LMFDB - Embedded newform 93.2.m.b.82.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(7,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 28]))

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

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

chi := DirichletCharacter("93.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.m (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			82.3
Character	$\chi$	$=$	93.82
Dual form			93.2.m.b.76.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.704349 + 2.16776i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-2.58506 + 1.87816i) q^{4} +(-0.398612 - 0.690417i) q^{5} +(-1.13966 + 1.97395i) q^{6} +(-0.477794 - 4.54591i) q^{7} +(-2.20416 - 1.60142i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(0.704349 + 2.16776i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-2.58506 + 1.87816i) q^{4} +(-0.398612 - 0.690417i) q^{5} +(-1.13966 + 1.97395i) q^{6} +(-0.477794 - 4.54591i) q^{7} +(-2.20416 - 1.60142i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(1.21590 - 1.35039i) q^{10} +(2.06856 + 0.920981i) q^{11} +(-3.12548 - 0.664342i) q^{12} +(-2.23546 + 0.475161i) q^{13} +(9.51792 - 4.23765i) q^{14} +(0.246356 - 0.758205i) q^{15} +(-0.0558146 + 0.171780i) q^{16} +(-2.35281 + 1.04754i) q^{17} +(-2.22951 + 0.473898i) q^{18} +(-4.27578 - 0.908845i) q^{19} +(2.32715 + 1.03611i) q^{20} +(3.05856 - 3.39688i) q^{21} +(-0.539483 + 5.13283i) q^{22} +(5.65996 + 4.11220i) q^{23} +(-0.284787 - 2.70957i) q^{24} +(2.18222 - 3.77971i) q^{25} +(-2.60458 - 4.51126i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(9.77304 + 10.8541i) q^{28} +(-2.52855 - 7.78207i) q^{29} +1.81713 q^{30} +(2.24947 + 5.09312i) q^{31} -5.86068 q^{32} +(0.699712 + 2.15349i) q^{33} +(-3.92802 - 4.36251i) q^{34} +(-2.94811 + 2.14193i) q^{35} +(-1.59765 - 2.76722i) q^{36} +(4.36455 - 7.55962i) q^{37} +(-1.04148 - 9.90903i) q^{38} +(-1.84893 - 1.34332i) q^{39} +(-0.227039 + 2.16013i) q^{40} +(-7.08260 + 7.86602i) q^{41} +(9.51792 + 4.23765i) q^{42} +(-1.92913 - 0.410048i) q^{43} +(-7.07709 + 1.50428i) q^{44} +(0.728301 - 0.324260i) q^{45} +(-4.92770 + 15.1659i) q^{46} +(-1.09764 + 3.37820i) q^{47} +(-0.165004 + 0.0734647i) q^{48} +(-13.5899 + 2.88863i) q^{49} +(9.73056 + 2.06829i) q^{50} +(-2.35281 - 1.04754i) q^{51} +(4.88636 - 5.42686i) q^{52} +(0.106558 - 1.01383i) q^{53} +(-1.84401 - 1.33975i) q^{54} +(-0.188692 - 1.79528i) q^{55} +(-6.22676 + 10.7851i) q^{56} +(-2.18565 - 3.78566i) q^{57} +(15.0887 - 10.9626i) q^{58} +(3.07829 + 3.41879i) q^{59} +(0.787183 + 2.42270i) q^{60} +0.251899 q^{61} +(-9.45628 + 8.46365i) q^{62} +4.57095 q^{63} +(-4.01633 - 12.3610i) q^{64} +(1.21914 + 1.35399i) q^{65} +(-4.17542 + 3.03362i) q^{66} +(1.98619 + 3.44018i) q^{67} +(4.11472 - 7.12690i) q^{68} +(0.731291 + 6.95777i) q^{69} +(-6.71970 - 4.88215i) q^{70} +(-0.804058 + 7.65010i) q^{71} +(1.82304 - 2.02469i) q^{72} +(8.35045 + 3.71786i) q^{73} +(19.4617 + 4.13670i) q^{74} +(4.26906 - 0.907417i) q^{75} +(12.7601 - 5.68116i) q^{76} +(3.19835 - 9.84350i) q^{77} +(1.60972 - 4.95421i) q^{78} +(8.02362 - 3.57235i) q^{79} +(0.140848 - 0.0299381i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-22.0403 - 9.81297i) q^{82} +(-1.85000 + 2.05463i) q^{83} +(-1.52670 + 14.5256i) q^{84} +(1.66110 + 1.20686i) q^{85} +(-0.469890 - 4.47071i) q^{86} +(4.09128 - 7.08630i) q^{87} +(-3.08456 - 5.34261i) q^{88} +(-1.10573 + 0.803361i) q^{89} +(1.21590 + 1.35039i) q^{90} +(3.22813 + 9.93515i) q^{91} -22.3547 q^{92} +(-2.27974 + 5.07964i) q^{93} -8.09627 q^{94} +(1.07690 + 3.31435i) q^{95} +(-3.92156 - 4.35533i) q^{96} +(-0.0532738 + 0.0387057i) q^{97} +(-15.8339 - 27.4252i) q^{98} +(-1.13216 + 1.96096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9 + 24 * q^10 - 22 * q^11 + 12 * q^12 - 8 * q^13 + 10 * q^14 - 8 * q^15 - 2 * q^16 - 17 * q^17 + 5 * q^19 - 22 * q^20 - 11 * q^21 - 37 * q^22 + 26 * q^23 + 26 * q^24 - 8 * q^25 + 4 * q^26 - 6 * q^27 - 36 * q^28 + 2 * q^29 + 42 * q^30 + 36 * q^32 + 14 * q^33 + 40 * q^34 + 9 * q^35 - 13 * q^36 - 13 * q^37 - q^38 - 19 * q^39 - 27 * q^40 + 36 * q^41 + 10 * q^42 - 11 * q^43 - 38 * q^44 - q^45 - 23 * q^46 - 13 * q^47 - 14 * q^48 - 22 * q^49 + 71 * q^50 - 17 * q^51 + 9 * q^52 - 20 * q^53 - 5 * q^54 + 26 * q^55 + 28 * q^56 - 15 * q^57 + 40 * q^58 - 16 * q^59 - 61 * q^60 + 70 * q^61 - 2 * q^62 + 12 * q^63 + 34 * q^64 + 94 * q^65 - 16 * q^66 + 4 * q^67 + 51 * q^68 - 13 * q^69 - 43 * q^70 - 5 * q^71 + q^72 - 12 * q^73 + 74 * q^74 - 8 * q^75 + 71 * q^76 + 25 * q^77 + 17 * q^78 - 29 * q^79 - 113 * q^80 + 3 * q^81 - 60 * q^82 - 11 * q^83 - 41 * q^84 + 16 * q^85 - 144 * q^86 + 14 * q^87 + 26 * q^88 - 27 * q^89 + 24 * q^90 - 81 * q^91 + 28 * q^92 - 36 * q^93 - 80 * q^94 - 56 * q^95 - 43 * q^96 - 21 * q^97 - 14 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{4}{15}\right)$

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 $

$2$	0.704349	+	2.16776i	0.498050	+	1.53284i	0.812149	+	0.583450i	$0.198298\pi$
$2$	0.704349	+	2.16776i	0.498050	+	1.53284i	−0.314099	+	0.949390i	$0.601702\pi$
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$4$	−2.58506	+	1.87816i	−1.29253	+	0.939078i
$5$	−0.398612	−	0.690417i	−0.178265	−	0.308764i	0.763021	−	0.646373i	$-0.223715\pi$
$5$	−0.398612	−	0.690417i	−0.178265	−	0.308764i	−0.941286	+	0.337609i	$0.890382\pi$
$6$	−1.13966	+	1.97395i	−0.465265	+	0.805862i
$7$	−0.477794	−	4.54591i	−0.180589	−	1.71819i	−0.591322	−	0.806436i	$-0.701394\pi$
$7$	−0.477794	−	4.54591i	−0.180589	−	1.71819i	0.410733	−	0.911756i	$-0.365273\pi$
$8$	−2.20416	−	1.60142i	−0.779289	−	0.566186i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	1.21590	−	1.35039i	0.384501	−	0.427031i
$11$	2.06856	+	0.920981i	0.623693	+	0.277686i	0.694152	−	0.719829i	$-0.255780\pi$
$11$	2.06856	+	0.920981i	0.623693	+	0.277686i	−0.0704586	+	0.997515i	$0.522446\pi$
$12$	−3.12548	−	0.664342i	−0.902249	−	0.191779i
$13$	−2.23546	+	0.475161i	−0.620004	+	0.131786i	−0.507196	−	0.861831i	$-0.669318\pi$
$13$	−2.23546	+	0.475161i	−0.620004	+	0.131786i	−0.112808	+	0.993617i	$0.535985\pi$
$14$	9.51792	−	4.23765i	2.54377	−	1.13256i
$15$	0.246356	−	0.758205i	0.0636088	−	0.195768i
$16$	−0.0558146	+	0.171780i	−0.0139536	+	0.0429449i
$17$	−2.35281	+	1.04754i	−0.570641	+	0.254066i	−0.671711	−	0.740814i	$-0.734440\pi$
$17$	−2.35281	+	1.04754i	−0.570641	+	0.254066i	0.101070	+	0.994879i	$0.467773\pi$
$18$	−2.22951	+	0.473898i	−0.525501	+	0.111699i
$19$	−4.27578	−	0.908845i	−0.980932	−	0.208503i	−0.310580	−	0.950547i	$-0.600523\pi$
$19$	−4.27578	−	0.908845i	−0.980932	−	0.208503i	−0.670351	+	0.742044i	$0.733857\pi$
$20$	2.32715	+	1.03611i	0.520366	+	0.231682i
$21$	3.05856	−	3.39688i	0.667433	−	0.741259i
$22$	−0.539483	+	5.13283i	−0.115018	+	1.09432i
$23$	5.65996	+	4.11220i	1.18018	+	0.857454i	0.992192	−	0.124717i	$-0.0398023\pi$
$23$	5.65996	+	4.11220i	1.18018	+	0.857454i	0.187991	+	0.982171i	$0.439802\pi$
$24$	−0.284787	−	2.70957i	−0.0581319	−	0.553088i
$25$	2.18222	−	3.77971i	0.436443	−	0.755942i
$26$	−2.60458	−	4.51126i	−0.510800	−	0.884732i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	9.77304	+	10.8541i	1.84693	+	2.05123i
$29$	−2.52855	−	7.78207i	−0.469540	−	1.44510i	−0.853182	−	0.521613i	$-0.825330\pi$
$29$	−2.52855	−	7.78207i	−0.469540	−	1.44510i	0.383642	−	0.923482i	$-0.374670\pi$
$30$	1.81713			0.331761
$31$	2.24947	+	5.09312i	0.404016	+	0.914752i
$31$	2.24947	+	5.09312i	0.404016	+	0.914752i
$32$	−5.86068			−1.03603
$33$	0.699712	+	2.15349i	0.121804	+	0.374875i
$34$	−3.92802	−	4.36251i	−0.673650	−	0.748164i
$35$	−2.94811	+	2.14193i	−0.498322	+	0.362052i
$36$	−1.59765	−	2.76722i	−0.266276	−	0.461203i
$37$	4.36455	−	7.55962i	0.717528	−	1.24279i	−0.244449	−	0.969662i	$-0.578607\pi$
$37$	4.36455	−	7.55962i	0.717528	−	1.24279i	0.961976	−	0.273132i	$-0.0880597\pi$
$38$	−1.04148	−	9.90903i	−0.168951	−	1.60746i
$39$	−1.84893	−	1.34332i	−0.296065	−	0.215104i
$40$	−0.227039	+	2.16013i	−0.0358981	+	0.341547i
$41$	−7.08260	+	7.86602i	−1.10612	+	1.22847i	−0.134750	+	0.990880i	$0.543023\pi$
$41$	−7.08260	+	7.86602i	−1.10612	+	1.22847i	−0.971366	+	0.237587i	$0.923644\pi$
$42$	9.51792	+	4.23765i	1.46865	+	0.653884i
$43$	−1.92913	−	0.410048i	−0.294189	−	0.0625318i	0.0584529	−	0.998290i	$-0.481383\pi$
$43$	−1.92913	−	0.410048i	−0.294189	−	0.0625318i	−0.352642	+	0.935758i	$0.614717\pi$
$44$	−7.07709	+	1.50428i	−1.06691	+	0.226779i
$45$	0.728301	−	0.324260i	0.108569	−	0.0483379i
$46$	−4.92770	+	15.1659i	−0.726549	+	2.23609i
$47$	−1.09764	+	3.37820i	−0.160108	+	0.492761i	−0.998643	−	0.0520869i	$-0.983413\pi$
$47$	−1.09764	+	3.37820i	−0.160108	+	0.492761i	0.838535	+	0.544848i	$0.183413\pi$
$48$	−0.165004	+	0.0734647i	−0.0238163	+	0.0106037i
$49$	−13.5899	+	2.88863i	−1.94142	+	0.412662i
$50$	9.73056	+	2.06829i	1.37611	+	0.292501i
$51$	−2.35281	−	1.04754i	−0.329460	−	0.146685i
$52$	4.88636	−	5.42686i	0.677617	−	0.752569i
$53$	0.106558	−	1.01383i	0.0146368	−	0.139260i	−0.984763	−	0.173902i	$-0.944362\pi$
$53$	0.106558	−	1.01383i	0.0146368	−	0.139260i	0.999400	+	0.0346420i	$0.0110291\pi$
$54$	−1.84401	−	1.33975i	−0.250938	−	0.182317i
$55$	−0.188692	−	1.79528i	−0.0254432	−	0.242075i
$56$	−6.22676	+	10.7851i	−0.832085	+	1.44121i
$57$	−2.18565	−	3.78566i	−0.289497	−	0.501423i
$58$	15.0887	−	10.9626i	1.98125	−	1.43946i
$59$	3.07829	+	3.41879i	0.400760	+	0.445089i	0.909420	−	0.415879i	$-0.136526\pi$
$59$	3.07829	+	3.41879i	0.400760	+	0.445089i	−0.508661	+	0.860967i	$0.669859\pi$
$60$	0.787183	+	2.42270i	0.101625	+	0.312769i
$61$	0.251899			0.0322523			0.0161262	−	0.999870i	$-0.494867\pi$
