LMFDB - Embedded newform 475.2.l.b.351.2

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:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} + \cdots + 361 $ x^18 + 12x^16 - 8x^15 + 96x^14 - 75x^13 + 448x^12 - 405x^11 + 1521x^10 - 1294x^9 + 3333x^8 - 2616x^7 + 5113x^6 - 3126x^5 + 4032x^4 - 1359x^3 + 1698x^2 - 513x + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			351.2
Root			$-0.359728 - 0.623068i$ of defining polynomial
Character	$\chi$	$=$	475.351
Dual form			475.2.l.b.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.124932 - 0.708527i) q^{2} +(0.945515 - 0.793382i) q^{3} +(1.39298 - 0.507004i) q^{4} +(-0.680257 - 0.570804i) q^{6} +(0.645970 - 1.11885i) q^{7} +(-1.25271 - 2.16976i) q^{8} +(-0.256400 + 1.45411i) q^{9} +O(q^{10})$	\(q+(-0.124932 - 0.708527i) q^{2} +(0.945515 - 0.793382i) q^{3} +(1.39298 - 0.507004i) q^{4} +(-0.680257 - 0.570804i) q^{6} +(0.645970 - 1.11885i) q^{7} +(-1.25271 - 2.16976i) q^{8} +(-0.256400 + 1.45411i) q^{9} +(-2.88381 - 4.99491i) q^{11} +(0.914839 - 1.58455i) q^{12} +(-1.80125 - 1.51143i) q^{13} +(-0.873439 - 0.317906i) q^{14} +(0.890312 - 0.747060i) q^{16} +(1.18948 + 6.74589i) q^{17} +1.06231 q^{18} +(2.40586 - 3.63481i) q^{19} +(-0.276903 - 1.57039i) q^{21} +(-3.17874 + 2.66728i) q^{22} +(5.32803 - 1.93925i) q^{23} +(-2.90591 - 1.05766i) q^{24} +(-0.845852 + 1.46506i) q^{26} +(2.76266 + 4.78507i) q^{27} +(0.332562 - 1.88605i) q^{28} +(-1.04556 + 5.92966i) q^{29} +(1.19445 - 2.06885i) q^{31} +(-4.47907 - 3.75839i) q^{32} +(-6.68956 - 2.43480i) q^{33} +(4.63104 - 1.68556i) q^{34} +(0.380082 + 2.15555i) q^{36} +4.53121 q^{37} +(-2.87593 - 1.25051i) q^{38} -2.90225 q^{39} +(-3.51177 + 2.94672i) q^{41} +(-1.07807 + 0.392386i) q^{42} +(0.260318 + 0.0947480i) q^{43} +(-6.54954 - 5.49572i) q^{44} +(-2.03965 - 3.53278i) q^{46} +(-0.0880430 + 0.499316i) q^{47} +(0.249100 - 1.41271i) q^{48} +(2.66545 + 4.61669i) q^{49} +(6.47674 + 5.43463i) q^{51} +(-3.27541 - 1.19215i) q^{52} +(-6.75604 + 2.45900i) q^{53} +(3.04520 - 2.55523i) q^{54} -3.23685 q^{56} +(-0.609016 - 5.34553i) q^{57} +4.33194 q^{58} +(1.00094 + 5.67662i) q^{59} +(6.77273 - 2.46507i) q^{61} +(-1.61506 - 0.587833i) q^{62} +(1.46131 + 1.22619i) q^{63} +(-0.941117 + 1.63006i) q^{64} +(-0.889378 + 5.04391i) q^{66} +(1.77501 - 10.0666i) q^{67} +(5.07713 + 8.79384i) q^{68} +(3.49918 - 6.06075i) q^{69} +(1.05207 + 0.382923i) q^{71} +(3.47627 - 1.26526i) q^{72} +(-1.83298 + 1.53805i) q^{73} +(-0.566094 - 3.21048i) q^{74} +(1.50845 - 6.28301i) q^{76} -7.45142 q^{77} +(0.362584 + 2.05632i) q^{78} +(-10.7969 + 9.05969i) q^{79} +(2.24603 + 0.817487i) q^{81} +(2.52657 + 2.12004i) q^{82} +(0.608609 - 1.05414i) q^{83} +(-1.18192 - 2.04714i) q^{84} +(0.0346093 - 0.196279i) q^{86} +(3.71589 + 6.43611i) q^{87} +(-7.22517 + 12.5144i) q^{88} +(-6.85239 - 5.74984i) q^{89} +(-2.85461 + 1.03899i) q^{91} +(6.43866 - 5.40267i) q^{92} +(-0.512015 - 2.90378i) q^{93} +0.364778 q^{94} -7.21687 q^{96} +(1.83977 + 10.4339i) q^{97} +(2.93805 - 2.46531i) q^{98} +(8.00258 - 2.91270i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 12 q^{8} - 21 q^{9}+O(q^{10}) $ 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 12 * q^8 - 21 * q^9	$ 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 12 q^{8} - 21 q^{9} - 6 q^{12} + 3 q^{13} + 24 q^{14} + 21 q^{16} + 24 q^{17} + 12 q^{18} - 12 q^{19} + 3 q^{21} - 15 q^{22} - 21 q^{23} + 21 q^{24} - 21 q^{26} - 6 q^{27} + 24 q^{28} - 9 q^{29} + 30 q^{31} - 45 q^{32} + 3 q^{33} + 24 q^{34} - 21 q^{36} + 60 q^{37} + 15 q^{38} + 12 q^{39} - 6 q^{41} - 39 q^{42} + 6 q^{43} - 30 q^{44} + 21 q^{46} - 33 q^{47} + 63 q^{48} - 3 q^{49} + 27 q^{51} - 9 q^{52} - 24 q^{53} + 30 q^{54} - 72 q^{56} + 30 q^{57} - 36 q^{58} + 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{63} - 24 q^{64} - 33 q^{66} + 24 q^{67} + 3 q^{68} + 27 q^{69} + 24 q^{71} - 18 q^{72} - 6 q^{73} - 39 q^{74} + 27 q^{76} - 24 q^{77} - 72 q^{78} + 9 q^{79} + 15 q^{81} + 57 q^{82} - 12 q^{84} - 33 q^{86} + 45 q^{87} - 39 q^{88} - 6 q^{89} - 6 q^{91} + 66 q^{92} + 72 q^{93} - 66 q^{94} - 18 q^{96} + 87 q^{97} - 39 q^{98} + 3 q^{99}+O(q^{100}) $ 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 12 * q^8 - 21 * q^9 - 6 * q^12 + 3 * q^13 + 24 * q^14 + 21 * q^16 + 24 * q^17 + 12 * q^18 - 12 * q^19 + 3 * q^21 - 15 * q^22 - 21 * q^23 + 21 * q^24 - 21 * q^26 - 6 * q^27 + 24 * q^28 - 9 * q^29 + 30 * q^31 - 45 * q^32 + 3 * q^33 + 24 * q^34 - 21 * q^36 + 60 * q^37 + 15 * q^38 + 12 * q^39 - 6 * q^41 - 39 * q^42 + 6 * q^43 - 30 * q^44 + 21 * q^46 - 33 * q^47 + 63 * q^48 - 3 * q^49 + 27 * q^51 - 9 * q^52 - 24 * q^53 + 30 * q^54 - 72 * q^56 + 30 * q^57 - 36 * q^58 + 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^63 - 24 * q^64 - 33 * q^66 + 24 * q^67 + 3 * q^68 + 27 * q^69 + 24 * q^71 - 18 * q^72 - 6 * q^73 - 39 * q^74 + 27 * q^76 - 24 * q^77 - 72 * q^78 + 9 * q^79 + 15 * q^81 + 57 * q^82 - 12 * q^84 - 33 * q^86 + 45 * q^87 - 39 * q^88 - 6 * q^89 - 6 * q^91 + 66 * q^92 + 72 * q^93 - 66 * q^94 - 18 * q^96 + 87 * q^97 - 39 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.124932	−	0.708527i	−0.0883405	−	0.501004i	−0.996586	−	0.0825655i	$-0.973689\pi$
$2$	−0.124932	−	0.708527i	−0.0883405	−	0.501004i	0.908245	−	0.418439i	$-0.137422\pi$
$3$	0.945515	−	0.793382i	0.545894	−	0.458059i	−0.327654	−	0.944798i	$-0.606258\pi$
$3$	0.945515	−	0.793382i	0.545894	−	0.458059i	0.873548	+	0.486739i	$0.161814\pi$
$4$	1.39298	−	0.507004i	0.696492	−	0.253502i
$5$		0			0
$5$		0			0
$6$	−0.680257	−	0.570804i	−0.277714	−	0.233030i
$7$	0.645970	−	1.11885i	0.244154	−	0.422886i	−0.717740	−	0.696311i	$-0.754823\pi$
$7$	0.645970	−	1.11885i	0.244154	−	0.422886i	0.961893	+	0.273425i	$0.0881566\pi$
$8$	−1.25271	−	2.16976i	−0.442900	−	0.767126i
$9$	−0.256400	+	1.45411i	−0.0854665	+	0.484705i
$10$		0			0
$11$	−2.88381	−	4.99491i	−0.869502	−	1.50602i	−0.862506	−	0.506046i	$-0.831107\pi$
$11$	−2.88381	−	4.99491i	−0.869502	−	1.50602i	−0.00699554	−	0.999976i	$-0.502227\pi$
$12$	0.914839	−	1.58455i	0.264091	−	0.457420i
$13$	−1.80125	−	1.51143i	−0.499576	−	0.419194i	0.357867	−	0.933773i	$-0.383504\pi$
$13$	−1.80125	−	1.51143i	−0.499576	−	0.419194i	−0.857443	+	0.514578i	$0.827949\pi$
$14$	−0.873439	−	0.317906i	−0.233436	−	0.0849639i
$15$		0			0
$16$	0.890312	−	0.747060i	0.222578	−	0.186765i
$17$	1.18948	+	6.74589i	0.288492	+	1.63612i	0.692539	+	0.721381i	$0.256492\pi$
$17$	1.18948	+	6.74589i	0.288492	+	1.63612i	−0.404047	+	0.914738i	$0.632397\pi$
$18$	1.06231			0.250389
$19$	2.40586	−	3.63481i	0.551942	−	0.833883i
$19$	2.40586	−	3.63481i	0.551942	−	0.833883i
$20$		0			0
$21$	−0.276903	−	1.57039i	−0.0604251	−	0.342688i
$22$	−3.17874	+	2.66728i	−0.677711	+	0.568667i
$23$	5.32803	−	1.93925i	1.11097	−	0.404361i	0.279622	−	0.960110i	$-0.409791\pi$
$23$	5.32803	−	1.93925i	1.11097	−	0.404361i	0.831350	+	0.555749i	$0.187569\pi$
$24$	−2.90591	−	1.05766i	−0.593166	−	0.215895i
$25$		0			0
$26$	−0.845852	+	1.46506i	−0.165885	+	0.287322i
$27$	2.76266	+	4.78507i	0.531675	+	0.920887i
$28$	0.332562	−	1.88605i	0.0628483	−	0.356430i
$29$	−1.04556	+	5.92966i	−0.194155	+	1.10111i	0.719461	+	0.694533i	$0.244389\pi$
$29$	−1.04556	+	5.92966i	−0.194155	+	1.10111i	−0.913617	+	0.406577i	$0.866722\pi$
$30$		0			0
$31$	1.19445	−	2.06885i	0.214529	−	0.371576i	−0.738598	−	0.674147i	$-0.764512\pi$
$31$	1.19445	−	2.06885i	0.214529	−	0.371576i	0.953127	+	0.302571i	$0.0978449\pi$
$32$	−4.47907	−	3.75839i	−0.791796	−	0.664395i
$33$	−6.68956	−	2.43480i	−1.16450	−	0.423844i
$34$	4.63104	−	1.68556i	0.794217	−	0.289071i
$35$		0			0
$36$	0.380082	+	2.15555i	0.0633470	+	0.359259i
$37$	4.53121			0.744926			0.372463	−	0.928047i	$-0.378513\pi$
$37$	4.53121			0.744926			0.372463	+	0.928047i	$0.378513\pi$
$38$	−2.87593	−	1.25051i	−0.466537	−	0.202859i
$39$	−2.90225			−0.464731
$40$		0			0
$41$	−3.51177	+	2.94672i	−0.548446	+	0.460201i	−0.874414	−	0.485180i	$-0.838754\pi$
$41$	−3.51177	+	2.94672i	−0.548446	+	0.460201i	0.325968	+	0.945381i	$0.394310\pi$
$42$	−1.07807	+	0.392386i	−0.166350	+	0.0605464i
$43$	0.260318	+	0.0947480i	0.0396981	+	0.0144489i	0.361793	−	0.932258i	$-0.382165\pi$
$43$	0.260318	+	0.0947480i	0.0396981	+	0.0144489i	−0.322095	+	0.946707i	$0.604387\pi$
$44$	−6.54954	−	5.49572i	−0.987381	−	0.828511i
$45$		0			0
$46$	−2.03965	−	3.53278i	−0.300730	−	0.520880i
$47$	−0.0880430	+	0.499316i	−0.0128424	+	0.0728328i	−0.990555	−	0.137113i	$-0.956218\pi$
$47$	−0.0880430	+	0.499316i	−0.0128424	+	0.0728328i	0.977713	+	0.209946i	$0.0673288\pi$
$48$	0.249100	−	1.41271i	0.0359544	−	0.203908i
$49$	2.66545	+	4.61669i	0.380778	+	0.659527i
$50$		0			0
$51$	6.47674	+	5.43463i	0.906925	+	0.761001i
$52$	−3.27541	−	1.19215i	−0.454217	−	0.165322i
