LMFDB - Embedded newform 241.2.m.a.121.11

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			121.11
Character	$\chi$	$=$	241.121
Dual form			241.2.m.a.2.11

$q$-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 $\left(\mathbb{Z}/241\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{5}{24}\right)$

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	−0.951562	−	0.307458i	$-0.900522\pi$
$2$	0.0371148	−	0.138514i	0.0262441	−	0.0979444i	0.977806	+	0.209514i	$0.0671882\pi$
$3$	0.407739	−	0.109253i	0.235408	−	0.0630774i	−0.139186	−	0.990266i	$-0.544449\pi$
$3$	0.407739	−	0.109253i	0.235408	−	0.0630774i	0.374594	+	0.927189i	$0.377782\pi$
$4$	1.71424	+	0.989718i	0.857121	+	0.494859i
$5$	2.06635	−	2.06635i	0.924102	−	0.924102i	−0.0732144	−	0.997316i	$-0.523326\pi$
$5$	2.06635	−	2.06635i	0.924102	−	0.924102i	0.997316	+	0.0732144i	$0.0233257\pi$
$6$		−	0.0605326i		−	0.0247123i
$7$	0.858916	+	0.659069i	0.324640	+	0.249105i	0.758203	−	0.652018i	$-0.226077\pi$
$7$	0.858916	+	0.659069i	0.324640	+	0.249105i	−0.433564	+	0.901123i	$0.642744\pi$
$8$	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	0.120210	−	0.992748i	$-0.461643\pi$
$11$	−2.67850	−	2.05529i	−0.807599	−	0.619692i	−0.927809	+	0.373056i	$0.878310\pi$
$12$	0.807093	+	0.216260i	0.232988	+	0.0624289i
$13$	−1.13790	+	0.873139i	−0.315596	+	0.242165i	−0.754396	−	0.656419i	$-0.772070\pi$
$13$	−1.13790	+	0.873139i	−0.315596	+	0.242165i	0.438800	+	0.898585i	$0.355403\pi$
$14$	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	0.246090	−	0.969247i	$-0.420854\pi$
$17$	−1.09369	−	0.453021i	−0.265259	−	0.109874i	−0.511349	+	0.859373i	$0.670854\pi$
$18$	0.104731	+	0.390861i	0.0246853	+	0.0921269i
$19$	0.756125	−	0.985401i	0.173467	−	0.226066i	−0.698526	−	0.715584i	$-0.746161\pi$
$19$	0.756125	−	0.985401i	0.173467	−	0.226066i	0.871993	+	0.489518i	$0.162827\pi$
$20$	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	−0.115873	−	0.993264i	$-0.536967\pi$
$23$	2.41967	−	1.00226i	0.504536	−	0.208986i	0.620409	+	0.784278i	$0.286967\pi$
$24$	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	0.151681	−	0.988429i	$-0.451531\pi$
$29$	−1.13720	−	0.304713i	−0.211174	−	0.0565838i	−0.362855	+	0.931846i	$0.618198\pi$
$30$	−0.125082	−	0.125082i	−0.0228367	−	0.0228367i
$31$	0.800612	+	6.08125i	0.143794	+	1.09223i	0.899377	+	0.437173i	$0.144020\pi$
$31$	0.800612	+	6.08125i	0.143794	+	1.09223i	−0.755583	+	0.655053i	$0.772646\pi$
$32$	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	0.259434	−	0.965761i	$-0.416464\pi$
$37$	−3.68782	−	2.82976i	−0.606273	−	0.465210i	−0.865707	+	0.500551i	$0.833131\pi$
$38$	−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	0.150142	−	0.988664i	$-0.452027\pi$
$41$	−5.36916	−	5.36916i	−0.838522	−	0.838522i	−0.988664	+	0.150142i	$0.952027\pi$
$42$	0.0398951	−	0.0519924i	0.00615596	−	0.00802260i
$43$	−0.0807644	+	0.194982i	−0.0123165	+	0.0297345i	−0.929918	−	0.367767i	$-0.880123\pi$
$43$	−0.0807644	+	0.194982i	−0.0123165	+	0.0297345i	0.917602	+	0.397501i	$0.130123\pi$
$44$	−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	−0.0807512	+	0.996734i	$0.525732\pi$
$47$	−7.38687	+	7.38687i	−1.07749	+	1.07749i	−0.996734	+	0.0807512i	$0.974268\pi$
$48$	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	0.474768	−	0.880111i	$-0.342532\pi$
$53$	9.65332	−	2.58660i	1.32599	−	0.355297i	0.851217	+	0.524814i	$0.175865\pi$
$54$	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	0.691905	+	0.721989i	$0.256772\pi$
$59$	−2.06083	+	7.69111i	−0.268297	+	1.00130i	−0.960201	+	0.279308i	$0.909895\pi$
$60$	2.11461	−	1.22087i	0.272995	−	0.157614i
$61$	−1.73613	+	1.73613i	−0.222288	+	0.222288i	−0.809461	−	0.587173i	$-0.800241\pi$
$61$	−1.73613	+	1.73613i	−0.222288	+	0.222288i	0.587173	+	0.809461i	$0.300241\pi$
$62$	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	−0.974626	−	0.223842i	$-0.928140\pi$
