LMFDB - Embedded newform 483.2.q.c.400.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
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} - 8 x^{19} + 40 x^{18} - 117 x^{17} + 295 x^{16} - 575 x^{15} + 1777 x^{14} - 1560 x^{13} + \cdots + 2374681 $ x^20 - 8x^19 + 40x^18 - 117x^17 + 295x^16 - 575x^15 + 1777x^14 - 1560x^13 + 4383x^12 - 6446x^11 + 7261x^10 + 7700x^9 + 7852x^8 - 39430x^7 - 101709x^6 + 156742x^5 + 999838x^4 + 2029154x^3 + 3616480x^2 + 4299390*x + 2374681
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			400.2
Root			$-1.22309 - 0.359132i$ of defining polynomial
Character	$\chi$	$=$	483.400
Dual form			483.2.q.c.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.273100 - 0.0801894i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(-1.61435 + 1.03748i) q^{4} +(0.454513 + 3.16121i) q^{5} +(-0.239446 - 0.153882i) q^{6} +(0.415415 - 0.909632i) q^{7} +(-0.730471 + 0.843008i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.273100 - 0.0801894i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(-1.61435 + 1.03748i) q^{4} +(0.454513 + 3.16121i) q^{5} +(-0.239446 - 0.153882i) q^{6} +(0.415415 - 0.909632i) q^{7} +(-0.730471 + 0.843008i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.377623 + 0.826879i) q^{10} +(-3.73000 - 1.09523i) q^{11} +(1.84125 + 0.540641i) q^{12} +(-1.84701 - 4.04439i) q^{13} +(0.0405070 - 0.281733i) q^{14} +(2.09144 - 2.41365i) q^{15} +(1.46246 - 3.20234i) q^{16} +(-2.23654 - 1.43733i) q^{17} +(0.0405070 + 0.281733i) q^{18} +(-4.23642 + 2.72258i) q^{19} +(-4.01344 - 4.63175i) q^{20} +(-0.959493 + 0.281733i) q^{21} -1.10649 q^{22} +(-4.38081 + 1.95154i) q^{23} +1.11546 q^{24} +(-4.98917 + 1.46495i) q^{25} +(-0.828736 - 0.956413i) q^{26} +(0.841254 - 0.540641i) q^{27} +(0.273100 + 1.89945i) q^{28} +(3.44308 + 2.21273i) q^{29} +(0.377623 - 0.826879i) q^{30} +(-0.0545500 + 0.0629540i) q^{31} +(0.460097 - 3.20005i) q^{32} +(1.61491 + 3.53617i) q^{33} +(-0.726057 - 0.213190i) q^{34} +(3.06434 + 0.899773i) q^{35} +(-0.797176 - 1.74557i) q^{36} +(-0.916586 + 6.37500i) q^{37} +(-0.938644 + 1.08325i) q^{38} +(-1.84701 + 4.04439i) q^{39} +(-2.99693 - 1.92601i) q^{40} +(0.804363 + 5.59447i) q^{41} +(-0.239446 + 0.153882i) q^{42} +(-7.78299 - 8.98205i) q^{43} +(7.15782 - 2.10172i) q^{44} -3.19371 q^{45} +(-1.03991 + 0.884260i) q^{46} -4.31364 q^{47} +(-3.37787 + 0.991834i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(-1.24507 + 0.800158i) q^{50} +(0.378355 + 2.63151i) q^{51} +(7.17771 + 4.61284i) q^{52} +(0.873996 - 1.91378i) q^{53} +(0.186393 - 0.215109i) q^{54} +(1.76690 - 12.2891i) q^{55} +(0.463379 + 1.01466i) q^{56} +(4.83185 + 1.41876i) q^{57} +(1.11774 + 0.328199i) q^{58} +(4.32749 + 9.47587i) q^{59} +(-0.872204 + 6.06631i) q^{60} +(-1.07121 + 1.23624i) q^{61} +(-0.00984935 + 0.0215671i) q^{62} +(0.841254 + 0.540641i) q^{63} +(0.871076 + 6.05846i) q^{64} +(11.9457 - 7.67701i) q^{65} +(0.724596 + 0.836229i) q^{66} +(1.83941 - 0.540100i) q^{67} +5.10177 q^{68} +(4.34369 + 2.03281i) q^{69} +0.909025 q^{70} +(6.43184 - 1.88856i) q^{71} +(-0.730471 - 0.843008i) q^{72} +(-6.47684 + 4.16241i) q^{73} +(0.260888 + 1.81451i) q^{74} +(4.37435 + 2.81122i) q^{75} +(4.01445 - 8.79042i) q^{76} +(-2.54575 + 2.93795i) q^{77} +(-0.180102 + 1.25263i) q^{78} +(-7.15552 - 15.6684i) q^{79} +(10.7880 + 3.16763i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(0.668289 + 1.46335i) q^{82} +(-1.19449 + 8.30784i) q^{83} +(1.25667 - 1.45027i) q^{84} +(3.52717 - 7.72344i) q^{85} +(-2.84580 - 1.82889i) q^{86} +(-0.582466 - 4.05114i) q^{87} +(3.64794 - 2.34439i) q^{88} +(4.98867 + 5.75723i) q^{89} +(-0.872204 + 0.256102i) q^{90} -4.44618 q^{91} +(5.04749 - 7.69548i) q^{92} +0.0833001 q^{93} +(-1.17806 + 0.345909i) q^{94} +(-10.5321 - 12.1547i) q^{95} +(-2.71973 + 1.74787i) q^{96} +(0.625311 + 4.34913i) q^{97} +(-0.239446 - 0.153882i) q^{98} +(1.61491 - 3.53617i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9} + 9 q^{10} + 3 q^{11} + 18 q^{12} - 2 q^{13} + 18 q^{14} - q^{15} + 8 q^{16} + 8 q^{17} + 18 q^{18} + 6 q^{19} - 2 q^{20} - 2 q^{21} + 6 q^{22} + 11 q^{23} + 9 q^{25} + 7 q^{26} - 2 q^{27} - 4 q^{28} + 23 q^{29} + 9 q^{30} + q^{31} - 28 q^{32} + 14 q^{33} - 28 q^{34} + 10 q^{35} - 4 q^{36} - 9 q^{37} + 34 q^{38} - 2 q^{39} - 15 q^{41} - 4 q^{42} - 23 q^{43} - 16 q^{44} - 12 q^{45} + 11 q^{46} - 66 q^{47} - 36 q^{48} - 2 q^{49} - 26 q^{50} - 14 q^{51} + 7 q^{52} + 9 q^{53} - 4 q^{54} - 62 q^{55} + 22 q^{56} - 27 q^{57} - 20 q^{58} + 49 q^{59} - 2 q^{60} + 46 q^{61} - 9 q^{62} - 2 q^{63} + 16 q^{64} + 11 q^{65} - 16 q^{66} + 14 q^{67} + 38 q^{68} + 11 q^{69} - 2 q^{70} + 36 q^{71} - q^{73} + 4 q^{74} - 2 q^{75} + 34 q^{76} - 8 q^{77} - 15 q^{78} - 22 q^{79} + 15 q^{80} - 2 q^{81} - 30 q^{82} + 8 q^{83} - 4 q^{84} - 32 q^{85} - 68 q^{86} + q^{87} - 11 q^{88} - 2 q^{89} - 2 q^{90} - 24 q^{91} + 11 q^{92} - 32 q^{93} + 33 q^{94} - 107 q^{95} + 16 q^{96} + 18 q^{97} - 4 q^{98} + 14 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9 + 9 * q^10 + 3 * q^11 + 18 * q^12 - 2 * q^13 + 18 * q^14 - q^15 + 8 * q^16 + 8 * q^17 + 18 * q^18 + 6 * q^19 - 2 * q^20 - 2 * q^21 + 6 * q^22 + 11 * q^23 + 9 * q^25 + 7 * q^26 - 2 * q^27 - 4 * q^28 + 23 * q^29 + 9 * q^30 + q^31 - 28 * q^32 + 14 * q^33 - 28 * q^34 + 10 * q^35 - 4 * q^36 - 9 * q^37 + 34 * q^38 - 2 * q^39 - 15 * q^41 - 4 * q^42 - 23 * q^43 - 16 * q^44 - 12 * q^45 + 11 * q^46 - 66 * q^47 - 36 * q^48 - 2 * q^49 - 26 * q^50 - 14 * q^51 + 7 * q^52 + 9 * q^53 - 4 * q^54 - 62 * q^55 + 22 * q^56 - 27 * q^57 - 20 * q^58 + 49 * q^59 - 2 * q^60 + 46 * q^61 - 9 * q^62 - 2 * q^63 + 16 * q^64 + 11 * q^65 - 16 * q^66 + 14 * q^67 + 38 * q^68 + 11 * q^69 - 2 * q^70 + 36 * q^71 - q^73 + 4 * q^74 - 2 * q^75 + 34 * q^76 - 8 * q^77 - 15 * q^78 - 22 * q^79 + 15 * q^80 - 2 * q^81 - 30 * q^82 + 8 * q^83 - 4 * q^84 - 32 * q^85 - 68 * q^86 + q^87 - 11 * q^88 - 2 * q^89 - 2 * q^90 - 24 * q^91 + 11 * q^92 - 32 * q^93 + 33 * q^94 - 107 * q^95 + 16 * q^96 + 18 * q^97 - 4 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{11}\right)$

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 $

$2$	0.273100	−	0.0801894i	0.193111	−	0.0567025i	−0.183747	−	0.982974i	$-0.558823\pi$
$2$	0.273100	−	0.0801894i	0.193111	−	0.0567025i	0.376858	+	0.926271i	$0.377005\pi$
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$4$	−1.61435	+	1.03748i	−0.807177	+	0.518741i
$5$	0.454513	+	3.16121i	0.203264	+	1.41373i	0.794514	+	0.607246i	$0.207726\pi$
$5$	0.454513	+	3.16121i	0.203264	+	1.41373i	−0.591250	+	0.806488i	$0.701365\pi$
$6$	−0.239446	−	0.153882i	−0.0977533	−	0.0628222i
$7$	0.415415	−	0.909632i	0.157012	−	0.343809i
$7$	0.415415	−	0.909632i	0.157012	−	0.343809i
$8$	−0.730471	+	0.843008i	−0.258260	+	0.298048i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	0.377623	+	0.826879i	0.119415	+	0.261482i
$11$	−3.73000	−	1.09523i	−1.12464	−	0.330223i	−0.334039	−	0.942559i	$-0.608412\pi$
$11$	−3.73000	−	1.09523i	−1.12464	−	0.330223i	−0.790598	+	0.612336i	$0.790230\pi$
$12$	1.84125	+	0.540641i	0.531524	+	0.156070i
$13$	−1.84701	−	4.04439i	−0.512269	−	1.12171i	−0.972284	−	0.233801i	$-0.924884\pi$
$13$	−1.84701	−	4.04439i	−0.512269	−	1.12171i	0.460016	−	0.887911i	$-0.347844\pi$
$14$	0.0405070	−	0.281733i	0.0108260	−	0.0752962i
$15$	2.09144	−	2.41365i	0.540007	−	0.623201i
$16$	1.46246	−	3.20234i	0.365615	−	0.800585i
$17$	−2.23654	−	1.43733i	−0.542440	−	0.348605i	0.240553	−	0.970636i	$-0.422671\pi$
$17$	−2.23654	−	1.43733i	−0.542440	−	0.348605i	−0.782992	+	0.622031i	$0.786308\pi$
$18$	0.0405070	+	0.281733i	0.00954760	+	0.0664050i
$19$	−4.23642	+	2.72258i	−0.971901	+	0.624603i	−0.927267	−	0.374401i	$-0.877848\pi$
$19$	−4.23642	+	2.72258i	−0.971901	+	0.624603i	−0.0446338	+	0.999003i	$0.514212\pi$
$20$	−4.01344	−	4.63175i	−0.897432	−	1.03569i
$21$	−0.959493	+	0.281733i	−0.209379	+	0.0614791i
$22$	−1.10649			−0.235904
$23$	−4.38081	+	1.95154i	−0.913462	+	0.406924i
$23$	−4.38081	+	1.95154i	−0.913462	+	0.406924i
$24$	1.11546			0.227692
$25$	−4.98917	+	1.46495i	−0.997835	+	0.292991i
$26$	−0.828736	−	0.956413i	−0.162529	−	0.187568i
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$	0.273100	+	1.89945i	0.0516111	+	0.358963i
$29$	3.44308	+	2.21273i	0.639364	+	0.410894i	0.819766	−	0.572699i	$-0.194103\pi$
$29$	3.44308	+	2.21273i	0.639364	+	0.410894i	−0.180402	+	0.983593i	$0.557740\pi$
$30$	0.377623	−	0.826879i	0.0689442	−	0.150967i
$31$	−0.0545500	+	0.0629540i	−0.00979746	+	0.0113069i	−0.760627	−	0.649189i	$-0.775108\pi$
$31$	−0.0545500	+	0.0629540i	−0.00979746	+	0.0113069i	0.750830	+	0.660496i	$0.229654\pi$
$32$	0.460097	−	3.20005i	0.0813344	−	0.565693i
$33$	1.61491	+	3.53617i	0.281120	+	0.615567i
$34$	−0.726057	−	0.213190i	−0.124518	−	0.0365617i
$35$	3.06434	+	0.899773i	0.517969	+	0.152089i
$36$	−0.797176	−	1.74557i	−0.132863	−	0.290929i
$37$	−0.916586	+	6.37500i	−0.150686	+	1.04804i	0.764388	+	0.644756i	$0.223041\pi$
$37$	−0.916586	+	6.37500i	−0.150686	+	1.04804i	−0.915074	+	0.403286i	$0.867868\pi$
$38$	−0.938644	+	1.08325i	−0.152268	+	0.175727i
$39$	−1.84701	+	4.04439i	−0.295758	+	0.647621i
$40$	−2.99693	−	1.92601i	−0.473856	−	0.304529i
$41$	0.804363	+	5.59447i	0.125620	+	0.873709i	0.951013	+	0.309150i	$0.100045\pi$
$41$	0.804363	+	5.59447i	0.125620	+	0.873709i	−0.825393	+	0.564559i	$0.809046\pi$
$42$	−0.239446	+	0.153882i	−0.0369473	+	0.0237446i
$43$	−7.78299	−	8.98205i	−1.18690	−	1.36975i	−0.912984	−	0.407995i	$-0.866228\pi$
$43$	−7.78299	−	8.98205i	−1.18690	−	1.36975i	−0.273911	−	0.961755i	$-0.588317\pi$
$44$	7.15782	−	2.10172i	1.07908	−	0.316847i
$45$	−3.19371			−0.476091
$46$	−1.03991	+	0.884260i	−0.153326	+	0.130377i
$47$	−4.31364			−0.629209			−0.314605	−	0.949223i	$-0.601872\pi$
$47$	−4.31364			−0.629209			−0.314605	+	0.949223i	$0.601872\pi$
