LMFDB - Embedded newform 945.2.bt.a.106.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(106,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 0, 0]))

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

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

chi := DirichletCharacter("945.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bt (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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			106.12
Character	$\chi$	$=$	945.106
Dual form			945.2.bt.a.526.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.234962 - 1.33254i) q^{2} +(-1.29175 - 1.15386i) q^{3} +(0.158937 + 0.0578482i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-1.84107 + 1.45019i) q^{6} +(0.939693 - 0.342020i) q^{7} +(1.46752 - 2.54182i) q^{8} +(0.337236 + 2.98098i) q^{9} +O(q^{10})$	\(q+(0.234962 - 1.33254i) q^{2} +(-1.29175 - 1.15386i) q^{3} +(0.158937 + 0.0578482i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-1.84107 + 1.45019i) q^{6} +(0.939693 - 0.342020i) q^{7} +(1.46752 - 2.54182i) q^{8} +(0.337236 + 2.98098i) q^{9} +(0.676547 + 1.17181i) q^{10} +(2.63140 + 2.20800i) q^{11} +(-0.138558 - 0.258115i) q^{12} +(0.565901 + 3.20939i) q^{13} +(-0.234962 - 1.33254i) q^{14} +(1.73122 + 0.0535834i) q^{15} +(-2.78313 - 2.33532i) q^{16} +(3.55581 + 6.15885i) q^{17} +(4.05151 + 0.251039i) q^{18} +(-1.42685 + 2.47138i) q^{19} +(-0.158937 + 0.0578482i) q^{20} +(-1.60849 - 0.642465i) q^{21} +(3.56053 - 2.98764i) q^{22} +(5.00999 + 1.82349i) q^{23} +(-4.82857 + 1.59009i) q^{24} +(0.173648 - 0.984808i) q^{25} +4.40959 q^{26} +(3.00400 - 4.23981i) q^{27} +0.169137 q^{28} +(-0.278150 + 1.57747i) q^{29} +(0.478174 - 2.29433i) q^{30} +(-7.80675 - 2.84142i) q^{31} +(0.730914 - 0.613309i) q^{32} +(-0.851390 - 5.88844i) q^{33} +(9.04238 - 3.29116i) q^{34} +(-0.500000 + 0.866025i) q^{35} +(-0.118845 + 0.493296i) q^{36} +(0.540564 + 0.936284i) q^{37} +(2.95795 + 2.48202i) q^{38} +(2.97216 - 4.79869i) q^{39} +(0.509665 + 2.89046i) q^{40} +(0.0256375 + 0.145398i) q^{41} +(-1.23404 + 1.99242i) q^{42} +(-2.49781 - 2.09591i) q^{43} +(0.290496 + 0.503154i) q^{44} +(-2.17448 - 2.06680i) q^{45} +(3.60703 - 6.24755i) q^{46} +(2.24702 - 0.817850i) q^{47} +(0.900484 + 6.22798i) q^{48} +(0.766044 - 0.642788i) q^{49} +(-1.27149 - 0.462785i) q^{50} +(2.51320 - 12.0586i) q^{51} +(-0.0957148 + 0.542825i) q^{52} +13.1043 q^{53} +(-4.94388 - 4.99914i) q^{54} -3.43504 q^{55} +(0.509665 - 2.89046i) q^{56} +(4.69476 - 1.54603i) q^{57} +(2.03668 + 0.741291i) q^{58} +(-1.56176 + 1.31047i) q^{59} +(0.272055 + 0.108664i) q^{60} +(8.01488 - 2.91718i) q^{61} +(-5.62060 + 9.73516i) q^{62} +(1.33646 + 2.68587i) q^{63} +(-4.27864 - 7.41082i) q^{64} +(-2.49646 - 2.09478i) q^{65} +(-8.04661 - 0.249052i) q^{66} +(-0.598598 - 3.39482i) q^{67} +(0.208871 + 1.18456i) q^{68} +(-4.36762 - 8.13630i) q^{69} +(1.03653 + 0.869752i) q^{70} +(-6.05707 - 10.4912i) q^{71} +(8.07204 + 3.51747i) q^{72} +(-0.185854 + 0.321908i) q^{73} +(1.37465 - 0.500330i) q^{74} +(-1.36064 + 1.07176i) q^{75} +(-0.369744 + 0.310252i) q^{76} +(3.22789 + 1.17485i) q^{77} +(-5.69609 - 5.08803i) q^{78} +(-1.15275 + 6.53760i) q^{79} +3.63312 q^{80} +(-8.77254 + 2.01059i) q^{81} +0.199771 q^{82} +(2.69764 - 15.2991i) q^{83} +(-0.218482 - 0.195159i) q^{84} +(-6.68274 - 2.43232i) q^{85} +(-3.37978 + 2.83597i) q^{86} +(2.17947 - 1.71675i) q^{87} +(9.47399 - 3.44825i) q^{88} +(-7.71577 + 13.3641i) q^{89} +(-3.26500 + 2.41195i) q^{90} +(1.62945 + 2.82229i) q^{91} +(0.690786 + 0.579638i) q^{92} +(6.80578 + 12.6783i) q^{93} +(-0.561850 - 3.18641i) q^{94} +(-0.495541 - 2.81035i) q^{95} +(-1.65183 - 0.0511261i) q^{96} +(0.0136097 + 0.0114199i) q^{97} +(-0.676547 - 1.17181i) q^{98} +(-5.69462 + 8.58877i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 3 q^{3} + 9 q^{8} + 3 q^{9}+O(q^{10}) $ 96 * q - 3 * q^3 + 9 * q^8 + 3 * q^9	$ 96 q - 3 q^{3} + 9 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{11} + 60 q^{12} - 6 q^{13} + 6 q^{15} - 12 q^{16} - 72 q^{18} - 6 q^{19} + 9 q^{22} - 6 q^{23} - 60 q^{24} + 54 q^{26} + 36 q^{27} - 78 q^{28} - 18 q^{29} + 3 q^{30} - 51 q^{32} + 39 q^{34} - 48 q^{35} + 42 q^{36} + 54 q^{37} + 105 q^{38} + 45 q^{39} - 9 q^{40} + 45 q^{41} - 3 q^{42} + 9 q^{43} - 48 q^{44} - 12 q^{45} + 24 q^{46} - 6 q^{47} + 6 q^{48} - 6 q^{51} + 3 q^{52} - 36 q^{53} + 90 q^{54} - 24 q^{55} - 9 q^{56} - 30 q^{57} - 27 q^{58} + 12 q^{59} - 15 q^{60} + 24 q^{61} - 27 q^{62} - 3 q^{63} + 15 q^{64} - 12 q^{65} - 27 q^{66} + 30 q^{67} + 69 q^{68} - 42 q^{69} - 42 q^{71} - 177 q^{72} + 6 q^{73} - 51 q^{74} - 24 q^{76} - 15 q^{78} - 48 q^{79} - 42 q^{80} + 99 q^{81} - 36 q^{82} + 30 q^{83} + 12 q^{84} - 21 q^{85} - 75 q^{86} - 18 q^{87} + 87 q^{88} - 75 q^{89} - 9 q^{90} - 18 q^{91} + 123 q^{92} + 24 q^{93} - 3 q^{94} - 21 q^{95} + 24 q^{96} + 102 q^{97} + 3 q^{98} - 75 q^{99}+O(q^{100}) $ 96 * q - 3 * q^3 + 9 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^11 + 60 * q^12 - 6 * q^13 + 6 * q^15 - 12 * q^16 - 72 * q^18 - 6 * q^19 + 9 * q^22 - 6 * q^23 - 60 * q^24 + 54 * q^26 + 36 * q^27 - 78 * q^28 - 18 * q^29 + 3 * q^30 - 51 * q^32 + 39 * q^34 - 48 * q^35 + 42 * q^36 + 54 * q^37 + 105 * q^38 + 45 * q^39 - 9 * q^40 + 45 * q^41 - 3 * q^42 + 9 * q^43 - 48 * q^44 - 12 * q^45 + 24 * q^46 - 6 * q^47 + 6 * q^48 - 6 * q^51 + 3 * q^52 - 36 * q^53 + 90 * q^54 - 24 * q^55 - 9 * q^56 - 30 * q^57 - 27 * q^58 + 12 * q^59 - 15 * q^60 + 24 * q^61 - 27 * q^62 - 3 * q^63 + 15 * q^64 - 12 * q^65 - 27 * q^66 + 30 * q^67 + 69 * q^68 - 42 * q^69 - 42 * q^71 - 177 * q^72 + 6 * q^73 - 51 * q^74 - 24 * q^76 - 15 * q^78 - 48 * q^79 - 42 * q^80 + 99 * q^81 - 36 * q^82 + 30 * q^83 + 12 * q^84 - 21 * q^85 - 75 * q^86 - 18 * q^87 + 87 * q^88 - 75 * q^89 - 9 * q^90 - 18 * q^91 + 123 * q^92 + 24 * q^93 - 3 * q^94 - 21 * q^95 + 24 * q^96 + 102 * q^97 + 3 * q^98 - 75 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$	$1$

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 $

$2$	0.234962	−	1.33254i	0.166143	−	0.942246i	−0.781734	−	0.623612i	$-0.785665\pi$
$2$	0.234962	−	1.33254i	0.166143	−	0.942246i	0.947878	−	0.318634i	$-0.103224\pi$
$3$	−1.29175	−	1.15386i	−0.745792	−	0.666179i
$3$	−1.29175	−	1.15386i	−0.745792	−	0.666179i
$4$	0.158937	+	0.0578482i	0.0794683	+	0.0289241i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$6$	−1.84107	+	1.45019i	−0.751613	+	0.592039i
$7$	0.939693	−	0.342020i	0.355170	−	0.129271i
$7$	0.939693	−	0.342020i	0.355170	−	0.129271i
$8$	1.46752	−	2.54182i	0.518848	−	0.898671i
$9$	0.337236	+	2.98098i	0.112412	+	0.993662i
$10$	0.676547	+	1.17181i	0.213943	+	0.370560i
$11$	2.63140	+	2.20800i	0.793396	+	0.665738i	0.946584	−	0.322459i	$-0.104509\pi$
$11$	2.63140	+	2.20800i	0.793396	+	0.665738i	−0.153187	+	0.988197i	$0.548954\pi$
$12$	−0.138558	−	0.258115i	−0.0399982	−	0.0745114i
$13$	0.565901	+	3.20939i	0.156953	+	0.890124i	0.956979	+	0.290158i	$0.0937079\pi$
$13$	0.565901	+	3.20939i	0.156953	+	0.890124i	−0.800026	+	0.599965i	$0.795181\pi$
$14$	−0.234962	−	1.33254i	−0.0627963	−	0.356136i
$15$	1.73122	+	0.0535834i	0.447000	+	0.0138352i
$16$	−2.78313	−	2.33532i	−0.695783	−	0.583831i
$17$	3.55581	+	6.15885i	0.862411	+	1.49374i	0.869595	+	0.493766i	$0.164380\pi$
$17$	3.55581	+	6.15885i	0.862411	+	1.49374i	−0.00718327	+	0.999974i	$0.502287\pi$
$18$	4.05151	+	0.251039i	0.954951	+	0.0591704i
$19$	−1.42685	+	2.47138i	−0.327343	+	0.566974i	−0.981984	−	0.188966i	$-0.939486\pi$
$19$	−1.42685	+	2.47138i	−0.327343	+	0.566974i	0.654641	+	0.755940i	$0.272820\pi$
$20$	−0.158937	+	0.0578482i	−0.0355393	+	0.0129352i
$21$	−1.60849	−	0.642465i	−0.351001	−	0.140197i
$22$	3.56053	−	2.98764i	0.759107	−	0.636966i
$23$	5.00999	+	1.82349i	1.04466	+	0.380224i	0.806643	−	0.591038i	$-0.201282\pi$
$23$	5.00999	+	1.82349i	1.04466	+	0.380224i	0.238013	+	0.971262i	$0.423504\pi$
$24$	−4.82857	+	1.59009i	−0.985628	+	0.324576i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	4.40959			0.864792
$27$	3.00400	−	4.23981i	0.578120	−	0.815952i
$28$	0.169137			0.0319638
$29$	−0.278150	+	1.57747i	−0.0516512	+	0.292929i	−0.999681	−	0.0252527i	$-0.991961\pi$
$29$	−0.278150	+	1.57747i	−0.0516512	+	0.292929i	0.948030	+	0.318181i	$0.103072\pi$
$30$	0.478174	−	2.29433i	0.0873022	−	0.418885i
$31$	−7.80675	−	2.84142i	−1.40213	−	0.510335i	−0.473323	−	0.880889i	$-0.656946\pi$
$31$	−7.80675	−	2.84142i	−1.40213	−	0.510335i	−0.928811	+	0.370554i	$0.879168\pi$
$32$	0.730914	−	0.613309i	0.129209	−	0.108419i
$33$	−0.851390	−	5.88844i	−0.148208	−	1.02505i
$34$	9.04238	−	3.29116i	1.55076	−	0.564429i
$35$	−0.500000	+	0.866025i	−0.0845154	+	0.146385i
$36$	−0.118845	+	0.493296i	−0.0198076	+	0.0822160i
$37$	0.540564	+	0.936284i	0.0888681	+	0.153924i	0.907033	−	0.421060i	$-0.138342\pi$
$37$	0.540564	+	0.936284i	0.0888681	+	0.153924i	−0.818165	+	0.574984i	$0.805008\pi$
$38$	2.95795	+	2.48202i	0.479843	+	0.402636i
$39$	2.97216	−	4.79869i	0.475927	−	0.768406i
$40$	0.509665	+	2.89046i	0.0805852	+	0.457021i
$41$	0.0256375	+	0.145398i	0.00400391	+	0.0227073i	0.986744	−	0.162283i	$-0.0518857\pi$
$41$	0.0256375	+	0.145398i	0.00400391	+	0.0227073i	−0.982740	+	0.184990i	$0.940775\pi$
$42$	−1.23404	+	1.99242i	−0.190417	+	0.307437i
$43$	−2.49781	−	2.09591i	−0.380913	−	0.319624i	0.432148	−	0.901803i	$-0.357756\pi$
$43$	−2.49781	−	2.09591i	−0.380913	−	0.319624i	−0.813061	+	0.582179i	$0.802200\pi$
$44$	0.290496	+	0.503154i	0.0437940	+	0.0758534i
$45$	−2.17448	−	2.06680i	−0.324152	−	0.308100i
$46$	3.60703	−	6.24755i	0.531827	−	0.921151i
$47$	2.24702	−	0.817850i	0.327762	−	0.119296i	−0.172898	−	0.984940i	$-0.555313\pi$
$47$	2.24702	−	0.817850i	0.327762	−	0.119296i	0.500660	+	0.865644i	$0.333091\pi$
$48$	0.900484	+	6.22798i	0.129974	+	0.898932i
$49$	0.766044	−	0.642788i	0.109435	−	0.0918268i
