LMFDB - Embedded newform 241.2.m.a.2.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [241,2,Mod(2,241)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(241, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([19]))

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

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

chi := DirichletCharacter("241.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	241.m (of order $24$, 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:	$1.92439468871$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			2.11
Character	$\chi$	$=$	241.2
Dual form			241.2.m.a.121.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0371148 + 0.138514i) q^{2} +(0.407739 + 0.109253i) q^{3} +(1.71424 - 0.989718i) q^{4} +(2.06635 + 2.06635i) q^{5} +0.0605326i q^{6} +(0.858916 - 0.659069i) q^{7} +(0.403513 + 0.403513i) q^{8} +(-2.44376 - 1.41091i) q^{9} +O(q^{10})$	\(q+(0.0371148 + 0.138514i) q^{2} +(0.407739 + 0.109253i) q^{3} +(1.71424 - 0.989718i) q^{4} +(2.06635 + 2.06635i) q^{5} +0.0605326i q^{6} +(0.858916 - 0.659069i) q^{7} +(0.403513 + 0.403513i) q^{8} +(-2.44376 - 1.41091i) q^{9} +(-0.209527 + 0.362912i) q^{10} +(-2.67850 + 2.05529i) q^{11} +(0.807093 - 0.216260i) q^{12} +(-1.13790 - 0.873139i) q^{13} +(0.123169 + 0.0945109i) q^{14} +(0.616777 + 1.06829i) q^{15} +(1.93852 - 3.35762i) q^{16} +(-1.09369 + 0.453021i) q^{17} +(0.104731 - 0.390861i) q^{18} +(0.756125 + 0.985401i) q^{19} +(5.58734 + 1.49712i) q^{20} +(0.422219 - 0.174889i) q^{21} +(-0.384099 - 0.294729i) q^{22} +(2.41967 + 1.00226i) q^{23} +(0.120443 + 0.208613i) q^{24} +3.53964i q^{25} +(0.0787094 - 0.190021i) q^{26} +(-1.73773 - 1.73773i) q^{27} +(0.820097 - 1.97989i) q^{28} +(-1.13720 + 0.304713i) q^{29} +(-0.125082 + 0.125082i) q^{30} +(0.800612 - 6.08125i) q^{31} +(1.63944 + 0.439288i) q^{32} +(-1.31668 + 0.545385i) q^{33} +(-0.103342 - 0.134678i) q^{34} +(3.13669 + 0.412954i) q^{35} -5.58560 q^{36} +(-3.68782 + 2.82976i) q^{37} +(-0.108429 + 0.141307i) q^{38} +(-0.368571 - 0.480331i) q^{39} +1.66760i q^{40} +(-5.36916 + 5.36916i) q^{41} +(0.0398951 + 0.0519924i) q^{42} +(-0.0807644 - 0.194982i) q^{43} +(-2.55745 + 6.17422i) q^{44} +(-2.13424 - 7.96511i) q^{45} +(-0.0490218 + 0.372358i) q^{46} +(-7.38687 - 7.38687i) q^{47} +(1.15724 - 1.15724i) q^{48} +(-1.50837 + 5.62931i) q^{49} +(-0.490291 + 0.131373i) q^{50} +(-0.495434 + 0.0652251i) q^{51} +(-2.81479 - 0.370574i) q^{52} +(9.65332 + 2.58660i) q^{53} +(0.176205 - 0.305195i) q^{54} +(-9.78169 - 1.28778i) q^{55} +(0.612526 + 0.0806406i) q^{56} +(0.200643 + 0.484395i) q^{57} +(-0.0844143 - 0.146210i) q^{58} +(-2.06083 - 7.69111i) q^{59} +(2.11461 + 1.22087i) q^{60} +(-1.73613 - 1.73613i) q^{61} +(0.872055 - 0.114808i) q^{62} +(-3.02887 + 0.398758i) q^{63} -7.51069i q^{64} +(-0.547083 - 4.15551i) q^{65} +(-0.124412 - 0.162137i) q^{66} +(-0.152692 - 0.569854i) q^{67} +(-1.42649 + 1.85903i) q^{68} +(0.877094 + 0.673018i) q^{69} +(0.0592178 + 0.449804i) q^{70} +(-0.110934 + 0.842630i) q^{71} +(-0.416770 - 1.55541i) q^{72} +(-8.56081 - 3.54600i) q^{73} +(-0.528835 - 0.405789i) q^{74} +(-0.386717 + 1.44325i) q^{75} +(2.27145 + 0.940865i) q^{76} +(-0.946031 + 3.53064i) q^{77} +(0.0528533 - 0.0688798i) q^{78} +(2.05523 - 2.05523i) q^{79} +(10.9437 - 2.93235i) q^{80} +(3.71403 + 6.43289i) q^{81} +(-0.942981 - 0.544430i) q^{82} +(7.30614 + 4.21820i) q^{83} +(0.550694 - 0.717679i) q^{84} +(-3.19606 - 1.32385i) q^{85} +(0.0240103 - 0.0184238i) q^{86} -0.496973 q^{87} +(-1.91015 - 0.251475i) q^{88} +(-1.97719 + 15.0182i) q^{89} +(1.02407 - 0.591247i) q^{90} -1.55282 q^{91} +(5.13986 - 0.676675i) q^{92} +(0.990838 - 2.39209i) q^{93} +(0.749025 - 1.29735i) q^{94} +(-0.473766 + 3.59861i) q^{95} +(0.620471 + 0.358229i) q^{96} +(0.317174 - 0.183120i) q^{97} -0.835723 q^{98} +(9.44544 - 1.24352i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 8 q^{2} - 8 q^{3} - 36 q^{4} - 8 q^{5} + 8 q^{7} - 16 q^{8} - 36 q^{9}+O(q^{10}) $ 160 * q - 8 * q^2 - 8 * q^3 - 36 * q^4 - 8 * q^5 + 8 * q^7 - 16 * q^8 - 36 * q^9	\( 160 q - 8 q^{2} - 8 q^{3} - 36 q^{4} - 8 q^{5} + 8 q^{7} - 16 q^{8} - 36 q^{9} + 4 q^{10} - 8 q^{11} - 24 q^{12} - 8 q^{13} + 16 q^{14} - 20 q^{15} + 80 q^{16} - 24 q^{17} + 8 q^{18} + 4 q^{19} - 16 q^{20} + 16 q^{22} + 20 q^{23} - 12 q^{24} + 20 q^{26} + 4 q^{27} - 48 q^{28} - 24 q^{29} + 84 q^{30} - 16 q^{31} + 24 q^{32} + 20 q^{33} - 52 q^{34} + 8 q^{35} - 376 q^{36} - 36 q^{37} - 60 q^{38} - 32 q^{39} - 20 q^{41} - 64 q^{42} - 116 q^{44} + 32 q^{45} + 120 q^{46} + 8 q^{47} + 204 q^{48} - 36 q^{49} + 224 q^{50} + 56 q^{51} + 32 q^{52} - 32 q^{53} - 12 q^{54} + 36 q^{55} - 80 q^{56} + 72 q^{57} - 24 q^{58} + 20 q^{59} + 36 q^{60} + 48 q^{61} + 32 q^{62} - 112 q^{63} - 68 q^{65} + 12 q^{66} - 28 q^{67} - 72 q^{68} + 12 q^{69} + 28 q^{70} + 68 q^{72} - 36 q^{74} + 20 q^{75} - 40 q^{76} + 40 q^{77} - 100 q^{78} - 40 q^{79} + 152 q^{80} + 52 q^{81} + 96 q^{82} - 96 q^{83} + 56 q^{84} - 60 q^{85} + 92 q^{86} + 40 q^{87} + 44 q^{88} - 64 q^{89} - 12 q^{90} - 8 q^{91} - 188 q^{92} - 56 q^{93} - 52 q^{94} + 8 q^{95} - 168 q^{96} - 72 q^{97} + 144 q^{98} + 108 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 - 8 * q^3 - 36 * q^4 - 8 * q^5 + 8 * q^7 - 16 * q^8 - 36 * q^9 + 4 * q^10 - 8 * q^11 - 24 * q^12 - 8 * q^13 + 16 * q^14 - 20 * q^15 + 80 * q^16 - 24 * q^17 + 8 * q^18 + 4 * q^19 - 16 * q^20 + 16 * q^22 + 20 * q^23 - 12 * q^24 + 20 * q^26 + 4 * q^27 - 48 * q^28 - 24 * q^29 + 84 * q^30 - 16 * q^31 + 24 * q^32 + 20 * q^33 - 52 * q^34 + 8 * q^35 - 376 * q^36 - 36 * q^37 - 60 * q^38 - 32 * q^39 - 20 * q^41 - 64 * q^42 - 116 * q^44 + 32 * q^45 + 120 * q^46 + 8 * q^47 + 204 * q^48 - 36 * q^49 + 224 * q^50 + 56 * q^51 + 32 * q^52 - 32 * q^53 - 12 * q^54 + 36 * q^55 - 80 * q^56 + 72 * q^57 - 24 * q^58 + 20 * q^59 + 36 * q^60 + 48 * q^61 + 32 * q^62 - 112 * q^63 - 68 * q^65 + 12 * q^66 - 28 * q^67 - 72 * q^68 + 12 * q^69 + 28 * q^70 + 68 * q^72 - 36 * q^74 + 20 * q^75 - 40 * q^76 + 40 * q^77 - 100 * q^78 - 40 * q^79 + 152 * q^80 + 52 * q^81 + 96 * q^82 - 96 * q^83 + 56 * q^84 - 60 * q^85 + 92 * q^86 + 40 * q^87 + 44 * q^88 - 64 * q^89 - 12 * q^90 - 8 * q^91 - 188 * q^92 - 56 * q^93 - 52 * q^94 + 8 * q^95 - 168 * q^96 - 72 * q^97 + 144 * q^98 + 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/241\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{19}{24}\right)$

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 $

$2$	0.0371148	+	0.138514i	0.0262441	+	0.0979444i	0.977806	−	0.209514i	$-0.0671882\pi$
$2$	0.0371148	+	0.138514i	0.0262441	+	0.0979444i	−0.951562	+	0.307458i	$0.900522\pi$
$3$	0.407739	+	0.109253i	0.235408	+	0.0630774i	0.374594	−	0.927189i	$-0.377782\pi$
$3$	0.407739	+	0.109253i	0.235408	+	0.0630774i	−0.139186	+	0.990266i	$0.544449\pi$
$4$	1.71424	−	0.989718i	0.857121	−	0.494859i
$5$	2.06635	+	2.06635i	0.924102	+	0.924102i	0.997316	−	0.0732144i	$-0.0233257\pi$
$5$	2.06635	+	2.06635i	0.924102	+	0.924102i	−0.0732144	+	0.997316i	$0.523326\pi$
$6$			0.0605326i			0.0247123i
$7$	0.858916	−	0.659069i	0.324640	−	0.249105i	−0.433564	−	0.901123i	$-0.642744\pi$
$7$	0.858916	−	0.659069i	0.324640	−	0.249105i	0.758203	+	0.652018i	$0.226077\pi$
$8$	0.403513	+	0.403513i	0.142663	+	0.142663i
$9$	−2.44376	−	1.41091i	−0.814587	−	0.470302i
$10$	−0.209527	+	0.362912i	−0.0662584	+	0.114763i
$11$	−2.67850	+	2.05529i	−0.807599	+	0.619692i	−0.927809	−	0.373056i	$-0.878310\pi$
$11$	−2.67850	+	2.05529i	−0.807599	+	0.619692i	0.120210	+	0.992748i	$0.461643\pi$
$12$	0.807093	−	0.216260i	0.232988	−	0.0624289i
$13$	−1.13790	−	0.873139i	−0.315596	−	0.242165i	0.438800	−	0.898585i	$-0.355403\pi$
$13$	−1.13790	−	0.873139i	−0.315596	−	0.242165i	−0.754396	+	0.656419i	$0.772070\pi$
$14$	0.123169	+	0.0945109i	0.0329183	+	0.0252591i
$15$	0.616777	+	1.06829i	0.159251	+	0.275831i
$16$	1.93852	−	3.35762i	0.484630	−	0.839404i
$17$	−1.09369	+	0.453021i	−0.265259	+	0.109874i	−0.511349	−	0.859373i	$-0.670854\pi$
$17$	−1.09369	+	0.453021i	−0.265259	+	0.109874i	0.246090	+	0.969247i	$0.420854\pi$
$18$	0.104731	−	0.390861i	0.0246853	−	0.0921269i
$19$	0.756125	+	0.985401i	0.173467	+	0.226066i	0.871993	−	0.489518i	$-0.162827\pi$
$19$	0.756125	+	0.985401i	0.173467	+	0.226066i	−0.698526	+	0.715584i	$0.746161\pi$
$20$	5.58734	+	1.49712i	1.24937	+	0.334767i
$21$	0.422219	−	0.174889i	0.0921357	−	0.0381638i
$22$	−0.384099	−	0.294729i	−0.0818901	−	0.0628365i
$23$	2.41967	+	1.00226i	0.504536	+	0.208986i	0.620409	−	0.784278i	$-0.286967\pi$
$23$	2.41967	+	1.00226i	0.504536	+	0.208986i	−0.115873	+	0.993264i	$0.536967\pi$
$24$	0.120443	+	0.208613i	0.0245853	+	0.0425829i
$25$			3.53964i			0.707928i
$26$	0.0787094	−	0.190021i	0.0154362	−	0.0372662i
$27$	−1.73773	−	1.73773i	−0.334426	−	0.334426i
$28$	0.820097	−	1.97989i	0.154984	−	0.374164i
$29$	−1.13720	+	0.304713i	−0.211174	+	0.0565838i	−0.362855	−	0.931846i	$-0.618198\pi$
$29$	−1.13720	+	0.304713i	−0.211174	+	0.0565838i	0.151681	+	0.988429i	$0.451531\pi$
$30$	−0.125082	+	0.125082i	−0.0228367	+	0.0228367i
$31$	0.800612	−	6.08125i	0.143794	−	1.09223i	−0.755583	−	0.655053i	$-0.772646\pi$
$31$	0.800612	−	6.08125i	0.143794	−	1.09223i	0.899377	−	0.437173i	$-0.144020\pi$
$32$	1.63944	+	0.439288i	0.289815	+	0.0776558i
$33$	−1.31668	+	0.545385i	−0.229204	+	0.0949394i
$34$	−0.103342	−	0.134678i	−0.0177230	−	0.0230971i
$35$	3.13669	+	0.412954i	0.530198	+	0.0698019i
$36$	−5.58560			−0.930933
$37$	−3.68782	+	2.82976i	−0.606273	+	0.465210i	−0.865707	−	0.500551i	$-0.833131\pi$
$37$	−3.68782	+	2.82976i	−0.606273	+	0.465210i	0.259434	+	0.965761i	$0.416464\pi$
$38$	−0.108429	+	0.141307i	−0.0175895	+	0.0229230i
$39$	−0.368571	−	0.480331i	−0.0590186	−	0.0769146i
$40$			1.66760i			0.263671i
$41$	−5.36916	+	5.36916i	−0.838522	+	0.838522i	−0.988664	−	0.150142i	$-0.952027\pi$
$41$	−5.36916	+	5.36916i	−0.838522	+	0.838522i	0.150142	+	0.988664i	$0.452027\pi$
$42$	0.0398951	+	0.0519924i	0.00615596	+	0.00802260i
$43$	−0.0807644	−	0.194982i	−0.0123165	−	0.0297345i	0.917602	−	0.397501i	$-0.130123\pi$
