0.445782i
$285$	23.2257	+	12.7117i	1.37577	+	0.752976i
$286$	14.1022	+	8.14189i	0.833879	+	0.481440i
$287$		0			0
$288$	0.701384	+	15.3557i	0.0413295	+	0.904844i
$289$	−14.3709			−0.845346
$290$	−0.578190	+	1.00145i	−0.0339525	+	0.0588074i
$291$	0.522942	+	22.9099i	0.0306554	+	1.34300i
$292$	3.40119	−	1.96368i	0.199040	−	0.114916i
$293$	−14.9237	−	25.8485i	−0.871849	−	1.51009i	−0.860082	−	0.510156i	$-0.829588\pi$
$293$	−14.9237	−	25.8485i	−0.871849	−	1.51009i	−0.0117671	−	0.999931i	$-0.503746\pi$
$294$		0			0
$295$	−7.68873	+	13.3173i	−0.447655	+	0.775362i
$296$			23.6706i			1.37583i
$297$	19.0800	+	9.33776i	1.10713	+	0.541832i
$298$	16.6648			0.965363
$299$	−8.74598	+	15.1485i	−0.505793	+	0.876060i
$300$	1.36292	+	2.24095i	0.0786884	+	0.129381i
$301$		0			0
$302$	1.65892	−	0.957777i	0.0954600	−	0.0551139i
$303$	−1.81783	+	0.0414938i	−0.104432	+	0.00238376i
$304$	6.00272	+	3.46567i	0.344280	+	0.198770i
$305$		−	7.04349i		−	0.403309i
$306$	−4.02200	+	2.57368i	−0.229922	+	0.147127i
$307$		−	2.68853i		−	0.153442i	−0.997053	−	0.0767212i	$-0.975555\pi$
$307$		−	2.68853i		−	0.153442i	0.997053	−	0.0767212i	$-0.0244451\pi$
$308$		0			0
$309$	−2.49016	−	1.36290i	−0.141661	−	0.0775324i
$310$	3.94297	+	6.82943i	0.223946	+	0.387886i
$311$	−5.53763	−	9.59145i	−0.314010	−	0.543881i	0.665217	−	0.746650i	$-0.268339\pi$
$311$	−5.53763	−	9.59145i	−0.314010	−	0.543881i	−0.979227	+	0.202769i	$0.935006\pi$
$312$	−10.0576	+	18.3764i	−0.569400	+	1.04036i
$313$	14.4970	+	8.36987i	0.819421	+	0.473093i	0.850217	−	0.526433i	$-0.176471\pi$
$313$	14.4970	+	8.36987i	0.819421	+	0.473093i	−0.0307957	+	0.999526i	$0.509804\pi$
$314$	−9.34619			−0.527436
$315$		0			0
$316$	8.66584			0.487492
$317$	−2.54774	−	1.47094i	−0.143095	−	0.0826160i	0.426743	−	0.904373i	$-0.359661\pi$
$317$	−2.54774	−	1.47094i	−0.143095	−	0.0826160i	−0.569838	+	0.821757i	$0.692994\pi$
$318$	−14.2294	+	0.324800i	−0.797944	+	0.0182139i
$319$	−1.28001	−	2.21704i	−0.0716668	−	0.124131i
$320$	−6.33562	−	10.9736i	−0.354172	−	0.613444i
$321$	5.08400	−	3.09205i	0.283761	−	0.172581i
$322$		0			0
$323$		−	13.1758i		−	0.733118i
$324$	−3.90806	+	8.46962i	−0.217114	+	0.470534i
$325$			5.92883i			0.328872i
$326$	−0.943801	−	0.544904i	−0.0522723	−	0.0301794i
$327$	−3.32163	−	5.46150i	−0.183687	−	0.302021i
$328$	4.70839	−	2.71839i	0.259977	−	0.150098i
$329$		0			0
$330$	−13.0722	+	0.298385i	−0.719598	+	0.0164255i
$331$	−2.44077	+	4.22753i	−0.134157	+	0.232366i	−0.925275	−	0.379297i	$-0.876166\pi$
$331$	−2.44077	+	4.22753i	−0.134157	+	0.232366i	0.791118	+	0.611663i	$0.209499\pi$
$332$	9.08526			0.498618
$333$	−10.9585	+	21.1547i	−0.600520	+	1.15927i
$334$		−	13.7590i		−	0.752859i
$335$	11.7868	−	20.4154i	0.643982	−	1.11541i
$336$		0			0
$337$	6.51421	+	11.2830i	0.354852	+	0.614621i	0.987093	−	0.160151i	$-0.0511980\pi$
$337$	6.51421	+	11.2830i	0.354852	+	0.614621i	−0.632241	+	0.774772i	$0.717865\pi$
$338$	−2.94622	+	1.70100i	−0.160253	+	0.0925221i
$339$	−26.4668	−	14.4856i	−1.43748	−	0.786748i
$340$	−1.58068	+	2.73782i	−0.0857245	+	0.148479i
$341$	−17.4581			−0.945409
$342$	12.8979	+	20.1561i	0.697440	+	1.08992i
$343$		0			0
$344$	−18.2556	−	10.5399i	−0.984275	−	0.568272i
$345$	−0.320524	−	14.0421i	−0.0172564	−	0.755999i
$346$	6.05081	−	3.49344i	0.325293	−	0.187808i
$347$	−1.86351	+	1.07590i	−0.100039	+	0.0577573i	−0.549185	−	0.835701i	$-0.685062\pi$
$347$	−1.86351	+	1.07590i	−0.100039	+	0.0577573i	0.449146	+	0.893458i	$0.351728\pi$
$348$	0.960450	−	0.584137i	0.0514855	−	0.0313130i
$349$	−25.2919	−	14.6023i	−1.35384	−	0.781642i	−0.365058	−	0.930985i	$-0.618951\pi$
$349$	−25.2919	−	14.6023i	−1.35384	−	0.781642i	−0.988785	+	0.149343i	$0.952284\pi$
$350$		0			0
$351$	−17.4961	+	11.7670i	−0.933870	+	0.628075i
$352$	20.9470			1.11648
$353$	−5.41764	+	9.38362i	−0.288352	+	0.499440i	−0.973416	−	0.229042i	$-0.926441\pi$
$353$	−5.41764	+	9.38362i	−0.288352	+	0.499440i	0.685065	+	0.728482i	$0.259774\pi$
$354$	−11.8744	+	7.22190i	−0.631117	+	0.383840i
$355$	−23.6179	+	13.6358i	−1.25351	+	0.723713i
$356$	−5.08239	−	8.80295i	−0.269366	−	0.466556i
$357$		0			0
$358$	−2.94617	+	5.10291i	−0.155710	+	0.269697i
$359$			20.9492i			1.10566i	0.833295	+	0.552829i	$0.186452\pi$
$359$			20.9492i			1.10566i	−0.833295	+	0.552829i	$0.813548\pi$
$360$	−0.767529	−	16.8039i	−0.0404523	−	0.885641i
$361$	−47.0300			−2.47526
$362$	0.639442	−	1.10755i	0.0336083	−	0.0582113i
$363$	4.75037	−	8.67947i	0.249330	−	0.455554i
$364$		0			0
$365$	−6.17348	+	3.56426i	−0.323135	+	0.186562i
$366$	3.05630	−	5.58421i	0.159755	−	0.291891i
$367$	4.97835	+	2.87425i	0.259868	+	0.150035i	0.624274	−	0.781205i	$-0.285395\pi$
$367$	4.97835	+	2.87425i	0.259868	+	0.150035i	−0.364407	+	0.931240i	$0.618728\pi$
$368$		−	3.67702i		−	0.191678i
$369$	5.46644	−	0.249684i	0.284571	−	0.0129980i
$370$		−	14.6650i		−	0.762398i
$371$		0			0
$372$	−0.174940	−	7.66405i	−0.00907019	−	0.397363i
$373$	−14.4467	−	25.0224i	−0.748023	−	1.29561i	−0.948769	−	0.315970i	$-0.897670\pi$
$373$	−14.4467	−	25.0224i	−0.748023	−	1.29561i	0.200747	−	0.979643i	$-0.435663\pi$
$374$	3.25342	+	5.63509i	0.168230	+	0.291383i
$375$	−10.9395	−	17.9869i	−0.564913	−	0.928842i
$376$	20.4886	+	11.8291i	1.05662	+	0.610039i
$377$	2.54104			0.130870
$378$		0			0
$379$	−0.411434			−0.0211339			−0.0105670	−	0.999944i	$-0.503364\pi$
$379$	−0.411434			−0.0211339			−0.0105670	+	0.999944i	$0.503364\pi$
$380$	13.7205	+	7.92156i	0.703849	+	0.406367i
$381$	9.11619	+	14.9890i	0.467037	+	0.767911i
$382$	−2.81376	−	4.87358i	−0.143965	−	0.249354i
$383$	−12.4007	−	21.4787i	−0.633648	−	1.09751i	−0.986800	−	0.161944i	$-0.948223\pi$
$383$	−12.4007	−	21.4787i	−0.633648	−	1.09751i	0.353152	−	0.935566i	$-0.385110\pi$
