LMFDB - Embedded newform 64.2.i.a.37.4

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			37.4
Character	$\chi$	$=$	64.37
Dual form			64.2.i.a.45.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.466807 + 1.33495i) q^{2} +(-0.572535 + 0.856859i) q^{3} +(-1.56418 - 1.24633i) q^{4} +(-0.690473 + 3.47124i) q^{5} +(-0.876601 - 1.16429i) q^{6} +(0.983337 - 2.37399i) q^{7} +(2.39396 - 1.50631i) q^{8} +(0.741639 + 1.79047i) q^{9} +O(q^{10})$	\(q+(-0.466807 + 1.33495i) q^{2} +(-0.572535 + 0.856859i) q^{3} +(-1.56418 - 1.24633i) q^{4} +(-0.690473 + 3.47124i) q^{5} +(-0.876601 - 1.16429i) q^{6} +(0.983337 - 2.37399i) q^{7} +(2.39396 - 1.50631i) q^{8} +(0.741639 + 1.79047i) q^{9} +(-4.31162 - 2.54215i) q^{10} +(1.29020 - 0.862086i) q^{11} +(1.96348 - 0.626717i) q^{12} +(-0.115716 - 0.581745i) q^{13} +(2.71012 + 2.42090i) q^{14} +(-2.57905 - 2.57905i) q^{15} +(0.893330 + 3.89897i) q^{16} +(4.30936 - 4.30936i) q^{17} +(-2.73640 + 0.154244i) q^{18} +(3.59299 - 0.714690i) q^{19} +(5.40633 - 4.56910i) q^{20} +(1.47118 + 2.20177i) q^{21} +(0.548565 + 2.12478i) q^{22} +(-7.79200 + 3.22755i) q^{23} +(-0.0799298 + 2.91370i) q^{24} +(-6.95338 - 2.88018i) q^{25} +(0.830617 + 0.117087i) q^{26} +(-4.99100 - 0.992772i) q^{27} +(-4.49689 + 2.48779i) q^{28} +(-0.373179 - 0.249351i) q^{29} +(4.64682 - 2.23898i) q^{30} -1.08345i q^{31} +(-5.62194 - 0.627516i) q^{32} +1.59910i q^{33} +(3.74114 + 7.76442i) q^{34} +(7.56172 + 5.05258i) q^{35} +(1.07146 - 3.72495i) q^{36} +(-4.16040 - 0.827556i) q^{37} +(-0.723158 + 5.13008i) q^{38} +(0.564725 + 0.233917i) q^{39} +(3.57580 + 9.35007i) q^{40} +(5.15990 - 2.13730i) q^{41} +(-3.62601 + 0.936145i) q^{42} +(-1.55896 - 2.33315i) q^{43} +(-3.09255 - 0.259557i) q^{44} +(-6.72725 + 1.33813i) q^{45} +(-0.671258 - 11.9086i) q^{46} +(6.43269 - 6.43269i) q^{47} +(-3.85233 - 1.46684i) q^{48} +(0.280888 + 0.280888i) q^{49} +(7.09079 - 7.93792i) q^{50} +(1.22526 + 6.15978i) q^{51} +(-0.544044 + 1.05417i) q^{52} +(-1.22184 + 0.816410i) q^{53} +(3.65514 - 6.19931i) q^{54} +(2.10166 + 5.07385i) q^{55} +(-1.22189 - 7.16443i) q^{56} +(-1.44472 + 3.48787i) q^{57} +(0.507073 - 0.381777i) q^{58} +(-1.46423 + 7.36119i) q^{59} +(0.819759 + 7.24844i) q^{60} +(6.45980 - 9.66777i) q^{61} +(1.44635 + 0.505761i) q^{62} +4.97984 q^{63} +(3.46207 - 7.21208i) q^{64} +2.09928 q^{65} +(-2.13471 - 0.746470i) q^{66} +(3.30637 - 4.94834i) q^{67} +(-12.1115 + 1.36974i) q^{68} +(1.69564 - 8.52453i) q^{69} +(-10.2748 + 7.73593i) q^{70} +(-3.75143 + 9.05676i) q^{71} +(4.47246 + 3.16918i) q^{72} +(-1.19724 - 2.89039i) q^{73} +(3.04685 - 5.16762i) q^{74} +(6.44896 - 4.30906i) q^{75} +(-6.51083 - 3.36014i) q^{76} +(-0.777876 - 3.91064i) q^{77} +(-0.575885 + 0.644685i) q^{78} +(-0.934789 - 0.934789i) q^{79} +(-14.1511 + 0.408832i) q^{80} +(-0.402918 + 0.402918i) q^{81} +(0.444510 + 7.88591i) q^{82} +(-16.5833 + 3.29862i) q^{83} +(0.442943 - 5.27754i) q^{84} +(11.9833 + 17.9343i) q^{85} +(3.84237 - 0.992002i) q^{86} +(0.427317 - 0.177000i) q^{87} +(1.79012 - 4.00724i) q^{88} +(-6.15337 - 2.54881i) q^{89} +(1.35399 - 9.60520i) q^{90} +(-1.49484 - 0.297343i) q^{91} +(16.2107 + 4.66291i) q^{92} +(0.928361 + 0.620311i) q^{93} +(5.58449 + 11.5901i) q^{94} +12.9656i q^{95} +(3.75645 - 4.45794i) q^{96} +5.79443i q^{97} +(-0.506092 + 0.243851i) q^{98} +(2.50041 + 1.67072i) 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 $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{9}{16}\right)$	$1$

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 $

$2$	−0.466807	+	1.33495i	−0.330083	+	0.943952i
$2$	−0.466807	+	1.33495i	−0.330083	+	0.943952i
$3$	−0.572535	+	0.856859i	−0.330553	+	0.494708i	−0.959101	−	0.283063i	$-0.908650\pi$
$3$	−0.572535	+	0.856859i	−0.330553	+	0.494708i	0.628548	+	0.777771i	$0.283650\pi$
$4$	−1.56418	−	1.24633i	−0.782091	−	0.623164i
$5$	−0.690473	+	3.47124i	−0.308789	+	1.55239i	0.445158	+	0.895452i	$0.353147\pi$
$5$	−0.690473	+	3.47124i	−0.308789	+	1.55239i	−0.753947	+	0.656935i	$0.771853\pi$
$6$	−0.876601	−	1.16429i	−0.357871	−	0.475321i
$7$	0.983337	−	2.37399i	0.371667	−	0.897283i	−0.621802	−	0.783175i	$-0.713599\pi$
$7$	0.983337	−	2.37399i	0.371667	−	0.897283i	0.993468	−	0.114108i	$-0.0364010\pi$
$8$	2.39396	−	1.50631i	0.846392	−	0.532561i
$9$	0.741639	+	1.79047i	0.247213	+	0.596825i
$10$	−4.31162	−	2.54215i	−1.36345	−	0.803898i
$11$	1.29020	−	0.862086i	0.389011	−	0.259929i	−0.345650	−	0.938364i	$-0.612341\pi$
$11$	1.29020	−	0.862086i	0.389011	−	0.259929i	0.734660	+	0.678435i	$0.237341\pi$
$12$	1.96348	−	0.626717i	0.566807	−	0.180918i
$13$	−0.115716	−	0.581745i	−0.0320939	−	0.161347i	0.961415	−	0.275103i	$-0.0887119\pi$
$13$	−0.115716	−	0.581745i	−0.0320939	−	0.161347i	−0.993509	+	0.113756i	$0.963712\pi$
$14$	2.71012	+	2.42090i	0.724311	+	0.647013i
$15$	−2.57905	−	2.57905i	−0.665907	−	0.665907i
$16$	0.893330	+	3.89897i	0.223333	+	0.974742i
$17$	4.30936	−	4.30936i	1.04517	−	1.04517i	0.0462432	−	0.998930i	$-0.485275\pi$
$17$	4.30936	−	4.30936i	1.04517	−	1.04517i	0.998930	−	0.0462432i	$-0.0147249\pi$
$18$	−2.73640	+	0.154244i	−0.644975	+	0.0363557i
$19$	3.59299	−	0.714690i	0.824288	−	0.163961i	0.235115	−	0.971968i	$-0.424453\pi$
$19$	3.59299	−	0.714690i	0.824288	−	0.163961i	0.589174	+	0.808006i	$0.299453\pi$
$20$	5.40633	−	4.56910i	1.20889	−	1.02168i
$21$	1.47118	+	2.20177i	0.321037	+	0.480466i
$22$	0.548565	+	2.12478i	0.116955	+	0.453005i
$23$	−7.79200	+	3.22755i	−1.62474	+	0.672991i	−0.994628	−	0.103510i	$-0.966993\pi$
$23$	−7.79200	+	3.22755i	−1.62474	+	0.672991i	−0.630116	+	0.776501i	$0.716993\pi$
$24$	−0.0799298	+	2.91370i	−0.0163156	+	0.594757i
$25$	−6.95338	−	2.88018i	−1.39068	−	0.576037i
$26$	0.830617	+	0.117087i	0.162897	+	0.0229627i
$27$	−4.99100	−	0.992772i	−0.960519	−	0.191059i
$28$	−4.49689	+	2.48779i	−0.849832	+	0.470147i
$29$	−0.373179	−	0.249351i	−0.0692977	−	0.0463032i	0.520439	−	0.853899i	$-0.325768\pi$
$29$	−0.373179	−	0.249351i	−0.0692977	−	0.0463032i	−0.589736	+	0.807596i	$0.700768\pi$
$30$	4.64682	−	2.23898i	0.848389	−	0.408780i
$31$		−	1.08345i		−	0.194593i	−0.995255	−	0.0972963i	$-0.968981\pi$
$31$		−	1.08345i		−	0.194593i	0.995255	−	0.0972963i	$-0.0310195\pi$
$32$	−5.62194	−	0.627516i	−0.993828	−	0.110930i
$33$			1.59910i			0.278367i
$34$	3.74114	+	7.76442i	0.641600	+	1.33159i
$35$	7.56172	+	5.05258i	1.27816	+	0.854041i
$36$	1.07146	−	3.72495i	0.178577	−	0.620825i
$37$	−4.16040	−	0.827556i	−0.683966	−	0.136049i	−0.159136	−	0.987257i	$-0.550871\pi$
$37$	−4.16040	−	0.827556i	−0.683966	−	0.136049i	−0.524830	+	0.851207i	$0.675871\pi$
$38$	−0.723158	+	5.13008i	−0.117312	+	0.832209i
$39$	0.564725	+	0.233917i	0.0904284	+	0.0374567i
$40$	3.57580	+	9.35007i	0.565384	+	1.47838i
$41$	5.15990	−	2.13730i	0.805841	−	0.333790i	0.0585477	−	0.998285i	$-0.481353\pi$
$41$	5.15990	−	2.13730i	0.805841	−	0.333790i	0.747293	+	0.664494i	$0.231353\pi$
$42$	−3.62601	+	0.936145i	−0.559506	+	0.144450i
$43$	−1.55896	−	2.33315i	−0.237739	−	0.355802i	0.693345	−	0.720605i	$-0.256136\pi$
$43$	−1.55896	−	2.33315i	−0.237739	−	0.355802i	−0.931084	+	0.364804i	$0.881136\pi$
$44$	−3.09255	−	0.259557i	−0.466220	−	0.0391297i
$45$	−6.72725	+	1.33813i	−1.00284	+	0.199477i
$46$	−0.671258	−	11.9086i	−0.0989715	−	1.75582i
$47$	6.43269	−	6.43269i	0.938304	−	0.938304i	−0.0599006	−	0.998204i	$-0.519078\pi$
$47$	6.43269	−	6.43269i	0.938304	−	0.938304i	0.998204	+	0.0599006i	$0.0190784\pi$
$48$	−3.85233	−	1.46684i	−0.556036	−	0.211720i
$49$	0.280888	+	0.280888i	0.0401268	+	0.0401268i
$50$	7.09079	−	7.93792i	1.00279	−	1.12259i
$51$	1.22526	+	6.15978i	0.171570	+	0.862541i
$52$	−0.544044	+	1.05417i	−0.0754453	+	0.146188i
$53$	−1.22184	+	0.816410i	−0.167833	+	0.112143i	−0.636650	−	0.771153i	$-0.719680\pi$
$53$	−1.22184	+	0.816410i	−0.167833	+	0.112143i	0.468817	+	0.883295i	$0.344680\pi$
$54$	3.65514	−	6.19931i	0.497401	−	0.843619i
$55$	2.10166	+	5.07385i	0.283388	+	0.684158i
$56$	−1.22189	−	7.16443i	−0.163282	−	0.957388i
$57$	−1.44472	+	3.48787i	−0.191358	+	0.461980i
$58$	0.507073	−	0.381777i	0.0665820	−	0.0501298i
$59$	−1.46423	+	7.36119i	−0.190627	+	0.958345i	0.760452	+	0.649395i	$0.224978\pi$
$59$	−1.46423	+	7.36119i	−0.190627	+	0.958345i	−0.951078	+	0.308950i	$0.900022\pi$
$60$	0.819759	+	7.24844i	0.105830	+	0.935769i
$61$	6.45980	−	9.66777i	0.827092	−	1.23783i	−0.141688	−	0.989911i	$-0.545253\pi$
$61$	6.45980	−	9.66777i	0.827092	−	1.23783i	0.968781	−	0.247920i	$-0.0797470\pi$
$62$	1.44635	+	0.505761i	0.183686	+	0.0642317i
$63$	4.97984			0.627401
$64$	3.46207	−	7.21208i	0.432758	−	0.901510i
$65$	2.09928			0.260383
$66$	−2.13471	−	0.746470i	−0.262765	−	0.0918841i
$67$	3.30637	−	4.94834i	0.403938	−	0.604535i	−0.572612	−	0.819826i	$-0.694070\pi$
$67$	3.30637	−	4.94834i	0.403938	−	0.604535i	0.976550	+	0.215291i	$0.0690700\pi$
$68$	−12.1115	+	1.36974i	−1.46874	+	0.166106i
$69$	1.69564	−	8.52453i	0.204131	−	1.02623i
$70$	−10.2748	+	7.73593i	−1.22807	+	0.924621i
$71$	−3.75143	+	9.05676i	−0.445213	+	1.07484i	0.528881	+	0.848696i	$0.322612\pi$
$71$	−3.75143	+	9.05676i	−0.445213	+	1.07484i	−0.974094	+	0.226143i	$0.927388\pi$
$72$	4.47246	+	3.16918i	0.527084	+	0.373492i
$73$	−1.19724	−	2.89039i	−0.140126	−	0.338295i	0.838200	−	0.545362i	$-0.183608\pi$
$73$	−1.19724	−	2.89039i	−0.140126	−	0.338295i	−0.978327	+	0.207068i	$0.933608\pi$