$50$	−1.27149	−	0.462785i	−0.179816	−	0.0654477i
$51$	2.51320	−	12.0586i	0.351918	−	1.68854i
$52$	−0.0957148	+	0.542825i	−0.0132732	+	0.0752763i
$53$	13.1043			1.80002			0.900009	−	0.435872i	$-0.143560\pi$
$53$	13.1043			1.80002			0.900009	+	0.435872i	$0.143560\pi$
$54$	−4.94388	−	4.99914i	−0.672777	−	0.680296i
$55$	−3.43504			−0.463181
$56$	0.509665	−	2.89046i	0.0681069	−	0.386253i
$57$	4.69476	−	1.54603i	0.621836	−	0.204776i
$58$	2.03668	+	0.741291i	0.267429	+	0.0973363i
$59$	−1.56176	+	1.31047i	−0.203324	+	0.170609i	−0.738764	−	0.673964i	$-0.764590\pi$
$59$	−1.56176	+	1.31047i	−0.203324	+	0.170609i	0.535440	+	0.844573i	$0.320146\pi$
$60$	0.272055	+	0.108664i	0.0351221	+	0.0140285i
$61$	8.01488	−	2.91718i	1.02620	−	0.373506i	0.226567	−	0.973996i	$-0.427250\pi$
$61$	8.01488	−	2.91718i	1.02620	−	0.373506i	0.799633	+	0.600489i	$0.205027\pi$
$62$	−5.62060	+	9.73516i	−0.713816	+	1.23637i
$63$	1.33646	+	2.68587i	0.168378	+	0.338388i
$64$	−4.27864	−	7.41082i	−0.534830	−	0.926353i
$65$	−2.49646	−	2.09478i	−0.309648	−	0.259825i
$66$	−8.04661	−	0.249052i	−0.990470	−	0.0306562i
$67$	−0.598598	−	3.39482i	−0.0731303	−	0.414743i	−0.999292	−	0.0376166i	$-0.988023\pi$
$67$	−0.598598	−	3.39482i	−0.0731303	−	0.414743i	0.926162	−	0.377126i	$-0.123088\pi$
$68$	0.208871	+	1.18456i	0.0253293	+	0.143649i
$69$	−4.36762	−	8.13630i	−0.525799	−	0.979495i
$70$	1.03653	+	0.869752i	0.123889	+	0.103955i
$71$	−6.05707	−	10.4912i	−0.718842	−	1.24507i	−0.961459	−	0.274949i	$-0.911339\pi$
$71$	−6.05707	−	10.4912i	−0.718842	−	1.24507i	0.242616	−	0.970122i	$-0.421994\pi$
$72$	8.07204	+	3.51747i	0.951299	+	0.414538i
$73$	−0.185854	+	0.321908i	−0.0217526	+	0.0376765i	−0.876697	−	0.481043i	$-0.840258\pi$
$73$	−0.185854	+	0.321908i	−0.0217526	+	0.0376765i	0.854944	+	0.518720i	$0.173591\pi$
$74$	1.37465	−	0.500330i	0.159799	−	0.0581622i
$75$	−1.36064	+	1.07176i	−0.157113	+	0.123756i
$76$	−0.369744	+	0.310252i	−0.0424126	+	0.0355884i
$77$	3.22789	+	1.17485i	0.367852	+	0.133887i
$78$	−5.69609	−	5.08803i	−0.644955	−	0.576106i
$79$	−1.15275	+	6.53760i	−0.129695	+	0.735537i	0.848713	+	0.528854i	$0.177378\pi$
$79$	−1.15275	+	6.53760i	−0.129695	+	0.735537i	−0.978408	+	0.206683i	$0.933733\pi$
$80$	3.63312			0.406195
$81$	−8.77254	+	2.01059i	−0.974727	+	0.223399i
$82$	0.199771			0.0220611
$83$	2.69764	−	15.2991i	0.296104	−	1.67929i	−0.366575	−	0.930389i	$-0.619470\pi$
$83$	2.69764	−	15.2991i	0.296104	−	1.67929i	0.662679	−	0.748903i	$-0.269419\pi$
$84$	−0.218482	−	0.195159i	−0.0238384	−	0.0212936i
$85$	−6.68274	−	2.43232i	−0.724845	−	0.263822i
$86$	−3.37978	+	2.83597i	−0.364451	+	0.305810i
$87$	2.17947	−	1.71675i	0.233664	−	0.184055i
$88$	9.47399	−	3.44825i	1.00993	−	0.367585i
$89$	−7.71577	+	13.3641i	−0.817870	+	1.41659i	0.0893792	+	0.995998i	$0.471512\pi$
$89$	−7.71577	+	13.3641i	−0.817870	+	1.41659i	−0.907249	+	0.420594i	$0.861822\pi$
$90$	−3.26500	+	2.41195i	−0.344162	+	0.254242i
$91$	1.62945	+	2.82229i	0.170813	+	0.295856i
$92$	0.690786	+	0.579638i	0.0720194	+	0.0604315i
$93$	6.80578	+	12.6783i	0.705726	+	1.31468i
$94$	−0.561850	−	3.18641i	−0.0579504	−	0.328653i
$95$	−0.495541	−	2.81035i	−0.0508414	−	0.288336i
$96$	−1.65183	−	0.0511261i	−0.168589	−	0.00521803i
$97$	0.0136097	+	0.0114199i	0.00138186	+	0.00115952i	0.643478	−	0.765464i	$-0.277491\pi$
$97$	0.0136097	+	0.0114199i	0.00138186	+	0.00115952i	−0.642096	+	0.766624i	$0.721935\pi$
$98$	−0.676547	−	1.17181i	−0.0683416	−	0.118371i
$99$	−5.69462	+	8.58877i	−0.572331	+	0.863204i
$100$	0.0845684	−	0.146477i	0.00845684	−	0.0146477i
$101$	5.09381	−	1.85400i	0.506853	−	0.184479i	−0.0759207	−	0.997114i	$-0.524190\pi$
$101$	5.09381	−	1.85400i	0.506853	−	0.184479i	0.582774	+	0.812634i	$0.301967\pi$
$102$	−15.4780	−	6.18224i	−1.53255	−	0.612133i
$103$	−10.8475	+	9.10215i	−1.06884	+	0.896861i	−0.994947	−	0.100405i	$-0.967986\pi$
$103$	−10.8475	+	9.10215i	−1.06884	+	0.896861i	−0.0738912	+	0.997266i	$0.523542\pi$
$104$	8.98817	+	3.27143i	0.881363	+	0.320790i
$105$	1.64514	−	0.541761i	0.160550	−	0.0528704i
$106$	3.07902	−	17.4620i	0.299061	−	1.69606i
$107$	3.99875			0.386574			0.193287	−	0.981142i	$-0.438085\pi$
$107$	3.99875			0.386574			0.193287	+	0.981142i	$0.438085\pi$
$108$	0.722711	−	0.500085i	0.0695429	−	0.0481207i
$109$	−17.5269			−1.67877			−0.839385	−	0.543537i	$-0.817085\pi$
$109$	−17.5269			−1.67877			−0.839385	+	0.543537i	$0.817085\pi$
$110$	−0.807106	+	4.57733i	−0.0769545	+	0.436431i
$111$	0.382063	−	1.83318i	0.0362638	−	0.173997i
$112$	−3.41402	−	1.24260i	−0.322594	−	0.117415i
$113$	−8.31763	+	6.97932i	−0.782457	+	0.656559i	−0.943866	−	0.330328i	$-0.892841\pi$
$113$	−8.31763	+	6.97932i	−0.782457	+	0.656559i	0.161409	+	0.986888i	$0.448396\pi$
$114$	−0.957048	−	6.61920i	−0.0896357	−	0.619945i
$115$	−5.00999	+	1.82349i	−0.467184	+	0.170041i
$116$	−0.135462	+	0.234627i	−0.0125773	+	0.0217846i
$117$	−9.37629	+	2.76927i	−0.866838	+	0.256019i
$118$	1.37930	+	2.38901i	0.126975	+	0.219926i
$119$	5.44782	+	4.57127i	0.499401	+	0.419047i
$120$	2.67681	−	4.32183i	0.244358	−	0.394527i
$121$	0.138838	+	0.787387i	0.0126216	+	0.0715807i
$122$	−2.00405	−	11.3656i	−0.181438	−	1.02899i
$123$	0.134650	−	0.217399i	0.0121410	−	0.0196022i
$124$	−1.07641	−	0.903213i	−0.0966642	−	0.0811109i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	3.89304	−	1.14980i	0.346819	−	0.102432i
$127$	7.48647	−	12.9669i	0.664316	−	1.15063i	−0.315154	−	0.949041i	$-0.602056\pi$
$127$	7.48647	−	12.9669i	0.664316	−	1.15063i	0.979470	−	0.201589i	$-0.0646106\pi$
$128$	−9.08732	+	3.30751i	−0.803213	+	0.292346i
$129$	0.808169	+	5.58951i	0.0711553	+	0.492129i
$130$	−3.37794	+	2.83443i	−0.296265	+	0.248596i
$131$	10.3928	+	3.78266i	0.908021	+	0.330493i	0.753463	−	0.657491i	$-0.228382\pi$
$131$	10.3928	+	3.78266i	0.908021	+	0.330493i	0.154559	+	0.987984i	$0.450604\pi$
$132$	0.205319	−	0.985140i	0.0178707	−	0.0857454i
$133$	−0.495541	+	2.81035i	−0.0429689	+	0.243689i
$134$	−4.66437			−0.402940
$135$	0.424100	+	5.17882i	0.0365007	+	0.445722i
$136$	20.8730			1.78984
$137$	3.57917	−	20.2985i	0.305789	−	1.73422i	−0.313977	−	0.949431i	$-0.601662\pi$
$137$	3.57917	−	20.2985i	0.305789	−	1.73422i	0.619766	−	0.784786i	$-0.287227\pi$
$138$	−11.8681	+	3.90829i	−1.01028	+	0.332696i
$139$	1.57205	+	0.572179i	0.133339	+	0.0485316i	0.407828	−	0.913059i	$-0.366286\pi$
$139$	1.57205	+	0.572179i	0.133339	+	0.0485316i	−0.274489	+	0.961590i	$0.588509\pi$
$140$	−0.129566	+	0.108719i	−0.0109504	+	0.00918844i
$141$	−3.84627	−	1.53628i	−0.323915	−	0.129378i
$142$	−15.4030	+	5.60625i	−1.29259	+	0.470466i
$143$	−5.59723	+	9.69468i	−0.468064	+	0.810710i
$144$	6.02299	−	9.08403i	0.501916	−	0.757002i
$145$	−0.800902	−	1.38720i	−0.0665113	−	0.115201i
$146$	0.385286	+	0.323294i	0.0318865	+	0.0267560i
$147$	−1.73122	−	0.0535834i	−0.142789	−	0.00441948i
$148$	0.0317530	+	0.180080i	0.00261008	+	0.0148025i
$149$	3.72171	+	21.1068i	0.304894	+	1.72914i	0.624003	+	0.781422i	$0.285505\pi$
$149$	3.72171	+	21.1068i	0.304894	+	1.72914i	−0.319109	+	0.947718i	$0.603384\pi$
$150$	1.10846	+	2.06492i	0.0905056	+	0.168600i
$151$	3.91026	+	3.28109i	0.318212	+	0.267012i	0.787876	−	0.615833i	$-0.211181\pi$
$151$	3.91026	+	3.28109i	0.318212	+	0.267012i	−0.469664	+	0.882845i	$0.655625\pi$
$152$	4.18788	+	7.25362i	0.339682	+	0.588347i
$153$	−17.1603	+	12.6768i	−1.38733	+	1.02486i
$154$	2.32397	−	4.02523i	0.187271	−	0.324363i
$155$	7.80675	−	2.84142i	0.627053	−	0.228229i
$156$	0.749981	−	0.590754i	0.0600466	−	0.0472982i
$157$	−9.93664	+	8.33783i	−0.793030	+	0.665431i	−0.946493	−	0.322723i	$-0.895402\pi$
$157$	−9.93664	+	8.33783i	−0.793030	+	0.665431i	0.153463	+	0.988154i	$0.450957\pi$
$158$	8.44074	+	3.07218i	0.671509	+	0.244409i
$159$	−16.9275	−	15.1205i	−1.34244	−	1.19913i
$160$	−0.165685	+	0.939645i	−0.0130985	+	0.0742854i
$161$	5.33152			0.420183
$162$	0.617975	+	12.1622i	0.0485527	+	0.955549i
$163$	20.8065			1.62969			0.814844	−	0.579681i	$-0.196823\pi$
$163$	20.8065			1.62969			0.814844	+	0.579681i	$0.196823\pi$
$164$	−0.00433625	+	0.0245921i	−0.000338604	+	0.00192032i
$165$	4.43722	+	3.96354i	0.345437	+	0.308562i
$166$	−19.7527	−	7.18941i	−1.53311	−	0.558007i
$167$	8.08710	−	6.78588i	0.625799	−	0.525107i	−0.273822	−	0.961780i	$-0.588288\pi$
$167$	8.08710	−	6.78588i	0.625799	−	0.525107i	0.899620	+	0.436673i	$0.143843\pi$
$168$	−3.99353	+	3.14567i	−0.308107	+	0.242693i
$169$	2.23609	−	0.813869i	0.172007	−	0.0626053i
$170$	−4.81135	+	8.33350i	−0.369014	+	0.639150i
$171$	−7.84834	−	3.41999i	−0.600178	−	0.261533i
$172$	−0.275749	−	0.477612i	−0.0210257	−	0.0364175i
$173$	−0.765990	−	0.642742i	−0.0582372	−	0.0488668i	0.613204	−	0.789924i	$-0.289880\pi$
$173$	−0.765990	−	0.642742i	−0.0582372	−	0.0488668i	−0.671442	+	0.741057i	$0.734325\pi$
$174$	−1.77554	−	3.30760i	−0.134603	−	0.250748i
$175$	−0.173648	−	0.984808i	−0.0131266	−	0.0744445i
$176$	−2.16712	−	12.2903i	−0.163353	−	0.926418i
$177$	3.52949	+	0.109242i	0.265293	+	0.00821114i
$178$	15.9952	+	13.4216i	1.19889	+	1.00599i
$179$	11.2552	+	19.4946i	0.841255	+	1.45710i	0.888835	+	0.458228i	$0.151516\pi$
$179$	11.2552	+	19.4946i	0.841255	+	1.45710i	−0.0475799	+	0.998867i	$0.515151\pi$
$180$	−0.226044	−	0.454279i	−0.0168483	−	0.0338600i
$181$	−2.00245	+	3.46835i	−0.148841	+	0.257800i	−0.930799	−	0.365530i	$-0.880888\pi$
$181$	−2.00245	+	3.46835i	−0.148841	+	0.257800i	0.781958	+	0.623331i	$0.214221\pi$
$182$	4.14366	−	1.50817i	0.307149	−	0.111793i
$183$	−13.7192	−	5.47974i	−1.01415	−	0.405074i
$184$	11.9873	−	10.0585i	0.883713	−	0.741523i
$185$	−1.01593	−	0.369767i	−0.0746925	−	0.0271858i
$186$	18.4934	−	6.09004i	1.35600	−	0.446543i
$187$	−4.24201	+	24.0576i	−0.310206	+	1.75927i
$188$	0.404445			0.0294972
$189$	1.37274	−	5.01155i	0.0998519	−	0.364536i
$190$	−3.86133			−0.280131
$191$	−0.0166510	+	0.0944324i	−0.00120482	+	0.00683289i	−0.985404	−	0.170231i	$-0.945549\pi$