$43$	−0.0807644	−	0.194982i	−0.0123165	−	0.0297345i	−0.929918	+	0.367767i	$0.880123\pi$
$44$	−2.55745	+	6.17422i	−0.385550	+	0.930799i
$45$	−2.13424	−	7.96511i	−0.318154	−	1.18737i
$46$	−0.0490218	+	0.372358i	−0.00722787	+	0.0549012i
$47$	−7.38687	−	7.38687i	−1.07749	−	1.07749i	−0.996734	−	0.0807512i	$-0.974268\pi$
$47$	−7.38687	−	7.38687i	−1.07749	−	1.07749i	−0.0807512	−	0.996734i	$-0.525732\pi$
$48$	1.15724	−	1.15724i	0.167033	−	0.167033i
$49$	−1.50837	+	5.62931i	−0.215481	+	0.804187i
$50$	−0.490291	+	0.131373i	−0.0693376	+	0.0185790i
$51$	−0.495434	+	0.0652251i	−0.0693747	+	0.00913335i
$52$	−2.81479	−	0.370574i	−0.390341	−	0.0513894i
$53$	9.65332	+	2.58660i	1.32599	+	0.355297i	0.851217	−	0.524814i	$-0.175865\pi$
$53$	9.65332	+	2.58660i	1.32599	+	0.355297i	0.474768	+	0.880111i	$0.342532\pi$
$54$	0.176205	−	0.305195i	0.0239784	−	0.0415318i
$55$	−9.78169	−	1.28778i	−1.31896	−	0.173645i
$56$	0.612526	+	0.0806406i	0.0818523	+	0.0107761i
$57$	0.200643	+	0.484395i	0.0265758	+	0.0641597i
$58$	−0.0844143	−	0.146210i	−0.0110841	−	0.0191983i
$59$	−2.06083	−	7.69111i	−0.268297	−	1.00130i	−0.960201	−	0.279308i	$-0.909895\pi$
$59$	−2.06083	−	7.69111i	−0.268297	−	1.00130i	0.691905	−	0.721989i	$-0.256772\pi$
$60$	2.11461	+	1.22087i	0.272995	+	0.157614i
$61$	−1.73613	−	1.73613i	−0.222288	−	0.222288i	0.587173	−	0.809461i	$-0.300241\pi$
$61$	−1.73613	−	1.73613i	−0.222288	−	0.222288i	−0.809461	+	0.587173i	$0.800241\pi$
$62$	0.872055	−	0.114808i	0.110751	−	0.0145807i
$63$	−3.02887	+	0.398758i	−0.381602	+	0.0502388i
$64$		−	7.51069i		−	0.938836i
$65$	−0.547083	−	4.15551i	−0.0678573	−	0.515428i
$66$	−0.124412	−	0.162137i	−0.0153140	−	0.0199576i
$67$	−0.152692	−	0.569854i	−0.0186543	−	0.0696187i	0.955971	−	0.293460i	$-0.0948068\pi$
$67$	−0.152692	−	0.569854i	−0.0186543	−	0.0696187i	−0.974626	+	0.223842i	$0.928140\pi$
$68$	−1.42649	+	1.85903i	−0.172987	+	0.225441i
$69$	0.877094	+	0.673018i	0.105590	+	0.0810218i
$70$	0.0592178	+	0.449804i	0.00707788	+	0.0537618i
$71$	−0.110934	+	0.842630i	−0.0131655	+	0.100002i	−0.996766	−	0.0803592i	$-0.974393\pi$
$71$	−0.110934	+	0.842630i	−0.0131655	+	0.100002i	0.983600	+	0.180361i	$0.0577266\pi$
$72$	−0.416770	−	1.55541i	−0.0491169	−	0.183307i
$73$	−8.56081	−	3.54600i	−1.00197	−	0.415028i	−0.179449	−	0.983767i	$-0.557431\pi$
$73$	−8.56081	−	3.54600i	−1.00197	−	0.415028i	−0.822518	+	0.568739i	$0.807431\pi$
$74$	−0.528835	−	0.405789i	−0.0614758	−	0.0471721i
$75$	−0.386717	+	1.44325i	−0.0446543	+	0.166652i
$76$	2.27145	+	0.940865i	0.260553	+	0.107925i
$77$	−0.946031	+	3.53064i	−0.107810	+	0.402353i
$78$	0.0528533	−	0.0688798i	0.00598446	−	0.00779910i
$79$	2.05523	−	2.05523i	0.231231	−	0.231231i	−0.581975	−	0.813206i	$-0.697720\pi$
$79$	2.05523	−	2.05523i	0.231231	−	0.231231i	0.813206	+	0.581975i	$0.197720\pi$
$80$	10.9437	−	2.93235i	1.22354	−	0.327847i
$81$	3.71403	+	6.43289i	0.412670	+	0.714766i
$82$	−0.942981	−	0.544430i	−0.104135	−	0.0601223i
$83$	7.30614	+	4.21820i	0.801953	+	0.463008i	0.844154	−	0.536101i	$-0.180104\pi$
$83$	7.30614	+	4.21820i	0.801953	+	0.463008i	−0.0422005	+	0.999109i	$0.513437\pi$
$84$	0.550694	−	0.717679i	0.0600857	−	0.0783052i
$85$	−3.19606	−	1.32385i	−0.346661	−	0.143592i
$86$	0.0240103	−	0.0184238i	0.00258910	−	0.00198668i
$87$	−0.496973			−0.0532811
$88$	−1.91015	−	0.251475i	−0.203622	−	0.0268074i
$89$	−1.97719	+	15.0182i	−0.209582	+	1.59193i	0.486312	+	0.873785i	$0.338342\pi$
$89$	−1.97719	+	15.0182i	−0.209582	+	1.59193i	−0.695894	+	0.718145i	$0.744992\pi$
$90$	1.02407	−	0.591247i	0.107946	−	0.0623229i
$91$	−1.55282			−0.162779
$92$	5.13986	−	0.676675i	0.535867	−	0.0705483i
$93$	0.990838	−	2.39209i	0.102745	−	0.248049i
$94$	0.749025	−	1.29735i	0.0772560	−	0.133811i
$95$	−0.473766	+	3.59861i	−0.0486074	+	0.369210i
$96$	0.620471	+	0.358229i	0.0633266	+	0.0365616i
$97$	0.317174	−	0.183120i	0.0322041	−	0.0185931i	−0.483812	−	0.875172i	$-0.660748\pi$
$97$	0.317174	−	0.183120i	0.0322041	−	0.0185931i	0.516016	+	0.856579i	$0.327415\pi$
$98$	−0.835723			−0.0844208
$99$	9.44544	−	1.24352i	0.949302	−	0.124978i
$100$	3.50325	+	6.06780i	0.350325	+	0.606780i
$101$	−3.61216	+	1.49620i	−0.359423	+	0.148878i	−0.555085	−	0.831793i	$-0.687314\pi$
$101$	−3.61216	+	1.49620i	−0.359423	+	0.148878i	0.195662	+	0.980671i	$0.437314\pi$
$102$	−0.0274226	−	0.0662039i	−0.00271524	−	0.00655516i
$103$	1.39246	−	3.36170i	0.137204	−	0.331239i	−0.840312	−	0.542104i	$-0.817628\pi$
$103$	1.39246	−	3.36170i	0.137204	−	0.331239i	0.977515	+	0.210865i	$0.0676280\pi$
$104$	−0.106833	−	0.811479i	−0.0104759	−	0.0795720i
$105$	1.23384	+	0.511071i	0.120410	+	0.0498755i
$106$			1.43312i			0.139197i
$107$	12.0875	−	6.97872i	1.16854	−	0.674658i	0.215206	−	0.976569i	$-0.430958\pi$
$107$	12.0875	−	6.97872i	1.16854	−	0.674658i	0.953336	+	0.301911i	$0.0976244\pi$
$108$	−4.69874	−	1.25902i	−0.452137	−	0.121150i
$109$	−10.6285	+	13.8514i	−1.01803	+	1.32672i	−0.0738559	+	0.997269i	$0.523530\pi$
$109$	−10.6285	+	13.8514i	−1.01803	+	1.32672i	−0.944172	+	0.329452i	$0.893136\pi$
$110$	−0.184669	−	1.40270i	−0.0176075	−	0.133742i
$111$	−1.81283	+	0.750898i	−0.172066	+	0.0712720i
$112$	−0.547875	−	4.16153i	−0.0517694	−	0.393227i
$113$	8.06915	−	2.16212i	0.759081	−	0.203395i	0.141539	−	0.989933i	$-0.454795\pi$
$113$	8.06915	−	2.16212i	0.759081	−	0.203395i	0.617543	+	0.786537i	$0.288128\pi$
$114$	−0.0596489	+	0.0457702i	−0.00558663	+	0.00428677i
$115$	2.92887	+	7.07092i	0.273119	+	0.659367i
$116$	−1.64786	+	1.64786i	−0.153000	+	0.153000i
$117$	1.54883	+	3.73921i	0.143189	+	0.345690i
$118$	0.988842	−	0.570908i	0.0910303	−	0.0525563i
$119$	−0.640815	+	1.10992i	−0.0587435	+	0.101747i
$120$	−0.182191	+	0.679946i	−0.0166317	+	0.0620703i
$121$	0.103160	−	0.385000i	0.00937821	−	0.0350000i
$122$	0.176042	−	0.304914i	0.0159381	−	0.0276056i
$123$	−2.77581	+	1.60262i	−0.250287	+	0.144503i
$124$	−4.64628	−	11.2171i	−0.417249	−	1.00733i
$125$	3.01762	−	3.01762i	0.269904	−	0.269904i
$126$	−0.167650	−	0.404742i	−0.0149354	−	0.0360573i
$127$	14.9263	−	11.4533i	1.32449	−	1.01632i	0.327040	−	0.945011i	$-0.393949\pi$
$127$	14.9263	−	11.4533i	1.32449	−	1.01632i	0.997454	−	0.0713093i	$-0.0227177\pi$
$128$	4.31923	−	1.15733i	0.381769	−	0.102295i
$129$	−0.0116283	−	0.0883257i	−0.00102381	−	0.00777664i
$130$	0.555293	−	0.230010i	0.0487024	−	0.0201732i
$131$	1.50219	+	11.4103i	0.131247	+	0.996920i	0.922654	+	0.385630i	$0.126016\pi$
$131$	1.50219	+	11.4103i	0.131247	+	0.996920i	−0.791406	+	0.611290i	$0.790651\pi$
$132$	−1.71732	+	2.23806i	−0.149474	+	0.194798i
$133$	1.29889	+	0.348038i	0.112628	+	0.0301787i
$134$	0.0732658	−	0.0423000i	0.00632920	−	0.00365416i
$135$		−	7.18152i		−	0.618087i
$136$	−0.624118	−	0.258518i	−0.0535177	−	0.0221678i
$137$	−2.01086	−	15.2740i	−0.171799	−	1.30494i	−0.832387	−	0.554195i	$-0.813026\pi$
$137$	−2.01086	−	15.2740i	−0.171799	−	1.30494i	0.660588	−	0.750749i	$-0.270307\pi$
$138$	−0.0606694	+	0.146469i	−0.00516452	+	0.0124683i
$139$	5.73896	+	13.8551i	0.486772	+	1.17517i	0.956335	+	0.292272i	$0.0944114\pi$
$139$	5.73896	+	13.8551i	0.486772	+	1.17517i	−0.469563	+	0.882899i	$0.655589\pi$
$140$	5.78576	−	2.39654i	0.488986	−	0.202545i
$141$	−2.20487	−	3.81895i	−0.185684	−	0.321614i
$142$	−0.120834	+	0.0159081i	−0.0101401	+	0.00133497i
$143$	4.84241			0.404943
$144$	−9.47456	+	5.47014i	−0.789547	+	0.455845i
$145$	−2.97951	−	1.72022i	−0.247435	−	0.142857i
$146$	0.173440	−	1.31740i	0.0143540	−	0.109029i
$147$	−1.23004	+	2.13049i	−0.101452	+	0.175720i
$148$	−3.52115	+	8.50080i	−0.289436	+	0.698761i
$149$	6.57009	−	0.864969i	0.538243	−	0.0708610i	0.143496	−	0.989651i	$-0.454166\pi$
$149$	6.57009	−	0.864969i	0.538243	−	0.0708610i	0.394747	+	0.918790i	$0.370832\pi$
$150$	−0.214264			−0.0174946
$151$	−2.02197	+	1.16738i	−0.164545	+	0.0950004i	−0.580011	−	0.814608i	$-0.696952\pi$
$151$	−2.02197	+	1.16738i	−0.164545	+	0.0950004i	0.415466	+	0.909609i	$0.363619\pi$
$152$	−0.0925159	+	0.702728i	−0.00750403	+	0.0569988i
$153$	3.31189	+	0.436019i	0.267750	+	0.0352500i
$154$	−0.524155			−0.0422377
$155$	14.2204	−	10.9117i	1.14221	−	0.876447i
$156$	−1.10721	−	0.458623i	−0.0886480	−	0.0367192i
$157$	9.35678	−	12.1940i	0.746753	−	0.973187i	−0.253231	−	0.967406i	$-0.581493\pi$
$157$	9.35678	−	12.1940i	0.746753	−	0.973187i	0.999983	−	0.00578110i	$-0.00184019\pi$
$158$	0.360958	+	0.208399i	0.0287163	+	0.0165793i
$159$	3.65344	+	2.10931i	0.289736	+	0.167279i
$160$	2.47995	+	4.29540i	0.196057	+	0.339581i
$161$	2.73885	−	0.733873i	0.215852	−	0.0578373i
$162$	−0.753202	+	0.753202i	−0.0591772	+	0.0591772i
$163$	0.865490	−	1.12793i	0.0677904	−	0.0883462i	−0.758227	−	0.651990i	$-0.773934\pi$
$163$	0.865490	−	1.12793i	0.0677904	−	0.0883462i	0.826018	+	0.563644i	$0.190601\pi$
$164$	−3.89009	+	14.5180i	−0.303765	+	1.13367i
$165$	−3.84768	−	1.59376i	−0.299541	−	0.124074i
$166$	−0.313115	+	1.16856i	−0.0243025	+	0.0906981i
$167$	2.58319	+	1.98215i	0.199893	+	0.153384i	0.703858	−	0.710341i	$-0.251459\pi$
$167$	2.58319	+	1.98215i	0.199893	+	0.153384i	−0.503965	+	0.863724i	$0.668126\pi$
$168$	0.240941	+	0.0998008i	0.0185890	+	0.00769980i
$169$	−2.83221	−	10.5700i	−0.217862	−	0.813073i
$170$	0.0647512	−	0.491834i	0.00496619	−	0.0377219i
$171$	−0.457480	−	3.47491i	−0.0349844	−	0.265733i
$172$	−0.331427	−	0.254313i	−0.0252711	−	0.0193912i
$173$	−6.05833	+	7.89537i	−0.460606	+	0.600274i	−0.964692	−	0.263380i	$-0.915163\pi$
$173$	−6.05833	+	7.89537i	−0.460606	+	0.600274i	0.504086	+	0.863654i	$0.331830\pi$
$174$	−0.0184451	−	0.0688379i	−0.00139832	−	0.00521859i
$175$	2.33287	+	3.04025i	0.176348	+	0.229822i
$176$	1.70853	+	12.9776i	0.128786	+	0.978223i
$177$		−	3.36112i		−	0.252637i
$178$	−2.15362	+	0.283530i	−0.161421	+	0.0212515i
$179$	1.52510	−	0.200784i	0.113991	−	0.0150073i	−0.0733146	−	0.997309i	$-0.523358\pi$
$179$	1.52510	−	0.200784i	0.113991	−	0.0150073i	0.187306	+	0.982302i	$0.440024\pi$
$180$	−11.5418	−	11.5418i	−0.860277	−	0.860277i
$181$	17.9449	+	10.3605i	1.33383	+	0.770088i	0.985885	−	0.167426i	$-0.0535456\pi$
$181$	17.9449	+	10.3605i	1.33383	+	0.770088i	0.347947	+	0.937514i	$0.386879\pi$
