LMFDB - Embedded newform 99.2.e.e.34.2

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			34.2
Root			$-0.577806 - 2.22188i$ of defining polynomial
Character	$\chi$	$=$	99.34
Dual form			99.2.e.e.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07781 + 1.86682i) q^{2} +(-0.635299 - 1.61133i) q^{3} +(-1.32333 - 2.29208i) q^{4} +(-1.81197 - 3.13842i) q^{5} +(3.69279 + 0.550720i) q^{6} +(1.13530 - 1.96640i) q^{7} +1.39396 q^{8} +(-2.19279 + 2.04736i) q^{9} +O(q^{10})$	\(q+(-1.07781 + 1.86682i) q^{2} +(-0.635299 - 1.61133i) q^{3} +(-1.32333 - 2.29208i) q^{4} +(-1.81197 - 3.13842i) q^{5} +(3.69279 + 0.550720i) q^{6} +(1.13530 - 1.96640i) q^{7} +1.39396 q^{8} +(-2.19279 + 2.04736i) q^{9} +7.81179 q^{10} +(-0.500000 + 0.866025i) q^{11} +(-2.85259 + 3.58849i) q^{12} +(-0.619175 - 1.07244i) q^{13} +(2.44726 + 4.23879i) q^{14} +(-3.90590 + 4.91351i) q^{15} +(1.14425 - 1.98189i) q^{16} +5.69681 q^{17} +(-1.45863 - 6.30019i) q^{18} -2.89453 q^{19} +(-4.79567 + 8.30634i) q^{20} +(-3.88977 - 0.580097i) q^{21} +(-1.07781 - 1.86682i) q^{22} +(-2.95863 - 5.12450i) q^{23} +(-0.885582 - 2.24614i) q^{24} +(-4.06644 + 7.04328i) q^{25} +2.66940 q^{26} +(4.69205 + 2.23263i) q^{27} -6.00951 q^{28} +(1.75447 - 3.03884i) q^{29} +(-4.96282 - 12.5874i) q^{30} +(1.25447 + 2.17281i) q^{31} +(3.86051 + 6.68660i) q^{32} +(1.71311 + 0.255482i) q^{33} +(-6.14006 + 10.6349i) q^{34} -8.22849 q^{35} +(7.59450 + 2.31672i) q^{36} -0.333960 q^{37} +(3.11974 - 5.40355i) q^{38} +(-1.33470 + 1.67902i) q^{39} +(-2.52581 - 4.37483i) q^{40} +(4.98370 + 8.63203i) q^{41} +(5.27535 - 6.63625i) q^{42} +(3.57781 - 6.19694i) q^{43} +2.64667 q^{44} +(10.3987 + 3.17215i) q^{45} +12.7553 q^{46} +(4.34840 - 7.53166i) q^{47} +(-3.92042 - 0.584668i) q^{48} +(0.922194 + 1.59729i) q^{49} +(-8.76567 - 15.1826i) q^{50} +(-3.61917 - 9.17946i) q^{51} +(-1.63875 + 2.83840i) q^{52} +6.16513 q^{53} +(-9.22504 + 6.35284i) q^{54} +3.62393 q^{55} +(1.58256 - 2.74108i) q^{56} +(1.83889 + 4.66405i) q^{57} +(3.78196 + 6.55056i) q^{58} +(-1.45863 - 2.52642i) q^{59} +(16.4310 + 2.45041i) q^{60} +(-3.13530 + 5.43050i) q^{61} -5.40832 q^{62} +(1.53644 + 6.63625i) q^{63} -12.0666 q^{64} +(-2.24385 + 3.88646i) q^{65} +(-2.32333 + 2.92269i) q^{66} +(-4.68142 - 8.10846i) q^{67} +(-7.53877 - 13.0575i) q^{68} +(-6.37766 + 8.02293i) q^{69} +(8.86872 - 15.3611i) q^{70} -12.1230 q^{71} +(-3.05667 + 2.85394i) q^{72} +4.31271 q^{73} +(0.359945 - 0.623442i) q^{74} +(13.9325 + 2.07780i) q^{75} +(3.83043 + 6.63449i) q^{76} +(1.13530 + 1.96640i) q^{77} +(-1.69587 - 4.30130i) q^{78} +(-0.708348 + 1.22690i) q^{79} -8.29333 q^{80} +(0.616665 - 8.97885i) q^{81} -21.4859 q^{82} +(1.37840 - 2.38747i) q^{83} +(3.81784 + 9.68333i) q^{84} +(-10.3224 - 17.8790i) q^{85} +(7.71236 + 13.3582i) q^{86} +(-6.01119 - 0.896472i) q^{87} +(-0.696981 + 1.20721i) q^{88} +4.77116 q^{89} +(-17.1296 + 15.9935i) q^{90} -2.81179 q^{91} +(-7.83051 + 13.5628i) q^{92} +(2.70416 - 3.40176i) q^{93} +(9.37347 + 16.2353i) q^{94} +(5.24479 + 9.08424i) q^{95} +(8.32177 - 10.4686i) q^{96} +(1.27954 - 2.21624i) q^{97} -3.97578 q^{98} +(-0.676667 - 2.92269i) 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 $

$2$	−1.07781	+	1.86682i	−0.762124	+	1.32004i	0.179629	+	0.983734i	$0.442510\pi$
$2$	−1.07781	+	1.86682i	−0.762124	+	1.32004i	−0.941754	+	0.336303i	$0.890823\pi$
$3$	−0.635299	−	1.61133i	−0.366790	−	0.930304i
$3$	−0.635299	−	1.61133i	−0.366790	−	0.930304i
$4$	−1.32333	−	2.29208i	−0.661667	−	1.14604i
$5$	−1.81197	−	3.13842i	−0.810336	−	1.40354i	−0.912629	−	0.408788i	$-0.865951\pi$
$5$	−1.81197	−	3.13842i	−0.810336	−	1.40354i	0.102294	−	0.994754i	$-0.467382\pi$
$6$	3.69279	+	0.550720i	1.50758	+	0.224831i
$7$	1.13530	−	1.96640i	0.429103	−	0.743227i	−0.567691	−	0.823242i	$-0.692163\pi$
$7$	1.13530	−	1.96640i	0.429103	−	0.743227i	0.996794	+	0.0800141i	$0.0254965\pi$
$8$	1.39396			0.492840
$9$	−2.19279	+	2.04736i	−0.730930	+	0.682452i
$10$	7.81179			2.47031
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−2.85259	+	3.58849i	−0.823473	+	1.03591i
$13$	−0.619175	−	1.07244i	−0.171728	−	0.297442i	0.767296	−	0.641293i	$-0.221602\pi$
$13$	−0.619175	−	1.07244i	−0.171728	−	0.297442i	−0.939024	+	0.343851i	$0.888268\pi$
$14$	2.44726	+	4.23879i	0.654059	+	1.13286i
$15$	−3.90590	+	4.91351i	−1.00850	+	1.26866i
$16$	1.14425	−	1.98189i	0.286061	−	0.495473i
$17$	5.69681			1.38168			0.690839	−	0.723008i	$-0.257241\pi$
$17$	5.69681			1.38168			0.690839	+	0.723008i	$0.257241\pi$
$18$	−1.45863	−	6.30019i	−0.343803	−	1.48497i
$19$	−2.89453			−0.664050			−0.332025	−	0.943271i	$-0.607732\pi$
$19$	−2.89453			−0.664050			−0.332025	+	0.943271i	$0.607732\pi$
$20$	−4.79567	+	8.30634i	−1.07234	+	1.85735i
$21$	−3.88977	−	0.580097i	−0.848818	−	0.126587i
$22$	−1.07781	−	1.86682i	−0.229789	−	0.398006i
$23$	−2.95863	−	5.12450i	−0.616917	−	1.06853i	−0.990045	−	0.140752i	$-0.955048\pi$
$23$	−2.95863	−	5.12450i	−0.616917	−	1.06853i	0.373127	−	0.927780i	$-0.378285\pi$
$24$	−0.885582	−	2.24614i	−0.180769	−	0.458491i
$25$	−4.06644	+	7.04328i	−0.813288	+	1.40866i
$26$	2.66940			0.523513
$27$	4.69205	+	2.23263i	0.902986	+	0.429671i
$28$	−6.00951			−1.13569
$29$	1.75447	−	3.03884i	0.325798	−	0.564298i	−0.655876	−	0.754869i	$-0.727701\pi$
$29$	1.75447	−	3.03884i	0.325798	−	0.564298i	0.981673	+	0.190571i	$0.0610339\pi$
$30$	−4.96282	−	12.5874i	−0.906083	−	2.29813i
$31$	1.25447	+	2.17281i	0.225310	+	0.390248i	0.956412	−	0.292019i	$-0.0943272\pi$
$31$	1.25447	+	2.17281i	0.225310	+	0.390248i	−0.731102	+	0.682268i	$0.760994\pi$
$32$	3.86051	+	6.68660i	0.682448	+	1.18204i
$33$	1.71311	+	0.255482i	0.298213	+	0.0444737i
$34$	−6.14006	+	10.6349i	−1.05301	+	1.82387i
$35$	−8.22849			−1.39087
$36$	7.59450	+	2.31672i	1.26575	+	0.386120i
$37$	−0.333960			−0.0549027			−0.0274514	−	0.999623i	$-0.508739\pi$
$37$	−0.333960			−0.0549027			−0.0274514	+	0.999623i	$0.508739\pi$
$38$	3.11974	−	5.40355i	0.506089	−	0.876572i
$39$	−1.33470	+	1.67902i	−0.213723	+	0.268858i
$40$	−2.52581	−	4.37483i	−0.399366	−	0.691722i
$41$	4.98370	+	8.63203i	0.778324	+	1.34810i	0.932907	+	0.360116i	$0.117263\pi$
$41$	4.98370	+	8.63203i	0.778324	+	1.34810i	−0.154584	+	0.987980i	$0.549404\pi$
$42$	5.27535	−	6.63625i	0.814005	−	1.02400i
$43$	3.57781	−	6.19694i	0.545610	−	0.945025i	−0.452958	−	0.891532i	$-0.649631\pi$
$43$	3.57781	−	6.19694i	0.545610	−	0.945025i	0.998568	−	0.0534929i	$-0.0170355\pi$
$44$	2.64667			0.399000
$45$	10.3987	+	3.17215i	1.55015	+	0.472877i
$46$	12.7553			1.88067
$47$	4.34840	−	7.53166i	0.634280	−	1.09860i	−0.352387	−	0.935854i	$-0.614630\pi$
$47$	4.34840	−	7.53166i	0.634280	−	1.09860i	0.986667	−	0.162751i	$-0.0520366\pi$
$48$	−3.92042	−	0.584668i	−0.565865	−	0.0843895i
$49$	0.922194	+	1.59729i	0.131742	+	0.228184i
$50$	−8.76567	−	15.1826i	−1.23965	−	2.14714i
$51$	−3.61917	−	9.17946i	−0.506786	−	1.28538i
$52$	−1.63875	+	2.83840i	−0.227254	+	0.393615i
$53$	6.16513			0.846845			0.423423	−	0.905932i	$-0.360829\pi$
$53$	6.16513			0.846845			0.423423	+	0.905932i	$0.360829\pi$
$54$	−9.22504	+	6.35284i	−1.25537	+	0.864513i
$55$	3.62393			0.488651
$56$	1.58256	−	2.74108i	0.211479	−	0.366292i
$57$	1.83889	+	4.66405i	0.243567	+	0.617769i
$58$	3.78196	+	6.55056i	0.496596	+	0.860130i
$59$	−1.45863	−	2.52642i	−0.189898	−	0.328912i	0.755318	−	0.655358i	$-0.227482\pi$
$59$	−1.45863	−	2.52642i	−0.189898	−	0.328912i	−0.945216	+	0.326446i	$0.894149\pi$
$60$	16.4310	+	2.45041i	2.12123	+	0.316347i
$61$	−3.13530	+	5.43050i	−0.401434	+	0.695304i	−0.993899	−	0.110292i	$-0.964821\pi$
$61$	−3.13530	+	5.43050i	−0.401434	+	0.695304i	0.592465	+	0.805596i	$0.298155\pi$
$62$	−5.40832			−0.686857
$63$	1.53644	+	6.63625i	0.193573	+	0.836089i
$64$	−12.0666			−1.50832
$65$	−2.24385	+	3.88646i	−0.278315	+	0.482055i
$66$	−2.32333	+	2.92269i	−0.285983	+	0.359758i
$67$	−4.68142	−	8.10846i	−0.571927	−	0.990606i	−0.996368	−	0.0851510i	$-0.972863\pi$
$67$	−4.68142	−	8.10846i	−0.571927	−	0.990606i	0.424441	−	0.905456i	$-0.360471\pi$
$68$	−7.53877	−	13.0575i	−0.914211	−	1.58346i
$69$	−6.37766	+	8.02293i	−0.767781	+	0.965847i
$70$	8.86872	−	15.3611i	1.06001	−	1.83600i
$71$	−12.1230			−1.43874			−0.719369	−	0.694628i	$-0.755569\pi$
$71$	−12.1230			−1.43874			−0.719369	+	0.694628i	$0.755569\pi$
$72$	−3.05667	+	2.85394i	−0.360232	+	0.336340i
$73$	4.31271			0.504764			0.252382	−	0.967628i	$-0.418786\pi$
$73$	4.31271			0.504764			0.252382	+	0.967628i	$0.418786\pi$
$74$	0.359945	−	0.623442i	0.0418427	−	0.0724737i
$75$	13.9325	+	2.07780i	1.60878	+	0.239924i
$76$	3.83043	+	6.63449i	0.439380	+	0.761028i
$77$	1.13530	+	1.96640i	0.129379	+	0.224092i