$53$	−6.75604	+	2.45900i	−0.928013	+	0.337769i	−0.761422	−	0.648257i	$-0.775498\pi$
$53$	−6.75604	+	2.45900i	−0.928013	+	0.337769i	−0.166591	+	0.986026i	$0.553276\pi$
$54$	3.04520	−	2.55523i	0.414400	−	0.347723i
$55$		0			0
$56$	−3.23685			−0.432543
$57$	−0.609016	−	5.34553i	−0.0806662	−	0.708033i
$58$	4.33194			0.568812
$59$	1.00094	+	5.67662i	0.130312	+	0.739034i	0.978010	+	0.208556i	$0.0668763\pi$
$59$	1.00094	+	5.67662i	0.130312	+	0.739034i	−0.847699	+	0.530478i	$0.822013\pi$
$60$		0			0
$61$	6.77273	−	2.46507i	0.867160	−	0.315620i	0.130143	−	0.991495i	$-0.458456\pi$
$61$	6.77273	−	2.46507i	0.867160	−	0.315620i	0.737016	+	0.675875i	$0.236234\pi$
$62$	−1.61506	−	0.587833i	−0.205113	−	0.0746549i
$63$	1.46131	+	1.22619i	0.184108	+	0.154485i
$64$	−0.941117	+	1.63006i	−0.117640	+	0.203758i
$65$		0			0
$66$	−0.889378	+	5.04391i	−0.109475	+	0.620863i
$67$	1.77501	−	10.0666i	0.216852	−	1.22983i	−0.660811	−	0.750552i	$-0.729788\pi$
$67$	1.77501	−	10.0666i	0.216852	−	1.22983i	0.877663	−	0.479278i	$-0.159101\pi$
$68$	5.07713	+	8.79384i	0.615692	+	1.06641i
$69$	3.49918	−	6.06075i	0.421251	−	0.729629i
$70$		0			0
$71$	1.05207	+	0.382923i	0.124858	+	0.0454446i	0.403694	−	0.914894i	$-0.367726\pi$
$71$	1.05207	+	0.382923i	0.124858	+	0.0454446i	−0.278836	+	0.960339i	$0.589948\pi$
$72$	3.47627	−	1.26526i	0.409683	−	0.149112i
$73$	−1.83298	+	1.53805i	−0.214534	+	0.180016i	−0.743722	−	0.668489i	$-0.766941\pi$
$73$	−1.83298	+	1.53805i	−0.214534	+	0.180016i	0.529188	+	0.848505i	$0.322497\pi$
$74$	−0.566094	−	3.21048i	−0.0658071	−	0.373211i
$75$		0			0
$76$	1.50845	−	6.28301i	0.173032	−	0.720711i
$77$	−7.45142			−0.849168
$78$	0.362584	+	2.05632i	0.0410546	+	0.232832i
$79$	−10.7969	+	9.05969i	−1.21475	+	1.01929i	−0.215666	+	0.976467i	$0.569192\pi$
$79$	−10.7969	+	9.05969i	−1.21475	+	1.01929i	−0.999082	+	0.0428275i	$0.986363\pi$
$80$		0			0
$81$	2.24603	+	0.817487i	0.249559	+	0.0908319i
$82$	2.52657	+	2.12004i	0.279012	+	0.234119i
$83$	0.608609	−	1.05414i	0.0668035	−	0.115707i	−0.830689	−	0.556737i	$-0.812053\pi$
$83$	0.608609	−	1.05414i	0.0668035	−	0.115707i	0.897493	+	0.441030i	$0.145387\pi$
$84$	−1.18192	−	2.04714i	−0.128958	−	0.223361i
$85$		0			0
$86$	0.0346093	−	0.196279i	0.00373202	−	0.0211653i
$87$	3.71589	+	6.43611i	0.398385	+	0.690023i
$88$	−7.22517	+	12.5144i	−0.770206	+	1.33404i
$89$	−6.85239	−	5.74984i	−0.726352	−	0.609482i	0.202782	−	0.979224i	$-0.435002\pi$
$89$	−6.85239	−	5.74984i	−0.726352	−	0.609482i	−0.929135	+	0.369742i	$0.879446\pi$
$90$		0			0
$91$	−2.85461	+	1.03899i	−0.299245	+	0.108916i
$92$	6.43866	−	5.40267i	0.671276	−	0.563268i
$93$	−0.512015	−	2.90378i	−0.0530934	−	0.301108i
$94$	0.364778			0.0376240
$95$		0			0
$96$	−7.21687			−0.736568
$97$	1.83977	+	10.4339i	0.186801	+	1.05940i	0.923620	+	0.383309i	$0.125216\pi$
$97$	1.83977	+	10.4339i	0.186801	+	1.05940i	−0.736819	+	0.676090i	$0.763673\pi$
$98$	2.93805	−	2.46531i	0.296788	−	0.249034i
$99$	8.00258	−	2.91270i	0.804289	−	0.292737i
$100$		0			0
$101$	1.65550	+	1.38913i	0.164728	+	0.138223i	0.721426	−	0.692492i	$-0.243487\pi$
$101$	1.65550	+	1.38913i	0.164728	+	0.138223i	−0.556697	+	0.830715i	$0.687932\pi$
$102$	3.04143	−	5.26791i	0.301146	−	0.521600i
$103$	4.54154	+	7.86618i	0.447491	+	0.775078i	0.998222	−	0.0596051i	$-0.0189841\pi$
$103$	4.54154	+	7.86618i	0.447491	+	0.775078i	−0.550731	+	0.834683i	$0.685651\pi$
$104$	−1.02299	+	5.80166i	−0.100312	+	0.568899i
$105$		0			0
$106$	2.58631	+	4.47962i	0.251205	+	0.435099i
$107$	−1.93432	+	3.35035i	−0.186998	+	0.323890i	−0.944248	−	0.329235i	$-0.893209\pi$
$107$	−1.93432	+	3.35035i	−0.186998	+	0.323890i	0.757250	+	0.653125i	$0.226543\pi$
$108$	6.27439	+	5.26484i	0.603754	+	0.506610i
$109$	15.6852	+	5.70895i	1.50237	+	0.546818i	0.956673	−	0.291165i	$-0.0940429\pi$
$109$	15.6852	+	5.70895i	1.50237	+	0.546818i	0.545697	+	0.837983i	$0.316265\pi$
$110$		0			0
$111$	4.28433	−	3.59498i	0.406650	−	0.341220i
$112$	−0.260736	−	1.47871i	−0.0246372	−	0.139725i
$113$	18.0822			1.70103			0.850515	−	0.525951i	$-0.176291\pi$
$113$	18.0822			1.70103			0.850515	+	0.525951i	$0.176291\pi$
$114$	−3.71137	+	1.09933i	−0.347601	+	0.102962i
$115$		0			0
$116$	1.54992	+	8.79002i	0.143906	+	0.816133i
$117$	2.65963	−	2.23169i	0.245882	−	0.206320i
$118$	3.89699	−	1.41839i	0.358747	−	0.130573i
$119$	8.31603	+	3.02679i	0.762329	+	0.277465i
$120$		0			0
$121$	−11.1327	+	19.2825i	−1.01207	+	1.75295i
$122$	−2.59270	−	4.49070i	−0.234732	−	0.406568i
$123$	−0.982554	+	5.57234i	−0.0885940	+	0.502441i
$124$	0.614933	−	3.48746i	0.0552226	−	0.313183i
$125$		0			0
$126$	0.686221	−	1.18857i	0.0611334	−	0.105886i
$127$	−8.26770	−	6.93743i	−0.733640	−	0.615597i	0.197481	−	0.980307i	$-0.436724\pi$
$127$	−8.26770	−	6.93743i	−0.733640	−	0.615597i	−0.931121	+	0.364710i	$0.881168\pi$
$128$	−9.71627	−	3.53643i	−0.858805	−	0.312580i
$129$	0.321306	−	0.116946i	0.0282894	−	0.0102965i
$130$		0			0
$131$	2.19238	+	12.4336i	0.191549	+	1.08633i	0.917248	+	0.398317i	$0.130406\pi$
$131$	2.19238	+	12.4336i	0.191549	+	1.08633i	−0.725699	+	0.688013i	$0.758483\pi$
$132$	−10.5529			−0.918512
$133$	−2.51270	−	5.03978i	−0.217879	−	0.437004i
$134$	−7.35421			−0.635307
$135$		0			0
$136$	13.1469	−	11.0316i	1.12734	−	0.945948i
$137$	−8.64939	+	3.14812i	−0.738967	+	0.268962i	−0.683956	−	0.729524i	$-0.739742\pi$
$137$	−8.64939	+	3.14812i	−0.738967	+	0.268962i	−0.0550118	+	0.998486i	$0.517520\pi$
$138$	−4.73136	−	1.72208i	−0.402760	−	0.146593i
$139$	3.63122	+	3.04696i	0.307996	+	0.258440i	0.783663	−	0.621186i	$-0.213349\pi$
$139$	3.63122	+	3.04696i	0.307996	+	0.258440i	−0.475667	+	0.879625i	$0.657793\pi$
$140$		0			0
$141$	0.312903	+	0.541963i	0.0263511	+	0.0456415i
$142$	0.139873	−	0.793261i	0.0117379	−	0.0665690i
$143$	−2.35498	+	13.3557i	−0.196933	+	1.11686i
$144$	0.858036	+	1.48616i	0.0715030	+	0.123847i
$145$		0			0
$146$	1.31875	+	1.10656i	0.109141	+	0.0915798i
$147$	6.18302	+	2.25043i	0.509967	+	0.185613i
$148$	6.31189	−	2.29734i	0.518835	−	0.188840i
$149$	7.46788	−	6.26629i	0.611792	−	0.513355i	−0.283419	−	0.958996i	$-0.591469\pi$
$149$	7.46788	−	6.26629i	0.611792	−	0.513355i	0.895212	+	0.445641i	$0.147024\pi$
$150$		0			0
$151$	−13.0214			−1.05967			−0.529834	−	0.848101i	$-0.677746\pi$
$151$	−13.0214			−1.05967			−0.529834	+	0.848101i	$0.677746\pi$
$152$	−10.9005	−	0.666765i	−0.884148	−	0.0540818i
$153$	−10.1143			−0.817691
$154$	0.930923	+	5.27953i	0.0750160	+	0.425437i
$155$		0			0
$156$	−4.04278	+	1.47145i	−0.323681	+	0.117810i
$157$	17.4944	+	6.36745i	1.39621	+	0.508178i	0.927050	−	0.374938i	$-0.122336\pi$
$157$	17.4944	+	6.36745i	1.39621	+	0.508178i	0.469156	+	0.883115i	$0.344558\pi$
$158$	7.76792	+	6.51806i	0.617982	+	0.518549i
$159$	−4.43701	+	7.68513i	−0.351878	+	0.609471i
$160$		0			0
$161$	1.27202	−	7.21398i	0.100249	−	0.568541i
$162$	0.298610	−	1.69350i	0.0234610	−	0.133054i
$163$	−4.94380	−	8.56291i	−0.387228	−	0.670699i	0.604847	−	0.796341i	$-0.293234\pi$
$163$	−4.94380	−	8.56291i	−0.387228	−	0.670699i	−0.992076	+	0.125642i	$0.959901\pi$
$164$	−3.39783	+	5.88522i	−0.265326	+	0.459558i
$165$		0			0
$166$	−0.822923	−	0.299519i	−0.0638712	−	0.0232472i
$167$	−11.2804	+	4.10574i	−0.872905	+	0.317711i	−0.739343	−	0.673329i	$-0.764864\pi$
$167$	−11.2804	+	4.10574i	−0.872905	+	0.317711i	−0.133562	+	0.991040i	$0.542642\pi$
$168$	−3.06050	+	2.56806i	−0.236122	+	0.198130i
$169$	−1.29734	−	7.35759i	−0.0997956	−	0.565969i
$170$		0			0
$171$	4.66857	+	4.43036i	0.357014	+	0.338798i
$172$	0.410656			0.0313122
$173$	−2.86662	−	16.2574i	−0.217945	−	1.23603i	−0.875722	−	0.482815i	$-0.839614\pi$
$173$	−2.86662	−	16.2574i	−0.217945	−	1.23603i	0.657777	−	0.753213i	$-0.271497\pi$
$174$	4.09592	−	3.43688i	0.310511	−	0.260550i
$175$		0			0
$176$	−6.29899	−	2.29265i	−0.474804	−	0.172815i
$177$	5.45014	+	4.57321i	0.409657	+	0.343743i
$178$	−3.21783	+	5.57345i	−0.241187	+	0.417747i
$179$	−10.1073	−	17.5064i	−0.755458	−	1.30849i	−0.945146	−	0.326647i	$-0.894081\pi$
$179$	−10.1073	−	17.5064i	−0.755458	−	1.30849i	0.189688	−	0.981844i	$-0.439252\pi$
$180$		0			0
$181$	0.0414421	−	0.235030i	0.00308037	−	0.0174696i	−0.983229	−	0.182376i	$-0.941621\pi$
$181$	0.0414421	−	0.235030i	0.00308037	−	0.0174696i	0.986309	+	0.164907i	$0.0527322\pi$
$182$	1.09279	+	1.89277i	0.0810029	+	0.140301i
$183$	4.44798	−	7.70413i	0.328804	−	0.569506i
$184$	−10.8822	−	9.13124i	−0.802246	−	0.673164i
$185$		0			0
$186$	−1.99344	+	0.725552i	−0.146166	+	0.0532001i
$187$	30.2649	−	25.3952i	2.21319	−	1.85708i
$188$	0.130513	+	0.740178i	0.00951866	+	0.0539830i
$189$	7.13838			0.519241
$190$		0			0
$191$	−0.323227			−0.0233879			−0.0116939	−	0.999932i	$-0.503722\pi$
$191$	−0.323227			−0.0233879			−0.0116939	+	0.999932i	$0.503722\pi$
$192$	0.403421	+	2.28791i	0.0291144	+	0.165116i
