LMFDB - Embedded newform 41.2.g.a.20.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [41,2,Mod(2,41)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(41, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("41.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	41.g (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.327386648287$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			20.1
Character	$\chi$	$=$	41.20
Dual form			41.2.g.a.39.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.29671 - 0.746246i) q^{2} +(-1.67347 + 1.67347i) q^{3} +(3.09996 + 2.25225i) q^{4} +(-1.68856 + 2.32411i) q^{5} +(5.09230 - 2.59466i) q^{6} +(-1.86997 - 0.952797i) q^{7} +(-2.60008 - 3.57870i) q^{8} -2.60102i q^{9} +O(q^{10})$	\(q+(-2.29671 - 0.746246i) q^{2} +(-1.67347 + 1.67347i) q^{3} +(3.09996 + 2.25225i) q^{4} +(-1.68856 + 2.32411i) q^{5} +(5.09230 - 2.59466i) q^{6} +(-1.86997 - 0.952797i) q^{7} +(-2.60008 - 3.57870i) q^{8} -2.60102i q^{9} +(5.61249 - 4.07771i) q^{10} +(0.0609104 - 0.384573i) q^{11} +(-8.95677 + 1.41861i) q^{12} +(1.56991 + 3.08112i) q^{13} +(3.58375 + 3.58375i) q^{14} +(-1.06357 - 6.71509i) q^{15} +(0.932875 + 2.87109i) q^{16} +(5.05100 + 0.800000i) q^{17} +(-1.94100 + 5.97379i) q^{18} +(-2.92520 + 5.74102i) q^{19} +(-10.4689 + 3.40156i) q^{20} +(4.72382 - 1.53486i) q^{21} +(-0.426880 + 0.837799i) q^{22} +(0.410662 - 1.26389i) q^{23} +(10.3400 + 1.63770i) q^{24} +(-1.00514 - 3.09351i) q^{25} +(-1.30635 - 8.24798i) q^{26} +(-0.667682 - 0.667682i) q^{27} +(-3.65089 - 7.16527i) q^{28} +(0.589758 - 0.0934085i) q^{29} +(-2.56841 + 16.2163i) q^{30} +(-0.996546 + 0.724033i) q^{31} +1.55681i q^{32} +(0.541641 + 0.745505i) q^{33} +(-11.0037 - 5.60665i) q^{34} +(5.37196 - 2.73715i) q^{35} +(5.85815 - 8.06305i) q^{36} +(-2.07936 - 1.51074i) q^{37} +(11.0025 - 11.0025i) q^{38} +(-7.78337 - 2.52897i) q^{39} +12.7077 q^{40} +(1.91012 + 6.11158i) q^{41} -11.9946 q^{42} +(9.42697 + 3.06301i) q^{43} +(1.05497 - 1.05497i) q^{44} +(6.04504 + 4.39198i) q^{45} +(-1.88634 + 2.59633i) q^{46} +(-1.97205 + 1.00481i) q^{47} +(-6.36584 - 3.24356i) q^{48} +(-1.52553 - 2.09972i) q^{49} +7.85497i q^{50} +(-9.79148 + 7.11393i) q^{51} +(-2.07280 + 13.0872i) q^{52} +(-5.34140 + 0.845995i) q^{53} +(1.03522 + 2.03173i) q^{54} +(0.790938 + 0.790938i) q^{55} +(1.45229 + 9.16940i) q^{56} +(-4.71221 - 14.5027i) q^{57} +(-1.42421 - 0.225572i) q^{58} +(2.04191 - 6.28435i) q^{59} +(11.8271 - 23.2119i) q^{60} +(6.08019 - 1.97557i) q^{61} +(2.82908 - 0.919225i) q^{62} +(-2.47824 + 4.86383i) q^{63} +(3.02751 - 9.31772i) q^{64} +(-9.81174 - 1.55403i) q^{65} +(-0.687662 - 2.11640i) q^{66} +(0.874252 + 5.51981i) q^{67} +(13.8561 + 13.8561i) q^{68} +(1.42785 + 2.80231i) q^{69} +(-14.3804 + 2.27763i) q^{70} +(-1.09545 + 6.91639i) q^{71} +(-9.30827 + 6.76285i) q^{72} -14.4984i q^{73} +(3.64830 + 5.02146i) q^{74} +(6.85898 + 3.49482i) q^{75} +(-21.9982 + 11.2086i) q^{76} +(-0.480321 + 0.661105i) q^{77} +(15.9889 + 11.6166i) q^{78} +(4.23136 - 4.23136i) q^{79} +(-8.24794 - 2.67992i) q^{80} +10.0378 q^{81} +(0.173757 - 15.4619i) q^{82} +15.4232 q^{83} +(18.1005 + 5.88122i) q^{84} +(-10.3882 + 10.3882i) q^{85} +(-19.3653 - 14.0697i) q^{86} +(-0.830627 + 1.14326i) q^{87} +(-1.53464 + 0.781940i) q^{88} +(0.298137 + 0.151908i) q^{89} +(-10.6062 - 14.5982i) q^{90} -7.25741i q^{91} +(4.11963 - 2.99308i) q^{92} +(0.456043 - 2.87934i) q^{93} +(5.27906 - 0.836122i) q^{94} +(-8.40337 - 16.4925i) q^{95} +(-2.60527 - 2.60527i) q^{96} +(2.25597 + 14.2436i) q^{97} +(1.93680 + 5.96087i) q^{98} +(-1.00028 - 0.158429i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8}+O(q^{10}) $ 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8} + 6 q^{10} - 16 q^{11} + 2 q^{12} + 14 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{17} + 16 q^{19} + 20 q^{20} - 10 q^{21} + 6 q^{22} + 12 q^{23} + 68 q^{24} - 8 q^{25} - 28 q^{26} - 6 q^{27} + 18 q^{28} + 40 q^{29} - 36 q^{30} - 12 q^{31} + 10 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} + 46 q^{38} - 50 q^{39} - 44 q^{40} - 4 q^{41} - 40 q^{42} - 48 q^{44} + 16 q^{45} + 70 q^{46} - 12 q^{47} - 50 q^{48} - 30 q^{49} - 24 q^{51} + 20 q^{52} - 26 q^{53} + 68 q^{54} + 20 q^{55} + 106 q^{56} + 10 q^{57} - 20 q^{58} + 6 q^{59} + 76 q^{60} + 30 q^{61} - 10 q^{62} + 92 q^{63} + 70 q^{64} + 68 q^{65} + 34 q^{66} - 22 q^{67} - 20 q^{68} - 38 q^{69} - 20 q^{70} + 4 q^{71} - 74 q^{72} + 10 q^{74} + 4 q^{75} - 128 q^{76} - 20 q^{77} - 10 q^{78} - 2 q^{79} - 70 q^{80} + 28 q^{81} - 90 q^{82} + 80 q^{83} - 30 q^{84} - 56 q^{85} - 46 q^{86} - 10 q^{87} + 10 q^{88} - 72 q^{89} - 70 q^{90} - 6 q^{93} - 18 q^{94} - 40 q^{95} + 66 q^{96} - 22 q^{97} + 6 q^{98} + 14 q^{99}+O(q^{100}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8 + 6 * q^10 - 16 * q^11 + 2 * q^12 + 14 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^17 + 16 * q^19 + 20 * q^20 - 10 * q^21 + 6 * q^22 + 12 * q^23 + 68 * q^24 - 8 * q^25 - 28 * q^26 - 6 * q^27 + 18 * q^28 + 40 * q^29 - 36 * q^30 - 12 * q^31 + 10 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 + 46 * q^38 - 50 * q^39 - 44 * q^40 - 4 * q^41 - 40 * q^42 - 48 * q^44 + 16 * q^45 + 70 * q^46 - 12 * q^47 - 50 * q^48 - 30 * q^49 - 24 * q^51 + 20 * q^52 - 26 * q^53 + 68 * q^54 + 20 * q^55 + 106 * q^56 + 10 * q^57 - 20 * q^58 + 6 * q^59 + 76 * q^60 + 30 * q^61 - 10 * q^62 + 92 * q^63 + 70 * q^64 + 68 * q^65 + 34 * q^66 - 22 * q^67 - 20 * q^68 - 38 * q^69 - 20 * q^70 + 4 * q^71 - 74 * q^72 + 10 * q^74 + 4 * q^75 - 128 * q^76 - 20 * q^77 - 10 * q^78 - 2 * q^79 - 70 * q^80 + 28 * q^81 - 90 * q^82 + 80 * q^83 - 30 * q^84 - 56 * q^85 - 46 * q^86 - 10 * q^87 + 10 * q^88 - 72 * q^89 - 70 * q^90 - 6 * q^93 - 18 * q^94 - 40 * q^95 + 66 * q^96 - 22 * q^97 + 6 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/41\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{17}{20}\right)$

Coefficient data

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

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

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

$2$	−2.29671	−	0.746246i	−1.62402	−	0.527676i	−0.651133	−	0.758963i	$-0.725706\pi$
$2$	−2.29671	−	0.746246i	−1.62402	−	0.527676i	−0.972885	+	0.231288i	$0.925706\pi$
$3$	−1.67347	+	1.67347i	−0.966180	+	0.966180i	−0.999447	−	0.0332667i	$-0.989409\pi$
$3$	−1.67347	+	1.67347i	−0.966180	+	0.966180i	0.0332667	+	0.999447i	$0.489409\pi$
$4$	3.09996	+	2.25225i	1.54998	+	1.12613i
$5$	−1.68856	+	2.32411i	−0.755148	+	1.03937i	0.242455	+	0.970163i	$0.422047\pi$
$5$	−1.68856	+	2.32411i	−0.755148	+	1.03937i	−0.997602	+	0.0692088i	$0.977953\pi$
$6$	5.09230	−	2.59466i	2.07892	−	1.05926i
$7$	−1.86997	−	0.952797i	−0.706782	−	0.360123i	0.0633646	−	0.997990i	$-0.479817\pi$
$7$	−1.86997	−	0.952797i	−0.706782	−	0.360123i	−0.770146	+	0.637867i	$0.779817\pi$
$8$	−2.60008	−	3.57870i	−0.919266	−	1.26526i
$9$		−	2.60102i		−	0.867007i
$10$	5.61249	−	4.07771i	1.77483	−	1.28949i
$11$	0.0609104	−	0.384573i	0.0183652	−	0.115953i	−0.976803	−	0.214141i	$-0.931305\pi$
$11$	0.0609104	−	0.384573i	0.0183652	−	0.115953i	0.995168	+	0.0981881i	$0.0313047\pi$
$12$	−8.95677	+	1.41861i	−2.58560	+	0.409518i
$13$	1.56991	+	3.08112i	0.435415	+	0.854549i	0.999583	+	0.0288893i	$0.00919702\pi$
$13$	1.56991	+	3.08112i	0.435415	+	0.854549i	−0.564168	+	0.825660i	$0.690803\pi$
$14$	3.58375	+	3.58375i	0.957799	+	0.957799i
$15$	−1.06357	−	6.71509i	−0.274611	−	1.73383i
$16$	0.932875	+	2.87109i	0.233219	+	0.717774i
$17$	5.05100	+	0.800000i	1.22505	+	0.194028i	0.735243	−	0.677804i	$-0.237068\pi$
$17$	5.05100	+	0.800000i	1.22505	+	0.194028i	0.489804	+	0.871832i	$0.337068\pi$
$18$	−1.94100	+	5.97379i	−0.457498	+	1.40804i
$19$	−2.92520	+	5.74102i	−0.671086	+	1.31708i	0.264638	+	0.964348i	$0.414748\pi$
$19$	−2.92520	+	5.74102i	−0.671086	+	1.31708i	−0.935724	+	0.352733i	$0.885252\pi$
$20$	−10.4689	+	3.40156i	−2.34092	+	0.760613i
$21$	4.72382	−	1.53486i	1.03082	−	0.334934i
$22$	−0.426880	+	0.837799i	−0.0910111	+	0.178619i
$23$	0.410662	−	1.26389i	0.0856289	−	0.263539i	−0.899069	−	0.437806i	$-0.855756\pi$
$23$	0.410662	−	1.26389i	0.0856289	−	0.263539i	0.984698	+	0.174267i	$0.0557557\pi$
$24$	10.3400	+	1.63770i	2.11065	+	0.334294i
$25$	−1.00514	−	3.09351i	−0.201028	−	0.618701i
$26$	−1.30635	−	8.24798i	−0.256197	−	1.61756i
$27$	−0.667682	−	0.667682i	−0.128495	−	0.128495i
$28$	−3.65089	−	7.16527i	−0.689953	−	1.35411i
$29$	0.589758	−	0.0934085i	0.109515	−	0.0173455i	−0.101436	−	0.994842i	$-0.532344\pi$
$29$	0.589758	−	0.0934085i	0.109515	−	0.0173455i	0.210952	+	0.977497i	$0.432344\pi$
$30$	−2.56841	+	16.2163i	−0.468925	+	2.96068i
$31$	−0.996546	+	0.724033i	−0.178985	+	0.130040i	−0.673670	−	0.739032i	$-0.735283\pi$
$31$	−0.996546	+	0.724033i	−0.178985	+	0.130040i	0.494685	+	0.869072i	$0.335283\pi$
$32$			1.55681i			0.275207i
$33$	0.541641	+	0.745505i	0.0942876	+	0.129776i
$34$	−11.0037	−	5.60665i	−1.88712	−	0.961533i
$35$	5.37196	−	2.73715i	0.908027	−	0.462663i
$36$	5.85815	−	8.06305i	0.976358	−	1.34384i
$37$	−2.07936	−	1.51074i	−0.341845	−	0.248365i	0.403595	−	0.914938i	$-0.367761\pi$
$37$	−2.07936	−	1.51074i	−0.341845	−	0.248365i	−0.745440	+	0.666573i	$0.767761\pi$
$38$	11.0025	−	11.0025i	1.78485	−	1.78485i
$39$	−7.78337	−	2.52897i	−1.24634	−	0.404959i
$40$	12.7077			2.00926
$41$	1.91012	+	6.11158i	0.298310	+	0.954469i
$41$	1.91012	+	6.11158i	0.298310	+	0.954469i
$42$	−11.9946			−1.85081
$43$	9.42697	+	3.06301i	1.43760	+	0.467104i	0.921148	−	0.389212i	$-0.127253\pi$
$43$	9.42697	+	3.06301i	1.43760	+	0.467104i	0.516452	+	0.856316i	$0.327253\pi$
$44$	1.05497	−	1.05497i	0.159043	−	0.159043i
$45$	6.04504	+	4.39198i	0.901142	+	0.654718i
$46$	−1.88634	+	2.59633i	−0.278126	+	0.382808i
