LMFDB - Embedded newform 105.4.s.a.101.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(26,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("105.26");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.6
Character	$\chi$	$=$	105.101
Dual form			105.4.s.a.26.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35336 + 0.781362i) q^{2} +(-5.18197 - 0.383668i) q^{3} +(-2.77895 + 4.81328i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(7.31285 - 3.52975i) q^{6} +(-17.7664 - 5.23007i) q^{7} -21.1872i q^{8} +(26.7056 + 3.97631i) q^{9} +O(q^{10})$	\(q+(-1.35336 + 0.781362i) q^{2} +(-5.18197 - 0.383668i) q^{3} +(-2.77895 + 4.81328i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(7.31285 - 3.52975i) q^{6} +(-17.7664 - 5.23007i) q^{7} -21.1872i q^{8} +(26.7056 + 3.97631i) q^{9} +(6.76679 + 3.90681i) q^{10} +(26.1426 + 15.0935i) q^{11} +(16.2471 - 23.8761i) q^{12} +59.7880i q^{13} +(28.1309 - 6.80387i) q^{14} +(11.2936 + 23.3978i) q^{15} +(-5.67667 - 9.83227i) q^{16} +(59.7827 - 103.547i) q^{17} +(-39.2492 + 15.4854i) q^{18} +(102.212 - 59.0123i) q^{19} +27.7895 q^{20} +(90.0585 + 33.9185i) q^{21} -47.1738 q^{22} +(65.0867 - 37.5778i) q^{23} +(-8.12888 + 109.792i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-46.7161 - 80.9146i) q^{26} +(-136.862 - 30.8512i) q^{27} +(74.5457 - 70.9807i) q^{28} +189.451i q^{29} +(-33.5664 - 22.8412i) q^{30} +(-211.357 - 122.027i) q^{31} +(162.155 + 93.6200i) q^{32} +(-129.679 - 88.2439i) q^{33} +186.848i q^{34} +(21.7693 + 90.0061i) q^{35} +(-93.3525 + 117.491i) q^{36} +(-61.8489 - 107.125i) q^{37} +(-92.2200 + 159.730i) q^{38} +(22.9388 - 309.820i) q^{39} +(-91.7435 + 52.9681i) q^{40} +344.535 q^{41} +(-148.384 + 24.4645i) q^{42} +88.4283 q^{43} +(-145.298 + 83.8878i) q^{44} +(-49.5460 - 125.579i) q^{45} +(-58.7238 + 101.713i) q^{46} +(-278.061 - 481.616i) q^{47} +(25.6440 + 53.1285i) q^{48} +(288.293 + 185.839i) q^{49} -39.0681i q^{50} +(-349.519 + 513.639i) q^{51} +(-287.776 - 166.148i) q^{52} +(-78.7698 - 45.4778i) q^{53} +(209.329 - 65.1860i) q^{54} -150.935i q^{55} +(-110.811 + 376.422i) q^{56} +(-552.302 + 266.584i) q^{57} +(-148.030 - 256.395i) q^{58} +(136.583 - 236.569i) q^{59} +(-144.004 - 10.6619i) q^{60} +(368.048 - 212.492i) q^{61} +381.389 q^{62} +(-453.667 - 210.317i) q^{63} -201.778 q^{64} +(258.890 - 149.470i) q^{65} +(244.453 + 18.0991i) q^{66} +(60.2695 - 104.390i) q^{67} +(332.266 + 575.501i) q^{68} +(-351.695 + 169.755i) q^{69} +(-99.7890 - 104.801i) q^{70} -222.156i q^{71} +(84.2472 - 565.818i) q^{72} +(853.939 + 493.022i) q^{73} +(167.407 + 96.6527i) q^{74} +(73.0813 - 107.397i) q^{75} +655.969i q^{76} +(-385.522 - 404.885i) q^{77} +(211.037 + 437.221i) q^{78} +(335.113 + 580.432i) q^{79} +(-28.3833 + 49.1614i) q^{80} +(697.378 + 212.380i) q^{81} +(-466.279 + 269.206i) q^{82} +778.740 q^{83} +(-413.527 + 339.219i) q^{84} -597.827 q^{85} +(-119.675 + 69.0945i) q^{86} +(72.6863 - 981.728i) q^{87} +(319.789 - 553.890i) q^{88} +(-406.705 - 704.434i) q^{89} +(165.177 + 131.241i) q^{90} +(312.695 - 1062.22i) q^{91} +417.707i q^{92} +(1048.43 + 713.431i) q^{93} +(752.633 + 434.533i) q^{94} +(-511.062 - 295.062i) q^{95} +(-804.361 - 547.350i) q^{96} +288.573i q^{97} +(-535.371 - 26.2462i) q^{98} +(638.138 + 507.031i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9}+O(q^{10}) $ 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9	\( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9} + 36 q^{11} + 246 q^{12} + 18 q^{14} + 20 q^{15} - 376 q^{16} - 72 q^{17} - 442 q^{18} - 198 q^{19} - 640 q^{20} - 218 q^{21} + 204 q^{22} + 72 q^{23} - 50 q^{24} - 400 q^{25} - 312 q^{26} + 508 q^{27} + 350 q^{28} + 40 q^{30} + 510 q^{31} + 810 q^{32} + 290 q^{33} - 70 q^{35} - 612 q^{36} - 658 q^{37} - 192 q^{38} - 648 q^{39} - 1404 q^{41} + 1892 q^{42} + 332 q^{43} + 2034 q^{44} - 490 q^{45} - 468 q^{46} + 408 q^{47} + 2810 q^{48} + 980 q^{49} - 888 q^{51} + 3378 q^{52} + 1152 q^{53} + 2714 q^{54} - 3354 q^{56} - 816 q^{57} - 1080 q^{58} - 48 q^{59} - 420 q^{60} - 1662 q^{61} - 2076 q^{62} + 874 q^{63} - 1952 q^{64} + 870 q^{65} - 1892 q^{66} - 1298 q^{67} + 1182 q^{68} + 2450 q^{69} - 450 q^{70} - 2708 q^{72} + 378 q^{73} + 2898 q^{74} - 50 q^{75} - 3528 q^{77} - 1896 q^{78} - 326 q^{79} - 1880 q^{80} - 3308 q^{81} - 2916 q^{82} - 1536 q^{83} + 1380 q^{84} + 720 q^{85} + 5202 q^{86} - 1090 q^{87} + 1668 q^{88} - 1590 q^{89} + 910 q^{90} + 2082 q^{91} - 4950 q^{93} - 1152 q^{94} + 990 q^{95} + 7416 q^{96} - 7830 q^{98} + 3128 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9 + 36 * q^11 + 246 * q^12 + 18 * q^14 + 20 * q^15 - 376 * q^16 - 72 * q^17 - 442 * q^18 - 198 * q^19 - 640 * q^20 - 218 * q^21 + 204 * q^22 + 72 * q^23 - 50 * q^24 - 400 * q^25 - 312 * q^26 + 508 * q^27 + 350 * q^28 + 40 * q^30 + 510 * q^31 + 810 * q^32 + 290 * q^33 - 70 * q^35 - 612 * q^36 - 658 * q^37 - 192 * q^38 - 648 * q^39 - 1404 * q^41 + 1892 * q^42 + 332 * q^43 + 2034 * q^44 - 490 * q^45 - 468 * q^46 + 408 * q^47 + 2810 * q^48 + 980 * q^49 - 888 * q^51 + 3378 * q^52 + 1152 * q^53 + 2714 * q^54 - 3354 * q^56 - 816 * q^57 - 1080 * q^58 - 48 * q^59 - 420 * q^60 - 1662 * q^61 - 2076 * q^62 + 874 * q^63 - 1952 * q^64 + 870 * q^65 - 1892 * q^66 - 1298 * q^67 + 1182 * q^68 + 2450 * q^69 - 450 * q^70 - 2708 * q^72 + 378 * q^73 + 2898 * q^74 - 50 * q^75 - 3528 * q^77 - 1896 * q^78 - 326 * q^79 - 1880 * q^80 - 3308 * q^81 - 2916 * q^82 - 1536 * q^83 + 1380 * q^84 + 720 * q^85 + 5202 * q^86 - 1090 * q^87 + 1668 * q^88 - 1590 * q^89 + 910 * q^90 + 2082 * q^91 - 4950 * q^93 - 1152 * q^94 + 990 * q^95 + 7416 * q^96 - 7830 * q^98 + 3128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.35336	+	0.781362i	−0.478485	+	0.276253i	−0.719785	−	0.694197i	$-0.755759\pi$
$2$	−1.35336	+	0.781362i	−0.478485	+	0.276253i	0.241300	+	0.970451i	$0.422426\pi$
$3$	−5.18197	−	0.383668i	−0.997270	−	0.0738370i
$3$	−5.18197	−	0.383668i	−0.997270	−	0.0738370i
$4$	−2.77895	+	4.81328i	−0.347368	+	0.601660i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$	7.31285	−	3.52975i	0.497576	−	0.240169i
$7$	−17.7664	−	5.23007i	−0.959298	−	0.282397i
$7$	−17.7664	−	5.23007i	−0.959298	−	0.282397i
$8$		−	21.1872i		−	0.936353i
$9$	26.7056	+	3.97631i	0.989096	+	0.147271i
$10$	6.76679	+	3.90681i	0.213985	+	0.123544i
$11$	26.1426	+	15.0935i	0.716573	+	0.413713i	0.813490	−	0.581579i	$-0.197565\pi$
$11$	26.1426	+	15.0935i	0.716573	+	0.413713i	−0.0969173	+	0.995292i	$0.530898\pi$
$12$	16.2471	−	23.8761i	0.390845	−	0.574369i
$13$			59.7880i			1.27555i	0.770221	+	0.637777i	$0.220146\pi$
$13$			59.7880i			1.27555i	−0.770221	+	0.637777i	$0.779854\pi$
$14$	28.1309	−	6.80387i	0.537022	−	0.129886i
$15$	11.2936	+	23.3978i	0.194399	+	0.402752i
$16$	−5.67667	−	9.83227i	−0.0886979	−	0.153629i
$17$	59.7827	−	103.547i	0.852907	−	1.47728i	−0.0256655	−	0.999671i	$-0.508170\pi$
$17$	59.7827	−	103.547i	0.852907	−	1.47728i	0.878573	−	0.477608i	$-0.158496\pi$
$18$	−39.2492	+	15.4854i	−0.513951	+	0.202774i
$19$	102.212	−	59.0123i	1.23416	−	0.712545i	0.266269	−	0.963899i	$-0.414209\pi$
$19$	102.212	−	59.0123i	1.23416	−	0.712545i	0.967895	+	0.251354i	$0.0808757\pi$
$20$	27.7895			0.310696
$21$	90.0585	+	33.9185i	0.935828	+	0.352458i
$22$	−47.1738			−0.457159
$23$	65.0867	−	37.5778i	0.590066	−	0.340675i	−0.175058	−	0.984558i	$-0.556011\pi$
$23$	65.0867	−	37.5778i	0.590066	−	0.340675i	0.765124	+	0.643884i	$0.222678\pi$
$24$	−8.12888	+	109.792i	−0.0691375	+	0.933797i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−46.7161	−	80.9146i	−0.352376	−	0.610333i
$27$	−136.862	−	30.8512i	−0.975522	−	0.219901i
$28$	74.5457	−	70.9807i	0.503137	−	0.479075i
$29$			189.451i			1.21311i	0.795042	+	0.606554i	$0.207449\pi$
$29$			189.451i			1.21311i	−0.795042	+	0.606554i	$0.792551\pi$
$30$	−33.5664	−	22.8412i	−0.204279	−	0.139007i
$31$	−211.357	−	122.027i	−1.22454	−	0.706990i	−0.258660	−	0.965968i	$-0.583281\pi$
$31$	−211.357	−	122.027i	−1.22454	−	0.706990i	−0.965883	+	0.258978i	$0.916614\pi$
$32$	162.155	+	93.6200i	0.895786	+	0.517183i
$33$	−129.679	−	88.2439i	−0.684069	−	0.465494i
$34$			186.848i			0.942474i
$35$	21.7693	+	90.0061i	0.105134	+	0.434680i
$36$	−93.3525	+	117.491i	−0.432188	+	0.543942i
$37$	−61.8489	−	107.125i	−0.274808	−	0.475981i	0.695279	−	0.718740i	$-0.255281\pi$
$37$	−61.8489	−	107.125i	−0.274808	−	0.475981i	−0.970087	+	0.242759i	$0.921948\pi$
$38$	−92.2200	+	159.730i	−0.393686	+	0.681884i
$39$	22.9388	−	309.820i	0.0941832	−	1.27207i
$40$	−91.7435	+	52.9681i	−0.362648	+	0.209375i
$41$	344.535			1.31237			0.656186	−	0.754599i	$-0.272169\pi$
$41$	344.535			1.31237			0.656186	+	0.754599i	$0.272169\pi$
$42$	−148.384	+	24.4645i	−0.545147	+	0.0898798i
$43$	88.4283			0.313609			0.156805	−	0.987630i	$-0.449881\pi$
$43$	88.4283			0.313609			0.156805	+	0.987630i	$0.449881\pi$
$44$	−145.298	+	83.8878i	−0.497829	+	0.287422i
$45$	−49.5460	−	125.579i	−0.164131	−	0.416006i
$46$	−58.7238	+	101.713i	−0.188225	+	0.326015i
$47$	−278.061	−	481.616i	−0.862966	−	1.49470i	−0.869053	−	0.494720i	$-0.835271\pi$
$47$	−278.061	−	481.616i	−0.862966	−	1.49470i	0.00608661	−	0.999981i	$-0.498063\pi$
$48$	25.6440	+	53.1285i	0.0771123	+	0.159759i
$49$	288.293	+	185.839i	0.840504	+	0.541806i
$50$		−	39.0681i		−	0.110501i
$51$	−349.519	+	513.639i	−0.959657	+	1.41027i
