LMFDB - Embedded newform 25.5.f.a.2.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,5,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, 5, names="a")

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

chi := DirichletCharacter("25.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 5 $
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:	$2.58424907710$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ 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			25.5.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)

$f(q)$	$=$	$q+(-4.54749 - 0.720251i) q^{2} +(0.590325 + 1.15858i) q^{3} +(4.94395 + 1.60639i) q^{4} +(22.6193 + 10.6475i) q^{5} +(-1.85003 - 5.69380i) q^{6} +(49.8348 + 49.8348i) q^{7} +(44.3120 + 22.5781i) q^{8} +(46.6168 - 64.1625i) q^{9} +O(q^{10})$	\(q+(-4.54749 - 0.720251i) q^{2} +(0.590325 + 1.15858i) q^{3} +(4.94395 + 1.60639i) q^{4} +(22.6193 + 10.6475i) q^{5} +(-1.85003 - 5.69380i) q^{6} +(49.8348 + 49.8348i) q^{7} +(44.3120 + 22.5781i) q^{8} +(46.6168 - 64.1625i) q^{9} +(-95.1920 - 64.7107i) q^{10} +(-143.024 + 103.913i) q^{11} +(1.05741 + 6.67625i) q^{12} +(67.0443 - 10.6188i) q^{13} +(-190.730 - 262.517i) q^{14} +(1.01681 + 32.4917i) q^{15} +(-252.535 - 183.478i) q^{16} +(-66.5233 + 130.559i) q^{17} +(-258.202 + 258.202i) q^{18} +(497.602 - 161.681i) q^{19} +(94.7247 + 88.9759i) q^{20} +(-28.3188 + 87.1563i) q^{21} +(725.241 - 369.529i) q^{22} +(-36.0271 + 227.466i) q^{23} +64.6673i q^{24} +(398.263 + 481.676i) q^{25} -312.531 q^{26} +(205.884 + 32.6088i) q^{27} +(166.327 + 326.435i) q^{28} +(-908.493 - 295.187i) q^{29} +(18.7782 - 148.488i) q^{30} +(-163.015 - 501.708i) q^{31} +(453.592 + 453.592i) q^{32} +(-204.822 - 104.362i) q^{33} +(396.549 - 545.803i) q^{34} +(596.613 + 1657.84i) q^{35} +(333.541 - 242.332i) q^{36} +(-340.736 - 2151.32i) q^{37} +(-2379.29 + 376.843i) q^{38} +(51.8806 + 71.4075i) q^{39} +(761.905 + 982.510i) q^{40} +(-260.416 - 189.203i) q^{41} +(191.554 - 375.945i) q^{42} +(-167.975 + 167.975i) q^{43} +(-874.027 + 283.989i) q^{44} +(1737.61 - 954.959i) q^{45} +(327.665 - 1008.45i) q^{46} +(-1106.60 + 563.841i) q^{47} +(63.4953 - 400.894i) q^{48} +2566.02i q^{49} +(-1464.17 - 2477.26i) q^{50} -190.534 q^{51} +(348.522 + 55.2004i) q^{52} +(-804.513 - 1578.95i) q^{53} +(-912.769 - 296.577i) q^{54} +(-4341.50 + 827.593i) q^{55} +(1083.10 + 3333.45i) q^{56} +(481.067 + 481.067i) q^{57} +(3918.75 + 1996.70i) q^{58} +(3661.50 - 5039.63i) q^{59} +(-47.1672 + 162.271i) q^{60} +(-14.9795 + 10.8832i) q^{61} +(379.952 + 2398.92i) q^{62} +(5520.67 - 874.388i) q^{63} +(1199.64 + 1651.16i) q^{64} +(1629.56 + 473.663i) q^{65} +(856.257 + 622.107i) q^{66} +(-3038.35 + 5963.09i) q^{67} +(-538.617 + 538.617i) q^{68} +(-284.805 + 92.5388i) q^{69} +(-1519.03 - 7968.72i) q^{70} +(-958.321 + 2949.41i) q^{71} +(3514.35 - 1790.65i) q^{72} +(1202.72 - 7593.67i) q^{73} +10028.5i q^{74} +(-322.954 + 745.764i) q^{75} +2719.85 q^{76} +(-12306.0 - 1949.09i) q^{77} +(-184.495 - 362.092i) q^{78} +(-3086.48 - 1002.86i) q^{79} +(-3758.60 - 6838.99i) q^{80} +(-1901.38 - 5851.85i) q^{81} +(1047.96 + 1047.96i) q^{82} +(4385.29 + 2234.42i) q^{83} +(-280.014 + 385.406i) q^{84} +(-2894.83 + 2244.85i) q^{85} +(884.848 - 642.880i) q^{86} +(-194.309 - 1226.82i) q^{87} +(-8683.81 + 1375.38i) q^{88} +(-4866.16 - 6697.70i) q^{89} +(-8589.55 + 3091.15i) q^{90} +(3870.33 + 2811.96i) q^{91} +(-543.515 + 1066.71i) q^{92} +(485.037 - 485.037i) q^{93} +(5438.36 - 1767.03i) q^{94} +(12976.9 + 1641.10i) q^{95} +(-257.755 + 793.289i) q^{96} +(2729.29 - 1390.64i) q^{97} +(1848.18 - 11668.9i) q^{98} +14020.8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9}+O(q^{10}) $ 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9} - 6 q^{11} - 178 q^{12} - 288 q^{13} - 10 q^{14} + 410 q^{15} + 762 q^{16} + 1042 q^{17} - 28 q^{18} - 1310 q^{19} - 3790 q^{20} - 6 q^{21} - 3226 q^{22} - 578 q^{23} + 1110 q^{25} - 976 q^{26} + 5120 q^{27} + 10318 q^{28} + 3290 q^{29} + 5270 q^{30} - 6 q^{31} - 1298 q^{32} - 2806 q^{33} - 8010 q^{34} - 5360 q^{35} - 2758 q^{36} + 4692 q^{37} + 14480 q^{38} + 8790 q^{39} + 2540 q^{40} + 1434 q^{41} - 23886 q^{42} - 14958 q^{43} - 22060 q^{44} - 23420 q^{45} - 6 q^{46} - 12158 q^{47} - 14168 q^{48} + 8050 q^{50} - 16 q^{51} + 29372 q^{52} + 22852 q^{53} + 53940 q^{54} + 18070 q^{55} - 1030 q^{56} + 34150 q^{57} + 23000 q^{58} + 23240 q^{59} + 40610 q^{60} + 2634 q^{61} - 13716 q^{62} - 42428 q^{63} - 66060 q^{64} - 41870 q^{65} + 5178 q^{66} - 25558 q^{67} - 71982 q^{68} - 39560 q^{69} - 38130 q^{70} + 7974 q^{71} - 37860 q^{72} - 4228 q^{73} + 21210 q^{75} - 1040 q^{76} + 34374 q^{77} + 51844 q^{78} + 26590 q^{79} + 110710 q^{80} - 14368 q^{81} + 145614 q^{82} + 99832 q^{83} + 149990 q^{84} + 48860 q^{85} - 6 q^{86} - 31320 q^{87} - 95490 q^{88} - 93760 q^{89} - 207250 q^{90} - 6 q^{91} - 199958 q^{92} - 134396 q^{93} - 130410 q^{94} - 50290 q^{95} + 17694 q^{96} - 40108 q^{97} - 25052 q^{98}+O(q^{100}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9 - 6 * q^11 - 178 * q^12 - 288 * q^13 - 10 * q^14 + 410 * q^15 + 762 * q^16 + 1042 * q^17 - 28 * q^18 - 1310 * q^19 - 3790 * q^20 - 6 * q^21 - 3226 * q^22 - 578 * q^23 + 1110 * q^25 - 976 * q^26 + 5120 * q^27 + 10318 * q^28 + 3290 * q^29 + 5270 * q^30 - 6 * q^31 - 1298 * q^32 - 2806 * q^33 - 8010 * q^34 - 5360 * q^35 - 2758 * q^36 + 4692 * q^37 + 14480 * q^38 + 8790 * q^39 + 2540 * q^40 + 1434 * q^41 - 23886 * q^42 - 14958 * q^43 - 22060 * q^44 - 23420 * q^45 - 6 * q^46 - 12158 * q^47 - 14168 * q^48 + 8050 * q^50 - 16 * q^51 + 29372 * q^52 + 22852 * q^53 + 53940 * q^54 + 18070 * q^55 - 1030 * q^56 + 34150 * q^57 + 23000 * q^58 + 23240 * q^59 + 40610 * q^60 + 2634 * q^61 - 13716 * q^62 - 42428 * q^63 - 66060 * q^64 - 41870 * q^65 + 5178 * q^66 - 25558 * q^67 - 71982 * q^68 - 39560 * q^69 - 38130 * q^70 + 7974 * q^71 - 37860 * q^72 - 4228 * q^73 + 21210 * q^75 - 1040 * q^76 + 34374 * q^77 + 51844 * q^78 + 26590 * q^79 + 110710 * q^80 - 14368 * q^81 + 145614 * q^82 + 99832 * q^83 + 149990 * q^84 + 48860 * q^85 - 6 * q^86 - 31320 * q^87 - 95490 * q^88 - 93760 * q^89 - 207250 * q^90 - 6 * q^91 - 199958 * q^92 - 134396 * q^93 - 130410 * q^94 - 50290 * q^95 + 17694 * q^96 - 40108 * q^97 - 25052 * 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 $

$2$	−4.54749	−	0.720251i	−1.13687	−	0.180063i	−0.440506	−	0.897750i	$-0.645201\pi$
$2$	−4.54749	−	0.720251i	−1.13687	−	0.180063i	−0.696366	+	0.717687i	$0.745201\pi$
$3$	0.590325	+	1.15858i	0.0655917	+	0.128731i	0.921474	−	0.388439i	$-0.126986\pi$
$3$	0.590325	+	1.15858i	0.0655917	+	0.128731i	−0.855883	+	0.517170i	$0.826986\pi$
$4$	4.94395	+	1.60639i	0.308997	+	0.100399i
$5$	22.6193	+	10.6475i	0.904771	+	0.425898i
$5$	22.6193	+	10.6475i	0.904771	+	0.425898i
$6$	−1.85003	−	5.69380i	−0.0513897	−	0.158161i
$7$	49.8348	+	49.8348i	1.01704	+	1.01704i	0.999852	+	0.0171850i	$0.00547043\pi$
$7$	49.8348	+	49.8348i	1.01704	+	1.01704i	0.0171850	+	0.999852i	$0.494530\pi$
$8$	44.3120	+	22.5781i	0.692375	+	0.352782i
$9$	46.6168	−	64.1625i	0.575516	−	0.792130i
$10$	−95.1920	−	64.7107i	−0.951920	−	0.647107i
$11$	−143.024	+	103.913i	−1.18201	+	0.858784i	−0.992397	−	0.123075i	$-0.960725\pi$
$11$	−143.024	+	103.913i	−1.18201	+	0.858784i	−0.189617	+	0.981858i	$0.560725\pi$
$12$	1.05741	+	6.67625i	0.00734315	+	0.0463629i
$13$	67.0443	−	10.6188i	0.396712	−	0.0628330i	0.0451086	−	0.998982i	$-0.485637\pi$
$13$	67.0443	−	10.6188i	0.396712	−	0.0628330i	0.351603	+	0.936149i	$0.385637\pi$
$14$	−190.730	−	262.517i	−0.973110	−	1.33937i
$15$	1.01681	+	32.4917i	0.00451914	+	0.144407i
$16$	−252.535	−	183.478i	−0.986466	−	0.716710i
$17$	−66.5233	+	130.559i	−0.230184	+	0.451762i	−0.976991	−	0.213278i	$-0.931586\pi$
$17$	−66.5233	+	130.559i	−0.230184	+	0.451762i	0.746807	+	0.665041i	$0.231586\pi$
$18$	−258.202	+	258.202i	−0.796920	+	0.796920i
$19$	497.602	−	161.681i	1.37840	−	0.447869i	0.476257	−	0.879306i	$-0.341993\pi$
$19$	497.602	−	161.681i	1.37840	−	0.447869i	0.902143	+	0.431437i	$0.141993\pi$
$20$	94.7247	+	88.9759i	0.236812	+	0.222440i
$21$	−28.3188	+	87.1563i	−0.0642150	+	0.197633i
$22$	725.241	−	369.529i	1.49843	−	0.763490i
$23$	−36.0271	+	227.466i	−0.0681042	+	0.429993i	0.929952	+	0.367680i	$0.119848\pi$
$23$	−36.0271	+	227.466i	−0.0681042	+	0.429993i	−0.998057	+	0.0623131i	$0.980152\pi$
$24$			64.6673i			0.112270i
$25$	398.263	+	481.676i	0.637221	+	0.770681i
$26$	−312.531			−0.462324
$27$	205.884	+	32.6088i	0.282420	+	0.0447309i
$28$	166.327	+	326.435i	0.212152	+	0.416371i
$29$	−908.493	−	295.187i	−1.08025	−	0.350995i	−0.285780	−	0.958295i	$-0.592253\pi$
$29$	−908.493	−	295.187i	−1.08025	−	0.350995i	−0.794473	+	0.607300i	$0.792253\pi$
$30$	18.7782	−	148.488i	0.0208647	−	0.164986i
$31$	−163.015	−	501.708i	−0.169631	−	0.522069i	0.829717	−	0.558184i	$-0.188502\pi$
$31$	−163.015	−	501.708i	−0.169631	−	0.522069i	−0.999348	+	0.0361150i	$0.988502\pi$
$32$	453.592	+	453.592i	0.442961	+	0.442961i
$33$	−204.822	−	104.362i	−0.188082	−	0.0958327i
$34$	396.549	−	545.803i	0.343036	−	0.472148i
$35$	596.613	+	1657.84i	0.487031	+	1.35334i
$36$	333.541	−	242.332i	0.257362	−	0.186984i
$37$	−340.736	−	2151.32i	−0.248894	−	1.57145i	−0.722913	−	0.690939i	$-0.757197\pi$
$37$	−340.736	−	2151.32i	−0.248894	−	1.57145i	0.474019	−	0.880515i	$-0.342803\pi$
$38$	−2379.29	+	376.843i	−1.64771	+	0.260971i
$39$	51.8806	+	71.4075i	0.0341095	+	0.0469478i
$40$	761.905	+	982.510i	0.476191	+	0.614069i
$41$	−260.416	−	189.203i	−0.154917	−	0.112554i	0.507626	−	0.861577i	$-0.330523\pi$
$41$	−260.416	−	189.203i	−0.154917	−	0.112554i	−0.662544	+	0.749023i	$0.730523\pi$
$42$	191.554	−	375.945i	0.108591	−	0.213121i
$43$	−167.975	+	167.975i	−0.0908464	+	0.0908464i	−0.751070	−	0.660223i	$-0.770462\pi$
$43$	−167.975	+	167.975i	−0.0908464	+	0.0908464i	0.660223	+	0.751070i	$0.270462\pi$
$44$	−874.027	+	283.989i	−0.451460	+	0.146688i
