LMFDB - Embedded newform 240.2.s.c.61.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(61,240)]

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([0, 3, 0, 0]))

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

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

chi := DirichletCharacter("240.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.s (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:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^18 - 4x^17 + 7x^16 + 16x^15 + 6x^14 - 36x^13 - 42x^12 + 40x^11 + 136x^10 + 80x^9 - 168x^8 - 288x^7 + 96x^6 + 512x^5 + 448x^4 - 512x^3 - 512*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			61.4
Root			$-0.720859 - 1.21670i$ of defining polynomial
Character	$\chi$	$=$	240.61
Dual form			240.2.s.c.181.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.720859 - 1.21670i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.960724 + 1.75414i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.350613 - 1.37006i) q^{6} +0.0588949i q^{7} +(2.82681 - 0.0955746i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.720859 - 1.21670i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.960724 + 1.75414i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.350613 - 1.37006i) q^{6} +0.0588949i q^{7} +(2.82681 - 0.0955746i) q^{8} +1.00000i q^{9} +(-1.37006 - 0.350613i) q^{10} +(2.23289 - 2.23289i) q^{11} +(-1.91970 + 0.561030i) q^{12} +(2.84870 + 2.84870i) q^{13} +(0.0716575 - 0.0424550i) q^{14} +1.00000 q^{15} +(-2.15402 - 3.37049i) q^{16} +5.98228 q^{17} +(1.21670 - 0.720859i) q^{18} +(-0.617238 - 0.617238i) q^{19} +(0.561030 + 1.91970i) q^{20} +(-0.0416450 + 0.0416450i) q^{21} +(-4.32636 - 1.10716i) q^{22} -0.746698i q^{23} +(2.06644 + 1.93128i) q^{24} -1.00000i q^{25} +(1.41251 - 5.51953i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.103310 - 0.0565818i) q^{28} +(-1.13987 - 1.13987i) q^{29} +(-0.720859 - 1.21670i) q^{30} -8.55143 q^{31} +(-2.54813 + 5.05045i) q^{32} +3.15778 q^{33} +(-4.31238 - 7.27864i) q^{34} +(0.0416450 + 0.0416450i) q^{35} +(-1.75414 - 0.960724i) q^{36} +(-2.01811 + 2.01811i) q^{37} +(-0.306053 + 1.19594i) q^{38} +4.02867i q^{39} +(1.93128 - 2.06644i) q^{40} -7.71113i q^{41} +(0.0806897 + 0.0206493i) q^{42} +(-2.94233 + 2.94233i) q^{43} +(1.77161 + 6.06199i) q^{44} +(0.707107 + 0.707107i) q^{45} +(-0.908508 + 0.538264i) q^{46} -0.789616 q^{47} +(0.860175 - 3.90642i) q^{48} +6.99653 q^{49} +(-1.21670 + 0.720859i) q^{50} +(4.23011 + 4.23011i) q^{51} +(-7.73383 + 2.26021i) q^{52} +(-6.80791 + 6.80791i) q^{53} +(1.37006 + 0.350613i) q^{54} -3.15778i q^{55} +(0.00562886 + 0.166485i) q^{56} -0.872906i q^{57} +(-0.565194 + 2.20856i) q^{58} +(-9.36045 + 9.36045i) q^{59} +(-0.960724 + 1.75414i) q^{60} +(-0.814225 - 0.814225i) q^{61} +(6.16438 + 10.4045i) q^{62} -0.0588949 q^{63} +(7.98173 - 0.540343i) q^{64} +4.02867 q^{65} +(-2.27632 - 3.84208i) q^{66} +(5.46701 + 5.46701i) q^{67} +(-5.74732 + 10.4938i) q^{68} +(0.527995 - 0.527995i) q^{69} +(0.0206493 - 0.0806897i) q^{70} -7.40423i q^{71} +(0.0955746 + 2.82681i) q^{72} +11.6114i q^{73} +(3.91020 + 1.00066i) q^{74} +(0.707107 - 0.707107i) q^{75} +(1.67572 - 0.489727i) q^{76} +(0.131506 + 0.131506i) q^{77} +(4.90169 - 2.90410i) q^{78} -17.4027 q^{79} +(-3.90642 - 0.860175i) q^{80} -1.00000 q^{81} +(-9.38214 + 5.55864i) q^{82} +(-7.55090 - 7.55090i) q^{83} +(-0.0330419 - 0.113061i) q^{84} +(4.23011 - 4.23011i) q^{85} +(5.70095 + 1.45893i) q^{86} -1.61202i q^{87} +(6.09855 - 6.52537i) q^{88} -16.3007i q^{89} +(0.350613 - 1.37006i) q^{90} +(-0.167774 + 0.167774i) q^{91} +(1.30981 + 0.717370i) q^{92} +(-6.04678 - 6.04678i) q^{93} +(0.569202 + 0.960727i) q^{94} -0.872906 q^{95} +(-5.37301 + 1.76940i) q^{96} +12.3159 q^{97} +(-5.04351 - 8.51269i) q^{98} +(2.23289 + 2.23289i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4} + 12 q^{8}+O(q^{10}) $ 20 * q + 4 * q^4 + 12 * q^8	$ 20 q + 4 q^{4} + 12 q^{8} + 8 q^{11} - 4 q^{14} + 20 q^{15} - 20 q^{16} - 24 q^{17} - 4 q^{18} - 4 q^{19} - 8 q^{20} + 8 q^{22} + 28 q^{26} - 8 q^{28} + 16 q^{29} - 40 q^{32} + 16 q^{33} - 44 q^{34} + 16 q^{37} - 8 q^{38} + 12 q^{40} + 12 q^{42} - 8 q^{43} + 24 q^{44} - 12 q^{46} - 16 q^{48} - 52 q^{49} + 4 q^{50} + 4 q^{51} - 56 q^{52} - 16 q^{53} + 64 q^{56} + 72 q^{58} - 16 q^{59} + 4 q^{60} - 4 q^{61} - 44 q^{62} - 8 q^{63} - 56 q^{64} - 32 q^{66} - 8 q^{67} - 32 q^{68} - 4 q^{69} + 20 q^{70} + 4 q^{72} + 60 q^{74} + 28 q^{76} - 40 q^{77} - 28 q^{78} + 56 q^{79} - 16 q^{80} - 20 q^{81} - 24 q^{82} - 48 q^{83} + 24 q^{84} + 4 q^{85} + 64 q^{86} + 40 q^{88} - 8 q^{91} + 88 q^{92} + 16 q^{93} - 20 q^{94} + 56 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) $ 20 * q + 4 * q^4 + 12 * q^8 + 8 * q^11 - 4 * q^14 + 20 * q^15 - 20 * q^16 - 24 * q^17 - 4 * q^18 - 4 * q^19 - 8 * q^20 + 8 * q^22 + 28 * q^26 - 8 * q^28 + 16 * q^29 - 40 * q^32 + 16 * q^33 - 44 * q^34 + 16 * q^37 - 8 * q^38 + 12 * q^40 + 12 * q^42 - 8 * q^43 + 24 * q^44 - 12 * q^46 - 16 * q^48 - 52 * q^49 + 4 * q^50 + 4 * q^51 - 56 * q^52 - 16 * q^53 + 64 * q^56 + 72 * q^58 - 16 * q^59 + 4 * q^60 - 4 * q^61 - 44 * q^62 - 8 * q^63 - 56 * q^64 - 32 * q^66 - 8 * q^67 - 32 * q^68 - 4 * q^69 + 20 * q^70 + 4 * q^72 + 60 * q^74 + 28 * q^76 - 40 * q^77 - 28 * q^78 + 56 * q^79 - 16 * q^80 - 20 * q^81 - 24 * q^82 - 48 * q^83 + 24 * q^84 + 4 * q^85 + 64 * q^86 + 40 * q^88 - 8 * q^91 + 88 * q^92 + 16 * q^93 - 20 * q^94 + 56 * q^97 - 48 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.720859	−	1.21670i	−0.509724	−	0.860338i
$2$	−0.720859	−	1.21670i	−0.509724	−	0.860338i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−0.960724	+	1.75414i	−0.480362	+	0.877070i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	0.350613	−	1.37006i	0.143137	−	0.559326i
$7$			0.0588949i			0.0222602i	0.999938	+	0.0111301i	$0.00354289\pi$
$7$			0.0588949i			0.0222602i	−0.999938	+	0.0111301i	$0.996457\pi$
$8$	2.82681	−	0.0955746i	0.999429	−	0.0337907i
$9$			1.00000i			0.333333i
$10$	−1.37006	−	0.350613i	−0.433252	−	0.110874i
$11$	2.23289	−	2.23289i	0.673242	−	0.673242i	−0.285220	−	0.958462i	$-0.592067\pi$
$11$	2.23289	−	2.23289i	0.673242	−	0.673242i	0.958462	+	0.285220i	$0.0920668\pi$
$12$	−1.91970	+	0.561030i	−0.554169	+	0.161956i
$13$	2.84870	+	2.84870i	0.790087	+	0.790087i	0.981508	−	0.191421i	$-0.0613095\pi$
$13$	2.84870	+	2.84870i	0.790087	+	0.790087i	−0.191421	+	0.981508i	$0.561310\pi$
$14$	0.0716575	−	0.0424550i	0.0191513	−	0.0113466i
$15$	1.00000			0.258199
$16$	−2.15402	−	3.37049i	−0.538505	−	0.842622i
$17$	5.98228			1.45092			0.725458	−	0.688267i	$-0.241628\pi$
$17$	5.98228			1.45092			0.725458	+	0.688267i	$0.241628\pi$
$18$	1.21670	−	0.720859i	0.286779	−	0.169908i
$19$	−0.617238	−	0.617238i	−0.141604	−	0.141604i	0.632751	−	0.774355i	$-0.281926\pi$
$19$	−0.617238	−	0.617238i	−0.141604	−	0.141604i	−0.774355	+	0.632751i	$0.781926\pi$
$20$	0.561030	+	1.91970i	0.125450	+	0.429258i
$21$	−0.0416450	+	0.0416450i	−0.00908769	+	0.00908769i
$22$	−4.32636	−	1.10716i	−0.922383	−	0.236047i
$23$		−	0.746698i		−	0.155697i	−0.996965	−	0.0778486i	$-0.975195\pi$
$23$		−	0.746698i		−	0.155697i	0.996965	−	0.0778486i	$-0.0248051\pi$
$24$	2.06644	+	1.93128i	0.421810	+	0.394220i
$25$		−	1.00000i		−	0.200000i
$26$	1.41251	−	5.51953i	0.277015	−	1.08247i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−0.103310	−	0.0565818i	−0.0195238	−	0.0106930i
$29$	−1.13987	−	1.13987i	−0.211668	−	0.211668i	0.593308	−	0.804976i	$-0.297822\pi$
$29$	−1.13987	−	1.13987i	−0.211668	−	0.211668i	−0.804976	+	0.593308i	$0.797822\pi$
$30$	−0.720859	−	1.21670i	−0.131610	−	0.222138i
$31$	−8.55143			−1.53588			−0.767941	−	0.640520i	$-0.778719\pi$
$31$	−8.55143			−1.53588			−0.767941	+	0.640520i	$0.778719\pi$
$32$	−2.54813	+	5.05045i	−0.450451	+	0.892801i
$33$	3.15778			0.549700
$34$	−4.31238	−	7.27864i	−0.739567	−	1.24828i
$35$	0.0416450	+	0.0416450i	0.00703929	+	0.00703929i
$36$	−1.75414	−	0.960724i	−0.292357	−	0.160121i
$37$	−2.01811	+	2.01811i	−0.331774	+	0.331774i	−0.853260	−	0.521486i	$-0.825378\pi$
$37$	−2.01811	+	2.01811i	−0.331774	+	0.331774i	0.521486	+	0.853260i	$0.325378\pi$
$38$	−0.306053	+	1.19594i	−0.0496483	+	0.194006i
$39$			4.02867i			0.645104i
$40$	1.93128	−	2.06644i	0.305362	−	0.326733i
$41$		−	7.71113i		−	1.20428i	−0.798392	−	0.602138i	$-0.794316\pi$
$41$		−	7.71113i		−	1.20428i	0.798392	−	0.602138i	$-0.205684\pi$
$42$	0.0806897	+	0.0206493i	0.0124507	+	0.00318626i
$43$	−2.94233	+	2.94233i	−0.448701	+	0.448701i	−0.894923	−	0.446221i	$-0.852769\pi$
$43$	−2.94233	+	2.94233i	−0.448701	+	0.448701i	0.446221	+	0.894923i	$0.352769\pi$
$44$	1.77161	+	6.06199i	0.267081	+	0.913880i
$45$	0.707107	+	0.707107i	0.105409	+	0.105409i
$46$	−0.908508	+	0.538264i	−0.133952	+	0.0793627i
$47$	−0.789616			−0.115177			−0.0575887	−	0.998340i	$-0.518341\pi$
$47$	−0.789616			−0.115177			−0.0575887	+	0.998340i	$0.518341\pi$
$48$	0.860175	−	3.90642i	0.124156	−	0.563843i
$49$	6.99653			0.999504
$50$	−1.21670	+	0.720859i	−0.172068	+	0.101945i
$51$	4.23011	+	4.23011i	0.592334	+	0.592334i
$52$	−7.73383	+	2.26021i	−1.07249	+	0.313434i
$53$	−6.80791	+	6.80791i	−0.935138	+	0.935138i	−0.998021	−	0.0628826i	$-0.979971\pi$