$191$	−0.0166510	+	0.0944324i	−0.00120482	+	0.00683289i	0.984199	+	0.177064i	$0.0566598\pi$
$192$	−3.02408	+	14.5099i	−0.218244	+	1.04716i
$193$	3.61711	+	1.31652i	0.260365	+	0.0947652i	0.468905	−	0.883249i	$-0.344649\pi$
$193$	3.61711	+	1.31652i	0.260365	+	0.0947652i	−0.208539	+	0.978014i	$0.566871\pi$
$194$	0.0184152	−	0.0154522i	0.00132214	−	0.00110940i
$195$	0.807731	+	5.58648i	0.0578428	+	0.400056i
$196$	0.158937	−	0.0578482i	0.0113526	−	0.00413201i
$197$	−2.74287	+	4.75079i	−0.195421	+	0.338480i	−0.947039	−	0.321120i	$-0.895941\pi$
$197$	−2.74287	+	4.75079i	−0.195421	+	0.338480i	0.751617	+	0.659600i	$0.229274\pi$
$198$	10.1068	+	9.60634i	0.718262	+	0.682693i
$199$	7.47949	+	12.9549i	0.530207	+	0.918346i	0.999379	+	0.0352389i	$0.0112192\pi$
$199$	7.47949	+	12.9549i	0.530207	+	0.918346i	−0.469172	+	0.883107i	$0.655447\pi$
$200$	−2.24838	−	1.88661i	−0.158984	−	0.133404i
$201$	−3.14389	+	5.07595i	−0.221753	+	0.358030i
$202$	−1.27366	−	7.22331i	−0.0896147	−	0.508230i
$203$	0.278150	+	1.57747i	0.0195223	+	0.110717i
$204$	1.09701	−	1.77117i	0.0768058	−	0.124006i
$205$	−0.113099	−	0.0949015i	−0.00789919	−	0.00662821i
$206$	9.58020	+	16.5934i	0.667484	+	1.15612i
$207$	−3.74624	+	15.5497i	−0.260382	+	1.08078i
$208$	5.91998	−	10.2537i	0.410477	−	0.710967i
$209$	−9.21144	+	3.35269i	−0.637169	+	0.231911i
$210$	−0.335370	−	2.31951i	−0.0231427	−	0.160061i
$211$	11.5515	−	9.69290i	0.795241	−	0.667287i	−0.151795	−	0.988412i	$-0.548506\pi$
$211$	11.5515	−	9.69290i	0.795241	−	0.667287i	0.947037	+	0.321125i	$0.104061\pi$
$212$	2.08276	+	0.758061i	0.143044	+	0.0520639i
$213$	−4.28105	+	20.5409i	−0.293333	+	1.40744i
$214$	0.939556	−	5.32849i	0.0642267	−	0.364248i
$215$	3.26066			0.222375
$216$	−6.36841	−	13.8577i	−0.433316	−	0.942894i
$217$	−8.30777			−0.563968
$218$	−4.11816	+	23.3552i	−0.278917	+	1.58182i
$219$	0.611513	−	0.201377i	0.0413222	−	0.0136078i
$220$	−0.545954	−	0.198711i	−0.0368082	−	0.0133971i
$221$	−17.7539	+	14.8973i	−1.19426	+	1.00210i
$222$	−2.35301	−	0.939840i	−0.157923	−	0.0630780i
$223$	−14.3117	+	5.20905i	−0.958385	+	0.348824i	−0.773401	−	0.633918i	$-0.781446\pi$
$223$	−14.3117	+	5.20905i	−0.958385	+	0.348824i	−0.184985	+	0.982741i	$0.559224\pi$
$224$	0.477070	−	0.826310i	0.0318756	−	0.0552101i
$225$	2.99426	+	0.185530i	0.199617	+	0.0123686i
$226$	7.34588	+	12.7234i	0.488640	+	0.846350i
$227$	−12.5221	−	10.5073i	−0.831123	−	0.697395i	0.124425	−	0.992229i	$-0.460291\pi$
$227$	−12.5221	−	10.5073i	−0.831123	−	0.697395i	−0.955549	+	0.294834i	$0.904736\pi$
$228$	0.835603	+	0.0258629i	0.0553392	+	0.00171281i
$229$	−3.71230	−	21.0535i	−0.245316	−	1.39126i	−0.819758	−	0.572710i	$-0.805892\pi$
$229$	−3.71230	−	21.0535i	−0.245316	−	1.39126i	0.574442	−	0.818545i	$-0.305219\pi$
$230$	1.25271	+	7.10446i	0.0826011	+	0.468454i
$231$	−2.81401	−	5.24213i	−0.185148	−	0.344907i
$232$	3.60146	+	3.02198i	0.236447	+	0.198403i
$233$	2.98025	+	5.16195i	0.195243	+	0.338171i	0.946980	−	0.321292i	$-0.104117\pi$
$233$	2.98025	+	5.16195i	0.195243	+	0.338171i	−0.751737	+	0.659463i	$0.770784\pi$
$234$	1.48708	+	13.1449i	0.0972132	+	0.859311i
$235$	−1.19562	+	2.07087i	−0.0779934	+	0.135089i
$236$	−0.324029	+	0.117937i	−0.0210925	+	0.00767703i
$237$	9.03251	−	7.11483i	0.586725	−	0.462158i
$238$	7.37142	−	6.18535i	0.477818	−	0.400937i
$239$	−8.09372	−	2.94587i	−0.523539	−	0.190553i	0.0667122	−	0.997772i	$-0.478749\pi$
$239$	−8.09372	−	2.94587i	−0.523539	−	0.190553i	−0.590251	+	0.807220i	$0.700971\pi$
$240$	−4.69308	−	4.19209i	−0.302937	−	0.270598i
$241$	2.79195	−	15.8339i	0.179845	−	1.01995i	−0.752556	−	0.658528i	$-0.771179\pi$
$241$	2.79195	−	15.8339i	0.179845	−	1.01995i	0.932401	−	0.361425i	$-0.117709\pi$
$242$	1.08184			0.0695436
$243$	13.6519	+	7.52506i	0.875768	+	0.482733i
$244$	1.44261			0.0923537
$245$	−0.173648	+	0.984808i	−0.0110940	+	0.0629171i
$246$	−0.258055	−	0.230507i	−0.0164530	−	0.0146966i
$247$	−8.73908	−	3.18077i	−0.556054	−	0.202387i
$248$	−18.6790	+	15.6735i	−1.18612	+	0.995270i
$249$	−21.1376	+	16.6499i	−1.33954	+	1.05514i
$250$	1.27149	−	0.462785i	0.0804162	−	0.0292691i
$251$	3.09944	−	5.36838i	0.195635	−	0.338849i	−0.751474	−	0.659763i	$-0.770657\pi$
$251$	3.09944	−	5.36838i	0.195635	−	0.338849i	0.947108	+	0.320914i	$0.103990\pi$
$252$	0.0570391	+	0.504194i	0.00359313	+	0.0317613i
$253$	9.15701	+	15.8604i	0.575696	+	0.997135i
$254$	−15.5199	−	13.0227i	−0.973805	−	0.817119i
$255$	5.82589	+	10.8529i	0.364831	+	0.679633i
$256$	−0.699704	−	3.96822i	−0.0437315	−	0.248014i
$257$	−3.83813	−	21.7671i	−0.239416	−	1.35780i	−0.833111	−	0.553106i	$-0.813443\pi$
$257$	−3.83813	−	21.7671i	−0.239416	−	1.35780i	0.593695	−	0.804690i	$-0.297668\pi$
$258$	7.63812	+	0.236409i	0.475529	+	0.0147182i
$259$	0.828192	+	0.694935i	0.0514613	+	0.0431812i
$260$	−0.275600	−	0.477353i	−0.0170920	−	0.0296042i
$261$	−4.79621	−	0.297182i	−0.296878	−	0.0183951i
$262$	7.48245	−	12.9600i	0.462267	−	0.800671i
$263$	−8.70094	+	3.16688i	−0.536523	+	0.195278i	−0.596049	−	0.802948i	$-0.703263\pi$
$263$	−8.70094	+	3.16688i	−0.536523	+	0.195278i	0.0595255	+	0.998227i	$0.481041\pi$
$264$	−16.2168	−	6.47734i	−0.998076	−	0.398653i
$265$	−10.0385	+	8.42330i	−0.616660	+	0.517439i
$266$	3.62847	+	1.32065i	0.222476	+	0.0809745i
$267$	25.3871	−	8.36020i	1.55366	−	0.511636i
$268$	0.101245	−	0.574188i	0.00618452	−	0.0350741i
$269$	4.68621			0.285723			0.142862	−	0.989743i	$-0.454370\pi$
$269$	4.68621			0.285723			0.142862	+	0.989743i	$0.454370\pi$
$270$	7.00061	+	0.651698i	0.426044	+	0.0396611i
$271$	−12.2696			−0.745325			−0.372662	−	0.927967i	$-0.621555\pi$
$271$	−12.2696			−0.745325			−0.372662	+	0.927967i	$0.621555\pi$
$272$	4.48662	−	25.4449i	0.272041	−	1.54282i
$273$	1.15167	−	5.52584i	0.0697023	−	0.334439i
$274$	−26.2075	−	9.53876i	−1.58325	−	0.576257i
$275$	2.63140	−	2.20800i	0.158679	−	0.133148i
$276$	−0.223504	−	1.54581i	−0.0134534	−	0.0930471i
$277$	11.8986	−	4.33074i	0.714918	−	0.260209i	0.0411511	−	0.999153i	$-0.486898\pi$
$277$	11.8986	−	4.33074i	0.714918	−	0.260209i	0.673767	+	0.738944i	$0.264675\pi$
$278$	1.13182	−	1.96037i	0.0678821	−	0.117575i
$279$	5.83752	−	24.2300i	0.349483	−	1.45061i
$280$	1.46752	+	2.54182i	0.0877013	+	0.151903i
$281$	−24.4018	−	20.4755i	−1.45569	−	1.22147i	−0.928294	−	0.371846i	$-0.878725\pi$
$281$	−24.4018	−	20.4755i	−1.45569	−	1.22147i	−0.527394	−	0.849621i	$-0.676831\pi$
$282$	−2.95088	+	4.76434i	−0.175723	+	0.283712i
$283$	−3.84307	−	21.7951i	−0.228447	−	1.29558i	−0.855986	−	0.517000i	$-0.827049\pi$
$283$	−3.84307	−	21.7951i	−0.228447	−	1.29558i	0.627539	−	0.778585i	$-0.284062\pi$
$284$	−0.355796	−	2.01782i	−0.0211126	−	0.119736i
$285$	−2.60263	+	4.20206i	−0.154166	+	0.248908i
$286$	11.6034	+	9.73640i	0.686123	+	0.575725i
$287$	0.0738203	+	0.127860i	0.00435747	+	0.00754736i
$288$	2.07476	+	1.97201i	0.122256	+	0.116202i
$289$	−16.7876	+	29.0770i	−0.987507	+	1.71041i
$290$	−2.03668	+	0.741291i	−0.119598	+	0.0435301i
$291$	−0.00440343	−	0.0304553i	−0.000258134	−	0.00178532i
$292$	−0.0481608	+	0.0404117i	−0.00281840	+	0.00236492i
$293$	−0.849799	−	0.309302i	−0.0496458	−	0.0180696i	0.317078	−	0.948400i	$-0.397298\pi$
$293$	−0.849799	−	0.309302i	−0.0496458	−	0.0180696i	−0.366724	+	0.930330i	$0.619521\pi$
$294$	−0.478174	+	2.29433i	−0.0278877	+	0.133808i
$295$	0.354022	−	2.00776i	0.0206119	−	0.116896i
$296$	3.17316			0.184436
$297$	17.2662	−	4.52378i	1.00189	−	0.262496i
$298$	29.0001			1.67993
$299$	−3.01712	+	17.1109i	−0.174484	+	0.989550i
$300$	−0.278254	+	0.0916317i	−0.0160650	+	0.00529036i
$301$	−3.06402	−	1.11521i	−0.176607	−	0.0642798i
$302$	5.29094	−	4.43963i	0.304460	−	0.255472i
$303$	−8.71917	−	3.48262i	−0.500903	−	0.200071i
$304$	9.74260	−	3.54602i	0.558776	−	0.203378i
$305$	−4.26463	+	7.38655i	−0.244192	+	0.422953i
$306$	12.8603	+	25.8453i	0.735175	+	1.47748i
$307$	−3.08987	−	5.35181i	−0.176348	−	0.305444i	0.764279	−	0.644886i	$-0.223095\pi$
$307$	−3.08987	−	5.35181i	−0.176348	−	0.305444i	−0.940627	+	0.339442i	$0.889762\pi$
$308$	0.445066	+	0.373455i	0.0253600	+	0.0212796i
$309$	24.5148	+	0.758764i	1.39460	+	0.0431646i
$310$	−1.95201	−	11.0704i	−0.110867	−	0.628757i
$311$	4.38869	+	24.8895i	0.248860	+	1.41135i	0.811355	+	0.584554i	$0.198730\pi$
$311$	4.38869	+	24.8895i	0.248860	+	1.41135i	−0.562495	+	0.826801i	$0.690159\pi$
$312$	−7.83572	−	14.5969i	−0.443610	−	0.826387i
$313$	7.61248	+	6.38763i	0.430283	+	0.361050i	0.832058	−	0.554688i	$-0.187162\pi$
$313$	7.61248	+	6.38763i	0.430283	+	0.361050i	−0.401776	+	0.915738i	$0.631607\pi$
$314$	8.77573	+	15.2000i	0.495243	+	0.857787i
$315$	−2.75023	−	1.19844i	−0.154958	−	0.0675243i
$316$	−0.561403	+	0.972379i	−0.0315814	+	0.0547006i
$317$	−28.9422	+	10.5341i	−1.62556	+	0.591654i	−0.984429	−	0.175781i	$-0.943755\pi$
$317$	−28.9422	+	10.5341i	−1.62556	+	0.591654i	−0.641127	+	0.767435i	$0.721533\pi$
$318$	−24.1259	+	19.0038i	−1.35292	+	1.06568i
$319$	−4.21498	+	3.53679i	−0.235994	+	0.198022i
$320$	8.04121	+	2.92676i	0.449517	+	0.163611i
$321$	−5.16539	−	4.61398i	−0.288304	−	0.257527i
$322$	1.25271	−	7.10446i	0.0698106	−	0.395916i
$323$	−20.2945			−1.12922
$324$	−1.51059	−	0.187919i	−0.0839215	−	0.0104399i
$325$	3.25890			0.180771
$326$	4.88873	−	27.7254i	0.270762	−	1.53557i
$327$	22.6403	+	20.2235i	1.25201	+	1.11836i
$328$	0.407199	+	0.148208i	0.0224838	+	0.00818343i
$329$	1.83179	−	1.53705i	0.100990	−	0.0847406i
$330$	6.32415	−	4.98148i	0.348133	−	0.274221i
$331$	2.58402	−	0.940507i	0.142031	−	0.0516950i	−0.270027	−	0.962853i	$-0.587033\pi$
$331$	2.58402	−	0.940507i	0.142031	−	0.0516950i	0.412057	+	0.911158i	$0.364810\pi$
$332$	1.31378	−	2.27553i	0.0721029	−	0.124886i
$333$	−2.60875	+	1.92716i	−0.142959	+	0.105608i
$334$	−7.14228	−	12.3708i	−0.390808	−	0.676900i
$335$	2.64070	+	2.21581i	0.144277	+	0.121063i