$48$	−3.37787	+	0.991834i	−0.487554	+	0.143159i
$49$	−0.654861	−	0.755750i	−0.0935515	−	0.107964i
$50$	−1.24507	+	0.800158i	−0.176080	+	0.113159i
$51$	0.378355	+	2.63151i	0.0529803	+	0.368486i
$52$	7.17771	+	4.61284i	0.995370	+	0.639685i
$53$	0.873996	−	1.91378i	0.120053	−	0.262878i	−0.840059	−	0.542495i	$-0.817480\pi$
$53$	0.873996	−	1.91378i	0.120053	−	0.262878i	0.960112	+	0.279616i	$0.0902072\pi$
$54$	0.186393	−	0.215109i	0.0253648	−	0.0292726i
$55$	1.76690	−	12.2891i	0.238249	−	1.65706i
$56$	0.463379	+	1.01466i	0.0619216	+	0.135589i
$57$	4.83185	+	1.41876i	0.639995	+	0.187919i
$58$	1.11774	+	0.328199i	0.146767	+	0.0430947i
$59$	4.32749	+	9.47587i	0.563391	+	1.23365i	0.950242	+	0.311512i	$0.100835\pi$
$59$	4.32749	+	9.47587i	0.563391	+	1.23365i	−0.386852	+	0.922142i	$0.626437\pi$
$60$	−0.872204	+	6.06631i	−0.112601	+	0.783157i
$61$	−1.07121	+	1.23624i	−0.137154	+	0.158284i	−0.820171	−	0.572118i	$-0.806122\pi$
$61$	−1.07121	+	1.23624i	−0.137154	+	0.158284i	0.683017	+	0.730402i	$0.260667\pi$
$62$	−0.00984935	+	0.0215671i	−0.00125087	+	0.00273902i
$63$	0.841254	+	0.540641i	0.105988	+	0.0681143i
$64$	0.871076	+	6.05846i	0.108884	+	0.757308i
$65$	11.9457	−	7.67701i	1.48168	−	0.952216i
$66$	0.724596	+	0.836229i	0.0891916	+	0.102933i
$67$	1.83941	−	0.540100i	0.224720	−	0.0659837i	−0.167434	−	0.985883i	$-0.553548\pi$
$67$	1.83941	−	0.540100i	0.224720	−	0.0659837i	0.392154	+	0.919900i	$0.371730\pi$
$68$	5.10177			0.618680
$69$	4.34369	+	2.03281i	0.522919	+	0.244722i
$70$	0.909025			0.108649
$71$	6.43184	−	1.88856i	0.763319	−	0.224131i	0.123174	−	0.992385i	$-0.460693\pi$
$71$	6.43184	−	1.88856i	0.763319	−	0.224131i	0.640145	+	0.768254i	$0.278874\pi$
$72$	−0.730471	−	0.843008i	−0.0860868	−	0.0993495i
$73$	−6.47684	+	4.16241i	−0.758056	+	0.487173i	−0.861685	−	0.507443i	$-0.830591\pi$
$73$	−6.47684	+	4.16241i	−0.758056	+	0.487173i	0.103629	+	0.994616i	$0.466955\pi$
$74$	0.260888	+	1.81451i	0.0303276	+	0.210933i
$75$	4.37435	+	2.81122i	0.505107	+	0.324612i
$76$	4.01445	−	8.79042i	0.460489	−	1.00833i
$77$	−2.54575	+	2.93795i	−0.290115	+	0.334811i
$78$	−0.180102	+	1.25263i	−0.0203925	+	0.141833i
$79$	−7.15552	−	15.6684i	−0.805059	−	1.76283i	−0.627330	−	0.778754i	$-0.715852\pi$
$79$	−7.15552	−	15.6684i	−0.805059	−	1.76283i	−0.177729	−	0.984079i	$-0.556875\pi$
$80$	10.7880	+	3.16763i	1.20613	+	0.354152i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	0.668289	+	1.46335i	0.0738001	+	0.161600i
$83$	−1.19449	+	8.30784i	−0.131112	+	0.911904i	0.812996	+	0.582269i	$0.197835\pi$
$83$	−1.19449	+	8.30784i	−0.131112	+	0.911904i	−0.944108	+	0.329635i	$0.893074\pi$
$84$	1.25667	−	1.45027i	0.137114	−	0.158238i
$85$	3.52717	−	7.72344i	0.382576	−	0.837724i
$86$	−2.84580	−	1.82889i	−0.306871	−	0.197214i
$87$	−0.582466	−	4.05114i	−0.0624469	−	0.434328i
$88$	3.64794	−	2.34439i	0.388872	−	0.249913i
$89$	4.98867	+	5.75723i	0.528798	+	0.610266i	0.955812	−	0.293980i	$-0.0949798\pi$
$89$	4.98867	+	5.75723i	0.528798	+	0.610266i	−0.427014	+	0.904245i	$0.640434\pi$
$90$	−0.872204	+	0.256102i	−0.0919383	+	0.0269955i
$91$	−4.44618			−0.466087
$92$	5.04749	−	7.69548i	0.526237	−	0.802310i
$93$	0.0833001			0.00863782
$94$	−1.17806	+	0.345909i	−0.121507	+	0.0356777i
$95$	−10.5321	−	12.1547i	−1.08057	−	1.24705i
$96$	−2.71973	+	1.74787i	−0.277582	+	0.178391i
$97$	0.625311	+	4.34913i	0.0634907	+	0.441587i	0.996627	+	0.0820647i	$0.0261514\pi$
$97$	0.625311	+	4.34913i	0.0634907	+	0.441587i	−0.933136	+	0.359523i	$0.882940\pi$
$98$	−0.239446	−	0.153882i	−0.0241877	−	0.0155445i
$99$	1.61491	−	3.53617i	0.162305	−	0.355398i
$100$	6.53443	−	7.54113i	0.653443	−	0.754113i
$101$	−1.02948	+	7.16017i	−0.102437	+	0.712464i	0.872278	+	0.489011i	$0.162642\pi$
$101$	−1.02948	+	7.16017i	−0.102437	+	0.712464i	−0.974715	+	0.223453i	$0.928267\pi$
$102$	0.314348	+	0.688327i	0.0311251	+	0.0681545i
$103$	−15.2106	−	4.46624i	−1.49875	−	0.440072i	−0.573426	−	0.819257i	$-0.694386\pi$
$103$	−15.2106	−	4.46624i	−1.49875	−	0.440072i	−0.925321	+	0.379186i	$0.876204\pi$
$104$	4.75864	+	1.39726i	0.466623	+	0.137013i
$105$	−1.32672	−	2.90510i	−0.129474	−	0.283509i
$106$	0.0852231	−	0.592740i	0.00827760	−	0.0575720i
$107$	9.12999	−	10.5366i	0.882629	−	1.01861i	−0.117046	−	0.993127i	$-0.537342\pi$
$107$	9.12999	−	10.5366i	0.882629	−	1.01861i	0.999675	−	0.0254821i	$-0.00811208\pi$
$108$	−0.797176	+	1.74557i	−0.0767083	+	0.167968i
$109$	14.3579	+	9.22729i	1.37524	+	0.883814i	0.999086	−	0.0427432i	$-0.0136097\pi$
$109$	14.3579	+	9.22729i	1.37524	+	0.883814i	0.376155	+	0.926557i	$0.377246\pi$
$110$	−0.502913	−	3.49784i	−0.0479509	−	0.333506i
$111$	5.41814	−	3.48202i	0.514267	−	0.330499i
$112$	−2.30542	−	2.66060i	−0.217842	−	0.251403i
$113$	0.815872	−	0.239562i	0.0767508	−	0.0225361i	−0.243132	−	0.969993i	$-0.578175\pi$
$113$	0.815872	−	0.239562i	0.0767508	−	0.0225361i	0.319883	+	0.947457i	$0.396357\pi$
$114$	1.43335			0.134245
$115$	−8.16034	−	12.9616i	−0.760956	−	1.20868i
$116$	−7.85402			−0.729228
$117$	4.26608	−	1.25263i	0.394399	−	0.115806i
$118$	1.94170	+	2.24084i	0.178748	+	0.206286i
$119$	−2.23654	+	1.43733i	−0.205023	+	0.131760i
$120$	0.506991	+	3.52620i	0.0462817	+	0.321896i
$121$	3.45958	+	2.22334i	0.314507	+	0.202122i
$122$	−0.193414	+	0.423517i	−0.0175108	+	0.0383434i
$123$	3.70127	−	4.27149i	0.333732	−	0.385148i
$124$	0.0227493	−	0.158225i	0.00204294	−	0.0142090i
$125$	−0.265079	−	0.580443i	−0.0237094	−	0.0519164i
$126$	0.273100	+	0.0801894i	0.0243297	+	0.00714384i
$127$	−4.37471	−	1.28453i	−0.388193	−	0.113984i	0.0818116	−	0.996648i	$-0.473929\pi$
$127$	−4.37471	−	1.28453i	−0.388193	−	0.113984i	−0.470004	+	0.882664i	$0.655748\pi$
$128$	3.40975	+	7.46631i	0.301382	+	0.659935i
$129$	−1.69141	+	11.7640i	−0.148920	+	1.03576i
$130$	2.64675	−	3.05451i	0.232135	−	0.267898i
$131$	−6.88944	+	15.0858i	−0.601933	+	1.31805i	0.326024	+	0.945362i	$0.394291\pi$
$131$	−6.88944	+	15.0858i	−0.601933	+	1.31805i	−0.927957	+	0.372688i	$0.878436\pi$
$132$	−6.27575	−	4.03318i	−0.546234	−	0.351043i
$133$	0.716675	+	4.98458i	0.0621436	+	0.432218i
$134$	0.459033	−	0.295003i	0.0396544	−	0.0254843i
$135$	2.09144	+	2.41365i	0.180002	+	0.207734i
$136$	2.84541	−	0.835487i	0.243992	−	0.0716424i
$137$	5.91771			0.505584			0.252792	−	0.967521i	$-0.418651\pi$
$137$	5.91771			0.505584			0.252792	+	0.967521i	$0.418651\pi$
$138$	1.34927	+	0.206842i	0.114858	+	0.0176076i
$139$	15.0236			1.27429			0.637144	−	0.770744i	$-0.280115\pi$
$139$	15.0236			1.27429			0.637144	+	0.770744i	$0.280115\pi$
$140$	−5.88043	+	1.72665i	−0.496987	+	0.145929i
$141$	2.82483	+	3.26003i	0.237894	+	0.274544i
$142$	1.60509	−	1.03153i	0.134696	−	0.0865642i
$143$	2.45983	+	17.1085i	0.205701	+	1.43068i
$144$	2.96162	+	1.90331i	0.246801	+	0.158610i
$145$	−5.42998	+	11.8900i	−0.450935	+	0.987411i
$146$	−1.43504	+	1.65613i	−0.118765	+	0.137062i
$147$	−0.142315	+	0.989821i	−0.0117379	+	0.0816391i
$148$	−5.13425	−	11.2424i	−0.422033	−	0.924123i
$149$	−22.3665	−	6.56739i	−1.83233	−	0.538021i	−0.832461	−	0.554083i	$-0.813069\pi$
$149$	−22.3665	−	6.56739i	−1.83233	−	0.538021i	−0.999871	+	0.0160618i	$0.994887\pi$
$150$	1.42007	+	0.416969i	0.115948	+	0.0340454i
$151$	7.34419	+	16.0815i	0.597662	+	1.30870i	0.930700	+	0.365783i	$0.119199\pi$
$151$	7.34419	+	16.0815i	0.597662	+	1.30870i	−0.333038	+	0.942913i	$0.608074\pi$
$152$	0.799422	−	5.56010i	0.0648417	−	0.450984i
$153$	1.74100	−	2.00922i	0.140751	−	0.162436i
$154$	−0.459652	+	1.00650i	−0.0370398	+	0.0811059i
$155$	−0.223804	−	0.143830i	−0.0179764	−	0.0115527i
$156$	−1.21425	−	8.44532i	−0.0972181	−	0.676167i
$157$	−4.71970	+	3.03317i	−0.376673	+	0.242073i	−0.715255	−	0.698864i	$-0.753689\pi$
$157$	−4.71970	+	3.03317i	−0.376673	+	0.242073i	0.338581	+	0.940937i	$0.390053\pi$
$158$	−3.21061	−	3.70525i	−0.255423	−	0.294774i
$159$	−2.01869	+	0.592740i	−0.160092	+	0.0470073i
$160$	10.3251			0.816272
$161$	−0.0446736	+	4.79562i	−0.00352077	+	0.377948i
$162$	−0.284630			−0.0223626
$163$	−5.76985	+	1.69418i	−0.451929	+	0.132698i	−0.499773	−	0.866156i	$-0.666583\pi$
$163$	−5.76985	+	1.69418i	−0.451929	+	0.132698i	0.0478437	+	0.998855i	$0.484765\pi$
$164$	−7.10268	−	8.19693i	−0.554626	−	0.640073i
$165$	−10.4445	+	6.71230i	−0.813107	+	0.522552i
$166$	0.339986	+	2.36466i	0.0263881	+	0.183533i
$167$	−0.554261	−	0.356202i	−0.0428900	−	0.0275637i	0.519020	−	0.854762i	$-0.326297\pi$
$167$	−0.554261	−	0.356202i	−0.0428900	−	0.0275637i	−0.561910	+	0.827198i	$0.689933\pi$
$168$	0.463379	−	1.01466i	0.0357504	−	0.0782826i
$169$	−4.43245	+	5.11532i	−0.340958	+	0.393486i
$170$	0.343934	−	2.39211i	0.0263785	−	0.183467i
$171$	−2.09196	−	4.58076i	−0.159976	−	0.350300i
$172$	21.8832	+	6.42549i	1.66858	+	0.489939i
$173$	9.37221	+	2.75193i	0.712556	+	0.209225i	0.617868	−	0.786282i	$-0.287997\pi$
$173$	9.37221	+	2.75193i	0.712556	+	0.209225i	0.0946876	+	0.995507i	$0.469815\pi$
$174$	−0.483930	−	1.05966i	−0.0366866	−	0.0803325i
$175$	−0.740009	+	5.14687i	−0.0559394	+	0.389067i
$176$	−8.96226	+	10.3430i	−0.675556	+	0.779633i
$177$	4.32749	−	9.47587i	0.325274	−	0.712250i
$178$	1.82408	+	1.17226i	0.136720	+	0.0878648i
$179$	3.12141	+	21.7099i	0.233305	+	1.62267i	0.683646	+	0.729814i	$0.260393\pi$
$179$	3.12141	+	21.7099i	0.233305	+	1.62267i	−0.450341	+	0.892857i	$0.648697\pi$
$180$	5.15578	−	3.31342i	0.384289	−	0.246968i
$181$	0.254978	+	0.294260i	0.0189523	+	0.0218722i	0.765147	−	0.643856i	$-0.222666\pi$
$181$	0.254978	+	0.294260i	0.0189523	+	0.0218722i	−0.746194	+	0.665728i	$0.768121\pi$
$182$	−1.21425	+	0.356537i	−0.0900064	+	0.0264283i
$183$	1.63578			0.120920
$184$	1.55489	−	5.11860i	0.114628	−	0.377348i
$185$	−20.5693			−1.51228
$186$	0.0227493	−	0.00667979i	0.00166806	−	0.000489786i
$187$	6.76807	+	7.81077i	0.494930	+	0.571180i
$188$	6.96374	−	4.47533i	0.507883	−	0.326397i
