LMFDB - Embedded newform 99.2.e.e.67.1

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			67.1
Root			$-0.734668 - 0.348716i$ of defining polynomial
Character	$\chi$	$=$	99.67
Dual form			99.2.e.e.34.1

$q$-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 $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

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

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	−0.858834	−	0.512254i	$-0.828811\pi$
$2$	−1.23467	−	2.13851i	−0.873042	−	1.51215i	−0.0142076	−	0.999899i	$-0.504523\pi$
$3$	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	−0.453853	−	0.891076i	$-0.649951\pi$
$5$	1.21814	−	2.10988i	0.544768	−	0.943566i	0.998621	−	0.0524895i	$-0.0167156\pi$
$6$	−1.07333	−	4.14015i	−0.438185	−	1.69021i
$7$	−1.16933	−	2.02534i	−0.441965	−	0.765506i	0.555870	−	0.831269i	$-0.312385\pi$
$7$	−1.16933	−	2.02534i	−0.441965	−	0.765506i	−0.997835	+	0.0657628i	$0.979052\pi$
$8$	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	0.329127	+	0.944286i	$0.393246\pi$
$13$	−2.35519	+	4.07931i	−0.653212	+	1.13140i	−0.982339	+	0.187111i	$0.940088\pi$
$14$	−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	−0.973246	−	0.229765i	$-0.926204\pi$
$23$	−1.37948	+	2.38932i	−0.287641	+	0.498209i	0.685605	+	0.727973i	$0.259538\pi$
$24$	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	0.954871	−	0.297020i	$-0.0959928\pi$
$29$	1.18586	+	2.05397i	0.220209	+	0.381413i	−0.734663	+	0.678433i	$0.762660\pi$
$30$	−10.0427	−	2.77868i	−1.83353	−	0.507315i
$31$	0.685860	−	1.18794i	0.123184	−	0.213361i	−0.797838	−	0.602872i	$-0.794023\pi$
$31$	0.685860	−	1.18794i	0.123184	−	0.213361i	0.921022	+	0.389511i	$0.127356\pi$
$32$	−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	−0.970624	−	0.240600i	$-0.922656\pi$
$41$	−1.77332	+	3.07149i	−0.276947	+	0.479686i	0.693678	+	0.720285i	$0.255989\pi$
$42$	−7.13013	+	7.01505i	−1.10020	+	1.08245i
$43$	3.73467	+	6.46863i	0.569531	+	0.986457i	0.996612	+	0.0822439i	$0.0262087\pi$
$43$	3.73467	+	6.46863i	0.569531	+	0.986457i	−0.427081	+	0.904213i	$0.640458\pi$
$44$	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	0.858341	−	0.513079i	$-0.171495\pi$
$47$	−0.103993	−	0.180122i	−0.0151690	−	0.0262735i	−0.873510	+	0.486806i	$0.838162\pi$
$48$	−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	−0.858073	−	0.513527i	$-0.828339\pi$
$59$	0.120523	−	0.208751i	0.0156907	−	0.0271771i	0.873764	+	0.486350i	$0.161672\pi$
$60$	4.33921	+	16.7376i	0.560189	+	2.16082i
$61$	−0.830670	−	1.43876i	−0.106356	−	0.184215i	0.807935	−	0.589271i	$-0.200585\pi$
$61$	−0.830670	−	1.43876i	−0.106356	−	0.184215i	−0.914292	+	0.405057i	$0.867252\pi$
$62$	−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	−0.530214	−	0.847864i	$-0.677889\pi$
$67$	3.84027	−	6.65155i	0.469164	−	0.812616i	0.999379	+	0.0352474i	$0.0112219\pi$
$68$	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	−0.962884	−	0.269916i	$-0.913004\pi$
$79$	−6.35680	−	11.0103i	−0.715196	−	1.23876i	0.247687	−	0.968840i	$-0.420329\pi$
$80$	−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	−0.995898	−	0.0904812i	$-0.971159\pi$