$78$	−1.69587	−	4.30130i	−0.192019	−	0.487026i
$79$	−0.708348	+	1.22690i	−0.0796954	+	0.138037i	−0.903119	−	0.429391i	$-0.858728\pi$
$79$	−0.708348	+	1.22690i	−0.0796954	+	0.138037i	0.823423	+	0.567428i	$0.192061\pi$
$80$	−8.29333			−0.927223
$81$	0.616665	−	8.97885i	0.0685184	−	0.997650i
$82$	−21.4859			−2.37272
$83$	1.37840	−	2.38747i	0.151300	−	0.262059i	−0.780406	−	0.625273i	$-0.784988\pi$
$83$	1.37840	−	2.38747i	0.151300	−	0.262059i	0.931705	+	0.363215i	$0.118321\pi$
$84$	3.81784	+	9.68333i	0.416560	+	1.05654i
$85$	−10.3224	−	17.8790i	−1.11962	−	1.93924i
$86$	7.71236	+	13.3582i	0.831646	+	1.44045i
$87$	−6.01119	−	0.896472i	−0.644468	−	0.0961119i
$88$	−0.696981	+	1.20721i	−0.0742984	+	0.128689i
$89$	4.77116			0.505742			0.252871	−	0.967500i	$-0.418625\pi$
$89$	4.77116			0.505742			0.252871	+	0.967500i	$0.418625\pi$
$90$	−17.1296	+	15.9935i	−1.80562	+	1.68587i
$91$	−2.81179			−0.294756
$92$	−7.83051	+	13.5628i	−0.816387	+	1.41402i
$93$	2.70416	−	3.40176i	0.280408	−	0.352746i
$94$	9.37347	+	16.2353i	0.966800	+	1.67455i
$95$	5.24479	+	9.08424i	0.538104	+	0.932023i
$96$	8.32177	−	10.4686i	0.849337	−	1.06844i
$97$	1.27954	−	2.21624i	0.129918	−	0.225025i	−0.793727	−	0.608275i	$-0.791862\pi$
$97$	1.27954	−	2.21624i	0.129918	−	0.225025i	0.923645	+	0.383250i	$0.125195\pi$
$98$	−3.97578			−0.401615
$99$	−0.676667	−	2.92269i	−0.0680076	−	0.293741i
$100$	21.5250			2.15250
$101$	9.16681	−	15.8774i	0.912131	−	1.57986i	0.101084	−	0.994878i	$-0.467769\pi$
$101$	9.16681	−	15.8774i	0.912131	−	1.57986i	0.811048	−	0.584980i	$-0.198898\pi$
$102$	21.0371	+	3.13735i	2.08299	+	0.310644i
$103$	2.28122	+	3.95120i	0.224776	+	0.389323i	0.956252	−	0.292544i	$-0.0945017\pi$
$103$	2.28122	+	3.95120i	0.224776	+	0.389323i	−0.731476	+	0.681867i	$0.761168\pi$
$104$	−0.863106	−	1.49494i	−0.0846345	−	0.146591i
$105$	5.22755	+	13.2588i	0.510156	+	1.29393i
$106$	−6.64481	+	11.5092i	−0.645401	+	1.11787i
$107$	−5.11014			−0.494016			−0.247008	−	0.969013i	$-0.579447\pi$
$107$	−5.11014			−0.494016			−0.247008	+	0.969013i	$0.579447\pi$
$108$	−1.09177	−	13.7091i	−0.105055	−	1.31916i
$109$	4.67891			0.448159			0.224079	−	0.974571i	$-0.428063\pi$
$109$	4.67891			0.448159			0.224079	+	0.974571i	$0.428063\pi$
$110$	−3.90590	+	6.76521i	−0.372413	+	0.645038i
$111$	0.212165	+	0.538121i	0.0201378	+	0.0510762i
$112$	−2.59812	−	4.50008i	−0.245499	−	0.425217i
$113$	0.765841	+	1.32648i	0.0720442	+	0.124784i	0.899797	−	0.436309i	$-0.143714\pi$
$113$	0.765841	+	1.32648i	0.0720442	+	0.124784i	−0.827753	+	0.561093i	$0.810381\pi$
$114$	−10.6889	−	1.59407i	−1.00111	−	0.149299i
$115$	−10.7219	+	18.5708i	−0.999820	+	1.73174i
$116$	−9.28701			−0.862277
$117$	3.55339	+	1.08397i	0.328511	+	0.100213i
$118$	6.28849			0.578902
$119$	6.46758	−	11.2022i	0.592882	−	1.02690i
$120$	−5.44467	+	6.84925i	−0.497028	+	0.625248i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−6.75849	−	11.7060i	−0.611885	−	1.05982i
$123$	10.7429	−	13.5143i	0.968658	−	1.21855i
$124$	3.32017	−	5.75071i	0.298160	−	0.516429i
$125$	11.3533			1.01547
$126$	−14.0446	−	4.28435i	−1.25120	−	0.381680i
$127$	8.72758			0.774447			0.387224	−	0.921986i	$-0.373434\pi$
$127$	8.72758			0.774447			0.387224	+	0.921986i	$0.373434\pi$
$128$	5.28439	−	9.15282i	0.467078	−	0.809003i
$129$	−12.2583	−	1.82813i	−1.07928	−	0.160958i
$130$	−4.83686	−	8.37769i	−0.424221	−	0.734772i
$131$	1.84439	+	3.19457i	0.161145	+	0.279111i	0.935280	−	0.353910i	$-0.115148\pi$
$131$	1.84439	+	3.19457i	0.161145	+	0.279111i	−0.774135	+	0.633021i	$0.781815\pi$
$132$	−1.68142	−	4.26466i	−0.146349	−	0.371191i
$133$	−3.28615	+	5.69179i	−0.284946	+	0.493541i
$134$	20.1827			1.74352
$135$	−1.49490	−	18.7711i	−0.128660	−	1.61556i
$136$	7.94113			0.680946
$137$	−10.9843	+	19.0253i	−0.938449	+	1.62544i	−0.170085	+	0.985429i	$0.554404\pi$
$137$	−10.9843	+	19.0253i	−0.938449	+	1.62544i	−0.768364	+	0.640013i	$0.778929\pi$
$138$	−8.10344	−	20.5531i	−0.689811	−	1.74960i
$139$	0.644985	+	1.11715i	0.0547070	+	0.0947552i	0.892082	−	0.451874i	$-0.149244\pi$
$139$	0.644985	+	1.11715i	0.0547070	+	0.0947552i	−0.837375	+	0.546629i	$0.815911\pi$
$140$	10.8890	+	18.8604i	0.920291	+	1.59399i
$141$	−14.8985	−	2.22188i	−1.25468	−	0.187116i
$142$	13.0663	−	22.6314i	1.09650	−	1.89919i
$143$	1.23835			0.103556
$144$	1.54855	+	6.68855i	0.129045	+	0.557379i
$145$	−12.7162			−1.05602
$146$	−4.64826	+	8.05103i	−0.384693	+	0.666308i
$147$	1.98789	−	2.50072i	0.163959	−	0.206256i
$148$	0.441941	+	0.765464i	0.0363273	+	0.0629207i
$149$	5.47234	+	9.47836i	0.448311	+	0.776498i	0.998276	−	0.0586899i	$-0.0186923\pi$
$149$	5.47234	+	9.47836i	0.448311	+	0.776498i	−0.549965	+	0.835188i	$0.685359\pi$
$150$	−18.8954	+	23.7699i	−1.54280	+	1.94080i
$151$	−1.06886	+	1.85132i	−0.0869826	+	0.150658i	−0.906234	−	0.422776i	$-0.861056\pi$
$151$	−1.06886	+	1.85132i	−0.0869826	+	0.150658i	0.819252	+	0.573434i	$0.194389\pi$
$152$	−4.03486			−0.327271
$153$	−12.4919	+	11.6634i	−1.00991	+	0.942930i
$154$	−4.89453			−0.394412
$155$	4.54612	−	7.87412i	0.365154	−	0.632464i
$156$	5.61470	+	0.837341i	0.449535	+	0.0670409i
$157$	−4.75028	−	8.22773i	−0.379114	−	0.656645i	0.611820	−	0.790997i	$-0.290438\pi$
$157$	−4.75028	−	8.22773i	−0.379114	−	0.656645i	−0.990934	+	0.134353i	$0.957104\pi$
$158$	−1.52692	−	2.64471i	−0.121476	−	0.210402i
$159$	−3.91670	−	9.93407i	−0.310614	−	0.787823i
$160$	13.9902	−	24.2318i	1.10602	−	1.91569i
$161$	−13.4357			−1.05888
$162$	16.0972	+	10.8287i	1.26472	+	0.850780i
$163$	−19.4713			−1.52511			−0.762556	−	0.646922i	$-0.776056\pi$
$163$	−19.4713			−1.52511			−0.762556	+	0.646922i	$0.776056\pi$
$164$	13.1902	−	22.8461i	1.02998	−	1.78398i
$165$	−2.30228	−	5.83936i	−0.179232	−	0.454594i
$166$	2.97131	+	5.14645i	0.230618	+	0.399442i
$167$	7.64900	+	13.2485i	0.591898	+	1.02520i	0.993977	+	0.109592i	$0.0349543\pi$
$167$	7.64900	+	13.2485i	0.591898	+	1.02520i	−0.402079	+	0.915605i	$0.631712\pi$
$168$	−5.42219	−	0.808632i	−0.418331	−	0.0623873i
$169$	5.73325	−	9.93027i	0.441019	−	0.763867i
$170$	44.5023			3.41317
$171$	6.34710	−	5.92613i	0.485375	−	0.453183i
$172$	−18.9385			−1.44405
$173$	−7.01045	+	12.1425i	−0.532995	+	0.923174i	0.466263	+	0.884646i	$0.345600\pi$
$173$	−7.01045	+	12.1425i	−0.532995	+	0.923174i	−0.999258	+	0.0385279i	$0.987733\pi$
$174$	8.15245	−	10.2556i	0.618036	−	0.777472i
$175$	9.23325	+	15.9925i	0.697968	+	1.20892i
$176$	1.14425	+	1.98189i	0.0862507	+	0.149391i
$177$	−3.14425	+	3.95538i	−0.236336	+	0.297304i
$178$	−5.14239	+	8.90688i	−0.385439	+	0.667599i
$179$	3.94951			0.295200			0.147600	−	0.989047i	$-0.452845\pi$
$179$	3.94951			0.295200			0.147600	+	0.989047i	$0.452845\pi$
$180$	−6.49014	−	28.0325i	−0.483746	−	2.08942i
$181$	13.3662			0.993502			0.496751	−	0.867893i	$-0.334526\pi$
$181$	13.3662			0.993502			0.496751	+	0.867893i	$0.334526\pi$
$182$	3.03057	−	5.24910i	0.224641	−	0.389089i
$183$	10.7422	+	1.60202i	0.794086	+	0.118425i
$184$	−4.12422	−	7.14336i	−0.304042	−	0.526615i
$185$	0.605125	+	1.04811i	0.0444896	+	0.0770583i
$186$	3.43590	+	8.71460i	0.251932	+	0.638986i
$187$	−2.84840	+	4.93358i	−0.208296	+	0.360779i
$188$	−23.0175			−1.67873
$189$	9.71712	−	6.69172i	0.706817	−	0.486751i
$190$	−22.6115			−1.64041
$191$	−9.46023	+	16.3856i	−0.684518	+	1.18562i	0.289070	+	0.957308i	$0.406654\pi$
$191$	−9.46023	+	16.3856i	−0.684518	+	1.18562i	−0.973588	+	0.228312i	$0.926679\pi$
$192$	7.66587	+	19.4432i	0.553236	+	1.40320i
$193$	1.03225	+	1.78791i	0.0743029	+	0.128696i	0.900783	−	0.434270i	$-0.142994\pi$
$193$	1.03225	+	1.78791i	0.0743029	+	0.128696i	−0.826480	+	0.562966i	$0.809660\pi$
$194$	2.75820	+	4.77734i	0.198027	+	0.342993i
$195$	7.68789	+	1.14652i	0.550541	+	0.0821043i
$196$	2.44074	−	4.22748i	0.174338	−	0.301963i
$197$	−6.00148			−0.427588			−0.213794	−	0.976879i	$-0.568582\pi$
$197$	−6.00148			−0.427588			−0.213794	+	0.976879i	$0.568582\pi$
$198$	6.18544	+	1.88688i	0.439580	+	0.134095i
$199$	19.7132			1.39743			0.698717	−	0.715399i	$-0.253755\pi$
$199$	19.7132			1.39743			0.698717	+	0.715399i	$0.253755\pi$
$200$	−5.66846	+	9.81806i	−0.400821	+	0.694242i
$201$	−10.0913	+	12.6946i	−0.711788	+	0.895410i
$202$	19.7601	+	34.2255i	1.39031	+	2.40810i
$203$	−3.98370	−	6.89998i	−0.279601	−	0.484283i
$204$	−16.2507	+	20.4429i	−1.13777	+	1.43129i
$205$	18.0606	−	31.2819i	1.26141	−	2.18482i
$206$	−9.83487			−0.685228
$207$	16.9793	+	5.17959i	1.18015	+	0.360006i
$208$	−2.83395			−0.196499
$209$	1.44726	−	2.50674i	0.100109	−	0.173395i
$210$	−30.3861	−	4.53159i	−2.09684	−	0.312710i
$211$	5.84123	+	10.1173i	0.402127	+	0.696504i	0.993982	−	0.109540i	$-0.0349378\pi$
