LMFDB - Embedded newform 841.2.d.g.190.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(190,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("841.190");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.d (of order $7$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	12.0.4413675765625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 2x^{10} - 3x^{9} + 5x^{8} - 8x^{7} + 13x^{6} + 8x^{5} + 5x^{4} + 3x^{3} + 2x^{2} + x + 1 $ x^12 - x^11 + 2x^10 - 3x^9 + 5x^8 - 8x^7 + 13x^6 + 8x^5 + 5x^4 + 3x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			190.2
Root			$-0.556829 - 0.268155i$ of defining polynomial
Character	$\chi$	$=$	841.190
Dual form			841.2.d.g.571.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.556829 + 0.268155i) q^{2} +(0.385338 - 0.483198i) q^{3} +(-1.00883 - 1.26503i) q^{4} +(-3.47243 - 1.67223i) q^{5} +(0.344139 - 0.165729i) q^{6} +(-1.39417 + 1.74823i) q^{7} +(-0.497572 - 2.18001i) q^{8} +(0.582567 + 2.55239i) q^{9} +O(q^{10})$	\(q+(0.556829 + 0.268155i) q^{2} +(0.385338 - 0.483198i) q^{3} +(-1.00883 - 1.26503i) q^{4} +(-3.47243 - 1.67223i) q^{5} +(0.344139 - 0.165729i) q^{6} +(-1.39417 + 1.74823i) q^{7} +(-0.497572 - 2.18001i) q^{8} +(0.582567 + 2.55239i) q^{9} +(-1.48513 - 1.86230i) q^{10} +(-0.307516 + 1.34732i) q^{11} -1.00000 q^{12} +(0.0525301 - 0.230149i) q^{13} +(-1.24511 + 0.599613i) q^{14} +(-2.14608 + 1.03350i) q^{15} +(-0.412577 + 1.80762i) q^{16} +4.38197 q^{17} +(-0.360046 + 1.57747i) q^{18} +(3.02648 + 3.79509i) q^{19} +(1.38766 + 6.07972i) q^{20} +(0.307516 + 1.34732i) q^{21} +(-0.532524 + 0.667764i) q^{22} +(1.11366 - 0.536310i) q^{23} +(-1.24511 - 0.599613i) q^{24} +(6.14393 + 7.70425i) q^{25} +(0.0909659 - 0.114068i) q^{26} +(3.12829 + 1.50650i) q^{27} +3.61803 q^{28} -1.47214 q^{30} +(-9.09093 - 4.37796i) q^{31} +(-3.50279 + 4.39236i) q^{32} +(0.532524 + 0.667764i) q^{33} +(2.44001 + 1.17505i) q^{34} +(7.76458 - 3.73922i) q^{35} +(2.64115 - 3.31189i) q^{36} +(1.04767 + 4.59016i) q^{37} +(0.667563 + 2.92478i) q^{38} +(-0.0909659 - 0.114068i) q^{39} +(-1.91769 + 8.40196i) q^{40} -3.85410 q^{41} +(-0.190056 + 0.832688i) q^{42} +(-6.51947 + 3.13961i) q^{43} +(2.01463 - 0.970194i) q^{44} +(2.24527 - 9.83719i) q^{45} +0.763932 q^{46} +(-1.55765 + 6.82450i) q^{47} +(0.714456 + 0.895899i) q^{48} +(0.445042 + 1.94986i) q^{49} +(1.35519 + 5.93748i) q^{50} +(1.68854 - 2.11736i) q^{51} +(-0.344139 + 0.165729i) q^{52} +(1.80194 + 0.867767i) q^{53} +(1.33795 + 1.67773i) q^{54} +(3.32086 - 4.16422i) q^{55} +(4.50484 + 2.16942i) q^{56} +3.00000 q^{57} +6.09017 q^{59} +(3.47243 + 1.67223i) q^{60} +(0.385338 - 0.483198i) q^{61} +(-3.88812 - 4.87555i) q^{62} +(-5.27436 - 2.54000i) q^{63} +(0.212690 - 0.102426i) q^{64} +(-0.567270 + 0.711334i) q^{65} +(0.117461 + 0.514629i) q^{66} +(0.339982 + 1.48956i) q^{67} +(-4.42065 - 5.54332i) q^{68} +(0.169991 - 0.744779i) q^{69} +5.32624 q^{70} +(-2.33027 + 10.2096i) q^{71} +(5.27436 - 2.54000i) q^{72} +(-12.3507 + 5.94777i) q^{73} +(-0.647498 + 2.83687i) q^{74} +6.09017 q^{75} +(1.74770 - 7.65718i) q^{76} +(-1.92669 - 2.41599i) q^{77} +(-0.0200647 - 0.0879092i) q^{78} +(-1.35519 - 5.93748i) q^{79} +(4.45539 - 5.58689i) q^{80} +(-5.14291 + 2.47670i) q^{81} +(-2.14608 - 1.03350i) q^{82} +(-6.20015 - 7.77474i) q^{83} +(1.39417 - 1.74823i) q^{84} +(-15.2161 - 7.32766i) q^{85} -4.47214 q^{86} +3.09017 q^{88} +(4.24195 + 2.04281i) q^{89} +(3.88812 - 4.87555i) q^{90} +(0.329118 + 0.412701i) q^{91} +(-1.80194 - 0.867767i) q^{92} +(-5.61850 + 2.70573i) q^{93} +(-2.69737 + 3.38239i) q^{94} +(-4.16297 - 18.2392i) q^{95} +(0.772623 + 3.38508i) q^{96} +(-2.22106 - 2.78512i) q^{97} +(-0.275051 + 1.20508i) q^{98} -3.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} + q^{3} + q^{4} - q^{5} + 3 q^{6} + 3 q^{9}+O(q^{10}) $ 12 * q - q^2 + q^3 + q^4 - q^5 + 3 * q^6 + 3 * q^9	$ 12 q - q^{2} + q^{3} + q^{4} - q^{5} + 3 q^{6} + 3 q^{9} + 7 q^{10} - 5 q^{11} - 12 q^{12} - 4 q^{13} - 5 q^{14} - 7 q^{15} + 3 q^{16} + 66 q^{17} - q^{18} - 3 q^{19} + 8 q^{20} + 5 q^{21} - 5 q^{22} - 2 q^{23} - 5 q^{24} - 13 q^{25} - 7 q^{26} - 2 q^{27} + 30 q^{28} + 36 q^{30} - 9 q^{31} + 9 q^{32} + 5 q^{33} - 8 q^{34} + 15 q^{35} - 4 q^{36} - 4 q^{37} + 6 q^{38} + 7 q^{39} - 15 q^{40} - 6 q^{41} + 5 q^{42} - 10 q^{43} + 9 q^{45} + 36 q^{46} - 14 q^{47} - 9 q^{48} + 4 q^{49} + q^{50} + 8 q^{51} - 3 q^{52} + 4 q^{53} - 11 q^{54} + 5 q^{55} + 10 q^{56} + 36 q^{57} + 6 q^{59} + q^{60} + q^{61} + 8 q^{62} - 5 q^{63} - 4 q^{64} + 13 q^{65} + 10 q^{66} + 12 q^{67} + 3 q^{68} + 6 q^{69} - 30 q^{70} - 12 q^{71} + 5 q^{72} - 14 q^{73} - 17 q^{74} + 6 q^{75} + 9 q^{76} - 5 q^{77} + 11 q^{78} - q^{79} - 21 q^{80} + 2 q^{81} - 7 q^{82} + 2 q^{83} + 2 q^{85} - 30 q^{88} - 4 q^{89} - 8 q^{90} - 10 q^{91} - 4 q^{92} - 8 q^{93} - 7 q^{94} - 24 q^{95} - 2 q^{96} - 13 q^{97} + 2 q^{98} - 30 q^{99}+O(q^{100}) $ 12 * q - q^2 + q^3 + q^4 - q^5 + 3 * q^6 + 3 * q^9 + 7 * q^10 - 5 * q^11 - 12 * q^12 - 4 * q^13 - 5 * q^14 - 7 * q^15 + 3 * q^16 + 66 * q^17 - q^18 - 3 * q^19 + 8 * q^20 + 5 * q^21 - 5 * q^22 - 2 * q^23 - 5 * q^24 - 13 * q^25 - 7 * q^26 - 2 * q^27 + 30 * q^28 + 36 * q^30 - 9 * q^31 + 9 * q^32 + 5 * q^33 - 8 * q^34 + 15 * q^35 - 4 * q^36 - 4 * q^37 + 6 * q^38 + 7 * q^39 - 15 * q^40 - 6 * q^41 + 5 * q^42 - 10 * q^43 + 9 * q^45 + 36 * q^46 - 14 * q^47 - 9 * q^48 + 4 * q^49 + q^50 + 8 * q^51 - 3 * q^52 + 4 * q^53 - 11 * q^54 + 5 * q^55 + 10 * q^56 + 36 * q^57 + 6 * q^59 + q^60 + q^61 + 8 * q^62 - 5 * q^63 - 4 * q^64 + 13 * q^65 + 10 * q^66 + 12 * q^67 + 3 * q^68 + 6 * q^69 - 30 * q^70 - 12 * q^71 + 5 * q^72 - 14 * q^73 - 17 * q^74 + 6 * q^75 + 9 * q^76 - 5 * q^77 + 11 * q^78 - q^79 - 21 * q^80 + 2 * q^81 - 7 * q^82 + 2 * q^83 + 2 * q^85 - 30 * q^88 - 4 * q^89 - 8 * q^90 - 10 * q^91 - 4 * q^92 - 8 * q^93 - 7 * q^94 - 24 * q^95 - 2 * q^96 - 13 * q^97 + 2 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{7}\right)$

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 $

$2$	0.556829	+	0.268155i	0.393738	+	0.189614i	0.620268	−	0.784390i	$-0.287024\pi$
$2$	0.556829	+	0.268155i	0.393738	+	0.189614i	−0.226530	+	0.974004i	$0.572738\pi$
$3$	0.385338	−	0.483198i	0.222475	−	0.278975i	−0.658050	−	0.752974i	$-0.728619\pi$
$3$	0.385338	−	0.483198i	0.222475	−	0.278975i	0.880525	+	0.473999i	$0.157190\pi$
$4$	−1.00883	−	1.26503i	−0.504414	−	0.632515i
$5$	−3.47243	−	1.67223i	−1.55292	−	0.747845i	−0.556374	−	0.830932i	$-0.687808\pi$
$5$	−3.47243	−	1.67223i	−1.55292	−	0.747845i	−0.996542	+	0.0830872i	$0.973522\pi$
$6$	0.344139	−	0.165729i	0.140494	−	0.0676585i
$7$	−1.39417	+	1.74823i	−0.526945	+	0.660768i	−0.972067	−	0.234702i	$-0.924589\pi$
$7$	−1.39417	+	1.74823i	−0.526945	+	0.660768i	0.445122	+	0.895470i	$0.353160\pi$
$8$	−0.497572	−	2.18001i	−0.175918	−	0.770748i
$9$	0.582567	+	2.55239i	0.194189	+	0.850798i
$10$	−1.48513	−	1.86230i	−0.469640	−	0.588910i
$11$	−0.307516	+	1.34732i	−0.0927197	+	0.406231i	−0.999895	−	0.0145224i	$-0.995377\pi$
$11$	−0.307516	+	1.34732i	−0.0927197	+	0.406231i	0.907175	+	0.420754i	$0.138234\pi$
$12$	−1.00000			−0.288675
$13$	0.0525301	−	0.230149i	0.0145692	−	0.0638319i	−0.967121	−	0.254318i	$-0.918149\pi$
$13$	0.0525301	−	0.230149i	0.0145692	−	0.0638319i	0.981690	+	0.190486i	$0.0610063\pi$
$14$	−1.24511	+	0.599613i	−0.332769	+	0.160253i
$15$	−2.14608	+	1.03350i	−0.554115	+	0.266848i
$16$	−0.412577	+	1.80762i	−0.103144	+	0.451904i
$17$	4.38197			1.06278			0.531391	−	0.847126i	$-0.321669\pi$
$17$	4.38197			1.06278			0.531391	+	0.847126i	$0.321669\pi$
$18$	−0.360046	+	1.57747i	−0.0848638	+	0.371812i
