LMFDB - Embedded newform 64.2.i.a.21.2

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			21.2
Character	$\chi$	$=$	64.21
Dual form			64.2.i.a.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27161 + 0.618873i) q^{2} +(-0.216111 - 1.08646i) q^{3} +(1.23399 - 1.57393i) q^{4} +(1.50133 - 1.00316i) q^{5} +(0.947192 + 1.24781i) q^{6} +(1.15320 + 0.477669i) q^{7} +(-0.595096 + 2.76512i) q^{8} +(1.63794 - 0.678457i) q^{9} +O(q^{10})$	\(q+(-1.27161 + 0.618873i) q^{2} +(-0.216111 - 1.08646i) q^{3} +(1.23399 - 1.57393i) q^{4} +(1.50133 - 1.00316i) q^{5} +(0.947192 + 1.24781i) q^{6} +(1.15320 + 0.477669i) q^{7} +(-0.595096 + 2.76512i) q^{8} +(1.63794 - 0.678457i) q^{9} +(-1.28828 + 2.20476i) q^{10} +(-4.61589 - 0.918157i) q^{11} +(-1.97670 - 1.00054i) q^{12} +(1.18288 + 0.790377i) q^{13} +(-1.76203 + 0.106272i) q^{14} +(-1.41435 - 1.41435i) q^{15} +(-0.954524 - 3.88444i) q^{16} +(-4.96238 + 4.96238i) q^{17} +(-1.66295 + 1.87641i) q^{18} +(0.306314 - 0.458431i) q^{19} +(0.273730 - 3.60088i) q^{20} +(0.269752 - 1.35613i) q^{21} +(6.43784 - 1.68911i) q^{22} +(2.28905 + 5.52625i) q^{23} +(3.13280 + 0.0489777i) q^{24} +(-0.665746 + 1.60725i) q^{25} +(-1.99331 - 0.272999i) q^{26} +(-2.93739 - 4.39612i) q^{27} +(2.17485 - 1.22561i) q^{28} +(4.74895 - 0.944625i) q^{29} +(2.67380 + 0.923200i) q^{30} +2.53878i q^{31} +(3.61776 + 4.34877i) q^{32} +5.21341i q^{33} +(3.23914 - 9.38131i) q^{34} +(2.21051 - 0.439697i) q^{35} +(0.953361 - 3.41522i) q^{36} +(-1.95294 - 2.92279i) q^{37} +(-0.105802 + 0.772515i) q^{38} +(0.603082 - 1.45597i) q^{39} +(1.88041 + 4.74833i) q^{40} +(-2.30661 - 5.56864i) q^{41} +(0.496255 + 1.89142i) q^{42} +(-1.76341 + 8.86527i) q^{43} +(-7.14109 + 6.13209i) q^{44} +(1.77849 - 2.66170i) q^{45} +(-6.33083 - 5.61062i) q^{46} +(6.66340 - 6.66340i) q^{47} +(-4.01402 + 1.87653i) q^{48} +(-3.84805 - 3.84805i) q^{49} +(-0.148115 - 2.45582i) q^{50} +(6.46387 + 4.31902i) q^{51} +(2.70367 - 0.886458i) q^{52} +(-13.5160 - 2.68850i) q^{53} +(6.45586 + 3.77228i) q^{54} +(-7.85103 + 3.25200i) q^{55} +(-2.00707 + 2.90446i) q^{56} +(-0.564266 - 0.233726i) q^{57} +(-5.45422 + 4.14019i) q^{58} +(4.57469 - 3.05671i) q^{59} +(-3.97138 + 0.480793i) q^{60} +(1.79525 + 9.02535i) q^{61} +(-1.57118 - 3.22835i) q^{62} +2.21295 q^{63} +(-7.29172 - 3.29102i) q^{64} +2.56877 q^{65} +(-3.22644 - 6.62944i) q^{66} +(-0.821008 - 4.12749i) q^{67} +(1.68691 + 13.9340i) q^{68} +(5.50938 - 3.68125i) q^{69} +(-2.53879 + 1.92715i) q^{70} +(11.2155 + 4.64562i) q^{71} +(0.901281 + 4.93284i) q^{72} +(7.67366 - 3.17854i) q^{73} +(4.29222 + 2.50803i) q^{74} +(1.89010 + 0.375964i) q^{75} +(-0.343550 - 1.04782i) q^{76} +(-4.88445 - 3.26368i) q^{77} +(0.134173 + 2.22466i) q^{78} +(-7.40915 - 7.40915i) q^{79} +(-5.32976 - 4.87429i) q^{80} +(-0.380539 + 0.380539i) q^{81} +(6.37939 + 5.65365i) q^{82} +(3.58524 - 5.36570i) q^{83} +(-1.80159 - 2.09803i) q^{84} +(-2.47213 + 12.4282i) q^{85} +(-3.24410 - 12.3645i) q^{86} +(-2.05260 - 4.95541i) q^{87} +(5.28570 - 12.2171i) q^{88} +(0.0401804 - 0.0970042i) q^{89} +(-0.614296 + 4.48531i) q^{90} +(0.986557 + 1.47649i) q^{91} +(11.5226 + 3.21655i) q^{92} +(2.75829 - 0.548659i) q^{93} +(-4.34946 + 12.5971i) q^{94} -0.995537i q^{95} +(3.94294 - 4.87038i) q^{96} -7.44456i q^{97} +(7.27469 + 2.51177i) q^{98} +(-8.18348 + 1.62780i) 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 $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{13}{16}\right)$	$1$

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 $

$2$	−1.27161	+	0.618873i	−0.899165	+	0.437609i
$2$	−1.27161	+	0.618873i	−0.899165	+	0.437609i
$3$	−0.216111	−	1.08646i	−0.124772	−	0.627270i	−0.991672	−	0.128788i	$-0.958891\pi$
$3$	−0.216111	−	1.08646i	−0.124772	−	0.627270i	0.866900	−	0.498481i	$-0.166109\pi$
$4$	1.23399	−	1.57393i	0.616996	−	0.786966i
$5$	1.50133	−	1.00316i	0.671416	−	0.448626i	−0.172566	−	0.984998i	$-0.555206\pi$
$5$	1.50133	−	1.00316i	0.671416	−	0.448626i	0.843981	+	0.536372i	$0.180206\pi$
$6$	0.947192	+	1.24781i	0.386689	+	0.509418i
$7$	1.15320	+	0.477669i	0.435867	+	0.180542i	0.589818	−	0.807536i	$-0.299200\pi$
$7$	1.15320	+	0.477669i	0.435867	+	0.180542i	−0.153950	+	0.988079i	$0.549200\pi$
$8$	−0.595096	+	2.76512i	−0.210398	+	0.977616i
$9$	1.63794	−	0.678457i	0.545980	−	0.226152i
$10$	−1.28828	+	2.20476i	−0.407391	+	0.697206i
$11$	−4.61589	−	0.918157i	−1.39174	−	0.276835i	−0.558391	−	0.829578i	$-0.688581\pi$
$11$	−4.61589	−	0.918157i	−1.39174	−	0.276835i	−0.833351	+	0.552743i	$0.813581\pi$
$12$	−1.97670	−	1.00054i	−0.570624	−	0.288832i
$13$	1.18288	+	0.790377i	0.328073	+	0.219211i	0.708688	−	0.705522i	$-0.249288\pi$
$13$	1.18288	+	0.790377i	0.328073	+	0.219211i	−0.380615	+	0.924734i	$0.624288\pi$
$14$	−1.76203	+	0.106272i	−0.470924	+	0.0284023i
$15$	−1.41435	−	1.41435i	−0.365183	−	0.365183i
$16$	−0.954524	−	3.88444i	−0.238631	−	0.971110i
$17$	−4.96238	+	4.96238i	−1.20355	+	1.20355i	−0.230477	+	0.973078i	$0.574029\pi$
$17$	−4.96238	+	4.96238i	−1.20355	+	1.20355i	−0.973078	+	0.230477i	$0.925971\pi$
$18$	−1.66295	+	1.87641i	−0.391960	+	0.442274i
$19$	0.306314	−	0.458431i	0.0702731	−	0.105171i	−0.794669	−	0.607044i	$-0.792355\pi$
$19$	0.306314	−	0.458431i	0.0702731	−	0.105171i	0.864942	+	0.501872i	$0.167355\pi$
$20$	0.273730	−	3.60088i	0.0612079	−	0.805182i
$21$	0.269752	−	1.35613i	0.0588647	−	0.295933i
$22$	6.43784	−	1.68911i	1.37255	−	0.360119i
$23$	2.28905	+	5.52625i	0.477300	+	1.15230i	0.960871	+	0.276998i	$0.0893395\pi$
$23$	2.28905	+	5.52625i	0.477300	+	1.15230i	−0.483571	+	0.875305i	$0.660660\pi$
$24$	3.13280	+	0.0489777i	0.639480	+	0.00999753i
$25$	−0.665746	+	1.60725i	−0.133149	+	0.321451i
$26$	−1.99331	−	0.272999i	−0.390921	−	0.0535394i
$27$	−2.93739	−	4.39612i	−0.565301	−	0.846033i
$28$	2.17485	−	1.22561i	0.411009	−	0.231619i
$29$	4.74895	−	0.944625i	0.881858	−	0.175412i	0.266665	−	0.963789i	$-0.414078\pi$
$29$	4.74895	−	0.944625i	0.881858	−	0.175412i	0.615193	+	0.788377i	$0.289078\pi$
$30$	2.67380	+	0.923200i	0.488167	+	0.168552i
$31$			2.53878i			0.455979i	0.973664	+	0.227990i	$0.0732152\pi$
$31$			2.53878i			0.455979i	−0.973664	+	0.227990i	$0.926785\pi$
$32$	3.61776	+	4.34877i	0.639536	+	0.768761i
$33$			5.21341i			0.907539i
$34$	3.23914	−	9.38131i	0.555508	−	1.60888i
$35$	2.21051	−	0.439697i	0.373644	−	0.0743224i
$36$	0.953361	−	3.41522i	0.158894	−	0.569203i
$37$	−1.95294	−	2.92279i	−0.321062	−	0.480503i	0.635472	−	0.772124i	$-0.280806\pi$
$37$	−1.95294	−	2.92279i	−0.321062	−	0.480503i	−0.956534	+	0.291621i	$0.905806\pi$
$38$	−0.105802	+	0.772515i	−0.0171633	+	0.125318i
$39$	0.603082	−	1.45597i	0.0965704	−	0.233141i
$40$	1.88041	+	4.74833i	0.297319	+	0.750777i
$41$	−2.30661	−	5.56864i	−0.360232	−	0.869676i	−0.995266	−	0.0971918i	$-0.969014\pi$
$41$	−2.30661	−	5.56864i	−0.360232	−	0.869676i	0.635034	−	0.772484i	$-0.280986\pi$
$42$	0.496255	+	1.89142i	0.0765738	+	0.291852i
$43$	−1.76341	+	8.86527i	−0.268918	+	1.35194i	0.576177	+	0.817325i	$0.304544\pi$
$43$	−1.76341	+	8.86527i	−0.268918	+	1.35194i	−0.845095	+	0.534616i	$0.820456\pi$
$44$	−7.14109	+	6.13209i	−1.07656	+	0.924448i
$45$	1.77849	−	2.66170i	0.265122	−	0.396783i
$46$	−6.33083	−	5.61062i	−0.933430	−	0.827240i
$47$	6.66340	−	6.66340i	0.971957	−	0.971957i	−0.0276606	−	0.999617i	$-0.508806\pi$
$47$	6.66340	−	6.66340i	0.971957	−	0.971957i	0.999617	+	0.0276606i	$0.00880576\pi$
$48$	−4.01402	+	1.87653i	−0.579374	+	0.270853i
$49$	−3.84805	−	3.84805i	−0.549722	−	0.549722i
$50$	−0.148115	−	2.45582i	−0.0209466	−	0.347305i
$51$	6.46387	+	4.31902i	0.905123	+	0.604784i
$52$	2.70367	−	0.886458i	0.374932	−	0.122930i
$53$	−13.5160	−	2.68850i	−1.85657	−	0.369294i	−0.865310	−	0.501237i	$-0.832878\pi$
$53$	−13.5160	−	2.68850i	−1.85657	−	0.369294i	−0.991257	+	0.131943i	$0.957878\pi$
$54$	6.45586	+	3.77228i	0.878531	+	0.513342i
$55$	−7.85103	+	3.25200i	−1.05863	+	0.438500i
$56$	−2.00707	+	2.90446i	−0.268206	+	0.388125i
$57$	−0.564266	−	0.233726i	−0.0747388	−	0.0309578i
$58$	−5.45422	+	4.14019i	−0.716174	+	0.543634i
$59$	4.57469	−	3.05671i	0.595574	−	0.397950i	−0.220930	−	0.975290i	$-0.570909\pi$
$59$	4.57469	−	3.05671i	0.595574	−	0.397950i	0.816504	+	0.577340i	$0.195909\pi$
$60$	−3.97138	+	0.480793i	−0.512703	+	0.0620701i
$61$	1.79525	+	9.02535i	0.229859	+	1.15558i	0.907457	+	0.420145i	$0.138021\pi$
$61$	1.79525	+	9.02535i	0.229859	+	1.15558i	−0.677598	+	0.735432i	$0.736979\pi$
$62$	−1.57118	−	3.22835i	−0.199541	−	0.410001i
$63$	2.21295			0.278805
$64$	−7.29172	−	3.29102i	−0.911465	−	0.411377i
$65$	2.56877			0.318617
$66$	−3.22644	−	6.62944i	−0.397147	−	0.816027i
$67$	−0.821008	−	4.12749i	−0.100302	−	0.504253i	−0.997976	−	0.0635922i	$-0.979744\pi$
$67$	−0.821008	−	4.12749i	−0.100302	−	0.504253i	0.897674	−	0.440660i	$-0.145256\pi$
$68$	1.68691	+	13.9340i	0.204568	+	1.68975i
$69$	5.50938	−	3.68125i	0.663251	−	0.443170i
$70$	−2.53879	+	1.92715i	−0.303443	+	0.230338i
$71$	11.2155	+	4.64562i	1.33104	+	0.551334i	0.930951	−	0.365143i	$-0.118980\pi$
$71$	11.2155	+	4.64562i	1.33104	+	0.551334i	0.400087	+	0.916477i	$0.368980\pi$
$72$	0.901281	+	4.93284i	0.106217	+	0.581341i
$73$	7.67366	−	3.17854i	0.898134	−	0.372019i	0.114632	−	0.993408i	$-0.463431\pi$
$73$	7.67366	−	3.17854i	0.898134	−	0.372019i	0.783503	+	0.621389i	$0.213431\pi$
$74$	4.29222	+	2.50803i	0.498961	+	0.291552i