$211$	5.84123	+	10.1173i	0.402127	+	0.696504i	−0.591856	+	0.806044i	$0.701605\pi$
$212$	−8.15852	−	14.1310i	−0.560329	−	0.970519i
$213$	7.70174	+	19.5342i	0.527714	+	1.33846i
$214$	5.50774	−	9.53969i	0.376502	−	0.652120i
$215$	−25.9314			−1.76851
$216$	6.54054	+	3.11221i	0.445027	+	0.211759i
$217$	5.69681			0.386724
$218$	−5.04296	+	8.73467i	−0.341553	+	0.591586i
$219$	−2.73986	−	6.94921i	−0.185142	−	0.469584i
$220$	−4.79567	−	8.30634i	−0.323324	−	0.560013i
$221$	−3.52732	−	6.10949i	−0.237273	−	0.410969i
$222$	−1.23325	−	0.183919i	−0.0827700	−	0.0123438i
$223$	9.06168	−	15.6953i	0.606815	−	1.05103i	−0.384947	−	0.922939i	$-0.625780\pi$
$223$	9.06168	−	15.6953i	0.606815	−	1.05103i	0.991762	−	0.128096i	$-0.0408865\pi$
$224$	17.5313			1.17136
$225$	−5.50325	−	23.7699i	−0.366883	−	1.58466i
$226$	−3.30171			−0.219627
$227$	−8.75373	+	15.1619i	−0.581006	+	1.00633i	0.414355	+	0.910115i	$0.364007\pi$
$227$	−8.75373	+	15.1619i	−0.581006	+	1.00633i	−0.995360	+	0.0962159i	$0.969326\pi$
$228$	8.25691	−	10.3870i	0.546827	−	0.687894i
$229$	−2.27134	−	3.93407i	−0.150094	−	0.259971i	0.781168	−	0.624321i	$-0.214624\pi$
$229$	−2.27134	−	3.93407i	−0.150094	−	0.259971i	−0.931262	+	0.364350i	$0.881291\pi$
$230$	−23.1122	−	40.0315i	−1.52397	−	2.63960i
$231$	2.44726	−	3.07859i	0.161018	−	0.202557i
$232$	2.44567	−	4.23602i	0.160566	−	0.278109i
$233$	−8.16962			−0.535210			−0.267605	−	0.963529i	$-0.586232\pi$
$233$	−8.16962			−0.535210			−0.267605	+	0.963529i	$0.586232\pi$
$234$	−5.85344	+	5.46521i	−0.382651	+	0.357272i
$235$	−31.5166			−2.05592
$236$	−3.86051	+	6.68660i	−0.251298	+	0.435261i
$237$	2.42695	+	0.361940i	0.157647	+	0.0235106i
$238$	13.9416	+	24.1475i	0.903699	+	1.56525i
$239$	−9.30042	−	16.1088i	−0.601594	−	1.04199i	−0.992580	−	0.121595i	$-0.961199\pi$
$239$	−9.30042	−	16.1088i	−0.601594	−	1.04199i	0.390985	−	0.920397i	$-0.372134\pi$
$240$	5.26874	+	13.3633i	0.340096	+	0.862599i
$241$	−14.1763	+	24.5541i	−0.913177	+	1.58167i	−0.103629	+	0.994616i	$0.533045\pi$
$241$	−14.1763	+	24.5541i	−0.913177	+	1.58167i	−0.809548	+	0.587053i	$0.800288\pi$
$242$	2.15561			0.138568
$243$	−14.8597	+	4.71060i	−0.953249	+	0.302185i
$244$	16.5962			1.06246
$245$	3.34197	−	5.78846i	0.213510	−	0.369811i
$246$	13.6499	+	34.6209i	0.870289	+	2.20735i
$247$	1.79222	+	3.10421i	0.114036	+	0.197516i
$248$	1.74869	+	3.02882i	0.111042	+	0.192330i
$249$	−4.72270	−	0.704315i	−0.299289	−	0.0446341i
$250$	−12.2367	+	21.1946i	−0.773917	+	1.34046i
$251$	4.93812			0.311691			0.155846	−	0.987781i	$-0.450190\pi$
$251$	4.93812			0.311691			0.155846	+	0.987781i	$0.450190\pi$
$252$	13.1776	−	12.3036i	0.830111	−	0.775055i
$253$	5.91726			0.372015
$254$	−9.40664	+	16.2928i	−0.590225	+	1.02230i
$255$	−22.2511	+	27.9913i	−1.39342	+	1.75289i
$256$	−0.675465	−	1.16994i	−0.0422166	−	0.0731212i
$257$	−8.55675	−	14.8207i	−0.533756	−	0.924492i	−0.999222	−	0.0394264i	$-0.987447\pi$
$257$	−8.55675	−	14.8207i	−0.533756	−	0.924492i	0.465467	−	0.885065i	$-0.345886\pi$
$258$	16.6249	−	20.9136i	1.03502	−	1.30203i
$259$	−0.379145	+	0.656698i	−0.0235589	+	0.0408052i
$260$	11.8774			0.736606
$261$	2.37439	+	10.2556i	0.146971	+	0.634804i
$262$	−7.95157			−0.491250
$263$	2.22279	−	3.84999i	0.137063	−	0.237400i	−0.789321	−	0.613981i	$-0.789567\pi$
$263$	2.22279	−	3.84999i	0.137063	−	0.237400i	0.926384	+	0.376581i	$0.122900\pi$
$264$	2.38800	+	0.356132i	0.146971	+	0.0219184i
$265$	−11.1710	−	19.3487i	−0.686229	−	1.18858i
$266$	−7.08368	−	12.2693i	−0.434328	−	0.752278i
$267$	−3.03111	−	7.68794i	−0.185501	−	0.470494i
$268$	−12.3902	+	21.4604i	−0.756850	+	1.31090i
$269$	19.5899			1.19441			0.597207	−	0.802087i	$-0.296277\pi$
$269$	19.5899			1.19441			0.597207	+	0.802087i	$0.296277\pi$
$270$	36.6533	+	17.4409i	2.23065	+	1.06142i
$271$	6.77601			0.411613			0.205807	−	0.978593i	$-0.434018\pi$
$271$	6.77601			0.411613			0.205807	+	0.978593i	$0.434018\pi$
$272$	6.51855	−	11.2905i	0.395245	−	0.684584i
$273$	1.78633	+	4.53074i	0.108113	+	0.274213i
$274$	−23.6778	−	41.0112i	−1.43043	−	2.47758i
$275$	−4.06644	−	7.04328i	−0.245215	−	0.424726i
$276$	26.8290	+	4.00111i	1.61491	+	0.240838i
$277$	−0.738261	+	1.27871i	−0.0443578	+	0.0768300i	−0.887352	−	0.461093i	$-0.847457\pi$
$277$	−0.738261	+	1.27871i	−0.0443578	+	0.0768300i	0.842994	+	0.537923i	$0.180791\pi$
$278$	−2.78068			−0.166774
$279$	−7.19932	−	2.19617i	−0.431012	−	0.131481i
$280$	−11.4702			−0.685476
$281$	3.67342	−	6.36255i	0.219138	−	0.379558i	−0.735407	−	0.677626i	$-0.763009\pi$
$281$	3.67342	−	6.36255i	0.219138	−	0.379558i	0.954545	+	0.298068i	$0.0963423\pi$
$282$	20.2056	−	25.4181i	1.20322	−	1.51362i
$283$	7.35809	+	12.7446i	0.437393	+	0.757587i	0.997488	−	0.0708417i	$-0.0225685\pi$
$283$	7.35809	+	12.7446i	0.437393	+	0.757587i	−0.560094	+	0.828429i	$0.689235\pi$
$284$	16.0428	+	27.7869i	0.951964	+	1.64885i
$285$	11.3057	−	14.2223i	0.669694	−	0.842457i
$286$	−1.33470	+	2.31177i	−0.0789225	+	0.136698i
$287$	22.6320			1.33592
$288$	−22.1552	−	6.75848i	−1.30550	−	0.398247i
$289$	15.4536			0.909036
$290$	13.7056	−	23.7388i	0.804819	−	1.39399i
$291$	−4.38399	−	0.653801i	−0.256994	−	0.0383265i
$292$	−5.70715	−	9.88507i	−0.333985	−	0.578480i
$293$	0.988066	+	1.71138i	0.0577234	+	0.0999799i	0.893443	−	0.449176i	$-0.148283\pi$
$293$	0.988066	+	1.71138i	0.0577234	+	0.0999799i	−0.835720	+	0.549156i	$0.814949\pi$
$294$	2.52581	+	6.40631i	0.147308	+	0.373624i
$295$	−5.28598	+	9.15559i	−0.307762	+	0.533059i
$296$	−0.465528			−0.0270583
$297$	−4.27954	+	2.94712i	−0.248324	+	0.171009i
$298$	−23.5925			−1.36668
$299$	−3.66382	+	6.34592i	−0.211884	+	0.366994i
$300$	−13.6748	−	34.6840i	−0.789516	−	2.00248i
$301$	−8.12376	−	14.0708i	−0.468246	−	0.811025i
$302$	−2.30405	−	3.99073i	−0.132583	−	0.229641i
$303$	−31.4074	−	4.68391i	−1.80431	−	0.269083i
$304$	−3.31205	+	5.73664i	−0.189959	+	0.329019i
$305$	22.7242			1.30118
$306$	−8.30954	−	35.8910i	−0.475025	−	2.05175i
$307$	11.9708			0.683208			0.341604	−	0.939844i	$-0.389030\pi$
$307$	11.9708			0.683208			0.341604	+	0.939844i	$0.389030\pi$
$308$	3.00476	−	5.20439i	0.171212	−	0.296548i
$309$	4.91744	−	6.18600i	0.279743	−	0.351909i
$310$	9.79968	+	16.9736i	0.556585	+	0.964033i
$311$	−1.69866	−	2.94217i	−0.0963223	−	0.166835i	0.813837	−	0.581093i	$-0.197375\pi$
$311$	−1.69866	−	2.94217i	−0.0963223	−	0.166835i	−0.910160	+	0.414258i	$0.864041\pi$
$312$	−1.86052	+	2.34049i	−0.105331	+	0.132504i
$313$	11.3482	−	19.6557i	0.641440	−	1.11101i	−0.343672	−	0.939090i	$-0.611671\pi$
$313$	11.3482	−	19.6557i	0.641440	−	1.11101i	0.985112	−	0.171917i	$-0.0549960\pi$
$314$	20.4795			1.15573
$315$	18.0434	−	16.8466i	1.01663	−	0.949201i
$316$	3.74952			0.210927
$317$	−7.42547	+	12.8613i	−0.417056	+	0.722362i	−0.995642	−	0.0932594i	$-0.970271\pi$
$317$	−7.42547	+	12.8613i	−0.417056	+	0.722362i	0.578586	+	0.815621i	$0.303605\pi$
$318$	22.7665	+	3.39526i	1.27668	+	0.190397i
$319$	1.75447	+	3.03884i	0.0982316	+	0.170142i
$320$	21.8642	+	37.8699i	1.22224	+	2.11699i
$321$	3.24647	+	8.23414i	0.181200	+	0.459585i
$322$	14.4811	−	25.0820i	0.807001	−	1.39777i
$323$	−16.4896			−0.917504
$324$	−21.3963	+	10.4686i	−1.18868	+	0.581587i
$325$	10.0713			0.558658
$326$	20.9863	−	36.3494i	1.16233	−	2.01321i
$327$	−2.97251	−	7.53929i	−0.164380	−	0.416924i
$328$	6.94709	+	12.0327i	0.383589	+	0.664396i
$329$	−9.87347	−	17.1014i	−0.544342	−	0.942828i
$330$	13.3824	+	1.99577i	0.736678	+	0.109864i
$331$	−8.10140	+	14.0320i	−0.445293	+	0.771270i	−0.998073	−	0.0620574i	$-0.980234\pi$
$331$	−8.10140	+	14.0320i	−0.445293	+	0.771270i	0.552780	+	0.833328i	$0.313567\pi$
$332$	−7.29635			−0.400439
$333$	0.732305	−	0.683736i	0.0401301	−	0.0374685i
$334$	−32.9766			−1.80440
$335$	−16.9652	+	29.3845i	−0.926906	+	1.60545i
$336$	−5.60054	+	7.04533i	−0.305535	+	0.384354i
$337$	5.63111	+	9.75337i	0.306746	+	0.531300i	0.977649	−	0.210246i	$-0.0674264\pi$
$337$	5.63111	+	9.75337i	0.306746	+	0.531300i	−0.670903	+	0.741546i	$0.734093\pi$
$338$	12.3587	+	21.4058i	0.672222	+	1.16432i
$339$	1.65086	−	2.07673i	0.0896622	−	0.112793i
$340$	−27.3200	+	47.3196i	−1.48163	+	2.56627i
$341$	−2.50895			−0.135867
$342$	4.22205	+	18.2361i	0.228302	+	0.986094i
$343$	20.0820			1.08433
$344$	4.98733	−	8.63830i	0.268899	−	0.465746i
$345$	36.7354	+	5.47849i	1.97777	+	0.294952i
$346$	−15.1118	−	26.1744i	−0.812417	−	1.40715i
$347$	8.53718	+	14.7868i	0.458300	+	0.793798i	0.998871	−	0.0474996i	$-0.0151253\pi$
$347$	8.53718	+	14.7868i	0.458300	+	0.793798i	−0.540572	+	0.841298i	$0.681792\pi$
$348$	5.90003	+	14.9645i	0.316275	+	0.802180i
$349$	−11.4862	+	19.8947i	−0.614843	+	1.06494i	0.375569	+	0.926794i	$0.377447\pi$