$19$	3.02648	+	3.79509i	0.694323	+	0.870653i	0.996585	−	0.0825715i	$-0.0263133\pi$
$19$	3.02648	+	3.79509i	0.694323	+	0.870653i	−0.302262	+	0.953225i	$0.597742\pi$
$20$	1.38766	+	6.07972i	0.310289	+	1.35947i
$21$	0.307516	+	1.34732i	0.0671056	+	0.294009i
$22$	−0.532524	+	0.667764i	−0.113534	+	0.142368i
$23$	1.11366	−	0.536310i	0.232214	−	0.111828i	−0.314159	−	0.949370i	$-0.601722\pi$
$23$	1.11366	−	0.536310i	0.232214	−	0.111828i	0.546373	+	0.837542i	$0.316008\pi$
$24$	−1.24511	−	0.599613i	−0.254157	−	0.122395i
$25$	6.14393	+	7.70425i	1.22879	+	1.54085i
$26$	0.0909659	−	0.114068i	0.0178399	−	0.0223705i
$27$	3.12829	+	1.50650i	0.602039	+	0.289927i
$28$	3.61803			0.683744
$29$		0			0
$29$		0			0
$30$	−1.47214			−0.268774
$31$	−9.09093	−	4.37796i	−1.63278	−	0.786305i	−0.999928	−	0.0120317i	$-0.996170\pi$
$31$	−9.09093	−	4.37796i	−1.63278	−	0.786305i	−0.632851	−	0.774273i	$-0.718116\pi$
$32$	−3.50279	+	4.39236i	−0.619211	+	0.776466i
$33$	0.532524	+	0.667764i	0.0927005	+	0.116243i
$34$	2.44001	+	1.17505i	0.418458	+	0.201519i
$35$	7.76458	−	3.73922i	1.31245	−	0.632044i
$36$	2.64115	−	3.31189i	0.440191	−	0.551982i
$37$	1.04767	+	4.59016i	0.172237	+	0.754618i	0.985075	+	0.172128i	$0.0550642\pi$
$37$	1.04767	+	4.59016i	0.172237	+	0.754618i	−0.812838	+	0.582490i	$0.802079\pi$
$38$	0.667563	+	2.92478i	0.108293	+	0.474463i
$39$	−0.0909659	−	0.114068i	−0.0145662	−	0.0182654i
$40$	−1.91769	+	8.40196i	−0.303214	+	1.32847i
$41$	−3.85410			−0.601910			−0.300955	−	0.953638i	$-0.597305\pi$
$41$	−3.85410			−0.601910			−0.300955	+	0.953638i	$0.597305\pi$
$42$	−0.190056	+	0.832688i	−0.0293262	+	0.128487i
$43$	−6.51947	+	3.13961i	−0.994210	+	0.478786i	−0.858970	−	0.512026i	$-0.828895\pi$
$43$	−6.51947	+	3.13961i	−0.994210	+	0.478786i	−0.135240	+	0.990813i	$0.543181\pi$
$44$	2.01463	−	0.970194i	0.303717	−	0.146262i
$45$	2.24527	−	9.83719i	0.334706	−	1.46644i
$46$	0.763932			0.112636
$47$	−1.55765	+	6.82450i	−0.227206	+	0.995455i	0.724700	+	0.689065i	$0.241978\pi$
$47$	−1.55765	+	6.82450i	−0.227206	+	0.995455i	−0.951906	+	0.306390i	$0.900879\pi$
$48$	0.714456	+	0.895899i	0.103123	+	0.129312i
$49$	0.445042	+	1.94986i	0.0635774	+	0.278551i
$50$	1.35519	+	5.93748i	0.191653	+	0.839686i
$51$	1.68854	−	2.11736i	0.236443	−	0.296490i
$52$	−0.344139	+	0.165729i	−0.0477236	+	0.0229825i
$53$	1.80194	+	0.867767i	0.247515	+	0.119197i	0.553529	−	0.832830i	$-0.313281\pi$
$53$	1.80194	+	0.867767i	0.247515	+	0.119197i	−0.306013	+	0.952027i	$0.598995\pi$
$54$	1.33795	+	1.67773i	0.182071	+	0.228310i
$55$	3.32086	−	4.16422i	0.447784	−	0.561503i
$56$	4.50484	+	2.16942i	0.601985	+	0.289901i
$57$	3.00000			0.397360
$58$		0			0
$59$	6.09017			0.792873			0.396436	−	0.918062i	$-0.370247\pi$
$59$	6.09017			0.792873			0.396436	+	0.918062i	$0.370247\pi$
$60$	3.47243	+	1.67223i	0.448288	+	0.215884i
$61$	0.385338	−	0.483198i	0.0493375	−	0.0618672i	−0.756551	−	0.653935i	$-0.773117\pi$
$61$	0.385338	−	0.483198i	0.0493375	−	0.0618672i	0.805888	+	0.592068i	$0.201688\pi$
$62$	−3.88812	−	4.87555i	−0.493792	−	0.619196i
$63$	−5.27436	−	2.54000i	−0.664507	−	0.320010i
$64$	0.212690	−	0.102426i	0.0265862	−	0.0128033i
$65$	−0.567270	+	0.711334i	−0.0703612	+	0.0882301i
$66$	0.117461	+	0.514629i	0.0144584	+	0.0633465i
$67$	0.339982	+	1.48956i	0.0415354	+	0.181978i	0.991440	−	0.130561i	$-0.0416777\pi$
$67$	0.339982	+	1.48956i	0.0415354	+	0.181978i	−0.949905	+	0.312539i	$0.898821\pi$
$68$	−4.42065	−	5.54332i	−0.536082	−	0.672226i
$69$	0.169991	−	0.744779i	0.0204645	−	0.0896608i
$70$	5.32624			0.636607
$71$	−2.33027	+	10.2096i	−0.276552	+	1.21165i	0.625568	+	0.780169i	$0.284867\pi$
$71$	−2.33027	+	10.2096i	−0.276552	+	1.21165i	−0.902120	+	0.431484i	$0.857990\pi$
$72$	5.27436	−	2.54000i	0.621590	−	0.299342i
$73$	−12.3507	+	5.94777i	−1.44554	+	0.696133i	−0.981814	−	0.189847i	$-0.939201\pi$
$73$	−12.3507	+	5.94777i	−1.44554	+	0.696133i	−0.463722	+	0.885981i	$0.653486\pi$
$74$	−0.647498	+	2.83687i	−0.0752701	+	0.329780i
$75$	6.09017			0.703232
$76$	1.74770	−	7.65718i	0.200475	−	0.878339i
$77$	−1.92669	−	2.41599i	−0.219567	−	0.275328i
$78$	−0.0200647	−	0.0879092i	−0.00227188	−	0.00995376i
$79$	−1.35519	−	5.93748i	−0.152471	−	0.668018i	−0.992162	−	0.124955i	$-0.960121\pi$
$79$	−1.35519	−	5.93748i	−0.152471	−	0.668018i	0.839692	−	0.543064i	$-0.182736\pi$
$80$	4.45539	−	5.58689i	0.498128	−	0.624633i
$81$	−5.14291	+	2.47670i	−0.571435	+	0.275189i
$82$	−2.14608	−	1.03350i	−0.236995	−	0.114131i
$83$	−6.20015	−	7.77474i	−0.680555	−	0.853389i	0.314850	−	0.949141i	$-0.398046\pi$
$83$	−6.20015	−	7.77474i	−0.680555	−	0.853389i	−0.995405	+	0.0957523i	$0.969474\pi$
$84$	1.39417	−	1.74823i	0.152116	−	0.190747i
$85$	−15.2161	−	7.32766i	−1.65041	−	0.794797i
$86$	−4.47214			−0.482243
$87$		0			0
$88$	3.09017			0.329413
$89$	4.24195	+	2.04281i	0.449645	+	0.216538i	0.644981	−	0.764199i	$-0.276865\pi$
$89$	4.24195	+	2.04281i	0.449645	+	0.216538i	−0.195336	+	0.980736i	$0.562580\pi$
$90$	3.88812	−	4.87555i	0.409844	−	0.513929i
$91$	0.329118	+	0.412701i	0.0345009	+	0.0432628i
$92$	−1.80194	−	0.867767i	−0.187865	−	0.0904710i
$93$	−5.61850	+	2.70573i	−0.582612	+	0.280571i
$94$	−2.69737	+	3.38239i	−0.278212	+	0.348867i
$95$	−4.16297	−	18.2392i	−0.427111	−	1.87130i
$96$	0.772623	+	3.38508i	0.0788555	+	0.345489i
$97$	−2.22106	−	2.78512i	−0.225515	−	0.282786i	0.656183	−	0.754602i	$-0.272170\pi$
$97$	−2.22106	−	2.78512i	−0.225515	−	0.282786i	−0.881697	+	0.471816i	$0.843599\pi$
$98$	−0.275051	+	1.20508i	−0.0277843	+	0.121731i
$99$	−3.61803			−0.363626
$100$	3.54793	−	15.5445i	0.354793	−	1.55445i
$101$	−0.556829	+	0.268155i	−0.0554066	+	0.0266824i	−0.461382	−	0.887202i	$-0.652646\pi$
$101$	−0.556829	+	0.268155i	−0.0554066	+	0.0266824i	0.405975	+	0.913884i	$0.366932\pi$
$102$	1.50801	−	0.726218i	0.149315	−	0.0719063i
$103$	−2.04282	+	8.95017i	−0.201285	+	0.881886i	0.768871	+	0.639404i	$0.220819\pi$
$103$	−2.04282	+	8.95017i	−0.201285	+	0.881886i	−0.970156	+	0.242482i	$0.922038\pi$
$104$	−0.527864			−0.0517613
$105$	1.18520	−	5.19270i	0.115664	−	0.506755i
$106$	0.770676	+	0.966397i	0.0748546	+	0.0938648i
$107$	−1.50512	−	6.59435i	−0.145505	−	0.637500i	−0.994101	−	0.108458i	$-0.965409\pi$
$107$	−1.50512	−	6.59435i	−0.145505	−	0.637500i	0.848596	−	0.529042i	$-0.177448\pi$
$108$	−1.25013	−	5.47718i	−0.120294	−	0.527042i
$109$	−8.96701	+	11.2443i	−0.858884	+	1.07701i	0.137369	+	0.990520i	$0.456135\pi$
$109$	−8.96701	+	11.2443i	−0.858884	+	1.07701i	−0.996253	+	0.0864862i	$0.972436\pi$
$110$	2.96581	−	1.42826i	0.282778	−	0.136179i
$111$	2.62167	+	1.26253i	0.248838	+	0.119834i
$112$	−2.58493	−	3.24139i	−0.244252	−	0.306283i
$113$	−4.95317	+	6.21108i	−0.465955	+	0.584289i	−0.958175	−	0.286181i	$-0.907614\pi$
$113$	−4.95317	+	6.21108i	−0.465955	+	0.584289i	0.492220	+	0.870471i	$0.336185\pi$
$114$	1.67049	+	0.804465i	0.156456	+	0.0753450i
$115$	−4.76393			−0.444239
$116$		0			0
$117$	0.618034			0.0571373
$118$	3.39119	+	1.63311i	0.312184	+	0.150340i
$119$	−6.10919	+	7.66068i	−0.560028	+	0.702253i
$120$	3.32086	+	4.16422i	0.303151	+	0.380140i
$121$	8.18996	+	3.94408i	0.744542	+	0.358552i
$122$	0.344139	−	0.165729i	0.0311569	−	0.0150044i
$123$	−1.48513	+	1.86230i	−0.133910	+	0.167918i
$124$	3.63293	+	15.9169i	0.326247	+	1.42938i
$125$	−4.16297	−	18.2392i	−0.372347	−	1.63136i
$126$	−2.25581	−	2.82869i	−0.200963	−	0.252000i
$127$	3.54793	−	15.5445i	0.314828	−	1.37935i	−0.531666	−	0.846954i	$-0.678434\pi$
$127$	3.54793	−	15.5445i	0.314828	−	1.37935i	0.846494	−	0.532398i	$-0.178709\pi$
$128$	11.3820			1.00603
$129$	−0.995144	+	4.36001i	−0.0876175	+	0.383877i
$130$	−0.506620	+	0.243975i	−0.0444335	+	0.0213981i