$47$	−1.97205	+	1.00481i	−0.287653	+	0.146567i	−0.591863	−	0.806038i	$-0.701607\pi$
$47$	−1.97205	+	1.00481i	−0.287653	+	0.146567i	0.304210	+	0.952605i	$0.401607\pi$
$48$	−6.36584	−	3.24356i	−0.918830	−	0.468167i
$49$	−1.52553	−	2.09972i	−0.217934	−	0.299960i
$50$			7.85497i			1.11086i
$51$	−9.79148	+	7.11393i	−1.37108	+	0.996149i
$52$	−2.07280	+	13.0872i	−0.287446	+	1.81486i
$53$	−5.34140	+	0.845995i	−0.733698	+	0.116206i	−0.512093	−	0.858930i	$-0.671130\pi$
$53$	−5.34140	+	0.845995i	−0.733698	+	0.116206i	−0.221605	+	0.975136i	$0.571130\pi$
$54$	1.03522	+	2.03173i	0.140875	+	0.276483i
$55$	0.790938	+	0.790938i	0.106650	+	0.106650i
$56$	1.45229	+	9.16940i	0.194070	+	1.22531i
$57$	−4.71221	−	14.5027i	−0.624147	−	1.92093i
$58$	−1.42421	−	0.225572i	−0.187008	−	0.0296191i
$59$	2.04191	−	6.28435i	0.265834	−	0.818153i	−0.725666	−	0.688047i	$-0.758468\pi$
$59$	2.04191	−	6.28435i	0.265834	−	0.818153i	0.991500	−	0.130106i	$-0.0415317\pi$
$60$	11.8271	−	23.2119i	1.52687	−	2.99664i
$61$	6.08019	−	1.97557i	0.778489	−	0.252946i	0.107294	−	0.994227i	$-0.465781\pi$
$61$	6.08019	−	1.97557i	0.778489	−	0.252946i	0.671195	+	0.741281i	$0.265781\pi$
$62$	2.82908	−	0.919225i	0.359294	−	0.116742i
$63$	−2.47824	+	4.86383i	−0.312229	+	0.612785i
$64$	3.02751	−	9.31772i	0.378439	−	1.16472i
$65$	−9.81174	−	1.55403i	−1.21700	−	0.192753i
$66$	−0.687662	−	2.11640i	−0.0846453	−	0.260511i
$67$	0.874252	+	5.51981i	0.106807	+	0.674352i	0.981757	+	0.190139i	$0.0608940\pi$
$67$	0.874252	+	5.51981i	0.106807	+	0.674352i	−0.874950	+	0.484213i	$0.839106\pi$
$68$	13.8561	+	13.8561i	1.68030	+	1.68030i
$69$	1.42785	+	2.80231i	0.171893	+	0.337359i
$70$	−14.3804	+	2.27763i	−1.71879	+	0.272229i
$71$	−1.09545	+	6.91639i	−0.130006	+	0.820824i	0.833379	+	0.552702i	$0.186403\pi$
$71$	−1.09545	+	6.91639i	−0.130006	+	0.820824i	−0.963385	+	0.268123i	$0.913597\pi$
$72$	−9.30827	+	6.76285i	−1.09699	+	0.797010i
$73$		−	14.4984i		−	1.69692i	−0.529263	−	0.848458i	$-0.677532\pi$
$73$		−	14.4984i		−	1.69692i	0.529263	−	0.848458i	$-0.322468\pi$
$74$	3.64830	+	5.02146i	0.424106	+	0.583732i
$75$	6.85898	+	3.49482i	0.792006	+	0.403547i
$76$	−21.9982	+	11.2086i	−2.52337	+	1.28572i
$77$	−0.480321	+	0.661105i	−0.0547376	+	0.0753399i
$78$	15.9889	+	11.6166i	1.81039	+	1.31532i
$79$	4.23136	−	4.23136i	0.476066	−	0.476066i	−0.427805	−	0.903871i	$-0.640713\pi$
$79$	4.23136	−	4.23136i	0.476066	−	0.476066i	0.903871	+	0.427805i	$0.140713\pi$
$80$	−8.24794	−	2.67992i	−0.922148	−	0.299624i
$81$	10.0378			1.11531
$82$	0.173757	−	15.4619i	0.0191882	−	1.70749i
$83$	15.4232			1.69292			0.846458	−	0.532456i	$-0.178731\pi$
$83$	15.4232			1.69292			0.846458	+	0.532456i	$0.178731\pi$
$84$	18.1005	+	5.88122i	1.97493	+	0.641694i
$85$	−10.3882	+	10.3882i	−1.12676	+	1.12676i
$86$	−19.3653	−	14.0697i	−2.08821	−	1.51717i
$87$	−0.830627	+	1.14326i	−0.0890526	+	0.122570i
$88$	−1.53464	+	0.781940i	−0.163594	+	0.0833551i
$89$	0.298137	+	0.151908i	0.0316024	+	0.0161022i	0.469720	−	0.882815i	$-0.344355\pi$
$89$	0.298137	+	0.151908i	0.0316024	+	0.0161022i	−0.438118	+	0.898918i	$0.644355\pi$
$90$	−10.6062	−	14.5982i	−1.11799	−	1.53879i
$91$		−	7.25741i		−	0.760783i
$92$	4.11963	−	2.99308i	0.429501	−	0.312050i
$93$	0.456043	−	2.87934i	0.0472895	−	0.298574i
$94$	5.27906	−	0.836122i	0.544494	−	0.0862394i
$95$	−8.40337	−	16.4925i	−0.862167	−	1.69210i
$96$	−2.60527	−	2.60527i	−0.265900	−	0.265900i
$97$	2.25597	+	14.2436i	0.229059	+	1.44622i	0.787315	+	0.616551i	$0.211470\pi$
$97$	2.25597	+	14.2436i	0.229059	+	1.44622i	−0.558257	+	0.829668i	$0.688530\pi$
$98$	1.93680	+	5.96087i	0.195647	+	0.602139i
$99$	−1.00028	−	0.158429i	−0.100532	−	0.0159227i
$100$	3.85146	−	11.8536i	0.385146	−	1.18536i
$101$	−5.20975	+	10.2247i	−0.518389	+	1.01740i	0.472323	+	0.881425i	$0.343415\pi$
$101$	−5.20975	+	10.2247i	−0.518389	+	1.01740i	−0.990713	+	0.135971i	$0.956585\pi$
$102$	27.7969	−	9.03177i	2.75231	−	0.894279i
$103$	−12.4376	+	4.04121i	−1.22551	+	0.398192i	−0.849085	−	0.528256i	$-0.822846\pi$
$103$	−12.4376	+	4.04121i	−1.22551	+	0.398192i	−0.376423	+	0.926448i	$0.622846\pi$
$104$	6.94452	−	13.6294i	0.680966	−	1.33647i
$105$	−4.40928	+	13.5704i	−0.430302	+	1.32433i
$106$	12.8990	+	2.04300i	1.25286	+	0.198433i
$107$	−2.13126	−	6.55935i	−0.206037	−	0.634116i	−0.999669	−	0.0257185i	$-0.991813\pi$
$107$	−2.13126	−	6.55935i	−0.206037	−	0.634116i	0.793632	−	0.608397i	$-0.208187\pi$
$108$	−0.565998	−	3.57357i	−0.0544632	−	0.343867i
$109$	−5.79514	−	5.79514i	−0.555074	−	0.555074i	0.372827	−	0.927901i	$-0.378389\pi$
$109$	−5.79514	−	5.79514i	−0.555074	−	0.555074i	−0.927901	+	0.372827i	$0.878389\pi$
$110$	−1.22632	−	2.40679i	−0.116925	−	0.229478i
$111$	6.00794	−	0.951565i	0.570249	−	0.0903185i
$112$	0.991122	−	6.25770i	0.0936522	−	0.591297i
$113$	−2.92382	+	2.12428i	−0.275049	+	0.199835i	−0.716755	−	0.697325i	$-0.754374\pi$
$113$	−2.92382	+	2.12428i	−0.275049	+	0.199835i	0.441706	+	0.897160i	$0.354374\pi$
$114$			36.8249i			3.44897i
$115$	2.24398	+	3.08857i	0.209252	+	0.288011i
$116$	2.03860	+	1.03872i	0.189280	+	0.0964428i
$117$	8.01406	−	4.08337i	0.740900	−	0.377507i
$118$	−9.37935	+	12.9096i	−0.863439	+	1.18842i
$119$	−8.68297	−	6.30855i	−0.795967	−	0.578304i
$120$	−21.2659	+	21.2659i	−1.94130	+	1.94130i
$121$	10.3174	+	3.35234i	0.937949	+	0.304758i
$122$	−15.4387			−1.39775
$123$	−13.4241	−	7.03103i	−1.21041	−	0.633967i
$124$	−4.71995			−0.423864
$125$	−4.77387	−	1.55112i	−0.426988	−	0.138737i
$126$	9.32142	−	9.32142i	0.830418	−	0.830418i
$127$	8.27813	+	6.01442i	0.734566	+	0.533693i	0.891004	−	0.453995i	$-0.150001\pi$
$127$	8.27813	+	6.01442i	0.734566	+	0.533693i	−0.156439	+	0.987688i	$0.550001\pi$
$128$	−12.0765	+	16.6219i	−1.06742	+	1.46918i
$129$	−20.9016	+	10.6499i	−1.84029	+	0.937673i
$130$	21.3750	+	10.8911i	1.87471	+	0.955214i
$131$	6.10182	+	8.39844i	0.533119	+	0.733775i	0.987602	−	0.156981i	$-0.0501760\pi$
$131$	6.10182	+	8.39844i	0.533119	+	0.733775i	−0.454483	+	0.890755i	$0.650176\pi$
$132$			3.53094i			0.307329i
$133$	10.9401	−	7.94842i	0.948623	−	0.689215i
$134$	2.11124	−	13.3298i	0.182383	−	1.15152i
$135$	2.67919	−	0.424341i	0.230588	−	0.0365215i
$136$	−10.2700	−	20.1561i	−0.880648	−	1.72837i
$137$	2.71426	+	2.71426i	0.231895	+	0.231895i	0.813483	−	0.581588i	$-0.197569\pi$
$137$	2.71426	+	2.71426i	0.231895	+	0.231895i	−0.581588	+	0.813483i	$0.697569\pi$
$138$	−1.18814	−	7.50162i	−0.101141	−	0.638581i
$139$	2.09647	+	6.45229i	0.177821	+	0.547276i	0.999751	−	0.0223122i	$-0.00710280\pi$
$139$	2.09647	+	6.45229i	0.177821	+	0.547276i	−0.821930	+	0.569588i	$0.807103\pi$
$140$	22.8176	+	3.61395i	1.92844	+	0.305434i
$141$	1.61865	−	4.98170i	0.136315	−	0.419534i
$142$	7.67726	−	15.0675i	0.644261	−	1.26443i
$143$	1.28054	−	0.416073i	0.107084	−	0.0347938i
$144$	7.46778	−	2.42643i	0.622315	−	0.202202i
$145$	−0.778751	+	1.52839i	−0.0646718	+	0.126926i
$146$	−10.8194	+	33.2987i	−0.895421	+	2.75582i
$147$	6.06676	+	0.960881i	0.500378	+	0.0792521i
$148$	−3.04336	−	9.36648i	−0.250162	−	0.769920i
$149$	−1.99565	−	12.6001i	−0.163490	−	1.03224i	−0.923856	−	0.382741i	$-0.874980\pi$
$149$	−1.99565	−	12.6001i	−0.163490	−	1.03224i	0.760365	−	0.649496i	$-0.225020\pi$
$150$	−13.1451	−	13.1451i	−1.07329	−	1.07329i
$151$	1.21997	+	2.39432i	0.0992794	+	0.194847i	0.935304	−	0.353845i	$-0.115126\pi$
$151$	1.21997	+	2.39432i	0.0992794	+	0.194847i	−0.836025	+	0.548692i	$0.815126\pi$
$152$	28.1511	−	4.45870i	2.28336	−	0.361648i
$153$	2.08081	−	13.1377i	0.168224	−	1.06212i
$154$	1.59650	−	1.15993i	0.128650	−	0.0934697i
$155$		−	3.53865i		−	0.284231i
$156$	−18.4322	−	25.3698i	−1.47576	−	2.03121i
$157$	9.25397	+	4.71513i	0.738547	+	0.376308i	0.782438	−	0.622728i	$-0.213976\pi$
$157$	9.25397	+	4.71513i	0.738547	+	0.376308i	−0.0438917	+	0.999036i	$0.513976\pi$
$158$	−12.8759	+	6.56057i	−1.02435	+	0.521931i
$159$	7.52294	−	10.3544i	0.596608	−	0.821160i
$160$	−3.61818	−	2.62876i	−0.286042	−	0.207822i
$161$	−1.97215	+	1.97215i	−0.155427	+	0.155427i
$162$	−23.0538	−	7.49064i	−1.81128	−	0.588520i
$163$	3.48663			0.273094			0.136547	−	0.990634i	$-0.456399\pi$
$163$	3.48663			0.273094			0.136547	+	0.990634i	$0.456399\pi$
$164$	−7.84353	+	23.2477i	−0.612477	+	1.81534i
$165$	−2.64723			−0.206086
$166$	−35.4226	−	11.5095i	−2.74933	−	0.893310i
$167$	13.8248	−	13.8248i	1.06980	−	1.06980i	0.0724237	−	0.997374i	$-0.476927\pi$
$167$	13.8248	−	13.8248i	1.06980	−	1.06980i	0.997374	−	0.0724237i	$-0.0230734\pi$
$168$	−17.7751	−	12.9144i	−1.37138	−	0.996365i
$169$	0.612517	−	0.843057i	0.0471167	−	0.0648505i
$170$	31.6108	−	16.1065i	2.42444	−	1.23531i
$171$	14.9325	+	7.60850i	1.14192	+	0.581836i
$172$	22.3245	+	30.7271i	1.70223	+	2.34292i
$173$		−	12.0871i		−	0.918962i	−0.888187	−	0.459481i	$-0.848035\pi$
$173$		−	12.0871i		−	0.918962i	0.888187	−	0.459481i	$-0.151965\pi$
$174$	2.76086	−	2.00588i	0.209300	−	0.152066i
$175$	−1.06790	+	6.74246i	−0.0807257	+	0.509682i
$176$	1.16097	−	0.183879i	0.0875113	−	0.0138604i
$177$	7.09961	+	13.9338i	0.533639	+	1.04733i
$178$	−0.571372	−	0.571372i	−0.0428262	−	0.0428262i
$179$	0.311865	+	1.96904i	0.0233099	+	0.147173i	0.996598	−	0.0824133i	$-0.0262628\pi$
$179$	0.311865	+	1.96904i	0.0233099	+	0.147173i	−0.973288	+	0.229586i	$0.926263\pi$
$180$	8.84753	+	27.2299i	0.659456	+	2.02960i
$181$	−16.0347	−	2.53965i	−1.19185	−	0.188771i	−0.471174	−	0.882040i	$-0.656170\pi$
$181$	−16.0347	−	2.53965i	−1.19185	−	0.188771i	−0.720678	+	0.693269i	$0.756170\pi$
$182$	−5.41581	+	16.6682i	−0.401447	+	1.23553i
$183$	−6.86897	+	13.4811i	−0.507769	+	0.996552i
$184$	−5.59083	+	1.81657i	−0.412161	+	0.133919i
$185$	7.02226	−	2.28167i	0.516287	−	0.167752i
$186$	−3.19610	+	6.27269i	−0.234349	+	0.459936i
$187$	0.615317	−	1.89375i	0.0449964	−	0.138485i