$52$	−287.776	−	166.148i	−0.767450	−	0.443087i
$53$	−78.7698	−	45.4778i	−0.204148	−	0.117865i	0.394441	−	0.918921i	$-0.370938\pi$
$53$	−78.7698	−	45.4778i	−0.204148	−	0.117865i	−0.598589	+	0.801056i	$0.704272\pi$
$54$	209.329	−	65.1860i	0.527521	−	0.164272i
$55$		−	150.935i		−	0.370036i
$56$	−110.811	+	376.422i	−0.264423	+	0.898241i
$57$	−552.302	+	266.584i	−1.28341	+	0.619473i
$58$	−148.030	−	256.395i	−0.335125	−	0.580453i
$59$	136.583	−	236.569i	0.301384	−	0.522012i	−0.675066	−	0.737757i	$-0.735885\pi$
$59$	136.583	−	236.569i	0.301384	−	0.522012i	0.976450	+	0.215746i	$0.0692182\pi$
$60$	−144.004	−	10.6619i	−0.309848	−	0.0229408i
$61$	368.048	−	212.492i	0.772519	−	0.446014i	−0.0612533	−	0.998122i	$-0.519510\pi$
$61$	368.048	−	212.492i	0.772519	−	0.446014i	0.833773	+	0.552108i	$0.186176\pi$
$62$	381.389			0.781233
$63$	−453.667	−	210.317i	−0.907249	−	0.420594i
$64$	−201.778			−0.394098
$65$	258.890	−	149.470i	0.494020	−	0.285223i
$66$	244.453	+	18.0991i	0.455911	+	0.0337552i
$67$	60.2695	−	104.390i	0.109897	−	0.190347i	−0.805831	−	0.592145i	$-0.798281\pi$
$67$	60.2695	−	104.390i	0.109897	−	0.190347i	0.915728	+	0.401798i	$0.131615\pi$
$68$	332.266	+	575.501i	0.592546	+	1.02632i
$69$	−351.695	+	169.755i	−0.613609	+	0.296176i
$70$	−99.7890	−	104.801i	−0.170387	−	0.178944i
$71$		−	222.156i		−	0.371340i	−0.982612	−	0.185670i	$-0.940555\pi$
$71$		−	222.156i		−	0.371340i	0.982612	−	0.185670i	$-0.0594455\pi$
$72$	84.2472	−	565.818i	0.137898	−	0.926143i
$73$	853.939	+	493.022i	1.36912	+	0.790463i	0.990816	−	0.135217i	$-0.0431731\pi$
$73$	853.939	+	493.022i	1.36912	+	0.790463i	0.378307	+	0.925680i	$0.376506\pi$
$74$	167.407	+	96.6527i	0.262983	+	0.151833i
$75$	73.0813	−	107.397i	0.112516	−	0.165349i
$76$			655.969i			0.990063i
$77$	−385.522	−	404.885i	−0.570575	−	0.599232i
$78$	211.037	+	437.221i	0.306349	+	0.634686i
$79$	335.113	+	580.432i	0.477255	+	0.826629i	0.999660	−	0.0260680i	$-0.00829864\pi$
$79$	335.113	+	580.432i	0.477255	+	0.826629i	−0.522406	+	0.852697i	$0.674965\pi$
$80$	−28.3833	+	49.1614i	−0.0396669	+	0.0687051i
$81$	697.378	+	212.380i	0.956623	+	0.291330i
$82$	−466.279	+	269.206i	−0.627950	+	0.362547i
$83$	778.740			1.02985			0.514927	−	0.857234i	$-0.327819\pi$
$83$	778.740			1.02985			0.514927	+	0.857234i	$0.327819\pi$
$84$	−413.527	+	339.219i	−0.537137	+	0.440617i
$85$	−597.827			−0.762864
$86$	−119.675	+	69.0945i	−0.150057	+	0.0866355i
$87$	72.6863	−	981.728i	0.0895722	−	1.20980i
$88$	319.789	−	553.890i	0.387382	−	0.670965i
$89$	−406.705	−	704.434i	−0.484390	−	0.838988i	0.515450	−	0.856920i	$-0.327625\pi$
$89$	−406.705	−	704.434i	−0.484390	−	0.838988i	−0.999839	+	0.0179324i	$0.994292\pi$
$90$	165.177	+	131.241i	0.193457	+	0.153711i
$91$	312.695	−	1062.22i	0.360213	−	1.22364i
$92$			417.707i			0.473358i
$93$	1048.43	+	713.431i	1.16900	+	0.795477i
$94$	752.633	+	434.533i	0.825832	+	0.476794i
$95$	−511.062	−	295.062i	−0.551935	−	0.318660i
$96$	−804.361	−	547.350i	−0.855154	−	0.581913i
$97$			288.573i			0.302064i	0.988529	+	0.151032i	$0.0482596\pi$
$97$			288.573i			0.302064i	−0.988529	+	0.151032i	$0.951740\pi$
$98$	−535.371	−	26.2462i	−0.551844	−	0.0270537i
$99$	638.138	+	507.031i	0.647831	+	0.514733i
$100$	−69.4737	−	120.332i	−0.0694737	−	0.120332i
$101$	528.273	−	914.996i	0.520447	−	0.901440i	−0.479270	−	0.877667i	$-0.659099\pi$
$101$	528.273	−	914.996i	0.520447	−	0.901440i	0.999717	−	0.0237732i	$-0.00756797\pi$
$102$	71.6875	−	968.238i	0.0695894	−	0.939901i
$103$	−76.6945	+	44.2796i	−0.0733682	+	0.0423592i	−0.536235	−	0.844069i	$-0.680154\pi$
$103$	−76.6945	+	44.2796i	−0.0733682	+	0.0423592i	0.462867	+	0.886428i	$0.346821\pi$
$104$	1266.74			1.19437
$105$	−78.2751	−	474.761i	−0.0727511	−	0.441256i
$106$	142.138			0.130242
$107$	730.279	−	421.627i	0.659801	−	0.380936i	−0.132400	−	0.991196i	$-0.542268\pi$
$107$	730.279	−	421.627i	0.659801	−	0.380936i	0.792201	+	0.610260i	$0.208935\pi$
$108$	528.828	−	573.021i	0.471171	−	0.510546i
$109$	−126.194	+	218.574i	−0.110891	+	0.192070i	−0.916130	−	0.400881i	$-0.868704\pi$
$109$	−126.194	+	218.574i	−0.110891	+	0.192070i	0.805238	+	0.592951i	$0.202037\pi$
$110$	117.935	+	204.269i	0.102224	+	0.177057i
$111$	279.398	+	578.850i	0.238913	+	0.494973i
$112$	49.4307	+	204.374i	0.0417032	+	0.172424i
$113$			370.182i			0.308175i	0.988057	+	0.154087i	$0.0492437\pi$
$113$			370.182i			0.308175i	−0.988057	+	0.154087i	$0.950756\pi$
$114$	539.164	−	792.332i	0.442959	−	0.650954i
$115$	−325.433	−	187.889i	−0.263885	−	0.152354i
$116$	−911.879	−	526.474i	−0.729878	−	0.421395i
$117$	−237.736	+	1596.67i	−0.187852	+	1.26165i
$118$			426.884i			0.333033i
$119$	−1603.68	+	1526.99i	−1.23537	+	1.17629i
$120$	495.734	−	239.280i	0.377118	−	0.182026i
$121$	−209.875	−	363.515i	−0.157682	−	0.273114i
$122$	−332.067	+	575.157i	−0.246426	+	0.426822i
$123$	−1785.37	−	132.187i	−1.30879	−	0.0969017i
$124$	1174.70	−	678.213i	0.850735	−	0.491172i
$125$	125.000			0.0894427
$126$	778.308	−	69.8439i	0.550295	−	0.0493824i
$127$	−1584.79			−1.10730			−0.553651	−	0.832749i	$-0.686766\pi$
$127$	−1584.79			−1.10730			−0.553651	+	0.832749i	$0.686766\pi$
$128$	−1024.16	+	591.299i	−0.707217	+	0.408312i
$129$	−458.233	−	33.9271i	−0.312753	−	0.0231560i
$130$	−233.580	+	404.573i	−0.157587	+	0.272949i
$131$	−283.491	−	491.022i	−0.189075	−	0.327487i	0.755867	−	0.654725i	$-0.227215\pi$
$131$	−283.491	−	491.022i	−0.189075	−	0.327487i	−0.944942	+	0.327238i	$0.893882\pi$
$132$	785.114	−	378.958i	0.517693	−	0.249879i
$133$	−2124.59	+	513.862i	−1.38515	+	0.335019i
$134$			188.369i			0.121437i
$135$	208.565	+	669.758i	0.132966	+	0.426989i
$136$	−2193.87	−	1266.63i	−1.38325	−	0.798622i
$137$	1356.67	+	783.273i	0.846044	+	0.488463i	0.859314	−	0.511448i	$-0.170891\pi$
$137$	1356.67	+	783.273i	0.846044	+	0.488463i	−0.0132704	+	0.999912i	$0.504224\pi$
$138$	343.329	−	504.541i	0.211783	−	0.311227i
$139$		−	143.032i		−	0.0872791i	−0.999047	−	0.0436396i	$-0.986105\pi$
$139$		−	143.032i		−	0.0872791i	0.999047	−	0.0436396i	$-0.0138953\pi$
$140$	−493.720	−	145.341i	−0.298050	−	0.0877395i
$141$	1256.12	+	2602.40i	0.750246	+	1.55434i
$142$	173.585	+	300.657i	0.102584	+	0.177680i
$143$	−902.408	+	1563.02i	−0.527714	+	0.914028i
$144$	−112.503	−	285.149i	−0.0651056	−	0.165017i
$145$	820.346	−	473.627i	0.469835	−	0.271259i
$146$	−1540.91			−0.873472
$147$	−1422.62	−	1073.62i	−0.798204	−	0.602387i
$148$	687.499			0.381838
$149$	−55.1209	+	31.8240i	−0.0303066	+	0.0174975i	−0.515077	−	0.857144i	$-0.672237\pi$
$149$	−55.1209	+	31.8240i	−0.0303066	+	0.0174975i	0.484770	+	0.874642i	$0.338903\pi$
$150$	−14.9892	+	202.450i	−0.00815908	+	0.110200i
$151$	412.551	−	714.560i	0.222337	−	0.385100i	−0.733180	−	0.680035i	$-0.761965\pi$
$151$	412.551	−	714.560i	0.222337	−	0.385100i	0.955517	+	0.294935i	$0.0952980\pi$
$152$	−1250.31	−	2165.60i	−0.667194	−	1.15561i
$153$	2008.27	−	2527.56i	1.06117	−	1.33556i
$154$	838.111	+	246.722i	0.438551	+	0.129100i
$155$			1220.27i			0.632351i
$156$	1427.50	+	971.383i	0.732639	+	0.498544i
$157$	2597.70	+	1499.78i	1.32050	+	0.762393i	0.983809	−	0.179220i	$-0.0573574\pi$
$157$	2597.70	+	1499.78i	1.32050	+	0.762393i	0.336695	+	0.941614i	$0.390691\pi$
$158$	−907.055	−	523.688i	−0.456718	−	0.263686i
$159$	390.734	+	265.886i	0.194888	+	0.132617i
$160$		−	936.200i		−	0.462582i
$161$	−1352.89	+	327.216i	−0.662254	+	0.160176i
$162$	−1109.75	+	257.479i	−0.538210	+	0.124873i
$163$	−453.105	−	784.801i	−0.217730	−	0.377119i	0.736384	−	0.676564i	$-0.236532\pi$
$163$	−453.105	−	784.801i	−0.217730	−	0.377119i	−0.954114	+	0.299445i	$0.903198\pi$
$164$	−957.443	+	1658.34i	−0.455877	+	0.789602i
$165$	−57.9088	+	782.138i	−0.0273224	+	0.369026i
$166$	−1053.91	+	608.478i	−0.492769	+	0.284500i
$167$	−2643.69			−1.22500			−0.612499	−	0.790471i	$-0.709836\pi$
$167$	−2643.69			−1.22500			−0.612499	+	0.790471i	$0.709836\pi$
$168$	718.639	−	1908.09i	0.330025	−	0.876265i
$169$	−1377.61			−0.627040
$170$	809.074	−	467.119i	0.365018	−	0.210743i
$171$	2964.29	−	1169.53i	1.32564	−	0.523019i
$172$	−245.738	+	425.630i	−0.108938	+	0.188686i
$173$	−657.338	−	1138.54i	−0.288881	−	0.500357i	0.684662	−	0.728861i	$-0.259950\pi$
$173$	−657.338	−	1138.54i	−0.288881	−	0.500357i	−0.973543	+	0.228504i	$0.926617\pi$
$174$	668.714	+	1385.42i	0.291351	+	0.603613i
$175$	335.315	−	319.279i	0.144842	−	0.137916i
$176$		−	342.722i		−	0.146782i
$177$	−798.534	+	1173.49i	−0.339105	+	0.498333i
$178$	1100.84	+	635.568i	0.463546	+	0.267628i
$179$	−691.886	−	399.461i	−0.288905	−	0.166799i	0.348543	−	0.937293i	$-0.386677\pi$
$179$	−691.886	−	399.461i	−0.288905	−	0.166799i	−0.637448	+	0.770493i	$0.720010\pi$
$180$	742.134	+	110.500i	0.307308	+	0.0457564i
$181$		−	1315.45i		−	0.540200i	−0.962832	−	0.270100i	$-0.912943\pi$
$181$		−	1315.45i		−	0.540200i	0.962832	−	0.270100i	$-0.0870568\pi$
$182$	406.790	+	1681.89i	0.165677	+	0.685001i
$183$	−1988.74	+	959.921i	−0.803343	+	0.387756i
$184$	−796.170	−	1379.01i	−0.318992	−	0.552510i
$185$	−309.244	+	535.627i	−0.122898	+	0.212865i
$186$	−1976.35	−	146.327i	−0.779101	−	0.0576839i
$187$	3125.75	−	1804.65i	1.22234	−	0.705718i
$188$	3090.87			1.19907
$189$	2270.20	+	1263.91i	0.873717	+	0.486435i
$190$	922.200			0.352123
$191$	847.363	−	489.225i	0.321011	−	0.185336i	−0.330832	−	0.943690i	$-0.607329\pi$
$191$	847.363	−	489.225i	0.321011	−	0.185336i	0.651843	+	0.758354i	$0.273996\pi$
