LMFDB - Embedded newform 841.2.d.i.571.1

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			571.1
Root			$-0.556829 + 0.268155i$ of defining polynomial
Character	$\chi$	$=$	841.571
Dual form			841.2.d.i.190.1

$q$-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 $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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	$-0.712976\pi$
$2$	−0.556829	+	0.268155i	−0.393738	+	0.189614i	0.226530	+	0.974004i	$0.427262\pi$
$3$	−0.385338	−	0.483198i	−0.222475	−	0.278975i	0.658050	−	0.752974i	$-0.271381\pi$
$3$	−0.385338	−	0.483198i	−0.222475	−	0.278975i	−0.880525	+	0.473999i	$0.842810\pi$
$4$	−1.00883	+	1.26503i	−0.504414	+	0.632515i
$5$	−3.47243	+	1.67223i	−1.55292	+	0.747845i	−0.996542	−	0.0830872i	$-0.973522\pi$
$5$	−3.47243	+	1.67223i	−1.55292	+	0.747845i	−0.556374	+	0.830932i	$0.687808\pi$
$6$	0.344139	+	0.165729i	0.140494	+	0.0676585i
$7$	−1.39417	−	1.74823i	−0.526945	−	0.660768i	0.445122	−	0.895470i	$-0.353160\pi$
$7$	−1.39417	−	1.74823i	−0.526945	−	0.660768i	−0.972067	+	0.234702i	$0.924589\pi$
$8$	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	$-0.00462277\pi$
$11$	0.307516	+	1.34732i	0.0927197	+	0.406231i	−0.907175	+	0.420754i	$0.861766\pi$
$12$	1.00000			0.288675
$13$	0.0525301	+	0.230149i	0.0145692	+	0.0638319i	0.981690	−	0.190486i	$-0.0610063\pi$
$13$	0.0525301	+	0.230149i	0.0145692	+	0.0638319i	−0.967121	+	0.254318i	$0.918149\pi$
$14$	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	−0.996585	−	0.0825715i	$-0.973687\pi$
$19$	−3.02648	+	3.79509i	−0.694323	+	0.870653i	0.302262	+	0.953225i	$0.402258\pi$
$20$	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	0.546373	−	0.837542i	$-0.316008\pi$
$23$	1.11366	+	0.536310i	0.232214	+	0.111828i	−0.314159	+	0.949370i	$0.601722\pi$
$24$	−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	0.632851	−	0.774273i	$-0.281884\pi$
$31$	9.09093	−	4.37796i	1.63278	−	0.786305i	0.999928	−	0.0120317i	$-0.00382990\pi$
$32$	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	0.812838	+	0.582490i	$0.197921\pi$
$37$	−1.04767	+	4.59016i	−0.172237	+	0.754618i	−0.985075	+	0.172128i	$0.944936\pi$
$38$	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	0.858970	−	0.512026i	$-0.171105\pi$
$43$	6.51947	+	3.13961i	0.994210	+	0.478786i	0.135240	+	0.990813i	$0.456819\pi$
$44$	−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	0.951906	+	0.306390i	$0.0991213\pi$
$47$	1.55765	+	6.82450i	0.227206	+	0.995455i	−0.724700	+	0.689065i	$0.758022\pi$
$48$	−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	−0.306013	−	0.952027i	$-0.598995\pi$
$53$	1.80194	−	0.867767i	0.247515	−	0.119197i	0.553529	+	0.832830i	$0.313281\pi$
$54$	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	$-0.226883\pi$
$61$	−0.385338	−	0.483198i	−0.0493375	−	0.0618672i	−0.805888	+	0.592068i	$0.798312\pi$
$62$	−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	−0.949905	−	0.312539i	$-0.898821\pi$
$67$	0.339982	−	1.48956i	0.0415354	−	0.181978i	0.991440	+	0.130561i	$0.0416777\pi$
$68$	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	−0.902120	−	0.431484i	$-0.857990\pi$
