LMFDB - Embedded newform 209.2.j.a.188.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(23,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(18))

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("209.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.j (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			188.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	209.188
Dual form			209.2.j.a.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.439693 + 2.49362i) q^{2} +(-1.53209 - 1.28558i) q^{3} +(-4.14543 - 1.50881i) q^{4} +(3.64543 - 1.32683i) q^{5} +(3.87939 - 3.25519i) q^{6} +(1.76604 + 3.05888i) q^{7} +(3.05303 - 5.28801i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.439693 + 2.49362i) q^{2} +(-1.53209 - 1.28558i) q^{3} +(-4.14543 - 1.50881i) q^{4} +(3.64543 - 1.32683i) q^{5} +(3.87939 - 3.25519i) q^{6} +(1.76604 + 3.05888i) q^{7} +(3.05303 - 5.28801i) q^{8} +(0.173648 + 0.984808i) q^{9} +(1.70574 + 9.67372i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(4.41147 + 7.64090i) q^{12} +(2.52094 - 2.11532i) q^{13} +(-8.40420 + 3.05888i) q^{14} +(-7.29086 - 2.65366i) q^{15} +(5.08512 + 4.26692i) q^{16} +(-0.602196 + 3.41523i) q^{17} -2.53209 q^{18} +(2.77719 + 3.35965i) q^{19} -17.1138 q^{20} +(1.22668 - 6.95686i) q^{21} +(-1.93969 - 1.62760i) q^{22} +(4.91147 + 1.78763i) q^{23} +(-11.4757 + 4.17680i) q^{24} +(7.69846 - 6.45978i) q^{25} +(4.16637 + 7.21637i) q^{26} +(-2.00000 + 3.46410i) q^{27} +(-2.70574 - 15.3450i) q^{28} +(-0.162504 - 0.921605i) q^{29} +(9.82295 - 17.0138i) q^{30} +(-2.62449 - 4.54574i) q^{31} +(-3.52094 + 2.95442i) q^{32} +(1.87939 - 0.684040i) q^{33} +(-8.25150 - 3.00330i) q^{34} +(10.4966 + 8.80769i) q^{35} +(0.766044 - 4.34445i) q^{36} -2.65270 q^{37} +(-9.59879 + 5.44804i) q^{38} -6.58172 q^{39} +(4.11334 - 23.3279i) q^{40} +(-2.61334 - 2.19285i) q^{41} +(16.8084 + 6.11776i) q^{42} +(0.992726 - 0.361323i) q^{43} +(3.37939 - 2.83564i) q^{44} +(1.93969 + 3.35965i) q^{45} +(-6.61721 + 11.4613i) q^{46} +(-1.13816 - 6.45480i) q^{47} +(-2.30541 - 13.0746i) q^{48} +(-2.73783 + 4.74205i) q^{49} +(12.7233 + 22.0374i) q^{50} +(5.31315 - 4.45826i) q^{51} +(-13.6420 + 4.96529i) q^{52} +(4.77719 + 1.73875i) q^{53} +(-7.75877 - 6.51038i) q^{54} +(-0.673648 + 3.82045i) q^{55} +21.5672 q^{56} +(0.0641778 - 8.71756i) q^{57} +2.36959 q^{58} +(-2.01114 + 11.4058i) q^{59} +(26.2199 + 22.0011i) q^{60} +(-1.09967 - 0.400247i) q^{61} +(12.4893 - 4.54574i) q^{62} +(-2.70574 + 2.27038i) q^{63} +(0.819078 + 1.41868i) q^{64} +(6.38326 - 11.0561i) q^{65} +(0.879385 + 4.98724i) q^{66} +(-2.52481 - 14.3189i) q^{67} +(7.64930 - 13.2490i) q^{68} +(-5.22668 - 9.05288i) q^{69} +(-26.5783 + 22.3019i) q^{70} +(-14.2417 + 5.18355i) q^{71} +(5.73783 + 2.08840i) q^{72} +(-10.5077 - 8.81704i) q^{73} +(1.16637 - 6.61484i) q^{74} -20.0993 q^{75} +(-6.44356 - 18.1174i) q^{76} -3.53209 q^{77} +(2.89393 - 16.4123i) q^{78} +(-7.38326 - 6.19529i) q^{79} +(24.1989 + 8.80769i) q^{80} +(10.3366 - 3.76222i) q^{81} +(6.61721 - 5.55250i) q^{82} +(-2.51367 - 4.35381i) q^{83} +(-15.5817 + 26.9883i) q^{84} +(2.33615 + 13.2490i) q^{85} +(0.464508 + 2.63435i) q^{86} +(-0.935822 + 1.62089i) q^{87} +(3.05303 + 5.28801i) q^{88} +(-0.922618 + 0.774169i) q^{89} +(-9.23055 + 3.35965i) q^{90} +(10.9226 + 3.97551i) q^{91} +(-17.6630 - 14.8210i) q^{92} +(-1.82295 + 10.3385i) q^{93} +16.5963 q^{94} +(14.5817 + 8.56250i) q^{95} +9.19253 q^{96} +(1.50727 - 8.54818i) q^{97} +(-10.6211 - 8.91215i) q^{98} +(-0.939693 - 0.342020i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 12 q^{6} + 6 q^{7} + 6 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 12 * q^6 + 6 * q^7 + 6 * q^8	\( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 12 q^{6} + 6 q^{7} + 6 q^{8} - 3 q^{11} + 6 q^{12} + 12 q^{13} - 12 q^{14} - 12 q^{15} + 9 q^{16} - 3 q^{17} - 6 q^{18} + 6 q^{19} - 30 q^{20} - 6 q^{21} - 6 q^{22} + 9 q^{23} - 30 q^{24} + 18 q^{25} + 6 q^{26} - 12 q^{27} - 6 q^{28} - 6 q^{29} + 18 q^{30} - 3 q^{31} - 18 q^{32} - 9 q^{34} + 21 q^{35} - 18 q^{37} - 15 q^{38} + 24 q^{39} + 18 q^{40} - 9 q^{41} + 24 q^{42} - 12 q^{43} + 9 q^{44} + 6 q^{45} - 9 q^{46} + 27 q^{47} - 18 q^{48} + 3 q^{49} + 21 q^{50} - 12 q^{51} - 24 q^{52} + 18 q^{53} - 24 q^{54} - 3 q^{55} + 30 q^{56} - 18 q^{57} - 6 q^{59} + 60 q^{60} - 21 q^{61} + 15 q^{62} - 6 q^{63} - 12 q^{64} + 3 q^{65} - 6 q^{66} + 12 q^{67} + 6 q^{68} - 18 q^{69} - 54 q^{70} - 42 q^{71} + 15 q^{72} - 15 q^{73} - 12 q^{74} - 12 q^{75} - 9 q^{76} - 12 q^{77} + 42 q^{78} - 9 q^{79} + 51 q^{80} + 9 q^{82} + 6 q^{83} - 30 q^{84} + 18 q^{85} - 30 q^{86} - 24 q^{87} + 6 q^{88} + 21 q^{89} - 18 q^{90} + 39 q^{91} - 45 q^{92} + 30 q^{93} + 72 q^{94} + 24 q^{95} + 27 q^{97} - 9 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 12 * q^6 + 6 * q^7 + 6 * q^8 - 3 * q^11 + 6 * q^12 + 12 * q^13 - 12 * q^14 - 12 * q^15 + 9 * q^16 - 3 * q^17 - 6 * q^18 + 6 * q^19 - 30 * q^20 - 6 * q^21 - 6 * q^22 + 9 * q^23 - 30 * q^24 + 18 * q^25 + 6 * q^26 - 12 * q^27 - 6 * q^28 - 6 * q^29 + 18 * q^30 - 3 * q^31 - 18 * q^32 - 9 * q^34 + 21 * q^35 - 18 * q^37 - 15 * q^38 + 24 * q^39 + 18 * q^40 - 9 * q^41 + 24 * q^42 - 12 * q^43 + 9 * q^44 + 6 * q^45 - 9 * q^46 + 27 * q^47 - 18 * q^48 + 3 * q^49 + 21 * q^50 - 12 * q^51 - 24 * q^52 + 18 * q^53 - 24 * q^54 - 3 * q^55 + 30 * q^56 - 18 * q^57 - 6 * q^59 + 60 * q^60 - 21 * q^61 + 15 * q^62 - 6 * q^63 - 12 * q^64 + 3 * q^65 - 6 * q^66 + 12 * q^67 + 6 * q^68 - 18 * q^69 - 54 * q^70 - 42 * q^71 + 15 * q^72 - 15 * q^73 - 12 * q^74 - 12 * q^75 - 9 * q^76 - 12 * q^77 + 42 * q^78 - 9 * q^79 + 51 * q^80 + 9 * q^82 + 6 * q^83 - 30 * q^84 + 18 * q^85 - 30 * q^86 - 24 * q^87 + 6 * q^88 + 21 * q^89 - 18 * q^90 + 39 * q^91 - 45 * q^92 + 30 * q^93 + 72 * q^94 + 24 * q^95 + 27 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

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 $

$2$	−0.439693	+	2.49362i	−0.310910	+	1.76326i	0.283383	+	0.959007i	$0.408543\pi$
$2$	−0.439693	+	2.49362i	−0.310910	+	1.76326i	−0.594292	+	0.804249i	$0.702568\pi$
$3$	−1.53209	−	1.28558i	−0.884552	−	0.742227i	0.0825579	−	0.996586i	$-0.473691\pi$
$3$	−1.53209	−	1.28558i	−0.884552	−	0.742227i	−0.967110	+	0.254359i	$0.918135\pi$
$4$	−4.14543	−	1.50881i	−2.07271	−	0.754407i
$5$	3.64543	−	1.32683i	1.63029	−	0.593375i	0.644984	−	0.764196i	$-0.276864\pi$
$5$	3.64543	−	1.32683i	1.63029	−	0.593375i	0.985302	+	0.170821i	$0.0546420\pi$
$6$	3.87939	−	3.25519i	1.58375	−	1.32893i
$7$	1.76604	+	3.05888i	0.667502	+	1.15615i	0.978600	+	0.205770i	$0.0659698\pi$
$7$	1.76604	+	3.05888i	0.667502	+	1.15615i	−0.311098	+	0.950378i	$0.600697\pi$
$8$	3.05303	−	5.28801i	1.07941	−	1.86959i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	1.70574	+	9.67372i	0.539401	+	3.05910i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	4.41147	+	7.64090i	1.27348	+	2.20574i
$13$	2.52094	−	2.11532i	0.699184	−	0.586685i	−0.222357	−	0.974965i	$-0.571375\pi$
$13$	2.52094	−	2.11532i	0.699184	−	0.586685i	0.921541	+	0.388280i	$0.126931\pi$
$14$	−8.40420	+	3.05888i	−2.24612	+	0.817520i
$15$	−7.29086	−	2.65366i	−1.88249	−	0.685171i
$16$	5.08512	+	4.26692i	1.27128	+	1.06673i
$17$	−0.602196	+	3.41523i	−0.146054	+	0.828314i	0.820461	+	0.571703i	$0.193717\pi$
$17$	−0.602196	+	3.41523i	−0.146054	+	0.828314i	−0.966515	+	0.256611i	$0.917394\pi$
$18$	−2.53209			−0.596819
$19$	2.77719	+	3.35965i	0.637131	+	0.770756i
$19$	2.77719	+	3.35965i	0.637131	+	0.770756i
$20$	−17.1138			−3.82676
$21$	1.22668	−	6.95686i	0.267684	−	1.51811i
$22$	−1.93969	−	1.62760i	−0.413544	−	0.347004i
$23$	4.91147	+	1.78763i	1.02411	+	0.372747i	0.798837	−	0.601548i	$-0.205449\pi$
$23$	4.91147	+	1.78763i	1.02411	+	0.372747i	0.225277	+	0.974295i	$0.427671\pi$