$74$	3.04685	−	5.16762i	0.354189	−	0.600724i
$75$	6.44896	−	4.30906i	0.744662	−	0.497567i
$76$	−6.51083	−	3.36014i	−0.746843	−	0.385435i
$77$	−0.777876	−	3.91064i	−0.0886472	−	0.445659i
$78$	−0.575885	+	0.644685i	−0.0652061	+	0.0729963i
$79$	−0.934789	−	0.934789i	−0.105172	−	0.105172i	0.652563	−	0.757735i	$-0.273694\pi$
$79$	−0.934789	−	0.934789i	−0.105172	−	0.105172i	−0.757735	+	0.652563i	$0.773694\pi$
$80$	−14.1511	+	0.408832i	−1.58214	+	0.0457088i
$81$	−0.402918	+	0.402918i	−0.0447687	+	0.0447687i
$82$	0.444510	+	7.88591i	0.0490879	+	0.870854i
$83$	−16.5833	+	3.29862i	−1.82025	+	0.362070i	−0.982834	−	0.184494i	$-0.940936\pi$
$83$	−16.5833	+	3.29862i	−1.82025	+	0.362070i	−0.837417	+	0.546564i	$0.815936\pi$
$84$	0.442943	−	5.27754i	0.0483290	−	0.575827i
$85$	11.9833	+	17.9343i	1.29978	+	1.94525i
$86$	3.84237	−	0.992002i	0.414333	−	0.106970i
$87$	0.427317	−	0.177000i	0.0458132	−	0.0189764i
$88$	1.79012	−	4.00724i	0.190828	−	0.427173i
$89$	−6.15337	−	2.54881i	−0.652256	−	0.270173i	0.0319199	−	0.999490i	$-0.489838\pi$
$89$	−6.15337	−	2.54881i	−0.652256	−	0.270173i	−0.684176	+	0.729317i	$0.739838\pi$
$90$	1.35399	−	9.60520i	0.142723	−	1.01248i
$91$	−1.49484	−	0.297343i	−0.156702	−	0.0311700i
$92$	16.2107	+	4.66291i	1.69008	+	0.486142i
$93$	0.928361	+	0.620311i	0.0962666	+	0.0643233i
$94$	5.58449	+	11.5901i	0.575996	+	1.19543i
$95$			12.9656i			1.33024i
$96$	3.75645	−	4.45794i	0.383391	−	0.454986i
$97$			5.79443i			0.588336i	0.955754	+	0.294168i	$0.0950425\pi$
$97$			5.79443i			0.588336i	−0.955754	+	0.294168i	$0.904958\pi$
$98$	−0.506092	+	0.243851i	−0.0511230	+	0.0246326i
$99$	2.50041	+	1.67072i	0.251300	+	0.167914i
$100$	7.28669	+	13.1713i	0.728669	+	1.31713i
$101$	0.921112	+	0.183220i	0.0916540	+	0.0182311i	0.240704	−	0.970599i	$-0.422622\pi$
$101$	0.921112	+	0.183220i	0.0916540	+	0.0182311i	−0.149050	+	0.988830i	$0.547622\pi$
$102$	−8.79495	−	1.23977i	−0.870830	−	0.122756i
$103$	12.7902	+	5.29788i	1.26026	+	0.522015i	0.909988	−	0.414634i	$-0.136090\pi$
$103$	12.7902	+	5.29788i	1.26026	+	0.522015i	0.350268	+	0.936649i	$0.386090\pi$
$104$	−1.15331	−	1.21837i	−0.113091	−	0.119471i
$105$	−8.65870	+	3.58655i	−0.845002	+	0.350011i
$106$	−0.519501	−	2.01221i	−0.0504584	−	0.195443i
$107$	−8.24793	−	12.3439i	−0.797358	−	1.19333i	−0.977758	−	0.209737i	$-0.932739\pi$
$107$	−8.24793	−	12.3439i	−0.797358	−	1.19333i	0.180400	−	0.983593i	$-0.442261\pi$
$108$	6.56952	+	7.77331i	0.632152	+	0.747987i
$109$	−6.63883	+	1.32055i	−0.635885	+	0.126485i	−0.502497	−	0.864579i	$-0.667585\pi$
$109$	−6.63883	+	1.32055i	−0.635885	+	0.126485i	−0.133387	+	0.991064i	$0.542585\pi$
$110$	−7.75441	+	0.437097i	−0.739354	+	0.0416756i
$111$	3.09108	−	3.09108i	0.293392	−	0.293392i
$112$	10.1345	+	1.71325i	0.957625	+	0.161887i
$113$	−3.62032	−	3.62032i	−0.340571	−	0.340571i	0.516011	−	0.856582i	$-0.327416\pi$
$113$	−3.62032	−	3.62032i	−0.340571	−	0.340571i	−0.856582	+	0.516011i	$0.827416\pi$
$114$	−3.98173	−	3.55680i	−0.372923	−	0.333125i
$115$	−5.82345	−	29.2765i	−0.543039	−	2.73004i
$116$	0.272948	+	0.855134i	0.0253426	+	0.0793972i
$117$	0.955779	−	0.638631i	0.0883618	−	0.0590415i
$118$	−9.14330	−	5.39093i	−0.841709	−	0.496275i
$119$	−5.99281	−	14.4679i	−0.549360	−	1.32627i
$120$	−10.0590	−	2.28929i	−0.918254	−	0.208982i
$121$	−3.28809	+	7.93814i	−0.298917	+	0.721649i
$122$	9.89051	+	13.1365i	0.895445	+	1.18932i
$123$	−1.12286	+	5.64499i	−0.101245	+	0.508991i
$124$	−1.35033	+	1.69471i	−0.121263	+	0.152189i
$125$	4.96743	−	7.43428i	0.444300	−	0.664942i
$126$	−2.32463	+	6.64784i	−0.207094	+	0.592237i
$127$	−5.27774			−0.468324			−0.234162	−	0.972198i	$-0.575235\pi$
$127$	−5.27774			−0.468324			−0.234162	+	0.972198i	$0.575235\pi$
$128$	8.01165	+	7.98834i	0.708136	+	0.706076i
$129$	2.89174			0.254603
$130$	−0.979957	+	2.80243i	−0.0859479	+	0.245789i
$131$	−3.19779	+	4.78583i	−0.279392	+	0.418140i	−0.944452	−	0.328651i	$-0.893406\pi$
$131$	−3.19779	+	4.78583i	−0.279392	+	0.418140i	0.665060	+	0.746790i	$0.268406\pi$
$132$	1.99300	−	2.50128i	0.173468	−	0.217708i
$133$	1.83646	−	9.23249i	0.159241	−	0.800558i
$134$	5.06234	+	6.72376i	0.437320	+	0.580844i
$135$	6.89231	−	16.6395i	0.593195	−	1.43210i
$136$	3.82520	−	16.8077i	0.328008	−	1.44124i
$137$	3.78991	+	9.14965i	0.323794	+	0.781707i	0.999027	+	0.0441030i	$0.0140430\pi$
$137$	3.78991	+	9.14965i	0.323794	+	0.781707i	−0.675233	+	0.737604i	$0.735957\pi$
$138$	10.5883	+	6.24290i	0.901335	+	0.531431i
$139$	−1.75609	+	1.17338i	−0.148950	+	0.0995250i	−0.627812	−	0.778365i	$-0.716049\pi$
$139$	−1.75609	+	1.17338i	−0.148950	+	0.0995250i	0.478862	+	0.877890i	$0.341049\pi$
$140$	−5.53073	−	17.3275i	−0.467432	−	1.46444i
$141$	1.82897	+	9.19485i	0.154027	+	0.774346i
$142$	−10.3391	−	9.23573i	−0.867640	−	0.775046i
$143$	−0.650811	−	0.650811i	−0.0544236	−	0.0544236i
$144$	−6.31848	+	4.49111i	−0.526540	+	0.374259i
$145$	1.12323	−	1.12323i	0.0932789	−	0.0932789i
$146$	4.41740	−	0.248998i	0.365587	−	0.0206073i
$147$	−0.401500	+	0.0798632i	−0.0331151	+	0.00658701i
$148$	5.47622	+	6.47968i	0.450143	+	0.532626i
$149$	−10.0124	−	14.9845i	−0.820244	−	1.22758i	−0.971016	−	0.239013i	$-0.923176\pi$
$149$	−10.0124	−	14.9845i	−0.820244	−	1.22758i	0.150772	−	0.988569i	$-0.451824\pi$
$150$	2.74196	+	10.6205i	0.223880	+	0.867164i
$151$	−4.99222	+	2.06785i	−0.406261	+	0.168279i	−0.576450	−	0.817133i	$-0.695562\pi$
$151$	−4.99222	+	2.06785i	−0.406261	+	0.168279i	0.170188	+	0.985412i	$0.445562\pi$
$152$	7.52492	−	7.12309i	0.610352	−	0.577759i
$153$	10.9118	+	4.51981i	0.882166	+	0.365405i
$154$	5.58363	+	0.787093i	0.449942	+	0.0634257i
$155$	3.76090	+	0.748090i	0.302083	+	0.0600881i
$156$	−0.591795	−	1.06972i	−0.0473816	−	0.0856462i
$157$	7.04496	+	4.70729i	0.562249	+	0.375683i	0.803976	−	0.594662i	$-0.202714\pi$
$157$	7.04496	+	4.70729i	0.562249	+	0.375683i	−0.241727	+	0.970344i	$0.577714\pi$
$158$	1.68426	−	0.811530i	0.133993	−	0.0645619i
$159$		−	1.51437i		−	0.120098i
$160$	6.06006	−	19.0818i	0.479090	−	1.50855i
$161$			21.6719i			1.70798i
$162$	−0.349790	−	0.725960i	−0.0274821	−	0.0570368i
$163$	0.919897	+	0.614656i	0.0720519	+	0.0481435i	0.591074	−	0.806617i	$-0.298704\pi$
$163$	0.919897	+	0.614656i	0.0720519	+	0.0481435i	−0.519023	+	0.854761i	$0.673704\pi$
$164$	−10.7348	−	3.08780i	−0.838247	−	0.241117i
$165$	−5.55085	−	1.10413i	−0.432133	−	0.0859567i
$166$	3.33770	−	23.6777i	0.259056	−	1.83774i
$167$	−2.61833	−	1.08455i	−0.202612	−	0.0839247i	0.279070	−	0.960271i	$-0.409974\pi$
$167$	−2.61833	−	1.08455i	−0.202612	−	0.0839247i	−0.481682	+	0.876346i	$0.659974\pi$
$168$	6.83849	+	3.05490i	0.527601	+	0.235691i
$169$	11.6854	−	4.84025i	0.898877	−	0.372327i
$170$	−29.5353	+	7.62528i	−2.26526	+	0.584832i
$171$	3.94433	+	5.90311i	0.301631	+	0.451422i
$172$	−0.469373	+	5.59244i	−0.0357893	+	0.426420i
$173$	10.2464	−	2.03813i	0.779016	−	0.154956i	0.210462	−	0.977602i	$-0.432503\pi$
$173$	10.2464	−	2.03813i	0.779016	−	0.154956i	0.568554	+	0.822646i	$0.307503\pi$
$174$	0.0368121	+	0.653071i	0.00279072	+	0.0495092i
$175$	−13.6750	+	13.6750i	−1.03374	+	1.03374i
$176$	4.51382	+	4.26033i	0.340242	+	0.321135i
$177$	−5.46918	−	5.46918i	−0.411089	−	0.411089i
$178$	6.27497	−	7.02464i	0.470329	−	0.526519i
$179$	3.79507	+	19.0791i	0.283657	+	1.42604i	0.815284	+	0.579061i	$0.196581\pi$
$179$	3.79507	+	19.0791i	0.283657	+	1.42604i	−0.531627	+	0.846979i	$0.678419\pi$
$180$	12.1904	+	6.29128i	0.908619	+	0.468925i
$181$	3.32947	−	2.22468i	0.247477	−	0.165359i	−0.425645	−	0.904890i	$-0.639953\pi$
$181$	3.32947	−	2.22468i	0.247477	−	0.165359i	0.673122	+	0.739531i	$0.264953\pi$
$182$	1.09474	−	1.85674i	0.0811476	−	0.137631i
$183$	4.58546	+	11.0703i	0.338967	+	0.818339i
$184$	−13.7920	+	19.4638i	−1.01676	+	1.43489i
$185$	5.74529	−	13.8704i	0.422402	−	1.01977i
$186$	−1.26145	+	0.949750i	−0.0924940	+	0.0696390i
$187$	1.84491	−	9.27499i	0.134913	−	0.678254i
$188$	−18.0791	+	2.04465i	−1.31856	+	0.149121i
$189$	−7.26467	+	10.8723i	−0.528427	+	0.790847i
$190$	−17.3084	−	6.05244i	−1.25569	−	0.439090i
$191$	16.2586			1.17643			0.588215	−	0.808704i	$-0.299831\pi$
$191$	16.2586			1.17643			0.588215	+	0.808704i	$0.299831\pi$
$192$	4.19758	+	7.09567i	0.302935	+	0.512086i
$193$	−24.9345			−1.79482			−0.897411	−	0.441196i	$-0.854554\pi$
$193$	−24.9345			−1.79482			−0.897411	+	0.441196i	$0.854554\pi$
$194$	−7.73528	−	2.70488i	−0.555361	−	0.194199i
$195$	−1.20191	+	1.79878i	−0.0860705	+	0.128814i
$196$	−0.0892812	−	0.789438i	−0.00637723	−	0.0563885i
$197$	−0.816489	+	4.10477i	−0.0581724	+	0.292452i	−0.998910	−	0.0466836i	$-0.985135\pi$
$197$	−0.816489	+	4.10477i	−0.0581724	+	0.292452i	0.940737	+	0.339136i	$0.110135\pi$
$198$	−3.39753	+	2.55801i	−0.241452	+	0.181790i
$199$	−0.744172	+	1.79659i	−0.0527529	+	0.127357i	−0.948059	−	0.318095i	$-0.896957\pi$
$199$	−0.744172	+	1.79659i	−0.0527529	+	0.127357i	0.895306	+	0.445452i	$0.146957\pi$
$200$	−20.9845	+	3.57890i	−1.48383	+	0.253066i
$201$	2.34701	+	5.66619i	0.165546	+	0.399662i
$202$	−0.674572	+	1.14411i	−0.0474627	+	0.0804992i
$203$	−0.958916	+	0.640727i	−0.0673027	+	0.0449702i
$204$	5.76058	−	11.1621i	0.403321	−	0.781502i
$205$	3.85632	+	19.3870i	0.269337	+	1.35405i
$206$	−13.0430	+	14.6012i	−0.908746	+	1.01731i
$207$	−11.5577	−	11.5577i	−0.803315	−	0.803315i
$208$	2.16483	−	0.970864i	0.150104	−	0.0673173i