$182$	−0.0576324	−	0.215087i	−0.00427200	−	0.0159433i
$183$	−0.518208	−	0.897563i	−0.0383071	−	0.0663498i
$184$	0.571943	+	1.38079i	0.0421642	+	0.101793i
$185$	−13.4676	−	1.77305i	−0.990160	−	0.130357i
$186$	0.368114	+	0.0484631i	0.0269914	+	0.00355349i
$187$	1.99836	−	3.46127i	0.146135	−	0.253113i
$188$	−19.9738	−	5.35196i	−1.45674	−	0.390332i
$189$	−2.63784	−	0.347279i	−0.191875	−	0.0252608i
$190$	−0.516043	+	0.0679383i	−0.0374377	+	0.00492876i
$191$	−19.2765	+	5.16512i	−1.39480	+	0.373735i	−0.876474	−	0.481449i	$-0.840111\pi$
$191$	−19.2765	+	5.16512i	−1.39480	+	0.373735i	−0.518325	+	0.855184i	$0.673444\pi$
$192$	0.820568	−	3.06240i	0.0592194	−	0.221010i
$193$	−11.4374	+	11.4374i	−0.823281	+	0.823281i	−0.986577	−	0.163296i	$-0.947787\pi$
$193$	−11.4374	+	11.4374i	−0.823281	+	0.823281i	0.163296	+	0.986577i	$0.447787\pi$
$194$	0.0371366	+	0.0371366i	0.00266626	+	0.00266626i
$195$	0.230936	−	1.75413i	0.0165377	−	0.125616i
$196$	2.98572	+	11.1429i	0.213266	+	0.795919i
$197$	−2.60680	+	6.29337i	−0.185727	+	0.448384i	−0.989129	−	0.147053i	$-0.953021\pi$
$197$	−2.60680	+	6.29337i	−0.185727	+	0.448384i	0.803402	+	0.595437i	$0.203021\pi$
$198$	0.522810	+	1.26218i	0.0371545	+	0.0896989i
$199$	6.23705	+	8.12828i	0.442132	+	0.576198i	0.960261	−	0.279105i	$-0.0900377\pi$
$199$	6.23705	+	8.12828i	0.442132	+	0.576198i	−0.518128	+	0.855303i	$0.673371\pi$
$200$	−1.42829	+	1.42829i	−0.100995	+	0.100995i
$201$		−	0.249034i		−	0.0175655i
$202$	−0.341310	−	0.444804i	−0.0240145	−	0.0312963i
$203$	−0.775936	+	1.01122i	−0.0544600	+	0.0709737i
$204$	−0.784740	+	0.602152i	−0.0549428	+	0.0421591i
$205$	−22.1892			−1.54976
$206$	0.517325	+	0.0681072i	0.0360438	+	0.00474525i
$207$	−4.49900	−	5.86322i	−0.312702	−	0.407522i
$208$	−5.13750	+	2.12802i	−0.356221	+	0.147552i
$209$	−4.05056	−	1.08535i	−0.280183	−	0.0750749i
$210$	−0.0249971	+	0.189872i	−0.00172497	+	0.0131024i
$211$	12.6588	−	12.6588i	0.871468	−	0.871468i	−0.121165	−	0.992632i	$-0.538663\pi$
$211$	12.6588	−	12.6588i	0.871468	−	0.871468i	0.992632	+	0.121165i	$0.0386629\pi$
$212$	19.1081	−	5.12001i	1.31235	−	0.351644i
$213$	−0.137292	+	0.331453i	−0.00940712	+	0.0227108i
$214$	1.41528	+	1.41528i	0.0967464	+	0.0967464i
$215$	0.236015	−	0.569791i	0.0160961	−	0.0388594i
$216$		−	1.40239i		−	0.0954206i
$217$	−3.32031	−	5.75094i	−0.225397	−	0.390399i
$218$	−2.31309	−	0.958113i	−0.156662	−	0.0648916i
$219$	−3.10316	−	2.38114i	−0.209692	−	0.160903i
$220$	−18.0427	+	7.47354i	−1.21644	+	0.503866i
$221$	1.64006	+	0.439452i	0.110322	+	0.0295607i
$222$	−0.171293	−	0.223233i	−0.0114964	−	0.0149824i
$223$	7.12286	−	26.5829i	0.476982	−	1.78012i	−0.136748	−	0.990606i	$-0.543665\pi$
$223$	7.12286	−	26.5829i	0.476982	−	1.78012i	0.613730	−	0.789516i	$-0.289668\pi$
$224$	1.69766	−	0.703196i	0.113430	−	0.0469842i
$225$	4.99410	−	8.65004i	0.332940	−	0.576669i
$226$	0.598970	+	1.03745i	0.0398429	+	0.0690099i
$227$	−14.0161	−	10.7550i	−0.930284	−	0.713832i	0.0280128	−	0.999608i	$-0.491082\pi$
$227$	−14.0161	−	10.7550i	−0.930284	−	0.713832i	−0.958297	+	0.285776i	$0.907749\pi$
$228$	0.823366	+	0.631791i	0.0545287	+	0.0418414i
$229$	4.21516	−	1.12945i	0.278546	−	0.0746360i	−0.116842	−	0.993151i	$-0.537277\pi$
$229$	4.21516	−	1.12945i	0.278546	−	0.0746360i	0.395387	+	0.918514i	$0.370610\pi$
$230$	−0.870720	+	0.668127i	−0.0574136	+	0.0440550i
$231$	−0.771467	+	1.33622i	−0.0507588	+	0.0879168i
$232$	−0.581833	−	0.335921i	−0.0381992	−	0.0220543i
$233$	6.96656	+	6.96656i	0.456395	+	0.456395i	0.897470	−	0.441075i	$-0.145403\pi$
$233$	6.96656	+	6.96656i	0.456395	+	0.456395i	−0.441075	+	0.897470i	$0.645403\pi$
$234$	−0.460449	+	0.353315i	−0.0301005	+	0.0230969i
$235$		−	30.5278i		−	1.99141i
$236$	−11.1448	−	11.1448i	−0.725464	−	0.725464i
$237$	1.06254	−	0.613456i	0.0690192	−	0.0398482i
$238$	−0.177524	−	0.0475675i	−0.0115072	−	0.00308334i
$239$	7.44550	+	27.7870i	0.481609	+	1.79739i	0.594866	+	0.803825i	$0.297205\pi$
$239$	7.44550	+	27.7870i	0.481609	+	1.79739i	−0.113257	+	0.993566i	$0.536128\pi$
$240$	4.78254			0.308711
$241$	−6.88354	−	13.9146i	−0.443408	−	0.896320i
$241$	−6.88354	−	13.9146i	−0.443408	−	0.896320i
$242$	0.0571568			0.00367418
$243$	2.71970	+	10.1500i	0.174469	+	0.651126i
$244$	−4.69442	−	1.25786i	−0.300529	−	0.0805265i
$245$	−14.7490	+	8.51533i	−0.942278	+	0.544024i
$246$	−0.325009	−	0.325009i	−0.0207218	−	0.0207218i
$247$		−	1.78149i		−	0.113353i
$248$	2.77692	−	2.13081i	0.176335	−	0.135306i
$249$	2.51814	+	2.51814i	0.159581	+	0.159581i
$250$	0.529982	+	0.305985i	0.0335190	+	0.0193522i
$251$	2.44560	−	4.23591i	0.154365	−	0.267368i	−0.778463	−	0.627691i	$-0.784000\pi$
$251$	2.44560	−	4.23591i	0.154365	−	0.267368i	0.932828	+	0.360323i	$0.117333\pi$
$252$	−4.79756	+	3.68130i	−0.302218	+	0.231900i
$253$	−8.54103	+	2.28856i	−0.536970	+	0.143881i
$254$	2.14044	+	1.64242i	0.134303	+	0.103054i
$255$	−1.15852	−	0.888964i	−0.0725494	−	0.0556691i
$256$	−7.19008	−	12.4536i	−0.449380	−	0.778349i
$257$	2.64692	−	4.58459i	0.165110	−	0.285979i	−0.771584	−	0.636127i	$-0.780535\pi$
$257$	2.64692	−	4.58459i	0.165110	−	0.285979i	0.936694	+	0.350148i	$0.113869\pi$
$258$	0.0118028	−	0.00488888i	0.000734810	−	0.000304368i
$259$	−1.30252	+	4.86105i	−0.0809344	+	0.302051i
$260$	−5.05062	−	6.58209i	−0.313226	−	0.408204i
$261$	3.20898	+	0.859843i	0.198631	+	0.0532230i
$262$	−1.52473	+	0.631565i	−0.0941983	+	0.0390182i
$263$	6.68108	+	5.12658i	0.411973	+	0.316118i	0.793871	−	0.608086i	$-0.208063\pi$
$263$	6.68108	+	5.12658i	0.411973	+	0.316118i	−0.381898	+	0.924205i	$0.624729\pi$
$264$	−0.751366	−	0.311226i	−0.0462434	−	0.0191546i
$265$	14.6023	+	25.2920i	0.897015	+	1.55368i
$266$			0.192833i			0.0118233i
$267$	−2.44697	+	5.90750i	−0.149752	+	0.361533i
$268$	−0.825745	−	0.825745i	−0.0504404	−	0.0504404i
$269$	1.01470	−	2.44971i	0.0618676	−	0.149362i	−0.889922	−	0.456112i	$-0.849242\pi$
$269$	1.01470	−	2.44971i	0.0618676	−	0.149362i	0.951790	+	0.306750i	$0.0992416\pi$
$270$	0.994743	−	0.266541i	0.0605381	−	0.0162211i
$271$	−11.1059	+	11.1059i	−0.674635	+	0.674635i	−0.958781	−	0.284146i	$-0.908290\pi$
$271$	−11.1059	+	11.1059i	−0.674635	+	0.674635i	0.284146	+	0.958781i	$0.408290\pi$
$272$	−0.599069	+	4.55038i	−0.0363239	+	0.275908i
$273$	−0.633143	−	0.169650i	−0.0383196	−	0.0102677i
$274$	2.04103	−	0.845423i	0.123303	−	0.0510739i
$275$	−7.27498	−	9.48094i	−0.438698	−	0.571722i
$276$	2.16965	+	0.285640i	0.130597	+	0.0171935i
$277$	24.9969			1.50192			0.750960	−	0.660348i	$-0.229591\pi$
$277$	24.9969			1.50192			0.750960	+	0.660348i	$0.229591\pi$
$278$	−1.70612	+	1.30916i	−0.102327	+	0.0785179i
$279$	−10.5366	+	13.7315i	−0.630809	+	0.822086i
$280$	1.09906	+	1.43233i	0.0656817	+	0.0855980i
$281$		−	22.5092i		−	1.34278i	−0.741103	−	0.671392i	$-0.765697\pi$
$281$		−	22.5092i		−	1.34278i	0.741103	−	0.671392i	$-0.234303\pi$
$282$	0.447146	−	0.447146i	0.0266272	−	0.0266272i
$283$	18.9444	+	24.6889i	1.12613	+	1.46760i	0.864639	+	0.502394i	$0.167547\pi$
$283$	18.9444	+	24.6889i	1.12613	+	1.46760i	0.261490	+	0.965206i	$0.415786\pi$
$284$	0.643798	+	1.55427i	0.0382024	+	0.0922287i
$285$	−0.586333	+	1.41553i	−0.0347313	+	0.0838489i
$286$	0.179725	+	0.670743i	0.0106274	+	0.0396619i
$287$	−1.07301	+	8.15031i	−0.0633377	+	0.481097i
$288$	−3.38662	−	3.38662i	−0.199558	−	0.199558i
$289$	−11.0299	+	11.0299i	−0.648817	+	0.648817i
$290$	0.127691	−	0.476551i	0.00749830	−	0.0279840i
$291$	0.149331	−	0.0400130i	0.00875391	−	0.00234560i
$292$	−18.1848	+	2.39408i	−1.06419	+	0.140103i
$293$	−23.0937	−	3.04034i	−1.34915	−	0.177618i	−0.578918	−	0.815386i	$-0.696525\pi$
$293$	−23.0937	−	3.04034i	−1.34915	−	0.177618i	−0.770229	+	0.637768i	$0.779858\pi$
$294$	−0.340757	−	0.0913055i	−0.0198733	−	0.00532504i
$295$	11.6342	−	20.1510i	0.677367	−	1.17323i
$296$	−2.62993	−	0.346237i	−0.152861	−	0.0201246i
$297$	8.22603	+	1.08298i	0.477323	+	0.0628407i
$298$	0.363658	+	0.877949i	0.0210662	+	0.0508582i
$299$	−1.87822	−	3.25318i	−0.108620	−	0.188136i
$300$	0.765483	+	2.85682i	0.0441952	+	0.164939i
$301$	−0.197877	−	0.114244i	−0.0114054	−	0.00658492i
$302$	−0.236744	−	0.236744i	−0.0136231	−	0.0136231i
$303$	−1.63628	+	0.215421i	−0.0940019	+	0.0123756i
$304$	4.77436	−	0.628557i	0.273828	−	0.0360502i
$305$		−	7.17490i		−	0.410834i
$306$	0.0625253	+	0.474927i	0.00357433	+	0.0271498i
$307$	−9.02600	−	11.7629i	−0.515141	−	0.671345i	0.461271	−	0.887259i	$-0.347393\pi$
$307$	−9.02600	−	11.7629i	−0.515141	−	0.671345i	−0.976412	+	0.215914i	$0.930727\pi$
$308$	1.87261	+	6.98867i	0.106702	+	0.398216i
$309$	0.935039	−	1.21857i	0.0531925	−	0.0693218i
$310$	2.03921	+	1.56474i	0.115819	+	0.0888713i
$311$	1.32378	+	10.0551i	0.0750645	+	0.570171i	0.987105	+	0.160072i	$0.0511726\pi$
$311$	1.32378	+	10.0551i	0.0750645	+	0.570171i	−0.912041	+	0.410099i	$0.865494\pi$
$312$	0.0450967	−	0.342543i	0.00255310	−	0.0193927i
$313$	7.42506	+	27.7107i	0.419689	+	1.56630i	0.775254	+	0.631649i	$0.217622\pi$
$313$	7.42506	+	27.7107i	0.419689	+	1.56630i	−0.355565	+	0.934651i	$0.615712\pi$
$314$	2.03632	+	0.843471i	0.114916	+	0.0475998i
$315$	−7.08269	−	5.43474i	−0.399065	−	0.306213i
$316$	1.48906	−	5.55725i	0.0837663	−	0.312620i
$317$	2.96154	+	1.22671i	0.166337	+	0.0688990i	0.464298	−	0.885679i	$-0.346307\pi$
$317$	2.96154	+	1.22671i	0.166337	+	0.0688990i	−0.297961	+	0.954578i	$0.596307\pi$
$318$	−0.156573	+	0.584340i	−0.00878020	+	0.0327682i
$319$	2.41973	−	3.15346i	0.135479	−	0.176560i
$320$	15.5197	−	15.5197i	0.867580	−	0.867580i
$321$	5.69099	−	1.52490i	0.317640	−	0.0851114i
$322$	0.203304	+	0.352133i	0.0113297	+	0.0196236i
$323$	−1.27337	−	0.735183i	−0.0708524	−	0.0409067i
$324$	12.7335	+	7.35169i	0.707417	+	0.408427i
$325$	3.09060	−	4.02775i	0.171436	−	0.223419i
$326$	0.188357	+	0.0780199i	0.0104321	+	0.00432113i
$327$	−5.84697	+	4.48654i	−0.323338	+	0.248106i
$328$	−4.33305			−0.239253
$329$	−11.2132	−	1.47624i	−0.618201	−	0.0813877i
$330$	0.0779529	−	0.592111i	0.00429116	−	0.0325946i
$331$	24.3958	−	14.0849i	1.34091	−	0.774176i	0.353971	−	0.935256i	$-0.384831\pi$