$24$	−11.4757	+	4.17680i	−2.34246	+	0.852585i
$25$	7.69846	−	6.45978i	1.53969	−	1.29196i
$26$	4.16637	+	7.21637i	0.817093	+	1.41525i
$27$	−2.00000	+	3.46410i	−0.384900	+	0.666667i
$28$	−2.70574	−	15.3450i	−0.511336	−	2.89993i
$29$	−0.162504	−	0.921605i	−0.0301762	−	0.171138i	0.965995	−	0.258560i	$-0.0832481\pi$
$29$	−0.162504	−	0.921605i	−0.0301762	−	0.171138i	−0.996171	+	0.0874226i	$0.972137\pi$
$30$	9.82295	−	17.0138i	1.79342	−	3.10629i
$31$	−2.62449	−	4.54574i	−0.471371	−	0.816439i	0.528092	−	0.849187i	$-0.322908\pi$
$31$	−2.62449	−	4.54574i	−0.471371	−	0.816439i	−0.999464	+	0.0327477i	$0.989574\pi$
$32$	−3.52094	+	2.95442i	−0.622421	+	0.522273i
$33$	1.87939	−	0.684040i	0.327159	−	0.119076i
$34$	−8.25150	−	3.00330i	−1.41512	−	0.515062i
$35$	10.4966	+	8.80769i	1.77425	+	1.48877i
$36$	0.766044	−	4.34445i	0.127674	−	0.724076i
$37$	−2.65270			−0.436102			−0.218051	−	0.975937i	$-0.569970\pi$
$37$	−2.65270			−0.436102			−0.218051	+	0.975937i	$0.569970\pi$
$38$	−9.59879	+	5.44804i	−1.55713	+	0.883789i
$39$	−6.58172			−1.05392
$40$	4.11334	−	23.3279i	0.650376	−	3.68847i
$41$	−2.61334	−	2.19285i	−0.408135	−	0.342466i	0.415493	−	0.909596i	$-0.363609\pi$
$41$	−2.61334	−	2.19285i	−0.408135	−	0.342466i	−0.823628	+	0.567130i	$0.808054\pi$
$42$	16.8084	+	6.11776i	2.59359	+	0.943990i
$43$	0.992726	−	0.361323i	0.151389	−	0.0551012i	−0.265214	−	0.964190i	$-0.585443\pi$
$43$	0.992726	−	0.361323i	0.151389	−	0.0551012i	0.416603	+	0.909088i	$0.363220\pi$
$44$	3.37939	−	2.83564i	0.509461	−	0.427489i
$45$	1.93969	+	3.35965i	0.289152	+	0.500826i
$46$	−6.61721	+	11.4613i	−0.975655	+	1.68988i
$47$	−1.13816	−	6.45480i	−0.166017	−	0.941530i	−0.948010	−	0.318242i	$-0.896908\pi$
$47$	−1.13816	−	6.45480i	−0.166017	−	0.941530i	0.781993	−	0.623288i	$-0.214203\pi$
$48$	−2.30541	−	13.0746i	−0.332757	−	1.88716i
$49$	−2.73783	+	4.74205i	−0.391118	+	0.677436i
$50$	12.7233	+	22.0374i	1.79934	+	3.11655i
$51$	5.31315	−	4.45826i	0.743990	−	0.624281i
$52$	−13.6420	+	4.96529i	−1.89181	+	0.688562i
$53$	4.77719	+	1.73875i	0.656197	+	0.238836i	0.648594	−	0.761135i	$-0.275357\pi$
$53$	4.77719	+	1.73875i	0.656197	+	0.238836i	0.00760361	+	0.999971i	$0.497580\pi$
$54$	−7.75877	−	6.51038i	−1.05583	−	0.885951i
$55$	−0.673648	+	3.82045i	−0.0908347	+	0.515149i
$56$	21.5672			2.88203
$57$	0.0641778	−	8.71756i	0.00850055	−	1.15467i
$58$	2.36959			0.311142
$59$	−2.01114	+	11.4058i	−0.261829	+	1.48490i	0.516087	+	0.856536i	$0.327388\pi$
$59$	−2.01114	+	11.4058i	−0.261829	+	1.48490i	−0.777916	+	0.628368i	$0.783723\pi$
$60$	26.2199	+	22.0011i	3.38497	+	2.84033i
$61$	−1.09967	−	0.400247i	−0.140798	−	0.0512464i	0.270660	−	0.962675i	$-0.412758\pi$
$61$	−1.09967	−	0.400247i	−0.140798	−	0.0512464i	−0.411458	+	0.911429i	$0.634980\pi$
$62$	12.4893	−	4.54574i	1.58615	−	0.577310i
$63$	−2.70574	+	2.27038i	−0.340891	+	0.286041i
$64$	0.819078	+	1.41868i	0.102385	+	0.177336i
$65$	6.38326	−	11.0561i	0.791745	−	1.37134i
$66$	0.879385	+	4.98724i	0.108245	+	0.613887i
$67$	−2.52481	−	14.3189i	−0.308455	−	1.74934i	−0.606778	−	0.794871i	$-0.707538\pi$
$67$	−2.52481	−	14.3189i	−0.308455	−	1.74934i	0.298323	−	0.954465i	$-0.403573\pi$
$68$	7.64930	−	13.2490i	0.927614	−	1.60667i
$69$	−5.22668	−	9.05288i	−0.629219	−	1.08984i
$70$	−26.5783	+	22.3019i	−3.17672	+	2.66558i
$71$	−14.2417	+	5.18355i	−1.69018	+	0.615175i	−0.994648	−	0.103322i	$-0.967053\pi$
$71$	−14.2417	+	5.18355i	−1.69018	+	0.615175i	−0.695530	+	0.718497i	$0.744831\pi$
$72$	5.73783	+	2.08840i	0.676209	+	0.246120i
$73$	−10.5077	−	8.81704i	−1.22984	−	1.03196i	−0.998250	−	0.0591428i	$-0.981163\pi$
$73$	−10.5077	−	8.81704i	−1.22984	−	1.03196i	−0.231589	−	0.972814i	$-0.574392\pi$
$74$	1.16637	−	6.61484i	0.135588	−	0.768959i
$75$	−20.0993			−2.32086
$76$	−6.44356	−	18.1174i	−0.739127	−	2.07821i
$77$	−3.53209			−0.402519
$78$	2.89393	−	16.4123i	0.327673	−	1.85833i
$79$	−7.38326	−	6.19529i	−0.830681	−	0.697024i	0.124766	−	0.992186i	$-0.460182\pi$
$79$	−7.38326	−	6.19529i	−0.830681	−	0.697024i	−0.955447	+	0.295162i	$0.904626\pi$
$80$	24.1989	+	8.80769i	2.70552	+	0.984730i
$81$	10.3366	−	3.76222i	1.14851	−	0.418025i
$82$	6.61721	−	5.55250i	0.730749	−	0.613171i
$83$	−2.51367	−	4.35381i	−0.275911	−	0.477892i	0.694453	−	0.719538i	$-0.255646\pi$
$83$	−2.51367	−	4.35381i	−0.275911	−	0.477892i	−0.970365	+	0.241645i	$0.922313\pi$
$84$	−15.5817	+	26.9883i	−1.70010	+	2.94467i
$85$	2.33615	+	13.2490i	0.253391	+	1.43705i
$86$	0.464508	+	2.63435i	0.0500891	+	0.284070i
$87$	−0.935822	+	1.62089i	−0.100331	+	0.173778i
$88$	3.05303	+	5.28801i	0.325454	+	0.563704i
$89$	−0.922618	+	0.774169i	−0.0977974	+	0.0820617i	−0.690375	−	0.723451i	$-0.742555\pi$
$89$	−0.922618	+	0.774169i	−0.0977974	+	0.0820617i	0.592578	+	0.805513i	$0.298110\pi$
$90$	−9.23055	+	3.35965i	−0.972986	+	0.354138i
$91$	10.9226	+	3.97551i	1.14500	+	0.416746i
$92$	−17.6630	−	14.8210i	−1.84149	−	1.54520i
$93$	−1.82295	+	10.3385i	−0.189031	+	1.07205i
$94$	16.5963			1.71177
$95$	14.5817	+	8.56250i	1.49605	+	0.878494i
$96$	9.19253			0.938209
$97$	1.50727	−	8.54818i	0.153040	−	0.867936i	−0.807515	−	0.589847i	$-0.799188\pi$
$97$	1.50727	−	8.54818i	0.153040	−	0.867936i	0.960555	−	0.278089i	$-0.0897009\pi$
$98$	−10.6211	−	8.91215i	−1.07289	−	0.900263i
$99$	−0.939693	−	0.342020i	−0.0944427	−	0.0343743i
$100$	−41.6600	+	15.1630i	−4.16600	+	1.51630i
$101$	−8.91534	+	7.48086i	−0.887110	+	0.744374i	−0.967628	−	0.252380i	$-0.918787\pi$
$101$	−8.91534	+	7.48086i	−0.887110	+	0.744374i	0.0805184	+	0.996753i	$0.474342\pi$
$102$	8.78106	+	15.2092i	0.869454	+	1.50594i
$103$	0.0603074	−	0.104455i	0.00594226	−	0.0102923i	−0.863039	−	0.505137i	$-0.831442\pi$
$103$	0.0603074	−	0.104455i	0.00594226	−	0.0102923i	0.868981	+	0.494845i	$0.164775\pi$
$104$	−3.48932	−	19.7889i	−0.342156	−	1.94046i
$105$	−4.75877	−	26.9883i	−0.464408	−	2.63379i
$106$	−6.43629	+	11.1480i	−0.625148	+	1.08279i
$107$	7.91147	+	13.7031i	0.764831	+	1.32473i	0.940336	+	0.340248i	$0.110511\pi$
$107$	7.91147	+	13.7031i	0.764831	+	1.32473i	−0.175505	+	0.984479i	$0.556156\pi$
$108$	13.5175	−	11.3426i	1.30073	−	1.09144i
$109$	−0.291737	+	0.106183i	−0.0279433	+	0.0101705i	−0.355954	−	0.934503i	$-0.615844\pi$
$109$	−0.291737	+	0.106183i	−0.0279433	+	0.0101705i	0.328011	+	0.944674i	$0.393622\pi$
$110$	−9.23055	−	3.35965i	−0.880099	−	0.320330i
$111$	4.06418	+	3.41025i	0.385755	+	0.323687i
$112$	−4.07145	+	23.0904i	−0.384716	+	2.18183i
$113$	−5.04458			−0.474554			−0.237277	−	0.971442i	$-0.576255\pi$
$113$	−5.04458			−0.474554			−0.237277	+	0.971442i	$0.576255\pi$
$114$	21.7101	+	3.99308i	2.03333	+	0.373986i
$115$	20.2763			1.89078
$116$	−0.716881	+	4.06564i	−0.0665608	+	0.377485i
$117$	2.52094	+	2.11532i	0.233061	+	0.195562i
$118$	−27.5574	−	10.0301i	−2.53686	−	0.923342i
$119$	−11.5103	+	4.18939i	−1.05514	+	0.384041i
$120$	−36.2918	+	30.4524i	−3.31297	+	2.77991i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	1.48158	−	2.56617i	0.134136	−	0.232331i
$123$	1.18479	+	6.71929i	0.106829	+	0.605858i
$124$	4.02094	+	22.8039i	0.361091	+	2.04785i
$125$	9.79473	−	16.9650i	0.876067	−	1.51739i
$126$	−4.47178	−	7.74535i	−0.398378	−	0.690011i
$127$	−0.392589	+	0.329421i	−0.0348366	+	0.0292314i	−0.660040	−	0.751231i	$-0.729461\pi$
$127$	−0.392589	+	0.329421i	−0.0348366	+	0.0292314i	0.625203	+	0.780462i	$0.285016\pi$
$128$	−12.5360	+	4.56272i	−1.10803	+	0.403291i
$129$	−1.98545	−	0.722645i	−0.174809	−	0.0636254i
$130$	24.7631	+	20.7787i	2.17187	+	1.82241i
$131$	−1.00727	+	5.71253i	−0.0880059	+	0.499106i	0.908661	+	0.417534i	$0.137105\pi$
$131$	−1.00727	+	5.71253i	−0.0880059	+	0.499106i	−0.996667	+	0.0815728i	$0.974006\pi$
$132$	−8.82295			−0.767939