$75$	1.89010	+	0.375964i	0.218250	+	0.0434125i
$76$	−0.343550	−	1.04782i	−0.0394079	−	0.120193i
$77$	−4.88445	−	3.26368i	−0.556634	−	0.371931i
$78$	0.134173	+	2.22466i	0.0151921	+	0.251893i
$79$	−7.40915	−	7.40915i	−0.833594	−	0.833594i	0.154412	−	0.988007i	$-0.450652\pi$
$79$	−7.40915	−	7.40915i	−0.833594	−	0.833594i	−0.988007	+	0.154412i	$0.950652\pi$
$80$	−5.32976	−	4.87429i	−0.595886	−	0.544963i
$81$	−0.380539	+	0.380539i	−0.0422821	+	0.0422821i
$82$	6.37939	+	5.65365i	0.704486	+	0.624342i
$83$	3.58524	−	5.36570i	0.393532	−	0.588962i	−0.580809	−	0.814040i	$-0.697264\pi$
$83$	3.58524	−	5.36570i	0.393532	−	0.588962i	0.974341	+	0.225078i	$0.0722637\pi$
$84$	−1.80159	−	2.09803i	−0.196570	−	0.228914i
$85$	−2.47213	+	12.4282i	−0.268140	+	1.34803i
$86$	−3.24410	−	12.3645i	−0.349820	−	1.33330i
$87$	−2.05260	−	4.95541i	−0.220062	−	0.531276i
$88$	5.28570	−	12.2171i	0.563458	−	1.30234i
$89$	0.0401804	−	0.0970042i	0.00425912	−	0.0102824i	−0.921736	−	0.387819i	$-0.873229\pi$
$89$	0.0401804	−	0.0970042i	0.00425912	−	0.0102824i	0.925995	+	0.377536i	$0.123229\pi$
$90$	−0.614296	+	4.48531i	−0.0647525	+	0.472793i
$91$	0.986557	+	1.47649i	0.103419	+	0.154778i
$92$	11.5226	+	3.21655i	1.20132	+	0.335348i
$93$	2.75829	−	0.548659i	0.286022	−	0.0568933i
$94$	−4.34946	+	12.5971i	−0.448613	+	1.29929i
$95$		−	0.995537i		−	0.102140i
$96$	3.94294	−	4.87038i	0.402425	−	0.497081i
$97$		−	7.44456i		−	0.755881i	−0.925830	−	0.377940i	$-0.876632\pi$
$97$		−	7.44456i		−	0.755881i	0.925830	−	0.377940i	$-0.123368\pi$
$98$	7.27469	+	2.51177i	0.734854	+	0.253728i
$99$	−8.18348	+	1.62780i	−0.822471	+	0.163600i
$100$	1.70818	+	3.03118i	0.170818	+	0.303118i
$101$	−1.00131	−	1.49857i	−0.0996342	−	0.149113i	0.778303	−	0.627889i	$-0.216081\pi$
$101$	−1.00131	−	1.49857i	−0.0996342	−	0.149113i	−0.877937	+	0.478776i	$0.841081\pi$
$102$	−10.8925	−	1.49180i	−1.07851	−	0.147710i
$103$	−1.67198	+	4.03651i	−0.164745	+	0.397729i	−0.984595	−	0.174848i	$-0.944056\pi$
$103$	−1.67198	+	4.03651i	−0.164745	+	0.397729i	0.819851	+	0.572578i	$0.194056\pi$
$104$	−2.88941	+	2.80046i	−0.283330	+	0.274608i
$105$	−0.955430	−	2.30661i	−0.0932404	−	0.225102i
$106$	18.8510	−	4.94596i	1.83097	−	0.480394i
$107$	−0.549321	+	2.76162i	−0.0531048	+	0.266976i	−0.998211	−	0.0597869i	$-0.980958\pi$
$107$	−0.549321	+	2.76162i	−0.0531048	+	0.266976i	0.945106	+	0.326763i	$0.105958\pi$
$108$	−10.5439	−	0.801521i	−1.01459	−	0.0771264i
$109$	−4.02240	+	6.01994i	−0.385276	+	0.576606i	−0.972524	−	0.232801i	$-0.925211\pi$
$109$	−4.02240	+	6.01994i	−0.385276	+	0.576606i	0.587249	+	0.809407i	$0.300211\pi$
$110$	7.97089	−	8.99408i	0.759994	−	0.857551i
$111$	−2.75345	+	2.75345i	−0.261346	+	0.261346i
$112$	0.754725	−	4.93547i	0.0713148	−	0.466358i
$113$	−0.851587	−	0.851587i	−0.0801105	−	0.0801105i	0.665916	−	0.746027i	$-0.268041\pi$
$113$	−0.851587	−	0.851587i	−0.0801105	−	0.0801105i	−0.746027	+	0.665916i	$0.768041\pi$
$114$	0.862174	−	0.0519994i	0.0807500	−	0.00487019i
$115$	8.98032	+	6.00046i	0.837419	+	0.559546i
$116$	4.37339	−	8.64018i	0.406059	−	0.802221i
$117$	2.47373	+	0.492055i	0.228696	+	0.0454905i
$118$	−3.92552	+	6.71811i	−0.361373	+	0.618452i
$119$	−8.09298	+	3.35222i	−0.741882	+	0.307298i
$120$	4.75251	−	3.06916i	0.433842	−	0.280175i
$121$	10.3007	+	4.26670i	0.936429	+	0.387882i
$122$	−7.86841	−	10.3657i	−0.712372	−	0.938467i
$123$	−5.55164	+	3.70949i	−0.500575	+	0.334473i
$124$	3.99587	+	3.13284i	0.358840	+	0.281337i
$125$	2.37413	+	11.9356i	0.212349	+	1.06755i
$126$	−2.81401	+	1.36953i	−0.250692	+	0.122008i
$127$	−8.83208			−0.783721			−0.391860	−	0.920025i	$-0.628168\pi$
$127$	−8.83208			−0.783721			−0.391860	+	0.920025i	$0.628168\pi$
$128$	11.3090	−	0.327756i	0.999580	−	0.0289698i
$129$	10.0129			0.881585
$130$	−3.26648	+	1.58974i	−0.286489	+	0.139430i
$131$	−0.0801792	−	0.403088i	−0.00700529	−	0.0352180i	0.977125	−	0.212668i	$-0.0682152\pi$
$131$	−0.0801792	−	0.403088i	−0.00700529	−	0.0352180i	−0.984130	+	0.177450i	$0.943215\pi$
$132$	8.20556	+	6.43331i	0.714202	+	0.559948i
$133$	0.572218	−	0.382344i	0.0496176	−	0.0331534i
$134$	3.59839	+	4.74046i	0.310854	+	0.409513i
$135$	−8.81999	−	3.65336i	−0.759104	−	0.314431i
$136$	−10.7685	−	16.6747i	−0.923389	−	1.42984i
$137$	−0.924279	+	0.382849i	−0.0789665	+	0.0327090i	−0.421817	−	0.906681i	$-0.638608\pi$
$137$	−0.924279	+	0.382849i	−0.0789665	+	0.0327090i	0.342851	+	0.939390i	$0.388608\pi$
$138$	−4.72757	+	8.09073i	−0.402437	+	0.688728i
$139$	−1.84020	−	0.366038i	−0.156084	−	0.0310469i	0.116430	−	0.993199i	$-0.462855\pi$
$139$	−1.84020	−	0.366038i	−0.156084	−	0.0310469i	−0.272513	+	0.962152i	$0.587855\pi$
$140$	2.03570	−	4.02177i	0.172048	−	0.339902i
$141$	−8.67957	−	5.79950i	−0.730952	−	0.488406i
$142$	−17.1368	+	1.03356i	−1.43809	+	0.0867342i
$143$	−4.73436	−	4.73436i	−0.395907	−	0.395907i
$144$	−4.19888	−	5.71488i	−0.349907	−	0.476240i
$145$	6.18214	−	6.18214i	0.513399	−	0.513399i
$146$	−7.79081	+	8.79089i	−0.644772	+	0.727539i
$147$	−3.34916	+	5.01238i	−0.276234	+	0.413414i
$148$	−7.01019	−	0.532897i	−0.576234	−	0.0438038i
$149$	−0.535159	+	2.69043i	−0.0438419	+	0.220408i	−0.996495	−	0.0836507i	$-0.973342\pi$
$149$	−0.535159	+	2.69043i	−0.0438419	+	0.220408i	0.952653	+	0.304059i	$0.0983420\pi$
$150$	−2.63614	+	0.691650i	−0.215240	+	0.0564730i
$151$	−7.23693	−	17.4715i	−0.588933	−	1.42181i	−0.884524	−	0.466495i	$-0.845516\pi$
$151$	−7.23693	−	17.4715i	−0.588933	−	1.42181i	0.295591	−	0.955315i	$-0.404484\pi$
$152$	1.08533	+	1.11980i	0.0880317	+	0.0908279i
$153$	−4.76133	+	11.4949i	−0.384930	+	0.929304i
$154$	8.23092	+	1.12729i	0.663267	+	0.0908393i
$155$	2.54680	+	3.81156i	0.204564	+	0.306152i
$156$	−1.54740	−	2.74586i	−0.123891	−	0.219845i
$157$	−4.96179	+	0.986961i	−0.395994	+	0.0787680i	−0.389070	−	0.921208i	$-0.627204\pi$
$157$	−4.96179	+	0.986961i	−0.395994	+	0.0787680i	−0.00692319	+	0.999976i	$0.502204\pi$
$158$	14.0069	+	4.83624i	1.11433	+	0.384751i
$159$			15.2657i			1.21065i
$160$	9.79396	+	2.89976i	0.774280	+	0.229246i
$161$			7.46626i			0.588424i
$162$	0.248392	−	0.719403i	0.0195155	−	0.0565216i
$163$	−7.76612	+	1.54478i	−0.608290	+	0.120996i	−0.489618	−	0.871937i	$-0.662864\pi$
$163$	−7.76612	+	1.54478i	−0.608290	+	0.120996i	−0.118672	+	0.992934i	$0.537864\pi$
$164$	−11.6110	−	3.24122i	−0.906667	−	0.253097i
$165$	5.22987	+	7.82706i	0.407145	+	0.609336i
$166$	−1.23835	+	9.04189i	−0.0961149	+	0.701787i
$167$	7.46970	−	18.0335i	0.578023	−	1.39547i	−0.316562	−	0.948572i	$-0.602529\pi$
$167$	7.46970	−	18.0335i	0.578023	−	1.39547i	0.894585	−	0.446898i	$-0.147471\pi$
$168$	3.58934	+	1.55292i	0.276924	+	0.119811i
$169$	−4.20037	−	10.1406i	−0.323105	−	0.780045i
$170$	−4.54791	−	17.3338i	−0.348809	−	1.32944i
$171$	0.190698	−	0.958703i	0.0145830	−	0.0733138i
$172$	11.7773	+	13.7152i	0.898011	+	1.04577i
$173$	11.1777	−	16.7286i	0.849823	−	1.27185i	−0.110758	−	0.993847i	$-0.535328\pi$
$173$	11.1777	−	16.7286i	0.849823	−	1.27185i	0.960580	−	0.278002i	$-0.0896723\pi$
$174$	5.67688	+	5.03106i	0.430363	+	0.381404i
$175$	−1.53547	+	1.53547i	−0.116071	+	0.116071i
$176$	0.839450	+	18.8065i	0.0632759	+	1.41760i
$177$	−4.30965	−	4.30965i	−0.323933	−	0.323933i
$178$	0.00893933	+	0.148218i	0.000670031	+	0.0111094i
$179$	−0.527103	−	0.352199i	−0.0393975	−	0.0263246i	0.535716	−	0.844399i	$-0.320042\pi$
$179$	−0.527103	−	0.352199i	−0.0393975	−	0.0263246i	−0.575113	+	0.818074i	$0.695042\pi$
$180$	−1.99469	−	6.08375i	−0.148676	−	0.453456i
$181$	20.6333	+	4.10421i	1.53366	+	0.305064i	0.888461	−	0.458952i	$-0.151775\pi$
$181$	20.6333	+	4.10421i	1.53366	+	0.305064i	0.645198	+	0.764016i	$0.276775\pi$
$182$	−2.16828	−	1.26696i	−0.160723	−	0.0939137i
$183$	9.41773	−	3.90095i	0.696179	−	0.288367i
$184$	−16.6429	+	3.04083i	−1.22693	+	0.224173i
$185$	−5.86403	−	2.42896i	−0.431132	−	0.178581i
$186$	−3.16793	+	2.40471i	−0.232284	+	0.176322i
$187$	27.4620	−	18.3496i	2.00822	−	1.34185i
$188$	−2.26515	−	18.7103i	−0.165203	−	1.36459i
$189$	−1.28750	−	6.47269i	−0.0936517	−	0.470819i
$190$	0.616111	+	1.26594i	0.0446974	+	0.0918407i
$191$	16.5260			1.19578			0.597890	−	0.801578i	$-0.296006\pi$
$191$	16.5260			1.19578			0.597890	+	0.801578i	$0.296006\pi$
$192$	−1.99975	+	8.63341i	−0.144319	+	0.623063i
$193$	6.98415			0.502730			0.251365	−	0.967892i	$-0.419121\pi$
$193$	6.98415			0.502730			0.251365	+	0.967892i	$0.419121\pi$
$194$	4.60724	+	9.46659i	0.330780	+	0.679662i
$195$	−0.555140	−	2.79088i	−0.0397544	−	0.199859i
$196$	−10.8050	+	1.30811i	−0.771789	+	0.0934361i
$197$	−2.97854	+	1.99020i	−0.212212	+	0.141796i	−0.657134	−	0.753774i	$-0.728231\pi$
$197$	−2.97854	+	1.99020i	−0.212212	+	0.141796i	0.444922	+	0.895569i	$0.353231\pi$
$198$	9.39881	−	7.13446i	0.667944	−	0.507024i
$199$	4.92695	+	2.04081i	0.349262	+	0.144669i	0.550416	−	0.834890i	$-0.314469\pi$
$199$	4.92695	+	2.04081i	0.349262	+	0.144669i	−0.201154	+	0.979560i	$0.564469\pi$
$200$	−4.04806	−	2.79734i	−0.286241	−	0.197801i
$201$	−4.30693	+	1.78399i	−0.303788	+	0.125833i
$202$	2.20070	+	1.28591i	0.154841	+	0.0904765i
$203$	5.92769	+	1.17909i	0.416042	+	0.0827559i
$204$	14.7742	−	4.84405i	1.03440	−	0.339152i
$205$	−9.04921	−	6.04649i	−0.632024	−	0.422305i
$206$	−0.371981	−	6.16761i	−0.0259171	−	0.429718i
$207$	7.49865	+	7.49865i	0.521192	+	0.521192i
$208$	1.94108	−	5.34927i	0.134590	−	0.370905i
