LMFDB - Embedded newform 77.2.f.b.64.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(15,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("77.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.f (of order $5$, degree $4$, 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:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.2
Root			$0.435488 - 1.34029i$ of defining polynomial
Character	$\chi$	$=$	77.64
Dual form			77.2.f.b.71.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.435488 + 1.34029i) q^{2} +(1.75021 - 1.27160i) q^{3} +(0.0112975 + 0.00820814i) q^{4} +(-0.565930 - 1.74175i) q^{5} +(0.942126 + 2.89957i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-2.29616 + 1.66826i) q^{8} +(0.519216 - 1.59798i) q^{9} +O(q^{10})$	\(q+(-0.435488 + 1.34029i) q^{2} +(1.75021 - 1.27160i) q^{3} +(0.0112975 + 0.00820814i) q^{4} +(-0.565930 - 1.74175i) q^{5} +(0.942126 + 2.89957i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-2.29616 + 1.66826i) q^{8} +(0.519216 - 1.59798i) q^{9} +2.58091 q^{10} +(-2.26009 + 2.42734i) q^{11} +0.0302106 q^{12} +(-1.43602 + 4.41961i) q^{13} +(1.14012 - 0.828347i) q^{14} +(-3.20531 - 2.32880i) q^{15} +(-1.22738 - 3.77748i) q^{16} +(-1.69039 - 5.20248i) q^{17} +(1.91565 + 1.39180i) q^{18} +(4.69325 - 3.40985i) q^{19} +(0.00790293 - 0.0243227i) q^{20} -2.16338 q^{21} +(-2.26911 - 4.08626i) q^{22} -0.719682 q^{23} +(-1.89741 + 5.83962i) q^{24} +(1.33166 - 0.967509i) q^{25} +(-5.29821 - 3.84937i) q^{26} +(0.882303 + 2.71545i) q^{27} +(-0.00431527 - 0.0132810i) q^{28} +(0.948551 + 0.689163i) q^{29} +(4.51715 - 3.28190i) q^{30} +(-0.404153 + 1.24385i) q^{31} -0.0789938 q^{32} +(-0.869026 + 7.12230i) q^{33} +7.70900 q^{34} +(-0.565930 + 1.74175i) q^{35} +(0.0189823 - 0.0137915i) q^{36} +(-1.69468 - 1.23126i) q^{37} +(2.52634 + 7.77528i) q^{38} +(3.10666 + 9.56131i) q^{39} +(4.20516 + 3.05523i) q^{40} +(0.741582 - 0.538791i) q^{41} +(0.942126 - 2.89957i) q^{42} +8.02379 q^{43} +(-0.0454574 + 0.00887181i) q^{44} -3.07713 q^{45} +(0.313413 - 0.964586i) q^{46} +(-4.83455 + 3.51251i) q^{47} +(-6.95163 - 5.05065i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.716823 + 2.20615i) q^{50} +(-9.57403 - 6.95594i) q^{51} +(-0.0525003 + 0.0381437i) q^{52} +(3.13496 - 9.64840i) q^{53} -4.02373 q^{54} +(5.50688 + 2.56282i) q^{55} +2.83822 q^{56} +(3.87821 - 11.9359i) q^{57} +(-1.33676 + 0.971215i) q^{58} +(6.21390 + 4.51466i) q^{59} +(-0.0170971 - 0.0526193i) q^{60} +(-1.93943 - 5.96895i) q^{61} +(-1.49113 - 1.08337i) q^{62} +(-1.35932 + 0.987607i) q^{63} +(2.48916 - 7.66083i) q^{64} +8.51056 q^{65} +(-9.16752 - 4.26643i) q^{66} -15.4673 q^{67} +(0.0236055 - 0.0726501i) q^{68} +(-1.25960 + 0.915151i) q^{69} +(-2.08800 - 1.51702i) q^{70} +(4.29593 + 13.2215i) q^{71} +(1.47365 + 4.53542i) q^{72} +(-4.86593 - 3.53531i) q^{73} +(2.38826 - 1.73517i) q^{74} +(1.10040 - 3.38669i) q^{75} +0.0810106 q^{76} +(3.25521 - 0.635311i) q^{77} -14.1679 q^{78} +(-4.83332 + 14.8754i) q^{79} +(-5.88482 + 4.27557i) q^{80} +(9.07517 + 6.59349i) q^{81} +(0.399188 + 1.22857i) q^{82} +(-1.35217 - 4.16157i) q^{83} +(-0.0244409 - 0.0177573i) q^{84} +(-8.10479 + 5.88848i) q^{85} +(-3.49426 + 10.7542i) q^{86} +2.53651 q^{87} +(1.14011 - 9.34400i) q^{88} +15.3437 q^{89} +(1.34005 - 4.12425i) q^{90} +(3.75955 - 2.73147i) q^{91} +(-0.00813063 - 0.00590725i) q^{92} +(0.874336 + 2.69093i) q^{93} +(-2.60240 - 8.00937i) q^{94} +(-8.59515 - 6.24474i) q^{95} +(-0.138256 + 0.100449i) q^{96} +(0.745114 - 2.29323i) q^{97} -1.40927 q^{98} +(2.70537 + 4.87190i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} + 3 q^{6} - 4 q^{7} - 5 q^{8} - 12 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 + 3 * q^6 - 4 * q^7 - 5 * q^8 - 12 * q^9	\( 16 q - 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} + 3 q^{6} - 4 q^{7} - 5 q^{8} - 12 q^{9} + 12 q^{10} - 3 q^{11} + 18 q^{12} - 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} - 5 q^{17} + 11 q^{18} + 19 q^{19} + q^{20} + 8 q^{21} - 33 q^{22} + 32 q^{23} - 35 q^{24} + 7 q^{25} - 27 q^{26} + 10 q^{27} + 4 q^{28} + 3 q^{29} - 2 q^{30} - 7 q^{31} + 32 q^{32} - 26 q^{33} - 24 q^{34} - 5 q^{35} + 52 q^{36} + 4 q^{37} - 5 q^{38} + 11 q^{39} - 10 q^{40} - 10 q^{41} + 3 q^{42} - 8 q^{43} - 38 q^{44} + 70 q^{45} - 42 q^{46} - 23 q^{47} - 36 q^{48} - 4 q^{49} + 52 q^{50} - 29 q^{51} + 33 q^{52} + 4 q^{53} + 60 q^{54} - 12 q^{55} - 11 q^{57} + 20 q^{58} + 17 q^{59} - 30 q^{60} - 7 q^{61} + 79 q^{62} - 2 q^{63} + 7 q^{64} - 8 q^{65} + 8 q^{66} - 38 q^{67} - 2 q^{68} + 10 q^{69} - 18 q^{70} - 14 q^{71} - 35 q^{73} - 29 q^{74} + 9 q^{75} + 52 q^{76} - 3 q^{77} - 58 q^{78} + 15 q^{79} - 87 q^{80} - 14 q^{81} + 19 q^{82} + 5 q^{83} + 8 q^{84} + 6 q^{85} - 52 q^{86} - 72 q^{87} + 55 q^{88} + 74 q^{89} - 14 q^{90} + 13 q^{91} - 55 q^{92} + 32 q^{93} - 24 q^{94} + 32 q^{95} - 42 q^{96} + 20 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 + 3 * q^6 - 4 * q^7 - 5 * q^8 - 12 * q^9 + 12 * q^10 - 3 * q^11 + 18 * q^12 - 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 - 5 * q^17 + 11 * q^18 + 19 * q^19 + q^20 + 8 * q^21 - 33 * q^22 + 32 * q^23 - 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 + 4 * q^28 + 3 * q^29 - 2 * q^30 - 7 * q^31 + 32 * q^32 - 26 * q^33 - 24 * q^34 - 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 + 11 * q^39 - 10 * q^40 - 10 * q^41 + 3 * q^42 - 8 * q^43 - 38 * q^44 + 70 * q^45 - 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 + 52 * q^50 - 29 * q^51 + 33 * q^52 + 4 * q^53 + 60 * q^54 - 12 * q^55 - 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 - 7 * q^61 + 79 * q^62 - 2 * q^63 + 7 * q^64 - 8 * q^65 + 8 * q^66 - 38 * q^67 - 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 - 35 * q^73 - 29 * q^74 + 9 * q^75 + 52 * q^76 - 3 * q^77 - 58 * q^78 + 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 + 5 * q^83 + 8 * q^84 + 6 * q^85 - 52 * q^86 - 72 * q^87 + 55 * q^88 + 74 * q^89 - 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 - 24 * q^94 + 32 * q^95 - 42 * q^96 + 20 * q^97 + 2 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.435488	+	1.34029i	−0.307936	+	0.947730i	0.670629	+	0.741793i	$0.266024\pi$
$2$	−0.435488	+	1.34029i	−0.307936	+	0.947730i	−0.978565	+	0.205937i	$0.933976\pi$
$3$	1.75021	−	1.27160i	1.01049	−	0.734161i	0.0461746	−	0.998933i	$-0.485297\pi$
$3$	1.75021	−	1.27160i	1.01049	−	0.734161i	0.964311	+	0.264773i	$0.0852969\pi$
$4$	0.0112975	+	0.00820814i	0.00564876	+	0.00410407i
$5$	−0.565930	−	1.74175i	−0.253091	−	0.778935i	−0.994200	−	0.107550i	$-0.965700\pi$
$5$	−0.565930	−	1.74175i	−0.253091	−	0.778935i	0.741108	−	0.671385i	$-0.234300\pi$
$6$	0.942126	+	2.89957i	0.384621	+	1.18374i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	−2.29616	+	1.66826i	−0.811817	+	0.589819i
$9$	0.519216	−	1.59798i	0.173072	−	0.532661i
$10$	2.58091			0.816157
$11$	−2.26009	+	2.42734i	−0.681444	+	0.731871i
$11$	−2.26009	+	2.42734i	−0.681444	+	0.731871i
$12$	0.0302106			0.00872104
$13$	−1.43602	+	4.41961i	−0.398280	+	1.22578i	0.528097	+	0.849184i	$0.322906\pi$
$13$	−1.43602	+	4.41961i	−0.398280	+	1.22578i	−0.926377	+	0.376596i	$0.877094\pi$
$14$	1.14012	−	0.828347i	0.304710	−	0.221385i
$15$	−3.20531	−	2.32880i	−0.827609	−	0.601293i
$16$	−1.22738	−	3.77748i	−0.306844	−	0.944370i
$17$	−1.69039	−	5.20248i	−0.409980	−	1.26179i	−0.916665	−	0.399656i	$-0.869129\pi$
$17$	−1.69039	−	5.20248i	−0.409980	−	1.26179i	0.506685	−	0.862131i	$-0.330871\pi$
$18$	1.91565	+	1.39180i	0.451524	+	0.328051i
$19$	4.69325	−	3.40985i	1.07671	−	0.782272i	0.0995999	−	0.995028i	$-0.468244\pi$
$19$	4.69325	−	3.40985i	1.07671	−	0.782272i	0.977106	+	0.212755i	$0.0682437\pi$
$20$	0.00790293	−	0.0243227i	0.00176715	−	0.00543873i
$21$	−2.16338			−0.472088
$22$	−2.26911	−	4.08626i	−0.483775	−	0.871194i
$23$	−0.719682			−0.150064			−0.0750321	−	0.997181i	$-0.523906\pi$
$23$	−0.719682			−0.150064			−0.0750321	+	0.997181i	$0.523906\pi$
$24$	−1.89741	+	5.83962i	−0.387307	+	1.19201i
$25$	1.33166	−	0.967509i	0.266332	−	0.193502i
$26$	−5.29821	−	3.84937i	−1.03906	−	0.754924i
$27$	0.882303	+	2.71545i	0.169799	+	0.522588i
$28$	−0.00431527	−	0.0132810i	−0.000815510	−	0.00250988i
$29$	0.948551	+	0.689163i	0.176142	+	0.127974i	0.672363	−	0.740222i	$-0.265280\pi$
$29$	0.948551	+	0.689163i	0.176142	+	0.127974i	−0.496221	+	0.868196i	$0.665280\pi$
$30$	4.51715	−	3.28190i	0.824714	−	0.599190i
$31$	−0.404153	+	1.24385i	−0.0725879	+	0.223403i	−0.980768	−	0.195177i	$-0.937472\pi$
$31$	−0.404153	+	1.24385i	−0.0725879	+	0.223403i	0.908180	+	0.418580i	$0.137472\pi$
$32$	−0.0789938			−0.0139643
$33$	−0.869026	+	7.12230i	−0.151278	+	1.23983i
$34$	7.70900			1.32208
$35$	−0.565930	+	1.74175i	−0.0956595	+	0.294410i
$36$	0.0189823	−	0.0137915i	0.00316372	−	0.00229858i
$37$	−1.69468	−	1.23126i	−0.278604	−	0.202417i	0.439705	−	0.898142i	$-0.355083\pi$
$37$	−1.69468	−	1.23126i	−0.278604	−	0.202417i	−0.718308	+	0.695725i	$0.755083\pi$
$38$	2.52634	+	7.77528i	0.409827	+	1.26132i
$39$	3.10666	+	9.56131i	0.497463	+	1.53103i
$40$	4.20516	+	3.05523i	0.664895	+	0.483074i
$41$	0.741582	−	0.538791i	0.115816	−	0.0841449i	−0.528370	−	0.849014i	$-0.677197\pi$
$41$	0.741582	−	0.538791i	0.115816	−	0.0841449i	0.644185	+	0.764869i	$0.277197\pi$
$42$	0.942126	−	2.89957i	0.145373	−	0.447413i
$43$	8.02379			1.22362			0.611808	−	0.791006i	$-0.290442\pi$
$43$	8.02379			1.22362			0.611808	+	0.791006i	$0.290442\pi$
$44$	−0.0454574	+	0.00887181i	−0.00685296	+	0.00133748i
$45$	−3.07713			−0.458711
$46$	0.313413	−	0.964586i	0.0462102	−	0.142220i
$47$	−4.83455	+	3.51251i	−0.705192	+	0.512352i	−0.881619	−	0.471962i	$-0.843546\pi$
$47$	−4.83455	+	3.51251i	−0.705192	+	0.512352i	0.176427	+	0.984314i	$0.443546\pi$
