LMFDB - Embedded newform 841.2.d.i.190.1

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			190.1
Root			$-0.556829 - 0.268155i$ of defining polynomial
Character	$\chi$	$=$	841.190
Dual form			841.2.d.i.571.1

$q$-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	0.226530	−	0.974004i	$-0.427262\pi$
$2$	−0.556829	−	0.268155i	−0.393738	−	0.189614i	−0.620268	+	0.784390i	$0.712976\pi$
$3$	−0.385338	+	0.483198i	−0.222475	+	0.278975i	−0.880525	−	0.473999i	$-0.842810\pi$
$3$	−0.385338	+	0.483198i	−0.222475	+	0.278975i	0.658050	+	0.752974i	$0.271381\pi$
$4$	−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	−0.907175	−	0.420754i	$-0.861766\pi$
$11$	0.307516	−	1.34732i	0.0927197	−	0.406231i	0.999895	+	0.0145224i	$0.00462277\pi$
$12$	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	$-0.678331\pi$
$17$	−4.38197			−1.06278			−0.531391	+	0.847126i	$0.678331\pi$
$18$	0.360046	−	1.57747i	0.0848638	−	0.371812i
$19$	−3.02648	−	3.79509i	−0.694323	−	0.870653i	0.302262	−	0.953225i	$-0.402258\pi$
$19$	−3.02648	−	3.79509i	−0.694323	−	0.870653i	−0.996585	+	0.0825715i	$0.973687\pi$
$20$	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	$0.00382990\pi$
$31$	9.09093	+	4.37796i	1.63278	+	0.786305i	0.632851	+	0.774273i	$0.281884\pi$
$32$	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	$-0.944936\pi$
$37$	−1.04767	−	4.59016i	−0.172237	−	0.754618i	0.812838	−	0.582490i	$-0.197921\pi$
$38$	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	$-0.402695\pi$
$41$	3.85410			0.601910			0.300955	+	0.953638i	$0.402695\pi$
$42$	−0.190056	+	0.832688i	−0.0293262	+	0.128487i
$43$	6.51947	−	3.13961i	0.994210	−	0.478786i	0.135240	−	0.990813i	$-0.456819\pi$
$43$	6.51947	−	3.13961i	0.994210	−	0.478786i	0.858970	+	0.512026i	$0.171105\pi$
$44$	−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	$-0.758022\pi$
$47$	1.55765	−	6.82450i	0.227206	−	0.995455i	0.951906	−	0.306390i	$-0.0991213\pi$
$48$	−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	−0.805888	−	0.592068i	$-0.798312\pi$
$61$	−0.385338	+	0.483198i	−0.0493375	+	0.0618672i	0.756551	+	0.653935i	$0.226883\pi$
$62$	−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	0.463722	−	0.885981i	$-0.346514\pi$
$73$	12.3507	−	5.94777i	1.44554	−	0.696133i	0.981814	+	0.189847i	$0.0607992\pi$
$74$	−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	$0.0398786\pi$
$79$	1.35519	+	5.93748i	0.152471	+	0.668018i	−0.839692	+	0.543064i	$0.817264\pi$
$80$	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	0.195336	−	0.980736i	$-0.437420\pi$
$89$	−4.24195	−	2.04281i	−0.449645	−	0.216538i	−0.644981	+	0.764199i	$0.723135\pi$
$90$	−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	0.881697	−	0.471816i	$-0.156401\pi$
$97$	2.22106	+	2.78512i	0.225515	+	0.282786i	−0.656183	+	0.754602i	$0.727830\pi$
$98$	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	−0.405975	−	0.913884i	$-0.633068\pi$
$101$	0.556829	−	0.268155i	0.0554066	−	0.0266824i	0.461382	+	0.887202i	$0.347354\pi$
$102$	−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	−0.492220	−	0.870471i	$-0.663815\pi$
$113$	4.95317	−	6.21108i	0.465955	−	0.584289i	0.958175	+	0.286181i	$0.0923860\pi$
$114$	−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	$0.321566\pi$
$127$	−3.54793	+	15.5445i	−0.314828	+	1.37935i	−0.846494	+	0.532398i	$0.821291\pi$
$128$	−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	−0.902273	−	0.431165i	$-0.858103\pi$
$131$	−12.9075	+	6.21592i	−1.12773	+	0.543088i	−0.225460	+	0.974252i	$0.572388\pi$
$132$	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	$-0.972686\pi$
$137$	−1.59011	−	6.96674i	−0.135852	−	0.595208i	0.860468	−	0.509504i	$-0.170171\pi$
$138$	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	$-0.302623\pi$
$157$	14.5623			1.16220			0.581099	+	0.813833i	$0.302623\pi$
$158$	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	$-0.852628\pi$
$163$	1.34279	−	5.88315i	0.105175	−	0.460804i	0.999899	−	0.0141841i	$-0.00451508\pi$
$164$	−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	$-0.288637\pi$
$191$	17.0344			1.23257			0.616284	+	0.787524i	$0.288637\pi$