$209$	−1.83482	+	1.83482i	−0.126917	+	0.126917i
$210$	2.64243	+	2.34182i	0.182345	+	0.161601i
$211$	−7.38307	+	11.0495i	−0.508271	+	0.760682i	−0.993515	−	0.113697i	$-0.963731\pi$
$211$	−7.38307	+	11.0495i	−0.508271	+	0.760682i	0.485244	+	0.874379i	$0.338731\pi$
$212$	−20.9102	+	17.9557i	−1.43612	+	1.23320i
$213$	2.62350	−	13.1892i	0.179759	−	0.903711i
$214$	−1.01057	−	3.85167i	−0.0690812	−	0.263295i
$215$	6.24580	+	15.0787i	0.425960	+	1.02836i
$216$	13.9038	−	5.50612i	0.946033	−	0.374644i
$217$	−1.21270	+	2.92772i	−0.0823234	+	0.198746i
$218$	1.38935	−	10.1444i	0.0940985	−	0.687064i
$219$	−5.11172	−	7.65024i	−0.345418	−	0.516955i
$220$	−4.56968	+	16.3699i	−0.308088	+	1.10366i
$221$	−9.79208	+	1.94777i	−0.658686	+	0.131021i
$222$	1.79728	−	5.20535i	0.120626	−	0.349360i
$223$			3.90815i			0.261709i	0.991402	+	0.130855i	$0.0417721\pi$
$223$			3.90815i			0.261709i	−0.991402	+	0.130855i	$0.958228\pi$
$224$	2.09471	+	6.74308i	0.139959	+	0.450541i
$225$			3.08427i			0.205618i
$226$	1.60991	+	0.555864i	0.107090	+	0.0369755i
$227$	−0.796815	+	0.158496i	−0.0528864	+	0.0105198i	−0.221463	−	0.975169i	$-0.571083\pi$
$227$	−0.796815	+	0.158496i	−0.0528864	+	0.0105198i	0.168576	+	0.985689i	$0.446083\pi$
$228$	−1.06417	+	0.599699i	−0.0704763	+	0.0397160i
$229$	1.29249	+	1.93435i	0.0854101	+	0.127825i	0.871715	−	0.490014i	$-0.163008\pi$
$229$	1.29249	+	1.93435i	0.0854101	+	0.127825i	−0.786305	+	0.617839i	$0.788008\pi$
$230$	−15.1330	−	2.07258i	−0.997841	−	0.136662i
$231$	−2.49029	+	6.01209i	−0.163849	+	0.395566i
$232$	−0.214082	+	13.6935i	−0.0140552	+	0.899024i
$233$	2.58378	+	6.23780i	0.169269	+	0.408652i	0.985636	−	0.168881i	$-0.0540155\pi$
$233$	2.58378	+	6.23780i	0.169269	+	0.408652i	−0.816367	+	0.577533i	$0.804015\pi$
$234$	−3.45014	+	0.905221i	−0.225543	+	0.0591761i
$235$	3.31953	−	16.6884i	0.216542	−	1.08863i
$236$	0.834080	−	10.9722i	0.0542940	−	0.714231i
$237$	−6.44857	+	9.65097i	−0.418880	+	0.626898i
$238$	8.21653	−	9.27125i	0.532599	−	0.600966i
$239$	−10.1603	+	10.1603i	−0.657213	+	0.657213i	−0.954720	−	0.297507i	$-0.903845\pi$
$239$	−10.1603	+	10.1603i	−0.657213	+	0.657213i	0.297507	+	0.954720i	$0.403845\pi$
$240$	−4.14392	+	6.84398i	−0.267489	+	0.441777i
$241$	−0.721160	−	0.721160i	−0.0464540	−	0.0464540i	0.683498	−	0.729952i	$-0.260458\pi$
$241$	−0.721160	−	0.721160i	−0.0464540	−	0.0464540i	−0.729952	+	0.683498i	$0.760458\pi$
$242$	−15.7391	+	0.949254i	−1.01174	+	0.0610203i
$243$	−12.6927	−	8.48097i	−0.814235	−	0.544055i
$244$	16.4206	+	8.31160i	1.05122	+	0.532096i
$245$	−9.63741	−	1.91700i	−0.615711	−	0.122473i
$246$	4.76383	−	8.15279i	0.303731	−	0.519803i
$247$	0.724666	−	0.300167i	0.0461094	−	0.0190991i
$248$	−7.02003	−	1.51082i	−0.445772	−	0.0959371i
$249$	−6.60444	−	2.73565i	−0.418539	−	0.173365i
$250$	−10.4056	−	13.7081i	−0.658107	−	0.866978i
$251$	−22.8359	+	15.2584i	−1.44139	+	0.963104i	−0.443627	+	0.896211i	$0.646309\pi$
$251$	−22.8359	+	15.2584i	−1.44139	+	0.963104i	−0.997760	+	0.0668929i	$0.978691\pi$
$252$	2.73076	−	3.48303i	0.172022	−	0.219410i
$253$	−5.49202	−	27.6103i	−0.345280	−	1.73584i
$254$	11.2310	−	5.46594i	0.704694	−	0.342963i
$255$	14.0371			0.879036
$256$	−14.1778	+	7.41559i	−0.886110	+	0.463474i
$257$	−17.9165			−1.11760			−0.558802	−	0.829301i	$-0.688739\pi$
$257$	−17.9165			−1.11760			−0.558802	+	0.829301i	$0.688739\pi$
$258$	−12.7325	+	6.19670i	−0.792691	+	0.385790i
$259$	−0.856001	−	4.30341i	−0.0531893	−	0.267401i
$260$	3.16985	−	4.04307i	0.196586	−	0.250741i
$261$	7.13761	−	4.76920i	0.441807	−	0.295206i
$262$	0.351417	+	0.462951i	0.0217106	+	0.0286012i
$263$	−5.26516	−	2.18090i	−0.324664	−	0.134480i	0.214398	−	0.976746i	$-0.431221\pi$
$263$	−5.26516	−	2.18090i	−0.324664	−	0.134480i	−0.539062	+	0.842266i	$0.681221\pi$
$264$	−14.4157	−	3.10248i	−0.887224	−	0.190944i
$265$	−22.9890	+	9.52236i	−1.41220	+	0.584954i
$266$	−0.491017	+	0.840323i	−0.0301062	+	0.0515235i
$267$	−0.114075	−	0.0226909i	−0.00698127	−	0.00138866i
$268$	−7.50950	−	3.80108i	−0.458716	−	0.232188i
$269$	17.3522	+	11.5943i	1.05798	+	0.706919i	0.957621	−	0.288032i	$-0.0930009\pi$
$269$	17.3522	+	11.5943i	1.05798	+	0.706919i	0.100359	+	0.994951i	$0.468001\pi$
$270$	13.4766	−	0.812799i	0.820158	−	0.0494654i
$271$	21.9244	+	21.9244i	1.33181	+	1.33181i	0.903748	+	0.428065i	$0.140804\pi$
$271$	21.9244	+	21.9244i	1.33181	+	1.33181i	0.428065	+	0.903748i	$0.359196\pi$
$272$	24.0128	+	14.5394i	1.45599	+	0.881579i
$273$	1.39094	−	1.39094i	0.0841837	−	0.0841837i
$274$	0.938389	−	1.05885i	0.0566902	−	0.0639672i
$275$	4.54872	−	6.80764i	0.274298	−	0.410516i
$276$	1.00450	−	13.2140i	0.0604636	−	0.795391i
$277$	−1.26542	+	6.36169i	−0.0760317	+	0.382237i	−1.00000		0.000231952i	$-0.999926\pi$
$277$	−1.26542	+	6.36169i	−0.0760317	+	0.382237i	0.923968	+	0.382469i	$0.124926\pi$
$278$	2.56655	−	0.673390i	0.153931	−	0.0403873i
$279$	1.72246	+	4.15838i	0.103121	+	0.248956i
$280$	−0.0996496	+	6.37397i	−0.00595520	+	0.380917i
$281$	−4.97401	+	12.0083i	−0.296725	+	0.716357i	0.703260	+	0.710932i	$0.251727\pi$
$281$	−4.97401	+	12.0083i	−0.296725	+	0.716357i	−0.999985	+	0.00542477i	$0.998273\pi$
$282$	14.6262	+	2.00317i	0.870978	+	0.119287i
$283$	11.1712	+	16.7189i	0.664058	+	0.993834i	0.998674	+	0.0514789i	$0.0163935\pi$
$283$	11.1712	+	16.7189i	0.664058	+	0.993834i	−0.334616	+	0.942355i	$0.608607\pi$
$284$	21.1518	−	11.9198i	1.25513	−	0.707311i
$285$	−1.08161	+	0.215146i	−0.0640693	+	0.0127442i
$286$	8.95024	+	3.09030i	0.529239	+	0.182733i
$287$		−	7.52353i		−	0.444100i
$288$	8.87613	+	4.66853i	0.523031	+	0.275096i
$289$		−	32.2505i		−	1.89709i
$290$	−4.03532	+	11.6872i	−0.236962	+	0.686298i
$291$	−8.08824	+	1.60885i	−0.474141	+	0.0943125i
$292$	4.46645	−	16.0001i	0.261379	−	0.936336i
$293$	−0.206488	−	0.309031i	−0.0120632	−	0.0180538i	0.825389	−	0.564564i	$-0.190956\pi$
$293$	−0.206488	−	0.309031i	−0.0120632	−	0.0180538i	−0.837452	+	0.546511i	$0.815956\pi$
$294$	1.15681	−	8.44650i	0.0674665	−	0.492610i
$295$	3.80177	−	9.17828i	0.221347	−	0.534380i
$296$	9.24403	−	3.66078i	0.537298	−	0.212778i
$297$	9.52234	+	22.9890i	0.552542	+	1.33395i
$298$	−0.984517	−	3.75237i	−0.0570316	−	0.217369i
$299$	−1.66015	+	8.34612i	−0.0960088	+	0.482669i
$300$	2.92411	−	2.51095i	0.168823	−	0.144970i
$301$	−6.26823	+	9.38107i	−0.361295	+	0.540716i
$302$	20.0152	+	17.7382i	1.15175	+	1.02072i
$303$	−1.41174	+	1.41174i	−0.0811026	+	0.0811026i
$304$	−2.07313	−	0.752274i	−0.118902	−	0.0431459i
$305$	11.7491	+	11.7491i	0.672752	+	0.672752i
$306$	−1.05930	−	17.5636i	−0.0605560	−	1.00405i
$307$	−14.4357	−	9.64562i	−0.823888	−	0.550505i	0.0706472	−	0.997501i	$-0.477494\pi$
$307$	−14.4357	−	9.64562i	−0.823888	−	0.550505i	−0.894536	+	0.446997i	$0.852494\pi$
$308$	−11.1642	+	3.66043i	−0.636139	+	0.208572i
$309$	4.74685	+	0.944207i	0.270039	+	0.0537141i
$310$	−5.59741	−	3.27067i	−0.317911	−	0.185762i
$311$	9.24907	−	3.83109i	0.524466	−	0.217241i	−0.104711	−	0.994503i	$-0.533392\pi$
$311$	9.24907	−	3.83109i	0.524466	−	0.217241i	0.629178	+	0.777262i	$0.283392\pi$
$312$	3.66703	+	2.53403i	0.207605	+	0.143461i
$313$	−3.99356	−	1.65419i	−0.225730	−	0.0935003i	0.266952	−	0.963710i	$-0.413983\pi$
$313$	−3.99356	−	1.65419i	−0.225730	−	0.0935003i	−0.492682	+	0.870209i	$0.663983\pi$
$314$	5.69866	−	4.32575i	0.321594	−	0.244116i
$315$	3.32236	−	2.21993i	0.187194	−	0.125079i
$316$	−20.8043	+	2.51866i	−1.17034	+	0.141686i
$317$	−1.65371	−	8.31376i	−0.0928816	−	0.466947i	−0.999032	−	0.0439915i	$-0.985993\pi$
$317$	−1.65371	−	8.31376i	−0.0928816	−	0.466947i	0.906150	−	0.422956i	$-0.139007\pi$
$318$	−9.44751	−	19.4120i	−0.529790	−	1.08857i
$319$	−22.7879			−1.27588
$320$	−14.2487	+	2.37384i	−0.796526	+	0.132702i
$321$	3.11911			0.174092
$322$	−4.62067	−	9.49418i	−0.257500	−	0.529090i
$323$	0.754863	+	3.79495i	0.0420017	+	0.211157i
$324$	0.129360	+	1.06852i	0.00718667	+	0.0593624i
$325$	−2.05784	+	1.37500i	−0.114148	+	0.0762714i
$326$	8.91947	−	6.77060i	0.494004	−	0.374989i
$327$	7.40973	+	3.06921i	0.409759	+	0.169728i
$328$	16.7706	−	3.06416i	0.926001	−	0.169190i
$329$	10.8671	−	4.50130i	0.599123	−	0.248165i
$330$	−11.4943	−	6.71635i	−0.632742	−	0.369723i
$331$	12.2281	+	2.43233i	0.672119	+	0.133693i	0.519340	−	0.854568i	$-0.326178\pi$
$331$	12.2281	+	2.43233i	0.672119	+	0.133693i	0.152779	+	0.988260i	$0.451178\pi$
$332$	−4.02108	−	12.2642i	−0.220685	−	0.673083i
$333$	−5.18179	−	3.46236i	−0.283961	−	0.189736i
$334$	1.66186	+	27.5543i	0.0909327	+	1.50771i
$335$	−5.37312	−	5.37312i	−0.293565	−	0.293565i
$336$	−5.52531	+	0.246628i	−0.301430	+	0.0134547i
$337$	1.88399	−	1.88399i	0.102628	−	0.102628i	−0.653929	−	0.756556i	$-0.726880\pi$
$337$	1.88399	−	1.88399i	0.102628	−	0.102628i	0.756556	+	0.653929i	$0.226880\pi$
$338$	11.6170	+	10.2954i	0.631880	+	0.559996i
$339$	−0.741180	+	1.10925i	−0.0402554	+	0.0602464i
$340$	16.5106	+	19.2273i	0.895413	+	1.04275i
$341$	2.33100	−	11.7187i	0.126231	−	0.634605i
$342$	0.350822	+	1.33712i	0.0189703	+	0.0723029i
$343$	−5.94315	−	14.3480i	−0.320900	−	0.774721i
$344$	−23.4641	−	10.1517i	−1.26510	−	0.547344i
$345$	4.57853	−	11.0536i	0.246500	−	0.595103i
$346$	−3.86080	+	28.1898i	−0.207558	+	1.51549i
$347$	−9.08589	−	13.5980i	−0.487756	−	0.729979i	0.503199	−	0.864170i	$-0.332156\pi$
