LMFDB - Embedded newform 475.2.l.c.351.3

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} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} + \cdots + 1 $ x^18 - 3x^17 + 15x^16 - 14x^15 + 72x^14 - 51x^13 + 231x^12 - 93x^11 + 438x^10 - 156x^9 + 582x^8 - 138x^7 + 437x^6 - 132x^5 + 198x^4 - 16x^3 + 15x^2 + 1
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			351.3
Root			$1.61137 - 2.79097i$ of defining polynomial
Character	$\chi$	$=$	475.351
Dual form			475.2.l.c.226.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.385975 + 2.18897i) q^{2} +(-0.794389 + 0.666572i) q^{3} +(-2.76323 + 1.00573i) q^{4} +(-1.76572 - 1.48162i) q^{6} +(-1.01254 + 1.75377i) q^{7} +(-1.04532 - 1.81055i) q^{8} +(-0.334208 + 1.89539i) q^{9} +O(q^{10})$	\(q+(0.385975 + 2.18897i) q^{2} +(-0.794389 + 0.666572i) q^{3} +(-2.76323 + 1.00573i) q^{4} +(-1.76572 - 1.48162i) q^{6} +(-1.01254 + 1.75377i) q^{7} +(-1.04532 - 1.81055i) q^{8} +(-0.334208 + 1.89539i) q^{9} +(-0.0424078 - 0.0734524i) q^{11} +(1.52469 - 2.64084i) q^{12} +(-4.38252 - 3.67737i) q^{13} +(-4.22977 - 1.53951i) q^{14} +(-0.945441 + 0.793319i) q^{16} +(0.439455 + 2.49227i) q^{17} -4.27795 q^{18} +(3.21565 - 2.94271i) q^{19} +(-0.364663 - 2.06811i) q^{21} +(0.144417 - 0.121180i) q^{22} +(-0.290447 + 0.105714i) q^{23} +(2.03725 + 0.741500i) q^{24} +(6.35811 - 11.0126i) q^{26} +(-2.55342 - 4.42266i) q^{27} +(1.03406 - 5.86442i) q^{28} +(0.455678 - 2.58428i) q^{29} +(-4.03639 + 6.99123i) q^{31} +(-5.30452 - 4.45102i) q^{32} +(0.0826495 + 0.0300820i) q^{33} +(-5.28589 + 1.92391i) q^{34} +(-0.982763 - 5.57352i) q^{36} +5.01303 q^{37} +(7.68268 + 5.90316i) q^{38} +5.93265 q^{39} +(-4.50461 + 3.77982i) q^{41} +(4.38627 - 1.59647i) q^{42} +(0.611288 + 0.222491i) q^{43} +(0.191056 + 0.160315i) q^{44} +(-0.343511 - 0.594978i) q^{46} +(-1.19865 + 6.79791i) q^{47} +(0.222244 - 1.26041i) q^{48} +(1.44953 + 2.51066i) q^{49} +(-2.01037 - 1.68690i) q^{51} +(15.8084 + 5.75378i) q^{52} +(13.6767 - 4.97790i) q^{53} +(8.69551 - 7.29640i) q^{54} +4.23372 q^{56} +(-0.592951 + 4.48112i) q^{57} +5.83278 q^{58} +(1.29773 + 7.35981i) q^{59} +(-12.5139 + 4.55468i) q^{61} +(-16.8615 - 6.13710i) q^{62} +(-2.98568 - 2.50528i) q^{63} +(6.46156 - 11.1918i) q^{64} +(-0.0339479 + 0.192528i) q^{66} +(-1.54242 + 8.74750i) q^{67} +(-3.72088 - 6.44475i) q^{68} +(0.160262 - 0.277582i) q^{69} +(13.4720 + 4.90340i) q^{71} +(3.78105 - 1.37619i) q^{72} +(-8.31526 + 6.97733i) q^{73} +(1.93490 + 10.9734i) q^{74} +(-5.92601 + 11.3655i) q^{76} +0.171758 q^{77} +(2.28985 + 12.9864i) q^{78} +(0.0887829 - 0.0744977i) q^{79} +(-0.449247 - 0.163512i) q^{81} +(-10.0126 - 8.40155i) q^{82} +(-1.48776 + 2.57688i) q^{83} +(3.08761 + 5.34790i) q^{84} +(-0.251084 + 1.42397i) q^{86} +(1.36062 + 2.35666i) q^{87} +(-0.0886595 + 0.153563i) q^{88} +(-8.52291 - 7.15157i) q^{89} +(10.8867 - 3.96245i) q^{91} +(0.696253 - 0.584226i) q^{92} +(-1.45369 - 8.24430i) q^{93} -15.3431 q^{94} +7.18078 q^{96} +(0.0392276 + 0.222471i) q^{97} +(-4.93627 + 4.14202i) q^{98} +(0.153394 - 0.0558308i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9	$ 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) $ 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9 + 18 * q^12 + 3 * q^13 - 12 * q^14 - 3 * q^16 - 24 * q^17 - 48 * q^18 - 21 * q^21 - 9 * q^22 + 9 * q^23 - 15 * q^24 + 3 * q^26 + 24 * q^27 + 12 * q^28 + 15 * q^29 - 18 * q^31 - 15 * q^32 + 33 * q^33 - 12 * q^34 + 75 * q^36 - 36 * q^37 + 33 * q^38 + 36 * q^39 - 30 * q^41 + 9 * q^42 + 36 * q^43 + 42 * q^44 + 9 * q^46 - 21 * q^47 - 33 * q^48 + 9 * q^49 - 45 * q^51 + 39 * q^52 + 12 * q^53 - 66 * q^54 - 72 * q^57 - 12 * q^58 + 18 * q^59 - 30 * q^61 + 24 * q^62 - 54 * q^63 + 36 * q^64 + 39 * q^66 - 51 * q^68 + 15 * q^69 - 12 * q^71 + 66 * q^72 - 24 * q^73 - 15 * q^74 - 33 * q^76 + 60 * q^77 + 48 * q^78 - 51 * q^79 + 27 * q^81 + 15 * q^82 + 48 * q^84 + 63 * q^86 + 15 * q^87 + 27 * q^88 - 54 * q^89 + 30 * q^91 + 42 * q^92 - 72 * q^93 + 30 * q^94 - 66 * q^96 - 27 * q^97 + 3 * q^98 - 93 * 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 $

$2$	0.385975	+	2.18897i	0.272925	+	1.54784i	0.745476	+	0.666533i	$0.232222\pi$
$2$	0.385975	+	2.18897i	0.272925	+	1.54784i	−0.472551	+	0.881304i	$0.656667\pi$
$3$	−0.794389	+	0.666572i	−0.458641	+	0.384845i	−0.842631	−	0.538492i	$-0.818994\pi$
$3$	−0.794389	+	0.666572i	−0.458641	+	0.384845i	0.383990	+	0.923337i	$0.374550\pi$
$4$	−2.76323	+	1.00573i	−1.38162	+	0.502867i
$5$		0			0
$5$		0			0
$6$	−1.76572	−	1.48162i	−0.720852	−	0.604867i
$7$	−1.01254	+	1.75377i	−0.382704	+	0.662863i	−0.991448	−	0.130504i	$-0.958340\pi$
$7$	−1.01254	+	1.75377i	−0.382704	+	0.662863i	0.608744	+	0.793367i	$0.291674\pi$
$8$	−1.04532	−	1.81055i	−0.369577	−	0.640126i
$9$	−0.334208	+	1.89539i	−0.111403	+	0.631796i
$10$		0			0
$11$	−0.0424078	−	0.0734524i	−0.0127864	−	0.0221467i	0.859561	−	0.511032i	$-0.170737\pi$
$11$	−0.0424078	−	0.0734524i	−0.0127864	−	0.0221467i	−0.872348	+	0.488886i	$0.837403\pi$
$12$	1.52469	−	2.64084i	0.440139	−	0.762344i
$13$	−4.38252	−	3.67737i	−1.21549	−	1.01992i	−0.999048	−	0.0436233i	$-0.986110\pi$
$13$	−4.38252	−	3.67737i	−1.21549	−	1.01992i	−0.216443	−	0.976295i	$-0.569446\pi$
$14$	−4.22977	−	1.53951i	−1.13045	−	0.411451i
$15$		0			0
$16$	−0.945441	+	0.793319i	−0.236360	+	0.198330i
$17$	0.439455	+	2.49227i	0.106583	+	0.604464i	0.990576	+	0.136964i	$0.0437344\pi$
$17$	0.439455	+	2.49227i	0.106583	+	0.604464i	−0.883993	+	0.467501i	$0.845155\pi$
$18$	−4.27795			−1.00832
$19$	3.21565	−	2.94271i	0.737722	−	0.675105i
$19$	3.21565	−	2.94271i	0.737722	−	0.675105i
$20$		0			0
$21$	−0.364663	−	2.06811i	−0.0795760	−	0.451298i
$22$	0.144417	−	0.121180i	0.0307898	−	0.0258357i
$23$	−0.290447	+	0.105714i	−0.0605624	+	0.0220429i	−0.372124	−	0.928183i	$-0.621370\pi$
$23$	−0.290447	+	0.105714i	−0.0605624	+	0.0220429i	0.311561	+	0.950226i	$0.399148\pi$
$24$	2.03725	+	0.741500i	0.415853	+	0.151358i
$25$		0			0
$26$	6.35811	−	11.0126i	1.24693	−	2.15974i
$27$	−2.55342	−	4.42266i	−0.491406	−	0.851141i
$28$	1.03406	−	5.86442i	0.195418	−	1.10827i
$29$	0.455678	−	2.58428i	0.0846172	−	0.479888i	−0.912821	−	0.408359i	$-0.866101\pi$
$29$	0.455678	−	2.58428i	0.0846172	−	0.479888i	0.997439	−	0.0715288i	$-0.0227878\pi$
$30$		0			0
$31$	−4.03639	+	6.99123i	−0.724957	+	1.25566i	0.234035	+	0.972228i	$0.424807\pi$
$31$	−4.03639	+	6.99123i	−0.724957	+	1.25566i	−0.958992	+	0.283434i	$0.908526\pi$
$32$	−5.30452	−	4.45102i	−0.937716	−	0.786837i
$33$	0.0826495	+	0.0300820i	0.0143874	+	0.00523660i
$34$	−5.28589	+	1.92391i	−0.906523	+	0.329947i
$35$		0			0
$36$	−0.982763	−	5.57352i	−0.163794	−	0.928921i
$37$	5.01303			0.824136			0.412068	−	0.911153i	$-0.364807\pi$
$37$	5.01303			0.824136			0.412068	+	0.911153i	$0.364807\pi$
$38$	7.68268	+	5.90316i	1.24629	+	0.957619i
$39$	5.93265			0.949985
$40$		0			0
$41$	−4.50461	+	3.77982i	−0.703502	+	0.590309i	−0.922768	−	0.385357i	$-0.874078\pi$
$41$	−4.50461	+	3.77982i	−0.703502	+	0.590309i	0.219265	+	0.975665i	$0.429634\pi$
$42$	4.38627	−	1.59647i	0.676817	−	0.246341i
$43$	0.611288	+	0.222491i	0.0932205	+	0.0339295i	0.388209	−	0.921571i	$-0.373094\pi$
$43$	0.611288	+	0.222491i	0.0932205	+	0.0339295i	−0.294989	+	0.955501i	$0.595316\pi$
$44$	0.191056	+	0.160315i	0.0288028	+	0.0241684i
$45$		0			0
$46$	−0.343511	−	0.594978i	−0.0506479	−	0.0877247i
$47$	−1.19865	+	6.79791i	−0.174842	+	0.991576i	0.763485	+	0.645826i	$0.223487\pi$
$47$	−1.19865	+	6.79791i	−0.174842	+	0.991576i	−0.938326	+	0.345751i	$0.887624\pi$
$48$	0.222244	−	1.26041i	0.0320782	−	0.181924i
$49$	1.44953	+	2.51066i	0.207075	+	0.358665i
$50$		0			0
$51$	−2.01037	−	1.68690i	−0.281509	−	0.236214i
$52$	15.8084	+	5.75378i	2.19223	+	0.797905i
$53$	13.6767	−	4.97790i	1.87864	−	0.683767i	0.929659	−	0.368422i	$-0.120102\pi$
$53$	13.6767	−	4.97790i	1.87864	−	0.683767i	0.948977	−	0.315345i	$-0.102120\pi$
$54$	8.69551	−	7.29640i	1.18331	−	0.992915i
$55$		0			0
$56$	4.23372			0.565754
$57$	−0.592951	+	4.48112i	−0.0785382	+	0.593539i
$58$	5.83278			0.765882
$59$	1.29773	+	7.35981i	0.168950	+	0.958166i	0.944897	+	0.327367i	$0.106161\pi$
$59$	1.29773	+	7.35981i	0.168950	+	0.958166i	−0.775947	+	0.630799i	$0.782727\pi$
$60$		0			0
$61$	−12.5139	+	4.55468i	−1.60224	+	0.583167i	−0.979884	−	0.199567i	$-0.936046\pi$
$61$	−12.5139	+	4.55468i	−1.60224	+	0.583167i	−0.622355	+	0.782735i	$0.713824\pi$
$62$	−16.8615	−	6.13710i	−2.14142	−	0.779412i
$63$	−2.98568	−	2.50528i	−0.376160	−	0.315636i
$64$	6.46156	−	11.1918i	0.807695	−	1.39897i