$189$	−0.142315	−	0.989821i	−0.0103519	−	0.0719989i
$190$	−3.85101	−	2.47489i	−0.279382	−	0.179548i
$191$	9.26532	−	20.2882i	0.670415	−	1.46800i	−0.202074	−	0.979370i	$-0.564768\pi$
$191$	9.26532	−	20.2882i	0.670415	−	1.46800i	0.872489	−	0.488634i	$-0.162504\pi$
$192$	4.00825	−	4.62576i	0.289270	−	0.333836i
$193$	0.700781	−	4.87404i	0.0504433	−	0.350841i	−0.948931	−	0.315483i	$-0.897834\pi$
$193$	0.700781	−	4.87404i	0.0504433	−	0.350841i	0.999375	−	0.0353585i	$-0.0112573\pi$
$194$	0.519527	+	1.13761i	0.0372999	+	0.0816753i
$195$	−13.6246	−	4.00055i	−0.975681	−	0.286486i
$196$	1.84125	+	0.540641i	0.131518	+	0.0386172i
$197$	0.400714	+	0.877441i	0.0285497	+	0.0625151i	0.923370	−	0.383912i	$-0.125423\pi$
$197$	0.400714	+	0.877441i	0.0285497	+	0.0625151i	−0.894820	+	0.446427i	$0.852696\pi$
$198$	0.157470	−	1.09523i	0.0111909	−	0.0778344i
$199$	14.2238	−	16.4152i	1.00830	−	1.16364i	0.0218213	−	0.999762i	$-0.493054\pi$
$199$	14.2238	−	16.4152i	1.00830	−	1.16364i	0.986480	−	0.163880i	$-0.0524010\pi$
$200$	2.40948	−	5.27602i	0.170376	−	0.373071i
$201$	−1.61274	−	1.03644i	−0.113754	−	0.0731051i
$202$	0.293020	+	2.03800i	0.0206168	+	0.143393i
$203$	3.44308	−	2.21273i	0.241657	−	0.155303i
$204$	−3.34095	−	3.85566i	−0.233913	−	0.269950i
$205$	−17.3197	+	5.08551i	−1.20966	+	0.355188i
$206$	−4.51217			−0.314378
$207$	−1.30822	−	4.61395i	−0.0909275	−	0.320692i
$208$	−15.6527			−1.08532
$209$	18.7837	−	5.51538i	1.29929	−	0.381507i
$210$	−0.595285	−	0.686996i	−0.0410786	−	0.0474072i
$211$	−21.0679	+	13.5395i	−1.45038	+	0.932100i	−0.451163	+	0.892441i	$0.648991\pi$
$211$	−21.0679	+	13.5395i	−1.45038	+	0.932100i	−0.999213	+	0.0396590i	$0.987373\pi$
$212$	0.574578	+	3.99628i	0.0394622	+	0.274466i
$213$	−5.63924	−	3.62412i	−0.386394	−	0.248320i
$214$	1.64848	−	3.60967i	0.112688	−	0.246752i
$215$	24.8566	−	28.6861i	1.69521	−	1.95638i
$216$	−0.158746	+	1.10411i	−0.0108013	+	0.0751249i
$217$	0.0346041	+	0.0757724i	0.00234908	+	0.00514377i
$218$	4.66109	+	1.36862i	0.315689	+	0.0926945i
$219$	7.38717	+	2.16907i	0.499178	+	0.146572i
$220$	9.89730	+	21.6721i	0.667276	+	1.46113i
$221$	−1.68223	+	11.7002i	−0.113159	+	0.787040i
$222$	1.20047	−	1.38542i	0.0805704	−	0.0929832i
$223$	−3.48666	+	7.63472i	−0.233484	+	0.511259i	−0.989716	−	0.143045i	$-0.954311\pi$
$223$	−3.48666	+	7.63472i	−0.233484	+	0.511259i	0.756232	+	0.654303i	$0.227038\pi$
$224$	−2.71973	−	1.74787i	−0.181720	−	0.116784i
$225$	−0.740009	−	5.14687i	−0.0493339	−	0.343125i
$226$	0.203605	−	0.130849i	0.0135436	−	0.00870392i
$227$	−1.25427	−	1.44751i	−0.0832489	−	0.0960744i	0.712597	−	0.701574i	$-0.247519\pi$
$227$	−1.25427	−	1.44751i	−0.0832489	−	0.0960744i	−0.795846	+	0.605499i	$0.792973\pi$
$228$	−9.27226	+	2.72258i	−0.614070	+	0.180307i
$229$	−18.2491			−1.20593			−0.602967	−	0.797766i	$-0.706015\pi$
$229$	−18.2491			−1.20593			−0.602967	+	0.797766i	$0.706015\pi$
$230$	−3.26798	−	2.88545i	−0.215484	−	0.190261i
$231$	3.88747			0.255777
$232$	−4.38042	+	1.28621i	−0.287589	+	0.0844437i
$233$	−11.8123	−	13.6321i	−0.773848	−	0.893068i	0.222801	−	0.974864i	$-0.428480\pi$
$233$	−11.8123	−	13.6321i	−0.773848	−	0.893068i	−0.996649	+	0.0817957i	$0.973934\pi$
$234$	1.06462	−	0.684189i	0.0695964	−	0.0447269i
$235$	−1.96060	−	13.6363i	−0.127896	−	0.889535i
$236$	−16.8171	−	10.8077i	−1.09470	−	0.703523i
$237$	−7.15552	+	15.6684i	−0.464801	+	1.01777i
$238$	−0.495539	+	0.571883i	−0.0321210	+	0.0370697i
$239$	3.40140	−	23.6573i	0.220019	−	1.53026i	−0.517940	−	0.855417i	$-0.673301\pi$
$239$	3.40140	−	23.6573i	0.220019	−	1.53026i	0.737959	−	0.674846i	$-0.235790\pi$
$240$	−4.67068	−	10.2274i	−0.301491	−	0.660173i
$241$	−15.9833	−	4.69311i	−1.02957	−	0.302310i	−0.277035	−	0.960860i	$-0.589352\pi$
$241$	−15.9833	−	4.69311i	−1.02957	−	0.302310i	−0.752537	+	0.658550i	$0.771170\pi$
$242$	1.12310	+	0.329772i	0.0721956	+	0.0211985i
$243$	0.415415	+	0.909632i	0.0266489	+	0.0583529i
$244$	0.446732	−	3.10709i	0.0285991	−	0.198911i
$245$	2.09144	−	2.41365i	0.133617	−	0.154202i
$246$	0.668289	−	1.46335i	0.0426085	−	0.0932997i
$247$	18.8359	+	12.1051i	1.19850	+	0.770228i
$248$	−0.0132236	−	0.0919721i	−0.000839699	−	0.00584023i
$249$	7.06087	−	4.53774i	0.447464	−	0.287568i
$250$	−0.118939	−	0.137262i	−0.00752233	−	0.00868124i
$251$	−26.0546	+	7.65033i	−1.64455	+	0.482885i	−0.967463	−	0.253014i	$-0.918578\pi$
$251$	−26.0546	+	7.65033i	−1.64455	+	0.482885i	−0.677091	+	0.735899i	$0.736760\pi$
$252$	−1.91899			−0.120885
$253$	18.4778	−	2.48125i	1.16169	−	0.155995i
$254$	−1.29774			−0.0814274
$255$	−8.14679	+	2.39211i	−0.510172	+	0.149800i
$256$	−6.48657	−	7.48590i	−0.405411	−	0.467869i
$257$	−0.328114	+	0.210866i	−0.0204672	+	0.0131535i	−0.550834	−	0.834615i	$-0.685690\pi$
$257$	−0.328114	+	0.210866i	−0.0204672	+	0.0131535i	0.530367	+	0.847768i	$0.322054\pi$
$258$	0.481424	+	3.34838i	0.0299722	+	0.208461i
$259$	5.41814	+	3.48202i	0.336667	+	0.216362i
$260$	−11.3198	+	24.7868i	−0.702022	+	1.53721i
$261$	−2.68021	+	3.09313i	−0.165901	+	0.191460i
$262$	−0.671788	+	4.67239i	−0.0415032	+	0.288661i
$263$	−1.93475	−	4.23650i	−0.119302	−	0.261234i	0.840555	−	0.541727i	$-0.182229\pi$
$263$	−1.93475	−	4.23650i	−0.119302	−	0.261234i	−0.959856	+	0.280493i	$0.909502\pi$
$264$	−4.16066	−	1.22168i	−0.256071	−	0.0751893i
$265$	6.44711	+	1.89304i	0.396043	+	0.116289i
$266$	0.595435	+	1.30382i	0.0365085	+	0.0799424i
$267$	1.08414	−	7.54037i	0.0663484	−	0.461463i
$268$	−2.40912	+	2.78027i	−0.147160	+	0.169832i
$269$	−1.85501	+	4.06190i	−0.113102	+	0.247659i	−0.957715	−	0.287719i	$-0.907103\pi$
$269$	−1.85501	+	4.06190i	−0.113102	+	0.247659i	0.844613	+	0.535377i	$0.179830\pi$
$270$	0.764721	+	0.491456i	0.0465394	+	0.0299091i
$271$	2.34636	+	16.3193i	0.142531	+	0.991325i	0.928042	+	0.372477i	$0.121491\pi$
$271$	2.34636	+	16.3193i	0.142531	+	0.991325i	−0.785511	+	0.618848i	$0.787600\pi$
$272$	−7.87368	+	5.06010i	−0.477412	+	0.306814i
$273$	2.91163	+	3.36020i	0.176220	+	0.203369i
$274$	1.61613	−	0.474538i	0.0976338	−	0.0286679i
$275$	20.2141			1.21895
$276$	−9.12126	+	1.22483i	−0.549036	+	0.0737261i
$277$	−1.49772			−0.0899892			−0.0449946	−	0.998987i	$-0.514327\pi$
$277$	−1.49772			−0.0899892			−0.0449946	+	0.998987i	$0.514327\pi$
$278$	4.10296	−	1.20474i	0.246079	−	0.0722554i
$279$	−0.0545500	−	0.0629540i	−0.00326582	−	0.00376896i
$280$	−2.99693	+	1.92601i	−0.179101	+	0.115101i
$281$	−0.791233	−	5.50315i	−0.0472010	−	0.328290i	−0.999717	−	0.0238008i	$-0.992423\pi$
$281$	−0.791233	−	5.50315i	−0.0472010	−	0.328290i	0.952516	−	0.304489i	$-0.0984858\pi$
$282$	1.03288	+	0.663794i	0.0615073	+	0.0395283i
$283$	1.81392	−	3.97193i	0.107826	−	0.236106i	−0.848026	−	0.529955i	$-0.822209\pi$
$283$	1.81392	−	3.97193i	0.107826	−	0.236106i	0.955852	+	0.293848i	$0.0949361\pi$
$284$	−8.42392	+	9.72172i	−0.499868	+	0.576878i
$285$	−2.28885	+	15.9193i	−0.135580	+	0.942979i
$286$	2.04370	+	4.47507i	0.120846	+	0.264617i
$287$	5.42305	+	1.59235i	0.320112	+	0.0939935i
$288$	3.10199	+	0.910828i	0.182787	+	0.0536710i
$289$	−4.12589	−	9.03445i	−0.242700	−	0.531438i
$290$	−0.529476	+	3.68259i	−0.0310919	+	0.216249i
$291$	2.87736	−	3.32065i	0.168674	−	0.194660i
$292$	6.13748	−	13.4392i	0.359169	−	0.786470i
$293$	−24.5886	−	15.8021i	−1.43648	−	0.923169i	−0.999722	−	0.0235904i	$-0.992490\pi$
$293$	−24.5886	−	15.8021i	−1.43648	−	0.923169i	−0.436758	−	0.899579i	$-0.643873\pi$
$294$	0.0405070	+	0.281733i	0.00236242	+	0.0164310i
$295$	−27.9883	+	17.9870i	−1.62954	+	1.04724i
$296$	−4.70463	−	5.42944i	−0.273451	−	0.315580i
$297$	−3.73000	+	1.09523i	−0.216436	+	0.0635515i
$298$	−6.63492			−0.384351
$299$	15.9842	+	14.1132i	0.924389	+	0.816187i
$300$	−9.97835			−0.576100
$301$	−11.4035	+	3.34838i	−0.657289	+	0.192997i
$302$	3.29527	+	3.80294i	0.189621	+	0.218835i
$303$	6.08546	−	3.91089i	0.349601	−	0.224675i
$304$	2.52304	+	17.5481i	0.144706	+	1.00645i
$305$	−4.39488	−	2.82442i	−0.251650	−	0.161726i
$306$	0.314348	−	0.688327i	0.0179701	−	0.0393490i
$307$	10.0926	−	11.6475i	0.576016	−	0.664758i	−0.390728	−	0.920506i	$-0.627777\pi$
$307$	10.0926	−	11.6475i	0.576016	−	0.664758i	0.966743	+	0.255749i	$0.0823220\pi$
$308$	1.06167	−	7.38407i	0.0604942	−	0.420746i
$309$	6.58548	+	14.4202i	0.374635	+	0.820335i
$310$	−0.0726546	−	0.0213333i	−0.00412651	−	0.00121165i
$311$	−13.8562	−	4.06856i	−0.785715	−	0.230707i	−0.135823	−	0.990733i	$-0.543368\pi$
$311$	−13.8562	−	4.06856i	−0.785715	−	0.230707i	−0.649892	+	0.760027i	$0.725186\pi$
$312$	−2.06027	−	4.51135i	−0.116640	−	0.255405i
$313$	0.601548	−	4.18386i	0.0340015	−	0.236486i	−0.965733	−	0.259538i	$-0.916430\pi$
$313$	0.601548	−	4.18386i	0.0340015	−	0.236486i	0.999734	+	0.0230530i	$0.00733865\pi$
$314$	−1.04572	+	1.20683i	−0.0590136	+	0.0681053i
$315$	−1.32672	+	2.90510i	−0.0747520	+	0.163684i
$316$	27.8072	+	17.8706i	1.56428	+	1.00530i
$317$	0.319731	+	2.22378i	0.0179579	+	0.124900i	0.996828	−	0.0795814i	$-0.0253584\pi$
$317$	0.319731	+	2.22378i	0.0179579	+	0.124900i	−0.978870	+	0.204481i	$0.934449\pi$
$318$	−0.503772	+	0.323755i	−0.0282501	+	0.0181553i
$319$	−10.4192	−	12.0244i	−0.583366	−	0.673240i
$320$	−18.7561	+	5.50730i	−1.04850	+	0.307867i
$321$	−13.9419			−0.778160
$322$	0.372358	+	1.31327i	0.0207507	+	0.0731856i
$323$	13.3882			0.744937
$324$	1.84125	−	0.540641i	0.102292	−	0.0300356i
$325$	15.1399	+	17.4724i	0.839811	+	0.969193i
$326$	−1.43989	+	0.925362i	−0.0797482	+	0.0512510i
$327$	−2.42893	−	16.8936i	−0.134320	−	0.934218i
$328$	−5.30374	−	3.40851i	−0.292850	−	0.188203i
$329$	−1.79195	+	3.92383i	−0.0987935	+	0.216328i
$330$	−2.31415	+	2.67067i	−0.127390	+	0.147016i
$331$	4.08365	−	28.4024i	0.224458	−	1.56114i	−0.496425	−	0.868079i	$-0.665354\pi$
$331$	4.08365	−	28.4024i	0.224458	−	1.56114i	0.720883	−	0.693057i	$-0.243737\pi$
$332$	−6.69091	−	14.6510i	−0.367211	−	0.804081i
