LMFDB - Embedded newform 64.2.i.a.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,2,Mod(5,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("64.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	64.i (of order $16$, degree $8$, 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:	$0.511042572936$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			61.1
Character	$\chi$	$=$	64.61
Dual form			64.2.i.a.21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30780 + 0.538195i) q^{2} +(0.344545 - 1.73215i) q^{3} +(1.42069 - 1.40771i) q^{4} +(-2.21982 - 1.48324i) q^{5} +(0.481636 + 2.45074i) q^{6} +(2.90595 - 1.20368i) q^{7} +(-1.10036 + 2.60561i) q^{8} +(-0.109979 - 0.0455548i) q^{9} +O(q^{10})$	\(q+(-1.30780 + 0.538195i) q^{2} +(0.344545 - 1.73215i) q^{3} +(1.42069 - 1.40771i) q^{4} +(-2.21982 - 1.48324i) q^{5} +(0.481636 + 2.45074i) q^{6} +(2.90595 - 1.20368i) q^{7} +(-1.10036 + 2.60561i) q^{8} +(-0.109979 - 0.0455548i) q^{9} +(3.70136 + 0.745083i) q^{10} +(1.75553 - 0.349197i) q^{11} +(-1.94886 - 2.94586i) q^{12} +(-5.20730 + 3.47941i) q^{13} +(-3.15259 + 3.13815i) q^{14} +(-3.33401 + 3.33401i) q^{15} +(0.0367288 - 3.99983i) q^{16} +(0.895276 + 0.895276i) q^{17} +(0.168348 + 0.000386458i) q^{18} +(2.36339 + 3.53706i) q^{19} +(-5.24165 + 1.01763i) q^{20} +(-1.08373 - 5.44826i) q^{21} +(-2.10795 + 1.40150i) q^{22} +(-0.709741 + 1.71347i) q^{23} +(4.13417 + 2.80374i) q^{24} +(0.814201 + 1.96565i) q^{25} +(4.93752 - 7.35293i) q^{26} +(2.82675 - 4.23052i) q^{27} +(2.43403 - 5.80079i) q^{28} +(7.36008 + 1.46401i) q^{29} +(2.56588 - 6.15458i) q^{30} +1.14161i q^{31} +(2.10466 + 5.25075i) q^{32} -3.16115i q^{33} +(-1.65268 - 0.689010i) q^{34} +(-8.23605 - 1.63825i) q^{35} +(-0.220374 + 0.0900988i) q^{36} +(-1.36011 + 2.03555i) q^{37} +(-4.99448 - 3.35381i) q^{38} +(4.23269 + 10.2186i) q^{39} +(6.30735 - 4.15189i) q^{40} +(-3.08221 + 7.44112i) q^{41} +(4.34952 + 6.54198i) q^{42} +(-1.56753 - 7.88051i) q^{43} +(2.00250 - 2.96737i) q^{44} +(0.176565 + 0.264249i) q^{45} +(0.00602099 - 2.62285i) q^{46} +(-6.65222 - 6.65222i) q^{47} +(-6.91564 - 1.44174i) q^{48} +(2.04595 - 2.04595i) q^{49} +(-2.12272 - 2.13249i) q^{50} +(1.85921 - 1.24228i) q^{51} +(-2.49999 + 12.2735i) q^{52} +(-0.674026 + 0.134072i) q^{53} +(-1.41997 + 7.05403i) q^{54} +(-4.41491 - 1.82872i) q^{55} +(-0.0612673 + 8.89627i) q^{56} +(6.94100 - 2.87506i) q^{57} +(-10.4135 + 2.04653i) q^{58} +(-2.59120 - 1.73138i) q^{59} +(-0.0432946 + 9.42992i) q^{60} +(0.360949 - 1.81461i) q^{61} +(-0.614409 - 1.49300i) q^{62} -0.374427 q^{63} +(-5.57841 - 5.73423i) q^{64} +16.7201 q^{65} +(1.70132 + 4.13416i) q^{66} +(-2.13440 + 10.7304i) q^{67} +(2.53219 + 0.0116258i) q^{68} +(2.72344 + 1.81974i) q^{69} +(11.6528 - 2.29009i) q^{70} +(1.97842 - 0.819489i) q^{71} +(0.239715 - 0.236436i) q^{72} +(-13.1646 - 5.45295i) q^{73} +(0.683231 - 3.39409i) q^{74} +(3.68533 - 0.733058i) q^{75} +(8.33679 + 1.69812i) q^{76} +(4.68117 - 3.12785i) q^{77} +(-11.0351 - 11.0859i) q^{78} +(0.102033 - 0.102033i) q^{79} +(-6.01423 + 8.82444i) q^{80} +(-6.60646 - 6.60646i) q^{81} +(0.0261475 - 11.3903i) q^{82} +(5.13230 + 7.68102i) q^{83} +(-9.20918 - 6.21473i) q^{84} +(-0.659446 - 3.31526i) q^{85} +(6.29128 + 9.46251i) q^{86} +(5.07176 - 12.2443i) q^{87} +(-1.02185 + 4.95847i) q^{88} +(-4.64776 - 11.2207i) q^{89} +(-0.373130 - 0.250558i) q^{90} +(-10.9441 + 16.3790i) q^{91} +(1.40373 + 3.43341i) q^{92} +(1.97743 + 0.393336i) q^{93} +(12.2800 + 5.11959i) q^{94} -11.3571i q^{95} +(9.82022 - 1.83645i) q^{96} +12.8041i q^{97} +(-1.57458 + 3.77683i) q^{98} +(-0.208979 - 0.0415685i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{3}{16}\right)$	$1$

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 $

$2$	−1.30780	+	0.538195i	−0.924756	+	0.380562i
$2$	−1.30780	+	0.538195i	−0.924756	+	0.380562i
$3$	0.344545	−	1.73215i	0.198923	−	1.00005i	−0.744287	−	0.667860i	$-0.767211\pi$
$3$	0.344545	−	1.73215i	0.198923	−	1.00005i	0.943211	−	0.332195i	$-0.107789\pi$
$4$	1.42069	−	1.40771i	0.710346	−	0.703853i
$5$	−2.21982	−	1.48324i	−0.992735	−	0.663324i	−0.0506563	−	0.998716i	$-0.516131\pi$
$5$	−2.21982	−	1.48324i	−0.992735	−	0.663324i	−0.942079	+	0.335392i	$0.891131\pi$
$6$	0.481636	+	2.45074i	0.196627	+	1.00051i
$7$	2.90595	−	1.20368i	1.09835	−	0.454950i	0.241437	−	0.970417i	$-0.422381\pi$
$7$	2.90595	−	1.20368i	1.09835	−	0.454950i	0.856910	+	0.515466i	$0.172381\pi$
$8$	−1.10036	+	2.60561i	−0.389037	+	0.921222i
$9$	−0.109979	−	0.0455548i	−0.0366597	−	0.0151849i
$10$	3.70136	+	0.745083i	1.17047	+	0.235616i
$11$	1.75553	−	0.349197i	0.529312	−	0.105287i	0.0768028	−	0.997046i	$-0.475529\pi$
$11$	1.75553	−	0.349197i	0.529312	−	0.105287i	0.452510	+	0.891760i	$0.350529\pi$
$12$	−1.94886	−	2.94586i	−0.562587	−	0.850397i
$13$	−5.20730	+	3.47941i	−1.44425	+	0.965015i	−0.446724	+	0.894672i	$0.647409\pi$
$13$	−5.20730	+	3.47941i	−1.44425	+	0.965015i	−0.997523	+	0.0703427i	$0.977591\pi$
$14$	−3.15259	+	3.13815i	−0.842566	+	0.838706i
$15$	−3.33401	+	3.33401i	−0.860839	+	0.860839i
$16$	0.0367288	−	3.99983i	0.00918220	−	0.999958i
$17$	0.895276	+	0.895276i	0.217136	+	0.217136i	0.807290	−	0.590154i	$-0.200933\pi$
$17$	0.895276	+	0.895276i	0.217136	+	0.217136i	−0.590154	+	0.807290i	$0.700933\pi$
$18$	0.168348		0.000386458i	0.0396800		9.10890e-5i
$19$	2.36339	+	3.53706i	0.542199	+	0.811458i	0.996858	−	0.0792076i	$-0.0252390\pi$
$19$	2.36339	+	3.53706i	0.542199	+	0.811458i	−0.454659	+	0.890665i	$0.650239\pi$
$20$	−5.24165	+	1.01763i	−1.17207	+	0.227550i
$21$	−1.08373	−	5.44826i	−0.236488	−	1.18891i
$22$	−2.10795	+	1.40150i	−0.449416	+	0.298800i
$23$	−0.709741	+	1.71347i	−0.147991	+	0.357282i	−0.980440	−	0.196820i	$-0.936938\pi$
$23$	−0.709741	+	1.71347i	−0.147991	+	0.357282i	0.832448	+	0.554103i	$0.186938\pi$
$24$	4.13417	+	2.80374i	0.843884	+	0.572311i
$25$	0.814201	+	1.96565i	0.162840	+	0.393131i
$26$	4.93752	−	7.35293i	0.968328	−	1.44203i
$27$	2.82675	−	4.23052i	0.544007	−	0.814165i
$28$	2.43403	−	5.80079i	0.459988	−	1.09625i
$29$	7.36008	+	1.46401i	1.36673	+	0.271860i	0.823307	−	0.567597i	$-0.192127\pi$
$29$	7.36008	+	1.46401i	1.36673	+	0.271860i	0.543426	+	0.839457i	$0.317127\pi$
$30$	2.56588	−	6.15458i	0.468463	−	1.12367i
$31$			1.14161i			0.205039i	0.994731	+	0.102520i	$0.0326904\pi$
$31$			1.14161i			0.205039i	−0.994731	+	0.102520i	$0.967310\pi$
$32$	2.10466	+	5.25075i	0.372054	+	0.928211i
$33$		−	3.16115i		−	0.550285i
$34$	−1.65268	−	0.689010i	−0.283432	−	0.118164i
$35$	−8.23605	−	1.63825i	−1.39215	−	0.276915i
$36$	−0.220374	+	0.0900988i	−0.0367290	+	0.0150165i
$37$	−1.36011	+	2.03555i	−0.223600	+	0.334642i	−0.926260	−	0.376884i	$-0.876995\pi$
$37$	−1.36011	+	2.03555i	−0.223600	+	0.334642i	0.702660	+	0.711526i	$0.251995\pi$
$38$	−4.99448	−	3.35381i	−0.810211	−	0.544060i
$39$	4.23269	+	10.2186i	0.677773	+	1.63629i
$40$	6.30735	−	4.15189i	0.997280	−	0.656472i
$41$	−3.08221	+	7.44112i	−0.481361	+	1.16211i	0.477602	+	0.878576i	$0.341506\pi$
$41$	−3.08221	+	7.44112i	−0.481361	+	1.16211i	−0.958963	+	0.283532i	$0.908494\pi$
$42$	4.34952	+	6.54198i	0.671146	+	1.00945i
$43$	−1.56753	−	7.88051i	−0.239046	−	1.20177i	−0.894687	−	0.446694i	$-0.852601\pi$
$43$	−1.56753	−	7.88051i	−0.239046	−	1.20177i	0.655641	−	0.755073i	$-0.272399\pi$
$44$	2.00250	−	2.96737i	0.301888	−	0.447348i
$45$	0.176565	+	0.264249i	0.0263208	+	0.0393919i
$46$	0.00602099	−	2.62285i	0.000887746	−	0.386719i
$47$	−6.65222	−	6.65222i	−0.970325	−	0.970325i	0.0292469	−	0.999572i	$-0.490689\pi$
$47$	−6.65222	−	6.65222i	−0.970325	−	0.970325i	−0.999572	+	0.0292469i	$0.990689\pi$
$48$	−6.91564	−	1.44174i	−0.998186	−	0.208098i
$49$	2.04595	−	2.04595i	0.292279	−	0.292279i
$50$	−2.12272	−	2.13249i	−0.300198	−	0.301579i
$51$	1.85921	−	1.24228i	0.260342	−	0.173955i
$52$	−2.49999	+	12.2735i	−0.346686	+	1.70203i
$53$	−0.674026	+	0.134072i	−0.0925846	+	0.0184162i	−0.241165	−	0.970484i	$-0.577530\pi$
$53$	−0.674026	+	0.134072i	−0.0925846	+	0.0184162i	0.148581	+	0.988900i	$0.452530\pi$
$54$	−1.41997	+	7.05403i	−0.193234	+	0.959931i
$55$	−4.41491	−	1.82872i	−0.595306	−	0.246584i
$56$	−0.0612673	+	8.89627i	−0.00818719	+	1.18881i
$57$	6.94100	−	2.87506i	0.919358	−	0.380811i
$58$	−10.4135	+	2.04653i	−1.36735	+	0.268722i
$59$	−2.59120	−	1.73138i	−0.337345	−	0.225407i	0.375346	−	0.926885i	$-0.377524\pi$
$59$	−2.59120	−	1.73138i	−0.337345	−	0.225407i	−0.712691	+	0.701478i	$0.752524\pi$
$60$	−0.0432946	+	9.42992i	−0.00558931	+	1.21740i
$61$	0.360949	−	1.81461i	0.0462147	−	0.232337i	−0.950774	−	0.309886i	$-0.899709\pi$
$61$	0.360949	−	1.81461i	0.0462147	−	0.232337i	0.996989	+	0.0775484i	$0.0247092\pi$
$62$	−0.614409	−	1.49300i	−0.0780300	−	0.189611i
$63$	−0.374427			−0.0471734
$64$	−5.57841	−	5.73423i	−0.697301	−	0.716779i
$65$	16.7201			2.07387
$66$	1.70132	+	4.13416i	0.209417	+	0.508879i
$67$	−2.13440	+	10.7304i	−0.260759	+	1.31092i	0.599217	+	0.800587i	$0.295479\pi$
$67$	−2.13440	+	10.7304i	−0.260759	+	1.31092i	−0.859976	+	0.510335i	$0.829521\pi$
$68$	2.53219	+	0.0116258i	0.307074	+	0.00140984i
$69$	2.72344	+	1.81974i	0.327863	+	0.219071i
$70$	11.6528	−	2.29009i	1.39278	−	0.273719i
$71$	1.97842	−	0.819489i	0.234795	−	0.0972554i	−0.262184	−	0.965018i	$-0.584443\pi$
$71$	1.97842	−	0.819489i	0.234795	−	0.0972554i	0.496979	+	0.867763i	$0.334443\pi$
$72$	0.239715	−	0.236436i	0.0282507	−	0.0278642i
