LMFDB - Embedded newform 441.2.ba.a.22.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(22,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([14, 24]))

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

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

chi := DirichletCharacter("441.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.ba (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			22.19
Character	$\chi$	$=$	441.22
Dual form			441.2.ba.a.421.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.912794 - 0.622332i) q^{2} +(-0.609005 + 1.62145i) q^{3} +(-0.284787 - 0.725626i) q^{4} +(-1.69424 - 1.57203i) q^{5} +(1.56498 - 1.10105i) q^{6} +(-1.84008 - 1.90108i) q^{7} +(-0.683292 + 2.99370i) q^{8} +(-2.25823 - 1.97495i) q^{9} +O(q^{10})$	\(q+(-0.912794 - 0.622332i) q^{2} +(-0.609005 + 1.62145i) q^{3} +(-0.284787 - 0.725626i) q^{4} +(-1.69424 - 1.57203i) q^{5} +(1.56498 - 1.10105i) q^{6} +(-1.84008 - 1.90108i) q^{7} +(-0.683292 + 2.99370i) q^{8} +(-2.25823 - 1.97495i) q^{9} +(0.568171 + 2.48932i) q^{10} +(2.79542 + 1.90589i) q^{11} +(1.35001 - 0.0198593i) q^{12} +(-0.0571828 + 0.763052i) q^{13} +(0.496507 + 2.88044i) q^{14} +(3.58077 - 1.78976i) q^{15} +(1.34394 - 1.24699i) q^{16} +(4.56015 + 5.71825i) q^{17} +(0.832220 + 3.20809i) q^{18} -1.37458 q^{19} +(-0.658205 + 1.67708i) q^{20} +(4.20313 - 1.82583i) q^{21} +(-1.36555 - 3.47936i) q^{22} +(0.0694554 + 0.176969i) q^{23} +(-4.43801 - 2.93110i) q^{24} +(0.0255375 + 0.340774i) q^{25} +(0.527068 - 0.660922i) q^{26} +(4.57756 - 2.45885i) q^{27} +(-0.855443 + 1.87661i) q^{28} +(-2.59373 + 6.60872i) q^{29} +(-4.38233 - 0.594745i) q^{30} +(-4.84451 + 8.39094i) q^{31} +(4.07000 - 0.613454i) q^{32} +(-4.79273 + 3.37195i) q^{33} +(-0.603827 - 8.05751i) q^{34} +(0.128985 + 6.11355i) q^{35} +(-0.789959 + 2.20107i) q^{36} +(1.37600 + 1.72545i) q^{37} +(1.25471 + 0.855446i) q^{38} +(-1.20243 - 0.557422i) q^{39} +(5.86384 - 3.99790i) q^{40} +(-1.77467 - 1.64665i) q^{41} +(-4.97287 - 0.949137i) q^{42} +(5.35328 - 4.96712i) q^{43} +(0.586860 - 2.57120i) q^{44} +(0.721310 + 6.89603i) q^{45} +(0.0467353 - 0.204761i) q^{46} +(7.35030 + 5.01135i) q^{47} +(1.20347 + 2.93855i) q^{48} +(-0.228226 + 6.99628i) q^{49} +(0.188764 - 0.326950i) q^{50} +(-12.0490 + 3.91163i) q^{51} +(0.569975 - 0.175814i) q^{52} +(-5.33824 + 6.69394i) q^{53} +(-5.70859 - 0.604335i) q^{54} +(-1.74002 - 7.62352i) q^{55} +(6.94857 - 4.20964i) q^{56} +(0.837127 - 2.22882i) q^{57} +(6.48036 - 4.41823i) q^{58} +(-6.38688 - 1.97009i) q^{59} +(-2.31846 - 2.08860i) q^{60} +(-1.91897 + 4.88946i) q^{61} +(9.64400 - 4.64430i) q^{62} +(0.400773 + 7.92713i) q^{63} +(-7.40041 - 3.56385i) q^{64} +(1.29642 - 1.20290i) q^{65} +(6.47325 - 0.0952250i) q^{66} +(5.88544 - 10.1939i) q^{67} +(2.85063 - 4.93744i) q^{68} +(-0.329247 + 0.00484339i) q^{69} +(3.68692 - 5.66068i) q^{70} +(4.46715 - 5.60163i) q^{71} +(7.45542 - 5.41098i) q^{72} +(3.02841 + 1.45840i) q^{73} +(-0.182202 - 2.43131i) q^{74} +(-0.568102 - 0.166126i) q^{75} +(0.391463 + 0.997431i) q^{76} +(-1.52055 - 8.82131i) q^{77} +(0.750668 + 1.25712i) q^{78} +(-1.77676 - 3.07744i) q^{79} -4.23726 q^{80} +(1.19916 + 8.91975i) q^{81} +(0.595141 + 2.60748i) q^{82} +(0.847472 + 11.3087i) q^{83} +(-2.52187 - 2.52993i) q^{84} +(1.26324 - 16.8568i) q^{85} +(-7.97765 + 1.20244i) q^{86} +(-9.13614 - 8.23036i) q^{87} +(-7.61574 + 7.06637i) q^{88} +(6.74063 + 3.24612i) q^{89} +(3.63322 - 6.74355i) q^{90} +(1.55584 - 1.29537i) q^{91} +(0.108634 - 0.100797i) q^{92} +(-10.6552 - 12.9653i) q^{93} +(-3.59058 - 9.14866i) q^{94} +(2.32887 + 2.16088i) q^{95} +(-1.48396 + 6.97291i) q^{96} +(7.80322 + 13.5156i) q^{97} +(4.56233 - 6.24413i) q^{98} +(-2.54867 - 9.82474i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 5 q^{2} - 10 q^{3} + 47 q^{4} - 9 q^{5} - 34 q^{6} - 7 q^{7} - 28 q^{8}+O(q^{10}) $ 648 * q - 5 * q^2 - 10 * q^3 + 47 * q^4 - 9 * q^5 - 34 * q^6 - 7 * q^7 - 28 * q^8	\( 648 q - 5 q^{2} - 10 q^{3} + 47 q^{4} - 9 q^{5} - 34 q^{6} - 7 q^{7} - 28 q^{8} - 28 q^{10} - 5 q^{11} + 5 q^{12} - 7 q^{13} - 38 q^{14} - 22 q^{15} + 47 q^{16} - 16 q^{17} - 46 q^{18} - 44 q^{19} - 29 q^{20} - 12 q^{21} - 13 q^{22} - 20 q^{23} - 2 q^{24} + 41 q^{25} - 20 q^{26} - 13 q^{27} - 28 q^{28} - 35 q^{29} - 6 q^{30} - 20 q^{31} - 25 q^{32} - 22 q^{33} - q^{34} - 44 q^{35} - 28 q^{36} - 30 q^{37} - 7 q^{38} - 8 q^{39} + 5 q^{40} - 29 q^{41} - 104 q^{42} - 13 q^{43} - 88 q^{44} + 63 q^{45} + 32 q^{46} - 55 q^{47} - 14 q^{48} - q^{49} + 6 q^{50} - 18 q^{51} + 3 q^{52} - 136 q^{53} + 30 q^{54} - 100 q^{55} + 145 q^{56} - 96 q^{57} + 17 q^{58} - 19 q^{59} + 118 q^{60} + 42 q^{61} + 96 q^{62} - 6 q^{63} - 124 q^{64} - 11 q^{65} + 120 q^{66} - 26 q^{67} + 166 q^{68} - 134 q^{69} - 7 q^{70} - 22 q^{71} + 32 q^{72} + 8 q^{73} - 45 q^{74} - 36 q^{75} - 41 q^{76} + q^{77} - 18 q^{78} - 26 q^{79} - 440 q^{80} + 64 q^{81} - 28 q^{82} + 61 q^{83} - 86 q^{84} + 5 q^{85} + 15 q^{86} + 34 q^{87} - q^{88} + 22 q^{89} + 96 q^{90} - 16 q^{91} - 43 q^{92} - 110 q^{93} - q^{94} - 38 q^{95} - 165 q^{96} - 14 q^{97} - 144 q^{98} - 196 q^{99}+O(q^{100}) \) 648 * q - 5 * q^2 - 10 * q^3 + 47 * q^4 - 9 * q^5 - 34 * q^6 - 7 * q^7 - 28 * q^8 - 28 * q^10 - 5 * q^11 + 5 * q^12 - 7 * q^13 - 38 * q^14 - 22 * q^15 + 47 * q^16 - 16 * q^17 - 46 * q^18 - 44 * q^19 - 29 * q^20 - 12 * q^21 - 13 * q^22 - 20 * q^23 - 2 * q^24 + 41 * q^25 - 20 * q^26 - 13 * q^27 - 28 * q^28 - 35 * q^29 - 6 * q^30 - 20 * q^31 - 25 * q^32 - 22 * q^33 - q^34 - 44 * q^35 - 28 * q^36 - 30 * q^37 - 7 * q^38 - 8 * q^39 + 5 * q^40 - 29 * q^41 - 104 * q^42 - 13 * q^43 - 88 * q^44 + 63 * q^45 + 32 * q^46 - 55 * q^47 - 14 * q^48 - q^49 + 6 * q^50 - 18 * q^51 + 3 * q^52 - 136 * q^53 + 30 * q^54 - 100 * q^55 + 145 * q^56 - 96 * q^57 + 17 * q^58 - 19 * q^59 + 118 * q^60 + 42 * q^61 + 96 * q^62 - 6 * q^63 - 124 * q^64 - 11 * q^65 + 120 * q^66 - 26 * q^67 + 166 * q^68 - 134 * q^69 - 7 * q^70 - 22 * q^71 + 32 * q^72 + 8 * q^73 - 45 * q^74 - 36 * q^75 - 41 * q^76 + q^77 - 18 * q^78 - 26 * q^79 - 440 * q^80 + 64 * q^81 - 28 * q^82 + 61 * q^83 - 86 * q^84 + 5 * q^85 + 15 * q^86 + 34 * q^87 - q^88 + 22 * q^89 + 96 * q^90 - 16 * q^91 - 43 * q^92 - 110 * q^93 - q^94 - 38 * q^95 - 165 * q^96 - 14 * q^97 - 144 * q^98 - 196 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.912794	−	0.622332i	−0.645443	−	0.440055i	0.195851	−	0.980634i	$-0.437253\pi$
$2$	−0.912794	−	0.622332i	−0.645443	−	0.440055i	−0.841294	+	0.540578i	$0.818205\pi$
$3$	−0.609005	+	1.62145i	−0.351609	+	0.936147i
$3$	−0.609005	+	1.62145i	−0.351609	+	0.936147i
$4$	−0.284787	−	0.725626i	−0.142394	−	0.362813i
$5$	−1.69424	−	1.57203i	−0.757688	−	0.703032i	0.203454	−	0.979084i	$-0.434783\pi$
$5$	−1.69424	−	1.57203i	−0.757688	−	0.703032i	−0.961143	+	0.276052i	$0.910974\pi$
$6$	1.56498	−	1.10105i	0.638900	−	0.449502i
$7$	−1.84008	−	1.90108i	−0.695484	−	0.718541i
$7$	−1.84008	−	1.90108i	−0.695484	−	0.718541i
$8$	−0.683292	+	2.99370i	−0.241580	+	1.05843i
$9$	−2.25823	−	1.97495i	−0.752742	−	0.658316i
$10$	0.568171	+	2.48932i	0.179671	+	0.787192i
$11$	2.79542	+	1.90589i	0.842852	+	0.574647i	0.905962	−	0.423360i	$-0.139149\pi$
$11$	2.79542	+	1.90589i	0.842852	+	0.574647i	−0.0631098	+	0.998007i	$0.520102\pi$
$12$	1.35001	−	0.0198593i	0.389713	−	0.00573289i
$13$	−0.0571828	+	0.763052i	−0.0158597	+	0.211632i	0.983644	+	0.180124i	$0.0576500\pi$
$13$	−0.0571828	+	0.763052i	−0.0158597	+	0.211632i	−0.999503	+	0.0315080i	$0.989969\pi$
$14$	0.496507	+	2.88044i	0.132697	+	0.769829i
$15$	3.58077	−	1.78976i	0.924552	−	0.462115i
$16$	1.34394	−	1.24699i	0.335984	−	0.311748i
$17$	4.56015	+	5.71825i	1.10600	+	1.38688i	0.914112	+	0.405461i	$0.132889\pi$
$17$	4.56015	+	5.71825i	1.10600	+	1.38688i	0.191887	+	0.981417i	$0.438539\pi$
$18$	0.832220	+	3.20809i	0.196156	+	0.756153i
$19$	−1.37458			−0.315350			−0.157675	−	0.987491i	$-0.550400\pi$
$19$	−1.37458			−0.315350			−0.157675	+	0.987491i	$0.550400\pi$
$20$	−0.658205	+	1.67708i	−0.147179	+	0.375006i
$21$	4.20313	−	1.82583i	0.917199	−	0.398429i
$22$	−1.36555	−	3.47936i	−0.291136	−	0.741803i
$23$	0.0694554	+	0.176969i	0.0144825	+	0.0369007i	0.937932	−	0.346819i	$-0.112738\pi$
$23$	0.0694554	+	0.176969i	0.0144825	+	0.0369007i	−0.923450	+	0.383720i	$0.874643\pi$
$24$	−4.43801	−	2.93110i	−0.905906	−	0.598309i
$25$	0.0255375	+	0.340774i	0.00510750	+	0.0681549i
$26$	0.527068	−	0.660922i	0.103366	−	0.129617i
$27$	4.57756	−	2.45885i	0.880951	−	0.473207i
$28$	−0.855443	+	1.87661i	−0.161664	+	0.354646i
$29$	−2.59373	+	6.60872i	−0.481644	+	1.22721i	0.459189	+	0.888338i	$0.348140\pi$
$29$	−2.59373	+	6.60872i	−0.481644	+	1.22721i	−0.940833	+	0.338870i	$0.889955\pi$
$30$	−4.38233	−	0.594745i	−0.800101	−	0.108585i
$31$	−4.84451	+	8.39094i	−0.870100	+	1.50706i	−0.00820813	+	0.999966i	$0.502613\pi$
$31$	−4.84451	+	8.39094i	−0.870100	+	1.50706i	−0.861892	+	0.507092i	$0.830721\pi$
$32$	4.07000	−	0.613454i	0.719481	−	0.108444i
$33$	−4.79273	+	3.37195i	−0.834308	+	0.586982i
$34$	−0.603827	−	8.05751i	−0.103555	−	1.38185i
$35$	0.128985	+	6.11355i	0.0218025	+	1.03338i
$36$	−0.789959	+	2.20107i	−0.131660	+	0.366844i
$37$	1.37600	+	1.72545i	0.226213	+	0.283663i	0.881966	−	0.471313i	$-0.156220\pi$
$37$	1.37600	+	1.72545i	0.226213	+	0.283663i	−0.655752	+	0.754976i	$0.727648\pi$
$38$	1.25471	+	0.855446i	0.203541	+	0.138772i
$39$	−1.20243	−	0.557422i	−0.192543	−	0.0892589i
$40$	5.86384	−	3.99790i	0.927154	−	0.632123i
$41$	−1.77467	−	1.64665i	−0.277156	−	0.257164i	0.529330	−	0.848416i	$-0.322443\pi$
$41$	−1.77467	−	1.64665i	−0.277156	−	0.257164i	−0.806487	+	0.591252i	$0.798634\pi$
$42$	−4.97287	−	0.949137i	−0.767330	−	0.146455i
$43$	5.35328	−	4.96712i	0.816368	−	0.757479i	−0.156786	−	0.987633i	$-0.550113\pi$
$43$	5.35328	−	4.96712i	0.816368	−	0.757479i	0.973154	+	0.230154i	$0.0739228\pi$
$44$	0.586860	−	2.57120i	0.0884725	−	0.387623i
$45$	0.721310	+	6.89603i	0.107526	+	1.02800i
$46$	0.0467353	−	0.204761i	0.00689075	−	0.0301904i
$47$	7.35030	+	5.01135i	1.07215	+	0.730980i	0.964732	−	0.263233i	$-0.0847889\pi$