$333$	−6.17966	−	1.81451i	−0.338643	−	0.0994347i
$334$	−0.179932	−	0.0528329i	−0.00984547	−	0.00289089i
$335$	2.54340	+	5.56927i	0.138961	+	0.304282i
$336$	−0.501016	+	3.48465i	−0.0273327	+	0.190103i
$337$	22.7044	−	26.2022i	1.23679	−	1.42733i	0.369711	−	0.929147i	$-0.379457\pi$
$337$	22.7044	−	26.2022i	1.23679	−	1.42733i	0.867074	−	0.498179i	$-0.165998\pi$
$338$	−0.800309	+	1.75243i	−0.0435310	+	0.0953197i
$339$	−0.715331	−	0.459715i	−0.0388515	−	0.0249683i
$340$	2.31882	+	16.1277i	0.125756	+	0.874649i
$341$	0.272420	−	0.175074i	0.0147524	−	0.00948078i
$342$	−0.938644	−	1.08325i	−0.0507561	−	0.0585756i
$343$	−0.959493	+	0.281733i	−0.0518078	+	0.0152121i
$344$	13.2572			0.714780
$345$	−4.45187	+	14.6552i	−0.239680	+	0.789012i
$346$	2.78023			0.149466
$347$	17.0429	−	5.00423i	0.914909	−	0.268641i	0.209803	−	0.977744i	$-0.432718\pi$
$347$	17.0429	−	5.00423i	0.914909	−	0.268641i	0.705106	+	0.709102i	$0.250900\pi$
$348$	5.14329	+	5.93567i	0.275709	+	0.318185i
$349$	19.2913	−	12.3977i	1.03264	−	0.663636i	0.0894822	−	0.995988i	$-0.471479\pi$
$349$	19.2913	−	12.3977i	1.03264	−	0.663636i	0.943155	+	0.332353i	$0.107842\pi$
$350$	0.210628	+	1.46495i	0.0112586	+	0.0783050i
$351$	−3.74037	−	2.40379i	−0.199646	−	0.128305i
$352$	−5.22094	+	11.4323i	−0.278277	+	0.609341i
$353$	4.96886	−	5.73437i	0.264466	−	0.305210i	−0.607949	−	0.793976i	$-0.708008\pi$
$353$	4.96886	−	5.73437i	0.264466	−	0.305210i	0.872415	+	0.488766i	$0.162553\pi$
$354$	0.421972	−	2.93488i	0.0224276	−	0.155987i
$355$	8.89347	+	19.4740i	0.472017	+	1.03357i
$356$	−14.0265	−	4.11855i	−0.743403	−	0.218283i
$357$	2.55088	+	0.749007i	0.135007	+	0.0396417i
$358$	2.59336	+	5.67866i	0.137063	+	0.300127i
$359$	−0.881807	+	6.13310i	−0.0465400	+	0.323693i	0.953230	+	0.302246i	$0.0977363\pi$
$359$	−0.881807	+	6.13310i	−0.0465400	+	0.323693i	−0.999770	+	0.0214468i	$0.993173\pi$
$360$	2.33291	−	2.69233i	0.122955	−	0.141898i
$361$	2.64191	−	5.78497i	0.139048	−	0.304472i
$362$	0.0932310	+	0.0599159i	0.00490011	+	0.00314911i
$363$	−0.585257	−	4.07055i	−0.0307180	−	0.213649i
$364$	7.17771	−	4.61284i	0.376214	−	0.241778i
$365$	−16.1020	−	18.5827i	−0.842819	−	0.972665i
$366$	0.446732	−	0.131172i	0.0233510	−	0.00685648i
$367$	−7.72041			−0.403002			−0.201501	−	0.979488i	$-0.564582\pi$
$367$	−7.72041			−0.403002			−0.201501	+	0.979488i	$0.564582\pi$
$368$	−0.157272	+	16.8829i	−0.00819839	+	0.880082i
$369$	−5.65199			−0.294231
$370$	−5.61747	+	1.64944i	−0.292038	+	0.0857502i
$371$	−1.37777	−	1.59003i	−0.0715301	−	0.0825502i
$372$	−0.134476	+	0.0864223i	−0.00697225	+	0.00448079i
$373$	2.85969	+	19.8896i	0.148069	+	1.02985i	0.919376	+	0.393381i	$0.128695\pi$
$373$	2.85969	+	19.8896i	0.148069	+	1.02985i	−0.771306	+	0.636464i	$0.780396\pi$
$374$	2.47470	+	1.59039i	0.127964	+	0.0822373i
$375$	−0.265079	+	0.580443i	−0.0136886	+	0.0299739i
$376$	3.15099	−	3.63644i	0.162500	−	0.187535i
$377$	2.58975	−	18.0121i	0.133379	−	0.927670i
$378$	−0.118239	−	0.258908i	−0.00608158	−	0.0133168i
$379$	−1.66847	−	0.489908i	−0.0857037	−	0.0251649i	0.238600	−	0.971118i	$-0.423312\pi$
$379$	−1.66847	−	0.489908i	−0.0857037	−	0.0251649i	−0.324303	+	0.945953i	$0.605130\pi$
$380$	29.6129	+	8.69514i	1.51911	+	0.446051i
$381$	1.89404	+	4.14737i	0.0970347	+	0.212476i
$382$	0.903459	−	6.28370i	0.0462250	−	0.321502i
$383$	−18.2093	+	21.0147i	−0.930454	+	1.07380i	0.0666519	+	0.997776i	$0.478768\pi$
$383$	−18.2093	+	21.0147i	−0.930454	+	1.07380i	−0.997106	+	0.0760249i	$0.975777\pi$
$384$	3.40975	−	7.46631i	0.174003	−	0.381014i
$385$	−10.4445	−	6.71230i	−0.532303	−	0.342091i
$386$	−0.199463	−	1.38730i	−0.0101524	−	0.0706115i
$387$	9.99826	−	6.42549i	0.508240	−	0.326626i
$388$	−5.52162	−	6.37229i	−0.280318	−	0.323504i
$389$	−30.7299	+	9.02312i	−1.55807	+	0.457490i	−0.943500	−	0.331373i	$-0.892488\pi$
$389$	−30.7299	+	9.02312i	−1.55807	+	0.457490i	−0.614569	+	0.788863i	$0.710670\pi$
$390$	−4.04169			−0.204659
$391$	12.6029	+	1.93201i	0.637354	+	0.0977057i
$392$	1.11546			0.0563392
$393$	15.9127	−	4.67239i	0.802689	−	0.235691i
$394$	0.179797	+	0.207496i	0.00905802	+	0.0104535i
$395$	46.2788	−	29.7416i	2.32854	−	1.49646i
$396$	1.06167	+	7.38407i	0.0533508	+	0.371063i
$397$	−12.3537	−	7.93926i	−0.620016	−	0.398460i	0.192585	−	0.981280i	$-0.438313\pi$
$397$	−12.3537	−	7.93926i	−0.620016	−	0.398460i	−0.812601	+	0.582820i	$0.801949\pi$
$398$	2.56821	−	5.62359i	0.128733	−	0.281885i
$399$	3.29777	−	3.80583i	0.165095	−	0.190530i
$400$	−2.60519	+	18.1195i	−0.130259	+	0.905973i
$401$	8.89415	+	19.4755i	0.444153	+	0.972559i	0.990817	+	0.135207i	$0.0431699\pi$
$401$	8.89415	+	19.4755i	0.444153	+	0.972559i	−0.546665	+	0.837352i	$0.684103\pi$
$402$	−0.523551	−	0.153728i	−0.0261123	−	0.00766728i
$403$	0.355365	+	0.104345i	0.0177020	+	0.00519777i
$404$	−5.76661	−	12.6271i	−0.286900	−	0.628222i
$405$	0.454513	−	3.16121i	0.0225849	−	0.157082i
$406$	0.762868	−	0.880397i	0.0378605	−	0.0436933i
$407$	10.4009	−	22.7749i	0.515555	−	1.12891i
$408$	−2.49477	−	1.60329i	−0.123509	−	0.0793746i
$409$	0.589011	+	4.09666i	0.0291247	+	0.202567i	0.999188	−	0.0402844i	$-0.0128264\pi$
$409$	0.589011	+	4.09666i	0.0291247	+	0.202567i	−0.970064	+	0.242851i	$0.921917\pi$
$410$	−4.32220	+	2.77771i	−0.213458	+	0.137181i
$411$	−3.87528	−	4.47231i	−0.191153	−	0.220603i
$412$	29.1890	−	8.57065i	1.43804	−	0.422246i
$413$	10.4173			0.512600
$414$	−0.727265	−	1.15517i	−0.0357431	−	0.0567733i
$415$	−26.8057			−1.31584
$416$	−13.7920	+	4.04971i	−0.676210	+	0.198553i
$417$	−9.83840	−	11.3541i	−0.481788	−	0.556013i
$418$	4.68755	−	3.01250i	0.229276	−	0.147346i
$419$	−0.233941	−	1.62709i	−0.0114287	−	0.0794887i	0.983309	−	0.181944i	$-0.0582391\pi$
$419$	−0.233941	−	1.62709i	−0.0114287	−	0.0794887i	−0.994738	+	0.102456i	$0.967330\pi$
$420$	5.15578	+	3.31342i	0.251576	+	0.161678i
$421$	−10.8057	+	23.6613i	−0.526639	+	1.15318i	0.440225	+	0.897888i	$0.354899\pi$
$421$	−10.8057	+	23.6613i	−0.526639	+	1.15318i	−0.966864	+	0.255292i	$0.917828\pi$
$422$	−4.66793	+	5.38708i	−0.227231	+	0.262239i
$423$	0.613895	−	4.26973i	0.0298486	−	0.207602i
$424$	0.974907	+	2.13475i	0.0473457	+	0.103673i
$425$	13.2641	+	3.89469i	0.643403	+	0.188920i
$426$	−1.83069	−	0.537540i	−0.0886973	−	0.0260439i
$427$	0.679527	+	1.48796i	0.0328846	+	0.0720073i
$428$	−3.80753	+	26.4820i	−0.184044	+	1.28005i
$429$	11.3189	−	13.0627i	0.546480	−	0.630672i
$430$	4.48803	−	9.82742i	0.216432	−	0.473920i
$431$	−6.62350	−	4.25666i	−0.319043	−	0.205036i	0.371311	−	0.928509i	$-0.378909\pi$
$431$	−6.62350	−	4.25666i	−0.319043	−	0.205036i	−0.690353	+	0.723472i	$0.742545\pi$
$432$	−0.501016	−	3.48465i	−0.0241052	−	0.167655i
$433$	20.7339	−	13.3249i	0.996410	−	0.640354i	0.0625683	−	0.998041i	$-0.480071\pi$
$433$	20.7339	−	13.3249i	0.996410	−	0.640354i	0.933842	+	0.357687i	$0.116434\pi$
$434$	0.0155265	+	0.0179186i	0.000745298	+	0.000860119i
$435$	12.5417	−	3.68259i	0.601331	−	0.176567i
$436$	−32.7519			−1.56853
$437$	13.2457	−	20.1946i	0.633629	−	0.966040i
$438$	2.19137			0.104708
$439$	37.6970	−	11.0688i	1.79918	−	0.528286i	0.801601	−	0.597860i	$-0.203982\pi$
$439$	37.6970	−	11.0688i	1.79918	−	0.528286i	0.997577	+	0.0695734i	$0.0221638\pi$
$440$	9.06913	+	10.4663i	0.432354	+	0.498963i
$441$	0.841254	−	0.540641i	0.0400597	−	0.0257448i
$442$	0.478814	+	3.33022i	0.0227748	+	0.158403i
$443$	5.38533	+	3.46094i	0.255865	+	0.164434i	0.662285	−	0.749252i	$-0.269587\pi$
$443$	5.38533	+	3.46094i	0.255865	+	0.164434i	−0.406420	+	0.913686i	$0.633223\pi$
$444$	−5.13425	+	11.2424i	−0.243661	+	0.533543i
$445$	−15.9324	+	18.3870i	−0.755267	+	0.871625i
$446$	−0.339983	+	2.36464i	−0.0160987	+	0.111969i
$447$	9.68362	+	21.2042i	0.458020	+	1.00292i
$448$	5.87283	+	1.72442i	0.277465	+	0.0814711i
$449$	−22.9856	−	6.74917i	−1.08476	−	0.318513i	−0.309976	−	0.950744i	$-0.600321\pi$
$449$	−22.9856	−	6.74917i	−1.08476	−	0.318513i	−0.774779	+	0.632232i	$0.782139\pi$
$450$	−0.614822	−	1.34627i	−0.0289830	−	0.0634638i
$451$	3.12693	−	21.7483i	0.147242	−	1.02409i
$452$	−1.06857	+	1.23319i	−0.0502611	+	0.0580044i
$453$	7.34419	−	16.0815i	0.345060	−	0.755576i
$454$	−0.458617	−	0.294735i	−0.0215239	−	0.0138326i
$455$	−2.02085	−	14.0553i	−0.0947387	−	0.658922i
$456$	−4.72555	+	3.03693i	−0.221294	+	0.142217i
$457$	15.3668	+	17.7342i	0.718828	+	0.829571i	0.991166	−	0.132630i	$-0.0423423\pi$
$457$	15.3668	+	17.7342i	0.718828	+	0.829571i	−0.272338	+	0.962202i	$0.587797\pi$
$458$	−4.98383	+	1.46338i	−0.232879	+	0.0683795i
$459$	−2.65858			−0.124092
$460$	26.6212	+	12.4585i	1.24122	+	0.580879i
$461$	−17.1359			−0.798100			−0.399050	−	0.916929i	$-0.630660\pi$
$461$	−17.1359			−0.798100			−0.399050	+	0.916929i	$0.630660\pi$
$462$	1.06167	−	0.311734i	0.0493933	−	0.0145032i
$463$	18.0539	+	20.8353i	0.839037	+	0.968300i	0.999825	−	0.0186885i	$-0.00594907\pi$
$463$	18.0539	+	20.8353i	0.839037	+	0.968300i	−0.160788	+	0.986989i	$0.551404\pi$
$464$	12.1213	−	7.78988i	0.562717	−	0.361636i
$465$	0.0378609	+	0.263329i	0.00175576	+	0.0122116i
$466$	−4.31909	−	2.77571i	−0.200078	−	0.128582i
$467$	−13.9519	+	30.5505i	−0.645619	+	1.41371i	0.249718	+	0.968319i	$0.419662\pi$
$467$	−13.9519	+	30.5505i	−0.645619	+	1.41371i	−0.895337	+	0.445389i	$0.853065\pi$
$468$	−5.58738	+	6.44818i	−0.258277	+	0.298067i
$469$	0.272827	−	1.89755i	0.0125980	−	0.0876208i
$470$	−1.62893	−	3.56686i	−0.0751369	−	0.164527i
$471$	5.38306	+	1.58061i	0.248038	+	0.0728306i
$472$	−11.1493	−	3.27374i	−0.513190	−	0.150686i
$473$	19.1932	+	42.0272i	0.882503	+	1.93241i
$474$	−0.697733	+	4.85284i	−0.0320479	+	0.222898i
$475$	17.1478	−	19.7896i	0.786793	−	0.908008i
$476$	2.11935	−	4.64073i	0.0971403	−	0.212708i
$477$	1.76992	+	1.13746i	0.0810391	+	0.0520807i
$478$	−0.968140	−	6.73356i	−0.0442817	−	0.307986i
$479$	−7.16123	+	4.60224i	−0.327205	+	0.210282i	−0.693921	−	0.720051i	$-0.744118\pi$