$67$	−0.152692	+	0.569854i	−0.0186543	+	0.0696187i	0.955971	+	0.293460i	$0.0948068\pi$
$68$	−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	0.983600	−	0.180361i	$-0.0577266\pi$
$71$	−0.110934	−	0.842630i	−0.0131655	−	0.100002i	−0.996766	+	0.0803592i	$0.974393\pi$
$72$	−0.416770	+	1.55541i	−0.0491169	+	0.183307i
$73$	−8.56081	+	3.54600i	−1.00197	+	0.415028i	−0.822518	−	0.568739i	$-0.807431\pi$
$73$	−8.56081	+	3.54600i	−1.00197	+	0.415028i	−0.179449	+	0.983767i	$0.557431\pi$
$74$	−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	0.813206	−	0.581975i	$-0.197720\pi$
$79$	2.05523	+	2.05523i	0.231231	+	0.231231i	−0.581975	+	0.813206i	$0.697720\pi$
$80$	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	−0.0422005	−	0.999109i	$-0.513437\pi$
$83$	7.30614	−	4.21820i	0.801953	−	0.463008i	0.844154	+	0.536101i	$0.180104\pi$
$84$	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	−0.695894	−	0.718145i	$-0.744992\pi$
$89$	−1.97719	−	15.0182i	−0.209582	−	1.59193i	0.486312	−	0.873785i	$-0.338342\pi$
$90$	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	0.516016	−	0.856579i	$-0.327415\pi$
$97$	0.317174	+	0.183120i	0.0322041	+	0.0185931i	−0.483812	+	0.875172i	$0.660748\pi$
$98$	−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	0.195662	−	0.980671i	$-0.437314\pi$
$101$	−3.61216	−	1.49620i	−0.359423	−	0.148878i	−0.555085	+	0.831793i	$0.687314\pi$
$102$	−0.0274226	+	0.0662039i	−0.00271524	+	0.00655516i
$103$	1.39246	+	3.36170i	0.137204	+	0.331239i	0.977515	−	0.210865i	$-0.0676280\pi$
$103$	1.39246	+	3.36170i	0.137204	+	0.331239i	−0.840312	+	0.542104i	$0.817628\pi$
$104$	−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	0.953336	−	0.301911i	$-0.0976244\pi$
$107$	12.0875	+	6.97872i	1.16854	+	0.674658i	0.215206	+	0.976569i	$0.430958\pi$
$108$	−4.69874	+	1.25902i	−0.452137	+	0.121150i
$109$	−10.6285	−	13.8514i	−1.01803	−	1.32672i	−0.944172	−	0.329452i	$-0.893136\pi$
$109$	−10.6285	−	13.8514i	−1.01803	−	1.32672i	−0.0738559	−	0.997269i	$-0.523530\pi$
$110$	−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	0.617543	−	0.786537i	$-0.288128\pi$
$113$	8.06915	+	2.16212i	0.759081	+	0.203395i	0.141539	+	0.989933i	$0.454795\pi$
$114$	−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	0.997454	+	0.0713093i	$0.0227177\pi$
$127$	14.9263	+	11.4533i	1.32449	+	1.01632i	0.327040	+	0.945011i	$0.393949\pi$
$128$	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	−0.791406	−	0.611290i	$-0.790651\pi$
$131$	1.50219	−	11.4103i	0.131247	−	0.996920i	0.922654	−	0.385630i	$-0.126016\pi$
$132$	−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	0.660588	+	0.750749i	$0.270307\pi$
$137$	−2.01086	+	15.2740i	−0.171799	+	1.30494i	−0.832387	+	0.554195i	$0.813026\pi$
$138$	−0.0606694	−	0.146469i	−0.00516452	−	0.0124683i
$139$	5.73896	−	13.8551i	0.486772	−	1.17517i	−0.469563	−	0.882899i	$-0.655589\pi$
$139$	5.73896	−	13.8551i	0.486772	−	1.17517i	0.956335	−	0.292272i	$-0.0944114\pi$
$140$	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	0.394747	−	0.918790i	$-0.370832\pi$
$149$	6.57009	+	0.864969i	0.538243	+	0.0708610i	0.143496	+	0.989651i	$0.454166\pi$
$150$	−0.214264			−0.0174946
$151$	−2.02197	−	1.16738i	−0.164545	−	0.0950004i	0.415466	−	0.909609i	$-0.363619\pi$
$151$	−2.02197	−	1.16738i	−0.164545	−	0.0950004i	−0.580011	+	0.814608i	$0.696952\pi$
$152$	−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	0.999983	+	0.00578110i	$0.00184019\pi$
$157$	9.35678	+	12.1940i	0.746753	+	0.973187i	−0.253231	+	0.967406i	$0.581493\pi$
$158$	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	0.826018	−	0.563644i	$-0.190601\pi$
$163$	0.865490	+	1.12793i	0.0677904	+	0.0883462i	−0.758227	+	0.651990i	$0.773934\pi$
$164$	−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	−0.503965	−	0.863724i	$-0.668126\pi$
$167$	2.58319	−	1.98215i	0.199893	−	0.153384i	0.703858	+	0.710341i	$0.251459\pi$
