LMFDB - Embedded newform 45.2.l.a.23.4

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			23.4
Root			$-0.347596 - 1.29724i$ of defining polynomial
Character	$\chi$	$=$	45.23
Dual form			45.2.l.a.2.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.347596 - 1.29724i) q^{2} +(-1.18953 - 1.25897i) q^{3} +(0.170031 + 0.0981673i) q^{4} +(-1.59371 + 1.56847i) q^{5} +(-2.04667 + 1.10550i) q^{6} +(1.97869 + 0.530190i) q^{7} +(2.08575 - 2.08575i) q^{8} +(-0.170031 + 2.99518i) q^{9} +O(q^{10})$	\(q+(0.347596 - 1.29724i) q^{2} +(-1.18953 - 1.25897i) q^{3} +(0.170031 + 0.0981673i) q^{4} +(-1.59371 + 1.56847i) q^{5} +(-2.04667 + 1.10550i) q^{6} +(1.97869 + 0.530190i) 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} +(-0.0786668 - 0.330837i) q^{12} +(-5.36743 + 1.43820i) q^{13} +(1.37557 - 2.38256i) q^{14} +(3.87043 + 0.140687i) q^{15} +(-1.78439 - 3.09066i) q^{16} +(-1.13610 - 1.13610i) q^{17} +(3.82638 + 1.26168i) q^{18} -1.52456i q^{19} +(-0.424952 + 0.110239i) q^{20} +(-1.68622 - 3.12180i) q^{21} +(0.305956 + 1.14184i) q^{22} +(0.410850 + 1.53331i) q^{23} +(-5.10696 - 0.144840i) q^{24} +(0.0797919 - 4.99936i) q^{25} +7.46278i q^{26} +(3.97311 - 3.34879i) q^{27} +(0.284392 + 0.284392i) q^{28} +(0.796583 + 1.37972i) q^{29} +(1.52785 - 4.97199i) q^{30} +(3.49518 - 6.05383i) q^{31} +(1.06878 - 0.286379i) q^{32} +(1.46084 + 0.436175i) 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} +(-1.97773 - 0.529931i) q^{38} +(8.19538 + 5.04667i) q^{39} +(-0.0526301 + 6.59550i) q^{40} +(3.11546 + 1.79871i) q^{41} +(-4.63586 + 1.10232i) q^{42} +(0.497959 - 1.85841i) q^{43} -0.172815 q^{44} +(-4.42687 - 5.04012i) q^{45} +2.13189 q^{46} +(-2.14344 + 7.99942i) q^{47} +(-1.76847 + 5.92294i) q^{48} +(-2.42805 - 1.40183i) q^{49} +(-6.45766 - 1.84127i) q^{50} +(-0.0788937 + 2.78174i) q^{51} +(-1.05381 - 0.282368i) 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} +(-1.91938 + 1.81351i) q^{57} +(2.06672 - 0.553777i) q^{58} +(3.81780 - 6.61262i) q^{59} +(0.644281 + 0.403871i) q^{60} +(6.64002 + 11.5008i) q^{61} +(-6.63838 - 6.63838i) q^{62} +(-1.92445 + 5.83639i) q^{63} -8.62358i q^{64} +(6.29833 - 10.7107i) q^{65} +(1.07361 - 1.74345i) q^{66} +(-0.859733 - 3.20857i) q^{67} +(-0.0816439 - 0.304699i) q^{68} +(1.44168 - 2.34117i) q^{69} +(1.54472 + 5.95464i) q^{70} -5.89798i q^{71} +(5.89254 + 6.60182i) q^{72} +(1.58900 + 1.58900i) q^{73} +(4.04309 + 7.00284i) q^{74} +(-6.38898 + 5.84644i) q^{75} +(0.149662 - 0.259222i) q^{76} +(-1.74166 + 0.466676i) q^{77} +(9.39544 - 8.87721i) 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} +(-9.59770 - 2.57170i) q^{83} +(0.0197489 - 0.696335i) q^{84} +(3.59254 + 0.0286674i) q^{85} +(-2.23772 - 1.29195i) q^{86} +(0.789474 - 2.64410i) q^{87} +(-0.671981 + 2.50787i) q^{88} -4.62765 q^{89} +(-8.07703 + 3.99081i) q^{90} -11.3830 q^{91} +(-0.0806641 + 0.301043i) q^{92} +(-11.7792 + 2.80088i) q^{93} +(9.63215 + 5.56112i) q^{94} +(2.39123 + 2.42970i) q^{95} +(-1.63189 - 1.00491i) q^{96} +(3.82988 + 1.02621i) 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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.347596	−	1.29724i	0.245787	−	0.917290i	−0.727199	−	0.686427i	$-0.759178\pi$
$2$	0.347596	−	1.29724i	0.245787	−	0.917290i	0.972986	−	0.230863i	$-0.0741551\pi$
$3$	−1.18953	−	1.25897i	−0.686776	−	0.726869i
$3$	−1.18953	−	1.25897i	−0.686776	−	0.726869i
$4$	0.170031	+	0.0981673i	0.0850154	+	0.0490837i
$5$	−1.59371	+	1.56847i	−0.712727	+	0.701442i
$5$	−1.59371	+	1.56847i	−0.712727	+	0.701442i
$6$	−2.04667	+	1.10550i	−0.835551	+	0.451318i
$7$	1.97869	+	0.530190i	0.747876	+	0.200393i	0.612576	−	0.790412i	$-0.290133\pi$
$7$	1.97869	+	0.530190i	0.747876	+	0.200393i	0.135300	+	0.990805i	$0.456800\pi$
$8$	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	$0.375697\pi$
$12$	−0.0786668	−	0.330837i	−0.0227092	−	0.0955045i
$13$	−5.36743	+	1.43820i	−1.48866	+	0.398885i	−0.909283	−	0.416177i	$-0.863370\pi$
$13$	−5.36743	+	1.43820i	−1.48866	+	0.398885i	−0.579374	+	0.815062i	$0.696703\pi$
$14$	1.37557	−	2.38256i	0.367637	−	0.636766i
$15$	3.87043	+	0.140687i	0.999340	+	0.0363252i
$16$	−1.78439	−	3.09066i	−0.446098	−	0.772664i
$17$	−1.13610	−	1.13610i	−0.275544	−	0.275544i	0.555783	−	0.831327i	$-0.312418\pi$
$17$	−1.13610	−	1.13610i	−0.275544	−	0.275544i	−0.831327	+	0.555783i	$0.812418\pi$
$18$	3.82638	+	1.26168i	0.901885	+	0.297381i
$19$		−	1.52456i		−	0.349758i	−0.984590	−	0.174879i	$-0.944047\pi$
$19$		−	1.52456i		−	0.349758i	0.984590	−	0.174879i	$-0.0559535\pi$
$20$	−0.424952	+	0.110239i	−0.0950221	+	0.0246501i
$21$	−1.68622	−	3.12180i	−0.367964	−	0.681233i
$22$	0.305956	+	1.14184i	0.0652300	+	0.243442i
$23$	0.410850	+	1.53331i	0.0856682	+	0.319718i	0.995440	−	0.0953909i	$-0.0304101\pi$
$23$	0.410850	+	1.53331i	0.0856682	+	0.319718i	−0.909772	+	0.415109i	$0.863743\pi$
$24$	−5.10696	−	0.144840i	−1.04245	−	0.0295653i
$25$	0.0797919	−	4.99936i	0.0159584	−	0.999873i
$26$			7.46278i			1.46357i
$27$	3.97311	−	3.34879i	0.764625	−	0.644476i
$28$	0.284392	+	0.284392i	0.0537450	+	0.0537450i
$29$	0.796583	+	1.37972i	0.147922	+	0.256208i	0.930459	−	0.366396i	$-0.119408\pi$
$29$	0.796583	+	1.37972i	0.147922	+	0.256208i	−0.782537	+	0.622603i	$0.786075\pi$
$30$	1.52785	−	4.97199i	0.278946	−	0.907757i
$31$	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	$-0.0493583\pi$
$32$	1.06878	−	0.286379i	0.188936	−	0.0506251i
$33$	1.46084	+	0.436175i	0.254299	+	0.0759284i
$34$	−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	−0.964393	−	0.264472i	$-0.914802\pi$
$37$	−4.25746	+	4.25746i	−0.699922	+	0.699922i	0.264472	+	0.964393i	$0.414802\pi$
$38$	−1.97773	−	0.529931i	−0.320830	−	0.0859661i
$39$	8.19538	+	5.04667i	1.31231	+	0.808114i
$40$	−0.0526301	+	6.59550i	−0.00832155	+	1.04284i
$41$	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	$0.576030\pi$
$42$	−4.63586	+	1.10232i	−0.715329	+	0.170092i
$43$	0.497959	−	1.85841i	0.0759380	−	0.283404i	−0.917506	−	0.397721i	$-0.869801\pi$
$43$	0.497959	−	1.85841i	0.0759380	−	0.283404i	0.993444	+	0.114317i	$0.0364679\pi$
$44$	−0.172815			−0.0260528
$45$	−4.42687	−	5.04012i	−0.659919	−	0.751337i
$46$	2.13189			0.314330
$47$	−2.14344	+	7.99942i	−0.312652	+	1.16683i	0.613503	+	0.789693i	$0.289760\pi$
$47$	−2.14344	+	7.99942i	−0.312652	+	1.16683i	−0.926155	+	0.377142i	$0.876907\pi$
$48$	−1.76847	+	5.92294i	−0.255256	+	0.854902i
$49$	−2.42805	−	1.40183i	−0.346864	−	0.200262i
$50$	−6.45766	−	1.84127i	−0.913251	−	0.260394i
$51$	−0.0788937	+	2.78174i	−0.0110473	+	0.389522i
$52$	−1.05381	−	0.282368i	−0.146137	−	0.0391574i
$53$	4.65601	−	4.65601i	0.639552	−	0.639552i	−0.310893	−	0.950445i	$-0.600628\pi$
$53$	4.65601	−	4.65601i	0.639552	−	0.639552i	0.950445	+	0.310893i	$0.100628\pi$
$54$	−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
$57$	−1.91938	+	1.81351i	−0.254229	+	0.240206i
$58$	2.06672	−	0.553777i	0.271374	−	0.0727145i
$59$	3.81780	−	6.61262i	0.497035	−	0.860890i	−0.502959	−	0.864310i	$-0.667755\pi$
$59$	3.81780	−	6.61262i	0.497035	−	0.860890i	0.999994	+	0.00342048i	$0.00108877\pi$
$60$	0.644281	+	0.403871i	0.0831763	+	0.0521395i
$61$	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
$63$	−1.92445	+	5.83639i	−0.242458	+	0.735317i
$64$		−	8.62358i		−	1.07795i
$65$	6.29833	−	10.7107i	0.781211	−	1.32850i
$66$	1.07361	−	1.74345i	0.132152	−	0.214604i
$67$	−0.859733	−	3.20857i	−0.105033	−	0.391989i	0.893316	−	0.449429i	$-0.148373\pi$
$67$	−0.859733	−	3.20857i	−0.105033	−	0.391989i	−0.998349	+	0.0574406i	$0.981706\pi$
$68$	−0.0816439	−	0.304699i	−0.00990078	−	0.0369502i
$69$	1.44168	−	2.34117i	0.173558	−	0.281844i
$70$	1.54472	+	5.95464i	0.184630	+	0.711716i
$71$		−	5.89798i		−	0.699961i	−0.936757	−	0.349980i	$-0.886188\pi$
$71$		−	5.89798i		−	0.699961i	0.936757	−	0.349980i	$-0.113812\pi$
$72$	5.89254	+	6.60182i	0.694442	+	0.778032i
$73$	1.58900	+	1.58900i	0.185979	+	0.185979i	0.793955	−	0.607976i	$-0.208018\pi$
$73$	1.58900	+	1.58900i	0.185979	+	0.185979i	−0.607976	+	0.793955i	$0.708018\pi$
$74$	4.04309	+	7.00284i	0.470000	+	0.814063i
$75$	−6.38898	+	5.84644i	−0.737736	+	0.675089i
$76$	0.149662	−	0.259222i	0.0171674	−	0.0297348i
$77$	−1.74166	+	0.466676i	−0.198480	+	0.0531827i
