LMFDB - Embedded newform 690.2.m.c.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (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:	$5.50967773947$
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} - 4 x^{19} - 3 x^{18} + 66 x^{17} - 163 x^{16} - 52 x^{15} + 1567 x^{14} - 6182 x^{13} + \cdots + 529 $ x^20 - 4x^19 - 3x^18 + 66x^17 - 163x^16 - 52x^15 + 1567x^14 - 6182x^13 + 17043x^12 - 35832x^11 + 60906x^10 - 87666x^9 + 106197x^8 - 102542x^7 + 92618x^6 - 8374x^5 + 38352x^4 + 60038x^3 + 32919x^2 + 5681*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			361.2
Root			$-0.103821 + 0.119816i$ of defining polynomial
Character	$\chi$	$=$	690.361
Dual form			690.2.m.c.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.142315 - 0.989821i) q^{6} +(2.42713 - 0.712670i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.142315 - 0.989821i) q^{6} +(2.42713 - 0.712670i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-0.959493 - 0.281733i) q^{10} +(-3.14672 - 3.63151i) q^{11} +(0.654861 + 0.755750i) q^{12} +(3.41824 + 1.00368i) q^{13} +(-1.05083 + 2.30100i) q^{14} +(-0.841254 - 0.540641i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.684717 - 4.76231i) q^{17} +(0.415415 + 0.909632i) q^{18} +(-0.0293102 - 0.203857i) q^{19} +(0.841254 - 0.540641i) q^{20} +(-1.65653 + 1.91174i) q^{21} +4.80517 q^{22} +(-1.83550 - 4.43068i) q^{23} -1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(-2.99700 + 1.92606i) q^{26} +(0.142315 + 0.989821i) q^{27} +(-1.05083 - 2.30100i) q^{28} +(0.860936 - 5.98794i) q^{29} +(0.959493 - 0.281733i) q^{30} +(5.39365 + 3.46629i) q^{31} +(0.415415 - 0.909632i) q^{32} +(4.61053 + 1.35377i) q^{33} +(3.15072 + 3.63613i) q^{34} +(1.65653 + 1.91174i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(1.60149 - 3.50677i) q^{37} +(0.173259 + 0.111347i) q^{38} +(-3.41824 + 1.00368i) q^{39} +(-0.142315 + 0.989821i) q^{40} +(4.17325 + 9.13813i) q^{41} +(-0.359999 - 2.50385i) q^{42} +(1.62206 - 1.04243i) q^{43} +(-3.14672 + 3.63151i) q^{44} +1.00000 q^{45} +(4.55048 + 1.51430i) q^{46} -5.35602 q^{47} +(0.654861 - 0.755750i) q^{48} +(-0.505710 + 0.325000i) q^{49} +(-0.142315 - 0.989821i) q^{50} +(1.99868 + 4.37650i) q^{51} +(0.507003 - 3.52628i) q^{52} +(12.5315 - 3.67959i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(1.99614 - 4.37094i) q^{55} +(2.42713 + 0.712670i) q^{56} +(0.134870 + 0.155649i) q^{57} +(3.96159 + 4.57192i) q^{58} +(7.41817 + 2.17817i) q^{59} +(-0.415415 + 0.909632i) q^{60} +(9.22714 + 5.92992i) q^{61} +(-6.15174 + 1.80631i) q^{62} +(0.359999 - 2.50385i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.507003 + 3.52628i) q^{65} +(-4.04237 + 2.59787i) q^{66} +(6.71185 - 7.74589i) q^{67} -4.81128 q^{68} +(3.93953 + 2.73498i) q^{69} -2.52960 q^{70} +(-1.47222 + 1.69903i) q^{71} +(0.841254 - 0.540641i) q^{72} +(0.534127 + 3.71493i) q^{73} +(1.60149 + 3.50677i) q^{74} +(0.142315 - 0.989821i) q^{75} +(-0.197610 + 0.0580236i) q^{76} +(-10.2256 - 6.57157i) q^{77} +(1.47993 - 3.24060i) q^{78} +(-9.22543 - 2.70883i) q^{79} +(-0.654861 - 0.755750i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-9.63903 - 2.83028i) q^{82} +(0.629887 - 1.37926i) q^{83} +(2.12803 + 1.36760i) q^{84} +(4.61639 - 1.35550i) q^{85} +(-0.274403 + 1.90852i) q^{86} +(2.51306 + 5.50283i) q^{87} +(-0.683847 - 4.75626i) q^{88} +(-11.8738 + 7.63085i) q^{89} +(-0.654861 + 0.755750i) q^{90} +9.01180 q^{91} +(-4.12437 + 2.44737i) q^{92} -6.41145 q^{93} +(3.50744 - 4.04781i) q^{94} +(0.173259 - 0.111347i) q^{95} +(0.142315 + 0.989821i) q^{96} +(0.356457 + 0.780532i) q^{97} +(0.0855510 - 0.595020i) q^{98} +(-4.61053 + 1.35377i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$2$	−0.654861	+	0.755750i	−0.463056	+	0.534396i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	0.415415	+	0.909632i	0.185779	+	0.406800i
$5$	0.415415	+	0.909632i	0.185779	+	0.406800i
$6$	0.142315	−	0.989821i	0.0580998	−	0.404093i
$7$	2.42713	−	0.712670i	0.917369	−	0.269364i	0.211229	−	0.977436i	$-0.432253\pi$
$7$	2.42713	−	0.712670i	0.917369	−	0.269364i	0.706140	+	0.708073i	$0.250435\pi$
$8$	0.841254	+	0.540641i	0.297428	+	0.191145i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	−0.959493	−	0.281733i	−0.303418	−	0.0890917i
$11$	−3.14672	−	3.63151i	−0.948772	−	1.09494i	−0.995379	−	0.0960274i	$-0.969386\pi$
$11$	−3.14672	−	3.63151i	−0.948772	−	1.09494i	0.0466071	−	0.998913i	$-0.485159\pi$
$12$	0.654861	+	0.755750i	0.189042	+	0.218166i
$13$	3.41824	+	1.00368i	0.948048	+	0.278372i	0.718974	−	0.695037i	$-0.244612\pi$
$13$	3.41824	+	1.00368i	0.948048	+	0.278372i	0.229074	+	0.973409i	$0.426430\pi$
$14$	−1.05083	+	2.30100i	−0.280847	+	0.614969i
$15$	−0.841254	−	0.540641i	−0.217211	−	0.139593i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.684717	−	4.76231i	0.166068	−	1.15503i	−0.720846	−	0.693096i	$-0.756246\pi$
$17$	0.684717	−	4.76231i	0.166068	−	1.15503i	0.886914	−	0.461935i	$-0.152845\pi$
$18$	0.415415	+	0.909632i	0.0979143	+	0.214402i
$19$	−0.0293102	−	0.203857i	−0.00672421	−	0.0467679i	0.986183	−	0.165659i	$-0.0529751\pi$
$19$	−0.0293102	−	0.203857i	−0.00672421	−	0.0467679i	−0.992907	+	0.118891i	$0.962066\pi$
$20$	0.841254	−	0.540641i	0.188110	−	0.120891i
$21$	−1.65653	+	1.91174i	−0.361485	+	0.417176i
$22$	4.80517			1.02447
$23$	−1.83550	−	4.43068i	−0.382728	−	0.923861i
$23$	−1.83550	−	4.43068i	−0.382728	−	0.923861i
$24$	−1.00000			−0.204124
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	−2.99700	+	1.92606i	−0.587760	+	0.377731i
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$	−1.05083	−	2.30100i	−0.198589	−	0.434849i
$29$	0.860936	−	5.98794i	0.159872	−	1.11193i	−0.738995	−	0.673711i	$-0.764699\pi$
$29$	0.860936	−	5.98794i	0.159872	−	1.11193i	0.898867	−	0.438222i	$-0.144392\pi$
$30$	0.959493	−	0.281733i	0.175179	−	0.0514371i
$31$	5.39365	+	3.46629i	0.968728	+	0.622564i	0.926400	−	0.376540i	$-0.122886\pi$
$31$	5.39365	+	3.46629i	0.968728	+	0.622564i	0.0423280	+	0.999104i	$0.486523\pi$
$32$	0.415415	−	0.909632i	0.0734357	−	0.160802i
$33$	4.61053	+	1.35377i	0.802590	+	0.235662i
$34$	3.15072	+	3.63613i	0.540344	+	0.623590i
$35$	1.65653	+	1.91174i	0.280005	+	0.323143i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	1.60149	−	3.50677i	0.263283	−	0.576509i	−0.731110	−	0.682260i	$-0.760997\pi$
$37$	1.60149	−	3.50677i	0.263283	−	0.576509i	0.994393	+	0.105751i	$0.0337246\pi$
$38$	0.173259	+	0.111347i	0.0281063	+	0.0180628i
$39$	−3.41824	+	1.00368i	−0.547356	+	0.160718i
$40$	−0.142315	+	0.989821i	−0.0225020	+	0.156505i
$41$	4.17325	+	9.13813i	0.651751	+	1.42714i	0.890013	+	0.455936i	$0.150695\pi$
$41$	4.17325	+	9.13813i	0.651751	+	1.42714i	−0.238261	+	0.971201i	$0.576577\pi$
$42$	−0.359999	−	2.50385i	−0.0555491	−	0.386352i
$43$	1.62206	−	1.04243i	0.247361	−	0.158970i	−0.411085	−	0.911597i	$-0.634850\pi$
$43$	1.62206	−	1.04243i	0.247361	−	0.158970i	0.658447	+	0.752627i	$0.271214\pi$
$44$	−3.14672	+	3.63151i	−0.474386	+	0.547470i
$45$	1.00000			0.149071
$46$	4.55048	+	1.51430i	0.670932	+	0.223272i
$47$	−5.35602			−0.781255			−0.390628	−	0.920549i	$-0.627742\pi$
$47$	−5.35602			−0.781255			−0.390628	+	0.920549i	$0.627742\pi$
$48$	0.654861	−	0.755750i	0.0945210	−	0.109083i
$49$	−0.505710	+	0.325000i	−0.0722443	+	0.0464286i
$50$	−0.142315	−	0.989821i	−0.0201264	−	0.139982i
$51$	1.99868	+	4.37650i	0.279871	+	0.612832i
$52$	0.507003	−	3.52628i	0.0703086	−	0.489007i
$53$	12.5315	−	3.67959i	1.72134	−	0.505430i	0.736137	−	0.676833i	$-0.236648\pi$
$53$	12.5315	−	3.67959i	1.72134	−	0.505430i	0.985201	+	0.171402i	$0.0548298\pi$
$54$	−0.841254	−	0.540641i	−0.114480	−	0.0735719i
$55$	1.99614	−	4.37094i	0.269160	−	0.589377i
$56$	2.42713	+	0.712670i	0.324339	+	0.0952345i
$57$	0.134870	+	0.155649i	0.0178640	+	0.0206162i
$58$	3.96159	+	4.57192i	0.520182	+	0.600322i
$59$	7.41817	+	2.17817i	0.965763	+	0.283574i	0.726335	−	0.687340i	$-0.241222\pi$
$59$	7.41817	+	2.17817i	0.965763	+	0.283574i	0.239428	+	0.970914i	$0.423040\pi$
$60$	−0.415415	+	0.909632i	−0.0536298	+	0.117433i
$61$	9.22714	+	5.92992i	1.18141	+	0.759249i	0.975646	−	0.219352i	$-0.0703944\pi$
$61$	9.22714	+	5.92992i	1.18141	+	0.759249i	0.205768	+	0.978601i	$0.434031\pi$
$62$	−6.15174	+	1.80631i	−0.781271	+	0.229402i
$63$	0.359999	−	2.50385i	0.0453556	−	0.315455i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	0.507003	+	3.52628i	0.0628860	+	0.437381i
$66$	−4.04237	+	2.59787i	−0.497581	+	0.319776i
$67$	6.71185	−	7.74589i	0.819983	−	0.946311i	−0.179314	−	0.983792i	$-0.557388\pi$
$67$	6.71185	−	7.74589i	0.819983	−	0.946311i	0.999297	+	0.0374805i	$0.0119332\pi$
$68$	−4.81128			−0.583454
$69$	3.93953	+	2.73498i	0.474263	+	0.329253i
$70$	−2.52960			−0.302345
$71$	−1.47222	+	1.69903i	−0.174720	+	0.201638i	−0.836355	−	0.548189i	$-0.815318\pi$
$71$	−1.47222	+	1.69903i	−0.174720	+	0.201638i	0.661635	+	0.749826i	$0.269863\pi$
$72$	0.841254	−	0.540641i	0.0991427	−	0.0637151i
$73$	0.534127	+	3.71493i	0.0625148	+	0.434800i	0.996909	+	0.0785603i	$0.0250323\pi$
$73$	0.534127	+	3.71493i	0.0625148	+	0.434800i	−0.934395	+	0.356240i	$0.884059\pi$
$74$	1.60149	+	3.50677i	0.186169	+	0.407653i
$75$	0.142315	−	0.989821i	0.0164331	−	0.114295i
$76$	−0.197610	+	0.0580236i	−0.0226675	+	0.00665577i
$77$	−10.2256	−	6.57157i	−1.16531	−	0.748900i
$78$	1.47993	−	3.24060i	0.167570	−	0.366926i
$79$	−9.22543	−	2.70883i	−1.03794	−	0.304767i	−0.282006	−	0.959413i	$-0.591000\pi$
