LMFDB - Embedded newform 25.3.f.a.2.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,3,Mod(2,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(20))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("25.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	25.f (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.681200660901$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			2.3
Character	$\chi$	$=$	25.2
Dual form			25.3.f.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.287585 + 0.0455490i) q^{2} +(1.72787 + 3.39113i) q^{3} +(-3.72360 - 1.20987i) q^{4} +(2.36408 - 4.40581i) q^{5} +(0.342446 + 1.05394i) q^{6} +(-2.38950 - 2.38950i) q^{7} +(-2.05348 - 1.04630i) q^{8} +(-3.22416 + 4.43767i) q^{9} +O(q^{10})$	\(q+(0.287585 + 0.0455490i) q^{2} +(1.72787 + 3.39113i) q^{3} +(-3.72360 - 1.20987i) q^{4} +(2.36408 - 4.40581i) q^{5} +(0.342446 + 1.05394i) q^{6} +(-2.38950 - 2.38950i) q^{7} +(-2.05348 - 1.04630i) q^{8} +(-3.22416 + 4.43767i) q^{9} +(0.880552 - 1.15936i) q^{10} +(-15.4985 + 11.2603i) q^{11} +(-2.33105 - 14.7177i) q^{12} +(16.2234 - 2.56953i) q^{13} +(-0.578344 - 0.796023i) q^{14} +(19.0255 + 0.404238i) q^{15} +(12.1270 + 8.81080i) q^{16} +(-2.10364 + 4.12863i) q^{17} +(-1.12935 + 1.12935i) q^{18} +(1.02742 - 0.333828i) q^{19} +(-14.1333 + 13.5452i) q^{20} +(3.97436 - 12.2318i) q^{21} +(-4.97001 + 2.53235i) q^{22} +(-1.81434 + 11.4553i) q^{23} -8.77147i q^{24} +(-13.8223 - 20.8313i) q^{25} +4.78263 q^{26} +(13.2122 + 2.09261i) q^{27} +(6.00654 + 11.7885i) q^{28} +(-17.5664 - 5.70767i) q^{29} +(5.45302 + 0.982843i) q^{30} +(-6.76718 - 20.8272i) q^{31} +(9.60482 + 9.60482i) q^{32} +(-64.9643 - 33.1010i) q^{33} +(-0.793031 + 1.09151i) q^{34} +(-16.1766 + 4.87872i) q^{35} +(17.3745 - 12.6233i) q^{36} +(7.13692 + 45.0607i) q^{37} +(0.310675 - 0.0492062i) q^{38} +(36.7454 + 50.5757i) q^{39} +(-9.46437 + 6.57370i) q^{40} +(-13.3733 - 9.71629i) q^{41} +(1.70011 - 3.33666i) q^{42} +(41.9589 - 41.9589i) q^{43} +(71.3335 - 23.1776i) q^{44} +(11.9294 + 24.6960i) q^{45} +(-1.04356 + 3.21173i) q^{46} +(20.1364 - 10.2600i) q^{47} +(-8.92468 + 56.3482i) q^{48} -37.5806i q^{49} +(-3.02624 - 6.62037i) q^{50} -17.6355 q^{51} +(-63.5180 - 10.0603i) q^{52} +(-21.6364 - 42.4637i) q^{53} +(3.70431 + 1.20360i) q^{54} +(12.9711 + 94.9034i) q^{55} +(2.40665 + 7.40691i) q^{56} +(2.90730 + 2.90730i) q^{57} +(-4.79186 - 2.44157i) q^{58} +(-27.2616 + 37.5224i) q^{59} +(-70.3541 - 24.5235i) q^{60} +(45.3825 - 32.9723i) q^{61} +(-0.997479 - 6.29783i) q^{62} +(18.3079 - 2.89969i) q^{63} +(-32.9185 - 45.3084i) q^{64} +(27.0324 - 77.5516i) q^{65} +(-17.1750 - 12.4784i) q^{66} +(2.50707 - 4.92040i) q^{67} +(12.8282 - 12.8282i) q^{68} +(-41.9814 + 13.6406i) q^{69} +(-4.87437 + 0.666216i) q^{70} +(-20.2891 + 62.4433i) q^{71} +(11.2639 - 5.73923i) q^{72} +(-16.1217 + 101.788i) q^{73} +13.2839i q^{74} +(46.7586 - 82.8669i) q^{75} -4.22958 q^{76} +(63.9400 + 10.1271i) q^{77} +(8.26375 + 16.2185i) q^{78} +(-81.7963 - 26.5772i) q^{79} +(67.4879 - 32.6000i) q^{80} +(30.9880 + 95.3712i) q^{81} +(-3.40340 - 3.40340i) q^{82} +(19.1762 + 9.77074i) q^{83} +(-29.5978 + 40.7379i) q^{84} +(13.2168 + 19.0286i) q^{85} +(13.9779 - 10.1556i) q^{86} +(-10.9970 - 69.4320i) q^{87} +(43.6074 - 6.90673i) q^{88} +(52.7361 + 72.5850i) q^{89} +(2.30583 + 7.64557i) q^{90} +(-44.9056 - 32.6258i) q^{91} +(20.6153 - 40.4599i) q^{92} +(58.9350 - 58.9350i) q^{93} +(6.25825 - 2.03343i) q^{94} +(0.958111 - 5.31580i) q^{95} +(-15.9753 + 49.1670i) q^{96} +(-83.7126 + 42.6537i) q^{97} +(1.71176 - 10.8076i) q^{98} -105.082i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) $ 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 2 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 - 6 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 + 4 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 6 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 58 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 - 86 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 - 6 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 16 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 70 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 114 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 138 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 - 66 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 80 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 62 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 - 6 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 - 6 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 174 * q^96 + 270 * q^97 + 170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{20}\right)$

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 $

$2$	0.287585	+	0.0455490i	0.143792	+	0.0227745i	0.227916	−	0.973681i	$-0.426809\pi$
$2$	0.287585	+	0.0455490i	0.143792	+	0.0227745i	−0.0841233	+	0.996455i	$0.526809\pi$
$3$	1.72787	+	3.39113i	0.575955	+	1.13038i	0.976785	+	0.214223i	$0.0687220\pi$
$3$	1.72787	+	3.39113i	0.575955	+	1.13038i	−0.400829	+	0.916153i	$0.631278\pi$
$4$	−3.72360	−	1.20987i	−0.930899	−	0.302467i
$5$	2.36408	−	4.40581i	0.472815	−	0.881162i
$5$	2.36408	−	4.40581i	0.472815	−	0.881162i
$6$	0.342446	+	1.05394i	0.0570743	+	0.175657i
$7$	−2.38950	−	2.38950i	−0.341357	−	0.341357i	0.515520	−	0.856877i	$-0.327599\pi$
$7$	−2.38950	−	2.38950i	−0.341357	−	0.341357i	−0.856877	+	0.515520i	$0.827599\pi$
$8$	−2.05348	−	1.04630i	−0.256685	−	0.130787i
$9$	−3.22416	+	4.43767i	−0.358240	+	0.493075i
$10$	0.880552	−	1.15936i	0.0880552	−	0.115936i
$11$	−15.4985	+	11.2603i	−1.40895	+	1.02366i	−0.415476	+	0.909604i	$0.636385\pi$
$11$	−15.4985	+	11.2603i	−1.40895	+	1.02366i	−0.993474	+	0.114058i	$0.963615\pi$
$12$	−2.33105	−	14.7177i	−0.194254	−	1.22647i
$13$	16.2234	−	2.56953i	1.24795	−	0.197656i	0.502712	−	0.864454i	$-0.332336\pi$
$13$	16.2234	−	2.56953i	1.24795	−	0.197656i	0.745239	+	0.666798i	$0.232336\pi$
$14$	−0.578344	−	0.796023i	−0.0413103	−	0.0568588i
$15$	19.0255	+	0.404238i	1.26836	+	0.0269492i
$16$	12.1270	+	8.81080i	0.757939	+	0.550675i
$17$	−2.10364	+	4.12863i	−0.123744	+	0.242861i	−0.944565	−	0.328324i	$-0.893516\pi$
$17$	−2.10364	+	4.12863i	−0.123744	+	0.242861i	0.820821	+	0.571185i	$0.193516\pi$
$18$	−1.12935	+	1.12935i	−0.0627417	+	0.0627417i
$19$	1.02742	−	0.333828i	0.0540747	−	0.0175699i	−0.281855	−	0.959457i	$-0.590950\pi$
$19$	1.02742	−	0.333828i	0.0540747	−	0.0175699i	0.335929	+	0.941887i	$0.390950\pi$
$20$	−14.1333	+	13.5452i	−0.706666	+	0.677261i
$21$	3.97436	−	12.2318i	0.189255	−	0.582468i
$22$	−4.97001	+	2.53235i	−0.225910	+	0.115107i
$23$	−1.81434	+	11.4553i	−0.0788845	+	0.498057i	0.916336	+	0.400409i	$0.131132\pi$
$23$	−1.81434	+	11.4553i	−0.0788845	+	0.498057i	−0.995221	+	0.0976482i	$0.968868\pi$
$24$		−	8.77147i		−	0.365478i
$25$	−13.8223	−	20.8313i	−0.552892	−	0.833253i
$26$	4.78263			0.183947
$27$	13.2122	+	2.09261i	0.489341	+	0.0775040i
$28$	6.00654	+	11.7885i	0.214519	+	0.421018i
$29$	−17.5664	−	5.70767i	−0.605738	−	0.196816i	−0.00994032	−	0.999951i	$-0.503164\pi$
$29$	−17.5664	−	5.70767i	−0.605738	−	0.196816i	−0.595798	+	0.803134i	$0.703164\pi$
$30$	5.45302	+	0.982843i	0.181767	+	0.0327614i
$31$	−6.76718	−	20.8272i	−0.218296	−	0.671846i	−0.998903	−	0.0468241i	$-0.985090\pi$
$31$	−6.76718	−	20.8272i	−0.218296	−	0.671846i	0.780607	−	0.625022i	$-0.214910\pi$
$32$	9.60482	+	9.60482i	0.300151	+	0.300151i
$33$	−64.9643	−	33.1010i	−1.96862	−	1.00306i
$34$	−0.793031	+	1.09151i	−0.0233244	+	0.0321033i
$35$	−16.1766	+	4.87872i	−0.462189	+	0.139392i
$36$	17.3745	−	12.6233i	0.482624	−	0.350647i
$37$	7.13692	+	45.0607i	0.192890	+	1.21786i	0.874091	+	0.485762i	$0.161458\pi$
$37$	7.13692	+	45.0607i	0.192890	+	1.21786i	−0.681201	+	0.732096i	$0.738542\pi$
$38$	0.310675	−	0.0492062i	0.00817567	−	0.00129490i
$39$	36.7454	+	50.5757i	0.942190	+	1.29681i
$40$	−9.46437	+	6.57370i	−0.236609	+	0.164342i
$41$	−13.3733	−	9.71629i	−0.326179	−	0.236983i	0.412629	−	0.910899i	$-0.364611\pi$
$41$	−13.3733	−	9.71629i	−0.326179	−	0.236983i	−0.738807	+	0.673917i	$0.764611\pi$
$42$	1.70011	−	3.33666i	0.0404789	−	0.0794443i
$43$	41.9589	−	41.9589i	0.975789	−	0.975789i	−0.0239244	−	0.999714i	$-0.507616\pi$
$43$	41.9589	−	41.9589i	0.975789	−	0.975789i	0.999714	+	0.0239244i	$0.00761609\pi$
$44$	71.3335	−	23.1776i	1.62121	−	0.526765i
$45$	11.9294	+	24.6960i	0.265097	+	0.548801i
$46$	−1.04356	+	3.21173i	−0.0226860	+	0.0698203i
$47$	20.1364	−	10.2600i	0.428434	−	0.218298i	−0.226457	−	0.974021i	$-0.572714\pi$
$47$	20.1364	−	10.2600i	0.428434	−	0.218298i	0.654891	+	0.755723i	$0.272714\pi$
$48$	−8.92468	+	56.3482i	−0.185931	+	1.17392i
$49$		−	37.5806i		−	0.766951i
$50$	−3.02624	−	6.62037i	−0.0605247	−	0.132407i
$51$	−17.6355			−0.345795
$52$	−63.5180	−	10.0603i	−1.22150	−	0.193467i
$53$	−21.6364	−	42.4637i	−0.408233	−	0.801203i	0.591755	−	0.806118i	$-0.298435\pi$
$53$	−21.6364	−	42.4637i	−0.408233	−	0.801203i	−0.999988	+	0.00491533i	$0.998435\pi$
$54$	3.70431	+	1.20360i	0.0685984	+	0.0222890i
$55$	12.9711	+	94.9034i	0.235839	+	1.72552i
$56$	2.40665	+	7.40691i	0.0429759	+	0.132266i
$57$	2.90730	+	2.90730i	0.0510052	+	0.0510052i
$58$	−4.79186	−	2.44157i	−0.0826182	−	0.0420961i
$59$	−27.2616	+	37.5224i	−0.462062	+	0.635973i	−0.974935	−	0.222491i	$-0.928581\pi$
$59$	−27.2616	+	37.5224i	−0.462062	+	0.635973i	0.512873	+	0.858464i	$0.328581\pi$
$60$	−70.3541	−	24.5235i	−1.17257	−	0.408726i
$61$	45.3825	−	32.9723i	0.743975	−	0.540529i	−0.149979	−	0.988689i	$-0.547920\pi$