$188$	−8.37636	−	1.32668i	−0.610909	−	0.0967584i
$189$	0.612379	+	1.88471i	0.0445440	+	0.137092i
$190$	6.99260	+	44.1495i	0.507297	+	3.20294i
$191$	3.91166	+	3.91166i	0.283038	+	0.283038i	0.834319	−	0.551282i	$-0.185861\pi$
$191$	3.91166	+	3.91166i	0.283038	+	0.283038i	−0.551282	+	0.834319i	$0.685861\pi$
$192$	10.5265	+	20.6594i	0.759684	+	1.49096i
$193$	−8.30947	+	1.31609i	−0.598129	+	0.0947343i	−0.448155	−	0.893956i	$-0.647919\pi$
$193$	−8.30947	+	1.31609i	−0.598129	+	0.0947343i	−0.149974	+	0.988690i	$0.547919\pi$
$194$	5.44794	−	34.3969i	0.391139	−	2.46956i
$195$	19.0203	−	13.8191i	1.36207	−	0.989603i
$196$		−	9.94492i		−	0.710352i
$197$	−15.4090	−	21.2087i	−1.09785	−	1.51106i	−0.838206	−	0.545354i	$-0.816395\pi$
$197$	−15.4090	−	21.2087i	−1.09785	−	1.51106i	−0.259643	−	0.965705i	$-0.583605\pi$
$198$	2.17913	+	1.11032i	0.154864	+	0.0789072i
$199$	10.0682	−	5.13001i	0.713716	−	0.363657i	−0.0591296	−	0.998250i	$-0.518833\pi$
$199$	10.0682	−	5.13001i	0.713716	−	0.363657i	0.772846	+	0.634594i	$0.218833\pi$
$200$	−8.45729	+	11.6405i	−0.598020	+	0.823105i
$201$	−10.7003	−	7.77422i	−0.754740	−	0.548351i
$202$	19.5954	−	19.5954i	1.37873	−	1.37873i
$203$	−1.19183	−	0.387249i	−0.0836500	−	0.0271795i
$204$	−46.3755			−3.24694
$205$	−17.4293	−	5.88047i	−1.21732	−	0.410710i
$206$	31.5812			2.20036
$207$	−3.28740	−	1.06814i	−0.228490	−	0.0742409i
$208$	−7.38166	+	7.38166i	−0.511826	+	0.511826i
$209$	2.02967	+	1.47464i	0.140395	+	0.102003i
$210$	20.2537	−	27.8768i	1.39764	−	1.92368i
$211$	−4.73888	+	2.41458i	−0.326238	+	0.166226i	−0.609437	−	0.792835i	$-0.708604\pi$
$211$	−4.73888	+	2.41458i	−0.326238	+	0.166226i	0.283199	+	0.959061i	$0.408604\pi$
$212$	−18.4635	−	9.40763i	−1.26808	−	0.646119i
$213$	−9.74118	−	13.4076i	−0.667455	−	0.918673i
$214$			16.6554i			1.13854i
$215$	−23.0368	+	16.7372i	−1.57110	+	1.14147i
$216$	−0.653408	+	4.12546i	−0.0444588	+	0.280702i
$217$	2.55337	−	0.404414i	0.173334	−	0.0274534i
$218$	8.98516	+	17.6344i	0.608552	+	1.19435i
$219$	24.2628	+	24.2628i	1.63953	+	1.63953i
$220$	0.670483	+	4.23326i	0.0452040	+	0.285407i
$221$	5.46472	+	16.8187i	0.367597	+	1.13135i
$222$	−14.5086	−	2.29794i	−0.973754	−	0.154227i
$223$	2.16692	−	6.66908i	0.145107	−	0.446595i	−0.851917	−	0.523676i	$-0.824560\pi$
$223$	2.16692	−	6.66908i	0.145107	−	0.446595i	0.997025	+	0.0770815i	$0.0245602\pi$
$224$	1.48332	−	2.91118i	0.0991085	−	0.194511i
$225$	−8.04627	+	2.61439i	−0.536418	+	0.174293i
$226$	8.30039	−	2.69696i	0.552134	−	0.179399i
$227$	−9.20507	+	18.0660i	−0.610962	+	1.19908i	0.353643	+	0.935380i	$0.384943\pi$
$227$	−9.20507	+	18.0660i	−0.610962	+	1.19908i	−0.964605	+	0.263699i	$0.915057\pi$
$228$	18.0560	−	55.5707i	1.19579	−	3.68026i
$229$	0.332243	+	0.0526221i	0.0219552	+	0.00347736i	0.167402	−	0.985889i	$-0.446462\pi$
$229$	0.332243	+	0.0526221i	0.0219552	+	0.00347736i	−0.145447	+	0.989366i	$0.546462\pi$
$230$	−2.84893	−	8.76812i	−0.187853	−	0.578153i
$231$	−0.302537	−	1.91014i	−0.0199055	−	0.125678i
$232$	−1.86770	−	1.86770i	−0.122620	−	0.122620i
$233$	5.88436	+	11.5487i	0.385497	+	0.756581i	0.999464	−	0.0327513i	$-0.0104269\pi$
$233$	5.88436	+	11.5487i	0.385497	+	0.756581i	−0.613966	+	0.789332i	$0.710427\pi$
$234$	−21.4532	+	3.39785i	−1.40244	+	0.222124i
$235$	0.994645	−	6.27994i	0.0648835	−	0.409658i
$236$	20.4838	−	14.8823i	1.33338	−	0.968757i
$237$			14.1621i			0.919930i
$238$	15.2345	+	20.9685i	0.987508	+	1.35919i
$239$	−10.5772	−	5.38936i	−0.684183	−	0.348609i	0.0771047	−	0.997023i	$-0.475432\pi$
$239$	−10.5772	−	5.38936i	−0.684183	−	0.348609i	−0.761288	+	0.648414i	$0.775432\pi$
$240$	18.2875	−	9.31794i	1.18045	−	0.601470i
$241$	15.9932	−	22.0128i	1.03021	−	1.41797i	0.125428	−	0.992103i	$-0.459970\pi$
$241$	15.9932	−	22.0128i	1.03021	−	1.41797i	0.904787	−	0.425865i	$-0.140030\pi$
$242$	−21.1945	−	15.3987i	−1.36243	−	0.989865i
$243$	−14.7949	+	14.7949i	−0.949091	+	0.949091i
$244$	23.2978	+	7.56992i	1.49149	+	0.484615i
$245$	7.45593			0.476342
$246$	25.5844	+	26.1659i	1.63120	+	1.66828i
$247$	−22.2811			−1.41771
$248$	5.18219	+	1.68380i	0.329070	+	0.106921i
$249$	−25.8103	+	25.8103i	−1.63566	+	1.63566i
$250$	9.80667	+	7.12496i	0.620228	+	0.450622i
$251$	−0.796453	+	1.09622i	−0.0502716	+	0.0691930i	−0.833413	−	0.552651i	$-0.813616\pi$
$251$	−0.796453	+	1.09622i	−0.0502716	+	0.0691930i	0.783141	+	0.621844i	$0.213616\pi$
$252$	−18.6370	+	9.49603i	−1.17402	+	0.598193i
$253$	−0.461044	−	0.234914i	−0.0289856	−	0.0147689i
$254$	−14.5242	−	19.9909i	−0.911331	−	1.25434i
$255$		−	34.7687i		−	2.17730i
$256$	24.2879	−	17.6462i	1.51800	−	1.10289i
$257$	−0.826496	+	5.21829i	−0.0515554	+	0.325508i	0.948409	+	0.317050i	$0.102692\pi$
$257$	−0.826496	+	5.21829i	−0.0515554	+	0.325508i	−0.999964	+	0.00845795i	$0.997308\pi$
$258$	55.9525	−	8.86200i	3.48345	−	0.551724i
$259$	2.44891	+	4.80625i	0.152168	+	0.298646i
$260$	−26.9159	−	26.9159i	−1.66925	−	1.66925i
$261$	−0.242957	−	1.53397i	−0.0150387	−	0.0949505i
$262$	−7.74681	−	23.8422i	−0.478599	−	1.47298i
$263$	−2.33090	−	0.369179i	−0.143730	−	0.0227645i	0.0841550	−	0.996453i	$-0.473181\pi$
$263$	−2.33090	−	0.369179i	−0.143730	−	0.0227645i	−0.227885	+	0.973688i	$0.573181\pi$
$264$	1.25963	−	3.87674i	0.0775248	−	0.238597i
$265$	7.05310	−	13.8425i	0.433269	−	0.850338i
$266$	−31.0576	+	10.0912i	−1.90426	+	0.618733i
$267$	−0.753138	+	0.244709i	−0.0460913	+	0.0149760i
$268$	−9.72186	+	19.0802i	−0.593857	+	1.16551i
$269$	−5.22162	+	16.0705i	−0.318368	+	0.979835i	0.655978	+	0.754780i	$0.272256\pi$
$269$	−5.22162	+	16.0705i	−0.318368	+	0.979835i	−0.974346	+	0.225055i	$0.927744\pi$
$270$	−6.46997	−	1.02474i	−0.393750	−	0.0623639i
$271$	6.54109	+	20.1314i	0.397343	+	1.22290i	0.927122	+	0.374760i	$0.122275\pi$
$271$	6.54109	+	20.1314i	0.397343	+	1.22290i	−0.529779	+	0.848136i	$0.677725\pi$
$272$	2.41508	+	15.2482i	0.146436	+	0.924558i
$273$	12.1451	+	12.1451i	0.735053	+	0.735053i
$274$	−4.20836	−	8.25937i	−0.254236	−	0.498967i
$275$	−1.25090	+	0.198124i	−0.0754323	+	0.0119473i
$276$	−1.88524	+	11.9029i	−0.113478	+	0.716472i
$277$	−9.22338	+	6.70118i	−0.554179	+	0.402635i	−0.829324	−	0.558768i	$-0.811274\pi$
$277$	−9.22338	+	6.70118i	−0.554179	+	0.402635i	0.275145	+	0.961403i	$0.411274\pi$
$278$		−	16.3835i		−	0.982618i
$279$	1.88322	+	2.59204i	0.112746	+	0.155181i
$280$	−23.7629	−	12.1078i	−1.42011	−	0.723581i
$281$	24.0979	−	12.2785i	1.43756	−	0.732474i	0.450494	−	0.892779i	$-0.351248\pi$
$281$	24.0979	−	12.2785i	1.43756	−	0.732474i	0.987068	+	0.160305i	$0.0512477\pi$
$282$	−7.43514	+	10.2336i	−0.442756	+	0.609402i
$283$	−9.07709	−	6.59489i	−0.539577	−	0.392026i	0.284351	−	0.958720i	$-0.408222\pi$
$283$	−9.07709	−	6.59489i	−0.539577	−	0.392026i	−0.823928	+	0.566695i	$0.808222\pi$
$284$	−18.9733	+	18.9733i	−1.12586	+	1.12586i
$285$	41.6626	+	13.5370i	2.46788	+	0.801863i
$286$	−3.25152			−0.192267
$287$	2.25123	−	13.2484i	0.132886	−	0.782030i
$288$	4.04928			0.238606
$289$	8.70462	+	2.82830i	0.512037	+	0.166371i
$290$	2.92912	−	2.92912i	0.172004	−	0.172004i
$291$	−27.6116	−	20.0610i	−1.61862	−	1.17600i
$292$	32.6541	−	44.9446i	1.91094	−	2.63018i
$293$	19.3154	−	9.84170i	1.12842	−	0.574958i	0.212837	−	0.977088i	$-0.431730\pi$
$293$	19.3154	−	9.84170i	1.12842	−	0.574958i	0.915583	+	0.402129i	$0.131730\pi$
$294$	−13.2165	−	6.73416i	−0.770804	−	0.392744i
$295$	11.1576	+	15.3571i	0.649621	+	0.894127i
$296$			11.3695i			0.660837i
$297$	−0.297441	+	0.216104i	−0.0172593	+	0.0125396i
$298$	−4.81931	+	30.4279i	−0.279175	+	1.76264i
$299$	4.53889	−	0.718890i	0.262491	−	0.0415745i
$300$	13.3913	+	26.2819i	0.773148	+	1.51739i
$301$	−14.7097	−	14.7097i	−0.847854	−	0.847854i
$302$	−1.01516	−	6.40945i	−0.0584157	−	0.368822i
$303$	−8.39239	−	25.8291i	−0.482130	−	1.48385i
$304$	−19.2119	−	3.04286i	−1.10188	−	0.174520i
$305$	−5.67534	+	17.4669i	−0.324969	+	1.00015i
$306$	−14.5830	+	28.6208i	−0.833656	+	1.63614i
$307$	−16.4573	+	5.34729i	−0.939267	+	0.305186i	−0.738347	−	0.674421i	$-0.764393\pi$
$307$	−16.4573	+	5.34729i	−0.939267	+	0.305186i	−0.200920	+	0.979608i	$0.564393\pi$
$308$	−2.97795	+	0.967594i	−0.169684	+	0.0551338i
$309$	14.0511	−	27.5767i	0.799337	−	1.56879i
$310$	−2.64071	+	8.12726i	−0.149982	+	0.461597i
$311$	−11.9416	−	1.89137i	−0.677148	−	0.107250i	−0.191618	−	0.981470i	$-0.561373\pi$
$311$	−11.9416	−	1.89137i	−0.677148	−	0.107250i	−0.485530	+	0.874220i	$0.661373\pi$
$312$	11.1869	+	34.4299i	0.633336	+	1.94921i
$313$	−3.39130	−	21.4118i	−0.191688	−	1.21027i	−0.876447	−	0.481499i	$-0.840093\pi$
$313$	−3.39130	−	21.4118i	−0.191688	−	1.21027i	0.684759	−	0.728770i	$-0.259907\pi$
$314$	−17.7350	−	17.7350i	−1.00085	−	1.00085i
$315$	−7.11938	−	13.9726i	−0.401132	−	0.787265i
$316$	22.6471	−	3.58695i	1.27400	−	0.201782i
$317$	−3.09471	+	19.5392i	−0.173816	+	1.09743i	0.734334	+	0.678788i	$0.237494\pi$
$317$	−3.09471	+	19.5392i	−0.173816	+	1.09743i	−0.908150	+	0.418644i	$0.862506\pi$
$318$	−25.0050	+	18.1672i	−1.40221	+	1.01876i
$319$		−	0.232495i		−	0.0130172i
$320$	16.5432	+	22.7698i	0.924795	+	1.27287i
$321$	14.5435	+	7.41028i	0.811739	+	0.413601i
$322$	6.00117	−	3.05775i	0.334432	−	0.170402i
$323$	−19.3680	+	26.6577i	−1.07766	+	1.48328i
$324$	31.1166	+	22.6075i	1.72870	+	1.25597i
$325$	7.95349	−	7.95349i	0.441180	−	0.441180i
$326$	−8.00778	−	2.60189i	−0.443510	−	0.144105i
$327$	19.3960			1.07260
$328$	16.9051	−	22.7263i	0.933426	−	1.25485i
$329$	4.64505			0.256090
$330$	6.07991	+	1.97548i	0.334688	+	0.108747i
$331$	20.3952	−	20.3952i	1.12102	−	1.12102i	0.129436	−	0.991588i	$-0.458683\pi$
$331$	20.3952	−	20.3952i	1.12102	−	1.12102i	0.991588	−	0.129436i	$-0.0413166\pi$
$332$	47.8112	+	34.7369i	2.62398	+	1.90643i
$333$	−3.92948	+	5.40846i	−0.215334	+	0.296382i
$334$	−42.0683	+	21.4349i	−2.30188	+	1.17287i