$168$	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	0.504086	−	0.863654i	$-0.331830\pi$
$173$	−6.05833	−	7.89537i	−0.460606	−	0.600274i	−0.964692	+	0.263380i	$0.915163\pi$
$174$	−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	0.187306	−	0.982302i	$-0.440024\pi$
$179$	1.52510	+	0.200784i	0.113991	+	0.0150073i	−0.0733146	+	0.997309i	$0.523358\pi$
$180$	−11.5418	+	11.5418i	−0.860277	+	0.860277i
$181$	17.9449	−	10.3605i	1.33383	−	0.770088i	0.347947	−	0.937514i	$-0.386879\pi$
$181$	17.9449	−	10.3605i	1.33383	−	0.770088i	0.985885	+	0.167426i	$0.0535456\pi$
$182$	−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	−0.518325	−	0.855184i	$-0.673444\pi$
$191$	−19.2765	−	5.16512i	−1.39480	−	0.373735i	−0.876474	+	0.481449i	$0.840111\pi$
$192$	0.820568	+	3.06240i	0.0592194	+	0.221010i
$193$	−11.4374	−	11.4374i	−0.823281	−	0.823281i	0.163296	−	0.986577i	$-0.447787\pi$
$193$	−11.4374	−	11.4374i	−0.823281	−	0.823281i	−0.986577	+	0.163296i	$0.947787\pi$
$194$	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	0.803402	−	0.595437i	$-0.203021\pi$
$197$	−2.60680	−	6.29337i	−0.185727	−	0.448384i	−0.989129	+	0.147053i	$0.953021\pi$
$198$	0.522810	−	1.26218i	0.0371545	−	0.0896989i
$199$	6.23705	−	8.12828i	0.442132	−	0.576198i	−0.518128	−	0.855303i	$-0.673371\pi$
$199$	6.23705	−	8.12828i	0.442132	−	0.576198i	0.960261	+	0.279105i	$0.0900377\pi$
$200$	−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	0.992632	−	0.121165i	$-0.0386629\pi$
$211$	12.6588	+	12.6588i	0.871468	+	0.871468i	−0.121165	+	0.992632i	$0.538663\pi$
$212$	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	0.613730	+	0.789516i	$0.289668\pi$
$223$	7.12286	+	26.5829i	0.476982	+	1.78012i	−0.136748	+	0.990606i	$0.543665\pi$
$224$	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	−0.958297	−	0.285776i	$-0.907749\pi$
$227$	−14.0161	+	10.7550i	−0.930284	+	0.713832i	0.0280128	+	0.999608i	$0.491082\pi$
$228$	0.823366	−	0.631791i	0.0545287	−	0.0418414i
$229$	4.21516	+	1.12945i	0.278546	+	0.0746360i	0.395387	−	0.918514i	$-0.370610\pi$
$229$	4.21516	+	1.12945i	0.278546	+	0.0746360i	−0.116842	+	0.993151i	$0.537277\pi$
$230$	−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	−0.441075	−	0.897470i	$-0.645403\pi$
$233$	6.96656	−	6.96656i	0.456395	−	0.456395i	0.897470	+	0.441075i	$0.145403\pi$
$234$	−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	−0.113257	−	0.993566i	$-0.536128\pi$
$239$	7.44550	−	27.7870i	0.481609	−	1.79739i	0.594866	−	0.803825i	$-0.297205\pi$
$240$	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	0.932828	−	0.360323i	$-0.117333\pi$
$251$	2.44560	+	4.23591i	0.154365	+	0.267368i	−0.778463	+	0.627691i	$0.784000\pi$
$252$	−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	0.936694	−	0.350148i	$-0.113869\pi$
$257$	2.64692	+	4.58459i	0.165110	+	0.285979i	−0.771584	+	0.636127i	$0.780535\pi$
$258$	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	−0.381898	−	0.924205i	$-0.624729\pi$
$263$	6.68108	−	5.12658i	0.411973	−	0.316118i	0.793871	+	0.608086i	$0.208063\pi$
$264$	−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	0.951790	−	0.306750i	$-0.0992416\pi$
$269$	1.01470	+	2.44971i	0.0618676	+	0.149362i	−0.889922	+	0.456112i	$0.849242\pi$
$270$	0.994743	+	0.266541i	0.0605381	+	0.0162211i
$271$	−11.1059	−	11.1059i	−0.674635	−	0.674635i	0.284146	−	0.958781i	$-0.408290\pi$
$271$	−11.1059	−	11.1059i	−0.674635	−	0.674635i	−0.958781	+	0.284146i	$0.908290\pi$
$272$	−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	$0.234303\pi$
$281$			22.5092i			1.34278i	−0.741103	+	0.671392i	$0.765697\pi$
$282$	0.447146	+	0.447146i	0.0266272	+	0.0266272i
$283$	18.9444	−	24.6889i	1.12613	−	1.46760i	0.261490	−	0.965206i	$-0.415786\pi$
$283$	18.9444	−	24.6889i	1.12613	−	1.46760i	0.864639	−	0.502394i	$-0.167547\pi$
$284$	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	−0.770229	−	0.637768i	$-0.779858\pi$