$336$	2.97627	+	5.54441i	0.162369	+	0.302472i
$337$	−1.96195	−	11.1268i	−0.106874	−	0.606114i	−0.990455	−	0.137835i	$-0.955985\pi$
$337$	−1.96195	−	11.1268i	−0.106874	−	0.606114i	0.883581	−	0.468279i	$-0.155126\pi$
$338$	−0.559115	−	3.17090i	−0.0304118	−	0.172474i
$339$	18.7974	+	0.581803i	1.02094	+	0.0315992i
$340$	−0.921427	−	0.773169i	−0.0499714	−	0.0419310i
$341$	−14.2688	−	24.7142i	−0.772698	−	1.33835i
$342$	−6.40133	+	9.65464i	−0.346144	+	0.522063i
$343$	0.500000	−	0.866025i	0.0269975	−	0.0467610i
$344$	−8.99305	+	3.27320i	−0.484873	+	0.176479i
$345$	8.57570	+	3.42532i	0.461700	+	0.184413i
$346$	−1.03646	+	0.869691i	−0.0557203	+	0.0467549i
$347$	9.75176	+	3.54935i	0.523502	+	0.190539i	0.590235	−	0.807232i	$-0.299035\pi$
$347$	9.75176	+	3.54935i	0.523502	+	0.190539i	−0.0667327	+	0.997771i	$0.521257\pi$
$348$	0.445709	−	0.146776i	0.0238925	−	0.00786802i
$349$	4.48781	−	25.4516i	0.240227	−	1.36240i	−0.591094	−	0.806603i	$-0.701304\pi$
$349$	4.48781	−	25.4516i	0.240227	−	1.36240i	0.831321	−	0.555793i	$-0.187585\pi$
$350$	−1.35309			−0.0723259
$351$	15.3072	+	7.24168i	0.817036	+	0.386532i
$352$	3.27751			0.174692
$353$	0.485755	−	2.75486i	0.0258541	−	0.146626i	−0.969148	−	0.246479i	$-0.920726\pi$
$353$	0.485755	−	2.75486i	0.0258541	−	0.146626i	0.995002	+	0.0998533i	$0.0318373\pi$
$354$	0.974867	−	4.67751i	0.0518136	−	0.248607i
$355$	11.3836	+	4.14328i	0.604177	+	0.219903i
$356$	−1.99941	+	1.67770i	−0.105968	+	0.0889180i
$357$	−1.76265	−	12.1909i	−0.0932891	−	0.645212i
$358$	28.6219	−	10.4175i	1.51271	−	0.550582i
$359$	10.4756	−	18.1443i	0.552882	−	0.957619i	−0.445183	−	0.895440i	$-0.646861\pi$
$359$	10.4756	−	18.1443i	0.552882	−	0.957619i	0.998065	−	0.0621798i	$-0.0198052\pi$
$360$	−8.44453	+	2.49407i	−0.445066	+	0.131449i
$361$	5.42818	+	9.40188i	0.285694	+	0.494836i
$362$	4.15120	+	3.48327i	0.218182	+	0.183077i
$363$	0.729187	−	1.17731i	0.0382724	−	0.0617925i
$364$	0.0957148	+	0.542825i	0.00501682	+	0.0284518i
$365$	−0.0645464	−	0.366061i	−0.00337851	−	0.0191605i
$366$	−10.5255	+	16.9938i	−0.550175	+	0.888282i
$367$	−18.2824	−	15.3407i	−0.954332	−	0.800780i	0.0256894	−	0.999670i	$-0.491822\pi$
$367$	−18.2824	−	15.3407i	−0.954332	−	0.800780i	−0.980022	+	0.198890i	$0.936266\pi$
$368$	−9.68503	−	16.7750i	−0.504867	−	0.874456i
$369$	−0.424782	+	0.125458i	−0.0221133	+	0.00653110i
$370$	−0.731434	+	1.26688i	−0.0380254	+	0.0658620i
$371$	12.3140	−	4.48194i	0.639313	−	0.232691i
$372$	0.348272	+	2.40874i	0.0180571	+	0.124887i
$373$	−8.04031	+	6.74662i	−0.416311	+	0.349327i	−0.826758	−	0.562558i	$-0.809817\pi$
$373$	−8.04031	+	6.74662i	−0.416311	+	0.349327i	0.410446	+	0.911885i	$0.365373\pi$
$374$	31.0610	+	11.3053i	1.60613	+	0.584582i
$375$	0.353393	−	1.69562i	0.0182491	−	0.0875612i
$376$	1.21873	−	6.91175i	0.0628511	−	0.356446i
$377$	−5.22011			−0.268849
$378$	−6.35553	−	3.00675i	−0.326893	−	0.154650i
$379$	3.08171			0.158297			0.0791483	−	0.996863i	$-0.474780\pi$
$379$	3.08171			0.158297			0.0791483	+	0.996863i	$0.474780\pi$
$380$	0.0838142	−	0.475334i	0.00429958	−	0.0243841i
$381$	−24.6326	+	8.11175i	−1.26197	+	0.415577i
$382$	0.121922	+	0.0443761i	0.00623809	+	0.00227048i
$383$	14.5802	−	12.2343i	0.745016	−	0.625142i	−0.189164	−	0.981946i	$-0.560578\pi$
$383$	14.5802	−	12.2343i	0.745016	−	0.625142i	0.934180	+	0.356803i	$0.116133\pi$
$384$	15.5549	+	6.21297i	0.793785	+	0.317054i
$385$	−3.22789	+	1.17485i	−0.164508	+	0.0598761i
$386$	2.60420	−	4.51060i	0.132550	−	0.229584i
$387$	5.40554	−	8.15276i	0.274779	−	0.414428i
$388$	0.00150246	+	0.00260234i	7.62759e−5	+	0.000132114i
$389$	2.48602	+	2.08602i	0.126046	+	0.105765i	0.703632	−	0.710565i	$-0.251561\pi$
$389$	2.48602	+	2.08602i	0.126046	+	0.105765i	−0.577585	+	0.816330i	$0.696005\pi$
$390$	7.63398	+	0.236281i	0.386562	+	0.0119646i
$391$	6.58401	+	37.3398i	0.332968	+	1.88835i
$392$	−0.509665	−	2.89046i	−0.0257420	−	0.145990i
$393$	−9.06023	−	16.8780i	−0.457028	−	0.851383i
$394$	5.68614	+	4.77123i	0.286463	+	0.240371i
$395$	−3.31922	−	5.74907i	−0.167008	−	0.289267i
$396$	−1.40193	+	1.03565i	−0.0704496	+	0.0520432i
$397$	1.14532	−	1.98376i	0.0574821	−	0.0995620i	−0.835852	−	0.548954i	$-0.815026\pi$
$397$	1.14532	−	1.98376i	0.0574821	−	0.0995620i	0.893335	+	0.449392i	$0.148359\pi$
$398$	19.0202	−	6.92280i	0.953398	−	0.347009i
$399$	3.88286	−	3.05849i	0.194386	−	0.153116i
$400$	−2.78313	+	2.33532i	−0.139157	+	0.116766i
$401$	−10.6188	−	3.86493i	−0.530278	−	0.193005i	0.0629844	−	0.998015i	$-0.479938\pi$
$401$	−10.6188	−	3.86493i	−0.530278	−	0.193005i	−0.593263	+	0.805009i	$0.702160\pi$
$402$	6.02520	+	5.38200i	0.300509	+	0.268430i
$403$	4.70138	−	26.6628i	0.234192	−	1.32817i
$404$	0.916843			0.0456147
$405$	5.42777	−	7.17909i	0.269708	−	0.356732i
$406$	2.16739			0.107566
$407$	−0.644881	+	3.65730i	−0.0319656	+	0.181286i
$408$	−26.9626	−	24.0844i	−1.33485	−	1.19235i
$409$	−26.8214	−	9.76218i	−1.32623	−	0.482709i	−0.420782	−	0.907162i	$-0.638244\pi$
$409$	−26.8214	−	9.76218i	−1.32623	−	0.482709i	−0.905450	+	0.424453i	$0.860466\pi$
$410$	−0.153034	+	0.128411i	−0.00755780	+	0.00634175i
$411$	−28.0449	+	22.0907i	−1.38335	+	1.08966i
$412$	−2.25061	+	0.819155i	−0.110880	+	0.0403569i
$413$	−1.01936	+	1.76559i	−0.0501597	+	0.0868791i
$414$	19.8403	+	8.64559i	0.975097	+	0.424908i
$415$	7.76754	+	13.4538i	0.381294	+	0.660420i
$416$	2.38197	+	1.99871i	0.116786	+	0.0979949i
$417$	−1.37048	−	2.55303i	−0.0671128	−	0.125022i
$418$	2.30324	+	13.0623i	0.112655	+	0.638900i
$419$	−3.97012	−	22.5157i	−0.193953	−	1.09996i	−0.913902	−	0.405936i	$-0.866946\pi$
$419$	−3.97012	−	22.5157i	−0.193953	−	1.09996i	0.719948	−	0.694028i	$-0.244166\pi$
$420$	0.292813	+	0.00906292i	0.0142878	+	0.000442225i
$421$	−11.2962	−	9.47863i	−0.550543	−	0.461960i	0.324582	−	0.945858i	$-0.394776\pi$
$421$	−11.2962	−	9.47863i	−0.550543	−	0.461960i	−0.875125	+	0.483897i	$0.839221\pi$
$422$	−10.2020	−	17.6703i	−0.496624	−	0.860178i
$423$	3.19578	+	6.42254i	0.155384	+	0.312274i
$424$	19.2309	−	33.3089i	0.933935	−	1.61762i
$425$	6.68274	−	2.43232i	0.324161	−	0.117985i
$426$	26.3657	+	10.5310i	1.27742	+	0.510229i
$427$	6.53379	−	5.48250i	0.316192	−	0.265317i
$428$	0.635548	+	0.231321i	0.0307204	+	0.0111813i
$429$	18.4165	−	6.06472i	0.889156	−	0.292807i
$430$	0.766133	−	4.34496i	0.0369462	−	0.209532i
$431$	−32.1874			−1.55041			−0.775207	−	0.631707i	$-0.782354\pi$
$431$	−32.1874			−1.55041			−0.775207	+	0.631707i	$0.782354\pi$
$432$	−18.2619	+	4.78463i	−0.878624	+	0.230201i
$433$	−29.1573			−1.40121			−0.700604	−	0.713550i	$-0.747086\pi$
$433$	−29.1573			−1.40121			−0.700604	+	0.713550i	$0.747086\pi$
$434$	−1.95201	+	11.0704i	−0.0936996	+	0.531397i
$435$	−0.566066	+	2.71604i	−0.0271408	+	0.130224i
$436$	−2.78566	−	1.01390i	−0.133409	−	0.0485569i
$437$	−11.6551	+	9.77976i	−0.557537	+	0.467829i
$438$	−0.124660	−	0.862179i	−0.00595647	−	0.0411965i
$439$	15.8769	−	5.77871i	0.757762	−	0.275803i	0.0658938	−	0.997827i	$-0.479010\pi$
$439$	15.8769	−	5.77871i	0.757762	−	0.275803i	0.691868	+	0.722024i	$0.256788\pi$
$440$	−5.04101	+	8.73128i	−0.240321	+	0.416247i
$441$	2.17448	+	2.06680i	0.103547	+	0.0984188i
$442$	15.6797	+	27.1580i	0.745807	+	1.29178i
$443$	−27.5591	−	23.1248i	−1.30937	−	1.09869i	−0.988443	−	0.151591i	$-0.951560\pi$
$443$	−27.5591	−	23.1248i	−1.30937	−	1.09869i	−0.320929	−	0.947103i	$-0.603995\pi$
$444$	0.166770	−	0.269257i	0.00791454	−	0.0127784i
$445$	−2.67966	−	15.1971i	−0.127028	−	0.720411i
$446$	3.57853	+	20.2949i	0.169448	+	0.960990i
$447$	19.5467	−	31.5591i	0.924528	−	1.49269i
$448$	−6.55526	−	5.50051i	−0.309707	−	0.259875i
$449$	17.9906	+	31.1607i	0.849030	+	1.47056i	0.882075	+	0.471109i	$0.156146\pi$
$449$	17.9906	+	31.1607i	0.849030	+	1.47056i	−0.0330454	+	0.999454i	$0.510521\pi$
$450$	0.950763	−	3.94637i	0.0448194	−	0.186034i
$451$	−0.253576	+	0.439206i	−0.0119404	+	0.0206814i
$452$	−1.72572	+	0.628110i	−0.0811709	+	0.0295438i
$453$	−1.26517	−	8.75022i	−0.0594427	−	0.411121i
$454$	−16.9436	+	14.2174i	−0.795204	+	0.667255i
$455$	−3.06236	−	1.11461i	−0.143566	−	0.0522536i
$456$	2.95993	−	14.2021i	0.138612	−	0.665073i
$457$	−7.33838	+	41.6180i	−0.343275	+	1.94681i	−0.0222053	+	0.999753i	$0.507069\pi$
$457$	−7.33838	+	41.6180i	−0.343275	+	1.94681i	−0.321070	+	0.947056i	$0.604042\pi$
$458$	−28.9269			−1.35166
$459$	36.7940	+	3.42521i	1.71740	+	0.159875i
$460$	−0.901757			−0.0420446
$461$	4.15653	−	23.5728i	0.193589	−	1.09790i	−0.720826	−	0.693116i	$-0.756237\pi$
$461$	4.15653	−	23.5728i	0.193589	−	1.09790i	0.914414	−	0.404780i	$-0.132652\pi$
$462$	−7.64652	+	2.51807i	−0.355748	+	0.117151i
$463$	17.8465	+	6.49559i	0.829397	+	0.301876i	0.721611	−	0.692298i	$-0.243402\pi$
$463$	17.8465	+	6.49559i	0.829397	+	0.301876i	0.107786	+	0.994174i	$0.465624\pi$
$464$	4.45803	−	3.74073i	0.206959	−	0.173659i
$465$	−13.3630	−	5.33745i	−0.619692	−	0.247518i
$466$	7.57874	−	2.75844i	0.351078	−	0.127782i
$467$	2.44130	−	4.22846i	0.112970	−	0.195670i	−0.803997	−	0.594634i	$-0.797297\pi$
$467$	2.44130	−	4.22846i	0.112970	−	0.195670i	0.916966	+	0.398964i	$0.130630\pi$
$468$	−1.65043	−	0.102264i	−0.0762913	−	0.00472714i
$469$	−1.72359	−	2.98535i	−0.0795881	−	0.137851i
$470$	2.47859	+	2.07978i	0.114329	+	0.0959331i
$471$	22.4563	+	0.695050i	1.03473	+	0.0320262i
$472$	1.03907	+	5.89286i	0.0478271	+	0.271241i
$473$	−1.94495	−	11.0304i	−0.0894290	−	0.507177i
$474$	−7.35848	−	13.7079i	−0.337986	−	0.629624i
$475$	2.18607	+	1.83433i	0.100304	+	0.0841647i
$476$	0.601419	+	1.04169i	0.0275660	+	0.0477457i
$477$	4.41926	+	39.0638i	0.202344	+	1.78861i
$478$	−5.82720	+	10.0930i	−0.266530	+	0.461644i
$479$	−33.2531	+	12.1031i	−1.51937	+	0.553007i	−0.960992	−	0.276577i	$-0.910800\pi$
$479$	−33.2531	+	12.1031i	−1.51937	+	0.553007i	−0.558382	+	0.829584i	$0.688578\pi$
$480$	1.29824	−	1.02261i	0.0592561	−	0.0466755i