$45$	1737.61	−	954.959i	0.858077	−	0.471585i
$46$	327.665	−	1008.45i	0.154851	−	0.476583i
$47$	−1106.60	+	563.841i	−0.500951	+	0.255247i	−0.686158	−	0.727452i	$-0.740704\pi$
$47$	−1106.60	+	563.841i	−0.500951	+	0.255247i	0.185207	+	0.982699i	$0.440704\pi$
$48$	63.4953	−	400.894i	0.0275587	−	0.173999i
$49$			2566.02i			1.06873i
$50$	−1464.17	−	2477.26i	−0.585667	−	0.990905i
$51$	−190.534			−0.0732540
$52$	348.522	+	55.2004i	0.128891	+	0.0204144i
$53$	−804.513	−	1578.95i	−0.286406	−	0.562103i	0.702316	−	0.711865i	$-0.252149\pi$
$53$	−804.513	−	1578.95i	−0.286406	−	0.562103i	−0.988722	+	0.149762i	$0.952149\pi$
$54$	−912.769	−	296.577i	−0.313021	−	0.101707i
$55$	−4341.50	+	827.593i	−1.43521	+	0.273584i
$56$	1083.10	+	3333.45i	0.345378	+	1.06296i
$57$	481.067	+	481.067i	0.148066	+	0.148066i
$58$	3918.75	+	1996.70i	1.16491	+	0.593550i
$59$	3661.50	−	5039.63i	1.05185	−	1.44775i	0.164663	−	0.986350i	$-0.447346\pi$
$59$	3661.50	−	5039.63i	1.05185	−	1.44775i	0.887191	−	0.461403i	$-0.152654\pi$
$60$	−47.1672	+	162.271i	−0.0131020	+	0.0450752i
$61$	−14.9795	+	10.8832i	−0.00402566	+	0.00292482i	−0.589796	−	0.807552i	$-0.700792\pi$
$61$	−14.9795	+	10.8832i	−0.00402566	+	0.00292482i	0.585771	+	0.810477i	$0.300792\pi$
$62$	379.952	+	2398.92i	0.0988429	+	0.624070i
$63$	5520.67	−	874.388i	1.39095	−	0.220304i
$64$	1199.64	+	1651.16i	0.292881	+	0.403116i
$65$	1629.56	+	473.663i	0.385694	+	0.112110i
$66$	856.257	+	622.107i	0.196569	+	0.142816i
$67$	−3038.35	+	5963.09i	−0.676843	+	1.32838i	0.255502	+	0.966808i	$0.417759\pi$
$67$	−3038.35	+	5963.09i	−0.676843	+	1.32838i	−0.932345	+	0.361570i	$0.882241\pi$
$68$	−538.617	+	538.617i	−0.116483	+	0.116483i
$69$	−284.805	+	92.5388i	−0.0598204	+	0.0194368i
$70$	−1519.03	−	7968.72i	−0.310006	−	1.62627i
$71$	−958.321	+	2949.41i	−0.190105	+	0.585084i	−0.999999	−	0.00149280i	$-0.999525\pi$
$71$	−958.321	+	2949.41i	−0.190105	+	0.585084i	0.809894	+	0.586577i	$0.199525\pi$
$72$	3514.35	−	1790.65i	0.677922	−	0.345418i
$73$	1202.72	−	7593.67i	0.225693	−	1.42497i	−0.571180	−	0.820825i	$-0.693514\pi$
$73$	1202.72	−	7593.67i	0.225693	−	1.42497i	0.796873	−	0.604147i	$-0.206486\pi$
$74$			10028.5i			1.83136i
$75$	−322.954	+	745.764i	−0.0574141	+	0.132580i
$76$	2719.85			0.470887
$77$	−12306.0	−	1949.09i	−2.07557	−	0.328738i
$78$	−184.495	−	362.092i	−0.0303246	−	0.0595154i
$79$	−3086.48	−	1002.86i	−0.494549	−	0.160689i	0.0511147	−	0.998693i	$-0.483723\pi$
$79$	−3086.48	−	1002.86i	−0.494549	−	0.160689i	−0.545664	+	0.838004i	$0.683723\pi$
$80$	−3758.60	−	6838.99i	−0.587281	−	1.06859i
$81$	−1901.38	−	5851.85i	−0.289800	−	0.891914i
$82$	1047.96	+	1047.96i	0.155854	+	0.155854i
$83$	4385.29	+	2234.42i	0.636564	+	0.324346i	0.742319	−	0.670047i	$-0.233726\pi$
$83$	4385.29	+	2234.42i	0.636564	+	0.324346i	−0.105755	+	0.994392i	$0.533726\pi$
$84$	−280.014	+	385.406i	−0.0396845	+	0.0546210i
$85$	−2894.83	+	2244.85i	−0.400669	+	0.310706i
$86$	884.848	−	642.880i	0.119639	−	0.0869226i
$87$	−194.309	−	1226.82i	−0.0256716	−	0.162084i
$88$	−8683.81	+	1375.38i	−1.12136	+	0.177606i
$89$	−4866.16	−	6697.70i	−0.614337	−	0.845562i	0.382589	−	0.923919i	$-0.375033\pi$
$89$	−4866.16	−	6697.70i	−0.614337	−	0.845562i	−0.996925	+	0.0783567i	$0.975033\pi$
$90$	−8589.55	+	3091.15i	−1.06044	+	0.381623i
$91$	3870.33	+	2811.96i	0.467374	+	0.339567i
$92$	−543.515	+	1066.71i	−0.0642150	+	0.126029i
$93$	485.037	−	485.037i	0.0560801	−	0.0560801i
$94$	5438.36	−	1767.03i	0.615478	−	0.199981i
$95$	12976.9	+	1641.10i	1.43788	+	0.181839i
$96$	−257.755	+	793.289i	−0.0279682	+	0.0860774i
$97$	2729.29	−	1390.64i	0.290073	−	0.147799i	−0.302899	−	0.953023i	$-0.597955\pi$
$97$	2729.29	−	1390.64i	0.290073	−	0.147799i	0.592972	+	0.805223i	$0.297955\pi$
$98$	1848.18	−	11668.9i	0.192438	−	1.21501i
$99$			14020.8i			1.43055i
$100$	1195.24	+	3021.15i	0.119524	+	0.302115i
$101$	7811.83			0.765791			0.382895	−	0.923792i	$-0.374927\pi$
$101$	7811.83			0.765791			0.382895	+	0.923792i	$0.374927\pi$
$102$	866.449	+	137.232i	0.0832804	+	0.0131903i
$103$	3023.10	+	5933.17i	0.284956	+	0.559258i	0.988469	−	0.151425i	$-0.0483861\pi$
$103$	3023.10	+	5933.17i	0.284956	+	0.559258i	−0.703512	+	0.710683i	$0.748386\pi$
$104$	3210.62	+	1043.19i	0.296840	+	0.0964490i
$105$	−1568.54	+	1669.89i	−0.142272	+	0.151464i
$106$	2521.28	+	7759.69i	0.224393	+	0.690609i
$107$	4886.82	+	4886.82i	0.426833	+	0.426833i	0.887548	−	0.460715i	$-0.152407\pi$
$107$	4886.82	+	4886.82i	0.426833	+	0.426833i	−0.460715	+	0.887548i	$0.652407\pi$
$108$	965.500	+	491.947i	0.0827760	+	0.0421765i
$109$	670.477	−	922.833i	0.0564327	−	0.0776730i	−0.779868	−	0.625944i	$-0.784714\pi$
$109$	670.477	−	922.833i	0.0564327	−	0.0776730i	0.836301	+	0.548271i	$0.184714\pi$
$110$	20339.0	−	636.496i	1.68091	−	0.0526030i
$111$	2291.33	−	1664.75i	0.185969	−	0.135115i
$112$	−3441.48	−	21728.6i	−0.274353	−	1.73219i
$113$	−12532.5	+	1984.95i	−0.981478	+	0.155451i	−0.626498	−	0.779423i	$-0.715512\pi$
$113$	−12532.5	+	1984.95i	−0.981478	+	0.155451i	−0.354980	+	0.934874i	$0.615512\pi$
$114$	−1841.16	−	2534.13i	−0.141671	−	0.194993i
$115$	−3236.84	+	4761.52i	−0.244752	+	0.360040i
$116$	−4017.36	−	2918.78i	−0.298555	−	0.216913i
$117$	2444.06	−	4796.74i	0.178542	−	0.350409i
$118$	−20280.4	+	20280.4i	−1.45651	+	1.45651i
$119$	−9821.58	+	3191.23i	−0.693566	+	0.225353i
$120$	−688.543	+	1462.73i	−0.0478155	+	0.101578i
$121$	5133.59	−	15799.6i	0.350631	−	1.07913i
$122$	75.9577	−	38.7024i	0.00510331	−	0.00260027i
$123$	65.4767	−	413.404i	0.00432789	−	0.0273253i
$124$		−	2742.29i		−	0.178349i
$125$	3879.80	+	15135.6i	0.248307	+	0.968681i
$126$	−25734.9			−1.62100
$127$	11792.9	+	1867.82i	0.731164	+	0.115805i	0.510906	−	0.859637i	$-0.329310\pi$
$127$	11792.9	+	1867.82i	0.731164	+	0.115805i	0.220258	+	0.975442i	$0.429310\pi$
$128$	−8925.68	−	17517.6i	−0.544780	−	1.06919i
$129$	−293.772	−	95.4523i	−0.0176535	−	0.00573597i
$130$	−7069.23	−	3327.66i	−0.418297	−	0.196903i
$131$	−5071.99	−	15610.0i	−0.295554	−	0.909620i	−0.983035	−	0.183418i	$-0.941284\pi$
$131$	−5071.99	−	15610.0i	−0.295554	−	0.909620i	0.687481	−	0.726202i	$-0.258716\pi$
$132$	−844.983	−	844.983i	−0.0484954	−	0.0484954i
$133$	32855.3	+	16740.6i	1.85738	+	0.946384i
$134$	18111.8	−	24928.7i	1.00867	−	1.38832i
$135$	4309.75	+	2929.73i	0.236475	+	0.160753i
$136$	−5895.56	+	4283.37i	−0.318748	+	0.231584i
$137$	4613.22	+	29126.7i	0.245789	+	1.55185i	0.734014	+	0.679134i	$0.237644\pi$
$137$	4613.22	+	29126.7i	0.245789	+	1.55185i	−0.488225	+	0.872718i	$0.662356\pi$
$138$	1361.80	−	215.688i	0.0715080	−	0.0113258i
$139$	−13312.4	−	18322.9i	−0.689010	−	0.948341i	0.310988	−	0.950414i	$-0.399340\pi$
$139$	−13312.4	−	18322.9i	−0.689010	−	0.948341i	−0.999998	+	0.00207271i	$0.999340\pi$
$140$	286.491	+	9154.69i	0.0146169	+	0.467076i
$141$	−1306.51	−	949.234i	−0.0657165	−	0.0477458i
$142$	6482.26	−	12722.2i	0.321477	−	0.630934i
$143$	−8485.50	+	8485.50i	−0.414959	+	0.414959i
$144$	−23544.8	+	7650.16i	−1.13545	+	0.368931i
$145$	−17406.5	−	16350.1i	−0.827893	−	0.777649i
$146$	−10938.7	+	33665.9i	−0.513169	+	1.57937i
$147$	−2972.94	+	1514.79i	−0.137579	+	0.0700998i
$148$	1771.27	−	11183.4i	0.0808653	−	0.510564i
$149$		−	36399.6i		−	1.63955i	−0.572686	−	0.819774i	$-0.694099\pi$
$149$		−	36399.6i		−	1.63955i	0.572686	−	0.819774i	$-0.305901\pi$
$150$	2005.77	−	3158.74i	0.0891452	−	0.140389i
$151$	−14149.6			−0.620568			−0.310284	−	0.950644i	$-0.600424\pi$
$151$	−14149.6			−0.620568			−0.310284	+	0.950644i	$0.600424\pi$
$152$	25700.2	+	4070.51i	1.11237	+	0.176182i
$153$	5275.91	+	10354.6i	0.225380	+	0.442332i
$154$	54557.7	+	17726.9i	2.30046	+	0.747465i
$155$	1654.64	−	13084.0i	0.0688717	−	0.544598i
$156$	141.787	+	436.376i	0.00582623	+	0.0179313i
$157$	−13278.9	−	13278.9i	−0.538720	−	0.538720i	0.384433	−	0.923153i	$-0.374397\pi$
$157$	−13278.9	−	13278.9i	−0.538720	−	0.538720i	−0.923153	+	0.384433i	$0.874397\pi$
$158$	13313.4	+	6783.53i	0.533305	+	0.271732i
$159$	1354.41	−	1864.18i	0.0535742	−	0.0737385i
$160$	5430.32	+	15089.5i	0.212122	+	0.589435i
$161$	−13131.1	+	9540.33i	−0.506583	+	0.368054i
$162$	4431.70	+	27980.7i	0.168865	+	1.06617i
$163$	−18499.6	+	2930.05i	−0.696285	+	0.110281i	−0.494537	−	0.869157i	$-0.664662\pi$
$163$	−18499.6	+	2930.05i	−0.696285	+	0.110281i	−0.201748	+	0.979437i	$0.564662\pi$
$164$	−983.551	−	1353.74i	−0.0365687	−	0.0503324i
$165$	−3521.73	−	4541.42i	−0.129356	−	0.166811i
$166$	−18332.7	−	13319.5i	−0.665289	−	0.483361i
$167$	324.049	−	635.983i	0.0116193	−	0.0228041i	−0.885124	−	0.465355i	$-0.845927\pi$
$167$	324.049	−	635.983i	0.0116193	−	0.0228041i	0.896743	+	0.442551i	$0.145927\pi$
$168$	−3222.68	+	3222.68i	−0.114182	+	0.114182i
$169$	−22780.9	+	7401.98i	−0.797624	+	0.259164i
$170$	14781.1	−	8123.43i	0.511456	−	0.281088i
$171$	12822.8	−	39464.4i	0.438520	−	1.34963i
$172$	−1100.29	+	560.628i	−0.0371922	+	0.0189504i
$173$	3438.83	−	21711.9i	0.114900	−	0.725447i	−0.861223	−	0.508227i	$-0.830301\pi$
$173$	3438.83	−	21711.9i	0.114900	−	0.725447i	0.976123	−	0.217220i	$-0.0696989\pi$
$174$			5718.88i			0.188892i
$175$	−4156.85	+	43851.6i	−0.135734	+	1.43189i
$176$	55184.2			1.78152
$177$	8000.28	+	1267.12i	0.255363	+	0.0404456i
$178$	17304.8	+	33962.5i	0.546168	+	1.07191i
$179$	11830.8	+	3844.07i	0.369241	+	0.119974i	0.487759	−	0.872978i	$-0.337814\pi$
$179$	11830.8	+	3844.07i	0.369241	+	0.119974i	−0.118518	+	0.992952i	$0.537814\pi$
$180$	10124.7	−	1930.00i	0.312490	−	0.0595680i
$181$	11933.3	+	36726.9i	0.364253	+	1.12105i	0.950448	+	0.310884i	$0.100625\pi$
$181$	11933.3	+	36726.9i	0.364253	+	1.12105i	−0.586195	+	0.810170i	$0.699375\pi$
$182$	−15574.9	−	15574.9i	−0.470201	−	0.470201i
$183$	−21.4519	−	10.9303i	−0.000640564	−	0.000326384i
$184$	−6732.18	+	9266.05i	−0.198847	+	0.273690i
$185$	15198.9	−	52289.3i	0.444088	−	1.52781i
$186$	−2555.05	+	1856.35i	−0.0738538	+	0.0536579i
$187$	−4052.38	−	25585.7i	−0.115885	−	0.731668i
$188$	−6376.73	+	1009.98i	−0.180419	+	0.0285756i