$384$	0.143710	+	6.29589i	0.00733366	+	0.321286i
$385$		0			0
$386$			1.53038i			0.0778944i
$387$	−11.4358	−	17.8711i	−0.581312	−	0.908441i
$388$			13.7123i			0.696139i
$389$	3.82694	+	2.20948i	0.194033	+	0.112025i	0.593869	−	0.804561i	$-0.297600\pi$
$389$	3.82694	+	2.20948i	0.194033	+	0.112025i	−0.399836	+	0.916587i	$0.630933\pi$
$390$	6.23113	−	11.3850i	0.315526	−	0.576501i
$391$	−6.05319	+	3.49481i	−0.306123	+	0.176740i
$392$		0			0
$393$	4.13873	−	7.56193i	0.208772	−	0.381449i
$394$	−9.59554	+	16.6200i	−0.483416	+	0.837302i
$395$	−15.7293			−0.791427
$396$	11.2865	+	5.84658i	0.567169	+	0.293802i
$397$		−	22.2603i		−	1.11721i	−0.829434	−	0.558605i	$-0.811337\pi$
$397$		−	22.2603i		−	1.11721i	0.829434	−	0.558605i	$-0.188663\pi$
$398$	−0.479229	+	0.830049i	−0.0240216	+	0.0416066i
$399$		0			0
$400$	−0.623155	−	1.07934i	−0.0311578	−	0.0539668i
$401$	−5.31899	+	3.07092i	−0.265617	+	0.153354i	−0.626894	−	0.779104i	$-0.715674\pi$
$401$	−5.31899	+	3.07092i	−0.265617	+	0.153354i	0.361277	+	0.932459i	$0.382341\pi$
$402$	18.2034	−	11.0712i	0.907904	−	0.552179i
$403$	8.66434	−	15.0071i	0.431602	−	0.747556i
$404$	−1.08803			−0.0541317
$405$	7.09349	−	15.3731i	0.352478	−	0.763898i
$406$		0			0
$407$	28.1162	+	16.2329i	1.39367	+	0.804633i
$408$	−7.15200	+	4.34978i	−0.354077	+	0.215346i
$409$	−0.765886	+	0.442185i	−0.0378706	+	0.0218646i	−0.518816	−	0.854886i	$-0.673627\pi$
$409$	−0.765886	+	0.442185i	−0.0378706	+	0.0218646i	0.480945	+	0.876751i	$0.340294\pi$
$410$	−2.91706	+	1.68416i	−0.144063	+	0.0831749i
$411$	−0.0332276	−	1.45569i	−0.00163900	−	0.0718040i
$412$	−1.47106	−	0.849316i	−0.0724739	−	0.0418428i
$413$		0			0
$414$	5.83899	−	11.2719i	0.286971	−	0.553983i
$415$	−16.4906			−0.809491
$416$	−10.3959	+	18.0062i	−0.509700	+	0.882827i
$417$	−10.0773	−	5.51540i	−0.493485	−	0.270090i
$418$	28.2401	−	16.3044i	1.38127	−	0.797476i
$419$	7.59365	+	13.1526i	0.370974	+	0.642546i	0.989716	−	0.143049i	$-0.0456905\pi$
$419$	7.59365	+	13.1526i	0.370974	+	0.642546i	−0.618742	+	0.785595i	$0.712357\pi$
$420$		0			0
$421$	13.3318	−	23.0914i	0.649753	−	1.12541i	−0.333428	−	0.942775i	$-0.608206\pi$
$421$	13.3318	−	23.0914i	0.649753	−	1.12541i	0.983182	−	0.182630i	$-0.0584611\pi$
$422$		−	23.5103i		−	1.14446i
$423$	12.8346	+	20.0571i	0.624039	+	0.975211i
$424$	−24.9517			−1.21176
$425$	−1.18455	+	2.05170i	−0.0574592	+	0.0995222i
$426$	−24.6415	+	0.562467i	−1.19389	+	0.0272516i
$427$		0			0
$428$	3.08358	−	1.78031i	0.149050	−	0.0860543i
$429$	14.9303	+	24.5487i	0.720841	+	1.18522i
$430$	11.3102	+	6.52992i	0.545424	+	0.314901i
$431$		−	4.69715i		−	0.226254i	−0.993581	−	0.113127i	$-0.963913\pi$
$431$		−	4.69715i		−	0.226254i	0.993581	−	0.113127i	$-0.0360866\pi$
$432$	1.94836	−	3.98110i	0.0937404	−	0.191541i
$433$			8.97714i			0.431414i	0.976458	+	0.215707i	$0.0692056\pi$
$433$			8.97714i			0.431414i	−0.976458	+	0.215707i	$0.930794\pi$
$434$		0			0
$435$	−1.74331	+	1.06026i	−0.0835851	+	0.0508357i
$436$	−1.91250	−	3.31254i	−0.0915919	−	0.158642i
$437$	17.5142	+	30.3354i	0.837816	+	1.45114i
$438$	−6.44105	+	0.147023i	−0.307765	+	0.00702504i
$439$	−14.3012	−	8.25679i	−0.682558	−	0.394075i	0.118260	−	0.992983i	$-0.462268\pi$
$439$	−14.3012	−	8.25679i	−0.682558	−	0.394075i	−0.800818	+	0.598907i	$0.795602\pi$
$440$	−22.9225			−1.09279
$441$		0			0
$442$	−6.45861			−0.307205
$443$	0.921171	+	0.531838i	0.0437661	+	0.0252684i	0.521723	−	0.853115i	$-0.325289\pi$
$443$	0.921171	+	0.531838i	0.0437661	+	0.0252684i	−0.477957	+	0.878383i	$0.658623\pi$
$444$	−6.84445	+	12.5056i	−0.324823	+	0.593488i
$445$	9.22500	+	15.9782i	0.437307	+	0.757438i
$446$	−1.52110	−	2.63461i	−0.0720260	−	0.124753i
$447$	25.7940	+	14.1174i	1.22002	+	0.667728i
$448$		0			0
$449$			15.9081i			0.750749i	0.926873	+	0.375374i	$0.122486\pi$
$449$			15.9081i			0.750749i	−0.926873	+	0.375374i	$0.877514\pi$
$450$	−0.196326	−	4.29825i	−0.00925489	−	0.202621i
$451$		−	7.45688i		−	0.351131i
$452$	−15.6352	−	9.02697i	−0.735417	−	0.424593i
$453$	3.37908	−	0.0771307i	0.158763	−	0.00362392i
$454$	−18.5309	+	10.6988i	−0.869698	+	0.502121i
$455$		0			0
$456$	21.7988	+	35.8421i	1.02082	+	1.67846i
$457$	16.3963	−	28.3992i	0.766985	−	1.32846i	−0.172206	−	0.985061i	$-0.555090\pi$
$457$	16.3963	−	28.3992i	0.766985	−	1.32846i	0.939191	−	0.343395i	$-0.111577\pi$
$458$	−12.6734			−0.592191
$459$	−8.40558	+	0.576398i	−0.392339	+	0.0269040i
$460$		−	8.40463i		−	0.391868i
$461$	9.23690	−	15.9988i	0.430205	−	0.745138i	−0.566685	−	0.823934i	$-0.691774\pi$
$461$	9.23690	−	15.9988i	0.430205	−	0.745138i	0.996891	+	0.0787967i	$0.0251078\pi$
$462$		0			0
$463$	−0.201921	−	0.349738i	−0.00938408	−	0.0162537i	0.861295	−	0.508105i	$-0.169654\pi$
$463$	−0.201921	−	0.349738i	−0.00938408	−	0.0162537i	−0.870679	+	0.491851i	$0.836320\pi$
$464$	−0.462594	+	0.267079i	−0.0214754	+	0.0123988i
$465$	0.317531	+	13.9110i	0.0147252	+	0.645106i
$466$	−0.396580	+	0.686897i	−0.0183712	+	0.0318199i
$467$	15.0257			0.695304			0.347652	−	0.937624i	$-0.386979\pi$
$467$	15.0257			0.695304			0.347652	+	0.937624i	$0.386979\pi$
$468$	−10.6272	+	6.80035i	−0.491242	+	0.314346i
$469$		0			0
$470$	−12.6936	−	7.32866i	−0.585512	−	0.338046i
$471$	−14.4662	−	7.91753i	−0.666568	−	0.364820i
$472$	−21.1002	+	12.1822i	−0.971216	+	0.560732i
$473$	−25.0387	+	14.4561i	−1.15128	+	0.664691i
$474$	−12.4705	−	6.82524i	−0.572789	−	0.313494i
$475$	10.2821	+	5.93635i	0.471773	+	0.272379i
$476$		0			0
$477$	−22.2997	−	11.5515i	−1.02103	−	0.528908i
$478$	−13.8321			−0.632664
$479$	15.5400	−	26.9161i	0.710041	−	1.22983i	−0.254800	−	0.966994i	$-0.582010\pi$
$479$	15.5400	−	26.9161i	0.710041	−	1.22983i	0.964841	−	0.262833i	$-0.0846569\pi$
$480$	−0.380989	−	16.6910i	−0.0173897	−	0.761838i
$481$	−27.9077	+	16.1125i	−1.27248	+	0.734669i
