LMFDB - Embedded newform 11.5.d.a.6.1

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			6.1
Root			$-4.56289i$ of defining polynomial
Character	$\chi$	$=$	11.6
Dual form			11.5.d.a.2.1

$q$-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 $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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	−0.897510	−	0.440995i	$-0.854626\pi$
$2$	−5.45760	+	1.77328i	−1.36440	+	0.443321i	−0.466891	+	0.884315i	$0.654626\pi$
$3$	−10.4040	−	7.55891i	−1.15599	−	0.839879i	−0.166728	−	0.986003i	$-0.553320\pi$
$3$	−10.4040	−	7.55891i	−1.15599	−	0.839879i	−0.989266	+	0.146124i	$0.953320\pi$
$4$	13.6966	−	9.95117i	0.856038	−	0.621948i
$5$	−9.33639	+	28.7345i	−0.373456	+	1.14938i	0.571059	+	0.820909i	$0.306533\pi$
$5$	−9.33639	+	28.7345i	−0.373456	+	1.14938i	−0.944515	+	0.328470i	$0.893467\pi$
$6$	70.1847	+	22.8044i	1.94958	+	0.633455i
$7$	−33.6132	−	46.2646i	−0.685983	−	0.944175i	0.314003	−	0.949422i	$-0.398330\pi$
$7$	−33.6132	−	46.2646i	−0.685983	−	0.944175i	−0.999986	+	0.00524700i	$0.998330\pi$
$8$	−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	−0.371027	−	0.928622i	$-0.620994\pi$
$13$	−21.1866	+	6.88395i	−0.125365	+	0.0407335i	0.245663	+	0.969355i	$0.420994\pi$
$14$	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	−0.0126306	−	0.999920i	$-0.504021\pi$
$17$	−176.460	−	57.3353i	−0.610587	−	0.198392i	−0.597957	+	0.801528i	$0.704021\pi$
$18$	−284.610	−	391.732i	−0.878426	−	1.20905i
$19$	169.409	−	233.171i	0.469276	−	0.645903i	−0.507124	−	0.861873i	$-0.669291\pi$
$19$	169.409	−	233.171i	0.469276	−	0.645903i	0.976400	+	0.215970i	$0.0692914\pi$
$20$	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	0.483514	−	0.875337i	$-0.339360\pi$
$29$	−419.150	−	576.911i	−0.498395	−	0.685982i	−0.981909	+	0.189355i	$0.939360\pi$
$30$	−1310.54	+	1803.81i	−1.45616	+	2.00423i
$31$	−28.3476	−	87.2449i	−0.0294980	−	0.0907855i	0.935224	−	0.354058i	$-0.115198\pi$
$31$	−28.3476	−	87.2449i	−0.0294980	−	0.0907855i	−0.964722	+	0.263272i	$0.915198\pi$
$32$		−	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	−0.895314	−	0.445436i	$-0.853049\pi$
$37$	−1024.49	+	744.333i	−0.748347	+	0.543706i	0.146967	+	0.989141i	$0.453049\pi$
$38$	−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	−0.695684	−	0.718348i	$-0.744899\pi$
$41$	340.375	−	468.486i	0.202484	−	0.278695i	0.898168	+	0.439653i	$0.144899\pi$
$42$	−1304.10	−	4013.59i	−0.739283	−	2.27528i
$43$			1410.60i			0.762899i	0.924390	+	0.381450i	$0.124575\pi$
$43$			1410.60i			0.762899i	−0.924390	+	0.381450i	$0.875425\pi$
$44$	−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	−0.960949	−	0.276726i	$-0.910751\pi$
$47$	−3360.07	−	2441.23i	−1.52108	−	1.10513i	−0.560132	−	0.828404i	$-0.689249\pi$
$48$	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	0.921141	+	0.389230i	$0.127259\pi$
$53$	1136.82	+	3498.77i	0.404706	+	1.24556i	−0.516435	+	0.856327i	$0.672741\pi$
$54$			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	−0.640844	−	0.767671i	$-0.721416\pi$
$59$	−378.655	+	275.109i	−0.108778	+	0.0790315i	0.532067	+	0.846702i	$0.321416\pi$
$60$	2032.71	−	6256.04i	0.564642	−	1.73779i
$61$	777.208	+	252.530i	0.208871	+	0.0678662i	0.411584	−	0.911372i	$-0.364976\pi$
$61$	777.208	+	252.530i	0.208871	+	0.0678662i	−0.202713	+	0.979238i	$0.564976\pi$
$62$	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	−0.770007	−	0.638035i	$-0.779748\pi$
$71$	1149.19	−	3536.85i	0.227969	−	0.701617i	0.997977	−	0.0635821i	$-0.0202525\pi$
$72$	−428.248	−	139.146i	−0.0826096	−	0.0268415i
$73$	−1264.79	−	1740.83i	−0.237340	−	0.326671i	0.673687	−	0.739017i	$-0.264710\pi$