$209$	4.01956	−	4.01956i	0.278039	−	0.278039i
$210$	−0.745921	−	13.2332i	−0.0514734	−	0.913174i
$211$	14.6646	−	2.91696i	1.00955	−	0.200812i	0.337507	−	0.941323i	$-0.390416\pi$
$211$	14.6646	−	2.91696i	1.00955	−	0.200812i	0.672044	+	0.740511i	$0.265416\pi$
$212$	2.92870	+	0.245805i	0.201144	+	0.0168820i
$213$	−5.61254	−	8.39976i	−0.384565	−	0.575542i
$214$	20.3287	−	5.24835i	1.38964	−	0.358770i
$215$	9.17534	−	3.80055i	0.625753	−	0.259195i
$216$	−13.4437	+	5.14134i	−0.914726	+	0.349824i
$217$	−2.57209	−	1.06539i	−0.174605	−	0.0723236i
$218$	1.33619	−	9.47894i	0.0904984	−	0.641995i
$219$	3.16212	+	0.628985i	0.213676	+	0.0425028i
$220$	3.03631	−	10.5558i	0.204708	−	0.711671i
$221$	−3.00561	−	2.00828i	−0.202179	−	0.135092i
$222$	2.68349	+	5.56937i	0.180104	+	0.373791i
$223$			14.8634i			0.995330i	0.867369	+	0.497665i	$0.165809\pi$
$223$			14.8634i			0.995330i	−0.867369	+	0.497665i	$0.834191\pi$
$224$	−7.01798	+	12.7294i	−0.468909	+	0.850516i
$225$		−	14.5859i		−	0.972393i
$226$	6.52294	−	3.14296i	0.433900	−	0.209066i
$227$	−6.90248	−	4.61209i	−0.458133	−	0.306115i	0.305004	−	0.952351i	$-0.401342\pi$
$227$	−6.90248	−	4.61209i	−0.458133	−	0.306115i	−0.763138	+	0.646236i	$0.776342\pi$
$228$	6.60685	−	3.65507i	0.437549	−	0.242063i
$229$	−3.63468	−	0.722983i	−0.240187	−	0.0477761i	0.0735290	−	0.997293i	$-0.476574\pi$
$229$	−3.63468	−	0.722983i	−0.240187	−	0.0477761i	−0.313716	+	0.949517i	$0.601574\pi$
$230$	41.8010	+	5.89245i	2.75628	+	0.388537i
$231$	3.79623	+	1.57245i	0.249774	+	0.103460i
$232$	−1.26897	−	0.0348110i	−0.0833123	−	0.00228546i
$233$	17.7828	−	7.36589i	1.16499	−	0.482556i	0.285458	−	0.958391i	$-0.407854\pi$
$233$	17.7828	−	7.36589i	1.16499	−	0.482556i	0.879534	+	0.475836i	$0.157854\pi$
$234$	0.406376	+	1.57403i	0.0265656	+	0.102898i
$235$	17.8878	+	26.7710i	1.16687	+	1.74635i
$236$	11.4648	−	9.68932i	0.746294	−	0.630721i
$237$	1.33618	−	0.265783i	0.0867944	−	0.0172645i
$238$	22.1114	−	1.24637i	1.43327	−	0.0807901i
$239$	−1.69651	+	1.69651i	−0.109738	+	0.109738i	−0.759844	−	0.650106i	$-0.774725\pi$
$239$	−1.69651	+	1.69651i	−0.109738	+	0.109738i	0.650106	+	0.759844i	$0.274725\pi$
$240$	7.75168	−	12.3596i	0.500369	−	0.797807i
$241$	−12.7520	−	12.7520i	−0.821432	−	0.821432i	0.164882	−	0.986313i	$-0.447276\pi$
$241$	−12.7520	−	12.7520i	−0.821432	−	0.821432i	−0.986313	+	0.164882i	$0.947276\pi$
$242$	−9.06212	−	8.09501i	−0.582535	−	0.520367i
$243$	−3.09288	−	15.5489i	−0.198408	−	0.997465i
$244$	−22.1535	+	7.07112i	−1.41823	+	0.452682i
$245$	−1.16898	+	0.781085i	−0.0746831	+	0.0499017i
$246$	−7.01162	−	4.13408i	−0.447044	−	0.263579i
$247$	−0.831534	−	2.00750i	−0.0529093	−	0.127734i
$248$	−1.63200	−	2.59372i	−0.103632	−	0.164702i
$249$	6.66806	−	16.0981i	0.422571	−	1.02018i
$250$	7.60556	+	10.1016i	0.481018	+	0.638884i
$251$	0.0325488	−	0.163634i	0.00205446	−	0.0103285i	−0.979744	−	0.200252i	$-0.935824\pi$
$251$	0.0325488	−	0.163634i	0.00205446	−	0.0103285i	0.981799	+	0.189923i	$0.0608240\pi$
$252$	−7.78938	−	6.20652i	−0.490685	−	0.390974i
$253$	−7.27083	+	10.8816i	−0.457113	+	0.684118i
$254$	2.46369	−	7.04552i	0.154586	−	0.442076i
$255$	−22.2281			−1.39198
$256$	−14.4039	+	6.96613i	−0.900245	+	0.435383i
$257$	1.30561			0.0814417			0.0407209	−	0.999171i	$-0.487035\pi$
$257$	1.30561			0.0814417			0.0407209	+	0.999171i	$0.487035\pi$
$258$	−1.34988	+	3.86033i	−0.0840402	+	0.240333i
$259$	−6.05569	+	9.06297i	−0.376282	+	0.563146i
$260$	−3.28365	−	2.61639i	−0.203643	−	0.162261i
$261$	0.169691	−	0.853096i	0.0105036	−	0.0528053i
$262$	−4.89609	−	6.50295i	−0.302481	−	0.401753i
$263$	4.45700	−	10.7602i	0.274831	−	0.663500i	−0.724846	−	0.688910i	$-0.758089\pi$
$263$	4.45700	−	10.7602i	0.274831	−	0.663500i	0.999677	+	0.0254106i	$0.00808933\pi$
$264$	2.40873	+	3.82817i	0.148247	+	0.235608i
$265$	−1.99031	−	4.80503i	−0.122264	−	0.295170i
$266$	11.4676	+	6.76137i	0.703126	+	0.414566i
$267$	5.70699	−	3.81329i	0.349262	−	0.233370i
$268$	−11.3390	+	3.61927i	−0.692641	+	0.221082i
$269$	−2.48406	−	12.4882i	−0.151456	−	0.761419i	−0.979608	−	0.200916i	$-0.935608\pi$
$269$	−2.48406	−	12.4882i	−0.151456	−	0.761419i	0.828153	−	0.560502i	$-0.189392\pi$
$270$	18.9955	+	16.9683i	1.15603	+	1.03266i
$271$	5.90740	+	5.90740i	0.358849	+	0.358849i	0.863389	−	0.504540i	$-0.168338\pi$
$271$	5.90740	+	5.90740i	0.358849	+	0.358849i	−0.504540	+	0.863389i	$0.668338\pi$
$272$	20.6517	+	12.9524i	1.25220	+	0.785354i
$273$	1.11063	−	1.11063i	0.0672184	−	0.0672184i
$274$	−13.9835	+	0.788215i	−0.844773	+	0.0476178i
$275$	−11.4542	+	2.27839i	−0.690716	+	0.137392i
$276$	−13.2767	+	11.2206i	−0.799161	+	0.675401i
$277$	−0.0619322	−	0.0926880i	−0.00372114	−	0.00556908i	0.829604	−	0.558352i	$-0.188566\pi$
$277$	−0.0619322	−	0.0926880i	−0.00372114	−	0.00556908i	−0.833326	+	0.552783i	$0.813566\pi$
$278$	−0.746651	−	2.89204i	−0.0447811	−	0.173453i
$279$	1.93988	−	0.803526i	0.116138	−	0.0481058i
$280$	25.7132	+	0.705374i	1.53666	+	0.0421542i
$281$	−8.41645	−	3.48621i	−0.502083	−	0.207970i	0.117243	−	0.993103i	$-0.462594\pi$
$281$	−8.41645	−	3.48621i	−0.502083	−	0.207970i	−0.619327	+	0.785133i	$0.712594\pi$
$282$	−13.1284	−	1.85064i	−0.781787	−	0.110204i
$283$	11.6331	+	2.31397i	0.691518	+	0.137551i	0.528324	−	0.849043i	$-0.322821\pi$
$283$	11.6331	+	2.31397i	0.691518	+	0.137551i	0.163193	+	0.986594i	$0.447821\pi$
$284$	17.1556	−	9.49090i	1.01800	−	0.563181i
$285$	−11.1097	−	7.42327i	−0.658082	−	0.439717i
$286$	1.17260	−	0.564997i	0.0693375	−	0.0334090i
$287$		−	14.3512i		−	0.847126i
$288$	−3.04590	−	10.5313i	−0.179481	−	0.620565i
$289$		−	20.1412i		−	1.18478i
$290$	0.975121	+	2.02378i	0.0572611	+	0.118841i
$291$	−4.96502	−	3.31752i	−0.291054	−	0.194476i
$292$	−1.72968	+	6.01325i	−0.101222	+	0.351899i
$293$	0.100300	+	0.0199510i	0.00585961	+	0.00116555i	0.198019	−	0.980198i	$-0.436549\pi$
$293$	0.100300	+	0.0199510i	0.00585961	+	0.00116555i	−0.192160	+	0.981364i	$0.561549\pi$
$294$	0.0808095	−	0.573263i	0.00471291	−	0.0334334i
$295$	−24.5415	−	10.1654i	−1.42886	−	0.591853i
$296$	−11.2064	+	4.28572i	−0.651358	+	0.249102i
$297$	−7.29526	+	3.02180i	−0.423314	+	0.175342i
$298$	24.6775	−	6.37109i	1.42953	−	0.369068i
$299$	2.77927	+	4.15947i	0.160729	+	0.240549i
$300$	−15.4579	−	1.29737i	−0.892460	−	0.0749040i
$301$	−7.07185	+	1.40668i	−0.407614	+	0.0810795i
$302$	−0.430065	−	7.62965i	−0.0247475	−	0.439037i
$303$	−0.684363	+	0.684363i	−0.0393156	+	0.0393156i
$304$	5.99628	+	13.3705i	0.343910	+	0.766851i
$305$	29.0989	+	29.0989i	1.66620	+	1.66620i
$306$	−11.1274	+	12.4568i	−0.636112	+	0.712108i
$307$	4.46728	+	22.4585i	0.254961	+	1.28178i	0.869911	+	0.493209i	$0.164176\pi$
$307$	4.46728	+	22.4585i	0.254961	+	1.28178i	−0.614950	+	0.788566i	$0.710824\pi$
$308$	−3.65721	+	7.08645i	−0.208389	+	0.403788i
$309$	−11.8624	+	7.92619i	−0.674827	+	0.450905i
$310$	−2.75428	+	4.67140i	−0.156433	+	0.265318i
$311$	−6.48708	−	15.6612i	−0.367848	−	0.888064i	−0.994102	−	0.108445i	$-0.965413\pi$
$311$	−6.48708	−	15.6612i	−0.367848	−	0.888064i	0.626254	−	0.779619i	$-0.284587\pi$
$312$	1.70428	−	0.290664i	0.0964858	−	0.0164556i
$313$	−6.94583	+	16.7687i	−0.392602	+	0.947824i	0.596770	+	0.802413i	$0.296451\pi$
$313$	−6.94583	+	16.7687i	−0.392602	+	0.947824i	−0.989371	+	0.145411i	$0.953549\pi$
$314$	−9.57264	+	7.20727i	−0.540215	+	0.406730i
$315$	−3.43845	+	17.2862i	−0.193735	+	0.973970i
$316$	0.297126	+	2.62724i	0.0167146	+	0.147794i
$317$	−10.9936	+	16.4530i	−0.617459	+	0.924093i	0.382541	+	0.923939i	$0.375049\pi$
$317$	−10.9936	+	16.4530i	−0.617459	+	0.924093i	−1.00000		0.000154534i	$0.999951\pi$
$318$	2.02161	+	0.706920i	0.113366	+	0.0396421i
$319$	−0.696439			−0.0389931
$320$	22.6444	+	16.9974i	1.26586	+	0.950185i
$321$	15.2992			0.853919
$322$	−28.9309	−	10.1166i	−1.61225	−	0.563775i
$323$	12.4036	−	18.5633i	0.690156	−	1.03289i
$324$	1.13241	−	0.128069i	0.0629114	−	0.00711494i
$325$	−0.870913	+	4.37837i	−0.0483095	+	0.242868i
$326$	−1.24995	+	0.941091i	−0.0692283	+	0.0521222i
$327$	2.66944	−	6.44460i	0.147620	−	0.356387i
$328$	9.13315	−	12.8890i	0.504294	−	0.711677i
$329$	−8.94561	−	21.5966i	−0.493187	−	1.19066i
$330$	4.06514	−	6.89469i	0.223779	−	0.379540i
$331$	−5.97462	+	3.99211i	−0.328395	+	0.219426i	−0.708827	−	0.705382i	$-0.750775\pi$
$331$	−5.97462	+	3.99211i	−0.328395	+	0.219426i	0.380432	+	0.924809i	$0.375775\pi$
$332$	30.0504	+	15.5086i	1.64923	+	0.851143i
$333$	−1.60380	−	8.06284i	−0.0878876	−	0.441841i
$334$	2.67007	−	2.98906i	0.146100	−	0.163554i
$335$	14.8939	+	14.8939i	0.813741	+	0.813741i
$336$	−7.27040	+	7.70299i	−0.396633	+	0.420232i
$337$	−18.4718	+	18.4718i	−1.00622	+	1.00622i	−0.00624304	+	0.999981i	$0.501987\pi$
$337$	−18.4718	+	18.4718i	−1.00622	+	1.00622i	−0.999981	+	0.00624304i	$0.998013\pi$
$338$	1.00666	+	17.8589i	0.0547552	+	0.971395i
$339$	5.17487	−	1.02935i	0.281060	−	0.0559064i
$340$	3.60795	−	42.9877i	0.195669	−	2.33134i
$341$	−0.934023	−	1.39786i	−0.0505802	−	0.0756986i
$342$	−9.72160	+	2.50987i	−0.525684	+	0.135718i
$343$	17.5609	−	7.27398i	0.948201	−	0.392758i
$344$	−7.24653	−	3.23718i	−0.390706	−	0.174537i
$345$	28.4199	+	11.7719i	1.53008	+	0.633779i
$346$	−2.06228	+	14.6298i	−0.110869	+	0.786502i
$347$	9.12297	+	1.81467i	0.489747	+	0.0974167i	0.433785	−	0.901016i	$-0.357178\pi$
$347$	9.12297	+	1.81467i	0.489747	+	0.0974167i	0.0559615	+	0.998433i	$0.482178\pi$