$189$	8635.15	+	11885.3i	0.241739	+	0.332725i
$190$	−57830.2	−	16809.5i	−1.60195	−	0.465637i
$191$	17570.7	+	12765.8i	0.481639	+	0.349931i	0.801960	−	0.597378i	$-0.203791\pi$
$191$	17570.7	+	12765.8i	0.481639	+	0.349931i	−0.320321	+	0.947309i	$0.603791\pi$
$192$	−1204.82	+	2364.60i	−0.0326829	+	0.0641439i
$193$	6502.07	−	6502.07i	0.174557	−	0.174557i	−0.614421	−	0.788978i	$-0.710610\pi$
$193$	6502.07	−	6502.07i	0.174557	−	0.174557i	0.788978	+	0.614421i	$0.210610\pi$
$194$	−13413.0	+	4358.16i	−0.356388	+	0.115798i
$195$	413.193	+	2167.58i	0.0108663	+	0.0570042i
$196$	−4122.03	+	12686.3i	−0.107300	+	0.330235i
$197$	−49166.0	+	25051.3i	−1.26687	+	0.645503i	−0.952714	−	0.303868i	$-0.901722\pi$
$197$	−49166.0	+	25051.3i	−1.26687	+	0.645503i	−0.314157	+	0.949371i	$0.601722\pi$
$198$	10098.5	−	63759.6i	0.257589	−	1.62635i
$199$			9413.31i			0.237704i	0.992912	+	0.118852i	$0.0379214\pi$
$199$			9413.31i			0.237704i	−0.992912	+	0.118852i	$0.962079\pi$
$200$	6772.51	+	30336.0i	0.169313	+	0.758400i
$201$	−8702.32			−0.215399
$202$	−35524.2	−	5626.48i	−0.870606	−	0.137890i
$203$	−30564.0	−	59985.2i	−0.741682	−	1.45563i
$204$	−941.990	−	306.071i	−0.0226353	−	0.00735465i
$205$	−3875.89	−	7052.41i	−0.0922281	−	0.167815i
$206$	−9474.14	−	29158.4i	−0.223257	−	0.687115i
$207$	12915.3	+	12915.3i	0.301415	+	0.301415i
$208$	−18879.4	−	9619.52i	−0.436376	−	0.222345i
$209$	−54368.2	+	74831.4i	−1.24467	+	1.71313i
$210$	8335.67	−	6464.05i	0.189017	−	0.146577i
$211$	42907.1	−	31173.8i	0.963749	−	0.700205i	0.00973088	−	0.999953i	$-0.496903\pi$
$211$	42907.1	−	31173.8i	0.963749	−	0.700205i	0.954018	+	0.299748i	$0.0969025\pi$
$212$	−1441.08	−	9098.60i	−0.0320638	−	0.202443i
$213$	−3982.84	+	630.820i	−0.0877878	+	0.0139042i
$214$	−18703.0	−	25742.5i	−0.408398	−	0.562112i
$215$	−5587.98	+	2010.96i	−0.120887	+	0.0435038i
$216$	8386.89	+	6093.43i	0.179760	+	0.130603i
$217$	16878.7	−	33126.4i	0.358443	−	0.703484i
$218$	−3713.66	+	3713.66i	−0.0781428	+	0.0781428i
$219$	9507.86	−	3089.29i	0.198242	−	0.0644126i
$220$	−22793.6	−	2882.55i	−0.470942	−	0.0595569i
$221$	−3073.63	+	9459.66i	−0.0629313	+	0.193683i
$222$	−11618.8	+	5920.08i	−0.235752	+	0.120122i
$223$	−9075.20	+	57298.6i	−0.182493	+	1.15222i	0.711017	+	0.703174i	$0.248235\pi$
$223$	−9075.20	+	57298.6i	−0.182493	+	1.15222i	−0.893511	+	0.449042i	$0.851765\pi$
$224$			45209.4i			0.901016i
$225$	49471.3	−	3099.38i	0.977210	−	0.0612224i
$226$	58421.0			1.14381
$227$	−1066.87	−	168.976i	−0.0207043	−	0.00327924i	0.146074	−	0.989274i	$-0.453336\pi$
$227$	−1066.87	−	168.976i	−0.0207043	−	0.00327924i	−0.166778	+	0.985994i	$0.553336\pi$
$228$	1605.59	+	3151.15i	0.0308863	+	0.0606178i
$229$	80669.6	+	26211.2i	1.53829	+	0.499822i	0.950905	−	0.309483i	$-0.100156\pi$
$229$	80669.6	+	26211.2i	1.53829	+	0.499822i	0.587388	+	0.809305i	$0.300156\pi$
$230$	18149.0	−	19321.6i	0.343081	−	0.365248i
$231$	−5006.40	−	15408.1i	−0.0938213	−	0.288752i
$232$	−33592.3	−	33592.3i	−0.624115	−	0.624115i
$233$	61524.9	+	31348.5i	1.13328	+	0.577437i	0.916998	−	0.398892i	$-0.130605\pi$
$233$	61524.9	+	31348.5i	1.13328	+	0.577437i	0.216287	+	0.976330i	$0.430605\pi$
$234$	−14569.2	+	20052.8i	−0.266075	+	0.366221i
$235$	−31034.0	+	971.191i	−0.561956	+	0.0175861i
$236$	26197.9	−	19033.9i	0.470373	−	0.341746i
$237$	−660.138	−	4167.95i	−0.0117527	−	0.0742037i
$238$	46962.0	−	7438.05i	0.829072	−	0.131312i
$239$	2958.27	+	4071.71i	0.0517896	+	0.0712823i	0.834126	−	0.551573i	$-0.185972\pi$
$239$	2958.27	+	4071.71i	0.0517896	+	0.0712823i	−0.782337	+	0.622856i	$0.785972\pi$
$240$	5704.72	−	8391.86i	0.0990402	−	0.145692i
$241$	83470.8	+	60645.1i	1.43714	+	1.04415i	0.988630	+	0.150371i	$0.0480468\pi$
$241$	83470.8	+	60645.1i	1.43714	+	1.04415i	0.448515	+	0.893776i	$0.351953\pi$
$242$	−34724.6	+	68150.8i	−0.592934	+	1.16370i
$243$	17596.5	−	17596.5i	0.297999	−	0.297999i
$244$	−91.5406	+	29.7434i	−0.00153757	+	0.000499586i
$245$	−27321.6	+	58041.5i	−0.455170	+	0.966956i
$246$	−595.509	+	1832.79i	−0.00984052	+	0.0302860i
$247$	31644.5	−	16123.7i	0.518687	−	0.264284i
$248$	4104.10	−	25912.3i	0.0667290	−	0.421310i
$249$			6399.74i			0.103220i
$250$	−6741.86	−	71623.6i	−0.107870	−	1.14598i
$251$	−122599.			−1.94599			−0.972996	−	0.230821i	$-0.925859\pi$
$251$	−122599.			−1.94599			−0.972996	+	0.230821i	$0.925859\pi$
$252$	28698.5	+	4545.40i	0.451917	+	0.0715766i
$253$	−18483.9	−	36276.7i	−0.288771	−	0.566744i
$254$	−52282.9	−	16987.8i	−0.810387	−	0.263311i
$255$	−4309.73	−	2028.70i	−0.0662781	−	0.0311988i
$256$	17881.3	+	55033.0i	0.272847	+	0.839736i
$257$	35139.9	+	35139.9i	0.532028	+	0.532028i	0.921176	−	0.389147i	$-0.127230\pi$
$257$	35139.9	+	35139.9i	0.532028	+	0.532028i	−0.389147	+	0.921176i	$0.627230\pi$
$258$	1267.17	+	645.658i	0.0190369	+	0.00969980i
$259$	90230.2	−	124191.i	1.34509	−	1.85136i
$260$	7295.57	+	4959.47i	0.107923	+	0.0733649i
$261$	−61291.0	+	44530.5i	−0.899737	+	0.653697i
$262$	11821.7	+	74639.3i	0.172218	+	1.08734i
$263$	−31722.4	+	5024.34i	−0.458622	+	0.0726386i	−0.381471	−	0.924381i	$-0.624582\pi$
$263$	−31722.4	+	5024.34i	−0.458622	+	0.0726386i	−0.0771510	+	0.997019i	$0.524582\pi$
$264$	−6719.76	−	9248.96i	−0.0964153	−	0.132704i
$265$	−1385.74	−	44280.7i	−0.0197328	−	0.630554i
$266$	−137351.	−	99791.6i	−1.94120	−	1.41036i
$267$	4887.19	−	9591.65i	0.0685546	−	0.134546i
$268$	−24600.5	+	24600.5i	−0.342511	+	0.342511i
$269$	7255.07	−	2357.32i	0.100262	−	0.0325772i	−0.258456	−	0.966023i	$-0.583214\pi$
$269$	7255.07	−	2357.32i	0.100262	−	0.0325772i	0.358719	+	0.933446i	$0.383214\pi$
$270$	−17488.4	−	16427.0i	−0.239895	−	0.225336i
$271$	−17413.0	+	53591.8i	−0.237102	+	0.729726i	0.759733	+	0.650235i	$0.225330\pi$
$271$	−17413.0	+	53591.8i	−0.237102	+	0.729726i	−0.996836	+	0.0794913i	$0.974670\pi$
$272$	40754.2	−	20765.3i	0.550852	−	0.280673i
$273$	−973.121	+	6144.04i	−0.0130569	+	0.0824383i
$274$		−	135776.i		−	1.80851i
$275$	−107013.	−	27506.4i	−1.41505	−	0.363721i
$276$	−1556.72			−0.0204358
$277$	−53426.3	−	8461.90i	−0.696299	−	0.110283i	−0.201756	−	0.979436i	$-0.564665\pi$
$277$	−53426.3	−	8461.90i	−0.696299	−	0.110283i	−0.494543	+	0.869153i	$0.664665\pi$
$278$	47340.7	+	92911.4i	0.612555	+	1.20221i
$279$	−39790.1	−	12928.6i	−0.511171	−	0.166090i
$280$	−10993.8	+	86932.6i	−0.140227	+	1.10883i
$281$	498.279	+	1533.54i	0.00631044	+	0.0194215i	0.954162	−	0.299290i	$-0.0967498\pi$
$281$	498.279	+	1533.54i	0.00631044	+	0.0194215i	−0.947852	+	0.318712i	$0.896750\pi$
$282$	5257.64	+	5257.64i	0.0661139	+	0.0661139i
$283$	−68761.1	−	35035.5i	−0.858558	−	0.437457i	−0.0314537	−	0.999505i	$-0.510014\pi$
$283$	−68761.1	−	35035.5i	−0.858558	−	0.437457i	−0.827105	+	0.562048i	$0.810014\pi$
$284$	−9475.79	+	13042.3i	−0.117484	+	0.161703i
$285$	5759.24	+	16003.5i	0.0709048	+	0.197027i
$286$	44699.4	−	32476.0i	0.546474	−	0.397036i
$287$	−3548.87	−	22406.7i	−0.0430850	−	0.272028i
$288$	50248.6	−	7958.60i	0.605814	−	0.0959515i
$289$	36472.0	+	50199.4i	0.436681	+	0.601040i
$290$	67379.4	+	86888.7i	0.801182	+	1.03316i
$291$	3222.34	+	2341.17i	0.0380527	+	0.0276469i
$292$	18144.6	−	35610.7i	0.212805	−	0.417653i
$293$	56554.7	−	56554.7i	0.658770	−	0.658770i	−0.296319	−	0.955089i	$-0.595759\pi$
$293$	56554.7	−	56554.7i	0.658770	−	0.658770i	0.955089	+	0.296319i	$0.0957592\pi$
$294$	14610.4	−	4747.21i	0.169032	−	0.0549217i
$295$	136480.	−	75007.0i	1.56828	−	0.861902i
$296$	33474.0	−	103022.i	0.382054	−	1.17584i
$297$	−32834.8	+	16730.2i	−0.372239	+	0.189665i
$298$	−26216.9	+	165527.i	−0.295222	+	1.86396i
$299$			15632.9i			0.174862i
$300$	−2794.66	+	3168.23i	−0.0310518	+	0.0352026i
$301$	−16742.0			−0.184788
$302$	64344.9	+	10191.2i	0.705506	+	0.111741i
$303$	4611.52	+	9050.62i	0.0502295	+	0.0985810i
$304$	−155327.	−	50468.8i	−1.68074	−	0.546105i
$305$	−454.704	+	86.6774i	−0.00488798	+	0.000931764i
$306$	−16534.2	−	50887.2i	−0.176580	−	0.543458i
$307$	32914.7	+	32914.7i	0.349231	+	0.349231i	0.859823	−	0.510592i	$-0.170574\pi$
$307$	32914.7	+	32914.7i	0.349231	+	0.349231i	−0.510592	+	0.859823i	$0.670574\pi$
$308$	−57709.5	−	29404.5i	−0.608339	−	0.309964i
$309$	−5089.43	+	7005.00i	−0.0533031	+	0.0733654i
$310$	−16948.2	+	58307.4i	−0.176360	+	0.606737i
$311$	−119250.	+	86640.2i	−1.23293	+	0.895775i	−0.997106	−	0.0760216i	$-0.975778\pi$
$311$	−119250.	+	86640.2i	−1.23293	+	0.895775i	−0.235822	+	0.971796i	$0.575778\pi$
$312$	686.687	+	4335.57i	0.00705423	+	0.0445387i
$313$	−89128.7	+	14116.6i	−0.909764	+	0.144092i	−0.593738	−	0.804658i	$-0.702349\pi$
$313$	−89128.7	+	14116.6i	−0.909764	+	0.144092i	−0.316026	+	0.948751i	$0.602349\pi$
$314$	50821.5	+	69949.8i	0.515452	+	0.709459i
$315$	134183.	+	39003.1i	1.35232	+	0.393077i
$316$	−13648.5	−	9916.18i	−0.136681	−	0.0993048i
$317$	69646.7	−	136689.i	0.693078	−	1.36024i	−0.229072	−	0.973409i	$-0.573569\pi$
$317$	69646.7	−	136689.i	0.693078	−	1.36024i	0.922150	−	0.386832i	$-0.126431\pi$
$318$	−7501.83	+	7501.83i	−0.0741845	+	0.0741845i
$319$	160610.	−	52185.3i	1.57830	−	0.512822i
$320$	9554.29	+	50121.2i	0.0933036	+	0.489465i
$321$	−2776.95	+	8546.57i	−0.0269499	+	0.0829434i
$322$	66585.1	−	33926.8i	0.642193	−	0.327214i
$323$	−11993.2	+	75722.2i	−0.114956	+	0.725802i
$324$		−	31985.6i		−	0.304695i
$325$	31816.1	+	28064.5i	0.301217	+	0.265700i
$326$	86237.0			0.811444
$327$	1464.97	+	232.029i	0.0137004	+	0.00216994i
$328$	−7267.70	−	14263.7i	−0.0675537	−	0.132582i
$329$	−83246.2	−	27048.3i	−0.769082	−	0.249890i
$330$	12744.0	+	23188.6i	0.117025	+	0.212934i
$331$	−19018.8	−	58533.9i	−0.173591	−	0.534259i	0.825975	−	0.563707i	$-0.190625\pi$
$331$	−19018.8	−	58533.9i	−0.173591	−	0.534259i	−0.999566	+	0.0294478i	$0.990625\pi$
$332$	18091.3	+	18091.3i	0.164132	+	0.164132i
$333$	−153918.	−	78425.2i	−1.38804	−	0.707240i
$334$	−1931.68	+	2658.72i	−0.0173158	+	0.0238331i
$335$	−132217.	+	102530.i	−1.17814	+	0.913612i
$336$	23142.7	−	16814.2i	0.204992	−	0.148935i