$482$	9.07944	+	15.7261i	0.413557	+	0.716302i
$483$		0			0
$484$	2.96029	−	5.12738i	0.134559	−	0.233063i
$485$		−	24.8892i		−	1.13016i
$486$	12.2945	−	9.11012i	0.557692	−	0.413243i
$487$	13.4956			0.611546			0.305773	−	0.952104i	$-0.401085\pi$
$487$	13.4956			0.611546			0.305773	+	0.952104i	$0.401085\pi$
$488$	5.57994	−	9.66474i	0.252592	−	0.437502i
$489$	−0.999224	−	1.64294i	−0.0451865	−	0.0742965i
$490$		0			0
$491$	−7.07098	+	4.08243i	−0.319109	+	0.184238i	−0.650995	−	0.759082i	$-0.725648\pi$
$491$	−7.07098	+	4.08243i	−0.319109	+	0.184238i	0.331886	+	0.943319i	$0.392315\pi$
$492$	3.27355	−	0.0747220i	0.147583	−	0.00336873i
$493$	0.879342	+	0.507688i	0.0396036	+	0.0228651i
$494$			32.3672i			1.45627i
$495$	−20.4861	−	10.6121i	−0.920781	−	0.476978i
$496$			3.64269i			0.163562i
$497$		0			0
$498$	−13.0740	−	7.15558i	−0.585862	−	0.320649i
$499$	14.0097	+	24.2655i	0.627159	+	1.08627i	0.988119	+	0.153690i	$0.0491158\pi$
$499$	14.0097	+	24.2655i	0.627159	+	1.08627i	−0.360960	+	0.932581i	$0.617551\pi$
$500$	−6.29863	−	10.9095i	−0.281683	−	0.487890i
$501$	11.6558	−	21.2964i	0.520742	−	0.951455i
$502$	−18.8497	−	10.8829i	−0.841305	−	0.485727i
$503$	5.89656			0.262915			0.131457	−	0.991322i	$-0.458034\pi$
$503$	5.89656			0.262915			0.131457	+	0.991322i	$0.458034\pi$
$504$		0			0
$505$	1.97488			0.0878811
$506$	−14.9811	−	8.64936i	−0.665992	−	0.384511i
$507$	−6.00119	+	0.136983i	−0.266522	+	0.00608363i
$508$	5.24883	+	9.09123i	0.232879	+	0.403358i
$509$	7.01957	+	12.1582i	0.311137	+	0.538905i	0.978609	−	0.205730i	$-0.0659569\pi$
$509$	7.01957	+	12.1582i	0.311137	+	0.538905i	−0.667472	+	0.744635i	$0.732624\pi$
$510$	4.43098	−	2.69488i	0.196207	−	0.119331i
$511$		0			0
$512$		−	9.45558i		−	0.417882i
$513$	2.88861	+	42.1244i	0.127535	+	1.85984i
$514$		−	3.98335i		−	0.175698i
$515$	2.67011	+	1.54159i	0.117659	+	0.0679305i
$516$	−6.59708	−	10.8470i	−0.290420	−	0.477515i
$517$	28.1014	−	16.2243i	1.23590	−	0.713546i
$518$		0			0
$519$	12.3250	−	0.281330i	0.541007	−	0.0123490i
$520$	11.3763	−	19.7043i	0.498883	−	0.864090i
$521$	38.4458			1.68434			0.842170	−	0.539213i	$-0.181278\pi$
$521$	38.4458			1.68434			0.842170	+	0.539213i	$0.181278\pi$
$522$	−1.84219	+	0.0841435i	−0.0806306	+	0.00368286i
$523$			10.4932i			0.458834i	0.973328	+	0.229417i	$0.0736819\pi$
$523$			10.4932i			0.458834i	−0.973328	+	0.229417i	$0.926318\pi$
$524$	2.57914	−	4.46720i	0.112670	−	0.195150i
$525$		0			0
$526$	4.88879	+	8.46764i	0.213161	+	0.369207i
$527$	5.99668	−	3.46219i	0.261220	−	0.150815i
$528$	−5.29825	−	2.89979i	−0.230577	−	0.126197i
$529$	−2.20889	+	3.82591i	−0.0960388	+	0.166344i
$530$	15.4587			0.671483
$531$	−24.4974	+	1.11894i	−1.06309	+	0.0485576i
$532$		0			0
$533$	6.40998	+	3.70080i	0.277647	+	0.160300i
$534$	0.380525	+	16.6707i	0.0164669	+	0.721412i
$535$	−5.59698	+	3.23142i	−0.241979	+	0.139706i
$536$	32.3466	−	18.6753i	1.39716	−	0.806650i
$537$	−8.88301	+	5.40257i	−0.383330	+	0.233138i
$538$	8.47388	+	4.89240i	0.365335	+	0.210926i
$539$		0			0
$540$	4.45339	−	9.09968i	0.191644	−	0.391588i
$541$	45.1565			1.94143			0.970715	−	0.240232i	$-0.0772235\pi$
$541$	45.1565			1.94143			0.970715	+	0.240232i	$0.0772235\pi$
$542$	−9.34112	+	16.1793i	−0.401236	+	0.694960i
$543$	1.92799	−	1.17258i	0.0827378	−	0.0503204i
$544$	−7.19510	+	4.15409i	−0.308487	+	0.178105i
$545$	3.47136	+	6.01257i	0.148697	+	0.257550i
$546$		0			0
$547$	−4.05733	+	7.02751i	−0.173479	+	0.300475i	−0.939634	−	0.342181i	$-0.888834\pi$
$547$	−4.05733	+	7.02751i	−0.173479	+	0.300475i	0.766155	+	0.642656i	$0.222168\pi$
$548$		−	0.871279i		−	0.0372192i
$549$	9.46121	−	6.05423i	0.403794	−	0.258388i
$550$	−5.86333			−0.250013
$551$	2.54427	−	4.40680i	0.108389	−	0.187736i
$552$	10.6845	−	19.5217i	0.454762	−	0.830901i
$553$		0			0
$554$	−13.2818	+	7.66827i	−0.564291	+	0.325794i
$555$	12.4233	−	22.6988i	0.527340	−	0.963510i
$556$	−5.95311	−	3.43703i	−0.252468	−	0.145763i
$557$		−	16.2727i		−	0.689494i	−0.938696	−	0.344747i	$-0.887965\pi$
$557$		−	16.2727i		−	0.689494i	0.938696	−	0.344747i	$-0.112035\pi$
$558$	−5.78449	+	11.1667i	−0.244877	+	0.472722i
$559$		−	28.6978i		−	1.21379i
$560$		0			0
$561$	0.262001	+	11.4782i	0.0110617	+	0.484610i
$562$	11.8324	+	20.4942i	0.499118	+	0.864498i
$563$	−5.13594	−	8.89572i	−0.216454	−	0.374910i	0.737267	−	0.675601i	$-0.236116\pi$
$563$	−5.13594	−	8.89572i	−0.216454	−	0.374910i	−0.953721	+	0.300692i	$0.902783\pi$
$564$	7.40404	+	12.1739i	0.311766	+	0.512612i
$565$	28.3793	+	16.3848i	1.19393	+	0.689314i
$566$	−2.96233			−0.124516
$567$		0			0
$568$	−43.2098			−1.81304
$569$	−17.8537	−	10.3079i	−0.748468	−	0.432128i	0.0766722	−	0.997056i	$-0.475571\pi$
$569$	−17.8537	−	10.3079i	−0.748468	−	0.432128i	−0.825140	+	0.564928i	$0.808904\pi$
$570$	−13.5054	−	22.2058i	−0.565677	−	0.930097i
$571$	−2.12828	−	3.68628i	−0.0890656	−	0.154266i	0.818051	−	0.575146i	$-0.195055\pi$
$571$	−2.12828	−	3.68628i	−0.0890656	−	0.154266i	−0.907116	+	0.420880i	$0.861721\pi$
$572$	8.59640	+	14.8894i	0.359434	+	0.622557i
$573$	−0.226595	−	9.92706i	−0.00946614	−	0.414709i
$574$		0			0
$575$		−	6.29836i		−	0.262660i
$576$	9.29458	−	17.9427i	0.387274	−	0.747614i
$577$		−	16.9289i		−	0.704760i	−0.935857	−	0.352380i	$-0.885372\pi$
$577$		−	16.9289i		−	0.704760i	0.935857	−	0.352380i	$-0.114628\pi$
$578$	12.2168	+	7.05338i	0.508153	+	0.293382i
$579$	−1.29645	+	2.36875i	−0.0538785	+	0.0984421i
$580$	−1.05736	+	0.610467i	−0.0439045	+	0.0253483i
$581$		0			0
$582$	10.7999	−	19.7326i	0.447669	−	0.817943i
$583$	−17.1114	+	29.6378i	−0.708682	+	1.22747i
$584$	−11.2946			−0.467374
$585$	19.2893	−	12.3433i	0.797516	−	0.510331i
$586$			29.2988i			1.21032i
$587$	−12.0558	+	20.8812i	−0.497594	+	0.861858i	−0.999996	−	0.00277589i	$-0.999116\pi$