$131$	12.9075	−	6.21592i	1.12773	−	0.543088i	0.225460	−	0.974252i	$-0.427612\pi$
$131$	12.9075	−	6.21592i	1.12773	−	0.543088i	0.902273	+	0.431165i	$0.141897\pi$
$132$	0.307516	−	1.34732i	0.0267659	−	0.117269i
$133$	−10.8541			−0.941170
$134$	−0.210120	+	0.920597i	−0.0181516	+	0.0795275i
$135$	−8.34352	−	10.4624i	−0.718096	−	0.900464i
$136$	−2.18034	−	9.55271i	−0.186963	−	0.819138i
$137$	1.59011	+	6.96674i	0.135852	+	0.595208i	0.996321	+	0.0857042i	$0.0273140\pi$
$137$	1.59011	+	6.96674i	0.135852	+	0.595208i	−0.860468	+	0.509504i	$0.829829\pi$
$138$	0.294372	−	0.369131i	0.0250586	−	0.0314225i
$139$	−1.16387	+	0.560489i	−0.0987180	+	0.0475401i	−0.482591	−	0.875846i	$-0.660304\pi$
$139$	−1.16387	+	0.560489i	−0.0987180	+	0.0475401i	0.383873	+	0.923386i	$0.374590\pi$
$140$	−12.5634	−	6.05019i	−1.06180	−	0.511335i
$141$	2.69737	+	3.38239i	0.227159	+	0.284849i
$142$	−4.03531	+	5.06012i	−0.338636	+	0.424636i
$143$	0.293930	+	0.141549i	0.0245797	+	0.0118369i
$144$	−4.85410			−0.404508
$145$		0			0
$146$	−8.47214			−0.701159
$147$	1.11366	+	0.536310i	0.0918530	+	0.0442341i
$148$	4.74977	−	5.95602i	0.390428	−	0.489582i
$149$	5.99675	+	7.51968i	0.491273	+	0.616036i	0.964236	−	0.265046i	$-0.0853871\pi$
$149$	5.99675	+	7.51968i	0.491273	+	0.616036i	−0.472963	+	0.881082i	$0.656816\pi$
$150$	3.39119	+	1.63311i	0.276889	+	0.133343i
$151$	−2.40898	+	1.16010i	−0.196040	+	0.0944078i	−0.529328	−	0.848417i	$-0.677556\pi$
$151$	−2.40898	+	1.16010i	−0.196040	+	0.0944078i	0.333288	+	0.942825i	$0.391842\pi$
$152$	6.76742	−	8.48608i	0.548910	−	0.688312i
$153$	2.55279	+	11.1845i	0.206381	+	0.904214i
$154$	−0.424977	−	1.86195i	−0.0342456	−	0.150040i
$155$	24.2466	+	30.4043i	1.94753	+	2.44213i
$156$	−0.0525301	+	0.230149i	−0.00420577	+	0.0184267i
$157$	−14.5623			−1.16220			−0.581099	−	0.813833i	$-0.697377\pi$
$157$	−14.5623			−1.16220			−0.581099	+	0.813833i	$0.697377\pi$
$158$	0.837554	−	3.66956i	0.0666322	−	0.291935i
$159$	1.11366	−	0.536310i	0.0883189	−	0.0425321i
$160$	19.5082	−	9.39466i	1.54226	−	0.742713i
$161$	−0.615033	+	2.69463i	−0.0484714	+	0.212367i
$162$	−3.52786			−0.277175
$163$	−1.34279	+	5.88315i	−0.105175	+	0.460804i	0.894724	+	0.446619i	$0.147372\pi$
$163$	−1.34279	+	5.88315i	−0.105175	+	0.460804i	−0.999899	+	0.0141841i	$0.995485\pi$
$164$	3.88812	+	4.87555i	0.303612	+	0.380717i
$165$	−0.732494	−	3.20926i	−0.0570245	−	0.249841i
$166$	−1.36759	−	5.99181i	−0.106146	−	0.465054i
$167$	6.56402	−	8.23102i	0.507939	−	0.636935i	−0.460061	−	0.887888i	$-0.652172\pi$
$167$	6.56402	−	8.23102i	0.507939	−	0.636935i	0.967999	+	0.250952i	$0.0807438\pi$
$168$	2.78415	−	1.34077i	0.214802	−	0.103443i
$169$	11.6624	+	5.61631i	0.897107	+	0.432024i
$170$	−6.50780	−	8.16052i	−0.499125	−	0.625883i
$171$	−7.92344	+	9.93567i	−0.605920	+	0.759800i
$172$	10.5487	+	5.08000i	0.804333	+	0.387346i
$173$	4.09017			0.310970			0.155485	−	0.987838i	$-0.450306\pi$
$173$	4.09017			0.310970			0.155485	+	0.987838i	$0.450306\pi$
$174$		0			0
$175$	−22.0344			−1.66565
$176$	−2.30856	−	1.11174i	−0.174014	−	0.0838008i
$177$	2.34677	−	2.94276i	0.176394	−	0.221191i
$178$	1.81425	+	2.27500i	0.135984	+	0.170518i
$179$	14.4155	+	6.94214i	1.07747	+	0.518880i	0.886506	−	0.462718i	$-0.153126\pi$
$179$	14.4155	+	6.94214i	1.07747	+	0.518880i	0.190960	+	0.981598i	$0.438840\pi$
$180$	−14.7094	+	7.08369i	−1.09638	+	0.527987i
$181$	3.70619	−	4.64742i	0.275479	−	0.345440i	−0.624775	−	0.780805i	$-0.714809\pi$
$181$	3.70619	−	4.64742i	0.275479	−	0.345440i	0.900254	+	0.435365i	$0.143381\pi$
$182$	0.0725948	+	0.318058i	0.00538108	+	0.0235761i
$183$	−0.0849954	−	0.372389i	−0.00628304	−	0.0275278i
$184$	−1.72328	−	2.16093i	−0.127042	−	0.159306i
$185$	4.03784	−	17.6909i	0.296868	−	1.30066i
$186$	−3.85410			−0.282596
$187$	−1.34753	+	5.90390i	−0.0985409	+	0.431736i
$188$	10.2046	−	4.91427i	0.744246	−	0.358410i
$189$	−6.99506	+	3.36864i	−0.508816	+	0.245033i
$190$	2.57286	−	11.2724i	0.186655	−	0.817787i
$191$	−17.0344			−1.23257			−0.616284	−	0.787524i	$-0.711363\pi$
$191$	−17.0344			−1.23257			−0.616284	+	0.787524i	$0.711363\pi$
$192$	0.0324654	−	0.142240i	0.00234299	−	0.0102653i
$193$	−7.77625	−	9.75111i	−0.559747	−	0.701900i	0.418764	−	0.908095i	$-0.362463\pi$
$193$	−7.77625	−	9.75111i	−0.559747	−	0.701900i	−0.978511	+	0.206195i	$0.933892\pi$
$194$	−0.489908	−	2.14643i	−0.0351733	−	0.154104i
$195$	0.125125	+	0.548208i	0.00896038	+	0.0392580i
$196$	2.01766	−	2.53006i	0.144118	−	0.180719i
$197$	5.66871	−	2.72991i	0.403879	−	0.194498i	−0.220905	−	0.975295i	$-0.570901\pi$
$197$	5.66871	−	2.72991i	0.403879	−	0.194498i	0.624784	+	0.780797i	$0.285187\pi$
$198$	−2.01463	−	0.970194i	−0.143173	−	0.0689487i
$199$	−3.64997	−	4.57692i	−0.258740	−	0.324449i	0.635446	−	0.772145i	$-0.280816\pi$
$199$	−3.64997	−	4.57692i	−0.258740	−	0.324449i	−0.894186	+	0.447696i	$0.852245\pi$
$200$	13.7382	−	17.2272i	0.971441	−	1.21815i
$201$	0.850760	+	0.409704i	0.0600080	+	0.0288983i
$202$	−0.381966			−0.0268750
$203$		0			0
$204$	−4.38197			−0.306799
$205$	13.3831	+	6.44495i	0.934715	+	0.450135i
$206$	−3.53753	+	4.43593i	−0.246472	+	0.309066i
$207$	2.01766	+	2.53006i	0.140237	+	0.175851i
$208$	0.394349	+	0.189908i	0.0273432	+	0.0131678i
$209$	−6.04388	+	2.91058i	−0.418064	+	0.201329i
$210$	2.05240	−	2.57363i	0.141629	−	0.177597i
$211$	−2.59292	−	11.3603i	−0.178504	−	0.782077i	−0.982322	−	0.187201i	$-0.940058\pi$
$211$	−2.59292	−	11.3603i	−0.178504	−	0.782077i	0.803818	−	0.594876i	$-0.202799\pi$
$212$	−0.720093	−	3.15493i	−0.0494562	−	0.216682i
$213$	4.03531	+	5.06012i	0.276495	+	0.346714i
$214$	0.930213	−	4.07553i	0.0635881	−	0.278597i
$215$	27.8885			1.90198
$216$	1.72764	−	7.56927i	0.117551	−	0.515024i
$217$	20.3279	−	9.78942i	1.37995	−	0.664549i
$218$	−8.00830	+	3.85659i	−0.542391	+	0.261202i
$219$	−1.88523	+	8.25972i	−0.127392	+	0.558140i
$220$	−8.61803			−0.581028
$221$	0.230185	−	1.00851i	0.0154839	−	0.0678395i
$222$	1.12127	+	1.40603i	0.0752546	+	0.0943662i
$223$	−0.594968	−	2.60673i	−0.0398420	−	0.174559i	0.951092	−	0.308907i	$-0.0999632\pi$
$223$	−0.594968	−	2.60673i	−0.0398420	−	0.174559i	−0.990934	+	0.134348i	$0.957106\pi$
$224$	−2.79538	−	12.2473i	−0.186774	−	0.818310i
$225$	−16.0850	+	20.1700i	−1.07233	+	1.34467i
$226$	−4.42360	+	2.13030i	−0.294254	+	0.141705i
$227$	18.8199	+	9.06320i	1.24912	+	0.601546i	0.937276	−	0.348587i	$-0.113338\pi$
$227$	18.8199	+	9.06320i	1.24912	+	0.601546i	0.311846	+	0.950133i	$0.399053\pi$
$228$	−3.02648	−	3.79509i	−0.200434	−	0.251336i
$229$	−1.42891	+	1.79180i	−0.0944251	+	0.118405i	−0.826799	−	0.562497i	$-0.809841\pi$
$229$	−1.42891	+	1.79180i	−0.0944251	+	0.118405i	0.732374	+	0.680902i	$0.238412\pi$
$230$	−2.65270	−	1.27747i	−0.174914	−	0.0842340i
$231$	−1.90983			−0.125658
$232$		0			0
$233$	15.2361			0.998148			0.499074	−	0.866559i	$-0.333674\pi$
$233$	15.2361			0.998148			0.499074	+	0.866559i	$0.333674\pi$
$234$	0.344139	+	0.165729i	0.0224971	+	0.0108340i
$235$	16.8210	−	21.0928i	1.09728	−	1.37594i
$236$	−6.14393	−	7.70425i	−0.399936	−	0.501504i
$237$	−3.39119	−	1.63311i	−0.220281	−	0.106082i
$238$	−5.45602	+	2.62748i	−0.353661	+	0.170314i
$239$	−17.2973	+	21.6901i	−1.11887	+	1.40301i	−0.214255	+	0.976778i	$0.568732\pi$
$239$	−17.2973	+	21.6901i	−1.11887	+	1.40301i	−0.904612	+	0.426236i	$0.859839\pi$
$240$	−0.982743	−	4.30568i	−0.0634358	−	0.277930i
$241$	1.03527	+	4.53583i	0.0666878	+	0.292178i	0.997264	−	0.0739193i	$-0.0235507\pi$
$241$	1.03527	+	4.53583i	0.0666878	+	0.292178i	−0.930576	+	0.366098i	$0.880694\pi$
$242$	3.50279	+	4.39236i	0.225168	+	0.282351i
$243$	−3.10289	+	13.5947i	−0.199051	+	0.872098i
$244$	−1.00000			−0.0640184
$245$	1.71524	−	7.51494i	0.109582	−	0.480112i