$481$	−2.69899	+	2.26472i	−0.123063	+	0.103262i
$482$	−20.4433	−	7.44075i	−0.931166	−	0.338917i
$483$	−6.88700	−	6.15181i	−0.313369	−	0.279917i
$484$	−0.0234825	+	0.133176i	−0.00106739	+	0.00605346i
$485$	−0.0177662			−0.000806723
$486$	13.2351	−	16.4235i	0.600356	−	0.744986i
$487$	−24.6900			−1.11881			−0.559404	−	0.828895i	$-0.688970\pi$
$487$	−24.6900			−1.11881			−0.559404	+	0.828895i	$0.688970\pi$
$488$	4.34707	−	24.6534i	0.196782	−	1.11601i
$489$	−26.8767	−	24.0076i	−1.21541	−	1.08566i
$490$	1.27149	+	0.462785i	0.0574402	+	0.0209065i
$491$	29.6187	−	24.8530i	1.33667	−	1.12160i	0.354204	−	0.935168i	$-0.384752\pi$
$491$	29.6187	−	24.8530i	1.33667	−	1.12160i	0.982468	−	0.186432i	$-0.0596924\pi$
$492$	0.0339770	−	0.0267634i	0.00153180	−	0.00120659i
$493$	−10.7044	+	3.89610i	−0.482104	+	0.175471i
$494$	−6.29184	+	10.8978i	−0.283083	+	0.490315i
$495$	−1.15842	−	10.2398i	−0.0520672	−	0.460246i
$496$	15.0916	+	26.1393i	0.677631	+	1.17369i
$497$	−9.27998	−	7.78682i	−0.416264	−	0.349287i
$498$	17.2201	+	32.0787i	0.771650	+	1.43748i
$499$	3.11323	+	17.6560i	0.139367	+	0.790392i	0.971718	+	0.236143i	$0.0758833\pi$
$499$	3.11323	+	17.6560i	0.139367	+	0.790392i	−0.832351	+	0.554249i	$0.813006\pi$
$500$	0.0293703	+	0.166567i	0.00131348	+	0.00744911i
$501$	−18.2764	−	0.565678i	−0.816531	−	0.0252726i
$502$	−6.42532	−	5.39148i	−0.286776	−	0.240634i
$503$	−0.902416	−	1.56303i	−0.0402367	−	0.0696921i	0.845206	−	0.534441i	$-0.179478\pi$
$503$	−0.902416	−	1.56303i	−0.0402367	−	0.0696921i	−0.885442	+	0.464749i	$0.846145\pi$
$504$	8.78828	+	0.544538i	0.391461	+	0.0242556i
$505$	−2.71036	+	4.69448i	−0.120609	+	0.208902i
$506$	23.2861	−	8.47546i	1.03520	−	0.376780i
$507$	−3.82755	−	1.52880i	−0.169988	−	0.0678966i
$508$	1.93999	−	1.62784i	0.0860730	−	0.0722238i
$509$	34.2694	+	12.4730i	1.51896	+	0.552857i	0.960889	−	0.276934i	$-0.0893183\pi$
$509$	34.2694	+	12.4730i	1.51896	+	0.552857i	0.558074	+	0.829791i	$0.311541\pi$
$510$	15.8307	−	5.21320i	0.700996	−	0.230844i
$511$	−0.0645464	+	0.366061i	−0.00285536	+	0.0161936i
$512$	−24.7932			−1.09572
$513$	6.19193	+	13.4736i	0.273380	+	0.594875i
$514$	−29.9073			−1.31916
$515$	2.45893	−	13.9453i	0.108354	−	0.614503i
$516$	−0.194896	+	0.935129i	−0.00857980	+	0.0411668i
$517$	7.71863	+	2.80935i	0.339465	+	0.123555i
$518$	1.12062	−	0.940313i	0.0492373	−	0.0413150i
$519$	0.247837	+	1.71410i	0.0108788	+	0.0752408i
$520$	−8.98817	+	3.27143i	−0.394157	+	0.143462i
$521$	−4.46285	+	7.72989i	−0.195521	+	0.338653i	−0.947071	−	0.321023i	$-0.895973\pi$
$521$	−4.46285	+	7.72989i	−0.195521	+	0.338653i	0.751550	+	0.659676i	$0.229307\pi$
$522$	−1.52294	+	6.32131i	−0.0666571	+	0.276676i
$523$	4.72752	+	8.18830i	0.206720	+	0.358049i	0.950679	−	0.310175i	$-0.100388\pi$
$523$	4.72752	+	8.18830i	0.206720	+	0.358049i	−0.743959	+	0.668225i	$0.767054\pi$
$524$	1.43297	+	1.20241i	0.0625997	+	0.0525274i
$525$	−0.912015	+	1.47249i	−0.0398036	+	0.0642647i
$526$	2.17560	+	12.3384i	0.0948606	+	0.537981i
$527$	−10.2594	−	58.1842i	−0.446908	−	2.53454i
$528$	−11.3819	+	18.3766i	−0.495333	+	0.799738i
$529$	4.15590	+	3.48722i	0.180691	+	0.151618i
$530$	8.86569	+	15.3558i	0.385101	+	0.667014i
$531$	−4.43317	−	4.21364i	−0.192383	−	0.182856i
$532$	−0.241333	+	0.418002i	−0.0104631	+	0.0181227i
$533$	−0.452129	+	0.164561i	−0.0195839	+	0.00712794i
$534$	−5.17527	−	35.7936i	−0.223956	−	1.54894i
$535$	−3.06322	+	2.57035i	−0.132435	+	0.111126i
$536$	−9.50748	−	3.46044i	−0.410661	−	0.149468i
$537$	7.95503	−	38.1691i	0.343285	−	1.64712i
$538$	1.10108	−	6.24455i	0.0474710	−	0.269222i
$539$	3.43504			0.147958
$540$	−0.232180	+	0.847637i	−0.00999144	+	0.0364765i
$541$	−22.9241			−0.985582			−0.492791	−	0.870148i	$-0.664023\pi$
$541$	−22.9241			−0.985582			−0.492791	+	0.870148i	$0.664023\pi$
$542$	−2.88289	+	16.3497i	−0.123831	+	0.702280i
$543$	6.58864	−	2.16970i	0.282745	−	0.0931107i
$544$	6.37627	+	2.32077i	0.273380	+	0.0995024i
$545$	13.4264	−	11.2661i	0.575122	−	0.482585i
$546$	−7.09279	−	2.83301i	−0.303543	−	0.121242i
$547$	0.523127	−	0.190403i	0.0223673	−	0.00814104i	−0.330812	−	0.943697i	$-0.607323\pi$
$547$	0.523127	−	0.190403i	0.0223673	−	0.00814104i	0.353180	+	0.935556i	$0.385100\pi$
$548$	1.74309	−	3.01912i	0.0744612	−	0.128971i
$549$	11.3990	+	22.9085i	0.486496	+	0.977709i
$550$	−2.32397	−	4.02523i	−0.0990944	−	0.171637i
$551$	−3.50165	−	2.93823i	−0.149175	−	0.125173i
$552$	−27.0906	−	0.838487i	−1.15305	−	0.0356884i
$553$	1.15275	+	6.53760i	0.0490201	+	0.278007i
$554$	−2.97515	−	16.8729i	−0.126402	−	0.716861i
$555$	0.885666	+	1.64988i	0.0375944	+	0.0700335i
$556$	0.216756	+	0.181880i	0.00919252	+	0.00771344i
$557$	2.92950	+	5.07404i	0.124127	+	0.214994i	0.921391	−	0.388636i	$-0.127054\pi$
$557$	2.92950	+	5.07404i	0.124127	+	0.214994i	−0.797264	+	0.603630i	$0.793720\pi$
$558$	−30.9158	−	13.4719i	−1.30877	−	0.570309i
$559$	5.31308	−	9.20253i	0.224719	−	0.389226i
$560$	3.41402	−	1.24260i	0.144268	−	0.0525094i
$561$	33.2386	−	26.1818i	1.40334	−	1.10540i
$562$	−33.0179	+	27.7053i	−1.39278	+	1.16868i
$563$	28.7133	+	10.4508i	1.21012	+	0.440448i	0.866746	−	0.498751i	$-0.166208\pi$
$563$	28.7133	+	10.4508i	1.21012	+	0.440448i	0.343375	+	0.939198i	$0.388430\pi$
$564$	−0.522442	−	0.466672i	−0.0219988	−	0.0196504i
$565$	1.88545	−	10.6929i	0.0793216	−	0.449855i
$566$	−29.9458			−1.25871
$567$	−7.55583	+	4.88973i	−0.317315	+	0.205349i
$568$	−35.5556			−1.49188
$569$	−1.57107	+	8.90997i	−0.0658626	+	0.373525i	0.934005	+	0.357260i	$0.116289\pi$
$569$	−1.57107	+	8.90997i	−0.0658626	+	0.373525i	−0.999868	+	0.0162658i	$0.994822\pi$
$570$	4.98788	+	4.45542i	0.208919	+	0.186617i
$571$	−10.4771	−	3.81337i	−0.438455	−	0.159584i	0.113355	−	0.993555i	$-0.463840\pi$
$571$	−10.4771	−	3.81337i	−0.438455	−	0.159584i	−0.551810	+	0.833970i	$0.686062\pi$
$572$	−1.45042	+	1.21705i	−0.0606453	+	0.0508874i
$573$	0.130470	−	0.102770i	0.00545047	−	0.00429329i
$574$	0.187724	−	0.0683259i	0.00783544	−	0.00285187i
$575$	2.66576	−	4.61724i	0.111170	−	0.192552i
$576$	20.6486	−	15.2538i	0.860360	−	0.635573i
$577$	14.8261	+	25.6795i	0.617218	+	1.06905i	0.989991	+	0.141130i	$0.0450737\pi$
$577$	14.8261	+	25.6795i	0.617218	+	1.06905i	−0.372773	+	0.927923i	$0.621593\pi$
$578$	34.8017	+	29.2021i	1.44756	+	1.21465i
$579$	−3.15333	−	5.87424i	−0.131048	−	0.244125i
$580$	−0.0470455	−	0.266808i	−0.00195346	−	0.0110786i
$581$	−2.69764	−	15.2991i	−0.111917	−	0.634713i
$582$	−0.0416175	−	0.00128811i	−0.00172510	−	5.33939e-5i
$583$	34.4827	+	28.9344i	1.42813	+	1.19834i
$584$	0.545490	+	0.944816i	0.0225725	+	0.0390968i
$585$	5.40261	−	8.14834i	0.223370	−	0.336893i
$586$	−0.611827	+	1.05972i	−0.0252743	+	0.0437764i
$587$	22.7837	−	8.29260i	0.940385	−	0.342272i	0.174067	−	0.984734i	$-0.444309\pi$
$587$	22.7837	−	8.29260i	0.940385	−	0.342272i	0.766318	+	0.642462i	$0.222087\pi$
$588$	−0.272055	−	0.108664i	−0.0112194	−	0.00448124i
$589$	18.1613	−	15.2392i	0.748325	−	0.627919i
$590$	−2.59223	−	0.943494i	−0.106720	−	0.0388430i
$591$	9.02483	−	2.97196i	0.371232	−	0.122250i
$592$	0.682067	−	3.86819i	0.0280328	−	0.158982i
$593$	27.1109			1.11331			0.556656	−	0.830743i	$-0.312084\pi$
$593$	27.1109			1.11331			0.556656	+	0.830743i	$0.312084\pi$
$594$	−1.97119	−	24.0708i	−0.0808789	−	0.987638i
$595$	−7.11163			−0.291548
$596$	−0.629477	+	3.56994i	−0.0257844	+	0.146231i
$597$	5.28640	−	25.3647i	0.216358	−	1.03811i
$598$	22.0920	+	8.04084i	0.903410	+	0.328815i
$599$	13.7959	−	11.5762i	0.563687	−	0.472989i	−0.315857	−	0.948807i	$-0.602292\pi$
$599$	13.7959	−	11.5762i	0.563687	−	0.472989i	0.879544	+	0.475817i	$0.157848\pi$
$600$	0.727463	+	5.03133i	0.0296986	+	0.205403i
$601$	17.4633	−	6.35612i	0.712343	−	0.259272i	0.0396714	−	0.999213i	$-0.487369\pi$
$601$	17.4633	−	6.35612i	0.712343	−	0.259272i	0.672672	+	0.739941i	$0.265147\pi$
$602$	−2.20599	+	3.82089i	−0.0899095	+	0.155728i
$603$	9.91803	−	2.92927i	0.403893	−	0.119289i
$604$	0.431677	+	0.747687i	0.0175647	+	0.0304230i
$605$	−0.612479	−	0.513931i	−0.0249008	−	0.0208942i
$606$	−6.68940	+	10.8003i	−0.271738	+	0.438734i
$607$	−5.16364	−	29.2844i	−0.209586	−	1.18862i	−0.890059	−	0.455846i	$-0.849337\pi$
$607$	−5.16364	−	29.2844i	−0.209586	−	1.18862i	0.680473	−	0.732773i	$-0.261774\pi$
$608$	0.472816	+	2.68147i	0.0191752	+	0.108748i
$609$	1.46087	−	2.35864i	0.0591974	−	0.0955769i
$610$	8.84083	+	7.41834i	0.357955	+	0.300360i
$611$	3.89639	+	6.74875i	0.157631	+	0.273025i
$612$	−3.46073	+	1.02212i	−0.139892	+	0.0413167i
$613$	5.64352	−	9.77487i	0.227940	−	0.394803i	−0.729258	−	0.684239i	$-0.760134\pi$
$613$	5.64352	−	9.77487i	0.227940	−	0.394803i	0.957197	+	0.289436i	$0.0934678\pi$
$614$	−7.85750	+	2.85990i	−0.317103	+	0.115416i
$615$	0.0365933	+	0.253089i	0.00147558	+	0.0102055i
$616$	7.72327	−	6.48059i	0.311179	−	0.261111i
$617$	−0.293118	−	0.106686i	−0.0118005	−	0.00429502i	0.336113	−	0.941822i	$-0.390888\pi$
$617$	−0.293118	−	0.106686i	−0.0118005	−	0.00429502i	−0.347914	+	0.937527i	$0.613110\pi$
$618$	6.77115	−	32.4887i	0.272375	−	1.30689i
$619$	−2.68189	+	15.2098i	−0.107794	+	0.611333i	0.882273	+	0.470738i	$0.156012\pi$
$619$	−2.68189	+	15.2098i	−0.107794	+	0.611333i	−0.990067	+	0.140594i	$0.955099\pi$
$620$	1.40515			0.0564322
$621$	22.7813	−	15.7637i	0.914181	−	0.632574i
$622$	34.1974			1.37119
$623$	−2.67966	+	15.1971i	−0.107358	+	0.608859i
$624$	−19.4784	+	6.41443i	−0.779761	+	0.256783i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	10.3004	−	8.64306i	0.411687	−	0.345446i
$627$	15.7674	+	6.29783i	0.629689	+	0.251511i
$628$	−2.06162	+	0.750370i	−0.0822677	+	0.0299430i
$629$	−3.84429	+	6.65850i	−0.153282	+	0.265492i
$630$	−2.24316	+	3.38319i	−0.0893697	+	0.134790i
$631$	−3.38085	−	5.85580i	−0.134590	−	0.233116i	0.790851	−	0.612009i	$-0.209638\pi$
$631$	−3.38085	−	5.85580i	−0.134590	−	0.233116i	−0.925441	+	0.378893i	$0.876305\pi$