$71$	−2.33027	−	10.2096i	−0.276552	−	1.21165i	0.625568	−	0.780169i	$-0.284867\pi$
$72$	−5.27436	−	2.54000i	−0.621590	−	0.299342i
$73$	12.3507	+	5.94777i	1.44554	+	0.696133i	0.981814	−	0.189847i	$-0.0607992\pi$
$73$	12.3507	+	5.94777i	1.44554	+	0.696133i	0.463722	+	0.885981i	$0.346514\pi$
$74$	−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	−0.839692	−	0.543064i	$-0.817264\pi$
$79$	1.35519	−	5.93748i	0.152471	−	0.668018i	0.992162	−	0.124955i	$-0.0398786\pi$
$80$	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	−0.995405	−	0.0957523i	$-0.969474\pi$
$83$	−6.20015	+	7.77474i	−0.680555	+	0.853389i	0.314850	+	0.949141i	$0.398046\pi$
$84$	−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	$-0.723135\pi$
$89$	−4.24195	+	2.04281i	−0.449645	+	0.216538i	0.195336	+	0.980736i	$0.437420\pi$
$90$	−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	$-0.727830\pi$
$97$	2.22106	−	2.78512i	0.225515	−	0.282786i	0.881697	+	0.471816i	$0.156401\pi$
$98$	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	$-0.347354\pi$
$101$	0.556829	+	0.268155i	0.0554066	+	0.0266824i	−0.405975	+	0.913884i	$0.633068\pi$
$102$	−1.50801	−	0.726218i	−0.149315	−	0.0719063i
$103$	−2.04282	−	8.95017i	−0.201285	−	0.881886i	−0.970156	−	0.242482i	$-0.922038\pi$
$103$	−2.04282	−	8.95017i	−0.201285	−	0.881886i	0.768871	−	0.639404i	$-0.220819\pi$
$104$	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	0.848596	+	0.529042i	$0.177448\pi$
$107$	−1.50512	+	6.59435i	−0.145505	+	0.637500i	−0.994101	+	0.108458i	$0.965409\pi$
$108$	1.25013	−	5.47718i	0.120294	−	0.527042i
$109$	−8.96701	−	11.2443i	−0.858884	−	1.07701i	−0.996253	−	0.0864862i	$-0.972436\pi$
$109$	−8.96701	−	11.2443i	−0.858884	−	1.07701i	0.137369	−	0.990520i	$-0.456135\pi$
$110$	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	$-0.0923860\pi$
$113$	4.95317	+	6.21108i	0.465955	+	0.584289i	−0.492220	+	0.870471i	$0.663815\pi$
$114$	−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	−0.846494	−	0.532398i	$-0.821291\pi$
$127$	−3.54793	−	15.5445i	−0.314828	−	1.37935i	0.531666	−	0.846954i	$-0.321566\pi$
$128$	−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	$-0.572388\pi$
$131$	−12.9075	−	6.21592i	−1.12773	−	0.543088i	−0.902273	+	0.431165i	$0.858103\pi$
$132$	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	0.860468	+	0.509504i	$0.170171\pi$
$137$	−1.59011	+	6.96674i	−0.135852	+	0.595208i	−0.996321	+	0.0857042i	$0.972686\pi$
$138$	0.294372	+	0.369131i	0.0250586	+	0.0314225i
$139$	−1.16387	−	0.560489i	−0.0987180	−	0.0475401i	0.383873	−	0.923386i	$-0.374590\pi$
$139$	−1.16387	−	0.560489i	−0.0987180	−	0.0475401i	−0.482591	+	0.875846i	$0.660304\pi$
$140$	−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	−0.472963	−	0.881082i	$-0.656816\pi$
$149$	5.99675	−	7.51968i	0.491273	−	0.616036i	0.964236	+	0.265046i	$0.0853871\pi$
$150$	3.39119	−	1.63311i	0.276889	−	0.133343i
$151$	−2.40898	−	1.16010i	−0.196040	−	0.0944078i	0.333288	−	0.942825i	$-0.391842\pi$
$151$	−2.40898	−	1.16010i	−0.196040	−	0.0944078i	−0.529328	+	0.848417i	$0.677556\pi$
$152$	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	0.999899	+	0.0141841i	$0.00451508\pi$