$47$	7.35030	+	5.01135i	1.07215	+	0.730980i	0.107419	+	0.994214i	$0.465741\pi$
$48$	1.20347	+	2.93855i	0.173706	+	0.424144i
$49$	−0.228226	+	6.99628i	−0.0326037	+	0.999468i
$50$	0.188764	−	0.326950i	0.0266953	−	0.0462377i
$51$	−12.0490	+	3.91163i	−1.68720	+	0.547738i
$52$	0.569975	−	0.175814i	0.0790413	−	0.0243810i
$53$	−5.33824	+	6.69394i	−0.733264	+	0.919484i	−0.999007	−	0.0445600i	$-0.985811\pi$
$53$	−5.33824	+	6.69394i	−0.733264	+	0.919484i	0.265743	+	0.964044i	$0.414383\pi$
$54$	−5.70859	−	0.604335i	−0.776841	−	0.0822395i
$55$	−1.74002	−	7.62352i	−0.234624	−	1.02795i
$56$	6.94857	−	4.20964i	0.928542	−	0.562537i
$57$	0.837127	−	2.22882i	0.110880	−	0.295214i
$58$	6.48036	−	4.41823i	0.850913	−	0.580143i
$59$	−6.38688	−	1.97009i	−0.831500	−	0.256484i	−0.150355	−	0.988632i	$-0.548042\pi$
$59$	−6.38688	−	1.97009i	−0.831500	−	0.256484i	−0.681145	+	0.732148i	$0.738518\pi$
$60$	−2.31846	−	2.08860i	−0.299311	−	0.269637i
$61$	−1.91897	+	4.88946i	−0.245699	+	0.626031i	−0.999518	−	0.0310513i	$-0.990114\pi$
$61$	−1.91897	+	4.88946i	−0.245699	+	0.626031i	0.753819	+	0.657083i	$0.228210\pi$
$62$	9.64400	−	4.64430i	1.22479	−	0.589827i
$63$	0.400773	+	7.92713i	0.0504926	+	0.998724i
$64$	−7.40041	−	3.56385i	−0.925051	−	0.445481i
$65$	1.29642	−	1.20290i	0.160801	−	0.149202i
$66$	6.47325	−	0.0952250i	0.796802	−	0.0117214i
$67$	5.88544	−	10.1939i	0.719021	−	1.24538i	−0.242367	−	0.970185i	$-0.577924\pi$
$67$	5.88544	−	10.1939i	0.719021	−	1.24538i	0.961388	−	0.275197i	$-0.0887430\pi$
$68$	2.85063	−	4.93744i	0.345690	−	0.598753i
$69$	−0.329247	+	0.00484339i	−0.0396366	+	0.000583076i
$70$	3.68692	−	5.66068i	0.440671	−	0.676581i
$71$	4.46715	−	5.60163i	0.530153	−	0.664791i	−0.442577	−	0.896730i	$-0.645936\pi$
$71$	4.46715	−	5.60163i	0.530153	−	0.664791i	0.972730	+	0.231939i	$0.0745071\pi$
$72$	7.45542	−	5.41098i	0.878630	−	0.637690i
$73$	3.02841	+	1.45840i	0.354448	+	0.170693i	0.602631	−	0.798020i	$-0.294119\pi$
$73$	3.02841	+	1.45840i	0.354448	+	0.170693i	−0.248183	+	0.968713i	$0.579833\pi$
$74$	−0.182202	−	2.43131i	−0.0211805	−	0.282634i
$75$	−0.568102	−	0.166126i	−0.0655988	−	0.0191825i
$76$	0.391463	+	0.997431i	0.0449038	+	0.114413i
$77$	−1.52055	−	8.82131i	−0.173283	−	1.00528i
$78$	0.750668	+	1.25712i	0.0849964	+	0.142341i
$79$	−1.77676	−	3.07744i	−0.199901	−	0.346239i	0.748595	−	0.663027i	$-0.230729\pi$
$79$	−1.77676	−	3.07744i	−0.199901	−	0.346239i	−0.948496	+	0.316789i	$0.897395\pi$
$80$	−4.23726			−0.473740
$81$	1.19916	+	8.91975i	0.133240	+	0.991084i
$82$	0.595141	+	2.60748i	0.0657224	+	0.287948i
$83$	0.847472	+	11.3087i	0.0930221	+	1.24129i	0.827032	+	0.562155i	$0.190028\pi$
$83$	0.847472	+	11.3087i	0.0930221	+	1.24129i	−0.734010	+	0.679139i	$0.762353\pi$
$84$	−2.52187	−	2.52993i	−0.275158	−	0.276038i
$85$	1.26324	−	16.8568i	0.137018	−	1.82837i
$86$	−7.97765	+	1.20244i	−0.860252	+	0.129662i
$87$	−9.13614	−	8.23036i	−0.979497	−	0.882387i
$88$	−7.61574	+	7.06637i	−0.811840	+	0.753278i
$89$	6.74063	+	3.24612i	0.714506	+	0.344088i	0.755569	−	0.655069i	$-0.227360\pi$
$89$	6.74063	+	3.24612i	0.714506	+	0.344088i	−0.0410636	+	0.999157i	$0.513075\pi$
$90$	3.63322	−	6.74355i	0.382975	−	0.710833i
$91$	1.55584	−	1.29537i	0.163097	−	0.135791i
$92$	0.108634	−	0.100797i	0.0113258	−	0.0105088i
$93$	−10.6552	−	12.9653i	−1.10489	−	1.34444i
$94$	−3.59058	−	9.14866i	−0.370340	−	0.943612i
$95$	2.32887	+	2.16088i	0.238937	+	0.221701i
$96$	−1.48396	+	6.97291i	−0.151456	+	0.711670i
$97$	7.80322	+	13.5156i	0.792297	+	1.37230i	0.924541	+	0.381082i	$0.124448\pi$
$97$	7.80322	+	13.5156i	0.792297	+	1.37230i	−0.132244	+	0.991217i	$0.542218\pi$
$98$	4.56233	−	6.24413i	0.460865	−	0.630752i
$99$	−2.54867	−	9.82474i	−0.256151	−	0.987423i
$100$	0.240002	−	0.115579i	0.0240002	−	0.0115579i
$101$	−15.9012	+	4.90487i	−1.58223	+	0.488053i	−0.956437	−	0.291938i	$-0.905700\pi$
$101$	−15.9012	+	4.90487i	−1.58223	+	0.488053i	−0.625791	+	0.779991i	$0.715224\pi$
$102$	13.4326	+	3.92799i	1.33003	+	0.388929i
$103$	0.302320	+	0.280512i	0.0297884	+	0.0276396i	0.694927	−	0.719081i	$-0.255437\pi$
$103$	0.302320	+	0.280512i	0.0297884	+	0.0276396i	−0.665138	+	0.746720i	$0.731627\pi$
$104$	−2.24527	−	0.692575i	−0.220167	−	0.0679126i
$105$	−9.99139	−	3.51404i	−0.975060	−	0.342935i
$106$	9.03857	−	2.78803i	0.877904	−	0.270797i
$107$	−13.6103	−	6.55438i	−1.31576	−	0.633635i	−0.361430	−	0.932399i	$-0.617711\pi$
$107$	−13.6103	−	6.55438i	−1.31576	−	0.633635i	−0.954327	+	0.298764i	$0.903426\pi$
$108$	−3.08784	−	2.62134i	−0.297127	−	0.252239i
$109$	−2.03406	+	0.979550i	−0.194827	+	0.0938239i	−0.528754	−	0.848775i	$-0.677341\pi$
$109$	−2.03406	+	0.979550i	−0.194827	+	0.0938239i	0.333927	+	0.942599i	$0.391626\pi$
$110$	−3.15608	+	8.04157i	−0.300921	+	0.766733i
$111$	−3.63573	+	1.18032i	−0.345089	+	0.112031i
$112$	−4.84358	−	0.260373i	−0.457675	−	0.0246029i
$113$	−4.72283	+	3.21997i	−0.444287	+	0.302910i	−0.764721	−	0.644361i	$-0.777123\pi$
$113$	−4.72283	+	3.21997i	−0.444287	+	0.302910i	0.320435	+	0.947271i	$0.396171\pi$
$114$	−2.15119	+	1.51348i	−0.201477	+	0.141750i
$115$	0.160527	−	0.409015i	0.0149692	−	0.0381409i
$116$	5.53412			0.513830
$117$	1.63612	−	1.61021i	0.151259	−	0.148864i
$118$	4.60385	+	5.77304i	0.423819	+	0.531452i
$119$	2.47983	−	19.1912i	0.227325	−	1.75926i
$120$	2.91130	+	11.9427i	0.265764	+	1.09021i
$121$	0.163232	+	0.415908i	0.0148393	+	0.0378098i
$122$	4.79449	−	3.26883i	0.434073	−	0.295946i
$123$	3.75075	−	1.87472i	0.338194	−	0.169038i
$124$	7.46834	+	1.12567i	0.670677	+	0.101088i
$125$	−6.71267	+	8.41742i	−0.600399	+	0.752877i
$126$	4.56749	−	7.48525i	0.406904	−	0.666839i
$127$	−7.38312	−	9.25813i	−0.655146	−	0.821527i	0.337659	−	0.941268i	$-0.390365\pi$
$127$	−7.38312	−	9.25813i	−0.655146	−	0.821527i	−0.992805	+	0.119742i	$0.961793\pi$
$128$	0.421179	+	0.729504i	0.0372274	+	0.0644797i
$129$	4.79378	+	11.7051i	0.422069	+	1.03058i
$130$	−1.93197	+	0.291197i	−0.169445	+	0.0255397i
$131$	0.939242	+	0.289718i	0.0820620	+	0.0253128i	0.335514	−	0.942035i	$-0.391090\pi$
$131$	0.939242	+	0.289718i	0.0820620	+	0.0253128i	−0.253452	+	0.967348i	$0.581566\pi$
$132$	3.81169	+	2.51744i	0.331765	+	0.219115i
$133$	2.52933	+	2.61319i	0.219321	+	0.226592i
$134$	−11.7162	+	5.64221i	−1.01212	+	0.487413i
$135$	−11.6209	−	3.03015i	−1.00017	−	0.260794i
$136$	−20.2346	+	9.74448i	−1.73510	+	0.835582i
$137$	4.33542	−	4.02268i	0.370400	−	0.343681i	−0.472908	−	0.881112i	$-0.656796\pi$
$137$	4.33542	−	4.02268i	0.370400	−	0.343681i	0.843308	+	0.537431i	$0.180605\pi$
$138$	0.303548	+	0.200480i	0.0258398	+	0.0170660i
$139$	−2.74720	−	2.54903i	−0.233014	−	0.216206i	0.555020	−	0.831837i	$-0.312711\pi$
$139$	−2.74720	−	2.54903i	−0.233014	−	0.216206i	−0.788034	+	0.615631i	$0.788901\pi$
$140$	4.39941	−	1.83465i	0.371818	−	0.155057i
$141$	−12.6020	+	8.86623i	−1.06128	+	0.746672i
$142$	−7.56366	+	2.33308i	−0.634728	+	0.195788i
$143$	−1.61414	+	2.02407i	−0.134981	+	0.169261i
$144$	−5.49765	+	0.161782i	−0.458137	+	0.0134818i
$145$	14.7835	−	7.11936i	1.22770	−	0.591231i
$146$	−1.85670	−	3.21590i	−0.153661	−	0.266149i
$147$	−11.2052	−	4.63083i	−0.924185	−	0.381944i
$148$	0.860165	−	1.48985i	0.0707051	−	0.122465i
$149$	−0.0706146	+	0.942286i	−0.00578497	+	0.0771951i	−0.999349	−	0.0360766i	$-0.988514\pi$
$149$	−0.0706146	+	0.942286i	−0.00578497	+	0.0771951i	0.993564	+	0.113272i	$0.0361330\pi$
$150$	0.415175	+	0.505187i	0.0338989	+	0.0412483i
$151$	−19.0750	−	2.87509i	−1.55230	−	0.233972i	−0.683803	−	0.729667i	$-0.739675\pi$
$151$	−19.0750	−	2.87509i	−1.55230	−	0.233972i	−0.868497	+	0.495695i	$0.834913\pi$
$152$	0.939239	−	4.11508i	0.0761824	−	0.333777i
$153$	0.995393	−	21.9191i	0.0804728	−	1.77206i
$154$	−4.10184	+	8.99832i	−0.330535	+	0.725105i
$155$	21.3986	−	6.60059i	1.71878	−	0.530172i
$156$	−0.0620434	+	1.03126i	−0.00496745	+	0.0825668i
$157$	12.9411	+	3.99179i	1.03281	+	0.318579i	0.764411	−	0.644729i	$-0.223030\pi$
$157$	12.9411	+	3.99179i	1.03281	+	0.318579i	0.268397	+	0.963308i	$0.413506\pi$
$158$	−0.293374	+	3.91480i	−0.0233395	+	0.311445i
$159$	−7.60290	−	12.7324i	−0.602950	−	1.00974i
$160$	−7.85993	−	5.35881i	−0.621382	−	0.423651i
$161$	0.208630	−	0.457678i	0.0164424	−	0.0360701i
$162$	4.45646	−	8.88817i	0.350133	−	0.698321i
$163$	4.43842	+	19.4460i	0.347644	+	1.52313i	0.782514	+	0.622633i	$0.213937\pi$
$163$	4.43842	+	19.4460i	0.347644	+	1.52313i	−0.434870	+	0.900493i	$0.643206\pi$
$164$	−0.689449	+	1.75669i	−0.0538370	+	0.137174i
$165$	13.4209	+	1.82140i	1.04481	+	0.141796i
$166$	6.26422	−	10.8499i	0.486198	−	0.842119i
$167$	−15.9156	+	2.39889i	−1.23158	+	0.185631i	−0.732406	−	0.680868i	$-0.761603\pi$
$167$	−15.9156	+	2.39889i	−1.23158	+	0.185631i	−0.499178	+	0.866500i	$0.666365\pi$
$168$	2.59402	+	13.8305i	0.200133	+	1.06705i
$169$	12.2758	+	1.85028i	0.944294	+	0.142329i
$170$	−11.6436	+	14.6006i	−0.893023	+	1.11982i
$171$	3.10411	+	2.71472i	0.237377	+	0.207600i
$172$	−5.12882	−	2.46991i	−0.391069	−	0.188329i
$173$	17.7448	+	2.67460i	1.34911	+	0.203346i	0.783535	−	0.621348i	$-0.213414\pi$
$173$	17.7448	+	2.67460i	1.34911	+	0.203346i	0.565579	+	0.824694i	$0.308653\pi$
$174$	3.21739	+	13.1983i	0.243910	+	1.00056i
$175$	0.600849	−	0.675600i	0.0454199	−	0.0510706i
$176$	6.13349	−	0.924475i	0.462329	−	0.0696849i
$177$	7.08405	−	9.15623i	0.532470	−	0.688224i
$178$	−4.13264	−	7.15795i	−0.309755	−	0.536511i
$179$	6.77838	+	8.49982i	0.506640	+	0.635306i	0.967713	−	0.252056i	$-0.0811067\pi$
$179$	6.77838	+	8.49982i	0.506640	+	0.635306i	−0.461073	+	0.887362i	$0.652535\pi$
$180$	4.79852	−	2.48730i	0.357661	−	0.185393i
$181$	−7.95736	−	3.83206i	−0.591466	−	0.284835i	0.114111	−	0.993468i	$-0.463598\pi$
$181$	−7.95736	−	3.83206i	−0.591466	−	0.284835i	−0.705577	+	0.708633i	$0.749312\pi$
$182$	−2.22631	+	0.214149i	−0.165025	+	0.0158738i
$183$	−6.75937	−	6.08923i	−0.499667	−	0.450129i
$184$	−0.577251	+	0.0870066i	−0.0425555	+	0.00641421i
$185$	0.381177	−	5.08645i	0.0280247	−	0.373963i
$186$	1.65728	+	18.4657i	0.121518	+	1.35397i
$187$	1.84921	+	24.6760i	0.135228	+	1.80449i