$192$	1045.61	+	77.4158i	0.393022	+	0.0290990i
$193$	−1545.39	+	2676.70i	−0.576373	+	0.998307i	0.419518	+	0.907747i	$0.362199\pi$
$193$	−1545.39	+	2676.70i	−0.576373	+	0.998307i	−0.995891	+	0.0905601i	$0.971134\pi$
$194$	−225.480	−	390.543i	−0.0834461	−	0.144533i
$195$	−1398.91	+	675.221i	−0.513732	+	0.247967i
$196$	−1695.65	+	871.196i	−0.617947	+	0.317491i
$197$		−	413.844i		−	0.149671i	−0.997196	−	0.0748355i	$-0.976157\pi$
$197$		−	413.844i		−	0.149671i	0.997196	−	0.0748355i	$-0.0238432\pi$
$198$	−1259.80	−	187.578i	−0.452174	−	0.0673262i
$199$	−1284.54	−	741.630i	−0.457581	−	0.264185i	0.253446	−	0.967350i	$-0.418436\pi$
$199$	−1284.54	−	741.630i	−0.457581	−	0.264185i	−0.711027	+	0.703165i	$0.751769\pi$
$200$	458.717	+	264.841i	0.162181	+	0.0936353i
$201$	−352.366	+	517.821i	−0.123652	+	0.181713i
$202$			1651.09i			0.575100i
$203$	990.840	−	3365.87i	0.342578	−	1.16373i
$204$	−1500.99	−	3109.71i	−0.515148	−	1.06727i
$205$	−861.337	−	1491.88i	−0.293455	−	0.508280i
$206$	69.1967	−	119.852i	0.0234037	−	0.0405364i
$207$	1887.60	−	744.733i	0.633803	−	0.250060i
$208$	587.852	−	339.397i	0.195963	−	0.113139i
$209$	3562.80			1.17916
$210$	476.894	+	581.361i	0.156709	+	0.191037i
$211$	−1673.15			−0.545899			−0.272949	−	0.962028i	$-0.587999\pi$
$211$	−1673.15			−0.545899			−0.272949	+	0.962028i	$0.587999\pi$
$212$	437.794	−	252.761i	0.141829	−	0.0818852i
$213$	−85.2344	+	1151.21i	−0.0274186	+	0.370326i
$214$	−658.886	+	1141.22i	−0.210470	+	0.364544i
$215$	−221.071	−	382.906i	−0.0701251	−	0.121460i
$216$	−653.653	+	2899.73i	−0.205905	+	0.913433i
$217$	3116.85	+	3273.40i	0.975049	+	1.02402i
$218$		−	394.412i		−	0.122536i
$219$	−4235.93	−	2882.45i	−1.30702	−	0.889398i
$220$	726.490	+	419.439i	0.222636	+	0.128539i
$221$	6190.85	+	3574.29i	1.88435	+	1.08793i
$222$	−830.417	−	565.080i	−0.251054	−	0.170837i
$223$			543.549i			0.163223i	0.996664	+	0.0816115i	$0.0260067\pi$
$223$			543.549i			0.163223i	−0.996664	+	0.0816115i	$0.973993\pi$
$224$	−2391.27	−	2511.37i	−0.713275	−	0.749099i
$225$	−419.910	+	528.489i	−0.124418	+	0.156589i
$226$	−289.246	−	500.988i	−0.0851343	−	0.147457i
$227$	287.724	−	498.352i	0.0841272	−	0.145713i	−0.820892	−	0.571084i	$-0.806523\pi$
$227$	287.724	−	498.352i	0.0841272	−	0.145713i	0.905019	+	0.425371i	$0.139856\pi$
$228$	251.674	−	3399.21i	0.0731033	−	0.987360i
$229$	1476.87	−	852.672i	0.426176	−	0.246053i	−0.271540	−	0.962427i	$-0.587533\pi$
$229$	1476.87	−	852.672i	0.426176	−	0.246053i	0.697716	+	0.716374i	$0.254200\pi$
$230$	587.238			0.168353
$231$	1842.42	+	2246.01i	0.524772	+	0.639726i
$232$	4013.94			1.13590
$233$	724.681	−	418.395i	0.203757	−	0.117639i	−0.394650	−	0.918832i	$-0.629134\pi$
$233$	724.681	−	418.395i	0.203757	−	0.117639i	0.598407	+	0.801192i	$0.295801\pi$
$234$	−925.839	−	2346.63i	−0.258650	−	0.655573i
$235$	−1390.31	+	2408.08i	−0.385930	+	0.668451i
$236$	759.115	+	1314.83i	0.209382	+	0.362661i
$237$	−1513.85	−	3136.35i	−0.414916	−	0.859612i
$238$	977.225	−	3319.62i	0.266152	−	0.904113i
$239$		−	5557.24i		−	1.50405i	−0.659135	−	0.752024i	$-0.729078\pi$
$239$		−	5557.24i		−	1.50405i	0.659135	−	0.752024i	$-0.270922\pi$
$240$	165.943	−	243.863i	0.0446316	−	0.0655887i
$241$	−4496.86	−	2596.26i	−1.20194	−	0.693942i	−0.240956	−	0.970536i	$-0.577461\pi$
$241$	−4496.86	−	2596.26i	−1.20194	−	0.693942i	−0.960987	+	0.276594i	$0.910794\pi$
$242$	568.073	+	327.977i	0.150897	+	0.0871206i
$243$	−3532.31	−	1368.11i	−0.932500	−	0.361169i
$244$			2362.02i			0.619725i
$245$	83.9757	−	1712.94i	0.0218980	−	0.446677i
$246$	2519.53	−	1216.12i	0.653005	−	0.315191i
$247$	3528.23	+	6111.08i	0.908891	+	1.57424i
$248$	−2585.42	+	4478.07i	−0.661992	+	1.14660i
$249$	−4035.41	−	298.778i	−1.02704	−	0.0760413i
$250$	−169.170	+	97.6703i	−0.0427970	+	0.0247088i
$251$	−1150.64			−0.289354			−0.144677	−	0.989479i	$-0.546214\pi$
$251$	−1150.64			−0.289354			−0.144677	+	0.989479i	$0.546214\pi$
$252$	2273.03	−	1599.17i	0.568204	−	0.399754i
$253$	2268.72			0.563767
$254$	2144.79	−	1238.29i	0.529826	−	0.305895i
$255$	3097.92	+	229.367i	0.760781	+	0.0563276i
$256$	1731.15	−	2998.44i	0.422644	−	0.732040i
$257$	2826.64	+	4895.89i	0.686074	+	1.18832i	0.973098	+	0.230392i	$0.0740008\pi$
$257$	2826.64	+	4895.89i	0.686074	+	1.18832i	−0.287024	+	0.957923i	$0.592666\pi$
$258$	646.662	−	312.130i	0.156044	−	0.0753192i
$259$	538.562	+	2226.71i	0.129207	+	0.534213i
$260$			1661.48i			0.396309i
$261$	−753.316	+	5059.40i	−0.178655	+	1.19988i
$262$	767.331	+	443.019i	0.180938	+	0.104465i
$263$	5329.11	+	3076.77i	1.24946	+	0.721374i	0.971001	−	0.239075i	$-0.0768441\pi$
$263$	5329.11	+	3076.77i	1.24946	+	0.721374i	0.278456	+	0.960449i	$0.410177\pi$
$264$	−1869.65	+	2747.55i	−0.435866	+	0.640530i
$265$			454.778i			0.105422i
$266$	2473.82	−	2355.51i	0.570224	−	0.542954i
$267$	1837.27	+	3806.40i	0.421119	+	0.872463i
$268$	334.971	+	580.187i	0.0763494	+	0.132241i
$269$	2602.37	−	4507.43i	0.589848	−	1.02165i	−0.404404	−	0.914581i	$-0.632521\pi$
$269$	2602.37	−	4507.43i	0.589848	−	1.02165i	0.994252	−	0.107066i	$-0.0341457\pi$
$270$	−805.587	−	743.458i	−0.181579	−	0.167576i
$271$	2343.41	−	1352.97i	0.525283	−	0.303272i	−0.213810	−	0.976875i	$-0.568587\pi$
$271$	2343.41	−	1352.97i	0.525283	−	0.303272i	0.739094	+	0.673603i	$0.235254\pi$
$272$	−1357.46			−0.302604
$273$	−2027.92	+	5384.42i	−0.449579	+	1.19370i
$274$	−2448.08			−0.539758
$275$	−653.566	+	377.336i	−0.143315	+	0.0827427i
$276$	160.261	−	2164.54i	0.0349514	−	0.472066i
$277$	919.668	−	1592.91i	0.199486	−	0.345519i	−0.748876	−	0.662710i	$-0.769406\pi$
$277$	919.668	−	1592.91i	0.199486	−	0.345519i	0.948362	+	0.317191i	$0.102740\pi$
$278$	111.760	+	193.573i	0.0241111	+	0.0417617i
$279$	−5159.20	−	4099.23i	−1.10707	−	0.879621i
$280$	1906.98	−	461.231i	0.407014	−	0.0984421i
$281$		−	2505.86i		−	0.531983i	−0.963975	−	0.265992i	$-0.914301\pi$
$281$		−	2505.86i		−	0.531983i	0.963975	−	0.265992i	$-0.0856993\pi$
$282$	−3733.41	−	2540.50i	−0.788373	−	0.536470i
$283$	18.8941	+	10.9085i	0.00396868	+	0.00229132i	0.501983	−	0.864877i	$-0.332604\pi$
$283$	18.8941	+	10.9085i	0.00396868	+	0.00229132i	−0.498014	+	0.867169i	$0.665937\pi$
$284$	1069.30	+	617.361i	0.223420	+	0.128992i
$285$	2535.10	+	1725.08i	0.526900	+	0.358543i
$286$		−	2820.43i		−	0.583131i
$287$	−6121.15	−	1801.94i	−1.25896	−	0.370610i
$288$	3958.17	+	3144.96i	0.809853	+	0.643467i
$289$	−4691.43	−	8125.80i	−0.954902	−	1.65394i
$290$	−740.148	+	1281.97i	−0.149872	+	0.259587i
$291$	110.716	−	1495.38i	0.0223035	−	0.301239i
$292$	−4746.10	+	2740.16i	−0.951180	+	0.549164i
$293$	−6459.08			−1.28786			−0.643931	−	0.765084i	$-0.722698\pi$
$293$	−6459.08			−1.28786			−0.643931	+	0.765084i	$0.722698\pi$
$294$	2764.21	+	341.412i	0.548340	+	0.0677263i
$295$	−1365.83			−0.269566
$296$	−2269.69	+	1310.41i	−0.445686	+	0.257317i
$297$	−3112.28	−	2872.25i	−0.608057	−	0.561161i
$298$	49.7322	−	86.1387i	0.00966748	−	0.0167446i
$299$	2246.70	+	3891.40i	0.434549	+	0.752661i
$300$	313.843	+	650.211i	0.0603991	+	0.125133i
$301$	−1571.06	−	462.486i	−0.300844	−	0.0885622i
$302$			1289.41i			0.245686i
$303$	−3088.55	+	4538.80i	−0.585586	+	0.860552i
$304$	−1160.45	−	669.987i	−0.218936	−	0.126403i
$305$	−1840.24	−	1062.46i	−0.345481	−	0.199464i
$306$	−742.965	+	4989.88i	−0.138799	+	0.932197i
$307$		−	3494.94i		−	0.649728i	−0.945761	−	0.324864i	$-0.894681\pi$
$307$		−	3494.94i		−	0.649728i	0.945761	−	0.324864i	$-0.105319\pi$
$308$	3020.17	−	730.470i	0.558734	−	0.135138i
$309$	414.417	−	200.030i	0.0762957	−	0.0368263i
$310$	−953.473	−	1651.46i	−0.174689	−	0.302570i
$311$	−3709.12	+	6424.38i	−0.676285	+	1.17136i	0.299806	+	0.954000i	$0.403078\pi$
$311$	−3709.12	+	6424.38i	−0.676285	+	1.17136i	−0.976091	+	0.217360i	$0.930255\pi$
$312$	−6564.23	−	486.009i	−1.19111	−	0.0881887i
$313$	−8718.77	+	5033.79i	−1.57449	+	0.909030i	−0.578878	+	0.815414i	$0.696509\pi$
$313$	−8718.77	+	5033.79i	−1.57449	+	0.909030i	−0.995608	+	0.0936158i	$0.970157\pi$
$314$	−4687.50			−0.842455
$315$	223.468	+	2490.23i	0.0399715	+	0.445424i
$316$	−3725.04			−0.663133
$317$	4573.02	−	2640.23i	0.810241	−	0.467793i	−0.0367987	−	0.999323i	$-0.511716\pi$
$317$	4573.02	−	2640.23i	0.810241	−	0.467793i	0.847040	+	0.531530i	$0.178383\pi$
$318$	−736.557	−	54.5340i	−0.129887	−	0.00961671i
$319$	−2859.47	+	4952.74i	−0.501879	+	0.869280i
$320$	504.445	+	873.724i	0.0881229	+	0.152633i
$321$	−3946.05	+	1904.67i	−0.686127	+	0.331179i
$322$	1575.28	−	1499.94i	0.272629	−	0.259591i
$323$		−	14111.7i		−	2.43094i
$324$	−2960.22	+	2766.48i	−0.507582	+	0.474362i
$325$	−1294.45	−	747.350i	−0.220933	−	0.127555i
$326$	1226.43	+	708.078i	0.208361	+	0.120297i
$327$	737.792	−	1084.23i	0.124771	−	0.183357i
$328$		−	7299.74i		−	1.22884i
$329$	2421.27	+	10010.9i	0.405742	+	1.67756i
$330$	−532.762	−	1103.76i	−0.0888714	−	0.184121i
$331$	1454.72	+	2519.64i	0.241566	+	0.418405i	0.961161	−	0.275990i	$-0.0890055\pi$
$331$	1454.72	+	2519.64i	0.241566	+	0.418405i	−0.719594	+	0.694395i	$0.755672\pi$
$332$	−2164.08	+	3748.29i	−0.357738	+	0.619621i
$333$	−1225.75	−	3106.78i	−0.201713	−	0.511262i
$334$	3577.86	−	2065.68i	0.586142	−	0.338410i
$335$	−602.695			−0.0982947
$336$	−177.737	−	1078.02i	−0.0288581	−	0.175033i
$337$	5655.37			0.914147			0.457073	−	0.889429i	$-0.348898\pi$
$337$	5655.37			0.914147			0.457073	+	0.889429i	$0.348898\pi$