$193$	−1.12114	+	0.940747i	−0.0807013	+	0.0677164i	−0.682246	−	0.731123i	$-0.738997\pi$
$193$	−1.12114	+	0.940747i	−0.0807013	+	0.0677164i	0.601545	+	0.798839i	$0.294552\pi$
$194$	7.16283	−	2.60706i	0.514261	−	0.187176i
$195$		0			0
$196$	6.05360	+	5.07958i	0.432400	+	0.362827i
$197$	−4.77502	+	8.27058i	−0.340206	+	0.589255i	−0.984471	−	0.175548i	$-0.943830\pi$
$197$	−4.77502	+	8.27058i	−0.340206	+	0.589255i	0.644265	+	0.764803i	$0.277164\pi$
$198$	−3.06351	−	5.30615i	−0.217714	−	0.377092i
$199$	0.242795	−	1.37696i	0.0172113	−	0.0976101i	−0.974992	−	0.222240i	$-0.928663\pi$
$199$	0.242795	−	1.37696i	0.0172113	−	0.0976101i	0.992203	+	0.124630i	$0.0397743\pi$
$200$		0			0
$201$	−6.30835	−	10.9264i	−0.444957	−	0.770687i
$202$	0.777409	−	1.34651i	0.0546983	−	0.0947402i
$203$	5.95901	+	5.00020i	0.418241	+	0.350946i
$204$	11.7774	+	4.28661i	0.824581	+	0.300123i
$205$		0			0
$206$	5.00601	−	4.20054i	0.348786	−	0.292666i
$207$	1.45378	+	8.24479i	0.101045	+	0.573053i
$208$	−2.73280			−0.189486
$209$	−25.0936	−	1.53493i	−1.73576	−	0.106173i
$210$		0			0
$211$	−2.95007	−	16.7307i	−0.203091	−	1.15179i	−0.900415	−	0.435031i	$-0.856737\pi$
$211$	−2.95007	−	16.7307i	−0.203091	−	1.15179i	0.697324	−	0.716756i	$-0.254374\pi$
$212$	−8.16432	+	6.85068i	−0.560728	+	0.470507i
$213$	1.29855	−	0.472635i	0.0889755	−	0.0323844i
$214$	2.61547	+	0.951954i	0.178790	+	0.0650742i
$215$		0			0
$216$	6.92164	−	11.9886i	0.470958	−	0.815723i
$217$	−1.54316	−	2.67282i	−0.104756	−	0.181443i
$218$	2.08535	−	11.8266i	0.141238	−	0.800999i
$219$	−0.512848	+	2.90851i	−0.0346551	+	0.196539i
$220$		0			0
$221$	8.05337	−	13.9488i	0.541728	−	0.938301i
$222$	−3.08239	−	2.58643i	−0.206876	−	0.173590i
$223$	11.0581	+	4.02483i	0.740507	+	0.269523i	0.684606	−	0.728914i	$-0.259974\pi$
$223$	11.0581	+	4.02483i	0.740507	+	0.269523i	0.0559018	+	0.998436i	$0.482197\pi$
$224$	−7.09843	+	2.58362i	−0.474283	+	0.172625i
$225$		0			0
$226$	−2.25905	−	12.8117i	−0.150270	−	0.852223i
$227$	−27.5106			−1.82594			−0.912971	−	0.408025i	$-0.866218\pi$
$227$	−27.5106			−1.82594			−0.912971	+	0.408025i	$0.866218\pi$
$228$	−3.55856	−	7.13746i	−0.235671	−	0.472690i
$229$	−9.40958			−0.621802			−0.310901	−	0.950442i	$-0.600631\pi$
$229$	−9.40958			−0.621802			−0.310901	+	0.950442i	$0.600631\pi$
$230$		0			0
$231$	−7.04543	+	5.91182i	−0.463555	+	0.388969i
$232$	14.1757	−	5.15954i	0.930681	−	0.338740i
$233$	1.04994	+	0.382148i	0.0687841	+	0.0250354i	0.376183	−	0.926545i	$-0.377236\pi$
$233$	1.04994	+	0.382148i	0.0687841	+	0.0250354i	−0.307399	+	0.951581i	$0.599459\pi$
$234$	−1.91349	−	1.60561i	−0.125088	−	0.104962i
$235$		0			0
$236$	4.27237	+	7.39996i	0.278108	+	0.481696i
$237$	−3.02086	+	17.1322i	−0.196226	+	1.11285i
$238$	1.10562	−	6.27027i	0.0716666	−	0.406441i
$239$	6.48276	+	11.2285i	0.419335	+	0.726310i	0.995873	−	0.0907608i	$-0.0289299\pi$
$239$	6.48276	+	11.2285i	0.419335	+	0.726310i	−0.576538	+	0.817071i	$0.695597\pi$
$240$		0			0
$241$	−15.6540	−	13.1353i	−1.00836	−	0.846118i	−0.0202435	−	0.999795i	$-0.506444\pi$
$241$	−15.6540	−	13.1353i	−1.00836	−	0.846118i	−0.988121	+	0.153677i	$0.950889\pi$
$242$	15.0530	+	5.47884i	0.967643	+	0.352193i
$243$	−12.8041	+	4.66031i	−0.821382	+	0.298959i
$244$	8.18450	−	6.86761i	0.523959	−	0.439654i
$245$		0			0
$246$	4.07091			0.259552
$247$	−9.82729	+	2.91092i	−0.625296	+	0.185217i
$248$	−5.98520			−0.380061
$249$	−0.260887	−	1.47957i	−0.0165331	−	0.0937637i
$250$		0			0
$251$	15.5328	−	5.65348i	0.980422	−	0.356844i	0.198418	−	0.980118i	$-0.436420\pi$
$251$	15.5328	−	5.65348i	0.980422	−	0.356844i	0.782004	+	0.623273i	$0.214198\pi$
$252$	2.65727	+	0.967166i	0.167392	+	0.0609257i
$253$	−25.0514	−	21.0206i	−1.57497	−	1.32156i
$254$	−3.88245	+	6.72460i	−0.243606	+	0.421939i
$255$		0			0
$256$	−1.94547	+	11.0333i	−0.121592	+	0.689583i
$257$	2.02701	−	11.4958i	0.126442	−	0.717087i	−0.853999	−	0.520274i	$-0.825830\pi$
$257$	2.02701	−	11.4958i	0.126442	−	0.717087i	0.980441	−	0.196813i	$-0.0630591\pi$
$258$	−0.123001	−	0.213043i	−0.00765769	−	0.0132635i
$259$	2.92702	−	5.06975i	0.181876	−	0.315019i
$260$		0			0
$261$	−8.35432	−	3.04072i	−0.517119	−	0.188216i
$262$	8.53564	−	3.10672i	0.527334	−	0.191934i
$263$	5.34724	−	4.48687i	0.329725	−	0.276672i	−0.462863	−	0.886430i	$-0.653178\pi$
$263$	5.34724	−	4.48687i	0.329725	−	0.276672i	0.792588	+	0.609758i	$0.208733\pi$
$264$	3.09715	+	17.5648i	0.190617	+	1.08104i
$265$		0			0
$266$	−3.25690	+	2.40995i	−0.199693	+	0.147763i
$267$	−11.0409			−0.675690
$268$	−2.63125	−	14.9225i	−0.160729	−	0.911539i
$269$	−3.94311	+	3.30866i	−0.240416	+	0.201733i	−0.755032	−	0.655688i	$-0.772379\pi$
$269$	−3.94311	+	3.30866i	−0.240416	+	0.201733i	0.514617	+	0.857420i	$0.327934\pi$
$270$		0			0
$271$	3.24655	+	1.18165i	0.197214	+	0.0717801i	0.438739	−	0.898615i	$-0.355425\pi$
$271$	3.24655	+	1.18165i	0.197214	+	0.0717801i	−0.241525	+	0.970395i	$0.577648\pi$
$272$	6.09860	+	5.11733i	0.369782	+	0.310284i
$273$	−1.87476	+	3.24718i	−0.113466	+	0.196528i
$274$	3.31112	+	5.73502i	0.200032	+	0.346465i
$275$		0			0
$276$	1.80147	−	10.2166i	0.108436	−	0.614968i
$277$	4.09007	+	7.08421i	0.245749	+	0.425649i	0.962342	−	0.271842i	$-0.0876329\pi$
$277$	4.09007	+	7.08421i	0.245749	+	0.425649i	−0.716593	+	0.697491i	$0.754300\pi$
$278$	1.70519	−	2.95348i	0.102271	−	0.177138i
$279$	2.70208	+	2.26732i	0.161769	+	0.135741i
$280$		0			0
$281$	−10.5082	+	3.82467i	−0.626866	+	0.228160i	−0.635866	−	0.771799i	$-0.719357\pi$
$281$	−10.5082	+	3.82467i	−0.626866	+	0.228160i	0.00900091	+	0.999959i	$0.497135\pi$
$282$	0.344904	−	0.289409i	0.0205387	−	0.0172340i
$283$	−3.01728	−	17.1119i	−0.179359	−	1.01719i	−0.932992	−	0.359898i	$-0.882811\pi$
$283$	−3.01728	−	17.1119i	−0.179359	−	1.01719i	0.753633	−	0.657296i	$-0.228300\pi$
$284$	1.65966			0.0984829
$285$		0			0
$286$	9.75711			0.576950
$287$	1.02845	+	5.83264i	0.0607076	+	0.344290i
$288$	6.61356	−	5.54943i	0.389708	−	0.327004i
$289$	−28.1174	+	10.2339i	−1.65397	+	0.601994i
$290$		0			0
$291$	10.0176	+	8.40574i	0.587241	+	0.492753i
$292$	−1.77351	+	3.07181i	−0.103787	+	0.179764i
$293$	1.43049	+	2.47768i	0.0835699	+	0.144747i	0.904781	−	0.425877i	$-0.140034\pi$
$293$	1.43049	+	2.47768i	0.0835699	+	0.144747i	−0.821211	+	0.570625i	$0.806701\pi$
$294$	0.822034	−	4.66198i	0.0479420	−	0.271892i
$295$		0			0
$296$	−5.67630	−	9.83163i	−0.329928	−	0.571452i
$297$	15.9340	−	27.5985i	0.924584	−	1.60143i
$298$	−5.37282	−	4.50833i	−0.311239	−	0.261160i
$299$	−12.5281	−	4.55987i	−0.724521	−	0.263704i
$300$		0			0
$301$	0.274166	−	0.230053i	0.0158027	−	0.0132600i
$302$	1.62680	+	9.22602i	0.0936116	+	0.530898i
$303$	2.66741			0.153239
$304$	−0.573459	−	5.03344i	−0.0328901	−	0.288687i
$305$		0			0
$306$	1.26360	+	7.16624i	0.0722353	+	0.409667i
$307$	−21.4527	+	18.0009i	−1.22437	+	1.02737i	−0.225784	+	0.974177i	$0.572494\pi$
$307$	−21.4527	+	18.0009i	−1.22437	+	1.02737i	−0.998584	+	0.0531897i	$0.983061\pi$
$308$	−10.3797	+	3.77790i	−0.591438	+	0.215266i
$309$	10.5350	+	3.83442i	0.599314	+	0.218133i
$310$		0			0
$311$	10.9646	−	18.9912i	0.621744	−	1.07689i	−0.367417	−	0.930056i	$-0.619758\pi$
$311$	10.9646	−	18.9912i	0.621744	−	1.07689i	0.989161	−	0.146836i	$-0.0469090\pi$
$312$	3.63568	+	6.29718i	0.205830	+	0.356507i
$313$	−0.204904	+	1.16207i	−0.0115819	+	0.0656841i	−0.990051	−	0.140710i	$-0.955062\pi$
$313$	−0.204904	+	1.16207i	−0.0115819	+	0.0656841i	0.978469	+	0.206394i	$0.0661727\pi$
$314$	2.32589	−	13.1908i	0.131257	−	0.744398i
$315$		0			0
$316$	−10.4466	+	18.0941i	−0.587668	+	1.01787i
$317$	−22.7839	−	19.1180i	−1.27967	−	1.07377i	−0.993289	−	0.115660i	$-0.963102\pi$
$317$	−22.7839	−	19.1180i	−1.27967	−	1.07377i	−0.286385	−	0.958115i	$-0.592454\pi$
$318$	5.99945	+	2.18362i	0.336432	+	0.122451i
$319$	32.6333	−	11.8775i	1.82711	−	0.665015i
$320$		0			0
$321$	0.829171	+	4.70246i	0.0462798	+	0.262466i
$322$	−5.27021			−0.293697
$323$	27.3818	+	11.9061i	1.52356	+	0.662474i
$324$	3.54315			0.196842
$325$		0			0
$326$	−5.44941	+	4.57260i	−0.301815	+	0.253253i
$327$	19.3600	−	7.04645i	1.07061	−	0.389670i
$328$	10.7929	+	3.92830i	0.595939	+	0.216904i
$329$	0.501788	+	0.421050i	0.0276645	+	0.0232133i
$330$		0			0
$331$	12.7192	+	22.0304i	0.699113	+	1.21090i	0.968774	+	0.247944i	$0.0797549\pi$
$331$	12.7192	+	22.0304i	0.699113	+	1.21090i	−0.269662	+	0.962955i	$0.586912\pi$
$332$	0.313328	−	1.77697i	0.0171961	−	0.0975239i
$333$	−1.16180	+	6.58889i	−0.0636662	+	0.361069i
$334$	4.31831	+	7.47954i	0.236288	+	0.409262i
$335$		0			0
$336$	−1.41971	−	1.19128i	−0.0774514	−	0.0649894i
$337$	11.0931	+	4.03756i	0.604280	+	0.219940i	0.625998	−	0.779824i	$-0.284692\pi$
$337$	11.0931	+	4.03756i	0.604280	+	0.219940i	−0.0217189	+	0.999764i	$0.506914\pi$
$338$	−5.05097	+	1.83840i	−0.274737	+	0.0999960i
