LMFDB - Embedded newform 475.2.u.a.99.1

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			99.1
Root			$0.984808 - 0.173648i$ of defining polynomial
Character	$\chi$	$=$	475.99
Dual form			475.2.u.a.24.1

$q$-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 $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

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

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	−0.999458	−	0.0329100i	$-0.989523\pi$
$2$	−0.300767	+	0.826352i	−0.212675	+	0.584319i	0.786784	+	0.617229i	$0.211745\pi$
$3$	−0.524005	+	0.0923963i	−0.302535	+	0.0533450i	−0.322855	−	0.946449i	$-0.604643\pi$
$3$	−0.524005	+	0.0923963i	−0.302535	+	0.0533450i	0.0203202	+	0.999794i	$0.493531\pi$
$4$	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	0.159814	−	0.987147i	$-0.448910\pi$
$7$	−1.62760	−	0.939693i	−0.615173	−	0.355170i	−0.774987	+	0.631977i	$0.782244\pi$
$8$	−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	−0.999862	−	0.0165906i	$-0.994719\pi$
$11$	−1.70574	−	2.95442i	−0.514299	−	0.890792i	0.485563	−	0.874202i	$-0.338615\pi$
$12$	−0.565258	−	0.326352i	−0.163176	−	0.0942097i
$13$	−5.21048	−	0.918748i	−1.44513	−	0.254815i	−0.604576	−	0.796547i	$-0.706657\pi$
$13$	−5.21048	−	0.918748i	−1.44513	−	0.254815i	−0.840551	+	0.541733i	$0.817769\pi$
$14$	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	−0.989174	−	0.146748i	$-0.953119\pi$
$17$	−0.565258	+	1.55303i	−0.137095	+	0.376666i	0.852079	+	0.523414i	$0.175342\pi$
$18$		−	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	−0.870921	−	0.491424i	$-0.836477\pi$
$23$	−1.13052	+	1.34730i	−0.235729	+	0.280931i	0.635192	+	0.772354i	$0.280921\pi$
$24$	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	−0.626375	−	0.779522i	$-0.715462\pi$
$29$	−3.25877	+	1.18610i	−0.605138	+	0.220252i	0.0212363	+	0.999774i	$0.493240\pi$
$30$		0			0
$31$	−0.971782	+	1.68317i	−0.174537	+	0.302307i	−0.940001	−	0.341172i	$-0.889176\pi$
$31$	−0.971782	+	1.68317i	−0.174537	+	0.302307i	0.765464	+	0.643479i	$0.222510\pi$
$32$	−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	$0.0219304\pi$
$37$			0.837496i			0.137684i	−0.997628	+	0.0688418i	$0.978070\pi$
$38$	−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	−0.983173	−	0.182675i	$-0.941524\pi$
$41$	−0.779715	−	4.42198i	−0.121771	−	0.690598i	0.861402	−	0.507923i	$-0.169587\pi$
$42$	−0.565258	+	0.673648i	−0.0872212	+	0.103946i
$43$	3.08580	+	3.67752i	0.470581	+	0.560816i	0.948169	−	0.317768i	$-0.102933\pi$
$43$	3.08580	+	3.67752i	0.470581	+	0.560816i	−0.477588	+	0.878584i	$0.658489\pi$
$44$	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	0.956290	−	0.292422i	$-0.0944610\pi$
$47$	0.245188	+	0.673648i	0.0357643	+	0.0982617i	−0.920525	+	0.390683i	$0.872239\pi$
$48$	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	−0.425865	−	0.904787i	$-0.640030\pi$
$53$	3.92490	−	4.67752i	0.539127	−	0.642507i	0.964992	+	0.262280i	$0.0844745\pi$
$54$	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	−0.413962	−	0.910294i	$-0.635856\pi$
$59$	−10.1099	−	3.67972i	−1.31620	−	0.479058i	−0.902239	+	0.431236i	$0.858078\pi$
$60$		0			0
$61$	3.36231	+	2.82131i	0.430500	+	0.361232i	0.832140	−	0.554565i	$-0.187115\pi$
$61$	3.36231	+	2.82131i	0.430500	+	0.361232i	−0.401640	+	0.915797i	$0.631560\pi$
$62$	−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	0.763304	+	0.646040i	$0.223576\pi$
$67$	4.86084	+	13.3550i	0.593846	+	1.63158i	−0.169458	+	0.985537i	$0.554202\pi$
$68$	−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	−0.254252	+	0.967138i	$0.581829\pi$
$71$	−10.5398	+	8.84397i	−1.25085	+	1.04959i	−0.996595	+	0.0824479i	$0.973726\pi$
$72$	4.95534	−	5.90554i	0.583992	−	0.695975i
$73$	7.40333	−	1.30541i	0.866495	−	0.152786i	0.277306	−	0.960782i	$-0.410559\pi$
$73$	7.40333	−	1.30541i	0.866495	−	0.152786i	0.589189	+	0.807995i	$0.299447\pi$
$74$	−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	0.974131	+	0.225986i	$0.0725603\pi$
$79$	1.20914	+	6.85738i	0.136039	+	0.771515i	−0.838092	+	0.545529i	$0.816329\pi$