$133$	−5.37211	+	14.4284i	−0.465821	+	1.25110i
$134$	36.8161			3.18043
$135$	−2.69459	+	15.2818i	−0.231914	+	1.31525i
$136$	16.2212	+	13.6112i	1.39096	+	1.16715i
$137$	5.31655	+	1.93507i	0.454224	+	0.165324i	0.558993	−	0.829173i	$-0.311188\pi$
$137$	5.31655	+	1.93507i	0.454224	+	0.165324i	−0.104769	+	0.994497i	$0.533410\pi$
$138$	24.8726	−	9.05288i	2.11729	−	0.770632i
$139$	−9.16044	+	7.68653i	−0.776979	+	0.651963i	−0.942486	−	0.334246i	$-0.891518\pi$
$139$	−9.16044	+	7.68653i	−0.776979	+	0.651963i	0.165507	+	0.986209i	$0.447074\pi$
$140$	−30.2237	−	52.3491i	−2.55437	−	4.42430i
$141$	−6.55438	+	11.3525i	−0.551978	+	0.956054i
$142$	−6.66385	−	37.7926i	−0.559218	−	3.17148i
$143$	0.571452	+	3.24086i	0.0477872	+	0.271015i
$144$	−3.31908	+	5.74881i	−0.276590	+	0.479068i
$145$	−1.81521	−	3.14403i	−0.150745	−	0.261098i
$146$	26.6065	−	22.3255i	2.20197	−	1.84767i
$147$	10.2909	−	3.74557i	0.848776	−	0.308929i
$148$	10.9966	+	4.00243i	0.903915	+	0.328998i
$149$	4.88326	+	4.09754i	0.400052	+	0.335683i	0.820514	−	0.571627i	$-0.193687\pi$
$149$	4.88326	+	4.09754i	0.400052	+	0.335683i	−0.420462	+	0.907310i	$0.638132\pi$
$150$	8.83750	−	50.1199i	0.721579	−	4.09228i
$151$	−4.55438			−0.370630			−0.185315	−	0.982679i	$-0.559331\pi$
$151$	−4.55438			−0.370630			−0.185315	+	0.982679i	$0.559331\pi$
$152$	26.2447	−	4.42869i	2.12873	−	0.359214i
$153$	−3.46791			−0.280364
$154$	1.55303	−	8.80769i	0.125147	−	0.709744i
$155$	−15.5988	−	13.0889i	−1.25293	−	1.05133i
$156$	27.2841	+	9.93058i	2.18447	+	0.795083i
$157$	7.30453	−	2.65863i	0.582965	−	0.212182i	−0.0336675	−	0.999433i	$-0.510719\pi$
$157$	7.30453	−	2.65863i	0.582965	−	0.212182i	0.616632	+	0.787251i	$0.288496\pi$
$158$	18.6951	−	15.6870i	1.48730	−	1.24799i
$159$	−5.08378	−	8.80536i	−0.403170	−	0.698311i
$160$	−8.91534	+	15.4418i	−0.704820	+	1.22078i
$161$	3.20574	+	18.1806i	0.252647	+	1.43284i
$162$	4.83662	+	27.4298i	0.380001	+	2.15509i
$163$	4.78106	−	8.28104i	0.374481	−	0.648621i	−0.615768	−	0.787928i	$-0.711154\pi$
$163$	4.78106	−	8.28104i	0.374481	−	0.648621i	0.990249	+	0.139307i	$0.0444874\pi$
$164$	7.52481	+	13.0334i	0.587589	+	1.01773i
$165$	5.94356	−	4.98724i	0.462706	−	0.388256i
$166$	11.9620	−	4.35381i	0.928430	−	0.337921i
$167$	−3.10607	−	1.13052i	−0.240355	−	0.0874819i	0.219034	−	0.975717i	$-0.429709\pi$
$167$	−3.10607	−	1.13052i	−0.240355	−	0.0874819i	−0.459389	+	0.888235i	$0.651932\pi$
$168$	−33.0428	−	27.7262i	−2.54931	−	2.13912i
$169$	−0.376859	+	2.13727i	−0.0289892	+	0.164406i
$170$	−34.0651			−2.61267
$171$	−2.82635	+	3.31839i	−0.216137	+	0.253764i
$172$	−4.66044			−0.355356
$173$	−3.25237	+	18.4451i	−0.247273	+	1.40236i	0.567880	+	0.823112i	$0.307764\pi$
$173$	−3.25237	+	18.4451i	−0.247273	+	1.40236i	−0.815153	+	0.579246i	$0.803347\pi$
$174$	−3.63041	−	3.04628i	−0.275221	−	0.230938i
$175$	33.3555	+	12.1404i	2.52144	+	0.917729i
$176$	−6.23783	+	2.27038i	−0.470194	+	0.171137i
$177$	17.7442	−	14.8892i	1.33374	−	1.11914i
$178$	−1.52481	−	2.64106i	−0.114290	−	0.197956i
$179$	3.99407	−	6.91793i	0.298531	−	0.517071i	−0.677269	−	0.735735i	$-0.736837\pi$
$179$	3.99407	−	6.91793i	0.298531	−	0.517071i	0.975800	+	0.218665i	$0.0701701\pi$
$180$	−2.97178	−	16.8538i	−0.221504	−	1.25621i
$181$	−1.25759	−	7.13214i	−0.0934758	−	0.530128i	−0.995204	−	0.0978237i	$-0.968812\pi$
$181$	−1.25759	−	7.13214i	−0.0934758	−	0.530128i	0.901728	−	0.432304i	$-0.142299\pi$
$182$	−14.7160	+	25.4889i	−1.09082	+	1.88936i
$183$	1.17024	+	2.02692i	0.0865070	+	0.149834i
$184$	24.4479	−	20.5142i	1.80232	−	1.51233i
$185$	−9.67024	+	3.51968i	−0.710971	+	0.258772i
$186$	−24.9786	−	9.09148i	−1.83152	−	0.666620i
$187$	−2.65657	−	2.22913i	−0.194268	−	0.163010i
$188$	−5.02094	+	28.4752i	−0.366190	+	2.07677i
$189$	−14.1284			−1.02769
$190$	−27.7631	+	32.5964i	−2.01415	+	2.36479i
$191$	−15.2686			−1.10479			−0.552397	−	0.833581i	$-0.686287\pi$
$191$	−15.2686			−1.10479			−0.552397	+	0.833581i	$0.686287\pi$
$192$	0.568926	−	3.22654i	0.0410587	−	0.232855i
$193$	9.50980	+	7.97967i	0.684530	+	0.574389i	0.917326	−	0.398136i	$-0.130343\pi$
$193$	9.50980	+	7.97967i	0.684530	+	0.574389i	−0.232796	+	0.972526i	$0.574787\pi$
$194$	20.6532	+	7.51714i	1.48281	+	0.539699i
$195$	−23.9932	+	8.73281i	−1.71819	+	0.625369i
$196$	18.5043	−	15.5270i	1.32174	−	1.10907i
$197$	−2.91875	−	5.05542i	−0.207952	−	0.360184i	0.743117	−	0.669161i	$-0.233347\pi$
$197$	−2.91875	−	5.05542i	−0.207952	−	0.360184i	−0.951069	+	0.308978i	$0.900013\pi$
$198$	1.26604	−	2.19285i	0.0899739	−	0.155839i
$199$	−1.34343	−	7.61895i	−0.0952329	−	0.540093i	−0.994676	−	0.103054i	$-0.967138\pi$
$199$	−1.34343	−	7.61895i	−0.0952329	−	0.540093i	0.899443	−	0.437039i	$-0.143973\pi$
$200$	−10.6557	−	60.4315i	−0.753472	−	4.27315i
$201$	−14.5398	+	25.1837i	−1.02556	+	1.77632i
$202$	−14.7344	−	25.5208i	−1.03671	−	1.79563i
$203$	2.53209	−	2.12467i	0.177718	−	0.149123i
$204$	−28.7520	+	10.4649i	−2.01304	+	0.732687i
$205$	−12.4363	−	4.52644i	−0.868588	−	0.316140i
$206$	0.233956	+	0.196312i	0.0163005	+	0.0136777i
$207$	−0.907604	+	5.14728i	−0.0630828	+	0.357760i
$208$	21.8452			1.51469
$209$	−4.29813	+	0.725293i	−0.297308	+	0.0501696i
$210$	69.3911			4.78844
$211$	1.83750	−	10.4210i	0.126498	−	0.717408i	−0.853908	−	0.520424i	$-0.825774\pi$
$211$	1.83750	−	10.4210i	0.126498	−	0.717408i	0.980407	−	0.196985i	$-0.0631149\pi$
$212$	−17.1800	−	14.4158i	−1.17993	−	0.990079i
$213$	28.4834	+	10.3671i	1.95165	+	0.710342i
$214$	−37.6489	+	13.7031i	−2.57363	+	0.936723i
$215$	3.13950	−	2.63435i	0.214112	−	0.179661i
$216$	12.2121	+	21.1520i	0.830930	+	1.43921i
$217$	9.26991	−	16.0560i	0.629283	−	1.08995i
$218$	−0.136507	−	0.774169i	−0.00924541	−	0.0524333i
$219$	4.76382	+	27.0170i	0.321909	+	1.82564i
$220$	8.55690	−	14.8210i	0.576906	−	0.999231i
$221$	5.70620	+	9.88344i	0.383841	+	0.664832i
$222$	−10.2909	+	8.63506i	−0.690677	+	0.579547i
$223$	15.5496	−	5.65960i	1.04128	−	0.378995i	0.235915	−	0.971774i	$-0.424191\pi$
$223$	15.5496	−	5.65960i	1.04128	−	0.378995i	0.805365	+	0.592779i	$0.201969\pi$
$224$	−15.2554	−	5.55250i	−1.01929	−	0.370992i
$225$	7.69846	+	6.45978i	0.513231	+	0.430652i
$226$	2.21806	−	12.5793i	0.147543	−	0.836760i
$227$	−7.29767			−0.484363			−0.242182	−	0.970231i	$-0.577863\pi$
$227$	−7.29767			−0.484363			−0.242182	+	0.970231i	$0.577863\pi$
$228$	−13.4192	+	36.0412i	−0.888709	+	2.38689i
$229$	−23.2472			−1.53622			−0.768110	−	0.640318i	$-0.778802\pi$
$229$	−23.2472			−1.53622			−0.768110	+	0.640318i	$0.778802\pi$
$230$	−8.91534	+	50.5614i	−0.587860	+	3.33392i
$231$	5.41147	+	4.54077i	0.356049	+	0.298760i
$232$	−5.36959	−	1.95437i	−0.352531	−	0.128311i
$233$	15.2922	−	5.56591i	1.00183	−	0.364635i	0.211537	−	0.977370i	$-0.432153\pi$
$233$	15.2922	−	5.56591i	1.00183	−	0.364635i	0.790288	+	0.612735i	$0.209931\pi$
$234$	−6.38326	+	5.35619i	−0.417286	+	0.350145i
$235$	−12.7135	−	22.0204i	−0.829336	−	1.43645i
$236$	25.5462	−	44.2474i	1.66292	−	2.88026i
$237$	3.34730	+	18.9835i	0.217430	+	1.23311i
$238$	−5.38578	−	30.5443i	−0.349108	−	1.97989i
$239$	9.10607	−	15.7722i	0.589022	−	1.02022i	−0.405338	−	0.914167i	$-0.632846\pi$
$239$	9.10607	−	15.7722i	0.589022	−	1.02022i	0.994361	−	0.106050i	$-0.0338204\pi$
$240$	−25.7520	−	44.6037i	−1.66228	−	2.87916i
$241$	11.7999	−	9.90133i	0.760101	−	0.637801i	−0.178052	−	0.984021i	$-0.556980\pi$
$241$	11.7999	−	9.90133i	0.760101	−	0.637801i	0.938153	+	0.346220i	$0.112535\pi$
$242$	2.37939	−	0.866025i	0.152953	−	0.0556702i
$243$	−9.39693	−	3.42020i	−0.602813	−	0.219406i
$244$	3.95471	+	3.31839i	0.253174	+	0.212438i
$245$	−3.68866	+	20.9194i	−0.235660	+	1.33649i
$246$	−17.2763			−1.10150
$247$	14.1079	+	2.59483i	0.897663	+	0.165105i
$248$	−32.0506			−2.03521
$249$	−1.74598	+	9.90193i	−0.110647	+	0.627509i