$73$	−13.1646	−	5.45295i	−1.54080	−	0.638220i	−0.559176	−	0.829049i	$-0.688882\pi$
$73$	−13.1646	−	5.45295i	−1.54080	−	0.638220i	−0.981623	+	0.190829i	$0.938882\pi$
$74$	0.683231	−	3.39409i	0.0794240	−	0.394555i
$75$	3.68533	−	0.733058i	0.425545	−	0.0846462i
$76$	8.33679	+	1.69812i	0.956295	+	0.194787i
$77$	4.68117	−	3.12785i	0.533468	−	0.356452i
$78$	−11.0351	−	11.0859i	−1.24948	−	1.25523i
$79$	0.102033	−	0.102033i	0.0114796	−	0.0114796i	−0.701344	−	0.712823i	$-0.747416\pi$
$79$	0.102033	−	0.102033i	0.0114796	−	0.0114796i	0.712823	+	0.701344i	$0.247416\pi$
$80$	−6.01423	+	8.82444i	−0.672412	+	0.986602i
$81$	−6.60646	−	6.60646i	−0.734052	−	0.734052i
$82$	0.0261475	−	11.3903i	0.00288751	−	1.25785i
$83$	5.13230	+	7.68102i	0.563343	+	0.843102i	0.998356	−	0.0573223i	$-0.0182563\pi$
$83$	5.13230	+	7.68102i	0.563343	+	0.843102i	−0.435013	+	0.900424i	$0.643256\pi$
$84$	−9.20918	−	6.21473i	−1.00480	−	0.678082i
$85$	−0.659446	−	3.31526i	−0.0715270	−	0.359590i
$86$	6.29128	+	9.46251i	0.678406	+	1.02037i
$87$	5.07176	−	12.2443i	0.543750	−	1.31273i
$88$	−1.02185	+	4.95847i	−0.108929	+	0.528575i
$89$	−4.64776	−	11.2207i	−0.492662	−	1.18939i	−0.953360	−	0.301834i	$-0.902401\pi$
$89$	−4.64776	−	11.2207i	−0.492662	−	1.18939i	0.460699	−	0.887557i	$-0.347599\pi$
$90$	−0.373130	−	0.250558i	−0.0393313	−	0.0264112i
$91$	−10.9441	+	16.3790i	−1.14725	+	1.71698i
$92$	1.40373	+	3.43341i	0.146349	+	0.357958i
$93$	1.97743	+	0.393336i	0.205050	+	0.0407870i
$94$	12.2800	+	5.11959i	1.26658	+	0.528045i
$95$		−	11.3571i		−	1.16522i
$96$	9.82022	−	1.83645i	1.00227	−	0.187432i
$97$			12.8041i			1.30006i	0.759908	+	0.650031i	$0.225244\pi$
$97$			12.8041i			1.30006i	−0.759908	+	0.650031i	$0.774756\pi$
$98$	−1.57458	+	3.77683i	−0.159057	+	0.381517i
$99$	−0.208979	−	0.0415685i	−0.0210032	−	0.00417779i
$100$	3.92379	+	1.64643i	0.392379	+	0.164643i
$101$	−0.497823	+	0.745045i	−0.0495352	+	0.0741347i	−0.855411	−	0.517951i	$-0.826695\pi$
$101$	−0.497823	+	0.745045i	−0.0495352	+	0.0741347i	0.805875	+	0.592085i	$0.201695\pi$
$102$	−1.76289	+	2.62528i	−0.174552	+	0.259942i
$103$	−1.27589	−	3.08028i	−0.125718	−	0.303509i	0.848472	−	0.529240i	$-0.177523\pi$
$103$	−1.27589	−	3.08028i	−0.125718	−	0.303509i	−0.974190	+	0.225731i	$0.927523\pi$
$104$	−3.33606	−	17.3968i	−0.327128	−	1.70590i
$105$	−5.67538	+	13.7016i	−0.553861	+	1.33714i
$106$	0.809336	−	0.538097i	0.0786096	−	0.0522646i
$107$	−1.20029	−	6.03426i	−0.116036	−	0.583354i	−0.994428	−	0.105413i	$-0.966383\pi$
$107$	−1.20029	−	6.03426i	−0.116036	−	0.583354i	0.878392	−	0.477940i	$-0.158617\pi$
$108$	−1.93940	−	9.98949i	−0.186619	−	0.961239i
$109$	1.59700	+	2.39008i	0.152965	+	0.228928i	0.900035	−	0.435817i	$-0.143540\pi$
$109$	1.59700	+	2.39008i	0.152965	+	0.228928i	−0.747071	+	0.664744i	$0.768540\pi$
$110$	6.75803	+	0.0155136i	0.644353	+	0.00147917i
$111$	3.05724	+	3.05724i	0.290181	+	0.290181i
$112$	−4.70780	−	11.6675i	−0.444846	−	1.10248i
$113$	−0.395040	+	0.395040i	−0.0371623	+	0.0371623i	−0.725444	−	0.688281i	$-0.758365\pi$
$113$	−0.395040	+	0.395040i	−0.0371623	+	0.0371623i	0.688281	+	0.725444i	$0.258365\pi$
$114$	−7.53011	+	7.49562i	−0.705260	+	0.702029i
$115$	4.11698	−	2.75088i	0.383910	−	0.256521i
$116$	12.5173	−	8.28092i	1.16220	−	0.768864i
$117$	0.731198	−	0.145444i	0.0675993	−	0.0134463i
$118$	4.32060	+	0.869736i	0.397743	+	0.0800657i
$119$	3.67926	+	1.52400i	0.337277	+	0.139705i
$120$	−5.01852	−	12.3558i	−0.458126	−	1.12792i
$121$	−7.20273	+	2.98347i	−0.654793	+	0.271224i
$122$	0.504566	+	2.56741i	0.0456813	+	0.232443i
$123$	11.8271	+	7.90265i	1.06642	+	0.712558i
$124$	1.60705	+	1.62187i	0.144317	+	0.145649i
$125$	−1.49607	+	7.52124i	−0.133812	+	0.672720i
$126$	0.489677	−	0.201515i	0.0436239	−	0.0179524i
$127$	20.8005			1.84574			0.922872	−	0.385108i	$-0.125836\pi$
$127$	20.8005			1.84574			0.922872	+	0.385108i	$0.125836\pi$
$128$	10.3816	+	4.49696i	0.917611	+	0.397479i
$129$	−14.1903			−1.24938
$130$	−21.8666	+	8.99867i	−1.91782	+	0.789236i
$131$	0.204695	−	1.02907i	0.0178843	−	0.0899104i	−0.970812	−	0.239840i	$-0.922905\pi$
$131$	0.204695	−	1.02907i	0.0178843	−	0.0899104i	0.988697	+	0.149930i	$0.0479049\pi$
$132$	−4.44997	−	4.49102i	−0.387320	−	0.390893i
$133$	11.1254	+	7.43376i	0.964695	+	0.644589i
$134$	−2.98365	−	15.1819i	−0.257749	−	1.31152i
$135$	−12.5497	+	5.19828i	−1.08011	+	0.447396i
$136$	−3.31787	+	1.34761i	−0.284505	+	0.115557i
$137$	11.1139	+	4.60351i	0.949520	+	0.393304i	0.803051	−	0.595911i	$-0.203209\pi$
$137$	11.1139	+	4.60351i	0.949520	+	0.393304i	0.146470	+	0.989215i	$0.453209\pi$
$138$	−4.54109	−	0.914121i	−0.386563	−	0.0778151i
$139$	−6.58030	+	1.30890i	−0.558133	+	0.111020i	−0.466093	−	0.884736i	$-0.654339\pi$
$139$	−6.58030	+	1.30890i	−0.558133	+	0.111020i	−0.0920403	+	0.995755i	$0.529339\pi$
$140$	−14.0071	+	9.26649i	−1.18381	+	0.783161i
$141$	−13.8146	+	9.23062i	−1.16340	+	0.777358i
$142$	−2.14634	+	2.13651i	−0.180117	+	0.179292i
$143$	−7.92658	+	7.92658i	−0.662854	+	0.662854i
$144$	−0.186251	+	0.438224i	−0.0155209	+	0.0365187i
$145$	−14.1666	−	14.1666i	−1.17647	−	1.17647i
$146$	20.1514	+	0.0462594i	1.66775	+	0.00382845i
$147$	−2.83897	−	4.24881i	−0.234154	−	0.350436i
$148$	0.933155	+	4.80651i	0.0767049	+	0.395093i
$149$	−1.37106	−	6.89279i	−0.112322	−	0.564680i	−0.995429	−	0.0955079i	$-0.969552\pi$
$149$	−1.37106	−	6.89279i	−0.112322	−	0.564680i	0.883107	−	0.469172i	$-0.155448\pi$
$150$	−4.42515	+	2.94212i	−0.361312	+	0.240223i
$151$	3.32014	−	8.01552i	0.270189	−	0.652293i	−0.729302	−	0.684192i	$-0.760155\pi$
$151$	3.32014	−	8.01552i	0.270189	−	0.652293i	0.999491	+	0.0318981i	$0.0101552\pi$
$152$	−11.8168	+	2.26602i	−0.958468	+	0.183799i
$153$	−0.0576774	−	0.139246i	−0.00466294	−	0.0112573i
$154$	−4.43864	+	6.61000i	−0.357676	+	0.532649i
$155$	1.69328	−	2.53417i	0.136007	−	0.203549i
$156$	20.3982	+	8.55913i	1.63316	+	0.685279i
$157$	5.32031	+	1.05828i	0.424607	+	0.0844596i	0.402768	−	0.915302i	$-0.368048\pi$
$157$	5.32031	+	1.05828i	0.424607	+	0.0844596i	0.0218386	+	0.999762i	$0.493048\pi$
$158$	−0.0785254	+	0.188353i	−0.00624714	+	0.0149846i
$159$			1.21371i			0.0962531i
$160$	3.11615	−	14.7775i	0.246354	−	1.16826i
$161$			5.83356i			0.459749i
$162$	12.1955	+	5.08438i	0.958170	+	0.399466i
$163$	1.98707	+	0.395252i	0.155639	+	0.0309585i	0.272295	−	0.962214i	$-0.412217\pi$
$163$	1.98707	+	0.395252i	0.155639	+	0.0309585i	−0.116656	+	0.993172i	$0.537217\pi$
$164$	6.09604	+	14.9104i	0.476020	+	1.16431i
$165$	−4.68874	+	7.01719i	−0.365018	+	0.546288i
$166$	−10.8459	−	7.28308i	−0.841806	−	0.565277i
$167$	1.22945	+	2.96815i	0.0951375	+	0.229682i	0.964283	−	0.264874i	$-0.0853305\pi$
$167$	1.22945	+	2.96815i	0.0951375	+	0.229682i	−0.869145	+	0.494557i	$0.835330\pi$
$168$	15.3885	+	3.17129i	1.18725	+	0.244670i
$169$	10.0348	−	24.2263i	0.771911	−	1.86356i
$170$	2.64668	+	3.98079i	0.202991	+	0.305313i
$171$	−0.0987931	−	0.496666i	−0.00755490	−	0.0379810i
$172$	−13.3204	−	8.98915i	−1.01567	−	0.685417i
$173$	−8.03014	−	12.0180i	−0.610521	−	0.913709i	0.389453	−	0.921047i	$-0.372664\pi$
$173$	−8.03014	−	12.0180i	−0.610521	−	0.913709i	−0.999973	+	0.00733795i	$0.997664\pi$
$174$	−0.0430256	+	18.7427i	−0.00326176	+	1.42088i
$175$	4.73206	+	4.73206i	0.357710	+	0.357710i
$176$	−1.33225	−	7.03465i	−0.100422	−	0.530257i
$177$	−3.89179	+	3.89179i	−0.292525	+	0.292525i
$178$	12.1173	+	12.1730i	0.908228	+	0.912407i
$179$	−3.88955	+	2.59891i	−0.290719	+	0.194252i	−0.692374	−	0.721539i	$-0.743435\pi$
$179$	−3.88955	+	2.59891i	−0.290719	+	0.194252i	0.401655	+	0.915791i	$0.368435\pi$
$180$	0.622829	+	0.126864i	0.0464230	+	0.00945587i
$181$	6.66273	−	1.32530i	0.495237	−	0.0985088i	0.0588482	−	0.998267i	$-0.481257\pi$
$181$	6.66273	−	1.32530i	0.495237	−	0.0985088i	0.436389	+	0.899758i	$0.356257\pi$
$182$	5.49759	−	27.3105i	0.407509	−	2.02439i
$183$	−3.01881	−	1.25043i	−0.223157	−	0.0924345i
$184$	−3.68365	−	3.73474i	−0.271562	−	0.275329i
$185$	6.03840	−	2.50119i	0.443952	−	0.183891i
$186$	−2.79778	+	0.549840i	−0.205143	+	0.0403162i
$187$	1.88431	+	1.25906i	0.137794	+	0.0920713i
$188$	−18.8151	−	0.0863839i	−1.37223	−	0.00630019i
$189$	3.12217	−	15.6962i	0.227104	−	1.14173i
$190$	6.11235	+	14.8529i	0.443436	+	1.07754i
$191$	−11.5951			−0.838989			−0.419495	−	0.907758i	$-0.637793\pi$
$191$	−11.5951			−0.838989			−0.419495	+	0.907758i	$0.637793\pi$
$192$	−11.8545	+	7.68691i	−0.855527	+	0.554755i
$193$	−12.0011			−0.863855			−0.431927	−	0.901908i	$-0.642166\pi$
$193$	−12.0011			−0.863855			−0.431927	+	0.901908i	$0.642166\pi$
$194$	−6.89112	−	16.7453i	−0.494754	−	1.20224i
$195$	5.76083	−	28.9616i	0.412541	−	2.07399i
$196$	0.0265682	−	5.78677i	0.00189773	−	0.413341i
$197$	3.45531	+	2.30877i	0.246181	+	0.164493i	0.672539	−	0.740062i	$-0.265204\pi$
$197$	3.45531	+	2.30877i	0.246181	+	0.164493i	−0.426358	+	0.904554i	$0.640204\pi$
$198$	0.295675	−	0.0581082i	0.0210127	−	0.00412957i
$199$	16.6804	−	6.90923i	1.18244	−	0.489782i	0.297154	−	0.954830i	$-0.403963\pi$
$199$	16.6804	−	6.90923i	1.18244	−	0.489782i	0.885286	+	0.465047i	$0.153963\pi$
$200$	−6.01765	−	0.0414427i	−0.425512	−	0.00293044i
$201$	17.8511	+	7.39419i	1.25912	+	0.521546i
$202$	0.250074	−	1.24230i	0.0175952	−	0.0874077i
$203$	23.1503	−	4.60487i	1.62483	−	0.323199i
$204$	0.892593	−	4.38213i	0.0624940	−	0.306810i
$205$	17.8789	−	11.9463i	1.24872	−	0.834367i