$83$	−5.25042	−	9.09399i	−0.576308	−	0.998195i	0.419590	−	0.907714i	$-0.362174\pi$
$84$	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	0.545054	−	0.838401i	$-0.316509\pi$
$97$	−4.46694	−	7.73697i	−0.453549	−	0.785570i	−0.998603	+	0.0528305i	$0.983176\pi$
$98$	−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	0.961464	−	0.274932i	$-0.0886554\pi$
$101$	2.43844	+	4.22350i	0.242633	+	0.420254i	−0.718830	+	0.695186i	$0.755322\pi$
$102$	3.44322	+	13.2815i	0.340930	+	1.31507i
$103$	5.08509	−	8.80764i	0.501049	−	0.867843i	−0.498950	−	0.866631i	$-0.666281\pi$
$103$	5.08509	−	8.80764i	0.501049	−	0.867843i	0.999999	−	0.00121186i	$-0.000385748\pi$
$104$	−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	−0.618001	−	0.786177i	$-0.712057\pi$
$113$	3.95281	−	6.84646i	0.371849	−	0.644061i	0.989850	+	0.142116i	$0.0453907\pi$
$114$	−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	−0.791379	−	0.611326i	$-0.790636\pi$
$131$	1.53066	−	2.65119i	0.133735	−	0.231636i	0.925113	+	0.379691i	$0.123970\pi$
$132$	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	0.857999	+	0.513652i	$0.171708\pi$
$137$	10.2280	+	17.7154i	0.873835	+	1.51353i	0.0158365	+	0.999875i	$0.494959\pi$
$138$	11.3728	+	3.14671i	0.968116	+	0.267866i
$139$	−6.45442	+	11.1794i	−0.547457	+	0.948223i	0.450991	+	0.892528i	$0.351071\pi$
$139$	−6.45442	+	11.1794i	−0.547457	+	0.948223i	−0.998448	+	0.0556944i	$0.982263\pi$
$140$	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	−0.995207	−	0.0977899i	$-0.968823\pi$
$149$	−5.04027	+	8.73000i	−0.412915	+	0.715190i	0.582292	+	0.812980i	$0.302156\pi$
$150$	−2.85199	+	2.80596i	−0.232864	+	0.229105i
$151$	−2.36295	−	4.09275i	−0.192294	−	0.333063i	0.753716	−	0.657200i	$-0.228259\pi$
$151$	−2.36295	−	4.09275i	−0.192294	−	0.333063i	−0.946010	+	0.324137i	$0.894926\pi$
$152$	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	−0.750074	−	0.661354i	$-0.769982\pi$
$157$	2.47733	−	4.29086i	0.197712	−	0.342448i	0.947786	+	0.318906i	$0.103316\pi$
$158$	−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	−0.970821	−	0.239807i	$-0.922916\pi$
$167$	−3.58908	+	6.21646i	−0.277731	+	0.481044i	0.693089	+	0.720852i	$0.256249\pi$
$168$	−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	0.694632	−	0.719365i	$-0.255567\pi$
$173$	−3.62591	−	6.28026i	−0.275673	−	0.477479i	−0.970305	+	0.241886i	$0.922234\pi$
$174$	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	0.904640	−	0.426176i	$-0.140140\pi$
$191$	1.15041	+	1.99256i	0.0832406	+	0.144177i	−0.821400	+	0.570353i	$0.806806\pi$
$192$	−11.2704	−	3.11838i	−0.813372	−	0.225050i
$193$	−7.04904	+	12.2093i	−0.507401	+	0.878844i	0.492562	+	0.870277i	$0.336060\pi$
$193$	−7.04904	+	12.2093i	−0.507401	+	0.878844i	−0.999963	+	0.00856725i	$0.997273\pi$
$194$	−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	−0.679608	−	0.733575i	$-0.737850\pi$
$211$	4.29225	−	7.43439i	0.295490	−	0.511804i	0.975099	+	0.221771i	$0.0711836\pi$
$212$	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	0.842352	+	0.538927i	$0.181170\pi$
$223$	13.2592	+	22.9656i	0.887901	+	1.53789i	0.0455487	+	0.998962i	$0.485496\pi$