$78$	9.39544	−	8.87721i	1.06382	−	1.00515i
$79$	−6.69401	+	3.86479i	−0.753135	+	0.434823i	−0.826826	−	0.562458i	$-0.809856\pi$
$79$	−6.69401	+	3.86479i	−0.753135	+	0.434823i	0.0736905	+	0.997281i	$0.476522\pi$
$80$	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
$83$	−9.59770	−	2.57170i	−1.05348	−	0.282280i	−0.309794	−	0.950804i	$-0.600260\pi$
$83$	−9.59770	−	2.57170i	−1.05348	−	0.282280i	−0.743691	+	0.668523i	$0.766927\pi$
$84$	0.0197489	−	0.696335i	0.00215478	−	0.0759763i
$85$	3.59254	+	0.0286674i	0.389666	+	0.00310942i
$86$	−2.23772	−	1.29195i	−0.241299	−	0.139314i
$87$	0.789474	−	2.64410i	0.0846405	−	0.283477i
$88$	−0.671981	+	2.50787i	−0.0716334	+	0.267340i
$89$	−4.62765			−0.490530			−0.245265	−	0.969456i	$-0.578875\pi$
$89$	−4.62765			−0.490530			−0.245265	+	0.969456i	$0.578875\pi$
$90$	−8.07703	+	3.99081i	−0.851393	+	0.420669i
$91$	−11.3830			−1.19327
$92$	−0.0806641	+	0.301043i	−0.00840982	+	0.0313859i
$93$	−11.7792	+	2.80088i	−1.22145	+	0.290437i
$94$	9.63215	+	5.56112i	0.993480	+	0.573586i
$95$	2.39123	+	2.42970i	0.245335	+	0.249282i
$96$	−1.63189	−	1.00491i	−0.166554	−	0.102563i
$97$	3.82988	+	1.02621i	0.388865	+	0.104196i	0.447954	−	0.894057i	$-0.352153\pi$
$97$	3.82988	+	1.02621i	0.388865	+	0.104196i	−0.0590888	+	0.998253i	$0.518820\pi$
$98$	−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	$0.374260\pi$
$102$	3.58117	+	1.06927i	0.354589	+	0.105873i
$103$	12.6183	−	3.38106i	1.24332	−	0.333146i	0.423566	−	0.905865i	$-0.360778\pi$
$103$	12.6183	−	3.38106i	1.24332	−	0.333146i	0.819752	+	0.572719i	$0.194111\pi$
$104$	−8.19538	+	14.1948i	−0.803623	+	1.39192i
$105$	7.58380	+	2.33044i	0.740103	+	0.227427i
$106$	−4.42157	−	7.65839i	−0.429461	−	0.743848i
$107$	9.23034	+	9.23034i	0.892331	+	0.892331i	0.994742	−	0.102411i	$-0.0326557\pi$
$107$	9.23034	+	9.23034i	0.892331	+	0.892331i	−0.102411	+	0.994742i	$0.532656\pi$
$108$	1.00429	−	0.179369i	0.0966381	−	0.0172598i
$109$			8.05480i			0.771510i	0.922601	+	0.385755i	$0.126059\pi$
$109$			8.05480i			0.771510i	−0.922601	+	0.385755i	$0.873941\pi$
$110$	−2.27855	−	1.33988i	−0.217251	−	0.127752i
$111$	10.4244	+	0.295649i	0.989441	+	0.0280618i
$112$	−1.89213	−	7.06153i	−0.178790	−	0.667252i
$113$	3.10662	+	11.5941i	0.292246	+	1.09068i	0.943380	+	0.331714i	$0.107627\pi$
$113$	3.10662	+	11.5941i	0.292246	+	1.09068i	−0.651134	+	0.758963i	$0.725706\pi$
$114$	1.68540	+	3.12028i	0.157852	+	0.292241i
$115$	−3.05973	−	1.79924i	−0.285322	−	0.167780i
$116$			0.312794i			0.0290422i
$117$	−3.39503	−	16.3209i	−0.313871	−	1.50887i
$118$	−7.25113	−	7.25113i	−0.667521	−	0.667521i
$119$	−1.64564	−	2.85034i	−0.150856	−	0.261290i
$120$	8.36617	−	7.77929i	0.763723	−	0.710149i
$121$	−5.11262	+	8.85532i	−0.464784	+	0.805029i
$122$	17.2274	−	4.61608i	1.55970	−	0.417920i
$123$	−1.44140	−	6.06190i	−0.129967	−	0.546583i
$124$	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	−0.617651	−	0.786452i	$-0.711915\pi$
$127$	1.90230	−	1.90230i	0.168802	−	0.168802i	0.786452	+	0.617651i	$0.211915\pi$
$128$	−9.04933	−	2.42476i	−0.799855	−	0.214321i
$129$	−2.93202	+	1.58372i	−0.258150	+	0.139438i
$130$	−11.7052	−	11.8935i	−1.02661	−	1.04313i
$131$	−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	$-0.716821\pi$
$132$	0.205569	+	0.217569i	0.0178925	+	0.0189370i
$133$	0.808307	−	3.01664i	0.0700891	−	0.261576i
$134$	−4.46113			−0.385383
$135$	−1.07947	+	11.5687i	−0.0929063	+	0.995675i
$136$	−4.73922			−0.406385
$137$	1.77541	−	6.62594i	0.151684	−	0.566092i	−0.847683	−	0.530504i	$-0.822003\pi$
$137$	1.77541	−	6.62594i	0.151684	−	0.566092i	0.999367	−	0.0355883i	$-0.0113305\pi$
$138$	−2.53595	−	2.68400i	−0.215875	−	0.228477i
$139$	−1.24863	−	0.720896i	−0.105907	−	0.0611456i	0.446111	−	0.894978i	$-0.352809\pi$
$139$	−1.24863	−	0.720896i	−0.105907	−	0.0611456i	−0.552018	+	0.833832i	$0.686142\pi$
$140$	−0.899297	−	0.00717612i	−0.0760045	−	0.000606493i
$141$	12.6207	−	6.81703i	1.06286	−	0.574097i
$142$	−7.65111	−	2.05011i	−0.642067	−	0.172041i
$143$	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
$147$	1.12337	+	4.72437i	0.0926536	+	0.389659i
$148$	−1.14184	+	0.305956i	−0.0938589	+	0.0251494i
$149$	8.28457	−	14.3493i	0.678699	−	1.17554i	−0.296674	−	0.954979i	$-0.595878\pi$
$149$	8.28457	−	14.3493i	0.678699	−	1.17554i	0.975373	−	0.220562i	$-0.0707891\pi$
$150$	5.36348	+	10.3203i	0.437927	+	0.842646i
$151$	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
$153$	3.59599	−	3.20964i	0.290718	−	0.259484i
$154$			2.42157i			0.195136i
$155$	3.92497	+	15.1301i	0.315261	+	1.21528i
$156$	0.898049	+	1.66261i	0.0719014	+	0.133115i
$157$	2.18944	+	8.17112i	0.174737	+	0.652126i	0.996596	+	0.0824362i	$0.0262701\pi$
$157$	2.18944	+	8.17112i	0.174737	+	0.652126i	−0.821860	+	0.569690i	$0.807063\pi$
$158$	2.68677	+	10.0272i	0.213748	+	0.797717i
$159$	−11.4003	−	0.323326i	−0.904099	−	0.0256414i
$160$	−1.25414	+	2.13276i	−0.0991488	+	0.168609i
$161$			3.25179i			0.256277i
$162$	−4.42956	+	11.2461i	−0.348019	+	0.883581i
$163$	4.19302	+	4.19302i	0.328422	+	0.328422i	0.851986	−	0.523564i	$-0.175398\pi$
$163$	4.19302	+	4.19302i	0.328422	+	0.328422i	−0.523564	+	0.851986i	$0.675398\pi$
$164$	0.353149	+	0.611672i	0.0275763	+	0.0477635i
$165$	−3.01227	+	1.59614i	−0.234505	+	0.124260i
$166$	−6.67224	+	11.5567i	−0.517866	+	0.896970i
$167$	−5.76334	+	1.54428i	−0.445980	+	0.119500i	−0.474818	−	0.880084i	$-0.657486\pi$
$167$	−5.76334	+	1.54428i	−0.445980	+	0.119500i	0.0288375	+	0.999584i	$0.490819\pi$
$168$	−10.0283	−	2.99425i	−0.773702	−	0.231012i
$169$	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
$173$	13.1994	+	3.53677i	1.00353	+	0.268896i	0.722925	−	0.690927i	$-0.242797\pi$
$173$	13.1994	+	3.53677i	1.00353	+	0.268896i	0.280608	+	0.959822i	$0.409464\pi$
$174$	−3.15562	−	1.94322i	−0.239227	−	0.147315i
$175$	2.80849	−	9.84991i	0.212302	−	0.744583i
$176$	2.72042	+	1.57063i	0.205059	+	0.118391i
$177$	−12.8665	+	3.05941i	−0.967106	+	0.229959i
$178$	−1.60855	+	6.00319i	−0.120566	+	0.449958i
$179$	−17.2370			−1.28836			−0.644178	−	0.764875i	$-0.722801\pi$
$179$	−17.2370			−1.28836			−0.644178	+	0.764875i	$0.722801\pi$
$180$	−0.257930	−	1.29155i	−0.0192250	−	0.0962664i
$181$	14.7708			1.09790			0.548952	−	0.835854i	$-0.315027\pi$
$181$	14.7708			1.09790			0.548952	+	0.835854i	$0.315027\pi$
$182$	−3.95669	+	14.7666i	−0.293289	+	1.09457i
$183$	6.58076	−	22.0402i	0.486464	−	1.62926i
$184$	4.05503	+	2.34117i	0.298941	+	0.172594i
$185$	0.107429	−	13.4628i	0.00789837	−	0.989807i
$186$	−0.460987	+	16.2541i	−0.0338012	+	1.19181i
$187$	1.36603	+	0.366025i	0.0998937	+	0.0267664i
$188$	−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	$0.272216\pi$
$192$	−10.8569	+	10.2580i	−0.783527	+	0.740309i
$193$	−8.98952	+	2.40873i	−0.647080	+	0.173384i	−0.567408	−	0.823437i	$-0.692054\pi$
$193$	−8.98952	+	2.40873i	−0.647080	+	0.173384i	−0.0796715	+	0.996821i	$0.525387\pi$
$194$	2.66250	−	4.61158i	0.191156	−	0.331092i
$195$	−20.9766	+	4.81132i	−1.50216	+	0.344545i
$196$	−0.275228	−	0.476709i	−0.0196592	−	0.0340507i
$197$	−9.49539	−	9.49539i	−0.676519	−	0.676519i	0.282692	−	0.959211i	$-0.408773\pi$
$197$	−9.49539	−	9.49539i	−0.676519	−	0.676519i	−0.959211	+	0.282692i	$0.908773\pi$
$198$	−3.47204	+	0.722243i	−0.246747	+	0.0513276i
$199$			17.6342i			1.25005i	0.780604	+	0.625026i	$0.214912\pi$
$199$			17.6342i			1.25005i	−0.780604	+	0.625026i	$0.785088\pi$
$200$	−10.2610	−	10.5938i	−0.725561	−	0.749097i
$201$	−3.01682	+	4.89907i	−0.212790	+	0.345554i
$202$	0.895835	+	3.34330i	0.0630307	+	0.235234i
$203$	0.844680	+	3.15239i	0.0592849	+	0.221254i
$204$	−0.286490	+	0.465237i	−0.0200583	+	0.0325731i
$205$	−7.78634	+	2.01989i	−0.543822	+	0.141075i
$206$		−	17.5443i		−	1.22237i
$207$	−4.66240	+	0.969859i	−0.324060	+	0.0674098i
$208$	14.0226	+	14.0226i	0.972291	+	0.972291i
$209$	0.670964	+	1.16214i	0.0464116	+	0.0803872i
$210$	5.65924	−	9.02800i	0.390525	−	0.622991i
$211$	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	$0.165317\pi$
$212$	1.24873	−	0.334597i	0.0857633	−	0.0229802i
$213$	−7.42540	+	7.01583i	−0.508780	+	0.480716i
$214$	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
$218$	10.4490	+	2.79981i	0.707698	+	0.189627i
$219$	0.110345	−	3.89068i	0.00745640	−	0.262908i