$65$		0			0
$66$	−0.0339479	+	0.192528i	−0.00417870	+	0.0236986i
$67$	−1.54242	+	8.74750i	−0.188437	+	1.06868i	0.733023	+	0.680204i	$0.238109\pi$
$67$	−1.54242	+	8.74750i	−0.188437	+	1.06868i	−0.921460	+	0.388474i	$0.873002\pi$
$68$	−3.72088	−	6.44475i	−0.451223	−	0.781541i
$69$	0.160262	−	0.277582i	0.0192933	−	0.0334170i
$70$		0			0
$71$	13.4720	+	4.90340i	1.59883	+	0.581926i	0.979187	−	0.202958i	$-0.0650556\pi$
$71$	13.4720	+	4.90340i	1.59883	+	0.581926i	0.619642	+	0.784885i	$0.287278\pi$
$72$	3.78105	−	1.37619i	0.445601	−	0.162186i
$73$	−8.31526	+	6.97733i	−0.973227	+	0.816635i	−0.983054	−	0.183317i	$-0.941316\pi$
$73$	−8.31526	+	6.97733i	−0.973227	+	0.816635i	0.00982664	+	0.999952i	$0.496872\pi$
$74$	1.93490	+	10.9734i	0.224928	+	1.27563i
$75$		0			0
$76$	−5.92601	+	11.3655i	−0.679760	+	1.30371i
$77$	0.171758			0.0195737
$78$	2.28985	+	12.9864i	0.259275	+	1.47042i
$79$	0.0887829	−	0.0744977i	0.00998886	−	0.00838165i	−0.637780	−	0.770219i	$-0.720147\pi$
$79$	0.0887829	−	0.0744977i	0.00998886	−	0.00838165i	0.647768	+	0.761837i	$0.275702\pi$
$80$		0			0
$81$	−0.449247	−	0.163512i	−0.0499163	−	0.0181681i
$82$	−10.0126	−	8.40155i	−1.10570	−	0.927796i
$83$	−1.48776	+	2.57688i	−0.163303	+	0.282849i	−0.936051	−	0.351863i	$-0.885548\pi$
$83$	−1.48776	+	2.57688i	−0.163303	+	0.282849i	0.772748	+	0.634713i	$0.218882\pi$
$84$	3.08761	+	5.34790i	0.336886	+	0.583504i
$85$		0			0
$86$	−0.251084	+	1.42397i	−0.0270751	+	0.153550i
$87$	1.36062	+	2.35666i	0.145874	+	0.252661i
$88$	−0.0886595	+	0.153563i	−0.00945113	+	0.0163698i
$89$	−8.52291	−	7.15157i	−0.903427	−	0.758065i	0.0674305	−	0.997724i	$-0.478520\pi$
$89$	−8.52291	−	7.15157i	−0.903427	−	0.758065i	−0.970857	+	0.239659i	$0.922964\pi$
$90$		0			0
$91$	10.8867	−	3.96245i	1.14124	−	0.415377i
$92$	0.696253	−	0.584226i	0.0725894	−	0.0609097i
$93$	−1.45369	−	8.24430i	−0.150741	−	0.854894i
$94$	−15.3431			−1.58252
$95$		0			0
$96$	7.18078			0.732885
$97$	0.0392276	+	0.222471i	0.00398296	+	0.0225885i	0.986734	−	0.162343i	$-0.0519049\pi$
$97$	0.0392276	+	0.222471i	0.00398296	+	0.0225885i	−0.982752	+	0.184931i	$0.940794\pi$
$98$	−4.93627	+	4.14202i	−0.498639	+	0.418408i
$99$	0.153394	−	0.0558308i	0.0154167	−	0.00561121i
$100$		0			0
$101$	−9.65322	−	8.10001i	−0.960531	−	0.805981i	0.0205084	−	0.999790i	$-0.493472\pi$
$101$	−9.65322	−	8.10001i	−0.960531	−	0.805981i	−0.981039	+	0.193808i	$0.937916\pi$
$102$	2.91663	−	5.05175i	0.288790	−	0.500198i
$103$	8.86152	+	15.3486i	0.873152	+	1.51234i	0.858719	+	0.512447i	$0.171261\pi$
$103$	8.86152	+	15.3486i	0.873152	+	1.51234i	0.0144333	+	0.999896i	$0.495406\pi$
$104$	−2.07692	+	11.7788i	−0.203659	+	1.15501i
$105$		0			0
$106$	16.1753	+	28.0165i	1.57109	+	2.72120i
$107$	2.54806	−	4.41337i	0.246330	−	0.426657i	−0.716174	−	0.697921i	$-0.754109\pi$
$107$	2.54806	−	4.41337i	0.246330	−	0.426657i	0.962505	+	0.271265i	$0.0874418\pi$
$108$	11.5037	+	9.65277i	1.10695	+	0.928838i
$109$	5.76514	+	2.09834i	0.552200	+	0.200984i	0.603024	−	0.797723i	$-0.293962\pi$
$109$	5.76514	+	2.09834i	0.552200	+	0.200984i	−0.0508237	+	0.998708i	$0.516185\pi$
$110$		0			0
$111$	−3.98229	+	3.34154i	−0.377983	+	0.317165i
$112$	−0.434003	−	2.46135i	−0.0410094	−	0.232576i
$113$	−11.4316			−1.07539			−0.537697	−	0.843138i	$-0.680706\pi$
$113$	−11.4316			−1.07539			−0.537697	+	0.843138i	$0.680706\pi$
$114$	−10.0379	+	0.431649i	−0.940137	+	0.0404276i
$115$		0			0
$116$	1.33995	+	7.59925i	0.124411	+	0.705572i
$117$	8.43472	−	7.07757i	0.779790	−	0.654321i
$118$	−15.6095	+	5.68140i	−1.43697	+	0.523015i
$119$	−4.81583	−	1.75282i	−0.441467	−	0.160681i
$120$		0			0
$121$	5.49640	−	9.52005i	0.499673	−	0.865459i
$122$	−14.8001	−	25.6345i	−1.33994	−	2.32084i
$123$	1.05890	−	6.00529i	0.0954774	−	0.541479i
$124$	4.12216	−	23.3779i	0.370181	−	2.09940i
$125$		0			0
$126$	4.33159	−	7.50253i	0.385889	−	0.668379i
$127$	1.10293	+	0.925472i	0.0978696	+	0.0821224i	0.690410	−	0.723419i	$-0.257430\pi$
$127$	1.10293	+	0.925472i	0.0978696	+	0.0821224i	−0.592540	+	0.805541i	$0.701875\pi$
$128$	13.9785	+	5.08776i	1.23554	+	0.449699i
$129$	−0.633906	+	0.230723i	−0.0558123	+	0.0203140i
$130$		0			0
$131$	−0.174248	−	0.988207i	−0.0152241	−	0.0863400i	0.976249	−	0.216651i	$-0.0695135\pi$
$131$	−0.174248	−	0.988207i	−0.0152241	−	0.0863400i	−0.991473	+	0.130311i	$0.958402\pi$
$132$	−0.258634			−0.0225112
$133$	1.90487	+	8.61913i	0.165173	+	0.747373i
$134$	−19.7434			−1.70557
$135$		0			0
$136$	4.05301	−	3.40088i	0.347543	−	0.291623i
$137$	−9.81678	+	3.57301i	−0.838704	+	0.305263i	−0.725426	−	0.688300i	$-0.758357\pi$
$137$	−9.81678	+	3.57301i	−0.838704	+	0.305263i	−0.113278	+	0.993563i	$0.536135\pi$
$138$	0.669476	+	0.243669i	0.0569896	+	0.0207425i
$139$	8.18488	+	6.86793i	0.694233	+	0.582530i	0.920126	−	0.391622i	$-0.128086\pi$
$139$	8.18488	+	6.86793i	0.694233	+	0.582530i	−0.225894	+	0.974152i	$0.572530\pi$
$140$		0			0
$141$	−3.57909	−	6.19917i	−0.301414	−	0.522064i
$142$	−5.53355	+	31.3823i	−0.464366	+	2.63355i
$143$	−0.0842588	+	0.477855i	−0.00704607	+	0.0399603i
$144$	−1.18767	−	2.05711i	−0.0989729	−	0.171426i
$145$		0			0
$146$	−18.4826	−	15.5088i	−1.52963	−	1.28352i
$147$	−2.82502	−	1.02822i	−0.233004	−	0.0848064i
$148$	−13.8522	+	5.04177i	−1.13864	+	0.414431i
$149$	−3.86440	+	3.24262i	−0.316584	+	0.265645i	−0.787207	−	0.616689i	$-0.788474\pi$
$149$	−3.86440	+	3.24262i	−0.316584	+	0.265645i	0.470623	+	0.882334i	$0.344029\pi$
$150$		0			0
$151$	20.8114			1.69360			0.846802	−	0.531909i	$-0.178525\pi$
$151$	20.8114			1.69360			0.846802	+	0.531909i	$0.178525\pi$
$152$	−8.68933	−	2.74602i	−0.704797	−	0.222732i
$153$	−4.87069			−0.393772
$154$	0.0662943	+	0.375974i	0.00534214	+	0.0302968i
$155$		0			0
$156$	−16.3933	+	5.96667i	−1.31251	+	0.477716i
$157$	22.1916	+	8.07709i	1.77108	+	0.644622i	0.999969	+	0.00792593i	$0.00252293\pi$
$157$	22.1916	+	8.07709i	1.77108	+	0.644622i	0.771115	+	0.636696i	$0.219699\pi$
$158$	0.197341	+	0.165589i	0.0156996	+	0.0131736i
$159$	−7.54647	+	13.0709i	−0.598474	+	1.03659i
$160$		0			0
$161$	0.108691	−	0.616417i	0.00856605	−	0.0485805i
$162$	0.184526	−	1.04650i	0.0144977	−	0.0822208i
$163$	−0.106766	−	0.184925i	−0.00836258	−	0.0144844i	0.861814	−	0.507225i	$-0.169329\pi$
$163$	−0.106766	−	0.184925i	−0.00836258	−	0.0144844i	−0.870176	+	0.492740i	$0.835995\pi$
$164$	8.64580	−	14.9750i	0.675124	−	1.16935i
$165$		0			0
$166$	−6.21495	−	2.26206i	−0.482374	−	0.175570i
$167$	18.5353	−	6.74630i	1.43431	−	0.522045i	0.496144	−	0.868240i	$-0.334749\pi$
$167$	18.5353	−	6.74630i	1.43431	−	0.522045i	0.938162	+	0.346196i	$0.112527\pi$
$168$	−3.36322	+	2.82208i	−0.259478	+	0.217728i
$169$	3.42599	+	19.4298i	0.263538	+	1.49460i
$170$		0			0
$171$	4.50289	+	7.07839i	0.344345	+	0.541298i
$172$	−1.91290			−0.145857
$173$	−2.18361	−	12.3839i	−0.166017	−	0.941527i	−0.948010	−	0.318240i	$-0.896908\pi$
$173$	−2.18361	−	12.3839i	−0.166017	−	0.941527i	0.781993	−	0.623287i	$-0.214203\pi$
$174$	−4.63350	+	3.88797i	−0.351265	+	0.294746i
$175$		0			0
$176$	0.0983652	+	0.0358020i	0.00741456	+	0.00269868i
$177$	−5.93675	−	4.98152i	−0.446233	−	0.374434i
$178$	12.3650	−	21.4167i	0.926792	−	1.60525i
$179$	5.40914	+	9.36891i	0.404298	+	0.700265i	0.994240	−	0.107181i	$-0.0341825\pi$
$179$	5.40914	+	9.36891i	0.404298	+	0.700265i	−0.589941	+	0.807446i	$0.700849\pi$
$180$		0			0
$181$	−0.939769	+	5.32969i	−0.0698524	+	0.396153i	0.929756	+	0.368176i	$0.120018\pi$
$181$	−0.939769	+	5.32969i	−0.0698524	+	0.396153i	−0.999609	+	0.0279769i	$0.991094\pi$
$182$	12.8757	+	22.3013i	0.954409	+	1.65308i
$183$	6.90488	−	11.9596i	0.510423	−	0.884079i
$184$	0.495012	+	0.415364i	0.0364927	+	0.0306210i
$185$		0			0
$186$	17.4854	−	6.36418i	1.28209	−	0.466644i
$187$	0.164427	−	0.137971i	0.0120241	−	0.0100894i
$188$	−3.52473	−	19.9897i	−0.257067	−	1.45790i
$189$	10.3418			0.752253
$190$		0			0
$191$	4.87144			0.352485			0.176243	−	0.984347i	$-0.443606\pi$
$191$	4.87144			0.352485			0.176243	+	0.984347i	$0.443606\pi$
$192$	2.32711	+	13.1977i	0.167945	+	0.952462i
$193$	1.06031	−	0.889706i	0.0763228	−	0.0640424i	−0.603828	−	0.797115i	$-0.706359\pi$
$193$	1.06031	−	0.889706i	0.0763228	−	0.0640424i	0.680151	+	0.733072i	$0.261914\pi$
$194$	−0.471841	+	0.171736i	−0.0338762	+	0.0123299i
$195$		0			0
$196$	−6.53044	−	5.47969i	−0.466460	−	0.391406i
$197$	3.20375	−	5.54906i	0.228258	−	0.395354i	−0.729034	−	0.684477i	$-0.760030\pi$
$197$	3.20375	−	5.54906i	0.228258	−	0.395354i	0.957292	+	0.289123i	$0.0933638\pi$
$198$	0.181418	+	0.314225i	0.0128928	+	0.0223310i
