LMFDB - Embedded newform 240.2.bc.e.67.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(43,240)]

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, 1, 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("240.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bc (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			67.4
Root			$-1.40988 - 0.110627i$ of defining polynomial
Character	$\chi$	$=$	240.67
Dual form			240.2.bc.e.43.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.489639 - 1.32675i) q^{2} -1.00000i q^{3} +(-1.52051 + 1.29925i) q^{4} +(-0.849960 - 2.06823i) q^{5} +(-1.32675 + 0.489639i) q^{6} +(-2.08016 - 2.08016i) q^{7} +(2.46828 + 1.38116i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.489639 - 1.32675i) q^{2} -1.00000i q^{3} +(-1.52051 + 1.29925i) q^{4} +(-0.849960 - 2.06823i) q^{5} +(-1.32675 + 0.489639i) q^{6} +(-2.08016 - 2.08016i) q^{7} +(2.46828 + 1.38116i) q^{8} -1.00000 q^{9} +(-2.32784 + 2.14037i) q^{10} +(3.33354 + 3.33354i) q^{11} +(1.29925 + 1.52051i) q^{12} -6.13735 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} +(0.489639 + 1.32675i) q^{18} +(-0.834324 - 0.834324i) q^{19} +(3.97952 + 2.04044i) q^{20} +(-2.08016 + 2.08016i) q^{21} +(2.79053 - 6.05500i) 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} +1.00000i q^{27} +(5.86555 + 0.460244i) q^{28} +(0.576185 - 0.576185i) q^{29} +(2.14037 + 2.32784i) q^{30} -2.62300i q^{31} +(-5.54751 + 1.10685i) q^{32} +(3.33354 - 3.33354i) q^{33} +(-1.95159 + 4.23464i) q^{34} +(-2.53419 + 6.07029i) q^{35} +(1.52051 - 1.29925i) q^{36} +2.07309 q^{37} +(-0.698418 + 1.51545i) q^{38} +6.13735i q^{39} +(0.758619 - 6.27889i) q^{40} -10.8873i q^{41} +(3.77837 + 1.74131i) q^{42} +5.16088 q^{43} +(-9.39979 - 0.737562i) q^{44} +(0.849960 + 2.06823i) q^{45} +(-5.36024 - 2.47034i) q^{46} +(8.65772 - 8.65772i) q^{47} +(-3.95105 - 0.623885i) q^{48} +1.65411i q^{49} +(6.40534 + 2.99528i) q^{50} +(-2.33136 + 2.33136i) q^{51} +(9.33189 - 7.97397i) q^{52} +1.58490i 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} +(-1.04657 - 0.482328i) q^{58} +(-2.32603 + 2.32603i) q^{59} +(2.04044 - 3.97952i) q^{60} +(-7.22499 - 7.22499i) q^{61} +(-3.48006 + 1.28433i) 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} -0.885549 q^{67} +(6.57387 + 0.515823i) q^{68} +(-2.95105 - 2.95105i) q^{69} +(9.29457 + 0.389973i) q^{70} +2.56877 q^{71} +(-2.46828 - 1.38116i) q^{72} +(-7.35033 - 7.35033i) q^{73} +(-1.01507 - 2.75047i) q^{74} +(3.51582 + 3.55514i) q^{75} +(2.35259 + 0.184598i) q^{76} -13.8686i q^{77} +(8.14270 - 3.00509i) q^{78} +7.72612 q^{79} +(-8.70194 + 2.06790i) q^{80} +1.00000 q^{81} +(-14.4447 + 5.33084i) q^{82} +8.67714i q^{83} +(0.460244 - 5.86555i) q^{84} +(-2.84022 + 6.80334i) q^{85} +(-2.52697 - 6.84718i) q^{86} +(-0.576185 - 0.576185i) q^{87} +(3.62395 + 12.8323i) q^{88} +8.70590 q^{89} +(2.32784 - 2.14037i) q^{90} +(12.7667 + 12.7667i) q^{91} +(-0.652933 + 8.32124i) q^{92} -2.62300 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} +(2.19459 - 0.809919i) q^{98} +(-3.33354 - 3.33354i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9	$ 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9} - 2 q^{10} - 4 q^{12} - 8 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} - 8 q^{17} - 2 q^{18} - 8 q^{19} + 4 q^{20} - 4 q^{21} + 4 q^{24} - 32 q^{25} + 20 q^{26} + 12 q^{28} - 12 q^{29} + 2 q^{30} - 28 q^{32} + 12 q^{35} - 8 q^{36} - 24 q^{37} + 16 q^{38} + 16 q^{40} + 24 q^{42} + 24 q^{43} - 52 q^{44} + 8 q^{45} - 16 q^{46} + 32 q^{47} - 16 q^{48} + 6 q^{50} - 8 q^{51} + 24 q^{52} - 2 q^{54} - 4 q^{55} + 20 q^{56} - 8 q^{57} + 12 q^{58} + 24 q^{59} + 24 q^{60} + 40 q^{61} + 28 q^{62} + 4 q^{63} + 8 q^{64} - 4 q^{65} - 8 q^{66} + 16 q^{67} - 8 q^{68} + 12 q^{70} - 8 q^{72} - 8 q^{73} - 64 q^{74} + 24 q^{75} + 16 q^{76} + 12 q^{78} + 48 q^{79} + 16 q^{81} - 32 q^{82} - 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} + 24 q^{88} + 2 q^{90} - 40 q^{91} - 16 q^{92} - 32 q^{93} + 20 q^{94} - 8 q^{95} - 28 q^{96} + 48 q^{97} + 62 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9 - 2 * q^10 - 4 * q^12 - 8 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 - 8 * q^17 - 2 * q^18 - 8 * q^19 + 4 * q^20 - 4 * q^21 + 4 * q^24 - 32 * q^25 + 20 * q^26 + 12 * q^28 - 12 * q^29 + 2 * q^30 - 28 * q^32 + 12 * q^35 - 8 * q^36 - 24 * q^37 + 16 * q^38 + 16 * q^40 + 24 * q^42 + 24 * q^43 - 52 * q^44 + 8 * q^45 - 16 * q^46 + 32 * q^47 - 16 * q^48 + 6 * q^50 - 8 * q^51 + 24 * q^52 - 2 * q^54 - 4 * q^55 + 20 * q^56 - 8 * q^57 + 12 * q^58 + 24 * q^59 + 24 * q^60 + 40 * q^61 + 28 * q^62 + 4 * q^63 + 8 * q^64 - 4 * q^65 - 8 * q^66 + 16 * q^67 - 8 * q^68 + 12 * q^70 - 8 * q^72 - 8 * q^73 - 64 * q^74 + 24 * q^75 + 16 * q^76 + 12 * q^78 + 48 * q^79 + 16 * q^81 - 32 * q^82 - 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 + 24 * q^88 + 2 * q^90 - 40 * q^91 - 16 * q^92 - 32 * q^93 + 20 * q^94 - 8 * q^95 - 28 * q^96 + 48 * q^97 + 62 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.489639	−	1.32675i	−0.346227	−	0.938151i
$2$	−0.489639	−	1.32675i	−0.346227	−	0.938151i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.52051	+	1.29925i	−0.760254	+	0.649626i
$5$	−0.849960	−	2.06823i	−0.380114	−	0.924940i
$5$	−0.849960	−	2.06823i	−0.380114	−	0.924940i
$6$	−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	$0.937644\pi$
$8$	2.46828	+	1.38116i	0.872668	+	0.488314i
$9$	−1.00000			−0.333333
$10$	−2.32784	+	2.14037i	−0.736127	+	0.676843i
$11$	3.33354	+	3.33354i	1.00510	+	1.00510i	0.999987	+	0.00511408i	$0.00162787\pi$
$11$	3.33354	+	3.33354i	1.00510	+	1.00510i	0.00511408	+	0.999987i	$0.498372\pi$
$12$	1.29925	+	1.52051i	0.375062	+	0.438933i
$13$	−6.13735			−1.70220			−0.851098	−	0.525007i	$-0.824063\pi$
$13$	−6.13735			−1.70220			−0.851098	+	0.525007i	$0.824063\pi$
$14$	−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	$0.880929\pi$
$18$	0.489639	+	1.32675i	0.115409	+	0.312717i
$19$	−0.834324	−	0.834324i	−0.191407	−	0.191407i	0.604897	−	0.796304i	$-0.293214\pi$
$19$	−0.834324	−	0.834324i	−0.191407	−	0.191407i	−0.796304	+	0.604897i	$0.793214\pi$
$20$	3.97952	+	2.04044i	0.889848	+	0.456257i
$21$	−2.08016	+	2.08016i	−0.453928	+	0.453928i
$22$	2.79053	−	6.05500i	0.594943	−	1.29093i
$23$	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
$27$			1.00000i			0.192450i
$28$	5.86555	+	0.460244i	1.10848	+	0.0869780i
$29$	0.576185	−	0.576185i	0.106995	−	0.106995i	−0.651583	−	0.758578i	$-0.725895\pi$
$29$	0.576185	−	0.576185i	0.106995	−	0.106995i	0.758578	+	0.651583i	$0.225895\pi$
$30$	2.14037	+	2.32784i	0.390776	+	0.425003i
$31$		−	2.62300i		−	0.471106i	−0.971862	−	0.235553i	$-0.924310\pi$
$31$		−	2.62300i		−	0.471106i	0.971862	−	0.235553i	$-0.0756900\pi$
$32$	−5.54751	+	1.10685i	−0.980671	+	0.195665i
$33$	3.33354	−	3.33354i	0.580295	−	0.580295i
$34$	−1.95159	+	4.23464i	−0.334696	+	0.726235i
$35$	−2.53419	+	6.07029i	−0.428356	+	1.02607i
$36$	1.52051	−	1.29925i	0.253418	−	0.216542i
$37$	2.07309			0.340814			0.170407	−	0.985374i	$-0.445492\pi$
$37$	2.07309			0.340814			0.170407	+	0.985374i	$0.445492\pi$
$38$	−0.698418	+	1.51545i	−0.113298	+	0.245839i
$39$			6.13735i			0.982763i
$40$	0.758619	−	6.27889i	0.119948	−	0.992780i
$41$		−	10.8873i		−	1.70031i	−0.526533	−	0.850154i	$-0.676508\pi$
$41$		−	10.8873i		−	1.70031i	0.526533	−	0.850154i	$-0.323492\pi$
$42$	3.77837	+	1.74131i	0.583015	+	0.268691i
$43$	5.16088			0.787027			0.393514	−	0.919319i	$-0.371259\pi$
$43$	5.16088			0.787027			0.393514	+	0.919319i	$0.371259\pi$
$44$	−9.39979	−	0.737562i	−1.41707	−	0.111192i
$45$	0.849960	+	2.06823i	0.126705	+	0.308313i
$46$	−5.36024	−	2.47034i	−0.790324	−	0.364232i
$47$	8.65772	−	8.65772i	1.26286	−	1.26286i	0.313156	−	0.949702i	$-0.398614\pi$
$47$	8.65772	−	8.65772i	1.26286	−	1.26286i	0.949702	−	0.313156i	$-0.101386\pi$
$48$	−3.95105	−	0.623885i	−0.570284	−	0.0900500i