$73$	−1264.79	−	1740.83i	−0.237340	−	0.326671i	−0.911027	+	0.412346i	$0.864710\pi$
$74$	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	−0.981435	−	0.191796i	$-0.938569\pi$
$79$	−10376.9	+	3371.66i	−1.66270	+	0.540243i	−0.681263	+	0.732039i	$0.738569\pi$
$80$	−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	−0.0152885	−	0.999883i	$-0.504867\pi$
$83$	−4239.31	−	1377.44i	−0.615374	−	0.199947i	−0.600085	+	0.799936i	$0.704867\pi$
$84$	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	−0.398682	−	0.917089i	$-0.630532\pi$
$97$	−5788.35	−	17814.7i	−0.615193	−	1.89337i	−0.216511	−	0.976280i	$-0.569468\pi$
$98$		−	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	0.0807044	−	0.996738i	$-0.474283\pi$
$101$	7465.74	−	2425.77i	0.731863	−	0.237797i	0.651159	+	0.758941i	$0.274283\pi$
$102$	−11077.3	−	8048.12i	−1.06471	−	0.773560i
$103$	−7326.15	+	5322.76i	−0.690560	+	0.501721i	−0.876844	−	0.480775i	$-0.840355\pi$
$103$	−7326.15	+	5322.76i	−0.690560	+	0.501721i	0.186284	+	0.982496i	$0.440355\pi$
$104$	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	−0.113521	+	0.993536i	$0.536213\pi$
$107$	−11716.3	+	16126.1i	−1.02335	+	1.40852i	−0.909828	+	0.414984i	$0.863787\pi$
$108$	−227.359	−	699.739i	−0.0194924	−	0.0599913i
$109$			4222.52i			0.355401i	0.984085	+	0.177701i	$0.0568659\pi$
$109$			4222.52i			0.355401i	−0.984085	+	0.177701i	$0.943134\pi$
$110$	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	0.996543	+	0.0830819i	$0.0264763\pi$
$113$	17666.0	+	12835.1i	1.38351	+	1.00518i	0.386964	+	0.922095i	$0.373524\pi$
$114$	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	0.574942	−	0.818194i	$-0.305025\pi$
$127$	9018.65	+	2930.34i	0.559158	+	0.181681i	−0.0157845	+	0.999875i	$0.505025\pi$
$128$	−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	$-0.833405\pi$
$131$		−	17154.3i		−	0.999608i	0.866138	−	0.499804i	$-0.166595\pi$
$132$	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	−0.856529	−	0.516099i	$-0.827384\pi$
$137$	2623.40	−	8073.99i	0.139773	−	0.430177i	0.996302	+	0.0859221i	$0.0273836\pi$
$138$	−8181.99	−	2658.49i	−0.429636	−	0.139597i
$139$	−15617.1	−	21495.1i	−0.808298	−	1.11253i	−0.991584	−	0.129467i	$-0.958673\pi$
$139$	−15617.1	−	21495.1i	−0.808298	−	1.11253i	0.183286	−	0.983060i	$-0.441327\pi$
$140$	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	−0.301902	−	0.953339i	$-0.597622\pi$
$149$	−24565.5	−	7981.82i	−1.10650	−	0.359525i	−0.804602	+	0.593814i	$0.797622\pi$
$150$	−12485.4	−	17184.7i	−0.554907	−	0.763764i
$151$	−16028.5	+	22061.3i	−0.702972	+	0.967558i	0.296948	+	0.954894i	$0.404031\pi$
$151$	−16028.5	+	22061.3i	−0.702972	+	0.967558i	−0.999920	+	0.0126640i	$0.995969\pi$
$152$	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	0.838024	−	0.545633i	$-0.183711\pi$
$157$	14248.6	+	10352.2i	0.578061	+	0.419986i	−0.259964	+	0.965618i	$0.583711\pi$
$158$	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	0.908880	−	0.417058i	$-0.136939\pi$
$163$	−1901.28	−	5851.55i	−0.0715602	−	0.220240i	−0.980440	+	0.196819i	$0.936939\pi$
$164$		−	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	−0.374548	−	0.927208i	$-0.622202\pi$
$167$	−3697.07	+	1201.25i	−0.132564	+	0.0430726i	0.241984	+	0.970280i	$0.422202\pi$
$168$	−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	−0.368288	−	0.929712i	$-0.620056\pi$
$173$	18847.1	−	25940.8i	0.629728	−	0.866746i	0.998016	+	0.0629660i	$0.0200560\pi$
$174$	−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	0.479394	−	0.877600i	$-0.340857\pi$
$179$	−6636.09	−	4821.40i	−0.207112	−	0.150476i	−0.686506	+	0.727124i	$0.740857\pi$
$180$	−34917.7	+	25369.2i	−1.07771	+	0.783001i