$206$	3.32641	+	3.34172i	0.231762	+	0.232829i
$207$	0.156113	−	0.156113i	0.0108506	−	0.0108506i
$208$	13.7258	+	20.9561i	0.951713	+	1.45305i
$209$	5.38413	+	5.38413i	0.372428	+	0.372428i
$210$	0.0481463	−	20.9734i	0.00332241	−	1.44730i
$211$	−8.80598	−	13.1791i	−0.606229	−	0.907286i	0.393700	−	0.919239i	$-0.371195\pi$
$211$	−8.80598	−	13.1791i	−0.606229	−	0.907286i	−0.999929	+	0.0119535i	$0.996195\pi$
$212$	−0.768849	+	1.13931i	−0.0528048	+	0.0782478i
$213$	−0.737818	−	3.70926i	−0.0505545	−	0.254155i
$214$	4.81735	+	7.24562i	0.329307	+	0.495301i
$215$	−8.20904	+	19.8184i	−0.559852	+	1.35160i
$216$	7.91265	+	12.0205i	0.538388	+	0.817892i
$217$	1.37414	+	3.31746i	0.0932825	+	0.225204i
$218$	−3.37488	−	2.26625i	−0.228576	−	0.153490i
$219$	−13.9811	+	20.9242i	−0.944756	+	1.41393i
$220$	−8.84652	+	3.61685i	−0.596432	+	0.243848i
$221$	−7.77700	−	1.54694i	−0.523138	−	0.104059i
$222$	−5.64366	−	2.35287i	−0.378778	−	0.157915i
$223$		−	9.77843i		−	0.654812i	−0.944884	−	0.327406i	$-0.893826\pi$
$223$		−	9.77843i		−	0.654812i	0.944884	−	0.327406i	$-0.106174\pi$
$224$	12.4363	+	12.7251i	0.830934	+	0.850231i
$225$		−	0.253272i		−	0.0168848i
$226$	0.304026	−	0.729244i	0.0202235	−	0.0485086i
$227$	−8.30819	−	1.65260i	−0.551434	−	0.109687i	−0.0884942	−	0.996077i	$-0.528205\pi$
$227$	−8.30819	−	1.65260i	−0.551434	−	0.109687i	−0.462940	+	0.886390i	$0.653205\pi$
$228$	5.81379	−	13.8555i	0.385028	−	0.917600i
$229$	−7.11294	+	10.6453i	−0.470037	+	0.703459i	−0.988429	−	0.151683i	$-0.951531\pi$
$229$	−7.11294	+	10.6453i	−0.470037	+	0.703459i	0.518393	+	0.855143i	$0.326531\pi$
$230$	−3.90368	+	5.81334i	−0.257401	+	0.383320i
$231$	−3.80503	−	9.18615i	−0.250352	−	0.604404i
$232$	−11.9134	+	17.5666i	−0.782153	+	1.15330i
$233$	−1.63989	+	3.95906i	−0.107433	+	0.259366i	−0.968449	−	0.249211i	$-0.919829\pi$
$233$	−1.63989	+	3.95906i	−0.107433	+	0.259366i	0.861016	+	0.508578i	$0.169829\pi$
$234$	−0.877985	+	0.583740i	−0.0573957	+	0.0381603i
$235$	4.89992	+	24.6336i	0.319636	+	1.60692i
$236$	−6.11857	+	1.18788i	−0.398285	+	0.0773246i
$237$	−0.141581	−	0.211891i	−0.00919669	−	0.0137638i
$238$	−5.63195	−	0.0129286i	−0.365065	−	0.000838038i
$239$	10.5905	+	10.5905i	0.685040	+	0.685040i	0.961131	−	0.276091i	$-0.0890392\pi$
$239$	10.5905	+	10.5905i	0.685040	+	0.685040i	−0.276091	+	0.961131i	$0.589039\pi$
$240$	13.2130	+	13.4579i	0.852898	+	0.868707i
$241$	−2.17798	+	2.17798i	−0.140296	+	0.140296i	−0.773767	−	0.633471i	$-0.781630\pi$
$241$	−2.17798	+	2.17798i	−0.140296	+	0.140296i	0.633471	+	0.773767i	$0.281630\pi$
$242$	7.81405	−	7.77826i	0.502306	−	0.500005i
$243$	−1.02802	+	0.686898i	−0.0659472	+	0.0440645i
$244$	−2.04164	−	3.08611i	−0.130703	−	0.197568i
$245$	−7.57629	+	1.50702i	−0.484032	+	0.0962799i
$246$	−19.7207	−	3.96978i	−1.25735	−	0.253104i
$247$	−24.6138	−	10.1954i	−1.56614	−	0.648715i
$248$	−2.97459	−	1.25618i	−0.188887	−	0.0797677i
$249$	15.0730	−	6.24342i	0.955210	−	0.395661i
$250$	−2.09134	−	10.6415i	−0.132268	−	0.673025i
$251$	−20.0734	−	13.4126i	−1.26702	−	0.846596i	−0.273682	−	0.961820i	$-0.588241\pi$
$251$	−20.0734	−	13.4126i	−1.26702	−	0.846596i	−0.993340	+	0.115224i	$0.963241\pi$
$252$	−0.531946	+	0.527084i	−0.0335094	+	0.0332031i
$253$	−0.647635	+	3.25588i	−0.0407165	+	0.204695i
$254$	−27.2029	+	11.1947i	−1.70686	+	0.702419i
$255$	−5.96972			−0.373839
$256$	−15.9973	−	0.293818i	−0.999831	−	0.0183636i
$257$	19.3207			1.20519			0.602595	−	0.798047i	$-0.294134\pi$
$257$	19.3207			1.20519			0.602595	+	0.798047i	$0.294134\pi$
$258$	18.5581	−	7.63714i	1.15538	−	0.475468i
$259$	−1.50225	+	7.55234i	−0.0933455	+	0.469280i
$260$	23.7541	−	23.5370i	1.47317	−	1.45970i
$261$	−0.742762	−	0.496298i	−0.0459758	−	0.0307201i
$262$	0.286141	+	1.45599i	0.0176778	+	0.0899512i
$263$	−25.8007	+	10.6870i	−1.59094	+	0.658990i	−0.990098	−	0.140377i	$-0.955169\pi$
$263$	−25.8007	+	10.6870i	−1.59094	+	0.658990i	−0.600844	+	0.799366i	$0.705169\pi$
$264$	8.23672	+	3.47841i	0.506935	+	0.214081i
$265$	1.69508	+	0.702125i	0.104128	+	0.0431312i
$266$	−18.5506	−	3.73424i	−1.13741	−	0.228961i
$267$	−21.0372	+	4.18457i	−1.28746	+	0.256091i
$268$	12.0729	+	18.2491i	0.737467	+	1.11474i
$269$	−13.5221	+	9.03520i	−0.824459	+	0.550886i	−0.894712	−	0.446644i	$-0.852619\pi$
$269$	−13.5221	+	9.03520i	−0.824459	+	0.550886i	0.0702534	+	0.997529i	$0.477619\pi$
$270$	13.6149	−	13.5525i	0.828576	−	0.824781i
$271$	2.46801	−	2.46801i	0.149921	−	0.149921i	−0.628162	−	0.778083i	$-0.716192\pi$
$271$	2.46801	−	2.46801i	0.149921	−	0.149921i	0.778083	+	0.628162i	$0.216192\pi$
$272$	3.61383	−	3.54807i	0.219121	−	0.215133i
$273$	24.6000	+	24.6000i	1.48886	+	1.48886i
$274$	−17.0123	−	0.0390532i	−1.02775	−	0.00235929i
$275$	2.11575	+	3.16645i	0.127585	+	0.190944i
$276$	6.43082	−	1.24850i	0.387090	−	0.0751511i
$277$	5.37681	+	27.0311i	0.323061	+	1.62414i	0.711515	+	0.702671i	$0.248009\pi$
$277$	5.37681	+	27.0311i	0.323061	+	1.62414i	−0.388453	+	0.921468i	$0.626991\pi$
$278$	7.90128	−	5.25327i	0.473887	−	0.315070i
$279$	0.0520058	−	0.125553i	0.00311350	−	0.00751667i
$280$	13.3313	−	19.6573i	0.796697	−	1.17475i
$281$	5.74296	+	13.8647i	0.342596	+	0.827101i	0.997452	+	0.0713465i	$0.0227296\pi$
$281$	5.74296	+	13.8647i	0.342596	+	0.827101i	−0.654855	+	0.755754i	$0.727270\pi$
$282$	13.0989	−	19.5068i	0.780027	−	1.16161i
$283$	15.0536	−	22.5293i	0.894845	−	1.33923i	−0.0454844	−	0.998965i	$-0.514483\pi$
$283$	15.0536	−	22.5293i	0.894845	−	1.33923i	0.940329	−	0.340265i	$-0.110517\pi$
$284$	1.65713	−	3.94927i	0.0983324	−	0.234346i
$285$	−19.6722	−	3.91304i	−1.16528	−	0.231789i
$286$	6.10035	−	14.6325i	0.360721	−	0.865235i
$287$			25.3336i			1.49539i
$288$	0.00772899	−	0.673350i	0.000455435	−	0.0396775i
$289$		−	15.3970i		−	0.905704i
$290$	26.1515	+	10.9027i	1.53567	+	0.640229i
$291$	22.1786	+	4.41160i	1.30013	+	0.258613i
$292$	−26.3790	+	10.7849i	−1.54371	+	0.631139i
$293$	11.8816	−	17.7821i	0.694132	−	1.03884i	−0.302198	−	0.953245i	$-0.597720\pi$
$293$	11.8816	−	17.7821i	0.694132	−	1.03884i	0.996330	−	0.0855963i	$-0.0272795\pi$
$294$	5.99950	+	4.02869i	0.349898	+	0.234958i
$295$	3.18395	+	7.68673i	0.185377	+	0.447539i
$296$	−3.80723	−	5.78375i	−0.221291	−	0.336174i
$297$	3.48515	−	8.41390i	0.202229	−	0.488224i
$298$	5.50275	+	8.27651i	0.318766	+	0.479445i
$299$	−2.26601	−	11.3920i	−0.131047	−	0.658818i
$300$	4.20379	−	6.22931i	0.242706	−	0.359649i
$301$	−14.0408	−	21.0136i	−0.809300	−	1.21120i
$302$	−0.0281659	+	12.2696i	−0.00162077	+	0.706035i
$303$	1.11900	+	1.11900i	0.0642851	+	0.0642851i
$304$	14.2345	−	9.32325i	0.816402	−	0.534725i
$305$	−3.49274	+	3.49274i	−0.199994	+	0.199994i
$306$	0.150372	+	0.151064i	0.00859620	+	0.00863575i
$307$	20.8525	−	13.9332i	1.19011	−	0.795209i	0.207025	−	0.978336i	$-0.433622\pi$
$307$	20.8525	−	13.9332i	1.19011	−	0.795209i	0.983089	+	0.183127i	$0.0586219\pi$
$308$	2.24739	−	11.0334i	0.128057	−	0.628687i
$309$	−5.77510	+	1.14874i	−0.328534	+	0.0653495i
$310$	−0.850594	+	4.22551i	−0.0483105	+	0.239993i
$311$	12.4907	+	5.17383i	0.708284	+	0.293381i	0.707594	−	0.706619i	$-0.249780\pi$
$311$	12.4907	+	5.17383i	0.708284	+	0.293381i	0.000689814		1.00000i	$0.499780\pi$
$312$	−31.2832	−	0.215443i	−1.77107	−	0.0121971i
$313$	9.36192	−	3.87784i	0.529167	−	0.219188i	−0.102071	−	0.994777i	$-0.532547\pi$
$313$	9.36192	−	3.87784i	0.529167	−	0.219188i	0.631238	+	0.775589i	$0.282547\pi$
$314$	−7.52747	+	1.47935i	−0.424800	+	0.0834846i
$315$	0.831163	+	0.555365i	0.0468307	+	0.0312913i
$316$	0.00132497	−	0.288590i	7.45357e−5	−	0.0162345i
$317$	−1.93405	+	9.72312i	−0.108627	+	0.546105i	0.887696	+	0.460430i	$0.152305\pi$
$317$	−1.93405	+	9.72312i	−0.108627	+	0.546105i	−0.996323	+	0.0856750i	$0.972695\pi$
$318$	−0.653211	−	1.58729i	−0.0366302	−	0.0890106i
$319$	13.4321			0.752052
$320$	3.87784	+	21.0031i	0.216778	+	1.17411i
$321$	−10.8658			−0.606468
$322$	−3.13959	−	7.62913i	−0.174963	−	0.425155i
$323$	−1.05076	+	5.28253i	−0.0584659	+	0.293928i
$324$	−18.6857	−	0.0857898i	−1.03809	−	0.00476610i
$325$	−11.0791	−	7.40282i	−0.614558	−	0.410635i
$326$	−2.81141	+	0.552518i	−0.155710	+	0.0306012i
$327$	4.69020	−	1.94274i	0.259369	−	0.107434i
$328$	−15.9971	−	16.2190i	−0.883292	−	0.895543i
$329$	−27.3382	−	11.3238i	−1.50720	−	0.624304i
$330$	2.35532	−	11.7006i	0.129656	−	0.644094i
$331$	−17.7915	+	3.53895i	−0.977909	+	0.194518i	−0.658072	−	0.752955i	$-0.728628\pi$
$331$	−17.7915	+	3.53895i	−0.977909	+	0.194518i	−0.319836	+	0.947473i	$0.603628\pi$
$332$	18.1040	+	3.68760i	0.993588	+	0.202383i
$333$	0.242312	−	0.161908i	0.0132786	−	0.00887250i
$334$	−3.20532	−	3.22007i	−0.175387	−	0.176194i
$335$	20.6537	−	20.6537i	1.12843	−	1.12843i
$336$	−21.8319	+	4.13461i	−1.19103	+	0.225562i
$337$	6.93868	+	6.93868i	0.377974	+	0.377974i	0.870371	−	0.492397i	$-0.163879\pi$
$337$	6.93868	+	6.93868i	0.377974	+	0.377974i	−0.492397	+	0.870371i	$0.663879\pi$
$338$	−0.0851292	+	37.0839i	−0.00463042	+	2.01710i
$339$	0.548158	+	0.820377i	0.0297719	+	0.0445568i
$340$	−5.60378	−	3.78166i	−0.303908	−	0.205089i
$341$	0.398646	+	2.00413i	0.0215879	+	0.108530i
$342$	0.396505	+	0.596371i	0.0214406	+	0.0322481i
$343$	−4.94303	+	11.9335i	−0.266899	+	0.644350i
$344$	22.2584	+	4.58704i	1.20009	+	0.247317i
$345$	−3.34643	−	8.07901i	−0.180166	−	0.434959i
$346$	16.9698	+	11.3953i	0.912305	+	0.612616i
$347$	13.9556	−	20.8861i	0.749178	−	1.12122i	−0.239460	−	0.970906i	$-0.576970\pi$