$337$	−16377.5	−	103404.i	−0.144208	−	0.910491i	−0.948619	−	0.316419i	$-0.897519\pi$
$337$	−16377.5	−	103404.i	−0.144208	−	0.910491i	0.804412	−	0.594072i	$-0.202481\pi$
$338$	108927.	−	17252.4i	0.953462	−	0.151014i
$339$	−9697.97	−	13348.1i	−0.0843881	−	0.116150i
$340$	−17918.0	+	6448.22i	−0.155000	+	0.0557805i
$341$	75448.9	+	54816.9i	0.648850	+	0.471417i
$342$	−86735.7	+	170228.i	−0.741559	+	1.45539i
$343$	−8223.77	+	8223.77i	−0.0699009	+	0.0699009i
$344$	−11235.9	+	3650.75i	−0.0949487	+	0.0308507i
$345$	−7427.39	−	939.291i	−0.0624019	−	0.00789155i
$346$	−31276.0	+	96257.8i	−0.261252	+	0.804051i
$347$	152581.	−	77743.8i	1.26719	−	0.645665i	0.314397	−	0.949291i	$-0.398198\pi$
$347$	152581.	−	77743.8i	1.26719	−	0.645665i	0.952791	+	0.303627i	$0.0981976\pi$
$348$	1010.09	−	6377.46i	0.00834069	−	0.0526610i
$349$			141899.i			1.16500i	0.812829	+	0.582502i	$0.197926\pi$
$349$			141899.i			1.16500i	−0.812829	+	0.582502i	$0.802074\pi$
$350$	50487.4	−	196421.i	0.412142	−	1.60343i
$351$	14149.6			0.114850
$352$	−112008.	−	17740.4i	−0.903994	−	0.143179i
$353$	22551.1	+	44259.0i	0.180975	+	0.355183i	0.963616	−	0.267290i	$-0.0861281\pi$
$353$	22551.1	+	44259.0i	0.180975	+	0.355183i	−0.782641	+	0.622473i	$0.786128\pi$
$354$	−35468.5	−	11524.4i	−0.283033	−	0.0919629i
$355$	−53080.2	+	56509.8i	−0.421188	+	0.448402i
$356$	−13299.0	−	40930.1i	−0.104935	−	0.322955i
$357$	−9495.21	−	9495.21i	−0.0745020	−	0.0745020i
$358$	−51031.9	−	26002.0i	−0.398176	−	0.202881i
$359$	−9742.31	+	13409.1i	−0.0755915	+	0.104043i	−0.845138	−	0.534547i	$-0.820482\pi$
$359$	−9742.31	+	13409.1i	−0.0755915	+	0.104043i	0.769547	+	0.638590i	$0.220482\pi$
$360$	98557.9	−	3084.31i	0.760477	−	0.0237987i
$361$	116036.	−	84304.7i	0.890382	−	0.646901i
$362$	−27813.9	−	175610.i	−0.212248	−	1.34008i
$363$	21335.5	−	3379.22i	0.161916	−	0.0256450i
$364$	14617.6	+	20119.4i	0.110325	+	0.151849i
$365$	108058.	−	158957.i	0.811094	−	1.19315i
$366$	89.6794	+	65.1559i	0.000669469	+	0.000486398i
$367$	−59522.7	+	116820.i	−0.441927	+	0.867330i	0.557386	+	0.830254i	$0.311805\pi$
$367$	−59522.7	+	116820.i	−0.441927	+	0.867330i	−0.999312	+	0.0370766i	$0.988195\pi$
$368$	50833.1	−	50833.1i	0.375363	−	0.375363i
$369$	−24279.5	+	7888.89i	−0.178315	+	0.0579380i
$370$	−106778.	+	226838.i	−0.779972	+	1.65696i
$371$	38593.7	−	118779.i	0.280394	−	0.862965i
$372$	3177.16	−	1618.84i	0.0229590	−	0.0116982i
$373$	−12819.2	+	80937.2i	−0.0921389	+	0.581742i	0.897817	+	0.440368i	$0.145152\pi$
$373$	−12819.2	+	80937.2i	−0.0921389	+	0.581742i	−0.989956	+	0.141374i	$0.954848\pi$
$374$			119269.i			0.852679i
$375$	−15245.5	+	13430.0i	−0.108412	+	0.0955022i
$376$	−61766.1			−0.436893
$377$	−64043.8	−	10143.5i	−0.450603	−	0.0713685i
$378$	−30707.8	−	60267.5i	−0.214914	−	0.421793i
$379$	−131370.	−	42684.7i	−0.914571	−	0.297162i	−0.186333	−	0.982487i	$-0.559660\pi$
$379$	−131370.	−	42684.7i	−0.914571	−	0.297162i	−0.728238	+	0.685325i	$0.759660\pi$
$380$	61520.9	+	28959.5i	0.426045	+	0.200550i
$381$	4797.66	+	14765.7i	0.0330506	+	0.101719i
$382$	−70707.7	−	70707.7i	−0.484551	−	0.484551i
$383$	−63887.4	−	32552.2i	−0.435529	−	0.221913i	0.222458	−	0.974942i	$-0.428592\pi$
$383$	−63887.4	−	32552.2i	−0.435529	−	0.221913i	−0.657987	+	0.753029i	$0.728592\pi$
$384$	15026.5	−	20682.2i	0.101905	−	0.140260i
$385$	−257601.	−	175115.i	−1.73790	−	1.18141i
$386$	−34251.2	+	24884.9i	−0.229880	+	0.167017i
$387$	2947.24	+	18608.1i	0.0196786	+	0.124246i
$388$	15727.4	−	2490.98i	0.104471	−	0.0165465i
$389$	−1395.18	−	1920.30i	−0.00922002	−	0.0126903i	0.804382	−	0.594112i	$-0.202497\pi$
$389$	−1395.18	−	1920.30i	−0.00922002	−	0.0126903i	−0.813602	+	0.581422i	$0.802497\pi$
$390$	−317.784	−	10154.7i	−0.00208931	−	0.0667630i
$391$	−27301.2	−	19835.5i	−0.178578	−	0.129745i
$392$	−57935.8	+	113705.i	−0.377029	+	0.739961i
$393$	15091.3	−	15091.3i	0.0977104	−	0.0977104i
$394$	241625.	−	78508.7i	1.55650	−	0.505738i
$395$	−59136.1	−	55547.2i	−0.379017	−	0.356014i
$396$	−22522.9	+	69318.4i	−0.143626	+	0.442037i
$397$	−172877.	+	88085.4i	−1.09687	+	0.558885i	−0.906235	−	0.422775i	$-0.861056\pi$
$397$	−172877.	+	88085.4i	−1.09687	+	0.558885i	−0.190640	+	0.981660i	$0.561056\pi$
$398$	6779.95	−	42806.9i	0.0428016	−	0.270239i
$399$			47947.8i			0.301178i
$400$	−12198.8	−	194713.i	−0.0762424	−	1.21695i
$401$	48861.7			0.303864			0.151932	−	0.988391i	$-0.451450\pi$
$401$	48861.7			0.303864			0.151932	+	0.988391i	$0.451450\pi$
$402$	39573.7	+	6267.85i	0.244881	+	0.0387853i
$403$	−16256.8	−	31905.7i	−0.100098	−	0.196453i
$404$	38621.3	+	12548.8i	0.236627	+	0.0768848i
$405$	19299.5	−	152609.i	0.117662	−	0.930404i
$406$	95784.8	+	294795.i	0.581092	+	1.78842i
$407$	272283.	+	272283.i	1.64373	+	1.64373i
$408$	−8442.92	−	4301.88i	−0.0507192	−	0.0258427i
$409$	−87308.1	+	120169.i	−0.521925	+	0.718368i	−0.985873	−	0.167494i	$-0.946432\pi$
$409$	−87308.1	+	120169.i	−0.521925	+	0.718368i	0.463948	+	0.885862i	$0.346432\pi$
$410$	12546.0	+	34862.3i	0.0746343	+	0.207390i
$411$	−31022.3	+	22539.0i	−0.183650	+	0.133429i
$412$	5415.10	+	34189.6i	0.0319016	+	0.201419i
$413$	433619.	−	68678.6i	2.54219	−	0.402644i
$414$	−49430.0	−	68034.6i	−0.288396	−	0.396944i
$415$	75401.2	+	97233.1i	0.437807	+	0.564570i
$416$	35227.4	+	25594.2i	0.203560	+	0.147895i
$417$	13369.9	−	26239.9i	0.0768875	−	0.150900i
$418$	301136.	−	301136.i	1.72350	−	1.72350i
$419$	145935.	−	47417.2i	0.831250	−	0.270090i	0.137678	−	0.990477i	$-0.456036\pi$
$419$	145935.	−	47417.2i	0.831250	−	0.270090i	0.693572	+	0.720388i	$0.256036\pi$
$420$	−10437.3	+	5736.17i	−0.0591684	+	0.0325179i
$421$	−33879.7	+	104271.i	−0.191150	+	0.588301i	0.808849	+	0.588016i	$0.200091\pi$
$421$	−33879.7	+	104271.i	−0.191150	+	0.588301i	−1.00000		0.000284964i	$0.999909\pi$
$422$	−217572.	+	110859.i	−1.22174	+	0.622508i
$423$	−15408.7	+	97286.8i	−0.0861163	+	0.543717i
$424$		−	88130.6i		−	0.490225i
$425$	−89381.1	+	19954.3i	−0.494843	+	0.110474i
$426$	18566.3			0.102307
$427$	−1288.86	−	204.136i	−0.00706890	−	0.00111960i
$428$	16310.1	+	32010.3i	0.0890366	+	0.174744i
$429$	−14840.3	−	4821.91i	−0.0806359	−	0.0262002i
$430$	26859.6	−	5120.09i	0.145266	−	0.0276911i
$431$	−30261.3	−	93134.6i	−0.162904	−	0.501368i	0.835971	−	0.548773i	$-0.184905\pi$
$431$	−30261.3	−	93134.6i	−0.162904	−	0.501368i	−0.998876	+	0.0474050i	$0.984905\pi$
$432$	−46010.0	−	46010.0i	−0.246539	−	0.246539i
$433$	196339.	+	100040.i	1.04720	+	0.533576i	0.890931	−	0.454138i	$-0.150053\pi$
$433$	196339.	+	100040.i	1.04720	+	0.533576i	0.156270	+	0.987714i	$0.450053\pi$
$434$	−100615.	+	138485.i	−0.534175	+	0.735229i
$435$	8667.36	−	29818.6i	0.0458045	−	0.157583i
$436$	4797.24	−	3485.40i	0.0252359	−	0.0183349i
$437$	18849.7	+	119013.i	0.0987058	+	0.623204i
$438$	−45461.9	+	7200.46i	−0.236973	+	0.0375329i
$439$	155035.	+	213387.i	0.804453	+	1.10723i	0.992156	+	0.125008i	$0.0398957\pi$
$439$	155035.	+	213387.i	0.804453	+	1.10723i	−0.187703	+	0.982226i	$0.560104\pi$
$440$	−211066.	−	61350.5i	−1.09022	−	0.316893i
$441$	164642.	+	119620.i	0.846573	+	0.615071i
$442$	20790.6	−	40803.9i	0.106420	−	0.208861i
$443$	−61230.4	+	61230.4i	−0.312003	+	0.312003i	−0.845685	−	0.533682i	$-0.820808\pi$
$443$	−61230.4	+	61230.4i	−0.312003	+	0.312003i	0.533682	+	0.845685i	$0.320808\pi$
$444$	14002.5	−	4549.67i	0.0710294	−	0.0230789i
$445$	−38755.6	−	203309.i	−0.195711	−	1.02669i
$446$	82538.7	−	254028.i	0.414942	−	1.27706i
$447$	42171.8	−	21487.6i	0.211061	−	0.107541i
$448$	−22501.6	+	142069.i	−0.112113	+	0.707855i
$449$		−	329623.i		−	1.63503i	−0.575908	−	0.817514i	$-0.695351\pi$
$449$		−	329623.i		−	1.63503i	0.575908	−	0.817514i	$-0.304649\pi$
$450$	−227202.	−	21537.3i	−1.12199	−	0.106357i
$451$	56906.3			0.279774
$452$	−65148.7	−	10318.5i	−0.318881	−	0.0505058i
$453$	−8352.85	−	16393.4i	−0.0407041	−	0.0798863i
$454$	4729.88	+	1536.83i	0.0229477	+	0.00745615i
$455$	57603.8	+	104814.i	0.278245	+	0.506285i
$456$	10455.5	+	32178.6i	0.0502821	+	0.154752i
$457$	−145010.	−	145010.i	−0.694330	−	0.694330i	0.268852	−	0.963182i	$-0.413356\pi$
$457$	−145010.	−	145010.i	−0.694330	−	0.694330i	−0.963182	+	0.268852i	$0.913356\pi$
$458$	−347965.	−	177297.i	−1.65884	−	0.845222i
$459$	−17953.5	+	24710.9i	−0.0852165	+	0.117290i
$460$	−23651.7	+	18341.1i	−0.111775	+	0.0866783i
$461$	−20118.1	+	14616.7i	−0.0946641	+	0.0687775i	−0.634110	−	0.773242i	$-0.718634\pi$
$461$	−20118.1	+	14616.7i	−0.0946641	+	0.0687775i	0.539446	+	0.842020i	$0.318634\pi$
$462$	11668.8	+	73674.0i	0.0546692	+	0.345168i
$463$	−395165.	+	62588.1i	−1.84339	+	0.291964i	−0.977917	−	0.208994i	$-0.932981\pi$
$463$	−395165.	+	62588.1i	−1.84339	+	0.291964i	−0.865472	+	0.500958i	$0.832981\pi$
$464$	175266.	+	241233.i	0.814071	+	1.12047i
$465$	16135.6	−	5806.77i	0.0746241	−	0.0268552i
$466$	−257205.	−	186870.i	−1.18442	−	0.860534i
$467$	94499.3	−	185465.i	0.433306	−	0.850412i	−0.566349	−	0.824165i	$-0.691645\pi$
$467$	94499.3	−	185465.i	0.433306	−	0.850412i	0.999656	−	0.0262462i	$-0.00835537\pi$
$468$	19788.8	−	19788.8i	0.0903498	−	0.0903498i
$469$	−448585.	+	145754.i	−2.03938	+	0.662636i
$470$	141826.	+	17935.8i	0.642038	+	0.0811942i
$471$	7545.79	−	23223.5i	0.0340144	−	0.104686i
$472$	276034.	−	140646.i	1.23902	−	0.631312i
$473$	6569.65	−	41479.2i	0.0293643	−	0.185399i
$474$			19429.1i			0.0864762i
$475$	276054.	+	175291.i	1.22351	+	0.776915i
$476$	−53683.8			−0.236935
$477$	−138813.	−	21985.8i	−0.610089	−	0.0966286i
$478$	−10520.1	−	20646.8i	−0.0460428	−	0.0903641i
$479$	10286.0	+	3342.12i	0.0448306	+	0.0145663i	0.331346	−	0.943509i	$-0.392497\pi$
$479$	10286.0	+	3342.12i	0.0448306	+	0.0145663i	−0.286516	+	0.958075i	$0.592497\pi$
$480$	−14276.7	+	15199.2i	−0.0619651	+	0.0659687i
$481$	−45688.8	−	140616.i	−0.197478	−	0.607776i
$482$	−335902.	−	335902.i	−1.44584	−	1.44584i
$483$	−18804.9	−	9581.56i	−0.0806076	−	0.0410716i
$484$	50760.5	−	69865.8i	0.216688	−	0.298246i
$485$	76541.5	−	2395.32i	0.325397	−	0.0101831i
$486$	−92693.9	+	67346.0i	−0.392445	+	0.285128i