$250$	37.9975	+	31.8837i	2.40317	+	2.01650i
$251$	−14.4290	−	5.25173i	−0.910751	−	0.331486i	−0.156199	−	0.987726i	$-0.549924\pi$
$251$	−14.4290	−	5.25173i	−0.910751	−	0.331486i	−0.754553	+	0.656239i	$0.772146\pi$
$252$	14.6420	−	5.32926i	0.922361	−	0.335712i
$253$	−4.00387	+	3.35965i	−0.251721	+	0.211219i
$254$	−0.648833	−	1.12381i	−0.0407114	−	0.0705142i
$255$	13.4534	−	23.3019i	0.842482	−	1.45922i
$256$	−5.29679	−	30.0396i	−0.331049	−	1.87747i
$257$	0.748503	+	4.24497i	0.0466904	+	0.264794i	0.999213	−	0.0396747i	$-0.0126322\pi$
$257$	0.748503	+	4.24497i	0.0466904	+	0.264794i	−0.952522	+	0.304469i	$0.901521\pi$
$258$	2.67499	−	4.63322i	0.166538	−	0.288452i
$259$	−4.68479	−	8.11430i	−0.291099	−	0.504198i
$260$	−43.1430	+	36.2012i	−2.67561	+	2.24511i
$261$	0.879385	−	0.320070i	0.0544326	−	0.0198118i
$262$	−13.8020	−	5.02352i	−0.852691	−	0.310354i
$263$	−20.5535	−	17.2464i	−1.26738	−	1.06346i	−0.994855	−	0.101313i	$-0.967696\pi$
$263$	−20.5535	−	17.2464i	−1.26738	−	1.06346i	−0.272529	−	0.962148i	$-0.587860\pi$
$264$	2.12061	−	12.0266i	0.130515	−	0.740186i
$265$	19.7219			1.21151
$266$	−33.6168	−	19.7401i	−2.06118	−	1.21034i
$267$	2.40879			0.147415
$268$	−11.1382	+	63.1676i	−0.680371	+	3.85858i
$269$	20.4158	+	17.1309i	1.24477	+	1.04449i	0.997135	+	0.0756369i	$0.0240990\pi$
$269$	20.4158	+	17.1309i	1.24477	+	1.04449i	0.247639	+	0.968852i	$0.420345\pi$
$270$	−36.9222	−	13.4386i	−2.24701	−	0.817846i
$271$	9.90167	−	3.60391i	0.601484	−	0.218922i	−0.0232890	−	0.999729i	$-0.507414\pi$
$271$	9.90167	−	3.60391i	0.601484	−	0.218922i	0.624773	+	0.780807i	$0.285192\pi$
$272$	−17.6348	+	14.7973i	−1.06926	+	0.897219i
$273$	−11.6236	−	20.1327i	−0.703493	−	1.21849i
$274$	−7.16297	+	12.4066i	−0.432731	+	0.749512i
$275$	1.74510	+	9.89695i	0.105233	+	0.596809i
$276$	8.00774	+	45.4142i	0.482009	+	2.73361i
$277$	−11.1001	+	19.2260i	−0.666943	+	1.15518i	0.311812	+	0.950144i	$0.399064\pi$
$277$	−11.1001	+	19.2260i	−0.666943	+	1.15518i	−0.978755	+	0.205035i	$0.934269\pi$
$278$	−15.1395	−	26.2224i	−0.908007	−	1.57271i
$279$	4.02094	−	3.37397i	0.240728	−	0.201994i
$280$	78.6216	−	28.6159i	4.69854	−	1.71013i
$281$	10.2788	+	3.74119i	0.613184	+	0.223181i	0.629896	−	0.776680i	$-0.283098\pi$
$281$	10.2788	+	3.74119i	0.613184	+	0.223181i	−0.0167118	+	0.999860i	$0.505320\pi$
$282$	−25.4270	−	21.3357i	−1.51415	−	1.27053i
$283$	0.459760	−	2.60743i	0.0273299	−	0.154995i	−0.968089	−	0.250607i	$-0.919370\pi$
$283$	0.459760	−	2.60743i	0.0273299	−	0.154995i	0.995419	+	0.0956119i	$0.0304808\pi$
$284$	66.8590			3.96735
$285$	−11.3327	−	31.8644i	−0.671294	−	1.88748i
$286$	−8.33275			−0.492726
$287$	2.09240	−	11.8666i	0.123510	−	0.700461i
$288$	−3.52094	−	2.95442i	−0.207474	−	0.174091i
$289$	4.67365	+	1.70107i	0.274920	+	0.100063i
$290$	8.63816	−	3.14403i	0.507250	−	0.184624i
$291$	−13.2986	+	11.1589i	−0.779578	+	0.654143i
$292$	30.2558	+	52.4046i	1.77059	+	3.06675i
$293$	13.2194	−	22.8967i	0.772286	−	1.33764i	−0.164021	−	0.986457i	$-0.552447\pi$
$293$	13.2194	−	22.8967i	0.772286	−	1.33764i	0.936307	−	0.351182i	$-0.114220\pi$
$294$	4.81521	+	27.3084i	0.280829	+	1.59266i
$295$	7.80200	+	44.2474i	0.454250	+	2.57618i
$296$	−8.09879	+	14.0275i	−0.470733	+	0.815333i
$297$	−2.00000	−	3.46410i	−0.116052	−	0.201008i
$298$	−12.3648	+	10.3753i	−0.716276	+	0.601027i
$299$	16.1630	−	5.88284i	0.934729	−	0.340213i
$300$	83.3201	+	30.3260i	4.81049	+	1.75087i
$301$	2.85844	+	2.39852i	0.164758	+	0.138248i
$302$	2.00253	−	11.3569i	0.115232	−	0.653516i
$303$	23.2763			1.33719
$304$	−0.213011	+	28.9343i	−0.0122170	+	1.65949i
$305$	−4.53983			−0.259950
$306$	1.52481	−	8.64766i	0.0871679	−	0.494354i
$307$	4.07398	+	3.41847i	0.232514	+	0.195103i	0.751599	−	0.659620i	$-0.229283\pi$
$307$	4.07398	+	3.41847i	0.232514	+	0.195103i	−0.519085	+	0.854723i	$0.673727\pi$
$308$	14.6420	+	5.32926i	0.834307	+	0.303663i
$309$	−0.226682	+	0.0825054i	−0.0128955	+	0.00469357i
$310$	39.4975	−	33.1424i	2.24331	−	1.88236i
$311$	−11.8537	−	20.5312i	−0.672161	−	1.16422i	−0.977290	−	0.211906i	$-0.932033\pi$
$311$	−11.8537	−	20.5312i	−0.672161	−	1.16422i	0.305129	−	0.952311i	$-0.401301\pi$
$312$	−20.0942	+	34.8042i	−1.13761	+	1.97040i
$313$	2.49495	+	14.1496i	0.141023	+	0.799780i	0.970475	+	0.241202i	$0.0775417\pi$
$313$	2.49495	+	14.1496i	0.141023	+	0.799780i	−0.829452	+	0.558578i	$0.811347\pi$
$314$	3.41787	+	19.3837i	0.192882	+	1.09389i
$315$	−6.85117	+	11.8666i	−0.386020	+	0.668605i
$316$	21.2592	+	36.8221i	1.19593	+	2.07140i
$317$	−5.23190	+	4.39008i	−0.293853	+	0.246572i	−0.777780	−	0.628537i	$-0.783654\pi$
$317$	−5.23190	+	4.39008i	−0.293853	+	0.246572i	0.483928	+	0.875108i	$0.339210\pi$
$318$	24.1925	−	8.80536i	1.35665	−	0.493780i
$319$	0.879385	+	0.320070i	0.0492361	+	0.0179205i
$320$	4.86824	+	4.08494i	0.272143	+	0.228355i
$321$	5.49525	−	31.1651i	0.306715	−	1.73947i
$322$	−46.7452			−2.60501
$323$	−13.1464	+	7.46156i	−0.731483	+	0.415172i
$324$	−48.5262			−2.69590
$325$	5.74288	−	32.5695i	0.318558	−	1.80663i
$326$	18.5476	+	15.5633i	1.02725	+	0.861969i
$327$	0.583473	+	0.212367i	0.0322662	+	0.0117439i
$328$	−19.5744	+	7.12452i	−1.08082	+	0.393386i
$329$	17.7344	−	14.8809i	0.977730	−	0.820413i
$330$	9.82295	+	17.0138i	0.540736	+	0.936581i
$331$	1.77244	−	3.06996i	0.0974222	−	0.168740i	−0.813195	−	0.581992i	$-0.802274\pi$
$331$	1.77244	−	3.06996i	0.0974222	−	0.168740i	0.910617	+	0.413251i	$0.135607\pi$
$332$	3.85117	+	21.8411i	0.211360	+	1.19868i
$333$	−0.460637	−	2.61240i	−0.0252428	−	0.143159i
$334$	4.18479	−	7.24827i	0.228982	−	0.396608i
$335$	−28.2028	−	48.8487i	−1.54088	−	2.66889i
$336$	35.9222	−	30.1423i	1.95972	−	1.64440i
$337$	−6.41400	+	2.33451i	−0.349393	+	0.127169i	−0.510754	−	0.859727i	$-0.670634\pi$
$337$	−6.41400	+	2.33451i	−0.349393	+	0.127169i	0.161361	+	0.986895i	$0.448412\pi$
$338$	−5.16385	−	1.87949i	−0.280876	−	0.102231i
$339$	7.72874	+	6.48518i	0.419768	+	0.352227i
$340$	10.3059	−	58.4475i	0.558914	−	3.16976i
$341$	5.24897			0.284248
$342$	−7.03209	−	8.50692i	−0.380252	−	0.460002i
$343$	5.38413			0.290716
$344$	1.12015	−	6.35267i	0.0603943	−	0.342513i
$345$	−31.0651	−	26.0667i	−1.67249	−	1.40339i
$346$	−44.5651	−	16.2204i	−2.39584	−	0.872013i
$347$	2.66860	−	0.971289i	0.143258	−	0.0521415i	−0.269396	−	0.963029i	$-0.586824\pi$
$347$	2.66860	−	0.971289i	0.143258	−	0.0521415i	0.412654	+	0.910888i	$0.364602\pi$
$348$	6.32501	−	5.30731i	0.339056	−	0.284502i
$349$	−9.76604	−	16.9153i	−0.522764	−	0.905454i	−0.999649	−	0.0264886i	$-0.991567\pi$
$349$	−9.76604	−	16.9153i	−0.522764	−	0.905454i	0.476885	−	0.878966i	$-0.341766\pi$
$350$	−44.9397	+	77.8379i	−2.40213	+	4.16061i
$351$	2.28581	+	12.9635i	0.122007	+	0.691938i
$352$	−0.798133	−	4.52644i	−0.0425406	−	0.241260i
$353$	−3.63223	+	6.29120i	−0.193324	+	0.334847i	−0.946350	−	0.323144i	$-0.895260\pi$
$353$	−3.63223	+	6.29120i	−0.193324	+	0.334847i	0.753026	+	0.657991i	$0.228593\pi$
$354$	29.3259	+	50.7940i	1.55866	+	2.69967i
$355$	−45.0394	+	37.7926i	−2.39044	+	2.00582i
$356$	4.99273	−	1.81720i	0.264614	−	0.0963116i
$357$	23.0205	+	8.37879i	1.21838	+	0.443453i
$358$	15.4945	+	13.0015i	0.818912	+	0.687149i
$359$	−3.04963	+	17.2953i	−0.160953	+	0.912812i	0.792186	+	0.610280i	$0.208943\pi$
$359$	−3.04963	+	17.2953i	−0.160953	+	0.912812i	−0.953139	+	0.302532i	$0.902168\pi$
$360$	23.6878			1.24846
$361$	−3.57444	+	18.6607i	−0.188129	+	0.982144i
$362$	18.3378			0.963813
$363$	−0.347296	+	1.96962i	−0.0182283	+	0.103378i
$364$	−39.2806	−	32.9604i	−2.05887	−	1.72759i
$365$	−50.0039	−	18.1999i	−2.61733	−	0.952628i
$366$	−5.56893	+	2.02692i	−0.291092	+	0.105949i
$367$	−16.4231	+	13.7806i	−0.857278	+	0.719342i	−0.961380	−	0.275225i	$-0.911248\pi$
