LMFDB - Embedded newform 240.2.y.e.187.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(163,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("240.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.y (of order $4$, degree $2$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 $ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.1
Root			$-1.40988 - 0.110627i$ of defining polynomial
Character	$\chi$	$=$	240.187
Dual form			240.2.y.e.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32675 - 0.489639i) q^{2} +1.00000 q^{3} +(1.52051 + 1.29925i) q^{4} +(2.06823 - 0.849960i) q^{5} +(-1.32675 - 0.489639i) q^{6} +(-2.08016 - 2.08016i) q^{7} +(-1.38116 - 2.46828i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.32675 - 0.489639i) q^{2} +1.00000 q^{3} +(1.52051 + 1.29925i) q^{4} +(2.06823 - 0.849960i) q^{5} +(-1.32675 - 0.489639i) q^{6} +(-2.08016 - 2.08016i) q^{7} +(-1.38116 - 2.46828i) q^{8} +1.00000 q^{9} +(-3.16019 + 0.114996i) q^{10} +(3.33354 - 3.33354i) q^{11} +(1.52051 + 1.29925i) q^{12} +6.13735i q^{13} +(1.74131 + 3.77837i) q^{14} +(2.06823 - 0.849960i) q^{15} +(0.623885 + 3.95105i) q^{16} +(-2.33136 - 2.33136i) q^{17} +(-1.32675 - 0.489639i) q^{18} +(0.834324 - 0.834324i) q^{19} +(4.24907 + 1.39478i) q^{20} +(-2.08016 - 2.08016i) q^{21} +(-6.05500 + 2.79053i) q^{22} +(2.95105 - 2.95105i) q^{23} +(-1.38116 - 2.46828i) q^{24} +(3.55514 - 3.51582i) q^{25} +(3.00509 - 8.14270i) q^{26} +1.00000 q^{27} +(-0.460244 - 5.86555i) q^{28} +(-0.576185 - 0.576185i) q^{29} +(-3.16019 + 0.114996i) q^{30} +2.62300i q^{31} +(1.10685 - 5.54751i) q^{32} +(3.33354 - 3.33354i) q^{33} +(1.95159 + 4.23464i) q^{34} +(-6.07029 - 2.53419i) q^{35} +(1.52051 + 1.29925i) q^{36} +2.07309i q^{37} +(-1.51545 + 0.698418i) q^{38} +6.13735i q^{39} +(-4.95449 - 3.93103i) q^{40} +10.8873i q^{41} +(1.74131 + 3.77837i) q^{42} -5.16088i q^{43} +(9.39979 - 0.737562i) q^{44} +(2.06823 - 0.849960i) q^{45} +(-5.36024 + 2.47034i) q^{46} +(-8.65772 + 8.65772i) q^{47} +(0.623885 + 3.95105i) q^{48} +1.65411i q^{49} +(-6.43824 + 2.92387i) q^{50} +(-2.33136 - 2.33136i) q^{51} +(-7.97397 + 9.33189i) q^{52} -1.58490 q^{53} +(-1.32675 - 0.489639i) q^{54} +(4.06115 - 9.72791i) q^{55} +(-2.26137 + 8.00744i) q^{56} +(0.834324 - 0.834324i) q^{57} +(0.482328 + 1.04657i) q^{58} +(2.32603 + 2.32603i) q^{59} +(4.24907 + 1.39478i) q^{60} +(-7.22499 + 7.22499i) q^{61} +(1.28433 - 3.48006i) q^{62} +(-2.08016 - 2.08016i) q^{63} +(-4.18479 + 6.81818i) q^{64} +(5.21651 + 12.6934i) q^{65} +(-6.05500 + 2.79053i) q^{66} -0.885549i q^{67} +(-0.515823 - 6.57387i) q^{68} +(2.95105 - 2.95105i) q^{69} +(6.81290 + 6.33448i) q^{70} +2.56877 q^{71} +(-1.38116 - 2.46828i) q^{72} +(7.35033 + 7.35033i) q^{73} +(1.01507 - 2.75047i) q^{74} +(3.55514 - 3.51582i) q^{75} +(2.35259 - 0.184598i) q^{76} -13.8686 q^{77} +(3.00509 - 8.14270i) q^{78} -7.72612 q^{79} +(4.64857 + 7.64139i) q^{80} +1.00000 q^{81} +(5.33084 - 14.4447i) q^{82} -8.67714 q^{83} +(-0.460244 - 5.86555i) q^{84} +(-6.80334 - 2.84022i) q^{85} +(-2.52697 + 6.84718i) q^{86} +(-0.576185 - 0.576185i) q^{87} +(-12.8323 - 3.62395i) q^{88} -8.70590 q^{89} +(-3.16019 + 0.114996i) q^{90} +(12.7667 - 12.7667i) q^{91} +(8.32124 - 0.652933i) q^{92} +2.62300i q^{93} +(15.7257 - 7.24743i) q^{94} +(1.01643 - 2.43472i) q^{95} +(1.10685 - 5.54751i) q^{96} +(11.9985 + 11.9985i) q^{97} +(0.809919 - 2.19459i) q^{98} +(3.33354 - 3.33354i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9	$ 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9} - 14 q^{10} - 8 q^{12} - 4 q^{14} - 4 q^{15} - 8 q^{16} - 8 q^{17} + 2 q^{18} + 8 q^{19} - 12 q^{20} - 4 q^{21} - 8 q^{22} - 4 q^{24} + 32 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{28} + 12 q^{29} - 14 q^{30} - 28 q^{32} - 20 q^{35} - 8 q^{36} - 16 q^{38} - 44 q^{40} - 4 q^{42} + 52 q^{44} - 4 q^{45} - 16 q^{46} - 32 q^{47} - 8 q^{48} + 22 q^{50} - 8 q^{51} + 8 q^{52} + 16 q^{53} + 2 q^{54} - 4 q^{55} + 20 q^{56} + 8 q^{57} - 44 q^{58} - 24 q^{59} - 12 q^{60} + 40 q^{61} + 40 q^{62} - 4 q^{63} - 8 q^{64} - 4 q^{65} - 8 q^{66} + 24 q^{68} + 56 q^{70} - 4 q^{72} + 8 q^{73} + 64 q^{74} + 32 q^{75} + 16 q^{76} - 72 q^{77} + 20 q^{78} - 48 q^{79} + 16 q^{80} + 16 q^{81} + 8 q^{82} - 8 q^{83} + 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} - 16 q^{88} - 14 q^{90} - 40 q^{91} - 20 q^{94} + 8 q^{95} - 28 q^{96} + 48 q^{97} + 30 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9 - 14 * q^10 - 8 * q^12 - 4 * q^14 - 4 * q^15 - 8 * q^16 - 8 * q^17 + 2 * q^18 + 8 * q^19 - 12 * q^20 - 4 * q^21 - 8 * q^22 - 4 * q^24 + 32 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^28 + 12 * q^29 - 14 * q^30 - 28 * q^32 - 20 * q^35 - 8 * q^36 - 16 * q^38 - 44 * q^40 - 4 * q^42 + 52 * q^44 - 4 * q^45 - 16 * q^46 - 32 * q^47 - 8 * q^48 + 22 * q^50 - 8 * q^51 + 8 * q^52 + 16 * q^53 + 2 * q^54 - 4 * q^55 + 20 * q^56 + 8 * q^57 - 44 * q^58 - 24 * q^59 - 12 * q^60 + 40 * q^61 + 40 * q^62 - 4 * q^63 - 8 * q^64 - 4 * q^65 - 8 * q^66 + 24 * q^68 + 56 * q^70 - 4 * q^72 + 8 * q^73 + 64 * q^74 + 32 * q^75 + 16 * q^76 - 72 * q^77 + 20 * q^78 - 48 * q^79 + 16 * q^80 + 16 * q^81 + 8 * q^82 - 8 * q^83 + 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 - 16 * q^88 - 14 * q^90 - 40 * q^91 - 20 * q^94 + 8 * q^95 - 28 * q^96 + 48 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.32675	−	0.489639i	−0.938151	−	0.346227i
$2$	−1.32675	−	0.489639i	−0.938151	−	0.346227i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	1.52051	+	1.29925i	0.760254	+	0.649626i
$5$	2.06823	−	0.849960i	0.924940	−	0.380114i
$5$	2.06823	−	0.849960i	0.924940	−	0.380114i
$6$	−1.32675	−	0.489639i	−0.541642	−	0.199894i
$7$	−2.08016	−	2.08016i	−0.786226	−	0.786226i	0.194647	−	0.980873i	$-0.437644\pi$
$7$	−2.08016	−	2.08016i	−0.786226	−	0.786226i	−0.980873	+	0.194647i	$0.937644\pi$
$8$	−1.38116	−	2.46828i	−0.488314	−	0.872668i
$9$	1.00000			0.333333
$10$	−3.16019	+	0.114996i	−0.999339	+	0.0363648i
$11$	3.33354	−	3.33354i	1.00510	−	1.00510i	0.00511408	−	0.999987i	$-0.498372\pi$
$11$	3.33354	−	3.33354i	1.00510	−	1.00510i	0.999987	−	0.00511408i	$-0.00162787\pi$
$12$	1.52051	+	1.29925i	0.438933	+	0.375062i
$13$			6.13735i			1.70220i	0.525007	+	0.851098i	$0.324063\pi$
$13$			6.13735i			1.70220i	−0.525007	+	0.851098i	$0.675937\pi$
$14$	1.74131	+	3.77837i	0.465386	+	1.00981i
$15$	2.06823	−	0.849960i	0.534014	−	0.219459i
$16$	0.623885	+	3.95105i	0.155971	+	0.987762i
$17$	−2.33136	−	2.33136i	−0.565437	−	0.565437i	0.365410	−	0.930847i	$-0.380929\pi$
$17$	−2.33136	−	2.33136i	−0.565437	−	0.565437i	−0.930847	+	0.365410i	$0.880929\pi$
$18$	−1.32675	−	0.489639i	−0.312717	−	0.115409i
$19$	0.834324	−	0.834324i	0.191407	−	0.191407i	−0.604897	−	0.796304i	$-0.706786\pi$
$19$	0.834324	−	0.834324i	0.191407	−	0.191407i	0.796304	+	0.604897i	$0.206786\pi$
$20$	4.24907	+	1.39478i	0.950121	+	0.311882i
$21$	−2.08016	−	2.08016i	−0.453928	−	0.453928i
$22$	−6.05500	+	2.79053i	−1.29093	+	0.594943i
$23$	2.95105	−	2.95105i	0.615336	−	0.615336i	−0.328996	−	0.944331i	$-0.606710\pi$
$23$	2.95105	−	2.95105i	0.615336	−	0.615336i	0.944331	+	0.328996i	$0.106710\pi$
$24$	−1.38116	−	2.46828i	−0.281928	−	0.503835i
$25$	3.55514	−	3.51582i	0.711027	−	0.703165i
$26$	3.00509	−	8.14270i	0.589346	−	1.59692i
$27$	1.00000			0.192450
$28$	−0.460244	−	5.86555i	−0.0869780	−	1.10848i
$29$	−0.576185	−	0.576185i	−0.106995	−	0.106995i	0.651583	−	0.758578i	$-0.274105\pi$
$29$	−0.576185	−	0.576185i	−0.106995	−	0.106995i	−0.758578	+	0.651583i	$0.774105\pi$
$30$	−3.16019	+	0.114996i	−0.576968	+	0.0209953i
$31$			2.62300i			0.471106i	0.971862	+	0.235553i	$0.0756900\pi$
$31$			2.62300i			0.471106i	−0.971862	+	0.235553i	$0.924310\pi$
$32$	1.10685	−	5.54751i	0.195665	−	0.980671i
$33$	3.33354	−	3.33354i	0.580295	−	0.580295i
$34$	1.95159	+	4.23464i	0.334696	+	0.726235i
$35$	−6.07029	−	2.53419i	−1.02607	−	0.428356i
$36$	1.52051	+	1.29925i	0.253418	+	0.216542i
$37$			2.07309i			0.340814i	0.985374	+	0.170407i	$0.0545083\pi$
$37$			2.07309i			0.340814i	−0.985374	+	0.170407i	$0.945492\pi$
$38$	−1.51545	+	0.698418i	−0.245839	+	0.113298i
$39$			6.13735i			0.982763i
$40$	−4.95449	−	3.93103i	−0.783374	−	0.621550i
$41$			10.8873i			1.70031i	0.526533	+	0.850154i	$0.323492\pi$
$41$			10.8873i			1.70031i	−0.526533	+	0.850154i	$0.676508\pi$
$42$	1.74131	+	3.77837i	0.268691	+	0.583015i
$43$		−	5.16088i		−	0.787027i	−0.919319	−	0.393514i	$-0.871259\pi$
$43$		−	5.16088i		−	0.787027i	0.919319	−	0.393514i	$-0.128741\pi$
$44$	9.39979	−	0.737562i	1.41707	−	0.111192i
$45$	2.06823	−	0.849960i	0.308313	−	0.126705i
$46$	−5.36024	+	2.47034i	−0.790324	+	0.364232i
$47$	−8.65772	+	8.65772i	−1.26286	+	1.26286i	−0.313156	+	0.949702i	$0.601386\pi$
$47$	−8.65772	+	8.65772i	−1.26286	+	1.26286i	−0.949702	+	0.313156i	$0.898614\pi$
$48$	0.623885	+	3.95105i	0.0900500	+	0.570284i
$49$			1.65411i			0.236302i
$50$	−6.43824	+	2.92387i	−0.910505	+	0.413498i
$51$	−2.33136	−	2.33136i	−0.326455	−	0.326455i
$52$	−7.97397	+	9.33189i	−1.10579	+	1.29410i
$53$	−1.58490			−0.217703			−0.108851	−	0.994058i	$-0.534717\pi$
$53$	−1.58490			−0.217703			−0.108851	+	0.994058i	$0.534717\pi$
$54$	−1.32675	−	0.489639i	−0.180547	−	0.0666314i
$55$	4.06115	−	9.72791i	0.547605	−	1.31171i
$56$	−2.26137	+	8.00744i	−0.302189	+	1.07004i