$61$	45.3825	−	32.9723i	0.743975	−	0.540529i	0.893953	+	0.448160i	$0.147920\pi$
$62$	−0.997479	−	6.29783i	−0.0160884	−	0.101578i
$63$	18.3079	−	2.89969i	0.290602	−	0.0460269i
$64$	−32.9185	−	45.3084i	−0.514351	−	0.707944i
$65$	27.0324	−	77.5516i	0.415883	−	1.19310i
$66$	−17.1750	−	12.4784i	−0.260228	−	0.189067i
$67$	2.50707	−	4.92040i	0.0374190	−	0.0734388i	−0.871540	−	0.490324i	$-0.836878\pi$
$67$	2.50707	−	4.92040i	0.0374190	−	0.0734388i	0.908959	+	0.416885i	$0.136878\pi$
$68$	12.8282	−	12.8282i	0.188650	−	0.188650i
$69$	−41.9814	+	13.6406i	−0.608426	+	0.197690i
$70$	−4.87437	+	0.666216i	−0.0696339	+	0.00951737i
$71$	−20.2891	+	62.4433i	−0.285761	+	0.879483i	0.700408	+	0.713743i	$0.253001\pi$
$71$	−20.2891	+	62.4433i	−0.285761	+	0.879483i	−0.986169	+	0.165740i	$0.946999\pi$
$72$	11.2639	−	5.73923i	0.156443	−	0.0797115i
$73$	−16.1217	+	101.788i	−0.220845	+	1.39436i	0.589199	+	0.807988i	$0.299443\pi$
$73$	−16.1217	+	101.788i	−0.220845	+	1.39436i	−0.810044	+	0.586370i	$0.800557\pi$
$74$			13.2839i			0.179512i
$75$	46.7586	−	82.8669i	0.623449	−	1.10489i
$76$	−4.22958			−0.0556524
$77$	63.9400	+	10.1271i	0.830389	+	0.131521i
$78$	8.26375	+	16.2185i	0.105945	+	0.207930i
$79$	−81.7963	−	26.5772i	−1.03540	−	0.336421i	−0.258475	−	0.966018i	$-0.583220\pi$
$79$	−81.7963	−	26.5772i	−1.03540	−	0.336421i	−0.776922	+	0.629597i	$0.783220\pi$
$80$	67.4879	−	32.6000i	0.843599	−	0.407499i
$81$	30.9880	+	95.3712i	0.382568	+	1.17742i
$82$	−3.40340	−	3.40340i	−0.0415048	−	0.0415048i
$83$	19.1762	+	9.77074i	0.231038	+	0.117720i	0.565678	−	0.824626i	$-0.308615\pi$
$83$	19.1762	+	9.77074i	0.231038	+	0.117720i	−0.334640	+	0.942346i	$0.608615\pi$
$84$	−29.5978	+	40.7379i	−0.352355	+	0.484975i
$85$	13.2168	+	19.0286i	0.155492	+	0.223866i
$86$	13.9779	−	10.1556i	0.162534	−	0.118088i
$87$	−10.9970	−	69.4320i	−0.126402	−	0.798070i
$88$	43.6074	−	6.90673i	0.495538	−	0.0784855i
$89$	52.7361	+	72.5850i	0.592541	+	0.815562i	0.995000	−	0.0998756i	$-0.0318445\pi$
$89$	52.7361	+	72.5850i	0.592541	+	0.815562i	−0.402459	+	0.915438i	$0.631844\pi$
$90$	2.30583	+	7.64557i	0.0256204	+	0.0849508i
$91$	−44.9056	−	32.6258i	−0.493468	−	0.358525i
$92$	20.6153	−	40.4599i	0.224080	−	0.439781i
$93$	58.9350	−	58.9350i	0.633710	−	0.633710i
$94$	6.25825	−	2.03343i	0.0665772	−	0.0216322i
$95$	0.958111	−	5.31580i	0.0100854	−	0.0559558i
$96$	−15.9753	+	49.1670i	−0.166410	+	0.512156i
$97$	−83.7126	+	42.6537i	−0.863017	+	0.439729i	−0.828707	−	0.559682i	$-0.810923\pi$
$97$	−83.7126	+	42.6537i	−0.863017	+	0.439729i	−0.0343096	+	0.999411i	$0.510923\pi$
$98$	1.71176	−	10.8076i	0.0174669	−	0.110282i
$99$		−	105.082i		−	1.06143i
$100$	26.2654	+	94.2906i	0.262654	+	0.942906i
$101$	14.4367			0.142938			0.0714690	−	0.997443i	$-0.477231\pi$
$101$	14.4367			0.142938			0.0714690	+	0.997443i	$0.477231\pi$
$102$	−5.07171	−	0.803280i	−0.0497227	−	0.00787530i
$103$	39.3351	+	77.1995i	0.381894	+	0.749510i	0.999311	−	0.0371269i	$-0.0118206\pi$
$103$	39.3351	+	77.1995i	0.381894	+	0.749510i	−0.617416	+	0.786637i	$0.711821\pi$
$104$	−36.0028	−	11.6980i	−0.346181	−	0.112481i
$105$	−44.4954	−	46.4272i	−0.423766	−	0.442164i
$106$	−4.28811	−	13.1974i	−0.0404539	−	0.124504i
$107$	−120.842	−	120.842i	−1.12937	−	1.12937i	−0.990280	−	0.139087i	$-0.955583\pi$
$107$	−120.842	−	120.842i	−1.12937	−	1.12937i	−0.139087	−	0.990280i	$-0.544417\pi$
$108$	−46.6651	−	23.7771i	−0.432085	−	0.220158i
$109$	19.5764	−	26.9446i	0.179600	−	0.247198i	−0.709720	−	0.704484i	$-0.751178\pi$
$109$	19.5764	−	26.9446i	0.179600	−	0.247198i	0.889320	+	0.457286i	$0.151178\pi$
$110$	−0.592449	+	27.8836i	−0.00538590	+	0.253487i
$111$	−140.475	+	102.061i	−1.26554	+	0.919470i
$112$	−7.92412	−	50.0309i	−0.0707510	−	0.446705i
$113$	−25.8428	+	4.09310i	−0.228697	+	0.0362221i	−0.269731	−	0.962936i	$-0.586935\pi$
$113$	−25.8428	+	4.09310i	−0.228697	+	0.0362221i	0.0410338	+	0.999158i	$0.486935\pi$
$114$	0.703670	+	0.968519i	0.00617254	+	0.00849578i
$115$	46.1807	+	35.0749i	0.401571	+	0.304999i
$116$	58.5047	+	42.5061i	0.504351	+	0.366432i
$117$	−40.9040	+	80.2786i	−0.349607	+	0.686142i
$118$	−9.54914	+	9.54914i	−0.0809249	+	0.0809249i
$119$	14.8920	−	4.83871i	0.125143	−	0.0406614i
$120$	−38.6454	−	20.7364i	−0.322045	−	0.172803i
$121$	76.0170	−	233.956i	0.628240	−	1.93352i
$122$	14.5532	−	7.41521i	0.119288	−	0.0607804i
$123$	9.84186	−	62.1391i	0.0800151	−	0.505196i
$124$			85.7396i			0.691448i
$125$	−124.456	+	11.6515i	−0.995646	+	0.0932121i
$126$	5.39716			0.0428346
$127$	73.7930	+	11.6877i	0.581047	+	0.0920289i	0.440038	−	0.897979i	$-0.354965\pi$
$127$	73.7930	+	11.6877i	0.581047	+	0.0920289i	0.141010	+	0.990008i	$0.454965\pi$
$128$	−32.0698	−	62.9405i	−0.250545	−	0.491723i
$129$	214.788	+	69.7887i	1.66502	+	0.540998i
$130$	11.3065	−	21.0714i	0.0869731	−	0.162087i
$131$	−25.0313	−	77.0383i	−0.191078	−	0.588078i	−1.00000		0.000162070i	$-0.999948\pi$
$131$	−25.0313	−	77.0383i	−0.191078	−	0.588078i	0.808922	−	0.587916i	$-0.200052\pi$
$132$	201.853	+	201.853i	1.52919	+	1.52919i
$133$	−3.25270	−	1.65733i	−0.0244564	−	0.0124611i
$134$	0.945114	−	1.30084i	0.00705309	−	0.00970775i
$135$	40.4543	−	53.2634i	0.299661	−	0.394544i
$136$	8.63957	−	6.27701i	0.0635262	−	0.0461545i
$137$	24.7567	+	156.308i	0.180706	+	1.14093i	0.896638	+	0.442763i	$0.146002\pi$
$137$	24.7567	+	156.308i	0.180706	+	1.14093i	−0.715932	+	0.698170i	$0.753998\pi$
$138$	−12.6945	+	2.01062i	−0.0919893	+	0.0145697i
$139$	−92.2598	−	126.985i	−0.663739	−	0.913559i	0.335859	−	0.941912i	$-0.390974\pi$
$139$	−92.2598	−	126.985i	−0.663739	−	0.913559i	−0.999598	+	0.0283536i	$0.990974\pi$
$140$	66.1378	+	1.40524i	0.472413	+	0.0100375i
$141$	69.5860	+	50.5572i	0.493518	+	0.358561i
$142$	−8.67905	+	17.0336i	−0.0611201	+	0.119955i
$143$	−222.503	+	222.503i	−1.55597	+	1.55597i
$144$	−78.1989	+	25.4084i	−0.543048	+	0.176447i
$145$	−66.6753	+	63.9009i	−0.459829	+	0.440696i
$146$	−9.27269	+	28.5384i	−0.0635115	+	0.195468i
$147$	127.441	−	64.9342i	0.866943	−	0.441729i
$148$	27.9426	−	176.423i	0.188801	−	1.19205i
$149$			87.4028i			0.586596i	0.956021	+	0.293298i	$0.0947529\pi$
$149$			87.4028i			0.586596i	−0.956021	+	0.293298i	$0.905247\pi$
$150$	17.2216	−	21.7015i	0.114811	−	0.144676i
$151$	172.239			1.14066			0.570328	−	0.821417i	$-0.306816\pi$
$151$	172.239			1.14066			0.570328	+	0.821417i	$0.306816\pi$
$152$	−2.45906	−	0.389478i	−0.0161781	−	0.00256235i
$153$	−11.5390	−	22.6467i	−0.0754186	−	0.148017i
$154$	17.9269	+	5.82480i	0.116408	+	0.0378234i
$155$	−107.759	−	19.4223i	−0.695219	−	0.125305i
$156$	−75.6350	−	232.781i	−0.484840	−	1.49218i
$157$	−53.0884	−	53.0884i	−0.338143	−	0.338143i	0.517525	−	0.855668i	$-0.326853\pi$
$157$	−53.0884	−	53.0884i	−0.338143	−	0.338143i	−0.855668	+	0.517525i	$0.826853\pi$
$158$	−22.3128	−	11.3689i	−0.141220	−	0.0719553i
$159$	106.615	−	146.743i	0.670536	−	0.922914i
$160$	65.0235	−	19.6105i	0.406397	−	0.122565i
$161$	31.7078	−	23.0371i	0.196943	−	0.143088i
$162$	4.56762	+	28.8388i	0.0281952	+	0.178017i
$163$	1.91719	−	0.303653i	0.0117619	−	0.00186290i	−0.150551	−	0.988602i	$-0.548105\pi$
$163$	1.91719	−	0.303653i	0.0117619	−	0.00186290i	0.162313	+	0.986739i	$0.448105\pi$
$164$	38.0414	+	52.3595i	0.231960	+	0.319265i
$165$	−299.417	+	207.967i	−1.81465	+	1.26041i
$166$	5.06973	+	3.68337i	0.0305405	+	0.0221890i
$167$	−5.17831	+	10.1630i	−0.0310078	+	0.0608563i	−0.905991	−	0.423298i	$-0.860872\pi$
$167$	−5.17831	+	10.1630i	−0.0310078	+	0.0608563i	0.874983	+	0.484154i	$0.160872\pi$
$168$	−20.9594	+	20.9594i	−0.124758	+	0.124758i
$169$	95.8665	−	31.1489i	0.567257	−	0.184313i
$170$	2.93421	+	6.07436i	0.0172601	+	0.0357315i
$171$	−1.83114	+	5.63567i	−0.0107084	+	0.0329571i
$172$	−207.003	+	105.473i	−1.20351	+	0.613217i
$173$	31.2522	−	197.319i	0.180649	−	1.14057i	−0.716089	−	0.698009i	$-0.754070\pi$
$173$	31.2522	−	197.319i	0.180649	−	1.14057i	0.896738	−	0.442562i	$-0.145930\pi$
$174$		−	20.4685i		−	0.117635i
$175$	−16.7481	+	82.8048i	−0.0957034	+	0.473170i
$176$	−287.162			−1.63160
$177$	−174.348	−	27.6140i	−0.985016	−	0.156011i
$178$	11.8599	+	23.2764i	0.0666288	+	0.130766i
$179$	−51.8588	−	16.8499i	−0.289714	−	0.0941338i	0.160555	−	0.987027i	$-0.448672\pi$
$179$	−51.8588	−	16.8499i	−0.289714	−	0.0941338i	−0.450269	+	0.892893i	$0.648672\pi$
$180$	−14.5412	−	106.391i	−0.0807846	−	0.591061i
$181$	42.0315	+	129.360i	0.232218	+	0.714694i	0.997478	+	0.0709726i	$0.0226103\pi$
$181$	42.0315	+	129.360i	0.232218	+	0.714694i	−0.765260	+	0.643721i	$0.777390\pi$
$182$	−11.4281	−	11.4281i	−0.0627917	−	0.0627917i
$183$	190.228	+	96.9260i	1.03950	+	0.529650i
$184$	15.7114	−	21.6249i	0.0853881	−	0.117527i
$185$	215.401	+	75.0831i	1.16433	+	0.405855i
$186$	19.6332	−	14.2644i	0.105555	−	0.0766903i
$187$	−13.8864	−	87.6750i	−0.0742586	−	0.468850i
$188$	−87.3931	+	13.8417i	−0.464857	+	0.0736261i
$189$	−26.5703	−	36.5708i	−0.140583	−	0.193496i
$190$	0.517668	−	1.48510i	0.00272457	−	0.00781634i
$191$	73.9512	+	53.7287i	0.387179	+	0.281302i	0.764299	−	0.644863i	$-0.223085\pi$
$191$	73.9512	+	53.7287i	0.387179	+	0.281302i	−0.377119	+	0.926165i	$0.623085\pi$
$192$	96.7679	−	189.918i	0.503999	−	0.989155i
$193$	62.2572	−	62.2572i	0.322576	−	0.322576i	−0.527178	−	0.849755i	$-0.676750\pi$
$193$	62.2572	−	62.2572i	0.322576	−	0.322576i	0.849755	+	0.527178i	$0.176750\pi$
$194$	−26.0173	+	8.45354i	−0.134110	+	0.0435749i
$195$	309.696	−	42.3284i	1.58818	−	0.217069i
$196$	−45.4676	+	139.935i	−0.231978	+	0.713954i
$197$	232.265	−	118.345i	1.17901	−	0.600736i	0.249084	−	0.968482i	$-0.419870\pi$
$197$	232.265	−	118.345i	1.17901	−	0.600736i	0.929926	+	0.367746i	$0.119870\pi$