$61$	0.251899			0.0322523			0.0161262	+	0.999870i	$0.494867\pi$
$62$	−9.45628	+	8.46365i	−1.20095	+	1.07488i
$63$	4.57095			0.575885
$64$	−4.01633	−	12.3610i	−0.502042	−	1.54513i
$65$	1.21914	+	1.35399i	0.151216	+	0.167942i
$66$	−4.17542	+	3.03362i	−0.513959	+	0.373413i
$67$	1.98619	+	3.44018i	0.242652	+	0.420285i	0.961469	−	0.274914i	$-0.0886494\pi$
$67$	1.98619	+	3.44018i	0.242652	+	0.420285i	−0.718817	+	0.695199i	$0.755316\pi$
$68$	4.11472	−	7.12690i	0.498983	−	0.864263i
$69$	0.731291	+	6.95777i	0.0880371	+	0.837617i
$70$	−6.71970	−	4.88215i	−0.803158	−	0.583529i
$71$	−0.804058	+	7.65010i	−0.0954241	+	0.907900i	0.837163	+	0.546954i	$0.184213\pi$
$71$	−0.804058	+	7.65010i	−0.0954241	+	0.907900i	−0.932587	+	0.360946i	$0.882454\pi$
$72$	1.82304	−	2.02469i	0.214848	−	0.238612i
$73$	8.35045	+	3.71786i	0.977346	+	0.435143i	0.832326	−	0.554286i	$-0.187009\pi$
$73$	8.35045	+	3.71786i	0.977346	+	0.435143i	0.145020	+	0.989429i	$0.453675\pi$
$74$	19.4617	+	4.13670i	2.26237	+	0.480882i
$75$	4.26906	−	0.907417i	0.492949	−	0.104779i
$76$	12.7601	−	5.68116i	1.46368	−	0.651674i
$77$	3.19835	−	9.84350i	0.364486	−	1.12177i
$78$	1.60972	−	4.95421i	0.182265	−	0.560953i
$79$	8.02362	−	3.57235i	0.902728	−	0.401920i	0.0977404	−	0.995212i	$-0.468839\pi$
$79$	8.02362	−	3.57235i	0.902728	−	0.401920i	0.804988	+	0.593292i	$0.202172\pi$
$80$	0.140848	−	0.0299381i	0.0157473	−	0.00334719i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−22.0403	−	9.81297i	−2.43394	−	1.08366i
$83$	−1.85000	+	2.05463i	−0.203064	+	0.225525i	−0.836072	−	0.548620i	$-0.815153\pi$
$83$	−1.85000	+	2.05463i	−0.203064	+	0.225525i	0.633008	+	0.774145i	$0.281820\pi$
$84$	−1.52670	+	14.5256i	−0.166577	+	1.58487i
$85$	1.66110	+	1.20686i	0.180171	+	0.130902i
$86$	−0.469890	−	4.47071i	−0.0506696	−	0.482089i
$87$	4.09128	−	7.08630i	0.438631	−	0.759731i
$88$	−3.08456	−	5.34261i	−0.328815	−	0.569524i
$89$	−1.10573	+	0.803361i	−0.117207	+	0.0851561i	−0.644845	−	0.764314i	$-0.723078\pi$
$89$	−1.10573	+	0.803361i	−0.117207	+	0.0851561i	0.527637	+	0.849470i	$0.323078\pi$
$90$	1.21590	+	1.35039i	0.128167	+	0.142344i
$91$	3.22813	+	9.93515i	0.338400	+	1.04149i
$92$	−22.3547			−2.33064
$93$	−2.27974	+	5.07964i	−0.236398	+	0.526735i
$94$	−8.09627			−0.835066
$95$	1.07690	+	3.31435i	0.110487	+	0.340045i
$96$	−3.92156	−	4.35533i	−0.400242	−	0.444514i
$97$	−0.0532738	+	0.0387057i	−0.00540914	+	0.00392997i	−0.590487	−	0.807047i	$-0.701064\pi$
$97$	−0.0532738	+	0.0387057i	−0.00540914	+	0.00392997i	0.585077	+	0.810977i	$0.301064\pi$
$98$	−15.8339	−	27.4252i	−1.59947	−	2.77036i
$99$	−1.13216	+	1.96096i	−0.113786	+	0.197083i
$100$	1.45772	+	13.8693i	0.145772	+	1.38693i
$101$	−9.55254	−	6.94033i	−0.950513	−	0.690588i	0.000414784	−	1.00000i	$-0.499868\pi$
$101$	−9.55254	−	6.94033i	−0.950513	−	0.690588i	−0.950928	+	0.309411i	$0.899868\pi$
$102$	0.613617	−	5.83817i	0.0607571	−	0.578065i
$103$	12.1843	−	13.5320i	1.20055	−	1.33335i	0.271931	−	0.962317i	$-0.412338\pi$
$103$	12.1843	−	13.5320i	1.20055	−	1.33335i	0.928621	−	0.371030i	$-0.120995\pi$
$104$	5.68824	+	2.53257i	0.557778	+	0.248339i
$105$	−3.56444	−	0.757645i	−0.347854	−	0.0739386i
$106$	2.27279	−	0.483097i	0.220753	−	0.0469225i
$107$	5.71321	−	2.54368i	0.552317	−	0.245907i	−0.111549	−	0.993759i	$-0.535581\pi$
$107$	5.71321	−	2.54368i	0.552317	−	0.245907i	0.663866	+	0.747852i	$0.268915\pi$
$108$	0.987405	−	3.03892i	0.0950131	−	0.292420i
$109$	−2.99731	+	9.22477i	−0.287090	+	0.883573i	0.698674	+	0.715440i	$0.253774\pi$
$109$	−2.99731	+	9.22477i	−0.287090	+	0.883573i	−0.985764	+	0.168133i	$0.946226\pi$
$110$	3.75884	−	1.67354i	0.358391	−	0.159566i
$111$	8.53835	−	1.81488i	0.810424	−	0.172261i
$112$	0.807562	+	0.171653i	0.0763075	+	0.0162196i
$113$	−3.81080	−	1.69668i	−0.358490	−	0.159610i	0.219585	−	0.975593i	$-0.429530\pi$
$113$	−3.81080	−	1.69668i	−0.358490	−	0.159610i	−0.578076	+	0.815983i	$0.696196\pi$
$114$	6.66696	−	7.40441i	0.624418	−	0.693486i
$115$	0.583003	−	5.54691i	0.0543653	−	0.517252i
$116$	21.1524	+	15.3681i	1.96395	+	1.42689i
$117$	−0.238889	−	2.27288i	−0.0220853	−	0.210128i
$118$	−5.24294	+	9.08104i	−0.482652	+	0.835977i
$119$	5.88618	+	10.1952i	0.539585	+	0.934588i
$120$	−1.75721	+	1.27669i	−0.160411	+	0.116545i
$121$	−3.92972	−	4.36439i	−0.357247	−	0.396763i
$122$	0.177425	+	0.546057i	0.0160633	+	0.0494377i
$123$	−10.5848			−0.954397
$124$	−15.3807	−	8.94117i	−1.38123	−	0.802941i
$125$	−7.46555			−0.667739
$126$	3.21954	+	9.90873i	0.286820	+	0.882740i
$127$	13.6658	+	15.1774i	1.21264	+	1.34678i	0.920666	+	0.390352i	$0.127647\pi$
$127$	13.6658	+	15.1774i	1.21264	+	1.34678i	0.291978	+	0.956425i	$0.405687\pi$
$128$	14.4841	−	10.5233i	1.28022	−	0.930136i
$129$	−0.986112	−	1.70800i	−0.0868223	−	0.150381i
$130$	−2.07643	+	3.59649i	−0.182115	+	0.315433i
$131$	−0.245534	−	2.33610i	−0.0214524	−	0.204106i	0.978546	−	0.206030i	$-0.0660544\pi$
$131$	−0.245534	−	2.33610i	−0.0214524	−	0.204106i	−0.999998	+	0.00192351i	$0.999388\pi$
$132$	−5.85339	−	4.25274i	−0.509472	−	0.370153i
$133$	−2.08858	+	19.8715i	−0.181103	+	1.72308i
$134$	−6.05853	+	6.72868i	−0.523378	+	0.581270i
$135$	0.728301	+	0.324260i	0.0626821	+	0.0279079i
$136$	6.86352	+	1.45889i	0.588542	+	0.125099i
$137$	17.7257	−	3.76772i	1.51441	−	0.321898i	0.625591	−	0.780151i	$-0.284858\pi$
$137$	17.7257	−	3.76772i	1.51441	−	0.321898i	0.888822	+	0.458253i	$0.151525\pi$
$138$	−14.5677	+	6.48597i	−1.24009	+	0.552122i
$139$	−1.11458	+	3.43033i	−0.0945377	+	0.290957i	−0.987133	−	0.159902i	$-0.948882\pi$
$139$	−1.11458	+	3.43033i	−0.0945377	+	0.290957i	0.892595	+	0.450859i	$0.148882\pi$
$140$	3.59817	−	11.0740i	0.304101	−	0.935927i
$141$	−3.24496	+	1.44475i	−0.273275	+	0.121670i
$142$	−17.1499	+	3.64533i	−1.43919	+	0.305910i
$143$	−5.06178	−	1.07592i	−0.423288	−	0.0899726i
$144$	−0.165004	−	0.0734647i	−0.0137504	−	0.00612206i
$145$	−4.36496	+	4.84778i	−0.362490	+	0.402586i
$146$	−2.17781	+	20.7205i	−0.180237	+	1.71484i
$147$	−11.2401	−	8.16643i	−0.927070	−	0.673556i
$148$	2.91553	+	27.7394i	0.239655	+	2.28016i
$149$	−6.12004	+	10.6002i	−0.501373	+	0.868403i	0.498626	+	0.866817i	$0.333838\pi$
$149$	−6.12004	+	10.6002i	−0.501373	+	0.868403i	−0.999999	+	0.00158608i	$0.999495\pi$
$150$	4.97397	+	8.61518i	0.406123	+	0.703426i
$151$	−0.444224	+	0.322748i	−0.0361504	+	0.0262648i	−0.605714	−	0.795683i	$-0.707112\pi$
$151$	−0.444224	+	0.322748i	−0.0361504	+	0.0262648i	0.569563	+	0.821947i	$0.307112\pi$
$152$	7.96907	+	8.85055i	0.646377	+	0.717875i
$153$	−0.795865	−	2.44942i	−0.0643419	−	0.198024i
$154$	23.5911			1.90103
$155$	2.61971	−	3.58325i	0.210420	−	0.287814i
$156$	7.30255			0.584672
$157$	−2.61513	−	8.04854i	−0.208710	−	0.642343i	−0.999541	−	0.0303083i	$-0.990351\pi$
$157$	−2.61513	−	8.04854i	−0.208710	−	0.642343i	0.790831	−	0.612035i	$-0.209649\pi$
$158$	13.3954	+	14.8771i	1.06568	+	1.18356i
$159$	0.824721	−	0.599195i	0.0654047	−	0.0475193i
$160$	2.33614	+	4.04631i	0.184688	+	0.319889i
$161$	15.9894	−	27.6944i	1.26014	−	2.18263i
$162$	−0.238254	−	2.26684i	−0.0187190	−	0.178099i
$163$	−6.23819	−	4.53231i	−0.488613	−	0.354998i	0.316038	−	0.948747i	$-0.397647\pi$
$163$	−6.23819	−	4.53231i	−0.488613	−	0.354998i	−0.804651	+	0.593748i	$0.797647\pi$
$164$	3.53532	−	33.6364i	0.276062	−	2.62656i
$165$	1.20789	−	1.34150i	0.0940344	−	0.104436i
$166$	−5.75700	−	2.56318i	−0.446830	−	0.198941i
$167$	−17.2546	−	3.66757i	−1.33520	−	0.283805i	−0.515642	−	0.856804i	$-0.672447\pi$
$167$	−17.2546	−	3.66757i	−1.33520	−	0.283805i	−0.819556	+	0.572999i	$0.805780\pi$
$168$	−12.1814	+	2.58923i	−0.939814	+	0.199764i
$169$	−7.10460	+	3.16317i	−0.546508	+	0.243321i
$170$	−1.44619	+	4.45092i	−0.110918	+	0.341370i
$171$	1.35081	−	4.15736i	0.103299	−	0.317921i
$172$	5.75704	−	2.56320i	0.438970	−	0.195442i
$173$	21.5097	−	4.57204i	1.63536	−	0.347605i	0.703573	−	0.710623i	$-0.251587\pi$
$173$	21.5097	−	4.57204i	1.63536	−	0.347605i	0.931782	+	0.363018i	$0.118254\pi$
$174$	18.2431	+	3.87770i	1.38301	+	0.293967i
$175$	−18.2249	−	8.11423i	−1.37767	−	0.613378i
$176$	−0.273661	+	0.303932i	−0.0206280	+	0.0229097i
$177$	−0.480877	+	4.57523i	−0.0361449	+	0.343896i
$178$	−2.52032	−	1.83112i	−0.188906	−	0.137248i
$179$	−0.902491	−	8.58663i	−0.0674553	−	0.641795i	−0.975056	−	0.221960i	$-0.928755\pi$
$179$	−0.902491	−	8.58663i	−0.0674553	−	0.641795i	0.907600	−	0.419835i	$-0.137912\pi$
$180$	−1.27369	+	2.20609i	−0.0949352	+	0.164433i
$181$	−7.83047	−	13.5628i	−0.582034	−	1.00811i	−0.995238	−	0.0974742i	$-0.968924\pi$
$181$	−7.83047	−	13.5628i	−0.582034	−	1.00811i	0.413204	−	0.910639i	$-0.364410\pi$
$182$	−19.2633	+	13.9956i	−1.42789	+	1.03743i
$183$	0.168553	+	0.187197i	0.0124598	+	0.0138380i
$184$	−5.89012	−	18.1279i	−0.434225	−	1.33641i
$185$	−6.95905			−0.511640
$186$	−12.6172	−	1.36409i	−0.925138	−	0.100020i
$187$	−5.83169			−0.426455
$188$	−3.50731	−	10.7944i	−0.255797	−	0.787262i
$189$	3.05856	+	3.39688i	0.222478	+	0.247086i
$190$	−6.42621	+	4.66892i	−0.466206	+	0.338719i
$191$	4.38724	+	7.59893i	0.317450	+	0.549839i	0.979955	−	0.199218i	$-0.0638402\pi$
$191$	4.38724	+	7.59893i	0.317450	+	0.549839i	−0.662505	+	0.749057i	$0.730507\pi$
$192$	6.49857	−	11.2558i	0.468994	−	0.812321i
$193$	−0.234416	−	2.23032i	−0.0168737	−	0.160542i	0.982840	−	0.184458i	$-0.0590531\pi$
$193$	−0.234416	−	2.23032i	−0.0168737	−	0.160542i	−0.999714	+	0.0239164i	$0.992386\pi$
$194$	−0.121428	−	0.0882228i	−0.00871804	−	0.00633403i
$195$	−0.190448	+	1.81199i	−0.0136383	+	0.129760i
$196$	29.7055	−	32.9913i	2.12182	−	2.35652i
$197$	−6.87851	−	3.06251i	−0.490074	−	0.218195i	0.146795	−	0.989167i	$-0.453104\pi$
