LMFDB - Embedded newform 25.2.e.a.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,2,Mod(4,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("25.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	25.e (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.199626005053$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			9.2
Root			$1.66637 - 0.917186i$ of defining polynomial
Character	$\chi$	$=$	25.9
Dual form			25.2.e.a.14.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.666375 - 0.917186i) q^{2} +(-2.47539 + 0.804303i) q^{3} +(0.220859 + 0.679734i) q^{4} +(-1.07822 - 1.95894i) q^{5} +(-0.911842 + 2.80636i) q^{6} +0.407162i q^{7} +(2.92705 + 0.951057i) q^{8} +(3.05361 - 2.21858i) q^{9} +O(q^{10})$	\(q+(0.666375 - 0.917186i) q^{2} +(-2.47539 + 0.804303i) q^{3} +(0.220859 + 0.679734i) q^{4} +(-1.07822 - 1.95894i) q^{5} +(-0.911842 + 2.80636i) q^{6} +0.407162i q^{7} +(2.92705 + 0.951057i) q^{8} +(3.05361 - 2.21858i) q^{9} +(-2.51521 - 0.316463i) q^{10} +(-1.61803 - 1.17557i) q^{11} +(-1.09343 - 1.50497i) q^{12} +(-0.411842 - 0.566852i) q^{13} +(0.373443 + 0.271322i) q^{14} +(4.24459 + 3.98193i) q^{15} +(1.66637 - 1.21069i) q^{16} +(1.50527 + 0.489091i) q^{17} -4.27913i q^{18} +(-1.52988 + 4.70847i) q^{19} +(1.09343 - 1.16555i) q^{20} +(-0.327481 - 1.00788i) q^{21} +(-2.15643 + 0.700668i) q^{22} +(-0.706192 + 0.971990i) q^{23} -8.01054 q^{24} +(-2.67490 + 4.22433i) q^{25} -0.794350 q^{26} +(-1.18484 + 1.63079i) q^{27} +(-0.276762 + 0.0899253i) q^{28} +(-1.70239 - 5.23943i) q^{29} +(6.48066 - 1.23962i) q^{30} +(2.53514 - 7.80237i) q^{31} +3.82022i q^{32} +(4.95078 + 1.60861i) q^{33} +(1.45166 - 1.05469i) q^{34} +(0.797605 - 0.439008i) q^{35} +(2.18246 + 1.58565i) q^{36} +(3.01846 + 4.15456i) q^{37} +(3.29908 + 4.54079i) q^{38} +(1.47539 + 1.07193i) q^{39} +(-1.29293 - 6.75936i) q^{40} +(-5.83802 + 4.24157i) q^{41} +(-1.14264 - 0.371267i) q^{42} -9.16531i q^{43} +(0.441718 - 1.35947i) q^{44} +(-7.63851 - 3.58973i) q^{45} +(0.420907 + 1.29542i) q^{46} +(1.21092 - 0.393451i) q^{47} +(-3.15117 + 4.33721i) q^{48} +6.83422 q^{49} +(2.09201 + 5.26836i) q^{50} -4.11950 q^{51} +(0.294350 - 0.405138i) q^{52} +(-4.83133 + 1.56979i) q^{53} +(0.706192 + 2.17344i) q^{54} +(-0.558282 + 4.43715i) q^{55} +(-0.387234 + 1.19178i) q^{56} -12.8858i q^{57} +(-5.93997 - 1.93001i) q^{58} +(-5.25838 + 3.82044i) q^{59} +(-1.76920 + 3.76464i) q^{60} +(7.62101 + 5.53699i) q^{61} +(-5.46687 - 7.52450i) q^{62} +(0.903319 + 1.24331i) q^{63} +(6.83660 + 4.96708i) q^{64} +(-0.666375 + 1.41796i) q^{65} +(4.77447 - 3.46885i) q^{66} +(-2.93090 - 0.952307i) q^{67} +1.13120i q^{68} +(0.966327 - 2.97405i) q^{69} +(0.128852 - 1.02410i) q^{70} +(2.12183 + 6.53032i) q^{71} +(11.0481 - 3.58973i) q^{72} +(-0.320429 + 0.441032i) q^{73} +5.82193 q^{74} +(3.22378 - 12.6083i) q^{75} -3.53840 q^{76} +(0.478647 - 0.658801i) q^{77} +(1.96633 - 0.638898i) q^{78} +(-1.69390 - 5.21330i) q^{79} +(-4.16839 - 1.95894i) q^{80} +(-1.87783 + 5.77938i) q^{81} +8.18102i q^{82} +(-0.926457 - 0.301024i) q^{83} +(0.612766 - 0.445201i) q^{84} +(-0.664904 - 3.47608i) q^{85} +(-8.40629 - 6.10753i) q^{86} +(8.42819 + 11.6004i) q^{87} +(-3.61803 - 4.97980i) q^{88} +(-1.83363 - 1.33221i) q^{89} +(-8.38256 + 4.61383i) q^{90} +(0.230800 - 0.167686i) q^{91} +(-0.816664 - 0.265350i) q^{92} +21.3529i q^{93} +(0.446057 - 1.37282i) q^{94} +(10.8732 - 2.07982i) q^{95} +(-3.07261 - 9.45653i) q^{96} +(-14.4736 + 4.70276i) q^{97} +(4.55415 - 6.26825i) q^{98} -7.54893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} - 5 q^{3} - q^{4} - 9 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) $ 8 * q - 5 * q^2 - 5 * q^3 - q^4 - 9 * q^6 + 10 * q^8 + q^9	$ 8 q - 5 q^{2} - 5 q^{3} - q^{4} - 9 q^{6} + 10 q^{8} + q^{9} - 5 q^{10} - 4 q^{11} + 15 q^{12} - 5 q^{13} + 13 q^{14} + 15 q^{15} + 3 q^{16} - 10 q^{17} - 5 q^{19} - 15 q^{20} - 4 q^{21} + 5 q^{23} - 20 q^{24} - 10 q^{25} + 6 q^{26} - 5 q^{27} - 15 q^{28} - 5 q^{29} + 15 q^{30} - 9 q^{31} + 10 q^{33} + 13 q^{34} + 15 q^{35} + 23 q^{36} + 30 q^{37} + 15 q^{38} - 3 q^{39} + 10 q^{40} - 4 q^{41} - 15 q^{42} - 2 q^{44} - 15 q^{45} - 19 q^{46} - 30 q^{48} + 14 q^{49} - 15 q^{50} - 4 q^{51} - 10 q^{52} - 10 q^{53} - 5 q^{54} - 10 q^{55} + 10 q^{56} + 20 q^{58} - 10 q^{60} - 9 q^{61} - 30 q^{62} + 10 q^{63} + 4 q^{64} + 5 q^{65} + 12 q^{66} + 20 q^{67} + 17 q^{69} + 30 q^{70} + 6 q^{71} + 5 q^{72} + 15 q^{73} - 12 q^{74} - 10 q^{75} - 20 q^{76} + 10 q^{77} + 25 q^{78} + 15 q^{79} + 20 q^{80} + 28 q^{81} - 45 q^{83} + 18 q^{84} - 15 q^{85} - 9 q^{86} - 20 q^{87} - 20 q^{88} - 25 q^{89} - 25 q^{90} + 6 q^{91} + 30 q^{92} - 27 q^{94} + 15 q^{95} + 16 q^{96} - 60 q^{97} - 10 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q - 5 * q^2 - 5 * q^3 - q^4 - 9 * q^6 + 10 * q^8 + q^9 - 5 * q^10 - 4 * q^11 + 15 * q^12 - 5 * q^13 + 13 * q^14 + 15 * q^15 + 3 * q^16 - 10 * q^17 - 5 * q^19 - 15 * q^20 - 4 * q^21 + 5 * q^23 - 20 * q^24 - 10 * q^25 + 6 * q^26 - 5 * q^27 - 15 * q^28 - 5 * q^29 + 15 * q^30 - 9 * q^31 + 10 * q^33 + 13 * q^34 + 15 * q^35 + 23 * q^36 + 30 * q^37 + 15 * q^38 - 3 * q^39 + 10 * q^40 - 4 * q^41 - 15 * q^42 - 2 * q^44 - 15 * q^45 - 19 * q^46 - 30 * q^48 + 14 * q^49 - 15 * q^50 - 4 * q^51 - 10 * q^52 - 10 * q^53 - 5 * q^54 - 10 * q^55 + 10 * q^56 + 20 * q^58 - 10 * q^60 - 9 * q^61 - 30 * q^62 + 10 * q^63 + 4 * q^64 + 5 * q^65 + 12 * q^66 + 20 * q^67 + 17 * q^69 + 30 * q^70 + 6 * q^71 + 5 * q^72 + 15 * q^73 - 12 * q^74 - 10 * q^75 - 20 * q^76 + 10 * q^77 + 25 * q^78 + 15 * q^79 + 20 * q^80 + 28 * q^81 - 45 * q^83 + 18 * q^84 - 15 * q^85 - 9 * q^86 - 20 * q^87 - 20 * q^88 - 25 * q^89 - 25 * q^90 + 6 * q^91 + 30 * q^92 - 27 * q^94 + 15 * q^95 + 16 * q^96 - 60 * q^97 - 10 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	0.666375	−	0.917186i	0.471198	−	0.648548i	−0.505586	−	0.862776i	$-0.668724\pi$
$2$	0.666375	−	0.917186i	0.471198	−	0.648548i	0.976784	+	0.214228i	$0.0687236\pi$
$3$	−2.47539	+	0.804303i	−1.42917	+	0.464365i	−0.918503	−	0.395415i	$-0.870601\pi$
$3$	−2.47539	+	0.804303i	−1.42917	+	0.464365i	−0.510665	+	0.859780i	$0.670601\pi$
$4$	0.220859	+	0.679734i	0.110430	+	0.339867i
$5$	−1.07822	−	1.95894i	−0.482193	−	0.876065i
$5$	−1.07822	−	1.95894i	−0.482193	−	0.876065i
$6$	−0.911842	+	2.80636i	−0.372258	+	1.14569i
$7$			0.407162i			0.153893i	0.997035	+	0.0769463i	$0.0245170\pi$
$7$			0.407162i			0.153893i	−0.997035	+	0.0769463i	$0.975483\pi$
$8$	2.92705	+	0.951057i	1.03487	+	0.336249i
$9$	3.05361	−	2.21858i	1.01787	−	0.739525i
$10$	−2.51521	−	0.316463i	−0.795379	−	0.100074i
$11$	−1.61803	−	1.17557i	−0.487856	−	0.354448i	0.316503	−	0.948591i	$-0.397491\pi$
$11$	−1.61803	−	1.17557i	−0.487856	−	0.354448i	−0.804359	+	0.594144i	$0.797491\pi$
$12$	−1.09343	−	1.50497i	−0.315645	−	0.434448i
$13$	−0.411842	−	0.566852i	−0.114224	−	0.157216i	0.748077	−	0.663612i	$-0.230977\pi$
$13$	−0.411842	−	0.566852i	−0.114224	−	0.157216i	−0.862301	+	0.506396i	$0.830977\pi$
$14$	0.373443	+	0.271322i	0.0998068	+	0.0725139i
$15$	4.24459	+	3.98193i	1.09595	+	1.02813i
$16$	1.66637	−	1.21069i	0.416594	−	0.302673i
$17$	1.50527	+	0.489091i	0.365081	+	0.118622i	0.485812	−	0.874063i	$-0.338524\pi$
$17$	1.50527	+	0.489091i	0.365081	+	0.118622i	−0.120731	+	0.992685i	$0.538524\pi$
$18$		−	4.27913i		−	1.00860i
$19$	−1.52988	+	4.70847i	−0.350978	+	1.08020i	0.607328	+	0.794452i	$0.292242\pi$
$19$	−1.52988	+	4.70847i	−0.350978	+	1.08020i	−0.958305	+	0.285747i	$0.907758\pi$
$20$	1.09343	−	1.16555i	0.244497	−	0.260625i
$21$	−0.327481	−	1.00788i	−0.0714623	−	0.219938i
$22$	−2.15643	+	0.700668i	−0.459753	+	0.149383i
$23$	−0.706192	+	0.971990i	−0.147251	+	0.202674i	−0.876271	−	0.481819i	$-0.839976\pi$
$23$	−0.706192	+	0.971990i	−0.147251	+	0.202674i	0.729020	+	0.684493i	$0.239976\pi$
$24$	−8.01054			−1.63514
$25$	−2.67490	+	4.22433i	−0.534980	+	0.844865i
$26$	−0.794350			−0.155785
$27$	−1.18484	+	1.63079i	−0.228022	+	0.313846i
$28$	−0.276762	+	0.0899253i	−0.0523030	+	0.0169943i
$29$	−1.70239	−	5.23943i	−0.316127	−	0.972938i	−0.975288	−	0.220937i	$-0.929089\pi$
$29$	−1.70239	−	5.23943i	−0.316127	−	0.972938i	0.659161	−	0.752001i	$-0.270911\pi$
$30$	6.48066	−	1.23962i	1.18320	−	0.226323i
$31$	2.53514	−	7.80237i	0.455325	−	1.40135i	−0.415428	−	0.909626i	$-0.636368\pi$
$31$	2.53514	−	7.80237i	0.455325	−	1.40135i	0.870753	−	0.491721i	$-0.163632\pi$
$32$			3.82022i			0.675325i
$33$	4.95078	+	1.60861i	0.861821	+	0.280023i
$34$	1.45166	−	1.05469i	0.248958	−	0.180878i
$35$	0.797605	−	0.439008i	0.134820	−	0.0742060i
$36$	2.18246	+	1.58565i	0.363743	+	0.264275i
$37$	3.01846	+	4.15456i	0.496232	+	0.683005i	0.981522	−	0.191348i	$-0.0612859\pi$
$37$	3.01846	+	4.15456i	0.496232	+	0.683005i	−0.485290	+	0.874353i	$0.661286\pi$
$38$	3.29908	+	4.54079i	0.535181	+	0.736613i
$39$	1.47539	+	1.07193i	0.236252	+	0.171647i
$40$	−1.29293	−	6.75936i	−0.204430	−	1.06875i
$41$	−5.83802	+	4.24157i	−0.911745	+	0.662422i	−0.941456	−	0.337137i	$-0.890541\pi$
$41$	−5.83802	+	4.24157i	−0.911745	+	0.662422i	0.0297106	+	0.999559i	$0.490541\pi$
$42$	−1.14264	−	0.371267i	−0.176314	−	0.0572877i
$43$		−	9.16531i		−	1.39770i	−0.715270	−	0.698848i	$-0.753696\pi$
$43$		−	9.16531i		−	1.39770i	0.715270	−	0.698848i	$-0.246304\pi$
$44$	0.441718	−	1.35947i	0.0665915	−	0.204948i
$45$	−7.63851	−	3.58973i	−1.13868	−	0.535126i
$46$	0.420907	+	1.29542i	0.0620593	+	0.190999i
$47$	1.21092	−	0.393451i	0.176631	−	0.0573907i	−0.219367	−	0.975643i	$-0.570399\pi$
$47$	1.21092	−	0.393451i	0.176631	−	0.0573907i	0.395997	+	0.918252i	$0.370399\pi$
$48$	−3.15117	+	4.33721i	−0.454832	+	0.626022i
$49$	6.83422			0.976317
$50$	2.09201	+	5.26836i	0.295855	+	0.745059i
$51$	−4.11950			−0.576846