$198$	4.78638	−	30.2200i	0.0241736	−	0.152626i
$199$			198.360i			0.996782i	0.866952	+	0.498391i	$0.166076\pi$
$199$			198.360i			0.996782i	−0.866952	+	0.498391i	$0.833924\pi$
$200$	6.58796	+	57.2389i	0.0329398	+	0.286195i
$201$	21.0176			0.104565
$202$	4.15178	+	0.657578i	0.0205534	+	0.00325534i
$203$	28.3364	+	55.6134i	0.139588	+	0.273958i
$204$	65.6676	+	21.3367i	0.321900	+	0.104592i
$205$	−74.4236	+	35.9502i	−0.363042	+	0.175367i
$206$	7.79582	+	23.9931i	0.0378438	+	0.116471i
$207$	−44.9853	−	44.9853i	−0.217320	−	0.217320i
$208$	219.381	+	111.780i	1.05472	+	0.537404i
$209$	−12.1644	+	16.7429i	−0.0582028	+	0.0801093i
$210$	−10.6815	−	15.3785i	−0.0508642	−	0.0732309i
$211$	−32.1898	+	23.3872i	−0.152558	+	0.110840i	−0.661446	−	0.749993i	$-0.730057\pi$
$211$	−32.1898	+	23.3872i	−0.152558	+	0.110840i	0.508888	+	0.860833i	$0.330057\pi$
$212$	29.1895	+	184.295i	0.137686	+	0.869316i
$213$	−246.810	+	39.0909i	−1.15873	+	0.183525i
$214$	−29.2482	−	40.2566i	−0.136674	−	0.188115i
$215$	−85.6689	−	284.057i	−0.398460	−	1.32120i
$216$	−24.9415	−	18.1210i	−0.115470	−	0.0838937i
$217$	−33.5965	+	65.9368i	−0.154822	+	0.303856i
$218$	6.85717	−	6.85717i	0.0314549	−	0.0314549i
$219$	−373.033	+	121.206i	−1.70334	+	0.553450i
$220$	66.5215	−	369.075i	0.302370	−	1.67761i
$221$	−23.5195	+	72.3857i	−0.106423	+	0.327537i
$222$	−45.0473	+	22.9527i	−0.202916	+	0.103391i
$223$	−10.9708	+	69.2671i	−0.0491966	+	0.310615i	0.950803	+	0.309796i	$0.100261\pi$
$223$	−10.9708	+	69.2671i	−0.0491966	+	0.310615i	−1.00000		0.000819017i	$0.999739\pi$
$224$		−	45.9014i		−	0.204917i
$225$	137.008	+	5.82470i	0.608924	+	0.0258876i
$226$	−7.61844			−0.0337099
$227$	−46.0077	−	7.28690i	−0.202677	−	0.0321009i	0.0542703	−	0.998526i	$-0.482717\pi$
$227$	−46.0077	−	7.28690i	−0.202677	−	0.0321009i	−0.256947	+	0.966425i	$0.582717\pi$
$228$	−7.30815	−	14.3430i	−0.0320533	−	0.0629081i
$229$	−17.5687	−	5.70843i	−0.0767194	−	0.0249276i	0.270406	−	0.962746i	$-0.412842\pi$
$229$	−17.5687	−	5.70843i	−0.0767194	−	0.0249276i	−0.347125	+	0.937819i	$0.612842\pi$
$230$	11.6832	+	12.1905i	0.0507967	+	0.0530021i
$231$	76.1374	+	234.327i	0.329599	+	1.01440i
$232$	30.1003	+	30.1003i	0.129743	+	0.129743i
$233$	364.992	+	185.972i	1.56649	+	0.798165i	0.999670	−	0.0256786i	$-0.00817466\pi$
$233$	364.992	+	185.972i	1.56649	+	0.798165i	0.566817	+	0.823844i	$0.308175\pi$
$234$	−15.4200	+	21.2238i	−0.0658973	+	0.0906999i
$235$	2.40035	−	112.973i	0.0102143	−	0.480734i
$236$	146.909	−	106.735i	0.622494	−	0.452268i
$237$	−51.2063	−	323.304i	−0.216060	−	1.36415i
$238$	4.50311	−	0.713223i	0.0189206	−	0.00299674i
$239$	−241.175	−	331.949i	−1.00910	−	1.38891i	−0.919571	−	0.392924i	$-0.871463\pi$
$239$	−241.175	−	331.949i	−1.00910	−	1.38891i	−0.0895301	−	0.995984i	$-0.528537\pi$
$240$	227.161	+	172.532i	0.946503	+	0.718882i
$241$	−284.923	−	207.009i	−1.18225	−	0.858958i	−0.189830	−	0.981817i	$-0.560794\pi$
$241$	−284.923	−	207.009i	−1.18225	−	0.858958i	−0.992424	+	0.122859i	$0.960794\pi$
$242$	32.5178	−	63.8198i	0.134371	−	0.263718i
$243$	−184.743	+	184.743i	−0.760259	+	0.760259i
$244$	−208.878	+	67.8686i	−0.856058	+	0.278150i
$245$	−165.573	−	88.8434i	−0.675808	−	0.362626i
$246$	5.66074	−	17.4220i	0.0230111	−	0.0708210i
$247$	15.8104	−	8.05580i	0.0640097	−	0.0326146i
$248$	−7.89526	+	49.8487i	−0.0318357	+	0.201003i
$249$			81.9114i			0.328961i
$250$	−36.3223	−	2.31803i	−0.145289	−	0.00927214i
$251$	99.8650			0.397869			0.198934	−	0.980013i	$-0.436252\pi$
$251$	99.8650			0.397869			0.198934	+	0.980013i	$0.436252\pi$
$252$	−71.6796	−	11.3529i	−0.284443	−	0.0450513i
$253$	−100.871	−	197.970i	−0.398698	−	0.782489i
$254$	20.6894	+	6.72239i	0.0814543	+	0.0264661i
$255$	−41.6917	+	77.6988i	−0.163497	+	0.304701i
$256$	62.8692	+	193.491i	0.245583	+	0.755826i
$257$	−138.476	−	138.476i	−0.538818	−	0.538818i	0.384363	−	0.923182i	$-0.374421\pi$
$257$	−138.476	−	138.476i	−0.538818	−	0.538818i	−0.923182	+	0.384363i	$0.874421\pi$
$258$	58.5908	+	29.8535i	0.227096	+	0.115711i
$259$	90.6189	−	124.726i	0.349880	−	0.481568i
$260$	−194.485	+	256.065i	−0.748020	+	0.984866i
$261$	81.9657	−	59.5516i	0.314045	−	0.228167i
$262$	−3.68959	−	23.2952i	−0.0140824	−	0.0889129i
$263$	208.637	−	33.0448i	0.793296	−	0.125646i	0.253382	−	0.967366i	$-0.418457\pi$
$263$	208.637	−	33.0448i	0.793296	−	0.125646i	0.539914	+	0.841720i	$0.318457\pi$
$264$	98.7692	+	135.944i	0.374126	+	0.514940i
$265$	−238.237	−	5.06187i	−0.899008	−	0.0191014i
$266$	−0.859937	−	0.624781i	−0.00323284	−	0.00234880i
$267$	−155.024	+	304.252i	−0.580615	+	1.13952i
$268$	−15.2884	+	15.2884i	−0.0570461	+	0.0570461i
$269$	326.227	−	105.998i	1.21274	−	0.394043i	0.368307	−	0.929704i	$-0.379938\pi$
$269$	326.227	−	105.998i	1.21274	−	0.394043i	0.844433	+	0.535661i	$0.179938\pi$
$270$	14.0601	−	13.4751i	0.0520746	−	0.0499077i
$271$	−71.5216	+	220.121i	−0.263918	+	0.812255i	0.728023	+	0.685552i	$0.240439\pi$
$271$	−71.5216	+	220.121i	−0.263918	+	0.812255i	−0.991941	+	0.126702i	$0.959561\pi$
$272$	−61.8875	+	31.5333i	−0.227528	+	0.115931i
$273$	33.0475	−	208.654i	0.121053	−	0.764299i
$274$			46.0794i			0.168173i
$275$	448.791	+	167.210i	1.63197	+	0.608038i
$276$	172.825			0.626178
$277$	395.109	+	62.5791i	1.42639	+	0.225917i	0.821416	−	0.570330i	$-0.193185\pi$
$277$	395.109	+	62.5791i	1.42639	+	0.225917i	0.604971	+	0.796247i	$0.293185\pi$
$278$	−20.7485	−	40.7212i	−0.0746348	−	0.146479i
$279$	114.243	+	37.1198i	0.409473	+	0.133046i
$280$	38.3229	+	6.90726i	0.136868	+	0.0246688i
$281$	−41.2543	−	126.968i	−0.146813	−	0.451843i	0.850427	−	0.526093i	$-0.176344\pi$
$281$	−41.2543	−	126.968i	−0.146813	−	0.451843i	−0.997240	+	0.0742504i	$0.976344\pi$
$282$	17.7090	+	17.7090i	0.0627980	+	0.0627980i
$283$	−222.492	−	113.365i	−0.786190	−	0.400584i	0.0143241	−	0.999897i	$-0.495440\pi$
$283$	−222.492	−	113.365i	−0.786190	−	0.400584i	−0.800515	+	0.599313i	$0.795440\pi$
$284$	151.096	−	207.966i	0.532030	−	0.732276i
$285$	19.6821	−	5.93592i	0.0690599	−	0.0208278i
$286$	−74.1234	+	53.8538i	−0.259173	+	0.188300i
$287$	8.73848	+	55.1726i	0.0304477	+	0.192239i
$288$	−73.5905	+	11.6556i	−0.255523	+	0.0404708i
$289$	157.250	+	216.436i	0.544116	+	0.748912i
$290$	−22.0854	+	15.3399i	−0.0761566	+	0.0528963i
$291$	−289.288	−	210.180i	−0.994118	−	0.722269i
$292$	183.181	−	359.513i	0.627332	−	1.23121i
$293$	279.769	−	279.769i	0.954844	−	0.954844i	−0.0441800	−	0.999024i	$-0.514068\pi$
$293$	279.769	−	279.769i	0.954844	−	0.954844i	0.999024	+	0.0441800i	$0.0140675\pi$
$294$	39.6077	−	12.8693i	0.134720	−	0.0437732i
$295$	100.868	+	208.815i	0.341925	+	0.707849i
$296$	32.4915	−	99.9986i	0.109769	−	0.337833i
$297$	−228.332	+	116.341i	−0.768795	+	0.391721i
$298$	−3.98111	+	25.1357i	−0.0133594	+	0.0843481i
$299$			190.506i			0.637143i
$300$	−274.368	+	251.991i	−0.914561	+	0.839970i
$301$	−200.522			−0.666185
$302$	49.5333	+	7.84531i	0.164018	+	0.0259779i
$303$	24.9447	+	48.9568i	0.0823258	+	0.161574i
$304$	15.4008	+	5.00403i	0.0506606	+	0.0164606i
$305$	−37.9820	−	277.895i	−0.124531	−	0.911133i
$306$	−2.28692	−	7.03842i	−0.00747360	−	0.0230014i
$307$	292.963	+	292.963i	0.954277	+	0.954277i	0.998999	−	0.0447226i	$-0.0142404\pi$
$307$	292.963	+	292.963i	0.954277	+	0.954277i	−0.0447226	+	0.998999i	$0.514240\pi$
$308$	−225.834	−	115.068i	−0.733228	−	0.373598i
$309$	−193.828	+	266.781i	−0.627274	+	0.863368i
$310$	−30.1052	−	10.4939i	−0.0971134	−	0.0338511i
$311$	−56.9351	+	41.3658i	−0.183071	+	0.133009i	−0.675546	−	0.737318i	$-0.736092\pi$
$311$	−56.9351	+	41.3658i	−0.183071	+	0.133009i	0.492475	+	0.870326i	$0.336092\pi$
$312$	−22.5385	−	142.303i	−0.0722389	−	0.456098i
$313$	−551.569	+	87.3599i	−1.76220	+	0.279105i	−0.951788	−	0.306755i	$-0.900757\pi$
$313$	−551.569	+	87.3599i	−1.76220	+	0.279105i	−0.810412	+	0.585860i	$0.800757\pi$
$314$	−12.8493	−	17.6855i	−0.0409213	−	0.0563234i
$315$	30.5059	−	87.5164i	0.0968440	−	0.277830i
$316$	272.421	+	197.926i	0.862093	+	0.626347i
$317$	−283.718	+	556.827i	−0.895008	+	1.75655i	−0.297427	+	0.954744i	$0.596129\pi$
$317$	−283.718	+	556.827i	−0.895008	+	1.75655i	−0.597581	+	0.801808i	$0.703871\pi$
$318$	37.3449	−	37.3449i	0.117437	−	0.117437i
$319$	336.522	−	109.343i	1.05493	−	0.342767i
$320$	−277.442	+	37.9200i	−0.867006	+	0.118500i
$321$	200.992	−	618.591i	0.626144	−	1.92707i
$322$	10.1680	−	5.18086i	0.0315777	−	0.0160896i
$323$	−0.783067	+	4.94409i	−0.00242436	+	0.0153068i
$324$		−	392.615i		−	1.21178i
$325$	−277.771	−	302.437i	−0.854679	−	0.930577i
$326$	0.565186			0.00173370
$327$	125.198	+	19.8294i	0.382868	+	0.0606403i
$328$	17.2957	+	33.9447i	0.0527307	+	0.103490i
$329$	−72.6321	−	23.5996i	−0.220766	−	0.0717314i
$330$	−95.5805	+	46.1700i	−0.289638	+	0.139909i
$331$	−98.3145	−	302.581i	−0.297023	−	0.914142i	−0.982535	−	0.186080i	$-0.940421\pi$
$331$	−98.3145	−	302.581i	−0.297023	−	0.914142i	0.685512	−	0.728062i	$-0.259579\pi$
$332$	−59.5830	−	59.5830i	−0.179467	−	0.179467i
$333$	−222.975	−	113.612i	−0.669596	−	0.341176i
$334$	−1.95212	+	2.68686i	−0.00584466	+	0.00804448i
$335$	−15.7514	−	22.6779i	−0.0470192	−	0.0676951i
$336$	155.969	−	113.318i	0.464195	−	0.337257i
$337$	52.4267	+	331.009i	0.155569	+	0.982223i	0.934719	+	0.355387i	$0.115651\pi$
$337$	52.4267	+	331.009i	0.155569	+	0.982223i	−0.779151	+	0.626837i	$0.784349\pi$
$338$	28.9885	−	4.59133i	0.0857649	−	0.0135838i
$339$	−58.5331	−	80.5640i	−0.172664	−	0.237652i
$340$	−26.1918	−	86.8456i	−0.0770347	−	0.255428i
$341$	339.401	+	246.590i	0.995312	+	0.723136i
$342$	−0.783306	+	1.53733i	−0.00229037	+	0.00449510i