$347$	−9.08589	−	13.5980i	−0.487756	−	0.729979i	−0.990955	+	0.134192i	$0.957156\pi$
$348$	−10.3324	−	2.88429i	−0.553874	−	0.154614i
$349$	13.4591	−	2.67719i	0.720451	−	0.143307i	0.178770	−	0.983891i	$-0.442788\pi$
$349$	13.4591	−	2.67719i	0.720451	−	0.143307i	0.541681	+	0.840584i	$0.317788\pi$
$350$	1.00226	−	2.90279i	0.0535732	−	0.155160i
$351$		−	7.52174i		−	0.401481i
$352$	−12.7063	−	23.3951i	−0.677249	−	1.24696i
$353$			18.8115i			1.00124i	0.865668	+	0.500618i	$0.166894\pi$
$353$			18.8115i			1.00124i	−0.865668	+	0.500618i	$0.833106\pi$
$354$	8.14732	+	2.81307i	0.433025	+	0.149513i
$355$	21.4985	−	4.27632i	1.14102	−	0.226964i
$356$	−0.103096	−	0.182944i	−0.00546406	−	0.00969600i
$357$	5.39105	+	8.06827i	0.285324	+	0.427018i
$358$	0.888236	+	0.121650i	0.0469447	+	0.00642943i
$359$	−13.4509	+	32.4734i	−0.709913	+	1.71388i	−0.00969415	+	0.999953i	$0.503086\pi$
$359$	−13.4509	+	32.4734i	−0.709913	+	1.71388i	−0.700219	+	0.713928i	$0.746914\pi$
$360$	6.30154	+	6.50170i	0.332120	+	0.342670i
$361$	7.15465	+	17.2729i	0.376561	+	0.909098i
$362$	−28.7775	+	7.55041i	−1.51251	+	0.396841i
$363$	2.40951	−	12.1134i	0.126467	−	0.635790i
$364$	3.54130	+	0.269200i	0.185614	+	0.0141099i
$365$	8.33214	−	12.4699i	0.436124	−	0.652706i
$366$	−9.56150	+	10.7889i	−0.499788	+	0.563944i
$367$	21.5313	−	21.5313i	1.12393	−	1.12393i	0.132781	−	0.991145i	$-0.457609\pi$
$367$	21.5313	−	21.5313i	1.12393	−	1.12393i	0.991145	−	0.132781i	$-0.0423906\pi$
$368$	19.2814	−	14.1666i	1.00511	−	0.738486i
$369$	−7.55617	−	7.55617i	−0.393359	−	0.393359i
$370$	8.95999	−	0.540395i	0.465808	−	0.0280938i
$371$	−14.3024	−	9.55656i	−0.742544	−	0.496152i
$372$	2.54016	−	5.01841i	0.131701	−	0.260192i
$373$	7.27127	+	1.44635i	0.376492	+	0.0748889i	0.379709	−	0.925106i	$-0.376024\pi$
$373$	7.27127	+	1.44635i	0.376492	+	0.0748889i	−0.00321719	+	0.999995i	$0.501024\pi$
$374$	−23.5650	+	40.3290i	−1.21852	+	2.08536i
$375$	12.4545	−	5.15882i	0.643147	−	0.266400i
$376$	14.4597	+	22.3904i	0.745703	+	1.15470i
$377$	6.36406	+	2.63608i	0.327766	+	0.135765i
$378$	5.64297	+	7.43395i	0.290243	+	0.382361i
$379$	−0.0372684	+	0.0249019i	−0.00191435	+	0.00127913i	−0.556527	−	0.830829i	$-0.687866\pi$
$379$	−0.0372684	+	0.0249019i	−0.00191435	+	0.00127913i	0.554613	+	0.832109i	$0.312866\pi$
$380$	−1.56691	−	1.22849i	−0.0803807	−	0.0630200i
$381$	1.90871	+	9.59573i	0.0977861	+	0.491604i
$382$	−21.0147	+	10.2275i	−1.07520	+	0.523285i
$383$	−23.5166			−1.20164			−0.600822	−	0.799383i	$-0.705160\pi$
$383$	−23.5166			−1.20164			−0.600822	+	0.799383i	$0.705160\pi$
$384$	−2.80008	−	12.2159i	−0.142891	−	0.623392i
$385$	−10.6072			−0.540591
$386$	−8.88112	+	4.32230i	−0.452037	+	0.219999i
$387$	3.12634	+	15.7172i	0.158921	+	0.798950i
$388$	−11.7172	−	9.18653i	−0.594852	−	0.466376i
$389$	−5.29175	+	3.53583i	−0.268302	+	0.179274i	−0.682443	−	0.730939i	$-0.739082\pi$
$389$	−5.29175	+	3.53583i	−0.268302	+	0.179274i	0.414140	+	0.910213i	$0.364082\pi$
$390$	2.43312	+	3.20535i	0.123206	+	0.162309i
$391$	−38.7825	−	16.0642i	−1.96132	−	0.812404i
$392$	12.9303	−	8.35035i	0.653077	−	0.421757i
$393$	−0.420613	+	0.174224i	−0.0212171	+	0.00878842i
$394$	2.55587	−	4.37409i	0.128763	−	0.220364i
$395$	−18.5561	−	3.69104i	−0.933660	−	0.185717i
$396$	−7.53631	+	14.8889i	−0.378714	+	0.748197i
$397$	19.7084	+	13.1687i	0.989135	+	0.660919i	0.941171	−	0.337930i	$-0.109727\pi$
$397$	19.7084	+	13.1687i	0.989135	+	0.660919i	0.0479636	+	0.998849i	$0.484727\pi$
$398$	−7.52817	+	0.454039i	−0.377353	+	0.0227589i
$399$	−0.539065	−	0.539065i	−0.0269870	−	0.0269870i
$400$	6.87875	+	1.05189i	0.343938	+	0.0525945i
$401$	6.59727	−	6.59727i	0.329452	−	0.329452i	−0.522926	−	0.852378i	$-0.675160\pi$
$401$	6.59727	−	6.59727i	0.329452	−	0.329452i	0.852378	+	0.522926i	$0.175160\pi$
$402$	4.37268	−	4.93398i	0.218090	−	0.246085i
$403$	−2.00660	+	3.00308i	−0.0999557	+	0.149594i
$404$	−3.59426	−	0.273226i	−0.178821	−	0.0135935i
$405$	−0.189574	+	0.953055i	−0.00942003	+	0.0473577i
$406$	−8.26742	+	2.16914i	−0.410305	+	0.107653i
$407$	6.33099	+	15.2844i	0.313816	+	0.757618i
$408$	−15.7892	+	15.3031i	−0.781682	+	0.757617i
$409$	15.0322	−	36.2909i	0.743294	−	1.79447i	0.151371	−	0.988477i	$-0.451631\pi$
$409$	15.0322	−	36.2909i	0.743294	−	1.79447i	0.591924	−	0.805994i	$-0.298369\pi$
$410$	15.2491	+	2.08847i	0.753099	+	0.103142i
$411$	0.615698	+	0.921457i	0.0303701	+	0.0454521i
$412$	4.28998	+	7.61260i	0.211352	+	0.375046i
$413$	6.73562	−	1.33980i	0.331438	−	0.0659271i
$414$	−14.1761	−	4.89466i	−0.696717	−	0.240559i
$415$		−	11.6523i		−	0.571987i
$416$	0.842217	+	8.00348i	0.0412931	+	0.392403i
$417$			2.07841i			0.101780i
$418$	1.19766	−	3.46870i	0.0585794	−	0.169660i
$419$	20.0398	−	3.98617i	0.979009	−	0.194737i	0.320449	−	0.947266i	$-0.396166\pi$
$419$	20.0398	−	3.98617i	0.979009	−	0.194737i	0.658560	+	0.752529i	$0.271166\pi$
$420$	−4.80944	−	1.34256i	−0.234677	−	0.0655102i
$421$	−8.12329	−	12.1574i	−0.395905	−	0.592514i	0.578947	−	0.815365i	$-0.303464\pi$
$421$	−8.12329	−	12.1574i	−0.395905	−	0.592514i	−0.974853	+	0.222851i	$0.928464\pi$
$422$	2.55013	−	18.6199i	0.124139	−	0.906403i
$423$	6.39342	−	15.4351i	0.310859	−	0.750480i
$424$	15.4773	−	35.7734i	0.751646	−	1.73731i
$425$	−4.67212	−	11.2795i	−0.226631	−	0.547136i
$426$	4.82638	+	18.3952i	0.233839	+	0.891250i
$427$	−2.24085	+	11.2655i	−0.108443	+	0.545177i
$428$	3.66875	+	4.27241i	0.177336	+	0.206515i
$429$	−4.12056	+	6.16686i	−0.198943	+	0.297739i
$430$	−17.2740	−	15.3089i	−0.833027	−	0.738260i
$431$	−8.45642	+	8.45642i	−0.407332	+	0.407332i	−0.880807	−	0.473475i	$-0.842999\pi$
$431$	−8.45642	+	8.45642i	−0.407332	+	0.407332i	0.473475	+	0.880807i	$0.342999\pi$
$432$	−14.2726	+	15.6063i	−0.686693	+	0.750860i
$433$	27.5679	+	27.5679i	1.32483	+	1.32483i	0.909816	+	0.415011i	$0.136222\pi$
$433$	27.5679	+	27.5679i	1.32483	+	1.32483i	0.415011	+	0.909816i	$0.363778\pi$
$434$	−0.269801	−	4.47342i	−0.0129509	−	0.214731i
$435$	−8.05269	−	5.38064i	−0.386097	−	0.257982i
$436$	4.51137	+	13.7595i	0.216056	+	0.658963i
$437$	3.23457	+	0.643396i	0.154730	+	0.0307778i
$438$	11.2347	+	6.56462i	0.536812	+	0.313670i
$439$	−11.1369	+	4.61307i	−0.531537	+	0.220170i	−0.632276	−	0.774743i	$-0.717879\pi$
$439$	−11.1369	+	4.61307i	−0.531537	+	0.220170i	0.100739	+	0.994913i	$0.467879\pi$
$440$	−4.32005	−	23.6443i	−0.205950	−	1.12720i
$441$	−8.91363	−	3.69214i	−0.424458	−	0.175816i
$442$	11.2463	−	8.53685i	0.534932	−	0.406057i
$443$	−26.2614	+	17.5473i	−1.24772	+	0.833697i	−0.991139	−	0.132827i	$-0.957595\pi$
$443$	−26.2614	+	17.5473i	−1.24772	+	0.833697i	−0.256576	+	0.966524i	$0.582595\pi$
$444$	0.936006	+	7.73147i	0.0444209	+	0.366920i
$445$	−0.0369863	−	0.185943i	−0.00175332	−	0.00881453i
$446$	−2.41865	−	4.96966i	−0.114526	−	0.235320i
$447$	3.03870			0.143726
$448$	−6.83677	−	7.27822i	−0.323007	−	0.343864i
$449$	−16.3035			−0.769410			−0.384705	−	0.923040i	$-0.625697\pi$
$449$	−16.3035			−0.769410			−0.384705	+	0.923040i	$0.625697\pi$
$450$	−1.90877	−	3.92199i	−0.0899803	−	0.184884i
$451$	5.53415	+	27.8220i	0.260593	+	1.31009i
$452$	−2.39119	+	0.289488i	−0.112472	+	0.0136164i
$453$	−17.4182	+	11.6384i	−0.818376	+	0.546822i
$454$	0.915150	−	0.694673i	0.0429501	−	0.0326026i
$455$	2.96230	+	1.22702i	0.138875	+	0.0575238i
$456$	0.982072	−	1.42117i	0.0459898	−	0.0665524i
$457$	−7.96515	+	3.29927i	−0.372594	+	0.154333i	−0.561119	−	0.827735i	$-0.689629\pi$
$457$	−7.96515	+	3.29927i	−0.372594	+	0.154333i	0.188526	+	0.982068i	$0.439629\pi$
$458$	−2.84066	−	1.65985i	−0.132735	−	0.0775598i
$459$	36.3917	+	7.23876i	1.69862	+	0.337876i
$460$	20.5260	−	6.72989i	0.957028	−	0.313783i
$461$	16.5861	+	11.0825i	0.772494	+	0.516164i	0.878235	−	0.478230i	$-0.158721\pi$
$461$	16.5861	+	11.0825i	0.772494	+	0.516164i	−0.105741	+	0.994394i	$0.533721\pi$
$462$	−0.554039	−	9.18621i	−0.0257762	−	0.427381i
$463$	3.14804	+	3.14804i	0.146302	+	0.146302i	0.776464	−	0.630162i	$-0.217012\pi$
$463$	3.14804	+	3.14804i	0.146302	+	0.146302i	−0.630162	+	0.776464i	$0.717012\pi$
$464$	−8.20233	−	17.5453i	−0.380783	−	0.814522i
$465$	3.59072	−	3.59072i	0.166516	−	0.166516i
$466$	−7.14597	−	6.33302i	−0.331031	−	0.293372i
$467$	9.83500	−	14.7191i	0.455110	−	0.681120i	−0.530971	−	0.847390i	$-0.678173\pi$
$467$	9.83500	−	14.7191i	0.455110	−	0.681120i	0.986080	+	0.166271i	$0.0531725\pi$
$468$	3.82703	−	3.28629i	0.176904	−	0.151909i
$469$	1.02479	−	5.15197i	0.0473204	−	0.237896i
$470$	6.10685	+	23.2755i	0.281688	+	1.07362i
$471$	2.14459	+	5.17750i	0.0988176	+	0.238567i
$472$	5.72978	+	14.4686i	0.263735	+	0.665971i
$473$	16.2794	−	39.3020i	0.748529	−	1.80711i
$474$	2.22735	−	16.2631i	0.102306	−	0.746990i
$475$	0.532887	+	0.797522i	0.0244505	+	0.0365928i
$476$	−4.71051	+	16.8744i	−0.215906	+	0.773438i
$477$	−23.9625	+	4.76643i	−1.09717	+	0.218240i
$478$	6.63200	−	19.2078i	0.303341	−	0.878546i
$479$		−	25.4529i		−	1.16297i	−0.813556	−	0.581486i	$-0.802471\pi$
$479$		−	25.4529i		−	1.16297i	0.813556	−	0.581486i	$-0.197529\pi$
$480$	1.03390	−	11.2674i	0.0471911	−	0.514286i
$481$		−	5.00088i		−	0.228020i
$482$	1.36334	+	0.470729i	0.0620986	+	0.0214411i
$483$	8.11182	−	1.61354i	0.369100	−	0.0734186i
$484$	19.4265	−	10.9476i	0.883023	−	0.497616i
$485$	−7.46807	−	11.1768i	−0.339107	−	0.507510i
$486$	21.3888	+	2.92935i	0.970215	+	0.132878i
