LMFDB - Embedded newform 475.2.l.a.176.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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([0, 14]))

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

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 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:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			176.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	475.176
Dual form			475.2.l.a.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.826352 - 0.300767i) q^{2} +(-0.0923963 + 0.524005i) q^{3} +(-0.939693 + 0.788496i) q^{4} +(0.0812519 + 0.460802i) q^{6} +(-0.939693 - 1.62760i) q^{7} +(-1.41875 + 2.45734i) q^{8} +(2.55303 + 0.929228i) q^{9} +O(q^{10})$	\(q+(0.826352 - 0.300767i) q^{2} +(-0.0923963 + 0.524005i) q^{3} +(-0.939693 + 0.788496i) q^{4} +(0.0812519 + 0.460802i) q^{6} +(-0.939693 - 1.62760i) q^{7} +(-1.41875 + 2.45734i) q^{8} +(2.55303 + 0.929228i) q^{9} +(-1.70574 + 2.95442i) q^{11} +(-0.326352 - 0.565258i) q^{12} +(0.918748 + 5.21048i) q^{13} +(-1.26604 - 1.06234i) q^{14} +(-0.00727396 + 0.0412527i) q^{16} +(1.55303 - 0.565258i) q^{17} +2.38919 q^{18} +(-2.52094 + 3.55596i) q^{19} +(0.939693 - 0.342020i) q^{21} +(-0.520945 + 2.95442i) q^{22} +(-1.34730 + 1.13052i) q^{23} +(-1.15657 - 0.970481i) q^{24} +(2.32635 + 4.02936i) q^{26} +(-1.52094 + 2.63435i) q^{27} +(2.16637 + 0.788496i) q^{28} +(3.25877 + 1.18610i) q^{29} +(-0.971782 - 1.68317i) q^{31} +(-0.979055 - 5.55250i) q^{32} +(-1.39053 - 1.16679i) q^{33} +(1.11334 - 0.934204i) q^{34} +(-3.13176 + 1.13987i) q^{36} +0.837496 q^{37} +(-1.01367 + 3.69669i) q^{38} -2.81521 q^{39} +(-0.779715 + 4.42198i) q^{41} +(0.673648 - 0.565258i) q^{42} +(-3.67752 - 3.08580i) q^{43} +(-0.726682 - 4.12122i) q^{44} +(-0.773318 + 1.33943i) q^{46} +(0.673648 + 0.245188i) q^{47} +(-0.0209445 - 0.00762319i) q^{48} +(1.73396 - 3.00330i) q^{49} +(0.152704 + 0.866025i) q^{51} +(-4.97178 - 4.17182i) q^{52} +(4.67752 - 3.92490i) q^{53} +(-0.464508 + 2.63435i) q^{54} +5.33275 q^{56} +(-1.63041 - 1.64955i) q^{57} +3.04963 q^{58} +(10.1099 - 3.67972i) q^{59} +(3.36231 - 2.82131i) q^{61} +(-1.30928 - 1.09861i) q^{62} +(-0.886659 - 5.02849i) q^{63} +(-2.52094 - 4.36640i) q^{64} +(-1.50000 - 0.545955i) q^{66} +(13.3550 + 4.86084i) q^{67} +(-1.01367 + 1.75573i) q^{68} +(-0.467911 - 0.810446i) q^{69} +(-10.5398 - 8.84397i) q^{71} +(-5.90554 + 4.95534i) q^{72} +(1.30541 - 7.40333i) q^{73} +(0.692066 - 0.251892i) q^{74} +(-0.434945 - 5.32926i) q^{76} +6.41147 q^{77} +(-2.32635 + 0.846723i) q^{78} +(-1.20914 + 6.85738i) q^{79} +(5.00387 + 4.19875i) q^{81} +(0.685670 + 3.88863i) q^{82} +(1.25624 + 2.17588i) q^{83} +(-0.613341 + 1.06234i) q^{84} +(-3.96703 - 1.44388i) q^{86} +(-0.922618 + 1.59802i) q^{87} +(-4.84002 - 8.38316i) q^{88} +(-0.396459 - 2.24843i) q^{89} +(7.61721 - 6.39160i) q^{91} +(0.374638 - 2.12467i) q^{92} +(0.971782 - 0.353700i) q^{93} +0.630415 q^{94} +3.00000 q^{96} +(-1.71301 + 0.623485i) q^{97} +(0.529563 - 3.00330i) q^{98} +(-7.10014 + 5.95772i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 3 q^{3} + 3 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 3 * q^3 + 3 * q^6 - 6 * q^8 + 3 * q^9	$ 6 q + 6 q^{2} + 3 q^{3} + 3 q^{6} - 6 q^{8} + 3 q^{9} - 3 q^{12} + 3 q^{13} - 3 q^{14} - 18 q^{16} - 3 q^{17} + 6 q^{18} - 12 q^{19} - 6 q^{23} + 15 q^{24} + 15 q^{26} - 6 q^{27} - 6 q^{28} - 3 q^{29} + 9 q^{31} - 9 q^{32} + 9 q^{33} - 24 q^{36} + 15 q^{38} - 24 q^{39} + 21 q^{41} + 3 q^{42} + 3 q^{43} + 9 q^{44} - 18 q^{46} + 3 q^{47} + 3 q^{48} + 15 q^{49} + 3 q^{51} - 15 q^{52} + 3 q^{53} + 30 q^{54} - 6 q^{56} - 24 q^{57} - 36 q^{58} + 12 q^{59} - 12 q^{61} + 12 q^{62} - 12 q^{63} - 12 q^{64} - 9 q^{66} + 30 q^{67} + 15 q^{68} - 12 q^{69} - 6 q^{71} + 12 q^{72} + 12 q^{73} + 15 q^{74} + 36 q^{76} + 18 q^{77} - 15 q^{78} - 39 q^{79} + 6 q^{81} + 54 q^{82} + 3 q^{84} + 24 q^{86} + 21 q^{87} - 9 q^{88} - 12 q^{89} + 15 q^{91} - 42 q^{92} - 9 q^{93} + 18 q^{94} + 18 q^{96} - 18 q^{97} + 9 q^{98} + 9 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 3 * q^3 + 3 * q^6 - 6 * q^8 + 3 * q^9 - 3 * q^12 + 3 * q^13 - 3 * q^14 - 18 * q^16 - 3 * q^17 + 6 * q^18 - 12 * q^19 - 6 * q^23 + 15 * q^24 + 15 * q^26 - 6 * q^27 - 6 * q^28 - 3 * q^29 + 9 * q^31 - 9 * q^32 + 9 * q^33 - 24 * q^36 + 15 * q^38 - 24 * q^39 + 21 * q^41 + 3 * q^42 + 3 * q^43 + 9 * q^44 - 18 * q^46 + 3 * q^47 + 3 * q^48 + 15 * q^49 + 3 * q^51 - 15 * q^52 + 3 * q^53 + 30 * q^54 - 6 * q^56 - 24 * q^57 - 36 * q^58 + 12 * q^59 - 12 * q^61 + 12 * q^62 - 12 * q^63 - 12 * q^64 - 9 * q^66 + 30 * q^67 + 15 * q^68 - 12 * q^69 - 6 * q^71 + 12 * q^72 + 12 * q^73 + 15 * q^74 + 36 * q^76 + 18 * q^77 - 15 * q^78 - 39 * q^79 + 6 * q^81 + 54 * q^82 + 3 * q^84 + 24 * q^86 + 21 * q^87 - 9 * q^88 - 12 * q^89 + 15 * q^91 - 42 * q^92 - 9 * q^93 + 18 * q^94 + 18 * q^96 - 18 * q^97 + 9 * q^98 + 9 * 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 $

$2$	0.826352	−	0.300767i	0.584319	−	0.212675i	−0.0329100	−	0.999458i	$-0.510477\pi$
$2$	0.826352	−	0.300767i	0.584319	−	0.212675i	0.617229	+	0.786784i	$0.288255\pi$
$3$	−0.0923963	+	0.524005i	−0.0533450	+	0.302535i	−0.999794	−	0.0203202i	$-0.993531\pi$
$3$	−0.0923963	+	0.524005i	−0.0533450	+	0.302535i	0.946449	+	0.322855i	$0.104643\pi$
$4$	−0.939693	+	0.788496i	−0.469846	+	0.394248i
$5$		0			0
$5$		0			0
$6$	0.0812519	+	0.460802i	0.0331710	+	0.188122i
$7$	−0.939693	−	1.62760i	−0.355170	−	0.615173i	0.631977	−	0.774987i	$-0.282244\pi$
$7$	−0.939693	−	1.62760i	−0.355170	−	0.615173i	−0.987147	+	0.159814i	$0.948910\pi$
$8$	−1.41875	+	2.45734i	−0.501603	+	0.868802i
$9$	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	$0.994719\pi$
$12$	−0.326352	−	0.565258i	−0.0942097	−	0.163176i
$13$	0.918748	+	5.21048i	0.254815	+	1.44513i	0.796547	+	0.604576i	$0.206657\pi$
$13$	0.918748	+	5.21048i	0.254815	+	1.44513i	−0.541733	+	0.840551i	$0.682231\pi$
$14$	−1.26604	−	1.06234i	−0.338365	−	0.283922i
$15$		0			0
$16$	−0.00727396	+	0.0412527i	−0.00181849	+	0.0103132i
$17$	1.55303	−	0.565258i	0.376666	−	0.137095i	−0.146748	−	0.989174i	$-0.546881\pi$
$17$	1.55303	−	0.565258i	0.376666	−	0.137095i	0.523414	+	0.852079i	$0.324658\pi$
$18$	2.38919			0.563136
$19$	−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
$22$	−0.520945	+	2.95442i	−0.111066	+	0.629885i
$23$	−1.34730	+	1.13052i	−0.280931	+	0.235729i	−0.772354	−	0.635192i	$-0.780921\pi$
$23$	−1.34730	+	1.13052i	−0.280931	+	0.235729i	0.491424	+	0.870921i	$0.336477\pi$
$24$	−1.15657	−	0.970481i	−0.236085	−	0.198099i
$25$		0			0
$26$	2.32635	+	4.02936i	0.456235	+	0.790222i
$27$	−1.52094	+	2.63435i	−0.292706	+	0.506982i
$28$	2.16637	+	0.788496i	0.409406	+	0.149012i
$29$	3.25877	+	1.18610i	0.605138	+	0.220252i	0.626375	−	0.779522i	$-0.284538\pi$
$29$	3.25877	+	1.18610i	0.605138	+	0.220252i	−0.0212363	+	0.999774i	$0.506760\pi$
$30$		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	$0.889176\pi$
$32$	−0.979055	−	5.55250i	−0.173074	−	0.981553i
$33$	−1.39053	−	1.16679i	−0.242060	−	0.203113i
$34$	1.11334	−	0.934204i	0.190936	−	0.160215i
$35$		0			0
$36$	−3.13176	+	1.13987i	−0.521960	+	0.189978i
$37$	0.837496			0.137684			0.0688418	−	0.997628i	$-0.478070\pi$
$37$	0.837496			0.137684			0.0688418	+	0.997628i	$0.478070\pi$
$38$	−1.01367	+	3.69669i	−0.164439	+	0.599682i
$39$	−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	$0.941524\pi$
$42$	0.673648	−	0.565258i	0.103946	−	0.0872212i
$43$	−3.67752	−	3.08580i	−0.560816	−	0.470581i	0.317768	−	0.948169i	$-0.397067\pi$
$43$	−3.67752	−	3.08580i	−0.560816	−	0.470581i	−0.878584	+	0.477588i	$0.841511\pi$
$44$	−0.726682	−	4.12122i	−0.109551	−	0.621297i
$45$		0			0
$46$	−0.773318	+	1.33943i	−0.114020	+	0.197488i
$47$	0.673648	+	0.245188i	0.0982617	+	0.0357643i	0.390683	−	0.920525i	$-0.372239\pi$
$47$	0.673648	+	0.245188i	0.0982617	+	0.0357643i	−0.292422	+	0.956290i	$0.594461\pi$
$48$	−0.0209445	−	0.00762319i	−0.00302308	−	0.00110031i
$49$	1.73396	−	3.00330i	0.247708	−	0.429043i
$50$		0			0
$51$	0.152704	+	0.866025i	0.0213828	+	0.121268i
$52$	−4.97178	−	4.17182i	−0.689462	−	0.578527i
$53$	4.67752	−	3.92490i	0.642507	−	0.539127i	−0.262280	−	0.964992i	$-0.584474\pi$
$53$	4.67752	−	3.92490i	0.642507	−	0.539127i	0.904787	+	0.425865i	$0.140030\pi$
$54$	−0.464508	+	2.63435i	−0.0632115	+	0.358490i