$246$	−1.32635	+	0.638736i	−0.0845649	+	0.0407243i
$247$	1.03242	−	0.497187i	0.0656912	−	0.0316352i
$248$	−5.02059	+	21.9966i	−0.318807	+	1.39679i
$249$	−6.14590			−0.389480
$250$	2.57286	−	11.2724i	0.162722	−	0.712930i
$251$	12.2531	+	15.3649i	0.773410	+	0.969825i	0.999991	−	0.00416682i	$-0.00132634\pi$
$251$	12.2531	+	15.3649i	0.773410	+	0.969825i	−0.226581	+	0.973992i	$0.572755\pi$
$252$	2.10775	+	9.23465i	0.132776	+	0.581728i
$253$	0.380111	+	1.66538i	0.0238974	+	0.104701i
$254$	6.14393	−	7.70425i	0.385505	−	0.483407i
$255$	−9.40404	+	4.52875i	−0.588904	+	0.283601i
$256$	5.91243	+	2.84728i	0.369527	+	0.177955i
$257$	−14.4527	−	18.1231i	−0.901535	−	1.13049i	−0.990915	−	0.134492i	$-0.957060\pi$
$257$	−14.4527	−	18.1231i	−0.901535	−	1.13049i	0.0893797	−	0.995998i	$-0.471512\pi$
$258$	−1.72328	+	2.16093i	−0.107287	+	0.134534i
$259$	−9.48528	−	4.56787i	−0.589386	−	0.283834i
$260$	1.47214			0.0912980
$261$		0			0
$262$	8.85410			0.547008
$263$	−15.0536	−	7.24942i	−0.928243	−	0.447018i	−0.0922361	−	0.995737i	$-0.529401\pi$
$263$	−15.0536	−	7.24942i	−0.928243	−	0.447018i	−0.836007	+	0.548719i	$0.815116\pi$
$264$	1.19076	−	1.49317i	0.0732862	−	0.0918980i
$265$	−4.80599	−	6.02652i	−0.295229	−	0.370206i
$266$	−6.04388	−	2.91058i	−0.370574	−	0.178459i
$267$	2.62167	−	1.26253i	0.160443	−	0.0772655i
$268$	1.54135	−	1.93279i	0.0941530	−	0.118064i
$269$	−1.33513	−	5.84957i	−0.0814040	−	0.356654i	0.917778	−	0.397094i	$-0.129981\pi$
$269$	−1.33513	−	5.84957i	−0.0814040	−	0.356654i	−0.999182	+	0.0404396i	$0.987124\pi$
$270$	−1.84036	−	8.06315i	−0.112001	−	0.490708i
$271$	−6.34734	−	7.95931i	−0.385573	−	0.483494i	0.550731	−	0.834683i	$-0.314349\pi$
$271$	−6.34734	−	7.95931i	−0.385573	−	0.483494i	−0.936305	+	0.351189i	$0.885777\pi$
$272$	−1.80790	+	7.92091i	−0.109620	+	0.480276i
$273$	0.326238			0.0197448
$274$	−0.982743	+	4.30568i	−0.0593697	+	0.260116i
$275$	−12.2694	+	5.90864i	−0.739874	+	0.356305i
$276$	−1.11366	+	0.536310i	−0.0670344	+	0.0322821i
$277$	4.75794	−	20.8459i	0.285877	−	1.25251i	−0.604250	−	0.796795i	$-0.706527\pi$
$277$	4.75794	−	20.8459i	0.285877	−	1.25251i	0.890127	−	0.455713i	$-0.150616\pi$
$278$	−0.798374			−0.0478833
$279$	5.87820	−	25.7541i	0.351919	−	1.54186i
$280$	−12.0150	−	15.0663i	−0.718032	−	0.900383i
$281$	−5.14571	−	22.5448i	−0.306967	−	1.34491i	−0.859379	−	0.511340i	$-0.829149\pi$
$281$	−5.14571	−	22.5448i	−0.306967	−	1.34491i	0.552411	−	0.833572i	$-0.313708\pi$
$282$	0.594968	+	2.60673i	0.0354298	+	0.155228i
$283$	−3.26463	+	4.09372i	−0.194062	+	0.243347i	−0.869337	−	0.494220i	$-0.835454\pi$
$283$	−3.26463	+	4.09372i	−0.194062	+	0.243347i	0.675274	+	0.737567i	$0.264025\pi$
$284$	15.2663	−	7.35184i	0.905886	−	0.436252i
$285$	−10.4173	−	5.01670i	−0.617066	−	0.297163i
$286$	0.125712	+	0.157638i	0.00743350	+	0.00932131i
$287$	5.37326	−	6.73785i	0.317173	−	0.397723i
$288$	−13.2516	−	6.38165i	−0.780860	−	0.376042i
$289$	2.20163			0.129507
$290$		0			0
$291$	−2.20163			−0.129062
$292$	19.9838	+	9.62369i	1.16946	+	0.563184i
$293$	−5.31704	+	6.66735i	−0.310625	+	0.389511i	−0.912498	−	0.409080i	$-0.865850\pi$
$293$	−5.31704	+	6.66735i	−0.310625	+	0.389511i	0.601874	+	0.798591i	$0.294421\pi$
$294$	0.476304	+	0.597266i	0.0277786	+	0.0348333i
$295$	−21.1477	−	10.1842i	−1.23126	−	0.592946i
$296$	9.48528	−	4.56787i	0.551321	−	0.265502i
$297$	−2.99174	+	3.75152i	−0.173598	+	0.217685i
$298$	1.32272	+	5.79524i	0.0766234	+	0.335709i
$299$	−0.0649307	−	0.284480i	−0.00375504	−	0.0164519i
$300$	−6.14393	−	7.70425i	−0.354720	−	0.444805i
$301$	3.60046	−	15.7747i	0.207527	−	0.909237i
$302$	−1.65248			−0.0950893
$303$	−0.0849954	+	0.372389i	−0.00488286	+	0.0213932i
$304$	−8.10872	+	3.90495i	−0.465067	+	0.223964i
$305$	−2.14608	+	1.03350i	−0.122884	+	0.0591778i
$306$	−1.57771	+	6.91240i	−0.0901917	+	0.395156i
$307$	19.1803			1.09468			0.547340	−	0.836910i	$-0.315640\pi$
$307$	19.1803			1.09468			0.547340	+	0.836910i	$0.315640\pi$
$308$	−1.11260	+	4.87464i	−0.0633965	+	0.277758i
$309$	3.53753	+	4.43593i	0.201243	+	0.252351i
$310$	5.34817	+	23.4318i	0.303755	+	1.33084i
$311$	0.465107	+	2.03777i	0.0263738	+	0.115551i	0.986401	−	0.164354i	$-0.0525540\pi$
$311$	0.465107	+	2.03777i	0.0263738	+	0.115551i	−0.960028	+	0.279905i	$0.909697\pi$
$312$	−0.203406	+	0.255063i	−0.0115156	+	0.0144401i
$313$	11.6314	−	5.60137i	0.657443	−	0.316608i	−0.0752524	−	0.997165i	$-0.523976\pi$
$313$	11.6314	−	5.60137i	0.657443	−	0.316608i	0.732695	+	0.680557i	$0.238262\pi$
$314$	−8.10872	−	3.90495i	−0.457602	−	0.220369i
$315$	14.0674	+	17.6399i	0.792606	+	0.993897i
$316$	−6.14393	+	7.70425i	−0.345623	+	0.433398i
$317$	24.9642	+	12.0221i	1.40213	+	0.675231i	0.973592	−	0.228293i	$-0.0733144\pi$
$317$	24.9642	+	12.0221i	1.40213	+	0.675231i	0.428538	+	0.903524i	$0.359029\pi$
$318$	0.763932			0.0428392
$319$		0			0
$320$	−0.909830			−0.0508610
$321$	−3.76636	−	1.81378i	−0.210217	−	0.101235i
$322$	−1.06505	+	1.33553i	−0.0593528	+	0.0744260i
$323$	13.2619	+	16.6300i	0.737914	+	0.925315i
$324$	8.32141	+	4.00738i	0.462301	+	0.222632i
$325$	2.09587	−	1.00932i	0.116258	−	0.0559868i
$326$	−2.32530	+	2.91583i	−0.128786	+	0.161493i
$327$	1.97789	+	8.66569i	0.109377	+	0.479214i
$328$	1.91769	+	8.40196i	0.105887	+	0.463921i
$329$	−9.75916	−	12.2376i	−0.538040	−	0.674681i
$330$	0.452706	−	1.98343i	0.0249206	−	0.109184i
$331$	−21.1803			−1.16418			−0.582088	−	0.813126i	$-0.697764\pi$
$331$	−21.1803			−1.16418			−0.582088	+	0.813126i	$0.697764\pi$
$332$	−3.58040	+	15.6868i	−0.196500	+	0.860923i
$333$	−11.1056	+	5.34815i	−0.608581	+	0.293077i
$334$	5.86222	−	2.82310i	0.320767	−	0.154473i
$335$	1.31032	−	5.74091i	0.0715907	−	0.313659i
$336$	−2.56231			−0.139785
$337$	−7.58104	+	33.2147i	−0.412966	+	1.80932i	0.156938	+	0.987609i	$0.449838\pi$
$337$	−7.58104	+	33.2147i	−0.412966	+	1.80932i	−0.569903	+	0.821712i	$0.693019\pi$
$338$	4.98792	+	6.25465i	0.271307	+	0.340208i
$339$	1.09254	+	4.78673i	0.0593386	+	0.259980i
$340$	6.08066	+	26.6411i	0.329770	+	1.44482i
$341$	8.69411	−	10.9021i	0.470813	−	0.590380i
$342$	−7.07630	+	3.40777i	−0.382643	+	0.184271i
$343$	−18.1316	−	8.73174i	−0.979017	−	0.471470i
$344$	10.0883	+	12.6503i	0.543923	+	0.682058i
$345$	−1.83572	+	2.30192i	−0.0988320	+	0.123931i
$346$	2.27753	+	1.09680i	0.122441	+	0.0589643i
$347$	−32.1246			−1.72454			−0.862270	−	0.506449i	$-0.830958\pi$
$347$	−32.1246			−1.72454			−0.862270	+	0.506449i	$0.830958\pi$
$348$		0			0
$349$	4.52786			0.242371			0.121186	−	0.992630i	$-0.461330\pi$
$349$	4.52786			0.242371			0.121186	+	0.992630i	$0.461330\pi$
$350$	−12.2694	−	5.90864i	−0.655828	−	0.315830i
$351$	0.511050	−	0.640836i	0.0272778	−	0.0342053i
$352$	−4.84073	−	6.07009i	−0.258012	−	0.323537i
$353$	17.2307	+	8.29786i	0.917097	+	0.441650i	0.832034	−	0.554725i	$-0.187177\pi$
$353$	17.2307	+	8.29786i	0.917097	+	0.441650i	0.0850629	+	0.996376i	$0.472891\pi$
$354$	2.09587	−	1.00932i	0.111394	−	0.0536446i
$355$	25.1645	−	31.5553i	1.33559	−	1.67478i
$356$	−1.69517	−	7.42703i	−0.0898439	−	0.393632i
$357$	1.34753	+	5.90390i	0.0713187	+	0.312467i
$358$	6.16541	+	7.73117i	0.325852	+	0.408605i
$359$	−5.28797	+	23.1681i	−0.279089	+	1.22277i	0.619860	+	0.784712i	$0.287189\pi$
$359$	−5.28797	+	23.1681i	−0.279089	+	1.22277i	−0.898949	+	0.438054i	$0.855668\pi$
$360$	−22.5623			−1.18914
$361$	−1.01521	+	4.44792i	−0.0534320	+	0.234101i
$362$	3.30995	−	1.59399i	0.173967	−	0.0837780i
$363$	5.06167	−	2.43757i	0.265669	−	0.127939i
$364$	0.190056	−	0.832688i	0.00996162	−	0.0436447i
$365$	52.8328			2.76540
$366$	0.0525301	−	0.230149i	0.00274579	−	0.0120301i