$347$	13.9556	−	20.8861i	0.749178	−	1.12122i	0.988638	−	0.150318i	$-0.0480297\pi$
$348$	−10.0310	−	24.5349i	−0.537717	−	1.31521i
$349$	2.23013	+	0.443600i	0.119376	+	0.0237453i	0.254417	−	0.967095i	$-0.418117\pi$
$349$	2.23013	+	0.443600i	0.119376	+	0.0237453i	−0.135041	+	0.990840i	$0.543117\pi$
$350$	−8.73537	−	3.64182i	−0.466925	−	0.194664i
$351$			31.8650i			1.70083i
$352$	5.52834	+	8.48292i	0.294661	+	0.452141i
$353$		−	13.4949i		−	0.718259i	−0.933288	−	0.359129i	$-0.883074\pi$
$353$		−	13.4949i		−	0.718259i	0.933288	−	0.359129i	$-0.116926\pi$
$354$	2.99515	−	7.18424i	0.159190	−	0.381838i
$355$	−5.60724	−	1.11535i	−0.297601	−	0.0591966i
$356$	−22.3985	−	9.39846i	−1.18712	−	0.498117i
$357$	3.90746	−	5.84792i	0.206805	−	0.309505i
$358$	3.68804	−	5.49220i	0.194919	−	0.290272i
$359$	−7.94195	−	19.1736i	−0.419160	−	1.01194i	−0.982592	−	0.185779i	$-0.940519\pi$
$359$	−7.94195	−	19.1736i	−0.419160	−	1.01194i	0.563431	−	0.826163i	$-0.309481\pi$
$360$	−0.882815	+	0.169291i	−0.0465284	+	0.00892242i
$361$	0.345785	−	0.834799i	0.0181992	−	0.0439368i
$362$	−8.00027	+	5.31908i	−0.420485	+	0.279565i
$363$	2.68613	+	13.5041i	0.140986	+	0.708782i
$364$	7.50860	+	38.6755i	0.393558	+	2.02715i
$365$	21.1350	+	31.6308i	1.10626	+	1.65563i
$366$	4.62098	+	0.0106079i	0.241542	+	0.000554482i
$367$	−9.25700	−	9.25700i	−0.483212	−	0.483212i	0.422944	−	0.906156i	$-0.360997\pi$
$367$	−9.25700	−	9.25700i	−0.483212	−	0.483212i	−0.906156	+	0.422944i	$0.860997\pi$
$368$	6.82751	+	2.90178i	0.355908	+	0.151266i
$369$	0.677958	−	0.677958i	0.0352931	−	0.0352931i
$370$	−6.55090	+	6.52089i	−0.340565	+	0.339005i
$371$	−1.79731	+	1.20092i	−0.0933115	+	0.0623488i
$372$	3.36302	−	2.22484i	0.174365	−	0.115352i
$373$	12.7838	−	2.54286i	0.661920	−	0.131664i	0.147313	−	0.989090i	$-0.452938\pi$
$373$	12.7838	−	2.54286i	0.661920	−	0.131664i	0.514608	+	0.857426i	$0.327938\pi$
$374$	−3.14192	−	0.632469i	−0.162465	−	0.0327042i
$375$	12.5124	+	5.18281i	0.646139	+	0.267639i
$376$	24.6529	−	10.0132i	1.27138	−	0.516393i
$377$	−43.4201	+	17.9852i	−2.23625	+	0.926284i
$378$	4.36445	+	22.2079i	0.224483	+	1.14225i
$379$	4.61576	+	3.08415i	0.237096	+	0.158422i	0.668442	−	0.743764i	$-0.266961\pi$
$379$	4.61576	+	3.08415i	0.237096	+	0.158422i	−0.431347	+	0.902186i	$0.641961\pi$
$380$	−15.9875	−	16.1350i	−0.820141	−	0.827706i
$381$	7.16670	−	36.0294i	0.367161	−	1.84584i
$382$	15.1640	−	6.24041i	0.775860	−	0.319287i
$383$	−7.81378			−0.399265			−0.199633	−	0.979871i	$-0.563975\pi$
$383$	−7.81378			−0.399265			−0.199633	+	0.979871i	$0.563975\pi$
$384$	11.3663	−	16.4330i	0.580035	−	0.838594i
$385$	−15.0307			−0.766036
$386$	15.6950	−	6.45891i	0.798855	−	0.328750i
$387$	−0.186600	+	0.938100i	−0.00948539	+	0.0476863i
$388$	18.0244	+	18.1907i	0.915052	+	0.923493i
$389$	−18.4653	−	12.3381i	−0.936227	−	0.625567i	−0.00895652	−	0.999960i	$-0.502851\pi$
$389$	−18.4653	−	12.3381i	−0.936227	−	0.625567i	−0.927270	+	0.374393i	$0.877851\pi$
$390$	8.05300	+	40.9765i	0.407779	+	2.07493i
$391$	−2.16944	+	0.898611i	−0.109713	+	0.0454447i
$392$	3.07967	+	7.58225i	0.155547	+	0.382961i
$393$	−1.71197	−	0.709123i	−0.0863577	−	0.0357705i
$394$	−5.76143	−	1.15978i	−0.290257	−	0.0584286i
$395$	−0.377835	+	0.0751561i	−0.0190109	+	0.00378151i
$396$	−0.355411	+	0.235125i	−0.0178601	+	0.0118155i
$397$	24.6132	−	16.4460i	1.23530	−	0.825403i	0.245717	−	0.969342i	$-0.420977\pi$
$397$	24.6132	−	16.4460i	1.23530	−	0.825403i	0.989587	+	0.143938i	$0.0459767\pi$
$398$	−18.0961	+	18.0132i	−0.907075	+	0.902920i
$399$	16.7096	−	16.7096i	0.836524	−	0.836524i
$400$	7.89219	−	3.18447i	0.394610	−	0.159223i
$401$	−14.2585	−	14.2585i	−0.712035	−	0.712035i	0.254926	−	0.966961i	$-0.417949\pi$
$401$	−14.2585	−	14.2585i	−0.712035	−	0.712035i	−0.966961	+	0.254926i	$0.917949\pi$
$402$	−27.3253	−	0.0627275i	−1.36286	−	0.00312857i
$403$	−3.97213	−	5.94471i	−0.197866	−	0.296127i
$404$	0.341551	+	1.75927i	0.0169928	+	0.0875268i
$405$	4.86622	+	24.4641i	0.241804	+	1.21563i
$406$	−27.7976	+	18.4816i	−1.37957	+	0.917227i
$407$	−1.67691	+	4.04841i	−0.0831211	+	0.200672i
$408$	1.19110	+	6.21134i	0.0589684	+	0.307507i
$409$	5.63715	+	13.6093i	0.278739	+	0.672936i	0.999801	−	0.0199343i	$-0.00634571\pi$
$409$	5.63715	+	13.6093i	0.278739	+	0.672936i	−0.721062	+	0.692871i	$0.756346\pi$
$410$	−16.9526	+	25.2458i	−0.837231	+	1.24680i
$411$	11.8032	−	17.6647i	0.582208	−	0.871335i
$412$	−6.14878	−	2.58005i	−0.302929	−	0.127110i
$413$	−9.61394	−	1.91233i	−0.473071	−	0.0940997i
$414$	−0.120146	+	0.288185i	−0.00590484	+	0.0141635i
$415$		−	24.6629i		−	1.21066i
$416$	−29.2291	−	20.0193i	−1.43308	−	0.981528i
$417$			11.8490i			0.580248i
$418$	−9.93909	−	4.14366i	−0.486137	−	0.202673i
$419$	7.40447	+	1.47284i	0.361732	+	0.0719529i	0.372610	−	0.927988i	$-0.378463\pi$
$419$	7.40447	+	1.47284i	0.361732	+	0.0719529i	−0.0108785	+	0.999941i	$0.503463\pi$
$420$	11.2248	+	27.4550i	0.547716	+	1.33967i
$421$	1.83572	−	2.74735i	0.0894674	−	0.133897i	−0.784036	−	0.620715i	$-0.786842\pi$
$421$	1.83572	−	2.74735i	0.0894674	−	0.133897i	0.873504	+	0.486818i	$0.161842\pi$
$422$	18.6094	+	12.4963i	0.905892	+	0.608310i
$423$	0.428564	+	1.03464i	0.0208375	+	0.0503061i
$424$	0.392333	−	1.90378i	0.0190534	−	0.0924556i
$425$	−1.03087	+	2.48874i	−0.0500045	+	0.120721i
$426$	2.96123	+	4.45389i	0.143472	+	0.215792i
$427$	−1.13532	−	5.70764i	−0.0549420	−	0.276212i
$428$	−10.1997	−	6.88317i	−0.493021	−	0.332710i
$429$	10.9989	+	16.4611i	0.531033	+	0.794748i
$430$	0.0696402	−	30.3366i	0.00335835	−	1.46296i
$431$	−23.3124	−	23.3124i	−1.12292	−	1.12292i	−0.991300	−	0.131620i	$-0.957982\pi$
$431$	−23.3124	−	23.3124i	−1.12292	−	1.12292i	−0.131620	−	0.991300i	$-0.542018\pi$
$432$	−16.8176	−	11.4619i	−0.809135	−	0.551460i
$433$	4.04942	−	4.04942i	0.194603	−	0.194603i	−0.603079	−	0.797682i	$-0.706060\pi$
$433$	4.04942	−	4.04942i	0.194603	−	0.194603i	0.797682	+	0.603079i	$0.206060\pi$
$434$	−3.58254	−	3.59903i	−0.171968	−	0.172759i
$435$	−29.4197	+	19.6576i	−1.41056	+	0.942509i
$436$	5.63336	+	1.14746i	0.269789	+	0.0549533i
$437$	−7.73803	+	1.53919i	−0.370160	+	0.0736294i
$438$	7.02321	−	34.8893i	0.335582	−	1.66707i
$439$	20.7711	+	8.60367i	0.991350	+	0.410631i	0.818618	−	0.574338i	$-0.194740\pi$
$439$	20.7711	+	8.60367i	0.991350	+	0.410631i	0.172732	+	0.984969i	$0.444740\pi$
$440$	9.62292	−	9.49128i	0.458755	−	0.452479i
$441$	−0.318215	+	0.131809i	−0.0151531	+	0.00627662i
$442$	11.0033	−	2.16245i	0.523375	−	0.102857i
$443$	29.3173	+	19.5892i	1.39291	+	0.930711i	0.999938	+	0.0111603i	$0.00355252\pi$
$443$	29.3173	+	19.5892i	1.39291	+	0.930711i	0.392970	+	0.919551i	$0.371447\pi$
$444$	8.64710	+	0.0397005i	0.410373	+	0.00188410i
$445$	−6.32575	+	31.8017i	−0.299869	+	1.50754i
$446$	5.26270	+	12.7882i	0.249196	+	0.605541i
$447$	−12.4117			−0.587054
$448$	−23.1128	−	9.94876i	−1.09198	−	0.470035i
$449$	−4.34734			−0.205163			−0.102582	−	0.994725i	$-0.532710\pi$
$449$	−4.34734			−0.205163			−0.102582	+	0.994725i	$0.532710\pi$
$450$	0.136310	+	0.331229i	0.00642569	+	0.0156143i
$451$	−2.81250	+	14.1394i	−0.132436	+	0.665799i
$452$	−0.00512989	+	1.11733i	−0.000241290	+	0.0525548i
$453$	−12.7401	−	8.51267i	−0.598582	−	0.399960i
$454$	11.7549	−	2.31015i	0.551685	−	0.108421i
$455$	48.5878	−	20.1257i	2.27783	−	0.943508i
$456$	−0.146340	+	21.2491i	−0.00685299	+	0.995083i
$457$	4.60193	+	1.90618i	0.215269	+	0.0891674i	0.487712	−	0.873005i	$-0.337832\pi$
$457$	4.60193	+	1.90618i	0.215269	+	0.0891674i	−0.272443	+	0.962172i	$0.587832\pi$
$458$	3.57308	−	17.7501i	0.166959	−	0.829406i
$459$	6.31820	−	1.25677i	0.294908	−	0.0586609i
$460$	1.97653	−	9.70364i	0.0921562	−	0.452435i
$461$	−2.25897	+	1.50940i	−0.105211	+	0.0702997i	−0.607063	−	0.794654i	$-0.707652\pi$
$461$	−2.25897	+	1.50940i	−0.105211	+	0.0702997i	0.501852	+	0.864954i	$0.332652\pi$
$462$	9.92016	+	9.96581i	0.461528	+	0.463652i
$463$	−15.5966	+	15.5966i	−0.724834	+	0.724834i	−0.969586	−	0.244752i	$-0.921293\pi$
$463$	−15.5966	+	15.5966i	−0.724834	+	0.724834i	0.244752	+	0.969586i	$0.421293\pi$
$464$	6.12613	−	29.3853i	0.284398	−	1.36418i
$465$	−3.80614	−	3.80614i	−0.176506	−	0.176506i
$466$	0.0139118	−	6.06025i	0.000644453	−	0.280735i
$467$	4.30970	+	6.44993i	0.199429	+	0.298467i	0.917682	−	0.397315i	$-0.130058\pi$
$467$	4.30970	+	6.44993i	0.199429	+	0.298467i	−0.718253	+	0.695782i	$0.755058\pi$
$468$	0.834064	−	1.23594i	0.0385546	−	0.0571315i
$469$	6.71350	+	33.7511i	0.310001	+	1.55848i
$470$	−19.6658	−	29.5787i	−0.907115	−	1.36436i
$471$	3.66618	−	8.85093i	0.168928	−	0.407829i
$472$	7.36257	−	4.84650i	0.338890	−	0.223078i
$473$	−5.50370	−	13.2871i	−0.253060	−	0.610942i
$474$	0.299199	+	0.200914i	0.0137427	+	0.00922826i
$475$	−5.02837	+	7.52549i	−0.230717	+	0.345293i
$476$	7.37243	−	3.01418i	0.337915	−	0.138155i
$477$	0.0802364	+	0.0159600i	0.00367377	+	0.000730758i
$478$	−19.5500	−	8.15049i	−0.894195	−	0.372795i
$479$		−	2.22366i		−	0.101602i	−0.998709	−	0.0508009i	$-0.983823\pi$
$479$		−	2.22366i		−	0.101602i	0.998709	−	0.0508009i	$-0.0161774\pi$
$480$	−24.5230	−	10.4891i	−1.11932	−	0.478761i
$481$		−	15.3321i		−	0.699083i
$482$	1.67619	−	4.02055i	0.0763484	−	0.183131i
$483$	10.1046	+	2.00992i	0.459774	+	0.0914547i
$484$	−6.03301	+	14.3779i	−0.274228	+	0.653541i
$485$	18.9916	−	28.4229i	0.862363	−	1.29062i
$486$	0.974755	−	1.45160i	0.0442158	−	0.0658459i