$343$	−206.884	+	206.884i	−0.603161	+	0.603161i
$344$	−130.063	+	42.2601i	−0.378091	+	0.122849i
$345$	−39.1494	+	217.209i	−0.113477	+	0.629592i
$346$	17.9753	−	55.3224i	0.0519518	−	0.159891i
$347$	368.200	−	187.607i	1.06110	−	0.540655i	0.165815	−	0.986157i	$-0.446975\pi$
$347$	368.200	−	187.607i	1.06110	−	0.540655i	0.895281	+	0.445501i	$0.146975\pi$
$348$	−43.0555	+	271.842i	−0.123723	+	0.781154i
$349$		−	234.141i		−	0.670891i	−0.942060	−	0.335445i	$-0.891113\pi$
$349$		−	234.141i		−	0.670891i	0.942060	−	0.335445i	$-0.108887\pi$
$350$	−8.58817	+	23.0505i	−0.0245376	+	0.0658587i
$351$	219.723			0.625993
$352$	−257.013	−	40.7069i	−0.730150	−	0.115644i
$353$	93.3076	+	183.126i	0.264327	+	0.518772i	0.984579	−	0.174941i	$-0.0559736\pi$
$353$	93.3076	+	183.126i	0.264327	+	0.518772i	−0.720251	+	0.693713i	$0.755974\pi$
$354$	−48.8820	−	15.8827i	−0.138085	−	0.0448664i
$355$	227.148	+	237.010i	0.639854	+	0.667635i
$356$	−108.550	−	334.081i	−0.304914	−	0.938430i
$357$	42.1401	+	42.1401i	0.118039	+	0.118039i
$358$	−14.1463	−	7.20790i	−0.0395148	−	0.0201338i
$359$	−203.218	+	279.706i	−0.566068	+	0.779126i	−0.992082	−	0.125591i	$-0.959917\pi$
$359$	−203.218	+	279.706i	−0.566068	+	0.779126i	0.426014	+	0.904717i	$0.359917\pi$
$360$	1.34271	−	63.1944i	0.00372974	−	0.175540i
$361$	−291.111	+	211.505i	−0.806402	+	0.585885i
$362$	6.19542	+	39.1163i	0.0171144	+	0.108056i
$363$	924.723	−	146.462i	2.54745	−	0.403476i
$364$	127.737	+	175.815i	0.350927	+	0.483009i
$365$	410.346	+	311.664i	1.12424	+	0.853873i
$366$	50.2918	+	36.5391i	0.137409	+	0.0998337i
$367$	241.897	−	474.749i	0.659119	−	1.29359i	−0.283258	−	0.959044i	$-0.591415\pi$
$367$	241.897	−	474.749i	0.659119	−	1.29359i	0.942378	−	0.334551i	$-0.108585\pi$
$368$	−122.933	+	122.933i	−0.334058	+	0.334058i
$369$	86.2354	−	28.0196i	0.233700	−	0.0759338i
$370$	58.5262	+	31.4041i	0.158179	+	0.0848759i
$371$	−49.7670	+	153.167i	−0.134143	+	0.412849i
$372$	−290.754	+	148.146i	−0.781596	+	0.398243i
$373$	−9.51134	+	60.0522i	−0.0254996	+	0.160998i	−0.997152	−	0.0754151i	$-0.975972\pi$
$373$	−9.51134	+	60.0522i	−0.0254996	+	0.160998i	0.971653	+	0.236413i	$0.0759718\pi$
$374$		−	25.8465i		−	0.0691083i
$375$	−254.555	−	401.913i	−0.678812	−	1.07177i
$376$	−52.0847			−0.138523
$377$	−299.652	−	47.4603i	−0.794834	−	0.125889i
$378$	−5.97544	−	11.7275i	−0.0158080	−	0.0310250i
$379$	185.112	+	60.1464i	0.488421	+	0.158698i	0.542866	−	0.839819i	$-0.317339\pi$
$379$	185.112	+	60.1464i	0.488421	+	0.158698i	−0.0544453	+	0.998517i	$0.517339\pi$
$380$	−9.99905	+	18.6347i	−0.0263133	+	0.0490387i
$381$	87.8701	+	270.436i	0.230630	+	0.709807i
$382$	18.8200	+	18.8200i	0.0492669	+	0.0492669i
$383$	−446.637	−	227.573i	−1.16615	−	0.594186i	−0.239794	−	0.970824i	$-0.577080\pi$
$383$	−446.637	−	227.573i	−1.16615	−	0.594186i	−0.926361	+	0.376638i	$0.877080\pi$
$384$	158.027	−	217.506i	0.411529	−	0.566421i
$385$	195.777	−	257.766i	0.508512	−	0.669522i
$386$	20.7400	−	15.0685i	0.0537305	−	0.0390375i
$387$	50.9178	+	321.482i	0.131571	+	0.830704i
$388$	363.317	−	57.5438i	0.936385	−	0.148309i
$389$	96.3944	+	132.676i	0.247801	+	0.341068i	0.914739	−	0.404044i	$-0.132396\pi$
$389$	96.3944	+	132.676i	0.247801	+	0.341068i	−0.666939	+	0.745112i	$0.732396\pi$
$390$	90.9918	+	1.93332i	0.233312	+	0.00495724i
$391$	−43.4781	−	31.5887i	−0.111197	−	0.0807894i
$392$	−39.3205	+	77.1709i	−0.100307	+	0.196865i
$393$	217.996	−	217.996i	0.554697	−	0.554697i
$394$	72.1864	−	23.4548i	0.183214	−	0.0595299i
$395$	−310.467	+	297.548i	−0.785992	+	0.753287i
$396$	−127.136	+	391.283i	−0.321049	+	0.988089i
$397$	306.180	−	156.006i	0.771234	−	0.392963i	−0.0236537	−	0.999720i	$-0.507530\pi$
$397$	306.180	−	156.006i	0.771234	−	0.392963i	0.794887	+	0.606757i	$0.207530\pi$
$398$	−9.03507	+	57.0452i	−0.0227012	+	0.143330i
$399$		−	13.8940i		−	0.0348220i
$400$	15.9174	−	374.408i	0.0397936	−	0.936019i
$401$	−355.216			−0.885825			−0.442912	−	0.896565i	$-0.646055\pi$
$401$	−355.216			−0.885825			−0.442912	+	0.896565i	$0.646055\pi$
$402$	6.04434	+	0.957329i	0.0150357	+	0.00238142i
$403$	−163.303	−	320.499i	−0.405217	−	0.795283i
$404$	−53.7565	−	17.4666i	−0.133061	−	0.0432341i
$405$	493.445	+	88.9377i	1.21838	+	0.219599i
$406$	5.61600	+	17.2843i	0.0138325	+	0.0425721i
$407$	−618.008	−	618.008i	−1.51845	−	1.51845i
$408$	36.2142	+	18.4520i	0.0887602	+	0.0452256i
$409$	−221.160	+	304.400i	−0.540733	+	0.744255i	−0.988718	−	0.149786i	$-0.952142\pi$
$409$	−221.160	+	304.400i	−0.540733	+	0.744255i	0.447986	+	0.894041i	$0.352142\pi$
$410$	−23.0406	+	6.94882i	−0.0561966	+	0.0169484i
$411$	−487.283	+	354.032i	−1.18560	+	0.861392i
$412$	−53.0667	−	335.050i	−0.128803	−	0.813228i
$413$	154.801	−	24.5181i	0.374822	−	0.0593659i
$414$	−10.8880	−	14.9861i	−0.0262996	−	0.0361983i
$415$	88.3819	−	61.3877i	0.212969	−	0.147922i
$416$	180.502	+	131.143i	0.433900	+	0.315247i
$417$	271.209	−	532.277i	0.650381	−	1.27644i
$418$	−4.26091	+	4.26091i	−0.0101936	+	0.0101936i
$419$	−581.123	+	188.818i	−1.38693	+	0.450640i	−0.904941	−	0.425538i	$-0.860085\pi$
$419$	−581.123	+	188.818i	−1.38693	+	0.450640i	−0.481987	+	0.876178i	$0.660085\pi$
$420$	109.512	+	226.710i	0.260743	+	0.539785i
$421$	−63.7783	+	196.289i	−0.151492	+	0.466245i	−0.997789	−	0.0664671i	$-0.978827\pi$
$421$	−63.7783	+	196.289i	−0.151492	+	0.466245i	0.846296	+	0.532712i	$0.178827\pi$
$422$	−10.3226	+	5.25960i	−0.0244610	+	0.0124635i
$423$	−19.3924	+	122.439i	−0.0458449	+	0.289453i
$424$			109.836i			0.259048i
$425$	115.082	−	13.2455i	0.270781	−	0.0311658i
$426$	−72.7593			−0.170797
$427$	−187.229	−	29.6541i	−0.438474	−	0.0694475i
$428$	303.764	+	596.171i	0.709730	+	1.39292i
$429$	−1138.99	−	370.081i	−2.65500	−	0.862661i
$430$	−11.6986	−	85.5927i	−0.0272060	−	0.199053i
$431$	−75.3165	−	231.800i	−0.174748	−	0.537820i	0.824874	−	0.565317i	$-0.191246\pi$
$431$	−75.3165	−	231.800i	−0.174748	−	0.537820i	−0.999622	+	0.0274974i	$0.991246\pi$
$432$	141.787	+	141.787i	0.328211	+	0.328211i
$433$	−347.221	−	176.918i	−0.801896	−	0.408586i	0.00447992	−	0.999990i	$-0.498574\pi$
$433$	−347.221	−	176.918i	−0.801896	−	0.408586i	−0.806376	+	0.591404i	$0.798574\pi$
$434$	−12.6652	+	17.4321i	−0.0291825	+	0.0401662i
$435$	−331.902	−	115.692i	−0.762993	−	0.265959i
$436$	−105.494	+	76.6458i	−0.241959	+	0.175793i
$437$	1.96002	+	12.3751i	0.00448517	+	0.0283183i
$438$	−112.799	+	17.8657i	−0.257533	+	0.0407892i
$439$	213.132	+	293.351i	0.485494	+	0.668225i	0.979549	−	0.201206i	$-0.0644860\pi$
$439$	213.132	+	293.351i	0.485494	+	0.668225i	−0.494055	+	0.869430i	$0.664486\pi$
$440$	72.6614	−	208.454i	0.165140	−	0.473758i
$441$	166.770	+	121.166i	0.378164	+	0.274752i
$442$	−10.0610	+	19.7457i	−0.0227623	+	0.0446736i
$443$	464.820	−	464.820i	1.04926	−	1.04926i	0.0505328	−	0.998722i	$-0.483908\pi$
$443$	464.820	−	464.820i	1.04926	−	1.04926i	0.998722	−	0.0505328i	$-0.0160920\pi$
$444$	646.553	−	210.078i	1.45620	−	0.473148i
$445$	444.468	−	60.7487i	0.998804	−	0.136514i
$446$	−6.31009	+	19.4205i	−0.0141482	+	0.0435436i
$447$	−296.394	+	151.020i	−0.663074	+	0.337853i
$448$	−29.6057	+	186.923i	−0.0660842	+	0.417239i
$449$		−	516.794i		−	1.15099i	−0.817806	−	0.575495i	$-0.804810\pi$
$449$		−	516.794i		−	1.15099i	0.817806	−	0.575495i	$-0.195190\pi$
$450$	39.1361	+	7.91567i	0.0869691	+	0.0175904i
$451$	316.674			0.702160
$452$	101.180	+	16.0254i	0.223850	+	0.0354544i
$453$	297.606	+	584.085i	0.656967	+	1.28937i
$454$	−12.8992	−	4.19121i	−0.0284123	−	0.00923173i
$455$	−249.903	+	120.715i	−0.549238	+	0.265309i
$456$	−2.92817	−	9.01197i	−0.00642142	−	0.0197631i
$457$	276.799	+	276.799i	0.605687	+	0.605687i	0.941816	−	0.336129i	$-0.109118\pi$
$457$	276.799	+	276.799i	0.605687	+	0.605687i	−0.336129	+	0.941816i	$0.609118\pi$
$458$	−4.79249	−	2.44190i	−0.0104640	−	0.00533165i
$459$	−36.4334	+	50.1463i	−0.0793756	+	0.109251i
$460$	−129.522	−	186.477i	−0.281570	−	0.405386i
$461$	692.843	−	503.380i	1.50291	−	1.09193i	0.533711	−	0.845667i	$-0.320797\pi$
$461$	692.843	−	503.380i	1.50291	−	1.09193i	0.969203	−	0.246264i	$-0.0792029\pi$
$462$	11.2226	+	70.8568i	0.0242914	+	0.153370i
$463$	−138.978	+	22.0119i	−0.300168	+	0.0475419i	−0.304702	−	0.952448i	$-0.598557\pi$
$463$	−138.978	+	22.0119i	−0.300168	+	0.0475419i	0.00453395	+	0.999990i	$0.498557\pi$
$464$	−162.739	−	223.991i	−0.350731	−	0.482740i
$465$	−120.330	−	398.983i	−0.258773	−	0.858028i
$466$	96.4952	+	70.1078i	0.207071	+	0.150446i
$467$	−164.433	+	322.718i	−0.352105	+	0.691045i	−0.997336	−	0.0729424i	$-0.976761\pi$
$467$	−164.433	+	322.718i	−0.352105	+	0.691045i	0.645231	+	0.763987i	$0.276761\pi$
$468$	249.436	−	249.436i	0.532984	−	0.532984i
$469$	−17.7479	+	5.76665i	−0.0378421	+	0.0122956i
$470$	5.83609	−	32.3798i	0.0124172	−	0.0688933i
$471$	88.2999	−	271.759i	0.187473	−	0.576983i
$472$	95.2408	−	48.5276i	0.201781	−	0.102813i
$473$	−177.829	+	1122.77i	−0.375960	+	2.37372i
$474$		−	95.3096i		−	0.201075i
$475$	−21.1554	−	16.7882i	−0.0445376	−	0.0353436i
$476$	−61.3060			−0.128794
$477$	258.199	+	40.8948i	0.541298	+	0.0857333i
$478$	−54.2384	−	106.449i	−0.113469	−	0.222696i
$479$	326.819	+	106.190i	0.682293	+	0.221691i	0.629599	−	0.776920i	$-0.283219\pi$
$479$	326.819	+	106.190i	0.682293	+	0.221691i	0.0526943	+	0.998611i	$0.483219\pi$
$480$	178.854	+	186.619i	0.372612	+	0.388789i
$481$	231.570	+	712.698i	0.481434	+	1.48170i
$482$	−72.5106	−	72.5106i	−0.150437	−	0.150437i
$483$	132.909	+	67.7203i	0.275173	+	0.140208i
$484$	−566.113	+	779.188i	−1.16966	+	1.60989i
$485$	−9.97893	+	469.658i	−0.0205751	+	0.968368i
$486$	−61.5441	+	44.7144i	−0.126634	+	0.0920049i