$220$	0.275416	−	0.271055i	0.0185685	−	0.0182745i
$221$	7.73186	+	4.46399i	0.520101	+	0.300281i
$222$	4.00701	−	13.4202i	0.268933	−	0.900707i
$223$	0.648014	−	2.41842i	0.0433942	−	0.161949i	−0.940829	−	0.338883i	$-0.889951\pi$
$223$	0.648014	−	2.41842i	0.0433942	−	0.161949i	0.984223	+	0.176933i	$0.0566177\pi$
$224$	2.26663			0.151445
$225$	14.9604	+	1.08904i	0.997361	+	0.0726024i
$226$	16.1202			1.07230
$227$	3.94671	−	14.7293i	0.261952	−	0.977619i	−0.702137	−	0.712042i	$-0.747771\pi$
$227$	3.94671	−	14.7293i	0.261952	−	0.977619i	0.964090	−	0.265577i	$-0.0855626\pi$
$228$	−0.504382	+	0.119932i	−0.0334035	+	0.00794272i
$229$	−19.1083	−	11.0322i	−1.26271	−	0.729029i	−0.289116	−	0.957294i	$-0.593361\pi$
$229$	−19.1083	−	11.0322i	−1.26271	−	0.729029i	−0.973599	+	0.228265i	$0.926695\pi$
$230$	−3.39761	+	3.34381i	−0.224032	+	0.220485i
$231$	2.65929	+	1.63758i	0.174969	+	0.107745i
$232$	4.53922	+	1.21628i	0.298014	+	0.0798527i
$233$	−4.22173	+	4.22173i	−0.276575	+	0.276575i	−0.831740	−	0.555165i	$-0.812655\pi$
$233$	−4.22173	+	4.22173i	−0.276575	+	0.276575i	0.555165	+	0.831740i	$0.312655\pi$
$234$	−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
$237$	12.8284	+	3.83030i	0.833294	+	0.248805i
$238$	−4.26960	+	1.14404i	−0.276757	+	0.0741569i
$239$	−6.79199	+	11.7641i	−0.439338	+	0.760955i	−0.997639	−	0.0686835i	$-0.978120\pi$
$239$	−6.79199	+	11.7641i	−0.439338	+	0.760955i	0.558301	+	0.829639i	$0.311453\pi$
$240$	−6.47154	−	12.2132i	−0.417736	−	0.788359i
$241$	−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
$243$	9.35468	+	12.4696i	0.600103	+	0.799923i
$244$			2.60733i			0.166917i
$245$	6.06832	−	1.57421i	0.387691	−	0.100573i
$246$	−8.36479	−	0.237236i	−0.533319	−	0.0151256i
$247$	2.19262	+	8.18298i	0.139513	+	0.520670i
$248$	−5.33669	−	19.9168i	−0.338880	−	1.26472i
$249$	8.17907	+	15.1424i	0.518327	+	0.959609i
$250$	13.1796	−	7.19422i	0.833550	−	0.455003i
$251$			2.60221i			0.164250i	0.996622	+	0.0821251i	$0.0261707\pi$
$251$			2.60221i			0.164250i	−0.996622	+	0.0821251i	$0.973829\pi$
$252$	−0.900159	+	0.803448i	−0.0567047	+	0.0506125i
$253$	−0.987999	−	0.987999i	−0.0621150	−	0.0621150i
$254$	−1.80652	−	3.12898i	−0.113351	−	0.196329i
$255$	−4.23735	−	4.55702i	−0.265353	−	0.285371i
$256$	2.33257	−	4.04013i	0.145786	−	0.252508i
$257$	−10.1958	+	2.73197i	−0.635999	+	0.170415i	−0.562390	−	0.826872i	$-0.690118\pi$
$257$	−10.1958	+	2.73197i	−0.635999	+	0.170415i	−0.0736085	+	0.997287i	$0.523452\pi$
$258$	1.03531	+	4.35404i	0.0644555	+	0.271071i
$259$	−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
$263$	−8.12541	−	2.17720i	−0.501034	−	0.134252i	−0.000554412	−	1.00000i	$-0.500176\pi$
$263$	−8.12541	−	2.17720i	−0.501034	−	0.134252i	−0.500480	+	0.865748i	$0.666843\pi$
$264$	3.95668	−	2.13718i	0.243517	−	0.131534i
$265$	−0.117486	+	14.7231i	−0.00721711	+	0.904434i
$266$	−3.63236	−	2.09714i	−0.222714	−	0.128584i
$267$	5.50473	+	5.82609i	0.336884	+	0.356551i
$268$	0.168795	−	0.629953i	0.0103108	−	0.0384805i
$269$	26.7708			1.63225			0.816123	−	0.577878i	$-0.196119\pi$
$269$	26.7708			1.63225			0.816123	+	0.577878i	$0.196119\pi$
$270$	14.6322	+	5.42157i	0.890488	+	0.329946i
$271$	−18.5850			−1.12896			−0.564480	−	0.825447i	$-0.690923\pi$
$271$	−18.5850			−1.12896			−0.564480	+	0.825447i	$0.690923\pi$
$272$	−1.48405	+	5.53853i	−0.0899834	+	0.335823i
$273$	13.5405	+	14.3309i	0.819506	+	0.867347i
$274$	−7.97833	−	4.60629i	−0.481989	−	0.278276i
$275$	2.13941	+	3.84604i	0.129011	+	0.231925i
$276$	0.474957	−	0.256546i	0.0285891	−	0.0154422i
$277$	−26.3206	−	7.05259i	−1.58145	−	0.423749i	−0.642078	−	0.766640i	$-0.721927\pi$
$277$	−26.3206	−	7.05259i	−1.58145	−	0.423749i	−0.939375	+	0.342891i	$0.888594\pi$
$278$	−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	$0.619135\pi$
$282$	−4.45643	−	18.7418i	−0.265377	−	1.11606i
$283$	3.44050	−	0.921880i	0.204517	−	0.0548001i	−0.155106	−	0.987898i	$-0.549572\pi$
$283$	3.44050	−	0.921880i	0.204517	−	0.0548001i	0.359623	+	0.933098i	$0.382905\pi$
$284$	0.578988	−	1.00284i	0.0343566	−	0.0595074i
$285$	0.214486	−	5.90070i	0.0127050	−	0.349528i
$286$	−3.28439	−	5.68873i	−0.194210	−	0.336382i
$287$	5.21088	+	5.21088i	0.307589	+	0.307589i
$288$	0.676030	+	3.24988i	0.0398355	+	0.191501i
$289$		−	14.4186i		−	0.848151i
$290$	−2.42517	+	4.12416i	−0.142411	+	0.242179i
$291$	−3.26378	−	6.04243i	−0.191326	−	0.354213i
$292$	0.114191	+	0.426168i	0.00668254	+	0.0249396i
$293$	0.771199	+	2.87816i	0.0450539	+	0.168144i	0.984787	−	0.173765i	$-0.0555933\pi$
$293$	0.771199	+	2.87816i	0.0450539	+	0.168144i	−0.939733	+	0.341909i	$0.888927\pi$
$294$	6.51914	+	0.184891i	0.380204	+	0.0107831i
$295$	4.28726	+	16.5267i	0.249614	+	0.962220i
$296$			17.7600i			1.03228i
$297$	−1.55481	+	4.30130i	−0.0902192	+	0.249587i
$298$	−15.7349	−	15.7349i	−0.911496	−	0.911496i
$299$	−4.41042	−	7.63907i	−0.255061	−	0.441779i
$300$	−1.66025	+	0.366886i	−0.0958548	+	0.0211822i
$301$	1.97062	−	3.41321i	0.113584	−	0.196734i
$302$	0.00736135	−	0.00197247i	0.000423598	−	0.000113503i
$303$	4.27731	+	1.27712i	0.245725	+	0.0733684i
$304$	−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	0.286081	−	0.958205i	$-0.407647\pi$
$307$	21.8017	−	21.8017i	1.24429	−	1.24429i	0.958205	−	0.286081i	$-0.0923528\pi$
$308$	−0.341948	−	0.0916247i	−0.0194843	−	0.00522080i
$309$	−19.2665	−	11.8642i	−1.09603	−	0.674933i
$310$	20.9917	+	0.167508i	1.19225	+	0.00951380i
$311$	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	$0.254565\pi$
$312$	27.6196	−	6.56741i	1.56365	−	0.371806i
$313$	6.00279	−	22.4027i	0.339298	−	1.26628i	−0.559836	−	0.828603i	$-0.689136\pi$
$313$	6.00279	−	22.4027i	0.339298	−	1.26628i	0.899134	−	0.437673i	$-0.144197\pi$
$314$	11.3610			0.641137
$315$	−6.08721	−	12.3199i	−0.342976	−	0.694150i
$316$	−1.51758			−0.0853708
$317$	−1.03536	+	3.86401i	−0.0581515	+	0.217024i	−0.988887	−	0.148669i	$-0.952501\pi$
$317$	−1.03536	+	3.86401i	−0.0581515	+	0.217024i	0.930736	+	0.365693i	$0.119168\pi$
$318$	−4.38211	+	14.6765i	−0.245737	+	0.823019i
$319$	−1.21444	−	0.701157i	−0.0679956	−	0.0392573i
$320$	13.5258	+	13.7434i	0.756118	+	0.768282i
$321$	0.640980	−	22.6005i	0.0357760	−	1.26144i
$322$	4.21836	+	1.13031i	0.235080	+	0.0629896i
$323$	−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
$327$	10.1408	−	9.58143i	0.560786	−	0.529854i
$328$	10.2497	−	2.74640i	0.565945	−	0.151645i
$329$	−8.48242	+	14.6920i	−0.467651	+	0.809995i
$330$	1.02354	+	4.46246i	0.0563439	+	0.245650i
$331$	−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
$333$	−12.0279	−	13.4757i	−0.659127	−	0.738466i
$334$			8.01324i			0.438465i
$335$	6.40271	+	3.76504i	0.349817	+	0.205706i
$336$	−6.63954	+	10.7821i	−0.362216	+	0.588210i
$337$	−2.56397	−	9.56887i	−0.139668	−	0.521250i	−0.999935	−	0.0114051i	$-0.996370\pi$
$337$	−2.56397	−	9.56887i	−0.139668	−	0.521250i	0.860267	−	0.509845i	$-0.170297\pi$
$338$	−6.21422	−	23.1918i	−0.338009	−	1.26147i
$339$	10.9012	−	17.7026i	0.592072	−	0.961476i
$340$	0.608028	+	0.357545i	0.0329750	+	0.0193906i
$341$			6.15295i			0.333201i
$342$	1.92351	−	5.83354i	0.104012	−	0.315442i
$343$	−14.2007	−	14.2007i	−0.766764	−	0.766764i
$344$	−2.83755	−	4.91478i	−0.152990	−	0.264987i
$345$	1.37445	+	5.99238i	0.0739978	+	0.322619i
$346$	9.17611	−	15.8935i	0.493311	−	0.854440i
$347$	−10.2471	+	2.74569i	−0.550091	+	0.147396i	−0.523150	−	0.852241i	$-0.675243\pi$
$347$	−10.2471	+	2.74569i	−0.550091	+	0.147396i	−0.0269407	+	0.999637i	$0.508577\pi$
$348$	0.393799	−	0.372078i	0.0211098	−	0.0199455i
$349$	−8.08831	+	4.66979i	−0.432957	+	0.249968i	−0.700606	−	0.713549i	$-0.747087\pi$
$349$	−8.08831	+	4.66979i	−0.432957	+	0.249968i	0.267648	+	0.963517i	$0.413753\pi$
$350$	−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
$353$	−18.5470	−	4.96965i	−0.987156	−	0.264508i	−0.271100	−	0.962551i	$-0.587388\pi$
$353$	−18.5470	−	4.96965i	−0.987156	−	0.264508i	−0.716055	+	0.698043i	$0.754054\pi$
$354$	−0.503538	+	17.7544i	−0.0267627	+	0.943638i
$355$	9.25081	+	9.39963i	0.490982	+	0.498881i
$356$	−0.786842	−	0.454284i	−0.0417026	−	0.0240770i
$357$	−1.63096	+	5.46239i	−0.0863194	+	0.289100i
$358$	−5.99152	+	22.3606i	−0.316662	+	1.18180i
$359$	12.5944			0.664705			0.332352	−	0.943155i	$-0.392158\pi$