$48$	−6.95163	−	5.05065i	−1.00338	−	0.728999i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.716823	+	2.20615i	0.101374	+	0.311997i
$51$	−9.57403	−	6.95594i	−1.34063	−	0.974027i
$52$	−0.0525003	+	0.0381437i	−0.00728048	+	0.00528958i
$53$	3.13496	−	9.64840i	0.430619	−	1.32531i	−0.466890	−	0.884315i	$-0.654626\pi$
$53$	3.13496	−	9.64840i	0.430619	−	1.32531i	0.897510	−	0.440995i	$-0.145374\pi$
$54$	−4.02373			−0.547560
$55$	5.50688	+	2.56282i	0.742547	+	0.345570i
$56$	2.83822			0.379272
$57$	3.87821	−	11.9359i	0.513682	−	1.58095i
$58$	−1.33676	+	0.971215i	−0.175526	+	0.127527i
$59$	6.21390	+	4.51466i	0.808981	+	0.587759i	0.913535	−	0.406760i	$-0.133341\pi$
$59$	6.21390	+	4.51466i	0.808981	+	0.587759i	−0.104554	+	0.994519i	$0.533341\pi$
$60$	−0.0170971	−	0.0526193i	−0.00220722	−	0.00679312i
$61$	−1.93943	−	5.96895i	−0.248318	−	0.764246i	−0.995073	−	0.0991458i	$-0.968389\pi$
$61$	−1.93943	−	5.96895i	−0.248318	−	0.764246i	0.746754	−	0.665100i	$-0.231611\pi$
$62$	−1.49113	−	1.08337i	−0.189373	−	0.137588i
$63$	−1.35932	+	0.987607i	−0.171259	+	0.124427i
$64$	2.48916	−	7.66083i	0.311144	−	0.957604i
$65$	8.51056			1.05560
$66$	−9.16752	−	4.26643i	−1.12844	−	0.525161i
$67$	−15.4673			−1.88963			−0.944814	−	0.327608i	$-0.893758\pi$
$67$	−15.4673			−1.88963			−0.944814	+	0.327608i	$0.893758\pi$
$68$	0.0236055	−	0.0726501i	0.00286258	−	0.00881012i
$69$	−1.25960	+	0.915151i	−0.151638	+	0.110171i
$70$	−2.08800	−	1.51702i	−0.249564	−	0.181319i
$71$	4.29593	+	13.2215i	0.509833	+	1.56910i	0.792491	+	0.609883i	$0.208784\pi$
$71$	4.29593	+	13.2215i	0.509833	+	1.56910i	−0.282659	+	0.959221i	$0.591216\pi$
$72$	1.47365	+	4.53542i	0.173671	+	0.534504i
$73$	−4.86593	−	3.53531i	−0.569514	−	0.413776i	0.265414	−	0.964134i	$-0.414491\pi$
$73$	−4.86593	−	3.53531i	−0.569514	−	0.413776i	−0.834929	+	0.550358i	$0.814491\pi$
$74$	2.38826	−	1.73517i	0.277629	−	0.201709i
$75$	1.10040	−	3.38669i	0.127064	−	0.391061i
$76$	0.0810106			0.00929255
$77$	3.25521	−	0.635311i	0.370965	−	0.0724004i
$78$	−14.1679			−1.60420
$79$	−4.83332	+	14.8754i	−0.543791	+	1.67362i	0.180058	+	0.983656i	$0.442372\pi$
$79$	−4.83332	+	14.8754i	−0.543791	+	1.67362i	−0.723848	+	0.689959i	$0.757628\pi$
$80$	−5.88482	+	4.27557i	−0.657943	+	0.478024i
$81$	9.07517	+	6.59349i	1.00835	+	0.732610i
$82$	0.399188	+	1.22857i	0.0440829	+	0.135673i
$83$	−1.35217	−	4.16157i	−0.148420	−	0.456791i	0.849015	−	0.528370i	$-0.177196\pi$
$83$	−1.35217	−	4.16157i	−0.148420	−	0.456791i	−0.997435	+	0.0715783i	$0.977196\pi$
$84$	−0.0244409	−	0.0177573i	−0.00266672	−	0.00193748i
$85$	−8.10479	+	5.88848i	−0.879088	+	0.638695i
$86$	−3.49426	+	10.7542i	−0.376796	+	1.15966i
$87$	2.53651			0.271942
$88$	1.14011	−	9.34400i	0.121536	−	0.996073i
$89$	15.3437			1.62643			0.813215	−	0.581963i	$-0.197715\pi$
$89$	15.3437			1.62643			0.813215	+	0.581963i	$0.197715\pi$
$90$	1.34005	−	4.12425i	0.141254	−	0.434735i
$91$	3.75955	−	2.73147i	0.394108	−	0.286336i
$92$	−0.00813063	−	0.00590725i	−0.000847677	−	0.000615873i
$93$	0.874336	+	2.69093i	0.0906644	+	0.279036i
$94$	−2.60240	−	8.00937i	−0.268417	−	0.826104i
$95$	−8.59515	−	6.24474i	−0.881844	−	0.640697i
$96$	−0.138256	+	0.100449i	−0.0141107	+	0.0102520i
$97$	0.745114	−	2.29323i	0.0756549	−	0.232842i	−0.906077	−	0.423114i	$-0.860937\pi$
$97$	0.745114	−	2.29323i	0.0756549	−	0.232842i	0.981731	+	0.190272i	$0.0609370\pi$
$98$	−1.40927			−0.142358
$99$	2.70537	+	4.87190i	0.271900	+	0.489645i
$100$	0.0229859			0.00229859
$101$	3.67603	−	11.3136i	0.365778	−	1.12575i	−0.583714	−	0.811959i	$-0.698401\pi$
$101$	3.67603	−	11.3136i	0.365778	−	1.12575i	0.949492	−	0.313790i	$-0.101599\pi$
$102$	13.4924	−	9.80279i	1.33594	−	0.970620i
$103$	−0.320625	−	0.232947i	−0.0315921	−	0.0229530i	0.571877	−	0.820339i	$-0.306215\pi$
$103$	−0.320625	−	0.232947i	−0.0315921	−	0.0229530i	−0.603469	+	0.797386i	$0.706215\pi$
$104$	−4.07573	−	12.5438i	−0.399658	−	1.23002i
$105$	1.22432	+	3.76807i	0.119482	+	0.367726i
$106$	11.5665	+	8.40352i	1.12343	+	0.816222i
$107$	2.64496	−	1.92168i	0.255698	−	0.185776i	−0.452550	−	0.891739i	$-0.649486\pi$
$107$	2.64496	−	1.92168i	0.255698	−	0.185776i	0.708248	+	0.705963i	$0.249486\pi$
$108$	−0.0123209	+	0.0379199i	−0.00118558	+	0.00364885i
$109$	−2.84638			−0.272634			−0.136317	−	0.990665i	$-0.543527\pi$
$109$	−2.84638			−0.272634			−0.136317	+	0.990665i	$0.543527\pi$
$110$	−5.83310	+	6.26476i	−0.556165	+	0.597321i
$111$	−4.53172			−0.430132
$112$	−1.22738	+	3.77748i	−0.115976	+	0.356938i
$113$	−11.7668	+	8.54906i	−1.10692	+	0.804228i	−0.982177	−	0.187961i	$-0.939812\pi$
$113$	−11.7668	+	8.54906i	−1.10692	+	0.804228i	−0.124748	+	0.992188i	$0.539812\pi$
$114$	14.3087	+	10.3959i	1.34013	+	0.973663i
$115$	0.407290	+	1.25351i	0.0379799	+	0.116890i
$116$	0.00505954	+	0.0155717i	0.000469767	+	0.00144579i
$117$	6.31686	+	4.58947i	0.583994	+	0.424296i
$118$	−8.75705	+	6.36237i	−0.806152	+	0.585704i
$119$	−1.69039	+	5.20248i	−0.154958	+	0.476911i
$120$	11.2450			1.02652
$121$	−0.783964	−	10.9720i	−0.0712695	−	0.997457i
$122$	8.84474			0.800765
$123$	0.612797	−	1.88600i	0.0552541	−	0.170054i
$124$	−0.0147756	+	0.0107351i	−0.00132689	+	0.000964044i
$125$	−9.84690	−	7.15419i	−0.880734	−	0.639890i
$126$	−0.731714	−	2.25198i	−0.0651863	−	0.200623i
$127$	1.55524	+	4.78655i	0.138006	+	0.424737i	0.996045	−	0.0888458i	$-0.0283178\pi$
$127$	1.55524	+	4.78655i	0.138006	+	0.424737i	−0.858040	+	0.513583i	$0.828318\pi$
$128$	9.05595	+	6.57953i	0.800440	+	0.581554i
$129$	14.0433	−	10.2031i	1.23645	−	0.898331i
$130$	−3.70624	+	11.4066i	−0.325059	+	1.00043i
$131$	−0.180053			−0.0157313			−0.00786565	−	0.999969i	$-0.502504\pi$
$131$	−0.180053			−0.0157313			−0.00786565	+	0.999969i	$0.502504\pi$
$132$	−0.0682787	+	0.0733313i	−0.00594290	+	0.00638267i
$133$	−5.80118			−0.503026
$134$	6.73581	−	20.7307i	0.581885	−	1.79086i
$135$	4.23032	−	3.07350i	0.364088	−	0.264525i
$136$	12.5605	+	9.12574i	1.07705	+	0.782526i
$137$	2.57224	+	7.91655i	0.219762	+	0.676357i	0.998781	+	0.0493570i	$0.0157172\pi$
$137$	2.57224	+	7.91655i	0.219762	+	0.676357i	−0.779020	+	0.627000i	$0.784283\pi$
$138$	−0.678031	−	2.08677i	−0.0577179	−	0.177637i
$139$	5.63172	+	4.09169i	0.477677	+	0.347052i	0.800425	−	0.599432i	$-0.204607\pi$
$139$	5.63172	+	4.09169i	0.477677	+	0.347052i	−0.322749	+	0.946485i	$0.604607\pi$
$140$	−0.0206901	+	0.0150323i	−0.00174864	+	0.00127046i
$141$	−3.99497	+	12.2953i	−0.336438	+	1.03545i
$142$	−19.5915			−1.64408
$143$	−7.48237	−	13.4744i	−0.625707	−	1.12679i
$144$	−6.67362			−0.556135
$145$	0.663538	−	2.04216i	0.0551038	−	0.169592i
$146$	6.85740	−	4.98219i	0.567523	−	0.412329i
$147$	1.75021	+	1.27160i	0.144355	+	0.104880i
$148$	−0.00903937	−	0.0278203i	−0.000743031	−	0.00228682i
$149$	−0.993277	−	3.05699i	−0.0813724	−	0.250439i	0.902091	−	0.431546i	$-0.142032\pi$
$149$	−0.993277	−	3.05699i	−0.0813724	−	0.250439i	−0.983463	+	0.181108i	$0.942032\pi$
$150$	4.05995	+	2.94972i	0.331493	+	0.240844i
$151$	−18.0144	+	13.0882i	−1.46599	+	1.06510i	−0.484239	+	0.874936i	$0.660903\pi$
$151$	−18.0144	+	13.0882i	−1.46599	+	1.06510i	−0.981752	+	0.190168i	$0.939097\pi$
$152$	−5.08796	+	15.6591i	−0.412688	+	1.27012i
$153$	−9.19115			−0.743061
$154$	−0.566100	+	4.63960i	−0.0456177	+	0.373870i
$155$	2.39521			0.192388
$156$	−0.0433830	+	0.133519i	−0.00347342	+	0.0106901i
$157$	−10.7233	+	7.79096i	−0.855816	+	0.621786i	−0.926743	−	0.375695i	$-0.877404\pi$
$157$	−10.7233	+	7.79096i	−0.855816	+	0.621786i	0.0709277	+	0.997481i	$0.477404\pi$
$158$	−17.8326	−	12.9561i	−1.41868	−	1.03073i
$159$	−6.78211	−	20.8732i	−0.537856	−	1.65535i
$160$	0.0447049	+	0.137588i	0.00353423	+	0.0108773i
$161$	0.582235	+	0.423019i	0.0458866	+	0.0333385i
$162$	−12.7893	+	9.29200i	−1.00483	+	0.730048i
$163$	4.23920	−	13.0469i	0.332040	−	1.02191i	−0.636122	−	0.771589i	$-0.719462\pi$
$163$	4.23920	−	13.0469i	0.332040	−	1.02191i	0.968162	−	0.250325i	$-0.0805375\pi$
$164$	0.0128005			0.000999552
$165$	12.8971	−	2.51709i	1.00404	−	0.195955i
$166$	6.16657			0.478619
$167$	2.87651	−	8.85300i	0.222591	−	0.685066i	−0.775936	−	0.630812i	$-0.782722\pi$
$167$	2.87651	−	8.85300i	0.222591	−	0.685066i	0.998527	−	0.0542539i	$-0.0172780\pi$
$168$	4.96748	−	3.60908i	0.383249	−	0.278447i
$169$	−6.95361	−	5.05209i	−0.534893	−	0.388623i
$170$	−4.36275	−	13.4272i	−0.334608	−	1.02982i
$171$	−3.01206	−	9.27018i	−0.230338	−	0.708908i
$172$	0.0906490	+	0.0658604i	0.00691192	+	0.00502181i
$173$	−8.49927	+	6.17508i	−0.646188	+	0.469483i	−0.861970	−	0.506959i	$-0.830770\pi$
$173$	−8.49927	+	6.17508i	−0.646188	+	0.469483i	0.215783	+	0.976441i	$0.430770\pi$
$174$	−1.10462	+	3.39966i	−0.0837409	+	0.257728i
$175$	−1.64602			−0.124428
$176$	11.9432	+	5.55819i	0.900254	+	0.418964i
$177$	16.6165			1.24897
$178$	−6.68200	+	20.5651i	−0.500837	+	1.54142i
$179$	6.73370	−	4.89232i	0.503300	−	0.365669i	−0.306976	−	0.951717i	$-0.599317\pi$
$179$	6.73370	−	4.89232i	0.503300	−	0.365669i	0.810276	+	0.586048i	$0.199317\pi$
$180$	−0.0347639	−	0.0252575i	−0.00259115	−	0.00188258i
$181$	−4.57437	−	14.0785i	−0.340010	−	1.04644i	−0.964201	−	0.265172i	$-0.914571\pi$
$181$	−4.57437	−	14.0785i	−0.340010	−	1.04644i	0.624191	−	0.781272i	$-0.285429\pi$
$182$	2.02374	+	6.22842i	0.150009	+	0.461681i
$183$	−10.9845	−	7.98074i	−0.812001	−	0.589953i
$184$	1.65251	−	1.20062i	0.121825	−	0.0885107i
$185$	−1.18547	+	3.64852i	−0.0871578	+	0.268244i
$186$	−3.98740			−0.292370
$187$	16.4486	+	7.65494i	1.20284	+	0.559785i
$188$	−0.0834496			−0.00608619
$189$	0.882303	−	2.71545i	0.0641781	−	0.197520i
$190$	12.1129	−	8.80052i	0.878760	−	0.638457i
$191$	7.77203	+	5.64671i	0.562364	+	0.408582i	0.832324	−	0.554290i	$-0.187010\pi$
$191$	7.77203	+	5.64671i	0.562364	+	0.408582i	−0.269959	+	0.962872i	$0.587010\pi$