$197$	−6.87851	−	3.06251i	−0.490074	−	0.218195i	−0.636869	+	0.770972i	$0.719771\pi$
$198$	−5.04832	−	1.07305i	−0.358769	−	0.0762587i
$199$	−5.48522	+	1.16592i	−0.388837	+	0.0826499i	−0.398182	−	0.917306i	$-0.630359\pi$
$199$	−5.48522	+	1.16592i	−0.388837	+	0.0826499i	0.00934480	+	0.999956i	$0.497025\pi$
$200$	−10.8628	+	4.83645i	−0.768119	+	0.341989i
$201$	−1.22753	+	3.77796i	−0.0865835	+	0.266477i
$202$	8.31667	−	25.5961i	0.585159	−	1.80093i
$203$	−34.1685	+	15.2128i	−2.39816	+	1.06773i
$204$	8.04960	−	1.71100i	0.563585	−	0.119794i
$205$	8.25404	+	1.75445i	0.576487	+	0.122536i
$206$	37.9162	+	16.8814i	2.64174	+	1.17618i
$207$	−4.68130	+	5.19911i	−0.325373	+	0.361363i
$208$	0.0431481	−	0.410527i	0.00299178	−	0.0284649i
$209$	−8.00767	−	5.81791i	−0.553902	−	0.402433i
$210$	−0.868214	−	8.26051i	−0.0599125	−	0.570029i
$211$	1.35528	−	2.34741i	0.0933010	−	0.161602i	−0.815597	−	0.578620i	$-0.803591\pi$
$211$	1.35528	−	2.34741i	0.0933010	−	0.161602i	0.908898	+	0.417018i	$0.136925\pi$
$212$	1.62867	+	2.82094i	0.111857	+	0.193743i
$213$	−6.22315	+	4.52138i	−0.426403	+	0.309800i
$214$	9.53820	+	10.5932i	0.652018	+	0.724139i
$215$	0.485869	+	1.49535i	0.0331360	+	0.101982i
$216$	2.72449			0.185378
$217$	22.0781	−	12.6593i	1.49876	−	0.859372i
$218$	−22.1083			−1.49736
$219$	2.82463	+	8.69333i	0.190871	+	0.587441i
$220$	3.85959	+	4.28651i	0.260214	+	0.288997i
$221$	4.76186	−	3.45969i	0.320317	−	0.232724i
$222$	9.94822	+	17.2308i	0.667681	+	1.15646i
$223$	3.14107	−	5.44050i	0.210342	−	0.364323i	−0.741480	−	0.670975i	$-0.765876\pi$
$223$	3.14107	−	5.44050i	0.210342	−	0.364323i	0.951822	+	0.306652i	$0.0992089\pi$
$224$	2.80020	+	26.6421i	0.187096	+	1.78010i
$225$	3.53090	+	2.56535i	0.235393	+	0.171023i
$226$	0.993864	−	9.45598i	0.0661108	−	0.629002i
$227$	6.45159	−	7.16521i	0.428207	−	0.475572i	−0.489972	−	0.871738i	$-0.662993\pi$
$227$	6.45159	−	7.16521i	0.428207	−	0.475572i	0.918179	+	0.396166i	$0.129660\pi$
$228$	12.7601	+	5.68116i	0.845058	+	0.376244i
$229$	3.48220	+	0.740164i	0.230110	+	0.0489114i	0.321523	−	0.946902i	$-0.395805\pi$
$229$	3.48220	+	0.740164i	0.230110	+	0.0489114i	−0.0914134	+	0.995813i	$0.529138\pi$
$230$	12.4350	−	2.64315i	0.819941	−	0.174284i
$231$	9.45526	−	4.20975i	0.622111	−	0.276981i
$232$	−6.88902	+	21.2022i	−0.452286	+	1.39199i
$233$	0.691952	−	2.12961i	0.0453313	−	0.139515i	−0.925829	−	0.377942i	$-0.876632\pi$
$233$	0.691952	−	2.12961i	0.0453313	−	0.139515i	0.971160	+	0.238427i	$0.0766318\pi$
$234$	4.75880	−	2.11876i	0.311093	−	0.138507i
$235$	2.76990	−	0.588760i	0.180688	−	0.0384065i
$236$	−14.3786	−	3.05626i	−0.935966	−	0.198946i
$237$	8.02362	+	3.57235i	0.521190	+	0.232049i
$238$	−17.9548	+	19.9408i	−1.16383	+	1.29257i
$239$	1.56290	−	14.8700i	0.101096	−	0.961860i	−0.819958	−	0.572424i	$-0.806003\pi$
$239$	1.56290	−	14.8700i	0.101096	−	0.961860i	0.921053	−	0.389436i	$-0.127330\pi$
$240$	0.116494	+	0.0846379i	0.00751966	+	0.00546335i
$241$	0.0972398	+	0.925175i	0.00626377	+	0.0595958i	0.997207	−	0.0746837i	$-0.0237947\pi$
$241$	0.0972398	+	0.925175i	0.00626377	+	0.0595958i	−0.990944	+	0.134279i	$0.957128\pi$
$242$	6.69308	−	11.5928i	0.430247	−	0.745210i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−0.651173	+	0.473105i	−0.0416871	+	0.0302874i
$245$	7.41148	+	8.23128i	0.473502	+	0.525877i
$246$	−7.45538	−	22.9453i	−0.475338	−	1.46294i
$247$	9.99018			0.635660
$248$	3.19802	−	14.8284i	0.203075	−	0.941604i
$249$	−2.76478			−0.175211
$250$	−5.25836	−	16.1836i	−0.332568	−	1.02354i
$251$	9.74726	+	10.8254i	0.615241	+	0.683295i	0.967576	−	0.252579i	$-0.0812788\pi$
$251$	9.74726	+	10.8254i	0.615241	+	0.683295i	−0.352335	+	0.935874i	$0.614612\pi$
$252$	−11.8162	+	8.58495i	−0.744349	+	0.540801i
$253$	7.92069	+	13.7190i	0.497970	+	0.862509i
$254$	−23.2755	+	40.3144i	−1.46044	+	2.52955i
$255$	0.214621	+	2.04198i	0.0134401	+	0.127874i
$256$	11.9841	+	8.70692i	0.749003	+	0.544183i
$257$	−0.350300	+	3.33288i	−0.0218511	+	0.207899i	−1.00000		6.32408e-6i	$-0.999998\pi$
$257$	−0.350300	+	3.33288i	−0.0218511	+	0.207899i	0.978149	+	0.207906i	$0.0666647\pi$
$258$	3.00796	−	3.34068i	0.187268	−	0.207982i
$259$	−36.4507	−	16.2289i	−2.26494	−	1.00841i
$260$	−5.69455	−	1.21042i	−0.353161	−	0.0750668i
$261$	8.00375	−	1.70125i	0.495420	−	0.105305i
$262$	4.89118	−	2.17769i	0.302178	−	0.134538i
$263$	5.79482	−	17.8346i	0.357324	−	1.09973i	−0.597326	−	0.801999i	$-0.703770\pi$
$263$	5.79482	−	17.8346i	0.357324	−	1.09973i	0.954650	−	0.297731i	$-0.0962299\pi$
$264$	1.90636	−	5.86718i	0.117328	−	0.361100i
$265$	−0.742438	+	0.330555i	−0.0456076	+	0.0203058i
$266$	−44.5479	+	9.46895i	−2.73141	+	0.580579i
$267$	−1.33689	−	0.284165i	−0.0818165	−	0.0173906i
$268$	−11.5956	−	5.16270i	−0.708315	−	0.315362i
$269$	10.2024	−	11.3309i	0.622049	−	0.690856i	−0.346960	−	0.937880i	$-0.612786\pi$
$269$	10.2024	−	11.3309i	0.622049	−	0.690856i	0.969009	+	0.247024i	$0.0794527\pi$
$270$	−0.189942	+	1.80718i	−0.0115595	+	0.109981i
$271$	11.0514	+	8.02930i	0.671324	+	0.487745i	0.870468	−	0.492225i	$-0.163816\pi$
$271$	11.0514	+	8.02930i	0.671324	+	0.487745i	−0.199144	+	0.979970i	$0.563816\pi$
$272$	−0.0486247	−	0.462633i	−0.00294831	−	0.0280513i
$273$	−5.22322	+	9.04688i	−0.316124	+	0.547542i
$274$	20.6527	+	35.7714i	1.24767	+	2.16103i
$275$	7.99508	−	5.80876i	0.482121	−	0.350282i
$276$	−14.9582	−	16.6128i	−0.900378	−	0.999971i
$277$	2.94103	+	9.05156i	0.176709	+	0.543855i	0.999707	−	0.0241888i	$-0.00770030\pi$
$277$	2.94103	+	9.05156i	0.176709	+	0.543855i	−0.822998	+	0.568044i	$0.807700\pi$
$278$	−8.22121			−0.493075
$279$	−5.30035	+	1.70477i	−0.317324	+	0.102062i
$280$	9.92825			0.593326
$281$	4.26083	+	13.1135i	0.254180	+	0.782286i	0.993990	+	0.109470i	$0.0349153\pi$
$281$	4.26083	+	13.1135i	0.254180	+	0.782286i	−0.739810	+	0.672816i	$0.765085\pi$
$282$	−5.41746	−	6.01670i	−0.322605	−	0.358289i
$283$	−9.86758	+	7.16922i	−0.586567	+	0.426166i	−0.841086	−	0.540902i	$-0.818083\pi$
$283$	−9.86758	+	7.16922i	−0.586567	+	0.426166i	0.254519	+	0.967068i	$0.418083\pi$
$284$	−12.2895	−	21.2861i	−0.729250	−	1.26310i
$285$	−1.74246	+	3.01802i	−0.103214	+	0.178772i
$286$	−1.23293	−	11.7306i	−0.0729049	−	0.693643i
$287$	39.1422	+	28.4385i	2.31049	+	1.67867i
$288$	0.612608	−	5.82857i	0.0360982	−	0.343452i
$289$	−6.93684	+	7.70414i	−0.408049	+	0.453184i
$290$	−13.5833	−	6.04768i	−0.797639	−	0.355132i
$291$	−0.0644111	−	0.0136910i	−0.00377585	−	0.000802581i
$292$	−28.5691	+	6.07255i	−1.67188	+	0.355369i
$293$	−15.5981	+	6.94474i	−0.911253	+	0.405716i	−0.808165	−	0.588956i	$-0.799539\pi$
$293$	−15.5981	+	6.94474i	−0.911253	+	0.405716i	−0.103088	+	0.994672i	$0.532872\pi$
$294$	9.78592	−	30.1180i	0.570726	−	1.75651i
$295$	1.13334	−	3.48808i	0.0659859	−	0.203084i
$296$	−21.7263	+	9.67317i	−1.26281	+	0.562241i
$297$	−2.21484	+	0.470778i	−0.128518	+	0.0273173i
$298$	−27.2894	−	5.80054i	−1.58083	−	0.336016i
$299$	−14.6066	−	6.50326i	−0.844719	−	0.376093i
$300$	−9.33150	+	10.3637i	−0.538755	+	0.598348i
$301$	−0.942317	+	8.96554i	−0.0543142	+	0.516765i
$302$	−1.01253	−	0.735646i	−0.0582645	−	0.0423317i
$303$	−1.23423	−	11.7429i	−0.0709046	−	0.674612i
$304$	0.394772	−	0.683765i	0.0226417	−	0.0392166i
$305$	−0.100410	−	0.173915i	−0.00574945	−	0.00995834i
$306$	4.74920	−	3.45050i	0.271494	−	0.197252i
$307$	−20.1382	−	22.3657i	−1.14935	−	1.27648i	−0.955349	−	0.295478i	$-0.904521\pi$
$307$	−20.1382	−	22.3657i	−1.14935	−	1.27648i	−0.193998	−	0.981002i	$-0.562146\pi$
$308$	10.2197	+	31.4530i	0.582322	+	1.79220i
$309$	18.2091			1.03588
$310$	9.61283	+	3.15505i	0.545972	+	0.179195i
$311$	4.97560			0.282141			0.141070	−	0.990000i	$-0.454946\pi$
$311$	4.97560			0.282141			0.141070	+	0.990000i	$0.454946\pi$
$312$	1.92411	+	5.92180i	0.108931	+	0.335256i
$313$	9.79194	+	10.8751i	0.553473	+	0.614694i	0.953347	−	0.301876i	$-0.0976128\pi$
$313$	9.79194	+	10.8751i	0.553473	+	0.614694i	−0.399874	+	0.916570i	$0.630946\pi$
$314$	15.6054	−	11.3380i	0.880662	−	0.639838i
$315$	−1.82204	−	3.15586i	−0.102660	−	0.177812i
$316$	−14.0321	+	24.3043i	−0.789368	+	1.36723i
$317$	−3.33739	−	31.7532i	−0.187447	−	1.78344i	−0.534079	−	0.845434i	$-0.679342\pi$
$317$	−3.33739	−	31.7532i	−0.187447	−	1.78344i	0.346633	−	0.938001i	$-0.387325\pi$
$318$	1.87981	+	1.36576i	0.105414	+	0.0765880i
$319$	1.93669	−	18.4264i	0.108434	−	1.03168i
$320$	−6.93328	+	7.70019i	−0.387582	+	0.430454i
$321$	5.71321	+	2.54368i	0.318880	+	0.141975i
$322$	71.2971	+	15.1547i	3.97323	+	0.844537i
$323$	11.0122	−	2.34071i	0.612733	−	0.130240i
$324$	2.91906	−	1.29965i	0.162170	−	0.0722027i
$325$	−3.08228	+	9.48629i	−0.170974	+	0.526204i
$326$	5.43112	−	16.7153i	0.300802	−	0.925773i
$327$	−8.86093	+	3.94514i	−0.490011	+	0.218167i
$328$	28.2080	−	5.99579i	1.55752	−	0.331062i
$329$	15.8814	+	3.37570i	0.875572	+	0.186109i
$330$	3.75884	+	1.67354i	0.206917	+	0.0921255i
$331$	5.03356	−	5.59033i	0.276669	−	0.307272i	−0.588756	−	0.808311i	$-0.700382\pi$
$331$	5.03356	−	5.59033i	0.276669	−	0.307272i	0.865425	+	0.501039i	$0.167049\pi$
$332$	0.923438	−	8.78593i	0.0506802	−	0.482190i
$333$	7.06199	+	5.13084i	0.386995	+	0.281168i
$334$	−4.20281	−	39.9871i	−0.229968	−	2.18800i
$335$	1.58344	−	2.74260i	0.0865125	−	0.149844i
$336$	0.412802	+	0.714994i	0.0225202	+	0.0390061i
$337$	−6.38542	+	4.63928i	−0.347836	+	0.252717i	−0.747961	−	0.663743i	$-0.768967\pi$
$337$	−6.38542	+	4.63928i	−0.347836	+	0.252717i	0.400125	+	0.916461i	$0.368967\pi$
$338$	−11.8611	−	13.1731i	−0.645160	−	0.716523i
$339$	−1.28905	−	3.96728i	−0.0700114	−	0.215473i
$340$	−6.56070			−0.355804