$188$	1.54309	−	6.76073i	0.112542	−	0.493077i
$189$	−13.0975	−	4.17783i	−0.952706	−	0.303892i
$190$	−0.780996	−	3.42177i	−0.0566594	−	0.248241i
$191$	11.0213	−	3.39963i	0.797476	−	0.245989i	0.130871	−	0.991399i	$-0.458223\pi$
$191$	11.0213	−	3.39963i	0.797476	−	0.245989i	0.666606	+	0.745411i	$0.267747\pi$
$192$	10.2855	−	9.82902i	0.742293	−	0.709349i
$193$	13.2936	+	12.3347i	0.956897	+	0.887870i	0.993770	−	0.111450i	$-0.0355494\pi$
$193$	13.2936	+	12.3347i	0.956897	+	0.887870i	−0.0368736	+	0.999320i	$0.511740\pi$
$194$	1.28845	−	17.1931i	0.0925051	−	1.23439i
$195$	1.16092	+	2.83466i	0.0831354	+	0.202994i
$196$	5.14167	−	1.82684i	0.367262	−	0.130489i
$197$	−6.18981			−0.441006			−0.220503	−	0.975386i	$-0.570770\pi$
$197$	−6.18981			−0.441006			−0.220503	+	0.975386i	$0.570770\pi$
$198$	−3.78784	+	10.5541i	−0.269190	+	0.750045i
$199$	−0.981236	+	4.29907i	−0.0695580	+	0.304753i	−0.997725	−	0.0674096i	$-0.978527\pi$
$199$	−0.981236	+	4.29907i	−0.0695580	+	0.304753i	0.928167	+	0.372163i	$0.121384\pi$
$200$	−1.03762	−	0.156397i	−0.0733712	−	0.0110589i
$201$	12.9446	+	15.7511i	0.913045	+	1.11100i
$202$	17.5670	+	5.41869i	1.23601	+	0.381258i
$203$	17.3364	−	7.22966i	1.21678	−	0.507423i
$204$	6.26979	+	7.62910i	0.438973	+	0.534144i
$205$	0.418137	+	5.57965i	0.0292040	+	0.389700i
$206$	−0.101384	−	0.444193i	−0.00706376	−	0.0309484i
$207$	0.192660	−	0.536808i	0.0133908	−	0.0373107i
$208$	0.874668	+	1.09680i	0.0606473	+	0.0760493i
$209$	−3.84253	−	2.61979i	−0.265794	−	0.181215i
$210$	6.93318	+	9.42556i	0.478435	+	0.650425i
$211$	−17.9794	+	12.2581i	−1.23775	+	0.843886i	−0.992097	−	0.125472i	$-0.959956\pi$
$211$	−17.9794	+	12.2581i	−1.23775	+	0.843886i	−0.245656	+	0.969357i	$0.579003\pi$
$212$	6.37756	+	1.96722i	0.438013	+	0.135109i
$213$	6.36226	+	10.6547i	0.435935	+	0.730048i
$214$	8.34440	+	14.4529i	0.570411	+	0.987981i
$215$	−16.8782			−1.15108
$216$	4.23326	+	15.3839i	0.288037	+	1.04674i
$217$	24.8662	−	6.23017i	1.68802	−	0.422932i
$218$	2.46628	+	0.371732i	0.167038	+	0.0251769i
$219$	−4.20905	+	4.02224i	−0.284421	+	0.271798i
$220$	−5.03628	+	3.43368i	−0.339546	+	0.231499i
$221$	−4.62408	+	3.15264i	−0.311049	+	0.212070i
$222$	4.05322	+	1.18525i	0.272035	+	0.0795488i
$223$	−7.00277	−	1.05550i	−0.468940	−	0.0706814i	−0.0896784	−	0.995971i	$-0.528584\pi$
$223$	−7.00277	−	1.05550i	−0.468940	−	0.0706814i	−0.379262	+	0.925289i	$0.623822\pi$
$224$	−8.65534	−	6.60860i	−0.578309	−	0.441556i
$225$	0.615342	−	0.819981i	0.0410228	−	0.0546654i
$226$	6.31487			0.420059
$227$	−4.64867	−	8.05174i	−0.308543	−	0.534413i	0.669501	−	0.742812i	$-0.266508\pi$
$227$	−4.64867	−	8.05174i	−0.308543	−	0.534413i	−0.978044	+	0.208399i	$0.933175\pi$
$228$	−1.85569	+	0.0272982i	−0.122896	+	0.00180787i
$229$	1.97520	+	0.609268i	0.130525	+	0.0402615i	0.359329	−	0.933211i	$-0.383005\pi$
$229$	1.97520	+	0.609268i	0.130525	+	0.0402615i	−0.228805	+	0.973472i	$0.573482\pi$
$230$	−0.401071	+	0.273446i	−0.0264458	+	0.0180305i
$231$	15.2294	+	2.90672i	1.00202	+	0.191248i
$232$	−18.0122	−	12.2805i	−1.18256	−	0.806256i
$233$	10.2478	+	12.8504i	0.671359	+	0.841857i	0.994527	−	0.104485i	$-0.0333193\pi$
$233$	10.2478	+	12.8504i	0.671359	+	0.841857i	−0.323168	+	0.946342i	$0.604748\pi$
$234$	−2.49552	+	0.451580i	−0.163138	+	0.0295207i
$235$	−4.57521	−	20.0453i	−0.298454	−	1.30761i
$236$	0.389352	+	5.19554i	0.0253446	+	0.338201i
$237$	6.07198	−	1.00676i	0.394417	−	0.0653959i
$238$	−14.2069	+	15.9744i	−0.920896	+	1.03546i
$239$	5.21822	+	1.60961i	0.337539	+	0.104117i	0.458891	−	0.888493i	$-0.348247\pi$
$239$	5.21822	+	1.60961i	0.337539	+	0.104117i	−0.121352	+	0.992609i	$0.538723\pi$
$240$	2.58051	−	6.87052i	0.166571	−	0.443490i
$241$	23.9244	+	3.60602i	1.54111	+	0.232284i	0.863959	−	0.503563i	$-0.167978\pi$
$241$	23.9244	+	3.60602i	1.54111	+	0.232284i	0.677148	+	0.735847i	$0.263216\pi$
$242$	0.109836	−	0.481223i	0.00706052	−	0.0309342i
$243$	−15.1933	−	3.48779i	−0.974648	−	0.223742i
$244$	4.09442			0.262118
$245$	11.3850	−	11.4946i	0.727362	−	0.734364i
$246$	−4.59036	−	0.622977i	−0.292671	−	0.0397196i
$247$	0.0786024	−	1.04888i	0.00500135	−	0.0667384i
$248$	−21.8097	−	20.2365i	−1.38492	−	1.28502i
$249$	−18.8527	−	5.51294i	−1.19474	−	0.349368i
$250$	11.3657	−	3.50586i	0.718830	−	0.221730i
$251$	1.93483	+	8.47706i	0.122126	+	0.535067i	0.998565	+	0.0535548i	$0.0170552\pi$
$251$	1.93483	+	8.47706i	0.122126	+	0.535067i	−0.876439	+	0.481512i	$0.840088\pi$
$252$	5.63799	−	2.54836i	0.355160	−	0.160531i
$253$	−0.143127	+	0.627079i	−0.00899829	+	0.0394241i
$254$	0.977626	+	13.0455i	0.0613417	+	0.818549i
$255$	26.5632	+	12.3142i	1.66345	+	0.771142i
$256$	−1.15810	+	15.4537i	−0.0723811	+	0.965859i
$257$	−12.6743	+	1.91034i	−0.790599	+	0.119164i	−0.531914	−	0.846798i	$-0.678527\pi$
$257$	−12.6743	+	1.91034i	−0.790599	+	0.119164i	−0.258685	+	0.965962i	$0.583289\pi$
$258$	2.90873	−	13.6677i	0.181090	−	0.850912i
$259$	0.748275	−	5.79086i	0.0464955	−	0.359827i
$260$	−1.24206	−	0.598145i	−0.0770293	−	0.0370954i
$261$	18.9091	−	9.80149i	1.17044	−	0.606697i
$262$	−0.677034	−	0.848974i	−0.0418273	−	0.0524498i
$263$	−0.553145	−	0.958076i	−0.0341084	−	0.0590775i	0.848467	−	0.529248i	$-0.177526\pi$
$263$	−0.553145	−	0.958076i	−0.0341084	−	0.0590775i	−0.882576	+	0.470170i	$0.844192\pi$
$264$	−6.81977	−	16.6520i	−0.419728	−	1.02486i
$265$	19.5673	−	2.94930i	1.20201	−	0.181174i
$266$	−0.682489	−	3.95939i	−0.0418461	−	0.242766i
$267$	−9.36851	+	8.95272i	−0.573344	+	0.547898i
$268$	−9.07304	−	1.36754i	−0.554224	−	0.0835359i
$269$	−25.4069	−	12.2353i	−1.54909	−	0.746000i	−0.552898	−	0.833249i	$-0.686478\pi$
$269$	−25.4069	−	12.2353i	−1.54909	−	0.746000i	−0.996187	+	0.0872486i	$0.972193\pi$
$270$	8.72171	+	9.99795i	0.530786	+	0.608456i
$271$	13.6531	−	17.1204i	0.829366	−	1.03999i	−0.169153	−	0.985590i	$-0.554103\pi$
$271$	13.6531	−	17.1204i	0.829366	−	1.03999i	0.998519	−	0.0544020i	$-0.0173252\pi$
$272$	13.2591	+	1.99849i	0.803954	+	0.121177i
$273$	1.15286	+	3.31161i	0.0697741	+	0.200428i
$274$	−6.46078	+	0.973806i	−0.390310	+	0.0588298i
$275$	−0.578089	+	1.00128i	−0.0348601	+	0.0603795i
$276$	0.0972796	+	0.237530i	0.00585555	+	0.0142976i
$277$	−3.16945	+	8.07563i	−0.190434	+	0.485217i	−0.993920	−	0.110106i	$-0.964881\pi$
$277$	−3.16945	+	8.07563i	−0.190434	+	0.485217i	0.803486	+	0.595324i	$0.202976\pi$
$278$	0.921283	+	4.03641i	0.0552549	+	0.242087i
$279$	27.5117	−	9.38098i	1.64708	−	0.561625i
$280$	−18.3902	−	3.79119i	−1.09903	−	0.226567i
$281$	−21.1364	−	14.4106i	−1.26089	−	0.859663i	−0.266339	−	0.963879i	$-0.585814\pi$
$281$	−21.1364	−	14.4106i	−1.26089	−	0.859663i	−0.994555	+	0.104217i	$0.966766\pi$
$282$	17.0208	−	0.250385i	1.01357	−	0.0149102i
$283$	−1.70461	+	22.7465i	−0.101329	+	1.35214i	0.682375	+	0.731002i	$0.260947\pi$
$283$	−1.70461	+	22.7465i	−0.101329	+	1.35214i	−0.783704	+	0.621135i	$0.786672\pi$
$284$	−5.33687	−	1.64621i	−0.316685	−	0.0976844i
$285$	−4.92206	+	2.46017i	−0.291558	+	0.145728i
$286$	2.73302	−	0.843025i	0.161607	−	0.0498491i
$287$	0.135108	+	6.40375i	0.00797519	+	0.378002i
$288$	−10.4025	−	6.65272i	−0.612974	−	0.392015i
$289$	−8.12053	+	35.5783i	−0.477678	+	2.09284i
$290$	−17.9249	−	2.70174i	−1.05259	−	0.158652i
$291$	−26.6671	+	4.42151i	−1.56325	+	0.259193i
$292$	0.195804	−	2.61282i	0.0114586	−	0.152904i
$293$	−5.20926	+	9.02270i	−0.304328	+	0.527111i	−0.977111	−	0.212728i	$-0.931765\pi$
$293$	−5.20926	+	9.02270i	−0.304328	+	0.527111i	0.672784	+	0.739839i	$0.265099\pi$
$294$	7.34608	+	11.2003i	0.428432	+	0.653216i
$295$	7.72388	+	13.3782i	0.449702	+	0.778906i
$296$	−6.10569	+	2.94035i	−0.354886	+	0.170904i
$297$	17.4825	+	1.85077i	1.01444	+	0.107393i
$298$	0.650871	−	0.816167i	0.0377040	−	0.0472793i
$299$	−0.139008	+	0.0428784i	−0.00803907	+	0.00247972i
$300$	0.0412433	+	0.459540i	0.00238118	+	0.0265316i
$301$	−19.2934	−	1.03714i	−1.11205	−	0.0597798i
$302$	15.6223	+	14.4953i	0.898960	+	0.834113i
$303$	1.73089	−	28.7702i	0.0994372	−	1.65280i
$304$	−1.84735	+	1.71409i	−0.105953	+	0.0983097i
$305$	10.9376	−	5.26726i	0.626283	−	0.301602i
$306$	−14.5496	+	19.3882i	−0.831744	+	1.10835i
$307$	−14.0240	+	6.75360i	−0.800392	+	0.385449i	−0.788928	−	0.614486i	$-0.789364\pi$
$307$	−14.0240	+	6.75360i	−0.800392	+	0.385449i	−0.0114643	+	0.999934i	$0.503649\pi$
$308$	−5.96794	+	3.61554i	−0.340055	+	0.206015i
$309$	−0.638951	+	0.319364i	−0.0363487	+	0.0181680i
$310$	−23.6402	−	7.29205i	−1.34268	−	0.414161i
$311$	6.92765	−	1.04418i	0.392831	−	0.0592098i	0.0503431	−	0.998732i	$-0.483969\pi$
$311$	6.92765	−	1.04418i	0.392831	−	0.0592098i	0.342488	+	0.939522i	$0.388730\pi$
$312$	2.49036	−	3.21882i	0.140989	−	0.182230i
$313$	−6.11603	−	10.5933i	−0.345699	−	0.598767i	0.639782	−	0.768557i	$-0.279025\pi$
$313$	−6.11603	−	10.5933i	−0.345699	−	0.598767i	−0.985480	+	0.169789i	$0.945691\pi$
$314$	−9.32829	−	11.6973i	−0.526426	−	0.660117i
$315$	11.7827	−	14.0605i	0.663878	−	0.792220i
$316$	−1.72707	+	2.16568i	−0.0971552	+	0.121829i
$317$	15.5491	+	2.34364i	0.873322	+	0.131632i	0.570384	−	0.821378i	$-0.306794\pi$
$317$	15.5491	+	2.34364i	0.873322	+	0.131632i	0.302938	+	0.953010i	$0.402033\pi$
$318$	−0.983875	+	16.3536i	−0.0551730	+	0.917062i
$319$	−19.8460	+	13.5308i	−1.11117	+	0.757580i
$320$	6.93562	+	17.6717i	0.387713	+	0.987877i
$321$	18.9164	−	18.0768i	1.05581	−	1.00895i
$322$	−0.475264	+	0.287928i	−0.0264854	+	0.0160456i
$323$	−6.26829	−	7.86019i	−0.348777	−	0.437353i
$324$	6.13090	−	3.41037i	0.340605	−	0.189465i
$325$	−0.261489			−0.0145048
$326$	8.05050	−	20.5123i	0.445876	−	1.13607i
$327$	−0.349544	−	3.89468i	−0.0193298	−	0.215376i
$328$	6.14219	−	4.18767i	0.339146	−	0.231226i
$329$	−3.99814	−	23.1948i	−0.220425	−	1.27877i
$330$	−11.1170	−	10.0148i	−0.611969	−	0.551297i
$331$	5.64667	−	14.3875i	0.310369	−	0.790808i	−0.687538	−	0.726148i	$-0.741309\pi$
$331$	5.64667	−	14.3875i	0.310369	−	0.790808i	0.997907	−	0.0646595i	$-0.0205961\pi$
$332$	7.96455	−	3.83553i	0.437112	−	0.210502i
$333$	0.300355	−	6.61399i	0.0164594	−	0.362445i
$334$	16.0205	+	7.71508i	0.876605	+	0.422151i
$335$	−25.9964	+	8.01884i	−1.42034	+	0.438116i