$163$	1.34279	+	5.88315i	0.105175	+	0.460804i	−0.894724	+	0.446619i	$0.852628\pi$
$164$	−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	0.967999	−	0.250952i	$-0.0807438\pi$
$167$	6.56402	+	8.23102i	0.507939	+	0.636935i	−0.460061	+	0.887888i	$0.652172\pi$
$168$	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	0.190960	−	0.981598i	$-0.438840\pi$
$179$	14.4155	−	6.94214i	1.07747	−	0.518880i	0.886506	+	0.462718i	$0.153126\pi$
$180$	−14.7094	−	7.08369i	−1.09638	−	0.527987i
$181$	3.70619	+	4.64742i	0.275479	+	0.345440i	0.900254	−	0.435365i	$-0.143381\pi$
$181$	3.70619	+	4.64742i	0.275479	+	0.345440i	−0.624775	+	0.780805i	$0.714809\pi$
$182$	−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	−0.418764	−	0.908095i	$-0.637537\pi$
$193$	7.77625	−	9.75111i	0.559747	−	0.701900i	0.978511	+	0.206195i	$0.0661081\pi$
$194$	−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	0.624784	−	0.780797i	$-0.285187\pi$
$197$	5.66871	+	2.72991i	0.403879	+	0.194498i	−0.220905	+	0.975295i	$0.570901\pi$
$198$	−2.01463	+	0.970194i	−0.143173	+	0.0689487i
$199$	−3.64997	+	4.57692i	−0.258740	+	0.324449i	−0.894186	−	0.447696i	$-0.852245\pi$
$199$	−3.64997	+	4.57692i	−0.258740	+	0.324449i	0.635446	+	0.772145i	$0.280816\pi$
$200$	−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	−0.803818	−	0.594876i	$-0.797201\pi$
$211$	2.59292	−	11.3603i	0.178504	−	0.782077i	0.982322	−	0.187201i	$-0.0599416\pi$
$212$	−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	−0.990934	−	0.134348i	$-0.957106\pi$
$223$	−0.594968	+	2.60673i	−0.0398420	+	0.174559i	0.951092	+	0.308907i	$0.0999632\pi$
$224$	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	0.311846	−	0.950133i	$-0.399053\pi$
$227$	18.8199	−	9.06320i	1.24912	−	0.601546i	0.937276	+	0.348587i	$0.113338\pi$
$228$	−3.02648	+	3.79509i	−0.200434	+	0.251336i
$229$	1.42891	+	1.79180i	0.0944251	+	0.118405i	0.826799	−	0.562497i	$-0.190159\pi$
$229$	1.42891	+	1.79180i	0.0944251	+	0.118405i	−0.732374	+	0.680902i	$0.761588\pi$
$230$	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	−0.904612	−	0.426236i	$-0.859839\pi$
$239$	−17.2973	−	21.6901i	−1.11887	−	1.40301i	−0.214255	−	0.976778i	$-0.568732\pi$
$240$	0.982743	−	4.30568i	0.0634358	−	0.277930i
$241$	1.03527	−	4.53583i	0.0666878	−	0.292178i	−0.930576	−	0.366098i	$-0.880694\pi$
$241$	1.03527	−	4.53583i	0.0666878	−	0.292178i	0.997264	+	0.0739193i	$0.0235507\pi$
$242$	−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	$-0.998674\pi$
$251$	−12.2531	+	15.3649i	−0.773410	+	0.969825i	0.226581	+	0.973992i	$0.427245\pi$
$252$	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	0.0893797	+	0.995998i	$0.471512\pi$
$257$	−14.4527	+	18.1231i	−0.901535	+	1.13049i	−0.990915	+	0.134492i	$0.957060\pi$
$258$	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	$-0.470599\pi$
$263$	15.0536	−	7.24942i	0.928243	−	0.447018i	0.836007	+	0.548719i	$0.184884\pi$
$264$	−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	$-0.870019\pi$
$269$	1.33513	−	5.84957i	0.0814040	−	0.356654i	0.999182	+	0.0404396i	$0.0128758\pi$
