LMFDB - Embedded newform 11.5.d.a.2.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,5,Mod(2,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("11.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	11.d (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.13706959392$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 115x^{10} + 5030x^{8} + 102975x^{6} + 953170x^{4} + 2910655x^{2} + 73205 $ x^12 + 115x^10 + 5030x^8 + 102975x^6 + 953170x^4 + 2910655*x^2 + 73205
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			2.1
Root			$4.56289i$ of defining polynomial
Character	$\chi$	$=$	11.2
Dual form			11.5.d.a.6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.45760 - 1.77328i) q^{2} +(-10.4040 + 7.55891i) q^{3} +(13.6966 + 9.95117i) q^{4} +(-9.33639 - 28.7345i) q^{5} +(70.1847 - 22.8044i) q^{6} +(-33.6132 + 46.2646i) q^{7} +(-3.13669 - 4.31729i) q^{8} +(26.0747 - 80.2495i) q^{9} +O(q^{10})$	\(q+(-5.45760 - 1.77328i) q^{2} +(-10.4040 + 7.55891i) q^{3} +(13.6966 + 9.95117i) q^{4} +(-9.33639 - 28.7345i) q^{5} +(70.1847 - 22.8044i) q^{6} +(-33.6132 + 46.2646i) q^{7} +(-3.13669 - 4.31729i) q^{8} +(26.0747 - 80.2495i) q^{9} +173.377i q^{10} +(-104.338 - 61.2750i) q^{11} -217.719 q^{12} +(-21.1866 - 6.88395i) q^{13} +(265.488 - 192.888i) q^{14} +(314.337 + 228.379i) q^{15} +(-74.2432 - 228.497i) q^{16} +(-176.460 + 57.3353i) q^{17} +(-284.610 + 391.732i) q^{18} +(169.409 + 233.171i) q^{19} +(158.065 - 486.473i) q^{20} -735.413i q^{21} +(460.776 + 519.435i) q^{22} -116.578 q^{23} +(65.2680 + 21.2068i) q^{24} +(-232.866 + 169.187i) q^{25} +(103.421 + 75.1398i) q^{26} +(13.4294 + 41.3314i) q^{27} +(-920.774 + 299.177i) q^{28} +(-419.150 + 576.911i) q^{29} +(-1310.54 - 1803.81i) q^{30} +(-28.3476 + 87.2449i) q^{31} +1464.08i q^{32} +(1548.70 - 151.178i) q^{33} +1064.72 q^{34} +(1643.21 + 533.913i) q^{35} +(1155.71 - 839.673i) q^{36} +(-1024.49 - 744.333i) q^{37} +(-511.087 - 1572.96i) q^{38} +(272.460 - 88.5276i) q^{39} +(-94.7695 + 130.439i) q^{40} +(340.375 + 468.486i) q^{41} +(-1304.10 + 4013.59i) q^{42} -1410.60i q^{43} +(-819.316 - 1877.54i) q^{44} -2549.37 q^{45} +(636.236 + 206.726i) q^{46} +(-3360.07 + 2441.23i) q^{47} +(2499.61 + 1816.07i) q^{48} +(-268.615 - 826.712i) q^{49} +(1570.90 - 510.418i) q^{50} +(1402.49 - 1930.36i) q^{51} +(-221.682 - 305.119i) q^{52} +(1136.82 - 3498.77i) q^{53} -249.385i q^{54} +(-786.566 + 3570.18i) q^{55} +305.172 q^{56} +(-3525.04 - 1145.35i) q^{57} +(3310.58 - 2405.28i) q^{58} +(-378.655 - 275.109i) q^{59} +(2032.71 + 6256.04i) q^{60} +(777.208 - 252.530i) q^{61} +(309.420 - 425.880i) q^{62} +(2836.26 + 3903.77i) q^{63} +(1408.34 - 4334.43i) q^{64} +673.058i q^{65} +(-8720.26 - 1921.21i) q^{66} +6019.75 q^{67} +(-2987.45 - 970.683i) q^{68} +(1212.87 - 881.203i) q^{69} +(-8021.23 - 5827.76i) q^{70} +(1149.19 + 3536.85i) q^{71} +(-428.248 + 139.146i) q^{72} +(-1264.79 + 1740.83i) q^{73} +(4271.33 + 5878.98i) q^{74} +(1143.85 - 3520.42i) q^{75} +4879.47i q^{76} +(6341.99 - 2767.50i) q^{77} -1643.96 q^{78} +(-10376.9 - 3371.66i) q^{79} +(-5872.58 + 4266.68i) q^{80} +(5077.27 + 3688.85i) q^{81} +(-1026.87 - 3160.39i) q^{82} +(-4239.31 + 1377.44i) q^{83} +(7318.23 - 10072.7i) q^{84} +(3295.00 + 4535.17i) q^{85} +(-2501.39 + 7698.50i) q^{86} -9170.47i q^{87} +(62.7337 + 642.657i) q^{88} -1587.53 q^{89} +(13913.5 + 4520.75i) q^{90} +(1030.63 - 748.799i) q^{91} +(-1596.72 - 1160.09i) q^{92} +(-364.550 - 1121.97i) q^{93} +(22666.9 - 7364.92i) q^{94} +(5118.38 - 7044.84i) q^{95} +(-11066.9 - 15232.3i) q^{96} +(-5788.35 + 17814.7i) q^{97} +4988.20i q^{98} +(-7637.86 + 6775.33i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 5 q^{2} - 6 q^{3} + 7 q^{4} - 18 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} + q^{9}+O(q^{10}) $ 12 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 - 18 * q^5 + 75 * q^6 - 80 * q^7 - 245 * q^8 + q^9	\( 12 q - 5 q^{2} - 6 q^{3} + 7 q^{4} - 18 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} + q^{9} - 43 q^{11} + 594 q^{12} + 250 q^{13} + 610 q^{14} + 1134 q^{15} - 633 q^{16} - 1250 q^{17} - 3150 q^{18} - 1025 q^{19} + 752 q^{20} - 35 q^{22} + 1684 q^{23} + 5345 q^{24} + 197 q^{25} + 3490 q^{26} - 687 q^{27} - 3580 q^{28} - 2690 q^{29} - 6740 q^{30} - 1136 q^{31} + 5939 q^{33} + 2370 q^{34} + 3610 q^{35} - 514 q^{36} - 336 q^{37} + 1900 q^{38} - 6880 q^{39} - 2340 q^{40} - 4550 q^{41} + 1310 q^{42} - 6268 q^{44} + 5136 q^{45} + 4150 q^{46} + 24 q^{47} + 344 q^{48} + 827 q^{49} + 8895 q^{50} + 13155 q^{51} + 14070 q^{52} + 414 q^{53} - 2738 q^{55} - 21340 q^{56} - 26925 q^{57} + 2980 q^{58} - 10011 q^{59} - 6856 q^{60} + 9460 q^{61} - 6200 q^{62} + 9150 q^{63} - 2633 q^{64} - 3210 q^{66} + 12154 q^{67} - 9400 q^{68} - 9022 q^{69} - 9380 q^{70} + 17574 q^{71} + 43045 q^{72} + 27950 q^{73} + 43270 q^{74} - 1761 q^{75} + 4090 q^{77} - 42920 q^{78} - 41540 q^{79} - 2308 q^{80} - 21080 q^{81} - 28175 q^{82} - 18665 q^{83} + 26250 q^{84} - 4230 q^{85} - 10125 q^{86} - 15125 q^{88} + 5554 q^{89} + 18400 q^{90} + 7390 q^{91} + 3904 q^{92} + 36898 q^{93} + 18920 q^{94} + 14110 q^{95} - 21140 q^{96} + 20769 q^{97} - 3269 q^{99}+O(q^{100}) \) 12 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 - 18 * q^5 + 75 * q^6 - 80 * q^7 - 245 * q^8 + q^9 - 43 * q^11 + 594 * q^12 + 250 * q^13 + 610 * q^14 + 1134 * q^15 - 633 * q^16 - 1250 * q^17 - 3150 * q^18 - 1025 * q^19 + 752 * q^20 - 35 * q^22 + 1684 * q^23 + 5345 * q^24 + 197 * q^25 + 3490 * q^26 - 687 * q^27 - 3580 * q^28 - 2690 * q^29 - 6740 * q^30 - 1136 * q^31 + 5939 * q^33 + 2370 * q^34 + 3610 * q^35 - 514 * q^36 - 336 * q^37 + 1900 * q^38 - 6880 * q^39 - 2340 * q^40 - 4550 * q^41 + 1310 * q^42 - 6268 * q^44 + 5136 * q^45 + 4150 * q^46 + 24 * q^47 + 344 * q^48 + 827 * q^49 + 8895 * q^50 + 13155 * q^51 + 14070 * q^52 + 414 * q^53 - 2738 * q^55 - 21340 * q^56 - 26925 * q^57 + 2980 * q^58 - 10011 * q^59 - 6856 * q^60 + 9460 * q^61 - 6200 * q^62 + 9150 * q^63 - 2633 * q^64 - 3210 * q^66 + 12154 * q^67 - 9400 * q^68 - 9022 * q^69 - 9380 * q^70 + 17574 * q^71 + 43045 * q^72 + 27950 * q^73 + 43270 * q^74 - 1761 * q^75 + 4090 * q^77 - 42920 * q^78 - 41540 * q^79 - 2308 * q^80 - 21080 * q^81 - 28175 * q^82 - 18665 * q^83 + 26250 * q^84 - 4230 * q^85 - 10125 * q^86 - 15125 * q^88 + 5554 * q^89 + 18400 * q^90 + 7390 * q^91 + 3904 * q^92 + 36898 * q^93 + 18920 * q^94 + 14110 * q^95 - 21140 * q^96 + 20769 * q^97 - 3269 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−5.45760	−	1.77328i	−1.36440	−	0.443321i	−0.466891	−	0.884315i	$-0.654626\pi$
$2$	−5.45760	−	1.77328i	−1.36440	−	0.443321i	−0.897510	+	0.440995i	$0.854626\pi$
$3$	−10.4040	+	7.55891i	−1.15599	+	0.839879i	−0.989266	−	0.146124i	$-0.953320\pi$
$3$	−10.4040	+	7.55891i	−1.15599	+	0.839879i	−0.166728	+	0.986003i	$0.553320\pi$
$4$	13.6966	+	9.95117i	0.856038	+	0.621948i
$5$	−9.33639	−	28.7345i	−0.373456	−	1.14938i	−0.944515	−	0.328470i	$-0.893467\pi$
$5$	−9.33639	−	28.7345i	−0.373456	−	1.14938i	0.571059	−	0.820909i	$-0.306533\pi$
$6$	70.1847	−	22.8044i	1.94958	−	0.633455i
$7$	−33.6132	+	46.2646i	−0.685983	+	0.944175i	−0.999986	−	0.00524700i	$-0.998330\pi$
$7$	−33.6132	+	46.2646i	−0.685983	+	0.944175i	0.314003	+	0.949422i	$0.398330\pi$
$8$	−3.13669	−	4.31729i	−0.0490108	−	0.0674576i
$9$	26.0747	−	80.2495i	0.321909	−	0.990735i
$10$			173.377i			1.73377i
$11$	−104.338	−	61.2750i	−0.862296	−	0.506405i
$11$	−104.338	−	61.2750i	−0.862296	−	0.506405i
$12$	−217.719			−1.51194
$13$	−21.1866	−	6.88395i	−0.125365	−	0.0407335i	0.245663	−	0.969355i	$-0.420994\pi$
$13$	−21.1866	−	6.88395i	−0.125365	−	0.0407335i	−0.371027	+	0.928622i	$0.620994\pi$
$14$	265.488	−	192.888i	1.35453	−	0.984122i
$15$	314.337	+	228.379i	1.39705	+	1.01502i
$16$	−74.2432	−	228.497i	−0.290013	−	0.892567i
$17$	−176.460	+	57.3353i	−0.610587	+	0.198392i	−0.597957	−	0.801528i	$-0.704021\pi$
$17$	−176.460	+	57.3353i	−0.610587	+	0.198392i	−0.0126306	+	0.999920i	$0.504021\pi$
$18$	−284.610	+	391.732i	−0.878426	+	1.20905i
$19$	169.409	+	233.171i	0.469276	+	0.645903i	0.976400	−	0.215970i	$-0.0692914\pi$
$19$	169.409	+	233.171i	0.469276	+	0.645903i	−0.507124	+	0.861873i	$0.669291\pi$
$20$	158.065	−	486.473i	0.395162	−	1.21618i
$21$		−	735.413i		−	1.66760i
$22$	460.776	+	519.435i	0.952017	+	1.07321i
$23$	−116.578			−0.220374			−0.110187	−	0.993911i	$-0.535145\pi$
$23$	−116.578			−0.220374			−0.110187	+	0.993911i	$0.535145\pi$
$24$	65.2680	+	21.2068i	0.113312	+	0.0368174i
$25$	−232.866	+	169.187i	−0.372585	+	0.270699i
$26$	103.421	+	75.1398i	0.152990	+	0.111153i
$27$	13.4294	+	41.3314i	0.0184217	+	0.0566961i
$28$	−920.774	+	299.177i	−1.17446	+	0.381604i
$29$	−419.150	+	576.911i	−0.498395	+	0.685982i	−0.981909	−	0.189355i	$-0.939360\pi$
$29$	−419.150	+	576.911i	−0.498395	+	0.685982i	0.483514	+	0.875337i	$0.339360\pi$
$30$	−1310.54	−	1803.81i	−1.45616	−	2.00423i
$31$	−28.3476	+	87.2449i	−0.0294980	+	0.0907855i	−0.964722	−	0.263272i	$-0.915198\pi$
$31$	−28.3476	+	87.2449i	−0.0294980	+	0.0907855i	0.935224	+	0.354058i	$0.115198\pi$
$32$			1464.08i			1.42977i
$33$	1548.70	−	151.178i	1.42213	−	0.138823i
$34$	1064.72			0.921037
$35$	1643.21	+	533.913i	1.34140	+	0.435847i
$36$	1155.71	−	839.673i	0.891753	−	0.647896i
$37$	−1024.49	−	744.333i	−0.748347	−	0.543706i	0.146967	−	0.989141i	$-0.453049\pi$
$37$	−1024.49	−	744.333i	−0.748347	−	0.543706i	−0.895314	+	0.445436i	$0.853049\pi$
$38$	−511.087	−	1572.96i	−0.353938	−	1.08931i
$39$	272.460	−	88.5276i	0.179132	−	0.0582035i
$40$	−94.7695	+	130.439i	−0.0592309	+	0.0815244i
$41$	340.375	+	468.486i	0.202484	+	0.278695i	0.898168	−	0.439653i	$-0.144899\pi$