$359$	12.5944			0.664705			0.332352	+	0.943155i	$0.392158\pi$
$360$	−19.7457	−	1.27907i	−1.04069	−	0.0674131i
$361$	16.6757			0.877669
$362$	5.13426	−	19.1613i	0.269851	−	1.00710i
$363$	17.2302	−	4.09702i	0.904353	−	0.215038i
$364$	−1.93546	−	1.11744i	−0.101446	−	0.0585698i
$365$	−5.02471	−	0.0400957i	−0.263005	−	0.00209870i
$366$	−26.3041	−	16.1979i	−1.37494	−	0.846680i
$367$	27.3263	+	7.32206i	1.42642	+	0.382209i	0.887757	−	0.460312i	$-0.152262\pi$
$367$	27.3263	+	7.32206i	1.42642	+	0.382209i	0.538665	+	0.842520i	$0.318929\pi$
$368$	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
$372$	−2.27779	−	0.680100i	−0.118098	−	0.0352616i
$373$	−2.25734	+	0.604851i	−0.116880	+	0.0313180i	−0.316785	−	0.948497i	$-0.602603\pi$
$373$	−2.25734	+	0.604851i	−0.116880	+	0.0313180i	0.199905	+	0.979815i	$0.435937\pi$
$374$	0.949649	−	1.64484i	0.0491052	−	0.0850526i
$375$	1.01217	−	19.3384i	0.0522684	−	0.998633i
$376$	12.2141	+	21.1554i	0.629894	+	1.09101i
$377$	−6.25992	−	6.25992i	−0.322402	−	0.322402i
$378$	−2.51341	−	14.0727i	−0.129276	−	0.723820i
$379$		−	18.4618i		−	0.948320i	−0.880439	−	0.474160i	$-0.842752\pi$
$379$		−	18.4618i		−	0.948320i	0.880439	−	0.474160i	$-0.157248\pi$
$380$	0.168066	+	0.647865i	0.00862159	+	0.0332348i
$381$	−4.65779	−	0.132101i	−0.238626	−	0.00676772i
$382$	−1.83342	−	6.84241i	−0.0938059	−	0.350088i
$383$	−6.26481	−	23.3806i	−0.320117	−	1.19469i	−0.919131	−	0.393953i	$-0.871107\pi$
$383$	−6.26481	−	23.3806i	−0.320117	−	1.19469i	0.599014	−	0.800739i	$-0.295559\pi$
$384$	7.71175	+	14.2772i	0.393539	+	0.728580i
$385$	2.04372	−	3.47549i	0.104158	−	0.177127i
$386$			12.4989i			0.636176i
$387$	5.48159	+	1.80746i	0.278645	+	0.0918784i
$388$	0.550457	+	0.550457i	0.0279452	+	0.0279452i
$389$	13.5444	+	23.4596i	0.686729	+	1.18945i	0.972890	+	0.231268i	$0.0742876\pi$
$389$	13.5444	+	23.4596i	0.686729	+	1.18945i	−0.286161	+	0.958182i	$0.592379\pi$
$390$	−1.04992	+	28.8841i	−0.0531645	+	1.46261i
$391$	1.27523	−	2.20876i	0.0644911	−	0.111702i
$392$	−7.98815	+	2.14042i	−0.403463	+	0.108108i
$393$	8.56432	+	36.0177i	0.432013	+	1.81685i
$394$	−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	−0.996637	−	0.0819389i	$-0.973889\pi$
$397$	−18.2252	+	18.2252i	−0.914698	+	0.914698i	0.0819389	+	0.996637i	$0.473889\pi$
$398$	22.8758	+	6.12955i	1.14666	+	0.307247i
$399$	−4.75938	+	2.57075i	−0.238267	+	0.128699i
$400$	−15.5937	+	8.67421i	−0.779685	+	0.433711i
$401$	−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	$0.770645\pi$
$402$	5.30666	+	5.61645i	0.264672	+	0.280123i
$403$	−10.0535	+	37.5202i	−0.500801	+	1.86902i
$404$	−0.506000			−0.0251745
$405$	15.8488	−	12.4023i	0.787531	−	0.616275i
$406$	4.38302			0.217526
$407$	1.37166	−	5.11910i	0.0679906	−	0.253744i
$408$	5.63745	+	5.96656i	0.279096	+	0.295389i
$409$	22.2450	+	12.8431i	1.09994	+	0.635053i	0.936206	−	0.351451i	$-0.114312\pi$
$409$	22.2450	+	12.8431i	1.09994	+	0.635053i	0.163737	+	0.986504i	$0.447645\pi$
$410$	−0.0862038	+	10.8029i	−0.00425730	+	0.533517i
$411$	−10.4538	+	5.64656i	−0.515648	+	0.278524i
$412$	2.47741	+	0.663820i	0.122053	+	0.0327041i
$413$	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
$417$	0.577694	+	2.42952i	0.0282898	+	0.118974i
$418$	1.74081	−	0.466448i	0.0851457	−	0.0228147i
$419$	6.13243	−	10.6217i	0.299589	−	0.518903i	−0.676453	−	0.736486i	$-0.736484\pi$
$419$	6.13243	−	10.6217i	0.299589	−	0.518903i	0.976042	+	0.217583i	$0.0698172\pi$
$420$	1.06071	+	1.14073i	0.0517572	+	0.0556618i
$421$	−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
$423$	−23.5952	−	7.78012i	−1.14724	−	0.378283i
$424$		−	19.4225i		−	0.943240i
$425$	−5.77042	+	5.58911i	−0.279906	+	0.271112i
$426$	6.52020	+	12.0712i	0.315905	+	0.584853i
$427$	7.04094	+	26.2771i	0.340735	+	1.27164i
$428$	0.663324	+	2.47556i	0.0320630	+	0.119661i
$429$	−8.46824	−	0.240170i	−0.408850	−	0.0115955i
$430$	5.59265	−	1.45082i	0.269701	−	0.0699646i
$431$		−	35.9660i		−	1.73242i	−0.499678	−	0.866211i	$-0.666548\pi$
$431$		−	35.9660i		−	1.73242i	0.499678	−	0.866211i	$-0.333452\pi$
$432$	−17.4396	−	6.30395i	−0.839061	−	0.303299i
$433$	−0.331545	−	0.331545i	−0.0159331	−	0.0159331i	0.699095	−	0.715028i	$-0.253586\pi$
$433$	−0.331545	−	0.331545i	−0.0159331	−	0.0159331i	−0.715028	+	0.699095i	$0.753586\pi$
$434$	−9.61573	−	16.6549i	−0.461570	−	0.799462i
$435$	2.88901	+	5.45218i	0.138517	+	0.261412i
$436$	−0.790718	+	1.36956i	−0.0378685	+	0.0655902i
$437$	2.33763	−	0.626366i	0.111824	−	0.0299632i
$438$	−5.00881	−	1.49553i	−0.239330	−	0.0714591i
$439$	−1.28953	+	0.744511i	−0.0615459	+	0.0355336i	−0.530457	−	0.847712i	$-0.677980\pi$
$439$	−1.28953	+	0.744511i	−0.0615459	+	0.0355336i	0.468911	+	0.883245i	$0.344646\pi$
$440$	−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
$443$	30.9468	+	8.29218i	1.47033	+	0.393973i	0.903044	−	0.429548i	$-0.141327\pi$
$443$	30.9468	+	8.29218i	1.47033	+	0.393973i	0.567285	+	0.823522i	$0.307994\pi$
$444$	1.74345	+	1.07361i	0.0827403	+	0.0509511i
$445$	7.37510	−	7.25833i	0.349613	−	0.344078i
$446$	−2.91203	−	1.68126i	−0.137889	−	0.0796101i
$447$	−27.9202	+	6.63888i	−1.32058	+	0.314008i
$448$	4.57213	−	17.0634i	0.216013	−	0.806172i
$449$	−21.8283			−1.03014			−0.515071	−	0.857147i	$-0.672234\pi$
$449$	−21.8283			−1.03014			−0.515071	+	0.857147i	$0.672234\pi$
$450$	6.61292	−	19.0288i	0.311736	−	0.897025i
$451$	−3.16647			−0.149103
$452$	−0.609937	+	2.27631i	−0.0286890	+	0.107069i
$453$	0.00281198	−	0.00941786i	0.000132118	−	0.000442490i
$454$	−17.7357	−	10.2397i	−0.832376	−	0.480572i
$455$	18.1412	−	17.8540i	0.850472	−	0.837006i
$456$	−0.220817	+	7.78588i	−0.0103407	+	0.364607i
$457$	0.880339	+	0.235886i	0.0411805	+	0.0110343i	0.279351	−	0.960189i	$-0.409881\pi$
$457$	0.880339	+	0.235886i	0.0411805	+	0.0110343i	−0.238170	+	0.971223i	$0.576548\pi$
$458$	−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	$0.501362\pi$
$462$	3.04870	−	2.88054i	0.141838	−	0.134015i
$463$	−18.1245	+	4.85644i	−0.842316	+	0.225698i	−0.654079	−	0.756426i	$-0.726944\pi$
$463$	−18.1245	+	4.85644i	−0.842316	+	0.225698i	−0.188236	+	0.982124i	$0.560277\pi$
$464$	2.84283	−	4.92393i	0.131975	−	0.228588i
$465$	14.3795	−	22.9392i	0.666834	−	1.06378i
$466$	4.00916	+	6.94407i	0.185721	+	0.321678i
$467$	16.8295	+	16.8295i	0.778777	+	0.778777i	0.979623	−	0.200846i	$-0.0643691\pi$
$467$	16.8295	+	16.8295i	0.778777	+	0.778777i	−0.200846	+	0.979623i	$0.564369\pi$
$468$	1.02492	−	3.10834i	0.0473771	−	0.143683i
$469$		−	6.80460i		−	0.314207i
$470$	−24.0733	+	6.24496i	−1.11042	+	0.288059i
$471$	7.68281	−	12.4763i	0.354005	−	0.574875i
$472$	−5.82929	−	21.7552i	−0.268315	−	1.00136i
$473$	0.438306	+	1.63578i	0.0201533	+	0.0752133i
$474$	9.42793	−	15.3102i	0.433039	−	0.703220i
$475$	−7.62184	−	0.121648i	−0.349714	−	0.00558158i
$476$		−	0.646194i		−	0.0296182i
$477$	13.1539	+	14.7372i	0.602276	+	0.674772i
$478$	12.9000	+	12.9000i	0.590033	+	0.590033i
$479$	−8.91724	−	15.4451i	−0.407439	−	0.705705i	0.587163	−	0.809469i	$-0.300245\pi$
$479$	−8.91724	−	15.4451i	−0.407439	−	0.705705i	−0.994602	+	0.103764i	$0.966911\pi$
$480$	4.17693	−	0.958046i	0.190650	−	0.0437286i
$481$	16.7285	−	28.9747i	0.762756	−	1.32113i
$482$	−6.66078	+	1.78475i	−0.303390	+	0.0812931i
$483$	4.09392	−	3.86810i	0.186280	−	0.176005i
$484$	−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	−0.999939	−	0.0110354i	$-0.996487\pi$
$487$	−21.8232	+	21.8232i	−0.988904	+	0.988904i	0.0110354	+	0.999939i	$0.496487\pi$
$488$	37.8372	+	10.1385i	1.71281	+	0.458946i
$489$	0.291174	−	10.2666i	0.0131674	−	0.464273i
$490$	0.0671834	−	8.41929i	0.00303504	−	0.380345i
$491$	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	$0.297834\pi$
$492$	0.349997	−	1.17221i	0.0157791	−	0.0528472i
$493$	0.662503	−	2.47249i	0.0298376	−	0.111356i
$494$	11.3775			0.511896
$495$	5.59269	+	1.89371i	0.251373	+	0.0851157i
$496$	−24.9471			−1.12016
$497$	3.12705	−	11.6703i	0.140267	−	0.523484i
$498$	22.4864	−	5.34683i	1.00764	−	0.239597i
$499$	37.3397	+	21.5581i	1.67156	+	0.965073i	0.966768	+	0.255655i	$0.0822910\pi$
$499$	37.3397	+	21.5581i	1.67156	+	0.965073i	0.704788	+	0.709418i	$0.251042\pi$
$500$	0.517216	+	2.13328i	0.0231306	+	0.0954033i
$501$	8.79988	+	5.41892i	0.393150	+	0.242100i