$367$	−16.4231	+	13.7806i	−0.857278	+	0.719342i	0.104102	+	0.994567i	$0.466803\pi$
$368$	17.3478	+	30.0472i	0.904315	+	1.56632i
$369$	1.70574	−	2.95442i	0.0887971	−	0.153801i
$370$	−4.52481	−	25.6615i	−0.235234	−	1.33408i
$371$	3.11809	+	17.6836i	0.161883	+	0.918085i
$372$	23.1557	−	40.1068i	1.20057	−	2.07944i
$373$	18.7934	+	32.5511i	0.973085	+	1.68543i	0.686116	+	0.727492i	$0.259314\pi$
$373$	18.7934	+	32.5511i	0.973085	+	1.68543i	0.286968	+	0.957940i	$0.407353\pi$
$374$	6.72668	−	5.64436i	0.347828	−	0.291863i
$375$	−36.8161	+	13.4000i	−1.90118	+	0.691972i
$376$	−37.6079	−	13.6881i	−1.93948	−	0.705912i
$377$	−2.35916	−	1.97957i	−0.121503	−	0.101953i
$378$	6.21213	−	35.2308i	0.319518	−	1.81207i
$379$	5.38507			0.276612			0.138306	−	0.990390i	$-0.455834\pi$
$379$	5.38507			0.276612			0.138306	+	0.990390i	$0.455834\pi$
$380$	−47.5283	−	57.4963i	−2.43815	−	2.94950i
$381$	1.02498			0.0525112
$382$	6.71348	−	38.0740i	0.343491	−	1.94804i
$383$	20.3760	+	17.0975i	1.04116	+	0.873640i	0.992137	−	0.125157i	$-0.0399435\pi$
$383$	20.3760	+	17.0975i	1.04116	+	0.873640i	0.0490271	+	0.998797i	$0.484388\pi$
$384$	25.0719	+	9.12543i	1.27945	+	0.465680i
$385$	−12.8760	+	4.68647i	−0.656221	+	0.238845i
$386$	−24.0797	+	20.2052i	−1.22562	+	1.02842i
$387$	0.528218	+	0.914901i	0.0268509	+	0.0465070i
$388$	−19.1459	+	33.1617i	−0.971986	+	1.68353i
$389$	−3.40508	−	19.3112i	−0.172644	−	0.979114i	−0.940828	−	0.338885i	$-0.889950\pi$
$389$	−3.40508	−	19.3112i	−0.172644	−	0.979114i	0.768184	−	0.640230i	$-0.221161\pi$
$390$	−11.2267	−	63.6697i	−0.568485	−	3.22404i
$391$	−9.06283	+	15.6973i	−0.458327	+	0.793846i
$392$	16.7173	+	28.9553i	0.844354	+	1.46246i
$393$	8.88713	−	7.45718i	0.448296	−	0.376165i
$394$	13.8897	−	5.05542i	0.699751	−	0.254688i
$395$	−35.1352	−	12.7882i	−1.76784	−	0.643443i
$396$	3.37939	+	2.83564i	0.169820	+	0.142496i
$397$	4.11762	−	23.3522i	0.206658	−	1.17201i	−0.688153	−	0.725566i	$-0.741578\pi$
$397$	4.11762	−	23.3522i	0.206658	−	1.17201i	0.894810	−	0.446447i	$-0.147311\pi$
$398$	19.5895			0.981931
$399$	26.7793	−	15.1993i	1.34064	−	0.760916i
$400$	66.7110			3.33555
$401$	−3.94784	+	22.3893i	−0.197146	+	1.11807i	0.712184	+	0.701993i	$0.247706\pi$
$401$	−3.94784	+	22.3893i	−0.197146	+	1.11807i	−0.909329	+	0.416077i	$0.863405\pi$
$402$	−56.4056	−	47.3299i	−2.81326	−	2.36060i
$403$	−16.2319	−	5.90793i	−0.808568	−	0.294295i
$404$	48.2452	−	17.5598i	2.40029	−	0.873633i
$405$	32.6896	−	27.4298i	1.62436	−	1.36300i
$406$	4.18479	+	7.24827i	0.207688	+	0.359726i
$407$	1.32635	−	2.29731i	0.0657448	−	0.113873i
$408$	−7.35410	−	41.7072i	−0.364082	−	2.06481i
$409$	−0.0773815	−	0.438852i	−0.00382627	−	0.0216999i	0.982835	−	0.184488i	$-0.0590625\pi$
$409$	−0.0773815	−	0.438852i	−0.00382627	−	0.0216999i	−0.986661	+	0.162788i	$0.947951\pi$
$410$	16.7554	−	29.0211i	0.827489	−	1.43325i
$411$	−5.65776	−	9.79952i	−0.279077	−	0.483375i
$412$	−0.407604	+	0.342020i	−0.0200812	+	0.0168501i
$413$	−38.4406	+	13.9912i	−1.89154	+	0.688464i
$414$	−12.4363	−	4.52644i	−0.611210	−	0.222462i
$415$	−14.9402	−	12.5363i	−0.733384	−	0.615382i
$416$	−2.62654	+	14.8959i	−0.128777	+	0.730330i
$417$	23.9162			1.17118
$418$	0.0812519	−	11.0368i	0.00397416	−	0.539829i
$419$	−1.55344			−0.0758907			−0.0379454	−	0.999280i	$-0.512081\pi$
$419$	−1.55344			−0.0758907			−0.0379454	+	0.999280i	$0.512081\pi$
$420$	−20.9932	+	119.058i	−1.02436	+	5.80945i
$421$	18.8286	+	15.7991i	0.917651	+	0.770001i	0.973559	−	0.228435i	$-0.0733609\pi$
$421$	18.8286	+	15.7991i	0.917651	+	0.770001i	−0.0559079	+	0.998436i	$0.517805\pi$
$422$	25.1780	+	9.16404i	1.22565	+	0.446098i
$423$	6.15910	−	2.24173i	0.299466	−	0.108997i
$424$	23.7795	−	19.9533i	1.15483	−	0.969020i
$425$	17.4256	+	30.1820i	0.845266	+	1.46404i
$426$	−38.3756	+	66.4684i	−1.85930	+	3.22041i
$427$	−0.717759	−	4.07061i	−0.0347348	−	0.196991i
$428$	−12.1211	−	68.7421i	−0.585895	−	3.32277i
$429$	3.29086	−	5.69994i	0.158884	−	0.275195i
$430$	5.18866	+	8.98703i	0.250220	+	0.433393i
$431$	−2.82429	+	2.36986i	−0.136041	+	0.114152i	−0.708269	−	0.705942i	$-0.750524\pi$
$431$	−2.82429	+	2.36986i	−0.136041	+	0.114152i	0.572228	+	0.820095i	$0.306079\pi$
$432$	−24.9513	+	9.08153i	−1.20047	+	0.436935i
$433$	−8.30706	−	3.02352i	−0.399212	−	0.145301i	0.134609	−	0.990899i	$-0.457022\pi$
$433$	−8.30706	−	3.02352i	−0.399212	−	0.145301i	−0.533821	+	0.845598i	$0.679244\pi$
$434$	35.9616	+	30.1753i	1.72621	+	1.44846i
$435$	−1.26083	+	7.15052i	−0.0604522	+	0.342841i
$436$	1.36959			0.0655912
$437$	7.63429	+	21.4654i	0.365197	+	1.02683i
$438$	−69.4647			−3.31915
$439$	−0.975185	+	5.53055i	−0.0465430	+	0.263959i	−0.999196	−	0.0401024i	$-0.987232\pi$
$439$	−0.975185	+	5.53055i	−0.0465430	+	0.263959i	0.952653	+	0.304061i	$0.0983427\pi$
$440$	18.1459	+	15.2262i	0.865072	+	0.725881i
$441$	−5.14543	−	1.87278i	−0.245020	−	0.0891802i
$442$	−27.1545	+	9.88344i	−1.29161	+	0.470107i
$443$	2.83228	−	2.37657i	0.134566	−	0.112914i	−0.573021	−	0.819541i	$-0.694228\pi$
$443$	2.83228	−	2.37657i	0.134566	−	0.112914i	0.707586	+	0.706627i	$0.249784\pi$
$444$	−11.7023	−	20.2690i	−0.555368	−	0.961926i
$445$	−2.33615	+	4.04633i	−0.110744	+	0.191815i
$446$	7.27584	+	41.2634i	0.344521	+	1.95388i
$447$	−2.21389	−	12.5556i	−0.104713	−	0.593859i
$448$	−2.89306	+	5.01092i	−0.136684	+	0.236744i
$449$	−4.57145	−	7.91799i	−0.215740	−	0.373673i	0.737761	−	0.675062i	$-0.235883\pi$
$449$	−4.57145	−	7.91799i	−0.215740	−	0.373673i	−0.953501	+	0.301389i	$0.902550\pi$
$450$	−19.4932	+	16.3567i	−0.918918	+	0.771064i
$451$	3.20574	−	1.16679i	0.150952	−	0.0549421i
$452$	20.9119	+	7.61132i	0.983615	+	0.358007i
$453$	6.97771	+	5.85499i	0.327841	+	0.275092i
$454$	3.20873	−	18.1976i	0.150593	−	0.854056i
$455$	45.0925			2.11397
$456$	−45.9026	−	26.9544i	−2.14959	−	1.26225i
$457$	4.99319			0.233572			0.116786	−	0.993157i	$-0.462741\pi$
$457$	4.99319			0.233572			0.116786	+	0.993157i	$0.462741\pi$
$458$	10.2216	−	57.9697i	0.477625	−	2.70875i
$459$	−10.6263	−	8.91652i	−0.495993	−	0.416188i
$460$	−84.0540	−	30.5932i	−3.91904	−	1.42641i
$461$	−5.94996	+	2.16561i	−0.277117	+	0.100862i	−0.476840	−	0.878990i	$-0.658218\pi$
$461$	−5.94996	+	2.16561i	−0.277117	+	0.100862i	0.199723	+	0.979852i	$0.435996\pi$
$462$	−13.7023	+	11.4976i	−0.637490	+	0.534918i
$463$	−14.6609	−	25.3934i	−0.681350	−	1.18013i	−0.974569	−	0.224088i	$-0.928060\pi$
$463$	−14.6609	−	25.3934i	−0.681350	−	1.18013i	0.293219	−	0.956045i	$-0.405274\pi$
$464$	3.10607	−	5.37987i	0.144196	−	0.249754i
$465$	7.07192	+	40.1068i	0.327952	+	1.85991i
$466$	7.15539	+	40.5802i	0.331467	+	1.87984i
$467$	−13.9841	+	24.2212i	−0.647107	+	1.12082i	0.336703	+	0.941611i	$0.390688\pi$
$467$	−13.9841	+	24.2212i	−0.647107	+	1.12082i	−0.983810	+	0.179212i	$0.942645\pi$
$468$	−7.25877	−	12.5726i	−0.335537	−	0.581167i
$469$	39.3410	−	33.0110i	1.81660	−	1.52431i
$470$	60.5005	−	22.0204i	2.79068	−	1.01572i
$471$	−14.6091	−	5.31726i	−0.673150	−	0.245007i
$472$	54.1737	+	45.4571i	2.49355	+	2.09233i
$473$	−0.183448	+	1.04039i	−0.00843496	+	0.0478371i
$474$	−48.8093			−2.24189
$475$	43.0827	+	7.92409i	1.97677	+	0.363582i
$476$	54.0360			2.47674
$477$	−0.882789	+	5.00654i	−0.0404201	+	0.229234i
$478$	35.3259	+	29.6420i	1.61577	+	1.35579i
$479$	23.7062	+	8.62835i	1.08316	+	0.394239i	0.821084	−	0.570807i	$-0.193369\pi$
$479$	23.7062	+	8.62835i	1.08316	+	0.394239i	0.262080	+	0.965046i	$0.415592\pi$
$480$	33.5107	−	12.1969i	1.52955	−	0.556710i
$481$	−6.68732	+	5.61133i	−0.304915	+	0.255854i
$482$	19.5018	+	33.7781i	0.888283	+	1.53855i
$483$	18.4611	−	31.9756i	0.840009	−	1.45494i
$484$	0.766044	+	4.34445i	0.0348202	+	0.197475i
$485$	−5.84730	−	33.1617i	−0.265512	−	1.50579i
$486$	12.6604	−	21.9285i	0.574289	−	0.994698i