$41$	340.375	+	468.486i	0.202484	+	0.278695i	−0.695684	+	0.718348i	$0.744899\pi$
$42$	−1304.10	+	4013.59i	−0.739283	+	2.27528i
$43$		−	1410.60i		−	0.762899i	−0.924390	−	0.381450i	$-0.875425\pi$
$43$		−	1410.60i		−	0.762899i	0.924390	−	0.381450i	$-0.124575\pi$
$44$	−819.316	−	1877.54i	−0.423201	−	0.969805i
$45$	−2549.37			−1.25895
$46$	636.236	+	206.726i	0.300679	+	0.0976964i
$47$	−3360.07	+	2441.23i	−1.52108	+	1.10513i	−0.560132	+	0.828404i	$0.689249\pi$
$47$	−3360.07	+	2441.23i	−1.52108	+	1.10513i	−0.960949	+	0.276726i	$0.910751\pi$
$48$	2499.61	+	1816.07i	1.08490	+	0.788227i
$49$	−268.615	−	826.712i	−0.111876	−	0.344320i
$50$	1570.90	−	510.418i	0.628362	−	0.204167i
$51$	1402.49	−	1930.36i	0.539210	−	0.742160i
$52$	−221.682	−	305.119i	−0.0819829	−	0.112840i
$53$	1136.82	−	3498.77i	0.404706	−	1.24556i	−0.516435	−	0.856327i	$-0.672741\pi$
$53$	1136.82	−	3498.77i	0.404706	−	1.24556i	0.921141	−	0.389230i	$-0.127259\pi$
$54$		−	249.385i		−	0.0855228i
$55$	−786.566	+	3570.18i	−0.260022	+	1.18022i
$56$	305.172			0.0973124
$57$	−3525.04	−	1145.35i	−1.08496	−	0.352525i
$58$	3310.58	−	2405.28i	0.984120	−	0.715005i
$59$	−378.655	−	275.109i	−0.108778	−	0.0790315i	0.532067	−	0.846702i	$-0.321416\pi$
$59$	−378.655	−	275.109i	−0.108778	−	0.0790315i	−0.640844	+	0.767671i	$0.721416\pi$
$60$	2032.71	+	6256.04i	0.564642	+	1.73779i
$61$	777.208	−	252.530i	0.208871	−	0.0678662i	−0.202713	−	0.979238i	$-0.564976\pi$
$61$	777.208	−	252.530i	0.208871	−	0.0678662i	0.411584	+	0.911372i	$0.364976\pi$
$62$	309.420	−	425.880i	0.0804942	−	0.110791i
$63$	2836.26	+	3903.77i	0.714603	+	0.983566i
$64$	1408.34	−	4334.43i	0.343834	−	1.05821i
$65$			673.058i			0.159304i
$66$	−8720.26	−	1921.21i	−2.00190	−	0.441049i
$67$	6019.75			1.34100			0.670500	−	0.741909i	$-0.266080\pi$
$67$	6019.75			1.34100			0.670500	+	0.741909i	$0.266080\pi$
$68$	−2987.45	−	970.683i	−0.646076	−	0.209923i
$69$	1212.87	−	881.203i	0.254751	−	0.185088i
$70$	−8021.23	−	5827.76i	−1.63699	−	1.18934i
$71$	1149.19	+	3536.85i	0.227969	+	0.701617i	0.997977	+	0.0635821i	$0.0202525\pi$
$71$	1149.19	+	3536.85i	0.227969	+	0.701617i	−0.770007	+	0.638035i	$0.779748\pi$
$72$	−428.248	+	139.146i	−0.0826096	+	0.0268415i
$73$	−1264.79	+	1740.83i	−0.237340	+	0.326671i	−0.911027	−	0.412346i	$-0.864710\pi$
$73$	−1264.79	+	1740.83i	−0.237340	+	0.326671i	0.673687	+	0.739017i	$0.264710\pi$
$74$	4271.33	+	5878.98i	0.780009	+	1.07359i
$75$	1143.85	−	3520.42i	0.203352	−	0.625853i
$76$			4879.47i			0.844783i
$77$	6341.99	−	2767.50i	1.06966	−	0.466773i
$78$	−1643.96			−0.270211
$79$	−10376.9	−	3371.66i	−1.66270	−	0.540243i	−0.681263	−	0.732039i	$-0.738569\pi$
$79$	−10376.9	−	3371.66i	−1.66270	−	0.540243i	−0.981435	+	0.191796i	$0.938569\pi$
$80$	−5872.58	+	4266.68i	−0.917590	+	0.666668i
$81$	5077.27	+	3688.85i	0.773856	+	0.562240i
$82$	−1026.87	−	3160.39i	−0.152718	−	0.470016i
$83$	−4239.31	+	1377.44i	−0.615374	+	0.199947i	−0.600085	−	0.799936i	$-0.704867\pi$
$83$	−4239.31	+	1377.44i	−0.615374	+	0.199947i	−0.0152885	+	0.999883i	$0.504867\pi$
$84$	7318.23	−	10072.7i	1.03716	−	1.42753i
$85$	3295.00	+	4535.17i	0.456055	+	0.627706i
$86$	−2501.39	+	7698.50i	−0.338209	+	1.04090i
$87$		−	9170.47i		−	1.21158i
$88$	62.7337	+	642.657i	0.00810095	+	0.0829877i
$89$	−1587.53			−0.200421			−0.100210	−	0.994966i	$-0.531952\pi$
$89$	−1587.53			−0.200421			−0.100210	+	0.994966i	$0.531952\pi$
$90$	13913.5	+	4520.75i	1.71771	+	0.558118i
$91$	1030.63	−	748.799i	0.124458	−	0.0904237i
$92$	−1596.72	−	1160.09i	−0.188649	−	0.137061i
$93$	−364.550	−	1121.97i	−0.0421493	−	0.129722i
$94$	22666.9	−	7364.92i	2.56529	−	0.833513i
$95$	5118.38	−	7044.84i	0.567133	−	0.780592i
$96$	−11066.9	−	15232.3i	−1.20083	−	1.65281i
$97$	−5788.35	+	17814.7i	−0.615193	+	1.89337i	−0.216511	+	0.976280i	$0.569468\pi$
$97$	−5788.35	+	17814.7i	−0.615193	+	1.89337i	−0.398682	+	0.917089i	$0.630532\pi$
$98$			4988.20i			0.519388i
$99$	−7637.86	+	6775.33i	−0.779294	+	0.691290i
$100$	−4873.08			−0.487308
$101$	7465.74	+	2425.77i	0.731863	+	0.237797i	0.651159	−	0.758941i	$-0.274283\pi$
$101$	7465.74	+	2425.77i	0.731863	+	0.237797i	0.0807044	+	0.996738i	$0.474283\pi$
$102$	−11077.3	+	8048.12i	−1.06471	+	0.773560i
$103$	−7326.15	−	5322.76i	−0.690560	−	0.501721i	0.186284	−	0.982496i	$-0.440355\pi$
$103$	−7326.15	−	5322.76i	−0.690560	−	0.501721i	−0.876844	+	0.480775i	$0.840355\pi$
$104$	36.7359	+	113.062i	0.00339644	+	0.0104532i
$105$	−21131.7	+	6866.11i	−1.91671	+	0.622776i
$106$	−12408.6	+	17079.0i	−1.10436	+	1.52002i
$107$	−11716.3	−	16126.1i	−1.02335	−	1.40852i	−0.909828	−	0.414984i	$-0.863787\pi$
$107$	−11716.3	−	16126.1i	−1.02335	−	1.40852i	−0.113521	−	0.993536i	$-0.536213\pi$
$108$	−227.359	+	699.739i	−0.0194924	+	0.0599913i
$109$		−	4222.52i		−	0.355401i	−0.984085	−	0.177701i	$-0.943134\pi$
$109$		−	4222.52i		−	0.355401i	0.984085	−	0.177701i	$-0.0568659\pi$
$110$	10623.7	−	18089.8i	0.877992	−	1.49503i
$111$	16285.1			1.32173
$112$	13066.9	+	4245.68i	1.04168	+	0.338463i
$113$	17666.0	−	12835.1i	1.38351	−	1.00518i	0.386964	−	0.922095i	$-0.373524\pi$
$113$	17666.0	−	12835.1i	1.38351	−	1.00518i	0.996543	−	0.0830819i	$-0.0264763\pi$
$114$	17207.2	+	12501.8i	1.32404	+	0.961971i
$115$	1088.42	+	3349.81i	0.0823000	+	0.253293i
$116$	−11481.9	+	3730.69i	−0.853290	+	0.277251i
$117$	−1104.87	+	1520.72i	−0.0807121	+	0.111091i
$118$	1578.70	+	2172.89i	0.113380	+	0.156054i
$119$	3278.78	−	10091.1i	0.231536	−	0.712595i
$120$		−	2073.44i		−	0.143989i
$121$	7131.75	+	12786.6i	0.487108	+	0.873342i
$122$	−4689.50			−0.315070
$123$	−7082.49	−	2301.24i	−0.468140	−	0.152108i
$124$	−1256.45	+	912.868i	−0.0817153	+	0.0593697i
$125$	−8241.25	−	5987.62i	−0.527440	−	0.383208i
$126$	−8556.67	−	26334.7i	−0.538969	−	1.65878i
$127$	9018.65	−	2930.34i	0.559158	−	0.181681i	−0.0157845	−	0.999875i	$-0.505025\pi$
$127$	9018.65	−	2930.34i	0.559158	−	0.181681i	0.574942	+	0.818194i	$0.305025\pi$
$128$	−1603.27	+	2206.72i	−0.0978560	+	0.134687i
$129$	10662.6	+	14675.8i	0.640743	+	0.881907i
$130$	1193.52	−	3673.28i	0.0706226	−	0.217354i
$131$			17154.3i			0.999608i	0.866138	+	0.499804i	$0.166595\pi$
$131$			17154.3i			0.999608i	−0.866138	+	0.499804i	$0.833405\pi$
$132$	22716.3	+	13340.7i	1.30374	+	0.765653i
$133$	−16481.9			−0.931761
$134$	−32853.4	−	10674.7i	−1.82966	−	0.594493i
$135$	1062.25	−	771.773i	0.0582856	−	0.0423469i
$136$	801.032	+	581.984i	0.0433084	+	0.0314654i
$137$	2623.40	+	8073.99i	0.139773	+	0.430177i	0.996302	−	0.0859221i	$-0.0273836\pi$
$137$	2623.40	+	8073.99i	0.139773	+	0.430177i	−0.856529	+	0.516099i	$0.827384\pi$
$138$	−8181.99	+	2658.49i	−0.429636	+	0.139597i
$139$	−15617.1	+	21495.1i	−0.808298	+	1.11253i	0.183286	+	0.983060i	$0.441327\pi$
$139$	−15617.1	+	21495.1i	−0.808298	+	1.11253i	−0.991584	+	0.129467i	$0.958673\pi$
$140$	17193.4	+	23664.7i	0.877215	+	1.20738i
$141$	16504.9	−	50796.9i	0.830185	−	2.55505i
$142$		−	21340.6i		−	1.05835i
$143$	1788.75	+	2016.47i	0.0874738	+	0.0986096i
$144$	−20272.7			−0.977655
$145$	20490.6	+	6657.79i	0.974581	+	0.316661i
$146$	9989.69	−	7257.93i	0.468647	−	0.340492i
$147$	9043.71	+	6570.64i	0.418516	+	0.304069i
$148$	−6625.01	−	20389.7i	−0.302457	−	0.930866i
$149$	−24565.5	+	7981.82i	−1.10650	+	0.359525i	−0.804602	−	0.593814i	$-0.797622\pi$
$149$	−24565.5	+	7981.82i	−1.10650	+	0.359525i	−0.301902	+	0.953339i	$0.597622\pi$
$150$	−12485.4	+	17184.7i	−0.554907	+	0.763764i
$151$	−16028.5	−	22061.3i	−0.702972	−	0.967558i	−0.999920	−	0.0126640i	$-0.995969\pi$
$151$	−16028.5	−	22061.3i	−0.702972	−	0.967558i	0.296948	−	0.954894i	$-0.404031\pi$
$152$	475.283	−	1462.77i	0.0205715	−	0.0633124i
$153$			15655.8i			0.668794i
$154$	−39519.6	+	3857.75i	−1.66637	+	0.162665i
$155$	2771.60			0.115363
$156$	4612.73	+	1498.77i	0.189544	+	0.0615864i
$157$	14248.6	−	10352.2i	0.578061	−	0.419986i	−0.259964	−	0.965618i	$-0.583711\pi$
$157$	14248.6	−	10352.2i	0.578061	−	0.419986i	0.838024	+	0.545633i	$0.183711\pi$
$158$	50654.1	+	36802.3i	2.02908	+	1.47422i
$159$	14619.5	+	44994.1i	0.578279	+	1.77976i
$160$	42069.7	−	13669.3i	1.64335	−	0.533956i
$161$	3918.56	−	5393.43i	0.151173	−	0.208072i
$162$	−21168.3	−	29135.7i	−0.806598	−	1.11019i
$163$	−1901.28	+	5851.55i	−0.0715602	+	0.220240i	−0.980440	−	0.196819i	$-0.936939\pi$
$163$	−1901.28	+	5851.55i	−0.0715602	+	0.220240i	0.908880	+	0.417058i	$0.136939\pi$
$164$			9803.80i			0.364508i
$165$	−18803.3	−	43089.5i	−0.690662	−	1.58272i
$166$	25579.0			0.928257
$167$	−3697.07	−	1201.25i	−0.132564	−	0.0430726i	0.241984	−	0.970280i	$-0.422202\pi$
$167$	−3697.07	−	1201.25i	−0.132564	−	0.0430726i	−0.374548	+	0.927208i	$0.622202\pi$
$168$	−3174.99	+	2306.77i	−0.112493	+	0.0817306i
$169$	−22704.8	−	16496.0i	−0.794960	−	0.577572i
$170$	−9940.63	−	30594.1i	−0.343967	−	1.05862i
$171$	23129.1	−	7515.11i	0.790983	−	0.257006i
$172$	14037.1	−	19320.5i	0.474484	−	0.653071i
$173$	18847.1	+	25940.8i	0.629728	+	0.866746i	0.998016	−	0.0629660i	$-0.0200560\pi$
$173$	18847.1	+	25940.8i	0.629728	+	0.866746i	−0.368288	+	0.929712i	$0.620056\pi$
$174$	−16261.8	+	50048.8i	−0.537119	+	1.65308i
$175$		−	16460.3i		−	0.537480i
$176$	−6254.79	+	28390.1i	−0.201924	+	0.916520i
$177$	6019.03			0.192123
$178$	8664.11	+	2815.14i	0.273454	+	0.0888505i
$179$	−6636.09	+	4821.40i	−0.207112	+	0.150476i	−0.686506	−	0.727124i	$-0.740857\pi$
$179$	−6636.09	+	4821.40i	−0.207112	+	0.150476i	0.479394	+	0.877600i	$0.340857\pi$
$180$	−34917.7	−	25369.2i	−1.07771	−	0.783001i
$181$	−7947.12	−	24458.7i	−0.242579	−	0.746581i	−0.996025	−	0.0890713i	$-0.971610\pi$
$181$	−7947.12	−	24458.7i	−0.242579	−	0.746581i	0.753447	−	0.657509i	$-0.228390\pi$
$182$	−6952.62	+	2259.04i	−0.209897	+	0.0681996i
$183$	−6177.18	+	8502.16i	−0.184454	+	0.253879i