$338$	1864.40	−	1076.41i	0.300029	−	0.173222i
$339$	142.027	−	1918.27i	0.0227547	−	0.307334i
$340$	1661.33	−	2877.51i	0.264995	−	0.458984i
$341$	−3683.62	−	6380.21i	−0.584983	−	1.01322i
$342$	−3097.93	+	3898.98i	−0.489815	+	0.616470i
$343$	−4149.99	−	4809.49i	−0.653289	−	0.757109i
$344$		−	1873.55i		−	0.293649i
$345$	1614.30	+	1098.49i	0.251916	+	0.171423i
$346$	1779.23	+	1027.24i	0.276451	+	0.159609i
$347$	10001.4	+	5774.32i	1.54727	+	0.893320i	0.998348	+	0.0574490i	$0.0182966\pi$
$347$	10001.4	+	5774.32i	1.54727	+	0.893320i	0.548926	+	0.835871i	$0.315037\pi$
$348$	4523.34	+	3078.03i	0.696771	+	0.474137i
$349$			10206.0i			1.56538i	0.622413	+	0.782689i	$0.286153\pi$
$349$			10206.0i			1.56538i	−0.622413	+	0.782689i	$0.713847\pi$
$350$	−204.329	+	694.101i	−0.0312052	+	0.106004i
$351$	1844.53	−	8182.71i	0.280496	−	1.24433i
$352$	2826.10	+	4894.95i	0.427931	+	0.741198i
$353$	579.996	−	1004.58i	0.0874506	−	0.151469i	−0.818982	−	0.573819i	$-0.805461\pi$
$353$	579.996	−	1004.58i	0.0874506	−	0.151469i	0.906433	+	0.422350i	$0.138795\pi$
$354$	163.782	−	2212.10i	0.0245901	−	0.332124i
$355$	−961.965	+	555.391i	−0.143819	+	0.0830341i
$356$	4520.85			0.673047
$357$	8896.08	−	7297.52i	1.31885	−	1.08186i
$358$	1248.49			0.184315
$359$	1136.44	−	656.126i	0.167073	−	0.0964596i	−0.414132	−	0.910217i	$-0.635915\pi$
$359$	1136.44	−	656.126i	0.167073	−	0.0964596i	0.581205	+	0.813757i	$0.302581\pi$
$360$	−2660.68	+	1049.74i	−0.389528	+	0.153684i
$361$	3535.41	−	6123.51i	0.515441	−	0.892770i
$362$	1027.84	+	1780.27i	0.149232	+	0.258478i
$363$	948.099	+	1964.25i	0.137086	+	0.284011i
$364$	4243.80	+	4456.94i	0.611086	+	0.641778i
$365$		−	4930.22i		−	0.707012i
$366$	1941.43	−	2853.04i	0.277268	−	0.407461i
$367$	−3449.12	−	1991.35i	−0.490579	−	0.283236i	0.234235	−	0.972180i	$-0.424741\pi$
$367$	−3449.12	−	1991.35i	−0.490579	−	0.283236i	−0.724815	+	0.688944i	$0.758075\pi$
$368$	−738.951	−	426.633i	−0.104675	−	0.0604343i
$369$	9201.00	+	1369.98i	1.29806	+	0.193274i
$370$		−	966.527i		−	0.135804i
$371$	1161.61	+	1219.95i	0.162554	+	0.170719i
$372$	−6347.47	+	3063.78i	−0.884679	+	0.427016i
$373$	4645.84	+	8046.84i	0.644913	+	1.11702i	0.984322	+	0.176384i	$0.0564399\pi$
$373$	4645.84	+	8046.84i	0.644913	+	1.11702i	−0.339408	+	0.940639i	$0.610227\pi$
$374$	−2820.18	+	4884.69i	−0.389914	+	0.675351i
$375$	−647.746	−	47.9585i	−0.0891986	−	0.00660418i
$376$	−10204.1	+	5891.35i	−1.39957	+	0.808041i
$377$	−11326.9			−1.54739
$378$	−4059.96	+	63.3166i	−0.552439	+	0.00861548i
$379$	7489.57			1.01507			0.507537	−	0.861630i	$-0.330556\pi$
$379$	7489.57			1.01507			0.507537	+	0.861630i	$0.330556\pi$
$380$	2840.43	−	1639.92i	0.383450	−	0.221385i
$381$	8212.32	+	608.033i	1.10428	+	0.0817598i
$382$	−764.524	+	1324.20i	−0.102399	+	0.177361i
$383$	−653.621	−	1132.11i	−0.0872023	−	0.151039i	0.819125	−	0.573615i	$-0.194459\pi$
$383$	−653.621	−	1132.11i	−0.0872023	−	0.151039i	−0.906328	+	0.422576i	$0.861126\pi$
$384$	5534.02	−	2671.15i	0.735435	−	0.354979i
$385$	−789.397	+	2681.57i	−0.104497	+	0.354975i
$386$		−	4830.05i		−	0.636899i
$387$	2361.53	+	351.619i	0.310189	+	0.0461855i
$388$	−1388.98	−	801.930i	−0.181740	−	0.104927i
$389$	545.637	+	315.024i	0.0711179	+	0.0410600i	0.535137	−	0.844765i	$-0.320260\pi$
$389$	545.637	+	315.024i	0.0711179	+	0.0410600i	−0.464019	+	0.885825i	$0.653593\pi$
$390$	1365.63	−	2006.87i	0.177311	−	0.260569i
$391$		−	8986.01i		−	1.16226i
$392$	3937.42	−	6108.13i	0.507321	−	0.787008i
$393$	1280.65	+	2653.22i	0.164378	+	0.340553i
$394$	323.362	+	560.079i	0.0413471	+	0.0716152i
$395$	1675.56	−	2902.16i	0.213435	−	0.369680i
$396$	−4213.83	+	1662.52i	−0.534730	+	0.210972i
$397$	−3083.29	+	1780.14i	−0.389788	+	0.225044i	−0.682068	−	0.731288i	$-0.738919\pi$
$397$	−3083.29	+	1780.14i	−0.389788	+	0.225044i	0.292280	+	0.956333i	$0.405586\pi$
$398$	2317.92			0.291927
$399$	11206.7	−	1847.68i	1.40611	−	0.231829i
$400$	283.833			0.0354792
$401$	−2343.23	+	1352.86i	−0.291808	+	0.168476i	−0.638757	−	0.769408i	$-0.720551\pi$
$401$	−2343.23	+	1352.86i	−0.291808	+	0.168476i	0.346949	+	0.937884i	$0.387218\pi$
$402$	72.2713	−	976.123i	0.00896658	−	0.121106i
$403$	7295.75	−	12636.6i	0.901805	−	1.56197i
$404$	2936.09	+	5085.45i	0.361574	+	0.626264i
$405$	−823.813	−	3550.68i	−0.101076	−	0.435642i
$406$	1289.00	+	5329.43i	0.157566	+	0.651466i
$407$		−	3734.05i		−	0.454767i
$408$	10882.6	+	7405.35i	1.32051	+	0.898578i
$409$	3450.96	+	1992.41i	0.417210	+	0.240876i	0.693883	−	0.720088i	$-0.255899\pi$
$409$	3450.96	+	1992.41i	0.417210	+	0.240876i	−0.276673	+	0.960964i	$0.589232\pi$
$410$	2331.39	+	1346.03i	0.280828	+	0.162136i
$411$	−6729.69	−	4579.40i	−0.807667	−	0.549599i
$412$		−	492.202i		−	0.0588570i
$413$	−3663.87	+	3488.65i	−0.436531	+	0.415655i
$414$	−1972.69	+	2482.79i	−0.234185	+	0.294740i
$415$	−1946.85	−	3372.04i	−0.230282	−	0.398861i
$416$	−5597.36	+	9694.91i	−0.659695	+	1.14262i
$417$	−54.8768	+	741.186i	−0.00644443	+	0.0870409i
$418$	−4821.75	+	2783.84i	−0.564209	+	0.325746i
$419$	−3157.38			−0.368134			−0.184067	−	0.982914i	$-0.558926\pi$
$419$	−3157.38			−0.368134			−0.184067	+	0.982914i	$0.558926\pi$
$420$	2502.68	+	942.576i	0.290758	+	0.109507i
$421$	4973.53			0.575760			0.287880	−	0.957667i	$-0.407050\pi$
$421$	4973.53			0.575760			0.287880	+	0.957667i	$0.407050\pi$
$422$	2264.38	−	1307.34i	0.261204	−	0.150806i
$423$	−5510.73	−	13967.5i	−0.633430	−	1.60549i
$424$	−963.548	+	1668.91i	−0.110363	+	0.191155i
$425$	1494.57	+	2588.67i	0.170581	+	0.295456i
$426$	−784.157	−	1624.60i	−0.0891843	−	0.184770i
$427$	−7650.25	+	1850.32i	−0.867029	+	0.209703i
$428$			4686.71i			0.529301i
$429$	5275.93	−	7753.27i	0.593763	−	0.872568i
$430$	598.376	+	345.473i	0.0671076	+	0.0387446i
$431$	−2720.15	−	1570.48i	−0.304002	−	0.175516i	0.340237	−	0.940340i	$-0.389493\pi$
$431$	−2720.15	−	1570.48i	−0.304002	−	0.175516i	−0.644240	+	0.764824i	$0.722826\pi$
$432$	473.582	+	1520.80i	0.0527436	+	0.169374i
$433$			4935.94i			0.547820i	0.961755	+	0.273910i	$0.0883170\pi$
$433$			4935.94i			0.547820i	−0.961755	+	0.273910i	$0.911683\pi$
$434$	−6775.93	−	1994.69i	−0.749435	−	0.220618i
$435$	−4432.72	+	2139.58i	−0.488581	+	0.235827i
$436$	−701.371	−	1214.81i	−0.0770403	−	0.133438i
$437$	4435.11	−	7681.84i	0.485492	−	0.840897i
$438$	7984.97	+	591.200i	0.871088	+	0.0644946i
$439$	10952.1	−	6323.17i	1.19069	−	0.687445i	0.232227	−	0.972662i	$-0.425399\pi$
$439$	10952.1	−	6323.17i	1.19069	−	0.687445i	0.958463	+	0.285216i	$0.0920654\pi$
$440$	−3197.89			−0.346485
$441$	6960.08	+	6109.29i	0.751547	+	0.659680i
$442$	−11171.2			−1.20218
$443$	−8249.80	+	4763.02i	−0.884785	+	0.510831i	−0.872233	−	0.489090i	$-0.837329\pi$
$443$	−8249.80	+	4763.02i	−0.884785	+	0.510831i	−0.0125519	+	0.999921i	$0.503996\pi$
$444$	−3562.60	−	263.772i	−0.380796	−	0.0281938i
$445$	−2033.53	+	3522.17i	−0.216626	+	0.375207i
$446$	−424.708	−	735.616i	−0.0450909	−	0.0780997i
$447$	297.844	−	143.763i	0.0315158	−	0.0152120i
$448$	3584.88	+	1055.31i	0.378057	+	0.111292i
$449$		−	6905.07i		−	0.725769i	−0.931834	−	0.362884i	$-0.881792\pi$
$449$		−	6905.07i		−	0.725769i	0.931834	−	0.362884i	$-0.118208\pi$
$450$	155.347	−	1043.34i	0.0162736	−	0.109296i
$451$	9007.04	+	5200.22i	0.940410	+	0.542946i
$452$	−1781.79	−	1028.71i	−0.185416	−	0.107050i
$453$	−2411.98	+	3544.54i	−0.250165	+	0.367632i
$454$			899.265i			0.0929617i
$455$	−5381.29	+	1301.54i	−0.554459	+	0.134104i
$456$	5648.19	+	11701.8i	0.580045	+	1.20172i
$457$	−7884.86	−	13657.0i	−0.807085	−	1.39791i	−0.914874	−	0.403739i	$-0.867710\pi$
$457$	−7884.86	−	13657.0i	−0.807085	−	1.39791i	0.107789	−	0.994174i	$-0.465623\pi$
$458$	−1332.49	+	2307.94i	−0.135946	+	0.235465i
$459$	−11376.5	+	12327.2i	−1.15688	+	1.25356i
$460$	1808.72	−	1044.27i	0.183331	−	0.105846i
$461$	10091.7			1.01956			0.509782	−	0.860304i	$-0.329726\pi$
$461$	10091.7			1.01956			0.509782	+	0.860304i	$0.329726\pi$
$462$	−4248.40	−	1600.06i	−0.427822	−	0.161129i
$463$	7425.01			0.745290			0.372645	−	0.927974i	$-0.378451\pi$
$463$	7425.01			0.745290			0.372645	+	0.927974i	$0.378451\pi$
$464$	1862.73	−	1075.45i	0.186369	−	0.107600i
$465$	468.179	−	6323.40i	0.0466909	−	0.630625i
$466$	−653.835	+	1132.48i	−0.0649964	+	0.112577i
$467$	−3110.28	−	5387.17i	−0.308194	−	0.533808i	0.669773	−	0.742566i	$-0.266391\pi$
$467$	−3110.28	−	5387.17i	−0.308194	−	0.533808i	−0.977967	+	0.208758i	$0.933058\pi$
$468$	−7024.58	−	5581.36i	−0.693828	−	0.551279i
$469$	−1616.74	+	1539.42i	−0.159177	+	0.151565i
$470$		−	4345.33i		−	0.426458i
$471$	−12885.8	−	8768.49i	−1.26061	−	0.857814i
$472$	−5012.25	−	2893.82i	−0.488787	−	0.282201i
$473$	2311.75	+	1334.69i	0.224724	+	0.129744i
$474$	4499.41	+	3061.75i	0.436001	+	0.296689i
$475$			2950.62i			0.285018i
$476$	−2893.27	−	11962.4i	−0.278598	−	1.15188i
$477$	−1922.76	−	1527.72i	−0.184564	−	0.146645i
$478$	4342.21	+	7520.93i	0.415498	+	0.719664i
$479$	−9650.00	+	16714.3i	−0.920500	+	1.59435i	−0.121858	+	0.992548i	$0.538885\pi$
$479$	−9650.00	+	16714.3i	−0.920500	+	1.59435i	−0.798643	+	0.601806i	$0.794448\pi$
$480$	−359.190	+	4851.36i	−0.0341557	+	0.461319i
$481$	6404.82	−	3697.82i	0.607140	−	0.350533i
$482$	8114.48			0.766814
$483$	7136.19	−	1176.56i	0.672273	−	0.110839i
$484$	2332.93			0.219096
$485$	1249.56	−	721.434i	0.116989	−	0.0675435i
