LMFDB - Embedded newform 240.2.y.e.163.8

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			163.8
Root			$0.424183 + 1.34910i$ of defining polynomial
Character	$\chi$	$=$	240.163
Dual form			240.2.y.e.187.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20932 + 0.733173i) q^{2} +1.00000 q^{3} +(0.924916 + 1.77328i) q^{4} +(-2.15140 + 0.609492i) q^{5} +(1.20932 + 0.733173i) q^{6} +(0.566689 - 0.566689i) q^{7} +(-0.181602 + 2.82259i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.20932 + 0.733173i) q^{2} +1.00000 q^{3} +(0.924916 + 1.77328i) q^{4} +(-2.15140 + 0.609492i) q^{5} +(1.20932 + 0.733173i) q^{6} +(0.566689 - 0.566689i) q^{7} +(-0.181602 + 2.82259i) q^{8} +1.00000 q^{9} +(-3.04860 - 0.840275i) q^{10} +(3.64458 + 3.64458i) q^{11} +(0.924916 + 1.77328i) q^{12} -2.74185i q^{13} +(1.10079 - 0.269828i) q^{14} +(-2.15140 + 0.609492i) q^{15} +(-2.28906 + 3.28027i) q^{16} +(2.08381 - 2.08381i) q^{17} +(1.20932 + 0.733173i) q^{18} +(-5.79168 - 5.79168i) q^{19} +(-3.07066 - 3.25131i) q^{20} +(0.566689 - 0.566689i) q^{21} +(1.73536 + 7.07957i) q^{22} +(-4.28027 - 4.28027i) q^{23} +(-0.181602 + 2.82259i) q^{24} +(4.25704 - 2.62252i) q^{25} +(2.01025 - 3.31578i) q^{26} +1.00000 q^{27} +(1.52904 + 0.480760i) q^{28} +(-2.63716 + 2.63716i) q^{29} +(-3.04860 - 0.840275i) q^{30} -8.10909i q^{31} +(-5.17322 + 2.28863i) q^{32} +(3.64458 + 3.64458i) q^{33} +(4.04778 - 0.992201i) q^{34} +(-0.873782 + 1.56457i) q^{35} +(0.924916 + 1.77328i) q^{36} +2.28428i q^{37} +(-2.75770 - 11.2503i) q^{38} -2.74185i q^{39} +(-1.32965 - 6.18321i) q^{40} +2.27486i q^{41} +(1.10079 - 0.269828i) q^{42} +3.06480i q^{43} +(-3.09194 + 9.83379i) q^{44} +(-2.15140 + 0.609492i) q^{45} +(-2.03805 - 8.31441i) q^{46} +(1.80573 + 1.80573i) q^{47} +(-2.28906 + 3.28027i) q^{48} +6.35773i q^{49} +(7.07089 - 0.0503283i) q^{50} +(2.08381 - 2.08381i) q^{51} +(4.86207 - 2.53598i) q^{52} +6.32215 q^{53} +(1.20932 + 0.733173i) q^{54} +(-10.0623 - 5.61960i) q^{55} +(1.49662 + 1.70244i) q^{56} +(-5.79168 - 5.79168i) q^{57} +(-5.12267 + 1.25568i) q^{58} +(-5.56839 + 5.56839i) q^{59} +(-3.07066 - 3.25131i) q^{60} +(4.82071 + 4.82071i) q^{61} +(5.94536 - 9.80650i) q^{62} +(0.566689 - 0.566689i) q^{63} +(-7.93404 - 1.02518i) q^{64} +(1.67114 + 5.89881i) q^{65} +(1.73536 + 7.07957i) q^{66} -3.34296i q^{67} +(5.62252 + 1.76783i) q^{68} +(-4.28027 - 4.28027i) q^{69} +(-2.20378 + 1.25143i) q^{70} -2.81803 q^{71} +(-0.181602 + 2.82259i) q^{72} +(10.7052 - 10.7052i) q^{73} +(-1.67477 + 2.76243i) q^{74} +(4.25704 - 2.62252i) q^{75} +(4.91347 - 15.6271i) q^{76} +4.13068 q^{77} +(2.01025 - 3.31578i) q^{78} -12.1478 q^{79} +(2.92539 - 8.45234i) q^{80} +1.00000 q^{81} +(-1.66786 + 2.75103i) q^{82} -1.97640 q^{83} +(1.52904 + 0.480760i) q^{84} +(-3.21304 + 5.75316i) q^{85} +(-2.24703 + 3.70633i) q^{86} +(-2.63716 + 2.63716i) q^{87} +(-10.9490 + 9.62528i) q^{88} +10.0322 q^{89} +(-3.04860 - 0.840275i) q^{90} +(-1.55378 - 1.55378i) q^{91} +(3.63124 - 11.5490i) q^{92} -8.10909i q^{93} +(0.859794 + 3.50761i) q^{94} +(15.9902 + 8.93024i) q^{95} +(-5.17322 + 2.28863i) q^{96} +(-1.02135 + 1.02135i) q^{97} +(-4.66131 + 7.68853i) q^{98} +(3.64458 + 3.64458i) 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 $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.20932	+	0.733173i	0.855119	+	0.518431i
$2$	1.20932	+	0.733173i	0.855119	+	0.518431i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.924916	+	1.77328i	0.462458	+	0.886641i
$5$	−2.15140	+	0.609492i	−0.962135	+	0.272573i
$5$	−2.15140	+	0.609492i	−0.962135	+	0.272573i
$6$	1.20932	+	0.733173i	0.493703	+	0.299316i
$7$	0.566689	−	0.566689i	0.214188	−	0.214188i	−0.591856	−	0.806044i	$-0.701604\pi$
$7$	0.566689	−	0.566689i	0.214188	−	0.214188i	0.806044	+	0.591856i	$0.201604\pi$
$8$	−0.181602	+	2.82259i	−0.0642061	+	0.997937i
$9$	1.00000			0.333333
$10$	−3.04860	−	0.840275i	−0.964051	−	0.265718i
$11$	3.64458	+	3.64458i	1.09888	+	1.09888i	0.994542	+	0.104339i	$0.0332727\pi$
$11$	3.64458	+	3.64458i	1.09888	+	1.09888i	0.104339	+	0.994542i	$0.466727\pi$
$12$	0.924916	+	1.77328i	0.267000	+	0.511903i
$13$		−	2.74185i		−	0.760452i	−0.924894	−	0.380226i	$-0.875846\pi$
$13$		−	2.74185i		−	0.760452i	0.924894	−	0.380226i	$-0.124154\pi$
$14$	1.10079	−	0.269828i	0.294198	−	0.0721146i
$15$	−2.15140	+	0.609492i	−0.555489	+	0.157370i
$16$	−2.28906	+	3.28027i	−0.572266	+	0.820068i
$17$	2.08381	−	2.08381i	0.505397	−	0.505397i	−0.407713	−	0.913110i	$-0.633674\pi$
$17$	2.08381	−	2.08381i	0.505397	−	0.505397i	0.913110	+	0.407713i	$0.133674\pi$
$18$	1.20932	+	0.733173i	0.285040	+	0.172810i
$19$	−5.79168	−	5.79168i	−1.32870	−	1.32870i	−0.906502	−	0.422201i	$-0.861258\pi$
$19$	−5.79168	−	5.79168i	−1.32870	−	1.32870i	−0.422201	−	0.906502i	$-0.638742\pi$
$20$	−3.07066	−	3.25131i	−0.686622	−	0.727015i
$21$	0.566689	−	0.566689i	0.123662	−	0.123662i
$22$	1.73536	+	7.07957i	0.369980	+	1.50937i
$23$	−4.28027	−	4.28027i	−0.892499	−	0.892499i	0.102259	−	0.994758i	$-0.467393\pi$
$23$	−4.28027	−	4.28027i	−0.892499	−	0.892499i	−0.994758	+	0.102259i	$0.967393\pi$
$24$	−0.181602	+	2.82259i	−0.0370694	+	0.576159i
$25$	4.25704	−	2.62252i	0.851408	−	0.524505i
$26$	2.01025	−	3.31578i	0.394242	−	0.650277i
$27$	1.00000			0.192450
$28$	1.52904	+	0.480760i	0.288961	+	0.0908551i
$29$	−2.63716	+	2.63716i	−0.489709	+	0.489709i	−0.908214	−	0.418506i	$-0.862554\pi$
$29$	−2.63716	+	2.63716i	−0.489709	+	0.489709i	0.418506	+	0.908214i	$0.362554\pi$
$30$	−3.04860	−	0.840275i	−0.556595	−	0.153413i
$31$		−	8.10909i		−	1.45644i	−0.685346	−	0.728218i	$-0.740349\pi$
$31$		−	8.10909i		−	1.45644i	0.685346	−	0.728218i	$-0.259651\pi$
$32$	−5.17322	+	2.28863i	−0.914504	+	0.404576i
$33$	3.64458	+	3.64458i	0.634439	+	0.634439i
$34$	4.04778	−	0.992201i	0.694189	−	0.170161i
$35$	−0.873782	+	1.56457i	−0.147696	+	0.264460i
$36$	0.924916	+	1.77328i	0.154153	+	0.295547i
$37$			2.28428i			0.375534i	0.982214	+	0.187767i	$0.0601249\pi$
$37$			2.28428i			0.375534i	−0.982214	+	0.187767i	$0.939875\pi$
$38$	−2.75770	−	11.2503i	−0.447358	−	1.82504i
$39$		−	2.74185i		−	0.439047i
$40$	−1.32965	−	6.18321i	−0.210236	−	0.977651i
$41$			2.27486i			0.355273i	0.984096	+	0.177637i	$0.0568452\pi$
$41$			2.27486i			0.355273i	−0.984096	+	0.177637i	$0.943155\pi$
$42$	1.10079	−	0.269828i	0.169856	−	0.0416354i
$43$			3.06480i			0.467378i	0.972311	+	0.233689i	$0.0750797\pi$
$43$			3.06480i			0.467378i	−0.972311	+	0.233689i	$0.924920\pi$
$44$	−3.09194	+	9.83379i	−0.466127	+	1.48250i
$45$	−2.15140	+	0.609492i	−0.320712	+	0.0908578i
$46$	−2.03805	−	8.31441i	−0.300493	−	1.22589i
$47$	1.80573	+	1.80573i	0.263392	+	0.263392i	0.826431	−	0.563039i	$-0.190368\pi$
$47$	1.80573	+	1.80573i	0.263392	+	0.263392i	−0.563039	+	0.826431i	$0.690368\pi$
$48$	−2.28906	+	3.28027i	−0.330398	+	0.473467i
$49$			6.35773i			0.908247i
$50$	7.07089	−	0.0503283i	0.999975	−	0.00711749i
$51$	2.08381	−	2.08381i	0.291791	−	0.291791i
$52$	4.86207	−	2.53598i	0.674248	−	0.351677i
$53$	6.32215			0.868415			0.434207	−	0.900813i	$-0.357029\pi$
$53$	6.32215			0.868415			0.434207	+	0.900813i	$0.357029\pi$
$54$	1.20932	+	0.733173i	0.164568	+	0.0997722i
$55$	−10.0623	−	5.61960i	−1.35680	−	0.757746i
$56$	1.49662	+	1.70244i	0.199994	+	0.227498i
$57$	−5.79168	−	5.79168i	−0.767127	−	0.767127i
$58$	−5.12267	+	1.25568i	−0.672640	+	0.164879i
$59$	−5.56839	+	5.56839i	−0.724942	+	0.724942i	−0.969608	−	0.244665i	$-0.921322\pi$
$59$	−5.56839	+	5.56839i	−0.724942	+	0.724942i	0.244665	+	0.969608i	$0.421322\pi$
$60$	−3.07066	−	3.25131i	−0.396421	−	0.419742i
$61$	4.82071	+	4.82071i	0.617228	+	0.617228i	0.944820	−	0.327591i	$-0.106237\pi$
$61$	4.82071	+	4.82071i	0.617228	+	0.617228i	−0.327591	+	0.944820i	$0.606237\pi$
$62$	5.94536	−	9.80650i	0.755062	−	1.24543i
$63$	0.566689	−	0.566689i	0.0713961	−	0.0713961i
$64$	−7.93404	−	1.02518i	−0.991755	−	0.128147i
$65$	1.67114	+	5.89881i	0.207279	+	0.731658i
$66$	1.73536	+	7.07957i	0.213608	+	0.871434i
$67$		−	3.34296i		−	0.408407i	−0.978928	−	0.204204i	$-0.934539\pi$
$67$		−	3.34296i		−	0.408407i	0.978928	−	0.204204i	$-0.0654605\pi$
$68$	5.62252	+	1.76783i	0.681831	+	0.214381i
$69$	−4.28027	−	4.28027i	−0.515284	−	0.515284i
$70$	−2.20378	+	1.25143i	−0.263402	+	0.149575i
$71$	−2.81803			−0.334439			−0.167219	−	0.985920i	$-0.553479\pi$
$71$	−2.81803			−0.334439			−0.167219	+	0.985920i	$0.553479\pi$
$72$	−0.181602	+	2.82259i	−0.0214020	+	0.332646i
$73$	10.7052	−	10.7052i	1.25295	−	1.25295i	0.298559	−	0.954391i	$-0.403494\pi$
$73$	10.7052	−	10.7052i	1.25295	−	1.25295i	0.954391	−	0.298559i	$-0.0965059\pi$
$74$	−1.67477	+	2.76243i	−0.194688	+	0.321126i
$75$	4.25704	−	2.62252i	0.491560	−	0.302823i
$76$	4.91347	−	15.6271i	0.563614	−	1.79255i
$77$	4.13068			0.470735
$78$	2.01025	−	3.31578i	0.227616	−	0.375438i