$49$			1.65411i			0.236302i
$50$	6.40534	+	2.99528i	0.905851	+	0.423596i
$51$	−2.33136	+	2.33136i	−0.326455	+	0.326455i
$52$	9.33189	−	7.97397i	1.29410	−	1.10579i
$53$			1.58490i			0.217703i	0.994058	+	0.108851i	$0.0347173\pi$
$53$			1.58490i			0.217703i	−0.994058	+	0.108851i	$0.965283\pi$
$54$	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
$58$	−1.04657	−	0.482328i	−0.137422	−	0.0633328i
$59$	−2.32603	+	2.32603i	−0.302824	+	0.302824i	−0.842118	−	0.539294i	$-0.818691\pi$
$59$	−2.32603	+	2.32603i	−0.302824	+	0.302824i	0.539294	+	0.842118i	$0.318691\pi$
$60$	2.04044	−	3.97952i	0.263420	−	0.513754i
$61$	−7.22499	−	7.22499i	−0.925065	−	0.925065i	0.0723167	−	0.997382i	$-0.476961\pi$
$61$	−7.22499	−	7.22499i	−0.925065	−	0.925065i	−0.997382	+	0.0723167i	$0.976961\pi$
$62$	−3.48006	+	1.28433i	−0.441968	+	0.163109i
$63$	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
$67$	−0.885549			−0.108187			−0.0540935	−	0.998536i	$-0.517227\pi$
$67$	−0.885549			−0.108187			−0.0540935	+	0.998536i	$0.517227\pi$
$68$	6.57387	+	0.515823i	0.797198	+	0.0625528i
$69$	−2.95105	−	2.95105i	−0.355264	−	0.355264i
$70$	9.29457	+	0.389973i	1.11091	+	0.0466106i
$71$	2.56877			0.304857			0.152428	−	0.988315i	$-0.451291\pi$
$71$	2.56877			0.304857			0.152428	+	0.988315i	$0.451291\pi$
$72$	−2.46828	−	1.38116i	−0.290889	−	0.162771i
$73$	−7.35033	−	7.35033i	−0.860291	−	0.860291i	0.131081	−	0.991372i	$-0.458155\pi$
$73$	−7.35033	−	7.35033i	−0.860291	−	0.860291i	−0.991372	+	0.131081i	$0.958155\pi$
$74$	−1.01507	−	2.75047i	−0.117999	−	0.319735i
$75$	3.51582	+	3.55514i	0.405972	+	0.410512i
$76$	2.35259	+	0.184598i	0.269861	+	0.0211748i
$77$		−	13.8686i		−	1.58047i
$78$	8.14270	−	3.00509i	0.921980	−	0.340259i
$79$	7.72612			0.869256			0.434628	−	0.900610i	$-0.356880\pi$
$79$	7.72612			0.869256			0.434628	+	0.900610i	$0.356880\pi$
$80$	−8.70194	+	2.06790i	−0.972907	+	0.231198i
$81$	1.00000			0.111111
$82$	−14.4447	+	5.33084i	−1.59515	+	0.588693i
$83$			8.67714i			0.952440i	0.879326	+	0.476220i	$0.157993\pi$
$83$			8.67714i			0.952440i	−0.879326	+	0.476220i	$0.842007\pi$
$84$	0.460244	−	5.86555i	0.0502168	−	0.639984i
$85$	−2.84022	+	6.80334i	−0.308065	+	0.737926i
$86$	−2.52697	−	6.84718i	−0.272490	−	0.738350i
$87$	−0.576185	−	0.576185i	−0.0617735	−	0.0617735i
$88$	3.62395	+	12.8323i	0.386314	+	1.36792i
$89$	8.70590			0.922823			0.461412	−	0.887186i	$-0.347343\pi$
$89$	8.70590			0.922823			0.461412	+	0.887186i	$0.347343\pi$
$90$	2.32784	−	2.14037i	0.245376	−	0.225614i
$91$	12.7667	+	12.7667i	1.33831	+	1.33831i
$92$	−0.652933	+	8.32124i	−0.0680729	+	0.867550i
$93$	−2.62300			−0.271993
$94$	−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	$0.419562\pi$
$98$	2.19459	−	0.809919i	0.221687	−	0.0818142i
$99$	−3.33354	−	3.33354i	−0.335034	−	0.335034i
$100$	0.837666	−	9.96485i	0.0837666	−	0.996485i
$101$	−6.69380	+	6.69380i	−0.666058	+	0.666058i	−0.956801	−	0.290743i	$-0.906098\pi$
$101$	−6.69380	+	6.69380i	−0.666058	+	0.666058i	0.290743	+	0.956801i	$0.406098\pi$
$102$	4.23464	+	1.95159i	0.419292	+	0.193237i
$103$	−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
$107$		−	10.9567i		−	1.05922i	−0.848240	−	0.529612i	$-0.822337\pi$
$107$		−	10.9567i		−	1.05922i	0.848240	−	0.529612i	$-0.177663\pi$
$108$	−1.29925	−	1.52051i	−0.125021	−	0.146311i
$109$	−0.643941	+	0.643941i	−0.0616784	+	0.0616784i	−0.737273	−	0.675595i	$-0.763887\pi$
$109$	−0.643941	+	0.643941i	−0.0616784	+	0.0616784i	0.675595	+	0.737273i	$0.263887\pi$
$110$	−14.8950	−	0.624948i	−1.42018	−	0.0595865i
$111$		−	2.07309i		−	0.196769i
$112$	−9.51658	+	6.92102i	−0.899232	+	0.653975i
$113$	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
$115$	−8.61171	−	3.59517i	−0.803046	−	0.335251i
$116$	−0.127484	+	1.62470i	−0.0118366	+	0.150850i
$117$	6.13735			0.567398
$118$	4.22497	+	1.94714i	0.388940	+	0.179249i
$119$			9.69918i			0.889122i
$120$	−6.27889	−	0.758619i	−0.573182	−	0.0692521i
$121$			11.2250i			1.02046i
$122$	−6.04809	+	13.1234i	−0.547568	+	1.18813i
$123$	−10.8873			−0.981674
$124$	3.40795	+	3.98830i	0.306043	+	0.358160i
$125$	10.2932	+	4.36452i	0.920656	+	0.390375i
$126$	1.74131	−	3.77837i	0.155129	−	0.336604i
$127$	−4.80716	+	4.80716i	−0.426567	+	0.426567i	−0.887457	−	0.460890i	$-0.847530\pi$
$127$	−4.80716	+	4.80716i	−0.426567	+	0.426567i	0.460890	+	0.887457i	$0.347530\pi$
$128$	6.99695	−	8.89059i	0.618449	−	0.785825i
$129$		−	5.16088i		−	0.454391i
$130$	14.2868	−	13.1362i	1.25303	−	1.15212i
$131$	−3.53632	+	3.53632i	−0.308970	+	0.308970i	−0.844510	−	0.535540i	$-0.820108\pi$
$131$	−3.53632	+	3.53632i	−0.308970	+	0.308970i	0.535540	+	0.844510i	$0.320108\pi$
$132$	−0.737562	+	9.39979i	−0.0641965	+	0.818147i
$133$			3.47105i			0.300978i
$134$	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	−0.951696	−	0.307042i	$-0.900661\pi$
$137$	−7.54548	+	7.54548i	−0.644654	+	0.644654i	0.307042	+	0.951696i	$0.400661\pi$
$138$	−2.47034	+	5.36024i	−0.210289	+	0.456294i
$139$	2.84263	−	2.84263i	0.241109	−	0.241109i	−0.576200	−	0.817309i	$-0.695465\pi$
$139$	2.84263	−	2.84263i	0.241109	−	0.241109i	0.817309	+	0.576200i	$0.195465\pi$
$140$	−4.03359	−	12.5225i	−0.340901	−	1.05834i
$141$	−8.65772	−	8.65772i	−0.729111	−	0.729111i
$142$	−1.25777	−	3.40810i	−0.105550	−	0.286002i
$143$	−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
$147$	1.65411			0.136429
$148$	−3.15215	+	2.69347i	−0.259105	+	0.221402i
$149$	−3.20287	−	3.20287i	−0.262389	−	0.262389i	0.563635	−	0.826024i	$-0.309403\pi$
$149$	−3.20287	−	3.20287i	−0.262389	−	0.262389i	−0.826024	+	0.563635i	$0.809403\pi$
$150$	2.99528	−	6.40534i	0.244563	−	0.522993i
$151$	8.82773			0.718390			0.359195	−	0.933262i	$-0.383051\pi$
$151$	8.82773			0.718390			0.359195	+	0.933262i	$0.383051\pi$
$152$	−0.907007	−	3.21168i	−0.0735680	−	0.260502i
$153$	2.33136	+	2.33136i	0.188479	+	0.188479i
$154$	−18.4001	+	6.79060i	−1.48272	+	0.547202i
$155$	−5.42497	+	2.22945i	−0.435744	+	0.179074i
$156$	−7.97397	−	9.33189i	−0.638429	−	0.747149i
$157$			15.5186i			1.23852i	0.785187	+	0.619258i	$0.212567\pi$
$157$			15.5186i			1.23852i	−0.785187	+	0.619258i	$0.787433\pi$
$158$	−3.78301	−	10.2506i	−0.300960	−	0.815493i
$159$	1.58490			0.125691
$160$	7.00438	+	10.5327i	0.553745	+	0.832686i
$161$	−12.2773			−0.967586
$162$	−0.489639	−	1.32675i	−0.0384697	−	0.104239i
$163$		−	8.65221i		−	0.677694i	−0.940842	−	0.338847i	$-0.889963\pi$
$163$		−	8.65221i		−	0.677694i	0.940842	−	0.338847i	$-0.110037\pi$
$164$	14.1453	+	16.5542i	1.10457	+	1.29267i
$165$	−9.72791	−	4.06115i	−0.757316	−	0.316160i
$166$	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	$0.699873\pi$
$168$	−8.00744	+	2.26137i	−0.617787	+	0.174469i
$169$	24.6671			1.89747
$170$	10.4170	+	0.437066i	0.798946	+	0.0335214i
$171$	0.834324	+	0.834324i	0.0638024	+	0.0638024i
$172$	−7.84716	+	6.70529i	−0.598340	+	0.511274i
$173$	15.1143			1.14912			0.574558	−	0.818464i	$-0.305174\pi$
$173$	15.1143			1.14912			0.574558	+	0.818464i	$0.305174\pi$
$174$	−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
$178$	−4.26275	−	11.5505i	−0.319506	−	0.865747i
$179$	12.3666	+	12.3666i	0.924324	+	0.924324i	0.997331	−	0.0730070i	$-0.0232595\pi$
$179$	12.3666	+	12.3666i	0.924324	+	0.924324i	−0.0730070	+	0.997331i	$0.523260\pi$
$180$	−3.97952	−	2.04044i	−0.296616	−	0.152086i
$181$	−9.58991	+	9.58991i	−0.712813	+	0.712813i	−0.967123	−	0.254310i	$-0.918152\pi$
$181$	−9.58991	+	9.58991i	−0.712813	+	0.712813i	0.254310	+	0.967123i	$0.418152\pi$
$182$	10.6871	−	23.1892i	0.792177	−	1.71890i
$183$	−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
$187$		−	15.5434i		−	1.13664i
$188$	−1.91556	+	24.4127i	−0.139707	+	1.78048i
$189$	2.08016	−	2.08016i	0.151309	−	0.151309i
$190$	3.72793	+	0.156413i	0.270453	+	0.0113474i
$191$		−	14.5044i		−	1.04950i	−0.851257	−	0.524750i	$-0.824159\pi$
$191$		−	14.5044i		−	1.04950i	0.851257	−	0.524750i	$-0.175841\pi$
$192$	6.81818	−	4.18479i	0.492060	−	0.302011i