$224$	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	−0.928385	−	0.371621i	$-0.878802\pi$
$227$	−11.8427	−	20.5121i	−0.786025	−	1.36144i	0.142359	−	0.989815i	$-0.454531\pi$
$228$	−39.3349	+	38.7001i	−2.60502	+	2.56298i
$229$	5.99547	−	10.3845i	0.396192	−	0.686224i	−0.597061	−	0.802196i	$-0.703665\pi$
$229$	5.99547	−	10.3845i	0.396192	−	0.686224i	0.993253	+	0.115972i	$0.0369982\pi$
$230$	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	−0.463347	−	0.886177i	$-0.653352\pi$
$239$	8.28293	−	14.3465i	0.535778	−	0.927995i	0.999125	−	0.0418181i	$-0.0133150\pi$
$240$	−18.6885	−	5.17089i	−1.20634	−	0.333779i
$241$	8.14450	+	14.1067i	0.524633	+	0.908691i	0.999589	+	0.0286815i	$0.00913084\pi$
$241$	8.14450	+	14.1067i	0.524633	+	0.908691i	−0.474955	+	0.880010i	$0.657536\pi$
$242$	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	0.383147	+	0.923688i	$0.374840\pi$
$257$	−9.75281	+	16.8924i	−0.608364	+	1.05372i	−0.991510	+	0.130029i	$0.958493\pi$
$258$	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	0.683022	−	0.730398i	$-0.260665\pi$
$263$	−4.71975	−	8.17485i	−0.291032	−	0.504083i	−0.974054	+	0.226315i	$0.927332\pi$
$264$	−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	−0.980460	−	0.196718i	$-0.936972\pi$
$277$	−10.9945	−	19.0430i	−0.660593	−	1.14418i	0.319867	−	0.947462i	$-0.396362\pi$
$278$	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	0.999968	+	0.00796209i	$0.00253444\pi$
$281$	8.49685	+	14.7170i	0.506880	+	0.877941i	−0.493089	+	0.869979i	$0.664132\pi$
$282$	−0.634112	+	0.623878i	−0.0377608	+	0.0371514i
$283$	−1.88908	+	3.27199i	−0.112294	+	0.194499i	−0.916695	−	0.399588i	$-0.869153\pi$
$283$	−1.88908	+	3.27199i	−0.112294	+	0.194499i	0.804401	+	0.594087i	$0.202487\pi$
$284$	−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	−0.291319	−	0.956626i	$-0.594094\pi$
$293$	11.6877	−	20.2437i	0.682803	−	1.18265i	0.974122	−	0.226024i	$-0.0725727\pi$
$294$	−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	0.283818	+	0.958878i	$0.408399\pi$
$311$	−12.1419	+	21.0304i	−0.688504	+	1.19252i	−0.972322	+	0.233645i	$0.924935\pi$
$312$	−30.1239	+	29.6378i	−1.70543	+	1.67791i
$313$	−3.90184	−	6.75818i	−0.220545	−	0.381995i	0.734429	−	0.678686i	$-0.237450\pi$
$313$	−3.90184	−	6.75818i	−0.220545	−	0.381995i	−0.954974	+	0.296691i	$0.904117\pi$
$314$	−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	0.610014	−	0.792390i	$-0.291164\pi$
$317$	−6.78748	−	11.7563i	−0.381223	−	0.660298i	−0.991237	+	0.132093i	$0.957830\pi$
$318$	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	−0.996424	−	0.0844958i	$-0.973072\pi$
$331$	−10.3955	−	18.0055i	−0.571387	−	0.989672i	0.425036	−	0.905176i	$-0.360261\pi$
$332$	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	−0.942403	−	0.334480i	$-0.891439\pi$
$337$	−3.33252	+	5.77209i	−0.181534	+	0.314426i	0.760869	+	0.648905i	$0.224773\pi$
$338$	−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	−0.758179	−	0.652047i	$-0.773911\pi$
$347$	3.45734	−	5.98828i	0.185600	−	0.321468i	0.943778	+	0.330579i	$0.107244\pi$
$348$	−16.2232	−	4.48876i	−0.869655	−	0.240623i