$487$	−14.2601	−	34.4270i	−0.646187	−	1.56003i	−0.818196	−	0.574939i	$-0.805026\pi$
$487$	−14.2601	−	34.4270i	−0.646187	−	1.56003i	0.172009	−	0.985095i	$-0.444974\pi$
$488$	4.33099	+	2.93722i	0.196055	+	0.132962i
$489$	1.36927	−	3.30571i	0.0619204	−	0.149489i
$490$	9.09722	−	6.04841i	0.410970	−	0.273239i
$491$	7.46638	+	37.5360i	0.336953	+	1.69398i	0.662997	+	0.748622i	$0.269284\pi$
$491$	7.46638	+	37.5360i	0.336953	+	1.69398i	−0.326044	+	0.945355i	$0.605716\pi$
$492$	27.9273	−	5.42192i	1.25906	−	0.244439i
$493$	5.27861	+	7.89999i	0.237737	+	0.355798i
$494$	37.6770	+	0.0864909i	1.69517	+	0.00389141i
$495$	0.402241	+	0.402241i	0.0180794	+	0.0180794i
$496$	4.56624	+	0.0419299i	0.205030	+	0.00188271i
$497$	4.76279	−	4.76279i	0.213640	−	0.213640i
$498$	−16.3523	+	16.2774i	−0.732762	+	0.729406i
$499$	−18.1987	+	12.1600i	−0.814685	+	0.544355i	−0.891675	−	0.452677i	$-0.850469\pi$
$499$	−18.1987	+	12.1600i	−0.814685	+	0.544355i	0.0769897	+	0.997032i	$0.475469\pi$
$500$	8.46224	+	12.7914i	0.378443	+	0.572048i
$501$	5.56487	−	1.10692i	0.248620	−	0.0494536i
$502$	33.4706	+	6.73763i	1.49387	+	0.300715i
$503$	35.5491	+	14.7249i	1.58505	+	0.656551i	0.989204	−	0.146545i	$-0.0468153\pi$
$503$	35.5491	+	14.7249i	1.58505	+	0.656551i	0.595850	+	0.803096i	$0.296815\pi$
$504$	0.412006	−	0.975612i	0.0183522	−	0.0434572i
$505$	2.21016	−	0.915477i	0.0983507	−	0.0407382i
$506$	−0.905322	−	4.60660i	−0.0402465	−	0.204788i
$507$	−38.5060	−	25.7289i	−1.71011	−	1.14266i
$508$	29.5511	−	29.2809i	1.31112	−	1.29913i
$509$	−3.48480	+	17.5193i	−0.154461	+	0.776529i	0.823430	+	0.567417i	$0.192057\pi$
$509$	−3.48480	+	17.5193i	−0.154461	+	0.776529i	−0.977892	+	0.209112i	$0.932943\pi$
$510$	7.80721	−	3.21288i	0.345709	−	0.142269i
$511$	−44.8193			−1.98269
$512$	21.0794	−	8.22542i	0.931588	−	0.363516i
$513$	21.6443			0.955620
$514$	−25.2676	+	10.3983i	−1.11451	+	0.458649i
$515$	−1.73653	+	8.73014i	−0.0765207	+	0.384696i
$516$	−20.1600	+	19.9757i	−0.887495	+	0.879383i
$517$	−14.0011	−	9.35524i	−0.615768	−	0.411443i
$518$	−2.09998	−	10.6855i	−0.0922680	−	0.469493i
$519$	−23.5836	+	9.76865i	−1.03521	+	0.428796i
$520$	−18.3982	+	43.5660i	−0.806812	+	1.91050i
$521$	13.5272	+	5.60316i	0.592639	+	0.245479i	0.658785	−	0.752331i	$-0.271071\pi$
$521$	13.5272	+	5.60316i	0.592639	+	0.245479i	−0.0661468	+	0.997810i	$0.521071\pi$
$522$	1.23849	+	0.249308i	0.0542073	+	0.0109119i
$523$	−23.5557	+	4.68553i	−1.03002	+	0.204884i	−0.681040	−	0.732246i	$-0.738472\pi$
$523$	−23.5557	+	4.68553i	−1.03002	+	0.204884i	−0.348980	+	0.937130i	$0.613472\pi$
$524$	−1.15782	−	1.75014i	−0.0505796	−	0.0764553i
$525$	9.82702	−	6.56621i	0.428886	−	0.286573i
$526$	27.9906	−	27.8623i	1.22045	−	1.21486i
$527$	−1.02205	+	1.02205i	−0.0445214	+	0.0445214i
$528$	−12.6441	−	0.116105i	−0.550262	−	0.00505283i
$529$	13.8312	+	13.8312i	0.601357	+	0.601357i
$530$	−2.59471	−	0.00595638i	−0.112707	−	0.000258728i
$531$	0.206105	+	0.308457i	0.00894418	+	0.0133859i
$532$	26.2703	−	5.10022i	1.13896	−	0.221123i
$533$	−9.84069	−	49.4725i	−0.426247	−	2.14289i
$534$	25.2604	−	16.7947i	1.09313	−	0.726779i
$535$	−6.28581	+	15.1753i	−0.271759	+	0.656085i
$536$	−25.6105	−	17.3687i	−1.10621	−	0.750213i
$537$	3.16157	+	7.63271i	0.136432	+	0.329376i
$538$	12.8216	−	19.0938i	0.552777	−	0.823192i
$539$	2.87729	−	4.30618i	0.123934	−	0.185480i
$540$	−10.5117	+	25.0515i	−0.452351	+	1.07804i
$541$	12.8082	+	2.54771i	0.550668	+	0.109535i	0.462579	−	0.886578i	$-0.346924\pi$
$541$	12.8082	+	2.54771i	0.550668	+	0.109535i	0.0880890	+	0.996113i	$0.471924\pi$
$542$	−1.89939	+	4.55594i	−0.0815860	+	0.195694i
$543$		−	11.9975i		−	0.514860i
$544$	−2.81662	+	6.58512i	−0.120762	+	0.282335i
$545$		−	7.67427i		−	0.328730i
$546$	−45.4115	−	18.9323i	−1.94343	−	0.810229i
$547$	−26.9082	−	5.35238i	−1.15051	−	0.228851i	−0.417247	−	0.908793i	$-0.637005\pi$
$547$	−26.9082	−	5.35238i	−1.15051	−	0.228851i	−0.733266	+	0.679942i	$0.762005\pi$
$548$	22.2697	−	9.10487i	0.951316	−	0.388941i
$549$	−0.122361	+	0.183126i	−0.00522224	+	0.00781564i
$550$	−4.47116	−	3.00240i	−0.190651	−	0.128023i
$551$	12.2164	+	29.4931i	0.520438	+	1.25645i
$552$	−7.73830	+	5.09384i	−0.329364	+	0.216808i
$553$	0.173688	−	0.419319i	0.00738595	−	0.0178313i
$554$	−21.5798	−	32.4575i	−0.916838	−	1.37899i
$555$	−2.25192	−	11.3212i	−0.0955886	−	0.480556i
$556$	−7.50602	+	11.1227i	−0.318326	+	0.471706i
$557$	6.63444	+	9.92914i	0.281110	+	0.420711i	0.944976	−	0.327141i	$-0.106085\pi$
$557$	6.63444	+	9.92914i	0.281110	+	0.420711i	−0.663865	+	0.747852i	$0.731085\pi$
$558$	−0.000441184		0.192188i	−1.86768e−5		0.00813596i
$559$	35.5821	+	35.5821i	1.50496	+	1.50496i
$560$	−6.85523	+	32.8826i	−0.289686	+	1.38955i
$561$	2.83010	−	2.83010i	0.119487	−	0.119487i
$562$	−14.9726	−	15.0415i	−0.631581	−	0.634487i
$563$	−27.6327	+	18.4636i	−1.16458	+	0.778148i	−0.978875	−	0.204458i	$-0.934457\pi$
$563$	−27.6327	+	18.4636i	−1.16458	+	0.778148i	−0.185705	+	0.982606i	$0.559457\pi$
$564$	−6.63228	+	32.5607i	−0.279270	+	1.37105i
$565$	1.46286	−	0.290981i	0.0615429	−	0.0122417i
$566$	−7.56197	+	37.5657i	−0.317853	+	1.57900i
$567$	−27.1502	−	11.2460i	−1.14020	−	0.472286i
$568$	−0.0417118	+	6.05673i	−0.00175019	+	0.254135i
$569$	−31.9367	+	13.2286i	−1.33886	+	0.554572i	−0.933168	−	0.359440i	$-0.882968\pi$
$569$	−31.9367	+	13.2286i	−1.33886	+	0.554572i	−0.405687	+	0.914012i	$0.632968\pi$
$570$	27.8333	−	5.47000i	1.16581	−	0.229113i
$571$	18.6137	+	12.4373i	0.778959	+	0.520484i	0.880328	−	0.474365i	$-0.157322\pi$
$571$	18.6137	+	12.4373i	0.778959	+	0.520484i	−0.101369	+	0.994849i	$0.532322\pi$
$572$	−0.102932	+	22.4195i	−0.00430382	+	0.937408i
$573$	−3.99502	+	20.0843i	−0.166895	+	0.839035i
$574$	−13.6344	−	33.1313i	−0.569089	−	1.38287i
$575$	−3.94595			−0.164558
$576$	0.352286	+	0.884768i	0.0146786	+	0.0368653i
$577$	−46.1161			−1.91984			−0.959920	−	0.280274i	$-0.909575\pi$
$577$	−46.1161			−1.91984			−0.959920	+	0.280274i	$0.909575\pi$
$578$	8.28657	+	20.1362i	0.344676	+	0.837555i
$579$	−4.13491	+	20.7876i	−0.171841	+	0.863902i
$580$	−40.0688	−	0.183964i	−1.66377	−	0.00763867i
$581$	24.1597	+	16.1430i	1.00231	+	0.669725i
$582$	−31.3795	+	6.16693i	−1.30072	+	0.255627i
$583$	−1.13646	+	0.470735i	−0.0470672	+	0.0194959i
$584$	28.6941	−	28.3016i	1.18737	−	1.17113i
$585$	−1.83886	−	0.761680i	−0.0760275	−	0.0314916i
$586$	−5.96856	+	29.6501i	−0.246559	+	1.22483i
$587$	33.9240	−	6.74790i	1.40019	−	0.278516i	0.563468	−	0.826138i	$-0.309467\pi$
$587$	33.9240	−	6.74790i	1.40019	−	0.278516i	0.836726	+	0.547623i	$0.184467\pi$
$588$	−10.0144	−	2.03982i	−0.412986	−	0.0841209i
$589$	−4.03794	+	2.69807i	−0.166381	+	0.111172i
$590$	−8.30093	−	8.33913i	−0.341744	−	0.343317i
$591$	5.18963	−	5.18963i	0.213473	−	0.213473i
$592$	8.09188	+	5.51497i	0.332574	+	0.226664i
$593$	23.3579	+	23.3579i	0.959194	+	0.959194i	0.999199	−	0.0400057i	$-0.0127376\pi$
$593$	23.3579	+	23.3579i	0.959194	+	0.959194i	−0.0400057	+	0.999199i	$0.512738\pi$
$594$	−0.0295658	+	12.8794i	−0.00121310	+	0.528449i
$595$	−5.90685	−	8.84022i	−0.242157	−	0.362414i
$596$	−11.6509	−	7.86248i	−0.477239	−	0.322060i
$597$	−6.22066	−	31.2734i	−0.254595	−	1.27993i
$598$	9.09463	+	13.6789i	0.371907	+	0.559374i
$599$	16.4727	−	39.7685i	0.673055	−	1.62490i	−0.103336	−	0.994647i	$-0.532952\pi$
$599$	16.4727	−	39.7685i	0.673055	−	1.62490i	0.776391	−	0.630252i	$-0.217048\pi$
$600$	−2.14514	+	10.4092i	−0.0875748	+	0.424952i
$601$	14.2850	+	34.4871i	0.582698	+	1.40676i	0.890358	+	0.455260i	$0.150454\pi$
$601$	14.2850	+	34.4871i	0.582698	+	1.40676i	−0.307661	+	0.951496i	$0.599546\pi$
$602$	29.6720	+	19.9249i	1.20934	+	0.812078i
$603$	0.723559	−	1.08288i	0.0294656	−	0.0440984i
$604$	−6.56660	−	16.0613i	−0.267191	−	0.653527i
$605$	20.4140	+	4.06059i	0.829946	+	0.165086i
$606$	−2.06568	−	0.861192i	−0.0839124	−	0.0349835i
$607$		−	4.05117i		−	0.164432i	−0.996615	−	0.0822160i	$-0.973800\pi$
$607$		−	4.05117i		−	0.164432i	0.996615	−	0.0822160i	$-0.0261997\pi$
$608$	−13.5981	+	19.8539i	−0.551477	+	0.805181i
$609$		−	41.6862i		−	1.68921i
$610$	2.68804	−	6.44759i	0.108835	−	0.261055i
$611$	57.7859	+	11.4943i	2.33777	+	0.465011i
$612$	−0.277959	−	0.116632i	−0.0112358	−	0.00471458i
$613$	7.80817	−	11.6857i	0.315369	−	0.471983i	−0.639592	−	0.768715i	$-0.720897\pi$
$613$	7.80817	−	11.6857i	0.315369	−	0.471983i	0.954961	+	0.296732i	$0.0958967\pi$
$614$	−19.7721	+	29.4446i	−0.797939	+	1.18829i
$615$	−14.5327	−	35.0849i	−0.586013	−	1.41476i
$616$	2.99899	+	15.6391i	0.120833	+	0.630116i
$617$	15.0351	−	36.2979i	0.605289	−	1.46130i	−0.262781	−	0.964855i	$-0.584640\pi$
$617$	15.0351	−	36.2979i	0.605289	−	1.46130i	0.868070	−	0.496441i	$-0.165360\pi$
$618$	6.93444	−	4.61046i	0.278944	−	0.185460i
$619$	−3.87037	−	19.4577i	−0.155563	−	0.782070i	−0.977243	−	0.212121i	$-0.931963\pi$
$619$	−3.87037	−	19.4577i	−0.155563	−	0.782070i	0.821680	−	0.569949i	$-0.193037\pi$
$620$	−1.16174	−	5.98391i	−0.0466566	−	0.240320i
$621$	5.24260	+	7.84611i	0.210378	+	0.314853i
$622$	−19.1199	−	0.0438914i	−0.766639	−	0.00175989i
$623$	−27.0123	−	27.0123i	−1.08223	−	1.08223i
$624$	41.0282	−	16.5547i	1.64244	−	0.662720i
$625$	21.9990	−	21.9990i	0.879961	−	0.879961i
$626$	−10.1565	+	10.1100i	−0.405936	+	0.404076i
$627$	11.1812	−	7.47103i	0.446533	−	0.298364i
$628$	9.04826	−	5.98595i	0.361065	−	0.238865i
$629$	−3.04005	+	0.604703i	−0.121215	+	0.0241111i