$53$	−6.80791	+	6.80791i	−0.935138	+	0.935138i	0.0628826	+	0.998021i	$0.479971\pi$
$54$	1.37006	+	0.350613i	0.186442	+	0.0477124i
$55$		−	3.15778i		−	0.425795i
$56$	0.00562886	+	0.166485i	0.000752188	+	0.0222475i
$57$		−	0.872906i		−	0.115619i
$58$	−0.565194	+	2.20856i	−0.0742136	+	0.289998i
$59$	−9.36045	+	9.36045i	−1.21863	+	1.21863i	−0.250514	+	0.968113i	$0.580599\pi$
$59$	−9.36045	+	9.36045i	−1.21863	+	1.21863i	−0.968113	+	0.250514i	$0.919401\pi$
$60$	−0.960724	+	1.75414i	−0.124029	+	0.226459i
$61$	−0.814225	−	0.814225i	−0.104251	−	0.104251i	0.653057	−	0.757308i	$-0.273486\pi$
$61$	−0.814225	−	0.814225i	−0.104251	−	0.104251i	−0.757308	+	0.653057i	$0.773486\pi$
$62$	6.16438	+	10.4045i	0.782877	+	1.32138i
$63$	−0.0588949			−0.00742006
$64$	7.98173	−	0.540343i	0.997716	−	0.0675428i
$65$	4.02867			0.499695
$66$	−2.27632	−	3.84208i	−0.280195	−	0.472927i
$67$	5.46701	+	5.46701i	0.667901	+	0.667901i	0.957230	−	0.289329i	$-0.0934320\pi$
$67$	5.46701	+	5.46701i	0.667901	+	0.667901i	−0.289329	+	0.957230i	$0.593432\pi$
$68$	−5.74732	+	10.4938i	−0.696964	+	1.27255i
$69$	0.527995	−	0.527995i	0.0635631	−	0.0635631i
$70$	0.0206493	−	0.0806897i	0.00246807	−	0.00964427i
$71$		−	7.40423i		−	0.878720i	−0.898311	−	0.439360i	$-0.855205\pi$
$71$		−	7.40423i		−	0.878720i	0.898311	−	0.439360i	$-0.144795\pi$
$72$	0.0955746	+	2.82681i	0.0112636	+	0.333143i
$73$			11.6114i			1.35901i	0.733670	+	0.679506i	$0.237806\pi$
$73$			11.6114i			1.35901i	−0.733670	+	0.679506i	$0.762194\pi$
$74$	3.91020	+	1.00066i	0.454552	+	0.116325i
$75$	0.707107	−	0.707107i	0.0816497	−	0.0816497i
$76$	1.67572	−	0.489727i	0.192218	−	0.0561755i
$77$	0.131506	+	0.131506i	0.0149865	+	0.0149865i
$78$	4.90169	−	2.90410i	0.555007	−	0.328825i
$79$	−17.4027			−1.95796			−0.978978	−	0.203964i	$-0.934617\pi$
$79$	−17.4027			−1.95796			−0.978978	+	0.203964i	$0.934617\pi$
$80$	−3.90642	−	0.860175i	−0.436751	−	0.0961704i
$81$	−1.00000			−0.111111
$82$	−9.38214	+	5.55864i	−1.03608	+	0.613849i
$83$	−7.55090	−	7.55090i	−0.828819	−	0.828819i	0.158534	−	0.987354i	$-0.449323\pi$
$83$	−7.55090	−	7.55090i	−0.828819	−	0.828819i	−0.987354	+	0.158534i	$0.949323\pi$
$84$	−0.0330419	−	0.113061i	−0.00360516	−	0.0123359i
$85$	4.23011	−	4.23011i	0.458820	−	0.458820i
$86$	5.70095	+	1.45893i	0.614749	+	0.157321i
$87$		−	1.61202i		−	0.172826i
$88$	6.09855	−	6.52537i	0.650108	−	0.695607i
$89$		−	16.3007i		−	1.72788i	−0.503599	−	0.863938i	$-0.667991\pi$
$89$		−	16.3007i		−	1.72788i	0.503599	−	0.863938i	$-0.332009\pi$
$90$	0.350613	−	1.37006i	0.0369579	−	0.144417i
$91$	−0.167774	+	0.167774i	−0.0175875	+	0.0175875i
$92$	1.30981	+	0.717370i	0.136557	+	0.0747910i
$93$	−6.04678	−	6.04678i	−0.627021	−	0.627021i
$94$	0.569202	+	0.960727i	0.0587087	+	0.0990914i
$95$	−0.872906			−0.0895583
$96$	−5.37301	+	1.76940i	−0.548380	+	0.180589i
$97$	12.3159			1.25049			0.625247	−	0.780427i	$-0.284998\pi$
$97$	12.3159			1.25049			0.625247	+	0.780427i	$0.284998\pi$
$98$	−5.04351	−	8.51269i	−0.509472	−	0.859911i
$99$	2.23289	+	2.23289i	0.224414	+	0.224414i
$100$	1.75414	+	0.960724i	0.175414	+	0.0960724i
$101$	−0.663582	+	0.663582i	−0.0660289	+	0.0660289i	−0.739350	−	0.673321i	$-0.764867\pi$
$101$	−0.663582	+	0.663582i	−0.0660289	+	0.0660289i	0.673321	+	0.739350i	$0.264867\pi$
$102$	2.09747	−	8.19609i	0.207680	−	0.811534i
$103$		−	14.9036i		−	1.46850i	−0.678880	−	0.734249i	$-0.737534\pi$
$103$		−	14.9036i		−	1.46850i	0.678880	−	0.734249i	$-0.262466\pi$
$104$	8.32500	+	7.78048i	0.816334	+	0.762938i
$105$			0.0588949i			0.00574756i
$106$	13.1907	+	3.37565i	1.28120	+	0.327872i
$107$	3.43861	−	3.43861i	0.332423	−	0.332423i	−0.521083	−	0.853506i	$-0.674472\pi$
$107$	3.43861	−	3.43861i	0.332423	−	0.332423i	0.853506	+	0.521083i	$0.174472\pi$
$108$	−0.561030	−	1.91970i	−0.0539852	−	0.184723i
$109$	0.0571202	+	0.0571202i	0.00547113	+	0.00547113i	0.709837	−	0.704366i	$-0.248769\pi$
$109$	0.0571202	+	0.0571202i	0.00547113	+	0.00547113i	−0.704366	+	0.709837i	$0.748769\pi$
$110$	−3.84208	+	2.27632i	−0.366328	+	0.217038i
$111$	−2.85403			−0.270893
$112$	0.198505	−	0.126861i	0.0187569	−	0.0119872i
$113$	−14.9834			−1.40952			−0.704759	−	0.709447i	$-0.748945\pi$
$113$	−14.9834			−1.40952			−0.704759	+	0.709447i	$0.748945\pi$
$114$	−1.06207	+	0.629243i	−0.0994716	+	0.0589340i
$115$	−0.527995	−	0.527995i	−0.0492358	−	0.0492358i
$116$	3.09458	−	0.904390i	0.287325	−	0.0839705i
$117$	−2.84870	+	2.84870i	−0.263362	+	0.263362i
$118$	18.1364	+	4.64130i	1.66959	+	0.427267i
$119$			0.352326i			0.0322977i
$120$	2.82681	−	0.0955746i	0.258051	−	0.00872473i
$121$			1.02840i			0.0934912i
$122$	−0.403727	+	1.57761i	−0.0365517	+	0.142830i
$123$	5.45259	−	5.45259i	0.491644	−	0.491644i
$124$	8.21556	−	15.0004i	0.737779	−	1.34708i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	0.0424550	+	0.0716575i	0.00378219	+	0.00638376i
$127$	6.74629			0.598636			0.299318	−	0.954153i	$-0.403241\pi$
$127$	6.74629			0.598636			0.299318	+	0.954153i	$0.403241\pi$
$128$	−6.41114	−	9.32187i	−0.566670	−	0.823945i
$129$	−4.16109			−0.366363
$130$	−2.90410	−	4.90169i	−0.254707	−	0.429906i
$131$	10.2459	+	10.2459i	0.895185	+	0.895185i	0.995005	−	0.0998208i	$-0.0318269\pi$
$131$	10.2459	+	10.2459i	0.895185	+	0.895185i	−0.0998208	+	0.995005i	$0.531827\pi$
$132$	−3.03376	+	5.53920i	−0.264055	+	0.482125i
$133$	0.0363522	−	0.0363522i	0.00315214	−	0.00315214i
$134$	2.71077	−	10.5927i	0.234175	−	0.915066i
$135$			1.00000i			0.0860663i
$136$	16.9108	−	0.571754i	1.45009	−	0.0490275i
$137$		−	19.4514i		−	1.66185i	−0.556388	−	0.830923i	$-0.687813\pi$
$137$		−	19.4514i		−	1.66185i	0.556388	−	0.830923i	$-0.312187\pi$
$138$	−1.02302	−	0.261802i	−0.0870854	−	0.0222861i
$139$	−1.09587	+	1.09587i	−0.0929501	+	0.0929501i	−0.752053	−	0.659103i	$-0.770936\pi$
$139$	−1.09587	+	1.09587i	−0.0929501	+	0.0929501i	0.659103	+	0.752053i	$0.270936\pi$
$140$	−0.113061	+	0.0330419i	−0.00955536	+	0.00279255i
$141$	−0.558343	−	0.558343i	−0.0470210	−	0.0470210i
$142$	−9.00873	+	5.33741i	−0.755996	+	0.447905i
$143$	12.7217			1.06384
$144$	3.37049	−	2.15402i	0.280874	−	0.179502i
$145$	−1.61202			−0.133871
$146$	14.1276	−	8.37019i	1.16921	−	0.692722i
$147$	4.94729	+	4.94729i	0.408046	+	0.408046i
$148$	−1.60120	−	5.47888i	−0.131618	−	0.450361i
$149$	−13.6510	+	13.6510i	−1.11834	+	1.11834i	−0.126349	+	0.991986i	$0.540326\pi$
$149$	−13.6510	+	13.6510i	−1.11834	+	1.11834i	−0.991986	+	0.126349i	$0.959674\pi$
$150$	−1.37006	−	0.350613i	−0.111865	−	0.0286275i
$151$		−	13.4811i		−	1.09708i	−0.836125	−	0.548538i	$-0.815184\pi$
$151$		−	13.4811i		−	1.09708i	0.836125	−	0.548538i	$-0.184816\pi$
$152$	−1.80381	−	1.68582i	−0.146308	−	0.136738i
$153$			5.98228i			0.483638i
$154$	0.0652062	−	0.254801i	0.00525446	−	0.0205324i
$155$	−6.04678	+	6.04678i	−0.485689	+	0.485689i
$156$	−7.06685	−	3.87044i	−0.565801	−	0.309883i
$157$	11.1090	+	11.1090i	0.886593	+	0.886593i	0.994194	−	0.107602i	$-0.0343171\pi$
$157$	11.1090	+	11.1090i	0.886593	+	0.886593i	−0.107602	+	0.994194i	$0.534317\pi$
$158$	12.5449	+	21.1739i	0.998018	+	1.68450i
$159$	−9.62784			−0.763537
$160$	1.76940	+	5.37301i	0.139884	+	0.424774i
$161$	0.0439767			0.00346585
$162$	0.720859	+	1.21670i	0.0566361	+	0.0955931i
$163$	−1.97598	−	1.97598i	−0.154771	−	0.154771i	0.625474	−	0.780245i	$-0.284906\pi$
$163$	−1.97598	−	1.97598i	−0.154771	−	0.154771i	−0.780245	+	0.625474i	$0.784906\pi$
$164$	13.5264	+	7.40827i	1.05623	+	0.578488i
$165$	2.23289	−	2.23289i	0.173830	−	0.173830i
$166$	−3.74406	+	14.6303i	−0.290595	+	1.13553i
$167$		−	2.12777i		−	0.164652i	−0.996605	−	0.0823259i	$-0.973765\pi$
$167$		−	2.12777i		−	0.164652i	0.996605	−	0.0823259i	$-0.0262348\pi$
$168$	−0.113742	+	0.121703i	−0.00877542	+	0.00938958i
$169$			3.23018i			0.248476i
$170$	−8.19609	−	2.09747i	−0.628612	−	0.160868i
$171$	0.617238	−	0.617238i	0.0472014	−	0.0472014i
$172$	−2.33450	−	7.98803i	−0.178004	−	0.609082i
$173$	−9.21877	−	9.21877i	−0.700890	−	0.700890i	0.263711	−	0.964602i	$-0.415053\pi$
$173$	−9.21877	−	9.21877i	−0.700890	−	0.700890i	−0.964602	+	0.263711i	$0.915053\pi$
$174$	−1.96134	+	1.16204i	−0.148689	+	0.0880937i
$175$	0.0588949			0.00445204
$176$	−12.3356	−	2.71625i	−0.929832	−	0.204745i
$177$	−13.2377			−0.995004
$178$	−19.8331	+	11.7505i	−1.48656	+	0.880740i
$179$	5.02407	+	5.02407i	0.375516	+	0.375516i	0.869482	−	0.493965i	$-0.164453\pi$
$179$	5.02407	+	5.02407i	0.375516	+	0.375516i	−0.493965	+	0.869482i	$0.664453\pi$
$180$	−1.91970	+	0.561030i	−0.143086	+	0.0418167i
$181$	−15.1363	+	15.1363i	−1.12507	+	1.12507i	−0.134102	+	0.990967i	$0.542815\pi$
$181$	−15.1363	+	15.1363i	−1.12507	+	1.12507i	−0.990967	+	0.134102i	$0.957185\pi$
$182$	0.325072	+	0.0831894i	0.0240960	+	0.00616641i
$183$		−	1.15149i		−	0.0851205i
$184$	−0.0713653	−	2.11077i	−0.00526112	−	0.155608i
$185$			2.85403i			0.209833i
$186$	−2.99825	+	11.7160i	−0.219842	+	0.859058i
$187$	13.3578	−	13.3578i	0.976817	−	0.976817i
$188$	0.758603	−	1.38510i	0.0553268	−	0.101019i
$189$	−0.0416450	−	0.0416450i	−0.00302923	−	0.00302923i
$190$	0.629243	+	1.06207i	0.0456501	+	0.0770504i
$191$	12.4425			0.900310			0.450155	−	0.892950i	$-0.351369\pi$
$191$	12.4425			0.900310			0.450155	+	0.892950i	$0.351369\pi$