$270$	−1.84036	+	8.06315i	−0.112001	+	0.490708i
$271$	6.34734	−	7.95931i	0.385573	−	0.483494i	−0.550731	−	0.834683i	$-0.685651\pi$
$271$	6.34734	−	7.95931i	0.385573	−	0.483494i	0.936305	+	0.351189i	$0.114223\pi$
$272$	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	0.890127	+	0.455713i	$0.150616\pi$
$277$	4.75794	+	20.8459i	0.285877	+	1.25251i	−0.604250	+	0.796795i	$0.706527\pi$
$278$	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	0.552411	+	0.833572i	$0.313708\pi$
$281$	−5.14571	+	22.5448i	−0.306967	+	1.34491i	−0.859379	+	0.511340i	$0.829149\pi$
$282$	−0.594968	+	2.60673i	−0.0354298	+	0.155228i
$283$	−3.26463	−	4.09372i	−0.194062	−	0.243347i	0.675274	−	0.737567i	$-0.264025\pi$
$283$	−3.26463	−	4.09372i	−0.194062	−	0.243347i	−0.869337	+	0.494220i	$0.835454\pi$
$284$	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	$-0.134150\pi$
$293$	5.31704	+	6.66735i	0.310625	+	0.389511i	−0.601874	+	0.798591i	$0.705579\pi$
$294$	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	−0.986401	−	0.164354i	$-0.947446\pi$
$311$	−0.465107	+	2.03777i	−0.0263738	+	0.115551i	0.960028	+	0.279905i	$0.0903031\pi$
$312$	−0.203406	−	0.255063i	−0.0115156	−	0.0144401i
$313$	11.6314	+	5.60137i	0.657443	+	0.316608i	0.732695	−	0.680557i	$-0.238262\pi$
$313$	11.6314	+	5.60137i	0.657443	+	0.316608i	−0.0752524	+	0.997165i	$0.523976\pi$
$314$	−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	$-0.926686\pi$
$317$	−24.9642	+	12.0221i	−1.40213	+	0.675231i	−0.428538	+	0.903524i	$0.640971\pi$
$318$	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	0.569903	+	0.821712i	$0.306981\pi$
$337$	7.58104	+	33.2147i	0.412966	+	1.80932i	−0.156938	+	0.987609i	$0.550162\pi$
$338$	−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	0.0850629	−	0.996376i	$-0.472891\pi$
$353$	17.2307	−	8.29786i	0.917097	−	0.441650i	0.832034	+	0.554725i	$0.187177\pi$
$354$	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	0.898949	+	0.438054i	$0.144332\pi$
$359$	5.28797	+	23.1681i	0.279089	+	1.22277i	−0.619860	+	0.784712i	$0.712811\pi$
$360$	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	−0.105409	−	0.994429i	$-0.533615\pi$
$367$	17.0029	−	21.3209i	0.887543	−	1.11294i	0.992952	−	0.118515i	$-0.0378134\pi$
$368$	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	−0.328328	−	0.944564i	$-0.606485\pi$
$373$	12.8551	−	16.1198i	0.665614	−	0.834653i	0.993941	+	0.109911i	$0.0350565\pi$
$374$	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	$-0.428407\pi$
$379$	21.8862	−	10.5398i	1.12422	−	0.541394i	0.901192	+	0.433419i	$0.142693\pi$
$380$	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	0.957353	−	0.288920i	$-0.0932961\pi$
$383$	25.9966	+	12.5193i	1.32837	+	0.639708i	0.371013	+	0.928628i	$0.379010\pi$
$384$	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	−0.833782	−	0.552094i	$-0.813829\pi$
$397$	3.12769	−	13.7033i	0.156974	−	0.687750i	0.990756	−	0.135656i	$-0.0433141\pi$
$398$	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	−0.902326	−	0.431054i	$-0.858142\pi$
$401$	−22.5863	+	10.8770i	−1.12791	+	0.543171i	−0.225579	+	0.974225i	$0.572427\pi$