$632$	14.9257	+	12.5242i	0.593714	+	0.498185i
$633$	−26.1059	−	0.808009i	−1.03762	−	0.0321155i
$634$	7.23676	+	41.0417i	0.287408	+	1.62997i
$635$	2.60002	+	14.7455i	0.103179	+	0.585156i
$636$	−1.81571	−	3.38243i	−0.0719975	−	0.134122i
$637$	2.49646	+	2.09478i	0.0989133	+	0.0829981i
$638$	3.72254	+	6.44763i	0.147377	+	0.255264i
$639$	29.2313	−	21.5940i	1.15637	−	0.854247i
$640$	4.83526	−	8.37492i	0.191130	−	0.331048i
$641$	−29.0064	+	10.5575i	−1.14568	+	0.416995i	−0.843963	−	0.536402i	$-0.819783\pi$
$641$	−29.0064	+	10.5575i	−1.14568	+	0.416995i	−0.301721	+	0.953396i	$0.597561\pi$
$642$	−7.36197	+	5.79896i	−0.290554	+	0.228867i
$643$	−27.8195	+	23.3433i	−1.09709	+	0.920570i	−0.997226	−	0.0744309i	$-0.976286\pi$
$643$	−27.8195	+	23.3433i	−1.09709	+	0.920570i	−0.0998663	+	0.995001i	$0.531842\pi$
$644$	0.847374	+	0.308419i	0.0333912	+	0.0121534i
$645$	−4.21196	−	3.76233i	−0.165846	−	0.148142i
$646$	−4.76844	+	27.0432i	−0.187612	+	1.06400i
$647$	45.3306			1.78213			0.891065	−	0.453877i	$-0.149959\pi$
$647$	45.3306			1.78213			0.891065	+	0.453877i	$0.149959\pi$
$648$	−7.76333	+	25.2489i	−0.304972	+	0.991869i
$649$	−7.00313			−0.274897
$650$	0.765718	−	4.34260i	0.0300339	−	0.170331i
$651$	10.7316	+	9.58596i	0.420603	+	0.375703i
$652$	3.30691	+	1.20362i	0.129508	+	0.0471372i
$653$	13.8982	−	11.6620i	0.543879	−	0.456369i	−0.328983	−	0.944336i	$-0.606706\pi$
$653$	13.8982	−	11.6620i	0.543879	−	0.456369i	0.872862	+	0.487967i	$0.162261\pi$
$654$	32.2682	−	25.4174i	1.26179	−	0.993897i
$655$	−10.3928	+	3.78266i	−0.406080	+	0.147801i
$656$	0.268198	−	0.464532i	0.0104714	−	0.0181369i
$657$	−1.02228	−	0.445469i	−0.0398830	−	0.0173794i
$658$	−1.61778	−	2.80208i	−0.0630677	−	0.109236i
$659$	14.0048	+	11.7514i	0.545550	+	0.457771i	0.873431	−	0.486948i	$-0.161890\pi$
$659$	14.0048	+	11.7514i	0.545550	+	0.457771i	−0.327881	+	0.944719i	$0.606334\pi$
$660$	0.475953	+	0.886637i	0.0185264	+	0.0345123i
$661$	−5.78982	−	32.8357i	−0.225198	−	1.27716i	−0.862306	−	0.506387i	$-0.830981\pi$
$661$	−5.78982	−	32.8357i	−0.225198	−	1.27716i	0.637108	−	0.770774i	$-0.280130\pi$
$662$	−0.646113	−	3.66429i	−0.0251119	−	0.142417i
$663$	40.1229	+	1.24185i	1.55824	+	0.0482295i
$664$	−34.9287	−	29.3087i	−1.35550	−	1.13740i
$665$	−1.42685	−	2.47138i	−0.0553310	−	0.0958361i
$666$	1.95506	+	3.92907i	0.0757569	+	0.152248i
$667$	−4.27003	+	7.39590i	−0.165336	+	0.286371i
$668$	1.67789	−	0.610701i	0.0649194	−	0.0236287i
$669$	24.4977	+	9.78489i	0.947135	+	0.378306i
$670$	3.57311	−	2.99820i	0.138041	−	0.115830i
$671$	27.5315	+	10.0206i	1.06284	+	0.386842i
$672$	−1.56970	+	0.516916i	−0.0605524	+	0.0199405i
$673$	2.68544	−	15.2299i	0.103516	−	0.587069i	−0.888287	−	0.459290i	$-0.848104\pi$
$673$	2.68544	−	15.2299i	0.103516	−	0.587069i	0.991803	−	0.127779i	$-0.0407849\pi$
$674$	−15.2878			−0.588865
$675$	−3.65376	−	3.69460i	−0.140633	−	0.142205i
$676$	0.402477			0.0154799
$677$	0.305188	−	1.73081i	0.0117293	−	0.0665204i	−0.978381	−	0.206809i	$-0.933692\pi$
$677$	0.305188	−	1.73081i	0.0117293	−	0.0665204i	0.990111	+	0.140289i	$0.0448031\pi$
$678$	5.19196	−	24.9116i	0.199396	−	0.956723i
$679$	0.0166948	+	0.00607641i	0.000640687	+	0.000233191i
$680$	−15.9896	+	13.4169i	−0.613173	+	0.514514i
$681$	4.05154	+	28.0216i	0.155255	+	1.07379i
$682$	−36.2853	+	13.2068i	−1.38944	+	0.505713i
$683$	9.94399	−	17.2235i	0.380496	−	0.659039i	−0.610637	−	0.791911i	$-0.709087\pi$
$683$	9.94399	−	17.2235i	0.380496	−	0.659039i	0.991133	+	0.132872i	$0.0424199\pi$
$684$	−1.04955	−	0.997574i	−0.0401305	−	0.0381432i
$685$	10.3058	+	17.8502i	0.393765	+	0.682021i
$686$	−1.03653	−	0.869752i	−0.0395749	−	0.0332073i
$687$	−19.4973	+	31.4793i	−0.743870	+	1.20101i
$688$	2.05710	+	11.6664i	0.0784263	+	0.444778i
$689$	7.41576	+	42.0568i	0.282518	+	1.60224i
$690$	6.57933	−	10.6226i	0.250471	−	0.404396i
$691$	−4.60258	−	3.86202i	−0.175090	−	0.146918i	0.551031	−	0.834485i	$-0.314235\pi$
$691$	−4.60258	−	3.86202i	−0.175090	−	0.146918i	−0.726122	+	0.687566i	$0.758679\pi$
$692$	−0.0845624	−	0.146466i	−0.00321458	−	0.00556782i
$693$	−2.41366	+	10.0185i	−0.0916875	+	0.380571i
$694$	7.02094	−	12.1606i	0.266511	−	0.461611i
$695$	−1.57205	+	0.572179i	−0.0596312	+	0.0217040i
$696$	−1.16525	−	8.05920i	−0.0441688	−	0.305483i
$697$	−0.804319	+	0.674904i	−0.0304658	+	0.0255638i
$698$	−32.8608	−	11.9604i	−1.24380	−	0.452706i
$699$	2.10640	−	10.1067i	0.0796714	−	0.382272i
$700$	0.0293703	−	0.166567i	0.00111009	−	0.00629565i
$701$	−32.8851			−1.24205			−0.621027	−	0.783789i	$-0.713284\pi$
$701$	−32.8851			−1.24205			−0.621027	+	0.783789i	$0.713284\pi$
$702$	13.2464	−	18.6958i	0.499954	−	0.705629i
$703$	−3.08522			−0.116361
$704$	5.10433	−	28.9481i	0.192377	−	1.09102i
$705$	3.93392	−	1.29548i	0.148160	−	0.0487905i
$706$	−3.55681	−	1.29457i	−0.133862	−	0.0487219i
$707$	4.15251	−	3.48437i	0.156171	−	0.131043i
$708$	0.554646	+	0.221537i	0.0208449	+	0.00832588i
$709$	−19.2308	+	6.99942i	−0.722226	+	0.262869i	−0.676871	−	0.736102i	$-0.736664\pi$
$709$	−19.2308	+	6.99942i	−0.722226	+	0.262869i	−0.0453557	+	0.998971i	$0.514442\pi$
$710$	8.19579	−	14.1955i	0.307583	−	0.532749i
$711$	−19.8772	−	1.23163i	−0.745454	−	0.0461897i
$712$	22.6461	+	39.2242i	0.848700	+	1.46999i
$713$	−33.9305	−	28.4710i	−1.27071	−	1.06625i
$714$	−16.6590	−	0.515617i	−0.623448	−	0.0192965i
$715$	−1.94390	−	11.0244i	−0.0726976	−	0.412289i
$716$	0.661138	+	3.74950i	0.0247079	+	0.140125i
$717$	7.05595	+	13.1443i	0.263509	+	0.490883i
$718$	−21.7166	−	18.2224i	−0.810456	−	0.680053i
$719$	−12.2295	−	21.1821i	−0.456083	−	0.789959i	0.542667	−	0.839948i	$-0.317415\pi$
$719$	−12.2295	−	21.1821i	−0.456083	−	0.789959i	−0.998750	+	0.0499891i	$0.984081\pi$
$720$	1.22522	+	10.8303i	0.0456613	+	0.403620i
$721$	−7.08022	+	12.2633i	−0.263681	+	0.456709i
$722$	13.8038	−	5.02416i	0.513723	−	0.186980i
$723$	−21.8766	+	17.2320i	−0.813598	+	0.640864i
$724$	−0.518900	+	0.435409i	−0.0192848	+	0.0161819i
$725$	1.50520	+	0.547849i	0.0559018	+	0.0203466i
$726$	−1.39747	−	1.24829i	−0.0518651	−	0.0463285i
$727$	0.665639	−	3.77503i	0.0246872	−	0.140008i	−0.969973	−	0.243213i	$-0.921799\pi$
$727$	0.665639	−	3.77503i	0.0246872	−	0.140008i	0.994660	+	0.103205i	$0.0329097\pi$
$728$	9.56501			0.354503
$729$	−8.95197	−	25.4728i	−0.331554	−	0.943436i
$730$	−0.502956			−0.0186152
$731$	4.02666	−	22.8363i	0.148932	−	0.844633i
$732$	−1.86349	−	1.66456i	−0.0688767	−	0.0615241i
$733$	−2.37740	−	0.865303i	−0.0878113	−	0.0319607i	0.297741	−	0.954647i	$-0.403767\pi$
$733$	−2.37740	−	0.865303i	−0.0878113	−	0.0319607i	−0.385552	+	0.922686i	$0.625989\pi$
$734$	−24.7378	+	20.7575i	−0.913088	+	0.766172i
$735$	1.36064	−	1.07176i	0.0501878	−	0.0395325i
$736$	4.78024	−	1.73986i	0.176202	−	0.0641322i
$737$	5.92062	−	10.2548i	0.218089	−	0.377741i
$738$	0.0673702	+	0.595516i	0.00247993	+	0.0219212i
$739$	7.66277	+	13.2723i	0.281879	+	0.488229i	0.971848	−	0.235610i	$-0.0757089\pi$
$739$	7.66277	+	13.2723i	0.281879	+	0.488229i	−0.689968	+	0.723840i	$0.742376\pi$
$740$	−0.140078	−	0.117539i	−0.00514936	−	0.00432082i
$741$	7.61857	+	14.1924i	0.279875	+	0.521370i
$742$	−3.07902	−	17.4620i	−0.113034	−	0.641050i
$743$	−8.35428	−	47.3795i	−0.306489	−	1.73819i	−0.616412	−	0.787424i	$-0.711415\pi$
$743$	−8.35428	−	47.3795i	−0.306489	−	1.73819i	0.309923	−	0.950762i	$-0.399697\pi$
$744$	42.2136	+	1.30656i	1.54762	+	0.0479008i
$745$	−16.4182	−	13.7765i	−0.601517	−	0.504732i
$746$	7.10095	+	12.2992i	0.259984	+	0.450306i
$747$	46.5161	+	2.88222i	1.70193	+	0.105455i
$748$	−2.06590	+	3.57825i	−0.0755368	+	0.130834i
$749$	3.75760	−	1.36765i	0.137300	−	0.0499730i
$750$	−2.17644	−	0.869315i	−0.0794723	−	0.0317429i
$751$	−14.6145	+	12.2630i	−0.533291	+	0.447484i	−0.869236	−	0.494398i	$-0.835389\pi$
$751$	−14.6145	+	12.2630i	−0.533291	+	0.447484i	0.335945	+	0.941881i	$0.390944\pi$
$752$	−8.16371	−	2.97135i	−0.297700	−	0.108354i
$753$	−10.1980	+	3.35831i	−0.371637	+	0.122384i
$754$	−1.22653	+	6.95600i	−0.0446676	+	0.253322i
$755$	−5.10448			−0.185771
$756$	0.508087	−	0.717108i	0.0184789	−	0.0260810i
$757$	−9.78813			−0.355756			−0.177878	−	0.984053i	$-0.556923\pi$
$757$	−9.78813			−0.355756			−0.177878	+	0.984053i	$0.556923\pi$
$758$	0.724085	−	4.10649i	0.0262999	−	0.149154i
$759$	6.47205	−	31.0536i	0.234920	−	1.12717i
$760$	−7.87064	−	2.86468i	−0.285498	−	0.103913i
$761$	−6.22407	+	5.22262i	−0.225622	+	0.189320i	−0.748591	−	0.663033i	$-0.769269\pi$
$761$	−6.22407	+	5.22262i	−0.225622	+	0.189320i	0.522968	+	0.852352i	$0.324825\pi$
$762$	5.02147	+	34.7298i	0.181909	+	1.25813i
$763$	−16.4699	+	5.99455i	−0.596250	+	0.217017i
$764$	−0.00810919	+	0.0140455i	−0.000293380	+	0.000508150i
$765$	4.99704	−	20.7414i	0.180668	−	0.749908i
$766$	−12.8768	−	22.3033i	−0.465259	−	0.805851i
$767$	−5.08961	−	4.27069i	−0.183775	−	0.154206i
$768$	−3.67491	+	5.93330i	−0.132607	+	0.214100i
$769$	9.51050	+	53.9367i	0.342957	+	1.94501i	0.326662	+	0.945141i	$0.394076\pi$
$769$	9.51050	+	53.9367i	0.342957	+	1.94501i	0.0162954	+	0.999867i	$0.494813\pi$
$770$	0.807106	+	4.57733i	0.0290861	+	0.164955i
$771$	−20.1582	+	32.5463i	−0.725980	+	1.17213i
$772$	0.498733	+	0.418487i	0.0179498	+	0.0150617i
$773$	−17.3563	−	30.0620i	−0.624263	−	1.08125i	−0.988683	−	0.150020i	$-0.952066\pi$
$773$	−17.3563	−	30.0620i	−0.624263	−	1.08125i	0.364420	−	0.931235i	$-0.381267\pi$
$774$	−9.59377	−	9.11867i	−0.344841	−	0.327764i
$775$	−4.15388	+	7.19474i	−0.149212	+	0.258443i
$776$	0.0490000	−	0.0178345i	0.00175900	−	0.000640222i
$777$	−0.267962	−	1.85330i	−0.00961308	−	0.0664866i
$778$	3.36382	−	2.82258i	0.120599	−	0.101194i
$779$	−0.395914	−	0.144101i	−0.0141851	−	0.00516295i
$780$	−0.194790	+	0.934622i	−0.00697460	+	0.0334648i
$781$	7.22596	−	40.9805i	0.258565	−	1.46640i
$782$	51.3037			1.83461
$783$	5.85260	+	5.91802i	0.209155	+	0.211493i