$193$	−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
$195$	12.6934	−	5.21651i	0.908996	−	0.373562i
$196$	−2.14911	−	2.51509i	−0.153508	−	0.179649i
$197$	8.65121			0.616373			0.308187	−	0.951326i	$-0.400278\pi$
$197$	8.65121			0.616373			0.308187	+	0.951326i	$0.400278\pi$
$198$	−2.79053	+	6.05500i	−0.198314	+	0.430310i
$199$		−	22.3275i		−	1.58275i	−0.611328	−	0.791377i	$-0.709365\pi$
$199$		−	22.3275i		−	1.58275i	0.611328	−	0.791377i	$-0.290635\pi$
$200$	−13.6310	+	3.76781i	−0.963856	+	0.266425i
$201$			0.885549i			0.0624618i
$202$	12.1585	+	5.60343i	0.855471	+	0.394256i
$203$	−2.39711			−0.168244
$204$	0.515823	−	6.57387i	0.0361149	−	0.460263i
$205$	−22.5174	+	9.25376i	−1.57268	+	0.646311i
$206$	24.3834	+	11.2375i	1.69887	+	0.782951i
$207$	−2.95105	+	2.95105i	−0.205112	+	0.205112i
$208$	−3.82900	+	24.2490i	−0.265493	+	1.68136i
$209$		−	5.56251i		−	0.384767i
$210$	0.389973	−	9.29457i	0.0269107	−	0.641386i
$211$	5.27613	−	5.27613i	0.363224	−	0.363224i	−0.501775	−	0.864998i	$-0.667319\pi$
$211$	5.27613	−	5.27613i	0.363224	−	0.363224i	0.864998	+	0.501775i	$0.167319\pi$
$212$	−2.05919	−	2.40985i	−0.141426	−	0.165509i
$213$		−	2.56877i		−	0.176009i
$214$	−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
$218$	1.16964	+	0.539047i	0.0792183	+	0.0365089i
$219$	−7.35033	+	7.35033i	−0.496689	+	0.496689i
$220$	6.46400	+	20.0678i	0.435803	+	1.35297i
$221$	14.3084	+	14.3084i	0.962484	+	0.962484i
$222$	−2.75047	+	1.01507i	−0.184599	+	0.0681268i
$223$	−13.8202	−	13.8202i	−0.925469	−	0.925469i	0.0719400	−	0.997409i	$-0.477081\pi$
$223$	−13.8202	−	13.8202i	−0.925469	−	0.925469i	−0.997409	+	0.0719400i	$0.977081\pi$
$224$	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
$227$	−1.66286			−0.110368			−0.0551839	−	0.998476i	$-0.517575\pi$
$227$	−1.66286			−0.110368			−0.0551839	+	0.998476i	$0.517575\pi$
$228$	0.184598	−	2.35259i	0.0122253	−	0.155804i
$229$	−11.3744	−	11.3744i	−0.751643	−	0.751643i	0.223142	−	0.974786i	$-0.428368\pi$
$229$	−11.3744	−	11.3744i	−0.751643	−	0.751643i	−0.974786	+	0.223142i	$0.928368\pi$
$230$	−0.553240	+	13.1859i	−0.0364796	+	0.869451i
$231$	−13.8686			−0.912486
$232$	2.21799	−	0.626380i	0.145618	−	0.0411239i
$233$	−9.38976	−	9.38976i	−0.615143	−	0.615143i	0.329138	−	0.944282i	$-0.393242\pi$
$233$	−9.38976	−	9.38976i	−0.615143	−	0.615143i	−0.944282	+	0.329138i	$0.893242\pi$
$234$	−3.00509	−	8.14270i	−0.196449	−	0.532305i
$235$	−25.2649	−	10.5474i	−1.64810	−	0.688038i
$236$	0.514646	−	6.55886i	0.0335006	−	0.426945i
$237$		−	7.72612i		−	0.501865i
$238$	12.8683	−	4.74910i	0.834131	−	0.307838i
$239$	−8.88914			−0.574991			−0.287495	−	0.957782i	$-0.592823\pi$
$239$	−8.88914			−0.574991			−0.287495	+	0.957782i	$0.592823\pi$
$240$	2.06790	+	8.70194i	0.133482	+	0.561708i
$241$	20.5978			1.32682			0.663411	−	0.748255i	$-0.269108\pi$
$241$	20.5978			1.32682			0.663411	+	0.748255i	$0.269108\pi$
$242$	14.8927	−	5.49621i	0.957342	−	0.353309i
$243$		−	1.00000i		−	0.0641500i
$244$	20.3727	+	1.59856i	1.30423	+	0.102337i
$245$	3.42109	−	1.40593i	0.218565	−	0.0898217i
$246$	5.33084	+	14.4447i	0.339882	+	0.920958i
$247$	5.12054	+	5.12054i	0.325812	+	0.325812i
$248$	3.62279	−	6.47430i	0.230048	−	0.411119i
$249$	8.67714			0.549891
$250$	0.750632	−	15.7936i	0.0474742	−	0.998872i
$251$	16.8455	+	16.8455i	1.06328	+	1.06328i	0.997858	+	0.0654195i	$0.0208386\pi$
$251$	16.8455	+	16.8455i	1.06328	+	1.06328i	0.0654195	+	0.997858i	$0.479161\pi$
$252$	−5.86555	−	0.460244i	−0.369495	−	0.0289927i
$253$	19.6749			1.23695
$254$	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	$0.964546\pi$
$258$	−6.84718	+	2.52697i	−0.426287	+	0.157322i
$259$	−4.31236	−	4.31236i	−0.267957	−	0.267957i
$260$	−24.4237	−	12.5229i	−1.51470	−	0.776638i
$261$	−0.576185	+	0.576185i	−0.0356650	+	0.0356650i
$262$	6.42332	+	2.96028i	0.396834	+	0.182887i
$263$	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
$267$		−	8.70590i		−	0.532792i
$268$	1.34648	−	1.15055i	0.0822496	−	0.0702811i
$269$	10.2902	−	10.2902i	0.627403	−	0.627403i	−0.320011	−	0.947414i	$-0.603687\pi$
$269$	10.2902	−	10.2902i	0.627403	−	0.627403i	0.947414	+	0.320011i	$0.103687\pi$
$270$	−2.14037	−	2.32784i	−0.130259	−	0.141668i
$271$			21.3325i			1.29586i	0.761702	+	0.647928i	$0.224364\pi$
$271$			21.3325i			1.29586i	−0.761702	+	0.647928i	$0.775636\pi$
$272$	−10.6658	+	7.75680i	−0.646709	+	0.470325i
$273$	12.7667	−	12.7667i	0.772674	−	0.772674i
$274$	13.7055	+	6.31637i	0.827979	+	0.381586i
$275$	−23.5713	−	0.131048i	−1.42141	−	0.00790249i
$276$	8.32124	+	0.652933i	0.500880	+	0.0393019i
$277$	19.0041			1.14184			0.570922	−	0.821004i	$-0.306586\pi$
$277$	19.0041			1.14184			0.570922	+	0.821004i	$0.306586\pi$
$278$	−5.16331	−	2.37959i	−0.309675	−	0.142718i
$279$			2.62300i			0.157035i
$280$	−14.6391	+	11.4830i	−0.874856	+	0.686243i
$281$			3.86317i			0.230457i	0.993339	+	0.115229i	$0.0367600\pi$
$281$			3.86317i			0.230457i	−0.993339	+	0.115229i	$0.963240\pi$
$282$	−7.24743	+	15.7257i	−0.431578	+	0.936454i
$283$	−5.89151			−0.350214			−0.175107	−	0.984549i	$-0.556027\pi$
$283$	−5.89151			−0.350214			−0.175107	+	0.984549i	$0.556027\pi$
$284$	−3.90583	+	3.33748i	−0.231769	+	0.198043i
$285$	2.43472	+	1.01643i	0.144220	+	0.0602081i
$286$	−17.1265	+	37.1616i	−1.01271	+	2.19741i
$287$	−22.6473	+	22.6473i	−1.33683	+	1.33683i
$288$	5.54751	−	1.10685i	0.326890	−	0.0652218i
$289$		−	6.12955i		−	0.360562i
$290$	−0.108019	+	2.57451i	−0.00634309	+	0.151181i
$291$	11.9985	−	11.9985i	0.703364	−	0.703364i
$292$	20.7262	+	1.62629i	1.21291	+	0.0951716i
$293$			4.49132i			0.262386i	0.991357	+	0.131193i	$0.0418807\pi$
$293$			4.49132i			0.262386i	−0.991357	+	0.131193i	$0.958119\pi$
$294$	−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
$298$	−2.68114	+	5.81764i	−0.155314	+	0.337007i
$299$	−18.1116	+	18.1116i	−1.04742	+	1.04742i
$300$	−9.96485	−	0.837666i	−0.575321	−	0.0483627i
$301$	−10.7355	−	10.7355i	−0.618781	−	0.618781i
$302$	−4.32240	−	11.7121i	−0.248726	−	0.673958i
$303$	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
$307$	3.84487			0.219438			0.109719	−	0.993963i	$-0.465005\pi$
$307$	3.84487			0.219438			0.109719	+	0.993963i	$0.465005\pi$
$308$	18.0188	+	21.0873i	1.02672	+	1.20156i
$309$	13.4242	+	13.4242i	0.763674	+	0.763674i
$310$	5.61419	+	6.10593i	0.318865	+	0.346794i
$311$	−4.07103			−0.230847			−0.115423	−	0.993316i	$-0.536822\pi$
$311$	−4.07103			−0.230847			−0.115423	+	0.993316i	$0.536822\pi$
$312$	−8.47667	+	15.1487i	−0.479897	+	0.857626i
$313$	1.37922	+	1.37922i	0.0779584	+	0.0779584i	0.745011	−	0.667052i	$-0.232444\pi$
$313$	1.37922	+	1.37922i	0.0779584	+	0.0779584i	−0.667052	+	0.745011i	$0.732444\pi$
$314$	20.5892	−	7.59850i	1.16192	−	0.428808i
$315$	2.53419	−	6.07029i	0.142785	−	0.342022i
$316$	−11.7476	+	10.0382i	−0.660855	+	0.564692i
$317$			9.80915i			0.550937i	0.961310	+	0.275468i	$0.0888330\pi$
$317$			9.80915i			0.550937i	−0.961310	+	0.275468i	$0.911167\pi$
$318$	−0.776029	−	2.10276i	−0.0435176	−	0.117917i
$319$	3.84148			0.215081
$320$	10.5446	−	14.4503i	0.589464	−	0.807795i
$321$	−10.9567			−0.611543
$322$	6.01144	+	16.2888i	0.335004	+	0.907741i
$323$			3.89021i			0.216457i
$324$	−1.52051	+	1.29925i	−0.0844726	+	0.0721807i
$325$	21.8191	−	21.5778i	1.21031	−	1.19692i
$326$	−11.4793	+	4.23646i	−0.635779	+	0.234636i
$327$	0.643941	+	0.643941i	0.0356100	+	0.0356100i
$328$	15.0371	−	26.8729i	0.830285	−	1.48380i
$329$	−36.0188			−1.98578
$330$	−0.624948	+	14.8950i	−0.0344023	+	0.819940i
$331$	−7.17235	−	7.17235i	−0.394228	−	0.394228i	0.481963	−	0.876191i	$-0.339924\pi$
$331$	−7.17235	−	7.17235i	−0.394228	−	0.394228i	−0.876191	+	0.481963i	$0.839924\pi$
$332$	−11.2738	−	13.1937i	−0.618730	−	0.724096i
$333$	−2.07309			−0.113605
$334$	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	$-0.681273\pi$
$338$	−12.0780	−	32.7270i	−0.656955	−	1.78011i
$339$	−9.19571	−	9.19571i	−0.499442	−	0.499442i