$181$	−7947.12	+	24458.7i	−0.242579	+	0.746581i	0.753447	+	0.657509i	$0.228390\pi$
$181$	−7947.12	+	24458.7i	−0.242579	+	0.746581i	−0.996025	+	0.0890713i	$0.971610\pi$
$182$	−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	−0.612504	−	0.790467i	$-0.709838\pi$
$191$	−1824.03	+	1325.24i	−0.0499995	+	0.0363268i	0.562505	+	0.826794i	$0.309838\pi$
$192$	18111.3	−	55740.8i	0.491300	−	1.51206i
$193$	−19901.9	−	6466.53i	−0.534294	−	0.173603i	0.0294283	−	0.999567i	$-0.490631\pi$
$193$	−19901.9	−	6466.53i	−0.534294	−	0.173603i	−0.563723	+	0.825964i	$0.690631\pi$
$194$	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	$0.00687933\pi$
$197$			1677.35i			0.0432208i	−0.999766	+	0.0216104i	$0.993121\pi$
$198$	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	−0.219117	−	0.975699i	$-0.570318\pi$
$211$	7885.34	−	2562.10i	0.177115	−	0.0575482i	0.396232	+	0.918150i	$0.370318\pi$
$212$	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	0.888733	−	0.458426i	$-0.151587\pi$
$223$	36171.7	+	26280.3i	0.727377	+	0.528470i	−0.161356	+	0.986896i	$0.551587\pi$
$224$	−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	0.709622	−	0.704583i	$-0.248866\pi$
$227$	−9262.91	−	12749.3i	−0.179761	−	0.247420i	−0.889383	+	0.457163i	$0.848866\pi$
$228$	−36883.5	+	50765.7i	−0.709515	+	0.976564i
$229$	−126.968	−	390.768i	−0.00242117	−	0.00745158i	0.949839	−	0.312740i	$-0.101247\pi$
$229$	−126.968	−	390.768i	−0.00242117	−	0.00745158i	−0.952260	+	0.305289i	$0.901247\pi$
$230$			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	0.298076	−	0.954542i	$-0.403655\pi$
$233$	59733.7	−	19408.6i	1.10029	−	0.357506i	0.802214	+	0.597036i	$0.203655\pi$
$234$	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	−0.701155	−	0.713009i	$-0.747332\pi$
$239$	11060.1	−	15222.9i	0.193626	−	0.266503i	0.894781	+	0.446506i	$0.147332\pi$
$240$	28846.6	+	88780.6i	0.500809	+	1.54133i
$241$			52220.3i			0.899094i	0.893257	+	0.449547i	$0.148415\pi$
$241$			52220.3i			0.899094i	−0.893257	+	0.449547i	$0.851585\pi$
$242$	−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	0.818935	−	0.573886i	$-0.194565\pi$
$251$	−11398.1	−	35079.8i	−0.180919	−	0.556813i	−0.999854	+	0.0170739i	$0.994565\pi$
$252$		−	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	−0.399859	−	0.916577i	$-0.630941\pi$
$257$	23004.5	−	16713.8i	0.348295	−	0.253051i	0.748153	+	0.663526i	$0.230941\pi$
$258$	−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	$-0.867357\pi$
$263$		−	55993.0i		−	0.809510i	0.914425	−	0.404755i	$-0.132643\pi$
$264$	−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	−0.995694	−	0.0926960i	$-0.970452\pi$
$269$	−9817.61	+	30215.5i	−0.135675	+	0.417566i	0.860019	+	0.510262i	$0.170452\pi$
$270$	−7165.93	−	2328.35i	−0.0982981	−	0.0319390i
$271$	46838.5	+	64467.6i	0.637770	+	0.877815i	0.998494	−	0.0548576i	$-0.0174705\pi$
$271$	46838.5	+	64467.6i	0.637770	+	0.877815i	−0.360724	+	0.932672i	$0.617470\pi$
$272$	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	−0.998351	−	0.0574001i	$-0.981719\pi$
$277$	−135986.	+	44184.7i	−1.77230	+	0.575854i	−0.773944	+	0.633254i	$0.781719\pi$
$278$	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	0.488061	−	0.872809i	$-0.337704\pi$
$281$	29206.6	+	9489.80i	0.369886	+	0.120183i	−0.118175	+	0.992993i	$0.537704\pi$
$282$	−180155.	−	247961.i	−2.26541	−	3.11807i
$283$	−82477.7	+	113521.i	−1.02983	+	1.41743i	−0.124748	+	0.992188i	$0.539812\pi$
$283$	−82477.7	+	113521.i	−1.02983	+	1.41743i	−0.905078	+	0.425245i	$0.860188\pi$
$284$	−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	−0.975086	−	0.221825i	$-0.928799\pi$
