LMFDB - Embedded newform 45.2.l.a.32.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,2,Mod(2,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("45.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	45.l (of order $12$, degree $4$, 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:	$0.359326809096$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.4
Root			$-1.29724 + 0.347596i$ of defining polynomial
Character	$\chi$	$=$	45.32
Dual form			45.2.l.a.38.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29724 + 0.347596i) q^{2} +(-1.25897 + 1.18953i) q^{3} +(-0.170031 - 0.0981673i) q^{4} +(0.561484 - 2.16443i) q^{5} +(-2.04667 + 1.10550i) q^{6} +(-0.530190 + 1.97869i) q^{7} +(-2.08575 - 2.08575i) q^{8} +(0.170031 - 2.99518i) q^{9} +O(q^{10})$	\(q+(1.29724 + 0.347596i) q^{2} +(-1.25897 + 1.18953i) q^{3} +(-0.170031 - 0.0981673i) q^{4} +(0.561484 - 2.16443i) q^{5} +(-2.04667 + 1.10550i) q^{6} +(-0.530190 + 1.97869i) q^{7} +(-2.08575 - 2.08575i) q^{8} +(0.170031 - 2.99518i) q^{9} +(1.48073 - 2.61262i) q^{10} +(-0.762281 + 0.440103i) q^{11} +(0.330837 - 0.0786668i) q^{12} +(1.43820 + 5.36743i) q^{13} +(-1.37557 + 2.38256i) q^{14} +(1.86776 + 3.39286i) q^{15} +(-1.78439 - 3.09066i) q^{16} +(1.13610 - 1.13610i) q^{17} +(1.26168 - 3.82638i) q^{18} +1.52456i q^{19} +(-0.307945 + 0.312899i) q^{20} +(-1.68622 - 3.12180i) q^{21} +(-1.14184 + 0.305956i) q^{22} +(1.53331 - 0.410850i) q^{23} +(5.10696 + 0.144840i) q^{24} +(-4.36947 - 2.43058i) q^{25} +7.46278i q^{26} +(3.34879 + 3.97311i) q^{27} +(0.284392 - 0.284392i) q^{28} +(-0.796583 - 1.37972i) q^{29} +(1.24360 + 5.05059i) q^{30} +(3.49518 - 6.05383i) q^{31} +(0.286379 + 1.06878i) q^{32} +(0.436175 - 1.46084i) q^{33} +(1.86870 - 1.07889i) q^{34} +(3.98504 + 2.25856i) q^{35} +(-0.322939 + 0.492581i) q^{36} +(-4.25746 - 4.25746i) q^{37} +(-0.529931 + 1.97773i) q^{38} +(-8.19538 - 5.04667i) q^{39} +(-5.68555 + 3.34333i) q^{40} +(3.11546 + 1.79871i) q^{41} +(-1.10232 - 4.63586i) q^{42} +(-1.85841 - 0.497959i) q^{43} +0.172815 q^{44} +(-6.38737 - 2.04976i) q^{45} +2.13189 q^{46} +(-7.99942 - 2.14344i) q^{47} +(5.92294 + 1.76847i) q^{48} +(2.42805 + 1.40183i) q^{49} +(-4.82341 - 4.67186i) q^{50} +(-0.0788937 + 2.78174i) q^{51} +(0.282368 - 1.05381i) q^{52} +(-4.65601 - 4.65601i) q^{53} +(2.96317 + 6.31812i) q^{54} +(0.524562 + 1.89701i) q^{55} +(5.23290 - 3.02121i) q^{56} +(-1.81351 - 1.91938i) q^{57} +(-0.553777 - 2.06672i) q^{58} +(-3.81780 + 6.61262i) q^{59} +(0.0154914 - 0.760243i) q^{60} +(6.64002 + 11.5008i) q^{61} +(6.63838 - 6.63838i) q^{62} +(5.83639 + 1.92445i) q^{63} +8.62358i q^{64} +(12.4249 - 0.0991472i) q^{65} +(1.07361 - 1.74345i) q^{66} +(3.20857 - 0.859733i) q^{67} +(-0.304699 + 0.0816439i) q^{68} +(-1.44168 + 2.34117i) q^{69} +(4.38451 + 4.31509i) q^{70} -5.89798i q^{71} +(-6.60182 + 5.89254i) q^{72} +(1.58900 - 1.58900i) q^{73} +(-4.04309 - 7.00284i) q^{74} +(8.39230 - 2.13759i) q^{75} +(0.149662 - 0.259222i) q^{76} +(-0.466676 - 1.74166i) q^{77} +(-8.87721 - 9.39544i) q^{78} +(6.69401 - 3.86479i) q^{79} +(-7.69140 + 2.12683i) q^{80} +(-8.94218 - 1.01854i) q^{81} +(3.41628 + 3.41628i) q^{82} +(-2.57170 + 9.59770i) q^{83} +(-0.0197489 + 0.696335i) q^{84} +(-1.82110 - 3.09690i) q^{85} +(-2.23772 - 1.29195i) q^{86} +(2.64410 + 0.789474i) q^{87} +(2.50787 + 0.671981i) q^{88} +4.62765 q^{89} +(-7.57349 - 4.87926i) q^{90} -11.3830 q^{91} +(-0.301043 - 0.0806641i) q^{92} +(2.80088 + 11.7792i) q^{93} +(-9.63215 - 5.56112i) q^{94} +(3.29980 + 0.856017i) q^{95} +(-1.63189 - 1.00491i) q^{96} +(-1.02621 + 3.82988i) q^{97} +(2.66250 + 2.66250i) q^{98} +(1.18858 + 2.35800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 2 q^{7}+O(q^{10}) $ 16 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 2 * q^7	$ 16 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 2 q^{7} - 8 q^{10} - 6 q^{12} - 2 q^{13} - 6 q^{15} - 8 q^{16} + 36 q^{18} + 18 q^{20} - 12 q^{21} - 10 q^{22} + 18 q^{23} + 4 q^{25} + 18 q^{27} - 16 q^{28} + 30 q^{30} - 4 q^{31} + 30 q^{32} - 12 q^{33} - 48 q^{36} + 4 q^{37} - 30 q^{38} + 6 q^{40} - 24 q^{41} + 6 q^{42} - 2 q^{43} - 36 q^{45} + 32 q^{46} - 12 q^{47} - 30 q^{48} - 54 q^{50} + 36 q^{51} - 14 q^{52} - 16 q^{55} + 36 q^{56} - 6 q^{57} - 6 q^{58} + 18 q^{60} + 8 q^{61} + 36 q^{63} + 66 q^{65} + 36 q^{66} + 4 q^{67} + 42 q^{68} + 18 q^{70} + 18 q^{72} - 8 q^{73} + 42 q^{75} + 24 q^{76} - 6 q^{77} - 42 q^{78} - 48 q^{81} + 32 q^{82} - 66 q^{83} + 22 q^{85} - 48 q^{86} - 18 q^{87} + 18 q^{88} - 66 q^{90} - 40 q^{91} - 60 q^{92} - 18 q^{93} - 36 q^{95} - 24 q^{96} + 28 q^{97}+O(q^{100}) $ 16 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 2 * q^7 - 8 * q^10 - 6 * q^12 - 2 * q^13 - 6 * q^15 - 8 * q^16 + 36 * q^18 + 18 * q^20 - 12 * q^21 - 10 * q^22 + 18 * q^23 + 4 * q^25 + 18 * q^27 - 16 * q^28 + 30 * q^30 - 4 * q^31 + 30 * q^32 - 12 * q^33 - 48 * q^36 + 4 * q^37 - 30 * q^38 + 6 * q^40 - 24 * q^41 + 6 * q^42 - 2 * q^43 - 36 * q^45 + 32 * q^46 - 12 * q^47 - 30 * q^48 - 54 * q^50 + 36 * q^51 - 14 * q^52 - 16 * q^55 + 36 * q^56 - 6 * q^57 - 6 * q^58 + 18 * q^60 + 8 * q^61 + 36 * q^63 + 66 * q^65 + 36 * q^66 + 4 * q^67 + 42 * q^68 + 18 * q^70 + 18 * q^72 - 8 * q^73 + 42 * q^75 + 24 * q^76 - 6 * q^77 - 42 * q^78 - 48 * q^81 + 32 * q^82 - 66 * q^83 + 22 * q^85 - 48 * q^86 - 18 * q^87 + 18 * q^88 - 66 * q^90 - 40 * q^91 - 60 * q^92 - 18 * q^93 - 36 * q^95 - 24 * q^96 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.29724	+	0.347596i	0.917290	+	0.245787i	0.686427	−	0.727199i	$-0.259178\pi$
$2$	1.29724	+	0.347596i	0.917290	+	0.245787i	0.230863	+	0.972986i	$0.425845\pi$
$3$	−1.25897	+	1.18953i	−0.726869	+	0.686776i
$3$	−1.25897	+	1.18953i	−0.726869	+	0.686776i
$4$	−0.170031	−	0.0981673i	−0.0850154	−	0.0490837i
$5$	0.561484	−	2.16443i	0.251103	−	0.967960i
$5$	0.561484	−	2.16443i	0.251103	−	0.967960i
$6$	−2.04667	+	1.10550i	−0.835551	+	0.451318i
$7$	−0.530190	+	1.97869i	−0.200393	+	0.747876i	0.790412	+	0.612576i	$0.209867\pi$
$7$	−0.530190	+	1.97869i	−0.200393	+	0.747876i	−0.990805	+	0.135300i	$0.956800\pi$
$8$	−2.08575	−	2.08575i	−0.737423	−	0.737423i
$9$	0.170031	−	2.99518i	0.0566769	−	0.998393i
$10$	1.48073	−	2.61262i	0.468247	−	0.826183i
$11$	−0.762281	+	0.440103i	−0.229836	+	0.132696i	−0.610497	−	0.792019i	$-0.709030\pi$
$11$	−0.762281	+	0.440103i	−0.229836	+	0.132696i	0.380660	+	0.924715i	$0.375697\pi$
$12$	0.330837	−	0.0786668i	0.0955045	−	0.0227092i
$13$	1.43820	+	5.36743i	0.398885	+	1.48866i	0.815062	+	0.579374i	$0.196703\pi$
$13$	1.43820	+	5.36743i	0.398885	+	1.48866i	−0.416177	+	0.909283i	$0.636630\pi$
$14$	−1.37557	+	2.38256i	−0.367637	+	0.636766i
$15$	1.86776	+	3.39286i	0.482253	+	0.876032i
$16$	−1.78439	−	3.09066i	−0.446098	−	0.772664i
$17$	1.13610	−	1.13610i	0.275544	−	0.275544i	−0.555783	−	0.831327i	$-0.687582\pi$
$17$	1.13610	−	1.13610i	0.275544	−	0.275544i	0.831327	+	0.555783i	$0.187582\pi$
$18$	1.26168	−	3.82638i	0.297381	−	0.901885i
$19$			1.52456i			0.349758i	0.984590	+	0.174879i	$0.0559535\pi$
$19$			1.52456i			0.349758i	−0.984590	+	0.174879i	$0.944047\pi$
$20$	−0.307945	+	0.312899i	−0.0688587	+	0.0699665i
$21$	−1.68622	−	3.12180i	−0.367964	−	0.681233i
$22$	−1.14184	+	0.305956i	−0.243442	+	0.0652300i
$23$	1.53331	−	0.410850i	0.319718	−	0.0856682i	−0.0953909	−	0.995440i	$-0.530410\pi$
$23$	1.53331	−	0.410850i	0.319718	−	0.0856682i	0.415109	+	0.909772i	$0.363743\pi$
$24$	5.10696	+	0.144840i	1.04245	+	0.0295653i
$25$	−4.36947	−	2.43058i	−0.873894	−	0.486116i
$26$			7.46278i			1.46357i
$27$	3.34879	+	3.97311i	0.644476	+	0.764625i
$28$	0.284392	−	0.284392i	0.0537450	−	0.0537450i
$29$	−0.796583	−	1.37972i	−0.147922	−	0.256208i	0.782537	−	0.622603i	$-0.213925\pi$
$29$	−0.796583	−	1.37972i	−0.147922	−	0.256208i	−0.930459	+	0.366396i	$0.880592\pi$
$30$	1.24360	+	5.05059i	0.227048	+	0.922107i
$31$	3.49518	−	6.05383i	0.627752	−	1.08730i	−0.360249	−	0.932856i	$-0.617308\pi$
$31$	3.49518	−	6.05383i	0.627752	−	1.08730i	0.988002	−	0.154443i	$-0.0493583\pi$
$32$	0.286379	+	1.06878i	0.0506251	+	0.188936i
$33$	0.436175	−	1.46084i	0.0759284	−	0.254299i
$34$	1.86870	−	1.07889i	0.320479	−	0.185029i
$35$	3.98504	+	2.25856i	0.673595	+	0.381767i
$36$	−0.322939	+	0.492581i	−0.0538232	+	0.0820968i
$37$	−4.25746	−	4.25746i	−0.699922	−	0.699922i	0.264472	−	0.964393i	$-0.414802\pi$
$37$	−4.25746	−	4.25746i	−0.699922	−	0.699922i	−0.964393	+	0.264472i	$0.914802\pi$
$38$	−0.529931	+	1.97773i	−0.0859661	+	0.320830i
$39$	−8.19538	−	5.04667i	−1.31231	−	0.808114i
$40$	−5.68555	+	3.34333i	−0.898965	+	0.528627i
$41$	3.11546	+	1.79871i	0.486552	+	0.280911i	0.723143	−	0.690698i	$-0.242697\pi$
$41$	3.11546	+	1.79871i	0.486552	+	0.280911i	−0.236591	+	0.971609i	$0.576030\pi$
$42$	−1.10232	−	4.63586i	−0.170092	−	0.715329i
$43$	−1.85841	−	0.497959i	−0.283404	−	0.0759380i	0.114317	−	0.993444i	$-0.463532\pi$
$43$	−1.85841	−	0.497959i	−0.283404	−	0.0759380i	−0.397721	+	0.917506i	$0.630199\pi$
$44$	0.172815			0.0260528
$45$	−6.38737	−	2.04976i	−0.952173	−	0.305561i
$46$	2.13189			0.314330
$47$	−7.99942	−	2.14344i	−1.16683	−	0.312652i	−0.377142	−	0.926155i	$-0.623093\pi$
$47$	−7.99942	−	2.14344i	−1.16683	−	0.312652i	−0.789693	+	0.613503i	$0.789760\pi$
$48$	5.92294	+	1.76847i	0.854902	+	0.255256i
$49$	2.42805	+	1.40183i	0.346864	+	0.200262i
$50$	−4.82341	−	4.67186i	−0.682134	−	0.660701i
$51$	−0.0788937	+	2.78174i	−0.0110473	+	0.389522i
$52$	0.282368	−	1.05381i	0.0391574	−	0.146137i
$53$	−4.65601	−	4.65601i	−0.639552	−	0.639552i	0.310893	−	0.950445i	$-0.399372\pi$
$53$	−4.65601	−	4.65601i	−0.639552	−	0.639552i	−0.950445	+	0.310893i	$0.899372\pi$
$54$	2.96317	+	6.31812i	0.403236	+	0.859787i
$55$	0.524562	+	1.89701i	0.0707319	+	0.255793i
$56$	5.23290	−	3.02121i	0.699275	−	0.403727i
$57$	−1.81351	−	1.91938i	−0.240206	−	0.254229i