$630$	−1.38589	−	0.278980i	−0.0552152	−	0.0111148i
$631$	−1.83341	−	0.759422i	−0.0729868	−	0.0302321i	0.345891	−	0.938275i	$-0.387577\pi$
$631$	−1.83341	−	0.759422i	−0.0729868	−	0.0302321i	−0.418878	+	0.908042i	$0.637577\pi$
$632$	0.153585	+	0.378132i	0.00610929	+	0.0150413i
$633$	−25.8622	+	10.7125i	−1.02793	+	0.425782i
$634$	−2.70359	−	13.7568i	−0.107373	−	0.546353i
$635$	−46.1734	−	30.8521i	−1.83233	−	1.22433i
$636$	1.70854	+	1.72430i	0.0677480	+	0.0683730i
$637$	−3.53519	+	17.7726i	−0.140069	+	0.704177i
$638$	−17.5665	+	7.22908i	−0.695464	+	0.286202i
$639$	−0.254916			−0.0100843
$640$	−16.3752	−	25.3808i	−0.647287	−	1.00327i
$641$	9.28564			0.366761			0.183380	−	0.983042i	$-0.441296\pi$
$641$	9.28564			0.366761			0.183380	+	0.983042i	$0.441296\pi$
$642$	14.2103	−	5.84791i	0.560835	−	0.230798i
$643$	2.48018	−	12.4687i	0.0978086	−	0.491717i	−0.900566	−	0.434720i	$-0.856847\pi$
$643$	2.48018	−	12.4687i	0.0978086	−	0.491717i	0.998374	−	0.0569971i	$-0.0181526\pi$
$644$	8.21193	+	8.28768i	0.323595	+	0.326580i
$645$	31.4999	+	21.0476i	1.24031	+	0.828747i
$646$	−1.46885	−	7.47402i	−0.0577910	−	0.294061i
$647$	−3.35949	+	1.39155i	−0.132075	+	0.0547073i	−0.447742	−	0.894163i	$-0.647772\pi$
$647$	−3.35949	+	1.39155i	−0.132075	+	0.0547073i	0.315667	+	0.948870i	$0.397772\pi$
$648$	24.4834	−	9.94436i	0.961798	−	0.390651i
$649$	−5.15352	−	2.13466i	−0.202293	−	0.0837927i
$650$	18.4734	+	3.71870i	0.724588	+	0.145860i
$651$	6.21978	−	1.23719i	0.243772	−	0.0484893i
$652$	3.37941	−	2.23567i	0.132348	−	0.0875557i
$653$	3.60748	−	2.41044i	0.141172	−	0.0943279i	−0.482979	−	0.875632i	$-0.660445\pi$
$653$	3.60748	−	2.41044i	0.141172	−	0.0943279i	0.624151	+	0.781304i	$0.285445\pi$
$654$	−5.08827	+	5.06497i	−0.198967	+	0.198056i
$655$	−1.98074	+	1.98074i	−0.0773941	+	0.0773941i
$656$	29.6500	+	12.6016i	1.15764	+	0.492011i
$657$	1.19942	+	1.19942i	0.0467939	+	0.0467939i
$658$	41.8474	+	0.0960643i	1.63138	+	0.00374498i
$659$	−17.8435	−	26.7046i	−0.695083	−	1.04026i	−0.996235	−	0.0866888i	$-0.972371\pi$
$659$	−17.8435	−	26.7046i	−0.695083	−	1.04026i	0.301153	−	0.953576i	$-0.402629\pi$
$660$	3.21689	+	16.5696i	0.125217	+	0.644972i
$661$	−4.81079	−	24.1855i	−0.187118	−	0.940706i	−0.954203	−	0.299160i	$-0.903293\pi$
$661$	−4.81079	−	24.1855i	−0.187118	−	0.940706i	0.767085	−	0.641546i	$-0.221707\pi$
$662$	21.3631	−	14.2035i	0.830300	−	0.552036i
$663$	−5.35906	+	12.9379i	−0.208129	+	0.502467i
$664$	−25.6611	+	4.92085i	−0.995845	+	0.190966i
$665$	−13.6704	−	33.0033i	−0.530115	−	1.27981i
$666$	−0.229758	+	0.342155i	−0.00890295	+	0.0132582i
$667$	−7.73228	+	11.5722i	−0.299395	+	0.448077i
$668$	5.92495	+	2.48612i	0.229243	+	0.0961910i
$669$	−16.9377	−	3.36911i	−0.654848	−	0.130257i
$670$	−15.8952	+	38.1266i	−0.614085	+	1.47296i
$671$		−	3.31165i		−	0.127845i
$672$	26.3266	−	17.1571i	1.01557	−	0.661849i
$673$			44.2289i			1.70490i	0.522811	+	0.852449i	$0.324883\pi$
$673$			44.2289i			1.70490i	−0.522811	+	0.852449i	$0.675117\pi$
$674$	−12.8088	−	5.34006i	−0.493376	−	0.205691i
$675$	10.6173	+	2.11191i	0.408659	+	0.0812874i
$676$	−19.8470	−	48.5442i	−0.763347	−	1.86708i
$677$	−18.1929	+	27.2277i	−0.699212	+	1.04644i	0.296599	+	0.955002i	$0.404148\pi$
$677$	−18.1929	+	27.2277i	−0.699212	+	1.04644i	−0.995810	+	0.0914418i	$0.970852\pi$
$678$	−1.15841	−	0.777874i	−0.0444883	−	0.0298741i
$679$	15.4121	+	37.2082i	0.591463	+	1.42792i
$680$	9.36390	+	1.92973i	0.359089	+	0.0740017i
$681$	−5.72510	+	13.8216i	−0.219386	+	0.529645i
$682$	−1.59996	−	2.40646i	−0.0612658	−	0.0921479i
$683$	−2.97371	−	14.9498i	−0.113786	−	0.572040i	−0.995047	−	0.0994097i	$-0.968305\pi$
$683$	−2.97371	−	14.9498i	−0.113786	−	0.572040i	0.881261	−	0.472630i	$-0.156695\pi$
$684$	−0.839515	−	0.566538i	−0.0320996	−	0.0216621i
$685$	−17.8427	−	26.7035i	−0.681734	−	1.02029i
$686$	0.0419335	−	18.2670i	0.00160103	−	0.697438i
$687$	15.9884	+	15.9884i	0.609997	+	0.609997i
$688$	−31.5783	+	5.98042i	−1.20391	+	0.228001i
$689$	3.04337	−	3.04337i	0.115943	−	0.115943i
$690$	8.72456	+	8.76470i	0.332138	+	0.333667i
$691$	36.9458	−	24.6864i	1.40549	−	0.939115i	0.405802	−	0.913961i	$-0.366992\pi$
$691$	36.9458	−	24.6864i	1.40549	−	0.939115i	0.999684	−	0.0251542i	$-0.00800767\pi$
$692$	−28.3261	−	5.76973i	−1.07680	−	0.219332i
$693$	−0.657319	+	0.130749i	−0.0249695	+	0.00496674i
$694$	−7.01041	+	34.8257i	−0.266112	+	1.32197i
$695$	16.5485	+	6.85462i	0.627721	+	0.260010i
$696$	26.3231	+	26.6882i	0.997776	+	1.01161i
$697$	−9.42128	+	3.90242i	−0.356857	+	0.147815i
$698$	−3.15531	+	0.620103i	−0.119430	+	0.0234712i
$699$	6.29265	+	4.20461i	0.238010	+	0.159033i
$700$	13.3841	+	0.0614492i	0.505873	+	0.00232256i
$701$	6.76034	−	33.9865i	0.255335	−	1.28365i	−0.613951	−	0.789344i	$-0.710421\pi$
$701$	6.76034	−	33.9865i	0.255335	−	1.28365i	0.869286	−	0.494310i	$-0.164579\pi$
$702$	−17.1496	−	41.6731i	−0.647270	−	1.57285i
$703$	−10.4143			−0.392783
$704$	−11.7954	−	8.11865i	−0.444557	−	0.305983i
$705$	44.3572			1.67059
$706$	7.26287	+	17.6486i	0.273342	+	0.664214i
$707$	−0.549851	+	2.76429i	−0.0206793	+	0.103962i
$708$	−0.0505378	+	11.0075i	−0.00189933	+	0.413689i
$709$	−16.8515	−	11.2598i	−0.632870	−	0.422870i	0.197329	−	0.980337i	$-0.436773\pi$
$709$	−16.8515	−	11.2598i	−0.632870	−	0.422870i	−0.830199	+	0.557467i	$0.811773\pi$
$710$	7.93343	−	1.55913i	0.297736	−	0.0585133i
$711$	−0.0158696	+	0.00657341i	−0.000595157	+	0.000246522i
$712$	34.3510	+	0.236570i	1.28736	+	0.00886584i
$713$	−1.95611	−	0.810247i	−0.0732568	−	0.0303440i
$714$	−1.96286	+	9.75090i	−0.0734580	+	0.364918i
$715$	29.3526	−	5.83860i	1.09773	−	0.218351i
$716$	−1.86734	+	9.16760i	−0.0697859	+	0.342609i
$717$	21.9931	−	14.6953i	0.821348	−	0.548807i
$718$	20.7056	+	20.8009i	0.772727	+	0.776283i
$719$	−22.8834	+	22.8834i	−0.853406	+	0.853406i	−0.990551	−	0.137145i	$-0.956207\pi$
$719$	−22.8834	+	22.8834i	−0.853406	+	0.853406i	0.137145	+	0.990551i	$0.456207\pi$
$720$	1.06344	−	0.696526i	0.0396319	−	0.0259580i
$721$	−7.41538	−	7.41538i	−0.276163	−	0.276163i
$722$	−0.00293342	+	1.27785i	−0.000109171	+	0.0475567i
$723$	3.02217	+	4.52300i	0.112396	+	0.168212i
$724$	7.60006	−	11.2620i	0.282454	−	0.418549i
$725$	3.11484	+	15.6594i	0.115682	+	0.581575i
$726$	−10.7808	−	16.2150i	−0.400112	−	0.601796i
$727$	−13.3809	+	32.3043i	−0.496269	+	1.19810i	0.455210	+	0.890384i	$0.349564\pi$
$727$	−13.3809	+	32.3043i	−0.496269	+	1.19810i	−0.951479	+	0.307715i	$0.900436\pi$
$728$	−30.6347	−	46.5388i	−1.13540	−	1.72484i
$729$	−9.89057	−	23.8779i	−0.366317	−	0.884368i
$730$	−44.6640	−	29.9921i	−1.65309	−	1.11006i
$731$	5.65186	−	8.45860i	0.209042	−	0.312853i
$732$	−6.04903	+	2.47312i	−0.223579	+	0.0914090i
$733$	−41.3984	−	8.23465i	−1.52908	−	0.304154i	−0.642342	−	0.766418i	$-0.722037\pi$
$733$	−41.3984	−	8.23465i	−1.52908	−	0.304154i	−0.886742	+	0.462264i	$0.847037\pi$
$734$	17.0884	+	7.12425i	0.630744	+	0.262961i
$735$			13.6425i			0.503210i
$736$	−10.4908	−	0.120417i	−0.386694	−	0.00443864i
$737$			19.5828i			0.721341i
$738$	−0.521761	+	1.25151i	−0.0192063	+	0.0460686i
$739$	−9.79618	−	1.94858i	−0.360358	−	0.0716797i	0.0115908	−	0.999933i	$-0.496310\pi$
$739$	−9.79618	−	1.94858i	−0.360358	−	0.0716797i	−0.371949	+	0.928253i	$0.621310\pi$
$740$	5.05777	−	12.0537i	0.185927	−	0.443103i
$741$	−26.1404	+	39.1219i	−0.960292	+	1.43718i
$742$	1.70419	−	2.53787i	0.0625628	−	0.0931682i
$743$	10.3765	+	25.0512i	0.380678	+	0.919039i	0.991835	+	0.127529i	$0.0407046\pi$
$743$	10.3765	+	25.0512i	0.380678	+	0.919039i	−0.611157	+	0.791510i	$0.709295\pi$
$744$	−3.20077	+	4.71961i	−0.117346	+	0.173029i
$745$	−7.18014	+	17.3344i	−0.263060	+	0.635083i
$746$	−15.3501	+	10.2057i	−0.562008	+	0.373659i
$747$	−0.214537	−	1.07855i	−0.00784951	−	0.0394622i
$748$	4.44941	−	0.863825i	0.162686	−	0.0315846i
$749$	−10.7513	−	16.0905i	−0.392845	−	0.587934i
$750$	−19.1531	−	0.0439677i	−0.699374	−	0.00160547i
$751$	23.4465	+	23.4465i	0.855575	+	0.855575i	0.990813	−	0.135238i	$-0.0431800\pi$
$751$	23.4465	+	23.4465i	0.855575	+	0.855575i	−0.135238	+	0.990813i	$0.543180\pi$
$752$	−26.8521	+	26.3634i	−0.979194	+	0.961375i
$753$	−30.1488	+	30.1488i	−1.09868	+	1.09868i
$754$	47.1053	−	46.8896i	1.71547	−	1.70762i
$755$	−19.2590	+	12.8685i	−0.700908	+	0.468332i
$756$	−17.6600	−	26.6946i	−0.642288	−	0.970872i
$757$	−34.9718	+	6.95632i	−1.27107	+	0.252832i	−0.784127	−	0.620601i	$-0.786889\pi$
$757$	−34.9718	+	6.95632i	−1.27107	+	0.252832i	−0.486945	+	0.873433i	$0.661889\pi$
$758$	−7.69638	−	1.54928i	−0.279545	−	0.0562724i
$759$	5.41652	+	2.24360i	0.196607	+	0.0814374i
$760$	29.5922	+	12.4969i	1.07342	+	0.453312i
$761$	41.9043	−	17.3573i	1.51903	−	0.629202i	0.541632	−	0.840616i	$-0.317807\pi$
$761$	41.9043	−	17.3573i	1.51903	−	0.629202i	0.977397	+	0.211413i	$0.0678065\pi$
$762$	10.0183	+	50.9765i	0.362923	+	1.84668i
$763$	7.51770	+	5.02316i	0.272159	+	0.181851i
$764$	−16.4730	+	16.3224i	−0.595973	+	0.590525i
$765$	−0.0785008	+	0.394650i	−0.00283820	+	0.0142686i
$766$	10.2189	−	4.20534i	0.369223	−	0.151945i
$767$	19.5174			0.704731
$768$	−6.02073	+	27.6084i	−0.217254	+	0.996233i
$769$	−0.661601			−0.0238579			−0.0119290	−	0.999929i	$-0.503797\pi$
$769$	−0.661601			−0.0238579			−0.0119290	+	0.999929i	$0.503797\pi$
$770$	19.6572	−	8.08946i	0.708396	−	0.291524i
$771$	6.65684	−	33.4662i	0.239740	−	1.20526i
$772$	−17.0498	+	16.8940i	−0.613636	+	0.608027i