$335$	−14.3049	−	7.28869i	−0.781558	−	0.398224i
$336$	8.81347	+	12.1307i	0.480814	+	0.661784i
$337$			23.4367i			1.27668i	0.769754	+	0.638340i	$0.220379\pi$
$337$			23.4367i			1.27668i	−0.769754	+	0.638340i	$0.779621\pi$
$338$	−2.03590	+	1.47917i	−0.110738	+	0.0804561i
$339$	1.33801	−	8.44784i	0.0726706	−	0.458824i
$340$	−55.5998	+	8.80615i	−3.01532	+	0.477580i
$341$	0.217744	+	0.427346i	0.0117915	+	0.0231421i
$342$	−28.6178	−	28.6178i	−1.54748	−	1.54748i
$343$	3.15028	+	19.8901i	0.170099	+	1.07396i
$344$	−13.5493	−	41.7004i	−0.730528	−	2.24833i
$345$	−8.92388	−	1.41340i	−0.480446	−	0.0760951i
$346$	−9.01992	+	27.7605i	−0.484914	+	1.49241i
$347$	6.09771	−	11.9674i	0.327342	−	0.642445i	−0.667418	−	0.744684i	$-0.732600\pi$
$347$	6.09771	−	11.9674i	0.327342	−	0.642445i	0.994760	+	0.102238i	$0.0326004\pi$
$348$	−5.14982	+	1.67328i	−0.276059	+	0.0896971i
$349$	−10.5919	+	3.44151i	−0.566970	+	0.184220i	−0.578455	−	0.815714i	$-0.696344\pi$
$349$	−10.5919	+	3.44151i	−0.566970	+	0.184220i	0.0114848	+	0.999934i	$0.496344\pi$
$350$	7.48419	−	14.6885i	0.400047	−	0.785136i
$351$	1.00901	−	3.10541i	0.0538569	−	0.165755i
$352$	0.598706	+	0.0948257i	0.0319111	+	0.00505423i
$353$	−4.34026	−	13.3579i	−0.231009	−	0.710971i	−0.997626	−	0.0688670i	$-0.978062\pi$
$353$	−4.34026	−	13.3579i	−0.231009	−	0.710971i	0.766617	−	0.642104i	$-0.221938\pi$
$354$	−5.90772	−	37.2999i	−0.313992	−	1.98247i
$355$	−14.2247	−	14.2247i	−0.754968	−	0.754968i
$356$	0.582075	+	1.14239i	0.0308499	+	0.0605464i
$357$	25.0879	−	3.97353i	1.32779	−	0.210302i
$358$	0.753123	−	4.75503i	0.0398038	−	0.251311i
$359$	23.2237	−	16.8730i	1.22570	−	0.890521i	0.229137	−	0.973394i	$-0.426409\pi$
$359$	23.2237	−	16.8730i	1.22570	−	0.890521i	0.996560	+	0.0828726i	$0.0264095\pi$
$360$		−	33.0529i		−	1.74204i
$361$	−13.2346	−	18.2159i	−0.696560	−	0.958733i
$362$	34.9319	+	17.7987i	1.83598	+	0.935479i
$363$	−22.8760	+	11.6559i	−1.20068	+	0.611776i
$364$	16.3455	−	22.4976i	0.856737	−	1.17920i
$365$	33.6959	+	24.4815i	1.76373	+	1.28142i
$366$	25.8362	−	25.8362i	1.35048	−	1.35048i
$367$	−21.1292	−	6.86529i	−1.10293	−	0.358365i	−0.299703	−	0.954032i	$-0.596888\pi$
$367$	−21.1292	−	6.86529i	−1.10293	−	0.358365i	−0.803231	+	0.595667i	$0.796888\pi$
$368$	4.01184			0.209131
$369$	15.8963	−	4.96826i	0.827531	−	0.258637i
$370$	−17.8308			−0.926978
$371$	10.7943	+	3.50729i	0.560413	+	0.182089i
$372$	7.89871	−	7.89871i	0.409529	−	0.409529i
$373$	14.0050	+	10.1752i	0.725149	+	0.526852i	0.888025	−	0.459795i	$-0.152077\pi$
$373$	14.0050	+	10.1752i	0.725149	+	0.526852i	−0.162876	+	0.986647i	$0.552077\pi$
$374$	−2.82641	+	3.89022i	−0.146150	+	0.201158i
$375$	10.5847	−	5.39318i	0.546592	−	0.278502i
$376$	8.72340	+	4.44479i	0.449875	+	0.229223i
$377$	1.21367	+	1.67047i	0.0625072	+	0.0860337i
$378$		−	4.78562i		−	0.246146i
$379$	−2.13917	+	1.55420i	−0.109882	+	0.0798339i	−0.641369	−	0.767232i	$-0.721633\pi$
$379$	−2.13917	+	1.55420i	−0.109882	+	0.0798339i	0.531487	+	0.847066i	$0.321633\pi$
$380$	11.0952	−	70.0526i	0.569174	−	3.59362i
$381$	−23.9182	+	3.78827i	−1.22537	+	0.194079i
$382$	−6.06488	−	11.9030i	−0.310306	−	0.609011i
$383$	20.4903	+	20.4903i	1.04701	+	1.04701i	0.998839	+	0.0481661i	$0.0153377\pi$
$383$	20.4903	+	20.4903i	1.04701	+	1.04701i	0.0481661	+	0.998839i	$0.484662\pi$
$384$	−7.60656	−	48.0259i	−0.388170	−	2.45081i
$385$	−0.725426	−	2.23263i	−0.0369711	−	0.113785i
$386$	20.0666	+	3.17823i	1.02136	+	0.161768i
$387$	7.96695	−	24.5197i	0.404983	−	1.24641i
$388$	−25.0868	+	49.2356i	−1.27359	+	2.49956i
$389$	20.1771	−	6.55595i	1.02302	−	0.332400i	0.250994	−	0.967989i	$-0.419243\pi$
$389$	20.1771	−	6.55595i	1.02302	−	0.332400i	0.772028	+	0.635589i	$0.219243\pi$
$390$	−53.9965	+	17.5445i	−2.73422	+	0.888402i
$391$	3.08536	−	6.05536i	0.156033	−	0.306233i
$392$	−3.54775	+	10.9189i	−0.179189	+	0.551486i
$393$	−24.2658	−	3.84332i	−1.22405	−	0.193870i
$394$	19.5632	+	60.2092i	0.985578	+	3.03330i
$395$	2.68922	+	16.9791i	0.135309	+	0.854309i
$396$	−2.74401	−	2.74401i	−0.137892	−	0.137892i
$397$	2.06513	+	4.05305i	0.103646	+	0.203417i	0.937006	−	0.349315i	$-0.113586\pi$
$397$	2.06513	+	4.05305i	0.103646	+	0.203417i	−0.833359	+	0.552731i	$0.813586\pi$
$398$	−26.9520	+	4.26878i	−1.35098	+	0.213974i
$399$	−5.00643	+	31.6093i	−0.250635	+	1.58245i
$400$	7.94408	−	5.77171i	0.397204	−	0.288586i
$401$		−	7.53484i		−	0.376272i	−0.982143	−	0.188136i	$-0.939755\pi$
$401$		−	7.53484i		−	0.376272i	0.982143	−	0.188136i	$-0.0602446\pi$
$402$	18.7740	+	25.8402i	0.936361	+	1.28879i
$403$	−3.79532	−	1.93381i	−0.189058	−	0.0963301i
$404$	−39.1786	+	19.9625i	−1.94921	+	0.993171i
$405$	−16.9494	+	23.3288i	−0.842221	+	1.15922i
$406$	2.44830	+	1.77879i	0.121507	+	0.0882801i
$407$	−0.707647	+	0.707647i	−0.0350767	+	0.0350767i
$408$	50.9172	+	16.5440i	2.52078	+	0.819051i
$409$	1.03548			0.0512013			0.0256007	−	0.999672i	$-0.491850\pi$
$409$	1.03548			0.0512013			0.0256007	+	0.999672i	$0.491850\pi$
$410$	35.6418	+	26.5123i	1.76022	+	1.30935i
$411$	−9.08448			−0.448104
$412$	−47.6577	−	15.4849i	−2.34793	−	0.762887i
$413$	−9.80602	+	9.80602i	−0.482523	+	0.482523i
$414$	6.75310	+	4.90641i	0.331897	+	0.241137i
$415$	−26.0430	+	35.8451i	−1.27840	+	1.75957i
$416$	−4.79671	+	2.44405i	−0.235178	+	0.119829i
$417$	−14.3061	−	7.28933i	−0.700573	−	0.356960i
$418$	−3.56111	−	4.90145i	−0.174180	−	0.239738i
$419$			5.57406i			0.272310i	0.990688	+	0.136155i	$0.0434746\pi$
$419$			5.57406i			0.272310i	−0.990688	+	0.136155i	$0.956525\pi$
$420$	−44.2324	+	32.1367i	−2.15832	+	1.56811i
$421$	4.88611	−	30.8497i	0.238134	−	1.50352i	−0.521546	−	0.853223i	$-0.674644\pi$
$421$	4.88611	−	30.8497i	0.238134	−	1.50352i	0.759680	−	0.650297i	$-0.225356\pi$
$422$	12.6857	−	2.00922i	0.617530	−	0.0978071i
$423$	2.61353	+	5.12934i	0.127074	+	0.249397i
$424$	16.9156	+	16.9156i	0.821495	+	0.821495i
$425$	−2.60216	−	16.4294i	−0.126223	−	0.796944i
$426$	12.3673	+	38.0627i	0.599198	+	1.84414i
$427$	−13.2521	−	2.09893i	−0.641314	−	0.101574i
$428$	8.16647	−	25.1338i	0.394741	−	1.21489i
$429$	−1.44666	+	2.83924i	−0.0698456	+	0.137080i
$430$	65.3989	−	21.2494i	3.15381	−	1.02474i
$431$	14.2216	−	4.62089i	0.685031	−	0.222580i	0.0542346	−	0.998528i	$-0.482728\pi$
$431$	14.2216	−	4.62089i	0.685031	−	0.222580i	0.630797	+	0.775948i	$0.282728\pi$
$432$	1.29411	−	2.53984i	0.0622631	−	0.122198i
$433$	5.42213	−	16.6876i	0.260571	−	0.801955i	−0.732110	−	0.681187i	$-0.761464\pi$
$433$	5.42213	−	16.6876i	0.260571	−	0.801955i	0.992681	−	0.120769i	$-0.0385359\pi$
$434$	−6.16613	−	0.976620i	−0.295984	−	0.0468792i
$435$	−1.25449	−	3.86093i	−0.0601483	−	0.185117i
$436$	−4.91258	−	31.0168i	−0.235270	−	1.48544i
$437$	6.05474	+	6.05474i	0.289637	+	0.289637i
$438$	−37.6185	−	73.8305i	−1.79748	−	3.52776i
$439$	−6.74843	+	1.06885i	−0.322085	+	0.0510133i	−0.315384	−	0.948964i	$-0.602133\pi$
$439$	−6.74843	+	1.06885i	−0.322085	+	0.0510133i	−0.00670154	+	0.999978i	$0.502133\pi$
$440$	0.774029	−	4.88703i	0.0369004	−	0.232980i
$441$	−5.46141	+	3.96795i	−0.260067	+	0.188950i
$442$		−	42.7056i		−	2.03130i
$443$	4.96856	+	6.83863i	0.236063	+	0.324913i	0.910570	−	0.413356i	$-0.135643\pi$
$443$	4.96856	+	6.83863i	0.236063	+	0.324913i	−0.674506	+	0.738269i	$0.735643\pi$
$444$	20.7675	+	10.5816i	0.985583	+	0.502180i
$445$	−0.856473	+	0.436395i	−0.0406007	+	0.0206871i
$446$	−9.95355	+	13.6999i	−0.471314	+	0.648708i
$447$	24.4255	+	17.7462i	1.15529	+	0.839365i
$448$	−14.5392	+	14.5392i	−0.686915	+	0.686915i
$449$	2.96928	+	0.964777i	0.140129	+	0.0455307i	0.378242	−	0.925707i	$-0.376529\pi$
$449$	2.96928	+	0.964777i	0.140129	+	0.0455307i	−0.238113	+	0.971238i	$0.576529\pi$
$450$	20.4309			0.963123
$451$	2.46670	−	0.362322i	0.116152	−	0.0170611i
$452$	−13.8481			−0.651360
$453$	−6.04840	−	1.96525i	−0.284179	−	0.0923353i
$454$	34.6230	−	34.6230i	1.62494	−	1.62494i
$455$	16.8670	+	12.2546i	0.790736	+	0.574503i
$456$	−39.6486	+	54.5717i	−1.85672	+	2.55555i
$457$	9.87764	−	5.03291i	0.462057	−	0.235430i	−0.207436	−	0.978249i	$-0.566512\pi$
$457$	9.87764	−	5.03291i	0.462057	−	0.235430i	0.669492	+	0.742819i	$0.266512\pi$
$458$	−0.723796	−	0.368792i	−0.0338208	−	0.0172325i
$459$	−2.83832	−	3.90661i	−0.132481	−	0.182345i
$460$			14.6284i			0.682055i
$461$	−14.4831	+	10.5226i	−0.674543	+	0.490084i	−0.871543	−	0.490319i	$-0.836880\pi$
$461$	−14.4831	+	10.5226i	−0.674543	+	0.490084i	0.197000	+	0.980404i	$0.436880\pi$
$462$	−0.730598	+	4.61281i	−0.0339905	+	0.214607i
$463$	−16.2174	+	2.56859i	−0.753689	+	0.119373i	−0.521445	−	0.853285i	$-0.674607\pi$
$463$	−16.2174	+	2.56859i	−0.753689	+	0.119373i	−0.232244	+	0.972658i	$0.574607\pi$
$464$	0.818355	+	1.60611i	0.0379912	+	0.0745619i
$465$	5.92184	+	5.92184i	0.274619	+	0.274619i
$466$	−4.89649	−	30.9152i	−0.226825	−	1.43212i
$467$	−3.86982	−	11.9101i	−0.179074	−	0.551132i	0.820722	−	0.571327i	$-0.193571\pi$
$467$	−3.86982	−	11.9101i	−0.179074	−	0.551132i	−0.999796	+	0.0201950i	$0.993571\pi$
$468$	34.0400	+	5.39141i	1.57350	+	0.249218i
$469$	3.62443	−	11.1549i	0.167361	−	0.515084i
$470$	−6.97079	+	13.6809i	−0.321539	+	0.631055i
$471$	−23.3769	+	7.59561i	−1.07715	+	0.349987i
$472$	−27.7989	+	9.03242i	−1.27955	+	0.415751i
$473$	1.75215	−	3.43879i	0.0805640	−	0.158116i
$474$	10.5684	−	32.5263i	0.485425	−	1.49398i
$475$	20.7001	+	3.27858i	0.949787	+	0.150432i
$476$	−12.7084	−	39.1125i	−0.582489	−	1.79272i
$477$	2.20045	+	13.8931i	0.100752	+	0.636121i
$478$	20.2710	+	20.2710i	0.927174	+	0.927174i
$479$	−3.18557	−	6.25203i	−0.145552	−	0.285663i	0.806708	−	0.590951i	$-0.201247\pi$
$479$	−3.18557	−	6.25203i	−0.145552	−	0.285663i	−0.952260	+	0.305288i	$0.901247\pi$
$480$	10.4541	−	1.65577i	0.477162	−	0.0755750i
$481$	1.39038	−	8.77850i	0.0633958	−	0.400265i
