LMFDB - Embedded newform 99.2.e.e.34.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(34,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("99.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.e (of order $3$, degree $2$, 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:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.508277025.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 15x^{5} + 21x^{4} + 3x^{3} - 22x^{2} + 3x + 19 $ x^8 - 3x^7 + 5x^6 - 15x^5 + 21x^4 + 3x^3 - 22x^2 + 3*x + 19
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			34.1
Root			$-0.734668 + 0.348716i$ of defining polynomial
Character	$\chi$	$=$	99.34
Dual form			99.2.e.e.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23467 + 2.13851i) q^{2} +(1.66933 - 0.461883i) q^{3} +(-2.04881 - 3.54864i) q^{4} +(1.21814 + 2.10988i) q^{5} +(-1.07333 + 4.14015i) q^{6} +(-1.16933 + 2.02534i) q^{7} +5.17972 q^{8} +(2.57333 - 1.54207i) q^{9} +O(q^{10})$	\(q+(-1.23467 + 2.13851i) q^{2} +(1.66933 - 0.461883i) q^{3} +(-2.04881 - 3.54864i) q^{4} +(1.21814 + 2.10988i) q^{5} +(-1.07333 + 4.14015i) q^{6} +(-1.16933 + 2.02534i) q^{7} +5.17972 q^{8} +(2.57333 - 1.54207i) q^{9} -6.01598 q^{10} +(-0.500000 + 0.866025i) q^{11} +(-5.05919 - 4.97754i) q^{12} +(-2.35519 - 4.07931i) q^{13} +(-2.88747 - 5.00124i) q^{14} +(3.00799 + 2.95945i) q^{15} +(-2.29761 + 3.97958i) q^{16} -3.20799 q^{17} +(0.120523 + 7.40702i) q^{18} +7.77494 q^{19} +(4.99146 - 8.64547i) q^{20} +(-1.01653 + 3.92106i) q^{21} +(-1.23467 - 2.13851i) q^{22} +(-1.37948 - 2.38932i) q^{23} +(8.64666 - 2.39242i) q^{24} +(-0.467722 + 0.810117i) q^{25} +11.6315 q^{26} +(3.58348 - 3.76280i) q^{27} +9.58293 q^{28} +(1.18586 - 2.05397i) q^{29} +(-10.0427 + 2.77868i) q^{30} +(0.685860 + 1.18794i) q^{31} +(-0.493856 - 0.855383i) q^{32} +(-0.434663 + 1.67662i) q^{33} +(3.96080 - 6.86030i) q^{34} -5.69762 q^{35} +(-10.7445 - 5.97241i) q^{36} -8.47256 q^{37} +(-9.59946 + 16.6268i) q^{38} +(-5.81575 - 5.72189i) q^{39} +(6.30961 + 10.9286i) q^{40} +(-1.77332 - 3.07149i) q^{41} +(-7.13013 - 7.01505i) q^{42} +(3.73467 - 6.46863i) q^{43} +4.09762 q^{44} +(6.38825 + 3.55095i) q^{45} +6.81278 q^{46} +(-0.103993 + 0.180122i) q^{47} +(-1.99737 + 7.70446i) q^{48} +(0.765332 + 1.32559i) q^{49} +(-1.15496 - 2.00045i) q^{50} +(-5.35519 + 1.48171i) q^{51} +(-9.65066 + 16.7154i) q^{52} -9.11360 q^{53} +(3.62237 + 12.3091i) q^{54} -2.43628 q^{55} +(-6.05680 + 10.4907i) q^{56} +(12.9789 - 3.59111i) q^{57} +(2.92829 + 5.07194i) q^{58} +(0.120523 + 0.208751i) q^{59} +(4.33921 - 16.7376i) q^{60} +(-0.830670 + 1.43876i) q^{61} -3.38724 q^{62} +(0.114145 + 7.01505i) q^{63} -6.75145 q^{64} +(5.73789 - 9.93832i) q^{65} +(-3.04881 - 2.99960i) q^{66} +(3.84027 + 6.65155i) q^{67} +(6.57255 + 11.3840i) q^{68} +(-3.40639 - 3.35142i) q^{69} +(7.03467 - 12.1844i) q^{70} +1.07731 q^{71} +(13.3291 - 7.98749i) q^{72} -2.37495 q^{73} +(10.4608 - 18.1186i) q^{74} +(-0.406602 + 1.56839i) q^{75} +(-15.9294 - 27.5904i) q^{76} +(-1.16933 - 2.02534i) q^{77} +(19.4168 - 5.37239i) q^{78} +(-6.35680 + 11.0103i) q^{79} -11.1952 q^{80} +(4.24404 - 7.93651i) q^{81} +8.75786 q^{82} +(-5.25042 + 9.09399i) q^{83} +(15.9971 - 4.42619i) q^{84} +(-3.90777 - 6.76846i) q^{85} +(9.22215 + 15.9732i) q^{86} +(1.03090 - 3.97648i) q^{87} +(-2.58986 + 4.48577i) q^{88} -14.2933 q^{89} +(-15.4811 + 9.27707i) q^{90} +11.0160 q^{91} +(-5.65257 + 9.79053i) q^{92} +(1.69362 + 1.66628i) q^{93} +(-0.256795 - 0.444781i) q^{94} +(9.47095 + 16.4042i) q^{95} +(-1.21950 - 1.19981i) q^{96} +(-4.46694 + 7.73697i) q^{97} -3.77972 q^{98} +(0.0488078 + 2.99960i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 5 q^{3} - 11 q^{4} - 4 q^{5} + 17 q^{6} - q^{7} - 5 q^{9}+O(q^{10}) $ 8 * q - q^2 + 5 * q^3 - 11 * q^4 - 4 * q^5 + 17 * q^6 - q^7 - 5 * q^9	\( 8 q - q^{2} + 5 q^{3} - 11 q^{4} - 4 q^{5} + 17 q^{6} - q^{7} - 5 q^{9} + 2 q^{10} - 4 q^{11} - 2 q^{12} - 7 q^{13} - q^{14} - q^{15} - 17 q^{16} - 10 q^{17} - 2 q^{18} + 18 q^{19} + 10 q^{20} - 13 q^{21} - q^{22} - 14 q^{23} + 18 q^{24} - 14 q^{25} + 44 q^{26} + 5 q^{27} - 2 q^{28} + 6 q^{29} - 37 q^{30} + 2 q^{31} + 34 q^{32} - 4 q^{33} - 16 q^{34} - 16 q^{35} + 11 q^{36} + 6 q^{37} - 3 q^{38} - 22 q^{39} - 12 q^{40} + 2 q^{41} - q^{42} + 21 q^{43} + 22 q^{44} + 49 q^{45} + 4 q^{46} + 7 q^{47} - 59 q^{48} + 15 q^{49} - 23 q^{50} - 31 q^{51} + 10 q^{52} - 12 q^{53} - 37 q^{54} + 8 q^{55} - 18 q^{56} + 33 q^{57} + 21 q^{58} - 2 q^{59} + 73 q^{60} - 15 q^{61} - 40 q^{62} - 5 q^{63} + 32 q^{64} - 19 q^{65} - 19 q^{66} - 14 q^{67} + 7 q^{68} - 2 q^{69} + 38 q^{70} - 6 q^{71} + 75 q^{72} + 44 q^{73} + 36 q^{74} + 10 q^{75} - 42 q^{76} - q^{77} + 29 q^{78} - 11 q^{79} - 68 q^{80} + 7 q^{81} - 34 q^{82} - 18 q^{83} + 34 q^{84} - 13 q^{85} + 24 q^{86} - 9 q^{87} - 12 q^{89} - 80 q^{90} + 38 q^{91} - 67 q^{92} + 20 q^{93} + 19 q^{94} + 30 q^{95} - 50 q^{96} - 26 q^{97} + 30 q^{98} - 5 q^{99}+O(q^{100}) \) 8 * q - q^2 + 5 * q^3 - 11 * q^4 - 4 * q^5 + 17 * q^6 - q^7 - 5 * q^9 + 2 * q^10 - 4 * q^11 - 2 * q^12 - 7 * q^13 - q^14 - q^15 - 17 * q^16 - 10 * q^17 - 2 * q^18 + 18 * q^19 + 10 * q^20 - 13 * q^21 - q^22 - 14 * q^23 + 18 * q^24 - 14 * q^25 + 44 * q^26 + 5 * q^27 - 2 * q^28 + 6 * q^29 - 37 * q^30 + 2 * q^31 + 34 * q^32 - 4 * q^33 - 16 * q^34 - 16 * q^35 + 11 * q^36 + 6 * q^37 - 3 * q^38 - 22 * q^39 - 12 * q^40 + 2 * q^41 - q^42 + 21 * q^43 + 22 * q^44 + 49 * q^45 + 4 * q^46 + 7 * q^47 - 59 * q^48 + 15 * q^49 - 23 * q^50 - 31 * q^51 + 10 * q^52 - 12 * q^53 - 37 * q^54 + 8 * q^55 - 18 * q^56 + 33 * q^57 + 21 * q^58 - 2 * q^59 + 73 * q^60 - 15 * q^61 - 40 * q^62 - 5 * q^63 + 32 * q^64 - 19 * q^65 - 19 * q^66 - 14 * q^67 + 7 * q^68 - 2 * q^69 + 38 * q^70 - 6 * q^71 + 75 * q^72 + 44 * q^73 + 36 * q^74 + 10 * q^75 - 42 * q^76 - q^77 + 29 * q^78 - 11 * q^79 - 68 * q^80 + 7 * q^81 - 34 * q^82 - 18 * q^83 + 34 * q^84 - 13 * q^85 + 24 * q^86 - 9 * q^87 - 12 * q^89 - 80 * q^90 + 38 * q^91 - 67 * q^92 + 20 * q^93 + 19 * q^94 + 30 * q^95 - 50 * q^96 - 26 * q^97 + 30 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.23467	+	2.13851i	−0.873042	+	1.51215i	−0.0142076	+	0.999899i	$0.504523\pi$
$2$	−1.23467	+	2.13851i	−0.873042	+	1.51215i	−0.858834	+	0.512254i	$0.828811\pi$
$3$	1.66933	−	0.461883i	0.963788	−	0.266668i
$3$	1.66933	−	0.461883i	0.963788	−	0.266668i
$4$	−2.04881	−	3.54864i	−1.02440	−	1.77432i
$5$	1.21814	+	2.10988i	0.544768	+	0.943566i	0.998621	+	0.0524895i	$0.0167156\pi$
$5$	1.21814	+	2.10988i	0.544768	+	0.943566i	−0.453853	+	0.891076i	$0.649951\pi$
$6$	−1.07333	+	4.14015i	−0.438185	+	1.69021i
$7$	−1.16933	+	2.02534i	−0.441965	+	0.765506i	−0.997835	−	0.0657628i	$-0.979052\pi$
$7$	−1.16933	+	2.02534i	−0.441965	+	0.765506i	0.555870	+	0.831269i	$0.312385\pi$
$8$	5.17972			1.83131
$9$	2.57333	−	1.54207i	0.857776	−	0.514023i
$10$	−6.01598			−1.90242
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−5.05919	−	4.97754i	−1.46046	−	1.43689i
$13$	−2.35519	−	4.07931i	−0.653212	−	1.13140i	−0.982339	−	0.187111i	$-0.940088\pi$
$13$	−2.35519	−	4.07931i	−0.653212	−	1.13140i	0.329127	−	0.944286i	$-0.393246\pi$
$14$	−2.88747	−	5.00124i	−0.771708	−	1.33664i
$15$	3.00799	+	2.95945i	0.776660	+	0.764126i
$16$	−2.29761	+	3.97958i	−0.574403	+	0.994895i
$17$	−3.20799			−0.778051			−0.389026	−	0.921227i	$-0.627188\pi$
$17$	−3.20799			−0.778051			−0.389026	+	0.921227i	$0.627188\pi$
$18$	0.120523	+	7.40702i	0.0284075	+	1.74585i
$19$	7.77494			1.78369			0.891846	−	0.452338i	$-0.149410\pi$
$19$	7.77494			1.78369			0.891846	+	0.452338i	$0.149410\pi$
$20$	4.99146	−	8.64547i	1.11612	−	1.93318i
$21$	−1.01653	+	3.92106i	−0.221825	+	0.855644i
$22$	−1.23467	−	2.13851i	−0.263232	−	0.455931i
$23$	−1.37948	−	2.38932i	−0.287641	−	0.498209i	0.685605	−	0.727973i	$-0.259538\pi$
$23$	−1.37948	−	2.38932i	−0.287641	−	0.498209i	−0.973246	+	0.229765i	$0.926204\pi$
$24$	8.64666	−	2.39242i	1.76499	−	0.488351i
$25$	−0.467722	+	0.810117i	−0.0935443	+	0.162023i
$26$	11.6315			2.28113
$27$	3.58348	−	3.76280i	0.689641	−	0.724151i
$28$	9.58293			1.81100
$29$	1.18586	−	2.05397i	0.220209	−	0.381413i	−0.734663	−	0.678433i	$-0.762660\pi$
$29$	1.18586	−	2.05397i	0.220209	−	0.381413i	0.954871	+	0.297020i	$0.0959928\pi$
$30$	−10.0427	+	2.77868i	−1.83353	+	0.507315i
$31$	0.685860	+	1.18794i	0.123184	+	0.213361i	0.921022	−	0.389511i	$-0.127356\pi$
$31$	0.685860	+	1.18794i	0.123184	+	0.213361i	−0.797838	+	0.602872i	$0.794023\pi$
$32$	−0.493856	−	0.855383i	−0.0873022	−	0.151212i
$33$	−0.434663	+	1.67662i	−0.0756651	+	0.291863i
$34$	3.96080	−	6.86030i	0.679271	−	1.17653i
$35$	−5.69762			−0.963074
$36$	−10.7445	−	5.97241i	−1.79075	−	0.995401i
$37$	−8.47256			−1.39288			−0.696440	−	0.717615i	$-0.745234\pi$
$37$	−8.47256			−1.39288			−0.696440	+	0.717615i	$0.745234\pi$
$38$	−9.59946	+	16.6268i	−1.55724	+	2.69722i
$39$	−5.81575	−	5.72189i	−0.931266	−	0.916236i
$40$	6.30961	+	10.9286i	0.997637	+	1.72796i
$41$	−1.77332	−	3.07149i	−0.276947	−	0.479686i	0.693678	−	0.720285i	$-0.255989\pi$
$41$	−1.77332	−	3.07149i	−0.276947	−	0.479686i	−0.970624	+	0.240600i	$0.922656\pi$
$42$	−7.13013	−	7.01505i	−1.10020	−	1.08245i
$43$	3.73467	−	6.46863i	0.569531	−	0.986457i	−0.427081	−	0.904213i	$-0.640458\pi$