$341$	−0.0375157	+	12.6071i	−0.00203159	+	0.682714i
$342$	9.96361			0.538770
$343$	9.73715	+	29.9679i	0.525757	+	1.61811i
$344$	3.59545	+	3.99315i	0.193853	+	0.215296i
$345$	4.51226	−	3.27835i	0.242932	−	0.176500i
$346$	25.0615	+	43.4077i	1.34731	+	2.33361i
$347$	−16.7024	+	28.9294i	−0.896632	+	1.55301i	−0.0648612	+	0.997894i	$0.520660\pi$
$347$	−16.7024	+	28.9294i	−0.896632	+	1.55301i	−0.831771	+	0.555119i	$0.812673\pi$
$348$	2.73298	+	26.0026i	0.146503	+	1.39388i
$349$	6.03663	+	4.38587i	0.323134	+	0.234770i	0.737511	−	0.675335i	$-0.236001\pi$
$349$	6.03663	+	4.38587i	0.323134	+	0.234770i	−0.414378	+	0.910105i	$0.636001\pi$
$350$	4.75307	−	45.2224i	0.254062	−	2.41724i
$351$	1.52923	−	1.69838i	0.0816243	−	0.0906529i
$352$	−12.1231	−	5.39757i	−0.646166	−	0.287691i
$353$	−3.48905	−	0.741620i	−0.185703	−	0.0394725i	0.114121	−	0.993467i	$-0.463595\pi$
$353$	−3.48905	−	0.741620i	−0.185703	−	0.0394725i	−0.299825	+	0.953994i	$0.596928\pi$
$354$	−10.2567	+	2.18014i	−0.545139	+	0.115873i
$355$	5.60226	−	2.49429i	0.297337	−	0.132383i
$356$	1.34955	−	4.15347i	0.0715258	−	0.220134i
$357$	−3.63786	+	11.1962i	−0.192536	+	0.592564i
$358$	17.9781	−	8.00437i	0.950173	−	0.423044i
$359$	−23.1016	+	4.91039i	−1.21925	+	0.259161i	−0.772220	−	0.635356i	$-0.780853\pi$
$359$	−23.1016	+	4.91039i	−1.21925	+	0.259161i	−0.447035	+	0.894516i	$0.647520\pi$
$360$	−2.12457	−	0.451591i	−0.111975	−	0.0238009i
$361$	0.0989471	+	0.0440541i	0.00520774	+	0.00231864i
$362$	23.8855	−	26.5275i	1.25539	−	1.39426i
$363$	0.613882	−	5.84070i	0.0322204	−	0.306557i
$364$	−27.0047	−	19.6200i	−1.41543	−	1.02837i
$365$	−0.761719	−	7.24727i	−0.0398702	−	0.379340i
$366$	−0.287079	+	0.497236i	−0.0150059	+	0.0259909i
$367$	−10.8521	−	18.7965i	−0.566477	−	0.981167i	−0.996911	−	0.0785449i	$-0.974973\pi$
$367$	−10.8521	−	18.7965i	−0.566477	−	0.981167i	0.430433	−	0.902622i	$-0.358361\pi$
$368$	−1.02230	+	0.742745i	−0.0532911	+	0.0387183i
$369$	−7.08260	−	7.86602i	−0.368705	−	0.409489i
$370$	−4.90160	−	15.0856i	−0.254822	−	0.784262i
$371$	−4.65968			−0.241918
$372$	−3.64710	−	17.4129i	−0.189093	−	0.902816i
$373$	−15.7335			−0.814648			−0.407324	−	0.913284i	$-0.633538\pi$
$373$	−15.7335			−0.814648			−0.407324	+	0.913284i	$0.633538\pi$
$374$	−4.10754	−	12.6417i	−0.212396	−	0.653688i
$375$	−4.99543	−	5.54799i	−0.257963	−	0.286497i
$376$	7.82929	−	5.68831i	0.403765	−	0.293352i
$377$	9.35020	+	16.1950i	0.481560	+	0.834086i
$378$	−5.20933	+	9.02282i	−0.267939	+	0.464084i
$379$	0.674334	+	6.41586i	0.0346382	+	0.329560i	0.998095	+	0.0616965i	$0.0196511\pi$
$379$	0.674334	+	6.41586i	0.0346382	+	0.329560i	−0.963457	+	0.267864i	$0.913682\pi$
$380$	−9.00870	−	6.54520i	−0.462137	−	0.335762i
$381$	−2.13481	+	20.3113i	−0.109370	+	1.04058i
$382$	−13.3825	+	14.8628i	−0.684710	+	0.760448i
$383$	23.6292	+	10.5204i	1.20740	+	0.537568i	0.908969	−	0.416864i	$-0.136871\pi$
$383$	23.6292	+	10.5204i	1.20740	+	0.537568i	0.298428	+	0.954432i	$0.403538\pi$
$384$	17.5121	+	3.72230i	0.893659	+	0.189953i
$385$	−8.07102	+	1.71555i	−0.411337	+	0.0874324i
$386$	4.66970	−	2.07909i	0.237682	−	0.105823i
$387$	0.609451	−	1.87570i	0.0309801	−	0.0953470i
$388$	0.0650207	−	0.200113i	0.00330093	−	0.0101592i
$389$	−21.3927	+	9.52463i	−1.08465	+	0.482918i	−0.869636	−	0.493693i	$-0.835647\pi$
$389$	−21.3927	+	9.52463i	−1.08465	+	0.482918i	−0.215015	+	0.976611i	$0.568980\pi$
$390$	−4.06212	+	0.863430i	−0.205693	+	0.0437215i
$391$	−17.6245	−	3.74621i	−0.891310	−	0.189454i
$392$	34.5803	+	15.3962i	1.74657	+	0.777624i
$393$	1.57177	−	1.74563i	0.0792852	−	0.0880552i
$394$	1.79393	−	17.0681i	0.0903767	−	0.859877i
$395$	−5.66472	−	4.11566i	−0.285023	−	0.207081i
$396$	−0.756283	−	7.19556i	−0.0380047	−	0.361590i
$397$	8.92563	−	15.4596i	0.447964	−	0.775897i	−0.550289	−	0.834974i	$-0.685482\pi$
$397$	8.92563	−	15.4596i	0.447964	−	0.775897i	0.998253	+	0.0590773i	$0.0188158\pi$
$398$	−6.39095	−	11.0695i	−0.320350	−	0.554862i
$399$	−16.1650	+	11.7445i	−0.809261	+	0.587962i
$400$	0.527478	+	0.585823i	0.0263739	+	0.0292912i
$401$	2.83024	+	8.71058i	0.141335	+	0.434986i	0.996522	−	0.0833353i	$-0.0265573\pi$
$401$	2.83024	+	8.71058i	0.141335	+	0.434986i	−0.855186	+	0.518321i	$0.826557\pi$
$402$	−9.05433			−0.451589
$403$	−7.44864	−	10.3166i	−0.371043	−	0.513906i
$404$	37.7289			1.87708
$405$	0.246356	+	0.758205i	0.0122415	+	0.0376755i
$406$	−57.0442	−	63.3541i	−2.83106	−	3.14421i
$407$	15.9906	−	11.6178i	0.792624	−	0.575875i
$408$	3.50843	+	6.07678i	0.173693	+	0.300845i
$409$	18.2182	−	31.5548i	0.900830	−	1.56028i	0.0744102	−	0.997228i	$-0.476293\pi$
$409$	18.2182	−	31.5548i	0.900830	−	1.56028i	0.826419	−	0.563055i	$-0.190374\pi$
$410$	2.01049	+	19.1286i	0.0992912	+	0.944692i
$411$	14.6608	+	10.6517i	0.723164	+	0.525410i
$412$	−6.08185	+	57.8650i	−0.299631	+	2.85080i
$413$	14.0707	−	15.6271i	0.692375	−	0.768960i
$414$	−14.5677	−	6.48597i	−0.715965	−	0.318768i
$415$	2.15598	+	0.458268i	0.105833	+	0.0224955i
$416$	13.1013	−	2.78477i	0.642344	−	0.136534i
$417$	−3.29504	+	1.46704i	−0.161359	+	0.0718415i
$418$	6.97166	−	21.4566i	0.340995	−	1.04948i
$419$	−5.84627	+	17.9930i	−0.285609	+	0.879015i	0.700606	+	0.713548i	$0.252913\pi$
$419$	−5.84627	+	17.9930i	−0.285609	+	0.879015i	−0.986215	+	0.165467i	$0.947087\pi$
$420$	10.6373	−	4.73601i	0.519045	−	0.231094i
$421$	−6.01043	+	1.27756i	−0.292931	+	0.0622643i	−0.352033	−	0.935988i	$-0.614509\pi$
$421$	−6.01043	+	1.27756i	−0.292931	+	0.0622643i	0.0591024	+	0.998252i	$0.481176\pi$
$422$	6.04321	+	1.28452i	0.294179	+	0.0625296i
$423$	−3.24496	−	1.44475i	−0.157775	−	0.0702461i
$424$	−1.85843	+	2.06400i	−0.0902534	+	0.100237i
$425$	−1.17495	+	11.1789i	−0.0569935	+	0.542257i
$426$	−14.1846	−	10.3057i	−0.687244	−	0.499312i
$427$	−0.120356	−	1.14511i	−0.00582442	−	0.0554157i
$428$	−9.99155	+	17.3059i	−0.482960	+	0.836511i
$429$	−2.58743	−	4.48157i	−0.124922	−	0.216372i
$430$	−2.89935	+	2.10650i	−0.139819	+	0.101584i
$431$	−23.9890	−	26.6425i	−1.15551	−	1.28333i	−0.952633	−	0.304121i	$-0.901637\pi$
$431$	−23.9890	−	26.6425i	−1.15551	−	1.28333i	−0.202878	−	0.979204i	$-0.565029\pi$
$432$	−0.0558146	−	0.171780i	−0.00268538	−	0.00826475i
$433$	19.1352			0.919578			0.459789	−	0.888028i	$-0.347925\pi$
$433$	19.1352			0.919578			0.459789	+	0.888028i	$0.347925\pi$
$434$	42.9931	+	38.9435i	2.06374	+	1.86935i
$435$	−6.52333			−0.312770
$436$	−9.57733	−	29.4760i	−0.458671	−	1.41164i
$437$	−20.4634	−	22.7269i	−0.978897	−	1.08718i
$438$	−16.8556	+	12.2463i	−0.805390	+	0.585150i
$439$	11.6441	+	20.1682i	0.555743	+	0.962574i	0.997845	+	0.0656099i	$0.0208993\pi$
$439$	11.6441	+	20.1682i	0.555743	+	0.962574i	−0.442103	+	0.896964i	$0.645767\pi$
$440$	−2.45909	+	4.25926i	−0.117232	+	0.203052i
$441$	−1.45227	−	13.8174i	−0.0691558	−	0.657974i
$442$	10.8538	+	7.88576i	0.516263	+	0.375087i
$443$	1.04224	−	9.91621i	0.0495181	−	0.471133i	−0.941461	−	0.337121i	$-0.890547\pi$
$443$	1.04224	−	9.91621i	0.0495181	−	0.471133i	0.990980	−	0.134013i	$-0.0427863\pi$
$444$	−18.6635	+	20.7279i	−0.885731	+	0.983704i
$445$	0.995412	+	0.443186i	0.0471871	+	0.0210090i
$446$	14.0061	+	2.97710i	0.663210	+	0.140970i
$447$	−11.9726	+	2.54485i	−0.566284	+	0.120367i
$448$	−54.2730	+	24.1639i	−2.56416	+	1.14164i
$449$	−11.1274	+	34.2467i	−0.525136	+	1.61620i	0.238910	+	0.971042i	$0.423210\pi$
$449$	−11.1274	+	34.2467i	−0.525136	+	1.61620i	−0.764046	+	0.645161i	$0.776790\pi$
$450$	−3.07409	+	9.46106i	−0.144914	+	0.445999i
$451$	−21.8952	+	9.74838i	−1.03101	+	0.459033i
$452$	13.0378	−	2.77127i	0.613246	−	0.130349i
$453$	−0.537092	−	0.114162i	−0.0252348	−	0.00536382i
$454$	20.0767	+	8.93870i	0.942244	+	0.419514i
$455$	5.57262	−	6.18902i	0.261249	−	0.290146i
$456$	−1.24489	+	11.8444i	−0.0582974	+	0.554663i
$457$	−4.02430	−	2.92383i	−0.188249	−	0.136771i	0.489669	−	0.871908i	$-0.337118\pi$
$457$	−4.02430	−	2.92383i	−0.188249	−	0.136771i	−0.677918	+	0.735137i	$0.737118\pi$
$458$	0.848182	+	8.06991i	0.0396329	+	0.377082i
$459$	1.28774	−	2.23043i	0.0601064	−	0.104107i
$460$	8.91085	+	15.4340i	0.415471	+	0.719616i
$461$	−1.94226	+	1.41114i	−0.0904602	+	0.0657232i	−0.632096	−	0.774890i	$-0.717805\pi$
$461$	−1.94226	+	1.41114i	−0.0904602	+	0.0657232i	0.541636	+	0.840613i	$0.317805\pi$
$462$	15.7856	+	17.5316i	0.734411	+	0.815646i
$463$	−0.662128	−	2.03782i	−0.0307717	−	0.0947055i	0.934491	−	0.355986i	$-0.115855\pi$
$463$	−0.662128	−	2.03782i	−0.0307717	−	0.0947055i	−0.965263	+	0.261281i	$0.915855\pi$
$464$	1.47793			0.0686113
$465$	4.41580	−	0.450838i	0.204778	−	0.0209071i
$466$	5.10387			0.236432
$467$	1.79375	+	5.52060i	0.0830049	+	0.255463i	0.983942	−	0.178486i	$-0.0571199\pi$
$467$	1.79375	+	5.52060i	0.0830049	+	0.255463i	−0.900938	+	0.433949i	$0.857120\pi$
$468$	4.88636	+	5.42686i	0.225872	+	0.250856i
$469$	14.6898	−	10.6727i	0.678310	−	0.492821i
$470$	3.22727	+	5.58980i	0.148863	+	0.257838i
$471$	4.23137	−	7.32894i	0.194971	−	0.337700i
$472$	−1.31014	−	12.4652i	−0.0603043	−	0.573757i
$473$	−3.61286	−	2.62490i	−0.166119	−	0.120693i
$474$	−2.09257	+	19.9095i	−0.0961150	+	0.914474i
$475$	−12.7659	+	14.1779i	−0.585738	+	0.650528i
$476$	−34.3642	−	15.2999i	−1.57508	−	0.701271i
$477$	0.997135	+	0.211948i	0.0456557	+	0.00970442i
$478$	33.3355	−	7.08567i	1.52473	−	0.324091i
$479$	−9.45267	+	4.20860i	−0.431903	+	0.192296i	−0.611161	−	0.791506i	$-0.709297\pi$
$479$	−9.45267	+	4.20860i	−0.431903	+	0.192296i	0.179257	+	0.983802i	$0.442630\pi$
$480$	−1.44381	+	4.44360i	−0.0659007	+	0.202822i
$481$	−6.16473	+	18.9731i	−0.281087	+	0.865098i
$482$	−1.93707	+	0.862439i	−0.0882311	+	0.0392830i
$483$	31.2800	−	6.64876i	1.42329	−	0.302529i