$349$	−11.4862	+	19.8947i	−0.614843	+	1.06494i	−0.990412	+	0.138145i	$0.955886\pi$
$350$	−39.8066			−2.12775
$351$	−0.510828	−	6.41434i	−0.0272660	−	0.342372i
$352$	−7.72102			−0.411532
$353$	10.2567	−	17.7652i	0.545910	−	0.945544i	−0.452639	−	0.891694i	$-0.649517\pi$
$353$	10.2567	−	17.7652i	0.545910	−	0.945544i	0.998549	−	0.0538502i	$-0.0171494\pi$
$354$	−3.99507	−	10.1329i	−0.212336	−	0.538555i
$355$	21.9665	+	38.0471i	1.16586	+	2.01933i
$356$	−6.31384	−	10.9359i	−0.334633	−	0.579601i
$357$	−22.1593	−	3.30470i	−1.17279	−	0.174903i
$358$	−4.25681	+	7.37301i	−0.224979	+	0.389676i
$359$	−2.91840			−0.154027			−0.0770136	−	0.997030i	$-0.524538\pi$
$359$	−2.91840			−0.154027			−0.0770136	+	0.997030i	$0.524538\pi$
$360$	14.4954	+	4.42186i	0.763976	+	0.233052i
$361$	−10.6217			−0.559037
$362$	−14.4062	+	24.9522i	−0.757172	+	1.31146i
$363$	−1.07781	+	1.35585i	−0.0565702	+	0.0711638i
$364$	3.72094	+	6.44485i	0.195030	+	0.337802i
$365$	−7.81447	−	13.5351i	−0.409028	−	0.708458i
$366$	−14.5687	+	18.3270i	−0.761517	+	0.957969i
$367$	−3.37570	+	5.84688i	−0.176210	+	0.305204i	−0.940579	−	0.339574i	$-0.889717\pi$
$367$	−3.37570	+	5.84688i	−0.176210	+	0.305204i	0.764369	+	0.644779i	$0.223050\pi$
$368$	−13.5416			−0.705905
$369$	−28.6011	−	8.72482i	−1.48891	−	0.454196i
$370$	−2.60883			−0.135627
$371$	6.99926	−	12.1231i	0.363383	−	0.629399i
$372$	−11.3756	−	1.69649i	−0.589798	−	0.0879588i
$373$	11.1887	+	19.3794i	0.579330	+	1.00343i	0.995556	+	0.0941677i	$0.0300190\pi$
$373$	11.1887	+	19.3794i	0.579330	+	1.00343i	−0.416227	+	0.909261i	$0.636648\pi$
$374$	−6.14006	−	10.6349i	−0.317495	−	0.549917i
$375$	−7.21276	−	18.2940i	−0.372465	−	0.944698i
$376$	6.06151	−	10.4988i	0.312598	−	0.541436i
$377$	−4.34530			−0.223794
$378$	2.01903	+	25.3524i	0.103848	+	1.30399i
$379$	33.0321			1.69674			0.848372	−	0.529401i	$-0.177583\pi$
$379$	33.0321			1.69674			0.848372	+	0.529401i	$0.177583\pi$
$380$	13.8812	−	24.0429i	0.712090	−	1.23338i
$381$	−5.54462	−	14.0630i	−0.284059	−	0.720471i
$382$	−20.3926	−	35.3210i	−1.04338	−	1.80718i
$383$	−11.7421	−	20.3379i	−0.599993	−	1.03922i	−0.992821	−	0.119607i	$-0.961836\pi$
$383$	−11.7421	−	20.3379i	−0.599993	−	1.03922i	0.392828	−	0.919612i	$-0.371497\pi$
$384$	−18.1054	−	2.70013i	−0.923938	−	0.137790i
$385$	4.11424	−	7.12608i	0.209681	−	0.363179i
$386$	−4.45026			−0.226512
$387$	4.84197	+	20.9136i	0.246131	+	1.06310i
$388$	−6.77305			−0.343850
$389$	15.5207	−	26.8827i	0.786931	−	1.36300i	−0.140908	−	0.990023i	$-0.545002\pi$
$389$	15.5207	−	26.8827i	0.786931	−	1.36300i	0.927839	−	0.372982i	$-0.121665\pi$
$390$	−10.4264	+	13.1161i	−0.527961	+	0.664161i
$391$	−16.8548	−	29.1933i	−0.852382	−	1.47637i
$392$	1.28550	+	2.22656i	0.0649277	+	0.112458i
$393$	3.97578	−	5.00143i	0.200552	−	0.252289i
$394$	6.46843	−	11.2037i	0.325875	−	0.564432i
$395$	5.13401			0.258320
$396$	−5.80359	+	5.41867i	−0.291641	+	0.272298i
$397$	17.3804			0.872297			0.436148	−	0.899875i	$-0.356342\pi$
$397$	17.3804			0.872297			0.436148	+	0.899875i	$0.356342\pi$
$398$	−21.2470	+	36.8009i	−1.06502	+	1.84466i
$399$	11.2591	+	1.67911i	0.563658	+	0.0840604i
$400$	9.30601	+	16.1185i	0.465300	+	0.805924i
$401$	5.77396	+	10.0008i	0.288338	+	0.499416i	0.973413	−	0.229057i	$-0.0735641\pi$
$401$	5.77396	+	10.0008i	0.288338	+	0.499416i	−0.685075	+	0.728472i	$0.740231\pi$
$402$	−12.8220	−	32.5210i	−0.639505	−	1.62200i
$403$	1.55348	−	2.69070i	0.0773841	−	0.134033i
$404$	−48.5230			−2.41411
$405$	−29.2967	+	14.3340i	−1.45577	+	0.712263i
$406$	17.1746			0.852363
$407$	0.166980	−	0.289218i	0.00827690	−	0.0143360i
$408$	−5.04499	−	12.7958i	−0.249764	−	0.633487i
$409$	−17.3678	−	30.0819i	−0.858783	−	1.48746i	−0.873091	−	0.487558i	$-0.837888\pi$
$409$	−17.3678	−	30.0819i	−0.858783	−	1.48746i	0.0143082	−	0.999898i	$-0.495445\pi$
$410$	38.9316	+	67.4316i	1.92270	+	3.33021i
$411$	37.6344	+	5.61256i	1.85637	+	0.276847i
$412$	6.03764	−	10.4575i	0.297453	−	0.515204i
$413$	−6.62393			−0.325942
$414$	−27.9698	+	26.1147i	−1.37464	+	1.28347i
$415$	−9.99049			−0.490414
$416$	4.78066	−	8.28035i	0.234391	−	0.405977i
$417$	1.39034	−	1.74901i	0.0680852	−	0.0856493i
$418$	3.11974	+	5.40355i	0.152592	+	0.264296i
$419$	3.71535	+	6.43518i	0.181507	+	0.314379i	0.942394	−	0.334505i	$-0.108569\pi$
$419$	3.71535	+	6.43518i	0.181507	+	0.314379i	−0.760887	+	0.648884i	$0.775236\pi$
$420$	23.4725	−	29.5278i	1.14534	−	1.44081i
$421$	−5.92789	+	10.2674i	−0.288908	+	0.500403i	−0.973549	−	0.228477i	$-0.926625\pi$
$421$	−5.92789	+	10.2674i	−0.288908	+	0.500403i	0.684642	+	0.728880i	$0.259959\pi$
$422$	−25.1828			−1.22588
$423$	5.88484	+	25.4181i	0.286131	+	1.23587i
$424$	8.59395			0.417359
$425$	−23.1657	+	40.1242i	−1.12370	+	1.94631i
$426$	−44.7678	−	6.67639i	−2.16901	−	0.323472i
$427$	7.11900	+	12.3305i	0.344513	+	0.596713i
$428$	6.76242	+	11.7129i	0.326874	+	0.566162i
$429$	−0.786722	−	1.99539i	−0.0379833	−	0.0963385i
$430$	27.9491	−	48.4092i	1.34782	−	2.33450i
$431$	24.7496			1.19214			0.596072	−	0.802931i	$-0.296727\pi$
$431$	24.7496			1.19214			0.596072	+	0.802931i	$0.296727\pi$
$432$	9.79370	−	6.74445i	0.471199	−	0.324493i
$433$	19.0608			0.916003			0.458002	−	0.888951i	$-0.348565\pi$
$433$	19.0608			0.916003			0.458002	+	0.888951i	$0.348565\pi$
$434$	−6.14006	+	10.6349i	−0.294732	+	0.510491i
$435$	8.07857	+	20.4900i	0.387338	+	0.982421i
$436$	−6.19176	−	10.7244i	−0.296532	−	0.513608i
$437$	8.56384	+	14.8330i	0.409664	+	0.709559i
$438$	15.9259	+	2.37509i	0.760970	+	0.113486i
$439$	17.3742	−	30.0931i	0.829227	−	1.43626i	−0.0694179	−	0.997588i	$-0.522114\pi$
$439$	17.3742	−	30.0931i	0.829227	−	1.43626i	0.898645	−	0.438676i	$-0.144552\pi$
$440$	5.05162			0.240827
$441$	−5.29239	−	1.61446i	−0.252019	−	0.0768789i
$442$	15.2071			0.723326
$443$	0.679943	−	1.17770i	0.0323051	−	0.0559540i	−0.849421	−	0.527716i	$-0.823049\pi$
$443$	0.679943	−	1.17770i	0.0323051	−	0.0559540i	0.881726	+	0.471762i	$0.156382\pi$
$444$	0.952653	−	1.19841i	0.0452109	−	0.0568741i
$445$	−8.64519	−	14.9739i	−0.409821	−	0.709831i
$446$	19.5335	+	33.8330i	0.924937	+	1.60204i
$447$	11.7962	−	14.8393i	0.557943	−	0.701877i
$448$	−13.6991	+	23.7276i	−0.647224	+	1.12102i
$449$	31.7261			1.49725			0.748623	−	0.662995i	$-0.230715\pi$
$449$	31.7261			1.49725			0.748623	+	0.662995i	$0.230715\pi$
$450$	50.3054	+	15.3458i	2.37142	+	0.723407i
$451$	−9.96741			−0.469347
$452$	2.02692	−	3.51074i	0.0953385	−	0.165131i
$453$	3.66214	+	0.546149i	0.172062	+	0.0256603i
$454$	−18.8697	−	32.6832i	−0.885597	−	1.53390i
$455$	5.09487	+	8.82458i	0.238851	+	0.413702i
$456$	2.56334	+	6.50151i	0.120040	+	0.304461i
$457$	−17.6912	+	30.6421i	−0.827561	+	1.43338i	0.0723859	+	0.997377i	$0.476939\pi$
$457$	−17.6912	+	30.6421i	−0.827561	+	1.43338i	−0.899946	+	0.436000i	$0.856395\pi$
$458$	9.79225			0.457562
$459$	26.7297	+	12.7189i	1.24764	+	0.593667i
$460$	56.7545			2.64619
$461$	15.6183	−	27.0518i	0.727419	−	1.25993i	−0.230551	−	0.973060i	$-0.574053\pi$
$461$	15.6183	−	27.0518i	0.727419	−	1.25993i	0.957971	−	0.286867i	$-0.0926137\pi$
$462$	3.10949	+	7.88672i	0.144666	+	0.366923i
$463$	0.119348	+	0.206717i	0.00554657	+	0.00960693i	0.868785	−	0.495189i	$-0.164901\pi$
$463$	0.119348	+	0.206717i	0.00554657	+	0.00960693i	−0.863239	+	0.504796i	$0.831568\pi$
$464$	−4.01510	−	6.95435i	−0.186396	−	0.322848i
$465$	−15.5760	−	2.32291i	−0.722319	−	0.107722i
$466$	8.80527	−	15.2512i	0.407896	−	0.706497i
$467$	1.40269			0.0649087			0.0324543	−	0.999473i	$-0.489668\pi$
$467$	1.40269			0.0649087			0.0324543	+	0.999473i	$0.489668\pi$
$468$	−2.21777	−	9.57911i	−0.102517	−	0.442794i
$469$	−21.2593			−0.981661
$470$	33.9688	−	58.8357i	1.56687	−	2.71389i
$471$	−10.2398	+	12.8814i	−0.471824	+	0.593542i
$472$	−2.03328	−	3.52174i	−0.0935892	−	0.162101i
$473$	3.57781	+	6.19694i	0.164508	+	0.284936i
$474$	−3.29146	+	4.14057i	−0.151182	+	0.190183i
$475$	11.7704	−	20.3870i	0.540064	−	0.935418i
$476$	−34.2350			−1.56916
$477$	−13.5188	+	12.6222i	−0.618985	+	0.577931i
$478$	40.0962			1.83396
$479$	−12.4665	+	21.5926i	−0.569609	+	0.986591i	0.426996	+	0.904254i	$0.359572\pi$
$479$	−12.4665	+	21.5926i	−0.569609	+	0.986591i	−0.996605	+	0.0823374i	$0.973761\pi$
$480$	−47.9335	−	7.14850i	−2.18785	−	0.326283i
$481$	0.206780	+	0.358153i	0.00942834	+	0.0163304i
$482$	−30.5587	−	52.9291i	−1.39191	−	2.41086i
$483$	8.53570	+	21.6494i	0.388388	+	0.985083i
$484$	−1.32333	+	2.29208i	−0.0601515	+	0.104185i
$485$	−9.27396			−0.421109
$486$	7.22205	−	32.8174i	0.327599	−	1.48863i
$487$	−16.0432			−0.726989			−0.363494	−	0.931596i	$-0.618416\pi$