$43$	3.73467	−	6.46863i	0.569531	−	0.986457i	0.996612	−	0.0822439i	$-0.0262087\pi$
$44$	4.09762			0.617739
$45$	6.38825	+	3.55095i	0.952304	+	0.529345i
$46$	6.81278			1.00449
$47$	−0.103993	+	0.180122i	−0.0151690	+	0.0262735i	−0.873510	−	0.486806i	$-0.838162\pi$
$47$	−0.103993	+	0.180122i	−0.0151690	+	0.0262735i	0.858341	+	0.513079i	$0.171495\pi$
$48$	−1.99737	+	7.70446i	−0.288296	+	1.11204i
$49$	0.765332	+	1.32559i	0.109333	+	0.189371i
$50$	−1.15496	−	2.00045i	−0.163336	−	0.282907i
$51$	−5.35519	+	1.48171i	−0.749877	+	0.207481i
$52$	−9.65066	+	16.7154i	−1.33831	+	2.31801i
$53$	−9.11360			−1.25185			−0.625925	−	0.779884i	$-0.715278\pi$
$53$	−9.11360			−1.25185			−0.625925	+	0.779884i	$0.715278\pi$
$54$	3.62237	+	12.3091i	0.492942	+	1.67506i
$55$	−2.43628			−0.328507
$56$	−6.05680	+	10.4907i	−0.809374	+	1.40188i
$57$	12.9789	−	3.59111i	1.71910	−	0.475654i
$58$	2.92829	+	5.07194i	0.384503	+	0.665978i
$59$	0.120523	+	0.208751i	0.0156907	+	0.0271771i	0.873764	−	0.486350i	$-0.161672\pi$
$59$	0.120523	+	0.208751i	0.0156907	+	0.0271771i	−0.858073	+	0.513527i	$0.828339\pi$
$60$	4.33921	−	16.7376i	0.560189	−	2.16082i
$61$	−0.830670	+	1.43876i	−0.106356	+	0.184215i	−0.914292	−	0.405057i	$-0.867252\pi$
$61$	−0.830670	+	1.43876i	−0.106356	+	0.184215i	0.807935	+	0.589271i	$0.200585\pi$
$62$	−3.38724			−0.430179
$63$	0.114145	+	7.01505i	0.0143809	+	0.883814i
$64$	−6.75145			−0.843932
$65$	5.73789	−	9.93832i	0.711698	−	1.23270i
$66$	−3.04881	−	2.99960i	−0.375282	−	0.369226i
$67$	3.84027	+	6.65155i	0.469164	+	0.812616i	0.999379	−	0.0352474i	$-0.0112219\pi$
$67$	3.84027	+	6.65155i	0.469164	+	0.812616i	−0.530214	+	0.847864i	$0.677889\pi$
$68$	6.57255	+	11.3840i	0.797039	+	1.38051i
$69$	−3.40639	−	3.35142i	−0.410081	−	0.403463i
$70$	7.03467	−	12.1844i	0.840804	−	1.45632i
$71$	1.07731			0.127854			0.0639268	−	0.997955i	$-0.479638\pi$
$71$	1.07731			0.127854			0.0639268	+	0.997955i	$0.479638\pi$
$72$	13.3291	−	7.98749i	1.57085	−	0.941334i
$73$	−2.37495			−0.277966			−0.138983	−	0.990295i	$-0.544383\pi$
$73$	−2.37495			−0.277966			−0.138983	+	0.990295i	$0.544383\pi$
$74$	10.4608	−	18.1186i	1.21604	−	2.10625i
$75$	−0.406602	+	1.56839i	−0.0469504	+	0.181102i
$76$	−15.9294	−	27.5904i	−1.82722	−	3.16484i
$77$	−1.16933	−	2.02534i	−0.133258	−	0.230809i
$78$	19.4168	−	5.37239i	2.19852	−	0.608304i
$79$	−6.35680	+	11.0103i	−0.715196	+	1.23876i	0.247687	+	0.968840i	$0.420329\pi$
$79$	−6.35680	+	11.0103i	−0.715196	+	1.23876i	−0.962884	+	0.269916i	$0.913004\pi$
$80$	−11.1952			−1.25166
$81$	4.24404	−	7.93651i	0.471560	−	0.881834i
$82$	8.75786			0.967144
$83$	−5.25042	+	9.09399i	−0.576308	+	0.998195i	0.419590	+	0.907714i	$0.362174\pi$
$83$	−5.25042	+	9.09399i	−0.576308	+	0.998195i	−0.995898	+	0.0904812i	$0.971159\pi$
$84$	15.9971	−	4.42619i	1.74542	−	0.482937i
$85$	−3.90777	−	6.76846i	−0.423857	−	0.734142i
$86$	9.22215	+	15.9732i	0.994450	+	1.72244i
$87$	1.03090	−	3.97648i	0.110524	−	0.426324i
$88$	−2.58986	+	4.48577i	−0.276080	+	0.478184i
$89$	−14.2933			−1.51509			−0.757544	−	0.652784i	$-0.773601\pi$
$89$	−14.2933			−1.51509			−0.757544	+	0.652784i	$0.773601\pi$
$90$	−15.4811	+	9.27707i	−1.63185	+	0.977889i
$91$	11.0160			1.15479
$92$	−5.65257	+	9.79053i	−0.589321	+	1.02073i
$93$	1.69362	+	1.66628i	0.175620	+	0.172786i
$94$	−0.256795	−	0.444781i	−0.0264863	−	0.0458757i
$95$	9.47095	+	16.4042i	0.971699	+	1.68303i
$96$	−1.21950	−	1.19981i	−0.124464	−	0.122455i
$97$	−4.46694	+	7.73697i	−0.453549	+	0.785570i	−0.998603	−	0.0528305i	$-0.983176\pi$
$97$	−4.46694	+	7.73697i	−0.453549	+	0.785570i	0.545054	+	0.838401i	$0.316509\pi$
$98$	−3.77972			−0.381810
$99$	0.0488078	+	2.99960i	0.00490536	+	0.301471i
$100$	3.83309			0.383309
$101$	2.43844	−	4.22350i	0.242633	−	0.420254i	−0.718830	−	0.695186i	$-0.755322\pi$
$101$	2.43844	−	4.22350i	0.242633	−	0.420254i	0.961464	+	0.274932i	$0.0886554\pi$
$102$	3.44322	−	13.2815i	0.340930	−	1.31507i
$103$	5.08509	+	8.80764i	0.501049	+	0.867843i	0.999999	+	0.00121186i	$0.000385748\pi$
$103$	5.08509	+	8.80764i	0.501049	+	0.867843i	−0.498950	+	0.866631i	$0.666281\pi$
$104$	−12.1992	−	21.1297i	−1.19623	−	2.07193i
$105$	−9.51122	+	2.63164i	−0.928200	+	0.256821i
$106$	11.2523	−	19.4895i	1.09292	−	1.89299i
$107$	9.59845			0.927917			0.463959	−	0.885857i	$-0.346429\pi$
$107$	9.59845			0.927917			0.463959	+	0.885857i	$0.346429\pi$
$108$	−20.6947	−	5.00722i	−1.99135	−	0.481820i
$109$	−1.95143			−0.186913			−0.0934564	−	0.995623i	$-0.529792\pi$
$109$	−1.95143			−0.186913			−0.0934564	+	0.995623i	$0.529792\pi$
$110$	3.00799	−	5.20999i	0.286801	−	0.496753i
$111$	−14.1435	+	3.91333i	−1.34244	+	0.371437i
$112$	−5.37333	−	9.30689i	−0.507732	−	0.879418i
$113$	3.95281	+	6.84646i	0.371849	+	0.644061i	0.989850	−	0.142116i	$-0.0453907\pi$
$113$	3.95281	+	6.84646i	0.371849	+	0.644061i	−0.618001	+	0.786177i	$0.712057\pi$
$114$	−8.34506	+	32.1894i	−0.781587	+	3.01481i
$115$	3.36079	−	5.82106i	0.313395	−	0.542816i
$116$	−9.71839			−0.902330
$117$	−12.3513	−	6.86553i	−1.14187	−	0.634719i
$118$	−0.595222			−0.0547946
$119$	3.75120	−	6.49726i	0.343872	−	0.595603i
$120$	15.5805	+	15.3291i	1.42230	+	1.39935i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−2.05120	−	3.55278i	−0.185707	−	0.321654i
$123$	−4.37893	−	4.30826i	−0.394835	−	0.388463i
$124$	2.81039	−	4.86774i	0.252380	−	0.437136i
$125$	9.90238			0.885696
$126$	−15.1427	−	8.41716i	−1.34902	−	0.749860i
$127$	−0.943412			−0.0837142			−0.0418571	−	0.999124i	$-0.513327\pi$
$127$	−0.943412			−0.0837142			−0.0418571	+	0.999124i	$0.513327\pi$
$128$	9.32351	−	16.1488i	0.824090	−	1.42737i
$129$	3.24664	−	12.5233i	0.285851	−	1.10261i
$130$	14.1688	+	24.5411i	1.24268	+	2.15239i
$131$	1.53066	+	2.65119i	0.133735	+	0.231636i	0.925113	−	0.379691i	$-0.123970\pi$
$131$	1.53066	+	2.65119i	0.133735	+	0.231636i	−0.791379	+	0.611326i	$0.790636\pi$
$132$	6.84027	−	1.89262i	0.595369	−	0.164731i
$133$	−9.09147	+	15.7469i	−0.788331	+	1.36543i
$134$	−18.9658			−1.63840
$135$	12.3042	+	2.97709i	1.05898	+	0.256227i
$136$	−16.6165			−1.42485
$137$	10.2280	−	17.7154i	0.873835	−	1.51353i	0.0158365	−	0.999875i	$-0.494959\pi$
$137$	10.2280	−	17.7154i	0.873835	−	1.51353i	0.857999	−	0.513652i	$-0.171708\pi$
$138$	11.3728	−	3.14671i	0.968116	−	0.267866i
$139$	−6.45442	−	11.1794i	−0.547457	−	0.948223i	−0.998448	−	0.0556944i	$-0.982263\pi$
$139$	−6.45442	−	11.1794i	−0.547457	−	0.948223i	0.450991	−	0.892528i	$-0.351071\pi$
$140$	11.6733	+	20.2188i	0.986577	+	1.70880i
$141$	−0.0904042	+	0.348716i	−0.00761341	+	0.0293672i
$142$	−1.33012	+	2.30384i	−0.111621	+	0.193334i
$143$	4.71038			0.393902
$144$	0.224282	+	13.7838i	0.0186902	+	1.14865i
$145$	5.77816			0.479850
$146$	2.93227	−	5.07884i	0.242676	−	0.420328i
$147$	1.88986	+	1.85936i	0.155873	+	0.153358i
$148$	17.3587	+	30.0661i	1.42687	+	2.47142i
$149$	−5.04027	−	8.73000i	−0.412915	−	0.715190i	0.582292	−	0.812980i	$-0.302156\pi$
$149$	−5.04027	−	8.73000i	−0.412915	−	0.715190i	−0.995207	+	0.0977899i	$0.968823\pi$
$150$	−2.85199	−	2.80596i	−0.232864	−	0.229105i
$151$	−2.36295	+	4.09275i	−0.192294	+	0.333063i	−0.946010	−	0.324137i	$-0.894926\pi$
$151$	−2.36295	+	4.09275i	−0.192294	+	0.333063i	0.753716	+	0.657200i	$0.228259\pi$
$152$	40.2720			3.26649
$153$	−8.25520	+	4.94694i	−0.667394	+	0.399936i
$154$	5.77494			0.465358
$155$	−1.67094	+	2.89416i	−0.134213	+	0.232465i
$156$	−8.38957	+	32.3611i	−0.671703	+	2.59096i
$157$	2.47733	+	4.29086i	0.197712	+	0.342448i	0.947786	−	0.318906i	$-0.103316\pi$
$157$	2.47733	+	4.29086i	0.197712	+	0.342448i	−0.750074	+	0.661354i	$0.769982\pi$
$158$	−15.6971	−	27.1881i	−1.24879	−	2.16297i
$159$	−15.2136	+	4.20941i	−1.20652	+	0.333828i
$160$	1.20317	−	2.08395i	0.0951189	−	0.164751i
$161$	6.45226			0.508509
$162$	11.7323	+	18.8749i	0.921776	+	1.48295i
$163$	−8.60277			−0.673821			−0.336910	−	0.941537i	$-0.609382\pi$
$163$	−8.60277			−0.673821			−0.336910	+	0.941537i	$0.609382\pi$
$164$	−7.26640	+	12.5858i	−0.567410	+	0.982784i
$165$	−4.06695	+	1.12527i	−0.316612	+	0.0876025i
$166$	−12.9650	−	22.4561i	−1.00628	−	1.74293i
$167$	−3.58908	−	6.21646i	−0.277731	−	0.481044i	0.693089	−	0.720852i	$-0.256249\pi$
$167$	−3.58908	−	6.21646i	−0.277731	−	0.481044i	−0.970821	+	0.239807i	$0.922916\pi$
$168$	−5.26533	+	20.3100i	−0.406229	+	1.56695i
$169$	−4.59384	+	7.95677i	−0.353372	+	0.612059i
$170$	19.2992			1.48018
$171$	20.0075	−	11.9895i	1.53001	−	0.916860i
$172$	−30.6065			−2.33372
$173$	−3.62591	+	6.28026i	−0.275673	+	0.477479i	−0.970305	−	0.241886i	$-0.922234\pi$
$173$	−3.62591	+	6.28026i	−0.275673	+	0.477479i	0.694632	+	0.719365i	$0.255567\pi$
$174$	7.23092	+	7.11422i	0.548174	+	0.539327i
$175$	−1.09384	−	1.89459i	−0.0826867	−	0.143218i
$176$	−2.29761	−	3.97958i	−0.173189	−	0.299972i
$177$	0.297611	+	0.292808i	0.0223698	+	0.0220088i
$178$	17.6475	−	30.5663i	1.32274	−	2.29104i
$179$	−7.29009			−0.544887			−0.272443	−	0.962172i	$-0.587832\pi$
$179$	−7.29009			−0.544887			−0.272443	+	0.962172i	$0.587832\pi$
$180$	−0.487244	−	29.9448i	−0.0363170	−	2.23195i
$181$	13.4235			0.997762			0.498881	−	0.866670i	$-0.333744\pi$
$181$	13.4235			0.997762			0.498881	+	0.866670i	$0.333744\pi$
$182$	−13.6011	+	23.5578i	−1.00818	+	1.74622i
$183$	−0.722123	+	2.78544i	−0.0533808	+	0.205906i
$184$	−7.14530	−	12.3760i	−0.526758	−	0.912372i