$79$	−9.22543	−	2.70883i	−1.03794	−	0.304767i	−0.755936	+	0.654645i	$0.772818\pi$
$80$	−0.654861	−	0.755750i	−0.0732157	−	0.0844954i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−9.63903	−	2.83028i	−1.06445	−	0.312552i
$83$	0.629887	−	1.37926i	0.0691391	−	0.151394i	−0.871907	−	0.489671i	$-0.837117\pi$
$83$	0.629887	−	1.37926i	0.0691391	−	0.151394i	0.941046	+	0.338277i	$0.109844\pi$
$84$	2.12803	+	1.36760i	0.232187	+	0.149218i
$85$	4.61639	−	1.35550i	0.500718	−	0.147024i
$86$	−0.274403	+	1.90852i	−0.0295897	+	0.205801i
$87$	2.51306	+	5.50283i	0.269428	+	0.589966i
$88$	−0.683847	−	4.75626i	−0.0728984	−	0.507019i
$89$	−11.8738	+	7.63085i	−1.25862	+	0.808869i	−0.988095	−	0.153843i	$-0.950835\pi$
$89$	−11.8738	+	7.63085i	−1.25862	+	0.808869i	−0.270529	+	0.962712i	$0.587199\pi$
$90$	−0.654861	+	0.755750i	−0.0690284	+	0.0796630i
$91$	9.01180			0.944693
$92$	−4.12437	+	2.44737i	−0.429995	+	0.255156i
$93$	−6.41145			−0.664836
$94$	3.50744	−	4.04781i	0.361765	−	0.417499i
$95$	0.173259	−	0.111347i	0.0177760	−	0.0114239i
$96$	0.142315	+	0.989821i	0.0145249	+	0.101023i
$97$	0.356457	+	0.780532i	0.0361927	+	0.0792510i	0.926865	−	0.375395i	$-0.122493\pi$
$97$	0.356457	+	0.780532i	0.0361927	+	0.0792510i	−0.890672	+	0.454646i	$0.849766\pi$
$98$	0.0855510	−	0.595020i	0.00864196	−	0.0601061i
$99$	−4.61053	+	1.35377i	−0.463376	+	0.136059i
$100$	0.841254	+	0.540641i	0.0841254	+	0.0540641i
$101$	−2.71817	+	5.95197i	−0.270468	+	0.592243i	−0.995317	−	0.0966651i	$-0.969182\pi$
$101$	−2.71817	+	5.95197i	−0.270468	+	0.592243i	0.724849	+	0.688908i	$0.241910\pi$
$102$	−4.61639	−	1.35550i	−0.457091	−	0.134214i
$103$	−4.50767	−	5.20213i	−0.444154	−	0.512581i	0.488889	−	0.872346i	$-0.337402\pi$
$103$	−4.50767	−	5.20213i	−0.444154	−	0.512581i	−0.933043	+	0.359765i	$0.882857\pi$
$104$	2.33297	+	2.69239i	0.228766	+	0.264011i
$105$	−2.42713	−	0.712670i	−0.236864	−	0.0695495i
$106$	−5.42556	+	11.8803i	−0.526977	+	1.15392i
$107$	2.97364	+	1.91104i	0.287473	+	0.184747i	0.676427	−	0.736509i	$-0.263527\pi$
$107$	2.97364	+	1.91104i	0.287473	+	0.184747i	−0.388955	+	0.921257i	$0.627164\pi$
$108$	0.959493	−	0.281733i	0.0923273	−	0.0271097i
$109$	2.94833	−	20.5061i	0.282399	−	1.96413i	0.0175237	−	0.999846i	$-0.494422\pi$
$109$	2.94833	−	20.5061i	0.282399	−	1.96413i	0.264875	−	0.964283i	$-0.414669\pi$
$110$	1.99614	+	4.37094i	0.190325	+	0.416753i
$111$	0.548645	+	3.81591i	0.0520751	+	0.362190i
$112$	−2.12803	+	1.36760i	−0.201080	+	0.129226i
$113$	−5.31675	+	6.13585i	−0.500158	+	0.577213i	−0.948551	−	0.316624i	$-0.897451\pi$
$113$	−5.31675	+	6.13585i	−0.500158	+	0.577213i	0.448394	+	0.893836i	$0.351996\pi$
$114$	−0.205953			−0.0192893
$115$	3.26780	−	3.51020i	0.304724	−	0.327328i
$116$	−6.04952			−0.561683
$117$	2.33297	−	2.69239i	0.215683	−	0.248912i
$118$	−6.50402	+	4.17988i	−0.598743	+	0.384789i
$119$	−1.73206	−	12.0467i	−0.158778	−	1.10432i
$120$	−0.415415	−	0.909632i	−0.0379220	−	0.0830377i
$121$	−1.72054	+	11.9666i	−0.156413	+	1.08788i
$122$	−10.5240	+	3.09013i	−0.952800	+	0.279767i
$123$	−8.45121	−	5.43126i	−0.762020	−	0.489720i
$124$	2.66341	−	5.83206i	0.239181	−	0.523734i
$125$	−0.959493	−	0.281733i	−0.0858197	−	0.0251989i
$126$	1.65653	+	1.91174i	0.147576	+	0.170312i
$127$	−2.82820	−	3.26392i	−0.250963	−	0.289626i	0.616264	−	0.787539i	$-0.288645\pi$
$127$	−2.82820	−	3.26392i	−0.250963	−	0.289626i	−0.867227	+	0.497913i	$0.834100\pi$
$128$	−0.959493	−	0.281733i	−0.0848080	−	0.0249019i
$129$	−0.800980	+	1.75390i	−0.0705223	+	0.154422i
$130$	−2.99700	−	1.92606i	−0.262854	−	0.168926i
$131$	−8.04184	+	2.36130i	−0.702619	+	0.206307i	−0.613478	−	0.789712i	$-0.710230\pi$
$131$	−8.04184	+	2.36130i	−0.702619	+	0.206307i	−0.0891404	+	0.996019i	$0.528412\pi$
$132$	0.683847	−	4.75626i	0.0595213	−	0.413980i
$133$	−0.216422	−	0.473898i	−0.0187662	−	0.0410922i
$134$	1.45863	+	10.1450i	0.126006	+	0.876391i
$135$	−0.841254	+	0.540641i	−0.0724036	+	0.0465310i
$136$	3.15072	−	3.63613i	0.270172	−	0.311795i
$137$	17.2818			1.47648			0.738242	−	0.674536i	$-0.235656\pi$
$137$	17.2818			1.47648			0.738242	+	0.674536i	$0.235656\pi$
$138$	−4.64680	+	1.18626i	−0.395562	+	0.100981i
$139$	−5.98307			−0.507477			−0.253739	−	0.967273i	$-0.581660\pi$
$139$	−5.98307			−0.507477			−0.253739	+	0.967273i	$0.581660\pi$
$140$	1.65653	−	1.91174i	0.140003	−	0.161572i
$141$	4.50577	−	2.89568i	0.379454	−	0.243860i
$142$	−0.319944	−	2.22526i	−0.0268491	−	0.186739i
$143$	−7.11134	−	15.5717i	−0.594680	−	1.30217i
$144$	−0.142315	+	0.989821i	−0.0118596	+	0.0824851i
$145$	5.80447	−	1.70435i	0.482035	−	0.141538i
$146$	−3.15734	−	2.02910i	−0.261303	−	0.167929i
$147$	0.249722	−	0.546815i	0.0205967	−	0.0451006i
$148$	−3.69899	−	1.08612i	−0.304055	−	0.0892786i
$149$	−10.3327	−	11.9246i	−0.846487	−	0.976898i	0.153449	−	0.988157i	$-0.450962\pi$
$149$	−10.3327	−	11.9246i	−0.846487	−	0.976898i	−0.999937	+	0.0112582i	$0.996416\pi$
$150$	0.654861	+	0.755750i	0.0534692	+	0.0617067i
$151$	−2.78013	−	0.816319i	−0.226244	−	0.0664311i	0.166646	−	0.986017i	$-0.446706\pi$
$151$	−2.78013	−	0.816319i	−0.226244	−	0.0664311i	−0.392890	+	0.919586i	$0.628525\pi$
$152$	0.0855559	−	0.187341i	0.00693950	−	0.0151954i
$153$	−4.04751	−	2.60118i	−0.327222	−	0.210293i
$154$	11.6628	−	3.42450i	0.939814	−	0.275954i
$155$	−0.912444	+	6.34619i	−0.0732893	+	0.509738i
$156$	1.47993	+	3.24060i	0.118490	+	0.259456i
$157$	1.03032	+	7.16602i	0.0822283	+	0.571911i	0.988730	+	0.149709i	$0.0478336\pi$
$157$	1.03032	+	7.16602i	0.0822283	+	0.571911i	−0.906502	+	0.422202i	$0.861257\pi$
$158$	8.08857	−	5.19821i	0.643492	−	0.413547i
$159$	−8.55286	+	9.87052i	−0.678286	+	0.782783i
$160$	1.00000			0.0790569
$161$	−7.61260	−	9.44574i	−0.599957	−	0.744429i
$162$	1.00000			0.0785674
$163$	10.9865	−	12.6791i	0.860532	−	0.993107i	−0.139464	−	0.990227i	$-0.544538\pi$
$163$	10.9865	−	12.6791i	0.860532	−	0.993107i	0.999996	−	0.00287960i	$-0.000916606\pi$
$164$	8.45121	−	5.43126i	0.659928	−	0.424110i
$165$	0.683847	+	4.75626i	0.0532375	+	0.370275i
$166$	0.629887	+	1.37926i	0.0488887	+	0.107051i
$167$	3.21431	−	22.3560i	0.248730	−	1.72996i	−0.356839	−	0.934166i	$-0.616146\pi$
$167$	3.21431	−	22.3560i	0.248730	−	1.72996i	0.605570	−	0.795792i	$-0.292945\pi$
$168$	−2.42713	+	0.712670i	−0.187257	+	0.0549837i
$169$	−0.259347	−	0.166672i	−0.0199498	−	0.0128209i
$170$	−1.99868	+	4.37650i	−0.153292	+	0.335662i
$171$	−0.197610	−	0.0580236i	−0.0151116	−	0.00443718i
$172$	−1.26267	−	1.45719i	−0.0962773	−	0.111110i
$173$	13.7045	+	15.8159i	1.04194	+	1.20246i	0.978877	+	0.204449i	$0.0655402\pi$
$173$	13.7045	+	15.8159i	1.04194	+	1.20246i	0.0630592	+	0.998010i	$0.479914\pi$
$174$	−5.80447	−	1.70435i	−0.440036	−	0.129206i
$175$	−1.05083	+	2.30100i	−0.0794355	+	0.173939i
$176$	4.04237	+	2.59787i	0.304705	+	0.195822i
$177$	−7.41817	+	2.17817i	−0.557584	+	0.163721i
$178$	2.00870	−	13.9708i	0.150558	−	1.04716i
$179$	0.401437	+	0.879023i	0.0300048	+	0.0657013i	0.924041	−	0.382293i	$-0.124866\pi$
$179$	0.401437	+	0.879023i	0.0300048	+	0.0657013i	−0.894036	+	0.447995i	$0.852138\pi$
$180$	−0.142315	−	0.989821i	−0.0106075	−	0.0737769i
$181$	−18.1205	+	11.6453i	−1.34689	+	0.865591i	−0.997450	−	0.0713690i	$-0.977263\pi$
$181$	−18.1205	+	11.6453i	−1.34689	+	0.865591i	−0.349436	+	0.936960i	$0.613627\pi$
$182$	−5.90147	+	6.81066i	−0.437446	+	0.504840i
$183$	−10.9683			−0.810801
$184$	0.851290	−	4.71967i	0.0627579	−	0.347939i
$185$	3.85515			0.283436
$186$	4.19860	−	4.84545i	0.307857	−	0.355285i
$187$	−19.4490	+	12.4991i	−1.42225	+	0.914025i
$188$	0.762240	+	5.30150i	0.0555921	+	0.386652i
$189$	1.05083	+	2.30100i	0.0764368	+	0.167373i
$190$	−0.0293102	+	0.203857i	−0.00212638	+	0.0147893i
$191$	−21.9038	+	6.43153i	−1.58490	+	0.465369i	−0.951294	−	0.308286i	$-0.900245\pi$
$191$	−21.9038	+	6.43153i	−1.58490	+	0.465369i	−0.633607	+	0.773655i	$0.718426\pi$
$192$	−0.841254	−	0.540641i	−0.0607122	−	0.0390174i
$193$	−4.37582	+	9.58171i	−0.314978	+	0.689706i	−0.999218	−	0.0395512i	$-0.987407\pi$
$193$	−4.37582	+	9.58171i	−0.314978	+	0.689706i	0.684239	+	0.729258i	$0.260134\pi$
$194$	−0.823316	−	0.241748i	−0.0591107	−	0.0173565i
$195$	−2.33297	−	2.69239i	−0.167067	−	0.192806i
$196$	0.393662	+	0.454311i	0.0281187	+	0.0324508i
$197$	5.35944	+	1.57367i	0.381845	+	0.112120i	0.467021	−	0.884246i	$-0.345327\pi$
$197$	5.35944	+	1.57367i	0.381845	+	0.112120i	−0.0851765	+	0.996366i	$0.527145\pi$
$198$	1.99614	−	4.37094i	0.141860	−	0.310629i
$199$	−16.4113	−	10.5469i	−1.16337	−	0.747651i	−0.191112	−	0.981568i	$-0.561209\pi$
$199$	−16.4113	−	10.5469i	−1.16337	−	0.747651i	−0.972257	+	0.233917i	$0.924846\pi$
$200$	−0.959493	+	0.281733i	−0.0678464	+	0.0199215i
$201$	−1.45863	+	10.1450i	−0.102883	+	0.715570i
$202$	−2.71817	−	5.95197i	−0.191250	−	0.418779i
$203$	−2.17782	−	15.1471i	−0.152853	−	1.06312i
$204$	4.04751	−	2.60118i	0.283382	−	0.182119i
$205$	−6.57871	+	7.59224i	−0.459477	+	0.530265i
$206$	6.88341			0.479590
$207$	−4.79278	−	0.170946i	−0.333122	−	0.0118815i
$208$	−3.56254			−0.247018
$209$	−0.648076	+	0.747920i	−0.0448284	+	0.0517347i
$210$	2.12803	−	1.36760i	0.146848	−	0.0943736i
$211$	0.602751	+	4.19223i	0.0414951	+	0.288605i	0.999994	+	0.00350798i	$0.00111663\pi$
$211$	0.602751	+	4.19223i	0.0414951	+	0.288605i	−0.958499	+	0.285097i	$0.907974\pi$
$212$	−5.42556	−	11.8803i	−0.372629	−	0.815943i
$213$	0.319944	−	2.22526i	0.0219222	−	0.152472i
$214$	−3.39159	+	0.995861i	−0.231844	+	0.0680756i