$487$	−2.10472	−	3.64549i	−0.0953741	−	0.165193i	0.814391	−	0.580317i	$-0.197071\pi$
$487$	−2.10472	−	3.64549i	−0.0953741	−	0.165193i	−0.909765	+	0.415124i	$0.863738\pi$
$488$	−5.47384	+	4.59310i	−0.247789	+	0.207920i
$489$	−17.9709	+	6.54087i	−0.812672	+	0.295789i
$490$	−50.5433	−	18.3963i	−2.28331	−	0.831058i
$491$	21.9918	+	18.4534i	0.992478	+	0.832788i	0.985925	−	0.167190i	$-0.0534695\pi$
$491$	21.9918	+	18.4534i	0.992478	+	0.832788i	0.00655361	+	0.999979i	$0.497914\pi$
$492$	5.22668	−	29.6420i	0.235637	−	1.33636i
$493$	3.24535			0.146163
$494$	−12.6736	+	34.0388i	−0.570214	+	1.53148i
$495$	−3.87939			−0.174365
$496$	6.05051	−	34.3141i	0.271676	−	1.54075i
$497$	−41.0073	−	34.4092i	−1.83943	−	1.54347i
$498$	−23.9240	−	8.70761i	−1.07206	−	0.390197i
$499$	−4.29339	+	1.56266i	−0.192198	+	0.0699545i	−0.436326	−	0.899789i	$-0.643721\pi$
$499$	−4.29339	+	1.56266i	−0.192198	+	0.0699545i	0.244128	+	0.969743i	$0.421498\pi$
$500$	−66.2003	+	55.5487i	−2.96057	+	2.48421i
$501$	3.30541	+	5.72513i	0.147675	+	0.255780i
$502$	19.4402	−	33.6713i	0.867657	−	1.50283i
$503$	−5.51326	−	31.2673i	−0.245824	−	1.39414i	−0.818571	−	0.574405i	$-0.805233\pi$
$503$	−5.51326	−	31.2673i	−0.245824	−	1.39414i	0.572747	−	0.819732i	$-0.305878\pi$
$504$	3.74510	+	21.2395i	0.166820	+	0.946083i
$505$	−22.5744	+	39.1001i	−1.00455	+	1.73993i
$506$	−6.61721	−	11.4613i	−0.294171	−	0.509519i
$507$	3.32501	−	2.79001i	0.147669	−	0.123909i
$508$	2.12449	−	0.773249i	0.0942588	−	0.0343074i
$509$	−18.6830	−	6.80007i	−0.828111	−	0.301408i	−0.107028	−	0.994256i	$-0.534133\pi$
$509$	−18.6830	−	6.80007i	−0.828111	−	0.301408i	−0.721083	+	0.692848i	$0.756356\pi$
$510$	52.1908	+	43.7933i	2.31105	+	1.93920i
$511$	8.41312	−	47.7132i	0.372175	−	2.11071i
$512$	50.5553			2.23425
$513$	−17.1925	+	2.90117i	−0.759069	+	0.128090i
$514$	−10.9145			−0.481417
$515$	0.0812519	−	0.460802i	0.00358039	−	0.0203054i
$516$	7.14022	+	5.99135i	0.314330	+	0.263755i
$517$	6.15910	+	2.24173i	0.270877	+	0.0985911i
$518$	22.2939	−	8.11430i	0.979536	−	0.356522i
$519$	28.6955	−	24.0784i	1.25959	−	1.05692i
$520$	−38.9766	−	67.5094i	−1.70924	−	2.96048i
$521$	−3.59879	+	6.23329i	−0.157666	+	0.273085i	−0.934027	−	0.357204i	$-0.883730\pi$
$521$	−3.59879	+	6.23329i	−0.157666	+	0.273085i	0.776361	+	0.630289i	$0.217064\pi$
$522$	0.411474	+	2.33359i	0.0180097	+	0.102138i
$523$	−2.68836	−	15.2464i	−0.117554	−	0.666680i	−0.985454	−	0.169942i	$-0.945642\pi$
$523$	−2.68836	−	15.2464i	−0.117554	−	0.666680i	0.867900	−	0.496738i	$-0.165469\pi$
$524$	12.7947	−	22.1611i	0.558940	−	0.968113i
$525$	−35.4962	−	61.4812i	−1.54918	−	2.68326i
$526$	52.0433	−	43.6695i	2.26920	−	1.90408i
$527$	17.1052	−	6.22578i	0.745114	−	0.271199i
$528$	12.4757	+	4.54077i	0.542933	+	0.197611i
$529$	3.30793	+	2.77569i	0.143823	+	0.120682i
$530$	−8.67159	+	49.1790i	−0.376670	+	2.13620i
$531$	−11.5817			−0.502604
$532$	44.0394	−	51.7063i	1.90935	−	2.24175i
$533$	−11.2267			−0.486282
$534$	−1.05913	+	6.00660i	−0.0458328	+	0.259931i
$535$	47.0223	+	39.4564i	2.03295	+	1.70585i
$536$	−83.4270	−	30.3649i	−3.60350	−	1.31157i
$537$	−15.0128	+	5.46421i	−0.647850	+	0.235798i
$538$	−51.6946	+	43.3770i	−2.22871	+	1.87011i
$539$	−2.73783	−	4.74205i	−0.117927	−	0.204255i
$540$	34.2276	−	59.2840i	1.47292	−	2.55118i
$541$	−0.366592	−	2.07905i	−0.0157610	−	0.0893852i	0.975913	−	0.218162i	$-0.0700061\pi$
$541$	−0.366592	−	2.07905i	−0.0157610	−	0.0893852i	−0.991674	+	0.128777i	$0.958895\pi$
$542$	4.63310	+	26.2756i	0.199009	+	1.12864i
$543$	−7.24216	+	12.5438i	−0.310791	+	0.538306i
$544$	−7.96972	−	13.8040i	−0.341699	−	0.591840i
$545$	−0.922618	+	0.774169i	−0.0395206	+	0.0331617i
$546$	55.3141	−	20.1327i	2.36722	−	0.861599i
$547$	23.3926	+	8.51423i	1.00020	+	0.364042i	0.789661	−	0.613544i	$-0.210257\pi$
$547$	23.3926	+	8.51423i	1.00020	+	0.364042i	0.210537	+	0.977586i	$0.432479\pi$
$548$	−19.1197	−	16.0434i	−0.816755	−	0.685339i
$549$	0.203211	−	1.15247i	0.00867283	−	0.0491860i
$550$	−25.4466			−1.08504
$551$	2.64496	−	3.10543i	0.112679	−	0.132296i
$552$	−63.8289			−2.71674
$553$	5.91147	−	33.5256i	0.251381	−	1.42566i
$554$	−43.0617	−	36.1331i	−1.82952	−	1.53515i
$555$	19.3405	+	7.03936i	0.820958	+	0.298804i
$556$	49.5715	−	18.0426i	2.10230	−	0.765175i
$557$	30.7165	−	25.7742i	1.30150	−	1.09209i	0.311615	−	0.950209i	$-0.399130\pi$
$557$	30.7165	−	25.7742i	1.30150	−	1.09209i	0.989884	−	0.141878i	$-0.0453142\pi$
$558$	6.64543	+	11.5102i	0.281323	+	0.487267i
$559$	1.73829	−	3.01081i	0.0735220	−	0.127344i
$560$	15.7947	+	89.5764i	0.667449	+	3.78529i
$561$	1.20439	+	6.83045i	0.0508495	+	0.288382i
$562$	−13.8486	+	23.9865i	−0.584170	+	1.01181i
$563$	14.0826	+	24.3918i	0.593511	+	1.02799i	0.993755	+	0.111582i	$0.0355919\pi$
$563$	14.0826	+	24.3918i	0.593511	+	1.02799i	−0.400245	+	0.916408i	$0.631075\pi$
$564$	44.2995	−	37.1717i	1.86535	−	1.56521i
$565$	−18.3897	+	6.69329i	−0.773658	+	0.281589i
$566$	6.29978	+	2.29293i	0.264800	+	0.0963792i
$567$	29.7631	+	24.9742i	1.24993	+	1.04882i
$568$	−16.0697	+	91.1358i	−0.674270	+	3.82397i
$569$	−19.1111			−0.801180			−0.400590	−	0.916257i	$-0.631195\pi$
$569$	−19.1111			−0.801180			−0.400590	+	0.916257i	$0.631195\pi$
$570$	84.4407	−	14.2490i	3.53683	−	0.596826i
$571$	−34.1985			−1.43116			−0.715582	−	0.698529i	$-0.753838\pi$
$571$	−34.1985			−1.43116			−0.715582	+	0.698529i	$0.753838\pi$
$572$	2.52094	−	14.2970i	0.105406	−	0.597787i
$573$	23.3928	+	19.6289i	0.977249	+	0.820009i
$574$	28.6707	+	10.4353i	1.19669	+	0.435560i
$575$	49.3585	−	17.9650i	2.05839	−	0.749193i
$576$	−1.25490	+	1.05299i	−0.0522875	+	0.0438744i
$577$	13.6544	+	23.6500i	0.568438	+	0.984564i	0.996721	+	0.0809189i	$0.0257855\pi$
$577$	13.6544	+	23.6500i	0.568438	+	0.984564i	−0.428283	+	0.903645i	$0.640881\pi$
$578$	−6.29679	+	10.9064i	−0.261912	+	0.453645i
$579$	−4.31139	−	24.4511i	−0.179175	−	1.01615i
$580$	2.78106	+	15.7722i	0.115477	+	0.654904i
$581$	8.87851	−	15.3780i	0.368343	−	0.637988i
$582$	−21.9786	−	38.0681i	−0.911044	−	1.57797i
$583$	−3.89440	+	3.26779i	−0.161290	+	0.135338i
$584$	−78.7051	+	28.6463i	−3.25684	+	1.18539i
$585$	11.9966	+	4.36640i	0.495998	+	0.180529i
$586$	51.2832	+	43.0317i	2.11849	+	1.77762i
$587$	−7.47359	+	42.3848i	−0.308468	+	1.74941i	0.298245	+	0.954489i	$0.403599\pi$
$587$	−7.47359	+	42.3848i	−0.308468	+	1.74941i	−0.606713	+	0.794921i	$0.707512\pi$
$588$	−48.3114			−1.99233
$589$	7.98339	−	21.4417i	0.328950	−	0.883491i
$590$	−113.767			−4.68370
$591$	−2.02734	+	11.4976i	−0.0833937	+	0.472949i
$592$	−13.4893	−	11.3189i	−0.554408	−	0.465203i
$593$	9.84137	+	3.58196i	0.404136	+	0.147094i	0.536087	−	0.844163i	$-0.319902\pi$
$593$	9.84137	+	3.58196i	0.404136	+	0.147094i	−0.131951	+	0.991256i	$0.542124\pi$
$594$	9.51754	−	3.46410i	0.390509	−	0.142134i
$595$	−36.4013	+	30.5443i	−1.49231	+	1.25219i
$596$	−14.0608	−	24.3540i	−0.575952	−	0.997578i
$597$	−7.73648	+	13.4000i	−0.316633	+	0.548425i
$598$	7.56283	+	42.8910i	0.309267	+	1.75394i
$599$	−5.47148	−	31.0303i	−0.223558	−	1.26786i	−0.865422	−	0.501044i	$-0.832949\pi$
$599$	−5.47148	−	31.0303i	−0.223558	−	1.26786i	0.641863	−	0.766819i	$-0.278162\pi$
$600$	−61.3637	+	106.285i	−2.50516	+	4.33907i
$601$	4.53730	+	7.85884i	0.185080	+	0.320569i	0.943604	−	0.331077i	$-0.107412\pi$
$601$	4.53730	+	7.85884i	0.185080	+	0.320569i	−0.758523	+	0.651646i	$0.774079\pi$
$602$	−7.23783	+	6.07326i	−0.294992	+	0.247527i
$603$	13.6630	−	4.97291i	0.556399	−	0.202513i
$604$	18.8799	+	6.87170i	0.768210	+	0.279606i
$605$	−2.97178	−	2.49362i	−0.120820	−	0.101380i
$606$	−10.2344	+	58.0423i	−0.415745	+	2.35781i
$607$	−4.55438			−0.184856			−0.0924282	−	0.995719i	$-0.529463\pi$
$607$	−4.55438			−0.184856			−0.0924282	+	0.995719i	$0.529463\pi$
$608$	−19.7041	−	3.62414i	−0.799109	−	0.146978i