$487$	−9.97345	+	24.0780i	−0.451940	+	1.09108i	0.519643	+	0.854383i	$0.326065\pi$
$487$	−9.97345	+	24.0780i	−0.451940	+	1.09108i	−0.971584	+	0.236697i	$0.923935\pi$
$488$	−26.0245	−	0.406862i	−1.17807	−	0.0184178i
$489$	3.35669	+	8.10376i	0.151795	+	0.366465i
$490$	13.4414	−	3.52665i	0.607222	−	0.159318i
$491$	5.00023	−	25.1379i	0.225657	−	1.13446i	−0.687292	−	0.726382i	$-0.741201\pi$
$491$	5.00023	−	25.1379i	0.225657	−	1.13446i	0.912949	−	0.408074i	$-0.133799\pi$
$492$	−1.01220	+	13.3154i	−0.0456336	+	0.600304i
$493$	−18.8785	+	28.2537i	−0.850246	+	1.27248i
$494$	−0.735729	+	0.830172i	−0.0331020	+	0.0373512i
$495$	−10.6532	+	10.6532i	−0.478825	+	0.478825i
$496$	9.86176	−	2.42333i	0.442806	−	0.108811i
$497$	10.7146	+	10.7146i	0.480617	+	0.480617i
$498$	10.0913	−	0.608626i	0.452202	−	0.0272732i
$499$	27.4357	+	18.3319i	1.22819	+	0.820650i	0.988650	−	0.150236i	$-0.0480034\pi$
$499$	27.4357	+	18.3319i	1.22819	+	0.820650i	0.239540	+	0.970886i	$0.423003\pi$
$500$	21.7154	+	10.9917i	0.971144	+	0.491563i
$501$	−21.2070	−	4.21833i	−0.947457	−	0.188461i
$502$	19.5953	−	33.5353i	0.874582	−	1.49675i
$503$	24.2013	−	10.0245i	1.07908	−	0.446971i	0.228896	−	0.973451i	$-0.426488\pi$
$503$	24.2013	−	10.0245i	1.07908	−	0.446971i	0.850188	+	0.526480i	$0.176488\pi$
$504$	−1.31691	+	6.11905i	−0.0586600	+	0.272564i
$505$	−3.00660	−	1.24537i	−0.133792	−	0.0554184i
$506$	24.0710	+	31.7107i	1.07008	+	1.40971i
$507$	−10.1096	+	6.75504i	−0.448984	+	0.300002i
$508$	−10.8987	+	13.9011i	−0.483553	+	0.616761i
$509$	1.43336	+	7.20596i	0.0635324	+	0.319399i	0.999462	−	0.0327874i	$-0.0104384\pi$
$509$	1.43336	+	7.20596i	0.0635324	+	0.319399i	−0.935930	+	0.352186i	$0.885438\pi$
$510$	−17.8497	+	8.68716i	−0.790398	+	0.384674i
$511$	10.3675			0.458633
$512$	13.4393	−	18.2040i	0.593939	−	0.804510i
$513$	−2.91508			−0.128704
$514$	22.7829	−	11.0881i	1.00491	−	0.489074i
$515$	1.53906	+	7.73739i	0.0678192	+	0.340950i
$516$	12.3558	−	15.7596i	0.543935	−	0.693778i
$517$	−36.8755	+	24.6394i	−1.62178	+	1.08364i
$518$	3.75176	+	4.94251i	0.164843	+	0.217161i
$519$	−20.5906	−	8.52890i	−0.903827	−	0.374377i
$520$	−1.52867	+	7.10295i	−0.0670364	+	0.311485i
$521$	32.4056	−	13.4228i	1.41971	−	0.588065i	0.464925	−	0.885350i	$-0.346081\pi$
$521$	32.4056	−	13.4228i	1.41971	−	0.588065i	0.954789	+	0.297285i	$0.0960813\pi$
$522$	−6.12474	+	10.4818i	−0.268073	+	0.458778i
$523$	−39.1235	−	7.78216i	−1.71075	−	0.340290i	−0.759926	−	0.650010i	$-0.774765\pi$
$523$	−39.1235	−	7.78216i	−1.71075	−	0.340290i	−0.950828	+	0.309720i	$0.899765\pi$
$524$	−0.733374	−	0.371211i	−0.0320376	−	0.0162164i
$525$	2.00007	+	1.33640i	0.0872900	+	0.0583253i
$526$	8.04494	−	0.485206i	0.350776	−	0.0211560i
$527$	−12.5984	−	12.5984i	−0.548796	−	0.548796i
$528$	20.2512	−	4.97633i	0.881320	−	0.216567i
$529$	−9.03626	+	9.03626i	−0.392881	+	0.392881i
$530$	23.3400	−	26.3360i	1.01382	−	1.14396i
$531$	5.41923	−	8.11045i	0.235175	−	0.351964i
$532$	0.104330	−	1.37244i	0.00452326	−	0.0595029i
$533$	1.67288	−	8.41014i	0.0724606	−	0.364284i
$534$	0.159102	−	0.0417438i	0.00688500	−	0.00180643i
$535$	1.94563	+	4.69716i	0.0841169	+	0.203076i
$536$	11.9016	+	0.186067i	0.514069	+	0.00803686i
$537$	−0.268738	+	0.648791i	−0.0115969	+	0.0279974i
$538$	−29.2406	−	4.00472i	−1.26065	−	0.172656i
$539$	14.2291	+	21.2953i	0.612889	+	0.917253i
$540$	−16.6340	+	9.37385i	−0.715811	+	0.403386i
$541$	−21.8431	+	4.34486i	−0.939108	+	0.186800i	−0.640833	−	0.767680i	$-0.721411\pi$
$541$	−21.8431	+	4.34486i	−0.939108	+	0.186800i	−0.298274	+	0.954480i	$0.596411\pi$
$542$	−41.4478	−	14.3109i	−1.78033	−	0.614706i
$543$		−	23.3043i		−	1.00008i
$544$	−39.5330	−	3.62756i	−1.69496	−	0.155530i
$545$			13.0730i			0.559987i
$546$	−0.907922	+	2.62956i	−0.0388555	+	0.112535i
$547$	13.0083	−	2.58751i	0.556195	−	0.110634i	0.0910141	−	0.995850i	$-0.470989\pi$
$547$	13.0083	−	2.58751i	0.556195	−	0.110634i	0.465181	+	0.885215i	$0.345989\pi$
$548$	−0.537975	+	1.92719i	−0.0229812	+	0.0823253i
$549$	9.06383	+	13.5650i	0.386835	+	0.578939i
$550$	−1.57114	+	11.4718i	−0.0669937	+	0.489157i
$551$	1.02162	−	2.46641i	0.0435226	−	0.105073i
$552$	6.90047	+	17.4248i	0.293704	+	0.741647i
$553$	−5.00508	−	12.0833i	−0.212838	−	0.513835i
$554$	−2.32796	−	8.87274i	−0.0989055	−	0.376967i
$555$	−1.37170	+	6.89598i	−0.0582252	+	0.292718i
$556$	−2.84691	+	2.44466i	−0.120736	+	0.103677i
$557$	−1.47481	+	2.20722i	−0.0624899	+	0.0935227i	−0.861399	−	0.507930i	$-0.830411\pi$
$557$	−1.47481	+	2.20722i	−0.0624899	+	0.0935227i	0.798909	+	0.601452i	$0.205411\pi$
$558$	−4.76380	−	4.22186i	−0.201668	−	0.178726i
$559$	−9.09282	+	9.09282i	−0.384585	+	0.384585i
$560$	−3.81796	−	8.16688i	−0.161338	−	0.345114i
$561$	−25.8710	−	25.8710i	−1.09227	−	1.09227i
$562$	−1.10662	−	18.3482i	−0.0466798	−	0.773973i
$563$	14.8288	+	9.90826i	0.624958	+	0.417583i	0.827323	−	0.561727i	$-0.189863\pi$
$563$	14.8288	+	9.90826i	0.624958	+	0.417583i	−0.202365	+	0.979310i	$0.564863\pi$
$564$	−19.8386	+	6.50451i	−0.835354	+	0.273889i
$565$	−2.13279	−	0.424238i	−0.0897271	−	0.0178478i
$566$	−24.5523	−	14.3464i	−1.03201	−	0.603023i
$567$	−0.620607	+	0.257064i	−0.0260631	+	0.0107957i
$568$	−19.5200	+	28.2476i	−0.819041	+	1.18524i
$569$	−3.56901	−	1.47833i	−0.149621	−	0.0619750i	0.306616	−	0.951833i	$-0.400803\pi$
$569$	−3.56901	−	1.47833i	−0.149621	−	0.0619750i	−0.456237	+	0.889858i	$0.650803\pi$
$570$	1.24224	−	0.942964i	0.0520319	−	0.0394964i
$571$	−1.49113	+	0.996342i	−0.0624019	+	0.0416956i	−0.586380	−	0.810036i	$-0.699447\pi$
$571$	−1.49113	+	0.996342i	−0.0624019	+	0.0416956i	0.523978	+	0.851732i	$0.324447\pi$
$572$	−13.2937	+	1.60940i	−0.555839	+	0.0672923i
$573$	−3.57145	−	17.9549i	−0.149200	−	0.750077i
$574$	4.65611	+	9.56701i	0.194342	+	0.399319i
$575$	−10.4060			−0.433961
$576$	−14.1762	−	0.443366i	−0.590676	−	0.0184736i
$577$	−31.2426			−1.30065			−0.650323	−	0.759658i	$-0.725366\pi$
$577$	−31.2426			−1.30065			−0.650323	+	0.759658i	$0.725366\pi$
$578$	19.9590	+	41.0101i	0.830183	+	1.70580i
$579$	−1.50935	−	7.58802i	−0.0627265	−	0.315347i
$580$	−2.10155	−	17.3590i	−0.0872622	−	0.720792i
$581$	6.69752	−	4.47514i	0.277860	−	0.185660i
$582$	9.28943	−	7.05143i	0.385059	−	0.292291i
$583$	59.9199	+	24.8196i	2.48163	+	1.02792i
$584$	4.22245	+	23.1101i	0.174726	+	0.956303i
$585$	4.20750	−	1.74280i	0.173959	−	0.0720560i
$586$	0.453824	+	0.265178i	0.0187473	+	0.0109544i
$587$	4.26386	+	0.848135i	0.175988	+	0.0350063i	0.282298	−	0.959327i	$-0.408903\pi$
$587$	4.26386	+	0.848135i	0.175988	+	0.0350063i	−0.106309	+	0.994333i	$0.533903\pi$
$588$	3.75630	+	11.4566i	0.154907	+	0.472462i
$589$	1.16386	+	0.777664i	0.0479559	+	0.0320431i
$590$	0.845816	+	14.0240i	0.0348217	+	0.577360i
$591$	2.80597	+	2.80597i	0.115422	+	0.115422i
$592$	−9.48926	+	10.3760i	−0.390006	+	0.426450i
$593$	−5.65821	+	5.65821i	−0.232355	+	0.232355i	−0.813675	−	0.581320i	$-0.802536\pi$
$593$	−5.65821	+	5.65821i	−0.232355	+	0.232355i	0.581320	+	0.813675i	$0.302536\pi$
$594$	−26.3360	−	23.3399i	−1.08058	−	0.957648i
$595$	−8.78744	+	13.1513i	−0.360250	+	0.539152i
$596$	3.57417	+	4.16227i	0.146404	+	0.170493i
$597$	1.15250	−	5.79399i	0.0471686	−	0.237132i
$598$	−3.05413	−	11.6404i	−0.124893	−	0.476013i
$599$	−1.01558	−	2.45183i	−0.0414955	−	0.100179i	0.901773	−	0.432210i	$-0.142266\pi$
$599$	−1.01558	−	2.45183i	−0.0414955	−	0.100179i	−0.943268	+	0.332031i	$0.892266\pi$
$600$	−2.16437	+	5.00260i	−0.0883601	+	0.204230i
$601$	−8.80161	+	21.2490i	−0.359025	+	0.866764i	0.636412	+	0.771349i	$0.280418\pi$
$601$	−8.80161	+	21.2490i	−0.359025	+	0.866764i	−0.995438	+	0.0954147i	$0.969582\pi$
$602$	2.16506	−	15.8083i	0.0882415	−	0.644299i
$603$	−4.14508	−	6.20356i	−0.168801	−	0.252628i
$604$	−36.4293	−	10.1693i	−1.48229	−	0.413781i
$605$	19.7450	−	3.92752i	0.802747	−	0.159676i
$606$	0.921500	−	2.66888i	0.0374334	−	0.108416i
$607$			16.6530i			0.675924i	0.941160	+	0.337962i	$0.109738\pi$
$607$			16.6530i			0.675924i	−0.941160	+	0.337962i	$0.890262\pi$
$608$	3.10178	−	0.326404i	0.125794	−	0.0132374i
$609$		−	6.69503i		−	0.271296i
$610$	−22.2115	−	7.66910i	−0.899318	−	0.310513i
$611$	13.1486	−	2.61542i	0.531936	−	0.105809i
$612$	12.2167	+	21.6786i	0.493830	+	0.876304i
$613$	−6.62294	−	9.91193i	−0.267498	−	0.400339i	0.673266	−	0.739400i	$-0.264891\pi$
$613$	−6.62294	−	9.91193i	−0.267498	−	0.400339i	−0.940764	+	0.339061i	$0.889891\pi$
$614$	24.3260	+	3.33163i	0.981718	+	0.134453i
$615$	−4.61365	+	11.1383i	−0.186040	+	0.449141i
$616$	11.9312	−	11.5639i	0.480721	−	0.465921i
$617$	−8.25983	−	19.9410i	−0.332528	−	0.802794i	−0.998390	−	0.0567193i	$-0.981936\pi$
$617$	−8.25983	−	19.9410i	−0.332528	−	0.802794i	0.665862	−	0.746075i	$-0.268064\pi$
$618$	−6.62050	+	1.73703i	−0.266315	+	0.0698737i
$619$	6.14302	−	30.8830i	0.246909	−	1.24129i	−0.635978	−	0.771707i	$-0.719403\pi$
$619$	6.14302	−	30.8830i	0.246909	−	1.24129i	0.882886	−	0.469587i	$-0.155597\pi$
$620$	9.14186	+	0.694941i	0.367146	+	0.0279095i
$621$	17.5702	−	26.2957i	0.705068	−	1.05521i
$622$	−9.39026	+	10.5957i	−0.376515	+	0.424847i
$623$	0.0926719	−	0.0926719i	0.00371282	−	0.00371282i
$624$	−6.23128	−	0.952878i	−0.249451	−	0.0381457i
$625$	9.38693	+	9.38693i	0.375477	+	0.375477i
$626$	6.10200	−	0.368023i	0.243885	−	0.0147092i
$627$	2.38999	+	1.59694i	0.0954469	+	0.0637756i
$628$	−4.56940	+	9.02742i	−0.182339	+	0.360233i