$479$	−7.16123	+	4.60224i	−0.327205	+	0.210282i	0.366716	+	0.930333i	$0.380482\pi$
$480$	−6.76152	−	7.80321i	−0.308620	−	0.356166i
$481$	27.4759	−	8.06766i	1.25279	−	0.367853i
$482$	−4.74137			−0.215963
$483$	3.65355	−	3.10670i	0.166242	−	0.141360i
$484$	−7.89166			−0.358712
$485$	−13.4643	+	3.95347i	−0.611382	+	0.179518i
$486$	0.186393	+	0.215109i	0.00845495	+	0.00975753i
$487$	1.53818	−	0.988531i	0.0697018	−	0.0447946i	−0.505326	−	0.862929i	$-0.668628\pi$
$487$	1.53818	−	0.988531i	0.0697018	−	0.0447946i	0.575028	+	0.818134i	$0.304991\pi$
$488$	−0.259674	−	1.80607i	−0.0117549	−	0.0817571i
$489$	5.05882	+	3.25111i	0.228768	+	0.147020i
$490$	0.377623	−	0.826879i	0.0170593	−	0.0373546i
$491$	4.58896	−	5.29594i	0.207097	−	0.239002i	−0.642693	−	0.766123i	$-0.722183\pi$
$491$	4.58896	−	5.29594i	0.207097	−	0.239002i	0.849790	+	0.527121i	$0.176729\pi$
$492$	−1.54356	+	10.7357i	−0.0695891	+	0.484003i
$493$	−4.52013	−	9.89771i	−0.203577	−	0.445771i
$494$	6.11478	+	1.79546i	0.275117	+	0.0807817i
$495$	11.9125	+	3.49784i	0.535429	+	0.157216i
$496$	0.121823	+	0.266755i	0.00547002	+	0.0119777i
$497$	0.953989	−	6.63514i	0.0427923	−	0.297627i
$498$	1.56445	−	1.80547i	0.0701045	−	0.0809049i
$499$	−5.66094	+	12.3957i	−0.253418	+	0.554909i	−0.992994	−	0.118164i	$-0.962299\pi$
$499$	−5.66094	+	12.3957i	−0.253418	+	0.554909i	0.739576	+	0.673074i	$0.235026\pi$
$500$	1.03013	+	0.662025i	0.0460688	+	0.0296066i
$501$	0.0937644	+	0.652145i	0.00418908	+	0.0291357i
$502$	−6.50205	+	4.17861i	−0.290201	+	0.186501i
$503$	−10.8709	−	12.5457i	−0.484709	−	0.559384i	0.459735	−	0.888056i	$-0.347944\pi$
$503$	−10.8709	−	12.5457i	−0.484709	−	0.559384i	−0.944444	+	0.328672i	$0.893399\pi$
$504$	−1.07028	+	0.314261i	−0.0476739	+	0.0139983i
$505$	−23.1027			−1.02806
$506$	4.84732	−	2.15935i	0.215490	−	0.0959950i
$507$	6.76854			0.300601
$508$	8.39500	−	2.46500i	0.372468	−	0.109366i
$509$	25.1476	+	29.0218i	1.11465	+	1.28637i	0.954148	+	0.299334i	$0.0967645\pi$
$509$	25.1476	+	29.0218i	1.11465	+	1.28637i	0.160498	+	0.987036i	$0.448690\pi$
$510$	−2.03307	+	1.30657i	−0.0900258	+	0.0578560i
$511$	1.09569	+	7.62067i	0.0484703	+	0.337118i
$512$	−16.1819	−	10.3995i	−0.715145	−	0.459596i
$513$	−2.09196	+	4.58076i	−0.0923624	+	0.202246i
$514$	−0.0726987	+	0.0838988i	−0.00320660	+	0.00370062i
$515$	7.20528	−	50.1138i	0.317503	−	2.20828i
$516$	−9.47440	−	20.7460i	−0.417087	−	0.913293i
$517$	16.0899	+	4.72441i	0.707632	+	0.207780i
$518$	1.75892	+	0.516464i	0.0772823	+	0.0226921i
$519$	−4.05772	−	8.88517i	−0.178114	−	0.390016i
$520$	−2.25417	+	15.6781i	−0.0988520	+	0.687531i
$521$	10.4888	−	12.1047i	0.459521	−	0.530316i	−0.477946	−	0.878389i	$-0.658619\pi$
$521$	10.4888	−	12.1047i	0.459521	−	0.530316i	0.937467	+	0.348073i	$0.113164\pi$
$522$	−0.483930	+	1.05966i	−0.0211810	+	0.0463800i
$523$	−33.5373	−	21.5531i	−1.46649	−	0.942453i	−0.998267	−	0.0588404i	$-0.981260\pi$
$523$	−33.5373	−	21.5531i	−1.46649	−	0.942453i	−0.468218	−	0.883613i	$-0.655104\pi$
$524$	−4.52922	−	31.5014i	−0.197860	−	1.37615i
$525$	4.37435	−	2.81122i	0.190912	−	0.122692i
$526$	−0.868102	−	1.00184i	−0.0378511	−	0.0436825i
$527$	0.212489	−	0.0623924i	0.00925616	−	0.00271785i
$528$	13.6858			0.595596
$529$	15.3830	−	17.0986i	0.668826	−	0.743419i
$530$	1.91251			0.0830740
$531$	−9.99529	+	2.93488i	−0.433758	+	0.127363i
$532$	−6.32838	−	7.30334i	−0.274370	−	0.316640i
$533$	21.1405	−	13.5862i	0.915698	−	0.588484i
$534$	−0.308579	−	2.14621i	−0.0133535	−	0.0928758i
$535$	37.4580	+	24.0728i	1.61945	+	1.04076i
$536$	−0.888327	+	1.94517i	−0.0383699	+	0.0840183i
$537$	14.3631	−	16.5759i	0.619815	−	0.715304i
$538$	−0.180881	+	1.25806i	−0.00779835	+	0.0542387i
$539$	1.61491	+	3.53617i	0.0695592	+	0.152313i
$540$	−5.88043	−	1.72665i	−0.253054	−	0.0743032i
$541$	1.91162	+	0.561303i	0.0821870	+	0.0241323i	0.322568	−	0.946546i	$-0.395454\pi$
$541$	1.91162	+	0.561303i	0.0821870	+	0.0241323i	−0.240381	+	0.970679i	$0.577272\pi$
$542$	1.94942	+	4.26864i	0.0837349	+	0.183354i
$543$	0.0554120	−	0.385399i	0.00237795	−	0.0165390i
$544$	−5.62856	+	6.49570i	−0.241322	+	0.278501i
$545$	−22.6435	+	49.5823i	−0.969940	+	2.12387i
$546$	1.06462	+	0.684189i	0.0455615	+	0.0292806i
$547$	−2.40345	−	16.7164i	−0.102764	−	0.714740i	−0.974438	−	0.224655i	$-0.927875\pi$
$547$	−2.40345	−	16.7164i	−0.102764	−	0.714740i	0.871674	−	0.490085i	$-0.163034\pi$
$548$	−9.55328	+	6.13952i	−0.408096	+	0.262267i
$549$	−1.07121	−	1.23624i	−0.0457180	−	0.0527614i
$550$	5.52046	−	1.62095i	0.235393	−	0.0691177i
$551$	−20.6107			−0.878044
$552$	−4.88662	+	2.17686i	−0.207988	+	0.0926534i
$553$	−17.2250			−0.732481
$554$	−0.409027	+	0.120101i	−0.0173779	+	0.00510261i
$555$	13.4700	+	15.5452i	0.571770	+	0.659858i
$556$	−24.2535	+	15.5868i	−1.02858	+	0.661026i
$557$	2.55245	+	17.7527i	0.108151	+	0.752204i	0.969659	+	0.244461i	$0.0786111\pi$
$557$	2.55245	+	17.7527i	0.108151	+	0.752204i	−0.861508	+	0.507743i	$0.830480\pi$
$558$	−0.0199458	−	0.0128184i	−0.000844375	−	0.000542647i
$559$	−21.9516	+	48.0674i	−0.928456	+	2.03303i
$560$	7.36286	−	8.49719i	0.311138	−	0.359072i
$561$	1.47084	−	10.2299i	0.0620990	−	0.431908i
$562$	−0.657380	−	1.43946i	−0.0277299	−	0.0607200i
$563$	14.9096	+	4.37786i	0.628365	+	0.184505i	0.580383	−	0.814344i	$-0.302903\pi$
$563$	14.9096	+	4.37786i	0.628365	+	0.184505i	0.0479819	+	0.998848i	$0.484721\pi$
$564$	−7.94251	−	2.33213i	−0.334440	−	0.0982004i
$565$	1.12813	+	2.47026i	0.0474607	+	0.103924i
$566$	0.176875	−	1.23019i	0.00743460	−	0.0517088i
$567$	−0.654861	+	0.755750i	−0.0275016	+	0.0317385i
$568$	−3.10620	+	6.80163i	−0.130333	+	0.285390i
$569$	−1.19265	−	0.766472i	−0.0499986	−	0.0321322i	0.515403	−	0.856948i	$-0.327642\pi$
$569$	−1.19265	−	0.766472i	−0.0499986	−	0.0321322i	−0.565401	+	0.824816i	$0.691279\pi$
$570$	0.651475	+	4.53111i	0.0272873	+	0.189787i
$571$	16.1529	−	10.3808i	0.675977	−	0.434424i	−0.157099	−	0.987583i	$-0.550214\pi$
$571$	16.1529	−	10.3808i	0.675977	−	0.434424i	0.833076	+	0.553159i	$0.186578\pi$
$572$	−21.7208	−	25.0671i	−0.908190	−	1.04811i
$573$	−21.4003	+	6.28370i	−0.894010	+	0.262505i
$574$	1.60873			0.0671469
$575$	18.9977	−	16.1542i	0.792259	−	0.673678i
$576$	−6.12076			−0.255032
$577$	36.9537	−	10.8506i	1.53840	−	0.451715i	0.600792	−	0.799406i	$-0.294852\pi$
$577$	36.9537	−	10.8506i	1.53840	−	0.451715i	0.937609	+	0.347690i	$0.113034\pi$
$578$	−1.85125	−	2.13646i	−0.0770018	−	0.0888648i
$579$	−4.14247	+	2.66220i	−0.172155	+	0.110637i
$580$	−3.56975	−	24.8282i	−0.148226	−	1.03093i
$581$	7.06087	+	4.53774i	0.292934	+	0.188257i
$582$	0.519527	−	1.13761i	0.0215351	−	0.0471553i
$583$	−5.35603	+	6.18119i	−0.221824	+	0.255999i
$584$	1.22219	−	8.50054i	0.0505747	−	0.351755i
$585$	5.89882	+	12.9166i	0.243886	+	0.534037i
$586$	−7.98231	−	2.34382i	−0.329746	−	0.0968222i
$587$	36.0186	+	10.5760i	1.48665	+	0.436519i	0.921470	−	0.388450i	$-0.126990\pi$
$587$	36.0186	+	10.5760i	1.48665	+	0.436519i	0.565177	+	0.824969i	$0.308808\pi$
$588$	−0.797176	−	1.74557i	−0.0328750	−	0.0719861i
$589$	0.0596991	−	0.415216i	0.00245986	−	0.0171087i
$590$	−6.20124	+	7.15661i	−0.255301	+	0.294633i
$591$	0.400714	−	0.877441i	0.0164832	−	0.0360931i
$592$	19.0744	+	12.2584i	0.783954	+	0.503817i
$593$	−6.12907	−	42.6286i	−0.251691	−	1.75055i	−0.588061	−	0.808817i	$-0.700109\pi$
$593$	−6.12907	−	42.6286i	−0.251691	−	1.75055i	0.336371	−	0.941730i	$-0.390801\pi$
$594$	−0.930838	+	0.598213i	−0.0381927	+	0.0245450i
$595$	−5.56024	−	6.41686i	−0.227948	−	0.263066i
$596$	42.9209	−	12.6027i	1.75811	−	0.516228i
$597$	−21.7204			−0.888957
$598$	5.49701	+	2.57255i	0.224790	+	0.105200i
$599$	−4.96388			−0.202819			−0.101409	−	0.994845i	$-0.532335\pi$
$599$	−4.96388			−0.202819			−0.101409	+	0.994845i	$0.532335\pi$
$600$	−5.56522	+	1.63410i	−0.227199	+	0.0667117i
$601$	24.1674	+	27.8906i	0.985808	+	1.13768i	0.990475	+	0.137694i	$0.0439689\pi$
$601$	24.1674	+	27.8906i	0.985808	+	1.13768i	−0.00466714	+	0.999989i	$0.501486\pi$
$602$	−2.84580	+	1.82889i	−0.115986	+	0.0745398i
$603$	0.272827	+	1.89755i	0.0111104	+	0.0772743i
$604$	−28.5404	−	18.3418i	−1.16129	−	0.746318i
$605$	−5.45600	+	11.9470i	−0.221818	+	0.485714i
$606$	1.34833	−	1.55605i	0.0547721	−	0.0632104i
$607$	−1.54711	+	10.7604i	−0.0627951	+	0.436750i	0.934034	+	0.357183i	$0.116263\pi$
$607$	−1.54711	+	10.7604i	−0.0627951	+	0.436750i	−0.996830	+	0.0795667i	$0.974646\pi$
$608$	6.76322	+	14.8094i	0.274285	+	0.600600i
$609$	−3.92701	−	1.15307i	−0.159130	−	0.0467249i
$610$	−1.42673	−	0.418926i	−0.0577667	−	0.0169618i
$611$	7.96734	+	17.4460i	0.322324	+	0.705792i
$612$	−0.726057	+	5.04984i	−0.0293491	+	0.204128i
$613$	12.6414	−	14.5890i	0.510581	−	0.589242i	−0.440666	−	0.897671i	$-0.645258\pi$
$613$	12.6414	−	14.5890i	0.510581	−	0.589242i	0.951247	+	0.308429i	$0.0998031\pi$
$614$	1.82229	−	3.99025i	0.0735415	−	0.161034i
$615$	15.1853	+	9.75903i	0.612332	+	0.393522i
$616$	−0.617122	−	4.29218i	−0.0248645	−	0.172937i
$617$	−31.1639	+	20.0278i	−1.25461	+	0.806290i	−0.987537	−	0.157386i	$-0.949693\pi$
$617$	−31.1639	+	20.0278i	−1.25461	+	0.806290i	−0.267075	+	0.963676i	$0.586057\pi$
$618$	2.95484	+	3.41007i	0.118861	+	0.137173i
$619$	−11.5570	+	3.39343i	−0.464513	+	0.136393i	−0.505611	−	0.862762i	$-0.668733\pi$
$619$	−11.5570	+	3.39343i	−0.464513	+	0.136393i	0.0410973	+	0.999155i	$0.486915\pi$
$620$	0.510520			0.0205030
$621$	−2.63029	+	4.01018i	−0.105550	+	0.160923i
$622$	−4.11039			−0.164812
$623$	7.30933	−	2.14621i	0.292842	−	0.0859862i
$624$	10.2503	+	11.8295i	0.410342	+	0.473560i
$625$	−20.1573	+	12.9543i	−0.806294	+	0.518173i
$626$	−0.171218	−	1.19085i	−0.00684326	−	0.0475959i
$627$	−16.4689	−	10.5839i	−0.657706	−	0.422682i
$628$	4.47241	−	9.79321i	0.178469	−	0.390792i
$629$	11.2130	−	12.9405i	0.447091	−	0.515970i