$192$	−5.38499	−	16.5733i	−0.388628	−	1.19607i
$193$	−0.459758	−	1.41499i	−0.0330941	−	0.101853i	0.933145	−	0.359500i	$-0.117053\pi$
$193$	−0.459758	−	1.41499i	−0.0330941	−	0.101853i	−0.966239	+	0.257647i	$0.917053\pi$
$194$	2.74911	+	1.99734i	0.197374	+	0.143401i
$195$	14.8953	−	10.8221i	1.06667	−	0.774983i
$196$	−0.00431527	+	0.0132810i	−0.000308234	+	0.000948646i
$197$	−14.0434			−1.00055			−0.500274	−	0.865867i	$-0.666767\pi$
$197$	−14.0434			−1.00055			−0.500274	+	0.865867i	$0.666767\pi$
$198$	−7.70793	+	1.50434i	−0.547779	+	0.106909i
$199$	−4.28729			−0.303918			−0.151959	−	0.988387i	$-0.548558\pi$
$199$	−4.28729			−0.303918			−0.151959	+	0.988387i	$0.548558\pi$
$200$	−1.44366	+	4.44312i	−0.102082	+	0.314176i
$201$	−27.0710	+	19.6682i	−1.90944	+	1.38729i
$202$	13.5627	+	9.85391i	0.954271	+	0.693318i
$203$	−0.362314	−	1.11509i	−0.0254295	−	0.0782639i
$204$	−0.0510676	−	0.157170i	−0.00357545	−	0.0110041i
$205$	−1.35812	−	0.986734i	−0.0948554	−	0.0689165i
$206$	0.451846	−	0.328285i	0.0314816	−	0.0228727i
$207$	−0.373671	+	1.15004i	−0.0259719	+	0.0799333i
$208$	18.4575			1.27980
$209$	−2.33032	+	19.0987i	−0.161192	+	1.32108i
$210$	−5.58350			−0.385298
$211$	−0.449704	+	1.38405i	−0.0309589	+	0.0952816i	−0.965342	−	0.260988i	$-0.915952\pi$
$211$	−0.449704	+	1.38405i	−0.0309589	+	0.0952816i	0.934383	+	0.356270i	$0.115952\pi$
$212$	0.114613	−	0.0832710i	0.00787163	−	0.00571907i
$213$	24.3313	+	17.6777i	1.66715	+	1.21126i
$214$	1.42376	+	4.38189i	0.0973264	+	0.299540i
$215$	−4.54090	−	13.9755i	−0.309687	−	0.953118i
$216$	−6.55599	−	4.76320i	−0.446079	−	0.324095i
$217$	1.05809	−	0.768744i	0.0718275	−	0.0521857i
$218$	1.23957	−	3.81499i	0.0839540	−	0.258384i
$219$	−13.0119			−0.879264
$220$	0.0411782	+	0.0741547i	0.00277623	+	0.00499951i
$221$	25.4204			1.70996
$222$	1.97351	−	6.07383i	0.132453	−	0.407649i
$223$	3.92893	−	2.85453i	0.263101	−	0.191154i	−0.448412	−	0.893827i	$-0.648010\pi$
$223$	3.92893	−	2.85453i	0.263101	−	0.191154i	0.711513	+	0.702673i	$0.248010\pi$
$224$	0.0639073	+	0.0464314i	0.00426999	+	0.00310233i
$225$	−0.854642	−	2.63032i	−0.0569761	−	0.175354i
$226$	−6.33396	−	19.4939i	−0.421329	−	1.29672i
$227$	−0.321296	−	0.233435i	−0.0213252	−	0.0154936i	0.577072	−	0.816694i	$-0.304195\pi$
$227$	−0.321296	−	0.233435i	−0.0213252	−	0.0154936i	−0.598397	+	0.801200i	$0.704195\pi$
$228$	0.141786	−	0.103013i	0.00938999	−	0.00682223i
$229$	0.676634	−	2.08246i	0.0447132	−	0.137613i	−0.926208	−	0.377014i	$-0.876951\pi$
$229$	0.676634	−	2.08246i	0.0447132	−	0.137613i	0.970921	+	0.239401i	$0.0769509\pi$
$230$	−1.85744			−0.122476
$231$	4.88944	−	5.25126i	0.321702	−	0.345508i
$232$	−3.32773			−0.218476
$233$	−0.389410	+	1.19848i	−0.0255111	+	0.0785150i	−0.963001	−	0.269496i	$-0.913143\pi$
$233$	−0.389410	+	1.19848i	−0.0255111	+	0.0785150i	0.937490	+	0.348011i	$0.113143\pi$
$234$	−8.90215	+	6.46779i	−0.581952	+	0.422813i
$235$	8.85393	+	6.43276i	0.577567	+	0.419627i
$236$	0.0331448	+	0.102009i	0.00215754	+	0.00664023i
$237$	10.4563	+	32.1812i	0.679210	+	2.09039i
$238$	−6.23671	−	4.53123i	−0.404266	−	0.293716i
$239$	9.02997	−	6.56066i	0.584100	−	0.424374i	−0.256100	−	0.966650i	$-0.582438\pi$
$239$	9.02997	−	6.56066i	0.584100	−	0.424374i	0.840200	+	0.542277i	$0.182438\pi$
$240$	−4.86285	+	14.9663i	−0.313896	+	0.966072i
$241$	−21.4843			−1.38392			−0.691962	−	0.721934i	$-0.743254\pi$
$241$	−21.4843			−1.38392			−0.691962	+	0.721934i	$0.743254\pi$
$242$	15.0471	+	3.72744i	0.967267	+	0.239609i
$243$	15.7022			1.00730
$244$	0.0270832	−	0.0833535i	0.00173382	−	0.00533616i
$245$	1.48162	−	1.07646i	0.0946574	−	0.0687726i
$246$	2.26092	+	1.64266i	0.144151	+	0.104732i
$247$	8.33060	+	25.6390i	0.530063	+	1.63137i
$248$	−1.14707	−	3.53032i	−0.0728391	−	0.224176i
$249$	−7.65846	−	5.56419i	−0.485335	−	0.352616i
$250$	13.8769	−	10.0822i	0.877653	−	0.637652i
$251$	−0.130968	+	0.403077i	−0.00826660	+	0.0254420i	−0.955105	−	0.296268i	$-0.904258\pi$
$251$	−0.130968	+	0.403077i	−0.00826660	+	0.0254420i	0.946838	+	0.321710i	$0.104258\pi$
$252$	−0.0234634			−0.00147806
$253$	1.62655	−	1.74691i	0.102260	−	0.109828i
$254$	−7.09267			−0.445033
$255$	−6.69730	+	20.6122i	−0.419401	+	1.29078i
$256$	0.271127	−	0.196986i	0.0169455	−	0.0123116i
$257$	−14.1093	−	10.2510i	−0.880115	−	0.639441i	0.0531672	−	0.998586i	$-0.483068\pi$
$257$	−14.1093	−	10.2510i	−0.880115	−	0.639441i	−0.933282	+	0.359145i	$0.883068\pi$
$258$	7.55942	+	23.2655i	0.470629	+	1.44845i
$259$	0.647310	+	1.99221i	0.0402219	+	0.123790i
$260$	0.0961483	+	0.0698558i	0.00596286	+	0.00433227i
$261$	1.59377	−	1.15794i	0.0986521	−	0.0716749i
$262$	0.0784109	−	0.241324i	0.00484424	−	0.0149090i
$263$	1.51519			0.0934307			0.0467153	−	0.998908i	$-0.485125\pi$
$263$	1.51519			0.0934307			0.0467153	+	0.998908i	$0.485125\pi$
$264$	−9.88643	−	17.8037i	−0.608468	−	1.09574i
$265$	−18.5793			−1.14132
$266$	2.52634	−	7.77528i	0.154900	−	0.476733i
$267$	26.8548	−	19.5111i	1.64348	−	1.19406i
$268$	−0.174742	−	0.126957i	−0.0106741	−	0.00775516i
$269$	−0.627622	−	1.93162i	−0.0382668	−	0.117773i	0.930098	−	0.367311i	$-0.119721\pi$
$269$	−0.627622	−	1.93162i	−0.0382668	−	0.117773i	−0.968365	+	0.249538i	$0.919721\pi$
$270$	2.27715	+	7.00834i	0.138583	+	0.426514i
$271$	−6.15212	−	4.46978i	−0.373715	−	0.271520i	0.385035	−	0.922902i	$-0.374189\pi$
$271$	−6.15212	−	4.46978i	−0.373715	−	0.271520i	−0.758750	+	0.651382i	$0.774189\pi$
$272$	−17.5775	+	12.7708i	−1.06579	+	0.774344i
$273$	3.10666	−	9.56131i	0.188023	−	0.578677i
$274$	−11.7307			−0.708676
$275$	−0.661205	+	5.41905i	−0.0398722	+	0.326781i
$276$	−0.0217420			−0.00130872
$277$	4.45813	−	13.7207i	0.267863	−	0.824398i	−0.723157	−	0.690684i	$-0.757310\pi$
$277$	4.45813	−	13.7207i	0.267863	−	0.824398i	0.991020	−	0.133714i	$-0.0426903\pi$
$278$	−7.93661	+	5.76628i	−0.476006	+	0.345839i
$279$	1.77781	+	1.29166i	0.106435	+	0.0773295i
$280$	−1.60623	−	4.94347i	−0.0959906	−	0.295429i
$281$	5.48494	+	16.8809i	0.327204	+	1.00703i	0.970436	+	0.241359i	$0.0775933\pi$
$281$	5.48494	+	16.8809i	0.327204	+	1.00703i	−0.643232	+	0.765672i	$0.722407\pi$
$282$	−14.7395	−	10.7089i	−0.877725	−	0.637704i
$283$	25.1897	−	18.3014i	1.49737	−	1.08790i	0.525956	−	0.850512i	$-0.323708\pi$
$283$	25.1897	−	18.3014i	1.49737	−	1.08790i	0.971414	−	0.237392i	$-0.0762924\pi$
$284$	−0.0599905	+	0.184632i	−0.00355978	+	0.0109559i
$285$	−22.9842			−1.36147
$286$	21.3182	−	4.16062i	1.26057	−	0.246022i
$287$	−0.916645			−0.0541079
$288$	−0.0410148	+	0.126231i	−0.00241682	+	0.00743821i
$289$	−10.4551	+	7.59609i	−0.615007	+	0.446829i
$290$	2.44813	+	1.77867i	0.143759	+	0.104447i
$291$	−1.61197	−	4.96112i	−0.0944951	−	0.290826i
$292$	−0.0259547	−	0.0798805i	−0.00151889	−	0.00467465i
$293$	19.4409	+	14.1247i	1.13575	+	0.825171i	0.986522	−	0.163632i	$-0.0523209\pi$
$293$	19.4409	+	14.1247i	1.13575	+	0.825171i	0.149229	+	0.988803i	$0.452321\pi$
$294$	−2.46652	+	1.79203i	−0.143850	+	0.104513i
$295$	4.34679	−	13.3781i	0.253080	−	0.778901i
$296$	5.94532			0.345565
$297$	−8.58540	−	3.99552i	−0.498176	−	0.231843i
$298$	4.52983			0.262406
$299$	1.03348	−	3.18072i	0.0597676	−	0.183946i
$300$	0.0402302	−	0.0292290i	0.00232269	−	0.00168754i
$301$	−6.49138	−	4.71627i	−0.374157	−	0.271841i
$302$	−9.69701	−	29.8443i	−0.558000	−	1.71735i
$303$	−7.95265	−	24.4757i	−0.456868	−	1.40609i
$304$	−18.6410	−	13.5435i	−1.06914	−	0.776772i
$305$	−9.29885	+	6.75601i	−0.532450	+	0.386848i
$306$	4.00263	−	12.3188i	0.228815	−	0.704221i
$307$	−5.46298			−0.311789			−0.155894	−	0.987774i	$-0.549826\pi$
$307$	−5.46298			−0.311789			−0.155894	+	0.987774i	$0.549826\pi$
$308$	0.0419905	+	0.0195417i	0.00239263	+	0.00111349i
$309$	−0.857378			−0.0487745
$310$	−1.04308	+	3.21028i	−0.0592431	+	0.182332i
$311$	−11.2360	+	8.16342i	−0.637134	+	0.462905i	−0.858864	−	0.512203i	$-0.828830\pi$
$311$	−11.2360	+	8.16342i	−0.637134	+	0.462905i	0.221730	+	0.975108i	$0.428830\pi$
$312$	−23.0842	−	16.7716i	−1.30688	−	0.949506i
$313$	8.48207	+	26.1051i	0.479435	+	1.47555i	0.839882	+	0.542770i	$0.182624\pi$
$313$	8.48207	+	26.1051i	0.479435	+	1.47555i	−0.360447	+	0.932780i	$0.617376\pi$
$314$	−5.77229	−	17.7653i	−0.325749	−	1.00255i
$315$	2.48945	+	1.80869i	0.140265	+	0.101908i
$316$	−0.176704	+	0.128383i	−0.00994038	+	0.00722211i
$317$	2.41828	−	7.44269i	0.135824	−	0.418023i	−0.859893	−	0.510474i	$-0.829470\pi$
$317$	2.41828	−	7.44269i	0.135824	−	0.418023i	0.995717	+	0.0924507i	$0.0294701\pi$
$318$	30.9297			1.73445
$319$	−3.81665	+	0.744885i	−0.213691	+	0.0417056i
$320$	−14.7520			−0.824659
$321$	2.18563	−	6.72669i	0.121990	−	0.375447i
$322$	−0.820525	+	0.596147i	−0.0457261	+	0.0332220i
$323$	−25.6731	−	18.6526i	−1.42849	−	1.03786i
$324$	0.0484067	+	0.148980i	0.00268926	+	0.00827669i
$325$	2.36372	+	7.27479i	0.131116	+	0.403533i
$326$	15.6406	+	11.3635i	0.866252	+	0.629369i
$327$	−4.98178	+	3.61947i	−0.275493	+	0.200157i
$328$	−0.803950	+	2.47430i	−0.0443907	+	0.136621i
$329$	5.97584			0.329458
$330$	−2.24288	+	18.3820i	−0.123467	+	1.01190i
$331$	−28.1462			−1.54705			−0.773527	−	0.633764i	$-0.781509\pi$
$331$	−28.1462			−1.54705			−0.773527	+	0.633764i	$0.781509\pi$
$332$	0.0188825	−	0.0581143i	0.00103631	−	0.00318943i
$333$	−2.84743	+	2.06878i	−0.156038	+	0.113368i
$334$	10.6129	+	7.71075i	0.580714	+	0.421913i
$335$	8.75338	+	26.9401i	0.478248	+	1.47190i
$336$	2.65528	+	8.17213i	0.144858	+	0.445826i
$337$	20.2084	+	14.6823i	1.10082	+	0.799793i	0.981194	−	0.193025i	$-0.0618300\pi$
$337$	20.2084	+	14.6823i	1.10082	+	0.799793i	0.119628	+	0.992819i	$0.461830\pi$
$338$	9.79950	−	7.11975i	0.533022	−	0.387263i
$339$	−9.72333	+	29.9253i	−0.528099	+	1.62532i
$340$	−0.139898			−0.00758701
$341$	−2.10583	−	3.79224i	−0.114037	−	0.205361i
$342$	13.7365			0.742783