$293$	−23.0937	+	3.04034i	−1.34915	+	0.177618i	−0.578918	+	0.815386i	$0.696525\pi$
$294$	−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	−0.976412	−	0.215914i	$-0.930727\pi$
$307$	−9.02600	+	11.7629i	−0.515141	+	0.671345i	0.461271	+	0.887259i	$0.347393\pi$
$308$	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	−0.912041	−	0.410099i	$-0.865494\pi$
$311$	1.32378	−	10.0551i	0.0750645	−	0.570171i	0.987105	−	0.160072i	$-0.0511726\pi$
$312$	0.0450967	+	0.342543i	0.00255310	+	0.0193927i
$313$	7.42506	−	27.7107i	0.419689	−	1.56630i	−0.355565	−	0.934651i	$-0.615712\pi$
$313$	7.42506	−	27.7107i	0.419689	−	1.56630i	0.775254	−	0.631649i	$-0.217622\pi$
$314$	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	−0.297961	−	0.954578i	$-0.596307\pi$
$317$	2.96154	−	1.22671i	0.166337	−	0.0688990i	0.464298	+	0.885679i	$0.346307\pi$
$318$	−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	0.986941	−	0.161080i	$-0.0514978\pi$
$331$	24.3958	+	14.0849i	1.34091	+	0.774176i	0.353971	+	0.935256i	$0.384831\pi$
$332$	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	−0.208893	−	0.977938i	$-0.566986\pi$
$337$	9.79521	−	5.65527i	0.533579	−	0.308062i	0.742473	+	0.669876i	$0.233653\pi$
$338$	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	$0.426163\pi$
$347$			36.2580i			1.94643i	−0.229890	+	0.973217i	$0.573837\pi$
$348$	−0.851933	−	0.491864i	−0.0456684	−	0.0263667i
$349$	7.06892	−	1.89411i	0.378391	−	0.101389i	−0.0646104	−	0.997911i	$-0.520580\pi$
$349$	7.06892	−	1.89411i	0.378391	−	0.101389i	0.443001	+	0.896521i	$0.353914\pi$
$350$	−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	−0.604991	−	0.796232i	$-0.706823\pi$
$353$	3.48458	−	26.4680i	0.185465	−	1.40875i	0.790457	−	0.612518i	$-0.209843\pi$
$354$	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	0.611394	−	0.791327i	$-0.290609\pi$
$359$	4.39163	+	2.53551i	0.231782	+	0.133819i	−0.379612	+	0.925146i	$0.623943\pi$
$360$	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	0.200455	+	0.979703i	$0.435758\pi$
$367$	−12.1465	+	29.3243i	−0.634043	+	1.53071i	−0.834498	+	0.551011i	$0.814242\pi$
$368$	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	0.266101	−	0.963945i	$-0.414265\pi$
$373$	−14.1734	−	18.4711i	−0.733871	−	0.956399i	−0.999972	+	0.00754627i	$0.997598\pi$
$374$	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	0.998647	−	0.0520014i	$-0.0165600\pi$
$379$	4.97846	+	12.0191i	0.255726	+	0.617378i	−0.742921	+	0.669380i	$0.766560\pi$
$380$	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	−0.231857	−	0.972750i	$-0.574480\pi$
$383$	−13.8476	−	1.82307i	−0.707579	−	0.0931546i	−0.475723	+	0.879595i	$0.657813\pi$
$384$	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	0.807237	−	0.590228i	$-0.200962\pi$
$389$	−3.56829	−	8.61462i	−0.180920	−	0.436779i	−0.988157	+	0.153449i	$0.950962\pi$
$390$	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	−0.350523	−	0.936554i	$-0.613996\pi$
$397$	1.27249	−	0.527083i	0.0638645	−	0.0264536i	0.414387	+	0.910101i	$0.363996\pi$
$398$	−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	−0.924396	−	0.381435i	$-0.875430\pi$
$401$	−2.64061	+	4.57367i	−0.131866	+	0.228398i	0.792530	+	0.609833i	$0.208763\pi$
$402$	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	−0.417753	−	0.908561i	$-0.637182\pi$
$409$	−1.42982	+	0.592251i	−0.0707000	+	0.0292849i	0.347053	+	0.937845i	$0.387182\pi$
$410$	−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	−0.168444	−	0.985711i	$-0.553874\pi$
$419$	−12.0006	−	1.57991i	−0.586269	−	0.0771838i	−0.417825	+	0.908527i	$0.637208\pi$
$420$	2.62091	+	0.345049i	0.127887	+	0.0168367i
$421$	10.8465	−	10.8465i	0.528625	−	0.528625i	−0.391537	−	0.920162i	$-0.628057\pi$
$421$	10.8465	−	10.8465i	0.528625	−	0.528625i	0.920162	+	0.391537i	$0.128057\pi$