$215$	1.62206	+	1.04243i	0.110623	+	0.0710933i
$216$	−0.415415	+	0.909632i	−0.0282654	+	0.0618926i
$217$	15.5614	+	4.56924i	1.05638	+	0.310181i
$218$	13.5667	+	15.6568i	0.918855	+	1.06042i
$219$	−2.45778	−	2.83643i	−0.166081	−	0.191668i
$220$	−4.61053	−	1.35377i	−0.310842	−	0.0912714i
$221$	7.12038	−	15.5915i	0.478969	−	1.04880i
$222$	−3.24316	−	2.08425i	−0.217666	−	0.139886i
$223$	6.21810	−	1.82580i	0.416395	−	0.122265i	−0.0668227	−	0.997765i	$-0.521286\pi$
$223$	6.21810	−	1.82580i	0.416395	−	0.122265i	0.483218	+	0.875500i	$0.339468\pi$
$224$	0.359999	−	2.50385i	0.0240535	−	0.167295i
$225$	0.415415	+	0.909632i	0.0276943	+	0.0606421i
$226$	−1.15544	−	8.03626i	−0.0768587	−	0.534564i
$227$	−16.8142	+	10.8059i	−1.11600	+	0.717210i	−0.962592	−	0.270953i	$-0.912661\pi$
$227$	−16.8142	+	10.8059i	−1.11600	+	0.717210i	−0.153407	+	0.988163i	$0.549025\pi$
$228$	0.134870	−	0.155649i	0.00893202	−	0.0103081i
$229$	19.1324			1.26430			0.632152	−	0.774845i	$-0.282172\pi$
$229$	19.1324			1.26430			0.632152	+	0.774845i	$0.282172\pi$
$230$	0.512879	+	4.76833i	0.0338182	+	0.314414i
$231$	12.1552			0.799750
$232$	3.96159	−	4.57192i	0.260091	−	0.300161i
$233$	−15.1344	+	9.72631i	−0.991490	+	0.637192i	−0.932539	−	0.361069i	$-0.882412\pi$
$233$	−15.1344	+	9.72631i	−0.991490	+	0.637192i	−0.0589509	+	0.998261i	$0.518776\pi$
$234$	0.507003	+	3.52628i	0.0331438	+	0.230520i
$235$	−2.22497	−	4.87200i	−0.145141	−	0.317814i
$236$	1.10028	−	7.65265i	0.0716224	−	0.498145i
$237$	9.22543	−	2.70883i	0.599256	−	0.175957i
$238$	10.2386	+	6.57993i	0.663668	+	0.426513i
$239$	−5.81540	+	12.7340i	−0.376167	+	0.823691i	0.622973	+	0.782243i	$0.285924\pi$
$239$	−5.81540	+	12.7340i	−0.376167	+	0.823691i	−0.999141	+	0.0414484i	$0.986803\pi$
$240$	0.959493	+	0.281733i	0.0619350	+	0.0181858i
$241$	5.08468	+	5.86803i	0.327533	+	0.377993i	0.895503	−	0.445056i	$-0.146816\pi$
$241$	5.08468	+	5.86803i	0.327533	+	0.377993i	−0.567970	+	0.823049i	$0.692271\pi$
$242$	−7.91706	−	9.13678i	−0.508928	−	0.587334i
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$	4.55640	−	9.97713i	0.291694	−	0.638721i
$245$	−0.505710	−	0.325000i	−0.0323086	−	0.0207635i
$246$	9.63903	−	2.83028i	0.614562	−	0.180452i
$247$	0.104419	−	0.726248i	0.00664400	−	0.0462101i
$248$	2.66341	+	5.83206i	0.169127	+	0.370336i
$249$	0.215790	+	1.50085i	0.0136751	+	0.0951125i
$250$	0.841254	−	0.540641i	0.0532055	−	0.0341931i
$251$	9.09301	−	10.4939i	0.573946	−	0.662369i	−0.392346	−	0.919818i	$-0.628336\pi$
$251$	9.09301	−	10.4939i	0.573946	−	0.662369i	0.966292	+	0.257449i	$0.0828819\pi$
$252$	−2.52960			−0.159350
$253$	−10.3143	+	20.6077i	−0.648452	+	1.29560i
$254$	4.31879			0.270985
$255$	−3.15072	+	3.63613i	−0.197306	+	0.227703i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−3.05645	−	21.2581i	−0.190656	−	1.32604i	−0.830276	−	0.557353i	$-0.811817\pi$
$257$	−3.05645	−	21.2581i	−0.190656	−	1.32604i	0.639620	−	0.768692i	$-0.279092\pi$
$258$	−0.800980	−	1.75390i	−0.0498668	−	0.109193i
$259$	1.38785	−	9.65271i	0.0862368	−	0.599790i
$260$	3.41824	−	1.00368i	0.211990	−	0.0622459i
$261$	−5.08918	−	3.27062i	−0.315012	−	0.202446i
$262$	3.48174	−	7.62394i	0.215102	−	0.471008i
$263$	18.0033	+	5.28625i	1.11013	+	0.325964i	0.784871	−	0.619659i	$-0.212729\pi$
$263$	18.0033	+	5.28625i	1.11013	+	0.325964i	0.325262	+	0.945624i	$0.394547\pi$
$264$	3.14672	+	3.63151i	0.193667	+	0.223504i
$265$	8.55286	+	9.87052i	0.525398	+	0.606341i
$266$	0.499875	+	0.146776i	0.0306493	+	0.00899944i
$267$	5.86336	−	12.8390i	0.358832	−	0.785732i
$268$	−8.62225	−	5.54118i	−0.526688	−	0.338482i
$269$	29.3410	−	8.61530i	1.78895	−	0.525284i	0.792534	−	0.609828i	$-0.208762\pi$
$269$	29.3410	−	8.61530i	1.78895	−	0.525284i	0.996420	+	0.0845442i	$0.0269434\pi$
$270$	0.142315	−	0.989821i	0.00866101	−	0.0602386i
$271$	3.23821	+	7.09069i	0.196707	+	0.430728i	0.982123	−	0.188240i	$-0.0602782\pi$
$271$	3.23821	+	7.09069i	0.196707	+	0.430728i	−0.785416	+	0.618968i	$0.787551\pi$
$272$	0.684717	+	4.76231i	0.0415171	+	0.288758i
$273$	−7.58121	+	4.87215i	−0.458836	+	0.294876i
$274$	−11.3172	+	13.0607i	−0.683695	+	0.789026i
$275$	4.80517			0.289763
$276$	2.14649	−	4.28866i	0.129204	−	0.258147i
$277$	1.31361			0.0789272			0.0394636	−	0.999221i	$-0.487435\pi$
$277$	1.31361			0.0789272			0.0394636	+	0.999221i	$0.487435\pi$
$278$	3.91808	−	4.52170i	0.234991	−	0.271194i
$279$	5.39365	−	3.46629i	0.322909	−	0.207521i
$280$	0.359999	+	2.50385i	0.0215141	+	0.149634i
$281$	5.46294	+	11.9622i	0.325892	+	0.713604i	0.999679	−	0.0253215i	$-0.00806096\pi$
$281$	5.46294	+	11.9622i	0.325892	+	0.713604i	−0.673787	+	0.738925i	$0.735334\pi$
$282$	−0.762240	+	5.30150i	−0.0453908	+	0.315700i
$283$	−27.5648	+	8.09377i	−1.63856	+	0.481124i	−0.965919	−	0.258845i	$-0.916658\pi$
$283$	−27.5648	+	8.09377i	−1.63856	+	0.481124i	−0.672640	+	0.739969i	$0.734840\pi$
$284$	1.89126	+	1.21544i	0.112225	+	0.0721229i
$285$	−0.0855559	+	0.187341i	−0.00506790	+	0.0110971i
$286$	16.4252	+	4.82288i	0.971243	+	0.285183i
$287$	16.6415	+	19.2053i	0.982316	+	1.13365i
$288$	−0.654861	−	0.755750i	−0.0385880	−	0.0445330i
$289$	−5.89940	−	1.73222i	−0.347023	−	0.101895i
$290$	−2.51306	+	5.50283i	−0.147572	+	0.323138i
$291$	−0.721858	−	0.463910i	−0.0423161	−	0.0271949i
$292$	3.60111	−	1.05738i	0.210739	−	0.0618785i
$293$	−2.28734	+	15.9088i	−0.133628	+	0.929402i	0.807142	+	0.590357i	$0.201013\pi$
$293$	−2.28734	+	15.9088i	−0.133628	+	0.929402i	−0.940770	+	0.339045i	$0.889896\pi$
$294$	0.249722	+	0.546815i	0.0145641	+	0.0318909i
$295$	1.10028	+	7.65265i	0.0640611	+	0.445554i
$296$	3.24316	−	2.08425i	0.188505	−	0.121145i
$297$	3.14672	−	3.63151i	0.182591	−	0.210721i
$298$	15.7785			0.914022
$299$	−1.82715	−	16.9874i	−0.105667	−	0.982405i
$300$	−1.00000			−0.0577350
$301$	3.19403	−	3.68611i	0.184101	−	0.212464i
$302$	2.43753	−	1.56651i	0.140264	−	0.0901422i
$303$	−0.931205	−	6.47667i	−0.0534963	−	0.372075i
$304$	0.0855559	+	0.187341i	0.00490697	+	0.0107448i
$305$	−1.56095	+	10.8567i	−0.0893800	+	0.621651i
$306$	4.61639	−	1.35550i	0.263902	−	0.0774885i
$307$	−7.85616	−	5.04884i	−0.448374	−	0.288153i	0.296902	−	0.954908i	$-0.404046\pi$
$307$	−7.85616	−	5.04884i	−0.448374	−	0.288153i	−0.745277	+	0.666755i	$0.767683\pi$
$308$	−5.04943	+	11.0567i	−0.287718	+	0.630015i
$309$	6.60458	+	1.93928i	0.375722	+	0.110322i
$310$	−4.19860	−	4.84545i	−0.238465	−	0.275203i
$311$	14.2198	+	16.4105i	0.806330	+	0.930555i	0.998711	−	0.0507655i	$-0.0161661\pi$
$311$	14.2198	+	16.4105i	0.806330	+	0.930555i	−0.192380	+	0.981320i	$0.561621\pi$
$312$	−3.41824	−	1.00368i	−0.193519	−	0.0568224i
$313$	3.51477	−	7.69628i	0.198667	−	0.435020i	−0.783911	−	0.620874i	$-0.786778\pi$
$313$	3.51477	−	7.69628i	0.198667	−	0.435020i	0.982577	+	0.185854i	$0.0595052\pi$
$314$	−6.09043	−	3.91408i	−0.343703	−	0.220884i
$315$	2.42713	−	0.712670i	0.136753	−	0.0401544i
$316$	−1.36834	+	9.51703i	−0.0769753	+	0.535375i
$317$	9.03182	+	19.7769i	0.507277	+	1.11078i	0.974035	+	0.226397i	$0.0726947\pi$
$317$	9.03182	+	19.7769i	0.507277	+	1.11078i	−0.466758	+	0.884385i	$0.654578\pi$
$318$	−1.85871	−	12.9276i	−0.104231	−	0.724946i
$319$	−24.4544	+	15.7159i	−1.36918	+	0.879920i
$320$	−0.654861	+	0.755750i	−0.0366078	+	0.0422477i
$321$	−3.53477			−0.197292
$322$	12.1238	+	0.432424i	0.675634	+	0.0240980i
$323$	−0.990898			−0.0551350
$324$	−0.654861	+	0.755750i	−0.0363812	+	0.0419861i
$325$	−2.99700	+	1.92606i	−0.166244	+	0.106838i
$326$	2.38760	+	16.6061i	0.132237	+	0.919729i
$327$	8.60614	+	18.8448i	0.475921	+	1.04212i
$328$	−1.42969	+	9.94371i	−0.0789414	+	0.549050i
$329$	−12.9997	+	3.81707i	−0.716699	+	0.210442i
$330$	−4.04237	−	2.59787i	−0.222525	−	0.143008i
$331$	−2.65682	+	5.81762i	−0.146032	+	0.319765i	−0.968487	−	0.249065i	$-0.919877\pi$
$331$	−2.65682	+	5.81762i	−0.146032	+	0.319765i	0.822455	+	0.568830i	$0.192604\pi$
$332$	−1.45486	−	0.427187i	−0.0798460	−	0.0234449i
$333$	−2.52459	−	2.91353i	−0.138346	−	0.159660i
$334$	14.7906	+	17.0693i	0.809306	+	0.933989i
$335$	9.83412	+	2.88756i	0.537295	+	0.157764i
$336$	1.05083	−	2.30100i	0.0573276	−	0.125530i
$337$	−6.50646	−	4.18145i	−0.354429	−	0.227778i	0.351294	−	0.936265i	$-0.385742\pi$
$337$	−6.50646	−	4.18145i	−0.354429	−	0.227778i	−0.705724	+	0.708487i	$0.749378\pi$
$338$	0.295798	−	0.0868542i	0.0160893	−	0.00472425i
$339$	1.15544	−	8.03626i	0.0627549	−	0.436470i
$340$	−1.99868	−	4.37650i	−0.108394	−	0.237349i
$341$	−4.38445	−	30.4945i	−0.237431	−	1.65137i
$342$	0.173259	−	0.111347i	0.00936875	−	0.00602093i
$343$	−12.5915	+	14.5314i	−0.679879	+	0.784623i
$344$	1.92814			0.103959
$345$	−0.851290	+	4.71967i	−0.0458319	+	0.254099i
$346$	−20.9274			−1.12506
$347$	0.156342	−	0.180428i	0.00839287	−	0.00968589i	−0.751538	−	0.659690i	$-0.770687\pi$
$347$	0.156342	−	0.180428i	0.00839287	−	0.00968589i	0.759930	+	0.650004i	$0.225233\pi$
$348$	5.08918	−	3.27062i	0.272809	−	0.175323i
$349$	−1.12141	−	7.79958i	−0.0600277	−	0.417502i	−0.997572	−	0.0696372i	$-0.977816\pi$
$349$	−1.12141	−	7.79958i	−0.0600277	−	0.417502i	0.937545	−	0.347865i	$-0.113093\pi$
$350$	−1.05083	−	2.30100i	−0.0561694	−	0.122994i
$351$	−0.507003	+	3.52628i	−0.0270618	+	0.188219i
$352$	−4.61053	+	1.35377i	−0.245742	+	0.0721564i
$353$	6.04280	+	3.88347i	0.321626	+	0.206696i	0.691484	−	0.722392i	$-0.256957\pi$
$353$	6.04280	+	3.88347i	0.321626	+	0.206696i	−0.369858	+	0.929088i	$0.620594\pi$
$354$	3.21172	−	7.03268i	0.170701	−	0.373783i
$355$	−2.15707	−	0.633374i	−0.114486	−	0.0336160i