$192$	6.02602	+	5.26186i	0.434890	+	0.379742i
$193$	0.241933			0.0174147			0.00870734	−	0.999962i	$-0.497228\pi$
$193$	0.241933			0.0174147			0.00870734	+	0.999962i	$0.497228\pi$
$194$	−8.87806	−	14.9848i	−0.637408	−	1.07585i
$195$	2.84870	+	2.84870i	0.204000	+	0.204000i
$196$	−6.72173	+	12.2729i	−0.480124	+	0.876636i
$197$	−2.37260	+	2.37260i	−0.169041	+	0.169041i	−0.786558	−	0.617517i	$-0.788139\pi$
$197$	−2.37260	+	2.37260i	−0.169041	+	0.169041i	0.617517	+	0.786558i	$0.288139\pi$
$198$	1.10716	−	4.32636i	0.0786825	−	0.307461i
$199$			19.8275i			1.40553i	0.711420	+	0.702767i	$0.248052\pi$
$199$			19.8275i			1.40553i	−0.711420	+	0.702767i	$0.751948\pi$
$200$	−0.0955746	−	2.82681i	−0.00675814	−	0.199886i
$201$			7.73152i			0.545339i
$202$	1.28573	+	0.329032i	0.0904637	+	0.0231506i
$203$	0.0671324	−	0.0671324i	0.00471177	−	0.00471177i
$204$	−11.4842	+	3.35624i	−0.804053	+	0.234984i
$205$	−5.45259	−	5.45259i	−0.380826	−	0.380826i
$206$	−18.1333	+	10.7434i	−1.26340	+	0.748529i
$207$	0.746698			0.0518991
$208$	3.46536	−	15.7377i	0.240279	−	1.09121i
$209$	−2.75645			−0.190668
$210$	0.0716575	−	0.0424550i	0.00494484	−	0.00292967i
$211$	3.54907	+	3.54907i	0.244328	+	0.244328i	0.818638	−	0.574310i	$-0.194730\pi$
$211$	3.54907	+	3.54907i	0.244328	+	0.244328i	−0.574310	+	0.818638i	$0.694730\pi$
$212$	−5.40151	−	18.4826i	−0.370977	−	1.26939i
$213$	5.23558	−	5.23558i	0.358736	−	0.358736i
$214$	−6.66251	−	1.70501i	−0.455440	−	0.116552i
$215$			4.16109i			0.283784i
$216$	−1.93128	+	2.06644i	−0.131407	+	0.140603i
$217$		−	0.503636i		−	0.0341890i
$218$	0.0283226	−	0.110674i	0.00191825	−	0.00749578i
$219$	−8.21050	+	8.21050i	−0.554814	+	0.554814i
$220$	5.53920	+	3.03376i	0.373453	+	0.204536i
$221$	17.0417	+	17.0417i	1.14635	+	1.14635i
$222$	2.05736	+	3.47250i	0.138081	+	0.233059i
$223$	21.6789			1.45173			0.725864	−	0.687838i	$-0.241440\pi$
$223$	21.6789			1.45173			0.725864	+	0.687838i	$0.241440\pi$
$224$	−0.297446	−	0.150072i	−0.0198739	−	0.0100271i
$225$	1.00000			0.0666667
$226$	10.8009	+	18.2303i	0.718466	+	1.21266i
$227$	−10.2117	−	10.2117i	−0.677775	−	0.677775i	0.281721	−	0.959496i	$-0.409095\pi$
$227$	−10.2117	−	10.2117i	−0.677775	−	0.677775i	−0.959496	+	0.281721i	$0.909095\pi$
$228$	1.53120	+	0.838622i	0.101406	+	0.0555391i
$229$	17.0933	−	17.0933i	1.12956	−	1.12956i	0.139312	−	0.990249i	$-0.455511\pi$
$229$	17.0933	−	17.0933i	1.12956	−	1.12956i	0.990249	−	0.139312i	$-0.0444890\pi$
$230$	−0.261802	+	1.02302i	−0.0172627	+	0.0674561i
$231$			0.185977i			0.0122364i
$232$	−3.33113	−	3.11325i	−0.218700	−	0.204395i
$233$			24.2409i			1.58807i	0.607871	+	0.794036i	$0.292024\pi$
$233$			24.2409i			1.58807i	−0.607871	+	0.794036i	$0.707976\pi$
$234$	5.51953	+	1.41251i	0.360823	+	0.0923383i
$235$	−0.558343	+	0.558343i	−0.0364223	+	0.0364223i
$236$	−7.42674	−	25.4124i	−0.483439	−	1.65420i
$237$	−12.3056	−	12.3056i	−0.799332	−	0.799332i
$238$	0.428675	−	0.253977i	0.0277869	−	0.0164629i
$239$	21.0658			1.36263			0.681317	−	0.731989i	$-0.261408\pi$
$239$	21.0658			1.36263			0.681317	+	0.731989i	$0.261408\pi$
$240$	−2.15402	−	3.37049i	−0.139041	−	0.217564i
$241$	−22.0578			−1.42087			−0.710434	−	0.703764i	$-0.751501\pi$
$241$	−22.0578			−1.42087			−0.710434	+	0.703764i	$0.751501\pi$
$242$	1.25126	−	0.741334i	0.0804340	−	0.0476548i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	2.21051	−	0.646020i	0.141514	−	0.0413572i
$245$	4.94729	−	4.94729i	0.316071	−	0.316071i
$246$	−10.5647	−	2.70362i	−0.673582	−	0.172377i
$247$		−	3.51665i		−	0.223759i
$248$	−24.1733	+	0.817300i	−1.53501	+	0.0518986i
$249$		−	10.6786i		−	0.676728i
$250$	−0.350613	+	1.37006i	−0.0221747	+	0.0866503i
$251$	8.22942	−	8.22942i	0.519436	−	0.519436i	−0.397964	−	0.917401i	$-0.630283\pi$
$251$	8.22942	−	8.22942i	0.519436	−	0.519436i	0.917401	+	0.397964i	$0.130283\pi$
$252$	0.0565818	−	0.103310i	0.00356432	−	0.00650792i
$253$	−1.66729	−	1.66729i	−0.104822	−	0.104822i
$254$	−4.86312	−	8.20822i	−0.305140	−	0.515029i
$255$	5.98228			0.374625
$256$	−6.72040	+	14.5202i	−0.420025	+	0.907512i
$257$	7.32164			0.456712			0.228356	−	0.973578i	$-0.426665\pi$
$257$	7.32164			0.456712			0.228356	+	0.973578i	$0.426665\pi$
$258$	2.99956	+	5.06280i	0.186744	+	0.315196i
$259$	−0.118856	−	0.118856i	−0.00738536	−	0.00738536i
$260$	−3.87044	+	7.06685i	−0.240034	+	0.438268i
$261$	1.13987	−	1.13987i	0.0705560	−	0.0705560i
$262$	5.08033	−	19.8520i	0.313864	−	1.22646i
$263$			18.6430i			1.14958i	0.818302	+	0.574788i	$0.194915\pi$
$263$			18.6430i			1.14958i	−0.818302	+	0.574788i	$0.805085\pi$
$264$	8.92646	−	0.301804i	0.549386	−	0.0185747i
$265$			9.62784i			0.591433i
$266$	−0.0704346	−	0.0180249i	−0.00431862	−	0.00110518i
$267$	11.5264	−	11.5264i	0.705402	−	0.705402i
$268$	−14.8422	+	4.33762i	−0.906631	+	0.264962i
$269$	−3.22889	−	3.22889i	−0.196869	−	0.196869i	0.601787	−	0.798656i	$-0.294456\pi$
$269$	−3.22889	−	3.22889i	−0.196869	−	0.196869i	−0.798656	+	0.601787i	$0.794456\pi$
$270$	1.21670	−	0.720859i	0.0740461	−	0.0438701i
$271$	−27.9381			−1.69712			−0.848560	−	0.529099i	$-0.822530\pi$
$271$	−27.9381			−1.69712			−0.848560	+	0.529099i	$0.822530\pi$
$272$	−12.8859	−	20.1632i	−0.781325	−	1.22257i
$273$	−0.237268			−0.0143601
$274$	−23.6665	+	14.0217i	−1.42975	+	0.847083i
$275$	−2.23289	−	2.23289i	−0.134648	−	0.134648i
$276$	0.418920	+	1.43344i	0.0252160	+	0.0862827i
$277$	−1.58682	+	1.58682i	−0.0953431	+	0.0953431i	−0.753170	−	0.657826i	$-0.771476\pi$
$277$	−1.58682	+	1.58682i	−0.0953431	+	0.0953431i	0.657826	+	0.753170i	$0.271476\pi$
$278$	2.12330	+	0.543376i	0.127347	+	0.0325895i
$279$		−	8.55143i		−	0.511961i
$280$	0.121703	+	0.113742i	0.00727313	+	0.00679741i
$281$		−	6.36028i		−	0.379423i	−0.981840	−	0.189711i	$-0.939245\pi$
$281$		−	6.36028i		−	0.379423i	0.981840	−	0.189711i	$-0.0607552\pi$
$282$	−0.276850	+	1.08182i	−0.0164862	+	0.0644217i
$283$	3.64115	−	3.64115i	0.216444	−	0.216444i	−0.590554	−	0.806998i	$-0.701091\pi$
$283$	3.64115	−	3.64115i	0.216444	−	0.216444i	0.806998	+	0.590554i	$0.201091\pi$
$284$	12.9881	+	7.11342i	0.770699	+	0.422104i
$285$	−0.617238	−	0.617238i	−0.0365620	−	0.0365620i
$286$	−9.17053	−	15.4785i	−0.542265	−	0.915261i
$287$	0.454146			0.0268074
$288$	−5.05045	−	2.54813i	−0.297600	−	0.150150i
$289$	18.7876			1.10516
$290$	1.16204	+	1.96134i	0.0682371	+	0.115174i
$291$	8.70869	+	8.70869i	0.510512	+	0.510512i
$292$	−20.3680	−	11.1554i	−1.19195	−	0.652818i
$293$	−4.09157	+	4.09157i	−0.239032	+	0.239032i	−0.816449	−	0.577417i	$-0.804061\pi$
$293$	−4.09157	+	4.09157i	−0.239032	+	0.239032i	0.577417	+	0.816449i	$0.304061\pi$
$294$	2.45308	−	9.58568i	0.143066	−	0.559048i
$295$			13.2377i			0.770727i
$296$	−5.51192	+	5.89768i	−0.320374	+	0.342796i
$297$			3.15778i			0.183233i
$298$	26.4497	+	6.76875i	1.53219	+	0.392103i
$299$	2.12712	−	2.12712i	0.123014	−	0.123014i
$300$	0.561030	+	1.91970i	0.0323911	+	0.110834i
$301$	−0.173288	−	0.173288i	−0.00998818	−	0.00998818i
$302$	−16.4025	+	9.71798i	−0.943857	+	0.559207i
$303$	−0.938447			−0.0539124
$304$	−0.750852	+	3.40994i	−0.0430643	+	0.195573i
$305$	−1.15149			−0.0659341
$306$	7.27864	−	4.31238i	0.416092	−	0.246522i
$307$	0.832070	+	0.832070i	0.0474887	+	0.0474887i	0.730452	−	0.682964i	$-0.239309\pi$
$307$	0.832070	+	0.832070i	0.0474887	+	0.0474887i	−0.682964	+	0.730452i	$0.739309\pi$
$308$	−0.357021	+	0.104339i	−0.0203431	+	0.00594527i
$309$	10.5385	−	10.5385i	0.599512	−	0.599512i
$310$	11.7160	+	2.99825i	0.665424	+	0.170289i
$311$			13.8376i			0.784657i	0.919825	+	0.392329i	$0.128330\pi$
$311$			13.8376i			0.784657i	−0.919825	+	0.392329i	$0.871670\pi$
$312$	0.385039	+	11.3883i	0.0217985	+	0.644735i
$313$			5.09179i			0.287805i	0.989592	+	0.143902i	$0.0459651\pi$
$313$			5.09179i			0.287805i	−0.989592	+	0.143902i	$0.954035\pi$
$314$	5.50830	−	21.5243i	0.310851	−	1.21469i
$315$	−0.0416450	+	0.0416450i	−0.00234643	+	0.00234643i
$316$	16.7192	−	30.5268i	0.940528	−	1.71727i
$317$	16.3055	+	16.3055i	0.915811	+	0.915811i	0.996721	−	0.0809105i	$-0.0257828\pi$
$317$	16.3055	+	16.3055i	0.915811	+	0.915811i	−0.0809105	+	0.996721i	$0.525783\pi$
$318$	6.94032	+	11.7142i	0.389194	+	0.656900i
$319$	−5.09040			−0.285007
$320$	5.26186	−	6.02602i	0.294147	−	0.336865i
$321$	4.86293			0.271422
$322$	−0.0317010	−	0.0535065i	−0.00176663	−	0.00298180i
$323$	−3.69249	−	3.69249i	−0.205456	−	0.205456i
$324$	0.960724	−	1.75414i	0.0533735	−	0.0974523i
$325$	2.84870	−	2.84870i	0.158017	−	0.158017i
$326$	−0.979775	+	3.82859i	−0.0542647	+	0.212046i
$327$			0.0807802i			0.00446716i
$328$	−0.736988	−	21.7979i	−0.0406934	−	1.20359i
$329$		−	0.0465044i		−	0.00256387i
$330$	−4.32636	−	1.10716i	−0.238158	−	0.0609472i
$331$	5.33950	−	5.33950i	0.293485	−	0.293485i	−0.544970	−	0.838455i	$-0.683459\pi$
$331$	5.33950	−	5.33950i	0.293485	−	0.293485i	0.838455	+	0.544970i	$0.183459\pi$
$332$	20.4997	−	5.99101i	1.12507	−	0.328800i
$333$	−2.01811	−	2.01811i	−0.110591	−	0.110591i
$334$	−2.58886	+	1.53382i	−0.141656	+	0.0839270i
$335$	7.73152			0.422418
$336$	0.230068	+	0.0506599i	0.0125513	+	0.00276373i
$337$	−10.9232			−0.595023			−0.297512	−	0.954718i	$-0.596157\pi$
$337$	−10.9232			−0.595023			−0.297512	+	0.954718i	$0.596157\pi$
$338$	3.93017	−	2.32851i	0.213773	−	0.126654i