$486$	5849.46	−	908.471i	0.545961	−	0.0847923i
$487$	−7385.00	+	12791.2i	−0.687159	+	1.19019i	0.285594	+	0.958351i	$0.407809\pi$
$487$	−7385.00	+	12791.2i	−0.687159	+	1.19019i	−0.972753	+	0.231843i	$0.925524\pi$
$488$	−4502.13	−	7797.92i	−0.417627	−	0.723351i
$489$	2046.87	+	4240.66i	0.189290	+	0.392166i
$490$	1224.78	+	2383.84i	0.112918	+	0.219778i
$491$			7298.56i			0.670834i	0.942070	+	0.335417i	$0.108877\pi$
$491$			7298.56i			0.670834i	−0.942070	+	0.335417i	$0.891123\pi$
$492$	5597.69	−	8226.13i	0.512934	−	0.753786i
$493$	19617.0	+	11325.9i	1.79210	+	1.03467i
$494$	−9549.92	−	5513.65i	−0.869780	−	0.502168i
$495$	600.163	−	4030.80i	0.0544956	−	0.366002i
$496$			2770.83i			0.250834i
$497$	−1161.89	+	3946.93i	−0.104865	+	0.356225i
$498$	5694.81	−	2748.76i	0.512430	−	0.247339i
$499$	−4795.00	−	8305.19i	−0.430168	−	0.745073i	0.566720	−	0.823911i	$-0.308212\pi$
$499$	−4795.00	−	8305.19i	−0.430168	−	0.745073i	−0.996887	+	0.0788381i	$0.974879\pi$
$500$	−347.368	+	601.660i	−0.0310696	+	0.0538141i
$501$	13699.5	+	1014.30i	1.22165	+	0.0904502i
$502$	1557.23	−	899.067i	0.138451	−	0.0799349i
$503$	−1098.43			−0.0973687			−0.0486843	−	0.998814i	$-0.515503\pi$
$503$	−1098.43			−0.0973687			−0.0486843	+	0.998814i	$0.515503\pi$
$504$	−4456.04	+	9611.95i	−0.393825	+	0.849505i
$505$	−5282.73			−0.465502
$506$	−3070.39	+	1772.69i	−0.269754	+	0.155742i
$507$	7138.72	+	528.545i	0.625329	+	0.0462988i
$508$	4404.04	−	7628.03i	0.384641	−	0.666218i
$509$	−5648.10	−	9782.80i	−0.491842	−	0.851896i	0.508114	−	0.861290i	$-0.330343\pi$
$509$	−5648.10	−	9782.80i	−0.491842	−	0.851896i	−0.999956	+	0.00939431i	$0.997010\pi$
$510$	−4371.81	+	2110.18i	−0.379583	+	0.183216i
$511$	−12592.9	−	13225.4i	−1.09017	−	1.14493i
$512$		−	4050.17i		−	0.349597i
$513$	−15809.6	+	4923.17i	−1.36064	+	0.423710i
$514$	−7650.92	−	4417.26i	−0.656552	−	0.379060i
$515$	383.472	+	221.398i	0.0328113	+	0.0189436i
$516$	1436.70	−	2111.32i	0.122572	−	0.180127i
$517$		−	16787.6i		−	1.42808i
$518$	−2468.73	−	2592.73i	−0.209401	−	0.219919i
$519$	2969.48	+	6152.09i	0.251148	+	0.520322i
$520$	−3166.86	−	5485.16i	−0.267069	−	0.462577i
$521$	−5844.10	+	10122.3i	−0.491430	+	0.851181i	−0.999951	−	0.00986815i	$-0.996859\pi$
$521$	−5844.10	+	10122.3i	−0.491430	+	0.851181i	0.508522	+	0.861049i	$0.330192\pi$
$522$	−2933.71	−	7435.79i	−0.245987	−	0.623478i
$523$	−17162.9	+	9909.03i	−1.43496	+	0.828474i	−0.997493	−	0.0707615i	$-0.977457\pi$
$523$	−17162.9	+	9909.03i	−1.43496	+	0.828474i	−0.437465	+	0.899235i	$0.644124\pi$
$524$	3151.23			0.262714
$525$	−1860.09	+	1525.84i	−0.154630	+	0.126844i
$526$	−9616.27			−0.797128
$527$	−25271.0	+	14590.2i	−2.08884	+	1.20599i
$528$	−131.492	+	1775.97i	−0.0108379	+	0.146381i
$529$	−3259.32	+	5645.30i	−0.267882	+	0.463985i
$530$	−355.346	−	615.477i	−0.0291231	−	0.0504427i
$531$	4588.21	−	5774.62i	0.374974	−	0.471935i
$532$	3430.76	−	11654.2i	0.279591	−	0.949765i
$533$			20599.0i			1.67400i
$534$	−5460.65	−	3715.85i	−0.442520	−	0.301125i
$535$	−3651.39	−	2108.13i	−0.295072	−	0.170360i
$536$	−2211.73	−	1276.94i	−0.178232	−	0.102902i
$537$	3432.07	+	2335.45i	0.275800	+	0.187676i
$538$			8133.56i			0.651790i
$539$	4731.78	+	9209.66i	0.378130	+	0.735971i
$540$	−3803.32	−	857.339i	−0.303091	−	0.0683222i
$541$	10280.8	+	17806.8i	0.817014	+	1.41511i	0.907873	+	0.419246i	$0.137705\pi$
$541$	10280.8	+	17806.8i	0.817014	+	1.41511i	−0.0908589	+	0.995864i	$0.528961\pi$
$542$	−2114.31	+	3662.10i	−0.167560	+	0.290222i
$543$	−504.695	+	6816.60i	−0.0398868	+	0.538726i
$544$	19388.1	−	11193.7i	1.52805	−	0.882218i
$545$	1261.94			0.0991843
$546$	−1462.68	−	8871.59i	−0.114647	−	0.695365i
$547$	12770.7			0.998235			0.499117	−	0.866534i	$-0.333658\pi$
$547$	12770.7			0.998235			0.499117	+	0.866534i	$0.333658\pi$
$548$	−7540.22	+	4353.35i	−0.587778	+	0.339354i
$549$	10673.9	−	4211.26i	0.829781	−	0.327381i
$550$	589.673	−	1021.34i	0.0457159	−	0.0791822i
$551$	11179.9	+	19364.2i	0.864394	+	1.49717i
$552$	3596.65	+	7451.44i	0.277325	+	0.574555i
$553$	−2918.06	−	12064.9i	−0.224392	−	0.927759i
$554$			2874.38i			0.220434i
$555$	1808.00	−	2656.95i	0.138280	−	0.203210i
$556$	688.452	+	397.478i	0.0525123	+	0.0303180i
$557$	−4529.84	−	2615.31i	−0.344588	−	0.198948i	0.317711	−	0.948188i	$-0.397086\pi$
$557$	−4529.84	−	2615.31i	−0.344588	−	0.198948i	−0.662299	+	0.749240i	$0.730419\pi$
$558$	10185.2	+	1516.52i	0.772715	+	0.115053i
$559$			5286.95i			0.400026i
$560$	761.388	−	724.976i	0.0574545	−	0.0547068i
$561$	−16889.9	+	8152.41i	−1.27111	+	0.613538i
$562$	1957.99	+	3391.33i	0.146962	+	0.254546i
$563$	5287.56	−	9158.33i	0.395816	−	0.685573i	−0.597389	−	0.801951i	$-0.703795\pi$
$563$	5287.56	−	9158.33i	0.395816	−	0.685573i	0.993205	+	0.116379i	$0.0371286\pi$
$564$	−16016.8	−	1185.87i	−1.19580	−	0.0885356i
$565$	1602.93	−	925.454i	0.119356	−	0.0689100i
$566$	−34.0939			−0.00253193
$567$	−11279.2	−	7420.56i	−0.835415	−	0.549620i
$568$	−4706.88			−0.347705
$569$	12299.3	−	7101.00i	0.906174	−	0.523180i	0.0269761	−	0.999636i	$-0.491412\pi$
$569$	12299.3	−	7101.00i	0.906174	−	0.523180i	0.879198	+	0.476456i	$0.158079\pi$
$570$	−4778.81	−	353.819i	−0.351162	−	0.0259997i
$571$	−6745.01	+	11682.7i	−0.494343	+	0.856227i	−0.999979	−	0.00652001i	$-0.997925\pi$
$571$	−6745.01	+	11682.7i	−0.494343	+	0.856227i	0.505636	+	0.862747i	$0.331258\pi$
$572$	−5015.49	−	8687.08i	−0.366622	−	0.635009i
$573$	−4578.71	+	2210.04i	−0.333819	+	0.161127i
$574$	9692.08	−	2344.17i	0.704773	−	0.170459i
$575$			1878.89i			0.136270i
$576$	−5388.60	−	802.333i	−0.389800	−	0.0580391i
$577$	−13221.2	−	7633.28i	−0.953912	−	0.550741i	−0.0596179	−	0.998221i	$-0.518988\pi$
$577$	−13221.2	−	7633.28i	−0.953912	−	0.550741i	−0.894294	+	0.447480i	$0.852322\pi$
$578$	12698.4	+	7331.42i	0.913812	+	0.527589i
$579$	9035.15	−	13277.7i	0.648512	−	0.953024i
$580$			5264.74i			0.376907i
$581$	−13835.4	−	4072.86i	−0.987936	−	0.290828i
$582$	1018.59	+	2110.29i	0.0725464	+	0.150300i
$583$	−1372.83	−	2377.82i	−0.0975247	−	0.168918i
$584$	10445.8	−	18092.6i	0.740153	−	1.28198i
$585$	7508.15	−	2962.26i	0.530639	−	0.209358i
$586$	8741.45	−	5046.88i	0.616222	−	0.355776i
$587$	23928.9			1.68254			0.841270	−	0.540615i	$-0.181809\pi$
$587$	23928.9			1.68254			0.841270	+	0.540615i	$0.181809\pi$
$588$	9121.04	−	3863.94i	0.639703	−	0.270997i
$589$	−28804.4			−2.01505
$590$	1848.46	−	1067.21i	0.128983	−	0.0744684i
$591$	−158.779	+	2144.53i	−0.0110513	+	0.149262i
$592$	−702.191	+	1216.23i	−0.0487498	+	0.0844371i
$593$	−10698.3	−	18530.0i	−0.740853	−	1.28319i	−0.952107	−	0.305764i	$-0.901088\pi$
$593$	−10698.3	−	18530.0i	−0.740853	−	1.28319i	0.211254	−	0.977431i	$-0.432245\pi$
$594$	6456.30	+	1455.37i	0.445968	+	0.100530i
$595$	10621.3	+	3126.67i	0.731813	+	0.215430i
$596$		−	353.749i		−	0.0243123i
$597$	6371.91	+	4335.94i	0.436825	+	0.297250i
$598$	−6081.19	−	3510.98i	−0.415850	−	0.240091i
$599$	14601.1	+	8429.96i	0.995969	+	0.575023i	0.907053	−	0.421016i	$-0.138326\pi$
$599$	14601.1	+	8429.96i	0.995969	+	0.575023i	0.0889158	+	0.996039i	$0.471660\pi$
$600$	−2275.45	−	1548.39i	−0.154825	−	0.105355i
$601$			8040.78i			0.545741i	0.962051	+	0.272870i	$0.0879730\pi$
$601$			8040.78i			0.545741i	−0.962051	+	0.272870i	$0.912027\pi$
$602$	2487.57	−	601.654i	0.168415	−	0.0407336i
$603$	2024.62	−	2548.14i	0.136731	−	0.172087i
$604$	2292.92	+	3971.45i	0.154466	+	0.267543i
$605$	−1049.38	+	1817.57i	−0.0705178	+	0.122140i
$606$	633.471	−	8555.90i	0.0424637	−	0.573531i
$607$	−1911.63	+	1103.68i	−0.127827	+	0.0738007i	−0.562550	−	0.826763i	$-0.690180\pi$
$607$	−1911.63	+	1103.68i	−0.127827	+	0.0738007i	0.434723	+	0.900564i	$0.356846\pi$
$608$	22099.0			1.47406
$609$	−6425.88	+	17061.7i	−0.427569	+	1.13526i
$610$	3320.67			0.220410
$611$	28794.9	−	16624.7i	1.90657	−	1.10076i
$612$	6584.98	+	16690.3i	0.434938	+	1.10239i
$613$	6395.15	−	11076.7i	0.421366	−	0.729828i	−0.574707	−	0.818359i	$-0.694884\pi$
$613$	6395.15	−	11076.7i	0.421366	−	0.729828i	0.996073	+	0.0885314i	$0.0282174\pi$
$614$	2730.81	+	4729.90i	0.179490	+	0.310885i
$615$	3891.03	+	8061.34i	0.255125	+	0.528560i
$616$	−8578.39	+	8168.14i	−0.561093	+	0.534259i
$617$			2961.53i			0.193236i	0.995322	+	0.0966180i	$0.0308025\pi$
$617$			2961.53i			0.193236i	−0.995322	+	0.0966180i	$0.969197\pi$
$618$	−404.559	+	594.522i	−0.0263329	+	0.0386977i
$619$	−110.296	−	63.6792i	−0.00716181	−	0.00413487i	0.496415	−	0.868085i	$-0.334650\pi$
$619$	−110.296	−	63.6792i	−0.00716181	−	0.00413487i	−0.503577	+	0.863951i	$0.667983\pi$
$620$	−5873.50	−	3391.07i	−0.380460	−	0.219659i
$621$	−10067.2	+	3134.97i	−0.650537	+	0.202580i
$622$		−	11592.6i		−	0.747304i
$623$	3541.47	+	14642.4i	0.227746	+	0.941629i
$624$	−3176.45	+	1533.20i	−0.203782	+	0.0983609i
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	7866.42	−	13625.0i	0.502245	−	0.869914i
$627$	−18462.3	−	1366.93i	−1.17594	−	0.0870655i
$628$	−14437.7	+	8335.64i	−0.917403	+	0.529663i
$629$	−14790.0			−0.937543
$630$	−2248.20	−	3195.56i	−0.142175	−	0.202086i
$631$	25577.1			1.61364			0.806820	−	0.590797i	$-0.201187\pi$
$631$	25577.1			1.61364			0.806820	+	0.590797i	$0.201187\pi$
$632$	12297.8	−	7100.11i	0.774017	−	0.446879i
$633$	8670.23	+	641.936i	0.544408	+	0.0403075i
$634$	−4125.96	+	7146.37i	−0.258458	+	0.447663i
$635$	3961.97	+	6862.34i	0.247600	+	0.428856i
$636$	−2365.61	+	1141.83i	−0.147488	+	0.0711894i