$349$	−2.83783	−	4.91526i	−0.151905	−	0.263108i	0.780022	−	0.625751i	$-0.215208\pi$
$349$	−2.83783	−	4.91526i	−0.151905	−	0.263108i	−0.931928	+	0.362644i	$0.881874\pi$
$350$	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	0.948967	−	0.315374i	$-0.102130\pi$
$353$	3.78324	+	6.55277i	0.201362	+	0.348769i	−0.747606	+	0.664143i	$0.768797\pi$
$354$	−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	0.828450	+	0.560063i	$0.189223\pi$
$367$	17.2272	+	29.8384i	0.899254	+	1.55755i	0.0708032	+	0.997490i	$0.477444\pi$
$368$	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	−0.912143	−	0.409873i	$-0.865573\pi$
$373$	−1.95278	+	3.38232i	−0.101111	+	0.175130i	0.811031	+	0.585002i	$0.198906\pi$
$374$	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	−0.988101	−	0.153808i	$-0.950846\pi$
$383$	−7.06195	+	12.2317i	−0.360849	+	0.625009i	0.627252	+	0.778816i	$0.284180\pi$
$384$	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	0.627388	−	0.778707i	$-0.284124\pi$
$389$	−7.11383	−	12.3215i	−0.360686	−	0.624726i	−0.988074	+	0.153981i	$0.950791\pi$
$390$	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	0.101083	−	0.994878i	$-0.467769\pi$
$401$	18.2654	−	31.6366i	0.912131	−	1.57986i	0.811048	−	0.584979i	$-0.198897\pi$
$402$	−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	−0.995433	−	0.0954680i	$-0.969565\pi$
$409$	−8.39364	+	14.5382i	−0.415039	+	0.718868i	0.580394	+	0.814336i	$0.302899\pi$
$410$	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	−0.952306	−	0.305145i	$-0.901295\pi$
$419$	−4.33728	+	7.51239i	−0.211890	+	0.367004i	0.740416	+	0.672149i	$0.234629\pi$
$420$	28.8254	−	28.3602i	1.40653	−	1.38383i
$421$	−10.1827	−	17.6370i	−0.496275	−	0.859573i	0.503716	−	0.863869i	$-0.331966\pi$
$421$	−10.1827	−	17.6370i	−0.496275	−	0.859573i	−0.999991	+	0.00429609i	$0.998633\pi$
$422$	−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	0.997449	−	0.0713815i	$-0.0227408\pi$
$439$	9.15420	+	15.8555i	0.436906	+	0.756744i	−0.560543	+	0.828125i	$0.689407\pi$
$440$	−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	0.853243	−	0.521513i	$-0.174632\pi$
$443$	−0.526658	−	0.912198i	−0.0250223	−	0.0433398i	−0.878265	+	0.478174i	$0.841299\pi$
$444$	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	0.797127	−	0.603812i	$-0.206352\pi$
$457$	−2.65837	−	4.60443i	−0.124353	−	0.215386i	−0.921480	+	0.388426i	$0.873019\pi$
$458$	−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	0.934780	−	0.355227i	$-0.115596\pi$
$461$	3.43008	+	5.94107i	0.159755	+	0.276703i	−0.775025	+	0.631930i	$0.782263\pi$
$462$	9.64028	+	2.66734i	0.448506	+	0.124096i
$463$	12.6530	−	21.9157i	0.588036	−	1.01851i	−0.406453	−	0.913672i	$-0.633235\pi$
$463$	12.6530	−	21.9157i	0.588036	−	1.01851i	0.994489	−	0.104837i	$-0.0334322\pi$
$464$	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	0.990193	−	0.139709i	$-0.0446167\pi$
$479$	8.18768	+	14.1815i	0.374105	+	0.647969i	−0.616088	+	0.787678i	$0.711283\pi$
$480$	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	0.358946	+	0.933358i	$0.383136\pi$
$491$	−13.9341	+	24.1346i	−0.628839	+	1.08918i	−0.987785	+	0.155823i	$0.950197\pi$
