LMFDB - Embedded newform 475.2.u.a.24.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(24,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("475.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			24.1
Root			$0.984808 + 0.173648i$ of defining polynomial
Character	$\chi$	$=$	475.24
Dual form			475.2.u.a.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.300767 - 0.826352i) q^{2} +(-0.524005 - 0.0923963i) q^{3} +(0.939693 - 0.788496i) q^{4} +(0.0812519 + 0.460802i) q^{6} +(-1.62760 + 0.939693i) q^{7} +(-2.45734 - 1.41875i) q^{8} +(-2.55303 - 0.929228i) q^{9} +O(q^{10})$	\(q+(-0.300767 - 0.826352i) q^{2} +(-0.524005 - 0.0923963i) q^{3} +(0.939693 - 0.788496i) q^{4} +(0.0812519 + 0.460802i) q^{6} +(-1.62760 + 0.939693i) q^{7} +(-2.45734 - 1.41875i) q^{8} +(-2.55303 - 0.929228i) q^{9} +(-1.70574 + 2.95442i) q^{11} +(-0.565258 + 0.326352i) q^{12} +(-5.21048 + 0.918748i) q^{13} +(1.26604 + 1.06234i) q^{14} +(-0.00727396 + 0.0412527i) q^{16} +(-0.565258 - 1.55303i) q^{17} +2.38919i q^{18} +(2.52094 - 3.55596i) q^{19} +(0.939693 - 0.342020i) q^{21} +(2.95442 + 0.520945i) q^{22} +(-1.13052 - 1.34730i) q^{23} +(1.15657 + 0.970481i) q^{24} +(2.32635 + 4.02936i) q^{26} +(2.63435 + 1.52094i) q^{27} +(-0.788496 + 2.16637i) q^{28} +(-3.25877 - 1.18610i) q^{29} +(-0.971782 - 1.68317i) q^{31} +(-5.55250 + 0.979055i) q^{32} +(1.16679 - 1.39053i) q^{33} +(-1.11334 + 0.934204i) q^{34} +(-3.13176 + 1.13987i) q^{36} -0.837496i q^{37} +(-3.69669 - 1.01367i) q^{38} +2.81521 q^{39} +(-0.779715 + 4.42198i) q^{41} +(-0.565258 - 0.673648i) q^{42} +(3.08580 - 3.67752i) q^{43} +(0.726682 + 4.12122i) q^{44} +(-0.773318 + 1.33943i) q^{46} +(0.245188 - 0.673648i) q^{47} +(0.00762319 - 0.0209445i) q^{48} +(-1.73396 + 3.00330i) q^{49} +(0.152704 + 0.866025i) q^{51} +(-4.17182 + 4.97178i) q^{52} +(3.92490 + 4.67752i) q^{53} +(0.464508 - 2.63435i) q^{54} +5.33275 q^{56} +(-1.64955 + 1.63041i) q^{57} +3.04963i q^{58} +(-10.1099 + 3.67972i) q^{59} +(3.36231 - 2.82131i) q^{61} +(-1.09861 + 1.30928i) q^{62} +(5.02849 - 0.886659i) q^{63} +(2.52094 + 4.36640i) q^{64} +(-1.50000 - 0.545955i) q^{66} +(4.86084 - 13.3550i) q^{67} +(-1.75573 - 1.01367i) q^{68} +(0.467911 + 0.810446i) q^{69} +(-10.5398 - 8.84397i) q^{71} +(4.95534 + 5.90554i) q^{72} +(7.40333 + 1.30541i) q^{73} +(-0.692066 + 0.251892i) q^{74} +(-0.434945 - 5.32926i) q^{76} -6.41147i q^{77} +(-0.846723 - 2.32635i) q^{78} +(1.20914 - 6.85738i) q^{79} +(5.00387 + 4.19875i) q^{81} +(3.88863 - 0.685670i) q^{82} +(-2.17588 + 1.25624i) q^{83} +(0.613341 - 1.06234i) q^{84} +(-3.96703 - 1.44388i) q^{86} +(1.59802 + 0.922618i) q^{87} +(8.38316 - 4.84002i) q^{88} +(0.396459 + 2.24843i) q^{89} +(7.61721 - 6.39160i) q^{91} +(-2.12467 - 0.374638i) q^{92} +(0.353700 + 0.971782i) q^{93} -0.630415 q^{94} +3.00000 q^{96} +(0.623485 + 1.71301i) q^{97} +(3.00330 + 0.529563i) q^{98} +(7.10014 - 5.95772i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^6 - 6 * q^9	$ 12 q + 6 q^{6} - 6 q^{9} + 6 q^{14} - 36 q^{16} + 24 q^{19} - 30 q^{24} + 30 q^{26} + 6 q^{29} + 18 q^{31} - 48 q^{36} + 48 q^{39} + 42 q^{41} - 18 q^{44} - 36 q^{46} - 30 q^{49} + 6 q^{51} - 60 q^{54} - 12 q^{56} - 24 q^{59} - 24 q^{61} + 24 q^{64} - 18 q^{66} + 24 q^{69} - 12 q^{71} - 30 q^{74} + 72 q^{76} + 78 q^{79} + 12 q^{81} - 6 q^{84} + 48 q^{86} + 24 q^{89} + 30 q^{91} - 36 q^{94} + 36 q^{96} - 18 q^{99}+O(q^{100}) $ 12 * q + 6 * q^6 - 6 * q^9 + 6 * q^14 - 36 * q^16 + 24 * q^19 - 30 * q^24 + 30 * q^26 + 6 * q^29 + 18 * q^31 - 48 * q^36 + 48 * q^39 + 42 * q^41 - 18 * q^44 - 36 * q^46 - 30 * q^49 + 6 * q^51 - 60 * q^54 - 12 * q^56 - 24 * q^59 - 24 * q^61 + 24 * q^64 - 18 * q^66 + 24 * q^69 - 12 * q^71 - 30 * q^74 + 72 * q^76 + 78 * q^79 + 12 * q^81 - 6 * q^84 + 48 * q^86 + 24 * q^89 + 30 * q^91 - 36 * q^94 + 36 * q^96 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	−0.300767	−	0.826352i	−0.212675	−	0.584319i	0.786784	−	0.617229i	$-0.211745\pi$
$2$	−0.300767	−	0.826352i	−0.212675	−	0.584319i	−0.999458	+	0.0329100i	$0.989523\pi$
$3$	−0.524005	−	0.0923963i	−0.302535	−	0.0533450i	0.0203202	−	0.999794i	$-0.493531\pi$
$3$	−0.524005	−	0.0923963i	−0.302535	−	0.0533450i	−0.322855	+	0.946449i	$0.604643\pi$
$4$	0.939693	−	0.788496i	0.469846	−	0.394248i
$5$		0			0
$5$		0			0
$6$	0.0812519	+	0.460802i	0.0331710	+	0.188122i
$7$	−1.62760	+	0.939693i	−0.615173	+	0.355170i	−0.774987	−	0.631977i	$-0.782244\pi$
$7$	−1.62760	+	0.939693i	−0.615173	+	0.355170i	0.159814	+	0.987147i	$0.448910\pi$
$8$	−2.45734	−	1.41875i	−0.868802	−	0.501603i
$9$	−2.55303	−	0.929228i	−0.851011	−	0.309743i
$10$		0			0
$11$	−1.70574	+	2.95442i	−0.514299	+	0.890792i	0.485563	+	0.874202i	$0.338615\pi$
$11$	−1.70574	+	2.95442i	−0.514299	+	0.890792i	−0.999862	+	0.0165906i	$0.994719\pi$
$12$	−0.565258	+	0.326352i	−0.163176	+	0.0942097i
$13$	−5.21048	+	0.918748i	−1.44513	+	0.254815i	−0.840551	−	0.541733i	$-0.817769\pi$
$13$	−5.21048	+	0.918748i	−1.44513	+	0.254815i	−0.604576	+	0.796547i	$0.706657\pi$
$14$	1.26604	+	1.06234i	0.338365	+	0.283922i
$15$		0			0
$16$	−0.00727396	+	0.0412527i	−0.00181849	+	0.0103132i
$17$	−0.565258	−	1.55303i	−0.137095	−	0.376666i	0.852079	−	0.523414i	$-0.175342\pi$
$17$	−0.565258	−	1.55303i	−0.137095	−	0.376666i	−0.989174	+	0.146748i	$0.953119\pi$
$18$			2.38919i			0.563136i
$19$	2.52094	−	3.55596i	0.578344	−	0.815793i
$19$	2.52094	−	3.55596i	0.578344	−	0.815793i
$20$		0			0
$21$	0.939693	−	0.342020i	0.205058	−	0.0746349i
$22$	2.95442	+	0.520945i	0.629885	+	0.111066i
$23$	−1.13052	−	1.34730i	−0.235729	−	0.280931i	0.635192	−	0.772354i	$-0.280921\pi$
$23$	−1.13052	−	1.34730i	−0.235729	−	0.280931i	−0.870921	+	0.491424i	$0.836477\pi$
$24$	1.15657	+	0.970481i	0.236085	+	0.198099i
$25$		0			0
$26$	2.32635	+	4.02936i	0.456235	+	0.790222i
$27$	2.63435	+	1.52094i	0.506982	+	0.292706i
$28$	−0.788496	+	2.16637i	−0.149012	+	0.409406i
$29$	−3.25877	−	1.18610i	−0.605138	−	0.220252i	0.0212363	−	0.999774i	$-0.493240\pi$
$29$	−3.25877	−	1.18610i	−0.605138	−	0.220252i	−0.626375	+	0.779522i	$0.715462\pi$
$30$		0			0
$31$	−0.971782	−	1.68317i	−0.174537	−	0.302307i	0.765464	−	0.643479i	$-0.222510\pi$
$31$	−0.971782	−	1.68317i	−0.174537	−	0.302307i	−0.940001	+	0.341172i	$0.889176\pi$
$32$	−5.55250	+	0.979055i	−0.981553	+	0.173074i
$33$	1.16679	−	1.39053i	0.203113	−	0.242060i
$34$	−1.11334	+	0.934204i	−0.190936	+	0.160215i
$35$		0			0
$36$	−3.13176	+	1.13987i	−0.521960	+	0.189978i
$37$		−	0.837496i		−	0.137684i	−0.997628	−	0.0688418i	$-0.978070\pi$
$37$		−	0.837496i		−	0.137684i	0.997628	−	0.0688418i	$-0.0219304\pi$
$38$	−3.69669	−	1.01367i	−0.599682	−	0.164439i
$39$	2.81521			0.450794
$40$		0			0
$41$	−0.779715	+	4.42198i	−0.121771	+	0.690598i	0.861402	+	0.507923i	$0.169587\pi$
$41$	−0.779715	+	4.42198i	−0.121771	+	0.690598i	−0.983173	+	0.182675i	$0.941524\pi$
$42$	−0.565258	−	0.673648i	−0.0872212	−	0.103946i
$43$	3.08580	−	3.67752i	0.470581	−	0.560816i	−0.477588	−	0.878584i	$-0.658489\pi$
$43$	3.08580	−	3.67752i	0.470581	−	0.560816i	0.948169	+	0.317768i	$0.102933\pi$
$44$	0.726682	+	4.12122i	0.109551	+	0.621297i
$45$		0			0
$46$	−0.773318	+	1.33943i	−0.114020	+	0.197488i
$47$	0.245188	−	0.673648i	0.0357643	−	0.0982617i	−0.920525	−	0.390683i	$-0.872239\pi$
$47$	0.245188	−	0.673648i	0.0357643	−	0.0982617i	0.956290	+	0.292422i	$0.0944610\pi$
$48$	0.00762319	−	0.0209445i	0.00110031	−	0.00302308i
$49$	−1.73396	+	3.00330i	−0.247708	+	0.429043i
$50$		0			0
$51$	0.152704	+	0.866025i	0.0213828	+	0.121268i
$52$	−4.17182	+	4.97178i	−0.578527	+	0.689462i
$53$	3.92490	+	4.67752i	0.539127	+	0.642507i	0.964992	−	0.262280i	$-0.0844745\pi$
$53$	3.92490	+	4.67752i	0.539127	+	0.642507i	−0.425865	+	0.904787i	$0.640030\pi$
$54$	0.464508	−	2.63435i	0.0632115	−	0.358490i
$55$		0			0
$56$	5.33275			0.712618
$57$	−1.64955	+	1.63041i	−0.218488	+	0.215954i
$58$			3.04963i			0.400436i
$59$	−10.1099	+	3.67972i	−1.31620	+	0.479058i	−0.902239	−	0.431236i	$-0.858078\pi$
$59$	−10.1099	+	3.67972i	−1.31620	+	0.479058i	−0.413962	+	0.910294i	$0.635856\pi$
$60$		0			0
$61$	3.36231	−	2.82131i	0.430500	−	0.361232i	−0.401640	−	0.915797i	$-0.631560\pi$
$61$	3.36231	−	2.82131i	0.430500	−	0.361232i	0.832140	+	0.554565i	$0.187115\pi$
$62$	−1.09861	+	1.30928i	−0.139524	+	0.166278i
$63$	5.02849	−	0.886659i	0.633531	−	0.111709i
$64$	2.52094	+	4.36640i	0.315118	+	0.545801i
$65$		0			0
$66$	−1.50000	−	0.545955i	−0.184637	−	0.0672025i
$67$	4.86084	−	13.3550i	0.593846	−	1.63158i	−0.169458	−	0.985537i	$-0.554202\pi$
$67$	4.86084	−	13.3550i	0.593846	−	1.63158i	0.763304	−	0.646040i	$-0.223576\pi$
$68$	−1.75573	−	1.01367i	−0.212913	−	0.122926i
$69$	0.467911	+	0.810446i	0.0563299	+	0.0975662i
$70$		0			0
$71$	−10.5398	−	8.84397i	−1.25085	−	1.04959i	−0.996595	−	0.0824479i	$-0.973726\pi$