$422$	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	−0.0136542	−	0.999907i	$-0.504346\pi$
$431$	−5.93000	−	0.780700i	−0.285638	−	0.0376050i	−0.271984	+	0.962302i	$0.587680\pi$
$432$	−9.20324	−	2.46600i	−0.442791	−	0.118645i
$433$	7.38427	+	27.5585i	0.354865	+	1.32437i	0.880654	+	0.473760i	$0.157103\pi$
$433$	7.38427	+	27.5585i	0.354865	+	1.32437i	−0.525789	+	0.850615i	$0.676230\pi$
$434$	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	−0.711911	−	0.702269i	$-0.752170\pi$
$439$	6.03564	−	14.5713i	0.288066	−	0.695452i	0.999977	+	0.00681772i	$0.00217016\pi$
$440$	−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	−0.998263	−	0.0589133i	$-0.981236\pi$
$443$	−14.3752	+	18.7342i	−0.682988	+	0.890087i	0.315275	+	0.949000i	$0.397903\pi$
$444$	−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	0.210238	−	0.977650i	$-0.432576\pi$
$449$	−7.04351	−	2.91752i	−0.332404	−	0.137686i	−0.542642	+	0.839964i	$0.682576\pi$
$450$	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	$-0.751146\pi$
$457$		−	30.1234i		−	1.40911i	0.709648	−	0.704556i	$-0.248854\pi$
$458$	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	−0.365358	−	0.930867i	$-0.619053\pi$
$461$	−27.5241	−	11.4009i	−1.28193	−	0.530992i	−0.916569	+	0.399875i	$0.869053\pi$
$462$	−0.213719	+	0.0572657i	−0.00994309	+	0.00266424i
$463$	13.3286	−	17.3701i	0.619431	−	0.807258i	−0.373288	−	0.927716i	$-0.621770\pi$
$463$	13.3286	−	17.3701i	0.619431	−	0.807258i	0.992718	+	0.120458i	$0.0384362\pi$
$464$	−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	−0.945238	−	0.326380i	$-0.894171\pi$
$467$	−4.10519	+	7.11039i	−0.189965	+	0.329030i	0.755273	+	0.655410i	$0.227504\pi$
$468$	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	−0.387644	−	0.921809i	$-0.626711\pi$
$479$	−5.74397	+	1.53909i	−0.262448	+	0.0703229i	0.125195	+	0.992132i	$0.460044\pi$
$480$	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	−0.842055	−	0.539392i	$-0.818654\pi$
$487$	−6.67918	+	6.67918i	−0.302663	+	0.302663i	0.539392	+	0.842055i	$0.318654\pi$
$488$			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	−0.628612	+	0.777719i	$0.716376\pi$
$491$	−35.8180	+	20.6795i	−1.61644	+	0.933253i	−0.987831	+	0.155534i	$0.950290\pi$
$492$	−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	−0.482136	−	0.876097i	$-0.660139\pi$
$499$	−32.2241	−	13.3477i	−1.44255	−	0.597524i	−0.960415	+	0.278572i	$0.910139\pi$
$500$	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	−0.344473	−	0.938796i	$-0.611942\pi$
$503$	−28.0768	−	11.6298i	−1.25188	−	0.518546i	−0.907408	+	0.420250i	$0.861942\pi$
$504$	−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	−0.208989	+	0.977918i	$0.567017\pi$
$509$	−26.7778	+	26.7778i	−1.18691	+	1.18691i	−0.977918	+	0.208989i	$0.932983\pi$
$510$	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	−0.986001	−	0.166742i	$-0.946675\pi$
$521$	−13.0047	+	16.9480i	−0.569744	+	0.742505i	0.416256	+	0.909247i	$0.363342\pi$
$522$		−	0.476402i		−	0.0208516i
$523$	−10.5226	−	10.5226i	−0.460120	−	0.460120i	0.438575	−	0.898695i	$-0.355484\pi$
$523$	−10.5226	−	10.5226i	−0.460120	−	0.460120i	−0.898695	+	0.438575i	$0.855484\pi$
$524$	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	0.804183	+	0.594382i	$0.202603\pi$
$541$	−4.40652	+	16.4453i	−0.189451	+	0.707041i	−0.993634	+	0.112659i	$0.964063\pi$
$542$	−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	0.454404	+	0.890796i	$0.349852\pi$
$547$	−5.03010	+	38.2074i	−0.215072	+	1.63363i	−0.669475	+	0.742835i	$0.733481\pi$
$548$	−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	−0.998170	−	0.0604725i	$-0.980739\pi$
$557$	−3.86973	−	14.4420i	−0.163966	−	0.611928i	0.834204	−	0.551456i	$-0.185927\pi$
$558$	−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	−0.997711	−	0.0676189i	$-0.978460\pi$
$563$	−10.4472	+	18.0950i	−0.440296	+	0.762615i	0.557415	+	0.830234i	$0.311793\pi$