$339$	17.0970	−	14.3461i	0.928581	−	0.779172i
$340$		0			0
$341$	−13.7783			−0.746135
$342$	2.55577	−	3.86130i	0.138200	−	0.208795i
$343$	15.9308			0.860180
$344$	−0.120523	−	0.683519i	−0.00649816	−	0.0368529i
$345$		0			0
$346$	−11.1607	+	4.06215i	−0.600001	+	0.218383i
$347$	−4.62279	−	1.68256i	−0.248164	−	0.0903244i	0.214943	−	0.976627i	$-0.431043\pi$
$347$	−4.62279	−	1.68256i	−0.248164	−	0.0903244i	−0.463107	+	0.886302i	$0.653266\pi$
$348$	8.43931	+	7.08142i	0.452394	+	0.379604i
$349$	18.1158	−	31.3775i	0.969717	−	1.67960i	0.273349	−	0.961915i	$-0.411869\pi$
$349$	18.1158	−	31.3775i	0.969717	−	1.67960i	0.696368	−	0.717685i	$-0.254798\pi$
$350$		0			0
$351$	2.25604	−	12.7947i	0.120419	−	0.682928i
$352$	−5.85600	+	33.2110i	−0.312126	+	1.77015i
$353$	−12.7952	−	22.1620i	−0.681022	−	1.17957i	−0.974669	−	0.223651i	$-0.928202\pi$
$353$	−12.7952	−	22.1620i	−0.681022	−	1.17957i	0.293647	−	0.955914i	$-0.405131\pi$
$354$	2.55934	−	4.43291i	0.136027	−	0.235606i
$355$		0			0
$356$	−12.4605	−	4.53524i	−0.660403	−	0.240367i
$357$	10.2643	−	3.73591i	0.543246	−	0.197725i
$358$	−11.1410	+	9.34844i	−0.588822	+	0.494080i
$359$	5.34835	+	30.3320i	0.282275	+	1.60086i	0.714859	+	0.699269i	$0.246491\pi$
$359$	5.34835	+	30.3320i	0.282275	+	1.60086i	−0.432583	+	0.901594i	$0.642398\pi$
$360$		0			0
$361$	−7.42369	−	17.4897i	−0.390721	−	0.920509i
$362$	−0.171702			−0.00902447
$363$	4.77218	+	27.0644i	0.250475	+	1.42051i
$364$	−3.44965	+	2.89460i	−0.180811	+	0.151718i
$365$		0			0
$366$	−6.01428	−	2.18902i	−0.314371	−	0.114422i
$367$	−23.0842	−	19.3699i	−1.20499	−	1.01110i	−0.999473	−	0.0324481i	$-0.989670\pi$
$367$	−23.0842	−	19.3699i	−1.20499	−	1.01110i	−0.205512	−	0.978655i	$-0.565886\pi$
$368$	3.29488	−	5.70690i	0.171757	−	0.297493i
$369$	−3.38446	−	5.86205i	−0.176188	−	0.305166i
$370$		0			0
$371$	−1.61294	+	9.14744i	−0.0837397	+	0.474912i
$372$	−2.18546	−	3.78532i	−0.113311	−	0.196260i
$373$	−14.0122	+	24.2699i	−0.725526	+	1.25665i	0.233231	+	0.972421i	$0.425070\pi$
$373$	−14.0122	+	24.2699i	−0.725526	+	1.25665i	−0.958757	+	0.284227i	$0.908263\pi$
$374$	−21.7743	−	18.2708i	−1.12592	−	0.944760i
$375$		0			0
$376$	1.19369	−	0.434467i	0.0615598	−	0.0224059i
$377$	10.8456	−	9.10050i	0.558574	−	0.468699i
$378$	−0.891815	−	5.05773i	−0.0458700	−	0.260142i
$379$	−22.6159			−1.16170			−0.580851	−	0.814010i	$-0.697280\pi$
$379$	−22.6159			−1.16170			−0.580851	+	0.814010i	$0.697280\pi$
$380$		0			0
$381$	−13.3213			−0.682469
$382$	0.0403815	+	0.229015i	0.00206610	+	0.0117174i
$383$	−7.67822	+	6.44279i	−0.392339	+	0.329211i	−0.817523	−	0.575895i	$-0.804654\pi$
$383$	−7.67822	+	6.44279i	−0.392339	+	0.329211i	0.425185	+	0.905107i	$0.360209\pi$
$384$	−11.9926	+	4.36496i	−0.611996	+	0.222748i
$385$		0			0
$386$	0.806611	+	0.676827i	0.0410554	+	0.0344496i
$387$	−0.204520	+	0.354239i	−0.0103963	+	0.0180070i
$388$	7.85279	+	13.6014i	0.398665	+	0.690508i
$389$	−1.26793	+	7.19077i	−0.0642865	+	0.364587i	0.935646	+	0.352941i	$0.114818\pi$
$389$	−1.26793	+	7.19077i	−0.0642865	+	0.364587i	−0.999932	+	0.0116460i	$0.996293\pi$
$390$		0			0
$391$	19.4195	+	33.6356i	0.982089	+	1.70103i
$392$	6.67807	−	11.5668i	0.337294	−	0.584210i
$393$	11.9375	+	10.0168i	0.602168	+	0.505279i
$394$	6.45648	+	2.34997i	0.325273	+	0.118390i
$395$		0			0
$396$	9.67070	−	8.11468i	0.485971	−	0.407778i
$397$	6.31493	+	35.8137i	0.316937	+	1.79744i	0.561145	+	0.827717i	$0.310361\pi$
$397$	6.31493	+	35.8137i	0.316937	+	1.79744i	−0.244208	+	0.969723i	$0.578528\pi$
$398$	−1.00595			−0.0504235
$399$	−6.37427	−	2.77165i	−0.319112	−	0.138756i
$400$		0			0
$401$	1.58822	+	9.00726i	0.0793121	+	0.449801i	0.998440	+	0.0558411i	$0.0177840\pi$
$401$	1.58822	+	9.00726i	0.0793121	+	0.449801i	−0.919128	+	0.393960i	$0.871105\pi$
$402$	−6.95351	+	5.83469i	−0.346810	+	0.291008i
$403$	−5.27841	+	1.92118i	−0.262936	+	0.0957009i
$404$	3.01038	+	1.09569i	0.149772	+	0.0545125i
$405$		0			0
$406$	2.79830	−	4.84681i	0.138878	−	0.240543i
$407$	−13.0671	−	22.6330i	−0.647714	−	1.12187i
$408$	3.67836	−	20.8610i	0.182106	−	1.03277i
$409$	−0.814898	+	4.62152i	−0.0402941	+	0.228519i	−0.998304	−	0.0582158i	$-0.981459\pi$
$409$	−0.814898	+	4.62152i	−0.0402941	+	0.228519i	0.958010	+	0.286735i	$0.0925700\pi$
$410$		0			0
$411$	−5.68047	+	9.83887i	−0.280197	+	0.485315i
$412$	10.3145	+	8.65488i	0.508158	+	0.426395i
$413$	6.99788	+	2.54702i	0.344343	+	0.125331i
$414$	5.66003	−	2.06008i	0.278175	−	0.101248i
$415$		0			0
$416$	2.38739	+	13.5396i	0.117052	+	0.663832i
$417$	5.85078			0.286514
$418$	2.04746	+	17.9712i	0.100145	+	0.879002i
$419$	−0.588477			−0.0287490			−0.0143745	−	0.999897i	$-0.504576\pi$
$419$	−0.588477			−0.0287490			−0.0143745	+	0.999897i	$0.504576\pi$
$420$		0			0
$421$	−4.71306	+	3.95473i	−0.229701	+	0.192742i	−0.750373	−	0.661015i	$-0.770126\pi$
$421$	−4.71306	+	3.95473i	−0.229701	+	0.192742i	0.520672	+	0.853757i	$0.325681\pi$
$422$	−11.4856	+	4.18040i	−0.559109	+	0.203499i
$423$	−0.703489	−	0.256049i	−0.0342048	−	0.0124495i
$424$	13.7988	+	11.5786i	0.670129	+	0.562305i
$425$		0			0
$426$	−0.497106	−	0.861013i	−0.0240849	−	0.0417162i
$427$	1.61693	−	9.17005i	0.0782486	−	0.443770i
$428$	−0.995840	+	5.64769i	−0.0481358	+	0.272991i
$429$	8.36953	+	14.4965i	0.404085	+	0.699895i
$430$		0			0
$431$	−0.241775	−	0.202873i	−0.0116459	−	0.00977207i	0.636946	−	0.770908i	$-0.280197\pi$
$431$	−0.241775	−	0.202873i	−0.0116459	−	0.00977207i	−0.648592	+	0.761136i	$0.724642\pi$
$432$	6.03437	+	2.19633i	0.290329	+	0.105671i
$433$	32.1844	−	11.7142i	1.54668	−	0.562947i	0.579046	−	0.815295i	$-0.303425\pi$
$433$	32.1844	−	11.7142i	1.54668	−	0.562947i	0.967637	+	0.252348i	$0.0812028\pi$
$434$	−1.70098	+	1.42729i	−0.0816495	+	0.0685121i
$435$		0			0
$436$	24.7437			1.18501
$437$	5.76970	−	24.0319i	0.276002	−	1.14960i
$438$	2.12483			0.101528
$439$	−0.363229	−	2.05997i	−0.0173360	−	0.0983172i	0.974912	−	0.222590i	$-0.0714512\pi$
$439$	−0.363229	−	2.05997i	−0.0173360	−	0.0983172i	−0.992248	+	0.124273i	$0.960340\pi$
$440$		0			0
$441$	−7.39661	+	2.69215i	−0.352220	+	0.128197i
$442$	−10.8893	−	3.96336i	−0.517949	−	0.188518i
$443$	6.51336	+	5.46536i	0.309459	+	0.259667i	0.784268	−	0.620422i	$-0.213039\pi$
$443$	6.51336	+	5.46536i	0.309459	+	0.259667i	−0.474809	+	0.880089i	$0.657483\pi$
$444$	4.14532	−	7.17991i	0.196728	−	0.340744i
$445$		0			0
$446$	1.47018	−	8.33782i	0.0696151	−	0.394807i
$447$	2.08943	−	11.8498i	0.0988267	−	0.560474i
$448$	1.21587	+	2.10594i	0.0574443	+	0.0994964i
$449$	7.75850	−	13.4381i	0.366146	−	0.634184i	−0.622813	−	0.782371i	$-0.714010\pi$
$449$	7.75850	−	13.4381i	0.366146	−	0.634184i	0.988959	+	0.148187i	$0.0473437\pi$
$450$		0			0
$451$	24.8459	+	9.04316i	1.16995	+	0.425826i
$452$	25.1882	−	9.16775i	1.18475	−	0.431215i
$453$	−12.3120	+	10.3310i	−0.578466	+	0.485391i
$454$	3.43696	+	19.4920i	0.161305	+	0.914804i
$455$		0			0
$456$	−10.8356	+	8.01783i	−0.507424	+	0.375469i
$457$	−37.2930			−1.74449			−0.872247	−	0.489065i	$-0.837338\pi$
$457$	−37.2930			−1.74449			−0.872247	+	0.489065i	$0.837338\pi$
$458$	1.17556	+	6.66694i	0.0549303	+	0.311525i
$459$	−28.9934	+	24.3284i	−1.35330	+	1.13555i
$460$		0			0
$461$	16.4663	+	5.99324i	0.766912	+	0.279133i	0.695704	−	0.718328i	$-0.255092\pi$
$461$	16.4663	+	5.99324i	0.766912	+	0.279133i	0.0712079	+	0.997461i	$0.477315\pi$
$462$	5.06888	+	4.25330i	0.235826	+	0.197881i
$463$	−16.7188	+	28.9578i	−0.776987	+	1.34578i	0.156683	+	0.987649i	$0.449920\pi$
$463$	−16.7188	+	28.9578i	−0.776987	+	1.34578i	−0.933671	+	0.358133i	$0.883414\pi$
$464$	3.49894	+	6.06034i	0.162434	+	0.281344i
$465$		0			0
$466$	0.139590	−	0.791656i	0.00646640	−	0.0366728i
$467$	7.48091	+	12.9573i	0.346175	+	0.599593i	0.985567	−	0.169288i	$-0.0541469\pi$
$467$	7.48091	+	12.9573i	0.346175	+	0.599593i	−0.639391	+	0.768882i	$0.720814\pi$
$468$	2.57334	−	4.45715i	0.118953	−	0.206032i
$469$	−10.1164	−	8.48869i	−0.467133	−	0.391971i
$470$		0			0
$471$	21.5931	−	7.85923i	0.994955	−	0.362134i
$472$	11.0630	−	9.28298i	0.509217	−	0.427284i
$473$	−0.277450	−	1.57350i	−0.0127572	−	0.0723496i
$474$	12.5160			0.574878
$475$		0			0
$476$	13.1187			0.601294
$477$	−1.84342	−	10.4545i	−0.0844042	−	0.478680i
$478$	7.14577	−	5.99601i	0.326840	−	0.274251i
$479$	14.8807	−	5.41612i	0.679915	−	0.247469i	0.0211037	−	0.999777i	$-0.493282\pi$
$479$	14.8807	−	5.41612i	0.679915	−	0.247469i	0.658811	+	0.752309i	$0.271060\pi$
$480$		0			0
$481$	−8.16183	−	6.84858i	−0.372147	−	0.312269i
$482$	−7.35101	+	12.7323i	−0.334829	+	0.579941i
$483$	−4.52072	−	7.83012i	−0.205700	−	0.356283i
$484$	−5.73142	+	32.5045i	−0.260519	+	1.47748i
$485$		0			0
$486$	4.90160	+	8.48981i	0.222341	+	0.385106i
$487$	3.24767	−	5.62514i	0.147166	−	0.254899i	−0.783013	−	0.622006i	$-0.786318\pi$