$637$	−11111.0	+	17236.5i	−0.691103	+	1.07211i
$638$		−	8937.11i		−	0.554583i
$639$	883.364	−	5932.82i	0.0546875	−	0.367291i
$640$	5120.80	+	2956.49i	0.316277	+	0.182603i
$641$	−21519.0	−	12424.0i	−1.32598	−	0.765553i	−0.341302	−	0.939954i	$-0.610868\pi$
$641$	−21519.0	−	12424.0i	−1.32598	−	0.765553i	−0.984675	+	0.174401i	$0.944201\pi$
$642$	3852.18	−	5660.99i	0.236812	−	0.348009i
$643$		−	1572.93i		−	0.0964701i	−0.998836	−	0.0482350i	$-0.984640\pi$
$643$		−	1572.93i		−	0.0964701i	0.998836	−	0.0482350i	$-0.0153597\pi$
$644$	2184.64	−	7421.17i	0.133675	−	0.454092i
$645$	998.673	+	2069.02i	0.0609654	+	0.126307i
$646$	11026.3	+	19098.1i	0.671555	+	1.16317i
$647$	3345.51	−	5794.60i	0.203285	−	0.352101i	−0.746300	−	0.665610i	$-0.768171\pi$
$647$	3345.51	−	5794.60i	0.203285	−	0.352101i	0.949585	+	0.313509i	$0.101505\pi$
$648$	4499.74	−	14775.5i	0.272788	−	0.895736i
$649$	7141.29	−	4123.03i	0.431926	−	0.249373i
$650$	2335.80			0.140950
$651$	−14895.5	−	18158.5i	−0.896777	−	1.09322i
$652$	5036.62			0.302530
$653$	5469.11	−	3157.59i	0.327753	−	0.189229i	−0.327090	−	0.944993i	$-0.606068\pi$
$653$	5469.11	−	3157.59i	0.327753	−	0.189229i	0.654843	+	0.755765i	$0.272735\pi$
$654$	−151.323	+	2043.83i	−0.00904772	+	0.122202i
$655$	−1417.46	+	2455.11i	−0.0845567	+	0.146456i
$656$	−1955.81	−	3387.56i	−0.116405	−	0.201619i
$657$	20844.5	+	16562.0i	1.23778	+	0.983476i
$658$	−11099.0	−	11656.4i	−0.657573	−	0.690600i
$659$		−	4774.62i		−	0.282235i	−0.989993	−	0.141117i	$-0.954931\pi$
$659$		−	4774.62i		−	0.282235i	0.989993	−	0.141117i	$-0.0450695\pi$
$660$	−3603.72	−	2452.25i	−0.212537	−	0.144627i
$661$	7845.26	+	4529.46i	0.461642	+	0.266529i	0.712734	−	0.701434i	$-0.247457\pi$
$661$	7845.26	+	4529.46i	0.461642	+	0.266529i	−0.251093	+	0.967963i	$0.580790\pi$
$662$	−3937.51	−	2273.32i	−0.231172	−	0.133467i
$663$	−30709.4	−	20897.1i	−1.79888	−	1.22410i
$664$		−	16499.4i		−	0.964306i
$665$	7536.56	+	7915.08i	0.439481	+	0.461554i
$666$	4086.39	+	3246.83i	0.237755	+	0.188907i
$667$	7119.15	+	12330.7i	0.413275	+	0.715813i
$668$	7346.66	−	12724.8i	0.425525	−	0.737032i
$669$	208.542	−	2816.65i	0.0120519	−	0.162777i
$670$	815.662	−	470.923i	0.0470325	−	0.0271542i
$671$	12829.0			0.738088
$672$	11428.0	+	13931.3i	0.656017	+	0.799721i
$673$	−10257.3			−0.587503			−0.293752	−	0.955882i	$-0.594904\pi$
$673$	−10257.3			−0.587503			−0.293752	+	0.955882i	$0.594904\pi$
$674$	−7653.74	+	4418.89i	−0.437405	+	0.252536i
$675$	2378.72	−	2577.51i	0.135640	−	0.146975i
$676$	3828.30	−	6630.81i	0.217814	−	0.377265i
$677$	−3829.20	−	6632.36i	−0.217383	−	0.376518i	0.736624	−	0.676302i	$-0.236419\pi$
$677$	−3829.20	−	6632.36i	−0.217383	−	0.376518i	−0.954007	+	0.299784i	$0.903085\pi$
$678$	1306.65	+	2707.08i	0.0740141	+	0.153340i
$679$	1509.26	−	5126.92i	0.0853019	−	0.289769i
$680$			12666.3i			0.714309i
$681$	−1682.18	+	2472.05i	−0.0946566	+	0.139103i
$682$	9970.51	+	5756.48i	0.559810	+	0.323207i
$683$	22173.4	+	12801.8i	1.24223	+	0.717201i	0.969547	−	0.244904i	$-0.0787564\pi$
$683$	22173.4	+	12801.8i	1.24223	+	0.717201i	0.272681	+	0.962105i	$0.412090\pi$
$684$	−2608.34	+	17518.0i	−0.145807	+	0.979267i
$685$		−	7832.73i		−	0.436895i
$686$	9374.37	+	3266.33i	0.521742	+	0.181792i
$687$	−7980.24	+	3851.89i	−0.443181	+	0.213914i
$688$	−501.978	−	869.451i	−0.0278165	−	0.0481795i
$689$	2719.03	−	4709.49i	0.150343	−	0.260402i
$690$	−3043.05	−	225.304i	−0.167894	−	0.0124307i
$691$	−15375.4	+	8876.97i	−0.846463	+	0.488706i	−0.859456	−	0.511210i	$-0.829198\pi$
$691$	−15375.4	+	8876.97i	−0.846463	+	0.488706i	0.0129927	+	0.999916i	$0.495864\pi$
$692$	7306.83			0.401393
$693$	−8685.64	−	12345.6i	−0.476104	−	0.676727i
$694$	−18047.3			−0.987130
$695$	−619.346	+	357.579i	−0.0338031	+	0.0195162i
$696$	−20800.1	−	1540.02i	−1.13280	−	0.0838712i
$697$	20597.2	−	35675.4i	1.11933	−	1.93874i
$698$	−7974.62	−	13812.4i	−0.432441	−	0.749010i
$699$	−3915.80	+	1890.07i	−0.211887	+	0.102273i
$700$	604.956	+	2501.22i	0.0326646	+	0.135053i
$701$			14270.4i			0.768883i	0.923149	+	0.384441i	$0.125606\pi$
$701$			14270.4i			0.768883i	−0.923149	+	0.384441i	$0.874394\pi$
$702$	3897.34	+	12515.4i	0.209538	+	0.672882i
$703$	−12643.4	−	7299.69i	−0.678316	−	0.391626i
$704$	−5275.01	−	3045.53i	−0.282399	−	0.163043i
$705$	8128.43	−	11945.2i	0.434233	−	0.638130i
$706$			1812.75i			0.0966341i
$707$	−14171.0	+	13493.3i	−0.753828	+	0.717777i
$708$	−3429.25	−	7104.64i	−0.182033	−	0.377131i
$709$	−15078.8	−	26117.2i	−0.798723	−	1.38343i	−0.920448	−	0.390865i	$-0.872176\pi$
$709$	−15078.8	−	26117.2i	−0.798723	−	1.38343i	0.121725	−	0.992564i	$-0.461157\pi$
$710$	867.923	−	1503.29i	0.0458768	−	0.0794610i
$711$	6641.40	+	16833.3i	0.350312	+	0.887901i
$712$	−14925.0	+	8616.97i	−0.785588	+	0.453560i
$713$	−18342.0			−0.963415
$714$	−6337.58	+	16827.2i	−0.332182	+	0.881993i
$715$	9024.08			0.472002
$716$	3845.43	−	2220.16i	0.200713	−	0.115882i
$717$	−2132.14	+	28797.4i	−0.111054	+	1.49994i
$718$	−1025.34	+	1775.95i	−0.0532946	+	0.0923089i
$719$	13792.2	+	23888.7i	0.715384	+	1.23908i	0.962811	+	0.270176i	$0.0870817\pi$
$719$	13792.2	+	23888.7i	0.715384	+	1.23908i	−0.247427	+	0.968907i	$0.579585\pi$
$720$	−953.475	+	1200.02i	−0.0493526	+	0.0621142i
$721$	1594.17	−	385.573i	0.0823441	−	0.0199161i
$722$			11049.7i			0.569569i
$723$	22306.5	+	15179.1i	1.14742	+	0.780795i
$724$	6331.60	+	3655.55i	0.325017	+	0.187649i
$725$	−4101.73	−	2368.13i	−0.210116	−	0.121311i
$726$	−2817.90	−	1917.52i	−0.144053	−	0.0980246i
$727$			17049.4i			0.869777i	0.900484	+	0.434889i	$0.143212\pi$
$727$			17049.4i			0.869777i	−0.900484	+	0.434889i	$0.856788\pi$
$728$	−22505.5	−	6625.15i	−1.14576	−	0.337286i
$729$	17779.4	+	8444.72i	0.903287	+	0.429036i
$730$	3852.28	+	6672.35i	0.195314	+	0.338294i
$731$	5286.48	−	9156.45i	0.267479	−	0.463288i
$732$	906.232	−	12239.9i	0.0457586	−	0.618033i
$733$	14815.0	−	8553.46i	0.746529	−	0.431009i	−0.0779095	−	0.996960i	$-0.524825\pi$
$733$	14815.0	−	8553.46i	0.746529	−	0.431009i	0.824438	+	0.565952i	$0.191491\pi$
$734$	6223.86			0.312980
$735$	−1092.36	+	8844.20i	−0.0548195	+	0.443841i
$736$	14072.1			0.704764
$737$	3151.21	−	1819.35i	0.157498	−	0.0909316i
$738$	−13522.7	+	5335.24i	−0.674496	+	0.266115i
$739$	−127.113	+	220.166i	−0.00632738	+	0.0109593i	−0.869172	−	0.494510i	$-0.835347\pi$
$739$	−127.113	+	220.166i	−0.00632738	+	0.0109593i	0.862844	+	0.505470i	$0.168681\pi$
$740$	−1718.75	−	2976.96i	−0.0853816	−	0.147885i
$741$	−15938.6	−	33021.1i	−0.790172	−	1.63706i
$742$	−2525.29	−	743.393i	−0.124941	−	0.0367801i
$743$			31231.0i			1.54206i	0.636796	+	0.771032i	$0.280259\pi$
$743$			31231.0i			1.54206i	−0.636796	+	0.771032i	$0.719741\pi$
$744$	15115.6	−	22213.3i	0.744847	−	1.09459i
$745$	275.604	+	159.120i	0.0135535	+	0.00782512i
$746$	−12575.0	−	7260.17i	−0.617162	−	0.356319i
$747$	20796.7	+	3096.52i	1.01862	+	0.151667i
$748$			20060.1i			0.980577i
$749$	−15179.6	+	3671.40i	−0.740521	+	0.179105i
$750$	914.106	−	441.219i	0.0445046	−	0.0214814i
$751$	−805.681	−	1395.48i	−0.0391474	−	0.0678053i	0.845788	−	0.533519i	$-0.179131\pi$
$751$	−805.681	−	1395.48i	−0.0391474	−	0.0678053i	−0.884935	+	0.465714i	$0.845798\pi$
$752$	−3156.92	+	5467.95i	−0.153087	+	0.265154i
$753$	5962.58	+	441.464i	0.288564	+	0.0213650i
$754$	15329.3	−	8850.40i	0.740400	−	0.427470i
$755$	−4125.51			−0.198865
$756$	−12392.3	+	7414.73i	−0.596170	+	0.356708i
$757$	7794.46			0.374233			0.187116	−	0.982338i	$-0.440086\pi$
$757$	7794.46			0.374233			0.187116	+	0.982338i	$0.440086\pi$
$758$	−10136.1	+	5852.06i	−0.485697	+	0.280418i
$759$	−11756.4	−	870.435i	−0.562228	−	0.0416268i
$760$	−6251.54	+	10828.0i	−0.298378	+	0.516806i
$761$	−15580.5	−	26986.2i	−0.742170	−	1.28548i	−0.951505	−	0.307633i	$-0.900463\pi$
$761$	−15580.5	−	26986.2i	−0.742170	−	1.28548i	0.209335	−	0.977844i	$-0.432870\pi$
$762$	−11589.3	+	5593.91i	−0.550967	+	0.265940i
$763$	3385.17	−	3223.28i	0.160618	−	0.152936i
$764$			5438.13i			0.257519i
$765$	−15965.3	−	2377.15i	−0.754545	−	0.112348i
$766$	1769.17	+	1021.43i	0.0834500	+	0.0481799i
$767$	14144.0	+	8166.04i	0.665854	+	0.384431i
$768$	−10121.2	+	14873.6i	−0.475542	+	0.698835i
$769$			24931.9i			1.16914i	0.811343	+	0.584570i	$0.198737\pi$
$769$			24931.9i			1.16914i	−0.811343	+	0.584570i	$0.801263\pi$
$770$	−1026.94	−	4245.93i	−0.0480627	−	0.198718i
$771$	−12769.2	−	26454.8i	−0.596460	−	1.23573i
$772$	−8589.14	−	14876.8i	−0.400427	−	0.693561i
$773$	836.243	−	1448.42i	0.0389102	−	0.0673944i	−0.845914	−	0.533319i	$-0.820945\pi$
$773$	836.243	−	1448.42i	0.0389102	−	0.0673944i	0.884825	+	0.465924i	$0.154278\pi$
$774$	−3470.74	+	1369.34i	−0.161180	+	0.0635918i
$775$	5283.92	−	3050.68i	0.244909	−	0.141398i
$776$	6114.08			0.282838
$777$	−1936.49	−	11745.4i	−0.0894095	−	0.542295i
$778$	−984.590			−0.0453718
$779$	35215.7	−	20331.8i	1.61968	−	0.935125i
$780$	637.456	−	8609.72i	0.0292623	−	0.395228i
$781$	3353.11	−	5807.75i	0.153628	−	0.266092i
$782$	7021.33	+	12161.3i	0.321077	+	0.556121i
$783$	5844.79	−	25928.6i	0.266763	−	1.18341i
$784$	190.681	−	3889.52i	0.00868626	−	0.177183i
$785$		−	14997.8i		−	0.681905i
$786$	−3806.31	−	2590.11i	−0.172731	−	0.117540i
$787$	13357.2	+	7711.79i	0.604998	+	0.349296i	0.771005	−	0.636829i	$-0.219754\pi$
$787$	13357.2	+	7711.79i	0.604998	+	0.349296i	−0.166007	+	0.986125i	$0.553088\pi$