$630$	−0.129368	+	0.899773i	−0.00515414	+	0.0358478i
$631$	−16.2840	−	35.6569i	−0.648255	−	1.41948i	−0.893074	−	0.449911i	$-0.851456\pi$
$631$	−16.2840	−	35.6569i	−0.648255	−	1.41948i	0.244819	−	0.969569i	$-0.421271\pi$
$632$	18.4355	+	5.41315i	0.733325	+	0.215324i
$633$	24.0291	+	7.05557i	0.955070	+	0.280434i
$634$	0.265642	+	0.581675i	0.0105500	+	0.0231013i
$635$	2.07230	−	14.4132i	0.0822368	−	0.571970i
$636$	2.64392	−	3.05124i	0.104838	−	0.120990i
$637$	−1.84701	+	4.04439i	−0.0731812	+	0.160245i
$638$	−3.80973	−	2.44836i	−0.150829	−	0.0969317i
$639$	0.953989	+	6.63514i	0.0377392	+	0.262482i
$640$	−22.0528	+	14.1725i	−0.871712	+	0.560215i
$641$	28.1560	+	32.4938i	1.11210	+	1.28343i	0.955249	+	0.295804i	$0.0955876\pi$
$641$	28.1560	+	32.4938i	1.11210	+	1.28343i	0.156847	+	0.987623i	$0.449867\pi$
$642$	−3.80753	+	1.11799i	−0.150271	+	0.0441236i
$643$	13.2336			0.521883			0.260941	−	0.965355i	$-0.415967\pi$
$643$	13.2336			0.521883			0.260941	+	0.965355i	$0.415967\pi$
$644$	−4.90325	−	7.78818i	−0.193215	−	0.306897i
$645$	−37.9571			−1.49456
$646$	3.65631	−	1.07359i	0.143856	−	0.0422398i
$647$	0.175072	+	0.202044i	0.00688280	+	0.00794318i	0.759181	−	0.650880i	$-0.225600\pi$
$647$	0.175072	+	0.202044i	0.00688280	+	0.00794318i	−0.752298	+	0.658823i	$0.771054\pi$
$648$	0.938384	−	0.603063i	0.0368632	−	0.0236906i
$649$	−5.76329	−	40.0846i	−0.226229	−	1.57346i
$650$	5.53581	+	3.55765i	0.217132	+	0.139542i
$651$	0.0346041	−	0.0757724i	0.00135624	−	0.00296976i
$652$	7.55689	−	8.72112i	0.295951	−	0.341545i
$653$	−3.23763	+	22.5182i	−0.126698	+	0.881205i	0.823001	+	0.568040i	$0.192298\pi$
$653$	−3.23763	+	22.5182i	−0.126698	+	0.881205i	−0.949699	+	0.313165i	$0.898611\pi$
$654$	−2.01803	−	4.41887i	−0.0789112	−	0.172791i
$655$	−50.8205	−	14.9223i	−1.98572	−	0.583061i
$656$	19.0917	+	5.60584i	0.745407	+	0.218871i
$657$	−3.19829	−	7.00328i	−0.124777	−	0.273224i
$658$	−0.174733	+	1.21529i	−0.00681179	+	0.0473771i
$659$	−23.5585	+	27.1879i	−0.917707	+	1.05909i	0.0803489	+	0.996767i	$0.474397\pi$
$659$	−23.5585	+	27.1879i	−0.917707	+	1.05909i	−0.998056	+	0.0623236i	$0.980149\pi$
$660$	9.89730	−	21.6721i	0.385252	−	0.843584i
$661$	6.95477	+	4.46956i	0.270509	+	0.173846i	0.668862	−	0.743387i	$-0.266782\pi$
$661$	6.95477	+	4.46956i	0.270509	+	0.173846i	−0.398353	+	0.917232i	$0.630418\pi$
$662$	−1.16233	−	8.08416i	−0.0451751	−	0.314200i
$663$	9.94405	−	6.39065i	0.386195	−	0.248192i
$664$	−6.13104	−	7.07560i	−0.237930	−	0.274586i
$665$	−15.4315	+	4.53111i	−0.598410	+	0.175709i
$666$	−1.83317			−0.0710340
$667$	−19.4017	−	2.97427i	−0.751237	−	0.115164i
$668$	1.26433			0.0489183
$669$	8.05321	−	2.36464i	0.311355	−	0.0914221i
$670$	1.14120	+	1.31702i	0.0440884	+	0.0508807i
$671$	5.34957	−	3.43796i	0.206518	−	0.132721i
$672$	0.460097	+	3.20005i	0.0177486	+	0.123444i
$673$	−41.4957	−	26.6677i	−1.59954	−	1.02796i	−0.967447	−	0.253074i	$-0.918558\pi$
$673$	−41.4957	−	26.6677i	−1.59954	−	1.02796i	−0.632096	−	0.774890i	$-0.717805\pi$
$674$	4.09942	−	8.97648i	0.157904	−	0.345761i
$675$	−3.40515	+	3.92975i	−0.131064	+	0.151256i
$676$	1.84849	−	12.8565i	0.0710958	−	0.494482i
$677$	10.4386	+	22.8574i	0.401189	+	0.878480i	0.997148	+	0.0754662i	$0.0240445\pi$
$677$	10.4386	+	22.8574i	0.401189	+	0.878480i	−0.595960	+	0.803014i	$0.703228\pi$
$678$	−0.232221	−	0.0681864i	−0.00891841	−	0.00261868i
$679$	4.21587	+	1.23789i	0.161790	+	0.0475059i
$680$	3.93442	+	8.61518i	0.150878	+	0.330377i
$681$	−0.272579	+	1.89583i	−0.0104453	+	0.0726484i
$682$	0.0603589	−	0.0696579i	0.00231126	−	0.00266734i
$683$	0.490628	−	1.07433i	0.0187734	−	0.0411080i	−0.900013	−	0.435863i	$-0.856443\pi$
$683$	0.490628	−	1.07433i	0.0187734	−	0.0411080i	0.918786	+	0.394755i	$0.129171\pi$
$684$	8.12963	+	5.22459i	0.310844	+	0.199767i
$685$	2.68967	+	18.7071i	0.102767	+	0.714761i
$686$	−0.239446	+	0.153882i	−0.00914208	+	0.00587526i
$687$	11.9506	+	13.7917i	0.455944	+	0.526188i
$688$	−40.1459	+	11.7879i	−1.53055	+	0.449409i
$689$	−9.35437			−0.356373
$690$	−0.0406094	+	4.35934i	−0.00154597	+	0.165957i
$691$	−41.4241			−1.57585			−0.787923	−	0.615774i	$-0.788843\pi$
$691$	−41.4241			−1.57585			−0.787923	+	0.615774i	$0.788843\pi$
$692$	−17.9851	+	5.28091i	−0.683692	+	0.200750i
$693$	−2.54575	−	2.93795i	−0.0967051	−	0.111604i
$694$	4.25312	−	2.73331i	0.161446	−	0.103755i
$695$	6.82844	+	47.4928i	0.259017	+	1.80151i
$696$	3.84062	+	2.46821i	0.145578	+	0.0935574i
$697$	6.24213	−	13.6684i	0.236438	−	0.517726i
$698$	4.27428	−	4.93278i	0.161784	−	0.186708i
$699$	−2.56705	+	17.8542i	−0.0970949	+	0.675310i
$700$	−4.14515	−	9.07662i	−0.156672	−	0.343064i
$701$	−21.9506	−	6.44528i	−0.829064	−	0.243435i	−0.160449	−	0.987044i	$-0.551294\pi$
$701$	−21.9506	−	6.44528i	−0.829064	−	0.243435i	−0.668615	+	0.743609i	$0.733112\pi$
$702$	−1.21425	−	0.356537i	−0.0458290	−	0.0134566i
$703$	−13.4734	−	29.5026i	−0.508159	−	1.11271i
$704$	3.38628	−	23.5521i	0.127625	−	0.887653i
$705$	−9.02171	+	10.4116i	−0.339777	+	0.392124i
$706$	0.897160	−	1.96451i	0.0337651	−	0.0739352i
$707$	6.08546	+	3.91089i	0.228867	+	0.147084i
$708$	2.84496	+	19.7871i	0.106920	+	0.743645i
$709$	−5.56451	+	3.57609i	−0.208980	+	0.134303i	−0.640944	−	0.767588i	$-0.721457\pi$
$709$	−5.56451	+	3.57609i	−0.208980	+	0.134303i	0.431964	+	0.901891i	$0.357821\pi$
$710$	3.99042	+	4.60519i	0.149758	+	0.172830i
$711$	16.5273	−	4.85284i	0.619821	−	0.181996i
$712$	−8.49747			−0.318456
$713$	0.116116	−	0.382246i	0.00434858	−	0.0143152i
$714$	0.756709			0.0283191
$715$	−52.9654	+	15.5520i	−1.98079	+	0.581613i
$716$	−27.5626	−	31.8090i	−1.03006	−	1.18876i
$717$	−20.1064	+	12.9216i	−0.750888	+	0.482567i
$718$	0.250988	+	1.74566i	0.00936680	+	0.0651475i
$719$	−36.8973	−	23.7125i	−1.37604	−	0.884326i	−0.376917	−	0.926247i	$-0.623016\pi$
$719$	−36.8973	−	23.7125i	−1.37604	−	0.884326i	−0.999121	+	0.0419215i	$0.986652\pi$
$720$	−4.67068	+	10.2274i	−0.174066	+	0.381151i
$721$	−10.3814	+	11.9807i	−0.386622	+	0.446185i
$722$	0.257612	−	1.79173i	0.00958731	−	0.0666812i
$723$	6.91999	+	15.1527i	0.257357	+	0.563534i
$724$	−0.716914	−	0.210505i	−0.0266439	−	0.00782335i
$725$	−20.4197	−	5.99576i	−0.758368	−	0.222677i
$726$	−0.486249	−	1.06474i	−0.0180464	−	0.0395161i
$727$	−7.60997	+	52.9285i	−0.282238	+	1.96301i	−0.0130762	+	0.999915i	$0.504162\pi$
$727$	−7.60997	+	52.9285i	−0.282238	+	1.96301i	−0.269162	+	0.963095i	$0.586747\pi$
$728$	3.24781	−	3.74817i	0.120372	−	0.138916i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−5.88761	−	3.78374i	−0.217910	−	0.140042i
$731$	4.49673	+	31.2754i	0.166318	+	1.15676i
$732$	−2.64073	+	1.69709i	−0.0976040	+	0.0627263i
$733$	9.09097	+	10.4915i	0.335783	+	0.387514i	0.898381	−	0.439216i	$-0.144744\pi$
$733$	9.09097	+	10.4915i	0.335783	+	0.387514i	−0.562599	+	0.826730i	$0.690198\pi$
$734$	−2.10845	+	0.619095i	−0.0778241	+	0.0228512i
$735$	−3.19371			−0.117802
$736$	4.22941	+	14.9167i	0.155898	+	0.549836i
$737$	−7.45253			−0.274517
$738$	−1.54356	+	0.453230i	−0.0568193	+	0.0166836i
$739$	−18.6155	−	21.4834i	−0.684782	−	0.790281i	0.301830	−	0.953362i	$-0.402402\pi$
$739$	−18.6155	−	21.4834i	−0.684782	−	0.790281i	−0.986613	+	0.163081i	$0.947857\pi$
$740$	33.2061	−	21.3402i	1.22068	−	0.784483i
$741$	−3.18647	−	22.1624i	−0.117058	−	0.814155i
$742$	−0.503772	−	0.323755i	−0.0184941	−	0.0118854i
$743$	−9.84020	+	21.5470i	−0.361002	+	0.790484i	0.638776	+	0.769393i	$0.279441\pi$
$743$	−9.84020	+	21.5470i	−0.361002	+	0.790484i	−0.999778	+	0.0210907i	$0.993286\pi$
$744$	−0.0608483	+	0.0702227i	−0.00223081	+	0.00257449i
$745$	10.5950	−	73.6900i	0.388171	−	2.69979i
$746$	2.37592	+	5.20254i	0.0869886	+	0.190478i
$747$	−8.05328	−	2.36466i	−0.294654	−	0.0865183i
$748$	−19.0296	−	5.58759i	−0.695791	−	0.204303i
$749$	−5.79167	−	12.6820i	−0.211623	−	0.463389i
$750$	−0.0258478	+	0.179776i	−0.000943829	+	0.00656447i
$751$	−13.3089	+	15.3593i	−0.485648	+	0.560468i	−0.944698	−	0.327943i	$-0.893645\pi$
$751$	−13.3089	+	15.3593i	−0.485648	+	0.560468i	0.459049	+	0.888411i	$0.348190\pi$
$752$	−6.30853	+	13.8137i	−0.230048	+	0.503736i
$753$	22.8439	+	14.6809i	0.832478	+	0.535001i
$754$	−0.737120	−	5.12678i	−0.0268443	−	0.186706i
$755$	−47.4990	+	30.5258i	−1.72867	+	1.11095i
$756$	1.25667	+	1.45027i	0.0457046	+	0.0527459i
$757$	35.5486	−	10.4380i	1.29204	−	0.379376i	0.437711	−	0.899116i	$-0.355789\pi$
$757$	35.5486	−	10.4380i	1.29204	−	0.379376i	0.854325	+	0.519740i	$0.173971\pi$
$758$	−0.494946			−0.0179772
$759$	−13.9756	−	12.3397i	−0.507282	−	0.447903i
$760$	17.9400			0.650751
$761$	13.9451	−	4.09464i	0.505509	−	0.148431i	−0.0190275	−	0.999819i	$-0.506057\pi$
$761$	13.9451	−	4.09464i	0.505509	−	0.148431i	0.524536	+	0.851388i	$0.324239\pi$
$762$	0.849838	+	0.980766i	0.0307864	+	0.0355294i
$763$	14.3579	−	9.22729i	0.519792	−	0.334050i
$764$	6.09116	+	42.3650i	0.220370	+	1.53271i
$765$	7.14285	+	4.59043i	0.258250	+	0.165967i
$766$	−3.28782	+	7.19932i	−0.118794	+	0.260122i
$767$	30.3312	−	35.0041i	1.09520	−	1.26392i
$768$	−1.40967	+	9.80445i	−0.0508670	+	0.353788i
$769$	−3.35253	−	7.34101i	−0.120895	−	0.264724i	0.839503	−	0.543355i	$-0.182846\pi$
$769$	−3.35253	−	7.34101i	−0.120895	−	0.264724i	−0.960398	+	0.278632i	$0.910119\pi$
$770$	−3.39066	−	0.995589i	−0.122191	−	0.0358785i
$771$	0.374231	+	0.109884i	0.0134776	+	0.00395738i
$772$	3.92542	+	8.59547i	0.141279	+	0.309358i
$773$	1.33993	−	9.31944i	0.0481941	−	0.335197i	−0.951432	−	0.307858i	$-0.900388\pi$
$773$	1.33993	−	9.31944i	0.0481941	−	0.335197i	0.999626	−	0.0273386i	$-0.00870323\pi$
$774$	2.21527	−	2.55656i	0.0796263	−	0.0918936i
$775$	0.179934	−	0.394001i	0.00646344	−	0.0141530i
$776$	−4.12312	−	2.64977i	−0.148012	−	0.0951213i
$777$	−0.916586	−	6.37500i	−0.0328823	−	0.228702i
$778$	−7.66879	+	4.92843i	−0.274939	+	0.176693i
$779$	−18.6390	−	21.5106i	−0.667811	−	0.770695i