$487$	3.24767	−	5.62514i	0.147166	−	0.254899i	0.930179	+	0.367106i	$0.119651\pi$
$488$	−13.8329	−	11.6072i	−0.626186	−	0.525433i
$489$	−11.4681	−	4.17404i	−0.518605	−	0.188757i
$490$		0			0
$491$	−1.28942	+	1.08195i	−0.0581905	+	0.0488277i	−0.671419	−	0.741078i	$-0.734315\pi$
$491$	−1.28942	+	1.08195i	−0.0581905	+	0.0488277i	0.613229	+	0.789906i	$0.289870\pi$
$492$	1.45652	+	8.26034i	0.0656650	+	0.372405i
$493$	−41.2445			−1.85756
$494$	3.29021	+	6.59923i	0.148034	+	0.296914i
$495$		0			0
$496$	−0.482121	−	2.73424i	−0.0216479	−	0.122771i
$497$	1.10804	−	0.929757i	0.0497024	−	0.0417053i
$498$	−1.01572	+	0.369691i	−0.0455155	+	0.0165663i
$499$	−12.5320	−	4.56129i	−0.561011	−	0.204191i	0.0459208	−	0.998945i	$-0.485378\pi$
$499$	−12.5320	−	4.56129i	−0.561011	−	0.204191i	−0.606932	+	0.794754i	$0.707600\pi$
$500$		0			0
$501$	−7.40839	+	12.8317i	−0.330983	+	0.573279i
$502$	−5.94619	−	10.2991i	−0.265391	−	0.459672i
$503$	−1.32303	+	7.50329i	−0.0589911	+	0.334555i	−0.999993	−	0.00384718i	$-0.998775\pi$
$503$	−1.32303	+	7.50329i	−0.0589911	+	0.334555i	0.941001	+	0.338402i	$0.109887\pi$
$504$	0.829928	−	4.70676i	0.0369679	−	0.209656i
$505$		0			0
$506$	−11.7639	+	20.3757i	−0.522971	+	0.905812i
$507$	−7.06404	−	5.92743i	−0.313725	−	0.263246i
$508$	−15.0341	−	5.47196i	−0.667029	−	0.242779i
$509$	−17.8484	+	6.49628i	−0.791116	+	0.287943i	−0.705800	−	0.708411i	$-0.749412\pi$
$509$	−17.8484	+	6.49628i	−0.791116	+	0.287943i	−0.0853161	+	0.996354i	$0.527190\pi$
$510$		0			0
$511$	0.536805	+	3.04437i	0.0237468	+	0.134675i
$512$	−12.6192			−0.557696
$513$	24.0394	+	1.47045i	1.06137	+	0.0649219i
$514$	−8.39830			−0.370433
$515$		0			0
$516$	0.388282	−	0.325807i	0.0170931	−	0.0143429i
$517$	2.74794	−	1.00017i	0.120854	−	0.0439873i
$518$	−3.95773	−	1.44050i	−0.173893	−	0.0632918i
$519$	−15.6088	−	13.0973i	−0.685149	−	0.574908i
$520$		0			0
$521$	−10.1510	−	17.5821i	−0.444724	−	0.770285i	0.553308	−	0.832976i	$-0.313365\pi$
$521$	−10.1510	−	17.5821i	−0.444724	−	0.770285i	−0.998033	+	0.0626910i	$0.980032\pi$
$522$	−1.11071	+	6.29914i	−0.0486144	+	0.275706i
$523$	2.66928	−	15.1382i	0.116719	−	0.661948i	−0.869165	−	0.494522i	$-0.835343\pi$
$523$	2.66928	−	15.1382i	0.116719	−	0.661948i	0.985885	−	0.167426i	$-0.0535456\pi$
$524$	9.35784	+	16.2083i	0.408799	+	0.708061i
$525$		0			0
$526$	−3.84711	−	3.22811i	−0.167742	−	0.140752i
$527$	15.3770	+	5.59677i	0.669832	+	0.243799i
$528$	−7.77474	+	2.82977i	−0.338352	+	0.123150i
$529$	7.00825	−	5.88062i	0.304706	−	0.255679i
$530$		0			0
$531$	−8.51110			−0.369350
$532$	−6.05534	−	5.74637i	−0.262532	−	0.249137i
$533$	10.7793			0.466904
$534$	1.37936	+	7.82275i	0.0596908	+	0.338523i
$535$		0			0
$536$	−24.0657	+	8.75919i	−1.03948	+	0.378339i
$537$	−23.4459	−	8.53362i	−1.01177	−	0.368253i
$538$	2.83690	+	2.38044i	0.122307	+	0.102628i
$539$	15.3733	−	26.6273i	0.662175	−	1.14692i
$540$		0			0
$541$	2.26414	−	12.8406i	0.0973431	−	0.552060i	−0.896661	−	0.442718i	$-0.854014\pi$
$541$	2.26414	−	12.8406i	0.0973431	−	0.552060i	0.994004	−	0.109342i	$-0.0348745\pi$
$542$	0.431630	−	2.44790i	0.0185401	−	0.105146i
$543$	−0.147284	−	0.255104i	−0.00632057	−	0.0109475i
$544$	20.0259	−	34.6859i	0.858603	−	1.48714i
$545$		0			0
$546$	2.53493	+	0.922641i	0.108485	+	0.0394854i
$547$	13.7727	−	5.01285i	0.588878	−	0.214334i	−0.0303580	−	0.999539i	$-0.509665\pi$
$547$	13.7727	−	5.01285i	0.588878	−	0.214334i	0.619236	+	0.785205i	$0.287443\pi$
$548$	−10.4523	+	8.77056i	−0.446502	+	0.374660i
$549$	1.84797	+	10.4804i	0.0788695	+	0.447291i
$550$		0			0
$551$	19.0377	+	18.0663i	0.811034	+	0.769651i
$552$	−17.5338			−0.746290
$553$	3.16197	+	17.9324i	0.134461	+	0.762565i
$554$	4.50837	−	3.78297i	0.191542	−	0.160723i
$555$		0			0
$556$	6.60306	+	2.40332i	0.280032	+	0.101923i
$557$	23.1541	+	19.4286i	0.981071	+	0.823216i	0.984251	−	0.176779i	$-0.0565677\pi$
$557$	23.1541	+	19.4286i	0.981071	+	0.823216i	−0.00317970	+	0.999995i	$0.501012\pi$
$558$	1.26888	−	2.19776i	0.0537158	−	0.0930385i
$559$	−0.325692	−	0.564116i	−0.0137753	−	0.0238596i
$560$		0			0
$561$	8.46778	−	48.0232i	0.357510	−	2.02754i
$562$	4.02269	+	6.96750i	0.169687	+	0.293906i
$563$	9.01300	−	15.6110i	0.379853	−	0.657924i	−0.611188	−	0.791486i	$-0.709308\pi$
$563$	9.01300	−	15.6110i	0.379853	−	0.657924i	0.991041	+	0.133561i	$0.0426413\pi$
$564$	0.710646	+	0.596303i	0.0299236	+	0.0251089i
$565$		0			0
$566$	−11.7472	+	4.27565i	−0.493774	+	0.179719i
$567$	2.36551	−	1.98490i	0.0993422	−	0.0833580i
$568$	−0.487092	−	2.76244i	−0.0204379	−	0.115909i
$569$	−39.6582			−1.66256			−0.831280	−	0.555854i	$-0.812391\pi$
$569$	−39.6582			−1.66256			−0.831280	+	0.555854i	$0.812391\pi$
$570$		0			0
$571$	−31.2303			−1.30695			−0.653473	−	0.756950i	$-0.726689\pi$
$571$	−31.2303			−1.30695			−0.653473	+	0.756950i	$0.726689\pi$
$572$	3.49097	+	19.7983i	0.145965	+	0.827809i
$573$	−0.305616	+	0.256442i	−0.0127673	+	0.0107130i
$574$	4.00410	−	1.45737i	0.167128	−	0.0608295i
$575$		0			0
$576$	−2.12900	−	1.78644i	−0.0887082	−	0.0744350i
$577$	8.82708	−	15.2890i	0.367476	−	0.636488i	−0.621694	−	0.783260i	$-0.713555\pi$
$577$	8.82708	−	15.2890i	0.367476	−	0.636488i	0.989170	+	0.146773i	$0.0468886\pi$
$578$	10.7638	+	18.6434i	0.447714	+	0.775463i
$579$	−0.313682	+	1.77898i	−0.0130362	+	0.0739319i
$580$		0			0
$581$	−0.786286	−	1.36189i	−0.0326206	−	0.0565006i
$582$	4.70417	−	8.14787i	0.194994	−	0.337740i
$583$	31.7656	+	26.6545i	1.31560	+	1.10392i
$584$	5.63340	+	2.05039i	0.233112	+	0.0848458i
$585$		0			0
$586$	1.57679	−	1.32308i	0.0651364	−	0.0546559i
$587$	−0.824684	−	4.67702i	−0.0340384	−	0.193041i	0.963047	−	0.269333i	$-0.0868031\pi$
$587$	−0.824684	−	4.67702i	−0.0340384	−	0.193041i	−0.997086	+	0.0762916i	$0.975692\pi$
$588$	9.75382			0.402241
$589$	−4.64619	−	9.31895i	−0.191443	−	0.383980i
$590$		0			0
$591$	2.04687	+	11.6084i	0.0841970	+	0.477505i
$592$	4.03419	−	3.38509i	0.165804	−	0.139126i
$593$	4.38739	−	1.59688i	0.180168	−	0.0655760i	−0.250361	−	0.968153i	$-0.580549\pi$
$593$	4.38739	−	1.59688i	0.180168	−	0.0655760i	0.430529	+	0.902577i	$0.358327\pi$
$594$	−21.5449	−	7.84171i	−0.883999	−	0.321749i
$595$		0			0
$596$	7.22559	−	12.5151i	0.295972	−	0.512638i
$597$	−0.862889	−	1.49457i	−0.0353157	−	0.0611685i
$598$	−1.66562	+	9.44619i	−0.0681122	+	0.386284i
$599$	5.76250	−	32.6807i	0.235449	−	1.33530i	−0.606216	−	0.795300i	$-0.707313\pi$
$599$	5.76250	−	32.6807i	0.235449	−	1.33530i	0.841666	−	0.539999i	$-0.181575\pi$
$600$		0			0
$601$	9.35026	−	16.1951i	0.381405	−	0.660613i	−0.609858	−	0.792510i	$-0.708774\pi$
$601$	9.35026	−	16.1951i	0.381405	−	0.660613i	0.991263	+	0.131898i	$0.0421070\pi$
$602$	−0.197251	−	0.165513i	−0.00803935	−	0.00674581i
$603$	14.1829	+	5.16214i	0.577571	+	0.210219i
$604$	−18.1386	+	6.60192i	−0.738050	+	0.268628i
$605$		0			0
$606$	−0.333246	−	1.88993i	−0.0135372	−	0.0767731i
$607$	−8.41685			−0.341629			−0.170815	−	0.985303i	$-0.554640\pi$
$607$	−8.41685			−0.341629			−0.170815	+	0.985303i	$0.554640\pi$
$608$	−24.4370	+	7.23843i	−0.991053	+	0.293557i
$609$	9.60141			0.389069
$610$		0			0
$611$	0.913267	−	0.766322i	0.0369468	−	0.0310021i
$612$	−14.0890	+	5.12799i	−0.569515	+	0.207287i
$613$	−32.7815	−	11.9315i	−1.32403	−	0.481908i	−0.419283	−	0.907855i	$-0.637719\pi$
$613$	−32.7815	−	11.9315i	−1.32403	−	0.481908i	−0.904748	+	0.425947i	$0.859941\pi$
$614$	15.4343	+	12.9509i	0.622876	+	0.522655i
$615$		0			0
$616$	9.33448	+	16.1678i	0.376097	+	0.651419i
$617$	−7.14999	+	40.5496i	−0.287848	+	1.63247i	0.407084	+	0.913391i	$0.366546\pi$
$617$	−7.14999	+	40.5496i	−0.287848	+	1.63247i	−0.694932	+	0.719076i	$0.744565\pi$
$618$	1.40063	−	7.94336i	0.0563415	−	0.319529i
$619$	−8.59148	−	14.8809i	−0.345321	−	0.598113i	0.640091	−	0.768299i	$-0.278897\pi$
$619$	−8.59148	−	14.8809i	−0.345321	−	0.598113i	−0.985412	+	0.170186i	$0.945563\pi$
$620$		0			0
$621$	23.9990	+	20.1375i	0.963046	+	0.808092i
$622$	−14.8256	−	5.39608i	−0.594453	−	0.216363i
$623$	−10.8597	+	3.95259i	−0.435083	+	0.158357i
$624$	−2.58390	+	2.16815i	−0.103439	+	0.0867956i
$625$		0			0
$626$	0.848957			0.0339311
$627$	−24.9442	+	18.4575i	−0.996174	+	0.737121i
$628$	27.5978			1.10127
$629$	5.38979	+	30.5670i	0.214905	+	1.21879i
$630$		0			0
$631$	−9.86061	+	3.58897i	−0.392545	+	0.142875i	−0.530749	−	0.847529i	$-0.678089\pi$
$631$	−9.86061	+	3.58897i	−0.392545	+	0.142875i	0.138204	+	0.990404i	$0.455867\pi$
$632$	33.1828	+	12.0775i	1.31994	+	0.480419i
$633$	−16.0631	−	13.4786i	−0.638452	−	0.535725i
$634$	−10.6992	+	18.5315i	−0.424918	+	0.735980i
$635$		0			0
$636$	−2.28429	+	12.9548i	−0.0905780	+	0.513693i
$637$	2.17666	−	12.3444i	0.0862422	−	0.489104i
$638$	−12.4925	−	21.6377i	−0.494583	−	0.856643i
$639$	−0.826565	+	1.43165i	−0.0326984	+	0.0566353i