$487$	26551.6	+	167640.i	0.111952	+	0.706839i	0.978268	+	0.207343i	$0.0664816\pi$
$487$	26551.6	+	167640.i	0.111952	+	0.706839i	−0.866316	+	0.499496i	$0.833518\pi$
$488$	−909.493	+	144.050i	−0.00381909	+	0.000604884i
$489$	−14315.5	−	19703.6i	−0.0598671	−	0.0823999i
$490$	166049.	−	244265.i	0.691583	−	1.01735i
$491$	116907.	+	84937.6i	0.484927	+	0.352320i	0.803230	−	0.595669i	$-0.203113\pi$
$491$	116907.	+	84937.6i	0.484927	+	0.352320i	−0.318303	+	0.947989i	$0.603113\pi$
$492$	987.801	−	1938.67i	0.00408074	−	0.00800891i
$493$	98975.4	−	98975.4i	0.407224	−	0.407224i
$494$	−155516.	+	50530.3i	−0.637267	+	0.207061i
$495$	−149286.	+	317141.i	−0.609270	+	1.29432i
$496$	−50885.3	+	156609.i	−0.206837	+	0.636580i
$497$	−194741.	+	99225.5i	−0.788397	+	0.401708i
$498$	4609.42	−	29102.7i	0.0185861	−	0.117348i
$499$		−	293364.i		−	1.17816i	−0.808074	−	0.589081i	$-0.799490\pi$
$499$		−	293364.i		−	1.17816i	0.808074	−	0.589081i	$-0.200510\pi$
$500$	−5132.18	+	81062.4i	−0.0205287	+	0.324250i
$501$	928.130			0.00369771
$502$	557519.	+	88302.4i	2.21234	+	0.350401i
$503$	71687.2	+	140694.i	0.283338	+	0.556083i	0.988183	−	0.153279i	$-0.0489833\pi$
$503$	71687.2	+	140694.i	0.283338	+	0.556083i	−0.704845	+	0.709362i	$0.748983\pi$
$504$	264374.	+	85900.2i	1.04078	+	0.338168i
$505$	176698.	+	83176.2i	0.692865	+	0.326149i
$506$	57927.0	+	178281.i	0.226246	+	0.696312i
$507$	−22023.9	−	22023.9i	−0.0856799	−	0.0856799i
$508$	55303.3	+	28178.5i	0.214301	+	0.109192i
$509$	−45526.4	+	62661.7i	−0.175723	+	0.241861i	−0.887789	−	0.460251i	$-0.847760\pi$
$509$	−45526.4	+	62661.7i	−0.175723	+	0.241861i	0.712066	+	0.702112i	$0.247760\pi$
$510$	18137.3	+	12329.6i	0.0697319	+	0.0474032i
$511$	438367.	−	318492.i	1.67879	−	1.21971i
$512$	7531.90	+	47554.5i	0.0287319	+	0.181406i
$513$	107721.	−	17061.3i	0.409321	−	0.0648301i
$514$	−134489.	−	185108.i	−0.509049	−	0.700646i
$515$	5207.15	+	166392.i	0.0196330	+	0.627363i
$516$	−1299.06	−	943.824i	−0.00487900	−	0.00354480i
$517$	99679.9	−	195633.i	0.372929	−	0.731915i
$518$	−499769.	+	499769.i	−1.86256	+	1.86256i
$519$	27185.0	−	8832.93i	0.100924	−	0.0327922i
$520$	61514.5	+	57781.2i	0.227494	+	0.213688i
$521$	−41910.7	+	128988.i	−0.154401	+	0.475196i	−0.998100	−	0.0616203i	$-0.980373\pi$
$521$	−41910.7	+	128988.i	−0.154401	+	0.475196i	0.843699	+	0.536816i	$0.180373\pi$
$522$	310793.	−	158357.i	1.14059	−	0.581160i
$523$	17837.6	−	112622.i	0.0652127	−	0.411737i	−0.933389	−	0.358867i	$-0.883163\pi$
$523$	17837.6	−	112622.i	0.0652127	−	0.411737i	0.998601	−	0.0528698i	$-0.0168368\pi$
$524$		−	85322.7i		−	0.310743i
$525$	−53259.4	+	21070.7i	−0.193231	+	0.0764469i
$526$	147876.			0.534474
$527$	76347.0	+	12092.2i	0.274898	+	0.0435395i
$528$	32576.6	+	63935.3i	0.116853	+	0.229336i
$529$	215702.	+	70085.7i	0.770801	+	0.250448i
$530$	−25591.6	+	202364.i	−0.0911056	+	0.720412i
$531$	−152668.	−	469862.i	−0.541449	−	1.66641i
$532$	135543.	+	135543.i	0.478910	+	0.478910i
$533$	−19468.5	−	9919.70i	−0.0685296	−	0.0349176i
$534$	−29132.8	+	40097.9i	−0.102164	+	0.140617i
$535$	58504.0	+	162568.i	0.204399	+	0.567974i
$536$	−269270.	+	195636.i	−0.937257	+	0.680957i
$537$	2530.38	+	15976.2i	0.00877481	+	0.0554020i
$538$	−34690.2	+	5494.39i	−0.119851	+	0.0189826i
$539$	−266642.	−	367002.i	−0.917808	−	1.26325i
$540$	16600.9	+	21407.6i	0.0569304	+	0.0734142i
$541$	−314241.	−	228310.i	−1.07366	−	0.780063i	−0.0970972	−	0.995275i	$-0.530956\pi$
$541$	−314241.	−	228310.i	−1.07366	−	0.780063i	−0.976567	+	0.215212i	$0.930956\pi$
$542$	117785.	−	231166.i	0.400952	−	0.786912i
$543$	−35506.4	+	35506.4i	−0.120422	+	0.120422i
$544$	−89395.2	+	29046.2i	−0.302076	+	0.0981504i
$545$	24991.5	−	13734.9i	0.0841395	−	0.0462417i
$546$	8850.51	−	27239.1i	0.0296881	−	0.0913707i
$547$	−501622.	+	255589.i	−1.67649	+	0.854216i	−0.684344	+	0.729160i	$0.739911\pi$
$547$	−501622.	+	255589.i	−1.67649	+	0.854216i	−0.992150	+	0.125056i	$0.960089\pi$
$548$	−23981.3	+	151412.i	−0.0798566	+	0.504195i
$549$			1468.46i			0.00487212i
$550$	466830.	+	202161.i	1.54324	+	0.668302i
$551$	−499794.			−1.64622
$552$	−14709.6	−	2329.78i	−0.0482751	−	0.00764603i
$553$	−103837.	−	203792.i	−0.339549	−	0.666402i
$554$	236861.	+	76960.7i	0.771745	+	0.250755i
$555$	69553.5	−	13258.5i	0.225805	−	0.0430437i
$556$	−36382.0	−	111972.i	−0.117689	−	0.362211i
$557$	214097.	+	214097.i	0.690082	+	0.690082i	0.962250	−	0.272167i	$-0.0877405\pi$
$557$	214097.	+	214097.i	0.690082	+	0.690082i	−0.272167	+	0.962250i	$0.587740\pi$
$558$	171633.	+	87451.4i	0.551230	+	0.280866i
$559$	−9478.08	+	13045.5i	−0.0303317	+	0.0417480i
$560$	153511.	−	528129.i	0.489513	−	1.68409i
$561$	27250.8	−	19798.9i	0.0865873	−	0.0629093i
$562$	−1161.38	−	7332.65i	−0.00367706	−	0.0232161i
$563$	−165216.	+	26167.7i	−0.521237	+	0.0825559i	−0.411509	−	0.911406i	$-0.634998\pi$
$563$	−165216.	+	26167.7i	−0.521237	+	0.0825559i	−0.109728	+	0.993962i	$0.534998\pi$
$564$	−4934.48	−	6791.73i	−0.0155126	−	0.0213512i
$565$	−304611.	−	88541.1i	−0.954219	−	0.277363i
$566$	287456.	+	208849.i	0.897301	+	0.651927i
$567$	196871.	−	386381.i	0.612372	−	1.20185i
$568$	−109057.	+	109057.i	−0.338032	+	0.338032i
$569$	64698.0	−	21021.7i	0.199833	−	0.0649296i	−0.207391	−	0.978258i	$-0.566497\pi$
$569$	64698.0	−	21021.7i	0.199833	−	0.0649296i	0.407223	+	0.913329i	$0.366497\pi$
$570$	−14663.5	−	76923.9i	−0.0451324	−	0.236762i
$571$	−46470.4	+	143021.i	−0.142529	+	0.438660i	−0.996685	−	0.0813571i	$-0.974075\pi$
$571$	−46470.4	+	143021.i	−0.142529	+	0.438660i	0.854156	+	0.520017i	$0.174075\pi$
$572$	−55582.9	+	28320.9i	−0.169883	+	0.0865596i
$573$	−4417.81	+	27893.0i	−0.0134554	+	0.0849543i
$574$			104450.i			0.317019i
$575$	−123913.	+	73238.0i	−0.374785	+	0.221514i
$576$	161866.			0.487878
$577$	8567.46	+	1356.95i	0.0257336	+	0.00407580i	0.169288	−	0.985567i	$-0.445853\pi$
$577$	8567.46	+	1356.95i	0.0257336	+	0.00407580i	−0.143554	+	0.989642i	$0.545853\pi$
$578$	−129700.	−	254550.i	−0.388225	−	0.761935i
$579$	11371.5	+	3694.82i	0.0339203	+	0.0110214i
$580$	−59792.2	−	108795.i	−0.177741	−	0.323411i
$581$	107188.	+	329892.i	0.317538	+	0.977281i
$582$	−12967.3	−	12967.3i	−0.0382828	−	0.0382828i
$583$	279137.	+	142228.i	0.821260	+	0.418453i
$584$	224745.	−	309336.i	0.658969	−	0.906994i
$585$	106356.	−	82475.8i	0.310778	−	0.240999i
$586$	−297915.	+	216448.i	−0.867556	+	0.630317i
$587$	−44476.5	−	280814.i	−0.129079	−	0.814971i	−0.964253	−	0.264985i	$-0.914633\pi$
$587$	−44476.5	−	280814.i	−0.129079	−	0.814971i	0.835174	−	0.549986i	$-0.185367\pi$
$588$	−17131.4	+	2713.35i	−0.0495494	+	0.00784785i
$589$	−162233.	−	223295.i	−0.467637	−	0.643648i
$590$	−674664.	+	242793.i	−1.93813	+	0.697482i
$591$	−58047.9	−	42174.2i	−0.166192	−	0.120746i
$592$	−308672.	+	605802.i	−0.880751	+	1.72857i
$593$	131514.	−	131514.i	0.373992	−	0.373992i	−0.494937	−	0.868929i	$-0.664809\pi$
$593$	131514.	−	131514.i	0.373992	−	0.373992i	0.868929	+	0.494937i	$0.164809\pi$
$594$	161366.	−	52430.9i	0.457339	−	0.148598i
$595$	−256135.	−	32391.7i	−0.723495	−	0.0914956i
$596$	58471.9	−	179958.i	0.164610	−	0.506616i
$597$	−10906.1	+	5556.92i	−0.0305998	+	0.0155914i
$598$	11259.6	−	71090.3i	0.0314862	−	0.198796i
$599$		−	369785.i		−	1.03061i	−0.857006	−	0.515307i	$-0.827678\pi$
$599$		−	369785.i		−	1.03061i	0.857006	−	0.515307i	$-0.172322\pi$
$600$	−31148.7	+	25754.6i	−0.0865241	+	0.0715406i
$601$	−363323.			−1.00588			−0.502938	−	0.864323i	$-0.667747\pi$
$601$	−363323.			−1.00588			−0.502938	+	0.864323i	$0.667747\pi$
$602$	76134.0	+	12058.4i	0.210081	+	0.0332735i
$603$	240969.	+	472928.i	0.662714	+	1.30065i
$604$	−69954.8	−	22729.7i	−0.191754	−	0.0623046i
$605$	284343.	−	302715.i	0.776842	−	0.827034i
$606$	−14452.1	−	44479.0i	−0.0393537	−	0.121118i
$607$	179745.	+	179745.i	0.487842	+	0.487842i	0.907625	−	0.419783i	$-0.137894\pi$
$607$	179745.	+	179745.i	0.487842	+	0.487842i	−0.419783	+	0.907625i	$0.637894\pi$
$608$	299046.	+	152371.i	0.808966	+	0.412189i
$609$	51454.8	−	70821.5i	0.138737	−	0.190955i
$610$	2130.19	−	66.6630i	0.00572478	−	0.000179153i
$611$	−68204.0	+	49553.1i	−0.182695	+	0.132736i
$612$	9450.43	+	59667.6i	0.0252318	+	0.159307i
$613$	266343.	−	42184.5i	0.708794	−	0.112262i	0.208380	−	0.978048i	$-0.433181\pi$
$613$	266343.	−	42184.5i	0.708794	−	0.112262i	0.500414	+	0.865786i	$0.333181\pi$
$614$	−125972.	−	173386.i	−0.334147	−	0.459914i
$615$	5882.74	−	8653.73i	0.0155535	−	0.0228799i
$616$	−501298.	−	364215.i	−1.32110	−	0.959833i
$617$	−227157.	+	445821.i	−0.596700	+	1.17109i	0.373237	+	0.927736i	$0.378248\pi$
$617$	−227157.	+	445821.i	−0.596700	+	1.17109i	−0.969937	+	0.243354i	$0.921752\pi$
$618$	28189.5	−	28189.5i	0.0738091	−	0.0738091i
$619$	−80381.5	+	26117.5i	−0.209785	+	0.0681634i	−0.412024	−	0.911173i	$-0.635178\pi$
$619$	−80381.5	+	26117.5i	−0.209785	+	0.0681634i	0.202239	+	0.979336i	$0.435178\pi$
$620$	29198.4	−	62028.6i	0.0759584	−	0.161365i
$621$	−14834.8	+	45656.9i	−0.0384680	+	0.118392i
$622$	604690.	−	308105.i	1.56298	−	0.796376i
$623$	91274.3	−	576283.i	0.235165	−	1.48477i
$624$		−	27551.9i		−	0.0707590i
$625$	−73398.0	+	383667.i	−0.187899	+	0.982188i
$626$	415479.			1.06023
$627$	−118793.	−	18815.0i	−0.302173	−	0.0478595i
$628$	−44319.3	−	86981.5i	−0.112376	−	0.220550i
$629$	303542.	+	98626.7i	0.767215	+	0.249283i
$630$	−582105.	−	274012.i	−1.46663	−	0.690380i
$631$	112531.	+	346333.i	0.282626	+	0.869832i	0.987100	+	0.160103i	$0.0511827\pi$
$631$	112531.	+	346333.i	0.282626	+	0.869832i	−0.704475	+	0.709729i	$0.748817\pi$
$632$	−114126.	−	114126.i	−0.285725	−	0.285725i
$633$	61446.5	+	31308.5i	0.153352	+	0.0781367i
$634$	−415168.	+	571430.i	−1.03287	+	1.42162i
$635$	246860.	+	167814.i	0.612215	+	0.416179i
$636$	9690.74	−	7040.73i	0.0239576	−	0.0174062i
$637$	27248.0	+	172037.i	0.0671515	+	0.423978i
$638$	−767957.	+	121632.i	−1.88667	+	0.298819i
$639$	144568.	+	198980.i	0.354054	+	0.487313i
$640$	−15374.1	−	491272.i	−0.0375343	−	1.19939i