$587$	−12.0558	+	20.8812i	−0.497594	+	0.861858i	0.502402	+	0.864634i	$0.332450\pi$
$588$		0			0
$589$	−17.3507	−	30.0522i	−0.714922	−	1.23828i
$590$	13.0725	−	7.54743i	0.538187	−	0.310723i
$591$	−28.9316	+	17.5959i	−1.19009	+	0.723800i
$592$	3.38705	−	5.86654i	0.139207	−	0.241113i
$593$	38.5816			1.58436			0.792178	−	0.610290i	$-0.208947\pi$
$593$	38.5816			1.58436			0.792178	+	0.610290i	$0.208947\pi$
$594$	−11.6370	−	17.3028i	−0.477471	−	0.709941i
$595$		0			0
$596$	15.2378	+	8.79752i	0.624163	+	0.360360i
$597$	−1.44493	+	0.878792i	−0.0591369	+	0.0359666i
$598$	14.8701	−	8.58525i	0.608083	−	0.351077i
$599$	−29.2921	+	16.9118i	−1.19684	+	0.690997i	−0.959850	−	0.280514i	$-0.909495\pi$
$599$	−29.2921	+	16.9118i	−1.19684	+	0.690997i	−0.236992	+	0.971511i	$0.576162\pi$
$600$	−0.172132	−	7.54106i	−0.00702726	−	0.307862i
$601$	27.4855	+	15.8688i	1.12116	+	0.647300i	0.941696	−	0.336465i	$-0.109231\pi$
$601$	27.4855	+	15.8688i	1.12116	+	0.647300i	0.179461	+	0.983765i	$0.442565\pi$
$602$		0			0
$603$	37.5544	−	1.71533i	1.52933	−	0.0698534i
$604$	2.02249			0.0822939
$605$	−5.37320	+	9.30666i	−0.218452	+	0.378370i
$606$	1.56572	+	0.856938i	0.0636031	+	0.0348107i
$607$	0.169355	−	0.0977772i	0.00687391	−	0.00396865i	−0.496559	−	0.868003i	$-0.665403\pi$
$607$	0.169355	−	0.0977772i	0.00687391	−	0.00396865i	0.503433	+	0.864034i	$0.332070\pi$
$608$	20.8181	+	36.0581i	0.844287	+	1.46235i
$609$		0			0
$610$	−3.45702	+	5.98774i	−0.139971	+	0.242436i
$611$			32.2082i			1.30300i
$612$	−5.03627	+	0.230035i	−0.203579	+	0.00929863i
$613$	2.93328			0.118474			0.0592370	−	0.998244i	$-0.481133\pi$
$613$	2.93328			0.118474			0.0592370	+	0.998244i	$0.481133\pi$
$614$	−1.31956	+	2.28554i	−0.0532530	+	0.0922370i
$615$	−5.94180	+	0.135627i	−0.239596	+	0.00546902i
$616$		0			0
$617$	−7.86982	+	4.54365i	−0.316827	+	0.182920i	−0.649977	−	0.759953i	$-0.725222\pi$
$617$	−7.86982	+	4.54365i	−0.316827	+	0.182920i	0.333150	+	0.942874i	$0.391888\pi$
$618$	1.44799	+	2.38081i	0.0582466	+	0.0957702i
$619$	−24.8586	−	14.3521i	−0.999152	−	0.576861i	−0.0911550	−	0.995837i	$-0.529056\pi$
$619$	−24.8586	−	14.3521i	−0.999152	−	0.576861i	−0.907997	+	0.418976i	$0.862389\pi$
$620$			8.32617i			0.334387i
$621$	18.5866	−	12.5004i	0.745853	−	0.501623i
$622$			10.8717i			0.435916i
$623$		0			0
$624$	5.12217	−	3.11526i	0.205051	−	0.124710i
$625$	7.77986	+	13.4751i	0.311194	+	0.539004i
$626$	−8.21604	−	14.2306i	−0.328379	−	0.568769i
$627$	57.5227	−	1.31301i	2.29724	−	0.0524367i
$628$	−8.54588	−	4.93397i	−0.341018	−	0.196887i
$629$	−12.8768			−0.513433
$630$		0			0
$631$	−20.7691			−0.826805			−0.413403	−	0.910548i	$-0.635660\pi$
$631$	−20.7691			−0.826805			−0.413403	+	0.910548i	$0.635660\pi$
$632$	−21.5830	−	12.4609i	−0.858525	−	0.495670i
$633$	19.9165	−	36.3896i	0.791608	−	1.44636i
$634$	1.44390	+	2.50091i	0.0573447	+	0.0993240i
$635$	−9.52711	−	16.5014i	−0.378072	−	0.654839i
$636$	−13.1824	−	7.21487i	−0.522716	−	0.286088i
$637$		0			0
$638$			2.51297i			0.0994895i
$639$	−38.6171	−	20.0042i	−1.52767	−	0.791354i
$640$		−	6.83981i		−	0.270367i
$641$	39.7733	+	22.9632i	1.57095	+	0.906990i	0.996052	+	0.0887664i	$0.0282925\pi$
$641$	39.7733	+	22.9632i	1.57095	+	0.906990i	0.574900	+	0.818224i	$0.305041\pi$
$642$	−5.83957	+	0.133294i	−0.230469	+	0.00526069i
$643$	−9.15428	+	5.28523i	−0.361010	+	0.208429i	−0.669524	−	0.742791i	$-0.733502\pi$
$643$	−9.15428	+	5.28523i	−0.361010	+	0.208429i	0.308514	+	0.951220i	$0.400168\pi$
$644$		0			0
$645$	11.9743	+	19.6884i	0.471488	+	0.775230i
$646$	−6.46680	+	11.2008i	−0.254433	+	0.440691i
$647$	38.5123			1.51408			0.757038	−	0.653371i	$-0.226646\pi$
$647$	38.5123			1.51408			0.757038	+	0.653371i	$0.226646\pi$
$648$	21.9121	−	15.4747i	0.860790	−	0.607905i
$649$			33.4173i			1.31174i
$650$	2.90993	−	5.04015i	0.114137	−	0.197691i
$651$		0			0
$652$	−0.575323	−	0.996488i	−0.0225314	−	0.0390255i
$653$	−11.0867	+	6.40089i	−0.433855	+	0.250486i	−0.700988	−	0.713173i	$-0.747257\pi$
$653$	−11.0867	+	6.40089i	−0.433855	+	0.250486i	0.267133	+	0.963660i	$0.413924\pi$
$654$	0.143191	+	6.27316i	0.00559921	+	0.245300i
$655$	−4.68137	+	8.10837i	−0.182916	+	0.316820i
$656$	−1.55590			−0.0607479
$657$	−10.0941	−	5.22890i	−0.393809	−	0.203999i
$658$		0			0
$659$	41.5777	+	24.0049i	1.61964	+	0.935097i	0.987014	+	0.160636i	$0.0513546\pi$
$659$	41.5777	+	24.0049i	1.61964	+	0.935097i	0.632622	+	0.774461i	$0.281979\pi$
$660$	−12.1103	−	6.62811i	−0.471393	−	0.257999i
$661$	9.38011	−	5.41561i	0.364844	−	0.210643i	−0.306360	−	0.951916i	$-0.599111\pi$
$661$	9.38011	−	5.41561i	0.364844	−	0.210643i	0.671204	+	0.741273i	$0.265778\pi$
$662$	4.14983	−	2.39591i	0.161288	−	0.0931196i
$663$	−9.99675	−	5.47134i	−0.388242	−	0.212489i
$664$	−22.6276	−	13.0640i	−0.878121	−	0.506983i
$665$		0			0
$666$	19.6989	−	12.6053i	0.763315	−	0.488446i
$667$	−2.69942			−0.104522
$668$	7.26354	−	12.5808i	0.281035	−	0.486767i
$669$	−0.122495	−	5.36649i	−0.00473594	−	0.207480i
$670$	−20.0402	+	11.5702i	−0.774219	+	0.446995i
$671$	−7.65323	−	13.2558i	−0.295450	−	0.511734i
$672$		0			0
$673$	−6.19553	+	10.7310i	−0.238820	+	0.413649i	−0.960376	−	0.278707i	$-0.910094\pi$
$673$	−6.19553	+	10.7310i	−0.238820	+	0.413649i	0.721556	+	0.692356i	$0.243427\pi$
$674$		−	12.7890i		−	0.492613i
$675$	3.33734	−	6.81923i	0.128454	−	0.262472i
$676$	−3.59191			−0.138150
$677$	−14.4947	+	25.1056i	−0.557078	+	0.964888i	0.440660	+	0.897674i	$0.354744\pi$
$677$	−14.4947	+	25.1056i	−0.557078	+	0.964888i	−0.997739	+	0.0672139i	$0.978589\pi$
$678$	15.3900	+	25.3045i	0.591048	+	0.971813i
$679$		0			0
$680$	7.87364	−	4.54585i	0.301940	−	0.174325i
$681$	−37.7459	+	0.861586i	−1.44642	+	0.0330161i