$339$	−10.5948	−	10.5948i	−0.575433	−	0.575433i
$340$	3.35624	+	11.4842i	0.182018	+	0.622817i
$341$	−19.0944	+	19.0944i	−1.03402	+	1.03402i
$342$	−1.19594	−	0.306053i	−0.0646688	−	0.0165494i
$343$			0.824325i			0.0445094i
$344$	−8.03621	+	8.59863i	−0.433283	+	0.463607i
$345$		−	0.746698i		−	0.0402009i
$346$	−4.57105	+	17.8619i	−0.245741	+	0.960263i
$347$	−19.5294	+	19.5294i	−1.04839	+	1.04839i	−0.0496243	+	0.998768i	$0.515802\pi$
$347$	−19.5294	+	19.5294i	−1.04839	+	1.04839i	−0.998768	+	0.0496243i	$0.984198\pi$
$348$	2.82770	+	1.54870i	0.151581	+	0.0830191i
$349$	−9.27622	−	9.27622i	−0.496545	−	0.496545i	0.413816	−	0.910361i	$-0.364196\pi$
$349$	−9.27622	−	9.27622i	−0.496545	−	0.496545i	−0.910361	+	0.413816i	$0.864196\pi$
$350$	−0.0424550	−	0.0716575i	−0.00226931	−	0.00383026i
$351$	−4.02867			−0.215035
$352$	5.58739	+	16.9668i	0.297809	+	0.904333i
$353$	3.31510			0.176445			0.0882225	−	0.996101i	$-0.471881\pi$
$353$	3.31510			0.176445			0.0882225	+	0.996101i	$0.471881\pi$
$354$	9.54250	+	16.1063i	0.507178	+	0.856040i
$355$	−5.23558	−	5.23558i	−0.277876	−	0.277876i
$356$	28.5938	+	15.6605i	1.51547	+	0.830006i
$357$	−0.249132	+	0.249132i	−0.0131855	+	0.0131855i
$358$	2.49114	−	9.73443i	0.131661	−	0.514481i
$359$			4.61854i			0.243757i	0.992545	+	0.121879i	$0.0388919\pi$
$359$			4.61854i			0.243757i	−0.992545	+	0.121879i	$0.961108\pi$
$360$	2.06644	+	1.93128i	0.108911	+	0.101787i
$361$		−	18.2380i		−	0.959897i
$362$	29.3274	+	7.50520i	1.54142	+	0.394464i
$363$	−0.727191	+	0.727191i	−0.0381676	+	0.0381676i
$364$	−0.133115	−	0.455484i	−0.00697711	−	0.0238738i
$365$	8.21050	+	8.21050i	0.429757	+	0.429757i
$366$	−1.40102	+	0.830061i	−0.0732324	+	0.0433880i
$367$	−3.80336			−0.198534			−0.0992668	−	0.995061i	$-0.531650\pi$
$367$	−3.80336			−0.198534			−0.0992668	+	0.995061i	$0.531650\pi$
$368$	−2.51674	+	1.60840i	−0.131194	+	0.0838437i
$369$	7.71113			0.401425
$370$	3.47250	−	2.05736i	0.180527	−	0.106957i
$371$	−0.400951	−	0.400951i	−0.0208164	−	0.0208164i
$372$	16.4162	−	4.79761i	0.851139	−	0.248745i
$373$	18.4506	−	18.4506i	0.955338	−	0.955338i	−0.0437062	−	0.999044i	$-0.513917\pi$
$373$	18.4506	−	18.4506i	0.955338	−	0.955338i	0.999044	+	0.0437062i	$0.0139165\pi$
$374$	−25.8815	−	6.62334i	−1.33830	−	0.342485i
$375$		−	1.00000i		−	0.0516398i
$376$	−2.23210	+	0.0754673i	−0.115112	+	0.00389193i
$377$		−	6.49428i		−	0.334472i
$378$	−0.0206493	+	0.0806897i	−0.00106209	+	0.00415023i
$379$	2.95913	−	2.95913i	0.152000	−	0.152000i	−0.627010	−	0.779011i	$-0.715722\pi$
$379$	2.95913	−	2.95913i	0.152000	−	0.152000i	0.779011	+	0.627010i	$0.215722\pi$
$380$	0.838622	−	1.53120i	0.0430204	−	0.0785489i
$381$	4.77035	+	4.77035i	0.244392	+	0.244392i
$382$	−8.96932	−	15.1389i	−0.458910	−	0.774571i
$383$	37.0073			1.89099			0.945493	−	0.325642i	$-0.105580\pi$
$383$	37.0073			1.89099			0.945493	+	0.325642i	$0.105580\pi$
$384$	2.05820	−	11.1249i	0.105032	−	0.567716i
$385$	0.185977			0.00947829
$386$	−0.174399	−	0.294360i	−0.00887669	−	0.0149825i
$387$	−2.94233	−	2.94233i	−0.149567	−	0.149567i
$388$	−11.8322	+	21.6039i	−0.600690	+	1.09677i
$389$	18.0915	−	18.0915i	0.917276	−	0.917276i	−0.0795542	−	0.996831i	$-0.525350\pi$
$389$	18.0915	−	18.0915i	0.917276	−	0.917276i	0.996831	+	0.0795542i	$0.0253497\pi$
$390$	1.41251	−	5.51953i	0.0715250	−	0.279492i
$391$		−	4.46695i		−	0.225904i
$392$	19.7779	−	0.668691i	0.998934	−	0.0337740i
$393$			14.4898i			0.730915i
$394$	4.59706	+	1.17644i	0.231597	+	0.0592680i
$395$	−12.3056	+	12.3056i	−0.619160	+	0.619160i
$396$	−6.06199	+	1.77161i	−0.304627	+	0.0890269i
$397$	−17.0980	−	17.0980i	−0.858125	−	0.858125i	0.132992	−	0.991117i	$-0.457542\pi$
$397$	−17.0980	−	17.0980i	−0.858125	−	0.858125i	−0.991117	+	0.132992i	$0.957542\pi$
$398$	24.1242	−	14.2928i	1.20923	−	0.716435i
$399$	0.0514098			0.00257371
$400$	−3.37049	+	2.15402i	−0.168524	+	0.107701i
$401$	10.8173			0.540189			0.270094	−	0.962834i	$-0.412945\pi$
$401$	10.8173			0.540189			0.270094	+	0.962834i	$0.412945\pi$
$402$	9.40694	−	5.57333i	0.469176	−	0.277973i
$403$	−24.3605	−	24.3605i	−1.21348	−	1.21348i
$404$	−0.526497	−	1.80154i	−0.0261942	−	0.0896297i
$405$	−0.707107	+	0.707107i	−0.0351364	+	0.0351364i
$406$	−0.130073	−	0.0332871i	−0.00645542	−	0.00165201i
$407$			9.01241i			0.446729i
$408$	12.3620	+	11.5534i	0.612011	+	0.571980i
$409$			4.30551i			0.212894i	0.994318	+	0.106447i	$0.0339474\pi$
$409$			4.30551i			0.212894i	−0.994318	+	0.106447i	$0.966053\pi$
$410$	−2.70362	+	10.5647i	−0.133522	+	0.521755i
$411$	13.7542	−	13.7542i	0.678446	−	0.678446i
$412$	26.1431	+	14.3183i	1.28798	+	0.705411i
$413$	−0.551283	−	0.551283i	−0.0271269	−	0.0271269i
$414$	−0.538264	−	0.908508i	−0.0264542	−	0.0446507i
$415$	−10.6786			−0.524191
$416$	−21.6461	+	7.12834i	−1.06129	+	0.349495i
$417$	−1.54979			−0.0758934
$418$	1.98701	+	3.35378i	0.0971879	+	0.164039i
$419$	−16.3215	−	16.3215i	−0.797357	−	0.797357i	0.185321	−	0.982678i	$-0.440667\pi$
$419$	−16.3215	−	16.3215i	−0.797357	−	0.797357i	−0.982678	+	0.185321i	$0.940667\pi$
$420$	−0.103310	−	0.0565818i	−0.00504101	−	0.00276091i
$421$	7.16177	−	7.16177i	0.349043	−	0.349043i	−0.510710	−	0.859753i	$-0.670617\pi$
$421$	7.16177	−	7.16177i	0.349043	−	0.349043i	0.859753	+	0.510710i	$0.170617\pi$
$422$	1.75978	−	6.87653i	0.0856645	−	0.334744i
$423$		−	0.789616i		−	0.0383925i
$424$	−18.5940	+	19.8953i	−0.903005	+	0.966203i
$425$		−	5.98228i		−	0.290183i
$426$	−10.1443	−	2.59602i	−0.491491	−	0.125778i
$427$	0.0479538	−	0.0479538i	0.00232064	−	0.00232064i
$428$	2.72825	+	9.33536i	0.131875	+	0.451242i
$429$	8.99558	+	8.99558i	0.434311	+	0.434311i
$430$	5.06280	−	2.99956i	0.244150	−	0.144651i
$431$	−14.4255			−0.694851			−0.347426	−	0.937708i	$-0.612944\pi$
$431$	−14.4255			−0.694851			−0.347426	+	0.937708i	$0.612944\pi$
$432$	3.90642	+	0.860175i	0.187948	+	0.0413852i
$433$	−31.3821			−1.50813			−0.754063	−	0.656802i	$-0.771909\pi$
$433$	−31.3821			−1.50813			−0.754063	+	0.656802i	$0.771909\pi$
$434$	−0.612775	+	0.363051i	−0.0294141	+	0.0174270i
$435$	−1.13987	−	1.13987i	−0.0546524	−	0.0546524i
$436$	−0.155074	+	0.0453202i	−0.00742669	+	0.00217044i
$437$	−0.460890	+	0.460890i	−0.0220474	+	0.0220474i
$438$	15.9083	+	4.07111i	0.760130	+	0.194525i
$439$			7.91484i			0.377755i	0.982001	+	0.188877i	$0.0604849\pi$
$439$			7.91484i			0.377755i	−0.982001	+	0.188877i	$0.939515\pi$
$440$	−0.301804	−	8.92646i	−0.0143879	−	0.425552i
$441$			6.99653i			0.333168i
$442$	8.45000	−	33.0193i	0.401925	−	1.57057i
$443$	−11.2877	+	11.2877i	−0.536294	+	0.536294i	−0.922438	−	0.386144i	$-0.873807\pi$
$443$	−11.2877	+	11.2877i	−0.536294	+	0.536294i	0.386144	+	0.922438i	$0.373807\pi$
$444$	2.74194	−	5.00637i	0.130127	−	0.237592i
$445$	−11.5264	−	11.5264i	−0.546402	−	0.546402i
$446$	−15.6275	−	26.3768i	−0.739982	−	1.24898i
$447$	−19.3055			−0.913117
$448$	0.0318235	+	0.470084i	0.00150352	+	0.0222094i
$449$	−16.7071			−0.788458			−0.394229	−	0.919012i	$-0.628988\pi$
$449$	−16.7071			−0.788458			−0.394229	+	0.919012i	$0.628988\pi$
$450$	−0.720859	−	1.21670i	−0.0339816	−	0.0573558i
$451$	−17.2181	−	17.2181i	−0.810769	−	0.810769i
$452$	14.3949	−	26.2830i	0.677079	−	1.23625i
$453$	9.53258	−	9.53258i	0.447880	−	0.447880i
$454$	−5.06340	+	19.7858i	−0.237637	+	0.928594i
$455$			0.237268i			0.0111233i
$456$	−0.0834277	−	2.46754i	−0.00390686	−	0.115553i
$457$			25.5371i			1.19458i	0.802027	+	0.597288i	$0.203755\pi$
$457$			25.5371i			1.19458i	−0.802027	+	0.597288i	$0.796245\pi$
$458$	−33.1194	−	8.47560i	−1.54757	−	0.396039i
$459$	−4.23011	+	4.23011i	−0.197445	+	0.197445i
$460$	1.43344	−	0.418920i	0.0668343	−	0.0195323i
$461$	−1.05719	−	1.05719i	−0.0492382	−	0.0492382i	0.682059	−	0.731297i	$-0.261085\pi$
$461$	−1.05719	−	1.05719i	−0.0492382	−	0.0492382i	−0.731297	+	0.682059i	$0.761085\pi$
$462$	0.226279	−	0.134064i	0.0105275	−	0.00623720i
$463$	33.8953			1.57525			0.787623	−	0.616157i	$-0.211312\pi$
$463$	33.8953			1.57525			0.787623	+	0.616157i	$0.211312\pi$
$464$	−1.38661	+	6.29721i	−0.0643720	+	0.292340i
$465$	−8.55143			−0.396563
$466$	29.4939	−	17.4743i	1.36628	−	0.809479i
$467$	−15.8661	−	15.8661i	−0.734194	−	0.734194i	0.237253	−	0.971448i	$-0.423753\pi$
$467$	−15.8661	−	15.8661i	−0.734194	−	0.734194i	−0.971448	+	0.237253i	$0.923753\pi$
$468$	−2.26021	−	7.73383i	−0.104478	−	0.357497i
$469$	−0.321979	+	0.321979i	−0.0148676	+	0.0148676i
$470$	1.08182	+	0.276850i	0.0499008	+	0.0127701i
$471$			15.7105i			0.723900i
$472$	−25.5656	+	27.3548i	−1.17675	+	1.25911i
$473$			13.1398i			0.604169i
$474$	−6.10162	+	23.8428i	−0.280257	+	1.09514i
$475$	−0.617238	+	0.617238i	−0.0283208	+	0.0283208i
$476$	−0.618029	−	0.338488i	−0.0283273	−	0.0155146i
$477$	−6.80791	−	6.80791i	−0.311713	−	0.311713i
$478$	−15.1855	−	25.6308i	−0.694568	−	1.17233i
$479$	−1.85047			−0.0845500			−0.0422750	−	0.999106i	$-0.513461\pi$
$479$	−1.85047			−0.0845500			−0.0422750	+	0.999106i	$0.513461\pi$
$480$	−2.54813	+	5.05045i	−0.116306	+	0.230520i
$481$	−11.4980			−0.524261
$482$	15.9006	+	26.8378i	0.724251	+	1.22243i
$483$	0.0310962	+	0.0310962i	0.00141493	+	0.00141493i
$484$	−1.80396	−	0.988012i	−0.0819984	−	0.0449096i
$485$	8.70869	−	8.70869i	0.395441	−	0.395441i
