LMFDB - Embedded newform 605.2.s.b.416.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(16,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(110))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("605.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.s (of order $55$, degree $40$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$880$
Relative dimension:	$22$ over $\Q(\zeta_{55})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{55}]$

Embedding invariants

Embedding label			416.13
Character	$\chi$	$=$	605.416
Dual form			605.2.s.b.16.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.742152 - 0.0851540i) q^{2} +(0.230756 - 0.167654i) q^{3} +(-1.40448 + 0.326599i) q^{4} +(-0.564443 - 0.825472i) q^{5} +(0.156980 - 0.144075i) q^{6} +(0.473372 - 0.487088i) q^{7} +(-2.42169 + 0.864056i) q^{8} +(-0.901911 + 2.77580i) q^{9} +O(q^{10})$	\(q+(0.742152 - 0.0851540i) q^{2} +(0.230756 - 0.167654i) q^{3} +(-1.40448 + 0.326599i) q^{4} +(-0.564443 - 0.825472i) q^{5} +(0.156980 - 0.144075i) q^{6} +(0.473372 - 0.487088i) q^{7} +(-2.42169 + 0.864056i) q^{8} +(-0.901911 + 2.77580i) q^{9} +(-0.489195 - 0.564561i) q^{10} +(1.96261 + 2.67361i) q^{11} +(-0.269338 + 0.310832i) q^{12} +(3.10068 + 5.14191i) q^{13} +(0.309837 - 0.401803i) q^{14} +(-0.268642 - 0.0958514i) q^{15} +(0.864340 - 0.424968i) q^{16} +(-1.19068 - 0.973612i) q^{17} +(-0.432985 + 2.13686i) q^{18} +(0.461091 - 0.0263661i) q^{19} +(1.06235 + 0.975016i) q^{20} +(0.0275711 - 0.191761i) q^{21} +(1.68422 + 1.81710i) q^{22} +(0.0315878 + 0.219698i) q^{23} +(-0.413956 + 0.605392i) q^{24} +(-0.362808 + 0.931864i) q^{25} +(2.73903 + 3.55204i) q^{26} +(0.521675 + 1.60555i) q^{27} +(-0.505761 + 0.838711i) q^{28} +(3.59889 + 9.24368i) q^{29} +(-0.207536 - 0.0482604i) q^{30} +(7.36953 - 3.11439i) q^{31} +(4.93138 - 3.16920i) q^{32} +(0.901124 + 0.287912i) q^{33} +(-0.966571 - 0.621177i) q^{34} +(-0.669269 - 0.115822i) q^{35} +(0.360148 - 4.19313i) q^{36} +(-0.0106008 - 0.123423i) q^{37} +(0.339955 - 0.0588315i) q^{38} +(1.57756 + 0.666683i) q^{39} +(2.08016 + 1.51132i) q^{40} +(-7.96216 - 4.49644i) q^{41} +(0.00413271 - 0.144664i) q^{42} +(-9.47245 - 2.78136i) q^{43} +(-3.62965 - 3.11406i) q^{44} +(2.80042 - 0.822277i) q^{45} +(0.0421511 + 0.160359i) q^{46} +(1.96893 + 9.71705i) q^{47} +(0.128204 - 0.242974i) q^{48} +(0.186718 + 6.53600i) q^{49} +(-0.189907 + 0.722480i) q^{50} +(-0.437986 - 0.0250449i) q^{51} +(-6.03420 - 6.20905i) q^{52} +(-8.61725 - 4.23681i) q^{53} +(0.523881 + 1.14714i) q^{54} +(1.09921 - 3.12918i) q^{55} +(-0.725487 + 1.58859i) q^{56} +(0.101979 - 0.0833880i) q^{57} +(3.45806 + 6.55376i) q^{58} +(-6.23543 + 3.52131i) q^{59} +(0.408609 + 0.0468835i) q^{60} +(3.34920 + 0.384285i) q^{61} +(5.20411 - 2.93890i) q^{62} +(0.925118 + 1.75329i) q^{63} +(1.89871 - 1.55257i) q^{64} +(2.49434 - 5.46184i) q^{65} +(0.693288 + 0.136940i) q^{66} +(-1.32801 - 2.90794i) q^{67} +(1.99027 + 0.978549i) q^{68} +(0.0441223 + 0.0454007i) q^{69} +(-0.506562 - 0.0289663i) q^{70} +(0.492892 - 1.87516i) q^{71} +(-0.214298 - 7.50141i) q^{72} +(-2.45507 + 4.65287i) q^{73} +(-0.0183774 - 0.0906960i) q^{74} +(0.0725107 + 0.275859i) q^{75} +(-0.638984 + 0.187623i) q^{76} +(2.23133 + 0.309649i) q^{77} +(1.22756 + 0.360445i) q^{78} +(0.168040 - 5.88216i) q^{79} +(-0.838670 - 0.473619i) q^{80} +(-6.69414 - 4.86358i) q^{81} +(-6.29203 - 2.65903i) q^{82} +(7.21701 - 1.24895i) q^{83} +(0.0239058 + 0.278330i) q^{84} +(-0.131620 + 1.53242i) q^{85} +(-7.26685 - 1.25758i) q^{86} +(2.38021 + 1.52967i) q^{87} +(-7.06296 - 4.77884i) q^{88} +(5.44962 - 3.50226i) q^{89} +(2.00832 - 0.848722i) q^{90} +(3.97234 + 0.923727i) q^{91} +(-0.116118 - 0.298246i) q^{92} +(1.17842 - 1.95419i) q^{93} +(2.28869 + 7.04387i) q^{94} +(-0.282024 - 0.365736i) q^{95} +(0.606615 - 1.55808i) q^{96} +(5.36102 - 7.84025i) q^{97} +(0.695140 + 4.83481i) q^{98} +(-9.19148 + 3.03643i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 880 q + 4 q^{2} - q^{3} + 24 q^{4} + 22 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 217 q^{9}+O(q^{10}) $ 880 * q + 4 * q^2 - q^3 + 24 * q^4 + 22 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 217 * q^9	\( 880 q + 4 q^{2} - q^{3} + 24 q^{4} + 22 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 217 q^{9} - 6 q^{10} + 5 q^{11} - 5 q^{12} - 26 q^{13} - 108 q^{14} - 12 q^{15} + 34 q^{16} - q^{17} - 14 q^{18} + q^{19} + 19 q^{20} - 10 q^{21} + 275 q^{22} - 51 q^{23} + 283 q^{24} + 22 q^{25} - 16 q^{27} - 4 q^{28} - 19 q^{29} + q^{30} - 34 q^{31} - 122 q^{32} + 19 q^{33} + 52 q^{34} + 8 q^{35} - 21 q^{36} - 109 q^{37} - 10 q^{38} - 9 q^{39} - 64 q^{40} + 4 q^{41} - 49 q^{42} - 97 q^{43} + 17 q^{44} - 80 q^{45} - 91 q^{46} + 166 q^{47} - 159 q^{48} + 175 q^{49} + 4 q^{50} - 112 q^{51} - 128 q^{52} - 141 q^{53} - 37 q^{54} - 5 q^{55} + 79 q^{56} - 204 q^{57} - 190 q^{58} + 9 q^{59} - 22 q^{60} + 2 q^{61} - 105 q^{62} - q^{63} - 176 q^{64} - 14 q^{65} - 112 q^{66} - 13 q^{67} - 35 q^{68} - 53 q^{69} + 24 q^{70} - 50 q^{71} + 705 q^{72} + q^{73} + 40 q^{74} - q^{75} - 148 q^{76} - 104 q^{77} - 187 q^{78} - 83 q^{79} - q^{80} - 238 q^{81} - 54 q^{82} - 151 q^{83} + 4 q^{84} - 29 q^{85} - 39 q^{86} - 74 q^{87} - 143 q^{88} - 52 q^{89} - 28 q^{90} - 188 q^{91} - 253 q^{92} + 122 q^{93} - 187 q^{94} + 122 q^{95} - 155 q^{96} + 283 q^{97} - 92 q^{98} + 172 q^{99}+O(q^{100}) \) 880 * q + 4 * q^2 - q^3 + 24 * q^4 + 22 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 217 * q^9 - 6 * q^10 + 5 * q^11 - 5 * q^12 - 26 * q^13 - 108 * q^14 - 12 * q^15 + 34 * q^16 - q^17 - 14 * q^18 + q^19 + 19 * q^20 - 10 * q^21 + 275 * q^22 - 51 * q^23 + 283 * q^24 + 22 * q^25 - 16 * q^27 - 4 * q^28 - 19 * q^29 + q^30 - 34 * q^31 - 122 * q^32 + 19 * q^33 + 52 * q^34 + 8 * q^35 - 21 * q^36 - 109 * q^37 - 10 * q^38 - 9 * q^39 - 64 * q^40 + 4 * q^41 - 49 * q^42 - 97 * q^43 + 17 * q^44 - 80 * q^45 - 91 * q^46 + 166 * q^47 - 159 * q^48 + 175 * q^49 + 4 * q^50 - 112 * q^51 - 128 * q^52 - 141 * q^53 - 37 * q^54 - 5 * q^55 + 79 * q^56 - 204 * q^57 - 190 * q^58 + 9 * q^59 - 22 * q^60 + 2 * q^61 - 105 * q^62 - q^63 - 176 * q^64 - 14 * q^65 - 112 * q^66 - 13 * q^67 - 35 * q^68 - 53 * q^69 + 24 * q^70 - 50 * q^71 + 705 * q^72 + q^73 + 40 * q^74 - q^75 - 148 * q^76 - 104 * q^77 - 187 * q^78 - 83 * q^79 - q^80 - 238 * q^81 - 54 * q^82 - 151 * q^83 + 4 * q^84 - 29 * q^85 - 39 * q^86 - 74 * q^87 - 143 * q^88 - 52 * q^89 - 28 * q^90 - 188 * q^91 - 253 * q^92 + 122 * q^93 - 187 * q^94 + 122 * q^95 - 155 * q^96 + 283 * q^97 - 92 * q^98 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{53}{55}\right)$

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 $

$2$	0.742152	−	0.0851540i	0.524781	−	0.0602130i	0.152447	−	0.988312i	$-0.451285\pi$
$2$	0.742152	−	0.0851540i	0.524781	−	0.0602130i	0.372334	+	0.928099i	$0.378557\pi$
$3$	0.230756	−	0.167654i	0.133227	−	0.0967951i	−0.519176	−	0.854667i	$-0.673761\pi$
$3$	0.230756	−	0.167654i	0.133227	−	0.0967951i	0.652403	+	0.757872i	$0.273761\pi$
$4$	−1.40448	+	0.326599i	−0.702242	+	0.163299i
$5$	−0.564443	−	0.825472i	−0.252427	−	0.369162i
$5$	−0.564443	−	0.825472i	−0.252427	−	0.369162i
$6$	0.156980	−	0.144075i	0.0640867	−	0.0588182i
$7$	0.473372	−	0.487088i	0.178918	−	0.184102i	−0.621741	−	0.783223i	$-0.713574\pi$
$7$	0.473372	−	0.487088i	0.178918	−	0.184102i	0.800658	+	0.599121i	$0.204483\pi$
$8$	−2.42169	+	0.864056i	−0.856196	+	0.305490i
$9$	−0.901911	+	2.77580i	−0.300637	+	0.925265i
$10$	−0.489195	−	0.564561i	−0.154697	−	0.178530i
$11$	1.96261	+	2.67361i	0.591748	+	0.806123i
$11$	1.96261	+	2.67361i	0.591748	+	0.806123i
$12$	−0.269338	+	0.310832i	−0.0777511	+	0.0897295i
$13$	3.10068	+	5.14191i	0.859975	+	1.42611i	0.904211	+	0.427087i	$0.140460\pi$
$13$	3.10068	+	5.14191i	0.859975	+	1.42611i	−0.0442359	+	0.999021i	$0.514085\pi$
$14$	0.309837	−	0.401803i	0.0828073	−	0.107386i
$15$	−0.268642	−	0.0958514i	−0.0693632	−	0.0247487i
$16$	0.864340	−	0.424968i	0.216085	−	0.106242i
$17$	−1.19068	−	0.973612i	−0.288782	−	0.236135i	0.477513	−	0.878624i	$-0.341538\pi$
$17$	−1.19068	−	0.973612i	−0.288782	−	0.236135i	−0.766295	+	0.642489i	$0.777902\pi$
$18$	−0.432985	+	2.13686i	−0.102055	+	0.503664i
$19$	0.461091	−	0.0263661i	0.105782	−	0.00604881i	−0.00411786	−	0.999992i	$-0.501311\pi$
$19$	0.461091	−	0.0263661i	0.105782	−	0.00604881i	0.109899	+	0.993943i	$0.464947\pi$
$20$	1.06235	+	0.975016i	0.237549	+	0.218020i
$21$	0.0275711	−	0.191761i	0.00601651	−	0.0418457i
$22$	1.68422	+	1.81710i	0.359077	+	0.387407i
$23$	0.0315878	+	0.219698i	0.00658650	+	0.0458101i	0.992850	−	0.119372i	$-0.0380880\pi$
$23$	0.0315878	+	0.219698i	0.00658650	+	0.0458101i	−0.986263	+	0.165182i	$0.947179\pi$
$24$	−0.413956	+	0.605392i	−0.0844985	+	0.123575i
$25$	−0.362808	+	0.931864i	−0.0725615	+	0.186373i
$26$	2.73903	+	3.55204i	0.537169	+	0.696613i
$27$	0.521675	+	1.60555i	0.100396	+	0.308988i
$28$	−0.505761	+	0.838711i	−0.0955799	+	0.158501i
$29$	3.59889	+	9.24368i	0.668297	+	1.71651i	0.697151	+	0.716924i	$0.254451\pi$
$29$	3.59889	+	9.24368i	0.668297	+	1.71651i	−0.0288542	+	0.999584i	$0.509186\pi$
$30$	−0.207536	−	0.0482604i	−0.0378907	−	0.00881110i
$31$	7.36953	−	3.11439i	1.32361	−	0.559361i	0.391045	−	0.920372i	$-0.372114\pi$
$31$	7.36953	−	3.11439i	1.32361	−	0.559361i	0.932562	+	0.361011i	$0.117568\pi$
$32$	4.93138	−	3.16920i	0.871752	−	0.560241i
$33$	0.901124	+	0.287912i	0.156866	+	0.0501191i
$34$	−0.966571	−	0.621177i	−0.165765	−	0.106531i
$35$	−0.669269	−	0.115822i	−0.113127	−	0.0195774i
$36$	0.360148	−	4.19313i	0.0600246	−	0.698854i
$37$	−0.0106008	−	0.123423i	−0.00174276	−	0.0202906i	0.995409	−	0.0957159i	$-0.0305140\pi$
$37$	−0.0106008	−	0.123423i	−0.00174276	−	0.0202906i	−0.997151	+	0.0754253i	$0.975969\pi$
$38$	0.339955	−	0.0588315i	0.0551479	−	0.00954373i
$39$	1.57756	+	0.666683i	0.252612	+	0.106755i
$40$	2.08016	+	1.51132i	0.328902	+	0.238961i
$41$	−7.96216	−	4.49644i	−1.24348	−	0.702226i	−0.277472	−	0.960734i	$-0.589497\pi$
$41$	−7.96216	−	4.49644i	−1.24348	−	0.702226i	−0.966009	+	0.258508i	$0.916769\pi$
$42$	0.00413271	−	0.144664i	0.000637692	−	0.0223221i
$43$	−9.47245	−	2.78136i	−1.44454	−	0.424154i	−0.536805	−	0.843707i	$-0.680369\pi$
$43$	−9.47245	−	2.78136i	−1.44454	−	0.424154i	−0.907731	+	0.419553i	$0.862187\pi$