$80$		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	0.375807	−	0.926698i	$-0.377366\pi$
$83$	−2.17588	−	1.25624i	−0.238834	−	0.137891i	−0.614641	+	0.788807i	$0.710699\pi$
$84$	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	−0.956559	−	0.291539i	$-0.905833\pi$
$89$	0.396459	−	2.24843i	0.0420246	−	0.238333i	0.998584	+	0.0532055i	$0.0169438\pi$
$90$		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	−0.904007	−	0.427517i	$-0.859388\pi$
$97$	0.623485	−	1.71301i	0.0633053	−	0.173930i	0.967312	+	0.253587i	$0.0816105\pi$
$98$	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	0.836671	+	0.547705i	$0.184499\pi$
$101$	−1.37551	+	7.80093i	−0.136869	+	0.776222i	−0.973540	+	0.228516i	$0.926613\pi$
$102$	0.669713	+	0.386659i	0.0663115	+	0.0382850i
$103$	−0.0125989	+	0.00727396i	−0.00124140	+	0.000716725i	−0.500621	−	0.865667i	$-0.666895\pi$
$103$	−0.0125989	+	0.00727396i	−0.00124140	+	0.000716725i	0.499379	+	0.866384i	$0.333561\pi$
$104$	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	0.343776	−	0.939052i	$-0.388294\pi$
$107$	−3.07818	−	1.77719i	−0.297579	−	0.171807i	−0.641355	+	0.767244i	$0.721627\pi$
$108$	3.67474	+	0.647956i	0.353602	+	0.0623496i
$109$	−5.64543	+	4.73708i	−0.540734	+	0.453730i	−0.871789	−	0.489882i	$-0.837040\pi$
$109$	−5.64543	+	4.73708i	−0.540734	+	0.453730i	0.331055	+	0.943612i	$0.392596\pi$
$110$		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	$0.112800\pi$
$113$			7.37733i			0.694000i	−0.937865	+	0.347000i	$0.887200\pi$
$114$	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	0.178060	−	0.984020i	$-0.443018\pi$
$127$	0.0994798	+	0.0175410i	0.00882740	+	0.00155651i	−0.169233	+	0.985576i	$0.554129\pi$
$128$	−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	0.463661	−	0.886013i	$-0.346536\pi$
$131$	2.85369	+	1.03866i	0.249328	+	0.0907481i	−0.214333	+	0.976761i	$0.568758\pi$
$132$			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	0.114671	−	0.993404i	$-0.463419\pi$
$137$	12.5600	−	14.9684i	1.07307	−	1.27883i	0.958399	−	0.285431i	$-0.0921368\pi$
$138$	0.528981	+	0.630415i	0.0450298	+	0.0536645i
$139$	−2.67365	+	15.1630i	−0.226776	+	1.28611i	0.632485	+	0.774573i	$0.282035\pi$
$139$	−2.67365	+	15.1630i	−0.226776	+	1.28611i	−0.859261	+	0.511537i	$0.829076\pi$
$140$		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	0.999807	−	0.0196306i	$-0.00624903\pi$
$149$	0.654048	+	3.70929i	0.0535817	+	0.303877i	−0.946226	+	0.323507i	$0.895138\pi$
$150$		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	0.963425	−	0.267980i	$-0.0863560\pi$
$157$	6.66869	+	7.94743i	0.532219	+	0.634274i	−0.431205	+	0.902254i	$0.641912\pi$
$158$	−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	−0.567018	−	0.823706i	$-0.691903\pi$
$163$	−1.75135	+	1.01114i	−0.137177	+	0.0791989i	0.429841	+	0.902905i	$0.358570\pi$
$164$	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	−0.244218	+	0.969720i	$0.578531\pi$
$167$	−14.9491	+	17.8157i	−1.15680	+	1.37862i	−0.912580	+	0.408898i	$0.865913\pi$
$168$	−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	−0.927489	−	0.373850i	$-0.878037\pi$
$173$	0.306663	−	0.842549i	0.0233151	−	0.0640578i	0.950804	+	0.309793i	$0.100260\pi$
$174$	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	−0.921755	−	0.387773i	$-0.873245\pi$
$179$	−10.6591	−	18.4621i	−0.796699	−	1.37992i	0.125056	−	0.992150i	$-0.460089\pi$
$180$		0			0
$181$	15.1284	−	5.50627i	1.12448	−	0.409278i	0.288196	−	0.957571i	$-0.406945\pi$
$181$	15.1284	−	5.50627i	1.12448	−	0.409278i	0.836286	+	0.548294i	$0.184722\pi$
$182$	−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	−0.611080	−	0.791569i	$-0.709264\pi$
$193$	−12.7057	+	2.24035i	−0.914574	+	0.161264i	−0.303494	+	0.952833i	$0.598153\pi$
$194$	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	−0.434263	−	0.900786i	$-0.642991\pi$
$197$	−20.0920	−	11.6001i	−1.43150	−	0.826476i	−0.997235	+	0.0743108i	$0.976324\pi$
$198$	−7.05866	+	4.07532i	−0.501637	+	0.289621i
$199$	8.66550	−	3.15398i	0.614281	−	0.223580i	−0.0160945	−	0.999870i	$-0.505123\pi$