$629$	24.1953	+	4.81274i	0.964728	+	0.191896i
$630$	−2.85090	+	4.87901i	−0.113583	+	0.194385i
$631$	1.20930	−	0.500909i	0.0481415	−	0.0199409i	−0.358483	−	0.933536i	$-0.616706\pi$
$631$	1.20930	−	0.500909i	0.0481415	−	0.0199409i	0.406624	+	0.913595i	$0.366706\pi$
$632$	24.8963	−	16.0780i	0.990322	−	0.639548i
$633$	13.6005	+	5.63350i	0.540571	+	0.223912i
$634$	7.24804	+	9.54844i	0.287856	+	0.379217i
$635$	−13.2599	+	8.85997i	−0.526202	+	0.351597i
$636$	24.0271	+	18.8377i	0.952737	+	0.746964i
$637$	−1.51038	−	7.59321i	−0.0598436	−	0.300854i
$638$	28.9774	−	14.1028i	1.14723	−	0.558336i
$639$	21.5222			0.851406
$640$	16.6497	−	11.8367i	0.658137	−	0.467888i
$641$	28.7275			1.13467			0.567334	−	0.823488i	$-0.307975\pi$
$641$	28.7275			1.13467			0.567334	+	0.823488i	$0.307975\pi$
$642$	−3.96630	+	1.93034i	−0.156537	+	0.0761843i
$643$	−7.40711	−	37.2381i	−0.292108	−	1.46853i	−0.796283	−	0.604924i	$-0.793203\pi$
$643$	−7.40711	−	37.2381i	−0.292108	−	1.46853i	0.504175	−	0.863601i	$-0.331797\pi$
$644$	11.7514	+	9.21331i	0.463070	+	0.363055i
$645$	15.0327	−	10.0445i	0.591910	−	0.395502i
$646$	−3.30849	−	4.35854i	−0.130171	−	0.171485i
$647$	−15.7606	−	6.52825i	−0.619612	−	0.256652i	0.0507199	−	0.998713i	$-0.483848\pi$
$647$	−15.7606	−	6.52825i	−0.619612	−	0.256652i	−0.670332	+	0.742061i	$0.733848\pi$
$648$	−0.825776	−	1.27869i	−0.0324396	−	0.0502317i
$649$	−23.9228	+	9.90915i	−0.939052	+	0.388968i
$650$	1.76582	−	3.02201i	0.0692611	−	0.118533i
$651$	3.44293	+	0.684842i	0.134939	+	0.0268411i
$652$	−7.15196	+	14.1296i	−0.280093	+	0.553358i
$653$	15.5969	+	10.4215i	0.610353	+	0.407825i	0.821972	−	0.569527i	$-0.192874\pi$
$653$	15.5969	+	10.4215i	0.610353	+	0.407825i	−0.211620	+	0.977352i	$0.567874\pi$
$654$	−11.3218	+	0.682837i	−0.442715	+	0.0267010i
$655$	−0.524737	−	0.524737i	−0.0205032	−	0.0205032i
$656$	−19.4294	+	14.2753i	−0.758589	+	0.557356i
$657$	10.4125	−	10.4125i	0.406231	−	0.406231i
$658$	−11.0330	+	12.4493i	−0.430111	+	0.485323i
$659$	5.14889	−	7.70586i	0.200572	−	0.300178i	−0.717525	−	0.696533i	$-0.754725\pi$
$659$	5.14889	−	7.70586i	0.200572	−	0.300178i	0.918097	+	0.396355i	$0.129725\pi$
$660$	18.7729	+	1.42707i	0.730734	+	0.0555485i
$661$	5.30290	−	26.6595i	0.206259	−	1.03693i	−0.729416	−	0.684070i	$-0.760208\pi$
$661$	5.30290	−	26.6595i	0.206259	−	1.03693i	0.935675	−	0.352863i	$-0.114792\pi$
$662$	−17.0547	+	4.47468i	−0.662851	+	0.173914i
$663$	4.23235	+	10.2178i	0.164371	+	0.396826i
$664$	12.7032	+	13.1067i	0.492980	+	0.508639i
$665$	0.475538	−	1.14805i	0.0184406	−	0.0445194i
$666$	8.73199	+	1.19591i	0.338358	+	0.0463406i
$667$	16.0908	+	24.0816i	0.623039	+	0.932443i
$668$	−19.1659	−	34.0099i	−0.741550	−	1.31588i
$669$	4.24607	−	0.844595i	0.164162	−	0.0326539i
$670$	10.1578	+	3.50725i	0.392430	+	0.135497i
$671$		−	43.3083i		−	1.67190i
$672$	6.87342	−	3.73308i	0.265148	−	0.144007i
$673$			13.9409i			0.537384i	0.963226	+	0.268692i	$0.0865914\pi$
$673$			13.9409i			0.537384i	−0.963226	+	0.268692i	$0.913409\pi$
$674$	−1.22976	+	3.56166i	−0.0473684	+	0.137190i
$675$	9.02123	−	1.79443i	0.347227	−	0.0690678i
$676$	−21.1438	−	5.90231i	−0.813224	−	0.227012i
$677$	−13.7047	−	20.5105i	−0.526713	−	0.788281i	0.468760	−	0.883325i	$-0.344701\pi$
$677$	−13.7047	−	20.5105i	−0.526713	−	0.788281i	−0.995473	+	0.0950442i	$0.969701\pi$
$678$	0.256006	−	1.86924i	0.00983184	−	0.0717876i
$679$	3.55604	−	8.58504i	0.136468	−	0.329464i
$680$	−32.8943	−	14.2317i	−1.26144	−	0.545761i
$681$	0.344401	+	0.831457i	0.0131975	+	0.0318615i
$682$	4.28828	+	16.3443i	0.164207	+	0.625855i
$683$	−7.64710	+	38.4446i	−0.292608	+	1.47104i	0.502502	+	0.864576i	$0.332413\pi$
$683$	−7.64710	+	38.4446i	−0.292608	+	1.47104i	−0.795110	+	0.606465i	$0.792587\pi$
$684$	−1.27361	−	1.48318i	−0.0486978	−	0.0567107i
$685$	−1.00359	+	1.50198i	−0.0383453	+	0.0573877i
$686$	16.4370	+	14.5671i	0.627567	+	0.556173i
$687$	1.82228	−	1.82228i	0.0695241	−	0.0695241i
$688$	36.1198	−	1.61225i	1.37706	−	0.0614663i
$689$	−13.8629	−	13.8629i	−0.528136	−	0.528136i
$690$	1.01863	+	16.8894i	0.0387786	+	0.642967i
$691$	−15.7489	−	10.5231i	−0.599115	−	0.400316i	0.218704	−	0.975791i	$-0.429817\pi$
$691$	−15.7489	−	10.5231i	−0.599115	−	0.400316i	−0.817819	+	0.575475i	$0.804817\pi$
$692$	−12.5365	−	38.2358i	−0.476565	−	1.45351i
$693$	−10.2147	−	2.03183i	−0.388025	−	0.0771829i
$694$	19.9692	+	11.6684i	0.758019	+	0.442925i
$695$	−3.12994	+	1.29646i	−0.118725	+	0.0491777i
$696$	14.9238	−	2.72673i	0.565684	−	0.103356i
$697$	39.0800	+	16.1875i	1.48026	+	0.613144i
$698$	−15.4580	+	11.7338i	−0.585092	+	0.444132i
$699$	6.21875	−	4.15524i	0.235215	−	0.157165i
$700$	0.521968	+	4.31149i	0.0197285	+	0.162959i
$701$	4.38884	+	22.0642i	0.165764	+	0.833353i	0.970756	+	0.240067i	$0.0771695\pi$
$701$	4.38884	+	22.0642i	0.165764	+	0.833353i	−0.804992	+	0.593286i	$0.797830\pi$
$702$	4.65500	+	9.56473i	0.175692	+	0.360998i
$703$	−1.93811			−0.0730971
$704$	30.6361	+	21.8859i	1.15464	+	0.824856i
$705$	−18.8487			−0.709884
$706$	−11.6419	−	23.9210i	−0.438150	−	0.900277i
$707$	−0.438888	−	2.20644i	−0.0165061	−	0.0829817i
$708$	−12.1012	+	1.46502i	−0.454790	+	0.0550588i
$709$	−0.257873	+	0.172305i	−0.00968464	+	0.00647107i	−0.560403	−	0.828220i	$-0.689354\pi$
$709$	−0.257873	+	0.172305i	−0.00968464	+	0.00647107i	0.550718	+	0.834691i	$0.314354\pi$
$710$	−24.6913	+	18.7427i	−0.926647	+	0.703400i
$711$	−17.1625	−	7.10896i	−0.643646	−	0.266607i
$712$	0.244316	+	0.168830i	0.00915615	+	0.00632718i
$713$	−14.0300	+	5.81140i	−0.525426	+	0.217639i
$714$	−11.8486	−	6.92334i	−0.443421	−	0.259099i
$715$	−11.8572	−	2.35854i	−0.443433	−	0.0882043i
$716$	−1.20478	+	0.395013i	−0.0450246	+	0.0147623i
$717$	13.2345	+	8.84301i	0.494251	+	0.330248i
$718$	−2.99256	−	49.6180i	−0.111681	−	1.85173i
$719$	13.5820	+	13.5820i	0.506522	+	0.506522i	0.913457	−	0.406935i	$-0.133403\pi$
$719$	13.5820	+	13.5820i	0.506522	+	0.506522i	−0.406935	+	0.913457i	$0.633403\pi$
$720$	−12.0368	−	4.36779i	−0.448586	−	0.162778i
$721$	−3.85623	+	3.85623i	−0.143614	+	0.143614i
$722$	−19.7877	−	17.5366i	−0.736420	−	0.652643i
$723$	−0.627663	+	0.939365i	−0.0233431	+	0.0349353i
$724$	31.9211	−	27.4108i	1.18634	−	1.01871i
$725$	−1.64334	+	8.26165i	−0.0610323	+	0.306830i
$726$	4.43271	+	16.8948i	0.164513	+	0.627023i
$727$	−0.663094	−	1.60085i	−0.0245928	−	0.0593723i	0.911106	−	0.412172i	$-0.135230\pi$
$727$	−0.663094	−	1.60085i	−0.0245928	−	0.0593723i	−0.935699	+	0.352800i	$0.885230\pi$
$728$	−4.66975	+	1.84929i	−0.173073	+	0.0685394i
$729$	−7.08907	+	17.1145i	−0.262558	+	0.633872i
$730$	−2.87795	+	21.0134i	−0.106518	+	0.777742i
$731$	−35.2422	−	52.7436i	−1.30348	−	1.95079i
$732$	5.48158	−	19.6366i	0.202605	−	0.725790i
$733$	27.6629	−	5.50250i	1.02175	−	0.203239i	0.344343	−	0.938844i	$-0.388102\pi$
$733$	27.6629	−	5.50250i	1.02175	−	0.203239i	0.677411	+	0.735605i	$0.263102\pi$
$734$	−14.0543	+	40.7046i	−0.518755	+	1.50244i
$735$			10.8850i			0.401498i
$736$	−15.7512	+	29.9472i	−0.580596	+	1.10387i
$737$			19.8058i			0.729557i
$738$	14.2848	+	4.93221i	0.525832	+	0.181557i
$739$	−33.7821	+	6.71968i	−1.24269	+	0.247187i	−0.772294	−	0.635266i	$-0.780891\pi$
$739$	−33.7821	+	6.71968i	−1.24269	+	0.247187i	−0.470401	+	0.882453i	$0.655891\pi$
$740$	−11.0592	+	6.23227i	−0.406544	+	0.229103i
$741$	−0.482728	−	0.722454i	−0.0177335	−	0.0265400i
$742$	24.1014	+	3.30086i	0.884790	+	0.121178i
$743$	−10.3053	+	24.8793i	−0.378066	+	0.912733i	0.614262	+	0.789102i	$0.289454\pi$
$743$	−10.3053	+	24.8793i	−0.378066	+	0.912733i	−0.992328	+	0.123630i	$0.960546\pi$
$744$	−0.124344	+	7.95351i	−0.00455866	+	0.291590i
$745$	1.89547	+	4.57607i	0.0694447	+	0.167654i
$746$	−10.1413	+	2.66080i	−0.371301	+	0.0974189i
$747$	2.23202	−	11.2211i	0.0816654	−	0.410560i
$748$	5.00701	−	65.8666i	0.183075	−	2.40832i
$749$	−1.95262	+	2.92230i	−0.0713471	+	0.106778i
$750$	−12.6446	+	14.2678i	−0.461716	+	0.520985i
$751$	15.9076	−	15.9076i	0.580475	−	0.580475i	−0.354559	−	0.935034i	$-0.615369\pi$
$751$	15.9076	−	15.9076i	0.580475	−	0.580475i	0.935034	+	0.354559i	$0.115369\pi$
$752$	−32.2440	−	19.5232i	−1.17582	−	0.711938i
$753$	21.5128	+	21.5128i	0.783971	+	0.783971i
$754$	−9.72401	+	0.586474i	−0.354128	+	0.0213581i
$755$	−28.3917	−	18.9707i	−1.03328	−	0.690415i
$756$	−11.7763	−	5.96081i	−0.428301	−	0.216793i
$757$	46.5995	+	9.26922i	1.69369	+	0.336896i	0.945260	−	0.326319i	$-0.105808\pi$
$757$	46.5995	+	9.26922i	1.69369	+	0.336896i	0.748429	+	0.663215i	$0.230808\pi$
$758$	0.0319798	−	0.0547299i	0.00116156	−	0.00198788i
$759$	−28.8106	+	11.9338i	−1.04576	+	0.433168i
$760$	2.75277	+	0.592440i	0.0998536	+	0.0214900i
$761$	−20.7338	−	8.58822i	−0.751599	−	0.311323i	−0.0262054	−	0.999657i	$-0.508342\pi$
$761$	−20.7338	−	8.58822i	−0.751599	−	0.311323i	−0.725394	+	0.688334i	$0.758342\pi$
$762$	−8.36567	−	11.0208i	−0.303056	−	0.399241i
$763$	−7.51416	+	5.02080i	−0.272031	+	0.181765i
$764$	20.3930	−	26.0108i	0.737792	−	0.941039i
$765$	4.38282	+	22.0339i	0.158461	+	0.796639i
$766$	29.9040	−	14.5538i	1.08048	−	0.525851i
$767$	7.82729			0.282627
$768$	11.1207	+	13.8010i	0.401285	+	0.498002i
$769$	−4.49974			−0.162265			−0.0811325	−	0.996703i	$-0.525854\pi$
$769$	−4.49974			−0.162265			−0.0811325	+	0.996703i	$0.525854\pi$
$770$	13.4882	−	6.56448i	0.486081	−	0.236568i
$771$	3.87196	+	19.4657i	0.139445	+	0.701039i