$486$	−0.350613	+	1.37006i	−0.0159041	+	0.0621473i
$487$			7.72194i			0.349915i	0.984576	+	0.174957i	$0.0559787\pi$
$487$			7.72194i			0.349915i	−0.984576	+	0.174957i	$0.944021\pi$
$488$	−2.37948	−	2.22384i	−0.107714	−	0.100669i
$489$		−	2.79446i		−	0.126370i
$490$	−9.58568	−	2.45308i	−0.433037	−	0.110819i
$491$	16.2289	−	16.2289i	0.732399	−	0.732399i	−0.238696	−	0.971094i	$-0.576720\pi$
$491$	16.2289	−	16.2289i	0.732399	−	0.732399i	0.971094	+	0.238696i	$0.0767199\pi$
$492$	4.32618	+	14.8030i	0.195039	+	0.667373i
$493$	−6.81900	−	6.81900i	−0.307112	−	0.307112i
$494$	−4.27871	+	2.53501i	−0.192508	+	0.114056i
$495$	3.15778			0.141932
$496$	18.4199	+	28.8225i	0.827080	+	1.29417i
$497$	0.436071			0.0195605
$498$	−12.9927	+	7.69776i	−0.582215	+	0.344945i
$499$	20.2479	+	20.2479i	0.906418	+	0.906418i	0.995981	−	0.0895629i	$-0.0285470\pi$
$499$	20.2479	+	20.2479i	0.906418	+	0.906418i	−0.0895629	+	0.995981i	$0.528547\pi$
$500$	1.91970	−	0.561030i	0.0858516	−	0.0250900i
$501$	1.50456	−	1.50456i	0.0672188	−	0.0672188i
$502$	−15.9450	−	4.08049i	−0.711660	−	0.182121i
$503$		−	18.2912i		−	0.815566i	−0.913079	−	0.407783i	$-0.866302\pi$
$503$		−	18.2912i		−	0.815566i	0.913079	−	0.407783i	$-0.133698\pi$
$504$	−0.166485	+	0.00562886i	−0.00741583	+	0.000250729i
$505$			0.938447i			0.0417603i
$506$	−0.826714	+	3.23048i	−0.0367519	+	0.143612i
$507$	−2.28408	+	2.28408i	−0.101440	+	0.101440i
$508$	−6.48132	+	11.8339i	−0.287562	+	0.525046i
$509$	16.0470	+	16.0470i	0.711272	+	0.711272i	0.966801	−	0.255529i	$-0.0822496\pi$
$509$	16.0470	+	16.0470i	0.711272	+	0.711272i	−0.255529	+	0.966801i	$0.582250\pi$
$510$	−4.31238	−	7.27864i	−0.190955	−	0.322304i
$511$	−0.683853			−0.0302519
$512$	22.5112	−	2.29030i	0.994864	−	0.101218i
$513$	0.872906			0.0385398
$514$	−5.27787	−	8.90825i	−0.232797	−	0.392926i
$515$	−10.5385	−	10.5385i	−0.464380	−	0.464380i
$516$	3.99765	−	7.29913i	0.175987	−	0.321326i
$517$	−1.76313	+	1.76313i	−0.0775422	+	0.0775422i
$518$	−0.0589339	+	0.230291i	−0.00258941	+	0.0101184i
$519$		−	13.0373i		−	0.572275i
$520$	11.3883	−	0.385039i	0.499410	−	0.0168851i
$521$			8.02188i			0.351445i	0.984440	+	0.175722i	$0.0562261\pi$
$521$			8.02188i			0.351445i	−0.984440	+	0.175722i	$0.943774\pi$
$522$	−2.20856	−	0.565194i	−0.0966661	−	0.0247379i
$523$	−31.8339	+	31.8339i	−1.39200	+	1.39200i	−0.571158	+	0.820840i	$0.693506\pi$
$523$	−31.8339	+	31.8339i	−1.39200	+	1.39200i	−0.820840	+	0.571158i	$0.806494\pi$
$524$	−27.8161	+	8.12924i	−1.21515	+	0.355127i
$525$	0.0416450	+	0.0416450i	0.00181754	+	0.00181754i
$526$	22.6829	−	13.4390i	0.989023	−	0.585967i
$527$	−51.1570			−2.22844
$528$	−6.80193	−	10.6433i	−0.296016	−	0.463189i
$529$	22.4424			0.975758
$530$	11.7142	−	6.94032i	0.508832	−	0.301468i
$531$	−9.36045	−	9.36045i	−0.406209	−	0.406209i
$532$	0.0288424	+	0.0986913i	0.00125048	+	0.00427881i
$533$	21.9667	−	21.9667i	0.951483	−	0.951483i
$534$	−22.3330	−	5.71526i	−0.966445	−	0.247323i
$535$		−	4.86293i		−	0.210243i
$536$	15.9767	+	14.9317i	0.690089	+	0.644951i
$537$			7.10510i			0.306608i
$538$	−1.60102	+	6.25618i	−0.0690249	+	0.269723i
$539$	15.6225	−	15.6225i	0.672908	−	0.672908i
$540$	−1.75414	−	0.960724i	−0.0754862	−	0.0413430i
$541$	16.7467	+	16.7467i	0.719996	+	0.719996i	0.968604	−	0.248608i	$-0.0799730\pi$
$541$	16.7467	+	16.7467i	0.719996	+	0.719996i	−0.248608	+	0.968604i	$0.579973\pi$
$542$	20.1395	+	33.9924i	0.865064	+	1.46010i
$543$	−21.4059			−0.918616
$544$	−15.2436	+	30.2132i	−0.653566	+	1.29538i
$545$	0.0807802			0.00346024
$546$	0.171037	+	0.288685i	0.00731971	+	0.0123546i
$547$	24.8600	+	24.8600i	1.06294	+	1.06294i	0.997882	+	0.0650571i	$0.0207230\pi$
$547$	24.8600	+	24.8600i	1.06294	+	1.06294i	0.0650571	+	0.997882i	$0.479277\pi$
$548$	34.1205	+	18.6874i	1.45756	+	0.798287i
$549$	0.814225	−	0.814225i	0.0347503	−	0.0347503i
$550$	−1.10716	+	4.32636i	−0.0472095	+	0.184477i
$551$			1.40714i			0.0599461i
$552$	1.44208	−	1.54301i	0.0613790	−	0.0656747i
$553$		−	1.02493i		−	0.0435845i
$554$	3.07457	+	0.786814i	0.130626	+	0.0334285i
$555$	−2.01811	+	2.01811i	−0.0856638	+	0.0856638i
$556$	−0.869478	−	2.97513i	−0.0368741	−	0.126173i
$557$	12.0423	+	12.0423i	0.510248	+	0.510248i	0.914603	−	0.404354i	$-0.132504\pi$
$557$	12.0423	+	12.0423i	0.510248	+	0.510248i	−0.404354	+	0.914603i	$0.632504\pi$
$558$	−10.4045	+	6.16438i	−0.440459	+	0.260959i
$559$	−16.7636			−0.709026
$560$	0.0506599	−	0.230068i	0.00214077	−	0.00972216i
$561$	18.8907			0.797567
$562$	−7.73856	+	4.58487i	−0.326432	+	0.193401i
$563$	−15.2672	−	15.2672i	−0.643435	−	0.643435i	0.307963	−	0.951398i	$-0.400353\pi$
$563$	−15.2672	−	15.2672i	−0.643435	−	0.643435i	−0.951398	+	0.307963i	$0.900353\pi$
$564$	1.51583	−	0.442999i	0.0638278	−	0.0186536i
$565$	−10.5948	+	10.5948i	−0.445729	+	0.445729i
$566$	−7.05496	−	1.80544i	−0.296542	−	0.0758882i
$567$		−	0.0588949i		−	0.00247335i
$568$	−0.707656	−	20.9304i	−0.0296926	−	0.878218i
$569$		−	33.2847i		−	1.39537i	−0.716406	−	0.697683i	$-0.754214\pi$
$569$		−	33.2847i		−	1.39537i	0.716406	−	0.697683i	$-0.245786\pi$
$570$	−0.306053	+	1.19594i	−0.0128191	+	0.0500922i
$571$	−10.4781	+	10.4781i	−0.438494	+	0.438494i	−0.891505	−	0.453011i	$-0.850350\pi$
$571$	−10.4781	+	10.4781i	−0.438494	+	0.438494i	0.453011	+	0.891505i	$0.350350\pi$
$572$	−12.2220	+	22.3156i	−0.511028	+	0.933062i
$573$	8.79820	+	8.79820i	0.367550	+	0.367550i
$574$	−0.327376	−	0.552561i	−0.0136644	−	0.0230634i
$575$	−0.746698			−0.0311394
$576$	0.540343	+	7.98173i	0.0225143	+	0.332572i
$577$	−38.6407			−1.60863			−0.804316	−	0.594202i	$-0.797468\pi$
$577$	−38.6407			−1.60863			−0.804316	+	0.594202i	$0.797468\pi$
$578$	−13.5432	−	22.8589i	−0.563325	−	0.950807i
$579$	0.171072	+	0.171072i	0.00710952	+	0.00710952i
$580$	1.54870	−	2.82770i	0.0643063	−	0.117414i
$581$	0.444710	−	0.444710i	0.0184497	−	0.0184497i
$582$	4.31813	−	16.8736i	0.178992	−	0.699434i
$583$			30.4026i			1.25915i
$584$	1.10976	+	32.8233i	0.0459220	+	1.35824i
$585$			4.02867i			0.166565i
$586$	7.92767	+	2.02877i	0.327489	+	0.0838079i
$587$	−21.1392	+	21.1392i	−0.872507	+	0.872507i	−0.992745	−	0.120238i	$-0.961634\pi$
$587$	−21.1392	+	21.1392i	−0.872507	+	0.872507i	0.120238	+	0.992745i	$0.461634\pi$
$588$	−13.4312	+	3.92527i	−0.553895	+	0.161875i
$589$	5.27827	+	5.27827i	0.217487	+	0.217487i
$590$	16.1063	−	9.54250i	0.663086	−	0.392858i
$591$	−3.35537			−0.138021
$592$	11.1490	+	2.45497i	0.458223	+	0.100898i
$593$	−4.03330			−0.165628			−0.0828138	−	0.996565i	$-0.526391\pi$
$593$	−4.03330			−0.165628			−0.0828138	+	0.996565i	$0.526391\pi$
$594$	3.84208	−	2.27632i	0.157642	−	0.0933984i
$595$	0.249132	+	0.249132i	0.0102134	+	0.0102134i
$596$	−10.8309	−	37.0607i	−0.443653	−	1.51806i
$597$	−14.0202	+	14.0202i	−0.573807	+	0.573807i
$598$	−4.12142	−	1.05471i	−0.168537	−	0.0431305i
$599$			6.44275i			0.263244i	0.991300	+	0.131622i	$0.0420184\pi$
$599$			6.44275i			0.263244i	−0.991300	+	0.131622i	$0.957982\pi$
$600$	1.93128	−	2.06644i	0.0788440	−	0.0843620i
$601$		−	36.3011i		−	1.48075i	−0.672193	−	0.740376i	$-0.734648\pi$
$601$		−	36.3011i		−	1.48075i	0.672193	−	0.740376i	$-0.265352\pi$
$602$	−0.0859237	+	0.335757i	−0.00350199	+	0.0136844i
$603$	−5.46701	+	5.46701i	−0.222634	+	0.222634i
$604$	23.6478	+	12.9516i	0.962214	+	0.526994i
$605$	0.727191	+	0.727191i	0.0295645	+	0.0295645i
$606$	0.676488	+	1.14181i	0.0274805	+	0.0463828i
$607$	19.5463			0.793360			0.396680	−	0.917957i	$-0.370162\pi$
$607$	19.5463			0.793360			0.396680	+	0.917957i	$0.370162\pi$
$608$	4.69013	−	1.54452i	0.190210	−	0.0626386i
$609$	0.0949395			0.00384714
$610$	0.830061	+	1.40102i	0.0336082	+	0.0567256i
$611$	−2.24938	−	2.24938i	−0.0910002	−	0.0910002i
$612$	−10.4938	−	5.74732i	−0.424185	−	0.232321i
$613$	18.5711	−	18.5711i	0.750080	−	0.750080i	−0.224414	−	0.974494i	$-0.572047\pi$
$613$	18.5711	−	18.5711i	0.750080	−	0.750080i	0.974494	+	0.224414i	$0.0720467\pi$
$614$	0.412575	−	1.61219i	0.0166502	−	0.0650625i
$615$		−	7.71113i		−	0.310943i
$616$	0.384311	+	0.359174i	0.0154843	+	0.0144715i
$617$			19.7311i			0.794342i	0.917745	+	0.397171i	$0.130008\pi$
$617$			19.7311i			0.794342i	−0.917745	+	0.397171i	$0.869992\pi$
$618$	−20.4189	−	5.22541i	−0.821368	−	0.210197i
$619$	22.1910	−	22.1910i	0.891930	−	0.891930i	−0.102775	−	0.994705i	$-0.532772\pi$
$619$	22.1910	−	22.1910i	0.891930	−	0.891930i	0.994705	+	0.102775i	$0.0327721\pi$
$620$	−4.79761	−	16.4162i	−0.192677	−	0.659289i
$621$	0.527995	+	0.527995i	0.0211877	+	0.0211877i
$622$	16.8362	−	9.97495i	0.675070	−	0.399959i
$623$	0.960031			0.0384628
$624$	13.5786	−	8.67783i	0.543579	−	0.347391i
$625$	−1.00000			−0.0400000
$626$	6.19518	−	3.67046i	0.247609	−	0.146701i
$627$	−1.94910	−	1.94910i	−0.0778397	−	0.0778397i
$628$	−30.1594	+	8.81405i	−1.20349	+	0.351719i
$629$	−12.0729	+	12.0729i	−0.481377	+	0.481377i
$630$	0.0806897	+	0.0206493i	0.00321476	+	0.000822690i
$631$		−	13.1148i		−	0.522093i	−0.965326	−	0.261046i	$-0.915932\pi$
$631$		−	13.1148i		−	0.522093i	0.965326	−	0.261046i	$-0.0840676\pi$
$632$	−49.1942	+	1.66326i	−1.95684	+	0.0661608i
$633$			5.01914i			0.199493i
$634$	8.08498	−	31.5930i	0.321095	−	1.25472i
$635$	4.77035	−	4.77035i	0.189305	−	0.189305i
$636$	9.24969	−	16.8886i	0.366774	−	0.669676i
