LMFDB - Embedded newform 384.2.w.a.179.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(11,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([16, 21, 16]))

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

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

chi := DirichletCharacter("384.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.w (of order $32$, degree $16$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$62$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			179.17
Character	$\chi$	$=$	384.179
Dual form			384.2.w.a.251.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.879716 - 1.10729i) q^{2} +(1.68380 - 0.405958i) q^{3} +(-0.452199 + 1.94821i) q^{4} +(-0.324308 - 3.29275i) q^{5} +(-1.93078 - 1.50734i) q^{6} +(-3.28633 - 2.19586i) q^{7} +(2.55505 - 1.21315i) q^{8} +(2.67040 - 1.36711i) q^{9} +O(q^{10})$	\(q+(-0.879716 - 1.10729i) q^{2} +(1.68380 - 0.405958i) q^{3} +(-0.452199 + 1.94821i) q^{4} +(-0.324308 - 3.29275i) q^{5} +(-1.93078 - 1.50734i) q^{6} +(-3.28633 - 2.19586i) q^{7} +(2.55505 - 1.21315i) q^{8} +(2.67040 - 1.36711i) q^{9} +(-3.36075 + 3.25579i) q^{10} +(-0.281020 - 0.525751i) q^{11} +(0.0294756 + 3.46398i) q^{12} +(-0.187953 + 1.90832i) q^{13} +(0.459581 + 5.57067i) q^{14} +(-1.88279 - 5.41270i) q^{15} +(-3.59103 - 1.76196i) q^{16} +(-2.42180 + 5.84675i) q^{17} +(-3.86298 - 1.75425i) q^{18} +(-1.15540 + 0.948208i) q^{19} +(6.56162 + 0.857161i) q^{20} +(-6.42497 - 2.36328i) q^{21} +(-0.334943 + 0.773683i) q^{22} +(1.22716 - 6.16936i) q^{23} +(3.80971 - 3.07995i) q^{24} +(-5.83312 + 1.16028i) q^{25} +(2.27842 - 1.47066i) q^{26} +(3.94144 - 3.38601i) q^{27} +(5.76407 - 5.40950i) q^{28} +(3.15612 - 5.90468i) q^{29} +(-4.33712 + 6.84644i) q^{30} +(-1.04469 - 1.04469i) q^{31} +(1.20808 + 5.52635i) q^{32} +(-0.686615 - 0.771180i) q^{33} +(8.60457 - 2.46183i) q^{34} +(-6.16463 + 11.5332i) q^{35} +(1.45586 + 5.82069i) q^{36} +(0.353476 + 0.290090i) q^{37} +(2.06637 + 0.445208i) q^{38} +(0.458222 + 3.28954i) q^{39} +(-4.82323 - 8.01970i) q^{40} +(2.35149 - 11.8217i) q^{41} +(3.03530 + 9.19335i) q^{42} +(0.626022 - 2.06372i) q^{43} +(1.15135 - 0.309741i) q^{44} +(-5.36758 - 8.34959i) q^{45} +(-7.91085 + 4.06846i) q^{46} +(0.749553 - 1.80958i) q^{47} +(-6.76188 - 1.50898i) q^{48} +(3.29941 + 7.96549i) q^{49} +(6.41626 + 5.43826i) q^{50} +(-1.70431 + 10.8279i) q^{51} +(-3.63282 - 1.22911i) q^{52} +(5.62217 + 10.5183i) q^{53} +(-7.21666 - 1.38560i) q^{54} +(-1.64003 + 1.09583i) q^{55} +(-11.0606 - 1.62369i) q^{56} +(-1.56053 + 2.06564i) q^{57} +(-9.31470 + 1.69969i) q^{58} +(-0.520180 - 5.28148i) q^{59} +(11.3965 - 1.22045i) q^{60} +(3.82602 + 12.6127i) q^{61} +(-0.237748 + 2.07581i) q^{62} +(-11.7778 - 1.37104i) q^{63} +(5.05652 - 6.19932i) q^{64} +6.34459 q^{65} +(-0.249896 + 1.43870i) q^{66} +(4.28074 - 1.29855i) q^{67} +(-10.2956 - 7.36208i) q^{68} +(-0.438200 - 10.8862i) q^{69} +(18.1938 - 3.31990i) q^{70} +(-5.35095 - 3.57539i) q^{71} +(5.16447 - 6.73262i) q^{72} +(5.77379 + 8.64109i) q^{73} +(0.0102566 - 0.646598i) q^{74} +(-9.35080 + 4.32168i) q^{75} +(-1.32484 - 2.67973i) q^{76} +(-0.230950 + 2.34487i) q^{77} +(3.23938 - 3.40125i) q^{78} +(11.1761 - 4.62928i) q^{79} +(-4.63709 + 12.3958i) q^{80} +(5.26203 - 7.30144i) q^{81} +(-15.1588 + 7.79597i) q^{82} +(-2.60265 + 2.13594i) q^{83} +(7.50953 - 11.4485i) q^{84} +(20.0373 + 6.07825i) q^{85} +(-2.83587 + 1.12230i) q^{86} +(2.91723 - 11.2236i) q^{87} +(-1.35584 - 1.00240i) q^{88} +(12.0484 - 2.39657i) q^{89} +(-4.52350 + 13.2888i) q^{90} +(4.80808 - 5.85866i) q^{91} +(11.4643 + 5.18055i) q^{92} +(-2.18315 - 1.33495i) q^{93} +(-2.66313 + 0.761942i) q^{94} +(3.49692 + 3.49692i) q^{95} +(4.27764 + 8.81486i) q^{96} +(5.23719 - 5.23719i) q^{97} +(5.91759 - 10.6608i) q^{98} +(-1.46919 - 1.01978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 16 q^{3} - 32 q^{4} - 16 q^{6} - 32 q^{7} - 16 q^{9}+O(q^{10}) $ 992 * q - 16 * q^3 - 32 * q^4 - 16 * q^6 - 32 * q^7 - 16 * q^9	$ 992 q - 16 q^{3} - 32 q^{4} - 16 q^{6} - 32 q^{7} - 16 q^{9} - 32 q^{10} - 16 q^{12} - 32 q^{13} - 16 q^{15} - 32 q^{16} - 16 q^{18} - 32 q^{19} - 16 q^{21} - 32 q^{22} - 16 q^{24} - 32 q^{25} - 16 q^{27} - 32 q^{28} - 16 q^{30} - 32 q^{31} - 16 q^{33} - 32 q^{34} - 16 q^{36} - 32 q^{37} - 16 q^{39} - 32 q^{40} - 16 q^{42} - 32 q^{43} - 16 q^{45} - 32 q^{46} - 16 q^{48} - 32 q^{49} - 16 q^{51} - 128 q^{52} - 16 q^{54} - 32 q^{55} - 16 q^{57} - 320 q^{58} - 16 q^{60} - 32 q^{61} - 32 q^{63} - 224 q^{64} - 16 q^{66} - 32 q^{67} - 16 q^{69} - 224 q^{70} - 16 q^{72} - 32 q^{73} - 16 q^{75} - 256 q^{76} - 16 q^{78} - 32 q^{79} - 16 q^{81} - 32 q^{82} - 16 q^{84} - 32 q^{85} - 16 q^{87} - 32 q^{88} - 16 q^{90} - 32 q^{91} - 16 q^{93} - 32 q^{94} - 16 q^{96} - 32 q^{97} - 16 q^{99}+O(q^{100}) $ 992 * q - 16 * q^3 - 32 * q^4 - 16 * q^6 - 32 * q^7 - 16 * q^9 - 32 * q^10 - 16 * q^12 - 32 * q^13 - 16 * q^15 - 32 * q^16 - 16 * q^18 - 32 * q^19 - 16 * q^21 - 32 * q^22 - 16 * q^24 - 32 * q^25 - 16 * q^27 - 32 * q^28 - 16 * q^30 - 32 * q^31 - 16 * q^33 - 32 * q^34 - 16 * q^36 - 32 * q^37 - 16 * q^39 - 32 * q^40 - 16 * q^42 - 32 * q^43 - 16 * q^45 - 32 * q^46 - 16 * q^48 - 32 * q^49 - 16 * q^51 - 128 * q^52 - 16 * q^54 - 32 * q^55 - 16 * q^57 - 320 * q^58 - 16 * q^60 - 32 * q^61 - 32 * q^63 - 224 * q^64 - 16 * q^66 - 32 * q^67 - 16 * q^69 - 224 * q^70 - 16 * q^72 - 32 * q^73 - 16 * q^75 - 256 * q^76 - 16 * q^78 - 32 * q^79 - 16 * q^81 - 32 * q^82 - 16 * q^84 - 32 * q^85 - 16 * q^87 - 32 * q^88 - 16 * q^90 - 32 * q^91 - 16 * q^93 - 32 * q^94 - 16 * q^96 - 32 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{31}{32}\right)$	$-1$

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 $

$2$	−0.879716	−	1.10729i	−0.622053	−	0.782975i
$2$	−0.879716	−	1.10729i	−0.622053	−	0.782975i
$3$	1.68380	−	0.405958i	0.972145	−	0.234380i
$3$	1.68380	−	0.405958i	0.972145	−	0.234380i
$4$	−0.452199	+	1.94821i	−0.226100	+	0.974104i
$5$	−0.324308	−	3.29275i	−0.145035	−	1.47256i	−0.742056	−	0.670338i	$-0.766149\pi$
$5$	−0.324308	−	3.29275i	−0.145035	−	1.47256i	0.597021	−	0.802226i	$-0.296351\pi$
$6$	−1.93078	−	1.50734i	−0.788240	−	0.615368i
$7$	−3.28633	−	2.19586i	−1.24212	−	0.829956i	−0.251665	−	0.967814i	$-0.580978\pi$
$7$	−3.28633	−	2.19586i	−1.24212	−	0.829956i	−0.990452	+	0.137858i	$0.955978\pi$
$8$	2.55505	−	1.21315i	0.903345	−	0.428914i
$9$	2.67040	−	1.36711i	0.890132	−	0.455703i
$10$	−3.36075	+	3.25579i	−1.06276	+	1.02957i
$11$	−0.281020	−	0.525751i	−0.0847307	−	0.158520i	0.835987	−	0.548749i	$-0.184896\pi$
$11$	−0.281020	−	0.525751i	−0.0847307	−	0.158520i	−0.920718	+	0.390229i	$0.872396\pi$
$12$	0.0294756	+	3.46398i	0.00850888	+	0.999964i
$13$	−0.187953	+	1.90832i	−0.0521289	+	0.529273i	0.933290	+	0.359125i	$0.116925\pi$
$13$	−0.187953	+	1.90832i	−0.0521289	+	0.529273i	−0.985418	+	0.170149i	$0.945575\pi$
$14$	0.459581	+	5.57067i	0.122828	+	1.48882i
$15$	−1.88279	−	5.41270i	−0.486134	−	1.39755i
$16$	−3.59103	−	1.76196i	−0.897758	−	0.440489i
$17$	−2.42180	+	5.84675i	−0.587374	+	1.41805i	0.298631	+	0.954369i	$0.403470\pi$
$17$	−2.42180	+	5.84675i	−0.587374	+	1.41805i	−0.886004	+	0.463677i	$0.846530\pi$
$18$	−3.86298	−	1.75425i	−0.910513	−	0.413480i
$19$	−1.15540	+	0.948208i	−0.265066	+	0.217534i	−0.757533	−	0.652797i	$-0.773595\pi$
$19$	−1.15540	+	0.948208i	−0.265066	+	0.217534i	0.492467	+	0.870331i	$0.336095\pi$
$20$	6.56162	+	0.857161i	1.46722	+	0.191667i
$21$	−6.42497	−	2.36328i	−1.40204	−	0.515711i
$22$	−0.334943	+	0.773683i	−0.0714101	+	0.164950i
$23$	1.22716	−	6.16936i	0.255881	−	1.28640i	−0.612487	−	0.790480i	$-0.709831\pi$
$23$	1.22716	−	6.16936i	0.255881	−	1.28640i	0.868368	−	0.495920i	$-0.165169\pi$
$24$	3.80971	−	3.07995i	0.777654	−	0.628693i
$25$	−5.83312	+	1.16028i	−1.16662	+	0.232056i
$26$	2.27842	−	1.47066i	0.446835	−	0.288421i
$27$	3.94144	−	3.38601i	0.758530	−	0.651638i
$28$	5.76407	−	5.40950i	1.08931	−	1.02230i
$29$	3.15612	−	5.90468i	0.586076	−	1.09647i	−0.397775	−	0.917483i	$-0.630218\pi$
$29$	3.15612	−	5.90468i	0.586076	−	1.09647i	0.983851	−	0.178988i	$-0.0572824\pi$
$30$	−4.33712	+	6.84644i	−0.791847	+	1.24998i
$31$	−1.04469	−	1.04469i	−0.187632	−	0.187632i	0.607040	−	0.794671i	$-0.292357\pi$
$31$	−1.04469	−	1.04469i	−0.187632	−	0.187632i	−0.794671	+	0.607040i	$0.792357\pi$
$32$	1.20808	+	5.52635i	0.213561	+	0.976930i
$33$	−0.686615	−	0.771180i	−0.119524	−	0.134245i
$34$	8.60457	−	2.46183i	1.47567	−	0.422201i
$35$	−6.16463	+	11.5332i	−1.04201	+	1.94947i
$36$	1.45586	+	5.82069i	0.242643	+	0.970116i
$37$	0.353476	+	0.290090i	0.0581111	+	0.0476905i	0.663001	−	0.748619i	$-0.269283\pi$
$37$	0.353476	+	0.290090i	0.0581111	+	0.0476905i	−0.604889	+	0.796309i	$0.706783\pi$
$38$	2.06637	+	0.445208i	0.335209	+	0.0722223i
$39$	0.458222	+	3.28954i	0.0733742	+	0.526748i
$40$	−4.82323	−	8.01970i	−0.762620	−	1.26803i
$41$	2.35149	−	11.8217i	0.367240	−	1.84624i	−0.147721	−	0.989029i	$-0.547194\pi$
$41$	2.35149	−	11.8217i	0.367240	−	1.84624i	0.514962	−	0.857213i	$-0.327806\pi$
$42$	3.03530	+	9.19335i	0.468357	+	1.41856i
$43$	0.626022	−	2.06372i	0.0954675	−	0.314714i	−0.896180	−	0.443690i	$-0.853669\pi$
$43$	0.626022	−	2.06372i	0.0954675	−	0.314714i	0.991648	+	0.128976i	$0.0411690\pi$
$44$	1.15135	−	0.309741i	0.173572	−	0.0466952i
$45$	−5.36758	−	8.34959i	−0.800151	−	1.24468i
$46$	−7.91085	+	4.06846i	−1.16639	+	0.599861i
$47$	0.749553	−	1.80958i	0.109333	−	0.263954i	−0.859738	−	0.510736i	$-0.829373\pi$
$47$	0.749553	−	1.80958i	0.109333	−	0.263954i	0.969071	+	0.246782i	$0.0793730\pi$
$48$	−6.76188	−	1.50898i	−0.975993	−	0.217803i
$49$	3.29941	+	7.96549i	0.471345	+	1.13793i
$50$	6.41626	+	5.43826i	0.907396	+	0.769086i
$51$	−1.70431	+	10.8279i	−0.238651	+	1.51621i
$52$	−3.63282	−	1.22911i	−0.503781	−	0.170447i
$53$	5.62217	+	10.5183i	0.772265	+	1.44481i	0.892017	+	0.452003i	$0.149290\pi$