$44$	−3.62965	−	3.11406i	−0.547190	−	0.469462i
$45$	2.80042	−	0.822277i	0.417462	−	0.122578i
$46$	0.0421511	+	0.160359i	0.00621484	+	0.0236437i
$47$	1.96893	+	9.71705i	0.287198	+	1.41738i	0.820594	+	0.571511i	$0.193643\pi$
$47$	1.96893	+	9.71705i	0.287198	+	1.41738i	−0.533396	+	0.845865i	$0.679085\pi$
$48$	0.128204	−	0.242974i	0.0185047	−	0.0350703i
$49$	0.186718	+	6.53600i	0.0266741	+	0.933714i
$50$	−0.189907	+	0.722480i	−0.0268568	+	0.102174i
$51$	−0.437986	−	0.0250449i	−0.0613303	−	0.00350699i
$52$	−6.03420	−	6.20905i	−0.836793	−	0.861040i
$53$	−8.61725	−	4.23681i	−1.18367	−	0.581971i	−0.260167	−	0.965564i	$-0.583778\pi$
$53$	−8.61725	−	4.23681i	−1.18367	−	0.581971i	−0.923503	+	0.383592i	$0.874687\pi$
$54$	0.523881	+	1.14714i	0.0712912	+	0.156106i
$55$	1.09921	−	3.12918i	0.148217	−	0.421938i
$56$	−0.725487	+	1.58859i	−0.0969473	+	0.212285i
$57$	0.101979	−	0.0833880i	0.0135075	−	0.0110450i
$58$	3.45806	+	6.55376i	0.454066	+	0.860550i
$59$	−6.23543	+	3.52131i	−0.811784	+	0.458435i	−0.840933	−	0.541140i	$-0.817993\pi$
$59$	−6.23543	+	3.52131i	−0.811784	+	0.458435i	0.0291489	+	0.999575i	$0.490720\pi$
$60$	0.408609	+	0.0468835i	0.0527512	+	0.00605264i
$61$	3.34920	+	0.384285i	0.428821	+	0.0492027i	0.325716	−	0.945468i	$-0.394395\pi$
$61$	3.34920	+	0.384285i	0.428821	+	0.0492027i	0.103106	+	0.994670i	$0.467122\pi$
$62$	5.20411	−	2.93890i	0.660923	−	0.373240i
$63$	0.925118	+	1.75329i	0.116554	+	0.220894i
$64$	1.89871	−	1.55257i	0.237339	−	0.194071i
$65$	2.49434	−	5.46184i	0.309385	−	0.677458i
$66$	0.693288	+	0.136940i	0.0853379	+	0.0168562i
$67$	−1.32801	−	2.90794i	−0.162242	−	0.355261i	0.810999	−	0.585048i	$-0.198924\pi$
$67$	−1.32801	−	2.90794i	−0.162242	−	0.355261i	−0.973241	+	0.229787i	$0.926197\pi$
$68$	1.99027	+	0.978549i	0.241355	+	0.118666i
$69$	0.0441223	+	0.0454007i	0.00531170	+	0.00546561i
$70$	−0.506562	−	0.0289663i	−0.0605458	−	0.00346213i
$71$	0.492892	−	1.87516i	0.0584955	−	0.222540i	−0.931477	−	0.363800i	$-0.881479\pi$
$71$	0.492892	−	1.87516i	0.0584955	−	0.222540i	0.989972	+	0.141260i	$0.0451154\pi$
$72$	−0.214298	−	7.50141i	−0.0252553	−	0.884049i
$73$	−2.45507	+	4.65287i	−0.287344	+	0.544577i	−0.985147	−	0.171712i	$-0.945070\pi$
$73$	−2.45507	+	4.65287i	−0.287344	+	0.544577i	0.697803	+	0.716290i	$0.254161\pi$
$74$	−0.0183774	−	0.0906960i	−0.00213633	−	0.0105432i
$75$	0.0725107	+	0.275859i	0.00837282	+	0.0318535i
$76$	−0.638984	+	0.187623i	−0.0732965	+	0.0215218i
$77$	2.23133	+	0.309649i	0.254283	+	0.0352878i
$78$	1.22756	+	0.360445i	0.138994	+	0.0408123i
$79$	0.168040	−	5.88216i	0.0189059	−	0.661794i	−0.933782	−	0.357843i	$-0.883512\pi$
$79$	0.168040	−	5.88216i	0.0189059	−	0.661794i	0.952688	−	0.303951i	$-0.0983059\pi$
$80$	−0.838670	−	0.473619i	−0.0937661	−	0.0529522i
$81$	−6.69414	−	4.86358i	−0.743793	−	0.540398i
$82$	−6.29203	−	2.65903i	−0.694838	−	0.293641i
$83$	7.21701	−	1.24895i	0.792170	−	0.137090i	0.239946	−	0.970786i	$-0.422870\pi$
$83$	7.21701	−	1.24895i	0.792170	−	0.137090i	0.552224	+	0.833696i	$0.313779\pi$
$84$	0.0239058	+	0.278330i	0.00260834	+	0.0303683i
$85$	−0.131620	+	1.53242i	−0.0142761	+	0.166214i
$86$	−7.26685	−	1.25758i	−0.783604	−	0.135608i
$87$	2.38021	+	1.52967i	0.255185	+	0.163997i
$88$	−7.06296	−	4.77884i	−0.752914	−	0.509426i
$89$	5.44962	−	3.50226i	0.577658	−	0.371238i	−0.218948	−	0.975736i	$-0.570263\pi$
$89$	5.44962	−	3.50226i	0.577658	−	0.371238i	0.796607	+	0.604498i	$0.206626\pi$
$90$	2.00832	−	0.848722i	0.211695	−	0.0894631i
$91$	3.97234	+	0.923727i	0.416414	+	0.0968329i
$92$	−0.116118	−	0.298246i	−0.0121061	−	0.0310942i
$93$	1.17842	−	1.95419i	0.122197	−	0.202641i
$94$	2.28869	+	7.04387i	0.236060	+	0.726519i
$95$	−0.282024	−	0.365736i	−0.0289351	−	0.0375237i
$96$	0.606615	−	1.55808i	0.0619124	−	0.159021i
$97$	5.36102	−	7.84025i	0.544329	−	0.796057i	−0.451007	−	0.892520i	$-0.648935\pi$
$97$	5.36102	−	7.84025i	0.544329	−	0.796057i	0.995336	+	0.0964639i	$0.0307532\pi$
$98$	0.695140	+	4.83481i	0.0702198	+	0.488389i
$99$	−9.19148	+	3.03643i	−0.923779	+	0.305173i
$100$	0.205212	−	1.42728i	0.0205212	−	0.142728i
$101$	−0.834451	−	0.765852i	−0.0830309	−	0.0762051i	0.633585	−	0.773673i	$-0.281583\pi$
$101$	−0.834451	−	0.765852i	−0.0830309	−	0.0762051i	−0.716616	+	0.697468i	$0.754310\pi$
$102$	−0.327185	+	0.0187091i	−0.0323961	+	0.00185248i
$103$	−0.323981	+	1.59891i	−0.0319228	+	0.157545i	−0.992873	−	0.119175i	$-0.961975\pi$
$103$	−0.323981	+	1.59891i	−0.0319228	+	0.157545i	0.960950	+	0.276721i	$0.0892477\pi$
$104$	−11.9518	−	9.77292i	−1.17197	−	0.958314i
$105$	−0.173856	+	0.0854792i	−0.0169666	+	0.00834191i
$106$	−6.75609	−	2.41057i	−0.656210	−	0.234135i
$107$	4.10635	−	5.32521i	0.396976	−	0.514807i	−0.550413	−	0.834893i	$-0.685530\pi$
$107$	4.10635	−	5.32521i	0.396976	−	0.514807i	0.947389	+	0.320085i	$0.103712\pi$
$108$	−1.25706	−	2.08459i	−0.120960	−	0.200590i
$109$	7.99296	−	9.22437i	0.765587	−	0.883535i	−0.230394	−	0.973097i	$-0.574002\pi$
$109$	7.99296	−	9.22437i	0.765587	−	0.883535i	0.995981	+	0.0895628i	$0.0285470\pi$
$110$	0.549319	−	2.41593i	0.0523755	−	0.230350i
$111$	−0.0231386	−	0.0267033i	−0.00219622	−	0.00253457i
$112$	0.202158	−	0.622178i	0.0191021	−	0.0587903i
$113$	19.4582	−	6.94266i	1.83047	−	0.653111i	0.835922	−	0.548849i	$-0.184934\pi$
$113$	19.4582	−	6.94266i	1.83047	−	0.653111i	0.994550	−	0.104262i	$-0.0332482\pi$
$114$	0.0685833	−	0.0705705i	0.00642341	−	0.00660953i
$115$	0.163525	−	0.150082i	0.0152488	−	0.0139952i
$116$	−8.07356	−	11.8072i	−0.749612	−	1.09627i
$117$	−17.0694	+	3.96932i	−1.57807	+	0.366964i
$118$	−4.32779	+	3.14432i	−0.398405	+	0.289458i
$119$	−1.03787	+	0.119084i	−0.0951412	+	0.0109164i
$120$	0.733389			0.0669489
$121$	−3.29636	+	10.4945i	−0.299669	+	0.954043i
$122$	2.51834			0.228000
$123$	−2.59116	+	0.297308i	−0.233637	+	0.0268074i
$124$	−9.33323	+	6.78099i	−0.838149	+	0.608951i
$125$	0.974012	−	0.226497i	0.0871183	−	0.0202585i
$126$	0.835878	+	1.22243i	0.0744660	+	0.108903i
$127$	9.28949	−	8.52582i	0.824309	−	0.756544i	−0.148312	−	0.988941i	$-0.547384\pi$
$127$	9.28949	−	8.52582i	0.824309	−	0.756544i	0.972621	+	0.232397i	$0.0746568\pi$
$128$	−6.89388	+	7.09364i	−0.609339	+	0.626995i
$129$	−2.65213	+	0.946279i	−0.233507	+	0.0833152i
$130$	1.38608	−	4.26592i	0.121567	−	0.374146i
$131$	12.2366	+	14.1218i	1.06911	+	1.23382i	0.971109	+	0.238638i	$0.0767009\pi$
$131$	12.2366	+	14.1218i	1.06911	+	1.23382i	0.0980058	+	0.995186i	$0.468754\pi$
$132$	−1.35965	−	0.110062i	−0.118342	−	0.00957970i
$133$	0.205425	−	0.237073i	0.0178126	−	0.0205568i
$134$	−1.23321	−	2.04505i	−0.106533	−	0.176665i
$135$	1.03088	−	1.33687i	0.0887241	−	0.115059i
$136$	3.72470	+	1.32897i	0.319390	+	0.113958i
$137$	7.23589	−	3.55765i	0.618204	−	0.303950i	−0.105120	−	0.994460i	$-0.533523\pi$
$137$	7.23589	−	3.55765i	0.618204	−	0.303950i	0.723324	+	0.690509i	$0.242614\pi$
$138$	0.0366115	+	0.0299371i	0.00311658	+	0.00254841i
$139$	0.0642212	−	0.316944i	0.00544718	−	0.0268829i	−0.977267	−	0.212013i	$-0.931998\pi$
$139$	0.0642212	−	0.316944i	0.00544718	−	0.0268829i	0.982714	+	0.185130i	$0.0592707\pi$
$140$	0.977806	−	0.0559129i	0.0826397	−	0.00472551i
$141$	2.08344	+	1.91217i	0.175458	+	0.161034i
$142$	0.206124	−	1.43362i	0.0172975	−	0.120307i
$143$	−7.66202	+	18.3815i	−0.640731	+	1.53714i
$144$	0.400065	+	2.78251i	0.0333388	+	0.231876i
$145$	5.59903	−	8.18831i	0.464974	−	0.680002i
$146$	−1.42582	+	3.66220i	−0.118002	+	0.303086i
$147$	1.13887	+	1.47692i	0.0939327	+	0.121814i
$148$	0.0551985	+	0.169884i	0.00453729	+	0.0139643i
$149$	−11.0243	+	18.2817i	−0.903143	+	1.49769i	−0.0361668	+	0.999346i	$0.511515\pi$
$149$	−11.0243	+	18.2817i	−0.903143	+	1.49769i	−0.866976	+	0.498349i	$0.833940\pi$
$150$	0.0773045	+	0.198555i	0.00631189	+	0.0162120i
$151$	11.4781	+	2.66912i	0.934075	+	0.217210i	0.665798	−	0.746132i	$-0.268091\pi$
$151$	11.4781	+	2.66912i	0.934075	+	0.217210i	0.268277	+	0.963342i	$0.413546\pi$
$152$	−1.09384	+	0.462259i	−0.0887219	+	0.0374942i
$153$	3.77643	−	2.42696i	0.305306	−	0.196208i
$154$	1.68235	+	0.0398005i	0.135568	+	0.00320721i
$155$	−6.73052	−	4.32544i	−0.540608	−	0.347428i
$156$	−2.43340	−	0.421117i	−0.194828	−	0.0337163i
$157$	0.956073	−	11.1314i	0.0763030	−	0.888379i	−0.853685	−	0.520790i	$-0.825638\pi$
$157$	0.956073	−	11.1314i	0.0763030	−	0.888379i	0.929988	−	0.367590i	$-0.119817\pi$
$158$	−0.376178	−	4.37977i	−0.0299271	−	0.348435i
$159$	−2.69880	+	0.467046i	−0.214029	+	0.0370391i
$160$	−5.39957	−	2.28188i	−0.426873	−	0.180398i
$161$	0.121965	+	0.0886127i	0.00961218	+	0.00698366i
$162$	−5.38223	−	3.03948i	−0.422868	−	0.238804i
$163$	0.188957	−	6.61435i	0.0148002	−	0.518076i	−0.958045	−	0.286618i	$-0.907469\pi$
$163$	0.188957	−	6.61435i	0.0148002	−	0.518076i	0.972845	−	0.231457i	$-0.0743493\pi$
$164$	12.6513	+	3.71475i	0.987898	+	0.290073i
$165$	−0.270970	−	0.906363i	−0.0210950	−	0.0705603i
$166$	5.24977	−	1.54147i	0.407461	−	0.119641i
$167$	−2.49135	−	9.47808i	−0.192786	−	0.733436i	−0.991318	−	0.131483i	$-0.958026\pi$
$167$	−2.49135	−	9.47808i	−0.192786	−	0.733436i	0.798532	−	0.601952i	$-0.205610\pi$
$168$	0.0989239	+	0.488209i	0.00763214	+	0.0376661i
$169$	−10.7583	+	20.3892i	−0.827560	+	1.56840i
$170$	0.0328099	+	1.14850i	0.00251640	+	0.0880856i
$171$	−0.342676	+	1.30367i	−0.0262051	+	0.0996945i
$172$	14.2123	+	0.812689i	1.08368	+	0.0619670i
$173$	−11.2189	−	11.5439i	−0.852954	−	0.877669i	0.140711	−	0.990051i	$-0.455061\pi$
$173$	−11.2189	−	11.5439i	−0.852954	−	0.877669i	−0.993665	+	0.112382i	$0.964152\pi$
$174$	1.89673	+	0.932560i	0.143791	+	0.0706972i
$175$	0.282157	+	0.617838i	0.0213291	+	0.0467041i
$176$	2.83256	+	1.47686i	0.213512	+	0.111323i
$177$	−0.848501	+	1.85796i	−0.0637773	+	0.139653i
$178$	3.74622	−	3.06327i	0.280791	−	0.229601i
$179$	6.00905	+	11.3884i	0.449138	+	0.851211i	0.999863	+	0.0165244i	$0.00526011\pi$
$179$	6.00905	+	11.3884i	0.449138	+	0.851211i	−0.550726	+	0.834686i	$0.685649\pi$
$180$	−3.66459	+	2.06949i	−0.273142	+	0.154251i
$181$	−3.65490	−	0.419361i	−0.271667	−	0.0311709i	−0.0229125	−	0.999737i	$-0.507294\pi$
$181$	−3.65490	−	0.419361i	−0.271667	−	0.0311709i	−0.248754	+	0.968567i	$0.580021\pi$
$182$	3.02674	+	0.347286i	0.224357	+	0.0257425i
$183$	0.837275	−	0.472831i	0.0618932	−	0.0349527i
$184$	−0.266327	−	0.504745i	−0.0196339	−	0.0372103i