$502$	3.37571	+	0.904518i	0.150665	+	0.0403706i
$503$	−28.0936	+	28.0936i	−1.25263	+	1.25263i	−0.298093	+	0.954537i	$0.596351\pi$
$503$	−28.0936	+	28.0936i	−1.25263	+	1.25263i	−0.954537	+	0.298093i	$0.903649\pi$
$504$	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
$507$	−29.6708	−	8.85909i	−1.31773	−	0.393446i
$508$	0.510193	−	0.136706i	0.0226361	−	0.00606534i
$509$	7.39188	−	12.8031i	0.327639	−	0.567488i	−0.654404	−	0.756145i	$-0.727080\pi$
$509$	7.39188	−	12.8031i	0.327639	−	0.567488i	0.982043	+	0.188658i	$0.0604136\pi$
$510$	−7.38445	+	3.91288i	−0.326989	+	0.173265i
$511$	2.30168	+	3.98663i	0.101820	+	0.176358i
$512$	−17.6794	−	17.6794i	−0.781325	−	0.781325i
$513$	−5.10544	−	6.05725i	−0.225411	−	0.267434i
$514$			14.1761i			0.625282i
$515$	−14.8067	+	25.1799i	−0.652463	+	1.10956i
$516$	−0.654003	−	0.0185484i	−0.0287909	−	0.000816546i
$517$	−1.88667	−	7.04114i	−0.0829755	−	0.309669i
$518$	4.28721	+	16.0001i	0.188369	+	0.703003i
$519$	−11.2484	−	20.8248i	−0.493750	−	0.914108i
$520$	−9.20315	−	35.4766i	−0.403585	−	1.55575i
$521$			28.4812i			1.24778i	0.781511	+	0.623892i	$0.214449\pi$
$521$			28.4812i			1.24778i	−0.781511	+	0.623892i	$0.785551\pi$
$522$	1.30725	+	6.28437i	0.0572170	+	0.275059i
$523$	15.4076	+	15.4076i	0.673726	+	0.673726i	0.958573	−	0.284847i	$-0.0919428\pi$
$523$	15.4076	+	15.4076i	0.673726	+	0.673726i	−0.284847	+	0.958573i	$0.591943\pi$
$524$	−2.09829	−	3.63434i	−0.0916641	−	0.158767i
$525$	−15.7416	+	8.18095i	−0.687019	+	0.357046i
$526$	−5.64872	+	9.78386i	−0.246296	+	0.426597i
$527$	−10.8486	+	2.90687i	−0.472572	+	0.126625i
$528$	−1.25863	−	5.29325i	−0.0547750	−	0.230359i
$529$	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
$533$	−19.3089	−	5.17380i	−0.836361	−	0.224102i
$534$	9.47128	−	5.11586i	0.409862	−	0.221385i
$535$	−29.1880	−	0.232911i	−1.26191	−	0.0100696i
$536$	−8.48544	−	4.89907i	−0.366515	−	0.211608i
$537$	20.5040	+	21.7010i	0.884813	+	0.936466i
$538$	9.30542	−	34.7283i	0.401185	−	1.49724i
$539$	2.46780			0.106296
$540$	−1.31921	+	1.86107i	−0.0567698	+	0.0800875i
$541$	−1.11754			−0.0480466			−0.0240233	−	0.999711i	$-0.507648\pi$
$541$	−1.11754			−0.0480466			−0.0240233	+	0.999711i	$0.507648\pi$
$542$	−6.46008	+	24.1093i	−0.277484	+	1.03558i
$543$	−17.5703	−	18.5960i	−0.754015	−	0.798033i
$544$	−1.53959	−	0.888885i	−0.0660096	−	0.0381106i
$545$	−12.6337	−	12.8370i	−0.541169	−	0.549875i
$546$	23.2973	−	12.5839i	0.997033	−	0.538542i
$547$	−31.1213	−	8.33894i	−1.33065	−	0.356547i	−0.477694	−	0.878526i	$-0.658527\pi$
$547$	−31.1213	−	8.33894i	−1.33065	−	0.356547i	−0.852958	+	0.521979i	$0.825194\pi$
$548$	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
$552$	−1.87611	−	7.89008i	−0.0798526	−	0.335824i
$553$	−15.2945	+	4.09814i	−0.650387	+	0.174271i
$554$	−18.2979	+	31.6928i	−0.777402	+	1.34650i
$555$	−17.0772	+	15.8792i	−0.724885	+	0.674035i
$556$	−0.141537	−	0.245149i	−0.00600250	−	0.0103966i
$557$	30.4033	+	30.4033i	1.28823	+	1.28823i	0.935862	+	0.352366i	$0.114623\pi$
$557$	30.4033	+	30.4033i	1.28823	+	1.28823i	0.352366	+	0.935862i	$0.385377\pi$
$558$	21.0119	−	18.7544i	0.889503	−	0.793937i
$559$			10.6910i			0.452182i
$560$	14.0913	+	8.28625i	0.595467	+	0.350158i
$561$	−1.16411	−	2.15519i	−0.0491489	−	0.0909922i
$562$	9.11308	+	34.0105i	0.384412	+	1.43465i
$563$	0.300692	+	1.12220i	0.0126727	+	0.0472950i	0.971973	−	0.235094i	$-0.0755398\pi$
$563$	0.300692	+	1.12220i	0.0126727	+	0.0472950i	−0.959300	+	0.282389i	$0.908873\pi$
$564$	2.81512	+	0.0798405i	0.118538	+	0.00336189i
$565$	−23.1360	−	13.6049i	−0.973338	−	0.572361i
$566$		−	4.78361i		−	0.201070i
$567$	−17.1538	−	6.75644i	−0.720393	−	0.283744i
$568$	−12.3017	−	12.3017i	−0.516167	−	0.516167i
$569$	−0.145367	−	0.251784i	−0.00609412	−	0.0105553i	0.862962	−	0.505268i	$-0.168606\pi$
$569$	−0.145367	−	0.251784i	−0.00609412	−	0.0105553i	−0.869056	+	0.494713i	$0.835273\pi$
$570$	−7.58010	−	2.32930i	−0.317495	−	0.0975636i
$571$	−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	$0.983115\pi$
$572$	0.927572	−	0.248542i	0.0387837	−	0.0103921i
$573$	−8.75395	−	2.61375i	−0.365702	−	0.109191i
$574$	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	−0.757774	−	0.652517i	$-0.773713\pi$
$577$	−2.52834	+	2.52834i	−0.105256	+	0.105256i	0.652517	+	0.757774i	$0.273713\pi$
$578$	−18.7044	−	5.01183i	−0.778000	−	0.208465i
$579$	13.7258	+	8.45230i	0.570427	+	0.351266i
$580$	−0.490608	−	0.498501i	−0.0203714	−	0.0206991i
$581$	−17.6274	−	10.1772i	−0.731309	−	0.422222i
$582$	−8.97298	+	2.13360i	−0.371942	+	0.0884408i
$583$	−1.50006	+	5.59831i	−0.0621262	+	0.231858i
$584$	6.62852			0.274290
$585$	31.0096	+	20.6858i	1.28209	+	0.855251i
$586$	4.00174			0.165310
$587$	10.7212	−	40.0121i	0.442511	−	1.65147i	−0.279914	−	0.960025i	$-0.590306\pi$
$587$	10.7212	−	40.0121i	0.442511	−	1.65147i	0.722425	−	0.691449i	$-0.243027\pi$
$588$	−0.272772	+	0.913566i	−0.0112489	+	0.0376748i
$589$	−9.22943	−	5.32861i	−0.380292	−	0.219562i
$590$	22.9294	+	0.182969i	0.943987	+	0.00753273i
$591$	−0.659386	+	23.2495i	−0.0271235	+	0.956358i
$592$	20.7553	+	5.56137i	0.853038	+	0.228571i
$593$	26.6583	−	26.6583i	1.09473	−	1.09473i	0.0997087	−	0.995017i	$-0.468209\pi$
$593$	26.6583	−	26.6583i	1.09473	−	1.09473i	0.995017	−	0.0997087i	$-0.0317911\pi$
$594$	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
$597$	22.2009	−	20.9764i	0.908624	−	0.858506i
$598$	−11.4428	+	3.06608i	−0.467930	+	0.125382i
$599$	−13.2427	+	22.9370i	−0.541080	+	0.937178i	0.457762	+	0.889075i	$0.348651\pi$
$599$	−13.2427	+	22.9370i	−0.541080	+	0.937178i	−0.998842	+	0.0481037i	$0.984682\pi$
$600$	−1.13160	+	25.5200i	−0.0461974	+	1.04185i
$601$	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
$603$	9.75641	−	2.02950i	0.397312	−	0.0826475i
$604$			0.00111412i			4.53329e-5i
$605$	−5.74131	−	22.1318i	−0.233417	−	0.899784i
$606$	3.14351	−	5.10480i	0.127696	−	0.207368i
$607$	−11.9000	−	44.4113i	−0.483005	−	1.80260i	−0.588881	−	0.808220i	$-0.700431\pi$
$607$	−11.9000	−	44.4113i	−0.483005	−	1.80260i	0.105876	−	0.994379i	$-0.466235\pi$
$608$	−0.436602	−	1.62942i	−0.0177066	−	0.0660818i
$609$	2.96400	−	4.81329i	0.120107	−	0.195045i
$610$	−20.2153	+	34.3774i	−0.818493	+	1.39190i
$611$		−	46.0190i		−	1.86173i
$612$	0.926510	−	0.192730i	0.0374520	−	0.00779064i
$613$	17.3219	+	17.3219i	0.699625	+	0.699625i	0.964330	−	0.264705i	$-0.0852744\pi$
$613$	17.3219	+	17.3219i	0.699625	+	0.699625i	−0.264705	+	0.964330i	$0.585274\pi$
$614$	−20.7039	−	35.8602i	−0.835542	−	1.44720i
$615$	11.8051	+	7.40008i	0.476027	+	0.298400i
$616$	−2.65929	+	4.60603i	−0.107146	+	0.185582i
$617$	36.3708	−	9.74553i	1.46423	−	0.392340i	0.563284	−	0.826263i	$-0.309538\pi$
$617$	36.3708	−	9.74553i	1.46423	−	0.392340i	0.900950	+	0.433923i	$0.142871\pi$
$618$	−22.0878	+	20.8694i	−0.888500	+	0.839492i
$619$	8.57434	−	4.95040i	0.344632	−	0.198973i	−0.317687	−	0.948196i	$-0.602906\pi$
$619$	8.57434	−	4.95040i	0.344632	−	0.198973i	0.662318	+	0.749223i	$0.269573\pi$
$620$	−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
$623$	−9.15670	−	2.45353i	−0.366855	−	0.0982986i
$624$	0.973765	−	34.3344i	0.0389818	−	1.37447i
$625$	−24.9873	−	0.797817i	−0.999491	−	0.0319127i
$626$	−26.9753	−	15.5742i	−1.07815	−	0.622469i
$627$	0.664976	−	2.22713i	0.0265566	−	0.0889431i
$628$	−0.429864	+	1.60427i	−0.0171534	+	0.0640175i
$629$	9.67378			0.385719
$630$	−18.0979	+	3.61425i	−0.721036	+	0.143995i
$631$	−22.0279			−0.876918			−0.438459	−	0.898751i	$-0.644476\pi$
$631$	−22.0279			−0.876918			−0.438459	+	0.898751i	$0.644476\pi$
$632$	−5.90104	+	22.0230i	−0.234731	+	0.876027i
$633$	−0.207617	+	0.0493675i	−0.00825205	+	0.00196218i
$634$	4.65268	+	2.68622i	0.184781	+	0.106684i
$635$	−0.0480011	+	6.01540i	−0.00190487	+	0.238714i
$636$	−1.90665	−	1.17411i	−0.0756038	−	0.0465564i
$637$	15.0485	+	4.03223i	0.596242	+	0.159763i
$638$	−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	$0.167676\pi$
$642$	−29.0956	−	8.68736i	−1.14831	−	0.342863i
$643$	30.0492	−	8.05166i	1.18502	−	0.317526i	0.388107	−	0.921614i	$-0.373129\pi$
$643$	30.0492	−	8.05166i	1.18502	−	0.317526i	0.796918	+	0.604088i	$0.206462\pi$
$644$	−0.319219	+	0.552904i	−0.0125790	+	0.0217875i