$637$	19.9310	+	19.9310i	0.789696	+	0.789696i
$638$	3.66946	+	6.19349i	0.145275	+	0.245203i
$639$	7.40423			0.292907
$640$	−11.1249	−	2.05820i	−0.439751	−	0.0813574i
$641$	30.5395			1.20624			0.603119	−	0.797652i	$-0.293925\pi$
$641$	30.5395			1.20624			0.603119	+	0.797652i	$0.293925\pi$
$642$	−3.50549	−	5.91673i	−0.138350	−	0.233515i
$643$	−4.01306	−	4.01306i	−0.158260	−	0.158260i	0.623535	−	0.781795i	$-0.285696\pi$
$643$	−4.01306	−	4.01306i	−0.158260	−	0.158260i	−0.781795	+	0.623535i	$0.785696\pi$
$644$	−0.0422495	+	0.0771414i	−0.00166486	+	0.00303980i
$645$	−2.94233	+	2.94233i	−0.115854	+	0.115854i
$646$	−1.83089	+	7.15442i	−0.0720354	+	0.281487i
$647$		−	9.01207i		−	0.354301i	−0.984184	−	0.177151i	$-0.943312\pi$
$647$		−	9.01207i		−	0.354301i	0.984184	−	0.177151i	$-0.0566880\pi$
$648$	−2.82681	+	0.0955746i	−0.111048	+	0.00375452i
$649$			41.8017i			1.64086i
$650$	−5.51953	−	1.41251i	−0.216494	−	0.0554030i
$651$	0.356124	−	0.356124i	0.0139576	−	0.0139576i
$652$	5.36452	−	1.56778i	0.210091	−	0.0613989i
$653$	−25.2241	−	25.2241i	−0.987096	−	0.987096i	0.0128219	−	0.999918i	$-0.495919\pi$
$653$	−25.2241	−	25.2241i	−0.987096	−	0.987096i	−0.999918	+	0.0128219i	$0.995919\pi$
$654$	0.0982854	−	0.0582312i	0.00384326	−	0.00227702i
$655$	14.4898			0.566165
$656$	−25.9903	+	16.6099i	−1.01475	+	0.648508i
$657$	−11.6114			−0.453004
$658$	−0.0565820	+	0.0335231i	−0.00220579	+	0.00130687i
$659$	15.8387	+	15.8387i	0.616987	+	0.616987i	0.944757	−	0.327770i	$-0.106297\pi$
$659$	15.8387	+	15.8387i	0.616987	+	0.616987i	−0.327770	+	0.944757i	$0.606297\pi$
$660$	1.77161	+	6.06199i	0.0689599	+	0.235963i
$661$	8.25357	−	8.25357i	0.321027	−	0.321027i	−0.528134	−	0.849161i	$-0.677108\pi$
$661$	8.25357	−	8.25357i	0.321027	−	0.321027i	0.849161	+	0.528134i	$0.177108\pi$
$662$	−10.3456	−	2.64755i	−0.402093	−	0.102900i
$663$			24.1006i			0.935991i
$664$	−22.0667	−	20.6233i	−0.856353	−	0.800340i
$665$		−	0.0514098i		−	0.00199359i
$666$	−1.00066	+	3.91020i	−0.0387748	+	0.151517i
$667$	−0.851136	+	0.851136i	−0.0329561	+	0.0329561i
$668$	3.73241	+	2.04420i	0.144411	+	0.0790924i
$669$	15.3293	+	15.3293i	0.592666	+	0.592666i
$670$	−5.57333	−	9.40694i	−0.215317	−	0.363422i
$671$	−3.63615			−0.140372
$672$	−0.104209	−	0.316443i	−0.00401994	−	0.0122071i
$673$	29.8226			1.14958			0.574789	−	0.818302i	$-0.305084\pi$
$673$	29.8226			1.14958			0.574789	+	0.818302i	$0.305084\pi$
$674$	7.87407	+	13.2902i	0.303298	+	0.511921i
$675$	0.707107	+	0.707107i	0.0272166	+	0.0272166i
$676$	−5.66619	−	3.10331i	−0.217931	−	0.119358i
$677$	11.3009	−	11.3009i	0.434328	−	0.434328i	−0.455770	−	0.890098i	$-0.650636\pi$
$677$	11.3009	−	11.3009i	0.434328	−	0.434328i	0.890098	+	0.455770i	$0.150636\pi$
$678$	−5.25337	+	20.5282i	−0.201755	+	0.788379i
$679$			0.725347i			0.0278363i
$680$	11.5534	−	12.3620i	0.443054	−	0.474062i
$681$		−	14.4415i		−	0.553401i
$682$	36.9966	+	9.46781i	1.41667	+	0.362541i
$683$	24.7739	−	24.7739i	0.947949	−	0.947949i	−0.0507621	−	0.998711i	$-0.516165\pi$
$683$	24.7739	−	24.7739i	0.947949	−	0.947949i	0.998711	+	0.0507621i	$0.0161650\pi$
$684$	0.489727	+	1.67572i	0.0187252	+	0.0640727i
$685$	−13.7542	−	13.7542i	−0.525522	−	0.525522i
$686$	1.00296	−	0.594222i	0.0382931	−	0.0226875i
$687$	24.1736			0.922282
$688$	16.2549	+	3.57926i	0.619714	+	0.136458i
$689$	−38.7874			−1.47768
$690$	−0.908508	+	0.538264i	−0.0345863	+	0.0204914i
$691$	30.4140	+	30.4140i	1.15700	+	1.15700i	0.985117	+	0.171888i	$0.0549866\pi$
$691$	30.4140	+	30.4140i	1.15700	+	1.15700i	0.171888	+	0.985117i	$0.445013\pi$
$692$	25.0277	−	7.31433i	0.951411	−	0.278049i
$693$	−0.131506	+	0.131506i	−0.00499550	+	0.00499550i
$694$	37.8394	+	9.68349i	1.43636	+	0.367580i
$695$			1.54979i			0.0587868i
$696$	−0.154068	−	4.55686i	−0.00583992	−	0.172728i
$697$		−	46.1301i		−	1.74730i
$698$	−4.59954	+	17.9732i	−0.174095	+	0.680297i
$699$	−17.1409	+	17.1409i	−0.648328	+	0.648328i
$700$	−0.0565818	+	0.103310i	−0.00213859	+	0.00390475i
$701$	−9.35541	−	9.35541i	−0.353349	−	0.353349i	0.508005	−	0.861354i	$-0.330383\pi$
$701$	−9.35541	−	9.35541i	−0.353349	−	0.353349i	−0.861354	+	0.508005i	$0.830383\pi$
$702$	2.90410	+	4.90169i	0.109608	+	0.185002i
$703$	2.49130			0.0939612
$704$	16.6158	−	19.0289i	0.626232	−	0.717177i
$705$	−0.789616			−0.0297387
$706$	−2.38972	−	4.03349i	−0.0899384	−	0.151802i
$707$	−0.0390816	−	0.0390816i	−0.00146982	−	0.00146982i
$708$	12.7177	−	23.2207i	0.477962	−	0.872689i
$709$	15.6531	−	15.6531i	0.587866	−	0.587866i	−0.349187	−	0.937053i	$-0.613542\pi$
$709$	15.6531	−	15.6531i	0.587866	−	0.587866i	0.937053	+	0.349187i	$0.113542\pi$
$710$	−2.59602	+	10.1443i	−0.0974269	+	0.380707i
$711$		−	17.4027i		−	0.652652i
$712$	−1.55794	−	46.0791i	−0.0583862	−	1.72689i
$713$			6.38533i			0.239133i
$714$	0.482708	+	0.123530i	0.0180649	+	0.00462300i
$715$	8.99558	−	8.99558i	0.336416	−	0.336416i
$716$	−13.6397	+	3.98618i	−0.509738	+	0.148971i
$717$	14.8958	+	14.8958i	0.556293	+	0.556293i
$718$	5.61939	−	3.32932i	0.209714	−	0.124249i
$719$	51.4373			1.91829			0.959144	−	0.282919i	$-0.0913028\pi$
$719$	51.4373			1.91829			0.959144	+	0.282919i	$0.0913028\pi$
$720$	0.860175	−	3.90642i	0.0320568	−	0.145584i
$721$	0.877748			0.0326891
$722$	−22.1902	+	13.1471i	−0.825835	+	0.489283i
$723$	−15.5972	−	15.5972i	−0.580067	−	0.580067i
$724$	−12.0094	−	41.0929i	−0.446325	−	1.52721i
$725$	−1.13987	+	1.13987i	−0.0423336	+	0.0423336i
$726$	1.40898	+	0.360572i	0.0522920	+	0.0133821i
$727$			15.7975i			0.585898i	0.956128	+	0.292949i	$0.0946366\pi$
$727$			15.7975i			0.585898i	−0.956128	+	0.292949i	$0.905363\pi$
$728$	−0.458231	+	0.490300i	−0.0169832	+	0.0181717i
$729$		−	1.00000i		−	0.0370370i
$730$	4.07111	−	15.9083i	0.150679	−	0.588794i
$731$	−17.6018	+	17.6018i	−0.651028	+	0.651028i
$732$	2.01987	+	1.10626i	0.0746567	+	0.0408886i
$733$	28.7672	+	28.7672i	1.06254	+	1.06254i	0.997909	+	0.0646310i	$0.0205870\pi$
$733$	28.7672	+	28.7672i	1.06254	+	1.06254i	0.0646310	+	0.997909i	$0.479413\pi$
$734$	2.74168	+	4.62755i	0.101197	+	0.170806i
$735$	6.99653			0.258071
$736$	3.77116	+	1.90269i	0.139007	+	0.0701339i
$737$	24.4145			0.899318
$738$	−5.55864	−	9.38214i	−0.204616	−	0.345361i
$739$	6.12767	+	6.12767i	0.225410	+	0.225410i	0.810772	−	0.585362i	$-0.199048\pi$
$739$	6.12767	+	6.12767i	0.225410	+	0.225410i	−0.585362	+	0.810772i	$0.699048\pi$
$740$	−5.00637	−	2.74194i	−0.184038	−	0.100796i
$741$	2.48665	−	2.48665i	0.0913493	−	0.0913493i
$742$	−0.198809	+	0.776868i	−0.00729849	+	0.0285197i
$743$		−	22.0466i		−	0.808810i	−0.914580	−	0.404405i	$-0.867479\pi$
$743$		−	22.0466i		−	0.808810i	0.914580	−	0.404405i	$-0.132521\pi$
$744$	−17.6710	−	16.5152i	−0.647851	−	0.605476i
$745$			19.3055i			0.707297i
$746$	−35.7492	−	9.14861i	−1.30887	−	0.334954i
$747$	7.55090	−	7.55090i	0.276273	−	0.276273i
$748$	10.5983	+	36.2645i	0.387511	+	1.32596i
$749$	0.202517	+	0.202517i	0.00739980	+	0.00739980i
$750$	−1.21670	+	0.720859i	−0.0444276	+	0.0263221i
$751$	40.6203			1.48226			0.741128	−	0.671364i	$-0.234291\pi$
$751$	40.6203			1.48226			0.741128	+	0.671364i	$0.234291\pi$
$752$	1.70085	+	2.66139i	0.0620236	+	0.0970510i
$753$	11.6382			0.424118
$754$	−7.90160	+	4.68146i	−0.287759	+	0.170489i
$755$	−9.53258	−	9.53258i	−0.346926	−	0.346926i
$756$	0.113061	−	0.0330419i	0.00411197	−	0.00120172i
$757$	−12.9575	+	12.9575i	−0.470949	+	0.470949i	−0.902222	−	0.431272i	$-0.858065\pi$
$757$	−12.9575	+	12.9575i	−0.470949	+	0.470949i	0.431272	+	0.902222i	$0.358065\pi$
$758$	−5.73350	−	1.46726i	−0.208250	−	0.0532934i
$759$		−	2.35791i		−	0.0855867i
$760$	−2.46754	+	0.0834277i	−0.0895072	+	0.00302624i
$761$		−	33.9075i		−	1.22915i	−0.788860	−	0.614573i	$-0.789328\pi$
$761$		−	33.9075i		−	1.22915i	0.788860	−	0.614573i	$-0.210672\pi$
$762$	2.36534	−	9.24284i	0.0856872	−	0.334833i
$763$	−0.00336409	+	0.00336409i	−0.000121788	+	0.000121788i
$764$	−11.9538	+	21.8260i	−0.432475	+	0.789636i
$765$	4.23011	+	4.23011i	0.152940	+	0.152940i
$766$	−26.6771	−	45.0269i	−0.963882	−	1.62689i
$767$	−53.3302			−1.92564
$768$	−15.0194	+	5.51529i	−0.541965	+	0.199016i
$769$	8.30816			0.299600			0.149800	−	0.988716i	$-0.452137\pi$
$769$	8.30816			0.299600			0.149800	+	0.988716i	$0.452137\pi$
$770$	−0.134064	−	0.226279i	−0.00483132	−	0.00815453i
$771$	5.17718	+	5.17718i	0.186452	+	0.186452i
$772$	−0.232430	+	0.424384i	−0.00836535	+	0.0152739i
$773$	9.90838	−	9.90838i	0.356380	−	0.356380i	−0.506097	−	0.862477i	$-0.668912\pi$
$773$	9.90838	−	9.90838i	0.356380	−	0.356380i	0.862477	+	0.506097i	$0.168912\pi$
$774$	−1.45893	+	5.70095i	−0.0524402	+	0.204916i
$775$			8.55143i			0.307176i
$776$	34.8149	−	1.17709i	1.24978	−	0.0422551i
$777$		−	0.168088i		−	0.00603012i
$778$	−35.0534	−	8.97053i	−1.25673	−	0.321609i
$779$	−4.75960	+	4.75960i	−0.170530	+	0.170530i
$780$	−7.73383	+	2.26021i	−0.276916	+	0.0809284i
$781$	−16.5328	−	16.5328i	−0.591591	−	0.591591i
$782$	−5.43495	+	3.22004i	−0.194353	+	0.115149i
$783$	1.61202			0.0576087
$784$	−15.0707	−	23.5817i	−0.538238	−	0.842205i
$785$	15.7105			0.560730
$786$	17.6298	−	10.4451i	0.628834	−	0.372565i
$787$	32.2948	+	32.2948i	1.15119	+	1.15119i	0.986315	+	0.164872i	$0.0527209\pi$
$787$	32.2948	+	32.2948i	1.15119	+	1.15119i	0.164872	+	0.986315i	$0.447279\pi$