$788$	1991.95	+	1150.05i	0.0900509	+	0.0519909i
$789$	−26434.8	−	17988.3i	−1.19278	−	0.811661i
$790$			5236.88i			0.235848i
$791$	1936.07	−	6576.81i	0.0870276	−	0.295631i
$792$	10742.6	−	13520.4i	0.481971	−	0.606599i
$793$	12704.5	+	22004.8i	0.568916	+	0.985391i
$794$	2781.87	−	4818.33i	0.124338	−	0.215360i
$795$	174.484	−	2356.64i	0.00778403	−	0.105134i
$796$	7139.34	−	4121.90i	0.317898	−	0.183539i
$797$	−32042.5			−1.42410			−0.712048	−	0.702131i	$-0.752232\pi$
$797$	−32042.5			−1.42410			−0.712048	+	0.702131i	$0.752232\pi$
$798$	−13723.0	+	11257.1i	−0.608757	+	0.499368i
$799$	−66493.0			−2.94412
$800$	−4053.87	+	2340.50i	−0.179157	+	0.103437i
$801$	−8060.26	−	20429.5i	−0.355550	−	0.901176i
$802$	2114.15	−	3661.82i	0.0930839	−	0.161226i
$803$	14882.8	+	25777.8i	0.654051	+	1.13285i
$804$	−1513.21	−	3135.03i	−0.0663767	−	0.137517i
$805$	4799.12	+	5040.16i	0.210120	+	0.220674i
$806$			22802.5i			0.996506i
$807$	−15214.7	+	22358.9i	−0.663673	+	0.975305i
$808$	−19386.2	−	11192.7i	−0.844066	−	0.487322i
$809$	−31899.7	−	18417.3i	−1.38632	−	0.800393i	−0.393423	−	0.919357i	$-0.628709\pi$
$809$	−31899.7	−	18417.3i	−1.38632	−	0.800393i	−0.992899	+	0.118964i	$0.962043\pi$
$810$	3889.28	+	4161.65i	0.168711	+	0.180525i
$811$			12360.8i			0.535201i	0.963530	+	0.267600i	$0.0862307\pi$
$811$			12360.8i			0.535201i	−0.963530	+	0.267600i	$0.913769\pi$
$812$	13447.4	+	14122.7i	0.581169	+	0.610359i
$813$	−12662.5	+	6111.94i	−0.546242	+	0.263659i
$814$	2917.65	+	5053.51i	0.125631	+	0.217599i
$815$	−2265.53	+	3924.01i	−0.0973717	+	0.168653i
$816$	7034.34	+	520.816i	0.301778	+	0.0223434i
$817$	9038.46	−	5218.36i	0.387045	−	0.223461i
$818$	−6227.18			−0.266171
$819$	12574.4	−	27123.9i	0.536491	−	1.15725i
$820$	9574.43			0.407748
$821$	−31373.5	+	18113.5i	−1.33367	+	0.769996i	−0.985860	−	0.167569i	$-0.946408\pi$
$821$	−31373.5	+	18113.5i	−1.33367	+	0.769996i	−0.347811	+	0.937565i	$0.613075\pi$
$822$	12685.9	+	939.250i	0.538285	+	0.0398541i
$823$	14082.2	−	24391.2i	0.596447	−	1.03308i	−0.396894	−	0.917865i	$-0.629912\pi$
$823$	14082.2	−	24391.2i	0.596447	−	1.03308i	0.993341	−	0.115212i	$-0.0367548\pi$
$824$	938.162	+	1624.94i	0.0396631	+	0.0686986i
$825$	3531.53	−	1704.59i	0.149033	−	0.0719349i
$826$	2232.63	−	7584.21i	0.0940474	−	0.319477i
$827$		−	3521.78i		−	0.148083i	−0.997255	−	0.0740413i	$-0.976410\pi$
$827$		−	3521.78i		−	0.148083i	0.997255	−	0.0740413i	$-0.0235897\pi$
$828$	−1660.93	+	11155.1i	−0.0697119	+	0.468197i
$829$	−11756.6	−	6787.70i	−0.492551	−	0.284375i	0.233081	−	0.972457i	$-0.425119\pi$
$829$	−11756.6	−	6787.70i	−0.492551	−	0.284375i	−0.725632	+	0.688083i	$0.758453\pi$
$830$	5269.57	+	3042.39i	0.220373	+	0.127232i
$831$	−5376.84	+	7901.57i	−0.224453	+	0.329847i
$832$		−	12063.9i		−	0.502693i
$833$	36477.9	−	18741.8i	1.51727	−	0.779549i
$834$	−504.867	−	1045.97i	−0.0209618	−	0.0434280i
$835$	6609.22	+	11447.5i	0.273918	+	0.474440i
$836$	−9900.83	+	17148.7i	−0.409602	+	0.709452i
$837$	25162.1	+	23221.5i	1.03910	+	0.958963i
$838$	4273.07	−	2467.06i	0.176147	−	0.101698i
$839$	−18852.1			−0.775740			−0.387870	−	0.921714i	$-0.626789\pi$
$839$	−18852.1			−0.775740			−0.387870	+	0.921714i	$0.626789\pi$
$840$	−10058.9	+	1658.43i	−0.413172	+	0.0681207i
$841$	−11502.6			−0.471630
$842$	−6730.96	+	3886.12i	−0.275492	+	0.159055i
$843$	−961.420	+	12985.3i	−0.0392800	+	0.530531i
$844$	4649.60	−	8053.35i	0.189628	−	0.328445i
$845$	3444.02	+	5965.22i	0.140211	+	0.242852i
$846$	18371.7	+	14597.2i	0.746609	+	0.593216i
$847$	1827.53	+	7556.03i	0.0741378	+	0.306527i
$848$			1032.65i			0.0418176i
$849$	−93.7232	−	63.7765i	−0.00378866	−	0.00257810i
$850$	−4045.37	−	2335.60i	−0.163241	−	0.0942474i
$851$	−8051.08	−	4648.29i	−0.324309	−	0.187240i
$852$	−5304.22	−	3609.40i	−0.213286	−	0.145136i
$853$		−	16204.8i		−	0.650460i	−0.945635	−	0.325230i	$-0.894558\pi$
$853$		−	16204.8i		−	0.650460i	0.945635	−	0.325230i	$-0.105442\pi$
$854$	8907.76	−	8481.76i	0.356929	−	0.339859i
$855$	−12475.0	−	9911.94i	−0.498988	−	0.396469i
$856$	−8933.10	−	15472.6i	−0.356691	−	0.617806i
$857$	12940.6	−	22413.8i	0.515802	−	0.893395i	−0.484030	−	0.875051i	$-0.660827\pi$
$857$	12940.6	−	22413.8i	0.515802	−	0.893395i	0.999832	−	0.0183433i	$-0.00583920\pi$
$858$	−1082.11	+	14615.4i	−0.0430566	+	0.581539i
$859$	−31181.2	+	18002.5i	−1.23852	+	0.715060i	−0.968792	−	0.247876i	$-0.920267\pi$
$859$	−31181.2	+	18002.5i	−1.23852	+	0.715060i	−0.269729	+	0.962936i	$0.586934\pi$
$860$	2457.38			0.0974370
$861$	31028.3	+	11686.1i	1.22815	+	0.462556i
$862$	4908.45			0.193947
$863$	2904.67	−	1677.01i	0.114573	−	0.0661486i	−0.441619	−	0.897203i	$-0.645596\pi$
$863$	2904.67	−	1677.01i	0.114573	−	0.0661486i	0.556191	+	0.831054i	$0.312262\pi$
$864$	−19304.5	−	17815.7i	−0.760131	−	0.701507i
$865$	−3286.69	+	5692.72i	−0.129192	+	0.223767i
$866$	−3856.75	−	6680.09i	−0.151337	−	0.262123i
$867$	21193.2	+	43907.6i	0.830174	+	1.71993i
$868$	−24417.3	+	5905.68i	−0.954814	+	0.230935i
$869$			20232.0i			0.789786i
$870$	4327.28	−	6359.18i	0.168630	−	0.247812i
$871$	6241.26	+	3603.39i	0.242798	+	0.140179i
$872$	4630.98	+	2673.70i	0.179845	+	0.103834i
$873$	−1147.46	+	7706.53i	−0.0444852	+	0.298770i
$874$			13861.7i			0.536475i
$875$	−2220.81	−	653.758i	−0.0858022	−	0.0252584i
$876$	25645.5	−	12378.5i	0.989132	−	0.477433i
$877$	−18567.9	−	32160.6i	−0.714931	−	1.23830i	−0.962986	−	0.269551i	$-0.913125\pi$
$877$	−18567.9	−	32160.6i	−0.714931	−	1.23830i	0.248055	−	0.968746i	$-0.420208\pi$
$878$	−9881.37	+	17115.0i	−0.379818	+	0.657864i
$879$	33470.7	+	2478.14i	1.28435	+	0.0950919i
$880$	−1484.03	+	856.805i	−0.0568484	+	0.0328215i
$881$	10167.5			0.388821			0.194410	−	0.980920i	$-0.437721\pi$
$881$	10167.5			0.388821			0.194410	+	0.980920i	$0.437721\pi$
$882$	−14193.0	−	2829.72i	−0.541842	−	0.108029i
$883$	37365.6			1.42407			0.712035	−	0.702144i	$-0.247774\pi$
$883$	37365.6			1.42407			0.712035	+	0.702144i	$0.247774\pi$
$884$	−34408.1	+	19865.5i	−1.30913	+	0.755825i
$885$	7077.70	+	524.027i	0.268830	+	0.0199039i
$886$	7443.29	−	12892.2i	0.282237	−	0.488849i
$887$	−1048.46	−	1815.98i	−0.0396886	−	0.0687427i	0.845499	−	0.533977i	$-0.179303\pi$
$887$	−1048.46	−	1815.98i	−0.0396886	−	0.0687427i	−0.885187	+	0.465235i	$0.845970\pi$
$888$	12264.2	−	5919.68i	0.463469	−	0.223707i
$889$	28156.0	+	8288.55i	1.06223	+	0.312698i
$890$		−	6355.68i		−	0.239374i
$891$	15025.7	+	16078.0i	0.564962	+	0.604527i
$892$	−2616.25	−	1510.49i	−0.0982046	−	0.0566985i
$893$	−56842.6	−	32818.1i	−2.13008	−	1.22980i
$894$	−290.759	+	427.287i	−0.0108775	+	0.0159850i
$895$			3994.61i			0.149190i
$896$	21288.2	−	5148.85i	0.793738	−	0.191977i
$897$	−10149.3	−	21027.1i	−0.377789	−	0.782693i
$898$	5395.36	+	9345.03i	0.200496	+	0.347269i
$899$	23118.1	−	40041.7i	0.857655	−	1.48550i
$900$	−1376.86	−	3489.79i	−0.0509948	−	0.129251i
$901$	−9418.14	+	5437.56i	−0.348239	+	0.201056i
$902$	−16253.0			−0.599962
$903$	7963.72	+	2999.35i	0.293484	+	0.110534i
$904$	7843.13			0.288560
$905$	−5696.04	+	3288.61i	−0.209219	+	0.120792i
$906$	494.705	−	6681.67i	0.0181407	−	0.245015i
$907$	−12956.6	+	22441.6i	−0.474331	+	0.821565i	−0.999568	−	0.0293908i	$-0.990643\pi$
$907$	−12956.6	+	22441.6i	−0.474331	+	0.821565i	0.525237	+	0.850956i	$0.323977\pi$
$908$	1599.14	+	2769.79i	0.0584463	+	0.101232i
$909$	17746.2	−	22334.9i	0.647528	−	0.814965i
$910$	6265.84	−	5966.18i	0.228253	−	0.217337i
$911$		−	25814.5i		−	0.938829i	−0.882978	−	0.469414i	$-0.844465\pi$
$911$		−	25814.5i		−	0.938829i	0.882978	−	0.469414i	$-0.155535\pi$
$912$	5756.37	+	3917.08i	0.209005	+	0.142223i
$913$	20358.3	+	11753.9i	0.737965	+	0.426064i
$914$	21342.1	+	12321.9i	0.772356	+	0.445920i
$915$	9128.42	+	6211.69i	0.329810	+	0.224428i
$916$			9478.12i			0.341884i
$917$	2468.56	+	10206.4i	0.0888975	+	0.367551i
$918$	5764.48	−	25572.3i	0.207251	−	0.919404i
$919$	−22815.6	−	39517.7i	−0.818951	−	1.41847i	−0.906456	−	0.422301i	$-0.861223\pi$
$919$	−22815.6	−	39517.7i	−0.818951	−	1.41847i	0.0875045	−	0.996164i	$-0.472111\pi$
$920$	−3980.85	+	6895.04i	−0.142657	+	0.247090i
$921$	−1340.90	+	18110.7i	−0.0479740	+	0.647955i
$922$	−13657.7	+	7885.29i	−0.487845	+	0.281658i
$923$	13282.3			0.473664
$924$	−15930.7	+	2626.53i	−0.567187	+	0.0935135i
$925$	3092.44			0.109923
$926$	−10048.7	+	5801.62i	−0.356610	+	0.205889i
$927$	−2224.24	+	877.551i	−0.0788065	+	0.0310923i
$928$	−17736.4	+	30720.3i	−0.627398	+	1.08669i
$929$	−451.782	−	782.509i	−0.0159553	−	0.0276354i	0.857938	−	0.513754i	$-0.171746\pi$
$929$	−451.782	−	782.509i	−0.0159553	−	0.0276354i	−0.873893	+	0.486119i	$0.838412\pi$
$930$	4307.25	+	8923.65i	0.151871	+	0.314643i
$931$	40433.9	+	1982.24i	1.42338	+	0.0697802i
$932$			4650.79i			0.163457i
$933$	21685.4	−	31867.8i	0.760929	−	1.11823i
$934$	8418.65	+	4860.51i	0.294932	+	0.170279i
$935$	−15628.8	−	9023.27i	−0.546647	−	0.315607i
$936$	33829.1	+	5036.97i	1.18135	+	0.175896i
$937$		−	33159.0i		−	1.15609i	−0.816004	−	0.578046i	$-0.803815\pi$
$937$		−	33159.0i		−	1.15609i	0.816004	−	0.578046i	$-0.196185\pi$
$938$	985.183	−	3346.65i	0.0342936	−	0.116495i
$939$	47111.7	−	22739.8i	1.63731	−	0.790293i
$940$	−7727.17	−	13383.9i	−0.268120	−	0.464397i
$941$	1608.48	−	2785.97i	0.0557226	−	0.0965143i	−0.836819	−	0.547480i	$-0.815587\pi$
$941$	1608.48	−	2785.97i	0.0557226	−	0.0965143i	0.892541	+	0.450966i	$0.148920\pi$