$55$		0			0
$56$	5.33275			0.712618
$57$	−1.63041	−	1.64955i	−0.215954	−	0.218488i
$58$	3.04963			0.400436
$59$	10.1099	−	3.67972i	1.31620	−	0.479058i	0.413962	−	0.910294i	$-0.364144\pi$
$59$	10.1099	−	3.67972i	1.31620	−	0.479058i	0.902239	+	0.431236i	$0.141922\pi$
$60$		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	$0.187115\pi$
$62$	−1.30928	−	1.09861i	−0.166278	−	0.139524i
$63$	−0.886659	−	5.02849i	−0.111709	−	0.633531i
$64$	−2.52094	−	4.36640i	−0.315118	−	0.545801i
$65$		0			0
$66$	−1.50000	−	0.545955i	−0.184637	−	0.0672025i
$67$	13.3550	+	4.86084i	1.63158	+	0.593846i	0.985537	−	0.169458i	$-0.0542017\pi$
$67$	13.3550	+	4.86084i	1.63158	+	0.593846i	0.646040	+	0.763304i	$0.276424\pi$
$68$	−1.01367	+	1.75573i	−0.122926	+	0.212913i
$69$	−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	$-0.581829\pi$
$72$	−5.90554	+	4.95534i	−0.695975	+	0.583992i
$73$	1.30541	−	7.40333i	0.152786	−	0.866495i	−0.807995	−	0.589189i	$-0.799447\pi$
$73$	1.30541	−	7.40333i	0.152786	−	0.866495i	0.960782	−	0.277306i	$-0.0894415\pi$
$74$	0.692066	−	0.251892i	0.0804511	−	0.0292818i
$75$		0			0
$76$	−0.434945	−	5.32926i	−0.0498916	−	0.611308i
$77$	6.41147			0.730655
$78$	−2.32635	+	0.846723i	−0.263407	+	0.0958725i
$79$	−1.20914	+	6.85738i	−0.136039	+	0.771515i	0.838092	+	0.545529i	$0.183671\pi$
$79$	−1.20914	+	6.85738i	−0.136039	+	0.771515i	−0.974131	+	0.225986i	$0.927440\pi$
$80$		0			0
$81$	5.00387	+	4.19875i	0.555986	+	0.466527i
$82$	0.685670	+	3.88863i	0.0757196	+	0.429427i
$83$	1.25624	+	2.17588i	0.137891	+	0.238834i	0.926698	−	0.375807i	$-0.122634\pi$
$83$	1.25624	+	2.17588i	0.137891	+	0.238834i	−0.788807	+	0.614641i	$0.789301\pi$
$84$	−0.613341	+	1.06234i	−0.0669210	+	0.115911i
$85$		0			0
$86$	−3.96703	−	1.44388i	−0.427776	−	0.155698i
$87$	−0.922618	+	1.59802i	−0.0989151	+	0.171326i
$88$	−4.84002	−	8.38316i	−0.515948	−	0.893648i
$89$	−0.396459	−	2.24843i	−0.0420246	−	0.238333i	0.956559	−	0.291539i	$-0.0941673\pi$
$89$	−0.396459	−	2.24843i	−0.0420246	−	0.238333i	−0.998584	+	0.0532055i	$0.983056\pi$
$90$		0			0
$91$	7.61721	−	6.39160i	0.798501	−	0.670022i
$92$	0.374638	−	2.12467i	0.0390587	−	0.221513i
$93$	0.971782	−	0.353700i	0.100769	−	0.0366769i
$94$	0.630415			0.0650223
$95$		0			0
$96$	3.00000			0.306186
$97$	−1.71301	+	0.623485i	−0.173930	+	0.0633053i	−0.427517	−	0.904007i	$-0.640612\pi$
$97$	−1.71301	+	0.623485i	−0.173930	+	0.0633053i	0.253587	+	0.967312i	$0.418389\pi$
$98$	0.529563	−	3.00330i	0.0534939	−	0.303379i
$99$	−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	$-0.184499\pi$
$102$	0.386659	+	0.669713i	0.0382850	+	0.0663115i
$103$	−0.00727396	+	0.0125989i	−0.000716725	+	0.00124140i	−0.866384	−	0.499379i	$-0.833561\pi$
$103$	−0.00727396	+	0.0125989i	−0.000716725	+	0.00124140i	0.865667	+	0.500621i	$0.166895\pi$
$104$	−14.1074	−	5.13468i	−1.38335	−	0.503497i
$105$		0			0
$106$	2.68479	−	4.65020i	0.260770	−	0.451667i
$107$	−1.77719	−	3.07818i	−0.171807	−	0.297579i	0.767244	−	0.641355i	$-0.221627\pi$
$107$	−1.77719	−	3.07818i	−0.171807	−	0.297579i	−0.939052	+	0.343776i	$0.888294\pi$
$108$	−0.647956	−	3.67474i	−0.0623496	−	0.353602i
$109$	5.64543	+	4.73708i	0.540734	+	0.453730i	0.871789	−	0.489882i	$-0.162960\pi$
$109$	5.64543	+	4.73708i	0.540734	+	0.453730i	−0.331055	+	0.943612i	$0.607404\pi$
$110$		0			0
$111$	−0.0773815	+	0.438852i	−0.00734473	+	0.0416540i
$112$	0.0739780	−	0.0269258i	0.00699026	−	0.00254425i
$113$	−7.37733			−0.694000			−0.347000	−	0.937865i	$-0.612800\pi$
$113$	−7.37733			−0.694000			−0.347000	+	0.937865i	$0.612800\pi$
$114$	−1.84343	−	0.872729i	−0.172653	−	0.0817386i
$115$		0			0
$116$	−3.99747	+	1.45496i	−0.371156	+	0.135090i
$117$	−2.49613	+	14.1563i	−0.230767	+	1.30875i
$118$	7.24763	−	6.08148i	0.667198	−	0.559846i
$119$	−2.37939	−	1.99654i	−0.218118	−	0.183023i
$120$		0			0
$121$	−0.319078	−	0.552659i	−0.0290071	−	0.0502417i
$122$	1.92989	−	3.34267i	0.174724	−	0.302631i
$123$	−2.24510	−	0.817150i	−0.202434	−	0.0736799i
$124$	2.24035	+	0.815422i	0.201190	+	0.0732270i
$125$		0			0
$126$	−2.24510	−	3.88863i	−0.200009	−	0.346426i
$127$	0.0175410	+	0.0994798i	0.00155651	+	0.00882740i	0.985576	−	0.169233i	$-0.0541290\pi$
$127$	0.0175410	+	0.0994798i	0.00155651	+	0.00882740i	−0.984020	+	0.178060i	$0.943018\pi$
$128$	5.24170	+	4.39831i	0.463305	+	0.388759i
$129$	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	$0.346536\pi$
$132$	2.22668			0.193808
$133$	8.15657	+	0.761570i	0.707265	+	0.0660365i
$134$	12.4979			1.07966
$135$		0			0
$136$	−0.814330	+	4.61830i	−0.0698282	+	0.396016i
$137$	−14.9684	+	12.5600i	−1.27883	+	1.07307i	−0.285431	+	0.958399i	$0.592137\pi$
$137$	−14.9684	+	12.5600i	−1.27883	+	1.07307i	−0.993404	+	0.114671i	$0.963419\pi$
$138$	−0.630415	−	0.528981i	−0.0536645	−	0.0450298i
$139$	2.67365	+	15.1630i	0.226776	+	1.28611i	0.859261	+	0.511537i	$0.170924\pi$
$139$	2.67365	+	15.1630i	0.226776	+	1.28611i	−0.632485	+	0.774573i	$0.717965\pi$
$140$		0			0
$141$	−0.190722	+	0.330341i	−0.0160617	+	0.0278197i
$142$	−11.3696	−	4.13819i	−0.954114	−	0.347269i
$143$	−16.9611	−	6.17334i	−1.41836	−	0.516240i
$144$	−0.0569038	+	0.0985603i	−0.00474198	+	0.00821336i
$145$		0			0
$146$	−1.14796	−	6.51038i	−0.0950055	−	0.538803i
$147$	1.41353	+	1.18610i	0.116586	+	0.0978275i
$148$	−0.786989	+	0.660362i	−0.0646901	+	0.0542814i
$149$	−0.654048	+	3.70929i	−0.0535817	+	0.303877i	−0.999807	−	0.0196306i	$-0.993751\pi$
$149$	−0.654048	+	3.70929i	−0.0535817	+	0.303877i	0.946226	+	0.323507i	$0.104862\pi$
$150$		0			0
$151$	−14.5963			−1.18783			−0.593914	−	0.804529i	$-0.702418\pi$
$151$	−14.5963			−1.18783			−0.593914	+	0.804529i	$0.702418\pi$
$152$	−5.16163	−	11.2398i	−0.418663	−	0.911671i
$153$	4.49020			0.363011
$154$	5.29813	−	1.92836i	0.426936	−	0.155392i
$155$		0			0
$156$	2.64543	−	2.21978i	0.211804	−	0.177725i
$157$	7.94743	+	6.66869i	0.634274	+	0.532219i	0.902254	−	0.431205i	$-0.141912\pi$
$157$	7.94743	+	6.66869i	0.634274	+	0.532219i	−0.267980	+	0.963425i	$0.586356\pi$
$158$	1.06330	+	6.03028i	0.0845916	+	0.479743i
$159$	1.62449	+	2.81369i	0.128830	+	0.223140i
$160$		0			0
$161$	3.10607	+	1.13052i	0.244792	+	0.0890971i
$162$	5.39780	+	1.96464i	0.424091	+	0.154357i
$163$	−1.01114	+	1.75135i	−0.0791989	+	0.137177i	−0.902905	−	0.429841i	$-0.858570\pi$
$163$	−1.01114	+	1.75135i	−0.0791989	+	0.137177i	0.823706	+	0.567018i	$0.191903\pi$
$164$	−2.75402	−	4.77011i	−0.215053	−	0.372483i
$165$		0			0
$166$	1.69253	+	1.42020i	0.131366	+	0.110229i
$167$	17.8157	−	14.9491i	1.37862	−	1.15680i	0.408898	−	0.912580i	$-0.365913\pi$
$167$	17.8157	−	14.9491i	1.37862	−	1.15680i	0.969720	−	0.244218i	$-0.0785312\pi$
$168$	−0.492726	+	2.79439i	−0.0380146	+	0.215592i
$169$	−14.0890	+	5.12797i	−1.08377	+	0.394460i
$170$		0			0
$171$	−9.74035	+	6.73595i	−0.744863	+	0.515111i
$172$	5.88888			0.449023
$173$	0.842549	−	0.306663i	0.0640578	−	0.0233151i	−0.309793	−	0.950804i	$-0.600260\pi$
$173$	0.842549	−	0.306663i	0.0640578	−	0.0233151i	0.373850	+	0.927489i	$0.378037\pi$
$174$	−0.281774	+	1.59802i	−0.0213613	+	0.121146i
$175$		0			0
$176$	−0.109470	−	0.0918566i	−0.00825164	−	0.00692395i
$177$	0.994070	+	5.63765i	0.0747189	+	0.423752i
$178$	−1.00387	−	1.73875i	−0.0752433	−	0.130325i
$179$	10.6591	−	18.4621i	0.796699	−	1.37992i	−0.125056	−	0.992150i	$-0.539911\pi$
$179$	10.6591	−	18.4621i	0.796699	−	1.37992i	0.921755	−	0.387773i	$-0.126755\pi$
$180$		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	$0.406945\pi$
$182$	4.37211	−	7.57272i	0.324082	−	0.561327i
$183$	1.16772	+	2.02255i	0.0863202	+	0.149511i
$184$	−0.866592	−	4.91469i	−0.0638860	−	0.362316i
$185$		0			0
$186$	0.696652	−	0.584561i	0.0510810	−	0.0428621i
$187$	−0.979055	+	5.55250i	−0.0715956	+	0.406039i
$188$	−0.826352	+	0.300767i	−0.0602679	+	0.0219357i
$189$	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	$0.259568\pi$
$192$	2.52094	−	0.917549i	0.181934	−	0.0662184i
$193$	−2.24035	+	12.7057i	−0.161264	+	0.914574i	0.791569	+	0.611080i	$0.209264\pi$
$193$	−2.24035	+	12.7057i	−0.161264	+	0.914574i	−0.952833	+	0.303494i	$0.901847\pi$
$194$	−1.22803	+	1.03044i	−0.0881671	+	0.0739810i
$195$		0			0
$196$	0.738703	+	4.18939i	0.0527645	+	0.299242i
$197$	−11.6001	−	20.0920i	−0.826476	−	1.43150i	−0.900786	−	0.434263i	$-0.857009\pi$
$197$	−11.6001	−	20.0920i	−0.826476	−	1.43150i	0.0743108	−	0.997235i	$-0.476324\pi$