$79$	−12.1478			−1.36673			−0.683367	−	0.730075i	$-0.739485\pi$
$79$	−12.1478			−1.36673			−0.683367	+	0.730075i	$0.739485\pi$
$80$	2.92539	−	8.45234i	0.327068	−	0.945001i
$81$	1.00000			0.111111
$82$	−1.66786	+	2.75103i	−0.184185	+	0.303801i
$83$	−1.97640			−0.216938			−0.108469	−	0.994100i	$-0.534595\pi$
$83$	−1.97640			−0.216938			−0.108469	+	0.994100i	$0.534595\pi$
$84$	1.52904	+	0.480760i	0.166832	+	0.0524552i
$85$	−3.21304	+	5.75316i	−0.348503	+	0.624018i
$86$	−2.24703	+	3.70633i	−0.242303	+	0.399664i
$87$	−2.63716	+	2.63716i	−0.282733	+	0.282733i
$88$	−10.9490	+	9.62528i	−1.16717	+	1.02606i
$89$	10.0322			1.06341			0.531706	−	0.846929i	$-0.321551\pi$
$89$	10.0322			1.06341			0.531706	+	0.846929i	$0.321551\pi$
$90$	−3.04860	−	0.840275i	−0.321350	−	0.0885728i
$91$	−1.55378	−	1.55378i	−0.162880	−	0.162880i
$92$	3.63124	−	11.5490i	0.378583	−	1.20407i
$93$		−	8.10909i		−	0.840874i
$94$	0.859794	+	3.50761i	0.0886809	+	0.361782i
$95$	15.9902	+	8.93024i	1.64056	+	0.916223i
$96$	−5.17322	+	2.28863i	−0.527989	+	0.233582i
$97$	−1.02135	+	1.02135i	−0.103702	+	0.103702i	−0.757054	−	0.653352i	$-0.773362\pi$
$97$	−1.02135	+	1.02135i	−0.103702	+	0.103702i	0.653352	+	0.757054i	$0.273362\pi$
$98$	−4.66131	+	7.68853i	−0.470864	+	0.776659i
$99$	3.64458	+	3.64458i	0.366294	+	0.366294i
$100$	8.58788	+	5.12332i	0.858788	+	0.512332i
$101$	−13.1932	+	13.1932i	−1.31277	+	1.31277i	−0.393412	+	0.919362i	$0.628705\pi$
$101$	−13.1932	+	13.1932i	−1.31277	+	1.31277i	−0.919362	+	0.393412i	$0.871295\pi$
$102$	4.04778	−	0.992201i	0.400790	−	0.0982426i
$103$	4.51726	+	4.51726i	0.445099	+	0.445099i	0.893721	−	0.448623i	$-0.148085\pi$
$103$	4.51726	+	4.51726i	0.445099	+	0.445099i	−0.448623	+	0.893721i	$0.648085\pi$
$104$	7.73912	+	0.497926i	0.758883	+	0.0488257i
$105$	−0.873782	+	1.56457i	−0.0852723	+	0.152686i
$106$	7.64551	+	4.63523i	0.742598	+	0.450213i
$107$	3.88249			0.375334			0.187667	−	0.982233i	$-0.439907\pi$
$107$	3.88249			0.375334			0.187667	+	0.982233i	$0.439907\pi$
$108$	0.924916	+	1.77328i	0.0890000	+	0.170634i
$109$	−2.51614	+	2.51614i	−0.241003	+	0.241003i	−0.817265	−	0.576262i	$-0.804511\pi$
$109$	−2.51614	+	2.51614i	−0.241003	+	0.241003i	0.576262	+	0.817265i	$0.304511\pi$
$110$	−8.04839	−	14.1733i	−0.767384	−	1.35137i
$111$			2.28428i			0.216815i
$112$	0.561708	+	3.15608i	0.0530765	+	0.298222i
$113$	−3.89520	−	3.89520i	−0.366429	−	0.366429i	0.499744	−	0.866173i	$-0.333427\pi$
$113$	−3.89520	−	3.89520i	−0.366429	−	0.366429i	−0.866173	+	0.499744i	$0.833427\pi$
$114$	−2.75770	−	11.2503i	−0.258282	−	1.05369i
$115$	11.8174	+	6.59978i	1.10198	+	0.615433i
$116$	−7.11559	−	2.23728i	−0.660666	−	0.207726i
$117$		−	2.74185i		−	0.253484i
$118$	−10.8166	+	2.65138i	−0.995745	+	0.244079i
$119$		−	2.36174i		−	0.216500i
$120$	−1.32965	−	6.18321i	−0.121380	−	0.564447i
$121$			15.5659i			1.41508i
$122$	2.29537	+	9.36420i	0.207813	+	0.847795i
$123$			2.27486i			0.205117i
$124$	14.3797	−	7.50023i	1.29134	−	0.673540i
$125$	−7.56018	+	8.23673i	−0.676203	+	0.736715i
$126$	1.10079	−	0.269828i	0.0980661	−	0.0240382i
$127$	−3.11993	−	3.11993i	−0.276849	−	0.276849i	0.555001	−	0.831850i	$-0.312718\pi$
$127$	−3.11993	−	3.11993i	−0.276849	−	0.276849i	−0.831850	+	0.555001i	$0.812718\pi$
$128$	−8.84317	−	7.05679i	−0.781633	−	0.623738i
$129$			3.06480i			0.269841i
$130$	−2.30391	+	8.35879i	−0.202066	+	0.733115i
$131$	−8.69631	+	8.69631i	−0.759800	+	0.759800i	−0.976286	−	0.216486i	$-0.930541\pi$
$131$	−8.69631	+	8.69631i	−0.759800	+	0.759800i	0.216486	+	0.976286i	$0.430541\pi$
$132$	−3.09194	+	9.83379i	−0.269119	+	0.855921i
$133$	−6.56416			−0.569185
$134$	2.45097	−	4.04271i	0.211731	−	0.349237i
$135$	−2.15140	+	0.609492i	−0.185163	+	0.0524567i
$136$	5.50331	+	6.26016i	0.471905	+	0.536804i
$137$	−16.1963	−	16.1963i	−1.38375	−	1.38375i	−0.837856	−	0.545891i	$-0.816191\pi$
$137$	−16.1963	−	16.1963i	−1.38375	−	1.38375i	−0.545891	−	0.837856i	$-0.683809\pi$
$138$	−2.03805	−	8.31441i	−0.173490	−	0.707769i
$139$	−10.8859	+	10.8859i	−0.923329	+	0.923329i	−0.997263	−	0.0739337i	$-0.976445\pi$
$139$	−10.8859	+	10.8859i	−0.923329	+	0.923329i	0.0739337	+	0.997263i	$0.476445\pi$
$140$	−3.58259	−	0.102370i	−0.302784	−	0.00865180i
$141$	1.80573	+	1.80573i	0.152070	+	0.152070i
$142$	−3.40790	−	2.06610i	−0.285985	−	0.173383i
$143$	9.99288	−	9.99288i	0.835646	−	0.835646i
$144$	−2.28906	+	3.28027i	−0.190755	+	0.273356i
$145$	4.06626	−	7.28092i	0.337684	−	0.604647i
$146$	20.7948	−	5.09727i	1.72099	−	0.421853i
$147$			6.35773i			0.524377i
$148$	−4.05068	+	2.11277i	−0.332964	+	0.173669i
$149$	8.06960	+	8.06960i	0.661088	+	0.661088i	0.955636	−	0.294549i	$-0.0951694\pi$
$149$	8.06960	+	8.06960i	0.661088	+	0.661088i	−0.294549	+	0.955636i	$0.595169\pi$
$150$	7.07089	−	0.0503283i	0.577336	−	0.00410929i
$151$	10.9071			0.887609			0.443804	−	0.896124i	$-0.353628\pi$
$151$	10.9071			0.887609			0.443804	+	0.896124i	$0.353628\pi$
$152$	17.3993	−	15.2958i	1.41127	−	1.24065i
$153$	2.08381	−	2.08381i	0.168466	−	0.168466i
$154$	4.99532	+	3.02850i	0.402534	+	0.244044i
$155$	4.94243	+	17.4459i	0.396985	+	1.40129i
$156$	4.86207	−	2.53598i	0.389277	−	0.203041i
$157$	14.0713			1.12301			0.561507	−	0.827472i	$-0.310222\pi$
$157$	14.0713			1.12301			0.561507	+	0.827472i	$0.310222\pi$
$158$	−14.6906	−	8.90644i	−1.16872	−	0.708558i
$159$	6.32215			0.501379
$160$	9.73476	−	8.07679i	0.769600	−	0.638526i
$161$	−4.85117			−0.382325
$162$	1.20932	+	0.733173i	0.0950132	+	0.0576035i
$163$	2.82750			0.221467			0.110734	−	0.993850i	$-0.464680\pi$
$163$	2.82750			0.221467			0.110734	+	0.993850i	$0.464680\pi$
$164$	−4.03397	+	2.10405i	−0.315000	+	0.164299i
$165$	−10.0623	−	5.61960i	−0.783347	−	0.437485i
$166$	−2.39010	−	1.44904i	−0.185508	−	0.112468i
$167$	−5.12509	+	5.12509i	−0.396591	+	0.396591i	−0.877029	−	0.480438i	$-0.840478\pi$
$167$	−5.12509	+	5.12509i	−0.396591	+	0.396591i	0.480438	+	0.877029i	$0.340478\pi$
$168$	1.49662	+	1.70244i	0.115467	+	0.131346i
$169$	5.48226			0.421712
$170$	−8.10365	+	4.60171i	−0.621522	+	0.352935i
$171$	−5.79168	−	5.79168i	−0.442901	−	0.442901i
$172$	−5.43476	+	2.83468i	−0.414396	+	0.216143i
$173$			4.60016i			0.349743i	0.984591	+	0.174872i	$0.0559511\pi$
$173$			4.60016i			0.349743i	−0.984591	+	0.174872i	$0.944049\pi$
$174$	−5.12267	+	1.25568i	−0.388349	+	0.0951929i
$175$	0.926262	−	3.89857i	0.0700188	−	0.294704i
$176$	−20.2979	+	3.61254i	−1.53001	+	0.272306i
$177$	−5.56839	+	5.56839i	−0.418546	+	0.418546i
$178$	12.1322	+	7.35534i	0.909343	+	0.551306i
$179$	−3.06396	−	3.06396i	−0.229011	−	0.229011i	0.583268	−	0.812280i	$-0.301774\pi$
$179$	−3.06396	−	3.06396i	−0.229011	−	0.229011i	−0.812280	+	0.583268i	$0.801774\pi$
$180$	−3.07066	−	3.25131i	−0.228874	−	0.242338i
$181$	−3.08559	+	3.08559i	−0.229350	+	0.229350i	−0.812421	−	0.583071i	$-0.801851\pi$
$181$	−3.08559	+	3.08559i	−0.229350	+	0.229350i	0.583071	+	0.812421i	$0.301851\pi$
$182$	−0.739828	−	3.01820i	−0.0548397	−	0.223724i
$183$	4.82071	+	4.82071i	0.356357	+	0.356357i
$184$	12.8588	−	11.3042i	0.947961	−	0.833353i
$185$	−1.39225	−	4.91440i	−0.102360	−	0.361314i
$186$	5.94536	−	9.80650i	0.435935	−	0.719047i
$187$	15.1892			1.11074
$188$	−1.53192	+	4.87221i	−0.111727	+	0.355342i
$189$	0.566689	−	0.566689i	0.0412205	−	0.0412205i
$190$	12.7899	+	22.5231i	0.927876	+	1.63400i
$191$		−	21.0908i		−	1.52608i	−0.646353	−	0.763038i	$-0.723707\pi$
$191$		−	21.0908i		−	1.52608i	0.646353	−	0.763038i	$-0.276293\pi$
$192$	−7.93404	−	1.02518i	−0.572590	−	0.0739858i
$193$	15.2332	+	15.2332i	1.09651	+	1.09651i	0.994816	+	0.101692i	$0.0324255\pi$
$193$	15.2332	+	15.2332i	1.09651	+	1.09651i	0.101692	+	0.994816i	$0.467574\pi$
$194$	−1.98396	+	0.486314i	−0.142440	+	0.0349153i
$195$	1.67114	+	5.89881i	0.119673	+	0.422423i
$196$	−11.2740	+	5.88036i	−0.805289	+	0.420026i
$197$		−	14.0460i		−	1.00073i	−0.865814	−	0.500367i	$-0.833199\pi$
$197$		−	14.0460i		−	1.00073i	0.865814	−	0.500367i	$-0.166801\pi$
$198$	1.73536	+	7.07957i	0.123327	+	0.503123i
$199$		−	2.42066i		−	0.171596i	−0.996313	−	0.0857978i	$-0.972656\pi$
$199$		−	2.42066i		−	0.171596i	0.996313	−	0.0857978i	$-0.0273439\pi$
$200$	6.62922	+	12.4921i	0.468757	+	0.883327i
$201$		−	3.34296i		−	0.235794i
$202$	−25.6277	+	6.28193i	−1.80316	+	0.441995i
$203$			2.98890i			0.209780i
$204$	5.62252	+	1.76783i	0.393655	+	0.123773i
$205$	−1.38651	−	4.89413i	−0.0968380	−	0.341821i
$206$	2.15089	+	8.77474i	0.149859	+	0.611365i
$207$	−4.28027	−	4.28027i	−0.297500	−	0.297500i
$208$	8.99402	+	6.27626i	0.623623	+	0.435181i
$209$		−	42.2164i		−	2.92017i
$210$	−2.20378	+	1.25143i	−0.152075	+	0.0863569i
$211$	5.18795	−	5.18795i	0.357153	−	0.357153i	−0.505609	−	0.862762i	$-0.668732\pi$
$211$	5.18795	−	5.18795i	0.357153	−	0.357153i	0.862762	+	0.505609i	$0.168732\pi$
$212$	5.84746	+	11.2110i	0.401605	+	0.769972i