$185$	−0.0958987	+	0.0784160i	−0.00705061	+	0.00576526i
$186$	0.708162	−	1.55066i	0.0519249	−	0.113700i
$187$	0.266227	−	5.09422i	0.0194685	−	0.372526i
$188$	−5.93891	−	13.0044i	−0.433139	−	0.948443i
$189$	1.02899	+	0.505921i	0.0748481	+	0.0368003i
$190$	−0.240449	−	0.247416i	−0.0174440	−	0.0179494i
$191$	−24.9680	−	1.42772i	−1.80662	−	0.103306i	−0.878997	−	0.476828i	$-0.841786\pi$
$191$	−24.9680	−	1.42772i	−1.80662	−	0.103306i	−0.927621	+	0.373522i	$0.878150\pi$
$192$	0.177845	−	0.676592i	0.0128348	−	0.0488288i
$193$	−0.263745	−	9.23229i	−0.0189848	−	0.664555i	−0.952242	−	0.305345i	$-0.901228\pi$
$193$	−0.263745	−	9.23229i	−0.0189848	−	0.664555i	0.933257	−	0.359209i	$-0.116954\pi$
$194$	3.31107	−	6.27517i	0.237721	−	0.450531i
$195$	−0.340116	−	1.67854i	−0.0243562	−	0.120203i
$196$	−2.39689	−	9.11873i	−0.171207	−	0.651338i
$197$	−17.1698	+	5.04151i	−1.22330	+	0.359193i	−0.828717	−	0.559668i	$-0.810929\pi$
$197$	−17.1698	+	5.04151i	−1.22330	+	0.359193i	−0.394581	+	0.918861i	$0.629110\pi$
$198$	−6.56292	+	3.03619i	−0.466406	+	0.215773i
$199$	−11.0524	−	3.24527i	−0.783481	−	0.230051i	−0.134559	−	0.990906i	$-0.542962\pi$
$199$	−11.0524	−	3.24527i	−0.783481	−	0.230051i	−0.648922	+	0.760855i	$0.724780\pi$
$200$	0.0734238	−	2.57017i	0.00519185	−	0.181738i
$201$	−0.793974	−	0.448378i	−0.0560026	−	0.0316261i
$202$	−0.684505	−	0.497322i	−0.0481616	−	0.0349914i
$203$	6.20610	+	2.62272i	0.435583	+	0.184079i
$204$	0.623324	−	0.107870i	0.0436414	−	0.00755244i
$205$	0.782504	+	9.11053i	0.0546524	+	0.636307i
$206$	−0.104290	+	1.21422i	−0.00726621	+	0.0845990i
$207$	−0.638325	−	0.110467i	−0.0443667	−	0.00767795i
$208$	4.86519	+	3.12667i	0.337340	+	0.216795i
$209$	0.975433	+	1.18103i	0.0674721	+	0.0816936i
$210$	−0.121749	+	0.0782431i	−0.00840145	+	0.00539929i
$211$	−1.17134	+	0.495013i	−0.0806385	+	0.0340781i	−0.429216	−	0.903202i	$-0.641210\pi$
$211$	−1.17134	+	0.495013i	−0.0806385	+	0.0340781i	0.348578	+	0.937280i	$0.386665\pi$
$212$	13.4865	+	3.13616i	0.926259	+	0.215392i
$213$	−0.200640	−	0.515339i	−0.0137476	−	0.0353104i
$214$	2.59407	−	4.30179i	0.177327	−	0.294064i
$215$	3.05072	+	9.38917i	0.208058	+	0.640336i
$216$	−2.65062	−	3.43738i	−0.180352	−	0.233884i
$217$	1.97155	−	5.06387i	0.133837	−	0.343758i
$218$	5.14650	−	7.52652i	0.348565	−	0.509760i
$219$	0.213551	+	1.48528i	0.0144304	+	0.100366i
$220$	−0.521837	+	4.75388i	−0.0351823	+	0.320507i
$221$	1.31431	−	9.14121i	0.0884099	−	0.614904i
$222$	−0.0194462	−	0.0178476i	−0.00130515	−	0.00119785i
$223$	23.9406	−	1.36897i	1.60318	−	0.0916733i	0.767560	−	0.640977i	$-0.221471\pi$
$223$	23.9406	−	1.36897i	1.60318	−	0.0916733i	0.835623	+	0.549304i	$0.185107\pi$
$224$	0.790694	−	3.90223i	0.0528304	−	0.260728i
$225$	−2.25944	−	1.84754i	−0.150630	−	0.123169i
$226$	13.8497	−	6.80946i	0.921271	−	0.452958i
$227$	26.1784	+	9.34044i	1.73752	+	0.619947i	0.998552	−	0.0537917i	$-0.0171307\pi$
$227$	26.1784	+	9.34044i	1.73752	+	0.619947i	0.738970	+	0.673738i	$0.235313\pi$
$228$	−0.115994	+	0.150423i	−0.00768188	+	0.00996203i
$229$	2.51669	+	4.17346i	0.166307	+	0.275790i	0.928327	−	0.371764i	$-0.121247\pi$
$229$	2.51669	+	4.17346i	0.166307	+	0.275790i	−0.762020	+	0.647554i	$0.775792\pi$
$230$	0.108580	−	0.125308i	0.00715957	−	0.00826258i
$231$	0.566806	−	0.302637i	0.0372931	−	0.0199121i
$232$	−16.7024	−	19.2756i	−1.09657	−	1.26551i
$233$	2.02094	−	6.21983i	0.132396	−	0.407474i	−0.862779	−	0.505580i	$-0.831278\pi$
$233$	2.02094	−	6.21983i	0.132396	−	0.407474i	0.995176	+	0.0981059i	$0.0312784\pi$
$234$	−12.3301	+	4.39937i	−0.806044	+	0.287596i
$235$	6.90980	−	7.11002i	0.450746	−	0.463806i
$236$	7.60751	−	6.98211i	0.495207	−	0.454497i
$237$	−0.947391	−	1.38552i	−0.0615397	−	0.0899989i
$238$	−0.760115	+	0.176757i	−0.0492710	+	0.0114575i
$239$	−8.81050	+	6.40121i	−0.569904	+	0.414060i	−0.835070	−	0.550143i	$-0.814573\pi$
$239$	−8.81050	+	6.40121i	−0.569904	+	0.414060i	0.265166	+	0.964203i	$0.414573\pi$
$240$	−0.272932	+	0.0313160i	−0.0176177	+	0.00202144i
$241$	17.3431			1.11717			0.558585	−	0.829447i	$-0.311345\pi$
$241$	17.3431			1.11717			0.558585	+	0.829447i	$0.311345\pi$
$242$	−1.55276	+	8.06920i	−0.0998149	+	0.518708i
$243$	−7.42464			−0.476291
$244$	−4.82941	+	0.554123i	−0.309171	+	0.0354741i
$245$	5.28989	−	3.84333i	0.337959	−	0.245541i
$246$	−1.89772	+	0.441296i	−0.120994	+	0.0281360i
$247$	1.56527	+	2.28913i	0.0995957	+	0.145654i
$248$	−15.1557	+	13.9098i	−0.962387	+	0.883271i
$249$	1.45598	−	1.49816i	0.0922688	−	0.0949423i
$250$	0.703578	−	0.251036i	0.0444982	−	0.0158769i
$251$	−4.18583	+	12.8827i	−0.264207	+	0.813146i	0.727668	+	0.685930i	$0.240604\pi$
$251$	−4.18583	+	12.8827i	−0.264207	+	0.813146i	−0.991875	+	0.127217i	$0.959396\pi$
$252$	−1.87194	−	2.16033i	−0.117921	−	0.136088i
$253$	−0.525391	+	0.515633i	−0.0330311	+	0.0324176i
$254$	6.16821	−	7.11849i	0.387028	−	0.446654i
$255$	0.226544	+	0.375681i	0.0141867	+	0.0235261i
$256$	−7.50769	+	9.73615i	−0.469231	+	0.608509i
$257$	−11.6362	−	4.15180i	−0.725848	−	0.258982i	−0.0528254	−	0.998604i	$-0.516823\pi$
$257$	−11.6362	−	4.15180i	−0.725848	−	0.258982i	−0.673023	+	0.739622i	$0.735004\pi$
$258$	−1.88771	+	0.928123i	−0.117523	+	0.0577824i
$259$	−0.0651360	−	0.0532615i	−0.00404736	−	0.00330951i
$260$	−1.71943	+	8.48572i	−0.106635	+	0.526262i
$261$	−28.9044	+	1.65282i	−1.78914	+	0.102307i
$262$	10.2839	+	9.43850i	0.635343	+	0.583113i
$263$	1.91585	−	13.3250i	0.118137	−	0.821657i	−0.841468	−	0.540306i	$-0.818308\pi$
$263$	1.91585	−	13.3250i	0.118137	−	0.821657i	0.959605	−	0.281351i	$-0.0907826\pi$
$264$	−2.43101	+	0.0813882i	−0.149619	+	0.00500910i
$265$	1.36657	+	9.50474i	0.0839480	+	0.583871i
$266$	0.132269	−	0.193437i	0.00810993	−	0.0118604i
$267$	0.670365	−	1.72182i	0.0410256	−	0.105374i
$268$	2.81490	+	3.65043i	0.171947	+	0.222985i
$269$	−5.83510	−	17.9586i	−0.355772	−	1.09495i	−0.955560	−	0.294795i	$-0.904749\pi$
$269$	−5.83510	−	17.9586i	−0.355772	−	1.09495i	0.599788	−	0.800159i	$-0.295251\pi$
$270$	0.651231	−	1.07994i	0.0396326	−	0.0657233i
$271$	9.09284	+	23.3548i	0.552351	+	1.41870i	0.880486	+	0.474071i	$0.157216\pi$
$271$	9.09284	+	23.3548i	0.552351	+	1.41870i	−0.328135	+	0.944631i	$0.606420\pi$
$272$	−1.44290	−	0.335533i	−0.0874889	−	0.0203447i
$273$	1.07151	−	0.452823i	0.0648506	−	0.0274061i
$274$	5.06718	−	3.25648i	0.306120	−	0.196731i
$275$	−3.20349	+	0.858876i	−0.193178	+	0.0517921i
$276$	−0.0767969	−	0.0493544i	−0.00462263	−	0.00297078i
$277$	26.5311	+	4.59138i	1.59410	+	0.275869i	0.897308	−	0.441406i	$-0.145520\pi$
$277$	26.5311	+	4.59138i	1.59410	+	0.275869i	0.696790	+	0.717275i	$0.254611\pi$
$278$	0.0206729	−	0.240690i	0.00123988	−	0.0144356i
$279$	1.99825	+	23.2652i	0.119632	+	1.39285i
$280$	1.72084	−	0.297802i	0.102840	−	0.0177971i
$281$	11.3311	+	4.78855i	0.675954	+	0.285661i	0.700097	−	0.714048i	$-0.253140\pi$
$281$	11.3311	+	4.78855i	0.675954	+	0.285661i	−0.0241426	+	0.999709i	$0.507686\pi$
$282$	1.70906	+	1.24171i	0.101773	+	0.0739425i
$283$	21.0955	+	11.9132i	1.25400	+	0.708166i	0.968213	−	0.250127i	$-0.0804725\pi$
$283$	21.0955	+	11.9132i	1.25400	+	0.708166i	0.285786	+	0.958293i	$0.407745\pi$
$284$	−0.0798355	+	2.79461i	−0.00473736	+	0.165829i
$285$	−0.126396	−	0.0371132i	−0.00748704	−	0.00219839i
$286$	−4.12113	+	14.2944i	−0.243687	+	0.845243i
$287$	−5.95923	+	1.74979i	−0.351762	+	0.103287i
$288$	4.34940	+	16.5468i	0.256291	+	0.975031i
$289$	−2.90625	−	14.3429i	−0.170956	−	0.843699i
$290$	3.45806	−	6.55376i	0.203064	−	0.384850i
$291$	−0.0773608	−	2.70798i	−0.00453497	−	0.158745i
$292$	1.92848	−	7.33671i	0.112856	−	0.429349i
$293$	−20.5738	−	1.17645i	−1.20193	−	0.0687291i	−0.555380	−	0.831597i	$-0.687427\pi$
$293$	−20.5738	−	1.17645i	−1.20193	−	0.0687291i	−0.646554	+	0.762868i	$0.723791\pi$
$294$	0.970983	+	0.999118i	0.0566289	+	0.0582697i
$295$	6.42629	+	3.15959i	0.374153	+	0.183959i
$296$	0.132316	+	0.289732i	0.00769073	+	0.0168403i
$297$	−3.26877	+	4.54582i	−0.189673	+	0.263775i
$298$	−6.62493	+	14.5066i	−0.383772	+	0.840343i
$299$	−1.03172	+	0.843634i	−0.0596660	+	0.0487886i
$300$	−0.191936	−	0.363758i	−0.0110814	−	0.0210016i
$301$	−5.83876	+	3.29730i	−0.336541	+	0.190053i
$302$	8.74579	+	1.00349i	0.503264	+	0.0577441i
$303$	−0.320953	−	0.0368259i	−0.0184383	−	0.00211559i
$304$	0.387335	−	0.218738i	0.0222152	−	0.0125455i
$305$	−1.57322	−	2.98158i	−0.0900822	−	0.170725i
$306$	2.59602	−	2.12276i	0.148405	−	0.121350i
$307$	−1.53034	+	3.35097i	−0.0873409	+	0.191250i	−0.948262	−	0.317488i	$-0.897161\pi$
$307$	−1.53034	+	3.35097i	−0.0873409	+	0.191250i	0.860921	+	0.508738i	$0.169888\pi$
$308$	−3.23499	+	0.293851i	−0.184331	+	0.0167437i
$309$	0.193303	+	0.423275i	0.0109966	+	0.0240793i
$310$	−5.36340	−	2.63701i	−0.304621	−	0.149772i
$311$	−0.995074	−	1.02391i	−0.0564255	−	0.0580605i	0.688331	−	0.725397i	$-0.258344\pi$
$311$	−0.995074	−	1.02391i	−0.0564255	−	0.0580605i	−0.744757	+	0.667336i	$0.767434\pi$
$312$	−4.39641	−	0.251396i	−0.248898	−	0.0142325i
$313$	1.36776	−	5.20348i	0.0773101	−	0.294118i	−0.917246	−	0.398321i	$-0.869593\pi$
$313$	1.36776	−	5.20348i	0.0773101	−	0.294118i	0.994556	+	0.104203i	$0.0332292\pi$
$314$	−0.238328	−	8.34258i	−0.0134496	−	0.470799i
$315$	0.925118	−	1.75329i	0.0521245	−	0.0987869i
$316$	1.68510	+	8.31628i	0.0947941	+	0.467827i
$317$	−3.86180	−	14.6918i	−0.216900	−	0.825174i	−0.983176	−	0.182662i	$-0.941529\pi$
$317$	−3.86180	−	14.6918i	−0.216900	−	0.825174i	0.766276	−	0.642512i	$-0.222108\pi$
$318$	−1.96315	+	0.576433i	−0.110088	+	0.0323248i
$319$	−17.6508	+	27.7637i	−0.988253	+	1.55447i
$320$	−2.35332	−	0.690997i	−0.131555	−	0.0386279i
$321$	0.0547720	−	1.91727i	0.00305708	−	0.107012i
$322$	0.0980623	+	0.0553783i	0.00546480	+	0.00308611i
$323$	−0.574681	−	0.417530i	−0.0319761	−	0.0232320i
$324$	10.9903	+	4.64452i	0.610570	+	0.258029i
$325$	−5.91651	+	1.02389i	−0.328189	+	0.0567953i
$326$	−0.423004	−	4.92494i	−0.0234280	−	0.272767i
$327$	0.297921	−	3.46863i	0.0164751	−	0.191816i
$328$	23.1670	+	4.00921i	1.27919	+	0.221372i
$329$	5.66509	+	3.64073i	0.312327	+	0.200720i
$330$	−0.278281	−	0.649585i	−0.0153189	−	0.0357585i
$331$	3.10178	−	1.99340i	0.170490	−	0.109567i	−0.452613	−	0.891707i	$-0.649508\pi$
$331$	3.10178	−	1.99340i	0.170490	−	0.109567i	0.623103	+	0.782140i	$0.285872\pi$