$336$	3.37195	−	7.69507i	0.183955	−	0.419800i
$337$	−25.2064	−	7.77515i	−1.37308	−	0.423540i	−0.481519	−	0.876436i	$-0.659915\pi$
$337$	−25.2064	−	7.77515i	−1.37308	−	0.423540i	−0.891563	+	0.452896i	$0.850391\pi$
$338$	−10.0538	−	9.32857i	−0.546855	−	0.507407i
$339$	−2.34481	−	9.61884i	−0.127352	−	0.522424i
$340$	−12.5915	+	3.88395i	−0.682868	+	0.210637i
$341$	−29.5347	+	14.2231i	−1.59939	+	0.770226i
$342$	−1.14395	−	4.40977i	−0.0618579	−	0.238453i
$343$	13.7205	−	12.4398i	0.740835	−	0.671687i
$344$	11.2122	+	19.4201i	0.604522	+	1.04706i
$345$	0.565438	+	0.509379i	0.0304421	+	0.0274240i
$346$	−14.5329	−	13.4845i	−0.781292	−	0.724933i
$347$	5.23113	+	13.3287i	0.280822	+	0.715523i	0.999790	+	0.0204798i	$0.00651939\pi$
$347$	5.23113	+	13.3287i	0.280822	+	0.715523i	−0.718968	+	0.695043i	$0.755385\pi$
$348$	−3.37031	+	8.97332i	−0.180667	+	0.481020i
$349$	−4.60516	+	4.27297i	−0.246509	+	0.228727i	−0.793744	−	0.608252i	$-0.791871\pi$
$349$	−4.60516	+	4.27297i	−0.246509	+	0.228727i	0.547235	+	0.836979i	$0.315680\pi$
$350$	−0.968899	+	0.242756i	−0.0517898	+	0.0129759i
$351$	1.61448	+	3.63352i	0.0861743	+	0.193943i
$352$	12.5465	+	6.04210i	0.668733	+	0.322045i
$353$	8.86602	−	8.22647i	0.471891	−	0.437851i	−0.408032	−	0.912968i	$-0.633785\pi$
$353$	8.86602	−	8.22647i	0.471891	−	0.437851i	0.879923	+	0.475117i	$0.157594\pi$
$354$	−12.1645	+	3.94911i	−0.646536	+	0.209893i
$355$	−16.3744	+	2.46804i	−0.869060	+	0.130990i
$356$	0.435821	−	5.81563i	0.0230985	−	0.308228i
$357$	29.6075	+	15.7085i	1.56699	+	0.831381i
$358$	−0.897551	−	11.9770i	−0.0474370	−	0.633003i
$359$	6.29159	+	27.5653i	0.332057	+	1.45484i	0.815140	+	0.579264i	$0.196660\pi$
$359$	6.29159	+	27.5653i	0.332057	+	1.45484i	−0.483082	+	0.875575i	$0.660483\pi$
$360$	−21.1375	−	2.55262i	−1.11404	−	0.134535i
$361$	−17.1105			−0.900554
$362$	4.87861	+	8.45001i	0.256414	+	0.444122i
$363$	−0.773785	+	0.0113828i	−0.0406132	+	0.000597442i
$364$	−1.38303	−	0.760057i	−0.0724907	−	0.0398378i
$365$	−2.83820	−	7.23163i	−0.148558	−	0.378521i
$366$	2.38039	+	9.76479i	0.124425	+	0.510414i
$367$	−0.158594	−	2.11630i	−0.00827856	−	0.110470i	0.991534	−	0.129850i	$-0.0414497\pi$
$367$	−0.158594	−	2.11630i	−0.00827856	−	0.110470i	−0.999812	+	0.0193805i	$0.993831\pi$
$368$	0.314023	+	0.151225i	0.0163696	+	0.00788317i
$369$	0.755549	+	7.22338i	0.0393323	+	0.376034i
$370$	−3.51340	+	4.40566i	−0.182653	+	0.229039i
$371$	22.5485	−	2.16894i	1.17066	−	0.112606i
$372$	−6.37348	+	11.4240i	−0.330450	+	0.592308i
$373$	−4.05851	+	7.02955i	−0.210142	+	0.363976i	−0.951759	−	0.306847i	$-0.900726\pi$
$373$	−4.05851	+	7.02955i	−0.210142	+	0.363976i	0.741617	+	0.670824i	$0.234059\pi$
$374$	13.6687	−	23.6750i	0.706794	−	1.22420i
$375$	−9.56040	−	16.0105i	−0.493697	−	0.826780i
$376$	−20.0249	+	18.5804i	−1.03270	+	0.958209i
$377$	−4.89448	−	2.35706i	−0.252078	−	0.121395i
$378$	9.35536	+	11.9645i	0.481188	+	0.615389i
$379$	17.7260	−	8.53640i	0.910524	−	0.438485i	0.0808457	−	0.996727i	$-0.474238\pi$
$379$	17.7260	−	8.53640i	0.910524	−	0.438485i	0.829679	+	0.558241i	$0.188524\pi$
$380$	0.904756	−	2.30528i	0.0464130	−	0.118258i
$381$	19.5080	−	6.33313i	0.999425	−	0.324456i
$382$	−12.1759	−	3.75577i	−0.622974	−	0.192162i
$383$	17.4963	−	11.9288i	0.894021	−	0.609533i	−0.0267478	−	0.999642i	$-0.508515\pi$
$383$	17.4963	−	11.9288i	0.894021	−	0.609533i	0.920769	+	0.390109i	$0.127563\pi$
$384$	−1.43936	+	0.238651i	−0.0734519	+	0.0121786i
$385$	−11.2912	+	17.3358i	−0.575451	+	0.883513i
$386$	−4.45807	−	19.5321i	−0.226910	−	0.994157i
$387$	−21.8987	+	0.644424i	−1.11318	+	0.0327579i
$388$	7.58499	−	9.51128i	0.385070	−	0.482862i
$389$	11.5839	−	3.57316i	0.587327	−	0.181166i	0.0131722	−	0.999913i	$-0.495807\pi$
$389$	11.5839	−	3.57316i	0.587327	−	0.181166i	0.574155	+	0.818747i	$0.305331\pi$
$390$	0.704416	−	3.30994i	0.0356695	−	0.167605i
$391$	−0.695228	+	1.20417i	−0.0351592	+	0.0608975i
$392$	−20.7888	−	5.46374i	−1.04999	−	0.275960i
$393$	−1.04177	+	1.34650i	−0.0525502	+	0.0679219i
$394$	5.65002	+	3.85212i	0.284644	+	0.194067i
$395$	−1.82755	+	8.00704i	−0.0919542	+	0.402878i
$396$	−6.40325	+	4.64734i	−0.321776	+	0.233537i
$397$	4.09397	−	17.9369i	0.205470	−	0.900225i	−0.762067	−	0.647498i	$-0.775815\pi$
$397$	4.09397	−	17.9369i	0.205470	−	0.900225i	0.967538	−	0.252727i	$-0.0813274\pi$
$398$	3.57112	−	3.31351i	0.179004	−	0.166091i
$399$	−5.77754	+	2.50975i	−0.289239	+	0.125645i
$400$	0.459263	+	0.426134i	0.0229632	+	0.0213067i
$401$	−6.49686	+	4.42948i	−0.324438	+	0.221198i	−0.714575	−	0.699559i	$-0.753380\pi$
$401$	−6.49686	+	4.42948i	−0.324438	+	0.221198i	0.390137	+	0.920757i	$0.372428\pi$
$402$	−2.01338	−	22.4334i	−0.100418	−	1.11888i
$403$	−6.12570	−	4.17643i	−0.305143	−	0.208043i
$404$	8.08756	+	10.1415i	0.402371	+	0.504557i
$405$	11.9904	−	16.9973i	0.595809	−	0.844605i
$406$	−20.3238	−	4.18980i	−1.00865	−	0.207936i
$407$	0.557991	+	7.44587i	0.0276586	+	0.369078i
$408$	−3.47723	−	38.7439i	−0.172149	−	1.91811i
$409$	28.7663	−	4.33582i	1.42240	−	0.214392i	0.607650	−	0.794205i	$-0.292112\pi$
$409$	28.7663	−	4.33582i	1.42240	−	0.214392i	0.814750	+	0.579813i	$0.196874\pi$
$410$	3.09072	−	5.35329i	0.152640	−	0.264380i
$411$	3.88230	+	9.47951i	0.191500	+	0.467590i
$412$	0.117450	−	0.299257i	0.00578633	−	0.0147433i
$413$	8.00705	+	15.7671i	0.394001	+	0.775848i
$414$	−0.509931	+	0.370096i	−0.0250617	+	0.0181892i
$415$	16.3418	−	20.4920i	0.802188	−	1.00591i
$416$	0.235363	+	3.14070i	0.0115396	+	0.153985i
$417$	5.80619	−	2.90208i	0.284330	−	0.142116i
$418$	1.87706	+	4.78266i	0.0918099	+	0.233928i
$419$	4.93643	+	12.5778i	0.241160	+	0.614467i	0.999292	−	0.0376355i	$-0.0119826\pi$
$419$	4.93643	+	12.5778i	0.241160	+	0.614467i	−0.758131	+	0.652102i	$0.773887\pi$
$420$	0.295542	+	8.25076i	0.0144210	+	0.402596i
$421$	6.73170	−	17.1521i	0.328083	−	0.835942i	−0.667720	−	0.744413i	$-0.732729\pi$
$421$	6.73170	−	17.1521i	0.328083	−	0.835942i	0.995802	−	0.0915286i	$-0.0291753\pi$
$422$	24.0401			1.17025
$423$	−6.70148	−	25.8332i	−0.325837	−	1.25605i
$424$	−16.3921	−	20.5550i	−0.796069	−	0.998239i
$425$	−1.83218	+	1.70001i	−0.0888737	+	0.0824627i
$426$	0.823327	−	13.6850i	0.0398903	−	0.663040i
$427$	12.8263	−	5.34887i	0.620709	−	0.258850i
$428$	−0.879985	+	11.7426i	−0.0425357	+	0.567599i
$429$	−2.29891	−	3.84992i	−0.110993	−	0.185876i
$430$	15.4063	+	10.5039i	0.742959	+	0.506541i
$431$	−3.35581	−	14.7027i	−0.161644	−	0.708206i	−0.989169	−	0.146779i	$-0.953109\pi$
$431$	−3.35581	−	14.7027i	−0.161644	−	0.708206i	0.827526	−	0.561428i	$-0.189748\pi$
$432$	3.08578	−	9.01271i	0.148464	−	0.433624i
$433$	−5.11004	+	22.3886i	−0.245573	+	1.07593i	0.690282	+	0.723540i	$0.257486\pi$
$433$	−5.11004	+	22.3886i	−0.245573	+	1.07593i	−0.935855	+	0.352385i	$0.885371\pi$
$434$	−26.5749	−	9.78815i	−1.27564	−	0.469846i
$435$	2.54048	+	28.3065i	0.121807	+	1.35719i
$436$	1.29006	+	1.19700i	0.0617827	+	0.0573259i
$437$	−0.0954720	−	0.243259i	−0.00456705	−	0.0116366i
$438$	6.34516	−	1.05205i	0.303184	−	0.0502690i
$439$	−23.5700	−	16.0698i	−1.12494	−	0.766968i	−0.149830	−	0.988712i	$-0.547873\pi$
$439$	−23.5700	−	16.0698i	−1.12494	−	0.766968i	−0.975105	+	0.221744i	$0.928825\pi$
$440$	24.0114			1.14470
$441$	14.3327	−	15.3484i	0.682508	−	0.730878i
$442$	6.18282			0.294087
$443$	−19.9735	−	13.6177i	−0.948969	−	0.646996i	−0.0133134	−	0.999911i	$-0.504238\pi$
$443$	−19.9735	−	13.6177i	−0.948969	−	0.646996i	−0.935655	+	0.352916i	$0.885190\pi$
$444$	1.89188	+	2.30204i	0.0897845	+	0.109250i
$445$	−6.31728	−	16.0962i	−0.299468	−	0.763032i
$446$	5.73521	+	5.32150i	0.271570	+	0.251980i
$447$	−1.48487	−	0.688355i	−0.0702319	−	0.0325581i
$448$	6.84216	+	20.6266i	0.323262	+	0.974513i
$449$	2.26625	−	9.92910i	0.106951	−	0.468583i	−0.892882	−	0.450291i	$-0.851320\pi$
$449$	2.26625	−	9.92910i	0.106951	−	0.468583i	0.999833	−	0.0182917i	$-0.00582276\pi$
$450$	−1.07198	+	0.365526i	−0.0505337	+	0.0172311i
$451$	−1.82262	−	7.98540i	−0.0858236	−	0.376018i
$452$	3.68150	+	2.51000i	0.173163	+	0.118061i
$453$	16.2786	−	29.1782i	0.764835	−	1.37091i
$454$	−0.767577	+	10.2426i	−0.0360242	+	0.480709i
$455$	−4.67233	−	0.251167i	−0.219042	−	0.0117749i
$456$	6.10041	+	4.02904i	0.285678	+	0.188677i
$457$	27.7414	−	25.7402i	1.29769	−	1.20408i	0.332324	−	0.943165i	$-0.392167\pi$
$457$	27.7414	−	25.7402i	1.29769	−	1.20408i	0.965363	−	0.260912i	$-0.0840232\pi$
$458$	−1.42378	−	1.78536i	−0.0665289	−	0.0834246i
$459$	34.9347	+	14.9629i	1.63061	+	0.698406i
$460$	−0.342508			−0.0159695
$461$	−5.38816	+	13.7288i	−0.250952	+	0.639414i	−0.999726	−	0.0234106i	$-0.992547\pi$
$461$	−5.38816	+	13.7288i	−0.250952	+	0.639414i	0.748774	+	0.662825i	$0.230643\pi$
$462$	−12.0923	−	12.1310i	−0.562586	−	0.564384i
$463$	−0.479981	−	1.22297i	−0.0223066	−	0.0568363i	0.919287	−	0.393589i	$-0.128767\pi$
$463$	−0.479981	−	1.22297i	−0.0223066	−	0.0568363i	−0.941593	+	0.336753i	$0.890671\pi$
$464$	4.75520	+	12.1161i	0.220755	+	0.562474i
$465$	−2.32930	+	38.7166i	−0.108019	+	1.79544i
$466$	−1.35696	−	18.1073i	−0.0628598	−	0.838805i
$467$	6.81746	−	8.54883i	0.315474	−	0.395592i	−0.598660	−	0.801003i	$-0.704300\pi$
$467$	6.81746	−	8.54883i	0.315474	−	0.395592i	0.914135	+	0.405411i	$0.132871\pi$
$468$	−1.63435	−	0.728643i	−0.0755481	−	0.0336815i
$469$	−30.2091	+	7.56884i	−1.39493	+	0.349496i
$470$	−8.29862	+	21.1445i	−0.382787	+	0.975325i
$471$	−14.3537	+	18.5523i	−0.661382	+	0.854845i
$472$	10.2620	−	17.7742i	0.472345	−	0.818125i
$473$	24.4315	−	3.68245i	1.12336	−	0.169319i
$474$	−6.16900	−	2.85982i	−0.283351	−	0.131356i
$475$	−0.0351034	−	0.468422i	−0.00161065	−	0.0214927i
$476$	−14.6319	+	3.66599i	−0.670651	+	0.168030i
$477$	25.2751	−	4.57368i	1.15727	−	0.209415i
$478$	−3.76145	−	4.71671i	−0.172045	−	0.215737i
$479$	−4.52552	−	3.08544i	−0.206776	−	0.140978i	0.455504	−	0.890234i	$-0.349459\pi$
$479$	−4.52552	−	3.08544i	−0.206776	−	0.140978i	−0.662281	+	0.749256i	$0.730411\pi$
$480$	13.4758	−	9.48097i	0.615084	−	0.432745i
$481$	−1.39529	+	0.951295i	−0.0636199	+	0.0433753i
$482$	−19.5939	−	18.1805i	−0.892478	−	0.828098i