$199$	2.71594	−	15.4029i	0.192528	−	1.09188i	−0.723367	−	0.690464i	$-0.757406\pi$
$199$	2.71594	−	15.4029i	0.192528	−	1.09188i	0.915895	−	0.401418i	$-0.131482\pi$
$200$		0			0
$201$	−4.60555	−	7.97705i	−0.324851	−	0.562658i
$202$	14.0048	−	24.2570i	0.985374	−	1.70672i
$203$	4.07083	+	3.41583i	0.285716	+	0.239745i
$204$	7.25171	+	2.63941i	0.507721	+	0.184795i
$205$		0			0
$206$	−30.1773	+	25.3218i	−2.10255	+	1.76425i
$207$	−0.103300	−	0.585841i	−0.00717982	−	0.0407188i
$208$	7.06074			0.489574
$209$	−0.352518	−	0.111404i	−0.0243842	−	0.00770594i
$210$		0			0
$211$	1.33429	+	7.56711i	0.0918560	+	0.520941i	0.995666	+	0.0930062i	$0.0296477\pi$
$211$	1.33429	+	7.56711i	0.0918560	+	0.520941i	−0.903810	+	0.427935i	$0.859241\pi$
$212$	−32.7854	+	27.5102i	−2.25171	+	1.88941i
$213$	−13.9705	+	5.08483i	−0.957240	+	0.348407i
$214$	10.6442	+	3.87418i	0.727625	+	0.264834i
$215$		0			0
$216$	−5.33830	+	9.24620i	−0.363225	+	0.629124i
$217$	−8.17400	−	14.1578i	−0.554887	−	0.961093i
$218$	−2.36800	+	13.4296i	−0.160382	+	0.909569i
$219$	1.95466	−	11.0854i	0.132084	−	0.749084i
$220$		0			0
$221$	7.23908	−	12.5385i	0.486953	−	0.843428i
$222$	−8.85160	−	7.42737i	−0.594080	−	0.498493i
$223$	2.33040	+	0.848195i	0.156055	+	0.0567993i	0.418866	−	0.908048i	$-0.362428\pi$
$223$	2.33040	+	0.848195i	0.156055	+	0.0567993i	−0.262812	+	0.964847i	$0.584650\pi$
$224$	13.1771	−	4.79607i	0.880432	−	0.320451i
$225$		0			0
$226$	−4.41231	−	25.0234i	−0.293502	−	1.66453i
$227$	0.453554			0.0301034			0.0150517	−	0.999887i	$-0.495209\pi$
$227$	0.453554			0.0301034			0.0150517	+	0.999887i	$0.495209\pi$
$228$	−2.86836	−	12.9787i	−0.189962	−	0.859538i
$229$	0.993282			0.0656379			0.0328190	−	0.999461i	$-0.489552\pi$
$229$	0.993282			0.0656379			0.0328190	+	0.999461i	$0.489552\pi$
$230$		0			0
$231$	−0.136443	+	0.114489i	−0.00897727	+	0.00753283i
$232$	−5.15529	+	1.87637i	−0.338461	+	0.123190i
$233$	−4.00611	−	1.45810i	−0.262449	−	0.0955236i	0.207444	−	0.978247i	$-0.433485\pi$
$233$	−4.00611	−	1.45810i	−0.262449	−	0.0955236i	−0.469893	+	0.882723i	$0.655708\pi$
$234$	18.7482	+	15.7316i	1.22561	+	1.02841i
$235$		0			0
$236$	−10.9880	−	19.0317i	−0.715255	−	1.23886i
$237$	−0.0208701	+	0.118360i	−0.00135566	+	0.00768833i
$238$	1.97808	−	11.2183i	0.128220	−	0.727172i
$239$	−12.2291	−	21.1815i	−0.791037	−	1.37012i	−0.925325	−	0.379175i	$-0.876208\pi$
$239$	−12.2291	−	21.1815i	−0.791037	−	1.37012i	0.134288	−	0.990942i	$-0.457125\pi$
$240$		0			0
$241$	3.36665	+	2.82495i	0.216865	+	0.181971i	0.744748	−	0.667346i	$-0.232570\pi$
$241$	3.36665	+	2.82495i	0.216865	+	0.181971i	−0.527883	+	0.849317i	$0.677014\pi$
$242$	22.9606	+	8.35697i	1.47596	+	0.537206i
$243$	14.8625	−	5.40950i	0.953428	−	0.347019i
$244$	29.9980	−	25.1713i	1.92042	−	1.61143i
$245$		0			0
$246$	13.5541			0.864179
$247$	−24.9141	+	1.07135i	−1.58525	+	0.0681685i
$248$	16.8773			1.07171
$249$	−0.535813	−	3.03875i	−0.0339558	−	0.192573i
$250$		0			0
$251$	0.364101	−	0.132522i	0.0229818	−	0.00836471i	−0.330504	−	0.943805i	$-0.607219\pi$
$251$	0.364101	−	0.132522i	0.0229818	−	0.00836471i	0.353485	+	0.935440i	$0.384996\pi$
$252$	10.7698	+	3.91987i	0.678431	+	0.246929i
$253$	0.0200822	+	0.0168509i	0.00126256	+	0.00105941i
$254$	−1.60013	+	2.77150i	−0.100401	+	0.173899i
$255$		0			0
$256$	−1.25346	+	7.10870i	−0.0783410	+	0.444294i
$257$	0.495411	−	2.80962i	0.0309029	−	0.175259i	−0.965450	−	0.260589i	$-0.916083\pi$
$257$	0.495411	−	2.80962i	0.0309029	−	0.175259i	0.996353	+	0.0853298i	$0.0271944\pi$
$258$	−0.749718	−	1.29855i	−0.0466754	−	0.0808441i
$259$	−5.07589	+	8.79169i	−0.315400	+	0.546289i
$260$		0			0
$261$	4.74592	+	1.72737i	0.293765	+	0.106922i
$262$	2.09590	−	0.762846i	0.129485	−	0.0471288i
$263$	8.27900	−	6.94691i	0.510505	−	0.428365i	−0.350802	−	0.936450i	$-0.614091\pi$
$263$	8.27900	−	6.94691i	0.510505	−	0.428365i	0.861307	+	0.508085i	$0.169646\pi$
$264$	−0.0319304	−	0.181086i	−0.00196518	−	0.0111451i
$265$		0			0
$266$	−18.1318	+	7.49647i	−1.11173	+	0.459638i
$267$	11.5375			0.706086
$268$	−4.53560	−	25.7226i	−0.277056	−	1.57126i
$269$	2.12780	−	1.78544i	0.129734	−	0.108860i	−0.575612	−	0.817723i	$-0.695236\pi$
$269$	2.12780	−	1.78544i	0.129734	−	0.108860i	0.705346	+	0.708863i	$0.250792\pi$
$270$		0			0
$271$	−13.9661	−	5.08325i	−0.848381	−	0.308785i	−0.119001	−	0.992894i	$-0.537969\pi$
$271$	−13.9661	−	5.08325i	−0.848381	−	0.308785i	−0.729380	+	0.684109i	$0.760191\pi$
$272$	−2.39264	−	2.00767i	−0.145075	−	0.121733i
$273$	−6.00705	+	10.4045i	−0.363563	+	0.629709i
$274$	−11.6103	−	20.1095i	−0.701401	−	1.21486i
$275$		0			0
$276$	−0.163668	+	0.928205i	−0.00985163	+	0.0558714i
$277$	9.04379	+	15.6643i	0.543389	+	0.941177i	0.998706	+	0.0508480i	$0.0161924\pi$
$277$	9.04379	+	15.6643i	0.543389	+	0.941177i	−0.455318	+	0.890329i	$0.650474\pi$
$278$	−11.8745	+	20.5673i	−0.712188	+	1.23355i
$279$	−11.9021	−	9.98705i	−0.712560	−	0.597909i
$280$		0			0
$281$	3.65001	−	1.32850i	0.217741	−	0.0792514i	−0.230846	−	0.972990i	$-0.574149\pi$
$281$	3.65001	−	1.32850i	0.217741	−	0.0792514i	0.448588	+	0.893739i	$0.351927\pi$
$282$	12.1884	−	10.2273i	0.725807	−	0.609024i
$283$	3.86993	+	21.9474i	0.230043	+	1.30464i	0.852805	+	0.522229i	$0.174899\pi$
$283$	3.86993	+	21.9474i	0.230043	+	1.30464i	−0.622762	+	0.782411i	$0.713990\pi$
$284$	−42.1577			−2.50160
$285$		0			0
$286$	−1.07853			−0.0637750
$287$	−2.06783	−	11.7273i	−0.122060	−	0.692239i
$288$	10.2092	−	8.56656i	0.601585	−	0.504789i
$289$	9.95648	−	3.62386i	0.585675	−	0.213168i
$290$		0			0
$291$	−0.179455	−	0.150580i	−0.0105198	−	0.00882718i
$292$	15.9596	−	27.6429i	0.933968	−	1.61768i
$293$	−12.2257	−	21.1755i	−0.714232	−	1.23709i	−0.963255	−	0.268589i	$-0.913443\pi$
$293$	−12.2257	−	21.1755i	−0.714232	−	1.23709i	0.249023	−	0.968498i	$-0.419891\pi$
$294$	1.16037	−	6.58076i	0.0676739	−	0.383798i
$295$		0			0
$296$	−5.24022	−	9.07633i	−0.304582	−	0.527551i
$297$	−0.216570	+	0.375110i	−0.0125667	+	0.0217661i
$298$	−8.58955	−	7.20749i	−0.497580	−	0.417519i
$299$	1.66164	+	0.604788i	0.0960951	+	0.0349758i
$300$		0			0
$301$	−1.00915	+	0.846777i	−0.0581664	+	0.0488074i
$302$	8.03265	+	45.5554i	0.462227	+	2.62142i
$303$	13.0676			0.750717
$304$	−0.705699	+	5.33320i	−0.0404746	+	0.305880i
$305$		0			0
$306$	−1.87996	−	10.6618i	−0.107470	−	0.609495i
$307$	−4.92198	+	4.13004i	−0.280913	+	0.235714i	−0.772347	−	0.635201i	$-0.780917\pi$
$307$	−4.92198	+	4.13004i	−0.280913	+	0.235714i	0.491434	+	0.870915i	$0.336473\pi$
$308$	−0.474608	+	0.172743i	−0.0270433	+	0.00984295i
$309$	−17.2704	−	6.28593i	−0.982481	−	0.357594i
$310$		0			0
$311$	8.78200	−	15.2109i	0.497982	−	0.862529i	−0.502016	−	0.864858i	$-0.667408\pi$
$311$	8.78200	−	15.2109i	0.497982	−	0.862529i	0.999997	+	0.00232912i	$0.000741383\pi$
$312$	−6.20153	−	10.7414i	−0.351093	−	0.608110i
$313$	0.632703	−	3.58824i	0.0357625	−	0.202819i	−0.961691	−	0.274135i	$-0.911609\pi$
$313$	0.632703	−	3.58824i	0.0357625	−	0.202819i	0.997454	+	0.0713155i	$0.0227197\pi$
$314$	−9.11511	+	51.6944i	−0.514395	+	2.91728i
$315$		0			0
$316$	−0.170403	+	0.295146i	−0.00958591	+	0.0166033i
$317$	−3.44644	−	2.89191i	−0.193571	−	0.162426i	0.540851	−	0.841118i	$-0.318102\pi$
$317$	−3.44644	−	2.89191i	−0.193571	−	0.162426i	−0.734422	+	0.678693i	$0.762547\pi$
$318$	−31.5245	−	11.4740i	−1.76781	−	0.643429i
$319$	−0.209145	+	0.0761227i	−0.0117099	+	0.00426205i
$320$		0			0
$321$	0.917676	+	5.20440i	0.0512197	+	0.290481i
$322$	1.39127			0.0775325
$323$	8.74717	+	6.72109i	0.486706	+	0.373972i
$324$	1.40582			0.0781013
$325$		0			0
$326$	0.363586	−	0.305085i	0.0201371	−	0.0168971i
$327$	−5.97845	+	2.17598i	−0.330609	+	0.120332i
$328$	11.5523	+	4.20470i	0.637870	+	0.232166i
$329$	−10.7083	−	8.98531i	−0.590366	−	0.495376i
$330$		0			0
$331$	−17.0501	−	29.5317i	−0.937161	−	1.62321i	−0.770735	−	0.637156i	$-0.780111\pi$
$331$	−17.0501	−	29.5317i	−0.937161	−	1.62321i	−0.166426	−	0.986054i	$-0.553223\pi$
$332$	1.51938	−	8.61681i	0.0833866	−	0.472909i
$333$	−1.67539	+	9.50163i	−0.0918110	+	0.520686i
$334$	21.9216	+	37.9694i	1.19950	+	2.07759i
$335$		0			0
$336$	1.98544	+	1.66598i	0.108314	+	0.0908866i
$337$	−0.910498	−	0.331394i	−0.0495980	−	0.0180522i	0.317102	−	0.948391i	$-0.397290\pi$
$337$	−0.910498	−	0.331394i	−0.0495980	−	0.0180522i	−0.366700	+	0.930339i	$0.619512\pi$
$338$	−41.2088	+	14.9988i	−2.24146	+	0.815827i
$339$	9.08113	−	7.61998i	0.493220	−	0.413860i
$340$		0			0
$341$	0.684697			0.0370784
$342$	−13.7564	+	12.5888i	−0.743861	+	0.680723i