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	−18.4239	+	13.3858i	−0.993352	+	0.721713i
$345$	2.30681	+	1.67599i	0.124194	+	0.0902325i
$346$	−4.57509	−	14.0807i	−0.245959	−	0.756983i
$347$	6.38096	+	19.6386i	0.342548	+	1.05425i	0.962883	+	0.269918i	$0.0869965\pi$
$347$	6.38096	+	19.6386i	0.342548	+	1.05425i	−0.620335	+	0.784337i	$0.713003\pi$
$348$	0.0286563	+	0.0208200i	0.00153614	+	0.00111607i
$349$	4.85185	−	3.52507i	0.259713	−	0.188693i	−0.450307	−	0.892874i	$-0.648686\pi$
$349$	4.85185	−	3.52507i	0.259713	−	0.188693i	0.710021	+	0.704181i	$0.248686\pi$
$350$	0.716823	−	2.20615i	0.0383158	−	0.117924i
$351$	−13.2682			−0.708206
$352$	0.178533	−	0.191745i	0.00951585	−	0.0102200i
$353$	24.0382			1.27942			0.639712	−	0.768615i	$-0.279054\pi$
$353$	24.0382			1.27942			0.639712	+	0.768615i	$0.279054\pi$
$354$	−7.23629	+	22.2710i	−0.384604	+	1.18369i
$355$	20.5974	−	14.9649i	1.09320	−	0.794253i
$356$	0.173346	+	0.125943i	0.00918732	+	0.00667498i
$357$	3.65696	+	11.2550i	0.193547	+	0.595675i
$358$	3.62470	+	11.1557i	0.191571	+	0.589596i
$359$	8.85883	+	6.43632i	0.467551	+	0.339696i	0.796486	−	0.604657i	$-0.206690\pi$
$359$	8.85883	+	6.43632i	0.467551	+	0.339696i	−0.328935	+	0.944353i	$0.606690\pi$
$360$	7.06559	−	5.13345i	0.372389	−	0.270557i
$361$	4.52822	−	13.9364i	0.238328	−	0.733497i
$362$	20.8613			1.09645
$363$	−15.3242	−	18.2065i	−0.804311	−	0.955593i
$364$	0.0648939			0.00340136
$365$	−3.40385	+	10.4760i	−0.178166	+	0.548338i
$366$	15.4802	−	11.2470i	0.809161	−	0.587890i
$367$	−8.58995	−	6.24096i	−0.448392	−	0.325776i	0.340569	−	0.940220i	$-0.389380\pi$
$367$	−8.58995	−	6.24096i	−0.448392	−	0.325776i	−0.788960	+	0.614444i	$0.789380\pi$
$368$	0.883322	+	2.71859i	0.0460463	+	0.141716i
$369$	−0.475937	−	1.46478i	−0.0247763	−	0.0762535i
$370$	−4.37382	−	3.17777i	−0.227384	−	0.165204i
$371$	−8.20742	+	5.96304i	−0.426108	+	0.309586i
$372$	−0.0122097	+	0.0375775i	−0.000633042	+	0.00194830i
$373$	36.6036			1.89526			0.947631	−	0.319367i	$-0.103470\pi$
$373$	36.6036			1.89526			0.947631	+	0.319367i	$0.103470\pi$
$374$	−17.4230	+	18.7124i	−0.900924	+	0.967593i
$375$	−26.3315			−1.35975
$376$	5.24115	−	16.1306i	0.270292	−	0.831872i
$377$	−4.40797	+	3.20258i	−0.227022	+	0.164941i
$378$	3.25527	+	2.36509i	0.167433	+	0.121647i
$379$	−3.91147	−	12.0383i	−0.200919	−	0.618364i	−0.999856	−	0.0169501i	$-0.994604\pi$
$379$	−3.91147	−	12.0383i	−0.200919	−	0.618364i	0.798938	−	0.601414i	$-0.205396\pi$
$380$	−0.0458463	−	0.141100i	−0.00235187	−	0.00723830i
$381$	8.80860	+	6.39982i	0.451278	+	0.327873i
$382$	−10.9529	+	7.95773i	−0.560398	+	0.407153i
$383$	−4.77984	+	14.7108i	−0.244238	+	0.751688i	0.751522	+	0.659708i	$0.229320\pi$
$383$	−4.77984	+	14.7108i	−0.244238	+	0.751688i	−0.995761	+	0.0919809i	$0.970680\pi$
$384$	24.2164			1.23579
$385$	−2.94877	−	5.31022i	−0.150283	−	0.270634i
$386$	2.09672			0.106720
$387$	4.16608	−	12.8219i	0.211774	−	0.651773i
$388$	0.0272411	−	0.0197918i	0.00138296	−	0.00100478i
$389$	10.2850	+	7.47249i	0.521470	+	0.378870i	0.817157	−	0.576415i	$-0.195549\pi$
$389$	10.2850	+	7.47249i	0.521470	+	0.378870i	−0.295687	+	0.955285i	$0.595549\pi$
$390$	8.01801	+	24.6769i	0.406008	+	1.24956i
$391$	1.21654	+	3.74414i	0.0615232	+	0.189349i
$392$	−2.29616	−	1.66826i	−0.115974	−	0.0842599i
$393$	−0.315131	+	0.228956i	−0.0158963	+	0.0115493i
$394$	6.11571	−	18.8222i	0.308105	−	0.948250i
$395$	28.6446			1.44127
$396$	−0.00942522	+	0.0772465i	−0.000473635	+	0.00388178i
$397$	−18.9574			−0.951445			−0.475722	−	0.879596i	$-0.657813\pi$
$397$	−18.9574			−0.951445			−0.475722	+	0.879596i	$0.657813\pi$
$398$	1.86706	−	5.74622i	0.0935873	−	0.288032i
$399$	−10.1533	+	7.37680i	−0.508300	+	0.369302i
$400$	−5.28919	−	3.84282i	−0.264460	−	0.192141i
$401$	−2.68291	−	8.25715i	−0.133978	−	0.412343i	0.861451	−	0.507840i	$-0.169556\pi$
$401$	−2.68291	−	8.25715i	−0.133978	−	0.412343i	−0.995430	+	0.0954974i	$0.969556\pi$
$402$	−14.5721	−	44.8484i	−0.726791	−	2.23683i
$403$	−4.91698	−	3.57240i	−0.244932	−	0.177954i
$404$	0.134394	−	0.0976429i	0.00668635	−	0.00485792i
$405$	6.34833	−	19.5381i	0.315451	−	0.970858i
$406$	1.65233			0.0820037
$407$	6.81881	−	1.33081i	0.337996	−	0.0659658i
$408$	33.5879			1.66285
$409$	1.76574	−	5.43440i	0.0873104	−	0.268714i	−0.897863	−	0.440275i	$-0.854881\pi$
$409$	1.76574	−	5.43440i	0.0873104	−	0.268714i	0.985173	+	0.171561i	$0.0548811\pi$
$410$	1.91396	−	1.39057i	0.0945237	−	0.0686755i
$411$	14.5687	+	10.5848i	0.718620	+	0.522108i
$412$	−0.00171020	−	0.00526346i	−8.42556e−5	−	0.000259312i
$413$	−2.37350	−	7.30488i	−0.116792	−	0.359450i
$414$	−1.37866	−	1.00166i	−0.0677575	−	0.0492287i
$415$	−6.48318	+	4.71031i	−0.318247	+	0.231220i
$416$	0.113437	−	0.349122i	0.00556169	−	0.0171171i
$417$	15.0597			0.737477
$418$	−24.5830	−	11.4406i	−1.20239	−	0.559576i
$419$	−27.1909			−1.32836			−0.664181	−	0.747571i	$-0.731220\pi$
$419$	−27.1909			−1.32836			−0.664181	+	0.747571i	$0.731220\pi$
$420$	−0.0170971	+	0.0526193i	−0.000834251	+	0.00256756i
$421$	19.3881	−	14.0863i	0.944921	−	0.686525i	−0.00467947	−	0.999989i	$-0.501490\pi$
$421$	19.3881	−	14.0863i	0.944921	−	0.686525i	0.949600	+	0.313464i	$0.101490\pi$
$422$	−1.65919	−	1.20547i	−0.0807679	−	0.0586813i
$423$	3.10275	+	9.54928i	0.150861	+	0.464302i
$424$	8.89768	+	27.3842i	0.432110	+	1.32990i
$425$	−7.28447	−	5.29248i	−0.353349	−	0.256723i
$426$	−34.2893	+	24.9126i	−1.66132	+	1.20702i
$427$	−1.93943	+	5.96895i	−0.0938555	+	0.288858i
$428$	0.0456549			0.00220681
$429$	−30.2299	−	14.0685i	−1.45951	−	0.679235i
$430$	20.7087			0.998663
$431$	5.09049	−	15.6669i	0.245200	−	0.754649i	−0.750403	−	0.660980i	$-0.770141\pi$
$431$	5.09049	−	15.6669i	0.245200	−	0.754649i	0.995603	−	0.0936683i	$-0.0298593\pi$
$432$	9.17463	−	6.66576i	0.441415	−	0.320706i
$433$	−16.2539	−	11.8092i	−0.781113	−	0.567512i	0.124200	−	0.992257i	$-0.460364\pi$
$433$	−16.2539	−	11.8092i	−0.781113	−	0.567512i	−0.905313	+	0.424745i	$0.860364\pi$
$434$	0.569559	+	1.75292i	0.0273397	+	0.0841430i
$435$	−1.43548	−	4.41797i	−0.0688262	−	0.211825i
$436$	−0.0321571	−	0.0233635i	−0.00154005	−	0.00111891i
$437$	−3.37765	+	2.45401i	−0.161575	+	0.117391i
$438$	5.66653	−	17.4398i	0.270757	−	0.833306i
$439$	26.7682			1.27758			0.638788	−	0.769383i	$-0.279436\pi$
$439$	26.7682			1.27758			0.638788	+	0.769383i	$0.279436\pi$
$440$	−16.9201	+	3.30226i	−0.806636	+	0.157429i
$441$	1.68022			0.0800104
$442$	−11.0703	+	34.0708i	−0.526559	+	1.62058i
$443$	−21.2086	+	15.4090i	−1.00765	+	0.732103i	−0.963716	−	0.266931i	$-0.913990\pi$
$443$	−21.2086	+	15.4090i	−1.00765	+	0.732103i	−0.0439378	+	0.999034i	$0.513990\pi$
$444$	−0.0511972	−	0.0371970i	−0.00242971	−	0.00176529i
$445$	−8.68346	−	26.7249i	−0.411635	−	1.26688i
$446$	2.11491	+	6.50903i	0.100144	+	0.308212i
$447$	−5.62573	−	4.08733i	−0.266088	−	0.193324i
$448$	−6.51669	+	4.73465i	−0.307885	+	0.223691i
$449$	3.01211	−	9.27033i	0.142150	−	0.437494i	−0.854483	−	0.519479i	$-0.826126\pi$
$449$	3.01211	−	9.27033i	0.142150	−	0.437494i	0.996634	+	0.0819851i	$0.0261260\pi$
$450$	3.89758			0.183734
$451$	−0.368215	+	3.01779i	−0.0173386	+	0.142102i
$452$	−0.203107			−0.00955336
$453$	−14.8860	+	45.8143i	−0.699404	+	2.15254i
$454$	0.452792	−	0.328973i	0.0212506	−	0.0154395i
$455$	−6.88518	−	5.00238i	−0.322782	−	0.234515i
$456$	11.0072	+	33.8767i	0.515459	+	1.58642i
$457$	3.67276	+	11.3036i	0.171805	+	0.528760i	0.999473	−	0.0324572i	$-0.0103333\pi$
$457$	3.67276	+	11.3036i	0.171805	+	0.528760i	−0.827669	+	0.561217i	$0.810333\pi$
$458$	2.49645	+	1.81378i	0.116651	+	0.0847522i
$459$	12.6356	−	9.18033i	0.589781	−	0.428501i
$460$	−0.00568760	+	0.0175046i	−0.000265186	+	0.000816158i
$461$	9.14737			0.426035			0.213018	−	0.977048i	$-0.431671\pi$
$461$	9.14737			0.426035			0.213018	+	0.977048i	$0.431671\pi$
$462$	4.90894	+	8.84015i	0.228385	+	0.411281i
$463$	38.9342			1.80943			0.904713	−	0.426021i	$-0.140085\pi$
$463$	38.9342			1.80943			0.904713	+	0.426021i	$0.140085\pi$
$464$	1.43907	−	4.42899i	0.0668070	−	0.205611i
$465$	4.19212	−	3.04575i	0.194405	−	0.141243i
$466$	−1.43673	−	1.04385i	−0.0665553	−	0.0483552i
$467$	−6.42243	−	19.7662i	−0.297195	−	0.914671i	−0.982475	−	0.186392i	$-0.940320\pi$
$467$	−6.42243	−	19.7662i	−0.297195	−	0.914671i	0.685281	−	0.728279i	$-0.259680\pi$
$468$	0.0336939	+	0.103699i	0.00155750	+	0.00479350i
$469$	12.5133	+	9.09143i	0.577810	+	0.419803i
$470$	−12.4776	+	9.06548i	−0.575547	+	0.418159i
$471$	−8.86110	+	27.2717i	−0.408298	+	1.25661i
$472$	−21.7998			−1.00342
$473$	−18.1345	+	19.4765i	−0.833826	+	0.895529i
$474$	−47.6858			−2.19028
$475$	2.95076	−	9.08152i	0.135390	−	0.416689i
$476$	−0.0617999	+	0.0449003i	−0.00283259	+	0.00205800i
$477$	−13.7903	−	10.0192i	−0.631413	−	0.458748i
$478$	4.86076	+	14.9599i	0.222326	+	0.684249i
$479$	−7.58214	−	23.3354i	−0.346437	−	1.06622i	−0.960810	−	0.277207i	$-0.910591\pi$
$479$	−7.58214	−	23.3354i	−0.346437	−	1.06622i	0.614374	−	0.789015i	$-0.289409\pi$
$480$	0.253200	+	0.183960i	0.0115569	+	0.00839661i
$481$	7.87527	−	5.72172i	0.359081	−	0.260888i
$482$	9.35614	−	28.7952i	0.426161	−	1.31159i
$483$	1.55695			0.0708436
$484$	0.0812030	−	0.130392i	0.00369105	−	0.00592690i
$485$	−4.41591			−0.200516
$486$	−6.83811	+	21.0456i	−0.310183	+	0.954646i
$487$	10.0086	−	7.27168i	0.453533	−	0.329511i	−0.337456	−	0.941341i	$-0.609566\pi$
$487$	10.0086	−	7.27168i	0.453533	−	0.329511i	0.790989	+	0.611830i	$0.209566\pi$
$488$	14.4110	+	10.4702i	0.652356	+	0.473964i
$489$	−9.17101	−	28.2255i	−0.414727	−	1.27640i
$490$	0.797546	+	2.45459i	0.0360295	+	0.110887i
$491$	−13.3691	−	9.71320i	−0.603338	−	0.438350i	0.243724	−	0.969845i	$-0.421631\pi$
$491$	−13.3691	−	9.71320i	−0.603338	−	0.438350i	−0.847062	+	0.531494i	$0.821631\pi$