$348$	−0.889002	−	0.255716i	−0.0476555	−	0.0137078i
$349$	9.46721	+	6.32579i	0.506768	+	0.338612i	0.782528	−	0.622615i	$-0.213930\pi$
$349$	9.46721	+	6.32579i	0.506768	+	0.338612i	−0.275760	+	0.961226i	$0.588930\pi$
$350$	−11.8719	−	24.6391i	−0.634578	−	1.31701i
$351$			3.01837i			0.161109i
$352$	−7.79442	+	4.03697i	−0.415444	+	0.215171i
$353$		−	12.2587i		−	0.652465i	−0.945290	−	0.326233i	$-0.894221\pi$
$353$		−	12.2587i		−	0.652465i	0.945290	−	0.326233i	$-0.105779\pi$
$354$	9.85413	−	4.74803i	0.523741	−	0.252355i
$355$	−28.8479	−	19.2756i	−1.53109	−	1.02304i
$356$	6.44834	+	11.6559i	0.341761	+	0.617763i
$357$	15.8281	+	3.14840i	0.837710	+	0.166631i
$358$	−27.2412	−	3.84004i	−1.43974	−	0.202952i
$359$	−6.95121	−	2.87929i	−0.366871	−	0.151963i	0.191629	−	0.981467i	$-0.438623\pi$
$359$	−6.95121	−	2.87929i	−0.366871	−	0.151963i	−0.558500	+	0.829505i	$0.688623\pi$
$360$	−14.0891	+	13.3368i	−0.742562	+	0.702909i
$361$	−5.15492	+	2.13524i	−0.271311	+	0.112381i
$362$	1.41562	+	5.48317i	0.0744031	+	0.288189i
$363$	−4.91933	−	7.36230i	−0.258198	−	0.386420i
$364$	1.96762	+	2.32816i	0.103131	+	0.122029i
$365$	10.8599	−	2.16017i	0.568433	−	0.113068i
$366$	−16.9188	+	0.953672i	−0.884359	+	0.0498492i
$367$	−1.10049	+	1.10049i	−0.0574452	+	0.0574452i	−0.735246	−	0.677801i	$-0.762933\pi$
$367$	−1.10049	+	1.10049i	−0.0574452	+	0.0574452i	0.677801	+	0.735246i	$0.262933\pi$
$368$	−19.5450	−	27.4975i	−1.01885	−	1.43341i
$369$	7.65356	+	7.65356i	0.398429	+	0.398429i
$370$	15.8343	+	14.1445i	0.823186	+	0.735336i
$371$	0.736662	+	3.70345i	0.0382456	+	0.192273i
$372$	−0.679014	−	2.12732i	−0.0352052	−	0.110297i
$373$	29.9517	−	20.0131i	1.55084	−	1.03624i	0.574897	−	0.818226i	$-0.305042\pi$
$373$	29.9517	−	20.0131i	1.55084	−	1.03624i	0.975946	−	0.218014i	$-0.0699579\pi$
$374$	11.5204	+	6.79249i	0.595707	+	0.351231i
$375$	3.52611	+	8.51278i	0.182087	+	0.439598i
$376$	5.70996	−	25.0892i	0.294469	−	1.29388i
$377$	−0.101875	+	0.245949i	−0.00524685	+	0.0126670i
$378$	−11.1228	−	14.7733i	−0.572097	−	0.759854i
$379$	3.70680	−	18.6353i	0.190405	−	0.957233i	−0.760873	−	0.648900i	$-0.775229\pi$
$379$	3.70680	−	18.6353i	0.190405	−	0.957233i	0.951279	−	0.308332i	$-0.0997708\pi$
$380$	16.1594	−	20.2806i	0.828961	−	1.04037i
$381$	3.02169	−	4.52229i	0.154806	−	0.231684i
$382$	−7.58963	+	21.7044i	−0.388319	+	1.11049i
$383$	−22.9884			−1.17465			−0.587327	−	0.809350i	$-0.699820\pi$
$383$	−22.9884			−1.17465			−0.587327	+	0.809350i	$0.699820\pi$
$384$	−11.4318	+	2.29125i	−0.583378	+	0.116925i
$385$	14.1119			0.719209
$386$	11.6396	−	33.2863i	0.592439	−	1.69423i
$387$	3.02126	−	4.52163i	0.153579	−	0.229847i
$388$	7.22177	−	9.06355i	0.366630	−	0.460132i
$389$	−5.01123	+	25.1931i	−0.254079	+	1.27734i	0.617298	+	0.786729i	$0.288227\pi$
$389$	−5.01123	+	25.1931i	−0.254079	+	1.27734i	−0.871377	+	0.490614i	$0.836773\pi$
$390$	−1.84023	−	2.44417i	−0.0931835	−	0.123766i
$391$	−19.6698	+	47.4872i	−0.994747	+	2.40153i
$392$	1.09554	+	0.249330i	0.0553330	+	0.0125931i
$393$	−2.26994	−	5.48011i	−0.114503	−	0.276435i
$394$	−5.09851	−	3.00611i	−0.256859	−	0.151445i
$395$	3.89033	−	2.59943i	0.195744	−	0.130792i
$396$	−1.82883	−	5.72964i	−0.0919020	−	0.287925i
$397$	0.319222	+	1.60484i	0.0160213	+	0.0805445i	0.987969	−	0.154654i	$-0.0494261\pi$
$397$	0.319222	+	1.60484i	0.0160213	+	0.0805445i	−0.971947	+	0.235198i	$0.924426\pi$
$398$	−2.05097	−	1.83209i	−0.102806	−	0.0918345i
$399$	6.85951	+	6.85951i	0.343405	+	0.343405i
$400$	5.01808	−	29.6840i	0.250904	−	1.48420i
$401$	−21.7278	+	21.7278i	−1.08503	+	1.08503i	−0.0890025	+	0.996031i	$0.528368\pi$
$401$	−21.7278	+	21.7278i	−1.08503	+	1.08503i	−0.996031	+	0.0890025i	$0.971632\pi$
$402$	−8.65969	+	0.488126i	−0.431906	+	0.0243455i
$403$	−0.630289	+	0.125372i	−0.0313969	+	0.00624524i
$404$	−1.21243	−	1.43460i	−0.0603208	−	0.0713739i
$405$	−1.12042	−	1.67683i	−0.0556742	−	0.0833224i
$406$	−0.407710	−	1.57920i	−0.0202343	−	0.0783744i
$407$	−6.08119	+	2.51891i	−0.301433	+	0.124858i
$408$	12.2117	+	12.9006i	0.604571	+	0.638676i
$409$	17.9000	+	7.41442i	0.885097	+	0.366619i	0.778472	−	0.627680i	$-0.215995\pi$
$409$	17.9000	+	7.41442i	0.885097	+	0.366619i	0.106626	+	0.994299i	$0.465995\pi$
$410$	−27.6808	−	3.90201i	−1.36706	−	0.192707i
$411$	−10.0098	−	1.99108i	−0.493748	−	0.0982126i
$412$	−13.4033	−	24.2276i	−0.660334	−	1.19361i
$413$	16.0355	+	10.7146i	0.789056	+	0.527231i
$414$	20.8242	−	10.0337i	1.02345	−	0.493131i
$415$		−	59.8422i		−	2.93754i
$416$	0.285495	+	3.34315i	0.0139976	+	0.163911i
$417$		−	2.17653i		−	0.106585i
$418$	3.48955	+	7.24227i	0.170680	+	0.354231i
$419$	27.8129	+	18.5840i	1.35875	+	0.907886i	0.999677	−	0.0254236i	$-0.00809346\pi$
$419$	27.8129	+	18.5840i	1.35875	+	0.907886i	0.359071	+	0.933310i	$0.383093\pi$
$420$	18.0138	+	5.18157i	0.878983	+	0.252834i
$421$	19.7735	+	3.93320i	0.963703	+	0.191693i	0.651774	−	0.758413i	$-0.274025\pi$
$421$	19.7735	+	3.93320i	0.963703	+	0.191693i	0.311929	+	0.950105i	$0.399025\pi$
$422$	−2.95153	+	20.9381i	−0.143678	+	1.01925i
$423$	16.2883	+	6.74683i	0.791964	+	0.328042i
$424$	−1.69528	+	3.79493i	−0.0823299	+	0.184298i
$425$	−42.3764	+	17.5529i	−2.05556	+	0.851439i
$426$	13.8332	−	3.57139i	0.670222	−	0.173034i
$427$	−16.5990	−	24.8422i	−0.803282	−	1.20220i
$428$	−2.48329	+	29.5878i	−0.120035	+	1.43018i
$429$	0.930266	−	0.185041i	0.0449137	−	0.00893388i
$430$	0.790429	+	14.0227i	0.0381178	+	0.676237i
$431$	13.5229	−	13.5229i	0.651373	−	0.651373i	−0.301950	−	0.953324i	$-0.597638\pi$
$431$	13.5229	−	13.5229i	0.651373	−	0.651373i	0.953324	+	0.301950i	$0.0976377\pi$
$432$	−0.587825	−	20.3466i	−0.0282817	−	0.978928i
$433$	−17.9120	−	17.9120i	−0.860797	−	0.860797i	0.130634	−	0.991431i	$-0.458299\pi$
$433$	−17.9120	−	17.9120i	−0.860797	−	0.860797i	−0.991431	+	0.130634i	$0.958299\pi$
$434$	2.62291	−	2.93627i	0.125904	−	0.140946i
$435$	0.319361	+	1.60553i	0.0153122	+	0.0769795i
$436$	12.0302	+	6.20859i	0.576141	+	0.297338i
$437$	−25.6899	+	17.1654i	−1.22891	+	0.821134i
$438$	−2.31576	+	3.92766i	−0.110651	+	0.187671i
$439$	2.81785	+	6.80290i	0.134489	+	0.324685i	0.976749	−	0.214387i	$-0.0687753\pi$
$439$	2.81785	+	6.80290i	0.134489	+	0.324685i	−0.842260	+	0.539071i	$0.818775\pi$
$440$	12.6741	+	8.98084i	0.604213	+	0.428145i
$441$	−0.294605	+	0.711240i	−0.0140288	+	0.0338686i
$442$	4.08400	−	3.07486i	0.194256	−	0.146256i
$443$	5.64485	−	28.3786i	0.268195	−	1.34831i	−0.578263	−	0.815850i	$-0.696269\pi$
$443$	5.64485	−	28.3786i	0.268195	−	1.34831i	0.846458	−	0.532456i	$-0.178731\pi$
$444$	−8.68750	+	0.982509i	−0.412291	+	0.0466278i
$445$	13.0963	−	19.6000i	0.620823	−	0.929127i
$446$	−19.8419	−	6.93836i	−0.939543	−	0.328541i
$447$	18.5721			0.878429
$448$	−13.7170	−	15.3108i	−0.648067	−	0.723368i
$449$	−0.0955370			−0.00450867			−0.00225433	−	0.999997i	$-0.500718\pi$
$449$	−0.0955370			−0.00450867			−0.00225433	+	0.999997i	$0.500718\pi$
$450$	19.4714	+	6.80880i	0.917892	+	0.320970i
$451$	4.81478	−	7.20583i	0.226719	−	0.339309i
$452$	1.15073	+	10.1750i	0.0541259	+	0.478590i
$453$	1.08637	−	5.46155i	0.0510421	−	0.256606i
$454$	9.37903	−	7.06150i	0.440180	−	0.331413i
$455$	2.06430	−	4.98365i	0.0967757	−	0.233637i
$456$	1.79521	+	10.5260i	0.0840682	+	0.492926i
$457$	11.4359	+	27.6087i	0.534949	+	1.29148i	0.928211	+	0.372054i	$0.121346\pi$
$457$	11.4359	+	27.6087i	0.534949	+	1.29148i	−0.393262	+	0.919426i	$0.628654\pi$
$458$	2.66184	−	4.51463i	0.124380	−	0.210955i
$459$	−25.7862	+	17.2298i	−1.20360	+	0.804219i
$460$	−27.3792	+	53.0516i	−1.27656	+	2.47355i
$461$	−5.29789	−	26.6343i	−0.246747	−	1.24048i	−0.883137	−	0.469115i	$-0.844573\pi$
$461$	−5.29789	−	26.6343i	−0.246747	−	1.24048i	0.636390	−	0.771368i	$-0.280427\pi$
$462$	−3.87125	+	4.33375i	−0.180107	+	0.201624i
$463$	21.3463	+	21.3463i	0.992048	+	0.992048i	0.999969	−	0.00792071i	$-0.00252127\pi$
$463$	21.3463	+	21.3463i	0.992048	+	0.992048i	−0.00792071	+	0.999969i	$0.502521\pi$
$464$	0.638838	−	1.67777i	0.0296573	−	0.0778884i
$465$	−2.79426	+	2.79426i	−0.129581	+	0.129581i
$466$	1.53194	+	27.1776i	0.0709657	+	1.25898i
$467$	32.0458	−	6.37431i	1.48290	−	0.294968i	0.613746	−	0.789503i	$-0.289662\pi$
$467$	32.0458	−	6.37431i	1.48290	−	0.294968i	0.869157	+	0.494535i	$0.164662\pi$
$468$	−2.29096	−	0.192279i	−0.105900	−	0.00888812i
$469$	−8.49600	−	12.7152i	−0.392309	−	0.587132i
$470$	−44.0881	+	11.3824i	−2.03363	+	0.525033i
$471$	−8.06697	+	3.34145i	−0.371707	+	0.153966i
$472$	7.58291	+	19.8280i	0.349032	+	0.912655i
$473$	−4.02275	−	1.66628i	−0.184966	−	0.0766155i
$474$	−0.268933	+	1.90781i	−0.0123525	+	0.0876285i
$475$	−27.0418	−	5.37896i	−1.24077	−	0.246804i
$476$	−8.65794	+	30.0995i	−0.396836	+	1.37961i
$477$	−2.36793	−	1.58220i	−0.108420	−	0.0724439i
$478$	−1.47281	−	3.05670i	−0.0673649	−	0.139810i
$479$			0.620601i			0.0283560i	0.999899	+	0.0141780i	$0.00451315\pi$
$479$			0.620601i			0.0283560i	−0.999899	+	0.0141780i	$0.995487\pi$
$480$	12.8809	+	16.1176i	0.587928	+	0.735667i
$481$			2.51605i			0.114722i
$482$	22.9761	−	11.0706i	1.04653	−	0.504252i
$483$	−18.5697	−	12.4079i	−0.844953	−	0.564579i
$484$	15.0367	−	8.31866i	0.683486	−	0.378121i
$485$	−20.1139	−	4.00090i	−0.913325	−	0.181672i
$486$	22.2008	+	3.12952i	1.00705	+	0.141958i
$487$	−11.7418	−	4.86361i	−0.532072	−	0.220391i	0.100439	−	0.994943i	$-0.467975\pi$