$58$	−0.553777	−	2.06672i	−0.0727145	−	0.271374i
$59$	−3.81780	+	6.61262i	−0.497035	+	0.860890i	−0.999994	−	0.00342048i	$-0.998911\pi$
$59$	−3.81780	+	6.61262i	−0.497035	+	0.860890i	0.502959	+	0.864310i	$0.332245\pi$
$60$	0.0154914	−	0.760243i	0.00199993	−	0.0981469i
$61$	6.64002	+	11.5008i	0.850167	+	1.47253i	0.881057	+	0.473010i	$0.156833\pi$
$61$	6.64002	+	11.5008i	0.850167	+	1.47253i	−0.0308900	+	0.999523i	$0.509834\pi$
$62$	6.63838	−	6.63838i	0.843075	−	0.843075i
$63$	5.83639	+	1.92445i	0.735317	+	0.242458i
$64$			8.62358i			1.07795i
$65$	12.4249	−	0.0991472i	1.54112	−	0.0122977i
$66$	1.07361	−	1.74345i	0.132152	−	0.214604i
$67$	3.20857	−	0.859733i	0.391989	−	0.105033i	−0.0574406	−	0.998349i	$-0.518294\pi$
$67$	3.20857	−	0.859733i	0.391989	−	0.105033i	0.449429	+	0.893316i	$0.351627\pi$
$68$	−0.304699	+	0.0816439i	−0.0369502	+	0.00990078i
$69$	−1.44168	+	2.34117i	−0.173558	+	0.281844i
$70$	4.38451	+	4.31509i	0.524049	+	0.515752i
$71$		−	5.89798i		−	0.699961i	−0.936757	−	0.349980i	$-0.886188\pi$
$71$		−	5.89798i		−	0.699961i	0.936757	−	0.349980i	$-0.113812\pi$
$72$	−6.60182	+	5.89254i	−0.778032	+	0.694442i
$73$	1.58900	−	1.58900i	0.185979	−	0.185979i	−0.607976	−	0.793955i	$-0.708018\pi$
$73$	1.58900	−	1.58900i	0.185979	−	0.185979i	0.793955	+	0.607976i	$0.208018\pi$
$74$	−4.04309	−	7.00284i	−0.470000	−	0.814063i
$75$	8.39230	−	2.13759i	0.969060	−	0.246827i
$76$	0.149662	−	0.259222i	0.0171674	−	0.0297348i
$77$	−0.466676	−	1.74166i	−0.0531827	−	0.198480i
$78$	−8.87721	−	9.39544i	−1.00515	−	1.06382i
$79$	6.69401	−	3.86479i	0.753135	−	0.434823i	−0.0736905	−	0.997281i	$-0.523478\pi$
$79$	6.69401	−	3.86479i	0.753135	−	0.434823i	0.826826	+	0.562458i	$0.190144\pi$
$80$	−7.69140	+	2.12683i	−0.859925	+	0.237787i
$81$	−8.94218	−	1.01854i	−0.993575	−	0.113172i
$82$	3.41628	+	3.41628i	0.377265	+	0.377265i
$83$	−2.57170	+	9.59770i	−0.282280	+	1.05348i	0.668523	+	0.743691i	$0.266927\pi$
$83$	−2.57170	+	9.59770i	−0.282280	+	1.05348i	−0.950804	+	0.309794i	$0.899740\pi$
$84$	−0.0197489	+	0.696335i	−0.00215478	+	0.0759763i
$85$	−1.82110	−	3.09690i	−0.197526	−	0.335906i
$86$	−2.23772	−	1.29195i	−0.241299	−	0.139314i
$87$	2.64410	+	0.789474i	0.283477	+	0.0846405i
$88$	2.50787	+	0.671981i	0.267340	+	0.0716334i
$89$	4.62765			0.490530			0.245265	−	0.969456i	$-0.421125\pi$
$89$	4.62765			0.490530			0.245265	+	0.969456i	$0.421125\pi$
$90$	−7.57349	−	4.87926i	−0.798316	−	0.514320i
$91$	−11.3830			−1.19327
$92$	−0.301043	−	0.0806641i	−0.0313859	−	0.00840982i
$93$	2.80088	+	11.7792i	0.290437	+	1.22145i
$94$	−9.63215	−	5.56112i	−0.993480	−	0.573586i
$95$	3.29980	+	0.856017i	0.338552	+	0.0878255i
$96$	−1.63189	−	1.00491i	−0.166554	−	0.102563i
$97$	−1.02621	+	3.82988i	−0.104196	+	0.388865i	−0.998253	−	0.0590888i	$-0.981180\pi$
$97$	−1.02621	+	3.82988i	−0.104196	+	0.388865i	0.894057	+	0.447954i	$0.147847\pi$
$98$	2.66250	+	2.66250i	0.268953	+	0.268953i
$99$	1.18858	+	2.35800i	0.119456	+	0.236988i
$100$	0.504341	+	0.842213i	0.0504341	+	0.0842213i
$101$	−2.23195	+	1.28862i	−0.222087	+	0.128222i	−0.606916	−	0.794766i	$-0.707594\pi$
$101$	−2.23195	+	1.28862i	−0.222087	+	0.128222i	0.384829	+	0.922988i	$0.374260\pi$
$102$	−1.06927	+	3.58117i	−0.105873	+	0.354589i
$103$	−3.38106	−	12.6183i	−0.333146	−	1.24332i	−0.905865	−	0.423566i	$-0.860778\pi$
$103$	−3.38106	−	12.6183i	−0.333146	−	1.24332i	0.572719	−	0.819752i	$-0.305889\pi$
$104$	8.19538	−	14.1948i	0.803623	−	1.39192i
$105$	−7.70370	+	1.89686i	−0.751804	+	0.185115i
$106$	−4.42157	−	7.65839i	−0.429461	−	0.743848i
$107$	−9.23034	+	9.23034i	−0.892331	+	0.892331i	−0.994742	−	0.102411i	$-0.967344\pi$
$107$	−9.23034	+	9.23034i	−0.892331	+	0.892331i	0.102411	+	0.994742i	$0.467344\pi$
$108$	−0.179369	−	1.00429i	−0.0172598	−	0.0966381i
$109$		−	8.05480i		−	0.771510i	−0.922601	−	0.385755i	$-0.873941\pi$
$109$		−	8.05480i		−	0.771510i	0.922601	−	0.385755i	$-0.126059\pi$
$110$	0.0210921	+	2.64322i	0.00201105	+	0.252021i
$111$	10.4244	+	0.295649i	0.989441	+	0.0280618i
$112$	7.06153	−	1.89213i	0.667252	−	0.178790i
$113$	11.5941	−	3.10662i	1.09068	−	0.292246i	0.331714	−	0.943380i	$-0.392373\pi$
$113$	11.5941	−	3.10662i	1.09068	−	0.292246i	0.758963	+	0.651134i	$0.225706\pi$
$114$	−1.68540	−	3.12028i	−0.157852	−	0.292241i
$115$	−0.0283234	−	3.54943i	−0.00264117	−	0.330986i
$116$			0.312794i			0.0290422i
$117$	16.3209	−	3.39503i	1.50887	−	0.313871i
$118$	−7.25113	+	7.25113i	−0.667521	+	0.667521i
$119$	1.64564	+	2.85034i	0.150856	+	0.261290i
$120$	3.18097	−	10.9723i	0.290382	−	1.00163i
$121$	−5.11262	+	8.85532i	−0.464784	+	0.805029i
$122$	4.61608	+	17.2274i	0.417920	+	1.55970i
$123$	−6.06190	+	1.44140i	−0.546583	+	0.129967i
$124$	−1.18858	+	0.686224i	−0.106737	+	0.0616248i
$125$	−7.71420	+	8.09266i	−0.689979	+	0.723830i
$126$	6.90230	+	4.52519i	0.614906	+	0.403136i
$127$	1.90230	+	1.90230i	0.168802	+	0.168802i	0.786452	−	0.617651i	$-0.211915\pi$
$127$	1.90230	+	1.90230i	0.168802	+	0.168802i	−0.617651	+	0.786452i	$0.711915\pi$
$128$	−2.42476	+	9.04933i	−0.214321	+	0.799855i
$129$	2.93202	−	1.58372i	0.258150	−	0.139438i
$130$	16.1526	+	4.19023i	1.41668	+	0.367508i
$131$	−18.5109	−	10.6873i	−1.61731	−	0.933754i	−0.987613	−	0.156912i	$-0.949846\pi$
$131$	−18.5109	−	10.6873i	−1.61731	−	0.933754i	−0.629696	−	0.776841i	$-0.716821\pi$
$132$	−0.217569	+	0.205569i	−0.0189370	+	0.0178925i
$133$	−3.01664	−	0.808307i	−0.261576	−	0.0700891i
$134$	4.46113			0.385383
$135$	10.4798	−	5.01738i	0.901956	−	0.431827i
$136$	−4.73922			−0.406385
$137$	6.62594	+	1.77541i	0.566092	+	0.151684i	0.530504	−	0.847683i	$-0.322003\pi$
$137$	6.62594	+	1.77541i	0.566092	+	0.151684i	0.0355883	+	0.999367i	$0.488669\pi$
$138$	−2.68400	+	2.53595i	−0.228477	+	0.215875i
$139$	1.24863	+	0.720896i	0.105907	+	0.0611456i	0.552018	−	0.833832i	$-0.313858\pi$
$139$	1.24863	+	0.720896i	0.105907	+	0.0611456i	−0.446111	+	0.894978i	$0.647191\pi$
$140$	−0.455863	−	0.775226i	−0.0385275	−	0.0655186i
$141$	12.6207	−	6.81703i	1.06286	−	0.574097i
$142$	2.05011	−	7.65111i	0.172041	−	0.642067i
$143$	−3.45853	−	3.45853i	−0.289217	−	0.289217i
$144$	−9.56047	+	4.81906i	−0.796706	+	0.401589i
$145$	−3.43357	+	0.949452i	−0.285143	+	0.0788477i
$146$	2.61366	−	1.50900i	0.216308	−	0.124885i
$147$	−4.72437	+	1.12337i	−0.389659	+	0.0926536i
$148$	0.305956	+	1.14184i	0.0251494	+	0.0938589i
$149$	−8.28457	+	14.3493i	−0.678699	+	1.17554i	0.296674	+	0.954979i	$0.404122\pi$
$149$	−8.28457	+	14.3493i	−0.678699	+	1.17554i	−0.975373	+	0.220562i	$0.929211\pi$
$150$	11.6299	+	0.144155i	0.949576	+	0.0117702i
$151$	0.00283730	+	0.00491435i	0.000230896	+	0.000399924i	0.866141	−	0.499800i	$-0.166593\pi$
$151$	0.00283730	+	0.00491435i	0.000230896	+	0.000399924i	−0.865910	+	0.500200i	$0.833260\pi$
$152$	3.17985	−	3.17985i	0.257920	−	0.257920i
$153$	−3.20964	−	3.59599i	−0.259484	−	0.290718i
$154$		−	2.42157i		−	0.195136i
$155$	−11.1406	−	10.9642i	−0.894832	−	0.880664i
$156$	0.898049	+	1.66261i	0.0719014	+	0.133115i
$157$	−8.17112	+	2.18944i	−0.652126	+	0.174737i	−0.569690	−	0.821860i	$-0.692937\pi$
$157$	−8.17112	+	2.18944i	−0.652126	+	0.174737i	−0.0824362	+	0.996596i	$0.526270\pi$
$158$	10.0272	−	2.68677i	0.797717	−	0.213748i
$159$	11.4003	+	0.323326i	0.904099	+	0.0256414i
$160$	2.47409	−	0.0197425i	0.195594	−	0.00156078i
$161$			3.25179i			0.256277i
$162$	−11.2461	−	4.42956i	−0.883581	−	0.348019i
$163$	4.19302	−	4.19302i	0.328422	−	0.328422i	−0.523564	−	0.851986i	$-0.675398\pi$
$163$	4.19302	−	4.19302i	0.328422	−	0.328422i	0.851986	+	0.523564i	$0.175398\pi$
$164$	−0.353149	−	0.611672i	−0.0275763	−	0.0477635i
$165$	−2.91696	−	1.76430i	−0.227085	−	0.137351i
$166$	−6.67224	+	11.5567i	−0.517866	+	0.896970i
$167$	−1.54428	−	5.76334i	−0.119500	−	0.445980i	0.880084	−	0.474818i	$-0.157486\pi$
$167$	−1.54428	−	5.76334i	−0.119500	−	0.445980i	−0.999584	+	0.0288375i	$0.990819\pi$
$168$	−2.99425	+	10.0283i	−0.231012	+	0.773702i
$169$	−15.4826	+	8.93886i	−1.19097	+	0.687605i
$170$	−1.28594	−	4.65044i	−0.0986271	−	0.356672i
$171$	4.56633	+	0.259222i	0.349196	+	0.0198232i
$172$	0.267103	+	0.267103i	0.0203664	+	0.0203664i
$173$	3.53677	−	13.1994i	0.268896	−	1.00353i	−0.690927	−	0.722925i	$-0.742797\pi$
$173$	3.53677	−	13.1994i	0.268896	−	1.00353i	0.959822	−	0.280608i	$-0.0905361\pi$
$174$	3.15562	+	1.94322i	0.239227	+	0.147315i
$175$	7.12602	−	7.35718i	0.538677	−	0.556151i
$176$	2.72042	+	1.57063i	0.205059	+	0.118391i
$177$	−3.05941	−	12.8665i	−0.229959	−	0.967106i
$178$	6.00319	+	1.60855i	0.449958	+	0.120566i
$179$	17.2370			1.28836			0.644178	−	0.764875i	$-0.277199\pi$
$179$	17.2370			1.28836			0.644178	+	0.764875i	$0.277199\pi$
$180$	0.884829	+	0.975554i	0.0659513	+	0.0727135i
$181$	14.7708			1.09790			0.548952	−	0.835854i	$-0.315027\pi$
$181$	14.7708			1.09790			0.548952	+	0.835854i	$0.315027\pi$
$182$	−14.7666	−	3.95669i	−1.09457	−	0.293289i
$183$	−22.0402	−	6.58076i	−1.62926	−	0.486464i
$184$	−4.05503	−	2.34117i	−0.298941	−	0.172594i
$185$	−11.6054	+	6.82446i	−0.853249	+	0.501744i
$186$	−0.460987	+	16.2541i	−0.0338012	+	1.19181i
$187$	−0.366025	+	1.36603i	−0.0267664	+	0.0998937i
$188$	1.14973	+	1.14973i	0.0838528	+	0.0838528i
$189$	−9.63706	+	4.51974i	−0.700993	+	0.328763i
$190$	3.98310	+	2.25746i	0.288964	+	0.163773i
$191$	4.56792	−	2.63729i	0.330523	−	0.190827i	−0.325550	−	0.945525i	$-0.605550\pi$
$191$	4.56792	−	2.63729i	0.330523	−	0.190827i	0.656073	+	0.754697i	$0.272216\pi$
$192$	−10.2580	−	10.8569i	−0.740309	−	0.783527i
$193$	2.40873	+	8.98952i	0.173384	+	0.647080i	0.996821	+	0.0796715i	$0.0253871\pi$
$193$	2.40873	+	8.98952i	0.173384	+	0.647080i	−0.823437	+	0.567408i	$0.807946\pi$
$194$	−2.66250	+	4.61158i	−0.191156	+	0.331092i
$195$	−15.5247	+	14.9047i	−1.11175	+	1.06734i
$196$	−0.275228	−	0.476709i	−0.0196592	−	0.0340507i
$197$	9.49539	−	9.49539i	0.676519	−	0.676519i	−0.282692	−	0.959211i	$-0.591227\pi$