$293$	−75953.7	−	104541.i	−0.884736	−	1.21774i	0.0903501	−	0.995910i	$-0.471201\pi$
$294$	−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	$-0.803435\pi$
$307$		−	109144.i		−	1.15804i	0.815314	−	0.579020i	$-0.196565\pi$
$308$	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	0.455304	−	0.890336i	$-0.349531\pi$
$311$	−24253.7	−	17621.4i	−0.250760	−	0.182187i	−0.706063	+	0.708149i	$0.749531\pi$
$312$	−1236.82	+	898.603i	−0.0127057	+	0.00923121i
$313$	48065.9	−	147932.i	0.490623	−	1.50998i	−0.333045	−	0.942911i	$-0.608076\pi$
$313$	48065.9	−	147932.i	0.490623	−	1.50998i	0.823668	−	0.567072i	$-0.191924\pi$
$314$	−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	0.999800	+	0.0200029i	$0.00636756\pi$
$317$	20369.3	+	62690.4i	0.202702	+	0.623853i	−0.797098	+	0.603850i	$0.793632\pi$
$318$			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	−0.999811	−	0.0194335i	$-0.993814\pi$
$337$	−80558.5	−	110879.i	−0.709335	−	0.976316i	0.290476	−	0.956882i	$-0.406186\pi$
$338$	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	0.650526	−	0.759484i	$-0.274548\pi$
$347$	87946.7	+	28575.6i	0.730399	+	0.237321i	0.0798733	+	0.996805i	$0.474548\pi$
$348$	91256.9	+	125604.i	0.753542	+	1.03716i
$349$	−55119.1	+	75865.0i	−0.452534	+	0.622860i	−0.972940	−	0.231059i	$-0.925781\pi$
$349$	−55119.1	+	75865.0i	−0.452534	+	0.622860i	0.520405	+	0.853919i	$0.325781\pi$
$350$	−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	0.752120	−	0.659026i	$-0.229031\pi$
$359$	−13799.1	−	18992.8i	−0.107069	−	0.147367i	−0.859189	+	0.511659i	$0.829031\pi$
$360$	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	−0.638279	−	0.769805i	$-0.720353\pi$
$367$	−13925.4	+	10117.4i	−0.103389	+	0.0751166i	0.534890	+	0.844922i	$0.320353\pi$
$368$	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	$-0.928805\pi$
$373$		−	61718.8i		−	0.443609i	0.975091	−	0.221804i	$-0.0711946\pi$
$374$	−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	−0.527240	−	0.849717i	$-0.676773\pi$
$379$	57277.9	−	176283.i	0.398757	−	1.22725i	0.925997	−	0.377531i	$-0.123227\pi$
$380$	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	0.987546	+	0.157331i	$0.0502888\pi$
$383$	41231.5	+	126898.i	0.281081	+	0.865079i	−0.706465	+	0.707748i	$0.749711\pi$
$384$			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	−0.693975	−	0.719999i	$-0.744142\pi$
$389$	−33845.2	+	24589.9i	−0.223665	+	0.162502i	0.470310	+	0.882501i	$0.344142\pi$
$390$	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	0.725695	+	0.688016i	$0.241518\pi$
$401$	−42742.6	+	131548.i	−0.265810	+	0.818080i	−0.991506	+	0.130064i	$0.958482\pi$
$402$	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	0.406247	−	0.913763i	$-0.366837\pi$
$409$	212782.	−	69137.1i	1.27200	−	0.413299i	0.865757	+	0.500464i	$0.166837\pi$
$410$	−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	0.0989305	−	0.995094i	$-0.468458\pi$
$421$	−144786.	−	105193.i	−0.816889	−	0.593505i	−0.915820	+	0.401590i	$0.868458\pi$
$422$	−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	−0.537620	−	0.843187i	$-0.680676\pi$
$431$	−88598.8	+	28787.5i	−0.476951	+	0.154971i	0.0606693	+	0.998158i	$0.480676\pi$
$432$	8447.07	+	6137.16i	0.0452625	+	0.0328851i
$433$	46736.5	−	33956.1i	0.249276	−	0.181110i	−0.456130	−	0.889913i	$-0.650765\pi$
$433$	46736.5	−	33956.1i	0.249276	−	0.181110i	0.705406	+	0.708804i	$0.250765\pi$
$434$	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	$0.147961\pi$
$439$			172784.i			0.896548i	−0.893896	+	0.448274i	$0.852039\pi$
$440$	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	0.930570	−	0.366115i	$-0.119312\pi$
$443$	170724.	+	124038.i	0.869936	+	0.632046i	−0.0606337	+	0.998160i	$0.519312\pi$