$340$	−4.52068	−	14.0347i	−0.245169	−	0.761138i
$341$	8.74390	−	8.74390i	0.473509	−	0.473509i
$342$	0.698418	−	1.51545i	0.0377661	−	0.0819463i
$343$	−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
$347$		−	8.80549i		−	0.472704i	−0.971668	−	0.236352i	$-0.924048\pi$
$347$		−	8.80549i		−	0.472704i	0.971668	−	0.236352i	$-0.0759518\pi$
$348$	1.62470	+	0.127484i	0.0870933	+	0.00683384i
$349$	14.8110	−	14.8110i	0.792815	−	0.792815i	−0.189136	−	0.981951i	$-0.560569\pi$
$349$	14.8110	−	14.8110i	0.792815	−	0.792815i	0.981951	+	0.189136i	$0.0605687\pi$
$350$	−7.09346	−	19.5548i	−0.379162	−	1.04525i
$351$		−	6.13735i		−	0.327588i
$352$	−22.1826	−	14.8031i	−1.18234	−	0.789010i
$353$	−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
$355$	−2.18335	−	5.31280i	−0.115880	−	0.281974i
$356$	−13.2374	+	11.3112i	−0.701580	+	0.599490i
$357$	9.69918			0.513335
$358$	10.3522	−	22.4625i	0.547130	−	1.18718i
$359$			9.38977i			0.495573i	0.968815	+	0.247787i	$0.0797032\pi$
$359$			9.38977i			0.495573i	−0.968815	+	0.247787i	$0.920297\pi$
$360$	−0.758619	+	6.27889i	−0.0399827	+	0.330927i
$361$		−	17.6078i		−	0.926727i
$362$	17.4190	+	8.02778i	0.915521	+	0.421931i
$363$	11.2250			0.589161
$364$	−35.9989	−	2.82468i	−1.88686	−	0.148054i
$365$	−8.95467	+	21.4496i	−0.468709	+	1.12273i
$366$	13.1234	+	6.04809i	0.685969	+	0.316138i
$367$	0.129655	−	0.129655i	0.00676792	−	0.00676792i	−0.703715	−	0.710483i	$-0.748477\pi$
$367$	0.129655	−	0.129655i	0.00676792	−	0.00676792i	0.710483	+	0.703715i	$0.248477\pi$
$368$	−9.81861	−	13.5008i	−0.511830	−	0.703780i
$369$			10.8873i			0.566770i
$370$	−4.82582	+	4.43718i	−0.250883	+	0.230678i
$371$	3.29684	−	3.29684i	0.171164	−	0.171164i
$372$	3.98830	−	3.40795i	0.206784	−	0.176694i
$373$			2.85797i			0.147980i	0.997259	+	0.0739900i	$0.0235733\pi$
$373$			2.85797i			0.147980i	−0.997259	+	0.0739900i	$0.976427\pi$
$374$	−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
$378$	−3.77837	−	1.74131i	−0.194338	−	0.0895635i
$379$	14.8095	−	14.8095i	0.760713	−	0.760713i	−0.215739	−	0.976451i	$-0.569216\pi$
$379$	14.8095	−	14.8095i	0.760713	−	0.760713i	0.976451	+	0.215739i	$0.0692159\pi$
$380$	−1.61782	−	5.02260i	−0.0829924	−	0.257654i
$381$	4.80716	+	4.80716i	0.246278	+	0.246278i
$382$	−19.2436	+	7.10191i	−0.984589	+	0.363365i
$383$	22.2921	+	22.2921i	1.13907	+	1.13907i	0.988616	+	0.150458i	$0.0480749\pi$
$383$	22.2921	+	22.2921i	1.13907	+	1.13907i	0.150458	+	0.988616i	$0.451925\pi$
$384$	−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
$387$	−5.16088			−0.262342
$388$	−33.8328	−	2.65472i	−1.71760	−	0.134773i
$389$	−17.1132	−	17.1132i	−0.867671	−	0.867671i	0.124543	−	0.992214i	$-0.460254\pi$
$389$	−17.1132	−	17.1132i	−0.867671	−	0.867671i	−0.992214	+	0.124543i	$0.960254\pi$
$390$	−13.1362	−	14.2868i	−0.665176	−	0.723439i
$391$	−13.7599			−0.695867
$392$	−2.28460	+	4.08281i	−0.115390	+	0.206213i
$393$	3.53632	+	3.53632i	0.178384	+	0.178384i
$394$	−4.23597	−	11.4780i	−0.213405	−	0.578251i
$395$	−6.56689	−	15.9794i	−0.330416	−	0.804009i
$396$	9.39979	+	0.737562i	0.472357	+	0.0370639i
$397$			16.2806i			0.817099i	0.912736	+	0.408549i	$0.133965\pi$
$397$			16.2806i			0.817099i	−0.912736	+	0.408549i	$0.866035\pi$
$398$	−29.6229	+	10.9324i	−1.48486	+	0.547992i
$399$	3.47105			0.173770
$400$	11.6732	+	16.2400i	0.583659	+	0.811999i
$401$	5.13860			0.256609			0.128305	−	0.991735i	$-0.459046\pi$
$401$	5.13860			0.256609			0.128305	+	0.991735i	$0.459046\pi$
$402$	1.17490	−	0.433599i	0.0585986	−	0.0216260i
$403$			16.0983i			0.801914i
$404$	1.48103	−	18.8749i	0.0736842	−	0.939062i
$405$	−0.849960	−	2.06823i	−0.0422349	−	0.102771i
$406$	1.17372	+	3.18036i	0.0582507	+	0.157839i
$407$	6.91074	+	6.91074i	0.342553	+	0.342553i
$408$	−8.97441	+	2.53445i	−0.444300	+	0.125474i
$409$	3.88999			0.192348			0.0961738	−	0.995365i	$-0.469340\pi$
$409$	3.88999			0.192348			0.0961738	+	0.995365i	$0.469340\pi$
$410$	23.3028	+	25.3439i	1.15084	+	1.25164i
$411$	7.54548	+	7.54548i	0.372191	+	0.372191i
$412$	2.97016	−	37.8529i	0.146329	−	1.86488i
$413$	9.67703			0.476176
$414$	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
$418$	−7.38004	+	2.72362i	−0.360969	+	0.133217i
$419$	9.68913	+	9.68913i	0.473345	+	0.473345i	0.902995	−	0.429650i	$-0.141363\pi$
$419$	9.68913	+	9.68913i	0.473345	+	0.473345i	−0.429650	+	0.902995i	$0.641363\pi$
$420$	−12.5225	+	4.03359i	−0.611034	+	0.196819i
$421$	−19.2867	+	19.2867i	−0.939978	+	0.939978i	−0.998298	−	0.0583197i	$-0.981426\pi$
$421$	−19.2867	+	19.2867i	−0.939978	+	0.939978i	0.0583197	+	0.998298i	$0.481426\pi$
$422$	−9.58348	−	4.41668i	−0.466516	−	0.215001i
$423$	−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
$427$			30.0582i			1.45462i
$428$	14.2355	+	16.6597i	0.688100	+	0.805279i
$429$	−20.4591	+	20.4591i	−0.987776	+	0.987776i
$430$	−12.0137	+	11.0462i	−0.579352	+	0.532694i
$431$			4.13031i			0.198950i	0.995040	+	0.0994751i	$0.0317164\pi$
$431$			4.13031i			0.198950i	−0.995040	+	0.0994751i	$0.968284\pi$
$432$	3.95105	+	0.623885i	0.190095	+	0.0300167i
$433$	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
$435$	−0.701948	+	1.68142i	−0.0336558	+	0.0806178i
$436$	0.142475	−	1.81576i	0.00682331	−	0.0869591i
$437$	−4.92426			−0.235559
$438$	13.3510	+	6.15301i	0.637937	+	0.294002i
$439$			22.0770i			1.05368i	0.849965	+	0.526839i	$0.176623\pi$
$439$			22.0770i			1.05368i	−0.849965	+	0.526839i	$0.823377\pi$
$440$	23.4598	−	18.4021i	1.11840	−	0.877284i
$441$		−	1.65411i		−	0.0787673i
$442$	11.9776	−	25.9895i	0.569717	−	1.23619i
$443$	8.44869			0.401409			0.200705	−	0.979652i	$-0.435677\pi$
$443$	8.44869			0.401409			0.200705	+	0.979652i	$0.435677\pi$
$444$	2.69347	+	3.15215i	0.127826	+	0.149594i
$445$	−7.39967	−	18.0058i	−0.350778	−	0.853556i
$446$	−11.5690	+	25.1028i	−0.547807	+	1.18865i
$447$	−3.20287	+	3.20287i	−0.151491	+	0.151491i
$448$	5.47787	−	22.8879i	0.258805	−	1.08135i
$449$			12.3249i			0.581648i	0.956777	+	0.290824i	$0.0939293\pi$
$449$			12.3249i			0.581648i	−0.956777	+	0.290824i	$0.906071\pi$
$450$	−6.40534	−	2.99528i	−0.301950	−	0.141199i
$451$	36.2932	−	36.2932i	1.70898	−	1.70898i
$452$	−2.03459	+	25.9297i	−0.0956992	+	1.21963i
$453$		−	8.82773i		−	0.414763i
$454$	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	−0.909905	−	0.414816i	$-0.863846\pi$
$457$	−10.5838	+	10.5838i	−0.495089	+	0.495089i	0.414816	+	0.909905i	$0.363846\pi$
$458$	−9.52161	+	20.6603i	−0.444916	+	0.965394i
$459$	2.33136	−	2.33136i	0.108818	−	0.108818i
$460$	17.7652	−	5.72231i	0.828306	−	0.266804i
$461$	−6.77081	−	6.77081i	−0.315348	−	0.315348i	0.531629	−	0.846977i	$-0.321580\pi$
$461$	−6.77081	−	6.77081i	−0.315348	−	0.315348i	−0.846977	+	0.531629i	$0.821580\pi$
$462$	6.79060	+	18.4001i	0.315927	+	0.856050i
$463$	11.3573	+	11.3573i	0.527819	+	0.527819i	0.919921	−	0.392103i	$-0.128252\pi$
$463$	11.3573	+	11.3573i	0.527819	+	0.527819i	−0.392103	+	0.919921i	$0.628252\pi$
$464$	−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
$467$	3.11578			0.144181			0.0720906	−	0.997398i	$-0.477033\pi$
$467$	3.11578			0.144181			0.0720906	+	0.997398i	$0.477033\pi$
$468$	−9.33189	+	7.97397i	−0.431367	+	0.368597i
$469$	1.84208	+	1.84208i	0.0850594	+	0.0850594i
$470$	−1.62309	+	38.6845i	−0.0748673	+	1.78438i
$471$	15.5186			0.715058
$472$	−8.95392	+	2.52867i	−0.412138	+	0.116391i
$473$	17.2040	+	17.2040i	0.791042	+	0.791042i
$474$	−10.2506	+	3.78301i	−0.470825	+	0.173759i
$475$	5.89947	+	0.0327989i	0.270686	+	0.00150492i
$476$	−12.6017	−	14.7477i	−0.577597	−	0.675958i
$477$		−	1.58490i		−	0.0725676i
$478$	4.35247	+	11.7936i	0.199077	+	0.539428i
$479$	15.3508			0.701396			0.350698	−	0.936489i	$-0.385944\pi$
$479$	15.3508			0.701396			0.350698	+	0.936489i	$0.385944\pi$
$480$	10.5327	−	7.00438i	0.480752	−	0.319705i
$481$	−12.7233			−0.580132
$482$	−10.0855	−	27.3281i	−0.459382	−	1.24476i
$483$			12.2773i			0.558636i