$198$	−4.07532	+	7.05866i	−0.289621	+	0.501637i
$199$	−8.66550	−	3.15398i	−0.614281	−	0.223580i	0.0160945	−	0.999870i	$-0.494877\pi$
$199$	−8.66550	−	3.15398i	−0.614281	−	0.223580i	−0.630375	+	0.776291i	$0.717099\pi$
$200$		0			0
$201$	−3.78106	+	6.54899i	−0.266695	+	0.461930i
$202$	−3.48293	−	6.03260i	−0.245058	−	0.424453i
$203$	−1.13176	−	6.41852i	−0.0794339	−	0.450492i
$204$	−0.826352	−	0.693392i	−0.0578562	−	0.0485471i
$205$		0			0
$206$	−0.00222152	+	0.0125989i	−0.000154781	+	0.000877805i
$207$	−4.49020	+	1.63430i	−0.312090	+	0.113592i
$208$	−0.221629			−0.0153672
$209$	−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	$0.556794\pi$
$212$	−1.30066	+	7.37641i	−0.0893297	+	0.506614i
$213$	5.60813	−	4.70578i	0.384262	−	0.322435i
$214$	−2.39440	−	2.00914i	−0.163678	−	0.137342i
$215$		0			0
$216$	−4.31567	−	7.47497i	−0.293644	−	0.508607i
$217$	−1.82635	+	3.16333i	−0.123981	+	0.214741i
$218$	6.08987	+	2.21653i	0.412458	+	0.150122i
$219$	3.75877	+	1.36808i	0.253994	+	0.0924463i
$220$		0			0
$221$	4.37211	+	7.57272i	0.294100	+	0.509396i
$222$	0.0680482	+	0.385920i	0.00456709	+	0.0259013i
$223$	2.30928	+	1.93771i	0.154641	+	0.129759i	0.716825	−	0.697253i	$-0.245595\pi$
$223$	2.30928	+	1.93771i	0.154641	+	0.129759i	−0.562185	+	0.827012i	$0.690039\pi$
$224$	−8.11721	+	6.81115i	−0.542354	+	0.455089i
$225$		0			0
$226$	−6.09627	+	2.21886i	−0.405518	+	0.147596i
$227$	13.7219			0.910757			0.455378	−	0.890298i	$-0.349504\pi$
$227$	13.7219			0.910757			0.455378	+	0.890298i	$0.349504\pi$
$228$	2.83275	+	0.264490i	0.187603	+	0.0175163i
$229$	9.41416			0.622105			0.311053	−	0.950393i	$-0.399318\pi$
$229$	9.41416			0.622105			0.311053	+	0.950393i	$0.399318\pi$
$230$		0			0
$231$	−0.592396	+	3.35965i	−0.0389768	+	0.221048i
$232$	−7.53802	+	6.32515i	−0.494895	+	0.415266i
$233$	18.5273	+	15.5463i	1.21377	+	1.01847i	0.999127	+	0.0417777i	$0.0133021\pi$
$233$	18.5273	+	15.5463i	1.21377	+	1.01847i	0.214640	+	0.976693i	$0.431142\pi$
$234$	2.19506	+	12.4488i	0.143496	+	0.813804i
$235$		0			0
$236$	−6.59879	+	11.4294i	−0.429545	+	0.743993i
$237$	−3.48158	−	1.26719i	−0.226153	−	0.0823130i
$238$	−2.56670	−	0.934204i	−0.166375	−	0.0605554i
$239$	11.6630	−	20.2009i	0.754415	−	1.30668i	−0.191250	−	0.981541i	$-0.561254\pi$
$239$	11.6630	−	20.2009i	0.754415	−	1.30668i	0.945665	−	0.325143i	$-0.105413\pi$
$240$		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	$0.941393\pi$
$242$	−0.429892	−	0.360723i	−0.0276345	−	0.0231881i
$243$	−9.65317	+	8.09997i	−0.619251	+	0.519613i
$244$	−0.934945	+	5.30234i	−0.0598537	+	0.339447i
$245$		0			0
$246$	−2.10101			−0.133956
$247$	−20.8444	−	9.86830i	−1.32629	−	0.627905i
$248$	5.51485			0.350193
$249$	−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	$0.448573\pi$
$252$	4.79813	+	4.02611i	0.302254	+	0.253621i
$253$	−1.04189	−	5.90885i	−0.0655030	−	0.371486i
$254$	0.0444153	+	0.0769295i	0.00278686	+	0.00482699i
$255$		0			0
$256$	15.1300	+	5.50687i	0.945625	+	0.344179i
$257$	14.4290	+	5.25173i	0.900057	+	0.327594i	0.750276	−	0.661125i	$-0.229921\pi$
$257$	14.4290	+	5.25173i	0.900057	+	0.327594i	0.149782	+	0.988719i	$0.452143\pi$
$258$	1.12314	−	1.94534i	0.0699237	−	0.121111i
$259$	−0.786989	−	1.36310i	−0.0489011	−	0.0846992i
$260$		0			0
$261$	7.21760	+	6.05628i	0.446758	+	0.374874i
$262$	2.04576	−	1.71660i	0.126387	−	0.106052i
$263$	−1.67453	+	9.49671i	−0.103256	+	0.585592i	0.888647	+	0.458592i	$0.151646\pi$
$263$	−1.67453	+	9.49671i	−0.103256	+	0.585592i	−0.991903	+	0.127000i	$0.959465\pi$
$264$	4.84002	−	1.76162i	0.297883	−	0.108420i
$265$		0			0
$266$	6.96926	−	1.82391i	0.427312	−	0.111831i
$267$	1.21482			0.0743459
$268$	−16.3824	+	5.96270i	−1.00071	+	0.364230i
$269$	−3.17412	+	18.0013i	−0.193529	+	1.09756i	0.720969	+	0.692968i	$0.243697\pi$
$269$	−3.17412	+	18.0013i	−0.193529	+	1.09756i	−0.914498	+	0.404591i	$0.867414\pi$
$270$		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	$0.526838\pi$
$272$	0.0120217	+	0.0681784i	0.000728923	+	0.00413393i
$273$	2.64543	+	4.58202i	0.160109	+	0.277316i
$274$	−8.59152	+	14.8809i	−0.519033	+	0.898991i
$275$		0			0
$276$	1.07873	+	0.392624i	0.0649317	+	0.0236332i
$277$	6.88191	−	11.9198i	0.413494	−	0.716193i	−0.581775	−	0.813350i	$-0.697642\pi$
$277$	6.88191	−	11.9198i	0.413494	−	0.716193i	0.995269	+	0.0971571i	$0.0309749\pi$
$278$	6.76991	+	11.7258i	0.406033	+	0.703269i
$279$	−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	$0.149882\pi$
$282$	−0.0582480	+	0.330341i	−0.00346862	+	0.0196715i
$283$	−16.3293	+	5.94340i	−0.970679	+	0.353298i	−0.778209	−	0.628005i	$-0.783872\pi$
$283$	−16.3293	+	5.94340i	−0.970679	+	0.353298i	−0.192469	+	0.981303i	$0.561650\pi$
$284$	16.8776			1.00150
$285$		0			0
$286$	−15.8726			−0.938565
$287$	7.92989	−	2.88624i	0.468087	−	0.170370i
$288$	2.65998	−	15.0855i	0.156741	−	0.888921i
$289$	−10.9304	+	9.17166i	−0.642962	+	0.539509i
$290$		0			0
$291$	−0.168434	−	0.955234i	−0.00987375	−	0.0559968i
$292$	4.61081	+	7.98617i	0.269828	+	0.467355i
$293$	7.80200	−	13.5135i	0.455798	−	0.789465i	−0.542936	−	0.839774i	$-0.682687\pi$
$293$	7.80200	−	13.5135i	0.455798	−	0.789465i	0.998734	+	0.0503091i	$0.0160206\pi$
$294$	1.52481	+	0.554987i	0.0889290	+	0.0323675i
$295$		0			0
$296$	−1.18820	+	2.05802i	−0.0690625	+	0.119620i
$297$	−5.18866	−	8.98703i	−0.301077	−	0.521480i
$298$	0.575160	+	3.26189i	0.0333181	+	0.188956i
$299$	−7.12836	−	5.98140i	−0.412243	−	0.345913i
$300$		0			0
$301$	−1.56670	+	8.88522i	−0.0903033	+	0.512136i
$302$	−12.0617	+	4.39008i	−0.694070	+	0.252621i
$303$	4.21482			0.242135
$304$	−0.128356	−	0.129862i	−0.00736170	−	0.00744807i
$305$		0			0
$306$	3.71048	−	1.35051i	0.212114	−	0.0772033i
$307$	−3.73695	+	21.1933i	−0.213279	+	1.20956i	0.670589	+	0.741829i	$0.266041\pi$
$307$	−3.73695	+	21.1933i	−0.213279	+	1.20956i	−0.883868	+	0.467736i	$0.845070\pi$
$308$	−6.02481	+	5.05542i	−0.343296	+	0.288059i
$309$	−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	$0.968145\pi$
$312$	3.99407	−	6.91793i	0.226120	−	0.391651i
$313$	18.3414	+	6.67571i	1.03672	+	0.377334i	0.803634	−	0.595124i	$-0.202897\pi$
$313$	18.3414	+	6.67571i	1.03672	+	0.377334i	0.233081	+	0.972457i	$0.425119\pi$
$314$	8.57310	+	3.12035i	0.483808	+	0.176092i
$315$		0			0
$316$	−4.27079	−	7.39723i	−0.240251	−	0.416127i
$317$	−4.92246	−	27.9166i	−0.276473	−	1.56795i	−0.734245	−	0.678885i	$-0.762464\pi$
$317$	−4.92246	−	27.9166i	−0.276473	−	1.56795i	0.457772	−	0.889070i	$-0.348648\pi$
$318$	2.18866	+	1.83651i	0.122734	+	0.102986i
$319$	−9.06283	+	7.60462i	−0.507421	+	0.425777i
$320$		0			0
$321$	1.77719	−	0.646844i	0.0991930	−	0.0361033i
$322$	2.90673			0.161986
$323$	−1.90508	+	6.94751i	−0.106001	+	0.386570i
$324$	−8.01279			−0.445155
$325$		0			0
$326$	−0.308811	+	1.75135i	−0.0171035	+	0.0969985i
$327$	−3.00387	+	2.52055i	−0.166114	+	0.139387i
$328$	−9.76011	−	8.18971i	−0.538912	−	0.452201i
$329$	−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	$0.151702\pi$
$332$	−2.89615	−	1.05411i	−0.158947	−	0.0578520i
$333$	2.13816	+	0.778225i	0.117170	+	0.0426465i
$334$	10.2258	−	17.7116i	0.559531	−	0.969136i
$335$		0			0
$336$	0.00727396	+	0.0412527i	0.000396827	+	0.00225052i
$337$	−19.4873	−	16.3518i	−1.06154	−	0.890737i	−0.0672796	−	0.997734i	$-0.521432\pi$
$337$	−19.4873	−	16.3518i	−1.06154	−	0.890737i	−0.994259	+	0.106997i	$0.965876\pi$
$338$	−10.1001	+	8.47502i	−0.549375	+	0.460980i
$339$	0.681637	−	3.86576i	0.0370215	−	0.209959i
$340$		0			0
$341$	6.63041			0.359057
$342$	−6.02300	+	8.49584i	−0.325687	+	0.459403i
$343$	−19.6732			−1.06225
$344$	12.8004	−	4.65895i	0.690149	−	0.251194i
$345$		0			0
$346$	0.604007	−	0.506822i	0.0324716	−	0.0272469i
$347$	−5.90033	−	4.95096i	−0.316746	−	0.265782i	0.470527	−	0.882385i	$-0.344064\pi$
$347$	−5.90033	−	4.95096i	−0.316746	−	0.265782i	−0.787274	+	0.616604i	$0.788508\pi$
$348$	−0.393056	−	2.22913i	−0.0210700	−	0.119494i
$349$	−11.3785	−	19.7082i	−0.609078	−	1.05495i	−0.991393	−	0.130921i	$-0.958206\pi$
$349$	−11.3785	−	19.7082i	−0.609078	−	1.05495i	0.382315	−	0.924032i	$-0.375127\pi$
$350$		0			0
$351$	−15.1236	−	5.50454i	−0.807238	−	0.293811i
$352$	18.0744	+	6.57856i	0.963371	+	0.350638i
$353$	−5.72281	+	9.91220i	−0.304595	+	0.527573i	−0.977171	−	0.212454i	$-0.931854\pi$
$353$	−5.72281	+	9.91220i	−0.304595	+	0.527573i	0.672576	+	0.740028i	$0.265188\pi$