$199$	8.66550	−	3.15398i	0.614281	−	0.223580i	0.630375	+	0.776291i	$0.282901\pi$
$200$		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	−0.177478	−	0.984125i	$-0.556794\pi$
$211$	−13.7417	−	5.00157i	−0.946017	−	0.344322i	−0.768539	+	0.639803i	$0.779016\pi$
$212$	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	0.697253	−	0.716825i	$-0.254405\pi$
$223$	−1.93771	−	2.30928i	−0.129759	−	0.154641i	−0.827012	+	0.562185i	$0.809961\pi$
$224$	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	$0.150496\pi$
$227$			13.7219i			0.910757i	−0.890298	+	0.455378i	$0.849504\pi$
$228$	−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	−0.976693	−	0.214640i	$-0.931142\pi$
$233$	−15.5463	−	18.5273i	−1.01847	−	1.21377i	−0.0417777	−	0.999127i	$-0.513302\pi$
$234$	−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	−0.945665	−	0.325143i	$-0.894587\pi$
$239$	−11.6630	−	20.2009i	−0.754415	−	1.30668i	0.191250	−	0.981541i	$-0.438746\pi$
$240$		0			0
$241$	0.0516892	−	0.293144i	0.00332960	−	0.0188831i	−0.983098	−	0.183082i	$-0.941393\pi$
$241$	0.0516892	−	0.293144i	0.00332960	−	0.0188831i	0.986427	+	0.164199i	$0.0525038\pi$
$242$	−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	0.160859	−	0.986977i	$-0.448573\pi$
$251$	−12.4081	−	10.4116i	−0.783190	−	0.657175i	−0.944050	+	0.329802i	$0.893018\pi$
$252$	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	0.988719	+	0.149782i	$0.0478570\pi$
$257$	5.25173	+	14.4290i	0.327594	+	0.900057i	−0.661125	+	0.750276i	$0.729921\pi$
$258$	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	−0.458592	−	0.888647i	$-0.651646\pi$
$263$	−9.49671	+	1.67453i	−0.585592	+	0.103256i	−0.127000	+	0.991903i	$0.540535\pi$
$264$	−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	0.914498	+	0.404591i	$0.132586\pi$
$269$	3.17412	+	18.0013i	0.193529	+	1.09756i	−0.720969	+	0.692968i	$0.756303\pi$
$270$		0			0
$271$	14.5273	−	12.1899i	0.882473	−	0.740483i	−0.0842129	−	0.996448i	$-0.526838\pi$
$271$	14.5273	−	12.1899i	0.882473	−	0.740483i	0.966686	+	0.255965i	$0.0823932\pi$
$272$	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	−0.813350	−	0.581775i	$-0.802358\pi$
$277$	−11.9198	+	6.88191i	−0.716193	+	0.413494i	0.0971571	+	0.995269i	$0.469025\pi$
$278$	−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	0.891175	−	0.453661i	$-0.149882\pi$
$281$	10.0437	+	8.42767i	0.599157	+	0.502752i	−0.292018	+	0.956413i	$0.594327\pi$
$282$	0.330341	−	0.0582480i	0.0196715	−	0.00346862i
$283$	−5.94340	+	16.3293i	−0.353298	+	0.970679i	0.628005	+	0.778209i	$0.283872\pi$
$283$	−5.94340	+	16.3293i	−0.353298	+	0.970679i	−0.981303	+	0.192469i	$0.938350\pi$
$284$	−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	−0.0503091	−	0.998734i	$-0.516021\pi$
$293$	13.5135	−	7.80200i	0.789465	−	0.455798i	0.839774	+	0.542936i	$0.182687\pi$
$294$	−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	0.467736	−	0.883868i	$-0.345070\pi$
$307$	21.1933	−	3.73695i	1.20956	−	0.213279i	0.741829	+	0.670589i	$0.233959\pi$
$308$	−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	−0.994997	−	0.0999083i	$-0.968145\pi$
$311$	−7.24763	+	12.5533i	−0.410975	+	0.711830i	0.584021	+	0.811738i	$0.301478\pi$
$312$	−6.91793	+	3.99407i	−0.391651	+	0.226120i
$313$	−6.67571	−	18.3414i	−0.377334	−	1.03672i	−0.972457	−	0.233081i	$-0.925119\pi$
$313$	−6.67571	−	18.3414i	−0.377334	−	1.03672i	0.595124	−	0.803634i	$-0.297103\pi$
$314$	−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	−0.678885	−	0.734245i	$-0.737536\pi$
$317$	−27.9166	−	4.92246i	−1.56795	−	0.276473i	−0.889070	+	0.457772i	$0.848648\pi$
$318$	−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	0.888567	−	0.458747i	$-0.151702\pi$
$331$	0.855037	+	1.48097i	0.0469971	+	0.0814014i	−0.841570	+	0.540148i	$0.818368\pi$
$332$	−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	−0.997734	−	0.0672796i	$-0.978568\pi$
$337$	−16.3518	−	19.4873i	−0.890737	−	1.06154i	0.106997	−	0.994259i	$-0.465876\pi$
$338$	−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	0.616604	−	0.787274i	$-0.288508\pi$