$645$	2.18877	−	7.12277i	0.0861826	−	0.280459i
$646$	1.64484	+	2.84895i	0.0647154	+	0.112090i
$647$	−7.86580	−	7.86580i	−0.309237	−	0.309237i	0.535377	−	0.844613i	$-0.320170\pi$
$647$	−7.86580	−	7.86580i	−0.309237	−	0.309237i	−0.844613	+	0.535377i	$0.820170\pi$
$648$	−20.7755	+	16.5267i	−0.816140	+	0.649230i
$649$			6.72090i			0.263818i
$650$	37.3091	+	0.595469i	1.46339	+	0.0233562i
$651$	−24.7925	−	0.703147i	−0.971695	−	0.0275585i
$652$	0.301325	+	1.12456i	0.0118008	+	0.0440411i
$653$	0.0749391	+	0.279676i	0.00293259	+	0.0109446i	0.967377	−	0.253343i	$-0.0815300\pi$
$653$	0.0749391	+	0.279676i	0.00293259	+	0.0109446i	−0.964444	+	0.264287i	$0.914863\pi$
$654$	−8.90457	−	16.4855i	−0.348196	−	0.644635i
$655$	46.2637	−	12.0015i	1.80767	−	0.468937i
$656$		−	12.8384i		−	0.501256i
$657$	−5.02953	+	4.48917i	−0.196221	+	0.175139i
$658$	16.1106	+	16.1106i	0.628058	+	0.628058i
$659$	13.4009	+	23.2111i	0.522026	+	0.904175i	0.999672	+	0.0256228i	$0.00815688\pi$
$659$	13.4009	+	23.2111i	0.522026	+	0.904175i	−0.477646	+	0.878552i	$0.658510\pi$
$660$	−0.668868	−	0.0243128i	−0.0260356	−	0.000946374i
$661$	−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	$0.330323\pi$
$662$	−7.73611	+	2.07289i	−0.300673	+	0.0805650i
$663$	−3.57724	−	15.0443i	−0.138928	−	0.584271i
$664$	−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
$668$	−1.13154	−	0.303196i	−0.0437807	−	0.0117310i
$669$	−3.81556	+	2.06095i	−0.147518	+	0.0796811i
$670$	7.10973	−	6.99716i	0.274673	−	0.270324i
$671$	−10.1231	−	5.84458i	−0.390799	−	0.225628i
$672$	−2.69622	−	2.85362i	−0.104009	−	0.110081i
$673$	6.30290	−	23.5227i	0.242959	−	0.906735i	−0.731439	−	0.681906i	$-0.761151\pi$
$673$	6.30290	−	23.5227i	0.242959	−	0.906735i	0.974398	−	0.224829i	$-0.0721822\pi$
$674$	−13.3044			−0.512466
$675$	−16.4248	−	20.1302i	−0.632191	−	0.774812i
$676$	3.51002			0.135001
$677$	−0.240265	+	0.896681i	−0.00923414	+	0.0344623i	−0.970389	−	0.241547i	$-0.922345\pi$
$677$	−0.240265	+	0.896681i	−0.00923414	+	0.0344623i	0.961155	+	0.276009i	$0.0890120\pi$
$678$	−19.1754	−	20.2949i	−0.736429	−	0.779420i
$679$	7.03407	+	4.06112i	0.269943	+	0.155852i
$680$	7.55292	−	7.43334i	0.289641	−	0.285056i
$681$	−23.2386	+	12.5522i	−0.890503	+	0.481000i
$682$	7.98188	+	2.13874i	0.305642	+	0.0818966i
$683$	−22.2024	+	22.2024i	−0.849550	+	0.849550i	−0.990077	−	0.140526i	$-0.955120\pi$
$683$	−22.2024	+	22.2024i	−0.849550	+	0.849550i	0.140526	+	0.990077i	$0.455120\pi$
$684$	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
$687$	8.84071	+	37.1801i	0.337294	+	1.41851i
$688$	−6.63225	+	1.77711i	−0.252852	+	0.0677515i
$689$	−18.2945	+	31.6871i	−0.696966	+	1.20718i
$690$	8.25133	+	0.299929i	0.314123	+	0.0114181i
$691$	−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
$693$	−1.10164	−	5.29593i	−0.0418479	−	0.201176i
$694$			14.2473i			0.540821i
$695$	3.12065	−	0.809543i	0.118373	−	0.0307077i
$696$	−3.86828	−	7.16156i	−0.146627	−	0.271458i
$697$	−1.49595	−	5.58297i	−0.0566633	−	0.211470i
$698$	3.24640	+	12.1157i	0.122878	+	0.458586i
$699$	10.3369	+	0.293168i	0.390979	+	0.0110887i
$700$	1.44447	−	1.39909i	0.0545958	−	0.0528805i
$701$		−	19.6359i		−	0.741637i	−0.928705	−	0.370819i	$-0.879077\pi$
$701$		−	19.6359i		−	0.741637i	0.928705	−	0.370819i	$-0.120923\pi$
$702$	24.9913	+	29.6504i	0.943236	+	1.11908i
$703$	6.49076	+	6.49076i	0.244804	+	0.244804i
$704$	3.79526	+	6.57359i	0.143039	+	0.247752i
$705$	−9.42143	+	30.6596i	−0.354832	+	1.15471i
$706$	−12.8937	+	22.3325i	−0.485260	+	0.840496i
$707$	−5.09956	+	1.36642i	−0.191789	+	0.0513896i
$708$	−2.48804	−	0.742876i	−0.0935061	−	0.0279190i
$709$	−2.68383	+	1.54951i	−0.100793	+	0.0581931i	−0.549549	−	0.835461i	$-0.685201\pi$
$709$	−2.68383	+	1.54951i	−0.100793	+	0.0581931i	0.448756	+	0.893654i	$0.351867\pi$
$710$	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
$713$	10.7184	+	2.87199i	0.401408	+	0.107557i
$714$	6.51914	+	4.01445i	0.243973	+	0.150237i
$715$	−0.0872699	+	10.9365i	−0.00326371	+	0.409002i
$716$	−2.93083	−	1.69211i	−0.109530	−	0.0632373i
$717$	22.8900	−	5.44280i	0.854841	−	0.203265i
$718$	4.37774	−	16.3380i	0.163376	−	0.609727i
$719$	−20.3126			−0.757533			−0.378767	−	0.925492i	$-0.623652\pi$
$719$	−20.3126			−0.757533			−0.378767	+	0.925492i	$0.623652\pi$
$720$	−7.67800	+	22.6755i	−0.286142	+	0.845066i
$721$	26.7604			0.996608
$722$	5.79640	−	21.6325i	0.215720	−	0.805077i
$723$	−2.54437	+	8.52158i	−0.0946261	+	0.316921i
$724$	2.51149	+	1.45001i	0.0933388	+	0.0538892i
$725$	6.96129	−	3.87232i	0.258536	−	0.143814i
$726$	0.674315	−	23.7759i	0.0250262	−	0.882407i
$727$	−17.0647	−	4.57247i	−0.632895	−	0.169584i	−0.0719119	−	0.997411i	$-0.522910\pi$
$727$	−17.0647	−	4.57247i	−0.632895	−	0.169584i	−0.560983	+	0.827827i	$0.689577\pi$
$728$	−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
$732$	3.28256	−	3.10150i	0.121327	−	0.114635i
$733$	25.4785	−	6.82693i	0.941068	−	0.252158i	0.244500	−	0.969649i	$-0.421376\pi$
$733$	25.4785	−	6.82693i	0.941068	−	0.252158i	0.696568	+	0.717491i	$0.254709\pi$
$734$	18.9970	−	32.9038i	0.701192	−	1.21450i
$735$	−9.20035	−	5.76729i	−0.339360	−	0.212730i
$736$	0.878218	+	1.52112i	0.0323715	+	0.0560692i
$737$	2.06746	+	2.06746i	0.0761558	+	0.0761558i
$738$	9.65150	+	10.8133i	0.355277	+	0.398041i
$739$		−	6.41459i		−	0.235965i	−0.993016	−	0.117982i	$-0.962357\pi$
$739$		−	6.41459i		−	0.235965i	0.993016	−	0.117982i	$-0.0376426\pi$
$740$	1.33988	−	2.27855i	0.0492549	−	0.0837612i
$741$	7.69396	−	12.4944i	0.282645	−	0.458992i
$742$	−4.68854	−	17.4979i	−0.172122	−	0.642368i
$743$	−4.95625	−	18.4970i	−0.181827	−	0.678588i	−0.995288	−	0.0969677i	$-0.969086\pi$
$743$	−4.95625	−	18.4970i	−0.181827	−	0.678588i	0.813460	−	0.581620i	$-0.197581\pi$
$744$	−18.7266	+	30.4104i	−0.686549	+	1.11490i
$745$	9.30331	+	35.8627i	0.340847	+	1.31391i
$746$			3.13856i			0.114911i
$747$	9.33459	−	28.3096i	0.341535	−	1.03579i
$748$	0.196335	+	0.196335i	0.00717870	+	0.00717870i
$749$	13.3702	+	23.1579i	0.488536	+	0.846170i
$750$	−24.7349	−	8.03499i	−0.903189	−	0.293397i
$751$	−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	$0.189564\pi$
$752$	28.5482	−	7.64946i	1.04105	−	0.278947i
$753$	3.27612	−	3.09541i	0.119388	−	0.112803i
$754$	−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	−0.317049	−	0.948409i	$-0.602692\pi$
$757$	17.3710	−	17.3710i	0.631361	−	0.631361i	0.948409	+	0.317049i	$0.102692\pi$
$758$	−23.9495	−	6.41725i	−0.869885	−	0.233085i
$759$	−0.0686093	+	2.41912i	−0.00249036	+	0.0878085i
$760$	10.0552	+	0.0802378i	0.364742	+	0.00291053i
$761$	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	$0.619066\pi$
$762$	−1.79039	+	5.99637i	−0.0648591	+	0.217226i
$763$	−4.27057	+	15.9380i	−0.154605	+	0.576994i
$764$	1.03558			0.0374660
$765$	−0.696707	+	10.7554i	−0.0251895	+	0.388863i
$766$	−32.5079			−1.17456
$767$	−10.9815	+	40.9835i	−0.396519	+	1.47983i
$768$	−7.86108	+	1.86921i	−0.283662	+	0.0674495i
$769$	−1.91615	−	1.10629i	−0.0690983	−	0.0398939i	0.465053	−	0.885283i	$-0.346035\pi$
$769$	−1.91615	−	1.10629i	−0.0690983	−	0.0398939i	−0.534151	+	0.845389i	$0.679369\pi$
$770$	−3.79817	−	3.85927i	−0.136876	−	0.139078i
$771$	15.5677	+	9.58654i	0.560659	+	0.345251i
$772$	−1.76495	−	0.472918i	−0.0635221	−	0.0170207i
$773$	8.23173	−	8.23173i	0.296075	−	0.296075i	−0.543400	−	0.839474i	$-0.682863\pi$
$773$	8.23173	−	8.23173i	0.296075	−	0.296075i	0.839474	+	0.543400i	$0.182863\pi$
$774$	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
$777$	20.4700	+	6.11191i	0.734356	+	0.219264i
$778$	35.1408	−	9.41596i	1.25986	−	0.337579i
$779$	2.74224	−	4.74970i	0.0982511	−	0.170176i
$780$	−4.03898	−	1.24114i	−0.144619	−	0.0444401i
$781$	2.59572	+	4.49591i	0.0928820	+	0.160876i
$782$	−2.42204	−	2.42204i	−0.0866119	−	0.0866119i
$783$	7.78531	+	2.81419i	0.278224	+	0.100571i
$784$			10.0057i			0.357346i
$785$	−16.3055	−	9.58827i	−0.581968	−	0.342220i
$786$	49.7006	+	1.40957i	1.77276	+	0.0502778i
$787$	−9.07119	−	33.8541i	−0.323353	−	1.20677i	−0.915957	−	0.401276i	$-0.868567\pi$
$787$	−9.07119	−	33.8541i	−0.323353	−	1.20677i	0.592604	−	0.805494i	$-0.298100\pi$
$788$	−0.682372	−	2.54665i	−0.0243085	−	0.0907205i
$789$	6.92440	+	12.8195i	0.246515	+	0.456387i