$482$	−53.1587	+	38.6221i	−2.42131	+	1.75919i
$483$		−	6.60069i		−	0.300342i
$484$	24.4333	+	33.6295i	1.11060	+	1.52862i
$485$	−36.9130	−	18.8081i	−1.67613	−	0.854032i
$486$	45.0201	−	22.9389i	2.04215	−	1.04053i
$487$	17.4933	−	24.0774i	0.792695	−	1.09105i	−0.201072	−	0.979576i	$-0.564443\pi$
$487$	17.4933	−	24.0774i	0.792695	−	1.09105i	0.993767	−	0.111475i	$-0.0355575\pi$
$488$	−22.8790	−	16.6225i	−1.03568	−	0.752467i
$489$	−5.83479	+	5.83479i	−0.263858	+	0.263858i
$490$	−17.1241	−	5.56396i	−0.773588	−	0.251354i
$491$	−31.3635			−1.41542			−0.707708	−	0.706505i	$-0.750271\pi$
$491$	−31.3635			−1.41542			−0.707708	+	0.706505i	$0.750271\pi$
$492$	−25.7785	−	52.0303i	−1.16218	−	2.34571i
$493$	3.05359			0.137527
$494$	51.1732	+	16.6272i	2.30239	+	0.748092i
$495$	2.05725	−	2.05725i	0.0924663	−	0.0924663i
$496$	−3.00842	−	2.18575i	−0.135082	−	0.0981429i
$497$	8.63837	−	11.8897i	0.387484	−	0.533326i
$498$	78.5396	−	40.0179i	3.51944	−	1.79325i
$499$	23.9083	+	12.1819i	1.07028	+	0.545335i	0.898127	−	0.439735i	$-0.144928\pi$
$499$	23.9083	+	12.1819i	1.07028	+	0.545335i	0.172153	+	0.985070i	$0.444928\pi$
$500$	−11.3053	−	15.5604i	−0.505587	−	0.695881i
$501$			46.2710i			2.06723i
$502$	2.64727	−	1.92336i	0.118154	−	0.0858436i
$503$	3.75693	−	23.7203i	0.167513	−	1.05764i	−0.750437	−	0.660942i	$-0.770157\pi$
$503$	3.75693	−	23.7203i	0.167513	−	1.05764i	0.917950	−	0.396695i	$-0.129843\pi$
$504$	23.8498	−	3.77744i	1.06235	−	0.168260i
$505$	−14.9663	−	29.3731i	−0.665992	−	1.30708i
$506$	0.883580	+	0.883580i	0.0392799	+	0.0392799i
$507$	0.385803	+	2.43586i	0.0171341	+	0.108180i
$508$	12.1159	+	37.2889i	0.537555	+	1.65443i
$509$	−14.6108	−	2.31412i	−0.647612	−	0.102572i	−0.176017	−	0.984387i	$-0.556321\pi$
$509$	−14.6108	−	2.31412i	−0.647612	−	0.102572i	−0.471595	+	0.881815i	$0.656321\pi$
$510$	−25.9460	+	79.8537i	−1.14891	+	3.53598i
$511$	−13.8141	+	27.1116i	−0.611099	+	1.19935i
$512$	−29.8704	+	9.70548i	−1.32010	+	0.428926i
$513$	5.78628	−	1.88008i	0.255470	−	0.0830074i
$514$	5.79235	−	11.3681i	0.255489	−	0.501426i
$515$	11.6094	−	35.7300i	0.511571	−	1.57445i
$516$	−88.7805	−	14.0614i	−3.90834	−	0.619020i
$517$	0.266305	+	0.819602i	0.0117121	+	0.0360460i
$518$	−2.03778	−	12.8661i	−0.0895351	−	0.565302i
$519$	20.2274	+	20.2274i	0.887883	+	0.887883i
$520$	19.9499	+	39.1539i	0.874860	+	1.71701i
$521$	−16.0123	+	2.53611i	−0.701513	+	0.111109i	−0.496994	−	0.867754i	$-0.665563\pi$
$521$	−16.0123	+	2.53611i	−0.701513	+	0.111109i	−0.204519	+	0.978863i	$0.565563\pi$
$522$	−0.586718	+	3.70439i	−0.0256800	+	0.162137i
$523$	2.29692	−	1.66881i	0.100437	−	0.0729721i	−0.536433	−	0.843943i	$-0.680229\pi$
$523$	2.29692	−	1.66881i	0.100437	−	0.0729721i	0.636870	+	0.770971i	$0.280229\pi$
$524$			39.7776i			1.73769i
$525$	−9.49621	−	13.0704i	−0.414449	−	0.570440i
$526$	5.07791	+	2.58732i	0.221407	+	0.112813i
$527$	−5.61278	+	2.85985i	−0.244497	+	0.124577i
$528$	−1.63513	+	2.25057i	−0.0711600	+	0.0979433i
$529$	17.1786	+	12.4810i	0.746897	+	0.542652i
$530$	−26.5288	+	26.5288i	−1.15234	+	1.15234i
$531$	−16.3457	−	5.31105i	−0.709344	−	0.230480i
$532$	51.8155			2.24649
$533$	−15.8318	+	15.4799i	−0.685752	+	0.670511i
$534$	1.91235			0.0827555
$535$	18.8434	+	6.12258i	0.814670	+	0.264702i
$536$	17.4806	−	17.4806i	0.755048	−	0.755048i
$537$	−3.81703	−	2.77323i	−0.164717	−	0.119674i
$538$	23.9851	−	33.0126i	1.03407	−	1.42328i
$539$	−0.900417	+	0.458785i	−0.0387837	+	0.0197613i
$540$	9.26108	+	4.71876i	0.398534	+	0.203063i
$541$	15.1869	+	20.9030i	0.652938	+	0.898691i	0.999222	−	0.0394382i	$-0.0125568\pi$
$541$	15.1869	+	20.9030i	0.652938	+	0.898691i	−0.346284	+	0.938130i	$0.612557\pi$
$542$		−	51.1173i		−	2.19567i
$543$	31.0837	−	22.5836i	1.33393	−	0.969157i
$544$	−1.24544	+	7.86343i	−0.0533980	+	0.337142i
$545$	23.2540	−	3.68307i	0.996091	−	0.157765i
$546$	−18.8305	−	36.9569i	−0.805870	−	1.58161i
$547$	−31.0360	−	31.0360i	−1.32700	−	1.32700i	−0.907971	−	0.419032i	$-0.862369\pi$
$547$	−31.0360	−	31.0360i	−1.32700	−	1.32700i	−0.419032	−	0.907971i	$-0.637631\pi$
$548$	2.30090	+	14.5273i	0.0982894	+	0.620575i
$549$	−5.13851	−	15.8147i	−0.219306	−	0.674955i
$550$	3.02081	+	0.478450i	0.128808	+	0.0204012i
$551$	−1.18890	+	3.65905i	−0.0506488	+	0.155881i
$552$	6.31611	−	12.3961i	0.268832	−	0.527612i
$553$	−11.9441	+	3.88089i	−0.507917	+	0.165032i
$554$	26.1842	−	8.50775i	1.11246	−	0.361460i
$555$	−7.93324	+	15.5699i	−0.336747	+	0.660904i
$556$	−8.03318	+	24.7236i	−0.340683	+	1.04851i
$557$	36.1001	+	5.71769i	1.52961	+	0.242266i	0.863792	−	0.503849i	$-0.168083\pi$
$557$	36.1001	+	5.71769i	1.52961	+	0.242266i	0.665817	+	0.746115i	$0.268083\pi$
$558$	−2.39092	−	7.35850i	−0.101216	−	0.311510i
$559$	5.36199	+	33.8543i	0.226788	+	1.43188i
$560$	12.8700	+	12.8700i	0.543856	+	0.543856i
$561$	2.13942	+	4.19886i	0.0903265	+	0.177276i
$562$	−64.5087	+	10.2172i	−2.72114	+	0.430986i
$563$	1.70284	−	10.7513i	0.0717661	−	0.453113i	−0.925470	−	0.378820i	$-0.876330\pi$
$563$	1.70284	−	10.7513i	0.0717661	−	0.453113i	0.997236	−	0.0742931i	$-0.0236700\pi$
$564$	16.2378	−	11.7974i	0.683734	−	0.496762i
$565$		−	10.3822i		−	0.436784i
$566$	15.9260	+	21.9203i	0.669421	+	0.921379i
$567$	−18.7703	−	9.56394i	−0.788278	−	0.401648i
$568$	27.5999	−	14.0629i	1.15807	−	0.590065i
$569$	6.39245	−	8.79845i	0.267985	−	0.368850i	−0.653723	−	0.756734i	$-0.726794\pi$
$569$	6.39245	−	8.79845i	0.267985	−	0.368850i	0.921708	+	0.387884i	$0.126794\pi$
$570$	−85.5850	−	62.1811i	−3.58476	−	2.60448i
$571$	−3.44644	+	3.44644i	−0.144229	+	0.144229i	−0.775534	−	0.631305i	$-0.782519\pi$
$571$	−3.44644	+	3.44644i	−0.144229	+	0.144229i	0.631305	+	0.775534i	$0.282519\pi$
$572$	4.90672	+	1.59429i	0.205160	+	0.0666606i
$573$	−13.0921			−0.546931
$574$	−15.0570	+	28.7478i	−0.628468	+	1.19991i
$575$	−4.32262			−0.180266
$576$	−24.2356	−	7.87462i	−1.00982	−	0.328109i
$577$	−27.6070	+	27.6070i	−1.14930	+	1.14930i	−0.162605	+	0.986691i	$0.551989\pi$
$577$	−27.6070	+	27.6070i	−1.14930	+	1.14930i	−0.986691	+	0.162605i	$0.948011\pi$
$578$	−17.8814	−	12.9916i	−0.743767	−	0.540379i
$579$	11.7032	−	16.1081i	0.486370	−	0.669430i
$580$	−5.85640	+	2.98399i	−0.243174	+	0.123903i
$581$	−28.8409	−	14.6952i	−1.19652	−	0.609658i
$582$	48.4453	+	66.6793i	2.00812	+	2.76395i
$583$			2.10569i			0.0872088i
$584$	−51.8856	+	37.6971i	−2.14704	+	1.55992i
$585$	−4.04205	+	25.5205i	−0.167118	+	1.05514i
$586$	−51.7063	+	8.18947i	−2.13597	+	0.338304i
$587$	−2.56196	−	5.02813i	−0.105743	−	0.207533i	0.832072	−	0.554668i	$-0.187155\pi$
$587$	−2.56196	−	5.02813i	−0.105743	−	0.207533i	−0.937815	+	0.347135i	$0.887155\pi$
$588$	16.6426	+	16.6426i	0.686327	+	0.686327i
$589$	−1.24160	−	7.83913i	−0.0511591	−	0.323006i
$590$	−14.1656	−	43.5972i	−0.583188	−	1.79487i
$591$	61.2788	+	9.70561i	2.52067	+	0.399236i
$592$	2.39771	−	7.37938i	0.0985451	−	0.303291i
$593$	2.04888	−	4.02116i	0.0841376	−	0.165129i	−0.845104	−	0.534602i	$-0.820462\pi$
$593$	2.04888	−	4.02116i	0.0841376	−	0.165129i	0.929242	+	0.369473i	$0.120462\pi$
$594$	0.844403	−	0.274363i	0.0346463	−	0.0112573i
$595$	29.3235	−	9.52777i	1.20214	−	0.390601i
$596$	22.1920	−	43.5543i	0.909022	−	1.78406i
$597$	−8.26394	+	25.4338i	−0.338221	+	1.04094i
$598$	−10.9610	−	1.73605i	−0.448228	−	0.0709924i
$599$	9.38078	+	28.8711i	0.383288	+	1.17964i	0.937715	+	0.347407i	$0.112938\pi$
$599$	9.38078	+	28.8711i	0.383288	+	1.17964i	−0.554426	+	0.832233i	$0.687062\pi$
$600$	−5.32695	−	33.6330i	−0.217472	−	1.37306i
$601$	10.5900	+	10.5900i	0.431977	+	0.431977i	0.889300	−	0.457324i	$-0.151192\pi$
$601$	10.5900	+	10.5900i	0.431977	+	0.431977i	−0.457324	+	0.889300i	$0.651192\pi$
$602$	22.8069	+	44.7610i	0.929539	+	1.82432i
$603$	14.3571	−	2.27395i	0.584668	−	0.0926023i
$604$	−1.61076	+	10.1699i	−0.0655410	+	0.413809i
$605$	−25.2128	+	18.3182i	−1.02505	+	0.744740i
$606$			65.5848i			2.66420i
$607$	11.3274	+	15.5908i	0.459764	+	0.632811i	0.974460	−	0.224562i	$-0.0720950\pi$
$607$	11.3274	+	15.5908i	0.459764	+	0.632811i	−0.514696	+	0.857373i	$0.672095\pi$
$608$	−8.93766	−	4.55397i	−0.362470	−	0.184688i
$609$	2.64254	−	1.34644i	0.107081	−	0.0545606i
$610$	26.0692	−	35.8812i	1.05551	−	1.45279i
$611$	−6.19188	−	4.49867i	−0.250497	−	0.181997i
$612$	36.0399	−	36.0399i	1.45683	−	1.45683i
$613$	11.6005	+	3.76925i	0.468542	+	0.152238i	0.533766	−	0.845632i	$-0.320776\pi$
$613$	11.6005	+	3.76925i	0.468542	+	0.152238i	−0.0652243	+	0.997871i	$0.520776\pi$
$614$	41.7880			1.68643
$615$	39.0083	−	19.3267i	1.57297	−	0.779327i
$616$	3.61477			0.145643
$617$	−20.3958	−	6.62699i	−0.821104	−	0.266793i	−0.131810	−	0.991275i	$-0.542079\pi$
$617$	−20.3958	−	6.62699i	−0.821104	−	0.266793i	−0.689293	+	0.724482i	$0.742079\pi$
$618$	−52.8502	+	52.8502i	−2.12595	+	2.12595i
$619$	−36.9222	−	26.8256i	−1.48403	−	1.07821i	−0.976230	−	0.216735i	$-0.930459\pi$
$619$	−36.9222	−	26.8256i	−1.48403	−	1.07821i	−0.507799	−	0.861476i	$-0.669541\pi$
$620$	7.96993	−	10.9697i	0.320080	−	0.440553i
$621$	−1.11807	+	0.569683i	−0.0448665	+	0.0228606i
$622$	26.0150	+	13.2553i	1.04311	+	0.531490i
$623$	−0.412769	−	0.568127i	−0.0165372	−	0.0227615i
$624$		−	24.7060i		−	0.989032i
$625$	24.8234	−	18.0353i	0.992937	−	0.721411i
$626$	−8.18966	+	51.7075i	−0.327325	+	2.06665i
$627$	−5.86437	+	0.928824i	−0.234200	+	0.0370937i
$628$	18.0672	+	35.4589i	0.720961	+	1.41497i
$629$	−9.29426	−	9.29426i	−0.370586	−	0.370586i
$630$	5.92417	+	37.4037i	0.236025	+	1.49020i
$631$	8.35237	+	25.7059i	0.332502	+	1.02334i	0.967939	+	0.251184i	$0.0808200\pi$
$631$	8.35237	+	25.7059i	0.332502	+	1.02334i	−0.635437	+	0.772153i	$0.719180\pi$
$632$	−26.1447	−	4.14091i	−1.03998	−	0.164716i
$633$	3.88965	−	11.9711i	0.154600	−	0.475809i
$634$	21.6887	−	42.5665i	0.861369	−	1.69053i