$492$	−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	−0.209414	−	0.977827i	$-0.567156\pi$
$499$	16.5776	−	28.7133i	0.742116	−	1.28538i	0.951530	−	0.307556i	$-0.0995111\pi$
$500$	−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	−0.0816414	+	0.996662i	$0.526016\pi$
$509$	−20.3942	+	35.3237i	−0.903955	+	1.56570i	−0.822314	+	0.569034i	$0.807317\pi$
$510$	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	0.743595	−	0.668630i	$-0.233119\pi$
$547$	−4.84725	−	8.39569i	−0.207254	−	0.358974i	−0.950848	+	0.309657i	$0.899786\pi$
$548$	−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	−0.408718	−	0.912661i	$-0.634024\pi$
$563$	13.9051	−	24.0843i	0.586029	−	1.01503i	0.994746	−	0.102370i	$-0.0326427\pi$
$564$	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	−0.934346	−	0.356367i	$-0.884015\pi$
$569$	−18.5056	−	32.0527i	−0.775796	−	1.34372i	0.158550	−	0.987351i	$-0.449318\pi$
$570$	−78.0811	−	21.6041i	−3.27046	−	0.904894i
$571$	13.9640	−	24.1863i	0.584374	−	1.01217i	−0.410579	−	0.911825i	$-0.634673\pi$
$571$	13.9640	−	24.1863i	0.584374	−	1.01217i	0.994953	−	0.100340i	$-0.0319932\pi$
$572$	−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	0.998809	+	0.0487810i	$0.0155337\pi$
$587$	13.1231	+	22.7300i	0.541650	+	0.938166i	−0.457159	+	0.889385i	$0.651133\pi$
$588$	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	0.363961	+	0.931414i	$0.381424\pi$
$599$	−15.2879	+	26.4795i	−0.624648	+	1.08192i	−0.988609	+	0.150508i	$0.951909\pi$
$600$	−2.10608	−	8.12379i	−0.0859806	−	0.331653i
$601$	−13.9118	−	24.0959i	−0.567472	−	0.982891i	−0.996815	−	0.0797492i	$-0.974588\pi$
$601$	−13.9118	−	24.0959i	−0.567472	−	0.982891i	0.429343	−	0.903142i	$-0.358745\pi$
$602$	−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	−0.757566	−	0.652759i	$-0.773611\pi$
$607$	4.59543	−	7.95952i	0.186523	−	0.323067i	0.944089	+	0.329692i	$0.106945\pi$
$608$	−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	−0.970946	−	0.239297i	$-0.923083\pi$
$617$	−6.91123	+	11.9706i	−0.278236	+	0.481918i	0.692711	+	0.721216i	$0.256416\pi$
$618$	−41.9229	−	11.5995i	−1.68639	−	0.466602i
$619$	−22.6728	−	39.2705i	−0.911297	−	1.57841i	−0.812234	−	0.583332i	$-0.801749\pi$
$619$	−22.6728	−	39.2705i	−0.911297	−	1.57841i	−0.0990636	−	0.995081i	$-0.531585\pi$
$620$	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	0.974099	−	0.226123i	$-0.0726052\pi$
$641$	7.37312	+	12.7706i	0.291221	+	0.504409i	−0.682878	+	0.730533i	$0.739272\pi$
$642$	−10.3023	−	39.7390i	−0.406599	−	1.56837i
$643$	22.8328	−	39.5476i	0.900438	−	1.55960i	0.0735112	−	0.997294i	$-0.476580\pi$
$643$	22.8328	−	39.5476i	0.900438	−	1.55960i	0.826927	−	0.562310i	$-0.190087\pi$
$644$	−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	−0.598644	−	0.801016i	$-0.704293\pi$
$653$	10.0779	−	17.4554i	0.394378	−	0.683083i	0.993022	+	0.117933i	$0.0376267\pi$
$654$	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	0.756280	−	0.654248i	$-0.227015\pi$
$659$	−4.83783	−	8.37936i	−0.188455	−	0.326414i	−0.944735	+	0.327834i	$0.893681\pi$
$660$	12.3256	−	12.1267i	0.479773	−	0.472030i
$661$	−12.6736	+	21.9513i	−0.492945	+	0.853805i	−0.999967	−	0.00812759i	$-0.997413\pi$