$487$	−11.7418	−	4.86361i	−0.532072	−	0.220391i	−0.632510	+	0.774552i	$0.717975\pi$
$488$	0.901832	−	32.8747i	0.0408240	−	1.48817i
$489$	−1.05335	+	0.436311i	−0.0476340	+	0.0197306i
$490$	−0.497022	−	1.92514i	−0.0224532	−	0.0869689i
$491$	−11.9335	−	17.8598i	−0.538553	−	0.806002i	0.458000	−	0.888952i	$-0.348566\pi$
$491$	−11.9335	−	17.8598i	−0.538553	−	0.806002i	−0.996554	+	0.0829501i	$0.973566\pi$
$492$	8.79186	−	7.43034i	0.396368	−	0.334986i
$493$	−2.68271	+	0.533623i	−0.120823	+	0.0240332i
$494$	3.06808	−	0.172940i	0.138039	−	0.00778095i
$495$	−7.52593	+	7.52593i	−0.338266	+	0.338266i
$496$	4.22432	−	0.967875i	0.189678	−	0.0434589i
$497$	17.8117	+	17.8117i	0.798964	+	0.798964i
$498$	18.3775	+	16.4162i	0.823514	+	0.735629i
$499$	5.81742	+	29.2462i	0.260424	+	1.30924i	0.860564	+	0.509343i	$0.170112\pi$
$499$	5.81742	+	29.2462i	0.260424	+	1.30924i	−0.600140	+	0.799895i	$0.704888\pi$
$500$	−17.0355	+	5.43752i	−0.761852	+	0.243173i
$501$	2.42839	−	1.62260i	0.108492	−	0.0724923i
$502$	0.203249	+	0.119836i	0.00907144	+	0.00534856i
$503$	10.2519	+	24.7502i	0.457108	+	1.10356i	0.969563	+	0.244842i	$0.0787362\pi$
$503$	10.2519	+	24.7502i	0.457108	+	1.10356i	−0.512455	+	0.858714i	$0.671264\pi$
$504$	11.9215	−	7.50118i	0.531027	−	0.334129i
$505$	−1.27201	+	3.07089i	−0.0566035	+	0.136653i
$506$	−11.1323	−	14.7858i	−0.494890	−	0.657308i
$507$	−2.54289	+	12.7840i	−0.112934	+	0.567755i
$508$	8.25535	+	6.57780i	0.366272	+	0.291843i
$509$	−3.45815	+	5.17549i	−0.153280	+	0.229399i	−0.900160	−	0.435559i	$-0.856551\pi$
$509$	−3.45815	+	5.17549i	−0.153280	+	0.229399i	0.746880	+	0.664958i	$0.231551\pi$
$510$	10.3762	−	29.6734i	0.459467	−	1.31396i
$511$	−8.03904			−0.355626
$512$	−2.57558	−	22.4804i	−0.113826	−	0.993501i
$513$	−18.6421			−0.823071
$514$	−0.609468	+	1.74292i	−0.0268825	+	0.0768771i
$515$	−27.2215	+	40.7399i	−1.19952	+	1.79521i
$516$	−4.52321	−	3.60406i	−0.199123	−	0.158660i
$517$	2.75394	−	13.8450i	0.121118	−	0.608902i
$518$	−9.27178	−	12.3147i	−0.407378	−	0.541077i
$519$	−4.12001	+	9.94659i	−0.180848	+	0.436607i
$520$	5.02558	−	3.16216i	0.220386	−	0.138670i
$521$	−13.3796	−	32.3011i	−0.586169	−	1.41514i	−0.887138	−	0.461504i	$-0.847310\pi$
$521$	−13.3796	−	32.3011i	−0.586169	−	1.41514i	0.300969	−	0.953634i	$-0.402690\pi$
$522$	1.05963	+	0.624761i	0.0463786	+	0.0273450i
$523$	−29.7773	+	19.8966i	−1.30207	+	0.870016i	−0.996617	−	0.0821904i	$-0.973808\pi$
$523$	−29.7773	+	19.8966i	−1.30207	+	0.870016i	−0.305455	+	0.952207i	$0.598808\pi$
$524$	10.9666	−	3.50041i	0.479080	−	0.152916i
$525$	−3.88814	−	19.5470i	−0.169692	−	0.853102i
$526$	12.2837	+	10.9728i	0.535595	+	0.478437i
$527$	−4.66896	−	4.66896i	−0.203383	−	0.203383i
$528$	−6.23483	+	1.42852i	−0.271336	+	0.0621684i
$529$	34.0347	−	34.0347i	1.47977	−	1.47977i
$530$	7.34356	−	0.413939i	0.318984	−	0.0179803i
$531$	−14.2659	+	2.83767i	−0.619089	+	0.123145i
$532$	−14.3793	+	12.1525i	−0.623420	+	0.526876i
$533$	−1.84045	−	2.75442i	−0.0797186	−	0.119307i
$534$	2.42649	+	9.39862i	0.105004	+	0.406718i
$535$	48.5437	−	20.1074i	2.09873	−	0.869321i
$536$	0.461592	−	16.8265i	0.0199377	−	0.726795i
$537$	−18.5209	−	7.67162i	−0.799237	−	0.331055i
$538$	17.8307	+	2.51349i	0.768735	+	0.108364i
$539$	0.604552	+	0.120253i	0.0260399	+	0.00517966i
$540$	−31.5191	+	17.4371i	−1.35637	+	0.750374i
$541$	−33.4281	−	22.3359i	−1.43718	−	0.960296i	−0.998085	−	0.0618571i	$-0.980298\pi$
$541$	−33.4281	−	22.3359i	−1.43718	−	0.960296i	−0.439099	−	0.898439i	$-0.644702\pi$
$542$	−10.6437	+	5.12847i	−0.457186	+	0.220287i
$543$			4.12659i			0.177089i
$544$	−26.9312	+	21.5228i	−1.15466	+	0.922781i
$545$		−	23.9568i		−	1.02620i
$546$	0.964185	+	2.00109i	0.0412633	+	0.0856386i
$547$	−2.75272	−	1.83931i	−0.117698	−	0.0786432i	0.495328	−	0.868706i	$-0.335048\pi$
$547$	−2.75272	−	1.83931i	−0.117698	−	0.0786432i	−0.613026	+	0.790063i	$0.710048\pi$
$548$	5.47536	−	19.0352i	0.233896	−	0.813143i
$549$	22.1007	+	4.39611i	0.943236	+	0.187621i
$550$	2.30538	−	16.3544i	0.0983019	−	0.697353i
$551$	−1.51904	−	0.629206i	−0.0647132	−	0.0268051i
$552$	−8.78130	−	22.9615i	−0.373757	−	0.977307i
$553$	−3.13839	+	1.29996i	−0.133458	+	0.0552801i
$554$	0.152644	−	0.0394089i	0.00648523	−	0.00167432i
$555$	8.59557	+	12.8642i	0.364862	+	0.546054i
$556$	4.20927	+	0.353283i	0.178513	+	0.0149825i
$557$	42.1945	−	8.39301i	1.78784	−	0.355623i	0.813650	−	0.581355i	$-0.197477\pi$
$557$	42.1945	−	8.39301i	1.78784	−	0.355623i	0.974190	+	0.225731i	$0.0724772\pi$
$558$	0.167115	+	2.96474i	0.00707455	+	0.125507i
$559$	−1.17690	+	1.17690i	−0.0497775	+	0.0497775i
$560$	−12.9447	+	33.9965i	−0.547015	+	1.43662i
$561$	6.89108	+	6.89108i	0.290942	+	0.290942i
$562$	8.58278	−	9.60815i	0.362043	−	0.405296i
$563$	−2.34500	−	11.7891i	−0.0988299	−	0.496852i	−0.998217	−	0.0596975i	$-0.980986\pi$
$563$	−2.34500	−	11.7891i	−0.0988299	−	0.496852i	0.899387	−	0.437154i	$-0.144014\pi$
$564$	8.59896	−	16.6619i	0.362082	−	0.701593i
$565$	15.0668	−	10.0673i	0.633863	−	0.423534i
$566$	−8.51947	+	14.4495i	−0.358100	+	0.607356i
$567$	0.560318	+	1.35273i	0.0235311	+	0.0568092i
$568$	4.66151	+	27.3323i	0.195592	+	1.14684i
$569$	−2.83292	+	6.83927i	−0.118762	+	0.286717i	−0.972070	−	0.234690i	$-0.924593\pi$
$569$	−2.83292	+	6.83927i	−0.118762	+	0.286717i	0.853308	+	0.521407i	$0.174593\pi$
$570$	15.0958	−	11.3657i	0.632293	−	0.476055i
$571$	6.93430	−	34.8611i	0.290191	−	1.45889i	−0.510534	−	0.859858i	$-0.670552\pi$
$571$	6.93430	−	34.8611i	0.290191	−	1.45889i	0.800725	−	0.599032i	$-0.204448\pi$
$572$	0.206862	+	1.82911i	0.00864936	+	0.0764790i
$573$	−9.30862	+	13.9313i	−0.388873	+	0.581990i
$574$	19.1582	+	6.69925i	0.799646	+	0.279621i
$575$	63.4766			2.64716
$576$	15.4806	+	0.849982i	0.645027	+	0.0354159i
$577$	24.2433			1.00926			0.504632	−	0.863335i	$-0.331628\pi$
$577$	24.2433			1.00926			0.504632	+	0.863335i	$0.331628\pi$
$578$	26.8875	+	9.40205i	1.11837	+	0.391074i
$579$	14.2759	−	21.3653i	0.593284	−	0.887913i
$580$	−3.15684	+	0.357021i	−0.131081	+	0.0148245i
$581$	−8.47608	+	42.6121i	−0.351647	+	1.76785i
$582$	6.74643	−	5.07941i	0.279648	−	0.210548i
$583$	−0.872611	+	2.10667i	−0.0361398	+	0.0872493i
$584$	−7.21996	−	5.11606i	−0.298764	−	0.211704i
$585$	1.55690	+	3.75870i	0.0643701	+	0.155403i
$586$	−0.0734546	+	0.124583i	−0.00303438	+	0.00514647i
$587$	12.8222	−	8.56752i	0.529229	−	0.353619i	−0.262070	−	0.965049i	$-0.584405\pi$
$587$	12.8222	−	8.56752i	0.529229	−	0.353619i	0.791299	+	0.611429i	$0.209405\pi$
$588$	0.727554	+	0.375480i	0.0300038	+	0.0154845i
$589$	−0.774328	−	3.89281i	−0.0319056	−	0.160400i
$590$	25.0264	−	28.0163i	1.03032	−	1.15341i
$591$	−3.04974	−	3.04974i	−0.125450	−	0.125450i
$592$	−0.489999	−	16.9606i	−0.0201389	−	0.697075i
$593$	−7.17902	+	7.17902i	−0.294807	+	0.294807i	−0.838976	−	0.544169i	$-0.816845\pi$
$593$	−7.17902	+	7.17902i	−0.294807	+	0.294807i	0.544169	+	0.838976i	$0.316845\pi$
$594$	−0.628465	−	11.1494i	−0.0257862	−	0.457465i
$595$	54.3595	−	10.8128i	2.22852	−	0.443281i
$596$	−3.01453	+	35.9172i	−0.123480	+	1.47123i
$597$	−1.11336	−	1.66626i	−0.0455668	−	0.0681955i
$598$	−6.85007	+	1.76852i	−0.280120	+	0.0723200i
$599$	−37.8559	+	15.6804i	−1.54675	+	0.640685i	−0.982725	−	0.185073i	$-0.940748\pi$
$599$	−37.8559	+	15.6804i	−1.54675	+	0.640685i	−0.564025	+	0.825758i	$0.690748\pi$
$600$	8.94777	−	20.0298i	0.365291	−	0.817715i
$601$	−32.5429	−	13.4797i	−1.32745	−	0.549850i	−0.397526	−	0.917591i	$-0.630131\pi$
$601$	−32.5429	−	13.4797i	−1.32745	−	0.549850i	−0.929928	+	0.367741i	$0.880131\pi$
$602$	1.42335	−	10.0972i	0.0580112	−	0.411531i
$603$	11.3120	+	2.25010i	0.460660	+	0.0916310i
$604$	10.3860	+	2.98746i	0.422599	+	0.121558i
$605$	−25.2849	−	16.8948i	−1.02798	−	0.686872i
$606$	−0.594125	−	1.23306i	−0.0241347	−	0.0500895i
$607$			37.4709i			1.52090i	0.649399	+	0.760448i	$0.275021\pi$
$607$			37.4709i			1.52090i	−0.649399	+	0.760448i	$0.724979\pi$
$608$	−20.6481	+	1.76329i	−0.837389	+	0.0715107i
$609$		−	1.18850i		−	0.0481603i
$610$	−52.4291	+	25.2620i	−2.12279	+	1.02283i
$611$	−4.48655	−	2.99781i	−0.181506	−	0.121279i
$612$	−11.4349	−	20.6695i	−0.462226	−	0.835514i
$613$	3.83710	+	0.763246i	0.154979	+	0.0308272i	0.271970	−	0.962306i	$-0.412325\pi$
$613$	3.83710	+	0.763246i	0.154979	+	0.0308272i	−0.116991	+	0.993133i	$0.537325\pi$
$614$	−32.0664	−	4.52021i	−1.29409	−	0.182421i
$615$	−18.8198	−	7.79543i	−0.758889	−	0.314342i
$616$	−7.75284	−	8.19020i	−0.312371	−	0.329992i
$617$	−37.8776	+	15.6894i	−1.52490	+	0.631633i	−0.978565	−	0.205937i	$-0.933976\pi$
$617$	−37.8776	+	15.6894i	−1.52490	+	0.631633i	−0.546331	+	0.837569i	$0.683976\pi$
$618$	−5.04362	−	19.5357i	−0.202884	−	0.785840i
$619$	22.0632	+	33.0200i	0.886796	+	1.32718i	0.944384	+	0.328844i	$0.106659\pi$
$619$	22.0632	+	33.0200i	0.886796	+	1.32718i	−0.0575877	+	0.998340i	$0.518341\pi$
$620$	−4.95037	−	5.85747i	−0.198812	−	0.235242i
$621$	42.0941	−	8.37304i	1.68918	−	0.335998i
$622$	23.9351	−	1.34916i	0.959711	−	0.0540966i
$623$	−12.1017	+	12.1017i	−0.484843	+	0.484843i
$624$	−0.407548	+	2.41081i	−0.0163150	+	0.0965096i
$625$	−4.23310	−	4.23310i	−0.169324	−	0.169324i
$626$	−19.1430	−	17.1001i	−0.765109	−	0.683457i
$627$	1.14286	+	5.74554i	0.0456414	+	0.229455i
$628$	−5.15277	−	16.1434i	−0.205618	−	0.644192i