$487$	−109.417	−	690.831i	−0.224675	−	1.41854i	−0.799696	−	0.600405i	$-0.795006\pi$
$487$	−109.417	−	690.831i	−0.224675	−	1.41854i	0.575021	−	0.818139i	$-0.304994\pi$
$488$	−127.691	+	20.2242i	−0.261661	+	0.0414431i
$489$	4.34237	+	5.97676i	0.00888011	+	0.0122224i
$490$	−43.5695	−	33.0917i	−0.0889174	−	0.0675340i
$491$	−281.430	−	204.471i	−0.573177	−	0.416438i	0.263081	−	0.964774i	$-0.415261\pi$
$491$	−281.430	−	204.471i	−0.573177	−	0.416438i	−0.836258	+	0.548336i	$0.815261\pi$
$492$	−111.827	+	219.473i	−0.227291	+	0.446084i
$493$	60.5184	−	60.5184i	0.122755	−	0.122755i
$494$	4.91376	−	1.59658i	0.00994689	−	0.00323194i
$495$	−462.971	−	248.422i	−0.935296	−	0.501863i
$496$	101.439	−	312.197i	0.204514	−	0.629429i
$497$	197.689	−	100.727i	0.397764	−	0.202671i
$498$	−3.73098	+	23.5565i	−0.00749192	+	0.0473021i
$499$		−	90.5909i		−	0.181545i	−0.995872	−	0.0907724i	$-0.971066\pi$
$499$		−	90.5909i		−	0.181545i	0.995872	−	0.0907724i	$-0.0289336\pi$
$500$	477.520	+	107.190i	0.955040	+	0.214380i
$501$	−43.4114			−0.0866496
$502$	28.7197	+	4.54875i	0.0572105	+	0.00906125i
$503$	−360.023	−	706.585i	−0.715751	−	1.40474i	−0.906117	−	0.423028i	$-0.860967\pi$
$503$	−360.023	−	706.585i	−0.715751	−	1.40474i	0.190365	−	0.981713i	$-0.439033\pi$
$504$	−40.6289	−	13.2011i	−0.0806129	−	0.0261927i
$505$	34.1295	−	63.6055i	0.0675832	−	0.125951i
$506$	−19.9916	−	61.5277i	−0.0395090	−	0.121596i
$507$	271.274	+	271.274i	0.535058	+	0.535058i
$508$	−260.635	−	132.800i	−0.513061	−	0.261417i
$509$	361.411	−	497.439i	0.710041	−	0.977287i	−0.289756	−	0.957101i	$-0.593574\pi$
$509$	361.411	−	497.439i	0.710041	−	0.977287i	0.999796	−	0.0201863i	$-0.00642593\pi$
$510$	−15.5290	+	20.4460i	−0.0304490	+	0.0400901i
$511$	281.745	−	204.700i	0.551360	−	0.400587i
$512$	53.4689	+	337.589i	0.104431	+	0.659354i
$513$	14.2730	−	2.26063i	0.0278227	−	0.00440668i
$514$	−33.5162	−	46.1311i	−0.0652067	−	0.0897493i
$515$	433.117	+	9.20254i	0.841004	+	0.0178690i
$516$	−715.347	−	519.730i	−1.38633	−	1.00723i
$517$	−196.552	+	385.756i	−0.380179	+	0.746143i
$518$	31.7418	−	31.7418i	0.0612776	−	0.0612776i
$519$	723.133	−	234.960i	1.39332	−	0.452717i
$520$	−136.653	+	130.966i	−0.262793	+	0.251859i
$521$	−204.980	+	630.864i	−0.393436	+	1.21087i	0.536737	+	0.843749i	$0.319657\pi$
$521$	−204.980	+	630.864i	−0.393436	+	1.21087i	−0.930173	+	0.367121i	$0.880343\pi$
$522$	26.2846	−	13.3927i	0.0503537	−	0.0256565i
$523$	37.7042	−	238.055i	0.0720921	−	0.455172i	−0.925064	−	0.379811i	$-0.875989\pi$
$523$	37.7042	−	238.055i	0.0720921	−	0.455172i	0.997156	−	0.0753609i	$-0.0240109\pi$
$524$			317.144i			0.605237i
$525$	−309.740	+	86.2806i	−0.589981	+	0.164344i
$526$	61.5059			0.116931
$527$	100.224	+	15.8739i	0.190178	+	0.0301212i
$528$	−496.178	−	973.804i	−0.939731	−	1.84433i
$529$	375.176	+	121.902i	0.709218	+	0.230439i
$530$	−68.2828	−	12.3072i	−0.128835	−	0.0232211i
$531$	−78.6164	−	241.957i	−0.148054	−	0.455662i
$532$	10.1066	+	10.1066i	0.0189973	+	0.0189973i
$533$	−241.926	−	123.268i	−0.453896	−	0.231271i
$534$	−58.4410	+	80.4371i	−0.109440	+	0.150631i
$535$	−818.088	+	246.728i	−1.52914	+	0.461173i
$536$	−10.2964	+	7.48079i	−0.0192097	+	0.0139567i
$537$	−32.4647	−	204.974i	−0.0604557	−	0.381703i
$538$	98.6460	−	15.6240i	0.183357	−	0.0290409i
$539$	423.168	+	582.441i	0.785099	+	1.08060i
$540$	−215.077	+	149.387i	−0.398291	+	0.276642i
$541$	−755.213	−	548.694i	−1.39596	−	1.01422i	−0.995182	−	0.0980465i	$-0.968741\pi$
$541$	−755.213	−	548.694i	−1.39596	−	1.01422i	−0.400776	−	0.916176i	$-0.631259\pi$
$542$	−30.5948	+	60.0457i	−0.0564480	+	0.110785i
$543$	−366.050	+	366.050i	−0.674125	+	0.674125i
$544$	−59.8599	+	19.4497i	−0.110037	+	0.0357530i
$545$	−72.4326	−	149.949i	−0.132904	−	0.275135i
$546$	19.0079	−	58.5003i	0.0348130	−	0.107143i
$547$	−926.420	+	472.034i	−1.69364	+	0.862951i	−0.705623	+	0.708587i	$0.749333\pi$
$547$	−926.420	+	472.034i	−1.69364	+	0.862951i	−0.988014	+	0.154364i	$0.950667\pi$
$548$	96.9280	−	611.980i	0.176876	−	1.11675i
$549$			307.701i			0.560475i
$550$	121.449	+	68.5292i	0.220817	+	0.124598i
$551$	−19.9534			−0.0362131
$552$	100.480	+	15.9145i	0.182029	+	0.0288306i
$553$	131.946	+	258.958i	0.238600	+	0.468279i
$554$	110.777	+	35.9936i	0.199958	+	0.0649704i
$555$	117.568	+	860.187i	0.211834	+	1.54989i
$556$	189.903	+	584.462i	0.341552	+	1.05119i
$557$	−162.407	−	162.407i	−0.291575	−	0.291575i	0.546127	−	0.837702i	$-0.316102\pi$
$557$	−162.407	−	162.407i	−0.291575	−	0.291575i	−0.837702	+	0.546127i	$0.816102\pi$
$558$	31.1638	+	15.8787i	0.0558490	+	0.0284565i
$559$	572.900	−	788.530i	1.02487	−	1.41061i
$560$	−239.160	−	83.3647i	−0.427071	−	0.148866i
$561$	273.323	−	198.581i	0.487208	−	0.353977i
$562$	−6.08087	−	38.3931i	−0.0108201	−	0.0683151i
$563$	−228.223	+	36.1470i	−0.405370	+	0.0642043i	−0.355790	−	0.934566i	$-0.615788\pi$
$563$	−228.223	+	36.1470i	−0.405370	+	0.0642043i	−0.0495798	+	0.998770i	$0.515788\pi$
$564$	−197.942	−	272.444i	−0.350962	−	0.483057i
$565$	−43.0610	+	123.535i	−0.0762141	+	0.218646i
$566$	−58.8216	−	42.7364i	−0.103925	−	0.0755060i
$567$	153.844	−	301.935i	0.271329	−	0.532513i
$568$	106.997	−	106.997i	0.188376	−	0.188376i
$569$	−124.308	+	40.3900i	−0.218467	+	0.0709842i	−0.416205	−	0.909271i	$-0.636640\pi$
$569$	−124.308	+	40.3900i	−0.218467	+	0.0709842i	0.197739	+	0.980255i	$0.436640\pi$
$570$	5.93064	−	0.810583i	0.0104046	−	0.00142208i
$571$	154.922	−	476.802i	0.271318	−	0.835030i	−0.718853	−	0.695163i	$-0.755332\pi$
$571$	154.922	−	476.802i	0.271318	−	0.835030i	0.990170	−	0.139867i	$-0.0446677\pi$
$572$	1097.71	−	559.313i	1.91908	−	0.977819i
$573$	−54.4231	+	343.614i	−0.0949793	+	0.599675i
$574$			16.2648i			0.0283359i
$575$	263.708	−	120.544i	0.458623	−	0.209641i
$576$	307.199			0.533331
$577$	372.888	+	59.0596i	0.646252	+	0.102356i	0.470952	−	0.882159i	$-0.343910\pi$
$577$	372.888	+	59.0596i	0.646252	+	0.102356i	0.175300	+	0.984515i	$0.443910\pi$
$578$	35.3642	+	69.4061i	0.0611837	+	0.120080i
$579$	318.694	+	103.550i	0.550422	+	0.178843i
$580$	325.583	−	157.273i	0.561351	−	0.271160i
$581$	−22.4742	−	69.1686i	−0.0386820	−	0.119051i
$582$	−73.6215	−	73.6215i	−0.126497	−	0.126497i
$583$	813.484	+	414.491i	1.39534	+	0.710962i
$584$	139.606	−	192.152i	0.239052	−	0.329027i
$585$	256.992	+	370.000i	0.439302	+	0.632478i
$586$	93.2006	−	67.7142i	0.159045	−	0.115553i
$587$	138.085	+	871.835i	0.235239	+	1.48524i	0.768807	+	0.639481i	$0.220851\pi$
$587$	138.085	+	871.835i	0.235239	+	1.48524i	−0.533568	+	0.845757i	$0.679149\pi$
$588$	−553.099	+	87.6023i	−0.940645	+	0.148984i
$589$	−13.9054	−	19.1392i	−0.0236086	−	0.0324944i
$590$	19.4968	+	64.6466i	0.0330454	+	0.109570i
$591$	802.646	+	583.156i	1.35811	+	0.986728i
$592$	−310.472	+	609.335i	−0.524445	+	1.02928i
$593$	128.291	−	128.291i	0.216342	−	0.216342i	−0.590613	−	0.806955i	$-0.701114\pi$
$593$	128.291	−	128.291i	0.216342	−	0.216342i	0.806955	+	0.590613i	$0.201114\pi$
$594$	−70.9641	+	23.0576i	−0.119468	+	0.0388176i
$595$	13.8874	−	77.0504i	0.0233402	−	0.129496i
$596$	105.746	−	325.453i	0.177426	−	0.546062i
$597$	−672.663	+	342.739i	−1.12674	+	0.574102i
$598$	−8.67734	+	54.7866i	−0.0145106	+	0.0916164i
$599$		−	543.188i		−	0.906825i	−0.891301	−	0.453412i	$-0.850207\pi$
$599$		−	543.188i		−	0.906825i	0.891301	−	0.453412i	$-0.149793\pi$
$600$	−182.721	+	121.242i	−0.304536	+	0.202070i
$601$	228.860			0.380799			0.190399	−	0.981707i	$-0.439022\pi$
$601$	228.860			0.380799			0.190399	+	0.981707i	$0.439022\pi$
$602$	−57.6670	−	9.13355i	−0.0957923	−	0.0151720i
$603$	13.7519	+	26.9897i	0.0228059	+	0.0447591i
$604$	−641.349	−	208.387i	−1.06184	−	0.345011i
$605$	−851.056	−	888.007i	−1.40670	−	1.46778i
$606$	4.94380	+	15.2154i	0.00815808	+	0.0251080i
$607$	241.898	+	241.898i	0.398514	+	0.398514i	0.877709	−	0.479195i	$-0.159071\pi$
$607$	241.898	+	241.898i	0.398514	+	0.398514i	−0.479195	+	0.877709i	$0.659071\pi$
$608$	13.0745	+	6.66181i	0.0215042	+	0.0109569i
$609$	−139.631	+	192.185i	−0.229278	+	0.315575i
$610$	1.73480	−	81.6485i	0.00284394	−	0.133850i
$611$	300.317	−	218.193i	0.491517	−	0.357108i
$612$	15.5672	+	98.2877i	0.0254367	+	0.160601i
$613$	−58.4076	+	9.25086i	−0.0952816	+	0.0150911i	−0.203893	−	0.978993i	$-0.565360\pi$
$613$	−58.4076	+	9.25086i	−0.0952816	+	0.0150911i	0.108612	+	0.994084i	$0.465360\pi$
$614$	70.9075	+	97.5959i	0.115485	+	0.158951i
$615$	−250.506	−	190.263i	−0.407327	−	0.309370i
$616$	−120.703	−	87.6961i	−0.195947	−	0.142364i
$617$	352.094	−	691.024i	0.570656	−	1.11997i	−0.407714	−	0.913110i	$-0.633674\pi$
$617$	352.094	−	691.024i	0.570656	−	1.11997i	0.978370	−	0.206865i	$-0.0663260\pi$
$618$	−67.8934	+	67.8934i	−0.109860	+	0.109860i
$619$	−537.492	+	174.642i	−0.868323	+	0.282135i	−0.709100	−	0.705108i	$-0.750899\pi$
$619$	−537.492	+	174.642i	−0.868323	+	0.282135i	−0.159222	+	0.987243i	$0.550899\pi$
$620$	377.752	+	202.695i	0.609278	+	0.326927i
$621$	−47.9430	+	147.553i	−0.0772029	+	0.237606i
$622$	−18.2578	+	9.30283i	−0.0293534	+	0.0149563i
$623$	47.4290	−	299.455i	0.0761300	−	0.480666i
$624$			937.089i			1.50175i
$625$	−242.889	+	575.873i	−0.388622	+	0.921397i
$626$	−162.602			−0.259748
$627$	−77.7956	−	12.3216i	−0.124076	−	0.0196517i
$628$	133.450	+	261.910i	0.212500	+	0.417054i
$629$	−201.053	−	65.3260i	−0.319639	−	0.103857i
$630$	12.7593	−	23.7789i	0.0202529	−	0.0377442i
$631$	−187.092	−	575.810i	−0.296501	−	0.912536i	−0.982713	−	0.185134i	$-0.940728\pi$
$631$	−187.092	−	575.810i	−0.296501	−	0.912536i	0.686212	−	0.727401i	$-0.259272\pi$
$632$	140.159	+	140.159i	0.221771	+	0.221771i