$57$	0.834324	−	0.834324i	0.110509	−	0.110509i
$58$	0.482328	+	1.04657i	0.0633328	+	0.137422i
$59$	2.32603	+	2.32603i	0.302824	+	0.302824i	0.842118	−	0.539294i	$-0.181309\pi$
$59$	2.32603	+	2.32603i	0.302824	+	0.302824i	−0.539294	+	0.842118i	$0.681309\pi$
$60$	4.24907	+	1.39478i	0.548552	+	0.180065i
$61$	−7.22499	+	7.22499i	−0.925065	+	0.925065i	−0.997382	−	0.0723167i	$-0.976961\pi$
$61$	−7.22499	+	7.22499i	−0.925065	+	0.925065i	0.0723167	+	0.997382i	$0.476961\pi$
$62$	1.28433	−	3.48006i	0.163109	−	0.441968i
$63$	−2.08016	−	2.08016i	−0.262075	−	0.262075i
$64$	−4.18479	+	6.81818i	−0.523098	+	0.852272i
$65$	5.21651	+	12.6934i	0.647028	+	1.57443i
$66$	−6.05500	+	2.79053i	−0.745318	+	0.343491i
$67$		−	0.885549i		−	0.108187i	−0.998536	−	0.0540935i	$-0.982773\pi$
$67$		−	0.885549i		−	0.108187i	0.998536	−	0.0540935i	$-0.0172269\pi$
$68$	−0.515823	−	6.57387i	−0.0625528	−	0.797198i
$69$	2.95105	−	2.95105i	0.355264	−	0.355264i
$70$	6.81290	+	6.33448i	0.814297	+	0.757115i
$71$	2.56877			0.304857			0.152428	−	0.988315i	$-0.451291\pi$
$71$	2.56877			0.304857			0.152428	+	0.988315i	$0.451291\pi$
$72$	−1.38116	−	2.46828i	−0.162771	−	0.290889i
$73$	7.35033	+	7.35033i	0.860291	+	0.860291i	0.991372	−	0.131081i	$-0.0418447\pi$
$73$	7.35033	+	7.35033i	0.860291	+	0.860291i	−0.131081	+	0.991372i	$0.541845\pi$
$74$	1.01507	−	2.75047i	0.117999	−	0.319735i
$75$	3.55514	−	3.51582i	0.410512	−	0.405972i
$76$	2.35259	−	0.184598i	0.269861	−	0.0211748i
$77$	−13.8686			−1.58047
$78$	3.00509	−	8.14270i	0.340259	−	0.921980i
$79$	−7.72612			−0.869256			−0.434628	−	0.900610i	$-0.643120\pi$
$79$	−7.72612			−0.869256			−0.434628	+	0.900610i	$0.643120\pi$
$80$	4.64857	+	7.64139i	0.519726	+	0.854333i
$81$	1.00000			0.111111
$82$	5.33084	−	14.4447i	0.588693	−	1.59515i
$83$	−8.67714			−0.952440			−0.476220	−	0.879326i	$-0.657993\pi$
$83$	−8.67714			−0.952440			−0.476220	+	0.879326i	$0.657993\pi$
$84$	−0.460244	−	5.86555i	−0.0502168	−	0.639984i
$85$	−6.80334	−	2.84022i	−0.737926	−	0.308065i
$86$	−2.52697	+	6.84718i	−0.272490	+	0.738350i
$87$	−0.576185	−	0.576185i	−0.0617735	−	0.0617735i
$88$	−12.8323	−	3.62395i	−1.36792	−	0.386314i
$89$	−8.70590			−0.922823			−0.461412	−	0.887186i	$-0.652657\pi$
$89$	−8.70590			−0.922823			−0.461412	+	0.887186i	$0.652657\pi$
$90$	−3.16019	+	0.114996i	−0.333113	+	0.0121216i
$91$	12.7667	−	12.7667i	1.33831	−	1.33831i
$92$	8.32124	−	0.652933i	0.867550	−	0.0680729i
$93$			2.62300i			0.271993i
$94$	15.7257	−	7.24743i	1.62199	−	0.747516i
$95$	1.01643	−	2.43472i	0.104284	−	0.249797i
$96$	1.10685	−	5.54751i	0.112967	−	0.566191i
$97$	11.9985	+	11.9985i	1.21826	+	1.21826i	0.968240	+	0.250021i	$0.0804375\pi$
$97$	11.9985	+	11.9985i	1.21826	+	1.21826i	0.250021	+	0.968240i	$0.419562\pi$
$98$	0.809919	−	2.19459i	0.0818142	−	0.221687i
$99$	3.33354	−	3.33354i	0.335034	−	0.335034i
$100$	9.97355	−	0.726816i	0.997355	−	0.0726816i
$101$	−6.69380	−	6.69380i	−0.666058	−	0.666058i	0.290743	−	0.956801i	$-0.406098\pi$
$101$	−6.69380	−	6.69380i	−0.666058	−	0.666058i	−0.956801	+	0.290743i	$0.906098\pi$
$102$	1.95159	+	4.23464i	0.193237	+	0.419292i
$103$	−13.4242	+	13.4242i	−1.32272	+	1.32272i	−0.411158	+	0.911564i	$0.634876\pi$
$103$	−13.4242	+	13.4242i	−1.32272	+	1.32272i	−0.911564	+	0.411158i	$0.865124\pi$
$104$	15.1487	−	8.47667i	1.48545	−	0.831206i
$105$	−6.07029	−	2.53419i	−0.592400	−	0.247312i
$106$	2.10276	+	0.776029i	0.204238	+	0.0753746i
$107$	−10.9567			−1.05922			−0.529612	−	0.848240i	$-0.677663\pi$
$107$	−10.9567			−1.05922			−0.529612	+	0.848240i	$0.677663\pi$
$108$	1.52051	+	1.29925i	0.146311	+	0.125021i
$109$	0.643941	+	0.643941i	0.0616784	+	0.0616784i	0.737273	−	0.675595i	$-0.236113\pi$
$109$	0.643941	+	0.643941i	0.0616784	+	0.0616784i	−0.675595	+	0.737273i	$0.736113\pi$
$110$	−10.1513	+	10.9180i	−0.967886	+	1.04099i
$111$			2.07309i			0.196769i
$112$	6.92102	−	9.51658i	0.653975	−	0.899232i
$113$	9.19571	−	9.19571i	0.865060	−	0.865060i	−0.126861	−	0.991921i	$-0.540490\pi$
$113$	9.19571	−	9.19571i	0.865060	−	0.865060i	0.991921	+	0.126861i	$0.0404901\pi$
$114$	−1.51545	+	0.698418i	−0.141935	+	0.0654129i
$115$	3.59517	−	8.61171i	0.335251	−	0.803046i
$116$	−0.127484	−	1.62470i	−0.0118366	−	0.150850i
$117$			6.13735i			0.567398i
$118$	−1.94714	−	4.22497i	−0.179249	−	0.388940i
$119$			9.69918i			0.889122i
$120$	−4.95449	−	3.93103i	−0.452281	−	0.358852i
$121$		−	11.2250i		−	1.02046i
$122$	13.1234	−	6.04809i	1.18813	−	0.547568i
$123$			10.8873i			0.981674i
$124$	−3.40795	+	3.98830i	−0.306043	+	0.358160i
$125$	4.36452	−	10.2932i	0.390375	−	0.920656i
$126$	1.74131	+	3.77837i	0.155129	+	0.336604i
$127$	4.80716	−	4.80716i	0.426567	−	0.426567i	−0.460890	−	0.887457i	$-0.652470\pi$
$127$	4.80716	−	4.80716i	0.426567	−	0.426567i	0.887457	+	0.460890i	$0.152470\pi$
$128$	8.89059	−	6.99695i	0.785825	−	0.618449i
$129$		−	5.16088i		−	0.454391i
$130$	−0.705769	−	19.3952i	−0.0619001	−	1.70107i
$131$	−3.53632	−	3.53632i	−0.308970	−	0.308970i	0.535540	−	0.844510i	$-0.320108\pi$
$131$	−3.53632	−	3.53632i	−0.308970	−	0.308970i	−0.844510	+	0.535540i	$0.820108\pi$
$132$	9.39979	−	0.737562i	0.818147	−	0.0641965i
$133$	−3.47105			−0.300978
$134$	−0.433599	+	1.17490i	−0.0374573	+	0.101496i
$135$	2.06823	−	0.849960i	0.178005	−	0.0731529i
$136$	−2.53445	+	8.97441i	−0.217328	+	0.769550i
$137$	7.54548	−	7.54548i	0.644654	−	0.644654i	−0.307042	−	0.951696i	$-0.599339\pi$
$137$	7.54548	−	7.54548i	0.644654	−	0.644654i	0.951696	+	0.307042i	$0.0993392\pi$
$138$	−5.36024	+	2.47034i	−0.456294	+	0.210289i
$139$	−2.84263	−	2.84263i	−0.241109	−	0.241109i	0.576200	−	0.817309i	$-0.304535\pi$
$139$	−2.84263	−	2.84263i	−0.241109	−	0.241109i	−0.817309	+	0.576200i	$0.804535\pi$
$140$	−5.93737	−	11.7401i	−0.501799	−	0.992219i
$141$	−8.65772	+	8.65772i	−0.729111	+	0.729111i
$142$	−3.40810	−	1.25777i	−0.286002	−	0.105550i
$143$	20.4591	+	20.4591i	1.71088	+	1.71088i
$144$	0.623885	+	3.95105i	0.0519904	+	0.329254i
$145$	−1.68142	−	0.701948i	−0.139634	−	0.0582936i
$146$	−6.15301	−	13.3510i	−0.509227	−	1.10494i
$147$			1.65411i			0.136429i
$148$	−2.69347	+	3.15215i	−0.221402	+	0.259105i
$149$	3.20287	−	3.20287i	0.262389	−	0.262389i	−0.563635	−	0.826024i	$-0.690597\pi$
$149$	3.20287	−	3.20287i	0.262389	−	0.262389i	0.826024	+	0.563635i	$0.190597\pi$
$150$	−6.43824	+	2.92387i	−0.525680	+	0.238733i
$151$	8.82773			0.718390			0.359195	−	0.933262i	$-0.383051\pi$
$151$	8.82773			0.718390			0.359195	+	0.933262i	$0.383051\pi$
$152$	−3.21168	−	0.907007i	−0.260502	−	0.0735680i
$153$	−2.33136	−	2.33136i	−0.188479	−	0.188479i
$154$	18.4001	+	6.79060i	1.48272	+	0.547202i
$155$	2.22945	+	5.42497i	0.179074	+	0.435744i
$156$	−7.97397	+	9.33189i	−0.638429	+	0.747149i
$157$	15.5186			1.23852			0.619258	−	0.785187i	$-0.287433\pi$
$157$	15.5186			1.23852			0.619258	+	0.785187i	$0.287433\pi$
$158$	10.2506	+	3.78301i	0.815493	+	0.300960i
$159$	−1.58490			−0.125691
$160$	−2.42595	−	12.4143i	−0.191788	−	0.981436i
$161$	−12.2773			−0.967586
$162$	−1.32675	−	0.489639i	−0.104239	−	0.0384697i
$163$	8.65221			0.677694			0.338847	−	0.940842i	$-0.389963\pi$
$163$	8.65221			0.677694			0.338847	+	0.940842i	$0.389963\pi$
$164$	−14.1453	+	16.5542i	−1.10457	+	1.29267i
$165$	4.06115	−	9.72791i	0.316160	−	0.757316i
$166$	11.5124	+	4.24867i	0.893532	+	0.329760i
$167$	2.86613	+	2.86613i	0.221788	+	0.221788i	0.809251	−	0.587463i	$-0.199873\pi$
$167$	2.86613	+	2.86613i	0.221788	+	0.221788i	−0.587463	+	0.809251i	$0.699873\pi$
$168$	−2.26137	+	8.00744i	−0.174469	+	0.617787i
$169$	−24.6671			−1.89747
$170$	7.63562	+	7.09942i	0.585625	+	0.544501i
$171$	0.834324	−	0.834324i	0.0638024	−	0.0638024i
$172$	6.70529	−	7.84716i	0.511274	−	0.598340i
$173$		−	15.1143i		−	1.14912i	−0.818464	−	0.574558i	$-0.805174\pi$
$173$		−	15.1143i		−	1.14912i	0.818464	−	0.574558i	$-0.194826\pi$
$174$	0.482328	+	1.04657i	0.0365652	+	0.0793406i
$175$	−14.7087	−	0.0817750i	−1.11187	−	0.00618161i
$176$	15.2507	+	11.0912i	1.14957	+	0.836033i
$177$	2.32603	+	2.32603i	0.174835	+	0.174835i
$178$	11.5505	+	4.26275i	0.865747	+	0.319506i
$179$	−12.3666	+	12.3666i	−0.924324	+	0.924324i	−0.997331	−	0.0730070i	$-0.976740\pi$
$179$	−12.3666	+	12.3666i	−0.924324	+	0.924324i	0.0730070	+	0.997331i	$0.476740\pi$
$180$	4.24907	+	1.39478i	0.316707	+	0.103961i
$181$	−9.58991	−	9.58991i	−0.712813	−	0.712813i	0.254310	−	0.967123i	$-0.418152\pi$
$181$	−9.58991	−	9.58991i	−0.712813	−	0.712813i	−0.967123	+	0.254310i	$0.918152\pi$
$182$	−23.1892	+	10.6871i	−1.71890	+	0.792177i
$183$	−7.22499	+	7.22499i	−0.534087	+	0.534087i
$184$	−11.3599	−	3.20813i	−0.837461	−	0.236506i
$185$	1.76205	+	4.28763i	0.129548	+	0.315233i
$186$	1.28433	−	3.48006i	0.0941713	−	0.255170i
$187$	−15.5434			−1.13664
$188$	−24.4127	+	1.91556i	−1.78048	+	0.139707i
$189$	−2.08016	−	2.08016i	−0.151309	−	0.151309i
$190$	−2.54068	+	2.73256i	−0.184320	+	0.198241i
$191$			14.5044i			1.04950i	0.851257	+	0.524750i	$0.175841\pi$
$191$			14.5044i			1.04950i	−0.851257	+	0.524750i	$0.824159\pi$
$192$	−4.18479	+	6.81818i	−0.302011	+	0.492060i
$193$	−1.68153	+	1.68153i	−0.121039	+	0.121039i	−0.765032	−	0.643992i	$-0.777277\pi$
$193$	−1.68153	+	1.68153i	−0.121039	+	0.121039i	0.643992	+	0.765032i	$0.277277\pi$
$194$	−10.0440	−	21.7939i	−0.721118	−	1.56471i