$444$	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	0.954788	+	0.297287i	$0.0960820\pi$
$449$	71989.6	+	221561.i	0.357089	+	1.09901i	−0.597699	+	0.801721i	$0.703918\pi$
$450$			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	−0.335144	−	0.942167i	$-0.608785\pi$
$457$	−242280.	−	78721.6i	−1.16007	−	0.376931i	−0.824929	+	0.565236i	$0.808785\pi$
$458$	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	$-0.660474\pi$
$461$		−	372162.i		−	1.75118i	0.483058	−	0.875588i	$-0.339526\pi$
$462$	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	−0.924843	−	0.380349i	$-0.875804\pi$
$467$	10235.8	−	31502.6i	0.0469342	−	0.144449i	0.971777	+	0.235900i	$0.0758039\pi$
$468$	−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	−0.0538938	−	0.998547i	$-0.517163\pi$
$479$	−157035.	−	51023.9i	−0.684426	−	0.222383i	−0.630532	+	0.776163i	$0.717163\pi$
$480$	−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	0.825792	−	0.563975i	$-0.190729\pi$
$487$	129163.	+	93842.4i	0.544603	+	0.395677i	−0.281189	+	0.959653i	$0.590729\pi$
$488$	−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	0.983186	+	0.182609i	$0.0584543\pi$
$491$	205651.	+	283054.i	0.853036	+	1.17410i	−0.130149	+	0.991494i	$0.541546\pi$
$492$	−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	−0.321646	−	0.946860i	$-0.604236\pi$
$499$	119390.	−	86742.2i	0.479478	−	0.348361i	0.801123	+	0.598499i	$0.204236\pi$
$500$	−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	0.00821208	+	0.999966i	$0.497386\pi$
$503$	−239182.	+	329206.i	−0.945350	+	1.30116i	−0.953562	+	0.301196i	$0.902614\pi$
$504$	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	−0.0175338	−	0.999846i	$-0.505581\pi$
$509$	−252309.	−	183313.i	−0.973862	−	0.707552i	−0.956329	+	0.292294i	$0.905581\pi$
$510$	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	−0.0112174	−	0.999937i	$-0.503571\pi$
$521$	254154.	−	184653.i	0.936313	−	0.680271i	0.947530	+	0.319666i	$0.103571\pi$
$522$	−106700.	+	328389.i	−0.391583	+	1.20517i
$523$	363288.	+	118039.i	1.32815	+	0.431543i	0.885287	−	0.465046i	$-0.153962\pi$
$523$	363288.	+	118039.i	1.32815	+	0.431543i	0.442865	+	0.896588i	$0.353962\pi$
$524$	−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	−0.638179	−	0.769888i	$-0.720312\pi$
$541$	−205447.	+	66753.7i	−0.701947	+	0.228077i	−0.0637686	+	0.997965i	$0.520312\pi$
$542$	−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	−0.611361	−	0.791352i	$-0.709378\pi$
$547$	98792.7	−	135977.i	0.330180	−	0.454453i	0.941541	+	0.336898i	$0.109378\pi$
$548$	−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	0.466888	−	0.884317i	$-0.345375\pi$
$557$	−160840.	−	221378.i	−0.518424	−	0.713549i	−0.985311	+	0.170768i	$0.945375\pi$
$558$	−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	−0.749046	−	0.662518i	$-0.769488\pi$
$563$	−306071.	+	99448.5i	−0.965618	+	0.313748i	−0.216572	+	0.976267i	$0.569488\pi$
$564$	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	−0.189540	−	0.981873i	$-0.560700\pi$
$569$	259931.	−	357764.i	0.802848	−	1.10503i	0.992388	−	0.123153i	$-0.0393005\pi$
$570$	198578.	+	611161.i	0.611199	+	1.88108i
$571$			560951.i			1.72049i	0.509880	+	0.860246i	$0.329690\pi$
$571$			560951.i			1.72049i	−0.509880	+	0.860246i	$0.670310\pi$
$572$	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	−0.543508	−	0.839404i	$-0.682904\pi$
$577$	129705.	−	399192.i	0.389588	−	1.19903i	0.933097	−	0.359626i	$-0.117096\pi$
$578$	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	−0.654051	−	0.756451i	$-0.726932\pi$
$587$	−47114.9	+	34231.0i	−0.136736	+	0.0993444i	0.517315	+	0.855795i	$0.326932\pi$