$197$	9.49539	−	9.49539i	0.676519	−	0.676519i	0.959211	+	0.282692i	$0.0912274\pi$
$198$	0.722243	+	3.47204i	0.0513276	+	0.246747i
$199$		−	17.6342i		−	1.25005i	−0.780604	−	0.625026i	$-0.785088\pi$
$199$		−	17.6342i		−	1.25005i	0.780604	−	0.625026i	$-0.214912\pi$
$200$	4.04404	+	14.1832i	0.285957	+	1.00290i
$201$	−3.01682	+	4.89907i	−0.212790	+	0.345554i
$202$	−3.34330	+	0.895835i	−0.235234	+	0.0630307i
$203$	3.15239	−	0.844680i	0.221254	−	0.0592849i
$204$	0.286490	−	0.465237i	0.0200583	−	0.0325731i
$205$	5.64245	−	5.73322i	0.394086	−	0.400426i
$206$		−	17.5443i		−	1.22237i
$207$	−0.969859	−	4.66240i	−0.0674098	−	0.324060i
$208$	14.0226	−	14.0226i	0.972291	−	0.972291i
$209$	−0.670964	−	1.16214i	−0.0464116	−	0.0803872i
$210$	−10.6529	−	0.217074i	−0.735121	−	0.0149795i
$211$	0.0616050	−	0.106703i	0.00424106	−	0.00734574i	−0.863897	−	0.503668i	$-0.831983\pi$
$211$	0.0616050	−	0.106703i	0.00424106	−	0.00734574i	0.868138	+	0.496323i	$0.165317\pi$
$212$	0.334597	+	1.24873i	0.0229802	+	0.0857633i
$213$	7.01583	+	7.42540i	0.480716	+	0.508780i
$214$	−15.1824	+	8.76558i	−1.03785	+	0.599203i
$215$	−2.12126	+	3.74279i	−0.144669	+	0.255256i
$216$	1.30216	−	15.2716i	0.0886009	−	1.03910i
$217$	10.1256	+	10.1256i	0.687368	+	0.687368i
$218$	2.79981	−	10.4490i	0.189627	−	0.707698i
$219$	−0.110345	+	3.89068i	−0.00745640	+	0.262908i
$220$	0.0970328	−	0.374045i	0.00654195	−	0.0252181i
$221$	7.73186	+	4.46399i	0.520101	+	0.300281i
$222$	13.4202	+	4.00701i	0.900707	+	0.268933i
$223$	−2.41842	−	0.648014i	−0.161949	−	0.0433942i	0.176933	−	0.984223i	$-0.443382\pi$
$223$	−2.41842	−	0.648014i	−0.161949	−	0.0433942i	−0.338883	+	0.940829i	$0.610049\pi$
$224$	−2.26663			−0.151445
$225$	−8.02296	+	12.6741i	−0.534864	+	0.844938i
$226$	16.1202			1.07230
$227$	14.7293	+	3.94671i	0.977619	+	0.261952i	0.712042	−	0.702137i	$-0.247771\pi$
$227$	14.7293	+	3.94671i	0.977619	+	0.261952i	0.265577	+	0.964090i	$0.414437\pi$
$228$	0.119932	+	0.504382i	0.00794272	+	0.0334035i
$229$	19.1083	+	11.0322i	1.26271	+	0.729029i	0.973599	−	0.228265i	$-0.0733054\pi$
$229$	19.1083	+	11.0322i	1.26271	+	0.729029i	0.289116	+	0.957294i	$0.406639\pi$
$230$	1.19702	−	4.61432i	0.0789294	−	0.304259i
$231$	2.65929	+	1.63758i	0.174969	+	0.107745i
$232$	−1.21628	+	4.53922i	−0.0798527	+	0.298014i
$233$	4.22173	+	4.22173i	0.276575	+	0.276575i	0.831740	−	0.555165i	$-0.187345\pi$
$233$	4.22173	+	4.22173i	0.276575	+	0.276575i	−0.555165	+	0.831740i	$0.687345\pi$
$234$	22.3524	+	1.26890i	1.46122	+	0.0829507i
$235$	−9.13085	+	16.1106i	−0.595631	+	1.05094i
$236$	1.29829	−	0.749566i	0.0845112	−	0.0487926i
$237$	−3.83030	+	12.8284i	−0.248805	+	0.833294i
$238$	1.14404	+	4.26960i	0.0741569	+	0.276757i
$239$	6.79199	−	11.7641i	0.439338	−	0.760955i	−0.558301	−	0.829639i	$-0.688547\pi$
$239$	6.79199	−	11.7641i	0.439338	−	0.760955i	0.997639	+	0.0686835i	$0.0218799\pi$
$240$	7.15335	−	11.8268i	0.461747	−	0.763416i
$241$	−2.56728	−	4.44666i	−0.165373	−	0.286434i	0.771415	−	0.636333i	$-0.219549\pi$
$241$	−2.56728	−	4.44666i	−0.165373	−	0.286434i	−0.936788	+	0.349898i	$0.886216\pi$
$242$	−9.71038	+	9.71038i	−0.624207	+	0.624207i
$243$	12.4696	−	9.35468i	0.799923	−	0.600103i
$244$		−	2.60733i		−	0.166917i
$245$	4.39747	−	4.46822i	0.280944	−	0.285464i
$246$	−8.36479	−	0.237236i	−0.533319	−	0.0151256i
$247$	−8.18298	+	2.19262i	−0.520670	+	0.139513i
$248$	−19.9168	+	5.33669i	−1.26472	+	0.338880i
$249$	−8.17907	−	15.1424i	−0.518327	−	0.959609i
$250$	−12.8202	+	7.81674i	−0.810819	+	0.494374i
$251$			2.60221i			0.164250i	0.996622	+	0.0821251i	$0.0261707\pi$
$251$			2.60221i			0.164250i	−0.996622	+	0.0821251i	$0.973829\pi$
$252$	−0.803448	−	0.900159i	−0.0506125	−	0.0567047i
$253$	−0.987999	+	0.987999i	−0.0621150	+	0.0621150i
$254$	1.80652	+	3.12898i	0.113351	+	0.196329i
$255$	5.97657	+	1.73266i	0.374267	+	0.108504i
$256$	2.33257	−	4.04013i	0.145786	−	0.252508i
$257$	−2.73197	−	10.1958i	−0.170415	−	0.635999i	−0.997287	−	0.0736085i	$-0.976548\pi$
$257$	−2.73197	−	10.1958i	−0.170415	−	0.635999i	0.826872	−	0.562390i	$-0.190118\pi$
$258$	4.35404	−	1.03531i	0.271071	−	0.0644555i
$259$	10.6815	−	6.16695i	0.663714	−	0.383196i
$260$	−2.12235	−	1.20286i	−0.131623	−	0.0745984i
$261$	−4.26796	+	2.15131i	−0.264180	+	0.133163i
$262$	−20.2984	−	20.2984i	−1.25404	−	1.25404i
$263$	−2.17720	+	8.12541i	−0.134252	+	0.501034i	0.865748	+	0.500480i	$0.166843\pi$
$263$	−2.17720	+	8.12541i	−0.134252	+	0.501034i	−1.00000		0.000554412i	$0.999824\pi$
$264$	−3.95668	+	2.13718i	−0.243517	+	0.131534i
$265$	−12.6919	+	7.46331i	−0.779654	+	0.458467i
$266$	−3.63236	−	2.09714i	−0.222714	−	0.128584i
$267$	−5.82609	+	5.50473i	−0.356551	+	0.336884i
$268$	−0.629953	−	0.168795i	−0.0384805	−	0.0103108i
$269$	−26.7708			−1.63225			−0.816123	−	0.577878i	$-0.803881\pi$
$269$	−26.7708			−1.63225			−0.816123	+	0.577878i	$0.803881\pi$
$270$	15.3389	−	2.86603i	0.933493	−	0.174421i
$271$	−18.5850			−1.12896			−0.564480	−	0.825447i	$-0.690923\pi$
$271$	−18.5850			−1.12896			−0.564480	+	0.825447i	$0.690923\pi$
$272$	−5.53853	−	1.48405i	−0.335823	−	0.0899834i
$273$	14.3309	−	13.5405i	0.867347	−	0.819506i
$274$	7.97833	+	4.60629i	0.481989	+	0.278276i
$275$	4.40047	−	0.0702333i	0.265358	−	0.00423523i
$276$	0.474957	−	0.256546i	0.0285891	−	0.0154422i
$277$	7.05259	−	26.3206i	0.423749	−	1.58145i	−0.342891	−	0.939375i	$-0.611406\pi$
$277$	7.05259	−	26.3206i	0.423749	−	1.58145i	0.766640	−	0.642078i	$-0.221927\pi$
$278$	1.36920	+	1.36920i	0.0821189	+	0.0821189i
$279$	−17.5380	−	11.4980i	−1.04997	−	0.688368i
$280$	−3.60100	−	13.0226i	−0.215201	−	0.778248i
$281$	−22.7050	+	13.1087i	−1.35447	+	0.782002i	−0.988872	−	0.148772i	$-0.952468\pi$
$281$	−22.7050	+	13.1087i	−1.35447	+	0.782002i	−0.365595	+	0.930774i	$0.619135\pi$
$282$	18.7418	−	4.45643i	1.11606	−	0.265377i
$283$	−0.921880	−	3.44050i	−0.0548001	−	0.204517i	0.933098	−	0.359623i	$-0.117095\pi$
$283$	−0.921880	−	3.44050i	−0.0548001	−	0.204517i	−0.987898	+	0.155106i	$0.950428\pi$
$284$	−0.578988	+	1.00284i	−0.0343566	+	0.0595074i
$285$	−5.17262	+	2.84751i	−0.306400	+	0.168672i
$286$	−3.28439	−	5.68873i	−0.194210	−	0.336382i
$287$	−5.21088	+	5.21088i	−0.307589	+	0.307589i
$288$	3.24988	−	0.676030i	0.191501	−	0.0398355i
$289$			14.4186i			0.848151i
$290$	−4.78421	+	0.0381765i	−0.280938	+	0.00224180i
$291$	−3.26378	−	6.04243i	−0.191326	−	0.354213i
$292$	−0.426168	+	0.114191i	−0.0249396	+	0.00668254i
$293$	2.87816	−	0.771199i	0.168144	−	0.0450539i	−0.173765	−	0.984787i	$-0.555593\pi$
$293$	2.87816	−	0.771199i	0.168144	−	0.0450539i	0.341909	+	0.939733i	$0.388927\pi$
$294$	−6.51914	−	0.184891i	−0.380204	−	0.0107831i
$295$	12.1689	+	11.9762i	0.708500	+	0.697282i
$296$			17.7600i			1.03228i
$297$	−4.30130	−	1.55481i	−0.249587	−	0.0902192i
$298$	−15.7349	+	15.7349i	−0.911496	+	0.911496i
$299$	4.41042	+	7.63907i	0.255061	+	0.441779i
$300$	−1.63679	−	0.460394i	−0.0945002	−	0.0265809i
$301$	1.97062	−	3.41321i	0.113584	−	0.196734i
$302$	0.00197247	+	0.00736135i	0.000113503	+	0.000423598i
$303$	1.27712	−	4.27731i	0.0733684	−	0.245725i
$304$	4.71190	−	2.72042i	0.270246	−	0.156027i
$305$	28.6210	−	7.91428i	1.63883	−	0.453170i
$306$	−2.91374	−	5.78053i	−0.166568	−	0.330451i
$307$	21.8017	+	21.8017i	1.24429	+	1.24429i	0.958205	+	0.286081i	$0.0923528\pi$
$307$	21.8017	+	21.8017i	1.24429	+	1.24429i	0.286081	+	0.958205i	$0.407647\pi$
$308$	−0.0916247	+	0.341948i	−0.00522080	+	0.0194843i
$309$	19.2665	+	11.8642i	1.09603	+	0.674933i
$310$	−10.6409	−	18.0956i	−0.604365	−	1.02776i
$311$	29.3878	+	16.9671i	1.66643	+	0.962114i	0.969539	+	0.244939i	$0.0787679\pi$
$311$	29.3878	+	16.9671i	1.66643	+	0.962114i	0.696892	+	0.717176i	$0.254565\pi$
$312$	6.56741	+	27.6196i	0.371806	+	1.56365i
$313$	−22.4027	−	6.00279i	−1.26628	−	0.339298i	−0.437673	−	0.899134i	$-0.644197\pi$
$313$	−22.4027	−	6.00279i	−1.26628	−	0.339298i	−0.828603	+	0.559836i	$0.810864\pi$
$314$	−11.3610			−0.641137
$315$	7.44237	−	11.5519i	0.419330	−	0.650875i
$316$	−1.51758			−0.0853708
$317$	−3.86401	−	1.03536i	−0.217024	−	0.0581515i	0.148669	−	0.988887i	$-0.452501\pi$
$317$	−3.86401	−	1.03536i	−0.217024	−	0.0581515i	−0.365693	+	0.930736i	$0.619168\pi$
$318$	14.6765	+	4.38211i	0.823019	+	0.245737i
$319$	1.21444	+	0.701157i	0.0679956	+	0.0392573i
$320$	18.6651	+	4.84200i	1.04341	+	0.270676i
$321$	0.640980	−	22.6005i	0.0357760	−	1.26144i
$322$	−1.13031	+	4.21836i	−0.0629896	+	0.235080i
$323$	1.73205	+	1.73205i	0.0963739	+	0.0963739i
$324$	1.42046	+	1.05101i	0.0789143	+	0.0583896i
$325$	6.76180	−	26.9485i	0.375077	−	1.49483i
$326$	6.89684	−	3.98189i	0.381981	−	0.220537i
$327$	9.58143	+	10.1408i	0.529854	+	0.560786i
$328$	−2.74640	−	10.2497i	−0.151645	−	0.565945i
$329$	8.48242	−	14.6920i	0.467651	−	0.809995i
$330$	−3.17075	−	3.30266i	−0.174544	−	0.181805i
$331$	−2.98175	−	5.16454i	−0.163892	−	0.283869i	0.772369	−	0.635174i	$-0.219071\pi$
$331$	−2.98175	−	5.16454i	−0.163892	−	0.283869i	−0.936261	+	0.351305i	$0.885738\pi$
$332$	1.37945	−	1.37945i	0.0757071	−	0.0757071i
$333$	−13.4757	+	12.0279i	−0.738466	+	0.659127i
$334$		−	8.01324i		−	0.438465i
$335$	−0.0592686	−	7.42743i	−0.00323819	−	0.405804i
$336$	−6.63954	+	10.7821i	−0.362216	+	0.588210i
$337$	9.56887	−	2.56397i	0.521250	−	0.139668i	0.0114051	−	0.999935i	$-0.496370\pi$
$337$	9.56887	−	2.56397i	0.521250	−	0.139668i	0.509845	+	0.860267i	$0.329703\pi$
$338$	−23.1918	+	6.21422i	−1.26147	+	0.338009i
$339$	−10.9012	+	17.7026i	−0.592072	+	0.961476i
$340$	0.00562840	+	0.705340i	0.000305243	+	0.0382525i
$341$			6.15295i			0.333201i
$342$	5.83354	+	1.92351i	0.315442	+	0.104012i
$343$	−14.2007	+	14.2007i	−0.766764	+	0.766764i
$344$	2.83755	+	4.91478i	0.152990	+	0.264987i
$345$	4.25781	+	4.43495i	0.229233	+	0.238770i
$346$	9.17611	−	15.8935i	0.493311	−	0.854440i
$347$	−2.74569	−	10.2471i	−0.147396	−	0.550091i	−0.999637	−	0.0269407i	$-0.991423\pi$