$52$	0.294350	−	0.405138i	0.0408190	−	0.0561825i
$53$	−4.83133	+	1.56979i	−0.663634	+	0.215628i	−0.621416	−	0.783481i	$-0.713442\pi$
$53$	−4.83133	+	1.56979i	−0.663634	+	0.215628i	−0.0422180	+	0.999108i	$0.513442\pi$
$54$	0.706192	+	2.17344i	0.0961005	+	0.295767i
$55$	−0.558282	+	4.43715i	−0.0752787	+	0.598306i
$56$	−0.387234	+	1.19178i	−0.0517463	+	0.159259i
$57$		−	12.8858i		−	1.70677i
$58$	−5.93997	−	1.93001i	−0.779956	−	0.253423i
$59$	−5.25838	+	3.82044i	−0.684583	+	0.497379i	−0.874875	−	0.484349i	$-0.839057\pi$
$59$	−5.25838	+	3.82044i	−0.684583	+	0.497379i	0.190292	+	0.981728i	$0.439057\pi$
$60$	−1.76920	+	3.76464i	−0.228403	+	0.486013i
$61$	7.62101	+	5.53699i	0.975770	+	0.708938i	0.956759	−	0.290881i	$-0.0939483\pi$
$61$	7.62101	+	5.53699i	0.975770	+	0.708938i	0.0190107	+	0.999819i	$0.493948\pi$
$62$	−5.46687	−	7.52450i	−0.694293	−	0.955612i
$63$	0.903319	+	1.24331i	0.113807	+	0.156643i
$64$	6.83660	+	4.96708i	0.854575	+	0.620885i
$65$	−0.666375	+	1.41796i	−0.0826536	+	0.175877i
$66$	4.77447	−	3.46885i	0.587696	−	0.426986i
$67$	−2.93090	−	0.952307i	−0.358066	−	0.116343i	0.124459	−	0.992225i	$-0.460280\pi$
$67$	−2.93090	−	0.952307i	−0.358066	−	0.116343i	−0.482526	+	0.875882i	$0.660280\pi$
$68$			1.13120i			0.137178i
$69$	0.966327	−	2.97405i	0.116332	−	0.358033i
$70$	0.128852	−	1.02410i	0.0154007	−	0.122403i
$71$	2.12183	+	6.53032i	0.251815	+	0.775007i	0.994440	+	0.105300i	$0.0335803\pi$
$71$	2.12183	+	6.53032i	0.251815	+	0.775007i	−0.742625	+	0.669707i	$0.766420\pi$
$72$	11.0481	−	3.58973i	1.30203	−	0.423054i
$73$	−0.320429	+	0.441032i	−0.0375033	+	0.0516189i	−0.827357	−	0.561677i	$-0.810157\pi$
$73$	−0.320429	+	0.441032i	−0.0375033	+	0.0516189i	0.789854	+	0.613296i	$0.210157\pi$
$74$	5.82193			0.676786
$75$	3.22378	−	12.6083i	0.372250	−	1.45588i
$76$	−3.53840			−0.405882
$77$	0.478647	−	0.658801i	0.0545469	−	0.0750774i
$78$	1.96633	−	0.638898i	0.222643	−	0.0723410i
$79$	−1.69390	−	5.21330i	−0.190579	−	0.586542i	0.809421	−	0.587229i	$-0.199781\pi$
$79$	−1.69390	−	5.21330i	−0.190579	−	0.586542i	−1.00000		0.000687140i	$0.999781\pi$
$80$	−4.16839	−	1.95894i	−0.466040	−	0.219016i
$81$	−1.87783	+	5.77938i	−0.208648	+	0.642153i
$82$			8.18102i			0.903442i
$83$	−0.926457	−	0.301024i	−0.101692	−	0.0330417i	0.257729	−	0.966217i	$-0.417026\pi$
$83$	−0.926457	−	0.301024i	−0.101692	−	0.0330417i	−0.359421	+	0.933176i	$0.617026\pi$
$84$	0.612766	−	0.445201i	0.0668583	−	0.0485754i
$85$	−0.664904	−	3.47608i	−0.0721190	−	0.377033i
$86$	−8.40629	−	6.10753i	−0.906474	−	0.658592i
$87$	8.42819	+	11.6004i	0.903596	+	1.24369i
$88$	−3.61803	−	4.97980i	−0.385684	−	0.530848i
$89$	−1.83363	−	1.33221i	−0.194364	−	0.141214i	0.486347	−	0.873766i	$-0.338329\pi$
$89$	−1.83363	−	1.33221i	−0.194364	−	0.141214i	−0.680711	+	0.732552i	$0.738329\pi$
$90$	−8.38256	+	4.61383i	−0.883599	+	0.486340i
$91$	0.230800	−	0.167686i	0.0241945	−	0.0175783i
$92$	−0.816664	−	0.265350i	−0.0851431	−	0.0276647i
$93$			21.3529i			2.21420i
$94$	0.446057	−	1.37282i	0.0460073	−	0.141596i
$95$	10.8732	−	2.07982i	1.11556	−	0.213385i
$96$	−3.07261	−	9.45653i	−0.313597	−	0.965153i
$97$	−14.4736	+	4.70276i	−1.46957	+	0.477493i	−0.930979	−	0.365073i	$-0.881044\pi$
$97$	−14.4736	+	4.70276i	−1.46957	+	0.477493i	−0.538593	+	0.842566i	$0.681044\pi$
$98$	4.55415	−	6.26825i	0.460039	−	0.633189i
$99$	−7.54893			−0.758696
$100$	−3.46219	−	0.885239i	−0.346219	−	0.0885239i
$101$	18.3965			1.83052			0.915261	−	0.402861i	$-0.131984\pi$
$101$	18.3965			1.83052			0.915261	+	0.402861i	$0.131984\pi$
$102$	−2.74513	+	3.77835i	−0.271809	+	0.374113i
$103$	11.3026	−	3.67243i	1.11368	−	0.361856i	0.306326	−	0.951927i	$-0.400900\pi$
$103$	11.3026	−	3.67243i	1.11368	−	0.361856i	0.807351	+	0.590071i	$0.200900\pi$
$104$	−0.666375	−	2.05089i	−0.0653434	−	0.201106i
$105$	−1.62129	+	1.72823i	−0.158222	+	0.168658i
$106$	−1.77968	+	5.47730i	−0.172858	+	0.532002i
$107$			0.754919i			0.0729808i	0.999334	+	0.0364904i	$0.0116178\pi$
$107$			0.754919i			0.0729808i	−0.999334	+	0.0364904i	$0.988382\pi$
$108$	−1.37019	−	0.445201i	−0.131846	−	0.0428395i
$109$	−7.40859	+	5.38265i	−0.709614	+	0.515565i	−0.883049	−	0.469281i	$-0.844513\pi$
$109$	−7.40859	+	5.38265i	−0.709614	+	0.515565i	0.173435	+	0.984845i	$0.444513\pi$
$110$	3.69767	+	3.46885i	0.352559	+	0.330742i
$111$	−10.8134	−	7.85640i	−1.02636	−	0.745697i
$112$	0.492947	+	0.678484i	0.0465791	+	0.0641107i
$113$	−7.54710	−	10.3877i	−0.709971	−	0.977191i	−0.999798	−	0.0201123i	$-0.993598\pi$
$113$	−7.54710	−	10.3877i	−0.709971	−	0.977191i	0.289827	−	0.957079i	$-0.406402\pi$
$114$	−11.8187	−	8.58677i	−1.10692	−	0.804225i
$115$	2.66550	+	0.335373i	0.248559	+	0.0312737i
$116$	3.18543	−	2.31435i	0.295760	−	0.214882i
$117$	−2.51521	−	0.817241i	−0.232531	−	0.0755539i
$118$			7.36876i			0.678349i
$119$	−0.199139	+	0.612887i	−0.0182551	+	0.0561833i
$120$	8.63709	+	15.6922i	0.788455	+	1.43249i
$121$	−2.16312	−	6.65740i	−0.196647	−	0.605218i
$122$	10.1569	−	3.30017i	0.919562	−	0.298784i
$123$	11.0399	−	15.1951i	0.995432	−	1.37009i
$124$	5.86345			0.526553
$125$	11.1593	+	0.685229i	0.998120	+	0.0612887i
$126$	1.74230			0.155216
$127$	4.17632	−	5.74821i	0.370588	−	0.510071i	−0.582472	−	0.812850i	$-0.697915\pi$
$127$	4.17632	−	5.74821i	0.370588	−	0.510071i	0.953061	+	0.302780i	$0.0979146\pi$
$128$	1.84498	−	0.599472i	0.163075	−	0.0529863i
$129$	7.37169	+	22.6877i	0.649041	+	1.99754i
$130$	0.856481	+	1.55608i	0.0751184	+	0.136478i
$131$	0.739865	−	2.27707i	0.0646423	−	0.198949i	−0.913519	−	0.406796i	$-0.866646\pi$
$131$	0.739865	−	2.27707i	0.0646423	−	0.198949i	0.978161	+	0.207848i	$0.0666459\pi$
$132$			3.72049i			0.323827i
$133$	−1.91711	−	0.622907i	−0.166234	−	0.0540129i
$134$	−2.82652	+	2.05359i	−0.244174	+	0.177403i
$135$	4.47214	+	0.562683i	0.384900	+	0.0484281i
$136$	3.94084	+	2.86319i	0.337924	+	0.245516i
$137$	−11.1793	−	15.3870i	−0.955111	−	1.31460i	−0.949219	−	0.314615i	$-0.898125\pi$
$137$	−11.1793	−	15.3870i	−0.955111	−	1.31460i	−0.00589176	−	0.999983i	$-0.501875\pi$
$138$	−2.08382	−	2.86813i	−0.177386	−	0.244152i
$139$	−5.44849	−	3.95856i	−0.462135	−	0.335761i	0.332233	−	0.943197i	$-0.392198\pi$
$139$	−5.44849	−	3.95856i	−0.462135	−	0.335761i	−0.794368	+	0.607437i	$0.792198\pi$
$140$	0.474567	+	0.445201i	0.0401083	+	0.0376263i
$141$	−2.68104	+	1.94789i	−0.225784	+	0.164042i
$142$	7.40346	+	2.40553i	0.621284	+	0.201867i
$143$			1.40134i			0.117186i
$144$	2.40244	−	7.39396i	0.200204	−	0.616163i
$145$	−8.42819	+	8.98413i	−0.699923	+	0.746092i
$146$	0.190983	+	0.587785i	0.0158059	+	0.0486455i
$147$	−16.9174	+	5.49679i	−1.39532	+	0.453367i
$148$	−2.15734	+	2.96933i	−0.177332	+	0.244077i
$149$	0.720492			0.0590250			0.0295125	−	0.999564i	$-0.490605\pi$
$149$	0.720492			0.0590250			0.0295125	+	0.999564i	$0.490605\pi$
$150$	−9.41590	−	11.3586i	−0.768805	−	0.927430i
$151$	−15.5178			−1.26282			−0.631412	−	0.775447i	$-0.717524\pi$
$151$	−15.5178			−1.26282			−0.631412	+	0.775447i	$0.717524\pi$
$152$	−8.95605	+	12.3269i	−0.726432	+	0.999847i
$153$	5.68158	−	1.84606i	0.459329	−	0.149245i
$154$	−0.285285	−	0.878017i	−0.0229889	−	0.0707526i
$155$	−18.0178	+	3.44645i	−1.44723	+	0.276825i
$156$	−0.402777	+	1.23962i	−0.0322480	+	0.0992491i
$157$		−	2.78418i		−	0.222202i	−0.993809	−	0.111101i	$-0.964562\pi$
$157$		−	2.78418i		−	0.222202i	0.993809	−	0.111101i	$-0.0354376\pi$
$158$	−5.91034	−	1.92039i	−0.470201	−	0.152778i
$159$	10.6968	−	7.77171i	0.848315	−	0.616337i
$160$	7.48358	−	4.11902i	0.591629	−	0.325637i
$161$	−0.395757	−	0.287534i	−0.0311900	−	0.0226609i
$162$	4.04942	+	5.57355i	0.318153	+	0.437900i
$163$	14.2287	+	19.5842i	1.11448	+	1.53395i	0.814645	+	0.579960i	$0.196932\pi$
$163$	14.2287	+	19.5842i	1.11448	+	1.53395i	0.299835	+	0.953991i	$0.403068\pi$
$164$	−4.17252	−	3.03151i	−0.325819	−	0.236721i
$165$	−2.18685	−	11.4327i	−0.170246	−	0.890036i
$166$	−0.893462	+	0.649138i	−0.0693461	+	0.0503829i
$167$	18.1140	+	5.88559i	1.40170	+	0.455441i	0.909741	−	0.415176i	$-0.136280\pi$
$167$	18.1140	+	5.88559i	1.40170	+	0.455441i	0.491961	+	0.870617i	$0.336280\pi$
$168$		−	3.26158i		−	0.251637i
$169$	3.86551	−	11.8968i	0.297347	−	0.915141i
$170$	−3.63128	−	1.70653i	−0.278507	−	0.130885i
$171$	5.77447	+	17.7720i	0.441585	+	1.35906i
$172$	6.22998	−	2.02424i	0.475031	−	0.154347i
$173$	−7.78642	+	10.7171i	−0.591991	+	0.814805i	−0.994946	−	0.100415i	$-0.967983\pi$
$173$	−7.78642	+	10.7171i	−0.591991	+	0.814805i	0.402955	+	0.915220i	$0.367983\pi$
$174$	16.2561			1.23237
$175$	−1.71998	−	1.08912i	−0.130018	−	0.0823294i
$176$	−4.11950			−0.310519
$177$	9.94376	−	13.6864i	0.747419	−	1.02873i
$178$	−2.44376	+	0.794027i	−0.183168	+	0.0595148i
$179$	3.77772	+	11.6266i	0.282360	+	0.869016i	0.987177	+	0.159627i	$0.0510290\pi$
$179$	3.77772	+	11.6266i	0.282360	+	0.869016i	−0.704817	+	0.709389i	$0.748971\pi$
$180$	0.753030	−	5.98498i	0.0561275	−	0.446094i
$181$	3.37348	−	10.3825i	0.250748	−	0.771724i	−0.743889	−	0.668303i	$-0.767021\pi$
$181$	3.37348	−	10.3825i	0.250748	−	0.771724i	0.994638	−	0.103421i	$-0.0329790\pi$
$182$		−	0.323429i		−	0.0239741i
$183$	−23.3184	−	7.57661i	−1.72375	−	0.560079i
$184$	−2.99148	+	2.17344i	−0.220535	+	0.160228i
$185$	4.88398	−	10.3925i	0.359077	−	0.764072i
$186$	19.5846	+	14.2291i	1.43601	+	1.04333i
$187$	−1.86061	−	2.56091i	−0.136062	−	0.187273i
$188$	0.534884	+	0.736205i	0.0390105	+	0.0536933i
$189$	−0.663995	−	0.482421i	−0.0482986	−	0.0350910i
$190$	5.33802	−	11.3586i	0.387260	−	0.824043i
$191$	−1.26824	+	0.921429i	−0.0917665	+	0.0666723i	−0.632722	−	0.774379i	$-0.718063\pi$
$191$	−1.26824	+	0.921429i	−0.0917665	+	0.0666723i	0.540956	+	0.841051i	$0.318063\pi$
$192$	−20.9183	−	6.79677i	−1.50965	−	0.490514i
$193$			1.65786i			0.119335i	0.998218	+	0.0596675i	$0.0190040\pi$