$331$	24.3958	−	14.0849i	1.34091	−	0.774176i	0.986941	+	0.161080i	$0.0514978\pi$
$332$	16.6993			0.916495
$333$	13.0047	−	1.71210i	0.712652	−	0.0938224i
$334$	−0.178682	+	0.431376i	−0.00977704	+	0.0236039i
$335$	0.862004	−	1.49304i	0.0470963	−	0.0815732i
$336$	0.231270	−	1.75667i	0.0126168	−	0.0958344i
$337$	9.79521	+	5.65527i	0.533579	+	0.308062i	0.742473	−	0.669876i	$-0.233653\pi$
$337$	9.79521	+	5.65527i	0.533579	+	0.308062i	−0.208893	+	0.977938i	$0.566986\pi$
$338$	1.35897	−	0.784603i	0.0739184	−	0.0426768i
$339$	3.52632			0.191524
$340$	−6.78905	+	0.893795i	−0.368188	+	0.0484729i
$341$	10.3543	+	17.9341i	0.560716	+	0.971188i
$342$	0.464345	−	0.192338i	0.0251089	−	0.0104004i
$343$	5.31470	+	12.8308i	0.286967	+	0.692799i
$344$	0.0460885	−	0.111267i	0.00248492	−	0.00599914i
$345$	0.421693	+	3.20308i	0.0227032	+	0.172448i
$346$	−1.31848	−	0.546131i	−0.0708817	−	0.0293602i
$347$		−	36.2580i		−	1.94643i	−0.229890	−	0.973217i	$-0.573837\pi$
$347$		−	36.2580i		−	1.94643i	0.229890	−	0.973217i	$-0.426163\pi$
$348$	−0.851933	+	0.491864i	−0.0456684	+	0.0263667i
$349$	7.06892	+	1.89411i	0.378391	+	0.101389i	0.443001	−	0.896521i	$-0.353914\pi$
$349$	7.06892	+	1.89411i	0.378391	+	0.101389i	−0.0646104	+	0.997911i	$0.520580\pi$
$350$	−0.334535	+	0.435974i	−0.0178816	+	0.0233038i
$351$	0.460077	+	3.49463i	0.0245571	+	0.186529i
$352$	−5.29412	+	2.19289i	−0.282177	+	0.116882i
$353$	3.48458	+	26.4680i	0.185465	+	1.40875i	0.790457	+	0.612518i	$0.209843\pi$
$353$	3.48458	+	26.4680i	0.185465	+	1.40875i	−0.604991	+	0.796232i	$0.706823\pi$
$354$	0.465563	−	0.124747i	0.0247444	−	0.00663024i
$355$	−1.97040	+	1.51194i	−0.104578	+	0.0802456i
$356$	11.4744	+	27.7018i	0.608144	+	1.46819i
$357$	−0.382548	+	0.382548i	−0.0202466	+	0.0202466i
$358$	0.0844153	+	0.203796i	0.00446149	+	0.0107710i
$359$	4.39163	−	2.53551i	0.231782	−	0.133819i	−0.379612	−	0.925146i	$-0.623943\pi$
$359$	4.39163	−	2.53551i	0.231782	−	0.133819i	0.611394	+	0.791327i	$0.290609\pi$
$360$	2.35283	−	4.07522i	0.124005	−	0.214783i
$361$	4.51827	−	16.8624i	0.237804	−	0.887496i
$362$	−0.769054	+	2.87015i	−0.0404206	+	0.150852i
$363$	0.0841250	−	0.145709i	0.00441542	−	0.00764772i
$364$	−2.66190	+	1.53685i	−0.139522	+	0.0805528i
$365$	−10.3624	−	25.0170i	−0.542391	−	1.30945i
$366$	0.105092	−	0.105092i	0.00549326	−	0.00549326i
$367$	−12.1465	−	29.3243i	−0.634043	−	1.53071i	−0.834498	−	0.551011i	$-0.814242\pi$
$367$	−12.1465	−	29.3243i	−0.634043	−	1.53071i	0.200455	−	0.979703i	$-0.435758\pi$
$368$	8.05579	−	6.18142i	0.419937	−	0.322229i
$369$	20.6963	−	5.54557i	1.07741	−	0.288691i
$370$	−0.254256	−	1.93127i	−0.0132181	−	0.100402i
$371$	9.99613	−	4.14053i	0.518973	−	0.214966i
$372$	−0.668963	−	5.08128i	−0.0346841	−	0.263452i
$373$	−14.1734	+	18.4711i	−0.733871	+	0.956399i	−0.999972	−	0.00754627i	$-0.997598\pi$
$373$	−14.1734	+	18.4711i	−0.733871	+	0.956399i	0.266101	+	0.963945i	$0.414265\pi$
$374$	0.553604	+	0.148338i	0.0286262	+	0.00767036i
$375$	1.56008	−	0.900715i	0.0805624	−	0.0465127i
$376$		−	5.96139i		−	0.307435i
$377$	1.56008	+	0.646205i	0.0803481	+	0.0332813i
$378$	−0.0497999	−	0.378268i	−0.00256143	−	0.0194560i
$379$	4.97846	−	12.0191i	0.255726	−	0.617378i	−0.742921	−	0.669380i	$-0.766560\pi$
$379$	4.97846	−	12.0191i	0.255726	−	0.617378i	0.998647	+	0.0520014i	$0.0165600\pi$
$380$	2.74946	+	6.63778i	0.141044	+	0.340511i
$381$	7.33734	−	3.03923i	0.375903	−	0.155704i
$382$	−1.43089	−	2.47837i	−0.0732106	−	0.126804i
$383$	−13.8476	+	1.82307i	−0.707579	+	0.0931546i	−0.475723	−	0.879595i	$-0.657813\pi$
$383$	−13.8476	+	1.82307i	−0.707579	+	0.0931546i	−0.231857	+	0.972750i	$0.574480\pi$
$384$	1.88756			0.0963240
$385$	−9.25038	+	5.34071i	−0.471443	+	0.272188i
$386$	−2.00874	−	1.15975i	−0.102242	−	0.0590295i
$387$	−0.0777331	+	0.590442i	−0.00395140	+	0.0300138i
$388$	0.362475	−	0.627825i	0.0184019	−	0.0318730i
$389$	−3.56829	+	8.61462i	−0.180920	+	0.436779i	−0.988157	−	0.153449i	$-0.950962\pi$
$389$	−3.56829	+	8.61462i	−0.180920	+	0.436779i	0.807237	+	0.590228i	$0.200962\pi$
$390$	0.251544	−	0.0331164i	0.0127374	−	0.00167691i
$391$	−3.10042			−0.156795
$392$	−2.88015	+	1.66285i	−0.145469	+	0.0839868i
$393$	−0.634108	+	4.81653i	−0.0319865	+	0.242962i
$394$	−0.968473	−	0.127502i	−0.0487910	−	0.00642345i
$395$	8.49366			0.427362
$396$	14.9610	−	11.4800i	0.751821	−	0.576892i
$397$	1.27249	+	0.527083i	0.0638645	+	0.0264536i	0.414387	−	0.910101i	$-0.363996\pi$
$397$	1.27249	+	0.527083i	0.0638645	+	0.0264536i	−0.350523	+	0.936554i	$0.613996\pi$
$398$	−0.894396	+	1.16560i	−0.0448320	+	0.0584262i
$399$	0.491585	+	0.283817i	0.0246101	+	0.0142086i
$400$	11.8848	+	6.86167i	0.594238	+	0.343083i
$401$	−2.64061	−	4.57367i	−0.131866	−	0.228398i	0.792530	−	0.609833i	$-0.208763\pi$
$401$	−2.64061	−	4.57367i	−0.131866	−	0.228398i	−0.924396	+	0.381435i	$0.875430\pi$
$402$	0.0344947	−	0.00924283i	0.00172044	−	0.000460990i
$403$	−6.22079	+	6.22079i	−0.309880	+	0.309880i
$404$	−4.71129	+	6.13987i	−0.234395	+	0.305470i
$405$	−5.61813	+	20.9671i	−0.279167	+	1.04187i
$406$	−0.168867	−	0.0699470i	−0.00838073	−	0.00347141i
$407$	4.06185	−	15.1590i	0.201339	−	0.751406i
$408$	−0.226233	−	0.173595i	−0.0112002	−	0.00859423i
$409$	−1.42982	−	0.592251i	−0.0707000	−	0.0292849i	0.347053	−	0.937845i	$-0.387182\pi$
$409$	−1.42982	−	0.592251i	−0.0707000	−	0.0292849i	−0.417753	+	0.908561i	$0.637182\pi$
$410$	−0.823547	−	3.07352i	−0.0406721	−	0.151790i
$411$	0.848827	−	6.44748i	0.0418696	−	0.318031i
$412$	−0.940120	−	7.14092i	−0.0463164	−	0.351808i
$413$	−6.83905	−	5.24779i	−0.336528	−	0.258227i
$414$	0.645160	−	0.840788i	0.0317079	−	0.0413225i
$415$	6.38078	+	23.8134i	0.313220	+	1.16895i
$416$	−1.48196	−	1.93132i	−0.0726590	−	0.0946910i
$417$	0.826284	+	6.27625i	0.0404633	+	0.307349i
$418$		−	0.601343i		−	0.0294127i
$419$	−12.0006	+	1.57991i	−0.586269	+	0.0771838i	−0.417825	−	0.908527i	$-0.637208\pi$
$419$	−12.0006	+	1.57991i	−0.586269	+	0.0771838i	−0.168444	+	0.985711i	$0.553874\pi$
$420$	2.62091	−	0.345049i	0.127887	−	0.0168367i
$421$	10.8465	+	10.8465i	0.528625	+	0.528625i	0.920162	−	0.391537i	$-0.128057\pi$
$421$	10.8465	+	10.8465i	0.528625	+	0.528625i	−0.391537	+	0.920162i	$0.628057\pi$
$422$	2.22325	+	1.28360i	0.108226	+	0.0624845i
$423$	7.62957	+	28.4739i	0.370962	+	1.38445i
$424$	2.85151	+	4.93896i	0.138482	+	0.239857i
$425$	−1.60353	−	3.87127i	−0.0777828	−	0.187784i
$426$	−0.0510066	−	0.00671514i	−0.00247128	−	0.000325350i
$427$	−2.63541	−	0.346959i	−0.127537	−	0.0167905i
$428$	13.8139	−	23.9264i	0.667721	−	1.15653i
$429$	1.97444	+	0.529049i	0.0953268	+	0.0255427i
$430$	0.0876838	+	0.0115438i	0.00422849	+	0.000556691i
$431$	−5.93000	+	0.780700i	−0.285638	+	0.0376050i	−0.271984	−	0.962302i	$-0.587680\pi$
$431$	−5.93000	+	0.780700i	−0.285638	+	0.0376050i	−0.0136542	+	0.999907i	$0.504346\pi$
$432$	−9.20324	+	2.46600i	−0.442791	+	0.118645i
$433$	7.38427	−	27.5585i	0.354865	−	1.32437i	−0.525789	−	0.850615i	$-0.676230\pi$
$433$	7.38427	−	27.5585i	0.354865	−	1.32437i	0.880654	−	0.473760i	$-0.157103\pi$
$434$	0.673355	−	0.673355i	0.0323221	−	0.0323221i
$435$	−1.02692	−	1.02692i	−0.0492372	−	0.0492372i
$436$	−4.51092	+	34.2638i	−0.216034	+	1.64094i
$437$	0.841945	+	3.14218i	0.0402757	+	0.150311i
$438$	0.214649	−	0.518208i	0.0102563	−	0.0247609i
$439$	6.03564	+	14.5713i	0.288066	+	0.695452i	0.999977	−	0.00681772i	$-0.00217016\pi$
$439$	6.03564	+	14.5713i	0.288066	+	0.695452i	−0.711911	+	0.702269i	$0.752170\pi$
$440$	−3.42740	−	4.46667i	−0.163395	−	0.212940i
$441$	11.6285	−	11.6285i	0.553739	−	0.553739i
$442$			0.243482i			0.0115812i
$443$	−14.3752	−	18.7342i	−0.682988	−	0.890087i	0.315275	−	0.949000i	$-0.397903\pi$
$443$	−14.3752	−	18.7342i	−0.682988	−	0.890087i	−0.998263	+	0.0589133i	$0.981236\pi$
$444$	−2.36445	+	3.08141i	−0.112212	+	0.146237i
$445$	−35.1186	+	26.9474i	−1.66478	+	1.27743i
$446$	3.94647			0.186871
$447$	2.77338	+	0.365123i	0.131176	+	0.0172697i
$448$	−4.95006	−	6.45105i	−0.233869	−	0.304783i
$449$	−7.04351	+	2.91752i	−0.332404	+	0.137686i	−0.542642	−	0.839964i	$-0.682576\pi$
$449$	−7.04351	+	2.91752i	−0.332404	+	0.137686i	0.210238	+	0.977650i	$0.432576\pi$
$450$	1.38351	+	0.370710i	0.0652193	+	0.0174755i
$451$	3.34614	−	25.4165i	0.157564	−	1.19682i
$452$	11.6926	−	11.6926i	0.549973	−	0.549973i
$453$	−0.951976	+	0.255081i	−0.0447277	+	0.0119848i
$454$	0.969510	−	2.34060i	0.0455014	−	0.109850i
$455$	−3.20867	−	3.20867i	−0.150425	−	0.150425i
$456$	−0.114498	+	0.276422i	−0.00536185	+	0.0129446i
$457$			30.1234i			1.40911i	0.709648	+	0.704556i	$0.248854\pi$
$457$			30.1234i			1.40911i	−0.709648	+	0.704556i	$0.751146\pi$
$458$	0.312890	+	0.541941i	0.0146204	+	0.0253232i
$459$	2.68776	+	1.11331i	0.125454	+	0.0519648i
$460$	12.0190	+	9.22252i	0.560390	+	0.430002i
$461$	−27.5241	+	11.4009i	−1.28193	+	0.530992i	−0.916569	−	0.399875i	$-0.869053\pi$
$461$	−27.5241	+	11.4009i	−1.28193	+	0.530992i	−0.365358	+	0.930867i	$0.619053\pi$
$462$	−0.213719	−	0.0572657i	−0.00994309	−	0.00266424i
$463$	13.3286	+	17.3701i	0.619431	+	0.807258i	0.992718	−	0.120458i	$-0.0384362\pi$
$463$	13.3286	+	17.3701i	0.619431	+	0.807258i	−0.373288	+	0.927716i	$0.621770\pi$
$464$	−1.18139	+	4.40899i	−0.0548444	+	0.204682i
$465$	6.99034	−	2.89549i	0.324169	−	0.134275i
$466$	−0.706406	+	1.22353i	−0.0327236	+	0.0566790i
$467$	−4.10519	−	7.11039i	−0.189965	−	0.329030i	0.755273	−	0.655410i	$-0.227504\pi$
$467$	−4.10519	−	7.11039i	−0.189965	−	0.329030i	−0.945238	+	0.326380i	$0.894171\pi$
$468$	6.35583	+	4.87700i	0.293798	+	0.225439i
$469$	−0.506722	−	0.388822i	−0.0233983	−	0.0179541i
$470$	4.22853	−	1.13303i	0.195048	−	0.0522629i
$471$	5.14736	−	3.94971i	0.237178	−	0.181993i
$472$	2.27189	−	3.93503i	0.104572	−	0.181125i
$473$	0.617073	+	0.356267i	0.0283730	+	0.0163812i
$474$	0.124408	+	0.124408i	0.00571426	+	0.00571426i
$475$	−3.48797	+	2.67641i	−0.160039	+	0.122802i
$476$			2.53691i			0.116279i
$477$	−19.9410	−	19.9410i	−0.913034	−	0.913034i
$478$	−3.57256	+	2.06262i	−0.163405	+	0.0943419i
$479$	−5.74397	−	1.53909i	−0.262448	−	0.0703229i	0.125195	−	0.992132i	$-0.460044\pi$