$773$	−20.9389	−	13.9909i	−0.753119	−	0.503218i	0.118770	−	0.992922i	$-0.462105\pi$
$773$	−20.9389	−	13.9909i	−0.753119	−	0.503218i	−0.871889	+	0.489704i	$0.837105\pi$
$774$	−0.260846	−	1.32728i	−0.00937590	−	0.0477079i
$775$	−2.24401	+	0.929499i	−0.0806072	+	0.0333886i
$776$	−33.3626	−	14.0892i	−1.19765	−	0.505772i
$777$	12.5642	+	5.20425i	0.450737	+	0.186701i
$778$	30.7892	+	6.19787i	1.10385	+	0.222204i
$779$	−33.6042	+	6.68429i	−1.20399	+	0.239489i
$780$	−32.5851	−	49.2551i	−1.16673	−	1.76362i
$781$	3.18701	−	2.12950i	0.114040	−	0.0761993i
$782$	2.35357	−	2.34279i	0.0841634	−	0.0837779i
$783$	26.9986	−	26.9986i	0.964852	−	0.964852i
$784$	−8.10833	−	8.25862i	−0.289583	−	0.294951i
$785$	−10.2405	−	10.2405i	−0.365498	−	0.365498i
$786$	2.62057	+	0.00601575i	0.0934726	+	0.000214575i
$787$	24.2752	+	36.3304i	0.865318	+	1.29504i	0.954253	+	0.299002i	$0.0966537\pi$
$787$	24.2752	+	36.3304i	0.865318	+	1.29504i	−0.0889350	+	0.996037i	$0.528346\pi$
$788$	8.15900	−	1.58402i	0.290652	−	0.0564283i
$789$	9.62195	+	48.3728i	0.342551	+	1.72212i
$790$	0.453685	−	0.301638i	0.0161414	−	0.0107318i
$791$	−0.672464	+	1.62347i	−0.0239101	+	0.0577240i
$792$	0.338264	−	0.498778i	0.0120197	−	0.0177233i
$793$	4.43421	+	10.7051i	0.157463	+	0.380150i
$794$	−23.3381	+	34.7549i	−0.828237	+	1.23341i
$795$	1.80021	−	2.69421i	0.0638470	−	0.0955538i
$796$	13.9715	−	33.2969i	0.495206	−	1.18018i
$797$	−15.2693	−	3.03726i	−0.540867	−	0.107585i	−0.0829060	−	0.996557i	$-0.526420\pi$
$797$	−15.2693	−	3.03726i	−0.540867	−	0.107585i	−0.457961	+	0.888972i	$0.651420\pi$
$798$	−12.8598	+	30.8458i	−0.455231	+	1.09193i
$799$		−	11.9111i		−	0.421386i
$800$	−8.60756	+	8.41220i	−0.304323	+	0.297416i
$801$			1.44577i			0.0510837i
$802$	26.3211	+	10.9734i	0.929432	+	0.387485i
$803$	−25.0150	−	4.97579i	−0.882760	−	0.175592i
$804$	35.7698	−	14.6243i	1.26150	−	0.515759i
$805$	8.65255	−	12.9495i	0.304962	−	0.456408i
$806$	8.39417	+	5.63672i	0.295672	+	0.198545i
$807$	10.9913	+	26.5353i	0.386912	+	0.934088i
$808$	−1.39351	−	2.11695i	−0.0490235	−	0.0744741i
$809$	−11.9884	+	28.9426i	−0.421490	+	1.01757i	0.560419	+	0.828209i	$0.310640\pi$
$809$	−11.9884	+	28.9426i	−0.421490	+	1.01757i	−0.981908	+	0.189357i	$0.939360\pi$
$810$	−19.5305	−	29.3753i	−0.686233	−	1.03214i
$811$	−4.91692	−	24.7190i	−0.172656	−	0.868002i	−0.965864	−	0.259050i	$-0.916590\pi$
$811$	−4.91692	−	24.7190i	−0.172656	−	0.868002i	0.793208	−	0.608951i	$-0.208410\pi$
$812$	26.4071	−	39.1309i	0.926706	−	1.37322i
$813$	−3.42461	−	5.12529i	−0.120106	−	0.179752i
$814$	0.0142258	−	6.19702i	0.000498614	−	0.217205i
$815$	−3.82468	−	3.82468i	−0.133973	−	0.133973i
$816$	−4.90064	−	7.48216i	−0.171557	−	0.261928i
$817$	24.1692	−	24.1692i	0.845572	−	0.845572i
$818$	−14.6967	−	14.7644i	−0.513859	−	0.516224i
$819$	1.94976	−	1.30279i	0.0681300	−	0.0455230i
$820$	8.58354	−	42.1403i	0.299750	−	1.47160i
$821$	−26.8954	+	5.34982i	−0.938655	+	0.186710i	−0.640632	−	0.767848i	$-0.721327\pi$
$821$	−26.8954	+	5.34982i	−0.938655	+	0.186710i	−0.298024	+	0.954559i	$0.596327\pi$
$822$	−5.92915	+	29.4543i	−0.206803	+	1.02734i
$823$	−28.5108	−	11.8096i	−0.993824	−	0.411655i	−0.174295	−	0.984693i	$-0.555765\pi$
$823$	−28.5108	−	11.8096i	−0.993824	−	0.411655i	−0.819529	+	0.573038i	$0.805765\pi$
$824$	9.42996	+	0.0649428i	0.328508	+	0.00226239i
$825$	6.21373	−	2.57381i	0.216334	−	0.0896086i
$826$	13.6023	−	2.67323i	0.473286	−	0.0930135i
$827$	44.8557	+	29.9716i	1.55978	+	1.04221i	0.972520	+	0.232820i	$0.0747953\pi$
$827$	44.8557	+	29.9716i	1.55978	+	1.04221i	0.587265	+	0.809395i	$0.300205\pi$
$828$	0.00202724	−	0.441550i	7.04516e−5	−	0.0153449i
$829$	0.547508	−	2.75251i	0.0190157	−	0.0955985i	−0.970112	−	0.242658i	$-0.921981\pi$
$829$	0.547508	−	2.75251i	0.0190157	−	0.0955985i	0.989128	+	0.147059i	$0.0469808\pi$
$830$	13.2735	+	32.2542i	0.460729	+	1.11956i
$831$	48.6743			1.68849
$832$	49.0002	+	10.4503i	1.69878	+	0.362300i
$833$	3.66339			0.126929
$834$	−6.37708	−	15.4962i	−0.220820	−	0.536588i
$835$	1.67332	−	8.41233i	0.0579075	−	0.291121i
$836$	15.2285	+	0.0699169i	0.526688	+	0.00241813i
$837$	4.82960	+	3.22704i	0.166936	+	0.111543i
$838$	−10.4762	+	2.05887i	−0.361896	+	0.0711224i
$839$	−25.0080	+	10.3586i	−0.863371	+	0.357620i	−0.770025	−	0.638014i	$-0.779756\pi$
$839$	−25.0080	+	10.3586i	−0.863371	+	0.357620i	−0.0933462	+	0.995634i	$0.529756\pi$
$840$	−29.4560	−	29.8645i	−1.01633	−	1.03042i
$841$	25.2350	+	10.4527i	0.870171	+	0.360437i
$842$	−0.922146	+	4.58096i	−0.0317793	+	0.157870i
$843$	25.9945	−	5.17062i	0.895297	−	0.178086i
$844$	−31.0629	−	6.32718i	−1.06923	−	0.217791i
$845$	−58.2089	+	38.8939i	−2.00245	+	1.33799i
$846$	−1.11732	−	1.12246i	−0.0384142	−	0.0385909i
$847$	−17.3396	+	17.3396i	−0.595797	+	0.595797i
$848$	0.511510	+	2.70091i	0.0175653	+	0.0927498i
$849$	−33.8374	−	33.8374i	−1.16130	−	1.16130i
$850$	0.00874523	−	3.80958i	0.000299959	−	0.130668i
$851$	−2.52251	−	3.77521i	−0.0864707	−	0.129413i
$852$	−6.26976	−	4.23109i	−0.214799	−	0.144955i
$853$	−1.05082	−	5.28282i	−0.0359793	−	0.180880i	0.958617	−	0.284699i	$-0.0918937\pi$
$853$	−1.05082	−	5.28282i	−0.0359793	−	0.180880i	−0.994596	+	0.103819i	$0.966894\pi$
$854$	4.55660	+	6.85344i	0.155924	+	0.234520i
$855$	−0.517371	+	1.24905i	−0.0176937	+	0.0427164i
$856$	17.0437	+	3.51239i	0.582541	+	0.120051i
$857$	16.2865	+	39.3192i	0.556337	+	1.34312i	0.912647	+	0.408749i	$0.134035\pi$
$857$	16.2865	+	39.3192i	0.556337	+	1.34312i	−0.356310	+	0.934368i	$0.615965\pi$
$858$	−23.2437	−	15.6082i	−0.793527	−	0.532856i
$859$	−6.15821	+	9.21642i	−0.210116	+	0.314460i	−0.921526	−	0.388317i	$-0.873057\pi$
$859$	−6.15821	+	9.21642i	−0.210116	+	0.314460i	0.711411	+	0.702777i	$0.248057\pi$
$860$	16.2359	+	39.7117i	0.553640	+	1.35416i
$861$	43.8814	+	8.72856i	1.49547	+	0.297468i
$862$	43.0347	+	17.9414i	1.46577	+	0.611087i
$863$		−	8.38657i		−	0.285482i	−0.989760	−	0.142741i	$-0.954408\pi$
$863$		−	8.38657i		−	0.285482i	0.989760	−	0.142741i	$-0.0455916\pi$
$864$	28.1628	+	5.93875i	0.958117	+	0.202040i
$865$			38.5884i			1.31204i
$866$	−3.11646	+	7.47522i	−0.105902	+	0.254018i
$867$	−26.6698	−	5.30495i	−0.905753	−	0.180166i
$868$	6.62224	+	2.77871i	0.224773	+	0.0943155i
$869$	0.143493	−	0.214752i	0.00486766	−	0.00728496i
$870$	27.8955	−	41.5417i	0.945745	−	1.40840i
$871$	−26.2208	−	63.3027i	−0.888459	−	2.14493i
$872$	−7.98488	+	1.53120i	−0.270402	+	0.0518531i
$873$	0.583289	−	1.40818i	0.0197414	−	0.0476598i
$874$	9.29143	−	6.17753i	0.314287	−	0.208958i
$875$	4.70570	+	23.6572i	0.159082	+	0.799758i
$876$	9.59229	+	49.4081i	0.324093	+	1.66935i
$877$	−21.5743	−	32.2883i	−0.728514	−	1.09030i	−0.992074	−	0.125655i	$-0.959897\pi$
$877$	−21.5743	−	32.2883i	−0.728514	−	1.09030i	0.263560	−	0.964643i	$-0.415103\pi$
$878$	−31.7949	−	0.0729880i	−1.07303	−	0.00246323i
$879$	−26.7074	−	26.7074i	−0.900819	−	0.900819i
$880$	−7.47671	+	17.5917i	−0.252040	+	0.593017i
$881$	−2.03075	+	2.03075i	−0.0684177	+	0.0684177i	−0.740488	−	0.672070i	$-0.765405\pi$
$881$	−2.03075	+	2.03075i	−0.0684177	+	0.0684177i	0.672070	+	0.740488i	$0.265405\pi$
$882$	0.345223	−	0.343642i	0.0116243	−	0.0115710i
$883$	34.7885	−	23.2450i	1.17073	−	0.782255i	0.190804	−	0.981628i	$-0.438890\pi$
$883$	34.7885	−	23.2450i	1.17073	−	0.782255i	0.979924	+	0.199373i	$0.0638905\pi$
$884$	−13.2264	+	8.75001i	−0.444851	+	0.294295i
$885$	14.4115	−	2.86664i	0.484439	−	0.0963609i
$886$	−48.8841	−	9.84036i	−1.64229	−	0.330593i
$887$	−14.6194	−	6.05554i	−0.490870	−	0.203325i	0.123498	−	0.992345i	$-0.460589\pi$
$887$	−14.6194	−	6.05554i	−0.490870	−	0.203325i	−0.614368	+	0.789020i	$0.710589\pi$
$888$	−11.3301	+	4.60191i	−0.380212	+	0.154430i
$889$	60.4452	−	25.0372i	2.02727	−	0.839721i
$890$	−8.84269	−	44.9948i	−0.296408	−	1.50823i
$891$	−13.9048	−	9.29089i	−0.465828	−	0.311257i
$892$	−13.7651	−	13.8921i	−0.460891	−	0.465143i
$893$	7.80752	−	39.2511i	0.261269	−	1.31349i
$894$	16.2321	−	6.67993i	0.542882	−	0.223410i
$895$	12.4889			0.417459
$896$	35.5813	+	0.571808i	1.18869	+	0.0191028i
$897$	−20.5134			−0.684922
$898$	5.68545	−	2.33972i	0.189726	−	0.0780773i
$899$	−1.67133	+	8.40234i	−0.0557419	+	0.280234i
$900$	−0.356532	−	0.359821i	−0.0118844	−	0.0119940i
$901$	−0.723471	−	0.483408i	−0.0241023	−	0.0161046i
$902$	−3.93157	−	20.0052i	−0.130907	−	0.666101i
$903$	−41.2363	+	17.0806i	−1.37226	+	0.568408i
$904$	−0.594634	−	1.46401i	−0.0197772	−	0.0486922i
$905$	−16.7558	−	6.94049i	−0.556983	−	0.230710i
$906$	21.2430	+	4.27622i	0.705752	+	0.142068i
$907$	−33.2090	+	6.60568i	−1.10269	+	0.219338i	−0.712690	−	0.701479i	$-0.752524\pi$
$907$	−33.2090	+	6.60568i	−1.10269	+	0.219338i	−0.389996	+	0.920817i	$0.627524\pi$
$908$	−14.1298	+	9.34766i	−0.468913	+	0.310213i
$909$	0.0886904	−	0.0592611i	0.00294168	−	0.00196556i
$910$	−52.7116	+	52.4702i	−1.74737	+	1.73937i
$911$	−0.835916	+	0.835916i	−0.0276951	+	0.0276951i	−0.720819	−	0.693124i	$-0.756234\pi$
$911$	−0.835916	+	0.835916i	−0.0276951	+	0.0276951i	0.693124	+	0.720819i	$0.256234\pi$
$912$	−11.2448	−	27.8684i	−0.372353	−	0.922816i
$913$	11.6921	+	11.6921i	0.386952	+	0.386952i
$914$	−7.04431	−	0.0161708i	−0.233005	−	0.000534883i
$915$	4.84653	+	7.25335i	0.160221	+	0.239788i
$916$	4.88011	+	25.1366i	0.161243	+	0.830536i
$917$	−0.643843	−	3.23682i	−0.0212616	−	0.106889i
$918$	−7.58657	+	5.04403i	−0.250394	+	0.166478i