$193$			1.65786i			0.119335i	−0.998218	+	0.0596675i	$0.980996\pi$
$194$	−5.33154	+	16.4088i	−0.382782	+	1.17808i
$195$	0.509065	−	4.04598i	0.0364549	−	0.289739i
$196$	1.50940	+	4.64545i	0.107814	+	0.331818i
$197$	12.6330	−	4.10470i	0.900061	−	0.292448i	0.177799	−	0.984067i	$-0.443102\pi$
$197$	12.6330	−	4.10470i	0.900061	−	0.292448i	0.722262	+	0.691619i	$0.243102\pi$
$198$	−5.03042	+	6.92378i	−0.357496	+	0.492051i
$199$	−12.1025			−0.857921			−0.428960	−	0.903323i	$-0.641120\pi$
$199$	−12.1025			−0.857921			−0.428960	+	0.903323i	$0.641120\pi$
$200$	−11.8471	+	9.82084i	−0.837719	+	0.694438i
$201$	8.02107			0.565763
$202$	12.2590	−	16.8730i	0.862539	−	1.18718i
$203$	2.13330	−	0.693150i	0.149728	−	0.0486496i
$204$	−0.909830	−	2.80017i	−0.0637008	−	0.196051i
$205$	14.6036	+	6.86300i	1.01996	+	0.479333i
$206$	4.16345	−	12.8138i	0.290082	−	0.892779i
$207$			4.53482i			0.315192i
$208$	−1.37257	−	0.445974i	−0.0951704	−	0.0309227i
$209$	8.01054	−	5.81999i	0.554100	−	0.402577i
$210$	0.504726	+	2.63868i	0.0348294	+	0.182086i
$211$	5.42091	+	3.93852i	0.373191	+	0.271139i	0.758533	−	0.651635i	$-0.225917\pi$
$211$	5.42091	+	3.93852i	0.373191	+	0.271139i	−0.385342	+	0.922774i	$0.625917\pi$
$212$	−2.13409	−	2.93732i	−0.146570	−	0.201736i
$213$	−10.5047	−	14.4585i	−0.719772	−	0.990681i
$214$	0.692401	+	0.503059i	0.0473316	+	0.0343884i
$215$	−17.9543	+	9.88219i	−1.22447	+	0.673960i
$216$	−5.01906	+	3.64656i	−0.341504	+	0.248117i
$217$	3.17683	+	1.03221i	0.215657	+	0.0700712i
$218$			10.3819i			0.703152i
$219$	0.438463	−	1.34945i	0.0296286	−	0.0911873i
$220$	−3.13939	+	0.600502i	−0.211657	+	0.0404858i
$221$	−0.342690	−	1.05469i	−0.0230518	−	0.0709463i
$222$	−14.4116	+	4.68260i	−0.967241	+	0.314276i
$223$	−6.22564	+	8.56885i	−0.416900	+	0.573813i	−0.964884	−	0.262675i	$-0.915395\pi$
$223$	−6.22564	+	8.56885i	−0.416900	+	0.573813i	0.547985	+	0.836488i	$0.315395\pi$
$224$	−1.55545			−0.103928
$225$	1.20390	+	18.8339i	0.0802598	+	1.25559i
$226$	−14.5566			−0.968293
$227$	−11.5272	+	15.8658i	−0.765087	+	1.05305i	0.231687	+	0.972790i	$0.425575\pi$
$227$	−11.5272	+	15.8658i	−0.765087	+	1.05305i	−0.996774	+	0.0802612i	$0.974425\pi$
$228$	8.75892	−	2.84595i	0.580074	−	0.188477i
$229$	−2.73139	−	8.40637i	−0.180496	−	0.555508i	0.819346	−	0.573299i	$-0.194337\pi$
$229$	−2.73139	−	8.40637i	−0.180496	−	0.555508i	−0.999842	+	0.0177908i	$0.994337\pi$
$230$	2.08382	−	2.22127i	0.137403	−	0.146466i
$231$	−0.654963	+	2.01577i	−0.0430934	+	0.132628i
$232$		−	16.9552i		−	1.11316i
$233$	10.5210	+	3.41848i	0.689253	+	0.223952i	0.632642	−	0.774445i	$-0.281971\pi$
$233$	10.5210	+	3.41848i	0.689253	+	0.223952i	0.0566109	+	0.998396i	$0.481971\pi$
$234$	−2.42563	+	1.76233i	−0.158569	+	0.115207i
$235$	−2.07638	−	1.94789i	−0.135448	−	0.127066i
$236$	−3.75824	−	2.73052i	−0.244641	−	0.177742i
$237$	8.38615	+	11.5425i	0.544739	+	0.749769i
$238$	0.429430	+	0.591060i	0.0278358	+	0.0383127i
$239$	13.0296	+	9.46655i	0.842814	+	0.612340i	0.923155	−	0.384427i	$-0.125601\pi$
$239$	13.0296	+	9.46655i	0.842814	+	0.612340i	−0.0803411	+	0.996767i	$0.525601\pi$
$240$	11.8940	+	1.49650i	0.767753	+	0.0965985i
$241$	−4.84498	+	3.52009i	−0.312093	+	0.226749i	−0.732794	−	0.680451i	$-0.761784\pi$
$241$	−4.84498	+	3.52009i	−0.312093	+	0.226749i	0.420701	+	0.907199i	$0.361784\pi$
$242$	−7.54752	−	2.45234i	−0.485173	−	0.157642i
$243$		−	21.8639i		−	1.40257i
$244$	−2.08051	+	6.40315i	−0.133191	+	0.409920i
$245$	−7.36877	−	13.3878i	−0.470773	−	0.855317i
$246$	−6.58002	−	20.2512i	−0.419527	−	1.29117i
$247$	3.29908	−	1.07193i	0.209915	−	0.0682056i
$248$	14.8410	−	20.4269i	0.942404	−	1.29711i
$249$	2.53546			0.160678
$250$	8.06477	−	9.77855i	0.510061	−	0.618450i
$251$	3.73176			0.235547			0.117773	−	0.993041i	$-0.462424\pi$
$251$	3.73176			0.235547			0.117773	+	0.993041i	$0.462424\pi$
$252$	−0.645616	+	0.888614i	−0.0406700	+	0.0559774i
$253$	2.28528	−	0.742534i	0.143675	−	0.0466827i
$254$	−2.48918	−	7.66092i	−0.156185	−	0.480689i
$255$	4.44172	+	8.06987i	0.278151	+	0.505355i
$256$	−4.54307	+	13.9821i	−0.283942	+	0.873884i
$257$			23.5935i			1.47172i	0.677132	+	0.735862i	$0.263223\pi$
$257$			23.5935i			1.47172i	−0.677132	+	0.735862i	$0.736777\pi$
$258$	25.7212	+	8.35731i	1.60133	+	0.520304i
$259$	−1.69158	+	1.22900i	−0.105109	+	0.0763665i
$260$	−1.11101	−	0.139788i	−0.0689021	−	0.00866926i
$261$	−16.8225	−	12.2223i	−1.04129	−	0.756540i
$262$	−1.59547	−	2.19598i	−0.0985685	−	0.135668i
$263$	3.90363	+	5.37289i	0.240708	+	0.331307i	0.912230	−	0.409678i	$-0.134359\pi$
$263$	3.90363	+	5.37289i	0.240708	+	0.331307i	−0.671522	+	0.740985i	$0.734359\pi$
$264$	12.9613	+	9.41695i	0.797714	+	0.579573i
$265$	8.28436	+	7.77171i	0.508904	+	0.477413i
$266$	−1.84883	+	1.34326i	−0.113359	+	0.0823604i
$267$	5.61044	+	1.82294i	0.343353	+	0.111562i
$268$		−	2.20256i		−	0.134543i
$269$	4.03078	−	12.4055i	0.245761	−	0.756375i	−0.749749	−	0.661722i	$-0.769826\pi$
$269$	4.03078	−	12.4055i	0.245761	−	0.756375i	0.995510	−	0.0946532i	$-0.0301742\pi$
$270$	3.49620	−	3.72682i	0.212772	−	0.226807i
$271$	−3.66147	−	11.2689i	−0.222419	−	0.684534i	−0.998543	−	0.0539549i	$-0.982817\pi$
$271$	−3.66147	−	11.2689i	−0.222419	−	0.684534i	0.776125	−	0.630579i	$-0.217183\pi$
$272$	3.10048	−	1.00741i	0.187994	−	0.0610830i
$273$	−0.436451	+	0.600723i	−0.0264152	+	0.0363574i
$274$	−21.5623			−1.30263
$275$	9.29407	−	3.69057i	0.560453	−	0.222550i
$276$	2.23498			0.134530
$277$	−9.96641	+	13.7176i	−0.598824	+	0.824210i	−0.995600	−	0.0937053i	$-0.970129\pi$
$277$	−9.96641	+	13.7176i	−0.598824	+	0.824210i	0.396776	+	0.917915i	$0.370129\pi$
$278$	−7.26147	+	2.35939i	−0.435514	+	0.141507i
$279$	−9.56882	−	29.4498i	−0.572870	−	1.76311i
$280$	2.75215	−	0.526432i	0.164473	−	0.0314603i
$281$	−1.56826	+	4.82659i	−0.0935543	+	0.287930i	−0.986874	−	0.161491i	$-0.948370\pi$
$281$	−1.56826	+	4.82659i	−0.0935543	+	0.287930i	0.893320	+	0.449421i	$0.148370\pi$
$282$			3.75704i			0.223728i
$283$	11.2461	+	3.65408i	0.668511	+	0.217212i	0.623558	−	0.781777i	$-0.285686\pi$
$283$	11.2461	+	3.65408i	0.668511	+	0.217212i	0.0449525	+	0.998989i	$0.485686\pi$
$284$	−3.97026	+	2.88456i	−0.235592	+	0.171167i
$285$	−25.2425	+	13.8937i	−1.49524	+	0.822991i
$286$	1.28528	+	0.933814i	0.0760005	+	0.0552176i
$287$	−1.72700	−	2.37702i	−0.101942	−	0.140311i
$288$	8.47544	+	11.6654i	0.499420	+	0.687393i
$289$	−11.7267	−	8.51992i	−0.689804	−	0.501172i
$290$	2.62379	+	13.7170i	0.154074	+	0.805491i
$291$	32.0454	−	23.2823i	1.87853	−	1.36484i
$292$	−0.370554	−	0.120400i	−0.0216851	−	0.00704590i
$293$		−	19.4348i		−	1.13540i	−0.823237	−	0.567698i	$-0.807834\pi$
$293$		−	19.4348i		−	1.13540i	0.823237	−	0.567698i	$-0.192166\pi$
$294$	−6.23173	+	19.1793i	−0.363442	+	1.11856i
$295$	13.1537	+	6.18160i	0.765837	+	0.359907i
$296$	4.88398	+	15.0313i	0.283875	+	0.873679i
$297$	3.83422	−	1.24581i	0.222484	−	0.0722894i
$298$	0.480118	−	0.660825i	0.0278125	−	0.0382806i
$299$	0.841814			0.0486834
$300$	9.28229	−	0.593341i	0.535913	−	0.0342566i
$301$	3.73176			0.215095
$302$	−10.3407	+	14.2328i	−0.595040	+	0.819003i
$303$	−45.5386	+	14.7964i	−2.61612	+	0.850030i
$304$	3.15117	+	9.69829i	0.180732	+	0.556235i
$305$	2.62953	−	20.8992i	0.150566	−	1.19668i
$306$	2.09288	−	6.44123i	0.119642	−	0.368221i
$307$		−	25.4169i		−	1.45062i	−0.688423	−	0.725310i	$-0.741697\pi$
$307$		−	25.4169i		−	1.45062i	0.688423	−	0.725310i	$-0.258303\pi$
$308$	0.553523	+	0.179851i	0.0315399	+	0.0102479i
$309$	−25.0246	+	18.1814i	−1.42360	+	1.03431i
$310$	−8.84558	+	18.8223i	−0.502395	+	1.06904i
$311$	−12.8292	−	9.32097i	−0.727478	−	0.528544i	0.161287	−	0.986908i	$-0.448436\pi$
$311$	−12.8292	−	9.32097i	−0.727478	−	0.528544i	−0.888765	+	0.458364i	$0.848436\pi$
$312$	3.29908	+	4.54079i	0.186773	+	0.257072i
$313$	−4.12416	−	5.67642i	−0.233111	−	0.320850i	0.676396	−	0.736538i	$-0.263541\pi$
$313$	−4.12416	−	5.67642i	−0.233111	−	0.320850i	−0.909507	+	0.415688i	$0.863541\pi$
$314$	−2.55361	−	1.85530i	−0.144108	−	0.104701i
$315$	1.46160	−	3.11011i	0.0823519	−	0.175235i
$316$	3.16955	−	2.30281i	0.178301	−	0.129543i
$317$	−12.3958	−	4.02763i	−0.696215	−	0.226214i	−0.0605344	−	0.998166i	$-0.519280\pi$
$317$	−12.3958	−	4.02763i	−0.696215	−	0.226214i	−0.635681	+	0.771952i	$0.719280\pi$
$318$		−	14.9899i		−	0.840590i
$319$	−3.40479	+	10.4789i	−0.190632	+	0.586704i
$320$	2.35888	−	18.7481i	0.131865	−	1.04805i
$321$	−0.607184	−	1.86872i	−0.0338897	−	0.104302i
$322$	−0.527445	+	0.171377i	−0.0293933	+	0.00955047i
$323$	−4.60575	+	6.33927i	−0.256271	+	0.352726i
$324$	−4.34318			−0.241288
$325$	3.49620	−	0.223484i	0.193934	−	0.0123966i
$326$	27.4440			1.51998
$327$	14.0099	−	19.2829i	0.774747	−	1.06635i
$328$	−21.1221	+	6.86300i	−1.16628	+	0.378946i
$329$	0.160198	+	0.493039i	0.00883201	+	0.0271821i
$330$	−11.9432	−	5.61272i	−0.657451	−	0.308970i
$331$	−5.45225	+	16.7803i	−0.299683	+	0.922329i	0.681925	+	0.731422i	$0.261143\pi$
$331$	−5.45225	+	16.7803i	−0.299683	+	0.922329i	−0.981608	+	0.190907i	$0.938857\pi$
$332$		−	0.696229i		−	0.0382105i
$333$	18.4344	+	5.98970i	1.01020	+	0.328234i
$334$	17.4689	−	12.6919i	0.955855	−	0.694469i
$335$	1.29463	+	6.76825i	0.0707333	+	0.369789i
$336$	−1.76594	−	1.28303i	−0.0963401	−	0.0699952i
$337$	14.6062	+	20.1037i	0.795649	+	1.09512i	0.993382	+	0.114860i	$0.0366421\pi$
$337$	14.6062	+	20.1037i	0.795649	+	1.09512i	−0.197733	+	0.980256i	$0.563358\pi$
$338$	−8.33572	−	11.4731i	−0.453404	−	0.624056i
$339$	27.0369	+	19.6434i	1.46844	+	1.06689i
$340$	2.21596	−	1.21968i	0.120177	−	0.0661465i
$341$	−13.2742	+	9.64426i	−0.718837	+	0.522266i
$342$	20.1482	+	6.54654i	1.08949	+	0.353996i
$343$			5.63276i			0.304141i
$344$	8.71673	−	26.8273i	0.469974	−	1.44643i