$479$	−5.74397	−	1.53909i	−0.262448	−	0.0703229i	−0.387644	+	0.921809i	$0.626711\pi$
$480$	0.541885	+	2.02234i	0.0247335	+	0.0923068i
$481$	6.66713			0.303995
$482$	1.67189	−	1.46991i	0.0761527	−	0.0669525i
$483$	1.19691			0.0544615
$484$	−0.204199	−	0.762082i	−0.00928179	−	0.0346401i
$485$	1.03379	+	0.277002i	0.0469418	+	0.0125780i
$486$	−1.30499	+	0.753434i	−0.0591954	+	0.0341765i
$487$	−6.67918	−	6.67918i	−0.302663	−	0.302663i	0.539392	−	0.842055i	$-0.318654\pi$
$487$	−6.67918	−	6.67918i	−0.302663	−	0.302663i	−0.842055	+	0.539392i	$0.818654\pi$
$488$		−	1.40110i		−	0.0634248i
$489$	0.476124	−	0.365343i	0.0215311	−	0.0165214i
$490$	−1.72690	−	1.72690i	−0.0780134	−	0.0780134i
$491$	−35.8180	−	20.6795i	−1.61644	−	0.933253i	−0.987831	−	0.155534i	$-0.950290\pi$
$491$	−35.8180	−	20.6795i	−1.61644	−	0.933253i	−0.628612	−	0.777719i	$-0.716376\pi$
$492$	−3.17228	+	5.49455i	−0.143017	+	0.247713i
$493$	1.10571	−	0.848440i	0.0497986	−	0.0382118i
$494$	0.246761	−	0.0661195i	0.0111023	−	0.00297486i
$495$	22.0872	+	16.9481i	0.992744	+	0.761760i
$496$	−18.8665	−	14.4768i	−0.847131	−	0.650027i
$497$	0.460068	+	0.796862i	0.0206369	+	0.0357441i
$498$	−0.255339	+	0.442260i	−0.0114420	+	0.0198181i
$499$	−32.2241	+	13.3477i	−1.44255	+	0.597524i	−0.960415	−	0.278572i	$-0.910139\pi$
$499$	−32.2241	+	13.3477i	−1.44255	+	0.597524i	−0.482136	+	0.876097i	$0.660139\pi$
$500$	2.18634	−	8.15952i	0.0977759	−	0.364905i
$501$	0.836711	+	1.09042i	0.0373815	+	0.0487165i
$502$	0.677502	+	0.181536i	0.0302384	+	0.00810235i
$503$	−28.0768	+	11.6298i	−1.25188	+	0.518546i	−0.907408	−	0.420250i	$-0.861942\pi$
$503$	−28.0768	+	11.6298i	−1.25188	+	0.518546i	−0.344473	+	0.938796i	$0.611942\pi$
$504$	−1.38309	−	1.06128i	−0.0616078	−	0.0472733i
$505$	−10.5557	−	4.37231i	−0.469722	−	0.194565i
$506$	−0.633997	−	1.09812i	−0.0281846	−	0.0488172i
$507$		−	4.61921i		−	0.205146i
$508$	14.2517	−	34.4066i	0.632316	−	1.52655i
$509$	−26.7778	−	26.7778i	−1.18691	−	1.18691i	−0.977918	−	0.208989i	$-0.932983\pi$
$509$	−26.7778	−	26.7778i	−1.18691	−	1.18691i	−0.208989	−	0.977918i	$-0.567017\pi$
$510$	0.0801360	−	0.193465i	0.00354848	−	0.00856679i
$511$	−9.69008	+	2.59645i	−0.428664	+	0.114860i
$512$	7.78192	−	7.78192i	0.343916	−	0.343916i
$513$	0.398419	−	3.02630i	0.0175906	−	0.133614i
$514$	0.733272	+	0.196480i	0.0323432	+	0.00866634i
$515$	9.82380	−	4.06915i	0.432888	−	0.179308i
$516$	−0.107351	−	0.139903i	−0.00472588	−	0.00615888i
$517$	34.9679	+	4.60361i	1.53789	+	0.202466i
$518$	−0.721668			−0.0317083
$519$	−3.33281	+	2.55736i	−0.146294	+	0.112256i
$520$	1.45605	−	1.89756i	0.0638519	−	0.0832134i
$521$	−13.0047	−	16.9480i	−0.569744	−	0.742505i	0.416256	−	0.909247i	$-0.363342\pi$
$521$	−13.0047	−	16.9480i	−0.569744	−	0.742505i	−0.986001	+	0.166742i	$0.946675\pi$
$522$			0.476402i			0.0208516i
$523$	−10.5226	+	10.5226i	−0.460120	+	0.460120i	−0.898695	−	0.438575i	$-0.855484\pi$
$523$	−10.5226	+	10.5226i	−0.460120	+	0.460120i	0.438575	+	0.898695i	$0.355484\pi$
$524$	13.8681	+	18.0732i	0.605830	+	0.789533i
$525$	0.619043	+	1.49450i	0.0270173	+	0.0652255i
$526$	−0.462137	+	1.11570i	−0.0201501	+	0.0486467i
$527$	1.87932	+	7.01371i	0.0818643	+	0.305522i
$528$	−0.721210	+	5.47813i	−0.0313866	+	0.238405i
$529$	−11.4132	−	11.4132i	−0.496225	−	0.496225i
$530$	−2.96134	+	2.96134i	−0.128632	+	0.128632i
$531$	−5.81527	+	21.7029i	−0.252361	+	0.941824i
$532$	2.57108	−	0.688919i	0.111470	−	0.0298684i
$533$	10.7976	−	1.42153i	0.467695	−	0.0615732i
$534$	−0.909093	−	0.119684i	−0.0393403	−	0.00517925i
$535$	39.3976	+	10.5565i	1.70330	+	0.456399i
$536$	0.168330	−	0.291556i	0.00727076	−	0.0125933i
$537$	0.643780	+	0.0847552i	0.0277811	+	0.00365746i
$538$	0.376981	+	0.0496305i	0.0162528	+	0.00213972i
$539$	−7.52968	−	18.1783i	−0.324326	−	0.782993i
$540$	−7.10768	−	12.3109i	−0.305866	−	0.529775i
$541$	−4.40652	−	16.4453i	−0.189451	−	0.707041i	−0.993634	−	0.112659i	$-0.964063\pi$
$541$	−4.40652	−	16.4453i	−0.189451	−	0.707041i	0.804183	−	0.594382i	$-0.202603\pi$
$542$	−1.95052	−	1.12613i	−0.0837820	−	0.0483716i
$543$	6.18490	+	6.18490i	0.265420	+	0.265420i
$544$	−1.99205	+	0.262258i	−0.0854085	+	0.0112442i
$545$	−50.5841	+	6.65953i	−2.16679	+	0.285263i
$546$		−	0.0939959i		−	0.00402265i
$547$	−5.03010	−	38.2074i	−0.215072	−	1.63363i	−0.669475	−	0.742835i	$-0.733481\pi$
$547$	−5.03010	−	38.2074i	−0.215072	−	1.63363i	0.454404	−	0.890796i	$-0.349852\pi$
$548$	−18.5640	−	24.1931i	−0.793016	−	1.03348i
$549$	1.79317	+	6.69219i	0.0765305	+	0.285616i
$550$	1.04324	−	1.35957i	0.0444837	−	0.0579724i
$551$	−1.16013	−	0.890202i	−0.0494233	−	0.0379239i
$552$	0.0823473	+	0.625490i	0.00350493	+	0.0266226i
$553$	0.410730	−	3.11980i	0.0174660	−	0.132668i
$554$	0.927756	+	3.46243i	0.0394166	+	0.147105i
$555$	−5.29756	−	2.19432i	−0.224869	−	0.0931438i
$556$	23.5506	+	18.0710i	0.998767	+	0.766381i
$557$	−3.86973	+	14.4420i	−0.163966	+	0.611928i	0.834204	+	0.551456i	$0.185927\pi$
$557$	−3.86973	+	14.4420i	−0.163966	+	0.611928i	−0.998170	+	0.0604725i	$0.980739\pi$
$558$	−2.29308	−	0.949825i	−0.0970738	−	0.0402093i
$559$	−0.0783452	+	0.292388i	−0.00331365	+	0.0123667i
$560$	7.46709	−	9.73130i	0.315542	−	0.411222i
$561$	1.19297	−	1.19297i	0.0503670	−	0.0503670i
$562$	3.11784	−	0.835423i	0.131518	−	0.0352402i
$563$	−10.4472	−	18.0950i	−0.440296	−	0.762615i	0.557415	−	0.830234i	$-0.311793\pi$
$563$	−10.4472	−	18.0950i	−0.440296	−	0.762615i	−0.997711	+	0.0676189i	$0.978460\pi$
$564$	−7.55937	−	4.36441i	−0.318307	−	0.183775i
$565$	21.1414	+	12.2060i	0.889426	+	0.513511i
$566$	−2.71664	+	3.54040i	−0.114189	+	0.148814i
$567$	7.42976	+	3.07751i	0.312021	+	0.129243i
$568$	−0.384776	+	0.295249i	−0.0161448	+	0.0123884i
$569$	−27.4079			−1.14900			−0.574499	−	0.818506i	$-0.694803\pi$
$569$	−27.4079			−1.14900			−0.574499	+	0.818506i	$0.694803\pi$
$570$	−0.217833	−	0.0286783i	−0.00912402	−	0.00120120i
$571$	−1.52328	+	11.5705i	−0.0637475	+	0.484210i	0.929556	+	0.368680i	$0.120190\pi$
$571$	−1.52328	+	11.5705i	−0.0637475	+	0.484210i	−0.993304	+	0.115530i	$0.963143\pi$
$572$	8.30106	−	4.79262i	0.347085	−	0.200389i
$573$	−8.42409			−0.351921
$574$	−1.16876	+	0.153870i	−0.0487830	+	0.00642241i
$575$	−3.54764	+	8.56477i	−0.147947	+	0.357176i
$576$	−10.5969	+	18.3543i	−0.441537	+	0.764764i
$577$	2.64333	−	20.0781i	0.110043	−	0.835861i	−0.844032	−	0.536293i	$-0.819824\pi$
$577$	2.64333	−	20.0781i	0.110043	−	0.835861i	0.954075	−	0.299568i	$-0.0968425\pi$
$578$	−1.93717	−	1.11842i	−0.0805756	−	0.0465203i
$579$	−5.91304	+	3.41389i	−0.245737	+	0.141877i
$580$	−6.81014			−0.282776
$581$	9.05544	−	1.19217i	0.375683	−	0.0494596i
$582$	0.0110848	+	0.0191994i	0.000459478	+	0.000795839i
$583$	−31.1726	+	12.9121i	−1.29104	+	0.534766i
$584$	−2.02354	−	4.88526i	−0.0837347	−	0.202153i
$585$	−4.52610	+	10.9270i	−0.187131	+	0.451774i
$586$	−0.435986	−	3.31164i	−0.0180104	−	0.136803i
$587$	−0.105132	−	0.0435469i	−0.00433924	−	0.00179737i	0.380513	−	0.924776i	$-0.375748\pi$
$587$	−0.105132	−	0.0435469i	−0.00433924	−	0.00179737i	−0.384852	+	0.922978i	$0.625748\pi$
$588$			4.86958i			0.200818i
$589$	6.59784	−	3.80926i	0.271859	−	0.156958i
$590$	3.22300	+	0.863599i	0.132689	+	0.0355538i
$591$	−1.75047	+	2.28125i	−0.0720045	+	0.0938381i
$592$	2.35234	+	17.8678i	0.0966807	+	0.734363i
$593$	−15.0757	+	6.24456i	−0.619085	+	0.256433i	−0.670107	−	0.742264i	$-0.733752\pi$
$593$	−15.0757	+	6.24456i	−0.619085	+	0.256433i	0.0510224	+	0.998698i	$0.483752\pi$
$594$	0.155300	+	1.17962i	0.00637202	+	0.0484003i
$595$	−3.61765	+	0.969346i	−0.148309	+	0.0397393i
$596$	10.4067	−	7.98530i	0.426273	−	0.327091i
$597$	1.65504	+	3.99563i	0.0677365	+	0.163530i
$598$	0.380902	−	0.380902i	0.0155762	−	0.0155762i
$599$	15.6169	+	37.7026i	0.638090	+	1.54049i	0.829220	+	0.558922i	$0.188785\pi$
$599$	15.6169	+	37.7026i	0.638090	+	1.54049i	−0.191130	+	0.981565i	$0.561215\pi$
$600$	−0.738415	+	0.426324i	−0.0301457	+	0.0174046i
$601$	−8.48011	+	14.6880i	−0.345911	+	0.599135i	−0.985519	−	0.169566i	$-0.945763\pi$
$601$	−8.48011	+	14.6880i	−0.345911	+	0.599135i	0.639608	+	0.768701i	$0.279097\pi$
$602$	0.00848030	−	0.0316489i	0.000345631	−	0.00128991i
$603$	−0.430868	+	1.60802i	−0.0175463	+	0.0654837i
$604$	−2.31076	+	4.00236i	−0.0940236	+	0.162854i
$605$	1.00871	−	0.582380i	0.0410100	−	0.0236771i
$606$	−0.0905691	−	0.218653i	−0.00367912	−	0.00888218i
$607$	−18.8790	+	18.8790i	−0.766274	+	0.766274i	−0.977448	−	0.211174i	$-0.932271\pi$
$607$	−18.8790	+	18.8790i	−0.766274	+	0.766274i	0.211174	+	0.977448i	$0.432271\pi$
$608$	0.806749	+	1.94767i	0.0327180	+	0.0789883i
$609$	−0.426858	+	0.327540i	−0.0172972	+	0.0132726i
$610$	0.993827	−	0.266295i	0.0402389	−	0.0107820i
$611$	1.95573	+	14.8552i	0.0791204	+	0.600979i
$612$	6.10892	−	2.53040i	0.246938	−	0.102285i
$613$	−4.34337	−	32.9911i	−0.175427	−	1.33250i	−0.821930	−	0.569588i	$-0.807103\pi$
$613$	−4.34337	−	32.9911i	−0.175427	−	1.33250i	0.646503	−	0.762911i	$-0.276231\pi$
$614$	1.29433	−	1.68681i	0.0522350	−	0.0680740i
$615$	−9.04739	−	2.42424i	−0.364826	−	0.0977548i
$616$	−1.80639	+	1.04292i	−0.0727817	+	0.0420205i
$617$		−	34.1725i		−	1.37573i	−0.725837	−	0.687867i	$-0.758547\pi$
$617$		−	34.1725i		−	1.37573i	0.725837	−	0.687867i	$-0.241453\pi$
$618$	0.203493	+	0.0842894i	0.00818567	+	0.00339062i
$619$	3.92353	+	29.8022i	0.157700	+	1.19785i	0.868946	+	0.494908i	$0.164798\pi$
$619$	3.92353	+	29.8022i	0.157700	+	1.19785i	−0.711245	+	0.702944i	$0.751869\pi$
$620$	13.5777	−	32.7794i	0.545293	−	1.31645i
$621$	−2.46307	−	5.94638i	−0.0988397	−	0.238620i
$622$	−1.34364	+	0.556554i	−0.0538751	+	0.0223158i
$623$	8.19982	+	14.2025i	0.328519	+	0.569011i
$624$	−2.32725	+	0.306388i	−0.0931646	+	0.0122654i
$625$	30.1691			1.20677
$626$	−3.56275	+	2.05695i	−0.142396	+	0.0822124i
$627$	−1.53299	−	0.885075i	−0.0612219	−	0.0353465i
$628$	3.97117	−	30.1640i	0.158467	−	1.20368i
$629$	2.75139	−	4.76554i	0.109705	−	0.190015i
$630$	0.489917	−	1.18276i	0.0195188	−	0.0471224i
$631$	1.34978	−	0.177701i	0.0537337	−	0.00707418i	−0.103611	−	0.994618i	$-0.533040\pi$