$367$	−17.0029	−	21.3209i	−0.887543	−	1.11294i	−0.992952	−	0.118515i	$-0.962187\pi$
$367$	−17.0029	−	21.3209i	−0.887543	−	1.11294i	0.105409	−	0.994429i	$-0.466385\pi$
$368$	0.509973	+	2.23434i	0.0265842	+	0.116473i
$369$	−2.24527	−	9.83719i	−0.116884	−	0.512104i
$370$	6.99230	−	8.76807i	0.363512	−	0.455830i
$371$	−4.02926	+	1.94039i	−0.209189	+	0.100740i
$372$	9.09093	+	4.37796i	0.471343	+	0.226987i
$373$	12.8551	+	16.1198i	0.665614	+	0.834653i	0.993941	−	0.109911i	$-0.0350565\pi$
$373$	12.8551	+	16.1198i	0.665614	+	0.834653i	−0.328328	+	0.944564i	$0.606485\pi$
$374$	−2.33350	+	2.92612i	−0.120662	+	0.151306i
$375$	−10.4173	−	5.01670i	−0.537946	−	0.259061i
$376$	15.6525			0.807215
$377$		0			0
$378$	−4.79837			−0.246802
$379$	−21.8862	−	10.5398i	−1.12422	−	0.541394i	−0.223024	−	0.974813i	$-0.571593\pi$
$379$	−21.8862	−	10.5398i	−1.12422	−	0.541394i	−0.901192	+	0.433419i	$0.857307\pi$
$380$	−18.8734	+	23.6664i	−0.968183	+	1.21406i
$381$	−6.14393	−	7.70425i	−0.314763	−	0.394701i
$382$	−9.48528	−	4.56787i	−0.485309	−	0.233713i
$383$	25.9966	−	12.5193i	1.32837	−	0.639708i	0.371013	−	0.928628i	$-0.379010\pi$
$383$	25.9966	−	12.5193i	1.32837	−	0.639708i	0.957353	+	0.288920i	$0.0932961\pi$
$384$	4.38590	−	5.49975i	0.223817	−	0.280658i
$385$	2.65019	+	11.6112i	0.135066	+	0.591763i
$386$	−1.71524	−	7.51494i	−0.0873033	−	0.382501i
$387$	−11.8116	−	14.8112i	−0.600415	−	0.752897i
$388$	−1.28260	+	5.61942i	−0.0651139	+	0.285283i
$389$	19.1246			0.969656			0.484828	−	0.874609i	$-0.338882\pi$
$389$	19.1246			0.969656			0.484828	+	0.874609i	$0.338882\pi$
$390$	−0.0773314	+	0.338811i	−0.00391583	+	0.0171564i
$391$	4.88001	−	2.35009i	0.246793	−	0.118849i
$392$	4.02926	−	1.94039i	0.203508	−	0.0980043i
$393$	1.97022	−	8.63211i	0.0993846	−	0.435432i
$394$	3.88854			0.195902
$395$	−5.22304	+	22.8836i	−0.262800	+	1.15140i
$396$	3.64997	+	4.57692i	0.183418	+	0.229999i
$397$	3.12769	+	13.7033i	0.156974	+	0.687750i	0.990756	+	0.135656i	$0.0433141\pi$
$397$	3.12769	+	13.7033i	0.156974	+	0.687750i	−0.833782	+	0.552094i	$0.813829\pi$
$398$	−0.805088	−	3.52732i	−0.0403554	−	0.176809i
$399$	−4.18250	+	5.24469i	−0.209387	+	0.262563i
$400$	−16.4612	+	7.92728i	−0.823058	+	0.396364i
$401$	−22.5863	−	10.8770i	−1.12791	−	0.543171i	−0.225579	−	0.974225i	$-0.572427\pi$
$401$	−22.5863	−	10.8770i	−1.12791	−	0.543171i	−0.902326	+	0.431054i	$0.858142\pi$
$402$	0.363864	+	0.456271i	0.0181479	+	0.0227567i
$403$	−1.48513	+	1.86230i	−0.0739797	+	0.0927676i
$404$	0.900969	+	0.433884i	0.0448249	+	0.0215865i
$405$	22.0000			1.09319
$406$		0			0
$407$	−6.50658			−0.322519
$408$	−5.45602	−	2.62748i	−0.270113	−	0.130080i
$409$	−17.0939	+	21.4350i	−0.845237	+	1.05989i	0.152201	+	0.988350i	$0.451364\pi$
$409$	−17.0939	+	21.4350i	−0.845237	+	1.05989i	−0.997437	+	0.0715435i	$0.977208\pi$
$410$	5.72385	+	7.17748i	0.282681	+	0.354470i
$411$	3.97905	+	1.91621i	0.196272	+	0.0945195i
$412$	13.3831	−	6.44495i	0.659337	−	0.317520i
$413$	−8.49071	+	10.6470i	−0.417800	+	0.523905i
$414$	0.445042	+	1.94986i	0.0218726	+	0.0958302i
$415$	8.52839	+	37.3653i	0.418642	+	1.83419i
$416$	0.826896	+	1.03689i	0.0405419	+	0.0508379i
$417$	−0.177655	+	0.778357i	−0.00869980	+	0.0381163i
$418$	−4.14590			−0.202783
$419$	3.90798	−	17.1220i	0.190917	−	0.836464i	−0.785204	−	0.619237i	$-0.787442\pi$
$419$	3.90798	−	17.1220i	0.190917	−	0.836464i	0.976121	−	0.217226i	$-0.0697010\pi$
$420$	−7.76458	+	3.73922i	−0.378873	+	0.182455i
$421$	−27.9611	+	13.4653i	−1.36274	+	0.656261i	−0.965246	−	0.261345i	$-0.915834\pi$
$421$	−27.9611	+	13.4653i	−1.36274	+	0.656261i	−0.397493	+	0.917605i	$0.630120\pi$
$422$	1.60251	−	7.02107i	0.0780091	−	0.341780i
$423$	−18.3262			−0.891052
$424$	0.995144	−	4.36001i	0.0483285	−	0.211741i
$425$	26.9225	+	33.7597i	1.30593	+	1.63759i
$426$	0.890084	+	3.89971i	0.0431247	+	0.188942i
$427$	0.307516	+	1.34732i	0.0148818	+	0.0652013i
$428$	−6.82364	+	8.55658i	−0.329833	+	0.413598i
$429$	0.181659	−	0.0874823i	0.00877057	−	0.00422369i
$430$	15.5292	+	7.47845i	0.748883	+	0.360643i
$431$	9.10092	+	11.4122i	0.438376	+	0.549706i	0.951114	−	0.308839i	$-0.0999403\pi$
$431$	9.10092	+	11.4122i	0.438376	+	0.549706i	−0.512738	+	0.858545i	$0.671369\pi$
$432$	−4.01384	+	5.03319i	−0.193116	+	0.242160i
$433$	9.35383	+	4.50457i	0.449516	+	0.216476i	0.644924	−	0.764246i	$-0.276889\pi$
$433$	9.35383	+	4.50457i	0.449516	+	0.216476i	−0.195408	+	0.980722i	$0.562603\pi$
$434$	13.9443			0.669346
$435$		0			0
$436$	23.2705			1.11446
$437$	5.40581	+	2.60330i	0.258595	+	0.124533i
$438$	−3.26463	+	4.09372i	−0.155990	+	0.195606i
$439$	−13.0585	−	16.3749i	−0.623250	−	0.781531i	0.365548	−	0.930793i	$-0.380882\pi$
$439$	−13.0585	−	16.3749i	−0.623250	−	0.781531i	−0.988798	+	0.149262i	$0.952310\pi$
$440$	−10.7304	−	5.16748i	−0.511551	−	0.246350i
$441$	−4.71753	+	2.27184i	−0.224644	+	0.108183i
$442$	0.398610	−	0.499841i	0.0189599	−	0.0237750i
$443$	−0.424977	−	1.86195i	−0.0201913	−	0.0884638i	0.963828	−	0.266524i	$-0.0858751\pi$
$443$	−0.424977	−	1.86195i	−0.0201913	−	0.0884638i	−0.984020	+	0.178060i	$0.943018\pi$
$444$	−1.04767	−	4.59016i	−0.0497204	−	0.217839i
$445$	−11.3138	−	14.1870i	−0.536325	−	0.672530i
$446$	0.367710	−	1.61104i	0.0174116	−	0.0762852i
$447$	5.94427			0.281154
$448$	−0.117461	+	0.514629i	−0.00554950	+	0.0243140i
$449$	−23.5375	+	11.3350i	−1.11080	+	0.534934i	−0.897039	−	0.441952i	$-0.854286\pi$
$449$	−23.5375	+	11.3350i	−1.11080	+	0.534934i	−0.213763	+	0.976886i	$0.568572\pi$
$450$	−14.3653	+	6.91796i	−0.677186	+	0.326116i
$451$	1.18520	−	5.19270i	0.0558089	−	0.244515i
$452$	12.8541			0.604606
$453$	−0.367710	+	1.61104i	−0.0172765	+	0.0756935i
$454$	8.04915	+	10.0933i	0.377765	+	0.473703i
$455$	−0.452706	−	1.98343i	−0.0212232	−	0.0929848i
$456$	−1.49272	−	6.54002i	−0.0699028	−	0.306264i
$457$	11.6644	−	14.6267i	0.545636	−	0.684206i	−0.430194	−	0.902737i	$-0.641555\pi$
$457$	11.6644	−	14.6267i	0.545636	−	0.684206i	0.975830	+	0.218530i	$0.0701262\pi$
$458$	−1.27614	+	0.614556i	−0.0596301	+	0.0287163i
$459$	13.7080	+	6.60145i	0.639837	+	0.308129i
$460$	4.80599	+	6.02652i	0.224080	+	0.280988i
$461$	24.3028	−	30.4748i	1.13190	−	1.41935i	0.237893	−	0.971291i	$-0.423543\pi$
$461$	24.3028	−	30.4748i	1.13190	−	1.41935i	0.894003	−	0.448061i	$-0.147885\pi$
$462$	−1.06345	−	0.512130i	−0.0494761	−	0.0238265i
$463$	10.7082			0.497652			0.248826	−	0.968548i	$-0.419955\pi$
$463$	10.7082			0.497652			0.248826	+	0.968548i	$0.419955\pi$
$464$		0			0
$465$	24.0344			1.11457
$466$	8.48389	+	4.08563i	0.393009	+	0.189263i
$467$	11.1881	−	14.0294i	0.517722	−	0.649203i	−0.452401	−	0.891814i	$-0.649433\pi$
$467$	11.1881	−	14.0294i	0.517722	−	0.649203i	0.970124	+	0.242611i	$0.0780040\pi$
$468$	−0.623490	−	0.781831i	−0.0288208	−	0.0361402i
$469$	−3.07808	−	1.48232i	−0.142132	−	0.0684474i
$470$	15.0225	−	7.23447i	0.692938	−	0.333701i
$471$	−5.61141	+	7.03648i	−0.258560	+	0.324224i
$472$	−3.03030	−	13.2766i	−0.139481	−	0.611105i
$473$	−2.22521	−	9.74928i	−0.102315	−	0.448272i
$474$	−1.45039	−	1.81873i	−0.0666184	−	0.0835369i
$475$	−10.6438	+	46.6335i	−0.488371	+	2.13969i
$476$	15.8541			0.726672
$477$	−1.16513	+	5.10479i	−0.0533479	+	0.233732i
$478$	−15.4479	+	7.43933i	−0.706571	+	0.340267i
$479$	−10.0731	+	4.85097i	−0.460253	+	0.221646i	−0.649618	−	0.760260i	$-0.725071\pi$
$479$	−10.0731	+	4.85097i	−0.460253	+	0.221646i	0.189365	+	0.981907i	$0.439357\pi$
$480$	2.97777	−	13.0465i	0.135916	−	0.595486i
$481$	1.11146			0.0506780
$482$	−0.639834	+	2.80330i	−0.0291436	+	0.127687i
$483$	1.06505	+	1.33553i	0.0484613	+	0.0607686i
$484$	−3.27288	−	14.3394i	−0.148767	−	0.651793i
$485$	3.05510	+	13.3853i	0.138725	+	0.607793i