$71$	−10.5398	−	8.84397i	−1.25085	−	1.04959i	−0.254252	−	0.967138i	$-0.581829\pi$
$72$	4.95534	+	5.90554i	0.583992	+	0.695975i
$73$	7.40333	+	1.30541i	0.866495	+	0.152786i	0.589189	−	0.807995i	$-0.299447\pi$
$73$	7.40333	+	1.30541i	0.866495	+	0.152786i	0.277306	+	0.960782i	$0.410559\pi$
$74$	−0.692066	+	0.251892i	−0.0804511	+	0.0292818i
$75$		0			0
$76$	−0.434945	−	5.32926i	−0.0498916	−	0.611308i
$77$		−	6.41147i		−	0.730655i
$78$	−0.846723	−	2.32635i	−0.0958725	−	0.263407i
$79$	1.20914	−	6.85738i	0.136039	−	0.771515i	−0.838092	−	0.545529i	$-0.816329\pi$
$79$	1.20914	−	6.85738i	0.136039	−	0.771515i	0.974131	−	0.225986i	$-0.0725603\pi$
$80$		0			0
$81$	5.00387	+	4.19875i	0.555986	+	0.466527i
$82$	3.88863	−	0.685670i	0.429427	−	0.0757196i
$83$	−2.17588	+	1.25624i	−0.238834	+	0.137891i	−0.614641	−	0.788807i	$-0.710699\pi$
$83$	−2.17588	+	1.25624i	−0.238834	+	0.137891i	0.375807	+	0.926698i	$0.377366\pi$
$84$	0.613341	−	1.06234i	0.0669210	−	0.115911i
$85$		0			0
$86$	−3.96703	−	1.44388i	−0.427776	−	0.155698i
$87$	1.59802	+	0.922618i	0.171326	+	0.0989151i
$88$	8.38316	−	4.84002i	0.893648	−	0.515948i
$89$	0.396459	+	2.24843i	0.0420246	+	0.238333i	0.998584	−	0.0532055i	$-0.0169438\pi$
$89$	0.396459	+	2.24843i	0.0420246	+	0.238333i	−0.956559	+	0.291539i	$0.905833\pi$
$90$		0			0
$91$	7.61721	−	6.39160i	0.798501	−	0.670022i
$92$	−2.12467	−	0.374638i	−0.221513	−	0.0390587i
$93$	0.353700	+	0.971782i	0.0366769	+	0.100769i
$94$	−0.630415			−0.0650223
$95$		0			0
$96$	3.00000			0.306186
$97$	0.623485	+	1.71301i	0.0633053	+	0.173930i	0.967312	−	0.253587i	$-0.0816105\pi$
$97$	0.623485	+	1.71301i	0.0633053	+	0.173930i	−0.904007	+	0.427517i	$0.859388\pi$
$98$	3.00330	+	0.529563i	0.303379	+	0.0534939i
$99$	7.10014	−	5.95772i	0.713591	−	0.598774i
$100$		0			0
$101$	−1.37551	−	7.80093i	−0.136869	−	0.776222i	−0.973540	−	0.228516i	$-0.926613\pi$
$101$	−1.37551	−	7.80093i	−0.136869	−	0.776222i	0.836671	−	0.547705i	$-0.184499\pi$
$102$	0.669713	−	0.386659i	0.0663115	−	0.0382850i
$103$	−0.0125989	−	0.00727396i	−0.00124140	−	0.000716725i	0.499379	−	0.866384i	$-0.333561\pi$
$103$	−0.0125989	−	0.00727396i	−0.00124140	−	0.000716725i	−0.500621	+	0.865667i	$0.666895\pi$
$104$	14.1074	+	5.13468i	1.38335	+	0.503497i
$105$		0			0
$106$	2.68479	−	4.65020i	0.260770	−	0.451667i
$107$	−3.07818	+	1.77719i	−0.297579	+	0.171807i	−0.641355	−	0.767244i	$-0.721627\pi$
$107$	−3.07818	+	1.77719i	−0.297579	+	0.171807i	0.343776	+	0.939052i	$0.388294\pi$
$108$	3.67474	−	0.647956i	0.353602	−	0.0623496i
$109$	−5.64543	−	4.73708i	−0.540734	−	0.453730i	0.331055	−	0.943612i	$-0.392596\pi$
$109$	−5.64543	−	4.73708i	−0.540734	−	0.453730i	−0.871789	+	0.489882i	$0.837040\pi$
$110$		0			0
$111$	−0.0773815	+	0.438852i	−0.00734473	+	0.0416540i
$112$	−0.0269258	−	0.0739780i	−0.00254425	−	0.00699026i
$113$		−	7.37733i		−	0.694000i	−0.937865	−	0.347000i	$-0.887200\pi$
$113$		−	7.37733i		−	0.694000i	0.937865	−	0.347000i	$-0.112800\pi$
$114$	1.84343	+	0.872729i	0.172653	+	0.0817386i
$115$		0			0
$116$	−3.99747	+	1.45496i	−0.371156	+	0.135090i
$117$	14.1563	+	2.49613i	1.30875	+	0.230767i
$118$	6.08148	+	7.24763i	0.559846	+	0.667198i
$119$	2.37939	+	1.99654i	0.218118	+	0.183023i
$120$		0			0
$121$	−0.319078	−	0.552659i	−0.0290071	−	0.0502417i
$122$	−3.34267	−	1.92989i	−0.302631	−	0.174724i
$123$	0.817150	−	2.24510i	0.0736799	−	0.202434i
$124$	−2.24035	−	0.815422i	−0.201190	−	0.0732270i
$125$		0			0
$126$	−2.24510	−	3.88863i	−0.200009	−	0.346426i
$127$	0.0994798	−	0.0175410i	0.00882740	−	0.00155651i	−0.169233	−	0.985576i	$-0.554129\pi$
$127$	0.0994798	−	0.0175410i	0.00882740	−	0.00155651i	0.178060	+	0.984020i	$0.443018\pi$
$128$	−4.39831	+	5.24170i	−0.388759	+	0.463305i
$129$	−1.95677	+	1.64192i	−0.172284	+	0.144563i
$130$		0			0
$131$	2.85369	−	1.03866i	0.249328	−	0.0907481i	−0.214333	−	0.976761i	$-0.568758\pi$
$131$	2.85369	−	1.03866i	0.249328	−	0.0907481i	0.463661	+	0.886013i	$0.346536\pi$
$132$		−	2.22668i		−	0.193808i
$133$	−0.761570	+	8.15657i	−0.0660365	+	0.707265i
$134$	−12.4979			−1.07966
$135$		0			0
$136$	−0.814330	+	4.61830i	−0.0698282	+	0.396016i
$137$	12.5600	+	14.9684i	1.07307	+	1.27883i	0.958399	+	0.285431i	$0.0921368\pi$
$137$	12.5600	+	14.9684i	1.07307	+	1.27883i	0.114671	+	0.993404i	$0.463419\pi$
$138$	0.528981	−	0.630415i	0.0450298	−	0.0536645i
$139$	−2.67365	−	15.1630i	−0.226776	−	1.28611i	−0.859261	−	0.511537i	$-0.829076\pi$
$139$	−2.67365	−	15.1630i	−0.226776	−	1.28611i	0.632485	−	0.774573i	$-0.282035\pi$
$140$		0			0
$141$	−0.190722	+	0.330341i	−0.0160617	+	0.0278197i
$142$	−4.13819	+	11.3696i	−0.347269	+	0.954114i
$143$	6.17334	−	16.9611i	0.516240	−	1.41836i
$144$	0.0569038	−	0.0985603i	0.00474198	−	0.00821336i
$145$		0			0
$146$	−1.14796	−	6.51038i	−0.0950055	−	0.538803i
$147$	1.18610	−	1.41353i	0.0978275	−	0.116586i
$148$	−0.660362	−	0.786989i	−0.0542814	−	0.0646901i
$149$	0.654048	−	3.70929i	0.0535817	−	0.303877i	−0.946226	−	0.323507i	$-0.895138\pi$
$149$	0.654048	−	3.70929i	0.0535817	−	0.303877i	0.999807	+	0.0196306i	$0.00624903\pi$
$150$		0			0
$151$	−14.5963			−1.18783			−0.593914	−	0.804529i	$-0.702418\pi$
$151$	−14.5963			−1.18783			−0.593914	+	0.804529i	$0.702418\pi$
$152$	−11.2398	+	5.16163i	−0.911671	+	0.418663i
$153$			4.49020i			0.363011i
$154$	−5.29813	+	1.92836i	−0.426936	+	0.155392i
$155$		0			0
$156$	2.64543	−	2.21978i	0.211804	−	0.177725i
$157$	6.66869	−	7.94743i	0.532219	−	0.634274i	−0.431205	−	0.902254i	$-0.641912\pi$
$157$	6.66869	−	7.94743i	0.532219	−	0.634274i	0.963425	+	0.267980i	$0.0863560\pi$
$158$	−6.03028	+	1.06330i	−0.479743	+	0.0845916i
$159$	−1.62449	−	2.81369i	−0.128830	−	0.223140i
$160$		0			0
$161$	3.10607	+	1.13052i	0.244792	+	0.0890971i
$162$	1.96464	−	5.39780i	0.154357	−	0.424091i
$163$	−1.75135	−	1.01114i	−0.137177	−	0.0791989i	0.429841	−	0.902905i	$-0.358570\pi$
$163$	−1.75135	−	1.01114i	−0.137177	−	0.0791989i	−0.567018	+	0.823706i	$0.691903\pi$
$164$	2.75402	+	4.77011i	0.215053	+	0.372483i
$165$		0			0
$166$	1.69253	+	1.42020i	0.131366	+	0.110229i
$167$	−14.9491	−	17.8157i	−1.15680	−	1.37862i	−0.912580	−	0.408898i	$-0.865913\pi$
$167$	−14.9491	−	17.8157i	−1.15680	−	1.37862i	−0.244218	−	0.969720i	$-0.578531\pi$
$168$	−2.79439	−	0.492726i	−0.215592	−	0.0380146i
$169$	14.0890	−	5.12797i	1.08377	−	0.394460i
$170$		0			0
$171$	−9.74035	+	6.73595i	−0.744863	+	0.515111i
$172$		−	5.88888i		−	0.449023i
$173$	0.306663	+	0.842549i	0.0233151	+	0.0640578i	0.950804	−	0.309793i	$-0.100260\pi$
$173$	0.306663	+	0.842549i	0.0233151	+	0.0640578i	−0.927489	+	0.373850i	$0.878037\pi$
$174$	0.281774	−	1.59802i	0.0213613	−	0.121146i
$175$		0			0
$176$	−0.109470	−	0.0918566i	−0.00825164	−	0.00692395i
$177$	5.63765	−	0.994070i	0.423752	−	0.0747189i
$178$	1.73875	−	1.00387i	0.130325	−	0.0752433i
$179$	−10.6591	+	18.4621i	−0.796699	+	1.37992i	0.125056	+	0.992150i	$0.460089\pi$
$179$	−10.6591	+	18.4621i	−0.796699	+	1.37992i	−0.921755	+	0.387773i	$0.873245\pi$
$180$		0			0
$181$	15.1284	+	5.50627i	1.12448	+	0.409278i	0.836286	−	0.548294i	$-0.184722\pi$
$181$	15.1284	+	5.50627i	1.12448	+	0.409278i	0.288196	+	0.957571i	$0.406945\pi$
$182$	−7.57272	−	4.37211i	−0.561327	−	0.324082i
$183$	−2.02255	+	1.16772i	−0.149511	+	0.0863202i
$184$	0.866592	+	4.91469i	0.0638860	+	0.362316i
$185$		0			0
$186$	0.696652	−	0.584561i	0.0510810	−	0.0428621i
$187$	5.55250	+	0.979055i	0.406039	+	0.0715956i
$188$	−0.300767	−	0.826352i	−0.0219357	−	0.0602679i
$189$	−5.71688			−0.415842
$190$		0			0
$191$	18.9486			1.37107			0.685537	−	0.728038i	$-0.259568\pi$
$191$	18.9486			1.37107			0.685537	+	0.728038i	$0.259568\pi$
$192$	−0.917549	−	2.52094i	−0.0662184	−	0.181934i
$193$	−12.7057	−	2.24035i	−0.914574	−	0.161264i	−0.303494	−	0.952833i	$-0.598153\pi$
$193$	−12.7057	−	2.24035i	−0.914574	−	0.161264i	−0.611080	+	0.791569i	$0.709264\pi$
$194$	1.22803	−	1.03044i	0.0881671	−	0.0739810i
$195$		0			0
$196$	0.738703	+	4.18939i	0.0527645	+	0.299242i
$197$	−20.0920	+	11.6001i	−1.43150	+	0.826476i	−0.997235	−	0.0743108i	$-0.976324\pi$
$197$	−20.0920	+	11.6001i	−1.43150	+	0.826476i	−0.434263	+	0.900786i	$0.642991\pi$
$198$	−7.05866	−	4.07532i	−0.501637	−	0.289621i
$199$	8.66550	+	3.15398i	0.614281	+	0.223580i	0.630375	−	0.776291i	$-0.282901\pi$
$199$	8.66550	+	3.15398i	0.614281	+	0.223580i	−0.0160945	+	0.999870i	$0.505123\pi$
$200$		0			0
$201$	−3.78106	+	6.54899i	−0.266695	+	0.461930i
$202$	−6.03260	+	3.48293i	−0.424453	+	0.245058i
$203$	6.41852	−	1.13176i	0.450492	−	0.0794339i
$204$	0.826352	+	0.693392i	0.0578562	+	0.0485471i
$205$		0			0
$206$	−0.00222152	+	0.0125989i	−0.000154781	+	0.000877805i
$207$	1.63430	+	4.49020i	0.113592	+	0.312090i
$208$		−	0.221629i		−	0.0153672i
$209$	6.20574	+	13.5135i	0.429260	+	0.934746i
$210$		0			0