$629$	−21.4949	+	14.3624i	−0.857058	+	0.572668i
$630$	−21.4712	−	12.6595i	−0.855432	−	0.504367i
$631$	−0.295581	−	0.713596i	−0.0117669	−	0.0284078i	0.917887	−	0.396842i	$-0.129894\pi$
$631$	−0.295581	−	0.713596i	−0.0117669	−	0.0284078i	−0.929654	+	0.368434i	$0.879894\pi$
$632$	−3.64593	−	0.829765i	−0.145027	−	0.0330063i
$633$	−5.89655	+	14.2355i	−0.234367	+	0.565812i
$634$	−16.8321	−	22.3562i	−0.668487	−	0.887879i
$635$	3.64414	−	18.3203i	0.144613	−	0.727020i
$636$	−1.88741	+	2.36875i	−0.0748405	+	0.0939272i
$637$	0.130902	−	0.195908i	0.00518652	−	0.00776217i
$638$	0.325103	−	0.929711i	0.0128709	−	0.0368076i
$639$	−18.9981			−0.751553
$640$	−33.2613	+	22.2946i	−1.31477	+	0.881273i
$641$	20.3094			0.802172			0.401086	−	0.916040i	$-0.368633\pi$
$641$	20.3094			0.802172			0.401086	+	0.916040i	$0.368633\pi$
$642$	−7.14179	+	20.4237i	−0.281864	+	0.806059i
$643$	−6.26132	+	9.37072i	−0.246922	+	0.369545i	−0.934140	−	0.356906i	$-0.883832\pi$
$643$	−6.26132	+	9.37072i	−0.246922	+	0.369545i	0.687218	+	0.726451i	$0.258832\pi$
$644$	27.0103	−	33.8988i	1.06435	−	1.33580i
$645$	−1.99667	+	10.0379i	−0.0786187	+	0.395243i
$646$	18.9910	+	25.2237i	0.747192	+	0.992414i
$647$	−0.189930	+	0.458531i	−0.00746691	+	0.0180267i	−0.927569	−	0.373652i	$-0.878105\pi$
$647$	−0.189930	+	0.458531i	−0.00746691	+	0.0180267i	0.920102	+	0.391679i	$0.128105\pi$
$648$	−0.357650	+	1.57149i	−0.0140498	+	0.0617339i
$649$	4.45682	+	10.7597i	0.174945	+	0.422356i
$650$	−5.43836	−	3.20648i	−0.213310	−	0.125769i
$651$	2.38550	−	1.59394i	0.0934952	−	0.0624715i
$652$	−0.672824	−	2.10793i	−0.0263498	−	0.0825528i
$653$	4.73978	+	23.8285i	0.185482	+	0.932481i	0.955620	+	0.294603i	$0.0951875\pi$
$653$	4.73978	+	23.8285i	0.185482	+	0.932481i	−0.770138	+	0.637878i	$0.779813\pi$
$654$	7.35711	+	6.57196i	0.287686	+	0.256984i
$655$	−14.4048	−	14.4048i	−0.562842	−	0.562842i
$656$	12.9428	+	18.2090i	0.505330	+	0.710941i
$657$	4.28725	−	4.28725i	0.167262	−	0.167262i
$658$	33.0063	−	1.86048i	1.28672	−	0.0725292i
$659$	−38.0620	+	7.57099i	−1.48268	+	0.294924i	−0.869073	−	0.494685i	$-0.835284\pi$
$659$	−38.0620	+	7.57099i	−1.48268	+	0.294924i	−0.613611	+	0.789609i	$0.710284\pi$
$660$	7.30643	+	8.64525i	0.284402	+	0.336516i
$661$	5.84250	+	8.74392i	0.227247	+	0.340099i	0.927518	−	0.373778i	$-0.121938\pi$
$661$	5.84250	+	8.74392i	0.227247	+	0.340099i	−0.700271	+	0.713877i	$0.746938\pi$
$662$	−2.54027	−	9.83937i	−0.0987306	−	0.382418i
$663$	3.44164	−	1.42557i	0.133662	−	0.0553646i
$664$	−34.7309	+	32.8763i	−1.34782	+	1.27585i
$665$	30.7802	+	12.7496i	1.19360	+	0.494407i
$666$	11.5122	+	1.62280i	0.446087	+	0.0628823i
$667$	3.71261	+	0.738483i	0.143753	+	0.0285942i
$668$	2.74384	+	4.95972i	0.106162	+	0.191898i
$669$	−12.7359	−	8.50984i	−0.492398	−	0.329010i
$670$	−26.8352	+	12.9300i	−1.03673	+	0.499531i
$671$		−	18.0423i		−	0.696515i
$672$	−6.88923	−	13.3014i	−0.265758	−	0.513114i
$673$			40.4801i			1.56039i	0.625534	+	0.780197i	$0.284881\pi$
$673$			40.4801i			1.56039i	−0.625534	+	0.780197i	$0.715119\pi$
$674$	−16.0362	−	33.2817i	−0.617690	−	1.28196i
$675$	31.8450	+	21.2781i	1.22571	+	0.818995i
$676$	−24.3106	−	6.99281i	−0.935024	−	0.268954i
$677$	28.0273	+	5.57498i	1.07718	+	0.214264i	0.701632	−	0.712540i	$-0.252455\pi$
$677$	28.0273	+	5.57498i	1.07718	+	0.214264i	0.375546	+	0.926804i	$0.377455\pi$
$678$	−1.04154	+	7.38870i	−0.0400002	+	0.283761i
$679$	13.7559	+	5.69788i	0.527903	+	0.218665i
$680$	55.7023	+	24.8834i	2.13608	+	0.954236i
$681$	7.90382	−	3.27387i	0.302875	−	0.125455i
$682$	2.30209	−	0.594341i	0.0881515	−	0.0227585i
$683$	10.1966	+	15.2603i	0.390163	+	0.583920i	0.973606	−	0.228234i	$-0.0732950\pi$
$683$	10.1966	+	15.2603i	0.390163	+	0.583920i	−0.583443	+	0.812154i	$0.698295\pi$
$684$	1.18756	−	14.1495i	0.0454076	−	0.541019i
$685$	−34.3775	+	6.83811i	−1.31350	+	0.261271i
$686$	1.51282	+	26.8385i	0.0577598	+	1.02470i
$687$	2.70048	−	2.70048i	0.103030	−	0.103030i
$688$	7.70421	−	8.16261i	0.293720	−	0.311196i
$689$	0.616329	+	0.616329i	0.0234803	+	0.0234803i
$690$	−28.9816	+	32.4440i	−1.10331	+	1.23512i
$691$	−0.695696	−	3.49750i	−0.0264655	−	0.133051i	0.965294	−	0.261167i	$-0.0841072\pi$
$691$	−0.695696	−	3.49750i	−0.0264655	−	0.133051i	−0.991759	+	0.128115i	$0.959107\pi$
$692$	−18.5673	−	9.58233i	−0.705824	−	0.364265i
$693$	6.42501	−	4.29305i	0.244066	−	0.163080i
$694$	−6.68117	+	11.3316i	−0.253614	+	0.430142i
$695$	−2.86056	−	6.90601i	−0.108507	−	0.261960i
$696$	0.756361	−	1.06740i	0.0286698	−	0.0404598i
$697$	13.0255	−	31.4463i	0.493375	−	1.19111i
$698$	−12.8640	+	9.68533i	−0.486908	+	0.366595i
$699$	−3.86976	+	19.4546i	−0.146368	+	0.735841i
$700$	38.4338	−	4.34665i	1.45266	−	0.164288i
$701$	8.71090	−	13.0368i	0.329006	−	0.492393i	−0.629681	−	0.776853i	$-0.716815\pi$
$701$	8.71090	−	13.0368i	0.329006	−	0.492393i	0.958688	+	0.284461i	$0.0918146\pi$
$702$	−4.02937	−	1.40900i	−0.152079	−	0.0531792i
$703$	−15.5397			−0.586092
$704$	−1.75067	−	12.2896i	−0.0659807	−	0.463183i
$705$	−33.1804			−1.24965
$706$	16.3648	+	5.72245i	0.615896	+	0.215367i
$707$	1.34073	−	2.00654i	0.0504232	−	0.0754637i
$708$	1.73840	+	15.3712i	0.0653329	+	0.577684i
$709$	−0.737183	+	3.70607i	−0.0276855	+	0.139184i	−0.992156	−	0.125006i	$-0.960105\pi$
$709$	−0.737183	+	3.70607i	−0.0276855	+	0.139184i	0.964470	+	0.264191i	$0.0851048\pi$
$710$	39.1984	−	29.5126i	1.47109	−	1.10759i
$711$	0.980440	−	2.36699i	0.0367694	−	0.0887692i
$712$	−18.5702	+	3.16714i	−0.695948	+	0.118693i
$713$	3.49688	+	8.44221i	0.130959	+	0.316163i
$714$	−11.5916	+	19.6600i	−0.433805	+	0.735756i
$715$	2.70849	−	1.80976i	0.101292	−	0.0676810i
$716$	17.8427	−	34.5731i	0.666812	−	1.29206i
$717$	−0.482359	−	2.42498i	−0.0180140	−	0.0905627i
$718$	7.08858	−	7.93544i	0.264543	−	0.296148i
$719$	−36.7070	−	36.7070i	−1.36894	−	1.36894i	−0.861955	−	0.506985i	$-0.830760\pi$
$719$	−36.7070	−	36.7070i	−1.36894	−	1.36894i	−0.506985	−	0.861955i	$-0.669240\pi$
$720$	−11.2270	−	25.0340i	−0.418406	−	0.932960i
$721$	25.1542	−	25.1542i	0.936790	−	0.936790i
$722$	−0.444081	−	7.87830i	−0.0165270	−	0.293200i
$723$	18.2277	−	3.62572i	0.677896	−	0.134842i
$724$	−7.98058	−	0.669808i	−0.296596	−	0.0248932i
$725$	1.87668	+	2.80865i	0.0696982	+	0.104311i
$726$	12.1247	−	3.13028i	0.449989	−	0.116176i
$727$	−3.90063	+	1.61569i	−0.144666	+	0.0599228i	−0.453842	−	0.891082i	$-0.649947\pi$
$727$	−3.90063	+	1.61569i	−0.144666	+	0.0599228i	0.309176	+	0.951005i	$0.399947\pi$
$728$	−4.02648	+	1.53987i	−0.149231	+	0.0570713i
$729$	13.5147	+	5.59798i	0.500545	+	0.207333i
$730$	−2.18577	+	15.5058i	−0.0808988	+	0.573896i
$731$	−16.7725	−	3.33626i	−0.620353	−	0.123396i
$732$	6.62471	−	23.0309i	0.244856	−	0.851247i
$733$	10.5958	+	7.07991i	0.391366	+	0.261502i	0.735648	−	0.677364i	$-0.236878\pi$
$733$	10.5958	+	7.07991i	0.391366	+	0.261502i	−0.344282	+	0.938866i	$0.611878\pi$
$734$	−0.955384	−	1.98282i	−0.0352639	−	0.0731872i
$735$		−	1.44885i		−	0.0534415i
$736$	45.8315	−	13.2555i	1.68937	−	0.488604i
$737$		−	9.23473i		−	0.340166i
$738$	−13.7899	+	6.64438i	−0.507612	+	0.244583i
$739$	−5.97439	−	3.99196i	−0.219772	−	0.146847i	0.440811	−	0.897600i	$-0.354691\pi$
$739$	−5.97439	−	3.99196i	−0.219772	−	0.146847i	−0.660583	+	0.750753i	$0.729691\pi$
$740$	−26.2737	+	14.5352i	−0.965841	+	0.534326i
$741$	2.19623	+	0.436857i	0.0806805	+	0.0160483i
$742$	−5.28780	−	0.745390i	−0.194121	−	0.0273641i
$743$	−16.8050	−	6.96086i	−0.616515	−	0.255369i	0.0524960	−	0.998621i	$-0.483282\pi$
$743$	−16.8050	−	6.96086i	−0.616515	−	0.255369i	−0.669011	+	0.743252i	$0.733282\pi$
$744$	3.15684	+	0.0865996i	0.115735	+	0.00317490i
$745$	58.9283	−	24.4089i	2.15896	−	0.894272i
$746$	12.7348	+	49.3263i	0.466255	+	1.80597i
$747$	−18.2049	−	27.2455i	−0.666082	−	0.996862i
$748$	−14.4455	+	12.2084i	−0.528178	+	0.446383i
$749$	−37.4148	+	7.44226i	−1.36711	+	0.271934i
$750$	−13.0101	+	0.733350i	−0.475063	+	0.0267782i
$751$	25.4171	−	25.4171i	0.927482	−	0.927482i	−0.0700603	−	0.997543i	$-0.522319\pi$
$751$	25.4171	−	25.4171i	0.927482	−	0.927482i	0.997543	+	0.0700603i	$0.0223192\pi$
$752$	30.8274	+	19.3343i	1.12416	+	0.705051i
$753$	0.121576	+	0.121576i	0.00443047	+	0.00443047i
$754$	−0.280773	−	0.250809i	−0.0102252	−	0.00913394i
$755$	−3.73100	−	18.7570i	−0.135785	−	0.682638i
$756$	24.9138	−	7.95216i	0.906105	−	0.289217i
$757$	−28.3377	+	18.9346i	−1.02995	+	0.688192i	−0.951160	−	0.308700i	$-0.900106\pi$
$757$	−28.3377	+	18.9346i	−1.02995	+	0.688192i	−0.0787918	+	0.996891i	$0.525106\pi$
$758$	23.1469	+	13.6475i	0.840732	+	0.495699i
$759$	−5.16117	−	12.4602i	−0.187338	−	0.452275i
$760$	19.5302	+	31.0391i	0.708436	+	1.12591i
$761$	3.25313	−	7.85375i	0.117926	−	0.284698i	−0.853884	−	0.520463i	$-0.825759\pi$
$761$	3.25313	−	7.85375i	0.117926	−	0.284698i	0.971810	+	0.235765i	$0.0757594\pi$
$762$	4.62648	+	6.14485i	0.167600	+	0.222604i
$763$	−3.39325	+	17.0590i	−0.122844	+	0.617578i
$764$	−25.4314	−	20.2636i	−0.920076	−	0.733110i
$765$	−23.2237	+	34.7567i	−0.839653	+	1.25663i
$766$	10.7312	−	30.6884i	0.387733	−	1.10882i
$767$	4.45177			0.160744
$768$	2.27776	−	16.3305i	0.0821914	−	0.589276i
$769$	0.673777			0.0242970			0.0121485	−	0.999926i	$-0.496133\pi$
$769$	0.673777			0.0242970			0.0121485	+	0.999926i	$0.496133\pi$
$770$	−6.58754	+	18.8387i	−0.237398	+	0.678899i
$771$	−0.747508	+	1.11872i	−0.0269208	+	0.0402899i