$347$	−4.95096	−	5.90033i	−0.265782	−	0.316746i	−0.882385	+	0.470527i	$0.844064\pi$
$348$	2.22913	+	0.393056i	0.119494	+	0.0210700i
$349$	11.3785	−	19.7082i	0.609078	−	1.05495i	−0.382315	−	0.924032i	$-0.624873\pi$
$349$	11.3785	−	19.7082i	0.609078	−	1.05495i	0.991393	−	0.130921i	$-0.0417935\pi$
$350$		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	−0.740028	−	0.672576i	$-0.765188\pi$
$353$	−9.91220	+	5.72281i	−0.527573	+	0.304595i	0.212454	+	0.977171i	$0.431854\pi$
$354$	−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	0.586429	−	0.810000i	$-0.300533\pi$
$359$	9.75789	+	3.55158i	0.515002	+	0.187445i	−0.0714274	+	0.997446i	$0.522755\pi$
$360$		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	0.927930	−	0.372754i	$-0.121586\pi$
$367$	32.0388	+	5.64930i	1.67241	+	0.294891i	0.744480	+	0.667645i	$0.232697\pi$
$368$	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	−0.376469	−	0.926429i	$-0.622862\pi$
$373$	−26.4014	−	15.2429i	−1.36701	−	0.789246i	−0.990546	+	0.137183i	$0.956195\pi$
$374$	−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	0.451157	−	0.892445i	$-0.351012\pi$
$383$	23.0997	−	4.07310i	1.18034	−	0.208126i	0.729183	+	0.684319i	$0.239900\pi$
$384$	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	−0.247206	−	0.968963i	$-0.579512\pi$
$389$	3.67365	−	1.33710i	0.186261	−	0.0677936i	0.433467	+	0.901169i	$0.357290\pi$
$390$		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	−0.992530	−	0.122002i	$-0.961069\pi$
$397$	−3.06417	+	8.41875i	−0.153786	+	0.422525i	0.838743	+	0.544527i	$0.183291\pi$
$398$			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	0.389149	−	0.921175i	$-0.372769\pi$
$401$	1.90508	+	0.693392i	0.0951350	+	0.0346263i	−0.294014	+	0.955801i	$0.594991\pi$
$402$	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	−0.955162	−	0.296084i	$-0.904319\pi$
$409$	−30.2656	+	11.0158i	−1.49654	+	0.544696i	−0.541377	+	0.840780i	$0.682097\pi$
$410$		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	0.999862	−	0.0166178i	$-0.00528986\pi$
$421$	1.12061	+	6.35532i	0.0546154	+	0.309739i	−0.945246	+	0.326357i	$0.894179\pi$
$422$	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	0.868622	+	0.495475i	$0.165006\pi$
$431$	−2.43061	+	13.7847i	−0.117078	+	0.663984i	−0.985700	+	0.168508i	$0.946105\pi$
$432$	−0.0819052	−	0.0976108i	−0.00394067	−	0.00469630i
$433$	18.4434	−	21.9800i	0.886333	−	1.05629i	−0.111709	−	0.993741i	$-0.535632\pi$
$433$	18.4434	−	21.9800i	0.886333	−	1.05629i	0.998042	−	0.0625499i	$-0.0199232\pi$
$434$	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	0.0250271	−	0.999687i	$-0.492033\pi$
$439$	−12.5376	−	4.56332i	−0.598387	−	0.217795i	−0.623414	+	0.781892i	$0.714255\pi$
$440$		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	0.895728	−	0.444603i	$-0.146655\pi$
$443$	33.3682	+	5.88372i	1.58537	+	0.279544i	0.689646	+	0.724147i	$0.257766\pi$
$444$	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	−0.553460	−	0.832876i	$-0.686693\pi$
$449$	9.42009	−	16.3161i	0.444562	−	0.770003i	0.998022	+	0.0628725i	$0.0200261\pi$
$450$		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	$-0.891611\pi$
$457$		−	14.2790i		−	0.667943i	0.942583	−	0.333972i	$-0.108389\pi$
$458$	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	−0.856502	−	0.516144i	$-0.827367\pi$
$461$	−10.6695	+	8.95280i	−0.496930	+	0.416973i	0.359572	+	0.933117i	$0.382923\pi$
$462$	2.95442	+	0.520945i	0.137452	+	0.0242365i
$463$	1.52671	+	0.881445i	0.0709521	+	0.0409642i	0.535056	−	0.844816i	$-0.320290\pi$
$463$	1.52671	+	0.881445i	0.0709521	+	0.0409642i	−0.464104	+	0.885781i	$0.653624\pi$
$464$	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	−0.871754	−	0.489945i	$-0.837017\pi$
$467$	−19.0888	+	11.0209i	−0.883326	+	0.509988i	−0.0115724	+	0.999933i	$0.503684\pi$
$468$	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	0.968417	−	0.249337i	$-0.0802126\pi$
$479$	19.5012	+	16.3634i	0.891032	+	0.747664i	−0.0773851	+	0.997001i	$0.524657\pi$
$480$		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	−0.0116199	−	0.999932i	$-0.503699\pi$