$564$	−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	−0.993304	−	0.115530i	$-0.963143\pi$
$571$	−1.52328	−	11.5705i	−0.0637475	−	0.484210i	0.929556	−	0.368680i	$-0.120190\pi$
$572$	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	0.954075	+	0.299568i	$0.0968425\pi$
$577$	2.64333	+	20.0781i	0.110043	+	0.835861i	−0.844032	+	0.536293i	$0.819824\pi$
$578$	−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	−0.384852	−	0.922978i	$-0.625748\pi$
$587$	−0.105132	+	0.0435469i	−0.00433924	+	0.00179737i	0.380513	+	0.924776i	$0.375748\pi$
$588$		−	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	0.0510224	−	0.998698i	$-0.483752\pi$
$593$	−15.0757	−	6.24456i	−0.619085	−	0.256433i	−0.670107	+	0.742264i	$0.733752\pi$
$594$	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	−0.191130	−	0.981565i	$-0.561215\pi$
$599$	15.6169	−	37.7026i	0.638090	−	1.54049i	0.829220	−	0.558922i	$-0.188785\pi$
$600$	−0.738415	−	0.426324i	−0.0301457	−	0.0174046i
$601$	−8.48011	−	14.6880i	−0.345911	−	0.599135i	0.639608	−	0.768701i	$-0.279097\pi$
$601$	−8.48011	−	14.6880i	−0.345911	−	0.599135i	−0.985519	+	0.169566i	$0.945763\pi$
$602$	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	0.211174	−	0.977448i	$-0.432271\pi$
$607$	−18.8790	−	18.8790i	−0.766274	−	0.766274i	−0.977448	+	0.211174i	$0.932271\pi$
$608$	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	0.646503	+	0.762911i	$0.276231\pi$
$613$	−4.34337	+	32.9911i	−0.175427	+	1.33250i	−0.821930	+	0.569588i	$0.807103\pi$
$614$	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	$0.241453\pi$
$617$			34.1725i			1.37573i	−0.725837	+	0.687867i	$0.758547\pi$
$618$	0.203493	−	0.0842894i	0.00818567	−	0.00339062i
$619$	3.92353	−	29.8022i	0.157700	−	1.19785i	−0.711245	−	0.702944i	$-0.751869\pi$
$619$	3.92353	−	29.8022i	0.157700	−	1.19785i	0.868946	−	0.494908i	$-0.164798\pi$
$620$	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	0.157345	−	0.987544i	$-0.449706\pi$
$631$	1.34978	+	0.177701i	0.0537337	+	0.00707418i	−0.103611	+	0.994618i	$0.533040\pi$
$632$	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	−0.0700972	−	0.997540i	$-0.522331\pi$
$641$	19.2100	−	11.0909i	0.758749	−	0.438064i	0.828847	+	0.559476i	$0.188998\pi$
$642$	0.422440	−	0.731687i	0.0166724	−	0.0288774i
$643$	13.0505	+	3.49688i	0.514663	+	0.137903i	0.506797	−	0.862066i	$-0.330829\pi$
$643$	13.0505	+	3.49688i	0.514663	+	0.137903i	0.00786602	+	0.999969i	$0.497496\pi$
$644$	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	−0.658547	−	0.752539i	$-0.728829\pi$
$647$	−15.0604	+	6.23821i	−0.592085	+	0.245249i	0.0664625	+	0.997789i	$0.478829\pi$
$648$	−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	0.885699	+	0.464260i	$0.153680\pi$
$653$	−2.29933	+	17.4652i	−0.0899798	+	0.683465i	−0.975679	+	0.219205i	$0.929654\pi$
$654$	−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	$0.110648\pi$
$659$			17.4897i			0.681303i	−0.940190	+	0.340651i	$0.889352\pi$
$660$	−8.17323	−	1.07603i	−0.318142	−	0.0418842i
$661$	43.4068	+	5.71461i	1.68833	+	0.222273i	0.912617	−	0.408816i	$-0.134058\pi$
$661$	43.4068	+	5.71461i	1.68833	+	0.222273i	0.775711	+	0.631088i	$0.217391\pi$
$662$	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	0.733218	−	0.679994i	$-0.238018\pi$
$673$	26.6740	+	7.14727i	1.02821	+	0.275507i	0.294988	+	0.955501i	$0.404684\pi$
$674$	−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	−0.959327	−	0.282297i	$-0.908904\pi$
$677$	−2.75159	−	20.9004i	−0.105752	−	0.803268i	0.853575	−	0.520970i	$-0.174430\pi$
$678$	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	$0.111912\pi$
$683$			18.0004i			0.688766i	−0.938829	+	0.344383i	$0.888088\pi$
$684$	−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	−0.244672	−	0.969606i	$-0.578680\pi$
$691$	0.742327	−	0.198906i	0.0282395	−	0.00756674i	0.272911	+	0.962039i	$0.412014\pi$