$345$	−6.86789	+	1.31369i	−0.369755	+	0.0707267i
$346$	4.64089	+	14.2832i	0.249496	+	0.767869i
$347$	12.6276	−	4.10297i	0.677887	−	0.220259i	0.0502171	−	0.998738i	$-0.484009\pi$
$347$	12.6276	−	4.10297i	0.677887	−	0.220259i	0.627670	+	0.778479i	$0.284009\pi$
$348$	−6.02375	+	8.29098i	−0.322907	+	0.444443i
$349$	18.1283			0.970385			0.485192	−	0.874407i	$-0.338750\pi$
$349$	18.1283			0.970385			0.485192	+	0.874407i	$0.338750\pi$
$350$	−2.14507	+	0.851785i	−0.114659	+	0.0455298i
$351$	1.41238			0.0753875
$352$	4.49094	−	6.18124i	0.239368	−	0.329461i
$353$	16.8377	−	5.47091i	0.896182	−	0.291187i	0.175522	−	0.984476i	$-0.443839\pi$
$353$	16.8377	−	5.47091i	0.896182	−	0.291187i	0.720660	+	0.693288i	$0.243839\pi$
$354$	−5.92672	−	18.2406i	−0.315001	−	0.969475i
$355$	10.5047	−	11.1976i	0.557533	−	0.594309i
$356$	0.500574	−	1.54061i	0.0265304	−	0.0816521i
$357$		−	1.67730i		−	0.0887723i
$358$	13.1812	+	4.28282i	0.696646	+	0.226354i
$359$	26.3289	−	19.1291i	1.38959	−	1.00959i	0.393677	−	0.919249i	$-0.371203\pi$
$359$	26.3289	−	19.1291i	1.38959	−	1.00959i	0.995910	−	0.0903458i	$-0.0287972\pi$
$360$	−18.9443	−	17.7720i	−0.998451	−	0.936666i
$361$	−4.45789	−	3.23885i	−0.234626	−	0.170466i
$362$	−7.27467	−	10.0127i	−0.382348	−	0.526257i
$363$	10.7091	+	14.7399i	0.562084	+	0.773642i
$364$	0.164956	+	0.119848i	0.00864607	+	0.00628174i
$365$	1.20945	+	0.152172i	0.0633054	+	0.00796507i
$366$	−22.4879	+	16.3384i	−1.17546	+	0.854024i
$367$	−31.3355	−	10.1815i	−1.63570	−	0.531472i	−0.660129	−	0.751152i	$-0.729499\pi$
$367$	−31.3355	−	10.1815i	−1.63570	−	0.531472i	−0.975572	+	0.219680i	$0.929499\pi$
$368$			2.47468i			0.129002i
$369$	−8.41677	+	25.9042i	−0.438160	+	1.34852i
$370$	−6.27730	−	11.4048i	−0.326341	−	0.592908i
$371$	−0.639160	−	1.96713i	−0.0331835	−	0.102128i
$372$	−14.5143	+	4.71599i	−0.752533	+	0.244513i
$373$	2.03754	−	2.80444i	0.105500	−	0.145208i	−0.753003	−	0.658018i	$-0.771395\pi$
$373$	2.03754	−	2.80444i	0.105500	−	0.145208i	0.858503	+	0.512809i	$0.171395\pi$
$374$	−3.58870			−0.185567
$375$	−28.1748	+	7.27927i	−1.45494	+	0.375900i
$376$	3.91861			0.202087
$377$	−2.26886	+	3.12282i	−0.116852	+	0.160834i
$378$	−0.884939	+	0.287534i	−0.0455164	+	0.0147892i
$379$	0.595979	+	1.83424i	0.0306134	+	0.0942183i	0.965196	−	0.261528i	$-0.0842265\pi$
$379$	0.595979	+	1.83424i	0.0306134	+	0.0942183i	−0.934582	+	0.355747i	$0.884227\pi$
$380$	3.81516	+	6.93151i	0.195714	+	0.355579i
$381$	−5.71472	+	17.5881i	−0.292774	+	0.901065i
$382$			1.77723i			0.0909309i
$383$	−4.68874	−	1.52346i	−0.239583	−	0.0778454i	0.186764	−	0.982405i	$-0.440200\pi$
$383$	−4.68874	−	1.52346i	−0.239583	−	0.0778454i	−0.426348	+	0.904559i	$0.640200\pi$
$384$	−4.08490	+	2.96786i	−0.208457	+	0.151453i
$385$	−1.80664	−	0.227311i	−0.0920748	−	0.0115848i
$386$	1.52056	+	1.10475i	0.0773945	+	0.0562304i
$387$	−20.3339	−	27.9873i	−1.03363	−	1.42267i
$388$	−6.39326	−	8.79956i	−0.324568	−	0.446730i
$389$	10.8295	+	7.86809i	0.549077	+	0.398928i	0.827445	−	0.561547i	$-0.189793\pi$
$389$	10.8295	+	7.86809i	0.549077	+	0.398928i	−0.278368	+	0.960475i	$0.589793\pi$
$390$	−3.37169	−	3.16305i	−0.170732	−	0.160167i
$391$	−1.53840	+	1.11771i	−0.0778002	+	0.0565252i
$392$	20.0041	+	6.49973i	1.01036	+	0.328286i
$393$			6.23172i			0.314349i
$394$	4.65351	−	14.3220i	0.234441	−	0.721534i
$395$	−8.38615	+	8.93932i	−0.421953	+	0.449786i
$396$	−1.66725	−	5.13127i	−0.0837825	−	0.257856i
$397$	2.03418	−	0.660946i	0.102093	−	0.0331719i	−0.257525	−	0.966272i	$-0.582907\pi$
$397$	2.03418	−	0.660946i	0.102093	−	0.0331719i	0.359618	+	0.933100i	$0.382907\pi$
$398$	−8.06477	+	11.1002i	−0.404250	+	0.556403i
$399$	5.24660			0.262659
$400$	0.656975	+	10.2778i	0.0328487	+	0.513889i
$401$	−26.8213			−1.33939			−0.669696	−	0.742635i	$-0.733576\pi$
$401$	−26.8213			−1.33939			−0.669696	+	0.742635i	$0.733576\pi$
$402$	5.34504	−	7.35681i	0.266586	−	0.366924i
$403$	−5.46687	+	1.77629i	−0.272324	+	0.0884835i
$404$	4.06304	+	12.5048i	0.202144	+	0.622135i
$405$	13.3462	−	2.55286i	0.663177	−	0.126852i
$406$	0.785827	−	2.41853i	0.0389999	−	0.120029i
$407$		−	10.2706i		−	0.509097i
$408$	−12.0580	−	3.91788i	−0.596960	−	0.193964i
$409$	11.3248	−	8.22796i	0.559976	−	0.406847i	−0.271474	−	0.962446i	$-0.587511\pi$
$409$	11.3248	−	8.22796i	0.559976	−	0.406847i	0.831450	+	0.555599i	$0.187511\pi$
$410$	16.0261	−	8.82091i	0.791474	−	0.435634i
$411$	40.0489	+	29.0972i	1.97547	+	1.43526i
$412$	4.99256	+	6.87167i	0.245966	+	0.338543i
$413$	−1.55554	−	2.14101i	−0.0765429	−	0.105352i
$414$	4.15927	+	3.02189i	0.204417	+	0.148518i
$415$	0.409233	+	2.13944i	0.0200885	+	0.105021i
$416$	2.16550	−	1.57333i	0.106172	−	0.0771387i
$417$	16.6710	+	5.41674i	0.816384	+	0.265259i
$418$		−	11.2254i		−	0.549055i
$419$	−9.54925	+	29.3896i	−0.466511	+	1.43577i	0.390560	+	0.920577i	$0.372281\pi$
$419$	−9.54925	+	29.3896i	−0.466511	+	1.43577i	−0.857072	+	0.515197i	$0.827719\pi$
$420$	−1.53282	−	0.720350i	−0.0747938	−	0.0351495i
$421$	−2.54622	−	7.83646i	−0.124095	−	0.381926i	0.869640	−	0.493687i	$-0.164351\pi$
$421$	−2.54622	−	7.83646i	−0.124095	−	0.381926i	−0.993735	+	0.111761i	$0.964351\pi$
$422$	7.22471	−	2.34745i	0.351693	−	0.114272i
$423$	2.82477	−	3.88796i	0.137345	−	0.189039i
$424$	−15.6345			−0.759279
$425$	−6.09252	+	5.05047i	−0.295530	+	0.244984i
$426$	−20.2612			−0.981660
$427$	−2.25445	+	3.10298i	−0.109100	+	0.150164i
$428$	−0.513144	+	0.166731i	−0.0248038	+	0.00805923i
$429$	−1.12710	−	3.46885i	−0.0544168	−	0.167478i
$430$	−2.90048	+	23.0527i	−0.139874	+	1.11170i
$431$	8.38925	−	25.8194i	0.404096	−	1.24368i	−0.517552	−	0.855652i	$-0.673157\pi$
$431$	8.38925	−	25.8194i	0.404096	−	1.24368i	0.921648	−	0.388027i	$-0.126843\pi$
$432$			4.15198i			0.199762i
$433$	−20.4387	−	6.64093i	−0.982220	−	0.319143i	−0.226481	−	0.974016i	$-0.572722\pi$
$433$	−20.4387	−	6.64093i	−0.982220	−	0.319143i	−0.755739	+	0.654873i	$0.772722\pi$
$434$	3.06369	−	2.22590i	0.147062	−	0.106847i
$435$	13.6371	−	29.0181i	0.653849	−	1.39131i
$436$	−5.29503	−	3.84706i	−0.253586	−	0.184241i
$437$	−3.49620	−	4.81211i	−0.167246	−	0.230194i
$438$	−0.945515	−	1.30139i	−0.0451785	−	0.0621828i
$439$	−20.8691	−	15.1623i	−0.996027	−	0.723656i	−0.0347942	−	0.999394i	$-0.511078\pi$
$439$	−20.8691	−	15.1623i	−0.996027	−	0.723656i	−0.961233	+	0.275739i	$0.911078\pi$
$440$	−5.85410	+	12.4568i	−0.279083	+	0.593855i
$441$	20.8690	−	15.1622i	0.993763	−	0.722011i
$442$	−1.19571	−	0.388509i	−0.0568741	−	0.0184795i
$443$		−	3.18479i		−	0.151314i	−0.997134	−	0.0756570i	$-0.975895\pi$
$443$		−	3.18479i		−	0.151314i	0.997134	−	0.0756570i	$-0.0241054\pi$
$444$	2.95203	−	9.08540i	0.140097	−	0.431174i
$445$	−0.632669	+	5.02837i	−0.0299914	+	0.238368i
$446$	3.71063	+	11.4201i	0.175703	+	0.540759i
$447$	−1.78350	+	0.579494i	−0.0843566	+	0.0274091i
$448$	−2.02240	+	2.78360i	−0.0955496	+	0.131513i
$449$	−36.0785			−1.70265			−0.851325	−	0.524639i	$-0.824200\pi$
$449$	−36.0785			−1.70265			−0.851325	+	0.524639i	$0.824200\pi$
$450$	18.0764	+	11.4462i	0.852131	+	0.539581i
$451$	14.4324			0.679594
$452$	5.39402	−	7.42424i	0.253714	−	0.349207i
$453$	38.4127	−	12.4811i	1.80479	−	0.586411i
$454$	6.87048	+	21.1452i	0.322448	+	0.992392i
$455$	−0.577340	−	0.271322i	−0.0270661	−	0.0127198i
$456$	12.2551	−	37.7174i	0.573899	−	1.76628i
$457$			25.5245i			1.19399i	0.802246	+	0.596994i	$0.203638\pi$
$457$			25.5245i			1.19399i	−0.802246	+	0.596994i	$0.796362\pi$
$458$	−9.53033	−	3.09659i	−0.445323	−	0.144694i
$459$	−2.58111	+	1.87528i	−0.120476	+	0.0875307i
$460$	0.360735	+	1.88590i	0.0168194	+	0.0879306i
$461$	13.4614	+	9.78026i	0.626959	+	0.455512i	0.855345	−	0.518058i	$-0.173345\pi$
$461$	13.4614	+	9.78026i	0.626959	+	0.455512i	−0.228387	+	0.973571i	$0.573345\pi$
$462$	1.41238	+	1.94398i	0.0657100	+	0.0904421i
$463$	10.4730	+	14.4149i	0.486723	+	0.669916i	0.979779	−	0.200081i	$-0.0641205\pi$
$463$	10.4730	+	14.4149i	0.486723	+	0.669916i	−0.493057	+	0.869997i	$0.664120\pi$
$464$	−9.18017	−	6.66978i	−0.426178	−	0.309637i
$465$	41.8292	−	23.0231i	1.93978	−	1.06767i
$466$	10.1463	−	7.37171i	0.470018	−	0.341488i
$467$	−13.5507	−	4.40289i	−0.627051	−	0.203741i	−0.0217829	−	0.999763i	$-0.506934\pi$
$467$	−13.5507	−	4.40289i	−0.627051	−	0.203741i	−0.605269	+	0.796021i	$0.706934\pi$
$468$		−	1.89017i		−	0.0873731i
$469$	0.387743	−	1.19335i	0.0179043	−	0.0551038i
$470$	−3.17022	+	0.606401i	−0.146232	+	0.0279712i
$471$	2.23932	+	6.89193i	0.103183	+	0.317563i
$472$	−19.0250	+	6.18160i	−0.875697	+	0.284531i
$473$	−10.7745	+	14.8298i	−0.495411	+	0.681874i
$474$	16.1750			0.742941
$475$	−15.7979	−	19.0574i	−0.724856	−	0.874413i
$476$	−0.460582			−0.0211107
$477$	−11.2703	+	15.5122i	−0.516031	+	0.710255i
$478$	17.3652	−	5.64229i	0.794265	−	0.258072i
$479$	−0.898820	−	2.76628i	−0.0410681	−	0.126395i	0.928420	−	0.371531i	$-0.121167\pi$
$479$	−0.898820	−	2.76628i	−0.0410681	−	0.126395i	−0.969489	+	0.245137i	$0.921167\pi$
$480$	−15.2118	+	16.2153i	−0.694323	+	0.740122i
$481$	1.11189	−	3.42205i	0.0506978	−	0.156032i
$482$			6.78945i			0.309251i
$483$	1.21092	+	0.393451i	0.0550987	+	0.0179026i
$484$	4.04752	−	2.94069i	0.183978	−	0.133668i
$485$	24.8181	+	23.2823i	1.12693	+	1.05720i
$486$	−20.0532	−	14.5695i	−0.909633	−	0.660887i
$487$	10.0307	+	13.8060i	0.454533	+	0.625612i	0.973364	−	0.229266i	$-0.0736324\pi$
$487$	10.0307	+	13.8060i	0.454533	+	0.625612i	−0.518831	+	0.854877i	$0.673632\pi$
$488$	17.0411	+	23.4550i	0.771414	+	1.06176i
$489$	−50.9733	−	37.0343i	−2.30509	−	1.67475i
$490$	−17.1895	−	2.16278i	−0.776542	−	0.0977044i
$491$	−24.8990	+	18.0902i	−1.12368	+	0.816398i	−0.984762	−	0.173906i	$-0.944361\pi$
$491$	−24.8990	+	18.0902i	−1.12368	+	0.816398i	−0.138913	+	0.990305i	$0.544361\pi$