$211$	−13.7417	+	5.00157i	−0.946017	+	0.344322i	−0.768539	−	0.639803i	$-0.779016\pi$
$211$	−13.7417	+	5.00157i	−0.946017	+	0.344322i	−0.177478	+	0.984125i	$0.556794\pi$
$212$	7.37641	+	1.30066i	0.506614	+	0.0893297i
$213$	4.70578	+	5.60813i	0.322435	+	0.384262i
$214$	2.39440	+	2.00914i	0.163678	+	0.137342i
$215$		0			0
$216$	−4.31567	−	7.47497i	−0.293644	−	0.508607i
$217$	3.16333	+	1.82635i	0.214741	+	0.123981i
$218$	−2.21653	+	6.08987i	−0.150122	+	0.412458i
$219$	−3.75877	−	1.36808i	−0.253994	−	0.0924463i
$220$		0			0
$221$	4.37211	+	7.57272i	0.294100	+	0.509396i
$222$	0.385920	−	0.0680482i	0.0259013	−	0.00456709i
$223$	−1.93771	+	2.30928i	−0.129759	+	0.154641i	−0.827012	−	0.562185i	$-0.809961\pi$
$223$	−1.93771	+	2.30928i	−0.129759	+	0.154641i	0.697253	+	0.716825i	$0.254405\pi$
$224$	8.11721	−	6.81115i	0.542354	−	0.455089i
$225$		0			0
$226$	−6.09627	+	2.21886i	−0.405518	+	0.147596i
$227$		−	13.7219i		−	0.910757i	−0.890298	−	0.455378i	$-0.849504\pi$
$227$		−	13.7219i		−	0.910757i	0.890298	−	0.455378i	$-0.150496\pi$
$228$	−0.264490	+	2.83275i	−0.0175163	+	0.187603i
$229$	−9.41416			−0.622105			−0.311053	−	0.950393i	$-0.600682\pi$
$229$	−9.41416			−0.622105			−0.311053	+	0.950393i	$0.600682\pi$
$230$		0			0
$231$	−0.592396	+	3.35965i	−0.0389768	+	0.221048i
$232$	6.32515	+	7.53802i	0.415266	+	0.494895i
$233$	−15.5463	+	18.5273i	−1.01847	+	1.21377i	−0.0417777	+	0.999127i	$0.513302\pi$
$233$	−15.5463	+	18.5273i	−1.01847	+	1.21377i	−0.976693	+	0.214640i	$0.931142\pi$
$234$	−2.19506	−	12.4488i	−0.143496	−	0.813804i
$235$		0			0
$236$	−6.59879	+	11.4294i	−0.429545	+	0.743993i
$237$	−1.26719	+	3.48158i	−0.0823130	+	0.226153i
$238$	0.934204	−	2.56670i	0.0605554	−	0.166375i
$239$	−11.6630	+	20.2009i	−0.754415	+	1.30668i	0.191250	+	0.981541i	$0.438746\pi$
$239$	−11.6630	+	20.2009i	−0.754415	+	1.30668i	−0.945665	+	0.325143i	$0.894587\pi$
$240$		0			0
$241$	0.0516892	+	0.293144i	0.00332960	+	0.0188831i	0.986427	−	0.164199i	$-0.0525038\pi$
$241$	0.0516892	+	0.293144i	0.00332960	+	0.0188831i	−0.983098	+	0.183082i	$0.941393\pi$
$242$	−0.360723	+	0.429892i	−0.0231881	+	0.0276345i
$243$	−8.09997	−	9.65317i	−0.519613	−	0.619251i
$244$	0.934945	−	5.30234i	0.0598537	−	0.339447i
$245$		0			0
$246$	−2.10101			−0.133956
$247$	−9.86830	+	20.8444i	−0.627905	+	1.32629i
$248$			5.51485i			0.350193i
$249$	1.25624	−	0.457236i	0.0796112	−	0.0289761i
$250$		0			0
$251$	−12.4081	+	10.4116i	−0.783190	+	0.657175i	−0.944050	−	0.329802i	$-0.893018\pi$
$251$	−12.4081	+	10.4116i	−0.783190	+	0.657175i	0.160859	+	0.986977i	$0.448573\pi$
$252$	4.02611	−	4.79813i	0.253621	−	0.302254i
$253$	5.90885	−	1.04189i	0.371486	−	0.0655030i
$254$	−0.0444153	−	0.0769295i	−0.00278686	−	0.00482699i
$255$		0			0
$256$	15.1300	+	5.50687i	0.945625	+	0.344179i
$257$	5.25173	−	14.4290i	0.327594	−	0.900057i	−0.661125	−	0.750276i	$-0.729921\pi$
$257$	5.25173	−	14.4290i	0.327594	−	0.900057i	0.988719	−	0.149782i	$-0.0478570\pi$
$258$	1.94534	+	1.12314i	0.121111	+	0.0699237i
$259$	0.786989	+	1.36310i	0.0489011	+	0.0846992i
$260$		0			0
$261$	7.21760	+	6.05628i	0.446758	+	0.374874i
$262$	−1.71660	−	2.04576i	−0.106052	−	0.126387i
$263$	−9.49671	−	1.67453i	−0.585592	−	0.103256i	−0.127000	−	0.991903i	$-0.540535\pi$
$263$	−9.49671	−	1.67453i	−0.585592	−	0.103256i	−0.458592	+	0.888647i	$0.651646\pi$
$264$	−4.84002	+	1.76162i	−0.297883	+	0.108420i
$265$		0			0
$266$	6.96926	−	1.82391i	0.427312	−	0.111831i
$267$		−	1.21482i		−	0.0743459i
$268$	−5.96270	−	16.3824i	−0.364230	−	1.00071i
$269$	3.17412	−	18.0013i	0.193529	−	1.09756i	−0.720969	−	0.692968i	$-0.756303\pi$
$269$	3.17412	−	18.0013i	0.193529	−	1.09756i	0.914498	−	0.404591i	$-0.132586\pi$
$270$		0			0
$271$	14.5273	+	12.1899i	0.882473	+	0.740483i	0.966686	−	0.255965i	$-0.0823932\pi$
$271$	14.5273	+	12.1899i	0.882473	+	0.740483i	−0.0842129	+	0.996448i	$0.526838\pi$
$272$	0.0681784	−	0.0120217i	0.00413393	−	0.000728923i
$273$	−4.58202	+	2.64543i	−0.277316	+	0.160109i
$274$	8.59152	−	14.8809i	0.519033	−	0.898991i
$275$		0			0
$276$	1.07873	+	0.392624i	0.0649317	+	0.0236332i
$277$	−11.9198	−	6.88191i	−0.716193	−	0.413494i	0.0971571	−	0.995269i	$-0.469025\pi$
$277$	−11.9198	−	6.88191i	−0.716193	−	0.413494i	−0.813350	+	0.581775i	$0.802358\pi$
$278$	−11.7258	+	6.76991i	−0.703269	+	0.406033i
$279$	0.916937	+	5.20021i	0.0548956	+	0.311328i
$280$		0			0
$281$	10.0437	−	8.42767i	0.599157	−	0.502752i	−0.292018	−	0.956413i	$-0.594327\pi$
$281$	10.0437	−	8.42767i	0.599157	−	0.502752i	0.891175	+	0.453661i	$0.149882\pi$
$282$	0.330341	+	0.0582480i	0.0196715	+	0.00346862i
$283$	−5.94340	−	16.3293i	−0.353298	−	0.970679i	−0.981303	−	0.192469i	$-0.938350\pi$
$283$	−5.94340	−	16.3293i	−0.353298	−	0.970679i	0.628005	−	0.778209i	$-0.283872\pi$
$284$	−16.8776			−1.00150
$285$		0			0
$286$	−15.8726			−0.938565
$287$	−2.88624	−	7.92989i	−0.170370	−	0.468087i
$288$	15.0855	+	2.65998i	0.888921	+	0.156741i
$289$	10.9304	−	9.17166i	0.642962	−	0.539509i
$290$		0			0
$291$	−0.168434	−	0.955234i	−0.00987375	−	0.0559968i
$292$	7.98617	−	4.61081i	0.467355	−	0.269828i
$293$	13.5135	+	7.80200i	0.789465	+	0.455798i	0.839774	−	0.542936i	$-0.182687\pi$
$293$	13.5135	+	7.80200i	0.789465	+	0.455798i	−0.0503091	+	0.998734i	$0.516021\pi$
$294$	−1.52481	−	0.554987i	−0.0889290	−	0.0323675i
$295$		0			0
$296$	−1.18820	+	2.05802i	−0.0690625	+	0.119620i
$297$	−8.98703	+	5.18866i	−0.521480	+	0.301077i
$298$	−3.26189	+	0.575160i	−0.188956	+	0.0333181i
$299$	7.12836	+	5.98140i	0.412243	+	0.345913i
$300$		0			0
$301$	−1.56670	+	8.88522i	−0.0903033	+	0.512136i
$302$	4.39008	+	12.0617i	0.252621	+	0.694070i
$303$			4.21482i			0.242135i
$304$	0.128356	+	0.129862i	0.00736170	+	0.00744807i
$305$		0			0
$306$	3.71048	−	1.35051i	0.212114	−	0.0772033i
$307$	21.1933	+	3.73695i	1.20956	+	0.213279i	0.741829	−	0.670589i	$-0.233959\pi$
$307$	21.1933	+	3.73695i	1.20956	+	0.213279i	0.467736	+	0.883868i	$0.345070\pi$
$308$	−5.05542	−	6.02481i	−0.288059	−	0.343296i
$309$	0.00592979	+	0.00497568i	0.000337334	+	0.000283057i
$310$		0			0
$311$	−7.24763	−	12.5533i	−0.410975	−	0.711830i	0.584021	−	0.811738i	$-0.301478\pi$
$311$	−7.24763	−	12.5533i	−0.410975	−	0.711830i	−0.994997	+	0.0999083i	$0.968145\pi$
$312$	−6.91793	−	3.99407i	−0.391651	−	0.226120i
$313$	−6.67571	+	18.3414i	−0.377334	+	1.03672i	0.595124	+	0.803634i	$0.297103\pi$
$313$	−6.67571	+	18.3414i	−0.377334	+	1.03672i	−0.972457	+	0.233081i	$0.925119\pi$
$314$	−8.57310	−	3.12035i	−0.483808	−	0.176092i
$315$		0			0
$316$	−4.27079	−	7.39723i	−0.240251	−	0.416127i
$317$	−27.9166	+	4.92246i	−1.56795	+	0.276473i	−0.889070	−	0.457772i	$-0.848648\pi$
$317$	−27.9166	+	4.92246i	−1.56795	+	0.276473i	−0.678885	+	0.734245i	$0.737536\pi$
$318$	−1.83651	+	2.18866i	−0.102986	+	0.122734i
$319$	9.06283	−	7.60462i	0.507421	−	0.425777i
$320$		0			0
$321$	1.77719	−	0.646844i	0.0991930	−	0.0361033i
$322$		−	2.90673i		−	0.161986i
$323$	−6.94751	−	1.90508i	−0.386570	−	0.106001i
$324$	8.01279			0.445155
$325$		0			0
$326$	−0.308811	+	1.75135i	−0.0171035	+	0.0969985i
$327$	2.52055	+	3.00387i	0.139387	+	0.166114i
$328$	8.18971	−	9.76011i	0.452201	−	0.538912i
$329$	0.233956	+	1.32683i	0.0128984	+	0.0731504i
$330$		0			0
$331$	0.855037	−	1.48097i	0.0469971	−	0.0814014i	−0.841570	−	0.540148i	$-0.818368\pi$
$331$	0.855037	−	1.48097i	0.0469971	−	0.0814014i	0.888567	+	0.458747i	$0.151702\pi$
$332$	−1.05411	+	2.89615i	−0.0578520	+	0.158947i
$333$	−0.778225	+	2.13816i	−0.0426465	+	0.117170i
$334$	−10.2258	+	17.7116i	−0.559531	+	0.969136i
$335$		0			0
$336$	0.00727396	+	0.0412527i	0.000396827	+	0.00225052i
$337$	−16.3518	+	19.4873i	−0.890737	+	1.06154i	0.106997	+	0.994259i	$0.465876\pi$
$337$	−16.3518	+	19.4873i	−0.890737	+	1.06154i	−0.997734	+	0.0672796i	$0.978568\pi$
$338$	−8.47502	−	10.1001i	−0.460980	−	0.549375i
$339$	−0.681637	+	3.86576i	−0.0370215	+	0.209959i
$340$		0			0
$341$	6.63041			0.359057
$342$	8.49584	+	6.02300i	0.459403	+	0.325687i
$343$		−	19.6732i		−	1.06225i
$344$	−12.8004	+	4.65895i	−0.690149	+	0.251194i
$345$		0			0
$346$	0.604007	−	0.506822i	0.0324716	−	0.0272469i
$347$	−4.95096	+	5.90033i	−0.265782	+	0.316746i	−0.882385	−	0.470527i	$-0.844064\pi$
$347$	−4.95096	+	5.90033i	−0.265782	+	0.316746i	0.616604	+	0.787274i	$0.288508\pi$
$348$	2.22913	−	0.393056i	0.119494	−	0.0210700i
$349$	11.3785	+	19.7082i	0.609078	+	1.05495i	0.991393	+	0.130921i	$0.0417935\pi$
$349$	11.3785	+	19.7082i	0.609078	+	1.05495i	−0.382315	+	0.924032i	$0.624873\pi$
$350$		0			0
$351$	−15.1236	−	5.50454i	−0.807238	−	0.293811i
$352$	6.57856	−	18.0744i	0.350638	−	0.963371i
$353$	−9.91220	−	5.72281i	−0.527573	−	0.304595i	0.212454	−	0.977171i	$-0.431854\pi$
$353$	−9.91220	−	5.72281i	−0.527573	−	0.304595i	−0.740028	+	0.672576i	$0.765188\pi$
$354$	−2.51707	−	4.35970i	−0.133781	−	0.231715i