$641$	482431.	+	350507.i	1.17414	+	0.853061i	0.991498	−	0.130119i	$-0.0415359\pi$
$641$	482431.	+	350507.i	1.17414	+	0.853061i	0.182640	+	0.983180i	$0.441536\pi$
$642$	18783.8	−	36865.3i	0.0455736	−	0.0894433i
$643$	216686.	−	216686.i	0.524094	−	0.524094i	−0.394711	−	0.918805i	$-0.629155\pi$
$643$	216686.	−	216686.i	0.524094	−	0.524094i	0.918805	+	0.394711i	$0.129155\pi$
$644$	−80245.3	+	26073.3i	−0.193485	+	0.0628671i
$645$	−5628.58	−	5286.99i	−0.0135294	−	0.0127083i
$646$	109078.	−	335707.i	0.261380	−	0.804444i
$647$	−342625.	+	174576.i	−0.818484	+	0.417039i	−0.812513	−	0.582944i	$-0.801901\pi$
$647$	−342625.	+	174576.i	−0.818484	+	0.417039i	−0.00597169	+	0.999982i	$0.501901\pi$
$648$	47869.6	−	302236.i	0.114001	−	0.719775i
$649$			1.10126e6i			2.61458i
$650$	−124470.	−	150539.i	−0.294603	−	0.356304i
$651$	48343.4			0.114071
$652$	−96168.0	−	15231.5i	−0.226222	−	0.0358301i
$653$	61098.2	+	119912.i	0.143285	+	0.281214i	0.951485	−	0.307695i	$-0.0995577\pi$
$653$	61098.2	+	119912.i	0.143285	+	0.281214i	−0.808200	+	0.588909i	$0.799558\pi$
$654$	−6494.83	−	2110.30i	−0.0151849	−	0.00493388i
$655$	51482.0	−	407091.i	0.119998	−	0.948874i
$656$	31049.7	+	95561.0i	0.0721521	+	0.222061i
$657$	−431162.	−	431162.i	−0.998872	−	0.998872i
$658$	359079.	+	182960.i	0.829352	+	0.422576i
$659$	234057.	−	322152.i	0.538953	−	0.741806i	−0.449508	−	0.893276i	$-0.648401\pi$
$659$	234057.	−	322152.i	0.538953	−	0.741806i	0.988462	+	0.151470i	$0.0484008\pi$
$660$	−10116.0	−	28109.8i	−0.0232231	−	0.0645313i
$661$	638560.	−	463941.i	1.46150	−	1.06184i	0.478530	−	0.878071i	$-0.341170\pi$
$661$	638560.	−	463941.i	1.46150	−	1.06184i	0.982969	−	0.183771i	$-0.0588304\pi$
$662$	44328.7	+	279880.i	0.101151	+	0.638641i
$663$	−12774.2	+	2023.23i	−0.0290607	+	0.00460277i
$664$	143872.	+	198023.i	0.326317	+	0.449137i
$665$	564917.	+	728485.i	1.27744	+	1.64732i
$666$	643454.	+	467497.i	1.45067	+	1.05398i
$667$	99875.5	−	196017.i	0.224495	−	0.440597i
$668$	2623.72	−	2623.72i	0.00587983	−	0.00587983i
$669$	−71742.2	+	23310.5i	−0.160296	+	0.0520833i
$670$	675102.	−	371025.i	1.50390	−	0.826520i
$671$	1011.51	−	3113.12i	0.00224661	−	0.00691435i
$672$	−52378.6	+	26688.2i	−0.115989	+	0.0590992i
$673$	59433.8	−	375250.i	0.131221	−	0.828496i	−0.831009	−	0.556259i	$-0.812236\pi$
$673$	59433.8	−	375250.i	0.131221	−	0.828496i	0.962230	−	0.272238i	$-0.0877637\pi$
$674$			482022.i			1.06108i
$675$	66289.2	+	112156.i	0.145491	+	0.246159i
$676$	−124518.			−0.272483
$677$	−484296.	−	76705.0i	−1.05666	−	0.167358i	−0.396156	−	0.918183i	$-0.629656\pi$
$677$	−484296.	−	76705.0i	−1.05666	−	0.167358i	−0.660501	+	0.750825i	$0.729656\pi$
$678$	34487.4	+	67685.3i	0.0750241	+	0.147243i
$679$	205316.	+	66711.3i	0.445332	+	0.144697i
$680$	−178960.	+	34114.1i	−0.387025	+	0.0737761i
$681$	−434.030	−	1335.81i	−0.000935891	−	0.00288038i
$682$	−303621.	−	303621.i	−0.652774	−	0.652774i
$683$	−92845.6	−	47307.2i	−0.199031	−	0.101411i	0.351635	−	0.936137i	$-0.385626\pi$
$683$	−92845.6	−	47307.2i	−0.199031	−	0.101411i	−0.550665	+	0.834726i	$0.685626\pi$
$684$	126790.	−	174512.i	0.271003	−	0.373004i
$685$	−205778.	+	707944.i	−0.438548	+	1.50875i
$686$	43320.6	−	31474.3i	0.0920549	−	0.0668818i
$687$	17253.6	+	108935.i	0.0365567	+	0.230810i
$688$	73239.3	−	11600.0i	0.154727	−	0.0245064i
$689$	−70704.5	−	97316.4i	−0.148939	−	0.204997i
$690$	33099.4	+	9621.00i	0.0695220	+	0.0202079i
$691$	−469660.	−	341228.i	−0.983621	−	0.714642i	−0.0251061	−	0.999685i	$-0.507992\pi$
$691$	−469660.	−	341228.i	−0.983621	−	0.714642i	−0.958515	+	0.285042i	$0.907992\pi$
$692$	51879.2	−	101819.i	0.108338	−	0.212625i
$693$	−698726.	+	698726.i	−1.45492	+	1.45492i
$694$	−749854.	+	243642.i	−1.55689	+	0.505864i
$695$	−106024.	−	556194.i	−0.219499	−	1.15148i
$696$	19089.0	−	58749.8i	0.0394061	−	0.121280i
$697$	42026.0	−	21413.3i	0.0865072	−	0.0440776i
$698$	102203.	−	645282.i	0.209774	−	1.32446i
$699$			89787.2i			0.183764i
$700$	−90994.0	+	210123.i	−0.185702	+	0.428822i
$701$	941416.			1.91578			0.957890	−	0.287135i	$-0.0927030\pi$
$701$	941416.			1.91578			0.957890	+	0.287135i	$0.0927030\pi$
$702$	−64345.2	−	10191.3i	−0.130570	−	0.0206802i
$703$	−517378.	−	1.01541e6i	−1.04688	−	2.05462i
$704$	−343154.	−	111497.i	−0.692379	−	0.224967i
$705$	−19445.3	−	35382.0i	−0.0391235	−	0.0711876i
$706$	−70673.2	−	217510.i	−0.141790	−	0.436384i
$707$	389301.	+	389301.i	0.778838	+	0.778838i
$708$	37517.5	+	19116.1i	0.0748459	+	0.0381359i
$709$	145199.	−	199850.i	0.288850	−	0.397568i	−0.639790	−	0.768550i	$-0.720979\pi$
$709$	145199.	−	199850.i	0.288850	−	0.397568i	0.928640	+	0.370982i	$0.120979\pi$
$710$	282083.	−	218746.i	0.559577	−	0.433935i
$711$	−208228.	+	151286.i	−0.411907	+	0.299268i
$712$	−64408.1	−	406657.i	−0.127052	−	0.802173i
$713$	119995.	−	19005.3i	0.236038	−	0.0373848i
$714$	36340.4	+	50018.3i	0.0712842	+	0.0981143i
$715$	−282285.	+	101587.i	−0.552173	+	0.198712i
$716$	52316.1	+	38009.8i	0.102049	+	0.0741430i
$717$	−2971.06	+	5831.03i	−0.00577927	+	0.0113424i
$718$	53961.0	−	53961.0i	0.104672	−	0.104672i
$719$	−205772.	+	66859.4i	−0.398042	+	0.129332i	−0.501196	−	0.865334i	$-0.667106\pi$
$719$	−205772.	+	66859.4i	−0.398042	+	0.129332i	0.103154	+	0.994665i	$0.467106\pi$
$720$	−614021.	−	77651.0i	−1.18445	−	0.149790i
$721$	−145023.	+	446334.i	−0.278975	+	0.858598i
$722$	−588390.	+	299800.i	−1.12873	+	0.575118i
$723$	−20987.2	+	132508.i	−0.0401492	+	0.253492i
$724$			200745.i			0.382973i
$725$	−219635.	−	555161.i	−0.417854	−	1.05619i
$726$	−99456.9			−0.188696
$727$	−88134.5	−	13959.1i	−0.166754	−	0.0264113i	0.0724989	−	0.997368i	$-0.476903\pi$
$727$	−88134.5	−	13959.1i	−0.166754	−	0.0264113i	−0.239253	+	0.970957i	$0.576903\pi$
$728$	108013.	+	211988.i	0.203805	+	0.399989i
$729$	−443225.	−	144013.i	−0.834006	−	0.270985i
$730$	−605881.	+	645028.i	−1.13695	+	1.21041i
$731$	−10756.5	−	33105.0i	−0.0201296	−	0.0619524i
$732$	−88.4987	−	88.4987i	−0.000165164	−	0.000165164i
$733$	248887.	+	126814.i	0.463227	+	0.236026i	0.669997	−	0.742363i	$-0.266295\pi$
$733$	248887.	+	126814.i	0.463227	+	0.236026i	−0.206770	+	0.978390i	$0.566295\pi$
$734$	354818.	−	488365.i	0.658588	−	0.906468i
$735$	−83374.3	+	2609.15i	−0.154333	+	0.00482974i
$736$	−119518.	+	86835.3i	−0.220638	+	0.160303i
$737$	−185086.	−	1.16859e6i	−0.340752	−	2.15142i
$738$	116093.	−	18387.3i	0.213153	−	0.0337602i
$739$	170415.	+	234556.i	0.312047	+	0.429495i	0.936018	−	0.351952i	$-0.114482\pi$
$739$	170415.	+	234556.i	0.312047	+	0.429495i	−0.623972	+	0.781447i	$0.714482\pi$
$740$	159140.	−	234100.i	0.290613	−	0.427503i
$741$	37361.1	+	27144.5i	0.0680430	+	0.0494362i
$742$	−261055.	+	512350.i	−0.474160	+	0.930591i
$743$	−435154.	+	435154.i	−0.788253	+	0.788253i	−0.981208	−	0.192954i	$-0.938193\pi$
$743$	−435154.	+	435154.i	−0.788253	+	0.788253i	0.192954	+	0.981208i	$0.438193\pi$
$744$	32444.1	−	10541.7i	0.0586125	−	0.0190444i
$745$	387564.	−	823333.i	0.698281	−	1.48342i
$746$	116590.	−	358828.i	0.209500	−	0.644775i
$747$	347794.	−	177210.i	0.623277	−	0.317575i
$748$	21065.8	−	133004.i	0.0376509	−	0.237718i
$749$			487067.i			0.868211i
$750$	79001.6	−	50092.2i	0.140447	−	0.0890527i
$751$	55983.2			0.0992608			0.0496304	−	0.998768i	$-0.484196\pi$
$751$	55983.2			0.0992608			0.0496304	+	0.998768i	$0.484196\pi$
$752$	382908.	+	60646.7i	0.677110	+	0.107244i
$753$	−72373.5	−	142041.i	−0.127641	−	0.250509i
$754$	283932.	+	92255.2i	0.499427	+	0.162274i
$755$	−320053.	−	150657.i	−0.561472	−	0.264299i
$756$	23599.4	+	72631.6i	0.0412912	+	0.127081i
$757$	577553.	+	577553.i	1.00786	+	1.00786i	0.999969	+	0.00789025i	$0.00251157\pi$
$757$	577553.	+	577553.i	1.00786	+	1.00786i	0.00789025	+	0.999969i	$0.497488\pi$
$758$	566659.	+	288727.i	0.986242	+	0.502515i
$759$	31117.9	−	42830.1i	0.0540166	−	0.0743474i
$760$	537979.	+	365714.i	0.931404	+	0.633161i
$761$	−460941.	+	334893.i	−0.795932	+	0.578279i	−0.909718	−	0.415227i	$-0.863702\pi$
$761$	−460941.	+	334893.i	−0.795932	+	0.578279i	0.113786	+	0.993505i	$0.463702\pi$
$762$	−11182.3	−	70602.2i	−0.0192584	−	0.121593i
$763$	79402.3	−	12576.1i	0.136391	−	0.0216021i
$764$	66361.6	+	91339.0i	0.113692	+	0.156484i
$765$	9087.51	+	290388.i	0.0155282	+	0.496198i
$766$	267081.	+	194046.i	0.455182	+	0.330709i
$767$	191968.	−	376759.i	0.326316	−	0.640432i
$768$	−53204.2	+	53204.2i	−0.0902036	+	0.0902036i
$769$	100741.	−	32732.7i	0.170354	−	0.0553515i	−0.222598	−	0.974910i	$-0.571454\pi$
$769$	100741.	−	32732.7i	0.170354	−	0.0553515i	0.392952	+	0.919559i	$0.371454\pi$
$770$	1.04531e6	+	981870.i	1.76304	+	1.65605i
$771$	−19968.4	+	61456.4i	−0.0335919	+	0.103385i
$772$	42590.8	−	21701.1i	0.0714629	−	0.0364122i
$773$	−39272.2	+	247955.i	−0.0657243	+	0.414967i	0.932787	+	0.360427i	$0.117369\pi$
$773$	−39272.2	+	247955.i	−0.0657243	+	0.414967i	−0.998512	+	0.0545396i	$0.982631\pi$
$774$		−	86743.0i		−	0.144795i
$775$	176738.	−	278332.i	0.294257	−	0.463404i
$776$	152338.			0.252980
$777$	197150.	+	31225.6i	0.326554	+	0.0517211i
$778$	4961.47	+	9737.44i	0.00819693	+	0.0160874i
$779$	−160174.	−	52043.7i	−0.263947	−	0.0857617i
$780$	−1439.17	+	11380.2i	−0.00236551	+	0.0187051i
$781$	−169419.	−	521417.i	−0.277753	−	0.854837i
$782$	109865.	+	109865.i	0.179658	+	0.179658i
$783$	−177419.	−	90399.3i	−0.289385	−	0.147449i
$784$	470808.	−	648011.i	0.765969	−	1.05427i
$785$	−158973.	−	441746.i	−0.257978	−	0.716859i
$786$	−79496.9	+	57757.8i	−0.128678	+	0.0934902i
$787$	166094.	+	1.04868e6i	0.268166	+	1.69313i	0.642858	+	0.765985i	$0.277749\pi$
$787$	166094.	+	1.04868e6i	0.268166	+	1.69313i	−0.374692	+	0.927149i	$0.622251\pi$
$788$	−283317.	+	44872.9i	−0.456268	+	0.0722657i
$789$	−24547.6	−	33786.9i	−0.0394326	−	0.0542743i
$790$	228913.	+	295193.i	0.366788	+	0.472989i
$791$	−723474.	−	525635.i	−1.15630	−	0.840101i
$792$	−316564.	+	621291.i	−0.504674	+	0.990478i
$793$	−888.723	+	888.723i	−0.00141325	+	0.00141325i
$794$	849600.	−	276052.i	1.34764	−	0.437875i