$486$	−5.37326	+	6.73785i	−0.243736	+	0.305635i
$487$	−38.3473	+	18.4671i	−1.73768	+	0.836824i	−0.754009	+	0.656865i	$0.771882\pi$
$487$	−38.3473	+	18.4671i	−1.73768	+	0.836824i	−0.983674	+	0.179959i	$0.942403\pi$
$488$	−1.24511	−	0.599613i	−0.0563634	−	0.0271432i
$489$	2.32530	+	2.91583i	0.105154	+	0.131859i
$490$	2.97026	−	3.72459i	0.134183	−	0.168260i
$491$	−13.6268	−	6.56232i	−0.614969	−	0.296153i	0.100349	−	0.994952i	$-0.468004\pi$
$491$	−13.6268	−	6.56232i	−0.614969	−	0.296153i	−0.715318	+	0.698799i	$0.753718\pi$
$492$	3.85410			0.173756
$493$		0			0
$494$	0.708204			0.0318636
$495$	12.5634	+	6.05019i	0.564681	+	0.271936i
$496$	11.6644	−	14.6267i	0.523746	−	0.656757i
$497$	−14.5999	−	18.3077i	−0.654895	−	0.821212i
$498$	−3.42222	−	1.64805i	−0.153353	−	0.0738510i
$499$	−22.2421	+	10.7113i	−0.995695	+	0.479502i	−0.859475	−	0.511177i	$-0.829210\pi$
$499$	−22.2421	+	10.7113i	−0.995695	+	0.479502i	−0.136220	+	0.990679i	$0.543495\pi$
$500$	−18.8734	+	23.6664i	−0.844042	+	1.05840i
$501$	−1.44785	−	6.34344i	−0.0646852	−	0.283404i
$502$	2.70272	+	11.8414i	0.120628	+	0.528506i
$503$	−8.89752	−	11.1571i	−0.396721	−	0.497472i	0.542849	−	0.839831i	$-0.317346\pi$
$503$	−8.89752	−	11.1571i	−0.396721	−	0.497472i	−0.939569	+	0.342358i	$0.888774\pi$
$504$	−2.91284	+	12.7620i	−0.129748	+	0.568463i
$505$	2.38197			0.105996
$506$	−0.234922	+	1.02926i	−0.0104435	+	0.0457561i
$507$	7.20775	−	3.47107i	0.320107	−	0.154156i
$508$	−23.2435	+	11.1935i	−1.03126	+	0.496631i
$509$	−7.02327	+	30.7710i	−0.311301	+	1.36390i	0.541077	+	0.840973i	$0.318017\pi$
$509$	−7.02327	+	30.7710i	−0.311301	+	1.36390i	−0.852378	+	0.522926i	$0.824840\pi$
$510$	−6.45085			−0.285648
$511$	6.82082	−	29.8840i	0.301735	−	1.32199i
$512$	−11.6644	−	14.6267i	−0.515497	−	0.646413i
$513$	3.75039	+	16.4315i	0.165584	+	0.725470i
$514$	−3.18789	−	13.9670i	−0.140612	−	0.616060i
$515$	22.0603	−	27.6627i	0.972093	−	1.21897i
$516$	6.51947	−	3.13961i	0.287004	−	0.138214i
$517$	−8.71576	−	4.19729i	−0.383319	−	0.184597i
$518$	−4.05678	−	5.08705i	−0.178245	−	0.223512i
$519$	1.57610	−	1.97636i	0.0691830	−	0.0867527i
$520$	1.83297	+	0.882711i	0.0803810	+	0.0387094i
$521$	4.09017			0.179194			0.0895968	−	0.995978i	$-0.471442\pi$
$521$	4.09017			0.179194			0.0895968	+	0.995978i	$0.471442\pi$
$522$		0			0
$523$	−20.3820			−0.891241			−0.445621	−	0.895222i	$-0.647017\pi$
$523$	−20.3820			−0.891241			−0.445621	+	0.895222i	$0.647017\pi$
$524$	−20.8848	−	10.0576i	−0.912355	−	0.439367i
$525$	−8.49071	+	10.6470i	−0.370565	+	0.464674i
$526$	−6.43830	−	8.07338i	−0.280723	−	0.352016i
$527$	−39.8361	−	19.1841i	−1.73529	−	0.835671i
$528$	−1.42677	+	0.687095i	−0.0620921	+	0.0299020i
$529$	−13.3877	+	16.7876i	−0.582072	+	0.729895i
$530$	−1.06007	−	4.64449i	−0.0460467	−	0.201744i
$531$	3.54793	+	15.5445i	0.153967	+	0.674575i
$532$	10.9499	+	13.7308i	0.474739	+	0.595304i
$533$	−0.202456	+	0.887019i	−0.00876935	+	0.0384210i
$534$	1.79837			0.0778232
$535$	−5.80087	+	25.4153i	−0.250794	+	1.09880i
$536$	3.07808	−	1.48232i	0.132953	−	0.0640266i
$537$	8.90927	−	4.29048i	0.384463	−	0.185148i
$538$	0.825153	−	3.61523i	0.0355749	−	0.155864i
$539$	−2.76393			−0.119051
$540$	−4.81813	+	21.1096i	−0.207339	+	0.908413i
$541$	9.10092	+	11.4122i	0.391279	+	0.490649i	0.937985	−	0.346676i	$-0.112690\pi$
$541$	9.10092	+	11.4122i	0.391279	+	0.490649i	−0.546706	+	0.837325i	$0.684118\pi$
$542$	−1.40006	−	6.13405i	−0.0601376	−	0.263480i
$543$	−0.817489	−	3.58165i	−0.0350818	−	0.153703i
$544$	−15.3491	+	19.2472i	−0.658087	+	0.825215i
$545$	49.9403	−	24.0500i	2.13921	−	1.03019i
$546$	0.181659	+	0.0874823i	0.00777428	+	0.00374390i
$547$	4.60258	+	5.77145i	0.196792	+	0.246770i	0.870430	−	0.492292i	$-0.163841\pi$
$547$	4.60258	+	5.77145i	0.196792	+	0.246770i	−0.673638	+	0.739061i	$0.735269\pi$
$548$	7.20898	−	9.03977i	0.307952	−	0.386160i
$549$	1.45780	+	0.702039i	0.0622173	+	0.0299623i
$550$	−8.41641			−0.358877
$551$		0			0
$552$	−1.70820			−0.0727060
$553$	12.2694	+	5.90864i	0.521749	+	0.251261i
$554$	8.23928	−	10.3317i	0.350054	−	0.438953i
$555$	−6.99230	−	8.76807i	−0.296807	−	0.372184i
$556$	1.88318	+	0.906891i	0.0798645	+	0.0384607i
$557$	4.96126	−	2.38921i	0.210215	−	0.101234i	−0.325814	−	0.945434i	$-0.605638\pi$
$557$	4.96126	−	2.38921i	0.210215	−	0.101234i	0.536029	+	0.844200i	$0.319924\pi$
$558$	10.1792	−	12.7644i	0.430922	−	0.540359i
$559$	0.380111	+	1.66538i	0.0160770	+	0.0704379i
$560$	3.55560	+	15.5781i	0.150251	+	0.658295i
$561$	2.33350	+	2.92612i	0.0985205	+	0.123541i
$562$	3.18022	−	13.9335i	0.134150	−	0.587748i
$563$	−28.3951			−1.19671			−0.598356	−	0.801230i	$-0.704179\pi$
$563$	−28.3951			−1.19671			−0.598356	+	0.801230i	$0.704179\pi$
$564$	1.55765	−	6.82450i	0.0655888	−	0.287363i
$565$	27.5859	−	13.2847i	1.16055	−	0.558890i
$566$	−2.91560	+	1.40408i	−0.122552	+	0.0590178i
$567$	2.84024	−	12.4439i	0.119279	−	0.522595i
$568$	23.4164			0.982531
$569$	−0.432641	+	1.89552i	−0.0181373	+	0.0794645i	−0.983187	−	0.182604i	$-0.941547\pi$
$569$	−0.432641	+	1.89552i	−0.0181373	+	0.0794645i	0.965049	+	0.262068i	$0.0844046\pi$
$570$	−4.45539	−	5.58689i	−0.186616	−	0.234009i
$571$	7.67844	+	33.6414i	0.321333	+	1.40785i	0.835184	+	0.549971i	$0.185361\pi$
$571$	7.67844	+	33.6414i	0.321333	+	1.40785i	−0.513851	+	0.857879i	$0.671782\pi$
$572$	−0.117461	−	0.514629i	−0.00491128	−	0.0215177i
$573$	−6.56402	+	8.23102i	−0.274216	+	0.343856i
$574$	4.79877	−	2.31097i	0.200297	−	0.0964579i
$575$	10.9741	+	5.28485i	0.457652	+	0.220394i
$576$	0.385338	+	0.483198i	0.0160557	+	0.0201333i
$577$	1.72328	−	2.16093i	0.0717412	−	0.0899607i	−0.744666	−	0.667437i	$-0.767391\pi$
$577$	1.72328	−	2.16093i	0.0717412	−	0.0899607i	0.816407	+	0.577477i	$0.195963\pi$
$578$	1.22593	+	0.590377i	0.0509920	+	0.0245564i
$579$	−7.70820			−0.320342
$580$		0			0
$581$	22.2361			0.922508
$582$	−1.22593	−	0.590377i	−0.0508164	−	0.0244719i
$583$	−1.72328	+	2.16093i	−0.0713711	+	0.0894965i
$584$	19.1115	+	23.9651i	0.790840	+	0.991682i
$585$	−2.14608	−	1.03350i	−0.0887294	−	0.0427298i
$586$	−4.74857	+	2.28679i	−0.196161	+	0.0944664i
$587$	29.0659	−	36.4474i	1.19968	−	1.50435i	0.386542	−	0.922272i	$-0.373669\pi$
$587$	29.0659	−	36.4474i	1.19968	−	1.50435i	0.813135	−	0.582075i	$-0.197759\pi$
$588$	−0.445042	−	1.94986i	−0.0183532	−	0.0804107i
$589$	−10.8988	−	47.7507i	−0.449077	−	1.96753i
$590$	−9.04470	−	11.3417i	−0.372365	−	0.466930i
$591$	0.865282	−	3.79105i	0.0355930	−	0.155943i
$592$	−8.72949			−0.358780
$593$	3.21269	−	14.0757i	0.131929	−	0.578020i	−0.865141	−	0.501529i	$-0.832771\pi$
$593$	3.21269	−	14.0757i	0.131929	−	0.578020i	0.997070	−	0.0764913i	$-0.0243717\pi$
$594$	−2.67188	+	1.28671i	−0.109628	+	0.0527942i
$595$	34.0241	−	16.3852i	1.39485	−	0.671726i
$596$	3.46294	−	15.1721i	0.141848	−	0.621475i
$597$	−3.61803			−0.148076
$598$	0.0401294	−	0.175818i	0.00164101	−	0.00718975i
$599$	−8.14832	−	10.2177i	−0.332931	−	0.417482i	0.586985	−	0.809598i	$-0.300315\pi$
$599$	−8.14832	−	10.2177i	−0.332931	−	0.417482i	−0.919916	+	0.392115i	$0.871743\pi$
$600$	−3.03030	−	13.2766i	−0.123711	−	0.542015i
$601$	6.48850	+	28.4280i	0.264671	+	1.15960i	0.916119	+	0.400907i	$0.131305\pi$
$601$	6.48850	+	28.4280i	0.264671	+	1.15960i	−0.651447	+	0.758694i	$0.725838\pi$
$602$	6.23490	−	7.81831i	0.254115	−	0.318651i
$603$	−3.60388	+	1.73553i	−0.146761	+	0.0706764i
$604$	3.89781	+	1.87708i	0.158599	+	0.0763775i
$605$	−21.8436	−	27.3910i	−0.888069	−	1.11360i
$606$	−0.147186	+	0.184565i	−0.00597902	+	0.00749746i
$607$	9.89148	+	4.76349i	0.401483	+	0.193344i	0.623718	−	0.781649i	$-0.285621\pi$
$607$	9.89148	+	4.76349i	0.401483	+	0.193344i	−0.222236	+	0.974993i	$0.571335\pi$