$788$	−1.88246	−	6.44130i	−0.0670600	−	0.229462i
$789$	−13.1826	+	13.1826i	−0.469312	+	0.469312i
$790$	23.8428	+	6.10162i	0.848288	+	0.217086i
$791$		−	0.882445i		−	0.0313761i
$792$	6.52537	+	6.09855i	0.231869	+	0.216703i
$793$		−	4.63897i		−	0.164735i
$794$	−8.47792	+	33.1285i	−0.300870	+	1.17569i
$795$	−6.80791	+	6.80791i	−0.241452	+	0.241452i
$796$	−34.7802	−	19.0488i	−1.23275	−	0.675165i
$797$	−21.3637	−	21.3637i	−0.756740	−	0.756740i	0.218987	−	0.975728i	$-0.429725\pi$
$797$	−21.3637	−	21.3637i	−0.756740	−	0.756740i	−0.975728	+	0.218987i	$0.929725\pi$
$798$	−0.0370592	−	0.0625503i	−0.00131188	−	0.00221426i
$799$	−4.72370			−0.167113
$800$	5.05045	+	2.54813i	0.178560	+	0.0900902i
$801$	16.3007			0.575958
$802$	−7.79773	−	13.1614i	−0.275347	−	0.464745i
$803$	25.9270	+	25.9270i	0.914944	+	0.914944i
$804$	−13.5622	−	7.42785i	−0.478301	−	0.261960i
$805$	0.0310962	−	0.0310962i	0.00109600	−	0.00109600i
$806$	−12.0789	+	47.1999i	−0.425463	+	1.66254i
$807$		−	4.56635i		−	0.160743i
$808$	−1.81240	+	1.93924i	−0.0637600	+	0.0682223i
$809$			37.9895i			1.33564i	0.744323	+	0.667820i	$0.232772\pi$
$809$			37.9895i			1.33564i	−0.744323	+	0.667820i	$0.767228\pi$
$810$	1.37006	+	0.350613i	0.0481391	+	0.0123193i
$811$	6.45375	−	6.45375i	0.226622	−	0.226622i	−0.584658	−	0.811280i	$-0.698771\pi$
$811$	6.45375	−	6.45375i	0.226622	−	0.226622i	0.811280	+	0.584658i	$0.198771\pi$
$812$	0.0532640	+	0.182255i	0.00186920	+	0.00639591i
$813$	−19.7552	−	19.7552i	−0.692847	−	0.692847i
$814$	10.9654	−	6.49668i	0.384338	−	0.227709i
$815$	−2.79446			−0.0978857
$816$	5.14580	−	23.3693i	0.180139	−	0.818088i
$817$	3.63224			0.127076
$818$	5.23852	−	3.10367i	0.183161	−	0.108517i
$819$	−0.167774	−	0.167774i	−0.00586250	−	0.00586250i
$820$	14.8030	−	4.32618i	0.516945	−	0.151077i
$821$	−10.5389	+	10.5389i	−0.367809	+	0.367809i	−0.866677	−	0.498869i	$-0.833749\pi$
$821$	−10.5389	+	10.5389i	−0.367809	+	0.367809i	0.498869	+	0.866677i	$0.333749\pi$
$822$	−26.6496	−	6.81992i	−0.929513	−	0.237872i
$823$		−	35.0064i		−	1.22025i	−0.792306	−	0.610124i	$-0.791120\pi$
$823$		−	35.0064i		−	1.22025i	0.792306	−	0.610124i	$-0.208880\pi$
$824$	−1.42441	−	42.1298i	−0.0496216	−	1.46766i
$825$		−	3.15778i		−	0.109940i
$826$	−0.273349	+	1.06814i	−0.00951104	+	0.0371655i
$827$	13.0789	−	13.0789i	0.454799	−	0.454799i	−0.442145	−	0.896944i	$-0.645782\pi$
$827$	13.0789	−	13.0789i	0.454799	−	0.454799i	0.896944	+	0.442145i	$0.145782\pi$
$828$	−0.717370	+	1.30981i	−0.0249303	+	0.0455191i
$829$	−28.3502	−	28.3502i	−0.984642	−	0.984642i	0.0152419	−	0.999884i	$-0.495148\pi$
$829$	−28.3502	−	28.3502i	−0.984642	−	0.984642i	−0.999884	+	0.0152419i	$0.995148\pi$
$830$	7.69776	+	12.9927i	0.267193	+	0.450982i
$831$	−2.24411			−0.0778473
$832$	24.2768	+	21.1983i	0.841648	+	0.734918i
$833$	41.8552			1.45020
$834$	1.11718	+	1.88563i	0.0386847	+	0.0652940i
$835$	−1.50456	−	1.50456i	−0.0520674	−	0.0520674i
$836$	2.64819	−	4.83520i	0.0915895	−	0.167229i
$837$	6.04678	−	6.04678i	0.209007	−	0.209007i
$838$	−8.09288	+	31.6239i	−0.279564	+	1.09243i
$839$		−	52.5560i		−	1.81444i	−0.420661	−	0.907218i	$-0.638202\pi$
$839$		−	52.5560i		−	1.81444i	0.420661	−	0.907218i	$-0.361798\pi$
$840$	0.00562886	+	0.166485i	0.000194214	+	0.00574428i
$841$		−	26.4014i		−	0.910393i
$842$	−13.8764	−	3.55111i	−0.478211	−	0.122379i
$843$	4.49740	−	4.49740i	0.154899	−	0.154899i
$844$	−9.63523	+	2.81589i	−0.331658	+	0.0969269i
$845$	2.28408	+	2.28408i	0.0785749	+	0.0785749i
$846$	−0.960727	+	0.569202i	−0.0330305	+	0.0195696i
$847$	−0.0605677			−0.00208113
$848$	37.6104	+	8.28162i	1.29155	+	0.284392i
$849$	5.14937			0.176726
$850$	−7.27864	+	4.31238i	−0.249655	+	0.147913i
$851$	1.50691	+	1.50691i	0.0516564	+	0.0516564i
$852$	4.15400	+	14.2139i	0.142314	+	0.486960i
$853$	−33.3957	+	33.3957i	−1.14345	+	1.14345i	−0.155632	+	0.987815i	$0.549741\pi$
$853$	−33.3957	+	33.3957i	−1.14345	+	1.14345i	−0.987815	+	0.155632i	$0.950259\pi$
$854$	−0.0929133	−	0.0237775i	−0.00317943	−	0.000813649i
$855$		−	0.872906i		−	0.0298528i
$856$	9.39166	−	10.0489i	0.321000	−	0.343466i
$857$		−	6.36548i		−	0.217441i	−0.994072	−	0.108720i	$-0.965325\pi$
$857$		−	6.36548i		−	0.217441i	0.994072	−	0.108720i	$-0.0346753\pi$
$858$	4.46039	−	17.4295i	0.152275	−	0.595032i
$859$	30.2446	−	30.2446i	1.03193	−	1.03193i	0.0324590	−	0.999473i	$-0.489666\pi$
$859$	30.2446	−	30.2446i	1.03193	−	1.03193i	0.999473	−	0.0324590i	$-0.0103338\pi$
$860$	−7.29913	−	3.99765i	−0.248898	−	0.136319i
$861$	0.321130	+	0.321130i	0.0109441	+	0.0109441i
$862$	10.3987	+	17.5515i	0.354183	+	0.597807i
$863$	−16.2067			−0.551683			−0.275841	−	0.961203i	$-0.588956\pi$
$863$	−16.2067			−0.551683			−0.275841	+	0.961203i	$0.588956\pi$
$864$	−1.76940	−	5.37301i	−0.0601963	−	0.182793i
$865$	−13.0373			−0.443282
$866$	22.6221	+	38.1826i	0.768729	+	1.29750i
$867$	13.2849	+	13.2849i	0.451178	+	0.451178i
$868$	0.883448	+	0.483855i	0.0299862	+	0.0164231i
$869$	−38.8583	+	38.8583i	−1.31818	+	1.31818i
$870$	−0.565194	+	2.20856i	−0.0191619	+	0.0748772i
$871$			31.1477i			1.05540i
$872$	0.166927	+	0.156009i	0.00565288	+	0.00528313i
$873$			12.3159i			0.416832i
$874$	0.893003	+	0.228529i	0.0302063	+	0.00773010i
$875$	0.0416450	−	0.0416450i	0.00140786	−	0.00140786i
$876$	−6.51435	−	22.2904i	−0.220100	−	0.753123i
$877$	−7.08871	−	7.08871i	−0.239369	−	0.239369i	0.577220	−	0.816589i	$-0.304137\pi$
$877$	−7.08871	−	7.08871i	−0.239369	−	0.239369i	−0.816589	+	0.577220i	$0.804137\pi$
$878$	9.63000	−	5.70549i	0.324997	−	0.192551i
$879$	−5.78636			−0.195169
$880$	−10.6433	+	6.80193i	−0.358785	+	0.229293i
$881$	−46.7030			−1.57346			−0.786731	−	0.617296i	$-0.788228\pi$
$881$	−46.7030			−1.57346			−0.786731	+	0.617296i	$0.788228\pi$
$882$	8.51269	−	5.04351i	0.286637	−	0.169824i
$883$	35.6005	+	35.6005i	1.19805	+	1.19805i	0.974749	+	0.223303i	$0.0716840\pi$
$883$	35.6005	+	35.6005i	1.19805	+	1.19805i	0.223303	+	0.974749i	$0.428316\pi$
$884$	−46.2659	+	13.5212i	−1.55609	+	0.454767i
$885$	−9.36045	+	9.36045i	−0.314648	+	0.314648i
$886$	21.8706	+	5.59691i	0.734756	+	0.188032i
$887$			2.62187i			0.0880338i	0.999031	+	0.0440169i	$0.0140156\pi$
$887$			2.62187i			0.0880338i	−0.999031	+	0.0440169i	$0.985984\pi$
$888$	−8.06781	+	0.272773i	−0.270738	+	0.00915366i
$889$			0.397322i			0.0133258i
$890$	−5.71526	+	22.3330i	−0.191576	+	0.748605i
$891$	−2.23289	+	2.23289i	−0.0748046	+	0.0748046i
$892$	−20.8275	+	38.0279i	−0.697355	+	1.27327i
$893$	0.487381	+	0.487381i	0.0163096	+	0.0163096i
$894$	13.9165	+	23.4890i	0.465438	+	0.785589i
$895$	7.10510			0.237497
$896$	0.549011	−	0.377584i	0.0183412	−	0.0126142i
$897$	3.00820			0.100441
$898$	12.0435	+	20.3276i	0.401897	+	0.678341i
$899$	9.74749	+	9.74749i	0.325097	+	0.325097i
$900$	−0.960724	+	1.75414i	−0.0320241	+	0.0584714i
$901$	−40.7268	+	40.7268i	−1.35681	+	1.35681i
$902$	−8.53746	+	33.3611i	−0.284266	+	1.11080i
$903$		−	0.245067i		−	0.00815532i
$904$	−42.3552	+	1.43203i	−1.40871	+	0.0476286i
$905$			21.4059i			0.711557i
$906$	−18.4700	−	4.72665i	−0.613623	−	0.157033i
$907$	−11.1287	+	11.1287i	−0.369522	+	0.369522i	−0.867303	−	0.497781i	$-0.834148\pi$
$907$	−11.1287	+	11.1287i	−0.369522	+	0.369522i	0.497781	+	0.867303i	$0.334148\pi$
$908$	27.7234	−	8.10214i	0.920034	−	0.268879i
$909$	−0.663582	−	0.663582i	−0.0220096	−	0.0220096i
$910$	0.288685	−	0.171037i	0.00956980	−	0.00566982i
$911$	−40.1961			−1.33176			−0.665878	−	0.746061i	$-0.731943\pi$
$911$	−40.1961			−1.33176			−0.665878	+	0.746061i	$0.731943\pi$
$912$	−2.94212	+	1.88026i	−0.0974234	+	0.0622615i
$913$	−33.7207			−1.11599
$914$	31.0711	−	18.4087i	1.02774	−	0.608905i
$915$	−0.814225	−	0.814225i	−0.0269175	−	0.0269175i
$916$	13.5621	+	46.4061i	0.448106	+	1.53330i
$917$	−0.603429	+	0.603429i	−0.0199270	+	0.0199270i
$918$	8.19609	+	2.09747i	0.270511	+	0.0692267i
$919$			0.413348i			0.0136351i	0.999977	+	0.00681755i	$0.00217011\pi$
$919$			0.413348i			0.0136351i	−0.999977	+	0.00681755i	$0.997830\pi$
$920$	−1.54301	−	1.44208i	−0.0508714	−	0.0475440i
$921$			1.17672i			0.0387744i
$922$	−0.524199	+	2.04837i	−0.0172636	+	0.0674594i
$923$	21.0924	−	21.0924i	0.694266	−	0.694266i
$924$	−0.326231	−	0.178673i	−0.0107322	−	0.00587791i
$925$	2.01811	+	2.01811i	0.0663549	+	0.0663549i
$926$	−24.4337	−	41.2404i	−0.802941	−	1.35524i
$927$	14.9036			0.489499
$928$	8.66137	−	2.85230i	0.284323	−	0.0936314i
$929$	−28.8881			−0.947787			−0.473893	−	0.880582i	$-0.657152\pi$
$929$	−28.8881			−0.947787			−0.473893	+	0.880582i	$0.657152\pi$
$930$	6.16438	+	10.4045i	0.202138	+	0.341178i
$931$	−4.31853	−	4.31853i	−0.141534	−	0.141534i
$932$	−42.5219	−	23.2888i	−1.39285	−	0.762849i
$933$	−9.78465	+	9.78465i	−0.320335	+	0.320335i
$934$	−7.86707	+	30.7415i	−0.257418	+	1.00589i
$935$		−	18.8907i		−	0.617793i
$936$	−7.78048	+	8.32500i	−0.254313	+	0.272111i
$937$		−	5.60125i		−	0.182985i	−0.995806	−	0.0914925i	$-0.970836\pi$
$937$		−	5.60125i		−	0.182985i	0.995806	−	0.0914925i	$-0.0291637\pi$
$938$	0.623854	+	0.159651i	0.0203696	+	0.00521278i
$939$	−3.60044	+	3.60044i	−0.117496	+	0.117496i
$940$	−0.442999	−	1.51583i	−0.0144490	−	0.0494408i
$941$	−15.8730	−	15.8730i	−0.517446	−	0.517446i	0.399352	−	0.916798i	$-0.369235\pi$