$484$	18.3556	+	3.90159i	0.834343	+	0.177345i
$485$	0.0479587	+	0.0213526i	0.00217769	+	0.000969571i
$486$	1.52516	−	1.69387i	0.0691828	−	0.0768353i
$487$	−2.90167	+	27.6076i	−0.131487	+	1.25102i	0.707440	+	0.706774i	$0.249850\pi$
$487$	−2.90167	+	27.6076i	−0.131487	+	1.25102i	−0.838927	+	0.544244i	$0.816816\pi$
$488$	−0.555225	−	0.403395i	−0.0251339	−	0.0182608i
$489$	−0.806001	−	7.66859i	−0.0364486	−	0.346786i
$490$	−12.6232	+	21.8640i	−0.570258	+	0.987716i
$491$	−8.79259	−	15.2292i	−0.396804	−	0.687285i	0.596526	−	0.802594i	$-0.296547\pi$
$491$	−8.79259	−	15.2292i	−0.396804	−	0.687285i	−0.993330	+	0.115309i	$0.963214\pi$
$492$	27.3623	−	19.8799i	1.23359	−	0.896253i
$493$	14.1012	+	15.6610i	0.635087	+	0.705336i
$494$	7.03657	+	21.6563i	0.316590	+	0.974365i
$495$	1.80517			0.0811363
$496$	−1.00045	+	0.102142i	−0.0449214	+	0.00458632i
$497$	35.1608			1.57718
$498$	−1.94737	−	5.99339i	−0.0872637	−	0.268570i
$499$	24.6905	+	27.4215i	1.10530	+	1.22756i	0.971624	+	0.236531i	$0.0760104\pi$
$499$	24.6905	+	27.4215i	1.10530	+	1.22756i	0.133672	+	0.991026i	$0.457323\pi$
$500$	19.2989	−	14.0215i	0.863073	−	0.627059i
$501$	−8.82002	−	15.2767i	−0.394049	−	0.682514i
$502$	−16.6015	+	28.7546i	−0.740961	+	1.28338i
$503$	−0.596021	−	5.67076i	−0.0265753	−	0.252847i	−0.999741	−	0.0227430i	$-0.992760\pi$
$503$	−0.596021	−	5.67076i	−0.0265753	−	0.252847i	0.973166	−	0.230104i	$-0.0739066\pi$
$504$	−10.0751	−	7.31999i	−0.448781	−	0.326058i
$505$	−0.983958	+	9.36173i	−0.0437855	+	0.416592i
$506$	−24.1607	+	26.8332i	−1.07407	+	1.19288i
$507$	−7.10460	−	3.16317i	−0.315526	−	0.140481i
$508$	−63.8324	−	13.5680i	−2.83211	−	0.601983i
$509$	−11.8744	+	2.52398i	−0.526323	+	0.111873i	−0.463407	−	0.886145i	$-0.653373\pi$
$509$	−11.8744	+	2.52398i	−0.526323	+	0.111873i	−0.0629159	+	0.998019i	$0.520040\pi$
$510$	−4.27537	+	1.90352i	−0.189316	+	0.0842891i
$511$	12.9112	−	39.7367i	0.571160	−	1.75785i
$512$	0.631244	−	1.94277i	0.0278973	−	0.0858591i
$513$	3.99339	−	1.77797i	0.176312	−	0.0784993i
$514$	−7.47162	+	1.58814i	−0.329559	+	0.0700500i
$515$	−14.1995	−	3.01820i	−0.625705	−	0.132998i
$516$	5.75704	+	2.56320i	0.253439	+	0.112839i
$517$	−5.38180	+	5.97709i	−0.236691	+	0.262872i
$518$	9.50640	−	90.4473i	0.417687	−	3.97403i
$519$	17.7905	+	12.9256i	0.780917	+	0.567369i
$520$	−0.518875	−	4.93677i	−0.0227542	−	0.216492i
$521$	8.96419	−	15.5264i	0.392728	−	0.680225i	−0.600080	−	0.799940i	$-0.704865\pi$
$521$	8.96419	−	15.5264i	0.392728	−	0.680225i	0.992808	+	0.119715i	$0.0381980\pi$
$522$	9.32534	+	16.1520i	0.408159	+	0.706952i
$523$	34.5751	−	25.1203i	1.51186	−	1.09843i	0.546523	−	0.837444i	$-0.315951\pi$
$523$	34.5751	−	25.1203i	1.51186	−	1.09843i	0.965341	−	0.260990i	$-0.0840490\pi$
$524$	5.02229	+	5.57781i	0.219400	+	0.243668i
$525$	−6.16476	−	18.9732i	−0.269052	−	0.828058i
$526$	42.7428			1.86368
$527$	−10.6278	−	9.62675i	−0.462955	−	0.419348i
$528$	−0.408981			−0.0177986
$529$	8.01756	+	24.6755i	0.348590	+	1.07285i
$530$	−1.23950	−	1.37661i	−0.0538405	−	0.0597959i
$531$	−3.72183	+	2.70407i	−0.161514	+	0.117347i
$532$	−31.9227	−	55.2918i	−1.38403	−	2.39720i
$533$	12.0952	−	20.9495i	0.523902	−	0.907425i
$534$	−0.325636	−	3.09822i	−0.0140917	−	0.134073i
$535$	−4.03356	−	2.93055i	−0.174386	−	0.126699i
$536$	1.13128	−	10.7634i	0.0488640	−	0.464910i
$537$	5.77722	−	6.41626i	0.249306	−	0.276882i
$538$	31.7487	+	14.1354i	1.36878	+	0.609422i
$539$	−30.7720	−	6.54078i	−1.32544	−	0.281731i
$540$	−2.49171	+	0.529630i	−0.107226	+	0.0227916i
$541$	12.7300	−	5.66776i	0.547305	−	0.243676i	−0.114407	−	0.993434i	$-0.536497\pi$
$541$	12.7300	−	5.66776i	0.547305	−	0.243676i	0.661712	+	0.749758i	$0.269830\pi$
$542$	−9.62159	+	29.6122i	−0.413283	+	1.27195i
$543$	4.83950	−	14.8944i	0.207683	−	0.639181i
$544$	13.7891	−	6.13929i	0.591202	−	0.263220i
$545$	7.56370	−	1.60771i	0.323993	−	0.0688669i
$546$	−23.2905	−	4.95054i	−0.996740	−	0.211864i
$547$	32.0565	+	14.2725i	1.37064	+	0.610248i	0.954269	−	0.298948i	$-0.0966357\pi$
$547$	32.0565	+	14.2725i	1.37064	+	0.610248i	0.416369	+	0.909196i	$0.363302\pi$
$548$	−38.7457	+	43.0315i	−1.65514	+	1.83821i
$549$	−0.0263306	+	0.250519i	−0.00112376	+	0.0106919i
$550$	18.2234	+	13.2400i	0.777047	+	0.564557i
$551$	3.73882	+	35.5725i	0.159279	+	1.51544i
$552$	9.53041	−	16.5072i	0.405641	−	0.702591i
$553$	−20.0732	−	34.7678i	−0.853599	−	1.47848i
$554$	−17.5501	+	12.7509i	−0.745633	+	0.541734i
$555$	−4.65652	−	5.17158i	−0.197658	−	0.219522i
$556$	−3.56144	−	10.9610i	−0.151039	−	0.464849i
$557$	−43.7230			−1.85260			−0.926301	−	0.376784i	$-0.877030\pi$
$557$	−43.7230			−1.85260			−0.926301	+	0.376784i	$0.877030\pi$
$558$	−7.42884	−	10.2892i	−0.314488	−	0.435575i
$559$	4.50732			0.190639
$560$	−0.203392	−	0.625977i	−0.00859489	−	0.0264524i
$561$	−3.90216	−	4.33379i	−0.164749	−	0.182973i
$562$	−25.4259	+	18.4730i	−1.07252	+	0.779235i
$563$	8.80229	+	15.2460i	0.370972	+	0.642543i	0.989715	−	0.143051i	$-0.0456912\pi$
$563$	8.80229	+	15.2460i	0.370972	+	0.642543i	−0.618743	+	0.785593i	$0.712358\pi$
$564$	5.67495	−	9.82930i	0.238958	−	0.413888i
$565$	0.347618	+	3.30736i	0.0146244	+	0.139142i
$566$	−22.4914	−	16.3410i	−0.945384	−	0.686862i
$567$	−0.477794	+	4.54591i	−0.0200655	+	0.190910i
$568$	14.0233	−	15.5744i	0.588403	−	0.653488i
$569$	−14.8350	−	6.60498i	−0.621916	−	0.276895i	0.0714905	−	0.997441i	$-0.477224\pi$
$569$	−14.8350	−	6.60498i	−0.621916	−	0.276895i	−0.693407	+	0.720546i	$0.743891\pi$
$570$	−7.76966	−	1.65149i	−0.325435	−	0.0691734i
$571$	3.82722	−	0.813500i	0.160164	−	0.0340439i	−0.127132	−	0.991886i	$-0.540577\pi$
$571$	3.82722	−	0.813500i	0.160164	−	0.0340439i	0.287296	+	0.957842i	$0.407244\pi$
$572$	15.1057	−	6.72551i	0.631603	−	0.281208i
$573$	−2.71147	+	8.34503i	−0.113273	+	0.348619i
$574$	−34.0781	+	104.882i	−1.42239	+	4.37768i
$575$	27.8942	−	12.4193i	1.16327	−	0.517920i
$576$	12.7131	−	2.70226i	0.529713	−	0.112594i
$577$	−0.546751	−	0.116216i	−0.0227615	−	0.00483811i	0.196517	−	0.980500i	$-0.437037\pi$
$577$	−0.546751	−	0.116216i	−0.0227615	−	0.00483811i	−0.219278	+	0.975662i	$0.570370\pi$
$578$	−21.5867	−	9.61102i	−0.897888	−	0.399766i
$579$	1.50060	−	1.66658i	0.0623627	−	0.0692608i
$580$	2.17880	−	20.7299i	0.0904697	−	0.860761i
$581$	10.2241	+	7.42823i	0.424166	+	0.308175i
$582$	−0.0156891	−	0.149271i	−0.000650332	−	0.00618750i
$583$	1.15414	−	1.99902i	0.0477994	−	0.0827910i
$584$	−12.4519	−	21.5673i	−0.515263	−	0.892462i
$585$	−1.47401	+	1.07093i	−0.0609428	+	0.0442775i
$586$	−26.0411	−	28.9216i	−1.07575	−	1.19474i
$587$	5.25895	+	16.1854i	0.217060	+	0.668042i	0.999001	+	0.0446895i	$0.0142298\pi$
$587$	5.25895	+	16.1854i	0.217060	+	0.668042i	−0.781941	+	0.623353i	$0.785770\pi$
$588$	44.3942			1.83079
$589$	−4.98937	−	23.8215i	−0.205584	−	0.981548i
$590$	8.35960			0.344159
$591$	−2.32673	−	7.16095i	−0.0957090	−	0.294562i
$592$	1.05498	+	1.17168i	0.0433596	+	0.0481557i
$593$	−4.55171	+	3.30701i	−0.186916	+	0.135803i	−0.677308	−	0.735699i	$-0.736854\pi$
$593$	−4.55171	+	3.30701i	−0.186916	+	0.135803i	0.490392	+	0.871502i	$0.336854\pi$
$594$	−2.58055	−	4.46965i	−0.105881	−	0.183392i
$595$	4.69260	−	8.12783i	0.192378	−	0.333208i
$596$	−4.08819	−	38.8966i	−0.167459	−	1.59327i
$597$	−4.53678	−	3.29616i	−0.185678	−	0.134903i
$598$	3.80941	−	36.2441i	0.155778	−	1.48213i
$599$	23.7618	−	26.3901i	0.970881	−	1.07827i	−0.0260249	−	0.999661i	$-0.508285\pi$
$599$	23.7618	−	26.3901i	0.970881	−	1.07827i	0.996905	−	0.0786108i	$-0.0250484\pi$
$600$	−10.8628	−	4.83645i	−0.443474	−	0.197447i
$601$	−33.3120	−	7.08069i	−1.35883	−	0.288828i	−0.529841	−	0.848097i	$-0.677748\pi$
$601$	−33.3120	−	7.08069i	−1.35883	−	0.288828i	−0.828986	+	0.559270i	$0.811082\pi$
$602$	−20.0989	+	4.27215i	−0.819170	+	0.174120i
$603$	−3.62895	+	1.61571i	−0.147782	+	0.0657969i
$604$	0.542175	−	1.66864i	0.0220608	−	0.0678961i
$605$	−1.44682	+	4.45284i	−0.0588214	+	0.181034i
$606$	24.5865	−	10.9466i	0.998759	−	0.444676i
$607$	15.8914	−	3.37783i	0.645013	−	0.137102i	0.126221	−	0.992002i	$-0.459715\pi$
$607$	15.8914	−	3.37783i	0.645013	−	0.137102i	0.518792	+	0.854900i	$0.326382\pi$
$608$	25.0590	+	5.32645i	1.01628	+	0.216016i
$609$	−34.1685	−	15.2128i	−1.38458	−	0.616453i
$610$	0.306283	−	0.340162i	0.0124010	−	0.0137727i
$611$	0.848547	−	8.07338i	0.0343285	−	0.326614i
$612$	6.65775	+	4.83714i	0.269124	+	0.195530i
$613$	2.71534	+	25.8347i	0.109672	+	1.04346i	0.901520	+	0.432738i	$0.142452\pi$
$613$	2.71534	+	25.8347i	0.109672	+	1.04346i	−0.791848	+	0.610718i	$0.790881\pi$
$614$	34.2993	−	59.4082i	1.38421	−	2.39752i
$615$	4.21922	+	7.30791i	0.170135	+	0.294683i
$616$	−22.8132	+	16.5748i	−0.919171	+	0.667817i
$617$	22.1162	+	24.5625i	0.890363	+	0.988849i	0.999987	−	0.00512437i	$-0.00163114\pi$
$617$	22.1162	+	24.5625i	0.890363	+	0.988849i	−0.109623	+	0.993973i	$0.534964\pi$
$618$	12.8256	+	39.4730i	0.515920	+	1.58784i
$619$	−31.5958			−1.26994			−0.634970	−	0.772536i	$-0.718988\pi$
$619$	−31.5958			−1.26994			−0.634970	+	0.772536i	$0.718988\pi$
$620$	−0.0422055	+	14.1831i	−0.00169501	+	0.569609i
$621$	−6.99610			−0.280744
$622$	3.50456	+	10.7859i	0.140520	+	0.432477i
$623$	4.18032	+	4.64271i	0.167481	+	0.186006i
$624$	0.333953	−	0.242631i	0.0133688	−	0.00971301i
$625$	−7.93522	−	13.7442i	−0.317409	−	0.549768i
$626$	−16.6776	+	28.8864i	−0.666571	+	1.15453i
$627$	−1.03462	−	9.84380i	−0.0413189	−	0.393123i
$628$	21.8767	+	15.8943i	0.872974	+	0.634253i
$629$	−2.34996	+	22.3584i	−0.0936992	+	0.891488i
$630$	5.55781	−	6.17257i	0.221428	−	0.245921i
$631$	14.5383	+	6.47286i	0.578759	+	0.257680i	0.675171	−	0.737661i	$-0.264070\pi$