$635$	−27.9563	+	9.08354i	−1.10941	+	0.360469i
$636$	46.6416	−	15.1548i	1.84946	−	0.600926i
$637$	4.07454	−	7.99673i	0.161439	−	0.316842i
$638$	−0.173498	+	0.533973i	−0.00686886	+	0.0211402i
$639$	17.9897	+	2.84928i	0.711660	+	0.112716i
$640$	−18.2391	−	56.1341i	−0.720962	−	2.21889i
$641$	2.19761	+	13.8752i	0.0868005	+	0.548037i	0.992317	+	0.123725i	$0.0394840\pi$
$641$	2.19761	+	13.8752i	0.0868005	+	0.548037i	−0.905516	+	0.424312i	$0.860516\pi$
$642$	−27.8723	−	27.8723i	−1.10003	−	1.10003i
$643$	9.30874	+	18.2694i	0.367101	+	0.720476i	0.998487	−	0.0549930i	$-0.0175137\pi$
$643$	9.30874	+	18.2694i	0.367101	+	0.720476i	−0.631386	+	0.775469i	$0.717514\pi$
$644$	−10.5554	+	1.67181i	−0.415940	+	0.0658784i
$645$	10.5422	−	66.5607i	0.415098	−	2.62082i
$646$	64.3759	−	46.7718i	2.53283	−	1.84021i
$647$			15.8806i			0.624333i	0.950027	+	0.312166i	$0.101055\pi$
$647$			15.8806i			0.624333i	−0.950027	+	0.312166i	$0.898945\pi$
$648$	−26.0989	−	35.9221i	−1.02526	−	1.41115i
$649$	−2.29242	−	1.16805i	−0.0899854	−	0.0458498i
$650$	−24.2021	+	12.3316i	−0.949285	+	0.483685i
$651$	−3.59621	+	4.94976i	−0.140947	+	0.193997i
$652$	10.8084	+	7.85277i	0.423290	+	0.307538i
$653$	22.9902	−	22.9902i	0.899676	−	0.899676i	−0.0957311	−	0.995407i	$-0.530519\pi$
$653$	22.9902	−	22.9902i	0.899676	−	0.899676i	0.995407	+	0.0957311i	$0.0305189\pi$
$654$	−44.5470	−	14.4742i	−1.74193	−	0.565986i
$655$	−29.8222			−1.16525
$656$	−15.7650	+	11.1855i	−0.615521	+	0.436720i
$657$	−37.7108			−1.47124
$658$	−10.6683	−	3.46635i	−0.415895	−	0.135133i
$659$	1.46743	−	1.46743i	0.0571629	−	0.0571629i	−0.677947	−	0.735110i	$-0.737130\pi$
$659$	1.46743	−	1.46743i	0.0571629	−	0.0571629i	0.735110	+	0.677947i	$0.237130\pi$
$660$	−8.20628	−	5.96221i	−0.319429	−	0.232079i
$661$	−18.2310	+	25.0928i	−0.709103	+	0.975997i	0.290713	+	0.956810i	$0.406108\pi$
$661$	−18.2310	+	25.0928i	−0.709103	+	0.975997i	−0.999816	+	0.0191863i	$0.993892\pi$
$662$	−62.0618	+	31.6221i	−2.41210	+	1.22903i
$663$	−37.2906	−	19.0005i	−1.44825	−	0.737919i
$664$	−40.1015	−	55.1950i	−1.55624	−	2.14198i
$665$			38.8472i			1.50643i
$666$	13.0609	−	9.48931i	0.506100	−	0.367703i
$667$	0.124133	−	0.783747i	0.00480646	−	0.0303468i
$668$	73.9934	−	11.7194i	2.86289	−	0.453437i
$669$	7.53425	+	14.7868i	0.291291	+	0.571691i
$670$	27.4149	+	27.4149i	1.05913	+	1.05913i
$671$	−0.389406	−	2.45861i	−0.0150329	−	0.0949137i
$672$	2.38948	+	7.35407i	0.0921763	+	0.283690i
$673$	−1.93008	−	0.305695i	−0.0743992	−	0.0117837i	0.119124	−	0.992879i	$-0.461991\pi$
$673$	−1.93008	−	0.305695i	−0.0743992	−	0.0117837i	−0.193523	+	0.981096i	$0.561991\pi$
$674$	17.4896	−	53.8274i	0.673673	−	2.07335i
$675$	−1.39436	+	2.73659i	−0.0536691	+	0.105332i
$676$	3.79755	−	1.23390i	0.146060	−	0.0474576i
$677$	17.1066	−	5.55828i	0.657461	−	0.213622i	0.0387601	−	0.999249i	$-0.487659\pi$
$677$	17.1066	−	5.55828i	0.657461	−	0.213622i	0.618701	+	0.785626i	$0.287659\pi$
$678$	−9.37718	+	18.4038i	−0.360129	+	0.706792i
$679$	9.35267	−	28.7846i	0.358923	−	1.10465i
$680$	64.1864	+	10.1661i	2.46144	+	0.389853i
$681$	−14.8285	−	45.6373i	−0.568228	−	1.74883i
$682$	−0.181189	−	1.14398i	−0.00693807	−	0.0438053i
$683$	−11.2813	−	11.2813i	−0.431666	−	0.431666i	0.457529	−	0.889195i	$-0.348735\pi$
$683$	−11.2813	−	11.2813i	−0.431666	−	0.431666i	−0.889195	+	0.457529i	$0.848735\pi$
$684$	29.1539	+	57.2178i	1.11473	+	2.18778i
$685$	−10.8914	+	1.72503i	−0.416140	+	0.0659101i
$686$	7.60761	−	48.0326i	0.290460	−	1.83389i
$687$	−0.644061	+	0.467937i	−0.0245724	+	0.0178529i
$688$			29.9231i			1.14081i
$689$	−10.9921	−	15.1294i	−0.418767	−	0.576383i
$690$	19.4408	+	9.90559i	0.740099	+	0.377099i
$691$	39.1797	−	19.9630i	1.49046	−	0.759430i	0.496387	−	0.868102i	$-0.334660\pi$
$691$	39.1797	−	19.9630i	1.49046	−	0.759430i	0.994078	+	0.108672i	$0.0346598\pi$
$692$	27.2231	−	37.4694i	1.03487	−	1.42437i
$693$	1.71955	+	1.24932i	0.0653202	+	0.0474579i
$694$	−22.9353	+	22.9353i	−0.870613	+	0.870613i
$695$	−18.5358	−	6.02265i	−0.703104	−	0.228452i
$696$	6.25108			0.236947
$697$	4.75874	+	32.3977i	0.180250	+	1.22715i
$698$	26.8947			1.01798
$699$	−29.1738	−	9.47913i	−1.10345	−	0.358534i
$700$	−18.4961	+	18.4961i	−0.699089	+	0.699089i
$701$	−2.76681	−	2.01021i	−0.104501	−	0.0759245i	0.534308	−	0.845290i	$-0.320572\pi$
$701$	−2.76681	−	2.01021i	−0.104501	−	0.0759245i	−0.638809	+	0.769366i	$0.720572\pi$
$702$	−4.63480	+	6.37926i	−0.174929	+	0.240769i
$703$	14.7558	−	7.51844i	0.556524	−	0.283563i
$704$	−3.39894	−	1.73185i	−0.128102	−	0.0652714i
$705$	8.84479	+	12.1738i	0.333114	+	0.458492i
$706$			33.9182i			1.27653i
$707$	19.4841	−	14.1561i	0.732776	−	0.532393i
$708$	−9.37385	+	59.1842i	−0.352291	+	2.22428i
$709$	−4.54201	+	0.719383i	−0.170579	+	0.0270170i	−0.241139	−	0.970490i	$-0.577521\pi$
$709$	−4.54201	+	0.719383i	−0.170579	+	0.0270170i	0.0705608	+	0.997507i	$0.477521\pi$
$710$	22.0549	+	43.2851i	0.827704	+	1.62446i
$711$	−11.0059	−	11.0059i	−0.412752	−	0.412752i
$712$	−0.231545	−	1.46191i	−0.00867750	−	0.0547876i
$713$	0.505853	+	1.55686i	0.0189443	+	0.0583047i
$714$	−60.5848	−	9.59570i	−2.26733	−	0.359110i
$715$	−1.19527	+	3.67868i	−0.0447007	+	0.137575i
$716$	−3.46800	+	6.80632i	−0.129605	+	0.254364i
$717$	26.7196	−	8.68173i	0.997862	−	0.324225i
$718$	−65.9294	+	21.4218i	−2.46046	+	0.799453i
$719$	−4.48920	+	8.81056i	−0.167419	+	0.328578i	−0.959439	−	0.281917i	$-0.909030\pi$
$719$	−4.48920	+	8.81056i	−0.167419	+	0.328578i	0.792020	+	0.610496i	$0.209030\pi$
$720$	−6.97052	+	21.4531i	−0.259776	+	0.799509i
$721$	27.1083	+	4.29353i	1.00957	+	0.159899i
$722$	16.8026	+	51.7130i	0.625327	+	1.92456i
$723$	10.0736	+	63.6020i	0.374640	+	2.36538i
$724$	−43.9870	−	43.9870i	−1.63477	−	1.63477i
$725$	−0.881750	−	1.73053i	−0.0327474	−	0.0642703i
$726$	61.2377	−	9.69909i	2.27274	−	0.359967i
$727$	−1.74917	+	11.0438i	−0.0648730	+	0.409592i	0.933787	+	0.357831i	$0.116483\pi$
$727$	−1.74917	+	11.0438i	−0.0648730	+	0.409592i	−0.998659	+	0.0517612i	$0.983517\pi$
$728$	−25.9721	+	18.8698i	−0.962589	+	0.699362i
$729$		−	19.4043i		−	0.718678i
$730$	−59.1205	−	81.3724i	−2.18815	−	3.01173i
$731$	45.1652	+	23.0128i	1.67050	+	0.851160i
$732$	−51.6563	+	26.3202i	−1.90927	+	0.972823i
$733$	−17.4839	+	24.0645i	−0.645783	+	0.888844i	−0.998907	−	0.0467321i	$-0.985119\pi$
$733$	−17.4839	+	24.0645i	−0.645783	+	0.888844i	0.353124	+	0.935576i	$0.385119\pi$
$734$	43.4044	+	31.5351i	1.60209	+	1.16398i
$735$	−12.4773	+	12.4773i	−0.460232	+	0.460232i
$736$	1.96763	+	0.639321i	0.0725277	+	0.0235657i
$737$	2.17602			0.0801549
$738$	−40.2168	−	0.451945i	−1.48040	−	0.0166363i
$739$	17.1524			0.630961			0.315481	−	0.948932i	$-0.397834\pi$
$739$	17.1524			0.630961			0.315481	+	0.948932i	$0.397834\pi$
$740$	26.9076	+	8.74281i	0.989143	+	0.321392i
$741$	37.2868	−	37.2868i	1.36976	−	1.36976i
$742$	−22.1741	−	16.1104i	−0.814037	−	0.591433i
$743$	28.5351	−	39.2752i	1.04685	−	1.44087i	0.155343	−	0.987861i	$-0.450352\pi$
$743$	28.5351	−	39.2752i	1.04685	−	1.44087i	0.891508	−	0.453006i	$-0.149648\pi$
$744$	−11.4900	+	5.85447i	−0.421246	+	0.214635i
$745$	32.6536	+	16.6379i	1.19634	+	0.609564i
$746$	−24.5721	−	33.8206i	−0.899649	−	1.23826i
$747$		−	40.1160i		−	1.46777i
$748$	6.17266	−	4.48470i	0.225695	−	0.163977i
$749$	−2.26433	+	14.2964i	−0.0827369	+	0.522380i
$750$	−28.3346	+	4.48776i	−1.03463	+	0.163870i
$751$	−5.55343	−	10.8992i	−0.202647	−	0.397718i	0.767208	−	0.641398i	$-0.221645\pi$
$751$	−5.55343	−	10.8992i	−0.202647	−	0.397718i	−0.969856	+	0.243680i	$0.921645\pi$
$752$	−4.72458	−	4.72458i	−0.172288	−	0.172288i
$753$	−0.501657	−	3.16734i	−0.0182814	−	0.115424i
$754$	−1.54086	−	4.74229i	−0.0561149	−	0.172704i
$755$	−7.62463	−	1.20762i	−0.277489	−	0.0439499i
$756$	−2.34649	+	7.22175i	−0.0853410	+	0.262653i
$757$	16.8826	−	33.1340i	0.613609	−	1.20427i	−0.349948	−	0.936769i	$-0.613801\pi$
$757$	16.8826	−	33.1340i	0.613609	−	1.20427i	0.963556	−	0.267505i	$-0.0861993\pi$
$758$	6.07287	−	1.97320i	0.220577	−	0.0716697i
$759$	1.16467	−	0.378423i	0.0422747	−	0.0137359i
$760$	−37.1724	+	72.9550i	−1.34839	+	2.64636i
$761$	−2.87532	+	8.84933i	−0.104230	+	0.320788i	−0.989549	−	0.144197i	$-0.953940\pi$
$761$	−2.87532	+	8.84933i	−0.104230	+	0.320788i	0.885319	+	0.464985i	$0.153940\pi$
$762$	57.7601	+	9.14830i	2.09243	+	0.331408i
$763$	5.31514	+	16.3583i	0.192421	+	0.592211i
$764$	3.31594	+	20.9360i	0.119966	+	0.757438i
$765$	27.0199	+	27.0199i	0.976908	+	0.976908i
$766$	−31.7695	−	62.3511i	−1.14788	−	2.25284i
$767$	22.5685	−	3.57449i	0.814900	−	0.129067i
$768$	−11.1147	+	70.1757i	−0.401068	+	2.53225i
$769$	−32.0673	+	23.2983i	−1.15638	+	0.840157i	−0.989316	−	0.145789i	$-0.953428\pi$
$769$	−32.0673	+	23.2983i	−1.15638	+	0.840157i	−0.167062	+	0.985946i	$0.553428\pi$
$770$			5.66905i			0.204299i
$771$	−7.34954	−	10.1158i	−0.264687	−	0.364311i
$772$	−28.7232	−	14.6352i	−1.03377	−	0.526732i
$773$	−36.3471	+	18.5198i	−1.30731	+	0.666109i	−0.962172	−	0.272441i	$-0.912169\pi$
$773$	−36.3471	+	18.5198i	−1.30731	+	0.666109i	−0.345141	+	0.938551i	$0.612169\pi$
$774$	−36.5955	+	50.3694i	−1.31540	+	1.81049i
$775$	3.24147	+	2.35507i	0.116437	+	0.0845965i
$776$	45.1079	−	45.1079i	1.61928	−	1.61928i
$777$	−12.1413	−	3.94495i	−0.435567	−	0.141524i
$778$	−51.2334			−1.83681
$779$	−40.6742	−	6.91155i	−1.45730	−	0.247632i
$780$	90.0861			3.22560
$781$	2.59313	+	0.842560i	0.0927896	+	0.0301492i
$782$	−11.6050	+	11.6050i	−0.414993	+	0.414993i
$783$	−0.456138	−	0.331404i	−0.0163010	−	0.0118434i
$784$	4.60536	−	6.33873i	0.164477	−	0.226383i
$785$	−26.5843	+	13.5454i	−0.948836	+	0.483456i
$786$	52.8634	+	26.9352i	1.88557	+	0.960748i
$787$	−2.16421	−	2.97878i	−0.0771457	−	0.106182i	0.768700	−	0.639609i	$-0.220904\pi$