$483$	0.615047	+	0.617012i	0.0279856	+	0.0280750i
$484$	0.255307	−	0.236891i	0.0116049	−	0.0107678i
$485$	8.02631	−	35.1655i	0.364456	−	1.59679i
$486$	11.6978	+	12.6389i	0.530621	+	0.573312i
$487$	6.74076	−	29.5332i	0.305453	−	1.33828i	−0.556314	−	0.830972i	$-0.687785\pi$
$487$	6.74076	−	29.5332i	0.305453	−	1.33828i	0.861767	−	0.507305i	$-0.169358\pi$
$488$	−13.3263	−	9.08575i	−0.603255	−	0.411292i
$489$	−34.2338	−	4.64601i	−1.54810	−	0.210100i
$490$	−17.5456	+	3.40695i	−0.792631	+	0.153910i
$491$	−8.14343	+	14.1048i	−0.367508	+	0.636542i	−0.989175	−	0.146739i	$-0.953122\pi$
$491$	−8.14343	+	14.1048i	−0.367508	+	0.636542i	0.621667	+	0.783281i	$0.286456\pi$
$492$	−2.42851	−	2.18774i	−0.109486	−	0.0986311i
$493$	−49.6181	+	15.3052i	−2.23469	+	0.689309i
$494$	−0.724497	+	0.908490i	−0.0325967	+	0.0408749i
$495$	−11.1267	+	20.6521i	−0.500108	+	0.928241i
$496$	3.95271	+	17.3179i	0.177482	+	0.777599i
$497$	−18.8691	+	1.81502i	−0.846393	+	0.0814146i
$498$	13.7777	+	16.7648i	0.617395	+	0.751249i
$499$	20.9194	−	14.2626i	0.936483	−	0.638483i	0.00411373	−	0.999992i	$-0.498691\pi$
$499$	20.9194	−	14.2626i	0.936483	−	0.638483i	0.932369	+	0.361509i	$0.117738\pi$
$500$	8.01957	+	2.47371i	0.358646	+	0.110628i
$501$	5.80298	−	27.2673i	0.259258	−	1.21821i
$502$	3.50944	−	8.94191i	0.156634	−	0.399097i
$503$	1.37144	−	0.660451i	0.0611495	−	0.0294481i	−0.403059	−	0.915174i	$-0.632053\pi$
$503$	1.37144	−	0.660451i	0.0611495	−	0.0294481i	0.464209	+	0.885726i	$0.346339\pi$
$504$	−24.0053	−	4.21675i	−1.06928	−	0.187829i
$505$	34.6511	+	16.6871i	1.54195	+	0.742565i
$506$	0.520896	−	0.483321i	0.0231567	−	0.0214862i
$507$	−10.4762	+	18.7778i	−0.465264	+	0.833954i
$508$	−4.61532	+	7.99398i	−0.204772	+	0.354675i
$509$	−17.5793	+	30.4482i	−0.779187	+	1.34959i	0.153224	+	0.988192i	$0.451034\pi$
$509$	−17.5793	+	30.4482i	−0.779187	+	1.34959i	−0.932411	+	0.361400i	$0.882299\pi$
$510$	−16.5832	−	27.7714i	−0.734316	−	1.22974i
$511$	−2.79996	−	8.44082i	−0.123863	−	0.373400i
$512$	11.7249	−	14.7025i	0.518171	−	0.649766i
$513$	−6.29222	+	3.37989i	−0.277808	+	0.149226i
$514$	12.7579	+	6.14386i	0.562725	+	0.270994i
$515$	−0.0712309	−	0.950510i	−0.00313881	−	0.0418845i
$516$	7.12832	−	6.81195i	0.313807	−	0.299880i
$517$	10.9961	+	28.0177i	0.483609	+	1.23222i
$518$	−4.28686	+	4.82019i	−0.188354	+	0.211787i
$519$	−15.1434	+	27.1436i	−0.664723	+	1.19147i
$520$	2.71529	+	4.70302i	0.119073	+	0.206241i
$521$	26.4754			1.15991			0.579954	−	0.814649i	$-0.303070\pi$
$521$	26.4754			1.15991			0.579954	+	0.814649i	$0.303070\pi$
$522$	−23.3599	−	2.82100i	−1.02243	−	0.123472i
$523$	−2.27230	−	9.95561i	−0.0993609	−	0.435329i	−1.00000		0.000760113i	$-0.999758\pi$
$523$	−2.27230	−	9.95561i	−0.0993609	−	0.435329i	0.900639	−	0.434568i	$-0.143099\pi$
$524$	−0.0572574	−	0.764046i	−0.00250130	−	0.0333775i
$525$	0.729535	+	1.38569i	0.0318395	+	0.0604766i
$526$	−0.0913339	+	1.21877i	−0.00398235	+	0.0531407i
$527$	−70.0732	+	10.5618i	−3.05244	+	0.460081i
$528$	−2.23633	+	10.5082i	−0.0973240	+	0.457310i
$529$	16.8337	−	15.6194i	0.731900	−	0.679104i
$530$	−19.6964	−	9.48528i	−0.855557	−	0.412014i
$531$	10.5322	+	17.0627i	0.457058	+	0.740456i
$532$	1.17588	−	2.57955i	0.0509807	−	0.111838i
$533$	1.35796	−	1.26000i	0.0588198	−	0.0545768i
$534$	14.1231	−	2.34166i	0.611166	−	0.101334i
$535$	12.7555	+	32.5005i	0.551468	+	1.40512i
$536$	26.4959	+	24.5846i	1.14445	+	1.06189i
$537$	−17.9101	+	5.81440i	−0.772879	+	0.250910i
$538$	15.5768	+	26.9798i	0.671564	+	1.16318i
$539$	−13.9721	+	19.1226i	−0.601821	+	0.823668i
$540$	1.11072	+	9.29536i	0.0477979	+	0.400008i
$541$	19.0663	−	9.18187i	0.819726	−	0.394759i	0.0234743	−	0.999724i	$-0.492527\pi$
$541$	19.0663	−	9.18187i	0.819726	−	0.394759i	0.796252	+	0.604965i	$0.206813\pi$
$542$	−23.1170	+	7.13066i	−0.992962	+	0.306288i
$543$	11.0596	−	10.5687i	0.474612	−	0.453548i
$544$	22.0677	+	20.4758i	0.946144	+	0.877893i
$545$	4.98607	+	1.53800i	0.213580	+	0.0658806i
$546$	1.00860	−	3.74028i	0.0431642	−	0.160069i
$547$	20.9574	−	6.46449i	0.896072	−	0.276402i	0.187688	−	0.982229i	$-0.439901\pi$
$547$	20.9574	−	6.46449i	0.896072	−	0.276402i	0.708384	+	0.705827i	$0.249425\pi$
$548$	−4.15363	−	2.00028i	−0.177434	−	0.0854478i
$549$	13.9899	−	7.25163i	0.597074	−	0.309492i
$550$	1.15081	−	0.554199i	0.0490705	−	0.0236311i
$551$	3.56529	−	9.08422i	0.151887	−	0.387001i
$552$	0.210472	−	0.988974i	0.00895827	−	0.0420935i
$553$	−2.58108	+	9.04049i	−0.109759	+	0.384441i
$554$	7.91878	−	5.39893i	0.336437	−	0.229379i
$555$	8.01531	+	3.71574i	0.340231	+	0.157724i
$556$	−1.06727	+	2.71937i	−0.0452625	+	0.115327i
$557$	18.8933			0.800533			0.400267	−	0.916399i	$-0.368918\pi$
$557$	18.8933			0.800533			0.400267	+	0.916399i	$0.368918\pi$
$558$	−30.9506	−	8.55850i	−1.31024	−	0.362310i
$559$	3.48405	+	4.36887i	0.147360	+	0.184783i
$560$	7.79688	+	8.05537i	0.329478	+	0.340402i
$561$	−41.1373	−	12.0294i	−1.73682	−	0.507883i
$562$	10.3250	+	26.3078i	0.435535	+	1.10973i
$563$	8.03367	−	5.47727i	0.338579	−	0.230839i	−0.382080	−	0.924129i	$-0.624792\pi$
$563$	8.03367	−	5.47727i	0.338579	−	0.230839i	0.720659	+	0.693290i	$0.243840\pi$
$564$	10.0225	+	6.61938i	0.422022	+	0.278726i
$565$	13.0635	+	1.96901i	0.549586	+	0.0828368i
$566$	15.7118	−	19.7020i	0.660417	−	0.828137i
$567$	14.7506	−	18.6927i	0.619468	−	0.785022i
$568$	13.7172	+	17.2008i	0.575561	+	0.721731i
$569$	21.0252	+	36.4167i	0.881421	+	1.52667i	0.849762	+	0.527167i	$0.176746\pi$
$569$	21.0252	+	36.4167i	0.881421	+	1.52667i	0.0316592	+	0.999499i	$0.489921\pi$
$570$	6.02387	+	0.817525i	0.252312	+	0.0342424i
$571$	10.6229	−	1.60115i	0.444555	−	0.0670059i	0.0770495	−	0.997027i	$-0.475450\pi$
$571$	10.6229	−	1.60115i	0.444555	−	0.0670059i	0.367505	+	0.930021i	$0.380212\pi$
$572$	1.92840	+	0.594833i	0.0806305	+	0.0248712i
$573$	−1.19971	+	19.9410i	−0.0501184	+	0.833047i
$574$	3.86194	−	5.92939i	0.161194	−	0.247488i
$575$	−0.0585329	+	0.0281880i	−0.00244099	+	0.00117552i
$576$	9.67338	+	22.6634i	0.403057	+	0.944308i
$577$	9.81613	−	4.72720i	0.408651	−	0.196796i	−0.218253	−	0.975892i	$-0.570036\pi$
$577$	9.81613	−	4.72720i	0.408651	−	0.196796i	0.626904	+	0.779096i	$0.284322\pi$
$578$	29.5539	−	27.4220i	1.22928	−	1.14061i
$579$	−28.0960	+	14.0431i	−1.16763	+	0.583612i
$580$	−9.37614	−	8.69979i	−0.389323	−	0.361239i
$581$	19.9394	−	22.4201i	0.827226	−	0.930141i
$582$	27.0932	+	12.5599i	1.12305	+	0.520623i
$583$	−27.6805	+	8.53832i	−1.14641	+	0.353621i
$584$	−6.43530	+	8.06961i	−0.266295	+	0.333923i
$585$	−5.30328	+	0.156062i	−0.219263	+	0.00645236i
$586$	10.3701	−	4.99397i	0.428384	−	0.206299i
$587$	−20.3250	−	35.2040i	−0.838905	−	1.45303i	−0.890811	−	0.454373i	$-0.849863\pi$
$587$	−20.3250	−	35.2040i	−0.838905	−	1.45303i	0.0519068	−	0.998652i	$-0.483470\pi$
$588$	−0.169165	+	9.44955i	−0.00697624	+	0.389693i
$589$	6.65917	−	11.5340i	0.274386	−	0.475251i
$590$	1.27535	−	17.0183i	0.0525052	−	0.700633i
$591$	3.76963	−	10.0365i	0.155062	−	0.412846i
$592$	4.00088	+	0.603036i	0.164435	+	0.0247846i
$593$	−1.12280	+	4.91931i	−0.0461079	+	0.202012i	−0.992735	−	0.120318i	$-0.961609\pi$
$593$	−1.12280	+	4.91931i	−0.0461079	+	0.202012i	0.946628	+	0.322329i	$0.104466\pi$
$594$	−14.8061	−	12.5693i	−0.607503	−	0.515725i
$595$	−34.3706	+	28.6163i	−1.40906	+	1.17315i
$596$	0.703857	−	0.217111i	0.0288311	−	0.00889322i
$597$	−6.37317	−	4.20919i	−0.260837	−	0.172271i
$598$	0.153571	+	0.0473703i	0.00627997	+	0.00193712i
$599$	−0.706653	+	9.42963i	−0.0288731	+	0.385284i	0.963983	+	0.265965i	$0.0856904\pi$
$599$	−0.706653	+	9.42963i	−0.0288731	+	0.385284i	−0.992856	+	0.119320i	$0.961929\pi$
$600$	0.885509	−	1.58721i	0.0361508	−	0.0647978i
$601$	−9.60495	−	6.54855i	−0.391794	−	0.267121i	0.351361	−	0.936240i	$-0.385719\pi$
$601$	−9.60495	−	6.54855i	−0.391794	−	0.267121i	−0.743155	+	0.669119i	$0.766671\pi$
$602$	16.9654	+	12.9536i	0.691459	+	0.527949i
$603$	−33.4230	+	11.3966i	−1.36109	+	0.464107i
$604$	3.34607	+	14.6601i	0.136150	+	0.596510i
$605$	0.377265	−	0.961255i	0.0153380	−	0.0390806i
$606$	−19.4845	+	25.1840i	−0.791505	+	1.02303i
$607$	21.8805	−	37.8981i	0.888101	−	1.53824i	0.0459844	−	0.998942i	$-0.485358\pi$
$607$	21.8805	−	37.8981i	0.888101	−	1.53824i	0.842117	−	0.539295i	$-0.181309\pi$
$608$	−5.59454	+	0.843241i	−0.226889	+	0.0341979i
$609$	1.16462	+	32.5131i	0.0471926	+	1.31750i
$610$	−13.2617	−	1.99888i	−0.536952	−	0.0809324i
$611$	−4.24423	+	5.32210i	−0.171703	+	0.215309i
$612$	−16.1886	+	5.52001i	−0.654384	+	0.223133i
$613$	27.2267	+	13.1117i	1.09968	+	0.529577i	0.893557	−	0.448949i	$-0.148202\pi$
$613$	27.2267	+	13.1117i	1.09968	+	0.529577i	0.206121	+	0.978527i	$0.433916\pi$
$614$	17.0040	+	2.56294i	0.686226	+	0.103432i
$615$	−9.30179	−	2.72005i	−0.375085	−	0.109683i
$616$	27.4473	+	1.47547i	1.10588	+	0.0594482i
$617$	−5.57470	+	0.840251i	−0.224429	+	0.0338272i	−0.260294	−	0.965529i	$-0.583819\pi$
$617$	−5.57470	+	0.840251i	−0.224429	+	0.0338272i	0.0358650	+	0.999357i	$0.488581\pi$
$618$	0.781981	+	0.106126i	0.0314559	+	0.00426902i
$619$	−21.0038	−	36.3796i	−0.844213	−	1.46222i	−0.886303	−	0.463106i	$-0.846735\pi$
$619$	−21.0038	−	36.3796i	−0.844213	−	1.46222i	0.0420894	−	0.999114i	$-0.486599\pi$
$620$	−10.8836	−	13.6476i	−0.437096	−	0.548101i
$621$	0.753078	+	0.639307i	0.0302200	+	0.0256545i
$622$	−6.97334	−	3.35818i	−0.279605	−	0.134651i
$623$	−6.23216	−	18.7876i	−0.249686	−	0.752710i
$624$	−2.31109	+	0.750277i	−0.0925175	+	0.0300351i
$625$	26.2949	−	3.96331i	1.05179	−	0.158533i
$626$	−1.00986	+	13.4757i	−0.0403622	+	0.538597i
$627$	6.58800	−	4.63502i	0.263099	−	0.185105i
$628$	−0.788902	−	10.5272i	−0.0314806	−	0.420080i
$629$	−3.59179	+	15.7366i	−0.143214	+	0.627461i
$630$	−19.5054	+	5.50162i	−0.777116	+	0.219190i
$631$	4.50973	+	19.7584i	0.179529	+	0.786569i	0.981847	+	0.189673i	$0.0607427\pi$
$631$	4.50973	+	19.7584i	0.179529	+	0.786569i	−0.802318	+	0.596897i	$0.796400\pi$
$632$	10.4270	−	3.21629i	0.414762	−	0.127937i
$633$	−8.92647	−	36.6180i	−0.354795	−	1.45544i
$634$	−12.7346	−	11.8159i	−0.505754	−	0.469271i