$213$	−2.81803			−0.193088
$214$	4.69518	+	2.84653i	0.320956	+	0.194585i
$215$	−1.86797	−	6.59361i	−0.127395	−	0.449681i
$216$	−0.181602	+	2.82259i	−0.0123565	+	0.192053i
$217$	−4.59533	−	4.59533i	−0.311951	−	0.311951i
$218$	−4.88759	+	1.19806i	−0.331029	+	0.0811427i
$219$	10.7052	−	10.7052i	0.723391	−	0.723391i
$220$	0.658374	−	23.0409i	0.0443876	−	1.55342i
$221$	−5.71348	−	5.71348i	−0.384331	−	0.384331i
$222$	−1.67477	+	2.76243i	−0.112403	+	0.185402i
$223$	−11.3379	+	11.3379i	−0.759240	+	0.759240i	−0.976184	−	0.216944i	$-0.930391\pi$
$223$	−11.3379	+	11.3379i	−0.759240	+	0.759240i	0.216944	+	0.976184i	$0.430391\pi$
$224$	−1.63467	+	4.22854i	−0.109221	+	0.282532i
$225$	4.25704	−	2.62252i	0.283803	−	0.174835i
$226$	−1.85469	−	7.56640i	−0.123372	−	0.503309i
$227$		−	19.8951i		−	1.32049i	−0.751052	−	0.660243i	$-0.770453\pi$
$227$		−	19.8951i		−	1.32049i	0.751052	−	0.660243i	$-0.229547\pi$
$228$	4.91347	−	15.6271i	0.325403	−	1.03493i
$229$	−14.1933	−	14.1933i	−0.937918	−	0.937918i	0.0602643	−	0.998182i	$-0.480806\pi$
$229$	−14.1933	−	14.1933i	−0.937918	−	0.937918i	−0.998182	+	0.0602643i	$0.980806\pi$
$230$	9.45222	+	16.6454i	0.623261	+	1.09757i
$231$	4.13068			0.271779
$232$	−6.96472	−	7.92255i	−0.457256	−	0.520141i
$233$	−13.9475	+	13.9475i	−0.913734	+	0.913734i	−0.996564	−	0.0828295i	$-0.973604\pi$
$233$	−13.9475	+	13.9475i	−0.913734	+	0.913734i	0.0828295	+	0.996564i	$0.473604\pi$
$234$	2.01025	−	3.31578i	0.131414	−	0.216759i
$235$	−4.98541	−	2.78426i	−0.325212	−	0.181625i
$236$	−15.0246	−	4.72404i	−0.978019	−	0.307509i
$237$	−12.1478			−0.789085
$238$	1.73156	−	2.85610i	0.112241	−	0.185134i
$239$	16.4452			1.06375			0.531876	−	0.846822i	$-0.321487\pi$
$239$	16.4452			1.06375			0.531876	+	0.846822i	$0.321487\pi$
$240$	2.92539	−	8.45234i	0.188833	−	0.545596i
$241$	−4.70995			−0.303394			−0.151697	−	0.988427i	$-0.548474\pi$
$241$	−4.70995			−0.303394			−0.151697	+	0.988427i	$0.548474\pi$
$242$	−11.4125	+	18.8241i	−0.733621	+	1.21006i
$243$	1.00000			0.0641500
$244$	−4.08973	+	13.0072i	−0.261818	+	0.832702i
$245$	−3.87499	−	13.6780i	−0.247564	−	0.873856i
$246$	−1.66786	+	2.75103i	−0.106339	+	0.175400i
$247$	−15.8799	+	15.8799i	−1.01042	+	1.01042i
$248$	22.8887	+	1.47263i	1.45343	+	0.0935121i
$249$	−1.97640			−0.125249
$250$	−15.1816	+	4.41793i	−0.960171	+	0.279414i
$251$	−14.6935	−	14.6935i	−0.927448	−	0.927448i	0.0700924	−	0.997541i	$-0.477671\pi$
$251$	−14.6935	−	14.6935i	−0.927448	−	0.927448i	−0.997541	+	0.0700924i	$0.977671\pi$
$252$	1.52904	+	0.480760i	0.0963204	+	0.0302850i
$253$		−	31.1996i		−	1.96150i
$254$	−1.48555	−	6.06045i	−0.0932117	−	0.380266i
$255$	−3.21304	+	5.75316i	−0.201208	+	0.360277i
$256$	−5.52039	−	15.0175i	−0.345024	−	0.938594i
$257$	5.02979	−	5.02979i	0.313750	−	0.313750i	−0.532611	−	0.846360i	$-0.678789\pi$
$257$	5.02979	−	5.02979i	0.313750	−	0.313750i	0.846360	+	0.532611i	$0.178789\pi$
$258$	−2.24703	+	3.70633i	−0.139894	+	0.230746i
$259$	1.29448	+	1.29448i	0.0804349	+	0.0804349i
$260$	−8.91460	+	8.41930i	−0.552860	+	0.522143i
$261$	−2.63716	+	2.63716i	−0.163236	+	0.163236i
$262$	−16.8925	+	4.14073i	−1.04362	+	0.255815i
$263$	8.84851	+	8.84851i	0.545622	+	0.545622i	0.925172	−	0.379549i	$-0.123921\pi$
$263$	8.84851	+	8.84851i	0.545622	+	0.545622i	−0.379549	+	0.925172i	$0.623921\pi$
$264$	−10.9490	+	9.62528i	−0.673865	+	0.592395i
$265$	−13.6015	+	3.85330i	−0.835532	+	0.236707i
$266$	−7.93818	−	4.81267i	−0.486721	−	0.295083i
$267$	10.0322			0.613961
$268$	5.92801	−	3.09196i	0.362111	−	0.188871i
$269$	−4.66057	+	4.66057i	−0.284160	+	0.284160i	−0.834766	−	0.550605i	$-0.814397\pi$
$269$	−4.66057	+	4.66057i	−0.284160	+	0.284160i	0.550605	+	0.834766i	$0.314397\pi$
$270$	−3.04860	−	0.840275i	−0.185532	−	0.0511375i
$271$			3.87643i			0.235477i	0.993045	+	0.117738i	$0.0375644\pi$
$271$			3.87643i			0.235477i	−0.993045	+	0.117738i	$0.962436\pi$
$272$	2.06549	+	11.6054i	0.125239	+	0.703682i
$273$	−1.55378	−	1.55378i	−0.0940388	−	0.0940388i
$274$	−7.71187	−	31.4613i	−0.465891	−	1.90065i
$275$	25.0731	+	5.95712i	1.51196	+	0.359228i
$276$	3.63124	−	11.5490i	0.218575	−	0.695170i
$277$			14.6951i			0.882941i	0.897276	+	0.441471i	$0.145543\pi$
$277$			14.6951i			0.882941i	−0.897276	+	0.441471i	$0.854457\pi$
$278$	−21.1458	+	5.18330i	−1.26824	+	0.310874i
$279$		−	8.10909i		−	0.485479i
$280$	−4.25745	−	2.75046i	−0.254431	−	0.164371i
$281$			0.328587i			0.0196019i	0.999952	+	0.00980093i	$0.00311978\pi$
$281$			0.328587i			0.0196019i	−0.999952	+	0.00980093i	$0.996880\pi$
$282$	0.859794	+	3.50761i	0.0512000	+	0.208875i
$283$		−	22.9890i		−	1.36656i	−0.730158	−	0.683278i	$-0.760554\pi$
$283$		−	22.9890i		−	1.36656i	0.730158	−	0.683278i	$-0.239446\pi$
$284$	−2.60644	−	4.99716i	−0.154664	−	0.296527i
$285$	15.9902	+	8.93024i	0.947178	+	0.528981i
$286$	19.4111	−	4.75809i	1.14780	−	0.281352i
$287$	1.28914	+	1.28914i	0.0760953	+	0.0760953i
$288$	−5.17322	+	2.28863i	−0.304835	+	0.134859i
$289$			8.31550i			0.489147i
$290$	10.2556	−	5.82370i	0.602229	−	0.341979i
$291$	−1.02135	+	1.02135i	−0.0598725	+	0.0598725i
$292$	28.8848	+	9.08195i	1.69035	+	0.531481i
$293$	22.0162			1.28620			0.643101	−	0.765781i	$-0.277648\pi$
$293$	22.0162			1.28620			0.643101	+	0.765781i	$0.277648\pi$
$294$	−4.66131	+	7.68853i	−0.271853	+	0.448404i
$295$	8.58594	−	15.3737i	0.499893	−	0.895092i
$296$	−6.44760	−	0.414831i	−0.374759	−	0.0241116i
$297$	3.64458	+	3.64458i	0.211480	+	0.211480i
$298$	3.84233	+	15.6752i	0.222580	+	0.908037i
$299$	−11.7359	+	11.7359i	−0.678703	+	0.678703i
$300$	8.58788	+	5.12332i	0.495821	+	0.295795i
$301$	1.73679	+	1.73679i	0.100107	+	0.100107i
$302$	13.1902	+	7.99680i	0.759011	+	0.460164i
$303$	−13.1932	+	13.1932i	−0.757931	+	0.757931i
$304$	32.2558	−	5.74078i	1.85000	−	0.329256i
$305$	−13.3095	−	7.43308i	−0.762097	−	0.425617i
$306$	4.04778	−	0.992201i	0.231396	−	0.0567204i
$307$			3.08698i			0.176183i	0.996112	+	0.0880916i	$0.0280768\pi$
$307$			3.08698i			0.176183i	−0.996112	+	0.0880916i	$0.971923\pi$
$308$	3.82053	+	7.32486i	0.217695	+	0.417373i
$309$	4.51726	+	4.51726i	0.256978	+	0.256978i
$310$	−6.81387	+	24.7213i	−0.387002	+	1.40408i
$311$	24.3682			1.38179			0.690897	−	0.722953i	$-0.257216\pi$
$311$	24.3682			1.38179			0.690897	+	0.722953i	$0.257216\pi$
$312$	7.73912	+	0.497926i	0.438141	+	0.0281895i
$313$	−3.31911	+	3.31911i	−0.187607	+	0.187607i	−0.794661	−	0.607054i	$-0.792351\pi$
$313$	−3.31911	+	3.31911i	−0.187607	+	0.187607i	0.607054	+	0.794661i	$0.292351\pi$
$314$	17.0168	+	10.3167i	0.960311	+	0.582206i
$315$	−0.873782	+	1.56457i	−0.0492320	+	0.0881533i
$316$	−11.2357	−	21.5415i	−0.632057	−	1.21180i
$317$	5.35749			0.300907			0.150453	−	0.988617i	$-0.451927\pi$
$317$	5.35749			0.300907			0.150453	+	0.988617i	$0.451927\pi$
$318$	7.64551	+	4.63523i	0.428739	+	0.259931i
$319$	−19.2227			−1.07626
$320$	17.6941	−	2.63017i	0.989132	−	0.147031i
$321$	3.88249			0.216699
$322$	−5.86662	−	3.55674i	−0.326934	−	0.198210i
$323$	−24.1375			−1.34305
$324$	0.924916	+	1.77328i	0.0513842	+	0.0985157i
$325$	−7.19056	−	11.6722i	−0.398861	−	0.647455i
$326$	3.41936	+	2.07305i	0.189381	+	0.114816i
$327$	−2.51614	+	2.51614i	−0.139143	+	0.139143i
$328$	−6.42099	−	0.413119i	−0.354540	−	0.0228107i
$329$	2.04657			0.112831
$330$	−8.04839	−	14.1733i	−0.443049	−	0.780214i
$331$	−2.76903	−	2.76903i	−0.152200	−	0.152200i	0.626900	−	0.779100i	$-0.284323\pi$
$331$	−2.76903	−	2.76903i	−0.152200	−	0.152200i	−0.779100	+	0.626900i	$0.784323\pi$
$332$	−1.82800	−	3.50472i	−0.100325	−	0.192346i
$333$			2.28428i			0.125178i
$334$	−9.95545	+	2.44030i	−0.544738	+	0.133527i
$335$	2.03751	+	7.19204i	0.111321	+	0.392943i
$336$	0.561708	+	3.15608i	0.0306437	+	0.172178i
$337$	−7.30028	+	7.30028i	−0.397672	+	0.397672i	−0.877411	−	0.479739i	$-0.840731\pi$
$337$	−7.30028	+	7.30028i	−0.397672	+	0.397672i	0.479739	+	0.877411i	$0.340731\pi$
$338$	6.62981	+	4.01944i	0.360614	+	0.218629i
$339$	−3.89520	−	3.89520i	−0.211558	−	0.211558i
$340$	−13.1738	−	0.376429i	−0.714448	−	0.0204147i
$341$	29.5542	−	29.5542i	1.60045	−	1.60045i
$342$	−2.75770	−	11.2503i	−0.149119	−	0.608347i
$343$	7.56968	+	7.56968i	0.408724	+	0.408724i
$344$	−8.65068	−	0.556575i	−0.466413	−	0.0300085i
$345$	11.8174	+	6.59978i	0.636226	+	0.355320i
$346$	−3.37271	+	5.56307i	−0.181318	+	0.299072i
$347$	−17.0824			−0.917032			−0.458516	−	0.888686i	$-0.651619\pi$
$347$	−17.0824			−0.917032			−0.458516	+	0.888686i	$0.651619\pi$
$348$	−7.11559	−	2.23728i	−0.381435	−	0.119931i
$349$	1.38113	−	1.38113i	0.0739302	−	0.0739302i	−0.669175	−	0.743105i	$-0.733352\pi$
$349$	1.38113	−	1.38113i	0.0739302	−	0.0739302i	0.743105	+	0.669175i	$0.233352\pi$
$350$	3.97847	−	4.03551i	0.212658	−	0.215707i
$351$		−	2.74185i		−	0.146349i
$352$	−27.1953	−	10.5131i	−1.44951	−	0.560351i