$492$	0.0224036	−	0.0162772i	0.00101003	−	0.000733831i
$493$	1.98194	−	6.09977i	0.0892620	−	0.274720i
$494$	−37.9916			−1.70932
$495$	6.95459	−	7.46924i	0.312586	−	0.335717i
$496$	5.19468			0.233248
$497$	4.29593	−	13.2215i	0.192699	−	0.593065i
$498$	10.7928	−	7.84144i	0.483638	−	0.351383i
$499$	11.1167	+	8.07673i	0.497650	+	0.361564i	0.808119	−	0.589020i	$-0.200486\pi$
$499$	11.1167	+	8.07673i	0.497650	+	0.361564i	−0.310469	+	0.950584i	$0.600486\pi$
$500$	−0.0525231	−	0.161649i	−0.00234890	−	0.00722918i
$501$	−6.22300	−	19.1524i	−0.278023	−	0.855667i
$502$	−0.483206	−	0.351070i	−0.0215665	−	0.0156690i
$503$	18.2812	−	13.2820i	0.815117	−	0.592217i	−0.100193	−	0.994968i	$-0.531946\pi$
$503$	18.2812	−	13.2820i	0.815117	−	0.592217i	0.915310	+	0.402751i	$0.131946\pi$
$504$	1.47365	−	4.53542i	0.0656414	−	0.202024i
$505$	−21.7859			−0.969461
$506$	1.63304	+	2.94081i	0.0725973	+	0.130735i
$507$	−18.5946			−0.825813
$508$	−0.0217182	+	0.0668418i	−0.000963590	+	0.00296563i
$509$	17.3644	−	12.6160i	0.769664	−	0.559194i	−0.132195	−	0.991224i	$-0.542202\pi$
$509$	17.3644	−	12.6160i	0.769664	−	0.559194i	0.901859	+	0.432030i	$0.142202\pi$
$510$	−24.7098	−	17.9527i	−1.09417	−	0.794958i
$511$	1.85862	+	5.72025i	0.0822206	+	0.253049i
$512$	7.06408	+	21.7410i	0.312191	+	0.960825i
$513$	13.4001	+	9.73576i	0.591630	+	0.429844i
$514$	19.8838	−	14.4464i	0.877037	−	0.637204i
$515$	−0.224286	+	0.690280i	−0.00988321	+	0.0304174i
$516$	0.242403			0.0106712
$517$	2.40048	−	19.6737i	0.105573	−	0.865248i
$518$	−2.95205			−0.129706
$519$	−7.02327	+	21.6154i	−0.308287	+	0.948811i
$520$	−19.5416	+	14.1978i	−0.856957	+	0.622616i
$521$	−28.0822	−	20.4029i	−1.23031	−	0.893869i	−0.233393	−	0.972383i	$-0.574983\pi$
$521$	−28.0822	−	20.4029i	−1.23031	−	0.893869i	−0.996913	+	0.0785132i	$0.974983\pi$
$522$	0.857916	+	2.64039i	0.0375500	+	0.115567i
$523$	6.09633	+	18.7626i	0.266574	+	0.820430i	0.991327	+	0.131421i	$0.0419540\pi$
$523$	6.09633	+	18.7626i	0.266574	+	0.820430i	−0.724753	+	0.689009i	$0.758046\pi$
$524$	−0.00203415	−	0.00147790i	−8.88624e−5	−	6.45623e-5i
$525$	−2.88089	+	2.09309i	−0.125732	+	0.0913499i
$526$	−0.659847	+	2.03080i	−0.0287707	+	0.0885471i
$527$	7.15430			0.311646
$528$	27.9710	−	5.45902i	1.21728	−	0.237573i
$529$	−22.4821			−0.977481
$530$	8.09105	−	24.9017i	0.351453	−	1.08166i
$531$	10.4407	−	7.58562i	0.453088	−	0.329188i
$532$	−0.0655390	−	0.0476168i	−0.00284147	−	0.00206445i
$533$	1.31632	+	4.05122i	0.0570162	+	0.175478i
$534$	14.4557	+	44.4901i	0.625560	+	1.92527i
$535$	−4.84395	−	3.51933i	−0.209422	−	0.152154i
$536$	35.5154	−	25.8034i	1.53403	−	1.11454i
$537$	5.56431	−	17.1252i	0.240118	−	0.739006i
$538$	2.86226			0.123401
$539$	−3.00695	−	1.39939i	−0.129518	−	0.0602758i
$540$	0.0730199			0.00314227
$541$	−1.71487	+	5.27782i	−0.0737279	+	0.226911i	−0.981129	−	0.193355i	$-0.938063\pi$
$541$	−1.71487	+	5.27782i	−0.0737279	+	0.226911i	0.907401	+	0.420266i	$0.138063\pi$
$542$	8.66998	−	6.29911i	0.372408	−	0.270570i
$543$	−25.9083	−	18.8235i	−1.11183	−	0.807794i
$544$	0.133530	+	0.410964i	0.00572506	+	0.0176199i
$545$	1.61085	+	4.95770i	0.0690014	+	0.212364i
$546$	11.4620	+	8.32766i	0.490530	+	0.356391i
$547$	6.83353	−	4.96485i	0.292181	−	0.212282i	−0.432032	−	0.901858i	$-0.642203\pi$
$547$	6.83353	−	4.96485i	0.292181	−	0.212282i	0.724213	+	0.689576i	$0.242203\pi$
$548$	−0.0359201	+	0.110551i	−0.00153443	+	0.00472250i
$549$	−10.5453			−0.450061
$550$	−6.97518	−	3.24614i	−0.297422	−	0.138416i
$551$	6.80173			0.289763
$552$	1.36553	−	4.20267i	0.0581209	−	0.178878i
$553$	12.6538	−	9.19351i	0.538094	−	0.390948i
$554$	16.4483	+	11.9504i	0.698822	+	0.507724i
$555$	2.56463	+	7.89313i	0.108863	+	0.335045i
$556$	0.0300394	+	0.0924519i	0.00127396	+	0.00392083i
$557$	9.85665	+	7.16128i	0.417640	+	0.303433i	0.776687	−	0.629886i	$-0.216898\pi$
$557$	9.85665	+	7.16128i	0.417640	+	0.303433i	−0.359048	+	0.933319i	$0.616898\pi$
$558$	−2.50542	+	1.82029i	−0.106063	+	0.0770591i
$559$	−11.5223	+	35.4620i	−0.487342	+	1.49988i
$560$	7.27404			0.307384
$561$	38.5226	−	7.51837i	1.62643	−	0.317426i
$562$	−25.0140			−1.05515
$563$	−8.45270	+	26.0147i	−0.356239	+	1.09639i	0.599049	+	0.800713i	$0.295546\pi$
$563$	−8.45270	+	26.0147i	−0.356239	+	1.09639i	−0.955288	+	0.295678i	$0.904454\pi$
$564$	−0.146055	+	0.106115i	−0.00615001	+	0.00446824i
$565$	21.5495	+	15.6566i	0.906594	+	0.658679i
$566$	13.5594	+	41.7316i	0.569944	+	1.75411i
$567$	−3.46640	−	10.6685i	−0.145575	−	0.448035i
$568$	−31.9211	−	23.1920i	−1.33938	−	0.973115i
$569$	−5.77253	+	4.19399i	−0.241997	+	0.175821i	−0.702173	−	0.712007i	$-0.747786\pi$
$569$	−5.77253	+	4.19399i	−0.241997	+	0.175821i	0.460176	+	0.887828i	$0.347786\pi$
$570$	10.0093	−	30.8055i	0.419245	−	1.29030i
$571$	32.4839			1.35941			0.679705	−	0.733486i	$-0.262108\pi$
$571$	32.4839			1.35941			0.679705	+	0.733486i	$0.262108\pi$
$572$	0.0260678	−	0.213644i	0.00108995	−	0.00893291i
$573$	20.7831			0.868226
$574$	0.399188	−	1.22857i	0.0166618	−	0.0512797i
$575$	−0.958373	+	0.696299i	−0.0399669	+	0.0290377i
$576$	−10.9495	−	7.95525i	−0.456228	−	0.331469i
$577$	10.7482	+	33.0795i	0.447453	+	1.37712i	0.879771	+	0.475398i	$0.157696\pi$
$577$	10.7482	+	33.0795i	0.447453	+	1.37712i	−0.432317	+	0.901721i	$0.642304\pi$
$578$	−5.62791	−	17.3209i	−0.234090	−	0.720456i
$579$	−2.60398	−	1.89190i	−0.108218	−	0.0786248i
$580$	0.0242587	−	0.0176249i	0.00100729	−	0.000731836i
$581$	−1.35217	+	4.16157i	−0.0560977	+	0.172651i
$582$	7.35135			0.304723
$583$	16.3347	+	29.4159i	0.676513	+	1.21828i
$584$	17.0708			0.706395
$585$	4.41882	−	13.5997i	0.182696	−	0.562279i
$586$	−27.3975	+	19.9054i	−1.13178	+	0.822285i
$587$	11.7105	+	8.50816i	0.483343	+	0.351169i	0.802618	−	0.596493i	$-0.203440\pi$
$587$	11.7105	+	8.50816i	0.483343	+	0.351169i	−0.319276	+	0.947662i	$0.603440\pi$
$588$	0.00933558	+	0.0287320i	0.000384993	+	0.00118489i
$589$	2.34456	+	7.21581i	0.0966059	+	0.297322i
$590$	16.0375	+	11.6520i	0.660255	+	0.479704i
$591$	−24.5789	+	17.8576i	−1.01104	+	0.734563i
$592$	−2.57103	+	7.91283i	−0.105669	+	0.325215i
$593$	−15.0291			−0.617169			−0.308585	−	0.951197i	$-0.599855\pi$
$593$	−15.0291			−0.617169			−0.308585	+	0.951197i	$0.599855\pi$
$594$	9.09400	−	9.76696i	0.373131	−	0.400743i
$595$	10.0181			0.410701
$596$	0.0138706	−	0.0426894i	0.000568163	−	0.00174863i
$597$	−7.50366	+	5.45173i	−0.307104	+	0.223124i
$598$	3.81303	+	2.77033i	0.155926	+	0.113287i
$599$	0.544010	+	1.67429i	0.0222276	+	0.0684097i	0.961555	−	0.274612i	$-0.0885495\pi$
$599$	0.544010	+	1.67429i	0.0222276	+	0.0684097i	−0.939327	+	0.343022i	$0.888549\pi$
$600$	3.12318	+	9.61216i	0.127503	+	0.392415i
$601$	−18.9605	−	13.7756i	−0.773415	−	0.561919i	0.129581	−	0.991569i	$-0.458637\pi$
$601$	−18.9605	−	13.7756i	−0.773415	−	0.561919i	−0.902995	+	0.429650i	$0.858637\pi$
$602$	9.14810	−	6.64648i	0.372849	−	0.270890i
$603$	−8.03085	+	24.7164i	−0.327042	+	1.00653i
$604$	−0.310948			−0.0126523
$605$	−18.6669	+	7.57487i	−0.758917	+	0.307962i
$606$	36.2679			1.47328
$607$	−7.81149	+	24.0413i	−0.317059	+	0.975806i	0.657840	+	0.753158i	$0.271470\pi$
$607$	−7.81149	+	24.0413i	−0.317059	+	0.975806i	−0.974899	+	0.222649i	$0.928530\pi$
$608$	−0.370738	+	0.269357i	−0.0150354	+	0.0109239i
$609$	−2.05208	−	1.49092i	−0.0831544	−	0.0604152i
$610$	−5.00550	−	15.4053i	−0.202667	−	0.623744i
$611$	−8.58142	−	26.4109i	−0.347167	−	1.06847i
$612$	−0.103837	−	0.0754422i	−0.00419737	−	0.00304957i
$613$	−0.939222	+	0.682385i	−0.0379348	+	0.0275613i	−0.606591	−	0.795014i	$-0.707463\pi$
$613$	−0.939222	+	0.682385i	−0.0379348	+	0.0275613i	0.568656	+	0.822575i	$0.307463\pi$
$614$	2.37906	−	7.32199i	0.0960110	−	0.295492i
$615$	−3.63174			−0.146446
$616$	−6.41463	+	6.88931i	−0.258453	+	0.277578i
$617$	12.9711			0.522197			0.261098	−	0.965312i	$-0.415915\pi$
$617$	12.9711			0.522197			0.261098	+	0.965312i	$0.415915\pi$
$618$	0.373377	−	1.14914i	0.0150194	−	0.0462251i
$619$	−37.0465	+	26.9158i	−1.48902	+	1.08184i	−0.514517	+	0.857480i	$0.672029\pi$
$619$	−37.0465	+	26.9158i	−1.48902	+	1.08184i	−0.974507	+	0.224358i	$0.927971\pi$
$620$	0.0270599	+	0.0196602i	0.00108675	+	0.000789572i
$621$	−0.634978	−	1.95426i	−0.0254808	−	0.0784218i
$622$	−6.04824	−	18.6146i	−0.242512	−	0.746377i
$623$	−12.4133	−	9.01881i	−0.497329	−	0.361331i
$624$	32.3046	−	23.4707i	1.29322	−	0.939578i
$625$	−4.34493	+	13.3723i	−0.173797	+	0.534893i
$626$	−38.6824			−1.54606
$627$	20.2074	+	36.3900i	0.807006	+	1.45328i
$628$	−0.185097			−0.00738615
$629$	−3.54092	+	10.8978i	−0.141186	+	0.434525i
$630$	−3.50830	+	2.54893i	−0.139774	+	0.101552i
$631$	10.2103	+	7.41824i	0.406467	+	0.295316i	0.772170	−	0.635416i	$-0.219171\pi$
$631$	10.2103	+	7.41824i	0.406467	+	0.295316i	−0.365703	+	0.930732i	$0.619171\pi$
$632$	−13.7180	−	42.2196i	−0.545672	−	1.67941i
$633$	0.972881	+	2.99422i	0.0386685	+	0.119009i
$634$	8.92225	+	6.48240i	0.354348	+	0.257449i
$635$	7.45682	−	5.41770i	0.295915	−	0.214995i
$636$	0.0947088	−	0.291484i	0.00375545	−	0.0115581i
$637$	−4.64706			−0.184123
$638$	0.663738	−	5.43981i	0.0262776	−	0.215364i
$639$	23.3582			0.924038
$640$	6.33488	−	19.4968i	0.250408	−	0.770678i
$641$	−22.6175	+	16.4326i	−0.893336	+	0.649047i	−0.936746	−	0.350011i	$-0.886178\pi$
$641$	−22.6175	+	16.4326i	−0.893336	+	0.649047i	0.0434095	+	0.999057i	$0.486178\pi$
$642$	8.06392	+	5.85878i	0.318257	+	0.231228i
$643$	−15.3575	−	47.2657i	−0.605642	−	1.86398i	−0.492313	−	0.870418i	$-0.663848\pi$
$643$	−15.3575	−	47.2657i	−0.605642	−	1.86398i	−0.113330	−	0.993557i	$-0.536152\pi$
$644$	0.00310563	+	0.00955813i	0.000122379	+	0.000376643i
$645$	−25.7188	−	18.6858i	−1.01268	−	0.735752i
$646$	36.1802	−	26.2865i	1.42349	−	1.03423i
$647$	−3.40125	+	10.4680i	−0.133717	+	0.411539i	−0.995388	−	0.0959281i	$-0.969418\pi$