$184$	365.669	+	503.300i	0.0108007	+	0.0148659i
$185$	−11823.0	+	36387.5i	−0.345449	+	1.06318i
$186$			6769.71i			0.195679i
$187$	21924.6	+	4830.34i	0.626974	+	0.138132i
$188$	−70314.7			−1.98944
$189$	−2363.59	−	767.976i	−0.0661680	−	0.0214993i
$190$	−40426.5	+	29371.6i	−1.11985	+	0.813618i
$191$	−1824.03	−	1325.24i	−0.0499995	−	0.0363268i	0.562505	−	0.826794i	$-0.309838\pi$
$191$	−1824.03	−	1325.24i	−0.0499995	−	0.0363268i	−0.612504	+	0.790467i	$0.709838\pi$
$192$	18111.3	+	55740.8i	0.491300	+	1.51206i
$193$	−19901.9	+	6466.53i	−0.534294	+	0.173603i	−0.563723	−	0.825964i	$-0.690631\pi$
$193$	−19901.9	+	6466.53i	−0.534294	+	0.173603i	0.0294283	+	0.999567i	$0.490631\pi$
$194$	63181.0	−	86961.2i	1.67874	−	2.31059i
$195$	−5087.59	−	7002.46i	−0.133796	−	0.184154i
$196$	4547.64	−	13996.2i	0.118379	−	0.364333i
$197$		−	1677.35i		−	0.0432208i	−0.999766	−	0.0216104i	$-0.993121\pi$
$197$		−	1677.35i		−	0.0432208i	0.999766	−	0.0216104i	$-0.00687933\pi$
$198$	53699.0	−	23433.0i	1.36973	−	0.597719i
$199$	44006.7			1.11125			0.555626	−	0.831433i	$-0.312479\pi$
$199$	44006.7			1.11125			0.555626	+	0.831433i	$0.312479\pi$
$200$	1460.86	+	474.661i	0.0365214	+	0.0118665i
$201$	−62629.2	+	45502.8i	−1.55019	+	1.12628i
$202$	−36443.5	−	26477.7i	−0.893135	−	0.648900i
$203$	−12601.6	−	38783.6i	−0.305796	−	0.941144i
$204$	38418.6	−	12483.0i	0.923170	−	0.299956i
$205$	10283.8	−	14154.5i	0.244707	−	0.336810i
$206$	30544.5	+	42040.8i	0.719777	+	0.990688i
$207$	−3039.73	+	9355.33i	−0.0709405	+	0.218332i
$208$			5352.17i			0.123710i
$209$	−3388.17	−	34709.0i	−0.0775661	−	0.794603i
$210$	127504.			2.89125
$211$	7885.34	+	2562.10i	0.177115	+	0.0575482i	0.396232	−	0.918150i	$-0.370318\pi$
$211$	7885.34	+	2562.10i	0.177115	+	0.0575482i	−0.219117	+	0.975699i	$0.570318\pi$
$212$	50387.4	−	36608.6i	1.12112	−	0.814538i
$213$	−38690.9	−	28110.6i	−0.852805	−	0.619599i
$214$	35346.9	+	108786.i	0.771833	+	2.37546i
$215$	−40532.9	+	13169.9i	−0.876860	+	0.284909i
$216$	136.316	−	187.623i	0.00292172	−	0.00402140i
$217$	−3083.50	−	4244.07i	−0.0654823	−	0.0901286i
$218$	−7487.72	+	23044.8i	−0.157557	+	0.484910i
$219$		−	27671.9i		−	0.576967i
$220$	−46300.7	+	41072.1i	−0.956627	+	0.848597i
$221$	4133.28			0.0846273
$222$	−88877.4	−	28878.0i	−1.80337	−	0.585951i
$223$	36171.7	−	26280.3i	0.727377	−	0.528470i	−0.161356	−	0.986896i	$-0.551587\pi$
$223$	36171.7	−	26280.3i	0.727377	−	0.528470i	0.888733	+	0.458426i	$0.151587\pi$
$224$	−67735.2	−	49212.5i	−1.34995	−	0.980798i
$225$	7505.27	+	23098.9i	0.148252	+	0.456274i
$226$	−119174.	+	38722.1i	−2.33327	+	0.758126i
$227$	−9262.91	+	12749.3i	−0.179761	+	0.247420i	−0.889383	−	0.457163i	$-0.848866\pi$
$227$	−9262.91	+	12749.3i	−0.179761	+	0.247420i	0.709622	+	0.704583i	$0.248866\pi$
$228$	−36883.5	−	50765.7i	−0.709515	−	0.976564i
$229$	−126.968	+	390.768i	−0.00242117	+	0.00745158i	−0.952260	−	0.305289i	$-0.901247\pi$
$229$	−126.968	+	390.768i	−0.00242117	+	0.00745158i	0.949839	+	0.312740i	$0.101247\pi$
$230$		−	20212.0i		−	0.382079i
$231$	−45062.5	+	76731.4i	−0.844483	+	1.43797i
$232$	3805.43			0.0707014
$233$	59733.7	+	19408.6i	1.10029	+	0.357506i	0.802214	−	0.597036i	$-0.203655\pi$
$233$	59733.7	+	19408.6i	1.10029	+	0.357506i	0.298076	+	0.954542i	$0.403655\pi$
$234$	8726.60	−	6340.24i	0.159372	−	0.115791i
$235$	101518.	+	73757.4i	1.83827	+	1.33558i
$236$	−2448.63	−	7536.11i	−0.0439642	−	0.135308i
$237$	133447.	−	43359.5i	2.37581	−	0.771947i
$238$	−35788.6	+	49258.8i	−0.631816	+	0.869620i
$239$	11060.1	+	15222.9i	0.193626	+	0.266503i	0.894781	−	0.446506i	$-0.147332\pi$
$239$	11060.1	+	15222.9i	0.193626	+	0.266503i	−0.701155	+	0.713009i	$0.747332\pi$
$240$	28846.6	−	88780.6i	0.500809	−	1.54133i
$241$		−	52220.3i		−	0.899094i	−0.893257	−	0.449547i	$-0.851585\pi$
$241$		−	52220.3i		−	0.899094i	0.893257	−	0.449547i	$-0.148415\pi$
$242$	−16248.0	−	82430.8i	−0.277440	−	1.40753i
$243$	−84227.5			−1.42640
$244$	13158.1	+	4275.32i	0.221011	+	0.0718107i
$245$	−21247.2	+	15437.0i	−0.353973	+	0.257177i
$246$	34572.6	+	25118.5i	0.571298	+	0.415072i
$247$	−1984.06	−	6106.31i	−0.0325208	−	0.100089i
$248$	465.579	−	151.276i	0.00756989	−	0.00245961i
$249$	33693.7	−	46375.3i	0.543437	−	0.747977i
$250$	34359.7	+	47292.1i	0.549756	+	0.756674i
$251$	−11398.1	+	35079.8i	−0.180919	+	0.556813i	−0.999854	−	0.0170739i	$-0.994565\pi$
$251$	−11398.1	+	35079.8i	−0.180919	+	0.556813i	0.818935	+	0.573886i	$0.194565\pi$
$252$			81692.6i			1.28642i
$253$	12163.5	+	7143.32i	0.190028	+	0.111599i
$254$	−54416.5			−0.843458
$255$	−68561.9	−	22277.1i	−1.05439	−	0.342593i
$256$	−46330.2	+	33660.9i	−0.706943	+	0.513624i
$257$	23004.5	+	16713.8i	0.348295	+	0.253051i	0.748153	−	0.663526i	$-0.230941\pi$
$257$	23004.5	+	16713.8i	0.348295	+	0.253051i	−0.399859	+	0.916577i	$0.630941\pi$
$258$	−32167.9	−	99002.6i	−0.483263	−	1.48733i
$259$	68872.5	−	22378.0i	1.02671	−	0.333597i
$260$	−6697.71	+	9218.61i	−0.0990786	+	0.136370i
$261$	35367.6	+	48679.3i	0.519188	+	0.714601i
$262$	30419.4	−	93621.2i	0.443147	−	1.36387i
$263$			55993.0i			0.809510i	0.914425	+	0.404755i	$0.132643\pi$
$263$			55993.0i			0.809510i	−0.914425	+	0.404755i	$0.867357\pi$
$264$	−5510.47	−	6211.97i	−0.0790643	−	0.0891295i
$265$	−111149.			−1.58276
$266$	89951.7	+	29227.1i	1.27129	+	0.413069i
$267$	16516.6	−	12000.0i	0.231685	−	0.168329i
$268$	82450.2	+	59903.6i	1.14795	+	0.834033i
$269$	−9817.61	−	30215.5i	−0.135675	−	0.417566i	0.860019	−	0.510262i	$-0.170452\pi$
$269$	−9817.61	−	30215.5i	−0.135675	−	0.417566i	−0.995694	+	0.0926960i	$0.970452\pi$
$270$	−7165.93	+	2328.35i	−0.0982981	+	0.0319390i
$271$	46838.5	−	64467.6i	0.637770	−	0.877815i	−0.360724	−	0.932672i	$-0.617470\pi$
$271$	46838.5	−	64467.6i	0.637770	−	0.877815i	0.998494	+	0.0548576i	$0.0174705\pi$
$272$	26201.9	+	36063.8i	0.354156	+	0.487454i
$273$	−5062.55	+	15580.9i	−0.0679273	+	0.209059i
$274$		−	48716.7i		−	0.648898i
$275$	34663.6	−	3383.73i	0.458362	−	0.0447436i
$276$	25381.2			0.333192
$277$	−135986.	−	44184.7i	−1.77230	−	0.575854i	−0.773944	−	0.633254i	$-0.781719\pi$
$277$	−135986.	−	44184.7i	−1.77230	−	0.575854i	−0.998351	+	0.0574001i	$0.981719\pi$
$278$	123349.	−	89618.3i	1.59605	−	1.15960i
$279$	6262.21	+	4549.76i	0.0804487	+	0.0584494i
$280$	−2849.20	−	8768.94i	−0.0363419	−	0.111849i
$281$	29206.6	−	9489.80i	0.369886	−	0.120183i	−0.118175	−	0.992993i	$-0.537704\pi$
$281$	29206.6	−	9489.80i	0.369886	−	0.120183i	0.488061	+	0.872809i	$0.337704\pi$
$282$	−180155.	+	247961.i	−2.26541	+	3.11807i
$283$	−82477.7	−	113521.i	−1.02983	−	1.41743i	−0.905078	−	0.425245i	$-0.860188\pi$
$283$	−82477.7	−	113521.i	−1.02983	−	1.41743i	−0.124748	−	0.992188i	$-0.539812\pi$
$284$	−19455.8	+	59878.7i	−0.241219	+	0.742396i
$285$			111984.i			1.37868i
$286$	−6186.53	−	14177.0i	−0.0756336	−	0.173322i
$287$	−33115.4			−0.402037
$288$	117492.	+	38175.5i	1.41652	+	0.460256i
$289$	−39719.2	+	28857.7i	−0.475559	+	0.345514i
$290$	−100023.	−	72671.1i	−1.18934	−	0.864104i
$291$	−74438.1	−	229097.i	−0.879042	−	2.70541i
$292$	−34646.6	+	11257.4i	−0.406345	+	0.132030i
$293$	−75953.7	+	104541.i	−0.884736	+	1.21774i	0.0903501	+	0.995910i	$0.471201\pi$
$293$	−75953.7	+	104541.i	−0.884736	+	1.21774i	−0.975086	+	0.221825i	$0.928799\pi$
$294$	−37705.4	−	51897.0i	−0.436223	−	0.600409i
$295$	−4369.83	+	13449.0i	−0.0502135	+	0.154541i
$296$			6757.75i			0.0771291i
$297$	1131.39	−	5135.32i	0.0128262	−	0.0582176i
$298$	148223.			1.66910
$299$	2469.89	+	802.517i	0.0276271	+	0.00897660i
$300$	50699.3	−	36835.2i	0.563325	−	0.409280i
$301$	65260.8	+	47414.8i	0.720310	+	0.523336i
$302$	48356.1	+	148825.i	0.530197	+	1.63178i
$303$	−96009.3	+	31195.3i	−1.04575	+	0.339785i
$304$	40701.4	−	56020.7i	0.440415	−	0.606180i
$305$	−14512.6	−	19974.9i	−0.156008	−	0.214727i
$306$	27762.2	−	85443.2i	0.296490	−	0.912503i
$307$			109144.i			1.15804i	0.815314	+	0.579020i	$0.196565\pi$
$307$			109144.i			1.15804i	−0.815314	+	0.579020i	$0.803435\pi$
$308$	114404.	+	25204.9i	1.20597	+	0.265695i
$309$	116455.			1.21967
$310$	−15126.3	−	4914.83i	−0.157402	−	0.0511429i
$311$	−24253.7	+	17621.4i	−0.250760	+	0.182187i	−0.706063	−	0.708149i	$-0.749531\pi$
$311$	−24253.7	+	17621.4i	−0.250760	+	0.182187i	0.455304	+	0.890336i	$0.349531\pi$
$312$	−1236.82	−	898.603i	−0.0127057	−	0.00923121i
$313$	48065.9	+	147932.i	0.490623	+	1.50998i	0.823668	+	0.567072i	$0.191924\pi$
$313$	48065.9	+	147932.i	0.490623	+	1.50998i	−0.333045	+	0.942911i	$0.608076\pi$
$314$	−96120.7	+	31231.5i	−0.974894	+	0.316762i
$315$	85692.5	−	117946.i	0.863618	−	1.18867i
$316$	−108576.	−	149443.i	−1.08733	−	1.49658i
$317$	20369.3	−	62690.4i	0.202702	−	0.623853i	−0.797098	−	0.603850i	$-0.793632\pi$
$317$	20369.3	−	62690.4i	0.202702	−	0.623853i	0.999800	−	0.0200029i	$-0.00636756\pi$
$318$		−	271485.i		−	2.68467i
$319$	79083.4	−	34510.1i	0.777148	−	0.339129i
$320$	−137696.			−1.34469
$321$	243792.	+	79212.9i	2.36597	+	0.768751i
$322$	−30950.0	+	22486.5i	−0.298503	+	0.216875i
$323$	−43262.7	−	31432.2i	−0.414676	−	0.301280i
$324$	32833.0	+	101050.i	0.312767	+	0.962597i
$325$	6098.31	−	1981.46i	0.0577355	−	0.0187594i
$326$	20752.9	−	28563.9i	0.195274	−	0.268771i
$327$	31917.7	+	43930.9i	0.298494	+	0.410842i
$328$	954.936	−	2938.99i	0.00887619	−	0.0273181i
$329$		−	237510.i		−	2.19427i
$330$	26210.8	+	268509.i	0.240687	+	2.46565i
$331$	43362.4			0.395783			0.197891	−	0.980224i	$-0.436591\pi$
$331$	43362.4			0.395783			0.197891	+	0.980224i	$0.436591\pi$
$332$	−71771.3	−	23319.9i	−0.651140	−	0.211568i
$333$	−86445.5	+	62806.4i	−0.779568	+	0.566389i
$334$	18047.0	+	13111.9i	0.161775	+	0.117537i
$335$	−56202.8	−	172974.i	−0.500804	−	1.54132i