$682$	14.8413	+	8.56862i	0.568302	+	0.328109i
$683$			0.152476i			0.00583433i	0.999996	+	0.00291717i	$0.000928564\pi$
$683$			0.152476i			0.00583433i	−0.999996	+	0.00291717i	$0.999071\pi$
$684$	1.15282	+	25.2392i	0.0440791	+	0.965043i
$685$			1.58145i			0.0604242i
$686$		0			0
$687$	−19.6162	−	10.7362i	−0.748404	−	0.409610i
$688$	3.01631	+	5.22441i	0.114996	+	0.199179i
$689$	−16.9846	−	29.4181i	−0.647060	−	1.12074i
$690$	−6.61951	+	12.0946i	−0.252000	+	0.460433i
$691$	37.4428	+	21.6176i	1.42439	+	0.822373i	0.996670	−	0.0815369i	$-0.0259828\pi$
$691$	37.4428	+	21.6176i	1.42439	+	0.822373i	0.427722	+	0.903910i	$0.359316\pi$
$692$	7.37691			0.280428
$693$		0			0
$694$	2.11225			0.0801799
$695$	10.8055	+	6.23853i	0.409874	+	0.236641i
$696$	−3.23203	+	0.0737743i	−0.122510	+	0.00279641i
$697$	1.47880	+	2.56136i	0.0560137	+	0.0970186i
$698$	14.3339	+	24.8271i	0.542546	+	0.939718i
$699$	−1.19573	+	0.727234i	−0.0452267	+	0.0275065i
$700$		0			0
$701$		−	11.5821i		−	0.437451i	−0.975786	−	0.218726i	$-0.929810\pi$
$701$		−	11.5821i		−	0.437451i	0.975786	−	0.218726i	$-0.0701900\pi$
$702$	20.6489	−	1.41596i	0.779343	−	0.0534421i
$703$			64.5319i			2.43387i
$704$	−23.8472	−	13.7682i	−0.898774	−	0.518907i
$705$	−13.4390	−	22.0967i	−0.506142	−	0.832209i
$706$	9.21116	−	5.31807i	0.346667	−	0.200148i
$707$		0			0
$708$	−14.6701	+	0.334860i	−0.551337	+	0.0125848i
$709$	18.9474	−	32.8178i	0.711584	−	1.23250i	−0.252678	−	0.967550i	$-0.581311\pi$
$709$	18.9474	−	32.8178i	0.711584	−	1.23250i	0.964262	−	0.264949i	$-0.0853552\pi$
$710$	26.7704			1.00467
$711$	−13.5201	−	21.1285i	−0.507044	−	0.792380i
$712$			29.2326i			1.09554i
$713$	−9.20437	+	15.9424i	−0.344707	+	0.597049i
$714$		0			0
$715$	−15.6033	−	27.0256i	−0.583529	−	1.01070i
$716$	−5.38777	+	3.11063i	−0.201351	+	0.116250i
$717$	−21.4095	−	11.7177i	−0.799554	−	0.437605i
$718$	10.2821	−	17.8091i	0.383724	−	0.664630i
$719$	46.6317			1.73907			0.869534	−	0.493873i	$-0.164419\pi$
$719$	46.6317			1.73907			0.869534	+	0.493873i	$0.164419\pi$
$720$	−2.21425	+	4.27450i	−0.0825202	+	0.159301i
$721$		0			0
$722$	39.9806	+	23.0828i	1.48792	+	0.859054i
$723$	0.731176	+	32.0326i	0.0271927	+	1.19131i
$724$	1.16937	−	0.675138i	0.0434594	−	0.0250913i
$725$	−0.792377	+	0.457479i	−0.0294282	+	0.0169904i
$726$	−8.29831	+	5.04696i	−0.307979	+	0.187310i
$727$	3.72659	+	2.15155i	0.138212	+	0.0797965i	0.567511	−	0.823366i	$-0.307906\pi$
$727$	3.72659	+	2.15155i	0.138212	+	0.0797965i	−0.429300	+	0.903162i	$0.641240\pi$
$728$		0			0
$729$	26.7473	−	3.68562i	0.990639	−	0.136505i
$730$	6.99751			0.258989
$731$	5.73369	−	9.93104i	0.212068	−	0.367313i
$732$	5.74256	−	3.49258i	0.212251	−	0.129089i
$733$	−12.1337	+	7.00539i	−0.448168	+	0.258750i	−0.707056	−	0.707157i	$-0.749977\pi$
$733$	−12.1337	+	7.00539i	−0.448168	+	0.258750i	0.258888	+	0.965907i	$0.416644\pi$
$734$	−2.82143	−	4.88685i	−0.104141	−	0.180377i
$735$		0			0
$736$	11.0438	−	19.1285i	0.407081	−	0.705086i
$737$		−	51.2287i		−	1.88703i
$738$	−4.76962	−	2.47073i	−0.175572	−	0.0909488i
$739$	37.8627			1.39280			0.696401	−	0.717653i	$-0.254784\pi$
$739$	37.8627			1.39280			0.696401	+	0.717653i	$0.254784\pi$
$740$	7.74184	−	13.4093i	0.284596	−	0.492934i
$741$	−27.4195	+	50.0985i	−1.00728	+	1.84041i
$742$		0			0
$743$	−24.0489	+	13.8847i	−0.882269	+	0.509378i	−0.871406	−	0.490563i	$-0.836791\pi$
$743$	−24.0489	+	13.8847i	−0.882269	+	0.509378i	−0.0108634	+	0.999941i	$0.503458\pi$
$744$	−10.5847	+	19.3395i	−0.388055	+	0.709021i
$745$	−27.6579	−	15.9683i	−1.01331	−	0.585034i
$746$			28.3624i			1.03842i
$747$	−14.1745	−	22.1511i	−0.518617	−	0.810465i
$748$			6.87007i			0.251195i
$749$		0			0
$750$	0.471587	+	20.6601i	0.0172199	+	0.754400i
$751$	8.67540	+	15.0262i	0.316570	+	0.548315i	0.979770	−	0.200127i	$-0.0641355\pi$
$751$	8.67540	+	15.0262i	0.316570	+	0.548315i	−0.663200	+	0.748442i	$0.730802\pi$
$752$	−3.38527	−	5.86346i	−0.123448	−	0.213818i
$753$	−19.9566	−	32.8131i	−0.727260	−	1.19578i
$754$	−2.16017	−	1.24717i	−0.0786686	−	0.0454193i
$755$	−3.67100			−0.133601
$756$		0			0
$757$	18.8111			0.683701			0.341850	−	0.939754i	$-0.388946\pi$
$757$	18.8111			0.683701			0.341850	+	0.939754i	$0.388946\pi$
$758$	0.349764	+	0.201936i	0.0127040	+	0.00733465i
$759$	−15.8609	−	26.0787i	−0.575713	−	0.946598i
$760$	−22.7814	−	39.4586i	−0.826369	−	1.43131i
$761$	−4.22520	−	7.31825i	−0.153163	−	0.265286i	0.779225	−	0.626744i	$-0.215613\pi$
$761$	−4.22520	−	7.31825i	−0.153163	−	0.265286i	−0.932389	+	0.361457i	$0.882279\pi$
$762$	−0.392986	−	17.2166i	−0.0142364	−	0.623693i
$763$		0			0
$764$		−	5.94167i		−	0.214962i
$765$	9.14130	−	0.417536i	0.330504	−	0.0150960i
$766$			24.3457i			0.879644i
$767$	−28.7257	−	16.5848i	−1.03723	−	0.598843i
$768$	14.1704	−	25.8909i	0.511330	−	0.934257i
$769$	−19.8100	+	11.4373i	−0.714366	+	0.412440i	−0.812676	−	0.582716i	$-0.801990\pi$
$769$	−19.8100	+	11.4373i	−0.714366	+	0.412440i	0.0983092	+	0.995156i	$0.468657\pi$
$770$		0			0
$771$	3.37445	−	6.16550i	0.121528	−	0.222045i
$772$	−0.807907	+	1.39934i	−0.0290772	+	0.0503632i
$773$	−37.6747			−1.35507			−0.677533	−	0.735492i	$-0.736951\pi$
$773$	−37.6747			−1.35507			−0.677533	+	0.735492i	$0.736951\pi$
$774$	0.950294	+	20.8052i	0.0341576	+	0.747828i
$775$			6.23957i			0.224132i
$776$	19.7175	−	34.1517i	0.707817	−	1.22598i
$777$		0			0
$778$	−2.16888	−	3.75660i	−0.0777579	−	0.134681i
$779$	12.8362	−	7.41099i	0.459905	−	0.265526i
$780$	11.7078	−	7.12060i	0.419208	−	0.254958i
$781$	−29.6324	+	51.3249i	−1.06033	+	1.83655i
$782$	6.86116			0.245355
$783$	−2.92266	−	1.43035i	−0.104447	−	0.0511167i
$784$		0			0
$785$	15.5116	+	8.95561i	0.553632	+	0.319639i
$786$	−7.22985	+	4.39713i	−0.257880	+	0.156841i