$647$	−3.40125	+	10.4680i	−0.133717	+	0.411539i	0.861671	+	0.507467i	$0.169418\pi$
$648$	−31.8377			−1.25070
$649$	−25.0026	+	4.87970i	−0.981439	+	0.191545i
$650$	−10.7797			−0.422816
$651$	0.874336	−	2.69093i	0.0342679	−	0.105466i
$652$	0.154983	−	0.112602i	0.00606962	−	0.00440984i
$653$	−23.4100	−	17.0084i	−0.916106	−	0.665590i	0.0264458	−	0.999650i	$-0.491581\pi$
$653$	−23.4100	−	17.0084i	−0.916106	−	0.665590i	−0.942552	+	0.334060i	$0.891581\pi$
$654$	−2.68165	−	8.25328i	−0.104861	−	0.322729i
$655$	0.101897	+	0.313608i	0.00398146	+	0.0122537i
$656$	−2.94547	−	2.14001i	−0.115001	−	0.0835533i
$657$	−8.17583	+	5.94009i	−0.318969	+	0.231745i
$658$	−2.60240	+	8.00937i	−0.101452	+	0.312238i
$659$	10.8405			0.422288			0.211144	−	0.977455i	$-0.432281\pi$
$659$	10.8405			0.422288			0.211144	+	0.977455i	$0.432281\pi$
$660$	0.166366	+	0.0774241i	0.00647578	+	0.00301373i
$661$	20.3444			0.791305			0.395652	−	0.918400i	$-0.370519\pi$
$661$	20.3444			0.791305			0.395652	+	0.918400i	$0.370519\pi$
$662$	12.2573	−	37.7241i	0.476394	−	1.46619i
$663$	44.4911	−	32.3247i	1.72789	−	1.25539i
$664$	10.0474	+	7.29986i	0.389915	+	0.283289i
$665$	3.28306	+	10.1042i	0.127311	+	0.391824i
$666$	−1.53275	−	4.71732i	−0.0593929	−	0.182792i
$667$	−0.682656	−	0.495978i	−0.0264325	−	0.0192044i
$668$	0.105164	−	0.0764062i	0.00406892	−	0.00295625i
$669$	3.24662	−	9.99208i	0.125522	−	0.386316i
$670$	−39.9197			−1.54223
$671$	18.8720	+	8.78272i	0.728544	+	0.339053i
$672$	0.170894			0.00659237
$673$	−3.73255	+	11.4876i	−0.143879	+	0.442815i	−0.996865	−	0.0791188i	$-0.974789\pi$
$673$	−3.73255	+	11.4876i	−0.143879	+	0.442815i	0.852986	+	0.521934i	$0.174789\pi$
$674$	−28.4790	+	20.6912i	−1.09697	+	0.796996i
$675$	3.80215	+	2.76242i	0.146345	+	0.106326i
$676$	−0.0370903	−	0.114152i	−0.00142655	−	0.00439047i
$677$	1.04951	+	3.23007i	0.0403361	+	0.124142i	0.969197	−	0.246287i	$-0.0792107\pi$
$677$	1.04951	+	3.23007i	0.0403361	+	0.124142i	−0.928861	+	0.370429i	$0.879211\pi$
$678$	−35.8743	−	26.0642i	−1.37775	−	1.00099i
$679$	−1.95073	+	1.41729i	−0.0748623	+	0.0543906i
$680$	8.78642	−	27.0418i	0.336944	−	1.03701i
$681$	−0.859173			−0.0329236
$682$	5.99978	−	1.17096i	0.229743	−	0.0448384i
$683$	−4.75643			−0.182000			−0.0909999	−	0.995851i	$-0.529006\pi$
$683$	−4.75643			−0.182000			−0.0909999	+	0.995851i	$0.529006\pi$
$684$	0.0420620	−	0.129454i	0.00160828	−	0.00494978i
$685$	12.3330	−	8.96042i	0.471218	−	0.342360i
$686$	1.14012	+	0.828347i	0.0435300	+	0.0316264i
$687$	−1.46382	−	4.50516i	−0.0558481	−	0.171883i
$688$	−9.84822	−	30.3097i	−0.375460	−	1.15555i
$689$	38.1404	+	27.7106i	1.45303	+	1.05569i
$690$	−3.25091	+	2.36193i	−0.123760	+	0.0899170i
$691$	2.04998	−	6.30920i	0.0779850	−	0.240013i	−0.904462	−	0.426554i	$-0.859728\pi$
$691$	2.04998	−	6.30920i	0.0779850	−	0.240013i	0.982447	+	0.186540i	$0.0597275\pi$
$692$	−0.146707			−0.00557695
$693$	0.674941	−	5.53163i	0.0256389	−	0.210129i
$694$	−29.1003			−1.10463
$695$	3.93955	−	12.1247i	0.149435	−	0.459915i
$696$	−5.82424	+	4.23156i	−0.220767	+	0.160397i
$697$	−4.05661	−	2.94730i	−0.153655	−	0.111637i
$698$	2.61171	+	8.03802i	0.0988547	+	0.304244i
$699$	0.842441	+	2.59277i	0.0318641	+	0.0980675i
$700$	−0.0185960	−	0.0135108i	−0.000702863	−	0.000510660i
$701$	−2.45134	+	1.78101i	−0.0925860	+	0.0672677i	−0.633115	−	0.774058i	$-0.718224\pi$
$701$	−2.45134	+	1.78101i	−0.0925860	+	0.0672677i	0.540529	+	0.841325i	$0.318224\pi$
$702$	5.77815	−	17.7833i	0.218082	−	0.671188i
$703$	−12.1519			−0.458319
$704$	12.9697	+	23.3562i	0.488815	+	0.880270i
$705$	23.6762			0.891697
$706$	−10.4683	+	32.2182i	−0.393981	+	1.21255i
$707$	−9.62396	+	6.99222i	−0.361946	+	0.262969i
$708$	0.187726	+	0.136391i	0.00705516	+	0.00512587i
$709$	−4.22026	−	12.9886i	−0.158495	−	0.487798i	0.840003	−	0.542582i	$-0.182553\pi$
$709$	−4.22026	−	12.9886i	−0.158495	−	0.487798i	−0.998498	+	0.0547836i	$0.982553\pi$
$710$	11.0874	+	34.1236i	0.416103	+	1.28063i
$711$	21.2611	+	15.4471i	0.797354	+	0.579312i
$712$	−35.2317	+	25.5973i	−1.32036	+	0.959300i
$713$	0.290862	−	0.895180i	0.0108928	−	0.0335247i
$714$	−16.6775			−0.624140
$715$	−19.2346	+	20.6580i	−0.719335	+	0.772566i
$716$	0.116231			0.00434376
$717$	7.46181	−	22.9651i	0.278666	−	0.857647i
$718$	−12.4845	+	9.07050i	−0.465916	+	0.338508i
$719$	1.53737	+	1.11696i	0.0573341	+	0.0416557i	0.616083	−	0.787681i	$-0.288719\pi$
$719$	1.53737	+	1.11696i	0.0573341	+	0.0416557i	−0.558749	+	0.829337i	$0.688719\pi$
$720$	3.77680	+	11.6238i	0.140753	+	0.433193i
$721$	0.122468	+	0.376917i	0.00456094	+	0.0140371i
$722$	16.7069	+	12.1383i	0.621768	+	0.451741i
$723$	−37.6021	+	27.3195i	−1.39844	+	1.01602i
$724$	0.0638788	−	0.196599i	0.00237404	−	0.00730654i
$725$	1.92992			0.0716754
$726$	31.0755	−	12.6102i	1.15332	−	0.468008i
$727$	−13.8211			−0.512595			−0.256298	−	0.966598i	$-0.582503\pi$
$727$	−13.8211			−0.512595			−0.256298	+	0.966598i	$0.582503\pi$
$728$	−4.07573	+	12.5438i	−0.151057	+	0.464905i
$729$	0.256684	−	0.186492i	0.00950682	−	0.00690711i
$730$	−12.5586	−	9.12432i	−0.464813	−	0.337706i
$731$	−13.5633	−	41.7436i	−0.501658	−	1.54394i
$732$	−0.0585912	−	0.180325i	−0.00216559	−	0.00666502i
$733$	−39.1357	−	28.4337i	−1.44551	−	1.05022i	−0.986855	−	0.161610i	$-0.948331\pi$
$733$	−39.1357	−	28.4337i	−1.44551	−	1.05022i	−0.458655	−	0.888615i	$-0.651669\pi$
$734$	12.1055	−	8.79519i	0.446824	−	0.324636i
$735$	1.22432	−	3.76807i	0.0451598	−	0.138987i
$736$	0.0568504			0.00209553
$737$	34.9575	−	37.5443i	1.28767	−	1.38296i
$738$	2.17050			0.0798973
$739$	7.17170	−	22.0722i	0.263815	−	0.811939i	−0.728149	−	0.685419i	$-0.759619\pi$
$739$	7.17170	−	22.0722i	0.263815	−	0.811939i	0.991964	−	0.126520i	$-0.0403809\pi$
$740$	−0.0433404	+	0.0314887i	−0.00159323	+	0.00115755i
$741$	47.1829	+	34.2804i	1.73331	+	1.25932i
$742$	−4.41799	−	13.5972i	−0.162190	−	0.499168i
$743$	−13.8536	−	42.6369i	−0.508238	−	1.56420i	−0.795257	−	0.606272i	$-0.792664\pi$
$743$	−13.8536	−	42.6369i	−0.508238	−	1.56420i	0.287019	−	0.957925i	$-0.407336\pi$
$744$	−6.49679	−	4.72020i	−0.238184	−	0.173051i
$745$	−4.76240	+	3.46009i	−0.174481	+	0.126768i
$746$	−15.9404	+	49.0596i	−0.583620	+	1.79620i
$747$	−7.35218			−0.269002
$748$	0.122996	+	0.221495i	0.00449718	+	0.00809864i
$749$	−3.26935			−0.119460
$750$	11.4670	−	35.2919i	0.418717	−	1.28868i
$751$	33.3199	−	24.2083i	1.21586	−	0.883373i	0.220109	−	0.975475i	$-0.429359\pi$
$751$	33.3199	−	24.2083i	1.21586	−	0.883373i	0.995750	+	0.0921022i	$0.0293587\pi$
$752$	19.2022	+	13.9512i	0.700234	+	0.508750i
$753$	0.283333	+	0.872008i	0.0103252	+	0.0317777i
$754$	−2.37278	−	7.30266i	−0.0864115	−	0.265947i
$755$	32.9913	+	23.9696i	1.20068	+	0.872343i
$756$	0.0322566	−	0.0234358i	0.00117316	−	0.000852352i
$757$	−6.76401	+	20.8175i	−0.245842	+	0.756624i	0.749655	+	0.661829i	$0.230219\pi$
$757$	−6.76401	+	20.8175i	−0.245842	+	0.756624i	−0.995497	+	0.0947948i	$0.969781\pi$
$758$	17.8382			0.647912
$759$	0.625423	−	5.12580i	0.0227014	−	0.186055i
$760$	30.1537			1.09379
$761$	−11.0367	+	33.9673i	−0.400078	+	1.23131i	0.524857	+	0.851190i	$0.324119\pi$
$761$	−11.0367	+	33.9673i	−0.400078	+	1.23131i	−0.924935	+	0.380124i	$0.875881\pi$
$762$	−12.4137	+	9.01906i	−0.449700	+	0.326726i
$763$	2.30277	+	1.67306i	0.0833660	+	0.0605690i
$764$	0.0414558	+	0.127588i	0.00149982	+	0.00461596i
$765$	5.20154	+	16.0087i	0.188062	+	0.578796i
$766$	−17.6353	−	12.8128i	−0.637188	−	0.462944i
$767$	−28.8764	+	20.9799i	−1.04266	+	0.757540i
$768$	0.224043	−	0.689533i	0.00808445	−	0.0248814i
$769$	5.30246			0.191212			0.0956058	−	0.995419i	$-0.469521\pi$
$769$	5.30246			0.191212			0.0956058	+	0.995419i	$0.469521\pi$
$770$	8.40141	−	1.63968i	0.302766	−	0.0590900i
$771$	−37.7295			−1.35880
$772$	0.00642030	−	0.0197596i	0.000231072	−	0.000711165i
$773$	40.3628	−	29.3253i	1.45175	−	1.05476i	0.466332	−	0.884610i	$-0.345575\pi$
$773$	40.3628	−	29.3253i	1.45175	−	1.05476i	0.985418	−	0.170149i	$-0.0544248\pi$
$774$	15.3708	+	11.1675i	0.552492	+	0.401409i
$775$	0.665245	+	2.04741i	0.0238963	+	0.0735452i
$776$	2.11479	+	6.50867i	0.0759167	+	0.233648i
$777$	3.66624	+	2.66368i	0.131526	+	0.0955589i
$778$	−14.4943	+	10.5307i	−0.519646	+	0.377545i
$779$	1.64324	−	5.05736i	0.0588750	−	0.181199i
$780$	0.257109			0.00920597
$781$	−41.8023	−	19.4541i	−1.49580	−	0.696124i
$782$	−5.54803			−0.198397
$783$	−1.03448	+	3.18379i	−0.0369692	+	0.113779i
$784$	3.21332	−	2.33461i	0.114761	−	0.0833789i
$785$	19.6386	+	14.2683i	0.700931	+	0.509256i
$786$	−0.169633	−	0.522075i	−0.00605059	−	0.0186218i
$787$	11.0804	+	34.1020i	0.394974	+	1.21560i	0.928982	+	0.370125i	$0.120685\pi$
$787$	11.0804	+	34.1020i	0.394974	+	1.21560i	−0.534008	+	0.845479i	$0.679315\pi$
$788$	−0.158655	−	0.115270i	−0.00565186	−	0.00410632i
$789$	2.65191	−	1.92672i	0.0944103	−	0.0685931i
$790$	−12.4744	+	38.3922i	−0.443818	+	1.36593i
$791$	14.5445			0.517144
$792$	−14.3396	−	6.67342i	−0.509535	−	0.237130i
$793$	29.1655			1.03570
$794$	8.25571	−	25.4085i	0.292984	−	0.901713i
$795$	−32.5177	+	23.6255i	−1.15328	+	0.837910i
$796$	−0.0484357	−	0.0351906i	−0.00171676	−	0.00124730i
$797$	4.55530	+	14.0198i	0.161357	+	0.496606i	0.998749	−	0.0499962i	$-0.0159209\pi$
$797$	4.55530	+	14.0198i	0.161357	+	0.496606i	−0.837392	+	0.546602i	$0.815921\pi$
$798$	−5.46544	−	16.8209i	−0.193474	−	0.595453i
$799$	26.4460	+	19.2142i	0.935593	+	0.679748i
$800$	−0.105193	+	0.0764272i	−0.00371913	+	0.00270211i
$801$	7.96670	−	24.5190i	0.281489	−	0.866336i
$802$	12.2354			0.432046
$803$	19.5789	−	3.82116i	0.690923	−	0.134846i
$804$	−0.467275			−0.0164795
$805$	0.407290	−	1.25351i	0.0143551	−	0.0441804i
$806$	6.92934	−	5.03446i	0.244076	−	0.177331i
$807$	−3.55473	−	2.58266i	−0.125132	−	0.0909140i