$343$	−20.0464			−1.08240
$344$	−0.236162	−	1.33934i	−0.0127330	−	0.0722124i
$345$		0			0
$346$	26.2651	−	9.55971i	1.41202	−	0.513933i
$347$	−22.0888	−	8.03967i	−1.18579	−	0.431592i	−0.327546	−	0.944835i	$-0.606222\pi$
$347$	−22.0888	−	8.03967i	−1.18579	−	0.431592i	−0.858243	+	0.513243i	$0.828444\pi$
$348$	−6.12988	−	5.14358i	−0.328596	−	0.275725i
$349$	−9.71877	+	16.8334i	−0.520234	+	0.901071i	0.479490	+	0.877548i	$0.340822\pi$
$349$	−9.71877	+	16.8334i	−0.520234	+	0.901071i	−0.999723	+	0.0235237i	$0.992511\pi$
$350$		0			0
$351$	−5.07332	+	28.7723i	−0.270794	+	1.53575i
$352$	−0.101985	+	0.578388i	−0.00543584	+	0.0308282i
$353$	−5.98232	−	10.3617i	−0.318407	−	0.551497i	0.661749	−	0.749726i	$-0.269815\pi$
$353$	−5.98232	−	10.3617i	−0.318407	−	0.551497i	−0.980156	+	0.198229i	$0.936481\pi$
$354$	8.61297	−	14.9181i	0.457774	−	0.792888i
$355$		0			0
$356$	30.7434	+	11.1897i	1.62939	+	0.593051i
$357$	4.99403	−	1.81768i	0.264312	−	0.0962017i
$358$	−18.4205	+	15.4566i	−0.973552	+	0.816907i
$359$	2.98502	+	16.9289i	0.157543	+	0.893473i	0.956424	+	0.291983i	$0.0943150\pi$
$359$	2.98502	+	16.9289i	0.157543	+	0.893473i	−0.798880	+	0.601490i	$0.794574\pi$
$360$		0			0
$361$	1.68086	−	18.9255i	0.0884664	−	0.996079i
$362$	−12.0293			−0.632244
$363$	1.97951	+	11.2264i	0.103897	+	0.589232i
$364$	−26.0974	+	21.8983i	−1.36788	+	1.14778i
$365$		0			0
$366$	28.8443	+	10.4985i	1.50772	+	0.548764i
$367$	13.5002	+	11.3280i	0.704703	+	0.591316i	0.923107	−	0.384542i	$-0.125641\pi$
$367$	13.5002	+	11.3280i	0.704703	+	0.591316i	−0.218404	+	0.975858i	$0.570085\pi$
$368$	0.190736	−	0.330364i	0.00994279	−	0.0172214i
$369$	−5.65875	−	9.80124i	−0.294583	−	0.510232i
$370$		0			0
$371$	−5.11808	+	29.0261i	−0.265717	+	1.50696i
$372$	12.3085	+	21.3189i	0.638164	+	1.10533i
$373$	−1.32738	+	2.29909i	−0.0687292	+	0.119042i	−0.898342	−	0.439296i	$-0.855228\pi$
$373$	−1.32738	+	2.29909i	−0.0687292	+	0.119042i	0.829613	+	0.558339i	$0.188561\pi$
$374$	0.365478	+	0.306673i	0.0188984	+	0.0158577i
$375$		0			0
$376$	13.5609	−	4.93577i	0.699352	−	0.254543i
$377$	−11.5003	+	9.64994i	−0.592298	+	0.496997i
$378$	3.99166	+	22.6378i	0.205309	+	1.16436i
$379$	−18.9795			−0.974909			−0.487455	−	0.873148i	$-0.662075\pi$
$379$	−18.9795			−0.974909			−0.487455	+	0.873148i	$0.662075\pi$
$380$		0			0
$381$	−1.49305			−0.0764914
$382$	1.88025	+	10.6634i	0.0962021	+	0.545589i
$383$	9.13777	−	7.66750i	0.466918	−	0.391791i	−0.378751	−	0.925499i	$-0.623646\pi$
$383$	9.13777	−	7.66750i	0.466918	−	0.391791i	0.845669	+	0.533708i	$0.179202\pi$
$384$	−14.4957	+	5.27601i	−0.739732	+	0.269240i
$385$		0			0
$386$	2.35679	+	1.97758i	0.119958	+	0.100656i
$387$	−0.626003	+	1.08427i	−0.0318215	+	0.0551165i
$388$	−0.332142	−	0.575286i	−0.0168619	−	0.0292057i
$389$	−1.69579	+	9.61728i	−0.0859798	+	0.487616i	0.911161	+	0.412050i	$0.135187\pi$
$389$	−1.69579	+	9.61728i	−0.0859798	+	0.487616i	−0.997141	+	0.0755652i	$0.975924\pi$
$390$		0			0
$391$	−0.391107	−	0.677417i	−0.0197791	−	0.0342584i
$392$	3.03045	−	5.24889i	0.153061	−	0.265109i
$393$	0.797131	+	0.668872i	0.0402099	+	0.0337401i
$394$	13.3833	+	4.87112i	0.674240	+	0.245403i
$395$		0			0
$396$	−0.367712	+	0.308547i	−0.0184782	+	0.0155051i
$397$	−5.00846	−	28.4044i	−0.251368	−	1.42558i	−0.805227	−	0.592966i	$-0.797957\pi$
$397$	−5.00846	−	28.4044i	−0.251368	−	1.42558i	0.553860	−	0.832610i	$-0.313154\pi$
$398$	34.7648			1.74260
$399$	−7.25847	−	5.57721i	−0.363378	−	0.279210i
$400$		0			0
$401$	1.08900	+	6.17602i	0.0543820	+	0.308416i	0.999850	−	0.0172981i	$-0.00550645\pi$
$401$	1.08900	+	6.17602i	0.0543820	+	0.308416i	−0.945468	+	0.325714i	$0.894395\pi$
$402$	15.6839	−	13.1604i	0.782242	−	0.656379i
$403$	43.3989	−	15.7959i	2.16185	−	0.786849i
$404$	34.8205	+	12.6736i	1.73239	+	0.630537i
$405$		0			0
$406$	−5.90592	+	10.2294i	−0.293106	+	0.507675i
$407$	−0.212591	−	0.368219i	−0.0105378	−	0.0182519i
$408$	−0.952737	+	5.40324i	−0.0471675	+	0.267500i
$409$	1.94902	−	11.0534i	0.0963726	−	0.546556i	−0.897946	−	0.440107i	$-0.854941\pi$
$409$	1.94902	−	11.0534i	0.0963726	−	0.546556i	0.994318	−	0.106450i	$-0.0339483\pi$
$410$		0			0
$411$	5.41667	−	9.38195i	0.267185	−	0.462777i
$412$	−39.9231	−	33.4994i	−1.96687	−	1.65040i
$413$	−14.2214	−	5.17617i	−0.699790	−	0.254703i
$414$	1.24252	−	0.452240i	0.0610664	−	0.0222264i
$415$		0			0
$416$	6.87911	+	39.0134i	0.337276	+	1.91279i
$417$	−11.0800			−0.542588
$418$	0.107796	−	0.814651i	0.00527248	−	0.0398459i
$419$	−26.0754			−1.27387			−0.636934	−	0.770918i	$-0.719798\pi$
$419$	−26.0754			−1.27387			−0.636934	+	0.770918i	$0.719798\pi$
$420$		0			0
$421$	−19.3507	+	16.2372i	−0.943096	+	0.791351i	−0.978121	−	0.208035i	$-0.933293\pi$
$421$	−19.3507	+	16.2372i	−0.943096	+	0.791351i	0.0350258	+	0.999386i	$0.488849\pi$
$422$	−16.0492	+	5.84142i	−0.781262	+	0.284356i
$423$	−12.4841	−	4.54383i	−0.606996	−	0.220929i
$424$	−23.3093	−	19.5588i	−1.13200	−	0.949859i
$425$		0			0
$426$	−16.5228	−	28.6183i	−0.800532	−	1.38656i
$427$	4.68294	−	26.5583i	0.226623	−	1.28525i
$428$	−2.60221	+	14.7578i	−0.125782	+	0.713347i
$429$	−0.251591	−	0.435768i	−0.0121469	−	0.0210391i
$430$		0			0
$431$	29.2544	+	24.5474i	1.40914	+	1.18241i	0.956867	+	0.290525i	$0.0938299\pi$
$431$	29.2544	+	24.5474i	1.40914	+	1.18241i	0.452269	+	0.891881i	$0.350615\pi$
$432$	5.92269	+	2.15568i	0.284956	+	0.103715i
$433$	2.46296	−	0.896443i	0.118362	−	0.0430803i	−0.282160	−	0.959367i	$-0.591051\pi$
$433$	2.46296	−	0.896443i	0.118362	−	0.0430803i	0.400522	+	0.916287i	$0.368829\pi$
$434$	27.8360	−	23.3572i	1.33617	−	1.12118i
$435$		0			0
$436$	−18.0408			−0.863997
$437$	−0.622891	+	1.19464i	−0.0297969	+	0.0571476i
$438$	25.0201			1.19551
$439$	1.16634	+	6.61462i	0.0556662	+	0.315699i	0.999908	−	0.0135537i	$-0.00431442\pi$
$439$	1.16634	+	6.61462i	0.0556662	+	0.315699i	−0.944242	+	0.329252i	$0.893203\pi$
$440$		0			0
$441$	−5.24311	+	1.90834i	−0.249672	+	0.0908732i
$442$	30.2404	+	11.0066i	1.43839	+	0.523531i
$443$	19.9218	+	16.7163i	0.946511	+	0.794217i	0.978707	−	0.205264i	$-0.0658054\pi$
$443$	19.9218	+	16.7163i	0.946511	+	0.794217i	−0.0321953	+	0.999482i	$0.510250\pi$
$444$	7.64330	−	13.2386i	0.362735	−	0.628275i
$445$		0			0
$446$	−0.957200	+	5.42855i	−0.0453247	+	0.257049i
$447$	0.908401	−	5.15180i	0.0429659	−	0.243672i
$448$	13.0852	+	22.6642i	0.618216	+	1.07078i
$449$	13.7860	−	23.8781i	0.650602	−	1.12688i	−0.332376	−	0.943147i	$-0.607850\pi$
$449$	13.7860	−	23.8781i	0.650602	−	1.12688i	0.982977	−	0.183728i	$-0.0588165\pi$
$450$		0			0
$451$	0.468667	+	0.170581i	0.0220687	+	0.00803234i
$452$	31.5882	−	11.4971i	1.48578	−	0.540780i
$453$	−16.5323	+	13.8723i	−0.776756	+	0.651775i
$454$	0.175060	+	0.992816i	0.00821598	+	0.0465951i
$455$		0			0
$456$	8.73312	−	3.61065i	0.408966	−	0.169084i
$457$	−2.22524			−0.104092			−0.0520462	−	0.998645i	$-0.516574\pi$
$457$	−2.22524			−0.104092			−0.0520462	+	0.998645i	$0.516574\pi$
$458$	0.383382	+	2.17427i	0.0179143	+	0.101597i
$459$	9.90035	−	8.30738i	0.462109	−	0.387755i
$460$		0			0
$461$	−19.2217	−	6.99612i	−0.895243	−	0.325842i	−0.146898	−	0.989152i	$-0.546929\pi$
$461$	−19.2217	−	6.99612i	−0.895243	−	0.325842i	−0.748345	+	0.663310i	$0.769151\pi$
$462$	−0.303277	−	0.254479i	−0.0141097	−	0.0118395i
$463$	−16.2150	+	28.0852i	−0.753575	+	1.30523i	0.192505	+	0.981296i	$0.438339\pi$
$463$	−16.2150	+	28.0852i	−0.753575	+	1.30523i	−0.946080	+	0.323934i	$0.894994\pi$
$464$	1.61934	+	2.80478i	0.0751760	+	0.130209i
$465$		0			0
$466$	1.64549	−	9.33205i	0.0762259	−	0.432299i
$467$	−3.46049	−	5.99375i	−0.160132	−	0.277357i	0.774784	−	0.632227i	$-0.217859\pi$
$467$	−3.46049	−	5.99375i	−0.160132	−	0.277357i	−0.934916	+	0.354869i	$0.884525\pi$
$468$	−16.1889	+	28.0400i	−0.748333	+	1.29615i
$469$	−13.7793	−	11.5622i	−0.636271	−	0.533895i
$470$		0			0
$471$	−23.0127	+	8.37595i	−1.06037	+	0.385943i
$472$	11.9688	−	10.0430i	0.550907	−	0.462266i
$473$	−0.00958088	−	0.0543359i	−0.000440529	−	0.00249837i
$474$	−0.267143			−0.0122703
$475$		0			0
$476$	15.0701			0.690739
$477$	4.86420	+	27.5863i	0.222717	+	1.26309i
$478$	41.6455	−	34.9448i	1.90482	−	1.59834i
$479$	18.8350	−	6.85539i	0.860594	−	0.313231i	0.126242	−	0.991999i	$-0.459708\pi$
$479$	18.8350	−	6.85539i	0.860594	−	0.313231i	0.734352	+	0.678769i	$0.237486\pi$
$480$		0			0
$481$	−21.9697	−	18.4347i	−1.00173	−	0.840552i
$482$	−4.88430	+	8.45985i	−0.222474	+	0.385336i
$483$	0.324543	+	0.562126i	0.0147672	+	0.0255776i
$484$	−5.61320	+	31.8340i	−0.255145	+	1.44700i
$485$		0			0