$790$	−20.0092	−	11.7662i	−0.711896	−	0.418623i
$791$			24.5882i			0.874256i
$792$	−7.39725	−	2.43912i	−0.262850	−	0.0866703i
$793$	−52.1803	−	52.1803i	−1.85298	−	1.85298i
$794$	17.3076	+	29.9776i	0.614223	+	1.06387i
$795$	18.6758	−	17.3657i	0.662362	−	0.615898i
$796$	−1.73110	+	2.99835i	−0.0613571	+	0.106274i
$797$	−25.2788	+	6.77343i	−0.895421	+	0.239927i	−0.677049	−	0.735938i	$-0.736741\pi$
$797$	−25.2788	+	6.77343i	−0.895421	+	0.239927i	−0.218372	+	0.975866i	$0.570075\pi$
$798$	1.68056	+	7.06766i	0.0594910	+	0.250192i
$799$	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
$803$	−1.91059	−	0.511942i	−0.0674233	−	0.0180660i
$804$	−0.993882	+	0.536840i	−0.0350515	+	0.0189329i
$805$	−5.10034	−	5.18239i	−0.179763	−	0.182655i
$806$	45.1784	+	26.0837i	1.59134	+	0.918761i
$807$	−31.8447	−	33.7038i	−1.12099	−	1.18643i
$808$	−1.96755	+	7.34301i	−0.0692183	+	0.258326i
$809$	−40.3389			−1.41824			−0.709120	−	0.705088i	$-0.750908\pi$
$809$	−40.3389			−1.41824			−0.709120	+	0.705088i	$0.750908\pi$
$810$	−10.5799	−	24.8707i	−0.371738	−	0.873867i
$811$	−4.50040			−0.158030			−0.0790152	−	0.996873i	$-0.525178\pi$
$811$	−4.50040			−0.158030			−0.0790152	+	0.996873i	$0.525178\pi$
$812$	−0.165840	+	0.618923i	−0.00581984	+	0.0217199i
$813$	22.1075	+	23.3981i	0.775343	+	0.820606i
$814$	−6.16394	−	3.55875i	−0.216046	−	0.124734i
$815$	−13.2591	−	0.105803i	−0.464445	−	0.00370613i
$816$	8.73818	−	4.71988i	0.305898	−	0.165229i
$817$	−2.83326	−	0.759168i	−0.0991231	−	0.0265599i
$818$	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	$0.246901\pi$
$822$	3.69127	+	15.5238i	0.128748	+	0.541456i
$823$	−14.0723	+	3.77065i	−0.490528	+	0.131437i	−0.495601	−	0.868551i	$-0.665052\pi$
$823$	−14.0723	+	3.77065i	−0.490528	+	0.131437i	0.00507263	+	0.999987i	$0.498385\pi$
$824$	19.2665	−	33.3706i	0.671182	−	1.16252i
$825$	2.29716	−	7.26844i	0.0799769	−	0.253055i
$826$	−10.5033	−	18.1923i	−0.365457	−	0.632989i
$827$	3.31824	+	3.31824i	0.115387	+	0.115387i	0.762443	−	0.647056i	$-0.224000\pi$
$827$	3.31824	+	3.31824i	0.115387	+	0.115387i	−0.647056	+	0.762443i	$0.724000\pi$
$828$	−0.887961	−	0.292790i	−0.0308588	−	0.0101752i
$829$		−	33.9539i		−	1.17927i	−0.807671	−	0.589633i	$-0.799272\pi$
$829$		−	33.9539i		−	1.17927i	0.807671	−	0.589633i	$-0.200728\pi$
$830$	−7.49271	−	28.8831i	−0.260076	−	1.00255i
$831$	22.4302	+	41.5263i	0.778094	+	1.44053i
$832$	12.4024	+	46.2865i	0.429977	+	1.60469i
$833$	1.16588	+	4.35112i	0.0403953	+	0.150757i
$834$	3.35248	+	0.0950807i	0.116087	+	0.00329237i
$835$	6.76290	−	11.5008i	0.234040	−	0.398000i
$836$			0.263467i			0.00911220i
$837$	−6.38629	−	35.7571i	−0.220743	−	1.23595i
$838$	−11.6473	−	11.6473i	−0.402349	−	0.402349i
$839$	−5.71824	−	9.90428i	−0.197416	−	0.341934i	0.750274	−	0.661127i	$-0.229921\pi$
$839$	−5.71824	−	9.90428i	−0.197416	−	0.341934i	−0.947690	+	0.319193i	$0.896588\pi$
$840$	20.6786	−	10.9572i	0.713479	−	0.378059i
$841$	13.2309	−	22.9166i	0.456238	−	0.790228i
$842$	−18.7855	+	5.03357i	−0.647392	+	0.173468i
$843$	43.5119	+	12.9918i	1.49863	+	0.447460i
$844$	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
$848$	−22.6983	−	6.08198i	−0.779462	−	0.208856i
$849$	−5.25321	−	3.23490i	−0.180290	−	0.111021i
$850$	5.24467	+	9.42839i	0.179891	+	0.323391i
$851$	−8.27720	−	4.77884i	−0.283739	−	0.163817i
$852$	−1.95127	+	0.463975i	−0.0668494	+	0.0158955i
$853$	−6.18947	+	23.0994i	−0.211923	+	0.790909i	0.775304	+	0.631589i	$0.217597\pi$
$853$	−6.18947	+	23.0994i	−0.211923	+	0.790909i	−0.987227	+	0.159320i	$0.949070\pi$
$854$	36.5353			1.25021
$855$	−7.68397	+	6.74904i	−0.262786	+	0.230812i
$856$	38.5043			1.31605
$857$	−3.88189	+	14.4874i	−0.132603	+	0.494881i	−0.999996	−	0.00274224i	$-0.999127\pi$
$857$	−3.88189	+	14.4874i	−0.132603	+	0.494881i	0.867393	+	0.497623i	$0.165794\pi$
$858$	−3.25508	+	10.9019i	−0.111127	+	0.372184i
$859$	−37.5983	−	21.7074i	−1.28284	−	0.740646i	−0.305471	−	0.952201i	$-0.598814\pi$
$859$	−37.5983	−	21.7074i	−1.28284	−	0.740646i	−0.977366	+	0.211555i	$0.932147\pi$
$860$	−0.00673987	+	0.844627i	−0.000229828	+	0.0288015i
$861$	0.361857	−	12.7589i	0.0123321	−	0.434821i
$862$	−46.6567	−	12.5016i	−1.58913	−	0.425807i
$863$	2.78648	−	2.78648i	0.0948527	−	0.0948527i	−0.658088	−	0.752941i	$-0.728635\pi$
$863$	2.78648	−	2.78648i	0.0948527	−	0.0948527i	0.752941	+	0.658088i	$0.228635\pi$
$864$	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
$867$	−18.1526	+	17.1513i	−0.616495	+	0.582490i
$868$	2.71566	−	0.727658i	0.0921754	−	0.0246983i
$869$	3.40181	−	5.89211i	0.115399	−	0.199876i
$870$	8.07702	−	1.85259i	0.273837	−	0.0628088i
$871$	9.22911	+	15.9853i	0.312717	+	0.541641i
$872$	16.8003	+	16.8003i	0.568929	+	0.568929i
$873$	−3.72489	+	11.2967i	−0.126068	+	0.382335i
$874$		−	3.25020i		−	0.109940i
$875$	10.9734	+	20.1029i	0.370968	+	0.679602i
$876$	0.400700	−	0.650704i	0.0135384	−	0.0219852i
$877$	11.1359	+	41.5598i	0.376033	+	1.40338i	0.851829	+	0.523820i	$0.175493\pi$
$877$	11.1359	+	41.5598i	0.376033	+	1.40338i	−0.475796	+	0.879556i	$0.657840\pi$
$878$	0.517577	+	1.93163i	0.0174674	+	0.0651892i
$879$	2.70616	−	4.39458i	0.0912764	−	0.148225i
$880$	−6.79903	+	1.76377i	−0.229195	+	0.0594567i
$881$			47.0487i			1.58511i	0.609801	+	0.792555i	$0.291249\pi$
$881$			47.0487i			1.58511i	−0.609801	+	0.792555i	$0.708751\pi$
$882$	−7.52195	−	8.42736i	−0.253277	−	0.283764i
$883$	21.0669	+	21.0669i	0.708957	+	0.708957i	0.966316	−	0.257359i	$-0.0828523\pi$
$883$	21.0669	+	21.0669i	0.708957	+	0.708957i	−0.257359	+	0.966316i	$0.582852\pi$
$884$	0.876436	+	1.51803i	0.0294777	+	0.0510569i
$885$	15.7068	−	25.0565i	0.527979	−	0.842267i
$886$	21.5140	−	37.2633i	0.722776	−	1.25188i
$887$	3.50739	−	0.939801i	0.117766	−	0.0315554i	−0.199454	−	0.979907i	$-0.563917\pi$
$887$	3.50739	−	0.939801i	0.117766	−	0.0315554i	0.317221	+	0.948352i	$0.397250\pi$
$888$	22.3593	−	21.1260i	0.750330	−	0.708943i
$889$	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
$893$	12.1956	+	3.26780i	0.408110	+	0.109353i
$894$	−1.09267	+	38.5269i	−0.0365444	+	1.28853i
$895$	27.4708	−	27.0358i	0.918246	−	0.903707i
$896$	−16.6203	−	9.59572i	−0.555245	−	0.320571i
$897$	−4.37106	+	14.6395i	−0.145945	+	0.488799i
$898$	−7.58743	+	28.3167i	−0.253196	+	0.944939i
$899$	11.1368			0.371433
$900$	2.43682	+	1.65379i	0.0812274	+	0.0551264i
$901$	−10.5794			−0.352450
$902$	−1.10065	+	4.10768i	−0.0366477	+	0.136771i
$903$	−6.64125	+	1.57916i	−0.221007	+	0.0525512i
$904$	30.6619	+	17.7026i	1.01980	+	0.588781i
$905$	−23.5403	+	23.1676i	−0.782506	+	0.770116i
$906$	−0.0112398	−	0.00692143i	−0.000373419	−	0.000229949i
$907$	10.1363	+	2.71600i	0.336569	+	0.0901833i	0.423145	−	0.906062i	$-0.360926\pi$
$907$	10.1363	+	2.71600i	0.336569	+	0.0901833i	−0.0865764	+	0.996245i	$0.527593\pi$
$908$	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	$0.291965\pi$
$912$	9.02988	+	2.69614i	0.299009	+	0.0892780i
$913$	8.44796	−	2.26362i	0.279587	−	0.0749150i
$914$	0.612004	−	1.06002i	0.0202433	−	0.0350624i
$915$	24.0817	+	45.4474i	0.796116	+	1.50244i
$916$	−2.16600	−	3.75163i	−0.0715668	−	0.123957i
$917$	−30.9612	−	30.9612i	−1.02243	−	1.02243i
$918$	−3.81155	+	10.5444i	−0.125800	+	0.348019i
$919$			4.61000i			0.152070i	0.997105	+	0.0760349i	$0.0242260\pi$
$919$			4.61000i			0.152070i	−0.997105	+	0.0760349i	$0.975774\pi$
$920$	−10.1346	+	2.62906i	−0.334128	+	0.0866777i
$921$	−53.3815	−	1.51397i	−1.75898	−	0.0498869i
$922$	7.51842	+	28.0591i	0.247606	+	0.924078i
$923$	8.48246	+	31.6570i	0.279204	+	1.04200i
$924$	0.291405	+	0.539494i	0.00958651	+	0.0177481i
$925$	20.9449	+	21.6243i	0.688663	+	0.711002i
$926$			25.1999i			0.828122i
$927$	7.98139	+	38.3689i	0.262143	+	1.26020i
$928$	1.24650	+	1.24650i	0.0409182	+	0.0409182i
$929$	−15.7062	−	27.2039i	−0.515302	−	0.892530i	−0.999842	−	0.0177609i	$-0.994346\pi$
$929$	−15.7062	−	27.2039i	−0.515302	−	0.892530i	0.484540	−	0.874769i	$-0.338987\pi$
$930$	−24.7594	−	26.6273i	−0.811894	−	0.873144i
$931$	−2.13718	+	3.70170i	−0.0700433	+	0.121318i
$932$	−1.13226	+	0.303388i	−0.0370884	+	0.00993782i
$933$	−13.5966	−	57.1814i	−0.445134	−	1.87203i
$934$	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	−0.963948	−	0.266092i	$-0.914268\pi$
$937$	−21.3617	+	21.3617i	−0.697856	+	0.697856i	0.266092	+	0.963948i	$0.414268\pi$