$787$	20.3222	−	11.7330i	0.724408	−	0.418237i	−0.0919648	−	0.995762i	$-0.529315\pi$
$787$	20.3222	−	11.7330i	0.724408	−	0.418237i	0.816373	+	0.577525i	$0.195981\pi$
$788$	−17.5478	+	10.1312i	−0.625113	+	0.360909i
$789$	0.393699	+	17.2479i	0.0140161	+	0.614040i
$790$	13.3716	+	7.72011i	0.475741	+	0.274669i
$791$		0			0
$792$	−19.7030	−	30.7907i	−0.700116	−	1.09410i
$793$	15.1930			0.539519
$794$	−10.9256	+	18.9237i	−0.387734	+	0.671575i
$795$	23.9273	+	13.0957i	0.848612	+	0.464455i
$796$	−0.876386	+	0.505981i	−0.0310627	+	0.0179340i
$797$	22.8856	+	39.6390i	0.810648	+	1.40408i	0.912411	+	0.409275i	$0.134218\pi$
$797$	22.8856	+	39.6390i	0.810648	+	1.40408i	−0.101763	+	0.994809i	$0.532448\pi$
$798$		0			0
$799$	−6.43503	+	11.1458i	−0.227655	+	0.394310i
$800$		−	7.48653i		−	0.264689i
$801$	−13.5334	+	26.1256i	−0.478180	+	0.923102i
$802$	6.02896			0.212890
$803$	−7.74562	+	13.4158i	−0.273337	+	0.473433i
$804$	22.4893	−	0.513339i	0.793135	−	0.0181041i
$805$		0			0
$806$	−14.7313	+	8.50510i	−0.518887	+	0.299579i
$807$	8.97149	+	14.7511i	0.315811	+	0.519263i
$808$	2.70984	+	1.56453i	0.0953317	+	0.0550398i
$809$		−	13.2408i		−	0.465522i	−0.972534	−	0.232761i	$-0.925224\pi$
$809$		−	13.2408i		−	0.465522i	0.972534	−	0.232761i	$-0.0747761\pi$
$810$	−13.5755	+	9.58729i	−0.476996	+	0.336863i
$811$			56.0437i			1.96796i	0.178275	+	0.983981i	$0.442948\pi$
$811$			56.0437i			1.96796i	−0.178275	+	0.983981i	$0.557052\pi$
$812$		0			0
$813$	−28.1645	+	17.1294i	−0.987771	+	0.600754i
$814$	−15.9345	−	27.5994i	−0.558505	−	0.967359i
$815$	1.04426	+	1.80872i	0.0365790	+	0.0633566i
$816$	2.39497	−	0.0546674i	0.0838406	−	0.00191374i
$817$	−49.7692	−	28.7343i	−1.74120	−	1.00528i
$818$	0.868116			0.0303530
$819$		0			0
$820$	−3.55636			−0.124193
$821$	48.7766	+	28.1612i	1.70232	+	0.982833i	0.943407	+	0.331636i	$0.107601\pi$
$821$	48.7766	+	28.1612i	1.70232	+	0.982833i	0.758909	+	0.651197i	$0.225733\pi$
$822$	−0.686222	+	1.25381i	−0.0239347	+	0.0437315i
$823$	−8.52180	−	14.7602i	−0.297051	−	0.514508i	0.678409	−	0.734685i	$-0.262670\pi$
$823$	−8.52180	−	14.7602i	−0.297051	−	0.514508i	−0.975460	+	0.220177i	$0.929337\pi$
$824$	2.44253	+	4.23058i	0.0850895	+	0.147379i
$825$	−9.07537	−	4.96705i	−0.315964	−	0.172931i
$826$		0			0
$827$			45.7715i			1.59163i	0.605539	+	0.795816i	$0.292958\pi$
$827$			45.7715i			1.59163i	−0.605539	+	0.795816i	$0.707042\pi$
$828$	11.2896	−	7.22420i	0.392339	−	0.251058i
$829$		−	35.2839i		−	1.22546i	−0.790293	−	0.612730i	$-0.790071\pi$
$829$		−	35.2839i		−	1.22546i	0.790293	−	0.612730i	$-0.209929\pi$
$830$	14.0188	+	8.09376i	0.486600	+	0.280938i
$831$	−27.0540	+	0.617533i	−0.938492	+	0.0214220i
$832$	23.6704	−	13.6661i	0.820623	−	0.473787i
$833$		0			0
$834$	5.85975	+	9.63472i	0.202907	+	0.333623i
$835$	−13.1840	+	22.8354i	−0.456251	+	0.790250i
$836$	34.4292			1.19076
$837$	−18.4130	+	12.3837i	−0.636448	+	0.428043i
$838$		−	14.9082i		−	0.514995i
$839$	22.3195	−	38.6585i	0.770555	−	1.33464i	−0.166704	−	0.986007i	$-0.553312\pi$
$839$	22.3195	−	38.6585i	0.770555	−	1.33464i	0.937259	−	0.348634i	$-0.113354\pi$
$840$		0			0
$841$	−14.3039	−	24.7751i	−0.493239	−	0.854315i
$842$	−22.6670	+	13.0868i	−0.781157	+	0.451001i
$843$	0.952871	+	41.7450i	0.0328186	+	1.43778i
$844$	12.4114	−	21.4971i	0.427216	−	0.739960i
$845$	6.51965			0.224283
$846$	−1.06653	−	23.3501i	−0.0366682	−	0.802793i
$847$		0			0
$848$	6.18404	+	3.57036i	0.212361	+	0.122607i
$849$	−4.58515	−	2.50951i	−0.157362	−	0.0861260i
$850$	2.01400	−	1.16278i	0.0690795	−	0.0398831i
$851$	29.6472	−	17.1168i	1.01629	−	0.586757i
$852$	−22.8284	−	12.4943i	−0.782089	−	0.428046i
$853$	−47.7652	−	27.5772i	−1.63545	−	0.944227i	−0.982372	−	0.186935i	$-0.940145\pi$
$853$	−47.7652	−	27.5772i	−1.63545	−	0.944227i	−0.653077	−	0.757292i	$-0.726522\pi$
$854$		0			0
$855$	−2.09247	−	45.8114i	−0.0715610	−	1.56672i
$856$	−10.2399			−0.349992
$857$	−19.0771	+	33.0425i	−0.651660	+	1.12871i	0.331059	+	0.943610i	$0.392594\pi$
$857$	−19.0771	+	33.0425i	−0.651660	+	1.12871i	−0.982720	+	0.185099i	$0.940739\pi$
$858$	−0.643624	−	28.1970i	−0.0219730	−	0.962629i
$859$	35.0465	−	20.2341i	1.19577	−	0.690378i	0.236160	−	0.971714i	$-0.424111\pi$
$859$	35.0465	−	20.2341i	1.19577	−	0.690378i	0.959609	+	0.281336i	$0.0907776\pi$
$860$	6.89444	+	11.9415i	0.235099	+	0.407203i
$861$		0			0
$862$	−2.30541	+	3.99309i	−0.0785226	+	0.136005i
$863$		−	36.2021i		−	1.23233i	−0.787616	−	0.616167i	$-0.788685\pi$
$863$		−	36.2021i		−	1.23233i	0.787616	−	0.616167i	$-0.211315\pi$
$864$	22.0928	−	14.8585i	0.751614	−	0.505498i
$865$	−13.3898			−0.455266
$866$	4.40608	−	7.63155i	0.149725	−	0.259331i
$867$	12.9342	+	21.2667i	0.439269	+	0.722255i
$868$		0			0
$869$	−29.6024	+	17.0910i	−1.00419	+	0.579771i
$870$	2.00239	−	0.0457065i	0.0678873	−	0.00154959i
$871$	44.0365	+	25.4245i	1.49212	+	0.861475i
$872$			11.0002i			0.372514i
$873$	33.4325	−	21.3935i	1.13152	−	0.724060i
$874$		−	34.3846i		−	1.16307i
$875$		0			0
$876$	−5.96712	−	3.26587i	−0.201610	−	0.110344i
$877$	5.53439	+	9.58584i	0.186883	+	0.323691i	0.944209	−	0.329346i	$-0.106828\pi$
$877$	5.53439	+	9.58584i	0.186883	+	0.323691i	−0.757326	+	0.653036i	$0.773495\pi$
$878$	8.10505	+	14.0384i	0.273532	+	0.473771i
$879$	−24.8201	+	45.3492i	−0.837162	+	1.52959i
$880$	5.68111	+	3.27999i	0.191510	+	0.110568i
$881$	−8.87036			−0.298850			−0.149425	−	0.988773i	$-0.547742\pi$
$881$	−8.87036			−0.298850			−0.149425	+	0.988773i	$0.547742\pi$
$882$		0			0
$883$	−14.1903			−0.477540			−0.238770	−	0.971076i	$-0.576744\pi$
$883$	−14.1903			−0.477540			−0.238770	+	0.971076i	$0.576744\pi$
$884$	−5.90556	−	3.40958i	−0.198625	−	0.114676i
$885$	26.6276	−	0.607801i	0.895078	−	0.0204310i
$886$	−0.522064	−	0.904241i	−0.0175391	−	0.0303786i