$356$	9.24301	+	10.6670i	0.489878	+	0.565350i
$357$	7.97005	+	9.19793i	0.421820	+	0.486806i
$358$	−0.927207	−	0.272252i	−0.0490044	−	0.0143890i
$359$	7.16627	−	15.6919i	0.378221	−	0.828189i	−0.620800	−	0.783969i	$-0.713192\pi$
$359$	7.16627	−	15.6919i	0.378221	−	0.828189i	0.999022	−	0.0442205i	$-0.0140804\pi$
$360$	0.841254	+	0.540641i	0.0443380	+	0.0284943i
$361$	18.1897	−	5.34097i	0.957351	−	0.281104i
$362$	3.06544	−	21.3206i	0.161116	−	1.12059i
$363$	−5.02224	−	10.9972i	−0.263599	−	0.577202i
$364$	−1.28251	−	8.92007i	−0.0672219	−	0.467539i
$365$	−3.15734	+	2.02910i	−0.165263	+	0.106208i
$366$	7.18272	−	8.28930i	0.375447	−	0.433289i
$367$	−6.12805			−0.319881			−0.159941	−	0.987127i	$-0.551130\pi$
$367$	−6.12805			−0.319881			−0.159941	+	0.987127i	$0.551130\pi$
$368$	3.00941	+	3.73409i	0.156877	+	0.194653i
$369$	10.0460			0.522972
$370$	−2.52459	+	2.91353i	−0.131247	+	0.151467i
$371$	27.7933	−	17.8617i	1.44296	−	0.927333i
$372$	0.912444	+	6.34619i	0.0473080	+	0.329034i
$373$	−11.0230	−	24.1370i	−0.570748	−	1.24976i	−0.946398	−	0.323003i	$-0.895308\pi$
$373$	−11.0230	−	24.1370i	−0.570748	−	1.24976i	0.375650	−	0.926762i	$-0.377420\pi$
$374$	3.29018	−	22.8837i	0.170131	−	1.18329i
$375$	0.959493	−	0.281733i	0.0495480	−	0.0145486i
$376$	−4.50577	−	2.89568i	−0.232367	−	0.149333i
$377$	8.95288	−	19.6041i	0.461097	−	1.00966i
$378$	−2.42713	−	0.712670i	−0.124838	−	0.0366558i
$379$	13.3664	+	15.4257i	0.686588	+	0.792364i	0.986875	−	0.161484i	$-0.0516281\pi$
$379$	13.3664	+	15.4257i	0.686588	+	0.792364i	−0.300288	+	0.953849i	$0.597083\pi$
$380$	−0.134870	−	0.155649i	−0.00691871	−	0.00798462i
$381$	4.14385	+	1.21674i	0.212296	+	0.0623356i
$382$	9.48329	−	20.7655i	0.485207	−	1.06246i
$383$	22.1342	+	14.2248i	1.13100	+	0.726852i	0.965769	−	0.259402i	$-0.0835254\pi$
$383$	22.1342	+	14.2248i	1.13100	+	0.726852i	0.165235	+	0.986254i	$0.447162\pi$
$384$	0.959493	−	0.281733i	0.0489639	−	0.0143771i
$385$	1.72986	−	12.0314i	0.0881617	−	0.613178i
$386$	−4.37582	−	9.58171i	−0.222723	−	0.487696i
$387$	−0.274403	−	1.90852i	−0.0139487	−	0.0970154i
$388$	0.721858	−	0.463910i	0.0366468	−	0.0235515i
$389$	−7.19526	+	8.30377i	−0.364814	+	0.421018i	−0.908247	−	0.418435i	$-0.862579\pi$
$389$	−7.19526	+	8.30377i	−0.364814	+	0.421018i	0.543433	+	0.839453i	$0.317124\pi$
$390$	3.56254			0.180396
$391$	−22.3571	+	5.70744i	−1.13065	+	0.288638i
$392$	−0.601139			−0.0303621
$393$	5.48861	−	6.33420i	0.276864	−	0.319518i
$394$	−4.69899	+	3.01986i	−0.236732	+	0.152138i
$395$	−1.36834	−	9.51703i	−0.0688488	−	0.478854i
$396$	1.99614	+	4.37094i	0.100310	+	0.219648i
$397$	−3.64706	+	25.3658i	−0.183041	+	1.27308i	0.666481	+	0.745522i	$0.267800\pi$
$397$	−3.64706	+	25.3658i	−0.183041	+	1.27308i	−0.849522	+	0.527553i	$0.823109\pi$
$398$	18.7180	−	5.49609i	0.938247	−	0.275494i
$399$	0.438275	+	0.281662i	0.0219412	+	0.0141007i
$400$	0.415415	−	0.909632i	0.0207708	−	0.0454816i
$401$	−18.4177	−	5.40792i	−0.919735	−	0.270059i	−0.212602	−	0.977139i	$-0.568194\pi$
$401$	−18.4177	−	5.40792i	−0.919735	−	0.270059i	−0.707133	+	0.707080i	$0.750012\pi$
$402$	−6.71185	−	7.74589i	−0.334757	−	0.386330i
$403$	14.9577	+	17.2621i	0.745097	+	0.859887i
$404$	6.27822	+	1.84345i	0.312353	+	0.0917152i
$405$	0.415415	−	0.909632i	0.0206421	−	0.0452000i
$406$	12.8736	+	8.27334i	0.638904	+	0.410599i
$407$	−17.7743	+	5.21900i	−0.881038	+	0.258696i
$408$	−0.684717	+	4.76231i	−0.0338985	+	0.235770i
$409$	3.17599	+	6.95445i	0.157043	+	0.343876i	0.971756	−	0.235989i	$-0.0758328\pi$
$409$	3.17599	+	6.95445i	0.157043	+	0.343876i	−0.814713	+	0.579864i	$0.803106\pi$
$410$	−1.42969	−	9.94371i	−0.0706074	−	0.491085i
$411$	−14.5384	+	9.34324i	−0.717125	+	0.460868i
$412$	−4.50767	+	5.20213i	−0.222077	+	0.256291i
$413$	19.5572			0.962346
$414$	3.26780	−	3.51020i	0.160604	−	0.172517i
$415$	1.51628			0.0744315
$416$	2.33297	−	2.69239i	0.114383	−	0.132005i
$417$	5.03328	−	3.23469i	0.246481	−	0.158404i
$418$	−0.140840	−	0.979566i	−0.00688873	−	0.0479122i
$419$	1.27708	+	2.79641i	0.0623894	+	0.136614i	0.938258	−	0.345935i	$-0.112438\pi$
$419$	1.27708	+	2.79641i	0.0623894	+	0.136614i	−0.875869	+	0.482549i	$0.839711\pi$
$420$	−0.359999	+	2.50385i	−0.0175662	+	0.122175i
$421$	23.6639	−	6.94836i	1.15331	−	0.338642i	0.351481	−	0.936195i	$-0.385678\pi$
$421$	23.6639	−	6.94836i	1.15331	−	0.338642i	0.801830	+	0.597553i	$0.203860\pi$
$422$	−3.56299	−	2.28979i	−0.173444	−	0.111465i
$423$	−2.22497	+	4.87200i	−0.108182	+	0.236885i
$424$	12.5315	+	3.67959i	0.608585	+	0.178697i
$425$	3.15072	+	3.63613i	0.152832	+	0.176378i
$426$	1.47222	+	1.69903i	0.0713292	+	0.0823183i
$427$	26.6215	+	7.81679i	1.28831	+	0.378281i
$428$	1.46840	−	3.21534i	0.0709777	−	0.155419i
$429$	14.4011	+	9.25503i	0.695292	+	0.446837i
$430$	−1.85004	+	0.543221i	−0.0892169	+	0.0261964i
$431$	−0.587085	+	4.08326i	−0.0282789	+	0.196684i	−0.999063	−	0.0432688i	$-0.986223\pi$
$431$	−0.587085	+	4.08326i	−0.0282789	+	0.196684i	0.970785	+	0.239953i	$0.0771319\pi$
$432$	−0.415415	−	0.909632i	−0.0199867	−	0.0437647i
$433$	0.503735	+	3.50355i	0.0242079	+	0.168370i	0.998339	−	0.0576142i	$-0.0183493\pi$
$433$	0.503735	+	3.50355i	0.0242079	+	0.168370i	−0.974131	+	0.225984i	$0.927440\pi$
$434$	−13.6438	+	8.76832i	−0.654922	+	0.420893i
$435$	−3.96159	+	4.57192i	−0.189944	+	0.219207i
$436$	−20.7170			−0.992163
$437$	−0.849425	+	0.504042i	−0.0406335	+	0.0241116i
$438$	3.75314			0.179332
$439$	−10.2897	+	11.8749i	−0.491099	+	0.566758i	−0.946159	−	0.323702i	$-0.895072\pi$
$439$	−10.2897	+	11.8749i	−0.491099	+	0.566758i	0.455060	+	0.890461i	$0.349618\pi$
$440$	4.04237	−	2.59787i	0.192712	−	0.123849i
$441$	0.0855510	+	0.595020i	0.00407386	+	0.0283343i
$442$	7.12038	+	15.5915i	0.338682	+	0.741610i
$443$	1.76224	−	12.2566i	0.0837263	−	0.582329i	−0.904165	−	0.427183i	$-0.859506\pi$
$443$	1.76224	−	12.2566i	0.0837263	−	0.582329i	0.987891	−	0.155146i	$-0.0495849\pi$
$444$	3.69899	−	1.08612i	0.175546	−	0.0515450i
$445$	−11.8738	−	7.63085i	−0.562874	−	0.361737i
$446$	−2.69214	+	5.89497i	−0.127477	+	0.279135i
$447$	15.1393	+	4.44531i	0.716065	+	0.210256i
$448$	1.65653	+	1.91174i	0.0782639	+	0.0903213i
$449$	−21.7447	−	25.0947i	−1.02620	−	1.18429i	−0.982693	−	0.185240i	$-0.940694\pi$
$449$	−21.7447	−	25.0947i	−1.02620	−	1.18429i	−0.0435029	−	0.999053i	$-0.513852\pi$
$450$	−0.959493	−	0.281733i	−0.0452309	−	0.0132810i
$451$	20.0532	−	43.9103i	0.944267	−	2.06766i
$452$	6.83005	+	4.38941i	0.321259	+	0.206460i
$453$	2.78013	−	0.816319i	0.130622	−	0.0383540i
$454$	2.84446	−	19.7837i	0.133497	−	0.928494i
$455$	3.74364	+	8.19742i	0.175504	+	0.384301i
$456$	0.0293102	+	0.203857i	0.00137257	+	0.00954646i
$457$	−10.5476	+	6.77852i	−0.493395	+	0.317086i	−0.763569	−	0.645726i	$-0.776555\pi$
$457$	−10.5476	+	6.77852i	−0.493395	+	0.317086i	0.270175	+	0.962811i	$0.412919\pi$
$458$	−12.5290	+	14.4593i	−0.585444	+	0.675638i
$459$	4.81128			0.224572
$460$	−3.93953	−	2.73498i	−0.183681	−	0.127519i
$461$	−34.6704			−1.61476			−0.807382	−	0.590029i	$-0.799116\pi$
$461$	−34.6704			−1.61476			−0.807382	+	0.590029i	$0.799116\pi$
$462$	−7.95993	+	9.18625i	−0.370330	+	0.427383i
$463$	−11.8546	+	7.61847i	−0.550928	+	0.354060i	−0.786300	−	0.617845i	$-0.788006\pi$
$463$	−11.8546	+	7.61847i	−0.550928	+	0.354060i	0.235371	+	0.971906i	$0.424369\pi$
$464$	0.860936	+	5.98794i	0.0399679	+	0.277983i
$465$	−2.66341	−	5.83206i	−0.123513	−	0.270455i
$466$	2.56029	−	17.8072i	0.118603	−	0.824904i
$467$	7.61643	−	2.23639i	0.352446	−	0.103488i	−0.100717	−	0.994915i	$-0.532114\pi$
$467$	7.61643	−	2.23639i	0.352446	−	0.103488i	0.453163	+	0.891428i	$0.350295\pi$
$468$	−2.99700	−	1.92606i	−0.138536	−	0.0890320i
$469$	10.7703	−	23.5836i	0.497325	−	1.08899i
$470$	5.13906	+	1.50896i	0.237047	+	0.0696033i
$471$	−4.74100	−	5.47141i	−0.218454	−	0.252109i
$472$	5.06295	+	5.84296i	0.233041	+	0.268944i
$473$	−8.88976	−	2.61027i	−0.408752	−	0.120020i
$474$	−3.99417	+	8.74602i	−0.183458	+	0.401718i
$475$	0.173259	+	0.111347i	0.00794965	+	0.00510893i
$476$	−11.6776	+	3.42886i	−0.535243	+	0.157161i
$477$	1.85871	−	12.9276i	0.0851046	−	0.591916i
$478$	−5.81540	−	12.7340i	−0.265990	−	0.582438i
$479$	3.86075	+	26.8521i	0.176402	+	1.22690i	0.865004	+	0.501765i	$0.167316\pi$
$479$	3.86075	+	26.8521i	0.176402	+	1.22690i	−0.688602	+	0.725139i	$0.741775\pi$
$480$	−0.841254	+	0.540641i	−0.0383978	+	0.0246768i
$481$	8.99394	−	10.3796i	0.410089	−	0.473267i
$482$	−7.76452			−0.353664
$483$	11.5109	+	3.83058i	0.523763	+	0.174297i
$484$	12.0897			0.549531
$485$	−0.561919	+	0.648489i	−0.0255154	+	0.0294464i
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	−1.59935	−	11.1238i	−0.0724737	−	0.504065i	−0.993434	−	0.114409i	$-0.963503\pi$
$487$	−1.59935	−	11.1238i	−0.0724737	−	0.504065i	0.920960	−	0.389657i	$-0.127406\pi$
$488$	4.55640	+	9.97713i	0.206259	+	0.451644i
$489$	−2.38760	+	16.6061i	−0.107971	+	0.750956i
$490$	0.576789	−	0.169360i	0.0260567	−	0.00765092i
$491$	−20.1918	−	12.9765i	−0.911243	−	0.585621i	−0.00113891	−	0.999999i	$-0.500363\pi$
$491$	−20.1918	−	12.9765i	−0.911243	−	0.585621i	−0.910105	+	0.414379i	$0.863999\pi$
$492$	−4.17325	+	9.13813i	−0.188144	+	0.411979i
$493$	−27.9269	−	8.20009i	−1.25777	−	0.369314i
$494$	0.480482	+	0.554506i	0.0216179	+	0.0249484i
$495$	−3.14672	−	3.63151i	−0.141435	−	0.163224i
$496$	−6.15174	−	1.80631i	−0.276221	−	0.0811059i
$497$	−2.36242	+	5.17298i	−0.105969	+	0.232040i