$772$	8.61838	−	10.9926i	0.310182	−	0.395631i
$773$	−16.5712	+	11.0725i	−0.596024	+	0.398250i	−0.816671	−	0.577103i	$-0.804183\pi$
$773$	−16.5712	+	11.0725i	−0.596024	+	0.398250i	0.220647	+	0.975354i	$0.429183\pi$
$774$	−13.7024	−	18.0514i	−0.492524	−	0.648842i
$775$	−4.08047	−	1.69019i	−0.146575	−	0.0607133i
$776$	20.5851	+	4.43023i	0.738961	+	0.159036i
$777$	−4.49050	+	1.86003i	−0.161096	+	0.0667281i
$778$	4.54082	−	7.77112i	0.162796	−	0.278608i
$779$	−3.25938	−	0.648331i	−0.116779	−	0.0232289i
$780$	−5.07769	−	2.57017i	−0.181810	−	0.0920268i
$781$	−47.5042	−	31.7413i	−1.69983	−	1.13579i
$782$	59.2580	−	3.57397i	2.11906	−	0.127805i
$783$	−18.1022	−	18.1022i	−0.646920	−	0.646920i
$784$	−11.2745	+	18.6206i	−0.402660	+	0.665022i
$785$	−6.45921	+	6.45921i	−0.230539	+	0.230539i
$786$	0.427034	−	0.481851i	0.0152318	−	0.0171870i
$787$	−17.9715	+	26.8963i	−0.640615	+	0.958748i	0.359062	+	0.933314i	$0.383097\pi$
$787$	−17.9715	+	26.8963i	−0.640615	+	0.958748i	−0.999677	+	0.0254341i	$0.991903\pi$
$788$	−0.543061	+	7.14390i	−0.0193458	+	0.254491i
$789$	−1.23161	+	6.19172i	−0.0438465	+	0.220431i
$790$	25.8805	−	6.79031i	0.920786	−	0.241588i
$791$	−0.575269	−	1.38882i	−0.0204542	−	0.0493809i
$792$	0.368911	−	23.5970i	0.0131087	−	0.838481i
$793$	−5.00985	+	12.0949i	−0.177905	+	0.429501i
$794$	−33.2112	−	4.54851i	−1.17862	−	0.161421i
$795$	15.3139	+	22.9188i	0.543127	+	0.812847i
$796$	9.29192	−	5.23634i	0.329343	−	0.185597i
$797$	5.55329	−	1.10462i	0.196708	−	0.0391276i	−0.0957531	−	0.995405i	$-0.530526\pi$
$797$	5.55329	−	1.10462i	0.196708	−	0.0391276i	0.292461	+	0.956278i	$0.405526\pi$
$798$	1.01909	+	0.351869i	0.0360755	+	0.0124560i
$799$			66.1327i			2.33961i
$800$	−9.39809	+	2.91948i	−0.332273	+	0.103219i
$801$		−	0.186148i		−	0.00657721i
$802$	−4.30629	+	12.4720i	−0.152060	+	0.440403i
$803$	−38.3392	+	7.62613i	−1.35296	+	0.269120i
$804$	−2.50684	+	8.98025i	−0.0884096	+	0.316709i
$805$	7.48984	+	11.2093i	0.263982	+	0.395077i
$806$	0.693085	−	5.06059i	0.0244129	−	0.178252i
$807$	8.84683	−	21.3581i	0.311423	−	0.751842i
$808$	4.73959	−	1.87695i	0.166738	−	0.0660309i
$809$	10.2838	+	24.8272i	0.361558	+	0.872877i	0.995073	+	0.0991470i	$0.0316114\pi$
$809$	10.2838	+	24.8272i	0.361558	+	0.872877i	−0.633515	+	0.773730i	$0.718389\pi$
$810$	−0.348755	−	1.32924i	−0.0122540	−	0.0467047i
$811$	2.63030	−	13.2234i	0.0923624	−	0.464337i	−0.906729	−	0.421714i	$-0.861429\pi$
$811$	2.63030	−	13.2234i	0.0923624	−	0.464337i	0.999091	−	0.0426231i	$-0.0135715\pi$
$812$	9.17053	−	7.87479i	0.321823	−	0.276351i
$813$	19.0820	−	28.5582i	0.669233	−	1.00158i
$814$	−17.5096	−	15.5177i	−0.613713	−	0.543895i
$815$	−10.1099	+	10.1099i	−0.354133	+	0.354133i
$816$	10.6071	−	29.2311i	0.371321	−	1.02329i
$817$	3.52395	+	3.52395i	0.123288	+	0.123288i
$818$	3.34436	+	55.4510i	0.116933	+	1.93880i
$819$	2.61766	+	1.74906i	0.0914683	+	0.0611172i
$820$	−20.6834	+	6.78152i	−0.722296	+	0.236821i
$821$	−45.5370	−	9.05787i	−1.58925	−	0.316122i	−0.680272	−	0.732960i	$-0.738138\pi$
$821$	−45.5370	−	9.05787i	−1.58925	−	0.316122i	−0.908981	+	0.416838i	$0.863138\pi$
$822$	−1.35319	−	0.790697i	−0.0471980	−	0.0275787i
$823$	30.3233	−	12.5603i	1.05701	−	0.437826i	0.214618	−	0.976698i	$-0.431149\pi$
$823$	30.3233	−	12.5603i	1.05701	−	0.437826i	0.842388	+	0.538872i	$0.181149\pi$
$824$	−10.1664	−	7.02532i	−0.354164	−	0.244739i
$825$	−8.37928	−	3.47081i	−0.291729	−	0.120838i
$826$	−7.73593	+	5.87219i	−0.269167	+	0.204320i
$827$	37.9550	−	25.3607i	1.31982	−	0.881879i	0.321932	−	0.946763i	$-0.395668\pi$
$827$	37.9550	−	25.3607i	1.31982	−	0.881879i	0.997893	+	0.0648841i	$0.0206678\pi$
$828$	21.0556	−	2.54909i	0.731734	−	0.0885869i
$829$	−3.97771	−	19.9973i	−0.138152	−	0.694535i	−0.986324	−	0.164816i	$-0.947297\pi$
$829$	−3.97771	−	19.9973i	−0.138152	−	0.694535i	0.848173	−	0.529720i	$-0.177703\pi$
$830$	7.21126	+	14.8171i	0.250307	+	0.514310i
$831$	7.18522			0.249252
$832$	−6.02411	−	9.65610i	−0.208849	−	0.334765i
$833$	38.1910			1.32324
$834$	−1.28627	−	2.64293i	−0.0445400	−	0.0915173i
$835$	−6.87590	−	34.5675i	−0.237950	−	1.19626i
$836$	0.623728	+	5.15204i	0.0215721	+	0.178187i
$837$	11.1608	−	7.45740i	0.385773	−	0.257765i
$838$	−23.0159	+	17.4710i	−0.795072	+	0.603524i
$839$	20.2814	+	8.40084i	0.700193	+	0.290029i	0.704239	−	0.709963i	$-0.251288\pi$
$839$	20.2814	+	8.40084i	0.700193	+	0.290029i	−0.00404689	+	0.999992i	$0.501288\pi$
$840$	6.94662	−	1.26922i	0.239681	−	0.0437922i
$841$	−5.13231	+	2.12587i	−0.176976	+	0.0733059i
$842$	17.8535	+	10.4322i	0.615274	+	0.359516i
$843$	14.1215	+	2.80895i	0.486372	+	0.0967454i
$844$	8.28058	+	25.2555i	0.285029	+	0.869330i
$845$	−16.4787	−	11.0107i	−0.566886	−	0.378781i
$846$	1.42241	+	23.5842i	0.0489033	+	0.810840i
$847$	9.84068	+	9.84068i	0.338130	+	0.338130i
$848$	2.45804	+	55.0684i	0.0844093	+	1.89106i
$849$	15.7502	−	15.7502i	0.540546	−	0.540546i
$850$	12.9217	+	11.4517i	0.443211	+	0.392790i
$851$	11.6817	−	17.4829i	0.400443	−	0.599305i
$852$	−17.5216	−	20.4046i	−0.600279	−	0.699051i
$853$	−8.80554	+	44.2684i	−0.301496	+	1.51572i	0.471816	+	0.881697i	$0.343599\pi$
$853$	−8.80554	+	44.2684i	−0.301496	+	1.51572i	−0.773312	+	0.634025i	$0.781401\pi$
$854$	−4.12244	−	15.7122i	−0.141067	−	0.537660i
$855$	−0.675429	−	1.63063i	−0.0230992	−	0.0557664i
$856$	−7.30930	−	3.16236i	−0.249827	−	0.108087i
$857$	−6.43402	+	15.5331i	−0.219782	+	0.530600i	−0.994859	−	0.101266i	$-0.967711\pi$
$857$	−6.43402	+	15.5331i	−0.219782	+	0.530600i	0.775078	+	0.631866i	$0.217711\pi$
$858$	1.42325	−	10.3920i	0.0485891	−	0.354776i
$859$	−17.3896	−	26.0253i	−0.593324	−	0.887972i	0.406345	−	0.913720i	$-0.366803\pi$
$859$	−17.3896	−	26.0253i	−0.593324	−	0.887972i	−0.999668	+	0.0257480i	$0.991803\pi$
$860$	31.4401	+	8.77653i	1.07210	+	0.299277i
$861$	−8.17404	+	1.62592i	−0.278571	+	0.0554111i
$862$	5.51984	−	15.9867i	0.188006	−	0.544511i
$863$			29.5149i			1.00470i	0.864665	+	0.502349i	$0.167531\pi$
$863$			29.5149i			1.00470i	−0.864665	+	0.502349i	$0.832469\pi$
$864$	8.49093	−	28.6781i	0.288867	−	0.975650i
$865$		−	36.3281i		−	1.23519i
$866$	−52.1166	−	17.9946i	−1.77100	−	0.611482i
$867$	−35.0390	+	6.96969i	−1.18999	+	0.236703i
$868$	3.11156	+	5.52149i	0.105613	+	0.187411i
$869$	27.3970	+	41.0026i	0.929381	+	1.39092i
$870$	13.5698	+	1.85849i	0.460060	+	0.0630086i
$871$	2.29111	−	5.53124i	0.0776315	−	0.187419i
$872$	−14.2521	−	14.7048i	−0.482638	−	0.497968i
$873$	−5.05082	−	12.1937i	−0.170944	−	0.412696i
$874$	−4.51130	+	1.18364i	−0.152597	+	0.0400371i
$875$	−2.96342	+	14.8981i	−0.100182	+	0.503648i
$876$	−18.3488	−	1.39483i	−0.619948	−	0.0471269i
$877$	14.9195	−	22.3286i	0.503796	−	0.753983i	−0.489195	−	0.872174i	$-0.662709\pi$
$877$	14.9195	−	22.3286i	0.503796	−	0.753983i	0.992991	+	0.118191i	$0.0377095\pi$
$878$	11.3070	−	12.7584i	0.381592	−	0.430575i
$879$	−0.291127	+	0.291127i	−0.00981946	+	0.00981946i
$880$	20.1262	+	27.3928i	0.678455	+	0.923409i
$881$	−30.5958	−	30.5958i	−1.03080	−	1.03080i	−0.999510	−	0.0312894i	$-0.990039\pi$
$881$	−30.5958	−	30.5958i	−1.03080	−	1.03080i	−0.0312894	−	0.999510i	$-0.509961\pi$
$882$	13.6196	−	0.821427i	0.458597	−	0.0276589i
$883$	2.58481	+	1.72711i	0.0869856	+	0.0581219i	0.598302	−	0.801270i	$-0.295842\pi$
$883$	2.58481	+	1.72711i	0.0869856	+	0.0581219i	−0.511317	+	0.859392i	$0.670842\pi$
$884$	−9.01770	+	17.8156i	−0.303298	+	0.599203i
$885$	−10.7935	−	2.14695i	−0.362818	−	0.0721690i
$886$	22.5347	−	38.5658i	0.757069	−	1.29564i
$887$	−34.8607	+	14.4398i	−1.17051	+	0.484840i	−0.881360	−	0.472445i	$-0.843371\pi$
$887$	−34.8607	+	14.4398i	−1.17051	+	0.484840i	−0.289146	+	0.957285i	$0.593371\pi$
$888$	−5.97504	−	9.25217i	−0.200509	−	0.310482i
$889$	−10.1851	−	4.21882i	−0.341598	−	0.141495i
$890$	0.162107	+	0.213557i	0.00543384	+	0.00715845i
$891$	2.10592	−	1.40713i	0.0705509	−	0.0471406i
$892$	6.15117	+	4.82263i	0.205956	+	0.161474i
$893$	−1.01362	−	5.09580i	−0.0339194	−	0.170524i
$894$	−3.86405	+	1.88057i	−0.129233	+	0.0628957i
$895$	−1.14467			−0.0382620
$896$	13.1980	+	5.02398i	0.440915	+	0.167839i
$897$	9.42653			0.314743
$898$	20.7317	−	10.0898i	0.691827	−	0.336701i
$899$	2.39820	+	12.0566i	0.0799844	+	0.402109i
$900$	4.85443	+	3.80596i	0.161814	+	0.126865i
$901$	80.4130	−	53.7303i	2.67895	−	1.79001i
$902$	−24.2556	−	31.9539i	−0.807623	−	1.06395i
$903$	11.5468	+	4.78285i	0.384254	+	0.159163i
$904$	2.86151	−	1.84796i	0.0951724	−	0.0614622i
$905$	35.0945	−	14.5366i	1.16658	−	0.483214i
$906$	14.9464	−	25.5792i	0.496561	−	0.849812i
$907$	−20.2556	−	4.02908i	−0.672575	−	0.133783i	−0.153023	−	0.988223i	$-0.548901\pi$
$907$	−20.2556	−	4.02908i	−0.672575	−	0.133783i	−0.519552	+	0.854439i	$0.673901\pi$
$908$	−0.733801	+	1.44972i	−0.0243520	+	0.0481105i
$909$	−2.65680	−	1.77522i	−0.0881206	−	0.0588803i
$910$	−4.52627	+	0.272988i	−0.150044	+	0.00904946i
$911$	11.3454	+	11.3454i	0.375890	+	0.375890i	0.869617	−	0.493727i	$-0.164366\pi$
$911$	11.3454	+	11.3454i	0.375890	+	0.375890i	−0.493727	+	0.869617i	$0.664366\pi$
$912$	−0.369291	+	2.41495i	−0.0122285	+	0.0799671i
$913$	−21.4756	+	21.4756i	−0.710740	+	0.710740i
$914$	8.08675	−	9.12481i	0.267486	−	0.301822i
$915$	10.2259	−	15.3041i	0.338057	−	0.505938i
$916$	4.63945	+	0.352680i	0.153292	+	0.0116529i
$917$	0.100081	−	0.503139i	0.00330495	−	0.0166151i