$353$	−6.69565	−	6.69565i	−0.356373	−	0.356373i	0.506101	−	0.862474i	$-0.331086\pi$
$353$	−6.69565	−	6.69565i	−0.356373	−	0.356373i	−0.862474	+	0.506101i	$0.831086\pi$
$354$	−10.8166	+	2.65138i	−0.574894	+	0.140919i
$355$	6.06271	−	1.71757i	0.321775	−	0.0911590i
$356$	9.27894	+	17.7899i	0.491783	+	0.942864i
$357$		−	2.36174i		−	0.124997i
$358$	−1.45890	−	5.95173i	−0.0771054	−	0.314559i
$359$			1.90946i			0.100777i	0.998730	+	0.0503886i	$0.0160460\pi$
$359$			1.90946i			0.100777i	−0.998730	+	0.0503886i	$0.983954\pi$
$360$	−1.32965	−	6.18321i	−0.0700786	−	0.325884i
$361$			48.0872i			2.53090i
$362$	−5.99374	+	1.46920i	−0.315024	+	0.0772194i
$363$			15.5659i			0.816996i
$364$	1.31817	−	4.19239i	0.0690910	−	0.219741i
$365$	−16.5064	+	29.5559i	−0.863986	+	1.54703i
$366$	2.29537	+	9.36420i	0.119981	+	0.489474i
$367$	20.2767	+	20.2767i	1.05844	+	1.05844i	0.998183	+	0.0602537i	$0.0191910\pi$
$367$	20.2767	+	20.2767i	1.05844	+	1.05844i	0.0602537	+	0.998183i	$0.480809\pi$
$368$	23.8383	−	4.24266i	1.24266	−	0.221164i
$369$			2.27486i			0.118424i
$370$	1.91943	−	6.96385i	0.0997862	−	0.362034i
$371$	3.58269	−	3.58269i	0.186004	−	0.186004i
$372$	14.3797	−	7.50023i	0.745553	−	0.388869i
$373$	34.5736			1.79015			0.895076	−	0.445914i	$-0.147121\pi$
$373$	34.5736			1.79015			0.895076	+	0.445914i	$0.147121\pi$
$374$	18.3686	+	11.1363i	0.949818	+	0.575844i
$375$	−7.56018	+	8.23673i	−0.390406	+	0.425343i
$376$	−5.42475	+	4.76890i	−0.279760	+	0.245937i
$377$	7.23070	+	7.23070i	0.372400	+	0.372400i
$378$	1.10079	−	0.269828i	0.0566185	−	0.0138785i
$379$	21.2172	−	21.2172i	1.08986	−	1.08986i	0.0943133	−	0.995543i	$-0.469934\pi$
$379$	21.2172	−	21.2172i	1.08986	−	1.08986i	0.995543	−	0.0943133i	$-0.0300656\pi$
$380$	−1.04624	+	36.6149i	−0.0536709	+	1.87830i
$381$	−3.11993	−	3.11993i	−0.159839	−	0.159839i
$382$	15.4632	−	25.5056i	0.791166	−	1.30498i
$383$	3.13204	−	3.13204i	0.160040	−	0.160040i	−0.622544	−	0.782584i	$-0.713901\pi$
$383$	3.13204	−	3.13204i	0.160040	−	0.160040i	0.782584	+	0.622544i	$0.213901\pi$
$384$	−8.84317	−	7.05679i	−0.451276	−	0.360115i
$385$	−8.88674	+	2.51762i	−0.452910	+	0.128310i
$386$	7.25325	+	29.5903i	0.369181	+	1.50611i
$387$			3.06480i			0.155793i
$388$	−2.75580	−	0.866478i	−0.139905	−	0.0439888i
$389$	15.2777	+	15.2777i	0.774610	+	0.774610i	0.978909	−	0.204299i	$-0.0654913\pi$
$389$	15.2777	+	15.2777i	0.774610	+	0.774610i	−0.204299	+	0.978909i	$0.565491\pi$
$390$	−2.30391	+	8.35879i	−0.116663	+	0.423264i
$391$	−17.8385			−0.902133
$392$	−17.9453	−	1.15458i	−0.906373	−	0.0583150i
$393$	−8.69631	+	8.69631i	−0.438671	+	0.438671i
$394$	10.2981	−	16.9861i	0.518811	−	0.855746i
$395$	26.1348	−	7.40399i	1.31498	−	0.372535i
$396$	−3.09194	+	9.83379i	−0.155376	+	0.494166i
$397$	9.39676			0.471610			0.235805	−	0.971800i	$-0.424227\pi$
$397$	9.39676			0.471610			0.235805	+	0.971800i	$0.424227\pi$
$398$	1.77476	−	2.92735i	0.0889606	−	0.146735i
$399$	−6.56416			−0.328619
$400$	−1.14203	+	19.9674i	−0.0571017	+	0.998368i
$401$	0.722171			0.0360635			0.0180317	−	0.999837i	$-0.494260\pi$
$401$	0.722171			0.0360635			0.0180317	+	0.999837i	$0.494260\pi$
$402$	2.45097	−	4.04271i	0.122243	−	0.201632i
$403$	−22.2339			−1.10755
$404$	−35.5979	−	11.1927i	−1.77106	−	0.556857i
$405$	−2.15140	+	0.609492i	−0.106904	+	0.0302859i
$406$	−2.19138	+	3.61454i	−0.108756	+	0.179387i
$407$	−8.32524	+	8.32524i	−0.412667	+	0.412667i
$408$	5.50331	+	6.26016i	0.272454	+	0.309924i
$409$	20.7860			1.02780			0.513900	−	0.857850i	$-0.328200\pi$
$409$	20.7860			1.02780			0.513900	+	0.857850i	$0.328200\pi$
$410$	1.91151	−	6.93512i	0.0944026	−	0.342501i
$411$	−16.1963	−	16.1963i	−0.798907	−	0.798907i
$412$	−3.83229	+	12.1885i	−0.188803	+	0.600482i
$413$			6.31109i			0.310548i
$414$	−2.03805	−	8.31441i	−0.100164	−	0.408631i
$415$	4.25203	−	1.20460i	0.208724	−	0.0591315i
$416$	6.27507	+	14.1842i	0.307661	+	0.695437i
$417$	−10.8859	+	10.8859i	−0.533085	+	0.533085i
$418$	30.9519	−	51.0532i	1.51391	−	2.49710i
$419$	−6.25484	−	6.25484i	−0.305569	−	0.305569i	0.537619	−	0.843188i	$-0.319324\pi$
$419$	−6.25484	−	6.25484i	−0.305569	−	0.305569i	−0.843188	+	0.537619i	$0.819324\pi$
$420$	−3.58259	−	0.102370i	−0.174813	−	0.00499512i
$421$	16.2076	−	16.2076i	0.789909	−	0.789909i	−0.191570	−	0.981479i	$-0.561358\pi$
$421$	16.2076	−	16.2076i	0.789909	−	0.789909i	0.981479	+	0.191570i	$0.0613580\pi$
$422$	10.0776	−	2.47023i	0.490568	−	0.120249i
$423$	1.80573	+	1.80573i	0.0877974	+	0.0877974i
$424$	−1.14812	+	17.8449i	−0.0557575	+	0.866623i
$425$	3.40601	−	14.3357i	0.165216	−	0.695382i
$426$	−3.40790	−	2.06610i	−0.165113	−	0.100103i
$427$	5.46368			0.264406
$428$	3.59097	+	6.88475i	0.173576	+	0.332787i
$429$	9.99288	−	9.99288i	0.482461	−	0.482461i
$430$	2.57528	−	9.34334i	0.124191	−	0.450576i
$431$			16.1416i			0.777512i	0.921341	+	0.388756i	$0.127095\pi$
$431$			16.1416i			0.777512i	−0.921341	+	0.388756i	$0.872905\pi$
$432$	−2.28906	+	3.28027i	−0.110133	+	0.157822i
$433$	−23.9381	−	23.9381i	−1.15039	−	1.15039i	−0.986474	−	0.163919i	$-0.947586\pi$
$433$	−23.9381	−	23.9381i	−1.15039	−	1.15039i	−0.163919	−	0.986474i	$-0.552414\pi$
$434$	−2.18806	−	8.92640i	−0.105030	−	0.428481i
$435$	4.06626	−	7.28092i	0.194962	−	0.349093i
$436$	−6.78905	−	2.13461i	−0.325136	−	0.102229i
$437$			49.5800i			2.37173i
$438$	20.7948	−	5.09727i	0.993614	−	0.243557i
$439$			13.2194i			0.630927i	0.948938	+	0.315464i	$0.102160\pi$
$439$			13.2194i			0.630927i	−0.948938	+	0.315464i	$0.897840\pi$
$440$	17.6892	−	27.3812i	0.843297	−	1.30535i
$441$			6.35773i			0.302749i
$442$	−2.72047	−	11.0984i	−0.129399	−	0.527897i
$443$		−	7.03868i		−	0.334418i	−0.985921	−	0.167209i	$-0.946525\pi$
$443$		−	7.03868i		−	0.334418i	0.985921	−	0.167209i	$-0.0534754\pi$
$444$	−4.05068	+	2.11277i	−0.192237	+	0.100268i
$445$	−21.5833	+	6.11455i	−1.02315	+	0.289857i
$446$	−22.0237	+	5.39851i	−1.04285	+	0.255627i
$447$	8.06960	+	8.06960i	0.381679	+	0.381679i
$448$	−5.07709	+	3.91518i	−0.239870	+	0.184975i
$449$			28.2211i			1.33184i	0.746025	+	0.665918i	$0.231960\pi$
$449$			28.2211i			1.33184i	−0.746025	+	0.665918i	$0.768040\pi$
$450$	7.07089	−	0.0503283i	0.333325	−	0.00237250i
$451$	−8.29089	+	8.29089i	−0.390403	+	0.390403i
$452$	3.30456	−	10.5100i	0.155433	−	0.494350i
$453$	10.9071			0.512461
$454$	14.5866	−	24.0596i	0.684581	−	1.12917i
$455$	4.28981	+	2.39578i	0.201109	+	0.112316i
$456$	17.3993	−	15.2958i	0.814798	−	0.716290i
$457$	−27.6086	−	27.6086i	−1.29148	−	1.29148i	−0.933873	−	0.357605i	$-0.883594\pi$
$457$	−27.6086	−	27.6086i	−1.29148	−	1.29148i	−0.357605	−	0.933873i	$-0.616406\pi$
$458$	−6.75811	−	27.5704i	−0.315786	−	1.28828i
$459$	2.08381	−	2.08381i	0.0972638	−	0.0972638i
$460$	−0.773210	+	27.0598i	−0.0360511	+	1.26167i
$461$	−16.4823	−	16.4823i	−0.767657	−	0.767657i	0.210036	−	0.977694i	$-0.432642\pi$
$461$	−16.4823	−	16.4823i	−0.767657	−	0.767657i	−0.977694	+	0.210036i	$0.932642\pi$
$462$	4.99532	+	3.02850i	0.232403	+	0.140899i
$463$	−18.5827	+	18.5827i	−0.863610	+	0.863610i	−0.991755	−	0.128145i	$-0.959098\pi$
$463$	−18.5827	+	18.5827i	−0.863610	+	0.863610i	0.128145	+	0.991755i	$0.459098\pi$
$464$	−2.61399	−	14.6872i	−0.121351	−	0.681838i
$465$	4.94243	+	17.4459i	0.229200	+	0.809034i
$466$	−27.0930	+	6.64110i	−1.25506	+	0.307643i
$467$		−	11.5112i		−	0.532676i	−0.963880	−	0.266338i	$-0.914186\pi$
$467$		−	11.5112i		−	0.532676i	0.963880	−	0.266338i	$-0.0858137\pi$
$468$	4.86207	−	2.53598i	0.224749	−	0.117226i
$469$	−1.89442	−	1.89442i	−0.0874761	−	0.0874761i
$470$	−3.98762	−	7.02223i	−0.183935	−	0.323912i
$471$	14.0713			0.648373
$472$	−14.7061	−	16.7285i	−0.676901	−	0.769992i
$473$	−11.1699	+	11.1699i	−0.513593	+	0.513593i
$474$	−14.6906	−	8.90644i	−0.674761	−	0.409086i
$475$	−39.8442	−	9.46659i	−1.82818	−	0.434357i
$476$	4.18803	−	2.18441i	0.191958	−	0.100122i
$477$	6.32215			0.289472
$478$	19.8875	+	12.0572i	0.909634	+	0.551482i
$479$	−10.5991			−0.484286			−0.242143	−	0.970241i	$-0.577850\pi$
$479$	−10.5991			−0.484286			−0.242143	+	0.970241i	$0.577850\pi$
$480$	9.73476	−	8.07679i	0.444329	−	0.368653i
$481$	6.26316			0.285575
$482$	−5.69584	−	3.45321i	−0.259438	−	0.157289i
$483$	−4.85117			−0.220736
$484$	−27.6027	+	14.3971i	−1.25467	+	0.654414i
$485$	1.57482	−	2.81983i	0.0715091	−	0.128042i
$486$	1.20932	+	0.733173i	0.0548559	+	0.0332574i
$487$	23.1871	−	23.1871i	1.05071	−	1.05071i	0.0520644	−	0.998644i	$-0.483420\pi$
$487$	23.1871	−	23.1871i	1.05071	−	1.05071i	0.998644	−	0.0520644i	$-0.0165801\pi$
$488$	−14.4823	+	12.7314i	−0.655585	+	0.576325i
$489$	2.82750			0.127864
$490$	5.34224	−	19.3821i	0.241338	−	0.875596i
$491$	−17.0460	−	17.0460i	−0.769277	−	0.769277i	0.208702	−	0.977979i	$-0.433076\pi$
$491$	−17.0460	−	17.0460i	−0.769277	−	0.769277i	−0.977979	+	0.208702i	$0.933076\pi$
$492$	−4.03397	+	2.10405i	−0.181865	+	0.0948580i