$195$	5.21651	+	12.6934i	0.373562	+	0.908996i
$196$	−2.14911	+	2.51509i	−0.153508	+	0.179649i
$197$			8.65121i			0.616373i	0.951326	+	0.308187i	$0.0997221\pi$
$197$			8.65121i			0.616373i	−0.951326	+	0.308187i	$0.900278\pi$
$198$	−6.05500	+	2.79053i	−0.430310	+	0.198314i
$199$		−	22.3275i		−	1.58275i	−0.611328	−	0.791377i	$-0.709365\pi$
$199$		−	22.3275i		−	1.58275i	0.611328	−	0.791377i	$-0.290635\pi$
$200$	−13.5882	−	3.91914i	−0.960834	−	0.277125i
$201$		−	0.885549i		−	0.0624618i
$202$	5.60343	+	12.1585i	0.394256	+	0.855471i
$203$			2.39711i			0.168244i
$204$	−0.515823	−	6.57387i	−0.0361149	−	0.460263i
$205$	9.25376	+	22.5174i	0.646311	+	1.57268i
$206$	24.3834	−	11.2375i	1.69887	−	0.782951i
$207$	2.95105	−	2.95105i	0.205112	−	0.205112i
$208$	−24.2490	+	3.82900i	−1.68136	+	0.265493i
$209$		−	5.56251i		−	0.384767i
$210$	6.81290	+	6.33448i	0.470134	+	0.437120i
$211$	5.27613	+	5.27613i	0.363224	+	0.363224i	0.864998	−	0.501775i	$-0.167319\pi$
$211$	5.27613	+	5.27613i	0.363224	+	0.363224i	−0.501775	+	0.864998i	$0.667319\pi$
$212$	−2.40985	−	2.05919i	−0.165509	−	0.141426i
$213$	2.56877			0.176009
$214$	14.5368	+	5.36483i	0.993712	+	0.366732i
$215$	−4.38655	−	10.6739i	−0.299160	−	0.727953i
$216$	−1.38116	−	2.46828i	−0.0939761	−	0.167945i
$217$	5.45626	−	5.45626i	0.370395	−	0.370395i
$218$	−0.539047	−	1.16964i	−0.0365089	−	0.0792183i
$219$	7.35033	+	7.35033i	0.496689	+	0.496689i
$220$	18.8140	−	9.51489i	1.26844	−	0.641494i
$221$	14.3084	−	14.3084i	0.962484	−	0.962484i
$222$	1.01507	−	2.75047i	0.0681268	−	0.184599i
$223$	13.8202	+	13.8202i	0.925469	+	0.925469i	0.997409	−	0.0719400i	$-0.0229190\pi$
$223$	13.8202	+	13.8202i	0.925469	+	0.925469i	−0.0719400	+	0.997409i	$0.522919\pi$
$224$	−13.8421	+	9.23728i	−0.924866	+	0.617192i
$225$	3.55514	−	3.51582i	0.237009	−	0.234388i
$226$	−16.7029	+	7.69779i	−1.11106	+	0.512049i
$227$		−	1.66286i		−	0.110368i	−0.998476	−	0.0551839i	$-0.982425\pi$
$227$		−	1.66286i		−	0.110368i	0.998476	−	0.0551839i	$-0.0175745\pi$
$228$	2.35259	−	0.184598i	0.155804	−	0.0122253i
$229$	11.3744	−	11.3744i	0.751643	−	0.751643i	−0.223142	−	0.974786i	$-0.571632\pi$
$229$	11.3744	−	11.3744i	0.751643	−	0.751643i	0.974786	+	0.223142i	$0.0716315\pi$
$230$	−8.98650	+	9.66521i	−0.592552	+	0.637305i
$231$	−13.8686			−0.912486
$232$	−0.626380	+	2.21799i	−0.0411239	+	0.145618i
$233$	9.38976	+	9.38976i	0.615143	+	0.615143i	0.944282	−	0.329138i	$-0.106758\pi$
$233$	9.38976	+	9.38976i	0.615143	+	0.615143i	−0.329138	+	0.944282i	$0.606758\pi$
$234$	3.00509	−	8.14270i	0.196449	−	0.532305i
$235$	−10.5474	+	25.2649i	−0.688038	+	1.64810i
$236$	0.514646	+	6.55886i	0.0335006	+	0.426945i
$237$	−7.72612			−0.501865
$238$	4.74910	−	12.8683i	0.307838	−	0.834131i
$239$	8.88914			0.574991			0.287495	−	0.957782i	$-0.407177\pi$
$239$	8.88914			0.574991			0.287495	+	0.957782i	$0.407177\pi$
$240$	4.64857	+	7.64139i	0.300064	+	0.493249i
$241$	20.5978			1.32682			0.663411	−	0.748255i	$-0.269108\pi$
$241$	20.5978			1.32682			0.663411	+	0.748255i	$0.269108\pi$
$242$	−5.49621	+	14.8927i	−0.353309	+	0.957342i
$243$	1.00000			0.0641500
$244$	−20.3727	+	1.59856i	−1.30423	+	0.102337i
$245$	1.40593	+	3.42109i	0.0898217	+	0.218565i
$246$	5.33084	−	14.4447i	0.339882	−	0.920958i
$247$	5.12054	+	5.12054i	0.325812	+	0.325812i
$248$	6.47430	−	3.62279i	0.411119	−	0.230048i
$249$	−8.67714			−0.549891
$250$	−10.8306	+	11.5195i	−0.684986	+	0.728556i
$251$	16.8455	−	16.8455i	1.06328	−	1.06328i	0.0654195	−	0.997858i	$-0.479161\pi$
$251$	16.8455	−	16.8455i	1.06328	−	1.06328i	0.997858	−	0.0654195i	$-0.0208386\pi$
$252$	−0.460244	−	5.86555i	−0.0289927	−	0.369495i
$253$		−	19.6749i		−	1.23695i
$254$	−8.73165	+	4.02411i	−0.547873	+	0.252495i
$255$	−6.80334	−	2.84022i	−0.426042	−	0.177861i
$256$	−15.2215	+	4.93000i	−0.951346	+	0.308125i
$257$	−14.1500	−	14.1500i	−0.882653	−	0.882653i	0.111151	−	0.993804i	$-0.464546\pi$
$257$	−14.1500	−	14.1500i	−0.882653	−	0.882653i	−0.993804	+	0.111151i	$0.964546\pi$
$258$	−2.52697	+	6.84718i	−0.157322	+	0.426287i
$259$	4.31236	−	4.31236i	0.267957	−	0.267957i
$260$	−8.56026	+	26.0780i	−0.530885	+	1.61729i
$261$	−0.576185	−	0.576185i	−0.0356650	−	0.0356650i
$262$	2.96028	+	6.42332i	0.182887	+	0.396834i
$263$	11.1204	−	11.1204i	0.685712	−	0.685712i	−0.275569	−	0.961281i	$-0.588866\pi$
$263$	11.1204	−	11.1204i	0.685712	−	0.685712i	0.961281	+	0.275569i	$0.0888664\pi$
$264$	−12.8323	−	3.62395i	−0.789772	−	0.223039i
$265$	−3.27794	+	1.34710i	−0.201362	+	0.0827519i
$266$	4.60520	+	1.69956i	0.282363	+	0.104207i
$267$	−8.70590			−0.532792
$268$	1.15055	−	1.34648i	0.0702811	−	0.0822496i
$269$	−10.2902	−	10.2902i	−0.627403	−	0.627403i	0.320011	−	0.947414i	$-0.396313\pi$
$269$	−10.2902	−	10.2902i	−0.627403	−	0.627403i	−0.947414	+	0.320011i	$0.896313\pi$
$270$	−3.16019	+	0.114996i	−0.192323	+	0.00699842i
$271$		−	21.3325i		−	1.29586i	−0.761702	−	0.647928i	$-0.775636\pi$
$271$		−	21.3325i		−	1.29586i	0.761702	−	0.647928i	$-0.224364\pi$
$272$	7.75680	−	10.6658i	0.470325	−	0.646709i
$273$	12.7667	−	12.7667i	0.772674	−	0.772674i
$274$	−13.7055	+	6.31637i	−0.827979	+	0.381586i
$275$	0.131048	−	23.5713i	0.00790249	−	1.42141i
$276$	8.32124	−	0.652933i	0.500880	−	0.0393019i
$277$			19.0041i			1.14184i	0.821004	+	0.570922i	$0.193414\pi$
$277$			19.0041i			1.14184i	−0.821004	+	0.570922i	$0.806586\pi$
$278$	2.37959	+	5.16331i	0.142718	+	0.309675i
$279$			2.62300i			0.157035i
$280$	2.12897	+	18.4833i	0.127230	+	1.10459i
$281$		−	3.86317i		−	0.230457i	−0.993339	−	0.115229i	$-0.963240\pi$
$281$		−	3.86317i		−	0.230457i	0.993339	−	0.115229i	$-0.0367600\pi$
$282$	15.7257	−	7.24743i	0.936454	−	0.431578i
$283$			5.89151i			0.350214i	0.984549	+	0.175107i	$0.0560271\pi$
$283$			5.89151i			0.350214i	−0.984549	+	0.175107i	$0.943973\pi$
$284$	3.90583	+	3.33748i	0.231769	+	0.198043i
$285$	1.01643	−	2.43472i	0.0602081	−	0.144220i
$286$	−17.1265	−	37.1616i	−1.01271	−	2.19741i
$287$	22.6473	−	22.6473i	1.33683	−	1.33683i
$288$	1.10685	−	5.54751i	0.0652218	−	0.326890i
$289$		−	6.12955i		−	0.360562i
$290$	1.88711	+	1.75459i	0.110815	+	0.103033i
$291$	11.9985	+	11.9985i	0.703364	+	0.703364i
$292$	1.62629	+	20.7262i	0.0951716	+	1.21291i
$293$	−4.49132			−0.262386			−0.131193	−	0.991357i	$-0.541881\pi$
$293$	−4.49132			−0.262386			−0.131193	+	0.991357i	$0.541881\pi$
$294$	0.809919	−	2.19459i	0.0472354	−	0.127991i
$295$	6.78780	+	2.83373i	0.395201	+	0.164986i
$296$	5.11697	−	2.86327i	0.297418	−	0.166424i
$297$	3.33354	−	3.33354i	0.193432	−	0.193432i
$298$	−5.81764	+	2.68114i	−0.337007	+	0.155314i
$299$	18.1116	+	18.1116i	1.04742	+	1.04742i
$300$	9.97355	−	0.726816i	0.575823	−	0.0419627i
$301$	−10.7355	+	10.7355i	−0.618781	+	0.618781i
$302$	−11.7121	−	4.32240i	−0.673958	−	0.248726i
$303$	−6.69380	−	6.69380i	−0.384549	−	0.384549i
$304$	3.81698	+	2.77593i	0.218919	+	0.159211i
$305$	−8.80197	+	21.0839i	−0.503999	+	1.20726i
$306$	1.95159	+	4.23464i	0.111565	+	0.242078i
$307$			3.84487i			0.219438i	0.993963	+	0.109719i	$0.0349951\pi$
$307$			3.84487i			0.219438i	−0.993963	+	0.109719i	$0.965005\pi$
$308$	−21.0873	−	18.0188i	−1.20156	−	1.02672i
$309$	−13.4242	+	13.4242i	−0.763674	+	0.763674i
$310$	−0.301634	−	8.28918i	−0.0171317	−	0.470794i
$311$	−4.07103			−0.230847			−0.115423	−	0.993316i	$-0.536822\pi$
$311$	−4.07103			−0.230847			−0.115423	+	0.993316i	$0.536822\pi$
$312$	15.1487	−	8.47667i	0.857626	−	0.479897i
$313$	−1.37922	−	1.37922i	−0.0779584	−	0.0779584i	0.667052	−	0.745011i	$-0.267556\pi$
$313$	−1.37922	−	1.37922i	−0.0779584	−	0.0779584i	−0.745011	+	0.667052i	$0.767556\pi$
$314$	−20.5892	−	7.59850i	−1.16192	−	0.428808i
$315$	−6.07029	−	2.53419i	−0.342022	−	0.142785i
$316$	−11.7476	−	10.0382i	−0.660855	−	0.564692i
$317$	9.80915			0.550937			0.275468	−	0.961310i	$-0.411167\pi$
$317$	9.80915			0.550937			0.275468	+	0.961310i	$0.411167\pi$
$318$	2.10276	+	0.776029i	0.117917	+	0.0435176i
$319$	−3.84148			−0.215081
$320$	−2.85991	+	17.6585i	−0.159874	+	0.987137i
$321$	−10.9567			−0.611543
$322$	16.2888	+	6.01144i	0.907741	+	0.335004i
$323$	−3.89021			−0.216457
$324$	1.52051	+	1.29925i	0.0844726	+	0.0721807i
$325$	21.5778	+	21.8191i	1.19692	+	1.21031i
$326$	−11.4793	−	4.23646i	−0.635779	−	0.234636i
$327$	0.643941	+	0.643941i	0.0356100	+	0.0356100i
$328$	26.8729	−	15.0371i	1.48380	−	0.830285i
$329$	36.0188			1.98578
$330$	−10.1513	+	10.9180i	−0.558809	+	0.601014i
$331$	−7.17235	+	7.17235i	−0.394228	+	0.394228i	−0.876191	−	0.481963i	$-0.839924\pi$
$331$	−7.17235	+	7.17235i	−0.394228	+	0.394228i	0.481963	+	0.876191i	$0.339924\pi$
$332$	−13.1937	−	11.2738i	−0.724096	−	0.618730i
$333$			2.07309i			0.113605i
$334$	−2.39925	−	5.20599i	−0.131281	−	0.284859i
$335$	−0.752681	−	1.83152i	−0.0411234	−	0.100066i
$336$	6.92102	−	9.51658i	0.377573	−	0.519172i
$337$	−25.3587	−	25.3587i	−1.38138	−	1.38138i	−0.842178	−	0.539200i	$-0.818727\pi$
$337$	−25.3587	−	25.3587i	−1.38138	−	1.38138i	−0.539200	−	0.842178i	$-0.681273\pi$
$338$	32.7270	+	12.0780i	1.78011	+	0.656955i
$339$	9.19571	−	9.19571i	0.499442	−	0.499442i
$340$	−6.65436	−	13.1578i	−0.360884	−	0.713583i
$341$	8.74390	+	8.74390i	0.473509	+	0.473509i
$342$	−1.51545	+	0.698418i	−0.0819463	+	0.0377661i
$343$	−11.1203	+	11.1203i	−0.600439	+	0.600439i
$344$	−12.7385	+	7.12801i	−0.686814	+	0.384317i
$345$	3.59517	−	8.61171i	0.193557	−	0.463639i