$787$	−2.16421	−	2.97878i	−0.0771457	−	0.106182i	−0.845846	+	0.533427i	$0.820904\pi$
$788$		−	100.451i		−	3.57842i
$789$	4.51851	−	3.28289i	0.160863	−	0.116874i
$790$	6.49420	−	41.0028i	0.231053	−	1.45881i
$791$	7.49145	−	1.18653i	0.266365	−	0.0421881i
$792$	2.03384	+	3.99164i	0.0722694	+	0.141837i
$793$	15.6323	+	15.6323i	0.555121	+	0.555121i
$794$	−1.71844	−	10.8498i	−0.0609850	−	0.385044i
$795$	11.3619	+	34.9682i	0.402964	+	1.24019i
$796$	42.7651	+	6.77332i	1.51577	+	0.240074i
$797$	13.3156	−	40.9813i	0.471664	−	1.45163i	−0.378740	−	0.925503i	$-0.623643\pi$
$797$	13.3156	−	40.9813i	0.471664	−	1.45163i	0.850404	−	0.526130i	$-0.176357\pi$
$798$	35.0867	−	68.8614i	1.24205	−	2.43767i
$799$	−10.7647	+	3.49765i	−0.380827	+	0.123738i
$800$	4.81599	−	1.56481i	0.170271	−	0.0553244i
$801$	0.395116	−	0.775459i	0.0139607	−	0.0273995i
$802$	−5.62285	+	17.3053i	−0.198550	+	0.611073i
$803$	−5.57572	−	0.883107i	−0.196763	−	0.0311642i
$804$	−15.6610	−	48.1995i	−0.552319	−	1.69986i
$805$	−1.25339	−	7.91359i	−0.0441762	−	0.278918i
$806$	7.27365	+	7.27365i	0.256203	+	0.256203i
$807$	−18.1553	−	35.6317i	−0.639096	−	1.25430i
$808$	50.1369	−	7.94091i	1.76381	−	0.279360i
$809$	−2.96962	+	18.7494i	−0.104406	+	0.659195i	0.878868	+	0.477065i	$0.158299\pi$
$809$	−2.96962	+	18.7494i	−0.104406	+	0.659195i	−0.983274	+	0.182130i	$0.941701\pi$
$810$	56.3368	−	40.9311i	1.97947	−	1.43817i
$811$			8.79807i			0.308942i	0.987997	+	0.154471i	$0.0493673\pi$
$811$			8.79807i			0.308942i	−0.987997	+	0.154471i	$0.950633\pi$
$812$	−2.82244	−	3.88475i	−0.0990481	−	0.136328i
$813$	−44.6357	−	22.7430i	−1.56544	−	0.797633i
$814$	2.15334	−	1.09718i	0.0754744	−	0.0384561i
$815$	−5.88740	+	8.10330i	−0.206226	+	0.283846i
$816$	−29.5590	−	21.4759i	−1.03477	−	0.751806i
$817$	−45.1606	+	45.1606i	−1.57997	+	1.57997i
$818$	−2.37820	−	0.772725i	−0.0831519	−	0.0270177i
$819$	−18.8767			−0.659604
$820$	−40.7858	−	57.4844i	−1.42430	−	2.00744i
$821$	−54.2917			−1.89479			−0.947397	−	0.320060i	$-0.896297\pi$
$821$	−54.2917			−1.89479			−0.947397	+	0.320060i	$0.896297\pi$
$822$	20.8644	+	6.77926i	0.727730	+	0.236454i
$823$	2.69668	−	2.69668i	0.0940004	−	0.0940004i	−0.658543	−	0.752543i	$-0.728827\pi$
$823$	2.69668	−	2.69668i	0.0940004	−	0.0940004i	0.752543	+	0.658543i	$0.228827\pi$
$824$	46.8009	+	34.0028i	1.63039	+	1.18454i
$825$	1.76180	−	2.42491i	0.0613379	−	0.0844244i
$826$	29.8393	−	15.2039i	1.03824	−	0.529010i
$827$	−26.9294	−	13.7212i	−0.936428	−	0.477134i	−0.0819589	−	0.996636i	$-0.526118\pi$
$827$	−26.9294	−	13.7212i	−0.936428	−	0.477134i	−0.854469	+	0.519502i	$0.826118\pi$
$828$	−7.78507	−	10.7152i	−0.270550	−	0.372380i
$829$		−	42.4307i		−	1.47368i	−0.676067	−	0.736840i	$-0.736317\pi$
$829$		−	42.4307i		−	1.47368i	0.676067	−	0.736840i	$-0.263683\pi$
$830$	86.5625	−	62.8913i	3.00463	−	2.18299i
$831$	4.22084	−	26.6493i	0.146419	−	0.924455i
$832$	33.4619	−	5.29985i	1.16008	−	0.183739i
$833$	−6.02570	−	11.8261i	−0.208778	−	0.409750i
$834$	27.4174	+	27.4174i	0.949385	+	0.949385i
$835$	8.78629	+	55.4744i	0.304062	+	1.91977i
$836$	2.97063	+	9.14264i	0.102741	+	0.316205i
$837$	1.14880	+	0.181952i	0.0397083	+	0.00628918i
$838$	4.15962	−	12.8020i	0.143692	−	0.442237i
$839$	4.77141	−	9.36443i	0.164728	−	0.323296i	−0.793857	−	0.608105i	$-0.791930\pi$
$839$	4.77141	−	9.36443i	0.164728	−	0.323296i	0.958584	+	0.284809i	$0.0919301\pi$
$840$	60.0287	−	19.5045i	2.07119	−	0.672970i
$841$	−27.2415	+	8.85132i	−0.939364	+	0.305218i
$842$	−34.2434	+	67.2065i	−1.18011	+	2.31609i
$843$	−19.7795	+	60.8750i	−0.681241	+	2.09665i
$844$	−20.1285	−	3.18805i	−0.692853	−	0.109737i
$845$	0.925081	+	2.84711i	0.0318237	+	0.0979434i
$846$	−2.17477	−	13.7310i	−0.0747701	−	0.472080i
$847$	−16.0992	−	16.0992i	−0.553175	−	0.553175i
$848$	−7.41179	−	14.5465i	−0.254522	−	0.499528i
$849$	26.2266	−	4.15389i	0.900096	−	0.142561i
$850$	−6.28397	+	39.6754i	−0.215538	+	1.36086i
$851$	−2.76333	+	2.00767i	−0.0947256	+	0.0688222i
$852$		−	63.5025i		−	2.17556i
$853$	25.0919	+	34.5360i	0.859131	+	1.18249i	0.981776	+	0.190041i	$0.0608622\pi$
$853$	25.0919	+	34.5360i	0.859131	+	1.18249i	−0.122646	+	0.992451i	$0.539138\pi$
$854$	28.8699	+	14.7099i	0.987907	+	0.503364i
$855$	−42.8974	+	21.8573i	−1.46706	+	0.747505i
$856$	−17.9325	+	24.6819i	−0.612920	+	0.843612i
$857$	−0.509355	−	0.370068i	−0.0173992	−	0.0126413i	0.579052	−	0.815291i	$-0.303423\pi$
$857$	−0.509355	−	0.370068i	−0.0173992	−	0.0126413i	−0.596451	+	0.802650i	$0.703423\pi$
$858$	5.44133	−	5.44133i	0.185764	−	0.185764i
$859$	6.63785	+	2.15677i	0.226480	+	0.0735880i	0.420059	−	0.907497i	$-0.362009\pi$
$859$	6.63785	+	2.15677i	0.226480	+	0.0735880i	−0.193578	+	0.981085i	$0.562009\pi$
$860$	−109.109			−3.72060
$861$	18.4035	+	25.9383i	0.627189	+	0.883973i
$862$	−36.1113			−1.22995
$863$	33.7819	+	10.9764i	1.14995	+	0.373641i	0.821124	−	0.570749i	$-0.193347\pi$
$863$	33.7819	+	10.9764i	1.14995	+	0.373641i	0.328826	+	0.944391i	$0.393347\pi$
$864$	1.03945	−	1.03945i	0.0353629	−	0.0353629i
$865$	28.0916	+	20.4098i	0.955143	+	0.693952i
$866$	−24.9061	+	34.2803i	−0.846345	+	1.16489i
$867$	−19.3000	+	9.83386i	−0.655464	+	0.333975i
$868$	8.82617	+	4.49716i	0.299580	+	0.152643i
$869$	−1.36954	−	1.88500i	−0.0464583	−	0.0639444i
$870$			9.80360i			0.332373i
$871$	−15.6347	+	11.3593i	−0.529762	+	0.384895i
$872$	−5.67125	+	35.8069i	−0.192053	+	1.21257i
$873$	37.0479	−	5.86781i	1.25388	−	0.198595i
$874$	−9.38765	−	18.4243i	−0.317542	−	0.623211i
$875$	7.44908	+	7.44908i	0.251825	+	0.251825i
$876$	20.5677	+	129.859i	0.694918	+	4.38754i
$877$	5.53033	+	17.0206i	0.186746	+	0.574745i	0.999974	−	0.00720030i	$-0.00229195\pi$
$877$	5.53033	+	17.0206i	0.186746	+	0.574745i	−0.813228	+	0.581945i	$0.802292\pi$
$878$	16.2968	+	2.58116i	0.549991	+	0.0871100i
$879$	−15.8540	+	48.7937i	−0.534743	+	1.64577i
$880$	−1.53301	+	3.00870i	−0.0516778	+	0.101423i
$881$	20.2237	−	6.57108i	0.681354	−	0.221385i	0.0521659	−	0.998638i	$-0.483388\pi$
$881$	20.2237	−	6.57108i	0.681354	−	0.221385i	0.629188	+	0.777253i	$0.283388\pi$
$882$	15.5043	−	5.03766i	0.522058	−	0.169627i
$883$	18.3180	−	35.9511i	0.616449	−	1.20985i	−0.345961	−	0.938249i	$-0.612447\pi$
$883$	18.3180	−	35.9511i	0.616449	−	1.20985i	0.962410	−	0.271601i	$-0.0875530\pi$
$884$	−20.9395	+	64.4450i	−0.704270	+	2.16752i
$885$	−44.3717	−	7.02778i	−1.49154	−	0.236236i
$886$	−6.30803	−	19.4141i	−0.211922	−	0.652230i
$887$	−3.95846	−	24.9927i	−0.132912	−	0.839174i	−0.960590	−	0.277970i	$-0.910338\pi$
$887$	−3.95846	−	24.9927i	−0.132912	−	0.839174i	0.827678	−	0.561204i	$-0.189662\pi$
$888$	−19.0265	−	19.0265i	−0.638487	−	0.638487i
$889$	−9.74934	−	19.1341i	−0.326982	−	0.641739i
$890$	2.29273	−	0.363132i	0.0768524	−	0.0121722i
$891$	0.611404	−	3.86025i	0.0204828	−	0.129323i
$892$	21.7378	−	15.7934i	0.727835	−	0.528803i
$893$		−	14.2609i		−	0.477221i
$894$	−42.8553	−	58.9853i	−1.43330	−	1.97276i
$895$	−5.10285	−	2.60003i	−0.170569	−	0.0869095i
$896$	38.4199	−	19.5759i	1.28352	−	0.653986i
$897$	−6.39267	+	8.79876i	−0.213445	+	0.293782i
$898$	−6.09961	−	4.43163i	−0.203547	−	0.147885i
$899$	−0.520090	+	0.520090i	−0.0173460	+	0.0173460i
$900$	−30.8314	−	10.0177i	−1.02771	−	0.333924i
$901$	−27.6562			−0.921362
$902$	−5.93567	−	1.00862i	−0.197636	−	0.0335832i
$903$	49.2326			1.63836
$904$	15.2043	+	4.94017i	0.505687	+	0.164308i
$905$	32.9781	−	32.9781i	1.09623	−	1.09623i
$906$	12.4249	+	9.02720i	0.412789	+	0.299908i
$907$	23.2631	−	32.0189i	0.772438	−	1.06317i	−0.223638	−	0.974672i	$-0.571793\pi$
$907$	23.2631	−	32.0189i	0.772438	−	1.06317i	0.996076	−	0.0884974i	$-0.0282065\pi$
$908$	−69.2244	+	35.2716i	−2.29729	+	1.17053i
$909$	26.5947	+	13.5507i	0.882089	+	0.449447i
$910$	−29.5936	−	40.7321i	−0.981019	−	1.35026i
$911$			34.8374i			1.15422i	0.816668	+	0.577108i	$0.195819\pi$
$911$			34.8374i			1.15422i	−0.816668	+	0.577108i	$0.804181\pi$
$912$	37.2427	−	27.0584i	1.23323	−	0.895993i
$913$	0.939433	−	5.93135i	0.0310907	−	0.196299i
$914$	−26.4419	+	4.18798i	−0.874619	+	0.138526i
$915$	−19.7328	−	38.7279i	−0.652347	−	1.28030i
$916$	0.911420	+	0.911420i	0.0301142	+	0.0301142i
$917$	−3.40821	−	21.5186i	−0.112549	−	0.710607i
$918$	3.60350	+	11.0904i	0.118933	+	0.366038i
$919$	−23.4135	−	3.70833i	−0.772339	−	0.122326i	−0.242187	−	0.970229i	$-0.577865\pi$
$919$	−23.4135	−	3.70833i	−0.772339	−	0.122326i	−0.530151	+	0.847903i	$0.677865\pi$
$920$	5.21855	−	16.0611i	0.172051	−	0.529517i
$921$	18.5923	−	36.4894i	0.612636	−	1.20237i
$922$	41.1158	−	13.3593i	1.35408	−	0.439966i
$923$	−23.0300	+	7.48290i	−0.758041	+	0.246303i
$924$	3.36427	−	6.60275i	0.110676	−	0.217215i
$925$	−2.58345	+	7.95103i	−0.0849432	+	0.261428i
$926$	39.1636	+	6.20290i	1.28699	+	0.203840i
$927$	10.5113	+	32.3503i	0.345235	+	1.06252i
$928$	0.145419	+	0.918139i	0.00477361	+	0.0301394i
$929$	−13.5134	−	13.5134i	−0.443359	−	0.443359i	0.449780	−	0.893139i	$-0.351502\pi$
$929$	−13.5134	−	13.5134i	−0.443359	−	0.443359i	−0.893139	+	0.449780i	$0.851502\pi$
$930$	−9.18159	−	18.0199i	−0.301076	−	0.590895i
$931$	16.5170	−	2.61604i	0.541324	−	0.0857372i
$932$	−7.76932	+	49.0535i	−0.254492	+	1.60680i
$933$	23.1491	−	16.8188i	0.757869	−	0.550624i
$934$			30.2418i			0.989542i
$935$	3.36228	+	4.62778i	0.109958	+	0.151344i
$936$	−35.4503	−	18.0628i	−1.15873	−	0.590402i
$937$	−25.3987	+	12.9413i	−0.829739	+	0.422773i	−0.816644	−	0.577141i	$-0.804168\pi$
$937$	−25.3987	+	12.9413i	−0.829739	+	0.422773i	−0.0130943	+	0.999914i	$0.504168\pi$
$938$	−16.6485	+	22.9148i	−0.543594	+	0.748193i
$939$	41.5074	+	30.1569i	1.35454	+	0.984132i
$940$	17.2273	−	17.2273i	0.561894	−	0.561894i
$941$	6.31488	+	2.05183i	0.205859	+	0.0668877i	0.410131	−	0.912026i	$-0.365483\pi$
$941$	6.31488	+	2.05183i	0.205859	+	0.0668877i	−0.204272	+	0.978914i	$0.565483\pi$