$608$	−27.2705			−1.10597
$609$		0			0
$610$	−1.47214			−0.0596050
$611$	1.48883	+	0.716982i	0.0602316	+	0.0290060i
$612$	11.5734	−	14.5126i	0.467827	−	0.586637i
$613$	17.1715	+	21.5324i	0.693552	+	0.869687i	0.996523	−	0.0833128i	$-0.0265501\pi$
$613$	17.1715	+	21.5324i	0.693552	+	0.869687i	−0.302971	+	0.953000i	$0.597979\pi$
$614$	10.6802	+	5.14330i	0.431017	+	0.207567i
$615$	8.27120	−	3.98320i	0.333527	−	0.160618i
$616$	−4.30821	+	5.40232i	−0.173583	+	0.217666i
$617$	−3.15542	−	13.8248i	−0.127033	−	0.556566i	−0.997884	−	0.0650196i	$-0.979289\pi$
$617$	−3.15542	−	13.8248i	−0.127033	−	0.556566i	0.870851	−	0.491546i	$-0.163568\pi$
$618$	0.780287	+	3.41866i	0.0313877	+	0.137519i
$619$	−4.39917	−	5.51639i	−0.176818	−	0.221722i	0.685523	−	0.728051i	$-0.259574\pi$
$619$	−4.39917	−	5.51639i	−0.176818	−	0.221722i	−0.862341	+	0.506329i	$0.831002\pi$
$620$	14.0017	−	61.3454i	0.562321	−	2.46369i
$621$	4.29180			0.172224
$622$	−0.287452	+	1.25941i	−0.0115258	+	0.0504977i
$623$	−9.48528	+	4.56787i	−0.380020	+	0.183008i
$624$	0.243721	−	0.117370i	0.00975665	−	0.00469855i
$625$	−5.08078	+	22.2603i	−0.203231	+	0.890414i
$626$	7.97871			0.318894
$627$	−0.922549	+	4.04195i	−0.0368431	+	0.161420i
$628$	14.6909	+	18.4218i	0.586229	+	0.735108i
$629$	4.59087	+	20.1139i	0.183050	+	0.801995i
$630$	3.10289	+	13.5947i	0.123622	+	0.541624i
$631$	−17.5916	+	22.0592i	−0.700312	+	0.878163i	−0.997047	−	0.0767968i	$-0.975531\pi$
$631$	−17.5916	+	22.0592i	−0.700312	+	0.878163i	0.296735	+	0.954960i	$0.404102\pi$
$632$	−12.2694	+	5.90864i	−0.488052	+	0.235033i
$633$	−6.48844	−	3.12467i	−0.257892	−	0.124194i
$634$	10.6770	+	13.3886i	0.424039	+	0.531728i
$635$	−38.3140	+	48.0442i	−1.52044	+	1.90658i
$636$	−1.80194	−	0.867767i	−0.0714515	−	0.0344092i
$637$	0.472136			0.0187067
$638$		0			0
$639$	−27.4164			−1.08458
$640$	−39.5230	−	19.0333i	−1.56229	−	0.752357i
$641$	−6.89313	+	8.64372i	−0.272262	+	0.341406i	−0.899100	−	0.437744i	$-0.855778\pi$
$641$	−6.89313	+	8.64372i	−0.272262	+	0.341406i	0.626837	+	0.779150i	$0.284349\pi$
$642$	−1.61084	−	2.01993i	−0.0635749	−	0.0797204i
$643$	33.7110	+	16.2344i	1.32943	+	0.640221i	0.957606	−	0.288081i	$-0.0930173\pi$
$643$	33.7110	+	16.2344i	1.32943	+	0.640221i	0.371827	+	0.928302i	$0.378732\pi$
$644$	4.02926	−	1.94039i	0.158775	−	0.0764620i
$645$	10.7465	−	13.4757i	0.423144	−	0.530605i
$646$	2.92524	+	12.8163i	0.115092	+	0.504251i
$647$	6.79309	+	29.7625i	0.267064	+	1.17008i	0.913411	+	0.407039i	$0.133439\pi$
$647$	6.79309	+	29.7625i	0.267064	+	1.17008i	−0.646347	+	0.763044i	$0.723704\pi$
$648$	7.95818	+	9.97924i	0.312627	+	0.392022i
$649$	−1.87283	+	8.20539i	−0.0735149	+	0.322090i
$650$	1.43769			0.0563910
$651$	3.10289	−	13.5947i	0.121612	−	0.532817i
$652$	8.79700	−	4.23641i	0.344517	−	0.165911i
$653$	43.2584	−	20.8321i	1.69283	−	0.815224i	0.697729	−	0.716362i	$-0.254194\pi$
$653$	43.2584	−	20.8321i	1.69283	−	0.815224i	0.995101	−	0.0988626i	$-0.0315204\pi$
$654$	−1.22240	+	5.35569i	−0.0477997	+	0.209424i
$655$	−55.2148			−2.15742
$656$	1.59011	−	6.96674i	0.0620834	−	0.272005i
$657$	−22.3761	−	28.0588i	−0.872976	−	1.09468i
$658$	−2.15261	−	9.43122i	−0.0839177	−	0.367667i
$659$	−1.57005	−	6.87883i	−0.0611604	−	0.267961i	0.935098	−	0.354390i	$-0.115312\pi$
$659$	−1.57005	−	6.87883i	−0.0611604	−	0.267961i	−0.996258	+	0.0864291i	$0.972454\pi$
$660$	−3.32086	+	4.16422i	−0.129264	+	0.162092i
$661$	33.7420	−	16.2493i	1.31241	−	0.632025i	0.358900	−	0.933376i	$-0.383152\pi$
$661$	33.7420	−	16.2493i	1.31241	−	0.632025i	0.953513	+	0.301351i	$0.0974375\pi$
$662$	−11.7938	−	5.67961i	−0.458380	−	0.220744i
$663$	−0.398610	−	0.499841i	−0.0154807	−	0.0194122i
$664$	−13.8640	+	17.3849i	−0.538026	+	0.674663i
$665$	37.6901	+	18.1506i	1.46156	+	0.703849i
$666$	−7.61803			−0.295193
$667$		0			0
$668$	−17.0344			−0.659082
$669$	−1.48883	−	0.716982i	−0.0575615	−	0.0277201i
$670$	2.26908	−	2.84534i	0.0876622	−	0.109925i
$671$	0.532524	+	0.667764i	0.0205579	+	0.0257787i
$672$	−6.99506	−	3.36864i	−0.269840	−	0.129948i
$673$	5.83119	−	2.80815i	0.224776	−	0.108246i	−0.318107	−	0.948055i	$-0.603047\pi$
$673$	5.83119	−	2.80815i	0.224776	−	0.108246i	0.542883	+	0.839808i	$0.317333\pi$
$674$	−13.1280	+	16.4620i	−0.505673	+	0.634094i
$675$	7.61351	+	33.3569i	0.293044	+	1.28391i
$676$	−4.66054	−	20.4192i	−0.179251	−	0.785352i
$677$	25.4588	+	31.9244i	0.978463	+	1.22695i	0.973903	+	0.226964i	$0.0728800\pi$
$677$	25.4588	+	31.9244i	0.978463	+	1.22695i	0.00455972	+	0.999990i	$0.498549\pi$
$678$	−0.675227	+	2.95836i	−0.0259319	+	0.113615i
$679$	7.96556			0.305690
$680$	−8.40327	+	36.8171i	−0.322251	+	1.41187i
$681$	11.6314	−	5.60137i	0.445714	−	0.214645i
$682$	7.76458	−	3.73922i	0.297321	−	0.143182i
$683$	−4.64047	+	20.3312i	−0.177563	+	0.777954i	0.805188	+	0.593019i	$0.202064\pi$
$683$	−4.64047	+	20.3312i	−0.177563	+	0.777954i	−0.982751	+	0.184934i	$0.940793\pi$
$684$	20.5623			0.786219
$685$	6.12845	−	26.8505i	0.234156	−	1.02591i
$686$	−7.75478	−	9.72418i	−0.296079	−	0.371271i
$687$	0.315180	+	1.38090i	0.0120249	+	0.0526845i
$688$	−2.98543	−	13.0800i	−0.113819	−	0.498671i
$689$	0.294372	−	0.369131i	0.0112147	−	0.0140628i
$690$	−1.63946	+	0.789521i	−0.0624131	+	0.0300565i
$691$	−10.6610	−	5.13407i	−0.405563	−	0.195309i	0.219970	−	0.975507i	$-0.429404\pi$
$691$	−10.6610	−	5.13407i	−0.405563	−	0.195309i	−0.625533	+	0.780198i	$0.715118\pi$
$692$	−4.12628	−	5.17419i	−0.156858	−	0.196693i
$693$	5.04414	−	6.32515i	0.191611	−	0.240273i
$694$	−17.8879	−	8.61437i	−0.679016	−	0.326997i
$695$	4.97871			0.188853
$696$		0			0
$697$	−16.8885			−0.639699
$698$	2.52125	+	1.21417i	0.0954306	+	0.0459570i
$699$	5.87103	−	7.36204i	0.222063	−	0.278458i
$700$	22.2290	+	27.8742i	0.840176	+	1.05355i
$701$	18.9706	+	9.13574i	0.716508	+	0.345052i	0.756362	−	0.654153i	$-0.226975\pi$
$701$	18.9706	+	9.13574i	0.716508	+	0.345052i	−0.0398539	+	0.999206i	$0.512689\pi$
$702$	0.456411	−	0.219796i	0.0172261	−	0.00829566i
$703$	−14.2493	+	17.8681i	−0.537423	+	0.673907i
$704$	0.0725948	+	0.318058i	0.00273602	+	0.0119873i
$705$	−3.71026	−	16.2557i	−0.139737	−	0.612226i
$706$	7.36944	+	9.24098i	0.277352	+	0.347789i
$707$	0.307516	−	1.34732i	0.0115653	−	0.0506711i
$708$	−6.09017			−0.228883
$709$	9.23608	−	40.4659i	0.346868	−	1.51973i	−0.437377	−	0.899278i	$-0.644092\pi$
$709$	9.23608	−	40.4659i	0.346868	−	1.51973i	0.784245	−	0.620451i	$-0.213051\pi$
$710$	22.4740	−	10.8229i	0.843435	−	0.406177i
$711$	14.3653	−	6.91796i	0.538741	−	0.259444i
$712$	2.34267	−	10.2639i	0.0877953	−	0.384656i
$713$	−12.4721			−0.467085
$714$	−0.832817	+	3.64881i	−0.0311674	+	0.136553i
$715$	−0.783948	−	0.983039i	−0.0293180	−	0.0367636i
$716$	−5.76074	−	25.2395i	−0.215289	−	0.943243i
$717$	3.81532	+	16.7160i	0.142486	+	0.624271i
$718$	−9.15714	+	11.4827i	−0.341742	+	0.428530i
$719$	−7.66416	+	3.69087i	−0.285825	+	0.137646i	−0.571303	−	0.820739i	$-0.693562\pi$
$719$	−7.66416	+	3.69087i	−0.285825	+	0.137646i	0.285478	+	0.958385i	$0.407848\pi$
$720$	16.8555	+	8.11719i	0.628168	+	0.302510i
$721$	−12.7989	−	16.0493i	−0.476656	−	0.597708i
$722$	−1.75803	+	2.20450i	−0.0654271	+	0.0820430i
$723$	2.59064	+	1.24758i	0.0963468	+	0.0463982i
$724$	−9.61803			−0.357451
$725$		0			0
$726$	3.47214			0.128863
$727$	25.2773	+	12.1729i	0.937485	+	0.451469i	0.839281	−	0.543698i	$-0.182976\pi$
$727$	25.2773	+	12.1729i	0.937485	+	0.451469i	0.0982034	+	0.995166i	$0.468690\pi$
$728$	0.735930	−	0.922827i	0.0272754	−	0.0342022i
$729$	−5.30376	−	6.65071i	−0.196436	−	0.246323i
$730$	29.4189	+	14.1674i	1.08884	+	0.524358i
$731$	−28.5681	+	13.7577i	−1.05663	+	0.508846i