$192$	−0.0324654	+	0.142240i	−0.00234299	+	0.0102653i
$193$	7.77625	+	9.75111i	0.559747	+	0.701900i	0.978511	−	0.206195i	$-0.0661081\pi$
$193$	7.77625	+	9.75111i	0.559747	+	0.701900i	−0.418764	+	0.908095i	$0.637537\pi$
$194$	−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	$0.0599416\pi$
$211$	2.59292	+	11.3603i	0.178504	+	0.782077i	−0.803818	+	0.594876i	$0.797201\pi$
$212$	−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	−0.732374	−	0.680902i	$-0.761588\pi$
$229$	1.42891	−	1.79180i	0.0944251	−	0.118405i	0.826799	+	0.562497i	$0.190159\pi$
$230$	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	0.226581	−	0.973992i	$-0.427245\pi$
$251$	−12.2531	−	15.3649i	−0.773410	−	0.969825i	−0.999991	+	0.00416682i	$0.998674\pi$
$252$	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	0.836007	−	0.548719i	$-0.184884\pi$
$263$	15.0536	+	7.24942i	0.928243	+	0.447018i	0.0922361	+	0.995737i	$0.470599\pi$
$264$	−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	0.999182	−	0.0404396i	$-0.0128758\pi$
$269$	1.33513	+	5.84957i	0.0814040	+	0.356654i	−0.917778	+	0.397094i	$0.870019\pi$
$270$	−1.84036	−	8.06315i	−0.112001	−	0.490708i
$271$	6.34734	+	7.95931i	0.385573	+	0.483494i	0.936305	−	0.351189i	$-0.114223\pi$
$271$	6.34734	+	7.95931i	0.385573	+	0.483494i	−0.550731	+	0.834683i	$0.685651\pi$
$272$	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	−0.601874	−	0.798591i	$-0.705579\pi$
$293$	5.31704	−	6.66735i	0.310625	−	0.389511i	0.912498	+	0.409080i	$0.134150\pi$
$294$	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	$-0.684360\pi$
$307$	−19.1803			−1.09468			−0.547340	+	0.836910i	$0.684360\pi$
$308$	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	0.960028	−	0.279905i	$-0.0903031\pi$
$311$	−0.465107	−	2.03777i	−0.0263738	−	0.115551i	−0.986401	+	0.164354i	$0.947446\pi$
$312$	−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	−0.428538	−	0.903524i	$-0.640971\pi$
$317$	−24.9642	−	12.0221i	−1.40213	−	0.675231i	−0.973592	+	0.228293i	$0.926686\pi$
$318$	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	$-0.302236\pi$
$331$	21.1803			1.16418			0.582088	+	0.813126i	$0.302236\pi$
$332$	−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	$-0.550162\pi$
$337$	7.58104	−	33.2147i	0.412966	−	1.80932i	0.569903	−	0.821712i	$-0.306981\pi$
$338$	−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	$-0.712811\pi$
$359$	5.28797	−	23.1681i	0.279089	−	1.22277i	0.898949	−	0.438054i	$-0.144332\pi$
$360$	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	$0.0378134\pi$
$367$	17.0029	+	21.3209i	0.887543	+	1.11294i	−0.105409	+	0.994429i	$0.533615\pi$
$368$	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	0.901192	−	0.433419i	$-0.142693\pi$
$379$	21.8862	+	10.5398i	1.12422	+	0.541394i	0.223024	+	0.974813i	$0.428407\pi$
$380$	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	$-0.661118\pi$
$389$	−19.1246			−0.969656			−0.484828	+	0.874609i	$0.661118\pi$
$390$	−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	$-0.548636\pi$
$409$	17.0939	−	21.4350i	0.845237	−	1.05989i	0.997437	−	0.0715435i	$-0.0227925\pi$
$410$	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	0.397493	−	0.917605i	$-0.369880\pi$
$421$	27.9611	−	13.4653i	1.36274	−	0.656261i	0.965246	+	0.261345i	$0.0841659\pi$
$422$	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	0.195408	−	0.980722i	$-0.437397\pi$
$433$	−9.35383	−	4.50457i	−0.449516	−	0.216476i	−0.644924	+	0.764246i	$0.723111\pi$
$434$	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	0.984020	−	0.178060i	$-0.0569821\pi$
$443$	0.424977	+	1.86195i	0.0201913	+	0.0884638i	−0.963828	+	0.266524i	$0.914125\pi$
$444$	−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	0.213763	−	0.976886i	$-0.431428\pi$
$449$	23.5375	−	11.3350i	1.11080	−	0.534934i	0.897039	+	0.441952i	$0.145714\pi$
$450$	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	$0.576457\pi$
$461$	−24.3028	+	30.4748i	−1.13190	+	1.41935i	−0.894003	+	0.448061i	$0.852115\pi$
$462$	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	−0.970124	−	0.242611i	$-0.921996\pi$