$347$	−2.74569	−	10.2471i	−0.147396	−	0.550091i	0.852241	−	0.523150i	$-0.175243\pi$
$348$	−0.372078	−	0.393799i	−0.0199455	−	0.0211098i
$349$	8.08831	−	4.66979i	0.432957	−	0.249968i	−0.267648	−	0.963517i	$-0.586247\pi$
$349$	8.08831	−	4.66979i	0.432957	−	0.249968i	0.700606	+	0.713549i	$0.252913\pi$
$350$	11.8015	−	7.06709i	0.630818	−	0.377752i
$351$	−16.5091	+	23.6885i	−0.881193	+	1.26440i
$352$	−0.688675	−	0.688675i	−0.0367065	−	0.0367065i
$353$	−4.96965	+	18.5470i	−0.264508	+	0.987156i	0.698043	+	0.716055i	$0.254054\pi$
$353$	−4.96965	+	18.5470i	−0.264508	+	0.987156i	−0.962551	+	0.271100i	$0.912612\pi$
$354$	0.503538	−	17.7544i	0.0267627	−	0.943638i
$355$	−12.7657	−	3.31162i	−0.677534	−	0.175762i
$356$	−0.786842	−	0.454284i	−0.0417026	−	0.0240770i
$357$	−5.46239	−	1.63096i	−0.289100	−	0.0863194i
$358$	22.3606	+	5.99152i	1.18180	+	0.316662i
$359$	−12.5944			−0.664705			−0.332352	−	0.943155i	$-0.607842\pi$
$359$	−12.5944			−0.664705			−0.332352	+	0.943155i	$0.607842\pi$
$360$	9.04714	+	17.5977i	0.476826	+	0.927481i
$361$	16.6757			0.877669
$362$	19.1613	+	5.13426i	1.00710	+	0.269851i
$363$	−4.09702	−	17.2302i	−0.215038	−	0.904353i
$364$	1.93546	+	1.11744i	0.101446	+	0.0585698i
$365$	−2.54708	−	4.33148i	−0.133320	−	0.226720i
$366$	−26.3041	−	16.1979i	−1.37494	−	0.846680i
$367$	−7.32206	+	27.3263i	−0.382209	+	1.42642i	0.460312	+	0.887757i	$0.347738\pi$
$367$	−7.32206	+	27.3263i	−0.382209	+	1.42642i	−0.842520	+	0.538665i	$0.818929\pi$
$368$	−4.00583	−	4.00583i	−0.208818	−	0.208818i
$369$	5.91718	−	9.02551i	0.308036	−	0.469849i
$370$	−17.4272	+	4.81898i	−0.905999	+	0.250527i
$371$	11.6814	−	6.74425i	0.606467	−	0.350144i
$372$	0.680100	−	2.27779i	0.0352616	−	0.118098i
$373$	0.604851	+	2.25734i	0.0313180	+	0.116880i	0.979815	−	0.199905i	$-0.0640633\pi$
$373$	0.604851	+	2.25734i	0.0313180	+	0.116880i	−0.948497	+	0.316785i	$0.897397\pi$
$374$	−0.949649	+	1.64484i	−0.0491052	+	0.0850526i
$375$	0.0854972	−	19.3647i	0.00441505	−	0.999990i
$376$	12.2141	+	21.1554i	0.629894	+	1.09101i
$377$	6.25992	−	6.25992i	0.322402	−	0.322402i
$378$	−14.0727	+	2.51341i	−0.723820	+	0.129276i
$379$			18.4618i			0.948320i	0.880439	+	0.474160i	$0.157248\pi$
$379$			18.4618i			0.948320i	−0.880439	+	0.474160i	$0.842752\pi$
$380$	−0.477035	−	0.469482i	−0.0244714	−	0.0240839i
$381$	−4.65779	−	0.132101i	−0.238626	−	0.00676772i
$382$	6.84241	−	1.83342i	0.350088	−	0.0938059i
$383$	−23.3806	+	6.26481i	−1.19469	+	0.320117i	−0.800739	−	0.599014i	$-0.795559\pi$
$383$	−23.3806	+	6.26481i	−1.19469	+	0.320117i	−0.393953	+	0.919131i	$0.628893\pi$
$384$	−7.71175	−	14.2772i	−0.393539	−	0.728580i
$385$	−4.03172	+	0.0321719i	−0.205476	+	0.00163963i
$386$			12.4989i			0.636176i
$387$	−1.80746	+	5.48159i	−0.0918784	+	0.278645i
$388$	0.550457	−	0.550457i	0.0279452	−	0.0279452i
$389$	−13.5444	−	23.4596i	−0.686729	−	1.18945i	−0.972890	−	0.231268i	$-0.925712\pi$
$389$	−13.5444	−	23.4596i	−0.686729	−	1.18945i	0.286161	−	0.958182i	$-0.407621\pi$
$390$	−25.3201	+	13.9387i	−1.28214	+	0.705812i
$391$	1.27523	−	2.20876i	0.0644911	−	0.111702i
$392$	−2.14042	−	7.98815i	−0.108108	−	0.403463i
$393$	36.0177	−	8.56432i	1.81685	−	0.432013i
$394$	15.6184	−	9.01729i	0.786844	−	0.454284i
$395$	−4.60647	−	16.6587i	−0.231776	−	0.838190i
$396$	0.0293839	−	0.517611i	0.00147659	−	0.0260110i
$397$	−18.2252	−	18.2252i	−0.914698	−	0.914698i	0.0819389	−	0.996637i	$-0.473889\pi$
$397$	−18.2252	−	18.2252i	−0.914698	−	0.914698i	−0.996637	+	0.0819389i	$0.973889\pi$
$398$	6.12955	−	22.8758i	0.307247	−	1.14666i
$399$	4.75938	−	2.57075i	0.238267	−	0.128699i
$400$	0.284760	+	17.8416i	0.0142380	+	0.892082i
$401$	−11.1294	−	6.42558i	−0.555777	−	0.320878i	0.195672	−	0.980669i	$-0.437311\pi$
$401$	−11.1294	−	6.42558i	−0.555777	−	0.320878i	−0.751449	+	0.659791i	$0.770645\pi$
$402$	−5.61645	+	5.30666i	−0.280123	+	0.264672i
$403$	37.5202	+	10.0535i	1.86902	+	0.500801i
$404$	0.506000			0.0251745
$405$	−7.22545	+	18.7828i	−0.359036	+	0.933324i
$406$	4.38302			0.217526
$407$	5.11910	+	1.37166i	0.253744	+	0.0679906i
$408$	5.96656	−	5.63745i	0.295389	−	0.279096i
$409$	−22.2450	−	12.8431i	−1.09994	−	0.635053i	−0.163737	−	0.986504i	$-0.552355\pi$
$409$	−22.2450	−	12.8431i	−1.09994	−	0.635053i	−0.936206	+	0.351451i	$0.885688\pi$
$410$	9.31248	−	5.47610i	0.459911	−	0.270445i
$411$	−10.4538	+	5.64656i	−0.515648	+	0.278524i
$412$	−0.663820	+	2.47741i	−0.0327041	+	0.122053i
$413$	−11.0602	−	11.0602i	−0.544237	−	0.544237i
$414$	0.362487	−	6.38540i	0.0178153	−	0.313825i
$415$	19.3295	+	10.9552i	0.948850	+	0.537770i
$416$	−5.32474	+	3.07424i	−0.261067	+	0.150727i
$417$	−2.42952	+	0.577694i	−0.118974	+	0.0282898i
$418$	−0.466448	−	1.74081i	−0.0228147	−	0.0851457i
$419$	−6.13243	+	10.6217i	−0.299589	+	0.518903i	−0.976042	−	0.217583i	$-0.930183\pi$
$419$	−6.13243	+	10.6217i	−0.299589	+	0.518903i	0.676453	+	0.736486i	$0.263516\pi$
$420$	1.49608	+	0.433726i	0.0730010	+	0.0211637i
$421$	−7.24056	−	12.5410i	−0.352883	−	0.611212i	0.633870	−	0.773439i	$-0.281465\pi$
$421$	−7.24056	−	12.5410i	−0.352883	−	0.611212i	−0.986753	+	0.162228i	$0.948132\pi$
$422$	0.117006	−	0.117006i	0.00569577	−	0.00569577i
$423$	−7.78012	+	23.5952i	−0.378283	+	1.14724i
$424$			19.4225i			0.943240i
$425$	−7.72552	+	2.20277i	−0.374743	+	0.106850i
$426$	6.52020	+	12.0712i	0.315905	+	0.584853i
$427$	−26.2771	+	7.04094i	−1.27164	+	0.340735i
$428$	2.47556	−	0.663324i	0.119661	−	0.0320630i
$429$	8.46824	+	0.240170i	0.408850	+	0.0115955i
$430$	−4.05277	+	4.11797i	−0.195442	+	0.198586i
$431$		−	35.9660i		−	1.73242i	−0.499678	−	0.866211i	$-0.666548\pi$
$431$		−	35.9660i		−	1.73242i	0.499678	−	0.866211i	$-0.333452\pi$
$432$	6.30395	−	17.4396i	0.303299	−	0.839061i
$433$	−0.331545	+	0.331545i	−0.0159331	+	0.0159331i	−0.715028	−	0.699095i	$-0.753586\pi$
$433$	−0.331545	+	0.331545i	−0.0159331	+	0.0159331i	0.699095	+	0.715028i	$0.253586\pi$
$434$	9.61573	+	16.6549i	0.461570	+	0.799462i
$435$	3.19338	−	5.27968i	0.153111	−	0.253141i
$436$	−0.790718	+	1.36956i	−0.0378685	+	0.0655902i
$437$	0.626366	+	2.33763i	0.0299632	+	0.111824i
$438$	−1.49553	+	5.00881i	−0.0714591	+	0.239330i
$439$	1.28953	−	0.744511i	0.0615459	−	0.0355336i	−0.468911	−	0.883245i	$-0.655354\pi$
$439$	1.28953	−	0.744511i	0.0615459	−	0.0355336i	0.530457	+	0.847712i	$0.322020\pi$
$440$	2.86258	−	5.05078i	0.136468	−	0.240787i
$441$	4.61158	−	7.03407i	0.219599	−	0.334956i
$442$	8.47845	+	8.47845i	0.403279	+	0.403279i
$443$	8.29218	−	30.9468i	0.393973	−	1.47033i	−0.429548	−	0.903044i	$-0.641327\pi$
$443$	8.29218	−	30.9468i	0.393973	−	1.47033i	0.823522	−	0.567285i	$-0.192006\pi$
$444$	−1.74345	−	1.07361i	−0.0827403	−	0.0509511i
$445$	2.59835	−	10.0162i	0.123174	−	0.474813i
$446$	−2.91203	−	1.68126i	−0.137889	−	0.0796101i
$447$	−6.63888	−	27.9202i	−0.314008	−	1.32058i
$448$	−17.0634	−	4.57213i	−0.806172	−	0.216013i
$449$	21.8283			1.03014			0.515071	−	0.857147i	$-0.327766\pi$
$449$	21.8283			1.03014			0.515071	+	0.857147i	$0.327766\pi$
$450$	−14.8132	+	13.6526i	−0.698301	+	0.643591i
$451$	−3.16647			−0.149103
$452$	−2.27631	−	0.609937i	−0.107069	−	0.0286890i
$453$	−0.00941786	−	0.00281198i	−0.000442490	−	0.000132118i
$454$	17.7357	+	10.2397i	0.832376	+	0.480572i
$455$	−6.39139	+	24.6377i	−0.299633	+	1.15503i
$456$	−0.220817	+	7.78588i	−0.0103407	+	0.364607i
$457$	−0.235886	+	0.880339i	−0.0110343	+	0.0411805i	−0.971223	−	0.238170i	$-0.923452\pi$
$457$	−0.235886	+	0.880339i	−0.0110343	+	0.0411805i	0.960189	+	0.279351i	$0.0901191\pi$
$458$	20.9534	+	20.9534i	0.979090	+	0.979090i
$459$	8.31839	+	0.709282i	0.388269	+	0.0331065i
$460$	−0.343622	+	0.606293i	−0.0160215	+	0.0282685i
$461$	−18.7320	+	10.8149i	−0.872434	+	0.503700i	−0.868156	−	0.496291i	$-0.834695\pi$
$461$	−18.7320	+	10.8149i	−0.872434	+	0.503700i	−0.00427761	+	0.999991i	$0.501362\pi$
$462$	2.88054	+	3.04870i	0.134015	+	0.141838i
$463$	4.85644	+	18.1245i	0.225698	+	0.842316i	0.982124	+	0.188236i	$0.0602771\pi$
$463$	4.85644	+	18.1245i	0.225698	+	0.842316i	−0.756426	+	0.654079i	$0.773056\pi$
$464$	−2.84283	+	4.92393i	−0.131975	+	0.228588i
$465$	27.0679	+	0.551561i	1.25524	+	0.0255780i
$466$	4.00916	+	6.94407i	0.185721	+	0.321678i
$467$	−16.8295	+	16.8295i	−0.778777	+	0.778777i	−0.979623	−	0.200846i	$-0.935631\pi$
$467$	−16.8295	+	16.8295i	−0.778777	+	0.778777i	0.200846	+	0.979623i	$0.435631\pi$
$468$	−3.10834	−	1.02492i	−0.143683	−	0.0473771i
$469$			6.80460i			0.314207i
$470$	−17.4449	+	17.7256i	−0.804675	+	0.817620i
$471$	7.68281	−	12.4763i	0.354005	−	0.574875i
$472$	21.7552	−	5.82929i	1.00136	−	0.268315i
$473$	1.63578	−	0.438306i	0.0752133	−	0.0201533i
$474$	−9.42793	+	15.3102i	−0.433039	+	0.703220i
$475$	3.70557	−	6.66153i	0.170023	−	0.305652i
$476$		−	0.646194i		−	0.0296182i
$477$	−14.7372	+	13.1539i	−0.674772	+	0.602276i
$478$	12.9000	−	12.9000i	0.590033	−	0.590033i
$479$	8.91724	+	15.4451i	0.407439	+	0.705705i	0.994602	−	0.103764i	$-0.0330886\pi$
$479$	8.91724	+	15.4451i	0.407439	+	0.705705i	−0.587163	+	0.809469i	$0.699755\pi$
$480$	−3.09134	+	2.96787i	−0.141100	+	0.135464i
$481$	16.7285	−	28.9747i	0.762756	−	1.32113i
$482$	−1.78475	−	6.66078i	−0.0812931	−	0.303390i
$483$	−3.86810	−	4.09392i	−0.176005	−	0.186280i
$484$	1.73861	−	1.00378i	0.0790275	−	0.0456265i
$485$	7.71328	+	4.37158i	0.350242	+	0.198503i
$486$	19.4277	−	7.80094i	0.881259	−	0.353858i
$487$	−21.8232	−	21.8232i	−0.988904	−	0.988904i	0.0110354	−	0.999939i	$-0.496487\pi$
$487$	−21.8232	−	21.8232i	−0.988904	−	0.988904i	−0.999939	+	0.0110354i	$0.996487\pi$
$488$	10.1385	−	37.8372i	0.458946	−	1.71281i
$489$	−0.291174	+	10.2666i	−0.0131674	+	0.464273i
$490$	7.25773	−	4.26783i	0.327871	−	0.192801i
$491$	35.1670	+	20.3037i	1.58707	+	0.916292i	0.993787	+	0.111295i	$0.0354997\pi$
$491$	35.1670	+	20.3037i	1.58707	+	0.916292i	0.593278	+	0.804998i	$0.297834\pi$