$492$	12.7669	+	4.14821i	0.575575	+	0.187016i
$493$		−	8.71937i		−	0.392701i
$494$	1.21526	−	3.74018i	0.0546770	−	0.168278i
$495$	8.13939	+	14.7879i	0.365838	+	0.664667i
$496$	−5.22177	−	16.0709i	−0.234464	−	0.721607i
$497$	−2.65890	+	0.863928i	−0.119268	+	0.0387525i
$498$	1.68956	−	2.32549i	0.0757112	−	0.104208i
$499$	11.8824			0.531927			0.265964	−	0.963983i	$-0.414310\pi$
$499$	11.8824			0.531927			0.265964	+	0.963983i	$0.414310\pi$
$500$	1.99886	+	7.73671i	0.0893919	+	0.345996i
$501$	−49.5730			−2.21476
$502$	2.48675	−	3.42272i	0.110989	−	0.152763i
$503$	−2.83247	+	0.920324i	−0.126293	+	0.0410352i	−0.371482	−	0.928440i	$-0.621150\pi$
$503$	−2.83247	+	0.920324i	−0.126293	+	0.0410352i	0.245188	+	0.969475i	$0.421150\pi$
$504$	1.46160	+	4.49834i	0.0651049	+	0.200372i
$505$	−19.8354	−	36.0377i	−0.882665	−	1.60366i
$506$	0.841814	−	2.59084i	0.0374232	−	0.115177i
$507$			32.5584i			1.44597i
$508$	4.82963	+	1.56924i	0.214280	+	0.0696239i
$509$	−29.7038	+	21.5811i	−1.31660	+	0.956564i	−0.316629	+	0.948549i	$0.602551\pi$
$509$	−29.7038	+	21.5811i	−1.31660	+	0.956564i	−0.999968	+	0.00801464i	$0.997449\pi$
$510$	10.3614	+	1.30367i	0.458811	+	0.0577275i
$511$	−0.179571	−	0.130466i	−0.00794377	−	0.00577149i
$512$	12.0774	+	16.6231i	0.533749	+	0.734642i
$513$	−5.86588	−	8.07369i	−0.258985	−	0.356462i
$514$	21.6396	+	15.7221i	0.954484	+	0.693473i
$515$	−19.3807	−	18.1814i	−0.854017	−	0.801169i
$516$	−13.7935	+	10.0216i	−0.607226	+	0.441176i
$517$	−2.42184	−	0.786902i	−0.106512	−	0.0346079i
$518$			2.37047i			0.104152i
$519$	10.6546	−	32.7916i	0.467687	−	1.43939i
$520$	−3.29908	+	3.51669i	−0.144674	+	0.154217i
$521$	0.772662	+	2.37801i	0.0338509	+	0.104182i	0.966554	−	0.256462i	$-0.0825568\pi$
$521$	0.772662	+	2.37801i	0.0338509	+	0.104182i	−0.932703	+	0.360644i	$0.882557\pi$
$522$	−22.4202	+	7.28477i	−0.981306	+	0.318846i
$523$	24.7609	−	34.0805i	1.08272	−	1.49024i	0.226229	−	0.974074i	$-0.427360\pi$
$523$	24.7609	−	34.0805i	1.08272	−	1.49024i	0.856491	−	0.516162i	$-0.172640\pi$
$524$	1.71121			0.0747545
$525$	5.13361	+	1.31260i	0.224049	+	0.0572865i
$526$	7.52922			0.328290
$527$	7.63214	−	10.5047i	0.332461	−	0.457594i
$528$	10.1974	−	3.31333i	0.443784	−	0.144194i
$529$	6.66133	+	20.5015i	0.289623	+	0.891369i
$530$	12.6486	−	2.41942i	0.549420	−	0.105093i
$531$	−7.58111	+	23.3322i	−0.328992	+	1.01253i
$532$		−	1.44070i		−	0.0624623i
$533$	4.80868	+	1.56244i	0.208287	+	0.0676766i
$534$	5.41063	−	3.93105i	0.234141	−	0.170113i
$535$	1.47884	−	0.813966i	0.0639359	−	0.0351908i
$536$	−7.67320	−	5.57490i	−0.331432	−	0.240799i
$537$	−18.7027	−	25.7420i	−0.807080	−	1.11085i
$538$	−8.69212	−	11.9637i	−0.374744	−	0.515791i
$539$	−11.0580	−	8.03411i	−0.476302	−	0.346053i
$540$	0.605237	+	3.16414i	0.0260452	+	0.136163i
$541$	22.1259	−	16.0754i	0.951268	−	0.691137i	0.000161922	−	1.00000i	$-0.499948\pi$
$541$	22.1259	−	16.0754i	0.951268	−	0.691137i	0.951107	+	0.308863i	$0.0999485\pi$
$542$	−12.7756	−	4.15103i	−0.548757	−	0.178302i
$543$			28.4140i			1.21936i
$544$	−1.86843	+	5.75045i	−0.0801085	+	0.246549i
$545$	18.5324	+	8.70932i	0.793839	+	0.373066i
$546$	0.260135	+	0.800613i	0.0111327	+	0.0342631i
$547$	19.3437	−	6.28515i	0.827077	−	0.268734i	0.135263	−	0.990810i	$-0.456812\pi$
$547$	19.3437	−	6.28515i	0.827077	−	0.268734i	0.691814	+	0.722076i	$0.256812\pi$
$548$	7.99001	−	10.9973i	0.341316	−	0.469781i
$549$	35.5558			1.51748
$550$	2.80839	−	10.9837i	0.119750	−	0.468346i
$551$	27.2742			1.16192
$552$	5.65697	−	7.78616i	0.240777	−	0.331401i
$553$	2.12266	−	0.689692i	0.0902645	−	0.0293287i
$554$	5.94022	+	18.2821i	0.252376	+	0.776732i
$555$	−3.73103	+	29.6537i	−0.158373	+	1.25873i
$556$	1.48742	−	4.57781i	0.0630807	−	0.194142i
$557$		−	28.2605i		−	1.19744i	−0.800960	−	0.598718i	$-0.795677\pi$
$557$		−	28.2605i		−	1.19744i	0.800960	−	0.598718i	$-0.204323\pi$
$558$	−33.3873	−	10.8482i	−1.41340	−	0.459241i
$559$	−5.19537	+	3.77466i	−0.219741	+	0.159651i
$560$	0.797605	−	1.69721i	0.0337050	−	0.0717201i
$561$	6.66550	+	4.84277i	0.281418	+	0.204462i
$562$	3.38184	+	4.65470i	0.142654	+	0.196347i
$563$	−7.59738	−	10.4569i	−0.320192	−	0.440706i	0.618334	−	0.785915i	$-0.287808\pi$
$563$	−7.59738	−	10.4569i	−0.320192	−	0.440706i	−0.938526	+	0.345210i	$0.887808\pi$
$564$	−1.91618	−	1.39219i	−0.0806858	−	0.0586216i
$565$	−12.2115	+	25.9845i	−0.513740	+	1.09318i
$566$	10.8456	−	7.87977i	0.455874	−	0.331212i
$567$	−2.35314	−	0.764582i	−0.0988226	−	0.0321094i
$568$			21.1326i			0.886703i
$569$	0.953142	−	2.93347i	0.0399578	−	0.122977i	−0.929088	−	0.369859i	$-0.879406\pi$
$569$	0.953142	−	2.93347i	0.0399578	−	0.122977i	0.969046	+	0.246882i	$0.0794059\pi$
$570$	−4.07788	+	32.4105i	−0.170804	+	1.35753i
$571$	−1.27552	−	3.92564i	−0.0533788	−	0.164283i	0.920813	−	0.390004i	$-0.127526\pi$
$571$	−1.27552	−	3.92564i	−0.0533788	−	0.164283i	−0.974192	+	0.225721i	$0.927526\pi$
$572$	−0.952536	+	0.309498i	−0.0398275	+	0.0129407i
$573$	2.39828	−	3.30095i	0.100190	−	0.137899i
$574$	−3.33100			−0.139033
$575$	−2.21701	−	5.58316i	−0.0924557	−	0.232834i
$576$	31.8961			1.32901
$577$	−3.73579	+	5.14187i	−0.155523	+	0.214059i	−0.879667	−	0.475589i	$-0.842235\pi$
$577$	−3.73579	+	5.14187i	−0.155523	+	0.214059i	0.724145	+	0.689648i	$0.242235\pi$
$578$	−15.6287	+	5.07807i	−0.650068	+	0.211220i
$579$	−1.33342	−	4.10384i	−0.0554150	−	0.170550i
$580$	−7.96827	−	3.74470i	−0.330864	−	0.155490i
$581$	0.122565	−	0.377218i	0.00508487	−	0.0156496i
$582$		−	44.9063i		−	1.86143i
$583$	9.66266	+	3.13959i	0.400187	+	0.130028i
$584$	−1.35736	+	0.986178i	−0.0561679	+	0.0408083i
$585$	1.11101	+	5.80831i	0.0459348	+	0.240144i
$586$	−17.8254	−	12.9509i	−0.736359	−	0.534996i
$587$	−12.4046	−	17.0735i	−0.511992	−	0.704697i	0.472261	−	0.881459i	$-0.343438\pi$
$587$	−12.4046	−	17.0735i	−0.511992	−	0.704697i	−0.984254	+	0.176761i	$0.943438\pi$
$588$	−7.47271	−	10.2853i	−0.308169	−	0.424159i
$589$	32.8588	+	23.8733i	1.35392	+	0.983683i
$590$	14.4350	−	7.94512i	0.594278	−	0.327095i
$591$	−27.9701	+	20.3215i	−1.15054	+	0.835913i
$592$	10.0598	+	3.26862i	0.413455	+	0.134340i
$593$			21.6529i			0.889177i	0.895735	+	0.444589i	$0.146650\pi$
$593$			21.6529i			0.889177i	−0.895735	+	0.444589i	$0.853350\pi$
$594$	1.41238	−	4.34687i	0.0579508	−	0.178354i
$595$	1.41532	−	0.270723i	0.0580227	−	0.0110986i
$596$	0.159127	+	0.489743i	0.00651810	+	0.0200607i
$597$	29.9583	−	9.73405i	1.22611	−	0.398388i
$598$	0.560963	−	0.772100i	0.0229395	−	0.0315735i
$599$	3.38501			0.138308			0.0691539	−	0.997606i	$-0.477970\pi$
$599$	3.38501			0.138308			0.0691539	+	0.997606i	$0.477970\pi$
$600$	21.4274	−	33.8391i	0.874768	−	1.38148i
$601$	28.8265			1.17586			0.587928	−	0.808913i	$-0.299944\pi$
$601$	28.8265			1.17586			0.587928	+	0.808913i	$0.299944\pi$
$602$	2.48675	−	3.42272i	0.101352	−	0.139500i
$603$	−11.0626	+	3.59445i	−0.450503	+	0.146377i
$604$	−3.42726	−	10.5480i	−0.139453	−	0.429193i
$605$	−10.7091	+	11.4155i	−0.435388	+	0.464108i
$606$	−16.7747	+	51.6273i	−0.681427	+	2.09722i
$607$			15.6708i			0.636059i	0.948081	+	0.318029i	$0.103021\pi$
$607$			15.6708i			0.636059i	−0.948081	+	0.318029i	$0.896979\pi$
$608$	−17.9874	−	5.84446i	−0.729485	−	0.237024i
$609$	−4.72324	+	3.43163i	−0.191395	+	0.139057i
$610$	−17.4162	−	16.3384i	−0.705160	−	0.661524i
$611$	−0.721736	−	0.524372i	−0.0291983	−	0.0212138i
$612$	2.50966	+	3.45425i	0.101447	+	0.139630i
$613$	−22.4537	−	30.9048i	−0.906896	−	1.24823i	−0.968216	−	0.250117i	$-0.919531\pi$
$613$	−22.4537	−	30.9048i	−0.906896	−	1.24823i	0.0613201	−	0.998118i	$-0.480469\pi$
$614$	−23.3120	−	16.9372i	−0.940797	−	0.683529i
$615$	−41.6696	−	5.24287i	−1.68028	−	0.211413i
$616$	2.02758	−	1.47312i	0.0816936	−	0.0593539i
$617$	12.5842	+	4.08884i	0.506619	+	0.164611i	0.551164	−	0.834397i	$-0.314184\pi$
$617$	12.5842	+	4.08884i	0.506619	+	0.164611i	−0.0445449	+	0.999007i	$0.514184\pi$
$618$			35.0678i			1.41064i
$619$	−1.86789	+	5.74878i	−0.0750770	+	0.231063i	−0.981552	−	0.191197i	$-0.938763\pi$
$619$	−1.86789	+	5.74878i	−0.0750770	+	0.231063i	0.906475	+	0.422260i	$0.138763\pi$
$620$	−6.32207	−	11.4861i	−0.253900	−	0.461295i
$621$	−0.748388	−	2.30330i	−0.0300318	−	0.0924284i
$622$	−17.0981	+	5.55552i	−0.685572	+	0.222756i
$623$	0.542423	−	0.746582i	0.0217317	−	0.0299112i
$624$	3.75634			0.150374
$625$	−10.6898	−	22.5993i	−0.427594	−	0.903971i
$626$	−7.95456			−0.317928
$627$	−15.1482	+	20.8497i	−0.604960	+	0.832655i
$628$	1.89250	−	0.614911i	0.0755190	−	0.0245376i
$629$	2.51164	+	7.73003i	0.100146	+	0.308216i
$630$	−1.87857	−	3.41306i	−0.0748442	−	0.135979i
$631$	−11.6763	+	35.9361i	−0.464828	+	1.43059i	0.394371	+	0.918952i	$0.370963\pi$
$631$	−11.6763	+	35.9361i	−0.464828	+	1.43059i	−0.859199	+	0.511642i	$0.829037\pi$
$632$		−	16.8706i		−	0.671076i
$633$	−16.5866	−	5.38932i	−0.659259	−	0.214206i
$634$	−11.9543	+	8.68531i	−0.474766	+	0.344938i
$635$	−15.7634	−	1.98334i	−0.625550	−	0.0787066i
$636$	7.64520	+	5.55456i	0.303152	+	0.220253i
$637$	−2.81462	−	3.87399i	−0.111519	−	0.153493i
$638$	7.34220	+	10.1057i	0.290681	+	0.400087i
$639$	20.9673	+	15.2336i	0.829452	+	0.602632i
$640$	−3.16362	−	2.96786i	−0.125053	−	0.117315i
$641$	16.8737	−	12.2594i	0.666470	−	0.484219i	−0.202372	−	0.979309i	$-0.564865\pi$
$641$	16.8737	−	12.2594i	0.666470	−	0.484219i	0.868842	+	0.495090i	$0.164865\pi$
$642$	−2.11858	−	0.688367i	−0.0836135	−	0.0271677i
$643$			37.5552i			1.48103i	0.672039	+	0.740516i	$0.265419\pi$
$643$			37.5552i			1.48103i	−0.672039	+	0.740516i	$0.734581\pi$
$644$	0.108040	−	0.332514i	0.00425739	−	0.0131029i
$645$	36.4956	−	38.9030i	1.43701	−	1.53180i
$646$	2.74513	+	8.44865i	0.108006	+	0.332408i
$647$	26.0592	−	8.46714i	1.02449	−	0.332878i	0.251882	−	0.967758i	$-0.418951\pi$