$402$	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	0.997437	+	0.0715435i	$0.0227925\pi$
$409$	17.0939	+	21.4350i	0.845237	+	1.05989i	−0.152201	+	0.988350i	$0.548636\pi$
$410$	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	0.976121	+	0.217226i	$0.0697010\pi$
$419$	3.90798	+	17.1220i	0.190917	+	0.836464i	−0.785204	+	0.619237i	$0.787442\pi$
$420$	7.76458	+	3.73922i	0.378873	+	0.182455i
$421$	27.9611	+	13.4653i	1.36274	+	0.656261i	0.965246	−	0.261345i	$-0.0841659\pi$
$421$	27.9611	+	13.4653i	1.36274	+	0.656261i	0.397493	+	0.917605i	$0.369880\pi$
$422$	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	−0.512738	−	0.858545i	$-0.671369\pi$
$431$	9.10092	−	11.4122i	0.438376	−	0.549706i	0.951114	+	0.308839i	$0.0999403\pi$
$432$	4.01384	+	5.03319i	0.193116	+	0.242160i
$433$	−9.35383	+	4.50457i	−0.449516	+	0.216476i	−0.644924	−	0.764246i	$-0.723111\pi$
$433$	−9.35383	+	4.50457i	−0.449516	+	0.216476i	0.195408	+	0.980722i	$0.437397\pi$
$434$	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	−0.988798	−	0.149262i	$-0.952310\pi$
$439$	−13.0585	+	16.3749i	−0.623250	+	0.781531i	0.365548	+	0.930793i	$0.380882\pi$
$440$	−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	$-0.914125\pi$
$443$	0.424977	−	1.86195i	0.0201913	−	0.0884638i	0.984020	+	0.178060i	$0.0569821\pi$
$444$	−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	$-0.145714\pi$
$449$	23.5375	+	11.3350i	1.11080	+	0.534934i	0.213763	+	0.976886i	$0.431428\pi$
$450$	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	0.975830	−	0.218530i	$-0.0701262\pi$
$457$	11.6644	+	14.6267i	0.545636	+	0.684206i	−0.430194	+	0.902737i	$0.641555\pi$
$458$	−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	−0.894003	−	0.448061i	$-0.852115\pi$
$461$	−24.3028	−	30.4748i	−1.13190	−	1.41935i	−0.237893	−	0.971291i	$-0.576457\pi$
$462$	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	$-0.350567\pi$
$467$	−11.1881	−	14.0294i	−0.517722	−	0.649203i	−0.970124	+	0.242611i	$0.921996\pi$
$468$	−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	$-0.274929\pi$
$479$	10.0731	+	4.85097i	0.460253	+	0.221646i	−0.189365	+	0.981907i	$0.560643\pi$
$480$	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	−0.983674	−	0.179959i	$-0.942403\pi$
$487$	−38.3473	−	18.4671i	−1.73768	−	0.836824i	−0.754009	−	0.656865i	$-0.771882\pi$
$488$	−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	$-0.531996\pi$
$491$	13.6268	−	6.56232i	0.614969	−	0.296153i	0.715318	+	0.698799i	$0.246282\pi$
$492$	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	−0.136220	−	0.990679i	$-0.543495\pi$
$499$	−22.2421	−	10.7113i	−0.995695	−	0.479502i	−0.859475	+	0.511177i	$0.829210\pi$
$500$	−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	$-0.682654\pi$
$503$	8.89752	−	11.1571i	0.396721	−	0.497472i	0.939569	+	0.342358i	$0.111226\pi$
$504$	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	−0.852378	−	0.522926i	$-0.824840\pi$
$509$	−7.02327	−	30.7710i	−0.311301	−	1.36390i	0.541077	−	0.840973i	$-0.318017\pi$
$510$	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	$-0.887310\pi$
$541$	−9.10092	+	11.4122i	−0.391279	+	0.490649i	0.546706	+	0.837325i	$0.315882\pi$