$640$		0			0
$641$	3.51394	+	1.27897i	0.138792	+	0.0505163i	0.410482	−	0.911869i	$-0.365360\pi$
$641$	3.51394	+	1.27897i	0.138792	+	0.0505163i	−0.271690	+	0.962385i	$0.587583\pi$
$642$	3.22823	−	1.17498i	0.127408	−	0.0463728i
$643$	10.8122	−	9.07254i	0.426393	−	0.357786i	−0.404196	−	0.914672i	$-0.632449\pi$
$643$	10.8122	−	9.07254i	0.426393	−	0.357786i	0.830589	+	0.556886i	$0.188004\pi$
$644$	−1.88562	−	10.6939i	−0.0743037	−	0.421397i
$645$		0			0
$646$	5.01493	−	20.8882i	0.197310	−	0.821834i
$647$	41.4758			1.63058			0.815291	−	0.579052i	$-0.196577\pi$
$647$	41.4758			1.63058			0.815291	+	0.579052i	$0.196577\pi$
$648$	−1.03987	−	5.89742i	−0.0408501	−	0.231672i
$649$	25.4677	−	21.3699i	0.999694	−	0.838843i
$650$		0			0
$651$	−3.57965	−	1.30288i	−0.140297	−	0.0510641i
$652$	−11.2281	−	9.42146i	−0.439725	−	0.368973i
$653$	18.2540	−	31.6169i	0.714334	−	1.23726i	−0.248882	−	0.968534i	$-0.580063\pi$
$653$	18.2540	−	31.6169i	0.714334	−	1.23726i	0.963216	−	0.268729i	$-0.0866037\pi$
$654$	−7.41129	−	12.8367i	−0.289804	−	0.501956i
$655$		0			0
$656$	−0.925189	+	5.24700i	−0.0361225	+	0.204861i
$657$	−1.76653	−	3.05972i	−0.0689189	−	0.119371i
$658$	0.235636	−	0.408133i	0.00918604	−	0.0159107i
$659$	12.7965	+	10.7376i	0.498482	+	0.418276i	0.857055	−	0.515226i	$-0.172292\pi$
$659$	12.7965	+	10.7376i	0.498482	+	0.418276i	−0.358572	+	0.933502i	$0.616736\pi$
$660$		0			0
$661$	4.02830	−	1.46618i	0.156683	−	0.0570278i	−0.262488	−	0.964935i	$-0.584543\pi$
$661$	4.02830	−	1.46618i	0.156683	−	0.0570278i	0.419171	+	0.907907i	$0.362321\pi$
$662$	14.0201	−	11.7642i	0.544905	−	0.457230i
$663$	−3.45217	−	19.5782i	−0.134071	−	0.760356i
$664$	−3.04965			−0.118349
$665$		0			0
$666$	4.81355			0.186521
$667$	5.92829	+	33.6210i	0.229544	+	1.30181i
$668$	−13.6318	+	11.4384i	−0.527430	+	0.442567i
$669$	13.6489	−	4.96778i	0.527696	−	0.192065i
$670$		0			0
$671$	−31.8441	−	26.7204i	−1.22933	−	1.03153i
$672$	−4.66188	+	8.07461i	−0.179836	+	0.311485i
$673$	−11.8988	−	20.6094i	−0.458666	−	0.794434i	0.540224	−	0.841521i	$-0.318339\pi$
$673$	−11.8988	−	20.6094i	−0.458666	−	0.794434i	−0.998891	+	0.0470875i	$0.985006\pi$
$674$	1.47483	−	8.36418i	0.0568083	−	0.322176i
$675$		0			0
$676$	−5.53751	−	9.59125i	−0.212981	−	0.368894i
$677$	8.95247	−	15.5061i	0.344072	−	0.595949i	−0.641113	−	0.767446i	$-0.721527\pi$
$677$	8.95247	−	15.5061i	0.344072	−	0.595949i	0.985185	+	0.171497i	$0.0548604\pi$
$678$	−12.3005	−	10.3214i	−0.472400	−	0.396390i
$679$	12.8624	+	4.68153i	0.493613	+	0.179661i
$680$		0			0
$681$	−26.0117	+	21.8264i	−0.996770	+	0.836389i
$682$	1.72135	+	9.76227i	0.0659139	+	0.373817i
$683$	−8.10967			−0.310308			−0.155154	−	0.987890i	$-0.549587\pi$
$683$	−8.10967			−0.310308			−0.155154	+	0.987890i	$0.549587\pi$
$684$	8.74945	+	3.80443i	0.334544	+	0.145466i
$685$		0			0
$686$	−1.99027	−	11.2874i	−0.0759888	−	0.430954i
$687$	−8.89690	+	7.46539i	−0.339438	+	0.284822i
$688$	0.302547	−	0.110118i	0.0115345	−	0.00419821i
$689$	15.8859	+	5.78199i	0.605204	+	0.220276i
$690$		0			0
$691$	−4.61817	+	7.99890i	−0.175683	+	0.304293i	−0.940398	−	0.340077i	$-0.889547\pi$
$691$	−4.61817	+	7.99890i	−0.175683	+	0.304293i	0.764714	+	0.644370i	$0.222880\pi$
$692$	−12.2357	−	21.1929i	−0.465133	−	0.805633i
$693$	1.91054	−	10.8352i	0.0725754	−	0.411596i
$694$	−0.614601	+	3.48557i	−0.0233299	+	0.132311i
$695$		0			0
$696$	9.30988	−	16.1252i	0.352890	−	0.611223i
$697$	−24.0555	−	20.1849i	−0.911166	−	0.764559i
$698$	−24.4951	−	8.91547i	−0.927151	−	0.337456i
$699$	1.29593	−	0.471679i	0.0490165	−	0.0178405i
$700$		0			0
$701$	−7.42346	−	42.1005i	−0.280380	−	1.59011i	−0.721336	−	0.692586i	$-0.756471\pi$
$701$	−7.42346	−	42.1005i	−0.280380	−	1.59011i	0.440955	−	0.897529i	$-0.354640\pi$
$702$	−9.34721			−0.352788
$703$	10.9014	−	16.4701i	0.411156	−	0.621181i
$704$	10.8560			0.409152
$705$		0			0
$706$	−14.1038	+	11.8345i	−0.530805	+	0.445398i
$707$	2.62363	−	0.954923i	0.0986718	−	0.0359136i
$708$	9.91058	+	3.60716i	0.372463	+	0.135565i
$709$	17.4610	+	14.6515i	0.655762	+	0.550250i	0.908813	−	0.417203i	$-0.136990\pi$
$709$	17.4610	+	14.6515i	0.655762	+	0.550250i	−0.253051	+	0.967453i	$0.581434\pi$
$710$		0			0
$711$	−10.4055	−	18.0229i	−0.390237	−	0.675910i
$712$	−3.89170	+	22.0709i	−0.145848	+	0.827144i
$713$	2.35206	−	13.3392i	0.0880855	−	0.499557i
$714$	−3.92934	−	6.80581i	−0.147052	−	0.254701i
$715$		0			0
$716$	−22.9552	−	19.2617i	−0.857876	−	0.719843i
$717$	15.0380	+	5.47339i	0.561605	+	0.204408i
$718$	20.8229	−	7.57890i	0.777102	−	0.282842i
$719$	21.6987	−	18.2073i	0.809224	−	0.679019i	−0.141199	−	0.989981i	$-0.545096\pi$
$719$	21.6987	−	18.2073i	0.809224	−	0.679019i	0.950422	+	0.310962i	$0.100651\pi$
$720$		0			0
$721$	11.7348			0.437027
$722$	−11.4644	+	7.44491i	−0.426662	+	0.277071i
$723$	−25.2224			−0.938032
$724$	−0.0614330	−	0.348404i	−0.00228314	−	0.0129483i
$725$		0			0
$726$	18.5796	−	6.76244i	0.689555	−	0.250978i
$727$	27.2512	+	9.91861i	1.01069	+	0.367861i	0.793698	−	0.608312i	$-0.208153\pi$
$727$	27.2512	+	9.91861i	1.01069	+	0.367861i	0.216992	+	0.976173i	$0.430375\pi$
$728$	5.83038	+	4.89227i	0.216088	+	0.181320i
$729$	−11.9943	+	20.7748i	−0.444234	+	0.769436i
$730$		0			0
$731$	−0.329516	+	1.86878i	−0.0121876	+	0.0691192i
$732$	2.28994	−	12.9869i	0.0846384	−	0.480008i
$733$	8.37714	+	14.5096i	0.309417	+	0.535925i	0.978235	−	0.207501i	$-0.0665329\pi$
$733$	8.37714	+	14.5096i	0.309417	+	0.535925i	−0.668818	+	0.743426i	$0.733200\pi$
$734$	−10.8402	+	18.7757i	−0.400117	+	0.693024i
$735$		0			0
$736$	−31.1531	−	11.3388i	−1.14832	−	0.417954i
$737$	−55.4005	+	20.1641i	−2.04070	+	0.742756i
$738$	−3.73059	+	3.13034i	−0.137325	+	0.115229i
$739$	0.254943	+	1.44586i	0.00937824	+	0.0531866i	0.989138	−	0.146992i	$-0.0469590\pi$
$739$	0.254943	+	1.44586i	0.00937824	+	0.0531866i	−0.979760	+	0.200178i	$0.935848\pi$
$740$		0			0
$741$	−6.98239	+	10.5491i	−0.256505	+	0.387531i
$742$	6.68271			0.245330
$743$	−4.98854	−	28.2914i	−0.183012	−	1.03791i	−0.928483	−	0.371374i	$-0.878887\pi$
$743$	−4.98854	−	28.2914i	−0.183012	−	1.03791i	0.745472	−	0.666537i	$-0.232224\pi$
$744$	−5.65910	+	4.74855i	−0.207473	+	0.174090i
$745$		0			0
$746$	18.9465	+	6.89595i	0.693679	+	0.252479i
$747$	1.37680	+	1.15527i	0.0503743	+	0.0422691i
$748$	29.2830	−	50.7196i	1.07069	−	1.85449i
$749$	2.49903	+	4.32845i	0.0913126	+	0.158158i
$750$		0			0
$751$	−8.78054	+	49.7969i	−0.320406	+	1.81712i	0.219757	+	0.975555i	$0.429474\pi$
$751$	−8.78054	+	49.7969i	−0.320406	+	1.81712i	−0.540163	+	0.841560i	$0.681637\pi$
$752$	0.294634	+	0.510321i	0.0107442	+	0.0186095i
$753$	10.2011	−	17.6689i	0.371750	−	0.643890i
$754$	−7.80291	−	6.54741i	−0.284165	−	0.238443i
$755$		0			0
$756$	9.94365	−	3.61919i	0.361647	−	0.131629i
$757$	−5.88606	+	4.93899i	−0.213932	+	0.179511i	−0.743456	−	0.668784i	$-0.766815\pi$
$757$	−5.88606	+	4.93899i	−0.213932	+	0.179511i	0.529524	+	0.848295i	$0.322371\pi$
$758$	2.82546	+	16.0240i	0.102625	+	0.582017i
$759$	−40.3639			−1.46512
$760$		0			0
$761$	39.1347			1.41863			0.709315	−	0.704891i	$-0.249004\pi$
$761$	39.1347			1.41863			0.709315	+	0.704891i	$0.249004\pi$
$762$	1.66426	+	9.43847i	0.0602897	+	0.341920i
$763$	16.5196	−	13.8616i	0.598051	−	0.501824i
$764$	−0.450250	+	0.163878i	−0.0162895	+	0.00592888i
$765$		0			0
$766$	5.52415	+	4.63531i	0.199596	+	0.167481i
$767$	6.77686	−	11.7379i	0.244698	−	0.423829i
$768$	6.91417	+	11.9757i	0.249493	+	0.432135i
$769$	−5.81543	+	32.9809i	−0.209710	+	1.18932i	0.680145	+	0.733078i	$0.261917\pi$
$769$	−5.81543	+	32.9809i	−0.209710	+	1.18932i	−0.889854	+	0.456245i	$0.849194\pi$
$770$		0			0
$771$	−7.20396	−	12.4776i	−0.259444	−	0.449371i
$772$	−1.08476	+	1.87887i	−0.0390415	+	0.0676219i
$773$	−0.361162	−	0.303051i	−0.0129901	−	0.0109000i	0.636269	−	0.771467i	$-0.280477\pi$
$773$	−0.361162	−	0.303051i	−0.0129901	−	0.0109000i	−0.649260	+	0.760567i	$0.724921\pi$
$774$	0.276539	+	0.100652i	0.00993998	+	0.00361786i
$775$		0			0
$776$	20.3343	−	17.0625i	0.729959	−	0.612508i
$777$	−1.25470	−	7.11577i	−0.0450122	−	0.255277i
$778$	5.25326			0.188338
$779$	2.26197	+	19.8540i	0.0810433	+	0.711344i
$780$		0			0
$781$	−1.12131	−	6.35928i	−0.0401237	−	0.227553i
$782$	21.4056	−	17.9614i	0.765463	−	0.642300i
$783$	−31.2624	+	11.3786i	−1.11723	+	0.406637i
$784$	5.82202	+	2.11904i	0.207929	+	0.0756801i
$785$		0			0
$786$	5.60577	−	9.70947i	0.199951	−	0.346325i
$787$	−0.935856	−	1.62095i	−0.0333596	−	0.0577806i	0.848864	−	0.528612i	$-0.177287\pi$
$787$	−0.935856	−	1.62095i	−0.0333596	−	0.0577806i	−0.882223	+	0.470831i	$0.843954\pi$
$788$	−2.45831	+	13.9417i	−0.0875735	+	0.496654i
$789$	1.49610	−	8.48480i	0.0532626	−	0.302067i
$790$		0			0
$791$	11.6805	−	20.2313i	0.415312	−	0.719342i