$486$	17.5778	+	30.4456i	0.797344	+	1.38104i
$487$	3.56464	−	6.17413i	0.161529	−	0.279777i	−0.773888	−	0.633322i	$-0.781691\pi$
$487$	3.56464	−	6.17413i	0.161529	−	0.279777i	0.935417	+	0.353546i	$0.115024\pi$
$488$	21.3275	+	17.8959i	0.965452	+	0.810110i
$489$	0.208080	+	0.0757348i	0.00940968	+	0.00342484i
$490$		0			0
$491$	12.6437	−	10.6093i	0.570600	−	0.478790i	−0.311245	−	0.950330i	$-0.600746\pi$
$491$	12.6437	−	10.6093i	0.570600	−	0.478790i	0.881845	+	0.471539i	$0.156302\pi$
$492$	3.11376	+	17.6590i	0.140379	+	0.796129i
$493$	6.64096			0.299094
$494$	−11.9614	−	54.1227i	−0.538167	−	2.43510i
$495$		0			0
$496$	−1.73011	−	9.81194i	−0.0776842	−	0.440569i
$497$	−22.2403	+	18.6619i	−0.997615	+	0.837099i
$498$	6.44491	−	2.34576i	0.288804	−	0.105116i
$499$	28.5296	+	10.3839i	1.27716	+	0.464848i	0.889491	−	0.456952i	$-0.151059\pi$
$499$	28.5296	+	10.3839i	1.27716	+	0.464848i	0.387667	+	0.921800i	$0.373281\pi$
$500$		0			0
$501$	−10.2274	+	17.7143i	−0.456925	+	0.791417i
$502$	0.430620	+	0.745856i	0.0192195	+	0.0332892i
$503$	1.00185	−	5.68175i	0.0446701	−	0.253337i	−0.954293	−	0.298874i	$-0.903389\pi$
$503$	1.00185	−	5.68175i	0.0446701	−	0.253337i	0.998963	+	0.0455375i	$0.0145001\pi$
$504$	−1.41494	+	8.02454i	−0.0630266	+	0.357441i
$505$		0			0
$506$	−0.0291350	+	0.0504633i	−0.00129521	+	0.00224337i
$507$	−15.6729	−	13.1511i	−0.696058	−	0.584062i
$508$	−3.97844	−	1.44803i	−0.176515	−	0.0642462i
$509$	36.5216	−	13.2928i	1.61879	−	0.589191i	0.635638	−	0.771987i	$-0.280737\pi$
$509$	36.5216	−	13.2928i	1.61879	−	0.589191i	0.983151	+	0.182796i	$0.0585147\pi$
$510$		0			0
$511$	−3.81710	−	21.6479i	−0.168859	−	0.957645i
$512$	13.7067			0.605755
$513$	−21.2255	−	6.70774i	−0.937131	−	0.296154i
$514$	6.34139			0.279707
$515$		0			0
$516$	1.51958	−	1.27508i	0.0668960	−	0.0561324i
$517$	0.550155	−	0.200240i	0.0241958	−	0.00880654i
$518$	−21.2039	−	7.71760i	−0.931647	−	0.339092i
$519$	9.98936	+	8.38207i	0.438484	+	0.367932i
$520$		0			0
$521$	18.2553	+	31.6191i	0.799778	+	1.38526i	0.919761	+	0.392480i	$0.128383\pi$
$521$	18.2553	+	31.6191i	0.799778	+	1.38526i	−0.119983	+	0.992776i	$0.538284\pi$
$522$	−1.94936	+	11.0554i	−0.0853214	+	0.483881i
$523$	−4.82917	+	27.3876i	−0.211165	+	1.19758i	0.676274	+	0.736650i	$0.263593\pi$
$523$	−4.82917	+	27.3876i	−0.211165	+	1.19758i	−0.887439	+	0.460925i	$0.847518\pi$
$524$	1.47536	+	2.55540i	0.0644514	+	0.111633i
$525$		0			0
$526$	18.4021	+	15.4412i	0.802368	+	0.673267i
$527$	−19.1978	−	6.98744i	−0.836271	−	0.304378i
$528$	−0.102005	+	0.0371267i	−0.00443919	+	0.00161573i
$529$	−17.5458	+	14.7227i	−0.762863	+	0.640118i
$530$		0			0
$531$	−14.3834			−0.624187
$532$	−13.9321	−	21.9009i	−0.604035	−	0.949523i
$533$	33.6413			1.45717
$534$	4.45320	+	25.2553i	0.192709	+	1.09291i
$535$		0			0
$536$	17.4501	−	6.35132i	0.753730	−	0.274335i
$537$	−10.5420	−	3.83698i	−0.454921	−	0.165578i
$538$	4.72954	+	3.96856i	0.203905	+	0.171097i
$539$	0.122942	−	0.212943i	0.00529551	−	0.00917209i
$540$		0			0
$541$	−4.21069	+	23.8800i	−0.181032	+	1.02668i	0.749917	+	0.661532i	$0.230094\pi$
$541$	−4.21069	+	23.8800i	−0.181032	+	1.02668i	−0.930949	+	0.365150i	$0.881018\pi$
$542$	5.73652	−	32.5334i	0.246405	−	1.39743i
$543$	−2.80608	−	4.86027i	−0.120420	−	0.208574i
$544$	8.76205	−	15.1763i	0.375670	−	0.650679i
$545$		0			0
$546$	−25.0937	−	9.13337i	−1.07391	−	0.390872i
$547$	−0.556008	+	0.202370i	−0.0237732	+	0.00865274i	−0.353879	−	0.935291i	$-0.615138\pi$
$547$	−0.556008	+	0.202370i	−0.0237732	+	0.00865274i	0.330106	+	0.943944i	$0.392915\pi$
$548$	23.5325	−	19.7461i	1.00526	−	0.843513i
$549$	−4.45065	−	25.2409i	−0.189949	−	1.07726i
$550$		0			0
$551$	−6.13948	−	9.65107i	−0.261551	−	0.411149i
$552$	−0.670102			−0.0285214
$553$	0.0407556	+	0.231137i	0.00173311	+	0.00982893i
$554$	−30.7980	+	25.8426i	−1.30848	+	1.09795i
$555$		0			0
$556$	−29.5241	−	10.7459i	−1.25210	−	0.455727i
$557$	18.9312	+	15.8852i	0.802142	+	0.673077i	0.948719	−	0.316122i	$-0.102381\pi$
$557$	18.9312	+	15.8852i	0.802142	+	0.673077i	−0.146576	+	0.989199i	$0.546825\pi$
$558$	17.2675	−	29.9081i	0.730990	−	1.26611i
$559$	−1.86080	−	3.22300i	−0.0787034	−	0.136318i
$560$		0			0
$561$	−0.0386517	+	0.219205i	−0.00163188	+	0.00925483i
$562$	4.31685	+	7.47700i	0.182095	+	0.315398i
$563$	5.99775	−	10.3884i	0.252775	−	0.437819i	−0.711514	−	0.702672i	$-0.751990\pi$
$563$	5.99775	−	10.3884i	0.252775	−	0.437819i	0.964289	+	0.264853i	$0.0853234\pi$
$564$	16.1246	+	13.5301i	0.678968	+	0.569721i
$565$		0			0
$566$	−46.5486	+	16.9423i	−1.95658	+	0.712138i
$567$	0.741643	−	0.622313i	0.0311461	−	0.0261347i
$568$	−5.20470	−	29.5173i	−0.218384	−	1.23852i
$569$	33.9446			1.42303			0.711517	−	0.702669i	$-0.248009\pi$
$569$	33.9446			1.42303			0.711517	+	0.702669i	$0.248009\pi$
$570$		0			0
$571$	−3.81177			−0.159518			−0.0797588	−	0.996814i	$-0.525415\pi$
$571$	−3.81177			−0.159518			−0.0797588	+	0.996814i	$0.525415\pi$
$572$	−0.247769	−	1.40517i	−0.0103597	−	0.0587530i
$573$	−3.86982	+	3.24717i	−0.161664	+	0.135652i
$574$	24.8725	−	9.05286i	1.03816	−	0.377859i
$575$		0			0
$576$	19.0532	+	15.9875i	0.793884	+	0.666148i
$577$	0.827198	−	1.43275i	0.0344367	−	0.0596461i	−0.848293	−	0.529527i	$-0.822370\pi$
$577$	0.827198	−	1.43275i	0.0344367	−	0.0596461i	0.882730	+	0.469880i	$0.155703\pi$
$578$	11.7755	+	20.3957i	0.489795	+	0.848351i
$579$	−0.249246	+	1.41354i	−0.0103583	+	0.0587449i
$580$		0			0
$581$	−3.01284	−	5.21838i	−0.124993	−	0.216495i
$582$	0.260351	−	0.450941i	0.0107919	−	0.0186921i
$583$	−0.945636	−	0.793483i	−0.0391642	−	0.0328627i
$584$	21.3249	+	7.76164i	0.882432	+	0.321179i
$585$		0			0
$586$	41.6338	−	34.9349i	1.71987	−	1.44315i
$587$	5.10789	+	28.9683i	0.210825	+	1.19565i	0.888006	+	0.459832i	$0.152091\pi$
$587$	5.10789	+	28.9683i	0.210825	+	1.19565i	−0.677180	+	0.735817i	$0.736798\pi$
$588$	8.84031			0.364568
$589$	7.59356	+	34.3593i	0.312887	+	1.41575i
$590$		0			0
$591$	1.15382	+	6.54364i	0.0474618	+	0.269169i
$592$	−4.73952	+	3.97693i	−0.194793	+	0.163451i
$593$	44.0015	−	16.0152i	1.80693	−	0.657667i	0.809408	−	0.587247i	$-0.199788\pi$
$593$	44.0015	−	16.0152i	1.80693	−	0.657667i	0.997517	−	0.0704204i	$-0.0224341\pi$
$594$	−0.904695	−	0.329282i	−0.0371201	−	0.0135106i
$595$		0			0
$596$	7.41702	−	12.8467i	0.303813	−	0.526220i
$597$	8.10961	+	14.0463i	0.331904	+	0.574875i
$598$	−0.682511	+	3.87071i	−0.0279100	+	0.158285i
$599$	2.11359	−	11.9868i	0.0863589	−	0.489765i	−0.910696	−	0.413077i	$-0.864454\pi$
$599$	2.11359	−	11.9868i	0.0863589	−	0.489765i	0.997055	−	0.0766887i	$-0.0244348\pi$
$600$		0			0
$601$	−5.01956	+	8.69414i	−0.204752	+	0.354641i	−0.950054	−	0.312086i	$-0.898972\pi$
$601$	−5.01956	+	8.69414i	−0.204752	+	0.354641i	0.745302	+	0.666728i	$0.232306\pi$
$602$	−2.24308	−	1.88217i	−0.0914210	−	0.0767113i
$603$	−16.0644	−	5.84697i	−0.654194	−	0.238107i
$604$	−57.5066	+	20.9307i	−2.33991	+	0.851658i
$605$		0			0
$606$	5.04378	+	28.6047i	0.204890	+	1.16199i
$607$	−20.5318			−0.833358			−0.416679	−	0.909054i	$-0.636806\pi$
$607$	−20.5318			−0.833358			−0.416679	+	0.909054i	$0.636806\pi$
$608$	−30.1556	+	1.29675i	−1.22297	+	0.0525900i
$609$	−5.51072			−0.223306
$610$		0			0
$611$	30.2515	−	25.3840i	1.22385	−	1.02693i
$612$	13.4589	−	4.89862i	0.544042	−	0.198015i
$613$	−34.2734	−	12.4745i	−1.38429	−	0.503840i	−0.460813	−	0.887497i	$-0.652442\pi$
$613$	−34.2734	−	12.4745i	−1.38429	−	0.503840i	−0.923476	+	0.383657i	$0.874664\pi$
$614$	−10.9403	−	9.17999i	−0.441514	−	0.370474i
$615$		0			0
$616$	−0.179542	−	0.310977i	−0.00723397	−	0.0125296i
$617$	−3.71725	+	21.0816i	−0.149651	+	0.848712i	0.813864	+	0.581056i	$0.197360\pi$
$617$	−3.71725	+	21.0816i	−0.149651	+	0.848712i	−0.963514	+	0.267656i	$0.913751\pi$
$618$	7.09376	−	40.2307i	0.285353	−	1.61832i
$619$	7.68760	+	13.3153i	0.308991	+	0.535187i	0.978142	−	0.207939i	$-0.0666755\pi$
$619$	7.68760	+	13.3153i	0.308991	+	0.535187i	−0.669151	+	0.743126i	$0.733342\pi$
$620$		0			0
$621$	1.20917	+	1.01462i	0.0485224	+	0.0407151i
$622$	36.6858	+	13.3525i	1.47097	+	0.535388i
$623$	21.1720	−	7.70597i	0.848238	−	0.308733i
$624$	−5.60897	+	4.70649i	−0.224539	+	0.188410i
$625$		0			0
$626$	8.09876			0.323691
$627$	0.354295	−	0.146481i	0.0141492	−	0.00584988i
$628$	−69.4440			−2.77112
$629$	2.20300	+	12.4938i	0.0878392	+	0.498161i
$630$		0			0
$631$	27.9210	−	10.1624i	1.11152	−	0.404559i	0.279968	−	0.960009i	$-0.409676\pi$
$631$	27.9210	−	10.1624i	1.11152	−	0.404559i	0.831550	+	0.555450i	$0.187454\pi$