$887$	−19.5180	−	33.8062i	−0.655350	−	1.13510i	−0.981806	−	0.189887i	$-0.939188\pi$
$887$	−19.5180	−	33.8062i	−0.655350	−	1.13510i	0.326456	−	0.945213i	$-0.394146\pi$
$888$	35.0289	−	21.3043i	1.17549	−	0.714925i
$889$		0			0
$890$		−	18.1109i		−	0.607080i
$891$	−3.35409	−	36.6397i	−0.112366	−	1.22748i
$892$		−	3.21202i		−	0.107546i
$893$	55.8570	+	32.2490i	1.86918	+	1.07917i
$894$	−14.9988	−	24.6613i	−0.501634	−	0.824796i
$895$	9.77931	−	5.64609i	0.326886	−	0.188728i
$896$		0			0
$897$	30.2891	−	0.691378i	1.01132	−	0.0230844i
$898$	7.80786	−	13.5236i	0.260552	−	0.451288i
$899$	2.67422			0.0891904
$900$	2.08958	−	4.03384i	0.0696528	−	0.134461i
$901$		−	13.5737i		−	0.452207i
$902$	−3.65992	+	6.33916i	−0.121862	+	0.211071i
$903$		0			0
$904$	25.9605	+	44.9648i	0.863432	+	1.49551i
$905$	−2.12252	+	1.22544i	−0.0705550	+	0.0407350i
$906$	−2.91044	−	1.59292i	−0.0966929	−	0.0529211i
$907$	−4.93487	+	8.54745i	−0.163860	+	0.283813i	−0.936250	−	0.351335i	$-0.885728\pi$
$907$	−4.93487	+	8.54745i	−0.163860	+	0.283813i	0.772390	+	0.635148i	$0.219061\pi$
$908$	−22.5921			−0.749747
$909$	1.69751	+	2.65277i	0.0563028	+	0.0879868i
$910$		0			0
$911$	−46.6335	−	26.9239i	−1.54504	−	0.892028i	−0.998509	−	0.0545881i	$-0.982615\pi$
$911$	−46.6335	−	26.9239i	−1.54504	−	0.892028i	−0.546529	−	0.837440i	$-0.684051\pi$
$912$	−0.273965	−	12.0023i	−0.00907188	−	0.397437i
$913$	−31.0351	+	17.9181i	−1.02711	+	0.593004i
$914$	−27.8772	+	16.0949i	−0.922096	+	0.532373i
$915$	−10.4233	+	6.33935i	−0.344583	+	0.209573i
$916$	−11.5882	−	6.69046i	−0.382885	−	0.221059i
$917$		0			0
$918$	7.42857	+	3.63555i	0.245179	+	0.119991i
$919$	22.1799			0.731647			0.365824	−	0.930684i	$-0.380787\pi$
$919$	22.1799			0.731647			0.365824	+	0.930684i	$0.380787\pi$
$920$	−12.0853	+	20.9324i	−0.398442	+	0.690122i
$921$	−3.97861	+	2.41976i	−0.131100	+	0.0797337i
$922$	−15.7047	+	9.06714i	−0.517208	+	0.298610i
$923$	−29.4128	−	50.9444i	−0.968133	−	1.67686i
$924$		0			0
$925$	5.80167	−	10.0488i	0.190758	−	0.330402i
$926$			0.396421i			0.0130272i
$927$	0.224346	+	4.91171i	0.00736849	+	0.161322i
$928$	−3.20866			−0.105329
$929$	27.4954	−	47.6234i	0.902093	−	1.56247i	0.0773215	−	0.997006i	$-0.475363\pi$
$929$	27.4954	−	47.6234i	0.902093	−	1.56247i	0.824772	−	0.565466i	$-0.191303\pi$
$930$	6.55772	−	11.9817i	0.215036	−	0.392895i
$931$		0			0
$932$	−0.725243	+	0.418719i	−0.0237561	+	0.0137156i
$933$	−9.20985	+	16.8274i	−0.301517	+	0.550905i
$934$	−12.7734	−	7.37475i	−0.417960	−	0.241309i
$935$		−	12.4698i		−	0.407807i
$936$	36.2464	−	1.65558i	1.18475	−	0.0541143i
$937$		−	29.3132i		−	0.957622i	−0.877918	−	0.478811i	$-0.841068\pi$
$937$		−	29.3132i		−	0.957622i	0.877918	−	0.478811i	$-0.158932\pi$
$938$		0			0
$939$	−0.661646	−	28.9865i	−0.0215920	−	0.945940i
$940$	−7.73777	−	13.4022i	−0.252378	−	0.437132i
$941$	7.58758	+	13.1421i	0.247348	+	0.428419i	0.962789	−	0.270254i	$-0.0871076\pi$
$941$	7.58758	+	13.1421i	0.247348	+	0.428419i	−0.715441	+	0.698673i	$0.753774\pi$
$942$	8.41185	+	13.8309i	0.274073	+	0.450636i
$943$	−6.80950	−	3.93147i	−0.221748	−	0.128026i
$944$	6.97265			0.226940
$945$		0			0
$946$	28.3808			0.922739
$947$	2.27478	+	1.31335i	0.0739206	+	0.0426781i	0.536505	−	0.843897i	$-0.319744\pi$
$947$	2.27478	+	1.31335i	0.0739206	+	0.0426781i	−0.462584	+	0.886575i	$0.653078\pi$
$948$	−7.79952	−	12.8241i	−0.253317	−	0.416508i
$949$	−7.68820	−	13.3164i	−0.249570	−	0.432267i
$950$	−5.82725	−	10.0931i	−0.189061	−	0.327463i
$951$	0.116279	+	5.09415i	0.00377060	+	0.165189i
$952$		0			0
$953$		−	40.5520i		−	1.31361i	−0.754061	−	0.656805i	$-0.771908\pi$
$953$		−	40.5520i		−	1.31361i	0.754061	−	0.656805i	$-0.228092\pi$
$954$	13.2875	+	20.7650i	0.430199	+	0.672291i
$955$			10.7847i			0.348984i
$956$	−12.6476	−	7.30212i	−0.409054	−	0.236167i
$957$	−2.12884	+	3.88962i	−0.0688155	+	0.125734i
$958$	−26.4214	+	15.2544i	−0.853637	+	0.492847i
$959$		0			0
$960$	−10.5370	+	19.2523i	−0.340081	+	0.621366i
$961$	−6.38155	+	11.0532i	−0.205856	+	0.356554i
$962$	31.6328			1.01988
$963$	−9.15151	−	4.74061i	−0.294903	−	0.152764i
$964$			19.1726i			0.617507i
$965$	1.46643	−	2.53993i	0.0472059	−	0.0817631i
$966$		0			0
$967$	6.47468	+	11.2145i	0.208212	+	0.360633i	0.951151	−	0.308725i	$-0.0999023\pi$
$967$	6.47468	+	11.2145i	0.208212	+	0.360633i	−0.742939	+	0.669359i	$0.766569\pi$
$968$	−14.7457	+	8.51343i	−0.473945	+	0.273632i
$969$	−19.4981	+	11.8586i	−0.626369	+	0.380952i
$970$	−12.2159	+	21.1585i	−0.392228	+	0.679359i
$971$	16.5215			0.530202			0.265101	−	0.964221i	$-0.414595\pi$
$971$	16.5215			0.530202			0.265101	+	0.964221i	$0.414595\pi$
$972$	16.0511	−	1.83958i	0.514839	−	0.0590047i
$973$		0			0
$974$	−11.4728	−	6.62381i	−0.367611	−	0.212240i
$975$	8.77376	−	5.33612i	0.280985	−	0.170893i
$976$	−2.76587	+	1.59687i	−0.0885333	+	0.0511147i
$977$	5.50730	−	3.17964i	0.176194	−	0.101726i	−0.409309	−	0.912396i	$-0.634230\pi$
$977$	5.50730	−	3.17964i	0.176194	−	0.101726i	0.585503	+	0.810670i	$0.300897\pi$
$978$	0.0430752	+	1.88711i	0.00137739	+	0.0603432i
$979$	34.7227	+	20.0472i	1.10974	+	0.640711i
$980$		0			0
$981$	−5.09261	+	9.83102i	−0.162594	+	0.313880i
$982$	8.01481			0.255763
$983$	1.11487	−	1.93102i	0.0355590	−	0.0615899i	−0.847698	−	0.530479i	$-0.822012\pi$
$983$	1.11487	−	1.93102i	0.0355590	−	0.0615899i	0.883257	+	0.468889i	$0.155346\pi$
$984$	−8.26049	−	4.52106i	−0.263335	−	0.144126i
$985$	31.8508	−	18.3891i	1.01485	−	0.585924i
$986$	−0.498358	−	0.863181i	−0.0158709	−	0.0274893i
$987$		0			0
$988$	−17.0870	+	29.5956i	−0.543610	+	0.941561i
$989$			30.4865i			0.969415i
$990$	12.2069	+	19.0762i	0.387960	+	0.606282i
$991$	−49.4570			−1.57105			−0.785527	−	0.618828i	$-0.787608\pi$
$991$	−49.4570			−1.57105			−0.785527	+	0.618828i	$0.787608\pi$