$498$	−1.27558	−	0.819765i	−0.0571601	−	0.0367345i
$499$	−8.50852	+	2.49833i	−0.380894	+	0.111840i	−0.466574	−	0.884482i	$-0.654512\pi$
$499$	−8.50852	+	2.49833i	−0.380894	+	0.111840i	0.0856803	+	0.996323i	$0.472694\pi$
$500$	−0.142315	+	0.989821i	−0.00636451	+	0.0442662i
$501$	9.38251	+	20.5448i	0.419180	+	0.917875i
$502$	1.97610	+	13.7441i	0.0881977	+	0.613428i
$503$	29.7195	−	19.0995i	1.32513	−	0.851607i	0.329420	−	0.944183i	$-0.393147\pi$
$503$	29.7195	−	19.0995i	1.32513	−	0.851607i	0.995706	+	0.0925766i	$0.0295103\pi$
$504$	1.65653	−	1.91174i	0.0737879	−	0.0851558i
$505$	−6.54327			−0.291172
$506$	−8.81988	−	21.2902i	−0.392091	−	0.946465i
$507$	0.308286			0.0136915
$508$	−2.82820	+	3.26392i	−0.125481	+	0.144813i
$509$	−34.2295	+	21.9980i	−1.51720	+	0.975042i	−0.524897	+	0.851165i	$0.675896\pi$
$509$	−34.2295	+	21.9980i	−1.51720	+	0.975042i	−0.992298	+	0.123877i	$0.960467\pi$
$510$	−0.684717	−	4.76231i	−0.0303198	−	0.210879i
$511$	3.94392	+	8.63597i	0.174469	+	0.382033i
$512$	−0.142315	+	0.989821i	−0.00628949	+	0.0437443i
$513$	0.197610	−	0.0580236i	0.00872471	−	0.00256181i
$514$	18.0674	+	11.6112i	0.796917	+	0.512147i
$515$	2.85947	−	6.26137i	0.126003	−	0.275909i
$516$	1.85004	+	0.543221i	0.0814435	+	0.0239140i
$517$	16.8539	+	19.4504i	0.741233	+	0.855428i
$518$	6.38618	+	7.37005i	0.280593	+	0.323821i
$519$	−20.0797	−	5.89593i	−0.881401	−	0.258803i
$520$	−1.47993	+	3.24060i	−0.0648994	+	0.142110i
$521$	−16.2483	−	10.4421i	−0.711851	−	0.457479i	0.133943	−	0.990989i	$-0.457236\pi$
$521$	−16.2483	−	10.4421i	−0.711851	−	0.457479i	−0.845794	+	0.533510i	$0.820873\pi$
$522$	5.80447	−	1.70435i	0.254055	−	0.0745972i
$523$	2.41549	−	16.8001i	0.105622	−	0.734616i	−0.866336	−	0.499461i	$-0.833531\pi$
$523$	2.41549	−	16.8001i	0.105622	−	0.734616i	0.971958	−	0.235154i	$-0.0755596\pi$
$524$	3.48174	+	7.62394i	0.152100	+	0.333053i
$525$	−0.359999	−	2.50385i	−0.0157117	−	0.109277i
$526$	−15.7848	+	10.1442i	−0.688248	+	0.442310i
$527$	20.2007	−	23.3128i	0.879955	−	1.01552i
$528$	−4.80517			−0.209118
$529$	−16.2619	+	16.2650i	−0.707039	+	0.707174i
$530$	−13.0606			−0.567315
$531$	5.06295	−	5.84296i	0.219713	−	0.253563i
$532$	−0.438275	+	0.281662i	−0.0190016	+	0.0122116i
$533$	5.09333	+	35.4249i	0.220617	+	1.53442i
$534$	5.86336	+	12.8390i	0.253732	+	0.555596i
$535$	−0.503051	+	3.49879i	−0.0217488	+	0.151266i
$536$	9.83412	−	2.88756i	0.424769	−	0.124723i
$537$	−0.812946	−	0.522449i	−0.0350812	−	0.0225453i
$538$	−12.7033	+	27.8163i	−0.547677	+	1.19925i
$539$	2.77157	+	0.813806i	0.119380	+	0.0350531i
$540$	0.654861	+	0.755750i	0.0281807	+	0.0325223i
$541$	22.4457	+	25.9037i	0.965017	+	1.11369i	0.993470	+	0.114094i	$0.0363964\pi$
$541$	22.4457	+	25.9037i	0.965017	+	1.11369i	−0.0284532	+	0.999595i	$0.509058\pi$
$542$	−7.47936	−	2.19614i	−0.321266	−	0.0943322i
$543$	8.94799	−	19.5934i	0.383995	−	0.840832i
$544$	−4.04751	−	2.60118i	−0.173536	−	0.111525i
$545$	19.8778	−	5.83665i	0.851471	−	0.250015i
$546$	1.28251	−	8.92007i	0.0548865	−	0.381744i
$547$	−13.3785	−	29.2948i	−0.572023	−	1.25256i	−0.945713	−	0.325003i	$-0.894635\pi$
$547$	−13.3785	−	29.2948i	−0.572023	−	1.25256i	0.373690	−	0.927554i	$-0.378092\pi$
$548$	−2.45946	−	17.1059i	−0.105063	−	0.730727i
$549$	9.22714	−	5.92992i	0.393805	−	0.253083i
$550$	−3.14672	+	3.63151i	−0.134177	+	0.154848i
$551$	−1.24592			−0.0530778
$552$	1.83550	+	4.43068i	0.0781239	+	0.188582i
$553$	−24.3218			−1.03427
$554$	−0.860232	+	0.992761i	−0.0365478	+	0.0421784i
$555$	−3.24316	+	2.08425i	−0.137664	+	0.0884715i
$556$	0.851480	+	5.92217i	0.0361108	+	0.251156i
$557$	−4.88047	−	10.6867i	−0.206792	−	0.452811i	0.777610	−	0.628747i	$-0.216432\pi$
$557$	−4.88047	−	10.6867i	−0.206792	−	0.452811i	−0.984402	+	0.175936i	$0.943705\pi$
$558$	−0.912444	+	6.34619i	−0.0386268	+	0.268656i
$559$	6.59085	−	1.93525i	0.278763	−	0.0818522i
$560$	−2.12803	−	1.36760i	−0.0899258	−	0.0577918i
$561$	9.60400	−	21.0298i	0.405481	−	0.887880i
$562$	−12.6179	−	3.70494i	−0.532253	−	0.156284i
$563$	29.3144	+	33.8306i	1.23546	+	1.42579i	0.868600	+	0.495514i	$0.165020\pi$
$563$	29.3144	+	33.8306i	1.23546	+	1.42579i	0.366855	+	0.930278i	$0.380434\pi$
$564$	−3.50744	−	4.04781i	−0.147690	−	0.170443i
$565$	−7.79003	−	2.28736i	−0.327729	−	0.0962299i
$566$	11.9343	−	26.1324i	0.501635	−	1.09843i
$567$	−2.12803	−	1.36760i	−0.0893690	−	0.0574339i
$568$	−2.15707	+	0.633374i	−0.0905088	+	0.0265758i
$569$	−3.99159	+	27.7621i	−0.167336	+	1.16385i	0.717026	+	0.697047i	$0.245503\pi$
$569$	−3.99159	+	27.7621i	−0.167336	+	1.16385i	−0.884362	+	0.466802i	$0.845406\pi$
$570$	−0.0855559	−	0.187341i	−0.00358354	−	0.00784687i
$571$	4.53861	+	31.5667i	0.189935	+	1.32102i	0.832171	+	0.554519i	$0.187098\pi$
$571$	4.53861	+	31.5667i	0.189935	+	1.32102i	−0.642237	+	0.766506i	$0.721993\pi$
$572$	−14.4011	+	9.25503i	−0.602141	+	0.386972i
$573$	14.9495	−	17.2526i	0.624523	−	0.720738i
$574$	−25.4122			−1.06069
$575$	4.55048	+	1.51430i	0.189768	+	0.0631509i
$576$	1.00000			0.0416667
$577$	−0.221839	+	0.256016i	−0.00923528	+	0.0106581i	−0.760348	−	0.649515i	$-0.774972\pi$
$577$	−0.221839	+	0.256016i	−0.00923528	+	0.0106581i	0.751113	+	0.660173i	$0.229517\pi$
$578$	5.17241	−	3.32410i	0.215144	−	0.138265i
$579$	−1.49909	−	10.4264i	−0.0623000	−	0.433306i
$580$	−2.51306	−	5.50283i	−0.104349	−	0.228493i
$581$	0.545861	−	3.79655i	0.0226461	−	0.157507i
$582$	0.823316	−	0.241748i	0.0341276	−	0.0100208i
$583$	−52.7957	−	33.9297i	−2.18657	−	1.40523i
$584$	−1.55911	+	3.41397i	−0.0645164	+	0.141271i
$585$	3.41824	+	1.00368i	0.141327	+	0.0414972i
$586$	−10.5252	−	12.1467i	−0.434791	−	0.501776i
$587$	13.5435	+	15.6300i	0.558999	+	0.645119i	0.962956	−	0.269659i	$-0.0869110\pi$
$587$	13.5435	+	15.6300i	0.558999	+	0.645119i	−0.403957	+	0.914778i	$0.632366\pi$
$588$	−0.576789	−	0.169360i	−0.0237864	−	0.00698431i
$589$	0.548537	−	1.20113i	0.0226021	−	0.0494917i
$590$	−6.50402	−	4.17988i	−0.267766	−	0.172083i
$591$	−5.35944	+	1.57367i	−0.220458	+	0.0647323i
$592$	−0.548645	+	3.81591i	−0.0225492	+	0.156833i
$593$	−17.1200	−	37.4875i	−0.703033	−	1.53943i	−0.836255	−	0.548341i	$-0.815260\pi$
$593$	−17.1200	−	37.4875i	−0.703033	−	1.53943i	0.133222	−	0.991086i	$-0.457468\pi$
$594$	0.683847	+	4.75626i	0.0280586	+	0.195152i
$595$	10.2386	−	6.57993i	0.419740	−	0.269751i
$596$	−10.3327	+	11.9246i	−0.423244	+	0.488449i
$597$	19.5082			0.798417
$598$	14.0347	+	9.74350i	0.573923	+	0.398441i
$599$	−27.1986			−1.11131			−0.555653	−	0.831415i	$-0.687532\pi$
$599$	−27.1986			−1.11131			−0.555653	+	0.831415i	$0.687532\pi$
$600$	0.654861	−	0.755750i	0.0267346	−	0.0308533i
$601$	28.3609	−	18.2265i	1.15687	−	0.743472i	0.185871	−	0.982574i	$-0.440489\pi$
$601$	28.3609	−	18.2265i	1.15687	−	0.743472i	0.970995	+	0.239102i	$0.0768529\pi$
$602$	0.694130	+	4.82778i	0.0282906	+	0.196766i
$603$	−4.25771	−	9.32308i	−0.173387	−	0.379665i
$604$	−0.412357	+	2.86800i	−0.0167786	+	0.116697i
$605$	−11.6000	+	3.40606i	−0.471606	+	0.138476i
$606$	5.50455	+	3.53756i	0.223607	+	0.143704i
$607$	−11.9613	+	26.1916i	−0.485494	+	1.06308i	0.495422	+	0.868652i	$0.335013\pi$
$607$	−11.9613	+	26.1916i	−0.485494	+	1.06308i	−0.980916	+	0.194431i	$0.937714\pi$
$608$	−0.197610	−	0.0580236i	−0.00801416	−	0.00235317i
$609$	10.0212	+	11.5651i	0.406081	+	0.468642i
$610$	−7.18272	−	8.28930i	−0.290820	−	0.335624i
$611$	−18.3081	−	5.37575i	−0.740667	−	0.217480i
$612$	−1.99868	+	4.37650i	−0.0807918	+	0.176909i
$613$	−0.524012	−	0.336762i	−0.0211647	−	0.0136017i	0.530016	−	0.847988i	$-0.322186\pi$
$613$	−0.524012	−	0.336762i	−0.0211647	−	0.0136017i	−0.551180	+	0.834386i	$0.685822\pi$
$614$	8.96035	−	2.63100i	0.361610	−	0.106178i
$615$	1.42969	−	9.94371i	0.0576507	−	0.400969i
$616$	−5.04943	−	11.0567i	−0.203447	−	0.445488i
$617$	−5.05430	−	35.1534i	−0.203478	−	1.41522i	−0.793861	−	0.608099i	$-0.791932\pi$
$617$	−5.05430	−	35.1534i	−0.203478	−	1.41522i	0.590383	−	0.807123i	$-0.298977\pi$
$618$	−5.79069	+	3.72145i	−0.232936	+	0.149699i
$619$	−21.7922	+	25.1495i	−0.875901	+	1.01084i	0.123927	+	0.992291i	$0.460451\pi$
$619$	−21.7922	+	25.1495i	−0.875901	+	1.01084i	−0.999828	+	0.0185525i	$0.994094\pi$
$620$	6.41145			0.257490
$621$	4.12437	−	2.44737i	0.165505	−	0.0982094i
$622$	−21.7142			−0.870661
$623$	−23.3811	+	26.9832i	−0.936743	+	1.08106i
$624$	2.99700	−	1.92606i	0.119976	−	0.0771040i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	3.51477	+	7.69628i	0.140479	+	0.307605i
$627$	0.140840	−	0.979566i	0.00562462	−	0.0391201i
$628$	6.94645	−	2.03966i	0.277194	−	0.0813914i
$629$	−15.6037	−	10.0279i	−0.622162	−	0.399839i
$630$	−1.05083	+	2.30100i	−0.0418662	+	0.0916741i
$631$	3.58344	+	1.05219i	0.142655	+	0.0418872i	0.352280	−	0.935895i	$-0.385406\pi$
$631$	3.58344	+	1.05219i	0.142655	+	0.0418872i	−0.209626	+	0.977782i	$0.567225\pi$
$632$	−6.29642	−	7.26646i	−0.250458	−	0.289044i
$633$	−2.77355	−	3.20085i	−0.110239	−	0.127222i
$634$	−20.8610	−	6.12534i	−0.828495	−	0.243268i
$635$	1.79409	−	3.92851i	0.0711963	−	0.155898i
$636$	10.9873	+	7.06108i	0.435673	+	0.279990i
$637$	−2.05483	+	0.603354i	−0.0814155	+	0.0239057i
$638$	4.13695	−	28.7731i	0.163783	−	1.13914i
$639$	0.933911	+	2.04498i	0.0369449	+	0.0808982i
$640$	−0.142315	−	0.989821i	−0.00562549	−	0.0391261i
$641$	−5.65083	+	3.63157i	−0.223194	+	0.143438i	−0.647460	−	0.762099i	$-0.724169\pi$
$641$	−5.65083	+	3.63157i	−0.223194	+	0.143438i	0.424266	+	0.905538i	$0.360532\pi$
$642$	2.31478	−	2.67140i	0.0913572	−	0.105432i