$692$	−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	−0.945726	−	0.324964i	$-0.894648\pi$
$701$	−23.2094	+	17.8092i	−0.876608	+	0.672645i	0.0691189	+	0.997608i	$0.477981\pi$
$702$	−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	−0.806971	−	0.590591i	$-0.798895\pi$
$709$	−11.8587	+	9.09950i	−0.445363	+	0.341739i	0.361608	+	0.932330i	$0.382228\pi$
$710$	−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	0.397285	−	0.917695i	$-0.369952\pi$
$719$	−5.33119	−	3.07796i	−0.198820	−	0.114789i	−0.596105	+	0.802907i	$0.703286\pi$
$720$	−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	−0.0705332	−	0.997509i	$-0.522470\pi$
$727$	−26.1451	−	15.0949i	−0.969668	−	0.559838i	−0.899135	+	0.437671i	$0.855803\pi$
$728$	−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	0.651519	−	0.758632i	$-0.274132\pi$
$733$	−8.96785	−	15.5328i	−0.331235	−	0.573716i	−0.982754	+	0.184916i	$0.940799\pi$
$734$	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	0.972304	+	0.233720i	$0.0750897\pi$
$739$	18.7182	+	32.4208i	0.688559	+	1.19262i	−0.283745	+	0.958900i	$0.591577\pi$
$740$	−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	0.215075	−	0.976598i	$-0.431000\pi$
$743$	24.2497	−	6.49768i	0.889634	−	0.238377i	0.674559	+	0.738221i	$0.264334\pi$
$744$	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	−0.992755	−	0.120156i	$-0.961661\pi$
$751$	−10.2968	−	24.8586i	−0.375734	−	0.907103i	0.617021	−	0.786947i	$-0.288339\pi$
$752$	−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	−0.995134	−	0.0985342i	$-0.968585\pi$
$757$	−17.6747	+	23.0341i	−0.642397	+	0.837189i	0.352736	+	0.935723i	$0.385251\pi$
$758$	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	−0.963335	−	0.268302i	$-0.913538\pi$
$761$	−26.8460	−	34.9863i	−0.973165	−	1.26825i	−0.00983014	−	0.999952i	$-0.503129\pi$
$762$	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	0.943070	+	0.332594i	$0.107924\pi$
$769$	3.27823	+	24.9006i	0.118216	+	0.897939i	−0.824854	+	0.565345i	$0.808743\pi$
$770$	−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	0.974978	−	0.222303i	$-0.0713574\pi$
$773$	47.4924	+	12.7255i	1.70818	+	0.457706i	0.733204	+	0.680009i	$0.238024\pi$
$774$	−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	$-0.888685\pi$
$787$		−	19.2234i		−	0.685242i	0.939474	−	0.342621i	$-0.111315\pi$
$788$	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	−0.00878675	−	0.999961i	$-0.502797\pi$
$797$	26.9559	−	20.6840i	0.954828	−	0.732665i	0.963614	+	0.267296i	$0.0861303\pi$
$798$	−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	0.999872	−	0.0160211i	$-0.00509990\pi$
$809$	35.3597	+	27.1325i	1.24318	+	0.953927i	0.243311	+	0.969948i	$0.421767\pi$
$810$	−3.11277			−0.109371
$811$	−49.1246	+	6.46738i	−1.72500	+	0.227100i	−0.926869	−	0.375385i	$-0.877511\pi$
$811$	−49.1246	+	6.46738i	−1.72500	+	0.227100i	−0.798130	+	0.602485i	$0.794177\pi$
$812$	−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	−0.951999	−	0.306100i	$-0.900976\pi$
$823$	−6.05057	+	10.4799i	−0.210910	+	0.365306i	0.741090	+	0.671406i	$0.234309\pi$
$824$	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	−0.986882	−	0.161441i	$-0.948386\pi$
$827$	0.234567	−	1.78172i	0.00815670	−	0.0619563i	0.995039	+	0.0994843i	$0.0317193\pi$
$828$	−13.5153	+	5.59823i	−0.469690	+	0.194552i
$829$			50.4149i			1.75098i	0.483234	+	0.875491i	$0.339462\pi$
$829$			50.4149i			1.75098i	−0.483234	+	0.875491i	$0.660538\pi$
$830$	−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	0.604487	−	0.796615i	$-0.293378\pi$
$839$	−5.56510	−	5.56510i	−0.192129	−	0.192129i	−0.796615	+	0.604487i	$0.793378\pi$
$840$	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	0.809497	−	0.587124i	$-0.199740\pi$
$853$	28.2347	+	11.6952i	0.966738	+	0.400436i	0.157241	+	0.987560i	$0.449740\pi$
$854$	−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	0.147897	−	0.989003i	$-0.452750\pi$