$346$	−7.40053	+	20.0528i	−0.397855	+	1.07804i
$347$	−8.80549			−0.472704			−0.236352	−	0.971668i	$-0.575952\pi$
$347$	−8.80549			−0.472704			−0.236352	+	0.971668i	$0.575952\pi$
$348$	−0.127484	−	1.62470i	−0.00683384	−	0.0870933i
$349$	−14.8110	−	14.8110i	−0.792815	−	0.792815i	0.189136	−	0.981951i	$-0.439431\pi$
$349$	−14.8110	−	14.8110i	−0.792815	−	0.792815i	−0.981951	+	0.189136i	$0.939431\pi$
$350$	19.4747	+	7.31045i	1.04097	+	0.390760i
$351$			6.13735i			0.327588i
$352$	−14.8031	−	22.1826i	−0.789010	−	1.18234i
$353$	−21.3226	+	21.3226i	−1.13489	+	1.13489i	−0.145536	+	0.989353i	$0.546491\pi$
$353$	−21.3226	+	21.3226i	−1.13489	+	1.13489i	−0.989353	+	0.145536i	$0.953509\pi$
$354$	−1.94714	−	4.22497i	−0.103489	−	0.224555i
$355$	5.31280	−	2.18335i	0.281974	−	0.115880i
$356$	−13.2374	−	11.3112i	−0.701580	−	0.599490i
$357$			9.69918i			0.513335i
$358$	22.4625	−	10.3522i	1.18718	−	0.547130i
$359$			9.38977i			0.495573i	0.968815	+	0.247787i	$0.0797032\pi$
$359$			9.38977i			0.495573i	−0.968815	+	0.247787i	$0.920297\pi$
$360$	−4.95449	−	3.93103i	−0.261125	−	0.207183i
$361$			17.6078i			0.926727i
$362$	8.02778	+	17.4190i	0.421931	+	0.915521i
$363$		−	11.2250i		−	0.589161i
$364$	35.9989	−	2.82468i	1.88686	−	0.148054i
$365$	21.4496	+	8.95467i	1.12273	+	0.468709i
$366$	13.1234	−	6.04809i	0.685969	−	0.316138i
$367$	−0.129655	+	0.129655i	−0.00676792	+	0.00676792i	−0.710483	−	0.703715i	$-0.751523\pi$
$367$	−0.129655	+	0.129655i	−0.00676792	+	0.00676792i	0.703715	+	0.710483i	$0.251523\pi$
$368$	13.5008	+	9.81861i	0.703780	+	0.511830i
$369$			10.8873i			0.566770i
$370$	−0.238397	−	6.55136i	−0.0123937	−	0.340589i
$371$	3.29684	+	3.29684i	0.171164	+	0.171164i
$372$	−3.40795	+	3.98830i	−0.176694	+	0.206784i
$373$	−2.85797			−0.147980			−0.0739900	−	0.997259i	$-0.523573\pi$
$373$	−2.85797			−0.147980			−0.0739900	+	0.997259i	$0.523573\pi$
$374$	20.6221	+	7.61063i	1.06634	+	0.393536i
$375$	4.36452	−	10.2932i	0.225383	−	0.531541i
$376$	33.3274	+	9.41194i	1.71873	+	0.485384i
$377$	3.53625	−	3.53625i	0.182126	−	0.182126i
$378$	1.74131	+	3.77837i	0.0895635	+	0.194338i
$379$	−14.8095	−	14.8095i	−0.760713	−	0.760713i	0.215739	−	0.976451i	$-0.430784\pi$
$379$	−14.8095	−	14.8095i	−0.760713	−	0.760713i	−0.976451	+	0.215739i	$0.930784\pi$
$380$	4.70880	−	2.38140i	0.241556	−	0.122163i
$381$	4.80716	−	4.80716i	0.246278	−	0.246278i
$382$	7.10191	−	19.2436i	0.363365	−	0.984589i
$383$	−22.2921	−	22.2921i	−1.13907	−	1.13907i	−0.988616	−	0.150458i	$-0.951925\pi$
$383$	−22.2921	−	22.2921i	−1.13907	−	1.13907i	−0.150458	−	0.988616i	$-0.548075\pi$
$384$	8.89059	−	6.99695i	0.453696	−	0.357062i
$385$	−28.6834	+	11.7878i	−1.46184	+	0.600759i
$386$	3.05431	−	1.40762i	0.155460	−	0.0716461i
$387$		−	5.16088i		−	0.262342i
$388$	2.65472	+	33.8328i	0.134773	+	1.71760i
$389$	17.1132	−	17.1132i	0.867671	−	0.867671i	−0.124543	−	0.992214i	$-0.539746\pi$
$389$	17.1132	−	17.1132i	0.867671	−	0.867671i	0.992214	+	0.124543i	$0.0397465\pi$
$390$	−0.705769	−	19.3952i	−0.0357380	−	0.982113i
$391$	−13.7599			−0.695867
$392$	4.08281	−	2.28460i	0.206213	−	0.115390i
$393$	−3.53632	−	3.53632i	−0.178384	−	0.178384i
$394$	4.23597	−	11.4780i	0.213405	−	0.578251i
$395$	−15.9794	+	6.56689i	−0.804009	+	0.330416i
$396$	9.39979	−	0.737562i	0.472357	−	0.0370639i
$397$	16.2806			0.817099			0.408549	−	0.912736i	$-0.366035\pi$
$397$	16.2806			0.817099			0.408549	+	0.912736i	$0.366035\pi$
$398$	−10.9324	+	29.6229i	−0.547992	+	1.48486i
$399$	−3.47105			−0.173770
$400$	16.1092	+	11.8530i	0.805459	+	0.592652i
$401$	5.13860			0.256609			0.128305	−	0.991735i	$-0.459046\pi$
$401$	5.13860			0.256609			0.128305	+	0.991735i	$0.459046\pi$
$402$	−0.433599	+	1.17490i	−0.0216260	+	0.0585986i
$403$	−16.0983			−0.801914
$404$	−1.48103	−	18.8749i	−0.0736842	−	0.939062i
$405$	2.06823	−	0.849960i	0.102771	−	0.0422349i
$406$	1.17372	−	3.18036i	0.0582507	−	0.157839i
$407$	6.91074	+	6.91074i	0.342553	+	0.342553i
$408$	−2.53445	+	8.97441i	−0.125474	+	0.444300i
$409$	−3.88999			−0.192348			−0.0961738	−	0.995365i	$-0.530660\pi$
$409$	−3.88999			−0.192348			−0.0961738	+	0.995365i	$0.530660\pi$
$410$	−1.25199	−	34.4059i	−0.0618315	−	1.69918i
$411$	7.54548	−	7.54548i	0.372191	−	0.372191i
$412$	−37.8529	+	2.97016i	−1.86488	+	0.146329i
$413$		−	9.67703i		−	0.476176i
$414$	−5.36024	+	2.47034i	−0.263441	+	0.121411i
$415$	−17.9463	+	7.37522i	−0.880949	+	0.362035i
$416$	34.0470	+	6.79313i	1.66929	+	0.333061i
$417$	−2.84263	−	2.84263i	−0.139204	−	0.139204i
$418$	−2.72362	+	7.38004i	−0.133217	+	0.360969i
$419$	−9.68913	+	9.68913i	−0.473345	+	0.473345i	−0.902995	−	0.429650i	$-0.858637\pi$
$419$	−9.68913	+	9.68913i	−0.473345	+	0.473345i	0.429650	+	0.902995i	$0.358637\pi$
$420$	−5.93737	−	11.7401i	−0.289714	−	0.572858i
$421$	−19.2867	−	19.2867i	−0.939978	−	0.939978i	0.0583197	−	0.998298i	$-0.481426\pi$
$421$	−19.2867	−	19.2867i	−0.939978	−	0.939978i	−0.998298	+	0.0583197i	$0.981426\pi$
$422$	−4.41668	−	9.58348i	−0.215001	−	0.466516i
$423$	−8.65772	+	8.65772i	−0.420953	+	0.420953i
$424$	2.18900	+	3.91198i	0.106307	+	0.189982i
$425$	−16.4849	−	0.0916501i	−0.799636	−	0.00444568i
$426$	−3.40810	−	1.25777i	−0.165123	−	0.0609391i
$427$	30.0582			1.45462
$428$	−16.6597	−	14.2355i	−0.805279	−	0.688100i
$429$	20.4591	+	20.4591i	0.987776	+	0.987776i
$430$	0.593480	+	16.3094i	0.0286201	+	0.786507i
$431$		−	4.13031i		−	0.198950i	−0.995040	−	0.0994751i	$-0.968284\pi$
$431$		−	4.13031i		−	0.198950i	0.995040	−	0.0994751i	$-0.0317164\pi$
$432$	0.623885	+	3.95105i	0.0300167	+	0.190095i
$433$	13.3312	−	13.3312i	0.640655	−	0.640655i	−0.310062	−	0.950716i	$-0.600350\pi$
$433$	13.3312	−	13.3312i	0.640655	−	0.640655i	0.950716	+	0.310062i	$0.100350\pi$
$434$	−9.91067	+	4.56747i	−0.475728	+	0.219246i
$435$	−1.68142	−	0.701948i	−0.0806178	−	0.0336558i
$436$	0.142475	+	1.81576i	0.00682331	+	0.0869591i
$437$		−	4.92426i		−	0.235559i
$438$	−6.15301	−	13.3510i	−0.294002	−	0.637937i
$439$			22.0770i			1.05368i	0.849965	+	0.526839i	$0.176623\pi$
$439$			22.0770i			1.05368i	−0.849965	+	0.526839i	$0.823377\pi$
$440$	−29.6203	+	3.41177i	−1.41209	+	0.162650i
$441$			1.65411i			0.0787673i
$442$	−25.9895	+	11.9776i	−1.23619	+	0.569717i
$443$		−	8.44869i		−	0.401409i	−0.979652	−	0.200705i	$-0.935677\pi$
$443$		−	8.44869i		−	0.401409i	0.979652	−	0.200705i	$-0.0643231\pi$
$444$	−2.69347	+	3.15215i	−0.127826	+	0.149594i
$445$	−18.0058	+	7.39967i	−0.853556	+	0.350778i
$446$	−11.5690	−	25.1028i	−0.547807	−	1.18865i
$447$	3.20287	−	3.20287i	0.151491	−	0.151491i
$448$	22.8879	−	5.47787i	1.08135	−	0.258805i
$449$			12.3249i			0.581648i	0.956777	+	0.290824i	$0.0939293\pi$
$449$			12.3249i			0.581648i	−0.956777	+	0.290824i	$0.906071\pi$
$450$	−6.43824	+	2.92387i	−0.303502	+	0.137833i
$451$	36.2932	+	36.2932i	1.70898	+	1.70898i
$452$	25.9297	−	2.03459i	1.21963	−	0.0956992i
$453$	8.82773			0.414763
$454$	−0.814200	+	2.20619i	−0.0382123	+	0.103542i
$455$	15.5532	−	37.2555i	0.729146	−	1.74657i
$456$	−3.21168	−	0.907007i	−0.150401	−	0.0424745i
$457$	10.5838	−	10.5838i	0.495089	−	0.495089i	−0.414816	−	0.909905i	$-0.636154\pi$
$457$	10.5838	−	10.5838i	0.495089	−	0.495089i	0.909905	+	0.414816i	$0.136154\pi$
$458$	−20.6603	+	9.52161i	−0.965394	+	0.444916i
$459$	−2.33136	−	2.33136i	−0.108818	−	0.108818i
$460$	16.6553	−	8.42314i	0.776556	−	0.392731i
$461$	−6.77081	+	6.77081i	−0.315348	+	0.315348i	−0.846977	−	0.531629i	$-0.821580\pi$
$461$	−6.77081	+	6.77081i	−0.315348	+	0.315348i	0.531629	+	0.846977i	$0.321580\pi$
$462$	18.4001	+	6.79060i	0.856050	+	0.315927i
$463$	−11.3573	−	11.3573i	−0.527819	−	0.527819i	0.392103	−	0.919921i	$-0.371748\pi$
$463$	−11.3573	−	11.3573i	−0.527819	−	0.527819i	−0.919921	+	0.392103i	$0.871748\pi$
$464$	1.91706	−	2.63601i	0.0889973	−	0.122374i
$465$	2.22945	+	5.42497i	0.103388	+	0.251577i
$466$	−7.86023	−	17.0554i	−0.364118	−	0.790077i
$467$			3.11578i			0.144181i	0.997398	+	0.0720906i	$0.0229671\pi$
$467$			3.11578i			0.144181i	−0.997398	+	0.0720906i	$0.977033\pi$
$468$	−7.97397	+	9.33189i	−0.368597	+	0.431367i
$469$	−1.84208	+	1.84208i	−0.0850594	+	0.0850594i
$470$	26.3644	−	28.3556i	1.21610	−	1.30795i
$471$	15.5186			0.715058
$472$	2.52867	−	8.95392i	0.116391	−	0.412138i
$473$	−17.2040	−	17.2040i	−0.791042	−	0.791042i
$474$	10.2506	+	3.78301i	0.470825	+	0.173759i
$475$	0.0327989	−	5.89947i	0.00150492	−	0.270686i
$476$	−12.6017	+	14.7477i	−0.577597	+	0.675958i
$477$	−1.58490			−0.0725676
$478$	−11.7936	−	4.35247i	−0.539428	−	0.199077i
$479$	−15.3508			−0.701396			−0.350698	−	0.936489i	$-0.614056\pi$
$479$	−15.3508			−0.701396			−0.350698	+	0.936489i	$0.614056\pi$
$480$	−2.42595	−	12.4143i	−0.110729	−	0.566633i
$481$	−12.7233			−0.580132
$482$	−27.3281	−	10.0855i	−1.24476	−	0.459382i
$483$	−12.2773			−0.558636
$484$	14.5841	−	17.0677i	0.662915	−	0.775805i
$485$	35.0138	+	14.6174i	1.58990	+	0.663740i
$486$	−1.32675	−	0.489639i	−0.0601824	−	0.0222105i
$487$	8.51351	+	8.51351i	0.385784	+	0.385784i	0.873181	−	0.487397i	$-0.162053\pi$
$487$	8.51351	+	8.51351i	0.385784	+	0.385784i	−0.487397	+	0.873181i	$0.662053\pi$
$488$	27.8122	+	7.85440i	1.25900	+	0.355552i
$489$	8.65221			0.391267
$490$	−0.190216	−	5.22731i	−0.00859309	−	0.236146i
$491$	−6.16348	+	6.16348i	−0.278154	+	0.278154i	−0.832372	−	0.554218i	$-0.813017\pi$