$336$	−168040.	+	54599.5i	−1.48845	+	0.483626i
$337$	−80558.5	+	110879.i	−0.709335	+	0.976316i	0.290476	+	0.956882i	$0.406186\pi$
$337$	−80558.5	+	110879.i	−0.709335	+	0.976316i	−0.999811	+	0.0194335i	$0.993814\pi$
$338$	94661.9	+	130291.i	0.828594	+	1.14046i
$339$	−86776.8	+	267072.i	−0.755100	+	2.32396i
$340$			94905.6i			0.820982i
$341$	8303.66	−	7365.94i	0.0714103	−	0.0633460i
$342$	−139556.			−1.19315
$343$	−83307.3	−	27068.2i	−0.708101	−	0.230076i
$344$	−6089.97	+	4424.62i	−0.0514633	+	0.0373903i
$345$	−36644.7	−	26624.0i	−0.307874	−	0.223684i
$346$	−56859.6	−	174996.i	−0.474954	−	1.46176i
$347$	87946.7	−	28575.6i	0.730399	−	0.237321i	0.0798733	−	0.996805i	$-0.474548\pi$
$347$	87946.7	−	28575.6i	0.730399	−	0.237321i	0.650526	+	0.759484i	$0.274548\pi$
$348$	91256.9	−	125604.i	0.753542	−	1.03716i
$349$	−55119.1	−	75865.0i	−0.452534	−	0.622860i	0.520405	−	0.853919i	$-0.325781\pi$
$349$	−55119.1	−	75865.0i	−0.452534	−	0.622860i	−0.972940	+	0.231059i	$0.925781\pi$
$350$	−29188.8	+	89834.0i	−0.238276	+	0.733339i
$351$		−	968.121i		−	0.00785806i
$352$	89711.7	−	152759.i	0.724042	−	1.23288i
$353$	44676.1			0.358530			0.179265	−	0.983801i	$-0.442628\pi$
$353$	44676.1			0.358530			0.179265	+	0.983801i	$0.442628\pi$
$354$	−32849.4	−	10673.4i	−0.262133	−	0.0851721i
$355$	90900.2	−	66042.9i	0.721287	−	0.524046i
$356$	−21743.8	−	15797.8i	−0.171568	−	0.124651i
$357$	42165.1	+	129771.i	0.330839	+	1.01822i
$358$	44766.8	−	14545.6i	0.349293	−	0.113492i
$359$	−13799.1	+	18992.8i	−0.107069	+	0.147367i	−0.859189	−	0.511659i	$-0.829031\pi$
$359$	−13799.1	+	18992.8i	−0.107069	+	0.147367i	0.752120	+	0.659026i	$0.229031\pi$
$360$	7996.59	+	11006.4i	0.0617021	+	0.0849256i
$361$	14602.0	−	44940.3i	0.112046	−	0.344843i
$362$			147578.i			1.12617i
$363$	−170851.	−	79122.9i	−1.29660	−	0.600467i
$364$	21567.6			0.162779
$365$	61830.4	+	20089.9i	0.464105	+	0.150797i
$366$	48789.3	−	35447.5i	0.364219	−	0.264621i
$367$	−13925.4	−	10117.4i	−0.103389	−	0.0751166i	0.534890	−	0.844922i	$-0.320353\pi$
$367$	−13925.4	−	10117.4i	−0.103389	−	0.0751166i	−0.638279	+	0.769805i	$0.720353\pi$
$368$	8655.12	+	26637.7i	0.0639113	+	0.196699i
$369$	46470.9	−	15099.3i	0.341294	−	0.110893i
$370$	129051.	−	177623.i	0.942663	−	1.29746i
$371$	123657.	+	170199.i	0.898402	+	1.23654i
$372$	6171.81	−	18994.9i	0.0445991	−	0.137262i
$373$			61718.8i			0.443609i	0.975091	+	0.221804i	$0.0711946\pi$
$373$			61718.8i			0.443609i	−0.975091	+	0.221804i	$0.928805\pi$
$374$	−111090.	−	65240.6i	−0.794206	−	0.466418i
$375$	131002.			0.931566
$376$	21079.0	+	6848.98i	0.149099	+	0.0484451i
$377$	12851.8	−	9337.38i	0.0904235	−	0.0656965i
$378$	11537.7	+	8382.61i	0.0807485	+	0.0586672i
$379$	57277.9	+	176283.i	0.398757	+	1.22725i	0.925997	+	0.377531i	$0.123227\pi$
$379$	57277.9	+	176283.i	0.398757	+	1.22725i	−0.527240	+	0.849717i	$0.676773\pi$
$380$	140209.	−	45556.6i	0.970975	−	0.315489i
$381$	−71679.4	+	98658.3i	−0.493793	+	0.679647i
$382$	7604.82	+	10467.1i	0.0521149	+	0.0717301i
$383$	41231.5	−	126898.i	0.281081	−	0.865079i	−0.706465	−	0.707748i	$-0.749711\pi$
$383$	41231.5	−	126898.i	0.281081	−	0.865079i	0.987546	−	0.157331i	$-0.0502888\pi$
$384$		−	35077.6i		−	0.237885i
$385$	−138734.	−	156395.i	−0.935968	−	1.05512i
$386$	120084.			0.805953
$387$	−113200.	−	36780.9i	−0.755831	−	0.245584i
$388$	−256558.	+	186400.i	−1.70421	+	1.23818i
$389$	−33845.2	−	24589.9i	−0.223665	−	0.162502i	0.470310	−	0.882501i	$-0.344142\pi$
$389$	−33845.2	−	24589.9i	−0.223665	−	0.162502i	−0.693975	+	0.719999i	$0.744142\pi$
$390$	15348.7	+	47238.4i	0.100912	+	0.310574i
$391$	20571.3	−	6684.03i	0.134558	−	0.0437205i
$392$	−2726.59	+	3752.83i	−0.0177438	+	0.0244223i
$393$	−129668.	−	178472.i	−0.839550	−	1.15554i
$394$	−2974.42	+	9154.33i	−0.0191607	+	0.0589704i
$395$			329654.i			2.11283i
$396$	−172035.	+	16793.4i	−1.09705	+	0.107090i
$397$	−195481.			−1.24029			−0.620147	−	0.784486i	$-0.712927\pi$
$397$	−195481.			−1.24029			−0.620147	+	0.784486i	$0.712927\pi$
$398$	−240171.	−	78036.2i	−1.51619	−	0.492641i
$399$	171477.	−	124585.i	1.07711	−	0.782566i
$400$	55947.4	+	40648.2i	0.349671	+	0.254051i
$401$	−42742.6	−	131548.i	−0.265810	−	0.818080i	−0.991506	−	0.130064i	$-0.958482\pi$
$401$	−42742.6	−	131548.i	−0.265810	−	0.818080i	0.725695	−	0.688016i	$-0.241518\pi$
$402$	422494.	−	137277.i	2.61438	−	0.849464i
$403$	1201.18	−	1653.28i	0.00739602	−	0.0101797i
$404$	78116.1	+	107518.i	0.478606	+	0.658744i
$405$	58593.8	−	180333.i	0.357225	−	1.09943i
$406$			234012.i			1.41966i
$407$	61283.7	+	140438.i	0.369961	+	0.847802i
$408$	−12733.1			−0.0764914
$409$	212782.	+	69137.1i	1.27200	+	0.413299i	0.865757	−	0.500464i	$-0.166837\pi$
$409$	212782.	+	69137.1i	1.27200	+	0.413299i	0.406247	+	0.913763i	$0.366837\pi$
$410$	−81224.8	+	59013.3i	−0.483193	+	0.351061i
$411$	−88324.3	−	64171.4i	−0.522873	−	0.379890i
$412$	−47375.8	−	145808.i	−0.279101	−	0.858985i
$413$	25455.6	−	8271.02i	0.149239	−	0.0484907i
$414$	33179.3	−	45667.4i	0.193583	−	0.266444i
$415$	79159.7	+	108954.i	0.459630	+	0.632626i
$416$	10078.7	−	31019.0i	0.0582394	−	0.179243i
$417$		−	341683.i		−	1.96495i
$418$	−43057.7	+	195436.i	−0.246432	+	1.11854i
$419$	−202558.			−1.15378			−0.576889	−	0.816822i	$-0.695734\pi$
$419$	−202558.			−1.15378			−0.576889	+	0.816822i	$0.695734\pi$
$420$	−357759.	−	116243.i	−2.02811	−	0.658973i
$421$	−144786.	+	105193.i	−0.816889	+	0.593505i	−0.915820	−	0.401590i	$-0.868458\pi$
$421$	−144786.	+	105193.i	−0.816889	+	0.593505i	0.0989305	+	0.995094i	$0.468458\pi$
$422$	−38491.7	−	27965.9i	−0.216144	−	0.157038i
$423$	108295.	+	333298.i	0.605241	+	1.86274i
$424$	−18671.0	+	6066.59i	−0.103857	+	0.0337453i
$425$	31391.1	−	43206.1i	0.173791	−	0.239203i
$426$	161311.	+	222026.i	0.888886	+	1.22345i
$427$	−14441.2	+	44445.6i	−0.0792043	+	0.243766i
$428$		−	337465.i		−	1.84222i
$429$	−33852.4	−	7458.21i	−0.183939	−	0.0405247i
$430$	244566.			1.32269
$431$	−88598.8	−	28787.5i	−0.476951	−	0.154971i	0.0606693	−	0.998158i	$-0.480676\pi$
$431$	−88598.8	−	28787.5i	−0.476951	−	0.154971i	−0.537620	+	0.843187i	$0.680676\pi$
$432$	8447.07	−	6137.16i	0.0452625	−	0.0328851i
$433$	46736.5	+	33956.1i	0.249276	+	0.181110i	0.705406	−	0.708804i	$-0.250765\pi$
$433$	46736.5	+	33956.1i	0.249276	+	0.181110i	−0.456130	+	0.889913i	$0.650765\pi$
$434$	9302.56	+	28630.3i	0.0493882	+	0.152001i
$435$	−263509.	+	85619.1i	−1.39257	+	0.452472i
$436$	42019.0	−	57834.2i	0.221041	−	0.304237i
$437$	−19749.3	−	27182.6i	−0.103416	−	0.142340i
$438$	−49070.1	+	151022.i	−0.255781	+	0.787214i
$439$		−	172784.i		−	0.896548i	−0.893896	−	0.448274i	$-0.852039\pi$
$439$		−	172784.i		−	0.896548i	0.893896	−	0.448274i	$-0.147961\pi$
$440$	17880.7	−	7802.72i	0.0923590	−	0.0403033i
$441$	−73347.3			−0.377144
$442$	−22557.8	−	7329.47i	−0.115465	−	0.0375170i
$443$	170724.	−	124038.i	0.869936	−	0.632046i	−0.0606337	−	0.998160i	$-0.519312\pi$
$443$	170724.	−	124038.i	0.869936	−	0.632046i	0.930570	+	0.366115i	$0.119312\pi$
$444$	223050.	+	162055.i	1.13145	+	0.822049i
$445$	14821.8	+	45616.9i	0.0748482	+	0.230359i
$446$	−244013.	+	79284.7i	−1.22672	+	0.398584i
$447$	195244.	−	268731.i	0.977156	−	1.34494i
$448$	153192.	+	210850.i	0.763272	+	1.05055i
$449$	71989.6	−	221561.i	0.357089	−	1.09901i	−0.597699	−	0.801721i	$-0.703918\pi$
$449$	71989.6	−	221561.i	0.357089	−	1.09901i	0.954788	−	0.297287i	$-0.0960820\pi$
$450$		−	139373.i		−	0.688263i
$451$	−6807.49	−	69737.2i	−0.0334683	−	0.342856i
$452$	369689.			1.80950
$453$	333519.	+	108367.i	1.62526	+	0.528080i
$454$	73161.4	−	53154.8i	0.354952	−	0.257888i
$455$	−31138.7	−	22623.6i	−0.150411	−	0.109280i
$456$	6112.13	+	18811.2i	0.0293943	+	0.0904664i
$457$	−242280.	+	78721.6i	−1.16007	+	0.376931i	−0.824929	−	0.565236i	$-0.808785\pi$
$457$	−242280.	+	78721.6i	−1.16007	+	0.376931i	−0.335144	+	0.942167i	$0.608785\pi$
$458$	1385.89	−	1907.51i	0.00660688	−	0.00909359i
$459$	−4739.50	−	6523.36i	−0.0224961	−	0.0309632i
$460$	−18426.9	+	56712.0i	−0.0870834	+	0.268015i
$461$			372162.i			1.75118i	0.483058	+	0.875588i	$0.339526\pi$
$461$			372162.i			1.75118i	−0.483058	+	0.875588i	$0.660474\pi$
$462$	381999.	−	338861.i	1.78969	−	1.58759i
$463$	43261.0			0.201806			0.100903	−	0.994896i	$-0.467827\pi$
$463$	43261.0			0.201806			0.100903	+	0.994896i	$0.467827\pi$
$464$	162941.	+	52942.9i	0.756825	+	0.245907i
$465$	−28835.6	+	20950.3i	−0.133359	+	0.0968911i
$466$	−291586.	−	211849.i	−1.34275	−	0.975563i
$467$	10235.8	+	31502.6i	0.0469342	+	0.144449i	0.971777	−	0.235900i	$-0.0758039\pi$
$467$	10235.8	+	31502.6i	0.0469342	+	0.144449i	−0.924843	+	0.380349i	$0.875804\pi$
$468$	−30265.9	+	9833.99i	−0.138185	+	0.0448991i
$469$	−202343.	+	278501.i	−0.919904	+	1.26614i
$470$	−423254.	−	582559.i	−1.91604	−	2.63721i
$471$	−69990.3	+	215408.i	−0.315498	+	0.971002i
$472$			2497.69i			0.0112113i
$473$	−86434.6	+	147179.i	−0.386336	+	0.657845i
$474$	−805188.			−3.58377
$475$	−78898.9	−	25635.8i	−0.349690	−	0.113621i
$476$	145326.	−	105586.i	0.641401	−	0.466005i
$477$	−251132.	−	182458.i	−1.10374	−	0.801913i
$478$	−33367.1	−	102693.i	−0.146037	−	0.449456i
$479$	−157035.	+	51023.9i	−0.684426	+	0.222383i	−0.630532	−	0.776163i	$-0.717163\pi$
$479$	−157035.	+	51023.9i	−0.684426	+	0.222383i	−0.0538938	+	0.998547i	$0.517163\pi$
$480$	−334366.	+	460215.i	−1.45124	+	1.99746i
$481$	16581.5	+	22822.4i	0.0716692	+	0.0986443i
$482$	−92601.3	+	284998.i	−0.398587	+	1.22672i
$483$			85733.0i			0.367497i
$484$	−29560.8	+	246102.i	−0.126190	+	1.05057i
$485$	565939.			2.40595
$486$	459680.	+	149359.i	1.94618	+	0.632353i
$487$	129163.	−	93842.4i	0.544603	−	0.395677i	−0.281189	−	0.959653i	$-0.590729\pi$