$784$	−3.63312			−0.129754
$785$	2.25245	−	12.7743i	0.0803935	−	0.455934i
$786$	−24.6194	+	8.10740i	−0.878145	+	0.289181i
$787$	33.0476	+	12.0283i	1.17802	+	0.428764i	0.855502	−	0.517800i	$-0.173249\pi$
$787$	33.0476	+	12.0283i	1.17802	+	0.428764i	0.322517	+	0.946564i	$0.395471\pi$
$788$	−0.710767	+	0.596404i	−0.0253200	+	0.0212460i
$789$	14.8936	+	5.94880i	0.530225	+	0.211783i
$790$	−8.44074	+	3.07218i	−0.300308	+	0.109303i
$791$	−5.42895	+	9.40321i	−0.193031	+	0.334340i
$792$	13.4742	+	27.0790i	0.478784	+	0.962209i
$793$	13.8980	+	24.0720i	0.493532	+	0.854822i
$794$	−2.37432	−	1.99229i	−0.0842616	−	0.0707039i
$795$	22.6865	+	0.702174i	0.804607	+	0.0249036i
$796$	0.439350	+	2.49168i	0.0155723	+	0.0883151i
$797$	−4.68026	−	26.5431i	−0.165783	−	0.940205i	−0.948253	−	0.317516i	$-0.897151\pi$
$797$	−4.68026	−	26.5431i	−0.165783	−	0.940205i	0.782470	−	0.622689i	$-0.213960\pi$
$798$	−3.16323	−	5.89268i	−0.111977	−	0.208599i
$799$	13.0270	+	10.9310i	0.460863	+	0.386710i
$800$	−0.477070	−	0.826310i	−0.0168670	−	0.0292145i
$801$	−42.4402	−	18.4937i	−1.49955	−	0.653444i
$802$	−7.64519	+	13.2418i	−0.269961	+	0.467586i
$803$	−1.19983	+	0.436703i	−0.0423411	+	0.0154109i
$804$	−0.793313	+	0.624886i	−0.0279780	+	0.0220380i
$805$	−4.08418	+	3.42704i	−0.143949	+	0.120787i
$806$	−34.4246	−	12.5295i	−1.21255	−	0.441334i
$807$	−6.05341	−	5.40721i	−0.213090	−	0.190343i
$808$	2.76275	−	15.6684i	0.0971933	−	0.551211i
$809$	−11.7684			−0.413755			−0.206878	−	0.978367i	$-0.566330\pi$
$809$	−11.7684			−0.413755			−0.206878	+	0.978367i	$0.566330\pi$
$810$	−8.29108	−	8.91953i	−0.291319	−	0.313400i
$811$	6.97425			0.244899			0.122449	−	0.992475i	$-0.460925\pi$
$811$	6.97425			0.244899			0.122449	+	0.992475i	$0.460925\pi$
$812$	−0.0470455	+	0.266808i	−0.00165097	+	0.00936313i
$813$	15.8493	+	14.1573i	0.555858	+	0.496520i
$814$	4.72197	+	1.71866i	0.165505	+	0.0602389i
$815$	−15.9387	+	13.3741i	−0.558307	+	0.468475i
$816$	−35.1553	+	27.6915i	−1.23068	+	0.969396i
$817$	8.74382	−	3.18249i	0.305908	−	0.111341i
$818$	−19.3105	+	33.4467i	−0.675175	+	1.16944i
$819$	−7.86369	+	5.80914i	−0.274779	+	0.202988i
$820$	−0.0124857	−	0.0216259i	−0.000436020	−	0.000755209i
$821$	10.3301	+	8.66795i	0.360522	+	0.302513i	0.804999	−	0.593277i	$-0.202166\pi$
$821$	10.3301	+	8.66795i	0.360522	+	0.302513i	−0.444477	+	0.895790i	$0.646610\pi$
$822$	22.8472	+	42.5614i	0.796888	+	1.48450i
$823$	−0.297765	−	1.68871i	−0.0103794	−	0.0588647i	0.979178	−	0.203003i	$-0.0650701\pi$
$823$	−0.297765	−	1.68871i	−0.0103794	−	0.0588647i	−0.989558	+	0.144138i	$0.953959\pi$
$824$	7.21708	+	40.9301i	0.251419	+	1.42587i
$825$	−5.94682	−	0.184061i	−0.207042	−	0.00640820i
$826$	2.11320	+	1.77319i	0.0735278	+	0.0616972i
$827$	17.2364	+	29.8544i	0.599370	+	1.03814i	0.992914	+	0.118833i	$0.0379153\pi$
$827$	17.2364	+	29.8544i	0.599370	+	1.03814i	−0.393545	+	0.919305i	$0.628751\pi$
$828$	−1.49493	+	2.25470i	−0.0519526	+	0.0783561i
$829$	2.44207	−	4.22979i	0.0848167	−	0.146907i	−0.820496	−	0.571652i	$-0.806303\pi$
$829$	2.44207	−	4.22979i	0.0848167	−	0.146907i	0.905313	+	0.424745i	$0.139636\pi$
$830$	19.7527	−	7.18941i	0.685628	−	0.249548i
$831$	−20.3671	−	8.13503i	−0.706526	−	0.282201i
$832$	21.3629	−	17.9256i	0.740625	−	0.621458i
$833$	6.68274	+	2.43232i	0.231543	+	0.0842749i
$834$	−3.72402	+	1.22635i	−0.128952	+	0.0424651i
$835$	−1.83320	+	10.3966i	−0.0634404	+	0.359788i
$836$	−1.65798			−0.0573425
$837$	−35.4986	+	24.5635i	−1.22701	+	0.849038i
$838$	−30.9358			−1.06866
$839$	−5.55085	+	31.4804i	−0.191637	+	1.08682i	0.725491	+	0.688232i	$0.241613\pi$
$839$	−5.55085	+	31.4804i	−0.191637	+	1.08682i	−0.917128	+	0.398593i	$0.869498\pi$
$840$	1.03722	−	4.97671i	0.0357876	−	0.171713i
$841$	24.8400	+	9.04104i	0.856553	+	0.311760i
$842$	−15.2848	+	12.8255i	−0.526749	+	0.441995i
$843$	7.89521	+	54.6054i	0.271925	+	1.88071i
$844$	2.39668	−	0.872320i	0.0824971	−	0.0300265i
$845$	−1.18980	+	2.06079i	−0.0409303	+	0.0708933i
$846$	9.30916	−	2.74944i	0.320055	−	0.0945276i
$847$	0.399767	+	0.692417i	0.0137362	+	0.0237917i
$848$	−36.4710	−	30.6028i	−1.25242	−	1.05091i
$849$	−20.1841	+	32.5882i	−0.692717	+	1.11842i
$850$	−1.67096	−	9.47651i	−0.0573136	−	0.325042i
$851$	1.00092	+	5.67649i	0.0343110	+	0.194588i
$852$	−1.86867	+	3.01706i	−0.0640197	+	0.103363i
$853$	3.72225	+	3.12334i	0.127447	+	0.106941i	0.704284	−	0.709919i	$-0.251268\pi$
$853$	3.72225	+	3.12334i	0.127447	+	0.106941i	−0.576836	+	0.816860i	$0.695713\pi$
$854$	−5.77044	−	9.99470i	−0.197460	−	0.342012i
$855$	8.21051	−	2.42495i	0.280793	−	0.0829317i
$856$	5.86826	−	10.1641i	0.200573	−	0.347403i
$857$	−17.5001	+	6.36952i	−0.597792	+	0.217579i	−0.623153	−	0.782100i	$-0.714149\pi$
$857$	−17.5001	+	6.36952i	−0.597792	+	0.217579i	0.0253610	+	0.999678i	$0.491926\pi$
$858$	−3.75428	−	25.9656i	−0.128169	−	0.886452i
$859$	3.67806	−	3.08626i	0.125494	−	0.105302i	−0.577881	−	0.816121i	$-0.696120\pi$
$859$	3.67806	−	3.08626i	0.125494	−	0.105302i	0.703374	+	0.710819i	$0.251676\pi$
$860$	0.518239	+	0.188624i	0.0176718	+	0.00643201i
$861$	0.0521751	−	0.250342i	0.00177812	−	0.00853162i
$862$	−7.56283	+	42.8910i	−0.257591	+	1.46087i
$863$	−44.7134			−1.52206			−0.761030	−	0.648717i	$-0.775306\pi$
$863$	−44.7134			−1.52206			−0.761030	+	0.648717i	$0.775306\pi$
$864$	−0.404651	−	4.94132i	−0.0137665	−	0.168107i
$865$	0.999929			0.0339986
$866$	−6.85086	+	38.8531i	−0.232802	+	1.32028i
$867$	55.2361	−	18.1897i	1.87592	−	0.617756i
$868$	−1.32041	−	0.480589i	−0.0448176	−	0.0163123i
$869$	−17.4684	+	14.6577i	−0.592575	+	0.497229i
$870$	3.48623	+	1.39247i	0.118194	+	0.0472092i
$871$	10.5565	−	3.84226i	0.357694	−	0.130190i
$872$	−25.7211	+	44.5503i	−0.871026	+	1.50866i
$873$	−0.0294529	+	0.0444216i	−0.000996829	+	0.00150344i
$874$	10.2934	+	17.8287i	0.348179	+	0.603064i
$875$	0.766044	+	0.642788i	0.0258970	+	0.0217302i
$876$	0.108841	+	0.00336876i	0.00367740	+	0.000113820i
$877$	−6.64244	−	37.6711i	−0.224299	−	1.27206i	−0.864020	−	0.503457i	$-0.832061\pi$
$877$	−6.64244	−	37.6711i	−0.224299	−	1.27206i	0.639721	−	0.768607i	$-0.279050\pi$
$878$	−3.96988	−	22.5143i	−0.133977	−	0.759821i
$879$	0.740839	+	1.38009i	0.0249879	+	0.0465491i
$880$	9.56018	+	8.02194i	0.322274	+	0.270420i
$881$	−15.0271	−	26.0277i	−0.506277	−	0.876897i	−0.999974	−	0.00726281i	$-0.997688\pi$
$881$	−15.0271	−	26.0277i	−0.506277	−	0.876897i	0.493697	−	0.869634i	$-0.335645\pi$
$882$	3.26500	−	2.41195i	0.109938	−	0.0812147i
$883$	−20.5062	+	35.5178i	−0.690089	+	1.19527i	0.281719	+	0.959497i	$0.409095\pi$
$883$	−20.5062	+	35.5178i	−0.690089	+	1.19527i	−0.971808	+	0.235772i	$0.924238\pi$
$884$	−3.68352	+	1.34069i	−0.123890	+	0.0450924i
$885$	−2.77397	+	2.18503i	−0.0932459	+	0.0734490i
$886$	−37.2901	+	31.2901i	−1.25278	+	1.05121i
$887$	31.4100	+	11.4323i	1.05464	+	0.383859i	0.810414	−	0.585858i	$-0.199242\pi$
$887$	31.4100	+	11.4323i	1.05464	+	0.383859i	0.244230	+	0.969717i	$0.421465\pi$
$888$	−4.09893	−	3.66137i	−0.137551	−	0.122867i
$889$	2.60002	−	14.7455i	0.0872020	−	0.494547i
$890$	−20.8803			−0.699910
$891$	−27.5234	−	14.0791i	−0.922070	−	0.471669i
$892$	−2.57599			−0.0862507
$893$	−1.18495	+	6.72021i	−0.0396530	+	0.224883i
$894$	−37.4609	−	33.4619i	−1.25288	−	1.11913i
$895$	−21.1529	−	7.69902i	−0.707063	−	0.257350i
$896$	−7.40805	+	6.21609i	−0.247486	+	0.207665i
$897$	23.6409	−	18.6217i	0.789346	−	0.621761i
$898$	45.7499	−	16.6516i	1.52669	−	0.555671i
$899$	6.65371	−	11.5246i	0.221914	−	0.384366i
$900$	0.465165	+	0.202700i	0.0155055	+	0.00675666i
$901$	46.5965	+	80.7076i	1.55236	+	2.68876i
$902$	0.525678	+	0.441096i	0.0175032	+	0.0146869i
$903$	2.67116	+	4.97601i	0.0888905	+	0.165591i
$904$	5.53389	+	31.3843i	0.184055	+	1.04383i
$905$	−0.695444	−	3.94406i	−0.0231173	−	0.131105i
$906$	−11.9573	−	0.370092i	−0.397254	−	0.0122955i
$907$	−20.8158	−	17.4666i	−0.691179	−	0.579968i	0.228070	−	0.973645i	$-0.426758\pi$
$907$	−20.8158	−	17.4666i	−0.691179	−	0.579968i	−0.919249	+	0.393677i	$0.871203\pi$
$908$	−1.38240	−	2.39438i	−0.0458764	−	0.0794603i
$909$	7.24455	+	14.5593i	0.240287	+	0.482903i
$910$	−2.20480	+	3.81882i	−0.0730883	+	0.126593i
$911$	21.0247	−	7.65235i	0.696578	−	0.253534i	0.0306288	−	0.999531i	$-0.490249\pi$
$911$	21.0247	−	7.65235i	0.696578	−	0.253534i	0.665949	+	0.745997i	$0.268027\pi$
$912$	−16.6766	−	6.66098i	−0.552217	−	0.220567i
$913$	40.8790	−	34.3015i	1.35290	−	1.13522i
$914$	53.7333	+	19.5573i	1.77734	+	0.646899i
$915$	14.0318	−	4.62082i	0.463878	−	0.152759i
$916$	0.627887	−	3.56093i	0.0207460	−	0.117656i
$917$	11.0598			0.365226
$918$	13.2094	−	48.2246i	0.435976	−	1.59165i
$919$	−56.3352			−1.85833			−0.929163	−	0.369671i	$-0.879470\pi$
$919$	−56.3352			−1.85833			−0.929163	+	0.369671i	$0.879470\pi$
$920$	−2.71729	+	15.4105i	−0.0895865	+	0.508070i
$921$	−2.18388	+	10.4785i	−0.0719612	+	0.345277i
$922$	−30.4350	−	11.0775i	−1.00232	−	0.364816i
$923$	30.2425	−	25.3765i	0.995443	−	0.835276i
$924$	−0.144001	−	0.995952i	−0.00473730	−	0.0327644i
$925$	1.01593	−	0.369767i	0.0334035	−	0.0121579i
$926$	12.8489	−	22.2549i	0.422240	−	0.731342i
$927$	−30.7916	−	29.2667i	−1.01133	−	0.961245i
$928$	0.764173	+	1.32359i	0.0250852	+	0.0434488i
$929$	25.7899	+	21.6403i	0.846139	+	0.709995i	0.958936	−	0.283623i	$-0.0915365\pi$
$929$	25.7899	+	21.6403i	0.846139	+	0.709995i	−0.112797	+	0.993618i	$0.535981\pi$
$930$	−10.2521	+	16.5525i	−0.336181	+	0.542779i
$931$	0.495541	+	2.81035i	0.0162407	+	0.0921056i
$932$	0.175062	+	0.992825i	0.00573434	+	0.0325211i
$933$	23.0498	−	37.2149i	0.754616	−	1.21836i
$934$	−5.06096	−	4.24665i	−0.165600	−	0.138955i
$935$	−12.2144	−	21.1559i	−0.399453	−	0.691873i
$936$	−6.72093	+	27.8968i	−0.219681	+	0.911837i
$937$	−18.3558	+	31.7931i	−0.599656	+	1.03864i	0.393215	+	0.919447i	$0.371363\pi$
$937$	−18.3558	+	31.7931i	−0.599656	+	1.03864i	−0.992872	+	0.119189i	$0.961971\pi$