$491$	−6.16348	+	6.16348i	−0.278154	+	0.278154i	0.554218	+	0.832372i	$0.313017\pi$
$492$	−14.1453	+	16.5542i	−0.637721	+	0.746321i
$493$			2.68659i			0.120998i
$494$	−4.28644	−	9.30087i	−0.192856	−	0.418466i
$495$	4.06115	−	9.72791i	0.182535	−	0.437237i
$496$	−10.3636	+	1.63645i	−0.465340	+	0.0734789i
$497$	−5.34345	−	5.34345i	−0.239686	−	0.239686i
$498$	11.5124	+	4.24867i	0.515881	+	0.190387i
$499$	−16.1961	+	16.1961i	−0.725037	+	0.725037i	−0.969627	−	0.244589i	$-0.921347\pi$
$499$	−16.1961	+	16.1961i	−0.725037	+	0.725037i	0.244589	+	0.969627i	$0.421347\pi$
$500$	20.0098	−	9.98034i	0.894866	−	0.446335i
$501$	2.86613	+	2.86613i	0.128049	+	0.128049i
$502$	−30.5979	+	14.1015i	−1.36565	+	0.629379i
$503$	8.39462	−	8.39462i	0.374298	−	0.374298i	−0.494742	−	0.869040i	$-0.664737\pi$
$503$	8.39462	−	8.39462i	0.374298	−	0.374298i	0.869040	+	0.494742i	$0.164737\pi$
$504$	−2.26137	+	8.00744i	−0.100730	+	0.356680i
$505$	−19.5338	−	8.15485i	−0.869242	−	0.362886i
$506$	−9.63359	+	26.1036i	−0.428265	+	1.16044i
$507$	−24.6671			−1.09550
$508$	13.5550	−	1.06361i	0.601408	−	0.0471899i
$509$	5.50555	+	5.50555i	0.244029	+	0.244029i	0.818515	−	0.574486i	$-0.194798\pi$
$509$	5.50555	+	5.50555i	0.244029	+	0.244029i	−0.574486	+	0.818515i	$0.694798\pi$
$510$	7.63562	+	7.09942i	0.338111	+	0.314368i
$511$		−	30.5797i		−	1.35277i
$512$	22.6090	+	0.912208i	0.999187	+	0.0403143i
$513$	0.834324	−	0.834324i	0.0368363	−	0.0368363i
$514$	11.8451	+	25.7018i	0.522463	+	1.13366i
$515$	−16.3542	+	39.1742i	−0.720653	+	1.72622i
$516$	6.70529	−	7.84716i	0.295184	−	0.345452i
$517$			57.7217i			2.53860i
$518$	−7.83290	+	3.60990i	−0.344158	+	0.158610i
$519$		−	15.1143i		−	0.663442i
$520$	24.1261	−	30.4075i	1.05800	−	1.33346i
$521$			39.2289i			1.71865i	0.511430	+	0.859325i	$0.329116\pi$
$521$			39.2289i			1.71865i	−0.511430	+	0.859325i	$0.670884\pi$
$522$	0.482328	+	1.04657i	0.0211109	+	0.0458073i
$523$		−	16.7434i		−	0.732137i	−0.930588	−	0.366068i	$-0.880704\pi$
$523$		−	16.7434i		−	0.732137i	0.930588	−	0.366068i	$-0.119296\pi$
$524$	−0.782428	−	9.97158i	−0.0341805	−	0.435611i
$525$	−14.7087	−	0.0817750i	−0.641941	−	0.00356895i
$526$	−20.1989	+	9.30894i	−0.880713	+	0.405889i
$527$	6.11516	−	6.11516i	0.266381	−	0.266381i
$528$	15.2507	+	11.0912i	0.663703	+	0.482684i
$529$			5.58265i			0.242724i
$530$	5.00858	−	0.182257i	0.217559	−	0.00791673i
$531$	2.32603	+	2.32603i	0.100941	+	0.100941i
$532$	−5.27776	−	4.50977i	−0.228820	−	0.195524i
$533$	−66.8191			−2.89426
$534$	11.5505	+	4.26275i	0.499839	+	0.184467i
$535$	−22.6610	+	9.31276i	−0.979719	+	0.402626i
$536$	−2.18578	+	1.22309i	−0.0944113	+	0.0528293i
$537$	−12.3666	+	12.3666i	−0.533659	+	0.533659i
$538$	8.61398	+	18.6909i	0.371375	+	0.805823i
$539$	5.51406	+	5.51406i	0.237507	+	0.237507i
$540$	4.24907	+	1.39478i	0.182851	+	0.0600218i
$541$	3.45427	−	3.45427i	0.148511	−	0.148511i	−0.628942	−	0.777452i	$-0.716512\pi$
$541$	3.45427	−	3.45427i	0.148511	−	0.148511i	0.777452	+	0.628942i	$0.216512\pi$
$542$	−10.4452	+	28.3028i	−0.448660	+	1.21571i
$543$	−9.58991	−	9.58991i	−0.411543	−	0.411543i
$544$	−15.5137	+	10.3528i	−0.665144	+	0.443871i
$545$	1.87914	+	0.784493i	0.0804936	+	0.0336040i
$546$	−23.1892	+	10.6871i	−0.992405	+	0.457364i
$547$		−	18.1175i		−	0.774647i	−0.921944	−	0.387324i	$-0.873400\pi$
$547$		−	18.1175i		−	0.774647i	0.921944	−	0.387324i	$-0.126600\pi$
$548$	21.2764	−	1.66947i	0.908885	−	0.0713163i
$549$	−7.22499	+	7.22499i	−0.308355	+	0.308355i
$550$	−11.7153	+	31.2090i	−0.499543	+	1.33076i
$551$	−0.961451			−0.0409592
$552$	−11.3599	−	3.20813i	−0.483508	−	0.136547i
$553$	16.0715	+	16.0715i	0.683431	+	0.683431i
$554$	9.30514	−	25.2136i	0.395337	−	1.07122i
$555$	1.76205	+	4.28763i	0.0747947	+	0.182000i
$556$	−0.628946	−	8.01554i	−0.0266732	−	0.339935i
$557$	21.1776			0.897324			0.448662	−	0.893701i	$-0.351901\pi$
$557$	21.1776			0.897324			0.448662	+	0.893701i	$0.351901\pi$
$558$	1.28433	−	3.48006i	0.0543698	−	0.147323i
$559$	31.6742			1.33967
$560$	6.22554	−	25.5651i	0.263077	−	1.08032i
$561$	−15.5434			−0.656241
$562$	−1.89156	+	5.12544i	−0.0797905	+	0.216204i
$563$	44.5712			1.87845			0.939226	−	0.343298i	$-0.111544\pi$
$563$	44.5712			1.87845			0.939226	+	0.343298i	$0.111544\pi$
$564$	−24.4127	+	1.91556i	−1.02796	+	0.0806596i
$565$	11.2028	−	26.8348i	0.471307	−	1.12895i
$566$	2.88471	−	7.81653i	0.121253	−	0.328553i
$567$	−2.08016	−	2.08016i	−0.0873584	−	0.0873584i
$568$	−3.54788	−	6.34044i	−0.148866	−	0.266039i
$569$	−5.14194			−0.215562			−0.107781	−	0.994175i	$-0.534374\pi$
$569$	−5.14194			−0.215562			−0.107781	+	0.994175i	$0.534374\pi$
$570$	−2.54068	+	2.73256i	−0.106417	+	0.114454i
$571$	−17.4873	+	17.4873i	−0.731820	+	0.731820i	−0.970980	−	0.239160i	$-0.923128\pi$
$571$	−17.4873	+	17.4873i	−0.731820	+	0.731820i	0.239160	+	0.970980i	$0.423128\pi$
$572$	4.52668	+	57.6898i	0.189270	+	2.41213i
$573$			14.5044i			0.605929i
$574$	−41.1362	+	18.9582i	−1.71699	+	0.791299i
$575$	0.116011	−	20.8667i	0.00483801	−	0.870203i
$576$	−4.18479	+	6.81818i	−0.174366	+	0.284091i
$577$	−2.82131	−	2.82131i	−0.117453	−	0.117453i	0.645938	−	0.763390i	$-0.276467\pi$
$577$	−2.82131	−	2.82131i	−0.117453	−	0.117453i	−0.763390	+	0.645938i	$0.776467\pi$
$578$	−3.00127	+	8.13236i	−0.124836	+	0.338261i
$579$	−1.68153	+	1.68153i	−0.0698822	+	0.0698822i
$580$	−1.64460	−	3.25190i	−0.0682883	−	0.135028i
$581$	18.0498	+	18.0498i	0.748833	+	0.748833i
$582$	−10.0440	−	21.7939i	−0.416338	−	0.903385i
$583$	−5.28334	+	5.28334i	−0.218813	+	0.218813i
$584$	7.99066	−	28.2946i	0.330656	−	1.17084i
$585$	5.21651	+	12.6934i	0.215676	+	0.524809i
$586$	5.95884	+	2.19913i	0.246158	+	0.0908451i
$587$	−45.9941			−1.89838			−0.949191	−	0.314702i	$-0.898095\pi$
$587$	−45.9941			−1.89838			−0.949191	+	0.314702i	$0.898095\pi$
$588$	−2.14911	+	2.51509i	−0.0886279	+	0.103721i
$589$	2.18844	+	2.18844i	0.0901729	+	0.0901729i
$590$	−7.61818	−	7.08321i	−0.313636	−	0.291611i
$591$			8.65121i			0.355863i
$592$	−8.19088	+	1.29337i	−0.336643	+	0.0531572i
$593$	−7.77054	+	7.77054i	−0.319098	+	0.319098i	−0.848421	−	0.529323i	$-0.822446\pi$
$593$	−7.77054	+	7.77054i	−0.319098	+	0.319098i	0.529323	+	0.848421i	$0.322446\pi$
$594$	−6.05500	+	2.79053i	−0.248439	+	0.114497i
$595$	8.24392	+	20.0601i	0.337968	+	0.822385i
$596$	9.03132	−	0.708650i	0.369937	−	0.0290274i
$597$		−	22.3275i		−	0.913804i
$598$	−15.1613	−	32.8977i	−0.619994	−	1.34529i
$599$		−	16.1877i		−	0.661413i	−0.943734	−	0.330707i	$-0.892713\pi$
$599$		−	16.1877i		−	0.661413i	0.943734	−	0.330707i	$-0.107287\pi$
$600$	−13.5882	−	3.91914i	−0.554738	−	0.159998i
$601$			14.1986i			0.579174i	0.957152	+	0.289587i	$0.0935180\pi$
$601$			14.1986i			0.579174i	−0.957152	+	0.289587i	$0.906482\pi$
$602$	19.4997	−	8.98672i	0.794749	−	0.366271i
$603$		−	0.885549i		−	0.0360623i
$604$	13.4226	+	11.4694i	0.546159	+	0.466685i
$605$	−9.54082	−	23.2159i	−0.387889	−	0.943860i
$606$	5.60343	+	12.1585i	0.227624	+	0.493906i
$607$	22.9646	−	22.9646i	0.932105	−	0.932105i	−0.0657320	−	0.997837i	$-0.520938\pi$
$607$	22.9646	−	22.9646i	0.932105	−	0.932105i	0.997837	+	0.0657320i	$0.0209383\pi$
$608$	−3.70495	−	5.55190i	−0.150256	−	0.225159i
$609$			2.39711i			0.0971359i
$610$	22.0015	−	23.6632i	0.890813	−	0.958093i
$611$	−53.1355	−	53.1355i	−2.14963	−	2.14963i
$612$	−0.515823	−	6.57387i	−0.0208509	−	0.265733i
$613$	37.1155			1.49908			0.749541	−	0.661958i	$-0.230274\pi$
$613$	37.1155			1.49908			0.749541	+	0.661958i	$0.230274\pi$
$614$	1.88260	−	5.10116i	0.0759754	−	0.205866i
$615$	9.25376	+	22.5174i	0.373148	+	0.907989i
$616$	19.1548	+	34.2315i	0.771767	+	1.37923i
$617$	−1.45005	+	1.45005i	−0.0583767	+	0.0583767i	−0.735692	−	0.677316i	$-0.763143\pi$
$617$	−1.45005	+	1.45005i	−0.0583767	+	0.0583767i	0.677316	+	0.735692i	$0.263143\pi$
$618$	24.3834	−	11.2375i	0.980846	−	0.452037i
$619$	13.2111	+	13.2111i	0.530998	+	0.530998i	0.920869	−	0.389872i	$-0.127481\pi$
$619$	13.2111	+	13.2111i	0.530998	+	0.530998i	−0.389872	+	0.920869i	$0.627481\pi$
$620$	−3.65852	+	11.1453i	−0.146930	+	0.447607i
$621$	2.95105	−	2.95105i	0.118421	−	0.118421i
$622$	5.40122	+	1.99333i	0.216569	+	0.0799254i
$623$	18.1096	+	18.1096i	0.725548	+	0.725548i
$624$	−24.2490	+	3.82900i	−0.970735	+	0.153283i
$625$	0.277973	−	24.9985i	0.0111189	−	0.999938i
$626$	1.15456	+	2.50520i	0.0461454	+	0.100128i
$627$		−	5.56251i		−	0.222145i
$628$	23.5961	+	20.1625i	0.941587	+	0.804573i
$629$	4.83312	−	4.83312i	0.192709	−	0.192709i
$630$	6.81290	+	6.33448i	0.271432	+	0.252372i
$631$	11.6636			0.464322			0.232161	−	0.972677i	$-0.425420\pi$
$631$	11.6636			0.464322			0.232161	+	0.972677i	$0.425420\pi$
$632$	10.6710	+	19.0702i	0.424470	+	0.758572i
$633$	5.27613	+	5.27613i	0.209707	+	0.209707i
$634$	−13.0143	−	4.80294i	−0.516862	−	0.190749i
$635$	5.85641	−	14.0282i	0.232405	−	0.556692i
$636$	−2.40985	−	2.05919i	−0.0955569	−	0.0816521i
$637$	−10.1519			−0.402232
$638$	5.09666	+	1.88094i	0.201779	+	0.0744670i
$639$	2.56877			0.101619
$640$	12.4406	−	22.0279i	0.491760	−	0.870731i
$641$	−20.8880			−0.825025			−0.412512	−	0.910952i	$-0.635349\pi$
$641$	−20.8880			−0.825025			−0.412512	+	0.910952i	$0.635349\pi$
$642$	14.5368	+	5.36483i	0.573720	+	0.211733i
$643$	−36.6130			−1.44388			−0.721939	−	0.691957i	$-0.756749\pi$