$487$	129163.	−	93842.4i	0.544603	−	0.395677i	0.825792	+	0.563975i	$0.190729\pi$
$488$	−3528.11	−	2563.32i	−0.0148150	−	0.0107637i
$489$	−24450.5	−	75250.8i	−0.102251	−	0.314698i
$490$	143333.	−	46571.8i	0.596973	−	0.193968i
$491$	205651.	−	283054.i	0.853036	−	1.17410i	−0.130149	−	0.991494i	$-0.541546\pi$
$491$	205651.	−	283054.i	0.853036	−	1.17410i	0.983186	−	0.182609i	$-0.0584543\pi$
$492$	−74106.1	−	101998.i	−0.306142	−	0.421369i
$493$	40885.8	−	125834.i	0.168220	−	0.517729i
$494$			36844.1i			0.150978i
$495$	265996.	+	156213.i	1.08559	+	0.637538i
$496$	22039.8			0.0895869
$497$	−202259.	−	65717.9i	−0.818832	−	0.266055i
$498$	−266123.	+	193350.i	−1.07306	+	0.779623i
$499$	119390.	+	86742.2i	0.479478	+	0.348361i	0.801123	−	0.598499i	$-0.204236\pi$
$499$	119390.	+	86742.2i	0.479478	+	0.348361i	−0.321646	+	0.946860i	$0.604236\pi$
$500$	−53293.4	−	164020.i	−0.213174	−	0.656081i
$501$	47544.3	−	15448.1i	0.189419	−	0.0615459i
$502$	124413.	−	171239.i	0.493693	−	0.679510i
$503$	−239182.	−	329206.i	−0.945350	−	1.30116i	−0.953562	−	0.301196i	$-0.902614\pi$
$503$	−239182.	−	329206.i	−0.945350	−	1.30116i	0.00821208	−	0.999966i	$-0.497386\pi$
$504$	7957.24	−	24489.9i	0.0313258	−	0.0964108i
$505$		−	237172.i		−	0.929995i
$506$	−53716.4	−	60554.7i	−0.209800	−	0.236508i
$507$	360912.			1.40406
$508$	152685.	+	49610.5i	0.591657	+	0.192241i
$509$	−252309.	+	183313.i	−0.973862	+	0.707552i	−0.956329	−	0.292294i	$-0.905581\pi$
$509$	−252309.	+	183313.i	−0.973862	+	0.707552i	−0.0175338	+	0.999846i	$0.505581\pi$
$510$	334680.	+	243159.i	1.28674	+	0.934869i
$511$	−38025.2	−	117030.i	−0.145623	−	0.448182i
$512$	354049.	−	115037.i	1.35059	−	0.438833i
$513$	−7362.23	+	10133.2i	−0.0279753	+	0.0385047i
$514$	−95911.2	−	132010.i	−0.363031	−	0.499669i
$515$	−84546.8	+	260208.i	−0.318774	+	0.981086i
$516$			307114.i			1.15346i
$517$	500168.	−	48824.6i	1.87126	−	0.182666i
$518$	−415561.			−1.54873
$519$	−392169.	−	127423.i	−1.45592	−	0.473058i
$520$	2905.78	−	2111.17i	0.0107462	−	0.00780760i
$521$	254154.	+	184653.i	0.936313	+	0.680271i	0.947530	−	0.319666i	$-0.103571\pi$
$521$	254154.	+	184653.i	0.936313	+	0.680271i	−0.0112174	+	0.999937i	$0.503571\pi$
$522$	−106700.	−	328389.i	−0.391583	−	1.20517i
$523$	363288.	−	118039.i	1.32815	−	0.431543i	0.442865	−	0.896588i	$-0.353962\pi$
$523$	363288.	−	118039.i	1.32815	−	0.431543i	0.885287	+	0.465046i	$0.153962\pi$
$524$	−170705.	+	234956.i	−0.621705	+	0.855703i
$525$	124422.	+	171253.i	0.451419	+	0.621325i
$526$	99291.3	−	305587.i	0.358872	−	1.10450i
$527$		−	17020.5i		−	0.0612847i
$528$	−149524.	−	342649.i	−0.536344	−	1.22908i
$529$	−266251.			−0.951435
$530$	606607.	+	197099.i	2.15951	+	0.701668i
$531$	−31950.6	+	23213.5i	−0.113316	+	0.0823287i
$532$	−225746.	−	164014.i	−0.797623	−	0.579507i
$533$	−3986.36	−	12268.8i	−0.0140321	−	0.0431863i
$534$	−111420.	+	36202.7i	−0.390735	+	0.126957i
$535$	−353988.	+	487223.i	−1.23675	+	1.70224i
$536$	−18882.1	−	25989.0i	−0.0657235	−	0.0904606i
$537$	32597.0	−	100323.i	0.113039	−	0.347899i
$538$			182313.i			0.629875i
$539$	−22630.1	+	102717.i	−0.0778949	+	0.353560i
$540$	22229.3			0.0762323
$541$	−205447.	−	66753.7i	−0.701947	−	0.228077i	−0.0637686	−	0.997965i	$-0.520312\pi$
$541$	−205447.	−	66753.7i	−0.701947	−	0.228077i	−0.638179	+	0.769888i	$0.720312\pi$
$542$	−369945.	+	268781.i	−1.25933	+	0.914955i
$543$	267563.	+	194396.i	0.907457	+	0.659306i
$544$	−83943.6	−	258352.i	−0.283655	−	0.872999i
$545$	−121332.	+	39423.1i	−0.408491	+	0.132727i
$546$	55258.8	−	76057.2i	0.185360	−	0.255126i
$547$	98792.7	+	135977.i	0.330180	+	0.454453i	0.941541	−	0.336898i	$-0.109378\pi$
$547$	98792.7	+	135977.i	0.330180	+	0.454453i	−0.611361	+	0.791352i	$0.709378\pi$
$548$	−44414.0	+	136692.i	−0.147897	+	0.455180i
$549$		−	68955.2i		−	0.228782i
$550$	−195181.	−	43001.3i	−0.645225	−	0.142153i
$551$	−205526.			−0.676962
$552$	−7608.81	−	2472.25i	−0.0249711	−	0.00811362i
$553$	504789.	−	366751.i	1.65067	−	1.19928i
$554$	663808.	+	482285.i	2.16283	+	1.57139i
$555$	−152044.	−	467943.i	−0.493608	−	1.51917i
$556$	−427803.	+	139002.i	−1.38387	+	0.449646i
$557$	−160840.	+	221378.i	−0.518424	+	0.713549i	−0.985311	−	0.170768i	$-0.945375\pi$
$557$	−160840.	+	221378.i	−0.518424	+	0.713549i	0.466888	+	0.884317i	$0.345375\pi$
$558$	−26108.6	−	35935.4i	−0.0838524	−	0.115413i
$559$	−9710.51	+	29885.9i	−0.0310755	+	0.0956406i
$560$		−	415109.i		−	1.32369i
$561$	−264615.	+	115472.i	−0.840792	+	0.366902i
$562$	−176226.			−0.557953
$563$	−306071.	−	99448.5i	−0.965618	−	0.313748i	−0.216572	−	0.976267i	$-0.569488\pi$
$563$	−306071.	−	99448.5i	−0.965618	−	0.313748i	−0.749046	+	0.662518i	$0.769488\pi$
$564$	731550.	−	531502.i	2.29978	−	1.67089i
$565$	−533747.	−	387790.i	−1.67201	−	1.21478i
$566$	248826.	+	765808.i	0.776717	+	2.39049i
$567$	−341326.	+	110904.i	−1.06171	+	0.344969i
$568$	11664.9	−	16055.4i	0.0361564	−	0.0497651i
$569$	259931.	+	357764.i	0.802848	+	1.10503i	0.992388	+	0.123153i	$0.0393005\pi$
$569$	259931.	+	357764.i	0.802848	+	1.10503i	−0.189540	+	0.981873i	$0.560700\pi$
$570$	198578.	−	611161.i	0.611199	−	1.88108i
$571$		−	560951.i		−	1.72049i	−0.509880	−	0.860246i	$-0.670310\pi$
$571$		−	560951.i		−	1.72049i	0.509880	−	0.860246i	$-0.329690\pi$
$572$	4433.63	+	45419.0i	0.0135509	+	0.138818i
$573$	28994.5			0.0883093
$574$	180731.	+	58722.9i	0.548539	+	0.178231i
$575$	27147.0	−	19723.5i	0.0821082	−	0.0596551i
$576$	−311114.	−	226038.i	−0.937723	−	0.681296i
$577$	129705.	+	399192.i	0.389588	+	1.19903i	0.933097	+	0.359626i	$0.117096\pi$
$577$	129705.	+	399192.i	0.389588	+	1.19903i	−0.543508	+	0.839404i	$0.682904\pi$
$578$	267944.	−	87060.4i	0.802027	−	0.260594i
$579$	158179.	−	217714.i	0.471836	−	0.649427i
$580$	214399.	+	295094.i	0.637332	+	0.877213i
$581$	78770.2	−	242430.i	0.233351	−	0.718181i
$582$			1.38232e6i			4.08096i
$583$	−333000.	+	295395.i	−0.979732	+	0.869093i
$584$	11482.9			0.0336687
$585$	54012.6	+	17549.8i	0.157828	+	0.0512813i
$586$	599907.	−	435858.i	1.74698	−	1.26926i
$587$	−47114.9	−	34231.0i	−0.136736	−	0.0993444i	0.517315	−	0.855795i	$-0.326932\pi$
$587$	−47114.9	−	34231.0i	−0.136736	−	0.0993444i	−0.654051	+	0.756451i	$0.726932\pi$
$588$	58482.6	+	179991.i	0.169150	+	0.520590i
$589$	−25145.3	+	8170.20i	−0.0724813	+	0.0235506i
$590$	47697.6	−	65650.1i	0.137023	−	0.188596i
$591$	12679.0	+	17451.1i	0.0363002	+	0.0499630i
$592$	−94016.8	+	289354.i	−0.268264	+	0.825631i
$593$		−	59573.5i		−	0.169412i	−0.996406	−	0.0847060i	$-0.973005\pi$
$593$		−	59573.5i		−	0.169412i	0.996406	−	0.0847060i	$-0.0269951\pi$
$594$	−15281.0	+	26020.2i	−0.0433092	+	0.0737460i
$595$	−320573.			−0.905510
$596$	−415893.	−	135132.i	−1.17082	−	0.380421i
$597$	−457843.	+	332643.i	−1.28460	+	0.933317i
$598$	−12056.6	−	8759.64i	−0.0337150	−	0.0244954i
$599$	−39195.0	−	120630.i	−0.109239	−	0.336203i	0.881463	−	0.472253i	$-0.156559\pi$
$599$	−39195.0	−	120630.i	−0.109239	−	0.336203i	−0.990702	+	0.136050i	$0.956559\pi$
$600$	−18786.6	+	6104.13i	−0.0521850	+	0.0169559i
$601$	316638.	−	435815.i	0.876626	−	1.20657i	−0.100718	−	0.994915i	$-0.532114\pi$
$601$	316638.	−	435815.i	0.876626	−	1.20657i	0.977344	−	0.211657i	$-0.0678859\pi$
$602$	−272088.	−	374497.i	−0.750786	−	1.03337i
$603$	156963.	−	483082.i	0.431680	−	1.32858i
$604$		−	461667.i		−	1.26548i
$605$	300831.	−	324308.i	0.821887	−	0.886026i
$606$	579299.			1.57746
$607$	19437.1	+	6315.50i	0.0527539	+	0.0171408i	0.335275	−	0.942120i	$-0.391171\pi$
$607$	19437.1	+	6315.50i	0.0527539	+	0.0171408i	−0.282521	+	0.959261i	$0.591171\pi$
$608$	−341382.	+	248028.i	−0.923492	+	0.670956i
$609$	424268.	+	308249.i	1.14395	+	0.831125i
$610$	43783.0	+	134750.i	0.117665	+	0.362135i
$611$	87993.8	−	28590.9i	0.235706	−	0.0765854i
$612$	−155794.	+	214432.i	−0.415956	+	0.572514i
$613$	337448.	+	464458.i	0.898021	+	1.23602i	0.971095	+	0.238693i	$0.0767189\pi$
$613$	337448.	+	464458.i	0.898021	+	1.23602i	−0.0730746	+	0.997326i	$0.523281\pi$
$614$	193543.	−	595665.i	0.513383	−	1.58003i
$615$			224997.i			0.594875i
$616$	−31840.9	−	18699.4i	−0.0839120	−	0.0492795i
$617$	99904.0			0.262430			0.131215	−	0.991354i	$-0.458112\pi$
$617$	99904.0			0.262430			0.131215	+	0.991354i	$0.458112\pi$
$618$	−635566.	−	206508.i	−1.66412	−	0.540704i
$619$	−126477.	+	91890.9i	−0.330088	+	0.239823i	−0.740468	−	0.672091i	$-0.765396\pi$
$619$	−126477.	+	91890.9i	−0.330088	+	0.239823i	0.410380	+	0.911915i	$0.365396\pi$
$620$	37961.5	+	27580.7i	0.0987553	+	0.0717499i
$621$	−1565.57	−	4818.33i	−0.00405966	−	0.0124944i
$622$	163615.	−	53161.7i	0.422904	−	0.137410i
$623$	53362.0	−	73446.4i	0.137485	−	0.189232i
$624$	−40456.6	−	55683.7i	−0.103901	−	0.143008i
$625$	−150699.	+	463805.i	−0.385790	+	1.18734i
$626$		−	892586.i		−	2.27773i
$627$	297613.	+	335500.i	0.757036	+	0.853410i
$628$	298175.			0.756051
$629$	223457.	+	72605.7i	0.564798	+	0.183514i
$630$	−676826.	+	491743.i	−1.70528	+	1.23896i
$631$	158197.	+	114937.i	0.397320	+	0.288670i	0.768449	−	0.639912i	$-0.221029\pi$
$631$	158197.	+	114937.i	0.397320	+	0.288670i	−0.371128	+	0.928582i	$0.621029\pi$
$632$	17992.7	+	55375.9i	0.0450466	+	0.138639i
$633$	−101405.	+	32948.6i	−0.253078	+	0.0822299i
$634$	−222336.	+	306019.i	−0.553134	+	0.761324i
$635$	−168403.	−	231787.i	−0.417641	−	0.574834i
$636$	−247507.	+	761748.i	−0.611890	+	1.88320i
$637$			19364.4i			0.0477227i
$638$	−492802.	+	48105.5i	−1.21068	+	0.118182i
$639$	313795.			0.768502
$640$	78377.6	+	25466.4i	0.191352	+	0.0621739i
$641$	−384875.	+	279628.i	−0.936707	+	0.680558i	−0.947626	−	0.319383i	$-0.896524\pi$
$641$	−384875.	+	279628.i	−0.936707	+	0.680558i	0.0109187	+	0.999940i	$0.496524\pi$
$642$	−1.19005e6	−	864625.i	−2.88733	−	2.09777i