$938$	−4.38307	+	1.59531i	−0.143112	+	0.0520886i
$939$	−2.46302	−	17.0349i	−0.0803777	−	0.555913i
$940$	−0.309823	+	0.259973i	−0.0101053	+	0.00847937i
$941$	50.3555	+	18.3279i	1.64154	+	0.597473i	0.987308	−	0.158818i	$-0.0507681\pi$
$941$	50.3555	+	18.3279i	1.64154	+	0.597473i	0.654236	+	0.756291i	$0.272990\pi$
$942$	6.20256	−	29.7605i	0.202090	−	0.969651i
$943$	−0.136687	+	0.775190i	−0.00445114	+	0.0252437i
$944$	7.40695			0.241076
$945$	2.16978	+	4.72144i	0.0705830	+	0.153589i
$946$	−15.1554			−0.492743
$947$	2.22761	−	12.6334i	0.0723875	−	0.410530i	−0.926985	−	0.375099i	$-0.877609\pi$
$947$	2.22761	−	12.6334i	0.0723875	−	0.410530i	0.999372	−	0.0354306i	$-0.0112803\pi$
$948$	1.84718	−	0.608292i	0.0599935	−	0.0197564i
$949$	−1.13830	−	0.414309i	−0.0369509	−	0.0134490i
$950$	2.95795	−	2.48202i	0.0959687	−	0.0805273i
$951$	49.5409	+	19.7877i	1.60647	+	0.641660i
$952$	19.6142	−	7.13897i	0.635699	−	0.231375i
$953$	6.54797	−	11.3414i	0.212109	−	0.367384i	−0.740265	−	0.672315i	$-0.765300\pi$
$953$	6.54797	−	11.3414i	0.212109	−	0.367384i	0.952375	+	0.304931i	$0.0986333\pi$
$954$	53.0923	+	3.28969i	1.71893	+	0.106508i
$955$	−0.0479446	−	0.0830424i	−0.00155145	−	0.00268719i
$956$	−1.11597	−	0.936414i	−0.0360932	−	0.0302858i
$957$	9.52565	+	0.294830i	0.307920	+	0.00953051i
$958$	8.31467	+	47.1548i	0.268635	+	1.52350i
$959$	−3.57917	−	20.2985i	−0.115577	−	0.655472i
$960$	−7.01018	−	13.0590i	−0.226253	−	0.421479i
$961$	29.1243	+	24.4381i	0.939492	+	0.788327i
$962$	2.38367	+	4.12863i	0.0768525	+	0.133112i
$963$	1.34853	+	11.9202i	0.0434556	+	0.384124i
$964$	1.35971	−	2.35508i	0.0437932	−	0.0758520i
$965$	−3.61711	+	1.31652i	−0.116439	+	0.0423803i
$966$	−9.81570	+	7.73174i	−0.315815	+	0.248765i
$967$	24.3142	−	20.4021i	0.781893	−	0.656086i	−0.161832	−	0.986818i	$-0.551740\pi$
$967$	24.3142	−	20.4021i	0.781893	−	0.656086i	0.943725	+	0.330733i	$0.107296\pi$
$968$	2.20515	+	0.802608i	0.0708761	+	0.0257968i
$969$	26.2154	+	23.4169i	0.842161	+	0.752260i
$970$	−0.00417439	+	0.0236742i	−0.000134032	+	0.000760131i
$971$	16.7871			0.538723			0.269362	−	0.963039i	$-0.413187\pi$
$971$	16.7871			0.538723			0.269362	+	0.963039i	$0.413187\pi$
$972$	1.73447	+	1.98574i	0.0556332	+	0.0636927i
$973$	1.67294			0.0536319
$974$	−5.80121	+	32.9003i	−0.185883	+	1.05419i
$975$	−4.20968	−	3.76029i	−0.134818	−	0.120426i
$976$	−29.1190	−	10.5985i	−0.932077	−	0.339248i
$977$	−41.2057	+	34.5757i	−1.31829	+	1.10617i	−0.331621	+	0.943413i	$0.607596\pi$
$977$	−41.2057	+	34.5757i	−1.31829	+	1.10617i	−0.986666	+	0.162761i	$0.947960\pi$
$978$	−38.3061	+	30.1734i	−1.22489	+	0.964838i
$979$	−49.8112	+	18.1298i	−1.59197	+	0.579431i
$980$	−0.0845684	+	0.146477i	−0.00270144	+	0.00467903i
$981$	−5.91070	−	52.2474i	−0.188714	−	1.66813i
$982$	−26.1583	−	45.3075i	−0.834745	−	1.44582i
$983$	−35.6445	−	29.9093i	−1.13688	−	0.953958i	−0.137550	−	0.990495i	$-0.543923\pi$
$983$	−35.6445	−	29.9093i	−1.13688	−	0.953958i	−0.999332	+	0.0365373i	$0.988367\pi$
$984$	−0.354988	−	0.661296i	−0.0113166	−	0.0210813i
$985$	−0.952589	−	5.40240i	−0.0303520	−	0.172135i
$986$	2.67656	+	15.1795i	0.0852389	+	0.483414i
$987$	−4.13975	−	0.128130i	−0.131770	−	0.00407844i
$988$	−1.20496	−	1.01108i	−0.0383348	−	0.0321667i
$989$	−8.69215	−	15.0553i	−0.276394	−	0.478729i
$990$	−13.9171	−	0.862330i	−0.442315	−	0.0274066i
$991$	−9.83826	+	17.0404i	−0.312523	+	0.541305i	−0.978908	−	0.204303i	$-0.934507\pi$
$991$	−9.83826	+	17.0404i	−0.312523	+	0.541305i	0.666385	+	0.745608i	$0.267841\pi$
$992$	−7.44873	+	2.71112i	−0.236497	+	0.0860780i
$993$	−4.42312	−	1.76669i	−0.140363	−	0.0560641i
$994$	−12.5567	+	10.5363i	−0.398274	+	0.334191i
$995$	−14.0568	−	5.11627i	−0.445632	−	0.162197i
$996$	−4.32270	+	1.42351i	−0.136970	+	0.0451055i
$997$	−5.10296	+	28.9403i	−0.161612	+	0.916549i	0.790877	+	0.611975i	$0.209625\pi$
$997$	−5.10296	+	28.9403i	−0.161612	+	0.916549i	−0.952489	+	0.304573i	$0.901486\pi$
$998$	24.2588			0.767898
$999$	5.59352	+	0.520709i	0.176971	+	0.0164745i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bt.a.106.12	✓	96
27.13	even	9	inner	945.2.bt.a.526.12	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.bt.a.106.12	✓	96	1.1	even	1	trivial
945.2.bt.a.526.12	yes	96	27.13	even	9	inner

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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bt (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.234962 - 1.33254i) q^{2} +(-1.29175 - 1.15386i) q^{3} +(0.158937 + 0.0578482i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-1.84107 + 1.45019i) q^{6} +(0.939693 - 0.342020i) q^{7} +(1.46752 - 2.54182i) q^{8} +(0.337236 + 2.98098i) q^{9} +O(q^{10})\)	\(q+(0.234962 - 1.33254i) q^{2} +(-1.29175 - 1.15386i) q^{3} +(0.158937 + 0.0578482i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-1.84107 + 1.45019i) q^{6} +(0.939693 - 0.342020i) q^{7} +(1.46752 - 2.54182i) q^{8} +(0.337236 + 2.98098i) q^{9} +(0.676547 + 1.17181i) q^{10} +(2.63140 + 2.20800i) q^{11} +(-0.138558 - 0.258115i) q^{12} +(0.565901 + 3.20939i) q^{13} +(-0.234962 - 1.33254i) q^{14} +(1.73122 + 0.0535834i) q^{15} +(-2.78313 - 2.33532i) q^{16} +(3.55581 + 6.15885i) q^{17} +(4.05151 + 0.251039i) q^{18} +(-1.42685 + 2.47138i) q^{19} +(-0.158937 + 0.0578482i) q^{20} +(-1.60849 - 0.642465i) q^{21} +(3.56053 - 2.98764i) q^{22} +(5.00999 + 1.82349i) q^{23} +(-4.82857 + 1.59009i) q^{24} +(0.173648 - 0.984808i) q^{25} +4.40959 q^{26} +(3.00400 - 4.23981i) q^{27} +0.169137 q^{28} +(-0.278150 + 1.57747i) q^{29} +(0.478174 - 2.29433i) q^{30} +(-7.80675 - 2.84142i) q^{31} +(0.730914 - 0.613309i) q^{32} +(-0.851390 - 5.88844i) q^{33} +(9.04238 - 3.29116i) q^{34} +(-0.500000 + 0.866025i) q^{35} +(-0.118845 + 0.493296i) q^{36} +(0.540564 + 0.936284i) q^{37} +(2.95795 + 2.48202i) q^{38} +(2.97216 - 4.79869i) q^{39} +(0.509665 + 2.89046i) q^{40} +(0.0256375 + 0.145398i) q^{41} +(-1.23404 + 1.99242i) q^{42} +(-2.49781 - 2.09591i) q^{43} +(0.290496 + 0.503154i) q^{44} +(-2.17448 - 2.06680i) q^{45} +(3.60703 - 6.24755i) q^{46} +(2.24702 - 0.817850i) q^{47} +(0.900484 + 6.22798i) q^{48} +(0.766044 - 0.642788i) q^{49} +(-1.27149 - 0.462785i) q^{50} +(2.51320 - 12.0586i) q^{51} +(-0.0957148 + 0.542825i) q^{52} +13.1043 q^{53} +(-4.94388 - 4.99914i) q^{54} -3.43504 q^{55} +(0.509665 - 2.89046i) q^{56} +(4.69476 - 1.54603i) q^{57} +(2.03668 + 0.741291i) q^{58} +(-1.56176 + 1.31047i) q^{59} +(0.272055 + 0.108664i) q^{60} +(8.01488 - 2.91718i) q^{61} +(-5.62060 + 9.73516i) q^{62} +(1.33646 + 2.68587i) q^{63} +(-4.27864 - 7.41082i) q^{64} +(-2.49646 - 2.09478i) q^{65} +(-8.04661 - 0.249052i) q^{66} +(-0.598598 - 3.39482i) q^{67} +(0.208871 + 1.18456i) q^{68} +(-4.36762 - 8.13630i) q^{69} +(1.03653 + 0.869752i) q^{70} +(-6.05707 - 10.4912i) q^{71} +(8.07204 + 3.51747i) q^{72} +(-0.185854 + 0.321908i) q^{73} +(1.37465 - 0.500330i) q^{74} +(-1.36064 + 1.07176i) q^{75} +(-0.369744 + 0.310252i) q^{76} +(3.22789 + 1.17485i) q^{77} +(-5.69609 - 5.08803i) q^{78} +(-1.15275 + 6.53760i) q^{79} +3.63312 q^{80} +(-8.77254 + 2.01059i) q^{81} +0.199771 q^{82} +(2.69764 - 15.2991i) q^{83} +(-0.218482 - 0.195159i) q^{84} +(-6.68274 - 2.43232i) q^{85} +(-3.37978 + 2.83597i) q^{86} +(2.17947 - 1.71675i) q^{87} +(9.47399 - 3.44825i) q^{88} +(-7.71577 + 13.3641i) q^{89} +(-3.26500 + 2.41195i) q^{90} +(1.62945 + 2.82229i) q^{91} +(0.690786 + 0.579638i) q^{92} +(6.80578 + 12.6783i) q^{93} +(-0.561850 - 3.18641i) q^{94} +(-0.495541 - 2.81035i) q^{95} +(-1.65183 - 0.0511261i) q^{96} +(0.0136097 + 0.0114199i) q^{97} +(-0.676547 - 1.17181i) q^{98} +(-5.69462 + 8.58877i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 3 q^{3} + 9 q^{8} + 3 q^{9}+O(q^{10}) \) 96 * q - 3 * q^3 + 9 * q^8 + 3 * q^9	\( 96 q - 3 q^{3} + 9 q^{8} + 3 q^{9} - 3 q^{10} + 9 q^{11} + 60 q^{12} - 6 q^{13} + 6 q^{15} - 12 q^{16} - 72 q^{18} - 6 q^{19} + 9 q^{22} - 6 q^{23} - 60 q^{24} + 54 q^{26} + 36 q^{27} - 78 q^{28} - 18 q^{29} + 3 q^{30} - 51 q^{32} + 39 q^{34} - 48 q^{35} + 42 q^{36} + 54 q^{37} + 105 q^{38} + 45 q^{39} - 9 q^{40} + 45 q^{41} - 3 q^{42} + 9 q^{43} - 48 q^{44} - 12 q^{45} + 24 q^{46} - 6 q^{47} + 6 q^{48} - 6 q^{51} + 3 q^{52} - 36 q^{53} + 90 q^{54} - 24 q^{55} - 9 q^{56} - 30 q^{57} - 27 q^{58} + 12 q^{59} - 15 q^{60} + 24 q^{61} - 27 q^{62} - 3 q^{63} + 15 q^{64} - 12 q^{65} - 27 q^{66} + 30 q^{67} + 69 q^{68} - 42 q^{69} - 42 q^{71} - 177 q^{72} + 6 q^{73} - 51 q^{74} - 24 q^{76} - 15 q^{78} - 48 q^{79} - 42 q^{80} + 99 q^{81} - 36 q^{82} + 30 q^{83} + 12 q^{84} - 21 q^{85} - 75 q^{86} - 18 q^{87} + 87 q^{88} - 75 q^{89} - 9 q^{90} - 18 q^{91} + 123 q^{92} + 24 q^{93} - 3 q^{94} - 21 q^{95} + 24 q^{96} + 102 q^{97} + 3 q^{98} - 75 q^{99}+O(q^{100}) \) 96 * q - 3 * q^3 + 9 * q^8 + 3 * q^9 - 3 * q^10 + 9 * q^11 + 60 * q^12 - 6 * q^13 + 6 * q^15 - 12 * q^16 - 72 * q^18 - 6 * q^19 + 9 * q^22 - 6 * q^23 - 60 * q^24 + 54 * q^26 + 36 * q^27 - 78 * q^28 - 18 * q^29 + 3 * q^30 - 51 * q^32 + 39 * q^34 - 48 * q^35 + 42 * q^36 + 54 * q^37 + 105 * q^38 + 45 * q^39 - 9 * q^40 + 45 * q^41 - 3 * q^42 + 9 * q^43 - 48 * q^44 - 12 * q^45 + 24 * q^46 - 6 * q^47 + 6 * q^48 - 6 * q^51 + 3 * q^52 - 36 * q^53 + 90 * q^54 - 24 * q^55 - 9 * q^56 - 30 * q^57 - 27 * q^58 + 12 * q^59 - 15 * q^60 + 24 * q^61 - 27 * q^62 - 3 * q^63 + 15 * q^64 - 12 * q^65 - 27 * q^66 + 30 * q^67 + 69 * q^68 - 42 * q^69 - 42 * q^71 - 177 * q^72 + 6 * q^73 - 51 * q^74 - 24 * q^76 - 15 * q^78 - 48 * q^79 - 42 * q^80 + 99 * q^81 - 36 * q^82 + 30 * q^83 + 12 * q^84 - 21 * q^85 - 75 * q^86 - 18 * q^87 + 87 * q^88 - 75 * q^89 - 9 * q^90 - 18 * q^91 + 123 * q^92 + 24 * q^93 - 3 * q^94 - 21 * q^95 + 24 * q^96 + 102 * q^97 + 3 * q^98 - 75 * q^99

Introduction

L-functions

Modular forms

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