$631$	14.5383	+	6.47286i	0.578759	+	0.257680i	−0.0964116	+	0.995342i	$0.530737\pi$
$632$	−23.4062	−	4.97514i	−0.931048	−	0.197900i
$633$	2.65132	−	0.563555i	0.105380	−	0.0223993i
$634$	66.4827	−	29.6000i	2.64036	−	1.17557i
$635$	5.03138	−	15.4850i	0.199664	−	0.614503i
$636$	−1.00657	+	3.09791i	−0.0399132	+	0.122840i
$637$	29.0072	−	12.9148i	1.14931	−	0.511704i
$638$	41.3082	−	8.78033i	1.63541	−	0.347617i
$639$	−7.52414	−	1.59931i	−0.297650	−	0.0632676i
$640$	−13.0390	−	5.80533i	−0.515411	−	0.229476i
$641$	−4.53972	+	5.04187i	−0.179308	+	0.199142i	−0.826098	−	0.563526i	$-0.809444\pi$
$641$	−4.53972	+	5.04187i	−0.179308	+	0.199142i	0.646790	+	0.762668i	$0.276111\pi$
$642$	−1.49001	+	14.1765i	−0.0588061	+	0.559503i
$643$	−10.9460	−	7.95276i	−0.431670	−	0.313626i	0.350647	−	0.936508i	$-0.385962\pi$
$643$	−10.9460	−	7.95276i	−0.431670	−	0.313626i	−0.782316	+	0.622882i	$0.785962\pi$
$644$	10.6809	+	101.622i	0.420888	+	4.00448i
$645$	−0.786152	+	1.36166i	−0.0309547	+	0.0536151i
$646$	12.8305	+	22.2231i	0.504810	+	0.874356i
$647$	−18.0763	+	13.1332i	−0.710653	+	0.516320i	−0.883384	−	0.468649i	$-0.844741\pi$
$647$	−18.0763	+	13.1332i	−0.710653	+	0.516320i	0.172731	+	0.984969i	$0.444741\pi$
$648$	1.82304	+	2.02469i	0.0716158	+	0.0795375i
$649$	3.21898	+	9.90701i	0.126356	+	0.388884i
$650$	−22.7350			−0.891741
$651$	24.1808	+	7.93646i	0.947722	+	0.311054i
$652$	24.6385			0.964918
$653$	−1.53687	−	4.72998i	−0.0601422	−	0.185099i	0.916472	−	0.400100i	$-0.131024\pi$
$653$	−1.53687	−	4.72998i	−0.0601422	−	0.185099i	−0.976614	+	0.215001i	$0.931024\pi$
$654$	−14.7933	−	16.4297i	−0.578465	−	0.642450i
$655$	−1.51501	+	1.10072i	−0.0591964	+	0.0430087i
$656$	−0.955910	−	1.65569i	−0.0373220	−	0.0646436i
$657$	−4.57035	+	7.91608i	−0.178306	+	0.308836i
$658$	3.86835	+	36.8049i	0.150804	+	1.43480i
$659$	−15.7824	−	11.4666i	−0.614797	−	0.446676i	0.236304	−	0.971679i	$-0.424064\pi$
$659$	−15.7824	−	11.4666i	−0.614797	−	0.446676i	−0.851100	+	0.525003i	$0.824064\pi$
$660$	−0.602928	+	5.73647i	−0.0234689	+	0.223292i
$661$	−30.2738	+	33.6224i	−1.17751	+	1.30776i	−0.235621	+	0.971845i	$0.575713\pi$
$661$	−30.2738	+	33.6224i	−1.17751	+	1.30776i	−0.941892	+	0.335916i	$0.890954\pi$
$662$	15.6639	+	6.97402i	0.608795	+	0.271053i
$663$	5.75736	+	1.22376i	0.223597	+	0.0475271i
$664$	7.36801	−	1.56612i	0.285934	−	0.0607772i
$665$	14.5522	−	6.47905i	0.564309	−	0.251247i
$666$	−6.14834	+	18.9226i	−0.238243	+	0.733237i
$667$	17.6900	−	54.4442i	0.684959	−	2.10809i
$668$	51.4923	−	22.9259i	1.99230	−	0.887028i
$669$	6.14487	−	1.30613i	0.237574	−	0.0504980i
$670$	7.06060	+	1.50078i	0.272775	+	0.0579801i
$671$	0.521067	+	0.231994i	0.0201156	+	0.00895602i
$672$	−17.9252	+	19.9080i	−0.691481	+	0.767967i
$673$	2.48181	−	23.6129i	0.0956669	−	0.910210i	−0.836448	−	0.548047i	$-0.815372\pi$
$673$	2.48181	−	23.6129i	0.0956669	−	0.910210i	0.932115	−	0.362163i	$-0.117962\pi$
$674$	−14.5544	−	10.5744i	−0.560615	−	0.407311i
$675$	0.456208	+	4.34052i	0.0175594	+	0.167067i
$676$	12.4249	−	21.5205i	0.477880	−	0.827713i
$677$	10.3651	+	17.9529i	0.398365	+	0.689988i	0.993524	−	0.113620i	$-0.0362446\pi$
$677$	10.3651	+	17.9529i	0.398365	+	0.689988i	−0.595160	+	0.803607i	$0.702911\pi$
$678$	7.69219	−	5.58870i	0.295417	−	0.214633i
$679$	0.201407	+	0.223685i	0.00772927	+	0.00858423i
$680$	−1.72864	−	5.32022i	−0.0662905	−	0.204021i
$681$	9.64174			0.369472
$682$	−27.3557	+	8.79850i	−1.04750	+	0.336912i
$683$	−36.1171			−1.38198			−0.690991	−	0.722863i	$-0.742826\pi$
$683$	−36.1171			−1.38198			−0.690991	+	0.722863i	$0.742826\pi$
$684$	4.31625	+	13.2840i	0.165036	+	0.507928i
$685$	−9.66700	−	10.7363i	−0.369357	−	0.410213i
$686$	−58.1049	+	42.2157i	−2.21846	+	1.61180i
$687$	1.77999	+	3.08304i	0.0679110	+	0.117625i
$688$	0.178111	−	0.308498i	0.00679043	−	0.0117614i
$689$	0.243527	+	2.31700i	0.00927762	+	0.0882707i
$690$	10.2849	+	7.47241i	0.391539	+	0.284470i
$691$	−2.85500	+	27.1635i	−0.108609	+	1.03335i	0.795472	+	0.605990i	$0.207223\pi$
$691$	−2.85500	+	27.1635i	−0.108609	+	1.03335i	−0.904082	+	0.427359i	$0.859444\pi$
$692$	−47.0169	+	52.2176i	−1.78732	+	1.98502i
$693$	9.45526	+	4.20975i	0.359176	+	0.159915i
$694$	−74.4765	−	15.8305i	−2.82709	−	0.600916i
$695$	2.81264	−	0.597846i	0.106690	−	0.0226776i
$696$	−20.3660	+	9.06751i	−0.771970	+	0.343703i
$697$	8.42405	−	25.9266i	0.319084	−	0.982039i
$698$	−5.25564	+	16.1752i	−0.198929	+	0.612240i
$699$	2.04561	−	0.910766i	0.0773723	−	0.0344483i
$700$	62.3521	−	13.2534i	2.35669	−	0.500930i
$701$	−9.24866	−	1.96586i	−0.349317	−	0.0742496i	0.0299119	−	0.999553i	$-0.490477\pi$
$701$	−9.24866	−	1.96586i	−0.349317	−	0.0742496i	−0.379229	+	0.925303i	$0.623811\pi$
$702$	4.75880	+	2.11876i	0.179609	+	0.0799673i
$703$	−25.5324	+	28.3566i	−0.962973	+	1.06949i
$704$	3.07623	−	29.2684i	0.115940	−	1.10309i
$705$	2.29096	+	1.66448i	0.0862825	+	0.0626879i
$706$	−0.849851	−	8.08579i	−0.0319846	−	0.304313i
$707$	−26.9859	+	46.7410i	−1.01491	+	1.75788i
$708$	−7.34991	−	12.7304i	−0.276226	−	0.478438i
$709$	17.1142	−	12.4342i	0.642739	−	0.466977i	−0.218051	−	0.975937i	$-0.569970\pi$
$709$	17.1142	−	12.4342i	0.642739	−	0.466977i	0.860790	+	0.508960i	$0.169970\pi$
$710$	9.35297	+	10.3875i	0.351011	+	0.389837i
$711$	2.71408	+	8.35308i	0.101786	+	0.313265i
$712$	3.72373			0.139553
$713$	−8.21205	+	38.0771i	−0.307544	+	1.42600i
$714$	−26.8330			−1.00420
$715$	1.27486	+	3.92361i	0.0476770	+	0.146735i
$716$	18.4600	+	20.5019i	0.689883	+	0.766193i
$717$	12.0963	−	8.78851i	0.451746	−	0.328213i
$718$	−26.9162	−	46.6201i	−1.00450	−	1.73985i
$719$	2.51335	−	4.35324i	0.0937320	−	0.162349i	−0.815347	−	0.578973i	$-0.803454\pi$
$719$	2.51335	−	4.35324i	0.0937320	−	0.162349i	0.909079	+	0.416624i	$0.136787\pi$
$720$	0.0150515	+	0.143206i	0.000560937	+	0.00533696i
$721$	−67.3368	−	48.9230i	−2.50775	−	1.82199i
$722$	−0.0258055	+	0.245523i	−0.000960383	+	0.00913743i
$723$	−0.622473	+	0.691326i	−0.0231500	+	0.0257107i
$724$	45.7152	+	20.3537i	1.69899	+	0.756440i
$725$	−34.9318	−	7.42499i	−1.29734	−	0.275757i
$726$	13.0936	−	2.78314i	0.485951	−	0.103292i
$727$	−45.8048	+	20.3936i	−1.69880	+	0.756356i	−0.699683	+	0.714454i	$0.746675\pi$
$727$	−45.8048	+	20.3936i	−1.69880	+	0.756356i	−0.999122	+	0.0419028i	$0.986658\pi$
$728$	8.79501	−	27.0683i	0.325965	−	1.00322i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	15.1739	−	6.75584i	0.561610	−	0.250045i
$731$	4.96841	−	1.05607i	0.183763	−	0.0390601i
$732$	−0.787305	−	0.167347i	−0.0290996	−	0.00618532i
$733$	12.6915	+	5.65061i	0.468770	+	0.208710i	0.627507	−	0.778611i	$-0.284075\pi$
$733$	12.6915	+	5.65061i	0.468770	+	0.208710i	−0.158737	+	0.987321i	$0.550742\pi$
$734$	33.1026	−	36.7642i	1.22184	−	1.35699i
$735$	−1.15779	+	11.0156i	−0.0427056	+	0.406317i
$736$	−33.1712	−	24.1003i	−1.22271	−	0.888349i
$737$	0.940205	+	8.94546i	0.0346329	+	0.329510i
$738$	12.0631	−	20.8938i	0.444047	−	0.769112i
$739$	18.8073	+	32.5753i	0.691839	+	1.19830i	0.971235	+	0.238125i	$0.0765327\pi$
$739$	18.8073	+	32.5753i	0.691839	+	1.19830i	−0.279395	+	0.960176i	$0.590134\pi$
$740$	17.9896	−	13.0702i	0.661310	−	0.480469i
$741$	6.68473	+	7.42415i	0.245570	+	0.272733i
$742$	−3.28204	−	10.1011i	−0.120487	−	0.370822i
$743$	37.5735			1.37844			0.689219	−	0.724553i	$-0.257954\pi$
$743$	37.5735			1.37844			0.689219	+	0.724553i	$0.257954\pi$
$744$	13.1595	−	7.54554i	0.482452	−	0.276633i
$745$	9.75809			0.357509
$746$	−11.0819	−	34.1064i	−0.405735	−	1.24873i
$747$	−1.85000	−	2.05463i	−0.0676879	−	0.0751750i
$748$	15.0753	−	10.9528i	0.551206	−	0.400475i
$749$	−14.2931	−	24.7564i	−0.522258	−	0.904578i
$750$	8.50820	−	14.7366i	0.310676	−	0.538106i
$751$	−1.36433	−	12.9807i	−0.0497849	−	0.473672i	−0.990803	−	0.135315i	$-0.956795\pi$
$751$	−1.36433	−	12.9807i	−0.0497849	−	0.473672i	0.941018	−	0.338357i	$-0.109871\pi$
$752$	−0.519042	−	0.377106i	−0.0189275	−	0.0137516i
$753$	−1.52267	+	14.4872i	−0.0554892	+	0.527945i
$754$	−28.5212	+	31.6760i	−1.03868	+	1.15357i
$755$	0.399903	+	0.178048i	0.0145540	+	0.00647985i
$756$	−14.2864	−	3.03667i	−0.519592	−	0.110443i
$757$	6.14241	−	1.30561i	0.223250	−	0.0474532i	−0.0949286	−	0.995484i	$-0.530262\pi$
$757$	6.14241	−	1.30561i	0.223250	−	0.0474532i	0.318178	+	0.948031i	$0.396929\pi$
$758$	−13.4331	+	5.98080i	−0.487912	+	0.217232i
$759$	−4.89526	+	15.0661i	−0.177687	+	0.546863i
$760$	2.93400	−	9.02992i	0.106427	−	0.327550i
$761$	17.5388	−	7.80876i	0.635779	−	0.283067i	−0.0634276	−	0.997986i	$-0.520203\pi$
$761$	17.5388	−	7.80876i	0.635779	−	0.283067i	0.699207	+	0.714919i	$0.253537\pi$
$762$	−45.5338	+	9.67852i	−1.64952	+	0.350616i
$763$	43.3670	+	9.21795i	1.56999	+	0.333712i
$764$	−25.6133	−	11.4038i	−0.926655	−	0.412573i
$765$	−1.37388	+	1.52585i	−0.0496727	+	0.0551671i
$766$	−6.16254	+	58.6326i	−0.222661	+	2.11848i
$767$	−8.50587	−	6.17988i	−0.307129	−	0.223142i
$768$	1.54839	+	14.7320i	0.0558727	+	0.531594i
$769$	−8.75467	+	15.1635i	−0.315701	+	0.546811i	−0.979586	−	0.201024i	$-0.935573\pi$
$769$	−8.75467	+	15.1635i	−0.315701	+	0.546811i	0.663885	+	0.747835i	$0.268906\pi$
$770$	−9.40372	−	16.2877i	−0.338887	−	0.586969i
$771$	−2.71121	+	1.96981i	−0.0976417	+	0.0709409i
$772$	4.79487	+	5.32525i	0.172571	+	0.191660i
$773$	−8.17429	−	25.1579i	−0.294009	−	0.904866i	−0.983553	−	0.180622i	$-0.942189\pi$
$773$	−8.17429	−	25.1579i	−0.294009	−	0.904866i	0.689544	−	0.724244i	$-0.257811\pi$
$774$	4.49533			0.161581
$775$	24.1594	+	2.61196i	0.867830	+	0.0938244i
$776$	0.179408			0.00644038
$777$	−12.3299	−	37.9474i	−0.442331	−	1.36136i
$778$	−35.7151	−	39.6656i	−1.28045	−	1.42208i