$647$	26.0592	−	8.46714i	1.02449	−	0.332878i	0.772611	+	0.634880i	$0.218951\pi$
$648$	−10.9930	+	15.1306i	−0.431847	+	0.594387i
$649$	12.9994			0.510272
$650$	2.12480	−	3.35559i	0.0833417	−	0.131617i
$651$	−8.69410			−0.340749
$652$	−10.1695	+	13.9971i	−0.398268	+	0.548169i
$653$	21.9182	−	7.12164i	0.857724	−	0.278691i	0.153046	−	0.988219i	$-0.451092\pi$
$653$	21.9182	−	7.12164i	0.857724	−	0.278691i	0.704678	+	0.709528i	$0.251092\pi$
$654$	−8.35021	−	25.6993i	−0.326519	−	1.00492i
$655$	−5.25838	+	1.00582i	−0.205462	+	0.0393008i
$656$	−4.59309	+	14.1361i	−0.179330	+	0.551921i
$657$			2.05763i			0.0802760i
$658$	0.558961	+	0.181617i	0.0217906	+	0.00708018i
$659$	16.5717	−	12.0400i	0.645540	−	0.469012i	−0.216209	−	0.976347i	$-0.569369\pi$
$659$	16.5717	−	12.0400i	0.645540	−	0.469012i	0.861749	+	0.507335i	$0.169369\pi$
$660$	7.28823	−	4.01150i	0.283694	−	0.156147i
$661$	−11.3181	−	8.22311i	−0.440224	−	0.319842i	0.345500	−	0.938419i	$-0.387709\pi$
$661$	−11.3181	−	8.22311i	−0.440224	−	0.319842i	−0.785724	+	0.618577i	$0.787709\pi$
$662$	11.7574	+	16.1827i	0.456965	+	0.628959i
$663$	1.69659	+	2.33515i	0.0658899	+	0.0906897i
$664$	−2.42550	−	1.76223i	−0.0941275	−	0.0683876i
$665$	0.846822	+	4.42713i	0.0328384	+	0.171677i
$666$	17.7779	−	12.9164i	0.688880	−	0.500500i
$667$	6.29489	+	2.04533i	0.243739	+	0.0791957i
$668$			13.6126i			0.526687i
$669$	8.51893	−	26.2186i	0.329361	−	1.01367i
$670$	7.07046	+	3.32277i	0.273156	+	0.128370i
$671$	−5.82193	−	17.9181i	−0.224753	−	0.691719i
$672$	3.85034	−	1.25105i	0.148530	−	0.0482603i
$673$	−4.61160	+	6.34732i	−0.177764	+	0.244671i	−0.888596	−	0.458691i	$-0.848319\pi$
$673$	−4.61160	+	6.34732i	−0.177764	+	0.244671i	0.710832	+	0.703362i	$0.248319\pi$
$674$	28.1720			1.08514
$675$	−3.71967	−	9.36734i	−0.143170	−	0.360549i
$676$	8.94042			0.343862
$677$	8.46310	−	11.6485i	0.325263	−	0.447687i	−0.614802	−	0.788682i	$-0.710764\pi$
$677$	8.46310	−	11.6485i	0.325263	−	0.447687i	0.940065	+	0.340995i	$0.110764\pi$
$678$	36.0334	−	11.7080i	1.38385	−	0.449641i
$679$	−1.91478	−	5.89310i	−0.0734826	−	0.226156i
$680$	1.35974	−	10.8070i	0.0521435	−	0.414430i
$681$	15.7734	−	48.5455i	0.604437	−	1.86027i
$682$			18.6016i			0.712291i
$683$	12.0537	+	3.91647i	0.461221	+	0.149860i	0.530405	−	0.847744i	$-0.322040\pi$
$683$	12.0537	+	3.91647i	0.461221	+	0.149860i	−0.0691847	+	0.997604i	$0.522040\pi$
$684$	−10.8049	+	7.85021i	−0.413135	+	0.300160i
$685$	−18.0885	+	38.4901i	−0.691125	+	1.47063i
$686$	5.16629	+	3.75353i	0.197250	+	0.143310i
$687$	13.5225	+	18.6122i	0.515917	+	0.710099i
$688$	−11.0964	−	15.2728i	−0.423045	−	0.582271i
$689$	2.87959	+	2.09214i	0.109704	+	0.0797043i
$690$	−3.37169	+	7.17454i	−0.128358	+	0.273130i
$691$	−4.64805	+	3.37700i	−0.176820	+	0.128467i	−0.672675	−	0.739938i	$-0.734855\pi$
$691$	−4.64805	+	3.37700i	−0.176820	+	0.128467i	0.495855	+	0.868405i	$0.334855\pi$
$692$	−9.00448	−	2.92573i	−0.342299	−	0.111220i
$693$		−	3.07364i		−	0.116758i
$694$	4.65155	−	14.3160i	0.176571	−	0.543428i
$695$	−1.87993	+	14.9415i	−0.0713098	+	0.566762i
$696$	13.6371	+	41.9707i	0.516913	+	1.59089i
$697$	−10.8623	+	3.52937i	−0.411439	+	0.133685i
$698$	12.0802	−	16.6270i	0.457243	−	0.629342i
$699$	−28.7931			−1.08905
$700$	0.360435	−	1.40967i	0.0136232	−	0.0532806i
$701$	−30.5834			−1.15512			−0.577560	−	0.816348i	$-0.695995\pi$
$701$	−30.5834			−1.15512			−0.577560	+	0.816348i	$0.695995\pi$
$702$	0.941177	−	1.29542i	0.0355224	−	0.0488924i
$703$	−24.1795	+	7.85640i	−0.911948	+	0.296310i
$704$	−5.22270	−	16.0738i	−0.196838	−	0.605804i
$705$	6.70655	+	3.15175i	0.252583	+	0.118702i
$706$	6.20239	−	19.0890i	0.233430	−	0.718424i
$707$			7.49036i			0.281704i
$708$	11.4993	+	3.73635i	0.432170	+	0.140421i
$709$	−21.8998	+	15.9111i	−0.822464	+	0.597555i	−0.917417	−	0.397927i	$-0.869730\pi$
$709$	−21.8998	+	15.9111i	−0.822464	+	0.597555i	0.0949536	+	0.995482i	$0.469730\pi$
$710$	−3.27024	−	17.0966i	−0.122730	−	0.641624i
$711$	−16.7386	−	12.1613i	−0.627747	−	0.456085i
$712$	−4.10011	−	5.64332i	−0.153658	−	0.211492i
$713$	5.79353	+	7.97410i	0.216969	+	0.298633i
$714$	−1.53840	−	1.11771i	−0.0575731	−	0.0418293i
$715$	2.74513	−	1.51094i	0.102662	−	0.0565061i
$716$	−7.06868	+	5.13570i	−0.264169	+	0.191930i
$717$	−39.8673	−	12.9537i	−1.48887	−	0.483764i
$718$		−	36.8957i		−	1.37693i
$719$	5.16263	−	15.8889i	0.192534	−	0.592557i	−0.807463	−	0.589918i	$-0.799160\pi$
$719$	5.16263	−	15.8889i	0.192534	−	0.592557i	0.999997	−	0.00263916i	$-0.000840071\pi$
$720$	−17.0747	+	3.26605i	−0.636336	+	0.121718i
$721$	1.49527	+	4.60198i	0.0556869	+	0.171387i
$722$	−5.94125	+	1.93043i	−0.221110	+	0.0718431i
$723$	9.16202	−	12.6104i	0.340739	−	0.468987i
$724$	7.80240			0.289974
$725$	26.6868	+	6.82348i	0.991123	+	0.253418i
$726$	20.6555			0.766597
$727$	6.87743	−	9.46598i	0.255070	−	0.351074i	−0.662209	−	0.749319i	$-0.730381\pi$
$727$	6.87743	−	9.46598i	0.255070	−	0.351074i	0.917279	+	0.398246i	$0.130381\pi$
$728$	0.835044	−	0.271322i	0.0309488	−	0.0100559i
$729$	11.9517	+	36.7835i	0.442655	+	1.36235i
$730$	0.945515	−	1.00788i	0.0349951	−	0.0373035i
$731$	4.48267	−	13.7962i	0.165798	−	0.510272i
$732$		−	17.5237i		−	0.647694i
$733$	−32.4385	−	10.5399i	−1.19814	−	0.389300i	−0.359065	−	0.933312i	$-0.616904\pi$
$733$	−32.4385	−	10.5399i	−1.19814	−	0.389300i	−0.839077	+	0.544012i	$0.816904\pi$
$734$	−30.2196	+	21.9558i	−1.11542	+	0.810403i
$735$	29.0085	+	27.2134i	1.06999	+	1.00378i
$736$	−3.71321	−	2.69781i	−0.136871	−	0.0994425i
$737$	3.62279	+	4.98635i	0.133447	+	0.183674i
$738$	18.1502	+	24.9816i	0.668119	+	0.919586i
$739$	4.64794	+	3.37693i	0.170977	+	0.124222i	0.669983	−	0.742376i	$-0.266301\pi$
$739$	4.64794	+	3.37693i	0.170977	+	0.124222i	−0.499006	+	0.866599i	$0.666301\pi$
$740$	8.14282	+	1.02453i	0.299336	+	0.0376624i
$741$	−7.30434	+	5.30692i	−0.268332	+	0.194954i
$742$	−2.23015	−	0.724618i	−0.0818712	−	0.0266016i
$743$		−	36.4348i		−	1.33666i	−0.743863	−	0.668332i	$-0.767009\pi$
$743$		−	36.4348i		−	1.33666i	0.743863	−	0.668332i	$-0.232991\pi$
$744$	−20.3079	+	62.5012i	−0.744522	+	2.29140i
$745$	−0.776846	−	1.41140i	−0.0284615	−	0.0517097i
$746$	−1.21442	−	3.73761i	−0.0444632	−	0.136844i
$747$	−3.49688	+	1.13621i	−0.127944	+	0.0415716i
$748$	1.32981	−	1.83032i	0.0486226	−	0.0669233i
$749$	−0.307374			−0.0112312
$750$	−12.0985	+	30.6923i	−0.441776	+	1.12072i
$751$	1.48912			0.0543387			0.0271693	−	0.999631i	$-0.491351\pi$
$751$	1.48912			0.0543387			0.0271693	+	0.999631i	$0.491351\pi$
$752$	1.54149	−	2.12169i	0.0562125	−	0.0773699i
$753$	−9.23757	+	3.00147i	−0.336636	+	0.109380i
$754$	1.35230	+	4.16194i	0.0492477	+	0.151569i
$755$	16.7316	+	30.3985i	0.608925	+	1.10632i
$756$	0.181269	−	0.557888i	0.00659268	−	0.0202902i
$757$		−	5.53316i		−	0.201106i	−0.994932	−	0.100553i	$-0.967939\pi$
$757$		−	5.53316i		−	0.201106i	0.994932	−	0.100553i	$-0.0320612\pi$
$758$	2.07948	+	0.675664i	0.0755301	+	0.0245412i
$759$	−5.05975	+	3.67613i	−0.183657	+	0.133435i
$760$	33.8043	+	4.25325i	1.22621	+	0.154282i
$761$	15.1041	+	10.9738i	0.547523	+	0.397799i	0.826871	−	0.562391i	$-0.190118\pi$
$761$	15.1041	+	10.9738i	0.547523	+	0.397799i	−0.279348	+	0.960190i	$0.590118\pi$
$762$	12.3234	+	16.9617i	0.446430	+	0.614458i
$763$	−2.19161	−	3.01649i	−0.0793416	−	0.109204i
$764$	−0.906429	−	0.658559i	−0.0327935	−	0.0238258i
$765$	−9.74230	−	9.13943i	−0.352233	−	0.330437i
$766$	−4.52176	+	3.28525i	−0.163378	+	0.118701i
$767$	4.33125	+	1.40731i	0.156392	+	0.0508149i
$768$		−	38.2653i		−	1.38078i
$769$	4.06150	−	12.5000i	0.146462	−	0.450763i	−0.850734	−	0.525596i	$-0.823842\pi$
$769$	4.06150	−	12.5000i	0.146462	−	0.450763i	0.997196	+	0.0748333i	$0.0238425\pi$
$770$	−1.41238	+	1.50555i	−0.0508988	+	0.0542562i
$771$	−18.9764	−	58.4032i	−0.683417	−	2.10334i
$772$	−1.12690	+	0.366152i	−0.0405581	+	0.0131781i
$773$	−16.4425	+	22.6311i	−0.591394	+	0.813984i	−0.994887	−	0.100999i	$-0.967796\pi$
$773$	−16.4425	+	22.6311i	−0.591394	+	0.813984i	0.403493	+	0.914983i	$0.367796\pi$
$774$	−39.2195			−1.40972
$775$	26.1785	+	31.5798i	0.940359	+	1.13438i
$776$	−46.8376			−1.68137
$777$	3.19882	−	4.40280i	0.114757	−	0.157950i
$778$	14.4330	−	4.68957i	0.517448	−	0.168129i
$779$	−11.0399	−	33.9772i	−0.395544	−	1.21736i
$780$	2.86263	−	0.547563i	0.102498	−	0.0196059i
$781$	4.24366	−	13.0606i	0.151850	−	0.467347i
$782$			2.15581i			0.0770917i
$783$	10.5615	+	3.43163i	0.377437	+	0.122637i
$784$	11.3884	−	8.27413i	0.406727	−	0.295505i
$785$	−5.45404	+	3.00195i	−0.194663	+	0.107144i
$786$	5.71564	+	4.15266i	0.203870	+	0.148120i
$787$	−19.6126	−	26.9944i	−0.699114	−	0.962248i	−0.999963	−	0.00857605i	$-0.997270\pi$
$787$	−19.6126	−	26.9944i	−0.699114	−	0.962248i	0.300849	−	0.953672i	$-0.402730\pi$
$788$	5.58021	+	7.68050i	0.198787	+	0.273606i
$789$	−13.9845	−	10.1603i	−0.497860	−	0.361716i
$790$	2.61070	+	13.6486i	0.0928847	+	0.485595i
$791$	4.22947	−	3.07289i	0.150383	−	0.109259i
$792$	−22.0961	−	7.17946i	−0.785151	−	0.255111i
$793$		−	6.60035i		−	0.234385i
$794$	0.749317	−	2.30616i	0.0265923	−	0.0818426i
$795$	−26.7578	−	12.5749i	−0.949003	−	0.445986i
$796$	−2.67294	−	8.22646i	−0.0947398	−	0.291579i
$797$	−35.5682	+	11.5568i	−1.25989	+	0.409363i	−0.861455	−	0.507833i	$-0.830447\pi$
$797$	−35.5682	+	11.5568i	−1.25989	+	0.409363i	−0.398435	+	0.917197i	$0.630447\pi$
$798$	3.49620	−	4.81211i	0.123764	−	0.170347i
$799$	2.01519			0.0712923
$800$	−16.1378	−	10.2187i	−0.570559	−	0.361285i
$801$	−8.55478			−0.302268
$802$	−17.8730	+	24.6001i	−0.631119	+	0.868660i
$803$	1.03693	−	0.336919i	0.0365924	−	0.0118896i
$804$	1.77153	+	5.45220i	0.0624769	+	0.192284i
$805$	−0.136551	+	1.08529i	−0.00481278	+	0.0382514i
$806$	−2.01379	+	6.19781i	−0.0709328	+	0.218309i
$807$			33.9504i			1.19511i