$609$	−6.61081			−0.267884
$610$	1.99613	−	11.3206i	0.0808209	−	0.458358i
$611$	−16.5232	−	13.8646i	−0.668458	−	0.560903i
$612$	14.3760	+	5.23243i	0.581115	+	0.211508i
$613$	5.37686	−	1.95702i	0.217169	−	0.0790432i	−0.231144	−	0.972919i	$-0.574247\pi$
$613$	5.37686	−	1.95702i	0.217169	−	0.0790432i	0.448314	+	0.893876i	$0.352025\pi$
$614$	−10.3157	+	8.65588i	−0.416307	+	0.349323i
$615$	13.2344	+	22.9227i	0.533663	+	0.924332i
$616$	−10.7836	+	18.6777i	−0.434483	+	0.752547i
$617$	0.257588	+	1.46086i	0.0103701	+	0.0588119i	0.989554	−	0.144165i	$-0.0460495\pi$
$617$	0.257588	+	1.46086i	0.0103701	+	0.0588119i	−0.979184	+	0.202977i	$0.934938\pi$
$618$	−0.106067	−	0.601535i	−0.00426663	−	0.0241973i
$619$	18.9623	−	32.8436i	0.762159	−	1.32010i	−0.179577	−	0.983744i	$-0.557473\pi$
$619$	18.9623	−	32.8436i	0.762159	−	1.32010i	0.941736	−	0.336354i	$-0.109194\pi$
$620$	44.9149	+	77.7949i	1.80383	+	3.12432i
$621$	−16.0155	+	13.4386i	−0.642679	+	0.539272i
$622$	56.4090	−	20.5312i	2.26180	−	0.823226i
$623$	−3.99747	−	1.45496i	−0.160155	−	0.0582918i
$624$	−33.4688	−	28.0837i	−1.33983	−	1.12425i
$625$	4.47090	−	25.3558i	0.178836	−	1.01423i
$626$	−36.3806			−1.45406
$627$	7.51754	+	4.41436i	0.300222	+	0.176293i
$628$	−34.2918			−1.36839
$629$	1.59745	−	9.05958i	0.0636945	−	0.361229i
$630$	−26.5783	−	22.3019i	−1.05891	−	0.888527i
$631$	9.11633	+	3.31807i	0.362916	+	0.132090i	0.517041	−	0.855961i	$-0.327034\pi$
$631$	9.11633	+	3.31807i	0.362916	+	0.132090i	−0.154125	+	0.988051i	$0.549256\pi$
$632$	−55.3021	+	20.1283i	−2.19980	+	0.800661i
$633$	−16.2121	+	13.6036i	−0.644374	+	0.540694i
$634$	−8.64677	−	14.9767i	−0.343407	−	0.594799i
$635$	−0.994070	+	1.72178i	−0.0394485	+	0.0683268i
$636$	7.78880	+	44.1725i	0.308846	+	1.75155i
$637$	3.12907	+	17.7458i	0.123978	+	0.703116i
$638$	−1.18479	+	2.05212i	−0.0469064	+	0.0812442i
$639$	−7.57785	−	13.1252i	−0.299775	−	0.519226i
$640$	−39.6450	+	33.2661i	−1.56711	+	1.31496i
$641$	−37.7768	+	13.7496i	−1.49209	+	0.543077i	−0.954000	−	0.299808i	$-0.903077\pi$
$641$	−37.7768	+	13.7496i	−1.49209	+	0.543077i	−0.538093	+	0.842885i	$0.680855\pi$
$642$	75.2978	+	27.4062i	2.97177	+	1.08163i
$643$	−28.7429	−	24.1181i	−1.13351	−	0.951127i	−0.134301	−	0.990941i	$-0.542879\pi$
$643$	−28.7429	−	24.1181i	−1.13351	−	0.951127i	−0.999207	+	0.0398140i	$0.987323\pi$
$644$	14.1420	−	80.2034i	0.557274	−	3.16046i
$645$	−8.19665			−0.322743
$646$	−12.8259	−	36.0628i	−0.504630	−	1.41887i
$647$	40.2704			1.58319			0.791597	−	0.611043i	$-0.209250\pi$
$647$	40.2704			1.58319			0.791597	+	0.611043i	$0.209250\pi$
$648$	11.6634	−	66.1463i	0.458181	−	2.59847i
$649$	−8.87211	−	7.44459i	−0.348261	−	0.292226i
$650$	78.6908	+	28.6411i	3.08651	+	1.12340i
$651$	−34.8435	+	12.6820i	−1.36562	+	0.497046i
$652$	−32.3141	+	27.1147i	−1.26552	+	1.06189i
$653$	21.0214	+	36.4102i	0.822631	+	1.42484i	0.903716	+	0.428132i	$0.140828\pi$
$653$	21.0214	+	36.4102i	0.822631	+	1.42484i	−0.0810847	+	0.996707i	$0.525838\pi$
$654$	−0.786112	+	1.36159i	−0.0307394	+	0.0532422i
$655$	3.90760	+	22.1611i	0.152683	+	0.865907i
$656$	−3.93242	−	22.3019i	−0.153535	−	0.870741i
$657$	6.85844	−	11.8792i	0.267573	−	0.463450i
$658$	29.3097	+	50.7660i	1.14261	+	1.97906i
$659$	1.81521	−	1.52314i	0.0707104	−	0.0593331i	−0.606747	−	0.794895i	$-0.707526\pi$
$659$	1.81521	−	1.52314i	0.0707104	−	0.0593331i	0.677458	+	0.735562i	$0.263082\pi$
$660$	−32.1634	+	11.7065i	−1.25196	+	0.455676i
$661$	−20.3100	−	7.39225i	−0.789969	−	0.287525i	−0.0846460	−	0.996411i	$-0.526976\pi$
$661$	−20.3100	−	7.39225i	−0.789969	−	0.287525i	−0.705323	+	0.708886i	$0.749198\pi$
$662$	6.87598	+	5.76963i	0.267243	+	0.224243i
$663$	3.96349	−	22.4781i	0.153929	−	0.872975i
$664$	−30.6973			−1.19129
$665$	−0.439693	+	59.7255i	−0.0170505	+	2.31605i
$666$	6.71688			0.260274
$667$	0.849356	−	4.81694i	0.0328872	−	0.186512i
$668$	11.1702	+	9.37295i	0.432190	+	0.362650i
$669$	−31.0993	−	11.3192i	−1.20237	−	0.437626i
$670$	134.211	−	48.8487i	5.18501	−	1.88719i
$671$	0.896459	−	0.752219i	0.0346074	−	0.0290391i
$672$	16.2344	+	28.1188i	0.626256	+	1.08471i
$673$	10.3910	−	17.9977i	0.400543	−	0.693762i	−0.593248	−	0.805020i	$-0.702155\pi$
$673$	10.3910	−	17.9977i	0.400543	−	0.693762i	0.993792	+	0.111258i	$0.0354880\pi$
$674$	−3.00118	−	17.0205i	−0.115601	−	0.655607i
$675$	6.98040	+	39.5878i	0.268676	+	1.52374i
$676$	4.78699	−	8.29131i	0.184115	−	0.318896i
$677$	−9.13610	−	15.8242i	−0.351129	−	0.608173i	0.635319	−	0.772250i	$-0.280869\pi$
$677$	−9.13610	−	15.8242i	−0.351129	−	0.608173i	−0.986447	+	0.164077i	$0.947535\pi$
$678$	−19.5699	+	16.4211i	−0.751576	+	0.630647i
$679$	28.8097	−	10.4859i	1.10562	−	0.402412i
$680$	77.1931	+	28.0960i	2.96022	+	1.07743i
$681$	11.1807	+	9.38170i	0.428444	+	0.359507i
$682$	−2.30793	+	13.0889i	−0.0883753	+	0.501201i
$683$	42.7657			1.63638			0.818192	−	0.574945i	$-0.194977\pi$
$683$	42.7657			1.63638			0.818192	+	0.574945i	$0.194977\pi$
$684$	16.7233	−	9.49173i	0.639431	−	0.362925i
$685$	21.9486			0.838613
$686$	−2.36736	+	13.4260i	−0.0903864	+	0.512607i
$687$	35.6168	+	29.8860i	1.35887	+	1.14022i
$688$	6.58987	+	2.39852i	0.251236	+	0.0914426i
$689$	15.7211	−	5.72200i	0.598925	−	0.217991i
$690$	78.6596	−	66.0033i	2.99452	−	2.51270i
$691$	−24.9518	−	43.2177i	−0.949210	−	1.64408i	−0.747094	−	0.664719i	$-0.768551\pi$
$691$	−24.9518	−	43.2177i	−0.949210	−	1.64408i	−0.202116	−	0.979362i	$-0.564782\pi$
$692$	41.3127	−	71.5558i	1.57047	−	2.72014i
$693$	−0.613341	−	3.47843i	−0.0232989	−	0.132135i
$694$	1.24867	+	7.08153i	0.0473987	+	0.268811i
$695$	−23.1951	+	40.1750i	−0.879839	+	1.52393i
$696$	5.71419	+	9.89727i	0.216596	+	0.375155i
$697$	9.06283	−	7.60462i	0.343279	−	0.288046i
$698$	46.4744	−	16.9153i	1.75908	−	0.640253i
$699$	−30.5844	−	11.1318i	−1.15681	−	0.421044i
$700$	−119.955	−	100.654i	−4.53388	−	3.80438i
$701$	−3.88578	+	22.0374i	−0.146764	+	0.832340i	0.819170	+	0.573551i	$0.194435\pi$
$701$	−3.88578	+	22.0374i	−0.146764	+	0.832340i	−0.965934	+	0.258789i	$0.916677\pi$
$702$	−33.3310			−1.25800
$703$	−7.36706	−	8.91215i	−0.277854	−	0.336128i
$704$	−1.63816			−0.0617403
$705$	−8.83069	+	50.0813i	−0.332583	+	1.88617i
$706$	−14.0908	−	11.8236i	−0.530314	−	0.444987i
$707$	−38.6279	−	14.0594i	−1.45275	−	0.528759i
$708$	−96.0224	+	34.9493i	−3.60874	+	1.31347i
$709$	−5.31727	+	4.46172i	−0.199694	+	0.167563i	−0.737151	−	0.675728i	$-0.763829\pi$
$709$	−5.31727	+	4.46172i	−0.199694	+	0.167563i	0.537457	+	0.843291i	$0.319385\pi$
$710$	−74.4368	−	128.928i	−2.79356	−	4.83859i
$711$	4.81908	−	8.34689i	0.180730	−	0.313033i
$712$	1.27703	+	7.24238i	0.0478586	+	0.271420i
$713$	−4.76399	−	27.0179i	−0.178413	−	1.01183i
$714$	−31.0155	+	53.7204i	−1.16073	+	2.01044i
$715$	6.38326	+	11.0561i	0.238720	+	0.413476i
$716$	−26.9950	+	22.6515i	−1.00885	+	0.846526i
$717$	−34.2276	+	12.4578i	−1.27825	+	0.465246i
$718$	−41.7870	−	15.2092i	−1.55948	−	0.567604i
$719$	−19.3871	−	16.2677i	−0.723018	−	0.606684i	0.205201	−	0.978720i	$-0.434215\pi$
$719$	−19.3871	−	16.2677i	−0.723018	−	0.606684i	−0.928218	+	0.372036i	$0.878660\pi$
$720$	−4.47178	+	25.3607i	−0.166653	+	0.945139i
$721$	0.426022			0.0158659
$722$	−44.9612	−	17.1183i	−1.67328	−	0.637077i
$723$	−30.8075			−1.14574
$724$	−5.54782	+	31.4632i	−0.206183	+	1.16932i
$725$	−7.20439	−	6.04520i	−0.267564	−	0.224513i
$726$	−4.75877	−	1.73205i	−0.176615	−	0.0642824i
$727$	35.9102	−	13.0702i	1.33184	−	0.484748i	0.424603	−	0.905379i	$-0.360414\pi$
$727$	35.9102	−	13.0702i	1.33184	−	0.484748i	0.907232	+	0.420631i	$0.138191\pi$
$728$	54.3696	−	45.6215i	2.01507	−	1.69085i
$729$	−6.50000	−	11.2583i	−0.240741	−	0.416975i
$730$	67.3701	−	116.688i	2.49348	−	4.31883i
$731$	0.636183	+	3.60797i	0.0235301	+	0.133446i