$643$	−1.96479			−0.0774837			−0.0387418	−	0.999249i	$-0.512335\pi$
$643$	−1.96479			−0.0774837			−0.0387418	+	0.999249i	$0.512335\pi$
$644$	−8.26621	+	8.87939i	−0.325734	+	0.349897i
$645$	−1.92814			−0.0759206
$646$	0.648900	−	0.748871i	0.0255306	−	0.0294639i
$647$	−15.2562	+	9.80454i	−0.599782	+	0.385456i	−0.805013	−	0.593257i	$-0.797842\pi$
$647$	−15.2562	+	9.80454i	−0.599782	+	0.385456i	0.205231	+	0.978714i	$0.434205\pi$
$648$	−0.142315	−	0.989821i	−0.00559065	−	0.0388839i
$649$	−15.4328	−	33.7932i	−0.605792	−	1.32650i
$650$	0.507003	−	3.52628i	0.0198863	−	0.138312i
$651$	−15.5614	+	4.56924i	−0.609900	+	0.179083i
$652$	−14.1136	−	9.07028i	−0.552732	−	0.355220i
$653$	−14.9567	+	32.7506i	−0.585301	+	1.28163i	0.352939	+	0.935646i	$0.385182\pi$
$653$	−14.9567	+	32.7506i	−0.585301	+	1.28163i	−0.938240	+	0.345985i	$0.887545\pi$
$654$	−19.8778	−	5.83665i	−0.777283	−	0.228231i
$655$	−5.48861	−	6.33420i	−0.214458	−	0.247497i
$656$	−6.57871	−	7.59224i	−0.256855	−	0.296427i
$657$	3.60111	+	1.05738i	0.140493	+	0.0412523i
$658$	5.62828	−	12.3242i	0.219413	−	0.480447i
$659$	27.2769	+	17.5298i	1.06256	+	0.682863i	0.950464	−	0.310834i	$-0.100608\pi$
$659$	27.2769	+	17.5298i	1.06256	+	0.682863i	0.112092	+	0.993698i	$0.464245\pi$
$660$	4.61053	−	1.35377i	0.179465	−	0.0526956i
$661$	1.05362	−	7.32811i	0.0409812	−	0.285031i	−0.959017	−	0.283347i	$-0.908555\pi$
$661$	1.05362	−	7.32811i	0.0409812	−	0.285031i	0.999999	−	0.00168329i	$-0.000535809\pi$
$662$	−2.65682	−	5.81762i	−0.103260	−	0.226108i
$663$	2.43933	+	16.9659i	0.0947359	+	0.658903i
$664$	1.27558	−	0.819765i	0.0495021	−	0.0318131i
$665$	0.341168	−	0.393729i	0.0132299	−	0.0152682i
$666$	3.85515			0.149384
$667$	−28.1109	+	7.17631i	−1.08846	+	0.277868i
$668$	−22.5859			−0.873874
$669$	−4.24390	+	4.89772i	−0.164079	+	0.189357i
$670$	−8.62225	+	5.54118i	−0.333106	+	0.214075i
$671$	−7.50066	−	52.1682i	−0.289560	−	2.01393i
$672$	1.05083	+	2.30100i	0.0405367	+	0.0887631i
$673$	−6.25711	+	43.5192i	−0.241194	+	1.67754i	0.404960	+	0.914334i	$0.367285\pi$
$673$	−6.25711	+	43.5192i	−0.241194	+	1.67754i	−0.646154	+	0.763207i	$0.723624\pi$
$674$	7.42095	−	2.17899i	0.285844	−	0.0839315i
$675$	−0.841254	−	0.540641i	−0.0323799	−	0.0208093i
$676$	−0.128067	+	0.280427i	−0.00492564	+	0.0107856i
$677$	24.5983	+	7.22271i	0.945390	+	0.277591i	0.717866	−	0.696181i	$-0.245119\pi$
$677$	24.5983	+	7.22271i	0.945390	+	0.277591i	0.227524	+	0.973773i	$0.426937\pi$
$678$	5.31675	+	6.13585i	0.204188	+	0.235646i
$679$	1.42143	+	1.64042i	0.0545494	+	0.0629534i
$680$	4.61639	+	1.35550i	0.177031	+	0.0519809i
$681$	8.30295	−	18.1809i	0.318170	−	0.696694i
$682$	25.9174	+	16.6561i	0.992430	+	0.637796i
$683$	0.450025	−	0.132139i	0.0172197	−	0.00505617i	−0.273111	−	0.961982i	$-0.588053\pi$
$683$	0.450025	−	0.132139i	0.0172197	−	0.00505617i	0.290331	+	0.956926i	$0.406235\pi$
$684$	−0.0293102	+	0.203857i	−0.00112070	+	0.00779465i
$685$	7.17912	+	15.7201i	0.274300	+	0.600633i
$686$	−2.73640	−	19.0321i	−0.104476	−	0.726649i
$687$	−16.0952	+	10.3437i	−0.614070	+	0.394639i
$688$	−1.26267	+	1.45719i	−0.0481387	+	0.0555550i
$689$	46.5289			1.77261
$690$	−3.00941	−	3.73409i	−0.114566	−	0.142154i
$691$	−29.5192			−1.12296			−0.561482	−	0.827489i	$-0.689768\pi$
$691$	−29.5192			−1.12296			−0.561482	+	0.827489i	$0.689768\pi$
$692$	13.7045	−	15.8159i	0.520968	−	0.601229i
$693$	−10.2256	+	6.57157i	−0.388437	+	0.249633i
$694$	0.0339763	+	0.236311i	0.00128972	+	0.00897023i
$695$	−2.48546	−	5.44239i	−0.0942788	−	0.206442i
$696$	−0.860936	+	5.98794i	−0.0326337	+	0.226972i
$697$	46.3761	−	13.6173i	1.75662	−	0.515791i
$698$	6.62890	+	4.26014i	0.250908	+	0.161249i
$699$	7.47346	−	16.3646i	0.282672	−	0.618966i
$700$	2.42713	+	0.712670i	0.0917369	+	0.0269364i
$701$	−27.3814	−	31.5999i	−1.03418	−	1.19351i	−0.980816	−	0.194935i	$-0.937550\pi$
$701$	−27.3814	−	31.5999i	−1.03418	−	1.19351i	−0.0533666	−	0.998575i	$-0.516995\pi$
$702$	−2.33297	−	2.69239i	−0.0880523	−	0.101618i
$703$	−0.761817	−	0.223690i	−0.0287325	−	0.00843662i
$704$	1.99614	−	4.37094i	0.0752324	−	0.164736i
$705$	4.50577	+	2.89568i	0.169697	+	0.109058i
$706$	−6.89213	+	2.02371i	−0.259389	+	0.0761634i
$707$	−2.35557	+	16.3834i	−0.0885904	+	0.616160i
$708$	3.21172	+	7.03268i	0.120704	+	0.264304i
$709$	0.764294	+	5.31578i	0.0287037	+	0.199638i	0.999127	−	0.0417702i	$-0.0132997\pi$
$709$	0.764294	+	5.31578i	0.0287037	+	0.199638i	−0.970424	+	0.241408i	$0.922391\pi$
$710$	1.89126	−	1.21544i	0.0709776	−	0.0456145i
$711$	−6.29642	+	7.26646i	−0.236134	+	0.272513i
$712$	−14.1145			−0.528962
$713$	5.45800	−	30.2599i	0.204404	−	1.13324i
$714$	−12.1706			−0.455474
$715$	11.2103	−	12.9374i	0.419242	−	0.483831i
$716$	0.812946	−	0.522449i	0.0303812	−	0.0195248i
$717$	−1.99227	−	13.8565i	−0.0744026	−	0.517482i
$718$	7.16627	+	15.6919i	0.267443	+	0.585618i
$719$	2.82960	−	19.6803i	0.105526	−	0.733952i	−0.866516	−	0.499148i	$-0.833646\pi$
$719$	2.82960	−	19.6803i	0.105526	−	0.733952i	0.972043	−	0.234804i	$-0.0754447\pi$
$720$	−0.959493	+	0.281733i	−0.0357582	+	0.0104996i
$721$	−14.6481	−	9.41377i	−0.545524	−	0.350587i
$722$	−7.87526	+	17.2444i	−0.293087	+	0.641771i
$723$	−7.45000	−	2.18752i	−0.277068	−	0.0813546i
$724$	14.1056	+	16.2788i	0.524231	+	0.604995i
$725$	3.96159	+	4.57192i	0.147130	+	0.169797i
$726$	11.6000	+	3.40606i	0.430515	+	0.126411i
$727$	−4.02476	+	8.81299i	−0.149270	+	0.326856i	−0.969466	−	0.245228i	$-0.921137\pi$
$727$	−4.02476	+	8.81299i	−0.149270	+	0.326856i	0.820196	+	0.572083i	$0.193865\pi$
$728$	7.58121	+	4.87215i	0.280978	+	0.180574i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	0.534127	−	3.71493i	0.0197689	−	0.137496i
$731$	−3.85374	−	8.43852i	−0.142536	−	0.312110i
$732$	1.56095	+	10.8567i	0.0576945	+	0.401274i
$733$	41.7674	−	26.8423i	1.54271	−	0.991442i	0.555594	−	0.831453i	$-0.312491\pi$
$733$	41.7674	−	26.8423i	1.54271	−	0.991442i	0.987119	−	0.159988i	$-0.0511457\pi$
$734$	4.01302	−	4.63127i	0.148123	−	0.170943i
$735$	0.601139			0.0221733
$736$	−4.79278	−	0.170946i	−0.176664	−	0.00630114i
$737$	−49.2496			−1.81413
$738$	−6.57871	+	7.59224i	−0.242166	+	0.279474i
$739$	25.2454	−	16.2243i	0.928669	−	0.596819i	0.0135083	−	0.999909i	$-0.495700\pi$
$739$	25.2454	−	16.2243i	0.928669	−	0.596819i	0.915161	+	0.403090i	$0.132064\pi$
$740$	−0.548645	−	3.81591i	−0.0201686	−	0.140276i
$741$	0.304797	+	0.667412i	0.0111970	+	0.0245180i
$742$	−4.70180	+	32.7017i	−0.172608	+	1.20052i
$743$	−24.6264	+	7.23096i	−0.903455	+	0.265278i	−0.700283	−	0.713865i	$-0.746943\pi$
$743$	−24.6264	+	7.23096i	−0.903455	+	0.265278i	−0.203171	+	0.979143i	$0.565125\pi$
$744$	−5.39365	−	3.46629i	−0.197741	−	0.127080i
$745$	6.55461	−	14.3526i	0.240142	−	0.525838i
$746$	25.4600	+	7.47574i	0.932158	+	0.273706i
$747$	−0.992955	−	1.14593i	−0.0363303	−	0.0419274i
$748$	15.1398	+	17.4722i	0.553564	+	0.638847i
$749$	8.57935	+	2.51913i	0.313483	+	0.0920469i
$750$	−0.415415	+	0.909632i	−0.0151688	+	0.0332151i
$751$	−6.82017	−	4.38305i	−0.248871	−	0.159940i	0.410258	−	0.911970i	$-0.365439\pi$
$751$	−6.82017	−	4.38305i	−0.248871	−	0.159940i	−0.659129	+	0.752030i	$0.729075\pi$
$752$	5.13906	−	1.50896i	0.187402	−	0.0550263i
$753$	−1.97610	+	13.7441i	−0.0720131	+	0.500862i
$754$	8.95288	+	19.6041i	0.326045	+	0.713939i
$755$	−0.412357	−	2.86800i	−0.0150072	−	0.104377i
$756$	2.12803	−	1.36760i	0.0773958	−	0.0497393i
$757$	0.831572	−	0.959685i	0.0302240	−	0.0348804i	−0.740436	−	0.672127i	$-0.765381\pi$
$757$	0.831572	−	0.959685i	0.0302240	−	0.0348804i	0.770660	+	0.637246i	$0.219927\pi$
$758$	−20.4111			−0.741365
$759$	−2.46447	−	22.9126i	−0.0894546	−	0.831676i
$760$	0.205953			0.00747070
$761$	5.21101	−	6.01383i	0.188899	−	0.218001i	−0.653398	−	0.757014i	$-0.726657\pi$
$761$	5.21101	−	6.01383i	0.188899	−	0.218001i	0.842297	+	0.539013i	$0.181203\pi$
$762$	−3.63320	+	2.33491i	−0.131617	+	0.0845850i
$763$	−7.45810	−	51.8722i	−0.270001	−	1.87790i
$764$	9.48329	+	20.7655i	0.343093	+	0.751270i
$765$	0.684717	−	4.76231i	0.0247560	−	0.172182i
$766$	−25.2452	+	7.41266i	−0.912146	+	0.267830i
$767$	23.1708	+	14.8910i	0.836651	+	0.537683i
$768$	−0.415415	+	0.909632i	−0.0149900	+	0.0328235i
$769$	28.0980	+	8.25031i	1.01324	+	0.297514i	0.745878	−	0.666083i	$-0.232030\pi$
$769$	28.0980	+	8.25031i	1.01324	+	0.297514i	0.267361	+	0.963596i	$0.413848\pi$
$770$	7.95993	+	9.18625i	0.286856	+	0.331049i
$771$	14.0643	+	16.2310i	0.506512	+	0.584546i
$772$	10.1069	+	2.96766i	0.363756	+	0.106808i
$773$	−2.57133	+	5.63043i	−0.0924844	+	0.202513i	−0.950221	−	0.311577i	$-0.899143\pi$
$773$	−2.57133	+	5.63043i	−0.0924844	+	0.202513i	0.857737	+	0.514090i	$0.171870\pi$
$774$	1.62206	+	1.04243i	0.0583037	+	0.0374695i
$775$	−6.15174	+	1.80631i	−0.220977	+	0.0648847i
$776$	−0.122117	+	0.849340i	−0.00438373	+	0.0304895i
$777$	4.05112	+	8.87070i	0.145333	+	0.318235i
$778$	−1.56368	−	10.8756i	−0.0560606	−	0.389910i
$779$	1.74055	−	1.11858i	0.0623617	−	0.0400774i
$780$	−2.33297	+	2.69239i	−0.0835337	+	0.0964030i
$781$	10.8027			0.386551
$782$	10.3274	−	20.6339i	0.369306	−	0.737868i
$783$	6.04952			0.216192
$784$	0.393662	−	0.454311i	0.0140594	−	0.0162254i
$785$	−6.09043	+	3.91408i	−0.217377	+	0.139700i
$786$	1.19279	+	8.29603i	0.0425454	+	0.295910i
$787$	0.735040	+	1.60951i	0.0262013	+	0.0573729i	0.922280	−	0.386522i	$-0.126324\pi$
$787$	0.735040	+	1.60951i	0.0262013	+	0.0573729i	−0.896079	+	0.443895i	$0.853596\pi$