$484$	−14.5841	−	17.0677i	−0.662915	−	0.775805i
$485$	14.6174	−	35.0138i	0.663740	−	1.58990i
$486$	−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	$0.662053\pi$
$488$	−7.85440	−	27.8122i	−0.355552	−	1.25900i
$489$	−8.65221			−0.391267
$490$	−3.54041	−	3.85051i	−0.159939	−	0.173948i
$491$	−6.16348	−	6.16348i	−0.278154	−	0.278154i	0.554218	−	0.832372i	$-0.313017\pi$
$491$	−6.16348	−	6.16348i	−0.278154	−	0.278154i	−0.832372	+	0.554218i	$0.813017\pi$
$492$	16.5542	−	14.1453i	0.746321	−	0.637721i
$493$	−2.68659			−0.120998
$494$	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
$498$	−4.24867	−	11.5124i	−0.190387	−	0.515881i
$499$	16.1961	+	16.1961i	0.725037	+	0.725037i	0.969627	−	0.244589i	$-0.0786532\pi$
$499$	16.1961	+	16.1961i	0.725037	+	0.725037i	−0.244589	+	0.969627i	$0.578653\pi$
$500$	−21.3216	+	6.73725i	−0.953530	+	0.301299i
$501$	2.86613	−	2.86613i	0.128049	−	0.128049i
$502$	14.1015	−	30.5979i	0.629379	−	1.36565i
$503$	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
$507$		−	24.6671i		−	1.09550i
$508$	1.06361	−	13.5550i	0.0471899	−	0.601408i
$509$	−5.50555	+	5.50555i	−0.244029	+	0.244029i	−0.818515	−	0.574486i	$-0.805202\pi$
$509$	−5.50555	+	5.50555i	−0.244029	+	0.244029i	0.574486	+	0.818515i	$0.305202\pi$
$510$	0.437066	−	10.4170i	0.0193536	−	0.461272i
$511$			30.5797i			1.35277i
$512$	0.912208	+	22.6090i	0.0403143	+	0.999187i
$513$	0.834324	−	0.834324i	0.0368363	−	0.0368363i
$514$	−11.8451	+	25.7018i	−0.522463	+	1.13366i
$515$	39.1742	+	16.3542i	1.72622	+	0.720653i
$516$	6.70529	+	7.84716i	0.295184	+	0.345452i
$517$	57.7217			2.53860
$518$	−3.60990	+	7.83290i	−0.158610	+	0.344158i
$519$		−	15.1143i		−	0.663442i
$520$	−4.65591	+	38.5358i	−0.204175	+	1.68991i
$521$		−	39.2289i		−	1.71865i	−0.511430	−	0.859325i	$-0.670884\pi$
$521$		−	39.2289i		−	1.71865i	0.511430	−	0.859325i	$-0.329116\pi$
$522$	1.04657	+	0.482328i	0.0458073	+	0.0211109i
$523$	16.7434			0.732137			0.366068	−	0.930588i	$-0.380704\pi$
$523$	16.7434			0.732137			0.366068	+	0.930588i	$0.380704\pi$
$524$	0.782428	−	9.97158i	0.0341805	−	0.435611i
$525$	0.0817750	−	14.7087i	0.00356895	−	0.641941i
$526$	−20.1989	−	9.30894i	−0.880713	−	0.405889i
$527$	−6.11516	+	6.11516i	−0.266381	+	0.266381i
$528$	−11.0912	−	15.2507i	−0.482684	−	0.663703i
$529$			5.58265i			0.242724i
$530$	−3.39227	−	3.68939i	−0.147351	−	0.160257i
$531$	2.32603	−	2.32603i	0.100941	−	0.100941i
$532$	−4.50977	−	5.27776i	−0.195524	−	0.228820i
$533$			66.8191i			2.89426i
$534$	−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
$538$	−18.6909	−	8.61398i	−0.805823	−	0.371375i
$539$	−5.51406	+	5.51406i	−0.237507	+	0.237507i
$540$	−2.04044	+	3.97952i	−0.0878067	+	0.171251i
$541$	3.45427	+	3.45427i	0.148511	+	0.148511i	0.777452	−	0.628942i	$-0.216512\pi$
$541$	3.45427	+	3.45427i	0.148511	+	0.148511i	−0.628942	+	0.777452i	$0.716512\pi$
$542$	28.3028	−	10.4452i	1.21571	−	0.448660i
$543$	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
$547$	−18.1175			−0.774647			−0.387324	−	0.921944i	$-0.626600\pi$
$547$	−18.1175			−0.774647			−0.387324	+	0.921944i	$0.626600\pi$
$548$	1.66947	−	21.2764i	0.0713163	−	0.908885i
$549$	7.22499	+	7.22499i	0.308355	+	0.308355i
$550$	11.3676	+	31.3373i	0.484715	+	1.33623i
$551$	−0.961451			−0.0409592
$552$	−3.20813	−	11.3599i	−0.136547	−	0.483508i
$553$	−16.0715	−	16.0715i	−0.683431	−	0.683431i
$554$	−9.30514	−	25.2136i	−0.395337	−	1.07122i
$555$	−4.28763	+	1.76205i	−0.182000	+	0.0747947i
$556$	−0.628946	+	8.01554i	−0.0266732	+	0.339935i
$557$			21.1776i			0.897324i	0.893701	+	0.448662i	$0.148099\pi$
$557$			21.1776i			0.897324i	−0.893701	+	0.448662i	$0.851901\pi$
$558$	3.48006	−	1.28433i	0.147323	−	0.0543698i
$559$	−31.6742			−1.33967
$560$	22.4030	+	13.7999i	0.946698	+	0.583151i
$561$	−15.5434			−0.656241
$562$	5.12544	−	1.89156i	0.216204	−	0.0797905i
$563$		−	44.5712i		−	1.87845i	−0.343298	−	0.939226i	$-0.611544\pi$
$563$		−	44.5712i		−	1.87845i	0.343298	−	0.939226i	$-0.388456\pi$
$564$	24.4127	+	1.91556i	1.02796	+	0.0806596i
$565$	−26.8348	−	11.2028i	−1.12895	−	0.471307i
$566$	2.88471	+	7.81653i	0.121253	+	0.328553i
$567$	−2.08016	−	2.08016i	−0.0873584	−	0.0873584i
$568$	6.34044	+	3.54788i	0.266039	+	0.148866i
$569$	5.14194			0.215562			0.107781	−	0.994175i	$-0.465626\pi$
$569$	5.14194			0.215562			0.107781	+	0.994175i	$0.465626\pi$
$570$	0.156413	−	3.72793i	0.00655142	−	0.156146i
$571$	−17.4873	−	17.4873i	−0.731820	−	0.731820i	0.239160	−	0.970980i	$-0.423128\pi$
$571$	−17.4873	−	17.4873i	−0.731820	−	0.731820i	−0.970980	+	0.239160i	$0.923128\pi$
$572$	57.6898	+	4.52668i	2.41213	+	0.189270i
$573$	−14.5044			−0.605929
$574$	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	$0.776467\pi$
$578$	−8.13236	+	3.00127i	−0.338261	+	0.124836i
$579$	1.68153	+	1.68153i	0.0698822	+	0.0698822i
$580$	3.46861	−	1.11727i	0.144026	−	0.0463921i
$581$	18.0498	−	18.0498i	0.748833	−	0.748833i
$582$	−21.7939	−	10.0440i	−0.903385	−	0.416338i
$583$	−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
$587$		−	45.9941i		−	1.89838i	−0.314702	−	0.949191i	$-0.601905\pi$
$587$		−	45.9941i		−	1.89838i	0.314702	−	0.949191i	$-0.398095\pi$
$588$	−2.51509	+	2.14911i	−0.103721	+	0.0886279i
$589$	−2.18844	+	2.18844i	−0.0901729	+	0.0901729i
$590$	0.436068	−	10.3932i	0.0179526	−	0.427881i
$591$		−	8.65121i		−	0.355863i
$592$	1.29337	−	8.19088i	0.0531572	−	0.336643i
$593$	−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
$595$	20.0601	−	8.24392i	0.822385	−	0.337968i
$596$	9.03132	+	0.708650i	0.369937	+	0.0290274i
$597$	−22.3275			−0.913804
$598$	32.8977	+	15.1613i	1.34529	+	0.619994i
$599$		−	16.1877i		−	0.661413i	−0.943734	−	0.330707i	$-0.892713\pi$
$599$		−	16.1877i		−	0.661413i	0.943734	−	0.330707i	$-0.107287\pi$
$600$	3.76781	+	13.6310i	0.153820	+	0.556482i
$601$		−	14.1986i		−	0.579174i	−0.957152	−	0.289587i	$-0.906482\pi$
$601$		−	14.1986i		−	0.579174i	0.957152	−	0.289587i	$-0.0935180\pi$
$602$	−8.98672	+	19.4997i	−0.366271	+	0.794749i
$603$	0.885549			0.0360623
$604$	−13.4226	+	11.4694i	−0.546159	+	0.466685i
$605$	23.2159	−	9.54082i	0.943860	−	0.387889i
$606$	5.60343	−	12.1585i	0.227624	−	0.493906i
$607$	−22.9646	+	22.9646i	−0.932105	+	0.932105i	−0.997837	−	0.0657320i	$-0.979062\pi$
$607$	−22.9646	+	22.9646i	−0.932105	+	0.932105i	0.0657320	+	0.997837i	$0.479062\pi$
$608$	5.55190	+	3.70495i	0.225159	+	0.150256i
$609$			2.39711i			0.0971359i
$610$	32.2827	+	1.35449i	1.30709	+	0.0548416i
$611$	−53.1355	+	53.1355i	−2.14963	+	2.14963i
$612$	−6.57387	−	0.515823i	−0.265733	−	0.0208509i
$613$		−	37.1155i		−	1.49908i	−0.661958	−	0.749541i	$-0.730274\pi$
$613$		−	37.1155i		−	1.49908i	0.661958	−	0.749541i	$-0.269726\pi$
$614$	−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	−0.677316	−	0.735692i	$-0.736857\pi$
$617$	1.45005	−	1.45005i	0.0583767	−	0.0583767i	0.735692	+	0.677316i	$0.236857\pi$
$618$	11.2375	−	24.3834i	0.452037	−	0.980846i
$619$	−13.2111	+	13.2111i	−0.530998	+	0.530998i	−0.920869	−	0.389872i	$-0.872519\pi$
$619$	−13.2111	+	13.2111i	−0.530998	+	0.530998i	0.389872	+	0.920869i	$0.372519\pi$
$620$	5.35209	−	10.4383i	0.214945	−	0.419212i
$621$	2.95105	+	2.95105i	0.118421	+	0.118421i
$622$	1.99333	+	5.40122i	0.0799254	+	0.216569i
$623$	−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
$627$	−5.56251			−0.222145
$628$	−20.1625	−	23.5961i	−0.804573	−	0.941587i
$629$	−4.83312	−	4.83312i	−0.192709	−	0.192709i
$630$	−9.29457	−	0.389973i	−0.370305	−	0.0155369i
$631$	11.6636			0.464322			0.232161	−	0.972677i	$-0.425420\pi$
$631$	11.6636			0.464322			0.232161	+	0.972677i	$0.425420\pi$
$632$	19.0702	+	10.6710i	0.758572	+	0.424470i
$633$	−5.27613	−	5.27613i	−0.209707	−	0.209707i
$634$	13.0143	−	4.80294i	0.516862	−	0.190749i
$635$	14.0282	+	5.85641i	0.556692	+	0.232405i
$636$	−2.40985	+	2.05919i	−0.0955569	+	0.0816521i
$637$		−	10.1519i		−	0.402232i
$638$	−1.88094	−	5.09666i	−0.0744670	−	0.201779i