$185$	−10.3208	−	17.8761i	−0.758797	−	1.31427i
$186$	−5.65441	+	1.56451i	−0.414602	+	0.114715i
$187$	1.60399	−	2.77820i	0.117296	−	0.203162i
$188$	0.852250			0.0621567
$189$	3.43068	+	11.6577i	0.249545	+	0.847975i
$190$	−46.7739			−3.39333
$191$	1.15041	−	1.99256i	0.0832406	−	0.144177i	−0.821400	−	0.570353i	$-0.806806\pi$
$191$	1.15041	−	1.99256i	0.0832406	−	0.144177i	0.904640	+	0.426176i	$0.140140\pi$
$192$	−11.2704	+	3.11838i	−0.813372	+	0.225050i
$193$	−7.04904	−	12.2093i	−0.507401	−	0.878844i	−0.999963	−	0.00856725i	$-0.997273\pi$
$193$	−7.04904	−	12.2093i	−0.507401	−	0.878844i	0.492562	−	0.870277i	$-0.336060\pi$
$194$	−11.0304	−	19.1052i	−0.791935	−	1.37167i
$195$	4.98810	−	19.2406i	0.357205	−	1.37785i
$196$	3.13604	−	5.43178i	0.224003	−	0.387984i
$197$	1.31362			0.0935913			0.0467957	−	0.998904i	$-0.485099\pi$
$197$	1.31362			0.0935913			0.0467957	+	0.998904i	$0.485099\pi$
$198$	−6.47493	−	3.59914i	−0.460153	−	0.255779i
$199$	15.8491			1.12351			0.561755	−	0.827303i	$-0.310126\pi$
$199$	15.8491			1.12351			0.561755	+	0.827303i	$0.310126\pi$
$200$	−2.42266	+	4.19618i	−0.171308	+	0.296715i
$201$	9.48292	+	9.32988i	0.668874	+	0.658079i
$202$	6.02132	+	10.4292i	0.423658	+	0.733798i
$203$	2.77332	+	4.80354i	0.194649	+	0.337142i
$204$	16.2298	+	15.9679i	1.13631	+	1.11798i
$205$	4.32031	−	7.48299i	0.301743	−	0.522635i
$206$	−25.1136			−1.74975
$207$	−7.23435	−	4.02127i	−0.502822	−	0.279497i
$208$	21.6452			1.50083
$209$	−3.88747	+	6.73329i	−0.268902	+	0.465752i
$210$	6.11542	−	23.5890i	0.422004	−	1.62780i
$211$	4.29225	+	7.43439i	0.295490	+	0.511804i	0.975099	−	0.221771i	$-0.0711836\pi$
$211$	4.29225	+	7.43439i	0.295490	+	0.511804i	−0.679608	+	0.733575i	$0.737850\pi$
$212$	18.6720	+	32.3409i	1.28240	+	2.22118i
$213$	1.79839	−	0.497592i	0.123224	−	0.0340945i
$214$	−11.8509	+	20.5263i	−0.810110	+	1.40315i
$215$	18.1974			1.24105
$216$	18.5614	−	19.4902i	1.26294	−	1.32614i
$217$	−3.20799			−0.217772
$218$	2.40936	−	4.17314i	0.163183	−	0.282641i
$219$	−3.96457	+	1.09695i	−0.267901	+	0.0741248i
$220$	4.99146	+	8.64547i	0.336524	+	0.582877i
$221$	7.55542	+	13.0864i	0.508233	+	0.880285i
$222$	9.09384	−	35.0776i	0.610339	−	2.35426i
$223$	13.2592	−	22.9656i	0.887901	−	1.53789i	0.0455487	−	0.998962i	$-0.485496\pi$
$223$	13.2592	−	22.9656i	0.887901	−	1.53789i	0.842352	−	0.538927i	$-0.181170\pi$
$224$	2.30992			0.154338
$225$	0.0456569	+	2.80596i	0.00304379	+	0.187064i
$226$	−19.5216			−1.29856
$227$	−11.8427	+	20.5121i	−0.786025	+	1.36144i	0.142359	+	0.989815i	$0.454531\pi$
$227$	−11.8427	+	20.5121i	−0.786025	+	1.36144i	−0.928385	+	0.371621i	$0.878802\pi$
$228$	−39.3349	−	38.7001i	−2.60502	−	2.56298i
$229$	5.99547	+	10.3845i	0.396192	+	0.686224i	0.993253	−	0.115972i	$-0.0369982\pi$
$229$	5.99547	+	10.3845i	0.396192	+	0.686224i	−0.597061	+	0.802196i	$0.703665\pi$
$230$	8.29891	+	14.3741i	0.547214	+	0.947803i
$231$	−2.88747	−	2.84087i	−0.189981	−	0.186915i
$232$	6.14242	−	10.6390i	0.403269	−	0.698483i
$233$	18.9188			1.23941			0.619707	−	0.784833i	$-0.287251\pi$
$233$	18.9188			1.23941			0.619707	+	0.784833i	$0.287251\pi$
$234$	29.9317	−	17.9366i	1.95670	−	1.17255i
$235$	−0.506713			−0.0330543
$236$	0.493856	−	0.855383i	0.0321473	−	0.0556807i
$237$	−5.52613	+	21.3159i	−0.358961	+	1.38462i
$238$	9.26296	+	16.0439i	0.600429	+	1.03997i
$239$	8.28293	+	14.3465i	0.535778	+	0.927995i	0.999125	+	0.0418181i	$0.0133150\pi$
$239$	8.28293	+	14.3465i	0.535778	+	0.927995i	−0.463347	+	0.886177i	$0.653352\pi$
$240$	−18.6885	+	5.17089i	−1.20634	+	0.333779i
$241$	8.14450	−	14.1067i	0.524633	−	0.908691i	−0.474955	−	0.880010i	$-0.657536\pi$
$241$	8.14450	−	14.1067i	0.524633	−	0.908691i	0.999589	−	0.0286815i	$-0.00913084\pi$
$242$	2.46934			0.158735
$243$	3.41897	−	15.2089i	0.219327	−	0.975651i
$244$	6.80753			0.435807
$245$	−1.86456	+	3.22952i	−0.119122	+	0.206326i
$246$	14.6198	−	4.04511i	0.932122	−	0.257907i
$247$	−18.3115	−	31.7164i	−1.16513	−	2.01806i
$248$	3.55256	+	6.15321i	0.225588	+	0.390729i
$249$	−4.56432	+	17.6059i	−0.289252	+	1.11573i
$250$	−12.2262	+	21.1763i	−0.773250	+	1.33931i
$251$	−15.1248			−0.954671			−0.477336	−	0.878721i	$-0.658397\pi$
$251$	−15.1248			−0.954671			−0.477336	+	0.878721i	$0.658397\pi$
$252$	24.6600	−	14.7776i	1.55344	−	0.930899i
$253$	2.75895			0.173454
$254$	1.16480	−	2.01749i	0.0730860	−	0.126589i
$255$	−9.64960	−	9.49386i	−0.604281	−	0.594529i
$256$	16.2714	+	28.1829i	1.01696	+	1.76143i
$257$	−9.75281	−	16.8924i	−0.608364	−	1.05372i	−0.991510	−	0.130029i	$-0.958493\pi$
$257$	−9.75281	−	16.8924i	−0.608364	−	1.05372i	0.383147	−	0.923688i	$-0.374840\pi$
$258$	22.7726	+	22.4050i	1.41776	+	1.39488i
$259$	9.90723	−	17.1598i	0.615605	−	1.06626i
$260$	−47.0234			−2.91627
$261$	−0.115758	−	7.11422i	−0.00716526	−	0.440359i
$262$	−7.55945			−0.467024
$263$	−4.71975	+	8.17485i	−0.291032	+	0.504083i	−0.974054	−	0.226315i	$-0.927332\pi$
$263$	−4.71975	+	8.17485i	−0.291032	+	0.504083i	0.683022	+	0.730398i	$0.260665\pi$
$264$	−2.25143	+	8.68444i	−0.138566	+	0.534490i
$265$	−11.1016	−	19.2286i	−0.681967	−	1.18120i
$266$	−22.4499	−	38.8843i	−1.37649	−	2.38415i
$267$	−23.8603	+	6.60184i	−1.46022	+	0.404026i
$268$	15.7360	−	27.2555i	0.961227	−	1.66489i
$269$	7.33069			0.446960			0.223480	−	0.974708i	$-0.428258\pi$
$269$	7.33069			0.446960			0.223480	+	0.974708i	$0.428258\pi$
$270$	−21.5582	+	22.6369i	−1.31199	+	1.37764i
$271$	−2.50286			−0.152038			−0.0760190	−	0.997106i	$-0.524221\pi$
$271$	−2.50286			−0.152038			−0.0760190	+	0.997106i	$0.524221\pi$
$272$	7.37071	−	12.7664i	0.446915	−	0.774079i
$273$	18.3893	−	5.08809i	1.11297	−	0.307945i
$274$	25.2563	+	43.7452i	1.52579	+	2.64274i
$275$	−0.467722	−	0.810117i	−0.0282047	−	0.0488519i
$276$	−4.91392	+	18.9545i	−0.295783	+	1.14092i
$277$	−10.9945	+	19.0430i	−0.660593	+	1.14418i	0.319867	+	0.947462i	$0.396362\pi$
$277$	−10.9945	+	19.0430i	−0.660593	+	1.14418i	−0.980460	+	0.196718i	$0.936972\pi$
$278$	31.8762			1.91181
$279$	3.59684	+	1.99933i	0.215337	+	0.119697i
$280$	−29.5121			−1.76368
$281$	8.49685	−	14.7170i	0.506880	−	0.877941i	−0.493089	−	0.869979i	$-0.664132\pi$
$281$	8.49685	−	14.7170i	0.506880	−	0.877941i	0.999968	−	0.00796209i	$-0.00253444\pi$
$282$	−0.634112	−	0.623878i	−0.0377608	−	0.0371514i
$283$	−1.88908	−	3.27199i	−0.112294	−	0.194499i	0.804401	−	0.594087i	$-0.202487\pi$
$283$	−1.88908	−	3.27199i	−0.112294	−	0.194499i	−0.916695	+	0.399588i	$0.869153\pi$
$284$	−2.20721	−	3.82299i	−0.130974	−	0.226853i
$285$	23.3869	+	23.0095i	1.38532	+	1.36297i
$286$	−5.81575	+	10.0732i	−0.343893	+	0.595640i
$287$	8.29441			0.489603
$288$	−2.58991	−	1.43962i	−0.152612	−	0.0848305i
$289$	−6.70882			−0.394636
$290$	−7.13411	+	12.3566i	−0.418929	+	0.725607i
$291$	−3.88323	+	14.9788i	−0.227639	+	0.878071i
$292$	4.86581	+	8.42783i	0.284750	+	0.493201i
$293$	11.6877	+	20.2437i	0.682803	+	1.18265i	0.974122	+	0.226024i	$0.0725727\pi$
$293$	11.6877	+	20.2437i	0.682803	+	1.18265i	−0.291319	+	0.956626i	$0.594094\pi$
$294$	−6.30961	+	1.74579i	−0.367984	+	0.101817i
$295$	−0.293627	+	0.508576i	−0.0170956	+	0.0296105i
$296$	−43.8855			−2.55079
$297$	1.46694	+	4.98479i	0.0851206	+	0.289247i
$298$	24.8922			1.44197
$299$	−6.49786	+	11.2546i	−0.375781	+	0.650872i
$300$	6.39869	−	1.77044i	0.369428	−	0.102216i
$301$	8.73412	+	15.1279i	0.503426	+	0.871960i
$302$	−5.83491	−	10.1064i	−0.335761	−	0.581556i
$303$	2.11980	−	8.17668i	0.121779	−	0.469738i
$304$	−17.8638	+	30.9410i	−1.02456	+	1.77459i
$305$	−4.04748			−0.231758
$306$	−0.386635	−	23.7616i	−0.0221025	−	1.35836i
$307$	15.5574			0.887909			0.443954	−	0.896049i	$-0.353575\pi$
$307$	15.5574			0.887909			0.443954	+	0.896049i	$0.353575\pi$
$308$	−4.79147	+	8.29906i	−0.273019	+	0.472883i
$309$	12.5568	+	12.3541i	0.714331	+	0.702803i
$310$	−4.12612	−	7.14665i	−0.234348	−	0.405902i
$311$	−12.1419	−	21.0304i	−0.688504	−	1.19252i	−0.972322	−	0.233645i	$-0.924935\pi$
$311$	−12.1419	−	21.0304i	−0.688504	−	1.19252i	0.283818	−	0.958878i	$-0.408399\pi$
$312$	−30.1239	−	29.6378i	−1.70543	−	1.67791i
$313$	−3.90184	+	6.75818i	−0.220545	+	0.381995i	−0.954974	−	0.296691i	$-0.904117\pi$
$313$	−3.90184	+	6.75818i	−0.220545	+	0.381995i	0.734429	+	0.678686i	$0.237450\pi$
$314$	−12.2347			−0.690444
$315$	−14.6619	+	8.78614i	−0.826102	+	0.495043i
$316$	52.0955			2.93060
$317$	−6.78748	+	11.7563i	−0.381223	+	0.660298i	−0.991237	−	0.132093i	$-0.957830\pi$
$317$	−6.78748	+	11.7563i	−0.381223	+	0.660298i	0.610014	+	0.792390i	$0.291164\pi$
$318$	9.78188	−	37.7316i	0.548541	−	2.11588i
$319$	1.18586	+	2.05397i	0.0663954	+	0.115000i
$320$	−8.22420	−	14.2447i	−0.459747	−	0.796305i
$321$	16.0230	−	4.43336i	0.894316	−	0.247446i
$322$	−7.96640	+	13.7982i	−0.443950	+	0.768944i
$323$	−24.9419			−1.38780
$324$	−36.8590	+	1.19981i	−2.04772	+	0.0666563i
$325$	4.40629			0.244417
$326$	10.6216	−	18.3971i	0.588274	−	1.01892i
$327$	−3.25757	+	0.901330i	−0.180144	+	0.0498437i
$328$	−9.18531	−	15.9094i	−0.507174	−	0.878451i
$329$	−0.243205	−	0.421244i	−0.0134083	−	0.0232239i
$330$	2.61492	−	10.0865i	0.143947	−	0.555246i
$331$	−10.3955	+	18.0055i	−0.571387	+	0.989672i	0.425036	+	0.905176i	$0.360261\pi$
$331$	−10.3955	+	18.0055i	−0.571387	+	0.989672i	−0.996424	+	0.0844958i	$0.973072\pi$
$332$	43.0284			2.36149
$333$	−21.8027	+	13.0653i	−1.19478	+	0.715973i