$772$	39.0020	+	31.0765i	1.40371	+	1.11847i
$773$	9.93498	−	49.9465i	0.357336	−	1.79645i	−0.215198	−	0.976570i	$-0.569040\pi$
$773$	9.93498	−	49.9465i	0.357336	−	1.79645i	0.572534	−	0.819881i	$-0.305960\pi$
$774$	4.62580	+	6.14396i	0.166271	+	0.220840i
$775$	−3.12052	+	7.53361i	−0.112092	+	0.270615i
$776$	8.72821	+	13.8716i	0.313324	+	0.497963i
$777$	−4.29860	−	10.3777i	−0.154211	−	0.372299i
$778$	−31.2923	−	18.4501i	−1.12188	−	0.661467i
$779$	17.0120	−	11.3670i	0.609517	−	0.407266i
$780$	4.12188	−	1.31565i	0.147587	−	0.0471079i
$781$	2.96760	+	14.9191i	0.106189	+	0.533848i
$782$	−54.2110	−	48.4256i	−1.93858	−	1.73170i
$783$	1.61499	+	1.61499i	0.0577151	+	0.0577151i
$784$	−0.844248	+	1.34610i	−0.0301517	+	0.0480750i
$785$	−21.2045	+	21.2045i	−0.756821	+	0.756821i
$786$	8.37529	−	0.472095i	0.298737	−	0.0168391i
$787$	−50.7402	+	10.0929i	−1.80869	+	0.359772i	−0.979854	−	0.199715i	$-0.935999\pi$
$787$	−50.7402	+	10.0929i	−1.80869	+	0.359772i	−0.828840	+	0.559486i	$0.810999\pi$
$788$	6.39302	−	5.40299i	0.227742	−	0.192473i
$789$	6.66815	+	9.97959i	0.237393	+	0.355283i
$790$	1.65408	+	6.40683i	0.0588495	+	0.227945i
$791$	−12.1546	+	5.03460i	−0.432168	+	0.179010i
$792$	8.50249	+	0.233244i	0.302123	+	0.00828795i
$793$	−6.37168	−	2.63924i	−0.226265	−	0.0937220i
$794$	−2.29139	−	0.323004i	−0.0813185	−	0.0114630i
$795$	5.25675	+	1.04563i	0.186438	+	0.0370848i
$796$	3.40316	−	1.88271i	0.120622	−	0.0667309i
$797$	39.8300	+	26.6136i	1.41085	+	0.942701i	0.999513	+	0.0312188i	$0.00993885\pi$
$797$	39.8300	+	26.6136i	1.41085	+	0.942701i	0.411339	+	0.911482i	$0.365061\pi$
$798$	−12.3592	+	5.95503i	−0.437510	+	0.210806i
$799$		−	55.4415i		−	1.96138i
$800$	37.2841	+	20.5556i	1.31819	+	0.726749i
$801$		−	12.9077i		−	0.456073i
$802$	−18.8628	−	39.1482i	−0.666069	−	1.38237i
$803$	−4.03644	−	2.69707i	−0.142443	−	0.0951774i
$804$	3.39078	−	11.7881i	0.119584	−	0.415734i
$805$	−75.2283	−	14.9638i	−2.65145	−	0.527406i
$806$	0.126858	−	0.899929i	0.00446838	−	0.0316986i
$807$	12.1228	+	5.02144i	0.426744	+	0.176763i
$808$	2.48109	−	0.948857i	0.0872844	−	0.0333807i
$809$	14.9757	−	6.20314i	0.526518	−	0.218091i	−0.103559	−	0.994623i	$-0.533023\pi$
$809$	14.9757	−	6.20314i	0.526518	−	0.218091i	0.630077	+	0.776532i	$0.283023\pi$
$810$	2.76151	−	0.712951i	0.0970294	−	0.0250505i
$811$	0.427422	+	0.639682i	0.0150088	+	0.0224623i	0.838898	−	0.544288i	$-0.183200\pi$
$811$	0.427422	+	0.639682i	0.0150088	+	0.0224623i	−0.823889	+	0.566751i	$0.808200\pi$
$812$	2.29848	+	0.192911i	0.0806607	+	0.00676983i
$813$	−8.44401	+	1.67962i	−0.296144	+	0.0589068i
$814$	−0.523876	−	9.29392i	−0.0183618	−	0.325752i
$815$	−2.76878	+	2.76878i	−0.0969863	+	0.0969863i
$816$	−22.9222	+	10.2799i	−0.802438	+	0.359870i
$817$	−7.26880	−	7.26880i	−0.254303	−	0.254303i
$818$	−18.2537	+	20.4345i	−0.638226	+	0.714475i
$819$	−0.576248	−	2.89700i	−0.0201358	−	0.101229i
$820$	18.1306	−	35.1311i	0.633148	−	1.22683i
$821$	11.8401	−	7.91128i	0.413221	−	0.276105i	−0.331534	−	0.943443i	$-0.607566\pi$
$821$	11.8401	−	7.91128i	0.413221	−	0.276105i	0.744755	+	0.667338i	$0.232566\pi$
$822$	7.33064	−	12.4332i	0.255686	−	0.433656i
$823$	−20.8253	−	50.2767i	−0.725924	−	1.75254i	−0.655722	−	0.755003i	$-0.727636\pi$
$823$	−20.8253	−	50.2767i	−0.725924	−	1.75254i	−0.0702021	−	0.997533i	$-0.522364\pi$
$824$	38.5994	−	6.58311i	1.34468	−	0.229334i
$825$	4.60569	−	11.1191i	0.160350	−	0.387118i
$826$	−21.7889	+	16.4050i	−0.758134	+	0.570802i
$827$	−5.39604	+	27.1277i	−0.187639	+	0.943323i	0.766108	+	0.642712i	$0.222191\pi$
$827$	−5.39604	+	27.1277i	−0.187639	+	0.943323i	−0.953747	+	0.300611i	$0.902809\pi$
$828$	3.67365	+	32.4830i	0.127668	+	1.12886i
$829$	4.05663	−	6.07118i	0.140893	−	0.210861i	−0.754312	−	0.656516i	$-0.772029\pi$
$829$	4.05663	−	6.07118i	0.140893	−	0.210861i	0.895205	+	0.445656i	$0.147029\pi$
$830$	79.8863	+	27.9348i	2.77289	+	0.969630i
$831$	0.114879			0.00398511
$832$	−4.59621	−	1.17948i	−0.159345	−	0.0408912i
$833$	2.42089			0.0838790
$834$	2.90555	+	1.01602i	0.100611	+	0.0351818i
$835$	5.57261	−	8.34000i	0.192848	−	0.288618i
$836$	−11.2970	+	1.27763i	−0.390716	+	0.0441878i
$837$	−1.07562	+	5.40748i	−0.0371787	+	0.186910i
$838$	−37.7919	+	28.4537i	−1.30550	+	0.982916i
$839$	9.19848	−	22.2071i	0.317567	−	0.766674i	−0.681815	−	0.731524i	$-0.738809\pi$
$839$	9.19848	−	22.2071i	0.317567	−	0.766674i	0.999382	−	0.0351498i	$-0.0111908\pi$
$840$	−15.3261	+	21.6287i	−0.528801	+	0.746262i
$841$	−11.0207	−	26.6064i	−0.380025	−	0.917462i
$842$	−14.4811	+	24.5606i	−0.499050	+	0.846416i
$843$	7.80591	−	5.21574i	0.268850	−	0.179640i
$844$	−26.5736	−	13.7142i	−0.914699	−	0.472063i
$845$	8.73323	+	43.9049i	0.300432	+	1.51038i
$846$	−16.6102	+	18.5946i	−0.571069	+	0.639295i
$847$	15.6117	+	15.6117i	0.536426	+	0.536426i
$848$	−4.27467	−	4.03461i	−0.146793	−	0.138549i
$849$	−8.64313	+	8.64313i	−0.296631	+	0.296631i
$850$	−3.65060	−	64.7641i	−0.125214	−	2.22139i
$851$	35.0888	−	6.97960i	1.20283	−	0.239258i
$852$	−1.68983	+	20.1338i	−0.0578925	+	0.689774i
$853$	2.19782	+	3.28928i	0.0752521	+	0.112623i	0.867187	−	0.497983i	$-0.165926\pi$
$853$	2.19782	+	3.28928i	0.0752521	+	0.112623i	−0.791935	+	0.610606i	$0.790926\pi$
$854$	40.9116	−	10.5623i	1.39996	−	0.361435i
$855$	−23.2146	+	9.61580i	−0.793923	+	0.328853i
$856$	−38.3389	−	17.1268i	−1.31040	−	0.585384i
$857$	25.6461	+	10.6230i	0.876055	+	0.362874i	0.774966	−	0.632003i	$-0.217767\pi$
$857$	25.6461	+	10.6230i	0.876055	+	0.362874i	0.101089	+	0.994877i	$0.467767\pi$
$858$	−0.187234	+	1.32824i	−0.00639206	+	0.0453453i
$859$	48.0526	+	9.55825i	1.63953	+	0.326123i	0.926870	−	0.375383i	$-0.122489\pi$
$859$	48.0526	+	9.55825i	1.63953	+	0.326123i	0.712663	+	0.701506i	$0.247489\pi$
$860$	−19.0886	−	5.49074i	−0.650917	−	0.187233i
$861$	12.2970	+	8.21658i	0.419080	+	0.280020i
$862$	11.7398	+	24.3649i	0.399858	+	0.829872i
$863$			49.1366i			1.67263i	0.548250	+	0.836314i	$0.315294\pi$
$863$			49.1366i			1.67263i	−0.548250	+	0.836314i	$0.684706\pi$
$864$	27.4361	+	8.71324i	0.933397	+	0.296431i
$865$			36.9749i			1.25718i
$866$	32.2731	−	15.5502i	1.09668	−	0.528417i
$867$	17.2582	+	11.5315i	0.586118	+	0.391631i
$868$	2.69538	+	4.87213i	0.0914872	+	0.165371i
$869$	−2.01194	−	0.400199i	−0.0682503	−	0.0135758i
$870$	−2.29239	−	0.323145i	−0.0777192	−	0.0109556i
$871$	−3.26127	−	1.35086i	−0.110504	−	0.0457722i
$872$	−13.9039	+	13.1615i	−0.470846	+	0.445703i
$873$	−10.3748	+	4.29738i	−0.351133	+	0.145444i
$874$	−10.9228	−	42.3076i	−0.369468	−	1.43108i
$875$	−12.7642	−	19.1030i	−0.431510	−	0.645800i
$876$	−4.16221	−	4.92489i	−0.140628	−	0.166396i
$877$	−19.6791	+	3.91441i	−0.664515	+	0.132180i	−0.515812	−	0.856702i	$-0.672510\pi$
$877$	−19.6791	+	3.91441i	−0.664515	+	0.132180i	−0.148703	+	0.988882i	$0.547510\pi$
$878$	−10.3969	+	0.586049i	−0.350879	+	0.0197782i
$879$	−0.0745207	+	0.0745207i	−0.00251352	+	0.00251352i
$880$	−17.9053	+	12.7269i	−0.603588	+	0.429025i
$881$	−11.5209	−	11.5209i	−0.388150	−	0.388150i	0.485877	−	0.874027i	$-0.338500\pi$
$881$	−11.5209	−	11.5209i	−0.388150	−	0.388150i	−0.874027	+	0.485877i	$0.838500\pi$
$882$	−0.811946	−	0.725295i	−0.0273396	−	0.0244220i
$883$	−2.44651	−	12.2994i	−0.0823317	−	0.413909i	−0.999868	−	0.0162569i	$-0.994825\pi$
$883$	−2.44651	−	12.2994i	−0.0823317	−	0.413909i	0.917536	−	0.397652i	$-0.130175\pi$
$884$	2.19834	+	6.88730i	0.0739381	+	0.231645i
$885$	22.7612	−	15.2085i	0.765108	−	0.511229i
$886$	35.2489	+	20.7829i	1.18421	+	0.698215i
$887$	17.4593	+	42.1504i	0.586224	+	1.41527i	0.887087	+	0.461603i	$0.152726\pi$
$887$	17.4593	+	42.1504i	0.586224	+	1.41527i	−0.300862	+	0.953668i	$0.597274\pi$
$888$	2.74379	−	12.0560i	0.0920755	−	0.404574i
$889$	−5.18980	+	12.5293i	−0.174060	+	0.420219i
$890$	20.0515	+	26.6323i	0.672129	+	0.892716i
$891$	−0.172496	+	0.867196i	−0.00577883	+	0.0290522i
$892$	18.5247	−	23.2491i	0.620254	−	0.778438i
$893$	18.5152	−	27.7100i	0.619587	−	0.927278i
$894$	−8.66958	+	24.7928i	−0.289954	+	0.829195i
$895$	−68.8486			−2.30136
$896$	26.8424	−	11.1643i	0.896740	−	0.372974i
$897$	−5.15531			−0.172131
$898$	0.0445974	−	0.127537i	0.00148823	−	0.00425597i
$899$	−0.270158	+	0.404320i	−0.00901027	+	0.0134848i
$900$	−18.1788	+	22.8150i	−0.605961	+	0.760500i
$901$	−1.74716	+	8.78357i	−0.0582064	+	0.292623i
$902$	7.37184	+	9.79122i	0.245456	+	0.326012i
$903$	2.84356	−	6.86495i	0.0946276	−	0.228451i
$904$	−14.1202	−	3.21357i	−0.469632	−	0.106882i
$905$	5.42350	+	13.0935i	0.180283	+	0.435242i
$906$	6.78377	+	3.99974i	0.225376	+	0.132882i
$907$	−15.0921	+	10.0842i	−0.501125	+	0.334841i	−0.780306	−	0.625398i	$-0.784937\pi$
$907$	−15.0921	+	10.0842i	−0.501125	+	0.334841i	0.279182	+	0.960238i	$0.409937\pi$
$908$	5.04855	+	15.8169i	0.167542	+	0.524902i
$909$	0.355080	+	1.78511i	0.0117773	+	0.0592084i
$910$	5.68930	+	5.08214i	0.188598	+	0.168471i
$911$	36.0258	+	36.0258i	1.19359	+	1.19359i	0.976052	+	0.217537i	$0.0698022\pi$
$911$	36.0258	+	36.0258i	1.19359	+	1.19359i	0.217537	+	0.976052i	$0.430198\pi$
$912$	−14.8897	−	2.51711i	−0.493048	−	0.0833499i
$913$	−18.5521	+	18.5521i	−0.613985	+	0.613985i
$914$	−42.1946	+	2.37841i	−1.39567	+	0.0786707i
$915$	−41.5938	+	8.27351i	−1.37505	+	0.273514i
$916$	4.78423	+	5.66089i	0.158075	+	0.187041i
$917$	8.21699	+	12.2976i	0.271349	+	0.406102i