$542$	−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	−0.673638	−	0.739061i	$-0.735269\pi$
$547$	4.60258	−	5.77145i	0.196792	−	0.246770i	0.870430	+	0.492292i	$0.163841\pi$
$548$	−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	0.536029	−	0.844200i	$-0.319924\pi$
$557$	4.96126	+	2.38921i	0.210215	+	0.101234i	−0.325814	+	0.945434i	$0.605638\pi$
$558$	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	0.983187	−	0.182604i	$-0.0584526\pi$
$569$	0.432641	+	1.89552i	0.0181373	+	0.0794645i	−0.965049	+	0.262068i	$0.915595\pi$
$570$	4.45539	−	5.58689i	0.186616	−	0.234009i
$571$	7.67844	−	33.6414i	0.321333	−	1.40785i	−0.513851	−	0.857879i	$-0.671782\pi$
$571$	7.67844	−	33.6414i	0.321333	−	1.40785i	0.835184	−	0.549971i	$-0.185361\pi$
$572$	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	$-0.232609\pi$
$577$	−1.72328	−	2.16093i	−0.0717412	−	0.0899607i	−0.816407	+	0.577477i	$0.804037\pi$
$578$	−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	0.813135	+	0.582075i	$0.197759\pi$
$587$	29.0659	+	36.4474i	1.19968	+	1.50435i	0.386542	+	0.922272i	$0.373669\pi$
$588$	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	0.997070	+	0.0764913i	$0.0243717\pi$
$593$	3.21269	+	14.0757i	0.131929	+	0.578020i	−0.865141	+	0.501529i	$0.832771\pi$
$594$	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	$-0.699685\pi$
$599$	8.14832	−	10.2177i	0.332931	−	0.417482i	0.919916	+	0.392115i	$0.128257\pi$
$600$	−3.03030	+	13.2766i	−0.123711	+	0.542015i
$601$	−6.48850	+	28.4280i	−0.264671	+	1.15960i	0.651447	+	0.758694i	$0.274162\pi$
$601$	−6.48850	+	28.4280i	−0.264671	+	1.15960i	−0.916119	+	0.400907i	$0.868695\pi$
$602$	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	$-0.714379\pi$
$607$	−9.89148	+	4.76349i	−0.401483	+	0.193344i	0.222236	+	0.974993i	$0.428665\pi$
$608$	−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	−0.302971	−	0.953000i	$-0.597979\pi$
$613$	17.1715	−	21.5324i	0.693552	−	0.869687i	0.996523	+	0.0833128i	$0.0265501\pi$
$614$	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	−0.870851	−	0.491546i	$-0.836432\pi$
$617$	3.15542	−	13.8248i	0.127033	−	0.556566i	0.997884	−	0.0650196i	$-0.0207110\pi$
$618$	0.780287	−	3.41866i	0.0313877	−	0.137519i
$619$	4.39917	−	5.51639i	0.176818	−	0.221722i	−0.685523	−	0.728051i	$-0.740426\pi$
$619$	4.39917	−	5.51639i	0.176818	−	0.221722i	0.862341	+	0.506329i	$0.168998\pi$
$620$	−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	0.296735	−	0.954960i	$-0.404102\pi$
$631$	−17.5916	−	22.0592i	−0.700312	−	0.878163i	−0.997047	+	0.0767968i	$0.975531\pi$
$632$	−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	$-0.144222\pi$
$641$	6.89313	+	8.64372i	0.272262	+	0.341406i	−0.626837	+	0.779150i	$0.715651\pi$
$642$	−1.61084	+	2.01993i	−0.0635749	+	0.0797204i
$643$	33.7110	−	16.2344i	1.32943	−	0.640221i	0.371827	−	0.928302i	$-0.378732\pi$
$643$	33.7110	−	16.2344i	1.32943	−	0.640221i	0.957606	+	0.288081i	$0.0930173\pi$
$644$	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	−0.646347	−	0.763044i	$-0.723704\pi$
$647$	6.79309	−	29.7625i	0.267064	−	1.17008i	0.913411	−	0.407039i	$-0.133439\pi$