$779$	37.4326	−	27.1964i	1.34116	−	0.974412i
$780$	−2.91089	−	5.04180i	−0.104226	−	0.180526i
$781$	−8.70883	+	15.0841i	−0.311626	+	0.539753i
$782$	−4.29292	−	40.8444i	−0.153515	−	1.46059i
$783$	6.61983	+	4.80959i	0.236573	+	0.171881i
$784$	0.262309	−	2.49570i	0.00936818	−	0.0891323i
$785$	−4.51442	+	5.01377i	−0.161127	+	0.178949i
$786$	4.89118	+	2.17769i	0.174463	+	0.0776758i
$787$	5.20019	+	1.10533i	0.185367	+	0.0394009i	0.299660	−	0.954046i	$-0.403127\pi$
$787$	5.20019	+	1.10533i	0.185367	+	0.0394009i	−0.114293	+	0.993447i	$0.536460\pi$
$788$	23.5332	−	5.00214i	0.838337	−	0.178194i
$789$	17.1312	−	7.62730i	0.609887	−	0.271539i
$790$	4.93184	−	15.1786i	0.175467	−	0.540032i
$791$	−5.89217	+	18.1342i	−0.209501	+	0.644779i
$792$	5.63577	−	2.50921i	0.200258	−	0.0891607i
$793$	−0.563109	+	0.119692i	−0.0199966	+	0.00425040i
$794$	39.7996	+	8.45967i	1.41244	+	0.300222i
$795$	−0.742438	−	0.330555i	−0.0263316	−	0.0117236i
$796$	11.9898	−	13.3161i	0.424969	−	0.471976i
$797$	0.864143	−	8.22177i	0.0306095	−	0.291230i	−0.968499	−	0.249017i	$-0.919892\pi$
$797$	0.864143	−	8.22177i	0.0306095	−	0.291230i	0.999109	−	0.0422131i	$-0.0134408\pi$
$798$	−36.8452	−	26.7696i	−1.30431	−	0.947633i
$799$	−0.956248	−	9.09810i	−0.0338296	−	0.321868i
$800$	−12.7893	+	22.1517i	−0.452169	+	0.783180i
$801$	−0.683380	−	1.18365i	−0.0241460	−	0.0418222i
$802$	−16.8890	+	12.2706i	−0.596372	+	0.433289i
$803$	13.8493	+	15.3812i	0.488731	+	0.542791i
$804$	−3.92235	−	12.0717i	−0.138331	−	0.425738i
$805$	−25.4943			−0.898555
$806$	17.1175	−	23.4134i	0.602938	−	0.824701i
$807$	15.2472			0.536727
$808$	9.94099	+	30.5952i	0.349723	+	1.07634i
$809$	−6.33303	−	7.03354i	−0.222657	−	0.247286i	0.621458	−	0.783447i	$-0.286541\pi$
$809$	−6.33303	−	7.03354i	−0.222657	−	0.247286i	−0.844116	+	0.536161i	$0.819874\pi$
$810$	−1.47009	+	1.06808i	−0.0516537	+	0.0375286i
$811$	−10.2253	−	17.7108i	−0.359060	−	0.621910i	0.628744	−	0.777612i	$-0.283569\pi$
$811$	−10.2253	−	17.7108i	−0.359060	−	0.621910i	−0.987804	+	0.155702i	$0.950236\pi$
$812$	59.7555	−	103.500i	2.09701	−	3.63212i
$813$	1.42789	+	13.5854i	0.0500781	+	0.476462i
$814$	36.4477	+	26.4808i	1.27749	+	0.928152i
$815$	−0.642564	+	6.11359i	−0.0225080	+	0.214150i
$816$	0.311267	−	0.345697i	0.0108965	−	0.0121018i
$817$	7.87585	+	3.50655i	0.275541	+	0.122679i
$818$	81.2352	+	17.2671i	2.84032	+	0.603729i
$819$	−10.2182	+	2.17194i	−0.357051	+	0.0758936i
$820$	−24.6323	+	10.9670i	−0.860198	+	0.382985i
$821$	−14.2309	+	43.7981i	−0.496660	+	1.52856i	0.317693	+	0.948194i	$0.397092\pi$
$821$	−14.2309	+	43.7981i	−0.496660	+	1.52856i	−0.814353	+	0.580369i	$0.802908\pi$
$822$	−12.7640	+	39.2837i	−0.445197	+	1.37018i
$823$	−2.31682	+	1.03151i	−0.0807592	+	0.0359563i	−0.446719	−	0.894674i	$-0.647408\pi$
$823$	−2.31682	+	1.03151i	−0.0807592	+	0.0359563i	0.365960	+	0.930631i	$0.380741\pi$
$824$	−48.5265	+	10.3146i	−1.69050	+	0.359327i
$825$	9.66651	+	2.05468i	0.336545	+	0.0715347i
$826$	43.7866	+	19.4950i	1.52353	+	0.678319i
$827$	−29.1206	+	32.3417i	−1.01262	+	1.12463i	−0.0204461	+	0.999791i	$0.506509\pi$
$827$	−29.1206	+	32.3417i	−1.01262	+	1.12463i	−0.992177	+	0.124841i	$0.960158\pi$
$828$	2.33670	−	22.2322i	0.0812060	−	0.772623i
$829$	20.5250	+	14.9123i	0.712863	+	0.517926i	0.884096	−	0.467305i	$-0.154775\pi$
$829$	20.5250	+	14.9123i	0.712863	+	0.517926i	−0.171233	+	0.985231i	$0.554775\pi$
$830$	0.525147	+	4.99644i	0.0182281	+	0.173429i
$831$	−4.75868	+	8.24228i	−0.165077	+	0.285922i
$832$	14.8518	+	25.7241i	0.514894	+	0.891823i
$833$	28.9486	−	21.0324i	1.00301	−	0.728730i
$834$	−5.50106	−	6.10955i	−0.190486	−	0.211556i
$835$	4.34573	+	13.3748i	0.150390	+	0.462853i
$836$	31.6272			1.09385
$837$	−4.81352	−	2.79822i	−0.166380	−	0.0967206i
$838$	−43.1224			−1.48964
$839$	−8.53245	−	26.2602i	−0.294573	−	0.906602i	−0.983365	−	0.181643i	$-0.941859\pi$
$839$	−8.53245	−	26.2602i	−0.294573	−	0.906602i	0.688792	−	0.724959i	$-0.258141\pi$
$840$	6.64329	+	7.37812i	0.229215	+	0.254569i
$841$	−30.7056	+	22.3089i	−1.05881	+	0.769274i
$842$	−7.00288	−	12.1294i	−0.241335	−	0.418005i
$843$	−6.89417	+	11.9411i	−0.237448	+	0.411272i
$844$	0.905326	+	8.61360i	0.0311626	+	0.296492i
$845$	5.01589	+	3.64425i	0.172552	+	0.125366i
$846$	0.846290	−	8.05191i	0.0290961	−	0.276831i
$847$	−17.9625	+	19.9494i	−0.617200	+	0.685470i
$848$	0.168207	+	0.0748908i	0.00577627	+	0.00257176i
$849$	−11.9305	−	2.53590i	−0.409453	−	0.0870318i
$850$	−25.0608	+	5.32684i	−0.859578	+	0.182709i
$851$	55.7899	−	24.8393i	1.91245	−	0.851479i
$852$	7.59535	−	23.3761i	0.260212	−	0.800851i
$853$	11.0375	−	33.9700i	0.377917	−	1.16311i	−0.563572	−	0.826067i	$-0.690573\pi$
$853$	11.0375	−	33.9700i	0.377917	−	1.16311i	0.941489	−	0.337043i	$-0.109427\pi$
$854$	2.39755	−	1.06746i	0.0820425	−	0.0365277i
$855$	−3.40876	+	0.724554i	−0.116577	+	0.0247792i
$856$	−16.6663	−	3.54254i	−0.569644	−	0.121081i
$857$	23.1301	+	10.2982i	0.790108	+	0.351779i	0.761793	−	0.647820i	$-0.224319\pi$
$857$	23.1301	+	10.2982i	0.790108	+	0.351779i	0.0283146	+	0.999599i	$0.490986\pi$
$858$	7.89252	−	8.76553i	0.269446	−	0.299250i
$859$	−2.97861	+	28.3396i	−0.101629	+	0.966934i	0.818285	+	0.574813i	$0.194925\pi$
$859$	−2.97861	+	28.3396i	−0.101629	+	0.966934i	−0.919914	+	0.392121i	$0.871742\pi$
$860$	−4.06450	−	2.95303i	−0.138598	−	0.100698i
$861$	5.05734	+	48.1174i	0.172354	+	1.63984i
$862$	40.8580	−	70.7682i	1.39163	−	2.41037i
$863$	2.40701	+	4.16906i	0.0819355	+	0.141916i	0.904081	−	0.427361i	$-0.140557\pi$
$863$	2.40701	+	4.16906i	0.0819355	+	0.141916i	−0.822146	+	0.569277i	$0.807223\pi$
$864$	4.74139	−	3.44482i	0.161305	−	0.117195i
$865$	−11.7307	−	13.0282i	−0.398854	−	0.442972i
$866$	13.4778	+	41.4805i	0.457996	+	1.40957i
$867$	−10.3669			−0.352080
$868$	−33.2969	+	74.1912i	−1.13017	+	2.51821i
$869$	19.8874			0.674633
$870$	−4.59471	−	14.1410i	−0.155775	−	0.479426i
$871$	−6.07469	−	6.74662i	−0.205833	−	0.228601i
$872$	21.3793	−	15.5329i	0.723993	−	0.526012i
$873$	−0.0329250	−	0.0570279i	−0.00111434	−	0.00193010i
$874$	34.8532	−	60.3675i	1.17893	−	2.04196i
$875$	3.56700	+	33.9377i	0.120587	+	1.14730i
$876$	−23.6293	−	17.1677i	−0.798359	−	0.580042i
$877$	−1.28910	+	12.2650i	−0.0435299	+	0.414159i	0.950959	+	0.309317i	$0.100100\pi$
$877$	−1.28910	+	12.2650i	−0.0435299	+	0.414159i	−0.994489	+	0.104842i	$0.966566\pi$
$878$	−35.5183	+	39.4471i	−1.19869	+	1.33127i
$879$	−15.5981	−	6.94474i	−0.526112	−	0.234240i
$880$	0.318924	+	0.0677894i	0.0107509	+	0.00228518i
$881$	31.2620	−	6.64494i	1.05324	−	0.223874i	0.351415	−	0.936220i	$-0.385701\pi$
$881$	31.2620	−	6.64494i	1.05324	−	0.223874i	0.701828	+	0.712346i	$0.252367\pi$
$882$	28.9301	−	12.8805i	0.974126	−	0.433709i
$883$	−4.01391	+	12.3535i	−0.135079	+	0.415729i	−0.995602	−	0.0936812i	$-0.970137\pi$
$883$	−4.01391	+	12.3535i	−0.135079	+	0.415729i	0.860524	+	0.509411i	$0.170137\pi$
$884$	−5.81185	+	17.8870i	−0.195474	+	0.601606i
$885$	3.35050	−	1.49174i	0.112626	−	0.0501443i
$886$	22.2301	−	4.72515i	0.746835	−	0.158745i
$887$	−35.6625	−	7.58030i	−1.19743	−	0.254522i	−0.434301	−	0.900768i	$-0.643005\pi$
$887$	−35.6625	−	7.58030i	−1.19743	−	0.254522i	−0.763129	+	0.646246i	$0.776338\pi$
$888$	−21.7263	−	9.67317i	−0.729086	−	0.324610i
$889$	62.4656	−	69.3751i	2.09503	−	2.32677i
$890$	−0.259605	+	2.46998i	−0.00870198	+	0.0827938i
$891$	−1.83187	−	1.33093i	−0.0613700	−	0.0445879i
$892$	2.09824	+	19.9634i	0.0702544	+	0.668426i
$893$	7.76355	−	13.4469i	0.259797	−	0.449982i
$894$	−13.9495	−	24.1613i	−0.466542	−	0.808075i
$895$	−5.56861	+	4.04583i	−0.186138	+	0.135237i
$896$	−54.7583	−	60.8153i	−1.82935	−	2.03170i
$897$	−4.94083	−	15.2063i	−0.164970	−	0.507724i
$898$	−82.0764			−2.73893
$899$	33.9472	−	30.3837i	1.13220	−	1.01335i
$900$	−13.9457			−0.464857
$901$	0.811314	+	2.49697i	0.0270288	+	0.0831861i
$902$	−36.5541	−	40.5974i	−1.21712	−	1.35175i
$903$	−7.29323	+	5.29884i	−0.242704	+	0.176334i
$904$	5.68254	+	9.84244i	0.188998	+	0.327355i
$905$	−6.24264	+	10.8126i	−0.207512	+	0.359422i
$906$	−0.130823	−	1.24470i	−0.00434631	−	0.0413524i
$907$	−3.01894	−	2.19339i	−0.100242	−	0.0728304i	0.536535	−	0.843878i	$-0.319733\pi$
$907$	−3.01894	−	2.19339i	−0.100242	−	0.0728304i	−0.636777	+	0.771048i	$0.719733\pi$
$908$	−3.22035	+	30.6396i	−0.106871	+	1.01681i
$909$	7.90082	−	8.77475i	0.262054	−	0.291040i
$910$	17.3414	+	7.72090i	0.574862	+	0.255945i
$911$	20.6527	+	4.38986i	0.684253	+	0.145443i	0.536906	−	0.843642i	$-0.319593\pi$
$911$	20.6527	+	4.38986i	0.684253	+	0.145443i	0.147348	+	0.989085i	$0.452926\pi$
$912$	0.772291	−	0.164156i	0.0255731	−	0.00543573i
$913$	−5.71910	+	2.54631i	−0.189275	+	0.0842705i
$914$	3.50365	−	10.7831i	0.115891	−	0.356674i
$915$	0.0620567	−	0.190991i	0.00205153	−	0.00631397i
$916$	−10.3918	+	4.62674i	−0.343355	+	0.152872i
$917$	−10.5024	+	2.23235i	−0.346820	+	0.0737188i
$918$	5.74205	+	1.22051i	0.189516	+	0.0402829i
$919$	14.2973	+	6.36558i	0.471626	+	0.209981i	0.628765	−	0.777595i	$-0.283561\pi$
$919$	14.2973	+	6.36558i	0.471626	+	0.209981i	−0.157140	+	0.987576i	$0.550227\pi$
$920$	−10.1679	+	11.2926i	−0.335227	+	0.372307i
$921$	3.14590	−	29.9312i	0.103661	−	0.986267i
$922$	−4.42704	−	3.21644i	−0.145797	−	0.105928i
$923$	−1.83759	−	17.4835i	−0.0604851	−	0.575477i
$924$	−16.5358	+	28.6409i	−0.543989	+	0.942217i
$925$	−19.0488	−	32.9935i	−0.626320	−	1.08482i
$926$	3.95114	−	2.87067i	0.129843	−	0.0943362i
$927$	12.1843	+	13.5320i	0.400184	+	0.444449i
$928$	14.8190	+	45.6082i	0.486458	+	1.49716i
$929$	−55.1450			−1.80925			−0.904624	−	0.426211i	$-0.859848\pi$
$929$	−55.1450			−1.80925			−0.904624	+	0.426211i	$0.859848\pi$