$588$	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	$0.0269951\pi$
$593$			59573.5i			0.169412i	−0.996406	+	0.0847060i	$0.973005\pi$
$594$	−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	−0.990702	−	0.136050i	$-0.956559\pi$
$599$	−39195.0	+	120630.i	−0.109239	+	0.336203i	0.881463	+	0.472253i	$0.156559\pi$
$600$	−18786.6	−	6104.13i	−0.0521850	−	0.0169559i
$601$	316638.	+	435815.i	0.876626	+	1.20657i	0.977344	+	0.211657i	$0.0678859\pi$
$601$	316638.	+	435815.i	0.876626	+	1.20657i	−0.100718	+	0.994915i	$0.532114\pi$
$602$	−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	−0.282521	−	0.959261i	$-0.591171\pi$
$607$	19437.1	−	6315.50i	0.0527539	−	0.0171408i	0.335275	+	0.942120i	$0.391171\pi$
$608$	−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	−0.0730746	−	0.997326i	$-0.523281\pi$
$613$	337448.	−	464458.i	0.898021	−	1.23602i	0.971095	−	0.238693i	$-0.0767189\pi$
$614$	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	0.410380	−	0.911915i	$-0.365396\pi$
$619$	−126477.	−	91890.9i	−0.330088	−	0.239823i	−0.740468	+	0.672091i	$0.765396\pi$
$620$	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	−0.371128	−	0.928582i	$-0.621029\pi$
$631$	158197.	−	114937.i	0.397320	−	0.288670i	0.768449	+	0.639912i	$0.221029\pi$
$632$	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	0.0109187	−	0.999940i	$-0.496524\pi$
$641$	−384875.	−	279628.i	−0.936707	−	0.680558i	−0.947626	+	0.319383i	$0.896524\pi$
$642$	−1.19005e6	+	864625.i	−2.88733	+	2.09777i
$643$	32940.2	−	101379.i	0.0796717	−	0.245204i	−0.903285	−	0.429041i	$-0.858852\pi$
$643$	32940.2	−	101379.i	0.0796717	−	0.245204i	0.982957	+	0.183836i	$0.0588517\pi$
$644$	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	0.952811	+	0.303564i	$0.0981765\pi$
$647$	150867.	+	464321.i	0.360401	+	1.10920i	−0.592410	+	0.805637i	$0.701823\pi$
$648$			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	−0.923316	−	0.384040i	$-0.874532\pi$
$653$	−359630.	+	261287.i	−0.843393	+	0.612761i	0.0799236	+	0.996801i	$0.474532\pi$
$654$	−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	$-0.951382\pi$
$659$		−	132146.i		−	0.304287i	0.988358	−	0.152143i	$-0.0486175\pi$
$660$	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	0.188865	−	0.982003i	$-0.439519\pi$
$673$	416181.	−	135225.i	0.918866	−	0.298558i	0.730002	+	0.683445i	$0.239519\pi$
$674$	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	0.391953	−	0.919985i	$-0.371800\pi$
$677$	77134.7	+	25062.6i	0.168295	+	0.0546825i	−0.223657	+	0.974668i	$0.571800\pi$
$678$	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	−0.997795	−	0.0663705i	$-0.978858\pi$
$691$	−109617.	−	337366.i	−0.229573	−	0.706555i	0.768222	−	0.640184i	$-0.221142\pi$
$692$		−	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	−0.992645	−	0.121058i	$-0.961371\pi$
$701$	−280476.	+	386042.i	−0.570768	+	0.785595i	0.421877	+	0.906653i	$0.361371\pi$
$702$	−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	−0.958204	−	0.286084i	$-0.907646\pi$
$709$	−7462.11	+	22966.0i	−0.0148446	+	0.0456870i	0.943360	+	0.331771i	$0.107646\pi$
$710$	−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	−0.739423	−	0.673241i	$-0.764901\pi$
$719$	−169370.	+	123055.i	−0.327626	+	0.238034i	0.411796	+	0.911276i	$0.364901\pi$
$720$	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	0.955148	−	0.296128i	$-0.0956954\pi$
$733$	203287.	+	279801.i	0.378357	+	0.520764i	−0.576791	+	0.816892i	$0.695695\pi$
$734$	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	−0.351308	−	0.936260i	$-0.614263\pi$
$739$	−46530.6	+	15118.7i	−0.0852021	+	0.0276838i	0.266106	+	0.963944i	$0.414263\pi$