$992$	−10.9407	+	18.9499i	−0.347369	+	0.601661i
$993$	8.45286	−	0.192945i	0.268243	−	0.00612292i
$994$		0			0
$995$	1.59072	−	0.918403i	0.0504293	−	0.0291153i
$996$	−8.17701	−	13.4448i	−0.259098	−	0.426015i
$997$	−7.28219	−	4.20437i	−0.230629	−	0.133154i	0.380233	−	0.924891i	$-0.375844\pi$
$997$	−7.28219	−	4.20437i	−0.230629	−	0.133154i	−0.610862	+	0.791737i	$0.709177\pi$
$998$		−	27.5044i		−	0.870636i
$999$	41.1687	−	2.82307i	1.30252	−	0.0893180i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.o.e.146.9	✓	48
3.2	odd	2		1323.2.o.e.440.16		48
7.2	even	3		441.2.i.d.227.16		48
7.3	odd	6		441.2.s.d.362.16		48
7.4	even	3		441.2.s.d.362.15		48
7.5	odd	6		441.2.i.d.227.15		48
7.6	odd	2	inner	441.2.o.e.146.10	yes	48
9.4	even	3		1323.2.o.e.881.15		48
9.5	odd	6	inner	441.2.o.e.293.10	yes	48
21.2	odd	6		1323.2.i.d.521.8		48
21.5	even	6		1323.2.i.d.521.18		48
21.11	odd	6		1323.2.s.d.656.10		48
21.17	even	6		1323.2.s.d.656.9		48
21.20	even	2		1323.2.o.e.440.15		48
63.4	even	3		1323.2.i.d.1097.18		48
63.5	even	6		441.2.s.d.374.15		48
63.13	odd	6		1323.2.o.e.881.16		48
63.23	odd	6		441.2.s.d.374.16		48
63.31	odd	6		1323.2.i.d.1097.8		48
63.32	odd	6		441.2.i.d.68.9		48
63.40	odd	6		1323.2.s.d.962.10		48
63.41	even	6	inner	441.2.o.e.293.9	yes	48
63.58	even	3		1323.2.s.d.962.9		48
63.59	even	6		441.2.i.d.68.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.9		48	63.32	odd	6
441.2.i.d.68.10		48	63.59	even	6
441.2.i.d.227.15		48	7.5	odd	6
441.2.i.d.227.16		48	7.2	even	3
441.2.o.e.146.9	✓	48	1.1	even	1	trivial
441.2.o.e.146.10	yes	48	7.6	odd	2	inner
441.2.o.e.293.9	yes	48	63.41	even	6	inner
441.2.o.e.293.10	yes	48	9.5	odd	6	inner
441.2.s.d.362.15		48	7.4	even	3
441.2.s.d.362.16		48	7.3	odd	6
441.2.s.d.374.15		48	63.5	even	6
441.2.s.d.374.16		48	63.23	odd	6
1323.2.i.d.521.8		48	21.2	odd	6
1323.2.i.d.521.18		48	21.5	even	6
1323.2.i.d.1097.8		48	63.31	odd	6
1323.2.i.d.1097.18		48	63.4	even	3
1323.2.o.e.440.15		48	21.20	even	2
1323.2.o.e.440.16		48	3.2	odd	2
1323.2.o.e.881.15		48	9.4	even	3
1323.2.o.e.881.16		48	63.13	odd	6
1323.2.s.d.656.9		48	21.17	even	6
1323.2.s.d.656.10		48	21.11	odd	6
1323.2.s.d.962.9		48	63.58	even	3
1323.2.s.d.962.10		48	63.40	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.850109 - 0.490811i) q^{2} +(-0.900030 - 1.47985i) q^{3} +(-0.518210 - 0.897565i) q^{4} +(0.940599 + 1.62916i) q^{5} +(0.0387990 + 1.69978i) q^{6} +2.98061i q^{8} +(-1.37989 + 2.66381i) q^{9} +O(q^{10})\)	\(q+(-0.850109 - 0.490811i) q^{2} +(-0.900030 - 1.47985i) q^{3} +(-0.518210 - 0.897565i) q^{4} +(0.940599 + 1.62916i) q^{5} +(0.0387990 + 1.69978i) q^{6} +2.98061i q^{8} +(-1.37989 + 2.66381i) q^{9} -1.84662i q^{10} +(3.54040 + 2.04405i) q^{11} +(-0.861855 + 1.57471i) q^{12} +(-3.51415 + 2.02890i) q^{13} +(1.56435 - 2.85824i) q^{15} +(0.426498 - 0.738716i) q^{16} -1.62145 q^{17} +(2.48049 - 1.58727i) q^{18} +8.12588i q^{19} +(0.974855 - 1.68850i) q^{20} +(-2.00648 - 3.47533i) q^{22} +(3.73318 - 2.15535i) q^{23} +(4.41085 - 2.68264i) q^{24} +(0.730548 - 1.26535i) q^{25} +3.98322 q^{26} +(5.18398 - 0.355482i) q^{27} +(-0.542317 - 0.313107i) q^{29} +(-2.73272 + 1.66202i) q^{30} +(-3.69833 + 2.13523i) q^{31} +(4.43744 - 2.56195i) q^{32} +(-0.161584 - 7.07895i) q^{33} +(1.37841 + 0.795827i) q^{34} +(3.10602 - 0.141870i) q^{36} +7.94153 q^{37} +(3.98827 - 6.90789i) q^{38} +(6.16530 + 3.37434i) q^{39} +(-4.85591 + 2.80356i) q^{40} +(-0.912023 - 1.57967i) q^{41} +(-3.53614 + 6.12477i) q^{43} -4.23698i q^{44} +(-5.63771 + 0.257507i) q^{45} -4.23148 q^{46} +(3.96868 - 6.87396i) q^{47} +(-1.47705 + 0.0337151i) q^{48} +(-1.24209 + 0.717122i) q^{50} +(1.45936 + 2.39950i) q^{51} +(3.64214 + 2.10279i) q^{52} +8.37133i q^{53} +(-4.58142 - 2.24215i) q^{54} +7.69052i q^{55} +(12.0251 - 7.31354i) q^{57} +(0.307352 + 0.532350i) q^{58} +(4.08715 + 7.07915i) q^{59} +(-3.37612 + 0.0770632i) q^{60} +(-3.24253 - 1.87208i) q^{61} +4.19198 q^{62} -6.73573 q^{64} +(-6.61081 - 3.81676i) q^{65} +(-3.33706 + 6.09718i) q^{66} +(-6.26559 - 10.8523i) q^{67} +(0.840253 + 1.45536i) q^{68} +(-6.54957 - 3.58466i) q^{69} +14.4969i q^{71} +(-7.93980 - 4.11293i) q^{72} +3.78935i q^{73} +(-6.75117 - 3.89779i) q^{74} +(-2.53004 + 0.0577505i) q^{75} +(7.29351 - 4.21091i) q^{76} +(-3.58501 - 5.89455i) q^{78} +(-4.18066 + 7.24112i) q^{79} +1.60465 q^{80} +(-5.19179 - 7.35155i) q^{81} +1.79052i q^{82} +(-4.38300 + 7.59159i) q^{83} +(-1.52514 - 2.64162i) q^{85} +(6.01221 - 3.47115i) q^{86} +(0.0247514 + 1.08435i) q^{87} +(-6.09252 + 10.5526i) q^{88} +9.80759 q^{89} +(4.91906 + 2.54814i) q^{90} +(-3.86914 - 2.23385i) q^{92} +(6.48843 + 3.55119i) q^{93} +(-6.74762 + 3.89574i) q^{94} +(-13.2384 + 7.64320i) q^{95} +(-7.78512 - 4.26089i) q^{96} +(-11.4579 - 6.61525i) q^{97} +(-10.3303 + 6.61038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4} + 16 q^{9}+O(q^{10}) \) 48 * q + 24 * q^4 + 16 * q^9	\( 48 q + 24 q^{4} + 16 q^{9} - 24 q^{11} - 40 q^{15} - 24 q^{16} - 16 q^{18} - 48 q^{23} - 24 q^{25} - 24 q^{30} + 120 q^{32} - 8 q^{36} + 88 q^{39} + 48 q^{50} + 24 q^{51} + 80 q^{57} - 96 q^{60} - 48 q^{64} + 120 q^{65} + 56 q^{72} - 168 q^{74} - 88 q^{78} - 24 q^{79} - 96 q^{81} - 24 q^{85} + 24 q^{86} - 144 q^{92} - 32 q^{93} + 96 q^{95} - 72 q^{99}+O(q^{100}) \) 48 * q + 24 * q^4 + 16 * q^9 - 24 * q^11 - 40 * q^15 - 24 * q^16 - 16 * q^18 - 48 * q^23 - 24 * q^25 - 24 * q^30 + 120 * q^32 - 8 * q^36 + 88 * q^39 + 48 * q^50 + 24 * q^51 + 80 * q^57 - 96 * q^60 - 48 * q^64 + 120 * q^65 + 56 * q^72 - 168 * q^74 - 88 * q^78 - 24 * q^79 - 96 * q^81 - 24 * q^85 + 24 * q^86 - 144 * q^92 - 32 * q^93 + 96 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

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