$53$	5.62217	+	10.5183i	0.772265	+	1.44481i	−0.119752	+	0.992804i	$0.538210\pi$
$54$	−7.21666	−	1.38560i	−0.982062	−	0.188556i
$55$	−1.64003	+	1.09583i	−0.221142	+	0.147762i
$56$	−11.0606	−	1.62369i	−1.47804	−	0.216975i
$57$	−1.56053	+	2.06564i	−0.206697	+	0.273601i
$58$	−9.31470	+	1.69969i	−1.22308	+	0.223180i
$59$	−0.520180	−	5.28148i	−0.0677217	−	0.687590i	−0.967776	−	0.251812i	$-0.918973\pi$
$59$	−0.520180	−	5.28148i	−0.0677217	−	0.687590i	0.900054	−	0.435777i	$-0.143527\pi$
$60$	11.3965	−	1.22045i	1.47128	−	0.157559i
$61$	3.82602	+	12.6127i	0.489871	+	1.61489i	0.758519	+	0.651651i	$0.225923\pi$
$61$	3.82602	+	12.6127i	0.489871	+	1.61489i	−0.268648	+	0.963239i	$0.586577\pi$
$62$	−0.237748	+	2.07581i	−0.0301940	+	0.263628i
$63$	−11.7778	−	1.37104i	−1.48386	−	0.172735i
$64$	5.05652	−	6.19932i	0.632065	−	0.774915i
$65$	6.34459			0.786949
$66$	−0.249896	+	1.43870i	−0.0307601	+	0.177092i
$67$	4.28074	−	1.29855i	0.522975	−	0.158643i	−0.0177493	−	0.999842i	$-0.505650\pi$
$67$	4.28074	−	1.29855i	0.522975	−	0.158643i	0.540725	+	0.841200i	$0.318150\pi$
$68$	−10.2956	−	7.36208i	−1.24852	−	0.892783i
$69$	−0.438200	−	10.8862i	−0.0527531	−	1.31054i
$70$	18.1938	−	3.31990i	2.17457	−	0.396804i
$71$	−5.35095	−	3.57539i	−0.635041	−	0.424321i	0.195944	−	0.980615i	$-0.437223\pi$
$71$	−5.35095	−	3.57539i	−0.635041	−	0.424321i	−0.830985	+	0.556294i	$0.812223\pi$
$72$	5.16447	−	6.73262i	0.608639	−	0.793447i
$73$	5.77379	+	8.64109i	0.675771	+	1.01136i	0.997907	+	0.0646693i	$0.0205993\pi$
$73$	5.77379	+	8.64109i	0.675771	+	1.01136i	−0.322136	+	0.946693i	$0.604401\pi$
$74$	0.0102566	−	0.646598i	0.00119231	−	0.0751655i
$75$	−9.35080	+	4.32168i	−1.07974	+	0.499025i
$76$	−1.32484	−	2.67973i	−0.151969	−	0.307386i
$77$	−0.230950	+	2.34487i	−0.0263192	+	0.267223i
$78$	3.23938	−	3.40125i	0.366788	−	0.385116i
$79$	11.1761	−	4.62928i	1.25741	−	0.520835i	0.348294	−	0.937385i	$-0.386761\pi$
$79$	11.1761	−	4.62928i	1.25741	−	0.520835i	0.909112	+	0.416551i	$0.136761\pi$
$80$	−4.63709	+	12.3958i	−0.518442	+	1.38589i
$81$	5.26203	−	7.30144i	0.584670	−	0.811271i
$82$	−15.1588	+	7.79597i	−1.67400	+	0.860921i
$83$	−2.60265	+	2.13594i	−0.285678	+	0.234450i	−0.766308	−	0.642474i	$-0.777908\pi$
$83$	−2.60265	+	2.13594i	−0.285678	+	0.234450i	0.480630	+	0.876924i	$0.340408\pi$
$84$	7.50953	−	11.4485i	0.819357	−	1.24913i
$85$	20.0373	+	6.07825i	2.17335	+	0.659279i
$86$	−2.83587	+	1.12230i	−0.305799	+	0.121020i
$87$	2.91723	−	11.2236i	0.312760	−	1.20329i
$88$	−1.35584	−	1.00240i	−0.144532	−	0.106856i
$89$	12.0484	−	2.39657i	1.27712	−	0.254036i	0.490486	−	0.871449i	$-0.336819\pi$
$89$	12.0484	−	2.39657i	1.27712	−	0.254036i	0.786639	+	0.617413i	$0.211819\pi$
$90$	−4.52350	+	13.2888i	−0.476819	+	1.40076i
$91$	4.80808	−	5.85866i	0.504024	−	0.614155i
$92$	11.4643	+	5.18055i	1.19523	+	0.540109i
$93$	−2.18315	−	1.33495i	−0.226382	−	0.138428i
$94$	−2.66313	+	0.761942i	−0.274681	+	0.0785883i
$95$	3.49692	+	3.49692i	0.358776	+	0.358776i
$96$	4.27764	+	8.81486i	0.436585	+	0.899663i
$97$	5.23719	−	5.23719i	0.531756	−	0.531756i	−0.389339	−	0.921095i	$-0.627296\pi$
$97$	5.23719	−	5.23719i	0.531756	−	0.531756i	0.921095	+	0.389339i	$0.127296\pi$
$98$	5.91759	−	10.6608i	0.597767	−	1.07690i
$99$	−1.46919	−	1.01978i	−0.147659	−	0.102492i
$100$	0.377265	−	11.8888i	0.0377265	−	1.18888i
$101$	−7.30431	−	5.99449i	−0.726806	−	0.596474i	0.196516	−	0.980501i	$-0.437037\pi$
$101$	−7.30431	−	5.99449i	−0.726806	−	0.596474i	−0.923322	+	0.384026i	$0.874537\pi$
$102$	13.4890	−	7.63834i	1.33561	−	0.756309i
$103$	1.49458	+	7.51375i	0.147265	+	0.740352i	0.981878	+	0.189515i	$0.0606915\pi$
$103$	1.49458	+	7.51375i	0.147265	+	0.740352i	−0.834613	+	0.550837i	$0.814309\pi$
$104$	1.83486	+	5.10387i	0.179923	+	0.500475i
$105$	−5.69804	+	21.9223i	−0.556071	+	2.13939i
$106$	6.70099	−	15.4786i	0.650857	−	1.50341i
$107$	1.71247	−	5.64524i	0.165550	−	0.545746i	−0.834435	−	0.551106i	$-0.814206\pi$
$107$	1.71247	−	5.64524i	0.165550	−	0.545746i	0.999986	+	0.00535963i	$0.00170603\pi$
$108$	4.81434	+	9.20989i	0.463260	+	0.886222i
$109$	−4.14592	−	5.05182i	−0.397108	−	0.483877i	0.535620	−	0.844459i	$-0.320078\pi$
$109$	−4.14592	−	5.05182i	−0.397108	−	0.483877i	−0.932727	+	0.360582i	$0.882578\pi$
$110$	2.65617	+	0.851974i	0.253256	+	0.0812325i
$111$	0.712949	+	0.344959i	0.0676701	+	0.0327420i
$112$	7.93232	+	13.6758i	0.749534	+	1.29224i
$113$	5.45203	+	13.1624i	0.512884	+	1.23821i	0.942198	+	0.335056i	$0.108755\pi$
$113$	5.45203	+	13.1624i	0.512884	+	1.23821i	−0.429314	+	0.903155i	$0.641245\pi$
$114$	3.66009	−	0.0892144i	0.342799	−	0.00835569i
$115$	−20.7121	−	2.03997i	−1.93142	−	0.190228i
$116$	10.0763	+	8.81886i	0.935565	+	0.818811i
$117$	2.10697	+	5.35293i	0.194790	+	0.494878i
$118$	−5.39053	+	5.22219i	−0.496239	+	0.480742i
$119$	20.7975	−	13.8964i	1.90650	−	1.27388i
$120$	−11.3770	−	11.5456i	−1.03858	−	1.05396i
$121$	5.91383	−	8.85067i	0.537621	−	0.804607i
$122$	10.6001	−	15.3321i	0.959692	−	1.38810i
$123$	−0.839678	−	20.8601i	−0.0757112	−	1.88089i
$124$	2.50768	−	1.56286i	0.225196	−	0.140349i
$125$	0.909934	+	2.99965i	0.0813870	+	0.268297i
$126$	8.84297	+	14.2476i	0.787794	+	1.26928i
$127$			15.4496i			1.37093i	0.728104	+	0.685467i	$0.240402\pi$
$127$			15.4496i			1.37093i	−0.728104	+	0.685467i	$0.759598\pi$
$128$	−11.3128	−	0.145410i	−0.999917	−	0.0128525i
$129$	0.216316	−	3.72904i	0.0190456	−	0.328324i
$130$	−5.58143	−	7.02532i	−0.489524	−	0.616161i
$131$	−17.9308	+	5.43925i	−1.56662	+	0.475230i	−0.950058	−	0.312075i	$-0.898976\pi$
$131$	−17.9308	+	5.43925i	−1.56662	+	0.475230i	−0.616565	+	0.787304i	$0.711476\pi$
$132$	1.81291	−	0.988943i	0.157793	−	0.0860764i
$133$	5.87915	−	0.579045i	0.509787	−	0.0502096i
$134$	−5.20371	−	3.59768i	−0.449532	−	0.310792i
$135$	−12.4275	−	11.8801i	−1.06959	−	1.02247i
$136$	0.905183	+	17.8767i	0.0776188	+	1.53292i
$137$	6.76378	+	10.1227i	0.577869	+	0.864842i	0.999113	−	0.0421053i	$-0.0134065\pi$
$137$	6.76378	+	10.1227i	0.577869	+	0.864842i	−0.421244	+	0.906947i	$0.638407\pi$
$138$	−11.6687	+	10.0620i	−0.993306	+	0.856531i
$139$	−7.55153	+	4.03638i	−0.640513	+	0.342361i	−0.759474	−	0.650538i	$-0.774544\pi$
$139$	−7.55153	+	4.03638i	−0.640513	+	0.342361i	0.118961	+	0.992899i	$0.462044\pi$
$140$	−19.6815	−	17.2253i	−1.66339	−	1.45580i
$141$	0.527487	−	3.35127i	0.0444224	−	0.282228i
$142$	0.748309	+	9.07040i	0.0627967	+	0.761171i
$143$	1.05612	−	0.437460i	0.0883173	−	0.0365822i
$144$	−11.9983	+	0.204206i	−0.999855	+	0.0170172i
$145$	−20.4662	−	8.47737i	−1.69962	−	0.704008i
$146$	4.48893	−	13.9950i	0.371506	−	1.15823i
$147$	8.78922	+	12.0729i	0.724923	+	0.995756i
$148$	−0.724997	+	0.557466i	−0.0595944	+	0.0458234i
$149$	2.83990	+	0.861474i	0.232654	+	0.0705747i	0.404459	−	0.914556i	$-0.367460\pi$
$149$	2.83990	+	0.861474i	0.232654	+	0.0705747i	−0.171805	+	0.985131i	$0.554960\pi$
$150$	13.0114	+	6.55223i	1.06238	+	0.534988i
$151$	−13.2070	−	2.62704i	−1.07477	−	0.213785i	−0.374186	−	0.927354i	$-0.622078\pi$
$151$	−13.2070	−	2.62704i	−1.07477	−	0.213785i	−0.700585	+	0.713569i	$0.747078\pi$
$152$	−1.80177	+	3.82439i	−0.146143	+	0.310199i
$153$	1.52597	+	18.9240i	0.123367	+	1.52992i
$154$	2.79963	−	1.80709i	0.225601	−	0.145620i
$155$	−3.10110	+	3.77870i	−0.249086	+	0.303513i
$156$	−6.61592	−	0.594817i	−0.529698	−	0.0476235i
$157$	−7.52800	−	4.02380i	−0.600799	−	0.321134i	0.142808	−	0.989750i	$-0.454387\pi$
$157$	−7.52800	−	4.02380i	−0.600799	−	0.321134i	−0.743608	+	0.668616i	$0.766887\pi$
$158$	−14.9577	−	8.30274i	−1.18997	−	0.660531i
$159$	13.7367	+	15.4285i	1.08939	+	1.22356i
$160$	17.8051	−	5.77016i	1.40762	−	0.456171i
$161$	−17.5799	+	17.5799i	−1.38549	+	1.38549i
$162$	−12.7139	+	0.596579i	−0.998901	+	0.0468717i
$163$	−3.09813	−	1.65599i	−0.242664	−	0.129707i	0.345582	−	0.938389i	$-0.387681\pi$
$163$	−3.09813	−	1.65599i	−0.242664	−	0.129707i	−0.588246	+	0.808682i	$0.700181\pi$
$164$	21.9678	+	9.92696i	1.71540	+	0.775165i
$165$	−2.31663	+	2.51095i	−0.180349	+	0.195478i
$166$	4.65471	+	1.00288i	0.361275	+	0.0778385i
$167$	0.802727	+	4.03558i	0.0621169	+	0.312283i	0.999335	−	0.0364608i	$-0.0116084\pi$
$167$	0.802727	+	4.03558i	0.0621169	+	0.312283i	−0.937218	+	0.348744i	$0.886608\pi$
$168$	−19.2831	+	1.75618i	−1.48772	+	0.135492i
$169$	9.14384	+	1.81882i	0.703373	+	0.139909i
$170$	−10.8967	−	27.5343i	−0.835742	−	2.11179i
$171$	−1.78906	+	4.11164i	−0.136813	+	0.314425i
$172$	3.73747	+	2.15283i	0.284979	+	0.164152i
$173$	1.94768	+	2.37326i	0.148080	+	0.180435i	0.841768	−	0.539840i	$-0.181515\pi$
$173$	1.94768	+	2.37326i	0.148080	+	0.180435i	−0.693688	+	0.720276i	$0.744015\pi$
$174$	−14.9941	+	6.64333i	−1.13670	+	0.503629i
$175$	21.7174	+	8.99563i	1.64168	+	0.680006i
$176$	0.0828004	+	2.38313i	0.00624132	+	0.179635i
$177$	−3.01994	−	8.68180i	−0.226993	−	0.652564i
$178$	−13.2529	−	11.2328i	−0.993343	−	0.841933i
$179$	2.29275	+	0.225817i	0.171368	+	0.0168783i	0.183337	−	0.983050i	$-0.441310\pi$
$179$	2.29275	+	0.225817i	0.171368	+	0.0168783i	−0.0119689	+	0.999928i	$0.503810\pi$
$180$	18.6940	−	6.68148i	1.39337	−	0.498008i
$181$	13.0573	−	6.97925i	0.970538	−	0.518764i	0.0916501	−	0.995791i	$-0.470786\pi$
$181$	13.0573	−	6.97925i	0.970538	−	0.518764i	0.878888	+	0.477028i	$0.158286\pi$
$182$	−10.7170	−	0.169998i	−0.794398	−	0.0126011i
$183$	11.5625	+	19.6841i	0.854724	+	1.45509i
$184$	−4.34892	−	17.2517i	−0.320607	−	1.27181i
$185$	0.840560	−	1.25799i	0.0617992	−	0.0924890i
$186$	0.442370	+	3.59177i	0.0324361	+	0.263361i
$187$	3.75451	−	0.369787i	0.274557	−	0.0270415i
$188$	3.18649	+	2.27858i	0.232399	+	0.166182i
$189$	−20.3881	+	2.47273i	−1.48301	+	0.179864i
$190$	0.795821	−	6.94841i	0.0577349	−	0.504091i
$191$		−	15.9188i		−	1.15185i	−0.817504	−	0.575923i	$-0.804643\pi$
$191$		−	15.9188i		−	1.15185i	0.817504	−	0.575923i	$-0.195357\pi$