$795$	50484.6	−	27745.5i	0.0798775	−	0.0438993i
$796$	−15121.4	+	46539.0i	−0.0238653	+	0.0734498i
$797$	539412.	−	274844.i	0.849189	−	0.432683i	0.0254658	−	0.999676i	$-0.491893\pi$
$797$	539412.	−	274844.i	0.849189	−	0.432683i	0.823723	+	0.566992i	$0.191893\pi$
$798$	34534.4	−	218042.i	0.0542309	−	0.342400i
$799$		−	181986.i		−	0.285065i
$800$	−37835.3	+	399133.i	−0.0591177	+	0.623646i
$801$	−656586.			−1.02336
$802$	−222198.	−	35192.7i	−0.345455	−	0.0547147i
$803$	617063.	+	1.21105e6i	0.956970	+	1.87816i
$804$	−43023.9	−	13979.3i	−0.0665576	−	0.0216259i
$805$	−398597.	+	75982.1i	−0.615095	+	0.117252i
$806$	50947.2	+	156799.i	0.0784243	+	0.241365i
$807$	7013.99	+	7013.99i	0.0107701	+	0.0107701i
$808$	346158.	+	176376.i	0.530214	+	0.270158i
$809$	258255.	−	355458.i	0.394595	−	0.543114i	−0.564782	−	0.825240i	$-0.691040\pi$
$809$	258255.	−	355458.i	0.394595	−	0.543114i	0.959377	+	0.282126i	$0.0910398\pi$
$810$	−197681.	+	680089.i	−0.301297	+	1.03656i
$811$	645768.	−	469178.i	0.981826	−	0.713339i	0.0237104	−	0.999719i	$-0.492452\pi$
$811$	645768.	−	469178.i	0.981826	−	0.713339i	0.958116	+	0.286380i	$0.0924520\pi$
$812$	−54747.4	−	345662.i	−0.0830332	−	0.524251i
$813$	−72369.7	+	11462.2i	−0.109490	+	0.0173416i
$814$	−1.04209e6	−	1.43432e6i	−1.57274	−	2.16469i
$815$	−449645.	−	130698.i	−0.676947	−	0.196768i
$816$	48116.5	+	34958.7i	0.0722626	+	0.0525019i
$817$	−56426.4	+	110743.i	−0.0845353	+	0.165910i
$818$	483584.	−	483584.i	0.722713	−	0.722713i
$819$	360844.	−	117245.i	0.537963	−	0.174795i
$820$	−7833.29	−	41093.0i	−0.0116498	−	0.0611139i
$821$	−264028.	+	812595.i	−0.391709	+	1.20556i	0.539785	+	0.841803i	$0.318505\pi$
$821$	−264028.	+	812595.i	−0.391709	+	1.20556i	−0.931495	+	0.363755i	$0.881495\pi$
$822$	157307.	−	80151.9i	0.232812	−	0.118623i
$823$	−7069.79	+	44636.9i	−0.0104378	+	0.0659014i	−0.992357	−	0.123397i	$-0.960621\pi$
$823$	−7069.79	+	44636.9i	−0.0104378	+	0.0659014i	0.981920	+	0.189298i	$0.0606212\pi$
$824$			331166.i			0.487744i
$825$	−31304.3	−	140221.i	−0.0459935	−	0.206018i
$826$	−2.02134e6			−2.96265
$827$	−216985.	−	34367.1i	−0.317263	−	0.0502494i	−0.00422761	−	0.999991i	$-0.501346\pi$
$827$	−216985.	−	34367.1i	−0.317263	−	0.0502494i	−0.313035	+	0.949742i	$0.601346\pi$
$828$	43105.8	+	84599.8i	0.0628745	+	0.123398i
$829$	−849599.	−	276051.i	−1.23625	−	0.401681i	−0.383272	−	0.923635i	$-0.625203\pi$
$829$	−849599.	−	276051.i	−1.23625	−	0.401681i	−0.852973	+	0.521955i	$0.825203\pi$
$830$	−272854.	−	496474.i	−0.396072	−	0.720676i
$831$	−21735.1	−	66893.9i	−0.0314746	−	0.0968689i
$832$	97962.3	+	97962.3i	0.141518	+	0.141518i
$833$	−335018.	−	170700.i	−0.482812	−	0.246005i
$834$	−79698.7	+	109696.i	−0.114583	+	0.157710i
$835$	14101.4	−	10935.2i	0.0202250	−	0.0156838i
$836$	−389002.	+	282627.i	−0.556596	+	0.404390i
$837$	−17202.1	−	108610.i	−0.0245544	−	0.155030i
$838$	−697790.	+	110519.i	−0.993657	+	0.157380i
$839$	−254668.	−	350521.i	−0.361785	−	0.497955i	0.588860	−	0.808235i	$-0.299577\pi$
$839$	−254668.	−	350521.i	−0.361785	−	0.497955i	−0.950645	+	0.310280i	$0.899577\pi$
$840$	−107208.	+	38581.4i	−0.151939	+	0.0546788i
$841$	166021.	+	120621.i	0.234731	+	0.170542i
$842$	229169.	−	449769.i	0.323245	−	0.634403i
$843$	−1482.58	+	1482.58i	−0.00208624	+	0.00208624i
$844$	262208.	−	85196.5i	0.368096	−	0.119602i
$845$	−594101.	−	75131.9i	−0.832045	−	0.105223i
$846$	140142.	−	431312.i	0.195806	−	0.602630i
$847$	1.04320e6	−	531537.i	1.45412	−	0.740913i
$848$	−86533.4	+	546350.i	−0.120335	+	0.759765i
$849$		−	100347.i		−	0.139217i
$850$	420831.	−	26365.1i	0.582465	−	0.0364915i
$851$	501628.			0.692664
$852$	−20704.3	−	3279.24i	−0.0285221	−	0.00451746i
$853$	202834.	+	398085.i	0.278768	+	0.547114i	0.987358	−	0.158507i	$-0.0506681\pi$
$853$	202834.	+	398085.i	0.278768	+	0.547114i	−0.708589	+	0.705621i	$0.750668\pi$
$854$	5714.06	+	1856.61i	0.00783483	+	0.00254569i
$855$	710238.	−	756127.i	0.971565	−	1.03434i
$856$	106210.	+	326879.i	0.144949	+	0.446108i
$857$	842379.	+	842379.i	1.14695	+	1.14695i	0.987149	+	0.159806i	$0.0510867\pi$
$857$	842379.	+	842379.i	1.14695	+	1.14695i	0.159806	+	0.987149i	$0.448913\pi$
$858$	64013.1	+	32616.3i	0.0869550	+	0.0443058i
$859$	−457320.	+	629447.i	−0.619775	+	0.853047i	−0.997336	−	0.0729378i	$-0.976763\pi$
$859$	−457320.	+	629447.i	−0.619775	+	0.853047i	0.377562	+	0.925984i	$0.376763\pi$
$860$	−30857.1	+	965.655i	−0.0417213	+	0.00130564i
$861$	23864.9	−	17338.9i	0.0321924	−	0.0233892i
$862$	70532.4	+	445324.i	0.0949236	+	0.599324i
$863$	−172628.	+	27341.5i	−0.231787	+	0.0367114i	−0.271247	−	0.962510i	$-0.587436\pi$
$863$	−172628.	+	27341.5i	−0.231787	+	0.0367114i	0.0394604	+	0.999221i	$0.487436\pi$
$864$	78596.3	+	108179.i	0.105287	+	0.144915i
$865$	308961.	−	454493.i	0.412925	−	0.607428i
$866$	−820794.	−	596342.i	−1.09446	−	0.795169i
$867$	−36629.6	+	71889.7i	−0.0487298	+	0.0956375i
$868$	136662.	−	136662.i	0.181387	−	0.181387i
$869$	545650.	−	177292.i	0.722561	−	0.234774i
$870$	−60891.6	+	129357.i	−0.0804486	+	0.170904i
$871$	−140383.	+	432055.i	−0.185046	+	0.569512i
$872$	50546.0	−	25754.5i	0.0664743	−	0.0338703i
$873$	38003.7	−	239946.i	0.0498651	−	0.314836i
$874$		−	554785.i		−	0.726276i
$875$	−560933.	+	947631.i	−0.732648	+	1.23772i
$876$	51969.0			0.0677231
$877$	−488678.	−	77399.0i	−0.635366	−	0.100632i	−0.169561	−	0.985520i	$-0.554235\pi$
$877$	−488678.	−	77399.0i	−0.635366	−	0.100632i	−0.465805	+	0.884888i	$0.654235\pi$
$878$	−551327.	−	1.08204e6i	−0.715188	−	1.40363i
$879$	98908.8	+	32137.4i	0.128014	+	0.0415942i
$880$	1.24823e6	+	587572.i	1.61186	+	0.758745i
$881$	−224763.	−	691751.i	−0.289584	−	0.891247i	−0.984987	−	0.172627i	$-0.944774\pi$
$881$	−224763.	−	691751.i	−0.289584	−	0.891247i	0.695404	−	0.718619i	$-0.255226\pi$
$882$	−662552.	−	662552.i	−0.851693	−	0.851693i
$883$	−876825.	−	446765.i	−1.12458	−	0.573004i	−0.210121	−	0.977675i	$-0.567386\pi$
$883$	−876825.	−	446765.i	−1.12458	−	0.573004i	−0.914462	+	0.404672i	$0.867386\pi$
$884$	−30391.8	+	41830.7i	−0.0388912	+	0.0535291i
$885$	167469.	+	113844.i	0.213820	+	0.145353i
$886$	322545.	−	234343.i	0.410888	−	0.298528i
$887$	−106475.	−	672257.i	−0.135332	−	0.854453i	−0.958175	−	0.286184i	$-0.907613\pi$
$887$	−106475.	−	672257.i	−0.135332	−	0.854453i	0.822843	−	0.568269i	$-0.192387\pi$
$888$	139120.	−	22034.5i	0.176427	−	0.0279432i
$889$	494617.	+	680782.i	0.625843	+	0.861399i
$890$	29806.7	+	952460.i	0.0376299	+	1.20245i
$891$	880025.	+	639375.i	1.10851	+	0.805379i
$892$	−136911.	+	268703.i	−0.172072	+	0.337709i
$893$	−459485.	+	459485.i	−0.576194	+	0.576194i
$894$	−207252.	+	67340.3i	−0.259313	+	0.0842559i
$895$	226675.	+	212919.i	0.282982	+	0.265808i
$896$	428178.	−	1.31780e6i	0.533346	−	1.64147i
$897$	−18111.9	+	9228.48i	−0.0225102	+	0.0114695i
$898$	−237412.	+	1.49896e6i	−0.294408	+	1.85882i
$899$			503918.i			0.623506i
$900$	249563.	+	64146.8i	0.308102	+	0.0791936i
$901$	259665.			0.319863
$902$	−258781.	−	40986.8i	−0.318067	−	0.0503769i
$903$	−9883.23	−	19396.9i	−0.0121206	−	0.0237880i
$904$	−600156.	−	195002.i	−0.734391	−	0.238618i
$905$	−121126.	+	957794.i	−0.147890	+	1.16943i
$906$	26177.1	+	80564.8i	0.0318908	+	0.0981497i
$907$	−861176.	−	861176.i	−1.04683	−	1.04683i	−0.998848	−	0.0479850i	$-0.984720\pi$
$907$	−861176.	−	861176.i	−1.04683	−	1.04683i	−0.0479850	−	0.998848i	$-0.515280\pi$
$908$	−5003.13	−	2549.22i	−0.00606834	−	0.00309198i
$909$	364163.	−	501227.i	0.440725	−	0.606606i
$910$	−186460.	−	518127.i	−0.225166	−	0.625682i
$911$	−272571.	+	198035.i	−0.328430	+	0.238619i	−0.739764	−	0.672866i	$-0.765063\pi$
$911$	−272571.	+	198035.i	−0.328430	+	0.238619i	0.411334	+	0.911485i	$0.365063\pi$
$912$	−33221.4	−	209752.i	−0.0399418	−	0.252183i
$913$	−859385.	+	136113.i	−1.03097	+	0.163290i
$914$	554988.	+	763875.i	0.664341	+	0.914386i
$915$	−368.846	−	475.642i	−0.000440558	−	0.000568118i
$916$	356722.	+	259174.i	0.425147	+	0.308887i
$917$	525159.	−	1.03068e6i	0.624529	−	1.22571i
$918$	99441.2	−	99441.2i	0.118000	−	0.118000i
$919$	146377.	−	47560.8i	0.173317	−	0.0563143i	−0.221073	−	0.975257i	$-0.570956\pi$
$919$	146377.	−	47560.8i	0.173317	−	0.0563143i	0.394390	+	0.918943i	$0.370956\pi$
$920$	−250937.	+	137911.i	−0.296476	+	0.162938i
$921$	−18703.9	+	57564.6i	−0.0220502	+	0.0678635i
$922$	102015.	−	51979.0i	0.120005	−	0.0611457i
$923$	−32930.9	+	207917.i	−0.0386545	+	0.244055i
$924$		−	84219.2i		−	0.0986432i
$925$	900536.	−	1.02092e6i	1.05249	−	1.19318i
$926$	1.84209e6			2.14827
$927$	521614.	+	82615.6i	0.607002	+	0.0961397i
$928$	−278191.	−	545980.i	−0.323033	−	0.633987i
$929$	556198.	+	180720.i	0.644463	+	0.209399i	0.612971	−	0.790105i	$-0.289974\pi$
$929$	556198.	+	180720.i	0.644463	+	0.209399i	0.0314921	+	0.999504i	$0.489974\pi$
$930$	−77558.7	+	14784.5i	−0.0896736	+	0.0170939i
$931$	414876.	+	1.27686e6i	0.478651	+	1.47314i
$932$	253818.	+	253818.i	0.292207	+	0.292207i
$933$	−170776.	−	87014.6i	−0.196184	−	0.0999606i
$934$	−563316.	+	775338.i	−0.645741	+	0.888786i
$935$	180761.	−	621878.i	0.206767	−	0.711347i
$936$	216602.	−	157371.i	0.247236	−	0.179627i
$937$	95022.6	+	599949.i	0.108230	+	0.683337i	0.980825	+	0.194892i	$0.0624357\pi$
$937$	95022.6	+	599949.i	0.108230	+	0.683337i	−0.872595	+	0.488445i	$0.837564\pi$
$938$	2.14491e6	−	339721.i	2.43783	−	0.386115i
$939$	−68970.1	−	94929.2i	−0.0782221	−	0.107663i
$940$	−154991.	−	45051.1i	−0.175408	−	0.0509859i
$941$	−1.20854e6	−	878055.i	−1.36484	−	0.991614i	−0.998121	−	0.0612816i	$-0.980481\pi$
$941$	−1.20854e6	−	878055.i	−1.36484	−	0.991614i	−0.366719	−	0.930332i	$-0.619519\pi$
$942$	−51041.1	+	100174.i	−0.0575199	+	0.112889i
$943$	52419.4	−	52419.4i	0.0589479	−	0.0589479i
$944$	−1.84932e6	+	600880.i	−2.07524	+	0.674285i
$945$	68772.9	+	360778.i	0.0770112	+	0.403996i
$946$	−59750.8	+	183894.i	−0.0667669	+	0.205487i
$947$	−1.41349e6	+	720208.i	−1.57613	+	0.803079i	−0.999899	−	0.0142072i	$-0.995478\pi$