$639$	−2.56877			−0.101619
$640$	−24.3349	−	6.91465i	−0.961922	−	0.273325i
$641$	−20.8880			−0.825025			−0.412512	−	0.910952i	$-0.635349\pi$
$641$	−20.8880			−0.825025			−0.412512	+	0.910952i	$0.635349\pi$
$642$	5.36483	+	14.5368i	0.211733	+	0.573720i
$643$			36.6130i			1.44388i	0.691957	+	0.721939i	$0.256749\pi$
$643$			36.6130i			1.44388i	−0.691957	+	0.721939i	$0.743251\pi$
$644$	18.6677	−	15.9513i	0.735611	−	0.628569i
$645$	−10.6739	+	4.38655i	−0.420284	+	0.172720i
$646$	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	$0.519001\pi$
$648$	2.46828	+	1.38116i	0.0969631	+	0.0542571i
$649$	−15.5079			−0.608737
$650$	−39.3118	−	18.3831i	−1.54194	−	0.721043i
$651$	5.45626	+	5.45626i	0.213848	+	0.213848i
$652$	11.2414	+	13.1558i	0.440248	+	0.515219i
$653$	−22.3501			−0.874627			−0.437313	−	0.899309i	$-0.644070\pi$
$653$	−22.3501			−0.874627			−0.437313	+	0.899309i	$0.644070\pi$
$654$	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
$658$	17.6362	+	47.7878i	0.687532	+	1.86296i
$659$	−15.9700	−	15.9700i	−0.622102	−	0.622102i	0.323967	−	0.946068i	$-0.394983\pi$
$659$	−15.9700	−	15.9700i	−0.622102	−	0.622102i	−0.946068	+	0.323967i	$0.894983\pi$
$660$	20.0678	−	6.46400i	0.781138	−	0.251611i
$661$	−15.1592	+	15.1592i	−0.589624	+	0.589624i	−0.937530	−	0.347906i	$-0.886893\pi$
$661$	−15.1592	+	15.1592i	−0.589624	+	0.589624i	0.347906	+	0.937530i	$0.386893\pi$
$662$	−6.00402	+	13.0277i	−0.233353	+	0.506338i
$663$	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
$667$		−	3.40070i		−	0.131676i
$668$	−8.08179	−	0.634144i	−0.312694	−	0.0245358i
$669$	−13.8202	+	13.8202i	−0.534320	+	0.534320i
$670$	2.06141	−	1.89540i	0.0796394	−	0.0732256i
$671$		−	48.1696i		−	1.85957i
$672$	9.23728	−	13.8421i	0.356336	−	0.533971i
$673$	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
$675$	−3.51582	−	3.55514i	−0.135324	−	0.136837i
$676$	−37.5065	+	32.0488i	−1.44256	+	1.23265i
$677$	−3.95511			−0.152007			−0.0760036	−	0.997108i	$-0.524216\pi$
$677$	−3.95511			−0.152007			−0.0760036	+	0.997108i	$0.524216\pi$
$678$	−7.69779	+	16.7029i	−0.295632	+	0.641473i
$679$		−	49.9175i		−	1.91566i
$680$	−16.4069	+	12.8697i	−0.629178	+	0.493531i
$681$			1.66286i			0.0637209i
$682$	−15.8823	−	7.31957i	−0.608164	−	0.280281i
$683$	50.9345			1.94895			0.974476	−	0.224490i	$-0.0720717\pi$
$683$	50.9345			1.94895			0.974476	+	0.224490i	$0.0720717\pi$
$684$	−2.35259	−	0.184598i	−0.0899537	−	0.00705828i
$685$	22.0191	+	9.19242i	0.841308	+	0.351224i
$686$	20.1987	+	9.30886i	0.771191	+	0.355414i
$687$	−11.3744	+	11.3744i	−0.433962	+	0.433962i
$688$	3.21980	−	20.3909i	0.122754	−	0.777395i
$689$		−	9.72710i		−	0.370573i
$690$	13.1859	+	0.553240i	0.501978	+	0.0210615i
$691$	−13.5869	+	13.5869i	−0.516870	+	0.516870i	−0.916623	−	0.399753i	$-0.869096\pi$
$691$	−13.5869	+	13.5869i	−0.516870	+	0.516870i	0.399753	+	0.916623i	$0.369096\pi$
$692$	−22.9813	+	19.6372i	−0.873619	+	0.746496i
$693$			13.8686i			0.526824i
$694$	−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
$698$	−26.9025	−	12.3984i	−1.01827	−	0.469286i
$699$	−9.38976	+	9.38976i	−0.355153	+	0.355153i
$700$	−22.4709	+	18.9860i	−0.849322	+	0.717603i
$701$	−0.627254	−	0.627254i	−0.0236911	−	0.0236911i	0.695162	−	0.718853i	$-0.255333\pi$
$701$	−0.627254	−	0.627254i	−0.0236911	−	0.0236911i	−0.718853	+	0.695162i	$0.755333\pi$
$702$	−8.14270	+	3.00509i	−0.307327	+	0.113420i
$703$	−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
$707$	27.8483			1.04734
$708$	−6.55886	−	0.514646i	−0.246497	−	0.0193416i
$709$	−26.7170	−	26.7170i	−1.00338	−	1.00338i	−0.999994	−	0.00338478i	$-0.998923\pi$
$709$	−26.7170	−	26.7170i	−1.00338	−	1.00338i	−0.00338478	−	0.999994i	$-0.501077\pi$
$710$	−5.97968	+	5.49811i	−0.224413	+	0.206340i
$711$	−7.72612			−0.289752
$712$	21.4886	+	12.0243i	0.805318	+	0.450628i
$713$	−7.74061	−	7.74061i	−0.289888	−	0.289888i
$714$	−4.74910	−	12.8683i	−0.177730	−	0.481586i
$715$	−24.9247	+	59.7036i	−0.932131	+	2.23279i
$716$	−34.8709	−	2.73617i	−1.30319	−	0.102256i
$717$			8.88914i			0.331971i
$718$	12.4578	−	4.59760i	0.464922	−	0.171581i
$719$	27.5794			1.02854			0.514269	−	0.857629i	$-0.328063\pi$
$719$	27.5794			1.02854			0.514269	+	0.857629i	$0.328063\pi$
$720$	8.70194	−	2.06790i	0.324302	−	0.0770659i
$721$	55.8488			2.07992
$722$	−23.3611	+	8.62147i	−0.869409	+	0.320858i
$723$		−	20.5978i		−	0.766041i
$724$	2.12181	−	27.0413i	0.0788565	−	1.00498i
$725$	−0.0226510	+	4.07418i	−0.000841235	+	0.151311i
$726$	−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	$0.681695\pi$
$728$	13.8788	+	49.1445i	0.514384	+	1.82142i
$729$	−1.00000			−0.0370370
$730$	32.8428	+	1.37799i	1.21557	+	0.0510015i
$731$	−12.0319	−	12.0319i	−0.445014	−	0.445014i
$732$	1.59856	−	20.3727i	0.0590845	−	0.752998i
$733$	12.3271			0.455313			0.227656	−	0.973742i	$-0.426894\pi$
$733$	12.3271			0.455313			0.227656	+	0.973742i	$0.426894\pi$
$734$	−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
$738$	14.4447	−	5.33084i	0.531715	−	0.196231i
$739$	−24.8212	−	24.8212i	−0.913062	−	0.913062i	0.0834496	−	0.996512i	$-0.473406\pi$
$739$	−24.8212	−	24.8212i	−0.913062	−	0.913062i	−0.996512	+	0.0834496i	$0.973406\pi$
$740$	8.24991	+	4.23003i	0.303273	+	0.155499i
$741$	5.12054	−	5.12054i	0.188108	−	0.188108i
$742$	−5.98834	−	2.75981i	−0.219839	−	0.101316i
$743$	−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
$747$		−	8.67714i		−	0.317480i
$748$	20.1947	+	23.6338i	0.738393	+	0.864137i
$749$	−22.7917	+	22.7917i	−0.832789	+	0.832789i
$750$	−15.7936	−	0.750632i	−0.576699	−	0.0274092i
$751$		−	24.7594i		−	0.903484i	−0.892149	−	0.451742i	$-0.850803\pi$
$751$		−	24.7594i		−	0.903484i	0.892149	−	0.451742i	$-0.149197\pi$
$752$	−28.8056	−	39.6085i	−1.05043	−	1.44437i
$753$	16.8455	−	16.8455i	0.613883	−	0.613883i
$754$	6.42319	+	2.96022i	0.233919	+	0.107805i
$755$	−7.50322	−	18.2578i	−0.273070	−	0.664468i
$756$	−0.460244	+	5.86555i	−0.0167389	+	0.213328i
$757$	−35.5014			−1.29032			−0.645160	−	0.764047i	$-0.723209\pi$
$757$	−35.5014			−1.29032			−0.645160	+	0.764047i	$0.723209\pi$
$758$	−26.8997	−	12.3971i	−0.977042	−	0.450284i
$759$		−	19.6749i		−	0.714153i
$760$	−5.87157	+	4.60570i	−0.212984	+	0.167066i
$761$		−	19.8569i		−	0.719812i	−0.932989	−	0.359906i	$-0.882809\pi$
$761$		−	19.8569i		−	0.719812i	0.932989	−	0.359906i	$-0.117191\pi$
$762$	4.02411	−	8.73165i	0.145778	−	0.316314i
$763$	2.67900			0.0969862
$764$	18.8448	+	22.0540i	0.681782	+	0.797886i
$765$	2.84022	−	6.80334i	0.102688	−	0.245975i
$766$	18.6609	−	40.4911i	0.674245	−	1.46300i
$767$	14.2757	−	14.2757i	0.515465	−	0.515465i
$768$	−4.93000	+	15.2215i	−0.177896	+	0.549260i
$769$			37.1951i			1.34129i	0.741779	+	0.670644i	$0.233982\pi$
$769$			37.1951i			1.34129i	−0.741779	+	0.670644i	$0.766018\pi$
$770$	29.6839	+	32.2838i	1.06973	+	1.16343i
$771$	−14.1500	+	14.1500i	−0.509600	+	0.509600i
$772$	0.372047	−	4.74152i	0.0133903	−	0.170651i
$773$		−	13.2454i		−	0.476402i	−0.971216	−	0.238201i	$-0.923442\pi$
$773$		−	13.2454i		−	0.476402i	0.971216	−	0.238201i	$-0.0765578\pi$
$774$	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
$778$	−14.3255	+	31.0841i	−0.513595	+	1.11442i
$779$	−9.08353	+	9.08353i	−0.325451	+	0.325451i
$780$	−12.5229	+	24.4237i	−0.448392	+	0.874510i
$781$	8.56310	+	8.56310i	0.306412	+	0.306412i
$782$	6.73738	+	18.2559i	0.240928	+	0.652828i
$783$	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
$787$	−12.0292			−0.428794			−0.214397	−	0.976747i	$-0.568779\pi$
$787$	−12.0292			−0.428794			−0.214397	+	0.976747i	$0.568779\pi$
$788$	−13.1542	+	11.2401i	−0.468600	+	0.400412i
$789$	−11.1204	−	11.1204i	−0.395896	−	0.395896i
$790$	−17.9852	+	16.5367i	−0.639883	+	0.588350i
$791$	−38.2571			−1.36026
$792$	−3.62395	−	12.8323i	−0.128771	−	0.455975i
$793$	44.3423	+	44.3423i	1.57464	+	1.57464i
$794$	21.6002	−	7.97161i	0.766562	−	0.282902i
$795$	−1.34710	−	3.27794i	−0.0477768	−	0.116256i