$354$	2.51707	+	4.35970i	0.133781	+	0.231715i
$355$		0			0
$356$	2.14543	+	1.80023i	0.113708	+	0.0954120i
$357$	1.26604	−	1.06234i	0.0670062	−	0.0562249i
$358$	3.25537	−	18.4621i	0.172051	−	0.975752i
$359$	−9.75789	+	3.55158i	−0.515002	+	0.187445i	−0.586429	−	0.810000i	$-0.699467\pi$
$359$	−9.75789	+	3.55158i	−0.515002	+	0.187445i	0.0714274	+	0.997446i	$0.477245\pi$
$360$		0			0
$361$	−6.28968	−	17.9287i	−0.331036	−	0.943618i
$362$	14.1575			0.744099
$363$	0.319078	−	0.116135i	0.0167472	−	0.00609550i
$364$	−2.11809	+	12.0123i	−0.111018	+	0.629614i
$365$		0			0
$366$	1.57326	+	1.32012i	0.0822358	+	0.0690040i
$367$	5.64930	+	32.0388i	0.294891	+	1.67241i	0.667645	+	0.744480i	$0.267303\pi$
$367$	5.64930	+	32.0388i	0.294891	+	1.67241i	−0.372754	+	0.927930i	$0.621586\pi$
$368$	−0.0368366	−	0.0638029i	−0.00192024	−	0.00332596i
$369$	−6.09967	+	10.5649i	−0.317536	+	0.549989i
$370$		0			0
$371$	−10.7836	−	3.92490i	−0.559856	−	0.203771i
$372$	−0.634285	+	1.09861i	−0.0328862	+	0.0569605i
$373$	15.2429	+	26.4014i	0.789246	+	1.36701i	0.926429	+	0.376469i	$0.122862\pi$
$373$	15.2429	+	26.4014i	0.789246	+	1.36701i	−0.137183	+	0.990546i	$0.543805\pi$
$374$	0.860967	+	4.88279i	0.0445195	+	0.252483i
$375$		0			0
$376$	−1.55825	+	1.30753i	−0.0803605	+	0.0674305i
$377$	−3.18614	+	18.0695i	−0.164094	+	0.930626i
$378$	4.72416	−	1.71945i	0.242984	−	0.0884391i
$379$	17.8598			0.917396			0.458698	−	0.888592i	$-0.348316\pi$
$379$	17.8598			0.917396			0.458698	+	0.888592i	$0.348316\pi$
$380$		0			0
$381$	−0.0537486			−0.00275363
$382$	15.6582	−	5.69913i	0.801144	−	0.291593i
$383$	4.07310	−	23.0997i	0.208126	−	1.18034i	−0.684319	−	0.729183i	$-0.739900\pi$
$383$	4.07310	−	23.0997i	0.208126	−	1.18034i	0.892445	−	0.451157i	$-0.148988\pi$
$384$	−2.78905	+	2.34029i	−0.142328	+	0.119427i
$385$		0			0
$386$	1.97013	+	11.1732i	0.100277	+	0.568700i
$387$	−6.52141	−	11.2954i	−0.331502	−	0.574178i
$388$	1.11809	−	1.93659i	0.0567623	−	0.0983153i
$389$	−3.67365	−	1.33710i	−0.186261	−	0.0677936i	0.247206	−	0.968963i	$-0.420488\pi$
$389$	−3.67365	−	1.33710i	−0.186261	−	0.0677936i	−0.433467	+	0.901169i	$0.642710\pi$
$390$		0			0
$391$	−1.45336	+	2.51730i	−0.0734997	+	0.127305i
$392$	4.92009	+	8.52185i	0.248502	+	0.430418i
$393$	0.280592	+	1.59132i	0.0141540	+	0.0802714i
$394$	−15.6288	−	13.1141i	−0.787369	−	0.660681i
$395$		0			0
$396$	1.97431	−	11.1969i	0.0992127	−	0.562663i
$397$	8.41875	−	3.06417i	0.422525	−	0.153786i	−0.122002	−	0.992530i	$-0.538931\pi$
$397$	8.41875	−	3.06417i	0.422525	−	0.153786i	0.544527	+	0.838743i	$0.316709\pi$
$398$	−8.10936			−0.406486
$399$	−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	$0.372769\pi$
$402$	−1.15476	+	6.54899i	−0.0575943	+	0.326634i
$403$	7.87733	−	6.60986i	0.392398	−	0.329261i
$404$	7.44356	+	6.24589i	0.370331	+	0.310745i
$405$		0			0
$406$	−2.86571	−	4.96356i	−0.142223	−	0.246338i
$407$	−1.42855	+	2.47432i	−0.0708105	+	0.122647i
$408$	−2.34477	−	0.853427i	−0.116083	−	0.0422509i
$409$	30.2656	+	11.0158i	1.49654	+	0.544696i	0.955162	−	0.296084i	$-0.0956808\pi$
$409$	30.2656	+	11.0158i	1.49654	+	0.544696i	0.541377	+	0.840780i	$0.317903\pi$
$410$		0			0
$411$	−5.19846	−	9.00400i	−0.256421	−	0.444135i
$412$	−0.00309887	−	0.0175745i	−0.000152670	−	0.000865836i
$413$	−15.4893	−	12.9971i	−0.762180	−	0.639545i
$414$	−3.21894	+	2.70101i	−0.158202	+	0.132747i
$415$		0			0
$416$	28.0317	−	10.2027i	1.37437	−	0.500228i
$417$	−8.19253			−0.401190
$418$	−9.19253	−	9.30039i	−0.449622	−	0.454897i
$419$	−23.2499			−1.13583			−0.567916	−	0.823086i	$-0.692250\pi$
$419$	−23.2499			−1.13583			−0.567916	+	0.823086i	$0.692250\pi$
$420$		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	$0.00528986\pi$
$422$	−9.85117	+	8.26611i	−0.479547	+	0.402388i
$423$	1.49201	+	1.25195i	0.0725440	+	0.0608717i
$424$	3.00862	+	17.0627i	0.146111	+	0.828639i
$425$		0			0
$426$	3.21894	−	5.57537i	0.155958	−	0.270128i
$427$	−7.75150	−	2.82131i	−0.375121	−	0.136533i
$428$	4.09714	+	1.49124i	0.198043	+	0.0720817i
$429$	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	$-0.165006\pi$
$432$	−0.0976108	−	0.0819052i	−0.00469630	−	0.00394067i
$433$	21.9800	−	18.4434i	1.05629	−	0.886333i	0.0625499	−	0.998042i	$-0.480077\pi$
$433$	21.9800	−	18.4434i	1.05629	−	0.886333i	0.993741	+	0.111709i	$0.0356323\pi$
$434$	−0.557781	+	3.16333i	−0.0267744	+	0.151845i
$435$		0			0
$436$	−9.04013			−0.432944
$437$	−0.623608	−	7.64090i	−0.0298312	−	0.365514i
$438$	3.51754			0.168075
$439$	12.5376	−	4.56332i	0.598387	−	0.217795i	−0.0250271	−	0.999687i	$-0.507967\pi$
$439$	12.5376	−	4.56332i	0.598387	−	0.217795i	0.623414	+	0.781892i	$0.285745\pi$
$440$		0			0
$441$	7.21760	−	6.05628i	0.343695	−	0.288394i
$442$	5.89053	+	4.94274i	0.280184	+	0.235102i
$443$	−5.88372	−	33.3682i	−0.279544	−	1.58537i	−0.724147	−	0.689646i	$-0.757766\pi$
$443$	−5.88372	−	33.3682i	−0.279544	−	1.58537i	0.444603	−	0.895728i	$-0.353345\pi$
$444$	−0.273318	−	0.473401i	−0.0129711	−	0.0224666i
$445$		0			0
$446$	2.49108	+	0.906678i	0.117956	+	0.0429324i
$447$	−1.88326	−	0.685449i	−0.0890749	−	0.0324206i
$448$	−4.73783	+	8.20616i	−0.223841	+	0.387704i
$449$	−9.42009	−	16.3161i	−0.444562	−	0.770003i	0.553460	−	0.832876i	$-0.313307\pi$
$449$	−9.42009	−	16.3161i	−0.444562	−	0.770003i	−0.998022	+	0.0628725i	$0.979974\pi$
$450$		0			0
$451$	−11.7344	−	9.84635i	−0.552552	−	0.463646i
$452$	6.93242	−	5.81699i	0.326074	−	0.273608i
$453$	1.34864	−	7.64852i	0.0633647	−	0.359359i
$454$	11.3391	−	4.12711i	0.532172	−	0.193695i
$455$		0			0
$456$	6.36665	−	1.66620i	0.298146	−	0.0780270i
$457$	−14.2790			−0.667943			−0.333972	−	0.942583i	$-0.608389\pi$
$457$	−14.2790			−0.667943			−0.333972	+	0.942583i	$0.608389\pi$
$458$	7.77941	−	2.83147i	0.363508	−	0.132306i
$459$	−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	$0.827367\pi$
$462$	0.520945	+	2.95442i	0.0242365	+	0.137452i
$463$	−0.881445	−	1.52671i	−0.0409642	−	0.0709521i	0.844816	−	0.535056i	$-0.179710\pi$
$463$	−0.881445	−	1.52671i	−0.0409642	−	0.0709521i	−0.885781	+	0.464104i	$0.846376\pi$
$464$	−0.0726338	+	0.125805i	−0.00337194	+	0.00584037i
$465$		0			0
$466$	19.9859	+	7.27428i	0.925830	+	0.336974i
$467$	11.0209	−	19.0888i	0.509988	−	0.883326i	−0.489945	−	0.871754i	$-0.662983\pi$
$467$	11.0209	−	19.0888i	0.509988	−	0.883326i	0.999933	−	0.0115724i	$-0.00368368\pi$
$468$	−8.81655	−	15.2707i	−0.407545	−	0.705889i
$469$	−4.63816	−	26.3043i	−0.214170	−	1.21462i
$470$		0			0
$471$	−4.22874	+	3.54834i	−0.194850	+	0.163499i
$472$	−5.30113	+	30.0642i	−0.244004	+	1.38382i
$473$	15.3897	−	5.60138i	0.707617	−	0.257552i
$474$	−3.25814			−0.149651
$475$		0			0
$476$	3.81016			0.174638
$477$	15.5890	−	5.67393i	0.713771	−	0.259791i
$478$	3.56196	−	20.2009i	0.162920	−	0.923966i
$479$	−19.5012	+	16.3634i	−0.891032	+	0.747664i	−0.968417	−	0.249337i	$-0.919787\pi$
$479$	−19.5012	+	16.3634i	−0.891032	+	0.747664i	0.0773851	+	0.997001i	$0.475343\pi$
$480$		0			0
$481$	0.769448	+	4.36376i	0.0350838	+	0.198970i
$482$	0.130882	+	0.226694i	0.00596150	+	0.0103256i
$483$	−0.879385	+	1.52314i	−0.0400134	+	0.0693053i
$484$	0.735604	+	0.267738i	0.0334366	+	0.0121699i
$485$		0			0
$486$	−5.54071	+	9.59679i	−0.251332	+	0.435319i
$487$	−11.2554	−	19.4949i	−0.510029	−	0.883397i	−0.999932	−	0.0116199i	$-0.996301\pi$
$487$	−11.2554	−	19.4949i	−0.510029	−	0.883397i	0.489903	−	0.871777i	$-0.337032\pi$
$488$	2.16267	+	12.2651i	0.0978993	+	0.555214i
$489$	−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	$-0.0592071\pi$
$492$	2.75402	−	1.00238i	0.124161	−	0.0451909i
$493$	5.73143			0.258131
$494$	−20.1928	−	1.88538i	−0.908519	−	0.0848274i
$495$		0			0
$496$	0.0765042	−	0.0278452i	0.00343514	−	0.00125029i
$497$	−4.49020	+	25.4652i	−0.201413	+	1.14227i
$498$	−0.900578	+	0.755675i	−0.0403559	+	0.0338626i
$499$	−21.9217	−	18.3945i	−0.981352	−	0.823452i	0.00294090	−	0.999996i	$-0.499064\pi$
$499$	−21.9217	−	18.3945i	−0.981352	−	0.823452i	−0.984293	+	0.176544i	$0.943508\pi$
$500$		0			0
$501$	6.18732	+	10.7168i	0.276429	+	0.478789i
$502$	−7.12196	+	12.3356i	−0.317869	+	0.550565i
$503$	−23.5351	−	8.56607i	−1.04938	−	0.381942i	−0.240950	−	0.970538i	$-0.577459\pi$
$503$	−23.5351	−	8.56607i	−1.04938	−	0.381942i	−0.808428	+	0.588595i	$0.799681\pi$
$504$	13.6147	+	4.95534i	0.606446	+	0.220728i
$505$		0			0