$661$	−12.6736	+	21.9513i	−0.492945	+	0.853805i	0.507022	+	0.861933i	$0.330746\pi$
$662$	−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	0.880424	−	0.474187i	$-0.157258\pi$
$673$	0.766712	+	1.32798i	0.0295546	+	0.0511900i	−0.850870	+	0.525377i	$0.823924\pi$
$674$	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	0.907318	−	0.420445i	$-0.138126\pi$
$677$	2.32984	+	4.03539i	0.0895429	+	0.155093i	−0.817775	+	0.575538i	$0.804793\pi$
$678$	−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	0.999767	+	0.0215935i	$0.00687394\pi$
$691$	13.6320	+	23.6112i	0.518584	+	0.898214i	−0.481183	+	0.876620i	$0.659793\pi$
$692$	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	0.695764	−	0.718270i	$-0.255066\pi$
$709$	−7.30003	−	12.6440i	−0.274158	−	0.474856i	−0.969922	+	0.243414i	$0.921733\pi$
$710$	−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	0.986043	−	0.166492i	$-0.0532441\pi$
$727$	9.40561	+	16.2910i	0.348835	+	0.604200i	−0.637208	+	0.770692i	$0.719911\pi$
$728$	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	0.00855029	+	0.999963i	$0.497278\pi$
$733$	−23.3301	+	40.4090i	−0.861719	+	1.49254i	−0.870269	+	0.492577i	$0.836055\pi$
$734$	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	−0.113924	−	0.993489i	$-0.536342\pi$
$743$	21.8998	−	37.9315i	0.803425	−	1.39157i	0.917349	−	0.398083i	$-0.130325\pi$
$744$	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	−0.987864	−	0.155322i	$-0.950358\pi$
$751$	−9.84965	+	17.0601i	−0.359419	+	0.622531i	0.628445	+	0.777854i	$0.283692\pi$
$752$	−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	−0.964244	−	0.265017i	$-0.914622\pi$
$761$	−6.96855	+	12.0699i	−0.252610	+	0.437533i	0.711634	+	0.702551i	$0.247956\pi$
$762$	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	−0.816416	−	0.577464i	$-0.804042\pi$
$769$	2.54821	−	4.41363i	0.0918907	−	0.159159i	0.908307	+	0.418305i	$0.137376\pi$
$770$	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	−0.997070	−	0.0764950i	$-0.975627\pi$
$787$	−12.1272	+	21.0049i	−0.432288	+	0.748745i	0.564782	+	0.825240i	$0.308960\pi$
$788$	−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	0.277682	+	0.960673i	$0.410434\pi$
$797$	−19.5678	+	33.8924i	−0.693126	+	1.20053i	−0.970808	+	0.239857i	$0.922899\pi$
$798$	−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	−0.949674	−	0.313240i	$-0.898586\pi$
$821$	−21.3784	−	37.0284i	−0.746111	−	1.29230i	0.203563	−	0.979062i	$-0.434748\pi$
$822$	62.3663	−	61.3597i	2.17527	−	2.14017i
$823$	−7.90108	+	13.6851i	−0.275414	+	0.477032i	−0.970240	−	0.242147i	$-0.922148\pi$
$823$	−7.90108	+	13.6851i	−0.275414	+	0.477032i	0.694825	+	0.719179i	$0.255482\pi$
$824$	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	0.647463	−	0.762097i	$-0.275830\pi$
$839$	−9.74005	−	16.8703i	−0.336264	−	0.582426i	−0.983727	+	0.179671i	$0.942497\pi$
$840$	−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	−0.833794	−	0.552075i	$-0.813836\pi$
$853$	−26.1398	−	45.2754i	−0.895008	−	1.55020i	−0.0612137	−	0.998125i	$-0.519497\pi$
$854$	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	0.771829	+	0.635831i	$0.219342\pi$