$643$	−36.6130			−1.44388			−0.721939	+	0.691957i	$0.756749\pi$
$644$	−18.6677	−	15.9513i	−0.735611	−	0.628569i
$645$	−4.38655	−	10.6739i	−0.172720	−	0.420284i
$646$	5.16132	+	1.90480i	0.203070	+	0.0749434i
$647$	23.8735	+	23.8735i	0.938562	+	0.938562i	0.998219	−	0.0596566i	$-0.0190006\pi$
$647$	23.8735	+	23.8735i	0.938562	+	0.938562i	−0.0596566	+	0.998219i	$0.519001\pi$
$648$	−1.38116	−	2.46828i	−0.0542571	−	0.0969631i
$649$	15.5079			0.608737
$650$	−17.9448	−	39.5138i	−0.703854	−	1.54986i
$651$	5.45626	−	5.45626i	0.213848	−	0.213848i
$652$	13.1558	+	11.2414i	0.515219	+	0.440248i
$653$			22.3501i			0.874627i	0.899309	+	0.437313i	$0.144070\pi$
$653$			22.3501i			0.874627i	−0.899309	+	0.437313i	$0.855930\pi$
$654$	−0.539047	−	1.16964i	−0.0210784	−	0.0457367i
$655$	−10.3197	−	4.30819i	−0.403222	−	0.168335i
$656$	−43.0162	+	6.79241i	−1.67950	+	0.265199i
$657$	7.35033	+	7.35033i	0.286764	+	0.286764i
$658$	−47.7878	−	17.6362i	−1.86296	−	0.687532i
$659$	15.9700	−	15.9700i	0.622102	−	0.622102i	−0.323967	−	0.946068i	$-0.605017\pi$
$659$	15.9700	−	15.9700i	0.622102	−	0.622102i	0.946068	+	0.323967i	$0.105017\pi$
$660$	18.8140	−	9.51489i	0.732334	−	0.370367i
$661$	−15.1592	−	15.1592i	−0.589624	−	0.589624i	0.347906	−	0.937530i	$-0.386893\pi$
$661$	−15.1592	−	15.1592i	−0.589624	−	0.589624i	−0.937530	+	0.347906i	$0.886893\pi$
$662$	13.0277	−	6.00402i	0.506338	−	0.233353i
$663$	14.3084	−	14.3084i	0.555691	−	0.555691i
$664$	11.9845	+	21.4176i	0.465090	+	0.831164i
$665$	−7.17893	+	2.95026i	−0.278387	+	0.114406i
$666$	1.01507	−	2.75047i	0.0393330	−	0.106578i
$667$	−3.40070			−0.131676
$668$	0.634144	+	8.08179i	0.0245358	+	0.312694i
$669$	13.8202	+	13.8202i	0.534320	+	0.534320i
$670$	0.101834	+	2.79850i	0.00393420	+	0.108115i
$671$			48.1696i			1.85957i
$672$	−13.8421	+	9.23728i	−0.533971	+	0.356336i
$673$	15.2524	−	15.2524i	0.587938	−	0.587938i	−0.349134	−	0.937073i	$-0.613524\pi$
$673$	15.2524	−	15.2524i	0.587938	−	0.587938i	0.937073	+	0.349134i	$0.113524\pi$
$674$	21.2280	+	46.0612i	0.817670	+	1.77421i
$675$	3.55514	−	3.51582i	0.136837	−	0.135324i
$676$	−37.5065	−	32.0488i	−1.44256	−	1.23265i
$677$		−	3.95511i		−	0.152007i	−0.997108	−	0.0760036i	$-0.975784\pi$
$677$		−	3.95511i		−	0.152007i	0.997108	−	0.0760036i	$-0.0242161\pi$
$678$	−16.7029	+	7.69779i	−0.641473	+	0.295632i
$679$		−	49.9175i		−	1.91566i
$680$	2.38606	+	20.7153i	0.0915014	+	0.794396i
$681$		−	1.66286i		−	0.0637209i
$682$	−7.31957	−	15.8823i	−0.280281	−	0.608164i
$683$		−	50.9345i		−	1.94895i	−0.224490	−	0.974476i	$-0.572072\pi$
$683$		−	50.9345i		−	1.94895i	0.224490	−	0.974476i	$-0.427928\pi$
$684$	2.35259	−	0.184598i	0.0899537	−	0.00705828i
$685$	9.19242	−	22.0191i	0.351224	−	0.841308i
$686$	20.1987	−	9.30886i	0.771191	−	0.355414i
$687$	11.3744	−	11.3744i	0.433962	−	0.433962i
$688$	20.3909	−	3.21980i	0.777395	−	0.122754i
$689$		−	9.72710i		−	0.370573i
$690$	−8.98650	+	9.66521i	−0.342110	+	0.367948i
$691$	−13.5869	−	13.5869i	−0.516870	−	0.516870i	0.399753	−	0.916623i	$-0.369096\pi$
$691$	−13.5869	−	13.5869i	−0.516870	−	0.516870i	−0.916623	+	0.399753i	$0.869096\pi$
$692$	19.6372	−	22.9813i	0.746496	−	0.873619i
$693$	−13.8686			−0.526824
$694$	11.6826	+	4.31151i	0.443467	+	0.163663i
$695$	−8.29534	−	3.46309i	−0.314660	−	0.131362i
$696$	−0.626380	+	2.21799i	−0.0237429	+	0.0840727i
$697$	25.3822	−	25.3822i	0.961418	−	0.961418i
$698$	12.3984	+	26.9025i	0.469286	+	1.01827i
$699$	9.38976	+	9.38976i	0.355153	+	0.355153i
$700$	−22.2585	−	19.2347i	−0.841291	−	0.727002i
$701$	−0.627254	+	0.627254i	−0.0236911	+	0.0236911i	−0.718853	−	0.695162i	$-0.755333\pi$
$701$	−0.627254	+	0.627254i	−0.0236911	+	0.0236911i	0.695162	+	0.718853i	$0.255333\pi$
$702$	3.00509	−	8.14270i	0.113420	−	0.307327i
$703$	1.72963	+	1.72963i	0.0652343	+	0.0652343i
$704$	8.77853	+	36.6789i	0.330853	+	1.38239i
$705$	−10.5474	+	25.2649i	−0.397239	+	0.951529i
$706$	38.7301	−	17.8493i	1.45763	−	0.671768i
$707$			27.8483i			1.04734i
$708$	0.514646	+	6.55886i	0.0193416	+	0.246497i
$709$	26.7170	−	26.7170i	1.00338	−	1.00338i	0.00338478	−	0.999994i	$-0.498923\pi$
$709$	26.7170	−	26.7170i	1.00338	−	1.00338i	0.999994	−	0.00338478i	$-0.00107741\pi$
$710$	−8.11779	+	0.295398i	−0.304655	+	0.0110861i
$711$	−7.72612			−0.289752
$712$	12.0243	+	21.4886i	0.450628	+	0.805318i
$713$	7.74061	+	7.74061i	0.289888	+	0.289888i
$714$	4.74910	−	12.8683i	0.177730	−	0.481586i
$715$	59.7036	+	24.9247i	2.23279	+	0.932131i
$716$	−34.8709	+	2.73617i	−1.30319	+	0.102256i
$717$	8.88914			0.331971
$718$	4.59760	−	12.4578i	0.171581	−	0.464922i
$719$	−27.5794			−1.02854			−0.514269	−	0.857629i	$-0.671937\pi$
$719$	−27.5794			−1.02854			−0.514269	+	0.857629i	$0.671937\pi$
$720$	4.64857	+	7.64139i	0.173242	+	0.284778i
$721$	55.8488			2.07992
$722$	8.62147	−	23.3611i	0.320858	−	0.869409i
$723$	20.5978			0.766041
$724$	−2.12181	−	27.0413i	−0.0788565	−	1.00498i
$725$	−4.07418	−	0.0226510i	−0.151311	−	0.000841235i
$726$	−5.49621	+	14.8927i	−0.203983	+	0.552721i
$727$	8.11985	+	8.11985i	0.301148	+	0.301148i	0.841463	−	0.540315i	$-0.181695\pi$
$727$	8.11985	+	8.11985i	0.301148	+	0.301148i	−0.540315	+	0.841463i	$0.681695\pi$
$728$	−49.1445	−	13.8788i	−1.82142	−	0.514384i
$729$	1.00000			0.0370370
$730$	−24.0737	−	22.3831i	−0.891006	−	0.828437i
$731$	−12.0319	+	12.0319i	−0.445014	+	0.445014i
$732$	−20.3727	+	1.59856i	−0.752998	+	0.0590845i
$733$		−	12.3271i		−	0.455313i	−0.973742	−	0.227656i	$-0.926894\pi$
$733$		−	12.3271i		−	0.455313i	0.973742	−	0.227656i	$-0.0731063\pi$
$734$	0.235503	−	0.108535i	0.00869256	−	0.00400609i
$735$	1.40593	+	3.42109i	0.0518586	+	0.126189i
$736$	−13.1046	−	19.6373i	−0.483042	−	0.723842i
$737$	−2.95201	−	2.95201i	−0.108739	−	0.108739i
$738$	5.33084	−	14.4447i	0.196231	−	0.531715i
$739$	24.8212	−	24.8212i	0.913062	−	0.913062i	−0.0834496	−	0.996512i	$-0.526594\pi$
$739$	24.8212	−	24.8212i	0.913062	−	0.913062i	0.996512	+	0.0834496i	$0.0265938\pi$
$740$	−2.89151	+	8.80871i	−0.106294	+	0.323815i
$741$	5.12054	+	5.12054i	0.188108	+	0.188108i
$742$	−2.75981	−	5.98834i	−0.101316	−	0.219839i
$743$	−26.8731	+	26.8731i	−0.985877	+	0.985877i	−0.999902	−	0.0140246i	$-0.995536\pi$
$743$	−26.8731	+	26.8731i	−0.985877	+	0.985877i	0.0140246	+	0.999902i	$0.495536\pi$
$744$	6.47430	−	3.62279i	0.237359	−	0.132818i
$745$	3.90195	−	9.34658i	0.142957	−	0.342432i
$746$	3.79180	+	1.39937i	0.138828	+	0.0512347i
$747$	−8.67714			−0.317480
$748$	−23.6338	−	20.1947i	−0.864137	−	0.738393i
$749$	22.7917	+	22.7917i	0.832789	+	0.832789i
$750$	−10.8306	+	11.5195i	−0.395477	+	0.420632i
$751$			24.7594i			0.903484i	0.892149	+	0.451742i	$0.149197\pi$
$751$			24.7594i			0.903484i	−0.892149	+	0.451742i	$0.850803\pi$
$752$	−39.6085	−	28.8056i	−1.44437	−	1.05043i
$753$	16.8455	−	16.8455i	0.613883	−	0.613883i
$754$	−6.42319	+	2.96022i	−0.233919	+	0.107805i
$755$	18.2578	−	7.50322i	0.664468	−	0.273070i
$756$	−0.460244	−	5.86555i	−0.0167389	−	0.213328i
$757$		−	35.5014i		−	1.29032i	−0.764047	−	0.645160i	$-0.776791\pi$
$757$		−	35.5014i		−	1.29032i	0.764047	−	0.645160i	$-0.223209\pi$
$758$	12.3971	+	26.8997i	0.450284	+	0.977042i
$759$		−	19.6749i		−	0.714153i
$760$	−7.41341	+	0.853903i	−0.268913	+	0.0309743i
$761$			19.8569i			0.719812i	0.932989	+	0.359906i	$0.117191\pi$
$761$			19.8569i			0.719812i	−0.932989	+	0.359906i	$0.882809\pi$
$762$	−8.73165	+	4.02411i	−0.316314	+	0.145778i
$763$		−	2.67900i		−	0.0969862i
$764$	−18.8448	+	22.0540i	−0.681782	+	0.797886i
$765$	−6.80334	−	2.84022i	−0.245975	−	0.102688i
$766$	18.6609	+	40.4911i	0.674245	+	1.46300i
$767$	−14.2757	+	14.2757i	−0.515465	+	0.515465i
$768$	−15.2215	+	4.93000i	−0.549260	+	0.177896i
$769$			37.1951i			1.34129i	0.741779	+	0.670644i	$0.233982\pi$
$769$			37.1951i			1.34129i	−0.741779	+	0.670644i	$0.766018\pi$
$770$	43.8273	−	1.59483i	1.57943	−	0.0574736i
$771$	−14.1500	−	14.1500i	−0.509600	−	0.509600i
$772$	−4.74152	+	0.372047i	−0.170651	+	0.0133903i
$773$	13.2454			0.476402			0.238201	−	0.971216i	$-0.423442\pi$
$773$	13.2454			0.476402			0.238201	+	0.971216i	$0.423442\pi$
$774$	−2.52697	+	6.84718i	−0.0908301	+	0.246117i
$775$	9.22202	+	9.32514i	0.331265	+	0.334969i
$776$	13.0437	−	46.1874i	0.468243	−	1.65803i
$777$	4.31236	−	4.31236i	0.154705	−	0.154705i
$778$	−31.0841	+	14.3255i	−1.11442	+	0.513595i
$779$	9.08353	+	9.08353i	0.325451	+	0.325451i
$780$	−8.56026	+	26.0780i	−0.306506	+	0.933743i
$781$	8.56310	−	8.56310i	0.306412	−	0.306412i
$782$	18.2559	+	6.73738i	0.652828	+	0.240928i
$783$	−0.576185	−	0.576185i	−0.0205912	−	0.0205912i
$784$	−6.53548	+	1.03198i	−0.233410	+	0.0368563i
$785$	32.0959	−	13.1902i	1.14555	−	0.470777i
$786$	2.96028	+	6.42332i	0.105590	+	0.229112i
$787$		−	12.0292i		−	0.428794i	−0.976747	−	0.214397i	$-0.931221\pi$
$787$		−	12.0292i		−	0.428794i	0.976747	−	0.214397i	$-0.0687786\pi$
$788$	−11.2401	+	13.1542i	−0.400412	+	0.468600i
$789$	11.1204	−	11.1204i	0.395896	−	0.395896i
$790$	24.4160	−	0.888470i	0.868681	−	0.0316104i
$791$	−38.2571			−1.36026
$792$	−12.8323	−	3.62395i	−0.455975	−	0.128771i
$793$	−44.3423	−	44.3423i	−1.57464	−	1.57464i
$794$	−21.6002	−	7.97161i	−0.766562	−	0.282902i
$795$	−3.27794	+	1.34710i	−0.116256	+	0.0477768i
$796$	29.0091	−	33.9491i	1.02820	−	1.20329i
$797$	−45.2714			−1.60359			−0.801797	−	0.597597i	$-0.796122\pi$