$633$	−134.929	−	68.7496i	−0.213158	−	0.108609i
$634$	−106.956	+	147.212i	−0.168700	+	0.232196i
$635$	225.946	−	297.487i	0.355820	−	0.468484i
$636$	−574.532	+	417.422i	−0.903353	+	0.656324i
$637$	−96.5644	−	609.684i	−0.151592	−	0.957117i
$638$	101.759	−	16.1171i	0.159497	−	0.0252619i
$639$	−211.688	−	291.363i	−0.331280	−	0.455968i
$640$	−353.119	−	7.50280i	−0.551749	−	0.0117231i
$641$	621.687	+	451.682i	0.969870	+	0.704652i	0.955422	−	0.295244i	$-0.0954009\pi$
$641$	621.687	+	451.682i	0.969870	+	0.704652i	0.0144481	+	0.999896i	$0.495401\pi$
$642$	85.9785	−	168.742i	0.133923	−	0.262839i
$643$	−485.126	+	485.126i	−0.754472	+	0.754472i	−0.975310	−	0.220838i	$-0.929121\pi$
$643$	−485.126	+	485.126i	−0.754472	+	0.754472i	0.220838	+	0.975310i	$0.429121\pi$
$644$	−145.939	+	47.4185i	−0.226613	+	0.0736312i
$645$	815.250	−	781.327i	1.26395	−	1.21136i
$646$	−0.450396	+	1.38618i	−0.000697208	+	0.00214578i
$647$	438.563	−	223.459i	0.677840	−	0.345377i	−0.0809441	−	0.996719i	$-0.525794\pi$
$647$	438.563	−	223.459i	0.677840	−	0.345377i	0.758785	+	0.651342i	$0.225794\pi$
$648$	36.1537	−	228.265i	0.0557927	−	0.352261i
$649$		−	888.513i		−	1.36905i
$650$	−66.1069	−	99.6286i	−0.101703	−	0.153275i
$651$	−281.650			−0.432642
$652$	−7.50622	−	1.18887i	−0.0115126	−	0.00182342i
$653$	330.468	+	648.579i	0.506076	+	0.993230i	0.992812	+	0.119681i	$0.0381873\pi$
$653$	330.468	+	648.579i	0.506076	+	0.993230i	−0.486736	+	0.873549i	$0.661813\pi$
$654$	35.1018	+	11.4053i	0.0536725	+	0.0174392i
$655$	−398.592	−	71.8414i	−0.608537	−	0.109682i
$656$	−76.5704	−	235.659i	−0.116723	−	0.359237i
$657$	−399.724	−	399.724i	−0.608408	−	0.608408i
$658$	−19.8130	−	10.0952i	−0.0301109	−	0.0153423i
$659$	−285.023	+	392.301i	−0.432509	+	0.595297i	−0.968527	−	0.248909i	$-0.919928\pi$
$659$	−285.023	+	392.301i	−0.432509	+	0.595297i	0.536018	+	0.844206i	$0.319928\pi$
$660$	1366.52	−	412.130i	2.07049	−	0.624439i
$661$	−837.490	+	608.472i	−1.26700	+	0.920533i	−0.999079	−	0.0429071i	$-0.986338\pi$
$661$	−837.490	+	608.472i	−1.26700	+	0.920533i	−0.267925	+	0.963440i	$0.586338\pi$
$662$	−14.4915	−	91.4958i	−0.0218905	−	0.138211i
$663$	−286.108	+	45.3150i	−0.431535	+	0.0683484i
$664$	−29.1547	−	40.1280i	−0.0439077	−	0.0604337i
$665$	−14.9915	+	10.4127i	−0.0225436	+	0.0156582i
$666$	−58.9495	−	42.8293i	−0.0885127	−	0.0643083i
$667$	97.2548	−	190.873i	0.145809	−	0.286167i
$668$	31.5778	−	31.5778i	0.0472722	−	0.0472722i
$669$	−253.850	+	82.4808i	−0.379447	+	0.123290i
$670$	−3.49692	−	7.23927i	−0.00521929	−	0.0108049i
$671$	−332.081	+	1022.04i	−0.494904	+	1.52316i
$672$	155.658	−	79.3115i	0.231633	−	0.118023i
$673$	143.361	−	905.147i	0.213018	−	1.34494i	−0.616892	−	0.787048i	$-0.711609\pi$
$673$	143.361	−	905.147i	0.213018	−	1.34494i	0.829910	−	0.557897i	$-0.188391\pi$
$674$			97.5812i			0.144779i
$675$	−139.031	−	304.153i	−0.205972	−	0.450596i
$676$	−394.654			−0.583808
$677$	−1316.25	−	208.473i	−1.94424	−	0.307937i	−0.944451	−	0.328652i	$-0.893406\pi$
$677$	−1316.25	−	208.473i	−1.94424	−	0.307937i	−0.999785	+	0.0207152i	$0.993406\pi$
$678$	−13.1636	−	25.8351i	−0.0194154	−	0.0381049i
$679$	301.952	+	98.1102i	0.444701	+	0.144492i
$680$	−7.23072	−	52.9036i	−0.0106334	−	0.0777994i
$681$	−54.7843	−	168.609i	−0.0804469	−	0.247590i
$682$	86.3748	+	86.3748i	0.126649	+	0.126649i
$683$	553.314	+	281.927i	0.810123	+	0.412778i	0.809426	−	0.587222i	$-0.199778\pi$
$683$	553.314	+	281.927i	0.810123	+	0.412778i	0.000696453		1.00000i	$0.499778\pi$
$684$	13.6368	−	18.7695i	0.0199369	−	0.0274408i
$685$	747.189	+	260.450i	1.09079	+	0.380219i
$686$	−68.9201	+	50.0734i	−0.100467	+	0.0729933i
$687$	−10.9984	−	69.4413i	−0.0160093	−	0.101079i
$688$	878.529	−	139.145i	1.27693	−	0.202246i
$689$	−460.126	−	633.310i	−0.667818	−	0.919172i
$690$	−21.1524	+	60.6829i	−0.0306557	+	0.0879462i
$691$	651.607	+	473.420i	0.942992	+	0.685123i	0.949139	−	0.314858i	$-0.101957\pi$
$691$	651.607	+	473.420i	0.942992	+	0.685123i	−0.00614739	+	0.999981i	$0.501957\pi$
$692$	−355.101	+	696.924i	−0.513151	+	1.00712i
$693$	−251.093	+	251.093i	−0.362328	+	0.362328i
$694$	114.434	−	37.1819i	0.164891	−	0.0535762i
$695$	−777.579	+	106.277i	−1.11882	+	0.152917i
$696$	−50.0647	+	154.083i	−0.0719320	+	0.221384i
$697$	68.2477	−	34.7739i	0.0979163	−	0.0498908i
$698$	10.6649	−	67.3354i	0.0152792	−	0.0964690i
$699$			1559.07i			2.23043i
$700$	162.546	−	288.068i	0.232209	−	0.411526i
$701$	−570.439			−0.813751			−0.406876	−	0.913484i	$-0.633382\pi$
$701$	−570.439			−0.813751			−0.406876	+	0.913484i	$0.633382\pi$
$702$	63.1891	+	10.0082i	0.0900130	+	0.0142567i
$703$	22.3752	+	43.9137i	0.0318281	+	0.0624662i
$704$	1020.37	+	331.539i	1.44939	+	0.470936i
$705$	387.252	−	187.061i	0.549293	−	0.265335i
$706$	18.4926	+	56.9144i	0.0261935	+	0.0806154i
$707$	−34.4965	−	34.4965i	−0.0487928	−	0.0487928i
$708$	615.791	+	313.761i	0.869762	+	0.443166i
$709$	341.238	−	469.674i	0.481295	−	0.662445i	−0.497458	−	0.867488i	$-0.665733\pi$
$709$	341.238	−	469.674i	0.481295	−	0.662445i	0.978753	+	0.205043i	$0.0657333\pi$
$710$	54.5288	+	78.5070i	0.0768012	+	0.110573i
$711$	381.665	−	277.296i	0.536801	−	0.390009i
$712$	−32.3468	−	204.229i	−0.0454309	−	0.286839i
$713$	250.861	−	39.7324i	0.351838	−	0.0557257i
$714$	10.1994	+	14.0383i	0.0142849	+	0.0196615i
$715$	454.292	+	1506.32i	0.635374	+	2.10674i
$716$	172.715	+	125.485i	0.241222	+	0.175258i
$717$	708.963	−	1391.42i	0.988791	−	1.94061i
$718$	−71.1829	+	71.1829i	−0.0991405	+	0.0991405i
$719$	−497.061	+	161.505i	−0.691322	+	0.224624i	−0.633546	−	0.773705i	$-0.718401\pi$
$719$	−497.061	+	161.505i	−0.691322	+	0.224624i	−0.0577767	+	0.998330i	$0.518401\pi$
$720$	−72.9238	+	404.597i	−0.101283	+	0.561940i
$721$	90.4769	−	278.459i	0.125488	−	0.386213i
$722$	−93.3529	+	47.5657i	−0.129298	+	0.0658804i
$723$	209.684	−	1323.89i	0.290020	−	1.83111i
$724$		−	532.535i		−	0.735546i
$725$	123.910	+	444.825i	0.170910	+	0.613552i
$726$	272.607			0.375492
$727$	−412.828	−	65.3856i	−0.567852	−	0.0899389i	−0.134094	−	0.990969i	$-0.542813\pi$
$727$	−412.828	−	65.3856i	−0.567852	−	0.0899389i	−0.433757	+	0.901030i	$0.642813\pi$
$728$	58.0762	+	113.981i	0.0797751	+	0.156567i
$729$	−87.3564	−	28.3838i	−0.119830	−	0.0389353i
$730$	103.813	+	108.321i	0.142210	+	0.148384i
$731$	84.9664	+	261.500i	0.116233	+	0.357729i
$732$	−591.065	−	591.065i	−0.807465	−	0.807465i
$733$	641.297	+	326.757i	0.874894	+	0.445781i	0.832956	−	0.553340i	$-0.186647\pi$
$733$	641.297	+	326.757i	0.874894	+	0.445781i	0.0419378	+	0.999120i	$0.486647\pi$
$734$	91.1902	−	125.513i	0.124237	−	0.170998i
$735$	15.1915	−	714.988i	0.0206687	−	0.972773i
$736$	−127.453	+	92.5999i	−0.173170	+	0.125815i
$737$	16.5494	+	104.489i	0.0224551	+	0.141776i
$738$	26.0763	−	4.13007i	0.0353337	−	0.00559631i
$739$	−560.278	−	771.157i	−0.758158	−	1.04351i	−0.997365	−	0.0725458i	$-0.976888\pi$
$739$	−560.278	−	771.157i	−0.758158	−	1.04351i	0.239208	−	0.970968i	$-0.423112\pi$
$740$	−711.226	−	540.187i	−0.961117	−	0.729982i
$741$	54.6365	+	39.6957i	0.0737335	+	0.0535705i
$742$	−21.2888	+	41.7817i	−0.0286912	+	0.0563096i
$743$	−973.452	+	973.452i	−1.31016	+	1.31016i	−0.388872	+	0.921292i	$0.627135\pi$
$743$	−973.452	+	973.452i	−1.31016	+	1.31016i	−0.921292	+	0.388872i	$0.872865\pi$
$744$	−182.685	+	59.3581i	−0.245545	+	0.0797824i
$745$	385.080	+	206.627i	0.516886	+	0.277352i
$746$	−5.47063	+	16.8369i	−0.00733329	+	0.0225695i
$747$	−105.186	+	53.5951i	−0.140812	+	0.0717472i
$748$	−54.3682	+	343.267i	−0.0726847	+	0.458913i
$749$			577.505i			0.771034i
$750$	−54.8993	−	127.179i	−0.0731991	−	0.169572i
$751$	815.196			1.08548			0.542740	−	0.839901i	$-0.317387\pi$
$751$	815.196			1.08548			0.542740	+	0.839901i	$0.317387\pi$
$752$	334.593	+	52.9944i	0.444938	+	0.0704713i
$753$	172.553	+	338.655i	0.229155	+	0.449741i
$754$	−84.0137	−	27.2977i	−0.111424	−	0.0362039i
$755$	407.186	−	758.852i	0.539320	−	1.00510i
$756$	54.6910	+	168.322i	0.0723426	+	0.222648i
$757$	266.404	+	266.404i	0.351920	+	0.351920i	0.860824	−	0.508903i	$-0.169949\pi$
$757$	266.404	+	266.404i	0.351920	+	0.351920i	−0.508903	+	0.860824i	$0.669949\pi$
$758$	50.4957	+	25.7288i	0.0666170	+	0.0339430i
$759$	497.050	−	684.131i	0.654875	−	0.901358i
$760$	−7.52938	+	9.91341i	−0.00990708	+	0.0130440i
$761$	−875.638	+	636.188i	−1.15064	+	0.835989i	−0.988566	−	0.150789i	$-0.951819\pi$
$761$	−875.638	+	636.188i	−1.15064	+	0.835989i	−0.162075	+	0.986778i	$0.551819\pi$
$762$	12.9520	+	81.7758i	0.0169974	+	0.107317i
$763$	−111.162	+	17.6063i	−0.145690	+	0.0230751i
$764$	−210.360	−	289.535i	−0.275340	−	0.378973i
$765$	−127.056	−	2.69959i	−0.166086	−	0.00352887i
$766$	−118.080	−	85.7904i	−0.154152	−	0.111998i
$767$	−345.860	+	678.789i	−0.450926	+	0.884993i
$768$	−547.525	+	547.525i	−0.712923	+	0.712923i
$769$	−749.913	+	243.662i	−0.975180	+	0.316855i	−0.752905	−	0.658129i	$-0.771348\pi$
$769$	−749.913	+	243.662i	−0.975180	+	0.316855i	−0.222275	+	0.974984i	$0.571348\pi$
$770$	68.0435	−	65.2121i	0.0883681	−	0.0846911i
$771$	230.322	−	708.860i	0.298732	−	0.919403i
$772$	−307.144	+	156.498i	−0.397855	+	0.202717i
$773$	56.0962	−	354.177i	0.0725694	−	0.458185i	−0.924467	−	0.381261i	$-0.875490\pi$
$773$	56.0962	−	354.177i	0.0725694	−	0.458185i	0.997037	−	0.0769245i	$-0.0245100\pi$
$774$			94.7727i			0.122445i
$775$	−340.321	+	428.849i	−0.439124	+	0.553354i
$776$	216.531			0.279034
$777$	579.540	+	91.7901i	0.745869	+	0.118134i
$778$	21.6783	+	42.5461i	0.0278642	+	0.0546866i
$779$	−16.9836	−	5.51830i	−0.0218018	−	0.00708382i
$780$	−1204.39	−	217.078i	−1.54409	−	0.278305i