$740$	−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	0.703379	−	0.710815i	$-0.251674\pi$
$743$	471791.	+	153294.i	0.854618	+	0.277682i	0.151239	+	0.988497i	$0.451674\pi$
$744$	−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	−0.134893	−	0.990860i	$-0.543069\pi$
$751$	−631084.	−	458509.i	−1.11894	−	0.812958i	−0.984048	+	0.177902i	$0.943069\pi$
$752$	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	0.992554	+	0.121805i	$0.0388684\pi$
$757$	149655.	+	460592.i	0.261156	+	0.803757i	−0.731398	+	0.681951i	$0.761132\pi$
$758$			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	−0.790807	−	0.612066i	$-0.790339\pi$
$761$	−620134.	+	201494.i	−1.07082	+	0.347930i	−0.280013	+	0.959996i	$0.590339\pi$
$762$	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	$-0.940041\pi$
$769$		−	221470.i		−	0.374508i	0.982311	−	0.187254i	$-0.0599588\pi$
$770$	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	0.900933	−	0.433959i	$-0.142884\pi$
$773$	458076.	+	332812.i	0.766617	+	0.556980i	−0.134316	+	0.990939i	$0.542884\pi$
$774$	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	−0.0209765	−	0.999780i	$-0.506678\pi$
$787$	−387479.	−	125900.i	−0.625603	−	0.203271i	−0.604626	+	0.796509i	$0.706678\pi$
$788$	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	0.192239	+	0.981348i	$0.438425\pi$
$797$	−343081.	+	1.05590e6i	−0.540108	+	1.66228i	−0.732346	+	0.680932i	$0.761575\pi$
$798$	−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	−0.431987	−	0.901880i	$-0.642187\pi$
$809$	−858406.	−	278913.i	−1.31158	−	0.426159i	−0.879596	+	0.475721i	$0.842187\pi$
$810$	−639564.	−	880284.i	−0.974796	−	1.34169i
$811$	−316037.	+	434987.i	−0.480503	+	0.661355i	−0.978601	−	0.205765i	$-0.934032\pi$
$811$	−316037.	+	434987.i	−0.480503	+	0.661355i	0.498099	+	0.867120i	$0.334032\pi$
$812$	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	0.723775	−	0.690036i	$-0.242405\pi$
$821$	−105250.	−	144864.i	−0.156147	−	0.214918i	−0.879922	+	0.475118i	$0.842405\pi$
$822$	368245.	−	506846.i	0.544996	−	0.750122i
$823$	−200047.	−	615680.i	−0.295346	−	0.908982i	−0.983105	−	0.183043i	$-0.941405\pi$
$823$	−200047.	−	615680.i	−0.295346	−	0.908982i	0.687759	−	0.725939i	$-0.258595\pi$
$824$		−	48324.9i		−	0.0711733i
$825$	−335061.	−	297223.i	−0.492285	−	0.436692i
$826$	−153593.			−0.225119
$827$	239782.	−	77909.9i	0.350595	−	0.113915i	−0.128425	−	0.991719i	$-0.540992\pi$
$827$	239782.	−	77909.9i	0.350595	−	0.113915i	0.479020	+	0.877804i	$0.340992\pi$
$828$	−134730.	−	97887.4i	−0.196519	−	0.142780i
$829$	−28463.1	+	20679.7i	−0.0414165	+	0.0300909i	−0.608301	−	0.793706i	$-0.708149\pi$
$829$	−28463.1	+	20679.7i	−0.0414165	+	0.0300909i	0.566884	+	0.823797i	$0.308149\pi$
$830$	−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	0.276964	−	0.960880i	$-0.410672\pi$
$839$	−388072.	−	281951.i	−0.551301	−	0.400544i	−0.828265	+	0.560337i	$0.810672\pi$
$840$	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	−0.525875	−	0.850562i	$-0.676262\pi$
$853$	−1.05595e6	−	343100.i	−1.45127	−	0.471545i	−0.925390	+	0.379017i	$0.876262\pi$
$854$	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	$-0.939251\pi$
$857$		−	278639.i		−	0.379385i	0.981844	−	0.189692i	$-0.0607491\pi$
$858$	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	−0.986357	−	0.164621i	$-0.947360\pi$
$863$	−68232.4	+	209998.i	−0.0916155	+	0.281964i	0.894741	+	0.446585i	$0.147360\pi$
$864$	−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	−0.979845	−	0.199760i	$-0.935984\pi$
$877$	−374622.	+	515623.i	−0.487073	+	0.670399i	0.492772	+	0.870159i	$0.335984\pi$
$878$	−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	0.513319	−	0.858198i	$-0.328416\pi$