$631$	1.34978	−	0.177701i	0.0537337	−	0.00707418i	0.157345	+	0.987544i	$0.449706\pi$
$632$	1.65862			0.0659764
$633$	6.54450	−	3.77847i	0.260121	−	0.150181i
$634$	−0.0600000	+	0.455745i	−0.00238290	+	0.0181000i
$635$	54.5097	+	7.17633i	2.16315	+	0.284784i
$636$	8.35050			0.331119
$637$	6.63154	−	5.08856i	0.262751	−	0.201616i
$638$	0.526607	+	0.218128i	0.0208486	+	0.00863576i
$639$	1.45997	−	1.90267i	0.0577555	−	0.0752684i
$640$	11.3165	+	6.53359i	0.447324	+	0.258263i
$641$	19.2100	+	11.0909i	0.758749	+	0.438064i	0.828847	−	0.559476i	$-0.188998\pi$
$641$	19.2100	+	11.0909i	0.758749	+	0.438064i	−0.0700972	+	0.997540i	$0.522331\pi$
$642$	0.422440	+	0.731687i	0.0166724	+	0.0288774i
$643$	13.0505	−	3.49688i	0.514663	−	0.137903i	0.00786602	−	0.999969i	$-0.497496\pi$
$643$	13.0505	−	3.49688i	0.514663	−	0.137903i	0.506797	+	0.862066i	$0.330829\pi$
$644$	3.96873	−	3.96873i	0.156390	−	0.156390i
$645$	0.158484	−	0.206540i	0.00624030	−	0.00813252i
$646$	0.0545723	−	0.203667i	0.00214712	−	0.00801316i
$647$	−15.0604	−	6.23821i	−0.592085	−	0.245249i	0.0664625	−	0.997789i	$-0.478829\pi$
$647$	−15.0604	−	6.23821i	−0.592085	−	0.245249i	−0.658547	+	0.752539i	$0.728829\pi$
$648$	−1.09710	+	4.09442i	−0.0430980	+	0.160844i
$649$	21.3274	+	16.3651i	0.837172	+	0.642385i
$650$	0.672607	+	0.278603i	0.0263818	+	0.0109277i
$651$	−0.725509	−	2.70764i	−0.0284349	−	0.106121i
$652$	0.367328	−	2.79013i	0.0143857	−	0.109270i
$653$	−2.29933	−	17.4652i	−0.0899798	−	0.683465i	−0.975679	−	0.219205i	$-0.929654\pi$
$653$	−2.29933	−	17.4652i	−0.0899798	−	0.683465i	0.885699	−	0.464260i	$-0.153680\pi$
$654$	−0.838459	−	0.643372i	−0.0327863	−	0.0251578i
$655$	−20.4736	+	26.6817i	−0.799970	+	1.04254i
$656$	7.61935	+	28.4358i	0.297486	+	1.11023i
$657$	15.9175	+	20.7441i	0.621001	+	0.809304i
$658$	−0.211694	−	1.60797i	−0.00825268	−	0.0626853i
$659$		−	17.4897i		−	0.681303i	−0.940190	−	0.340651i	$-0.889352\pi$
$659$		−	17.4897i		−	0.681303i	0.940190	−	0.340651i	$-0.110648\pi$
$660$	−8.17323	+	1.07603i	−0.318142	+	0.0418842i
$661$	43.4068	−	5.71461i	1.68833	−	0.222273i	0.775711	−	0.631088i	$-0.217391\pi$
$661$	43.4068	−	5.71461i	1.68833	−	0.222273i	0.912617	+	0.408816i	$0.134058\pi$
$662$	2.85640	+	2.85640i	0.111017	+	0.111017i
$663$	0.620703	+	0.358363i	0.0241061	+	0.0139177i
$664$	1.24602	+	4.65022i	0.0483551	+	0.180464i
$665$	1.96481	+	3.40315i	0.0761920	+	0.131968i
$666$	0.719816	+	1.73779i	0.0278923	+	0.0673380i
$667$	−3.05706	−	0.402470i	−0.118370	−	0.0155837i
$668$	6.38999	+	0.841258i	0.247236	+	0.0325493i
$669$	5.80853	−	10.0607i	0.224571	−	0.388968i
$670$	0.238800	+	0.0639862i	0.00922564	+	0.00247200i
$671$	8.21846	+	1.08198i	0.317270	+	0.0417694i
$672$	0.769030	−	0.101245i	0.0296660	−	0.00390560i
$673$	26.6740	−	7.14727i	1.02821	−	0.275507i	0.294988	−	0.955501i	$-0.404684\pi$
$673$	26.6740	−	7.14727i	1.02821	−	0.275507i	0.733218	+	0.679994i	$0.238018\pi$
$674$	−0.419788	+	1.56667i	−0.0161696	+	0.0603459i
$675$	6.15093	−	6.15093i	0.236749	−	0.236749i
$676$	−15.3164	−	15.3164i	−0.589091	−	0.589091i
$677$	−2.75159	+	20.9004i	−0.105752	+	0.803268i	0.853575	+	0.520970i	$0.174430\pi$
$677$	−2.75159	+	20.9004i	−0.105752	+	0.803268i	−0.959327	+	0.282297i	$0.908904\pi$
$678$	0.130879	+	0.488446i	0.00502637	+	0.0187587i
$679$	0.151737	−	0.366324i	0.00582312	−	0.0140582i
$680$	−0.755459	−	1.82384i	−0.0289705	−	0.0699411i
$681$	−4.53991	−	5.91652i	−0.173970	−	0.226722i
$682$	−2.09984	+	2.09984i	−0.0804070	+	0.0804070i
$683$		−	18.0004i		−	0.688766i	−0.938829	−	0.344383i	$-0.888088\pi$
$683$		−	18.0004i		−	0.688766i	0.938829	−	0.344383i	$-0.111912\pi$
$684$	−4.22341	−	5.50405i	−0.161486	−	0.210453i
$685$	27.4063	−	35.7166i	1.04714	−	1.36466i
$686$	−1.58000	+	1.21238i	−0.0603246	+	0.0462887i
$687$	1.84208			0.0702797
$688$	−0.811240	−	0.106802i	−0.0309282	−	0.00407178i
$689$	−8.72601	−	11.3720i	−0.332435	−	0.433237i
$690$	−0.428021	+	0.177292i	−0.0162945	+	0.00674940i
$691$	0.742327	+	0.198906i	0.0282395	+	0.00756674i	0.272911	−	0.962039i	$-0.412014\pi$
$691$	0.742327	+	0.198906i	0.0282395	+	0.00756674i	−0.244672	+	0.969606i	$0.578680\pi$
$692$	−2.57125	+	19.5306i	−0.0977444	+	0.742443i
$693$	7.29327	−	7.29327i	0.277049	−	0.277049i
$694$	5.02226	−	1.34571i	0.190642	−	0.0510824i
$695$	−16.7708	+	40.4882i	−0.636151	+	1.53580i
$696$	−0.200535	−	0.200535i	−0.00760127	−	0.00760127i
$697$	3.43986	−	8.30455i	0.130294	−	0.314557i
$698$			1.04945i			0.0397221i
$699$	2.07942	+	3.60166i	0.0786508	+	0.136227i
$700$	7.00810	+	2.90285i	0.264881	+	0.109717i
$701$	−23.2094	−	17.8092i	−0.876608	−	0.672645i	0.0691189	−	0.997608i	$-0.477981\pi$
$701$	−23.2094	−	17.8092i	−0.876608	−	0.672645i	−0.945726	+	0.324964i	$0.894648\pi$
$702$	−0.466980	+	0.193430i	−0.0176250	+	0.00730053i
$703$	−5.57690	−	1.49433i	−0.210337	−	0.0563596i
$704$	15.4366	+	20.1174i	0.581790	+	0.758203i
$705$	3.33526	−	12.4474i	0.125613	−	0.468795i
$706$	−3.53687	+	1.46502i	−0.133112	+	0.0551367i
$707$	−2.11644	+	3.66577i	−0.0795968	+	0.137866i
$708$	−3.32656	−	5.76177i	−0.125020	−	0.216540i
$709$	−11.8587	−	9.09950i	−0.445363	−	0.341739i	0.361608	−	0.932330i	$-0.382228\pi$
$709$	−11.8587	−	9.09950i	−0.445363	−	0.341739i	−0.806971	+	0.590591i	$0.798895\pi$
$710$	−0.282557	−	0.216813i	−0.0106042	−	0.00813686i
$711$	−7.92222	+	2.12275i	−0.297106	+	0.0796094i
$712$	−6.85787	+	5.26223i	−0.257010	+	0.197210i
$713$	8.03222	−	13.9122i	0.300809	−	0.521017i
$714$	−0.0671866	−	0.0387902i	−0.00251440	−	0.00145169i
$715$	10.0061	+	10.0061i	0.374208	+	0.374208i
$716$	2.41568	−	1.85361i	0.0902780	−	0.0692728i
$717$			12.1433i			0.453499i
$718$	0.514199	+	0.514199i	0.0191897	+	0.0191897i
$719$	−5.33119	+	3.07796i	−0.198820	+	0.114789i	−0.596105	−	0.802907i	$-0.703286\pi$
$719$	−5.33119	+	3.07796i	−0.198820	+	0.114789i	0.397285	+	0.917695i	$0.369952\pi$
$720$	−30.8811	−	8.27455i	−1.15087	−	0.308374i
$721$	−1.01959	−	3.80515i	−0.0379714	−	0.141711i
$722$	2.50338			0.0931662
$723$	−1.28647	−	6.42558i	−0.0478443	−	0.238970i
$724$	41.0158			1.52434
$725$	−1.07858	−	4.02530i	−0.0400573	−	0.149496i
$726$	0.0233050	+	0.00624456i	0.000864931	+	0.000231757i
$727$	−26.1451	+	15.0949i	−0.969668	+	0.559838i	−0.899135	−	0.437671i	$-0.855803\pi$
$727$	−26.1451	+	15.0949i	−0.969668	+	0.559838i	−0.0705332	+	0.997509i	$0.522470\pi$
$728$	−0.626581	−	0.626581i	−0.0232226	−	0.0232226i
$729$		−	17.8485i		−	0.661055i
$730$	3.08061	−	2.36384i	0.114019	−	0.0874895i
$731$	0.176662	+	0.176662i	0.00653410	+	0.00653410i
$732$	−1.77667	−	1.02576i	−0.0656676	−	0.0379132i
$733$	−8.96785	+	15.5328i	−0.331235	+	0.573716i	−0.982754	−	0.184916i	$-0.940799\pi$
$733$	−8.96785	+	15.5328i	−0.331235	+	0.573716i	0.651519	+	0.758632i	$0.274132\pi$
$734$	3.61102	−	2.77083i	0.133285	−	0.102273i
$735$	−6.94406	+	1.86065i	−0.256135	+	0.0686313i
$736$	3.52663	+	2.70608i	0.129993	+	0.0997475i
$737$	1.58020	+	1.21253i	0.0582074	+	0.0446641i
$738$	1.53628	+	2.66092i	0.0565513	+	0.0979497i
$739$	18.7182	−	32.4208i	0.688559	−	1.19262i	−0.283745	−	0.958900i	$-0.591577\pi$
$739$	18.7182	−	32.4208i	0.688559	−	1.19262i	0.972304	−	0.233720i	$-0.0750897\pi$
$740$	−24.8416	+	10.2897i	−0.913195	+	0.378258i
$741$	0.194633	−	0.726381i	0.00715003	−	0.0266843i
$742$	0.944528	+	1.23093i	0.0346747	+	0.0451889i
$743$	24.2497	+	6.49768i	0.889634	+	0.238377i	0.674559	−	0.738221i	$-0.264334\pi$
$743$	24.2497	+	6.49768i	0.889634	+	0.238377i	0.215075	+	0.976598i	$0.431000\pi$
$744$	1.36506	−	0.565425i	0.0500454	−	0.0207295i
$745$	15.3635	+	11.7888i	0.562874	+	0.431908i
$746$	−3.08456	−	1.27767i	−0.112934	−	0.0467787i
$747$	−11.9030	−	20.6166i	−0.435507	−	0.754321i
$748$		−	7.91127i		−	0.289265i
$749$	5.78268	−	13.9606i	0.211295	−	0.510110i
$750$	0.182664	+	0.182664i	0.00666995	+	0.00666995i
$751$	−10.2968	+	24.8586i	−0.375734	+	0.907103i	0.617021	+	0.786947i	$0.288339\pi$
$751$	−10.2968	+	24.8586i	−0.375734	+	0.907103i	−0.992755	+	0.120156i	$0.961661\pi$
$752$	−39.1219	+	10.4827i	−1.42663	+	0.382264i
$753$	1.45995	−	1.45995i	0.0532037	−	0.0532037i
$754$	−0.0316067	+	0.240077i	−0.00115105	+	0.00874309i
$755$	−6.59033	−	1.76587i	−0.239847	−	0.0642668i
$756$	−4.86561	+	2.01540i	−0.176960	+	0.0732994i
$757$	−17.6747	−	23.0341i	−0.642397	−	0.837189i	0.352736	−	0.935723i	$-0.385251\pi$
$757$	−17.6747	−	23.0341i	−0.642397	−	0.837189i	−0.995134	+	0.0985342i	$0.968585\pi$
$758$	1.84959	+	0.243503i	0.0671801	+	0.00884442i
$759$	−3.73254			−0.135483
$760$	−1.64326	+	1.26091i	−0.0596072	+	0.0457382i
$761$	−26.8460	+	34.9863i	−0.973165	+	1.26825i	−0.00983014	+	0.999952i	$0.503129\pi$
$761$	−26.8460	+	34.9863i	−0.973165	+	1.26825i	−0.963335	+	0.268302i	$0.913538\pi$
$762$	0.693300	+	0.903527i	0.0251156	+	0.0327313i
$763$			18.9021i			0.684302i
$764$	−27.9326	+	27.9326i	−1.01057	+	1.01057i
$765$	5.94257	+	7.74451i	0.214854	+	0.280003i
$766$	−0.766473	−	1.85043i	−0.0276938	−	0.0668587i
$767$	−4.37040	+	10.5511i	−0.157806	+	0.380977i
$768$	−1.57108	−	5.86335i	−0.0566914	−	0.211575i
$769$	3.27823	−	24.9006i	0.118216	−	0.897939i	−0.824854	−	0.565345i	$-0.808743\pi$
$769$	3.27823	−	24.9006i	0.118216	−	0.897939i	0.943070	−	0.332594i	$-0.107924\pi$
$770$	−1.08309	−	1.08309i	−0.0390319	−	0.0390319i
$771$	1.58013	−	1.58013i	0.0569071	−	0.0569071i
$772$	−8.28666	+	30.9262i	−0.298243	+	1.11306i
$773$	47.4924	−	12.7255i	1.70818	−	0.457706i	0.733204	−	0.680009i	$-0.238024\pi$
$773$	47.4924	−	12.7255i	1.70818	−	0.457706i	0.974978	+	0.222303i	$0.0713574\pi$
$774$	−0.0846697	+	0.0111470i	−0.00304339	+	0.000400670i
$775$	21.5255	+	2.83388i	0.773217	+	0.101796i
$776$	0.201875	+	0.0540923i	0.00724690	+	0.00194180i
$777$	−1.06217	+	1.83974i	−0.0381052	+	0.0660002i
$778$	−1.32569	−	0.174530i	−0.0475281	−	0.00625719i
$779$	−9.35053	−	1.23102i	−0.335018	−	0.0441059i
$780$	−1.34022	−	3.23557i	−0.0479875	−	0.115852i
$781$	−1.43471	−	2.48499i	−0.0513379	−	0.0889199i
$782$	−0.115071	−	0.429452i	−0.00411494	−	0.0153572i
$783$	2.50566	+	1.44664i	0.0895450	+	0.0516988i
$784$	15.9771	+	15.9771i	0.570609	+	0.570609i