$781$	−388.680	−	1196.24i	−0.497670	−	1.53167i
$782$	−11.0648	−	11.0648i	−0.0141494	−	0.0141494i
$783$	−220.147	−	112.171i	−0.281159	−	0.143257i
$784$	331.115	−	455.741i	0.422341	−	0.581302i
$785$	−359.402	+	108.392i	−0.457837	+	0.138079i
$786$	72.6218	−	52.7628i	0.0923942	−	0.0671283i
$787$	197.057	+	1244.17i	0.250390	+	1.58090i	0.717410	+	0.696651i	$0.245327\pi$
$787$	197.057	+	1244.17i	0.250390	+	1.58090i	−0.467021	+	0.884246i	$0.654673\pi$
$788$	−1008.04	+	159.658i	−1.27924	+	0.202612i
$789$	472.556	+	650.417i	0.598930	+	0.824356i
$790$	−102.839	+	71.4289i	−0.130175	+	0.0904163i
$791$	71.5318	+	51.9709i	0.0904321	+	0.0657028i
$792$	−109.947	+	215.784i	−0.138822	+	0.272454i
$793$	651.533	−	651.533i	0.821605	−	0.821605i
$794$	95.1586	−	30.9189i	0.119847	−	0.0389407i
$795$	−394.476	−	816.639i	−0.496197	−	1.02722i
$796$	239.989	−	738.611i	0.301494	−	0.927903i
$797$	748.686	−	381.474i	0.939380	−	0.478638i	0.0839000	−	0.996474i	$-0.473262\pi$
$797$	748.686	−	381.474i	0.939380	−	0.478638i	0.855480	+	0.517836i	$0.173262\pi$
$798$	0.632855	−	3.99569i	0.000793052	−	0.00500713i
$799$			104.719i			0.131063i
$800$	67.3206	−	332.842i	0.0841507	−	0.416052i
$801$	−492.138			−0.614405
$802$	−102.155	−	16.1797i	−0.127375	−	0.0201742i
$803$	−896.303	−	1759.09i	−1.11619	−	2.19065i
$804$	−78.2610	−	25.4285i	−0.0973396	−	0.0316275i
$805$	−26.5373	−	194.160i	−0.0329656	−	0.241193i
$806$	−32.3649	−	99.6090i	−0.0401550	−	0.123584i
$807$	923.128	+	923.128i	1.14390	+	1.14390i
$808$	−29.6455	−	15.1051i	−0.0366900	−	0.0186945i
$809$	−668.124	+	919.594i	−0.825864	+	1.13670i	0.162814	+	0.986657i	$0.447943\pi$
$809$	−668.124	+	919.594i	−0.825864	+	1.13670i	−0.988679	+	0.150048i	$0.952057\pi$
$810$	137.856	+	48.0531i	0.170193	+	0.0593248i
$811$	1006.65	−	731.378i	1.24125	−	0.901822i	0.243570	−	0.969883i	$-0.421681\pi$
$811$	1006.65	−	731.378i	1.24125	−	0.901822i	0.997681	+	0.0680614i	$0.0216814\pi$
$812$	−38.2285	−	241.365i	−0.0470794	−	0.297248i
$813$	−870.038	+	137.801i	−1.07016	+	0.169496i
$814$	−149.580	−	205.879i	−0.183759	−	0.252923i
$815$	3.19454	−	9.16463i	0.00391969	−	0.0112449i
$816$	−213.867	−	155.383i	−0.262091	−	0.190421i
$817$	29.1023	−	57.1165i	0.0356209	−	0.0699100i
$818$	−77.4673	+	77.4673i	−0.0947033	+	0.0947033i
$819$	289.566	−	94.0855i	0.353560	−	0.114879i
$820$	320.619	−	43.8213i	0.390998	−	0.0534406i
$821$	3.49825	−	10.7665i	0.00426096	−	0.0131139i	−0.948903	−	0.315567i	$-0.897805\pi$
$821$	3.49825	−	10.7665i	0.00426096	−	0.0131139i	0.953164	+	0.302453i	$0.0978054\pi$
$822$	−156.261	+	79.6190i	−0.190099	+	0.0968601i
$823$	−65.6724	+	414.639i	−0.0797964	+	0.503815i	0.915126	+	0.403168i	$0.132091\pi$
$823$	−65.6724	+	414.639i	−0.0797964	+	0.503815i	−0.994922	+	0.100646i	$0.967909\pi$
$824$		−	199.684i		−	0.242335i
$825$	208.418	+	1810.82i	0.252628	+	2.19494i
$826$	45.6353			0.0552485
$827$	1100.78	+	174.346i	1.33105	+	0.210817i	0.781113	−	0.624390i	$-0.214652\pi$
$827$	1100.78	+	174.346i	1.33105	+	0.210817i	0.549936	+	0.835207i	$0.314652\pi$
$828$	113.081	+	221.933i	0.136571	+	0.268035i
$829$	494.260	+	160.595i	0.596213	+	0.193721i	0.591551	−	0.806268i	$-0.298516\pi$
$829$	494.260	+	160.595i	0.596213	+	0.193721i	0.00466205	+	0.999989i	$0.498516\pi$
$830$	28.2135	−	13.6285i	0.0339921	−	0.0164198i
$831$	470.482	+	1447.99i	0.566163	+	1.74247i
$832$	−650.470	−	650.470i	−0.781815	−	0.781815i
$833$	155.156	+	79.0562i	0.186262	+	0.0949054i
$834$	102.240	−	140.722i	0.122590	−	0.168731i
$835$	32.5343	+	46.8407i	0.0389632	+	0.0560967i
$836$	65.5520	−	47.6263i	0.0784114	−	0.0569692i
$837$	−45.8261	−	289.335i	−0.0547504	−	0.345681i
$838$	−175.723	+	27.8317i	−0.209693	+	0.0332121i
$839$	657.552	+	905.043i	0.783733	+	1.07872i	0.994860	+	0.101257i	$0.0322865\pi$
$839$	657.552	+	905.043i	0.783733	+	1.07872i	−0.211127	+	0.977459i	$0.567713\pi$
$840$	42.7935	+	141.893i	0.0509446	+	0.168920i
$841$	−404.382	−	293.801i	−0.480835	−	0.349347i
$842$	−27.2824	+	53.5448i	−0.0324019	+	0.0635924i
$843$	359.282	−	359.282i	0.426194	−	0.426194i
$844$	148.157	−	48.1392i	0.175542	−	0.0570370i
$845$	89.3995	−	496.008i	0.105798	−	0.586991i
$846$	−11.1539	+	34.3282i	−0.0131843	+	0.0405771i
$847$	−740.681	+	377.396i	−0.874475	+	0.445567i
$848$	111.755	−	705.593i	0.131786	−	0.832067i
$849$		−	950.378i		−	1.11941i
$850$	33.6992	+	1.43267i	0.0396461	+	0.00168550i
$851$	−529.134			−0.621779
$852$	966.315	+	153.049i	1.13417	+	0.179635i
$853$	281.083	+	551.657i	0.329523	+	0.646725i	0.995020	−	0.0996751i	$-0.0317803\pi$
$853$	281.083	+	551.657i	0.329523	+	0.646725i	−0.665497	+	0.746401i	$0.731780\pi$
$854$	−52.4934	−	17.0561i	−0.0614677	−	0.0199721i
$855$	20.5007	+	21.3908i	0.0239774	+	0.0250185i
$856$	121.710	+	374.584i	0.142184	+	0.437598i
$857$	312.684	+	312.684i	0.364858	+	0.364858i	0.865598	−	0.500740i	$-0.166939\pi$
$857$	312.684	+	312.684i	0.364858	+	0.364858i	−0.500740	+	0.865598i	$0.666939\pi$
$858$	−310.700	−	158.310i	−0.362122	−	0.184510i
$859$	59.1889	−	81.4665i	0.0689044	−	0.0948387i	−0.773174	−	0.634194i	$-0.781332\pi$
$859$	59.1889	−	81.4665i	0.0689044	−	0.0948387i	0.842078	+	0.539355i	$0.181332\pi$
$860$	−24.6757	+	1161.36i	−0.0286927	+	1.35042i
$861$	−171.998	+	124.964i	−0.199766	+	0.145138i
$862$	−11.1016	−	70.0928i	−0.0128789	−	0.0813142i
$863$	−158.959	+	25.1766i	−0.184194	+	0.0291734i	−0.247850	−	0.968798i	$-0.579724\pi$
$863$	−158.959	+	25.1766i	−0.184194	+	0.0291734i	0.0636561	+	0.997972i	$0.479724\pi$
$864$	106.802	+	147.000i	0.123613	+	0.170139i
$865$	−795.466	−	604.168i	−0.919614	−	0.698460i
$866$	−91.7970	−	66.6944i	−0.106001	−	0.0770144i
$867$	−462.254	+	907.225i	−0.533165	+	1.04640i
$868$	204.875	−	204.875i	0.236031	−	0.236031i
$869$	1566.98	−	509.144i	1.80320	−	0.585896i
$870$	−90.1803	−	48.3891i	−0.103656	−	0.0556197i
$871$	28.0300	−	86.2675i	0.0321814	−	0.0990442i
$872$	−68.3917	+	34.8473i	−0.0784309	+	0.0399625i
$873$	80.6196	−	509.012i	0.0923477	−	0.583061i
$874$			3.64816i			0.00417410i
$875$	325.228	+	269.546i	0.371689	+	0.308052i
$876$	1535.67			1.75304
$877$	−889.491	−	140.882i	−1.01424	−	0.160640i	−0.372882	−	0.927879i	$-0.621630\pi$
$877$	−889.491	−	140.882i	−1.01424	−	0.160640i	−0.641362	+	0.767239i	$0.721630\pi$
$878$	47.9316	+	94.0711i	0.0545918	+	0.107143i
$879$	1432.14	+	465.329i	1.62928	+	0.529385i
$880$	−678.874	+	1265.18i	−0.771447	+	1.43771i
$881$	−310.239	−	954.819i	−0.352145	−	1.08379i	−0.957647	−	0.287946i	$-0.907028\pi$
$881$	−310.239	−	954.819i	−0.352145	−	1.08379i	0.605502	−	0.795844i	$-0.292972\pi$
$882$	42.4417	+	42.4417i	0.0481198	+	0.0481198i
$883$	322.466	+	164.305i	0.365193	+	0.186075i	0.626952	−	0.779058i	$-0.284302\pi$
$883$	322.466	+	164.305i	0.365193	+	0.186075i	−0.261758	+	0.965133i	$0.584302\pi$
$884$	175.154	−	241.079i	0.198139	−	0.272714i
$885$	−533.833	+	702.861i	−0.603201	+	0.794193i
$886$	154.847	−	112.503i	0.174771	−	0.126979i
$887$	−172.488	−	1089.05i	−0.194463	−	1.22779i	−0.870964	−	0.491347i	$-0.836505\pi$
$887$	−172.488	−	1089.05i	−0.194463	−	1.22779i	0.676501	−	0.736442i	$-0.263495\pi$
$888$	395.249	−	62.6013i	0.445100	−	0.0704969i
$889$	−148.401	−	204.256i	−0.166930	−	0.229759i
$890$	130.589	+	2.77466i	0.146730	+	0.00311759i
$891$	−1554.17	−	1129.17i	−1.74430	−	1.26731i
$892$	124.655	−	244.649i	0.139748	−	0.274271i
$893$	17.2634	−	17.2634i	0.0193319	−	0.0193319i
$894$	−92.1173	+	29.9307i	−0.103039	+	0.0334796i
$895$	−196.836	+	188.645i	−0.219928	+	0.210777i
$896$	−73.7656	+	227.027i	−0.0823276	+	0.253378i
$897$	−646.030	+	329.169i	−0.720211	+	0.366966i
$898$	23.5394	−	148.622i	0.0262132	−	0.165503i
$899$			404.485i			0.449927i
$900$	−503.115	−	187.451i	−0.559017	−	0.208278i
$901$	220.832			0.245097
$902$	91.0706	+	14.4242i	0.100965	+	0.0159913i
$903$	−346.475	−	679.995i	−0.383693	−	0.753039i
$904$	57.3502	+	18.6342i	0.0634405	+	0.0206131i
$905$	669.299	+	120.633i	0.739557	+	0.133296i
$906$	58.9825	+	181.530i	0.0651021	+	0.200364i
$907$	183.638	+	183.638i	0.202468	+	0.202468i	0.801056	−	0.598589i	$-0.204272\pi$
$907$	183.638	+	183.638i	0.202468	+	0.202468i	−0.598589	+	0.801056i	$0.704272\pi$
$908$	162.498	+	82.7968i	0.178962	+	0.0911859i
$909$	−46.5463	+	64.0655i	−0.0512061	+	0.0704791i
$910$	−77.3669	+	23.3331i	−0.0850185	+	0.0256408i
$911$	922.010	−	669.880i	1.01209	−	0.735323i	0.0474403	−	0.998874i	$-0.484894\pi$
$911$	922.010	−	669.880i	1.01209	−	0.735323i	0.964646	+	0.263551i	$0.0848936\pi$
$912$	9.64125	+	60.8725i	0.0105715	+	0.0667461i
$913$	−407.222	+	64.4977i	−0.446027	+	0.0706437i
$914$	66.9953	+	92.2111i	0.0732990	+	0.100887i
$915$	876.751	−	608.968i	0.958198	−	0.665539i
$916$	58.5124	+	42.5118i	0.0638782	+	0.0464102i
$917$	−124.271	+	243.895i	−0.135519	+	0.265971i
$918$	−12.7618	+	12.7618i	−0.0139017	+	0.0139017i
$919$	−1036.37	+	336.736i	−1.12771	+	0.366416i	−0.812706	−	0.582674i	$-0.802007\pi$
$919$	−1036.37	+	336.736i	−1.12771	+	0.366416i	−0.315006	+	0.949090i	$0.602007\pi$
$920$	−58.1322	−	120.344i	−0.0631872	−	0.130809i
$921$	−487.274	+	1499.68i	−0.529071	+	1.62831i
$922$	222.180	−	113.206i	0.240976	−	0.122783i
$923$	−168.707	+	1065.17i	−0.182781	+	1.15403i
$924$		−	964.655i		−	1.04400i
$925$	840.027	−	771.514i	0.908137	−	0.834069i
$926$	−40.9705			−0.0442446
$927$	−469.409	−	74.3471i	−0.506374	−	0.0802018i
$928$	−113.901	−	223.543i	−0.122738	−	0.240887i
$929$	−832.928	−	270.635i	−0.896585	−	0.291318i	−0.175758	−	0.984433i	$-0.556238\pi$
$929$	−832.928	−	270.635i	−0.896585	−	0.291318i	−0.720827	+	0.693115i	$0.756238\pi$
$930$	−16.4317	−	120.222i	−0.0176685	−	0.129271i
$931$	−12.5455	−	38.6110i	−0.0134753	−	0.0414726i