$487$	−16.0432			−0.726989			−0.363494	+	0.931596i	$0.618416\pi$
$488$	−4.37049	+	7.56991i	−0.197843	+	0.342673i
$489$	12.3701	+	31.3748i	0.559396	+	1.41882i
$490$	7.20399	+	12.4777i	0.325443	+	0.563684i
$491$	−5.03989	−	8.72934i	−0.227447	−	0.393950i	0.729604	−	0.683870i	$-0.239704\pi$
$491$	−5.03989	−	8.72934i	−0.227447	−	0.393950i	−0.957051	+	0.289920i	$0.906371\pi$
$492$	−45.1924	−	6.73971i	−2.03743	−	0.303850i
$493$	9.99490	−	17.3117i	0.450148	−	0.779678i
$494$	−7.72666			−0.347639
$495$	−7.94652	+	7.41948i	−0.357170	+	0.333481i
$496$	5.74170			0.257810
$497$	−13.7632	+	23.8386i	−0.617366	+	1.06931i
$498$	6.40499	−	8.05730i	0.287014	−	0.361056i
$499$	−16.6268	−	28.7985i	−0.744319	−	1.28920i	−0.950512	−	0.310687i	$-0.899441\pi$
$499$	−16.6268	−	28.7985i	−0.744319	−	1.28920i	0.206193	−	0.978511i	$-0.433893\pi$
$500$	−15.0242	−	26.0228i	−0.671905	−	1.16377i
$501$	16.4883	−	20.7418i	0.736642	−	0.926676i
$502$	−5.32233	+	9.21855i	−0.237547	+	0.411444i
$503$	−23.0498			−1.02774			−0.513870	−	0.857868i	$-0.671789\pi$
$503$	−23.0498			−1.02774			−0.513870	+	0.857868i	$0.671789\pi$
$504$	2.14174	+	9.25069i	0.0954005	+	0.412058i
$505$	−66.4398			−2.95653
$506$	−6.37766	+	11.0464i	−0.283522	+	0.491074i
$507$	−19.6433	−	2.92948i	−0.872390	−	0.130103i
$508$	−11.5495	−	20.0043i	−0.512426	−	0.887547i
$509$	7.94615	+	13.7631i	0.352207	+	0.610040i	0.986636	−	0.162941i	$-0.0520980\pi$
$509$	7.94615	+	13.7631i	0.352207	+	0.610040i	−0.634429	+	0.772981i	$0.718765\pi$
$510$	−28.2722	−	71.7080i	−1.25192	−	3.17528i
$511$	4.89621	−	8.48048i	0.216596	−	0.375155i
$512$	24.0496			1.06285
$513$	−13.5813	−	6.46243i	−0.599628	−	0.285323i
$514$	36.8901			1.62715
$515$	8.26700	−	14.3189i	0.364288	−	0.630965i
$516$	12.0316	+	30.5163i	0.529662	+	1.34340i
$517$	4.34840	+	7.53166i	0.191243	+	0.331242i
$518$	−0.817289	−	1.41559i	−0.0359096	−	0.0621973i
$519$	24.0193	+	3.58209i	1.05433	+	0.157236i
$520$	−3.12784	+	5.41757i	−0.137165	+	0.237576i
$521$	−4.07140			−0.178371			−0.0891855	−	0.996015i	$-0.528426\pi$
$521$	−4.07140			−0.178371			−0.0891855	+	0.996015i	$0.528426\pi$
$522$	−21.7044	−	6.62097i	−0.949975	−	0.289792i
$523$	1.94690			0.0851319			0.0425659	−	0.999094i	$-0.486447\pi$
$523$	1.94690			0.0851319			0.0425659	+	0.999094i	$0.486447\pi$
$524$	4.88148	−	8.45497i	0.213248	−	0.369357i
$525$	19.9033	−	25.0378i	0.868651	−	1.09274i
$526$	4.79148	+	8.29908i	0.208918	+	0.361857i
$527$	7.14649	+	12.3781i	0.311306	+	0.539198i
$528$	2.46655	−	3.10285i	0.107343	−	0.135034i
$529$	−6.00700	+	10.4044i	−0.261174	+	0.452367i
$530$	48.1607			2.09197
$531$	8.37097	+	2.55358i	0.363269	+	0.110816i
$532$	17.3947			0.754156
$533$	6.17156	−	10.6895i	0.267320	−	0.463012i
$534$	17.6189	+	2.62758i	0.762445	+	0.113706i
$535$	9.25940	+	16.0378i	0.400319	+	0.693373i
$536$	−6.52573	−	11.3029i	−0.281868	−	0.488210i
$537$	−2.50912	−	6.36398i	−0.108277	−	0.274626i
$538$	−21.1141	+	36.5706i	−0.910292	+	1.57667i
$539$	−1.84439			−0.0794434
$540$	−41.0465	+	28.2668i	−1.76636	+	1.21641i
$541$	−39.4039			−1.69411			−0.847053	−	0.531508i	$-0.821626\pi$
$541$	−39.4039			−1.69411			−0.847053	+	0.531508i	$0.821626\pi$
$542$	−7.30322	+	12.6496i	−0.313700	+	0.543345i
$543$	−8.49154	−	21.5374i	−0.364407	−	0.924259i
$544$	21.9926	+	38.0923i	0.942925	+	1.63319i
$545$	−8.47803	−	14.6844i	−0.363159	−	0.629010i
$546$	−10.3834	−	1.54851i	−0.444367	−	0.0662701i
$547$	12.5777	−	21.7853i	0.537785	−	0.931470i	−0.461238	−	0.887276i	$-0.652595\pi$
$547$	12.5777	−	21.7853i	0.537785	−	0.931470i	0.999023	−	0.0441939i	$-0.0140719\pi$
$548$	58.1434			2.48376
$549$	−4.24311	−	18.3270i	−0.181091	−	0.782178i
$550$	17.5313			0.747539
$551$	−5.07837	+	8.79600i	−0.216346	+	0.374722i
$552$	−8.89022	+	11.1837i	−0.378393	+	0.476008i
$553$	1.60837	+	2.78579i	0.0683950	+	0.118464i
$554$	−1.59140	−	2.75639i	−0.0676123	−	0.117108i
$555$	1.30441	−	1.64092i	0.0553693	−	0.0696531i
$556$	1.70706	−	2.95672i	0.0723955	−	0.125393i
$557$	−30.0269			−1.27228			−0.636140	−	0.771574i	$-0.719470\pi$
$557$	−30.0269			−1.27228			−0.636140	+	0.771574i	$0.719470\pi$
$558$	11.8593	−	11.0728i	0.502045	−	0.468747i
$559$	−8.86115			−0.374787
$560$	−9.41541	+	16.3080i	−0.397874	+	0.689137i
$561$	9.75923	+	1.45543i	0.412035	+	0.0614484i
$562$	7.91847	+	13.7152i	0.334020	+	0.578540i
$563$	−9.16988	−	15.8827i	−0.386464	−	0.669376i	0.605507	−	0.795840i	$-0.292970\pi$
$563$	−9.16988	−	15.8827i	−0.386464	−	0.669376i	−0.991971	+	0.126464i	$0.959637\pi$
$564$	14.6230	+	37.0889i	0.615740	+	1.56173i
$565$	2.77535	−	4.80705i	0.116760	−	0.202234i
$566$	−31.7224			−1.33339
$567$	−16.9559	−	11.4063i	−0.712079	−	0.479019i
$568$	−16.8990			−0.709067
$569$	−16.1135	+	27.9094i	−0.675513	+	1.17002i	0.300805	+	0.953686i	$0.402745\pi$
$569$	−16.1135	+	27.9094i	−0.675513	+	1.17002i	−0.976319	+	0.216338i	$0.930589\pi$
$570$	14.3650	+	36.4346i	0.601685	+	1.52608i
$571$	18.6411	+	32.2873i	0.780105	+	1.35118i	0.931880	+	0.362767i	$0.118168\pi$
$571$	18.6411	+	32.2873i	0.780105	+	1.35118i	−0.151775	+	0.988415i	$0.548499\pi$
$572$	−1.63875	−	2.83840i	−0.0685195	−	0.118679i
$573$	32.4127	+	4.83383i	1.35406	+	0.201936i
$574$	−24.3929	+	42.2497i	−1.01814	+	1.76347i
$575$	48.1244			2.00693
$576$	26.4594	−	24.7045i	1.10248	−	1.02936i
$577$	−2.91538			−0.121369			−0.0606845	−	0.998157i	$-0.519328\pi$
$577$	−2.91538			−0.121369			−0.0606845	+	0.998157i	$0.519328\pi$
$578$	−16.6560	+	28.8490i	−0.692799	+	1.19996i
$579$	2.22513	−	2.79915i	0.0924731	−	0.116329i
$580$	16.8277	+	29.1465i	0.698734	+	1.21024i
$581$	−3.12980	−	5.42098i	−0.129846	−	0.224900i
$582$	5.94561	−	7.47942i	0.246454	−	0.310032i
$583$	−3.08256	+	5.33916i	−0.127667	+	0.221125i
$584$	6.01175			0.248768
$585$	−3.03667	−	13.1161i	−0.125551	−	0.542286i
$586$	−4.25977			−0.175970
$587$	9.62094	−	16.6640i	0.397099	−	0.687795i	−0.596268	−	0.802786i	$-0.703350\pi$
$587$	9.62094	−	16.6640i	0.397099	−	0.687795i	0.993367	+	0.114990i	$0.0366837\pi$
$588$	−8.36248	−	1.24713i	−0.344863	−	0.0514307i
$589$	−3.63111	−	6.28927i	−0.149617	−	0.259145i
$590$	−11.3945	−	19.7359i	−0.469105	−	0.812514i
$591$	3.81273	+	9.67039i	0.156835	+	0.397787i
$592$	−0.382133	+	0.661873i	−0.0157056	+	0.0272028i
$593$	14.7811			0.606986			0.303493	−	0.952834i	$-0.401847\pi$
$593$	14.7811			0.606986			0.303493	+	0.952834i	$0.401847\pi$
$594$	−0.889205	−	11.1655i	−0.0364845	−	0.458128i
$595$	−46.8761			−1.92173
$596$	14.4834	−	25.0861i	0.593265	−	1.02757i
$597$	−12.5238	−	31.7646i	−0.512564	−	1.30004i
$598$	−7.89777	−	13.6793i	−0.322964	−	0.559390i
$599$	8.74025	+	15.1386i	0.357117	+	0.618545i	0.987478	−	0.157758i	$-0.0504264\pi$
$599$	8.74025	+	15.1386i	0.357117	+	0.618545i	−0.630361	+	0.776302i	$0.717093\pi$
$600$	19.4213	+	2.89638i	0.792873	+	0.118244i
$601$	−11.8922	+	20.5979i	−0.485093	+	0.840205i	−0.999853	−	0.0171288i	$-0.994547\pi$
$601$	−11.8922	+	20.5979i	−0.485093	+	0.840205i	0.514761	+	0.857334i	$0.327881\pi$
$602$	35.0234			1.42745
$603$	26.8663	+	8.19563i	1.09408	+	0.333752i
$604$	5.65783			0.230214
$605$	−1.81197	+	3.13842i	−0.0736669	+	0.127595i
$606$	42.5951	−	53.5835i	1.73031	−	2.17668i
$607$	−19.5986	−	33.9458i	−0.795484	−	1.37782i	−0.922532	−	0.385922i	$-0.873883\pi$
$607$	−19.5986	−	33.9458i	−0.795484	−	1.37782i	0.127048	−	0.991897i	$-0.459450\pi$
$608$	−11.1744	−	19.3546i	−0.453180	−	0.784931i
$609$	−8.58732	+	10.8026i	−0.347976	+	0.437744i
$610$	−24.4923	+	42.4219i	−0.991664	+	1.71761i
$611$	−10.7697			−0.435695
$612$	43.2644	+	13.1979i	1.74886	+	0.533494i
$613$	9.34643			0.377499			0.188749	−	0.982025i	$-0.439557\pi$
$613$	9.34643			0.377499			0.188749	+	0.982025i	$0.439557\pi$
$614$	−12.9022	+	22.3472i	−0.520689	+	0.901860i
$615$	−61.8794	−	9.22831i	−2.49522	−	0.372121i
$616$	1.58256	+	2.74108i	0.0637633	+	0.110441i
$617$	1.85481	+	3.21263i	0.0746720	+	0.129336i	0.900944	−	0.433936i	$-0.142876\pi$
$617$	1.85481	+	3.21263i	0.0746720	+	0.129336i	−0.826272	+	0.563272i	$0.809542\pi$
$618$	6.24808	+	15.8473i	0.251335	+	0.637470i
$619$	−15.1420	+	26.2268i	−0.608609	+	1.05414i	0.382861	+	0.923806i	$0.374939\pi$
$619$	−15.1420	+	26.2268i	−0.608609	+	1.05414i	−0.991470	+	0.130336i	$0.958394\pi$
$620$	−24.0642			−0.966440
$621$	−2.44091	−	30.6500i	−0.0979504	−	1.22994i
$622$	7.32331			0.293638
$623$	5.41670	−	9.38199i	0.217015	−	0.375882i
$624$	1.80040	+	4.56644i	0.0720739	+	0.182804i
$625$	−0.239656	−	0.415097i	−0.00958625	−	0.0166039i
$626$	24.4624	+	42.3701i	0.977714	+	1.69345i
$627$	−4.95863	−	0.739500i	−0.198029	−	0.0295328i
$628$	−12.5724	+	21.7761i	−0.501694	+	0.868959i
$629$	−1.90251			−0.0758580
$630$	12.0023	+	51.8410i	0.478185	+	2.06540i