$930$	4.08758	+	9.25487i	0.134037	+	0.303479i
$931$	60.7330			1.99044
$932$	2.21100	+	6.80476i	0.0724237	+	0.222897i
$933$	3.32933	+	3.69759i	0.108997	+	0.121054i
$934$	−10.7039	+	7.77685i	−0.350243	+	0.254466i
$935$	2.32458	+	4.02629i	0.0760220	+	0.131674i
$936$	−3.11328	+	5.39235i	−0.101761	+	0.176255i
$937$	1.53783	+	14.6315i	0.0502388	+	0.477990i	0.990498	+	0.137530i	$0.0439163\pi$
$937$	1.53783	+	14.6315i	0.0502388	+	0.477990i	−0.940259	+	0.340460i	$0.889417\pi$
$938$	33.4827	+	24.3266i	1.09325	+	0.794292i
$939$	−1.52965	+	14.5537i	−0.0499183	+	0.474941i
$940$	−6.05457	+	6.72428i	−0.197478	+	0.219322i
$941$	39.1925	+	17.4496i	1.27764	+	0.568842i	0.929576	−	0.368630i	$-0.120173\pi$
$941$	39.1925	+	17.4496i	1.27764	+	0.568842i	0.348063	+	0.937471i	$0.386840\pi$
$942$	18.8678	+	4.01047i	0.614746	+	0.130668i
$943$	−72.4339	+	15.3963i	−2.35877	+	0.501373i
$944$	−0.759092	+	0.337970i	−0.0247064	+	0.0110000i
$945$	1.12608	−	3.46572i	0.0366314	−	0.112740i
$946$	3.14544	−	9.68067i	0.102267	−	0.314746i
$947$	−8.81007	+	3.92249i	−0.286289	+	0.127464i	−0.544857	−	0.838529i	$-0.683416\pi$
$947$	−8.81007	+	3.92249i	−0.286289	+	0.127464i	0.258568	+	0.965993i	$0.416749\pi$
$948$	−27.4510	+	5.83488i	−0.891566	+	0.189508i
$949$	−20.4337	−	4.34331i	−0.663305	−	0.140990i
$950$	−39.7260	−	17.6872i	−1.28888	−	0.573847i
$951$	21.3640	−	23.7272i	0.692777	−	0.769406i
$952$	3.35261	−	31.8980i	0.108659	−	1.03382i
$953$	−2.89137	−	2.10071i	−0.0936608	−	0.0680485i	0.539969	−	0.841685i	$-0.318436\pi$
$953$	−2.89137	−	2.10071i	−0.0936608	−	0.0680485i	−0.633630	+	0.773636i	$0.718436\pi$
$954$	0.242879	+	2.31084i	0.00786350	+	0.0748162i
$955$	3.49762	−	6.05805i	0.113180	−	0.196034i
$956$	23.8880	+	41.3752i	0.772592	+	1.33817i
$957$	14.9894	−	10.8904i	0.484538	−	0.352038i
$958$	−15.7812	−	17.5268i	−0.509868	−	0.566266i
$959$	−25.5970	−	78.7794i	−0.826570	−	2.54392i
$960$	−10.3616			−0.334420
$961$	−20.8798	+	22.9136i	−0.673542	+	0.739149i
$962$	−45.4713			−1.46605
$963$	1.93256	+	5.94780i	0.0622758	+	0.191665i
$964$	−1.98899	−	2.20900i	−0.0640612	−	0.0711471i
$965$	−1.44641	+	1.05088i	−0.0465616	+	0.0338290i
$966$	36.4450	+	63.1246i	1.17260	+	2.03100i
$967$	−9.22296	+	15.9746i	−0.296591	+	0.513710i	−0.975354	−	0.220647i	$-0.929183\pi$
$967$	−9.22296	+	15.9746i	−0.296591	+	0.513710i	0.678763	+	0.734357i	$0.262516\pi$
$968$	1.67252	+	15.9129i	0.0537567	+	0.511461i
$969$	9.10806	+	6.61739i	0.292593	+	0.212581i
$970$	−0.0125077	+	0.119003i	−0.000401598	+	0.00382095i
$971$	29.3554	−	32.6025i	0.942059	−	1.04626i	−0.0567938	−	0.998386i	$-0.518088\pi$
$971$	29.3554	−	32.6025i	0.942059	−	1.04626i	0.998853	−	0.0478770i	$-0.0152456\pi$
$972$	2.91906	+	1.29965i	0.0936289	+	0.0416863i
$973$	16.1265	+	3.42780i	0.516992	+	0.109890i
$974$	−61.8905	+	13.1552i	−1.98310	+	0.421521i
$975$	−9.11213	+	4.05698i	−0.291822	+	0.129927i
$976$	−0.0140596	+	0.0432711i	−0.000450037	+	0.00138507i
$977$	−14.8680	+	45.7590i	−0.475670	+	1.46396i	0.369382	+	0.929278i	$0.379569\pi$
$977$	−14.8680	+	45.7590i	−0.475670	+	1.46396i	−0.845052	+	0.534684i	$0.820431\pi$
$978$	16.0560	−	7.14859i	0.513414	−	0.228587i
$979$	−3.02715	+	0.643441i	−0.0967481	+	0.0205644i
$980$	−34.6187	−	7.35844i	−1.10585	−	0.235057i
$981$	−8.86093	−	3.94514i	−0.282908	−	0.125959i
$982$	26.8203	−	29.7869i	0.855870	−	0.950540i
$983$	0.919652	−	8.74990i	0.0293323	−	0.279078i	−0.970018	−	0.243034i	$-0.921857\pi$
$983$	0.919652	−	8.74990i	0.0293323	−	0.279078i	0.999350	−	0.0360448i	$-0.0114759\pi$
$984$	23.3306	+	16.9506i	0.743751	+	0.540367i
$985$	0.627450	+	5.96979i	0.0199922	+	0.190213i
$986$	−24.0172	+	41.5990i	−0.764862	+	1.32478i
$987$	8.11812	+	14.0610i	0.258403	+	0.447566i
$988$	−25.8252	+	18.7631i	−0.821609	+	0.596934i
$989$	−9.23258	−	10.2538i	−0.293579	−	0.326052i
$990$	1.27147	+	3.91318i	0.0404099	+	0.124369i
$991$	9.56580			0.303868			0.151934	−	0.988391i	$-0.451450\pi$
$991$	9.56580			0.303868			0.151934	+	0.988391i	$0.451450\pi$
$992$	−13.1834	−	29.8491i	−0.418574	−	0.947711i
$993$	7.52253			0.238720
$994$	24.7655	+	76.2203i	0.785513	+	2.41756i
$995$	2.99145	+	3.32234i	0.0948353	+	0.105325i
$996$	7.14712	−	5.19268i	0.226465	−	0.164536i
$997$	−11.7010	−	20.2668i	−0.370576	−	0.641856i	0.619079	−	0.785329i	$-0.287506\pi$
$997$	−11.7010	−	20.2668i	−0.370576	−	0.641856i	−0.989654	+	0.143473i	$0.954173\pi$
$998$	−42.0527	+	72.8374i	−1.33115	+	2.30563i
$999$	0.912440	+	8.68128i	0.0288683	+	0.274664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.m.b.82.3	yes	24
3.2	odd	2		279.2.y.d.82.1		24
31.13	odd	30		2883.2.a.s.1.10		12
31.14	even	15	inner	93.2.m.b.76.3	✓	24
31.18	even	15		2883.2.a.t.1.10		12
93.14	odd	30		279.2.y.d.262.1		24
93.44	even	30		8649.2.a.bl.1.3		12
93.80	odd	30		8649.2.a.bk.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.b.76.3	✓	24	31.14	even	15	inner
93.2.m.b.82.3	yes	24	1.1	even	1	trivial
279.2.y.d.82.1		24	3.2	odd	2
279.2.y.d.262.1		24	93.14	odd	30
2883.2.a.s.1.10		12	31.13	odd	30
2883.2.a.t.1.10		12	31.18	even	15
8649.2.a.bk.1.3		12	93.80	odd	30
8649.2.a.bl.1.3		12	93.44	even	30

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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.704349 + 2.16776i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-2.58506 + 1.87816i) q^{4} +(-0.398612 - 0.690417i) q^{5} +(-1.13966 + 1.97395i) q^{6} +(-0.477794 - 4.54591i) q^{7} +(-2.20416 - 1.60142i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.704349 + 2.16776i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-2.58506 + 1.87816i) q^{4} +(-0.398612 - 0.690417i) q^{5} +(-1.13966 + 1.97395i) q^{6} +(-0.477794 - 4.54591i) q^{7} +(-2.20416 - 1.60142i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(1.21590 - 1.35039i) q^{10} +(2.06856 + 0.920981i) q^{11} +(-3.12548 - 0.664342i) q^{12} +(-2.23546 + 0.475161i) q^{13} +(9.51792 - 4.23765i) q^{14} +(0.246356 - 0.758205i) q^{15} +(-0.0558146 + 0.171780i) q^{16} +(-2.35281 + 1.04754i) q^{17} +(-2.22951 + 0.473898i) q^{18} +(-4.27578 - 0.908845i) q^{19} +(2.32715 + 1.03611i) q^{20} +(3.05856 - 3.39688i) q^{21} +(-0.539483 + 5.13283i) q^{22} +(5.65996 + 4.11220i) q^{23} +(-0.284787 - 2.70957i) q^{24} +(2.18222 - 3.77971i) q^{25} +(-2.60458 - 4.51126i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(9.77304 + 10.8541i) q^{28} +(-2.52855 - 7.78207i) q^{29} +1.81713 q^{30} +(2.24947 + 5.09312i) q^{31} -5.86068 q^{32} +(0.699712 + 2.15349i) q^{33} +(-3.92802 - 4.36251i) q^{34} +(-2.94811 + 2.14193i) q^{35} +(-1.59765 - 2.76722i) q^{36} +(4.36455 - 7.55962i) q^{37} +(-1.04148 - 9.90903i) q^{38} +(-1.84893 - 1.34332i) q^{39} +(-0.227039 + 2.16013i) q^{40} +(-7.08260 + 7.86602i) q^{41} +(9.51792 + 4.23765i) q^{42} +(-1.92913 - 0.410048i) q^{43} +(-7.07709 + 1.50428i) q^{44} +(0.728301 - 0.324260i) q^{45} +(-4.92770 + 15.1659i) q^{46} +(-1.09764 + 3.37820i) q^{47} +(-0.165004 + 0.0734647i) q^{48} +(-13.5899 + 2.88863i) q^{49} +(9.73056 + 2.06829i) q^{50} +(-2.35281 - 1.04754i) q^{51} +(4.88636 - 5.42686i) q^{52} +(0.106558 - 1.01383i) q^{53} +(-1.84401 - 1.33975i) q^{54} +(-0.188692 - 1.79528i) q^{55} +(-6.22676 + 10.7851i) q^{56} +(-2.18565 - 3.78566i) q^{57} +(15.0887 - 10.9626i) q^{58} +(3.07829 + 3.41879i) q^{59} +(0.787183 + 2.42270i) q^{60} +0.251899 q^{61} +(-9.45628 + 8.46365i) q^{62} +4.57095 q^{63} +(-4.01633 - 12.3610i) q^{64} +(1.21914 + 1.35399i) q^{65} +(-4.17542 + 3.03362i) q^{66} +(1.98619 + 3.44018i) q^{67} +(4.11472 - 7.12690i) q^{68} +(0.731291 + 6.95777i) q^{69} +(-6.71970 - 4.88215i) q^{70} +(-0.804058 + 7.65010i) q^{71} +(1.82304 - 2.02469i) q^{72} +(8.35045 + 3.71786i) q^{73} +(19.4617 + 4.13670i) q^{74} +(4.26906 - 0.907417i) q^{75} +(12.7601 - 5.68116i) q^{76} +(3.19835 - 9.84350i) q^{77} +(1.60972 - 4.95421i) q^{78} +(8.02362 - 3.57235i) q^{79} +(0.140848 - 0.0299381i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-22.0403 - 9.81297i) q^{82} +(-1.85000 + 2.05463i) q^{83} +(-1.52670 + 14.5256i) q^{84} +(1.66110 + 1.20686i) q^{85} +(-0.469890 - 4.47071i) q^{86} +(4.09128 - 7.08630i) q^{87} +(-3.08456 - 5.34261i) q^{88} +(-1.10573 + 0.803361i) q^{89} +(1.21590 + 1.35039i) q^{90} +(3.22813 + 9.93515i) q^{91} -22.3547 q^{92} +(-2.27974 + 5.07964i) q^{93} -8.09627 q^{94} +(1.07690 + 3.31435i) q^{95} +(-3.92156 - 4.35533i) q^{96} +(-0.0532738 + 0.0387057i) q^{97} +(-15.8339 - 27.4252i) q^{98} +(-1.13216 + 1.96096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9 + 24 * q^10 - 22 * q^11 + 12 * q^12 - 8 * q^13 + 10 * q^14 - 8 * q^15 - 2 * q^16 - 17 * q^17 + 5 * q^19 - 22 * q^20 - 11 * q^21 - 37 * q^22 + 26 * q^23 + 26 * q^24 - 8 * q^25 + 4 * q^26 - 6 * q^27 - 36 * q^28 + 2 * q^29 + 42 * q^30 + 36 * q^32 + 14 * q^33 + 40 * q^34 + 9 * q^35 - 13 * q^36 - 13 * q^37 - q^38 - 19 * q^39 - 27 * q^40 + 36 * q^41 + 10 * q^42 - 11 * q^43 - 38 * q^44 - q^45 - 23 * q^46 - 13 * q^47 - 14 * q^48 - 22 * q^49 + 71 * q^50 - 17 * q^51 + 9 * q^52 - 20 * q^53 - 5 * q^54 + 26 * q^55 + 28 * q^56 - 15 * q^57 + 40 * q^58 - 16 * q^59 - 61 * q^60 + 70 * q^61 - 2 * q^62 + 12 * q^63 + 34 * q^64 + 94 * q^65 - 16 * q^66 + 4 * q^67 + 51 * q^68 - 13 * q^69 - 43 * q^70 - 5 * q^71 + q^72 - 12 * q^73 + 74 * q^74 - 8 * q^75 + 71 * q^76 + 25 * q^77 + 17 * q^78 - 29 * q^79 - 113 * q^80 + 3 * q^81 - 60 * q^82 - 11 * q^83 - 41 * q^84 + 16 * q^85 - 144 * q^86 + 14 * q^87 + 26 * q^88 - 27 * q^89 + 24 * q^90 - 81 * q^91 + 28 * q^92 - 36 * q^93 - 80 * q^94 - 56 * q^95 - 43 * q^96 - 21 * q^97 - 14 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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