$492$	1.17221	+	0.349997i	0.0528472	+	0.0157791i
$493$	−2.47249	−	0.662503i	−0.111356	−	0.0298376i
$494$	−11.3775			−0.511896
$495$	5.77107	−	1.24860i	0.259391	−	0.0561206i
$496$	−24.9471			−1.12016
$497$	11.6703	+	3.12705i	0.523484	+	0.140267i
$498$	−5.34683	−	22.4864i	−0.239597	−	1.00764i
$499$	−37.3397	−	21.5581i	−1.67156	−	0.965073i	−0.966768	−	0.255655i	$-0.917709\pi$
$499$	−37.3397	−	21.5581i	−1.67156	−	0.965073i	−0.704788	−	0.709418i	$-0.748958\pi$
$500$	2.10609	−	0.618720i	0.0941870	−	0.0276700i
$501$	8.79988	+	5.41892i	0.393150	+	0.242100i
$502$	−0.904518	+	3.37571i	−0.0403706	+	0.150665i
$503$	28.0936	+	28.0936i	1.25263	+	1.25263i	0.954537	+	0.298093i	$0.0963506\pi$
$503$	28.0936	+	28.0936i	1.25263	+	1.25263i	0.298093	+	0.954537i	$0.403649\pi$
$504$	−8.15932	−	16.1872i	−0.363445	−	0.721033i
$505$	1.53591	+	5.55443i	0.0683471	+	0.247169i
$506$	−1.62510	+	0.938252i	−0.0722445	+	0.0417104i
$507$	8.85909	−	29.6708i	0.393446	−	1.31773i
$508$	−0.136706	−	0.510193i	−0.00606534	−	0.0226361i
$509$	−7.39188	+	12.8031i	−0.327639	+	0.567488i	−0.982043	−	0.188658i	$-0.939586\pi$
$509$	−7.39188	+	12.8031i	−0.327639	+	0.567488i	0.654404	+	0.756145i	$0.272920\pi$
$510$	7.15081	+	4.32512i	0.316643	+	0.191519i
$511$	2.30168	+	3.98663i	0.101820	+	0.176358i
$512$	17.6794	−	17.6794i	0.781325	−	0.781325i
$513$	−6.05725	+	5.10544i	−0.267434	+	0.225411i
$514$		−	14.1761i		−	0.625282i
$515$	−29.2098	+	0.233085i	−1.28714	+	0.0102710i
$516$	−0.654003	−	0.0185484i	−0.0287909	−	0.000816546i
$517$	7.04114	−	1.88667i	0.309669	−	0.0829755i
$518$	16.0001	−	4.28721i	0.703003	−	0.188369i
$519$	11.2484	+	20.8248i	0.493750	+	0.914108i
$520$	−26.1220	−	25.7084i	−1.14553	−	1.12739i
$521$			28.4812i			1.24778i	0.781511	+	0.623892i	$0.214449\pi$
$521$			28.4812i			1.24778i	−0.781511	+	0.623892i	$0.785551\pi$
$522$	−6.28437	+	1.30725i	−0.275059	+	0.0572170i
$523$	15.4076	−	15.4076i	0.673726	−	0.673726i	−0.284847	−	0.958573i	$-0.591943\pi$
$523$	15.4076	−	15.4076i	0.673726	−	0.673726i	0.958573	+	0.284847i	$0.0919428\pi$
$524$	2.09829	+	3.63434i	0.0916641	+	0.158767i
$525$	−0.219881	+	17.7391i	−0.00959638	+	0.774199i
$526$	−5.64872	+	9.78386i	−0.246296	+	0.426597i
$527$	−2.90687	−	10.8486i	−0.126625	−	0.472572i
$528$	−5.29325	+	1.25863i	−0.230359	+	0.0547750i
$529$	−17.7363	+	10.2401i	−0.771145	+	0.445221i
$530$	−19.0586	+	5.27010i	−0.827855	+	0.228918i
$531$	19.1568	+	12.5593i	0.831335	+	0.545028i
$532$	0.433573	+	0.433573i	0.0187978	+	0.0187978i
$533$	−5.17380	+	19.3089i	−0.224102	+	0.836361i
$534$	−9.47128	+	5.11586i	−0.409862	+	0.221385i
$535$	14.7957	+	25.1611i	0.639674	+	1.08781i
$536$	−8.48544	−	4.89907i	−0.366515	−	0.211608i
$537$	−21.7010	+	20.5040i	−0.936466	+	0.884813i
$538$	−34.7283	−	9.30542i	−1.49724	−	0.401185i
$539$	−2.46780			−0.106296
$540$	−2.27443	−	0.175664i	−0.0978758	−	0.00755939i
$541$	−1.11754			−0.0480466			−0.0240233	−	0.999711i	$-0.507648\pi$
$541$	−1.11754			−0.0480466			−0.0240233	+	0.999711i	$0.507648\pi$
$542$	−24.1093	−	6.46008i	−1.03558	−	0.277484i
$543$	−18.5960	+	17.5703i	−0.798033	+	0.754015i
$544$	1.53959	+	0.888885i	0.0660096	+	0.0381106i
$545$	−17.4340	−	4.52264i	−0.746791	−	0.193729i
$546$	23.2973	−	12.5839i	0.997033	−	0.538542i
$547$	8.33894	−	31.1213i	0.356547	−	1.33065i	−0.521979	−	0.852958i	$-0.674806\pi$
$547$	8.33894	−	31.1213i	0.356547	−	1.33065i	0.878526	−	0.477694i	$-0.158527\pi$
$548$	−0.952326	−	0.952326i	−0.0406813	−	0.0406813i
$549$	35.5761	−	17.9325i	1.51835	−	0.765342i
$550$	5.73290	+	1.43847i	0.244452	+	0.0613367i
$551$	2.10347	−	1.21444i	0.0896109	−	0.0517369i
$552$	7.89008	−	1.87611i	0.335824	−	0.0798526i
$553$	4.09814	+	15.2945i	0.174271	+	0.650387i
$554$	18.2979	−	31.6928i	0.777402	−	1.34650i
$555$	6.49305	−	22.3969i	0.275615	−	0.950693i
$556$	−0.141537	−	0.245149i	−0.00600250	−	0.0103966i
$557$	−30.4033	+	30.4033i	−1.28823	+	1.28823i	−0.352366	+	0.935862i	$0.614623\pi$
$557$	−30.4033	+	30.4033i	−1.28823	+	1.28823i	−0.935862	+	0.352366i	$0.885377\pi$
$558$	−18.7544	−	21.0119i	−0.793937	−	0.889503i
$559$		−	10.6910i		−	0.452182i
$560$	−0.130441	−	16.3466i	−0.00551212	−	0.690768i
$561$	−1.16411	−	2.15519i	−0.0491489	−	0.0909922i
$562$	−34.0105	+	9.11308i	−1.43465	+	0.384412i
$563$	1.12220	−	0.300692i	0.0472950	−	0.0126727i	−0.235094	−	0.971973i	$-0.575540\pi$
$563$	1.12220	−	0.300692i	0.0472950	−	0.0126727i	0.282389	+	0.959300i	$0.408873\pi$
$564$	−2.81512	−	0.0798405i	−0.118538	−	0.00336189i
$565$	−0.214165	−	26.8388i	−0.00901001	−	1.12912i
$566$		−	4.78361i		−	0.201070i
$567$	6.75644	−	17.1538i	0.283744	−	0.720393i
$568$	−12.3017	+	12.3017i	−0.516167	+	0.516167i
$569$	0.145367	+	0.251784i	0.00609412	+	0.0105553i	0.869056	−	0.494713i	$-0.164727\pi$
$569$	0.145367	+	0.251784i	0.00609412	+	0.0105553i	−0.862962	+	0.505268i	$0.831394\pi$
$570$	−7.69993	+	1.89594i	−0.322515	+	0.0794121i
$571$	−13.0283	+	22.5656i	−0.545215	+	0.944341i	0.453378	+	0.891318i	$0.350219\pi$
$571$	−13.0283	+	22.5656i	−0.545215	+	0.944341i	−0.998593	+	0.0530223i	$0.983115\pi$
$572$	0.248542	+	0.927572i	0.0103921	+	0.0387837i
$573$	−2.61375	+	8.75395i	−0.109191	+	0.365702i
$574$	−8.57106	+	4.94851i	−0.357749	+	0.206547i
$575$	−7.69838	−	1.93164i	−0.321044	−	0.0805551i
$576$	25.8292	+	1.46627i	1.07621	+	0.0610948i
$577$	−2.52834	−	2.52834i	−0.105256	−	0.105256i	0.652517	−	0.757774i	$-0.273713\pi$
$577$	−2.52834	−	2.52834i	−0.105256	−	0.105256i	−0.757774	+	0.652517i	$0.773713\pi$
$578$	−5.01183	+	18.7044i	−0.208465	+	0.778000i
$579$	−13.7258	−	8.45230i	−0.570427	−	0.351266i
$580$	0.677018	+	0.175629i	0.0281116	+	0.00729258i
$581$	−17.6274	−	10.1772i	−0.731309	−	0.422222i
$582$	−2.13360	−	8.97298i	−0.0884408	−	0.371942i
$583$	5.59831	+	1.50006i	0.231858	+	0.0621262i
$584$	−6.62852			−0.274290
$585$	1.81566	−	37.2317i	0.0750682	−	1.53934i
$586$	4.00174			0.165310
$587$	40.0121	+	10.7212i	1.65147	+	0.442511i	0.960025	−	0.279914i	$-0.0903059\pi$
$587$	40.0121	+	10.7212i	1.65147	+	0.442511i	0.691449	+	0.722425i	$0.256973\pi$
$588$	0.913566	+	0.272772i	0.0376748	+	0.0112489i
$589$	9.22943	+	5.32861i	0.380292	+	0.219562i
$590$	11.6231	+	19.7659i	0.478517	+	0.813750i
$591$	−0.659386	+	23.2495i	−0.0271235	+	0.956358i
$592$	−5.56137	+	20.7553i	−0.228571	+	0.853038i
$593$	−26.6583	−	26.6583i	−1.09473	−	1.09473i	−0.995017	−	0.0997087i	$-0.968209\pi$
$593$	−26.6583	−	26.6583i	−1.09473	−	1.09473i	−0.0997087	−	0.995017i	$-0.531791\pi$
$594$	−5.03939	−	3.51208i	−0.206769	−	0.144102i
$595$	7.09335	−	1.96145i	0.290799	−	0.0804117i
$596$	2.81726	−	1.62655i	0.115400	−	0.0666260i
$597$	20.9764	+	22.2009i	0.858506	+	0.908624i
$598$	3.06608	+	11.4428i	0.125382	+	0.467930i
$599$	13.2427	−	22.9370i	0.541080	−	0.937178i	−0.457762	−	0.889075i	$-0.651349\pi$
$599$	13.2427	−	22.9370i	0.541080	−	0.937178i	0.998842	−	0.0481037i	$-0.0153178\pi$
$600$	−21.9627	−	13.0457i	−0.896622	−	0.532590i
$601$	4.26710	+	7.39084i	0.174059	+	0.301479i	0.939835	−	0.341628i	$-0.110978\pi$
$601$	4.26710	+	7.39084i	0.174059	+	0.301479i	−0.765776	+	0.643107i	$0.777645\pi$
$602$	3.74279	−	3.74279i	0.152545	−	0.152545i
$603$	−2.02950	−	9.75641i	−0.0826475	−	0.397312i
$604$		−	0.00111412i		−	4.53329e-5i
$605$	16.2960	+	16.0380i	0.662527	+	0.652037i
$606$	3.14351	−	5.10480i	0.127696	−	0.207368i
$607$	44.4113	−	11.9000i	1.80260	−	0.483005i	0.808220	−	0.588881i	$-0.200431\pi$
$607$	44.4113	−	11.9000i	1.80260	−	0.483005i	0.994379	+	0.105876i	$0.0337645\pi$
$608$	−1.62942	+	0.436602i	−0.0660818	+	0.0177066i
$609$	−2.96400	+	4.81329i	−0.120107	+	0.195045i
$610$	39.8794	−	0.318225i	1.61467	−	0.0128846i
$611$		−	46.0190i		−	1.86173i
$612$	0.192730	+	0.926510i	0.00779064	+	0.0374520i
$613$	17.3219	−	17.3219i	0.699625	−	0.699625i	−0.264705	−	0.964330i	$-0.585274\pi$
$613$	17.3219	−	17.3219i	0.699625	−	0.699625i	0.964330	+	0.264705i	$0.0852744\pi$
$614$	20.7039	+	35.8602i	0.835542	+	1.44720i
$615$	−0.283848	+	13.9299i	−0.0114458	+	0.561706i
$616$	−2.65929	+	4.60603i	−0.107146	+	0.185582i
$617$	9.74553	+	36.3708i	0.392340	+	1.46423i	0.826263	+	0.563284i	$0.190462\pi$
$617$	9.74553	+	36.3708i	0.392340	+	1.46423i	−0.433923	+	0.900950i	$0.642871\pi$
$618$	20.8694	+	22.0878i	0.839492	+	0.888500i
$619$	−8.57434	+	4.95040i	−0.344632	+	0.198973i	−0.662318	−	0.749223i	$-0.730427\pi$
$619$	−8.57434	+	4.95040i	−0.344632	+	0.198973i	0.317687	+	0.948196i	$0.397094\pi$
$620$	0.817915	+	2.95789i	0.0328483	+	0.118792i
$621$	6.76710	+	4.71617i	0.271554	+	0.189253i
$622$	32.2255	+	32.2255i	1.29213	+	1.29213i
$623$	−2.45353	+	9.15670i	−0.0982986	+	0.366855i
$624$	−0.973765	+	34.3344i	−0.0389818	+	1.37447i
$625$	13.1846	+	21.2407i	0.527383	+	0.849628i
$626$	−26.9753	−	15.5742i	−1.07815	−	0.622469i
$627$	2.22713	+	0.664976i	0.0889431	+	0.0265566i
$628$	1.60427	+	0.429864i	0.0640175	+	0.0171534i
$629$	−9.67378			−0.385719
$630$	13.6700	−	12.3987i	0.544624	−	0.493976i
$631$	−22.0279			−0.876918			−0.438459	−	0.898751i	$-0.644476\pi$
$631$	−22.0279			−0.876918			−0.438459	+	0.898751i	$0.644476\pi$
$632$	−22.0230	−	5.90104i	−0.876027	−	0.234731i
$633$	0.0493675	+	0.207617i	0.00196218	+	0.00825205i
$634$	−4.65268	−	2.68622i	−0.184781	−	0.106684i
$635$	5.18549	−	3.04927i	0.205780	−	0.121007i
$636$	−1.90665	−	1.17411i	−0.0756038	−	0.0465564i
$637$	−4.03223	+	15.0485i	−0.159763	+	0.596242i
$638$	1.33171	+	1.33171i	0.0527227	+	0.0527227i
$639$	−17.6655	−	1.00284i	−0.698836	−	0.0396716i
$640$	18.2251	+	10.3293i	0.720412	+	0.408300i
$641$	21.8054	−	12.5894i	0.861263	−	0.497251i	−0.00317173	−	0.999995i	$-0.501010\pi$
$641$	21.8054	−	12.5894i	0.861263	−	0.497251i	0.864435	+	0.502744i	$0.167676\pi$
$642$	8.68736	−	29.0956i	0.342863	−	1.14831i
$643$	−8.05166	−	30.0492i	−0.317526	−	1.18502i	−0.921614	−	0.388107i	$-0.873129\pi$
$643$	−8.05166	−	30.0492i	−0.317526	−	1.18502i	0.604088	−	0.796918i	$-0.293538\pi$