$808$	53.8476	+	17.4961i	1.89435	+	0.615512i
$809$	27.1844	−	19.7506i	0.955751	−	0.694394i	0.00359108	−	0.999994i	$-0.498857\pi$
$809$	27.1844	−	19.7506i	0.955751	−	0.694394i	0.952160	+	0.305600i	$0.0988569\pi$
$810$	6.55211	−	13.9421i	0.230218	−	0.489875i
$811$	30.7471	+	22.3391i	1.07968	+	0.784432i	0.977627	−	0.210347i	$-0.0674594\pi$
$811$	30.7471	+	22.3391i	1.07968	+	0.784432i	0.102051	+	0.994779i	$0.467459\pi$
$812$	0.942315	+	1.29699i	0.0330688	+	0.0455153i
$813$	18.1272	+	24.9499i	0.635747	+	0.875031i
$814$	−9.42008	−	6.84409i	−0.330174	−	0.239885i
$815$	23.0226	−	48.9892i	0.806446	−	1.71602i
$816$	−6.86464	+	4.98745i	−0.240310	+	0.174596i
$817$	43.1546	+	14.0218i	1.50979	+	0.490560i
$818$		−	15.8699i		−	0.554877i
$819$	0.332749	−	1.02410i	0.0116272	−	0.0357848i
$820$	−1.43967	+	11.4423i	−0.0502756	+	0.399584i
$821$	7.70479	+	23.7129i	0.268899	+	0.827587i	0.990769	+	0.135558i	$0.0432827\pi$
$821$	7.70479	+	23.7129i	0.268899	+	0.827587i	−0.721870	+	0.692028i	$0.756717\pi$
$822$	53.3751	−	17.3426i	1.86167	−	0.604894i
$823$	14.9653	−	20.5980i	0.521659	−	0.718002i	−0.464172	−	0.885745i	$-0.653648\pi$
$823$	14.9653	−	20.5980i	0.521659	−	0.718002i	0.985831	+	0.167743i	$0.0536479\pi$
$824$	36.5760			1.27418
$825$	−20.0381	+	16.6109i	−0.697638	+	0.578316i
$826$	−3.00027			−0.104393
$827$	−19.0082	+	26.1626i	−0.660980	+	0.909761i	−0.999513	−	0.0311933i	$-0.990069\pi$
$827$	−19.0082	+	26.1626i	−0.660980	+	0.909761i	0.338533	+	0.940954i	$0.390069\pi$
$828$	−3.08247	+	1.00156i	−0.107123	+	0.0348065i
$829$	−7.71962	−	23.7585i	−0.268113	−	0.825168i	−0.990960	−	0.134159i	$-0.957167\pi$
$829$	−7.71962	−	23.7585i	−0.268113	−	0.825168i	0.722846	−	0.691009i	$-0.242833\pi$
$830$	2.23497	+	1.05033i	0.0775769	+	0.0364574i
$831$	13.6377	−	41.9724i	0.473085	−	1.45601i
$832$		−	5.92099i		−	0.205273i
$833$	10.2873	+	3.34256i	0.356435	+	0.115813i
$834$	16.0773	−	11.6808i	0.556712	−	0.404475i
$835$	−8.00128	−	41.8302i	−0.276896	−	1.44759i
$836$	5.72525	+	4.15964i	0.198012	+	0.143864i
$837$	9.72030	+	13.3788i	0.335983	+	0.462440i
$838$	20.5923	+	28.3429i	0.711350	+	0.979089i
$839$	15.6566	+	11.3752i	0.540524	+	0.392714i	0.824280	−	0.566183i	$-0.191580\pi$
$839$	15.6566	+	11.3752i	0.540524	+	0.392714i	−0.283755	+	0.958897i	$0.591580\pi$
$840$	−6.38925	+	3.51669i	−0.220450	+	0.121337i
$841$	−1.09201	+	0.793390i	−0.0376554	+	0.0273583i
$842$	−8.88423	−	2.88666i	−0.306171	−	0.0994809i
$843$		−	13.2091i		−	0.454944i
$844$	−1.47989	+	4.55463i	−0.0509399	+	0.156777i
$845$	−27.4730	+	5.25505i	−0.945101	+	0.180779i
$846$	−1.68363	−	5.18167i	−0.0578843	−	0.178150i
$847$	2.71064	−	0.880739i	0.0931385	−	0.0302625i
$848$	−6.15027	+	8.46512i	−0.211201	+	0.290693i
$849$	−30.7775			−1.05628
$850$	0.572323	+	8.95348i	0.0196305	+	0.307102i
$851$	−6.16980			−0.211498
$852$	7.50789	−	10.3337i	0.257216	−	0.354027i
$853$	−25.4765	+	8.27783i	−0.872300	+	0.283427i	−0.710756	−	0.703438i	$-0.751647\pi$
$853$	−25.4765	+	8.27783i	−0.872300	+	0.283427i	−0.161543	+	0.986866i	$0.551647\pi$
$854$	1.34370	+	4.13550i	0.0459806	+	0.141514i
$855$	28.5881	−	30.4739i	0.977694	−	1.04218i
$856$	−0.717971	+	2.20969i	−0.0245397	+	0.0755255i
$857$			47.5186i			1.62320i	0.584210	+	0.811602i	$0.301404\pi$
$857$			47.5186i			1.62320i	−0.584210	+	0.811602i	$0.698596\pi$
$858$	−3.93265	−	1.27780i	−0.134259	−	0.0436233i
$859$	9.32717	−	6.77658i	0.318239	−	0.231214i	−0.417185	−	0.908822i	$-0.636983\pi$
$859$	9.32717	−	6.77658i	0.318239	−	0.231214i	0.735424	+	0.677608i	$0.236983\pi$
$860$	−10.6826	−	10.0216i	−0.364275	−	0.341733i
$861$	6.18685	+	4.49501i	0.210847	+	0.153190i
$862$	−18.0908	−	24.8999i	−0.616177	−	0.848095i
$863$	−10.5835	−	14.5669i	−0.360266	−	0.495864i	0.589957	−	0.807435i	$-0.299145\pi$
$863$	−10.5835	−	14.5669i	−0.360266	−	0.495864i	−0.950223	+	0.311571i	$0.899145\pi$
$864$	−6.22998	−	4.52634i	−0.211948	−	0.153989i
$865$	29.3896	+	3.69779i	0.999276	+	0.125729i
$866$	−19.7108	+	14.3207i	−0.669799	+	0.486638i
$867$	35.8807	+	11.6583i	1.21857	+	0.395938i
$868$			2.38737i			0.0810327i
$869$	−3.38781	+	10.4266i	−0.114924	+	0.353698i
$870$	−17.5275	−	31.8446i	−0.594240	−	1.07963i
$871$	0.667251	+	2.05359i	0.0226089	+	0.0695831i
$872$	−26.8045	+	8.70932i	−0.907716	+	0.294935i
$873$	−33.7633	+	46.4712i	−1.14271	+	1.57281i
$874$	−6.74338			−0.228098
$875$	−0.278999	+	4.54365i	−0.00943188	+	0.153603i
$876$	1.01411			0.0342635
$877$	10.0495	−	13.8320i	0.339349	−	0.467074i	−0.604902	−	0.796300i	$-0.706788\pi$
$877$	10.0495	−	13.8320i	0.339349	−	0.467074i	0.944251	+	0.329226i	$0.106788\pi$
$878$	−27.8132	+	9.03707i	−0.938652	+	0.304986i
$879$	15.6315	+	48.1088i	0.527238	+	1.62267i
$880$	4.44172	+	8.06987i	0.149730	+	0.272035i
$881$	−11.7516	+	36.1678i	−0.395923	+	1.21853i	0.532318	+	0.846545i	$0.321321\pi$
$881$	−11.7516	+	36.1678i	−0.395923	+	1.21853i	−0.928240	+	0.371981i	$0.878679\pi$
$882$		−	29.2445i		−	0.984714i
$883$	−35.0458	−	11.3871i	−1.17939	−	0.383206i	−0.347247	−	0.937774i	$-0.612884\pi$
$883$	−35.0458	−	11.3871i	−1.17939	−	0.383206i	−0.832138	+	0.554568i	$0.812884\pi$
$884$	0.641224	−	0.465877i	0.0215667	−	0.0156691i
$885$	−37.5324	−	4.72232i	−1.26164	−	0.158739i
$886$	−2.92104	−	2.12226i	−0.0981344	−	0.0712988i
$887$	17.5594	+	24.1684i	0.589586	+	0.811495i	0.994705	−	0.102769i	$-0.0327701\pi$
$887$	17.5594	+	24.1684i	0.589586	+	0.811495i	−0.405120	+	0.914264i	$0.632770\pi$
$888$	−24.1795	−	33.2802i	−0.811411	−	1.11681i
$889$	2.34045	+	1.70044i	0.0784961	+	0.0570308i
$890$	4.19036	+	3.93105i	0.140461	+	0.131769i
$891$	9.83247	−	7.14371i	0.329400	−	0.239323i
$892$	−7.19953	−	2.33927i	−0.241058	−	0.0783246i
$893$			6.30351i			0.210939i
$894$	−0.656975	+	2.02196i	−0.0219725	+	0.0676245i
$895$	18.7027	−	19.9364i	0.625162	−	0.666399i
$896$	0.244082	+	0.751207i	0.00815420	+	0.0250961i
$897$	−2.08382	+	0.677074i	−0.0695767	+	0.0226068i
$898$	−24.0418	+	33.0907i	−0.802285	+	1.10425i
$899$	−45.1958			−1.50736
$900$	−12.5362	+	4.97797i	−0.417872	+	0.165932i
$901$	−8.04022			−0.267859
$902$	9.61736	−	13.2372i	0.320223	−	0.440749i
$903$	−9.23757	+	3.00147i	−0.307407	+	0.0998826i
$904$	−12.2115	−	37.5830i	−0.406147	−	1.24999i
$905$	−23.9760	+	4.58613i	−0.796990	+	0.152448i
$906$	14.1498	−	43.5487i	0.470097	−	1.44681i
$907$		−	43.4897i		−	1.44405i	−0.691866	−	0.722026i	$-0.743211\pi$
$907$		−	43.4897i		−	1.44405i	0.691866	−	0.722026i	$-0.256789\pi$
$908$	−13.3304	−	4.33132i	−0.442386	−	0.143740i
$909$	56.1758	−	40.8141i	1.86323	−	1.35372i
$910$	−0.633578	+	0.348726i	−0.0210029	+	0.0115602i
$911$	19.7150	+	14.3238i	0.653186	+	0.474568i	0.864355	−	0.502882i	$-0.167727\pi$
$911$	19.7150	+	14.3238i	0.653186	+	0.474568i	−0.211169	+	0.977450i	$0.567727\pi$
$912$	−15.6007	−	21.4726i	−0.516592	−	0.711028i
$913$	1.14516	+	1.57618i	0.0378994	+	0.0521640i
$914$	23.4107	+	17.0089i	0.774358	+	0.562604i
$915$	10.3002	+	53.8486i	0.340513	+	1.78018i
$916$	5.11084	−	3.71325i	0.168867	−	0.122689i
$917$	0.927136	+	0.301245i	0.0306167	+	0.00994797i
$918$			3.61699i			0.119379i
$919$	−14.0647	+	43.2867i	−0.463952	+	1.42790i	0.396344	+	0.918102i	$0.370279\pi$
$919$	−14.0647	+	43.2867i	−0.463952	+	1.42790i	−0.860296	+	0.509795i	$0.829721\pi$
$920$	7.48309	+	3.51669i	0.246710	+	0.115942i
$921$	20.4429	+	62.9168i	0.673617	+	2.07318i
$922$	17.9406	−	5.82926i	0.590843	−	0.191977i
$923$	2.82787	−	3.89223i	0.0930804	−	0.128114i
$924$	−1.51484			−0.0498346
$925$	−25.6243	+	1.63795i	−0.842522	+	0.0538555i
$926$	20.2001			0.663816
$927$	26.3661	−	36.2898i	0.865977	−	1.19191i
$928$	20.0158	−	6.50352i	0.657050	−	0.213488i
$929$	−2.79288	−	8.59560i	−0.0916314	−	0.282012i	0.894730	−	0.446608i	$-0.147368\pi$
$929$	−2.79288	−	8.59560i	−0.0916314	−	0.282012i	−0.986361	+	0.164596i	$0.947368\pi$
$930$	6.75742	−	53.7071i	0.221585	−	1.76113i
$931$	−10.4555	+	32.1787i	−0.342665	+	1.05462i
$932$			7.90648i			0.258985i
$933$	39.2542	+	12.7545i	1.28513	+	0.417562i
$934$	−13.0681	+	9.49453i	−0.427601	+	0.310671i
$935$	−3.01054	+	6.40605i	−0.0984550	+	0.209500i
$936$	−6.58490	−	4.78421i	−0.215234	−	0.156377i
$937$	−19.5892	−	26.9623i	−0.639953	−	0.880819i	0.358661	−	0.933468i	$-0.383234\pi$
$937$	−19.5892	−	26.9623i	−0.639953	−	0.880819i	−0.998613	+	0.0526490i	$0.983234\pi$
$938$	−0.836142	−	1.15085i	−0.0273010	−	0.0375766i
$939$	14.7745	+	10.7343i	0.482147	+	0.350300i
$940$	0.865461	−	1.84160i	0.0282282	−	0.0600662i
$941$	23.7050	−	17.2227i	0.772762	−	0.561444i	−0.130036	−	0.991509i	$-0.541509\pi$
$941$	23.7050	−	17.2227i	0.772762	−	0.561444i	0.902798	+	0.430065i	$0.141509\pi$
$942$	7.81341	+	2.53873i	0.254575	+	0.0827163i
$943$		−	8.66985i		−	0.282329i
$944$	−4.13706	+	12.7326i	−0.134650	+	0.414410i
$945$	−0.229103	+	1.82088i	−0.00745272	+	0.0592333i
$946$	6.42184	+	19.7644i	0.208792	+	0.642595i
$947$	−54.0634	+	17.5663i	−1.75682	+	0.570827i	−0.996863	−	0.0791426i	$-0.974782\pi$
$947$	−54.0634	+	17.5663i	−1.75682	+	0.570827i	−0.759961	+	0.649969i	$0.774782\pi$
$948$	−5.99371	+	8.24963i	−0.194667	+	0.267936i
$949$	0.381966			0.0123991
$950$	−28.0065	+	1.79022i	−0.908649	+	0.0580825i
$951$	33.9238			1.10005
$952$	−1.16578	+	1.60456i	−0.0377832	+	0.0520041i
$953$	18.1051	−	5.88270i	0.586481	−	0.190559i	−0.000720915	−	1.00000i	$-0.500229\pi$
$953$	18.1051	−	5.88270i	0.586481	−	0.190559i	0.587202	+	0.809441i	$0.300229\pi$
$954$	6.71735	+	20.6739i	0.217482	+	0.669342i
$955$	3.17246	+	1.49090i	0.102658	+	0.0482445i
$956$	−3.55704	+	10.9474i	−0.115043	+	0.354065i
$957$		−	28.6778i		−	0.927021i
$958$	−3.13615	−	1.01900i	−0.101324	−	0.0329223i
$959$	6.26498	−	4.55178i	0.202307	−	0.146985i
$960$	9.23999	+	48.3061i	0.298219	+	1.55907i
$961$	−29.3705	−	21.3389i	−0.947435	−	0.688352i