$796$	29.0091	+	33.9491i	1.02820	+	1.20329i
$797$		−	45.2714i		−	1.60359i	−0.597597	−	0.801797i	$-0.703878\pi$
$797$		−	45.2714i		−	1.60359i	0.597597	−	0.801797i	$-0.296122\pi$
$798$	−1.69956	−	4.60520i	−0.0601639	−	0.163022i
$799$	−40.3685			−1.42813
$800$	15.8307	−	23.4391i	0.559698	−	0.828696i
$801$	−8.70590			−0.307608
$802$	−2.51606	−	6.81762i	−0.0888451	−	0.240738i
$803$		−	49.0053i		−	1.72936i
$804$	−1.15055	−	1.34648i	−0.0405768	−	0.0474868i
$805$	10.4352	+	25.3922i	0.367793	+	0.894958i
$806$	21.3584	−	7.88236i	0.752316	−	0.277644i
$807$	−10.2902	−	10.2902i	−0.362231	−	0.362231i
$808$	−25.7674	+	7.27694i	−0.906494	+	0.256002i
$809$	−5.16391			−0.181553			−0.0907767	−	0.995871i	$-0.528935\pi$
$809$	−5.16391			−0.181553			−0.0907767	+	0.995871i	$0.528935\pi$
$810$	−2.32784	+	2.14037i	−0.0817919	+	0.0752048i
$811$	15.7171	+	15.7171i	0.551903	+	0.551903i	0.926990	−	0.375087i	$-0.122387\pi$
$811$	15.7171	+	15.7171i	0.551903	+	0.551903i	−0.375087	+	0.926990i	$0.622387\pi$
$812$	3.64483	−	3.11446i	0.127908	−	0.109296i
$813$	21.3325			0.748163
$814$	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
$818$	−1.90469	−	5.16103i	−0.0665959	−	0.180451i
$819$	−12.7667	−	12.7667i	−0.446103	−	0.446103i
$820$	22.2149	−	43.3262i	0.775778	−	1.51302i
$821$	−15.6816	+	15.6816i	−0.547293	+	0.547293i	−0.925657	−	0.378364i	$-0.876487\pi$
$821$	−15.6816	+	15.6816i	−0.547293	+	0.547293i	0.378364	+	0.925657i	$0.376487\pi$
$822$	6.31637	−	13.7055i	0.220309	−	0.478034i
$823$	−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
$827$			14.0926i			0.490046i	0.969517	+	0.245023i	$0.0787956\pi$
$827$			14.0926i			0.490046i	−0.969517	+	0.245023i	$0.921204\pi$
$828$	0.652933	−	8.32124i	0.0226910	−	0.289183i
$829$	12.1216	−	12.1216i	0.421000	−	0.421000i	−0.464548	−	0.885548i	$-0.653783\pi$
$829$	12.1216	−	12.1216i	0.421000	−	0.421000i	0.885548	+	0.464548i	$0.153783\pi$
$830$	−18.5723	−	20.1990i	−0.644652	−	0.701117i
$831$		−	19.0041i		−	0.659244i
$832$	−25.6835	−	41.8456i	−0.890415	−	1.45073i
$833$	3.85633	−	3.85633i	0.133614	−	0.133614i
$834$	−2.37959	+	5.16331i	−0.0823983	+	0.178791i
$835$	3.49171	−	8.36390i	0.120836	−	0.289445i
$836$	7.22711	+	8.45784i	0.249955	+	0.292520i
$837$	2.62300			0.0906643
$838$	8.11083	−	17.5992i	0.280184	−	0.607954i
$839$			14.6206i			0.504759i	0.967628	+	0.252380i	$0.0812132\pi$
$839$			14.6206i			0.504759i	−0.967628	+	0.252380i	$0.918787\pi$
$840$	11.4830	+	14.6391i	0.396203	+	0.505098i
$841$			28.3360i			0.977104i
$842$	35.0321	+	16.1451i	1.20729	+	0.556395i
$843$	3.86317			0.133054
$844$	−1.16737	+	14.8774i	−0.0401825	+	0.512102i
$845$	−20.9661	−	51.0172i	−0.721254	−	1.75504i
$846$	15.7257	+	7.24743i	0.540662	+	0.249172i
$847$	23.3498	−	23.3498i	0.802309	−	0.802309i
$848$	6.26202	+	0.988796i	0.215039	+	0.0339554i
$849$			5.89151i			0.202196i
$850$	−7.95007	−	21.9162i	−0.272685	−	0.751719i
$851$	6.11779	−	6.11779i	0.209715	−	0.209715i
$852$	3.33748	+	3.90583i	0.114340	+	0.133812i
$853$		−	13.7252i		−	0.469940i	−0.972003	−	0.234970i	$-0.924501\pi$
$853$		−	13.7252i		−	0.469940i	0.972003	−	0.234970i	$-0.0754992\pi$
$854$	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	−0.951029	−	0.309102i	$-0.899972\pi$
$857$	−18.7921	+	18.7921i	−0.641927	+	0.641927i	0.309102	+	0.951029i	$0.399972\pi$
$858$	37.1616	+	17.1265i	1.26868	+	0.584688i
$859$	−23.1774	+	23.1774i	−0.790803	+	0.790803i	−0.981625	−	0.190822i	$-0.938885\pi$
$859$	−23.1774	+	23.1774i	−0.790803	+	0.790803i	0.190822	+	0.981625i	$0.438885\pi$
$860$	20.5379	+	10.5305i	0.700335	+	0.359087i
$861$	22.6473	+	22.6473i	0.771817	+	0.771817i
$862$	5.47988	−	2.02236i	0.186645	−	0.0688820i
$863$	8.96863	+	8.96863i	0.305296	+	0.305296i	0.843082	−	0.537786i	$-0.180739\pi$
$863$	8.96863	+	8.96863i	0.305296	+	0.305296i	−0.537786	+	0.843082i	$0.680739\pi$
$864$	−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
$867$	−6.12955			−0.208171
$868$	1.20722	−	15.3854i	0.0409758	−	0.522213i
$869$	25.7553	+	25.7553i	0.873690	+	0.873690i
$870$	2.57451	+	0.108019i	0.0872842	+	0.00366219i
$871$	5.43492			0.184155
$872$	−2.47881	+	0.700039i	−0.0839431	+	0.0237063i
$873$	−11.9985	−	11.9985i	−0.406087	−	0.406087i
$874$	2.41111	+	6.53324i	0.0815570	+	0.220990i
$875$	−12.3327	−	30.4905i	−0.416921	−	1.03077i
$876$	1.62629	−	20.7262i	0.0549474	−	0.700272i
$877$		−	47.1944i		−	1.59364i	−0.604215	−	0.796822i	$-0.706513\pi$
$877$		−	47.1944i		−	1.59364i	0.604215	−	0.796822i	$-0.293487\pi$
$878$	29.2906	−	10.8098i	0.988510	−	0.364812i
$879$	4.49132			0.151489
$880$	−35.9017	−	22.1149i	−1.21025	−	0.745492i
$881$	51.5667			1.73733			0.868663	−	0.495403i	$-0.164980\pi$
$881$	51.5667			1.73733			0.868663	+	0.495403i	$0.164980\pi$
$882$	−2.19459	+	0.809919i	−0.0738956	+	0.0272714i
$883$			33.7083i			1.13438i	0.823589	+	0.567188i	$0.191969\pi$
$883$			33.7083i			1.13438i	−0.823589	+	0.567188i	$0.808031\pi$
$884$	−40.3461	−	3.16579i	−1.35699	−	0.106477i
$885$	2.83373	−	6.78780i	0.0952548	−	0.228170i
$886$	−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	$0.712793\pi$
$888$	2.86327	−	5.11697i	0.0960852	−	0.171714i
$889$	19.9993			0.670755
$890$	−20.2659	+	18.6338i	−0.679315	+	0.624607i
$891$	3.33354	+	3.33354i	0.111678	+	0.111678i
$892$	38.9696	+	3.05778i	1.30480	+	0.102382i
$893$	−14.4467			−0.483440
$894$	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
$898$	16.3520	−	6.03475i	0.545673	−	0.201382i
$899$	−1.51134	−	1.51134i	−0.0504059	−	0.0504059i
$900$	−0.837666	+	9.96485i	−0.0279222	+	0.332162i
$901$	3.69497	−	3.69497i	0.123097	−	0.123097i
$902$	−65.9225	−	30.3813i	−2.19498	−	1.01159i
$903$	−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
$907$		−	39.4081i		−	1.30852i	−0.756268	−	0.654262i	$-0.772979\pi$
$907$		−	39.4081i		−	1.30852i	0.756268	−	0.654262i	$-0.227021\pi$
$908$	2.52839	−	2.16047i	0.0839075	−	0.0716978i
$909$	6.69380	−	6.69380i	0.222019	−	0.222019i
$910$	−57.0441	−	2.39340i	−1.89099	−	0.0793404i
$911$		−	7.29607i		−	0.241729i	−0.992669	−	0.120865i	$-0.961433\pi$
$911$		−	7.29607i		−	0.241729i	0.992669	−	0.120865i	$-0.0385667\pi$
$912$	2.77593	+	3.81698i	0.0919203	+	0.126393i
$913$	−28.9256	+	28.9256i	−0.957298	+	0.957298i
$914$	19.2243	+	8.85977i	0.635882	+	0.293055i
$915$	21.0839	+	8.80197i	0.697012	+	0.290984i
$916$	32.0732	+	2.51664i	1.05973	+	0.0831523i
$917$	14.7122			0.485840
$918$	−4.23464	−	1.95159i	−0.139764	−	0.0644122i
$919$			52.5346i			1.73296i	0.499215	+	0.866478i	$0.333622\pi$
$919$			52.5346i			1.73296i	−0.499215	+	0.866478i	$0.666378\pi$
$920$	−16.2906	−	20.7680i	−0.537085	−	0.684702i
$921$		−	3.84487i		−	0.126693i
$922$	−5.66789	+	12.2984i	−0.186662	+	0.405026i
$923$	−15.7654			−0.518926
$924$	21.0873	−	18.0188i	0.693721	−	0.592775i
$925$	−7.37012	+	7.28862i	−0.242328	+	0.239648i
$926$	9.50727	−	20.6292i	0.312428	−	0.677918i
$927$	13.4242	−	13.4242i	0.440907	−	0.440907i
$928$	−2.55864	+	3.83415i	−0.0839916	+	0.125862i
$929$		−	48.7878i		−	1.60068i	−0.599549	−	0.800338i	$-0.704654\pi$
$929$		−	48.7878i		−	1.60068i	0.599549	−	0.800338i	$-0.295346\pi$
$930$	6.10593	−	5.61419i	0.200221	−	0.184097i
$931$	1.38007	−	1.38007i	0.0452299	−	0.0452299i
$932$	26.4769	+	2.07753i	0.867278	+	0.0680517i
$933$			4.07103i			0.133279i
$934$	−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	−0.0414198	−	0.999142i	$-0.513188\pi$
$937$	29.3163	−	29.3163i	0.957722	−	0.957722i	0.999142	+	0.0414198i	$0.0131881\pi$
$938$	1.54202	−	3.34593i	0.0503487	−	0.109248i
$939$	1.37922	−	1.37922i	0.0450093	−	0.0450093i
$940$	52.1192	−	16.7880i	1.69994	−	0.547564i
$941$	−7.65378	−	7.65378i	−0.249506	−	0.249506i	0.571262	−	0.820768i	$-0.306454\pi$
$941$	−7.65378	−	7.65378i	−0.249506	−	0.249506i	−0.820768	+	0.571262i	$0.806454\pi$
$942$	−7.59850	−	20.5892i	−0.247572	−	0.670832i
$943$	−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
$947$	39.6694			1.28908			0.644541	−	0.764569i	$-0.277048\pi$