$192$	5.99753	−	12.4912i	0.432834	−	0.901474i
$193$		−	1.79727i		−	0.129370i	−0.997906	−	0.0646851i	$-0.979396\pi$
$193$		−	1.79727i		−	0.129370i	0.997906	−	0.0646851i	$-0.0206043\pi$
$194$	−10.4063	−	1.19187i	−0.747132	−	0.0855711i
$195$	10.6830	−	2.57564i	0.765029	−	0.184445i
$196$	−17.0104	+	2.82596i	−1.21503	+	0.201854i
$197$	−9.82672	+	0.967847i	−0.700125	+	0.0689563i	−0.441815	−	0.897106i	$-0.645665\pi$
$197$	−9.82672	+	0.967847i	−0.700125	+	0.0689563i	−0.258309	+	0.966062i	$0.583165\pi$
$198$	0.163277	+	2.52394i	0.0116036	+	0.179369i
$199$	2.15652	−	3.22746i	0.152871	−	0.228788i	−0.747127	−	0.664681i	$-0.768567\pi$
$199$	2.15652	−	3.22746i	0.152871	−	0.228788i	0.899999	+	0.435893i	$0.143567\pi$
$200$	−13.4963	+	10.0410i	−0.954331	+	0.710008i
$201$	6.68077	−	3.92430i	0.471225	−	0.276799i
$202$	−0.211945	+	13.3615i	−0.0149124	+	0.940109i
$203$	−23.3379	+	12.4744i	−1.63800	+	0.875528i
$204$	−20.3244	−	8.21674i	−1.42299	−	0.575287i
$205$	−39.6886	−	3.90899i	−2.77197	−	0.273015i
$206$	7.00512	−	8.26490i	0.488070	−	0.575843i
$207$	−5.15717	−	18.1523i	−0.358448	−	1.26167i
$208$	4.03733	−	6.52168i	0.279938	−	0.452197i
$209$	0.823211	+	0.340985i	0.0569427	+	0.0235864i
$210$	29.2870	−	12.9760i	2.02100	−	0.895427i
$211$	−1.08800	−	1.32573i	−0.0749011	−	0.0912673i	0.734212	−	0.678921i	$-0.237552\pi$
$211$	−1.08800	−	1.32573i	−0.0749011	−	0.0912673i	−0.809113	+	0.587653i	$0.800052\pi$
$212$	−23.0343	+	6.19678i	−1.58200	+	0.425597i
$213$	−10.4614	−	3.84800i	−0.716804	−	0.263661i
$214$	−7.75743	+	3.07001i	−0.530287	+	0.209861i
$215$	−6.99834	−	1.39206i	−0.477283	−	0.0949375i
$216$	5.96280	−	13.4330i	0.405717	−	0.913999i
$217$	1.13921	+	5.72719i	0.0773345	+	0.388787i
$218$	−1.94662	+	9.03493i	−0.131842	+	0.611922i
$219$	13.2299	+	12.2060i	0.893991	+	0.824804i
$220$	−1.39329	−	3.69066i	−0.0939357	−	0.248824i
$221$	−10.7023	−	5.72050i	−0.719915	−	0.384802i
$222$	−0.245222	−	1.09291i	−0.0164582	−	0.0733513i
$223$	9.67171	−	9.67171i	0.647666	−	0.647666i	−0.304763	−	0.952428i	$-0.598577\pi$
$223$	9.67171	−	9.67171i	0.647666	−	0.647666i	0.952428	+	0.304763i	$0.0985771\pi$
$224$	8.16491	−	20.8142i	0.545541	−	1.39071i
$225$	−13.9905	+	11.0729i	−0.932700	+	0.738194i
$226$	9.77837	−	17.6161i	0.650447	−	1.17181i
$227$	16.6493	+	8.89925i	1.10505	+	0.590664i	0.919942	−	0.392054i	$-0.128235\pi$
$227$	16.6493	+	8.89925i	1.10505	+	0.590664i	0.185112	+	0.982717i	$0.440735\pi$
$228$	−3.31863	−	3.97431i	−0.219781	−	0.263205i
$229$	−12.7948	+	15.5905i	−0.845503	+	1.03025i	0.153610	+	0.988132i	$0.450910\pi$
$229$	−12.7948	+	15.5905i	−0.845503	+	1.03025i	−0.999113	+	0.0421167i	$0.986590\pi$
$230$	15.9620	+	24.7290i	1.05250	+	1.63058i
$231$	0.563046	+	4.04206i	0.0370457	+	0.265948i
$232$	0.900745	−	18.9156i	0.0591368	−	1.24187i
$233$	−4.88894	−	0.972470i	−0.320285	−	0.0637086i	0.0323297	−	0.999477i	$-0.489707\pi$
$233$	−4.88894	−	0.972470i	−0.320285	−	0.0637086i	−0.352615	+	0.935769i	$0.614707\pi$
$234$	4.07373	−	7.04209i	0.266308	−	0.460356i
$235$	−6.20159	−	1.88123i	−0.404547	−	0.122718i
$236$	10.5246	+	1.37486i	0.685096	+	0.0894958i
$237$	16.9390	−	12.3318i	1.10031	−	0.801038i
$238$	−33.6833	−	10.8040i	−2.18337	−	0.700320i
$239$	−6.86113	−	2.84197i	−0.443810	−	0.183832i	0.149576	−	0.988750i	$-0.452209\pi$
$239$	−6.86113	−	2.84197i	−0.443810	−	0.183832i	−0.593386	+	0.804918i	$0.702209\pi$
$240$	−2.77578	+	22.7546i	−0.179176	+	1.46880i
$241$	15.4006	−	6.37915i	0.992042	−	0.410917i	0.173169	−	0.984892i	$-0.444599\pi$
$241$	15.4006	−	6.37915i	0.992042	−	0.410917i	0.818873	+	0.573975i	$0.194599\pi$
$242$	−15.0028	+	1.23773i	−0.964416	+	0.0795644i
$243$	5.89616	−	14.4304i	0.378239	−	0.925708i
$244$	−26.3023	+	1.75043i	−1.68383	+	0.112060i
$245$	25.1584	−	13.4474i	1.60731	−	0.859124i
$246$	−22.3595	+	19.2807i	−1.42559	+	1.22929i
$247$	−1.59233	−	2.38309i	−0.101317	−	0.151632i
$248$	−3.93660	−	1.40186i	−0.249974	−	0.0890183i
$249$	−3.51525	+	4.65307i	−0.222770	+	0.294877i
$250$	2.52101	−	3.64641i	0.159443	−	0.230619i
$251$	−8.18956	+	0.806601i	−0.516920	+	0.0509122i	−0.353114	−	0.935580i	$-0.614877\pi$
$251$	−8.18956	+	0.806601i	−0.516920	+	0.0509122i	−0.163806	+	0.986493i	$0.552377\pi$
$252$	7.99697	−	22.3256i	0.503762	−	1.40638i
$253$	−3.58840	+	1.08853i	−0.225601	+	0.0684353i
$254$	17.1073	−	13.5913i	1.07341	−	0.852793i
$255$	36.2064	+	2.10028i	2.26734	+	0.131525i
$256$	9.79102	+	12.6545i	0.611939	+	0.790905i
$257$		−	1.57386i		−	0.0981745i	−0.998794	−	0.0490872i	$-0.984369\pi$
$257$		−	1.57386i		−	0.0981745i	0.998794	−	0.0490872i	$-0.0156312\pi$
$258$	−4.31944	+	3.04097i	−0.268917	+	0.189323i
$259$	−0.524643	−	1.72952i	−0.0325997	−	0.107467i
$260$	−2.86902	+	12.3606i	−0.177929	+	0.766570i
$261$	0.355748	−	20.0826i	0.0220203	−	1.24308i
$262$	21.7969	+	15.0697i	1.34662	+	0.931008i
$263$	−8.16712	+	12.2230i	−0.503606	+	0.753700i	−0.992968	−	0.118381i	$-0.962230\pi$
$263$	−8.16712	+	12.2230i	−0.503606	+	0.753700i	0.489362	+	0.872081i	$0.337230\pi$
$264$	−2.68989	−	1.13743i	−0.165551	−	0.0700040i
$265$	32.8110	−	21.9236i	2.01556	−	1.34676i
$266$	−5.81315	−	6.00055i	−0.356427	−	0.367917i
$267$	19.3142	−	8.92649i	1.18201	−	0.546292i
$268$	0.594095	+	8.92697i	0.0362901	+	0.545302i
$269$	−15.1040	−	1.48761i	−0.920906	−	0.0907013i	−0.373558	−	0.927607i	$-0.621862\pi$
$269$	−15.1040	−	1.48761i	−0.920906	−	0.0907013i	−0.547348	+	0.836905i	$0.684362\pi$
$270$	−2.22202	+	24.2120i	−0.135228	+	1.47350i
$271$	10.0242	+	24.2005i	0.608926	+	1.47008i	0.864170	+	0.503200i	$0.167844\pi$
$271$	10.0242	+	24.2005i	0.608926	+	1.47008i	−0.255244	+	0.966877i	$0.582156\pi$
$272$	18.9985	−	16.7288i	1.15195	−	1.01433i
$273$	5.71750	−	11.8167i	0.346039	−	0.715181i
$274$	5.25861	−	16.3946i	0.317684	−	0.990435i
$275$	2.24924	+	2.74071i	0.135634	+	0.165271i
$276$	21.4067	+	4.06901i	1.28853	+	0.244926i
$277$	−7.76707	+	25.6046i	−0.466678	+	1.53843i	0.335908	+	0.941895i	$0.390957\pi$
$277$	−7.76707	+	25.6046i	−0.466678	+	1.53843i	−0.802586	+	0.596536i	$0.796543\pi$
$278$	11.1127	+	4.81090i	0.666493	+	0.288538i
$279$	−4.21794	−	1.36153i	−0.252521	−	0.0815127i
$280$	−1.75937	+	36.9465i	−0.105142	+	2.20798i
$281$	2.69961	+	13.5719i	0.161046	+	0.809631i	0.973867	+	0.227118i	$0.0729303\pi$
$281$	2.69961	+	13.5719i	0.161046	+	0.809631i	−0.812822	+	0.582513i	$0.802070\pi$
$282$	−4.17488	+	2.36408i	−0.248610	+	0.140779i
$283$	21.8762	+	17.9533i	1.30040	+	1.06721i	0.993303	+	0.115537i	$0.0368589\pi$
$283$	21.8762	+	17.9533i	1.30040	+	1.06721i	0.307101	+	0.951677i	$0.400641\pi$
$284$	9.38530	−	8.80798i	0.556915	−	0.522657i
$285$	7.30773	+	4.46853i	0.432873	+	0.264693i
$286$	−1.41348	−	0.784596i	−0.0835810	−	0.0463941i
$287$	−33.6866	+	33.6866i	−1.98846	+	1.98846i
$288$	10.7812	+	13.1060i	0.635287	+	0.772276i
$289$	−16.2986	−	16.2986i	−0.958739	−	0.958739i
$290$	8.61749	+	30.1198i	0.506037	+	1.76869i
$291$	6.69232	−	10.9445i	0.392311	−	0.641577i
$292$	−19.4455	+	7.34105i	−1.13796	+	0.429603i
$293$	5.09003	−	6.20222i	0.297363	−	0.362338i	−0.602799	−	0.797893i	$-0.705948\pi$
$293$	5.09003	−	6.20222i	0.297363	−	0.362338i	0.900162	+	0.435555i	$0.143448\pi$
$294$	5.63623	−	20.3530i	0.328712	−	1.18701i
$295$	−17.2219	+	3.42565i	−1.00270	+	0.199449i
$296$	1.25507	+	0.312373i	0.0729495	+	0.0181563i
$297$	−2.88782	−	1.12068i	−0.167568	−	0.0650284i
$298$	−1.54440	−	3.90246i	−0.0894647	−	0.226063i
$299$	11.5425	+	3.50137i	0.667518	+	0.202490i
$300$	−4.19111	−	20.1716i	−0.241974	−	1.16461i
$301$	−6.58895	+	5.40742i	−0.379781	+	0.311678i
$302$	8.70951	+	16.9351i	0.501176	+	0.974505i
$303$	−14.7325	−	7.12831i	−0.846362	−	0.409511i
$304$	5.81976	−	1.36929i	0.333786	−	0.0785342i
$305$	40.2897	−	16.6885i	2.30698	−	0.955582i
$306$	19.6120	−	18.3375i	1.12114	−	1.04828i
$307$	−2.62801	+	26.6826i	−0.149988	+	1.52286i	0.565801	+	0.824542i	$0.308567\pi$
$307$	−2.62801	+	26.6826i	−0.149988	+	1.52286i	−0.715789	+	0.698316i	$0.753933\pi$
$308$	−4.46387	−	1.51029i	−0.254352	−	0.0860567i
$309$	5.56684	+	12.0450i	0.316687	+	0.685213i
$310$	6.91222	+	0.109645i	0.392588	+	0.00622740i
$311$	−2.00925	−	3.00705i	−0.113934	−	0.170514i	0.770120	−	0.637899i	$-0.220196\pi$
$311$	−2.00925	−	3.00705i	−0.113934	−	0.170514i	−0.884054	+	0.467385i	$0.845196\pi$
$312$	5.16150	+	7.84904i	0.292212	+	0.444364i
$313$	−6.86076	−	4.58421i	−0.387793	−	0.259115i	0.346356	−	0.938103i	$-0.387419\pi$
$313$	−6.86076	−	4.58421i	−0.387793	−	0.259115i	−0.734149	+	0.678988i	$0.762419\pi$
$314$	2.16697	+	11.8755i	0.122289	+	0.670173i
$315$	−0.694860	+	39.2260i	−0.0391509	+	2.21013i
$316$	3.96499	+	23.8667i	0.223048	+	1.34261i
$317$	−16.2017	+	4.91473i	−0.909978	+	0.276039i	−0.710363	−	0.703836i	$-0.751469\pi$
$317$	−16.2017	+	4.91473i	−0.909978	+	0.276039i	−0.199615	+	0.979874i	$0.563969\pi$
$318$	4.99951	−	28.7832i	0.280358	−	1.61408i
$319$	−3.99132			−0.223471
$320$	−22.0527	−	14.6394i	−1.23278	−	0.818366i
$321$	0.591726	−	10.2007i	0.0330269	−	0.569346i
$322$	34.9314	+	4.00079i	1.94665	+	0.222956i
$323$	−2.74580	−	9.05169i	−0.152780	−	0.503649i
$324$	11.8452	+	13.5532i	0.658069	+	0.752958i
$325$	−1.11783	−	11.3495i	−0.0620062	−	0.629559i
$326$	0.891813	+	4.88734i	0.0493930	+	0.270685i
$327$	−9.03175	−	6.82321i	−0.499457	−	0.377325i
$328$	−8.33340	−	33.0577i	−0.460135	−	1.82531i
$329$	−6.43686	+	4.30097i	−0.354876	+	0.237120i
$330$	4.81834	+	0.356263i	0.265241	+	0.0196116i
$331$	−8.72229	−	16.3183i	−0.479420	−	0.896932i	−0.999094	−	0.0425673i	$-0.986446\pi$
$331$	−8.72229	−	16.3183i	−0.479420	−	0.896932i	0.519673	−	0.854365i	$-0.326054\pi$
$332$	−2.98434	−	6.03638i	−0.163787	−	0.331289i
$333$	1.34050	+	0.291416i	0.0734592	+	0.0159695i
$334$	3.76240	−	4.43902i	0.205870	−	0.242892i
$335$	−5.66407	−	13.6743i	−0.309461	−	0.747106i
$336$	18.9083	+	19.8071i	1.03153	+	1.08057i
$337$	8.70559	−	21.0172i	0.474224	−	1.14488i	−0.488055	−	0.872813i	$-0.662293\pi$