$332$	−9.72828	+	4.11120i	−0.533909	+	0.225632i
$333$	0.352158	+	0.0818909i	0.0192981	+	0.00448759i
$334$	−2.65606	−	6.82203i	−0.145333	−	0.373285i
$335$	−1.65083	+	2.73760i	−0.0901947	+	0.149571i
$336$	−0.0576615	−	0.177464i	−0.00314569	−	0.00968144i
$337$	4.14174	+	5.37111i	0.225615	+	0.292583i	0.891080	−	0.453846i	$-0.149948\pi$
$337$	4.14174	+	5.37111i	0.225615	+	0.292583i	−0.665465	+	0.746429i	$0.731767\pi$
$338$	−6.24806	+	16.0480i	−0.339850	+	0.872897i
$339$	3.32613	−	4.86430i	0.180650	−	0.264193i
$340$	−0.315629	−	2.19525i	−0.0171174	−	0.119054i
$341$	22.7901	+	13.5909i	1.23415	+	0.735989i
$342$	−0.143305	+	0.996705i	−0.00774903	+	0.0538957i
$343$	6.77484	+	6.21790i	0.365807	+	0.335735i
$344$	25.3426	−	1.44914i	1.36638	−	0.0781324i
$345$	0.0125725	−	0.0620478i	0.000676882	−	0.00334054i
$346$	−9.30911	−	7.61203i	−0.500461	−	0.409225i
$347$	19.2691	−	9.47399i	1.03442	−	0.508590i	0.156641	−	0.987656i	$-0.449933\pi$
$347$	19.2691	−	9.47399i	1.03442	−	0.508590i	0.877779	+	0.479065i	$0.159024\pi$
$348$	−3.84255	−	1.37102i	−0.205982	−	0.0734943i
$349$	11.0713	−	14.3575i	0.592632	−	0.768538i	−0.396105	−	0.918205i	$-0.629638\pi$
$349$	11.0713	−	14.3575i	0.592632	−	0.768538i	0.988736	+	0.149667i	$0.0478202\pi$
$350$	0.262015	+	0.434503i	0.0140053	+	0.0232252i
$351$	−6.63804	+	7.66071i	−0.354312	+	0.408898i
$352$	18.1516	+	6.96467i	0.967481	+	0.371218i
$353$	−3.55197	−	4.09919i	−0.189052	−	0.218178i	0.653309	−	0.757092i	$-0.273380\pi$
$353$	−3.55197	−	4.09919i	−0.189052	−	0.218178i	−0.842361	+	0.538914i	$0.818835\pi$
$354$	−0.471504	+	1.45114i	−0.0250602	+	0.0771273i
$355$	−1.82610	+	0.651550i	−0.0969192	+	0.0345807i
$356$	−6.51007	+	6.69871i	−0.345033	+	0.355031i
$357$	−0.219529	+	0.201482i	−0.0116187	+	0.0106636i
$358$	5.42940	+	7.94025i	0.286953	+	0.419655i
$359$	−0.755870	+	0.175770i	−0.0398933	+	0.00927679i	−0.246396	−	0.969169i	$-0.579246\pi$
$359$	−0.755870	+	0.175770i	−0.0398933	+	0.00927679i	0.206503	+	0.978446i	$0.433792\pi$
$360$	−6.07124	+	4.41102i	−0.319983	+	0.232481i
$361$	−18.6642	+	2.14152i	−0.982329	+	0.112712i
$362$	−2.74821			−0.144443
$363$	0.998786	+	2.97431i	0.0524227	+	0.156111i
$364$	−5.88078			−0.308236
$365$	5.22656	−	0.599692i	0.273571	−	0.0313893i
$366$	0.581122	−	0.422210i	0.0303757	−	0.0220693i
$367$	2.60248	−	0.605182i	0.135849	−	0.0315902i	−0.158021	−	0.987436i	$-0.550511\pi$
$367$	2.60248	−	0.605182i	0.135849	−	0.0315902i	0.293870	+	0.955846i	$0.405057\pi$
$368$	0.120667	+	0.176470i	0.00629020	+	0.00919912i
$369$	19.6624	−	18.0459i	1.02358	−	0.939434i
$370$	−0.0644940	+	0.0663628i	−0.00335288	+	0.00345004i
$371$	−6.14286	+	2.19177i	−0.318922	+	0.113791i
$372$	−1.01684	+	3.12951i	−0.0527207	+	0.162257i
$373$	8.75228	+	10.1007i	0.453176	+	0.522993i	0.935656	−	0.352914i	$-0.114809\pi$
$373$	8.75228	+	10.1007i	0.453176	+	0.522993i	−0.482480	+	0.875907i	$0.660264\pi$
$374$	−0.236212	−	3.80336i	−0.0122142	−	0.196667i
$375$	0.186786	−	0.215563i	0.00964559	−	0.0111316i
$376$	−13.1642	−	21.8304i	−0.678892	−	1.12582i
$377$	−36.3711	+	47.1669i	−1.87321	+	2.42922i
$378$	0.806749	+	0.287847i	0.0414947	+	0.0148053i
$379$	33.9003	−	16.6677i	1.74134	−	0.856160i	0.763790	−	0.645464i	$-0.223336\pi$
$379$	33.9003	−	16.6677i	1.74134	−	0.856160i	0.977552	−	0.210696i	$-0.0675730\pi$
$380$	0.515548	+	0.421561i	0.0264470	+	0.0216256i
$381$	0.714218	−	3.52480i	0.0365905	−	0.180581i
$382$	−18.6516	+	1.06654i	−0.954299	+	0.0545688i
$383$	−16.2497	−	14.9138i	−0.830319	−	0.762060i	0.143436	−	0.989660i	$-0.454185\pi$
$383$	−16.2497	−	14.9138i	−0.830319	−	0.762060i	−0.973755	+	0.227600i	$0.926912\pi$
$384$	−0.401528	+	2.79269i	−0.0204904	+	0.142514i
$385$	−1.00385	−	2.01668i	−0.0511609	−	0.102779i
$386$	−0.981906	−	6.82930i	−0.0499777	−	0.347602i
$387$	16.2638	−	23.7850i	0.826735	−	1.20906i
$388$	−4.96886	+	12.7624i	−0.252256	+	0.647913i
$389$	−17.7083	−	22.9645i	−0.897845	−	1.16435i	−0.985750	−	0.168217i	$-0.946199\pi$
$389$	−17.7083	−	22.9645i	−0.897845	−	1.16435i	0.0879047	−	0.996129i	$-0.471983\pi$
$390$	−0.395352	−	1.21677i	−0.0200194	−	0.0616135i
$391$	0.176289	−	0.292343i	0.00891534	−	0.0147844i
$392$	−6.09964	−	15.6668i	−0.308078	−	0.791293i
$393$	5.19123	+	1.20717i	0.261863	+	0.0608936i
$394$	−12.3133	+	5.20365i	−0.620336	+	0.262156i
$395$	−4.95040	+	3.18143i	−0.249082	+	0.160075i
$396$	11.9176	−	7.26656i	0.598882	−	0.365158i
$397$	1.36368	+	0.876385i	0.0684413	+	0.0439845i	0.574414	−	0.818565i	$-0.305230\pi$
$397$	1.36368	+	0.876385i	0.0684413	+	0.0439845i	−0.505973	+	0.862549i	$0.668866\pi$
$398$	−8.47889	−	1.46733i	−0.425008	−	0.0735506i
$399$	0.00765679	−	0.0891464i	0.000383319	−	0.00446290i
$400$	0.0824226	+	0.959629i	0.00412113	+	0.0479815i
$401$	−23.2250	+	4.01924i	−1.15980	+	0.200711i	−0.717765	−	0.696286i	$-0.754835\pi$
$401$	−23.2250	+	4.01924i	−1.15980	+	0.200711i	−0.442036	+	0.896997i	$0.645744\pi$
$402$	−0.627431	−	0.265154i	−0.0312934	−	0.0132247i
$403$	38.8645	+	28.2367i	1.93598	+	1.40657i
$404$	1.42210	+	0.803097i	0.0707521	+	0.0399556i
$405$	−0.236285	+	8.27104i	−0.0117411	+	0.410991i
$406$	4.82921	+	1.41798i	0.239669	+	0.0703733i
$407$	0.309180	−	0.270573i	0.0153255	−	0.0134118i
$408$	1.08230	−	0.317793i	0.0535821	−	0.0157331i
$409$	−1.69898	−	6.46357i	−0.0840089	−	0.319603i	0.911849	−	0.410526i	$-0.134655\pi$
$409$	−1.69898	−	6.46357i	−0.0840089	−	0.319603i	−0.995858	+	0.0909226i	$0.971018\pi$
$410$	1.35654	+	6.69477i	0.0669945	+	0.330631i
$411$	1.07327	−	2.03407i	0.0529406	−	0.100334i
$412$	−0.0671758	−	2.35146i	−0.00330951	−	0.115848i
$413$	−1.23649	+	4.70409i	−0.0608437	+	0.231473i
$414$	−0.483141	−	0.0276270i	−0.0237451	−	0.00135779i
$415$	−5.10457	−	5.25248i	−0.250573	−	0.257834i
$416$	31.5864	+	15.5300i	1.54865	+	0.761420i
$417$	−0.0383176	−	0.0839038i	−0.00187642	−	0.00410879i
$418$	0.824489	+	0.793443i	0.0403271	+	0.0388086i
$419$	−11.5084	+	25.1999i	−0.562223	+	1.23110i	0.388613	+	0.921401i	$0.372954\pi$
$419$	−11.5084	+	25.1999i	−0.562223	+	1.23110i	−0.950836	+	0.309695i	$0.899773\pi$
$420$	0.216260	−	0.176835i	0.0105524	−	0.00862868i
$421$	0.686819	+	1.30167i	0.0334735	+	0.0634394i	0.900601	−	0.434647i	$-0.143127\pi$
$421$	0.686819	+	1.30167i	0.0334735	+	0.0634394i	−0.867127	+	0.498087i	$0.834036\pi$
$422$	−0.827162	+	0.467120i	−0.0402656	+	0.0227390i
$423$	−28.7483	−	3.29856i	−1.39779	−	0.160382i
$424$	24.5291	+	2.81445i	1.19124	+	0.136682i
$425$	1.33926	−	0.756315i	0.0649637	−	0.0366867i
$426$	−0.192788	−	0.365375i	−0.00934063	−	0.0177025i
$427$	1.77260	−	1.44945i	0.0857820	−	0.0701436i
$428$	−4.02810	+	8.82031i	−0.194706	+	0.426346i
$429$	1.31368	+	5.52622i	0.0634252	+	0.266808i
$430$	3.06363	+	6.70841i	0.147741	+	0.323508i
$431$	14.8495	+	7.30099i	0.715274	+	0.351676i	0.762306	−	0.647217i	$-0.224067\pi$
$431$	14.8495	+	7.30099i	0.715274	+	0.351676i	−0.0470322	+	0.998893i	$0.514976\pi$
$432$	1.13321	+	1.16605i	0.0545217	+	0.0561015i
$433$	−17.5657	−	1.00444i	−0.844152	−	0.0482704i	−0.370340	−	0.928896i	$-0.620759\pi$
$433$	−17.5657	−	1.00444i	−0.844152	−	0.0482704i	−0.473812	+	0.880626i	$0.657122\pi$
$434$	1.03198	−	3.92605i	0.0495365	−	0.188456i
$435$	−0.0807952	−	2.82820i	−0.00387383	−	0.135602i
$436$	−8.21333	+	15.5660i	−0.393347	+	0.745475i
$437$	0.0203574	+	0.100468i	0.000973827	+	0.00480603i
$438$	0.284965	+	1.08412i	0.0136162	+	0.0518012i
$439$	12.9431	−	3.80044i	0.617741	−	0.181385i	0.0421347	−	0.999112i	$-0.486584\pi$
$439$	12.9431	−	3.80044i	0.617741	−	0.181385i	0.575607	+	0.817727i	$0.304766\pi$
$440$	0.0418429	+	8.52766i	0.00199478	+	0.406540i
$441$	−18.3110	−	5.37659i	−0.871952	−	0.256028i
$442$	0.197005	−	6.89609i	0.00937059	−	0.328013i
$443$	−23.1759	−	13.0880i	−1.10112	−	0.621832i	−0.169598	−	0.985513i	$-0.554247\pi$
$443$	−23.1759	−	13.0880i	−1.10112	−	0.621832i	−0.931523	+	0.363682i	$0.881520\pi$
$444$	0.0412191	+	0.0299474i	0.00195617	+	0.00142124i
$445$	−5.96701	−	2.52168i	−0.282864	−	0.119539i
$446$	17.6510	−	3.05463i	0.835800	−	0.144641i
$447$	0.521084	+	6.06687i	0.0246464	+	0.286953i
$448$	0.142559	−	1.65978i	0.00673528	−	0.0784174i
$449$	−33.4410	−	5.78720i	−1.57818	−	0.273115i	−0.686963	−	0.726692i	$-0.741057\pi$
$449$	−33.4410	−	5.78720i	−1.57818	−	0.273115i	−0.891217	+	0.453578i	$0.850147\pi$
$450$	−1.83418	−	1.17875i	−0.0864639	−	0.0555670i
$451$	−3.60486	−	30.1124i	−0.169746	−	1.41794i
$452$	−25.0613	+	16.1059i	−1.17878	+	0.757557i
$453$	3.09613	−	1.30844i	0.145469	−	0.0614757i
$454$	20.2237	+	4.70283i	0.949147	+	0.220715i
$455$	−1.47965	−	3.80044i	−0.0693670	−	0.178168i
$456$	−0.174910	+	0.290055i	−0.00819090	+	0.0135831i
$457$	−0.689669	−	2.12258i	−0.0322614	−	0.0992902i	0.933629	−	0.358241i	$-0.116623\pi$
$457$	−0.689669	−	2.12258i	−0.0322614	−	0.0992902i	−0.965891	+	0.258951i	$0.916623\pi$
$458$	2.22315	+	2.88304i	0.103881	+	0.134715i
$459$	0.942036	−	2.41960i	0.0439705	−	0.112937i
$460$	−0.180652	+	0.264194i	−0.00842292	+	0.0123181i
$461$	2.95020	+	20.5191i	0.137405	+	0.955670i	0.935547	+	0.353201i	$0.114907\pi$
$461$	2.95020	+	20.5191i	0.137405	+	0.955670i	−0.798143	+	0.602468i	$0.794184\pi$
$462$	0.394885	−	0.272869i	0.0183717	−	0.0126950i
$463$	3.87084	−	26.9223i	0.179893	−	1.25118i	−0.677113	−	0.735879i	$-0.736769\pi$
$463$	3.87084	−	26.9223i	0.179893	−	1.25118i	0.857006	−	0.515306i	$-0.172322\pi$
$464$	7.03893	+	6.46027i	0.326774	+	0.299911i
$465$	−2.27829	+	0.130277i	−0.105653	+	0.00604146i
$466$	0.970205	−	4.78815i	0.0449439	−	0.221807i
$467$	18.0291	+	14.7423i	0.834286	+	0.682192i	0.950395	−	0.311044i	$-0.100679\pi$
$467$	18.0291	+	14.7423i	0.834286	+	0.682192i	−0.116110	+	0.993236i	$0.537042\pi$
$468$	22.6774	−	11.1497i	1.04826	−	0.515395i
$469$	−2.04506	−	0.729678i	−0.0944323	−	0.0336934i
$470$	4.52268	−	5.86511i	0.208616	−	0.270537i
$471$	−1.64560	−	2.72892i	−0.0758252	−	0.125742i
$472$	12.0577	−	13.9153i	0.554998	−	0.640502i
$473$	−11.1544	−	30.7843i	−0.512880	−	1.41547i
$474$	−0.821091	−	0.947589i	−0.0377139	−	0.0435242i
$475$	−0.142718	+	0.439240i	−0.00654834	+	0.0201537i
$476$	1.41878	−	0.506218i	0.0650295	−	0.0232025i
$477$	19.5325	−	20.0985i	0.894332	−	0.920246i
$478$	−5.99365	+	5.50092i	−0.274143	+	0.251606i
$479$	2.84161	+	4.15573i	0.129837	+	0.189880i	0.884912	−	0.465758i	$-0.154218\pi$