$334$	17.7253			0.969884
$335$	−9.35597	+	16.2050i	−0.511171	+	0.885375i
$336$	−13.2686	−	13.0544i	−0.723859	−	0.712177i
$337$	−3.33252	−	5.77209i	−0.181534	−	0.314426i	0.760869	−	0.648905i	$-0.224773\pi$
$337$	−3.33252	−	5.77209i	−0.181534	−	0.314426i	−0.942403	+	0.334480i	$0.891439\pi$
$338$	−11.3437	−	19.6479i	−0.617018	−	1.06871i
$339$	9.76080	+	9.60327i	0.530134	+	0.521578i
$340$	−16.0125	+	27.7345i	−0.868402	+	1.50412i
$341$	−1.37172			−0.0742828
$342$	0.937057	+	57.5892i	0.0506702	+	3.11406i
$343$	−19.9503			−1.07722
$344$	19.3445	−	33.5057i	1.04299	−	1.80651i
$345$	2.92162	−	11.2696i	0.157295	−	0.606732i
$346$	−8.95359	−	15.5081i	−0.481348	−	0.833719i
$347$	3.45734	+	5.98828i	0.185600	+	0.321468i	0.943778	−	0.330579i	$-0.107244\pi$
$347$	3.45734	+	5.98828i	0.185600	+	0.321468i	−0.758179	+	0.652047i	$0.773911\pi$
$348$	−16.2232	+	4.48876i	−0.869655	+	0.240623i
$349$	−2.83783	+	4.91526i	−0.151905	+	0.263108i	−0.931928	−	0.362644i	$-0.881874\pi$
$349$	−2.83783	+	4.91526i	−0.151905	+	0.263108i	0.780022	+	0.625751i	$0.215208\pi$
$350$	5.40213			0.288756
$351$	−23.7894	−	5.75601i	−1.26978	−	0.307233i
$352$	0.987711			0.0526452
$353$	3.78324	−	6.55277i	0.201362	−	0.348769i	−0.747606	−	0.664143i	$-0.768797\pi$
$353$	3.78324	−	6.55277i	0.201362	−	0.348769i	0.948967	+	0.315374i	$0.102130\pi$
$354$	−0.993622	+	0.274923i	−0.0528104	+	0.0146120i
$355$	1.31232	+	2.27300i	0.0696505	+	0.120638i
$356$	29.2843	+	50.7218i	1.55206	+	2.68825i
$357$	3.26101	−	12.5787i	0.172591	−	0.665735i
$358$	9.00083	−	15.5899i	0.475709	−	0.823952i
$359$	29.1504			1.53850			0.769248	−	0.638950i	$-0.220631\pi$
$359$	29.1504			1.53850			0.769248	+	0.638950i	$0.220631\pi$
$360$	33.0893	+	18.3929i	1.74396	+	0.969392i
$361$	41.4497			2.18156
$362$	−16.5736	+	28.7063i	−0.871088	+	1.50877i
$363$	−1.23467	−	1.21474i	−0.0648032	−	0.0637574i
$364$	−22.5696	−	39.0917i	−1.18297	−	2.04896i
$365$	−2.89301	−	5.01085i	−0.151427	−	0.262280i
$366$	−5.06510	−	4.98336i	−0.264757	−	0.260484i
$367$	17.2272	−	29.8384i	0.899254	−	1.55755i	0.0708032	−	0.997490i	$-0.477444\pi$
$367$	17.2272	−	29.8384i	0.899254	−	1.55755i	0.828450	−	0.560063i	$-0.189223\pi$
$368$	12.6780			0.660887
$369$	−9.29979	−	5.16936i	−0.484128	−	0.269106i
$370$	50.9708			2.64985
$371$	10.6568	−	18.4581i	0.553274	−	0.958299i
$372$	2.44314	−	9.42393i	0.126671	−	0.488608i
$373$	−1.95278	−	3.38232i	−0.101111	−	0.175130i	0.811031	−	0.585002i	$-0.198906\pi$
$373$	−1.95278	−	3.38232i	−0.101111	−	0.175130i	−0.912143	+	0.409873i	$0.865573\pi$
$374$	3.96080	+	6.86030i	0.204808	+	0.354738i
$375$	16.5304	−	4.57374i	0.853624	−	0.236187i
$376$	−0.538656	+	0.932980i	−0.0277791	+	0.0481148i
$377$	−11.1717			−0.575372
$378$	−29.1659	−	7.05688i	−1.50013	−	0.362967i
$379$	−10.2129			−0.524600			−0.262300	−	0.964986i	$-0.584481\pi$
$379$	−10.2129			−0.524600			−0.262300	+	0.964986i	$0.584481\pi$
$380$	38.8083	−	67.2180i	1.99082	−	3.44821i
$381$	−1.57487	+	0.435746i	−0.0806828	+	0.0223239i
$382$	2.84074	+	4.92031i	0.145345	+	0.251745i
$383$	−7.06195	−	12.2317i	−0.360849	−	0.625009i	0.627252	−	0.778816i	$-0.284180\pi$
$383$	−7.06195	−	12.2317i	−0.360849	−	0.625009i	−0.988101	+	0.153808i	$0.950846\pi$
$384$	8.10517	−	31.2640i	0.413615	−	1.59544i
$385$	2.84881	−	4.93429i	0.145189	−	0.251475i
$386$	34.8129			1.77193
$387$	−0.364562	−	22.4050i	−0.0185317	−	1.13891i
$388$	36.6076			1.85847
$389$	−7.11383	+	12.3215i	−0.360686	+	0.624726i	−0.988074	−	0.153981i	$-0.950791\pi$
$389$	−7.11383	+	12.3215i	−0.360686	+	0.624726i	0.627388	+	0.778707i	$0.284124\pi$
$390$	34.9875	+	34.4228i	1.77166	+	1.74307i
$391$	4.42535	+	7.66492i	0.223799	+	0.387632i
$392$	3.96420	+	6.86620i	0.200223	+	0.346796i
$393$	3.77972	+	3.71872i	0.190662	+	0.187585i
$394$	−1.62188	+	2.80918i	−0.0817091	+	0.141524i
$395$	−30.9739			−1.55846
$396$	10.5445	−	6.31881i	0.529882	−	0.317532i
$397$	−23.5328			−1.18108			−0.590539	−	0.807009i	$-0.701085\pi$
$397$	−23.5328			−1.18108			−0.590539	+	0.807009i	$0.701085\pi$
$398$	−19.5683	+	33.8933i	−0.980872	+	1.69892i
$399$	−7.90345	+	30.4860i	−0.395667	+	1.52621i
$400$	−2.14928	−	3.72267i	−0.107464	−	0.186133i
$401$	18.2654	+	31.6366i	0.912131	+	1.57986i	0.811048	+	0.584979i	$0.198897\pi$
$401$	18.2654	+	31.6366i	0.912131	+	1.57986i	0.101083	+	0.994878i	$0.467769\pi$
$402$	−31.6603	+	8.76000i	−1.57907	+	0.436909i
$403$	3.23066	−	5.59567i	0.160931	−	0.278740i
$404$	−19.9835			−0.994219
$405$	21.9149	−	0.713361i	1.08896	−	0.0354472i
$406$	−13.6965			−0.679747
$407$	4.23628	−	7.33745i	0.209985	−	0.363704i
$408$	−27.7384	+	7.67486i	−1.37325	+	0.379962i
$409$	−8.39364	−	14.5382i	−0.415039	−	0.718868i	0.580394	−	0.814336i	$-0.302899\pi$
$409$	−8.39364	−	14.5382i	−0.415039	−	0.718868i	−0.995433	+	0.0954680i	$0.969565\pi$
$410$	10.6683	+	18.4780i	0.526869	+	0.912564i
$411$	8.89145	−	34.2969i	0.438583	−	1.69174i
$412$	20.8368	−	36.0903i	1.02655	−	1.77804i
$413$	−0.563724			−0.0277390
$414$	17.5315	−	10.5058i	0.861628	−	0.516331i
$415$	−25.5829			−1.25582
$416$	−2.32625	+	4.02918i	−0.114054	+	0.197547i
$417$	−15.9381	−	15.6809i	−0.780493	−	0.767897i
$418$	−9.59946	−	16.6268i	−0.469525	−	0.813241i
$419$	−4.33728	−	7.51239i	−0.211890	−	0.367004i	0.740416	−	0.672149i	$-0.234629\pi$
$419$	−4.33728	−	7.51239i	−0.211890	−	0.367004i	−0.952306	+	0.305145i	$0.901295\pi$
$420$	28.8254	+	28.3602i	1.40653	+	1.38383i
$421$	−10.1827	+	17.6370i	−0.496275	+	0.859573i	−0.999991	−	0.00429609i	$-0.998633\pi$
$421$	−10.1827	+	17.6370i	−0.496275	+	0.859573i	0.503716	+	0.863869i	$0.331966\pi$
$422$	−21.1980			−1.03190
$423$	0.0101514	+	0.623878i	0.000493577	+	0.0303340i
$424$	−47.2058			−2.29252
$425$	1.50044	−	2.59885i	0.0727822	−	0.126063i
$426$	−1.15631	+	4.46023i	−0.0560234	+	0.216099i
$427$	−1.94265	−	3.36478i	−0.0940116	−	0.162833i
$428$	−19.6654	−	34.0614i	−0.950562	−	1.64642i
$429$	7.86318	−	2.17564i	0.379638	−	0.105041i
$430$	−22.4677	+	38.9152i	−1.08349	+	1.87666i
$431$	−30.7365			−1.48053			−0.740263	−	0.672318i	$-0.765299\pi$
$431$	−30.7365			−1.48053			−0.740263	+	0.672318i	$0.765299\pi$
$432$	6.74092	+	22.9062i	0.324323	+	1.10207i
$433$	−35.7978			−1.72033			−0.860167	−	0.510012i	$-0.829641\pi$
$433$	−35.7978			−1.72033			−0.860167	+	0.510012i	$0.829641\pi$
$434$	3.96080	−	6.86030i	0.190124	−	0.329305i
$435$	9.64567	−	2.66884i	0.462474	−	0.127961i
$436$	3.99810	+	6.92491i	0.191474	+	0.331643i
$437$	−10.7253	−	18.5769i	−0.513063	−	0.888651i
$438$	2.54910	−	9.83263i	0.121801	−	0.469821i
$439$	9.15420	−	15.8555i	0.436906	−	0.756744i	−0.560543	−	0.828125i	$-0.689407\pi$
$439$	9.15420	−	15.8555i	0.436906	−	0.756744i	0.997449	+	0.0713815i	$0.0227408\pi$
$440$	−12.6192			−0.601598
$441$	4.01361	+	2.23099i	0.191124	+	0.106238i
$442$	−37.3137			−1.77483
$443$	−0.526658	+	0.912198i	−0.0250223	+	0.0433398i	−0.878265	−	0.478174i	$-0.841299\pi$
$443$	−0.526658	+	0.912198i	−0.0250223	+	0.0433398i	0.853243	+	0.521513i	$0.174632\pi$
$444$	42.8643	+	42.1725i	2.03425	+	2.00142i
$445$	−17.4112	−	30.1571i	−0.825372	−	1.42959i
$446$	32.7414	+	56.7097i	1.55035	+	2.68528i
$447$	−12.4461	−	12.2452i	−0.588681	−	0.579180i
$448$	7.89468	−	13.6740i	0.372989	−	0.646035i
$449$	29.3702			1.38607			0.693033	−	0.720906i	$-0.256274\pi$
$449$	29.3702			1.38607			0.693033	+	0.720906i	$0.256274\pi$
$450$	−6.05693	−	3.36679i	−0.285526	−	0.158712i
$451$	3.54665			0.167005
$452$	16.1971	−	28.0542i	0.761846	−	1.31956i
$453$	−2.05417	+	7.92355i	−0.0965134	+	0.372281i
$454$	−29.2435	−	50.6513i	−1.37247	−	2.37718i
$455$	13.4190	+	23.2424i	0.629092	+	1.08962i
$456$	67.2272	−	18.6009i	3.14820	−	0.871068i
$457$	−2.65837	+	4.60443i	−0.124353	+	0.215386i	−0.921480	−	0.388426i	$-0.873019\pi$
$457$	−2.65837	+	4.60443i	−0.124353	+	0.215386i	0.797127	+	0.603812i	$0.206352\pi$
$458$	−29.6096			−1.38357
$459$	−11.4958	+	12.0710i	−0.536576	+	0.563427i
$460$	−27.5424			−1.28417
$461$	3.43008	−	5.94107i	0.159755	−	0.276703i	−0.775025	−	0.631930i	$-0.782263\pi$
$461$	3.43008	−	5.94107i	0.159755	−	0.276703i	0.934780	+	0.355227i	$0.115596\pi$
$462$	9.64028	−	2.66734i	0.448506	−	0.124096i
$463$	12.6530	+	21.9157i	0.588036	+	1.01851i	0.994489	+	0.104837i	$0.0334322\pi$
$463$	12.6530	+	21.9157i	0.588036	+	1.01851i	−0.406453	+	0.913672i	$0.633235\pi$
$464$	5.44929	+	9.43844i	0.252977	+	0.438169i
$465$	−1.45259	+	5.60309i	−0.0673625	+	0.259837i
$466$	−23.3585	+	40.4581i	−1.08206	+	1.87418i
$467$	40.1018			1.85569			0.927844	−	0.372967i	$-0.121660\pi$
$467$	40.1018			1.85569			0.927844	+	0.372967i	$0.121660\pi$
$468$	0.942055	+	57.8963i	0.0435465	+	2.67626i
$469$	−17.9622			−0.829417
$470$	0.625623	−	1.08361i	0.0288578	−	0.0499832i
$471$	6.11735	+	6.01862i	0.281873	+	0.277323i
$472$	0.624273	+	1.08127i	0.0287345	+	0.0497696i
$473$	3.73467	+	6.46863i	0.171720	+	0.297428i
$474$	−38.7613	−	38.1358i	−1.78037	−	1.75163i
$475$	−3.63651	+	6.29861i	−0.166854	+	0.289000i
$476$	−30.7419			−1.40905
$477$	−23.4523	+	14.0538i	−1.07381	+	0.643480i
$478$	−40.9067			−1.87103
$479$	8.18768	−	14.1815i	0.374105	−	0.647969i	−0.616088	−	0.787678i	$-0.711283\pi$
$479$	8.18768	−	14.1815i	0.374105	−	0.647969i	0.990193	+	0.139709i	$0.0446167\pi$
$480$	1.04595	−	4.03452i	0.0477407	−	0.184150i
$481$	19.9545	+	34.5622i	0.909847	+	1.57590i