$792$	−16.3448	−	13.7149i	−0.580786	−	0.487338i
$793$	−15.9251	−	5.79628i	−0.565519	−	0.205832i
$794$	24.5861	−	8.94859i	0.872526	−	0.317574i
$795$		0			0
$796$	−0.359915	−	2.04118i	−0.0127569	−	0.0723478i
$797$	38.5450			1.36533			0.682666	−	0.730730i	$-0.260820\pi$
$797$	38.5450			1.36533			0.682666	+	0.730730i	$0.260820\pi$
$798$	−1.16744	+	4.86261i	−0.0413268	+	0.172134i
$799$	−3.47306			−0.122868
$800$		0			0
$801$	10.1179	−	8.48991i	0.357498	−	0.299976i
$802$	6.18346	−	2.25060i	0.218346	−	0.0794713i
$803$	12.9684	+	4.72011i	0.457645	+	0.166569i
$804$	−14.3271	−	12.0219i	−0.505280	−	0.423980i
$805$		0			0
$806$	2.02065	+	3.49987i	0.0711745	+	0.123278i
$807$	−1.10324	+	6.25678i	−0.0388359	+	0.220249i
$808$	0.940213	−	5.33221i	0.0330766	−	0.187587i
$809$	−8.78371	−	15.2138i	−0.308819	−	0.534890i	0.669285	−	0.743005i	$-0.266600\pi$
$809$	−8.78371	−	15.2138i	−0.308819	−	0.534890i	−0.978104	+	0.208115i	$0.933267\pi$
$810$		0			0
$811$	−27.2855	−	22.8953i	−0.958125	−	0.803962i	0.0225221	−	0.999746i	$-0.492830\pi$
$811$	−27.2855	−	22.8953i	−0.958125	−	0.803962i	−0.980647	+	0.195784i	$0.937275\pi$
$812$	10.8359	+	3.94396i	0.380267	+	0.138406i
$813$	4.00716	−	1.45849i	0.140537	−	0.0511514i
$814$	−14.4035	+	12.0860i	−0.504844	+	0.423614i
$815$		0			0
$816$	9.82632			0.343990
$817$	0.970679	−	0.718256i	0.0339598	−	0.0251286i
$818$	3.37628			0.118049
$819$	−0.778895	−	4.41733i	−0.0272168	−	0.154354i
$820$		0			0
$821$	24.1772	−	8.79979i	0.843791	−	0.307115i	0.116285	−	0.993216i	$-0.462901\pi$
$821$	24.1772	−	8.79979i	0.843791	−	0.307115i	0.727506	+	0.686101i	$0.240679\pi$
$822$	7.68077	+	2.79557i	0.267898	+	0.0975068i
$823$	10.2945	+	8.63812i	0.358844	+	0.301106i	0.804330	−	0.594183i	$-0.202525\pi$
$823$	10.2945	+	8.63812i	0.358844	+	0.301106i	−0.445486	+	0.895289i	$0.646969\pi$
$824$	11.3785	−	19.7081i	0.396388	−	0.686565i
$825$		0			0
$826$	0.930370	−	5.27639i	0.0323717	−	0.183589i
$827$	1.48361	−	8.41399i	0.0515903	−	0.292583i	−0.948086	−	0.318013i	$-0.896984\pi$
$827$	1.48361	−	8.41399i	0.0515903	−	0.292583i	0.999677	+	0.0254301i	$0.00809552\pi$
$828$	6.20524	+	10.7478i	0.215647	+	0.373511i
$829$	6.74559	−	11.6837i	0.234284	−	0.405792i	−0.724780	−	0.688980i	$-0.758059\pi$
$829$	6.74559	−	11.6837i	0.234284	−	0.405792i	0.959064	+	0.283188i	$0.0913921\pi$
$830$		0			0
$831$	9.48771	+	3.45324i	0.329125	+	0.119792i
$832$	4.15891	−	1.51372i	0.144184	−	0.0524787i
$833$	−27.9732	+	23.4723i	−0.969213	+	0.813267i
$834$	−0.730952	−	4.14543i	−0.0253108	−	0.143545i
$835$		0			0
$836$	−35.7332	+	10.5844i	−1.23586	+	0.366070i
$837$	13.1994			0.456239
$838$	0.0735198	+	0.416952i	0.00253970	+	0.0144034i
$839$	−1.90844	+	1.60137i	−0.0658865	+	0.0552853i	−0.675136	−	0.737693i	$-0.735915\pi$
$839$	−1.90844	+	1.60137i	−0.0658865	+	0.0552853i	0.609250	+	0.792978i	$0.291471\pi$
$840$		0			0
$841$	−6.81655	−	2.48102i	−0.235054	−	0.0855525i
$842$	3.39084	+	2.84526i	0.116856	+	0.0980540i
$843$	−6.90123	+	11.9533i	−0.237691	+	0.411693i
$844$	−12.5919	−	21.8098i	−0.433432	−	0.750726i
$845$		0			0
$846$	−0.0935290	+	0.530430i	−0.00321559	+	0.0182365i
$847$	14.3828	+	24.9118i	0.494200	+	0.855979i
$848$	−4.17796	+	7.23644i	−0.143472	+	0.248500i
$849$	−16.4291	−	13.7857i	−0.563846	−	0.473123i
$850$		0			0
$851$	24.1424	−	8.78712i	0.827592	−	0.301219i
$852$	1.56924	−	1.31675i	0.0537612	−	0.0451110i
$853$	5.82355	+	33.0270i	0.199395	+	1.13082i	0.906020	+	0.423235i	$0.139106\pi$
$853$	5.82355	+	33.0270i	0.199395	+	1.13082i	−0.706625	+	0.707588i	$0.749783\pi$
$854$	−6.69923			−0.229243
$855$		0			0
$856$	9.69260			0.331286
$857$	−1.76650	−	10.0183i	−0.0603425	−	0.342219i	−1.00000		0.000102570i	$-0.999967\pi$
$857$	−1.76650	−	10.0183i	−0.0603425	−	0.342219i	0.939658	−	0.342117i	$-0.111144\pi$
$858$	9.22550	−	7.74111i	0.314953	−	0.264277i
$859$	−25.6251	+	9.32677i	−0.874317	+	0.318225i	−0.739914	−	0.672702i	$-0.765134\pi$
$859$	−25.6251	+	9.32677i	−0.874317	+	0.318225i	−0.134403	+	0.990927i	$0.542912\pi$
$860$		0			0
$861$	5.59993	+	4.69890i	0.190845	+	0.160138i
$862$	−0.113536	+	0.196650i	−0.00386704	+	0.00669791i
$863$	9.37937	+	16.2455i	0.319278	+	0.553005i	0.980337	−	0.197328i	$-0.0632265\pi$
$863$	9.37937	+	16.2455i	0.319278	+	0.553005i	−0.661060	+	0.750333i	$0.729893\pi$
$864$	5.60999	−	31.8158i	0.190856	−	1.08240i
$865$		0			0
$866$	−12.3207	−	21.3400i	−0.418673	−	0.725163i
$867$	−18.4661	+	31.9842i	−0.627140	+	1.08624i
$868$	−3.50472	−	2.94081i	−0.118958	−	0.0998177i
$869$	76.3886	+	27.8032i	2.59131	+	0.943158i
$870$		0			0
$871$	−18.4122	+	15.4496i	−0.623872	+	0.523491i
$872$	−7.26199	−	41.1848i	−0.245922	−	1.39469i
$873$	−15.6438			−0.529461
$874$	−17.7481	−	1.08562i	−0.600338	−	0.0367216i
$875$		0			0
$876$	0.760237	+	4.31152i	0.0256860	+	0.145673i
$877$	−17.6865	+	14.8407i	−0.597230	+	0.501135i	−0.890554	−	0.454878i	$-0.849683\pi$
$877$	−17.6865	+	14.8407i	−0.597230	+	0.501135i	0.293324	+	0.956013i	$0.405239\pi$
$878$	−1.41417	+	0.514715i	−0.0477258	+	0.0173708i
$879$	3.31829	+	1.20776i	0.111923	+	0.0407367i
$880$		0			0
$881$	−27.3103	+	47.3029i	−0.920108	+	1.59367i	−0.120863	+	0.992669i	$0.538566\pi$
$881$	−27.3103	+	47.3029i	−0.920108	+	1.59367i	−0.799245	+	0.601005i	$0.794767\pi$
$882$	2.83153	+	4.90436i	0.0953427	+	0.165138i
$883$	3.22999	−	18.3182i	0.108698	−	0.616456i	−0.880981	−	0.473152i	$-0.843116\pi$
$883$	3.22999	−	18.3182i	0.108698	−	0.616456i	0.989679	−	0.143304i	$-0.0457727\pi$
$884$	4.14608	−	23.5136i	0.139448	−	0.790848i
$885$		0			0
$886$	3.05862	−	5.29769i	0.102756	−	0.177979i
$887$	2.87998	+	2.41659i	0.0967001	+	0.0811410i	0.689856	−	0.723947i	$-0.257674\pi$
$887$	2.87998	+	2.41659i	0.0967001	+	0.0811410i	−0.593156	+	0.805088i	$0.702118\pi$
$888$	−13.1673	−	4.79249i	−0.441864	−	0.160825i
$889$	−13.1026	+	4.76897i	−0.439448	+	0.159946i
$890$		0			0
$891$	−2.39385	−	13.5762i	−0.0801969	−	0.454819i
$892$	17.4444			0.584082
$893$	1.60310	+	1.52130i	0.0536458	+	0.0509085i
$894$	−8.65690			−0.289530
$895$		0			0
$896$	−10.2332	+	8.58664i	−0.341866	+	0.286860i
$897$	−15.4633	+	5.62817i	−0.516303	+	0.187919i
$898$	−10.4905	−	3.81825i	−0.350074	−	0.127417i
$899$	11.0187	+	9.24577i	0.367494	+	0.308364i
$900$		0			0
$901$	−24.6243	−	42.6506i	−0.820355	−	1.42090i
$902$	3.30327	−	18.7338i	0.109987	−	0.623766i
$903$	0.0767088	−	0.435037i	0.00255271	−	0.0144771i
$904$	−22.6518	−	39.2340i	−0.753387	−	1.30490i
$905$		0			0
$906$	8.85792	+	7.43268i	0.294285	+	0.246934i
$907$	−22.7463	−	8.27896i	−0.755277	−	0.274898i	−0.0644525	−	0.997921i	$-0.520530\pi$
$907$	−22.7463	−	8.27896i	−0.755277	−	0.274898i	−0.690825	+	0.723022i	$0.742752\pi$
$908$	−38.3218	+	13.9480i	−1.27175	+	0.462880i
$909$	−2.44442	+	2.05111i	−0.0810763	+	0.0680311i
$910$		0			0
$911$	29.7647			0.986148			0.493074	−	0.869987i	$-0.335873\pi$
$911$	29.7647			0.986148			0.493074	+	0.869987i	$0.335873\pi$
$912$	−4.53565	−	4.30422i	−0.150190	−	0.142527i
$913$	−7.02046			−0.232343
$914$	4.65911	+	26.4231i	0.154110	+	0.873999i
$915$		0			0
$916$	−13.1074	+	4.77070i	−0.433080	+	0.157628i
$917$	15.3276	+	5.57878i	0.506161	+	0.184228i
$918$	20.8595	+	17.5032i	0.688467	+	0.577692i
$919$	−22.8174	+	39.5210i	−0.752678	+	1.30368i	0.193842	+	0.981033i	$0.437905\pi$
$919$	−22.8174	+	39.5210i	−0.752678	+	1.30368i	−0.946520	+	0.322644i	$0.895428\pi$
$920$		0			0
$921$	−6.00222	+	34.0403i	−0.197780	+	1.12167i
$922$	2.18920	−	12.4156i	0.0720974	−	0.408885i
$923$	−1.31628	−	2.27987i	−0.0433260	−	0.0750428i
$924$	−6.81685	+	11.8071i	−0.224258	+	0.388426i
$925$		0			0
$926$	22.6061	+	8.22793i	0.742881	+	0.270387i
$927$	−12.6028	+	4.58704i	−0.413930	+	0.150658i
$928$	26.9691	−	22.6297i	0.885304	−	0.742858i
$929$	−4.73685	−	26.8640i	−0.155411	−	0.881380i	−0.958409	−	0.285398i	$-0.907874\pi$
$929$	−4.73685	−	26.8640i	−0.155411	−	0.881380i	0.802998	−	0.595982i	$-0.203237\pi$
$930$		0			0
$931$	23.1935	+	1.41870i	0.760135	+	0.0464962i
$932$	1.65631			0.0542541
$933$	−4.70010	−	26.6556i	−0.153874	−	0.872664i
$934$	8.24600	−	6.91922i	0.269817	−	0.226404i
$935$		0			0
$936$	−8.17398	−	2.97509i	−0.267175	−	0.0972437i
$937$	−33.5860	−	28.1820i	−1.09721	−	0.920666i	−0.0999724	−	0.994990i	$-0.531875\pi$
$937$	−33.5860	−	28.1820i	−1.09721	−	0.920666i	−0.997234	+	0.0743247i	$0.976320\pi$
$938$	−4.75059	+	8.22827i	−0.155112	+	0.268663i
$939$	0.728225	+	1.26132i	0.0237647	+	0.0411617i
$940$		0			0
$941$	−7.61144	+	43.1666i	−0.248126	+	1.40719i	0.564994	+	0.825095i	$0.308878\pi$
$941$	−7.61144	+	43.1666i	−0.248126	+	1.40719i	−0.813120	+	0.582096i	$0.802233\pi$
$942$	−8.26614	−	14.3174i	−0.269326	−	0.466486i
$943$	−12.9964	+	22.5104i	−0.423221	+	0.733040i
$944$	5.13193	+	4.30620i	0.167030	+	0.140155i
$945$		0			0
$946$	−1.08020	+	0.393162i	−0.0351205	+	0.0127828i