$932$	−1134.08	−	1134.08i	−1.21682	−	1.21682i
$933$	−238.653	−	121.600i	−0.255791	−	0.130332i
$934$	−61.9879	+	85.3190i	−0.0663682	+	0.0913480i
$935$	−419.108	−	146.090i	−0.448244	−	0.156246i
$936$	167.991	−	122.052i	0.179477	−	0.130398i
$937$	10.8140	+	68.2770i	0.0115411	+	0.0728676i	0.992787	−	0.119894i	$-0.0382555\pi$
$937$	10.8140	+	68.2770i	0.0115411	+	0.0728676i	−0.981246	+	0.192762i	$0.938256\pi$
$938$	−5.36670	+	0.850002i	−0.00572143	+	0.000906185i
$939$	−1249.29	−	1719.49i	−1.33044	−	1.83120i
$940$	−145.620	+	417.760i	−0.154915	+	0.444425i
$941$	−300.146	−	218.068i	−0.318964	−	0.231741i	0.416769	−	0.909012i	$-0.363162\pi$
$941$	−300.146	−	218.068i	−0.318964	−	0.231741i	−0.735733	+	0.677271i	$0.763162\pi$
$942$	37.7721	−	74.1318i	0.0400977	−	0.0786962i
$943$	135.567	−	135.567i	0.143761	−	0.143761i
$944$	−661.205	+	214.839i	−0.700429	+	0.227583i
$945$	−223.938	+	30.6073i	−0.236972	+	0.0323886i
$946$	−102.282	+	314.791i	−0.108120	+	0.332760i
$947$	−47.7905	+	24.3505i	−0.0504651	+	0.0257133i	−0.479041	−	0.877793i	$-0.659015\pi$
$947$	−47.7905	+	24.3505i	−0.0504651	+	0.0257133i	0.428576	+	0.903506i	$0.359015\pi$
$948$	−200.484	+	1265.80i	−0.211481	+	1.33524i
$949$			1692.77i			1.78374i
$950$	−5.31928	−	5.79164i	−0.00559924	−	0.00609647i
$951$	−2378.50			−2.50105
$952$	−35.6431	−	5.64532i	−0.0374403	−	0.00592996i
$953$	−62.8579	−	123.366i	−0.0659580	−	0.129450i	0.855674	−	0.517516i	$-0.173143\pi$
$953$	−62.8579	−	123.366i	−0.0659580	−	0.129450i	−0.921632	+	0.388066i	$0.873143\pi$
$954$	72.3915	+	23.5214i	0.0758821	+	0.0246556i
$955$	411.545	−	198.796i	0.430937	−	0.208163i
$956$	496.424	+	1527.83i	0.519272	+	1.59815i
$957$	952.261	+	952.261i	0.995048	+	0.995048i
$958$	89.1512	+	45.4248i	0.0930597	+	0.0474163i
$959$	314.341	−	432.653i	0.327780	−	0.451151i
$960$	−607.974	−	875.321i	−0.633307	−	0.911792i
$961$	389.487	−	282.979i	0.405293	−	0.294463i
$962$	34.1333	+	215.509i	0.0354816	+	0.224022i
$963$	925.873	−	146.644i	0.961447	−	0.152278i
$964$	810.485	+	1115.54i	0.840752	+	1.15720i
$965$	−127.113	−	421.474i	−0.131723	−	0.436761i
$966$	35.1379	+	25.5292i	0.0363747	+	0.0264277i
$967$	358.090	−	702.791i	0.370310	−	0.726775i	−0.628382	−	0.777905i	$-0.716282\pi$
$967$	358.090	−	702.791i	0.370310	−	0.726775i	0.998692	+	0.0511303i	$0.0162824\pi$
$968$	−400.887	+	400.887i	−0.414140	+	0.414140i
$969$	−18.1191	+	5.88724i	−0.0186987	+	0.00607559i
$970$	−24.2622	+	134.612i	−0.0250126	+	0.138775i
$971$	295.128	−	908.310i	0.303942	−	0.935438i	−0.676128	−	0.736784i	$-0.736343\pi$
$971$	295.128	−	908.310i	0.303942	−	0.935438i	0.980070	−	0.198653i	$-0.0636567\pi$
$972$	911.422	−	464.393i	0.937677	−	0.477771i
$973$	−82.9751	+	523.884i	−0.0852776	+	0.538422i
$974$		−	203.656i		−	0.209093i
$975$	545.654	−	1464.53i	0.559645	−	1.50208i
$976$	840.867			0.861544
$977$	699.516	+	110.792i	0.715984	+	0.113401i	0.503789	−	0.863827i	$-0.331939\pi$
$977$	699.516	+	110.792i	0.715984	+	0.113401i	0.212195	+	0.977227i	$0.431939\pi$
$978$	0.976565	+	1.91662i	0.000998533	+	0.00195973i
$979$	−1634.66	−	531.132i	−1.66972	−	0.542525i
$980$	509.038	+	531.138i	0.519426	+	0.541978i
$981$	56.4539	+	173.747i	0.0575473	+	0.177112i
$982$	−71.6216	−	71.6216i	−0.0729344	−	0.0729344i
$983$	375.050	+	191.097i	0.381536	+	0.194402i	0.634231	−	0.773144i	$-0.281317\pi$
$983$	375.050	+	191.097i	0.381536	+	0.194402i	−0.252695	+	0.967546i	$0.581317\pi$
$984$	−85.2261	+	117.304i	−0.0866119	+	0.119211i
$985$	27.6871	−	1303.09i	0.0281087	−	1.32294i
$986$	20.1607	−	14.6476i	0.0204470	−	0.0148556i
$987$	−45.4693	−	287.082i	−0.0460682	−	0.290863i
$988$	−68.6180	+	10.8680i	−0.0694514	+	0.0110000i
$989$	404.525	+	556.781i	0.409024	+	0.562974i
$990$	−121.828	−	92.5303i	−0.123059	−	0.0934649i
$991$	984.068	+	714.967i	0.993005	+	0.721460i	0.960577	−	0.278014i	$-0.0896761\pi$
$991$	984.068	+	714.967i	0.993005	+	0.721460i	0.0324279	+	0.999474i	$0.489676\pi$
$992$	135.044	−	265.039i	0.136133	−	0.267177i
$993$	856.216	−	856.216i	0.862252	−	0.862252i
$994$	61.4403	−	19.9632i	0.0618112	−	0.0200837i
$995$	873.934	+	468.937i	0.878326	+	0.471294i
$996$	99.1021	−	305.005i	0.0995001	−	0.306230i
$997$	31.4577	−	16.0285i	0.0315523	−	0.0160767i	−0.438143	−	0.898905i	$-0.644364\pi$
$997$	31.4577	−	16.0285i	0.0315523	−	0.0160767i	0.469695	+	0.882828i	$0.344364\pi$
$998$	4.12632	−	26.0526i	0.00413459	−	0.0261048i
$999$			610.287i			0.610898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.3.f.a.2.3	✓	32
3.2	odd	2		225.3.r.a.127.2		32
4.3	odd	2		400.3.bg.c.177.1		32
5.2	odd	4		125.3.f.b.93.2		32
5.3	odd	4		125.3.f.a.93.3		32
5.4	even	2		125.3.f.c.32.2		32
25.9	even	10		125.3.f.b.82.2		32
25.12	odd	20		125.3.f.c.43.2		32
25.13	odd	20	inner	25.3.f.a.13.3	yes	32
25.16	even	5		125.3.f.a.82.3		32
75.38	even	20		225.3.r.a.163.2		32
100.63	even	20		400.3.bg.c.113.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.2.3	✓	32	1.1	even	1	trivial
25.3.f.a.13.3	yes	32	25.13	odd	20	inner
125.3.f.a.82.3		32	25.16	even	5
125.3.f.a.93.3		32	5.3	odd	4
125.3.f.b.82.2		32	25.9	even	10
125.3.f.b.93.2		32	5.2	odd	4
125.3.f.c.32.2		32	5.4	even	2
125.3.f.c.43.2		32	25.12	odd	20
225.3.r.a.127.2		32	3.2	odd	2
225.3.r.a.163.2		32	75.38	even	20
400.3.bg.c.113.1		32	100.63	even	20
400.3.bg.c.177.1		32	4.3	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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.287585 + 0.0455490i) q^{2} +(1.72787 + 3.39113i) q^{3} +(-3.72360 - 1.20987i) q^{4} +(2.36408 - 4.40581i) q^{5} +(0.342446 + 1.05394i) q^{6} +(-2.38950 - 2.38950i) q^{7} +(-2.05348 - 1.04630i) q^{8} +(-3.22416 + 4.43767i) q^{9} +O(q^{10})\)	\(q+(0.287585 + 0.0455490i) q^{2} +(1.72787 + 3.39113i) q^{3} +(-3.72360 - 1.20987i) q^{4} +(2.36408 - 4.40581i) q^{5} +(0.342446 + 1.05394i) q^{6} +(-2.38950 - 2.38950i) q^{7} +(-2.05348 - 1.04630i) q^{8} +(-3.22416 + 4.43767i) q^{9} +(0.880552 - 1.15936i) q^{10} +(-15.4985 + 11.2603i) q^{11} +(-2.33105 - 14.7177i) q^{12} +(16.2234 - 2.56953i) q^{13} +(-0.578344 - 0.796023i) q^{14} +(19.0255 + 0.404238i) q^{15} +(12.1270 + 8.81080i) q^{16} +(-2.10364 + 4.12863i) q^{17} +(-1.12935 + 1.12935i) q^{18} +(1.02742 - 0.333828i) q^{19} +(-14.1333 + 13.5452i) q^{20} +(3.97436 - 12.2318i) q^{21} +(-4.97001 + 2.53235i) q^{22} +(-1.81434 + 11.4553i) q^{23} -8.77147i q^{24} +(-13.8223 - 20.8313i) q^{25} +4.78263 q^{26} +(13.2122 + 2.09261i) q^{27} +(6.00654 + 11.7885i) q^{28} +(-17.5664 - 5.70767i) q^{29} +(5.45302 + 0.982843i) q^{30} +(-6.76718 - 20.8272i) q^{31} +(9.60482 + 9.60482i) q^{32} +(-64.9643 - 33.1010i) q^{33} +(-0.793031 + 1.09151i) q^{34} +(-16.1766 + 4.87872i) q^{35} +(17.3745 - 12.6233i) q^{36} +(7.13692 + 45.0607i) q^{37} +(0.310675 - 0.0492062i) q^{38} +(36.7454 + 50.5757i) q^{39} +(-9.46437 + 6.57370i) q^{40} +(-13.3733 - 9.71629i) q^{41} +(1.70011 - 3.33666i) q^{42} +(41.9589 - 41.9589i) q^{43} +(71.3335 - 23.1776i) q^{44} +(11.9294 + 24.6960i) q^{45} +(-1.04356 + 3.21173i) q^{46} +(20.1364 - 10.2600i) q^{47} +(-8.92468 + 56.3482i) q^{48} -37.5806i q^{49} +(-3.02624 - 6.62037i) q^{50} -17.6355 q^{51} +(-63.5180 - 10.0603i) q^{52} +(-21.6364 - 42.4637i) q^{53} +(3.70431 + 1.20360i) q^{54} +(12.9711 + 94.9034i) q^{55} +(2.40665 + 7.40691i) q^{56} +(2.90730 + 2.90730i) q^{57} +(-4.79186 - 2.44157i) q^{58} +(-27.2616 + 37.5224i) q^{59} +(-70.3541 - 24.5235i) q^{60} +(45.3825 - 32.9723i) q^{61} +(-0.997479 - 6.29783i) q^{62} +(18.3079 - 2.89969i) q^{63} +(-32.9185 - 45.3084i) q^{64} +(27.0324 - 77.5516i) q^{65} +(-17.1750 - 12.4784i) q^{66} +(2.50707 - 4.92040i) q^{67} +(12.8282 - 12.8282i) q^{68} +(-41.9814 + 13.6406i) q^{69} +(-4.87437 + 0.666216i) q^{70} +(-20.2891 + 62.4433i) q^{71} +(11.2639 - 5.73923i) q^{72} +(-16.1217 + 101.788i) q^{73} +13.2839i q^{74} +(46.7586 - 82.8669i) q^{75} -4.22958 q^{76} +(63.9400 + 10.1271i) q^{77} +(8.26375 + 16.2185i) q^{78} +(-81.7963 - 26.5772i) q^{79} +(67.4879 - 32.6000i) q^{80} +(30.9880 + 95.3712i) q^{81} +(-3.40340 - 3.40340i) q^{82} +(19.1762 + 9.77074i) q^{83} +(-29.5978 + 40.7379i) q^{84} +(13.2168 + 19.0286i) q^{85} +(13.9779 - 10.1556i) q^{86} +(-10.9970 - 69.4320i) q^{87} +(43.6074 - 6.90673i) q^{88} +(52.7361 + 72.5850i) q^{89} +(2.30583 + 7.64557i) q^{90} +(-44.9056 - 32.6258i) q^{91} +(20.6153 - 40.4599i) q^{92} +(58.9350 - 58.9350i) q^{93} +(6.25825 - 2.03343i) q^{94} +(0.958111 - 5.31580i) q^{95} +(-15.9753 + 49.1670i) q^{96} +(-83.7126 + 42.6537i) q^{97} +(1.71176 - 10.8076i) q^{98} -105.082i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 2 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 - 6 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 + 4 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 6 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 58 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 - 86 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 - 6 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 16 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 70 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 114 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 138 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 - 66 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 80 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 62 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 - 6 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 - 6 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 174 * q^96 + 270 * q^97 + 170 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more