$482$	20.1115	+	34.8341i	0.916053	+	1.58665i
$483$	10.7710	−	2.98019i	0.490095	−	0.135603i
$484$	−2.04881	+	3.54864i	−0.0931276	+	0.161302i
$485$	−21.7654			−0.988316
$486$	28.3031	+	26.0894i	1.28385	+	1.18344i
$487$	14.9456			0.677249			0.338625	−	0.940922i	$-0.390038\pi$
$487$	14.9456			0.677249			0.338625	+	0.940922i	$0.390038\pi$
$488$	−4.30263	+	7.45238i	−0.194771	+	0.337353i
$489$	−14.3609	+	3.97347i	−0.649421	+	0.179687i
$490$	−4.60423	−	7.97476i	−0.207998	−	0.360263i
$491$	−13.9341	−	24.1346i	−0.628839	−	1.08918i	−0.987785	−	0.155823i	$-0.950197\pi$
$491$	−13.9341	−	24.1346i	−0.628839	−	1.08918i	0.358946	−	0.933358i	$-0.383136\pi$
$492$	−6.31687	+	24.3660i	−0.284786	+	1.09851i
$493$	−3.80422	+	6.58911i	−0.171334	+	0.296758i
$494$	90.4342			4.06883
$495$	−6.26934	+	3.75691i	−0.281786	+	0.168861i
$496$	−6.30336			−0.283029
$497$	−1.25973	+	2.18192i	−0.0565068	+	0.0978727i
$498$	−32.0150	−	31.4983i	−1.43463	−	1.41147i
$499$	16.5776	+	28.7133i	0.742116	+	1.28538i	0.951530	+	0.307556i	$0.0995111\pi$
$499$	16.5776	+	28.7133i	0.742116	+	1.28538i	−0.209414	+	0.977827i	$0.567156\pi$
$500$	−20.2881	−	35.1400i	−0.907311	−	1.57151i
$501$	−8.86264	−	8.71960i	−0.395953	−	0.389563i
$502$	18.6741	−	32.3446i	0.833468	−	1.44361i
$503$	8.90129			0.396889			0.198444	−	0.980112i	$-0.436411\pi$
$503$	8.90129			0.396889			0.198444	+	0.980112i	$0.436411\pi$
$504$	0.591238	+	36.3360i	0.0263358	+	1.61853i
$505$	11.8814			0.528716
$506$	−3.40639	+	5.90004i	−0.151433	+	0.262289i
$507$	−3.99355	+	15.4043i	−0.177360	+	0.684129i
$508$	1.93287	+	3.34783i	0.0857572	+	0.148536i
$509$	−20.3942	−	35.3237i	−0.903955	−	1.56570i	−0.822314	−	0.569034i	$-0.807317\pi$
$509$	−20.3942	−	35.3237i	−0.903955	−	1.56570i	−0.0816414	−	0.996662i	$-0.526016\pi$
$510$	32.2167	−	8.91397i	1.42658	−	0.394717i
$511$	2.77710	−	4.81007i	0.122852	−	0.212785i
$512$	−43.0651			−1.90323
$513$	27.8613	−	29.2555i	1.23011	−	1.29166i
$514$	48.1659			2.12451
$515$	−12.3887	+	21.4578i	−0.545911	+	0.945546i
$516$	−51.0923	+	14.1366i	−2.24921	+	0.622329i
$517$	−0.103993	−	0.180122i	−0.00457363	−	0.00792175i
$518$	24.4643	+	42.3733i	1.07490	+	1.86178i
$519$	−3.15210	+	12.1586i	−0.138362	+	0.533702i
$520$	29.7207	−	51.4777i	1.30334	−	2.25745i
$521$	−8.54191			−0.374228			−0.187114	−	0.982338i	$-0.559913\pi$
$521$	−8.54191			−0.374228			−0.187114	+	0.982338i	$0.559913\pi$
$522$	15.3567	+	8.53614i	0.672146	+	0.373617i
$523$	26.9328			1.17769			0.588845	−	0.808246i	$-0.299583\pi$
$523$	26.9328			1.17769			0.588845	+	0.808246i	$0.299583\pi$
$524$	6.27208	−	10.8636i	0.273997	−	0.474577i
$525$	−2.70106	−	2.65747i	−0.117884	−	0.115981i
$526$	−11.6546	−	20.1864i	−0.508167	−	0.880171i
$527$	−2.20023	−	3.81091i	−0.0958435	−	0.166006i
$528$	−5.67357	−	5.58201i	−0.246910	−	0.242926i
$529$	7.69408	−	13.3265i	0.334525	−	0.579415i
$530$	54.8273			2.38154
$531$	0.632054	+	0.351332i	0.0274288	+	0.0152465i
$532$	74.5067			3.23028
$533$	−8.35303	+	14.4679i	−0.361810	+	0.626673i
$534$	15.3414	−	59.1764i	0.663888	−	2.56081i
$535$	11.6922	+	20.2515i	0.505500	+	0.875551i
$536$	19.8915	+	34.4531i	0.859183	+	1.48815i
$537$	−12.1696	+	3.36717i	−0.525155	+	0.145304i
$538$	−9.05097	+	15.6767i	−0.390215	+	0.675872i
$539$	−1.53066			−0.0659304
$540$	−14.6444	−	49.7627i	−0.630193	−	2.14145i
$541$	44.5039			1.91337			0.956686	−	0.291121i	$-0.0940284\pi$
$541$	44.5039			1.91337			0.956686	+	0.291121i	$0.0940284\pi$
$542$	3.09020	−	5.35239i	0.132736	−	0.229905i
$543$	22.4083	−	6.20009i	0.961632	−	0.266071i
$544$	1.58428	+	2.74406i	0.0679256	+	0.117651i
$545$	−2.37711	−	4.11727i	−0.101824	−	0.176364i
$546$	−11.8238	+	45.6078i	−0.506011	+	1.95183i
$547$	−4.84725	+	8.39569i	−0.207254	+	0.358974i	−0.950848	−	0.309657i	$-0.899786\pi$
$547$	−4.84725	+	8.39569i	−0.207254	+	0.358974i	0.743595	+	0.668630i	$0.233119\pi$
$548$	−83.8206			−3.58064
$549$	0.0810862	+	4.98336i	0.00346068	+	0.212685i
$550$	2.30992			0.0984954
$551$	9.21999	−	15.9695i	0.392785	−	0.680323i
$552$	−17.6441	−	17.3594i	−0.750984	−	0.738864i
$553$	−14.8664	−	25.7494i	−0.632184	−	1.09497i
$554$	−27.1490	−	47.0234i	−1.15345	−	1.99783i
$555$	−25.4854	−	25.0741i	−1.08179	−	1.06434i
$556$	−26.4477	+	45.8088i	−1.12163	+	1.94273i
$557$	44.5990			1.88972			0.944861	−	0.327473i	$-0.106197\pi$
$557$	44.5990			1.88972			0.944861	+	0.327473i	$0.106197\pi$
$558$	−8.71647	+	5.22335i	−0.368998	+	0.221122i
$559$	−35.1834			−1.48810
$560$	13.0909	−	22.6741i	0.553193	−	0.958158i
$561$	1.39439	−	5.37859i	0.0588713	−	0.227084i
$562$	20.9816	+	36.3411i	0.885054	+	1.53296i
$563$	13.9051	+	24.0843i	0.586029	+	1.01503i	0.994746	+	0.102370i	$0.0326427\pi$
$563$	13.9051	+	24.0843i	0.586029	+	1.01503i	−0.408718	+	0.912661i	$0.634024\pi$
$564$	1.42269	−	0.393640i	0.0599059	−	0.0165752i
$565$	−9.63013	+	16.6799i	−0.405143	+	0.701727i
$566$	9.32955			0.392150
$567$	11.1114	+	17.8760i	0.466637	+	0.750722i
$568$	5.58017			0.234139
$569$	−18.5056	+	32.0527i	−0.775796	+	1.34372i	0.158550	+	0.987351i	$0.449318\pi$
$569$	−18.5056	+	32.0527i	−0.775796	+	1.34372i	−0.934346	+	0.356367i	$0.884015\pi$
$570$	−78.0811	+	21.6041i	−3.27046	+	0.904894i
$571$	13.9640	+	24.1863i	0.584374	+	1.01217i	0.994953	+	0.100340i	$0.0319932\pi$
$571$	13.9640	+	24.1863i	0.584374	+	1.01217i	−0.410579	+	0.911825i	$0.634673\pi$
$572$	−9.65066	−	16.7154i	−0.403515	−	0.698908i
$573$	1.00008	−	3.85760i	0.0417789	−	0.161154i
$574$	−10.2408	+	17.7376i	−0.427444	+	0.740355i
$575$	2.58084			0.107629
$576$	−17.3737	+	10.4112i	−0.723904	+	0.433801i
$577$	24.6587			1.02656			0.513278	−	0.858222i	$-0.328431\pi$
$577$	24.6587			1.02656			0.513278	+	0.858222i	$0.328431\pi$
$578$	8.28316	−	14.3469i	0.344534	−	0.596751i
$579$	−17.4064	−	17.1255i	−0.723387	−	0.711712i
$580$	−11.8383	−	20.5046i	−0.491561	−	0.851408i
$581$	−12.2789	−	21.2678i	−0.509416	−	0.882335i
$582$	−27.2377	−	26.7981i	−1.12904	−	1.11082i
$583$	4.55680	−	7.89261i	0.188723	−	0.326878i
$584$	−12.3015			−0.509042
$585$	−0.560108	−	34.4228i	−0.0231576	−	1.42321i
$586$	−57.7217			−2.38446
$587$	13.1231	−	22.7300i	0.541650	−	0.938166i	−0.457159	−	0.889385i	$-0.651133\pi$
$587$	13.1231	−	22.7300i	0.541650	−	0.938166i	0.998809	−	0.0487810i	$-0.0155337\pi$
$588$	2.72624	−	10.5159i	0.112428	−	0.433669i
$589$	5.33252	+	9.23619i	0.219723	+	0.380571i
$590$	−0.725063	−	1.25585i	−0.0298504	−	0.0517023i
$591$	2.19286	−	0.606737i	0.0902022	−	0.0249578i
$592$	19.4667	−	33.7172i	0.800074	−	1.38577i
$593$	11.8551			0.486829			0.243414	−	0.969922i	$-0.421733\pi$
$593$	11.8551			0.486829			0.243414	+	0.969922i	$0.421733\pi$
$594$	−12.4712	−	3.01749i	−0.511699	−	0.123809i
$595$	18.2779			0.749321
$596$	−20.6531	+	35.7722i	−0.845983	+	1.46529i
$597$	26.4573	−	7.32041i	1.08283	−	0.299605i
$598$	−16.0454	−	27.7914i	−0.656145	−	1.13648i
$599$	−15.2879	−	26.4795i	−0.624648	−	1.08192i	−0.988609	−	0.150508i	$-0.951909\pi$
$599$	−15.2879	−	26.4795i	−0.624648	−	1.08192i	0.363961	−	0.931414i	$-0.381424\pi$
$600$	−2.10608	+	8.12379i	−0.0859806	+	0.331653i
$601$	−13.9118	+	24.0959i	−0.567472	+	0.982891i	0.429343	+	0.903142i	$0.358745\pi$
$601$	−13.9118	+	24.0959i	−0.567472	+	0.982891i	−0.996815	+	0.0797492i	$0.974588\pi$
$602$	−43.1349			−1.75805
$603$	20.1394	+	11.1947i	0.820142	+	0.455881i
$604$	19.3649			0.787947
$605$	1.21814	−	2.10988i	0.0495244	−	0.0857787i
$606$	14.8686	+	14.6287i	0.603998	+	0.594250i
$607$	4.59543	+	7.95952i	0.186523	+	0.323067i	0.944089	−	0.329692i	$-0.106945\pi$
$607$	4.59543	+	7.95952i	0.186523	+	0.323067i	−0.757566	+	0.652759i	$0.773611\pi$
$608$	−3.83970	−	6.65055i	−0.155720	−	0.269715i
$609$	6.84827	+	6.73774i	0.277506	+	0.273027i
$610$	4.99729	−	8.65557i	0.202335	−	0.350454i
$611$	0.979697			0.0396343
$612$	34.4682	+	19.1594i	1.39330	+	0.774473i
$613$	−12.7376			−0.514467			−0.257234	−	0.966349i	$-0.582811\pi$
$613$	−12.7376			−0.514467			−0.257234	+	0.966349i	$0.582811\pi$
$614$	−19.2082	+	33.2697i	−0.775182	+	1.34265i
$615$	3.75576	−	14.4871i	0.151447	−	0.584175i
$616$	−6.05680	−	10.4907i	−0.244035	−	0.422682i
$617$	−6.91123	−	11.9706i	−0.278236	−	0.481918i	0.692711	−	0.721216i	$-0.256416\pi$
$617$	−6.91123	−	11.9706i	−0.278236	−	0.481918i	−0.970946	+	0.239297i	$0.923083\pi$
$618$	−41.9229	+	11.5995i	−1.68639	+	0.466602i
$619$	−22.6728	+	39.2705i	−0.911297	+	1.57841i	−0.0990636	+	0.995081i	$0.531585\pi$
$619$	−22.6728	+	39.2705i	−0.911297	+	1.57841i	−0.812234	+	0.583332i	$0.801749\pi$
$620$	13.6938			0.549955
$621$	−13.9339	−	3.37140i	−0.559147	−	0.135290i
$622$	59.9648			2.40437
$623$	16.7136	−	28.9488i	0.669617	−	1.15981i
$624$	36.1331	−	9.99757i	1.44648	−	0.400223i
$625$	14.4011	+	24.9434i	0.576043	+	0.997736i
$626$	−9.63495	−	16.6882i	−0.385090	−	0.666995i
$627$	−3.37948	+	13.0356i	−0.134963	+	0.520594i
$628$	10.1511	−	17.5823i	0.405074	−	0.701609i
$629$	27.1799			1.08373
$630$	−0.686693	−	42.2024i	−0.0273585	−	1.68139i
$631$	−48.0257			−1.91187			−0.955936	−	0.293576i	$-0.905155\pi$
$631$	−48.0257			−1.91187			−0.955936	+	0.293576i	$0.905155\pi$
$632$	−32.9264	+	57.0303i	−1.30974	+	2.26854i
$633$	10.5990	+	10.4279i	0.421272	+	0.414473i
$634$	−16.7606	−	29.0302i	−0.665647	−	1.15293i
$635$	−1.14921	−	1.99048i	−0.0456048	−	0.0789899i
$636$	46.1075	+	45.3633i	1.82828	+	1.79877i