$479$	2.84161	+	4.15573i	0.129837	+	0.189880i	−0.755076	+	0.655638i	$0.772400\pi$
$480$	−1.62855	+	0.378703i	−0.0743328	+	0.0172853i
$481$	0.601760	−	0.437204i	0.0274379	−	0.0199348i
$482$	12.8712	−	1.47684i	0.586269	−	0.0672681i
$483$	0.0430004			0.00195659
$484$	1.20220	−	15.8159i	0.0546457	−	0.718905i
$485$	−9.49790			−0.431277
$486$	−5.51021	+	0.632238i	−0.249948	+	0.0286789i
$487$	−17.4807	+	12.7005i	−0.792128	+	0.575515i	−0.908594	−	0.417680i	$-0.862843\pi$
$487$	−17.4807	+	12.7005i	−0.792128	+	0.575515i	0.116466	+	0.993195i	$0.462843\pi$
$488$	−8.44276	+	1.96328i	−0.382186	+	0.0888735i
$489$	−1.06532	−	1.55798i	−0.0481754	−	0.0704543i
$490$	3.59863	−	3.30279i	0.162570	−	0.149205i
$491$	15.8512	−	16.3105i	0.715357	−	0.736085i	−0.257807	−	0.966196i	$-0.583000\pi$
$491$	15.8512	−	16.3105i	0.715357	−	0.736085i	0.973164	+	0.230112i	$0.0739091\pi$
$492$	3.54215	−	1.26384i	0.159692	−	0.0569781i
$493$	4.71463	−	14.5102i	0.212336	−	0.653504i
$494$	1.35660	+	1.56560i	0.0610362	+	0.0704395i
$495$	7.69456	+	5.87342i	0.345845	+	0.263990i
$496$	5.04627	−	5.82370i	0.226584	−	0.261492i
$497$	−0.680045	−	1.12773i	−0.0305042	−	0.0505855i
$498$	0.952982	−	1.23585i	0.0427041	−	0.0553797i
$499$	35.6870	+	12.7331i	1.59757	+	0.570012i	0.976832	−	0.214007i	$-0.0686515\pi$
$499$	35.6870	+	12.7331i	1.59757	+	0.570012i	0.620737	+	0.784019i	$0.286833\pi$
$500$	−1.29401	+	0.636223i	−0.0578700	+	0.0284527i
$501$	−2.16393	−	1.76944i	−0.0966773	−	0.0790527i
$502$	−2.00951	+	9.91734i	−0.0896890	+	0.442632i
$503$	−4.91855	+	0.281253i	−0.219307	+	0.0125405i	−0.166397	−	0.986059i	$-0.553213\pi$
$503$	−4.91855	+	0.281253i	−0.219307	+	0.0125405i	−0.0529103	+	0.998599i	$0.516850\pi$
$504$	−3.75529	−	3.44657i	−0.167274	−	0.153523i
$505$	−0.161189	+	1.12110i	−0.00717283	+	0.0498881i
$506$	−0.346012	+	0.427417i	−0.0153821	+	0.0190010i
$507$	0.935796	+	6.50860i	0.0415601	+	0.289057i
$508$	−10.2624	+	15.0083i	−0.455321	+	0.665886i
$509$	−1.95131	+	5.01191i	−0.0864905	+	0.222149i	−0.968466	−	0.249147i	$-0.919850\pi$
$509$	−1.95131	+	5.01191i	−0.0864905	+	0.222149i	0.881975	+	0.471296i	$0.156214\pi$
$510$	0.200121	+	0.259522i	0.00886151	+	0.0114918i
$511$	1.10420	+	3.39837i	0.0488469	+	0.150335i
$512$	5.47330	−	9.07644i	0.241888	−	0.401126i
$513$	0.282872	+	0.726551i	0.0124891	+	0.0320780i
$514$	−8.98940	−	2.09040i	−0.396505	−	0.0922034i
$515$	1.50273	−	0.635057i	0.0662180	−	0.0279840i
$516$	3.41583	−	2.19522i	0.150373	−	0.0966391i
$517$	−22.1153	+	24.3349i	−0.972632	+	1.07025i
$518$	−0.0528763	−	0.0339815i	−0.00232325	−	0.00149306i
$519$	−4.52421	−	0.782945i	−0.198591	−	0.0343675i
$520$	−1.32117	+	15.3821i	−0.0579372	+	0.674550i
$521$	−0.144568	−	1.68317i	−0.00633363	−	0.0737411i	0.992482	−	0.122387i	$-0.0390549\pi$
$521$	−0.144568	−	1.68317i	−0.00633363	−	0.0737411i	−0.998816	+	0.0486458i	$0.984509\pi$
$522$	−21.3107	+	3.68797i	−0.932746	+	0.161418i
$523$	16.3235	+	6.89836i	0.713776	+	0.301644i	0.715753	−	0.698354i	$-0.246084\pi$
$523$	16.3235	+	6.89836i	0.713776	+	0.301644i	−0.00197668	+	0.999998i	$0.500629\pi$
$524$	−21.7982	−	15.8373i	−0.952260	−	0.691858i
$525$	0.168692	+	0.0952650i	0.00736234	+	0.00415770i
$526$	0.287173	−	10.0524i	0.0125213	−	0.438304i
$527$	−11.8069	−	3.46683i	−0.514318	−	0.151017i
$528$	0.901231	−	0.134094i	0.0392211	−	0.00583570i
$529$	22.0211	−	6.46597i	0.957438	−	0.281129i
$530$	1.82357	+	6.93759i	0.0792110	+	0.301350i
$531$	−4.15063	−	20.4842i	−0.180122	−	0.888938i
$532$	−0.211088	+	0.400057i	−0.00915185	+	0.0173447i
$533$	−1.56787	−	54.8827i	−0.0679121	−	2.37723i
$534$	0.350893	−	1.33494i	0.0151846	−	0.0577683i
$535$	−6.71361	−	0.383898i	−0.290255	−	0.0165974i
$536$	5.72865	+	5.89464i	0.247440	+	0.254610i
$537$	3.29594	+	1.62050i	0.142230	+	0.0699299i
$538$	−5.85978	−	12.8311i	−0.252633	−	0.553189i
$539$	−17.1082	+	13.3268i	−0.736904	+	0.574026i
$540$	−1.01124	+	2.21430i	−0.0435167	+	0.0952882i
$541$	9.56495	−	7.82122i	0.411229	−	0.336261i	−0.404661	−	0.914467i	$-0.632611\pi$
$541$	9.56495	−	7.82122i	0.411229	−	0.336261i	0.815891	+	0.578206i	$0.196247\pi$
$542$	8.73703	+	16.5585i	0.375288	+	0.711249i
$543$	−0.913699	+	0.515989i	−0.0392106	+	0.0221432i
$544$	−8.95725	−	1.02775i	−0.384039	−	0.0440644i
$545$	−12.1260	−	1.39133i	−0.519422	−	0.0595981i
$546$	0.756662	−	0.427307i	0.0323821	−	0.0182870i
$547$	−10.6412	−	20.1673i	−0.454985	−	0.862293i	−0.999719	−	0.0236839i	$-0.992460\pi$
$547$	−10.6412	−	20.1673i	−0.454985	−	0.862293i	0.544734	−	0.838609i	$-0.316630\pi$
$548$	−9.00077	+	7.35990i	−0.384494	+	0.314399i
$549$	−4.08738	+	8.95010i	−0.174445	+	0.381981i
$550$	−2.30434	+	0.910206i	−0.0982573	+	0.0388113i
$551$	1.90314	+	4.16729i	0.0810764	+	0.177532i
$552$	−0.146079	−	0.0718223i	−0.00621754	−	0.00305696i
$553$	−2.78558	−	2.86630i	−0.118455	−	0.121887i
$554$	20.0811	+	1.14828i	0.853163	+	0.0487856i
$555$	−0.00898244	+	0.0341728i	−0.000381284	+	0.00145055i
$556$	0.0133159	+	0.466118i	0.000564721	+	0.0197678i
$557$	−5.97789	+	11.3294i	−0.253291	+	0.480041i	−0.977887	−	0.209134i	$-0.932936\pi$
$557$	−5.97789	+	11.3294i	−0.253291	+	0.480041i	0.724596	+	0.689174i	$0.242027\pi$
$558$	3.46413	+	17.0962i	0.146648	+	0.723738i
$559$	−15.0696	−	57.3306i	−0.637375	−	2.42483i
$560$	−0.627697	+	0.184308i	−0.0265250	+	0.00778845i
$561$	−0.792633	−	1.22016i	−0.0334650	−	0.0515150i
$562$	8.81714	+	2.58894i	0.371928	+	0.109208i
$563$	0.950450	−	33.2701i	0.0400567	−	1.40217i	−0.692479	−	0.721438i	$-0.743481\pi$
$563$	0.950450	−	33.2701i	0.0400567	−	1.40217i	0.732536	−	0.680729i	$-0.238337\pi$
$564$	−3.55068	−	2.00516i	−0.149511	−	0.0844325i
$565$	−16.7140	−	12.1434i	−0.703164	−	0.510878i
$566$	16.6706	+	7.04504i	0.700716	+	0.296125i
$567$	−5.53781	+	0.958356i	−0.232566	+	0.0402472i
$568$	0.426610	+	4.96693i	0.0179001	+	0.208408i
$569$	−1.49430	+	17.3978i	−0.0626442	+	0.729353i	0.895871	+	0.444313i	$0.146552\pi$
$569$	−1.49430	+	17.3978i	−0.0626442	+	0.729353i	−0.958516	+	0.285040i	$0.907993\pi$
$570$	−0.0969653	−	0.0167805i	−0.00406143	−	0.000702858i
$571$	11.1182	+	7.14523i	0.465282	+	0.299019i	0.752198	−	0.658937i	$-0.228994\pi$
$571$	11.1182	+	7.14523i	0.465282	+	0.299019i	−0.286916	+	0.957956i	$0.592630\pi$
$572$	4.75780	−	28.3190i	0.198934	−	1.18408i
$573$	−6.00087	+	3.85652i	−0.250690	+	0.161109i
$574$	−4.27365	+	1.80606i	−0.178379	+	0.0753835i
$575$	−0.216189	−	0.0502725i	−0.00901569	−	0.00209651i
$576$	2.59715	+	6.67072i	0.108215	+	0.277947i
$577$	−9.21321	+	15.2784i	−0.383551	+	0.636048i	−0.986882	−	0.161443i	$-0.948385\pi$
$577$	−9.21321	+	15.2784i	−0.383551	+	0.636048i	0.603331	+	0.797491i	$0.293840\pi$
$578$	−3.37823	−	10.3971i	−0.140516	−	0.432464i
$579$	−1.60869	−	2.08619i	−0.0668549	−	0.0866990i
$580$	−5.18945	+	13.3290i	−0.215480	+	0.553457i
$581$	2.80798	−	4.10654i	0.116495	−	0.170368i
$582$	−0.288009	−	2.00315i	−0.0119384	−	0.0830331i
$583$	−5.58467	−	31.3543i	−0.231293	−	1.29856i
$584$	1.92506	−	13.3891i	0.0796597	−	0.554046i
$585$	12.9113	+	11.8499i	0.533816	+	0.489932i
$586$	−15.3691	+	0.878835i	−0.634890	+	0.0363043i
$587$	−4.66773	+	23.0361i	−0.192658	+	0.950803i	0.760733	+	0.649065i	$0.224840\pi$
$587$	−4.66773	+	23.0361i	−0.192658	+	0.950803i	−0.953391	+	0.301738i	$0.902433\pi$
$588$	−2.08189	−	1.70235i	−0.0858557	−	0.0702038i
$589$	3.31591	−	1.63032i	0.136630	−	0.0671763i
$590$	5.03834	+	1.79768i	0.207425	+	0.0740091i
$591$	−3.11681	+	4.04195i	−0.128208	+	0.166263i
$592$	−0.0616135	−	0.102175i	−0.00253230	−	0.00419935i
$593$	14.0843	−	16.2541i	0.578371	−	0.667476i	−0.388883	−	0.921287i	$-0.627139\pi$
$593$	14.0843	−	16.2541i	0.578371	−	0.667476i	0.967254	+	0.253812i	$0.0816843\pi$
$594$	−2.03883	+	3.65204i	−0.0836542	+	0.149845i
$595$	0.684118	+	0.789514i	0.0280461	+	0.0323669i
$596$	9.51264	−	29.2769i	0.389653	−	1.19923i
$597$	−3.09448	+	1.10411i	−0.126649	+	0.0451882i
$598$	−0.693855	+	0.713960i	−0.0283739	+	0.0291960i
$599$	10.2465	−	9.40414i	0.418660	−	0.384243i	−0.438977	−	0.898498i	$-0.644659\pi$
$599$	10.2465	−	9.40414i	0.418660	−	0.384243i	0.857637	+	0.514256i	$0.171932\pi$
$600$	−0.413956	−	0.605392i	−0.0168997	−	0.0247150i
$601$	−32.6564	+	7.59393i	−1.33208	+	0.309763i	−0.831307	−	0.555814i	$-0.812407\pi$
$601$	−32.6564	+	7.59393i	−1.33208	+	0.309763i	−0.500777	+	0.865577i	$0.666952\pi$
$602$	−4.05247	+	2.94429i	−0.165166	+	0.120000i
$603$	9.26958	−	1.06359i	0.377487	−	0.0433126i
$604$	−16.9926			−0.691417
$605$	10.5235	−	3.20248i	0.427841	−	0.130199i
$606$	−0.241332			−0.00980343
$607$	−22.5318	+	2.58528i	−0.914538	+	0.104933i	−0.558468	−	0.829526i	$-0.688611\pi$
$607$	−22.5318	+	2.58528i	−0.914538	+	0.104933i	−0.356070	+	0.934459i	$0.615883\pi$
$608$	2.19025	−	1.59131i	0.0888265	−	0.0645363i
$609$	1.87180	−	0.435269i	0.0758493	−	0.0176380i
$610$	−1.42146	−	2.07882i	−0.0575532	−	0.0841689i
$611$	−43.8591	+	40.2535i	−1.77435	+	1.62848i
$612$	−4.51130	+	4.64201i	−0.182358	+	0.187642i
$613$	31.1737	−	11.1227i	1.25909	−	0.449243i	0.379598	−	0.925152i	$-0.376062\pi$
$613$	31.1737	−	11.1227i	1.25909	−	0.449243i	0.879495	+	0.475908i	$0.157881\pi$
$614$	−0.850394	+	2.61724i	−0.0343191	+	0.105623i
$615$	1.70798	+	1.97112i	0.0688726	+	0.0794832i
$616$	−5.67112	+	1.17812i	−0.228496	+	0.0474677i
$617$	−10.8276	+	12.4957i	−0.435904	+	0.503060i	−0.930616	−	0.365997i	$-0.880728\pi$
$617$	−10.8276	+	12.4957i	−0.435904	+	0.503060i	0.494712	+	0.869057i	$0.335273\pi$
$618$	0.179504	+	0.297674i	0.00722071	+	0.0119742i
$619$	25.9306	−	33.6275i	1.04224	−	1.35160i	0.108322	−	0.994116i	$-0.465452\pi$
$619$	25.9306	−	33.6275i	1.04224	−	1.35160i	0.933919	−	0.357486i	$-0.116366\pi$
$620$	10.8656	+	3.87684i	0.436373	+	0.155698i
$621$	−0.336257	+	0.165326i	−0.0134935	+	0.00663432i
$622$	−0.825687	−	0.675161i	−0.0331070	−	0.0270715i
$623$	0.873788	−	4.31231i	0.0350076	−	0.172769i
$624$	1.64687	−	0.0941714i	0.0659275	−	0.00376987i
$625$	−0.736741	−	0.676175i	−0.0294696	−	0.0270470i
$626$	0.571986	−	3.97825i	0.0228611	−	0.159003i
$627$	0.423092	+	0.108995i	0.0168966	+	0.00435283i
$628$	2.29270	+	15.9461i	0.0914887	+	0.636318i
$629$	−0.107544	+	0.157278i	−0.00428806	+	0.00627109i
$630$	0.537278	−	1.37999i	0.0214057	−	0.0549800i
$631$	4.52804	+	5.87207i	0.180258	+	0.233763i	0.873358	−	0.487078i	$-0.161937\pi$
$631$	4.52804	+	5.87207i	0.180258	+	0.233763i	−0.693100	+	0.720842i	$0.743756\pi$