$883$	−112471.	−	81715.2i	−0.144252	−	0.104805i	−0.657570	+	0.753393i	$0.728416\pi$
$884$	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	0.999576	+	0.0291196i	$0.00927036\pi$
$887$	565203.	+	777935.i	0.718384	+	0.988771i	−0.281192	+	0.959652i	$0.590730\pi$
$888$	−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	−0.397864	−	0.917444i	$-0.630248\pi$
$907$	381113.	−	1.17294e6i	0.463275	−	1.42581i	0.861139	−	0.508369i	$-0.169752\pi$
$908$	−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	−0.932790	−	0.360421i	$-0.882633\pi$
$911$	−323667.	−	996144.i	−0.389997	−	1.20029i	0.542792	−	0.839867i	$-0.317367\pi$
$912$		−	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	0.190878	−	0.981614i	$-0.438866\pi$
$919$	−195664.	−	63575.2i	−0.231676	−	0.0752760i	−0.422554	+	0.906338i	$0.638866\pi$
$920$	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	−0.740294	−	0.672283i	$-0.765314\pi$
$929$	219018.	−	674067.i	0.253774	−	0.781037i	0.994069	−	0.108754i	$-0.0346861\pi$
$930$	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	−0.560326	−	0.828272i	$-0.689324\pi$
$937$	−462509.	+	150278.i	−0.526794	+	0.171166i	0.0335325	+	0.999438i	$0.489324\pi$
$938$	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	0.962851	−	0.270034i	$-0.0870351\pi$
$941$	1.40180e6	+	455471.i	1.58309	+	0.514377i	0.620240	+	0.784412i	$0.287035\pi$
$942$	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	0.655642	−	0.755072i	$-0.272398\pi$
$953$	−240747.	−	331360.i	−0.265079	−	0.364850i	−0.920721	+	0.390222i	$0.872398\pi$
$954$	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	$-0.960483\pi$
$967$		−	231580.i		−	0.247656i	0.992304	−	0.123828i	$-0.0395171\pi$
$968$	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	0.995652	−	0.0931474i	$-0.0296928\pi$
$971$	1.14530e6	+	832112.i	1.21474	+	0.882558i	0.219085	+	0.975706i	$0.429693\pi$
$972$	−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	0.988596	+	0.150595i	$0.0481190\pi$
$977$	264712.	+	814701.i	0.277323	+	0.853511i	−0.711273	+	0.702916i	$0.751881\pi$
$978$		−	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	−0.656803	−	0.754063i	$-0.728092\pi$
$983$	−137802.	+	100119.i	−0.142610	+	0.103612i	0.514193	+	0.857675i	$0.328092\pi$
$984$	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	0.559432	−	0.828876i	$-0.311019\pi$
$997$	−399343.	−	549649.i	−0.401750	−	0.552962i	−0.961182	+	0.275915i	$0.911019\pi$
$998$	−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.6.1	yes	12
3.2	odd	2		99.5.k.a.28.3		12
4.3	odd	2		176.5.n.a.17.3		12
11.2	odd	10	inner	11.5.d.a.2.1	✓	12
11.3	even	5		121.5.b.b.120.11		12
11.4	even	5		121.5.d.c.118.1		12
11.5	even	5		121.5.d.e.40.3		12
11.6	odd	10		121.5.d.c.40.1		12
11.7	odd	10		121.5.d.e.118.3		12
11.8	odd	10		121.5.b.b.120.2		12
11.9	even	5		121.5.d.d.112.3		12
11.10	odd	2		121.5.d.d.94.3		12
33.2	even	10		99.5.k.a.46.3		12
44.35	even	10		176.5.n.a.145.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.5.d.a.2.1	✓	12	11.2	odd	10	inner
11.5.d.a.6.1	yes	12	1.1	even	1	trivial
99.5.k.a.28.3		12	3.2	odd	2
99.5.k.a.46.3		12	33.2	even	10
121.5.b.b.120.2		12	11.8	odd	10
121.5.b.b.120.11		12	11.3	even	5
121.5.d.c.40.1		12	11.6	odd	10
121.5.d.c.118.1		12	11.4	even	5
121.5.d.d.94.3		12	11.10	odd	2
121.5.d.d.112.3		12	11.9	even	5
121.5.d.e.40.3		12	11.5	even	5
121.5.d.e.118.3		12	11.7	odd	10
176.5.n.a.17.3		12	4.3	odd	2
176.5.n.a.145.3		12	44.35	even	10

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:	\( N \)	\(=\)	\( 11 \)
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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