$942$	59.3581			1.93399
$943$	8.50877	+	0.0956191i	0.277084	+	0.00311379i
$944$	19.9478			0.649246
$945$	−5.41430	−	1.75921i	−0.176127	−	0.0572272i
$946$	−6.59037	+	6.59037i	−0.214271	+	0.214271i
$947$	−24.7639	−	17.9920i	−0.804719	−	0.584663i	0.107575	−	0.994197i	$-0.465691\pi$
$947$	−24.7639	−	17.9920i	−0.804719	−	0.584663i	−0.912295	+	0.409534i	$0.865691\pi$
$948$	−31.8967	+	43.9020i	−1.03596	+	1.42587i
$949$	44.6715	−	22.7613i	1.45010	−	0.738862i
$950$	−45.0956	−	22.9773i	−1.46309	−	0.745483i
$951$	−27.5194	−	37.8772i	−0.892379	−	1.22825i
$952$			47.4765i			1.53872i
$953$	−20.8531	+	15.1507i	−0.675499	+	0.490778i	−0.871861	−	0.489753i	$-0.837087\pi$
$953$	−20.8531	+	15.1507i	−0.675499	+	0.490778i	0.196363	+	0.980531i	$0.437087\pi$
$954$	5.31387	−	33.5505i	0.172043	−	1.08624i
$955$	−15.6962	+	2.48603i	−0.507917	+	0.0804461i
$956$	−20.6507	−	40.5293i	−0.667892	−	1.31081i
$957$	0.389074	+	0.389074i	0.0125770	+	0.0125770i
$958$	2.65077	+	16.7363i	0.0856426	+	0.540726i
$959$	−2.48944	−	7.66172i	−0.0803883	−	0.247410i
$960$	−65.7893	−	10.4200i	−2.12334	−	0.336304i
$961$	−9.11065	+	28.0397i	−0.293892	+	0.904506i
$962$	−9.74421	+	19.1241i	−0.314166	+	0.616586i
$963$	−17.0610	+	5.54345i	−0.549783	+	0.178635i
$964$	99.1566	−	32.2179i	3.19362	−	1.03767i
$965$	10.9723	−	21.5344i	0.353211	−	0.693217i
$966$	−4.92574	+	15.1599i	−0.158483	+	0.487761i
$967$	23.6731	+	3.74945i	0.761274	+	0.120574i	0.524988	−	0.851109i	$-0.324070\pi$
$967$	23.6731	+	3.74945i	0.761274	+	0.120574i	0.236286	+	0.971684i	$0.424070\pi$
$968$	−14.8291	−	45.6393i	−0.476626	−	1.46690i
$969$	−12.1992	−	77.0228i	−0.391895	−	2.47433i
$970$	70.7429	+	70.7429i	2.27142	+	2.27142i
$971$	5.16430	+	10.1355i	0.165730	+	0.325264i	0.958904	−	0.283732i	$-0.0915725\pi$
$971$	5.16430	+	10.1355i	0.165730	+	0.325264i	−0.793173	+	0.608996i	$0.791573\pi$
$972$	−79.1852	+	12.5417i	−2.53986	+	0.402275i
$973$	2.22737	−	14.0631i	0.0714063	−	0.450842i
$974$	−58.1446	+	42.2445i	−1.86307	+	1.35360i
$975$			26.6199i			0.852519i
$976$	11.3441	+	15.6138i	0.363117	+	0.499787i
$977$	31.3256	+	15.9612i	1.00219	+	0.510644i	0.876488	−	0.481424i	$-0.159880\pi$
$977$	31.3256	+	15.9612i	1.00219	+	0.510644i	0.125707	+	0.992067i	$0.459880\pi$
$978$	17.7550	−	9.04662i	0.567742	−	0.289279i
$979$	0.0765795	−	0.105403i	0.00244749	−	0.00336868i
$980$	23.1130	+	16.7926i	0.738319	+	0.536420i
$981$	−15.0733	+	15.0733i	−0.481253	+	0.481253i
$982$	72.0329	+	23.4049i	2.29866	+	0.746880i
$983$	58.6885			1.87187			0.935937	−	0.352169i	$-0.114556\pi$
$983$	58.6885			1.87187			0.935937	+	0.352169i	$0.114556\pi$
$984$	9.74173	+	66.3220i	0.310555	+	2.11427i
$985$	75.3104			2.39959
$986$	−7.01322	−	2.27873i	−0.223346	−	0.0725696i
$987$	−7.77337	+	7.77337i	−0.247429	+	0.247429i
$988$	−69.0704	−	50.1826i	−2.19742	−	1.59652i
$989$	7.74260	−	10.6568i	0.246200	−	0.338866i
$990$	−6.26011	+	3.18968i	−0.198959	+	0.101375i
$991$	−47.5172	−	24.2112i	−1.50943	−	0.769095i	−0.513406	−	0.858146i	$-0.671617\pi$
$991$	−47.5172	−	24.2112i	−1.50943	−	0.769095i	−0.996027	+	0.0890509i	$0.971617\pi$
$992$	−1.12718	−	1.55143i	−0.0357880	−	0.0492579i
$993$			68.2617i			2.16622i
$994$	−28.7125	+	20.8608i	−0.910704	+	0.661665i
$995$	−5.07811	+	32.0619i	−0.160987	+	1.01643i
$996$	−138.142	+	21.8795i	−4.37720	+	0.693280i
$997$	20.4658	+	40.1663i	0.648157	+	1.27208i	0.948054	+	0.318108i	$0.103048\pi$
$997$	20.4658	+	40.1663i	0.648157	+	1.27208i	−0.299897	+	0.953971i	$0.596952\pi$
$998$	−45.8196	−	45.8196i	−1.45040	−	1.45040i
$999$	0.379655	+	2.39705i	0.0120118	+	0.0758393i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.2.g.a.20.1	✓	24
3.2	odd	2		369.2.u.a.307.3		24
4.3	odd	2		656.2.bs.d.225.3		24
41.11	odd	40		1681.2.a.m.1.1		24
41.30	odd	40		1681.2.a.m.1.2		24
41.39	even	20	inner	41.2.g.a.39.1	yes	24
123.80	odd	20		369.2.u.a.244.3		24
164.39	odd	20		656.2.bs.d.449.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.20.1	✓	24	1.1	even	1	trivial
41.2.g.a.39.1	yes	24	41.39	even	20	inner
369.2.u.a.244.3		24	123.80	odd	20
369.2.u.a.307.3		24	3.2	odd	2
656.2.bs.d.225.3		24	4.3	odd	2
656.2.bs.d.449.3		24	164.39	odd	20
1681.2.a.m.1.1		24	41.11	odd	40
1681.2.a.m.1.2		24	41.30	odd	40

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:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	41.g (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.29671 - 0.746246i) q^{2} +(-1.67347 + 1.67347i) q^{3} +(3.09996 + 2.25225i) q^{4} +(-1.68856 + 2.32411i) q^{5} +(5.09230 - 2.59466i) q^{6} +(-1.86997 - 0.952797i) q^{7} +(-2.60008 - 3.57870i) q^{8} -2.60102i q^{9} +O(q^{10})\)	\(q+(-2.29671 - 0.746246i) q^{2} +(-1.67347 + 1.67347i) q^{3} +(3.09996 + 2.25225i) q^{4} +(-1.68856 + 2.32411i) q^{5} +(5.09230 - 2.59466i) q^{6} +(-1.86997 - 0.952797i) q^{7} +(-2.60008 - 3.57870i) q^{8} -2.60102i q^{9} +(5.61249 - 4.07771i) q^{10} +(0.0609104 - 0.384573i) q^{11} +(-8.95677 + 1.41861i) q^{12} +(1.56991 + 3.08112i) q^{13} +(3.58375 + 3.58375i) q^{14} +(-1.06357 - 6.71509i) q^{15} +(0.932875 + 2.87109i) q^{16} +(5.05100 + 0.800000i) q^{17} +(-1.94100 + 5.97379i) q^{18} +(-2.92520 + 5.74102i) q^{19} +(-10.4689 + 3.40156i) q^{20} +(4.72382 - 1.53486i) q^{21} +(-0.426880 + 0.837799i) q^{22} +(0.410662 - 1.26389i) q^{23} +(10.3400 + 1.63770i) q^{24} +(-1.00514 - 3.09351i) q^{25} +(-1.30635 - 8.24798i) q^{26} +(-0.667682 - 0.667682i) q^{27} +(-3.65089 - 7.16527i) q^{28} +(0.589758 - 0.0934085i) q^{29} +(-2.56841 + 16.2163i) q^{30} +(-0.996546 + 0.724033i) q^{31} +1.55681i q^{32} +(0.541641 + 0.745505i) q^{33} +(-11.0037 - 5.60665i) q^{34} +(5.37196 - 2.73715i) q^{35} +(5.85815 - 8.06305i) q^{36} +(-2.07936 - 1.51074i) q^{37} +(11.0025 - 11.0025i) q^{38} +(-7.78337 - 2.52897i) q^{39} +12.7077 q^{40} +(1.91012 + 6.11158i) q^{41} -11.9946 q^{42} +(9.42697 + 3.06301i) q^{43} +(1.05497 - 1.05497i) q^{44} +(6.04504 + 4.39198i) q^{45} +(-1.88634 + 2.59633i) q^{46} +(-1.97205 + 1.00481i) q^{47} +(-6.36584 - 3.24356i) q^{48} +(-1.52553 - 2.09972i) q^{49} +7.85497i q^{50} +(-9.79148 + 7.11393i) q^{51} +(-2.07280 + 13.0872i) q^{52} +(-5.34140 + 0.845995i) q^{53} +(1.03522 + 2.03173i) q^{54} +(0.790938 + 0.790938i) q^{55} +(1.45229 + 9.16940i) q^{56} +(-4.71221 - 14.5027i) q^{57} +(-1.42421 - 0.225572i) q^{58} +(2.04191 - 6.28435i) q^{59} +(11.8271 - 23.2119i) q^{60} +(6.08019 - 1.97557i) q^{61} +(2.82908 - 0.919225i) q^{62} +(-2.47824 + 4.86383i) q^{63} +(3.02751 - 9.31772i) q^{64} +(-9.81174 - 1.55403i) q^{65} +(-0.687662 - 2.11640i) q^{66} +(0.874252 + 5.51981i) q^{67} +(13.8561 + 13.8561i) q^{68} +(1.42785 + 2.80231i) q^{69} +(-14.3804 + 2.27763i) q^{70} +(-1.09545 + 6.91639i) q^{71} +(-9.30827 + 6.76285i) q^{72} -14.4984i q^{73} +(3.64830 + 5.02146i) q^{74} +(6.85898 + 3.49482i) q^{75} +(-21.9982 + 11.2086i) q^{76} +(-0.480321 + 0.661105i) q^{77} +(15.9889 + 11.6166i) q^{78} +(4.23136 - 4.23136i) q^{79} +(-8.24794 - 2.67992i) q^{80} +10.0378 q^{81} +(0.173757 - 15.4619i) q^{82} +15.4232 q^{83} +(18.1005 + 5.88122i) q^{84} +(-10.3882 + 10.3882i) q^{85} +(-19.3653 - 14.0697i) q^{86} +(-0.830627 + 1.14326i) q^{87} +(-1.53464 + 0.781940i) q^{88} +(0.298137 + 0.151908i) q^{89} +(-10.6062 - 14.5982i) q^{90} -7.25741i q^{91} +(4.11963 - 2.99308i) q^{92} +(0.456043 - 2.87934i) q^{93} +(5.27906 - 0.836122i) q^{94} +(-8.40337 - 16.4925i) q^{95} +(-2.60527 - 2.60527i) q^{96} +(2.25597 + 14.2436i) q^{97} +(1.93680 + 5.96087i) q^{98} +(-1.00028 - 0.158429i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8}+O(q^{10}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8} + 6 q^{10} - 16 q^{11} + 2 q^{12} + 14 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{17} + 16 q^{19} + 20 q^{20} - 10 q^{21} + 6 q^{22} + 12 q^{23} + 68 q^{24} - 8 q^{25} - 28 q^{26} - 6 q^{27} + 18 q^{28} + 40 q^{29} - 36 q^{30} - 12 q^{31} + 10 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} + 46 q^{38} - 50 q^{39} - 44 q^{40} - 4 q^{41} - 40 q^{42} - 48 q^{44} + 16 q^{45} + 70 q^{46} - 12 q^{47} - 50 q^{48} - 30 q^{49} - 24 q^{51} + 20 q^{52} - 26 q^{53} + 68 q^{54} + 20 q^{55} + 106 q^{56} + 10 q^{57} - 20 q^{58} + 6 q^{59} + 76 q^{60} + 30 q^{61} - 10 q^{62} + 92 q^{63} + 70 q^{64} + 68 q^{65} + 34 q^{66} - 22 q^{67} - 20 q^{68} - 38 q^{69} - 20 q^{70} + 4 q^{71} - 74 q^{72} + 10 q^{74} + 4 q^{75} - 128 q^{76} - 20 q^{77} - 10 q^{78} - 2 q^{79} - 70 q^{80} + 28 q^{81} - 90 q^{82} + 80 q^{83} - 30 q^{84} - 56 q^{85} - 46 q^{86} - 10 q^{87} + 10 q^{88} - 72 q^{89} - 70 q^{90} - 6 q^{93} - 18 q^{94} - 40 q^{95} + 66 q^{96} - 22 q^{97} + 6 q^{98} + 14 q^{99}+O(q^{100}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8 + 6 * q^10 - 16 * q^11 + 2 * q^12 + 14 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^17 + 16 * q^19 + 20 * q^20 - 10 * q^21 + 6 * q^22 + 12 * q^23 + 68 * q^24 - 8 * q^25 - 28 * q^26 - 6 * q^27 + 18 * q^28 + 40 * q^29 - 36 * q^30 - 12 * q^31 + 10 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 + 46 * q^38 - 50 * q^39 - 44 * q^40 - 4 * q^41 - 40 * q^42 - 48 * q^44 + 16 * q^45 + 70 * q^46 - 12 * q^47 - 50 * q^48 - 30 * q^49 - 24 * q^51 + 20 * q^52 - 26 * q^53 + 68 * q^54 + 20 * q^55 + 106 * q^56 + 10 * q^57 - 20 * q^58 + 6 * q^59 + 76 * q^60 + 30 * q^61 - 10 * q^62 + 92 * q^63 + 70 * q^64 + 68 * q^65 + 34 * q^66 - 22 * q^67 - 20 * q^68 - 38 * q^69 - 20 * q^70 + 4 * q^71 - 74 * q^72 + 10 * q^74 + 4 * q^75 - 128 * q^76 - 20 * q^77 - 10 * q^78 - 2 * q^79 - 70 * q^80 + 28 * q^81 - 90 * q^82 + 80 * q^83 - 30 * q^84 - 56 * q^85 - 46 * q^86 - 10 * q^87 + 10 * q^88 - 72 * q^89 - 70 * q^90 - 6 * q^93 - 18 * q^94 - 40 * q^95 + 66 * q^96 - 22 * q^97 + 6 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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