$493$			10.9907i			0.494995i
$494$	−30.8467	+	7.56120i	−1.38786	+	0.340195i
$495$	−10.0623	−	5.61960i	−0.452266	−	0.252582i
$496$	26.6000	+	18.5622i	1.19438	+	0.833468i
$497$	−1.59695	+	1.59695i	−0.0716328	+	0.0716328i
$498$	−2.39010	−	1.44904i	−0.107103	−	0.0649332i
$499$	23.5253	+	23.5253i	1.05314	+	1.05314i	0.998507	+	0.0546291i	$0.0173976\pi$
$499$	23.5253	+	23.5253i	1.05314	+	1.05314i	0.0546291	+	0.998507i	$0.482602\pi$
$500$	−21.5986	−	5.78806i	−0.965918	−	0.258850i
$501$	−5.12509	+	5.12509i	−0.228972	+	0.228972i
$502$	−6.99631	−	28.5421i	−0.312261	−	1.27390i
$503$	−16.1405	−	16.1405i	−0.719669	−	0.719669i	0.248868	−	0.968537i	$-0.419941\pi$
$503$	−16.1405	−	16.1405i	−0.719669	−	0.719669i	−0.968537	+	0.248868i	$0.919941\pi$
$504$	1.49662	+	1.70244i	0.0666647	+	0.0758328i
$505$	20.3427	−	36.4250i	0.905239	−	1.62089i
$506$	22.8747	−	37.7303i	1.01690	−	1.67732i
$507$	5.48226			0.243476
$508$	2.64685	−	8.41819i	0.117435	−	0.373497i
$509$	29.4832	−	29.4832i	1.30682	−	1.30682i	0.383124	−	0.923697i	$-0.374848\pi$
$509$	29.4832	−	29.4832i	1.30682	−	1.30682i	0.923697	−	0.383124i	$-0.125152\pi$
$510$	−8.10365	+	4.60171i	−0.358836	+	0.203767i
$511$		−	12.1330i		−	0.536734i
$512$	4.33450	−	22.2084i	0.191560	−	0.981481i
$513$	−5.79168	−	5.79168i	−0.255709	−	0.255709i
$514$	9.77034	−	2.39493i	0.430951	−	0.105636i
$515$	−12.4717	−	6.96519i	−0.549567	−	0.306923i
$516$	−5.43476	+	2.83468i	−0.239252	+	0.124790i
$517$			13.1622i			0.578873i
$518$	0.616364	+	2.51451i	0.0270815	+	0.110481i
$519$			4.60016i			0.201924i
$520$	−16.9534	+	3.64570i	−0.743457	+	0.159874i
$521$			18.6350i			0.816416i	0.912889	+	0.408208i	$0.133846\pi$
$521$			18.6350i			0.816416i	−0.912889	+	0.408208i	$0.866154\pi$
$522$	−5.12267	+	1.25568i	−0.224213	+	0.0549597i
$523$		−	16.2282i		−	0.709611i	−0.934940	−	0.354805i	$-0.884547\pi$
$523$		−	16.2282i		−	0.709611i	0.934940	−	0.354805i	$-0.115453\pi$
$524$	−23.4644	−	7.37766i	−1.02505	−	0.322295i
$525$	0.926262	−	3.89857i	0.0404254	−	0.170148i
$526$	4.21320	+	17.1882i	0.183704	+	0.749440i
$527$	−16.8978	−	16.8978i	−0.736079	−	0.736079i
$528$	−20.2979	+	3.61254i	−0.883351	+	0.157216i
$529$			13.6415i			0.593108i
$530$	−19.2737	−	5.31235i	−0.837196	−	0.230754i
$531$	−5.56839	+	5.56839i	−0.241647	+	0.241647i
$532$	−6.07130	−	11.6401i	−0.263224	−	0.504663i
$533$	6.23732			0.270168
$534$	12.1322	+	7.35534i	0.525010	+	0.318297i
$535$	−8.35278	+	2.36635i	−0.361122	+	0.102306i
$536$	9.43581	+	0.607089i	0.407565	+	0.0262222i
$537$	−3.06396	−	3.06396i	−0.132220	−	0.132220i
$538$	−9.05314	+	2.21913i	−0.390308	+	0.0956733i
$539$	−23.1712	+	23.1712i	−0.998055	+	0.998055i
$540$	−3.07066	−	3.25131i	−0.132140	−	0.139914i
$541$	−12.4579	−	12.4579i	−0.535609	−	0.535609i	0.386627	−	0.922236i	$-0.373640\pi$
$541$	−12.4579	−	12.4579i	−0.535609	−	0.535609i	−0.922236	+	0.386627i	$0.873640\pi$
$542$	−2.84210	+	4.68785i	−0.122078	+	0.201361i
$543$	−3.08559	+	3.08559i	−0.132415	+	0.132415i
$544$	−6.01093	+	15.5490i	−0.257717	+	0.666660i
$545$	3.87966	−	6.94679i	0.166186	−	0.297568i
$546$	−0.739828	−	3.01820i	−0.0316617	−	0.129167i
$547$		−	1.52574i		−	0.0652358i	−0.999468	−	0.0326179i	$-0.989616\pi$
$547$		−	1.52574i		−	0.0652358i	0.999468	−	0.0326179i	$-0.0103844\pi$
$548$	13.7404	−	43.7010i	0.586963	−	1.86681i
$549$	4.82071	+	4.82071i	0.205743	+	0.205743i
$550$	25.9538	+	25.5870i	1.10667	+	1.09103i
$551$	30.5472			1.30135
$552$	12.8588	−	11.3042i	0.547306	−	0.481137i
$553$	−6.88402	+	6.88402i	−0.292738	+	0.292738i
$554$	−10.7740	+	17.7711i	−0.457744	+	0.755020i
$555$	−1.39225	−	4.91440i	−0.0590978	−	0.208605i
$556$	−29.3723	−	9.23523i	−1.24566	−	0.391661i
$557$	14.5277			0.615560			0.307780	−	0.951458i	$-0.400414\pi$
$557$	14.5277			0.615560			0.307780	+	0.951458i	$0.400414\pi$
$558$	5.94536	−	9.80650i	0.251687	−	0.415142i
$559$	8.40322			0.355419
$560$	−3.13207	−	6.44763i	−0.132354	−	0.272462i
$561$	15.1892			0.641288
$562$	−0.240911	+	0.397367i	−0.0101622	+	0.0167619i
$563$	−37.1864			−1.56722			−0.783610	−	0.621253i	$-0.786624\pi$
$563$	−37.1864			−1.56722			−0.783610	+	0.621253i	$0.786624\pi$
$564$	−1.53192	+	4.87221i	−0.0645054	+	0.205157i
$565$	10.7542	+	6.00603i	0.452434	+	0.252676i
$566$	16.8549	−	27.8011i	0.708466	−	1.16857i
$567$	0.566689	−	0.566689i	0.0237987	−	0.0237987i
$568$	0.511760	−	7.95414i	0.0214730	−	0.333748i
$569$	22.2439			0.932513			0.466256	−	0.884650i	$-0.345602\pi$
$569$	22.2439			0.932513			0.466256	+	0.884650i	$0.345602\pi$
$570$	12.7899	+	22.5231i	0.535710	+	0.943389i
$571$	32.0005	+	32.0005i	1.33918	+	1.33918i	0.896854	+	0.442327i	$0.145847\pi$
$571$	32.0005	+	32.0005i	1.33918	+	1.33918i	0.442327	+	0.896854i	$0.354153\pi$
$572$	26.9628	+	8.47763i	1.12737	+	0.354467i
$573$		−	21.0908i		−	0.881081i
$574$	0.613821	+	2.50414i	0.0256204	+	0.104521i
$575$	−29.4464	−	6.99617i	−1.22800	−	0.291761i
$576$	−7.93404	−	1.02518i	−0.330585	−	0.0427157i
$577$	3.38284	−	3.38284i	0.140830	−	0.140830i	−0.633177	−	0.774007i	$-0.718250\pi$
$577$	3.38284	−	3.38284i	0.140830	−	0.140830i	0.774007	+	0.633177i	$0.218250\pi$
$578$	−6.09670	+	10.0561i	−0.253589	+	0.418279i
$579$	15.2332	+	15.2332i	0.633069	+	0.633069i
$580$	16.6721	+	0.476390i	0.692270	+	0.0197810i
$581$	−1.12000	+	1.12000i	−0.0464656	+	0.0464656i
$582$	−1.98396	+	0.486314i	−0.0822379	+	0.0201583i
$583$	23.0416	+	23.0416i	0.954284	+	0.954284i
$584$	28.2723	+	32.1605i	1.16992	+	1.33081i
$585$	1.67114	+	5.89881i	0.0690930	+	0.243886i
$586$	26.6247	+	16.1417i	1.09986	+	0.666807i
$587$	5.27446			0.217700			0.108850	−	0.994058i	$-0.465283\pi$
$587$	5.27446			0.217700			0.108850	+	0.994058i	$0.465283\pi$
$588$	−11.2740	+	5.88036i	−0.464934	+	0.242502i
$589$	−46.9653	+	46.9653i	−1.93517	+	1.93517i
$590$	21.6547	−	12.2968i	0.891512	−	0.506251i
$591$		−	14.0460i		−	0.577774i
$592$	−7.49307	−	5.22886i	−0.307963	−	0.214905i
$593$	20.6039	+	20.6039i	0.846101	+	0.846101i	0.989644	−	0.143543i	$-0.0458495\pi$
$593$	20.6039	+	20.6039i	0.846101	+	0.846101i	−0.143543	+	0.989644i	$0.545850\pi$
$594$	1.73536	+	7.07957i	0.0712027	+	0.290478i
$595$	1.43946	+	5.08105i	0.0590122	+	0.208303i
$596$	−6.84598	+	21.7734i	−0.280422	+	0.891873i
$597$		−	2.42066i		−	0.0990708i
$598$	−22.7968	+	5.58802i	−0.932233	+	0.228511i
$599$		−	31.6423i		−	1.29287i	−0.762969	−	0.646435i	$-0.776259\pi$
$599$		−	31.6423i		−	1.29287i	0.762969	−	0.646435i	$-0.223741\pi$
$600$	6.62922	+	12.4921i	0.270637	+	0.509989i
$601$		−	12.1679i		−	0.496338i	−0.968717	−	0.248169i	$-0.920171\pi$
$601$		−	12.1679i		−	0.496338i	0.968717	−	0.248169i	$-0.0798289\pi$
$602$	0.826969	+	3.37370i	0.0337048	+	0.137502i
$603$		−	3.34296i		−	0.136136i
$604$	10.0882	+	19.3414i	0.410482	+	0.786991i
$605$	−9.48727	−	33.4884i	−0.385712	−	1.36150i
$606$	−25.6277	+	6.28193i	−1.04106	+	0.255186i
$607$	19.4977	+	19.4977i	0.791387	+	0.791387i	0.981720	−	0.190332i	$-0.0609565\pi$
$607$	19.4977	+	19.4977i	0.791387	+	0.791387i	−0.190332	+	0.981720i	$0.560957\pi$
$608$	43.2166	+	16.7066i	1.75267	+	0.677544i
$609$			2.98890i			0.121116i
$610$	−10.6457	−	18.7471i	−0.431031	−	0.759049i
$611$	4.95103	−	4.95103i	0.200297	−	0.200297i
$612$	5.62252	+	1.76783i	0.227277	+	0.0714604i
$613$	−40.9232			−1.65287			−0.826437	−	0.563029i	$-0.809636\pi$
$613$	−40.9232			−1.65287			−0.826437	+	0.563029i	$0.809636\pi$
$614$	−2.26329	+	3.73315i	−0.0913389	+	0.150658i
$615$	−1.38651	−	4.89413i	−0.0559094	−	0.197350i
$616$	−0.750141	+	11.6592i	−0.0302240	+	0.469763i
$617$	12.9650	+	12.9650i	0.521952	+	0.521952i	0.918160	−	0.396209i	$-0.129674\pi$
$617$	12.9650	+	12.9650i	0.521952	+	0.521952i	−0.396209	+	0.918160i	$0.629674\pi$
$618$	2.15089	+	8.77474i	0.0865213	+	0.352972i
$619$	12.2565	−	12.2565i	0.492632	−	0.492632i	−0.416503	−	0.909135i	$-0.636744\pi$
$619$	12.2565	−	12.2565i	0.492632	−	0.492632i	0.909135	+	0.416503i	$0.136744\pi$
$620$	−26.3652	+	24.9003i	−1.05885	+	1.00002i
$621$	−4.28027	−	4.28027i	−0.171761	−	0.171761i
$622$	29.4690	+	17.8661i	1.18160	+	0.716366i
$623$	5.68514	−	5.68514i	0.227770	−	0.227770i
$624$	8.99402	+	6.27626i	0.360049	+	0.251252i
$625$	11.2447	−	22.3284i	0.449790	−	0.893134i
$626$	−6.44735	+	1.58039i	−0.257688	+	0.0631650i
$627$		−	42.2164i		−	1.68596i
$628$	13.0148	+	24.9524i	0.519347	+	0.995711i
$629$	4.76000	+	4.76000i	0.189794	+	0.189794i
$630$	−2.20378	+	1.25143i	−0.0878007	+	0.0498582i
$631$	7.42406			0.295547			0.147774	−	0.989021i	$-0.452789\pi$
$631$	7.42406			0.295547			0.147774	+	0.989021i	$0.452789\pi$
$632$	2.20607	−	34.2883i	0.0877527	−	1.36391i
$633$	5.18795	−	5.18795i	0.206202	−	0.206202i
$634$	6.47892	+	3.92796i	0.257311	+	0.155999i
$635$	8.61379	+	4.81064i	0.341828	+	0.190905i
$636$	5.84746	+	11.2110i	0.231867	+	0.444544i
$637$	17.4319			0.690678
$638$	−23.2464	−	14.0935i	−0.920333	−	0.557969i