$947$	39.6694			1.28908			0.644541	+	0.764569i	$0.277048\pi$
$948$	10.0382	+	11.7476i	0.326025	+	0.381545i
$949$	45.1116	+	45.1116i	1.46438	+	1.46438i
$950$	−2.84510	−	7.84316i	−0.0923071	−	0.254466i
$951$	9.80915			0.318084
$952$	−13.3961	+	23.9403i	−0.434171	+	0.775908i
$953$	−8.83095	−	8.83095i	−0.286063	−	0.286063i	0.549458	−	0.835521i	$-0.314834\pi$
$953$	−8.83095	−	8.83095i	−0.286063	−	0.286063i	−0.835521	+	0.549458i	$0.814834\pi$
$954$	−2.10276	+	0.776029i	−0.0680794	+	0.0251249i
$955$	−29.9983	+	12.3281i	−0.970724	+	0.398929i
$956$	13.5160	−	11.5492i	0.437139	−	0.373529i
$957$		−	3.84148i		−	0.124177i
$958$	−7.51635	−	20.3666i	−0.242842	−	0.658015i
$959$	31.3916			1.01369
$960$	−14.4503	−	10.5446i	−0.466381	−	0.340327i
$961$	24.1198			0.778060
$962$	6.22982	+	16.8806i	0.200858	+	0.544252i
$963$			10.9567i			0.353075i
$964$	−31.3191	+	26.7618i	−1.00872	+	0.861938i
$965$	4.90703	+	2.04856i	0.157963	+	0.0659455i
$966$	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	$0.767548\pi$
$968$	−15.5036	+	27.7065i	−0.498303	+	0.890519i
$969$	3.89021			0.124972
$970$	−53.6117	−	2.24939i	−1.72137	−	0.0722235i
$971$	21.9788	+	21.9788i	0.705334	+	0.705334i	0.965550	−	0.260216i	$-0.0837939\pi$
$971$	21.9788	+	21.9788i	0.705334	+	0.705334i	−0.260216	+	0.965550i	$0.583794\pi$
$972$	1.29925	+	1.52051i	0.0416735	+	0.0487703i
$973$	−11.8263			−0.379132
$974$	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	$0.484736\pi$
$978$	4.23646	+	11.4793i	0.135467	+	0.367067i
$979$	29.0215	+	29.0215i	0.927531	+	0.927531i
$980$	−3.37513	+	6.58258i	−0.107814	+	0.210273i
$981$	0.643941	−	0.643941i	0.0205595	−	0.0205595i
$982$	−5.15949	+	11.1952i	−0.164646	+	0.357255i
$983$	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
$987$			36.0188i			1.14649i
$988$	−14.4387	−	1.13294i	−0.459356	−	0.0360437i
$989$	15.2300	−	15.2300i	0.484286	−	0.484286i
$990$	14.8950	+	0.624948i	0.473393	+	0.0198622i
$991$		−	24.6172i		−	0.781991i	−0.920393	−	0.390996i	$-0.872131\pi$
$991$		−	24.6172i		−	0.781991i	0.920393	−	0.390996i	$-0.127869\pi$
$992$	2.90327	+	14.5511i	0.0921790	+	0.461999i
$993$	−7.17235	+	7.17235i	−0.227608	+	0.227608i
$994$	−4.47303	+	9.70575i	−0.141876	+	0.307848i
$995$	−46.1784	+	18.9775i	−1.46395	+	0.601627i
$996$	−13.1937	+	11.2738i	−0.418057	+	0.357224i
$997$	−36.9465			−1.17011			−0.585053	−	0.810995i	$-0.698926\pi$
$997$	−36.9465			−1.17011			−0.585053	+	0.810995i	$0.698926\pi$
$998$	13.5579	−	29.4184i	0.429167	−	0.931222i
$999$			2.07309i			0.0655897i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.1	✓	16	5.3	odd	4
240.2.y.e.187.1	yes	16	16.11	odd	4
240.2.bc.e.43.4	yes	16	80.43	even	4	inner
240.2.bc.e.67.4	yes	16	1.1	even	1	trivial
720.2.z.f.163.8		16	15.8	even	4
720.2.z.f.667.8		16	48.11	even	4
720.2.bd.f.307.5		16	3.2	odd	2
720.2.bd.f.523.5		16	240.203	odd	4
960.2.y.e.847.7		16	16.5	even	4
960.2.y.e.943.7		16	20.3	even	4
960.2.bc.e.367.3		16	4.3	odd	2
960.2.bc.e.463.3		16	80.53	odd	4
1920.2.y.i.223.2		16	40.13	odd	4
1920.2.y.i.1567.2		16	16.3	odd	4
1920.2.y.j.223.2		16	40.3	even	4
1920.2.y.j.1567.2		16	16.13	even	4
1920.2.bc.i.607.6		16	8.5	even	2
1920.2.bc.i.1183.6		16	80.3	even	4
1920.2.bc.j.607.6		16	8.3	odd	2
1920.2.bc.j.1183.6		16	80.13	odd	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.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.489639 - 1.32675i) q^{2} -1.00000i q^{3} +(-1.52051 + 1.29925i) q^{4} +(-0.849960 - 2.06823i) q^{5} +(-1.32675 + 0.489639i) q^{6} +(-2.08016 - 2.08016i) q^{7} +(2.46828 + 1.38116i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.489639 - 1.32675i) q^{2} -1.00000i q^{3} +(-1.52051 + 1.29925i) q^{4} +(-0.849960 - 2.06823i) q^{5} +(-1.32675 + 0.489639i) q^{6} +(-2.08016 - 2.08016i) q^{7} +(2.46828 + 1.38116i) q^{8} -1.00000 q^{9} +(-2.32784 + 2.14037i) q^{10} +(3.33354 + 3.33354i) q^{11} +(1.29925 + 1.52051i) q^{12} -6.13735 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} +(0.489639 + 1.32675i) q^{18} +(-0.834324 - 0.834324i) q^{19} +(3.97952 + 2.04044i) q^{20} +(-2.08016 + 2.08016i) q^{21} +(2.79053 - 6.05500i) 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} +1.00000i q^{27} +(5.86555 + 0.460244i) q^{28} +(0.576185 - 0.576185i) q^{29} +(2.14037 + 2.32784i) q^{30} -2.62300i q^{31} +(-5.54751 + 1.10685i) q^{32} +(3.33354 - 3.33354i) q^{33} +(-1.95159 + 4.23464i) q^{34} +(-2.53419 + 6.07029i) q^{35} +(1.52051 - 1.29925i) q^{36} +2.07309 q^{37} +(-0.698418 + 1.51545i) q^{38} +6.13735i q^{39} +(0.758619 - 6.27889i) q^{40} -10.8873i q^{41} +(3.77837 + 1.74131i) q^{42} +5.16088 q^{43} +(-9.39979 - 0.737562i) q^{44} +(0.849960 + 2.06823i) q^{45} +(-5.36024 - 2.47034i) q^{46} +(8.65772 - 8.65772i) q^{47} +(-3.95105 - 0.623885i) q^{48} +1.65411i q^{49} +(6.40534 + 2.99528i) q^{50} +(-2.33136 + 2.33136i) q^{51} +(9.33189 - 7.97397i) q^{52} +1.58490i 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} +(-1.04657 - 0.482328i) q^{58} +(-2.32603 + 2.32603i) q^{59} +(2.04044 - 3.97952i) q^{60} +(-7.22499 - 7.22499i) q^{61} +(-3.48006 + 1.28433i) 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} -0.885549 q^{67} +(6.57387 + 0.515823i) q^{68} +(-2.95105 - 2.95105i) q^{69} +(9.29457 + 0.389973i) q^{70} +2.56877 q^{71} +(-2.46828 - 1.38116i) q^{72} +(-7.35033 - 7.35033i) q^{73} +(-1.01507 - 2.75047i) q^{74} +(3.51582 + 3.55514i) q^{75} +(2.35259 + 0.184598i) q^{76} -13.8686i q^{77} +(8.14270 - 3.00509i) q^{78} +7.72612 q^{79} +(-8.70194 + 2.06790i) q^{80} +1.00000 q^{81} +(-14.4447 + 5.33084i) q^{82} +8.67714i q^{83} +(0.460244 - 5.86555i) q^{84} +(-2.84022 + 6.80334i) q^{85} +(-2.52697 - 6.84718i) q^{86} +(-0.576185 - 0.576185i) q^{87} +(3.62395 + 12.8323i) q^{88} +8.70590 q^{89} +(2.32784 - 2.14037i) q^{90} +(12.7667 + 12.7667i) q^{91} +(-0.652933 + 8.32124i) q^{92} -2.62300 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} +(2.19459 - 0.809919i) q^{98} +(-3.33354 - 3.33354i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9	\( 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9} - 2 q^{10} - 4 q^{12} - 8 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} - 8 q^{17} - 2 q^{18} - 8 q^{19} + 4 q^{20} - 4 q^{21} + 4 q^{24} - 32 q^{25} + 20 q^{26} + 12 q^{28} - 12 q^{29} + 2 q^{30} - 28 q^{32} + 12 q^{35} - 8 q^{36} - 24 q^{37} + 16 q^{38} + 16 q^{40} + 24 q^{42} + 24 q^{43} - 52 q^{44} + 8 q^{45} - 16 q^{46} + 32 q^{47} - 16 q^{48} + 6 q^{50} - 8 q^{51} + 24 q^{52} - 2 q^{54} - 4 q^{55} + 20 q^{56} - 8 q^{57} + 12 q^{58} + 24 q^{59} + 24 q^{60} + 40 q^{61} + 28 q^{62} + 4 q^{63} + 8 q^{64} - 4 q^{65} - 8 q^{66} + 16 q^{67} - 8 q^{68} + 12 q^{70} - 8 q^{72} - 8 q^{73} - 64 q^{74} + 24 q^{75} + 16 q^{76} + 12 q^{78} + 48 q^{79} + 16 q^{81} - 32 q^{82} - 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} + 24 q^{88} + 2 q^{90} - 40 q^{91} - 16 q^{92} - 32 q^{93} + 20 q^{94} - 8 q^{95} - 28 q^{96} + 48 q^{97} + 62 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9 - 2 * q^10 - 4 * q^12 - 8 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 - 8 * q^17 - 2 * q^18 - 8 * q^19 + 4 * q^20 - 4 * q^21 + 4 * q^24 - 32 * q^25 + 20 * q^26 + 12 * q^28 - 12 * q^29 + 2 * q^30 - 28 * q^32 + 12 * q^35 - 8 * q^36 - 24 * q^37 + 16 * q^38 + 16 * q^40 + 24 * q^42 + 24 * q^43 - 52 * q^44 + 8 * q^45 - 16 * q^46 + 32 * q^47 - 16 * q^48 + 6 * q^50 - 8 * q^51 + 24 * q^52 - 2 * q^54 - 4 * q^55 + 20 * q^56 - 8 * q^57 + 12 * q^58 + 24 * q^59 + 24 * q^60 + 40 * q^61 + 28 * q^62 + 4 * q^63 + 8 * q^64 - 4 * q^65 - 8 * q^66 + 16 * q^67 - 8 * q^68 + 12 * q^70 - 8 * q^72 - 8 * q^73 - 64 * q^74 + 24 * q^75 + 16 * q^76 + 12 * q^78 + 48 * q^79 + 16 * q^81 - 32 * q^82 - 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 + 24 * q^88 + 2 * q^90 - 40 * q^91 - 16 * q^92 - 32 * q^93 + 20 * q^94 - 8 * q^95 - 28 * q^96 + 48 * q^97 + 62 * q^98

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