$631$	−10.7233			−0.426886			−0.213443	−	0.976956i	$-0.568468\pi$
$631$	−10.7233			−0.426886			−0.213443	+	0.976956i	$0.568468\pi$
$632$	−0.987411	+	1.71025i	−0.0392771	+	0.0680299i
$633$	12.5914	−	15.8397i	0.500464	−	0.629570i
$634$	−16.0064	−	27.7240i	−0.635697	−	1.10106i
$635$	−15.8141	−	27.3908i	−0.627562	−	1.08697i
$636$	−17.5866	+	22.1235i	−0.697354	+	0.877253i
$637$	1.14200	−	1.97800i	0.0452476	−	0.0783711i
$638$	−7.56393			−0.299459
$639$	26.5832	−	24.8201i	1.05162	−	0.981869i
$640$	−38.3005			−1.51396
$641$	21.9083	−	37.9462i	0.865324	−	1.49879i	−0.00140071	−	0.999999i	$-0.500446\pi$
$641$	21.9083	−	37.9462i	0.865324	−	1.49879i	0.866725	−	0.498786i	$-0.166221\pi$
$642$	−18.8707	−	2.81426i	−0.744767	−	0.111070i
$643$	−16.0895	−	27.8678i	−0.634507	−	1.09900i	−0.986619	−	0.163041i	$-0.947870\pi$
$643$	−16.0895	−	27.8678i	−0.634507	−	1.09900i	0.352112	−	0.935958i	$-0.385464\pi$
$644$	17.7799	+	30.7958i	0.700628	+	1.21352i
$645$	16.4742	+	41.7842i	0.648672	+	1.64525i
$646$	17.7726	−	30.7830i	0.699252	−	1.21114i
$647$	10.9108			0.428946			0.214473	−	0.976730i	$-0.431197\pi$
$647$	10.9108			0.428946			0.214473	+	0.976730i	$0.431197\pi$
$648$	0.859608	−	12.5162i	0.0337686	−	0.491682i
$649$	2.91726			0.114513
$650$	−10.8550	+	18.8013i	−0.425766	+	0.737449i
$651$	−3.61917	−	9.17946i	−0.141847	−	0.359771i
$652$	25.7671	+	44.6299i	1.00912	+	1.74784i
$653$	23.5331	+	40.7605i	0.920922	+	1.59508i	0.797992	+	0.602667i	$0.205895\pi$
$653$	23.5331	+	40.7605i	0.920922	+	1.59508i	0.122929	+	0.992415i	$0.460771\pi$
$654$	17.2783	+	2.57677i	0.675633	+	0.100760i
$655$	6.68393	−	11.5769i	0.261163	−	0.452347i
$656$	22.8103			0.890593
$657$	−9.45686	+	8.82964i	−0.368947	+	0.344477i
$658$	42.5668			1.65943
$659$	−13.4862	+	23.3588i	−0.525348	+	0.909930i	0.474216	+	0.880409i	$0.342732\pi$
$659$	−13.4862	+	23.3588i	−0.525348	+	0.909930i	−0.999564	+	0.0295212i	$0.990602\pi$
$660$	−10.3376	+	13.0044i	−0.402391	+	0.506197i
$661$	−4.53345	−	7.85217i	−0.176331	−	0.305414i	0.764290	−	0.644872i	$-0.223090\pi$
$661$	−4.53345	−	7.85217i	−0.176331	−	0.305414i	−0.940621	+	0.339459i	$0.889756\pi$
$662$	−17.4635	−	30.2476i	−0.678737	−	1.17561i
$663$	−7.60353	+	9.56504i	−0.295297	+	0.371475i
$664$	1.92144	−	3.32804i	0.0745665	−	0.129153i
$665$	23.8176			0.923607
$666$	0.487125	+	2.10401i	0.0188757	+	0.0815289i
$667$	−20.7634			−0.803961
$668$	20.2444	−	35.0643i	0.783278	−	1.35668i
$669$	−31.0472	−	4.63019i	−1.20036	−	0.179014i
$670$	−36.5703	−	63.3416i	−1.41283	−	2.44710i
$671$	−3.13530	−	5.43050i	−0.121037	−	0.209642i
$672$	−11.1376	−	28.2488i	−0.429644	−	1.08972i
$673$	4.36695	−	7.56378i	0.168334	−	0.291562i	−0.769501	−	0.638646i	$-0.779495\pi$
$673$	4.36695	−	7.56378i	0.168334	−	0.291562i	0.937834	+	0.347084i	$0.112828\pi$
$674$	−24.2770			−0.935114
$675$	−34.8050	+	23.9685i	−1.33965	+	0.922550i
$676$	−30.3480			−1.16723
$677$	17.8921	−	30.9900i	0.687650	−	1.19104i	−0.284947	−	0.958543i	$-0.591976\pi$
$677$	17.8921	−	30.9900i	0.687650	−	1.19104i	0.972596	−	0.232501i	$-0.0746908\pi$
$678$	2.09757	+	5.32016i	0.0805568	+	0.204319i
$679$	−2.90533	−	5.03218i	−0.111496	−	0.193117i
$680$	−14.3891	−	24.9226i	−0.551795	−	0.955737i
$681$	29.9921	+	4.47284i	1.14930	+	0.171400i
$682$	2.70416	−	4.68374i	0.103548	−	0.179350i
$683$	−40.9545			−1.56708			−0.783541	−	0.621340i	$-0.786588\pi$
$683$	−40.9545			−1.56708			−0.783541	+	0.621340i	$0.786588\pi$
$684$	−21.9825	−	6.70581i	−0.840522	−	0.256403i
$685$	79.6125			3.04184
$686$	−21.6446	+	37.4895i	−0.826393	+	1.43135i
$687$	−4.89612	+	6.15919i	−0.186799	+	0.234988i
$688$	−8.18778	−	14.1816i	−0.312156	−	0.540670i
$689$	−3.81729	−	6.61174i	−0.145427	−	0.251887i
$690$	−49.8210	+	62.6735i	−1.89665	+	2.38594i
$691$	−19.9963	+	34.6346i	−0.760696	+	1.31756i	0.181797	+	0.983336i	$0.441809\pi$
$691$	−19.9963	+	34.6346i	−0.760696	+	1.31756i	−0.942492	+	0.334228i	$0.891525\pi$
$692$	37.1087			1.41066
$693$	−6.51538	−	1.98753i	−0.247499	−	0.0755001i
$694$	−36.8057			−1.39713
$695$	2.33738	−	4.04847i	0.0886620	−	0.153567i
$696$	−8.37938	−	1.24965i	−0.317619	−	0.0473678i
$697$	28.3912	+	49.1750i	1.07539	+	1.86264i
$698$	−24.7598	−	42.8853i	−0.937173	−	1.62323i
$699$	5.19015	+	13.1640i	0.196309	+	0.497908i
$700$	24.4373	−	42.3267i	0.923644	−	1.59980i
$701$	−28.4894			−1.07603			−0.538015	−	0.842935i	$-0.680826\pi$
$701$	−28.4894			−1.07603			−0.538015	+	0.842935i	$0.680826\pi$
$702$	12.5250	+	5.95980i	0.472724	+	0.224938i
$703$	0.966658			0.0364582
$704$	6.03328	−	10.4499i	0.227388	−	0.393847i
$705$	20.0225	+	50.7838i	0.754090	+	1.91263i
$706$	22.1095	+	38.2948i	0.832103	+	1.44124i
$707$	−20.8141	−	36.0511i	−0.782796	−	1.35584i
$708$	13.2269	+	1.97258i	0.497098	+	0.0741342i
$709$	−19.2455	+	33.3341i	−0.722779	+	1.25189i	0.237103	+	0.971485i	$0.423802\pi$
$709$	−19.2455	+	33.3341i	−0.722779	+	1.25189i	−0.959882	+	0.280405i	$0.909531\pi$
$710$	−94.7025			−3.55412
$711$	−0.958632	−	4.14057i	−0.0359515	−	0.155283i
$712$	6.65082			0.249250
$713$	7.42305	−	12.8571i	0.277995	−	0.481502i
$714$	30.0527	−	37.8055i	1.12469	−	1.41483i
$715$	−2.24385	−	3.88646i	−0.0839151	−	0.145345i
$716$	−5.22652	−	9.05260i	−0.195324	−	0.338311i
$717$	−20.0481	+	25.2200i	−0.748711	+	0.941858i
$718$	3.14547	−	5.44811i	0.117388	−	0.203322i
$719$	19.0764			0.711430			0.355715	−	0.934594i	$-0.384237\pi$
$719$	19.0764			0.711430			0.355715	+	0.934594i	$0.384237\pi$
$720$	18.1855	−	16.9794i	0.677735	−	0.632785i
$721$	10.3595			0.385807
$722$	11.4481	−	19.8288i	0.426056	−	0.737950i
$723$	48.5711	+	7.24359i	1.80638	+	0.269392i
$724$	−17.6879	−	30.6364i	−0.657367	−	1.13859i
$725$	14.2689	+	24.7145i	0.529934	+	0.917873i
$726$	−1.36946	−	3.47341i	−0.0508254	−	0.128910i
$727$	3.03168	−	5.25103i	0.112439	−	0.194750i	−0.804314	−	0.594204i	$-0.797467\pi$
$727$	3.03168	−	5.25103i	0.112439	−	0.194750i	0.916753	+	0.399454i	$0.130800\pi$
$728$	−3.91953			−0.145267
$729$	17.0307	+	20.9513i	0.630766	+	0.775973i
$730$	33.6900			1.24692
$731$	20.3821	−	35.3028i	0.753858	−	1.30572i
$732$	−10.5435	−	26.7420i	−0.389700	−	0.988412i
$733$	−18.8883	−	32.7155i	−0.697655	−	1.20837i	−0.969277	−	0.245970i	$-0.920894\pi$
$733$	−18.8883	−	32.7155i	−0.697655	−	1.20837i	0.271622	−	0.962404i	$-0.412440\pi$
$734$	−7.27669	−	12.6036i	−0.268588	−	0.465207i
$735$	−11.4503	−	1.70762i	−0.422350	−	0.0629867i
$736$	22.8437	−	39.5664i	0.842029	−	1.45844i
$737$	9.36285			0.344885
$738$	47.1140	−	43.9892i	1.73429	−	1.61927i
$739$	−11.0030			−0.404752			−0.202376	−	0.979308i	$-0.564866\pi$
$739$	−11.0030			−0.404752			−0.202376	+	0.979308i	$0.564866\pi$
$740$	1.60156	−	2.77399i	0.0588746	−	0.101974i
$741$	3.86333	−	4.85996i	0.141923	−	0.178535i
$742$	15.0877	+	26.1327i	0.553887	+	0.959360i
$743$	−8.83265	−	15.2986i	−0.324038	−	0.561251i	0.657279	−	0.753647i	$-0.271707\pi$
$743$	−8.83265	−	15.2986i	−0.324038	−	0.561251i	−0.981317	+	0.192397i	$0.938374\pi$
$744$	3.76949	−	4.74192i	0.138196	−	0.173847i
$745$	19.8314	−	34.3489i	0.726565	−	1.25845i
$746$	−48.2371			−1.76608
$747$	1.86544	+	8.05730i	0.0682529	+	0.294801i
$748$	15.0775			0.551290
$749$	−5.80154	+	10.0486i	−0.211984	+	0.367166i
$750$	41.9255	+	6.25251i	1.53090	+	0.228309i
$751$	2.14256	+	3.71103i	0.0781833	+	0.135417i	0.902466	−	0.430761i	$-0.141755\pi$
$751$	2.14256	+	3.71103i	0.0781833	+	0.135417i	−0.824283	+	0.566178i	$0.808421\pi$
$752$	−9.95128	−	17.2361i	−0.362886	−	0.628537i
$753$	−3.13718	−	7.95695i	−0.114325	−	0.289968i
$754$	4.68339	−	8.11187i	0.170559	−	0.295417i
$755$	7.74695			0.281940
$756$	−28.1969	−	13.4170i	−1.02551	−	0.487973i
$757$	−8.95117			−0.325336			−0.162668	−	0.986681i	$-0.552010\pi$
$757$	−8.95117			−0.325336			−0.162668	+	0.986681i	$0.552010\pi$
$758$	−35.6022	+	61.6648i	−1.29313	+	2.23977i
$759$	−3.75923	−	9.53468i	−0.136451	−	0.346087i
$760$	7.31103	+	12.6631i	0.265199	+	0.459338i
$761$	2.69037	+	4.65986i	0.0975258	+	0.168920i	0.910660	−	0.413157i	$-0.135574\pi$
$761$	2.69037	+	4.65986i	0.0975258	+	0.168920i	−0.813134	+	0.582076i	$0.802240\pi$
$762$	32.2291	+	4.80645i	1.16754	+	0.174119i
$763$	5.31197	−	9.20059i	0.192306	−	0.333084i
$764$	50.0761			1.81169
$765$	59.2395	+	18.0711i	2.14181	+	0.653364i
$766$	50.6229			1.82908
$767$	−1.80630	+	3.12860i	−0.0652215	+	0.112967i
$768$	−1.45604	+	1.83166i	−0.0525403	+	0.0660943i
$769$	7.72456	+	13.3793i	0.278555	+	0.482471i	0.971026	−	0.238975i	$-0.0768113\pi$
$769$	7.72456	+	13.3793i	0.278555	+	0.482471i	−0.692471	+	0.721446i	$0.743478\pi$
$770$	8.86872	+	15.3611i	0.319606	+	0.553575i
$771$	−18.4450	+	23.2034i	−0.664282	+	0.835649i