$639$	−2.81803			−0.111480
$640$	23.3263	+	9.79213i	0.922051	+	0.387068i
$641$	−28.7869			−1.13702			−0.568508	−	0.822678i	$-0.692479\pi$
$641$	−28.7869			−1.13702			−0.568508	+	0.822678i	$0.692479\pi$
$642$	4.69518	+	2.84653i	0.185304	+	0.112344i
$643$	−5.25971			−0.207423			−0.103711	−	0.994607i	$-0.533072\pi$
$643$	−5.25971			−0.207423			−0.103711	+	0.994607i	$0.533072\pi$
$644$	−4.48692	−	8.60249i	−0.176809	−	0.338986i
$645$	−1.86797	−	6.59361i	−0.0735514	−	0.259623i
$646$	−29.1900	−	17.6969i	−1.14846	−	0.696277i
$647$	−32.0670	+	32.0670i	−1.26068	+	1.26068i	−0.309923	+	0.950762i	$0.600303\pi$
$647$	−32.0670	+	32.0670i	−1.26068	+	1.26068i	−0.950762	+	0.309923i	$0.899697\pi$
$648$	−0.181602	+	2.82259i	−0.00713401	+	0.110882i
$649$	−40.5888			−1.59325
$650$	−0.137993	−	19.3873i	−0.00541251	−	0.760433i
$651$	−4.59533	−	4.59533i	−0.180105	−	0.180105i
$652$	2.61520	+	5.01396i	0.102419	+	0.196362i
$653$			31.6376i			1.23807i	0.785362	+	0.619037i	$0.212477\pi$
$653$			31.6376i			1.23807i	−0.785362	+	0.619037i	$0.787523\pi$
$654$	−4.88759	+	1.19806i	−0.191120	+	0.0468477i
$655$	13.4089	−	24.0096i	0.523929	−	0.938131i
$656$	−7.46216	−	5.20729i	−0.291348	−	0.203311i
$657$	10.7052	−	10.7052i	0.417650	−	0.417650i
$658$	2.47496	+	1.50049i	0.0964840	+	0.0584951i
$659$	12.8616	+	12.8616i	0.501015	+	0.501015i	0.911753	−	0.410738i	$-0.134729\pi$
$659$	12.8616	+	12.8616i	0.501015	+	0.501015i	−0.410738	+	0.911753i	$0.634729\pi$
$660$	0.658374	−	23.0409i	0.0256272	−	0.896866i
$661$	28.8603	−	28.8603i	1.12254	−	1.12254i	0.131178	−	0.991359i	$-0.458124\pi$
$661$	28.8603	−	28.8603i	1.12254	−	1.12254i	0.991359	−	0.131178i	$-0.0418761\pi$
$662$	−1.31847	−	5.37883i	−0.0512438	−	0.209054i
$663$	−5.71348	−	5.71348i	−0.221893	−	0.221893i
$664$	0.358919	−	5.57857i	0.0139287	−	0.216491i
$665$	14.1221	−	4.00081i	0.547633	−	0.155145i
$666$	−1.67477	+	2.76243i	−0.0648962	+	0.107042i
$667$	22.5756			0.874129
$668$	−13.8285	−	4.34795i	−0.535041	−	0.168227i
$669$	−11.3379	+	11.3379i	−0.438347	+	0.438347i
$670$	−2.80901	+	10.1913i	−0.108521	+	0.393726i
$671$			35.1389i			1.35652i
$672$	−1.63467	+	4.22854i	−0.0630586	+	0.163120i
$673$	8.69401	+	8.69401i	0.335130	+	0.335130i	0.854531	−	0.519401i	$-0.173845\pi$
$673$	8.69401	+	8.69401i	0.335130	+	0.335130i	−0.519401	+	0.854531i	$0.673845\pi$
$674$	−14.1808	+	3.47602i	−0.546222	+	0.133891i
$675$	4.25704	−	2.62252i	0.163853	−	0.100941i
$676$	5.07063	+	9.72160i	0.195024	+	0.373908i
$677$		−	13.3965i		−	0.514871i	−0.966295	−	0.257435i	$-0.917123\pi$
$677$		−	13.3965i		−	0.514871i	0.966295	−	0.257435i	$-0.0828775\pi$
$678$	−1.85469	−	7.56640i	−0.0712291	−	0.290586i
$679$			1.15757i			0.0444236i
$680$	−15.6553	−	10.1139i	−0.600355	−	0.387849i
$681$		−	19.8951i		−	0.762383i
$682$	57.4089	−	14.0722i	2.19830	−	0.538852i
$683$		−	20.0009i		−	0.765312i	−0.923891	−	0.382656i	$-0.875009\pi$
$683$		−	20.0009i		−	0.765312i	0.923891	−	0.382656i	$-0.124991\pi$
$684$	4.91347	−	15.6271i	0.187871	−	0.597517i
$685$	44.7164	+	24.9733i	1.70852	+	0.954179i
$686$	3.60429	+	14.7040i	0.137612	+	0.561403i
$687$	−14.1933	−	14.1933i	−0.541507	−	0.541507i
$688$	−10.0534	−	7.01552i	−0.383282	−	0.267464i
$689$		−	17.3344i		−	0.660388i
$690$	9.45222	+	16.6454i	0.359840	+	0.633681i
$691$	−29.3786	+	29.3786i	−1.11761	+	1.11761i	−0.125524	+	0.992091i	$0.540061\pi$
$691$	−29.3786	+	29.3786i	−1.11761	+	1.11761i	−0.992091	+	0.125524i	$0.959939\pi$
$692$	−8.15738	+	4.25476i	−0.310097	+	0.161742i
$693$	4.13068			0.156912
$694$	−20.6581	−	12.5244i	−0.784172	−	0.475418i
$695$	16.7850	−	30.0548i	0.636693	−	1.14004i
$696$	−6.96472	−	7.92255i	−0.263997	−	0.300303i
$697$	4.74036	+	4.74036i	0.179554	+	0.179554i
$698$	2.68284	−	0.657623i	0.101547	−	0.0248914i
$699$	−13.9475	+	13.9475i	−0.527545	+	0.527545i
$700$	7.76998	−	1.96333i	0.293678	−	0.0742067i
$701$	22.4862	+	22.4862i	0.849291	+	0.849291i	0.990045	−	0.140754i	$-0.0449525\pi$
$701$	22.4862	+	22.4862i	0.849291	+	0.849291i	−0.140754	+	0.990045i	$0.544953\pi$
$702$	2.01025	−	3.31578i	0.0758720	−	0.125146i
$703$	13.2298	−	13.2298i	0.498973	−	0.498973i
$704$	−25.1799	−	32.6526i	−0.949002	−	1.23064i
$705$	−4.98541	−	2.78426i	−0.187762	−	0.104861i
$706$	−3.18812	−	13.0063i	−0.119987	−	0.489497i
$707$			14.9529i			0.562362i
$708$	−15.0246	−	4.72404i	−0.564660	−	0.177540i
$709$	−3.15802	−	3.15802i	−0.118602	−	0.118602i	0.645315	−	0.763917i	$-0.276726\pi$
$709$	−3.15802	−	3.15802i	−0.118602	−	0.118602i	−0.763917	+	0.645315i	$0.776726\pi$
$710$	8.59103	+	2.36792i	0.322416	+	0.0888665i
$711$	−12.1478			−0.455578
$712$	−1.82187	+	28.3168i	−0.0682775	+	1.06122i
$713$	−34.7091	+	34.7091i	−1.29987	+	1.29987i
$714$	1.73156	−	2.85610i	0.0648021	−	0.106887i
$715$	−15.4081	+	27.5893i	−0.576230	+	1.03178i
$716$	2.59937	−	8.26718i	0.0971429	−	0.308959i
$717$	16.4452			0.614157
$718$	−1.39996	+	2.30914i	−0.0522461	+	0.0861765i
$719$	−1.88866			−0.0704352			−0.0352176	−	0.999380i	$-0.511212\pi$
$719$	−1.88866			−0.0704352			−0.0352176	+	0.999380i	$0.511212\pi$
$720$	2.92539	−	8.45234i	0.109023	−	0.315000i
$721$	5.11976			0.190670
$722$	−35.2562	+	58.1528i	−1.31210	+	2.16422i
$723$	−4.70995			−0.175165
$724$	−8.32554	−	2.61771i	−0.309416	−	0.0972866i
$725$	−4.31048	+	18.1425i	−0.160087	+	0.673796i
$726$	−11.4125	+	18.8241i	−0.423556	+	0.698629i
$727$	−0.978984	+	0.978984i	−0.0363085	+	0.0363085i	−0.725028	−	0.688719i	$-0.758173\pi$
$727$	−0.978984	+	0.978984i	−0.0363085	+	0.0363085i	0.688719	+	0.725028i	$0.258173\pi$
$728$	4.66784	−	4.10350i	0.173002	−	0.152086i
$729$	1.00000			0.0370370
$730$	−41.6312	+	23.6405i	−1.54084	+	0.874976i
$731$	6.38645	+	6.38645i	0.236211	+	0.236211i
$732$	−4.08973	+	13.0072i	−0.151161	+	0.480761i
$733$		−	18.1447i		−	0.670189i	−0.942185	−	0.335094i	$-0.891232\pi$
$733$		−	18.1447i		−	0.670189i	0.942185	−	0.335094i	$-0.108768\pi$
$734$	9.65474	+	39.3874i	0.356363	+	1.45382i
$735$	−3.87499	−	13.6780i	−0.142931	−	0.504521i
$736$	31.9387	+	12.3468i	1.17728	+	0.455111i
$737$	12.1837	−	12.1837i	0.448791	−	0.448791i
$738$	−1.66786	+	2.75103i	−0.0613949	+	0.101267i
$739$	−18.8493	−	18.8493i	−0.693383	−	0.693383i	0.269592	−	0.962975i	$-0.413111\pi$
$739$	−18.8493	−	18.8493i	−0.693383	−	0.693383i	−0.962975	+	0.269592i	$0.913111\pi$
$740$	7.42691	−	7.01427i	0.273019	−	0.257850i
$741$	−15.8799	+	15.8799i	−0.583364	+	0.583364i
$742$	6.95936	−	1.70589i	0.255486	−	0.0626254i
$743$	−6.80504	−	6.80504i	−0.249653	−	0.249653i	0.571175	−	0.820828i	$-0.306488\pi$
$743$	−6.80504	−	6.80504i	−0.249653	−	0.249653i	−0.820828	+	0.571175i	$0.806488\pi$
$744$	22.8887	+	1.47263i	0.839139	+	0.0539892i
$745$	−22.2793	−	12.4426i	−0.816250	−	0.455861i
$746$	41.8106	+	25.3484i	1.53079	+	0.928071i
$747$	−1.97640			−0.0723127
$748$	14.0487	+	26.9347i	0.513672	+	0.984830i
$749$	2.20016	−	2.20016i	0.0803922	−	0.0803922i
$750$	−15.1816	+	4.41793i	−0.554355	+	0.161320i
$751$		−	1.26232i		−	0.0460627i	−0.999735	−	0.0230313i	$-0.992668\pi$
$751$		−	1.26232i		−	0.0460627i	0.999735	−	0.0230313i	$-0.00733175\pi$
$752$	−10.0567	+	1.78986i	−0.366730	+	0.0652693i
$753$	−14.6935	−	14.6935i	−0.535462	−	0.535462i
$754$	3.44289	+	14.0456i	0.125383	+	0.511510i
$755$	−23.4656	+	6.64781i	−0.854000	+	0.241938i
$756$	1.52904	+	0.480760i	0.0556106	+	0.0174851i
$757$		−	29.2534i		−	1.06323i	−0.846985	−	0.531617i	$-0.821585\pi$
$757$		−	29.2534i		−	1.06323i	0.846985	−	0.531617i	$-0.178415\pi$
$758$	41.2143	−	10.1026i	1.49697	−	0.366941i
$759$		−	31.1996i		−	1.13247i
$760$	−28.1103	+	43.5121i	−1.01967	+	1.57835i
$761$		−	43.1952i		−	1.56583i	−0.622131	−	0.782913i	$-0.713733\pi$
$761$		−	43.1952i		−	1.56583i	0.622131	−	0.782913i	$-0.286267\pi$
$762$	−1.48555	−	6.06045i	−0.0538158	−	0.219547i
$763$			2.85174i			0.103240i
$764$	37.3999	−	19.5072i	1.35308	−	0.705746i
$765$	−3.21304	+	5.75316i	−0.116168	+	0.208006i
$766$	6.08397	−	1.49132i	0.219823	−	0.0538835i
$767$	15.2677	+	15.2677i	0.551284	+	0.551284i
$768$	−5.52039	−	15.0175i	−0.199200	−	0.541897i
$769$			22.3663i			0.806550i	0.915079	+	0.403275i	$0.132128\pi$
$769$			22.3663i			0.806550i	−0.915079	+	0.403275i	$0.867872\pi$
$770$	−12.5928	−	3.47091i	−0.453812	−	0.125083i
$771$	5.02979	−	5.02979i	0.181143	−	0.181143i
$772$	−12.9233	+	41.1021i	−0.465120	+	1.47930i
$773$	−25.3081			−0.910270			−0.455135	−	0.890422i	$-0.650409\pi$
$773$	−25.3081			−0.910270			−0.455135	+	0.890422i	$0.650409\pi$
$774$	−2.24703	+	3.70633i	−0.0807678	+	0.133221i
$775$	−21.2663	−	34.5207i	−0.763907	−	1.24002i
$776$	−2.69737	−	3.06833i	−0.0968299	−	0.110147i
$777$	1.29448	+	1.29448i	0.0464391	+	0.0464391i
$778$	7.27445	+	29.6768i	0.260802	+	1.06397i
$779$	13.1753	−	13.1753i	0.472053	−	0.472053i
$780$	−8.91460	+	8.41930i	−0.319194	+	0.301459i
$781$	−10.2705	−	10.2705i	−0.367508	−	0.367508i