$643$	32940.2	+	101379.i	0.0796717	+	0.245204i	0.982957	−	0.183836i	$-0.0588517\pi$
$643$	32940.2	+	101379.i	0.0796717	+	0.245204i	−0.903285	+	0.429041i	$0.858852\pi$
$644$	107342.	−	34877.5i	0.258820	−	0.0840957i
$645$	322152.	−	443404.i	0.774356	−	1.06581i
$646$	180372.	+	248261.i	0.432220	+	0.594900i
$647$	150867.	−	464321.i	0.360401	−	1.10920i	−0.592410	−	0.805637i	$-0.701823\pi$
$647$	150867.	−	464321.i	0.360401	−	1.10920i	0.952811	−	0.303564i	$-0.0981765\pi$
$648$		−	33490.8i		−	0.0797583i
$649$	22650.7	+	51906.3i	0.0537764	+	0.123234i
$650$	−36795.9			−0.0870908
$651$	64161.1	+	20847.2i	0.151394	+	0.0491910i
$652$	−84270.9	+	61226.4i	−0.198236	+	0.144027i
$653$	−359630.	−	261287.i	−0.843393	−	0.612761i	0.0799236	−	0.996801i	$-0.474532\pi$
$653$	−359630.	−	261287.i	−0.843393	−	0.612761i	−0.923316	+	0.384040i	$0.874532\pi$
$654$	−96292.0	−	296356.i	−0.225131	−	0.692881i
$655$	492919.	−	160159.i	1.14893	−	0.373309i
$656$	81777.1	−	112557.i	0.190031	−	0.261555i
$657$	106722.	+	146890.i	0.247242	+	0.340300i
$658$	−421172.	+	1.29623e6i	−0.972764	+	2.99386i
$659$			132146.i			0.304287i	0.988358	+	0.152143i	$0.0486175\pi$
$659$			132146.i			0.304287i	−0.988358	+	0.152143i	$0.951382\pi$
$660$	171250.	−	777295.i	0.393137	−	1.78442i
$661$	−502482.			−1.15005			−0.575026	−	0.818135i	$-0.695008\pi$
$661$	−502482.			−1.15005			−0.575026	+	0.818135i	$0.695008\pi$
$662$	−236655.	−	76893.7i	−0.540006	−	0.175459i
$663$	−43002.5	+	31243.1i	−0.0978287	+	0.0710767i
$664$	19244.2	+	13981.7i	0.0436479	+	0.0317121i
$665$	153882.	+	473599.i	0.347971	+	1.07095i
$666$	583159.	−	189480.i	1.31474	−	0.427183i
$667$	48863.7	−	67255.1i	0.109833	−	0.151173i
$668$	−38683.5	−	53243.3i	−0.0866908	−	0.119320i
$669$	−177678.	+	546838.i	−0.396993	+	1.22182i
$670$			1.04369e6i			2.32499i
$671$	−96566.0	−	21275.0i	−0.214476	−	0.0472525i
$672$	1.07671e6			2.38429
$673$	416181.	+	135225.i	0.918866	+	0.298558i	0.730002	−	0.683445i	$-0.239519\pi$
$673$	416181.	+	135225.i	0.918866	+	0.298558i	0.188865	+	0.982003i	$0.439519\pi$
$674$	636276.	−	462282.i	1.40064	−	1.01762i
$675$	−10120.0	−	7352.60i	−0.0222112	−	0.0161374i
$676$	−146825.	−	451880.i	−0.321296	−	0.988848i
$677$	77134.7	−	25062.6i	0.168295	−	0.0546825i	−0.223657	−	0.974668i	$-0.571800\pi$
$677$	77134.7	−	25062.6i	0.168295	−	0.0546825i	0.391953	+	0.919985i	$0.371800\pi$
$678$	947186.	−	1.30369e6i	2.06052	−	2.83606i
$679$	−629625.	−	866605.i	−1.36566	−	1.87967i
$680$	9244.25	−	28450.9i	0.0199919	−	0.0615287i
$681$		−	202661.i		−	0.436994i
$682$	−58379.9	+	25475.6i	−0.125515	+	0.0547717i
$683$	441204.			0.945797			0.472899	−	0.881117i	$-0.343208\pi$
$683$	441204.			0.945797			0.472899	+	0.881117i	$0.343208\pi$
$684$	391575.	+	127230.i	0.836956	+	0.271943i
$685$	207509.	−	150764.i	0.442237	−	0.321304i
$686$	406659.	+	295455.i	0.864135	+	0.627831i
$687$	−1632.81	−	5025.28i	−0.00345957	−	0.0106475i
$688$	−322318.	+	104728.i	−0.680939	+	0.221250i
$689$	−48170.7	+	66301.3i	−0.101472	+	0.139664i
$690$	152781.	+	210284.i	0.320900	+	0.441681i
$691$	−109617.	+	337366.i	−0.229573	+	0.706555i	0.768222	+	0.640184i	$0.221142\pi$
$691$	−109617.	+	337366.i	−0.229573	+	0.706555i	−0.997795	+	0.0663705i	$0.978858\pi$
$692$			542853.i			1.13363i
$693$	−56725.1	−	581103.i	−0.118116	−	1.21000i
$694$	−530651.			−1.10177
$695$	763459.	+	248063.i	1.58058	+	0.513561i
$696$	−39591.5	+	28764.9i	−0.0817304	+	0.0593806i
$697$	−86923.2	−	63153.4i	−0.178925	−	0.129996i
$698$	166288.	+	511783.i	0.341311	+	1.05045i
$699$	−768174.	+	249595.i	−1.57219	+	0.510836i
$700$	163800.	−	225451.i	0.334285	−	0.460104i
$701$	−280476.	−	386042.i	−0.570768	−	0.785595i	0.421877	−	0.906653i	$-0.361371\pi$
$701$	−280476.	−	386042.i	−0.570768	−	0.785595i	−0.992645	+	0.121058i	$0.961371\pi$
$702$	−1716.75	+	5283.62i	−0.00348364	+	0.0107215i
$703$		−	364977.i		−	0.738507i
$704$	−412536.	+	365949.i	−0.832370	+	0.738372i
$705$	−1.61372e6			−3.24675
$706$	−243824.	−	79223.3i	−0.489178	−	0.158944i
$707$	−363174.	+	263862.i	−0.726568	+	0.527883i
$708$	82440.3	+	59896.4i	0.164465	+	0.119491i
$709$	−7462.11	−	22966.0i	−0.0148446	−	0.0456870i	0.943360	−	0.331771i	$-0.107646\pi$
$709$	−7462.11	−	22966.0i	−0.0148446	−	0.0456870i	−0.958204	+	0.286084i	$0.907646\pi$
$710$	−613210.	+	199244.i	−1.21644	+	0.395247i
$711$	−541148.	+	744826.i	−1.07048	+	1.47338i
$712$	4979.59	+	6853.82i	0.00982277	+	0.0135199i
$713$	3304.70	−	10170.8i	0.00650060	−	0.0200068i
$714$		−	783008.i		−	1.53593i
$715$	41241.6	−	70225.4i	0.0806722	−	0.137367i
$716$	−138870.			−0.270884
$717$	−230138.	−	74776.3i	−0.447661	−	0.145454i
$718$	108990.	−	79185.6i	0.211415	−	0.153602i
$719$	−169370.	−	123055.i	−0.327626	−	0.238034i	0.411796	−	0.911276i	$-0.364901\pi$
$719$	−169370.	−	123055.i	−0.327626	−	0.238034i	−0.739423	+	0.673241i	$0.764901\pi$
$720$	189273.	+	582524.i	0.365111	+	1.12370i
$721$	492510.	−	160026.i	0.947425	−	0.307837i
$722$	−159384.	+	219373.i	−0.305752	+	0.420832i
$723$	394729.	+	543297.i	0.755131	+	1.03935i
$724$	134544.	−	414085.i	0.256678	−	0.789973i
$725$		−	205257.i		−	0.390502i
$726$	792130.	+	734788.i	1.50288	+	1.39408i
$727$	873464.			1.65263			0.826316	−	0.563206i	$-0.190432\pi$
$727$	873464.			1.65263			0.826316	+	0.563206i	$0.190432\pi$
$728$	−6465.56	−	2100.79i	−0.0121995	−	0.00396387i
$729$	465040.	−	337871.i	0.875055	−	0.635765i
$730$	−301820.	−	219285.i	−0.566374	−	0.411495i
$731$	80877.1	+	248914.i	0.151353	+	0.465817i
$732$	−169213.	+	54980.6i	−0.315800	+	0.102609i
$733$	203287.	−	279801.i	0.378357	−	0.520764i	−0.576791	−	0.816892i	$-0.695695\pi$
$733$	203287.	−	279801.i	0.378357	−	0.520764i	0.955148	+	0.296128i	$0.0956954\pi$
$734$	58058.2	+	79910.3i	0.107763	+	0.148324i
$735$	104368.	−	321212.i	0.193194	−	0.594590i
$736$		−	170680.i		−	0.315084i
$737$	−628087.	−	368860.i	−1.15634	−	0.679089i
$738$	−280395.			−0.514823
$739$	−46530.6	−	15118.7i	−0.0852021	−	0.0276838i	0.266106	−	0.963944i	$-0.414263\pi$
$739$	−46530.6	−	15118.7i	−0.0852021	−	0.0276838i	−0.351308	+	0.936260i	$0.614263\pi$
$740$	−524033.	+	380732.i	−0.956963	+	0.695275i
$741$	66799.1	+	48532.4i	0.121656	+	0.0883884i
$742$	−373059.	−	1.14816e6i	−0.677595	−	2.08542i
$743$	471791.	−	153294.i	0.854618	−	0.277682i	0.151239	−	0.988497i	$-0.451674\pi$
$743$	471791.	−	153294.i	0.854618	−	0.277682i	0.703379	+	0.710815i	$0.251674\pi$
$744$	−3700.38	+	5093.13i	−0.00668498	+	0.00920109i
$745$	458707.	+	631355.i	0.826461	+	1.13753i
$746$	109445.	−	336837.i	0.196661	−	0.605260i
$747$			376119.i			0.674037i
$748$	252226.	+	284335.i	0.450802	+	0.508191i
$749$	1.13989e6			2.03189
$750$	−714954.	−	232303.i	−1.27103	−	0.412982i
$751$	−631084.	+	458509.i	−1.11894	+	0.812958i	−0.984048	−	0.177902i	$-0.943069\pi$
$751$	−631084.	+	458509.i	−1.11894	+	0.812958i	−0.134893	+	0.990860i	$0.543069\pi$
$752$	807276.	+	586521.i	1.42753	+	1.03716i
$753$	−146579.	−	451125.i	−0.258513	−	0.795623i
$754$	−86697.8	+	28169.8i	−0.152499	+	0.0495498i
$755$	−484271.	+	666542.i	−0.849561	+	1.16932i
$756$	−24730.9	−	34039.1i	−0.0432709	−	0.0595573i
$757$	149655.	−	460592.i	0.261156	−	0.803757i	−0.731398	−	0.681951i	$-0.761132\pi$
$757$	149655.	−	460592.i	0.261156	−	0.803757i	0.992554	−	0.121805i	$-0.0388684\pi$
$758$		−	1.06365e6i		−	1.85123i
$759$	−180544.	+	17624.0i	−0.313400	+	0.0305930i
$760$	−46469.4			−0.0804525
$761$	−620134.	−	201494.i	−1.07082	−	0.347930i	−0.280013	−	0.959996i	$-0.590339\pi$
$761$	−620134.	−	201494.i	−1.07082	−	0.347930i	−0.790807	+	0.612066i	$0.790339\pi$
$762$	566147.	−	411330.i	0.975033	−	0.708403i
$763$	195353.	+	141932.i	0.335561	+	0.243799i
$764$	−11795.4	−	36302.5i	−0.0202081	−	0.0621942i
$765$	449861.	−	146169.i	0.768698	−	0.249765i
$766$	−450050.	+	619441.i	−0.767014	+	1.05570i
$767$	6128.58	+	8435.27i	0.0104176	+	0.0143386i
$768$	227578.	−	700413.i	0.385840	−	1.18749i
$769$			221470.i			0.374508i	0.982311	+	0.187254i	$0.0599588\pi$
$769$			221470.i			0.374508i	−0.982311	+	0.187254i	$0.940041\pi$
$770$	479821.	+	1.09956e6i	0.809278	+	1.85454i
$771$	−365676.			−0.615159
$772$	−336939.	−	109478.i	−0.565348	−	0.183693i
$773$	458076.	−	332812.i	0.766617	−	0.556980i	−0.134316	−	0.990939i	$-0.542884\pi$
$773$	458076.	−	332812.i	0.766617	−	0.556980i	0.900933	+	0.433959i	$0.142884\pi$
$774$	552578.	+	401471.i	0.922383	+	0.670151i
$775$	−8159.51	−	25112.4i	−0.0135850	−	0.0418104i
$776$	95067.5	−	30889.3i	0.157873	−	0.0512961i
$777$	−547393.	+	753421.i	−0.906686	+	1.24795i
$778$	141108.	+	194219.i	0.233128	+	0.320873i
$779$	−51574.8	+	158731.i	−0.0849890	+	0.261569i
$780$		−	146537.i		−	0.240857i
$781$	96816.4	−	439444.i	0.158726	−	0.720446i
$782$	−124123.			−0.202973
$783$	−29473.5	−	9576.51i	−0.0480737	−	0.0156201i
$784$	−168959.	+	122756.i	−0.274883	+	0.199714i
$785$	−430496.	−	312774.i	−0.698602	−	0.507564i
$786$	391193.	+	1.20397e6i	0.633207	+	1.94881i
$787$	−387479.	+	125900.i	−0.625603	+	0.203271i	−0.604626	−	0.796509i	$-0.706678\pi$
$787$	−387479.	+	125900.i	−0.625603	+	0.203271i	−0.0209765	+	0.999780i	$0.506678\pi$
$788$	16691.6	−	22974.1i	0.0268811	−	0.0369986i
$789$	−423246.	−	582548.i	−0.679890	−	0.935789i
$790$	584569.	−	1.79912e6i	0.936659	−	2.88274i
$791$			1.24874e6i			1.99581i
$792$	53208.7	+	11722.7i	0.0848266	+	0.0186886i
$793$	−18204.8			−0.0289495
$794$	1.06686e6	+	346644.i	1.69226	+	0.549848i
$795$	1.15639e6	−	840166.i	1.82966	−	1.32932i
$796$	602742.	+	437918.i	0.951274	+	0.691141i
$797$	−343081.	−	1.05590e6i	−0.540108	−	1.66228i	−0.732346	−	0.680932i	$-0.761575\pi$
$797$	−343081.	−	1.05590e6i	−0.540108	−	1.66228i	0.192239	−	0.981348i	$-0.438425\pi$
$798$	−1.15678e6	+	375860.i	−1.81654	+	0.590229i