$808$	10.4334	+	32.1106i	0.367044	+	1.12965i
$809$	−8.33599	−	25.6556i	−0.293078	−	0.902001i	−0.983860	−	0.178938i	$-0.942734\pi$
$809$	−8.33599	−	25.6556i	−0.293078	−	0.902001i	0.690782	−	0.723063i	$-0.257266\pi$
$810$	23.4222	+	17.0172i	0.822973	+	0.597925i
$811$	−1.18472	+	0.860750i	−0.0416012	+	0.0302250i	−0.608392	−	0.793637i	$-0.708185\pi$
$811$	−1.18472	+	0.860750i	−0.0416012	+	0.0302250i	0.566790	+	0.823862i	$0.308185\pi$
$812$	0.00505954	−	0.0155717i	0.000177555	−	0.000546459i
$813$	−16.4513			−0.576972
$814$	−1.18583	+	9.71876i	−0.0415634	+	0.340642i
$815$	−25.1236			−0.880041
$816$	−14.5250	+	44.7033i	−0.508476	+	1.56493i
$817$	37.6577	−	27.3599i	1.31747	−	0.957201i
$818$	6.51473	+	4.73323i	0.227782	+	0.165493i
$819$	−2.41283	−	7.42591i	−0.0843110	−	0.259482i
$820$	−0.00724418	−	0.0222953i	−0.000252978	−	0.000778586i
$821$	−24.7791	−	18.0031i	−0.864797	−	0.628312i	0.0643886	−	0.997925i	$-0.479490\pi$
$821$	−24.7791	−	18.0031i	−0.864797	−	0.628312i	−0.929186	+	0.369613i	$0.879490\pi$
$822$	−20.5312	+	14.9168i	−0.716107	+	0.520282i
$823$	−7.58137	+	23.3330i	−0.264270	+	0.813339i	0.727591	+	0.686011i	$0.240640\pi$
$823$	−7.58137	+	23.3330i	−0.264270	+	0.813339i	−0.991861	+	0.127328i	$0.959360\pi$
$824$	1.12482			0.0391851
$825$	5.73364	+	10.3253i	0.199620	+	0.359480i
$826$	10.8243			0.376626
$827$	−2.02927	+	6.24545i	−0.0705646	+	0.217176i	−0.980119	−	0.198408i	$-0.936423\pi$
$827$	−2.02927	+	6.24545i	−0.0705646	+	0.217176i	0.909555	+	0.415584i	$0.136423\pi$
$828$	−0.0136612	+	0.00992547i	−0.000474761	+	0.000344934i
$829$	16.0543	+	11.6642i	0.557590	+	0.405113i	0.830576	−	0.556905i	$-0.188011\pi$
$829$	16.0543	+	11.6642i	0.557590	+	0.405113i	−0.272986	+	0.962018i	$0.588011\pi$
$830$	−3.48985	−	10.7406i	−0.121134	−	0.372813i
$831$	−9.64463	−	29.6831i	−0.334569	−	1.02970i
$832$	30.2834	+	22.0022i	1.04989	+	0.762789i
$833$	4.42550	−	3.21531i	0.153334	−	0.111404i
$834$	−6.55832	+	20.1844i	−0.227096	+	0.698930i
$835$	−17.0476			−0.589958
$836$	−0.183091	+	0.196640i	−0.00633235	+	0.00680095i
$837$	−3.73421			−0.129073
$838$	11.8413	−	36.4438i	0.409051	−	1.25893i
$839$	6.44019	−	4.67907i	0.222340	−	0.161539i	−0.471039	−	0.882112i	$-0.656121\pi$
$839$	6.44019	−	4.67907i	0.222340	−	0.161539i	0.693379	+	0.720573i	$0.256121\pi$
$840$	−9.09737	−	6.60963i	−0.313889	−	0.228054i
$841$	−8.53669	−	26.2732i	−0.294369	−	0.905973i
$842$	10.4365	+	32.1202i	0.359665	+	1.10694i
$843$	31.0656	+	22.5705i	1.06996	+	0.777370i
$844$	−0.0164410	+	0.0119451i	−0.000565922	+	0.000411166i
$845$	−4.86424	+	14.9706i	−0.167335	+	0.515004i
$846$	−14.1500			−0.486489
$847$	−5.81496	+	9.33736i	−0.199804	+	0.320835i
$848$	−40.2944			−1.38372
$849$	20.8152	−	64.0625i	0.714375	−	2.19862i
$850$	10.2658	−	7.45852i	0.352113	−	0.255825i
$851$	1.21963	+	0.886114i	0.0418084	+	0.0303756i
$852$	0.129782	+	0.399429i	0.00444627	+	0.0136842i
$853$	10.5292	+	32.4055i	0.360513	+	1.10954i	0.952744	+	0.303776i	$0.0982473\pi$
$853$	10.5292	+	32.4055i	0.360513	+	1.10954i	−0.592231	+	0.805768i	$0.701753\pi$
$854$	−7.15554	−	5.19881i	−0.244858	−	0.177900i
$855$	−14.4417	+	10.4925i	−0.493897	+	0.358837i
$856$	−2.86741	+	8.82497i	−0.0980060	+	0.301631i
$857$	24.8539			0.848992			0.424496	−	0.905430i	$-0.360451\pi$
$857$	24.8539			0.848992			0.424496	+	0.905430i	$0.360451\pi$
$858$	32.0207	−	34.3902i	1.09317	−	1.17406i
$859$	2.05654			0.0701683			0.0350841	−	0.999384i	$-0.488830\pi$
$859$	2.05654			0.0701683			0.0350841	+	0.999384i	$0.488830\pi$
$860$	0.0634115	−	0.195160i	0.00216231	−	0.00665491i
$861$	−1.60432	+	1.16561i	−0.0546752	+	0.0397239i
$862$	18.7814	+	13.6455i	0.639697	+	0.464767i
$863$	−0.0801824	−	0.246776i	−0.00272944	−	0.00840035i	0.949683	−	0.313214i	$-0.101406\pi$
$863$	−0.0801824	−	0.246776i	−0.00272944	−	0.00840035i	−0.952412	+	0.304814i	$0.901406\pi$
$864$	−0.0696964	−	0.214504i	−0.00237112	−	0.00729756i
$865$	15.5655	+	11.3090i	0.529241	+	0.384516i
$866$	22.9061	−	16.6423i	0.778381	−	0.565527i
$867$	−8.63946	+	26.5895i	−0.293412	+	0.903028i
$868$	0.0182637			0.000619910
$869$	−25.1840	−	45.3519i	−0.854307	−	1.53846i
$870$	6.54651			0.221947
$871$	22.2113	−	68.3593i	0.752601	−	2.31627i
$872$	6.53577	−	4.74851i	0.221329	−	0.160805i
$873$	−3.27766	−	2.38136i	−0.110932	−	0.0805968i
$874$	−1.81816	−	5.59573i	−0.0615003	−	0.189278i
$875$	3.76118	+	11.5757i	0.127151	+	0.391331i
$876$	−0.147003	−	0.106804i	−0.00496676	−	0.00360856i
$877$	−15.0420	+	10.9287i	−0.507934	+	0.369035i	−0.812039	−	0.583603i	$-0.801642\pi$
$877$	−15.0420	+	10.9287i	−0.507934	+	0.369035i	0.304106	+	0.952638i	$0.401642\pi$
$878$	−11.6572	+	35.8772i	−0.393412	+	1.21080i
$879$	51.9867			1.75347
$880$	2.92197	−	23.9477i	0.0984996	−	0.807275i
$881$	6.45292			0.217404			0.108702	−	0.994074i	$-0.465330\pi$
$881$	6.45292			0.217404			0.108702	+	0.994074i	$0.465330\pi$
$882$	−0.731714	+	2.25198i	−0.0246381	+	0.0758283i
$883$	0.225301	−	0.163691i	0.00758198	−	0.00550863i	−0.583988	−	0.811762i	$-0.698508\pi$
$883$	0.225301	−	0.163691i	0.00758198	−	0.00550863i	0.591570	+	0.806254i	$0.298508\pi$
$884$	0.287188	+	0.208654i	0.00965917	+	0.00701779i
$885$	−9.40377	−	28.9418i	−0.316104	−	0.972869i
$886$	−11.4165	−	35.1362i	−0.383543	−	1.18042i
$887$	−24.7211	−	17.9609i	−0.830054	−	0.603069i	0.0895209	−	0.995985i	$-0.471466\pi$
$887$	−24.7211	−	17.9609i	−0.830054	−	0.603069i	−0.919575	+	0.392916i	$0.871466\pi$
$888$	10.4056	−	7.56009i	0.349188	−	0.253700i
$889$	1.55524	−	4.78655i	0.0521612	−	0.160536i
$890$	39.6008			1.32742
$891$	−36.5154	+	7.12661i	−1.22331	+	0.238750i
$892$	0.0678176			0.00227070
$893$	−10.7127	+	32.9702i	−0.358485	+	1.10330i
$894$	7.92816	−	5.76014i	0.265157	−	0.192648i
$895$	−12.3320	−	8.95972i	−0.412213	−	0.299491i
$896$	−3.45907	−	10.6459i	−0.115559	−	0.355655i
$897$	−2.23581	−	6.88111i	−0.0746514	−	0.229753i
$898$	11.1132	+	8.07423i	0.370853	+	0.269441i
$899$	−1.24058	+	0.901332i	−0.0413756	+	0.0300611i
$900$	0.0119347	−	0.0367311i	0.000397822	−	0.00122437i
$901$	−55.4949			−1.84880
$902$	−3.88437	−	1.80773i	−0.129335	−	0.0601907i
$903$	−17.3585			−0.577655
$904$	12.7564	−	39.2601i	0.424271	−	1.30577i
$905$	−21.9324	+	15.9348i	−0.729058	+	0.529692i
$906$	−54.9220	−	39.9031i	−1.82466	−	1.32569i
$907$	9.86836	+	30.3717i	0.327674	+	1.00848i	0.970219	+	0.242228i	$0.0778782\pi$
$907$	9.86836	+	30.3717i	0.327674	+	1.00848i	−0.642546	+	0.766247i	$0.722122\pi$
$908$	−0.00171378	−	0.00527448i	−5.68739e−5	−	0.000175040i
$909$	−16.1704	−	11.7484i	−0.536337	−	0.389671i
$910$	9.70307	−	7.04969i	0.321654	−	0.233695i
$911$	0.865378	−	2.66336i	0.0286713	−	0.0882411i	−0.935697	−	0.352805i	$-0.885228\pi$
$911$	0.865378	−	2.66336i	0.0286713	−	0.0882411i	0.964368	+	0.264564i	$0.0852280\pi$
$912$	−49.8477			−1.65062
$913$	13.1576	+	6.12334i	0.435452	+	0.202653i
$914$	−16.7496			−0.554027
$915$	−7.68399	+	23.6489i	−0.254025	+	0.781808i
$916$	0.0247374	−	0.0179728i	0.000817348	−	0.000593838i
$917$	0.145666	+	0.105832i	0.00481031	+	0.00349490i
$918$	6.80167	+	20.9334i	0.224488	+	0.690904i
$919$	−4.89293	−	15.0589i	−0.161403	−	0.496747i	0.837350	−	0.546667i	$-0.184104\pi$
$919$	−4.89293	−	15.0589i	−0.161403	−	0.496747i	−0.998753	+	0.0499194i	$0.984104\pi$
$920$	−3.02638	−	2.19880i	−0.0997769	−	0.0724922i
$921$	−9.56137	+	6.94674i	−0.315058	+	0.228903i
$922$	−3.98356	+	12.2602i	−0.131192	+	0.403767i
$923$	−64.6030			−2.12643
$924$	0.0983417	−	0.0191931i	0.00323520	−	0.000631407i
$925$	−3.44799			−0.113369
$926$	−16.9554	+	52.1833i	−0.557188	+	1.71485i
$927$	−0.538719	+	0.391402i	−0.0176939	+	0.0128553i
$928$	−0.0749296	−	0.0544396i	−0.00245969	−	0.00178707i
$929$	−8.49282	−	26.1382i	−0.278640	−	0.857567i	−0.988233	−	0.152955i	$-0.951121\pi$
$929$	−8.49282	−	26.1382i	−0.278640	−	0.857567i	0.709593	−	0.704612i	$-0.248879\pi$
$930$	2.25659	+	6.94506i	0.0739964	+	0.227737i
$931$	4.69325	+	3.40985i	0.153815	+	0.111753i
$932$	−0.0142366	+	0.0103435i	−0.000466337	+	0.000338814i
$933$	−9.28472	+	28.5754i	−0.303968	+	0.935517i
$934$	29.2894			0.958379
$935$	4.02424	−	32.9816i	0.131607	−	1.07861i
$936$	−22.1610			−0.724354
$937$	−3.80357	+	11.7062i	−0.124257	+	0.382425i	−0.993765	−	0.111495i	$-0.964436\pi$
$937$	−3.80357	+	11.7062i	−0.124257	+	0.382425i	0.869508	+	0.493919i	$0.164436\pi$
$938$	−17.6346	+	12.8123i	−0.575789	+	0.418335i
$939$	48.0408	+	34.9037i	1.56775	+	1.13904i
$940$	0.0472266	+	0.145349i	0.00154036	+	0.00474075i
$941$	0.451208	+	1.38867i	0.0147089	+	0.0452695i	0.958142	−	0.286295i	$-0.0924236\pi$
$941$	0.451208	+	1.38867i	0.0147089	+	0.0452695i	−0.943433	+	0.331564i	$0.892424\pi$
$942$	−32.6931	−	23.7530i	−1.06520	−	0.773913i
$943$	−0.533703	+	0.387758i	−0.0173798	+	0.0126271i
$944$	9.42725	−	29.0141i	0.306831	−	0.944328i
$945$	−5.22896			−0.170098
$946$	−18.2068	−	32.7873i	−0.591955	−	1.06601i
$947$	11.0714			0.359771			0.179885	−	0.983688i	$-0.442427\pi$
$947$	11.0714			0.359771			0.179885	+	0.983688i	$0.442427\pi$
$948$	−0.146017	+	0.449395i	−0.00474242	+	0.0145957i
$949$	22.6123	−	16.4288i	0.734025	−	0.533301i
$950$	10.8869	+	7.90978i	0.353217	+	0.256627i
$951$	−5.23165	−	16.1014i	−0.169648	−	0.522123i
$952$	−4.79769	−	14.7658i	−0.155494	−	0.478561i
$953$	11.9924	+	8.71296i	0.388471	+	0.282240i	0.764828	−	0.644234i	$-0.222824\pi$
$953$	11.9924	+	8.71296i	0.388471	+	0.282240i	−0.376358	+	0.926474i	$0.622824\pi$
$954$	19.4342	−	14.1197i	0.629204	−	0.457144i
$955$	5.43675	−	16.7326i	0.175929	−	0.541454i
$956$	0.155867			0.00504110
$957$	−5.73274	+	6.15697i	−0.185313	+	0.199027i
$958$	34.5782			1.11717
$959$	2.57224	−	7.91655i	0.0830621	−	0.255639i
$960$	−25.8191	+	18.7586i	−0.833306	+	0.605432i
$961$	23.6957	+	17.2159i	0.764377	+	0.555353i
$962$	4.23920	+	13.0469i	0.136677	+	0.420649i
$963$	−1.69750	−	5.22437i	−0.0547012	−	0.168353i