$506$	−2.63816	−	4.56942i	−0.117280	−	0.203135i
$507$	−1.38532	−	7.85651i	−0.0615240	−	0.348920i
$508$	−0.0949225	−	0.0796494i	−0.00421150	−	0.00353387i
$509$	25.6787	−	21.5470i	1.13819	−	0.955053i	0.138810	−	0.990319i	$-0.455672\pi$
$509$	25.6787	−	21.5470i	1.13819	−	0.955053i	0.999378	+	0.0352655i	$0.0112277\pi$
$510$		0			0
$511$	−13.2763	+	4.83218i	−0.587309	+	0.213763i
$512$	0.473897			0.0209435
$513$	−5.53343	−	12.0495i	−0.244307	−	0.531997i
$514$	13.5030			0.595591
$515$		0			0
$516$	−0.544111	+	3.08580i	−0.0239531	+	0.135845i
$517$	−1.87346	+	1.57202i	−0.0823945	+	0.0691372i
$518$	−1.06031	−	0.889704i	−0.0465872	−	0.0390913i
$519$	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	$-0.0389323\pi$
$522$	7.78581	+	2.83380i	0.340776	+	0.124032i
$523$	−9.73277	−	3.54244i	−0.425584	−	0.154900i	0.120343	−	0.992732i	$-0.461600\pi$
$523$	−9.73277	−	3.54244i	−0.425584	−	0.154900i	−0.545928	+	0.837832i	$0.683823\pi$
$524$	−1.86262	+	3.22615i	−0.0813687	+	0.140935i
$525$		0			0
$526$	1.47255	+	8.35126i	0.0642064	+	0.364132i
$527$	−2.46064	−	2.06472i	−0.107187	−	0.0899406i
$528$	0.0582480	−	0.0488759i	0.00253492	−	0.00212705i
$529$	−3.45677	+	19.6043i	−0.150294	+	0.852361i
$530$		0			0
$531$	29.2303			1.26849
$532$	−8.26517	+	5.71578i	−0.358340	+	0.247811i
$533$	−23.7570			−1.02903
$534$	1.00387	−	0.365379i	0.0434417	−	0.0158115i
$535$		0			0
$536$	−30.8922	+	25.9216i	−1.33434	+	1.11964i
$537$	8.68938	+	7.29125i	0.374974	+	0.314641i
$538$	2.79127	+	15.8301i	0.120340	+	0.682483i
$539$	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	$0.628393\pi$
$542$	15.6710	+	5.70378i	0.673128	+	0.244998i
$543$	−4.28312	+	7.41858i	−0.183806	+	0.318362i
$544$	−4.65910	−	8.06980i	−0.199757	−	0.345990i
$545$		0			0
$546$	3.56418	+	2.99070i	0.152533	+	0.127990i
$547$	−5.87939	+	4.93339i	−0.251384	+	0.210937i	−0.759768	−	0.650194i	$-0.774688\pi$
$547$	−5.87939	+	4.93339i	−0.251384	+	0.210937i	0.508384	+	0.861131i	$0.330243\pi$
$548$	4.16220	−	23.6050i	0.177800	−	1.00836i
$549$	11.2057	−	4.07855i	0.478249	−	0.174068i
$550$		0			0
$551$	−12.4329	+	8.59797i	−0.529659	+	0.366286i
$552$	2.65539			0.113021
$553$	12.2973	−	4.47584i	0.522933	−	0.190332i
$554$	2.10179	−	11.9198i	0.0892963	−	0.506425i
$555$		0			0
$556$	−14.4684	−	12.1404i	−0.613596	−	0.514868i
$557$	−0.565360	−	3.20631i	−0.0239551	−	0.135856i	0.970485	−	0.241163i	$-0.0775287\pi$
$557$	−0.565360	−	3.20631i	−0.0239551	−	0.135856i	−0.994440	+	0.105307i	$0.966418\pi$
$558$	−2.32177	−	4.02142i	−0.0982882	−	0.170240i
$559$	12.6998	−	21.9967i	0.537145	−	0.930362i
$560$		0			0
$561$	−2.81908	−	1.02606i	−0.119022	−	0.0433203i
$562$	5.76486	−	9.98503i	0.243176	−	0.421193i
$563$	2.62954	+	4.55449i	0.110822	+	0.191949i	0.916102	−	0.400946i	$-0.131318\pi$
$563$	2.62954	+	4.55449i	0.110822	+	0.191949i	−0.805280	+	0.592895i	$0.797985\pi$
$564$	−0.0812519	−	0.460802i	−0.00342132	−	0.0194033i
$565$		0			0
$566$	−11.7062	+	9.82267i	−0.492048	+	0.412878i
$567$	2.13176	−	12.0898i	0.0895255	−	0.507724i
$568$	36.6860	−	13.3526i	1.53931	−	0.560264i
$569$	−29.9564			−1.25584			−0.627918	−	0.778280i	$-0.716093\pi$
$569$	−29.9564			−1.25584			−0.627918	+	0.778280i	$0.716093\pi$
$570$		0			0
$571$	−16.7101			−0.699295			−0.349647	−	0.936881i	$-0.613699\pi$
$571$	−16.7101			−0.699295			−0.349647	+	0.936881i	$0.613699\pi$
$572$	20.8059	−	7.57272i	0.869937	−	0.316631i
$573$	−1.75078	+	9.92917i	−0.0731399	+	0.414797i
$574$	5.68479	−	4.77011i	0.237279	−	0.199100i
$575$		0			0
$576$	−2.37867	−	13.4901i	−0.0991113	−	0.562088i
$577$	−6.84002	−	11.8473i	−0.284754	−	0.493208i	0.687796	−	0.725904i	$-0.258579\pi$
$577$	−6.84002	−	11.8473i	−0.284754	−	0.493208i	−0.972549	+	0.232696i	$0.925245\pi$
$578$	−6.27379	+	10.8665i	−0.260955	+	0.451987i
$579$	−6.45084	−	2.34791i	−0.268088	−	0.0975759i
$580$		0			0
$581$	2.36097	−	4.08931i	0.0979494	−	0.169653i
$582$	−0.426489	−	0.738700i	−0.0176785	−	0.0306201i
$583$	3.61721	+	20.5142i	0.149810	+	0.849612i
$584$	16.3405	+	13.7113i	0.676174	+	0.567378i
$585$		0			0
$586$	2.38279	−	13.5135i	0.0984321	−	0.558236i
$587$	−22.5872	+	8.22108i	−0.932275	+	0.339320i	−0.763111	−	0.646268i	$-0.776329\pi$
$587$	−22.5872	+	8.22108i	−0.932275	+	0.339320i	−0.169164	+	0.985588i	$0.554107\pi$
$588$	−2.26352			−0.0933459
$589$	8.43511	+	0.787576i	0.347563	+	0.0324515i
$590$		0			0
$591$	11.6001	−	4.22210i	0.477166	−	0.173674i
$592$	−0.00609191	+	0.0345490i	−0.000250376	+	0.00141995i
$593$	3.24897	−	2.72621i	0.133419	−	0.111952i	−0.573636	−	0.819110i	$-0.694468\pi$
$593$	3.24897	−	2.72621i	0.133419	−	0.111952i	0.707055	+	0.707158i	$0.250023\pi$
$594$	−6.99067	−	5.86587i	−0.286831	−	0.240679i
$595$		0			0
$596$	−2.31016	−	4.00131i	−0.0946276	−	0.163900i
$597$	2.45336	−	4.24935i	0.100409	−	0.173914i
$598$	−7.68954	−	2.79876i	−0.314449	−	0.114450i
$599$	24.6894	+	8.98622i	1.00878	+	0.367167i	0.792965	−	0.609267i	$-0.208536\pi$
$599$	24.6894	+	8.98622i	1.00878	+	0.367167i	0.215818	+	0.976434i	$0.430758\pi$
$600$		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	$0.502864\pi$
$602$	1.37774	+	7.81353i	0.0561523	+	0.318456i
$603$	29.5790	+	24.8198i	1.20455	+	1.01074i
$604$	13.7160	−	11.5091i	0.558096	−	0.468298i
$605$		0			0
$606$	3.48293	−	1.26768i	0.141484	−	0.0514960i
$607$	22.0969			0.896885			0.448443	−	0.893812i	$-0.351979\pi$
$607$	22.0969			0.896885			0.448443	+	0.893812i	$0.351979\pi$
$608$	22.2126	+	10.5161i	0.900840	+	0.426483i
$609$	3.46791			0.140527
$610$		0			0
$611$	−0.658633	+	3.73530i	−0.0266455	+	0.151114i
$612$	−4.21941	+	3.54050i	−0.170559	+	0.143116i
$613$	−5.49794	−	4.61332i	−0.222060	−	0.186330i	0.524970	−	0.851121i	$-0.324076\pi$
$613$	−5.49794	−	4.61332i	−0.222060	−	0.186330i	−0.747030	+	0.664790i	$0.768521\pi$
$614$	3.28622	+	18.6371i	0.132621	+	0.752131i
$615$		0			0
$616$	−9.09627	+	15.7552i	−0.366499	+	0.634795i
$617$	−46.3953	−	16.8865i	−1.86781	−	0.679826i	−0.971811	−	0.235761i	$-0.924242\pi$
$617$	−46.3953	−	16.8865i	−1.86781	−	0.679826i	−0.895995	−	0.444065i	$-0.853536\pi$
$618$	−0.00639661	−	0.00232818i	−0.000257310	−	9.36530e-5i
$619$	−13.2490	+	22.9479i	−0.532521	+	0.922354i	0.466758	+	0.884385i	$0.345422\pi$
$619$	−13.2490	+	22.9479i	−0.532521	+	0.922354i	−0.999279	+	0.0379684i	$0.987911\pi$
$620$		0			0
$621$	−0.929015	−	5.26871i	−0.0372801	−	0.211426i
$622$	−9.76470	−	8.19356i	−0.391529	−	0.328532i
$623$	−3.28699	+	2.75811i	−0.131690	+	0.110501i
$624$	0.0204777	−	0.116135i	0.000819764	−	0.00464911i
$625$		0			0
$626$	17.1643			0.686022
$627$	7.65451	−	2.00324i	0.305692	−	0.0800019i
$628$	−12.7264			−0.507838
$629$	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	$0.0469579\pi$
$632$	−15.1355	−	12.7002i	−0.602057	−	0.505185i
$633$	−1.35117	−	7.66285i	−0.0537041	−	0.304571i
$634$	−12.4641	−	21.5884i	−0.495013	−	0.857387i
$635$		0			0
$636$	−3.74510	−	1.36310i	−0.148503	−	0.0540506i
$637$	17.2417	+	6.27546i	0.683141	+	0.248643i
$638$	−5.20187	+	9.00990i	−0.205944	+	0.356705i
$639$	−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	$0.723078\pi$
$642$	1.27403	−	1.06904i	0.0502821	−	0.0421917i
$643$	−8.36602	+	47.4461i	−0.329924	+	1.87109i	0.142613	+	0.989779i	$0.454450\pi$
$643$	−8.36602	+	47.4461i	−0.329924	+	1.87109i	−0.472536	+	0.881311i	$0.656661\pi$
$644$	−3.81016	+	1.38678i	−0.150141	+	0.0546469i
$645$		0			0
$646$	0.515319	+	6.31407i	0.0202750	+	0.248424i
$647$	36.9718			1.45351			0.726756	−	0.686895i	$-0.241027\pi$
$647$	36.9718			1.45351			0.726756	+	0.686895i	$0.241027\pi$
$648$	−17.4170	+	6.33927i	−0.684204	+	0.249030i
$649$	−6.37346	+	36.1457i	−0.250180	+	1.41884i
$650$		0			0
$651$	−1.48886	−	1.24930i	−0.0583529	−	0.0489639i
$652$	−0.430770	−	2.44302i	−0.0168702	−	0.0956759i
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	0.999456	+	0.0329874i	$0.0105021\pi$
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	−0.471160	+	0.882048i	$0.656165\pi$
$654$	−1.72416	+	2.98632i	−0.0674198	+	0.116775i
$655$		0			0
$656$	−0.176747	−	0.0643307i	−0.00690081	−	0.00251169i
$657$	10.2121	−	17.6879i	0.398413	−	0.690072i
$658$	−0.592396	−	1.02606i	−0.0230940	−	0.0400000i
$659$	3.27760	+	18.5882i	0.127677	+	0.724093i	0.979682	+	0.200559i	$0.0642757\pi$
$659$	3.27760	+	18.5882i	0.127677	+	0.724093i	−0.852005	+	0.523534i	$0.824613\pi$
$660$		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	$0.480756\pi$