$919$	16.7837	−	40.5195i	0.553645	−	1.33662i	−0.361079	−	0.932535i	$-0.617591\pi$
$919$	16.7837	−	40.5195i	0.553645	−	1.33662i	0.914723	−	0.404081i	$-0.132409\pi$
$920$	2.63754	+	13.7542i	0.0869572	+	0.453462i
$921$	−16.9497	−	40.9202i	−0.558511	−	1.34837i
$922$	2.14194	−	3.18976i	0.0705410	−	0.105049i
$923$	−7.45090	+	11.1511i	−0.245249	+	0.367042i
$924$	−18.3372	−	7.69432i	−0.603248	−	0.253125i
$925$	−5.10858	−	1.01616i	−0.167969	−	0.0334111i
$926$	12.0032	−	28.7912i	0.394450	−	0.946138i
$927$			0.396889i			0.0130356i
$928$	7.80328	+	41.7272i	0.256155	+	1.36976i
$929$		−	24.2586i		−	0.795898i	−0.917407	−	0.397949i	$-0.869722\pi$
$929$		−	24.2586i		−	0.795898i	0.917407	−	0.397949i	$-0.130278\pi$
$930$	7.02613	+	2.92923i	0.230396	+	0.0960533i
$931$	12.0721	+	2.40128i	0.395646	+	0.0786988i
$932$	3.24340	+	7.93309i	0.106241	+	0.259857i
$933$	13.2654	−	19.8531i	0.434291	−	0.649963i
$934$	−9.10756	−	6.11576i	−0.298008	−	0.200114i
$935$	−2.31536	−	5.58976i	−0.0757202	−	0.182805i
$936$	−0.425612	+	2.06526i	−0.0139116	+	0.0675051i
$937$	15.6361	−	37.7490i	0.510810	−	1.23320i	−0.432603	−	0.901585i	$-0.642405\pi$
$937$	15.6361	−	37.7490i	0.510810	−	1.23320i	0.943413	−	0.331620i	$-0.107595\pi$
$938$	−26.9446	−	40.5265i	−0.879772	−	1.32324i
$939$	−3.49137	−	17.5523i	−0.113937	−	0.572798i
$940$	41.6381	+	28.0990i	1.35808	+	0.916490i
$941$	32.3350	+	48.3927i	1.05409	+	1.57756i	0.790048	+	0.613045i	$0.210055\pi$
$941$	32.3350	+	48.3927i	1.05409	+	1.57756i	0.264041	+	0.964511i	$0.414945\pi$
$942$	−0.0311015	+	13.5484i	−0.00101334	+	0.441430i
$943$	−10.5625	−	10.5625i	−0.343964	−	0.343964i
$944$	−7.02041	+	10.3008i	−0.228495	+	0.335261i
$945$	−30.2119	+	30.2119i	−0.982793	+	0.982793i
$946$	14.3488	+	14.4148i	0.466520	+	0.468667i
$947$	22.2642	−	14.8765i	0.723489	−	0.483420i	−0.138490	−	0.990364i	$-0.544225\pi$
$947$	22.2642	−	14.8765i	0.723489	−	0.483420i	0.861979	+	0.506944i	$0.169225\pi$
$948$	−0.499424	−	0.101727i	−0.0162205	−	0.00330395i
$949$	87.5251	−	17.4098i	2.84119	−	0.565147i
$950$	2.52593	−	12.5481i	0.0819520	−	0.407114i
$951$	16.1755	+	6.70011i	0.524526	+	0.217266i
$952$	−8.01946	+	7.90976i	−0.259912	+	0.256357i
$953$	26.8881	−	11.1374i	0.870992	−	0.360777i	0.0979952	−	0.995187i	$-0.468757\pi$
$953$	26.8881	−	11.1374i	0.870992	−	0.360777i	0.772996	+	0.634410i	$0.218757\pi$
$954$	−0.113523	+	0.0223103i	−0.00367544	+	0.000722323i
$955$	25.7390	+	17.1982i	0.832894	+	0.556522i
$956$	29.9540	+	0.137525i	0.968783	+	0.00444787i
$957$	4.62796	−	23.2663i	0.149601	−	0.752093i
$958$	1.19677	+	2.90811i	0.0386657	+	0.0939568i
$959$	37.8375			1.22184
$960$	37.7165	+	0.519521i	1.21729	+	0.0167675i
$961$	29.6967			0.957959
$962$	8.25165	+	20.0513i	0.266044	+	0.646481i
$963$	−0.142883	+	0.718321i	−0.00460434	+	0.0231476i
$964$	−0.0282827	+	6.16021i	−0.000910925	+	0.198407i
$965$	26.6402	+	17.8004i	0.857579	+	0.573016i
$966$	−14.2965	+	2.80965i	−0.459982	+	0.0903990i
$967$	55.2681	−	22.8928i	1.77730	−	0.736183i	0.783984	−	0.620781i	$-0.213184\pi$
$967$	55.2681	−	22.8928i	1.77730	−	0.736183i	0.993319	−	0.115402i	$-0.0368157\pi$
$968$	0.151858	−	22.0504i	0.00488090	−	0.708726i
$969$	8.78808	+	3.64014i	0.282314	+	0.116938i
$970$	−9.54014	+	47.3927i	−0.306315	+	1.52169i
$971$	−38.4459	+	7.64736i	−1.23379	+	0.245415i	−0.768561	−	0.639777i	$-0.779027\pi$
$971$	−38.4459	+	7.64736i	−1.23379	+	0.245415i	−0.465226	+	0.885192i	$0.654027\pi$
$972$	−0.493543	+	2.42301i	−0.0158304	+	0.0777182i
$973$	−17.5465	+	11.7242i	−0.562516	+	0.375861i
$974$	37.1778	+	37.3489i	1.19125	+	1.19674i
$975$	−16.6400	+	16.6400i	−0.532907	+	0.532907i
$976$	−7.24488	−	1.51038i	−0.231903	−	0.0483461i
$977$	−13.4608	−	13.4608i	−0.430651	−	0.430651i	0.458199	−	0.888850i	$-0.348495\pi$
$977$	−13.4608	−	13.4608i	−0.430651	−	0.430651i	−0.888850	+	0.458199i	$0.848495\pi$
$978$	−0.0116160	+	5.06014i	−0.000371438	+	0.161805i
$979$	−12.0775	−	18.0753i	−0.385999	−	0.577688i
$980$	−8.64214	+	12.8062i	−0.276063	+	0.409079i
$981$	−0.0667568	−	0.335609i	−0.00213138	−	0.0107152i
$982$	−29.9663	−	45.0713i	−0.956262	−	1.43828i
$983$	5.14323	−	12.4169i	0.164044	−	0.396036i	−0.820387	−	0.571808i	$-0.806242\pi$
$983$	5.14323	−	12.4169i	0.164044	−	0.396036i	0.984431	+	0.175772i	$0.0562421\pi$
$984$	−33.6054	+	22.1212i	−1.07130	+	0.705197i
$985$	−4.24573	−	10.2501i	−0.135280	−	0.326595i
$986$	−11.1551	−	7.49071i	−0.355251	−	0.238553i
$987$	−29.0338	+	43.4522i	−0.924156	+	1.38310i
$988$	−49.3207	+	20.1645i	−1.56910	+	0.641518i
$989$	14.6155	+	2.90721i	0.464747	+	0.0924439i
$990$	−0.742535	−	0.309567i	−0.0235993	−	0.00983868i
$991$			48.2518i			1.53277i	0.642382	+	0.766385i	$0.277946\pi$
$991$			48.2518i			1.53277i	−0.642382	+	0.766385i	$0.722054\pi$
$992$	−5.99431	+	2.40270i	−0.190320	+	0.0762857i
$993$			32.0368i			1.01666i
$994$	−3.66547	+	8.79210i	−0.116262	+	0.278868i
$995$	−47.2755	−	9.40368i	−1.49873	−	0.298117i
$996$	12.6251	−	30.0883i	0.400042	−	0.953383i
$997$	−9.52673	+	14.2578i	−0.301715	+	0.451548i	−0.951087	−	0.308923i	$-0.900032\pi$
$997$	−9.52673	+	14.2578i	−0.301715	+	0.451548i	0.649373	+	0.760470i	$0.275032\pi$
$998$	17.2558	−	25.6973i	0.546224	−	0.813433i
$999$	4.76674	+	11.5079i	0.150813	+	0.364095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.61.1	yes	56
3.2	odd	2		576.2.bd.a.253.7		56
4.3	odd	2		256.2.i.a.81.2		56
8.3	odd	2		512.2.i.a.417.6		56
8.5	even	2		512.2.i.b.417.2		56
64.11	odd	16		512.2.i.a.97.6		56
64.21	even	16	inner	64.2.i.a.21.1	✓	56
64.43	odd	16		256.2.i.a.177.2		56
64.53	even	16		512.2.i.b.97.2		56
192.149	odd	16		576.2.bd.a.469.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.21.1	✓	56	64.21	even	16	inner
64.2.i.a.61.1	yes	56	1.1	even	1	trivial
256.2.i.a.81.2		56	4.3	odd	2
256.2.i.a.177.2		56	64.43	odd	16
512.2.i.a.97.6		56	64.11	odd	16
512.2.i.a.417.6		56	8.3	odd	2
512.2.i.b.97.2		56	64.53	even	16
512.2.i.b.417.2		56	8.5	even	2
576.2.bd.a.253.7		56	3.2	odd	2
576.2.bd.a.469.7		56	192.149	odd	16

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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	64.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30780 + 0.538195i) q^{2} +(0.344545 - 1.73215i) q^{3} +(1.42069 - 1.40771i) q^{4} +(-2.21982 - 1.48324i) q^{5} +(0.481636 + 2.45074i) q^{6} +(2.90595 - 1.20368i) q^{7} +(-1.10036 + 2.60561i) q^{8} +(-0.109979 - 0.0455548i) q^{9} +O(q^{10})\)	\(q+(-1.30780 + 0.538195i) q^{2} +(0.344545 - 1.73215i) q^{3} +(1.42069 - 1.40771i) q^{4} +(-2.21982 - 1.48324i) q^{5} +(0.481636 + 2.45074i) q^{6} +(2.90595 - 1.20368i) q^{7} +(-1.10036 + 2.60561i) q^{8} +(-0.109979 - 0.0455548i) q^{9} +(3.70136 + 0.745083i) q^{10} +(1.75553 - 0.349197i) q^{11} +(-1.94886 - 2.94586i) q^{12} +(-5.20730 + 3.47941i) q^{13} +(-3.15259 + 3.13815i) q^{14} +(-3.33401 + 3.33401i) q^{15} +(0.0367288 - 3.99983i) q^{16} +(0.895276 + 0.895276i) q^{17} +(0.168348 + 0.000386458i) q^{18} +(2.36339 + 3.53706i) q^{19} +(-5.24165 + 1.01763i) q^{20} +(-1.08373 - 5.44826i) q^{21} +(-2.10795 + 1.40150i) q^{22} +(-0.709741 + 1.71347i) q^{23} +(4.13417 + 2.80374i) q^{24} +(0.814201 + 1.96565i) q^{25} +(4.93752 - 7.35293i) q^{26} +(2.82675 - 4.23052i) q^{27} +(2.43403 - 5.80079i) q^{28} +(7.36008 + 1.46401i) q^{29} +(2.56588 - 6.15458i) q^{30} +1.14161i q^{31} +(2.10466 + 5.25075i) q^{32} -3.16115i q^{33} +(-1.65268 - 0.689010i) q^{34} +(-8.23605 - 1.63825i) q^{35} +(-0.220374 + 0.0900988i) q^{36} +(-1.36011 + 2.03555i) q^{37} +(-4.99448 - 3.35381i) q^{38} +(4.23269 + 10.2186i) q^{39} +(6.30735 - 4.15189i) q^{40} +(-3.08221 + 7.44112i) q^{41} +(4.34952 + 6.54198i) q^{42} +(-1.56753 - 7.88051i) q^{43} +(2.00250 - 2.96737i) q^{44} +(0.176565 + 0.264249i) q^{45} +(0.00602099 - 2.62285i) q^{46} +(-6.65222 - 6.65222i) q^{47} +(-6.91564 - 1.44174i) q^{48} +(2.04595 - 2.04595i) q^{49} +(-2.12272 - 2.13249i) q^{50} +(1.85921 - 1.24228i) q^{51} +(-2.49999 + 12.2735i) q^{52} +(-0.674026 + 0.134072i) q^{53} +(-1.41997 + 7.05403i) q^{54} +(-4.41491 - 1.82872i) q^{55} +(-0.0612673 + 8.89627i) q^{56} +(6.94100 - 2.87506i) q^{57} +(-10.4135 + 2.04653i) q^{58} +(-2.59120 - 1.73138i) q^{59} +(-0.0432946 + 9.42992i) q^{60} +(0.360949 - 1.81461i) q^{61} +(-0.614409 - 1.49300i) q^{62} -0.374427 q^{63} +(-5.57841 - 5.73423i) q^{64} +16.7201 q^{65} +(1.70132 + 4.13416i) q^{66} +(-2.13440 + 10.7304i) q^{67} +(2.53219 + 0.0116258i) q^{68} +(2.72344 + 1.81974i) q^{69} +(11.6528 - 2.29009i) q^{70} +(1.97842 - 0.819489i) q^{71} +(0.239715 - 0.236436i) q^{72} +(-13.1646 - 5.45295i) q^{73} +(0.683231 - 3.39409i) q^{74} +(3.68533 - 0.733058i) q^{75} +(8.33679 + 1.69812i) q^{76} +(4.68117 - 3.12785i) q^{77} +(-11.0351 - 11.0859i) q^{78} +(0.102033 - 0.102033i) q^{79} +(-6.01423 + 8.82444i) q^{80} +(-6.60646 - 6.60646i) q^{81} +(0.0261475 - 11.3903i) q^{82} +(5.13230 + 7.68102i) q^{83} +(-9.20918 - 6.21473i) q^{84} +(-0.659446 - 3.31526i) q^{85} +(6.29128 + 9.46251i) q^{86} +(5.07176 - 12.2443i) q^{87} +(-1.02185 + 4.95847i) q^{88} +(-4.64776 - 11.2207i) q^{89} +(-0.373130 - 0.250558i) q^{90} +(-10.9441 + 16.3790i) q^{91} +(1.40373 + 3.43341i) q^{92} +(1.97743 + 0.393336i) q^{93} +(12.2800 + 5.11959i) q^{94} -11.3571i q^{95} +(9.82022 - 1.83645i) q^{96} +12.8041i q^{97} +(-1.57458 + 3.77683i) q^{98} +(-0.208979 - 0.0415685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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