$632$	−0.227689	−	0.0828718i	−0.00905696	−	0.00329647i
$633$	−6.10396	−	5.12183i	−0.242611	−	0.203575i
$634$	5.00006	−	8.66036i	0.198578	−	0.343947i
$635$		0			0
$636$	7.70683	−	43.7076i	0.305596	−	1.73312i
$637$	2.88003	−	16.3334i	0.114111	−	0.647154i
$638$	−0.247355	−	0.428432i	−0.00979289	−	0.0169618i
$639$	−13.7963	+	23.8959i	−0.545773	+	0.945306i
$640$		0			0
$641$	−17.9574	−	6.53597i	−0.709275	−	0.258155i	−0.0379095	−	0.999281i	$-0.512070\pi$
$641$	−17.9574	−	6.53597i	−0.709275	−	0.258155i	−0.671366	+	0.741126i	$0.734292\pi$
$642$	−11.0381	+	4.01753i	−0.435638	+	0.158559i
$643$	−12.4316	+	10.4314i	−0.490256	+	0.411374i	−0.854118	−	0.520079i	$-0.825902\pi$
$643$	−12.4316	+	10.4314i	−0.490256	+	0.411374i	0.363862	+	0.931453i	$0.381458\pi$
$644$	0.319614	+	1.81262i	0.0125945	+	0.0714272i
$645$		0			0
$646$	−11.3361	+	21.7415i	−0.446012	+	0.855407i
$647$	−26.6353			−1.04714			−0.523571	−	0.851982i	$-0.675400\pi$
$647$	−26.6353			−1.04714			−0.523571	+	0.851982i	$0.675400\pi$
$648$	0.173560	+	0.984307i	0.00681808	+	0.0386672i
$649$	0.485562	−	0.407435i	0.0190600	−	0.0159932i
$650$		0			0
$651$	15.9305	+	5.79823i	0.624366	+	0.227251i
$652$	0.481005	+	0.403611i	0.0188376	+	0.0158066i
$653$	−20.4238	+	35.3751i	−0.799245	+	1.38433i	0.120863	+	0.992669i	$0.461434\pi$
$653$	−20.4238	+	35.3751i	−0.799245	+	1.38433i	−0.920108	+	0.391664i	$0.871899\pi$
$654$	−7.07069	−	12.2468i	−0.276486	−	0.478887i
$655$		0			0
$656$	1.26024	−	7.14719i	0.0492042	−	0.279051i
$657$	−10.4457	−	18.0925i	−0.407527	−	0.705857i
$658$	15.5355	−	26.9082i	0.605635	−	1.04899i
$659$	−14.0538	−	11.7926i	−0.547460	−	0.459373i	0.326620	−	0.945156i	$-0.394090\pi$
$659$	−14.0538	−	11.7926i	−0.547460	−	0.459373i	−0.874080	+	0.485782i	$0.838535\pi$
$660$		0			0
$661$	22.8442	−	8.31460i	0.888536	−	0.323400i	0.142886	−	0.989739i	$-0.454362\pi$
$661$	22.8442	−	8.31460i	0.888536	−	0.323400i	0.745649	+	0.666339i	$0.232139\pi$
$662$	58.0632	−	48.7208i	2.25669	−	1.89359i
$663$	2.60713	+	14.7858i	0.101253	+	0.574232i
$664$	6.22076			0.241412
$665$		0			0
$666$	−21.4455			−0.830995
$667$	0.140844	+	0.798767i	0.00545351	+	0.0309284i
$668$	−44.4324	+	37.2832i	−1.71914	+	1.44253i
$669$	−2.41662	+	0.879579i	−0.0934321	+	0.0340065i
$670$		0			0
$671$	0.865238	+	0.726021i	0.0334022	+	0.0280277i
$672$	−7.27082	+	12.5934i	−0.280478	+	0.485802i
$673$	−15.7847	−	27.3400i	−0.608457	−	1.05388i	−0.991495	−	0.130146i	$-0.958455\pi$
$673$	−15.7847	−	27.3400i	−0.608457	−	1.05388i	0.383038	−	0.923733i	$-0.374878\pi$
$674$	0.373983	−	2.12096i	0.0144053	−	0.0816965i
$675$		0			0
$676$	−29.0080	−	50.2433i	−1.11569	−	1.93243i
$677$	−6.21268	+	10.7607i	−0.238773	+	0.413566i	−0.960362	−	0.278755i	$-0.910078\pi$
$677$	−6.21268	+	10.7607i	−0.238773	+	0.413566i	0.721590	+	0.692321i	$0.243412\pi$
$678$	20.1850	+	16.9372i	0.775200	+	0.650470i
$679$	−0.429882	−	0.156464i	−0.0164974	−	0.00600455i
$680$		0			0
$681$	−0.360298	+	0.302326i	−0.0138066	+	0.0115852i
$682$	0.264276	+	1.49878i	0.0101196	+	0.0573913i
$683$	−9.71494			−0.371732			−0.185866	−	0.982575i	$-0.559509\pi$
$683$	−9.71494			−0.371732			−0.185866	+	0.982575i	$0.559509\pi$
$684$	−19.5615	−	15.0305i	−0.747953	−	0.574707i
$685$		0			0
$686$	−7.73739	−	43.8809i	−0.295415	−	1.67538i
$687$	−0.789053	+	0.662094i	−0.0301042	+	0.0252605i
$688$	−0.754443	+	0.274595i	−0.0287629	+	0.0104688i
$689$	−78.2438	−	28.4784i	−2.98085	−	1.08494i
$690$		0			0
$691$	−19.2944	+	33.4189i	−0.733994	+	1.27132i	0.221169	+	0.975235i	$0.429013\pi$
$691$	−19.2944	+	33.4189i	−0.733994	+	1.27132i	−0.955163	+	0.296080i	$0.904321\pi$
$692$	18.4887	+	32.0233i	0.702834	+	1.21734i
$693$	−0.0574030	+	0.325548i	−0.00218056	+	0.0123666i
$694$	9.07288	−	51.4549i	0.344402	−	1.95320i
$695$		0			0
$696$	2.84457	−	4.92694i	0.107823	−	0.186755i
$697$	−11.3999	−	9.56566i	−0.431802	−	0.362325i
$698$	−40.5990	−	14.7768i	−1.53670	−	0.559312i
$699$	4.15434	−	1.51206i	0.157132	−	0.0571912i
$700$		0			0
$701$	−3.17615	−	18.0129i	−0.119962	−	0.680336i	−0.984173	−	0.177208i	$-0.943293\pi$
$701$	−3.17615	−	18.0129i	−0.119962	−	0.680336i	0.864212	−	0.503128i	$-0.167818\pi$
$702$	−64.9398			−2.45099
$703$	16.1202	−	14.7519i	0.607983	−	0.556379i
$704$	−1.09608			−0.0413101
$705$		0			0
$706$	20.3724	−	17.0945i	0.766726	−	0.643359i
$707$	23.9798	−	8.72794i	0.901854	−	0.328248i
$708$	21.4147	+	7.79431i	0.804814	+	0.292928i
$709$	−8.38460	−	7.03551i	−0.314890	−	0.264224i	0.471620	−	0.881802i	$-0.343670\pi$
$709$	−8.38460	−	7.03551i	−0.314890	−	0.264224i	−0.786510	+	0.617578i	$0.788114\pi$
$710$		0			0
$711$	0.111530	+	0.193176i	0.00418271	+	0.00724466i
$712$	−4.03910	+	22.9068i	−0.151371	+	0.858470i
$713$	0.433286	−	2.45729i	0.0162267	−	0.0920261i
$714$	5.90641	+	10.2302i	0.221042	+	0.382856i
$715$		0			0
$716$	−24.3693	−	20.4483i	−0.910725	−	0.764189i
$717$	23.8337	+	8.67475i	0.890085	+	0.323965i
$718$	−35.9047	+	13.0683i	−1.33995	+	0.487703i
$719$	−6.11975	+	5.13508i	−0.228228	+	0.191506i	−0.749730	−	0.661744i	$-0.769817\pi$
$719$	−6.11975	+	5.13508i	−0.228228	+	0.191506i	0.521502	+	0.853250i	$0.325372\pi$
$720$		0			0
$721$	−35.8906			−1.33663
$722$	42.0762	−	3.62541i	1.56591	−	0.134924i
$723$	−4.55746			−0.169494
$724$	−2.76346	−	15.6723i	−0.102703	−	0.582458i
$725$		0			0
$726$	−23.8102	+	8.66619i	−0.883678	+	0.321632i
$727$	−12.7269	−	4.63222i	−0.472016	−	0.171800i	0.0950496	−	0.995473i	$-0.469699\pi$
$727$	−12.7269	−	4.63222i	−0.472016	−	0.171800i	−0.567065	+	0.823673i	$0.691921\pi$
$728$	−18.5543	−	15.5689i	−0.687670	−	0.577023i
$729$	−7.48365	+	12.9621i	−0.277172	+	0.480076i
$730$		0			0
$731$	−0.285873	+	1.62127i	−0.0105734	+	0.0599648i
$732$	−7.05160	+	39.9916i	−0.260635	+	1.47813i
$733$	6.11770	+	10.5962i	0.225962	+	0.391378i	0.956608	−	0.291379i	$-0.0941140\pi$
$733$	6.11770	+	10.5962i	0.225962	+	0.391378i	−0.730645	+	0.682757i	$0.760781\pi$
$734$	−19.5859	+	33.9238i	−0.722929	+	1.25215i
$735$		0			0
$736$	2.01122	+	0.732024i	0.0741345	+	0.0269828i
$737$	0.707935	−	0.257667i	0.0260771	−	0.00949130i
$738$	19.2705	−	16.1699i	0.709357	−	0.595221i
$739$	−0.942774	−	5.34674i	−0.0346805	−	0.196683i	0.962545	−	0.271122i	$-0.0873946\pi$
$739$	−0.942774	−	5.34674i	−0.0346805	−	0.196683i	−0.997226	+	0.0744387i	$0.976283\pi$
$740$		0			0
$741$	19.0774	−	17.4581i	0.700824	−	0.641339i
$742$	−65.5126			−2.40505
$743$	0.655059	+	3.71503i	0.0240318	+	0.136291i	0.994463	−	0.105086i	$-0.0335119\pi$
$743$	0.655059	+	3.71503i	0.0240318	+	0.136291i	−0.970431	+	0.241377i	$0.922401\pi$
$744$	−13.4071	+	11.2499i	−0.491530	+	0.412442i
$745$		0			0
$746$	−5.54498	−	2.01821i	−0.203016	−	0.0738918i
$747$	−4.38697	−	3.68110i	−0.160511	−	0.134684i
$748$	−0.315588	+	0.546615i	−0.0115390	+	0.0199862i
$749$	5.16003	+	8.93743i	0.188543	+	0.326566i
$750$		0			0
$751$	−1.09106	+	6.18771i	−0.0398133	+	0.225793i	−0.998222	−	0.0596070i	$-0.981015\pi$
$751$	−1.09106	+	6.18771i	−0.0398133	+	0.225793i	0.958409	+	0.285400i	$0.0921264\pi$
$752$	−4.25965	−	7.37794i	−0.155334	−	0.269046i
$753$	−0.200902	+	0.347973i	−0.00732129	+	0.0126809i
$754$	−25.5623	−	21.4493i	−0.930923	−	0.781137i
$755$		0			0
$756$	−28.5767	+	10.4011i	−1.03932	+	0.378283i
$757$	38.9320	−	32.6678i	1.41501	−	1.18733i	0.461055	−	0.887372i	$-0.347471\pi$
$757$	38.9320	−	32.6678i	1.41501	−	1.18733i	0.953952	−	0.299960i	$-0.0969732\pi$
$758$	−7.32559	−	41.5455i	−0.266077	−	1.50900i
$759$	−0.0271854			−0.000986768
$760$		0			0
$761$	−10.2538			−0.371701			−0.185850	−	0.982578i	$-0.559504\pi$
$761$	−10.2538			−0.371701			−0.185850	+	0.982578i	$0.559504\pi$
$762$	−0.576280	−	3.26825i	−0.0208764	−	0.118396i
$763$	−9.51743	+	7.98607i	−0.344554	+	0.289115i
$764$	−13.4609	+	4.89938i	−0.486999	+	0.177253i
$765$		0			0
$766$	20.3109	+	17.0429i	0.733862	+	0.615783i
$767$	21.3774	−	37.0267i	0.771893	−	1.33696i
$768$	−3.74273	−	6.48259i	−0.135054	−	0.233920i
$769$	−0.261207	+	1.48138i	−0.00941937	+	0.0534199i	−0.989155	−	0.146874i	$-0.953079\pi$
$769$	−0.261207	+	1.48138i	−0.00941937	+	0.0534199i	0.979736	+	0.200294i	$0.0641898\pi$
$770$		0			0
$771$	1.47926	+	2.56216i	0.0532743	+	0.0922738i
$772$	−2.03508	+	3.52485i	−0.0732440	+	0.126862i
$773$	−28.5905	−	23.9903i	−1.02833	−	0.862872i	−0.0376792	−	0.999290i	$-0.511997\pi$
$773$	−28.5905	−	23.9903i	−1.02833	−	0.862872i	−0.990651	+	0.136418i	$0.956441\pi$
$774$	−2.61506	−	0.951803i	−0.0939963	−	0.0342118i
$775$		0			0
$776$	0.361789	−	0.303577i	0.0129875	−	0.0108978i
$777$	−1.82806	−	10.3675i	−0.0655814	−	0.371931i
$778$	−21.7065			−0.778215