$355$		0			0
$356$	2.14543	+	1.80023i	0.113708	+	0.0954120i
$357$	−1.06234	−	1.26604i	−0.0562249	−	0.0670062i
$358$	18.4621	+	3.25537i	0.975752	+	0.172051i
$359$	9.75789	−	3.55158i	0.515002	−	0.187445i	−0.0714274	−	0.997446i	$-0.522755\pi$
$359$	9.75789	−	3.55158i	0.515002	−	0.187445i	0.586429	+	0.810000i	$0.300533\pi$
$360$		0			0
$361$	−6.28968	−	17.9287i	−0.331036	−	0.943618i
$362$		−	14.1575i		−	0.744099i
$363$	0.116135	+	0.319078i	0.00609550	+	0.0167472i
$364$	2.11809	−	12.0123i	0.111018	−	0.629614i
$365$		0			0
$366$	1.57326	+	1.32012i	0.0822358	+	0.0690040i
$367$	32.0388	−	5.64930i	1.67241	−	0.294891i	0.744480	−	0.667645i	$-0.232697\pi$
$367$	32.0388	−	5.64930i	1.67241	−	0.294891i	0.927930	+	0.372754i	$0.121586\pi$
$368$	0.0638029	−	0.0368366i	0.00332596	−	0.00192024i
$369$	6.09967	−	10.5649i	0.317536	−	0.549989i
$370$		0			0
$371$	−10.7836	−	3.92490i	−0.559856	−	0.203771i
$372$	1.09861	+	0.634285i	0.0569605	+	0.0328862i
$373$	−26.4014	+	15.2429i	−1.36701	+	0.789246i	−0.990546	−	0.137183i	$-0.956195\pi$
$373$	−26.4014	+	15.2429i	−1.36701	+	0.789246i	−0.376469	+	0.926429i	$0.622862\pi$
$374$	−0.860967	−	4.88279i	−0.0445195	−	0.252483i
$375$		0			0
$376$	−1.55825	+	1.30753i	−0.0803605	+	0.0674305i
$377$	18.0695	+	3.18614i	0.930626	+	0.164094i
$378$	1.71945	+	4.72416i	0.0884391	+	0.242984i
$379$	−17.8598			−0.917396			−0.458698	−	0.888592i	$-0.651684\pi$
$379$	−17.8598			−0.917396			−0.458698	+	0.888592i	$0.651684\pi$
$380$		0			0
$381$	−0.0537486			−0.00275363
$382$	−5.69913	−	15.6582i	−0.291593	−	0.801144i
$383$	23.0997	+	4.07310i	1.18034	+	0.208126i	0.729183	−	0.684319i	$-0.239900\pi$
$383$	23.0997	+	4.07310i	1.18034	+	0.208126i	0.451157	+	0.892445i	$0.351012\pi$
$384$	2.78905	−	2.34029i	0.142328	−	0.119427i
$385$		0			0
$386$	1.97013	+	11.1732i	0.100277	+	0.568700i
$387$	−11.2954	+	6.52141i	−0.574178	+	0.331502i
$388$	1.93659	+	1.11809i	0.0983153	+	0.0567623i
$389$	3.67365	+	1.33710i	0.186261	+	0.0677936i	0.433467	−	0.901169i	$-0.357290\pi$
$389$	3.67365	+	1.33710i	0.186261	+	0.0677936i	−0.247206	+	0.968963i	$0.579512\pi$
$390$		0			0
$391$	−1.45336	+	2.51730i	−0.0734997	+	0.127305i
$392$	8.52185	−	4.92009i	0.430418	−	0.248502i
$393$	−1.59132	+	0.280592i	−0.0802714	+	0.0141540i
$394$	15.6288	+	13.1141i	0.787369	+	0.660681i
$395$		0			0
$396$	1.97431	−	11.1969i	0.0992127	−	0.562663i
$397$	−3.06417	−	8.41875i	−0.153786	−	0.422525i	0.838743	−	0.544527i	$-0.183291\pi$
$397$	−3.06417	−	8.41875i	−0.153786	−	0.422525i	−0.992530	+	0.122002i	$0.961069\pi$
$398$		−	8.10936i		−	0.406486i
$399$	1.15270	−	4.20372i	0.0577074	−	0.210449i
$400$		0			0
$401$	1.90508	−	0.693392i	0.0951350	−	0.0346263i	−0.294014	−	0.955801i	$-0.594991\pi$
$401$	1.90508	−	0.693392i	0.0951350	−	0.0346263i	0.389149	+	0.921175i	$0.372769\pi$
$402$	6.54899	+	1.15476i	0.326634	+	0.0575943i
$403$	6.60986	+	7.87733i	0.329261	+	0.392398i
$404$	−7.44356	−	6.24589i	−0.370331	−	0.310745i
$405$		0			0
$406$	−2.86571	−	4.96356i	−0.142223	−	0.246338i
$407$	2.47432	+	1.42855i	0.122647	+	0.0708105i
$408$	0.853427	−	2.34477i	0.0422509	−	0.116083i
$409$	−30.2656	−	11.0158i	−1.49654	−	0.544696i	−0.541377	−	0.840780i	$-0.682097\pi$
$409$	−30.2656	−	11.0158i	−1.49654	−	0.544696i	−0.955162	+	0.296084i	$0.904319\pi$
$410$		0			0
$411$	−5.19846	−	9.00400i	−0.256421	−	0.444135i
$412$	−0.0175745	+	0.00309887i	−0.000865836	+	0.000152670i
$413$	12.9971	−	15.4893i	0.639545	−	0.762180i
$414$	3.21894	−	2.70101i	0.158202	−	0.132747i
$415$		0			0
$416$	28.0317	−	10.2027i	1.37437	−	0.500228i
$417$			8.19253i			0.401190i
$418$	9.30039	−	9.19253i	0.454897	−	0.449622i
$419$	23.2499			1.13583			0.567916	−	0.823086i	$-0.307750\pi$
$419$	23.2499			1.13583			0.567916	+	0.823086i	$0.307750\pi$
$420$		0			0
$421$	1.12061	−	6.35532i	0.0546154	−	0.309739i	−0.945246	−	0.326357i	$-0.894179\pi$
$421$	1.12061	−	6.35532i	0.0546154	−	0.309739i	0.999862	+	0.0166178i	$0.00528986\pi$
$422$	8.26611	+	9.85117i	0.402388	+	0.479547i
$423$	−1.25195	+	1.49201i	−0.0608717	+	0.0725440i
$424$	−3.00862	−	17.0627i	−0.146111	−	0.828639i
$425$		0			0
$426$	3.21894	−	5.57537i	0.155958	−	0.270128i
$427$	−2.82131	+	7.75150i	−0.136533	+	0.375121i
$428$	−1.49124	+	4.09714i	−0.0720817	+	0.198043i
$429$	−4.80200	+	8.31731i	−0.231843	+	0.401564i
$430$		0			0
$431$	−2.43061	−	13.7847i	−0.117078	−	0.663984i	−0.985700	−	0.168508i	$-0.946105\pi$
$431$	−2.43061	−	13.7847i	−0.117078	−	0.663984i	0.868622	−	0.495475i	$-0.165006\pi$
$432$	−0.0819052	+	0.0976108i	−0.00394067	+	0.00469630i
$433$	18.4434	+	21.9800i	0.886333	+	1.05629i	0.998042	+	0.0625499i	$0.0199232\pi$
$433$	18.4434	+	21.9800i	0.886333	+	1.05629i	−0.111709	+	0.993741i	$0.535632\pi$
$434$	0.557781	−	3.16333i	0.0267744	−	0.151845i
$435$		0			0
$436$	−9.04013			−0.432944
$437$	−7.64090	+	0.623608i	−0.365514	+	0.0298312i
$438$			3.51754i			0.168075i
$439$	−12.5376	+	4.56332i	−0.598387	+	0.217795i	−0.623414	−	0.781892i	$-0.714255\pi$
$439$	−12.5376	+	4.56332i	−0.598387	+	0.217795i	0.0250271	+	0.999687i	$0.492033\pi$
$440$		0			0
$441$	7.21760	−	6.05628i	0.343695	−	0.288394i
$442$	4.94274	−	5.89053i	0.235102	−	0.280184i
$443$	33.3682	−	5.88372i	1.58537	−	0.279544i	0.689646	−	0.724147i	$-0.257766\pi$
$443$	33.3682	−	5.88372i	1.58537	−	0.279544i	0.895728	+	0.444603i	$0.146655\pi$
$444$	0.273318	+	0.473401i	0.0129711	+	0.0224666i
$445$		0			0
$446$	2.49108	+	0.906678i	0.117956	+	0.0429324i
$447$	−0.685449	+	1.88326i	−0.0324206	+	0.0890749i
$448$	−8.20616	−	4.73783i	−0.387704	−	0.223841i
$449$	9.42009	+	16.3161i	0.444562	+	0.770003i	0.998022	−	0.0628725i	$-0.0200261\pi$
$449$	9.42009	+	16.3161i	0.444562	+	0.770003i	−0.553460	+	0.832876i	$0.686693\pi$
$450$		0			0
$451$	−11.7344	−	9.84635i	−0.552552	−	0.463646i
$452$	−5.81699	−	6.93242i	−0.273608	−	0.326074i
$453$	7.64852	+	1.34864i	0.359359	+	0.0633647i
$454$	−11.3391	+	4.12711i	−0.532172	+	0.193695i
$455$		0			0
$456$	6.36665	−	1.66620i	0.298146	−	0.0780270i
$457$			14.2790i			0.667943i	0.942583	+	0.333972i	$0.108389\pi$
$457$			14.2790i			0.667943i	−0.942583	+	0.333972i	$0.891611\pi$
$458$	2.83147	+	7.77941i	0.132306	+	0.363508i
$459$	0.872989	−	4.95096i	0.0407476	−	0.231091i
$460$		0			0
$461$	−10.6695	−	8.95280i	−0.496930	−	0.416973i	0.359572	−	0.933117i	$-0.382923\pi$
$461$	−10.6695	−	8.95280i	−0.496930	−	0.416973i	−0.856502	+	0.516144i	$0.827367\pi$
$462$	2.95442	−	0.520945i	0.137452	−	0.0242365i
$463$	1.52671	−	0.881445i	0.0709521	−	0.0409642i	−0.464104	−	0.885781i	$-0.653624\pi$
$463$	1.52671	−	0.881445i	0.0709521	−	0.0409642i	0.535056	+	0.844816i	$0.320290\pi$
$464$	0.0726338	−	0.125805i	0.00337194	−	0.00584037i
$465$		0			0
$466$	19.9859	+	7.27428i	0.925830	+	0.336974i
$467$	−19.0888	−	11.0209i	−0.883326	−	0.509988i	−0.0115724	−	0.999933i	$-0.503684\pi$
$467$	−19.0888	−	11.0209i	−0.883326	−	0.509988i	−0.871754	+	0.489945i	$0.837017\pi$
$468$	15.2707	−	8.81655i	0.705889	−	0.407545i
$469$	4.63816	+	26.3043i	0.214170	+	1.21462i
$470$		0			0
$471$	−4.22874	+	3.54834i	−0.194850	+	0.163499i
$472$	30.0642	+	5.30113i	1.38382	+	0.244004i
$473$	5.60138	+	15.3897i	0.257552	+	0.707617i
$474$	3.25814			0.149651
$475$		0			0
$476$	3.81016			0.174638
$477$	−5.67393	−	15.5890i	−0.259791	−	0.713771i
$478$	20.2009	+	3.56196i	0.923966	+	0.162920i
$479$	19.5012	−	16.3634i	0.891032	−	0.747664i	−0.0773851	−	0.997001i	$-0.524657\pi$
$479$	19.5012	−	16.3634i	0.891032	−	0.747664i	0.968417	+	0.249337i	$0.0802126\pi$
$480$		0			0
$481$	0.769448	+	4.36376i	0.0350838	+	0.198970i
$482$	0.226694	−	0.130882i	0.0103256	−	0.00596150i
$483$	−1.52314	−	0.879385i	−0.0693053	−	0.0400134i
$484$	−0.735604	−	0.267738i	−0.0334366	−	0.0121699i
$485$		0			0
$486$	−5.54071	+	9.59679i	−0.251332	+	0.435319i
$487$	−19.4949	+	11.2554i	−0.883397	+	0.510029i	−0.871777	−	0.489903i	$-0.837032\pi$
$487$	−19.4949	+	11.2554i	−0.883397	+	0.510029i	−0.0116199	+	0.999932i	$0.503699\pi$
$488$	−12.2651	+	2.16267i	−0.555214	+	0.0978993i
$489$	0.824292	+	0.691663i	0.0372758	+	0.0312781i
$490$		0			0
$491$	2.71482	−	15.3965i	0.122518	−	0.694835i	−0.860233	−	0.509902i	$-0.829682\pi$
$491$	2.71482	−	15.3965i	0.122518	−	0.694835i	0.982751	−	0.184934i	$-0.0592071\pi$
$492$	−1.00238	−	2.75402i	−0.0451909	−	0.124161i
$493$			5.73143i			0.258131i
$494$	20.1928	+	1.88538i	0.908519	+	0.0848274i
$495$		0			0
$496$	0.0765042	−	0.0278452i	0.00343514	−	0.00125029i
$497$	25.4652	+	4.49020i	1.14227	+	0.201413i
$498$	−0.755675	−	0.900578i	−0.0338626	−	0.0403559i
$499$	21.9217	+	18.3945i	0.981352	+	0.823452i	0.984293	−	0.176544i	$-0.0564917\pi$
$499$	21.9217	+	18.3945i	0.981352	+	0.823452i	−0.00294090	+	0.999996i	$0.500936\pi$
$500$		0			0
$501$	6.18732	+	10.7168i	0.276429	+	0.478789i
$502$	12.3356	+	7.12196i	0.550565	+	0.317869i