$632$	4.67557	+	14.3899i	0.185984	+	0.572401i
$633$	−0.187303	+	0.310607i	−0.00744463	+	0.0123455i
$634$	−4.11711	−	10.5747i	−0.163511	−	0.419975i
$635$	−12.2812	−	2.85587i	−0.487365	−	0.113332i
$636$	3.63789	−	1.53738i	0.144252	−	0.0609613i
$637$	−33.0285	+	21.2261i	−1.30864	+	0.841010i
$638$	−10.7354	+	22.1079i	−0.425017	+	0.875262i
$639$	4.76050	+	3.05939i	0.188323	+	0.121028i
$640$	9.74680	+	1.68675i	0.385276	+	0.0666747i
$641$	3.31142	−	38.5542i	0.130793	−	1.52280i	−0.577214	−	0.816593i	$-0.695860\pi$
$641$	3.31142	−	38.5542i	0.130793	−	1.52280i	0.708007	−	0.706205i	$-0.249594\pi$
$642$	−0.122614	−	1.42757i	−0.00483920	−	0.0563417i
$643$	−16.1802	+	2.80009i	−0.638084	+	0.110425i	−0.480378	−	0.877062i	$-0.659501\pi$
$643$	−16.1802	+	2.80009i	−0.638084	+	0.110425i	−0.157705	+	0.987486i	$0.550410\pi$
$644$	−0.200239	−	0.0846216i	−0.00789051	−	0.00333456i
$645$	2.27810	+	1.65514i	0.0897003	+	0.0651711i
$646$	−0.462055	−	0.260935i	−0.0181793	−	0.0102663i
$647$	−0.277570	+	9.71621i	−0.0109124	+	0.381984i	0.975720	+	0.219022i	$0.0702866\pi$
$647$	−0.277570	+	9.71621i	−0.0109124	+	0.381984i	−0.986632	+	0.162962i	$0.947895\pi$
$648$	20.4135	+	5.99395i	0.801919	+	0.235465i
$649$	−21.6523	−	9.76016i	−0.849927	−	0.383120i
$650$	−4.30376	+	1.26370i	−0.168807	+	0.0495663i
$651$	−0.394033	−	1.49906i	−0.0154434	−	0.0587527i
$652$	1.89485	+	9.35146i	0.0742081	+	0.366232i
$653$	−6.33034	+	11.9973i	−0.247726	+	0.469492i	−0.976574	−	0.215183i	$-0.930965\pi$
$653$	−6.33034	+	11.9973i	−0.247726	+	0.469492i	0.728848	+	0.684675i	$0.240056\pi$
$654$	−0.0742652	−	2.59962i	−0.00290400	−	0.101653i
$655$	4.75026	−	18.0719i	0.185608	−	0.706127i
$656$	−8.79286	−	0.502794i	−0.343303	−	0.0196308i
$657$	−10.7012	−	11.0112i	−0.417492	−	0.429589i
$658$	4.51439	+	2.21957i	0.175989	+	0.0865280i
$659$	5.28134	+	11.5645i	0.205732	+	0.450490i	0.984169	−	0.177233i	$-0.0567145\pi$
$659$	5.28134	+	11.5645i	0.205732	+	0.450490i	−0.778437	+	0.627723i	$0.783987\pi$
$660$	0.676590	+	1.18447i	0.0263362	+	0.0461056i
$661$	18.9278	−	41.4461i	0.736206	−	1.61207i	−0.0534911	−	0.998568i	$-0.517035\pi$
$661$	18.9278	−	41.4461i	0.736206	−	1.61207i	0.789697	−	0.613497i	$-0.210238\pi$
$662$	2.13225	−	1.74353i	0.0828723	−	0.0677643i
$663$	−1.22928	−	2.32974i	−0.0477411	−	0.0904795i
$664$	−16.3982	+	9.26048i	−0.636373	+	0.359376i
$665$	−0.311648	−	0.0357583i	−0.0120852	−	0.00138665i
$666$	0.268328	+	0.0307878i	0.0103975	+	0.00119300i
$667$	−1.91713	+	1.08265i	−0.0742317	+	0.0419206i
$668$	6.59459	+	12.4981i	0.255152	+	0.483568i
$669$	5.29493	−	4.32964i	0.204714	−	0.167394i
$670$	−0.992052	+	2.17229i	−0.0383263	+	0.0839230i
$671$	5.54573	+	9.70865i	0.214091	+	0.374798i
$672$	−0.471767	−	1.03303i	−0.0181988	−	0.0398498i
$673$	−0.358599	−	0.176311i	−0.0138230	−	0.00679629i	0.434297	−	0.900770i	$-0.356997\pi$
$673$	−0.358599	−	0.176311i	−0.0138230	−	0.00679629i	−0.448119	+	0.893974i	$0.647906\pi$
$674$	3.53118	+	3.63349i	0.136016	+	0.139957i
$675$	−1.68542	−	0.0963759i	−0.0648719	−	0.00370951i
$676$	8.45075	−	32.1500i	0.325029	−	1.23654i
$677$	−0.105245	−	3.68406i	−0.00404490	−	0.141590i	−0.999105	−	0.0423106i	$-0.986528\pi$
$677$	−0.105245	−	3.68406i	−0.00404490	−	0.141590i	0.995060	−	0.0992792i	$-0.0316537\pi$
$678$	2.05428	−	3.89329i	0.0788940	−	0.149521i
$679$	−1.28113	−	6.32264i	−0.0491654	−	0.242641i
$680$	−1.00535	−	3.82476i	−0.0385536	−	0.146673i
$681$	7.60679	−	2.23355i	0.291493	−	0.0855900i
$682$	18.0711	+	8.14586i	0.691977	+	0.311921i
$683$	35.5226	+	10.4304i	1.35924	+	0.399107i	0.878493	−	0.477755i	$-0.158549\pi$
$683$	35.5226	+	10.4304i	1.35924	+	0.399107i	0.480742	+	0.876862i	$0.340367\pi$
$684$	0.0555044	−	1.94291i	0.00212227	−	0.0742890i
$685$	−7.02099	−	3.96493i	−0.268258	−	0.151492i
$686$	5.55745	+	4.03772i	0.212184	+	0.154161i
$687$	1.28044	+	0.541118i	0.0488518	+	0.0206449i
$688$	−9.36941	+	1.62144i	−0.357205	+	0.0618168i
$689$	−4.93405	−	57.4461i	−0.187972	−	2.18852i
$690$	0.00404710	−	0.0471195i	0.000154071	−	0.00179381i
$691$	−27.5226	−	4.76297i	−1.04701	−	0.181192i	−0.379039	−	0.925381i	$-0.623745\pi$
$691$	−27.5226	−	4.76297i	−1.04701	−	0.181192i	−0.667970	+	0.744189i	$0.732836\pi$
$692$	19.5270	+	12.5492i	0.742303	+	0.477049i
$693$	−2.87198	+	5.91443i	−0.109097	+	0.224670i
$694$	13.4939	−	8.67199i	0.512221	−	0.329184i
$695$	−0.297878	+	0.125884i	−0.0112992	+	0.00477506i
$696$	−7.08583	−	1.64774i	−0.268588	−	0.0624574i
$697$	5.10258	+	13.1059i	0.193274	+	0.496420i
$698$	6.99397	−	11.5982i	0.264726	−	0.438998i
$699$	−0.576434	−	1.77408i	−0.0218027	−	0.0671020i
$700$	−0.598070	−	0.775591i	−0.0226049	−	0.0293146i
$701$	−0.908789	+	2.33421i	−0.0343245	+	0.0881617i	−0.947983	−	0.318321i	$-0.896881\pi$
$701$	−0.908789	+	2.33421i	−0.0343245	+	0.0881617i	0.913659	+	0.406482i	$0.133245\pi$
$702$	−4.27410	+	6.25067i	−0.161315	+	0.235916i
$703$	−0.00814213	−	0.0566298i	−0.000307086	−	0.00213583i
$704$	7.87739	+	2.02933i	0.296890	+	0.0764834i
$705$	0.402455	−	2.79913i	0.0151573	−	0.105422i
$706$	−2.98516	−	2.73976i	−0.112348	−	0.103112i
$707$	−0.768043	+	0.0439183i	−0.0288852	+	0.00165172i
$708$	0.584900	−	2.88659i	0.0219819	−	0.108485i
$709$	−35.8346	−	29.3018i	−1.34580	−	1.10045i	−0.985877	−	0.167470i	$-0.946440\pi$
$709$	−35.8346	−	29.3018i	−1.34580	−	1.10045i	−0.359920	−	0.932983i	$-0.617196\pi$
$710$	−1.29976	+	0.639049i	−0.0487791	+	0.0239831i
$711$	16.1761	+	5.77162i	0.606651	+	0.216453i
$712$	−10.1711	+	13.1901i	−0.381179	+	0.494322i
$713$	0.917011	+	1.52069i	0.0343423	+	0.0569503i
$714$	−0.145767	+	0.168224i	−0.00545520	+	0.00629563i
$715$	19.4982	−	4.05055i	0.729192	−	0.151482i
$716$	−12.1591	−	14.0323i	−0.454406	−	0.524412i
$717$	−0.959889	+	2.95423i	−0.0358477	+	0.110328i
$718$	−0.546003	+	0.194813i	−0.0203767	+	0.00727037i
$719$	−13.0520	+	13.4302i	−0.486758	+	0.500863i	−0.915363	−	0.402630i	$-0.868096\pi$
$719$	−13.0520	+	13.4302i	−0.486758	+	0.500863i	0.428605	+	0.903492i	$0.359005\pi$
$720$	2.07107	−	1.90081i	0.0771843	−	0.0708392i
$721$	0.625447	+	0.914687i	0.0232929	+	0.0340647i
$722$	−13.6694	+	3.17867i	−0.508721	+	0.118298i
$723$	4.00203	−	2.90765i	0.148837	−	0.108137i
$724$	5.27022	−	0.604702i	0.195866	−	0.0224736i
$725$	−9.91955			−0.368403
$726$	0.994526	+	2.12234i	0.0369103	+	0.0787675i
$727$	−46.8662			−1.73817			−0.869086	−	0.494661i	$-0.835292\pi$
$727$	−46.8662			−1.73817			−0.869086	+	0.494661i	$0.835292\pi$
$728$	−10.4179	+	1.19534i	−0.386113	+	0.0443024i
$729$	18.3691	−	13.3460i	0.680339	−	0.494295i
$730$	3.82784	−	0.890126i	0.141675	−	0.0329450i
$731$	8.57066	+	12.5342i	0.316997	+	0.463594i
$732$	−1.02151	+	0.937537i	−0.0377563	+	0.0346524i
$733$	16.4084	−	16.8839i	0.606060	−	0.623621i	−0.342766	−	0.939421i	$-0.611364\pi$
$733$	16.4084	−	16.8839i	0.606060	−	0.623621i	0.948826	+	0.315800i	$0.102273\pi$
$734$	1.87991	−	0.670749i	0.0693886	−	0.0247578i
$735$	0.576324	−	1.77374i	0.0212580	−	0.0654255i
$736$	0.852038	+	0.983304i	0.0314065	+	0.0362451i
$737$	5.16832	−	9.25771i	0.190378	−	0.341012i
$738$	13.0558	−	15.0672i	0.480590	−	0.554630i
$739$	16.0955	+	26.6914i	0.592082	+	0.981859i	0.997698	+	0.0678147i	$0.0216027\pi$
$739$	16.0955	+	26.6914i	0.592082	+	0.981859i	−0.405615	+	0.914044i	$0.632943\pi$
$740$	0.109078	−	0.141454i	0.00400978	−	0.00519997i
$741$	0.744978	+	0.265808i	0.0273675	+	0.00976469i
$742$	−4.37230	+	2.14972i	−0.160512	+	0.0789186i
$743$	7.74351	+	6.33184i	0.284082	+	0.232293i	0.764307	−	0.644853i	$-0.223081\pi$
$743$	7.74351	+	6.33184i	0.284082	+	0.232293i	−0.480225	+	0.877145i	$0.659445\pi$
$744$	−1.16524	+	5.75067i	−0.0427197	+	0.210830i
$745$	21.3136	−	1.21876i	0.780870	−	0.0446518i
$746$	7.35564	+	6.75094i	0.269309	+	0.247170i
$747$	−3.04226	+	21.1594i	−0.111311	+	0.774182i
$748$	1.28985	+	7.24170i	0.0471617	+	0.264783i
$749$	−0.650016	−	4.52096i	−0.0237511	−	0.165192i
$750$	0.120268	−	0.175886i	0.00439155	−	0.00642244i
$751$	−1.16514	+	2.99263i	−0.0425164	+	0.109202i	−0.951521	−	0.307583i	$-0.900480\pi$
$751$	−1.16514	+	2.99263i	−0.0425164	+	0.109202i	0.909005	+	0.416786i	$0.136843\pi$
$752$	5.83125	+	7.56210i	0.212644	+	0.275762i
$753$	1.19393	+	3.67452i	0.0435090	+	0.133907i
$754$	−22.9764	+	38.1021i	−0.836752	+	1.38760i
$755$	−4.27546	−	10.9814i	−0.155600	−	0.399655i
$756$	−1.61044	−	0.374491i	−0.0585710	−	0.0136201i
$757$	30.9453	−	13.0776i	1.12472	−	0.475312i	0.254059	−	0.967189i	$-0.418234\pi$
$757$	30.9453	−	13.0776i	1.12472	−	0.475312i	0.870665	+	0.491876i	$0.163689\pi$
$758$	23.7399	−	15.2567i	0.862271	−	0.554148i
$759$	−0.0347892	+	0.207069i	−0.00126277	+	0.00751614i
$760$	0.998991	+	0.642012i	0.0362372	+	0.0232882i
$761$	−3.24187	−	0.561027i	−0.117518	−	0.0203372i	0.111460	−	0.993769i	$-0.464447\pi$
$761$	−3.24187	−	0.561027i	−0.117518	−	0.0203372i	−0.228978	+	0.973432i	$0.573538\pi$
$762$	0.229907	−	2.67676i	0.00832866	−	0.0969688i
$763$	−0.709438	−	8.25984i	−0.0256834	−	0.299026i
$764$	35.5334	−	6.14930i	1.28555	−	0.222474i
$765$	−4.13497	−	1.74745i	−0.149500	−	0.0631793i
$766$	−13.3297	−	9.68459i	−0.481621	−	0.349918i
$767$	−37.4403	−	21.1435i	−1.35189	−	0.763449i
$768$	−0.100140	+	3.50537i	−0.00361350	+	0.126489i
$769$	−20.7193	−	6.08372i	−0.747155	−	0.219385i	−0.114077	−	0.993472i	$-0.536391\pi$
$769$	−20.7193	−	6.08372i	−0.747155	−	0.219385i	−0.633079	+	0.774087i	$0.718209\pi$
$770$	−0.916737	−	1.41120i	−0.0330369	−	0.0508561i
$771$	−3.38120	+	0.992809i	−0.121771	+	0.0357551i
$772$	3.38568	+	12.8805i	0.121853	+	0.463578i
$773$	−4.69980	−	23.1944i	−0.169040	−	0.834246i	−0.971408	−	0.237416i	$-0.923700\pi$
$773$	−4.69980	−	23.1944i	−0.169040	−	0.834246i	0.802368	−	0.596830i	$-0.203573\pi$
$774$	10.0448	−	19.0371i	0.361054	−	0.684273i
$775$	0.228465	+	7.99732i	0.00820671	+	0.287272i
$776$	−6.20831	+	23.6188i	−0.222865	+	0.847867i
$777$	−0.0239600	−	0.00137008i	−0.000859561	−	4.91515e-5i
$778$	−15.0978	−	15.5352i	−0.541281	−	0.556965i
$779$	−3.78984	−	1.86334i	−0.135785	−	0.0667610i
$780$	1.02590	+	2.24640i	0.0367330	+	0.0804340i
$781$	5.98078	−	2.36239i	0.214009	−	0.0845330i
$782$	0.105939	−	0.231975i	0.00378838	−	0.00829540i
$783$	−12.9637	+	10.6004i	−0.463286	+	0.378827i
$784$	2.93897	+	5.56998i	0.104963	+	0.198928i
$785$	−9.72827	+	5.49381i	−0.347217	+	0.196082i
$786$	3.95548	+	0.453849i	0.141087	+	0.0161883i