$337$	8.70559	−	21.0172i	0.474224	−	1.14488i	0.962279	−	0.272065i	$-0.0877065\pi$
$338$	−6.03001	−	11.7250i	−0.327989	−	0.637754i
$339$	14.5235	+	19.9496i	0.788809	+	1.08351i
$340$	−20.9026	+	36.2883i	−1.13360	+	1.96801i
$341$	−0.255668	+	0.842825i	−0.0138452	+	0.0456415i
$342$	6.12666	−	1.63606i	0.331292	−	0.0884681i
$343$	1.25053	−	6.28684i	0.0675223	−	0.339457i
$344$	−0.904091	−	6.03236i	−0.0487453	−	0.325243i
$345$	−35.7034	+	4.97335i	−1.92220	+	0.267756i
$346$	0.914486	−	4.24445i	0.0491631	−	0.228183i
$347$	−1.79621	−	1.47411i	−0.0964258	−	0.0791346i	0.584945	−	0.811073i	$-0.301116\pi$
$347$	−1.79621	−	1.47411i	−0.0964258	−	0.0791346i	−0.681371	+	0.731938i	$0.738616\pi$
$348$	20.5467	+	10.7587i	1.10142	+	0.576725i
$349$	−8.61947	+	16.1259i	−0.461390	+	0.863199i	0.538400	+	0.842689i	$0.319029\pi$
$349$	−8.61947	+	16.1259i	−0.461390	+	0.863199i	−0.999790	+	0.0205099i	$0.993471\pi$
$350$	−9.14432	−	31.9611i	−0.488784	−	1.70839i
$351$	5.72079	+	8.15794i	0.305353	+	0.435439i
$352$	2.56599	−	2.18817i	0.136768	−	0.116630i
$353$	−20.7553	−	20.7553i	−1.10469	−	1.10469i	−0.993836	−	0.110857i	$-0.964641\pi$
$353$	−20.7553	−	20.7553i	−1.10469	−	1.10469i	−0.110857	−	0.993836i	$-0.535359\pi$
$354$	−6.95662	+	10.9815i	−0.369740	+	0.583659i
$355$	−10.0375	+	18.7789i	−0.532736	+	0.996680i
$356$	−0.779246	+	24.5565i	−0.0413000	+	1.30149i
$357$	29.3776	−	31.8418i	1.55482	−	1.68525i
$358$	−1.76693	−	2.73741i	−0.0933850	−	0.144676i
$359$	24.0249	−	4.77884i	1.26798	−	0.252218i	0.485140	−	0.874436i	$-0.338769\pi$
$359$	24.0249	−	4.77884i	1.26798	−	0.252218i	0.782843	+	0.622219i	$0.213769\pi$
$360$	−23.8437	−	14.8219i	−1.25668	−	0.781182i
$361$	−3.27088	+	16.4438i	−0.172151	+	0.865464i
$362$	−19.2148	−	8.31846i	−1.00991	−	0.437209i
$363$	6.36473	−	17.3036i	0.334062	−	0.908202i
$364$	9.23969	+	12.0164i	0.484291	+	0.629832i
$365$	26.5805	−	21.8140i	1.39129	−	1.14180i
$366$	11.6244	−	30.1195i	0.607616	−	1.57437i
$367$	11.5833	−	27.9646i	0.604645	−	1.45974i	−0.264106	−	0.964494i	$-0.585077\pi$
$367$	11.5833	−	27.9646i	0.604645	−	1.45974i	0.868751	−	0.495249i	$-0.164923\pi$
$368$	−15.2769	+	19.9922i	−0.796365	+	1.04216i
$369$	−9.88217	−	34.7834i	−0.514445	−	1.81075i
$370$	−2.13241	+	0.175924i	−0.110859	+	0.00914587i
$371$	4.62046	−	46.9123i	0.239882	−	2.43557i
$372$	3.58799	−	3.64957i	0.186028	−	0.189221i
$373$	−13.2010	−	24.6973i	−0.683522	−	1.27878i	−0.949187	−	0.314714i	$-0.898091\pi$
$373$	−13.2010	−	24.6973i	−0.683522	−	1.27878i	0.265665	−	0.964065i	$-0.414409\pi$
$374$	−3.71237	−	3.83204i	−0.191962	−	0.198150i
$375$	2.74988	+	4.68143i	0.142003	+	0.241748i
$376$	−0.280156	−	5.53288i	−0.0144479	−	0.285337i
$377$	10.6748	+	7.13269i	0.549781	+	0.367352i
$378$	20.6738	+	20.4003i	1.06334	+	1.04928i
$379$	−0.252166	−	2.56028i	−0.0129529	−	0.131513i	0.986533	−	0.163559i	$-0.0522975\pi$
$379$	−0.252166	−	2.56028i	−0.0129529	−	0.131513i	−0.999486	+	0.0320465i	$0.989798\pi$
$380$	−8.39403	+	5.23142i	−0.430605	+	0.268366i
$381$	6.27190	+	26.0142i	0.321319	+	1.33275i
$382$	−17.6268	+	14.0041i	−0.901867	+	0.716510i
$383$	−13.6906			−0.699559			−0.349779	−	0.936832i	$-0.613743\pi$
$383$	−13.6906			−0.699559			−0.349779	+	0.936832i	$0.613743\pi$
$384$	−19.1075	+	4.34767i	−0.975077	+	0.221866i
$385$	7.79599			0.397320
$386$	−1.99010	+	1.58109i	−0.101294	+	0.0804751i
$387$	−1.14960	−	6.36679i	−0.0584374	−	0.323642i
$388$	7.83488	+	12.5714i	0.397756	+	0.638215i
$389$	1.42902	+	14.5090i	0.0724539	+	0.735637i	0.960944	+	0.276742i	$0.0892547\pi$
$389$	1.42902	+	14.5090i	0.0724539	+	0.735637i	−0.888490	+	0.458895i	$0.848245\pi$
$390$	−12.2500	−	9.56344i	−0.620304	−	0.484264i
$391$	33.0988	+	22.1159i	1.67388	+	1.11845i
$392$	18.0935	+	16.3495i	0.913860	+	0.825774i
$393$	−27.9839	+	16.4378i	−1.41160	+	0.829177i
$394$	9.71642	+	10.0296i	0.489506	+	0.505286i
$395$	−18.8676	−	35.2987i	−0.949330	−	1.77607i
$396$	2.65111	−	2.40115i	0.133223	−	0.120662i
$397$	−1.58664	+	16.1094i	−0.0796312	+	0.808509i	0.869564	+	0.493821i	$0.164400\pi$
$397$	−1.58664	+	16.1094i	−0.0796312	+	0.808509i	−0.949195	+	0.314689i	$0.898100\pi$
$398$	−5.47086	+	0.451347i	−0.274230	+	0.0226240i
$399$	9.66427	−	3.36169i	0.483818	−	0.168295i
$400$	22.9913	+	6.11110i	1.14956	+	0.305555i
$401$	0.00672810	−	0.0162431i	0.000335985	−	0.000811140i	−0.923711	−	0.383089i	$-0.874860\pi$
$401$	0.00672810	−	0.0162431i	0.000335985	−	0.000811140i	0.924047	+	0.382278i	$0.124860\pi$
$402$	−10.2225	−	3.94531i	−0.509854	−	0.196774i
$403$	2.18996	−	1.79725i	0.109089	−	0.0895274i
$404$	14.9815	−	11.5196i	0.745358	−	0.573122i
$405$	−25.7484	−	14.9587i	−1.27945	−	0.743301i
$406$	34.3435	+	14.8680i	1.70444	+	0.737886i
$407$	0.0531815	−	0.267361i	0.00263611	−	0.0132526i
$408$	8.78136	+	29.7335i	0.434742	+	1.47203i
$409$	−3.70841	+	0.737648i	−0.183369	+	0.0364743i	−0.285920	−	0.958253i	$-0.592299\pi$
$409$	−3.70841	+	0.737648i	−0.183369	+	0.0364743i	0.102552	+	0.994728i	$0.467299\pi$
$410$	30.5863	+	47.3857i	1.51055	+	2.34021i
$411$	15.4983	+	14.2989i	0.764474	+	0.705311i
$412$	−15.3142	−	0.485963i	−0.754476	−	0.0239417i
$413$	−9.88789	+	18.4989i	−0.486551	+	0.910273i
$414$	−15.5631	+	21.6794i	−0.764884	+	1.06548i
$415$	7.87718	+	7.87718i	0.386676	+	0.386676i
$416$	−10.7731	+	1.26672i	−0.528195	+	0.0621060i
$417$	−11.0767	+	9.86208i	−0.542429	+	0.482948i
$418$	−0.346621	−	1.21151i	−0.0169538	−	0.0592567i
$419$	−16.0453	+	30.0187i	−0.783866	+	1.46651i	0.0980904	+	0.995178i	$0.468727\pi$
$419$	−16.0453	+	30.0187i	−0.783866	+	1.46651i	−0.881956	+	0.471332i	$0.843773\pi$
$420$	−40.1325	−	21.0142i	−1.95827	−	1.02539i
$421$	0.217124	+	0.178189i	0.0105820	+	0.00868441i	0.639669	−	0.768650i	$-0.279071\pi$
$421$	0.217124	+	0.178189i	0.0105820	+	0.00868441i	−0.629087	+	0.777335i	$0.716571\pi$
$422$	−0.510844	+	2.37101i	−0.0248675	+	0.115419i
$423$	−0.472289	−	5.85702i	−0.0229635	−	0.284778i
$424$	27.1253	+	20.0543i	1.31732	+	0.973923i
$425$	7.34280	−	36.9148i	0.356178	−	1.79063i
$426$	4.94221	+	14.9690i	0.239451	+	0.725251i
$427$	15.1221	−	49.8509i	0.731810	−	2.41245i
$428$	10.2237	+	5.88901i	0.494183	+	0.284656i
$429$	1.60071	−	1.16534i	0.0772831	−	0.0562630i
$430$	4.61514	+	8.97383i	0.222562	+	0.432757i
$431$	10.2218	−	24.6777i	0.492368	−	1.18868i	−0.461144	−	0.887325i	$-0.652561\pi$
$431$	10.2218	−	24.6777i	0.492368	−	1.18868i	0.953512	−	0.301356i	$-0.0974392\pi$
$432$	−20.1198	+	5.21463i	−0.968016	+	0.250889i
$433$	−0.0200990	−	0.0485232i	−0.000965894	−	0.00233188i	0.923396	−	0.383849i	$-0.125402\pi$
$433$	−0.0200990	−	0.0485232i	−0.000965894	−	0.00233188i	−0.924362	+	0.381517i	$0.875402\pi$
$434$	5.33950	−	6.29974i	0.256304	−	0.302397i
$435$	−37.9025	−	5.96583i	−1.81729	−	0.286040i
$436$	11.7168	−	5.79269i	0.561132	−	0.277420i
$437$	4.43198	+	8.29165i	0.212010	+	0.396644i
$438$	1.87710	−	25.3871i	0.0896913	−	1.21304i
$439$	10.8799	−	7.26975i	0.519271	−	0.346966i	−0.268154	−	0.963376i	$-0.586414\pi$
$439$	10.8799	−	7.26975i	0.519271	−	0.346966i	0.787425	+	0.616410i	$0.211414\pi$
$440$	−2.86094	+	4.78951i	−0.136390	+	0.228331i
$441$	19.7004	+	16.7604i	0.938116	+	0.798112i
$442$	3.08071	+	16.8830i	0.146535	+	0.803043i
$443$	−0.861845	−	8.75046i	−0.0409475	−	0.415747i	−0.993706	−	0.112018i	$-0.964268\pi$
$443$	−0.861845	−	8.75046i	−0.0409475	−	0.415747i	0.952759	−	0.303728i	$-0.0982316\pi$
$444$	−0.994446	+	1.23298i	−0.0471943	+	0.0585147i
$445$	−11.7987	−	38.8951i	−0.559312	−	1.84380i
$446$	−19.2178	−	2.20107i	−0.909989	−	0.104224i
$447$	5.13156	+	0.297674i	0.242714	+	0.0140795i
$448$	−30.2302	+	9.26964i	−1.42824	+	0.437949i
$449$	5.31942			0.251039			0.125519	−	0.992091i	$-0.459940\pi$
$449$	5.31942			0.251039			0.125519	+	0.992091i	$0.459940\pi$
$450$	24.5686	+	5.75059i	1.15818	+	0.271085i
$451$	−6.87610	+	2.08584i	−0.323783	+	0.0982184i
$452$	−28.1084	+	4.66968i	−1.32211	+	0.219643i
$453$	−23.3045	+	0.938073i	−1.09494	+	0.0440745i
$454$	−4.79259	−	26.2645i	−0.224928	−	1.23265i
$455$	−20.8504	−	13.9318i	−0.977483	−	0.653133i
$456$	−1.48128	+	7.17096i	−0.0693674	+	0.335811i
$457$	−13.7933	−	20.6431i	−0.645222	−	0.965643i	−0.999534	−	0.0305162i	$-0.990285\pi$
$457$	−13.7933	−	20.6431i	−0.645222	−	0.965643i	0.354312	−	0.935127i	$-0.384715\pi$
$458$	28.5190	+	0.452381i	1.33261	+	0.0211384i
$459$	10.2518	+	31.2449i	0.478512	+	1.45839i
$460$	13.3403	−	39.4291i	0.621995	−	1.83839i
$461$	−1.07803	+	10.9454i	−0.0502089	+	0.509780i	0.936885	+	0.349638i	$0.113695\pi$
$461$	−1.07803	+	10.9454i	−0.0502089	+	0.509780i	−0.987094	+	0.160142i	$0.948805\pi$
$462$	3.98043	−	4.17933i	0.185186	−	0.194440i
$463$	−19.8008	+	8.20175i	−0.920220	+	0.381167i	−0.791960	−	0.610573i	$-0.790939\pi$
$463$	−19.8008	+	8.20175i	−0.920220	+	0.381167i	−0.128260	+	0.991741i	$0.540939\pi$
$464$	−21.7375	+	15.6429i	−1.00914	+	0.726205i
$465$	−3.68765	+	7.62151i	−0.171011	+	0.353439i
$466$	3.22407	+	6.26899i	0.149352	+	0.290405i
$467$	19.8906	−	16.3238i	0.920429	−	0.755377i	−0.0494975	−	0.998774i	$-0.515762\pi$
$467$	19.8906	−	16.3238i	0.920429	−	0.755377i	0.969927	+	0.243398i	$0.0782620\pi$
$468$	−11.3814	+	1.68423i	−0.526105	+	0.0778536i
$469$	−16.9194	−	5.13243i	−0.781264	−	0.236994i
$470$	3.37256	+	8.52193i	0.155565	+	0.393087i
$471$	−14.3092	−	3.71924i	−0.659332	−	0.171373i
$472$	−7.73632	−	12.8634i	−0.356093	−	0.592084i
$473$	−1.26093	+	0.250814i	−0.0579775	+	0.0115324i
$474$	−28.5565	−	7.90798i	−1.31164	−	0.363226i
$475$	5.63937	−	6.87159i	0.258752	−	0.315290i
$476$	17.6686	+	46.8018i	0.809837	+	2.14516i
$477$	29.3932	+	20.4020i	1.34582	+	0.934145i
$478$	2.88895	+	10.0974i	0.132137	+	0.461845i
$479$	28.1032	+	28.1032i	1.28407	+	1.28407i	0.938331	+	0.345738i	$0.112371\pi$
$479$	28.1032	+	28.1032i	1.28407	+	1.28407i	0.345738	+	0.938331i	$0.387629\pi$
$480$	27.6379	−	16.9440i	1.26149	−	0.773382i
$481$	−0.620022	+	0.620022i	−0.0282706	+	0.0282706i