$732$	−1.79292	−	10.1681i	−0.0662682	−	0.375826i
$733$	−23.2927	+	40.3441i	−0.860334	+	1.49014i	0.0112719	+	0.999936i	$0.496412\pi$
$733$	−23.2927	+	40.3441i	−0.860334	+	1.49014i	−0.871606	+	0.490206i	$0.836921\pi$
$734$	−27.1425	−	47.0122i	−1.00185	−	1.73525i
$735$	32.5449	−	27.3084i	1.20044	−	1.00729i
$736$	−22.5744	+	8.21643i	−0.832105	+	0.302861i
$737$	13.6630	+	4.97291i	0.503282	+	0.183180i
$738$	6.61721	+	5.55250i	0.243583	+	0.204390i
$739$	−8.88507	+	50.3897i	−0.326842	+	1.85362i	0.169556	+	0.985521i	$0.445767\pi$
$739$	−8.88507	+	50.3897i	−0.326842	+	1.85362i	−0.496398	+	0.868095i	$0.665344\pi$
$740$	45.3979			1.66886
$741$	−18.2787	−	22.1122i	−0.671484	−	0.812314i
$742$	−45.4671			−1.66915
$743$	1.43598	−	8.14387i	0.0526812	−	0.298770i	−0.947071	−	0.321024i	$-0.895973\pi$
$743$	1.43598	−	8.14387i	0.0526812	−	0.298770i	0.999752	+	0.0222539i	$0.00708423\pi$
$744$	49.1043	+	41.2034i	1.80025	+	1.51059i
$745$	23.2383	+	8.45805i	0.851385	+	0.309879i
$746$	−89.4334	+	32.5511i	−3.27439	+	1.19178i
$747$	3.85117	−	3.23151i	0.140907	−	0.118235i
$748$	7.64930	+	13.2490i	0.279686	+	0.484431i
$749$	−27.9440	+	48.4005i	−1.02105	+	1.76852i
$750$	−17.2267	−	97.6974i	−0.629029	−	3.56740i
$751$	3.26723	+	18.5294i	0.119223	+	0.676146i	0.984572	+	0.174977i	$0.0559852\pi$
$751$	3.26723	+	18.5294i	0.119223	+	0.676146i	−0.865350	+	0.501169i	$0.832904\pi$
$752$	21.7545	−	37.6799i	0.793305	−	1.37404i
$753$	15.3550	+	26.5957i	0.559569	+	0.969201i
$754$	5.97359	−	5.01244i	0.217545	−	0.182542i
$755$	−16.6027	+	6.04288i	−0.604233	+	0.219923i
$756$	58.5681	+	21.3170i	2.13010	+	0.775293i
$757$	30.4800	+	25.5757i	1.10781	+	0.929566i	0.997926	−	0.0643776i	$-0.0205062\pi$
$757$	30.4800	+	25.5757i	1.10781	+	0.929566i	0.109888	+	0.993944i	$0.464951\pi$
$758$	−2.36777	+	13.4283i	−0.0860014	+	0.487738i
$759$	10.4534			0.379433
$760$	89.7971	−	50.9667i	3.25728	−	1.84875i
$761$	−7.02910			−0.254805			−0.127402	−	0.991851i	$-0.540664\pi$
$761$	−7.02910			−0.254805			−0.127402	+	0.991851i	$0.540664\pi$
$762$	−0.450675	+	2.55590i	−0.0163262	+	0.0925906i
$763$	−0.840022	−	0.704862i	−0.0304109	−	0.0255177i
$764$	63.2948	+	23.0374i	2.28992	+	0.833465i

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.j (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.439693 + 2.49362i) q^{2} +(-1.53209 - 1.28558i) q^{3} +(-4.14543 - 1.50881i) q^{4} +(3.64543 - 1.32683i) q^{5} +(3.87939 - 3.25519i) q^{6} +(1.76604 + 3.05888i) q^{7} +(3.05303 - 5.28801i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.439693 + 2.49362i) q^{2} +(-1.53209 - 1.28558i) q^{3} +(-4.14543 - 1.50881i) q^{4} +(3.64543 - 1.32683i) q^{5} +(3.87939 - 3.25519i) q^{6} +(1.76604 + 3.05888i) q^{7} +(3.05303 - 5.28801i) q^{8} +(0.173648 + 0.984808i) q^{9} +(1.70574 + 9.67372i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(4.41147 + 7.64090i) q^{12} +(2.52094 - 2.11532i) q^{13} +(-8.40420 + 3.05888i) q^{14} +(-7.29086 - 2.65366i) q^{15} +(5.08512 + 4.26692i) q^{16} +(-0.602196 + 3.41523i) q^{17} -2.53209 q^{18} +(2.77719 + 3.35965i) q^{19} -17.1138 q^{20} +(1.22668 - 6.95686i) q^{21} +(-1.93969 - 1.62760i) q^{22} +(4.91147 + 1.78763i) q^{23} +(-11.4757 + 4.17680i) q^{24} +(7.69846 - 6.45978i) q^{25} +(4.16637 + 7.21637i) q^{26} +(-2.00000 + 3.46410i) q^{27} +(-2.70574 - 15.3450i) q^{28} +(-0.162504 - 0.921605i) q^{29} +(9.82295 - 17.0138i) q^{30} +(-2.62449 - 4.54574i) q^{31} +(-3.52094 + 2.95442i) q^{32} +(1.87939 - 0.684040i) q^{33} +(-8.25150 - 3.00330i) q^{34} +(10.4966 + 8.80769i) q^{35} +(0.766044 - 4.34445i) q^{36} -2.65270 q^{37} +(-9.59879 + 5.44804i) q^{38} -6.58172 q^{39} +(4.11334 - 23.3279i) q^{40} +(-2.61334 - 2.19285i) q^{41} +(16.8084 + 6.11776i) q^{42} +(0.992726 - 0.361323i) q^{43} +(3.37939 - 2.83564i) q^{44} +(1.93969 + 3.35965i) q^{45} +(-6.61721 + 11.4613i) q^{46} +(-1.13816 - 6.45480i) q^{47} +(-2.30541 - 13.0746i) q^{48} +(-2.73783 + 4.74205i) q^{49} +(12.7233 + 22.0374i) q^{50} +(5.31315 - 4.45826i) q^{51} +(-13.6420 + 4.96529i) q^{52} +(4.77719 + 1.73875i) q^{53} +(-7.75877 - 6.51038i) q^{54} +(-0.673648 + 3.82045i) q^{55} +21.5672 q^{56} +(0.0641778 - 8.71756i) q^{57} +2.36959 q^{58} +(-2.01114 + 11.4058i) q^{59} +(26.2199 + 22.0011i) q^{60} +(-1.09967 - 0.400247i) q^{61} +(12.4893 - 4.54574i) q^{62} +(-2.70574 + 2.27038i) q^{63} +(0.819078 + 1.41868i) q^{64} +(6.38326 - 11.0561i) q^{65} +(0.879385 + 4.98724i) q^{66} +(-2.52481 - 14.3189i) q^{67} +(7.64930 - 13.2490i) q^{68} +(-5.22668 - 9.05288i) q^{69} +(-26.5783 + 22.3019i) q^{70} +(-14.2417 + 5.18355i) q^{71} +(5.73783 + 2.08840i) q^{72} +(-10.5077 - 8.81704i) q^{73} +(1.16637 - 6.61484i) q^{74} -20.0993 q^{75} +(-6.44356 - 18.1174i) q^{76} -3.53209 q^{77} +(2.89393 - 16.4123i) q^{78} +(-7.38326 - 6.19529i) q^{79} +(24.1989 + 8.80769i) q^{80} +(10.3366 - 3.76222i) q^{81} +(6.61721 - 5.55250i) q^{82} +(-2.51367 - 4.35381i) q^{83} +(-15.5817 + 26.9883i) q^{84} +(2.33615 + 13.2490i) q^{85} +(0.464508 + 2.63435i) q^{86} +(-0.935822 + 1.62089i) q^{87} +(3.05303 + 5.28801i) q^{88} +(-0.922618 + 0.774169i) q^{89} +(-9.23055 + 3.35965i) q^{90} +(10.9226 + 3.97551i) q^{91} +(-17.6630 - 14.8210i) q^{92} +(-1.82295 + 10.3385i) q^{93} +16.5963 q^{94} +(14.5817 + 8.56250i) q^{95} +9.19253 q^{96} +(1.50727 - 8.54818i) q^{97} +(-10.6211 - 8.91215i) q^{98} +(-0.939693 - 0.342020i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 12 q^{6} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 12 * q^6 + 6 * q^7 + 6 * q^8	\( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 12 q^{6} + 6 q^{7} + 6 q^{8} - 3 q^{11} + 6 q^{12} + 12 q^{13} - 12 q^{14} - 12 q^{15} + 9 q^{16} - 3 q^{17} - 6 q^{18} + 6 q^{19} - 30 q^{20} - 6 q^{21} - 6 q^{22} + 9 q^{23} - 30 q^{24} + 18 q^{25} + 6 q^{26} - 12 q^{27} - 6 q^{28} - 6 q^{29} + 18 q^{30} - 3 q^{31} - 18 q^{32} - 9 q^{34} + 21 q^{35} - 18 q^{37} - 15 q^{38} + 24 q^{39} + 18 q^{40} - 9 q^{41} + 24 q^{42} - 12 q^{43} + 9 q^{44} + 6 q^{45} - 9 q^{46} + 27 q^{47} - 18 q^{48} + 3 q^{49} + 21 q^{50} - 12 q^{51} - 24 q^{52} + 18 q^{53} - 24 q^{54} - 3 q^{55} + 30 q^{56} - 18 q^{57} - 6 q^{59} + 60 q^{60} - 21 q^{61} + 15 q^{62} - 6 q^{63} - 12 q^{64} + 3 q^{65} - 6 q^{66} + 12 q^{67} + 6 q^{68} - 18 q^{69} - 54 q^{70} - 42 q^{71} + 15 q^{72} - 15 q^{73} - 12 q^{74} - 12 q^{75} - 9 q^{76} - 12 q^{77} + 42 q^{78} - 9 q^{79} + 51 q^{80} + 9 q^{82} + 6 q^{83} - 30 q^{84} + 18 q^{85} - 30 q^{86} - 24 q^{87} + 6 q^{88} + 21 q^{89} - 18 q^{90} + 39 q^{91} - 45 q^{92} + 30 q^{93} + 72 q^{94} + 24 q^{95} + 27 q^{97} - 9 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 12 * q^6 + 6 * q^7 + 6 * q^8 - 3 * q^11 + 6 * q^12 + 12 * q^13 - 12 * q^14 - 12 * q^15 + 9 * q^16 - 3 * q^17 - 6 * q^18 + 6 * q^19 - 30 * q^20 - 6 * q^21 - 6 * q^22 + 9 * q^23 - 30 * q^24 + 18 * q^25 + 6 * q^26 - 12 * q^27 - 6 * q^28 - 6 * q^29 + 18 * q^30 - 3 * q^31 - 18 * q^32 - 9 * q^34 + 21 * q^35 - 18 * q^37 - 15 * q^38 + 24 * q^39 + 18 * q^40 - 9 * q^41 + 24 * q^42 - 12 * q^43 + 9 * q^44 + 6 * q^45 - 9 * q^46 + 27 * q^47 - 18 * q^48 + 3 * q^49 + 21 * q^50 - 12 * q^51 - 24 * q^52 + 18 * q^53 - 24 * q^54 - 3 * q^55 + 30 * q^56 - 18 * q^57 - 6 * q^59 + 60 * q^60 - 21 * q^61 + 15 * q^62 - 6 * q^63 - 12 * q^64 + 3 * q^65 - 6 * q^66 + 12 * q^67 + 6 * q^68 - 18 * q^69 - 54 * q^70 - 42 * q^71 + 15 * q^72 - 15 * q^73 - 12 * q^74 - 12 * q^75 - 9 * q^76 - 12 * q^77 + 42 * q^78 - 9 * q^79 + 51 * q^80 + 9 * q^82 + 6 * q^83 - 30 * q^84 + 18 * q^85 - 30 * q^86 - 24 * q^87 + 6 * q^88 + 21 * q^89 - 18 * q^90 + 39 * q^91 - 45 * q^92 + 30 * q^93 + 72 * q^94 + 24 * q^95 + 27 * q^97 - 9 * q^98

Introduction

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