$787$	−17.6740	−	2.02791i	−0.630011	−	0.0722870i	−0.206896	−	0.978363i	$-0.566336\pi$
$787$	−17.6740	−	2.02791i	−0.630011	−	0.0722870i	−0.423115	+	0.906076i	$0.639063\pi$
$788$	22.4682	−	12.6884i	0.800396	−	0.452004i
$789$	−1.79190	−	3.39603i	−0.0637934	−	0.120902i
$790$	−3.40304	+	2.78265i	−0.121075	+	0.0990024i
$791$	5.82927	−	12.7643i	0.207265	−	0.453847i
$792$	19.6352	−	15.2953i	0.697708	−	0.543493i
$793$	8.40885	+	18.4128i	0.298607	+	0.653858i
$794$	1.08669	+	0.534288i	0.0385651	+	0.0189612i
$795$	1.90885	+	1.96416i	0.0677000	+	0.0696617i
$796$	16.5828	+	0.948238i	0.587761	+	0.0336094i
$797$	−9.20960	+	35.0370i	−0.326221	+	1.24107i	0.578717	+	0.815529i	$0.303554\pi$
$797$	−9.20960	+	35.0370i	−0.326221	+	1.24107i	−0.904938	+	0.425544i	$0.860083\pi$
$798$	−0.00190867	−	0.0668122i	−6.75662e−5	−	0.00236513i
$799$	7.11627	−	13.4868i	0.251756	−	0.477130i
$800$	1.16413	+	5.74518i	0.0411580	+	0.203123i
$801$	4.80648	+	18.2857i	0.169829	+	0.646095i
$802$	−16.8942	+	4.96059i	−0.596556	+	0.175165i
$803$	−17.2583	+	2.56786i	−0.609032	+	0.0906178i
$804$	1.26156	+	0.370429i	0.0444919	+	0.0130640i
$805$	0.00430502	−	0.150695i	0.000151732	−	0.00531132i
$806$	31.2478	+	17.6465i	1.10066	+	0.621570i
$807$	−4.35731	−	3.16577i	−0.153385	−	0.111440i
$808$	2.68252	+	1.13364i	0.0943706	+	0.0398814i
$809$	46.7560	−	8.09144i	1.64385	−	0.284480i	0.727876	−	0.685709i	$-0.240508\pi$
$809$	46.7560	−	8.09144i	1.64385	−	0.284480i	0.915978	+	0.401229i	$0.131417\pi$
$810$	0.528953	+	6.15849i	0.0185855	+	0.216387i
$811$	−0.366621	+	4.26849i	−0.0128738	+	0.149887i	−0.999946	−	0.0103892i	$-0.996693\pi$
$811$	−0.366621	+	4.26849i	−0.0128738	+	0.149887i	0.987072	+	0.160276i	$0.0512384\pi$
$812$	−9.57295	−	1.65666i	−0.335945	−	0.0581375i
$813$	6.01375	+	3.86480i	0.210912	+	0.135545i
$814$	0.206418	−	0.227134i	0.00723495	−	0.00796106i
$815$	−5.56661	+	3.57744i	−0.194990	+	0.125312i
$816$	−0.389212	+	0.164482i	−0.0136251	+	0.00575803i
$817$	−4.44100	−	1.03271i	−0.155371	−	0.0361299i
$818$	−1.81130	−	4.65228i	−0.0633306	−	0.162663i
$819$	−6.14677	+	10.1933i	−0.214786	+	0.356182i
$820$	−4.07450	−	12.5400i	−0.142288	−	0.437917i
$821$	4.04943	+	5.25140i	0.141326	+	0.183275i	0.857245	−	0.514908i	$-0.172174\pi$
$821$	4.04943	+	5.25140i	0.141326	+	0.183275i	−0.715919	+	0.698183i	$0.753992\pi$
$822$	0.623321	−	1.60099i	0.0217408	−	0.0558408i
$823$	22.3765	−	32.7246i	0.779997	−	1.14071i	−0.206742	−	0.978395i	$-0.566286\pi$
$823$	22.3765	−	32.7246i	0.779997	−	1.14071i	0.986739	−	0.162314i	$-0.0518957\pi$
$824$	−0.596968	−	4.15200i	−0.0207963	−	0.144642i
$825$	−0.595230	+	0.735268i	−0.0207232	+	0.0255988i
$826$	−0.517091	+	3.59645i	−0.0179919	+	0.125136i
$827$	25.0857	+	23.0234i	0.872315	+	0.800604i	0.981108	−	0.193461i	$-0.0619712\pi$
$827$	25.0857	+	23.0234i	0.872315	+	0.800604i	−0.108793	+	0.994064i	$0.534698\pi$
$828$	0.932596	−	0.0533278i	0.0324100	−	0.00185327i
$829$	−6.92426	+	34.1726i	−0.240490	+	1.18686i	0.659756	+	0.751480i	$0.270660\pi$
$829$	−6.92426	+	34.1726i	−0.240490	+	1.18686i	−0.900246	+	0.435383i	$0.856613\pi$
$830$	−4.23564	−	3.46346i	−0.147021	−	0.120219i
$831$	6.89197	−	3.38855i	0.239080	−	0.117548i
$832$	13.8705	+	4.94898i	0.480872	+	0.171575i
$833$	6.14120	−	7.96405i	0.212780	−	0.275938i
$834$	−0.0355822	−	0.0590065i	−0.00123211	−	0.00204323i
$835$	−6.41766	+	7.40637i	−0.222092	+	0.256308i
$836$	−1.75570	−	1.34016i	−0.0607223	−	0.0463506i
$837$	8.84480	+	10.2074i	0.305721	+	0.352821i
$838$	−6.39512	+	19.6822i	−0.220916	+	0.679909i
$839$	19.6228	−	7.00141i	0.677455	−	0.241716i	0.0251633	−	0.999683i	$-0.491989\pi$
$839$	19.6228	−	7.00141i	0.677455	−	0.241716i	0.652292	+	0.757968i	$0.273808\pi$
$840$	0.347166	−	0.357225i	0.0119784	−	0.0123254i
$841$	−51.1280	+	46.9249i	−1.76304	+	1.61810i
$842$	0.620567	+	0.907550i	0.0213861	+	0.0312762i
$843$	3.41753	−	0.794712i	0.117706	−	0.0273713i
$844$	1.48346	−	1.07780i	0.0510628	−	0.0370993i
$845$	22.9032	−	2.62789i	0.787893	−	0.0904022i
$846$	−21.6165			−0.743191
$847$	3.55133	+	6.57341i	0.122025	+	0.225865i
$848$	−9.24874			−0.317603
$849$	6.86522	−	0.787710i	0.235614	−	0.0270341i
$850$	0.929532	−	0.675344i	0.0318827	−	0.0231641i
$851$	0.0267809	−	0.00622763i	0.000918037	−	0.000213480i
$852$	0.450105	+	0.658257i	0.0154203	+	0.0225515i
$853$	−30.3850	+	27.8871i	−1.04036	+	0.954836i	−0.999018	−	0.0443089i	$-0.985891\pi$
$853$	−30.3850	+	27.8871i	−1.04036	+	0.954836i	−0.0413446	+	0.999145i	$0.513164\pi$
$854$	1.19211	−	1.22665i	0.0407932	−	0.0419752i
$855$	1.26957	−	0.452981i	0.0434183	−	0.0154916i
$856$	−5.34301	+	16.4441i	−0.182620	+	0.562048i
$857$	−30.5522	−	35.2591i	−1.04364	−	1.20443i	−0.978435	−	0.206557i	$-0.933774\pi$
$857$	−30.5522	−	35.2591i	−1.04364	−	1.20443i	−0.0652084	−	0.997872i	$-0.520771\pi$
$858$	1.44553	+	3.98943i	0.0493497	+	0.136197i
$859$	−7.02188	+	8.10368i	−0.239583	+	0.276494i	−0.862789	−	0.505564i	$-0.831284\pi$
$859$	−7.02188	+	8.10368i	−0.239583	+	0.276494i	0.623206	+	0.782058i	$0.285830\pi$
$860$	−7.35119	−	12.1906i	−0.250673	−	0.415695i
$861$	−1.08177	+	1.40286i	−0.0368666	+	0.0478094i
$862$	11.6423	+	4.15396i	0.396537	+	0.141484i
$863$	−18.1325	+	8.91517i	−0.617239	+	0.303476i	−0.722928	−	0.690923i	$-0.757204\pi$
$863$	−18.1325	+	8.91517i	−0.617239	+	0.303476i	0.105689	+	0.994399i	$0.466295\pi$
$864$	7.66089	+	6.26428i	0.260629	+	0.213115i
$865$	−3.19678	+	15.7767i	−0.108694	+	0.536426i
$866$	−13.1219	+	0.750339i	−0.445902	+	0.0254976i
$867$	−3.07528	−	2.82246i	−0.104442	−	0.0958559i
$868$	−1.11515	+	7.75604i	−0.0378507	+	0.263257i
$869$	16.0564	−	11.0951i	0.544675	−	0.376375i
$870$	−0.300795	−	2.09208i	−0.0101979	−	0.0709280i
$871$	10.8346	−	15.8451i	0.367116	−	0.536891i
$872$	−11.3861	+	29.2449i	−0.385581	+	0.990358i
$873$	16.9278	+	21.9523i	0.572918	+	0.742973i
$874$	0.0236635	+	0.0728289i	0.000800431	+	0.00246347i
$875$	0.350746	−	0.581647i	0.0118574	−	0.0196633i
$876$	−0.785020	−	2.01631i	−0.0265234	−	0.0681247i
$877$	3.75603	+	0.873426i	0.126832	+	0.0294935i	0.289432	−	0.957199i	$-0.406534\pi$
$877$	3.75603	+	0.873426i	0.126832	+	0.0294935i	−0.162600	+	0.986692i	$0.551988\pi$
$878$	9.28214	−	3.92267i	0.313257	−	0.132384i
$879$	−4.94476	+	3.17781i	−0.166783	+	0.107185i
$880$	−0.379707	−	3.17180i	−0.0127999	−	0.106921i
$881$	40.5169	+	26.0386i	1.36505	+	0.877263i	0.998585	−	0.0531703i	$-0.0169326\pi$
$881$	40.5169	+	26.0386i	1.36505	+	0.877263i	0.366462	+	0.930433i	$0.380569\pi$
$882$	−14.0474	−	2.43100i	−0.473000	−	0.0818559i
$883$	−3.03259	+	35.3078i	−0.102055	+	1.18820i	0.748798	+	0.662798i	$0.230631\pi$
$883$	−3.03259	+	35.3078i	−0.102055	+	1.18820i	−0.850853	+	0.525404i	$0.823914\pi$
$884$	1.13958	+	13.2679i	0.0383284	+	0.446249i
$885$	2.01262	−	0.348298i	0.0676536	−	0.0117079i
$886$	−18.3146	−	7.73980i	−0.615290	−	0.260024i
$887$	20.6532	+	15.0054i	0.693466	+	0.503833i	0.877798	−	0.479031i	$-0.159012\pi$
$887$	20.6532	+	15.0054i	0.693466	+	0.503833i	−0.184332	+	0.982864i	$0.559012\pi$
$888$	0.0791076	+	0.0446741i	0.00265468	+	0.00149916i
$889$	0.244559	−	8.56068i	0.00820225	−	0.287116i
$890$	−4.64317	−	1.36336i	−0.155639	−	0.0456998i
$891$	−0.134654	−	27.4428i	−0.00451109	−	0.919368i
$892$	−33.1771	+	9.74169i	−1.11085	+	0.326176i
$893$	1.16406	+	4.42853i	0.0389537	+	0.148195i
$894$	0.903343	+	4.45817i	0.0302123	+	0.149104i
$895$	6.00905	−	11.3884i	0.200860	−	0.380673i
$896$	0.191857	+	6.71586i	0.00640948	+	0.224361i
$897$	−0.0966371	+	0.367646i	−0.00322662	+	0.0122753i
$898$	−25.3111	−	1.44734i	−0.844644	−	0.0482985i
$899$	55.3105	+	56.9132i	1.84471	+	1.89816i
$900$	3.77676	+	1.85691i	0.125892	+	0.0618969i
$901$	6.13534	+	13.4345i	0.204398	+	0.447569i
$902$	−5.23955	−	22.0411i	−0.174458	−	0.733887i
$903$	−0.794524	+	1.73976i	−0.0264401	+	0.0578957i
$904$	−41.1228	+	33.6259i	−1.36772	+	1.11838i
$905$	1.71682	+	3.25373i	0.0570689	+	0.108158i
$906$	2.18638	−	1.23471i	0.0726377	−	0.0410204i
$907$	42.1146	+	4.83220i	1.39839	+	0.160451i	0.780177	−	0.625558i	$-0.215129\pi$
$907$	42.1146	+	4.83220i	1.39839	+	0.160451i	0.618215	+	0.786009i	$0.287856\pi$
$908$	−39.8178	−	4.56866i	−1.32140	−	0.151616i
$909$	2.87845	−	1.62553i	0.0954721	−	0.0539156i
$910$	−1.42175	−	2.69451i	−0.0471305	−	0.0893222i
$911$	3.67760	−	3.00716i	0.121844	−	0.0996316i	−0.570127	−	0.821557i	$-0.693106\pi$
$911$	3.67760	−	3.00716i	0.121844	−	0.0996316i	0.691971	+	0.721925i	$0.256742\pi$
$912$	0.0527075	−	0.115413i	0.00174532	−	0.00382172i
$913$	17.5034	+	16.8443i	0.579277	+	0.557464i
$914$	−0.692586	−	1.51655i	−0.0229087	−	0.0501631i
$915$	−0.862903	−	0.424261i	−0.0285267	−	0.0140256i
$916$	−4.89770	−	5.03961i	−0.161825	−	0.166514i
$917$	12.6710	+	0.724553i	0.418433	+	0.0239269i
$918$	0.493096	−	1.87593i	0.0162746	−	0.0619149i
$919$	0.687883	+	24.0791i	0.0226912	+	0.794295i	0.928656	+	0.370942i	$0.120965\pi$
$919$	0.687883	+	24.0791i	0.0226912	+	0.794295i	−0.905965	+	0.423353i	$0.860853\pi$
$920$	−0.266327	+	0.504745i	−0.00878053	+	0.0166410i
$921$	0.208669	+	1.02982i	0.00687589	+	0.0339338i
$922$	3.93678	+	14.9771i	0.129651	+	0.493244i
$923$	11.1702	−	3.27986i	0.367671	−	0.107958i
$924$	−0.697229	+	0.610168i	−0.0229371	+	0.0200730i
$925$	0.118860	+	0.0349003i	0.00390808	+	0.00114752i
$926$	0.580212	−	20.3101i	0.0190669	−	0.667430i
$927$	−4.14605	−	2.34138i	−0.136174	−	0.0769010i
$928$	47.0426	+	34.1784i	1.54425	+	1.12196i
$929$	5.92530	+	2.50405i	0.194403	+	0.0821554i	0.484298	−	0.874903i	$-0.339075\pi$
$929$	5.92530	+	2.50405i	0.194403	+	0.0821554i	−0.289895	+	0.957058i	$0.593620\pi$
$930$	−1.67974	+	0.290691i	−0.0550809	+	0.00953212i
$931$	0.258423	+	3.00877i	0.00846948	+	0.0986084i
$932$	−0.806997	+	9.39569i	−0.0264341	+	0.307766i
$933$	−0.401282	−	0.0694445i	−0.0131374	−	0.00227351i
$934$	14.6357	+	9.40578i	0.478894	+	0.307767i
$935$	−4.35540	+	2.65563i	−0.142437	+	0.0868485i
$936$	37.9071	−	24.3614i	1.23903	−	0.796277i
$937$	8.28403	−	3.50086i	0.270627	−	0.114368i	−0.249733	−	0.968315i	$-0.580343\pi$
$937$	8.28403	−	3.50086i	0.270627	−	0.114368i	0.520361	+	0.853947i	$0.325798\pi$
$938$	−1.57988	−	0.367386i	−0.0515851	−	0.0119956i
$939$	−0.556767	−	1.43004i	−0.0181694	−	0.0466677i
$940$	−7.38259	+	12.2426i	−0.240793	+	0.399311i
$941$	−1.40284	−	4.31749i	−0.0457312	−	0.140746i	0.925584	−	0.378543i	$-0.123575\pi$