$482$	−20.6118	−	11.4412i	−0.938841	−	0.521132i
$483$	−22.4644	+	36.7378i	−1.02217	+	1.67163i
$484$	14.5687	+	15.5236i	0.662215	+	0.705620i
$485$	−18.9432	−	15.5463i	−0.860167	−	0.705921i
$486$	−21.1656	+	6.16585i	−0.960091	+	0.279688i
$487$	−2.51031	−	12.6202i	−0.113753	−	0.571876i	−0.995055	−	0.0993226i	$-0.968332\pi$
$487$	−2.51031	−	12.6202i	−0.113753	−	0.571876i	0.881302	−	0.472553i	$-0.156668\pi$
$488$	25.0768	+	27.5845i	1.13517	+	1.24869i
$489$	−5.88891	−	1.53065i	−0.266306	−	0.0692182i
$490$	−37.0225	−	16.0278i	−1.67250	−	0.724061i
$491$	−1.75007	+	5.76922i	−0.0789797	+	0.260361i	−0.987534	−	0.157406i	$-0.949687\pi$
$491$	−1.75007	+	5.76922i	−0.0789797	+	0.260361i	0.908554	+	0.417767i	$0.137187\pi$
$492$	41.0195	+	7.79704i	1.84930	+	0.351518i
$493$	26.8797	+	32.7530i	1.21060	+	1.47512i
$494$	−1.23798	+	3.85961i	−0.0556994	+	0.173652i
$495$	−2.88141	+	5.16841i	−0.129510	+	0.232303i
$496$	1.91081	+	5.59221i	0.0857981	+	0.251098i
$497$	9.73396	+	23.4999i	0.436628	+	1.05411i
$498$	8.24475	−	0.200965i	0.369456	−	0.00900545i
$499$	35.7171	+	3.51783i	1.59892	+	0.157480i	0.857832	−	0.513930i	$-0.171811\pi$
$499$	35.7171	+	3.51783i	1.59892	+	0.157480i	0.741086	+	0.671410i	$0.234311\pi$
$500$	−6.25542	+	0.416302i	−0.279751	+	0.0186176i
$501$	2.98991	+	6.46926i	0.133579	+	0.289025i
$502$	8.09763	+	8.35867i	0.361415	+	0.373066i
$503$	−10.9992	+	7.34945i	−0.490431	+	0.327696i	−0.776075	−	0.630640i	$-0.782792\pi$
$503$	−10.9992	+	7.34945i	−0.490431	+	0.327696i	0.285644	+	0.958336i	$0.407792\pi$
$504$	−31.7561	+	10.7852i	−1.41453	+	0.480411i
$505$	−17.3695	+	25.9953i	−0.772934	+	1.15678i
$506$	4.36210	+	3.01582i	0.193919	+	0.134070i
$507$	16.1348	−	0.649473i	0.716572	−	0.0288441i
$508$	−30.0991	−	6.98631i	−1.33543	−	0.309967i
$509$	2.66082	+	8.77154i	0.117939	+	0.388792i	0.995957	−	0.0898361i	$-0.0286343\pi$
$509$	2.66082	+	8.77154i	0.117939	+	0.388792i	−0.878018	+	0.478628i	$0.841134\pi$
$510$	−29.5258	−	41.9388i	−1.30742	−	1.85708i
$511$		−	41.0759i		−	1.81709i
$512$	5.39892	−	21.9739i	0.238601	−	0.971118i
$513$	−1.34327	+	7.64949i	−0.0593070	+	0.337733i
$514$	−1.74272	+	1.38455i	−0.0768682	+	0.0610698i
$515$	24.2562	−	7.35804i	1.06886	−	0.324234i
$516$	7.16713	+	2.10770i	0.315515	+	0.0927862i
$517$	−1.16203	+	0.114450i	−0.0511059	+	0.00503349i
$518$	−1.45355	+	2.10242i	−0.0638651	+	0.0923749i
$519$	4.24296	+	3.20542i	0.186245	+	0.140703i
$520$	16.2107	−	7.69695i	0.710887	−	0.337534i
$521$	−1.86065	−	2.78467i	−0.0815168	−	0.121998i	0.788471	−	0.615072i	$-0.210873\pi$
$521$	−1.86065	−	2.78467i	−0.0815168	−	0.121998i	−0.869987	+	0.493074i	$0.835873\pi$
$522$	−22.5503	+	17.2730i	−0.986999	+	0.756021i
$523$	−30.9639	+	16.5506i	−1.35396	+	0.723705i	−0.979100	−	0.203377i	$-0.934808\pi$
$523$	−30.9639	+	16.5506i	−1.35396	+	0.723705i	−0.374857	+	0.927083i	$0.622308\pi$
$524$	−2.48850	−	37.3926i	−0.108711	−	1.63350i
$525$	40.2197	+	6.33054i	1.75533	+	0.276288i
$526$	20.7191	−	1.70933i	0.903398	−	0.0745304i
$527$	8.63807	−	3.57801i	0.376280	−	0.155860i
$528$	1.10687	+	3.97912i	0.0481704	+	0.173169i
$529$	−15.3058	−	6.33988i	−0.665471	−	0.275647i
$530$	−53.1402	−	17.0449i	−2.30826	−	0.740382i
$531$	−8.60943	−	13.3925i	−0.373618	−	0.581185i
$532$	−1.53044	+	11.7156i	−0.0663532	+	0.507938i
$533$	22.1177	+	6.70932i	0.958023	+	0.290613i
$534$	−26.8753	−	13.5337i	−1.16301	−	0.585661i
$535$	−19.1438	−	3.80793i	−0.827657	−	0.164631i
$536$	9.36215	−	8.51104i	0.404383	−	0.367621i
$537$	3.95222	−	0.550531i	0.170551	−	0.0237572i
$538$	11.6400	+	18.0332i	0.501836	+	0.777467i
$539$	3.26066	−	3.97313i	0.140447	−	0.171135i
$540$	28.7646	−	18.8393i	1.23783	−	0.810713i
$541$	17.3254	+	9.26062i	0.744877	+	0.398145i	0.799738	−	0.600349i	$-0.204972\pi$
$541$	17.3254	+	9.26062i	0.744877	+	0.398145i	−0.0548609	+	0.998494i	$0.517472\pi$
$542$	17.9786	−	32.3893i	0.772249	−	1.39124i
$543$	19.1526	−	17.0524i	0.821916	−	0.731788i
$544$	−35.2369	−	6.32036i	−1.51077	−	0.270983i
$545$	−15.2898	+	15.2898i	−0.654945	+	0.654945i
$546$	−18.1144	+	4.06441i	−0.775223	+	0.173941i
$547$	−14.1983	−	7.58915i	−0.607076	−	0.324489i	0.139059	−	0.990284i	$-0.455592\pi$
$547$	−14.1983	−	7.58915i	−0.607076	−	0.324489i	−0.746134	+	0.665795i	$0.768092\pi$
$548$	−22.7797	+	8.59977i	−0.973102	+	0.367364i
$549$	27.4599	+	28.4503i	1.17196	+	1.21423i
$550$	1.05607	−	4.90161i	0.0450312	−	0.209005i
$551$	1.95230	+	9.81489i	0.0831709	+	0.418128i
$552$	−14.3262	−	27.2831i	−0.609764	−	1.16124i
$553$	−46.8935	−	9.32771i	−1.99412	−	0.396654i
$554$	35.1846	−	13.9243i	1.49485	−	0.591589i
$555$	0.904649	−	2.45944i	0.0384002	−	0.104397i
$556$	−4.44891	−	16.5372i	−0.188676	−	0.701334i
$557$	−2.51777	−	3.06791i	−0.106681	−	0.129991i	0.716933	−	0.697143i	$-0.245546\pi$
$557$	−2.51777	−	3.06791i	−0.106681	−	0.129991i	−0.823614	+	0.567151i	$0.808046\pi$
$558$	2.20297	+	5.86826i	0.0932592	+	0.248423i
$559$	3.82058	+	1.58254i	0.161593	+	0.0669341i
$560$	42.4584	−	30.5543i	1.79420	−	1.29116i
$561$	6.17175	−	2.14682i	0.260571	−	0.0906390i
$562$	12.6532	−	14.9287i	0.533742	−	0.629728i
$563$	32.8836	+	3.23875i	1.38588	+	0.136497i	0.763292	−	0.646054i	$-0.223582\pi$
$563$	32.8836	+	3.23875i	1.38588	+	0.136497i	0.622586	+	0.782551i	$0.286082\pi$
$564$	6.29044	+	2.54309i	0.264875	+	0.107084i
$565$	41.5723	−	22.2208i	1.74896	−	0.934838i
$566$	0.634770	−	40.0172i	0.0266814	−	1.68205i
$567$	−33.3257	+	12.4403i	−1.39955	+	0.522443i
$568$	−18.0094	−	2.64377i	−0.755659	−	0.110930i
$569$	−11.2767	+	16.8767i	−0.472743	+	0.707510i	−0.988834	−	0.149024i	$-0.952387\pi$
$569$	−11.2767	+	16.8767i	−0.472743	+	0.707510i	0.516090	+	0.856534i	$0.327387\pi$
$570$	−1.48076	−	12.0228i	−0.0620221	−	0.503581i
$571$	−8.31363	+	0.818821i	−0.347915	+	0.0342666i	−0.270465	−	0.962730i	$-0.587178\pi$
$571$	−8.31363	+	0.818821i	−0.347915	+	0.0342666i	−0.0774492	+	0.996996i	$0.524678\pi$
$572$	0.374685	+	2.25536i	0.0156664	+	0.0943014i
$573$	−6.46238	−	26.8042i	−0.269970	−	1.11976i
$574$	66.9356	+	7.66632i	2.79384	+	0.319986i
$575$			37.4104i			1.56012i
$576$	5.02777	−	23.4675i	0.209490	−	0.977811i
$577$		−	9.05047i		−	0.376776i	−0.982095	−	0.188388i	$-0.939674\pi$
$577$		−	9.05047i		−	0.376776i	0.982095	−	0.188388i	$-0.0603262\pi$
$578$	−3.70919	+	32.3854i	−0.154282	+	1.34706i
$579$	−0.729615	−	3.02625i	−0.0303218	−	0.125767i
$580$	25.7705	−	36.0389i	1.07006	−	1.49644i
$581$	13.2434	−	1.30436i	0.549429	−	0.0541140i
$582$	−18.0061	+	2.21767i	−0.746377	+	0.0919252i
$583$	3.95009	−	5.91173i	0.163596	−	0.244839i
$584$	25.2353	+	15.0739i	1.04424	+	0.623762i
$585$	16.9426	−	8.67373i	0.700489	−	0.358615i
$586$	−11.3455	−	0.179967i	−0.468677	−	0.00743435i
$587$	16.1140	−	8.61312i	0.665097	−	0.355502i	−0.104052	−	0.994572i	$-0.533181\pi$
$587$	16.1140	−	8.61312i	0.665097	−	0.355502i	0.769148	+	0.639070i	$0.220681\pi$
$588$	−27.4950	+	11.6639i	−1.13388	+	0.481010i
$589$	2.19761	+	0.216446i	0.0905510	+	0.00891850i
$590$	18.9436	+	16.0561i	0.779895	+	0.661019i
$591$	−16.1534	+	5.61890i	−0.664461	+	0.231131i
$592$	−0.758217	−	1.66453i	−0.0311625	−	0.0684118i
$593$	22.0148	+	9.11883i	0.904040	+	0.374465i	0.785772	−	0.618516i	$-0.212266\pi$
$593$	22.0148	+	9.11883i	0.904040	+	0.374465i	0.118268	+	0.992982i	$0.462266\pi$
$594$	1.29954	+	4.18355i	0.0533209	+	0.171653i
$595$	−52.5023	−	63.9743i	−2.15239	−	2.62269i
$596$	−2.96253	+	5.14316i	−0.121350	+	0.210672i
$597$	2.32094	−	6.30986i	0.0949898	−	0.258245i
$598$	−6.27705	−	15.8611i	−0.256688	−	0.648610i
$599$	8.42861	+	1.67656i	0.344384	+	0.0685022i	0.364252	−	0.931300i	$-0.381325\pi$
$599$	8.42861	+	1.67656i	0.344384	+	0.0685022i	−0.0198682	+	0.999803i	$0.506325\pi$
$600$	−18.6489	+	22.3861i	−0.761337	+	0.913907i
$601$	1.39211	+	6.99863i	0.0567855	+	0.285480i	0.998736	−	0.0502732i	$-0.0160092\pi$
$601$	1.39211	+	6.99863i	0.0567855	+	0.285480i	−0.941950	+	0.335753i	$0.891009\pi$
$602$	11.7840	+	2.53892i	0.480280	+	0.103479i
$603$	9.65601	−	9.31987i	0.393223	−	0.379534i
$604$	11.0902	−	24.5421i	0.451254	−	0.998602i
$605$	−31.0610	−	16.6024i	−1.26281	−	0.674985i
$606$	5.06732	+	22.5841i	0.205846	+	0.917418i
$607$	−2.36253	+	2.36253i	−0.0958923	+	0.0958923i	−0.753426	−	0.657533i	$-0.771600\pi$
$607$	−2.36253	+	2.36253i	−0.0958923	+	0.0958923i	0.657533	+	0.753426i	$0.271600\pi$
$608$	−6.63595	−	5.23960i	−0.269123	−	0.212494i
$609$	−34.2324	+	30.4786i	−1.38717	+	1.23505i
$610$	−53.9226	−	29.9313i	−2.18326	−	1.21188i
$611$	3.31238	+	1.77050i	0.134005	+	0.0716269i
$612$	−37.5580	−	5.58453i	−1.51819	−	0.225741i
$613$	1.44970	−	1.76646i	0.0585528	−	0.0713468i	−0.742910	−	0.669391i	$-0.766555\pi$
$613$	1.44970	−	1.76646i	0.0585528	−	0.0713468i	0.801463	+	0.598044i	$0.204055\pi$
$614$	31.8574	−	20.5632i	1.28566	−	0.829862i
$615$	−68.4147	+	9.52994i	−2.75875	+	0.384284i
$616$	2.25460	+	6.27144i	0.0908405	+	0.252683i
$617$	−21.6635	−	4.30914i	−0.872139	−	0.173479i	−0.261323	−	0.965251i	$-0.584159\pi$
$617$	−21.6635	−	4.30914i	−0.872139	−	0.173479i	−0.610817	+	0.791772i	$0.709159\pi$
$618$	8.44006	−	16.7603i	0.339509	−	0.674197i
$619$	10.2301	+	3.10327i	0.411182	+	0.124731i	0.489097	−	0.872229i	$-0.337326\pi$
$619$	10.2301	+	3.10327i	0.411182	+	0.124731i	−0.0779150	+	0.996960i	$0.524826\pi$
$620$	−5.95939	−	7.75032i	−0.239335	−	0.311260i
$621$	−16.0527	−	28.4713i	−0.644174	−	1.14251i
$622$	−1.56212	+	4.87018i	−0.0626354	+	0.195276i
$623$	−44.8575	−	18.5806i	−1.79718	−	0.744415i
$624$	4.15054	−	12.6202i	0.166155	−	0.505213i
$625$	−17.8914	+	7.41085i	−0.715655	+	0.296434i
$626$	0.959449	+	11.6297i	0.0383473	+	0.464815i
$627$	1.52455	+	0.239963i	0.0608847	+	0.00958321i
$628$	11.2434	−	12.8465i	0.448659	−	0.512633i
$629$	−2.55213	+	1.36414i	−0.101760	+	0.0543920i
$630$	44.0460	−	33.7383i	1.75483	−	1.34417i
$631$	2.27400	+	3.40328i	0.0905265	+	0.135482i	0.873969	−	0.485982i	$-0.161538\pi$