$732$	−0.385338	+	0.483198i	−0.0142425	+	0.0178595i
$733$	3.29768	+	14.4481i	0.121803	+	0.533653i	0.998605	+	0.0528016i	$0.0168151\pi$
$733$	3.29768	+	14.4481i	0.121803	+	0.533653i	−0.876802	+	0.480851i	$0.840328\pi$
$734$	−3.75039	−	16.4315i	−0.138429	−	0.606499i
$735$	−2.97026	−	3.72459i	−0.109560	−	0.137384i
$736$	−1.54525	+	6.77016i	−0.0569585	+	0.249552i
$737$	−2.11146			−0.0777765
$738$	1.38766	−	6.07972i	0.0510803	−	0.223797i
$739$	−45.1105	+	21.7241i	−1.65942	+	0.799133i	−0.660588	+	0.750749i	$0.729693\pi$
$739$	−45.1105	+	21.7241i	−1.65942	+	0.799133i	−0.998829	+	0.0483844i	$0.984593\pi$
$740$	−26.4531	+	12.7391i	−0.972434	+	0.468299i
$741$	0.157590	−	0.690448i	0.00578922	−	0.0253642i
$742$	−2.76393			−0.101467
$743$	7.84076	−	34.3526i	0.287650	−	1.26028i	−0.600091	−	0.799932i	$-0.704869\pi$
$743$	7.84076	−	34.3526i	0.287650	−	1.26028i	0.887741	−	0.460344i	$-0.152274\pi$
$744$	8.69411	+	10.9021i	0.318742	+	0.399689i
$745$	−8.24860	−	36.1395i	−0.302205	−	1.32405i
$746$	2.83551	+	12.4232i	0.103815	+	0.454844i
$747$	16.2322	−	20.3545i	0.593905	−	0.744734i
$748$	8.82803	−	4.25136i	0.322785	−	0.155445i
$749$	13.6268	+	6.56232i	0.497913	+	0.239782i
$750$	−4.45539	−	5.58689i	−0.162688	−	0.204004i
$751$	11.5519	−	14.4857i	0.421536	−	0.528590i	−0.525037	−	0.851080i	$-0.675948\pi$
$751$	11.5519	−	14.4857i	0.421536	−	0.528590i	0.946573	+	0.322490i	$0.104520\pi$
$752$	−11.6934	−	5.63125i	−0.426415	−	0.205351i
$753$	12.1459			0.442621
$754$		0			0
$755$	10.3050			0.375036
$756$	11.3182	+	5.45058i	0.411641	+	0.198236i
$757$	0.0132718	−	0.0166422i	0.000482370	−	0.000604873i	−0.781590	−	0.623792i	$-0.785591\pi$
$757$	0.0132718	−	0.0166422i	0.000482370	−	0.000604873i	0.782073	+	0.623187i	$0.214163\pi$
$758$	−9.36055	−	11.7378i	−0.339990	−	0.426335i
$759$	0.951178	+	0.458063i	0.0345256	+	0.0166266i
$760$	−37.6901	+	18.1506i	−1.36716	+	0.658391i
$761$	15.7130	−	19.7034i	0.569594	−	0.714249i	−0.410705	−	0.911768i	$-0.634717\pi$
$761$	15.7130	−	19.7034i	0.569594	−	0.714249i	0.980299	+	0.197520i	$0.0632887\pi$
$762$	−1.35519	−	5.93748i	−0.0490934	−	0.215092i
$763$	−7.15606	−	31.3528i	−0.259067	−	1.13505i
$764$	17.1848	+	21.5491i	0.621725	+	0.779618i
$765$	9.83871	−	43.1062i	0.355719	−	1.55851i
$766$	17.8328			0.644326
$767$	0.319917	−	1.40165i	0.0115515	−	0.0506106i
$768$	3.65408	−

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.d (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.556829 + 0.268155i) q^{2} +(0.385338 - 0.483198i) q^{3} +(-1.00883 - 1.26503i) q^{4} +(-3.47243 - 1.67223i) q^{5} +(0.344139 - 0.165729i) q^{6} +(-1.39417 + 1.74823i) q^{7} +(-0.497572 - 2.18001i) q^{8} +(0.582567 + 2.55239i) q^{9} +O(q^{10})\)	\(q+(0.556829 + 0.268155i) q^{2} +(0.385338 - 0.483198i) q^{3} +(-1.00883 - 1.26503i) q^{4} +(-3.47243 - 1.67223i) q^{5} +(0.344139 - 0.165729i) q^{6} +(-1.39417 + 1.74823i) q^{7} +(-0.497572 - 2.18001i) q^{8} +(0.582567 + 2.55239i) q^{9} +(-1.48513 - 1.86230i) q^{10} +(-0.307516 + 1.34732i) q^{11} -1.00000 q^{12} +(0.0525301 - 0.230149i) q^{13} +(-1.24511 + 0.599613i) q^{14} +(-2.14608 + 1.03350i) q^{15} +(-0.412577 + 1.80762i) q^{16} +4.38197 q^{17} +(-0.360046 + 1.57747i) q^{18} +(3.02648 + 3.79509i) q^{19} +(1.38766 + 6.07972i) q^{20} +(0.307516 + 1.34732i) q^{21} +(-0.532524 + 0.667764i) q^{22} +(1.11366 - 0.536310i) q^{23} +(-1.24511 - 0.599613i) q^{24} +(6.14393 + 7.70425i) q^{25} +(0.0909659 - 0.114068i) q^{26} +(3.12829 + 1.50650i) q^{27} +3.61803 q^{28} -1.47214 q^{30} +(-9.09093 - 4.37796i) q^{31} +(-3.50279 + 4.39236i) q^{32} +(0.532524 + 0.667764i) q^{33} +(2.44001 + 1.17505i) q^{34} +(7.76458 - 3.73922i) q^{35} +(2.64115 - 3.31189i) q^{36} +(1.04767 + 4.59016i) q^{37} +(0.667563 + 2.92478i) q^{38} +(-0.0909659 - 0.114068i) q^{39} +(-1.91769 + 8.40196i) q^{40} -3.85410 q^{41} +(-0.190056 + 0.832688i) q^{42} +(-6.51947 + 3.13961i) q^{43} +(2.01463 - 0.970194i) q^{44} +(2.24527 - 9.83719i) q^{45} +0.763932 q^{46} +(-1.55765 + 6.82450i) q^{47} +(0.714456 + 0.895899i) q^{48} +(0.445042 + 1.94986i) q^{49} +(1.35519 + 5.93748i) q^{50} +(1.68854 - 2.11736i) q^{51} +(-0.344139 + 0.165729i) q^{52} +(1.80194 + 0.867767i) q^{53} +(1.33795 + 1.67773i) q^{54} +(3.32086 - 4.16422i) q^{55} +(4.50484 + 2.16942i) q^{56} +3.00000 q^{57} +6.09017 q^{59} +(3.47243 + 1.67223i) q^{60} +(0.385338 - 0.483198i) q^{61} +(-3.88812 - 4.87555i) q^{62} +(-5.27436 - 2.54000i) q^{63} +(0.212690 - 0.102426i) q^{64} +(-0.567270 + 0.711334i) q^{65} +(0.117461 + 0.514629i) q^{66} +(0.339982 + 1.48956i) q^{67} +(-4.42065 - 5.54332i) q^{68} +(0.169991 - 0.744779i) q^{69} +5.32624 q^{70} +(-2.33027 + 10.2096i) q^{71} +(5.27436 - 2.54000i) q^{72} +(-12.3507 + 5.94777i) q^{73} +(-0.647498 + 2.83687i) q^{74} +6.09017 q^{75} +(1.74770 - 7.65718i) q^{76} +(-1.92669 - 2.41599i) q^{77} +(-0.0200647 - 0.0879092i) q^{78} +(-1.35519 - 5.93748i) q^{79} +(4.45539 - 5.58689i) q^{80} +(-5.14291 + 2.47670i) q^{81} +(-2.14608 - 1.03350i) q^{82} +(-6.20015 - 7.77474i) q^{83} +(1.39417 - 1.74823i) q^{84} +(-15.2161 - 7.32766i) q^{85} -4.47214 q^{86} +3.09017 q^{88} +(4.24195 + 2.04281i) q^{89} +(3.88812 - 4.87555i) q^{90} +(0.329118 + 0.412701i) q^{91} +(-1.80194 - 0.867767i) q^{92} +(-5.61850 + 2.70573i) q^{93} +(-2.69737 + 3.38239i) q^{94} +(-4.16297 - 18.2392i) q^{95} +(0.772623 + 3.38508i) q^{96} +(-2.22106 - 2.78512i) q^{97} +(-0.275051 + 1.20508i) q^{98} -3.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + q^{3} + q^{4} - q^{5} + 3 q^{6} + 3 q^{9}+O(q^{10}) \) 12 * q - q^2 + q^3 + q^4 - q^5 + 3 * q^6 + 3 * q^9	\( 12 q - q^{2} + q^{3} + q^{4} - q^{5} + 3 q^{6} + 3 q^{9} + 7 q^{10} - 5 q^{11} - 12 q^{12} - 4 q^{13} - 5 q^{14} - 7 q^{15} + 3 q^{16} + 66 q^{17} - q^{18} - 3 q^{19} + 8 q^{20} + 5 q^{21} - 5 q^{22} - 2 q^{23} - 5 q^{24} - 13 q^{25} - 7 q^{26} - 2 q^{27} + 30 q^{28} + 36 q^{30} - 9 q^{31} + 9 q^{32} + 5 q^{33} - 8 q^{34} + 15 q^{35} - 4 q^{36} - 4 q^{37} + 6 q^{38} + 7 q^{39} - 15 q^{40} - 6 q^{41} + 5 q^{42} - 10 q^{43} + 9 q^{45} + 36 q^{46} - 14 q^{47} - 9 q^{48} + 4 q^{49} + q^{50} + 8 q^{51} - 3 q^{52} + 4 q^{53} - 11 q^{54} + 5 q^{55} + 10 q^{56} + 36 q^{57} + 6 q^{59} + q^{60} + q^{61} + 8 q^{62} - 5 q^{63} - 4 q^{64} + 13 q^{65} + 10 q^{66} + 12 q^{67} + 3 q^{68} + 6 q^{69} - 30 q^{70} - 12 q^{71} + 5 q^{72} - 14 q^{73} - 17 q^{74} + 6 q^{75} + 9 q^{76} - 5 q^{77} + 11 q^{78} - q^{79} - 21 q^{80} + 2 q^{81} - 7 q^{82} + 2 q^{83} + 2 q^{85} - 30 q^{88} - 4 q^{89} - 8 q^{90} - 10 q^{91} - 4 q^{92} - 8 q^{93} - 7 q^{94} - 24 q^{95} - 2 q^{96} - 13 q^{97} + 2 q^{98} - 30 q^{99}+O(q^{100}) \) 12 * q - q^2 + q^3 + q^4 - q^5 + 3 * q^6 + 3 * q^9 + 7 * q^10 - 5 * q^11 - 12 * q^12 - 4 * q^13 - 5 * q^14 - 7 * q^15 + 3 * q^16 + 66 * q^17 - q^18 - 3 * q^19 + 8 * q^20 + 5 * q^21 - 5 * q^22 - 2 * q^23 - 5 * q^24 - 13 * q^25 - 7 * q^26 - 2 * q^27 + 30 * q^28 + 36 * q^30 - 9 * q^31 + 9 * q^32 + 5 * q^33 - 8 * q^34 + 15 * q^35 - 4 * q^36 - 4 * q^37 + 6 * q^38 + 7 * q^39 - 15 * q^40 - 6 * q^41 + 5 * q^42 - 10 * q^43 + 9 * q^45 + 36 * q^46 - 14 * q^47 - 9 * q^48 + 4 * q^49 + q^50 + 8 * q^51 - 3 * q^52 + 4 * q^53 - 11 * q^54 + 5 * q^55 + 10 * q^56 + 36 * q^57 + 6 * q^59 + q^60 + q^61 + 8 * q^62 - 5 * q^63 - 4 * q^64 + 13 * q^65 + 10 * q^66 + 12 * q^67 + 3 * q^68 + 6 * q^69 - 30 * q^70 - 12 * q^71 + 5 * q^72 - 14 * q^73 - 17 * q^74 + 6 * q^75 + 9 * q^76 - 5 * q^77 + 11 * q^78 - q^79 - 21 * q^80 + 2 * q^81 - 7 * q^82 + 2 * q^83 + 2 * q^85 - 30 * q^88 - 4 * q^89 - 8 * q^90 - 10 * q^91 - 4 * q^92 - 8 * q^93 - 7 * q^94 - 24 * q^95 - 2 * q^96 - 13 * q^97 + 2 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more