$942$	24290.5	+	1798.44i	0.840155	+	0.0622043i
$943$	22424.6	−	12946.9i	0.774386	−	0.447092i
$944$	−3101.35			−0.106928
$945$	−202.584	−	12990.0i	−0.00697360	−	0.447159i
$946$	−4171.50			−0.143369
$947$	222.937	−	128.713i	0.00764991	−	0.00441668i	−0.496170	−	0.868225i	$-0.665261\pi$
$947$	222.937	−	128.713i	0.00764991	−	0.00441668i	0.503820	+	0.863809i	$0.331927\pi$
$948$	19303.0	+	1429.18i	0.661322	+	0.0489637i
$949$	−29476.8	+	51055.3i	−1.00828	+	1.74639i
$950$	−2305.50	−	3993.24i	−0.0787372	−	0.136377i
$951$	−24710.2	+	11927.1i	−0.842570	+	0.406690i
$952$	32352.7	+	33977.6i	1.10142	+	1.15674i
$953$		−	1742.82i		−	0.0592396i	−0.999561	−	0.0296198i	$-0.990570\pi$
$953$		−	1742.82i		−	0.0592396i	0.999561	−	0.0296198i	$-0.00942966\pi$
$954$	3795.89	+	565.187i	0.128822	+	0.0191809i
$955$	−4236.82	−	2446.13i	−0.143560	−	0.0828846i
$956$	26748.5	+	15443.3i	0.904925	+	0.522459i
$957$	16717.9	−	24567.9i	0.564694	−	0.829850i
$958$		−	30160.6i		−	1.01716i
$959$	−20006.6	−	21011.4i	−0.673667	−	0.707502i
$960$	−2278.80	−	4721.15i	−0.0766124	−	0.158723i
$961$	14885.7	+	25782.8i	0.499670	+	0.865455i
$962$	−5778.68	+	10009.0i	−0.193671	+	0.335449i
$963$	21179.0	−	8355.97i	0.708707	−	0.279613i
$964$	24993.1	−	14429.7i	0.835033	−	0.482107i
$965$	15453.9			0.515524
$966$	−8738.51	+	7168.26i	−0.291053	+	0.238753i
$967$	24711.2			0.821778			0.410889	−	0.911685i	$-0.365218\pi$
$967$	24711.2			0.821778			0.410889	+	0.911685i	$0.365218\pi$
$968$	−7701.88	+	4446.68i	−0.255731	+	0.147646i
$969$	−5414.20	+	73126.2i	−0.179493	+	2.42430i
$970$	−1127.40	+	1952.72i	−0.0373182	+	0.0646371i
$971$	10314.7	+	17865.6i	0.340901	+	0.590458i	0.984600	−	0.174821i	$-0.0559346\pi$
$971$	10314.7	+	17865.6i	0.340901	+	0.590458i	−0.643699	+	0.765278i	$0.722601\pi$
$972$	16401.2	−	13200.1i	0.541222	−	0.435589i
$973$	−748.066	+	2541.17i	−0.0246474	+	0.0837266i
$974$		−	23081.4i		−	0.759319i
$975$	6421.06	+	4369.38i	0.210911	+	0.143520i
$976$	−4178.57	−	2412.50i	−0.137042	−	0.0791210i
$977$	−16823.8	−	9713.22i	−0.550912	−	0.318069i	0.198578	−	0.980085i	$-0.436368\pi$
$977$	−16823.8	−	9713.22i	−0.550912	−	0.318069i	−0.749490	+	0.662016i	$0.769701\pi$
$978$	−6083.64	−	4139.78i	−0.198909	−	0.135353i
$979$		−	24554.4i		−	0.801594i
$980$	8011.50	+	5164.38i	0.261141	+	0.168337i
$981$	−4239.20	+	5335.36i	−0.137969	+	0.173644i
$982$	−5702.82	−	9877.57i	−0.185320	−	0.320984i
$983$	13984.4	−	24221.7i	0.453747	−	0.785913i	−0.544868	−	0.838522i	$-0.683420\pi$
$983$	13984.4	−	24221.7i	0.453747	−	0.785913i	0.998615	+	0.0526088i	$0.0167536\pi$
$984$	−2800.68	+	37827.0i	−0.0907341	+	1.22549i
$985$	−1792.00	+	1034.61i	−0.0579673	+	0.0334674i
$986$	−35398.4			−1.14332
$987$	−8706.11	−	52805.1i	−0.280768	−	1.70294i
$988$	−39219.1			−1.26288
$989$	5755.50	−	3322.94i	0.185050	−	0.106839i
$990$	2337.28	+	5924.06i	0.0750338	+	0.190181i
$991$	−29164.8	+	50514.9i	−0.934865	+	1.61923i	−0.159990	+	0.987119i	$0.551146\pi$
$991$	−29164.8	+	50514.9i	−0.934865	+	1.61923i	−0.774875	+	0.632115i	$0.782187\pi$
$992$	−22848.3	−	39574.5i	−0.731286	−	1.26662i
$993$	−6571.59	−	13614.8i	−0.210013	−	0.435100i
$994$	−1511.52	−	6249.47i	−0.0482320	−	0.199418i
$995$			7416.30i			0.236294i
$996$	12652.3	−	18593.2i	0.402513	−	0.591516i
$997$	−41676.8	−	24062.1i	−1.32389	−	0.764348i	−0.339542	−	0.940591i	$-0.610272\pi$
$997$	−41676.8	−	24062.1i	−1.32389	−	0.764348i	−0.984347	+	0.176243i	$0.943606\pi$
$998$	12978.7	+	7493.27i	0.411657	+	0.237671i
$999$	5159.81	+	16569.5i	0.163413	+	0.524761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.s.a.101.6	yes	32
3.2	odd	2		105.4.s.b.101.11	yes	32
7.5	odd	6		105.4.s.b.26.11	yes	32
21.5	even	6	inner	105.4.s.a.26.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.s.a.26.6	✓	32	21.5	even	6	inner
105.4.s.a.101.6	yes	32	1.1	even	1	trivial
105.4.s.b.26.11	yes	32	7.5	odd	6
105.4.s.b.101.11	yes	32	3.2	odd	2

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35336 + 0.781362i) q^{2} +(-5.18197 - 0.383668i) q^{3} +(-2.77895 + 4.81328i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(7.31285 - 3.52975i) q^{6} +(-17.7664 - 5.23007i) q^{7} -21.1872i q^{8} +(26.7056 + 3.97631i) q^{9} +O(q^{10})\)	\(q+(-1.35336 + 0.781362i) q^{2} +(-5.18197 - 0.383668i) q^{3} +(-2.77895 + 4.81328i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(7.31285 - 3.52975i) q^{6} +(-17.7664 - 5.23007i) q^{7} -21.1872i q^{8} +(26.7056 + 3.97631i) q^{9} +(6.76679 + 3.90681i) q^{10} +(26.1426 + 15.0935i) q^{11} +(16.2471 - 23.8761i) q^{12} +59.7880i q^{13} +(28.1309 - 6.80387i) q^{14} +(11.2936 + 23.3978i) q^{15} +(-5.67667 - 9.83227i) q^{16} +(59.7827 - 103.547i) q^{17} +(-39.2492 + 15.4854i) q^{18} +(102.212 - 59.0123i) q^{19} +27.7895 q^{20} +(90.0585 + 33.9185i) q^{21} -47.1738 q^{22} +(65.0867 - 37.5778i) q^{23} +(-8.12888 + 109.792i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-46.7161 - 80.9146i) q^{26} +(-136.862 - 30.8512i) q^{27} +(74.5457 - 70.9807i) q^{28} +189.451i q^{29} +(-33.5664 - 22.8412i) q^{30} +(-211.357 - 122.027i) q^{31} +(162.155 + 93.6200i) q^{32} +(-129.679 - 88.2439i) q^{33} +186.848i q^{34} +(21.7693 + 90.0061i) q^{35} +(-93.3525 + 117.491i) q^{36} +(-61.8489 - 107.125i) q^{37} +(-92.2200 + 159.730i) q^{38} +(22.9388 - 309.820i) q^{39} +(-91.7435 + 52.9681i) q^{40} +344.535 q^{41} +(-148.384 + 24.4645i) q^{42} +88.4283 q^{43} +(-145.298 + 83.8878i) q^{44} +(-49.5460 - 125.579i) q^{45} +(-58.7238 + 101.713i) q^{46} +(-278.061 - 481.616i) q^{47} +(25.6440 + 53.1285i) q^{48} +(288.293 + 185.839i) q^{49} -39.0681i q^{50} +(-349.519 + 513.639i) q^{51} +(-287.776 - 166.148i) q^{52} +(-78.7698 - 45.4778i) q^{53} +(209.329 - 65.1860i) q^{54} -150.935i q^{55} +(-110.811 + 376.422i) q^{56} +(-552.302 + 266.584i) q^{57} +(-148.030 - 256.395i) q^{58} +(136.583 - 236.569i) q^{59} +(-144.004 - 10.6619i) q^{60} +(368.048 - 212.492i) q^{61} +381.389 q^{62} +(-453.667 - 210.317i) q^{63} -201.778 q^{64} +(258.890 - 149.470i) q^{65} +(244.453 + 18.0991i) q^{66} +(60.2695 - 104.390i) q^{67} +(332.266 + 575.501i) q^{68} +(-351.695 + 169.755i) q^{69} +(-99.7890 - 104.801i) q^{70} -222.156i q^{71} +(84.2472 - 565.818i) q^{72} +(853.939 + 493.022i) q^{73} +(167.407 + 96.6527i) q^{74} +(73.0813 - 107.397i) q^{75} +655.969i q^{76} +(-385.522 - 404.885i) q^{77} +(211.037 + 437.221i) q^{78} +(335.113 + 580.432i) q^{79} +(-28.3833 + 49.1614i) q^{80} +(697.378 + 212.380i) q^{81} +(-466.279 + 269.206i) q^{82} +778.740 q^{83} +(-413.527 + 339.219i) q^{84} -597.827 q^{85} +(-119.675 + 69.0945i) q^{86} +(72.6863 - 981.728i) q^{87} +(319.789 - 553.890i) q^{88} +(-406.705 - 704.434i) q^{89} +(165.177 + 131.241i) q^{90} +(312.695 - 1062.22i) q^{91} +417.707i q^{92} +(1048.43 + 713.431i) q^{93} +(752.633 + 434.533i) q^{94} +(-511.062 - 295.062i) q^{95} +(-804.361 - 547.350i) q^{96} +288.573i q^{97} +(-535.371 - 26.2462i) q^{98} +(638.138 + 507.031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9}+O(q^{10}) \) 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9	\( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9} + 36 q^{11} + 246 q^{12} + 18 q^{14} + 20 q^{15} - 376 q^{16} - 72 q^{17} - 442 q^{18} - 198 q^{19} - 640 q^{20} - 218 q^{21} + 204 q^{22} + 72 q^{23} - 50 q^{24} - 400 q^{25} - 312 q^{26} + 508 q^{27} + 350 q^{28} + 40 q^{30} + 510 q^{31} + 810 q^{32} + 290 q^{33} - 70 q^{35} - 612 q^{36} - 658 q^{37} - 192 q^{38} - 648 q^{39} - 1404 q^{41} + 1892 q^{42} + 332 q^{43} + 2034 q^{44} - 490 q^{45} - 468 q^{46} + 408 q^{47} + 2810 q^{48} + 980 q^{49} - 888 q^{51} + 3378 q^{52} + 1152 q^{53} + 2714 q^{54} - 3354 q^{56} - 816 q^{57} - 1080 q^{58} - 48 q^{59} - 420 q^{60} - 1662 q^{61} - 2076 q^{62} + 874 q^{63} - 1952 q^{64} + 870 q^{65} - 1892 q^{66} - 1298 q^{67} + 1182 q^{68} + 2450 q^{69} - 450 q^{70} - 2708 q^{72} + 378 q^{73} + 2898 q^{74} - 50 q^{75} - 3528 q^{77} - 1896 q^{78} - 326 q^{79} - 1880 q^{80} - 3308 q^{81} - 2916 q^{82} - 1536 q^{83} + 1380 q^{84} + 720 q^{85} + 5202 q^{86} - 1090 q^{87} + 1668 q^{88} - 1590 q^{89} + 910 q^{90} + 2082 q^{91} - 4950 q^{93} - 1152 q^{94} + 990 q^{95} + 7416 q^{96} - 7830 q^{98} + 3128 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9 + 36 * q^11 + 246 * q^12 + 18 * q^14 + 20 * q^15 - 376 * q^16 - 72 * q^17 - 442 * q^18 - 198 * q^19 - 640 * q^20 - 218 * q^21 + 204 * q^22 + 72 * q^23 - 50 * q^24 - 400 * q^25 - 312 * q^26 + 508 * q^27 + 350 * q^28 + 40 * q^30 + 510 * q^31 + 810 * q^32 + 290 * q^33 - 70 * q^35 - 612 * q^36 - 658 * q^37 - 192 * q^38 - 648 * q^39 - 1404 * q^41 + 1892 * q^42 + 332 * q^43 + 2034 * q^44 - 490 * q^45 - 468 * q^46 + 408 * q^47 + 2810 * q^48 + 980 * q^49 - 888 * q^51 + 3378 * q^52 + 1152 * q^53 + 2714 * q^54 - 3354 * q^56 - 816 * q^57 - 1080 * q^58 - 48 * q^59 - 420 * q^60 - 1662 * q^61 - 2076 * q^62 + 874 * q^63 - 1952 * q^64 + 870 * q^65 - 1892 * q^66 - 1298 * q^67 + 1182 * q^68 + 2450 * q^69 - 450 * q^70 - 2708 * q^72 + 378 * q^73 + 2898 * q^74 - 50 * q^75 - 3528 * q^77 - 1896 * q^78 - 326 * q^79 - 1880 * q^80 - 3308 * q^81 - 2916 * q^82 - 1536 * q^83 + 1380 * q^84 + 720 * q^85 + 5202 * q^86 - 1090 * q^87 + 1668 * q^88 - 1590 * q^89 + 910 * q^90 + 2082 * q^91 - 4950 * q^93 - 1152 * q^94 + 990 * q^95 + 7416 * q^96 - 7830 * q^98 + 3128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more