$631$	2.27400	+	3.40328i	0.0905265	+	0.135482i	−0.783442	+	0.621465i	$0.786538\pi$
$632$	22.9394	−	25.3863i	0.912478	−	1.00981i
$633$	−2.37017	−	1.79059i	−0.0942060	−	0.0711697i
$634$	19.6949	+	13.6165i	0.782186	+	0.540779i
$635$	50.8718	−	5.01044i	2.01879	−	0.198833i
$636$	−36.2696	+	19.7851i	−1.43818	+	0.784531i
$637$	−15.8209	+	4.79920i	−0.626845	+	0.190151i
$638$	3.51123	+	4.41957i	0.139011	+	0.174972i
$639$	−19.1771	−	2.23238i	−0.758635	−	0.0883117i
$640$	3.19002	+	37.2973i	0.126097	+	1.47431i
$641$		−	27.2228i		−	1.07523i	−0.843189	−	0.537617i	$-0.819324\pi$
$641$		−	27.2228i		−	1.07523i	0.843189	−	0.537617i	$-0.180676\pi$
$642$	−11.8157	+	8.31848i	−0.466328	+	0.328304i
$643$	7.16421	+	23.6172i	0.282529	+	0.931373i	0.977249	+	0.212093i	$0.0680281\pi$
$643$	7.16421	+	23.6172i	0.282529	+	0.931373i	−0.694720	+	0.719280i	$0.744472\pi$
$644$	−26.2997	−	42.1989i	−1.03635	−	1.66287i
$645$	−12.3490	+	0.497081i	−0.486240	+	0.0195726i
$646$	−7.60735	+	11.0033i	−0.299307	+	0.432920i
$647$	−25.5496	+	38.2376i	−1.00446	+	1.50328i	−0.146727	+	0.989177i	$0.546874\pi$
$647$	−25.5496	+	38.2376i	−1.00446	+	1.50328i	−0.857731	+	0.514099i	$0.828126\pi$
$648$	4.58697	−	25.0392i	0.180193	−	0.983631i
$649$	−2.63056	+	1.75768i	−0.103259	+	0.0689952i
$650$	−11.5839	+	11.2221i	−0.454358	+	0.440169i
$651$	4.24320	+	9.18099i	0.166304	+	0.359831i
$652$	4.62718	−	5.28697i	0.181214	−	0.207054i
$653$	30.9219	+	3.04554i	1.21007	+	0.119181i	0.682856	−	0.730553i	$-0.260738\pi$
$653$	30.9219	+	3.04554i	1.21007	+	0.119181i	0.527211	+	0.849734i	$0.323238\pi$
$654$	0.390079	+	16.0033i	0.0152533	+	0.625778i
$655$	23.7252	+	57.2777i	0.927021	+	2.23803i
$656$	−29.2736	+	38.3090i	−1.14294	+	1.49571i
$657$	27.2316	+	15.1817i	1.06241	+	0.592296i
$658$	10.4251	+	3.34386i	0.406411	+	0.130357i
$659$	−6.31593	−	7.69598i	−0.246034	−	0.299793i	0.635321	−	0.772248i	$-0.280868\pi$
$659$	−6.31593	−	7.69598i	−0.246034	−	0.299793i	−0.881355	+	0.472455i	$0.843368\pi$
$660$	−3.84428	−	5.64873i	−0.149639	−	0.219876i
$661$	0.659604	−	2.17442i	0.0256556	−	0.0845753i	−0.943178	−	0.332289i	$-0.892179\pi$
$661$	0.659604	−	2.17442i	0.0256556	−	0.0845753i	0.968833	+	0.247713i	$0.0796792\pi$
$662$	−10.3960	+	24.0136i	−0.404051	+	0.933314i
$663$	−20.3429	−	5.28752i	−0.790051	−	0.205350i
$664$	−4.05867	+	8.61484i	−0.157507	+	0.334321i
$665$	−3.81331	−	19.1708i	−0.147874	−	0.743411i
$666$	−0.856581	−	1.74070i	−0.0331918	−	0.0674506i
$667$	−32.5550	−	26.7172i	−1.26053	−	1.03449i
$668$	−8.22515	−	0.261007i	−0.318241	−	0.0100987i
$669$	12.3590	−	20.2116i	0.477825	−	0.781425i
$670$	−10.1587	+	18.3013i	−0.392464	+	0.707040i
$671$	5.55595	−	5.55595i	0.214485	−	0.214485i
$672$	5.29842	−	38.3617i	0.204391	−	1.47983i
$673$	10.9849	+	10.9849i	0.423435	+	0.423435i	0.886385	−	0.462949i	$-0.153209\pi$
$673$	10.9849	+	10.9849i	0.423435	+	0.423435i	−0.462949	+	0.886385i	$0.653209\pi$
$674$	−30.9306	+	8.84948i	−1.19140	+	0.340869i
$675$	−19.0621	+	24.3242i	−0.733702	+	0.936238i
$676$	−7.67829	+	16.9916i	−0.295319	+	0.653525i
$677$	14.8217	−	18.0603i	0.569644	−	0.694113i	−0.405900	−	0.913918i	$-0.633042\pi$
$677$	14.8217	−	18.0603i	0.569644	−	0.694113i	0.975544	+	0.219804i	$0.0705418\pi$
$678$	9.31344	−	33.6317i	0.357681	−	1.29162i
$679$	−28.7113	+	5.71103i	−1.10184	+	0.219169i
$680$	58.5701	−	8.77811i	2.24606	−	0.336625i
$681$	31.6469	+	8.22567i	1.21271	+	0.315208i
$682$	1.15817	−	0.458347i	0.0443486	−	0.0175510i
$683$	−40.4530	−	12.2713i	−1.54789	−	0.469547i	−0.603221	−	0.797574i	$-0.706116\pi$
$683$	−40.4530	−	12.2713i	−1.54789	−	0.469547i	−0.944668	+	0.328027i	$0.893616\pi$
$684$	−7.20132	−	5.34474i	−0.275350	−	0.204361i
$685$	31.1380	−	25.5543i	1.18972	−	0.976381i
$686$	−8.06149	+	4.14593i	−0.307789	+	0.158292i
$687$	−15.2148	+	31.4455i	−0.580482	+	1.19972i
$688$	−5.88425	+	6.30786i	−0.224335	+	0.240485i
$689$	−21.1291	+	8.75196i	−0.804955	+	0.333423i
$690$	36.9158	+	35.1590i	1.40536	+	1.33848i
$691$	−1.15627	+	11.7398i	−0.0439865	+	0.446602i	0.947816	+	0.318819i	$0.103286\pi$
$691$	−1.15627	+	11.7398i	−0.0439865	+	0.446602i	−0.991802	+	0.127783i	$0.959214\pi$
$692$	−5.50434	+	2.72130i	−0.209244	+	0.103448i
$693$	2.58897	+	6.57747i	0.0983467	+	0.249858i
$694$	−0.0521198	+	3.28574i	−0.00197844	+	0.124725i
$695$	15.7398	+	23.5563i	0.597045	+	0.893541i
$696$	−6.16225	−	32.2158i	−0.233579	−	1.22114i
$697$	63.4238	+	42.3784i	2.40235	+	1.60520i
$698$	25.4388	−	4.64192i	0.962872	−	0.175699i
$699$	−8.62680	+	0.347254i	−0.326295	+	0.0131343i
$700$	−27.3459	+	38.2422i	−1.03358	+	1.44542i
$701$	18.8505	−	5.71824i	0.711974	−	0.215975i	0.0865357	−	0.996249i	$-0.472420\pi$
$701$	18.8505	−	5.71824i	0.711974	−	0.215975i	0.625438	+	0.780274i	$0.284920\pi$
$702$	4.00057	−	13.5113i	0.150992	−	0.509950i
$703$	−0.683470			−0.0257776
$704$	−4.68028	−	0.916339i	−0.176395	−	0.0345358i
$705$	−11.2060	−	0.650041i	−0.422041	−	0.0244820i
$706$	−4.72344	+	41.2410i	−0.177769	+	1.55212i
$707$	10.8413	+	35.7391i	0.407731	+	1.34411i
$708$	18.2796	−	1.95757i	0.686988	−	0.0735698i
$709$	1.46977	+	14.9229i	0.0551985	+	0.560440i	0.982518	+	0.186169i	$0.0596071\pi$
$709$	1.46977	+	14.9229i	0.0551985	+	0.560440i	−0.927319	+	0.374271i	$0.877893\pi$
$710$	29.6239	−	5.40560i	1.11177	−	0.202869i
$711$	23.5158	−	27.6409i	0.881912	−	1.03662i
$712$	27.8767	−	20.7399i	1.04472	−	0.777259i
$713$	−7.72706	+	5.16306i	−0.289381	+	0.193358i
$714$	−61.1021	−	4.51783i	−2.28669	−	0.169076i
$715$	−1.78295	−	3.33567i	−0.0666787	−	0.124747i
$716$	−1.47672	+	4.36465i	−0.0551876	+	0.163115i
$717$	−12.7065	−	2.00000i	−0.474534	−	0.0746913i
$718$	−26.4266	−	22.3986i	−0.986233	−	0.835907i
$719$	19.2802	+	46.5466i	0.719031	+	1.73589i	0.676092	+	0.736817i	$0.263672\pi$
$719$	19.2802	+	46.5466i	0.719031	+	1.73589i	0.0429389	+	0.999078i	$0.486328\pi$
$720$	4.56353	+	39.4411i	0.170073	+	1.46988i
$721$	11.5874	−	27.9746i	0.431539	−	1.04183i
$722$	21.0856	−	10.8441i	0.784724	−	0.403574i
$723$	23.3420	−	16.9933i	0.868098	−	0.631986i
$724$	7.69255	+	28.5943i	0.285891	+	1.06270i
$725$	−11.5589	+	38.1046i	−0.429287	+	1.41517i
$726$	−24.7593	+	8.17460i	−0.918904	+	0.303388i
$727$	3.45867	−	17.3879i	0.128275	−	0.644882i	−0.862130	−	0.506687i	$-0.830870\pi$
$727$	3.45867	−	17.3879i	0.128275	−	0.644882i	0.990405	−	0.138195i	$-0.0441300\pi$
$728$	5.17741	−	20.8021i	0.191888	−	0.770977i
$729$	4.06985	−	26.6915i	0.150735	−	0.988574i
$730$	−47.5378	−	10.2422i	−1.75945	−	0.379082i
$731$	10.5500	+	8.65812i	0.390204	+	0.320232i
$732$	−43.5773	+	13.6250i	−1.61066	+	0.503595i
$733$	−1.32394	+	2.47691i	−0.0489008	+	0.0914869i	−0.905185	−	0.425019i	$-0.860267\pi$
$733$	−1.32394	+	2.47691i	−0.0489008	+	0.0914869i	0.856284	+	0.516506i	$0.172767\pi$
$734$	−41.1551	+	11.7748i	−1.51906	+	0.434615i
$735$	36.9027	−	32.8561i	1.36118	−	1.21191i
$736$	35.5765	−	0.671384i	1.31137	−	0.0247475i
$737$	−1.88569	−	1.88569i	−0.0694601	−	0.0694601i
$738$	−29.8220	+	41.5420i	−1.09776	+	1.52918i
$739$	20.2602	−	37.9042i	0.745285	−	1.39433i	−0.167493	−	0.985873i	$-0.553567\pi$
$739$	20.2602	−	37.9042i	0.745285	−	1.39433i	0.912778	−	0.408456i	$-0.133933\pi$
$740$	2.07072	+	2.20645i	0.0761212	+	0.0811106i
$741$	−3.64860	−	3.36623i	−0.134035	−	0.123662i
$742$	−56.0104	+	36.1533i	−2.05621	+	1.32723i
$743$	−12.8386	+	2.55377i	−0.471004	+	0.0936886i	−0.424885	−	0.905247i	$-0.639685\pi$
$743$	−12.8386	+	2.55377i	−0.471004	+	0.0936886i	−0.0461194	+	0.998936i	$0.514685\pi$
$744$	−7.19756	−	0.762368i	−0.263875	−	0.0279498i
$745$	1.91562	−	9.63047i	0.0701829	−	0.352833i
$746$	−15.7341	+	36.3440i	−0.576065	+	1.33065i
$747$	−4.03005	+	9.26191i	−0.147452	+	0.338876i
$748$	−0.977365	+	7.48179i	−0.0357360	+	0.273561i
$749$	−18.0239	+	14.7918i	−0.658579	+	0.540481i
$750$	2.76460	−	7.16326i	0.100949	−	0.261565i
$751$	−2.17195	+	5.24355i	−0.0792556	+	0.191340i	−0.958541	−	0.284956i	$-0.908021\pi$
$751$	−2.17195	+	5.24355i	−0.0792556	+	0.191340i	0.879285	+	0.476296i	$0.158021\pi$
$752$	−5.88007	+	5.17758i	−0.214424	+	0.188807i
$753$	−13.4622	+	4.68278i	−0.490589	+	0.170650i
$754$	−1.49283	−	18.0949i	−0.0543657	−	0.658978i
$755$	−4.36705	+	44.3394i	−0.158933	+	1.61367i
$756$	4.40208	−	40.8384i	0.160102	−	1.48528i
$757$	1.03019	+	1.92735i	0.0374428	+	0.0700506i	0.899947	−	0.436000i	$-0.143605\pi$
$757$	1.03019	+	1.92735i	0.0374428	+	0.0700506i	−0.862504	+	0.506050i	$0.831105\pi$
$758$	−2.61315	+	2.53154i	−0.0949140	+	0.0919498i
$759$	−5.60027	+	3.28961i	−0.203277	+	0.119405i
$760$	13.1771	+	4.69249i	0.477983	+	0.170215i
$761$	−24.9470	−	16.6691i	−0.904329	−	0.604253i	0.0140733	−	0.999901i	$-0.495520\pi$
$761$	−24.9470	−	16.6691i	−0.904329	−	0.604253i	−0.918402	+	0.395648i	$0.870520\pi$
$762$	23.2878	−	29.8299i	0.843629	−	1.08062i
$763$	2.53180	+	25.7058i	0.0916575	+	0.930614i
$764$	31.0132	+	7.19848i	1.12202	+	0.260432i
$765$	61.8172	−	11.1618i	2.23501	−	0.403557i
$766$	12.0439	+	15.1596i	0.435163	+	0.547737i
$767$	10.1765			0.367453
$768$	21.6234	+	17.3329i	0.780265	+	0.625449i
$769$	20.0483			0.722959			0.361479	−	0.932380i	$-0.382272\pi$
$769$	20.0483			0.722959			0.361479	+	0.932380i	$0.382272\pi$
$770$	−6.85825	−	8.63245i	−0.247154	−	0.311092i
$771$	−0.638920	−	2.65007i	−0.0230101	−	0.0954398i
$772$	3.50145	+	0.812723i	0.126020	+	0.0292505i
$773$	1.36987	+	13.9086i	0.0492709	+	0.500256i	0.987874	+	0.155257i	$0.0496207\pi$
$773$	1.36987	+	13.9086i	0.0492709	+	0.500256i	−0.938603	+	0.344999i	$0.887879\pi$
$774$	−6.03859	+	6.87391i	−0.217052	+	0.247078i
$775$	7.30592	+	4.88166i	0.262437	+	0.175354i
$776$	7.02775	−	19.7348i	0.252281	−	0.708437i
$777$	−1.58551	−	2.69918i	−0.0568797	−	0.0968327i
$778$	14.8086	−	14.3462i	0.530915	−	0.514335i
$779$	8.49256	+	15.8885i	0.304277	+	0.569263i
$780$	0.187011	+	21.9775i	0.00669606	+	0.786921i
$781$	−0.376043	+	3.81802i	−0.0134559	+	0.136620i