$779$	−3.36235	+	25.4104i	−0.120469	+	0.910421i
$780$		0			0
$781$	−0.211150	−	1.19749i	−0.00755554	−	0.0428496i
$782$	1.33189	−	1.11759i	0.0476282	−	0.0399648i
$783$	−12.5929	+	4.58344i	−0.450034	+	0.163799i
$784$	−3.36220	−	1.22374i	−0.120078	−	0.0437050i
$785$		0			0
$786$	−1.15647	+	2.00306i	−0.0412499	+	0.0714469i
$787$	16.4647	+	28.5177i	0.586903	+	1.01655i	0.994635	+	0.103444i	$0.0329863\pi$
$787$	16.4647	+	28.5177i	0.586903	+	1.01655i	−0.407732	+	0.913101i	$0.633680\pi$
$788$	−3.27183	+	18.5555i	−0.116554	+	0.661011i
$789$	−1.94614	+	11.0371i	−0.0692844	+	0.392931i
$790$		0			0
$791$	11.5749	−	20.0484i	0.411558	−	0.712839i
$792$	−0.261430	−	0.219366i	−0.00928952	−	0.00779484i
$793$	71.5916	+	26.0572i	2.54229	+	0.925318i
$794$	60.2433	−	21.9268i	2.13795	−	0.778152i
$795$		0			0
$796$	7.98643	+	45.2933i	0.283071	+	1.60538i
$797$	18.1078			0.641410			0.320705	−	0.947179i	$-0.396080\pi$
$797$	18.1078			0.641410			0.320705	+	0.947179i	$0.396080\pi$
$798$	9.40677	−	18.0413i	0.332996	−	0.638653i
$799$	−17.4690			−0.618008
$800$		0			0
$801$	16.4034	−	13.7641i	0.579587	−	0.486331i
$802$	−13.0988	+	4.76758i	−0.462535	+	0.168349i
$803$	0.865133	+	0.314883i	0.0305299	+	0.0111120i
$804$	20.7490	+	17.4105i	0.731761	+	0.614021i
$805$		0			0
$806$	51.3276	+	88.9020i	1.80794	+	3.13144i
$807$	−0.500180	+	2.83666i	−0.0176072	+	0.0998552i
$808$	−4.57476	+	25.9448i	−0.160939	+	0.912733i
$809$	3.92768	+	6.80294i	0.138090	+	0.239179i	0.926774	−	0.375620i	$-0.122570\pi$
$809$	3.92768	+	6.80294i	0.138090	+	0.239179i	−0.788684	+	0.614799i	$0.789237\pi$
$810$		0			0
$811$	−14.9626	−	12.5551i	−0.525409	−	0.440870i	0.341104	−	0.940026i	$-0.389199\pi$
$811$	−14.9626	−	12.5551i	−0.525409	−	0.440870i	−0.866513	+	0.499155i	$0.833644\pi$
$812$	−14.6841	−	5.34457i	−0.515310	−	0.187558i
$813$	14.4829	−	5.27134i	0.507937	−	0.184874i
$814$	0.723965	−	0.607479i	0.0253750	−	0.0212921i
$815$		0			0
$816$	3.23895			0.113386
$817$	2.62042	−	1.08339i	0.0916767	−	0.0379031i
$818$	24.9479			0.872282
$819$	3.87194	+	21.9589i	0.135297	+	0.767305i
$820$		0			0
$821$	17.1492	−	6.24180i	0.598511	−	0.217840i	−0.0249577	−	0.999689i	$-0.507945\pi$
$821$	17.1492	−	6.24180i	0.598511	−	0.217840i	0.623469	+	0.781848i	$0.285723\pi$
$822$	22.6275	+	8.23574i	0.789225	+	0.287254i
$823$	−12.6885	−	10.6469i	−0.442294	−	0.371128i	0.394273	−	0.918993i	$-0.370996\pi$
$823$	−12.6885	−	10.6469i	−0.442294	−	0.371128i	−0.836567	+	0.547865i	$0.815441\pi$
$824$	18.5263	−	32.0885i	0.645394	−	1.11785i
$825$		0			0
$826$	5.84139	−	33.1282i	0.203248	−	1.15268i
$827$	−2.91020	+	16.5046i	−0.101198	+	0.573921i	0.891473	+	0.453073i	$0.149672\pi$
$827$	−2.91020	+	16.5046i	−0.101198	+	0.573921i	−0.992671	+	0.120848i	$0.961439\pi$
$828$	0.874641	+	1.51492i	0.0303959	+	0.0526472i
$829$	4.99915	−	8.65878i	0.173628	−	0.300732i	−0.766058	−	0.642772i	$-0.777784\pi$
$829$	4.99915	−	8.65878i	0.173628	−	0.300732i	0.939685	+	0.342040i	$0.111118\pi$
$830$		0			0
$831$	−17.6257	−	6.41522i	−0.611428	−	0.222542i
$832$	−69.4741	+	25.2865i	−2.40858	+	0.876652i
$833$	−5.62023	+	4.71593i	−0.194730	+	0.163397i
$834$	−4.27658	−	24.2537i	−0.148086	−	0.839837i
$835$		0			0
$836$	1.08613	−	0.0467056i	0.0375647	−	0.00161535i
$837$	41.2264			1.42499
$838$	−10.0645	−	57.0784i	−0.347671	−	1.97174i
$839$	34.8926	−	29.2783i	1.20463	−	1.01080i	0.205139	−	0.978733i	$-0.434235\pi$
$839$	34.8926	−	29.2783i	1.20463	−	1.01080i	0.999486	−	0.0320678i	$-0.0102092\pi$
$840$		0			0
$841$	20.7802	+	7.56339i	0.716560	+	0.260807i
$842$	−43.0116	−	36.0910i	−1.48228	−	1.24378i
$843$	−2.01399	+	3.48834i	−0.0693656	+	0.120145i
$844$	−11.2974	−	19.5677i	−0.388874	−	0.673549i
$845$		0			0
$846$	5.12778	−	29.0811i	0.176297	−	0.999828i
$847$	11.1306	+	19.2789i	0.382454	+	0.662429i
$848$	−8.98142	+	15.5563i	−0.308423	+	0.534205i
$849$	−17.7038	−	14.8552i	−0.607592	−	0.509830i
$850$		0			0
$851$	−1.45602	+	0.529948i	−0.0499117	+	0.0181664i
$852$	33.4896	−	28.1011i	1.14734	−	0.962729i
$853$	−4.42816	−	25.1133i	−0.151617	−	0.859864i	−0.961814	−	0.273706i	$-0.911751\pi$
$853$	−4.42816	−	25.1133i	−0.151617	−	0.859864i	0.810196	−	0.586159i	$-0.199360\pi$
$854$	59.9428			2.05120
$855$		0			0
$856$	−10.6542			−0.364152
$857$	1.25811	+	7.13511i	0.0429763	+	0.243731i	0.998727	−	0.0504481i	$-0.0160650\pi$
$857$	1.25811	+	7.13511i	0.0429763	+	0.243731i	−0.955750	+	0.294179i	$0.904954\pi$
$858$	0.856775	−	0.718920i	0.0292498	−	0.0245435i
$859$	28.2917	−	10.2973i	0.965300	−	0.351340i	0.189192	−	0.981940i	$-0.439413\pi$
$859$	28.2917	−	10.2973i	0.965300	−	0.351340i	0.776108	+	0.630600i	$0.217191\pi$
$860$		0			0
$861$	9.45973	+	7.93766i	0.322387	+	0.270515i
$862$	−42.4421	+	73.5118i	−1.44558	+	2.50382i
$863$	3.73981	+	6.47754i	0.127305	+	0.220498i	0.922631	−	0.385683i	$-0.126034\pi$
$863$	3.73981	+	6.47754i	0.127305	+	0.220498i	−0.795327	+	0.606181i	$0.792701\pi$
$864$	−6.14066	+	34.8254i	−0.208910	+	1.18478i
$865$		0			0
$866$	2.91293	+	5.04534i	0.0989853	+	0.171448i
$867$	−5.49376	+	9.51547i	−0.186578	+	0.323162i
$868$	36.8256	+	30.9004i	1.24994	+	1.04883i
$869$	−0.00923712	−	0.00336204i	−0.000313348	−	0.000114049i
$870$		0			0
$871$	38.9275	−	32.6640i	1.31901	−	1.10678i
$872$	−2.22728	−	12.6315i	−0.0754251	−	0.427757i
$873$	−0.434779			−0.0147150
$874$	−2.85546	−	0.902389i	−0.0965874	−	0.0305238i
$875$		0			0
$876$	5.74782	+	32.5975i	0.194201	+	1.10137i
$877$	18.9058	−	15.8639i	0.638404	−	0.535684i	−0.265124	−	0.964214i	$-0.585413\pi$
$877$	18.9058	−	15.8639i	0.638404	−	0.535684i	0.903528	+	0.428530i	$0.140968\pi$
$878$	−14.0290	+	5.10615i	−0.473457	+	0.172324i
$879$	23.8269	+	8.67230i	0.803663	+	0.292509i
$880$		0			0
$881$	−3.65124	+	6.32413i	−0.123013	+	0.213065i	−0.920955	−	0.389670i	$-0.872589\pi$
$881$	−3.65124	+	6.32413i	−0.123013	+	0.213065i	0.797941	+	0.602735i	$0.205922\pi$
$882$	−6.20100	−	10.7405i	−0.208799	−	0.361650i
$883$	7.60832	−	43.1489i	0.256040	−	1.45208i	−0.537347	−	0.843361i	$-0.680574\pi$
$883$	7.60832	−	43.1489i	0.256040	−	1.45208i	0.793388	−	0.608717i	$-0.208315\pi$
$884$	−7.39291	+	41.9273i	−0.248650	+	1.41017i
$885$		0			0
$886$	−28.9023	+	50.0602i	−0.970991	+	1.68181i
$887$	37.8365	+	31.7486i	1.27042	+	1.06601i	0.994489	+	0.104836i	$0.0334319\pi$
$887$	37.8365	+	31.7486i	1.27042	+	1.06601i	0.275935	+	0.961176i	$0.411013\pi$
$888$	10.2128	+	3.71716i	0.342719	+	0.124740i
$889$	−2.73983	+	0.997216i	−0.0918909	+	0.0334456i
$890$		0			0
$891$	0.00704117	+	0.0399325i	0.000235888	+	0.00133779i
$892$	−7.29249			−0.244170
$893$	16.1498	+	25.3870i	0.540434	+	0.849544i
$894$	11.6278			0.388890
$895$		0			0
$896$	−23.0765	+	19.3635i	−0.770933	+	0.646890i
$897$	−1.72312	+	0.627165i	−0.0575334	+	0.0209404i
$898$	57.5894	+	20.9608i	1.92178	+	0.699472i
$899$	16.2280	+	13.6169i	0.541233	+	0.454149i
$900$		0			0
$901$	18.4166	+	31.8984i	0.613544	+	1.06269i
$902$	−0.192503	+	1.09174i	−0.00640965	+	0.0363509i
$903$	0.237220	−	1.34534i	0.00789419	−	0.0447702i
$904$	11.9497	+	20.6975i	0.397441	+	0.688388i
$905$		0			0
$906$	−36.7470	−	30.8344i	−1.22084	−	1.02440i
$907$	−9.99581	−	3.63818i	−0.331905	−	0.120804i	0.170692	−	0.985325i	$-0.445400\pi$
$907$	−9.99581	−	3.63818i	−0.331905	−	0.120804i	−0.502597	+	0.864521i	$0.667622\pi$
$908$	−1.25327	+	0.456154i	−0.0415914	+	0.0151380i
$909$	18.5789	−	15.5895i	0.616222	−	0.517071i
$910$		0			0
$911$	−40.5583			−1.34376			−0.671878	−	0.740662i	$-0.734512\pi$
$911$	−40.5583			−1.34376			−0.671878	+	0.740662i	$0.734512\pi$
$912$	−2.99436	−	4.70704i	−0.0991532	−	0.155866i
$913$	0.252371			0.00835225
$914$	−0.858886	−	4.87099i	−0.0284094	−	0.161118i
$915$		0			0
$916$	−2.74467	+	0.998978i	−0.0906864	+	0.0330072i
$917$	1.90952	+	0.695008i	0.0630579	+	0.0229512i
$918$	22.0059	+	18.4651i	0.726303	+	0.609440i
$919$	−19.1728	+	33.2083i	−0.632453	+	1.09544i	0.354596	+	0.935020i	$0.384618\pi$
$919$	−19.1728	+	33.2083i	−0.632453	+	1.09544i	−0.987049	+	0.160421i	$0.948715\pi$
$920$		0			0
$921$	1.15701	−	6.56171i	0.0381247	−	0.216216i
$922$	7.89522	−	44.7760i	0.260015	−	1.47462i
$923$	−41.0096	−	71.0306i	−1.34985	−	2.33800i
$924$	0.261877	−	0.453585i	0.00861514	−	0.0149219i
$925$		0			0
$926$	−67.7363	−	24.6540i	−2.22595	−	0.810180i
$927$	−32.0532	+	11.6664i	−1.05276	+	0.383175i
$928$	−13.9198	+	11.6801i	−0.456940	+	0.383419i
$929$	7.57843	+	42.9794i	0.248640	+	1.41011i	0.811884	+	0.583818i	$0.198442\pi$
$929$	7.57843	+	42.9794i	0.248640	+	1.41011i	−0.563244	+	0.826290i	$0.690447\pi$
$930$		0			0
$931$	12.0493	+	3.80785i	0.394901	+	0.124797i