$782$	−21.5725	−	13.0787i	−0.771431	−	0.467694i
$783$	−2.63716	+	2.63716i	−0.0942445	+	0.0942445i
$784$	−20.8551	−	14.5532i	−0.744824	−	0.519758i
$785$	−30.2731	+	8.57637i	−1.08049	+	0.306104i
$786$	−16.8925	+	4.14073i	−0.602536	+	0.147695i
$787$		−	28.2019i		−	1.00529i	−0.864493	−	0.502645i	$-0.832360\pi$
$787$		−	28.2019i		−	1.00529i	0.864493	−	0.502645i	$-0.167640\pi$
$788$	24.9075	−	12.9913i	0.887291	−	0.462797i
$789$	8.84851	+	8.84851i	0.315015	+	0.315015i
$790$	37.0337	+	10.2075i	1.31760	+	0.363166i
$791$	−4.41473			−0.156970
$792$	−10.9490	+	9.62528i	−0.389056	+	0.342020i
$793$	13.2177	−	13.2177i	0.469373	−	0.469373i
$794$	11.3637	+	6.88945i	0.403283	+	0.244497i
$795$	−13.6015	+	3.85330i	−0.482395	+	0.136663i
$796$	4.29251	−	2.23890i	0.152144	−	0.0793558i
$797$	15.2969			0.541846			0.270923	−	0.962601i	$-0.412671\pi$
$797$	15.2969			0.541846			0.270923	+	0.962601i	$0.412671\pi$
$798$	−7.93818	−	4.81267i	−0.281009	−	0.170367i
$799$	7.52557			0.266235
$800$	−16.0206	+	23.3097i	−0.566414	+	0.824121i
$801$	10.0322			0.354470
$802$	0.873336	+	0.529476i	0.0308386	+	0.0186964i
$803$	78.0319			2.75369
$804$	5.92801	−	3.09196i	0.209065	−	0.109045i
$805$	10.4368	−	2.95675i	0.367849	−	0.104212i
$806$	−26.8879	−	16.3013i	−0.947087	−	0.574189i
$807$	−4.66057	+	4.66057i	−0.164060	+	0.164060i
$808$	−34.8431	−	39.6350i	−1.22578	−	1.39435i
$809$	6.74990			0.237314			0.118657	−	0.992935i	$-0.462141\pi$
$809$	6.74990			0.237314			0.118657	+	0.992935i	$0.462141\pi$
$810$	−3.04860	−	0.840275i	−0.107117	−	0.0295243i
$811$	−4.99242	−	4.99242i	−0.175307	−	0.175307i	0.613999	−	0.789307i	$-0.289560\pi$
$811$	−4.99242	−	4.99242i	−0.175307	−	0.175307i	−0.789307	+	0.613999i	$0.789560\pi$
$812$	−5.30017	+	2.76448i	−0.185999	+	0.0970143i
$813$			3.87643i			0.135952i
$814$	−16.1717	+	3.96405i	−0.566819	+	0.138940i
$815$	−6.08309	+	1.72334i	−0.213081	+	0.0603660i
$816$	2.06549	+	11.6054i	0.0723067	+	0.406271i
$817$	17.7504	−	17.7504i	0.621006	−	0.621006i
$818$	25.1369	+	15.2397i	0.878892	+	0.532844i
$819$	−1.55378	−	1.55378i	−0.0542933	−	0.0542933i
$820$	7.39627	−	6.98533i	0.258289	−	0.243938i
$821$	−28.2761	+	28.2761i	−0.986842	+	0.986842i	−0.999915	−	0.0130724i	$-0.995839\pi$
$821$	−28.2761	+	28.2761i	−0.986842	+	0.986842i	0.0130724	+	0.999915i	$0.495839\pi$
$822$	−7.71187	−	31.4613i	−0.268982	−	1.09734i
$823$	20.7586	+	20.7586i	0.723599	+	0.723599i	0.969336	−	0.245738i	$-0.0790302\pi$
$823$	20.7586	+	20.7586i	0.723599	+	0.723599i	−0.245738	+	0.969336i	$0.579030\pi$
$824$	−13.5707	+	11.9300i	−0.472758	+	0.415602i
$825$	25.0731	+	5.95712i	0.872933	+	0.207400i
$826$	−4.62712	+	7.63213i	−0.160998	+	0.265556i
$827$	17.1914			0.597804			0.298902	−	0.954284i	$-0.403380\pi$
$827$	17.1914			0.597804			0.298902	+	0.954284i	$0.403380\pi$
$828$	3.63124	−	11.5490i	0.126194	−	0.401356i
$829$	21.3409	−	21.3409i	0.741201	−	0.741201i	−0.231608	−	0.972809i	$-0.574399\pi$
$829$	21.3409	−	21.3409i	0.741201	−	0.741201i	0.972809	+	0.231608i	$0.0743987\pi$
$830$	6.02525	+	1.66072i	0.209139	+	0.0576444i
$831$			14.6951i			0.509766i
$832$	−2.81088	+	21.7539i	−0.0974498	+	0.754182i
$833$	13.2483	+	13.2483i	0.459025	+	0.459025i
$834$	−21.1458	+	5.18330i	−0.732219	+	0.179483i
$835$	7.90241	−	14.1498i	0.273474	−	0.489674i
$836$	74.8617	−	39.0467i	2.58915	−	1.35046i
$837$		−	8.10909i		−	0.280291i
$838$	−2.97824	−	12.1500i	−0.102881	−	0.419715i
$839$			24.3978i			0.842305i	0.906990	+	0.421153i	$0.138374\pi$
$839$			24.3978i			0.842305i	−0.906990	+	0.421153i	$0.861626\pi$
$840$	−4.25745	−	2.75046i	−0.146896	−	0.0948998i
$841$			15.0907i			0.520371i
$842$	31.4831	−	7.71721i	1.08498	−	0.265953i
$843$			0.328587i			0.0113171i
$844$	13.9981	+	4.40128i	0.481835	+	0.151498i
$845$	−11.7945	+	3.34140i	−0.405744	+	0.114947i
$846$	0.859794	+	3.50761i	0.0295603	+	0.120594i
$847$	8.82100	+	8.82100i	0.303093	+	0.303093i
$848$	−14.4718	+	20.7384i	−0.496964	+	0.712159i
$849$		−	22.9890i		−	0.788982i
$850$	14.6295	−	14.8392i	0.501787	−	0.508982i
$851$	9.77735	−	9.77735i	0.335163	−	0.335163i
$852$	−2.60644	−	4.99716i	−0.0892951	−	0.171200i
$853$	−57.1946			−1.95831			−0.979153	−	0.203124i	$-0.934891\pi$
$853$	−57.1946			−1.95831			−0.979153	+	0.203124i	$0.934891\pi$
$854$	6.60735	+	4.00582i	0.226099	+	0.137076i
$855$	15.9902	+	8.93024i	0.546854	+	0.305408i
$856$	−0.705069	+	10.9587i	−0.0240987	+	0.374560i
$857$	13.4584	+	13.4584i	0.459731	+	0.459731i	0.898567	−	0.438836i	$-0.144609\pi$
$857$	13.4584	+	13.4584i	0.459731	+	0.459731i	−0.438836	+	0.898567i	$0.644609\pi$
$858$	19.4111	−	4.75809i	0.662684	−	0.162439i
$859$	2.91627	−	2.91627i	0.0995019	−	0.0995019i	−0.655603	−	0.755105i	$-0.727586\pi$
$859$	2.91627	−	2.91627i	0.0995019	−	0.0995019i	0.755105	+	0.655603i	$0.227586\pi$
$860$	9.96462	−	9.41098i	0.339791	−	0.320912i
$861$	1.28914	+	1.28914i	0.0439337	+	0.0439337i
$862$	−11.8346	+	19.5203i	−0.403086	+	0.664865i
$863$	25.5234	−	25.5234i	0.868825	−	0.868825i	−0.123517	−	0.992342i	$-0.539417\pi$
$863$	25.5234	−	25.5234i	0.868825	−	0.868825i	0.992342	+	0.123517i	$0.0394174\pi$
$864$	−5.17322	+	2.28863i	−0.175996	+	0.0778607i
$865$	−2.80376	−	9.89677i	−0.0953307	−	0.336500i
$866$	−11.3981	−	46.4997i	−0.387323	−	1.58012i
$867$			8.31550i			0.282409i
$868$	3.89853	−	12.3991i	0.132325	−	0.420853i
$869$	−44.2736	−	44.2736i	−1.50188	−	1.50188i
$870$	10.2556	−	5.82370i	0.347697	−	0.197442i
$871$	−9.16589			−0.310574
$872$	−6.64510	−	7.55898i	−0.225032	−	0.255979i
$873$	−1.02135	+	1.02135i	−0.0345674	+	0.0345674i
$874$	−36.3507	+	59.9581i	−1.22958	+	2.02811i
$875$	0.383390	+	8.95193i	0.0129609	+	0.302631i
$876$	28.8848	+	9.08195i	0.975926	+	0.306851i
$877$	−52.9978			−1.78961			−0.894804	−	0.446460i	$-0.852685\pi$
$877$	−52.9978			−1.78961			−0.894804	+	0.446460i	$0.852685\pi$
$878$	−9.69210	+	15.9865i	−0.327093	+	0.539518i
$879$	22.0162			0.742589
$880$	41.4670	−	20.1434i	1.39785	−	0.679035i
$881$	42.2460			1.42331			0.711653	−	0.702531i	$-0.247947\pi$
$881$	42.2460			1.42331			0.711653	+	0.702531i	$0.247947\pi$
$882$	−4.66131	+	7.68853i	−0.156955	+	0.258886i
$883$	23.6484			0.795830			0.397915	−	0.917422i	$-0.369734\pi$
$883$	23.6484			0.795830			0.397915	+	0.917422i	$0.369734\pi$
$884$	4.84713	−	15.4161i	0.163027	−	0.518500i
$885$	8.58594	−	15.3737i	0.288613	−	0.516782i
$886$	5.16057	−	8.51203i	0.173373	−	0.285967i
$887$	−30.6018	+	30.6018i	−1.02751	+	1.02751i	−0.0278982	+	0.999611i	$0.508881\pi$
$887$	−30.6018	+	30.6018i	−1.02751	+	1.02751i	−0.999611	+	0.0278982i	$0.991119\pi$
$888$	−6.44760	−	0.414831i	−0.216367	−	0.0139208i
$889$	−3.53606			−0.118596
$890$	−30.5841	−	8.42981i	−1.02518	−	0.282568i
$891$	3.64458	+	3.64458i	0.122098	+	0.122098i
$892$	−30.5918	−	9.61868i	−1.02429	−	0.322057i
$893$		−	20.9164i		−	0.699940i
$894$	3.84233	+	15.6752i	0.128507	+	0.524256i
$895$	8.45927	+	4.72435i	0.282762	+	0.157918i
$896$	−9.01033	+	1.01232i	−0.301014	+	0.0338193i
$897$	−11.7359	+	11.7359i	−0.391849	+	0.391849i
$898$	−20.6909	+	34.1284i	−0.690465	+	1.13888i
$899$	21.3850	+	21.3850i	0.713229	+	0.713229i
$900$	8.58788	+	5.12332i	0.286263	+	0.170777i
$901$	13.1741	−	13.1741i	0.438894	−	0.438894i
$902$	−16.1050	+	3.94770i	−0.536238	+	0.131444i
$903$	1.73679	+	1.73679i	0.0577967	+	0.0577967i
$904$	11.7019	−	10.2872i	0.389200	−	0.342146i
$905$	4.75770	−	8.51898i	0.158151	−	0.283181i
$906$	13.1902	+	7.99680i	0.438215	+	0.265676i
$907$	−34.6654			−1.15105			−0.575523	−	0.817785i	$-0.695202\pi$
$907$	−34.6654			−1.15105			−0.575523	+	0.817785i	$0.695202\pi$
$908$	35.2797	−	18.4013i	1.17080	−	0.610669i
$909$	−13.1932	+	13.1932i	−0.437591	+	0.437591i
$910$	3.43124	+	6.04243i	0.113744	+	0.200305i
$911$			19.8125i			0.656418i	0.944605	+	0.328209i	$0.106445\pi$
$911$			19.8125i			0.656418i	−0.944605	+	0.328209i	$0.893555\pi$
$912$	32.2558	−	5.74078i	1.06810	−	0.190096i
$913$	−7.20314	−	7.20314i	−0.238389	−	0.238389i
$914$	−13.1458	−	53.6296i	−0.434825	−	1.77391i
$915$	−13.3095	−	7.43308i	−0.439997	−	0.245730i
$916$	12.0411	−	38.2963i	0.397849	−	1.26534i
$917$			9.85620i			0.325480i
$918$	4.04778	−	0.992201i	0.133597	−	0.0327475i
$919$			16.7104i			0.551226i	0.961269	+	0.275613i	$0.0888808\pi$
$919$			16.7104i			0.551226i	−0.961269	+	0.275613i	$0.911119\pi$
$920$	−20.7746	+	32.1571i	−0.684917	+	1.06019i
$921$			3.08698i			0.101719i
$922$	−7.84802	−	32.0168i	−0.258461	−	1.05442i
$923$			7.72661i			0.254325i
$924$	3.82053	+	7.32486i	0.125686	+	0.240970i
$925$	5.99058	+	9.72428i	0.196969	+	0.319732i
$926$	−36.0967	+	8.84811i	−1.18621	+	0.290767i
$927$	4.51726	+	4.51726i	0.148366	+	0.148366i
$928$	7.60714	−	19.6781i	0.249717	−	0.645965i
$929$			9.62355i			0.315739i	0.987460	+	0.157869i	$0.0504625\pi$
$929$			9.62355i			0.315739i	−0.987460	+	0.157869i	$0.949538\pi$
$930$	−6.81387	+	24.7213i	−0.223436	+	0.810645i