$797$	−45.2714			−1.60359			−0.801797	+	0.597597i	$0.796122\pi$
$798$	4.60520	+	1.69956i	0.163022	+	0.0601639i
$799$	40.3685			1.42813
$800$	−15.5691	−	23.6136i	−0.550450	−	0.834868i
$801$	−8.70590			−0.307608
$802$	−6.81762	−	2.51606i	−0.240738	−	0.0888451i
$803$	49.0053			1.72936
$804$	1.15055	−	1.34648i	0.0405768	−	0.0474868i
$805$	−25.3922	+	10.4352i	−0.894958	+	0.367793i
$806$	21.3584	+	7.88236i	0.752316	+	0.277644i
$807$	−10.2902	−	10.2902i	−0.362231	−	0.362231i
$808$	−7.27694	+	25.7674i	−0.256002	+	0.906494i
$809$	5.16391			0.181553			0.0907767	−	0.995871i	$-0.471065\pi$
$809$	5.16391			0.181553			0.0907767	+	0.995871i	$0.471065\pi$
$810$	−3.16019	+	0.114996i	−0.111038	+	0.00404054i
$811$	15.7171	−	15.7171i	0.551903	−	0.551903i	−0.375087	−	0.926990i	$-0.622387\pi$
$811$	15.7171	−	15.7171i	0.551903	−	0.551903i	0.926990	+	0.375087i	$0.122387\pi$
$812$	−3.11446	+	3.64483i	−0.109296	+	0.127908i
$813$		−	21.3325i		−	0.748163i
$814$	−5.78503	−	12.5526i	−0.202765	−	0.439967i
$815$	17.8947	−	7.35404i	0.626826	−	0.257601i
$816$	7.75680	−	10.6658i	0.271542	−	0.373378i
$817$	−4.30585	−	4.30585i	−0.150643	−	0.150643i
$818$	5.16103	+	1.90469i	0.180451	+	0.0665959i
$819$	12.7667	−	12.7667i	0.446103	−	0.446103i
$820$	−15.1854	+	46.2608i	−0.530296	+	1.61550i
$821$	−15.6816	−	15.6816i	−0.547293	−	0.547293i	0.378364	−	0.925657i	$-0.376487\pi$
$821$	−15.6816	−	15.6816i	−0.547293	−	0.547293i	−0.925657	+	0.378364i	$0.876487\pi$
$822$	−13.7055	+	6.31637i	−0.478034	+	0.220309i
$823$	−3.65203	+	3.65203i	−0.127302	+	0.127302i	−0.767887	−	0.640585i	$-0.778692\pi$
$823$	−3.65203	+	3.65203i	−0.127302	+	0.127302i	0.640585	+	0.767887i	$0.278692\pi$
$824$	51.6755	+	14.5936i	1.80020	+	0.508393i
$825$	0.131048	−	23.5713i	0.00456251	−	0.820649i
$826$	−4.73825	+	12.8390i	−0.164865	+	0.446725i
$827$	14.0926			0.490046			0.245023	−	0.969517i	$-0.421204\pi$
$827$	14.0926			0.490046			0.245023	+	0.969517i	$0.421204\pi$
$828$	8.32124	−	0.652933i	0.289183	−	0.0226910i
$829$	−12.1216	−	12.1216i	−0.421000	−	0.421000i	0.464548	−	0.885548i	$-0.346217\pi$
$829$	−12.1216	−	12.1216i	−0.421000	−	0.421000i	−0.885548	+	0.464548i	$0.846217\pi$
$830$	27.4214	−	0.997834i	0.951810	−	0.0346353i
$831$			19.0041i			0.659244i
$832$	−41.8456	−	25.6835i	−1.45073	−	0.890415i
$833$	3.85633	−	3.85633i	0.133614	−	0.133614i
$834$	2.37959	+	5.16331i	0.0823983	+	0.178791i
$835$	8.36390	+	3.49171i	0.289445	+	0.120836i
$836$	7.22711	−	8.45784i	0.249955	−	0.292520i
$837$			2.62300i			0.0906643i
$838$	17.5992	−	8.11083i	0.607954	−	0.280184i
$839$			14.6206i			0.504759i	0.967628	+	0.252380i	$0.0812132\pi$
$839$			14.6206i			0.504759i	−0.967628	+	0.252380i	$0.918787\pi$
$840$	2.12897	+	18.4833i	0.0734565	+	0.637734i
$841$		−	28.3360i		−	0.977104i
$842$	16.1451	+	35.0321i	0.556395	+	1.20729i
$843$		−	3.86317i		−	0.133054i
$844$	1.16737	+	14.8774i	0.0401825	+	0.512102i
$845$	−51.0172	+	20.9661i	−1.75504	+	0.721254i
$846$	15.7257	−	7.24743i	0.540662	−	0.249172i
$847$	−23.3498	+	23.3498i	−0.802309	+	0.802309i
$848$	−0.988796	−	6.26202i	−0.0339554	−	0.215039i
$849$			5.89151i			0.202196i
$850$	21.8264	+	8.19326i	0.748640	+	0.281026i
$851$	6.11779	+	6.11779i	0.209715	+	0.209715i
$852$	3.90583	+	3.33748i	0.133812	+	0.114340i
$853$	13.7252			0.469940			0.234970	−	0.972003i	$-0.424501\pi$
$853$	13.7252			0.469940			0.234970	+	0.972003i	$0.424501\pi$
$854$	−39.8796	−	14.7177i	−1.36465	−	0.503629i
$855$	1.01643	−	2.43472i	0.0347612	−	0.0832655i
$856$	15.1330	+	27.0442i	0.517234	+	0.924351i
$857$	18.7921	−	18.7921i	0.641927	−	0.641927i	−0.309102	−	0.951029i	$-0.600028\pi$
$857$	18.7921	−	18.7921i	0.641927	−	0.641927i	0.951029	+	0.309102i	$0.100028\pi$
$858$	−17.1265	−	37.1616i	−0.584688	−	1.26868i
$859$	23.1774	+	23.1774i	0.790803	+	0.790803i	0.981625	−	0.190822i	$-0.0611152\pi$
$859$	23.1774	+	23.1774i	0.790803	+	0.790803i	−0.190822	+	0.981625i	$0.561115\pi$
$860$	7.19830	−	21.9290i	0.245460	−	0.747771i
$861$	22.6473	−	22.6473i	0.771817	−	0.771817i
$862$	−2.02236	+	5.47988i	−0.0688820	+	0.186645i
$863$	−8.96863	−	8.96863i	−0.305296	−	0.305296i	0.537786	−	0.843082i	$-0.319261\pi$
$863$	−8.96863	−	8.96863i	−0.305296	−	0.305296i	−0.843082	+	0.537786i	$0.819261\pi$
$864$	1.10685	−	5.54751i	0.0376558	−	0.188730i
$865$	−12.8465	−	31.2597i	−0.436795	−	1.06286i
$866$	−24.2145	+	11.1596i	−0.822843	+	0.379219i
$867$		−	6.12955i		−	0.208171i
$868$	15.3854	−	1.20722i	0.522213	−	0.0409758i
$869$	−25.7553	+	25.7553i	−0.873690	+	0.873690i
$870$	1.88711	+	1.75459i	0.0639791	+	0.0594863i
$871$	5.43492			0.184155
$872$	0.700039	−	2.47881i	0.0237063	−	0.0839431i
$873$	11.9985	+	11.9985i	0.406087	+	0.406087i
$874$	−2.41111	+	6.53324i	−0.0815570	+	0.220990i
$875$	−30.4905	+	12.3327i	−1.03077	+	0.416921i
$876$	1.62629	+	20.7262i	0.0549474	+	0.700272i
$877$	−47.1944			−1.59364			−0.796822	−	0.604215i	$-0.793487\pi$
$877$	−47.1944			−1.59364			−0.796822	+	0.604215i	$0.793487\pi$
$878$	10.8098	−	29.2906i	0.364812	−	0.988510i
$879$	−4.49132			−0.151489
$880$	40.9691	+	9.97669i	1.38107	+	0.336314i
$881$	51.5667			1.73733			0.868663	−	0.495403i	$-0.164980\pi$
$881$	51.5667			1.73733			0.868663	+	0.495403i	$0.164980\pi$
$882$	0.809919	−	2.19459i	0.0272714	−	0.0738956i
$883$	−33.7083			−1.13438			−0.567188	−	0.823589i	$-0.691969\pi$
$883$	−33.7083			−1.13438			−0.567188	+	0.823589i	$0.691969\pi$
$884$	40.3461	−	3.16579i	1.35699	−	0.106477i
$885$	6.78780	+	2.83373i	0.228170	+	0.0952548i
$886$	−4.13681	+	11.2093i	−0.138979	+	0.376582i
$887$	4.91204	+	4.91204i	0.164930	+	0.164930i	0.784747	−	0.619817i	$-0.212793\pi$
$887$	4.91204	+	4.91204i	0.164930	+	0.164930i	−0.619817	+	0.784747i	$0.712793\pi$
$888$	5.11697	−	2.86327i	0.171714	−	0.0960852i
$889$	−19.9993			−0.670755
$890$	27.5123	−	1.00114i	0.922213	−	0.0335583i
$891$	3.33354	−	3.33354i	0.111678	−	0.111678i
$892$	3.05778	+	38.9696i	0.102382	+	1.30480i
$893$			14.4467i			0.483440i
$894$	−5.81764	+	2.68114i	−0.194571	+	0.0896708i
$895$	−15.0659	+	36.0881i	−0.503596	+	1.20629i
$896$	−33.0486	−	3.93907i	−1.10408	−	0.131595i
$897$	18.1116	+	18.1116i	0.604729	+	0.604729i
$898$	6.03475	−	16.3520i	0.201382	−	0.545673i
$899$	1.51134	−	1.51134i	0.0504059	−	0.0504059i
$900$	9.97355	−	0.726816i	0.332452	−	0.0242272i
$901$	3.69497	+	3.69497i	0.123097	+	0.123097i
$902$	−30.3813	−	65.9225i	−1.01159	−	2.19498i
$903$	−10.7355	+	10.7355i	−0.357254	+	0.357254i
$904$	−35.3983	−	9.99680i	−1.17733	−	0.332489i
$905$	−27.9852	−	11.6831i	−0.930259	−	0.388359i
$906$	−11.7121	−	4.32240i	−0.389110	−	0.143602i
$907$	−39.4081			−1.30852			−0.654262	−	0.756268i	$-0.727021\pi$
$907$	−39.4081			−1.30852			−0.654262	+	0.756268i	$0.727021\pi$
$908$	2.16047	−	2.52839i	0.0716978	−	0.0839075i
$909$	−6.69380	−	6.69380i	−0.222019	−	0.222019i
$910$	−38.8769	+	41.8131i	−1.28876	+	1.38609i
$911$			7.29607i			0.241729i	0.992669	+	0.120865i	$0.0385667\pi$
$911$			7.29607i			0.241729i	−0.992669	+	0.120865i	$0.961433\pi$
$912$	3.81698	+	2.77593i	0.126393	+	0.0919203i
$913$	−28.9256	+	28.9256i	−0.957298	+	0.957298i
$914$	−19.2243	+	8.85977i	−0.635882	+	0.293055i
$915$	−8.80197	+	21.0839i	−0.290984	+	0.697012i
$916$	32.0732	−	2.51664i	1.05973	−	0.0831523i
$917$			14.7122i			0.485840i
$918$	1.95159	+	4.23464i	0.0644122	+	0.139764i
$919$			52.5346i			1.73296i	0.499215	+	0.866478i	$0.333622\pi$
$919$			52.5346i			1.73296i	−0.499215	+	0.866478i	$0.666378\pi$
$920$	−26.2216	+	3.02030i	−0.864500	+	0.0995762i
$921$			3.84487i			0.126693i
$922$	12.2984	−	5.66789i	0.405026	−	0.186662i
$923$			15.7654i			0.518926i
$924$	−21.0873	−	18.0188i	−0.693721	−	0.592775i
$925$	7.28862	+	7.37012i	0.239648	+	0.242328i
$926$	9.50727	+	20.6292i	0.312428	+	0.677918i
$927$	−13.4242	+	13.4242i	−0.440907	+	0.440907i
$928$	−3.83415	+	2.55864i	−0.125862	+	0.0839916i
$929$		−	48.7878i		−	1.60068i	−0.599549	−	0.800338i	$-0.704654\pi$
$929$		−	48.7878i		−	1.60068i	0.599549	−	0.800338i	$-0.295346\pi$
$930$	−0.301634	−	8.28918i	−0.00989098	−	0.271813i
$931$	1.38007	+	1.38007i	0.0452299	+	0.0452299i
$932$	2.07753	+	26.4769i	0.0680517	+	0.867278i
$933$	−4.07103			−0.133279
$934$	1.52561	−	4.13385i	0.0499194	−	0.135264i
$935$	−32.1472	+	13.2112i	−1.05133	+	0.432054i
$936$	15.1487	−	8.47667i	0.495150	−	0.277069i
$937$	−29.3163	+	29.3163i	−0.957722	+	0.957722i	−0.999142	−	0.0414198i	$-0.986812\pi$
$937$	−29.3163	+	29.3163i	−0.957722	+	0.957722i	0.0414198	+	0.999142i	$0.486812\pi$
$938$	3.34593	−	1.54202i	0.109248	−	0.0503487i
$939$	−1.37922	−	1.37922i	−0.0450093	−	0.0450093i
$940$	−48.8629	+	24.7116i	−1.59373	+	0.806004i
$941$	−7.65378	+	7.65378i	−0.249506	+	0.249506i	−0.820768	−	0.571262i	$-0.806454\pi$
$941$	−7.65378	+	7.65378i	−0.249506	+	0.249506i	0.571262	+	0.820768i	$0.306454\pi$
$942$	−20.5892	−	7.59850i	−0.670832	−	0.247572i
$943$	32.1289	+	32.1289i	1.04626	+	1.04626i
$944$	−7.73909	+	10.6414i	−0.251886	+	0.346349i
$945$	−6.07029	−	2.53419i	−0.197467	−	0.0824372i
$946$	14.4016	+	31.2491i	0.468237	+	1.01600i
$947$			39.6694i			1.28908i	0.764569	+	0.644541i	$0.222952\pi$
$947$			39.6694i			1.28908i	−0.764569	+	0.644541i	$0.777048\pi$
$948$	−11.7476	−	10.0382i	−0.381545	−	0.326025i
$949$	−45.1116	+	45.1116i	−1.46438	+	1.46438i
$950$	−2.93213	+	7.81104i	−0.0951308	+	0.253424i
$951$	9.80915			0.318084