$635$	−2.04525	+	27.2920i	−0.0811634	+	1.08305i
$636$	−7.07372	+	9.14287i	−0.280491	+	0.362539i
$637$	−5.32547	−	0.574215i	−0.211003	−	0.0227512i
$638$	26.5360			1.05057
$639$	−21.1508	+	3.82735i	−0.836711	+	0.151408i
$640$	0.433221	−	1.89806i	0.0171245	−	0.0750275i
$641$	−39.5914	−	5.96744i	−1.56377	−	0.235700i	−0.690642	−	0.723197i	$-0.742672\pi$
$641$	−39.5914	−	5.96744i	−1.56377	−	0.235700i	−0.873125	+	0.487497i	$0.837910\pi$
$642$	−28.5165	+	4.72815i	−1.12546	+	0.186605i
$643$	14.2727	+	4.40255i	0.562861	+	0.173620i	0.563112	−	0.826380i	$-0.309604\pi$
$643$	14.2727	+	4.40255i	0.562861	+	0.173620i	−0.000251255		1.00000i	$0.500080\pi$
$644$	−0.391518	−	0.0210466i	−0.0154280	−	0.000829351i
$645$	10.2789	−	27.3673i	0.404732	−	1.07758i
$646$	0.830008	+	11.0757i	0.0326562	+	0.435767i
$647$	−7.03921	−	30.8408i	−0.276740	−	1.21248i	−0.901888	−	0.431970i	$-0.857819\pi$
$647$	−7.03921	−	30.8408i	−0.276740	−	1.21248i	0.625148	−	0.780506i	$-0.285039\pi$
$648$	−27.5224	−	2.50486i	−1.08118	−	0.0984004i
$649$	−14.0992	−	17.6799i	−0.553444	−	0.693997i
$650$	0.238685	+	0.162733i	0.00936201	+	0.00638291i
$651$	−5.04168	+	44.1135i	−0.197599	+	1.72895i
$652$	12.8465	−	8.75859i	0.503108	−	0.343013i
$653$	−5.25136	−	1.61983i	−0.205502	−	0.0633889i	0.190295	−	0.981727i	$-0.439055\pi$
$653$	−5.25136	−	1.61983i	−0.205502	−	0.0633889i	−0.395797	+	0.918338i	$0.629532\pi$
$654$	−2.10472	+	3.77257i	−0.0823012	+	0.147519i
$655$	−1.13586	−	1.96737i	−0.0443817	−	0.0768714i
$656$	−4.43839			−0.173290
$657$	−3.95855	−	9.27434i	−0.154438	−	0.361827i
$658$	−10.7854	+	23.6602i	−0.420458	+	0.922372i
$659$	−0.237847	−	0.0358497i	−0.00926521	−	0.00139651i	0.144408	−	0.989518i	$-0.453872\pi$
$659$	−0.237847	−	0.0358497i	−0.00926521	−	0.00139651i	−0.153673	+	0.988122i	$0.549110\pi$
$660$	−2.50043	−	10.2572i	−0.0973292	−	0.399262i
$661$	−37.5714	+	25.6158i	−1.46136	+	0.996338i	−0.467703	+	0.883886i	$0.654918\pi$
$661$	−37.5714	+	25.6158i	−1.46136	+	0.996338i	−0.993657	+	0.112453i	$0.964129\pi$
$662$	−14.1080	+	9.61870i	−0.548325	+	0.373841i
$663$	−2.29578	−	9.41771i	−0.0891606	−	0.365753i
$664$	−34.4340	−	5.19009i	−1.33630	−	0.201414i
$665$	−0.177301	−	8.40356i	−0.00687543	−	0.325876i
$666$	−4.39026	+	5.85029i	−0.170119	+	0.226694i
$667$	−1.34969			−0.0522602
$668$	6.27324	+	10.8656i	0.242719	+	0.420402i
$669$	5.97616	−	10.7119i	0.231052	−	0.414145i
$670$	28.7198	+	8.85888i	1.10954	+	0.342248i
$671$	−14.6831	+	10.0108i	−0.566835	+	0.386461i
$672$	15.9867	−	10.0096i	0.616700	−	0.386127i
$673$	−28.1443	−	19.1884i	−1.08488	−	0.739659i	−0.117522	−	0.993070i	$-0.537495\pi$
$673$	−28.1443	−	19.1884i	−1.08488	−	0.739659i	−0.967359	+	0.253411i	$0.918448\pi$
$674$	18.1695	+	22.7839i	0.699865	+	0.877603i
$675$	0.954814	+	1.49712i	0.0367508	+	0.0576242i
$676$	−2.15338	−	9.43459i	−0.0828224	−	0.362869i
$677$	2.28930	+	30.5485i	0.0879848	+	1.17408i	0.850096	+	0.526629i	$0.176544\pi$
$677$	2.28930	+	30.5485i	0.0879848	+	1.17408i	−0.762111	+	0.647447i	$0.775837\pi$
$678$	−3.84579	+	10.2393i	−0.147697	+	0.393237i
$679$	11.3357	−	39.7043i	0.435024	−	1.52371i
$680$	49.6009	+	15.2999i	1.90211	+	0.586723i
$681$	15.8866	−	2.63406i	0.608776	−	0.100937i
$682$	35.8106	+	5.39757i	1.37126	+	0.206684i
$683$	−2.39720	+	10.5028i	−0.0917262	+	0.401879i	−0.999859	−	0.0168039i	$-0.994651\pi$
$683$	−2.39720	+	10.5028i	−0.0917262	+	0.401879i	0.908133	+	0.418683i	$0.137508\pi$
$684$	1.08586	−	3.02554i	0.0415190	−	0.115684i
$685$	−13.6690			−0.522266
$686$	−20.2656	+	2.81631i	−0.773746	+	0.107527i
$687$	−2.19080	+	2.83164i	−0.0835844	+	0.108034i
$688$	1.00052	−	13.3510i	0.0381444	−	0.509002i
$689$	−4.80257	−	4.45613i	−0.182963	−	0.169765i
$690$	−0.199125	−	0.816848i	−0.00758056	−	0.0310969i
$691$	−8.65708	+	2.67035i	−0.329331	+	0.101585i	−0.455011	−	0.890486i	$-0.650365\pi$
$691$	−8.65708	+	2.67035i	−0.329331	+	0.101585i	0.125681	+	0.992071i	$0.459889\pi$
$692$	−3.11274	−	13.6378i	−0.118329	−	0.518431i
$693$	−13.9879	+	22.9235i	−0.531356	+	0.870792i
$694$	3.51994	−	15.4219i	0.133615	−	0.585406i
$695$	0.647279	+	8.63734i	0.0245527	+	0.327633i
$696$	30.8819	−	21.7271i	1.17057	−	0.823563i
$697$	1.32321	−	17.6570i	0.0501200	−	0.668805i
$698$	6.86277	−	1.03440i	0.259760	−	0.0391524i
$699$	−27.0773	+	8.79045i	−1.02416	+	0.332485i
$700$	−0.661347	−	0.243589i	−0.0249966	−	0.00920681i
$701$	6.09727	+	2.93629i	0.230291	+	0.110902i	0.545471	−	0.838130i	$-0.316351\pi$
$701$	6.09727	+	2.93629i	0.230291	+	0.110902i	−0.315181	+	0.949032i	$0.602065\pi$
$702$	0.787572	−	4.32139i	0.0297250	−	0.163100i
$703$	−1.89143	−	2.37177i	−0.0713365	−	0.0894531i
$704$	−13.8950	−	24.0668i	−0.523687	−	0.907052i
$705$	35.2889	+	4.78921i	1.32906	+	0.180372i
$706$	−13.2124	+	1.99146i	−0.497257	+	0.0749494i
$707$	38.5840	+	21.2041i	1.45110	+	0.797464i
$708$	−8.66144	−	2.53279i	−0.325517	−	0.0951882i
$709$	6.29932	+	0.949470i	0.236576	+	0.0356581i	0.266260	−	0.963901i	$-0.414212\pi$
$709$	6.29932	+	0.949470i	0.236576	+	0.0356581i	−0.0296840	+	0.999559i	$0.509450\pi$
$710$	16.4823	+	7.93748i	0.618571	+	0.297888i
$711$	−2.06545	+	10.4585i	−0.0774606	+	0.392226i
$712$	−14.3237	+	17.9614i	−0.536804	+	0.673131i
$713$	−1.82142	−	0.274535i	−0.0682127	−	0.0102814i
$714$	−17.2496	−	32.7643i	−0.645551	−	1.22617i
$715$	5.91664	−	0.891789i	0.221270	−	0.0333510i
$716$	4.23729	−	7.33920i	0.158355	−	0.274279i
$717$	−5.78783	+	7.48084i	−0.216150	+	0.279377i
$718$	11.4118	−	29.0769i	0.425886	−	1.08514i
$719$	−1.49264	−	6.53967i	−0.0556660	−	0.243889i	0.939438	−	0.342718i	$-0.111347\pi$
$719$	−1.49264	−	6.53967i	−0.0556660	−	0.243889i	−0.995104	+	0.0988291i	$0.968490\pi$
$720$	9.56868	+	8.36836i	0.356604	+	0.311870i
$721$	−0.0230161	−	1.09090i	−0.000857164	−	0.0406272i
$722$	15.6184	+	10.6484i	0.581256	+	0.396294i
$723$	−20.4171	+	36.5962i	−0.759320	+	1.36103i
$724$	−0.514490	+	6.86539i	−0.0191209	+	0.255150i
$725$	−2.31832	−	0.715107i	−0.0861002	−	0.0265584i
$726$	0.713390	+	0.471161i	0.0264764	+	0.0174864i
$727$	32.7766	−	10.1102i	1.21562	−	0.374968i	0.380365	−	0.924836i	$-0.375798\pi$
$727$	32.7766	−	10.1102i	1.21562	−	0.374968i	0.835251	+	0.549868i	$0.185322\pi$
$728$	2.81484	+	5.54284i	0.104325	+	0.205431i
$729$	14.9081	−	22.5111i	0.552151	−	0.833744i
$730$	−1.90978	+	8.36729i	−0.0706841	+	0.309687i
$731$	52.8150	+	7.96058i	1.95343	+	0.294433i
$732$	−2.49352	+	6.63891i	−0.0921632	+	0.245381i
$733$	1.83205	−	24.4470i	0.0676683	−	0.902970i	−0.855310	−	0.518117i	$-0.826633\pi$
$733$	1.83205	−	24.4470i	0.0676683	−	0.902970i	0.922978	−	0.384853i	$-0.125748\pi$
$734$	−1.17228	+	2.03044i	−0.0432695	+	0.0749449i
$735$	11.7045	+	25.4606i	0.431725	+	0.939127i
$736$	0.391246	+	0.677658i	0.0144215	+	0.0249788i
$737$	35.8807	−	17.2792i	1.32168	−	0.636489i
$738$	3.80568	−	7.06366i	0.140089	−	0.260017i
$739$	−10.1977	+	12.7875i	−0.375128	+	0.470396i	−0.933180	−	0.359410i	$-0.882978\pi$
$739$	−10.1977	+	12.7875i	−0.375128	+	0.470396i	0.558051	+	0.829806i	$0.311549\pi$
$740$	−3.79941	+	1.17196i	−0.139669	+	0.0430822i
$741$	1.65283	+	0.766221i	0.0607184	+	0.0281478i
$742$	−21.9319	−	12.0529i	−0.805147	−	0.442475i
$743$	31.7263	+	29.4377i	1.16393	+	1.07997i	0.995549	+	0.0942435i	$0.0300432\pi$
$743$	31.7263	+	29.4377i	1.16393	+	1.07997i	0.168377	+	0.985723i	$0.446147\pi$
$744$	46.0947	−	23.0393i	1.68992	−	0.844664i
$745$	1.60094	−	1.48545i	0.0586538	−	0.0544228i
$746$	8.07930	−	3.89078i	0.295804	−	0.142452i
$747$	20.4204	−	27.2114i	0.747142	−	0.995612i
$748$	17.3789	−	8.36926i	0.635437	−	0.306010i
$749$	12.5836	+	37.9349i	0.459795	+	1.38611i
$750$	−1.23719	+	20.5641i	−0.0451758	+	0.750893i
$751$	−27.5214	−	8.48924i	−1.00427	−	0.309777i	−0.251356	−	0.967895i	$-0.580877\pi$
$751$	−27.5214	−	8.48924i	−1.00427	−	0.309777i	−0.752915	+	0.658118i	$0.771353\pi$
$752$	16.1274	−	2.43082i	0.588107	−	0.0886429i
$753$	−14.9235	−	2.02533i	−0.543842	−	0.0738071i
$754$	3.00078	+	5.19750i	0.109282	+	0.189282i
$755$	27.7979	+	34.8575i	1.01167	+	1.26859i
$756$	0.698473	+	10.6937i	0.0254032	+	0.388926i
$757$	−4.75977	+	5.96857i	−0.172997	+	0.216931i	−0.860770	−	0.508995i	$-0.830017\pi$
$757$	−4.75977	+	5.96857i	−0.172997	+	0.216931i	0.687773	+	0.725926i	$0.258589\pi$
$758$	−21.4927	−	3.23950i	−0.780649	−	0.117664i
$759$	−0.929614	−	0.613967i	−0.0337429	−	0.0222856i
$760$	−8.06031	+	5.49543i	−0.292378	+	0.199340i
$761$	−15.0376	−	38.3151i	−0.545111	−	1.38892i	−0.892435	−	0.451175i	$-0.851005\pi$
$761$	−15.0376	−	38.3151i	−0.545111	−	1.38892i	0.347324	−	0.937745i	$-0.387090\pi$
$762$	−21.7481	−	6.35961i	−0.787850	−	0.230384i
$763$	5.60503	+	2.06446i	0.202916	+	0.0747385i
$764$	−5.60560	−	7.02919i	−0.202803	−	0.254307i
$765$	−36.1439	+	35.5716i	−1.30679	+	1.28609i
$766$	−23.3942			−0.845267
$767$	1.86850	−	4.76086i	0.0674676	−	0.171905i
$768$	−24.3522	−	11.2892i	−0.878736	−	0.407364i
$769$	21.2104	−	14.4610i	0.764868	−	0.521478i	−0.116910	−	0.993142i	$-0.537299\pi$
$769$	21.2104	−	14.4610i	0.764868	−	0.521478i	0.881778	+	0.471664i	$0.156347\pi$
$770$	21.0951	−	8.79714i	0.760215	−	0.317027i
$771$	4.62117	−	21.7141i	0.166427	−	0.782016i
$772$	5.16451	−	13.1590i	0.185875	−	0.473601i
$773$	−15.8947	+	7.65451i	−0.571694	+	0.275314i	−0.697315	−	0.716765i	$-0.745622\pi$
$773$	−15.8947	+	7.65451i	−0.571694	+	0.275314i	0.125621	+	0.992078i	$0.459908\pi$
$774$	20.3901	+	13.0401i	0.732906	+	0.468715i
$775$	−2.98314	−	1.43660i	−0.107157	−	0.0516043i
$776$	−45.7934	+	14.1254i	−1.64389	+	0.507072i
$777$	8.93391	+	4.73996i	0.320502	+	0.170045i
$778$	−12.7974	−	3.94747i	−0.458809	−	0.141524i
$779$	2.43942	+	2.26345i	0.0874014	+	0.0810966i
$780$	1.72628	−	1.64967i	0.0618109	−	0.0590677i
$781$	23.1636	−	7.14504i	0.828860	−	0.255670i
$782$	1.38399	−	0.666496i	0.0494915	−	0.0238339i
$783$	4.37693	+	36.6294i	0.156419	+	1.30903i
$784$	8.41757	+	9.68714i	0.300627	+	0.345969i
$785$	−15.6501	−	27.1067i	−0.558576	−	0.967481i
$786$	1.78889	−	0.580750i	0.0638075	−	0.0207147i
$787$	16.8042	+	15.5920i	0.599005	+	0.555796i	0.920315	−	0.391179i	$-0.127933\pi$
$787$	16.8042	+	15.5920i	0.599005	+	0.555796i	−0.321310	+	0.946974i	$0.604123\pi$