$947$	−10.4462	+	8.76541i	−0.339456	+	0.284838i	−0.796540	−	0.604586i	$-0.793339\pi$
$947$	−10.4462	+	8.76541i	−0.339456	+	0.284838i	0.457083	+	0.889424i	$0.348894\pi$
$948$	4.47807	+	25.3964i	0.145441	+	0.824836i
$949$	5.62631			0.182638
$950$		0			0
$951$	−36.7104			−1.19042
$952$	−3.85018	−	21.8355i	−0.124785	−	0.707692i
$953$	−9.46945	+	7.94581i	−0.306746	+	0.257390i	−0.783145	−	0.621839i	$-0.786386\pi$
$953$	−9.46945	+	7.94581i	−0.306746	+	0.257390i	0.476400	+	0.879229i	$0.341941\pi$
$954$	−7.17701	+	2.61222i	−0.232364	+	0.0845737i
$955$		0			0
$956$	14.7233	+	12.3543i	0.476185	+	0.399566i
$957$	21.4319	−	37.1211i	0.692793	−	1.19995i
$958$	−5.69654	−	9.86669i	−0.184047	−	0.318778i
$959$	−2.06496	+	11.7110i	−0.0666811	+	0.378167i
$960$		0			0
$961$	12.6466	+	21.9045i	0.407954	+	0.706598i
$962$	−3.83273	+	6.63848i	−0.123572	+	0.214033i
$963$	−4.37583	−	3.67176i	−0.141009	−	0.118321i
$964$	−28.4655	−	10.3606i	−0.916810	−	0.333692i
$965$		0			0
$966$	−4.98307	+	4.18129i	−0.160327	+	0.134531i
$967$	2.82125	+	16.0001i	0.0907254	+	0.514529i	0.995974	+	0.0896462i	$0.0285736\pi$
$967$	2.82125	+	16.0001i	0.0907254	+	0.514529i	−0.905248	+	0.424883i	$0.860315\pi$
$968$	55.7845			1.79298
$969$	35.3360	−	10.4668i	1.13516	−	0.336241i
$970$		0			0
$971$	5.64449	+	32.0115i	0.181140	+	1.02730i	0.930815	+	0.365491i	$0.119099\pi$
$971$	5.64449	+	32.0115i	0.181140	+	1.02730i	−0.749674	+	0.661807i	$0.769790\pi$
$972$	−15.4731	+	12.9835i	−0.496299	+	0.416445i
$973$	5.75476	−	2.09456i	0.184489	−	0.0671485i
$974$	−4.39130	−	1.59830i	−0.140706	−	0.0512129i
$975$		0			0
$976$	4.18829	−	7.25433i	0.134064	−	0.232205i
$977$	6.29447	+	10.9023i	0.201378	+	0.348797i	0.948973	−	0.315359i	$-0.102125\pi$
$977$	6.29447	+	10.9023i	0.201378	+	0.348797i	−0.747595	+	0.664155i	$0.768791\pi$
$978$	−1.52469	+	8.64692i	−0.0487541	+	0.276498i
$979$	−8.95892	+	50.8085i	−0.286328	+	1.62385i
$980$		0			0
$981$	−12.3231	+	21.3443i	−0.393448	+	0.681471i
$982$	0.927679	+	0.778415i	0.0296034	+	0.0248402i
$983$	29.9686	+	10.9077i	0.955850	+	0.347901i	0.772406	−	0.635129i	$-0.219053\pi$
$983$	29.9686	+	10.9077i	0.955850	+	0.347901i	0.183444	+	0.983030i	$0.441275\pi$
$984$	13.3215	−	4.84863i	0.424674	−	0.154569i
$985$		0			0
$986$	5.15277	+	29.2228i	0.164098	+	0.930645i
$987$	0.808502			0.0257349
$988$	−12.2134	+	9.03734i	−0.388560	+	0.287516i
$989$	1.57072			0.0499461
$990$		0			0
$991$	6.27678	−	5.26685i	0.199389	−	0.167307i	−0.537627	−	0.843183i	$-0.680679\pi$
$991$	6.27678	−	5.26685i	0.199389	−	0.167307i	0.737015	+	0.675876i	$0.236235\pi$
$992$	−13.1255	+	4.77731i	−0.416737	+	0.151680i
$993$	29.5047	+	10.7388i	0.936305	+	0.340787i
$994$	−0.797188	−	0.668920i	−0.0252853	−	0.0212168i
$995$		0			0
$996$	−1.11356	−	1.92874i	−0.0352845	−	0.0611145i
$997$	2.85615	−	16.1980i	0.0904552	−	0.512997i	−0.905590	−	0.424153i	$-0.860572\pi$
$997$	2.85615	−	16.1980i	0.0904552	−	0.512997i	0.996046	−	0.0888435i	$-0.0283171\pi$
$998$	−1.66614	+	9.44914i	−0.0527407	+	0.299107i
$999$	12.5182	+	21.6821i	0.396058	+	0.685993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.b.351.2		18
5.2	odd	4		475.2.u.c.199.4		36
5.3	odd	4		475.2.u.c.199.3		36
5.4	even	2		95.2.k.b.66.2	yes	18
15.14	odd	2		855.2.bs.b.541.2		18
19.6	even	9		9025.2.a.ce.1.4		9
19.13	odd	18		9025.2.a.cd.1.6		9
19.17	even	9	inner	475.2.l.b.226.2		18
95.17	odd	36		475.2.u.c.74.3		36
95.44	even	18		1805.2.a.t.1.6		9
95.74	even	18		95.2.k.b.36.2	✓	18
95.89	odd	18		1805.2.a.u.1.4		9
95.93	odd	36		475.2.u.c.74.4		36
285.74	odd	18		855.2.bs.b.226.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.36.2	✓	18	95.74	even	18
95.2.k.b.66.2	yes	18	5.4	even	2
475.2.l.b.226.2		18	19.17	even	9	inner
475.2.l.b.351.2		18	1.1	even	1	trivial
475.2.u.c.74.3		36	95.17	odd	36
475.2.u.c.74.4		36	95.93	odd	36
475.2.u.c.199.3		36	5.3	odd	4
475.2.u.c.199.4		36	5.2	odd	4
855.2.bs.b.226.2		18	285.74	odd	18
855.2.bs.b.541.2		18	15.14	odd	2
1805.2.a.t.1.6		9	95.44	even	18
1805.2.a.u.1.4		9	95.89	odd	18
9025.2.a.cd.1.6		9	19.13	odd	18
9025.2.a.ce.1.4		9	19.6	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)

\(f(q)\)	\(=\)	\(q+(-0.124932 - 0.708527i) q^{2} +(0.945515 - 0.793382i) q^{3} +(1.39298 - 0.507004i) q^{4} +(-0.680257 - 0.570804i) q^{6} +(0.645970 - 1.11885i) q^{7} +(-1.25271 - 2.16976i) q^{8} +(-0.256400 + 1.45411i) q^{9} +O(q^{10})\)	\(q+(-0.124932 - 0.708527i) q^{2} +(0.945515 - 0.793382i) q^{3} +(1.39298 - 0.507004i) q^{4} +(-0.680257 - 0.570804i) q^{6} +(0.645970 - 1.11885i) q^{7} +(-1.25271 - 2.16976i) q^{8} +(-0.256400 + 1.45411i) q^{9} +(-2.88381 - 4.99491i) q^{11} +(0.914839 - 1.58455i) q^{12} +(-1.80125 - 1.51143i) q^{13} +(-0.873439 - 0.317906i) q^{14} +(0.890312 - 0.747060i) q^{16} +(1.18948 + 6.74589i) q^{17} +1.06231 q^{18} +(2.40586 - 3.63481i) q^{19} +(-0.276903 - 1.57039i) q^{21} +(-3.17874 + 2.66728i) q^{22} +(5.32803 - 1.93925i) q^{23} +(-2.90591 - 1.05766i) q^{24} +(-0.845852 + 1.46506i) q^{26} +(2.76266 + 4.78507i) q^{27} +(0.332562 - 1.88605i) q^{28} +(-1.04556 + 5.92966i) q^{29} +(1.19445 - 2.06885i) q^{31} +(-4.47907 - 3.75839i) q^{32} +(-6.68956 - 2.43480i) q^{33} +(4.63104 - 1.68556i) q^{34} +(0.380082 + 2.15555i) q^{36} +4.53121 q^{37} +(-2.87593 - 1.25051i) q^{38} -2.90225 q^{39} +(-3.51177 + 2.94672i) q^{41} +(-1.07807 + 0.392386i) q^{42} +(0.260318 + 0.0947480i) q^{43} +(-6.54954 - 5.49572i) q^{44} +(-2.03965 - 3.53278i) q^{46} +(-0.0880430 + 0.499316i) q^{47} +(0.249100 - 1.41271i) q^{48} +(2.66545 + 4.61669i) q^{49} +(6.47674 + 5.43463i) q^{51} +(-3.27541 - 1.19215i) q^{52} +(-6.75604 + 2.45900i) q^{53} +(3.04520 - 2.55523i) q^{54} -3.23685 q^{56} +(-0.609016 - 5.34553i) q^{57} +4.33194 q^{58} +(1.00094 + 5.67662i) q^{59} +(6.77273 - 2.46507i) q^{61} +(-1.61506 - 0.587833i) q^{62} +(1.46131 + 1.22619i) q^{63} +(-0.941117 + 1.63006i) q^{64} +(-0.889378 + 5.04391i) q^{66} +(1.77501 - 10.0666i) q^{67} +(5.07713 + 8.79384i) q^{68} +(3.49918 - 6.06075i) q^{69} +(1.05207 + 0.382923i) q^{71} +(3.47627 - 1.26526i) q^{72} +(-1.83298 + 1.53805i) q^{73} +(-0.566094 - 3.21048i) q^{74} +(1.50845 - 6.28301i) q^{76} -7.45142 q^{77} +(0.362584 + 2.05632i) q^{78} +(-10.7969 + 9.05969i) q^{79} +(2.24603 + 0.817487i) q^{81} +(2.52657 + 2.12004i) q^{82} +(0.608609 - 1.05414i) q^{83} +(-1.18192 - 2.04714i) q^{84} +(0.0346093 - 0.196279i) q^{86} +(3.71589 + 6.43611i) q^{87} +(-7.22517 + 12.5144i) q^{88} +(-6.85239 - 5.74984i) q^{89} +(-2.85461 + 1.03899i) q^{91} +(6.43866 - 5.40267i) q^{92} +(-0.512015 - 2.90378i) q^{93} +0.364778 q^{94} -7.21687 q^{96} +(1.83977 + 10.4339i) q^{97} +(2.93805 - 2.46531i) q^{98} +(8.00258 - 2.91270i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 12 q^{8} - 21 q^{9}+O(q^{10}) \) 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 12 * q^8 - 21 * q^9	\( 18 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 12 q^{8} - 21 q^{9} - 6 q^{12} + 3 q^{13} + 24 q^{14} + 21 q^{16} + 24 q^{17} + 12 q^{18} - 12 q^{19} + 3 q^{21} - 15 q^{22} - 21 q^{23} + 21 q^{24} - 21 q^{26} - 6 q^{27} + 24 q^{28} - 9 q^{29} + 30 q^{31} - 45 q^{32} + 3 q^{33} + 24 q^{34} - 21 q^{36} + 60 q^{37} + 15 q^{38} + 12 q^{39} - 6 q^{41} - 39 q^{42} + 6 q^{43} - 30 q^{44} + 21 q^{46} - 33 q^{47} + 63 q^{48} - 3 q^{49} + 27 q^{51} - 9 q^{52} - 24 q^{53} + 30 q^{54} - 72 q^{56} + 30 q^{57} - 36 q^{58} + 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{63} - 24 q^{64} - 33 q^{66} + 24 q^{67} + 3 q^{68} + 27 q^{69} + 24 q^{71} - 18 q^{72} - 6 q^{73} - 39 q^{74} + 27 q^{76} - 24 q^{77} - 72 q^{78} + 9 q^{79} + 15 q^{81} + 57 q^{82} - 12 q^{84} - 33 q^{86} + 45 q^{87} - 39 q^{88} - 6 q^{89} - 6 q^{91} + 66 q^{92} + 72 q^{93} - 66 q^{94} - 18 q^{96} + 87 q^{97} - 39 q^{98} + 3 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 12 * q^8 - 21 * q^9 - 6 * q^12 + 3 * q^13 + 24 * q^14 + 21 * q^16 + 24 * q^17 + 12 * q^18 - 12 * q^19 + 3 * q^21 - 15 * q^22 - 21 * q^23 + 21 * q^24 - 21 * q^26 - 6 * q^27 + 24 * q^28 - 9 * q^29 + 30 * q^31 - 45 * q^32 + 3 * q^33 + 24 * q^34 - 21 * q^36 + 60 * q^37 + 15 * q^38 + 12 * q^39 - 6 * q^41 - 39 * q^42 + 6 * q^43 - 30 * q^44 + 21 * q^46 - 33 * q^47 + 63 * q^48 - 3 * q^49 + 27 * q^51 - 9 * q^52 - 24 * q^53 + 30 * q^54 - 72 * q^56 + 30 * q^57 - 36 * q^58 + 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^63 - 24 * q^64 - 33 * q^66 + 24 * q^67 + 3 * q^68 + 27 * q^69 + 24 * q^71 - 18 * q^72 - 6 * q^73 - 39 * q^74 + 27 * q^76 - 24 * q^77 - 72 * q^78 + 9 * q^79 + 15 * q^81 + 57 * q^82 - 12 * q^84 - 33 * q^86 + 45 * q^87 - 39 * q^88 - 6 * q^89 - 6 * q^91 + 66 * q^92 + 72 * q^93 - 66 * q^94 - 18 * q^96 + 87 * q^97 - 39 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

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