$799$	452948.	−	623429.i	0.709504	−	0.976548i
$800$	−247704.	−	340935.i	−0.387037	−	0.532711i
$801$	−41394.3	+	127399.i	−0.0645172	+	0.198564i
$802$			793731.i			1.23403i
$803$	238634.	−	104135.i	0.370086	−	0.161497i
$804$	−1.31061e6			−2.02751
$805$	−191563.	−	62242.4i	−0.295610	−	0.0960494i
$806$	−9487.30	+	6892.92i	−0.0146040	+	0.0106104i
$807$	330538.	+	240150.i	0.507545	+	0.368753i
$808$	−12945.0	−	39840.6i	−0.0198280	−	0.0610244i
$809$	−858406.	+	278913.i	−1.31158	+	0.426159i	−0.879596	−	0.475721i	$-0.842187\pi$
$809$	−858406.	+	278913.i	−1.31158	+	0.426159i	−0.431987	+	0.901880i	$0.642187\pi$
$810$	−639564.	+	880284.i	−0.974796	+	1.34169i
$811$	−316037.	−	434987.i	−0.480503	−	0.661355i	0.498099	−	0.867120i	$-0.334032\pi$
$811$	−316037.	−	434987.i	−0.480503	−	0.661355i	−0.978601	+	0.205765i	$0.934032\pi$
$812$	213344.	−	656604.i	0.323570	−	0.995845i
$813$			1.02477e6i			1.55040i
$814$	−85426.4	−	875125.i	−0.128927	−	1.32075i
$815$	185892.			0.279863
$816$	−545206.	−	177148.i	−0.818805	−	0.266046i
$817$	328911.	−	238968.i	0.492759	−	0.358010i
$818$	−1.03868e6	−	754646.i	−1.55230	−	1.12781i
$819$	−33217.4	−	102233.i	−0.0495219	−	0.152413i
$820$	281707.	−	91532.1i	0.418957	−	0.136127i
$821$	−105250.	+	144864.i	−0.156147	+	0.214918i	−0.879922	−	0.475118i	$-0.842405\pi$
$821$	−105250.	+	144864.i	−0.156147	+	0.214918i	0.723775	+	0.690036i	$0.242405\pi$
$822$	368245.	+	506846.i	0.544996	+	0.750122i
$823$	−200047.	+	615680.i	−0.295346	+	0.908982i	0.687759	+	0.725939i	$0.258595\pi$
$823$	−200047.	+	615680.i	−0.295346	+	0.908982i	−0.983105	+	0.183043i	$0.941405\pi$
$824$			48324.9i			0.0711733i
$825$	−335061.	+	297223.i	−0.492285	+	0.436692i
$826$	−153593.			−0.225119
$827$	239782.	+	77909.9i	0.350595	+	0.113915i	0.479020	−	0.877804i	$-0.340992\pi$
$827$	239782.	+	77909.9i	0.350595	+	0.113915i	−0.128425	+	0.991719i	$0.540992\pi$
$828$	−134730.	+	97887.4i	−0.196519	+	0.142780i
$829$	−28463.1	−	20679.7i	−0.0414165	−	0.0300909i	0.566884	−	0.823797i	$-0.308149\pi$
$829$	−28463.1	−	20679.7i	−0.0414165	−	0.0300909i	−0.608301	+	0.793706i	$0.708149\pi$
$830$	−238816.	−	735000.i	−0.346663	−	1.06692i
$831$	1.74878e6	−	568215.i	2.53241	−	0.822830i
$832$	−59676.1	+	82137.0i	−0.0862092	+	0.118657i
$833$	94799.5	+	130480.i	0.136621	+	0.188042i
$834$	−605900.	+	1.86477e6i	−0.871101	+	2.68097i
$835$			117449.i			0.168452i
$836$	298989.	−	509113.i	0.427802	−	0.728453i
$837$	−3986.65			−0.00569059
$838$	1.10548e6	+	359193.i	1.57422	+	0.511494i
$839$	−388072.	+	281951.i	−0.551301	+	0.400544i	−0.828265	−	0.560337i	$-0.810672\pi$
$839$	−388072.	+	281951.i	−0.551301	+	0.400544i	0.276964	+	0.960880i	$0.410672\pi$
$840$	95926.6	+	69694.8i	0.135950	+	0.0987738i
$841$	61422.8	+	189040.i	0.0868436	+	0.267277i
$842$	976723.	−	317357.i	1.37768	−	0.447634i
$843$	−232132.	+	319502.i	−0.326647	+	0.449591i
$844$	82506.5	+	113561.i	0.115825	+	0.159420i
$845$	−262023.	+	806425.i	−0.366967	+	1.12941i
$846$		−	2.01105e6i		−	2.80984i
$847$	−831287.	−	99851.0i	−1.15874	−	0.139183i
$848$	−883860.			−1.22911
$849$	1.71619e6	+	557623.i	2.38095	+	0.773616i
$850$	−247936.	+	180136.i	−0.343165	+	0.249324i
$851$	119433.	+	86772.9i	0.164916	+	0.119819i
$852$	−250201.	−	770040.i	−0.344675	−	1.06080i
$853$	−1.05595e6	+	343100.i	−1.45127	+	0.471545i	−0.925390	−	0.379017i	$-0.876262\pi$
$853$	−1.05595e6	+	343100.i	−1.45127	+	0.471545i	−0.525875	+	0.850562i	$0.676262\pi$
$854$	157629.	−	216958.i	0.216133	−	0.297481i
$855$	−431885.	−	594439.i	−0.590794	−	0.813158i
$856$	−32870.7	+	101165.i	−0.0448602	+	0.138065i
$857$			278639.i			0.379385i	0.981844	+	0.189692i	$0.0607491\pi$
$857$			278639.i			0.379385i	−0.981844	+	0.189692i	$0.939251\pi$
$858$	171527.	+	100734.i	0.233002	+	0.136836i
$859$	−625873.			−0.848203			−0.424101	−	0.905615i	$-0.639410\pi$
$859$	−625873.			−0.848203			−0.424101	+	0.905615i	$0.639410\pi$
$860$	−686219.	−	222966.i	−0.927825	−	0.301468i
$861$	344531.	−	250316.i	0.464752	−	0.337662i
$862$	432489.	+	314222.i	0.582050	+	0.422884i
$863$	−68232.4	−	209998.i	−0.0916155	−	0.281964i	0.894741	−	0.446585i	$-0.147360\pi$
$863$	−68232.4	−	209998.i	−0.0916155	−	0.281964i	−0.986357	+	0.164621i	$0.947360\pi$
$864$	−60512.7	+	19661.8i	−0.0810623	+	0.0263387i
$865$	569432.	−	783756.i	0.761044	−	1.04749i
$866$	−194856.	−	268196.i	−0.259823	−	0.357615i
$867$	195104.	−	600468.i	0.259554	−	0.798825i
$868$		−	88813.7i		−	0.117880i
$869$	876104.	+	987636.i	1.16016	+	1.30785i
$870$	1.58995e6			2.10061
$871$	−127538.	−	41439.7i	−0.168114	−	0.0546236i
$872$	−18229.8	+	13244.7i	−0.0239745	+	0.0174185i
$873$	1.27869e6	+	929025.i	1.67779	+	1.21899i
$874$	59581.4	+	183373.i	0.0779988	+	0.240056i
$875$	554030.	−	180015.i	0.723630	−	0.235122i
$876$	275368.	−	379012.i	0.358844	−	0.493906i
$877$	−374622.	−	515623.i	−0.487073	−	0.670399i	0.492772	−	0.870159i	$-0.335984\pi$
$877$	−374622.	−	515623.i	−0.487073	−	0.670399i	−0.979845	+	0.199760i	$0.935984\pi$
$878$	−306394.	+	942984.i	−0.397458	+	1.22325i
$879$		−	1.66177e6i		−	2.15077i
$880$	874173.	−	85333.4i	1.12884	−	0.110193i
$881$	280859.			0.361857			0.180928	−	0.983496i	$-0.442090\pi$
$881$	280859.			0.361857			0.180928	+	0.983496i	$0.442090\pi$
$882$	400301.	+	130066.i	0.514575	+	0.167196i
$883$	−112471.	+	81715.2i	−0.144252	+	0.104805i	−0.657570	−	0.753393i	$-0.728416\pi$
$883$	−112471.	+	81715.2i	−0.144252	+	0.104805i	0.513319	+	0.858198i	$0.328416\pi$
$884$	56612.0	+	41131.0i	0.0724442	+	0.0526338i
$885$	−56196.0	−	172953.i	−0.0717495	−	0.220822i
$886$	−1.15170e6	+	374210.i	−1.46714	+	0.476703i
$887$	565203.	−	777935.i	0.718384	−	0.988771i	−0.281192	−	0.959652i	$-0.590730\pi$
$887$	565203.	−	777935.i	0.718384	−	0.988771i	0.999576	−	0.0291196i	$-0.00927036\pi$
$888$	−51081.2	−	70307.3i	−0.0647791	−	0.0891608i
$889$	−167575.	+	515742.i	−0.212034	+	0.652573i
$890$		−	275242.i		−	0.347484i
$891$	−303717.	−	695997.i	−0.382572	−	0.876701i
$892$	756950.			0.951344
$893$	−1.13845e6	−	369904.i	−1.42761	−	0.463859i
$894$	−1.54210e6	+	1.12040e6i	−1.92947	+	1.40184i
$895$	200497.	+	145670.i	0.250301	+	0.181854i
$896$	−48201.7	−	148350.i	−0.0600408	−	0.184786i
$897$	−31762.8	+	10320.4i	−0.0394761	+	0.0128266i
$898$	−785781.	+	1.08153e6i	−0.974426	+	1.34118i
$899$	−38450.6	−	52922.7i	−0.0475756	−	0.0654821i
$900$	−127064.	+	391062.i	−0.156869	+	0.482793i
$901$			682572.i			0.840812i
$902$	−86511.3	+	392670.i	−0.106331	+	0.482630i
$903$	−1.03737e6			−1.27221
$904$	−110826.	−	36009.4i	−0.135614	−	0.0440635i
$905$	−628611.	+	456713.i	−0.767511	+	0.557630i
$906$	−1.62805e6	−	1.18285e6i	−1.98340	−	1.44103i
$907$	381113.	+	1.17294e6i	0.463275	+	1.42581i	0.861139	+	0.508369i	$0.169752\pi$
$907$	381113.	+	1.17294e6i	0.463275	+	1.42581i	−0.397864	+	0.917444i	$0.630248\pi$
$908$	−253741.	+	82445.4i	−0.307765	+	0.0999988i
$909$	389333.	−	535871.i	0.471187	−	0.648534i
$910$	129825.	+	178688.i	0.156774	+	0.215781i
$911$	−323667.	+	996144.i	−0.389997	+	1.20029i	0.542792	+	0.839867i	$0.317367\pi$
$911$	−323667.	+	996144.i	−0.389997	+	1.20029i	−0.932790	+	0.360421i	$0.882633\pi$
$912$			890495.i			1.07064i
$913$	526722.	+	116045.i	0.631888	+	0.139215i
$914$	1.46186e6			1.74991
$915$	301978.	+	98118.5i	0.360689	+	0.117195i
$916$	−5627.64	+	4088.72i	−0.00670711	+	0.00487300i
$917$	−793635.	−	576610.i	−0.943805	−	0.685715i
$918$	14298.5	+	44006.3i	0.0169670	+	0.0522192i
$919$	−195664.	+	63575.2i	−0.231676	+	0.0752760i	−0.422554	−	0.906338i	$-0.638866\pi$
$919$	−195664.	+	63575.2i	−0.231676	+	0.0752760i	0.190878	+	0.981614i	$0.438866\pi$
$920$	11048.0	−	15206.3i	0.0130530	−	0.0179659i
$921$	−825010.	−	1.13553e6i	−0.972613	−	1.33869i
$922$	659948.	−	2.03111e6i	0.776332	−	2.38931i
$923$		−	82845.0i		−	0.0972440i
$924$	−1.38077e6	+	602536.i	−1.61725	+	0.705731i
$925$	364499.			0.426003
$926$	−236101.	−	76714.0i	−0.275345	−	0.0894649i
$927$	−618176.	+	449131.i	−0.719370	+	0.522653i
$928$	−844645.	−	613671.i	−0.980795	−	0.712590i
$929$	219018.	+	674067.i	0.253774	+	0.781037i	0.994069	+	0.108754i	$0.0346861\pi$
$929$	219018.	+	674067.i	0.253774	+	0.781037i	−0.740294	+	0.672283i	$0.765314\pi$
$930$	194524.	−	63204.6i	0.224909	−	0.0730774i
$931$	147260.	−	202685.i	0.169896	−	0.233842i
$932$	625010.	+	860253.i	0.719541	+	0.990363i
$933$	119136.	−	366663.i	0.136861	−	0.421215i
$934$		−	190080.i		−	0.217893i
$935$	−65899.8	−	675091.i	−0.0753809	−	0.772216i
$936$	10031.0			0.0114497
$937$	−462509.	−	150278.i	−0.526794	−	0.171166i	0.0335325	−	0.999438i	$-0.489324\pi$
$937$	−462509.	−	150278.i	−0.526794	−	0.171166i	−0.560326	+	0.828272i	$0.689324\pi$
$938$	1.59817e6	−	1.16114e6i	1.81642	−	1.31971i
$939$	−1.61828e6	−	1.17575e6i	−1.83536	−	1.33347i
$940$	656485.	+	2.02045e6i	0.742967	+	2.28662i
$941$	1.40180e6	−	455471.i	1.58309	−	0.514377i	0.620240	−	0.784412i	$-0.287035\pi$
$941$	1.40180e6	−	455471.i	1.58309	−	0.514377i	0.962851	+	0.270034i	$0.0870351\pi$
$942$	763959.	−	1.05150e6i	0.860930	−	1.18497i
$943$	−39680.2	−	54615.1i	−0.0446222	−	0.0614171i
$944$	−34749.0	+	106946.i	−0.0389940	+	0.120011i
$945$			75086.5i			0.0840811i
$946$	732715.	−	649971.i	0.818753	−	0.726293i
$947$	−453271.			−0.505426			−0.252713	−	0.967541i	$-0.581323\pi$
$947$	−453271.			−0.505426			−0.252713	+	0.967541i	$0.581323\pi$
$948$	2.25925e6	+	734074.i	2.51389	+	0.816814i
$949$	38780.4	−	28175.6i	0.0430606	−	0.0312853i
$950$	385139.	+	279820.i	0.426747	+	0.310050i
$951$	261950.	+	806198.i	0.289639	+	0.891416i
$952$	−53850.5	+	17497.1i	−0.0594177	+	0.0193060i
$953$	−240747.	+	331360.i	−0.265079	+	0.364850i	−0.920721	−	0.390222i	$-0.872398\pi$
$953$	−240747.	+	331360.i	−0.265079	+	0.364850i	0.655642	+	0.755072i	$0.272398\pi$