$637$	3.60501	−	6.24406i	0.142836	−	0.247398i
$638$	−5.85657			−0.231864
$639$	2.77228	−	1.66129i	0.109670	−	0.0657197i
$640$	45.4293			1.79575
$641$	7.37312	−	12.7706i	0.291221	−	0.504409i	−0.682878	−	0.730533i	$-0.739272\pi$
$641$	7.37312	−	12.7706i	0.291221	−	0.504409i	0.974099	+	0.226123i	$0.0726052\pi$
$642$	−10.3023	+	39.7390i	−0.406599	+	1.56837i
$643$	22.8328	+	39.5476i	0.900438	+	1.55960i	0.826927	+	0.562310i	$0.190087\pi$
$643$	22.8328	+	39.5476i	0.900438	+	1.55960i	0.0735112	+	0.997294i	$0.476580\pi$
$644$	−13.2194	−	22.8967i	−0.520919	−	0.902258i
$645$	30.3774	−	8.40505i	1.19611	−	0.330949i
$646$	30.7950	−	53.3384i	1.21161	−	2.09857i
$647$	18.8503			0.741081			0.370540	−	0.928816i	$-0.379173\pi$
$647$	18.8503			0.741081			0.370540	+	0.928816i	$0.379173\pi$
$648$	21.9829	−	41.1088i	0.863570	−	1.61491i
$649$	−0.241045			−0.00946186
$650$	−5.44031	+	9.42289i	−0.213386	+	0.369596i
$651$	−5.35519	+	1.48171i	−0.209886	+	0.0580730i
$652$	17.6254	+	30.5281i	0.690265	+	1.19557i
$653$	10.0779	+	17.4554i	0.394378	+	0.683083i	0.993022	−	0.117933i	$-0.0376267\pi$
$653$	10.0779	+	17.4554i	0.394378	+	0.683083i	−0.598644	+	0.801016i	$0.704293\pi$
$654$	2.09452	−	8.07919i	0.0819023	−	0.315921i
$655$	−3.72912	+	6.45903i	−0.145709	+	0.252375i
$656$	16.2976			0.636316
$657$	−6.11152	+	3.66233i	−0.238433	+	0.142881i
$658$	1.20111			0.0468242
$659$	−4.83783	+	8.37936i	−0.188455	+	0.326414i	−0.944735	−	0.327834i	$-0.893681\pi$
$659$	−4.83783	+	8.37936i	−0.188455	+	0.326414i	0.756280	+	0.654248i	$0.227015\pi$
$660$	12.3256	+	12.1267i	0.479773	+	0.472030i
$661$	−12.6736	−	21.9513i	−0.492945	−	0.853805i	0.507022	−	0.861933i	$-0.330746\pi$
$661$	−12.6736	−	21.9513i	−0.492945	−	0.853805i	−0.999967	+	0.00812759i	$0.997413\pi$
$662$	−25.6699	−	44.4616i	−0.997690	−	1.72805i
$663$	18.6569	+	18.3558i	0.724572	+	0.712879i
$664$	−27.1957	+	47.1043i	−1.05540	+	1.82800i
$665$	−44.2987			−1.71783
$666$	−1.02114	−	62.7565i	−0.0395682	−	2.43176i
$667$	−6.54347			−0.253364
$668$	−14.7067	+	25.4727i	−0.569018	+	0.985568i
$669$	11.5266	−	44.4613i	0.445642	−	1.71897i
$670$	−23.1030	−	40.0156i	−0.892548	−	1.54594i
$671$	−0.830670	−	1.43876i	−0.0320676	−	0.0555428i
$672$	3.85602	−	1.06691i	0.148749	−	0.0411571i
$673$	0.766712	−	1.32798i	0.0295546	−	0.0511900i	−0.850870	−	0.525377i	$-0.823924\pi$
$673$	0.766712	−	1.32798i	0.0295546	−	0.0511900i	0.880424	+	0.474187i	$0.157258\pi$
$674$	16.4582			0.633946
$675$	1.37224	+	4.66298i	0.0528175	+	0.179478i
$676$	37.6476			1.44798
$677$	2.32984	−	4.03539i	0.0895429	−	0.155093i	−0.817775	−	0.575538i	$-0.804793\pi$
$677$	2.32984	−	4.03539i	0.0895429	−	0.155093i	0.907318	+	0.420445i	$0.138126\pi$
$678$	−32.5880	+	9.01669i	−1.25153	+	0.346284i
$679$	−10.4467	−	18.0941i	−0.400906	−	0.694390i
$680$	−20.2411	−	35.0587i	−0.776212	−	1.34444i
$681$	−10.2951	+	39.7114i	−0.394511	+	1.52174i
$682$	1.69362	−	2.93343i	0.0648520	−	0.112327i
$683$	−25.9322			−0.992269			−0.496134	−	0.868246i	$-0.665248\pi$
$683$	−25.9322			−0.992269			−0.496134	+	0.868246i	$0.665248\pi$
$684$	−83.5379	−	46.4351i	−3.19415	−	1.77549i
$685$	49.8364			1.90415
$686$	24.6320	−	42.6639i	0.940455	−	1.62892i
$687$	14.8048	+	14.5659i	0.564839	+	0.555723i
$688$	17.1616	+	29.7248i	0.654281	+	1.13325i
$689$	21.4643	+	37.1772i	0.817723	+	1.41634i
$690$	20.4928	+	20.1621i	0.780147	+	0.767556i
$691$	13.6320	−	23.6112i	0.518584	−	0.898214i	−0.481183	−	0.876620i	$-0.659793\pi$
$691$	13.6320	−	23.6112i	0.518584	−	0.898214i	0.999767	−	0.0215935i	$-0.00687394\pi$
$692$	29.7152			1.12960
$693$	−6.13229	−	3.40867i	−0.232946	−	0.129485i
$694$	−17.0746			−0.648145
$695$	15.7247	−	27.2361i	0.596474	−	1.03312i
$696$	5.33976	−	20.5970i	0.202403	−	0.780729i
$697$	5.68880	+	9.85329i	0.215479	+	0.373220i
$698$	−7.00755	−	12.1374i	−0.265240	−	0.459408i
$699$	31.5818	−	8.73829i	1.19453	−	0.330512i
$700$	−4.48214	+	7.76330i	−0.169409	+	0.293425i
$701$	−1.77806			−0.0671563			−0.0335782	−	0.999436i	$-0.510690\pi$
$701$	−1.77806			−0.0671563			−0.0335782	+	0.999436i	$0.510690\pi$
$702$	41.6813	−	43.7670i	1.57316	−	1.65188i
$703$	−65.8736			−2.48447
$704$	3.37573	−	5.84693i	0.127227	−	0.220364i
$705$	−0.845872	+	0.234042i	−0.0318574	+	0.00881454i
$706$	9.34209	+	16.1810i	0.351594	+	0.608979i
$707$	5.70268	+	9.87732i	0.214471	+	0.371475i
$708$	0.429322	−	1.65602i	0.0161349	−	0.0622371i
$709$	−7.30003	+	12.6440i	−0.274158	+	0.474856i	−0.969922	−	0.243414i	$-0.921733\pi$
$709$	−7.30003	+	12.6440i	−0.274158	+	0.474856i	0.695764	+	0.718270i	$0.255066\pi$
$710$	−6.48110			−0.243231
$711$	0.620523	+	38.1358i	0.0232714	+	1.43020i
$712$	−74.0353			−2.77459
$713$	1.89226	−	3.27748i	0.0708655	−	0.122743i
$714$	22.8734	+	22.5042i	0.856014	+	0.842199i
$715$	5.73789	+	9.93832i	0.214585	+	0.371672i
$716$	14.9360	+	25.8699i	0.558184	+	0.966803i
$717$	20.4533	+	20.1232i	0.763843	+	0.751516i
$718$	−35.9910	+	62.3382i	−1.34317	+	2.32644i
$719$	19.7642			0.737081			0.368540	−	0.929612i	$-0.379858\pi$
$719$	19.7642			0.737081			0.368540	+	0.929612i	$0.379858\pi$
$720$	−28.8090	+	17.2638i	−1.07365	+	0.643385i
$721$	−23.7846			−0.885785
$722$	−51.1765	+	88.6404i	−1.90459	+	3.29885i
$723$	7.08022	−	27.3105i	0.263316	−	1.01569i
$724$	−27.5022	−	47.6352i	−1.02211	−	1.77035i
$725$	1.10930	+	1.92137i	0.0411985	+	0.0713579i
$726$	4.12214	−	1.14054i	0.152987	−	0.0423295i
$727$	9.40561	−	16.2910i	0.348835	−	0.604200i	−0.637208	−	0.770692i	$-0.719911\pi$
$727$	9.40561	−	16.2910i	0.348835	−	0.604200i	0.986043	+	0.166492i	$0.0532441\pi$
$728$	57.0597			2.11477
$729$	−1.31734	−	26.9678i	−0.0487905	−	0.998809i
$730$	14.2876			0.528809
$731$	−11.9808	+	20.7513i	−0.443125	+	0.767514i
$732$	11.3640	−	3.14428i	0.420026	−	0.116216i
$733$	−23.3301	−	40.4090i	−0.861719	−	1.49254i	−0.870269	−	0.492577i	$-0.836055\pi$
$733$	−23.3301	−	40.4090i	−0.861719	−	1.49254i	0.00855029	−	0.999963i	$-0.497278\pi$
$734$	42.5398	+	73.6811i	1.57017	+	2.71962i
$735$	−1.62091	+	6.25234i	−0.0597882	+	0.230621i
$736$	−1.36253	+	2.35996i	−0.0502234	+	0.0869894i
$737$	−7.68055			−0.282917
$738$	22.5369	−	13.5052i	0.829593	−	0.497135i
$739$	−6.50838			−0.239415			−0.119707	−	0.992809i	$-0.538196\pi$
$739$	−6.50838			−0.239415			−0.119707	+	0.992809i	$0.538196\pi$
$740$	−42.2905	+	73.2492i	−1.55463	+	2.69270i
$741$	−45.2171	−	44.4874i	−1.66109	−	1.63428i
$742$	26.3152	+	45.5793i	0.966062	+	1.67327i
$743$	21.8998	+	37.9315i	0.803425	+	1.39157i	0.917349	+	0.398083i	$0.130325\pi$
$743$	21.8998	+	37.9315i	0.803425	+	1.39157i	−0.113924	+	0.993489i	$0.536342\pi$
$744$	8.77246	+	8.63088i	0.321614	+	0.316423i
$745$	12.2795	−	21.2687i	0.449886	−	0.779225i
$746$	9.64415			0.353097
$747$	0.512522	+	31.4983i	0.0187522	+	1.15246i
$748$	−13.1451			−0.480632
$749$	−11.2238	+	19.4401i	−0.410107	+	0.710327i
$750$	−10.6285	+	40.9973i	−0.388098	+	1.49701i
$751$	−9.84965	−	17.0601i	−0.359419	−	0.622531i	0.628445	−	0.777854i	$-0.283692\pi$
$751$	−9.84965	−	17.0601i	−0.359419	−	0.622531i	−0.987864	+	0.155322i	$0.950358\pi$
$752$	−0.477873	−	0.827700i	−0.0174262	−	0.0301831i
$753$	−25.2484	+	6.98590i	−0.920101	+	0.254580i
$754$	13.7933	−	23.8908i	0.502324	−	0.870050i
$755$	−11.5136			−0.419022
$756$	34.3402	−	36.0587i	1.24894	−	1.31144i
$757$	23.1719			0.842195			0.421098	−	0.907015i	$-0.361645\pi$
$757$	23.1719			0.842195			0.421098	+	0.907015i	$0.361645\pi$
$758$	12.6095	−	21.8403i	0.457998	−	0.793276i
$759$	4.60561	−	1.27431i	0.167173	−	0.0462547i
$760$	49.0568	+	84.9689i	1.77948	+	3.08215i
$761$	−6.96855	−	12.0699i	−0.252610	−	0.437533i	0.711634	−	0.702551i	$-0.247956\pi$
$761$	−6.96855	−	12.0699i	−0.252610	−	0.437533i	−0.964244	+	0.265017i	$0.914622\pi$
$762$	1.01259	−	3.90586i	0.0366823	−	0.141494i
$763$	2.28186	−	3.95230i	0.0826089	−	0.143083i
$764$	−9.42786			−0.341088
$765$	−20.4934	−	11.3914i	−0.740941	−	0.411857i
$766$	34.8767			1.26014
$767$	0.567708	−	0.983299i	0.0204987	−	0.0355049i
$768$	40.1796	+	39.5311i	1.44986	+	1.42646i
$769$	2.54821	+	4.41363i	0.0918907	+	0.159159i	0.908307	−	0.418305i	$-0.137376\pi$
$769$	2.54821	+	4.41363i	0.0918907	+	0.159159i	−0.816416	+	0.577464i	$0.804042\pi$
$770$	7.03467	+	12.1844i	0.253512	+	0.439096i
$771$	−24.0830	−	23.6943i	−0.867326	−	0.853329i
$772$	−28.8843	+	50.0290i	−1.03957	+	1.80058i
$773$	−20.5798			−0.740202			−0.370101	−	0.928991i	$-0.620677\pi$
$773$	−20.5798			−0.740202			−0.370101	+	0.928991i	$0.620677\pi$
$774$	48.3634	+	26.8832i	1.73839	+	0.966295i
$775$	−1.28317			−0.0460927
$776$	−23.1375	+	40.0753i	−0.830587	+	1.43862i
$777$	8.61261	−	33.2214i	0.308976	−	1.19181i
$778$	−17.5664	−	30.4260i	−0.629787	−	1.09082i
$779$	−13.7875	−	23.8806i	−0.493988	−	0.855612i
$780$	−78.4975	+	21.7193i	−2.81066	+	0.777675i
$781$	−0.538656	+	0.932980i	−0.0192746	+	0.0333847i
$782$	−21.8553			−0.781545
$783$	−3.47917	−	11.8225i	−0.124336	−	0.422502i
$784$	−7.03375			−0.251205
$785$	−6.03545	+	10.4537i	−0.215415	+	0.373109i
$786$	−12.6192	+	3.49158i	−0.450113	+	0.124541i
$787$	−12.1272	−	21.0049i	−0.432288	−	0.748745i	0.564782	−	0.825240i	$-0.308960\pi$
$787$	−12.1272	−	21.0049i	−0.432288	−	0.748745i	−0.997070	+	0.0764950i	$0.975627\pi$
$788$	−2.69135	−	4.66155i	−0.0958753	−	0.166061i
$789$	−4.10300	+	15.8265i	−0.146071	+	0.563438i
$790$	38.2424	−	66.2378i	1.36060	−	2.35664i