$503$	8.56607	−	23.5351i	0.381942	−	1.04938i	−0.588595	−	0.808428i	$-0.700319\pi$
$503$	8.56607	−	23.5351i	0.381942	−	1.04938i	0.970538	−	0.240950i	$-0.0774589\pi$
$504$	−13.6147	−	4.95534i	−0.606446	−	0.220728i
$505$		0			0
$506$	−2.63816	−	4.56942i	−0.117280	−	0.203135i
$507$	−7.85651	+	1.38532i	−0.348920	+	0.0615240i
$508$	0.0796494	−	0.0949225i	0.00353387	−	0.00421150i
$509$	−25.6787	+	21.5470i	−1.13819	+	0.955053i	−0.999378	−	0.0352655i	$-0.988772\pi$
$509$	−25.6787	+	21.5470i	−1.13819	+	0.955053i	−0.138810	+	0.990319i	$0.544328\pi$
$510$		0			0
$511$	−13.2763	+	4.83218i	−0.587309	+	0.213763i
$512$		−	0.473897i		−	0.0209435i
$513$	12.0495	−	5.53343i	0.531997	−	0.244307i
$514$	−13.5030			−0.595591
$515$		0			0
$516$	−0.544111	+	3.08580i	−0.0239531	+	0.135845i
$517$	1.57202	+	1.87346i	0.0691372	+	0.0823945i
$518$	0.889704	−	1.06031i	0.0390913	−	0.0465872i
$519$	−0.0828445	−	0.469834i	−0.00363647	−	0.0206234i
$520$		0			0
$521$	13.7392	−	23.7969i	0.601924	−	1.04256i	−0.390606	−	0.920558i	$-0.627734\pi$
$521$	13.7392	−	23.7969i	0.601924	−	1.04256i	0.992530	−	0.122005i	$-0.0389323\pi$
$522$	2.83380	−	7.78581i	0.124032	−	0.340776i
$523$	3.54244	−	9.73277i	0.154900	−	0.425584i	−0.837832	−	0.545928i	$-0.816177\pi$
$523$	3.54244	−	9.73277i	0.154900	−	0.425584i	0.992732	+	0.120343i	$0.0383995\pi$
$524$	1.86262	−	3.22615i	0.0813687	−	0.140935i
$525$		0			0
$526$	1.47255	+	8.35126i	0.0642064	+	0.364132i
$527$	−2.06472	+	2.46064i	−0.0899406	+	0.107187i
$528$	0.0488759	+	0.0582480i	0.00212705	+	0.00253492i
$529$	3.45677	−	19.6043i	0.150294	−	0.852361i
$530$		0			0
$531$	29.2303			1.26849
$532$	5.71578	+	8.26517i	0.247811	+	0.358340i
$533$		−	23.7570i		−	1.02903i
$534$	−1.00387	+	0.365379i	−0.0434417	+	0.0158115i
$535$		0			0
$536$	−30.8922	+	25.9216i	−1.33434	+	1.11964i
$537$	7.29125	−	8.68938i	0.314641	−	0.374974i
$538$	−15.8301	+	2.79127i	−0.682483	+	0.120340i
$539$	−5.91534	−	10.2457i	−0.254792	−	0.441313i
$540$		0			0
$541$	−2.37211	−	0.863378i	−0.101985	−	0.0371195i	0.290524	−	0.956868i	$-0.406170\pi$
$541$	−2.37211	−	0.863378i	−0.101985	−	0.0371195i	−0.392509	+	0.919748i	$0.628393\pi$
$542$	5.70378	−	15.6710i	0.244998	−	0.673128i
$543$	−7.41858	−	4.28312i	−0.318362	−	0.183806i
$544$	4.65910	+	8.06980i	0.199757	+	0.345990i
$545$		0			0
$546$	3.56418	+	2.99070i	0.152533	+	0.127990i
$547$	4.93339	+	5.87939i	0.210937	+	0.251384i	0.861131	−	0.508384i	$-0.169757\pi$
$547$	4.93339	+	5.87939i	0.210937	+	0.251384i	−0.650194	+	0.759768i	$0.725312\pi$
$548$	23.6050	+	4.16220i	1.00836	+	0.177800i
$549$	−11.2057	+	4.07855i	−0.478249	+	0.174068i
$550$		0			0
$551$	−12.4329	+	8.59797i	−0.529659	+	0.366286i
$552$		−	2.65539i		−	0.113021i
$553$	4.47584	+	12.2973i	0.190332	+	0.522933i
$554$	−2.10179	+	11.9198i	−0.0892963	+	0.506425i
$555$		0			0
$556$	−14.4684	−	12.1404i	−0.613596	−	0.514868i
$557$	−3.20631	+	0.565360i	−0.135856	+	0.0239551i	−0.241163	−	0.970485i	$-0.577529\pi$
$557$	−3.20631	+	0.565360i	−0.135856	+	0.0239551i	0.105307	+	0.994440i	$0.466418\pi$
$558$	4.02142	−	2.32177i	0.170240	−	0.0982882i
$559$	−12.6998	+	21.9967i	−0.537145	+	0.930362i
$560$		0			0
$561$	−2.81908	−	1.02606i	−0.119022	−	0.0433203i
$562$	−9.98503	−	5.76486i	−0.421193	−	0.243176i
$563$	−4.55449	+	2.62954i	−0.191949	+	0.110822i	−0.592895	−	0.805280i	$-0.702015\pi$
$563$	−4.55449	+	2.62954i	−0.191949	+	0.110822i	0.400946	+	0.916102i	$0.368682\pi$
$564$	0.0812519	+	0.460802i	0.00342132	+	0.0194033i
$565$		0			0
$566$	−11.7062	+	9.82267i	−0.492048	+	0.412878i
$567$	−12.0898	−	2.13176i	−0.507724	−	0.0895255i
$568$	13.3526	+	36.6860i	0.560264	+	1.53931i
$569$	29.9564			1.25584			0.627918	−	0.778280i	$-0.283907\pi$
$569$	29.9564			1.25584			0.627918	+	0.778280i	$0.283907\pi$
$570$		0			0
$571$	−16.7101			−0.699295			−0.349647	−	0.936881i	$-0.613699\pi$
$571$	−16.7101			−0.699295			−0.349647	+	0.936881i	$0.613699\pi$
$572$	−7.57272	−	20.8059i	−0.316631	−	0.869937i
$573$	−9.92917	−	1.75078i	−0.414797	−	0.0731399i
$574$	−5.68479	+	4.77011i	−0.237279	+	0.199100i
$575$		0			0
$576$	−2.37867	−	13.4901i	−0.0991113	−	0.562088i
$577$	−11.8473	+	6.84002i	−0.493208	+	0.284754i	−0.725904	−	0.687796i	$-0.758579\pi$
$577$	−11.8473	+	6.84002i	−0.493208	+	0.284754i	0.232696	+	0.972549i	$0.425245\pi$
$578$	−10.8665	−	6.27379i	−0.451987	−	0.260955i
$579$	6.45084	+	2.34791i	0.268088	+	0.0975759i
$580$		0			0
$581$	2.36097	−	4.08931i	0.0979494	−	0.169653i
$582$	−0.738700	+	0.426489i	−0.0306201	+	0.0176785i
$583$	−20.5142	+	3.61721i	−0.849612	+	0.149810i
$584$	−16.3405	−	13.7113i	−0.676174	−	0.567378i
$585$		0			0
$586$	2.38279	−	13.5135i	0.0984321	−	0.558236i
$587$	8.22108	+	22.5872i	0.339320	+	0.932275i	0.985588	+	0.169164i	$0.0541068\pi$
$587$	8.22108	+	22.5872i	0.339320	+	0.932275i	−0.646268	+	0.763111i	$0.723671\pi$
$588$		−	2.26352i		−	0.0933459i
$589$	−8.43511	−	0.787576i	−0.347563	−	0.0324515i
$590$		0			0
$591$	11.6001	−	4.22210i	0.477166	−	0.173674i
$592$	0.0345490	+	0.00609191i	0.00141995	+	0.000250376i
$593$	2.72621	+	3.24897i	0.111952	+	0.133419i	0.819110	−	0.573636i	$-0.194468\pi$
$593$	2.72621	+	3.24897i	0.111952	+	0.133419i	−0.707158	+	0.707055i	$0.750023\pi$
$594$	6.99067	+	5.86587i	0.286831	+	0.240679i
$595$		0			0
$596$	−2.31016	−	4.00131i	−0.0946276	−	0.163900i
$597$	−4.24935	−	2.45336i	−0.173914	−	0.100409i
$598$	2.79876	−	7.68954i	0.114450	−	0.314449i
$599$	−24.6894	−	8.98622i	−1.00878	−	0.367167i	−0.215818	−	0.976434i	$-0.569242\pi$
$599$	−24.6894	−	8.98622i	−1.00878	−	0.367167i	−0.792965	+	0.609267i	$0.791464\pi$
$600$		0			0
$601$	21.1197	+	36.5805i	0.861492	+	1.49215i	0.870489	+	0.492188i	$0.163803\pi$
$601$	21.1197	+	36.5805i	0.861492	+	1.49215i	−0.00899659	+	0.999960i	$0.502864\pi$
$602$	7.81353	−	1.37774i	0.318456	−	0.0561523i
$603$	−24.8198	+	29.5790i	−1.01074	+	1.20455i
$604$	−13.7160	+	11.5091i	−0.558096	+	0.468298i
$605$		0			0
$606$	3.48293	−	1.26768i	0.141484	−	0.0514960i
$607$		−	22.0969i		−	0.896885i	−0.893812	−	0.448443i	$-0.851979\pi$
$607$		−	22.0969i		−	0.896885i	0.893812	−	0.448443i	$-0.148021\pi$
$608$	−10.5161	+	22.2126i	−0.426483	+	0.900840i
$609$	−3.46791			−0.140527
$610$		0			0
$611$	−0.658633	+	3.73530i	−0.0266455	+	0.151114i
$612$	3.54050	+	4.21941i	0.143116	+	0.170559i
$613$	4.61332	−	5.49794i	0.186330	−	0.222060i	−0.664790	−	0.747030i	$-0.731479\pi$
$613$	4.61332	−	5.49794i	0.186330	−	0.222060i	0.851121	+	0.524970i	$0.175924\pi$
$614$	−3.28622	−	18.6371i	−0.132621	−	0.752131i
$615$		0			0
$616$	−9.09627	+	15.7552i	−0.366499	+	0.634795i
$617$	−16.8865	+	46.3953i	−0.679826	+	1.86781i	−0.235761	+	0.971811i	$0.575758\pi$
$617$	−16.8865	+	46.3953i	−0.679826	+	1.86781i	−0.444065	+	0.895995i	$0.646464\pi$
$618$	0.00232818	−	0.00639661i	9.36530e−5	−	0.000257310i
$619$	13.2490	−	22.9479i	0.532521	−	0.922354i	−0.466758	−	0.884385i	$-0.654578\pi$
$619$	13.2490	−	22.9479i	0.532521	−	0.922354i	0.999279	−	0.0379684i	$-0.0120886\pi$
$620$		0			0
$621$	−0.929015	−	5.26871i	−0.0372801	−	0.211426i
$622$	−8.19356	+	9.76470i	−0.328532	+	0.391529i
$623$	−2.75811	−	3.28699i	−0.110501	−	0.131690i
$624$	−0.0204777	+	0.116135i	−0.000819764	+	0.00464911i
$625$		0			0
$626$	17.1643			0.686022
$627$	−2.00324	−	7.65451i	−0.0800019	−	0.305692i
$628$		−	12.7264i		−	0.507838i
$629$	−1.30066	+	0.473401i	−0.0518607	+	0.0188757i
$630$		0			0
$631$	25.5253	−	21.4183i	1.01615	−	0.852647i	0.0270071	−	0.999635i	$-0.491402\pi$
$631$	25.5253	−	21.4183i	1.01615	−	0.852647i	0.989138	+	0.146988i	$0.0469579\pi$
$632$	−12.7002	+	15.1355i	−0.505185	+	0.602057i
$633$	7.66285	−	1.35117i	0.304571	−	0.0537041i
$634$	12.4641	+	21.5884i	0.495013	+	0.857387i
$635$		0			0
$636$	−3.74510	−	1.36310i	−0.148503	−	0.0540506i
$637$	6.27546	−	17.2417i	0.248643	−	0.683141i
$638$	−9.00990	−	5.20187i	−0.356705	−	0.205944i
$639$	18.6905	+	32.3729i	0.739384	+	1.28065i
$640$		0			0
$641$	−0.104256	−	0.0874810i	−0.00411786	−	0.00345529i	0.640726	−	0.767769i	$-0.278633\pi$
$641$	−0.104256	−	0.0874810i	−0.00411786	−	0.00345529i	−0.644844	+	0.764314i	$0.723078\pi$
$642$	−1.06904	−	1.27403i	−0.0421917	−	0.0502821i
$643$	−47.4461	−	8.36602i	−1.87109	−	0.329924i	−0.881311	−	0.472536i	$-0.843339\pi$
$643$	−47.4461	−	8.36602i	−1.87109	−	0.329924i	−0.989779	+	0.142613i	$0.954450\pi$
$644$	3.81016	−	1.38678i	0.150141	−	0.0546469i
$645$		0			0
$646$	0.515319	+	6.31407i	0.0202750	+	0.248424i
$647$		−	36.9718i		−	1.45351i	−0.686895	−	0.726756i	$-0.741027\pi$
$647$		−	36.9718i		−	1.45351i	0.686895	−	0.726756i	$-0.258973\pi$
$648$	−6.33927	−	17.4170i	−0.249030	−	0.684204i
$649$	6.37346	−	36.1457i	0.250180	−	1.41884i
$650$		0			0
$651$	−1.48886	−	1.24930i	−0.0583529	−	0.0489639i
$652$	−2.44302	+	0.430770i	−0.0956759	+	0.0168702i
$653$	−23.3827	+	13.5000i	−0.915035	+	0.528296i	−0.882048	−	0.471160i	$-0.843835\pi$