$487$	−19.4949	−	11.2554i	−0.883397	−	0.510029i	−0.871777	+	0.489903i	$0.837032\pi$
$488$	−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	0.982751	+	0.184934i	$0.0592071\pi$
$491$	2.71482	+	15.3965i	0.122518	+	0.694835i	−0.860233	+	0.509902i	$0.829682\pi$
$492$	−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	−0.00294090	−	0.999996i	$-0.500936\pi$
$499$	21.9217	−	18.3945i	0.981352	−	0.823452i	0.984293	+	0.176544i	$0.0564917\pi$
$500$		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	0.970538	+	0.240950i	$0.0774589\pi$
$503$	8.56607	+	23.5351i	0.381942	+	1.04938i	−0.588595	+	0.808428i	$0.700319\pi$
$504$	−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	−0.138810	−	0.990319i	$-0.544328\pi$
$509$	−25.6787	−	21.5470i	−1.13819	−	0.955053i	−0.999378	+	0.0352655i	$0.988772\pi$
$510$		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	0.992530	+	0.122005i	$0.0389323\pi$
$521$	13.7392	+	23.7969i	0.601924	+	1.04256i	−0.390606	+	0.920558i	$0.627734\pi$
$522$	2.83380	+	7.78581i	0.124032	+	0.340776i
$523$	3.54244	+	9.73277i	0.154900	+	0.425584i	0.992732	−	0.120343i	$-0.0383995\pi$
$523$	3.54244	+	9.73277i	0.154900	+	0.425584i	−0.837832	+	0.545928i	$0.816177\pi$
$524$	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	−0.392509	−	0.919748i	$-0.628393\pi$
$541$	−2.37211	+	0.863378i	−0.101985	+	0.0371195i	0.290524	+	0.956868i	$0.406170\pi$
$542$	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	−0.650194	−	0.759768i	$-0.725312\pi$
$547$	4.93339	−	5.87939i	0.210937	−	0.251384i	0.861131	+	0.508384i	$0.169757\pi$
$548$	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	0.105307	−	0.994440i	$-0.466418\pi$
$557$	−3.20631	−	0.565360i	−0.135856	−	0.0239551i	−0.241163	+	0.970485i	$0.577529\pi$
$558$	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	0.400946	−	0.916102i	$-0.368682\pi$
$563$	−4.55449	−	2.62954i	−0.191949	−	0.110822i	−0.592895	+	0.805280i	$0.702015\pi$
$564$	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	0.232696	−	0.972549i	$-0.425245\pi$
$577$	−11.8473	−	6.84002i	−0.493208	−	0.284754i	−0.725904	+	0.687796i	$0.758579\pi$
$578$	−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	−0.646268	−	0.763111i	$-0.723671\pi$
$587$	8.22108	−	22.5872i	0.339320	−	0.932275i	0.985588	−	0.169164i	$-0.0541068\pi$
$588$			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	−0.707158	−	0.707055i	$-0.750023\pi$
$593$	2.72621	−	3.24897i	0.111952	−	0.133419i	0.819110	+	0.573636i	$0.194468\pi$
$594$	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	−0.792965	−	0.609267i	$-0.791464\pi$
$599$	−24.6894	+	8.98622i	−1.00878	+	0.367167i	−0.215818	+	0.976434i	$0.569242\pi$
$600$		0			0
$601$	21.1197	−	36.5805i	0.861492	−	1.49215i	−0.00899659	−	0.999960i	$-0.502864\pi$
$601$	21.1197	−	36.5805i	0.861492	−	1.49215i	0.870489	−	0.492188i	$-0.163803\pi$
$602$	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	$0.148021\pi$
$607$			22.0969i			0.896885i	−0.893812	+	0.448443i	$0.851979\pi$
$608$	−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	0.851121	−	0.524970i	$-0.175924\pi$
$613$	4.61332	+	5.49794i	0.186330	+	0.222060i	−0.664790	+	0.747030i	$0.731479\pi$
$614$	−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	−0.444065	−	0.895995i	$-0.646464\pi$
$617$	−16.8865	−	46.3953i	−0.679826	−	1.86781i	−0.235761	−	0.971811i	$-0.575758\pi$
$618$	0.00232818	+	0.00639661i	9.36530e−5	+	0.000257310i
$619$	13.2490	+	22.9479i	0.532521	+	0.922354i	0.999279	+	0.0379684i	$0.0120886\pi$
$619$	13.2490	+	22.9479i	0.532521	+	0.922354i	−0.466758	+	0.884385i	$0.654578\pi$
$620$		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	0.989138	−	0.146988i	$-0.0469579\pi$
$631$	25.5253	+	21.4183i	1.01615	+	0.852647i	0.0270071	+	0.999635i	$0.491402\pi$
$632$	−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	−0.644844	−	0.764314i	$-0.723078\pi$
$641$	−0.104256	+	0.0874810i	−0.00411786	+	0.00345529i	0.640726	+	0.767769i	$0.278633\pi$
$642$	−1.06904	+	1.27403i	−0.0421917	+	0.0502821i
$643$	−47.4461	+	8.36602i	−1.87109	+	0.329924i	−0.989779	−	0.142613i	$-0.954450\pi$