$788$	0.794929	−	5.52885i	0.0283182	−	0.196957i
$789$	−18.0033	+	5.28625i	−0.640936	+	0.188196i
$790$	8.08857	+	5.19821i	0.287778	+	0.184944i
$791$	−8.53160	+	18.6816i	−0.303349	+	0.664241i
$792$	−4.61053	−	1.35377i	−0.163828	−	0.0481043i
$793$	25.5888	+	29.5310i	0.908683	+	1.04868i
$794$	−16.7819	−	19.3674i	−0.595568	−	0.687322i
$795$	−12.5315	−	3.67959i	−0.444448	−	0.130502i
$796$	−8.10399	+	17.7453i	−0.287238	+	0.628964i
$797$	14.4574	+	9.29120i	0.512107	+	0.329111i	0.771043	−	0.636783i	$-0.219735\pi$
$797$	14.4574	+	9.29120i	0.512107	+	0.329111i	−0.258936	+	0.965895i	$0.583372\pi$
$798$	−0.499875	+	0.146776i	−0.0176954	+	0.00519583i
$799$	−3.66736	+	25.5070i	−0.129742	+	0.902373i
$800$	0.415415	+	0.909632i	0.0146871	+	0.0321603i
$801$	2.00870	+	13.9708i	0.0709738	+	0.493634i
$802$	16.1480	−	10.3777i	0.570207	−	0.366450i
$803$	11.8101	−	13.6295i	0.416768	−	0.480976i
$804$	10.2493			0.361464
$805$	5.42976	−	10.8486i	0.191374	−	0.382362i
$806$	−22.8411			−0.804542
$807$	−20.0255	+	23.1106i	−0.704929	+	0.813532i
$808$	−5.50455	+	3.53756i	−0.193649	+	0.124451i
$809$	1.13509	+	7.89475i	0.0399078	+	0.277565i	0.999998	−	0.00212664i	$-0.000676929\pi$
$809$	1.13509	+	7.89475i	0.0399078	+	0.277565i	−0.960090	+	0.279691i	$0.909768\pi$
$810$	0.415415	+	0.909632i	0.0145962	+	0.0319612i
$811$	2.08635	−	14.5109i	0.0732616	−	0.509546i	−0.919840	−	0.392293i	$-0.871682\pi$
$811$	2.08635	−	14.5109i	0.0732616	−	0.509546i	0.993102	−	0.117253i	$-0.0374089\pi$
$812$	−14.6830	+	4.31131i	−0.515271	+	0.151297i
$813$	−6.55767	−	4.21436i	−0.229987	−	0.147804i
$814$	7.69542	−	16.8506i	0.269724	−	0.590614i
$815$	16.0973	+	4.72660i	0.563865	+	0.165566i
$816$	−3.15072	−	3.63613i	−0.110297	−	0.127290i
$817$	−0.260050	−	0.300113i	−0.00909799	−	0.0104996i
$818$	−7.33566	−	2.15394i	−0.256485	−	0.0753109i
$819$	3.74364	−	8.19742i	0.130813	−	0.286441i
$820$	8.45121	+	5.43126i	0.295129	+	0.189668i
$821$	−47.7527	+	14.0215i	−1.66658	+	0.489353i	−0.972957	−	0.230985i	$-0.925805\pi$
$821$	−47.7527	+	14.0215i	−1.66658	+	0.489353i	−0.693624	+	0.720337i	$0.743987\pi$
$822$	2.45946	−	17.1059i	0.0857834	−	0.596636i
$823$	14.4725	+	31.6903i	0.504478	+	1.10465i	0.974988	+	0.222259i	$0.0713429\pi$
$823$	14.4725	+	31.6903i	0.504478	+	1.10465i	−0.470509	+	0.882395i	$0.655930\pi$
$824$	−0.979611	−	6.81335i	−0.0341264	−	0.237354i
$825$	−4.04237	+	2.59787i	−0.140737	+	0.0904463i
$826$	−12.8072	+	14.7803i	−0.445621	+	0.514273i
$827$	24.2297			0.842548			0.421274	−	0.906933i	$-0.361583\pi$
$827$	24.2297			0.842548			0.421274	+	0.906933i	$0.361583\pi$
$828$	0.512879	+	4.76833i	0.0178238	+	0.165711i
$829$	−49.7946			−1.72944			−0.864719	−	0.502256i	$-0.832504\pi$
$829$	−49.7946			−1.72944			−0.864719	+	0.502256i	$0.832504\pi$
$830$	−0.992955	+	1.14593i	−0.0344660	+	0.0397758i
$831$	−1.10508	+	0.710192i	−0.0383348	+	0.0246363i
$832$	0.507003	+	3.52628i	0.0175772	+	0.122252i
$833$	1.20148	+	2.63088i	0.0416290	+	0.0911547i
$834$	−0.851480	+	5.92217i	−0.0294843	+	0.205068i
$835$	21.6710	−	6.36318i	0.749955	−	0.220207i
$836$	0.832538	+	0.535040i	0.0287939	+	0.0185047i
$837$	−2.66341	+	5.83206i	−0.0920610	+	0.201585i
$838$	−2.94970	−	0.866109i	−0.101896	−	0.0299192i
$839$	14.0469	+	16.2110i	0.484952	+	0.559665i	0.944510	−	0.328483i	$-0.106537\pi$
$839$	14.0469	+	16.2110i	0.484952	+	0.559665i	−0.459558	+	0.888148i	$0.651992\pi$
$840$	−1.65653	−	1.91174i	−0.0571558	−	0.0659614i
$841$	−7.28893	−	2.14022i	−0.251342	−	0.0738008i
$842$	−10.2454	+	22.4342i	−0.353079	+	0.773135i
$843$	−11.0630	−	7.10973i	−0.381029	−	0.244872i
$844$	4.06377	−	1.19323i	0.139881	−	0.0410727i
$845$	0.0438737	−	0.305148i	0.00150930	−	0.0104974i
$846$	−2.22497	−	4.87200i	−0.0764960	−	0.167503i
$847$	4.35228	+	30.2708i	0.149546	+	1.04012i
$848$	−10.9873	+	7.06108i	−0.377304	+	0.242478i
$849$	18.8132	−	21.7116i	0.645667	−	0.745140i
$850$	−4.81128			−0.165026
$851$	−18.4769	−	0.659021i	−0.633380	−	0.0225910i
$852$	−2.24814			−0.0770200
$853$	18.5711	−	21.4322i	0.635862	−	0.733824i	−0.342775	−	0.939417i	$-0.611367\pi$
$853$	18.5711	−	21.4322i	0.635862	−	0.733824i	0.978638	+	0.205593i	$0.0659123\pi$
$854$	−23.3409	+	15.0003i	−0.798710	+	0.513300i
$855$	−0.0293102	−	0.203857i	−0.00100239	−	0.00697175i
$856$	1.46840	+	3.21534i	0.0501888	+	0.109898i
$857$	−1.33053	+	9.25407i	−0.0454502	+	0.316113i	0.954395	+	0.298545i	$0.0965014\pi$
$857$	−1.33053	+	9.25407i	−0.0454502	+	0.316113i	−0.999846	+	0.0175678i	$0.994408\pi$
$858$	−16.4252	+	4.82288i	−0.560747	+	0.164650i
$859$	21.9485	+	14.1055i	0.748875	+	0.481273i	0.858572	−	0.512692i	$-0.171352\pi$
$859$	21.9485	+	14.1055i	0.748875	+	0.481273i	−0.109698	+	0.993965i	$0.534988\pi$
$860$	0.800980	−	1.75390i	0.0273132	−	0.0598075i
$861$	−24.3829	−	7.15946i	−0.830966	−	0.243994i
$862$	−2.70147	−	3.11766i	−0.0920123	−	0.106188i
$863$	33.2485	+	38.3708i	1.13179	+	1.30616i	0.946219	+	0.323527i	$0.104869\pi$
$863$	33.2485	+	38.3708i	1.13179	+	1.30616i	0.185573	+	0.982631i	$0.440586\pi$
$864$	0.959493	+	0.281733i	0.0326426	+	0.00958474i
$865$	−8.69356	+	19.0362i	−0.295590	+	0.647251i
$866$	−2.97768	−	1.91364i	−0.101186	−	0.0650282i
$867$	5.89940	−	1.73222i	0.200354	−	0.0588293i
$868$	2.30812	−	16.0533i	0.0783425	−	0.544884i
$869$	19.1927	+	42.0261i	0.651068	+	1.42564i
$870$	−0.860936	−	5.98794i	−0.0291885	−	0.203010i
$871$	30.7171	−	19.7407i	1.04081	−	0.668888i
$872$	13.5667	−	15.6568i	0.459428	−	0.530208i
$873$	0.858074			0.0290414
$874$	0.175326	−	0.972030i	0.00593048	−	0.0328794i
$875$	−2.52960			−0.0855160
$876$	−2.45778	+	2.83643i	−0.0830407	+	0.0958341i
$877$	−14.6941	+	9.44334i	−0.496185	+	0.318879i	−0.764689	−	0.644400i	$-0.777107\pi$
$877$	−14.6941	+	9.44334i	−0.496185	+	0.318879i	0.268504	+	0.963279i	$0.413471\pi$
$878$	−2.23616	−	15.5528i	−0.0754667	−	0.524882i
$879$	−6.67671	−	14.6200i	−0.225200	−	0.493119i
$880$	−0.683847	+	4.75626i	−0.0230525	+	0.160334i
$881$	30.2859	−	8.89275i	1.02036	−	0.299604i	0.271574	−	0.962418i	$-0.412456\pi$
$881$	30.2859	−	8.89275i	1.02036	−	0.299604i	0.748785	+	0.662813i	$0.230638\pi$
$882$	−0.505710	−	0.325000i	−0.0170282	−	0.0109433i
$883$	17.8982	−	39.1917i	0.602324	−	1.31891i	−0.325378	−	0.945584i	$-0.605492\pi$
$883$	17.8982	−	39.1917i	0.602324	−	1.31891i	0.927702	−	0.373321i	$-0.121781\pi$
$884$	−16.4461	−	4.82901i	−0.553142	−	0.162417i
$885$	−5.06295	−	5.84296i	−0.170189	−	0.196409i
$886$	8.10891	+	9.35818i	0.272424	+	0.314394i
$887$	4.30299	+	1.26347i	0.144480	+	0.0424233i	0.353173	−	0.935558i	$-0.385103\pi$
$887$	4.30299	+	1.26347i	0.144480	+	0.0424233i	−0.208693	+	0.977981i	$0.566921\pi$
$888$	−1.60149	+	3.50677i	−0.0537424	+	0.117679i
$889$	−9.19052	−	5.90639i	−0.308240	−	0.198094i
$890$	13.5427	−	3.97650i	0.453953	−	0.133293i
$891$	−0.683847	+	4.75626i	−0.0229098	+	0.159341i
$892$	−2.69214	−	5.89497i	−0.0901396	−	0.197378i
$893$	0.156986	+	1.09186i	0.00525333	+	0.0365377i
$894$	−13.2737	+	8.53048i	−0.443938	+	0.285302i
$895$	−0.632825	+	0.730319i	−0.0211530	+	0.0244119i
$896$	−2.52960			−0.0845079
$897$	10.7212	+	13.3029i	0.357969	+	0.444169i
$898$	33.2051			1.10807
$899$	25.3995	−	29.3126i	0.847122	−	0.977630i
$900$	0.841254	−	0.540641i	0.0280418	−	0.0180214i
$901$	−8.94280	−	62.1985i	−0.297928	−	2.07213i
$902$	20.0532	+	43.9103i	0.667697	+	1.46205i
$903$	−0.694130	+	4.82778i	−0.0230992	+	0.160658i
$904$	−7.79003	+	2.28736i	−0.259092	+	0.0760764i
$905$	−18.1205	−	11.6453i	−0.602346	−	0.387104i
$906$	−1.20366	+	2.63566i	−0.0399891	+	0.0875638i
$907$	−15.1652	−	4.45291i	−0.503552	−	0.147856i	0.0200838	−	0.999798i	$-0.493607\pi$
$907$	−15.1652	−	4.45291i	−0.503552	−	0.147856i	−0.523636	+	0.851942i	$0.675425\pi$
$908$	13.0888	+	15.1053i	0.434366	+	0.501286i
$909$	4.28493	+	4.94508i	0.142122	+	0.164018i
$910$	−8.64676	−	2.53892i	−0.286637	−	0.0841643i
$911$	−10.7858	+	23.6177i	−0.357351	+	0.782490i	0.642517	+	0.766271i	$0.277890\pi$
$911$	−10.7858	+	23.6177i	−0.357351	+	0.782490i	−0.999868	+	0.0162187i	$0.994837\pi$
$912$	−0.173259	−	0.111347i	−0.00573717	−	0.00368705i
$913$	−6.99087	+	2.05271i	−0.231364	+	0.0679346i
$914$	1.78433	−	12.4103i	0.0590205	−	0.410497i
$915$	−4.55640	−	9.97713i	−0.150630	−	0.329834i
$916$	−2.72282	−	18.9376i	−0.0899646	−	0.625717i
$917$	−17.8358	+	11.4624i	−0.588989	+	0.378520i
$918$	−3.15072	+	3.63613i	−0.103989	+	0.120010i
$919$	19.3870			0.639517			0.319759	−	0.947499i	$-0.396398\pi$
$919$	19.3870			0.639517			0.319759	+	0.947499i	$0.396398\pi$
$920$	4.64680	−	1.18626i	0.153201	−	0.0391099i
$921$	9.33863			0.307718
$922$	22.7043	−	26.2022i	0.747727	−	0.862923i
$923$	−6.73768	+	4.33004i	−0.221773	+	0.142525i
$924$	−1.72986	−	12.0314i	−0.0569082	−	0.395805i
$925$	1.60149	+	3.50677i	0.0526565	+	0.115302i
$926$	2.00544	−	13.9481i	0.0659027	−	0.458363i
$927$	−6.60458	+	1.93928i	−0.216923	+	0.0636943i
$928$	−5.08918	−	3.27062i	−0.167060	−	0.107363i
$929$	−20.1866	+	44.2024i	−0.662299	+	1.45023i	0.218064	+	0.975934i	$0.430026\pi$
$929$	−20.1866	+	44.2024i	−0.662299	+	1.45023i	−0.880364	+	0.474299i	$0.842702\pi$
$930$	6.15174	+	1.80631i	0.201723	+	0.0592313i
$931$	0.0810759	+	0.0935666i	0.00265716	+	0.00306652i
$932$	11.7812	+	13.5962i	0.385905	+	0.445358i
$933$	−20.8346	−	6.11760i	−0.682096	−	0.200281i
$934$	−3.29755	+	7.22064i	−0.107899	+	0.236266i
$935$	−19.4490	−	12.4991i	−0.636050	−	0.408764i
$936$	3.41824	−	1.00368i	0.111729	−	0.0328065i
$937$	−2.44818	+	17.0274i	−0.0799784	+	0.556262i	0.909953	+	0.414712i	$0.136118\pi$