$918$	−10.9637	−	42.4663i	−0.361857	−	1.40160i
$919$	23.4993	−	9.73374i	0.775171	−	0.321086i	0.0402060	−	0.999191i	$-0.487199\pi$
$919$	23.4993	−	9.73374i	0.775171	−	0.321086i	0.734965	+	0.678105i	$0.237199\pi$
$920$	−58.0405	−	61.3147i	−1.91354	−	2.02149i
$921$	−21.8015	−	9.03046i	−0.718383	−	0.297564i
$922$	38.0285	+	5.36066i	1.25240	+	0.176544i
$923$	5.70282	+	1.13436i	0.187711	+	0.0373380i
$924$	−3.97821	−	7.19096i	−0.130873	−	0.236565i
$925$	26.5453	+	17.7370i	0.872805	+	0.583190i
$926$	−38.4609	+	18.5317i	−1.26390	+	0.608988i
$927$			26.8296i			0.881201i
$928$	1.94152	+	1.63601i	0.0637336	+	0.0537047i
$929$		−	14.5115i		−	0.476107i	−0.971252	−	0.238053i	$-0.923491\pi$
$929$		−	14.5115i		−	0.476107i	0.971252	−	0.238053i	$-0.0765094\pi$
$930$	−2.42581	−	5.03458i	−0.0795456	−	0.165090i
$931$	1.20998	+	0.808480i	0.0396553	+	0.0264968i
$932$	−36.9959	−	10.6417i	−1.21184	−	0.348579i
$933$	17.1335	+	3.40807i	0.560926	+	0.111575i
$934$	−6.44984	+	45.7551i	−0.211045	+	1.49715i
$935$	30.9219	+	12.8083i	1.01125	+	0.418875i
$936$	1.32612	−	2.96855i	0.0433455	−	0.0970303i
$937$	15.1545	−	6.27722i	0.495077	−	0.205068i	−0.121153	−	0.992634i	$-0.538659\pi$
$937$	15.1545	−	6.27722i	0.495077	−	0.205068i	0.616230	+	0.787566i	$0.288659\pi$
$938$	20.9401	−	5.40620i	0.683719	−	0.176519i
$939$	−10.3917	−	15.5523i	−0.339120	−	0.507530i
$940$	5.38568	−	64.1688i	0.175661	−	2.09296i
$941$	−32.7794	+	6.52023i	−1.06858	+	0.212553i	−0.697891	−	0.716204i	$-0.745878\pi$
$941$	−32.7794	+	6.52023i	−1.06858	+	0.212553i	−0.370688	+	0.928758i	$0.620878\pi$
$942$	−0.694946	−	12.3288i	−0.0226426	−	0.401695i
$943$	−33.3077	+	33.3077i	−1.08465	+	1.08465i
$944$	−30.0091	+	0.866978i	−0.976712	+	0.0282177i
$945$	−32.7245	−	32.7245i	−1.06453	−	1.06453i
$946$	4.10224	−	4.59234i	0.133375	−	0.149310i
$947$	1.24368	+	6.25242i	0.0404143	+	0.203176i	0.995717	−	0.0924528i	$-0.0294707\pi$
$947$	1.24368	+	6.25242i	0.0404143	+	0.203176i	−0.955303	+	0.295629i	$0.904471\pi$
$948$	−2.42129	−	1.24959i	−0.0786397	−	0.0405848i
$949$	−1.54293	+	1.03095i	−0.0500856	+	0.0334661i
$950$	19.8040	−	33.5886i	0.642526	−	1.08976i
$951$	−7.80372	−	18.8399i	−0.253053	−	0.610924i
$952$	−36.1397	−	25.6086i	−1.17129	−	0.829978i
$953$	0.417863	−	1.00881i	0.0135359	−	0.0326786i	−0.916967	−	0.398963i	$-0.869370\pi$
$953$	0.417863	−	1.00881i	0.0135359	−	0.0326786i	0.930503	+	0.366284i	$0.119370\pi$
$954$	3.21752	−	2.42248i	0.104171	−	0.0784308i
$955$	−11.2261	+	56.4375i	−0.363269	+	1.82628i
$956$	4.76806	−	0.539242i	0.154210	−	0.0174403i
$957$	0.398736	−	0.596750i	0.0128893	−	0.0192902i
$958$	−0.828472	−	0.289701i	−0.0267667	−	0.00935982i
$959$	25.4479			0.821756
$960$	−27.5291	+	9.67146i	−0.888499	+	0.312145i
$961$	29.8261			0.962134
$962$	−3.35881	−	1.17451i	−0.108292	−	0.0378678i
$963$	15.9845	−	23.9224i	0.515092	−	0.770890i
$964$	4.05328	+	35.8398i	0.130547	+	1.15432i
$965$	17.2166	−	86.5536i	0.554221	−	2.78626i
$966$	25.2324	−	18.9976i	0.811840	−	0.611237i
$967$	12.0473	−	29.0848i	0.387416	−	0.935305i	−0.603069	−	0.797689i	$-0.706056\pi$
$967$	12.0473	−	29.0848i	0.387416	−	0.935305i	0.990486	−	0.137617i	$-0.0439442\pi$
$968$	4.08576	+	23.9565i	0.131321	+	0.769990i
$969$	8.80466	+	21.2563i	0.282847	+	0.682852i
$970$	14.7303	−	24.9834i	0.472962	−	0.802168i
$971$	25.2097	−	16.8446i	0.809017	−	0.540568i	−0.0808828	−	0.996724i	$-0.525774\pi$
$971$	25.2097	−	16.8446i	0.809017	−	0.540568i	0.889900	+	0.456156i	$0.150774\pi$
$972$	−14.5413	+	28.1761i	−0.466411	+	0.903749i
$973$	1.05876	+	5.32277i	0.0339424	+	0.170640i
$974$	11.9738	−	13.4043i	0.383667	−	0.429503i
$975$	−3.25302	−	3.25302i	−0.104180	−	0.104180i
$976$	43.4651	+	16.5500i	1.39128	+	0.529754i
$977$	27.6449	−	27.6449i	0.884440	−	0.884440i	−0.109543	−	0.993982i	$-0.534939\pi$
$977$	27.6449	−	27.6449i	0.884440	−	0.884440i	0.993982	+	0.109543i	$0.0349386\pi$
$978$	−0.0907427	−	1.60984i	−0.00290163	−	0.0514770i
$979$	−10.1364	+	2.01625i	−0.323960	+	0.0644397i
$980$	2.80198	+	0.235169i	0.0895059	+	0.00751221i
$981$	−7.28802	−	10.9073i	−0.232688	−	0.348243i
$982$	29.4126	−	7.59359i	0.938594	−	0.242321i
$983$	25.5539	−	10.5848i	0.815043	−	0.337602i	0.0640791	−	0.997945i	$-0.479589\pi$
$983$	25.5539	−	10.5848i	0.815043	−	0.337602i	0.750964	+	0.660343i	$0.229589\pi$
$984$	5.81502	+	15.2052i	0.185376	+	0.484725i
$985$	−13.6849	−	5.66846i	−0.436036	−	0.180612i
$986$	0.539946	−	3.83038i	0.0171954	−	0.121984i
$987$	23.6269	+	4.69969i	0.752054	+	0.149593i
$988$	−1.20134	+	4.17646i	−0.0382196	+	0.132871i
$989$	19.6778	+	13.1483i	0.625717	+	0.418090i
$990$	−6.53358	−	13.5599i	−0.207651	−	0.430962i
$991$			31.6905i			1.00668i	0.864088	+	0.503340i	$0.167896\pi$
$991$			31.6905i			1.00668i	−0.864088	+	0.503340i	$0.832104\pi$
$992$	−0.679880	+	6.09107i	−0.0215862	+	0.193392i
$993$		−	7.40504i		−	0.234992i
$994$	−32.0924	+	15.4631i	−1.01791	+	0.490459i
$995$	−5.72257	−	3.82370i	−0.181418	−	0.121219i
$996$	−30.4936	+	16.8698i	−0.966226	+	0.534540i
$997$	−21.6259	−	4.30166i	−0.684900	−	0.136235i	−0.159638	−	0.987176i	$-0.551033\pi$
$997$	−21.6259	−	4.30166i	−0.684900	−	0.136235i	−0.525262	+	0.850941i	$0.676033\pi$
$998$	−41.7578	−	5.88635i	−1.32182	−	0.186329i
$999$	19.9430	+	8.26066i	0.630969	+	0.261356i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.37.4	✓	56
3.2	odd	2		576.2.bd.a.37.4		56
4.3	odd	2		256.2.i.a.241.5		56
8.3	odd	2		512.2.i.a.225.3		56
8.5	even	2		512.2.i.b.225.5		56
64.13	even	16		512.2.i.b.289.5		56
64.19	odd	16		256.2.i.a.17.5		56
64.45	even	16	inner	64.2.i.a.45.4	yes	56
64.51	odd	16		512.2.i.a.289.3		56
192.173	odd	16		576.2.bd.a.109.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.37.4	✓	56	1.1	even	1	trivial
64.2.i.a.45.4	yes	56	64.45	even	16	inner
256.2.i.a.17.5		56	64.19	odd	16
256.2.i.a.241.5		56	4.3	odd	2
512.2.i.a.225.3		56	8.3	odd	2
512.2.i.a.289.3		56	64.51	odd	16
512.2.i.b.225.5		56	8.5	even	2
512.2.i.b.289.5		56	64.13	even	16
576.2.bd.a.37.4		56	3.2	odd	2
576.2.bd.a.109.4		56	192.173	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)

\(f(q)\)	\(=\)	\(q+(-0.466807 + 1.33495i) q^{2} +(-0.572535 + 0.856859i) q^{3} +(-1.56418 - 1.24633i) q^{4} +(-0.690473 + 3.47124i) q^{5} +(-0.876601 - 1.16429i) q^{6} +(0.983337 - 2.37399i) q^{7} +(2.39396 - 1.50631i) q^{8} +(0.741639 + 1.79047i) q^{9} +O(q^{10})\)	\(q+(-0.466807 + 1.33495i) q^{2} +(-0.572535 + 0.856859i) q^{3} +(-1.56418 - 1.24633i) q^{4} +(-0.690473 + 3.47124i) q^{5} +(-0.876601 - 1.16429i) q^{6} +(0.983337 - 2.37399i) q^{7} +(2.39396 - 1.50631i) q^{8} +(0.741639 + 1.79047i) q^{9} +(-4.31162 - 2.54215i) q^{10} +(1.29020 - 0.862086i) q^{11} +(1.96348 - 0.626717i) q^{12} +(-0.115716 - 0.581745i) q^{13} +(2.71012 + 2.42090i) q^{14} +(-2.57905 - 2.57905i) q^{15} +(0.893330 + 3.89897i) q^{16} +(4.30936 - 4.30936i) q^{17} +(-2.73640 + 0.154244i) q^{18} +(3.59299 - 0.714690i) q^{19} +(5.40633 - 4.56910i) q^{20} +(1.47118 + 2.20177i) q^{21} +(0.548565 + 2.12478i) q^{22} +(-7.79200 + 3.22755i) q^{23} +(-0.0799298 + 2.91370i) q^{24} +(-6.95338 - 2.88018i) q^{25} +(0.830617 + 0.117087i) q^{26} +(-4.99100 - 0.992772i) q^{27} +(-4.49689 + 2.48779i) q^{28} +(-0.373179 - 0.249351i) q^{29} +(4.64682 - 2.23898i) q^{30} -1.08345i q^{31} +(-5.62194 - 0.627516i) q^{32} +1.59910i q^{33} +(3.74114 + 7.76442i) q^{34} +(7.56172 + 5.05258i) q^{35} +(1.07146 - 3.72495i) q^{36} +(-4.16040 - 0.827556i) q^{37} +(-0.723158 + 5.13008i) q^{38} +(0.564725 + 0.233917i) q^{39} +(3.57580 + 9.35007i) q^{40} +(5.15990 - 2.13730i) q^{41} +(-3.62601 + 0.936145i) q^{42} +(-1.55896 - 2.33315i) q^{43} +(-3.09255 - 0.259557i) q^{44} +(-6.72725 + 1.33813i) q^{45} +(-0.671258 - 11.9086i) q^{46} +(6.43269 - 6.43269i) q^{47} +(-3.85233 - 1.46684i) q^{48} +(0.280888 + 0.280888i) q^{49} +(7.09079 - 7.93792i) q^{50} +(1.22526 + 6.15978i) q^{51} +(-0.544044 + 1.05417i) q^{52} +(-1.22184 + 0.816410i) q^{53} +(3.65514 - 6.19931i) q^{54} +(2.10166 + 5.07385i) q^{55} +(-1.22189 - 7.16443i) q^{56} +(-1.44472 + 3.48787i) q^{57} +(0.507073 - 0.381777i) q^{58} +(-1.46423 + 7.36119i) q^{59} +(0.819759 + 7.24844i) q^{60} +(6.45980 - 9.66777i) q^{61} +(1.44635 + 0.505761i) q^{62} +4.97984 q^{63} +(3.46207 - 7.21208i) q^{64} +2.09928 q^{65} +(-2.13471 - 0.746470i) q^{66} +(3.30637 - 4.94834i) q^{67} +(-12.1115 + 1.36974i) q^{68} +(1.69564 - 8.52453i) q^{69} +(-10.2748 + 7.73593i) q^{70} +(-3.75143 + 9.05676i) q^{71} +(4.47246 + 3.16918i) q^{72} +(-1.19724 - 2.89039i) q^{73} +(3.04685 - 5.16762i) q^{74} +(6.44896 - 4.30906i) q^{75} +(-6.51083 - 3.36014i) q^{76} +(-0.777876 - 3.91064i) q^{77} +(-0.575885 + 0.644685i) q^{78} +(-0.934789 - 0.934789i) q^{79} +(-14.1511 + 0.408832i) q^{80} +(-0.402918 + 0.402918i) q^{81} +(0.444510 + 7.88591i) q^{82} +(-16.5833 + 3.29862i) q^{83} +(0.442943 - 5.27754i) q^{84} +(11.9833 + 17.9343i) q^{85} +(3.84237 - 0.992002i) q^{86} +(0.427317 - 0.177000i) q^{87} +(1.79012 - 4.00724i) q^{88} +(-6.15337 - 2.54881i) q^{89} +(1.35399 - 9.60520i) q^{90} +(-1.49484 - 0.297343i) q^{91} +(16.2107 + 4.66291i) q^{92} +(0.928361 + 0.620311i) q^{93} +(5.58449 + 11.5901i) q^{94} +12.9656i q^{95} +(3.75645 - 4.45794i) q^{96} +5.79443i q^{97} +(-0.506092 + 0.243851i) q^{98} +(2.50041 + 1.67072i) 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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