$643$	−47.4461	+	8.36602i	−1.87109	+	0.329924i	−0.881311	+	0.472536i	$0.843339\pi$
$644$	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	$0.258973\pi$
$647$			36.9718i			1.45351i	−0.686895	+	0.726756i	$0.741027\pi$
$648$	−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	−0.0329874	−	0.999456i	$-0.510502\pi$
$653$	−23.3827	−	13.5000i	−0.915035	−	0.528296i	−0.882048	+	0.471160i	$0.843835\pi$
$654$	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	0.852005	+	0.523534i	$0.175387\pi$
$659$	−3.27760	+	18.5882i	−0.127677	+	0.724093i	−0.979682	+	0.200559i	$0.935724\pi$
$660$		0			0
$661$	−23.4500	−	19.6769i	−0.912098	−	0.765341i	0.0604192	−	0.998173i	$-0.480756\pi$
$661$	−23.4500	−	19.6769i	−0.912098	−	0.765341i	−0.972517	+	0.232832i	$0.925201\pi$
$662$	−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	−0.287865	−	0.957671i	$-0.592945\pi$
$673$	10.3139	−	5.95471i	0.397570	−	0.229537i	0.685435	+	0.728134i	$0.259612\pi$
$674$	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	0.593114	−	0.805119i	$-0.297898\pi$
$677$	5.00654	+	2.89053i	0.192417	+	0.111092i	−0.400696	+	0.916211i	$0.631232\pi$
$678$	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	$0.131935\pi$
$683$			21.0496i			0.805442i	−0.915323	+	0.402721i	$0.868065\pi$
$684$	−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	−0.361744	−	0.932278i	$-0.617818\pi$
$691$	16.4688	−	28.5249i	0.626504	−	1.08514i	0.988248	−	0.152860i	$-0.0488483\pi$
$692$	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	−0.0660380	−	0.997817i	$-0.521036\pi$
$701$	−20.0694	−	7.30466i	−0.758010	−	0.275893i	−0.691973	+	0.721924i	$0.743258\pi$
$702$		−	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	−0.889210	−	0.457499i	$-0.848745\pi$
$709$	2.73854	−	15.5310i	0.102848	−	0.583280i	0.992058	−	0.125781i	$-0.0401437\pi$
$710$		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	0.855314	+	0.518109i	$0.173364\pi$
$719$	6.13470	+	34.7916i	0.228786	+	1.29751i	−0.626529	+	0.779398i	$0.715525\pi$
$720$		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	−0.988877	−	0.148737i	$-0.952479\pi$
$727$	−25.9825	−	30.9647i	−0.963637	−	1.14842i	0.0252396	−	0.999681i	$-0.491965\pi$
$728$	−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	−0.951396	−	0.307970i	$-0.900350\pi$
$733$	−31.4162	+	18.1382i	−1.16038	+	0.669948i	−0.208988	+	0.977918i	$0.567017\pi$
$734$	−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	−0.0410304	−	0.999158i	$-0.513064\pi$
$739$	−19.4290	−	7.07158i	−0.714708	−	0.260132i	−0.673677	+	0.739026i	$0.735286\pi$
$740$		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	−0.890500	−	0.454982i	$-0.849646\pi$
$743$	2.29293	−	6.29978i	0.0841196	−	0.231117i	0.974620	+	0.223866i	$0.0718678\pi$
$744$	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	−0.519007	−	0.854770i	$-0.673698\pi$
$751$	−10.0617	+	3.66214i	−0.367155	+	0.133633i	0.151853	+	0.988403i	$0.451476\pi$
$752$	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	−0.245878	−	0.969301i	$-0.579076\pi$
$757$	−4.00071	+	0.705432i	−0.145408	+	0.0256394i	0.100470	+	0.994940i	$0.467965\pi$
$758$	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	0.0460191	−	0.998941i	$-0.485346\pi$
$769$	20.0599	−	7.30121i	0.723378	−	0.263288i	0.677359	+	0.735652i	$0.263124\pi$
$770$		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	0.481709	−	0.876331i	$-0.340016\pi$
$773$	17.6450	+	3.11128i	0.634645	+	0.111905i	0.152936	+	0.988236i	$0.451127\pi$
$774$	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	−0.507493	+	0.861656i	$0.669428\pi$
$787$	−42.2894	+	24.4158i	−1.50746	+	0.870330i	−0.999962	+	0.00867371i	$0.997239\pi$
$788$	−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	$0.168591\pi$
$797$			28.5262i			1.01045i	−0.862988	+	0.505225i	$0.831409\pi$
$798$	−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	0.705644	−	0.708567i	$-0.250658\pi$
$809$	−7.41834	−	12.8489i	−0.260815	−	0.451745i	−0.966459	+	0.256822i	$0.917325\pi$
$810$		0			0
$811$	−1.45471	+	8.25006i	−0.0510817	+	0.289699i	−0.999638	−	0.0269103i	$-0.991433\pi$