$785$	44.5316	−	5.86269i	1.58940	−	0.209248i
$786$	−0.690693	+	0.0909315i	−0.0246362	+	0.00324342i
$787$			19.2234i			0.685242i	0.939474	+	0.342621i	$0.111315\pi$
$787$			19.2234i			0.685242i	−0.939474	+	0.342621i	$0.888685\pi$
$788$	1.75998	+	13.3684i	0.0626966	+	0.476228i
$789$	2.16404	+	2.82023i	0.0770419	+	0.100403i
$790$	0.315240	+	1.17649i	0.0112158	+	0.0418578i
$791$	5.50573	−	7.17520i	0.195761	−	0.255121i
$792$	4.31313	+	3.30958i	0.153260	+	0.117601i
$793$	0.459653	+	3.49141i	0.0163227	+	0.123984i
$794$	−0.0257803	+	0.195821i	−0.000914909	+	0.00694943i
$795$	3.19071	+	11.9079i	0.113163	+	0.422329i
$796$	18.7365	+	7.76092i	0.664098	+	0.275078i
$797$	26.9559	+	20.6840i	0.954828	+	0.732665i	0.963614	−	0.267296i	$-0.0861303\pi$
$797$	26.9559	+	20.6840i	0.954828	+	0.732665i	−0.00878675	+	0.999961i	$0.502797\pi$
$798$	−0.0210676	+	0.0786254i	−0.000745786	+	0.00278331i
$799$	11.4254	+	4.73254i	0.404200	+	0.167425i
$800$	−1.55492	+	5.80304i	−0.0549747	+	0.205169i
$801$	26.0211	−	33.9114i	0.919410	−	1.19820i
$802$	0.535513	−	0.535513i	0.0189096	−	0.0189096i
$803$	30.2182	−	8.09694i	1.06638	−	0.285735i
$804$	−0.246473	−	0.426904i	−0.00869243	−	0.0150557i
$805$	7.17588	+	4.14300i	0.252917	+	0.146021i
$806$	−1.09255	−	0.630785i	−0.0384835	−	0.0222185i
$807$	0.681374	−	0.887984i	0.0239855	−	0.0312585i
$808$	−2.06129	−	0.853814i	−0.0725159	−	0.0300371i
$809$	35.3597	−	27.1325i	1.24318	−	0.953927i	0.243311	−	0.969948i	$-0.421767\pi$
$809$	35.3597	−	27.1325i	1.24318	−	0.953927i	0.999872	+	0.0160211i	$0.00509990\pi$
$810$	−3.11277			−0.109371
$811$	−49.1246	−	6.46738i	−1.72500	−	0.227100i	−0.798130	−	0.602485i	$-0.794177\pi$
$811$	−49.1246	−	6.46738i	−1.72500	−	0.227100i	−0.926869	+	0.375385i	$0.877511\pi$
$812$	−0.329320	+	2.50143i	−0.0115569	+	0.0877831i
$813$	−5.74166	+	3.31495i	−0.201369	+	0.116260i
$814$	2.25050			0.0788800
$815$	4.11911	−	0.542291i	0.144286	−	0.0189956i
$816$	−0.741408	+	1.78992i	−0.0259545	+	0.0626597i
$817$	0.131068	−	0.227016i	0.00458549	−	0.00794230i
$818$	0.0289677	−	0.220032i	0.00101283	−	0.00769323i
$819$	3.79471	+	2.19088i	0.132598	+	0.0765554i
$820$	−38.0376	+	21.9610i	−1.32833	+	0.766913i
$821$	6.82105			0.238056			0.119028	−	0.992891i	$-0.462022\pi$
$821$	6.82105			0.238056			0.119028	+	0.992891i	$0.462022\pi$
$822$	0.924573	−	0.121722i	0.0322482	−	0.00424555i
$823$	−6.05057	−	10.4799i	−0.210910	−	0.365306i	0.741090	−	0.671406i	$-0.234309\pi$
$823$	−6.05057	−	10.4799i	−0.210910	−	0.365306i	−0.951999	+	0.306100i	$0.900976\pi$
$824$	1.91837	−	0.794614i	0.0668295	−	0.0276817i
$825$	−1.93047	−	4.66056i	−0.0672103	−	0.162260i
$826$	0.473064	−	1.14208i	0.0164600	−	0.0397379i
$827$	0.234567	+	1.78172i	0.00815670	+	0.0619563i	0.995039	−	0.0994843i	$-0.0317193\pi$
$827$	0.234567	+	1.78172i	0.00815670	+	0.0619563i	−0.986882	+	0.161441i	$0.948386\pi$
$828$	−13.5153	−	5.59823i	−0.469690	−	0.194552i
$829$		−	50.4149i		−	1.75098i	−0.483234	−	0.875491i	$-0.660538\pi$
$829$		−	50.4149i		−	1.75098i	0.483234	−	0.875491i	$-0.339462\pi$
$830$	−3.06167	+	1.76766i	−0.106272	+	0.0613563i
$831$	10.1922	+	2.73100i	0.353564	+	0.0947372i
$832$	−6.55787	+	8.54639i	−0.227353	+	0.296293i
$833$	−0.900510	−	6.84005i	−0.0312008	−	0.236994i
$834$	−0.838683	+	0.347394i	−0.0290412	+	0.0120293i
$835$	1.24196	+	9.43362i	0.0429798	+	0.326464i
$836$	−8.01783	+	2.14837i	−0.277303	+	0.0743030i
$837$	−11.9588	+	9.17631i	−0.413357	+	0.317180i
$838$	−0.664242	−	1.60362i	−0.0229458	−	0.0553962i
$839$	−5.56510	+	5.56510i	−0.192129	+	0.192129i	−0.796615	−	0.604487i	$-0.793378\pi$
$839$	−5.56510	+	5.56510i	−0.192129	+	0.192129i	0.604487	+	0.796615i	$0.293378\pi$
$840$	0.291645	+	0.704092i	0.0100627	+	0.0242935i
$841$	−23.9144	+	13.8070i	−0.824633	+	0.476102i
$842$	−1.09983	+	1.90496i	−0.0379026	+	0.0656491i
$843$	2.45920	−	9.17785i	0.0846993	−	0.316102i
$844$	9.17161	−	34.2289i	0.315700	−	1.17821i
$845$	15.9889	−	27.6936i	0.550036	−	0.952690i
$846$	−3.66088	+	2.11361i	−0.125864	+	0.0726673i
$847$	−0.165135	−	0.398672i	−0.00567412	−	0.0136985i
$848$	27.3980	−	27.3980i	0.940850	−	0.940850i
$849$	5.02704	+	12.1363i	0.172528	+	0.416518i
$850$	0.476712	−	0.365794i	0.0163511	−	0.0125466i
$851$	−11.7595	+	3.15094i	−0.403109	+	0.108013i
$852$	0.0926928	+	0.704071i	0.00317560	+	0.0241211i
$853$	28.2347	−	11.6952i	0.966738	−	0.400436i	0.157241	−	0.987560i	$-0.449740\pi$
$853$	28.2347	−	11.6952i	0.966738	−	0.400436i	0.809497	+	0.587124i	$0.199740\pi$
$854$	−0.0497541	−	0.377920i	−0.00170255	−	0.0129321i
$855$	6.23507	−	8.12570i	0.213235	−	0.277893i
$856$	7.69346	+	2.06146i	0.262957	+	0.0704592i
$857$	−18.5793	+	10.7268i	−0.634656	+	0.366419i	−0.782553	−	0.622584i	$-0.786083\pi$
$857$	−18.5793	+	10.7268i	−0.634656	+	0.366419i	0.147897	+	0.989003i	$0.452750\pi$
$858$			0.293123i			0.0100071i
$859$	−25.6387	−	10.6199i	−0.874780	−	0.362346i	−0.100310	−	0.994956i	$-0.531984\pi$
$859$	−25.6387	−	10.6199i	−0.874780	−	0.362346i	−0.774470	+	0.632610i	$0.781984\pi$
$860$	−0.159345	−	1.21035i	−0.00543363	−	0.0412725i
$861$	−1.32795	+	3.20597i	−0.0452566	+	0.109259i
$862$	−0.328229	−	0.792415i	−0.0111795	−	0.0269897i
$863$	18.2635	−	7.56499i	0.621697	−	0.257515i	−0.0495237	−	0.998773i	$-0.515770\pi$
$863$	18.2635	−	7.56499i	0.621697	−	0.257515i	0.671221	+	0.741258i	$0.265770\pi$
$864$	−2.08554	−	3.61227i	−0.0709516	−	0.122892i
$865$	−28.8333	+	3.79598i	−0.980362	+	0.129067i
$866$	4.09131			0.139028
$867$	−5.70236	+	3.29226i	−0.193662	+	0.111811i
$868$	−11.3836	−	6.57234i	−0.386385	−	0.223080i
$869$	−1.28085	+	9.72902i	−0.0434498	+	0.330034i
$870$	0.104130	−	0.180358i	0.00353032	−	0.00611470i
$871$	−0.323814	+	0.781755i	−0.0109720	+	0.0264888i
$872$	−9.87795	+	1.30046i	−0.334510	+	0.0440390i
$873$	−1.03346			−0.0349774
$874$	−0.403988	+	0.233243i	−0.0136651	+	0.00788955i
$875$	0.603060	−	4.58070i	0.0203872	−	0.154856i
$876$	−7.67623	−	1.01059i	−0.259356	−	0.0341448i
$877$	12.0836			0.408036			0.204018	−	0.978967i	$-0.434600\pi$
$877$	12.0836			0.408036			0.204018	+	0.978967i	$0.434600\pi$
$878$	−1.79433	+	1.37684i	−0.0605556	+	0.0464659i
$879$	−9.08402	−	3.76272i	−0.306396	−	0.126913i
$880$	−23.2859	+	30.3468i	−0.784967	+	1.02299i
$881$	2.29745	+	1.32643i	0.0774030	+	0.0446886i	0.538202	−	0.842816i	$-0.319104\pi$
$881$	2.29745	+	1.32643i	0.0774030	+	0.0446886i	−0.460799	+	0.887505i	$0.652437\pi$
$882$	2.04231	+	1.17913i	0.0687681	+	0.0397033i
$883$	17.4301	+	30.1899i	0.586571	+	1.01597i	0.994678	+	0.103037i	$0.0328558\pi$
$883$	17.4301	+	30.1899i	0.586571	+	1.01597i	−0.408107	+	0.912934i	$0.633811\pi$
$884$	3.24639	−	0.869867i	0.109188	−	0.0292568i
$885$	6.94526	−	6.94526i	0.233462	−	0.233462i
$886$	2.06142	−	2.68649i	0.0692546	−	0.0902544i
$887$	−12.1109	+	45.1985i	−0.406645	+	1.51762i	0.394357	+	0.918957i	$0.370967\pi$
$887$	−12.1109	+	45.1985i	−0.406645	+	1.51762i	−0.801002	+	0.598662i	$0.795699\pi$
$888$	−1.03450	−	0.428502i	−0.0347154	−	0.0143796i
$889$	5.27188	−	19.6749i	0.176813	−	0.659875i
$890$	−5.03602	−	3.86428i	−0.168808	−	0.129531i
$891$	−23.1695	−	9.59712i	−0.776207	−	0.321516i
$892$	−14.0993	−	52.6191i	−0.472078	−	1.76182i
$893$	1.69363	−	12.8644i	0.0566753	−	0.430491i
$894$	0.0523588	+	0.397705i	0.00175114	+	0.0133012i
$895$	3.56629	+	2.73651i	0.119208	+	0.0914715i
$896$	2.94709	−	3.84072i	0.0984553	−	0.128309i
$897$	−0.410404	−	1.53165i	−0.0137030	−	0.0511402i
$898$	−0.665536	−	0.867344i	−0.0222092	−	0.0289436i
$899$	0.942578	+	7.15959i	0.0314367	+	0.238786i
$900$		−	19.7710i		−	0.659034i
$901$	−11.7295	+	1.54422i	−0.390767	+	0.0514455i
$902$	3.64474	−	0.479839i	0.121357	−	0.0159769i
$903$	−0.0682005	−	0.0682005i	−0.00226957	−	0.00226957i
$904$	4.12845	+	2.38356i	0.137310	+	0.0792761i
$905$	15.6720	+	58.4889i	0.520956	+	1.94424i
$906$	−0.0706648	−	0.122395i	−0.00234768	−	0.00406630i
$907$	4.02278	+	9.71184i	0.133574	+	0.322477i	0.976488	−	0.215572i	$-0.0691617\pi$
$907$	4.02278	+	9.71184i	0.133574	+	0.322477i	−0.842914	+	0.538049i	$0.819162\pi$
$908$	−34.6714	−	4.56458i	−1.15061	−	0.151481i
$909$	10.9383	+	1.44005i	0.362799	+	0.0477634i
$910$	0.325357	−	0.563535i	0.0107855	−	0.0186810i
$911$	32.2971	+	8.65399i	1.07005	+	0.286719i	0.750514	−	0.660854i	$-0.229806\pi$
$911$	32.2971	+	8.65399i	1.07005	+	0.286719i	0.319537	+	0.947574i	$0.396473\pi$
$912$	2.01536	+	0.265328i	0.0667354	+	0.00878588i
$913$	−28.2391	+	3.71775i	−0.934579	+	0.123040i
$914$	−4.17252	+	1.11802i	−0.138015	+	0.0369809i
$915$	0.783882	−	2.92549i	0.0259143	−	0.0967136i
$916$	6.10797	−	6.10797i	0.201813	−	0.201813i
$917$	8.81041	+	8.81041i	0.290945	+	0.290945i
$918$	−0.0544533	+	0.413614i	−0.00179723	+	0.0136513i
$919$	−0.343893	−	1.28343i	−0.0113440	−	0.0423363i	0.960022	−	0.279925i	$-0.0903096\pi$
$919$	−0.343893	−	1.28343i	−0.0113440	−	0.0423363i	−0.971366	+	0.237589i	$0.923643\pi$
$920$	−1.67137	+	4.03505i	−0.0551035	+	0.133032i
$921$	−2.39511	−	5.78231i	−0.0789217	−	0.190534i
$922$	−2.60074	−	3.38935i	−0.0856507	−	0.111622i
$923$	0.861965	−	0.861965i	0.0283719	−	0.0283719i
$924$			3.05414i			0.100474i
$925$	−10.0163	−	13.0536i	−0.329335	−	0.429198i
$926$	−1.91132	+	2.49089i	−0.0628100	+	0.0818556i
$927$	−8.14590	+	6.25057i	−0.267546	+	0.205296i
$928$	−1.99824			−0.0655954
$929$	−31.6695	−	4.16937i	−1.03904	−	0.136793i	−0.408351	−	0.912825i	$-0.633896\pi$
$929$	−31.6695	−	4.16937i	−1.03904	−	0.136793i	−0.630693	+	0.776033i	$0.717229\pi$
$930$	0.660512	+	0.860796i	0.0216590	+	0.0282266i
$931$	−6.68764	+	2.77011i	−0.219179	+	0.0907868i
$932$	18.8373	+	5.04744i	0.617037	+	0.165334i
$933$	−0.558796	+	4.24447i	−0.0182941	+	0.138958i
$934$	0.832528	−	0.832528i	0.0272412	−	0.0272412i
$935$	11.2815	−	3.02288i	0.368946	−	0.0988587i
$936$	−0.883845	+	2.13379i	−0.0288894	+	0.0697452i
$937$	−7.98048	−	7.98048i	−0.260711	−	0.260711i	0.564632	−	0.825343i	$-0.309018\pi$
$937$	−7.98048	−	7.98048i	−0.260711	−	0.260711i	−0.825343	+	0.564632i	$0.809018\pi$
$938$	0.0350505	−	0.0846193i	0.00114444	−	0.00276292i
$939$			12.1099i			0.395193i
$940$	−30.2139	−	52.3320i	−0.985469	−	1.70688i