$932$	12.5363			0.410639
$933$	3.16281	+	17.9372i	0.103546	+	0.587237i
$934$	11.7845	−	9.88835i	0.385600	−	0.323557i
$935$		0			0
$936$	−21.6313	−	7.87314i	−0.707041	−	0.257342i
$937$	27.5115	+	23.0849i	0.898760	+	0.754150i	0.969948	−	0.243313i	$-0.0782344\pi$
$937$	27.5115	+	23.0849i	0.898760	+	0.754150i	−0.0711873	+	0.997463i	$0.522679\pi$
$938$	19.9909	−	34.6253i	0.652727	−	1.13056i
$939$	1.88921	+	3.27220i	0.0616519	+	0.106784i
$940$		0			0
$941$	5.36936	−	30.4512i	0.175036	−	0.992680i	−0.763066	−	0.646321i	$-0.776307\pi$
$941$	5.36936	−	30.4512i	0.175036	−	0.992680i	0.938102	−	0.346359i	$-0.112582\pi$
$942$	−27.2170	−	47.1413i	−0.886779	−	1.53595i
$943$	0.908772	−	1.57404i	0.0295937	−	0.0512578i
$944$	−7.06561	−	5.92875i	−0.229966	−	0.192964i
$945$		0			0
$946$	0.115242	−	0.0419445i	0.00374683	−	0.00136373i
$947$	−8.55388	+	7.17756i	−0.277964	+	0.233239i	−0.771102	−	0.636712i	$-0.780294\pi$
$947$	−8.55388	+	7.17756i	−0.277964	+	0.233239i	0.493138	+	0.869951i	$0.335850\pi$
$948$	−0.0613701	−	0.348047i	−0.00199321	−	0.0113040i
$949$	62.1000			2.01585
$950$		0			0
$951$	4.66548			0.151288
$952$	1.86053	+	10.5516i	0.0603000	+	0.341978i
$953$	5.67166	−	4.75909i	0.183723	−	0.154162i	−0.546288	−	0.837598i	$-0.683959\pi$
$953$	5.67166	−	4.75909i	0.183723	−	0.154162i	0.730011	+	0.683436i	$0.239515\pi$
$954$	−58.5081	+	21.2952i	−1.89427	+	0.689458i
$955$		0			0
$956$	55.0949	+	46.2301i	1.78190	+	1.49519i
$957$	0.115402	−	0.199882i	0.00373041	−	0.00646125i
$958$	22.2761	+	38.5833i	0.719708	+	1.24657i
$959$	3.67363	−	20.8342i	0.118628	−	0.672771i
$960$		0			0
$961$	−17.0849	−	29.5918i	−0.551124	−	0.954575i
$962$	31.8734	−	55.2063i	1.02764	−	1.77992i
$963$	7.51347	+	6.30455i	0.242118	+	0.203161i
$964$	−12.1440	−	4.42005i	−0.391131	−	0.142360i
$965$		0			0
$966$	−1.10521	+	0.927382i	−0.0355596	+	0.0298380i
$967$	3.05244	+	17.3112i	0.0981598	+	0.556692i	0.993733	+	0.111778i	$0.0356545\pi$
$967$	3.05244	+	17.3112i	0.0981598	+	0.556692i	−0.895573	+	0.444914i	$0.853234\pi$
$968$	−22.9820			−0.738671
$969$	−11.4287	+	0.491457i	−0.367144	+	0.0157879i
$970$		0			0
$971$	−0.922819	−	5.23357i	−0.0296147	−	0.167953i	0.966413	−	0.256992i	$-0.0827315\pi$
$971$	−0.922819	−	5.23357i	−0.0296147	−	0.167953i	−0.996028	+	0.0890391i	$0.971620\pi$
$972$	−35.6279	+	29.8954i	−1.14277	+	0.958895i
$973$	−20.3323	+	7.40035i	−0.651823	+	0.237244i
$974$	14.8909	+	5.41983i	0.477134	+	0.173662i
$975$		0			0
$976$	8.21783	−	14.2337i	0.263046	−	0.455609i
$977$	6.82533	+	11.8218i	0.218362	+	0.378214i	0.954307	−	0.298827i	$-0.0965954\pi$
$977$	6.82533	+	11.8218i	0.218362	+	0.378214i	−0.735946	+	0.677041i	$0.763262\pi$
$978$	−0.0854678	+	0.484712i	−0.00273296	+	0.0154994i
$979$	−0.163862	+	0.929310i	−0.00523707	+	0.0297009i
$980$		0			0
$981$	−5.90392	+	10.2259i	−0.188498	+	0.326488i
$982$	28.1035	+	23.5817i	0.896820	+	0.752521i
$983$	27.0252	+	9.83639i	0.861972	+	0.313732i	0.734912	−	0.678163i	$-0.237224\pi$
$983$	27.0252	+	9.83639i	0.861972	+	0.313732i	0.127060	+	0.991895i	$0.459446\pi$
$984$	−11.9798	+	4.36028i	−0.381901	+	0.139001i
$985$		0			0
$986$	2.56324	+	14.5369i	0.0816303	+	0.462949i
$987$	14.4959			0.461409
$988$	67.7660	−	28.0174i	2.15592	−	0.891351i
$989$	−0.201067			−0.00639357
$990$		0			0
$991$	−43.2774	+	36.3141i	−1.37475	+	1.15355i	−0.403643	+	0.914916i	$0.632256\pi$
$991$	−43.2774	+	36.3141i	−1.37475	+	1.15355i	−0.971109	+	0.238638i	$0.923299\pi$
$992$	52.5292	−	19.1191i	1.66780	−	0.607031i
$993$	33.2295	+	12.0945i	1.05451	+	0.383808i
$994$	−49.4345	−	41.4804i	−1.56797	−	1.31568i
$995$		0			0
$996$	4.53675	+	7.85787i	0.143752	+	0.248986i
$997$	2.45126	−	13.9018i	0.0776323	−	0.440274i	−0.921072	−	0.389391i	$-0.872685\pi$
$997$	2.45126	−	13.9018i	0.0776323	−	0.440274i	0.998705	−	0.0508830i	$-0.0162035\pi$
$998$	−11.7184	+	66.4583i	−0.370939	+	2.10370i
$999$	−12.8004	−	22.1709i	−0.404986	−	0.701456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.c.351.3		18
5.2	odd	4		475.2.u.b.199.1		36
5.3	odd	4		475.2.u.b.199.6		36
5.4	even	2		95.2.k.a.66.1	yes	18
15.14	odd	2		855.2.bs.c.541.3		18
19.6	even	9		9025.2.a.cc.1.9		9
19.13	odd	18		9025.2.a.cf.1.1		9
19.17	even	9	inner	475.2.l.c.226.3		18
95.17	odd	36		475.2.u.b.74.6		36
95.44	even	18		1805.2.a.v.1.1		9
95.74	even	18		95.2.k.a.36.1	✓	18
95.89	odd	18		1805.2.a.s.1.9		9
95.93	odd	36		475.2.u.b.74.1		36
285.74	odd	18		855.2.bs.c.226.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.36.1	✓	18	95.74	even	18
95.2.k.a.66.1	yes	18	5.4	even	2
475.2.l.c.226.3		18	19.17	even	9	inner
475.2.l.c.351.3		18	1.1	even	1	trivial
475.2.u.b.74.1		36	95.93	odd	36
475.2.u.b.74.6		36	95.17	odd	36
475.2.u.b.199.1		36	5.2	odd	4
475.2.u.b.199.6		36	5.3	odd	4
855.2.bs.c.226.3		18	285.74	odd	18
855.2.bs.c.541.3		18	15.14	odd	2
1805.2.a.s.1.9		9	95.89	odd	18
1805.2.a.v.1.1		9	95.44	even	18
9025.2.a.cc.1.9		9	19.6	even	9
9025.2.a.cf.1.1		9	19.13	odd	18

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)

\(f(q)\)	\(=\)	\(q+(0.385975 + 2.18897i) q^{2} +(-0.794389 + 0.666572i) q^{3} +(-2.76323 + 1.00573i) q^{4} +(-1.76572 - 1.48162i) q^{6} +(-1.01254 + 1.75377i) q^{7} +(-1.04532 - 1.81055i) q^{8} +(-0.334208 + 1.89539i) q^{9} +O(q^{10})\)	\(q+(0.385975 + 2.18897i) q^{2} +(-0.794389 + 0.666572i) q^{3} +(-2.76323 + 1.00573i) q^{4} +(-1.76572 - 1.48162i) q^{6} +(-1.01254 + 1.75377i) q^{7} +(-1.04532 - 1.81055i) q^{8} +(-0.334208 + 1.89539i) q^{9} +(-0.0424078 - 0.0734524i) q^{11} +(1.52469 - 2.64084i) q^{12} +(-4.38252 - 3.67737i) q^{13} +(-4.22977 - 1.53951i) q^{14} +(-0.945441 + 0.793319i) q^{16} +(0.439455 + 2.49227i) q^{17} -4.27795 q^{18} +(3.21565 - 2.94271i) q^{19} +(-0.364663 - 2.06811i) q^{21} +(0.144417 - 0.121180i) q^{22} +(-0.290447 + 0.105714i) q^{23} +(2.03725 + 0.741500i) q^{24} +(6.35811 - 11.0126i) q^{26} +(-2.55342 - 4.42266i) q^{27} +(1.03406 - 5.86442i) q^{28} +(0.455678 - 2.58428i) q^{29} +(-4.03639 + 6.99123i) q^{31} +(-5.30452 - 4.45102i) q^{32} +(0.0826495 + 0.0300820i) q^{33} +(-5.28589 + 1.92391i) q^{34} +(-0.982763 - 5.57352i) q^{36} +5.01303 q^{37} +(7.68268 + 5.90316i) q^{38} +5.93265 q^{39} +(-4.50461 + 3.77982i) q^{41} +(4.38627 - 1.59647i) q^{42} +(0.611288 + 0.222491i) q^{43} +(0.191056 + 0.160315i) q^{44} +(-0.343511 - 0.594978i) q^{46} +(-1.19865 + 6.79791i) q^{47} +(0.222244 - 1.26041i) q^{48} +(1.44953 + 2.51066i) q^{49} +(-2.01037 - 1.68690i) q^{51} +(15.8084 + 5.75378i) q^{52} +(13.6767 - 4.97790i) q^{53} +(8.69551 - 7.29640i) q^{54} +4.23372 q^{56} +(-0.592951 + 4.48112i) q^{57} +5.83278 q^{58} +(1.29773 + 7.35981i) q^{59} +(-12.5139 + 4.55468i) q^{61} +(-16.8615 - 6.13710i) q^{62} +(-2.98568 - 2.50528i) q^{63} +(6.46156 - 11.1918i) q^{64} +(-0.0339479 + 0.192528i) q^{66} +(-1.54242 + 8.74750i) q^{67} +(-3.72088 - 6.44475i) q^{68} +(0.160262 - 0.277582i) q^{69} +(13.4720 + 4.90340i) q^{71} +(3.78105 - 1.37619i) q^{72} +(-8.31526 + 6.97733i) q^{73} +(1.93490 + 10.9734i) q^{74} +(-5.92601 + 11.3655i) q^{76} +0.171758 q^{77} +(2.28985 + 12.9864i) q^{78} +(0.0887829 - 0.0744977i) q^{79} +(-0.449247 - 0.163512i) q^{81} +(-10.0126 - 8.40155i) q^{82} +(-1.48776 + 2.57688i) q^{83} +(3.08761 + 5.34790i) q^{84} +(-0.251084 + 1.42397i) q^{86} +(1.36062 + 2.35666i) q^{87} +(-0.0886595 + 0.153563i) q^{88} +(-8.52291 - 7.15157i) q^{89} +(10.8867 - 3.96245i) q^{91} +(0.696253 - 0.584226i) q^{92} +(-1.45369 - 8.24430i) q^{93} -15.3431 q^{94} +7.18078 q^{96} +(0.0392276 + 0.222471i) q^{97} +(-4.93627 + 4.14202i) q^{98} +(0.153394 - 0.0558308i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9	\( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9 + 18 * q^12 + 3 * q^13 - 12 * q^14 - 3 * q^16 - 24 * q^17 - 48 * q^18 - 21 * q^21 - 9 * q^22 + 9 * q^23 - 15 * q^24 + 3 * q^26 + 24 * q^27 + 12 * q^28 + 15 * q^29 - 18 * q^31 - 15 * q^32 + 33 * q^33 - 12 * q^34 + 75 * q^36 - 36 * q^37 + 33 * q^38 + 36 * q^39 - 30 * q^41 + 9 * q^42 + 36 * q^43 + 42 * q^44 + 9 * q^46 - 21 * q^47 - 33 * q^48 + 9 * q^49 - 45 * q^51 + 39 * q^52 + 12 * q^53 - 66 * q^54 - 72 * q^57 - 12 * q^58 + 18 * q^59 - 30 * q^61 + 24 * q^62 - 54 * q^63 + 36 * q^64 + 39 * q^66 - 51 * q^68 + 15 * q^69 - 12 * q^71 + 66 * q^72 - 24 * q^73 - 15 * q^74 - 33 * q^76 + 60 * q^77 + 48 * q^78 - 51 * q^79 + 27 * q^81 + 15 * q^82 + 48 * q^84 + 63 * q^86 + 15 * q^87 + 27 * q^88 - 54 * q^89 + 30 * q^91 + 42 * q^92 - 72 * q^93 + 30 * q^94 - 66 * q^96 - 27 * q^97 + 3 * q^98 - 93 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more