$662$	0.261135	−	1.48097i	0.0101493	−	0.0575594i
$663$	−4.37211	+	1.59132i	−0.169799	+	0.0618017i
$664$	−7.12918			−0.276666
$665$		0			0
$666$	2.00093			0.0775346
$667$	−5.73143	+	2.08607i	−0.221922	+	0.0807729i
$668$	−4.95394	+	28.0952i	−0.191674	+	1.08703i
$669$	−1.22874	+	1.03104i	−0.0475059	+	0.0398622i
$670$		0			0
$671$	2.60014	+	14.7461i	0.100377	+	0.569267i
$672$	−2.81908	−	4.88279i	−0.108748	−	0.188358i
$673$	5.95471	−	10.3139i	0.229537	−	0.397570i	−0.728134	−	0.685435i	$-0.759612\pi$
$673$	5.95471	−	10.3139i	0.229537	−	0.397570i	0.957671	+	0.287865i	$0.0929454\pi$
$674$	−21.0214	−	7.65117i	−0.809715	−	0.294712i
$675$		0			0
$676$	9.19594	−	15.9278i	0.353690	−	0.612609i
$677$	2.89053	+	5.00654i	0.111092	+	0.192417i	0.916211	−	0.400696i	$-0.131232\pi$
$677$	2.89053	+	5.00654i	0.111092	+	0.192417i	−0.805119	+	0.593114i	$0.797898\pi$
$678$	−0.599422	−	3.39949i	−0.0230207	−	0.130557i
$679$	2.62449	+	2.20220i	0.100718	+	0.0845129i
$680$		0			0
$681$	−1.26786	+	7.19037i	−0.0485843	+	0.275535i
$682$	5.47906	−	1.99421i	0.209804	−	0.0763624i
$683$	−21.0496			−0.805442			−0.402721	−	0.915323i	$-0.631935\pi$
$683$	−21.0496			−0.805442			−0.402721	+	0.915323i	$0.631935\pi$
$684$	3.84167	−	14.0099i	0.146890	−	0.535684i
$685$		0			0
$686$	−16.2570	+	5.91707i	−0.620696	+	0.225915i
$687$	−0.869833	+	4.93307i	−0.0331862	+	0.188208i
$688$	0.154048	−	0.129261i	0.00587302	−	0.00492805i
$689$	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	$0.617818\pi$
$692$	−0.549935	+	0.952515i	−0.0209054	+	0.0362092i
$693$	16.3687	+	5.95772i	0.621796	+	0.226315i
$694$	−6.36484	−	2.31661i	−0.241606	−	0.0879374i
$695$		0			0
$696$	−2.61793	−	4.53438i	−0.0992322	−	0.171875i
$697$	1.28864	+	7.30823i	0.0488106	+	0.276819i
$698$	−15.3302	−	12.8636i	−0.580257	−	0.486894i
$699$	−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	$0.521036\pi$
$702$	−14.1530			−0.534171
$703$	−2.11128	+	2.97810i	−0.0796285	+	0.112321i
$704$	17.2003			0.648260
$705$		0			0
$706$	−1.74779	+	9.91220i	−0.0657789	+	0.373051i
$707$	−11.4042	+	9.56926i	−0.428899	+	0.359889i
$708$	−5.37939	−	4.51384i	−0.202170	−	0.169641i
$709$	−2.73854	−	15.5310i	−0.102848	−	0.583280i	−0.992058	−	0.125781i	$-0.959856\pi$
$709$	−2.73854	−	15.5310i	−0.102848	−	0.583280i	0.889210	−	0.457499i	$-0.151255\pi$
$710$		0			0
$711$	−9.45904	+	16.3835i	−0.354742	+	0.614431i
$712$	6.08765	+	2.21572i	0.228144	+	0.0830377i
$713$	3.21213	+	1.16912i	0.120295	+	0.0437839i
$714$	0.726682	−	1.25865i	0.0271954	−	0.0471038i
$715$		0			0
$716$	4.54101	+	25.7534i	0.169706	+	0.962448i
$717$	9.50774	+	7.97794i	0.355073	+	0.297942i
$718$	−6.99525	+	5.86971i	−0.261060	+	0.219056i
$719$	−6.13470	+	34.7916i	−0.228786	+	1.29751i	0.626529	+	0.779398i	$0.284475\pi$
$719$	−6.13470	+	34.7916i	−0.228786	+	1.29751i	−0.855314	+	0.518109i	$0.826636\pi$
$720$		0			0
$721$	0.0273411			0.00101824
$722$	−10.5899	−	12.9237i	−0.394114	−	0.480971i
$723$	−0.158385			−0.00589040
$724$	−18.5577	+	6.75444i	−0.689691	+	0.251027i
$725$		0			0
$726$	0.228741	−	0.191936i	0.00848937	−	0.00712343i
$727$	−30.9647	−	25.9825i	−1.14842	−	0.963637i	−0.148737	−	0.988877i	$-0.547521\pi$
$727$	−30.9647	−	25.9825i	−1.14842	−	0.963637i	−0.999681	+	0.0252396i	$0.991965\pi$
$728$	4.89945	+	27.7862i	0.181586	+	1.02982i
$729$	6.44562	+	11.1641i	0.238727	+	0.413487i
$730$		0			0
$731$	−7.45558	−	2.71361i	−0.275755	−	0.100367i
$732$	−2.69207	−	0.979832i	−0.0995016	−	0.0362156i
$733$	−18.1382	+	31.4162i	−0.669948	+	1.16038i	0.307970	+	0.951396i	$0.400350\pi$
$733$	−18.1382	+	31.4162i	−0.669948	+	1.16038i	−0.977918	+	0.208988i	$0.932983\pi$
$734$	14.3045	+	24.7762i	0.527990	+	0.914505i
$735$		0			0
$736$	7.59627	+	6.37402i	0.280002	+	0.234950i
$737$	−37.1411	+	31.1651i	−1.36811	+	1.14798i
$738$	−1.86288	+	10.5649i	−0.0685737	+	0.388901i
$739$	19.4290	−	7.07158i	0.714708	−	0.260132i	0.0410304	−	0.999158i	$-0.486936\pi$
$739$	19.4290	−	7.07158i	0.714708	−	0.260132i	0.673677	+	0.739026i	$0.264714\pi$
$740$		0			0
$741$	7.09698	−	10.0108i	0.260714	−	0.367754i
$742$	−10.0915			−0.370471
$743$	6.29978	−	2.29293i	0.231117	−	0.0841196i	−0.223866	−	0.974620i	$-0.571868\pi$
$743$	6.29978	−	2.29293i	0.231117	−	0.0841196i	0.454982	+	0.890500i	$0.349646\pi$
$744$	−0.509552	+	2.88981i	−0.0186811	+	0.105946i
$745$		0			0
$746$	20.5367	+	17.2323i	0.751901	+	0.630920i
$747$	1.18535	+	6.72243i	0.0433695	+	0.245961i
$748$	−3.45811	−	5.98962i	−0.126441	−	0.219002i
$749$	−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	$0.673698\pi$
$752$	−0.0150147	+	0.0260063i	−0.000547531	+	0.000948352i
$753$	−4.30928	−	7.46389i	−0.157039	−	0.271999i
$754$	2.80184	+	15.8900i	0.102037	+	0.578681i
$755$		0			0
$756$	−5.37211	+	4.50774i	−0.195382	+	0.163945i
$757$	0.705432	−	4.00071i	0.0256394	−	0.145408i	−0.969301	−	0.245878i	$-0.920924\pi$
$757$	0.705432	−	4.00071i	0.0256394	−	0.145408i	0.994940	+	0.100470i	$0.0320347\pi$
$758$	14.7585	−	5.37164i	0.536052	−	0.195107i
$759$	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	$0.563937\pi$
$762$	−0.0444153	+	0.0161658i	−0.00160900	+	0.000585627i
$763$	2.40508	−	13.6399i	0.0870697	−	0.493797i
$764$	−17.8059	+	14.9409i	−0.644194	+	0.540543i
$765$		0			0
$766$	−3.58182	−	20.3135i	−0.129417	−	0.733958i
$767$	28.4616	+	49.2969i	1.02769	+	1.78001i
$768$	−4.28359	+	7.41939i	−0.154571	+	0.267724i
$769$	−20.0599	−	7.30121i	−0.723378	−	0.263288i	−0.0460191	−	0.998941i	$-0.514654\pi$
$769$	−20.0599	−	7.30121i	−0.723378	−	0.263288i	−0.677359	+	0.735652i	$0.736876\pi$
$770$		0			0
$771$	−4.08512	+	7.07564i	−0.147122	+	0.254823i
$772$	−7.91312	−	13.7059i	−0.284800	−	0.493287i
$773$	−3.11128	−	17.6450i	−0.111905	−	0.634645i	−0.988236	−	0.152936i	$-0.951127\pi$
$773$	−3.11128	−	17.6450i	−0.111905	−	0.634645i	0.876331	−	0.481709i	$-0.159984\pi$
$774$	−8.78627	−	7.37256i	−0.315816	−	0.265001i
$775$		0			0
$776$	0.898214	−	5.09403i	0.0322440	−	0.182865i
$777$	0.786989	−	0.286441i	0.0282331	−	0.0102760i
$778$	−3.43788			−0.123254
$779$	−13.7588	−	13.9202i	−0.492959	−	0.498743i
$780$		0			0
$781$	44.1070	−	16.0536i	1.57827	−	0.574444i
$782$	−0.443868	+	2.51730i	−0.0158727	+	0.0900184i
$783$	−8.08100	+	6.78077i	−0.288792	+	0.242325i
$784$	0.111281	+	0.0933762i	0.00397434	+	0.00333486i
$785$		0			0
$786$	0.710485	+	1.23060i	0.0253422	+	0.0438939i
$787$	24.4158	−	42.2894i	0.870330	−	1.50746i	0.00867371	−	0.999962i	$-0.497239\pi$
$787$	24.4158	−	42.2894i	0.870330	−	1.50746i	0.861656	−	0.507493i	$-0.169428\pi$
$788$	26.7430	+	9.73367i	0.952681	+	0.346748i
$789$	−4.82160	−	1.75492i	−0.171654	−	0.0624768i
$790$		0			0
$791$	6.93242	+	12.0073i	0.246488	+	0.426930i
$792$	−4.56687	−	25.9000i	−0.162277	−	0.920316i
$793$	17.7895	+	14.9272i	0.631724	+	0.530080i
$794$	6.03524	−	5.06417i	0.214183	−	0.179721i
$795$		0			0
$796$	10.6298	−	3.86893i	0.376763	−	0.137131i
$797$	28.5262			1.01045			0.505225	−	0.862988i	$-0.331409\pi$
$797$	28.5262			1.01045			0.505225	+	0.862988i	$0.331409\pi$
$798$	0.311804	+	3.82045i	0.0110377	+	0.135242i
$799$	1.18479			0.0419149
$800$		0			0
$801$	1.07713	−	6.10873i	0.0380586	−	0.215841i
$802$	1.36571	−	1.14597i	0.0482251	−	0.0404656i
$803$	19.6459	+	16.4849i	0.693289	+	0.581738i
$804$	−1.61081	−	9.13538i	−0.0568091	−	0.322180i
$805$		0			0
$806$	4.52141	−	7.83131i	0.159260	−	0.275846i
$807$	−9.13950	−	3.32651i	−0.321726	−	0.117099i
$808$	21.1211	+	7.68745i	0.743037	+	0.270443i
$809$	7.41834	−	12.8489i	0.260815	−	0.451745i	−0.705644	−	0.708567i	$-0.749342\pi$
$809$	7.41834	−	12.8489i	0.260815	−	0.451745i	0.966459	+	0.256822i	$0.0826755\pi$
$810$		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	$0.991433\pi$
$812$	6.12449	+	5.13905i	0.214927	+	0.180345i
$813$	−7.72984	+	6.48610i	−0.271097	+	0.227478i
$814$	−0.436289	+	2.47432i	−0.0152919	+	0.0867248i
$815$		0			0
$816$	−0.0368366			−0.00128954
$817$	20.2438	−	5.29796i	0.708241	−	0.185352i
$818$	28.3233			0.990299
$819$	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	$0.242831\pi$
$822$	−7.00387	−	5.87695i	−0.244288	−	0.204982i
$823$	−1.91472	−	10.8589i	−0.0667428	−	0.378517i	−0.999822	−	0.0188472i	$-0.994000\pi$
$823$	−1.91472	−	10.8589i	−0.0667428	−	0.378517i	0.933080	−	0.359670i	$-0.117111\pi$
$824$	−0.0206398	−	0.0357492i	−0.000719023	−	0.00124538i
$825$		0			0
$826$	−16.7087	−	6.08148i	−0.581371	−	0.211602i