$772$	2.73202	−	4.73199i	0.0983274	−	0.170308i
$773$	−32.7213			−1.17690			−0.588451	−	0.808533i	$-0.700262\pi$
$773$	−32.7213			−1.17690			−0.588451	+	0.808533i	$0.700262\pi$
$774$	−44.2606	−	13.5018i	−1.59091	−	0.485312i
$775$	−20.4050			−0.732968
$776$	1.78364	−	3.08935i	0.0640288	−	0.110901i
$777$	1.29903	+	0.193729i	0.0466024	+	0.00695000i
$778$	33.4566	+	57.9486i	1.19948	+	2.07756i
$779$	−14.4255	−	24.9856i	−0.516846	−	0.895204i
$780$	−7.54571	−	19.1385i	−0.270180	−	0.685268i
$781$	6.06151	−	10.4988i	0.216898	−	0.375678i
$782$	72.6647			2.59848
$783$	15.0167	−	10.3413i	0.536653	−	0.369567i
$784$	4.22086			0.150745
$785$	−17.2147	+	29.8167i	−0.614419	+	1.06420i
$786$	5.05162	+	12.8126i	0.180185	+	0.457011i
$787$	12.4575	+	21.5771i	0.444063	+	0.769139i	0.997986	−	0.0634284i	$-0.0202035\pi$
$787$	12.4575	+	21.5771i	0.444063	+	0.769139i	−0.553924	+	0.832567i	$0.686870\pi$
$788$	7.94196	+	13.7559i	0.282921	+	0.490033i
$789$	−7.61575	−	1.13577i	−0.271128	−	0.0404343i
$790$	−5.53347	+	9.58425i	−0.196872	+	0.340992i
$791$	3.47783			0.123657
$792$	−0.943248	−	4.07412i	−0.0335169	−	0.144768i
$793$	7.76519			0.275750
$794$	−18.7327	+	32.4460i	−0.664799	+	1.15146i
$795$	−24.0803	+	30.2924i	−0.854042	+	1.07436i
$796$	−26.0872	−	45.1843i	−0.924635	−	1.60151i
$797$	−4.54547	−	7.87298i	−0.161009	−	0.278875i	0.774222	−	0.632914i	$-0.218141\pi$
$797$	−4.54547	−	7.87298i	−0.161009	−	0.278875i	−0.935231	+	0.354039i	$0.884808\pi$
$798$	−15.2697	+	19.2088i	−0.540540	+	0.679985i
$799$	24.7720	−	42.9064i	0.876371	−	1.51792i
$800$	−62.7941			−2.22011
$801$	−10.4622	+	9.76827i	−0.369662	+	0.345145i
$802$	−24.8928			−0.878997
$803$	−2.15635	+	3.73491i	−0.0760960	+	0.131802i
$804$	42.4513	+	6.33093i	1.49714	+	0.223275i
$805$	24.3451	+	42.1669i	0.858051	+	1.48619i
$806$	3.34869	+	5.80011i	0.117953	+	0.204300i
$807$	−12.4454	−	31.5658i	−0.438099	−	1.11117i
$808$	12.7782	−	22.1325i	0.449535	−	0.778617i
$809$	10.0563			0.353560			0.176780	−	0.984250i	$-0.443432\pi$
$809$	10.0563			0.353560			0.176780	+	0.984250i	$0.443432\pi$
$810$	4.81726	−	70.1409i	0.169261	−	2.46450i
$811$	−16.2533			−0.570730			−0.285365	−	0.958419i	$-0.592115\pi$
$811$	−16.2533			−0.570730			−0.285365	+	0.958419i	$0.592115\pi$
$812$	−10.5435	+	18.2619i	−0.370005	+	0.640868i
$813$	−4.30479	−	10.9184i	−0.150976	−	0.382925i
$814$	0.359945	+	0.623442i	0.0126161	+	0.0218516i
$815$	35.2814	+	61.1092i	1.23585	+	2.14056i
$816$	−22.3339	−	3.33074i	−0.781843	−	0.116599i
$817$	−10.3561	+	17.9372i	−0.362313	+	0.627544i
$818$	74.8765			2.61800
$819$	6.16567	−	5.75674i	0.215446	−	0.201157i
$820$	−95.6007			−3.33852
$821$	10.4445	−	18.0904i	0.364515	−	0.631359i	−0.624183	−	0.781278i	$-0.714568\pi$
$821$	10.4445	−	18.0904i	0.364515	−	0.631359i	0.988698	+	0.149919i	$0.0479013\pi$
$822$	−51.0402	+	64.2072i	−1.78023	+	2.23948i
$823$	6.73966	+	11.6734i	0.234930	+	0.406910i	0.959252	−	0.282551i	$-0.0911807\pi$
$823$	6.73966	+	11.6734i	0.234930	+	0.406910i	−0.724323	+	0.689461i	$0.757847\pi$
$824$	3.17994	+	5.50782i	0.110778	+	0.191874i
$825$	−8.76567	+	11.0270i	−0.305181	+	0.383910i
$826$	7.13932	−	12.3657i	0.248409	−	0.430256i
$827$	54.8435			1.90710			0.953548	−	0.301241i	$-0.0974008\pi$
$827$	54.8435			1.90710			0.953548	+	0.301241i	$0.0974008\pi$
$828$	−10.5973	−	45.7723i	−0.368281	−	1.59070i
$829$	1.57675			0.0547628			0.0273814	−	0.999625i	$-0.491283\pi$
$829$	1.57675			0.0547628			0.0273814	+	0.999625i	$0.491283\pi$
$830$	10.7678	−	18.6504i	0.373756	−	0.647365i
$831$	2.52944	+	0.377225i	0.0877452	+	0.0130858i
$832$	7.47130	+	12.9407i	0.259021	+	0.448637i
$833$	5.25356	+	9.09943i	0.182025	+	0.315277i
$834$	1.76656	+	4.48060i	0.0611710	+	0.155150i
$835$	27.7195	−	48.0115i	0.959271	−	1.66151i
$836$	−7.66085			−0.264956
$837$	1.03496	+	12.9957i	0.0357734	+	0.449198i
$838$	−16.0177			−0.553323
$839$	−14.5469	+	25.1960i	−0.502214	+	0.869861i	0.497782	+	0.867302i	$0.334148\pi$
$839$	−14.5469	+	25.1960i	−0.502214	+	0.869861i	−0.999997	+	0.00255896i	$0.999185\pi$
$840$	7.28700	+	18.4823i	0.251425	+	0.637701i
$841$	8.34365	+	14.4516i	0.287712	+	0.498332i
$842$	−12.7782	−	22.1326i	−0.440367	−	0.762738i
$843$	−12.5859	−	1.87698i	−0.433481	−	0.0646467i
$844$	15.4598	−	26.7771i	0.532147	−	0.921706i
$845$	−41.5538			−1.42949
$846$	−53.7936	−	16.4099i	−1.84946	−	0.564182i
$847$	−2.27060			−0.0780187
$848$	7.05442	−	12.2186i	0.242250	−	0.419589i
$849$	15.8612	−	19.9530i	0.544355	−	0.684784i
$850$	−49.9363	−	86.4922i	−1.71280	−	2.96666i
$851$	0.988066	+	1.71138i	0.0338705	+	0.0586653i
$852$	34.5820	−	43.5033i	1.18476	−	1.49040i
$853$	−12.8625	+	22.2785i	−0.440403	+	0.762800i	−0.997719	−	0.0675000i	$-0.978498\pi$
$853$	−12.8625	+	22.2785i	−0.440403	+	0.762800i	0.557316	+	0.830300i	$0.311831\pi$
$854$	−30.6916			−1.05025
$855$	−30.0994	−	9.18189i	−1.02938	−	0.314014i
$856$	−7.12334			−0.243471
$857$	23.0057	−	39.8470i	0.785860	−	1.36115i	−0.142625	−	0.989777i	$-0.545554\pi$
$857$	23.0057	−	39.8470i	0.785860	−	1.36115i	0.928484	−	0.371372i	$-0.121113\pi$
$858$	4.57296	+	0.681984i	0.156118	+	0.0232825i
$859$	22.0242	+	38.1470i	0.751455	+	1.30156i	0.947118	+	0.320886i	$0.103981\pi$
$859$	22.0242	+	38.1470i	0.751455	+	1.30156i	−0.195663	+	0.980671i	$0.562686\pi$
$860$	34.3159	+	59.4370i	1.17016	+	2.02678i
$861$	−14.3781	−	36.4676i	−0.490003	−	1.24281i
$862$	−26.6752	+	46.2029i	−0.908562	+	1.57368i
$863$	−13.4065			−0.456362			−0.228181	−	0.973619i	$-0.573278\pi$
$863$	−13.4065			−0.456362			−0.228181	+	0.973619i	$0.573278\pi$
$864$	3.18498	+	39.9930i	0.108355	+	1.36059i
$865$	50.8108			1.72762
$866$	−20.5438	+	35.5830i	−0.698108	+	1.20916i
$867$	−9.81766	−	24.9009i	−0.333425	−	0.845680i
$868$	−7.53877	−	13.0575i	−0.255883	−	0.443202i
$869$	−0.708348	−	1.22690i	−0.0240291	−	0.0416196i
$870$	−46.9582	−	7.00306i	−1.59203	−	0.237426i
$871$	−5.79724	+	10.0411i	−0.196432	+	0.340230i
$872$	6.52223			0.220871
$873$	1.73165	+	7.47942i	0.0586075	+	0.253140i
$874$	−36.9207			−1.24886
$875$	12.8894	−	22.3251i	0.435742	−	0.754727i
$876$	−12.3024	+	15.4761i	−0.415659	+	0.522889i
$877$	−6.18860	−	10.7190i	−0.208974	−	0.361954i	0.742417	−	0.669938i	$-0.233679\pi$
$877$	−6.18860	−	10.7190i	−0.208974	−	0.361954i	−0.951392	+	0.307984i	$0.900346\pi$
$878$	37.4521	+	64.8690i	1.26395	+	2.18922i
$879$	2.12989	−	2.67934i	0.0718393	−	0.0903719i
$880$	4.14667	−	7.18224i	0.139784	−	0.242113i
$881$	−31.1210			−1.04849			−0.524247	−	0.851566i	$-0.675653\pi$
$881$	−31.1210			−1.04849			−0.524247	+	0.851566i	$0.675653\pi$
$882$	8.71807	−	8.13985i	0.293553	−	0.274083i
$883$	−49.1130			−1.65278			−0.826392	−	0.563096i	$-0.809610\pi$
$883$	−49.1130			−1.65278			−0.826392	+	0.563096i	$0.809610\pi$
$884$	−9.33563	+	16.1698i	−0.313991	+	0.543849i
$885$	18.1109	+	2.70095i	0.608791	+	0.0907913i
$886$	1.46569	+	2.53866i	0.0492410	+	0.0852878i
$887$	23.1958	+	40.1763i	0.778839	+	1.34899i	0.932611	+	0.360882i	$0.117524\pi$
$887$	23.1958	+	40.1763i	0.778839	+	1.34899i	−0.153772	+	0.988106i	$0.549142\pi$
$888$	0.295749	+	0.750121i	0.00992470	+	0.0251724i
$889$	9.90841	−	17.1619i	0.332317	−	0.575590i
$890$	37.2713			1.24934
$891$	7.46758	+	5.02347i	0.250173	+	0.168293i
$892$	−47.9665			−1.60604
$893$	−12.5866	+	21.8006i	−0.421194	+	0.729529i
$894$	14.9883	+	38.0153i	0.501283	+	1.27142i
$895$	−7.15638	−	12.3952i	−0.239211	−	0.414326i
$896$	−11.9987	−	20.7824i	−0.400849	−	0.694291i
$897$	12.5530	+	1.87208i	0.419133	+	0.0625069i
$898$	−34.1946	+	59.2268i	−1.14109	+	1.97642i
$899$	8.80376			0.293622
$900$	−47.1999	+	44.0694i	−1.57333	+	1.46898i
$901$	35.1215			1.17007
$902$	10.7429	−	18.6073i	0.357701	−	0.619555i
$903$	−17.5117	+	22.0292i	−0.582752	+	0.733087i
$904$	1.06755	+	1.84906i	0.0355063	+	0.0614987i
$905$	−24.2191	−	41.9487i	−0.805070	−	1.39442i
$906$	−4.96663	+	6.24789i	−0.165005	+	0.207572i
$907$	3.71116	−	6.42792i	0.123227	−	0.213436i	−0.797811	−	0.602907i	$-0.794009\pi$
$907$	3.71116	−	6.42792i	0.123227	−	0.213436i	0.921039	+	0.389471i	$0.127342\pi$
$908$	46.3364			1.53773
$909$	12.4057	+	53.5835i	0.411473	+	1.77725i
$910$	−21.9651			−0.728137
$911$	−4.63530	+	8.02857i	−0.153574	+	0.265998i	−0.932539	−	0.361069i	$-0.882412\pi$
$911$	−4.63530	+	8.02857i	−0.153574	+	0.265998i	0.778965	+	0.627068i	$0.215745\pi$
$912$	11.3478	+	1.69234i	0.375763	+	0.0560389i
$913$	1.37840	+	2.38747i	0.0456185	+	0.0790136i
$914$	−38.1354	−	66.0525i	−1.26141	−	2.18482i
$915$	−14.4367	−	36.6163i	−0.477261	−	1.21050i
$916$	−6.01147	+	10.4122i	−0.198625	+	0.344028i
$917$	8.37572			0.276591
$918$	−52.5533	+	36.1909i	−1.73452	+	1.19448i