$653$	−23.3827	+	13.5000i	−0.915035	+	0.528296i	−0.0329874	+	0.999456i	$0.510502\pi$
$654$	1.72416	−	2.98632i	0.0674198	−	0.116775i
$655$		0			0
$656$	−0.176747	−	0.0643307i	−0.00690081	−	0.00251169i
$657$	−17.6879	−	10.2121i	−0.690072	−	0.398413i
$658$	1.02606	−	0.592396i	0.0400000	−	0.0230940i
$659$	−3.27760	−	18.5882i	−0.127677	−	0.724093i	−0.979682	−	0.200559i	$-0.935724\pi$
$659$	−3.27760	−	18.5882i	−0.127677	−	0.724093i	0.852005	−	0.523534i	$-0.175387\pi$
$660$		0			0
$661$	−23.4500	+	19.6769i	−0.912098	+	0.765341i	−0.972517	−	0.232832i	$-0.925201\pi$
$661$	−23.4500	+	19.6769i	−0.912098	+	0.765341i	0.0604192	+	0.998173i	$0.480756\pi$
$662$	−1.48097	−	0.261135i	−0.0575594	−	0.0101493i
$663$	−1.59132	−	4.37211i	−0.0618017	−	0.169799i
$664$	7.12918			0.276666
$665$		0			0
$666$	2.00093			0.0775346
$667$	2.08607	+	5.73143i	0.0807729	+	0.221922i
$668$	−28.0952	−	4.95394i	−1.08703	−	0.191674i
$669$	1.22874	−	1.03104i	0.0475059	−	0.0398622i
$670$		0			0
$671$	2.60014	+	14.7461i	0.100377	+	0.569267i
$672$	−4.88279	+	2.81908i	−0.188358	+	0.108748i
$673$	10.3139	+	5.95471i	0.397570	+	0.229537i	0.685435	−	0.728134i	$-0.259612\pi$
$673$	10.3139	+	5.95471i	0.397570	+	0.229537i	−0.287865	+	0.957671i	$0.592945\pi$
$674$	21.0214	+	7.65117i	0.809715	+	0.294712i
$675$		0			0
$676$	9.19594	−	15.9278i	0.353690	−	0.612609i
$677$	5.00654	−	2.89053i	0.192417	−	0.111092i	−0.400696	−	0.916211i	$-0.631232\pi$
$677$	5.00654	−	2.89053i	0.192417	−	0.111092i	0.593114	+	0.805119i	$0.297898\pi$
$678$	3.39949	−	0.599422i	0.130557	−	0.0230207i
$679$	−2.62449	−	2.20220i	−0.100718	−	0.0845129i
$680$		0			0
$681$	−1.26786	+	7.19037i	−0.0485843	+	0.275535i
$682$	−1.99421	−	5.47906i	−0.0763624	−	0.209804i
$683$		−	21.0496i		−	0.805442i	−0.915323	−	0.402721i	$-0.868065\pi$
$683$		−	21.0496i		−	0.805442i	0.915323	−	0.402721i	$-0.131935\pi$
$684$	−3.84167	+	14.0099i	−0.146890	+	0.535684i
$685$		0			0
$686$	−16.2570	+	5.91707i	−0.620696	+	0.225915i
$687$	4.93307	+	0.869833i	0.188208	+	0.0331862i
$688$	0.129261	+	0.154048i	0.00492805	+	0.00587302i
$689$	−24.7481	−	20.7661i	−0.942827	−	0.791126i
$690$		0			0
$691$	16.4688	+	28.5249i	0.626504	+	1.08514i	0.988248	+	0.152860i	$0.0488483\pi$
$691$	16.4688	+	28.5249i	0.626504	+	1.08514i	−0.361744	+	0.932278i	$0.617818\pi$
$692$	0.952515	+	0.549935i	0.0362092	+	0.0209054i
$693$	−5.95772	+	16.3687i	−0.226315	+	0.621796i
$694$	6.36484	+	2.31661i	0.241606	+	0.0879374i
$695$		0			0
$696$	−2.61793	−	4.53438i	−0.0992322	−	0.171875i
$697$	7.30823	−	1.28864i	0.276819	−	0.0488106i
$698$	12.8636	−	15.3302i	0.486894	−	0.580257i
$699$	9.85819	−	8.27201i	0.372871	−	0.312876i
$700$		0			0
$701$	−20.0694	+	7.30466i	−0.758010	+	0.275893i	−0.691973	−	0.721924i	$-0.743258\pi$
$701$	−20.0694	+	7.30466i	−0.758010	+	0.275893i	−0.0660380	+	0.997817i	$0.521036\pi$
$702$			14.1530i			0.534171i
$703$	−2.97810	−	2.11128i	−0.112321	−	0.0796285i
$704$	−17.2003			−0.648260
$705$		0			0
$706$	−1.74779	+	9.91220i	−0.0657789	+	0.373051i
$707$	9.56926	+	11.4042i	0.359889	+	0.428899i
$708$	4.51384	−	5.37939i	0.169641	−	0.202170i
$709$	2.73854	+	15.5310i	0.102848	+	0.583280i	0.992058	+	0.125781i	$0.0401437\pi$
$709$	2.73854	+	15.5310i	0.102848	+	0.583280i	−0.889210	+	0.457499i	$0.848745\pi$
$710$		0			0
$711$	−9.45904	+	16.3835i	−0.354742	+	0.614431i
$712$	2.21572	−	6.08765i	0.0830377	−	0.228144i
$713$	−1.16912	+	3.21213i	−0.0437839	+	0.120295i
$714$	−0.726682	+	1.25865i	−0.0271954	+	0.0471038i
$715$		0			0
$716$	4.54101	+	25.7534i	0.169706	+	0.962448i
$717$	7.97794	−	9.50774i	0.297942	−	0.355073i
$718$	−5.86971	−	6.99525i	−0.219056	−	0.261060i
$719$	6.13470	−	34.7916i	0.228786	−	1.29751i	−0.626529	−	0.779398i	$-0.715525\pi$
$719$	6.13470	−	34.7916i	0.228786	−	1.29751i	0.855314	−	0.518109i	$-0.173364\pi$
$720$		0			0
$721$	0.0273411			0.00101824
$722$	−12.9237	+	10.5899i	−0.480971	+	0.394114i
$723$		−	0.158385i		−	0.00589040i
$724$	18.5577	−	6.75444i	0.689691	−	0.251027i
$725$		0			0
$726$	0.228741	−	0.191936i	0.00848937	−	0.00712343i
$727$	−25.9825	+	30.9647i	−0.963637	+	1.14842i	0.0252396	+	0.999681i	$0.491965\pi$
$727$	−25.9825	+	30.9647i	−0.963637	+	1.14842i	−0.988877	+	0.148737i	$0.952479\pi$
$728$	−27.7862	+	4.89945i	−1.02982	+	0.181586i
$729$	−6.44562	−	11.1641i	−0.238727	−	0.413487i
$730$		0			0
$731$	−7.45558	−	2.71361i	−0.275755	−	0.100367i
$732$	−0.979832	+	2.69207i	−0.0362156	+	0.0995016i
$733$	−31.4162	−	18.1382i	−1.16038	−	0.669948i	−0.208988	−	0.977918i	$-0.567017\pi$
$733$	−31.4162	−	18.1382i	−1.16038	−	0.669948i	−0.951396	+	0.307970i	$0.900350\pi$
$734$	−14.3045	−	24.7762i	−0.527990	−	0.914505i
$735$		0			0
$736$	7.59627	+	6.37402i	0.280002	+	0.234950i
$737$	31.1651	+	37.1411i	1.14798	+	1.36811i
$738$	−10.5649	−	1.86288i	−0.388901	−	0.0685737i
$739$	−19.4290	+	7.07158i	−0.714708	+	0.260132i	−0.673677	−	0.739026i	$-0.735286\pi$
$739$	−19.4290	+	7.07158i	−0.714708	+	0.260132i	−0.0410304	+	0.999158i	$0.513064\pi$
$740$		0			0
$741$	7.09698	−	10.0108i	0.260714	−	0.367754i
$742$			10.0915i			0.370471i
$743$	2.29293	+	6.29978i	0.0841196	+	0.231117i	0.974620	−	0.223866i	$-0.0718678\pi$
$743$	2.29293	+	6.29978i	0.0841196	+	0.231117i	−0.890500	+	0.454982i	$0.849646\pi$
$744$	0.509552	−	2.88981i	0.0186811	−	0.105946i
$745$		0			0
$746$	20.5367	+	17.2323i	0.751901	+	0.630920i
$747$	6.72243	−	1.18535i	0.245961	−	0.0433695i
$748$	5.98962	−	3.45811i	0.219002	−	0.126441i
$749$	3.34002	−	5.78509i	0.122042	−	0.211383i
$750$		0			0
$751$	−10.0617	−	3.66214i	−0.367155	−	0.133633i	0.151853	−	0.988403i	$-0.451476\pi$
$751$	−10.0617	−	3.66214i	−0.367155	−	0.133633i	−0.519007	+	0.854770i	$0.673698\pi$
$752$	0.0260063	+	0.0150147i	0.000948352	+	0.000547531i
$753$	7.46389	−	4.30928i	0.271999	−	0.157039i
$754$	−2.80184	−	15.8900i	−0.102037	−	0.578681i
$755$		0			0
$756$	−5.37211	+	4.50774i	−0.195382	+	0.163945i
$757$	−4.00071	−	0.705432i	−0.145408	−	0.0256394i	0.100470	−	0.994940i	$-0.467965\pi$
$757$	−4.00071	−	0.705432i	−0.145408	−	0.0256394i	−0.245878	+	0.969301i	$0.579076\pi$
$758$	5.37164	+	14.7585i	0.195107	+	0.536052i
$759$	−3.19253			−0.115882
$760$		0			0
$761$	−11.0077			−0.399030			−0.199515	−	0.979895i	$-0.563937\pi$
$761$	−11.0077			−0.399030			−0.199515	+	0.979895i	$0.563937\pi$
$762$	0.0161658	+	0.0444153i	0.000585627	+	0.00160900i
$763$	13.6399	+	2.40508i	0.493797	+	0.0870697i
$764$	17.8059	−	14.9409i	0.644194	−	0.540543i
$765$		0			0
$766$	−3.58182	−	20.3135i	−0.129417	−	0.733958i
$767$	49.2969	−	28.4616i	1.78001	−	1.02769i
$768$	−7.41939	−	4.28359i	−0.267724	−	0.154571i
$769$	20.0599	+	7.30121i	0.723378	+	0.263288i	0.677359	−	0.735652i	$-0.263124\pi$
$769$	20.0599	+	7.30121i	0.723378	+	0.263288i	0.0460191	+	0.998941i	$0.485346\pi$
$770$		0			0
$771$	−4.08512	+	7.07564i	−0.147122	+	0.254823i
$772$	−13.7059	+	7.91312i	−0.493287	+	0.284800i
$773$	17.6450	−	3.11128i	0.634645	−	0.111905i	0.152936	−	0.988236i	$-0.451127\pi$
$773$	17.6450	−	3.11128i	0.634645	−	0.111905i	0.481709	+	0.876331i	$0.340016\pi$
$774$	8.78627	+	7.37256i	0.315816	+	0.265001i
$775$		0			0
$776$	0.898214	−	5.09403i	0.0322440	−	0.182865i
$777$	−0.286441	−	0.786989i	−0.0102760	−	0.0282331i
$778$		−	3.43788i		−	0.123254i
$779$	13.7588	+	13.9202i	0.492959	+	0.498743i
$780$		0			0
$781$	44.1070	−	16.0536i	1.57827	−	0.574444i
$782$	2.51730	+	0.443868i	0.0900184	+	0.0158727i
$783$	−6.78077	−	8.08100i	−0.242325	−	0.288792i
$784$	−0.111281	−	0.0933762i	−0.00397434	−	0.00333486i
$785$		0			0
$786$	0.710485	+	1.23060i	0.0253422	+	0.0438939i
$787$	−42.2894	−	24.4158i	−1.50746	−	0.870330i	−0.999962	−	0.00867371i	$-0.997239\pi$
$787$	−42.2894	−	24.4158i	−1.50746	−	0.870330i	−0.507493	−	0.861656i	$-0.669428\pi$
$788$	−9.73367	+	26.7430i	−0.346748	+	0.952681i
$789$	4.82160	+	1.75492i	0.171654	+	0.0624768i
$790$		0			0
$791$	6.93242	+	12.0073i	0.246488	+	0.426930i
$792$	−25.9000	+	4.56687i	−0.920316	+	0.162277i
$793$	−14.9272	+	17.7895i	−0.530080	+	0.631724i
$794$	−6.03524	+	5.06417i	−0.214183	+	0.179721i
$795$		0			0
$796$	10.6298	−	3.86893i	0.376763	−	0.137131i
$797$		−	28.5262i		−	1.01045i	−0.862988	−	0.505225i	$-0.831409\pi$
$797$		−	28.5262i		−	1.01045i	0.862988	−	0.505225i	$-0.168591\pi$
$798$	−3.82045	+	0.311804i	−0.135242	+	0.0110377i
$799$	−1.18479			−0.0419149
$800$		0			0
$801$	1.07713	−	6.10873i	0.0380586	−	0.215841i
$802$	−1.14597	−	1.36571i	−0.0404656	−	0.0482251i
$803$	−16.4849	+	19.6459i	−0.581738	+	0.693289i
$804$	1.61081	+	9.13538i	0.0568091	+	0.322180i
$805$		0			0
$806$	4.52141	−	7.83131i	0.159260	−	0.275846i
$807$	−3.32651	+	9.13950i	−0.117099	+	0.321726i
$808$	−7.68745	+	21.1211i	−0.270443	+	0.743037i
$809$	−7.41834	+	12.8489i	−0.260815	+	0.451745i	−0.966459	−	0.256822i	$-0.917325\pi$
$809$	−7.41834	+	12.8489i	−0.260815	+	0.451745i	0.705644	+	0.708567i	$0.250658\pi$