$827$	31.8892	+	11.6067i	1.10890	+	0.403606i	0.830589	−	0.556886i	$-0.188004\pi$
$827$	31.8892	+	11.6067i	1.10890	+	0.403606i	0.278309	+	0.960492i	$0.410226\pi$
$828$	2.93077	−	5.07624i	0.101851	−	0.176412i
$829$	10.1834	+	17.6382i	0.353686	+	0.612602i	0.986892	−	0.161381i	$-0.0515949\pi$
$829$	10.1834	+	17.6382i	0.353686	+	0.612602i	−0.633206	+	0.773983i	$0.718262\pi$
$830$		0			0
$831$	5.61019	+	4.70750i	0.194615	+	0.163302i
$832$	20.4349	−	17.1470i	0.708454	−	0.594464i
$833$	0.995252	−	5.64436i	0.0344834	−	0.195565i
$834$	−6.76991	+	2.46405i	−0.234423	+	0.0853230i
$835$		0			0
$836$	16.4868	+	7.80531i	0.570208	+	0.269952i
$837$	5.91210			0.204352
$838$	−19.2126	+	6.99281i	−0.663688	+	0.241563i
$839$	2.74526	−	15.5692i	0.0947770	−	0.537507i	−0.900038	−	0.435810i	$-0.856462\pi$
$839$	2.74526	−	15.5692i	0.0947770	−	0.537507i	0.994815	−	0.101697i	$-0.0324271\pi$
$840$		0			0
$841$	−13.0025	−	10.9104i	−0.448363	−	0.376221i
$842$	−0.985452	−	5.58878i	−0.0339609	−	0.192602i
$843$	3.48814	+	6.04164i	0.120138	+	0.208085i
$844$	8.96926	−	15.5352i	0.308734	−	0.534744i
$845$		0			0
$846$	1.60947	+	0.585799i	0.0553347	+	0.0201402i
$847$	−0.599670	+	1.03866i	−0.0206049	+	0.0356888i
$848$	0.127889	+	0.221510i	0.00439172	+	0.00760668i
$849$	−1.60560	−	9.10581i	−0.0551040	−	0.312511i
$850$		0			0
$851$	−1.12836	+	0.946803i	−0.0386795	+	0.0324560i
$852$	−1.55943	+	8.84397i	−0.0534252	+	0.302989i
$853$	−49.4741	+	18.0071i	−1.69396	+	0.616551i	−0.995115	−	0.0987227i	$-0.968524\pi$
$853$	−49.4741	+	18.0071i	−1.69396	+	0.616551i	−0.698845	+	0.715274i	$0.746302\pi$
$854$	−7.25402			−0.248228
$855$		0			0
$856$	10.0855			0.344716
$857$	−21.6386	+	7.87581i	−0.739161	+	0.269033i	−0.684038	−	0.729447i	$-0.739778\pi$
$857$	−21.6386	+	7.87581i	−0.739161	+	0.269033i	−0.0551238	+	0.998480i	$0.517555\pi$
$858$	1.46657	−	8.31731i	0.0500678	−	0.283948i
$859$	6.82501	−	5.72686i	0.232866	−	0.195398i	−0.518886	−	0.854843i	$-0.673653\pi$
$859$	6.82501	−	5.72686i	0.232866	−	0.195398i	0.751753	+	0.659445i	$0.229209\pi$
$860$		0			0
$861$	0.779715	+	4.42198i	0.0265726	+	0.150701i
$862$	−6.15451	−	10.6599i	−0.209624	−	0.363079i
$863$	14.8849	−	25.7814i	0.506688	−	0.877609i	−0.493282	−	0.869869i	$-0.664203\pi$
$863$	14.8849	−	25.7814i	0.506688	−	0.877609i	0.999970	−	0.00773998i	$-0.00246374\pi$
$864$	16.1163	+	5.86587i	0.548289	+	0.199561i
$865$		0			0
$866$	12.6160	−	21.8516i	0.428710	−	0.742548i
$867$	−3.79607	−	6.57499i	−0.128921	−	0.223298i
$868$	−0.778066	−	4.41263i	−0.0264093	−	0.149775i
$869$	−18.1971	−	15.2692i	−0.617295	−	0.517972i
$870$		0			0
$871$	−13.0574	+	74.0520i	−0.442432	+	2.50916i
$872$	−19.6501	+	7.15204i	−0.665435	+	0.242199i
$873$	−4.95273			−0.167625
$874$	−2.81345	−	6.12651i	−0.0951665	−	0.207232i
$875$		0			0
$876$	−4.61081	+	1.67820i	−0.155785	+	0.0567011i
$877$	4.34642	−	24.6498i	0.146768	−	0.832363i	−0.819162	−	0.573562i	$-0.805561\pi$
$877$	4.34642	−	24.6498i	0.146768	−	0.832363i	0.965930	−	0.258802i	$-0.0833276\pi$
$878$	8.98798	−	7.54181i	0.303330	−	0.254524i
$879$	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	$0.944973\pi$
$882$	4.14274	−	7.17544i	0.139493	−	0.241610i
$883$	−9.98710	−	3.63501i	−0.336093	−	0.122328i	0.168460	−	0.985708i	$-0.446120\pi$
$883$	−9.98710	−	3.63501i	−0.336093	−	0.122328i	−0.504553	+	0.863381i	$0.668343\pi$
$884$	−10.0795	−	3.66864i	−0.339010	−	0.123390i
$885$		0			0
$886$	−14.8981	−	25.8043i	−0.500512	−	0.866912i
$887$	9.78312	+	55.4828i	0.328485	+	1.86293i	0.483959	+	0.875091i	$0.339198\pi$
$887$	9.78312	+	55.4828i	0.328485	+	1.86293i	−0.155474	+	0.987840i	$0.549690\pi$
$888$	−0.968626	−	0.812774i	−0.0325050	−	0.0272749i
$889$	0.145430	−	0.122030i	0.00487756	−	0.00409275i
$890$		0			0
$891$	−20.9402	+	7.62159i	−0.701522	+	0.255333i
$892$	−3.69789			−0.123815
$893$	−2.57011	+	1.77736i	−0.0860054	+	0.0594771i
$894$	−1.76239			−0.0589432
$895$		0			0
$896$	2.23308	−	12.6644i	0.0746019	−	0.423088i
$897$	3.79292	−	3.18264i	0.126642	−	0.106265i
$898$	−12.6917	−	10.6496i	−0.423526	−	0.355381i
$899$	−1.17041	−	6.63771i	−0.0390353	−	0.221380i
$900$		0			0
$901$	5.04576	−	8.73951i	0.168099	−	0.291155i
$902$	−12.6582	−	4.60722i	−0.421473	−	0.153404i
$903$	−4.51114	−	1.64192i	−0.150121	−	0.0546398i
$904$	10.4666	−	18.1286i	0.348113	−	0.602949i
$905$		0			0
$906$	−1.18597	−	6.72600i	−0.0394014	−	0.223456i
$907$	4.53777	+	3.80764i	0.150674	+	0.126431i	0.715009	−	0.699116i	$-0.246423\pi$
$907$	4.53777	+	3.80764i	0.150674	+	0.126431i	−0.564334	+	0.825546i	$0.690867\pi$
$908$	−12.8944	+	10.8197i	−0.427916	+	0.359064i
$909$	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	$0.690821\pi$
$912$	0.0799077	−	0.0552603i	0.00264601	−	0.00182985i
$913$	−8.57129			−0.283668
$914$	−11.7995	+	4.29466i	−0.390292	+	0.142055i
$915$		0			0
$916$	−8.84642	+	7.42303i	−0.292294	+	0.245264i
$917$	−4.37211	−	3.66864i	−0.144380	−	0.121149i
$918$	0.767693	+	4.35381i	0.0253377	+	0.143697i
$919$	3.13697	+	5.43340i	0.103479	+	0.179231i	0.913116	−	0.407700i	$-0.133669\pi$
$919$	3.13697	+	5.43340i	0.103479	+	0.179231i	−0.809637	+	0.586931i	$0.800336\pi$
$920$		0			0
$921$	−10.7601	−	3.91636i	−0.354558	−	0.129048i
$922$	−11.5095	−	4.18911i	−0.379045	−	0.137961i
$923$	36.3979	−	63.0429i	1.19805	−	2.07508i
$924$	−2.09240	−	3.62414i	−0.0688348	−	0.119225i
$925$		0			0
$926$	−1.18757	−	0.996487i	−0.0390259	−	0.0327466i
$927$	−0.0302779	+	0.0254062i	−0.000994456	+	0.000834448i
$928$	3.39528	−	19.2556i	0.111455	−	0.632095i
$929$	−26.6152	+	9.68712i	−0.873215	+	0.317824i	−0.739468	−	0.673191i	$-0.764923\pi$
$929$	−26.6152	+	9.68712i	−0.873215	+	0.317824i	−0.133747	+	0.991016i	$0.542701\pi$
$930$		0			0
$931$	6.30840	+	13.7370i	0.206749	+	0.450213i
$932$	−29.6682			−0.971814
$933$	7.24763	−	2.63792i	0.237277	−	0.0863616i
$934$	3.36588	−	19.0888i	0.110135	−	0.624606i
$935$		0			0
$936$	−31.2454	−	26.2180i	−1.02129	−	0.856962i
$937$	3.48545	+	19.7670i	0.113865	+	0.645759i	0.987306	+	0.158830i	$0.0507720\pi$
$937$	3.48545	+	19.7670i	0.113865	+	0.645759i	−0.873441	+	0.486930i	$0.838117\pi$
$938$	−11.7442	−	20.3416i	−0.383462	−	0.664176i
$939$	−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	$0.639139\pi$
$942$	−2.42720	+	4.20404i	−0.0790826	+	0.136975i
$943$	−3.94862	−	6.83920i	−0.128585	−	0.222715i
$944$	0.0782589	+	0.443828i	0.00254711	+	0.0144454i
$945$		0			0
$946$	11.0326	−	9.25741i	0.358699	−	0.300984i
$947$	−1.15358	+	6.54228i	−0.0374863	+	0.212596i	−0.997797	−	0.0663359i	$-0.978869\pi$
$947$	−1.15358	+	6.54228i	−0.0374863	+	0.212596i	0.960311	+	0.278931i	$0.0899802\pi$
$948$	4.27079	−	1.55444i	0.138709	−	0.0504859i
$949$	39.7743			1.29113
$950$		0			0
$951$	15.0833			0.489109
$952$	8.28194	−	3.01438i	0.268419	−	0.0976966i
$953$	2.57414	−	14.5987i	0.0833846	−	0.472897i	−0.914309	−	0.405018i	$-0.867265\pi$
$953$	2.57414	−	14.5987i	0.0833846	−	0.472897i	0.997693	−	0.0678799i	$-0.0216235\pi$
$954$	11.1755	−	9.37732i	0.361819	−	0.303602i
$955$		0			0
$956$	4.96868	+	28.1788i	0.160699	+	0.911368i
$957$	−3.14749	−	5.45161i	−0.101744	−	0.176226i
$958$	−11.1932	+	19.3873i	−0.361637	+	0.626374i
$959$	34.5082	+	12.5600i	1.11433	+	0.405582i
$960$		0			0
$961$	13.6113	−	23.5754i	0.439074	−	0.760498i
$962$	1.94831	+	3.37457i	0.0628161	+	0.108801i
$963$	−1.67689	−	9.51011i	−0.0540370	−	0.306459i
$964$	−0.279715	−	0.234709i	−0.00900901	−	0.00755946i
$965$		0			0
$966$	−0.268571	+	1.52314i	−0.00864112	+	0.0490062i
$967$	19.9418	−	7.25822i	0.641285	−	0.233409i	−0.000850519	−	1.00000i	$-0.500271\pi$
$967$	19.9418	−	7.25822i	0.641285	−	0.233409i	0.642136	+	0.766591i	$0.278049\pi$
$968$	1.81076			0.0582002
$969$	−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	$0.182690\pi$
$972$	2.68422	−	15.2230i	0.0860964	−	0.488277i
$973$	22.1668	−	18.6002i	0.710636	−	0.596295i
$974$	−15.1643	−	12.7244i	−0.485896	−	0.407715i
$975$		0			0
$976$	0.0919294	+	0.159226i	0.00294259	+	0.00509671i
$977$	−23.0107	+	39.8558i	−0.736179	+	1.27510i	0.218026	+	0.975943i	$0.430038\pi$
$977$	−23.0107	+	39.8558i	−0.736179	+	1.27510i	−0.954204	+	0.299156i	$0.903295\pi$
$978$	−0.889185	−	0.323637i	−0.0284330	−	0.0103488i
$979$	7.31908	+	2.66393i	0.233919	+	0.0851395i
$980$		0			0
$981$	10.0111	+	17.3398i	0.319631	+	0.553618i
$982$	−2.38737	−	13.5395i	−0.0761842	−	0.432062i