$941$	−32.3674	−	13.4070i	−1.05515	−	0.437056i	−0.213421	−	0.976960i	$-0.568461\pi$
$941$	−32.3674	−	13.4070i	−1.05515	−	0.437056i	−0.841727	+	0.539904i	$0.818461\pi$
$942$	0.738134	+	0.566390i	0.0240497	+	0.0184540i
$943$	−18.3729	+	7.61031i	−0.598304	+	0.247826i
$944$	−29.8187	−	7.98991i	−0.970517	−	0.260049i
$945$	−4.73312	−	6.16832i	−0.153968	−	0.200655i
$946$	−0.0264456	+	0.0986962i	−0.000859819	+	0.00320889i
$947$	43.8685	−	18.1709i	1.42553	−	0.590475i	0.469289	−	0.883045i	$-0.344510\pi$
$947$	43.8685	−	18.1709i	1.42553	−	0.590475i	0.956244	+	0.292569i	$0.0945103\pi$
$948$	1.21430	−	2.10322i	0.0394385	−	0.0683095i
$949$	6.64516	+	11.5098i	0.215711	+	0.373623i
$950$	−0.500176	−	0.383799i	−0.0162279	−	0.0124521i
$951$	1.07351	+	0.823736i	0.0348111	+	0.0267115i
$952$	−0.706446	+	0.189292i	−0.0228961	+	0.00613498i
$953$	−30.4859	+	23.3927i	−0.987535	+	0.757762i	−0.970254	−	0.242088i	$-0.922168\pi$
$953$	−30.4859	+	23.3927i	−0.987535	+	0.757762i	−0.0172809	+	0.999851i	$0.505501\pi$
$954$	2.02200	−	3.50221i	0.0654648	−	0.113388i
$955$	−50.5051	−	29.1591i	−1.63431	−	0.943567i
$956$	40.2647	+	40.2647i	1.30225	+	1.30225i
$957$	1.33114	−	1.02142i	0.0430298	−	0.0330179i
$958$		−	0.852745i		−	0.0275509i
$959$	−11.7938	−	11.7938i	−0.380840	−	0.380840i
$960$	8.02359	−	4.63242i	0.258960	−	0.149511i
$961$	−6.39698	−	1.71407i	−0.206354	−	0.0552924i
$962$	0.247449	+	0.923493i	0.00797808	+	0.0297746i
$963$	−39.3853			−1.26917
$964$	−25.5716	−	17.0403i	−0.823606	−	0.548830i
$965$	−47.2674			−1.52159
$966$	0.0444232	+	0.165790i	0.00142929	+	0.00533420i
$967$	−34.6009	−	9.27130i	−1.11269	−	0.298145i	−0.344769	−	0.938688i	$-0.612043\pi$
$967$	−34.6009	−	9.27130i	−1.11269	−	0.298145i	−0.767922	+	0.640543i	$0.778709\pi$
$968$	0.196979	−	0.113726i	0.00633114	−	0.00365529i
$969$	−0.438883	−	0.438883i	−0.0140990	−	0.0140990i
$970$			0.153475i			0.00492778i
$971$	8.29583	−	6.36562i	0.266226	−	0.204282i	−0.467018	−	0.884248i	$-0.654672\pi$
$971$	8.29583	−	6.36562i	0.266226	−	0.204282i	0.733244	+	0.679965i	$0.238005\pi$
$972$	14.7079	+	14.7079i	0.471756	+	0.471756i
$973$	14.0607	+	8.11796i	0.450766	+	0.260250i
$974$	0.677266	−	1.17306i	0.0217010	−	0.0375872i
$975$	1.70020	−	1.30461i	0.0544500	−	0.0417810i
$976$	−9.19476	+	2.46373i	−0.294317	+	0.0788620i
$977$	31.7026	+	24.3263i	1.01426	+	0.778266i	0.975280	−	0.220974i	$-0.0709235\pi$
$977$	31.7026	+	24.3263i	1.01426	+	0.778266i	0.0389768	+	0.999240i	$0.487590\pi$
$978$	0.0682764	+	0.0523904i	0.00218324	+	0.00167526i
$979$	−25.5709	−	44.2901i	−0.817249	−	1.41552i
$980$	−16.8555	+	29.1947i	−0.538431	+	0.932589i
$981$	45.5166	−	18.8536i	1.45323	−	0.601949i
$982$	1.53503	−	5.72882i	0.0489848	−	0.182814i
$983$	−4.13102	−	5.38364i	−0.131759	−	0.171712i	0.722815	−	0.691042i	$-0.242848\pi$
$983$	−4.13102	−	5.38364i	−0.131759	−	0.171712i	−0.854574	+	0.519330i	$0.826181\pi$
$984$	−1.76675	−	0.473400i	−0.0563221	−	0.0150914i
$985$	−18.3909	+	7.61776i	−0.585983	+	0.242722i
$986$	0.158559	+	0.121667i	0.00504956	+	0.00387466i
$987$	−4.41075	−	1.82699i	−0.140396	−	0.0581539i
$988$	−1.76317	−	3.05390i	−0.0560939	−	0.0971574i
$989$		−	0.552740i		−	0.0175761i
$990$	−1.52779	+	3.68841i	−0.0485564	+	0.117225i
$991$	−32.8657	−	32.8657i	−1.04401	−	1.04401i	−0.998986	−	0.0450291i	$-0.985662\pi$
$991$	−32.8657	−	32.8657i	−1.04401	−	1.04401i	−0.0450291	−	0.998986i	$-0.514338\pi$
$992$	3.98398	−	9.61817i	0.126491	−	0.305377i
$993$	11.4859	−	3.07764i	0.364495	−	0.0976661i
$994$	−0.0933014	+	0.0933014i	−0.00295934	+	0.00295934i
$995$	−3.90795	+	29.6839i	−0.123890	+	0.941041i
$996$	6.80896	+	1.82446i	0.215750	+	0.0578101i
$997$	−38.9194	+	16.1210i	−1.23259	+	0.510556i	−0.901391	−	0.433005i	$-0.857453\pi$
$997$	−38.9194	+	16.1210i	−1.23259	+	0.510556i	−0.331199	+	0.943561i	$0.607453\pi$
$998$	−3.04484	−	3.96811i	−0.0963826	−	0.125608i
$999$	11.3258	+	1.49107i	0.358332	+	0.0471752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	241.2.m.a.2.11	✓	160
241.121	even	24	inner	241.2.m.a.121.11	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.m.a.2.11	✓	160	1.1	even	1	trivial
241.2.m.a.121.11	yes	160	241.121	even	24	inner

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:	\( N \)	\(=\)	\( 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	241.m (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0371148 + 0.138514i) q^{2} +(0.407739 + 0.109253i) q^{3} +(1.71424 - 0.989718i) q^{4} +(2.06635 + 2.06635i) q^{5} +0.0605326i q^{6} +(0.858916 - 0.659069i) q^{7} +(0.403513 + 0.403513i) q^{8} +(-2.44376 - 1.41091i) q^{9} +O(q^{10})\)	\(q+(0.0371148 + 0.138514i) q^{2} +(0.407739 + 0.109253i) q^{3} +(1.71424 - 0.989718i) q^{4} +(2.06635 + 2.06635i) q^{5} +0.0605326i q^{6} +(0.858916 - 0.659069i) q^{7} +(0.403513 + 0.403513i) q^{8} +(-2.44376 - 1.41091i) q^{9} +(-0.209527 + 0.362912i) q^{10} +(-2.67850 + 2.05529i) q^{11} +(0.807093 - 0.216260i) q^{12} +(-1.13790 - 0.873139i) q^{13} +(0.123169 + 0.0945109i) q^{14} +(0.616777 + 1.06829i) q^{15} +(1.93852 - 3.35762i) q^{16} +(-1.09369 + 0.453021i) q^{17} +(0.104731 - 0.390861i) q^{18} +(0.756125 + 0.985401i) q^{19} +(5.58734 + 1.49712i) q^{20} +(0.422219 - 0.174889i) q^{21} +(-0.384099 - 0.294729i) q^{22} +(2.41967 + 1.00226i) q^{23} +(0.120443 + 0.208613i) q^{24} +3.53964i q^{25} +(0.0787094 - 0.190021i) q^{26} +(-1.73773 - 1.73773i) q^{27} +(0.820097 - 1.97989i) q^{28} +(-1.13720 + 0.304713i) q^{29} +(-0.125082 + 0.125082i) q^{30} +(0.800612 - 6.08125i) q^{31} +(1.63944 + 0.439288i) q^{32} +(-1.31668 + 0.545385i) q^{33} +(-0.103342 - 0.134678i) q^{34} +(3.13669 + 0.412954i) q^{35} -5.58560 q^{36} +(-3.68782 + 2.82976i) q^{37} +(-0.108429 + 0.141307i) q^{38} +(-0.368571 - 0.480331i) q^{39} +1.66760i q^{40} +(-5.36916 + 5.36916i) q^{41} +(0.0398951 + 0.0519924i) q^{42} +(-0.0807644 - 0.194982i) q^{43} +(-2.55745 + 6.17422i) q^{44} +(-2.13424 - 7.96511i) q^{45} +(-0.0490218 + 0.372358i) q^{46} +(-7.38687 - 7.38687i) q^{47} +(1.15724 - 1.15724i) q^{48} +(-1.50837 + 5.62931i) q^{49} +(-0.490291 + 0.131373i) q^{50} +(-0.495434 + 0.0652251i) q^{51} +(-2.81479 - 0.370574i) q^{52} +(9.65332 + 2.58660i) q^{53} +(0.176205 - 0.305195i) q^{54} +(-9.78169 - 1.28778i) q^{55} +(0.612526 + 0.0806406i) q^{56} +(0.200643 + 0.484395i) q^{57} +(-0.0844143 - 0.146210i) q^{58} +(-2.06083 - 7.69111i) q^{59} +(2.11461 + 1.22087i) q^{60} +(-1.73613 - 1.73613i) q^{61} +(0.872055 - 0.114808i) q^{62} +(-3.02887 + 0.398758i) q^{63} -7.51069i q^{64} +(-0.547083 - 4.15551i) q^{65} +(-0.124412 - 0.162137i) q^{66} +(-0.152692 - 0.569854i) q^{67} +(-1.42649 + 1.85903i) q^{68} +(0.877094 + 0.673018i) q^{69} +(0.0592178 + 0.449804i) q^{70} +(-0.110934 + 0.842630i) q^{71} +(-0.416770 - 1.55541i) q^{72} +(-8.56081 - 3.54600i) q^{73} +(-0.528835 - 0.405789i) q^{74} +(-0.386717 + 1.44325i) q^{75} +(2.27145 + 0.940865i) q^{76} +(-0.946031 + 3.53064i) q^{77} +(0.0528533 - 0.0688798i) q^{78} +(2.05523 - 2.05523i) q^{79} +(10.9437 - 2.93235i) q^{80} +(3.71403 + 6.43289i) q^{81} +(-0.942981 - 0.544430i) q^{82} +(7.30614 + 4.21820i) q^{83} +(0.550694 - 0.717679i) q^{84} +(-3.19606 - 1.32385i) q^{85} +(0.0240103 - 0.0184238i) q^{86} -0.496973 q^{87} +(-1.91015 - 0.251475i) q^{88} +(-1.97719 + 15.0182i) q^{89} +(1.02407 - 0.591247i) q^{90} -1.55282 q^{91} +(5.13986 - 0.676675i) q^{92} +(0.990838 - 2.39209i) q^{93} +(0.749025 - 1.29735i) q^{94} +(-0.473766 + 3.59861i) q^{95} +(0.620471 + 0.358229i) q^{96} +(0.317174 - 0.183120i) q^{97} -0.835723 q^{98} +(9.44544 - 1.24352i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} - 8 q^{3} - 36 q^{4} - 8 q^{5} + 8 q^{7} - 16 q^{8} - 36 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 - 8 * q^3 - 36 * q^4 - 8 * q^5 + 8 * q^7 - 16 * q^8 - 36 * q^9	\( 160 q - 8 q^{2} - 8 q^{3} - 36 q^{4} - 8 q^{5} + 8 q^{7} - 16 q^{8} - 36 q^{9} + 4 q^{10} - 8 q^{11} - 24 q^{12} - 8 q^{13} + 16 q^{14} - 20 q^{15} + 80 q^{16} - 24 q^{17} + 8 q^{18} + 4 q^{19} - 16 q^{20} + 16 q^{22} + 20 q^{23} - 12 q^{24} + 20 q^{26} + 4 q^{27} - 48 q^{28} - 24 q^{29} + 84 q^{30} - 16 q^{31} + 24 q^{32} + 20 q^{33} - 52 q^{34} + 8 q^{35} - 376 q^{36} - 36 q^{37} - 60 q^{38} - 32 q^{39} - 20 q^{41} - 64 q^{42} - 116 q^{44} + 32 q^{45} + 120 q^{46} + 8 q^{47} + 204 q^{48} - 36 q^{49} + 224 q^{50} + 56 q^{51} + 32 q^{52} - 32 q^{53} - 12 q^{54} + 36 q^{55} - 80 q^{56} + 72 q^{57} - 24 q^{58} + 20 q^{59} + 36 q^{60} + 48 q^{61} + 32 q^{62} - 112 q^{63} - 68 q^{65} + 12 q^{66} - 28 q^{67} - 72 q^{68} + 12 q^{69} + 28 q^{70} + 68 q^{72} - 36 q^{74} + 20 q^{75} - 40 q^{76} + 40 q^{77} - 100 q^{78} - 40 q^{79} + 152 q^{80} + 52 q^{81} + 96 q^{82} - 96 q^{83} + 56 q^{84} - 60 q^{85} + 92 q^{86} + 40 q^{87} + 44 q^{88} - 64 q^{89} - 12 q^{90} - 8 q^{91} - 188 q^{92} - 56 q^{93} - 52 q^{94} + 8 q^{95} - 168 q^{96} - 72 q^{97} + 144 q^{98} + 108 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 - 8 * q^3 - 36 * q^4 - 8 * q^5 + 8 * q^7 - 16 * q^8 - 36 * q^9 + 4 * q^10 - 8 * q^11 - 24 * q^12 - 8 * q^13 + 16 * q^14 - 20 * q^15 + 80 * q^16 - 24 * q^17 + 8 * q^18 + 4 * q^19 - 16 * q^20 + 16 * q^22 + 20 * q^23 - 12 * q^24 + 20 * q^26 + 4 * q^27 - 48 * q^28 - 24 * q^29 + 84 * q^30 - 16 * q^31 + 24 * q^32 + 20 * q^33 - 52 * q^34 + 8 * q^35 - 376 * q^36 - 36 * q^37 - 60 * q^38 - 32 * q^39 - 20 * q^41 - 64 * q^42 - 116 * q^44 + 32 * q^45 + 120 * q^46 + 8 * q^47 + 204 * q^48 - 36 * q^49 + 224 * q^50 + 56 * q^51 + 32 * q^52 - 32 * q^53 - 12 * q^54 + 36 * q^55 - 80 * q^56 + 72 * q^57 - 24 * q^58 + 20 * q^59 + 36 * q^60 + 48 * q^61 + 32 * q^62 - 112 * q^63 - 68 * q^65 + 12 * q^66 - 28 * q^67 - 72 * q^68 + 12 * q^69 + 28 * q^70 + 68 * q^72 - 36 * q^74 + 20 * q^75 - 40 * q^76 + 40 * q^77 - 100 * q^78 - 40 * q^79 + 152 * q^80 + 52 * q^81 + 96 * q^82 - 96 * q^83 + 56 * q^84 - 60 * q^85 + 92 * q^86 + 40 * q^87 + 44 * q^88 - 64 * q^89 - 12 * q^90 - 8 * q^91 - 188 * q^92 - 56 * q^93 - 52 * q^94 + 8 * q^95 - 168 * q^96 - 72 * q^97 + 144 * q^98 + 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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