$952$	23.9403	−	13.3961i	0.775908	−	0.434171i
$953$	8.83095	+	8.83095i	0.286063	+	0.286063i	0.835521	−	0.549458i	$-0.185166\pi$
$953$	8.83095	+	8.83095i	0.286063	+	0.286063i	−0.549458	+	0.835521i	$0.685166\pi$
$954$	2.10276	+	0.776029i	0.0680794	+	0.0251249i
$955$	12.3281	+	29.9983i	0.398929	+	0.970724i
$956$	13.5160	+	11.5492i	0.437139	+	0.373529i
$957$	−3.84148			−0.124177
$958$	20.3666	+	7.51635i	0.658015	+	0.242842i
$959$	−31.3916			−1.01369
$960$	−2.85991	+	17.6585i	−0.0923033	+	0.569924i
$961$	24.1198			0.778060
$962$	16.8806	+	6.22982i	0.544252	+	0.200858i
$963$	−10.9567			−0.353075
$964$	31.3191	+	26.7618i	1.00872	+	0.861938i
$965$	−2.04856	+	4.90703i	−0.0659455	+	0.157963i
$966$	16.2888	+	6.01144i	0.524085	+	0.193415i
$967$	−2.42314	−	2.42314i	−0.0779231	−	0.0779231i	0.667071	−	0.744994i	$-0.267548\pi$
$967$	−2.42314	−	2.42314i	−0.0779231	−	0.0779231i	−0.744994	+	0.667071i	$0.767548\pi$
$968$	−27.7065	+	15.5036i	−0.890519	+	0.498303i
$969$	−3.89021			−0.124972
$970$	−39.2972	−	36.5377i	−1.26176	−	1.17315i
$971$	21.9788	−	21.9788i	0.705334	−	0.705334i	−0.260216	−	0.965550i	$-0.583794\pi$
$971$	21.9788	−	21.9788i	0.705334	−	0.705334i	0.965550	+	0.260216i	$0.0837939\pi$
$972$	1.52051	+	1.29925i	0.0487703	+	0.0416735i
$973$			11.8263i			0.379132i
$974$	−7.12671	−	15.4638i	−0.228355	−	0.495492i
$975$	21.5778	+	21.8191i	0.691044	+	0.698771i
$976$	−33.0538	−	24.0387i	−1.05803	−	0.769460i
$977$	32.7193	+	32.7193i	1.04678	+	1.04678i	0.998851	+	0.0479337i	$0.0152636\pi$
$977$	32.7193	+	32.7193i	1.04678	+	1.04678i	0.0479337	+	0.998851i	$0.484736\pi$
$978$	−11.4793	−	4.23646i	−0.367067	−	0.135467i
$979$	−29.0215	+	29.0215i	−0.927531	+	0.927531i
$980$	−2.30713	+	7.02845i	−0.0736984	+	0.224515i
$981$	0.643941	+	0.643941i	0.0205595	+	0.0205595i
$982$	11.1952	−	5.15949i	0.357255	−	0.164646i
$983$	27.7480	−	27.7480i	0.885023	−	0.885023i	−0.109017	−	0.994040i	$-0.534770\pi$
$983$	27.7480	−	27.7480i	0.885023	−	0.885023i	0.994040	+	0.109017i	$0.0347703\pi$
$984$	26.8729	−	15.0371i	0.856675	−	0.479365i
$985$	7.35318	+	17.8927i	0.234292	+	0.570108i
$986$	1.31546	−	3.56442i	0.0418927	−	0.113514i
$987$	36.0188			1.14649
$988$	1.13294	+	14.4387i	0.0360437	+	0.459356i
$989$	−15.2300	−	15.2300i	−0.484286	−	0.484286i
$990$	−10.1513	+	10.9180i	−0.322629	+	0.346996i
$991$			24.6172i			0.781991i	0.920393	+	0.390996i	$0.127869\pi$
$991$			24.6172i			0.781991i	−0.920393	+	0.390996i	$0.872131\pi$
$992$	14.5511	+	2.90327i	0.461999	+	0.0921790i
$993$	−7.17235	+	7.17235i	−0.227608	+	0.227608i
$994$	4.47303	+	9.70575i	0.141876	+	0.307848i
$995$	−18.9775	−	46.1784i	−0.601627	−	1.46395i
$996$	−13.1937	−	11.2738i	−0.418057	−	0.357224i
$997$		−	36.9465i		−	1.17011i	−0.810995	−	0.585053i	$-0.801074\pi$
$997$		−	36.9465i		−	1.17011i	0.810995	−	0.585053i	$-0.198926\pi$
$998$	29.4184	−	13.5579i	0.931222	−	0.429167i
$999$			2.07309i			0.0655897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.y.e.187.1	yes	16
3.2	odd	2		720.2.z.f.667.8		16
4.3	odd	2		960.2.y.e.847.7		16
5.3	odd	4		240.2.bc.e.43.4	yes	16
8.3	odd	2		1920.2.y.j.1567.2		16
8.5	even	2		1920.2.y.i.1567.2		16
15.8	even	4		720.2.bd.f.523.5		16
16.3	odd	4		240.2.bc.e.67.4	yes	16
16.5	even	4		1920.2.bc.j.607.6		16
16.11	odd	4		1920.2.bc.i.607.6		16
16.13	even	4		960.2.bc.e.367.3		16
20.3	even	4		960.2.bc.e.463.3		16
40.3	even	4		1920.2.bc.j.1183.6		16
40.13	odd	4		1920.2.bc.i.1183.6		16
48.35	even	4		720.2.bd.f.307.5		16
80.3	even	4	inner	240.2.y.e.163.1	✓	16
80.13	odd	4		960.2.y.e.943.7		16
80.43	even	4		1920.2.y.i.223.2		16
80.53	odd	4		1920.2.y.j.223.2		16
240.83	odd	4		720.2.z.f.163.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.1	✓	16	80.3	even	4	inner
240.2.y.e.187.1	yes	16	1.1	even	1	trivial
240.2.bc.e.43.4	yes	16	5.3	odd	4
240.2.bc.e.67.4	yes	16	16.3	odd	4
720.2.z.f.163.8		16	240.83	odd	4
720.2.z.f.667.8		16	3.2	odd	2
720.2.bd.f.307.5		16	48.35	even	4
720.2.bd.f.523.5		16	15.8	even	4
960.2.y.e.847.7		16	4.3	odd	2
960.2.y.e.943.7		16	80.13	odd	4
960.2.bc.e.367.3		16	16.13	even	4
960.2.bc.e.463.3		16	20.3	even	4
1920.2.y.i.223.2		16	80.43	even	4
1920.2.y.i.1567.2		16	8.5	even	2
1920.2.y.j.223.2		16	80.53	odd	4
1920.2.y.j.1567.2		16	8.3	odd	2
1920.2.bc.i.607.6		16	16.11	odd	4
1920.2.bc.i.1183.6		16	40.13	odd	4
1920.2.bc.j.607.6		16	16.5	even	4
1920.2.bc.j.1183.6		16	40.3	even	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32675 - 0.489639i) q^{2} +1.00000 q^{3} +(1.52051 + 1.29925i) q^{4} +(2.06823 - 0.849960i) q^{5} +(-1.32675 - 0.489639i) q^{6} +(-2.08016 - 2.08016i) q^{7} +(-1.38116 - 2.46828i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.32675 - 0.489639i) q^{2} +1.00000 q^{3} +(1.52051 + 1.29925i) q^{4} +(2.06823 - 0.849960i) q^{5} +(-1.32675 - 0.489639i) q^{6} +(-2.08016 - 2.08016i) q^{7} +(-1.38116 - 2.46828i) q^{8} +1.00000 q^{9} +(-3.16019 + 0.114996i) q^{10} +(3.33354 - 3.33354i) q^{11} +(1.52051 + 1.29925i) q^{12} +6.13735i q^{13} +(1.74131 + 3.77837i) q^{14} +(2.06823 - 0.849960i) q^{15} +(0.623885 + 3.95105i) q^{16} +(-2.33136 - 2.33136i) q^{17} +(-1.32675 - 0.489639i) q^{18} +(0.834324 - 0.834324i) q^{19} +(4.24907 + 1.39478i) q^{20} +(-2.08016 - 2.08016i) q^{21} +(-6.05500 + 2.79053i) q^{22} +(2.95105 - 2.95105i) q^{23} +(-1.38116 - 2.46828i) q^{24} +(3.55514 - 3.51582i) q^{25} +(3.00509 - 8.14270i) q^{26} +1.00000 q^{27} +(-0.460244 - 5.86555i) q^{28} +(-0.576185 - 0.576185i) q^{29} +(-3.16019 + 0.114996i) q^{30} +2.62300i q^{31} +(1.10685 - 5.54751i) q^{32} +(3.33354 - 3.33354i) q^{33} +(1.95159 + 4.23464i) q^{34} +(-6.07029 - 2.53419i) q^{35} +(1.52051 + 1.29925i) q^{36} +2.07309i q^{37} +(-1.51545 + 0.698418i) q^{38} +6.13735i q^{39} +(-4.95449 - 3.93103i) q^{40} +10.8873i q^{41} +(1.74131 + 3.77837i) q^{42} -5.16088i q^{43} +(9.39979 - 0.737562i) q^{44} +(2.06823 - 0.849960i) q^{45} +(-5.36024 + 2.47034i) q^{46} +(-8.65772 + 8.65772i) q^{47} +(0.623885 + 3.95105i) q^{48} +1.65411i q^{49} +(-6.43824 + 2.92387i) q^{50} +(-2.33136 - 2.33136i) q^{51} +(-7.97397 + 9.33189i) q^{52} -1.58490 q^{53} +(-1.32675 - 0.489639i) q^{54} +(4.06115 - 9.72791i) q^{55} +(-2.26137 + 8.00744i) q^{56} +(0.834324 - 0.834324i) q^{57} +(0.482328 + 1.04657i) q^{58} +(2.32603 + 2.32603i) q^{59} +(4.24907 + 1.39478i) q^{60} +(-7.22499 + 7.22499i) q^{61} +(1.28433 - 3.48006i) q^{62} +(-2.08016 - 2.08016i) q^{63} +(-4.18479 + 6.81818i) q^{64} +(5.21651 + 12.6934i) q^{65} +(-6.05500 + 2.79053i) q^{66} -0.885549i q^{67} +(-0.515823 - 6.57387i) q^{68} +(2.95105 - 2.95105i) q^{69} +(6.81290 + 6.33448i) q^{70} +2.56877 q^{71} +(-1.38116 - 2.46828i) q^{72} +(7.35033 + 7.35033i) q^{73} +(1.01507 - 2.75047i) q^{74} +(3.55514 - 3.51582i) q^{75} +(2.35259 - 0.184598i) q^{76} -13.8686 q^{77} +(3.00509 - 8.14270i) q^{78} -7.72612 q^{79} +(4.64857 + 7.64139i) q^{80} +1.00000 q^{81} +(5.33084 - 14.4447i) q^{82} -8.67714 q^{83} +(-0.460244 - 5.86555i) q^{84} +(-6.80334 - 2.84022i) q^{85} +(-2.52697 + 6.84718i) q^{86} +(-0.576185 - 0.576185i) q^{87} +(-12.8323 - 3.62395i) q^{88} -8.70590 q^{89} +(-3.16019 + 0.114996i) q^{90} +(12.7667 - 12.7667i) q^{91} +(8.32124 - 0.652933i) q^{92} +2.62300i q^{93} +(15.7257 - 7.24743i) q^{94} +(1.01643 - 2.43472i) q^{95} +(1.10685 - 5.54751i) q^{96} +(11.9985 + 11.9985i) q^{97} +(0.809919 - 2.19459i) q^{98} +(3.33354 - 3.33354i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9	\( 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9} - 14 q^{10} - 8 q^{12} - 4 q^{14} - 4 q^{15} - 8 q^{16} - 8 q^{17} + 2 q^{18} + 8 q^{19} - 12 q^{20} - 4 q^{21} - 8 q^{22} - 4 q^{24} + 32 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{28} + 12 q^{29} - 14 q^{30} - 28 q^{32} - 20 q^{35} - 8 q^{36} - 16 q^{38} - 44 q^{40} - 4 q^{42} + 52 q^{44} - 4 q^{45} - 16 q^{46} - 32 q^{47} - 8 q^{48} + 22 q^{50} - 8 q^{51} + 8 q^{52} + 16 q^{53} + 2 q^{54} - 4 q^{55} + 20 q^{56} + 8 q^{57} - 44 q^{58} - 24 q^{59} - 12 q^{60} + 40 q^{61} + 40 q^{62} - 4 q^{63} - 8 q^{64} - 4 q^{65} - 8 q^{66} + 24 q^{68} + 56 q^{70} - 4 q^{72} + 8 q^{73} + 64 q^{74} + 32 q^{75} + 16 q^{76} - 72 q^{77} + 20 q^{78} - 48 q^{79} + 16 q^{80} + 16 q^{81} + 8 q^{82} - 8 q^{83} + 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} - 16 q^{88} - 14 q^{90} - 40 q^{91} - 20 q^{94} + 8 q^{95} - 28 q^{96} + 48 q^{97} + 30 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9 - 14 * q^10 - 8 * q^12 - 4 * q^14 - 4 * q^15 - 8 * q^16 - 8 * q^17 + 2 * q^18 + 8 * q^19 - 12 * q^20 - 4 * q^21 - 8 * q^22 - 4 * q^24 + 32 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^28 + 12 * q^29 - 14 * q^30 - 28 * q^32 - 20 * q^35 - 8 * q^36 - 16 * q^38 - 44 * q^40 - 4 * q^42 + 52 * q^44 - 4 * q^45 - 16 * q^46 - 32 * q^47 - 8 * q^48 + 22 * q^50 - 8 * q^51 + 8 * q^52 + 16 * q^53 + 2 * q^54 - 4 * q^55 + 20 * q^56 + 8 * q^57 - 44 * q^58 - 24 * q^59 - 12 * q^60 + 40 * q^61 + 40 * q^62 - 4 * q^63 - 8 * q^64 - 4 * q^65 - 8 * q^66 + 24 * q^68 + 56 * q^70 - 4 * q^72 + 8 * q^73 + 64 * q^74 + 32 * q^75 + 16 * q^76 - 72 * q^77 + 20 * q^78 - 48 * q^79 + 16 * q^80 + 16 * q^81 + 8 * q^82 - 8 * q^83 + 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 - 16 * q^88 - 14 * q^90 - 40 * q^91 - 20 * q^94 + 8 * q^95 - 28 * q^96 + 48 * q^97 + 30 * q^98

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