$644$	0.319219	−	0.552904i	0.0125790	−	0.0217875i
$645$	−1.78155	−	7.23537i	−0.0701485	−	0.284893i
$646$	1.64484	+	2.84895i	0.0647154	+	0.112090i
$647$	7.86580	−	7.86580i	0.309237	−	0.309237i	−0.535377	−	0.844613i	$-0.679830\pi$
$647$	7.86580	−	7.86580i	0.309237	−	0.309237i	0.844613	+	0.535377i	$0.179830\pi$
$648$	16.5267	+	20.7755i	0.649230	+	0.816140i
$649$		−	6.72090i		−	0.263818i
$650$	18.1389	−	32.6084i	0.711465	−	1.27901i
$651$	−24.7925	−	0.703147i	−0.971695	−	0.0275585i
$652$	−1.12456	+	0.301325i	−0.0440411	+	0.0118008i
$653$	0.279676	−	0.0749391i	0.0109446	−	0.00293259i	−0.253343	−	0.967377i	$-0.581530\pi$
$653$	0.279676	−	0.0749391i	0.0109446	−	0.00293259i	0.264287	+	0.964444i	$0.414863\pi$
$654$	8.90457	+	16.4855i	0.348196	+	0.644635i
$655$	−33.5255	+	34.0648i	−1.30995	+	1.33102i
$656$		−	12.8384i		−	0.501256i
$657$	−4.48917	−	5.02953i	−0.175139	−	0.196221i
$658$	16.1106	−	16.1106i	0.628058	−	0.628058i
$659$	−13.4009	−	23.2111i	−0.522026	−	0.904175i	−0.999672	−	0.0256228i	$-0.991843\pi$
$659$	−13.4009	−	23.2111i	−0.522026	−	0.904175i	0.477646	−	0.878552i	$-0.341490\pi$
$660$	0.322776	+	0.586336i	0.0125641	+	0.0228231i
$661$	−12.6438	+	21.8997i	−0.491787	+	0.851800i	−0.999955	−	0.00945786i	$-0.996989\pi$
$661$	−12.6438	+	21.8997i	−0.491787	+	0.851800i	0.508168	+	0.861258i	$0.330323\pi$
$662$	−2.07289	−	7.73611i	−0.0805650	−	0.300673i
$663$	−15.0443	+	3.57724i	−0.584271	+	0.138928i
$664$	25.3823	−	14.6545i	0.985024	−	0.568704i
$665$	−3.44332	+	6.07544i	−0.133526	+	0.235596i
$666$	−21.6622	+	10.9191i	−0.839393	+	0.423106i
$667$	−1.78827	−	1.78827i	−0.0692421	−	0.0692421i
$668$	−0.303196	+	1.13154i	−0.0117310	+	0.0437807i
$669$	3.81556	−	2.06095i	0.147518	−	0.0796811i
$670$	2.50486	−	9.65579i	0.0967710	−	0.373036i
$671$	−10.1231	−	5.84458i	−0.390799	−	0.225628i
$672$	2.85362	−	2.69622i	0.110081	−	0.104009i
$673$	−23.5227	−	6.30290i	−0.906735	−	0.242959i	−0.224829	−	0.974398i	$-0.572182\pi$
$673$	−23.5227	−	6.30290i	−0.906735	−	0.242959i	−0.681906	+	0.731439i	$0.738849\pi$
$674$	13.3044			0.512466
$675$	−4.97550	−	25.4999i	−0.191507	−	0.981491i
$676$	3.51002			0.135001
$677$	−0.896681	−	0.240265i	−0.0344623	−	0.00923414i	0.241547	−	0.970389i	$-0.422345\pi$
$677$	−0.896681	−	0.240265i	−0.0344623	−	0.00923414i	−0.276009	+	0.961155i	$0.589012\pi$
$678$	−20.2949	+	19.1754i	−0.779420	+	0.736429i
$679$	−7.03407	−	4.06112i	−0.269943	−	0.155852i
$680$	−2.66100	+	10.2577i	−0.102045	+	0.393365i
$681$	−23.2386	+	12.5522i	−0.890503	+	0.481000i
$682$	−2.13874	+	7.98188i	−0.0818966	+	0.305642i
$683$	22.2024	+	22.2024i	0.849550	+	0.849550i	0.990077	−	0.140526i	$-0.0448795\pi$
$683$	22.2024	+	22.2024i	0.849550	+	0.849550i	−0.140526	+	0.990077i	$0.544880\pi$
$684$	−0.750970	−	0.492340i	−0.0287141	−	0.0188251i
$685$	7.56311	−	13.3445i	0.288972	−	0.509866i
$686$	−23.3578	+	13.4856i	−0.891805	+	0.514884i
$687$	−37.1801	+	8.84071i	−1.41851	+	0.337294i
$688$	1.77711	+	6.63225i	0.0677515	+	0.252852i
$689$	18.2945	−	31.6871i	0.696966	−	1.20718i
$690$	3.98186	+	7.23321i	0.151587	+	0.275363i
$691$	−4.05877	−	7.02999i	−0.154403	−	0.267433i	0.778439	−	0.627721i	$-0.216012\pi$
$691$	−4.05877	−	7.02999i	−0.154403	−	0.267433i	−0.932841	+	0.360287i	$0.882679\pi$
$692$	−1.89711	+	1.89711i	−0.0721173	+	0.0721173i
$693$	−5.29593	+	1.10164i	−0.201176	+	0.0418479i
$694$		−	14.2473i		−	0.540821i
$695$	2.26141	−	2.29779i	0.0857802	−	0.0871602i
$696$	−3.86828	−	7.16156i	−0.146627	−	0.271458i
$697$	5.58297	−	1.49595i	0.211470	−	0.0566633i
$698$	12.1157	−	3.24640i	0.458586	−	0.122878i
$699$	−10.3369	−	0.293168i	−0.390979	−	0.0110887i
$700$	−1.93388	+	0.551405i	−0.0730937	+	0.0208411i
$701$		−	19.6359i		−	0.741637i	−0.928705	−	0.370819i	$-0.879077\pi$
$701$		−	19.6359i		−	0.741637i	0.928705	−	0.370819i	$-0.120923\pi$
$702$	−29.6504	+	24.9913i	−1.11908	+	0.943236i
$703$	6.49076	−	6.49076i	0.244804	−	0.244804i
$704$	−3.79526	−	6.57359i	−0.143039	−	0.247752i
$705$	−7.66859	−	31.1443i	−0.288816	−	1.17296i
$706$	−12.8937	+	22.3325i	−0.485260	+	0.840496i
$707$	−1.36642	−	5.09956i	−0.0513896	−	0.191789i
$708$	−0.742876	+	2.48804i	−0.0279190	+	0.0935061i
$709$	2.68383	−	1.54951i	0.100793	−	0.0581931i	−0.448756	−	0.893654i	$-0.648133\pi$
$709$	2.68383	−	1.54951i	0.100793	−	0.0581931i	0.549549	+	0.835461i	$0.314799\pi$
$710$	−15.4092	−	8.73329i	−0.578295	−	0.327754i
$711$	−10.4375	−	20.7069i	−0.391438	−	0.776569i
$712$	−9.65210	−	9.65210i	−0.361728	−	0.361728i
$713$	2.87199	−	10.7184i	0.107557	−	0.401408i
$714$	−6.51914	−	4.01445i	−0.243973	−	0.150237i
$715$	−9.42765	+	5.54383i	−0.352574	+	0.207327i
$716$	−2.93083	−	1.69211i	−0.109530	−	0.0632373i
$717$	5.44280	+	22.8900i	0.203265	+	0.854841i
$718$	−16.3380	−	4.37774i	−0.609727	−	0.163376i
$719$	20.3126			0.757533			0.378767	−	0.925492i	$-0.376348\pi$
$719$	20.3126			0.757533			0.378767	+	0.925492i	$0.376348\pi$
$720$	5.06245	+	23.3987i	0.188666	+	0.872020i
$721$	26.7604			0.996608
$722$	21.6325	+	5.79640i	0.805077	+	0.215720i
$723$	8.52158	+	2.54437i	0.316921	+	0.0946261i
$724$	−2.51149	−	1.45001i	−0.0933388	−	0.0538892i
$725$	0.127122	+	7.96481i	0.00472118	+	0.295806i
$726$	0.674315	−	23.7759i	0.0250262	−	0.882407i
$727$	4.57247	−	17.0647i	0.169584	−	0.632895i	−0.827827	−	0.560983i	$-0.810423\pi$
$727$	4.57247	−	17.0647i	0.169584	−	0.632895i	0.997411	−	0.0719119i	$-0.0229101\pi$
$728$	23.7421	+	23.7421i	0.879941	+	0.879941i
$729$	−4.57117	+	26.6102i	−0.169303	+	0.985564i
$730$	−1.79858	−	6.50434i	−0.0665685	−	0.240736i
$731$	−2.67706	+	1.54560i	−0.0990147	+	0.0571662i
$732$	3.10150	+	3.28256i	0.114635	+	0.121327i
$733$	−6.82693	−	25.4785i	−0.252158	−	0.941068i	−0.969649	−	0.244500i	$-0.921376\pi$
$733$	−6.82693	−	25.4785i	−0.252158	−	0.941068i	0.717491	−	0.696568i	$-0.245291\pi$
$734$	−18.9970	+	32.9038i	−0.701192	+	1.21450i
$735$	−0.221218	+	10.8563i	−0.00815975	+	0.400440i
$736$	0.878218	+	1.52112i	0.0323715	+	0.0560692i
$737$	−2.06746	+	2.06746i	−0.0761558	+	0.0761558i
$738$	10.8133	−	9.65150i	0.398041	−	0.355277i
$739$			6.41459i			0.235965i	0.993016	+	0.117982i	$0.0376426\pi$
$739$			6.41459i			0.235965i	−0.993016	+	0.117982i	$0.962357\pi$
$740$	2.64322	−	0.0210921i	0.0971667	−	0.000775361i
$741$	7.69396	−	12.4944i	0.282645	−	0.458992i
$742$	17.4979	−	4.68854i	0.642368	−	0.172122i
$743$	−18.4970	+	4.95625i	−0.678588	+	0.181827i	−0.581620	−	0.813460i	$-0.697581\pi$
$743$	−18.4970	+	4.95625i	−0.678588	+	0.181827i	−0.0969677	+	0.995288i	$0.530914\pi$
$744$	18.7266	−	30.4104i	0.686549	−	1.11490i
$745$	26.4063	+	25.9882i	0.967453	+	0.952135i
$746$			3.13856i			0.114911i
$747$	28.3096	+	9.33459i	1.03579	+	0.341535i
$748$	0.196335	−	0.196335i	0.00717870	−	0.00717870i
$749$	−13.3702	−	23.1579i	−0.488536	−	0.846170i
$750$	6.84200	−	25.0911i	0.249835	−	0.916196i
$751$	−1.96958	+	3.41141i	−0.0718709	+	0.124484i	−0.899721	−	0.436465i	$-0.856230\pi$
$751$	−1.96958	+	3.41141i	−0.0718709	+	0.124484i	0.827850	+	0.560949i	$0.189564\pi$
$752$	7.64946	+	28.5482i	0.278947	+	1.04105i
$753$	−3.09541	−	3.27612i	−0.112803	−	0.119388i
$754$	10.2966	−	5.94472i	0.374979	−	0.216494i
$755$	0.0122298	−	0.00338180i	0.000445090	−	0.000123076i
$756$	2.08229	+	0.177550i	0.0757321	+	0.00645743i
$757$	17.3710	+	17.3710i	0.631361	+	0.631361i	0.948409	−	0.317049i	$-0.102692\pi$
$757$	17.3710	+	17.3710i	0.631361	+	0.631361i	−0.317049	+	0.948409i	$0.602692\pi$
$758$	−6.41725	+	23.9495i	−0.233085	+	0.869885i
$759$	0.0686093	−	2.41912i	0.00249036	−	0.0878085i
$760$	−5.09711	−	8.66798i	−0.184892	−	0.314421i
$761$	7.11860	+	4.10993i	0.258049	+	0.148985i	0.623444	−	0.781868i	$-0.285733\pi$
$761$	7.11860	+	4.10993i	0.258049	+	0.148985i	−0.365395	+	0.930853i	$0.619066\pi$
$762$	−5.99637	−	1.79039i	−0.217226	−	0.0648591i
$763$	15.9380	+	4.27057i	0.576994	+	0.154605i
$764$	−1.03558			−0.0374660
$765$	−9.58540	+	4.92794i	−0.346561	+	0.178170i
$766$	−32.5079			−1.17456
$767$	−40.9835	−	10.9815i	−1.47983	−	0.396519i
$768$	1.86921	+	7.86108i	0.0674495	+	0.283662i
$769$	1.91615	+	1.10629i	0.0690983	+	0.0398939i	0.534151	−	0.845389i	$-0.320631\pi$
$769$	1.91615	+	1.10629i	0.0690983	+	0.0398939i	−0.465053	+	0.885283i	$0.653965\pi$
$770$	−5.24131	−	1.35967i	−0.188884	−	0.0489992i
$771$	15.5677	+	9.58654i	0.560659	+	0.345251i
$772$	0.472918	−	1.76495i	0.0170207	−	0.0635221i
$773$	−8.23173	−	8.23173i	−0.296075	−	0.296075i	0.543400	−	0.839474i	$-0.317137\pi$
$773$	−8.23173	−	8.23173i	−0.296075	−	0.296075i	−0.839474	+	0.543400i	$0.817137\pi$
$774$	−4.25009	+	6.48270i	−0.152766	+	0.233016i
$775$	−29.9864	+	17.9567i	−1.07714	+	0.645024i
$776$	10.1286	−	5.84773i	0.363595	−	0.209921i
$777$	−6.11191	+	20.4700i	−0.219264	+	0.734356i
$778$	−9.41596	−	35.1408i	−0.337579	−	1.25986i
$779$	−2.74224	+	4.74970i	−0.0982511	+	0.170176i
$780$	4.10283	−	1.01023i	0.146905	−	0.0361721i
$781$	2.59572	+	4.49591i	0.0928820	+	0.160876i
$782$	2.42204	−	2.42204i	0.0866119	−	0.0866119i
$783$	2.81419	−	7.78531i	0.100571	−	0.278224i
$784$		−	10.0057i		−	0.357346i
$785$	0.150937	+	18.9151i	0.00538717	+	0.675109i
$786$	49.7006	+	1.40957i	1.77276	+	0.0502778i
$787$	33.8541	−	9.07119i	1.20677	−	0.323353i	0.401276	−	0.915957i	$-0.368567\pi$
$787$	33.8541	−	9.07119i	1.20677	−	0.323353i	0.805494	+	0.592604i	$0.201900\pi$
$788$	−2.54665	+	0.682372i	−0.0907205	+	0.0243085i
$789$	−6.92440	−	12.8195i	−0.246515	−	0.456387i
$790$	−0.185222	−	23.2116i	−0.00658989	−	0.825831i
$791$			24.5882i			0.874256i
$792$	2.43912	−	7.39725i	0.0866703	−	0.262850i
$793$	−52.1803	+	52.1803i	−1.85298	+	1.85298i
$794$	−17.3076	−	29.9776i	−0.614223	−	1.06387i
$795$	7.10088	−	24.4935i	0.251842	−	0.868694i
$796$	−1.73110	+	2.99835i	−0.0613571	+	0.106274i
$797$	−6.77343	−	25.2788i	−0.239927	−	0.895421i	−0.975866	−	0.218372i	$-0.929925\pi$
$797$	−6.77343	−	25.2788i	−0.239927	−	0.895421i	0.735938	−	0.677049i	$-0.236741\pi$