$962$	−2.39772	−	3.30017i	−0.0773055	−	0.106402i
$963$	1.67485	+	2.30523i	0.0539711	+	0.0742849i
$964$	−3.46278	−	2.51586i	−0.111529	−	0.0810304i
$965$	3.24764	−	1.78753i	0.104545	−	0.0575425i
$966$	1.16779	−	0.848451i	0.0375731	−	0.0272985i
$967$	−13.9905	−	4.54580i	−0.449906	−	0.146183i	0.0752956	−	0.997161i	$-0.476010\pi$
$967$	−13.9905	−	4.54580i	−0.449906	−	0.146183i	−0.525201	+	0.850978i	$0.676010\pi$
$968$		−	21.5438i		−	0.692443i
$969$	6.30233	−	19.3966i	0.202460	−	0.623108i
$970$	37.8924	−	7.24806i	1.21665	−	0.232721i
$971$	−12.0039	−	36.9441i	−0.385223	−	1.18559i	−0.936319	−	0.351151i	$-0.885790\pi$
$971$	−12.0039	−	36.9441i	−0.385223	−	1.18559i	0.551096	−	0.834442i	$-0.314210\pi$
$972$	14.8616	−	4.82884i	0.476687	−	0.154885i
$973$	1.61177	−	2.21842i	0.0516711	−	0.0711191i
$974$	19.3469			0.619914
$975$	−8.47472	+	3.36522i	−0.271408	+	0.107773i
$976$	19.4030			0.621076
$977$	34.3586	−	47.2906i	1.09923	−	1.51296i	0.262827	−	0.964843i	$-0.415345\pi$
$977$	34.3586	−	47.2906i	1.09923	−	1.51296i	0.836402	−	0.548116i	$-0.184655\pi$
$978$	−67.9346	+	22.0733i	−2.17231	+	0.705826i
$979$	1.40077	+	4.31111i	0.0447687	+	0.137784i
$980$	7.47271	−	7.96563i	0.238707	−	0.254453i
$981$	−10.6811	+	32.8730i	−0.341021	+	1.04955i
$982$			34.8918i			1.11344i
$983$	26.7812	+	8.70175i	0.854189	+	0.277543i	0.703199	−	0.710993i	$-0.251754\pi$
$983$	26.7812	+	8.70175i	0.854189	+	0.277543i	0.150989	+	0.988535i	$0.451754\pi$
$984$	46.7656	−	33.9772i	1.49083	−	1.08315i
$985$	−21.6619	−	20.3215i	−0.690206	−	0.647496i
$986$	−7.99729	−	5.81037i	−0.254685	−	0.185040i
$987$	−0.793106	−	1.09162i	−0.0252449	−	0.0347466i
$988$	1.45726	+	2.00575i	0.0463617	+	0.0638114i
$989$	8.90859	+	6.47247i	0.283277	+	0.205812i
$990$	18.9871	+	2.38896i	0.603451	+	0.0759261i
$991$	−31.8297	+	23.1256i	−1.01110	+	0.734610i	−0.964440	−	0.264300i	$-0.914859\pi$
$991$	−31.8297	+	23.1256i	−1.01110	+	0.734610i	−0.0466640	+	0.998911i	$0.514859\pi$
$992$	29.8068	+	9.68480i	0.946365	+	0.307493i
$993$		−	45.9231i		−	1.45733i
$994$	−0.979439	+	3.01440i	−0.0310659	+	0.0956110i
$995$	13.0491	+	23.7080i	0.413683	+	0.751594i
$996$	0.559979	+	1.72344i	0.0177436	+	0.0546092i
$997$	41.0074	−	13.3241i	1.29872	−	0.421979i	0.423583	−	0.905857i	$-0.360772\pi$
$997$	41.0074	−	13.3241i	1.29872	−	0.421979i	0.875136	+	0.483878i	$0.160772\pi$
$998$	7.91810	−	10.8983i	0.250643	−	0.344980i
$999$	−10.3516			−0.327511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.2.e.a.9.2	✓	8
3.2	odd	2		225.2.m.a.109.1		8
4.3	odd	2		400.2.y.c.209.2		8
5.2	odd	4		125.2.d.b.76.3		16
5.3	odd	4		125.2.d.b.76.2		16
5.4	even	2		125.2.e.b.49.1		8
25.2	odd	20		125.2.d.b.51.3		16
25.3	odd	20		625.2.d.o.126.3		16
25.4	even	10		625.2.e.i.499.2		8
25.6	even	5		625.2.b.c.624.6		8
25.8	odd	20		625.2.a.f.1.6		8
25.9	even	10		625.2.e.a.124.1		8
25.11	even	5		125.2.e.b.74.1		8
25.12	odd	20		625.2.d.o.501.2		16
25.13	odd	20		625.2.d.o.501.3		16
25.14	even	10	inner	25.2.e.a.14.2	yes	8
25.16	even	5		625.2.e.i.124.2		8
25.17	odd	20		625.2.a.f.1.3		8
25.19	even	10		625.2.b.c.624.3		8
25.21	even	5		625.2.e.a.499.1		8
25.22	odd	20		625.2.d.o.126.2		16
25.23	odd	20		125.2.d.b.51.2		16
75.8	even	20		5625.2.a.x.1.3		8
75.14	odd	10		225.2.m.a.64.1		8
75.17	even	20		5625.2.a.x.1.6		8
100.39	odd	10		400.2.y.c.289.2		8
100.67	even	20		10000.2.a.bj.1.1		8
100.83	even	20		10000.2.a.bj.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.9.2	✓	8	1.1	even	1	trivial
25.2.e.a.14.2	yes	8	25.14	even	10	inner
125.2.d.b.51.2		16	25.23	odd	20
125.2.d.b.51.3		16	25.2	odd	20
125.2.d.b.76.2		16	5.3	odd	4
125.2.d.b.76.3		16	5.2	odd	4
125.2.e.b.49.1		8	5.4	even	2
125.2.e.b.74.1		8	25.11	even	5
225.2.m.a.64.1		8	75.14	odd	10
225.2.m.a.109.1		8	3.2	odd	2
400.2.y.c.209.2		8	4.3	odd	2
400.2.y.c.289.2		8	100.39	odd	10
625.2.a.f.1.3		8	25.17	odd	20
625.2.a.f.1.6		8	25.8	odd	20
625.2.b.c.624.3		8	25.19	even	10
625.2.b.c.624.6		8	25.6	even	5
625.2.d.o.126.2		16	25.22	odd	20
625.2.d.o.126.3		16	25.3	odd	20
625.2.d.o.501.2		16	25.12	odd	20
625.2.d.o.501.3		16	25.13	odd	20
625.2.e.a.124.1		8	25.9	even	10
625.2.e.a.499.1		8	25.21	even	5
625.2.e.i.124.2		8	25.16	even	5
625.2.e.i.499.2		8	25.4	even	10
5625.2.a.x.1.3		8	75.8	even	20
5625.2.a.x.1.6		8	75.17	even	20
10000.2.a.bj.1.1		8	100.67	even	20
10000.2.a.bj.1.8		8	100.83	even	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	25.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.666375 - 0.917186i) q^{2} +(-2.47539 + 0.804303i) q^{3} +(0.220859 + 0.679734i) q^{4} +(-1.07822 - 1.95894i) q^{5} +(-0.911842 + 2.80636i) q^{6} +0.407162i q^{7} +(2.92705 + 0.951057i) q^{8} +(3.05361 - 2.21858i) q^{9} +O(q^{10})\)	\(q+(0.666375 - 0.917186i) q^{2} +(-2.47539 + 0.804303i) q^{3} +(0.220859 + 0.679734i) q^{4} +(-1.07822 - 1.95894i) q^{5} +(-0.911842 + 2.80636i) q^{6} +0.407162i q^{7} +(2.92705 + 0.951057i) q^{8} +(3.05361 - 2.21858i) q^{9} +(-2.51521 - 0.316463i) q^{10} +(-1.61803 - 1.17557i) q^{11} +(-1.09343 - 1.50497i) q^{12} +(-0.411842 - 0.566852i) q^{13} +(0.373443 + 0.271322i) q^{14} +(4.24459 + 3.98193i) q^{15} +(1.66637 - 1.21069i) q^{16} +(1.50527 + 0.489091i) q^{17} -4.27913i q^{18} +(-1.52988 + 4.70847i) q^{19} +(1.09343 - 1.16555i) q^{20} +(-0.327481 - 1.00788i) q^{21} +(-2.15643 + 0.700668i) q^{22} +(-0.706192 + 0.971990i) q^{23} -8.01054 q^{24} +(-2.67490 + 4.22433i) q^{25} -0.794350 q^{26} +(-1.18484 + 1.63079i) q^{27} +(-0.276762 + 0.0899253i) q^{28} +(-1.70239 - 5.23943i) q^{29} +(6.48066 - 1.23962i) q^{30} +(2.53514 - 7.80237i) q^{31} +3.82022i q^{32} +(4.95078 + 1.60861i) q^{33} +(1.45166 - 1.05469i) q^{34} +(0.797605 - 0.439008i) q^{35} +(2.18246 + 1.58565i) q^{36} +(3.01846 + 4.15456i) q^{37} +(3.29908 + 4.54079i) q^{38} +(1.47539 + 1.07193i) q^{39} +(-1.29293 - 6.75936i) q^{40} +(-5.83802 + 4.24157i) q^{41} +(-1.14264 - 0.371267i) q^{42} -9.16531i q^{43} +(0.441718 - 1.35947i) q^{44} +(-7.63851 - 3.58973i) q^{45} +(0.420907 + 1.29542i) q^{46} +(1.21092 - 0.393451i) q^{47} +(-3.15117 + 4.33721i) q^{48} +6.83422 q^{49} +(2.09201 + 5.26836i) q^{50} -4.11950 q^{51} +(0.294350 - 0.405138i) q^{52} +(-4.83133 + 1.56979i) q^{53} +(0.706192 + 2.17344i) q^{54} +(-0.558282 + 4.43715i) q^{55} +(-0.387234 + 1.19178i) q^{56} -12.8858i q^{57} +(-5.93997 - 1.93001i) q^{58} +(-5.25838 + 3.82044i) q^{59} +(-1.76920 + 3.76464i) q^{60} +(7.62101 + 5.53699i) q^{61} +(-5.46687 - 7.52450i) q^{62} +(0.903319 + 1.24331i) q^{63} +(6.83660 + 4.96708i) q^{64} +(-0.666375 + 1.41796i) q^{65} +(4.77447 - 3.46885i) q^{66} +(-2.93090 - 0.952307i) q^{67} +1.13120i q^{68} +(0.966327 - 2.97405i) q^{69} +(0.128852 - 1.02410i) q^{70} +(2.12183 + 6.53032i) q^{71} +(11.0481 - 3.58973i) q^{72} +(-0.320429 + 0.441032i) q^{73} +5.82193 q^{74} +(3.22378 - 12.6083i) q^{75} -3.53840 q^{76} +(0.478647 - 0.658801i) q^{77} +(1.96633 - 0.638898i) q^{78} +(-1.69390 - 5.21330i) q^{79} +(-4.16839 - 1.95894i) q^{80} +(-1.87783 + 5.77938i) q^{81} +8.18102i q^{82} +(-0.926457 - 0.301024i) q^{83} +(0.612766 - 0.445201i) q^{84} +(-0.664904 - 3.47608i) q^{85} +(-8.40629 - 6.10753i) q^{86} +(8.42819 + 11.6004i) q^{87} +(-3.61803 - 4.97980i) q^{88} +(-1.83363 - 1.33221i) q^{89} +(-8.38256 + 4.61383i) q^{90} +(0.230800 - 0.167686i) q^{91} +(-0.816664 - 0.265350i) q^{92} +21.3529i q^{93} +(0.446057 - 1.37282i) q^{94} +(10.8732 - 2.07982i) q^{95} +(-3.07261 - 9.45653i) q^{96} +(-14.4736 + 4.70276i) q^{97} +(4.55415 - 6.26825i) q^{98} -7.54893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} - 5 q^{3} - q^{4} - 9 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) \) 8 * q - 5 * q^2 - 5 * q^3 - q^4 - 9 * q^6 + 10 * q^8 + q^9	\( 8 q - 5 q^{2} - 5 q^{3} - q^{4} - 9 q^{6} + 10 q^{8} + q^{9} - 5 q^{10} - 4 q^{11} + 15 q^{12} - 5 q^{13} + 13 q^{14} + 15 q^{15} + 3 q^{16} - 10 q^{17} - 5 q^{19} - 15 q^{20} - 4 q^{21} + 5 q^{23} - 20 q^{24} - 10 q^{25} + 6 q^{26} - 5 q^{27} - 15 q^{28} - 5 q^{29} + 15 q^{30} - 9 q^{31} + 10 q^{33} + 13 q^{34} + 15 q^{35} + 23 q^{36} + 30 q^{37} + 15 q^{38} - 3 q^{39} + 10 q^{40} - 4 q^{41} - 15 q^{42} - 2 q^{44} - 15 q^{45} - 19 q^{46} - 30 q^{48} + 14 q^{49} - 15 q^{50} - 4 q^{51} - 10 q^{52} - 10 q^{53} - 5 q^{54} - 10 q^{55} + 10 q^{56} + 20 q^{58} - 10 q^{60} - 9 q^{61} - 30 q^{62} + 10 q^{63} + 4 q^{64} + 5 q^{65} + 12 q^{66} + 20 q^{67} + 17 q^{69} + 30 q^{70} + 6 q^{71} + 5 q^{72} + 15 q^{73} - 12 q^{74} - 10 q^{75} - 20 q^{76} + 10 q^{77} + 25 q^{78} + 15 q^{79} + 20 q^{80} + 28 q^{81} - 45 q^{83} + 18 q^{84} - 15 q^{85} - 9 q^{86} - 20 q^{87} - 20 q^{88} - 25 q^{89} - 25 q^{90} + 6 q^{91} + 30 q^{92} - 27 q^{94} + 15 q^{95} + 16 q^{96} - 60 q^{97} - 10 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 5 * q^3 - q^4 - 9 * q^6 + 10 * q^8 + q^9 - 5 * q^10 - 4 * q^11 + 15 * q^12 - 5 * q^13 + 13 * q^14 + 15 * q^15 + 3 * q^16 - 10 * q^17 - 5 * q^19 - 15 * q^20 - 4 * q^21 + 5 * q^23 - 20 * q^24 - 10 * q^25 + 6 * q^26 - 5 * q^27 - 15 * q^28 - 5 * q^29 + 15 * q^30 - 9 * q^31 + 10 * q^33 + 13 * q^34 + 15 * q^35 + 23 * q^36 + 30 * q^37 + 15 * q^38 - 3 * q^39 + 10 * q^40 - 4 * q^41 - 15 * q^42 - 2 * q^44 - 15 * q^45 - 19 * q^46 - 30 * q^48 + 14 * q^49 - 15 * q^50 - 4 * q^51 - 10 * q^52 - 10 * q^53 - 5 * q^54 - 10 * q^55 + 10 * q^56 + 20 * q^58 - 10 * q^60 - 9 * q^61 - 30 * q^62 + 10 * q^63 + 4 * q^64 + 5 * q^65 + 12 * q^66 + 20 * q^67 + 17 * q^69 + 30 * q^70 + 6 * q^71 + 5 * q^72 + 15 * q^73 - 12 * q^74 - 10 * q^75 - 20 * q^76 + 10 * q^77 + 25 * q^78 + 15 * q^79 + 20 * q^80 + 28 * q^81 - 45 * q^83 + 18 * q^84 - 15 * q^85 - 9 * q^86 - 20 * q^87 - 20 * q^88 - 25 * q^89 - 25 * q^90 + 6 * q^91 + 30 * q^92 - 27 * q^94 + 15 * q^95 + 16 * q^96 - 60 * q^97 - 10 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more