$788$	1.76278	+	4.49148i	0.0627963	+	0.160002i
$789$	1.89034	−	0.313426i	0.0672980	−	0.0111583i
$790$	6.65122	−	6.17143i	0.236640	−	0.219570i
$791$	14.8118	+	3.05349i	0.526648	+	0.108570i
$792$	31.1538	−	0.916776i	1.10700	−	0.0325762i
$793$	−3.62118	−	1.74387i	−0.128592	−	0.0619266i
$794$	−14.8996	+	13.8248i	−0.528768	+	0.490625i
$795$	−7.13446	+	33.5237i	−0.253033	+	1.18896i
$796$	3.39896	−	0.512311i	0.120473	−	0.0181584i
$797$	0.429884	−	5.73641i	0.0152273	−	0.203194i	−0.984401	−	0.175938i	$-0.943704\pi$
$797$	0.429884	−	5.73641i	0.0152273	−	0.203194i	0.999628	−	0.0272557i	$-0.00867684\pi$
$798$	6.83561	+	1.30467i	0.241978	+	0.0461846i
$799$	4.86233	+	64.8833i	0.172017	+	2.29541i
$800$	0.312987	+	1.37129i	0.0110658	+	0.0484823i
$801$	−8.81096	−	20.6429i	−0.311320	−	0.729380i
$802$	8.68690			0.306745
$803$	5.68612	+	9.84865i	0.200659	+	0.347551i
$804$	7.74294	−	13.8787i	0.273072	−	0.489463i
$805$	−1.07295	+	0.447445i	−0.0378166	+	0.0157704i
$806$	2.99237	+	7.62444i	0.105402	+	0.268559i
$807$	35.3119	−	33.7447i	1.24304	−	1.18787i
$808$	−3.81854	−	50.9548i	−0.134336	−	1.79258i
$809$	25.6509	+	12.3528i	0.901836	+	0.434301i	0.826552	−	0.562861i	$-0.190299\pi$
$809$	25.6509	+	12.3528i	0.901836	+	0.434301i	0.0752845	+	0.997162i	$0.476014\pi$
$810$	−21.5228	+	8.05304i	−0.756233	+	0.282955i
$811$	17.0288	−	21.3534i	0.597961	−	0.749819i	−0.387098	−	0.922039i	$-0.626522\pi$
$811$	17.0288	−	21.3534i	0.597961	−	0.749819i	0.985059	+	0.172220i	$0.0550939\pi$
$812$	−10.1832	−	10.5208i	−0.357361	−	0.369208i
$813$	19.4452	+	32.5643i	0.681972	+	1.14208i
$814$	4.12448	−	7.14380i	0.144563	−	0.250390i
$815$	23.0499	−	39.9235i	0.807401	−	1.39846i
$816$	−11.3154	+	20.2820i	−0.396117	+	0.710012i
$817$	−7.35852	+	6.82771i	−0.257442	+	0.238871i
$818$	−28.9560	−	13.9445i	−1.01242	−	0.487557i
$819$	−6.07173	−	0.147485i	−0.212163	−	0.00515355i
$820$	3.92966	−	1.89242i	0.137230	−	0.0660863i
$821$	4.95061	−	12.6140i	0.172778	−	0.440230i	−0.818086	−	0.575095i	$-0.804965\pi$
$821$	4.95061	−	12.6140i	0.172778	−	0.440230i	0.990864	+	0.134865i	$0.0430602\pi$
$822$	2.35567	−	11.0689i	0.0821634	−	0.386073i
$823$	3.37179	+	1.04006i	0.117533	+	0.0362542i	0.352964	−	0.935637i	$-0.385174\pi$
$823$	3.37179	+	1.04006i	0.117533	+	0.0362542i	−0.235431	+	0.971891i	$0.575650\pi$
$824$	−1.04634	+	0.713382i	−0.0364510	+	0.0248518i
$825$	−1.27147	−	1.54713i	−0.0442669	−	0.0538642i
$826$	2.50359	−	19.3751i	0.0871110	−	0.674148i
$827$	9.23090	+	40.4432i	0.320990	+	1.40635i	0.835795	+	0.549041i	$0.185007\pi$
$827$	9.23090	+	40.4432i	0.320990	+	1.40635i	−0.514805	+	0.857307i	$0.672136\pi$
$828$	−0.444388	+	0.0130772i	−0.0154436	+	0.000454465i
$829$	−16.5211	+	20.7168i	−0.573802	+	0.719525i	−0.981042	−	0.193796i	$-0.937920\pi$
$829$	−16.5211	+	20.7168i	−0.573802	+	0.719525i	0.407239	+	0.913321i	$0.366491\pi$
$830$	−27.6695	+	8.53492i	−0.960423	+	0.296251i
$831$	−11.1640	−	10.0572i	−0.387276	−	0.348881i
$832$	3.14258	−	5.44311i	0.108949	−	0.188706i
$833$	−41.0472	+	30.5990i	−1.42220	+	1.06019i
$834$	−7.10591	−	0.964374i	−0.246058	−	0.0333935i
$835$	30.7360	+	20.9554i	1.06366	+	0.725192i
$836$	−0.806686	+	3.53432i	−0.0278998	+	0.122237i
$837$	−1.54393	+	50.3220i	−0.0533660	+	1.73938i
$838$	3.32164	−	14.5531i	0.114744	−	0.502727i
$839$	−18.4379	+	17.1078i	−0.636546	+	0.590628i	−0.930992	−	0.365040i	$-0.881055\pi$
$839$	−18.4379	+	17.1078i	−0.636546	+	0.590628i	0.294446	+	0.955668i	$0.404865\pi$
$840$	17.3470	−	27.5101i	0.598528	−	0.949188i
$841$	−15.6892	−	14.5575i	−0.541008	−	0.501982i
$842$	−16.8189	+	11.4670i	−0.579619	+	0.395178i
$843$	36.2383	−	25.4956i	1.24811	−	0.878116i
$844$	14.0151	+	9.55535i	0.482421	+	0.328909i
$845$	−17.8895	−	22.4328i	−0.615419	−	0.771710i
$846$	−9.95977	+	27.7509i	−0.342424	+	0.954097i
$847$	0.490316	−	1.07562i	0.0168475	−	0.0369588i
$848$	1.17303	+	15.6530i	0.0402819	+	0.537525i
$849$	−35.8442	−	16.6167i	−1.23017	−	0.570282i
$850$	2.73037	−	0.411537i	0.0936510	−	0.0141156i
$851$	−0.209782	+	0.363352i	−0.00719122	+	0.0124556i
$852$	5.91943	−	7.65094i	0.202796	−	0.262117i
$853$	−11.3227	+	28.8499i	−0.387683	+	0.987800i	0.595201	+	0.803577i	$0.297072\pi$
$853$	−11.3227	+	28.8499i	−0.387683	+	0.987800i	−0.982884	+	0.184224i	$0.941023\pi$
$854$	−15.0366	−	3.09982i	−0.514540	−	0.106074i
$855$	−0.991498	−	9.47915i	−0.0339085	−	0.324180i
$856$	28.9216	−	36.2666i	0.988521	−	1.23957i
$857$	3.75255	+	50.0742i	0.128185	+	1.71050i	0.576888	+	0.816823i	$0.304267\pi$
$857$	3.75255	+	50.0742i	0.128185	+	1.71050i	−0.448704	+	0.893681i	$0.648114\pi$
$858$	−0.297497	+	4.94487i	−0.0101564	+	0.168815i
$859$	−6.44556	−	16.4230i	−0.219920	−	0.560346i	0.777750	−	0.628574i	$-0.216361\pi$
$859$	−6.44556	−	16.4230i	−0.219920	−	0.560346i	−0.997670	+	0.0682273i	$0.978266\pi$
$860$	4.80670	+	12.2473i	0.163907	+	0.417628i
$861$	−10.4657	−	3.68085i	−0.356669	−	0.125443i
$862$	−6.08684	+	15.5090i	−0.207318	+	0.528239i
$863$	−8.07166			−0.274762			−0.137381	−	0.990518i	$-0.543869\pi$
$863$	−8.07166			−0.274762			−0.137381	+	0.990518i	$0.543869\pi$
$864$	17.1223	−	12.8157i	0.582511	−	0.435997i
$865$	−25.8595	−	32.4268i	−0.879249	−	1.10254i
$866$	18.5975	−	17.2560i	0.631970	−	0.586383i
$867$	−52.7432	−	34.8345i	−1.79125	−	1.18304i
$868$	−11.6023	−	16.2692i	−0.393809	−	0.552214i
$869$	0.898454	−	11.9890i	0.0304780	−	0.406700i
$870$	15.2971	−	27.4190i	0.518620	−	0.929592i
$871$	7.44191	+	5.07381i	0.252160	+	0.171920i
$872$	−1.54262	−	6.75867i	−0.0522398	−	0.228877i
$873$	9.07112	−	45.9322i	0.307011	−	1.55457i
$874$	−0.0642415	+	0.281460i	−0.00217300	+	0.00952054i
$875$	28.3540	−	2.72737i	0.958541	−	0.0922021i
$876$	4.11733	+	1.90871i	0.139112	+	0.0644893i
$877$	23.8735	+	22.1513i	0.806150	+	0.747998i	0.971194	−	0.238289i	$-0.0765864\pi$
$877$	23.8735	+	22.1513i	0.806150	+	0.747998i	−0.165045	+	0.986286i	$0.552777\pi$
$878$	11.5138	+	29.3367i	0.388573	+	0.990067i
$879$	−11.4574	−	13.9414i	−0.386449	−	0.470233i
$880$	−11.8449	−	8.07573i	−0.399292	−	0.272233i
$881$	−25.8234			−0.870011			−0.435006	−	0.900428i	$-0.643254\pi$
$881$	−25.8234			−0.870011			−0.435006	+	0.900428i	$0.643254\pi$
$882$	−22.6346	+	5.09028i	−0.762147	+	0.171399i
$883$	−12.6475			−0.425624			−0.212812	−	0.977093i	$-0.568262\pi$
$883$	−12.6475			−0.425624			−0.212812	+	0.977093i	$0.568262\pi$
$884$	3.60452	+	2.45752i	0.121233	+	0.0826553i
$885$	−26.3959	+	4.37655i	−0.887290	+	0.147116i
$886$	9.75694	+	24.8603i	0.327791	+	0.835197i
$887$	−39.5375	−	36.6854i	−1.32754	−	1.23178i	−0.952416	−	0.304802i	$-0.901410\pi$
$887$	−39.5375	−	36.6854i	−1.32754	−	1.23178i	−0.375124	−	0.926975i	$-0.622400\pi$
$888$	−1.04924	−	11.6908i	−0.0352101	−	0.392317i
$889$	−4.01496	+	31.0716i	−0.134658	+	1.04211i
$890$	−4.25079	+	18.6239i	−0.142487	+	0.624276i
$891$	−13.6479	+	27.2200i	−0.457221	+	0.911903i
$892$	1.22840	+	5.38198i	0.0411299	+	0.180202i
$893$	−10.1036	−	6.88850i	−0.338103	−	0.230515i
$894$	0.926993	+	1.55241i	0.0310033	+	0.0519203i
$895$	1.87773	−	25.0566i	0.0627656	−	0.837548i
$896$	0.611844	−	2.14304i	0.0204403	−	0.0715940i
$897$	0.0151315	−	0.251509i	0.000505226	−	0.00839764i
$898$	−8.24782	+	7.65286i	−0.275233	+	0.255379i
$899$	−42.8880	−	53.7799i	−1.43040	−	1.79366i
$900$	−0.770240	−	0.212988i	−0.0256747	−	0.00709961i
$901$	−62.6208			−2.08620
$902$	−3.30590	+	8.42329i	−0.110074	+	0.280465i
$903$	13.4314	−	30.6517i	0.446970	−	1.02002i
$904$	−6.41255	−	16.3389i	−0.213278	−	0.543424i
$905$	7.45759	+	19.0016i	0.247899	+	0.631636i
$906$	−33.0176	+	16.5030i	−1.09693	+	0.548277i
$907$	−1.23671	−	16.5027i	−0.0410642	−	0.547964i	−0.979359	−	0.202128i	$-0.935214\pi$
$907$	−1.23671	−	16.5027i	−0.0410642	−	0.547964i	0.938295	−	0.345836i	$-0.112405\pi$
$908$	−4.51867	+	5.66623i	−0.149957	+	0.188040i
$909$	45.5953	+	20.3277i	1.51230	+	0.674228i
$910$	4.10856	+	3.13700i	0.136198	+	0.103991i
$911$	7.47361	−	19.0424i	0.247612	−	0.630904i	−0.751989	−	0.659176i	$-0.770905\pi$
$911$	7.47361	−	19.0424i	0.247612	−	0.630904i	0.999600	+	0.0282718i	$0.00900038\pi$
$912$	−1.65427	−	4.03928i	−0.0547784	−	0.133754i
$913$	−19.1841	+	33.2279i	−0.634902	+	1.09968i
$914$	−41.3411	+	6.23117i	−1.36744	+	0.206109i
$915$	1.87958	+	20.9426i	0.0621369	+	0.692339i
$916$	−0.120410	−	1.60676i	−0.00397847	−	0.0530890i
$917$	−1.17750	−	2.31868i	−0.0388845	−	0.0765696i
$918$	−22.5763	−	35.3990i	−0.745129	−	1.16834i
$919$	−11.9268	−	14.9558i	−0.393430	−	0.493345i	0.545184	−	0.838317i	$-0.316460\pi$
$919$	−11.9268	−	14.9558i	−0.393430	−	0.493345i	−0.938613	+	0.344972i	$0.887889\pi$
$920$	1.11478	+	0.760045i	0.0367532	+	0.0250579i
$921$	−2.40997	−	26.8523i	−0.0794111	−	0.884812i
$922$	13.4622	−	9.17835i	0.443353	−	0.302273i
$923$	4.01889	+	3.72898i	0.132283	+	0.122741i
$924$	−2.22793	−	11.8786i	−0.0732936	−	0.390778i
$925$	−0.552850	+	0.512970i	−0.0181776	+	0.0168664i
$926$	−0.322971	+	1.41503i	−0.0106135	+	0.0465007i
$927$	−0.128710	−	1.23052i	−0.00422739	−	0.0404157i
$928$	−6.50234	+	28.4886i	−0.213450	+	0.935185i
$929$	12.8656	+	8.77162i	0.422107	+	0.287787i	0.755685	−	0.654935i	$-0.227304\pi$
$929$	12.8656	+	8.77162i	0.422107	+	0.287787i	−0.333579	+	0.942722i	$0.608256\pi$
$930$	26.2208	−	33.8907i	0.859812	−	1.11132i
$931$	0.313715	−	9.61695i	0.0102816	−	0.315183i
$932$	6.40612	−	11.0957i	0.209839	−	0.363452i
$933$	−2.52589	+	11.8688i	−0.0826940	+	0.388566i
$934$	−11.5431	+	3.56059i	−0.377703	+	0.116506i
$935$	35.6584	−	44.7142i	1.16615	−	1.46231i
$936$	3.70253	+	5.99829i	0.121021	+	0.196060i
$937$	11.7399	+	51.4359i	0.383526	+	1.68034i	0.686336	+	0.727285i	$0.259218\pi$
$937$	11.7399	+	51.4359i	0.383526	+	1.68034i	−0.302810	+	0.953051i	$0.597925\pi$
$938$	32.2850	+	11.8913i	1.05414	+	0.388265i
$939$	20.9012	−	3.46550i	0.682085	−	0.113092i
$940$	−13.2424	+	9.02854i	−0.431921	+	0.294478i
$941$	5.24546	+	1.61801i	0.170997	+	0.0527456i	0.379072	−	0.925367i	$-0.376243\pi$
$941$	5.24546	+	1.61801i	0.170997	+	0.0527456i	−0.208074	+	0.978113i	$0.566720\pi$
$942$	24.6476	−	8.00167i	0.803063	−	0.260709i
$943$	0.168147	−	0.428431i	0.00547561	−	0.0139516i