$798$	7.06766	−	1.68056i	0.250192	−	0.0594910i
$799$	−11.5233	+	6.65297i	−0.407664	+	0.235365i
$800$	1.34643	−	5.36608i	0.0476036	−	0.189719i
$801$	0.786842	−	13.8606i	0.0278017	−	0.489741i
$802$	−12.2041	−	12.2041i	−0.430941	−	0.430941i
$803$	−0.511942	+	1.91059i	−0.0180660	+	0.0674233i
$804$	0.993882	−	0.536840i	0.0350515	−	0.0189329i
$805$	7.03825	+	1.82583i	0.248066	+	0.0643520i
$806$	45.1784	+	26.0837i	1.59134	+	0.918761i
$807$	33.7038	−	31.8447i	1.18643	−	1.12099i
$808$	7.34301	+	1.96755i	0.258326	+	0.0692183i
$809$	40.3389			1.41824			0.709120	−	0.705088i	$-0.249092\pi$
$809$	40.3389			1.41824			0.709120	+	0.705088i	$0.249092\pi$
$810$	−15.9020	+	21.8543i	−0.558739	+	0.767882i
$811$	−4.50040			−0.158030			−0.0790152	−	0.996873i	$-0.525178\pi$
$811$	−4.50040			−0.158030			−0.0790152	+	0.996873i	$0.525178\pi$
$812$	−0.618923	−	0.165840i	−0.0217199	−	0.00581984i
$813$	23.3981	−	22.1075i	0.820606	−	0.775343i
$814$	6.16394	+	3.55875i	0.216046	+	0.124734i
$815$	−6.72116	−	11.4298i	−0.235432	−	0.400368i
$816$	8.73818	−	4.71988i	0.305898	−	0.165229i
$817$	0.759168	−	2.83326i	0.0265599	−	0.0991231i
$818$	−24.3930	−	24.3930i	−0.852880	−	0.852880i
$819$	−1.93546	+	34.0942i	−0.0676306	+	1.19135i
$820$	−1.52221	+	0.420920i	−0.0531577	+	0.0146992i
$821$	13.3109	−	7.68503i	0.464552	−	0.268209i	−0.249404	−	0.968399i	$-0.580235\pi$
$821$	13.3109	−	7.68503i	0.464552	−	0.268209i	0.713956	+	0.700190i	$0.246901\pi$
$822$	−15.5238	+	3.69127i	−0.541456	+	0.128748i
$823$	3.77065	+	14.0723i	0.131437	+	0.490528i	0.999987	−	0.00507263i	$-0.00161467\pi$
$823$	3.77065	+	14.0723i	0.131437	+	0.490528i	−0.868551	+	0.495601i	$0.834948\pi$
$824$	−19.2665	+	33.3706i	−0.671182	+	1.16252i
$825$	−5.45653	+	5.32292i	−0.189972	+	0.185320i
$826$	−10.5033	−	18.1923i	−0.365457	−	0.632989i
$827$	−3.31824	+	3.31824i	−0.115387	+	0.115387i	−0.762443	−	0.647056i	$-0.776000\pi$
$827$	−3.31824	+	3.31824i	−0.115387	+	0.115387i	0.647056	+	0.762443i	$0.276000\pi$
$828$	−0.292790	+	0.887961i	−0.0101752	+	0.0308588i
$829$			33.9539i			1.17927i	0.807671	+	0.589633i	$0.200728\pi$
$829$			33.9539i			1.17927i	−0.807671	+	0.589633i	$0.799272\pi$
$830$	21.2672	+	20.9304i	0.738194	+	0.726506i
$831$	22.4302	+	41.5263i	0.778094	+	1.44053i
$832$	−46.2865	+	12.4024i	−1.60469	+	0.429977i
$833$	4.35112	−	1.16588i	0.150757	−	0.0403953i
$834$	−3.35248	−	0.0950807i	−0.116087	−	0.00329237i
$835$	−13.3414	+	0.106460i	−0.461698	+	0.00368421i
$836$			0.263467i			0.00911220i
$837$	35.7571	−	6.38629i	1.23595	−	0.220743i
$838$	−11.6473	+	11.6473i	−0.402349	+	0.402349i
$839$	5.71824	+	9.90428i	0.197416	+	0.341934i	0.947690	−	0.319193i	$-0.103412\pi$
$839$	5.71824	+	9.90428i	0.197416	+	0.341934i	−0.750274	+	0.661127i	$0.770079\pi$
$840$	20.0243	+	12.1116i	0.690905	+	0.417889i
$841$	13.2309	−	22.9166i	0.456238	−	0.790228i
$842$	−5.03357	−	18.7855i	−0.173468	−	0.647392i
$843$	12.9918	−	43.5119i	0.447460	−	1.49863i
$844$	−0.0209495	+	0.0120952i	−0.000721111	+	0.000416334i
$845$	10.6543	+	38.5299i	0.366519	+	1.32547i
$846$	−18.2943	+	27.9044i	−0.628972	+	0.959374i
$847$	−14.8113	−	14.8113i	−0.508923	−	0.508923i
$848$	−6.08198	+	22.6983i	−0.208856	+	0.779462i
$849$	5.25321	+	3.23490i	0.180290	+	0.111021i
$850$	−10.7876	+	0.172174i	−0.370010	+	0.00590552i
$851$	−8.27720	−	4.77884i	−0.283739	−	0.163817i
$852$	−0.463975	−	1.95127i	−0.0158955	−	0.0668494i
$853$	23.0994	+	6.18947i	0.790909	+	0.211923i	0.631589	−	0.775304i	$-0.282403\pi$
$853$	23.0994	+	6.18947i	0.790909	+	0.211923i	0.159320	+	0.987227i	$0.449070\pi$
$854$	−36.5353			−1.25021
$855$	3.12499	−	9.73794i	0.106872	−	0.333030i
$856$	38.5043			1.31605
$857$	−14.4874	−	3.88189i	−0.494881	−	0.132603i	0.00274224	−	0.999996i	$-0.499127\pi$
$857$	−14.4874	−	3.88189i	−0.494881	−	0.132603i	−0.497623	+	0.867393i	$0.665794\pi$
$858$	10.9019	+	3.25508i	0.372184	+	0.111127i
$859$	37.5983	+	21.7074i	1.28284	+	0.740646i	0.977366	−	0.211555i	$-0.0678529\pi$
$859$	37.5983	+	21.7074i	1.28284	+	0.740646i	0.305471	+	0.952201i	$0.401186\pi$
$860$	0.728099	−	0.428150i	0.0248280	−	0.0145998i
$861$	0.361857	−	12.7589i	0.0123321	−	0.434821i
$862$	12.5016	−	46.6567i	0.425807	−	1.58913i
$863$	−2.78648	−	2.78648i	−0.0948527	−	0.0948527i	0.658088	−	0.752941i	$-0.271365\pi$
$863$	−2.78648	−	2.78648i	−0.0948527	−	0.0948527i	−0.752941	+	0.658088i	$0.771365\pi$
$864$	−3.28736	+	4.71694i	−0.111838	+	0.160474i
$865$	−26.5833	−	15.0663i	−0.903859	−	0.512271i
$866$	−0.545339	+	0.314852i	−0.0185314	+	0.0106991i
$867$	−17.1513	−	18.1526i	−0.582490	−	0.616495i
$868$	−0.727658	−	2.71566i	−0.0246983	−	0.0921754i
$869$	−3.40181	+	5.89211i	−0.115399	+	0.199876i
$870$	5.97778	−	5.73903i	0.202666	−	0.194571i
$871$	9.22911	+	15.9853i	0.312717	+	0.541641i
$872$	−16.8003	+	16.8003i	−0.568929	+	0.568929i
$873$	11.2967	+	3.72489i	0.382335	+	0.126068i
$874$			3.25020i			0.109940i
$875$	−11.9229	−	19.5547i	−0.403068	−	0.661069i
$876$	0.400700	−	0.650704i	0.0135384	−	0.0219852i
$877$	−41.5598	+	11.1359i	−1.40338	+	0.376033i	−0.879556	−	0.475796i	$-0.842160\pi$
$877$	−41.5598	+	11.1359i	−1.40338	+	0.376033i	−0.523820	+	0.851829i	$0.675493\pi$
$878$	1.93163	−	0.517577i	0.0651892	−	0.0174674i
$879$	−2.70616	+	4.39458i	−0.0912764	+	0.148225i
$880$	4.92699	−	5.00625i	0.166089	−	0.168761i
$881$			47.0487i			1.58511i	0.609801	+	0.792555i	$0.291249\pi$
$881$			47.0487i			1.58511i	−0.609801	+	0.792555i	$0.708751\pi$
$882$	8.42736	−	7.52195i	0.283764	−	0.253277i
$883$	21.0669	−	21.0669i	0.708957	−	0.708957i	−0.257359	−	0.966316i	$-0.582852\pi$
$883$	21.0669	−	21.0669i	0.708957	−	0.708957i	0.966316	+	0.257359i	$0.0828523\pi$
$884$	−0.876436	−	1.51803i	−0.0294777	−	0.0510569i
$885$	−29.5664	−	0.602473i	−0.993863	−	0.0202519i
$886$	21.5140	−	37.2633i	0.722776	−	1.25188i
$887$	0.939801	+	3.50739i	0.0315554	+	0.117766i	0.979907	−	0.199454i	$-0.0639170\pi$
$887$	0.939801	+	3.50739i	0.0315554	+	0.117766i	−0.948352	+	0.317221i	$0.897250\pi$
$888$	−21.1260	−	22.3593i	−0.708943	−	0.750330i
$889$	−4.77265	+	2.75549i	−0.160069	+	0.0924161i
$890$	6.85228	−	12.0903i	0.229689	−	0.405267i
$891$	7.26472	−	3.15906i	0.243377	−	0.105833i
$892$	0.347592	+	0.347592i	0.0116382	+	0.0116382i
$893$	3.26780	−	12.1956i	0.109353	−	0.408110i
$894$	1.09267	−	38.5269i	0.0365444	−	1.28853i
$895$	9.67832	−	37.3083i	0.323511	−	1.24708i
$896$	−16.6203	−	9.59572i	−0.555245	−	0.320571i
$897$	−14.6395	−	4.37106i	−0.488799	−	0.145945i
$898$	28.3167	+	7.58743i	0.944939	+	0.253196i
$899$	−11.1368			−0.371433
$900$	2.60833	−	1.36739i	0.0869443	−	0.0455796i
$901$	−10.5794			−0.352450
$902$	−4.10768	−	1.10065i	−0.136771	−	0.0366477i
$903$	1.57916	+	6.64125i	0.0525512	+	0.221007i
$904$	−30.6619	−	17.7026i	−1.01980	−	0.588781i
$905$	8.29356	−	31.9703i	0.275687	−	1.06273i
$906$	−0.0112398	−	0.00692143i	−0.000373419	−	0.000229949i
$907$	−2.71600	+	10.1363i	−0.0901833	+	0.336569i	−0.996245	−	0.0865764i	$-0.972407\pi$
$907$	−2.71600	+	10.1363i	−0.0901833	+	0.336569i	0.906062	+	0.423145i	$0.139074\pi$
$908$	−2.11700	−	2.11700i	−0.0702551	−	0.0702551i
$909$	3.48014	+	6.90419i	0.115429	+	0.228998i
$910$	−16.8551	+	29.7395i	−0.558743	+	0.985855i
$911$	6.77512	−	3.91162i	0.224470	−	0.129598i	−0.383548	−	0.923521i	$-0.625298\pi$
$911$	6.77512	−	3.91162i	0.224470	−	0.129598i	0.608018	+	0.793923i	$0.291965\pi$
$912$	−2.69614	+	9.02988i	−0.0892780	+	0.299009i
$913$	−2.26362	−	8.44796i	−0.0749150	−	0.279587i
$914$	−0.612004	+	1.06002i	−0.0202433	+	0.0350624i
$915$	−26.6188	+	44.0094i	−0.879990	+	1.45491i
$916$	−2.16600	−	3.75163i	−0.0715668	−	0.123957i
$917$	30.9612	−	30.9612i	1.02243	−	1.02243i
$918$	10.5444	+	3.81155i	0.348019	+	0.125800i
$919$		−	4.61000i		−	0.152070i	−0.997105	−	0.0760349i	$-0.975774\pi$
$919$		−	4.61000i		−	0.152070i	0.997105	−	0.0760349i	$-0.0242260\pi$
$920$	−7.34413	+	7.46228i	−0.242129	+	0.246024i
$921$	−53.3815	−	1.51397i	−1.75898	−	0.0498869i
$922$	−28.0591	+	7.51842i	−0.924078	+	0.247606i
$923$	31.6570	−	8.48246i	1.04200	−	0.279204i
$924$	−0.291405	−	0.539494i	−0.00958651	−	0.0177481i
$925$	8.25475	+	28.9509i	0.271415	+	0.951901i
$926$			25.1999i			0.828122i
$927$	−38.3689	+	7.98139i	−1.26020	+	0.262143i
$928$	1.24650	−	1.24650i	0.0409182	−	0.0409182i
$929$	15.7062	+	27.2039i	0.515302	+	0.892530i	0.999842	+	0.0177609i	$0.00565375\pi$
$929$	15.7062	+	27.2039i	0.515302	+	0.892530i	−0.484540	+	0.874769i	$0.661013\pi$
$930$	34.9220	+	10.1242i	1.14514	+	0.331985i
$931$	−2.13718	+	3.70170i	−0.0700433	+	0.121318i
$932$	−0.303388	−	1.13226i	−0.00993782	−	0.0370884i
$933$	−57.1814	+	13.5966i	−1.87203	+	0.445134i
$934$	−27.6818	+	15.9821i	−0.905778	+	0.522951i
$935$	2.75114	+	1.55924i	0.0899720	+	0.0509925i
$936$	−41.1225	−	26.9602i	−1.34413	−	0.881221i
$937$	−21.3617	−	21.3617i	−0.697856	−	0.697856i	0.266092	−	0.963948i	$-0.414268\pi$
$937$	−21.3617	−	21.3617i	−0.697856	−	0.697856i	−0.963948	+	0.266092i	$0.914268\pi$
$938$	−2.36525	+	8.82722i	−0.0772281	+	0.288219i
$939$	35.3449	−	19.0914i	1.15344	−	0.623023i
$940$	3.13406	−	1.84295i	0.102222	−	0.0601105i
$941$	−5.77035	−	3.33151i	−0.188108	−	0.108604i	0.402989	−	0.915205i	$-0.367971\pi$
$941$	−5.77035	−	3.33151i	−0.188108	−	0.108604i	−0.591096	+	0.806601i	$0.701305\pi$
$942$	14.3032	−	13.5142i	0.466023	−	0.440318i
$943$	5.51597	+	1.47800i	0.179625	+	0.0481303i
$944$	27.2498			0.886905
$945$	4.37158	+	23.3965i	0.142208	+	0.761087i
$946$	2.27436			0.0739458
$947$	3.23873	+	0.867814i	0.105245	+	0.0282002i	0.311057	−	0.950391i	$-0.399317\pi$
$947$	3.23873	+	0.867814i	0.105245	+	0.0282002i	−0.205812	+	0.978591i	$0.565984\pi$
$948$	1.91060	−	1.80521i	0.0620534	−	0.0586306i
$949$	10.8142	+	6.24356i	0.351043	+	0.202675i
$950$	7.12255	−	7.35359i	0.231086	−	0.238582i
$951$	6.09628	−	3.29287i	0.197685	−	0.106779i
$952$	2.51269	−	9.37748i	0.0814367	−	0.303926i