$857$	−18.5793	−	10.7268i	−0.634656	−	0.366419i	−0.782553	+	0.622584i	$0.786083\pi$
$858$		−	0.293123i		−	0.0100071i
$859$	−25.6387	+	10.6199i	−0.874780	+	0.362346i	−0.774470	−	0.632610i	$-0.781984\pi$
$859$	−25.6387	+	10.6199i	−0.874780	+	0.362346i	−0.100310	+	0.994956i	$0.531984\pi$
$860$	−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	0.671221	−	0.741258i	$-0.265770\pi$
$863$	18.2635	+	7.56499i	0.621697	+	0.257515i	−0.0495237	+	0.998773i	$0.515770\pi$
$864$	−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	−0.460799	−	0.887505i	$-0.652437\pi$
$881$	2.29745	−	1.32643i	0.0774030	−	0.0446886i	0.538202	+	0.842816i	$0.319104\pi$
$882$	2.04231	−	1.17913i	0.0687681	−	0.0397033i
$883$	17.4301	−	30.1899i	0.586571	−	1.01597i	−0.408107	−	0.912934i	$-0.633811\pi$
$883$	17.4301	−	30.1899i	0.586571	−	1.01597i	0.994678	−	0.103037i	$-0.0328558\pi$
$884$	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	−0.801002	−	0.598662i	$-0.795699\pi$
$887$	−12.1109	−	45.1985i	−0.406645	−	1.51762i	0.394357	−	0.918957i	$-0.370967\pi$
$888$	−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	−0.842914	−	0.538049i	$-0.819162\pi$
$907$	4.02278	−	9.71184i	0.133574	−	0.322477i	0.976488	+	0.215572i	$0.0691617\pi$
$908$	−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	0.319537	−	0.947574i	$-0.396473\pi$
$911$	32.2971	−	8.65399i	1.07005	−	0.286719i	0.750514	+	0.660854i	$0.229806\pi$
$912$	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	−0.971366	−	0.237589i	$-0.923643\pi$
$919$	−0.343893	+	1.28343i	−0.0113440	+	0.0423363i	0.960022	+	0.279925i	$0.0903096\pi$
$920$	−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	−0.630693	−	0.776033i	$-0.717229\pi$
$929$	−31.6695	+	4.16937i	−1.03904	+	0.136793i	−0.408351	+	0.912825i	$0.633896\pi$
$930$	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	−0.825343	−	0.564632i	$-0.809018\pi$
$937$	−7.98048	+	7.98048i	−0.260711	+	0.260711i	0.564632	+	0.825343i	$0.309018\pi$
$938$	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	−0.841727	−	0.539904i	$-0.818461\pi$
$941$	−32.3674	+	13.4070i	−1.05515	+	0.437056i	−0.213421	+	0.976960i	$0.568461\pi$
$942$	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	0.956244	−	0.292569i	$-0.0945103\pi$
$947$	43.8685	+	18.1709i	1.42553	+	0.590475i	0.469289	+	0.883045i	$0.344510\pi$
$948$	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	−0.0172809	−	0.999851i	$-0.505501\pi$
$953$	−30.4859	−	23.3927i	−0.987535	−	0.757762i	−0.970254	+	0.242088i	$0.922168\pi$
$954$	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	−0.767922	−	0.640543i	$-0.778709\pi$
$967$	−34.6009	+	9.27130i	−1.11269	+	0.298145i	−0.344769	+	0.938688i	$0.612043\pi$
$968$	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	0.733244	−	0.679965i	$-0.238005\pi$
$971$	8.29583	+	6.36562i	0.266226	+	0.204282i	−0.467018	+	0.884248i	$0.654672\pi$
$972$	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	0.0389768	−	0.999240i	$-0.487590\pi$
$977$	31.7026	−	24.3263i	1.01426	−	0.778266i	0.975280	+	0.220974i	$0.0709235\pi$
$978$	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	−0.854574	−	0.519330i	$-0.826181\pi$
$983$	−4.13102	+	5.38364i	−0.131759	+	0.171712i	0.722815	+	0.691042i	$0.242848\pi$
$984$	−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	−0.0450291	+	0.998986i	$0.514338\pi$
$991$	−32.8657	+	32.8657i	−1.04401	+	1.04401i	−0.998986	+	0.0450291i	$0.985662\pi$
$992$	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	−0.331199	−	0.943561i	$-0.607453\pi$
$997$	−38.9194	−	16.1210i	−1.23259	−	0.510556i	−0.901391	+	0.433005i	$0.857453\pi$
$998$	−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.121.11	yes	160
241.2	even	24	inner	241.2.m.a.2.11	✓	160

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

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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