$791$	−18.4885			−0.657377
$792$	0.252810	+	15.5371i	0.00898322	+	0.552086i
$793$	7.82554			0.277893
$794$	29.0552	−	50.3251i	1.03113	−	1.78597i
$795$	−27.4136	−	26.9712i	−0.972261	−	0.956570i
$796$	−32.4717	−	56.2426i	−1.15093	−	1.99347i
$797$	−19.5678	−	33.8924i	−0.693126	−	1.20053i	−0.970808	−	0.239857i	$-0.922899\pi$
$797$	−19.5678	−	33.8924i	−0.693126	−	1.20053i	0.277682	−	0.960673i	$-0.410434\pi$
$798$	−55.4363	−	54.5416i	−1.96242	−	1.93075i
$799$	0.333610	−	0.577829i	0.0118023	−	0.0204421i
$800$	0.923948			0.0326665
$801$	−36.7814	+	22.0413i	−1.29961	+	0.778791i
$802$	−90.2068			−3.18531
$803$	1.18747	−	2.05676i	0.0419050	−	0.0725816i
$804$	13.6797	−	52.7666i	0.482445	−	1.86093i
$805$	7.85974	+	13.6135i	0.277020	+	0.479812i
$806$	7.97758	+	13.8176i	0.280998	+	0.486703i
$807$	12.2373	−	3.38592i	0.430775	−	0.119190i
$808$	12.6304	−	21.8765i	0.444336	−	0.769613i
$809$	−32.9926			−1.15996			−0.579979	−	0.814631i	$-0.696939\pi$
$809$	−32.9926			−1.15996			−0.579979	+	0.814631i	$0.696939\pi$
$810$	−25.5321	+	47.7459i	−0.897105	+	1.67762i
$811$	−32.0811			−1.12652			−0.563259	−	0.826280i	$-0.690453\pi$
$811$	−32.0811			−1.12652			−0.563259	+	0.826280i	$0.690453\pi$
$812$	11.3640	−	19.6831i	0.398799	−	0.690740i
$813$	−4.17810	+	1.15603i	−0.146532	+	0.0405437i
$814$	10.4608	+	18.1186i	0.366651	+	0.635058i
$815$	−10.4794	−	18.1508i	−0.367076	−	0.635794i
$816$	6.40755	−	24.7158i	0.224309	−	0.865226i
$817$	29.0368	−	50.2932i	1.01587	−	1.75954i
$818$	41.4534			1.44938
$819$	28.3477	−	16.9874i	0.990550	−	0.593588i
$820$	−35.4059			−1.23643
$821$	−21.3784	+	37.0284i	−0.746111	+	1.29230i	0.203563	+	0.979062i	$0.434748\pi$
$821$	−21.3784	+	37.0284i	−0.746111	+	1.29230i	−0.949674	+	0.313240i	$0.898586\pi$
$822$	62.3663	+	61.3597i	2.17527	+	2.14017i
$823$	−7.90108	−	13.6851i	−0.275414	−	0.477032i	0.694825	−	0.719179i	$-0.255482\pi$
$823$	−7.90108	−	13.6851i	−0.275414	−	0.477032i	−0.970240	+	0.242147i	$0.922148\pi$
$824$	26.3393	+	45.6211i	0.917574	+	1.58929i
$825$	−1.15496	−	1.13632i	−0.0402106	−	0.0395616i
$826$	0.696011	−	1.20553i	0.0242173	−	0.0419456i
$827$	−23.8246			−0.828461			−0.414230	−	0.910172i	$-0.635949\pi$
$827$	−23.8246			−0.828461			−0.414230	+	0.910172i	$0.635949\pi$
$828$	0.551778	+	33.9109i	0.0191756	+	1.17849i
$829$	−8.75791			−0.304175			−0.152087	−	0.988367i	$-0.548600\pi$
$829$	−8.75791			−0.304175			−0.152087	+	0.988367i	$0.548600\pi$
$830$	31.5864	−	54.7093i	1.09638	−	1.89899i
$831$	−9.55777	+	36.8671i	−0.331555	+	1.27891i
$832$	15.9010	+	27.5413i	0.551266	+	0.954822i
$833$	−2.45518	−	4.25249i	−0.0850668	−	0.147340i
$834$	53.2120	−	14.7231i	1.84258	−	0.509819i
$835$	8.74399	−	15.1450i	0.302598	−	0.524115i
$836$	31.8587			1.10186
$837$	6.92776	+	1.67622i	0.239458	+	0.0579386i
$838$	21.4204			0.739955
$839$	−9.74005	+	16.8703i	−0.336264	+	0.582426i	−0.983727	−	0.179671i	$-0.942497\pi$
$839$	−9.74005	+	16.8703i	−0.336264	+	0.582426i	0.647463	+	0.762097i	$0.275830\pi$
$840$	−49.2654	+	13.6311i	−1.69982	+	0.470318i
$841$	11.6875	+	20.2433i	0.403016	+	0.698045i
$842$	−25.1445	−	43.5516i	−0.866537	−	1.50089i
$843$	7.38653	−	28.4920i	0.254406	−	0.981318i
$844$	17.5880	−	30.4633i	0.605403	−	1.04859i
$845$	−22.3837			−0.770024
$846$	−1.34670	−	0.748573i	−0.0463005	−	0.0257365i
$847$	2.33866			0.0803573
$848$	20.9395	−	36.2683i	0.719066	−	1.24546i
$849$	−4.66478	−	4.58949i	−0.160095	−	0.157511i
$850$	3.70510	+	6.41742i	0.127084	+	0.220116i
$851$	11.6877	+	20.2437i	0.400649	+	0.693945i
$852$	−5.45033	−	5.36237i	−0.186725	−	0.183712i
$853$	−26.1398	+	45.2754i	−0.895008	+	1.55020i	−0.0612137	+	0.998125i	$0.519497\pi$
$853$	−26.1398	+	45.2754i	−0.895008	+	1.55020i	−0.833794	+	0.552075i	$0.813836\pi$
$854$	9.59413			0.328304
$855$	49.6682	+	27.6084i	1.69862	+	0.944189i
$856$	49.7172			1.69930
$857$	27.4174	−	47.4883i	0.936560	−	1.62217i	0.164731	−	0.986339i	$-0.447324\pi$
$857$	27.4174	−	47.4883i	0.936560	−	1.62217i	0.771829	−	0.635831i	$-0.219342\pi$
$858$	−5.05579	+	19.5017i	−0.172602	+	0.665776i
$859$	9.70616	+	16.8116i	0.331170	+	0.573603i	0.982742	−	0.184984i	$-0.0592233\pi$
$859$	9.70616	+	16.8116i	0.331170	+	0.573603i	−0.651572	+	0.758587i	$0.725890\pi$
$860$	−37.2829	−	64.5759i	−1.27134	−	2.20202i
$861$	13.8461	−	3.83104i	0.471874	−	0.130562i
$862$	37.9494	−	65.7302i	1.29256	−	2.23878i
$863$	2.89484			0.0985414			0.0492707	−	0.998785i	$-0.484310\pi$
$863$	2.89484			0.0985414			0.0492707	+	0.998785i	$0.484310\pi$
$864$	−4.98836	−	1.20697i	−0.169707	−	0.0410619i
$865$	−17.6674			−0.600711
$866$	44.1984	−	76.5539i	1.50192	−	2.60141i
$867$	−11.1992	+	3.09869i	−0.380346	+	0.105237i
$868$	6.57255	+	11.3840i	0.223087	+	0.386398i
$869$	−6.35680	−	11.0103i	−0.215640	−	0.373499i
$870$	−6.20187	+	23.9224i	−0.210263	+	0.811047i
$871$	18.0892	−	31.3313i	0.612928	−	1.06162i
$872$	−10.1078			−0.342294
$873$	0.436043	+	26.7981i	0.0147578	+	0.906978i
$874$	52.9690			1.79170
$875$	−11.5792	+	20.0557i	−0.391447	+	0.678006i
$876$	12.0153	+	11.8214i	0.405960	+	0.399408i
$877$	5.23651	+	9.06991i	0.176825	+	0.306269i	0.940791	−	0.338987i	$-0.110084\pi$
$877$	5.23651	+	9.06991i	0.176825	+	0.306269i	−0.763967	+	0.645256i	$0.776751\pi$
$878$	22.6048	+	39.1527i	0.762875	+	1.32134i
$879$	28.8609	+	28.3951i	0.973453	+	0.957742i
$880$	5.59762	−	9.69535i	0.188696	−	0.326830i
$881$	31.5232			1.06204			0.531022	−	0.847358i	$-0.321808\pi$
$881$	31.5232			1.06204			0.531022	+	0.847358i	$0.321808\pi$
$882$	−9.72647	+	5.82860i	−0.327507	+	0.196259i
$883$	5.25391			0.176808			0.0884040	−	0.996085i	$-0.471823\pi$
$883$	5.25391			0.176808			0.0884040	+	0.996085i	$0.471823\pi$
$884$	30.9592	−	53.6229i	1.04127	−	1.80353i
$885$	−0.255257	+	0.984603i	−0.00858038	+	0.0330971i
$886$	−1.30049	−	2.25252i	−0.0436910	−	0.0756750i
$887$	−10.4309	−	18.0669i	−0.350237	−	0.606628i	0.636054	−	0.771645i	$-0.280566\pi$
$887$	−10.4309	−	18.0669i	−0.350237	−	0.606628i	−0.986291	+	0.165017i	$0.947232\pi$
$888$	−73.2593	+	20.2699i	−2.45842	+	0.680215i
$889$	1.10316	−	1.91073i	0.0369988	−	0.0640838i
$890$	85.9883			2.88234
$891$	4.75120	+	7.64370i	0.159171	+	0.256074i
$892$	−108.662			−3.63828
$893$	−0.808542	+	1.40044i	−0.0270568	+	0.0468638i
$894$	41.5534	−	11.4973i	1.38975	−	0.384527i
$895$	−8.88033	−	15.3812i	−0.296837	−	0.514136i
$896$	21.8045	+	37.7666i	0.728438	+	1.26169i
$897$	−5.64876	+	21.7889i	−0.188607	+	0.727512i
$898$	−36.2624	+	62.8084i	−1.21009	+	2.09594i
$899$	3.25333			0.108505
$900$	9.86379	−	5.91089i	0.328793	−	0.197030i
$901$	29.2363			0.974002
$902$	−4.37893	+	7.58453i	−0.145802	+	0.252537i
$903$	21.5675	+	21.2194i	0.717721	+	0.706137i
$904$	20.4744	+	35.4627i	0.680969	+	1.17947i
$905$	16.3517	+	28.3220i	0.543549	+	0.941455i
$906$	−14.4083	−	14.1758i	−0.478685	−	0.470960i
$907$	−11.0005	+	19.0534i	−0.365265	+	0.632657i	−0.988819	−	0.149124i	$-0.952355\pi$
$907$	−11.0005	+	19.0534i	−0.365265	+	0.632657i	0.623554	+	0.781780i	$0.285688\pi$
$908$	97.0534			3.22083
$909$	−0.238029	−	14.6287i	−0.00789493	−	0.485203i
$910$	−66.2720			−2.19689
$911$	−2.33067	+	4.03684i	−0.0772185	+	0.133746i	−0.902049	−	0.431634i	$-0.857937\pi$
$911$	−2.33067	+	4.03684i	−0.0772185	+	0.133746i	0.824830	+	0.565380i	$0.191271\pi$
$912$	−15.5294	+	59.9017i	−0.514231	+	1.98354i
$913$	−5.25042	−	9.09399i	−0.173763	−	0.300967i
$914$	−6.56440	−	11.3699i	−0.217131	−	0.376082i
$915$	−6.75658	+	1.86946i	−0.223366	+	0.0618025i
$916$	24.5671	−	42.5515i	0.811721	−	1.40594i
$917$	−7.15941			−0.236425
$918$	−11.6205	−	39.4874i	−0.383534	−	1.30328i
$919$	−6.91941			−0.228250			−0.114125	−	0.993466i	$-0.536407\pi$
$919$	−6.91941			−0.228250			−0.114125	+	0.993466i	$0.536407\pi$
$920$	17.4079	−	30.1514i	0.573922	−	0.994063i
$921$	25.9705	−	7.18571i	0.855756	−	0.236777i
$922$	8.47001	+	14.6705i	0.278945	+	0.483147i
$923$	−2.53728	−	4.39469i	−0.0835155	−	0.144653i
$924$	−4.16535	+	16.0670i	−0.137030	+	0.528565i
$925$	3.96280	−	6.86377i	0.130296	−	0.225679i
$926$	−62.4892			−2.05352
$927$	26.6676	+	14.8234i	0.875879	+	0.486864i
$928$	−2.34257			−0.0768988
$929$	0.639189	−	1.10711i	0.0209711	−	0.0363230i	−0.855349	−	0.518052i	$-0.826658\pi$
$929$	0.639189	−	1.10711i	0.0209711	−	0.0363230i	0.876321	+	0.481729i	$0.159991\pi$
$930$	−10.1888	−	10.0243i	−0.334103	−	0.328711i
$931$	5.95041	+	10.3064i	0.195017	+	0.337779i
$932$	−38.7611	−	67.1361i	−1.26966	−	2.19912i
$933$	−29.9824	−	29.4985i	−0.981580	−	0.965738i
$934$	−49.5124	+	85.7579i	−1.62009	+	2.80609i
$935$	7.81554			0.255596
$936$	−63.9760	−	35.5615i	−2.09112	−	1.16236i
$937$	−47.7193			−1.55892			−0.779461	−	0.626450i	$-0.784507\pi$
$937$	−47.7193			−1.55892			−0.779461	+	0.626450i	$0.784507\pi$
$938$	22.1773	−	38.4123i	0.724116	−	1.25421i
$939$	−3.39197	+	13.0838i	−0.110693	+	0.426975i
$940$	1.03816	+	1.79814i	0.0338610	+	0.0586490i
$941$	4.06989	+	7.04926i	0.132675	+	0.229799i	0.924707	−	0.380680i	$-0.124310\pi$
$941$	4.06989	+	7.04926i	0.132675	+	0.229799i	−0.792032	+	0.610479i	$0.790977\pi$
$942$	−20.4238	+	5.65100i	−0.665442	+	0.184119i
$943$	−4.89252	+	8.47409i	−0.159322	+	0.275954i
$944$	−1.10766			−0.0360512
$945$	−20.4173	+	21.4390i	−0.664176	+	0.697412i
$946$	−18.4443			−0.599676
$947$	13.9845	−	24.2219i	0.454435	−	0.787105i	−0.544220	−	0.838942i	$-0.683174\pi$