$782$	−4.62873	−	56.1058i	−0.165523	−	2.00634i
$783$	−7.55367	−	33.9596i	−0.269946	−	1.21362i
$784$	2.18655	−	34.4178i	0.0780910	−	1.22921i
$785$	−10.8080	+	26.0928i	−0.385753	+	0.931291i
$786$	42.8193	+	16.5258i	1.52732	+	0.589455i
$787$	−31.0711	+	25.4994i	−1.10756	+	0.908955i	−0.996394	−	0.0848464i	$-0.972960\pi$
$787$	−31.0711	+	25.4994i	−1.10756	+	0.908955i	−0.111171	+	0.993801i	$0.535460\pi$
$788$	2.55807	−	19.5822i	0.0911274	−	0.697585i
$789$	−8.78982	+	23.8966i	−0.312926	+	0.850741i
$790$	−22.4880	+	51.9448i	−0.800086	+	1.84811i
$791$	10.9855	−	55.2278i	0.390599	−	1.96367i
$792$	−4.99100	−	0.823228i	−0.177348	−	0.0292521i
$793$	−24.7882	+	4.93068i	−0.880254	+	0.175093i
$794$	19.2337	−	12.4149i	0.682578	−	0.440587i
$795$	46.3473	−	50.2350i	1.64377	−	1.78165i
$796$	5.31258	+	5.66080i	0.188299	+	0.200642i
$797$	−12.7755	+	23.9013i	−0.452531	+	0.846626i	0.547421	+	0.836857i	$0.315610\pi$
$797$	−12.7755	+	23.9013i	−0.452531	+	0.846626i	−0.999952	+	0.00976908i	$0.996890\pi$
$798$	−12.2242	−	7.74385i	−0.432731	−	0.274129i
$799$	8.76490	+	8.76490i	0.310080	+	0.310080i
$800$	−13.4590	−	30.8341i	−0.475848	−	1.09015i
$801$	28.8976	−	22.8712i	1.02104	−	0.808115i
$802$	−0.0239047	+	0.00683931i	−0.000844103	+	0.000241504i
$803$	2.92051	−	5.46389i	0.103063	−	0.192817i
$804$	4.62432	+	14.7901i	0.163087	+	0.521607i
$805$	63.5876	+	52.1850i	2.24117	+	1.83928i
$806$	−3.91662	−	0.843855i	−0.137957	−	0.0297235i
$807$	−26.0361	+	3.62673i	−0.916513	+	0.127667i
$808$	−25.9351	−	6.45496i	−0.912393	−	0.227085i
$809$	3.30712	−	16.6260i	0.116272	−	0.584540i	−0.878089	−	0.478497i	$-0.841182\pi$
$809$	3.30712	−	16.6260i	0.116272	−	0.584540i	0.994362	−	0.106043i	$-0.0338182\pi$
$810$	6.08761	+	41.6704i	0.213897	+	1.46415i
$811$	9.54814	−	31.4760i	0.335280	−	1.10527i	−0.613595	−	0.789621i	$-0.710277\pi$
$811$	9.54814	−	31.4760i	0.335280	−	1.10527i	0.948876	−	0.315651i	$-0.102223\pi$
$812$	−13.7493	−	51.1080i	−0.482505	−	1.79354i
$813$	26.7032	+	36.6795i	0.936521	+	1.28641i
$814$	−0.342832	+	0.176315i	−0.0120163	+	0.00617982i
$815$	−4.44800	+	10.7384i	−0.155807	+	0.376151i
$816$	25.1986	−	35.8806i	0.882127	−	1.25607i
$817$	1.23353	+	2.97801i	0.0431559	+	0.104187i
$818$	4.07914	+	3.45737i	0.142624	+	0.120884i
$819$	4.83006	−	22.2181i	0.168776	−	0.776364i
$820$	25.5627	−	75.5540i	0.892687	−	2.63846i
$821$	14.2417	+	26.6443i	0.497037	+	0.929892i	0.997925	+	0.0643795i	$0.0205068\pi$
$821$	14.2417	+	26.6443i	0.497037	+	0.929892i	−0.500888	+	0.865512i	$0.666993\pi$
$822$	2.19895	−	29.7401i	0.0766973	−	1.03730i
$823$	44.8808	−	29.9884i	1.56445	−	1.04533i	0.593864	−	0.804566i	$-0.297602\pi$
$823$	44.8808	−	29.9884i	1.56445	−	1.04533i	0.970584	−	0.240765i	$-0.0773982\pi$
$824$	12.9340	+	17.3848i	0.450579	+	0.605629i
$825$	4.89989	+	3.70172i	0.170592	+	0.128877i
$826$	29.1823	−	5.32501i	1.01538	−	0.185281i
$827$	0.100137	+	1.01671i	0.00348210	+	0.0353543i	0.996769	−	0.0803245i	$-0.0255957\pi$
$827$	0.100137	+	1.01671i	0.00348210	+	0.0353543i	−0.993287	+	0.115679i	$0.963096\pi$
$828$	37.6965	−	1.83879i	1.31004	−	0.0639024i
$829$	−6.63031	−	21.8572i	−0.230280	−	0.759132i	−0.993584	−	0.113093i	$-0.963924\pi$
$829$	−6.63031	−	21.8572i	−0.230280	−	0.759132i	0.763304	−	0.646039i	$-0.223576\pi$
$830$	1.79267	−	15.6520i	0.0622245	−	0.543290i
$831$	−2.68384	+	46.2662i	−0.0931013	+	1.60496i
$832$	10.8799	+	10.8147i	0.377193	+	0.374931i
$833$	−54.5628			−1.89049
$834$	20.6646	+	3.58934i	0.715556	+	0.124289i
$835$	13.0278	−	3.95195i	0.450847	−	0.136763i
$836$	−1.03657	+	1.44959i	−0.0358504	+	0.0501352i
$837$	−7.65491	−	0.580247i	−0.264592	−	0.0200563i
$838$	47.3549	−	8.64104i	1.63585	−	0.298500i
$839$	17.4379	+	11.6516i	0.602022	+	0.402258i	0.818896	−	0.573941i	$-0.194586\pi$
$839$	17.4379	+	11.6516i	0.602022	+	0.402258i	−0.216875	+	0.976199i	$0.569586\pi$
$840$	12.0363	+	62.9250i	0.415292	+	2.17112i
$841$	−8.79261	−	13.1591i	−0.303193	−	0.453761i
$842$	0.00630018	−	0.397176i	0.000217118	−	0.0136876i
$843$	10.0552	+	21.7565i	0.346321	+	0.749332i
$844$	3.07480	−	1.52016i	0.105839	−	0.0523260i
$845$	3.02352	−	30.6983i	0.104012	−	1.05605i
$846$	−6.06996	+	5.67547i	−0.208689	+	0.195127i
$847$	−38.8696	+	16.1003i	−1.33558	+	0.553214i
$848$	−1.65653	−	47.6778i	−0.0568856	−	1.63726i
$849$	44.1235	+	21.3491i	1.51431	+	0.732698i
$850$	−47.3351	+	24.3439i	−1.62358	+	0.834988i
$851$	2.22344	−	1.82473i	0.0762186	−	0.0625510i
$852$	12.2273	−	18.6410i	0.418902	−	0.638629i
$853$	−41.9707	−	12.7317i	−1.43705	−	0.435924i	−0.526802	−	0.849988i	$-0.676609\pi$
$853$	−41.9707	−	12.7317i	−1.43705	−	0.435924i	−0.910248	+	0.414064i	$0.864109\pi$
$854$	−68.5028	+	27.1100i	−2.34412	+	0.927686i
$855$	14.1188	+	4.55749i	0.482854	+	0.155863i
$856$	−2.47311	−	16.5013i	−0.0845293	−	0.564004i
$857$	−2.92076	+	0.580975i	−0.0997711	+	0.0198457i	−0.244723	−	0.969593i	$-0.578697\pi$
$857$	−2.92076	+	0.580975i	−0.0997711	+	0.0198457i	0.144952	+	0.989439i	$0.453697\pi$
$858$	−2.69854	−	0.747292i	−0.0921267	−	0.0255121i
$859$	−9.79061	+	11.9299i	−0.334051	+	0.407043i	−0.912763	−	0.408490i	$-0.866056\pi$
$859$	−9.79061	+	11.9299i	−0.334051	+	0.407043i	0.578712	+	0.815532i	$0.303556\pi$
$860$	5.87666	−	13.0047i	0.200392	−	0.443458i
$861$	−43.0463	+	70.3970i	−1.46701	+	2.39912i
$862$	−36.3177	+	10.3908i	−1.23699	+	0.353911i
$863$	−8.67702	−	8.67702i	−0.295369	−	0.295369i	0.543828	−	0.839197i	$-0.316974\pi$
$863$	−8.67702	−	8.67702i	−0.295369	−	0.295369i	−0.839197	+	0.543828i	$0.816974\pi$
$864$	23.4739	+	17.6912i	0.798597	+	0.601866i
$865$	7.18290	−	7.18290i	0.244226	−	0.244226i
$866$	−0.0360480	+	0.0649421i	−0.00122496	+	0.00220682i
$867$	−34.0601	−	20.8271i	−1.15674	−	0.707324i
$868$	−11.6729	−	0.370414i	−0.396204	−	0.0125727i
$869$	−5.57455	−	4.57491i	−0.189104	−	0.155193i
$870$	26.7375	+	47.2175i	0.906487	+	1.60082i
$871$	1.67347	+	8.41309i	0.0567033	+	0.285067i
$872$	−16.7217	−	7.87800i	−0.566267	−	0.266783i
$873$	6.82556	−	21.1452i	0.231010	−	0.715655i
$874$	5.28241	−	12.2018i	0.178680	−	0.412732i
$875$	3.59646	−	11.8559i	0.121583	−	0.400804i
$876$	−29.7623	+	20.2550i	−1.00558	+	0.684352i
$877$	31.2376	+	38.0631i	1.05482	+	1.28530i	0.956997	+	0.290097i	$0.0936876\pi$
$877$	31.2376	+	38.0631i	1.05482	+	1.28530i	0.0978221	+	0.995204i	$0.468812\pi$
$878$	−17.6210	−	5.65198i	−0.594680	−	0.190745i
$879$	6.05278	−	12.5097i	0.204155	−	0.421941i
$880$	7.82022	−	1.04551i	0.263619	−	0.0352441i
$881$	−10.3647	−	25.0225i	−0.349194	−	0.843030i	−0.996716	−	0.0809823i	$-0.974194\pi$
$881$	−10.3647	−	25.0225i	−0.349194	−	0.843030i	0.647521	−	0.762047i	$-0.275806\pi$
$882$	1.22786	−	36.5585i	0.0413442	−	1.23099i
$883$	47.8419	+	4.71201i	1.61001	+	0.158572i	0.862632	−	0.505831i	$-0.168814\pi$
$883$	47.8419	+	4.71201i	1.61001	+	0.158572i	0.747374	+	0.664403i	$0.231314\pi$
$884$	15.9843	−	18.2635i	0.537610	−	0.614268i
$885$	−27.6076	+	12.7595i	−0.928021	+	0.428905i
$886$	−8.93115	+	8.65224i	−0.300048	+	0.290678i
$887$	40.1602	−	26.8342i	1.34845	−	0.901004i	0.349099	−	0.937086i	$-0.386488\pi$
$887$	40.1602	−	26.8342i	1.34845	−	0.901004i	0.999349	+	0.0360814i	$0.0114876\pi$
$888$	2.24010	+	0.0164698i	0.0751730	+	0.000552690i
$889$	33.9252	−	50.7727i	1.13781	−	1.70286i
$890$	−32.6888	+	47.2812i	−1.09573	+	1.58487i
$891$	−5.31748	−	0.714670i	−0.178142	−	0.0239423i
$892$	14.4690	+	23.2161i	0.484457	+	0.777331i
$893$	0.849830	+	2.80151i	0.0284385	+	0.0937490i
$894$	−4.18470	−	5.94401i	−0.139957	−	0.198797i
$895$		−	7.62271i		−	0.254799i
$896$	36.8583	+	25.3191i	1.23135	+	0.845852i
$897$	20.8567	+	1.20987i	0.696384	+	0.0403962i
$898$	−4.67958	−	5.89016i	−0.156160	−	0.196557i
$899$	−9.46571	+	2.87139i	−0.315699	+	0.0957663i
$900$	−15.2458	−	32.2636i	−0.508194	−	1.07545i
$901$	−75.1140	+	7.39808i	−2.50241	+	0.246466i
$902$	8.35865	+	5.77891i	0.278313	+	0.192417i
$903$	−8.89933	+	11.7799i	−0.296151	+	0.392010i
$904$	29.8981	+	27.0163i	0.994397	+	0.898549i
$905$	−27.2155	−	40.7309i	−0.904674	−	1.35394i
$906$	21.5401	+	24.9797i	0.715620	+	0.829894i
$907$	−22.7161	+	12.1420i	−0.754276	+	0.403169i	−0.803259	−	0.595631i	$-0.796902\pi$
$907$	−22.7161	+	12.1420i	−0.754276	+	0.403169i	0.0489821	+	0.998800i	$0.484402\pi$
$908$	−24.8664	+	28.4121i	−0.825221	+	0.942889i
$909$	−27.7005	−	6.02189i	−0.918768	−	0.199733i
$910$	2.91585	+	35.3436i	0.0966595	+	1.17163i
$911$	−21.0878	+	8.73487i	−0.698671	+	0.289399i	−0.703608	−	0.710589i	$-0.748429\pi$
$911$	−21.0878	+	8.73487i	−0.698671	+	0.289399i	0.00493643	+	0.999988i	$0.498429\pi$
$912$	9.24347	−	4.66820i	0.306082	−	0.154579i
$913$	1.85437	+	0.768105i	0.0613707	+	0.0254206i
$914$	−10.7238	+	33.4333i	−0.354712	+	1.10587i
$915$	61.0651	−	44.4561i	2.01875	−	1.46967i
$916$	−24.5877	−	31.9769i	−0.812401	−	1.05655i
$917$	70.8705	+	21.4983i	2.34035	+	0.709937i
$918$	25.5786	−	38.8383i	0.844219	−	1.28186i
$919$	3.48712	+	0.693631i	0.115029	+	0.0228808i	0.252269	−	0.967657i	$-0.418823\pi$
$919$	3.48712	+	0.693631i	0.115029	+	0.0228808i	−0.137240	+	0.990538i	$0.543823\pi$
$920$	−55.3953	+	19.9148i	−1.82633	+	0.656571i
$921$	6.40697	+	45.9952i	0.211117	+	1.51559i
$922$	13.0682	−	8.43518i	0.430377	−	0.277798i
$923$	7.82873	−	9.53933i	0.257686	−	0.313991i
$924$	−8.12939	−	0.730888i	−0.267437	−	0.0240445i
$925$	−2.39845	−	1.28200i	−0.0788606	−	0.0421519i
$926$	26.5008	+	14.7101i	0.870870	+	0.483403i
$927$	14.2632	+	18.0214i	0.468466	+	0.591902i
$928$	36.4442	+	10.3084i	1.19634	+	0.338391i
$929$	21.1359	−	21.1359i	0.693446	−	0.693446i	−0.269542	−	0.962989i	$-0.586872\pi$
$929$	21.1359	−	21.1359i	0.693446	−	0.693446i	0.962989	+	0.269542i	$0.0868724\pi$
$930$	11.6833	−	2.62145i	0.383112	−	0.0859608i
$931$	−11.3651	−	6.07476i	−0.372475	−	0.199092i
$932$	4.10535	−	9.08492i	0.134475	−	0.297586i
$933$	−4.60392	−	4.24762i	−0.150725	−	0.139061i
$934$	−35.5734	−	7.66445i	−1.16400	−	0.250788i