$983$	−46.4195	−	38.9506i	−1.48055	−	1.24233i	−0.905592	−	0.424150i	$-0.860573\pi$
$983$	−46.4195	−	38.9506i	−1.48055	−	1.24233i	−0.574961	−	0.818181i	$-0.694983\pi$
$984$	5.19325	−	4.35765i	0.165555	−	0.138917i
$985$		0			0
$986$	4.73618	−	1.72383i	0.150831	−	0.0548979i
$987$	0.716881			0.0228186
$988$	27.3684	−	7.16252i	0.870705	−	0.227870i
$989$	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	$-0.176213\pi$
$992$	−8.39440	+	7.04374i	−0.266522	+	0.223639i
$993$	0.697033	+	0.584880i	0.0221197	+	0.0185606i
$994$	3.94862	+	22.3937i	0.125242	+	0.710285i
$995$		0			0
$996$	0.819955	−	1.42020i	0.0259813	−	0.0450009i
$997$	31.6819	+	11.5313i	1.00337	+	0.365198i	0.790885	−	0.611965i	$-0.209621\pi$
$997$	31.6819	+	11.5313i	1.00337	+	0.365198i	0.212490	+	0.977163i	$0.431843\pi$
$998$	−23.6475	−	8.60700i	−0.748550	−	0.272450i
$999$	−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.l.a.176.1		6
5.2	odd	4		475.2.u.a.24.2		12
5.3	odd	4		475.2.u.a.24.1		12
5.4	even	2		19.2.e.a.5.1	yes	6
15.14	odd	2		171.2.u.c.100.1		6
19.2	odd	18		9025.2.a.x.1.3		3
19.4	even	9	inner	475.2.l.a.251.1		6
19.17	even	9		9025.2.a.bd.1.1		3
20.19	odd	2		304.2.u.b.81.1		6
35.4	even	6		931.2.x.a.765.1		6
35.9	even	6		931.2.v.b.214.1		6
35.19	odd	6		931.2.v.a.214.1		6
35.24	odd	6		931.2.x.b.765.1		6
35.34	odd	2		931.2.w.a.442.1		6
95.4	even	18		19.2.e.a.4.1	✓	6
95.9	even	18		361.2.e.f.234.1		6
95.14	odd	18		361.2.c.h.68.3		6
95.23	odd	36		475.2.u.a.99.2		12
95.24	even	18		361.2.c.i.68.1		6
95.29	odd	18		361.2.e.b.234.1		6
95.34	odd	18		361.2.e.h.99.1		6
95.42	odd	36		475.2.u.a.99.1		12
95.44	even	18		361.2.e.g.28.1		6
95.49	even	6		361.2.e.f.54.1		6
95.54	even	18		361.2.c.i.292.1		6
95.59	odd	18		361.2.a.h.1.1		3
95.64	even	6		361.2.e.g.245.1		6
95.69	odd	6		361.2.e.a.245.1		6
95.74	even	18		361.2.a.g.1.3		3
95.79	odd	18		361.2.c.h.292.3		6
95.84	odd	6		361.2.e.b.54.1		6
95.89	odd	18		361.2.e.a.28.1		6
95.94	odd	2		361.2.e.h.62.1		6
285.59	even	18		3249.2.a.s.1.3		3
285.74	odd	18		3249.2.a.z.1.1		3
285.194	odd	18		171.2.u.c.118.1		6
380.59	even	18		5776.2.a.bi.1.3		3
380.99	odd	18		304.2.u.b.289.1		6
380.359	odd	18		5776.2.a.br.1.1		3
665.4	even	18		931.2.v.b.422.1		6
665.194	odd	18		931.2.x.b.802.1		6
665.289	even	18		931.2.x.a.802.1		6
665.384	odd	18		931.2.w.a.99.1		6
665.479	odd	18		931.2.v.a.422.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.4.1	✓	6	95.4	even	18
19.2.e.a.5.1	yes	6	5.4	even	2
171.2.u.c.100.1		6	15.14	odd	2
171.2.u.c.118.1		6	285.194	odd	18
304.2.u.b.81.1		6	20.19	odd	2
304.2.u.b.289.1		6	380.99	odd	18
361.2.a.g.1.3		3	95.74	even	18
361.2.a.h.1.1		3	95.59	odd	18
361.2.c.h.68.3		6	95.14	odd	18
361.2.c.h.292.3		6	95.79	odd	18
361.2.c.i.68.1		6	95.24	even	18
361.2.c.i.292.1		6	95.54	even	18
361.2.e.a.28.1		6	95.89	odd	18
361.2.e.a.245.1		6	95.69	odd	6
361.2.e.b.54.1		6	95.84	odd	6
361.2.e.b.234.1		6	95.29	odd	18
361.2.e.f.54.1		6	95.49	even	6
361.2.e.f.234.1		6	95.9	even	18
361.2.e.g.28.1		6	95.44	even	18
361.2.e.g.245.1		6	95.64	even	6
361.2.e.h.62.1		6	95.94	odd	2
361.2.e.h.99.1		6	95.34	odd	18
475.2.l.a.176.1		6	1.1	even	1	trivial
475.2.l.a.251.1		6	19.4	even	9	inner
475.2.u.a.24.1		12	5.3	odd	4
475.2.u.a.24.2		12	5.2	odd	4
475.2.u.a.99.1		12	95.42	odd	36
475.2.u.a.99.2		12	95.23	odd	36
931.2.v.a.214.1		6	35.19	odd	6
931.2.v.a.422.1		6	665.479	odd	18
931.2.v.b.214.1		6	35.9	even	6
931.2.v.b.422.1		6	665.4	even	18
931.2.w.a.99.1		6	665.384	odd	18
931.2.w.a.442.1		6	35.34	odd	2
931.2.x.a.765.1		6	35.4	even	6
931.2.x.a.802.1		6	665.289	even	18
931.2.x.b.765.1		6	35.24	odd	6
931.2.x.b.802.1		6	665.194	odd	18
3249.2.a.s.1.3		3	285.59	even	18
3249.2.a.z.1.1		3	285.74	odd	18
5776.2.a.bi.1.3		3	380.59	even	18
5776.2.a.br.1.1		3	380.359	odd	18
9025.2.a.x.1.3		3	19.2	odd	18
9025.2.a.bd.1.1		3	19.17	even	9

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.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.826352 - 0.300767i) q^{2} +(-0.0923963 + 0.524005i) q^{3} +(-0.939693 + 0.788496i) q^{4} +(0.0812519 + 0.460802i) q^{6} +(-0.939693 - 1.62760i) q^{7} +(-1.41875 + 2.45734i) q^{8} +(2.55303 + 0.929228i) q^{9} +O(q^{10})\)	\(q+(0.826352 - 0.300767i) q^{2} +(-0.0923963 + 0.524005i) q^{3} +(-0.939693 + 0.788496i) q^{4} +(0.0812519 + 0.460802i) q^{6} +(-0.939693 - 1.62760i) q^{7} +(-1.41875 + 2.45734i) q^{8} +(2.55303 + 0.929228i) q^{9} +(-1.70574 + 2.95442i) q^{11} +(-0.326352 - 0.565258i) q^{12} +(0.918748 + 5.21048i) q^{13} +(-1.26604 - 1.06234i) q^{14} +(-0.00727396 + 0.0412527i) q^{16} +(1.55303 - 0.565258i) q^{17} +2.38919 q^{18} +(-2.52094 + 3.55596i) q^{19} +(0.939693 - 0.342020i) q^{21} +(-0.520945 + 2.95442i) q^{22} +(-1.34730 + 1.13052i) q^{23} +(-1.15657 - 0.970481i) q^{24} +(2.32635 + 4.02936i) q^{26} +(-1.52094 + 2.63435i) q^{27} +(2.16637 + 0.788496i) q^{28} +(3.25877 + 1.18610i) q^{29} +(-0.971782 - 1.68317i) q^{31} +(-0.979055 - 5.55250i) q^{32} +(-1.39053 - 1.16679i) q^{33} +(1.11334 - 0.934204i) q^{34} +(-3.13176 + 1.13987i) q^{36} +0.837496 q^{37} +(-1.01367 + 3.69669i) q^{38} -2.81521 q^{39} +(-0.779715 + 4.42198i) q^{41} +(0.673648 - 0.565258i) q^{42} +(-3.67752 - 3.08580i) q^{43} +(-0.726682 - 4.12122i) q^{44} +(-0.773318 + 1.33943i) q^{46} +(0.673648 + 0.245188i) q^{47} +(-0.0209445 - 0.00762319i) q^{48} +(1.73396 - 3.00330i) q^{49} +(0.152704 + 0.866025i) q^{51} +(-4.97178 - 4.17182i) q^{52} +(4.67752 - 3.92490i) q^{53} +(-0.464508 + 2.63435i) q^{54} +5.33275 q^{56} +(-1.63041 - 1.64955i) q^{57} +3.04963 q^{58} +(10.1099 - 3.67972i) q^{59} +(3.36231 - 2.82131i) q^{61} +(-1.30928 - 1.09861i) q^{62} +(-0.886659 - 5.02849i) q^{63} +(-2.52094 - 4.36640i) q^{64} +(-1.50000 - 0.545955i) q^{66} +(13.3550 + 4.86084i) q^{67} +(-1.01367 + 1.75573i) q^{68} +(-0.467911 - 0.810446i) q^{69} +(-10.5398 - 8.84397i) q^{71} +(-5.90554 + 4.95534i) q^{72} +(1.30541 - 7.40333i) q^{73} +(0.692066 - 0.251892i) q^{74} +(-0.434945 - 5.32926i) q^{76} +6.41147 q^{77} +(-2.32635 + 0.846723i) q^{78} +(-1.20914 + 6.85738i) q^{79} +(5.00387 + 4.19875i) q^{81} +(0.685670 + 3.88863i) q^{82} +(1.25624 + 2.17588i) q^{83} +(-0.613341 + 1.06234i) q^{84} +(-3.96703 - 1.44388i) q^{86} +(-0.922618 + 1.59802i) q^{87} +(-4.84002 - 8.38316i) q^{88} +(-0.396459 - 2.24843i) q^{89} +(7.61721 - 6.39160i) q^{91} +(0.374638 - 2.12467i) q^{92} +(0.971782 - 0.353700i) q^{93} +0.630415 q^{94} +3.00000 q^{96} +(-1.71301 + 0.623485i) q^{97} +(0.529563 - 3.00330i) q^{98} +(-7.10014 + 5.95772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 3 q^{3} + 3 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 3 * q^3 + 3 * q^6 - 6 * q^8 + 3 * q^9	\( 6 q + 6 q^{2} + 3 q^{3} + 3 q^{6} - 6 q^{8} + 3 q^{9} - 3 q^{12} + 3 q^{13} - 3 q^{14} - 18 q^{16} - 3 q^{17} + 6 q^{18} - 12 q^{19} - 6 q^{23} + 15 q^{24} + 15 q^{26} - 6 q^{27} - 6 q^{28} - 3 q^{29} + 9 q^{31} - 9 q^{32} + 9 q^{33} - 24 q^{36} + 15 q^{38} - 24 q^{39} + 21 q^{41} + 3 q^{42} + 3 q^{43} + 9 q^{44} - 18 q^{46} + 3 q^{47} + 3 q^{48} + 15 q^{49} + 3 q^{51} - 15 q^{52} + 3 q^{53} + 30 q^{54} - 6 q^{56} - 24 q^{57} - 36 q^{58} + 12 q^{59} - 12 q^{61} + 12 q^{62} - 12 q^{63} - 12 q^{64} - 9 q^{66} + 30 q^{67} + 15 q^{68} - 12 q^{69} - 6 q^{71} + 12 q^{72} + 12 q^{73} + 15 q^{74} + 36 q^{76} + 18 q^{77} - 15 q^{78} - 39 q^{79} + 6 q^{81} + 54 q^{82} + 3 q^{84} + 24 q^{86} + 21 q^{87} - 9 q^{88} - 12 q^{89} + 15 q^{91} - 42 q^{92} - 9 q^{93} + 18 q^{94} + 18 q^{96} - 18 q^{97} + 9 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 3 * q^3 + 3 * q^6 - 6 * q^8 + 3 * q^9 - 3 * q^12 + 3 * q^13 - 3 * q^14 - 18 * q^16 - 3 * q^17 + 6 * q^18 - 12 * q^19 - 6 * q^23 + 15 * q^24 + 15 * q^26 - 6 * q^27 - 6 * q^28 - 3 * q^29 + 9 * q^31 - 9 * q^32 + 9 * q^33 - 24 * q^36 + 15 * q^38 - 24 * q^39 + 21 * q^41 + 3 * q^42 + 3 * q^43 + 9 * q^44 - 18 * q^46 + 3 * q^47 + 3 * q^48 + 15 * q^49 + 3 * q^51 - 15 * q^52 + 3 * q^53 + 30 * q^54 - 6 * q^56 - 24 * q^57 - 36 * q^58 + 12 * q^59 - 12 * q^61 + 12 * q^62 - 12 * q^63 - 12 * q^64 - 9 * q^66 + 30 * q^67 + 15 * q^68 - 12 * q^69 - 6 * q^71 + 12 * q^72 + 12 * q^73 + 15 * q^74 + 36 * q^76 + 18 * q^77 - 15 * q^78 - 39 * q^79 + 6 * q^81 + 54 * q^82 + 3 * q^84 + 24 * q^86 + 21 * q^87 - 9 * q^88 - 12 * q^89 + 15 * q^91 - 42 * q^92 - 9 * q^93 + 18 * q^94 + 18 * q^96 - 18 * q^97 + 9 * q^98 + 9 * q^99

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