$953$	−30.7161	−	30.7161i	−0.994992	−	0.994992i	0.00499525	−	0.999988i	$-0.498410\pi$
$953$	−30.7161	−	30.7161i	−0.994992	−	0.994992i	−0.999988	+	0.00499525i	$0.998410\pi$
$954$	−23.6900	+	11.9412i	−0.766993	+	0.386612i
$955$	−3.14340	−	11.3677i	−0.101718	−	0.367850i
$956$	−2.30970	+	1.33350i	−0.0747009	+	0.0431286i
$957$	−2.36300	+	0.561875i	−0.0763848	+	0.0181629i
$958$	6.19919	+	23.1357i	0.200287	+	0.747480i
$959$	−7.02601	+	12.1694i	−0.226882	+	0.392970i
$960$	−29.2586	+	16.1068i	−0.944317	+	0.519843i
$961$	−8.93253	−	15.4716i	−0.288146	−	0.499084i
$962$	31.7725	−	31.7725i	1.02439	−	1.02439i
$963$	26.0771	+	29.2160i	0.840322	+	0.941471i
$964$			1.00809i			0.0324684i
$965$	20.8096	−	0.166054i	0.669885	−	0.00534548i
$966$	−3.59485	−	6.65535i	−0.115662	−	0.214132i
$967$	5.53906	−	1.48419i	0.178124	−	0.0477282i	−0.168654	−	0.985675i	$-0.553942\pi$
$967$	5.53906	−	1.48419i	0.178124	−	0.0477282i	0.346779	+	0.937947i	$0.387276\pi$
$968$	29.1336	−	7.80632i	0.936388	−	0.250904i
$969$	−4.24094	−	0.120278i	−0.136238	−	0.00386389i
$970$	8.48647	+	8.35210i	0.272484	+	0.268170i
$971$			14.2248i			0.456496i	0.973603	+	0.228248i	$0.0732998\pi$
$971$			14.2248i			0.456496i	−0.973603	+	0.228248i	$0.926700\pi$
$972$	−3.03853	+	0.366480i	−0.0974610	+	0.0117549i
$973$	−2.08844	+	2.08844i	−0.0669524	+	0.0669524i
$974$	−20.7244	−	35.8957i	−0.664052	−	1.15017i
$975$	23.5431	+	41.9708i	0.753984	+	1.34414i
$976$	23.6968	−	41.0440i	0.758516	−	1.31379i
$977$	8.07944	+	30.1529i	0.258484	+	0.964676i	0.966119	+	0.258097i	$0.0830956\pi$
$977$	8.07944	+	30.1529i	0.258484	+	0.964676i	−0.707635	+	0.706578i	$0.750238\pi$
$978$	−3.94636	+	13.2171i	−0.126191	+	0.422636i
$979$	−3.52757	+	2.03664i	−0.112742	+	0.0650913i
$980$	−1.18634	+	0.328046i	−0.0378962	+	0.0104791i
$981$	−24.1256	−	1.36956i	−0.770270	−	0.0437268i
$982$	38.5627	+	38.5627i	1.23059	+	1.23059i
$983$	2.66543	−	9.94750i	0.0850139	−	0.317276i	−0.910303	−	0.413943i	$-0.864151\pi$
$983$	2.66543	−	9.94750i	0.0850139	−	0.317276i	0.995317	+	0.0966666i	$0.0308181\pi$
$984$	15.6500	+	9.63718i	0.498903	+	0.307222i
$985$	−15.2206	−	25.8836i	−0.484967	−	0.824719i
$986$	−2.97715	−	1.71886i	−0.0948116	−	0.0547395i
$987$	6.79742	+	28.5869i	0.216364	+	0.909932i
$988$	1.60660	+	0.430488i	0.0511128	+	0.0136956i
$989$	−3.05411			−0.0971150
$990$	7.92050	+	0.386254i	0.251730	+	0.0122760i
$991$	37.9180			1.20450			0.602252	−	0.798306i	$-0.294270\pi$
$991$	37.9180			1.20450			0.602252	+	0.798306i	$0.294270\pi$
$992$	7.47116	+	2.00189i	0.237210	+	0.0635601i
$993$	9.89733	+	2.95514i	0.314082	+	0.0937785i
$994$	14.0523	+	8.11308i	0.445711	+	0.257331i
$995$	−38.1678	−	9.90130i	−1.21000	−	0.313892i
$996$	−0.0957926	+	3.37759i	−0.00303530	+	0.107023i
$997$	−8.06937	+	30.1153i	−0.255559	+	0.953761i	0.712219	+	0.701957i	$0.247690\pi$
$997$	−8.06937	+	30.1153i	−0.255559	+	0.953761i	−0.967778	+	0.251804i	$0.918976\pi$
$998$	−40.9452	−	40.9452i	−1.29610	−	1.29610i
$999$	2.65799	−	31.1727i	0.0840952	−	0.986260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.2.l.a.32.4	yes	16
3.2	odd	2		135.2.m.a.17.1		16
4.3	odd	2		720.2.cu.c.257.4		16
5.2	odd	4		225.2.p.b.68.1		16
5.3	odd	4	inner	45.2.l.a.23.4	yes	16
5.4	even	2		225.2.p.b.32.1		16
9.2	odd	6	inner	45.2.l.a.2.4	✓	16
9.4	even	3		405.2.f.a.242.3		16
9.5	odd	6		405.2.f.a.242.6		16
9.7	even	3		135.2.m.a.62.1		16
15.2	even	4		675.2.q.a.368.4		16
15.8	even	4		135.2.m.a.98.1		16
15.14	odd	2		675.2.q.a.557.4		16
20.3	even	4		720.2.cu.c.113.3		16
36.11	even	6		720.2.cu.c.497.3		16
45.2	even	12		225.2.p.b.218.1		16
45.7	odd	12		675.2.q.a.143.4		16
45.13	odd	12		405.2.f.a.323.6		16
45.23	even	12		405.2.f.a.323.3		16
45.29	odd	6		225.2.p.b.182.1		16
45.34	even	6		675.2.q.a.332.4		16
45.38	even	12	inner	45.2.l.a.38.4	yes	16
45.43	odd	12		135.2.m.a.8.1		16
180.83	odd	12		720.2.cu.c.353.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.4	✓	16	9.2	odd	6	inner
45.2.l.a.23.4	yes	16	5.3	odd	4	inner
45.2.l.a.32.4	yes	16	1.1	even	1	trivial
45.2.l.a.38.4	yes	16	45.38	even	12	inner
135.2.m.a.8.1		16	45.43	odd	12
135.2.m.a.17.1		16	3.2	odd	2
135.2.m.a.62.1		16	9.7	even	3
135.2.m.a.98.1		16	15.8	even	4
225.2.p.b.32.1		16	5.4	even	2
225.2.p.b.68.1		16	5.2	odd	4
225.2.p.b.182.1		16	45.29	odd	6
225.2.p.b.218.1		16	45.2	even	12
405.2.f.a.242.3		16	9.4	even	3
405.2.f.a.242.6		16	9.5	odd	6
405.2.f.a.323.3		16	45.23	even	12
405.2.f.a.323.6		16	45.13	odd	12
675.2.q.a.143.4		16	45.7	odd	12
675.2.q.a.332.4		16	45.34	even	6
675.2.q.a.368.4		16	15.2	even	4
675.2.q.a.557.4		16	15.14	odd	2
720.2.cu.c.113.3		16	20.3	even	4
720.2.cu.c.257.4		16	4.3	odd	2
720.2.cu.c.353.4		16	180.83	odd	12
720.2.cu.c.497.3		16	36.11	even	6

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	45.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29724 + 0.347596i) q^{2} +(-1.25897 + 1.18953i) q^{3} +(-0.170031 - 0.0981673i) q^{4} +(0.561484 - 2.16443i) q^{5} +(-2.04667 + 1.10550i) q^{6} +(-0.530190 + 1.97869i) q^{7} +(-2.08575 - 2.08575i) q^{8} +(0.170031 - 2.99518i) q^{9} +O(q^{10})\)	\(q+(1.29724 + 0.347596i) q^{2} +(-1.25897 + 1.18953i) q^{3} +(-0.170031 - 0.0981673i) q^{4} +(0.561484 - 2.16443i) q^{5} +(-2.04667 + 1.10550i) q^{6} +(-0.530190 + 1.97869i) q^{7} +(-2.08575 - 2.08575i) q^{8} +(0.170031 - 2.99518i) q^{9} +(1.48073 - 2.61262i) q^{10} +(-0.762281 + 0.440103i) q^{11} +(0.330837 - 0.0786668i) q^{12} +(1.43820 + 5.36743i) q^{13} +(-1.37557 + 2.38256i) q^{14} +(1.86776 + 3.39286i) q^{15} +(-1.78439 - 3.09066i) q^{16} +(1.13610 - 1.13610i) q^{17} +(1.26168 - 3.82638i) q^{18} +1.52456i q^{19} +(-0.307945 + 0.312899i) q^{20} +(-1.68622 - 3.12180i) q^{21} +(-1.14184 + 0.305956i) q^{22} +(1.53331 - 0.410850i) q^{23} +(5.10696 + 0.144840i) q^{24} +(-4.36947 - 2.43058i) q^{25} +7.46278i q^{26} +(3.34879 + 3.97311i) q^{27} +(0.284392 - 0.284392i) q^{28} +(-0.796583 - 1.37972i) q^{29} +(1.24360 + 5.05059i) q^{30} +(3.49518 - 6.05383i) q^{31} +(0.286379 + 1.06878i) q^{32} +(0.436175 - 1.46084i) q^{33} +(1.86870 - 1.07889i) q^{34} +(3.98504 + 2.25856i) q^{35} +(-0.322939 + 0.492581i) q^{36} +(-4.25746 - 4.25746i) q^{37} +(-0.529931 + 1.97773i) q^{38} +(-8.19538 - 5.04667i) q^{39} +(-5.68555 + 3.34333i) q^{40} +(3.11546 + 1.79871i) q^{41} +(-1.10232 - 4.63586i) q^{42} +(-1.85841 - 0.497959i) q^{43} +0.172815 q^{44} +(-6.38737 - 2.04976i) q^{45} +2.13189 q^{46} +(-7.99942 - 2.14344i) q^{47} +(5.92294 + 1.76847i) q^{48} +(2.42805 + 1.40183i) q^{49} +(-4.82341 - 4.67186i) q^{50} +(-0.0788937 + 2.78174i) q^{51} +(0.282368 - 1.05381i) q^{52} +(-4.65601 - 4.65601i) q^{53} +(2.96317 + 6.31812i) q^{54} +(0.524562 + 1.89701i) q^{55} +(5.23290 - 3.02121i) q^{56} +(-1.81351 - 1.91938i) q^{57} +(-0.553777 - 2.06672i) q^{58} +(-3.81780 + 6.61262i) q^{59} +(0.0154914 - 0.760243i) q^{60} +(6.64002 + 11.5008i) q^{61} +(6.63838 - 6.63838i) q^{62} +(5.83639 + 1.92445i) q^{63} +8.62358i q^{64} +(12.4249 - 0.0991472i) q^{65} +(1.07361 - 1.74345i) q^{66} +(3.20857 - 0.859733i) q^{67} +(-0.304699 + 0.0816439i) q^{68} +(-1.44168 + 2.34117i) q^{69} +(4.38451 + 4.31509i) q^{70} -5.89798i q^{71} +(-6.60182 + 5.89254i) q^{72} +(1.58900 - 1.58900i) q^{73} +(-4.04309 - 7.00284i) q^{74} +(8.39230 - 2.13759i) q^{75} +(0.149662 - 0.259222i) q^{76} +(-0.466676 - 1.74166i) q^{77} +(-8.87721 - 9.39544i) q^{78} +(6.69401 - 3.86479i) q^{79} +(-7.69140 + 2.12683i) q^{80} +(-8.94218 - 1.01854i) q^{81} +(3.41628 + 3.41628i) q^{82} +(-2.57170 + 9.59770i) q^{83} +(-0.0197489 + 0.696335i) q^{84} +(-1.82110 - 3.09690i) q^{85} +(-2.23772 - 1.29195i) q^{86} +(2.64410 + 0.789474i) q^{87} +(2.50787 + 0.671981i) q^{88} +4.62765 q^{89} +(-7.57349 - 4.87926i) q^{90} -11.3830 q^{91} +(-0.301043 - 0.0806641i) q^{92} +(2.80088 + 11.7792i) q^{93} +(-9.63215 - 5.56112i) q^{94} +(3.29980 + 0.856017i) q^{95} +(-1.63189 - 1.00491i) q^{96} +(-1.02621 + 3.82988i) q^{97} +(2.66250 + 2.66250i) q^{98} +(1.18858 + 2.35800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 2 q^{7}+O(q^{10}) \) 16 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 2 * q^7	\( 16 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 2 q^{7} - 8 q^{10} - 6 q^{12} - 2 q^{13} - 6 q^{15} - 8 q^{16} + 36 q^{18} + 18 q^{20} - 12 q^{21} - 10 q^{22} + 18 q^{23} + 4 q^{25} + 18 q^{27} - 16 q^{28} + 30 q^{30} - 4 q^{31} + 30 q^{32} - 12 q^{33} - 48 q^{36} + 4 q^{37} - 30 q^{38} + 6 q^{40} - 24 q^{41} + 6 q^{42} - 2 q^{43} - 36 q^{45} + 32 q^{46} - 12 q^{47} - 30 q^{48} - 54 q^{50} + 36 q^{51} - 14 q^{52} - 16 q^{55} + 36 q^{56} - 6 q^{57} - 6 q^{58} + 18 q^{60} + 8 q^{61} + 36 q^{63} + 66 q^{65} + 36 q^{66} + 4 q^{67} + 42 q^{68} + 18 q^{70} + 18 q^{72} - 8 q^{73} + 42 q^{75} + 24 q^{76} - 6 q^{77} - 42 q^{78} - 48 q^{81} + 32 q^{82} - 66 q^{83} + 22 q^{85} - 48 q^{86} - 18 q^{87} + 18 q^{88} - 66 q^{90} - 40 q^{91} - 60 q^{92} - 18 q^{93} - 36 q^{95} - 24 q^{96} + 28 q^{97}+O(q^{100}) \) 16 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 - 2 * q^7 - 8 * q^10 - 6 * q^12 - 2 * q^13 - 6 * q^15 - 8 * q^16 + 36 * q^18 + 18 * q^20 - 12 * q^21 - 10 * q^22 + 18 * q^23 + 4 * q^25 + 18 * q^27 - 16 * q^28 + 30 * q^30 - 4 * q^31 + 30 * q^32 - 12 * q^33 - 48 * q^36 + 4 * q^37 - 30 * q^38 + 6 * q^40 - 24 * q^41 + 6 * q^42 - 2 * q^43 - 36 * q^45 + 32 * q^46 - 12 * q^47 - 30 * q^48 - 54 * q^50 + 36 * q^51 - 14 * q^52 - 16 * q^55 + 36 * q^56 - 6 * q^57 - 6 * q^58 + 18 * q^60 + 8 * q^61 + 36 * q^63 + 66 * q^65 + 36 * q^66 + 4 * q^67 + 42 * q^68 + 18 * q^70 + 18 * q^72 - 8 * q^73 + 42 * q^75 + 24 * q^76 - 6 * q^77 - 42 * q^78 - 48 * q^81 + 32 * q^82 - 66 * q^83 + 22 * q^85 - 48 * q^86 - 18 * q^87 + 18 * q^88 - 66 * q^90 - 40 * q^91 - 60 * q^92 - 18 * q^93 - 36 * q^95 - 24 * q^96 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

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