$919$	−8.03556			−0.265069			−0.132534	−	0.991178i	$-0.542311\pi$
$919$	−8.03556			−0.265069			−0.132534	+	0.991178i	$0.542311\pi$
$920$	−14.9459	+	25.8870i	−0.492751	+	0.853470i
$921$	−7.60501	−	19.2889i	−0.250594	−	0.635591i
$922$	33.6671	+	58.3131i	1.10877	+	1.92044i
$923$	7.50626	+	13.0012i	0.247072	+	0.427941i
$924$	−10.2949	−	1.53532i	−0.338678	−	0.0505084i
$925$	1.35803	−	2.35218i	0.0446517	−	0.0773391i
$926$	−0.514536			−0.0169087
$927$	−13.0918	−	3.99367i	−0.429990	−	0.131169i
$928$	27.0927			0.889360
$929$	4.76732	−	8.25724i	0.156411	−	0.270911i	−0.777161	−	0.629302i	$-0.783341\pi$
$929$	4.76732	−	8.25724i	0.156411	−	0.270911i	0.933572	+	0.358390i	$0.116674\pi$
$930$	21.1243	−	26.5738i	0.692694	−	0.871390i
$931$	−2.66932	−	4.62339i	−0.0874833	−	0.151526i
$932$	10.8111	+	18.7254i	0.354130	+	0.613372i
$933$	−3.66166	+	4.60627i	−0.119877	+	0.150802i
$934$	−1.51183	+	2.61856i	−0.0494685	+	0.0856819i
$935$	20.6448			0.675158
$936$	4.95329	+	1.51101i	0.161903	+	0.0493890i
$937$	−17.8647			−0.583614			−0.291807	−	0.956477i	$-0.594256\pi$
$937$	−17.8647			−0.583614			−0.291807	+	0.956477i	$0.594256\pi$
$938$	22.9134	−	39.6871i	0.748148	−	1.29583i
$939$	−38.8814	−	5.79854i	−1.26885	−	0.189228i
$940$	41.7070	+	72.2386i	1.36033	+	2.35616i
$941$	24.4390	+	42.3296i	0.796689	+	1.37991i	0.921761	+	0.387758i	$0.126750\pi$
$941$	24.4390	+	42.3296i	0.796689	+	1.37991i	−0.125073	+	0.992148i	$0.539916\pi$
$942$	−13.0106	−	32.9994i	−0.423909	−	1.07518i
$943$	29.4899	−	51.0780i	0.960323	−	1.66333i
$944$	−6.67613			−0.217290
$945$	−38.6085	−	18.3712i	−1.25593	−	0.597616i
$946$	−15.4247			−0.501501
$947$	23.0552	−	39.9328i	0.749193	−	1.29764i	−0.199017	−	0.979996i	$-0.563775\pi$
$947$	23.0552	−	39.9328i	0.749193	−	1.29764i	0.948210	−	0.317644i	$-0.102892\pi$
$948$	−2.38207	−	6.04173i	−0.0773660	−	0.196226i
$949$	−2.67032	−	4.62513i	−0.0866822	−	0.150138i
$950$	25.3725	+	43.9464i	0.823192	+	1.42581i
$951$	25.4412	+	3.79415i	0.824988	+	0.123034i
$952$	9.01556	−	15.6154i	0.292196	−	0.506098i
$953$	−44.3793			−1.43759			−0.718793	−	0.695224i	$-0.755305\pi$
$953$	−44.3793			−1.43759			−0.718793	+	0.695224i	$0.755305\pi$
$954$	−8.99265	−	38.8415i	−0.291148	−	1.25754i
$955$	68.5664			2.21876
$956$	−24.6151	+	42.6346i	−0.796110	+	1.37890i
$957$	3.78196	−	4.75761i	0.122254	−	0.153792i
$958$	−26.8729	−	46.5453i	−0.868225	−	1.50381i
$959$	24.9409	+	43.1988i	0.805382	+	1.39496i
$960$	47.1307	−	59.2892i	1.52114	−	1.91355i
$961$	12.3526	−	21.3953i	0.398471	−	0.690172i
$962$	−0.891474			−0.0287423
$963$	11.2055	−	10.4623i	0.361091	−	0.337142i
$964$	75.0400			2.41687
$965$	3.74080	−	6.47925i	0.120421	−	0.208574i
$966$	−49.6153	−	7.39932i	−1.59635	−	0.238069i
$967$	−11.0831	−	19.1965i	−0.356409	−	0.617319i	0.630949	−	0.775825i	$-0.282666\pi$
$967$	−11.0831	−	19.1965i	−0.356409	−	0.617319i	−0.987358	+	0.158505i	$0.949332\pi$
$968$	−0.696981	−	1.20721i	−0.0224018	−	0.0388011i
$969$	10.4758	+	26.5702i	0.336531	+	0.853558i
$970$	9.99553	−	17.3128i	0.320937	−	0.555880i
$971$	23.1985			0.744476			0.372238	−	0.928137i	$-0.378591\pi$
$971$	23.1985			0.744476			0.372238	+	0.928137i	$0.378591\pi$
$972$	30.4614	+	27.8259i	0.977049	+	0.892516i
$973$	2.92900			0.0938996
$974$	17.2915	−	29.9498i	0.554056	−	0.959653i
$975$	−6.39831	−	16.2283i	−0.204910	−	0.519721i
$976$	7.17510	+	12.4276i	0.229669	+	0.397799i
$977$	−7.78410	−	13.4825i	−0.249035	−	0.431342i	0.714223	−	0.699918i	$-0.246780\pi$
$977$	−7.78410	−	13.4825i	−0.249035	−	0.431342i	−0.963258	+	0.268576i	$0.913447\pi$
$978$	−71.9036	−	10.7233i	−2.29922	−	0.342892i
$979$	−2.38558	+	4.13195i	−0.0762435	+	0.132058i
$980$	−17.6901			−0.565091
$981$	−10.2599	+	9.57940i	−0.327573	+	0.305847i
$982$	21.7281			0.693371
$983$	−14.7920	+	25.6206i	−0.471793	+	0.817169i	−0.999479	−	0.0322700i	$-0.989726\pi$
$983$	−14.7920	+	25.6206i	−0.471793	+	0.817169i	0.527686	+	0.849439i	$0.323060\pi$
$984$	14.9752	−	18.8384i	0.477393	−	0.600548i
$985$	10.8745	+	18.8351i	0.346490	+	0.600138i
$986$	21.5451	+	37.3173i	0.686137	+	1.18842i
$987$	−21.2834	+	26.7739i	−0.677458	+	0.852224i
$988$	4.74340	−	8.21582i	0.150908	−	0.261380i
$989$	−42.3416			−1.34639
$990$	−5.28598	−	22.8315i	−0.168000	−	0.725631i
$991$	−7.97155			−0.253225			−0.126612	−	0.991952i	$-0.540410\pi$
$991$	−7.97155			−0.253225			−0.126612	+	0.991952i	$0.540410\pi$
$992$	−9.68582	+	16.7763i	−0.307525	+	0.532649i
$993$	27.7571	+	4.13952i	0.880845	+	0.131364i
$994$	−29.6682	−	51.3869i	−0.941019	−	1.62989i
$995$	−35.7197	−	61.8683i	−1.13239	−	1.96136i
$996$	4.63536	+	11.7569i	0.146877	+	0.372530i
$997$	−23.9970	+	41.5641i	−0.759994	+	1.31635i	0.182860	+	0.983139i	$0.441465\pi$
$997$	−23.9970	+	41.5641i	−0.759994	+	1.31635i	−0.942853	+	0.333209i	$0.891869\pi$
$998$	71.6820			2.26905
$999$	−1.56696	−	0.745611i	−0.0495764	−	0.0235901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.e.e.34.2	✓	8
3.2	odd	2		297.2.e.e.100.3		8
9.2	odd	6		891.2.a.p.1.2		4
9.4	even	3	inner	99.2.e.e.67.2	yes	8
9.5	odd	6		297.2.e.e.199.3		8
9.7	even	3		891.2.a.q.1.3		4
11.10	odd	2		1089.2.e.i.727.3		8
99.43	odd	6		9801.2.a.bi.1.2		4
99.65	even	6		9801.2.a.bl.1.3		4
99.76	odd	6		1089.2.e.i.364.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.e.34.2	✓	8	1.1	even	1	trivial
99.2.e.e.67.2	yes	8	9.4	even	3	inner
297.2.e.e.100.3		8	3.2	odd	2
297.2.e.e.199.3		8	9.5	odd	6
891.2.a.p.1.2		4	9.2	odd	6
891.2.a.q.1.3		4	9.7	even	3
1089.2.e.i.364.3		8	99.76	odd	6
1089.2.e.i.727.3		8	11.10	odd	2
9801.2.a.bi.1.2		4	99.43	odd	6
9801.2.a.bl.1.3		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)

\(f(q)\)	\(=\)	\(q+(-1.07781 + 1.86682i) q^{2} +(-0.635299 - 1.61133i) q^{3} +(-1.32333 - 2.29208i) q^{4} +(-1.81197 - 3.13842i) q^{5} +(3.69279 + 0.550720i) q^{6} +(1.13530 - 1.96640i) q^{7} +1.39396 q^{8} +(-2.19279 + 2.04736i) q^{9} +O(q^{10})\)	\(q+(-1.07781 + 1.86682i) q^{2} +(-0.635299 - 1.61133i) q^{3} +(-1.32333 - 2.29208i) q^{4} +(-1.81197 - 3.13842i) q^{5} +(3.69279 + 0.550720i) q^{6} +(1.13530 - 1.96640i) q^{7} +1.39396 q^{8} +(-2.19279 + 2.04736i) q^{9} +7.81179 q^{10} +(-0.500000 + 0.866025i) q^{11} +(-2.85259 + 3.58849i) q^{12} +(-0.619175 - 1.07244i) q^{13} +(2.44726 + 4.23879i) q^{14} +(-3.90590 + 4.91351i) q^{15} +(1.14425 - 1.98189i) q^{16} +5.69681 q^{17} +(-1.45863 - 6.30019i) q^{18} -2.89453 q^{19} +(-4.79567 + 8.30634i) q^{20} +(-3.88977 - 0.580097i) q^{21} +(-1.07781 - 1.86682i) q^{22} +(-2.95863 - 5.12450i) q^{23} +(-0.885582 - 2.24614i) q^{24} +(-4.06644 + 7.04328i) q^{25} +2.66940 q^{26} +(4.69205 + 2.23263i) q^{27} -6.00951 q^{28} +(1.75447 - 3.03884i) q^{29} +(-4.96282 - 12.5874i) q^{30} +(1.25447 + 2.17281i) q^{31} +(3.86051 + 6.68660i) q^{32} +(1.71311 + 0.255482i) q^{33} +(-6.14006 + 10.6349i) q^{34} -8.22849 q^{35} +(7.59450 + 2.31672i) q^{36} -0.333960 q^{37} +(3.11974 - 5.40355i) q^{38} +(-1.33470 + 1.67902i) q^{39} +(-2.52581 - 4.37483i) q^{40} +(4.98370 + 8.63203i) q^{41} +(5.27535 - 6.63625i) q^{42} +(3.57781 - 6.19694i) q^{43} +2.64667 q^{44} +(10.3987 + 3.17215i) q^{45} +12.7553 q^{46} +(4.34840 - 7.53166i) q^{47} +(-3.92042 - 0.584668i) q^{48} +(0.922194 + 1.59729i) q^{49} +(-8.76567 - 15.1826i) q^{50} +(-3.61917 - 9.17946i) q^{51} +(-1.63875 + 2.83840i) q^{52} +6.16513 q^{53} +(-9.22504 + 6.35284i) q^{54} +3.62393 q^{55} +(1.58256 - 2.74108i) q^{56} +(1.83889 + 4.66405i) q^{57} +(3.78196 + 6.55056i) q^{58} +(-1.45863 - 2.52642i) q^{59} +(16.4310 + 2.45041i) q^{60} +(-3.13530 + 5.43050i) q^{61} -5.40832 q^{62} +(1.53644 + 6.63625i) q^{63} -12.0666 q^{64} +(-2.24385 + 3.88646i) q^{65} +(-2.32333 + 2.92269i) q^{66} +(-4.68142 - 8.10846i) q^{67} +(-7.53877 - 13.0575i) q^{68} +(-6.37766 + 8.02293i) q^{69} +(8.86872 - 15.3611i) q^{70} -12.1230 q^{71} +(-3.05667 + 2.85394i) q^{72} +4.31271 q^{73} +(0.359945 - 0.623442i) q^{74} +(13.9325 + 2.07780i) q^{75} +(3.83043 + 6.63449i) q^{76} +(1.13530 + 1.96640i) q^{77} +(-1.69587 - 4.30130i) q^{78} +(-0.708348 + 1.22690i) q^{79} -8.29333 q^{80} +(0.616665 - 8.97885i) q^{81} -21.4859 q^{82} +(1.37840 - 2.38747i) q^{83} +(3.81784 + 9.68333i) q^{84} +(-10.3224 - 17.8790i) q^{85} +(7.71236 + 13.3582i) q^{86} +(-6.01119 - 0.896472i) q^{87} +(-0.696981 + 1.20721i) q^{88} +4.77116 q^{89} +(-17.1296 + 15.9935i) q^{90} -2.81179 q^{91} +(-7.83051 + 13.5628i) q^{92} +(2.70416 - 3.40176i) q^{93} +(9.37347 + 16.2353i) q^{94} +(5.24479 + 9.08424i) q^{95} +(8.32177 - 10.4686i) q^{96} +(1.27954 - 2.21624i) q^{97} -3.97578 q^{98} +(-0.676667 - 2.92269i) 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

Introduction

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