$931$	36.8219	−	36.8219i	1.20679	−	1.20679i
$932$	−37.6332	−	11.8326i	−1.23272	−	0.387591i
$933$	24.3682			0.797780
$934$	8.43971	−	13.9208i	0.276156	−	0.455501i
$935$	−32.6780	+	9.25769i	−1.06868	+	0.302759i
$936$	7.73912	+	0.497926i	0.252961	+	0.0162752i
$937$	−19.6920	−	19.6920i	−0.643310	−	0.643310i	0.308057	−	0.951368i	$-0.400321\pi$
$937$	−19.6920	−	19.6920i	−0.643310	−	0.643310i	−0.951368	+	0.308057i	$0.900321\pi$
$938$	−0.902024	−	3.67990i	−0.0294521	−	0.120153i
$939$	−3.31911	+	3.31911i	−0.108315	+	0.108315i
$940$	0.326195	−	11.4158i	0.0106393	−	0.372341i
$941$	−19.3709	−	19.3709i	−0.631473	−	0.631473i	0.316965	−	0.948437i	$-0.397336\pi$
$941$	−19.3709	−	19.3709i	−0.631473	−	0.631473i	−0.948437	+	0.316965i	$0.897336\pi$
$942$	17.0168	+	10.3167i	0.554436	+	0.336137i
$943$	9.73702	−	9.73702i	0.317081	−	0.317081i
$944$	−5.51945	−	31.0122i	−0.179643	−	1.00936i
$945$	−0.873782	+	1.56457i	−0.0284241	+	0.0508954i
$946$	−21.6975	+	5.31853i	−0.705445	+	0.172920i
$947$			3.74620i			0.121735i	0.998146	+	0.0608676i	$0.0193867\pi$
$947$			3.74620i			0.121735i	−0.998146	+	0.0608676i	$0.980613\pi$
$948$	−11.2357	−	21.5415i	−0.364918	−	0.699635i
$949$	−29.3521	−	29.3521i	−0.952809	−	0.952809i
$950$	−41.2438	−	40.6609i	−1.33813	−	1.31921i
$951$	5.35749			0.173728
$952$	6.66623	+	0.428897i	0.216054	+	0.0139006i
$953$	11.3723	−	11.3723i	0.368385	−	0.368385i	−0.498503	−	0.866888i	$-0.666117\pi$
$953$	11.3723	−	11.3723i	0.368385	−	0.368385i	0.866888	+	0.498503i	$0.166117\pi$
$954$	7.64551	+	4.63523i	0.247533	+	0.150071i
$955$	12.8547	+	45.3747i	0.415968	+	1.46829i
$956$	15.2104	+	29.1620i	0.491940	+	0.943166i
$957$	−19.2227			−0.621381
$958$	−12.8177	−	7.77098i	−0.414122	−	0.251069i
$959$	−18.3566			−0.592765
$960$	17.6941	−	2.63017i	0.571076	−	0.0848884i
$961$	−34.7574			−1.12121
$962$	7.57417	+	4.59198i	0.244201	+	0.148051i
$963$	3.88249			0.125111
$964$	−4.35631	−	8.35207i	−0.140307	−	0.269002i
$965$	−42.0571	−	23.4881i	−1.35387	−	0.756110i
$966$	−5.86662	−	3.55674i	−0.188755	−	0.114436i
$967$	−7.94580	+	7.94580i	−0.255520	+	0.255520i	−0.823229	−	0.567709i	$-0.807830\pi$
$967$	−7.94580	+	7.94580i	−0.255520	+	0.255520i	0.567709	+	0.823229i	$0.307830\pi$
$968$	−43.9361	−	2.82680i	−1.41216	−	0.0908566i
$969$	−24.1375			−0.775408
$970$	3.97189	−	2.25547i	0.127530	−	0.0724186i
$971$	27.9413	+	27.9413i	0.896679	+	0.896679i	0.995141	−	0.0984615i	$-0.0313921\pi$
$971$	27.9413	+	27.9413i	0.896679	+	0.896679i	−0.0984615	+	0.995141i	$0.531392\pi$
$972$	0.924916	+	1.77328i	0.0296667	+	0.0568781i
$973$			12.3378i			0.395533i
$974$	45.0408	−	11.0405i	1.44320	−	0.353761i
$975$	−7.19056	−	11.6722i	−0.230282	−	0.373808i
$976$	−26.8481	+	4.77834i	−0.859388	+	0.152951i
$977$	−26.4111	+	26.4111i	−0.844968	+	0.844968i	−0.989500	−	0.144533i	$-0.953832\pi$
$977$	−26.4111	+	26.4111i	−0.844968	+	0.844968i	0.144533	+	0.989500i	$0.453832\pi$
$978$	3.41936	+	2.07305i	0.109339	+	0.0662888i
$979$	36.5631	+	36.5631i	1.16856	+	1.16856i
$980$	20.6709	−	19.5225i	0.660309	−	0.623622i
$981$	−2.51614	+	2.51614i	−0.0803342	+	0.0803342i
$982$	−8.11645	−	33.1118i	−0.259006	−	1.05664i
$983$	25.4583	+	25.4583i	0.811993	+	0.811993i	0.984932	−	0.172940i	$-0.0553265\pi$
$983$	25.4583	+	25.4583i	0.811993	+	0.811993i	−0.172940	+	0.984932i	$0.555327\pi$
$984$	−6.42099	−	0.413119i	−0.204694	−	0.0131698i
$985$	8.56090	+	30.2185i	0.272773	+	0.962840i
$986$	−8.05806	+	13.2913i	−0.256621	+	0.423280i
$987$	2.04657			0.0651430
$988$	−42.8472	−	13.4720i	−1.36315	−	0.428601i
$989$	13.1182	−	13.1182i	0.417134	−	0.417134i
$990$	−8.04839	−	14.1733i	−0.255795	−	0.450457i
$991$		−	29.0499i		−	0.922801i	−0.887192	−	0.461400i	$-0.847347\pi$
$991$		−	29.0499i		−	0.922801i	0.887192	−	0.461400i	$-0.152653\pi$
$992$	18.5587	+	41.9501i	0.589239	+	1.33192i
$993$	−2.76903	−	2.76903i	−0.0878726	−	0.0878726i
$994$	−3.10206	+	0.760383i	−0.0983913	+	0.0241179i
$995$	1.47537	+	5.20780i	0.0467724	+	0.165098i
$996$	−1.82800	−	3.50472i	−0.0579225	−	0.111051i
$997$			40.4803i			1.28202i	0.767531	+	0.641011i	$0.221485\pi$
$997$			40.4803i			1.28202i	−0.767531	+	0.641011i	$0.778515\pi$
$998$	11.2015	+	45.6977i	0.354578	+	1.44654i
$999$			2.28428i			0.0722715i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.y.e.163.8	✓	16
3.2	odd	2		720.2.z.f.163.1		16
4.3	odd	2		960.2.y.e.943.2		16
5.2	odd	4		240.2.bc.e.67.3	yes	16
8.3	odd	2		1920.2.y.j.223.7		16
8.5	even	2		1920.2.y.i.223.7		16
15.2	even	4		720.2.bd.f.307.6		16
16.3	odd	4		1920.2.bc.i.1183.4		16
16.5	even	4		960.2.bc.e.463.5		16
16.11	odd	4		240.2.bc.e.43.3	yes	16
16.13	even	4		1920.2.bc.j.1183.4		16
20.7	even	4		960.2.bc.e.367.5		16
40.27	even	4		1920.2.bc.j.607.4		16
40.37	odd	4		1920.2.bc.i.607.4		16
48.11	even	4		720.2.bd.f.523.6		16
80.27	even	4	inner	240.2.y.e.187.8	yes	16
80.37	odd	4		960.2.y.e.847.2		16
80.67	even	4		1920.2.y.i.1567.7		16
80.77	odd	4		1920.2.y.j.1567.7		16
240.107	odd	4		720.2.z.f.667.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.8	✓	16	1.1	even	1	trivial
240.2.y.e.187.8	yes	16	80.27	even	4	inner
240.2.bc.e.43.3	yes	16	16.11	odd	4
240.2.bc.e.67.3	yes	16	5.2	odd	4
720.2.z.f.163.1		16	3.2	odd	2
720.2.z.f.667.1		16	240.107	odd	4
720.2.bd.f.307.6		16	15.2	even	4
720.2.bd.f.523.6		16	48.11	even	4
960.2.y.e.847.2		16	80.37	odd	4
960.2.y.e.943.2		16	4.3	odd	2
960.2.bc.e.367.5		16	20.7	even	4
960.2.bc.e.463.5		16	16.5	even	4
1920.2.y.i.223.7		16	8.5	even	2
1920.2.y.i.1567.7		16	80.67	even	4
1920.2.y.j.223.7		16	8.3	odd	2
1920.2.y.j.1567.7		16	80.77	odd	4
1920.2.bc.i.607.4		16	40.37	odd	4
1920.2.bc.i.1183.4		16	16.3	odd	4
1920.2.bc.j.607.4		16	40.27	even	4
1920.2.bc.j.1183.4		16	16.13	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)

\(f(q)\)	\(=\)	\(q+(1.20932 + 0.733173i) q^{2} +1.00000 q^{3} +(0.924916 + 1.77328i) q^{4} +(-2.15140 + 0.609492i) q^{5} +(1.20932 + 0.733173i) q^{6} +(0.566689 - 0.566689i) q^{7} +(-0.181602 + 2.82259i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.20932 + 0.733173i) q^{2} +1.00000 q^{3} +(0.924916 + 1.77328i) q^{4} +(-2.15140 + 0.609492i) q^{5} +(1.20932 + 0.733173i) q^{6} +(0.566689 - 0.566689i) q^{7} +(-0.181602 + 2.82259i) q^{8} +1.00000 q^{9} +(-3.04860 - 0.840275i) q^{10} +(3.64458 + 3.64458i) q^{11} +(0.924916 + 1.77328i) q^{12} -2.74185i q^{13} +(1.10079 - 0.269828i) q^{14} +(-2.15140 + 0.609492i) q^{15} +(-2.28906 + 3.28027i) q^{16} +(2.08381 - 2.08381i) q^{17} +(1.20932 + 0.733173i) q^{18} +(-5.79168 - 5.79168i) q^{19} +(-3.07066 - 3.25131i) q^{20} +(0.566689 - 0.566689i) q^{21} +(1.73536 + 7.07957i) q^{22} +(-4.28027 - 4.28027i) q^{23} +(-0.181602 + 2.82259i) q^{24} +(4.25704 - 2.62252i) q^{25} +(2.01025 - 3.31578i) q^{26} +1.00000 q^{27} +(1.52904 + 0.480760i) q^{28} +(-2.63716 + 2.63716i) q^{29} +(-3.04860 - 0.840275i) q^{30} -8.10909i q^{31} +(-5.17322 + 2.28863i) q^{32} +(3.64458 + 3.64458i) q^{33} +(4.04778 - 0.992201i) q^{34} +(-0.873782 + 1.56457i) q^{35} +(0.924916 + 1.77328i) q^{36} +2.28428i q^{37} +(-2.75770 - 11.2503i) q^{38} -2.74185i q^{39} +(-1.32965 - 6.18321i) q^{40} +2.27486i q^{41} +(1.10079 - 0.269828i) q^{42} +3.06480i q^{43} +(-3.09194 + 9.83379i) q^{44} +(-2.15140 + 0.609492i) q^{45} +(-2.03805 - 8.31441i) q^{46} +(1.80573 + 1.80573i) q^{47} +(-2.28906 + 3.28027i) q^{48} +6.35773i q^{49} +(7.07089 - 0.0503283i) q^{50} +(2.08381 - 2.08381i) q^{51} +(4.86207 - 2.53598i) q^{52} +6.32215 q^{53} +(1.20932 + 0.733173i) q^{54} +(-10.0623 - 5.61960i) q^{55} +(1.49662 + 1.70244i) q^{56} +(-5.79168 - 5.79168i) q^{57} +(-5.12267 + 1.25568i) q^{58} +(-5.56839 + 5.56839i) q^{59} +(-3.07066 - 3.25131i) q^{60} +(4.82071 + 4.82071i) q^{61} +(5.94536 - 9.80650i) q^{62} +(0.566689 - 0.566689i) q^{63} +(-7.93404 - 1.02518i) q^{64} +(1.67114 + 5.89881i) q^{65} +(1.73536 + 7.07957i) q^{66} -3.34296i q^{67} +(5.62252 + 1.76783i) q^{68} +(-4.28027 - 4.28027i) q^{69} +(-2.20378 + 1.25143i) q^{70} -2.81803 q^{71} +(-0.181602 + 2.82259i) q^{72} +(10.7052 - 10.7052i) q^{73} +(-1.67477 + 2.76243i) q^{74} +(4.25704 - 2.62252i) q^{75} +(4.91347 - 15.6271i) q^{76} +4.13068 q^{77} +(2.01025 - 3.31578i) q^{78} -12.1478 q^{79} +(2.92539 - 8.45234i) q^{80} +1.00000 q^{81} +(-1.66786 + 2.75103i) q^{82} -1.97640 q^{83} +(1.52904 + 0.480760i) q^{84} +(-3.21304 + 5.75316i) q^{85} +(-2.24703 + 3.70633i) q^{86} +(-2.63716 + 2.63716i) q^{87} +(-10.9490 + 9.62528i) q^{88} +10.0322 q^{89} +(-3.04860 - 0.840275i) q^{90} +(-1.55378 - 1.55378i) q^{91} +(3.63124 - 11.5490i) q^{92} -8.10909i q^{93} +(0.859794 + 3.50761i) q^{94} +(15.9902 + 8.93024i) q^{95} +(-5.17322 + 2.28863i) q^{96} +(-1.02135 + 1.02135i) q^{97} +(-4.66131 + 7.68853i) q^{98} +(3.64458 + 3.64458i) 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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