$810$		0			0
$811$	−1.45471	−	8.25006i	−0.0510817	−	0.289699i	0.948556	−	0.316609i	$-0.102544\pi$
$811$	−1.45471	−	8.25006i	−0.0510817	−	0.289699i	−0.999638	+	0.0269103i	$0.991433\pi$
$812$	5.13905	−	6.12449i	0.180345	−	0.214927i
$813$	−6.48610	−	7.72984i	−0.227478	−	0.271097i
$814$	0.436289	−	2.47432i	0.0152919	−	0.0867248i
$815$		0			0
$816$	−0.0368366			−0.00128954
$817$	−5.29796	−	20.2438i	−0.185352	−	0.708241i
$818$			28.3233i			0.990299i
$819$	−25.3862	+	9.23984i	−0.887067	+	0.322866i
$820$		0			0
$821$	4.80999	−	4.03606i	0.167870	−	0.140860i	−0.554983	−	0.831862i	$-0.687275\pi$
$821$	4.80999	−	4.03606i	0.167870	−	0.140860i	0.722852	+	0.691002i	$0.242831\pi$
$822$	−5.87695	+	7.00387i	−0.204982	+	0.244288i
$823$	10.8589	−	1.91472i	0.378517	−	0.0667428i	0.0188472	−	0.999822i	$-0.494000\pi$
$823$	10.8589	−	1.91472i	0.378517	−	0.0667428i	0.359670	+	0.933080i	$0.382889\pi$
$824$	0.0206398	+	0.0357492i	0.000719023	+	0.00124538i
$825$		0			0
$826$	−16.7087	−	6.08148i	−0.581371	−	0.211602i
$827$	11.6067	−	31.8892i	0.403606	−	1.10890i	−0.556886	−	0.830589i	$-0.688004\pi$
$827$	11.6067	−	31.8892i	0.403606	−	1.10890i	0.960492	−	0.278309i	$-0.0897738\pi$
$828$	5.07624	+	2.93077i	0.176412	+	0.101851i
$829$	−10.1834	−	17.6382i	−0.353686	−	0.612602i	0.633206	−	0.773983i	$-0.281738\pi$
$829$	−10.1834	−	17.6382i	−0.353686	−	0.612602i	−0.986892	+	0.161381i	$0.948405\pi$
$830$		0			0
$831$	5.61019	+	4.70750i	0.194615	+	0.163302i
$832$	−17.1470	−	20.4349i	−0.594464	−	0.708454i
$833$	5.64436	+	0.995252i	0.195565	+	0.0344834i
$834$	6.76991	−	2.46405i	0.234423	−	0.0853230i
$835$		0			0
$836$	16.4868	+	7.80531i	0.570208	+	0.269952i
$837$		−	5.91210i		−	0.204352i
$838$	−6.99281	−	19.2126i	−0.241563	−	0.663688i
$839$	−2.74526	+	15.5692i	−0.0947770	+	0.537507i	0.900038	+	0.435810i	$0.143538\pi$
$839$	−2.74526	+	15.5692i	−0.0947770	+	0.537507i	−0.994815	+	0.101697i	$0.967573\pi$
$840$		0			0
$841$	−13.0025	−	10.9104i	−0.448363	−	0.376221i
$842$	−5.58878	+	0.985452i	−0.192602	+	0.0339609i
$843$	−6.04164	+	3.48814i	−0.208085	+	0.120138i
$844$	−8.96926	+	15.5352i	−0.308734	+	0.534744i
$845$		0			0
$846$	1.60947	+	0.585799i	0.0553347	+	0.0201402i
$847$	1.03866	+	0.599670i	0.0356888	+	0.0206049i
$848$	−0.221510	+	0.127889i	−0.00760668	+	0.00439172i
$849$	1.60560	+	9.10581i	0.0551040	+	0.312511i
$850$		0			0
$851$	−1.12836	+	0.946803i	−0.0386795	+	0.0324560i
$852$	8.84397	+	1.55943i	0.302989	+	0.0534252i
$853$	−18.0071	−	49.4741i	−0.616551	−	1.69396i	−0.715274	−	0.698845i	$-0.753698\pi$
$853$	−18.0071	−	49.4741i	−0.616551	−	1.69396i	0.0987227	−	0.995115i	$-0.468524\pi$
$854$	7.25402			0.248228
$855$		0			0
$856$	10.0855			0.344716
$857$	7.87581	+	21.6386i	0.269033	+	0.739161i	0.998480	+	0.0551238i	$0.0175553\pi$
$857$	7.87581	+	21.6386i	0.269033	+	0.739161i	−0.729447	+	0.684038i	$0.760222\pi$
$858$	8.31731	+	1.46657i	0.283948	+	0.0500678i
$859$	−6.82501	+	5.72686i	−0.232866	+	0.195398i	−0.751753	−	0.659445i	$-0.770791\pi$
$859$	−6.82501	+	5.72686i	−0.232866	+	0.195398i	0.518886	+	0.854843i	$0.326347\pi$
$860$		0			0
$861$	0.779715	+	4.42198i	0.0265726	+	0.150701i
$862$	−10.6599	+	6.15451i	−0.363079	+	0.209624i
$863$	25.7814	+	14.8849i	0.877609	+	0.506688i	0.869869	−	0.493282i	$-0.164203\pi$
$863$	25.7814	+	14.8849i	0.877609	+	0.506688i	0.00773998	+	0.999970i	$0.497536\pi$
$864$	−16.1163	−	5.86587i	−0.548289	−	0.199561i
$865$		0			0
$866$	12.6160	−	21.8516i	0.428710	−	0.742548i
$867$	−6.57499	+	3.79607i	−0.223298	+	0.128921i
$868$	4.41263	−	0.778066i	0.149775	−	0.0264093i
$869$	18.1971	+	15.2692i	0.617295	+	0.517972i
$870$		0			0
$871$	−13.0574	+	74.0520i	−0.442432	+	2.50916i
$872$	7.15204	+	19.6501i	0.242199	+	0.665435i
$873$		−	4.95273i		−	0.167625i
$874$	2.81345	+	6.12651i	0.0951665	+	0.207232i
$875$		0			0
$876$	−4.61081	+	1.67820i	−0.155785	+	0.0567011i
$877$	−24.6498	−	4.34642i	−0.832363	−	0.146768i	−0.258802	−	0.965930i	$-0.583328\pi$
$877$	−24.6498	−	4.34642i	−0.832363	−	0.146768i	−0.573562	+	0.819162i	$0.694439\pi$
$878$	7.54181	+	8.98798i	0.254524	+	0.303330i
$879$	−6.36025	−	5.33688i	−0.214526	−	0.180009i
$880$		0			0
$881$	−10.1980	−	17.6634i	−0.343579	−	0.595097i	0.641515	−	0.767110i	$-0.278306\pi$
$881$	−10.1980	−	17.6634i	−0.343579	−	0.595097i	−0.985095	+	0.172014i	$0.944973\pi$
$882$	−7.17544	−	4.14274i	−0.241610	−	0.139493i
$883$	3.63501	−	9.98710i	0.122328	−	0.336093i	−0.863381	−	0.504553i	$-0.831657\pi$
$883$	3.63501	−	9.98710i	0.122328	−	0.336093i	0.985708	+	0.168460i	$0.0538795\pi$
$884$	10.0795	+	3.66864i	0.339010	+	0.123390i
$885$		0			0
$886$	−14.8981	−	25.8043i	−0.500512	−	0.866912i
$887$	55.4828	−	9.78312i	1.86293	−	0.328485i	0.875091	−	0.483959i	$-0.160802\pi$
$887$	55.4828	−	9.78312i	1.86293	−	0.328485i	0.987840	+	0.155474i	$0.0496904\pi$
$888$	0.812774	−	0.968626i	0.0272749	−	0.0325050i
$889$	−0.145430	+	0.122030i	−0.00487756	+	0.00409275i
$890$		0			0
$891$	−20.9402	+	7.62159i	−0.701522	+	0.255333i
$892$			3.69789i			0.123815i
$893$	−1.77736	−	2.57011i	−0.0594771	−	0.0860054i
$894$	1.76239			0.0589432
$895$		0			0
$896$	2.23308	−	12.6644i	0.0746019	−	0.423088i
$897$	−3.18264	−	3.79292i	−0.106265	−	0.126642i
$898$	10.6496	−	12.6917i	0.355381	−	0.423526i
$899$	1.17041	+	6.63771i	0.0390353	+	0.221380i
$900$		0			0
$901$	5.04576	−	8.73951i	0.168099	−	0.291155i
$902$	−4.60722	+	12.6582i	−0.153404	+	0.421473i
$903$	1.64192	−	4.51114i	0.0546398	−	0.150121i
$904$	−10.4666	+	18.1286i	−0.348113	+	0.602949i
$905$		0			0
$906$	−1.18597	−	6.72600i	−0.0394014	−	0.223456i
$907$	3.80764	−	4.53777i	0.126431	−	0.150674i	−0.699116	−	0.715009i	$-0.746423\pi$
$907$	3.80764	−	4.53777i	0.126431	−	0.150674i	0.825546	+	0.564334i	$0.190867\pi$
$908$	−10.8197	−	12.8944i	−0.359064	−	0.427916i
$909$	−3.73711	+	21.1942i	−0.123952	+	0.702968i
$910$		0			0
$911$	−34.0591			−1.12843			−0.564215	−	0.825628i	$-0.690821\pi$
$911$	−34.0591			−1.12843			−0.564215	+	0.825628i	$0.690821\pi$
$912$	−0.0552603	−	0.0799077i	−0.00182985	−	0.00264601i
$913$		−	8.57129i		−	0.283668i
$914$	11.7995	−	4.29466i	0.390292	−	0.142055i
$915$		0			0
$916$	−8.84642	+	7.42303i	−0.292294	+	0.245264i
$917$	−3.66864	+	4.37211i	−0.121149	+	0.144380i
$918$	−4.35381	+	0.767693i	−0.143697	+	0.0253377i
$919$	−3.13697	−	5.43340i	−0.103479	−	0.179231i	0.809637	−	0.586931i	$-0.199664\pi$
$919$	−3.13697	−	5.43340i	−0.103479	−	0.179231i	−0.913116	+	0.407700i	$0.866331\pi$
$920$		0			0
$921$	−10.7601	−	3.91636i	−0.354558	−	0.129048i
$922$	−4.18911	+	11.5095i	−0.137961	+	0.379045i
$923$	63.0429	+	36.3979i	2.07508	+	1.19805i
$924$	2.09240	+	3.62414i	0.0688348	+	0.119225i
$925$		0			0
$926$	−1.18757	−	0.996487i	−0.0390259	−	0.0327466i
$927$	0.0254062	+	0.0302779i	0.000834448	+	0.000994456i
$928$	19.2556	+	3.39528i	0.632095	+	0.111455i
$929$	26.6152	−	9.68712i	0.873215	−	0.317824i	0.133747	−	0.991016i	$-0.457299\pi$
$929$	26.6152	−	9.68712i	0.873215	−	0.317824i	0.739468	+	0.673191i	$0.235077\pi$
$930$		0			0
$931$	6.30840	+	13.7370i	0.206749	+	0.450213i
$932$			29.6682i			0.971814i
$933$	2.63792	+	7.24763i	0.0863616	+	0.237277i
$934$	−3.36588	+	19.0888i	−0.110135	+	0.624606i
$935$		0			0
$936$	−31.2454	−	26.2180i	−1.02129	−	0.856962i
$937$	19.7670	−	3.48545i	0.645759	−	0.113865i	0.158830	−	0.987306i	$-0.449228\pi$
$937$	19.7670	−	3.48545i	0.645759	−	0.113865i	0.486930	+	0.873441i	$0.338117\pi$
$938$	20.3416	−	11.7442i	0.664176	−	0.383462i
$939$	5.19278	−	8.99416i	0.169460	−	0.293513i
$940$		0			0
$941$	−5.06980	−	1.84526i	−0.165271	−	0.0601537i	0.258060	−	0.966129i	$-0.416917\pi$
$941$	−5.06980	−	1.84526i	−0.165271	−	0.0601537i	−0.423331	+	0.905975i	$0.639139\pi$
$942$	4.20404	+	2.42720i	0.136975	+	0.0790826i
$943$	6.83920	−	3.94862i	0.222715	−	0.128585i
$944$	−0.0782589	−	0.443828i	−0.00254711	−	0.0144454i
$945$		0			0
$946$	11.0326	−	9.25741i	0.358699	−	0.300984i
$947$	6.54228	+	1.15358i	0.212596	+	0.0374863i	0.278931	−	0.960311i	$-0.410020\pi$
$947$	6.54228	+	1.15358i	0.212596	+	0.0374863i	−0.0663359	+	0.997797i	$0.521131\pi$
$948$	1.55444	+	4.27079i	0.0504859	+	0.138709i
$949$	−39.7743			−1.29113
$950$		0			0
$951$	15.0833			0.489109
$952$	−3.01438	−	8.28194i	−0.0976966	−	0.268419i
$953$	14.5987	+	2.57414i	0.472897	+	0.0833846i	0.405018	−	0.914309i	$-0.367265\pi$
$953$	14.5987	+	2.57414i	0.472897	+	0.0833846i	0.0678799	+	0.997693i	$0.478377\pi$
$954$	−11.1755	+	9.37732i	−0.361819	+	0.303602i
$955$		0			0
$956$	4.96868	+	28.1788i	0.160699	+	0.911368i
$957$	−5.45161	+	3.14749i	−0.176226	+	0.101744i
$958$	−19.3873	−	11.1932i	−0.626374	−	0.361637i
$959$	−34.5082	−	12.5600i	−1.11433	−	0.405582i
$960$		0			0
$961$	13.6113	−	23.5754i	0.439074	−	0.760498i
$962$	3.37457	−	1.94831i	0.108801	−	0.0628161i
$963$	9.51011	−	1.67689i	0.306459	−	0.0540370i