$811$	−1.45471	+	8.25006i	−0.0510817	+	0.289699i	0.948556	+	0.316609i	$0.102544\pi$
$812$	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	0.722852	−	0.691002i	$-0.242831\pi$
$821$	4.80999	+	4.03606i	0.167870	+	0.140860i	−0.554983	+	0.831862i	$0.687275\pi$
$822$	−5.87695	−	7.00387i	−0.204982	−	0.244288i
$823$	10.8589	+	1.91472i	0.378517	+	0.0667428i	0.359670	−	0.933080i	$-0.382889\pi$
$823$	10.8589	+	1.91472i	0.378517	+	0.0667428i	0.0188472	+	0.999822i	$0.494000\pi$
$824$	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	0.960492	+	0.278309i	$0.0897738\pi$
$827$	11.6067	+	31.8892i	0.403606	+	1.10890i	−0.556886	+	0.830589i	$0.688004\pi$
$828$	5.07624	−	2.93077i	0.176412	−	0.101851i
$829$	−10.1834	+	17.6382i	−0.353686	+	0.612602i	−0.986892	−	0.161381i	$-0.948405\pi$
$829$	−10.1834	+	17.6382i	−0.353686	+	0.612602i	0.633206	+	0.773983i	$0.281738\pi$
$830$		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	−0.994815	−	0.101697i	$-0.967573\pi$
$839$	−2.74526	−	15.5692i	−0.0947770	−	0.537507i	0.900038	−	0.435810i	$-0.143538\pi$
$840$		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	0.0987227	+	0.995115i	$0.468524\pi$
$853$	−18.0071	+	49.4741i	−0.616551	+	1.69396i	−0.715274	+	0.698845i	$0.753698\pi$
$854$	7.25402			0.248228
$855$		0			0
$856$	10.0855			0.344716
$857$	7.87581	−	21.6386i	0.269033	−	0.739161i	−0.729447	−	0.684038i	$-0.760222\pi$
$857$	7.87581	−	21.6386i	0.269033	−	0.739161i	0.998480	−	0.0551238i	$-0.0175553\pi$
$858$	8.31731	−	1.46657i	0.283948	−	0.0500678i
$859$	−6.82501	−	5.72686i	−0.232866	−	0.195398i	0.518886	−	0.854843i	$-0.326347\pi$
$859$	−6.82501	−	5.72686i	−0.232866	−	0.195398i	−0.751753	+	0.659445i	$0.770791\pi$
$860$		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	0.00773998	−	0.999970i	$-0.497536\pi$
$863$	25.7814	−	14.8849i	0.877609	−	0.506688i	0.869869	+	0.493282i	$0.164203\pi$
$864$	−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	−0.573562	−	0.819162i	$-0.694439\pi$
$877$	−24.6498	+	4.34642i	−0.832363	+	0.146768i	−0.258802	+	0.965930i	$0.583328\pi$
$878$	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	−0.985095	−	0.172014i	$-0.944973\pi$
$881$	−10.1980	+	17.6634i	−0.343579	+	0.595097i	0.641515	+	0.767110i	$0.278306\pi$
$882$	−7.17544	+	4.14274i	−0.241610	+	0.139493i
$883$	3.63501	+	9.98710i	0.122328	+	0.336093i	0.985708	−	0.168460i	$-0.0538795\pi$
$883$	3.63501	+	9.98710i	0.122328	+	0.336093i	−0.863381	+	0.504553i	$0.831657\pi$
$884$	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	0.987840	−	0.155474i	$-0.0496904\pi$
$887$	55.4828	+	9.78312i	1.86293	+	0.328485i	0.875091	+	0.483959i	$0.160802\pi$
$888$	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	0.825546	−	0.564334i	$-0.190867\pi$
$907$	3.80764	+	4.53777i	0.126431	+	0.150674i	−0.699116	+	0.715009i	$0.746423\pi$
$908$	−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	−0.913116	−	0.407700i	$-0.866331\pi$
$919$	−3.13697	+	5.43340i	−0.103479	+	0.179231i	0.809637	+	0.586931i	$0.199664\pi$
$920$		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	0.739468	−	0.673191i	$-0.235077\pi$
$929$	26.6152	+	9.68712i	0.873215	+	0.317824i	0.133747	+	0.991016i	$0.457299\pi$
$930$		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	0.486930	−	0.873441i	$-0.338117\pi$
$937$	19.7670	+	3.48545i	0.645759	+	0.113865i	0.158830	+	0.987306i	$0.449228\pi$
$938$	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	−0.423331	−	0.905975i	$-0.639139\pi$
$941$	−5.06980	+	1.84526i	−0.165271	+	0.0601537i	0.258060	+	0.966129i	$0.416917\pi$
$942$	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	−0.0663359	−	0.997797i	$-0.521131\pi$
$947$	6.54228	−	1.15358i	0.212596	−	0.0374863i	0.278931	+	0.960311i	$0.410020\pi$
$948$	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	0.0678799	−	0.997693i	$-0.478377\pi$
$953$	14.5987	−	2.57414i	0.472897	−	0.0833846i	0.405018	+	0.914309i	$0.367265\pi$
$954$	−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	−1.00000		0.000850519i	$-0.999729\pi$