$780$	26.1455	−	7.67701i	0.936159	−	0.274881i
$781$	−26.0591			−0.932470
$782$	3.59677	−	0.482985i	0.128620	−	0.0172715i
$783$	4.09280			0.146265
$784$	−3.37787	+	0.991834i	−0.120638	+	0.0354226i
$785$	−11.7336	−	13.5413i	−0.418791	−	0.483311i
$786$	3.97108	−	2.55206i	0.141644	−	0.0910289i
$787$	−4.95569	−	34.4676i	−0.176651	−	1.22864i	−0.864444	−	0.502729i	$-0.832329\pi$
$787$	−4.95569	−	34.4676i	−0.176651	−	1.22864i	0.687793	−	0.725907i	$-0.258580\pi$
$788$	−1.55722	−	1.00077i	−0.0554738	−	0.0356508i
$789$	−1.93475	+	4.23650i	−0.0688788	+	0.150824i
$790$	10.2538	−	11.8335i	0.364813	−	0.421017i
$791$	0.121013	−	0.841661i	0.00430271	−	0.0299260i
$792$	1.80137	+	3.94445i	0.0640089	+	0.140160i
$793$	6.97837	+	2.04903i	0.247809	+	0.0727633i
$794$	−4.01045	−	1.17758i	−0.142326	−	0.0417906i
$795$	−2.79129	−	6.11208i	−0.0989969	−	0.216773i
$796$	−5.93185	+	41.2569i	−0.210249	+	1.46231i
$797$	10.9924	−	12.6859i	0.389370	−	0.449357i	−0.526895	−	0.849931i	$-0.676644\pi$
$797$	10.9924	−	12.6859i	0.389370	−	0.449357i	0.916265	+	0.400574i	$0.131189\pi$
$798$	0.595435	−	1.30382i	0.0210782	−	0.0461547i
$799$	9.64761	+	6.20014i	0.341308	+	0.219345i
$800$	2.39241	+	16.6396i	0.0845846	+	0.588299i
$801$	−6.40860	+	4.11855i	−0.226437	+	0.145522i
$802$	3.99072	+	4.60554i	0.140917	+	0.162627i
$803$	28.7174	−	8.43218i	1.01341	−	0.297565i
$804$	3.67882			0.129742
$805$	−15.1803	+	2.03845i	−0.535034	+	0.0718459i
$806$	0.105418			0.00371317
$807$	4.28455	−	1.25806i	0.150823	−	0.0442857i
$808$	−5.28408	−	6.09815i	−0.185893	−	0.214532i
$809$	9.13588	−	5.87127i	0.321200	−	0.206423i	−0.370097	−	0.928993i	$-0.620676\pi$
$809$	9.13588	−	5.87127i	0.321200	−	0.206423i	0.691298	+	0.722570i	$0.257039\pi$
$810$	−0.129368	−	0.899773i	−0.00454552	−	0.0316148i
$811$	−12.7341	−	8.18370i	−0.447154	−	0.287368i	0.297621	−	0.954684i	$-0.403807\pi$
$811$	−12.7341	−	8.18370i	−0.447154	−	0.287368i	−0.744775	+	0.667316i	$0.767443\pi$
$812$	−3.26268	+	7.14427i	−0.114498	+	0.250715i
$813$	10.7967	−	12.4601i	0.378658	−	0.436995i
$814$	1.01419	−	7.05386i	0.0355474	−	0.247238i
$815$	−7.97812	−	17.4696i	−0.279461	−	0.611935i
$816$	8.98033	+	2.63686i	0.314375	+	0.0923087i
$817$	57.4264	+	16.8619i	2.00909	+	0.589923i
$818$	0.489368	+	1.07157i	0.0171103	+	0.0374664i
$819$	0.632758	−	4.40093i	0.0221103	−	0.153781i
$820$	22.6839	−	26.1787i	0.792157	−	0.914198i
$821$	−5.22663	+	11.4447i	−0.182411	+	0.399423i	−0.978643	−	0.205568i	$-0.934096\pi$
$821$	−5.22663	+	11.4447i	−0.182411	+	0.399423i	0.796232	+	0.604991i	$0.206823\pi$
$822$	−1.41697	−	0.910631i	−0.0494225	−	0.0317619i
$823$	−5.93582	−	41.2845i	−0.206910	−	1.43909i	−0.783163	−	0.621817i	$-0.786395\pi$
$823$	−5.93582	−	41.2845i	−0.206910	−	1.43909i	0.576253	−	0.817271i	$-0.304514\pi$
$824$	14.8760	−	9.56022i	0.518230	−	0.333046i
$825$	−13.2374	−	15.2768i	−0.460867	−	0.531869i
$826$	2.84496	−	0.835354i	0.0989887	−	0.0290657i
$827$	26.2893			0.914169			0.457085	−	0.889423i	$-0.348894\pi$
$827$	26.2893			0.914169			0.457085	+	0.889423i	$0.348894\pi$
$828$	6.89882	+	6.09130i	0.239751	+	0.211687i
$829$	1.28342			0.0445751			0.0222875	−	0.999752i	$-0.492905\pi$
$829$	1.28342			0.0445751			0.0222875	+	0.999752i	$0.492905\pi$
$830$	−7.32064	+	2.14953i	−0.254103	+	0.0746114i
$831$	0.980797	+	1.13190i	0.0340235	+	0.0392652i
$832$	22.8939	−	14.7130i	0.793703	−	0.510082i
$833$	0.378355	+	2.63151i	0.0131092	+	0.0911766i
$834$	−3.59735	−	2.31187i	−0.124566	−	0.0800537i
$835$	0.874109	−	1.91403i	0.0302498	−	0.0662378i
$836$	−24.6014	+	28.3915i	−0.850857	+	0.981941i
$837$	−0.0118548	+	0.0824522i	−0.000409763	+	0.00284997i
$838$	−0.194365	−	0.425600i	−0.00671422	−	0.0147021i
$839$	−28.2928	−	8.30752i	−0.976776	−	0.286807i	−0.245883	−	0.969299i	$-0.579078\pi$
$839$	−28.2928	−	8.30752i	−0.976776	−	0.286807i	−0.730893	+	0.682492i	$0.760896\pi$
$840$	3.41815	+	1.00366i	0.117937	+	0.0346296i
$841$	−5.08842	−	11.1421i	−0.175463	−	0.384210i
$842$	−1.05367	+	7.32840i	−0.0363117	+	0.252553i
$843$	−3.64085	+	4.20177i	−0.125398	+	0.144717i
$844$	19.9641	−	43.7152i	0.687192	−	1.50474i
$845$	−18.1852	−	11.6869i	−0.625590	−	0.402042i
$846$	−0.174733	−	1.21529i	−0.00600744	−	0.0417826i
$847$	3.45958	−	2.22334i	0.118873	−	0.0763948i
$848$	−4.85040	−	5.59766i	−0.166564	−	0.192225i
$849$	−4.18965	+	1.23019i	−0.143788	+	0.0422200i
$850$	3.93474			0.134960
$851$	−8.42565	−	29.7164i	−0.288828	−	1.01867i
$852$	12.8637			0.440702
$853$	30.7568	−	9.03102i	1.05309	−	0.309216i	0.291027	−	0.956715i	$-0.406003\pi$
$853$	30.7568	−	9.03102i	1.05309	−	0.309216i	0.762067	+	0.647499i	$0.224185\pi$
$854$	0.304897	+	0.351870i	0.0104334	+	0.0120408i
$855$	13.5299	−	8.69514i	0.462713	−	0.297367i
$856$	2.21322	+	15.3933i	0.0756464	+	0.526133i
$857$	−23.0174	−	14.7924i	−0.786258	−	0.505298i	0.0848469	−	0.996394i	$-0.472960\pi$
$857$	−23.0174	−	14.7924i	−0.786258	−	0.505298i	−0.871105	+	0.491096i	$0.836596\pi$
$858$	2.04370	−	4.47507i	0.0697707	−	0.152776i
$859$	16.5743	−	19.1278i	0.565508	−	0.652631i	−0.398917	−	0.916987i	$-0.630614\pi$
$859$	16.5743	−	19.1278i	0.565508	−	0.652631i	0.964425	+	0.264356i	$0.0851595\pi$
$860$	−10.3661	+	72.0978i	−0.353481	+	2.45852i
$861$	−2.34792	−	5.14124i	−0.0800170	−	0.175213i
$862$	−2.15022	−	0.631361i	−0.0732367	−	0.0215042i
$863$	17.7954	+	5.22521i	0.605764	+	0.177868i	0.570209	−	0.821499i	$-0.306862\pi$
$863$	17.7954	+	5.22521i	0.605764	+	0.177868i	0.0355545	+	0.999368i	$0.488680\pi$
$864$	−1.34302	−	2.94080i	−0.0456904	−	0.100048i
$865$	−4.43962	+	30.8783i	−0.150952	+	1.04989i
$866$	4.59393	−	5.30168i	0.156108	−	0.180158i
$867$	−4.12589	+	9.03445i	−0.140123	+	0.306826i
$868$	−0.134476	−	0.0864223i	−0.00456441	−	0.00293337i
$869$	9.52963	+	66.2800i	0.323271	+	2.24840i
$870$	3.12985	−	2.01143i	0.106112	−	0.0681939i
$871$	−5.58179	−	6.44172i	−0.189132	−	0.218269i
$872$	−18.2667	+	5.36360i	−0.618590	+	0.181634i
$873$	−4.39385			−0.148709
$874$	1.99801	−	6.57733i	0.0675838	−	0.222481i
$875$	−0.638107			−0.0215720
$876$	−14.1759	+	4.16241i	−0.478958	+	0.140635i
$877$	−8.86219	−	10.2275i	−0.299255	−	0.345358i	0.586130	−	0.810217i	$-0.300651\pi$
$877$	−8.86219	−	10.2275i	−0.299255	−	0.345358i	−0.885385	+	0.464858i	$0.846105\pi$
$878$	9.40744	−	6.04580i	0.317486	−	0.204036i
$879$	4.15965	+	28.9310i	0.140301	+	0.975818i
$880$	−36.7698	−	23.6305i	−1.23951	−	0.796585i
$881$	−9.90903	+	21.6977i	−0.333844	+	0.731016i	−0.999889	−	0.0148956i	$-0.995258\pi$
$881$	−9.90903	+	21.6977i	−0.333844	+	0.731016i	0.666045	+	0.745911i	$0.267986\pi$
$882$	0.186393	−	0.215109i	0.00627617	−	0.00724309i
$883$	−6.36413	+	44.2635i	−0.214170	+	1.48959i	0.544858	+	0.838528i	$0.316584\pi$
$883$	−6.36413	+	44.2635i	−0.214170	+	1.48959i	−0.759028	+	0.651058i	$0.774326\pi$
$884$	−9.42302	−	20.6335i	−0.316931	−	0.693981i
$885$	31.9221	+	9.37317i	1.07305	+	0.315076i
$886$	1.74827	+	0.513337i	0.0587342	+	0.0172459i
$887$	16.2991	+	35.6900i	0.547270	+	1.19835i	0.958045	+	0.286617i	$0.0925307\pi$
$887$	16.2991	+	35.6900i	0.547270	+	1.19835i	−0.410775	+	0.911737i	$0.634742\pi$
$888$	−1.02241	+	7.11105i	−0.0343100	+	0.238631i
$889$	−2.98577	+	3.44576i	−0.100139	+	0.115567i
$890$	−2.87670	+	6.29909i	−0.0964271	+	0.211146i
$891$	3.27035	+	2.10172i	0.109561	+	0.0704104i
$892$	−2.29218	−	15.9425i	−0.0767480	−	0.533794i
$893$	18.2744	−	11.7442i	0.611529	−	0.393006i
$894$	4.34495	+	5.01434i	0.145317	+	0.167705i
$895$	−67.2106	+	19.7348i	−2.24660	+	0.659662i
$896$	8.20806			0.274212
$897$	0.198627	−	21.3222i	0.00663196	−	0.711928i
$898$	−6.81857			−0.227539
$899$	−0.327120	+	0.0960512i	−0.0109101	+	0.00320349i
$900$	6.53443	+	7.54113i	0.217814	+	0.251371i
$901$	−4.70547	+	3.02402i	−0.156762	+	0.100745i
$902$	−0.890018	−	6.19021i	−0.0296344	−	0.206112i
$903$	9.99826	+	6.42549i	0.332721	+	0.213827i
$904$	−0.394018	+	0.862780i	−0.0131049	+	0.0286956i
$905$	−0.814326	+	0.939782i	−0.0270691	+	0.0312394i
$906$	0.716130	−	4.98080i	0.0237918	−	0.165476i
$907$	11.5511	+	25.2934i	0.383549	+	0.839854i	0.998677	+	0.0514272i	$0.0163770\pi$
$907$	11.5511	+	25.2934i	0.383549	+	0.839854i	−0.615128	+	0.788427i	$0.710896\pi$
$908$	3.52660	+	1.03550i	0.117034	+	0.0343644i
$909$	−6.94078	−	2.03800i	−0.230211	−	0.0675961i
$910$	−1.67898	−	3.67645i	−0.0556576	−	0.121873i
$911$	7.57122	−	52.6590i	0.250846	−	1.74467i	−0.342314	−	0.939585i	$-0.611211\pi$
$911$	7.57122	−	52.6590i	0.250846	−	1.74467i	0.593160	−	0.805084i	$-0.297880\pi$
$912$	11.6097	−	13.3984i	0.384437	−	0.443664i
$913$	13.5544	−	29.6800i	0.448585	−	0.982264i
$914$	5.61877	+	3.61096i	0.185852	+	0.119440i
$915$	0.743482	+	5.17103i	0.0245788	+	0.170949i
$916$	29.4605	−	18.9331i	0.973402	−	0.625567i
$917$	10.8605	+	12.5337i	0.358646	+	0.413899i
$918$	−0.726057	+	0.213190i	−0.0239635	+	0.00703631i
$919$	12.0361			0.397036			0.198518	−	0.980097i	$-0.436387\pi$
$919$	12.0361			0.397036			0.198518	+	0.980097i	$0.436387\pi$
$920$	16.8877	+	2.58886i	0.556770	+	0.0853523i
$921$	−15.4118			−0.507838
$922$	−4.67983	+	1.37412i	−0.154122	+	0.0452543i
$923$	−19.5177	−	22.5247i	−0.642434	−	0.741409i
$924$	−6.27575	+	4.03318i	−0.206457	+	0.132682i
$925$	−4.76606	−	33.1487i	−0.156707	−	1.08992i
$926$	6.60131	+	4.24240i	0.216932	+	0.139414i
$927$	6.58548	−	14.4202i	0.216295	−	0.473621i
$928$	8.66500	−	9.99994i	0.284443	−	0.328264i
$929$	−2.26360	+	15.7437i	−0.0742664	+	0.516534i	0.918401	+	0.395652i	$0.129481\pi$
$929$	−2.26360	+	15.7437i	−0.0742664	+	0.516534i	−0.992667	+	0.120882i	$0.961428\pi$
$930$	0.0314560	+	0.0688791i	0.00103148	+	0.00225863i
$931$	4.83185	+	1.41876i	0.158358	+	0.0464980i
$932$	33.2122	+	9.75200i	1.08790	+	0.319437i
$933$	5.99909	+	13.1362i	0.196401	+	0.430059i
$934$	−1.36045	+	9.46214i	−0.0445153	+	0.309611i
$935$	−21.6153	+	24.9453i	−0.706895	+	0.815800i
$936$	−2.06027	+	4.51135i	−0.0673419	+	0.147458i