$467$	−11.1881	+	14.0294i	−0.517722	+	0.649203i	0.452401	+	0.891814i	$0.350567\pi$
$468$	−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	−0.189365	−	0.981907i	$-0.560643\pi$
$479$	10.0731	−	4.85097i	0.460253	−	0.221646i	0.649618	+	0.760260i	$0.274929\pi$
$480$	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	0.715318	−	0.698799i	$-0.246282\pi$
$491$	13.6268	+	6.56232i	0.614969	+	0.296153i	−0.100349	+	0.994952i	$0.531996\pi$
$492$	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	0.939569	−	0.342358i	$-0.111226\pi$
$503$	8.89752	+	11.1571i	0.396721	+	0.497472i	−0.542849	+	0.839831i	$0.682654\pi$
$504$	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	0.546706	−	0.837325i	$-0.315882\pi$
$541$	−9.10092	−	11.4122i	−0.391279	−	0.490649i	−0.937985	+	0.346676i	$0.887310\pi$
$542$	−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	$-0.295821\pi$
$563$	28.3951			1.19671			0.598356	+	0.801230i	$0.295821\pi$
$564$	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	−0.965049	−	0.262068i	$-0.915595\pi$
$569$	0.432641	−	1.89552i	0.0181373	−	0.0794645i	0.983187	+	0.182604i	$0.0584526\pi$
$570$	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	−0.816407	−	0.577477i	$-0.804037\pi$
$577$	−1.72328	+	2.16093i	−0.0717412	+	0.0899607i	0.744666	+	0.667437i	$0.232609\pi$
$578$	−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	0.919916	−	0.392115i	$-0.128257\pi$
$599$	8.14832	+	10.2177i	0.332931	+	0.417482i	−0.586985	+	0.809598i	$0.699685\pi$
$600$	−3.03030	−	13.2766i	−0.123711	−	0.542015i
$601$	−6.48850	−	28.4280i	−0.264671	−	1.15960i	−0.916119	−	0.400907i	$-0.868695\pi$
$601$	−6.48850	−	28.4280i	−0.264671	−	1.15960i	0.651447	−	0.758694i	$-0.274162\pi$
$602$	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	0.222236	−	0.974993i	$-0.428665\pi$
$607$	−9.89148	−	4.76349i	−0.401483	−	0.193344i	−0.623718	+	0.781649i	$0.714379\pi$
$608$	−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	$0.0207110\pi$
$617$	3.15542	+	13.8248i	0.127033	+	0.556566i	−0.870851	+	0.491546i	$0.836432\pi$
$618$	0.780287	+	3.41866i	0.0313877	+	0.137519i
$619$	4.39917	+	5.51639i	0.176818	+	0.221722i	0.862341	−	0.506329i	$-0.168998\pi$
$619$	4.39917	+	5.51639i	0.176818	+	0.221722i	−0.685523	+	0.728051i	$0.740426\pi$
$620$	−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	−0.626837	−	0.779150i	$-0.715651\pi$
$641$	6.89313	−	8.64372i	0.272262	−	0.341406i	0.899100	+	0.437744i	$0.144222\pi$
$642$	−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	$0.745806\pi$
$653$	−43.2584	+	20.8321i	−1.69283	+	0.815224i	−0.995101	+	0.0988626i	$0.968480\pi$
$654$	−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	0.996258	−	0.0864291i	$-0.0275456\pi$
$659$	1.57005	+	6.87883i	0.0611604	+	0.267961i	−0.935098	+	0.354390i	$0.884688\pi$
$660$	−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	$-0.927120\pi$
$677$	−25.4588	−	31.9244i	−0.978463	−	1.22695i	−0.00455972	−	0.999990i	$-0.501451\pi$
$678$	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	−0.0982034	−	0.995166i	$-0.531310\pi$
$727$	−25.2773	−	12.1729i	−0.937485	−	0.451469i	−0.839281	+	0.543698i	$0.817024\pi$
$728$	−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	$-0.983185\pi$
$733$	−3.29768	−	14.4481i	−0.121803	−	0.533653i	0.876802	−	0.480851i	$-0.159672\pi$
$734$	−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	$-0.270307\pi$
$739$	45.1105	−	21.7241i	1.65942	−	0.799133i	0.998829	−	0.0483844i	$-0.0154072\pi$
$740$	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	$0.295131\pi$
$743$	−7.84076	+	34.3526i	−0.287650	+	1.26028i	−0.887741	+	0.460344i	$0.847726\pi$
$744$	−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	−0.946573	−	0.322490i	$-0.895480\pi$
$751$	−11.5519	+	14.4857i	−0.421536	+	0.528590i	0.525037	+	0.851080i	$0.324052\pi$
$752$	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	−0.782073	−	0.623187i	$-0.785837\pi$
$757$	−0.0132718	+	0.0166422i	−0.000482370	+	0.000604873i	0.781590	+	0.623792i	$0.214409\pi$
$758$	−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

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