$964$	0.279715	+	0.234709i	0.00900901	+	0.00755946i
$965$		0			0
$966$	−0.268571	+	1.52314i	−0.00864112	+	0.0490062i
$967$	−7.25822	−	19.9418i	−0.233409	−	0.641285i	0.766591	−	0.642136i	$-0.221951\pi$
$967$	−7.25822	−	19.9418i	−0.233409	−	0.641285i	−1.00000		0.000850519i	$0.999729\pi$
$968$			1.81076i			0.0582002i
$969$	3.46451	+	1.64019i	0.111296	+	0.0526906i
$970$		0			0
$971$	35.3387	−	12.8622i	1.13407	−	0.412769i	0.294304	−	0.955712i	$-0.404912\pi$
$971$	35.3387	−	12.8622i	1.13407	−	0.412769i	0.839770	+	0.542943i	$0.182690\pi$
$972$	−15.2230	−	2.68422i	−0.488277	−	0.0860964i
$973$	18.6002	+	22.1668i	0.596295	+	0.710636i
$974$	15.1643	+	12.7244i	0.485896	+	0.407715i
$975$		0			0
$976$	0.0919294	+	0.159226i	0.00294259	+	0.00509671i
$977$	39.8558	+	23.0107i	1.27510	+	0.736179i	0.975943	−	0.218026i	$-0.0699617\pi$
$977$	39.8558	+	23.0107i	1.27510	+	0.736179i	0.299156	+	0.954204i	$0.403295\pi$
$978$	0.323637	−	0.889185i	0.0103488	−	0.0284330i
$979$	−7.31908	−	2.66393i	−0.233919	−	0.0851395i
$980$		0			0
$981$	10.0111	+	17.3398i	0.319631	+	0.553618i
$982$	−13.5395	+	2.38737i	−0.432062	+	0.0761842i
$983$	38.9506	−	46.4195i	1.24233	−	1.48055i	0.424150	−	0.905592i	$-0.360573\pi$
$983$	38.9506	−	46.4195i	1.24233	−	1.48055i	0.818181	−	0.574961i	$-0.194983\pi$
$984$	−5.19325	+	4.35765i	−0.165555	+	0.138917i
$985$		0			0
$986$	4.73618	−	1.72383i	0.150831	−	0.0548979i
$987$		−	0.716881i		−	0.0228186i
$988$	7.16252	+	27.3684i	0.227870	+	0.870705i
$989$	−8.44326			−0.268480
$990$		0			0
$991$	7.27554	−	41.2616i	0.231115	−	1.31072i	−0.619528	−	0.784975i	$-0.712676\pi$
$991$	7.27554	−	41.2616i	0.231115	−	1.31072i	0.850643	−	0.525744i	$-0.176213\pi$
$992$	7.04374	+	8.39440i	0.223639	+	0.266522i
$993$	−0.584880	+	0.697033i	−0.0185606	+	0.0221197i
$994$	−3.94862	−	22.3937i	−0.125242	−	0.710285i
$995$		0			0
$996$	0.819955	−	1.42020i	0.0259813	−	0.0450009i
$997$	11.5313	−	31.6819i	0.365198	−	1.00337i	−0.611965	−	0.790885i	$-0.709621\pi$
$997$	11.5313	−	31.6819i	0.365198	−	1.00337i	0.977163	−	0.212490i	$-0.0681571\pi$
$998$	8.60700	−	23.6475i	0.272450	−	0.748550i
$999$	1.27379	−	2.20626i	0.0403008	−	0.0698030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.u.a.24.1		12
5.2	odd	4		475.2.l.a.176.1		6
5.3	odd	4		19.2.e.a.5.1	yes	6
5.4	even	2	inner	475.2.u.a.24.2		12
15.8	even	4		171.2.u.c.100.1		6
19.4	even	9	inner	475.2.u.a.99.2		12
20.3	even	4		304.2.u.b.81.1		6
35.3	even	12		931.2.x.b.765.1		6
35.13	even	4		931.2.w.a.442.1		6
35.18	odd	12		931.2.x.a.765.1		6
35.23	odd	12		931.2.v.b.214.1		6
35.33	even	12		931.2.v.a.214.1		6
95.2	even	36		9025.2.a.x.1.3		3
95.3	even	36		361.2.c.h.292.3		6
95.4	even	18	inner	475.2.u.a.99.1		12
95.8	even	12		361.2.e.b.54.1		6
95.13	even	36		361.2.e.a.28.1		6
95.17	odd	36		9025.2.a.bd.1.1		3
95.18	even	4		361.2.e.h.62.1		6
95.23	odd	36		19.2.e.a.4.1	✓	6
95.28	odd	36		361.2.e.f.234.1		6
95.33	even	36		361.2.c.h.68.3		6
95.42	odd	36		475.2.l.a.251.1		6
95.43	odd	36		361.2.c.i.68.1		6
95.48	even	36		361.2.e.b.234.1		6
95.53	even	36		361.2.e.h.99.1		6
95.63	odd	36		361.2.e.g.28.1		6
95.68	odd	12		361.2.e.f.54.1		6
95.73	odd	36		361.2.c.i.292.1		6
95.78	even	36		361.2.a.h.1.1		3
95.83	odd	12		361.2.e.g.245.1		6
95.88	even	12		361.2.e.a.245.1		6
95.93	odd	36		361.2.a.g.1.3		3
285.23	even	36		171.2.u.c.118.1		6
285.173	odd	36		3249.2.a.s.1.3		3
285.188	even	36		3249.2.a.z.1.1		3
380.23	even	36		304.2.u.b.289.1		6
380.283	even	36		5776.2.a.br.1.1		3
380.363	odd	36		5776.2.a.bi.1.3		3
665.23	odd	36		931.2.x.a.802.1		6
665.118	even	36		931.2.w.a.99.1		6
665.213	even	36		931.2.v.a.422.1		6
665.403	odd	36		931.2.v.b.422.1		6
665.593	even	36		931.2.x.b.802.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.4.1	✓	6	95.23	odd	36
19.2.e.a.5.1	yes	6	5.3	odd	4
171.2.u.c.100.1		6	15.8	even	4
171.2.u.c.118.1		6	285.23	even	36
304.2.u.b.81.1		6	20.3	even	4
304.2.u.b.289.1		6	380.23	even	36
361.2.a.g.1.3		3	95.93	odd	36
361.2.a.h.1.1		3	95.78	even	36
361.2.c.h.68.3		6	95.33	even	36
361.2.c.h.292.3		6	95.3	even	36
361.2.c.i.68.1		6	95.43	odd	36
361.2.c.i.292.1		6	95.73	odd	36
361.2.e.a.28.1		6	95.13	even	36
361.2.e.a.245.1		6	95.88	even	12
361.2.e.b.54.1		6	95.8	even	12
361.2.e.b.234.1		6	95.48	even	36
361.2.e.f.54.1		6	95.68	odd	12
361.2.e.f.234.1		6	95.28	odd	36
361.2.e.g.28.1		6	95.63	odd	36
361.2.e.g.245.1		6	95.83	odd	12
361.2.e.h.62.1		6	95.18	even	4
361.2.e.h.99.1		6	95.53	even	36
475.2.l.a.176.1		6	5.2	odd	4
475.2.l.a.251.1		6	95.42	odd	36
475.2.u.a.24.1		12	1.1	even	1	trivial
475.2.u.a.24.2		12	5.4	even	2	inner
475.2.u.a.99.1		12	95.4	even	18	inner
475.2.u.a.99.2		12	19.4	even	9	inner
931.2.v.a.214.1		6	35.33	even	12
931.2.v.a.422.1		6	665.213	even	36
931.2.v.b.214.1		6	35.23	odd	12
931.2.v.b.422.1		6	665.403	odd	36
931.2.w.a.99.1		6	665.118	even	36
931.2.w.a.442.1		6	35.13	even	4
931.2.x.a.765.1		6	35.18	odd	12
931.2.x.a.802.1		6	665.23	odd	36
931.2.x.b.765.1		6	35.3	even	12
931.2.x.b.802.1		6	665.593	even	36
3249.2.a.s.1.3		3	285.173	odd	36
3249.2.a.z.1.1		3	285.188	even	36
5776.2.a.bi.1.3		3	380.363	odd	36
5776.2.a.br.1.1		3	380.283	even	36
9025.2.a.x.1.3		3	95.2	even	36
9025.2.a.bd.1.1		3	95.17	odd	36

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.300767 - 0.826352i) q^{2} +(-0.524005 - 0.0923963i) q^{3} +(0.939693 - 0.788496i) q^{4} +(0.0812519 + 0.460802i) q^{6} +(-1.62760 + 0.939693i) q^{7} +(-2.45734 - 1.41875i) q^{8} +(-2.55303 - 0.929228i) q^{9} +O(q^{10})\)	\(q+(-0.300767 - 0.826352i) q^{2} +(-0.524005 - 0.0923963i) q^{3} +(0.939693 - 0.788496i) q^{4} +(0.0812519 + 0.460802i) q^{6} +(-1.62760 + 0.939693i) q^{7} +(-2.45734 - 1.41875i) q^{8} +(-2.55303 - 0.929228i) q^{9} +(-1.70574 + 2.95442i) q^{11} +(-0.565258 + 0.326352i) q^{12} +(-5.21048 + 0.918748i) q^{13} +(1.26604 + 1.06234i) q^{14} +(-0.00727396 + 0.0412527i) q^{16} +(-0.565258 - 1.55303i) q^{17} +2.38919i q^{18} +(2.52094 - 3.55596i) q^{19} +(0.939693 - 0.342020i) q^{21} +(2.95442 + 0.520945i) q^{22} +(-1.13052 - 1.34730i) q^{23} +(1.15657 + 0.970481i) q^{24} +(2.32635 + 4.02936i) q^{26} +(2.63435 + 1.52094i) q^{27} +(-0.788496 + 2.16637i) q^{28} +(-3.25877 - 1.18610i) q^{29} +(-0.971782 - 1.68317i) q^{31} +(-5.55250 + 0.979055i) q^{32} +(1.16679 - 1.39053i) q^{33} +(-1.11334 + 0.934204i) q^{34} +(-3.13176 + 1.13987i) q^{36} -0.837496i q^{37} +(-3.69669 - 1.01367i) q^{38} +2.81521 q^{39} +(-0.779715 + 4.42198i) q^{41} +(-0.565258 - 0.673648i) q^{42} +(3.08580 - 3.67752i) q^{43} +(0.726682 + 4.12122i) q^{44} +(-0.773318 + 1.33943i) q^{46} +(0.245188 - 0.673648i) q^{47} +(0.00762319 - 0.0209445i) q^{48} +(-1.73396 + 3.00330i) q^{49} +(0.152704 + 0.866025i) q^{51} +(-4.17182 + 4.97178i) q^{52} +(3.92490 + 4.67752i) q^{53} +(0.464508 - 2.63435i) q^{54} +5.33275 q^{56} +(-1.64955 + 1.63041i) q^{57} +3.04963i q^{58} +(-10.1099 + 3.67972i) q^{59} +(3.36231 - 2.82131i) q^{61} +(-1.09861 + 1.30928i) q^{62} +(5.02849 - 0.886659i) q^{63} +(2.52094 + 4.36640i) q^{64} +(-1.50000 - 0.545955i) q^{66} +(4.86084 - 13.3550i) q^{67} +(-1.75573 - 1.01367i) q^{68} +(0.467911 + 0.810446i) q^{69} +(-10.5398 - 8.84397i) q^{71} +(4.95534 + 5.90554i) q^{72} +(7.40333 + 1.30541i) q^{73} +(-0.692066 + 0.251892i) q^{74} +(-0.434945 - 5.32926i) q^{76} -6.41147i q^{77} +(-0.846723 - 2.32635i) q^{78} +(1.20914 - 6.85738i) q^{79} +(5.00387 + 4.19875i) q^{81} +(3.88863 - 0.685670i) q^{82} +(-2.17588 + 1.25624i) q^{83} +(0.613341 - 1.06234i) q^{84} +(-3.96703 - 1.44388i) q^{86} +(1.59802 + 0.922618i) q^{87} +(8.38316 - 4.84002i) q^{88} +(0.396459 + 2.24843i) q^{89} +(7.61721 - 6.39160i) q^{91} +(-2.12467 - 0.374638i) q^{92} +(0.353700 + 0.971782i) q^{93} -0.630415 q^{94} +3.00000 q^{96} +(0.623485 + 1.71301i) q^{97} +(3.00330 + 0.529563i) q^{98} +(7.10014 - 5.95772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^6 - 6 * q^9	\( 12 q + 6 q^{6} - 6 q^{9} + 6 q^{14} - 36 q^{16} + 24 q^{19} - 30 q^{24} + 30 q^{26} + 6 q^{29} + 18 q^{31} - 48 q^{36} + 48 q^{39} + 42 q^{41} - 18 q^{44} - 36 q^{46} - 30 q^{49} + 6 q^{51} - 60 q^{54} - 12 q^{56} - 24 q^{59} - 24 q^{61} + 24 q^{64} - 18 q^{66} + 24 q^{69} - 12 q^{71} - 30 q^{74} + 72 q^{76} + 78 q^{79} + 12 q^{81} - 6 q^{84} + 48 q^{86} + 24 q^{89} + 30 q^{91} - 36 q^{94} + 36 q^{96} - 18 q^{99}+O(q^{100}) \) 12 * q + 6 * q^6 - 6 * q^9 + 6 * q^14 - 36 * q^16 + 24 * q^19 - 30 * q^24 + 30 * q^26 + 6 * q^29 + 18 * q^31 - 48 * q^36 + 48 * q^39 + 42 * q^41 - 18 * q^44 - 36 * q^46 - 30 * q^49 + 6 * q^51 - 60 * q^54 - 12 * q^56 - 24 * q^59 - 24 * q^61 + 24 * q^64 - 18 * q^66 + 24 * q^69 - 12 * q^71 - 30 * q^74 + 72 * q^76 + 78 * q^79 + 12 * q^81 - 6 * q^84 + 48 * q^86 + 24 * q^89 + 30 * q^91 - 36 * q^94 + 36 * q^96 - 18 * q^99

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