$918$	−50.7560	+	13.3169i	−1.67520	+	0.439524i
$919$	−21.0148	−	50.7342i	−0.693215	−	1.67357i	−0.738201	−	0.674581i	$-0.764325\pi$
$919$	−21.0148	−	50.7342i	−0.693215	−	1.67357i	0.0449867	−	0.998988i	$-0.485675\pi$
$920$	−21.9361	+	21.2608i	−0.723212	+	0.700947i
$921$	−7.35990	+	17.7684i	−0.242517	+	0.585488i
$922$	−27.9498	−	3.82793i	−0.920478	−	0.126066i
$923$	9.59487	+	14.3597i	0.315819	+	0.472656i
$924$	6.38962	+	11.3384i	0.210203	+	0.373007i
$925$	5.99783	−	1.19304i	0.197207	−	0.0392270i
$926$	−5.95132	−	2.05485i	−0.195572	−	0.0675264i
$927$			7.74593i			0.254410i
$928$	21.2885	+	17.2347i	0.698830	+	0.565756i
$929$			0.531484i			0.0174374i	0.999962	+	0.00871870i	$0.00277529\pi$
$929$			0.531484i			0.0174374i	−0.999962	+	0.00871870i	$0.997225\pi$
$930$	−2.34380	+	6.78821i	−0.0768564	+	0.222594i
$931$	−2.94278	+	0.585355i	−0.0964456	+	0.0191842i
$932$	13.0062	+	3.63070i	0.426033	+	0.118928i
$933$	−6.16116	−	9.22083i	−0.201707	−	0.301876i
$934$	−3.39704	+	24.8036i	−0.111154	+	0.811599i
$935$	22.8221	−	55.0975i	0.746364	−	1.80188i
$936$	−2.83270	+	6.54733i	−0.0925896	+	0.214006i
$937$	6.58627	+	15.9007i	0.215164	+	0.519452i	0.994202	−	0.107524i	$-0.0342923\pi$
$937$	6.58627	+	15.9007i	0.215164	+	0.519452i	−0.779038	+	0.626976i	$0.784292\pi$
$938$	1.88528	+	7.18552i	0.0615566	+	0.234616i
$939$	−0.934162	+	4.69635i	−0.0304852	+	0.153260i
$940$	−22.1701	−	25.8181i	−0.723110	−	0.842093i
$941$	−21.5302	+	32.2222i	−0.701864	+	1.05041i	0.293660	+	0.955910i	$0.405127\pi$
$941$	−21.5302	+	32.2222i	−0.701864	+	1.05041i	−0.995524	+	0.0945042i	$0.969873\pi$
$942$	−5.93131	−	5.25654i	−0.193252	−	0.171267i
$943$	25.4938	−	25.4938i	0.830192	−	0.830192i
$944$	−16.2403	−	14.8524i	−0.528576	−	0.483405i
$945$	−8.42608	−	8.42608i	−0.274101	−	0.274101i
$946$	3.62184	+	60.0518i	0.117756	+	1.95245i
$947$	48.9270	+	32.6919i	1.58991	+	1.06235i	0.957787	+	0.287479i	$0.0928173\pi$
$947$	48.9270	+	32.6919i	1.58991	+	1.06235i	0.632125	+	0.774866i	$0.282183\pi$
$948$	7.23248	+	22.0588i	0.234900	+	0.716437i
$949$	11.5893	+	2.30525i	0.376204	+	0.0748317i
$950$	−1.17119	−	0.684349i	−0.0379984	−	0.0222032i
$951$	−8.67521	+	3.59339i	−0.281313	+	0.116524i
$952$	−4.45318	−	24.3729i	−0.144329	−	0.789931i
$953$	−39.6242	−	16.4129i	−1.28355	−	0.531665i	−0.366495	−	0.930420i	$-0.619442\pi$
$953$	−39.6242	−	16.4129i	−1.28355	−	0.531665i	−0.917057	+	0.398755i	$0.869442\pi$
$954$	27.5211	−	20.8908i	0.891030	−	0.676364i
$955$	24.8110	−	16.5782i	0.802866	−	0.536458i
$956$	3.45388	+	28.5293i	0.111706	+	0.922702i
$957$	4.92472	+	24.7582i	0.159194	+	0.800320i
$958$	15.7521	+	32.3662i	0.508927	+	1.04570i
$959$	−1.24875			−0.0403242
$960$	5.65839	+	14.9677i	0.182624	+	0.483079i
$961$	24.5546			0.792083
$962$	3.09491	+	6.35918i	0.0997839	+	0.205028i
$963$	0.973888	+	4.89606i	0.0313831	+	0.157773i
$964$	−2.02496	+	0.245151i	−0.0652197	+	0.00789578i
$965$	10.4855	−	7.00620i	0.337541	−	0.225538i
$966$	−9.31650	+	7.07198i	−0.299754	+	0.227537i
$967$	53.1360	+	22.0096i	1.70874	+	0.707782i	0.999997	+	0.00231245i	$0.000736076\pi$
$967$	53.1360	+	22.0096i	1.70874	+	0.707782i	0.708740	+	0.705470i	$0.249264\pi$
$968$	−17.9278	+	25.9436i	−0.576222	+	0.833858i
$969$	3.95994	−	1.64026i	0.127212	−	0.0526928i
$970$	16.4135	+	9.59070i	0.527005	+	0.307939i
$971$	41.3607	+	8.22715i	1.32733	+	0.264022i	0.807307	−	0.590132i	$-0.200924\pi$
$971$	41.3607	+	8.22715i	1.32733	+	0.264022i	0.520020	+	0.854154i	$0.325924\pi$
$972$	−29.0111	+	9.51194i	−0.930533	+	0.305096i
$973$	−1.94726	−	1.30112i	−0.0624264	−	0.0417120i
$974$	−2.21889	−	36.7902i	−0.0710978	−	1.17883i
$975$	1.93861	+	1.93861i	0.0620852	+	0.0620852i
$976$	33.3448	−	15.5885i	1.06734	−	0.498975i
$977$	17.1037	−	17.1037i	0.547194	−	0.547194i	−0.378434	−	0.925628i	$-0.623537\pi$
$977$	17.1037	−	17.1037i	0.547194	−	0.547194i	0.925628	+	0.378434i	$0.123537\pi$
$978$	−9.28360	−	8.22748i	−0.296857	−	0.263086i
$979$	−0.274533	+	0.410868i	−0.00877413	+	0.0131314i
$980$	−14.9097	+	12.8031i	−0.476274	+	0.408979i
$981$	−2.50417	+	12.5893i	−0.0799521	+	0.401947i
$982$	9.19879	+	35.0601i	0.293545	+	1.11881i
$983$	5.49950	+	13.2770i	0.175407	+	0.423469i	0.986993	−	0.160763i	$-0.0513956\pi$
$983$	5.49950	+	13.2770i	0.175407	+	0.423469i	−0.811586	+	0.584233i	$0.801396\pi$
$984$	−6.95340	−	17.5584i	−0.221666	−	0.559742i
$985$	−2.47529	+	5.97588i	−0.0788694	+	0.190408i
$986$	6.52069	−	47.6111i	0.207661	−	1.51625i
$987$	−7.23900	−	10.8339i	−0.230420	−	0.344848i
$988$	0.421791	−	1.51098i	0.0134190	−	0.0480706i
$989$	−53.0283	+	10.5480i	−1.68620	+	0.335406i
$990$	6.95374	−	20.1397i	0.221004	−	0.640081i
$991$			16.2665i			0.516722i	0.966048	+	0.258361i	$0.0831824\pi$
$991$			16.2665i			0.516722i	−0.966048	+	0.258361i	$0.916818\pi$
$992$	−11.0406	+	9.18471i	−0.350539	+	0.291615i
$993$		−	13.8111i		−	0.438281i
$994$	−20.2558	−	6.99386i	−0.642476	−	0.221832i
$995$	9.44424	−	1.87858i	0.299403	−	0.0595549i
$996$	−12.4556	+	7.01917i	−0.394669	+	0.222411i
$997$	−21.9051	−	32.7834i	−0.693743	−	1.03826i	−0.996368	−	0.0851498i	$-0.972863\pi$
$997$	−21.9051	−	32.7834i	−0.693743	−	1.03826i	0.302625	−	0.953110i	$-0.402137\pi$
$998$	−46.2327	−	6.33191i	−1.46347	−	0.200433i
$999$	−7.11235	+	17.1707i	−0.225025	+	0.543258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.21.2	✓	56
3.2	odd	2		576.2.bd.a.469.6		56
4.3	odd	2		256.2.i.a.177.5		56
8.3	odd	2		512.2.i.a.97.3		56
8.5	even	2		512.2.i.b.97.5		56
64.3	odd	16		256.2.i.a.81.5		56
64.29	even	16		512.2.i.b.417.5		56
64.35	odd	16		512.2.i.a.417.3		56
64.61	even	16	inner	64.2.i.a.61.2	yes	56
192.125	odd	16		576.2.bd.a.253.6		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.21.2	✓	56	1.1	even	1	trivial
64.2.i.a.61.2	yes	56	64.61	even	16	inner
256.2.i.a.81.5		56	64.3	odd	16
256.2.i.a.177.5		56	4.3	odd	2
512.2.i.a.97.3		56	8.3	odd	2
512.2.i.a.417.3		56	64.35	odd	16
512.2.i.b.97.5		56	8.5	even	2
512.2.i.b.417.5		56	64.29	even	16
576.2.bd.a.253.6		56	192.125	odd	16
576.2.bd.a.469.6		56	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-1.27161 + 0.618873i) q^{2} +(-0.216111 - 1.08646i) q^{3} +(1.23399 - 1.57393i) q^{4} +(1.50133 - 1.00316i) q^{5} +(0.947192 + 1.24781i) q^{6} +(1.15320 + 0.477669i) q^{7} +(-0.595096 + 2.76512i) q^{8} +(1.63794 - 0.678457i) q^{9} +O(q^{10})\)	\(q+(-1.27161 + 0.618873i) q^{2} +(-0.216111 - 1.08646i) q^{3} +(1.23399 - 1.57393i) q^{4} +(1.50133 - 1.00316i) q^{5} +(0.947192 + 1.24781i) q^{6} +(1.15320 + 0.477669i) q^{7} +(-0.595096 + 2.76512i) q^{8} +(1.63794 - 0.678457i) q^{9} +(-1.28828 + 2.20476i) q^{10} +(-4.61589 - 0.918157i) q^{11} +(-1.97670 - 1.00054i) q^{12} +(1.18288 + 0.790377i) q^{13} +(-1.76203 + 0.106272i) q^{14} +(-1.41435 - 1.41435i) q^{15} +(-0.954524 - 3.88444i) q^{16} +(-4.96238 + 4.96238i) q^{17} +(-1.66295 + 1.87641i) q^{18} +(0.306314 - 0.458431i) q^{19} +(0.273730 - 3.60088i) q^{20} +(0.269752 - 1.35613i) q^{21} +(6.43784 - 1.68911i) q^{22} +(2.28905 + 5.52625i) q^{23} +(3.13280 + 0.0489777i) q^{24} +(-0.665746 + 1.60725i) q^{25} +(-1.99331 - 0.272999i) q^{26} +(-2.93739 - 4.39612i) q^{27} +(2.17485 - 1.22561i) q^{28} +(4.74895 - 0.944625i) q^{29} +(2.67380 + 0.923200i) q^{30} +2.53878i q^{31} +(3.61776 + 4.34877i) q^{32} +5.21341i q^{33} +(3.23914 - 9.38131i) q^{34} +(2.21051 - 0.439697i) q^{35} +(0.953361 - 3.41522i) q^{36} +(-1.95294 - 2.92279i) q^{37} +(-0.105802 + 0.772515i) q^{38} +(0.603082 - 1.45597i) q^{39} +(1.88041 + 4.74833i) q^{40} +(-2.30661 - 5.56864i) q^{41} +(0.496255 + 1.89142i) q^{42} +(-1.76341 + 8.86527i) q^{43} +(-7.14109 + 6.13209i) q^{44} +(1.77849 - 2.66170i) q^{45} +(-6.33083 - 5.61062i) q^{46} +(6.66340 - 6.66340i) q^{47} +(-4.01402 + 1.87653i) q^{48} +(-3.84805 - 3.84805i) q^{49} +(-0.148115 - 2.45582i) q^{50} +(6.46387 + 4.31902i) q^{51} +(2.70367 - 0.886458i) q^{52} +(-13.5160 - 2.68850i) q^{53} +(6.45586 + 3.77228i) q^{54} +(-7.85103 + 3.25200i) q^{55} +(-2.00707 + 2.90446i) q^{56} +(-0.564266 - 0.233726i) q^{57} +(-5.45422 + 4.14019i) q^{58} +(4.57469 - 3.05671i) q^{59} +(-3.97138 + 0.480793i) q^{60} +(1.79525 + 9.02535i) q^{61} +(-1.57118 - 3.22835i) q^{62} +2.21295 q^{63} +(-7.29172 - 3.29102i) q^{64} +2.56877 q^{65} +(-3.22644 - 6.62944i) q^{66} +(-0.821008 - 4.12749i) q^{67} +(1.68691 + 13.9340i) q^{68} +(5.50938 - 3.68125i) q^{69} +(-2.53879 + 1.92715i) q^{70} +(11.2155 + 4.64562i) q^{71} +(0.901281 + 4.93284i) q^{72} +(7.67366 - 3.17854i) q^{73} +(4.29222 + 2.50803i) q^{74} +(1.89010 + 0.375964i) q^{75} +(-0.343550 - 1.04782i) q^{76} +(-4.88445 - 3.26368i) q^{77} +(0.134173 + 2.22466i) q^{78} +(-7.40915 - 7.40915i) q^{79} +(-5.32976 - 4.87429i) q^{80} +(-0.380539 + 0.380539i) q^{81} +(6.37939 + 5.65365i) q^{82} +(3.58524 - 5.36570i) q^{83} +(-1.80159 - 2.09803i) q^{84} +(-2.47213 + 12.4282i) q^{85} +(-3.24410 - 12.3645i) q^{86} +(-2.05260 - 4.95541i) q^{87} +(5.28570 - 12.2171i) q^{88} +(0.0401804 - 0.0970042i) q^{89} +(-0.614296 + 4.48531i) q^{90} +(0.986557 + 1.47649i) q^{91} +(11.5226 + 3.21655i) q^{92} +(2.75829 - 0.548659i) q^{93} +(-4.34946 + 12.5971i) q^{94} -0.995537i q^{95} +(3.94294 - 4.87038i) q^{96} -7.44456i q^{97} +(7.27469 + 2.51177i) q^{98} +(-8.18348 + 1.62780i) 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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