$947$	−1.41349e6	+	720208.i	−1.57613	+	0.803079i	−0.576232	+	0.817286i	$0.695478\pi$
$948$	3431.65	−	21666.6i	0.00381844	−	0.0241087i
$949$		−	521884.i		−	0.579484i
$950$	−1.12910e6	−	995964.i	−1.25108	−	1.10356i
$951$	199479.			0.220565
$952$	−507265.	−	80342.9i	−0.559708	−	0.0886490i
$953$	−194329.	−	381392.i	−0.213969	−	0.419938i	0.758928	−	0.651174i	$-0.225723\pi$
$953$	−194329.	−	381392.i	−0.213969	−	0.419938i	−0.972898	+	0.231236i	$0.925723\pi$
$954$	615415.	+	199960.i	0.676194	+	0.219709i
$955$	261512.	+	475837.i	0.286738	+	0.521736i
$956$	8084.82	+	24882.5i	0.00884615	+	0.0272257i
$957$	155273.	+	155273.i	0.169540	+	0.169540i
$958$	−44368.1	−	22606.7i	−0.0483437	−	0.0246324i
$959$	−1.22163e6	+	1.68142e6i	−1.32831	+	1.82827i
$960$	−52429.2	+	40657.2i	−0.0568894	+	0.0441159i
$961$	522007.	−	379260.i	0.565235	−	0.410668i
$962$	106490.	+	672355.i	0.115070	+	0.726521i
$963$	541358.	−	85742.7i	0.583757	−	0.0924580i
$964$	315256.	+	433913.i	0.339242	+	0.466927i
$965$	216302.	−	77841.5i	0.232277	−	0.0835904i
$966$	78613.7	+	57116.2i	0.0842450	+	0.0612076i
$967$	82688.2	−	162285.i	0.0884281	−	0.173550i	−0.842557	−	0.538607i	$-0.818951\pi$
$967$	82688.2	−	162285.i	0.0884281	−	0.173550i	0.930985	+	0.365057i	$0.118951\pi$
$968$	584204.	−	584204.i	0.623467	−	0.623467i
$969$	−94810.0	+	30805.6i	−0.100973	+	0.0328082i
$970$	−349796.	−	44236.4i	−0.371768	−	0.0470150i
$971$	−73557.8	+	226388.i	−0.0780172	+	0.240112i	−0.982457	−	0.186489i	$-0.940289\pi$
$971$	−73557.8	+	226388.i	−0.0780172	+	0.240112i	0.904440	+	0.426601i	$0.140289\pi$
$972$	115263.	−	58729.6i	0.122000	−	0.0621619i
$973$	249699.	−	1.57654e6i	0.263749	−	1.66525i
$974$		−	781466.i		−	0.823744i
$975$	−13733.1	+	53428.6i	−0.0144464	+	0.0562037i
$976$	5779.68			0.00606742
$977$	1.84641e6	+	292443.i	1.93437	+	0.306374i	0.998894	−	0.0470234i	$-0.0149735\pi$
$977$	1.84641e6	+	292443.i	1.93437	+	0.306374i	0.935473	+	0.353397i	$0.114974\pi$
$978$	50907.9	+	99912.4i	0.0532240	+	0.104458i
$979$	1.39195e6	+	452273.i	1.45231	+	0.471884i
$980$	−228314.	+	243066.i	−0.237728	+	0.253088i
$981$	−27955.8	−	86039.0i	−0.0290491	−	0.0894041i
$982$	−470455.	−	470455.i	−0.487860	−	0.487860i
$983$	45439.8	+	23152.7i	0.0470250	+	0.0239605i	0.477345	−	0.878716i	$-0.341599\pi$
$983$	45439.8	+	23152.7i	0.0470250	+	0.0239605i	−0.430320	+	0.902676i	$0.641599\pi$
$984$	12235.3	−	16840.4i	0.0126364	−	0.0173925i
$985$	−1.37883e6	+	43149.7i	−1.42115	+	0.0444740i
$986$	−521376.	+	378802.i	−0.536287	+	0.389635i
$987$	−17804.7	−	112415.i	−0.0182768	−	0.115395i
$988$	182350.	−	28881.4i	0.186807	−	0.0295873i
$989$	−32157.0	−	44260.3i	−0.0328763	−	0.0452503i
$990$	907299.	−	1.33467e6i	0.925721	−	1.36177i
$991$	913967.	+	664036.i	0.930644	+	0.676152i	0.946150	−	0.323728i	$-0.104936\pi$
$991$	913967.	+	664036.i	0.930644	+	0.676152i	−0.0155067	+	0.999880i	$0.504936\pi$
$992$	153629.	−	301513.i	0.156117	−	0.306396i
$993$	56588.9	−	56588.9i	0.0573895	−	0.0573895i
$994$	957049.	−	310964.i	0.968638	−	0.314730i
$995$	−100228.	+	212922.i	−0.101238	+	0.215068i
$996$	−10280.5	+	31640.0i	−0.0103632	+	0.0318947i
$997$	−1.22271e6	+	623003.i	−1.23008	+	0.626758i	−0.943524	−	0.331305i	$-0.892511\pi$
$997$	−1.22271e6	+	623003.i	−1.23008	+	0.626758i	−0.286558	+	0.958063i	$0.592511\pi$
$998$	−211295.	+	1.33407e6i	−0.212143	+	1.33942i
$999$		−	454034.i		−	0.454943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.5.f.a.2.3	✓	72
5.2	odd	4		125.5.f.a.93.7		72
5.3	odd	4		125.5.f.b.93.3		72
5.4	even	2		125.5.f.c.32.7		72
25.9	even	10		125.5.f.a.82.7		72
25.12	odd	20		125.5.f.c.43.7		72
25.13	odd	20	inner	25.5.f.a.13.3	yes	72
25.16	even	5		125.5.f.b.82.3		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.5.f.a.2.3	✓	72	1.1	even	1	trivial
25.5.f.a.13.3	yes	72	25.13	odd	20	inner
125.5.f.a.82.7		72	25.9	even	10
125.5.f.a.93.7		72	5.2	odd	4
125.5.f.b.82.3		72	25.16	even	5
125.5.f.b.93.3		72	5.3	odd	4
125.5.f.c.32.7		72	5.4	even	2
125.5.f.c.43.7		72	25.12	odd	20

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.54749 - 0.720251i) q^{2} +(0.590325 + 1.15858i) q^{3} +(4.94395 + 1.60639i) q^{4} +(22.6193 + 10.6475i) q^{5} +(-1.85003 - 5.69380i) q^{6} +(49.8348 + 49.8348i) q^{7} +(44.3120 + 22.5781i) q^{8} +(46.6168 - 64.1625i) q^{9} +O(q^{10})\)	\(q+(-4.54749 - 0.720251i) q^{2} +(0.590325 + 1.15858i) q^{3} +(4.94395 + 1.60639i) q^{4} +(22.6193 + 10.6475i) q^{5} +(-1.85003 - 5.69380i) q^{6} +(49.8348 + 49.8348i) q^{7} +(44.3120 + 22.5781i) q^{8} +(46.6168 - 64.1625i) q^{9} +(-95.1920 - 64.7107i) q^{10} +(-143.024 + 103.913i) q^{11} +(1.05741 + 6.67625i) q^{12} +(67.0443 - 10.6188i) q^{13} +(-190.730 - 262.517i) q^{14} +(1.01681 + 32.4917i) q^{15} +(-252.535 - 183.478i) q^{16} +(-66.5233 + 130.559i) q^{17} +(-258.202 + 258.202i) q^{18} +(497.602 - 161.681i) q^{19} +(94.7247 + 88.9759i) q^{20} +(-28.3188 + 87.1563i) q^{21} +(725.241 - 369.529i) q^{22} +(-36.0271 + 227.466i) q^{23} +64.6673i q^{24} +(398.263 + 481.676i) q^{25} -312.531 q^{26} +(205.884 + 32.6088i) q^{27} +(166.327 + 326.435i) q^{28} +(-908.493 - 295.187i) q^{29} +(18.7782 - 148.488i) q^{30} +(-163.015 - 501.708i) q^{31} +(453.592 + 453.592i) q^{32} +(-204.822 - 104.362i) q^{33} +(396.549 - 545.803i) q^{34} +(596.613 + 1657.84i) q^{35} +(333.541 - 242.332i) q^{36} +(-340.736 - 2151.32i) q^{37} +(-2379.29 + 376.843i) q^{38} +(51.8806 + 71.4075i) q^{39} +(761.905 + 982.510i) q^{40} +(-260.416 - 189.203i) q^{41} +(191.554 - 375.945i) q^{42} +(-167.975 + 167.975i) q^{43} +(-874.027 + 283.989i) q^{44} +(1737.61 - 954.959i) q^{45} +(327.665 - 1008.45i) q^{46} +(-1106.60 + 563.841i) q^{47} +(63.4953 - 400.894i) q^{48} +2566.02i q^{49} +(-1464.17 - 2477.26i) q^{50} -190.534 q^{51} +(348.522 + 55.2004i) q^{52} +(-804.513 - 1578.95i) q^{53} +(-912.769 - 296.577i) q^{54} +(-4341.50 + 827.593i) q^{55} +(1083.10 + 3333.45i) q^{56} +(481.067 + 481.067i) q^{57} +(3918.75 + 1996.70i) q^{58} +(3661.50 - 5039.63i) q^{59} +(-47.1672 + 162.271i) q^{60} +(-14.9795 + 10.8832i) q^{61} +(379.952 + 2398.92i) q^{62} +(5520.67 - 874.388i) q^{63} +(1199.64 + 1651.16i) q^{64} +(1629.56 + 473.663i) q^{65} +(856.257 + 622.107i) q^{66} +(-3038.35 + 5963.09i) q^{67} +(-538.617 + 538.617i) q^{68} +(-284.805 + 92.5388i) q^{69} +(-1519.03 - 7968.72i) q^{70} +(-958.321 + 2949.41i) q^{71} +(3514.35 - 1790.65i) q^{72} +(1202.72 - 7593.67i) q^{73} +10028.5i q^{74} +(-322.954 + 745.764i) q^{75} +2719.85 q^{76} +(-12306.0 - 1949.09i) q^{77} +(-184.495 - 362.092i) q^{78} +(-3086.48 - 1002.86i) q^{79} +(-3758.60 - 6838.99i) q^{80} +(-1901.38 - 5851.85i) q^{81} +(1047.96 + 1047.96i) q^{82} +(4385.29 + 2234.42i) q^{83} +(-280.014 + 385.406i) q^{84} +(-2894.83 + 2244.85i) q^{85} +(884.848 - 642.880i) q^{86} +(-194.309 - 1226.82i) q^{87} +(-8683.81 + 1375.38i) q^{88} +(-4866.16 - 6697.70i) q^{89} +(-8589.55 + 3091.15i) q^{90} +(3870.33 + 2811.96i) q^{91} +(-543.515 + 1066.71i) q^{92} +(485.037 - 485.037i) q^{93} +(5438.36 - 1767.03i) q^{94} +(12976.9 + 1641.10i) q^{95} +(-257.755 + 793.289i) q^{96} +(2729.29 - 1390.64i) q^{97} +(1848.18 - 11668.9i) q^{98} +14020.8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9}+O(q^{10}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9	\( 72 q - 8 q^{2} + 2 q^{3} - 10 q^{4} - 50 q^{5} - 6 q^{6} + 42 q^{7} + 50 q^{8} - 10 q^{9} - 6 q^{11} - 178 q^{12} - 288 q^{13} - 10 q^{14} + 410 q^{15} + 762 q^{16} + 1042 q^{17} - 28 q^{18} - 1310 q^{19} - 3790 q^{20} - 6 q^{21} - 3226 q^{22} - 578 q^{23} + 1110 q^{25} - 976 q^{26} + 5120 q^{27} + 10318 q^{28} + 3290 q^{29} + 5270 q^{30} - 6 q^{31} - 1298 q^{32} - 2806 q^{33} - 8010 q^{34} - 5360 q^{35} - 2758 q^{36} + 4692 q^{37} + 14480 q^{38} + 8790 q^{39} + 2540 q^{40} + 1434 q^{41} - 23886 q^{42} - 14958 q^{43} - 22060 q^{44} - 23420 q^{45} - 6 q^{46} - 12158 q^{47} - 14168 q^{48} + 8050 q^{50} - 16 q^{51} + 29372 q^{52} + 22852 q^{53} + 53940 q^{54} + 18070 q^{55} - 1030 q^{56} + 34150 q^{57} + 23000 q^{58} + 23240 q^{59} + 40610 q^{60} + 2634 q^{61} - 13716 q^{62} - 42428 q^{63} - 66060 q^{64} - 41870 q^{65} + 5178 q^{66} - 25558 q^{67} - 71982 q^{68} - 39560 q^{69} - 38130 q^{70} + 7974 q^{71} - 37860 q^{72} - 4228 q^{73} + 21210 q^{75} - 1040 q^{76} + 34374 q^{77} + 51844 q^{78} + 26590 q^{79} + 110710 q^{80} - 14368 q^{81} + 145614 q^{82} + 99832 q^{83} + 149990 q^{84} + 48860 q^{85} - 6 q^{86} - 31320 q^{87} - 95490 q^{88} - 93760 q^{89} - 207250 q^{90} - 6 q^{91} - 199958 q^{92} - 134396 q^{93} - 130410 q^{94} - 50290 q^{95} + 17694 q^{96} - 40108 q^{97} - 25052 q^{98}+O(q^{100}) \) 72 * q - 8 * q^2 + 2 * q^3 - 10 * q^4 - 50 * q^5 - 6 * q^6 + 42 * q^7 + 50 * q^8 - 10 * q^9 - 6 * q^11 - 178 * q^12 - 288 * q^13 - 10 * q^14 + 410 * q^15 + 762 * q^16 + 1042 * q^17 - 28 * q^18 - 1310 * q^19 - 3790 * q^20 - 6 * q^21 - 3226 * q^22 - 578 * q^23 + 1110 * q^25 - 976 * q^26 + 5120 * q^27 + 10318 * q^28 + 3290 * q^29 + 5270 * q^30 - 6 * q^31 - 1298 * q^32 - 2806 * q^33 - 8010 * q^34 - 5360 * q^35 - 2758 * q^36 + 4692 * q^37 + 14480 * q^38 + 8790 * q^39 + 2540 * q^40 + 1434 * q^41 - 23886 * q^42 - 14958 * q^43 - 22060 * q^44 - 23420 * q^45 - 6 * q^46 - 12158 * q^47 - 14168 * q^48 + 8050 * q^50 - 16 * q^51 + 29372 * q^52 + 22852 * q^53 + 53940 * q^54 + 18070 * q^55 - 1030 * q^56 + 34150 * q^57 + 23000 * q^58 + 23240 * q^59 + 40610 * q^60 + 2634 * q^61 - 13716 * q^62 - 42428 * q^63 - 66060 * q^64 - 41870 * q^65 + 5178 * q^66 - 25558 * q^67 - 71982 * q^68 - 39560 * q^69 - 38130 * q^70 + 7974 * q^71 - 37860 * q^72 - 4228 * q^73 + 21210 * q^75 - 1040 * q^76 + 34374 * q^77 + 51844 * q^78 + 26590 * q^79 + 110710 * q^80 - 14368 * q^81 + 145614 * q^82 + 99832 * q^83 + 149990 * q^84 + 48860 * q^85 - 6 * q^86 - 31320 * q^87 - 95490 * q^88 - 93760 * q^89 - 207250 * q^90 - 6 * q^91 - 199958 * q^92 - 134396 * q^93 - 130410 * q^94 - 50290 * q^95 + 17694 * q^96 - 40108 * q^97 - 25052 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more