$648$	−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	−0.995101	−	0.0988626i	$-0.968480\pi$
$653$	−43.2584	−	20.8321i	−1.69283	−	0.815224i	−0.697729	−	0.716362i	$-0.745806\pi$
$654$	−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	$-0.884688\pi$
$659$	1.57005	−	6.87883i	0.0611604	−	0.267961i	0.996258	+	0.0864291i	$0.0275456\pi$
$660$	−3.32086	−	4.16422i	−0.129264	−	0.162092i
$661$	33.7420	+	16.2493i	1.31241	+	0.632025i	0.953513	−	0.301351i	$-0.0974375\pi$
$661$	33.7420	+	16.2493i	1.31241	+	0.632025i	0.358900	+	0.933376i	$0.383152\pi$
$662$	−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	0.542883	−	0.839808i	$-0.317333\pi$
$673$	5.83119	+	2.80815i	0.224776	+	0.108246i	−0.318107	+	0.948055i	$0.603047\pi$
$674$	−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	−0.00455972	+	0.999990i	$0.501451\pi$
$677$	−25.4588	+	31.9244i	−0.978463	+	1.22695i	−0.973903	+	0.226964i	$0.927120\pi$
$678$	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	−0.982751	−	0.184934i	$-0.940793\pi$
$683$	−4.64047	−	20.3312i	−0.177563	−	0.777954i	0.805188	−	0.593019i	$-0.202064\pi$
$684$	−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	−0.625533	−	0.780198i	$-0.715118\pi$
$691$	−10.6610	+	5.13407i	−0.405563	+	0.195309i	0.219970	+	0.975507i	$0.429404\pi$
$692$	−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	−0.0398539	−	0.999206i	$-0.512689\pi$
$701$	18.9706	−	9.13574i	0.716508	−	0.345052i	0.756362	+	0.654153i	$0.226975\pi$
$702$	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	0.784245	+	0.620451i	$0.213051\pi$
$709$	9.23608	+	40.4659i	0.346868	+	1.51973i	−0.437377	+	0.899278i	$0.644092\pi$
$710$	−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	0.285478	−	0.958385i	$-0.407848\pi$
$719$	−7.66416	−	3.69087i	−0.285825	−	0.137646i	−0.571303	+	0.820739i	$0.693562\pi$
$720$	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	$-0.817024\pi$
$727$	−25.2773	+	12.1729i	−0.937485	+	0.451469i	−0.0982034	+	0.995166i	$0.531310\pi$
$728$	−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	0.876802	+	0.480851i	$0.159672\pi$
$733$	−3.29768	+	14.4481i	−0.121803	+	0.533653i	−0.998605	+	0.0528016i	$0.983185\pi$
$734$	−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	0.998829	+	0.0483844i	$0.0154072\pi$
$739$	45.1105	+	21.7241i	1.65942	+	0.799133i	0.660588	+	0.750749i	$0.270307\pi$
$740$	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	−0.887741	−	0.460344i	$-0.847726\pi$
$743$	−7.84076	−	34.3526i	−0.287650	−	1.26028i	0.600091	−	0.799932i	$-0.295131\pi$
$744$	−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	$-0.324052\pi$
$751$	−11.5519	−	14.4857i	−0.421536	−	0.528590i	−0.946573	+	0.322490i	$0.895480\pi$
$752$	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	$-0.214409\pi$
$757$	−0.0132718	−	0.0166422i	−0.000482370	−	0.000604873i	−0.782073	+	0.623187i	$0.785837\pi$
$758$	−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	0.980299	−	0.197520i	$-0.0632887\pi$
$761$	15.7130	+	19.7034i	0.569594	+	0.714249i	−0.410705	+	0.911768i	$0.634717\pi$
$762$	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