$941$	−15.8730	−	15.8730i	−0.517446	−	0.517446i	−0.916798	+	0.399352i	$0.869235\pi$
$942$	19.1149	−	11.3250i	0.622798	−	0.368989i
$943$	−5.75788			−0.187502
$944$	51.7119	+	11.3867i	1.68308	+	0.370606i
$945$	−0.0588949			−0.00191585
$946$	15.9872	−	9.47195i	0.519789	−	0.307960i
$947$	12.0697	+	12.0697i	0.392214	+	0.392214i	0.875476	−	0.483262i	$-0.160548\pi$
$947$	12.0697	+	12.0697i	0.392214	+	0.392214i	−0.483262	+	0.875476i	$0.660548\pi$
$948$	33.4079	−	9.76344i	1.08504	−	0.317102i
$949$	−33.0774	+	33.0774i	−1.07374	+	1.07374i
$950$	1.19594	+	0.306053i	0.0388013	+	0.00992966i
$951$			23.0595i			0.747756i
$952$	0.0336734	+	0.995959i	0.00109136	+	0.0322792i
$953$			5.02008i			0.162616i	0.996689	+	0.0813081i	$0.0259098\pi$
$953$			5.02008i			0.162616i	−0.996689	+	0.0813081i	$0.974090\pi$
$954$	−3.37565	+	13.1907i	−0.109291	+	0.427066i
$955$	8.79820	−	8.79820i	0.284703	−	0.284703i
$956$	−20.2384	+	36.9524i	−0.654557	+	1.19513i
$957$	−3.59945	−	3.59945i	−0.116354	−	0.116354i
$958$	1.33393	+	2.25147i	0.0430972	+	0.0727416i
$959$	1.14559			0.0369930
$960$	7.98173	−	0.540343i	0.257609	−	0.0174395i
$961$	42.1270			1.35893
$962$	8.28840	+	13.9896i	0.267229	+	0.451042i
$963$	3.43861	+	3.43861i	0.110808	+	0.110808i
$964$	21.1915	−	38.6925i	0.682531	−	1.24620i
$965$	0.171072	−	0.171072i	0.00550701	−	0.00550701i
$966$	0.0154188	−	0.0602508i	0.000496092	−	0.00193854i
$967$		−	33.9334i		−	1.09123i	−0.838038	−	0.545613i	$-0.816297\pi$
$967$		−	33.9334i		−	1.09123i	0.838038	−	0.545613i	$-0.183703\pi$
$968$	0.0982892	+	2.90710i	0.00315914	+	0.0934378i
$969$		−	5.22197i		−	0.167754i
$970$	−16.8736	−	4.31813i	−0.541779	−	0.138647i
$971$	1.06974	−	1.06974i	0.0343297	−	0.0343297i	−0.689734	−	0.724063i	$-0.742272\pi$
$971$	1.06974	−	1.06974i	0.0343297	−	0.0343297i	0.724063	+	0.689734i	$0.242272\pi$
$972$	1.91970	−	0.561030i	0.0615744	−	0.0179951i
$973$	−0.0645409	−	0.0645409i	−0.00206909	−	0.00206909i
$974$	9.39530	−	5.56643i	0.301045	−	0.178360i
$975$	4.02867			0.129021
$976$	−0.990481	+	4.49820i	−0.0317045	+	0.143984i
$977$	−1.01239			−0.0323891			−0.0161946	−	0.999869i	$-0.505155\pi$
$977$	−1.01239			−0.0323891			−0.0161946	+	0.999869i	$0.505155\pi$
$978$	−3.40002	+	2.01441i	−0.108721	+	0.0644138i
$979$	−36.3978	−	36.3978i	−1.16328	−	1.16328i
$980$	3.92527	+	13.4312i	0.125388	+	0.429045i
$981$	−0.0571202	+	0.0571202i	−0.00182371	+	0.00182371i
$982$	−31.4444	−	8.04696i	−1.00343	−	0.256789i
$983$			27.2297i			0.868494i	0.900794	+	0.434247i	$0.142985\pi$
$983$			27.2297i			0.868494i	−0.900794	+	0.434247i	$0.857015\pi$
$984$	14.8923	−	15.9346i	0.474750	−	0.507976i
$985$			3.35537i			0.106911i
$986$	−3.38115	+	13.2122i	−0.107678	+	0.420763i
$987$	0.0328836	−	0.0328836i	0.00104670	−	0.00104670i
$988$	6.16870	+	3.37853i	0.196253	+	0.107485i
$989$	2.19703	+	2.19703i	0.0698616	+	0.0698616i
$990$	−2.27632	−	3.84208i	−0.0723461	−	0.122109i
$991$	2.24865			0.0714308			0.0357154	−	0.999362i	$-0.488629\pi$
$991$	2.24865			0.0714308			0.0357154	+	0.999362i	$0.488629\pi$
$992$	21.7902	−	43.1885i	0.691839	−	1.37124i
$993$	7.55119			0.239630
$994$	−0.314346	−	0.530569i	−0.00997046	−	0.0168286i
$995$	14.0202	+	14.0202i	0.444469	+	0.444469i
$996$	18.7318	+	10.2592i	0.593538	+	0.325074i
$997$	−11.6266	+	11.6266i	−0.368220	+	0.368220i	−0.866828	−	0.498608i	$-0.833845\pi$
$997$	−11.6266	+	11.6266i	−0.368220	+	0.368220i	0.498608	+	0.866828i	$0.333845\pi$
$998$	10.0397	−	39.2314i	0.317802	−	1.24185i
$999$		−	2.85403i		−	0.0902976i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.s.c.61.4	✓	20
3.2	odd	2		720.2.t.d.541.7		20
4.3	odd	2		960.2.s.c.721.3		20
8.3	odd	2		1920.2.s.f.1441.8		20
8.5	even	2		1920.2.s.e.1441.3		20
12.11	even	2		2880.2.t.d.721.3		20
16.3	odd	4		1920.2.s.f.481.8		20
16.5	even	4	inner	240.2.s.c.181.4	yes	20
16.11	odd	4		960.2.s.c.241.3		20
16.13	even	4		1920.2.s.e.481.3		20
48.5	odd	4		720.2.t.d.181.7		20
48.11	even	4		2880.2.t.d.2161.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.c.61.4	✓	20	1.1	even	1	trivial
240.2.s.c.181.4	yes	20	16.5	even	4	inner
720.2.t.d.181.7		20	48.5	odd	4
720.2.t.d.541.7		20	3.2	odd	2
960.2.s.c.241.3		20	16.11	odd	4
960.2.s.c.721.3		20	4.3	odd	2
1920.2.s.e.481.3		20	16.13	even	4
1920.2.s.e.1441.3		20	8.5	even	2
1920.2.s.f.481.8		20	16.3	odd	4
1920.2.s.f.1441.8		20	8.3	odd	2
2880.2.t.d.721.3		20	12.11	even	2
2880.2.t.d.2161.3		20	48.11	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.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.720859 - 1.21670i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.960724 + 1.75414i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.350613 - 1.37006i) q^{6} +0.0588949i q^{7} +(2.82681 - 0.0955746i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.720859 - 1.21670i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.960724 + 1.75414i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.350613 - 1.37006i) q^{6} +0.0588949i q^{7} +(2.82681 - 0.0955746i) q^{8} +1.00000i q^{9} +(-1.37006 - 0.350613i) q^{10} +(2.23289 - 2.23289i) q^{11} +(-1.91970 + 0.561030i) q^{12} +(2.84870 + 2.84870i) q^{13} +(0.0716575 - 0.0424550i) q^{14} +1.00000 q^{15} +(-2.15402 - 3.37049i) q^{16} +5.98228 q^{17} +(1.21670 - 0.720859i) q^{18} +(-0.617238 - 0.617238i) q^{19} +(0.561030 + 1.91970i) q^{20} +(-0.0416450 + 0.0416450i) q^{21} +(-4.32636 - 1.10716i) q^{22} -0.746698i q^{23} +(2.06644 + 1.93128i) q^{24} -1.00000i q^{25} +(1.41251 - 5.51953i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.103310 - 0.0565818i) q^{28} +(-1.13987 - 1.13987i) q^{29} +(-0.720859 - 1.21670i) q^{30} -8.55143 q^{31} +(-2.54813 + 5.05045i) q^{32} +3.15778 q^{33} +(-4.31238 - 7.27864i) q^{34} +(0.0416450 + 0.0416450i) q^{35} +(-1.75414 - 0.960724i) q^{36} +(-2.01811 + 2.01811i) q^{37} +(-0.306053 + 1.19594i) q^{38} +4.02867i q^{39} +(1.93128 - 2.06644i) q^{40} -7.71113i q^{41} +(0.0806897 + 0.0206493i) q^{42} +(-2.94233 + 2.94233i) q^{43} +(1.77161 + 6.06199i) q^{44} +(0.707107 + 0.707107i) q^{45} +(-0.908508 + 0.538264i) q^{46} -0.789616 q^{47} +(0.860175 - 3.90642i) q^{48} +6.99653 q^{49} +(-1.21670 + 0.720859i) q^{50} +(4.23011 + 4.23011i) q^{51} +(-7.73383 + 2.26021i) q^{52} +(-6.80791 + 6.80791i) q^{53} +(1.37006 + 0.350613i) q^{54} -3.15778i q^{55} +(0.00562886 + 0.166485i) q^{56} -0.872906i q^{57} +(-0.565194 + 2.20856i) q^{58} +(-9.36045 + 9.36045i) q^{59} +(-0.960724 + 1.75414i) q^{60} +(-0.814225 - 0.814225i) q^{61} +(6.16438 + 10.4045i) q^{62} -0.0588949 q^{63} +(7.98173 - 0.540343i) q^{64} +4.02867 q^{65} +(-2.27632 - 3.84208i) q^{66} +(5.46701 + 5.46701i) q^{67} +(-5.74732 + 10.4938i) q^{68} +(0.527995 - 0.527995i) q^{69} +(0.0206493 - 0.0806897i) q^{70} -7.40423i q^{71} +(0.0955746 + 2.82681i) q^{72} +11.6114i q^{73} +(3.91020 + 1.00066i) q^{74} +(0.707107 - 0.707107i) q^{75} +(1.67572 - 0.489727i) q^{76} +(0.131506 + 0.131506i) q^{77} +(4.90169 - 2.90410i) q^{78} -17.4027 q^{79} +(-3.90642 - 0.860175i) q^{80} -1.00000 q^{81} +(-9.38214 + 5.55864i) q^{82} +(-7.55090 - 7.55090i) q^{83} +(-0.0330419 - 0.113061i) q^{84} +(4.23011 - 4.23011i) q^{85} +(5.70095 + 1.45893i) q^{86} -1.61202i q^{87} +(6.09855 - 6.52537i) q^{88} -16.3007i q^{89} +(0.350613 - 1.37006i) q^{90} +(-0.167774 + 0.167774i) q^{91} +(1.30981 + 0.717370i) q^{92} +(-6.04678 - 6.04678i) q^{93} +(0.569202 + 0.960727i) q^{94} -0.872906 q^{95} +(-5.37301 + 1.76940i) q^{96} +12.3159 q^{97} +(-5.04351 - 8.51269i) q^{98} +(2.23289 + 2.23289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} + 12 q^{8}+O(q^{10}) \) 20 * q + 4 * q^4 + 12 * q^8	\( 20 q + 4 q^{4} + 12 q^{8} + 8 q^{11} - 4 q^{14} + 20 q^{15} - 20 q^{16} - 24 q^{17} - 4 q^{18} - 4 q^{19} - 8 q^{20} + 8 q^{22} + 28 q^{26} - 8 q^{28} + 16 q^{29} - 40 q^{32} + 16 q^{33} - 44 q^{34} + 16 q^{37} - 8 q^{38} + 12 q^{40} + 12 q^{42} - 8 q^{43} + 24 q^{44} - 12 q^{46} - 16 q^{48} - 52 q^{49} + 4 q^{50} + 4 q^{51} - 56 q^{52} - 16 q^{53} + 64 q^{56} + 72 q^{58} - 16 q^{59} + 4 q^{60} - 4 q^{61} - 44 q^{62} - 8 q^{63} - 56 q^{64} - 32 q^{66} - 8 q^{67} - 32 q^{68} - 4 q^{69} + 20 q^{70} + 4 q^{72} + 60 q^{74} + 28 q^{76} - 40 q^{77} - 28 q^{78} + 56 q^{79} - 16 q^{80} - 20 q^{81} - 24 q^{82} - 48 q^{83} + 24 q^{84} + 4 q^{85} + 64 q^{86} + 40 q^{88} - 8 q^{91} + 88 q^{92} + 16 q^{93} - 20 q^{94} + 56 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) \) 20 * q + 4 * q^4 + 12 * q^8 + 8 * q^11 - 4 * q^14 + 20 * q^15 - 20 * q^16 - 24 * q^17 - 4 * q^18 - 4 * q^19 - 8 * q^20 + 8 * q^22 + 28 * q^26 - 8 * q^28 + 16 * q^29 - 40 * q^32 + 16 * q^33 - 44 * q^34 + 16 * q^37 - 8 * q^38 + 12 * q^40 + 12 * q^42 - 8 * q^43 + 24 * q^44 - 12 * q^46 - 16 * q^48 - 52 * q^49 + 4 * q^50 + 4 * q^51 - 56 * q^52 - 16 * q^53 + 64 * q^56 + 72 * q^58 - 16 * q^59 + 4 * q^60 - 4 * q^61 - 44 * q^62 - 8 * q^63 - 56 * q^64 - 32 * q^66 - 8 * q^67 - 32 * q^68 - 4 * q^69 + 20 * q^70 + 4 * q^72 + 60 * q^74 + 28 * q^76 - 40 * q^77 - 28 * q^78 + 56 * q^79 - 16 * q^80 - 20 * q^81 - 24 * q^82 - 48 * q^83 + 24 * q^84 + 4 * q^85 + 64 * q^86 + 40 * q^88 - 8 * q^91 + 88 * q^92 + 16 * q^93 - 20 * q^94 + 56 * q^97 - 48 * q^98 + 8 * q^99

Introduction

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