$947$	13.9845	−	24.2219i	0.454435	−	0.787105i	0.998656	+	0.0518372i	$0.0165077\pi$
$948$	86.9646	−	24.0620i	2.82448	−	0.781498i
$949$	5.59345	+	9.68814i	0.181571	+	0.314490i
$950$	−8.97975	−	15.5534i	−0.291342	−	0.504618i
$951$	−5.90053	+	22.7601i	−0.191338	+	0.738047i
$952$	19.4301	−	33.6540i	0.629734	−	1.09073i
$953$	−42.5121			−1.37710			−0.688551	−	0.725188i	$-0.741753\pi$
$953$	−42.5121			−1.37710			−0.688551	+	0.725188i	$0.741753\pi$
$954$	−1.09840	−	67.5046i	−0.0355619	−	2.18554i
$955$	5.60542			0.181387
$956$	33.9403	−	58.7863i	1.09771	−	1.90128i
$957$	2.92829	+	2.88103i	0.0946580	+	0.0931303i
$958$	20.2181	+	35.0188i	0.653218	+	1.13141i
$959$	23.9198	+	41.4303i	0.772410	+	1.33785i
$960$	−20.3083	−	19.9806i	−0.655448	−	0.644870i
$961$	14.5592	−	25.2173i	0.469651	−	0.813460i
$962$	−98.5487			−3.17734
$963$	24.7000	−	14.8015i	0.795945	−	0.476971i
$964$	−66.7460			−2.14975
$965$	17.1734	−	29.7452i	0.552832	−	0.957533i
$966$	−6.92539	+	26.7133i	−0.222821	+	0.859486i
$967$	11.0115	+	19.0724i	0.354104	+	0.613327i	0.986964	−	0.160940i	$-0.0514524\pi$
$967$	11.0115	+	19.0724i	0.354104	+	0.613327i	−0.632860	+	0.774266i	$0.718119\pi$
$968$	−2.58986	−	4.48577i	−0.0832412	−	0.144178i
$969$	−41.6363	+	11.5202i	−1.33755	+	0.370083i
$970$	26.8730	−	46.5455i	0.862841	−	1.49449i
$971$	−29.0719			−0.932963			−0.466482	−	0.884531i	$-0.654479\pi$
$971$	−29.0719			−0.932963			−0.466482	+	0.884531i	$0.654479\pi$
$972$	−60.9757	+	19.0274i	−1.95580	+	0.610305i
$973$	30.1894			0.967828
$974$	−18.4528	+	31.9612i	−0.591267	+	1.02410i
$975$	7.35556	−	2.03519i	0.235566	−	0.0651783i
$976$	−3.81711	−	6.61143i	−0.122183	−	0.211627i
$977$	21.6241	+	37.4540i	0.691815	+	1.19826i	0.971243	+	0.238092i	$0.0765219\pi$
$977$	21.6241	+	37.4540i	0.691815	+	1.19826i	−0.279428	+	0.960167i	$0.590145\pi$
$978$	9.23360	−	35.6167i	0.295258	−	1.13890i
$979$	7.14666	−	12.3784i	0.228408	−	0.395615i
$980$	15.2805			0.488118
$981$	−5.02166	+	3.00924i	−0.160329	+	0.0960775i
$982$	68.8161			2.19601
$983$	16.1093	−	27.9021i	0.513807	−	0.889940i	−0.486065	−	0.873923i	$-0.661568\pi$
$983$	16.1093	−	27.9021i	0.513807	−	0.889940i	0.999872	−	0.0160169i	$-0.00509856\pi$
$984$	−22.6816	−	22.3156i	−0.723064	−	0.711394i
$985$	1.60017	+	2.77157i	0.0509855	+	0.0883096i
$986$	−9.39390	−	16.2707i	−0.299163	−	0.518165i
$987$	−0.600556	−	0.590863i	−0.0191159	−	0.0188074i
$988$	−75.0333	+	129.962i	−2.38713	+	4.13463i
$989$	−20.6076			−0.655282
$990$	−0.293627	−	18.0456i	−0.00933207	−	0.573526i
$991$	38.9476			1.23721			0.618605	−	0.785702i	$-0.287698\pi$
$991$	38.9476			1.23721			0.618605	+	0.785702i	$0.287698\pi$
$992$	0.677432	−	1.17335i	0.0215085	−	0.0372538i
$993$	−9.03706	+	34.8586i	−0.286783	+	1.10621i
$994$	−3.11071	−	5.38790i	−0.0986656	−	0.170894i
$995$	19.3064	+	33.4396i	0.612053	+	1.06011i
$996$	71.8286	−	19.8741i	2.27598	−	0.629734i
$997$	18.3566	−	31.7945i	0.581358	−	1.00694i	−0.413960	−	0.910295i	$-0.635855\pi$
$997$	18.3566	−	31.7945i	0.581358	−	1.00694i	0.995319	−	0.0966472i	$-0.0308119\pi$
$998$	−81.8714			−2.59159
$999$	−30.3613	+	31.8806i	−0.960588	+	1.00866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.e.e.34.1	✓	8
3.2	odd	2		297.2.e.e.100.4		8
9.2	odd	6		891.2.a.p.1.1		4
9.4	even	3	inner	99.2.e.e.67.1	yes	8
9.5	odd	6		297.2.e.e.199.4		8
9.7	even	3		891.2.a.q.1.4		4
11.10	odd	2		1089.2.e.i.727.4		8
99.43	odd	6		9801.2.a.bi.1.1		4
99.65	even	6		9801.2.a.bl.1.4		4
99.76	odd	6		1089.2.e.i.364.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.e.34.1	✓	8	1.1	even	1	trivial
99.2.e.e.67.1	yes	8	9.4	even	3	inner
297.2.e.e.100.4		8	3.2	odd	2
297.2.e.e.199.4		8	9.5	odd	6
891.2.a.p.1.1		4	9.2	odd	6
891.2.a.q.1.4		4	9.7	even	3
1089.2.e.i.364.4		8	99.76	odd	6
1089.2.e.i.727.4		8	11.10	odd	2
9801.2.a.bi.1.1		4	99.43	odd	6
9801.2.a.bl.1.4		4	99.65	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23467 + 2.13851i) q^{2} +(1.66933 - 0.461883i) q^{3} +(-2.04881 - 3.54864i) q^{4} +(1.21814 + 2.10988i) q^{5} +(-1.07333 + 4.14015i) q^{6} +(-1.16933 + 2.02534i) q^{7} +5.17972 q^{8} +(2.57333 - 1.54207i) q^{9} +O(q^{10})\)	\(q+(-1.23467 + 2.13851i) q^{2} +(1.66933 - 0.461883i) q^{3} +(-2.04881 - 3.54864i) q^{4} +(1.21814 + 2.10988i) q^{5} +(-1.07333 + 4.14015i) q^{6} +(-1.16933 + 2.02534i) q^{7} +5.17972 q^{8} +(2.57333 - 1.54207i) q^{9} -6.01598 q^{10} +(-0.500000 + 0.866025i) q^{11} +(-5.05919 - 4.97754i) q^{12} +(-2.35519 - 4.07931i) q^{13} +(-2.88747 - 5.00124i) q^{14} +(3.00799 + 2.95945i) q^{15} +(-2.29761 + 3.97958i) q^{16} -3.20799 q^{17} +(0.120523 + 7.40702i) q^{18} +7.77494 q^{19} +(4.99146 - 8.64547i) q^{20} +(-1.01653 + 3.92106i) q^{21} +(-1.23467 - 2.13851i) q^{22} +(-1.37948 - 2.38932i) q^{23} +(8.64666 - 2.39242i) q^{24} +(-0.467722 + 0.810117i) q^{25} +11.6315 q^{26} +(3.58348 - 3.76280i) q^{27} +9.58293 q^{28} +(1.18586 - 2.05397i) q^{29} +(-10.0427 + 2.77868i) q^{30} +(0.685860 + 1.18794i) q^{31} +(-0.493856 - 0.855383i) q^{32} +(-0.434663 + 1.67662i) q^{33} +(3.96080 - 6.86030i) q^{34} -5.69762 q^{35} +(-10.7445 - 5.97241i) q^{36} -8.47256 q^{37} +(-9.59946 + 16.6268i) q^{38} +(-5.81575 - 5.72189i) q^{39} +(6.30961 + 10.9286i) q^{40} +(-1.77332 - 3.07149i) q^{41} +(-7.13013 - 7.01505i) q^{42} +(3.73467 - 6.46863i) q^{43} +4.09762 q^{44} +(6.38825 + 3.55095i) q^{45} +6.81278 q^{46} +(-0.103993 + 0.180122i) q^{47} +(-1.99737 + 7.70446i) q^{48} +(0.765332 + 1.32559i) q^{49} +(-1.15496 - 2.00045i) q^{50} +(-5.35519 + 1.48171i) q^{51} +(-9.65066 + 16.7154i) q^{52} -9.11360 q^{53} +(3.62237 + 12.3091i) q^{54} -2.43628 q^{55} +(-6.05680 + 10.4907i) q^{56} +(12.9789 - 3.59111i) q^{57} +(2.92829 + 5.07194i) q^{58} +(0.120523 + 0.208751i) q^{59} +(4.33921 - 16.7376i) q^{60} +(-0.830670 + 1.43876i) q^{61} -3.38724 q^{62} +(0.114145 + 7.01505i) q^{63} -6.75145 q^{64} +(5.73789 - 9.93832i) q^{65} +(-3.04881 - 2.99960i) q^{66} +(3.84027 + 6.65155i) q^{67} +(6.57255 + 11.3840i) q^{68} +(-3.40639 - 3.35142i) q^{69} +(7.03467 - 12.1844i) q^{70} +1.07731 q^{71} +(13.3291 - 7.98749i) q^{72} -2.37495 q^{73} +(10.4608 - 18.1186i) q^{74} +(-0.406602 + 1.56839i) q^{75} +(-15.9294 - 27.5904i) q^{76} +(-1.16933 - 2.02534i) q^{77} +(19.4168 - 5.37239i) q^{78} +(-6.35680 + 11.0103i) q^{79} -11.1952 q^{80} +(4.24404 - 7.93651i) q^{81} +8.75786 q^{82} +(-5.25042 + 9.09399i) q^{83} +(15.9971 - 4.42619i) q^{84} +(-3.90777 - 6.76846i) q^{85} +(9.22215 + 15.9732i) q^{86} +(1.03090 - 3.97648i) q^{87} +(-2.58986 + 4.48577i) q^{88} -14.2933 q^{89} +(-15.4811 + 9.27707i) q^{90} +11.0160 q^{91} +(-5.65257 + 9.79053i) q^{92} +(1.69362 + 1.66628i) q^{93} +(-0.256795 - 0.444781i) q^{94} +(9.47095 + 16.4042i) q^{95} +(-1.21950 - 1.19981i) q^{96} +(-4.46694 + 7.73697i) q^{97} -3.77972 q^{98} +(0.0488078 + 2.99960i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 5 q^{3} - 11 q^{4} - 4 q^{5} + 17 q^{6} - q^{7} - 5 q^{9}+O(q^{10}) \) 8 * q - q^2 + 5 * q^3 - 11 * q^4 - 4 * q^5 + 17 * q^6 - q^7 - 5 * q^9	\( 8 q - q^{2} + 5 q^{3} - 11 q^{4} - 4 q^{5} + 17 q^{6} - q^{7} - 5 q^{9} + 2 q^{10} - 4 q^{11} - 2 q^{12} - 7 q^{13} - q^{14} - q^{15} - 17 q^{16} - 10 q^{17} - 2 q^{18} + 18 q^{19} + 10 q^{20} - 13 q^{21} - q^{22} - 14 q^{23} + 18 q^{24} - 14 q^{25} + 44 q^{26} + 5 q^{27} - 2 q^{28} + 6 q^{29} - 37 q^{30} + 2 q^{31} + 34 q^{32} - 4 q^{33} - 16 q^{34} - 16 q^{35} + 11 q^{36} + 6 q^{37} - 3 q^{38} - 22 q^{39} - 12 q^{40} + 2 q^{41} - q^{42} + 21 q^{43} + 22 q^{44} + 49 q^{45} + 4 q^{46} + 7 q^{47} - 59 q^{48} + 15 q^{49} - 23 q^{50} - 31 q^{51} + 10 q^{52} - 12 q^{53} - 37 q^{54} + 8 q^{55} - 18 q^{56} + 33 q^{57} + 21 q^{58} - 2 q^{59} + 73 q^{60} - 15 q^{61} - 40 q^{62} - 5 q^{63} + 32 q^{64} - 19 q^{65} - 19 q^{66} - 14 q^{67} + 7 q^{68} - 2 q^{69} + 38 q^{70} - 6 q^{71} + 75 q^{72} + 44 q^{73} + 36 q^{74} + 10 q^{75} - 42 q^{76} - q^{77} + 29 q^{78} - 11 q^{79} - 68 q^{80} + 7 q^{81} - 34 q^{82} - 18 q^{83} + 34 q^{84} - 13 q^{85} + 24 q^{86} - 9 q^{87} - 12 q^{89} - 80 q^{90} + 38 q^{91} - 67 q^{92} + 20 q^{93} + 19 q^{94} + 30 q^{95} - 50 q^{96} - 26 q^{97} + 30 q^{98} - 5 q^{99}+O(q^{100}) \) 8 * q - q^2 + 5 * q^3 - 11 * q^4 - 4 * q^5 + 17 * q^6 - q^7 - 5 * q^9 + 2 * q^10 - 4 * q^11 - 2 * q^12 - 7 * q^13 - q^14 - q^15 - 17 * q^16 - 10 * q^17 - 2 * q^18 + 18 * q^19 + 10 * q^20 - 13 * q^21 - q^22 - 14 * q^23 + 18 * q^24 - 14 * q^25 + 44 * q^26 + 5 * q^27 - 2 * q^28 + 6 * q^29 - 37 * q^30 + 2 * q^31 + 34 * q^32 - 4 * q^33 - 16 * q^34 - 16 * q^35 + 11 * q^36 + 6 * q^37 - 3 * q^38 - 22 * q^39 - 12 * q^40 + 2 * q^41 - q^42 + 21 * q^43 + 22 * q^44 + 49 * q^45 + 4 * q^46 + 7 * q^47 - 59 * q^48 + 15 * q^49 - 23 * q^50 - 31 * q^51 + 10 * q^52 - 12 * q^53 - 37 * q^54 + 8 * q^55 - 18 * q^56 + 33 * q^57 + 21 * q^58 - 2 * q^59 + 73 * q^60 - 15 * q^61 - 40 * q^62 - 5 * q^63 + 32 * q^64 - 19 * q^65 - 19 * q^66 - 14 * q^67 + 7 * q^68 - 2 * q^69 + 38 * q^70 - 6 * q^71 + 75 * q^72 + 44 * q^73 + 36 * q^74 + 10 * q^75 - 42 * q^76 - q^77 + 29 * q^78 - 11 * q^79 - 68 * q^80 + 7 * q^81 - 34 * q^82 - 18 * q^83 + 34 * q^84 - 13 * q^85 + 24 * q^86 - 9 * q^87 - 12 * q^89 - 80 * q^90 + 38 * q^91 - 67 * q^92 + 20 * q^93 + 19 * q^94 + 30 * q^95 - 50 * q^96 - 26 * q^97 + 30 * q^98 - 5 * q^99

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