$937$	−21.0943	−	13.5565i	−0.689121	−	0.442871i	0.148652	−	0.988890i	$-0.452507\pi$
$937$	−21.0943	−	13.5565i	−0.689121	−	0.442871i	−0.837773	+	0.546018i	$0.816143\pi$
$938$	−0.0776546	−	0.540100i	−0.00253551	−	0.0176349i
$939$	−3.55588	+	2.28522i	−0.116042	+	0.0745754i
$940$	17.3125	+	19.9797i	0.564673	+	0.651667i
$941$	−43.7522	+	12.8468i	−1.42628	+	0.418794i	−0.901625	−	0.432519i	$-0.857625\pi$
$941$	−43.7522	+	12.8468i	−1.42628	+	0.418794i	−0.524658	+	0.851313i	$0.675807\pi$
$942$	1.59686			0.0520286
$943$	−14.4416	−	22.9386i	−0.470282	−	0.746982i
$944$	36.6737			1.19363
$945$	3.06434	−	0.899773i	0.0996831	−	0.0292696i
$946$	8.61179	+	9.93854i	0.279994	+	0.323130i
$947$	−40.7849	+	26.2108i	−1.32533	+	0.851738i	−0.995724	−	0.0923805i	$-0.970552\pi$
$947$	−40.7849	+	26.2108i	−1.32533	+	0.851738i	−0.329606	+	0.944118i	$0.606916\pi$
$948$	−4.70415	−	32.7181i	−0.152784	−	1.06263i
$949$	28.7972	+	18.5068i	0.934797	+	0.600757i
$950$	3.09614	−	6.77961i	0.100452	−	0.219959i
$951$	1.47124	−	1.69790i	0.0477082	−	0.0550582i
$952$	0.422039	−	2.93535i	0.0136784	−	0.0951352i
$953$	−14.4395	−	31.6182i	−0.467743	−	1.02421i	−0.985654	−	0.168779i	$-0.946018\pi$
$953$	−14.4395	−	31.6182i	−0.467743	−	1.02421i	0.517911	−	0.855434i	$-0.326710\pi$
$954$	0.574578	+	0.168711i	0.0186027	+	0.00546223i
$955$	68.3464	+	20.0683i	2.21164	+	0.649396i
$956$	19.0529	+	41.7201i	0.616216	+	1.34933i
$957$	−2.26432	+	15.7487i	−0.0731950	+	0.509082i
$958$	−1.58668	+	1.83113i	−0.0512633	+	0.0591610i
$959$	2.45831	−	5.38294i	0.0793828	−	0.173824i
$960$	16.4448	+	10.5684i	0.530753	+	0.341094i
$961$	4.41077	+	30.6776i	0.142283	+	0.989600i
$962$	6.85674	−	4.40656i	0.221070	−	0.142073i
$963$	9.12999	+	10.5366i	0.294210	+	0.339536i
$964$	30.6716	−	9.00601i	0.987867	−	0.290064i
$965$	15.7264			0.506249
$966$	0.748659	−	1.14142i	0.0240877	−	0.0367245i
$967$	32.3147			1.03917			0.519586	−	0.854418i	$-0.326086\pi$
$967$	32.3147			1.03917			0.519586	+	0.854418i	$0.326086\pi$
$968$	−4.40141	+	1.29237i	−0.141467	+	0.0415384i
$969$	−8.76738	−	10.1181i	−0.281649	−	0.325040i
$970$	−3.36007	+	2.15939i	−0.107885	+	0.0693338i
$971$	−2.65489	−	18.4652i	−0.0851995	−	0.592576i	−0.987036	−	0.160498i	$-0.948690\pi$
$971$	−2.65489	−	18.4652i	−0.0851995	−	0.592576i	0.901837	−	0.432077i	$-0.142219\pi$
$972$	−1.61435	−	1.03748i	−0.0517804	−	0.0332773i
$973$	6.24105	−	13.6660i	0.200079	−	0.438111i
$974$	0.340809	−	0.393314i	0.0109202	−	0.0126026i
$975$	3.29021	−	22.8839i	0.105371	−	0.732873i
$976$	2.39226	+	5.23832i	0.0765744	+	0.167675i
$977$	−24.6691	−	7.24351i	−0.789236	−	0.231740i	−0.137816	−	0.990458i	$-0.544008\pi$
$977$	−24.6691	−	7.24351i	−0.789236	−	0.231740i	−0.651420	+	0.758717i	$0.725826\pi$
$978$	1.64227	+	0.482214i	0.0525140	+	0.0154195i
$979$	−12.3023	−	26.9382i	−0.393182	−	0.860949i
$980$	−0.872204	+	6.06631i	−0.0278615	+	0.193781i
$981$	−11.1767	+	12.8986i	−0.356845	+	0.411821i
$982$	0.828567	−	1.81431i	0.0264406	−	0.0578969i
$983$	28.5621	+	18.3558i	0.910990	+	0.585458i	0.910030	−	0.414542i	$-0.136058\pi$
$983$	28.5621	+	18.3558i	0.910990	+	0.585458i	0.000959935		1.00000i	$0.499694\pi$
$984$	0.897234	+	6.24040i	0.0286028	+	0.198937i
$985$	−2.59164	+	1.66555i	−0.0825766	+	0.0530688i
$986$	−2.02814	−	2.34060i	−0.0645892	−	0.0745399i
$987$	4.13891	−	1.21529i	0.131743	−	0.0386832i
$988$	−42.9666			−1.36695
$989$	51.6246	+	24.1599i	1.64157	+	0.768239i
$990$	3.53381			0.112312
$991$	−15.0348	+	4.41462i	−0.477596	+	0.140235i	−0.511666	−	0.859185i	$-0.670971\pi$
$991$	−15.0348	+	4.41462i	−0.477596	+	0.140235i	0.0340696	+	0.999419i	$0.489153\pi$
$992$	0.176357	+	0.203527i	0.00559935	+	0.00646200i
$993$	−24.1393	+	15.5134i	−0.766038	+	0.492303i
$994$	−0.271534	−	1.88856i	−0.00861253	−	0.0599014i
$995$	58.3567	+	37.5036i	1.85003	+	1.18894i
$996$	−6.69091	+	14.6510i	−0.212010	+	0.464236i
$997$	−28.9502	+	33.4103i	−0.916861	+	1.05811i	0.0812515	+	0.996694i	$0.474108\pi$
$997$	−28.9502	+	33.4103i	−0.916861	+	1.05811i	−0.998112	+	0.0614198i	$0.980437\pi$
$998$	−0.551997	+	3.83922i	−0.0174732	+	0.121529i
$999$	2.67550	+	5.85853i	0.0846491	+	0.185356i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.c.400.2	yes	20
23.18	even	11	inner	483.2.q.c.64.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.c.64.2	✓	20	23.18	even	11	inner
483.2.q.c.400.2	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.273100 - 0.0801894i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(-1.61435 + 1.03748i) q^{4} +(0.454513 + 3.16121i) q^{5} +(-0.239446 - 0.153882i) q^{6} +(0.415415 - 0.909632i) q^{7} +(-0.730471 + 0.843008i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.273100 - 0.0801894i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(-1.61435 + 1.03748i) q^{4} +(0.454513 + 3.16121i) q^{5} +(-0.239446 - 0.153882i) q^{6} +(0.415415 - 0.909632i) q^{7} +(-0.730471 + 0.843008i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.377623 + 0.826879i) q^{10} +(-3.73000 - 1.09523i) q^{11} +(1.84125 + 0.540641i) q^{12} +(-1.84701 - 4.04439i) q^{13} +(0.0405070 - 0.281733i) q^{14} +(2.09144 - 2.41365i) q^{15} +(1.46246 - 3.20234i) q^{16} +(-2.23654 - 1.43733i) q^{17} +(0.0405070 + 0.281733i) q^{18} +(-4.23642 + 2.72258i) q^{19} +(-4.01344 - 4.63175i) q^{20} +(-0.959493 + 0.281733i) q^{21} -1.10649 q^{22} +(-4.38081 + 1.95154i) q^{23} +1.11546 q^{24} +(-4.98917 + 1.46495i) q^{25} +(-0.828736 - 0.956413i) q^{26} +(0.841254 - 0.540641i) q^{27} +(0.273100 + 1.89945i) q^{28} +(3.44308 + 2.21273i) q^{29} +(0.377623 - 0.826879i) q^{30} +(-0.0545500 + 0.0629540i) q^{31} +(0.460097 - 3.20005i) q^{32} +(1.61491 + 3.53617i) q^{33} +(-0.726057 - 0.213190i) q^{34} +(3.06434 + 0.899773i) q^{35} +(-0.797176 - 1.74557i) q^{36} +(-0.916586 + 6.37500i) q^{37} +(-0.938644 + 1.08325i) q^{38} +(-1.84701 + 4.04439i) q^{39} +(-2.99693 - 1.92601i) q^{40} +(0.804363 + 5.59447i) q^{41} +(-0.239446 + 0.153882i) q^{42} +(-7.78299 - 8.98205i) q^{43} +(7.15782 - 2.10172i) q^{44} -3.19371 q^{45} +(-1.03991 + 0.884260i) q^{46} -4.31364 q^{47} +(-3.37787 + 0.991834i) q^{48} +(-0.654861 - 0.755750i) q^{49} +(-1.24507 + 0.800158i) q^{50} +(0.378355 + 2.63151i) q^{51} +(7.17771 + 4.61284i) q^{52} +(0.873996 - 1.91378i) q^{53} +(0.186393 - 0.215109i) q^{54} +(1.76690 - 12.2891i) q^{55} +(0.463379 + 1.01466i) q^{56} +(4.83185 + 1.41876i) q^{57} +(1.11774 + 0.328199i) q^{58} +(4.32749 + 9.47587i) q^{59} +(-0.872204 + 6.06631i) q^{60} +(-1.07121 + 1.23624i) q^{61} +(-0.00984935 + 0.0215671i) q^{62} +(0.841254 + 0.540641i) q^{63} +(0.871076 + 6.05846i) q^{64} +(11.9457 - 7.67701i) q^{65} +(0.724596 + 0.836229i) q^{66} +(1.83941 - 0.540100i) q^{67} +5.10177 q^{68} +(4.34369 + 2.03281i) q^{69} +0.909025 q^{70} +(6.43184 - 1.88856i) q^{71} +(-0.730471 - 0.843008i) q^{72} +(-6.47684 + 4.16241i) q^{73} +(0.260888 + 1.81451i) q^{74} +(4.37435 + 2.81122i) q^{75} +(4.01445 - 8.79042i) q^{76} +(-2.54575 + 2.93795i) q^{77} +(-0.180102 + 1.25263i) q^{78} +(-7.15552 - 15.6684i) q^{79} +(10.7880 + 3.16763i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(0.668289 + 1.46335i) q^{82} +(-1.19449 + 8.30784i) q^{83} +(1.25667 - 1.45027i) q^{84} +(3.52717 - 7.72344i) q^{85} +(-2.84580 - 1.82889i) q^{86} +(-0.582466 - 4.05114i) q^{87} +(3.64794 - 2.34439i) q^{88} +(4.98867 + 5.75723i) q^{89} +(-0.872204 + 0.256102i) q^{90} -4.44618 q^{91} +(5.04749 - 7.69548i) q^{92} +0.0833001 q^{93} +(-1.17806 + 0.345909i) q^{94} +(-10.5321 - 12.1547i) q^{95} +(-2.71973 + 1.74787i) q^{96} +(0.625311 + 4.34913i) q^{97} +(-0.239446 - 0.153882i) q^{98} +(1.61491 - 3.53617i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9} + 9 q^{10} + 3 q^{11} + 18 q^{12} - 2 q^{13} + 18 q^{14} - q^{15} + 8 q^{16} + 8 q^{17} + 18 q^{18} + 6 q^{19} - 2 q^{20} - 2 q^{21} + 6 q^{22} + 11 q^{23} + 9 q^{25} + 7 q^{26} - 2 q^{27} - 4 q^{28} + 23 q^{29} + 9 q^{30} + q^{31} - 28 q^{32} + 14 q^{33} - 28 q^{34} + 10 q^{35} - 4 q^{36} - 9 q^{37} + 34 q^{38} - 2 q^{39} - 15 q^{41} - 4 q^{42} - 23 q^{43} - 16 q^{44} - 12 q^{45} + 11 q^{46} - 66 q^{47} - 36 q^{48} - 2 q^{49} - 26 q^{50} - 14 q^{51} + 7 q^{52} + 9 q^{53} - 4 q^{54} - 62 q^{55} + 22 q^{56} - 27 q^{57} - 20 q^{58} + 49 q^{59} - 2 q^{60} + 46 q^{61} - 9 q^{62} - 2 q^{63} + 16 q^{64} + 11 q^{65} - 16 q^{66} + 14 q^{67} + 38 q^{68} + 11 q^{69} - 2 q^{70} + 36 q^{71} - q^{73} + 4 q^{74} - 2 q^{75} + 34 q^{76} - 8 q^{77} - 15 q^{78} - 22 q^{79} + 15 q^{80} - 2 q^{81} - 30 q^{82} + 8 q^{83} - 4 q^{84} - 32 q^{85} - 68 q^{86} + q^{87} - 11 q^{88} - 2 q^{89} - 2 q^{90} - 24 q^{91} + 11 q^{92} - 32 q^{93} + 33 q^{94} - 107 q^{95} + 16 q^{96} + 18 q^{97} - 4 q^{98} + 14 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9 + 9 * q^10 + 3 * q^11 + 18 * q^12 - 2 * q^13 + 18 * q^14 - q^15 + 8 * q^16 + 8 * q^17 + 18 * q^18 + 6 * q^19 - 2 * q^20 - 2 * q^21 + 6 * q^22 + 11 * q^23 + 9 * q^25 + 7 * q^26 - 2 * q^27 - 4 * q^28 + 23 * q^29 + 9 * q^30 + q^31 - 28 * q^32 + 14 * q^33 - 28 * q^34 + 10 * q^35 - 4 * q^36 - 9 * q^37 + 34 * q^38 - 2 * q^39 - 15 * q^41 - 4 * q^42 - 23 * q^43 - 16 * q^44 - 12 * q^45 + 11 * q^46 - 66 * q^47 - 36 * q^48 - 2 * q^49 - 26 * q^50 - 14 * q^51 + 7 * q^52 + 9 * q^53 - 4 * q^54 - 62 * q^55 + 22 * q^56 - 27 * q^57 - 20 * q^58 + 49 * q^59 - 2 * q^60 + 46 * q^61 - 9 * q^62 - 2 * q^63 + 16 * q^64 + 11 * q^65 - 16 * q^66 + 14 * q^67 + 38 * q^68 + 11 * q^69 - 2 * q^70 + 36 * q^71 - q^73 + 4 * q^74 - 2 * q^75 + 34 * q^76 - 8 * q^77 - 15 * q^78 - 22 * q^79 + 15 * q^80 - 2 * q^81 - 30 * q^82 + 8 * q^83 - 4 * q^84 - 32 * q^85 - 68 * q^86 + q^87 - 11 * q^88 - 2 * q^89 - 2 * q^90 - 24 * q^91 + 11 * q^92 - 32 * q^93 + 33 * q^94 - 107 * q^95 + 16 * q^96 + 18 * q^97 - 4 * q^98 + 14 * q^99

Introduction

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