$857$	27.4174	+	47.4883i	0.936560	+	1.62217i	0.164731	+	0.986339i	$0.447324\pi$
$858$	−5.05579	−	19.5017i	−0.172602	−	0.665776i
$859$	9.70616	−	16.8116i	0.331170	−	0.573603i	−0.651572	−	0.758587i	$-0.725890\pi$
$859$	9.70616	−	16.8116i	0.331170	−	0.573603i	0.982742	+	0.184984i	$0.0592233\pi$
$860$	−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	−0.763967	−	0.645256i	$-0.776751\pi$
$877$	5.23651	−	9.06991i	0.176825	−	0.306269i	0.940791	+	0.338987i	$0.110084\pi$
$878$	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	−0.986291	−	0.165017i	$-0.947232\pi$
$887$	−10.4309	+	18.0669i	−0.350237	+	0.606628i	0.636054	+	0.771645i	$0.280566\pi$
$888$	−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	0.623554	−	0.781780i	$-0.285688\pi$
$907$	−11.0005	−	19.0534i	−0.365265	−	0.632657i	−0.988819	+	0.149124i	$0.952355\pi$
$908$	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	0.824830	−	0.565380i	$-0.191271\pi$
$911$	−2.33067	−	4.03684i	−0.0772185	−	0.133746i	−0.902049	+	0.431634i	$0.857937\pi$
$912$	−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	0.876321	−	0.481729i	$-0.159991\pi$
$929$	0.639189	+	1.10711i	0.0209711	+	0.0363230i	−0.855349	+	0.518052i	$0.826658\pi$
$930$	−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	−0.792032	−	0.610479i	$-0.790977\pi$
$941$	4.06989	−	7.04926i	0.132675	−	0.229799i	0.924707	+	0.380680i	$0.124310\pi$
$942$	−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	0.998656	−	0.0518372i	$-0.0165077\pi$
$947$	13.9845	+	24.2219i	0.454435	+	0.787105i	−0.544220	+	0.838942i	$0.683174\pi$
$948$	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	−0.632860	−	0.774266i	$-0.718119\pi$
$967$	11.0115	−	19.0724i	0.354104	−	0.613327i	0.986964	+	0.160940i	$0.0514524\pi$
$968$	−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	−0.279428	−	0.960167i	$-0.590145\pi$
$977$	21.6241	−	37.4540i	0.691815	−	1.19826i	0.971243	−	0.238092i	$-0.0765219\pi$
$978$	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	0.999872	+	0.0160169i	$0.00509856\pi$
$983$	16.1093	+	27.9021i	0.513807	+	0.889940i	−0.486065	+	0.873923i	$0.661568\pi$
$984$	−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	0.995319	+	0.0966472i	$0.0308119\pi$
$997$	18.3566	+	31.7945i	0.581358	+	1.00694i	−0.413960	+	0.910295i	$0.635855\pi$
$998$	−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.67.1	yes	8
3.2	odd	2		297.2.e.e.199.4		8
9.2	odd	6		297.2.e.e.100.4		8
9.4	even	3		891.2.a.q.1.4		4
9.5	odd	6		891.2.a.p.1.1		4
9.7	even	3	inner	99.2.e.e.34.1	✓	8
11.10	odd	2		1089.2.e.i.364.4		8
99.32	even	6		9801.2.a.bl.1.4		4
99.43	odd	6		1089.2.e.i.727.4		8
99.76	odd	6		9801.2.a.bi.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.e.34.1	✓	8	9.7	even	3	inner
99.2.e.e.67.1	yes	8	1.1	even	1	trivial
297.2.e.e.100.4		8	9.2	odd	6
297.2.e.e.199.4		8	3.2	odd	2
891.2.a.p.1.1		4	9.5	odd	6
891.2.a.q.1.4		4	9.4	even	3
1089.2.e.i.364.4		8	11.10	odd	2
1089.2.e.i.727.4		8	99.43	odd	6
9801.2.a.bi.1.1		4	99.76	odd	6
9801.2.a.bl.1.4		4	99.32	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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