$967$	−7.25822	+	19.9418i	−0.233409	+	0.641285i	0.766591	+	0.642136i	$0.221951\pi$
$968$		−	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	0.839770	−	0.542943i	$-0.182690\pi$
$971$	35.3387	+	12.8622i	1.13407	+	0.412769i	0.294304	+	0.955712i	$0.404912\pi$
$972$	−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	0.299156	−	0.954204i	$-0.403295\pi$
$977$	39.8558	−	23.0107i	1.27510	−	0.736179i	0.975943	+	0.218026i	$0.0699617\pi$
$978$	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	0.818181	+	0.574961i	$0.194983\pi$
$983$	38.9506	+	46.4195i	1.24233	+	1.48055i	0.424150	+	0.905592i	$0.360573\pi$
$984$	−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	0.850643	+	0.525744i	$0.176213\pi$
$991$	7.27554	+	41.2616i	0.231115	+	1.31072i	−0.619528	+	0.784975i	$0.712676\pi$
$992$	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	0.977163	+	0.212490i	$0.0681571\pi$
$997$	11.5313	+	31.6819i	0.365198	+	1.00337i	−0.611965	+	0.790885i	$0.709621\pi$
$998$	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.99.1		12
5.2	odd	4		19.2.e.a.4.1	✓	6
5.3	odd	4		475.2.l.a.251.1		6
5.4	even	2	inner	475.2.u.a.99.2		12
15.2	even	4		171.2.u.c.118.1		6
19.5	even	9	inner	475.2.u.a.24.2		12
20.7	even	4		304.2.u.b.289.1		6
35.2	odd	12		931.2.x.a.802.1		6
35.12	even	12		931.2.x.b.802.1		6
35.17	even	12		931.2.v.a.422.1		6
35.27	even	4		931.2.w.a.99.1		6
35.32	odd	12		931.2.v.b.422.1		6
95.2	even	36		361.2.e.b.54.1		6
95.7	odd	12		361.2.e.f.234.1		6
95.12	even	12		361.2.e.b.234.1		6
95.17	odd	36		361.2.e.f.54.1		6
95.22	even	36		361.2.e.a.245.1		6
95.24	even	18	inner	475.2.u.a.24.1		12
95.27	even	12		361.2.e.a.28.1		6
95.28	odd	36		9025.2.a.bd.1.1		3
95.32	even	36		361.2.c.h.68.3		6
95.37	even	4		361.2.e.h.99.1		6
95.42	odd	36		361.2.c.i.292.1		6
95.43	odd	36		475.2.l.a.176.1		6
95.47	odd	36		361.2.a.g.1.3		3
95.48	even	36		9025.2.a.x.1.3		3
95.52	even	36		361.2.e.h.62.1		6
95.62	odd	36		19.2.e.a.5.1	yes	6
95.67	even	36		361.2.a.h.1.1		3
95.72	even	36		361.2.c.h.292.3		6
95.82	odd	36		361.2.c.i.68.1		6
95.87	odd	12		361.2.e.g.28.1		6
95.92	odd	36		361.2.e.g.245.1		6
285.47	even	36		3249.2.a.z.1.1		3
285.62	even	36		171.2.u.c.100.1		6
285.257	odd	36		3249.2.a.s.1.3		3
380.47	even	36		5776.2.a.br.1.1		3
380.67	odd	36		5776.2.a.bi.1.3		3
380.347	even	36		304.2.u.b.81.1		6
665.62	even	36		931.2.w.a.442.1		6
665.157	even	36		931.2.x.b.765.1		6
665.347	odd	36		931.2.x.a.765.1		6
665.537	even	36		931.2.v.a.214.1		6
665.632	odd	36		931.2.v.b.214.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.4.1	✓	6	5.2	odd	4
19.2.e.a.5.1	yes	6	95.62	odd	36
171.2.u.c.100.1		6	285.62	even	36
171.2.u.c.118.1		6	15.2	even	4
304.2.u.b.81.1		6	380.347	even	36
304.2.u.b.289.1		6	20.7	even	4
361.2.a.g.1.3		3	95.47	odd	36
361.2.a.h.1.1		3	95.67	even	36
361.2.c.h.68.3		6	95.32	even	36
361.2.c.h.292.3		6	95.72	even	36
361.2.c.i.68.1		6	95.82	odd	36
361.2.c.i.292.1		6	95.42	odd	36
361.2.e.a.28.1		6	95.27	even	12
361.2.e.a.245.1		6	95.22	even	36
361.2.e.b.54.1		6	95.2	even	36
361.2.e.b.234.1		6	95.12	even	12
361.2.e.f.54.1		6	95.17	odd	36
361.2.e.f.234.1		6	95.7	odd	12
361.2.e.g.28.1		6	95.87	odd	12
361.2.e.g.245.1		6	95.92	odd	36
361.2.e.h.62.1		6	95.52	even	36
361.2.e.h.99.1		6	95.37	even	4
475.2.l.a.176.1		6	95.43	odd	36
475.2.l.a.251.1		6	5.3	odd	4
475.2.u.a.24.1		12	95.24	even	18	inner
475.2.u.a.24.2		12	19.5	even	9	inner
475.2.u.a.99.1		12	1.1	even	1	trivial
475.2.u.a.99.2		12	5.4	even	2	inner
931.2.v.a.214.1		6	665.537	even	36
931.2.v.a.422.1		6	35.17	even	12
931.2.v.b.214.1		6	665.632	odd	36
931.2.v.b.422.1		6	35.32	odd	12
931.2.w.a.99.1		6	35.27	even	4
931.2.w.a.442.1		6	665.62	even	36
931.2.x.a.765.1		6	665.347	odd	36
931.2.x.a.802.1		6	35.2	odd	12
931.2.x.b.765.1		6	665.157	even	36
931.2.x.b.802.1		6	35.12	even	12
3249.2.a.s.1.3		3	285.257	odd	36
3249.2.a.z.1.1		3	285.47	even	36
5776.2.a.bi.1.3		3	380.67	odd	36
5776.2.a.br.1.1		3	380.47	even	36
9025.2.a.x.1.3		3	95.48	even	36
9025.2.a.bd.1.1		3	95.28	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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