$937$	−2.44818	+	17.0274i	−0.0799784	+	0.556262i	−0.989931	+	0.141550i	$0.954791\pi$
$938$	10.7703	+	23.5836i	0.351662	+	0.770033i
$939$	1.20411	+	8.37475i	0.0392946	+	0.273300i
$940$	−4.50577	+	2.89568i	−0.146962	+	0.0944467i
$941$	−13.8040	+	15.9307i	−0.449999	+	0.519326i	−0.934741	−	0.355331i	$-0.884368\pi$
$941$	−13.8040	+	15.9307i	−0.449999	+	0.519326i	0.484742	+	0.874657i	$0.338914\pi$
$942$	7.23971			0.235882
$943$	32.8282	−	35.2633i	1.06903	−	1.14833i
$944$	−7.73134			−0.251634
$945$	−1.65653	+	1.91174i	−0.0538870	+	0.0621890i
$946$	7.79427	−	5.00907i	0.253413	−	0.162859i
$947$	5.33712	+	37.1205i	0.173433	+	1.20625i	0.871563	+	0.490283i	$0.163107\pi$
$947$	5.33712	+	37.1205i	0.173433	+	1.20625i	−0.698130	+	0.715971i	$0.745984\pi$
$948$	−3.99417	−	8.74602i	−0.129725	−	0.284058i
$949$	−1.90285	+	13.2346i	−0.0617691	+	0.429614i
$950$	−0.197610	+	0.0580236i	−0.00641133	+	0.00188254i
$951$	−18.2903	−	11.7544i	−0.593102	−	0.381164i
$952$	5.05585	−	11.0708i	0.163861	−	0.358806i
$953$	35.6386	+	10.4644i	1.15445	+	0.338977i	0.802273	−	0.596958i	$-0.203624\pi$
$953$	35.6386	+	10.4644i	1.15445	+	0.338977i	0.352175	+	0.935934i	$0.385442\pi$
$954$	8.55286	+	9.87052i	0.276909	+	0.319570i
$955$	−14.9495	−	17.2526i	−0.483754	−	0.558281i
$956$	13.4320	+	3.94398i	0.434421	+	0.127557i
$957$	12.0757	−	26.4421i	0.390352	−	0.854751i
$958$	−22.8217	−	14.6666i	−0.737336	−	0.473857i
$959$	41.9452	−	12.3162i	1.35448	−	0.397711i
$960$	0.142315	−	0.989821i	0.00459319	−	0.0319463i
$961$	4.19845	+	9.19333i	0.135434	+	0.296559i
$962$	1.95457	+	13.5943i	0.0630179	+	0.438299i
$963$	2.97364	−	1.91104i	0.0958242	−	0.0615825i
$964$	5.08468	−	5.86803i	0.163766	−	0.188997i
$965$	−10.5336			−0.339089
$966$	−10.4330	+	6.19085i	−0.335676	+	0.199187i
$967$	27.3976			0.881047			0.440523	−	0.897741i	$-0.354793\pi$
$967$	27.3976			0.881047			0.440523	+	0.897741i	$0.354793\pi$
$968$	−7.91706	+	9.13678i	−0.254464	+	0.293667i
$969$	0.833597	−	0.535720i	0.0267790	−	0.0172098i
$970$	−0.122117	−	0.849340i	−0.00392093	−	0.0272707i
$971$	19.7501	+	43.2467i	0.633811	+	1.38785i	0.905035	+	0.425336i	$0.139844\pi$
$971$	19.7501	+	43.2467i	0.633811	+	1.38785i	−0.271224	+	0.962516i	$0.587428\pi$
$972$	0.142315	−	0.989821i	0.00456475	−	0.0317485i
$973$	−14.5217	+	4.26395i	−0.465544	+	0.136696i
$974$	9.45413	+	6.07580i	0.302930	+	0.194681i
$975$	1.47993	−	3.24060i	0.0473958	−	0.103782i
$976$	−10.5240	−	3.09013i	−0.336866	−	0.0989127i
$977$	16.0949	+	18.5745i	0.514922	+	0.594252i	0.952352	−	0.305001i	$-0.0986567\pi$
$977$	16.0949	+	18.5745i	0.514922	+	0.594252i	−0.437430	+	0.899252i	$0.644111\pi$
$978$	−10.9865	−	12.6791i	−0.351311	−	0.405434i
$979$	65.0751	+	19.1078i	2.07981	+	0.610688i
$980$	−0.249722	+	0.546815i	−0.00797708	+	0.0174674i
$981$	−17.4282	−	11.2004i	−0.556441	−	0.357603i
$982$	23.0298	−	6.76216i	0.734910	−	0.215789i
$983$	6.11634	−	42.5401i	0.195081	−	1.35682i	−0.623229	−	0.782039i	$-0.714179\pi$
$983$	6.11634	−	42.5401i	0.195081	−	1.35682i	0.818310	−	0.574778i	$-0.194911\pi$
$984$	−4.17325	−	9.13813i	−0.133038	−	0.291313i
$985$	0.794929	+	5.52885i	0.0253285	+	0.176164i
$986$	24.4855	−	15.7359i	0.779776	−	0.501132i
$987$	8.87242	−	10.2393i	0.282412	−	0.325921i
$988$	−0.733716			−0.0233426
$989$	−7.59597	−	5.27344i	−0.241538	−	0.167686i
$990$	4.80517			0.152718
$991$	11.0198	−	12.7176i	0.350057	−	0.403987i	−0.553227	−	0.833031i	$-0.686604\pi$
$991$	11.0198	−	12.7176i	0.350057	−	0.403987i	0.903284	+	0.429043i	$0.141149\pi$
$992$	5.39365	−	3.46629i	0.171249	−	0.110055i
$993$	−0.910185	−	6.33048i	−0.0288839	−	0.200892i
$994$	−2.36242	−	5.17298i	−0.0749314	−	0.164077i
$995$	2.77630	−	19.3096i	0.0880148	−	0.612156i
$996$	1.45486	−	0.427187i	0.0460991	−	0.0135359i
$997$	4.81859	+	3.09672i	0.152606	+	0.0980740i	0.614715	−	0.788749i	$-0.289271\pi$
$997$	4.81859	+	3.09672i	0.152606	+	0.0980740i	−0.462109	+	0.886823i	$0.652907\pi$
$998$	3.68379	−	8.06636i	0.116608	−	0.255336i
$999$	3.69899	+	1.08612i	0.117031	+	0.0343633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.c.361.2	yes	20
23.13	even	11	inner	690.2.m.c.151.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.c.151.2	✓	20	23.13	even	11	inner
690.2.m.c.361.2	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.142315 - 0.989821i) q^{6} +(2.42713 - 0.712670i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.142315 - 0.989821i) q^{6} +(2.42713 - 0.712670i) q^{7} +(0.841254 + 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-0.959493 - 0.281733i) q^{10} +(-3.14672 - 3.63151i) q^{11} +(0.654861 + 0.755750i) q^{12} +(3.41824 + 1.00368i) q^{13} +(-1.05083 + 2.30100i) q^{14} +(-0.841254 - 0.540641i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.684717 - 4.76231i) q^{17} +(0.415415 + 0.909632i) q^{18} +(-0.0293102 - 0.203857i) q^{19} +(0.841254 - 0.540641i) q^{20} +(-1.65653 + 1.91174i) q^{21} +4.80517 q^{22} +(-1.83550 - 4.43068i) q^{23} -1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(-2.99700 + 1.92606i) q^{26} +(0.142315 + 0.989821i) q^{27} +(-1.05083 - 2.30100i) q^{28} +(0.860936 - 5.98794i) q^{29} +(0.959493 - 0.281733i) q^{30} +(5.39365 + 3.46629i) q^{31} +(0.415415 - 0.909632i) q^{32} +(4.61053 + 1.35377i) q^{33} +(3.15072 + 3.63613i) q^{34} +(1.65653 + 1.91174i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(1.60149 - 3.50677i) q^{37} +(0.173259 + 0.111347i) q^{38} +(-3.41824 + 1.00368i) q^{39} +(-0.142315 + 0.989821i) q^{40} +(4.17325 + 9.13813i) q^{41} +(-0.359999 - 2.50385i) q^{42} +(1.62206 - 1.04243i) q^{43} +(-3.14672 + 3.63151i) q^{44} +1.00000 q^{45} +(4.55048 + 1.51430i) q^{46} -5.35602 q^{47} +(0.654861 - 0.755750i) q^{48} +(-0.505710 + 0.325000i) q^{49} +(-0.142315 - 0.989821i) q^{50} +(1.99868 + 4.37650i) q^{51} +(0.507003 - 3.52628i) q^{52} +(12.5315 - 3.67959i) q^{53} +(-0.841254 - 0.540641i) q^{54} +(1.99614 - 4.37094i) q^{55} +(2.42713 + 0.712670i) q^{56} +(0.134870 + 0.155649i) q^{57} +(3.96159 + 4.57192i) q^{58} +(7.41817 + 2.17817i) q^{59} +(-0.415415 + 0.909632i) q^{60} +(9.22714 + 5.92992i) q^{61} +(-6.15174 + 1.80631i) q^{62} +(0.359999 - 2.50385i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.507003 + 3.52628i) q^{65} +(-4.04237 + 2.59787i) q^{66} +(6.71185 - 7.74589i) q^{67} -4.81128 q^{68} +(3.93953 + 2.73498i) q^{69} -2.52960 q^{70} +(-1.47222 + 1.69903i) q^{71} +(0.841254 - 0.540641i) q^{72} +(0.534127 + 3.71493i) q^{73} +(1.60149 + 3.50677i) q^{74} +(0.142315 - 0.989821i) q^{75} +(-0.197610 + 0.0580236i) q^{76} +(-10.2256 - 6.57157i) q^{77} +(1.47993 - 3.24060i) q^{78} +(-9.22543 - 2.70883i) q^{79} +(-0.654861 - 0.755750i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-9.63903 - 2.83028i) q^{82} +(0.629887 - 1.37926i) q^{83} +(2.12803 + 1.36760i) q^{84} +(4.61639 - 1.35550i) q^{85} +(-0.274403 + 1.90852i) q^{86} +(2.51306 + 5.50283i) q^{87} +(-0.683847 - 4.75626i) q^{88} +(-11.8738 + 7.63085i) q^{89} +(-0.654861 + 0.755750i) q^{90} +9.01180 q^{91} +(-4.12437 + 2.44737i) q^{92} -6.41145 q^{93} +(3.50744 - 4.04781i) q^{94} +(0.173259 - 0.111347i) q^{95} +(0.142315 + 0.989821i) q^{96} +(0.356457 + 0.780532i) q^{97} +(0.0855510 - 0.595020i) q^{98} +(-4.61053 + 1.35377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - 24 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 16 q^{17} - 2 q^{18} + 14 q^{19} - 2 q^{20} - 13 q^{21} - 2 q^{22} - 2 q^{23} - 20 q^{24} - 2 q^{25} + 7 q^{26} + 2 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} + 22 q^{31} - 2 q^{32} + 2 q^{33} - 17 q^{34} + 13 q^{35} - 2 q^{36} - 16 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{40} + 29 q^{41} + 9 q^{42} - 22 q^{43} - 24 q^{44} + 20 q^{45} - 2 q^{46} - 94 q^{47} + 2 q^{48} - 22 q^{49} - 2 q^{50} - 5 q^{51} - 4 q^{52} + 58 q^{53} + 2 q^{54} + 9 q^{55} + 2 q^{56} - 25 q^{57} - 4 q^{58} + 45 q^{59} + 2 q^{60} + q^{61} - 9 q^{63} - 2 q^{64} - 4 q^{65} - 9 q^{66} + 16 q^{67} - 6 q^{68} + 24 q^{69} + 2 q^{70} + 59 q^{71} - 2 q^{72} + 3 q^{73} - 16 q^{74} + 2 q^{75} - 8 q^{76} - 19 q^{77} - 18 q^{78} - 20 q^{79} - 2 q^{80} - 2 q^{81} - 37 q^{82} + 13 q^{83} + 9 q^{84} + 5 q^{85} - 22 q^{86} + 4 q^{87} + 9 q^{88} - 97 q^{89} - 2 q^{90} - 18 q^{91} + 9 q^{92} + 22 q^{93} + 27 q^{94} + 3 q^{95} + 2 q^{96} - 17 q^{97} - 11 q^{98} - 2 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - 24 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 16 * q^17 - 2 * q^18 + 14 * q^19 - 2 * q^20 - 13 * q^21 - 2 * q^22 - 2 * q^23 - 20 * q^24 - 2 * q^25 + 7 * q^26 + 2 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 22 * q^31 - 2 * q^32 + 2 * q^33 - 17 * q^34 + 13 * q^35 - 2 * q^36 - 16 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^40 + 29 * q^41 + 9 * q^42 - 22 * q^43 - 24 * q^44 + 20 * q^45 - 2 * q^46 - 94 * q^47 + 2 * q^48 - 22 * q^49 - 2 * q^50 - 5 * q^51 - 4 * q^52 + 58 * q^53 + 2 * q^54 + 9 * q^55 + 2 * q^56 - 25 * q^57 - 4 * q^58 + 45 * q^59 + 2 * q^60 + q^61 - 9 * q^63 - 2 * q^64 - 4 * q^65 - 9 * q^66 + 16 * q^67 - 6 * q^68 + 24 * q^69 + 2 * q^70 + 59 * q^71 - 2 * q^72 + 3 * q^73 - 16 * q^74 + 2 * q^75 - 8 * q^76 - 19 * q^77 - 18 * q^78 - 20 * q^79 - 2 * q^80 - 2 * q^81 - 37 * q^82 + 13 * q^83 + 9 * q^84 + 5 * q^85 - 22 * q^86 + 4 * q^87 + 9 * q^88 - 97 * q^89 - 2 * q^90 - 18 * q^91 + 9 * q^92 + 22 * q^93 + 27 * q^94 + 3 * q^95 + 2 * q^96 - 17 * q^97 - 11 * q^98 - 2 * q^99

Introduction

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