$954$	1.04703e6	+	1.44111e6i	1.15044	+	1.58344i
$955$	−21050.1	+	64785.5i	−0.0230806	+	0.0710348i
$956$			318564.i			0.348562i
$957$	−561921.	+	956826.i	−0.613551	+	1.04474i
$958$	947516.			1.03242
$959$	−461721.	−	150022.i	−0.502044	−	0.163124i
$960$	1.43259e6	−	1.04084e6i	1.55446	−	1.12938i
$961$	740336.	+	537886.i	0.801645	+	0.582429i
$962$	−50024.4	−	153959.i	−0.0540545	−	0.166363i
$963$	−1.59961e6	+	519746.i	−1.72490	+	0.560453i
$964$	519653.	−	715241.i	0.559190	−	0.769659i
$965$	371625.	+	511497.i	0.399071	+	0.549274i
$966$	152029.	−	467897.i	0.162919	−	0.501413i
$967$			231580.i			0.247656i	0.992304	+	0.123828i	$0.0395171\pi$
$967$			231580.i			0.247656i	−0.992304	+	0.123828i	$0.960483\pi$
$968$	32833.3	−	70897.4i	0.0350400	−	0.0756623i
$969$	687696.			0.732401
$970$	−3.08867e6	−	1.00357e6i	−3.28267	−	1.06661i
$971$	1.14530e6	−	832112.i	1.21474	−	0.882558i	0.219085	−	0.975706i	$-0.429693\pi$
$971$	1.14530e6	−	832112.i	1.21474	−	0.882558i	0.995652	+	0.0931474i	$0.0296928\pi$
$972$	−1.15363e6	−	838163.i	−1.22105	−	0.887147i
$973$	−469522.	−	1.44504e6i	−0.495941	−	1.52635i
$974$	−871329.	+	283112.i	−0.918468	+	0.298428i
$975$	−48468.9	+	66711.7i	−0.0509863	+	0.0701766i
$976$	−115405.	−	158841.i	−0.121150	−	0.166749i
$977$	264712.	−	814701.i	0.277323	−	0.853511i	−0.711273	−	0.702916i	$-0.751881\pi$
$977$	264712.	−	814701.i	0.277323	−	0.853511i	0.988596	−	0.150595i	$-0.0481190\pi$
$978$			454047.i			0.474704i
$979$	165639.	+	97276.0i	0.172822	+	0.101494i
$980$	−444632.			−0.462965
$981$	−338855.	−	110101.i	−0.352108	−	0.114407i
$982$	−1.62430e6	+	1.18012e6i	−1.68439	+	1.22378i
$983$	−137802.	−	100119.i	−0.142610	−	0.103612i	0.514193	−	0.857675i	$-0.328092\pi$
$983$	−137802.	−	100119.i	−0.142610	−	0.103612i	−0.656803	+	0.754063i	$0.728092\pi$
$984$	12280.5	+	37795.4i	0.0126831	+	0.0390345i
$985$	−48197.9	+	15660.4i	−0.0496770	+	0.0161410i
$986$	−446277.	+	614247.i	−0.459040	+	0.631814i
$987$	1.79531e6	+	2.47104e6i	1.84292	+	2.53656i
$988$	33590.0	−	103379.i	0.0344109	−	0.105906i
$989$			164445.i			0.168123i
$990$	−1.17469e6	−	1.32423e6i	−1.19854	−	1.35112i
$991$	−68489.3			−0.0697390			−0.0348695	−	0.999392i	$-0.511102\pi$
$991$	−68489.3			−0.0697390			−0.0348695	+	0.999392i	$0.511102\pi$
$992$	−127734.	−	41503.2i	−0.129802	−	0.0421753i
$993$	−451140.	+	327772.i	−0.457523	+	0.332410i
$994$	987312.	+	717324.i	0.999268	+	0.726010i
$995$	−410864.	−	1.26451e6i	−0.415003	−	1.27725i
$996$	922978.	−	299894.i	0.930406	−	0.302307i
$997$	−399343.	+	549649.i	−0.401750	+	0.552962i	−0.961182	−	0.275915i	$-0.911019\pi$
$997$	−399343.	+	549649.i	−0.401750	+	0.552962i	0.559432	+	0.828876i	$0.311019\pi$
$998$	−497767.	−	685118.i	−0.499764	−	0.687866i
$999$	17006.1	−	52339.5i	0.0170402	−	0.0524443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.5.d.a.2.1	✓	12
3.2	odd	2		99.5.k.a.46.3		12
4.3	odd	2		176.5.n.a.145.3		12
11.2	odd	10		121.5.d.c.118.1		12
11.3	even	5		121.5.d.c.40.1		12
11.4	even	5		121.5.b.b.120.2		12
11.5	even	5		121.5.d.d.94.3		12
11.6	odd	10	inner	11.5.d.a.6.1	yes	12
11.7	odd	10		121.5.b.b.120.11		12
11.8	odd	10		121.5.d.e.40.3		12
11.9	even	5		121.5.d.e.118.3		12
11.10	odd	2		121.5.d.d.112.3		12
33.17	even	10		99.5.k.a.28.3		12
44.39	even	10		176.5.n.a.17.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.5.d.a.2.1	✓	12	1.1	even	1	trivial
11.5.d.a.6.1	yes	12	11.6	odd	10	inner
99.5.k.a.28.3		12	33.17	even	10
99.5.k.a.46.3		12	3.2	odd	2
121.5.b.b.120.2		12	11.4	even	5
121.5.b.b.120.11		12	11.7	odd	10
121.5.d.c.40.1		12	11.3	even	5
121.5.d.c.118.1		12	11.2	odd	10
121.5.d.d.94.3		12	11.5	even	5
121.5.d.d.112.3		12	11.10	odd	2
121.5.d.e.40.3		12	11.8	odd	10
121.5.d.e.118.3		12	11.9	even	5
176.5.n.a.17.3		12	44.39	even	10
176.5.n.a.145.3		12	4.3	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	11.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.45760 - 1.77328i) q^{2} +(-10.4040 + 7.55891i) q^{3} +(13.6966 + 9.95117i) q^{4} +(-9.33639 - 28.7345i) q^{5} +(70.1847 - 22.8044i) q^{6} +(-33.6132 + 46.2646i) q^{7} +(-3.13669 - 4.31729i) q^{8} +(26.0747 - 80.2495i) q^{9} +O(q^{10})\)	\(q+(-5.45760 - 1.77328i) q^{2} +(-10.4040 + 7.55891i) q^{3} +(13.6966 + 9.95117i) q^{4} +(-9.33639 - 28.7345i) q^{5} +(70.1847 - 22.8044i) q^{6} +(-33.6132 + 46.2646i) q^{7} +(-3.13669 - 4.31729i) q^{8} +(26.0747 - 80.2495i) q^{9} +173.377i q^{10} +(-104.338 - 61.2750i) q^{11} -217.719 q^{12} +(-21.1866 - 6.88395i) q^{13} +(265.488 - 192.888i) q^{14} +(314.337 + 228.379i) q^{15} +(-74.2432 - 228.497i) q^{16} +(-176.460 + 57.3353i) q^{17} +(-284.610 + 391.732i) q^{18} +(169.409 + 233.171i) q^{19} +(158.065 - 486.473i) q^{20} -735.413i q^{21} +(460.776 + 519.435i) q^{22} -116.578 q^{23} +(65.2680 + 21.2068i) q^{24} +(-232.866 + 169.187i) q^{25} +(103.421 + 75.1398i) q^{26} +(13.4294 + 41.3314i) q^{27} +(-920.774 + 299.177i) q^{28} +(-419.150 + 576.911i) q^{29} +(-1310.54 - 1803.81i) q^{30} +(-28.3476 + 87.2449i) q^{31} +1464.08i q^{32} +(1548.70 - 151.178i) q^{33} +1064.72 q^{34} +(1643.21 + 533.913i) q^{35} +(1155.71 - 839.673i) q^{36} +(-1024.49 - 744.333i) q^{37} +(-511.087 - 1572.96i) q^{38} +(272.460 - 88.5276i) q^{39} +(-94.7695 + 130.439i) q^{40} +(340.375 + 468.486i) q^{41} +(-1304.10 + 4013.59i) q^{42} -1410.60i q^{43} +(-819.316 - 1877.54i) q^{44} -2549.37 q^{45} +(636.236 + 206.726i) q^{46} +(-3360.07 + 2441.23i) q^{47} +(2499.61 + 1816.07i) q^{48} +(-268.615 - 826.712i) q^{49} +(1570.90 - 510.418i) q^{50} +(1402.49 - 1930.36i) q^{51} +(-221.682 - 305.119i) q^{52} +(1136.82 - 3498.77i) q^{53} -249.385i q^{54} +(-786.566 + 3570.18i) q^{55} +305.172 q^{56} +(-3525.04 - 1145.35i) q^{57} +(3310.58 - 2405.28i) q^{58} +(-378.655 - 275.109i) q^{59} +(2032.71 + 6256.04i) q^{60} +(777.208 - 252.530i) q^{61} +(309.420 - 425.880i) q^{62} +(2836.26 + 3903.77i) q^{63} +(1408.34 - 4334.43i) q^{64} +673.058i q^{65} +(-8720.26 - 1921.21i) q^{66} +6019.75 q^{67} +(-2987.45 - 970.683i) q^{68} +(1212.87 - 881.203i) q^{69} +(-8021.23 - 5827.76i) q^{70} +(1149.19 + 3536.85i) q^{71} +(-428.248 + 139.146i) q^{72} +(-1264.79 + 1740.83i) q^{73} +(4271.33 + 5878.98i) q^{74} +(1143.85 - 3520.42i) q^{75} +4879.47i q^{76} +(6341.99 - 2767.50i) q^{77} -1643.96 q^{78} +(-10376.9 - 3371.66i) q^{79} +(-5872.58 + 4266.68i) q^{80} +(5077.27 + 3688.85i) q^{81} +(-1026.87 - 3160.39i) q^{82} +(-4239.31 + 1377.44i) q^{83} +(7318.23 - 10072.7i) q^{84} +(3295.00 + 4535.17i) q^{85} +(-2501.39 + 7698.50i) q^{86} -9170.47i q^{87} +(62.7337 + 642.657i) q^{88} -1587.53 q^{89} +(13913.5 + 4520.75i) q^{90} +(1030.63 - 748.799i) q^{91} +(-1596.72 - 1160.09i) q^{92} +(-364.550 - 1121.97i) q^{93} +(22666.9 - 7364.92i) q^{94} +(5118.38 - 7044.84i) q^{95} +(-11066.9 - 15232.3i) q^{96} +(-5788.35 + 17814.7i) q^{97} +4988.20i q^{98} +(-7637.86 + 6775.33i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 5 q^{2} - 6 q^{3} + 7 q^{4} - 18 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} + q^{9}+O(q^{10}) \) 12 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 - 18 * q^5 + 75 * q^6 - 80 * q^7 - 245 * q^8 + q^9	\( 12 q - 5 q^{2} - 6 q^{3} + 7 q^{4} - 18 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} + q^{9} - 43 q^{11} + 594 q^{12} + 250 q^{13} + 610 q^{14} + 1134 q^{15} - 633 q^{16} - 1250 q^{17} - 3150 q^{18} - 1025 q^{19} + 752 q^{20} - 35 q^{22} + 1684 q^{23} + 5345 q^{24} + 197 q^{25} + 3490 q^{26} - 687 q^{27} - 3580 q^{28} - 2690 q^{29} - 6740 q^{30} - 1136 q^{31} + 5939 q^{33} + 2370 q^{34} + 3610 q^{35} - 514 q^{36} - 336 q^{37} + 1900 q^{38} - 6880 q^{39} - 2340 q^{40} - 4550 q^{41} + 1310 q^{42} - 6268 q^{44} + 5136 q^{45} + 4150 q^{46} + 24 q^{47} + 344 q^{48} + 827 q^{49} + 8895 q^{50} + 13155 q^{51} + 14070 q^{52} + 414 q^{53} - 2738 q^{55} - 21340 q^{56} - 26925 q^{57} + 2980 q^{58} - 10011 q^{59} - 6856 q^{60} + 9460 q^{61} - 6200 q^{62} + 9150 q^{63} - 2633 q^{64} - 3210 q^{66} + 12154 q^{67} - 9400 q^{68} - 9022 q^{69} - 9380 q^{70} + 17574 q^{71} + 43045 q^{72} + 27950 q^{73} + 43270 q^{74} - 1761 q^{75} + 4090 q^{77} - 42920 q^{78} - 41540 q^{79} - 2308 q^{80} - 21080 q^{81} - 28175 q^{82} - 18665 q^{83} + 26250 q^{84} - 4230 q^{85} - 10125 q^{86} - 15125 q^{88} + 5554 q^{89} + 18400 q^{90} + 7390 q^{91} + 3904 q^{92} + 36898 q^{93} + 18920 q^{94} + 14110 q^{95} - 21140 q^{96} + 20769 q^{97} - 3269 q^{99}+O(q^{100}) \) 12 * q - 5 * q^2 - 6 * q^3 + 7 * q^4 - 18 * q^5 + 75 * q^6 - 80 * q^7 - 245 * q^8 + q^9 - 43 * q^11 + 594 * q^12 + 250 * q^13 + 610 * q^14 + 1134 * q^15 - 633 * q^16 - 1250 * q^17 - 3150 * q^18 - 1025 * q^19 + 752 * q^20 - 35 * q^22 + 1684 * q^23 + 5345 * q^24 + 197 * q^25 + 3490 * q^26 - 687 * q^27 - 3580 * q^28 - 2690 * q^29 - 6740 * q^30 - 1136 * q^31 + 5939 * q^33 + 2370 * q^34 + 3610 * q^35 - 514 * q^36 - 336 * q^37 + 1900 * q^38 - 6880 * q^39 - 2340 * q^40 - 4550 * q^41 + 1310 * q^42 - 6268 * q^44 + 5136 * q^45 + 4150 * q^46 + 24 * q^47 + 344 * q^48 + 827 * q^49 + 8895 * q^50 + 13155 * q^51 + 14070 * q^52 + 414 * q^53 - 2738 * q^55 - 21340 * q^56 - 26925 * q^57 + 2980 * q^58 - 10011 * q^59 - 6856 * q^60 + 9460 * q^61 - 6200 * q^62 + 9150 * q^63 - 2633 * q^64 - 3210 * q^66 + 12154 * q^67 - 9400 * q^68 - 9022 * q^69 - 9380 * q^70 + 17574 * q^71 + 43045 * q^72 + 27950 * q^73 + 43270 * q^74 - 1761 * q^75 + 4090 * q^77 - 42920 * q^78 - 41540 * q^79 - 2308 * q^80 - 21080 * q^81 - 28175 * q^82 - 18665 * q^83 + 26250 * q^84 - 4230 * q^85 - 10125 * q^86 - 15125 * q^88 + 5554 * q^89 + 18400 * q^90 + 7390 * q^91 + 3904 * q^92 + 36898 * q^93 + 18920 * q^94 + 14110 * q^95 - 21140 * q^96 + 20769 * q^97 - 3269 * q^99

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