$964$	−0.242719	−	0.176346i	−0.00781746	−	0.00567972i
$965$	−2.20437	+	1.60157i	−0.0709612	+	0.0515563i
$966$	−0.678031	+	2.08677i	−0.0218153	+	0.0671406i
$967$	16.5193			0.531224			0.265612	−	0.964080i	$-0.414426\pi$
$967$	16.5193			0.531224			0.265612	+	0.964080i	$0.414426\pi$
$968$	20.1043	+	23.8857i	0.646177	+	0.767716i
$969$	−68.6520			−2.20542
$970$	1.92308	−	5.91862i	0.0617462	−	0.190035i
$971$	−33.0073	+	23.9812i	−1.05926	+	0.769595i	−0.973951	−	0.226760i	$-0.927187\pi$
$971$	−33.0073	+	23.9812i	−1.05926	+	0.769595i	−0.0853055	+	0.996355i	$0.527187\pi$
$972$	0.177396	+	0.128886i	0.00568998	+	0.00413401i
$973$	−2.15113	−	6.62049i	−0.0689620	−	0.212243i
$974$	5.38755	+	16.5812i	0.172628	+	0.531296i
$975$	13.3877	+	9.72671i	0.428748	+	0.311504i
$976$	−20.1672	+	14.6523i	−0.645535	+	0.469009i
$977$	15.1772	−	46.7107i	0.485562	−	1.49441i	−0.345603	−	0.938381i	$-0.612326\pi$
$977$	15.1772	−	46.7107i	0.485562	−	1.49441i	0.831165	−	0.556025i	$-0.187674\pi$
$978$	41.8243			1.33739
$979$	−34.6782	+	37.2444i	−1.10832	+	1.19034i
$980$	0.0255744			0.000816945
$981$	−1.47789	+	4.54847i	−0.0471853	+	0.145222i
$982$	18.8406	−	13.6885i	0.601228	−	0.436817i
$983$	−0.895411	−	0.650554i	−0.0285592	−	0.0207495i	0.573414	−	0.819266i	$-0.305619\pi$
$983$	−0.895411	−	0.650554i	−0.0285592	−	0.0207495i	−0.601973	+	0.798516i	$0.705619\pi$
$984$	1.73925	+	5.35286i	0.0554453	+	0.170643i
$985$	7.94756	+	24.4601i	0.253230	+	0.779362i
$986$	7.31238	+	5.31275i	0.232874	+	0.169193i
$987$	10.4590	−	7.59889i	0.332913	−	0.241875i
$988$	−0.116333	+	0.358036i	−0.00370104	+	0.0113906i
$989$	−5.77458			−0.183621
$990$	6.98233	+	12.5740i	0.221913	+	0.399627i
$991$	41.7851			1.32735			0.663674	−	0.748022i	$-0.268996\pi$
$991$	41.7851			1.32735			0.663674	+	0.748022i	$0.268996\pi$
$992$	0.0319255	−	0.0982567i	0.00101364	−	0.00311965i
$993$	−49.2618	+	35.7908i	−1.56328	+	1.13579i
$994$	15.8499	+	11.5156i	0.502727	+	0.365253i
$995$	2.42630	+	7.46739i	0.0769189	+	0.236732i
$996$	−0.0408500	−	0.125723i	−0.00129438	−	0.00398369i
$997$	−35.7541	−	25.9769i	−1.13234	−	0.822695i	−0.146309	−	0.989239i	$-0.546739\pi$
$997$	−35.7541	−	25.9769i	−1.13234	−	0.822695i	−0.986034	+	0.166543i	$0.946739\pi$
$998$	−15.6664	+	11.3823i	−0.495910	+	0.360300i
$999$	1.84819	−	5.68816i	0.0584743	−	0.179965i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.f.b.64.2	✓	16
3.2	odd	2		693.2.m.i.64.3		16
7.2	even	3		539.2.q.g.361.3		32
7.3	odd	6		539.2.q.f.471.2		32
7.4	even	3		539.2.q.g.471.2		32
7.5	odd	6		539.2.q.f.361.3		32
7.6	odd	2		539.2.f.e.295.2		16
11.2	odd	10		847.2.f.v.729.2		16
11.3	even	5		847.2.f.w.323.3		16
11.4	even	5		847.2.a.p.1.3		8
11.5	even	5	inner	77.2.f.b.71.2	yes	16
11.6	odd	10		847.2.f.x.148.3		16
11.7	odd	10		847.2.a.o.1.6		8
11.8	odd	10		847.2.f.v.323.2		16
11.9	even	5		847.2.f.w.729.3		16
11.10	odd	2		847.2.f.x.372.3		16
33.5	odd	10		693.2.m.i.379.3		16
33.26	odd	10		7623.2.a.ct.1.6		8
33.29	even	10		7623.2.a.cw.1.3		8
77.5	odd	30		539.2.q.f.214.2		32
77.16	even	15		539.2.q.g.214.2		32
77.27	odd	10		539.2.f.e.148.2		16
77.38	odd	30		539.2.q.f.324.3		32
77.48	odd	10		5929.2.a.bt.1.3		8
77.60	even	15		539.2.q.g.324.3		32
77.62	even	10		5929.2.a.bs.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.64.2	✓	16	1.1	even	1	trivial
77.2.f.b.71.2	yes	16	11.5	even	5	inner
539.2.f.e.148.2		16	77.27	odd	10
539.2.f.e.295.2		16	7.6	odd	2
539.2.q.f.214.2		32	77.5	odd	30
539.2.q.f.324.3		32	77.38	odd	30
539.2.q.f.361.3		32	7.5	odd	6
539.2.q.f.471.2		32	7.3	odd	6
539.2.q.g.214.2		32	77.16	even	15
539.2.q.g.324.3		32	77.60	even	15
539.2.q.g.361.3		32	7.2	even	3
539.2.q.g.471.2		32	7.4	even	3
693.2.m.i.64.3		16	3.2	odd	2
693.2.m.i.379.3		16	33.5	odd	10
847.2.a.o.1.6		8	11.7	odd	10
847.2.a.p.1.3		8	11.4	even	5
847.2.f.v.323.2		16	11.8	odd	10
847.2.f.v.729.2		16	11.2	odd	10
847.2.f.w.323.3		16	11.3	even	5
847.2.f.w.729.3		16	11.9	even	5
847.2.f.x.148.3		16	11.6	odd	10
847.2.f.x.372.3		16	11.10	odd	2
5929.2.a.bs.1.6		8	77.62	even	10
5929.2.a.bt.1.3		8	77.48	odd	10
7623.2.a.ct.1.6		8	33.26	odd	10
7623.2.a.cw.1.3		8	33.29	even	10

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.435488 + 1.34029i) q^{2} +(1.75021 - 1.27160i) q^{3} +(0.0112975 + 0.00820814i) q^{4} +(-0.565930 - 1.74175i) q^{5} +(0.942126 + 2.89957i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-2.29616 + 1.66826i) q^{8} +(0.519216 - 1.59798i) q^{9} +O(q^{10})\)	\(q+(-0.435488 + 1.34029i) q^{2} +(1.75021 - 1.27160i) q^{3} +(0.0112975 + 0.00820814i) q^{4} +(-0.565930 - 1.74175i) q^{5} +(0.942126 + 2.89957i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-2.29616 + 1.66826i) q^{8} +(0.519216 - 1.59798i) q^{9} +2.58091 q^{10} +(-2.26009 + 2.42734i) q^{11} +0.0302106 q^{12} +(-1.43602 + 4.41961i) q^{13} +(1.14012 - 0.828347i) q^{14} +(-3.20531 - 2.32880i) q^{15} +(-1.22738 - 3.77748i) q^{16} +(-1.69039 - 5.20248i) q^{17} +(1.91565 + 1.39180i) q^{18} +(4.69325 - 3.40985i) q^{19} +(0.00790293 - 0.0243227i) q^{20} -2.16338 q^{21} +(-2.26911 - 4.08626i) q^{22} -0.719682 q^{23} +(-1.89741 + 5.83962i) q^{24} +(1.33166 - 0.967509i) q^{25} +(-5.29821 - 3.84937i) q^{26} +(0.882303 + 2.71545i) q^{27} +(-0.00431527 - 0.0132810i) q^{28} +(0.948551 + 0.689163i) q^{29} +(4.51715 - 3.28190i) q^{30} +(-0.404153 + 1.24385i) q^{31} -0.0789938 q^{32} +(-0.869026 + 7.12230i) q^{33} +7.70900 q^{34} +(-0.565930 + 1.74175i) q^{35} +(0.0189823 - 0.0137915i) q^{36} +(-1.69468 - 1.23126i) q^{37} +(2.52634 + 7.77528i) q^{38} +(3.10666 + 9.56131i) q^{39} +(4.20516 + 3.05523i) q^{40} +(0.741582 - 0.538791i) q^{41} +(0.942126 - 2.89957i) q^{42} +8.02379 q^{43} +(-0.0454574 + 0.00887181i) q^{44} -3.07713 q^{45} +(0.313413 - 0.964586i) q^{46} +(-4.83455 + 3.51251i) q^{47} +(-6.95163 - 5.05065i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.716823 + 2.20615i) q^{50} +(-9.57403 - 6.95594i) q^{51} +(-0.0525003 + 0.0381437i) q^{52} +(3.13496 - 9.64840i) q^{53} -4.02373 q^{54} +(5.50688 + 2.56282i) q^{55} +2.83822 q^{56} +(3.87821 - 11.9359i) q^{57} +(-1.33676 + 0.971215i) q^{58} +(6.21390 + 4.51466i) q^{59} +(-0.0170971 - 0.0526193i) q^{60} +(-1.93943 - 5.96895i) q^{61} +(-1.49113 - 1.08337i) q^{62} +(-1.35932 + 0.987607i) q^{63} +(2.48916 - 7.66083i) q^{64} +8.51056 q^{65} +(-9.16752 - 4.26643i) q^{66} -15.4673 q^{67} +(0.0236055 - 0.0726501i) q^{68} +(-1.25960 + 0.915151i) q^{69} +(-2.08800 - 1.51702i) q^{70} +(4.29593 + 13.2215i) q^{71} +(1.47365 + 4.53542i) q^{72} +(-4.86593 - 3.53531i) q^{73} +(2.38826 - 1.73517i) q^{74} +(1.10040 - 3.38669i) q^{75} +0.0810106 q^{76} +(3.25521 - 0.635311i) q^{77} -14.1679 q^{78} +(-4.83332 + 14.8754i) q^{79} +(-5.88482 + 4.27557i) q^{80} +(9.07517 + 6.59349i) q^{81} +(0.399188 + 1.22857i) q^{82} +(-1.35217 - 4.16157i) q^{83} +(-0.0244409 - 0.0177573i) q^{84} +(-8.10479 + 5.88848i) q^{85} +(-3.49426 + 10.7542i) q^{86} +2.53651 q^{87} +(1.14011 - 9.34400i) q^{88} +15.3437 q^{89} +(1.34005 - 4.12425i) q^{90} +(3.75955 - 2.73147i) q^{91} +(-0.00813063 - 0.00590725i) q^{92} +(0.874336 + 2.69093i) q^{93} +(-2.60240 - 8.00937i) q^{94} +(-8.59515 - 6.24474i) q^{95} +(-0.138256 + 0.100449i) q^{96} +(0.745114 - 2.29323i) q^{97} -1.40927 q^{98} +(2.70537 + 4.87190i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} + 3 q^{6} - 4 q^{7} - 5 q^{8} - 12 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 + 3 * q^6 - 4 * q^7 - 5 * q^8 - 12 * q^9	\( 16 q - 3 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} + 3 q^{6} - 4 q^{7} - 5 q^{8} - 12 q^{9} + 12 q^{10} - 3 q^{11} + 18 q^{12} - 7 q^{13} + 2 q^{14} - 18 q^{15} + 17 q^{16} - 5 q^{17} + 11 q^{18} + 19 q^{19} + q^{20} + 8 q^{21} - 33 q^{22} + 32 q^{23} - 35 q^{24} + 7 q^{25} - 27 q^{26} + 10 q^{27} + 4 q^{28} + 3 q^{29} - 2 q^{30} - 7 q^{31} + 32 q^{32} - 26 q^{33} - 24 q^{34} - 5 q^{35} + 52 q^{36} + 4 q^{37} - 5 q^{38} + 11 q^{39} - 10 q^{40} - 10 q^{41} + 3 q^{42} - 8 q^{43} - 38 q^{44} + 70 q^{45} - 42 q^{46} - 23 q^{47} - 36 q^{48} - 4 q^{49} + 52 q^{50} - 29 q^{51} + 33 q^{52} + 4 q^{53} + 60 q^{54} - 12 q^{55} - 11 q^{57} + 20 q^{58} + 17 q^{59} - 30 q^{60} - 7 q^{61} + 79 q^{62} - 2 q^{63} + 7 q^{64} - 8 q^{65} + 8 q^{66} - 38 q^{67} - 2 q^{68} + 10 q^{69} - 18 q^{70} - 14 q^{71} - 35 q^{73} - 29 q^{74} + 9 q^{75} + 52 q^{76} - 3 q^{77} - 58 q^{78} + 15 q^{79} - 87 q^{80} - 14 q^{81} + 19 q^{82} + 5 q^{83} + 8 q^{84} + 6 q^{85} - 52 q^{86} - 72 q^{87} + 55 q^{88} + 74 q^{89} - 14 q^{90} + 13 q^{91} - 55 q^{92} + 32 q^{93} - 24 q^{94} + 32 q^{95} - 42 q^{96} + 20 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 + 3 * q^6 - 4 * q^7 - 5 * q^8 - 12 * q^9 + 12 * q^10 - 3 * q^11 + 18 * q^12 - 7 * q^13 + 2 * q^14 - 18 * q^15 + 17 * q^16 - 5 * q^17 + 11 * q^18 + 19 * q^19 + q^20 + 8 * q^21 - 33 * q^22 + 32 * q^23 - 35 * q^24 + 7 * q^25 - 27 * q^26 + 10 * q^27 + 4 * q^28 + 3 * q^29 - 2 * q^30 - 7 * q^31 + 32 * q^32 - 26 * q^33 - 24 * q^34 - 5 * q^35 + 52 * q^36 + 4 * q^37 - 5 * q^38 + 11 * q^39 - 10 * q^40 - 10 * q^41 + 3 * q^42 - 8 * q^43 - 38 * q^44 + 70 * q^45 - 42 * q^46 - 23 * q^47 - 36 * q^48 - 4 * q^49 + 52 * q^50 - 29 * q^51 + 33 * q^52 + 4 * q^53 + 60 * q^54 - 12 * q^55 - 11 * q^57 + 20 * q^58 + 17 * q^59 - 30 * q^60 - 7 * q^61 + 79 * q^62 - 2 * q^63 + 7 * q^64 - 8 * q^65 + 8 * q^66 - 38 * q^67 - 2 * q^68 + 10 * q^69 - 18 * q^70 - 14 * q^71 - 35 * q^73 - 29 * q^74 + 9 * q^75 + 52 * q^76 - 3 * q^77 - 58 * q^78 + 15 * q^79 - 87 * q^80 - 14 * q^81 + 19 * q^82 + 5 * q^83 + 8 * q^84 + 6 * q^85 - 52 * q^86 - 72 * q^87 + 55 * q^88 + 74 * q^89 - 14 * q^90 + 13 * q^91 - 55 * q^92 + 32 * q^93 - 24 * q^94 + 32 * q^95 - 42 * q^96 + 20 * q^97 + 2 * q^98 + 16 * q^99

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