$941$	−1.40284	−	4.31749i	−0.0457312	−	0.140746i	−0.971315	+	0.237797i	$0.923575\pi$
$942$	−1.45366	−	1.88514i	−0.0473629	−	0.0614213i
$943$	0.736351	−	1.89130i	0.0239789	−	0.0615892i
$944$	−3.89309	+	5.69347i	−0.126709	+	0.185307i
$945$	−0.163184	−	1.13497i	−0.00530836	−	0.0369205i
$946$	−10.8997	−	21.8968i	−0.354379	−	0.711927i
$947$	−0.0127147	+	0.0884328i	−0.000413173	+	0.00287368i	−0.990027	−	0.140878i	$-0.955008\pi$
$947$	−0.0127147	+	0.0884328i	−0.000413173	+	0.00287368i	0.989614	+	0.143752i	$0.0459166\pi$
$948$	1.78310	+	1.63652i	0.0579125	+	0.0531516i
$949$	−31.5370	+	1.80335i	−1.02373	+	0.0585393i
$950$	−0.0685153	+	0.338136i	−0.00222293	+	0.0109706i
$951$	−3.35427	−	2.74278i	−0.108770	−	0.0889406i
$952$	2.41049	−	1.18516i	0.0781246	−	0.0384113i
$953$	−17.2969	−	6.17151i	−0.560301	−	0.199915i	0.0406886	−	0.999172i	$-0.487045\pi$
$953$	−17.2969	−	6.17151i	−0.560301	−	0.199915i	−0.600990	+	0.799257i	$0.705227\pi$
$954$	12.7846	−	16.5794i	0.413918	−	0.536778i
$955$	12.9145	+	21.4162i	0.417902	+	0.693012i
$956$	10.2836	−	11.8679i	0.332595	−	0.383835i
$957$	0.581679	+	9.36587i	0.0188030	+	0.302755i
$958$	2.46279	+	2.84221i	0.0795690	+	0.0918276i
$959$	1.69238	−	5.20861i	0.0546498	−	0.168195i
$960$	−0.658891	+	0.235092i	−0.0212656	+	0.00758756i
$961$	23.0055	−	23.6721i	0.742111	−	0.763615i
$962$	0.409368	−	0.375714i	0.0131985	−	0.0121135i
$963$	11.0781	+	16.2013i	0.356988	+	0.522078i
$964$	−24.3582	+	5.66425i	−0.784524	+	0.182433i
$965$	−7.47212	+	5.42882i	−0.240536	+	0.174760i
$966$	0.0319129	−	0.00366166i	0.00102678	−	0.000117812i
$967$	−39.1897			−1.26026			−0.630128	−	0.776491i	$-0.716998\pi$
$967$	−39.1897			−1.26026			−0.630128	+	0.776491i	$0.716998\pi$
$968$	−1.08506	−	28.2626i	−0.0348752	−	0.908393i
$969$	−0.202612			−0.00650883
$970$	−7.04889	+	0.808784i	−0.226326	+	0.0259685i
$971$	0.774357	−	0.562603i	0.0248503	−	0.0180548i	−0.575291	−	0.817949i	$-0.695111\pi$
$971$	0.774357	−	0.562603i	0.0248503	−	0.0180548i	0.600141	+	0.799894i	$0.295111\pi$
$972$	10.4278	−	2.42488i	0.334472	−	0.0777780i
$973$	−0.123979	−	0.181314i	−0.00397459	−	0.00581266i
$974$	−11.8919	+	10.9143i	−0.381040	+	0.349716i
$975$	−1.19361	+	1.22820i	−0.0382261	+	0.0393337i
$976$	3.05816	−	1.09115i	0.0978892	−	0.0349268i
$977$	−9.27890	+	28.5575i	−0.296858	+	0.913636i	0.685733	+	0.727854i	$0.259482\pi$
$977$	−9.27890	+	28.5575i	−0.296858	+	0.913636i	−0.982591	+	0.185782i	$0.940518\pi$
$978$	−0.923297	−	1.06554i	−0.0295238	−	0.0340723i
$979$	20.0591	+	7.69660i	0.641092	+	0.245984i
$980$	−6.17434	+	7.12557i	−0.197232	+	0.227618i
$981$	18.3960	+	30.5064i	0.587340	+	0.973994i
$982$	10.3751	−	13.4547i	0.331084	−	0.429357i
$983$	−53.1365	−	18.9591i	−1.69479	−	0.604701i	−0.700722	−	0.713435i	$-0.747138\pi$
$983$	−53.1365	−	18.9591i	−1.69479	−	0.604701i	−0.994071	+	0.108734i	$0.965320\pi$
$984$	6.01810	−	2.95890i	0.191850	−	0.0943262i
$985$	13.8530	+	11.3275i	0.441394	+	0.360926i
$986$	2.26338	−	11.1702i	0.0720807	−	0.355732i
$987$	1.91764	−	0.109655i	0.0610391	−	0.00349034i
$988$	−2.94603	−	2.70384i	−0.0937256	−	0.0860206i
$989$	0.311845	−	2.16893i	0.00991611	−	0.0689681i
$990$	6.21068	+	3.70375i	0.197388	+	0.117713i
$991$	5.04579	+	35.0943i	0.160285	+	1.11481i	0.898096	+	0.439799i	$0.144950\pi$
$991$	5.04579	+	35.0943i	0.160285	+	1.11481i	−0.737811	+	0.675007i	$0.764141\pi$
$992$	26.4718	−	38.7137i	0.840480	−	1.22916i
$993$	0.381555	−	0.980015i	0.0121083	−	0.0310998i
$994$	−0.600728	−	0.779037i	−0.0190539	−	0.0247096i
$995$	3.55956	+	10.9552i	0.112846	+	0.347303i
$996$	−1.55560	+	2.57967i	−0.0492910	+	0.0817400i
$997$	14.0174	+	36.0033i	0.443935	+	1.14024i	0.959080	+	0.283134i	$0.0913742\pi$
$997$	14.0174	+	36.0033i	0.443935	+	1.14024i	−0.515146	+	0.857103i	$0.672262\pi$
$998$	27.5695	+	6.41100i	0.872696	+	0.202937i
$999$	0.192632	−	0.0814068i	0.00609460	−	0.00257560i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.s.b.416.13	yes	880
121.16	even	55	inner	605.2.s.b.16.13	✓	880

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.s.b.16.13	✓	880	121.16	even	55	inner
605.2.s.b.416.13	yes	880	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.s (of order \(55\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(0.742152 - 0.0851540i) q^{2} +(0.230756 - 0.167654i) q^{3} +(-1.40448 + 0.326599i) q^{4} +(-0.564443 - 0.825472i) q^{5} +(0.156980 - 0.144075i) q^{6} +(0.473372 - 0.487088i) q^{7} +(-2.42169 + 0.864056i) q^{8} +(-0.901911 + 2.77580i) q^{9} +O(q^{10})\)	\(q+(0.742152 - 0.0851540i) q^{2} +(0.230756 - 0.167654i) q^{3} +(-1.40448 + 0.326599i) q^{4} +(-0.564443 - 0.825472i) q^{5} +(0.156980 - 0.144075i) q^{6} +(0.473372 - 0.487088i) q^{7} +(-2.42169 + 0.864056i) q^{8} +(-0.901911 + 2.77580i) q^{9} +(-0.489195 - 0.564561i) q^{10} +(1.96261 + 2.67361i) q^{11} +(-0.269338 + 0.310832i) q^{12} +(3.10068 + 5.14191i) q^{13} +(0.309837 - 0.401803i) q^{14} +(-0.268642 - 0.0958514i) q^{15} +(0.864340 - 0.424968i) q^{16} +(-1.19068 - 0.973612i) q^{17} +(-0.432985 + 2.13686i) q^{18} +(0.461091 - 0.0263661i) q^{19} +(1.06235 + 0.975016i) q^{20} +(0.0275711 - 0.191761i) q^{21} +(1.68422 + 1.81710i) q^{22} +(0.0315878 + 0.219698i) q^{23} +(-0.413956 + 0.605392i) q^{24} +(-0.362808 + 0.931864i) q^{25} +(2.73903 + 3.55204i) q^{26} +(0.521675 + 1.60555i) q^{27} +(-0.505761 + 0.838711i) q^{28} +(3.59889 + 9.24368i) q^{29} +(-0.207536 - 0.0482604i) q^{30} +(7.36953 - 3.11439i) q^{31} +(4.93138 - 3.16920i) q^{32} +(0.901124 + 0.287912i) q^{33} +(-0.966571 - 0.621177i) q^{34} +(-0.669269 - 0.115822i) q^{35} +(0.360148 - 4.19313i) q^{36} +(-0.0106008 - 0.123423i) q^{37} +(0.339955 - 0.0588315i) q^{38} +(1.57756 + 0.666683i) q^{39} +(2.08016 + 1.51132i) q^{40} +(-7.96216 - 4.49644i) q^{41} +(0.00413271 - 0.144664i) q^{42} +(-9.47245 - 2.78136i) q^{43} +(-3.62965 - 3.11406i) q^{44} +(2.80042 - 0.822277i) q^{45} +(0.0421511 + 0.160359i) q^{46} +(1.96893 + 9.71705i) q^{47} +(0.128204 - 0.242974i) q^{48} +(0.186718 + 6.53600i) q^{49} +(-0.189907 + 0.722480i) q^{50} +(-0.437986 - 0.0250449i) q^{51} +(-6.03420 - 6.20905i) q^{52} +(-8.61725 - 4.23681i) q^{53} +(0.523881 + 1.14714i) q^{54} +(1.09921 - 3.12918i) q^{55} +(-0.725487 + 1.58859i) q^{56} +(0.101979 - 0.0833880i) q^{57} +(3.45806 + 6.55376i) q^{58} +(-6.23543 + 3.52131i) q^{59} +(0.408609 + 0.0468835i) q^{60} +(3.34920 + 0.384285i) q^{61} +(5.20411 - 2.93890i) q^{62} +(0.925118 + 1.75329i) q^{63} +(1.89871 - 1.55257i) q^{64} +(2.49434 - 5.46184i) q^{65} +(0.693288 + 0.136940i) q^{66} +(-1.32801 - 2.90794i) q^{67} +(1.99027 + 0.978549i) q^{68} +(0.0441223 + 0.0454007i) q^{69} +(-0.506562 - 0.0289663i) q^{70} +(0.492892 - 1.87516i) q^{71} +(-0.214298 - 7.50141i) q^{72} +(-2.45507 + 4.65287i) q^{73} +(-0.0183774 - 0.0906960i) q^{74} +(0.0725107 + 0.275859i) q^{75} +(-0.638984 + 0.187623i) q^{76} +(2.23133 + 0.309649i) q^{77} +(1.22756 + 0.360445i) q^{78} +(0.168040 - 5.88216i) q^{79} +(-0.838670 - 0.473619i) q^{80} +(-6.69414 - 4.86358i) q^{81} +(-6.29203 - 2.65903i) q^{82} +(7.21701 - 1.24895i) q^{83} +(0.0239058 + 0.278330i) q^{84} +(-0.131620 + 1.53242i) q^{85} +(-7.26685 - 1.25758i) q^{86} +(2.38021 + 1.52967i) q^{87} +(-7.06296 - 4.77884i) q^{88} +(5.44962 - 3.50226i) q^{89} +(2.00832 - 0.848722i) q^{90} +(3.97234 + 0.923727i) q^{91} +(-0.116118 - 0.298246i) q^{92} +(1.17842 - 1.95419i) q^{93} +(2.28869 + 7.04387i) q^{94} +(-0.282024 - 0.365736i) q^{95} +(0.606615 - 1.55808i) q^{96} +(5.36102 - 7.84025i) q^{97} +(0.695140 + 4.83481i) q^{98} +(-9.19148 + 3.03643i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 880 q + 4 q^{2} - q^{3} + 24 q^{4} + 22 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 217 q^{9}+O(q^{10}) \) 880 * q + 4 * q^2 - q^3 + 24 * q^4 + 22 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 217 * q^9	\( 880 q + 4 q^{2} - q^{3} + 24 q^{4} + 22 q^{5} - 13 q^{6} + 3 q^{7} + 2 q^{8} - 217 q^{9} - 6 q^{10} + 5 q^{11} - 5 q^{12} - 26 q^{13} - 108 q^{14} - 12 q^{15} + 34 q^{16} - q^{17} - 14 q^{18} + q^{19} + 19 q^{20} - 10 q^{21} + 275 q^{22} - 51 q^{23} + 283 q^{24} + 22 q^{25} - 16 q^{27} - 4 q^{28} - 19 q^{29} + q^{30} - 34 q^{31} - 122 q^{32} + 19 q^{33} + 52 q^{34} + 8 q^{35} - 21 q^{36} - 109 q^{37} - 10 q^{38} - 9 q^{39} - 64 q^{40} + 4 q^{41} - 49 q^{42} - 97 q^{43} + 17 q^{44} - 80 q^{45} - 91 q^{46} + 166 q^{47} - 159 q^{48} + 175 q^{49} + 4 q^{50} - 112 q^{51} - 128 q^{52} - 141 q^{53} - 37 q^{54} - 5 q^{55} + 79 q^{56} - 204 q^{57} - 190 q^{58} + 9 q^{59} - 22 q^{60} + 2 q^{61} - 105 q^{62} - q^{63} - 176 q^{64} - 14 q^{65} - 112 q^{66} - 13 q^{67} - 35 q^{68} - 53 q^{69} + 24 q^{70} - 50 q^{71} + 705 q^{72} + q^{73} + 40 q^{74} - q^{75} - 148 q^{76} - 104 q^{77} - 187 q^{78} - 83 q^{79} - q^{80} - 238 q^{81} - 54 q^{82} - 151 q^{83} + 4 q^{84} - 29 q^{85} - 39 q^{86} - 74 q^{87} - 143 q^{88} - 52 q^{89} - 28 q^{90} - 188 q^{91} - 253 q^{92} + 122 q^{93} - 187 q^{94} + 122 q^{95} - 155 q^{96} + 283 q^{97} - 92 q^{98} + 172 q^{99}+O(q^{100}) \) 880 * q + 4 * q^2 - q^3 + 24 * q^4 + 22 * q^5 - 13 * q^6 + 3 * q^7 + 2 * q^8 - 217 * q^9 - 6 * q^10 + 5 * q^11 - 5 * q^12 - 26 * q^13 - 108 * q^14 - 12 * q^15 + 34 * q^16 - q^17 - 14 * q^18 + q^19 + 19 * q^20 - 10 * q^21 + 275 * q^22 - 51 * q^23 + 283 * q^24 + 22 * q^25 - 16 * q^27 - 4 * q^28 - 19 * q^29 + q^30 - 34 * q^31 - 122 * q^32 + 19 * q^33 + 52 * q^34 + 8 * q^35 - 21 * q^36 - 109 * q^37 - 10 * q^38 - 9 * q^39 - 64 * q^40 + 4 * q^41 - 49 * q^42 - 97 * q^43 + 17 * q^44 - 80 * q^45 - 91 * q^46 + 166 * q^47 - 159 * q^48 + 175 * q^49 + 4 * q^50 - 112 * q^51 - 128 * q^52 - 141 * q^53 - 37 * q^54 - 5 * q^55 + 79 * q^56 - 204 * q^57 - 190 * q^58 + 9 * q^59 - 22 * q^60 + 2 * q^61 - 105 * q^62 - q^63 - 176 * q^64 - 14 * q^65 - 112 * q^66 - 13 * q^67 - 35 * q^68 - 53 * q^69 + 24 * q^70 - 50 * q^71 + 705 * q^72 + q^73 + 40 * q^74 - q^75 - 148 * q^76 - 104 * q^77 - 187 * q^78 - 83 * q^79 - q^80 - 238 * q^81 - 54 * q^82 - 151 * q^83 + 4 * q^84 - 29 * q^85 - 39 * q^86 - 74 * q^87 - 143 * q^88 - 52 * q^89 - 28 * q^90 - 188 * q^91 - 253 * q^92 + 122 * q^93 - 187 * q^94 + 122 * q^95 - 155 * q^96 + 283 * q^97 - 92 * q^98 + 172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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