$935$	−2.43523	−	12.2428i	−0.0796407	−	0.400381i
$936$	11.8773	+	11.1209i	0.388223	+	0.363498i
$937$	29.6366	+	5.89510i	0.968187	+	0.192584i	0.653764	−	0.756699i	$-0.273189\pi$
$937$	29.6366	+	5.89510i	0.968187	+	0.192584i	0.314423	+	0.949283i	$0.398189\pi$
$938$	9.20113	+	23.2498i	0.300427	+	0.759133i
$939$	−13.4132	−	4.93374i	−0.437722	−	0.161006i
$940$	6.46938	−	11.2313i	0.211008	−	0.366324i
$941$	3.64899	+	4.44630i	0.118954	+	0.144945i	0.829082	−	0.559126i	$-0.188863\pi$
$941$	3.64899	+	4.44630i	0.118954	+	0.144945i	−0.710129	+	0.704072i	$0.751363\pi$
$942$	8.46971	+	19.1163i	0.275958	+	0.622844i
$943$	−70.0468	−	29.0143i	−2.28104	−	0.944836i
$944$	−7.43775	+	19.8825i	−0.242078	+	0.647120i
$945$	14.7541	+	66.3310i	0.479951	+	2.15775i
$946$	1.38698	+	1.17557i	0.0450947	+	0.0382211i
$947$	30.3312	+	2.98736i	0.985632	+	0.0970763i	0.577971	−	0.816057i	$-0.303845\pi$
$947$	30.3312	+	2.98736i	0.985632	+	0.0970763i	0.407661	+	0.913133i	$0.366345\pi$
$948$	16.3651	+	38.5772i	0.531515	+	1.25293i
$949$	−17.5752	+	9.39413i	−0.570514	+	0.304946i
$950$	−12.5699	−	0.199389i	−0.407822	−	0.00646904i
$951$	−25.2853	+	14.8527i	−0.819933	+	0.481630i
$952$	36.2801	−	60.7366i	1.17584	−	1.96848i
$953$	31.2128	−	46.7133i	1.01108	−	1.51319i	0.160716	−	0.987001i	$-0.448620\pi$
$953$	31.2128	−	46.7133i	1.01108	−	1.51319i	0.850366	−	0.526191i	$-0.176380\pi$
$954$	−3.26658	−	50.4949i	−0.105759	−	1.63483i
$955$	−52.4168	+	5.16260i	−1.69617	+	0.167058i
$956$	8.63936	−	12.0818i	0.279417	−	0.390753i
$957$	−6.72061	+	1.62031i	−0.217246	+	0.0523771i
$958$	6.39567	−	55.8414i	0.206635	−	1.80415i
$959$		−	48.1189i		−	1.55384i
$960$	−43.0754	−	15.6974i	−1.39025	−	0.506631i
$961$		−	28.8172i		−	0.929589i
$962$	1.23199	+	0.141103i	0.0397210	+	0.00454935i
$963$	−3.14469	−	17.4162i	−0.101336	−	0.561228i
$964$	5.46376	+	32.8883i	0.175976	+	1.05926i
$965$	−5.91796	+	0.582868i	−0.190506	+	0.0187632i
$966$	60.4419	−	7.44414i	1.94469	−	0.239511i
$967$	−1.29855	+	1.94341i	−0.0417584	+	0.0624959i	−0.851761	−	0.523930i	$-0.824465\pi$
$967$	−1.29855	+	1.94341i	−0.0417584	+	0.0624959i	0.810003	+	0.586426i	$0.199465\pi$
$968$	4.37289	−	29.7883i	0.140550	−	0.957431i
$969$	−8.29799	−	14.1266i	−0.266570	−	0.453812i
$970$	−0.549665	+	34.6520i	−0.0176487	+	1.11261i
$971$	−4.03297	+	2.15566i	−0.129424	+	0.0691786i	−0.534838	−	0.844955i	$-0.679627\pi$
$971$	−4.03297	+	2.15566i	−0.129424	+	0.0691786i	0.405414	+	0.914133i	$0.367127\pi$
$972$	25.4471	+	18.0123i	0.816217	+	0.577746i
$973$	33.6802	+	3.31721i	1.07974	+	0.106345i
$974$	−11.7659	+	13.8818i	−0.377004	+	0.444803i
$975$	−6.48965	−	18.6566i	−0.207835	−	0.597490i
$976$	8.48366	−	52.0339i	0.271555	−	1.66556i
$977$	−38.6316	−	16.0017i	−1.23593	−	0.511941i	−0.333492	−	0.942753i	$-0.608227\pi$
$977$	−38.6316	−	16.0017i	−1.23593	−	0.511941i	−0.902442	+	0.430812i	$0.858227\pi$
$978$	3.48569	+	7.86729i	0.111460	+	0.251568i
$979$	−4.64583	−	5.66096i	−0.148481	−	0.180925i
$980$	14.8218	+	55.0946i	0.473465	+	1.75993i
$981$	−17.9776	−	7.82244i	−0.573982	−	0.249751i
$982$	7.92778	−	3.13743i	0.252986	−	0.100119i
$983$	54.0512	+	10.7514i	1.72396	+	0.342918i	0.955052	−	0.296437i	$-0.0957986\pi$
$983$	54.0512	+	10.7514i	1.72396	+	0.342918i	0.768912	+	0.639355i	$0.220799\pi$
$984$	−27.4519	−	52.2798i	−0.875134	−	1.66662i
$985$	6.37376	+	32.0431i	0.203085	+	1.02098i
$986$	12.6207	−	58.5771i	0.401925	−	1.86547i
$987$	−9.09240	+	9.85510i	−0.289414	+	0.313691i
$988$	5.36280	−	2.02455i	0.170613	−	0.0644097i
$989$	−11.9636	−	6.39468i	−0.380420	−	0.203339i
$990$	8.25777	−	1.35617i	0.262449	−	0.0431018i
$991$	−21.8724	+	21.8724i	−0.694800	+	0.694800i	−0.963284	−	0.268484i	$-0.913477\pi$
$991$	−21.8724	+	21.8724i	−0.694800	+	0.694800i	0.268484	+	0.963284i	$0.413477\pi$
$992$	4.51124	−	7.03539i	0.143232	−	0.223374i
$993$	−21.3112	−	23.9359i	−0.676289	−	0.759582i
$994$	17.4581	−	31.4516i	0.553738	−	0.997583i
$995$	−11.3266	−	6.05419i	−0.359077	−	0.191931i
$996$	−7.47556	−	8.95256i	−0.236872	−	0.283673i
$997$	−37.3568	+	45.5194i	−1.18310	+	1.44161i	−0.312298	+	0.949984i	$0.601099\pi$
$997$	−37.3568	+	45.5194i	−1.18310	+	1.44161i	−0.870804	+	0.491630i	$0.836401\pi$
$998$	−27.5257	−	42.6440i	−0.871310	−	1.34987i
$999$	2.37545	−	0.0535013i	0.0751559	−	0.00169270i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.w.a.179.17	✓	992
3.2	odd	2	inner	384.2.w.a.179.46	yes	992
128.123	odd	32	inner	384.2.w.a.251.46	yes	992
384.251	even	32	inner	384.2.w.a.251.17	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.w.a.179.17	✓	992	1.1	even	1	trivial
384.2.w.a.179.46	yes	992	3.2	odd	2	inner
384.2.w.a.251.17	yes	992	384.251	even	32	inner
384.2.w.a.251.46	yes	992	128.123	odd	32	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.w (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.879716 - 1.10729i) q^{2} +(1.68380 - 0.405958i) q^{3} +(-0.452199 + 1.94821i) q^{4} +(-0.324308 - 3.29275i) q^{5} +(-1.93078 - 1.50734i) q^{6} +(-3.28633 - 2.19586i) q^{7} +(2.55505 - 1.21315i) q^{8} +(2.67040 - 1.36711i) q^{9} +O(q^{10})\)	\(q+(-0.879716 - 1.10729i) q^{2} +(1.68380 - 0.405958i) q^{3} +(-0.452199 + 1.94821i) q^{4} +(-0.324308 - 3.29275i) q^{5} +(-1.93078 - 1.50734i) q^{6} +(-3.28633 - 2.19586i) q^{7} +(2.55505 - 1.21315i) q^{8} +(2.67040 - 1.36711i) q^{9} +(-3.36075 + 3.25579i) q^{10} +(-0.281020 - 0.525751i) q^{11} +(0.0294756 + 3.46398i) q^{12} +(-0.187953 + 1.90832i) q^{13} +(0.459581 + 5.57067i) q^{14} +(-1.88279 - 5.41270i) q^{15} +(-3.59103 - 1.76196i) q^{16} +(-2.42180 + 5.84675i) q^{17} +(-3.86298 - 1.75425i) q^{18} +(-1.15540 + 0.948208i) q^{19} +(6.56162 + 0.857161i) q^{20} +(-6.42497 - 2.36328i) q^{21} +(-0.334943 + 0.773683i) q^{22} +(1.22716 - 6.16936i) q^{23} +(3.80971 - 3.07995i) q^{24} +(-5.83312 + 1.16028i) q^{25} +(2.27842 - 1.47066i) q^{26} +(3.94144 - 3.38601i) q^{27} +(5.76407 - 5.40950i) q^{28} +(3.15612 - 5.90468i) q^{29} +(-4.33712 + 6.84644i) q^{30} +(-1.04469 - 1.04469i) q^{31} +(1.20808 + 5.52635i) q^{32} +(-0.686615 - 0.771180i) q^{33} +(8.60457 - 2.46183i) q^{34} +(-6.16463 + 11.5332i) q^{35} +(1.45586 + 5.82069i) q^{36} +(0.353476 + 0.290090i) q^{37} +(2.06637 + 0.445208i) q^{38} +(0.458222 + 3.28954i) q^{39} +(-4.82323 - 8.01970i) q^{40} +(2.35149 - 11.8217i) q^{41} +(3.03530 + 9.19335i) q^{42} +(0.626022 - 2.06372i) q^{43} +(1.15135 - 0.309741i) q^{44} +(-5.36758 - 8.34959i) q^{45} +(-7.91085 + 4.06846i) q^{46} +(0.749553 - 1.80958i) q^{47} +(-6.76188 - 1.50898i) q^{48} +(3.29941 + 7.96549i) q^{49} +(6.41626 + 5.43826i) q^{50} +(-1.70431 + 10.8279i) q^{51} +(-3.63282 - 1.22911i) q^{52} +(5.62217 + 10.5183i) q^{53} +(-7.21666 - 1.38560i) q^{54} +(-1.64003 + 1.09583i) q^{55} +(-11.0606 - 1.62369i) q^{56} +(-1.56053 + 2.06564i) q^{57} +(-9.31470 + 1.69969i) q^{58} +(-0.520180 - 5.28148i) q^{59} +(11.3965 - 1.22045i) q^{60} +(3.82602 + 12.6127i) q^{61} +(-0.237748 + 2.07581i) q^{62} +(-11.7778 - 1.37104i) q^{63} +(5.05652 - 6.19932i) q^{64} +6.34459 q^{65} +(-0.249896 + 1.43870i) q^{66} +(4.28074 - 1.29855i) q^{67} +(-10.2956 - 7.36208i) q^{68} +(-0.438200 - 10.8862i) q^{69} +(18.1938 - 3.31990i) q^{70} +(-5.35095 - 3.57539i) q^{71} +(5.16447 - 6.73262i) q^{72} +(5.77379 + 8.64109i) q^{73} +(0.0102566 - 0.646598i) q^{74} +(-9.35080 + 4.32168i) q^{75} +(-1.32484 - 2.67973i) q^{76} +(-0.230950 + 2.34487i) q^{77} +(3.23938 - 3.40125i) q^{78} +(11.1761 - 4.62928i) q^{79} +(-4.63709 + 12.3958i) q^{80} +(5.26203 - 7.30144i) q^{81} +(-15.1588 + 7.79597i) q^{82} +(-2.60265 + 2.13594i) q^{83} +(7.50953 - 11.4485i) q^{84} +(20.0373 + 6.07825i) q^{85} +(-2.83587 + 1.12230i) q^{86} +(2.91723 - 11.2236i) q^{87} +(-1.35584 - 1.00240i) q^{88} +(12.0484 - 2.39657i) q^{89} +(-4.52350 + 13.2888i) q^{90} +(4.80808 - 5.85866i) q^{91} +(11.4643 + 5.18055i) q^{92} +(-2.18315 - 1.33495i) q^{93} +(-2.66313 + 0.761942i) q^{94} +(3.49692 + 3.49692i) q^{95} +(4.27764 + 8.81486i) q^{96} +(5.23719 - 5.23719i) q^{97} +(5.91759 - 10.6608i) q^{98} +(-1.46919 - 1.01978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 16 q^{3} - 32 q^{4} - 16 q^{6} - 32 q^{7} - 16 q^{9}+O(q^{10}) \) 992 * q - 16 * q^3 - 32 * q^4 - 16 * q^6 - 32 * q^7 - 16 * q^9	\( 992 q - 16 q^{3} - 32 q^{4} - 16 q^{6} - 32 q^{7} - 16 q^{9} - 32 q^{10} - 16 q^{12} - 32 q^{13} - 16 q^{15} - 32 q^{16} - 16 q^{18} - 32 q^{19} - 16 q^{21} - 32 q^{22} - 16 q^{24} - 32 q^{25} - 16 q^{27} - 32 q^{28} - 16 q^{30} - 32 q^{31} - 16 q^{33} - 32 q^{34} - 16 q^{36} - 32 q^{37} - 16 q^{39} - 32 q^{40} - 16 q^{42} - 32 q^{43} - 16 q^{45} - 32 q^{46} - 16 q^{48} - 32 q^{49} - 16 q^{51} - 128 q^{52} - 16 q^{54} - 32 q^{55} - 16 q^{57} - 320 q^{58} - 16 q^{60} - 32 q^{61} - 32 q^{63} - 224 q^{64} - 16 q^{66} - 32 q^{67} - 16 q^{69} - 224 q^{70} - 16 q^{72} - 32 q^{73} - 16 q^{75} - 256 q^{76} - 16 q^{78} - 32 q^{79} - 16 q^{81} - 32 q^{82} - 16 q^{84} - 32 q^{85} - 16 q^{87} - 32 q^{88} - 16 q^{90} - 32 q^{91} - 16 q^{93} - 32 q^{94} - 16 q^{96} - 32 q^{97} - 16 q^{99}+O(q^{100}) \) 992 * q - 16 * q^3 - 32 * q^4 - 16 * q^6 - 32 * q^7 - 16 * q^9 - 32 * q^10 - 16 * q^12 - 32 * q^13 - 16 * q^15 - 32 * q^16 - 16 * q^18 - 32 * q^19 - 16 * q^21 - 32 * q^22 - 16 * q^24 - 32 * q^25 - 16 * q^27 - 32 * q^28 - 16 * q^30 - 32 * q^31 - 16 * q^33 - 32 * q^34 - 16 * q^36 - 32 * q^37 - 16 * q^39 - 32 * q^40 - 16 * q^42 - 32 * q^43 - 16 * q^45 - 32 * q^46 - 16 * q^48 - 32 * q^49 - 16 * q^51 - 128 * q^52 - 16 * q^54 - 32 * q^55 - 16 * q^57 - 320 * q^58 - 16 * q^60 - 32 * q^61 - 32 * q^63 - 224 * q^64 - 16 * q^66 - 32 * q^67 - 16 * q^69 - 224 * q^70 - 16 * q^72 - 32 * q^73 - 16 * q^75 - 256 * q^76 - 16 * q^78 - 32 * q^79 - 16 * q^81 - 32 * q^82 - 16 * q^84 - 32 * q^85 - 16 * q^87 - 32 * q^88 - 16 * q^90 - 32 * q^91 - 16 * q^93 - 32 * q^94 - 16 * q^96 - 32 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more