$938$	−8.82722	−	2.36525i	−0.288219	−	0.0772281i
$939$	−35.3449	+	19.0914i	−1.15344	+	0.623023i
$940$	0.0290114	−	3.63565i	0.000946249	−	0.118582i
$941$	−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	$0.701305\pi$
$942$	−13.5142	−	14.3032i	−0.440318	−	0.466023i
$943$	−1.47800	+	5.51597i	−0.0481303	+	0.179625i
$944$	−27.2498			−0.886905
$945$	−8.26955	+	22.3186i	−0.269009	+	0.726024i
$946$	2.27436			0.0739458
$947$	0.867814	−	3.23873i	0.0282002	−	0.105245i	−0.950391	−	0.311057i	$-0.899317\pi$
$947$	0.867814	−	3.23873i	0.0282002	−	0.105245i	0.978591	+	0.205812i	$0.0659837\pi$
$948$	1.80521	+	1.91060i	0.0586306	+	0.0620534i
$949$	−10.8142	−	6.24356i	−0.351043	−	0.202675i
$950$	−2.80712	+	9.84510i	−0.0910751	+	0.319417i
$951$	6.09628	−	3.29287i	0.197685	−	0.106779i
$952$	−9.37748	−	2.51269i	−0.303926	−	0.0814367i
$953$	30.7161	−	30.7161i	0.994992	−	0.994992i	−0.00499525	−	0.999988i	$-0.501590\pi$
$953$	30.7161	−	30.7161i	0.994992	−	0.994992i	0.999988	+	0.00499525i	$0.00159004\pi$
$954$	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
$957$	0.561875	+	2.36300i	0.0181629	+	0.0763848i
$958$	−23.1357	+	6.19919i	−0.747480	+	0.200287i
$959$	7.02601	−	12.1694i	0.226882	−	0.392970i
$960$	1.21322	−	33.3769i	0.0391567	−	1.07724i
$961$	−8.93253	−	15.4716i	−0.288146	−	0.499084i
$962$	−31.7725	−	31.7725i	−1.02439	−	1.02439i
$963$	−29.2160	+	26.0771i	−0.941471	+	0.840322i
$964$		−	1.00809i		−	0.0324684i
$965$	10.5486	−	17.9386i	0.339572	−	0.577465i
$966$	−3.59485	−	6.65535i	−0.115662	−	0.214132i
$967$	−1.48419	−	5.53906i	−0.0477282	−	0.178124i	0.937947	−	0.346779i	$-0.112724\pi$
$967$	−1.48419	−	5.53906i	−0.0477282	−	0.178124i	−0.985675	+	0.168654i	$0.946058\pi$
$968$	7.80632	+	29.1336i	0.250904	+	0.936388i
$969$	4.24094	+	0.120278i	0.136238	+	0.00386389i
$970$	2.98990	+	11.5256i	0.0959999	+	0.370063i
$971$			14.2248i			0.456496i	0.973603	+	0.228248i	$0.0732998\pi$
$971$			14.2248i			0.456496i	−0.973603	+	0.228248i	$0.926700\pi$
$972$	0.366480	+	3.03853i	0.0117549	+	0.0974610i
$973$	−2.08844	−	2.08844i	−0.0669524	−	0.0669524i
$974$	20.7244	+	35.8957i	0.664052	+	1.15017i
$975$	25.8841	−	40.5690i	0.828954	−	1.29925i
$976$	23.6968	−	41.0440i	0.758516	−	1.31379i
$977$	30.1529	−	8.07944i	0.964676	−	0.258484i	0.258097	−	0.966119i	$-0.416904\pi$
$977$	30.1529	−	8.07944i	0.964676	−	0.258484i	0.706578	+	0.707635i	$0.250238\pi$
$978$	−13.2171	−	3.94636i	−0.422636	−	0.126191i
$979$	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
$983$	9.94750	+	2.66543i	0.317276	+	0.0850139i	0.413943	−	0.910303i	$-0.364151\pi$
$983$	9.94750	+	2.66543i	0.317276	+	0.0850139i	−0.0966666	+	0.995317i	$0.530818\pi$
$984$	−15.6500	−	9.63718i	−0.498903	−	0.307222i
$985$	30.0261	+	0.239599i	0.956712	+	0.00763427i
$986$	−2.97715	−	1.71886i	−0.0948116	−	0.0547395i
$987$	28.5869	−	6.79742i	0.909932	−	0.216364i
$988$	−0.430488	+	1.60660i	−0.0136956	+	0.0511128i
$989$	3.05411			0.0971150
$990$	4.40059	−	6.59684i	0.139860	−	0.209661i
$991$	37.9180			1.20450			0.602252	−	0.798306i	$-0.294270\pi$
$991$	37.9180			1.20450			0.602252	+	0.798306i	$0.294270\pi$
$992$	2.00189	−	7.47116i	0.0635601	−	0.237210i
$993$	−2.95514	+	9.89733i	−0.0937785	+	0.314082i
$994$	−14.0523	−	8.11308i	−0.445711	−	0.257331i
$995$	−27.6587	−	28.1036i	−0.876839	−	0.890945i
$996$	−0.0957926	+	3.37759i	−0.00303530	+	0.107023i
$997$	30.1153	+	8.06937i	0.953761	+	0.255559i	0.701957	−	0.712219i	$-0.252310\pi$
$997$	30.1153	+	8.06937i	0.953761	+	0.255559i	0.251804	+	0.967778i	$0.418976\pi$
$998$	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.23.4	yes	16
3.2	odd	2		135.2.m.a.98.1		16
4.3	odd	2		720.2.cu.c.113.3		16
5.2	odd	4	inner	45.2.l.a.32.4	yes	16
5.3	odd	4		225.2.p.b.32.1		16
5.4	even	2		225.2.p.b.68.1		16
9.2	odd	6	inner	45.2.l.a.38.4	yes	16
9.4	even	3		405.2.f.a.323.6		16
9.5	odd	6		405.2.f.a.323.3		16
9.7	even	3		135.2.m.a.8.1		16
15.2	even	4		135.2.m.a.17.1		16
15.8	even	4		675.2.q.a.557.4		16
15.14	odd	2		675.2.q.a.368.4		16
20.7	even	4		720.2.cu.c.257.4		16
36.11	even	6		720.2.cu.c.353.4		16
45.2	even	12	inner	45.2.l.a.2.4	✓	16
45.7	odd	12		135.2.m.a.62.1		16
45.22	odd	12		405.2.f.a.242.3		16
45.29	odd	6		225.2.p.b.218.1		16
45.32	even	12		405.2.f.a.242.6		16
45.34	even	6		675.2.q.a.143.4		16
45.38	even	12		225.2.p.b.182.1		16
45.43	odd	12		675.2.q.a.332.4		16
180.47	odd	12		720.2.cu.c.497.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.4	✓	16	45.2	even	12	inner
45.2.l.a.23.4	yes	16	1.1	even	1	trivial
45.2.l.a.32.4	yes	16	5.2	odd	4	inner
45.2.l.a.38.4	yes	16	9.2	odd	6	inner
135.2.m.a.8.1		16	9.7	even	3
135.2.m.a.17.1		16	15.2	even	4
135.2.m.a.62.1		16	45.7	odd	12
135.2.m.a.98.1		16	3.2	odd	2
225.2.p.b.32.1		16	5.3	odd	4
225.2.p.b.68.1		16	5.4	even	2
225.2.p.b.182.1		16	45.38	even	12
225.2.p.b.218.1		16	45.29	odd	6
405.2.f.a.242.3		16	45.22	odd	12
405.2.f.a.242.6		16	45.32	even	12
405.2.f.a.323.3		16	9.5	odd	6
405.2.f.a.323.6		16	9.4	even	3
675.2.q.a.143.4		16	45.34	even	6
675.2.q.a.332.4		16	45.43	odd	12
675.2.q.a.368.4		16	15.14	odd	2
675.2.q.a.557.4		16	15.8	even	4
720.2.cu.c.113.3		16	4.3	odd	2
720.2.cu.c.257.4		16	20.7	even	4
720.2.cu.c.353.4		16	36.11	even	6
720.2.cu.c.497.3		16	180.47	odd	12

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)

\(f(q)\)	\(=\)	\(q+(0.347596 - 1.29724i) q^{2} +(-1.18953 - 1.25897i) q^{3} +(0.170031 + 0.0981673i) q^{4} +(-1.59371 + 1.56847i) q^{5} +(-2.04667 + 1.10550i) q^{6} +(1.97869 + 0.530190i) q^{7} +(2.08575 - 2.08575i) q^{8} +(-0.170031 + 2.99518i) q^{9} +O(q^{10})\)	\(q+(0.347596 - 1.29724i) q^{2} +(-1.18953 - 1.25897i) q^{3} +(0.170031 + 0.0981673i) q^{4} +(-1.59371 + 1.56847i) q^{5} +(-2.04667 + 1.10550i) q^{6} +(1.97869 + 0.530190i) 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} +(-0.0786668 - 0.330837i) q^{12} +(-5.36743 + 1.43820i) q^{13} +(1.37557 - 2.38256i) q^{14} +(3.87043 + 0.140687i) q^{15} +(-1.78439 - 3.09066i) q^{16} +(-1.13610 - 1.13610i) q^{17} +(3.82638 + 1.26168i) q^{18} -1.52456i q^{19} +(-0.424952 + 0.110239i) q^{20} +(-1.68622 - 3.12180i) q^{21} +(0.305956 + 1.14184i) q^{22} +(0.410850 + 1.53331i) q^{23} +(-5.10696 - 0.144840i) q^{24} +(0.0797919 - 4.99936i) q^{25} +7.46278i q^{26} +(3.97311 - 3.34879i) q^{27} +(0.284392 + 0.284392i) q^{28} +(0.796583 + 1.37972i) q^{29} +(1.52785 - 4.97199i) q^{30} +(3.49518 - 6.05383i) q^{31} +(1.06878 - 0.286379i) q^{32} +(1.46084 + 0.436175i) 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} +(-1.97773 - 0.529931i) q^{38} +(8.19538 + 5.04667i) q^{39} +(-0.0526301 + 6.59550i) q^{40} +(3.11546 + 1.79871i) q^{41} +(-4.63586 + 1.10232i) q^{42} +(0.497959 - 1.85841i) q^{43} -0.172815 q^{44} +(-4.42687 - 5.04012i) q^{45} +2.13189 q^{46} +(-2.14344 + 7.99942i) q^{47} +(-1.76847 + 5.92294i) q^{48} +(-2.42805 - 1.40183i) q^{49} +(-6.45766 - 1.84127i) q^{50} +(-0.0788937 + 2.78174i) q^{51} +(-1.05381 - 0.282368i) 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} +(-1.91938 + 1.81351i) q^{57} +(2.06672 - 0.553777i) q^{58} +(3.81780 - 6.61262i) q^{59} +(0.644281 + 0.403871i) q^{60} +(6.64002 + 11.5008i) q^{61} +(-6.63838 - 6.63838i) q^{62} +(-1.92445 + 5.83639i) q^{63} -8.62358i q^{64} +(6.29833 - 10.7107i) q^{65} +(1.07361 - 1.74345i) q^{66} +(-0.859733 - 3.20857i) q^{67} +(-0.0816439 - 0.304699i) q^{68} +(1.44168 - 2.34117i) q^{69} +(1.54472 + 5.95464i) q^{70} -5.89798i q^{71} +(5.89254 + 6.60182i) q^{72} +(1.58900 + 1.58900i) q^{73} +(4.04309 + 7.00284i) q^{74} +(-6.38898 + 5.84644i) q^{75} +(0.149662 - 0.259222i) q^{76} +(-1.74166 + 0.466676i) q^{77} +(9.39544 - 8.87721i) 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} +(-9.59770 - 2.57170i) q^{83} +(0.0197489 - 0.696335i) q^{84} +(3.59254 + 0.0286674i) q^{85} +(-2.23772 - 1.29195i) q^{86} +(0.789474 - 2.64410i) q^{87} +(-0.671981 + 2.50787i) q^{88} -4.62765 q^{89} +(-8.07703 + 3.99081i) q^{90} -11.3830 q^{91} +(-0.0806641 + 0.301043i) q^{92} +(-11.7792 + 2.80088i) q^{93} +(9.63215 + 5.56112i) q^{94} +(2.39123 + 2.42970i) q^{95} +(-1.63189 - 1.00491i) q^{96} +(3.82988 + 1.02621i) 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

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