$944$	−11.0402	+	5.31670i	−0.359329	+	0.173044i
$945$	15.6228	+	27.6680i	0.508209	+	0.900039i
$946$	−24.5926	−	11.8432i	−0.799574	−	0.385055i
$947$	6.28891	−	5.83525i	0.204362	−	0.189620i	−0.571351	−	0.820705i	$-0.693581\pi$
$947$	6.28891	−	5.83525i	0.204362	−	0.189620i	0.775713	+	0.631085i	$0.217390\pi$
$948$	−2.45975	−	4.11927i	−0.0798889	−	0.133788i
$949$	−1.28601	+	2.22743i	−0.0417456	+	0.0723056i
$950$	−0.259472	+	0.449418i	−0.00841838	+	0.0145811i
$951$	−13.2696	+	23.7848i	−0.430295	+	0.771274i
$952$	55.7583	+	20.5371i	1.80714	+	0.665610i
$953$	23.9243	−	30.0001i	0.774984	−	0.971799i	−0.225013	−	0.974356i	$-0.572242\pi$
$953$	23.9243	−	30.0001i	0.774984	−	0.971799i	0.999997	+	0.00255660i	$0.000813792\pi$
$954$	−25.9173	−	11.5547i	−0.839105	−	0.374097i
$955$	−24.0171	−	11.5660i	−0.777176	−	0.374268i
$956$	−0.318109	−	4.24487i	−0.0102884	−	0.137289i
$957$	−9.85323	−	40.4198i	−0.318510	−	1.30659i
$958$	2.21069	+	5.63275i	0.0714242	+	0.181986i
$959$	−15.6249	−	0.839940i	−0.504556	−	0.0271231i
$960$	−32.8776	+	0.483648i	−1.06112	+	0.0156097i
$961$	−31.4386	−	54.4533i	−1.01415	−	1.75656i
$962$	1.86564			0.0601505
$963$	17.7906	+	41.6809i	0.573293	+	1.34315i
$964$	−4.19674	−	18.3871i	−0.135168	−	0.592209i
$965$	−3.13217	−	41.7959i	−0.100828	−	1.34546i
$966$	−0.177424	−	0.945969i	−0.00570853	−	0.0304360i
$967$	0.325292	−	4.34072i	0.0104607	−	0.139588i	−0.989528	−	0.144341i	$-0.953894\pi$
$967$	0.325292	−	4.34072i	0.0104607	−	0.139588i	0.999989	+	0.00475283i	$0.00151288\pi$
$968$	−1.35664	+	0.204480i	−0.0436040	+	0.00657225i
$969$	16.5624	−	5.37685i	0.532060	−	0.172729i
$970$	−29.2110	+	27.1039i	−0.937909	+	0.870252i
$971$	29.9666	+	14.4311i	0.961672	+	0.463117i	0.847764	−	0.530374i	$-0.177949\pi$
$971$	29.9666	+	14.4311i	0.961672	+	0.463117i	0.113909	+	0.993491i	$0.463663\pi$
$972$	1.79602	+	12.0179i	0.0576072	+	0.385474i
$973$	0.209149	+	9.91306i	0.00670500	+	0.317798i
$974$	−24.5324	+	22.7627i	−0.786068	+	0.729365i
$975$	0.159248	−	0.423992i	0.00510002	−	0.0135786i
$976$	3.51813	+	8.96406i	0.112613	+	0.286933i
$977$	−30.7065	−	28.4914i	−0.982386	−	0.911521i	0.0137000	−	0.999906i	$-0.495639\pi$
$977$	−30.7065	−	28.4914i	−0.982386	−	0.911521i	−0.996086	+	0.0883848i	$0.971829\pi$
$978$	28.3570	+	25.5456i	0.906757	+	0.816859i
$979$	12.6562	+	21.9212i	0.404493	+	0.700603i
$980$	−11.5831	−	4.98774i	−0.370008	−	0.159327i
$981$	6.52792	+	1.80511i	0.208420	+	0.0576328i
$982$	16.2112	−	7.80688i	0.517319	−	0.249128i
$983$	8.94965	−	2.76060i	0.285450	−	0.0880495i	−0.148724	−	0.988879i	$-0.547517\pi$
$983$	8.94965	−	2.76060i	0.285450	−	0.0880495i	0.434174	+	0.900829i	$0.357040\pi$
$984$	3.04949	+	12.5096i	0.0972143	+	0.398791i
$985$	10.4870	+	9.73055i	0.334145	+	0.310041i
$986$	54.8160	+	16.9085i	1.74570	+	0.538476i
$987$	40.0442	+	7.64296i	1.27462	+	0.243278i
$988$	−0.783476	+	0.241670i	−0.0249257	+	0.00768856i
$989$	1.25084	+	0.602374i	0.0397745	+	0.0191544i
$990$	23.0088	−	11.9266i	0.731268	−	0.379051i
$991$	31.8795	−	15.3524i	1.01269	−	0.487684i	0.147461	−	0.989068i	$-0.452890\pi$
$991$	31.8795	−	15.3524i	1.01269	−	0.487684i	0.865225	+	0.501384i	$0.167176\pi$
$992$	−14.5697	+	37.1230i	−0.462589	+	1.17866i
$993$	19.8898	+	17.9179i	0.631183	+	0.568606i
$994$	18.3531	+	10.0861i	0.582125	+	0.319911i
$995$	8.42072	−	5.74115i	0.266955	−	0.182007i
$996$	1.36868	+	15.2500i	0.0433681	+	0.483215i
$997$	−17.7177	+	45.1441i	−0.561126	+	1.42973i	0.315672	+	0.948868i	$0.397770\pi$
$997$	−17.7177	+	45.1441i	−0.561126	+	1.42973i	−0.876798	+	0.480858i	$0.840325\pi$
$998$	−27.9712			−0.885414
$999$	10.5414	+	4.51497i	0.333514	+	0.142847i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.ba.a.22.19	✓	648
9.7	even	3	inner	441.2.ba.a.169.19	yes	648
49.29	even	7	inner	441.2.ba.a.274.19	yes	648
441.421	even	21	inner	441.2.ba.a.421.19	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.ba.a.22.19	✓	648	1.1	even	1	trivial
441.2.ba.a.169.19	yes	648	9.7	even	3	inner
441.2.ba.a.274.19	yes	648	49.29	even	7	inner
441.2.ba.a.421.19	yes	648	441.421	even	21	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.ba (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.912794 - 0.622332i) q^{2} +(-0.609005 + 1.62145i) q^{3} +(-0.284787 - 0.725626i) q^{4} +(-1.69424 - 1.57203i) q^{5} +(1.56498 - 1.10105i) q^{6} +(-1.84008 - 1.90108i) q^{7} +(-0.683292 + 2.99370i) q^{8} +(-2.25823 - 1.97495i) q^{9} +O(q^{10})\)	\(q+(-0.912794 - 0.622332i) q^{2} +(-0.609005 + 1.62145i) q^{3} +(-0.284787 - 0.725626i) q^{4} +(-1.69424 - 1.57203i) q^{5} +(1.56498 - 1.10105i) q^{6} +(-1.84008 - 1.90108i) q^{7} +(-0.683292 + 2.99370i) q^{8} +(-2.25823 - 1.97495i) q^{9} +(0.568171 + 2.48932i) q^{10} +(2.79542 + 1.90589i) q^{11} +(1.35001 - 0.0198593i) q^{12} +(-0.0571828 + 0.763052i) q^{13} +(0.496507 + 2.88044i) q^{14} +(3.58077 - 1.78976i) q^{15} +(1.34394 - 1.24699i) q^{16} +(4.56015 + 5.71825i) q^{17} +(0.832220 + 3.20809i) q^{18} -1.37458 q^{19} +(-0.658205 + 1.67708i) q^{20} +(4.20313 - 1.82583i) q^{21} +(-1.36555 - 3.47936i) q^{22} +(0.0694554 + 0.176969i) q^{23} +(-4.43801 - 2.93110i) q^{24} +(0.0255375 + 0.340774i) q^{25} +(0.527068 - 0.660922i) q^{26} +(4.57756 - 2.45885i) q^{27} +(-0.855443 + 1.87661i) q^{28} +(-2.59373 + 6.60872i) q^{29} +(-4.38233 - 0.594745i) q^{30} +(-4.84451 + 8.39094i) q^{31} +(4.07000 - 0.613454i) q^{32} +(-4.79273 + 3.37195i) q^{33} +(-0.603827 - 8.05751i) q^{34} +(0.128985 + 6.11355i) q^{35} +(-0.789959 + 2.20107i) q^{36} +(1.37600 + 1.72545i) q^{37} +(1.25471 + 0.855446i) q^{38} +(-1.20243 - 0.557422i) q^{39} +(5.86384 - 3.99790i) q^{40} +(-1.77467 - 1.64665i) q^{41} +(-4.97287 - 0.949137i) q^{42} +(5.35328 - 4.96712i) q^{43} +(0.586860 - 2.57120i) q^{44} +(0.721310 + 6.89603i) q^{45} +(0.0467353 - 0.204761i) q^{46} +(7.35030 + 5.01135i) q^{47} +(1.20347 + 2.93855i) q^{48} +(-0.228226 + 6.99628i) q^{49} +(0.188764 - 0.326950i) q^{50} +(-12.0490 + 3.91163i) q^{51} +(0.569975 - 0.175814i) q^{52} +(-5.33824 + 6.69394i) q^{53} +(-5.70859 - 0.604335i) q^{54} +(-1.74002 - 7.62352i) q^{55} +(6.94857 - 4.20964i) q^{56} +(0.837127 - 2.22882i) q^{57} +(6.48036 - 4.41823i) q^{58} +(-6.38688 - 1.97009i) q^{59} +(-2.31846 - 2.08860i) q^{60} +(-1.91897 + 4.88946i) q^{61} +(9.64400 - 4.64430i) q^{62} +(0.400773 + 7.92713i) q^{63} +(-7.40041 - 3.56385i) q^{64} +(1.29642 - 1.20290i) q^{65} +(6.47325 - 0.0952250i) q^{66} +(5.88544 - 10.1939i) q^{67} +(2.85063 - 4.93744i) q^{68} +(-0.329247 + 0.00484339i) q^{69} +(3.68692 - 5.66068i) q^{70} +(4.46715 - 5.60163i) q^{71} +(7.45542 - 5.41098i) q^{72} +(3.02841 + 1.45840i) q^{73} +(-0.182202 - 2.43131i) q^{74} +(-0.568102 - 0.166126i) q^{75} +(0.391463 + 0.997431i) q^{76} +(-1.52055 - 8.82131i) q^{77} +(0.750668 + 1.25712i) q^{78} +(-1.77676 - 3.07744i) q^{79} -4.23726 q^{80} +(1.19916 + 8.91975i) q^{81} +(0.595141 + 2.60748i) q^{82} +(0.847472 + 11.3087i) q^{83} +(-2.52187 - 2.52993i) q^{84} +(1.26324 - 16.8568i) q^{85} +(-7.97765 + 1.20244i) q^{86} +(-9.13614 - 8.23036i) q^{87} +(-7.61574 + 7.06637i) q^{88} +(6.74063 + 3.24612i) q^{89} +(3.63322 - 6.74355i) q^{90} +(1.55584 - 1.29537i) q^{91} +(0.108634 - 0.100797i) q^{92} +(-10.6552 - 12.9653i) q^{93} +(-3.59058 - 9.14866i) q^{94} +(2.32887 + 2.16088i) q^{95} +(-1.48396 + 6.97291i) q^{96} +(7.80322 + 13.5156i) q^{97} +(4.56233 - 6.24413i) q^{98} +(-2.54867 - 9.82474i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 5 q^{2} - 10 q^{3} + 47 q^{4} - 9 q^{5} - 34 q^{6} - 7 q^{7} - 28 q^{8}+O(q^{10}) \) 648 * q - 5 * q^2 - 10 * q^3 + 47 * q^4 - 9 * q^5 - 34 * q^6 - 7 * q^7 - 28 * q^8	\( 648 q - 5 q^{2} - 10 q^{3} + 47 q^{4} - 9 q^{5} - 34 q^{6} - 7 q^{7} - 28 q^{8} - 28 q^{10} - 5 q^{11} + 5 q^{12} - 7 q^{13} - 38 q^{14} - 22 q^{15} + 47 q^{16} - 16 q^{17} - 46 q^{18} - 44 q^{19} - 29 q^{20} - 12 q^{21} - 13 q^{22} - 20 q^{23} - 2 q^{24} + 41 q^{25} - 20 q^{26} - 13 q^{27} - 28 q^{28} - 35 q^{29} - 6 q^{30} - 20 q^{31} - 25 q^{32} - 22 q^{33} - q^{34} - 44 q^{35} - 28 q^{36} - 30 q^{37} - 7 q^{38} - 8 q^{39} + 5 q^{40} - 29 q^{41} - 104 q^{42} - 13 q^{43} - 88 q^{44} + 63 q^{45} + 32 q^{46} - 55 q^{47} - 14 q^{48} - q^{49} + 6 q^{50} - 18 q^{51} + 3 q^{52} - 136 q^{53} + 30 q^{54} - 100 q^{55} + 145 q^{56} - 96 q^{57} + 17 q^{58} - 19 q^{59} + 118 q^{60} + 42 q^{61} + 96 q^{62} - 6 q^{63} - 124 q^{64} - 11 q^{65} + 120 q^{66} - 26 q^{67} + 166 q^{68} - 134 q^{69} - 7 q^{70} - 22 q^{71} + 32 q^{72} + 8 q^{73} - 45 q^{74} - 36 q^{75} - 41 q^{76} + q^{77} - 18 q^{78} - 26 q^{79} - 440 q^{80} + 64 q^{81} - 28 q^{82} + 61 q^{83} - 86 q^{84} + 5 q^{85} + 15 q^{86} + 34 q^{87} - q^{88} + 22 q^{89} + 96 q^{90} - 16 q^{91} - 43 q^{92} - 110 q^{93} - q^{94} - 38 q^{95} - 165 q^{96} - 14 q^{97} - 144 q^{98} - 196 q^{99}+O(q^{100}) \) 648 * q - 5 * q^2 - 10 * q^3 + 47 * q^4 - 9 * q^5 - 34 * q^6 - 7 * q^7 - 28 * q^8 - 28 * q^10 - 5 * q^11 + 5 * q^12 - 7 * q^13 - 38 * q^14 - 22 * q^15 + 47 * q^16 - 16 * q^17 - 46 * q^18 - 44 * q^19 - 29 * q^20 - 12 * q^21 - 13 * q^22 - 20 * q^23 - 2 * q^24 + 41 * q^25 - 20 * q^26 - 13 * q^27 - 28 * q^28 - 35 * q^29 - 6 * q^30 - 20 * q^31 - 25 * q^32 - 22 * q^33 - q^34 - 44 * q^35 - 28 * q^36 - 30 * q^37 - 7 * q^38 - 8 * q^39 + 5 * q^40 - 29 * q^41 - 104 * q^42 - 13 * q^43 - 88 * q^44 + 63 * q^45 + 32 * q^46 - 55 * q^47 - 14 * q^48 - q^49 + 6 * q^50 - 18 * q^51 + 3 * q^52 - 136 * q^53 + 30 * q^54 - 100 * q^55 + 145 * q^56 - 96 * q^57 + 17 * q^58 - 19 * q^59 + 118 * q^60 + 42 * q^61 + 96 * q^62 - 6 * q^63 - 124 * q^64 - 11 * q^65 + 120 * q^66 - 26 * q^67 + 166 * q^68 - 134 * q^69 - 7 * q^70 - 22 * q^71 + 32 * q^72 + 8 * q^73 - 45 * q^74 - 36 * q^75 - 41 * q^76 + q^77 - 18 * q^78 - 26 * q^79 - 440 * q^80 + 64 * q^81 - 28 * q^82 + 61 * q^83 - 86 * q^84 + 5 * q^85 + 15 * q^86 + 34 * q^87 - q^88 + 22 * q^89 + 96 * q^90 - 16 * q^91 - 43 * q^92 - 110 * q^93 - q^94 - 38 * q^95 - 165 * q^96 - 14 * q^97 - 144 * q^98 - 196 * q^99

Introduction

L-functions

Modular forms

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