LMFDB - Embedded newform 882.2.bb.b.121.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(25,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([28, 16]))

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

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

chi := DirichletCharacter("882.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.bb (of order $21$, degree $12$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			121.15
Character	$\chi$	$=$	882.121
Dual form			882.2.bb.b.277.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 - 0.433884i) q^{2} +(0.0351964 + 1.73169i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.94473 + 0.908329i) q^{5} +(0.783064 + 1.54493i) q^{6} +(-1.59747 - 2.10905i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-2.99752 + 0.121899i) q^{9} +O(q^{10})$	\(q+(0.900969 - 0.433884i) q^{2} +(0.0351964 + 1.73169i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.94473 + 0.908329i) q^{5} +(0.783064 + 1.54493i) q^{6} +(-1.59747 - 2.10905i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-2.99752 + 0.121899i) q^{9} +(-2.25900 + 2.09605i) q^{10} +(-0.310915 + 4.14887i) q^{11} +(1.37584 + 1.05218i) q^{12} +(0.420253 - 5.60788i) q^{13} +(-2.35436 - 1.20707i) q^{14} +(-1.67659 - 5.06740i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(1.61683 - 4.11961i) q^{17} +(-2.64778 + 1.41040i) q^{18} +(3.38128 - 5.85655i) q^{19} +(-1.12585 + 2.86862i) q^{20} +(3.59600 - 2.84056i) q^{21} +(1.52000 + 3.87291i) q^{22} +(-3.76283 - 0.567155i) q^{23} +(1.69611 + 0.351024i) q^{24} +(3.71518 - 2.53296i) q^{25} +(-2.05453 - 5.23487i) q^{26} +(-0.316593 - 5.18650i) q^{27} +(-2.64493 - 0.0660140i) q^{28} +(1.68907 - 4.30367i) q^{29} +(-3.70922 - 3.83812i) q^{30} -0.590748 q^{31} +(-0.623490 - 0.781831i) q^{32} +(-7.19552 - 0.392384i) q^{33} +(-0.330720 - 4.41315i) q^{34} +(6.61984 + 4.75954i) q^{35} +(-1.77362 + 2.41956i) q^{36} +(-6.18068 + 0.931588i) q^{37} +(0.505367 - 6.74366i) q^{38} +(9.72592 + 0.530371i) q^{39} +(0.230291 + 3.07302i) q^{40} +(3.83950 + 3.56253i) q^{41} +(2.00741 - 4.11950i) q^{42} +(-4.97839 + 4.61927i) q^{43} +(3.04987 + 2.82986i) q^{44} +(8.71617 - 3.08169i) q^{45} +(-3.63627 + 1.12164i) q^{46} +(-8.44580 + 4.06728i) q^{47} +(1.68044 - 0.419652i) q^{48} +(-1.89616 + 6.73829i) q^{49} +(2.24825 - 3.89408i) q^{50} +(7.19080 + 2.65485i) q^{51} +(-4.12240 - 3.82502i) q^{52} +(-5.81961 - 0.877164i) q^{53} +(-2.53558 - 4.53551i) q^{54} +(-2.85298 - 12.4997i) q^{55} +(-2.41164 + 1.08811i) q^{56} +(10.2608 + 5.64921i) q^{57} +(-0.345496 - 4.61033i) q^{58} +(0.383049 + 1.67825i) q^{59} +(-5.00719 - 1.84866i) q^{60} +(-6.86073 - 8.60309i) q^{61} +(-0.532245 + 0.256316i) q^{62} +(5.04555 + 6.12718i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(3.85627 + 16.8954i) q^{65} +(-6.65319 + 2.76849i) q^{66} -8.21095 q^{67} +(-2.21276 - 3.83262i) q^{68} +(0.849700 - 6.53602i) q^{69} +(8.02935 + 1.41596i) q^{70} +(-1.20071 + 1.50565i) q^{71} +(-0.548169 + 2.94949i) q^{72} +(-0.216525 - 2.88932i) q^{73} +(-5.16440 + 3.52103i) q^{74} +(4.51708 + 6.34440i) q^{75} +(-2.47064 - 6.29509i) q^{76} +(9.24685 - 5.97198i) q^{77} +(8.99287 - 3.74207i) q^{78} +11.6922 q^{79} +(1.54082 + 2.66878i) q^{80} +(8.97028 - 0.730789i) q^{81} +(5.00499 + 1.54384i) q^{82} +(-0.833374 - 11.1206i) q^{83} +(0.0212240 - 4.58253i) q^{84} +(-1.01916 + 13.5997i) q^{85} +(-2.48115 + 6.32186i) q^{86} +(7.51208 + 2.77347i) q^{87} +(3.97567 + 1.22633i) q^{88} +(13.4454 - 9.16694i) q^{89} +(6.51590 - 6.55831i) q^{90} +(-12.4986 + 8.07211i) q^{91} +(-2.78950 + 2.58828i) q^{92} +(-0.0207922 - 1.02299i) q^{93} +(-5.84467 + 7.32899i) q^{94} +(-4.63729 + 20.3173i) q^{95} +(1.33195 - 1.10721i) q^{96} +(1.51281 + 2.62027i) q^{97} +(1.21526 + 6.89370i) q^{98} +(0.426232 - 12.4742i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9}+O(q^{10}) $ 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9	\( 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9} - 2 q^{10} - 2 q^{12} + 19 q^{13} - 2 q^{14} + q^{15} - 56 q^{16} + 7 q^{17} + 2 q^{18} + 38 q^{19} + 2 q^{20} + 4 q^{21} - 42 q^{23} + 2 q^{24} + 24 q^{25} + 9 q^{26} + 35 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 88 q^{31} + 56 q^{32} + 26 q^{33} - 7 q^{34} - 2 q^{35} + 5 q^{36} + 52 q^{37} + 11 q^{38} - 60 q^{39} - 2 q^{40} + 3 q^{41} - 53 q^{42} + q^{43} + 108 q^{45} - 42 q^{46} + 3 q^{47} - 2 q^{48} + 70 q^{49} + 172 q^{50} + 13 q^{51} + 5 q^{52} - 78 q^{53} + 14 q^{54} + 23 q^{55} - 2 q^{56} - 30 q^{57} + 38 q^{58} - 28 q^{59} + q^{60} - 37 q^{61} - 24 q^{62} + 26 q^{63} - 56 q^{64} - 14 q^{65} + 2 q^{66} - 58 q^{67} - 21 q^{68} + 19 q^{69} + 44 q^{70} + 7 q^{71} + 2 q^{72} - 8 q^{73} + 4 q^{74} + q^{75} - 4 q^{76} - 13 q^{77} + 4 q^{78} + 18 q^{79} - 12 q^{80} - 87 q^{81} - 3 q^{82} + 185 q^{83} - 17 q^{84} - 159 q^{85} - q^{86} - 132 q^{87} + 47 q^{89} + 60 q^{90} + 45 q^{91} - 21 q^{92} + 53 q^{93} + 18 q^{94} + 26 q^{95} + 2 q^{96} + 111 q^{97} - 14 q^{98} - 157 q^{99}+O(q^{100}) \) 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9 - 2 * q^10 - 2 * q^12 + 19 * q^13 - 2 * q^14 + q^15 - 56 * q^16 + 7 * q^17 + 2 * q^18 + 38 * q^19 + 2 * q^20 + 4 * q^21 - 42 * q^23 + 2 * q^24 + 24 * q^25 + 9 * q^26 + 35 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 88 * q^31 + 56 * q^32 + 26 * q^33 - 7 * q^34 - 2 * q^35 + 5 * q^36 + 52 * q^37 + 11 * q^38 - 60 * q^39 - 2 * q^40 + 3 * q^41 - 53 * q^42 + q^43 + 108 * q^45 - 42 * q^46 + 3 * q^47 - 2 * q^48 + 70 * q^49 + 172 * q^50 + 13 * q^51 + 5 * q^52 - 78 * q^53 + 14 * q^54 + 23 * q^55 - 2 * q^56 - 30 * q^57 + 38 * q^58 - 28 * q^59 + q^60 - 37 * q^61 - 24 * q^62 + 26 * q^63 - 56 * q^64 - 14 * q^65 + 2 * q^66 - 58 * q^67 - 21 * q^68 + 19 * q^69 + 44 * q^70 + 7 * q^71 + 2 * q^72 - 8 * q^73 + 4 * q^74 + q^75 - 4 * q^76 - 13 * q^77 + 4 * q^78 + 18 * q^79 - 12 * q^80 - 87 * q^81 - 3 * q^82 + 185 * q^83 - 17 * q^84 - 159 * q^85 - q^86 - 132 * q^87 + 47 * q^89 + 60 * q^90 + 45 * q^91 - 21 * q^92 + 53 * q^93 + 18 * q^94 + 26 * q^95 + 2 * q^96 + 111 * q^97 - 14 * q^98 - 157 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$3$	0.0351964	+	1.73169i	0.0203207	+	0.999794i
$3$	0.0351964	+	1.73169i	0.0203207	+	0.999794i
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	−2.94473	+	0.908329i	−1.31692	+	0.406217i	−0.872068	−	0.489385i	$-0.837221\pi$
$5$	−2.94473	+	0.908329i	−1.31692	+	0.406217i	−0.444855	+	0.895602i	$0.646745\pi$
$6$	0.783064	+	1.54493i	0.319685	+	0.630715i
$7$	−1.59747	−	2.10905i	−0.603788	−	0.797145i
$7$	−1.59747	−	2.10905i	−0.603788	−	0.797145i
$8$	0.222521	−	0.974928i	0.0786730	−	0.344689i
$9$	−2.99752	+	0.121899i	−0.999174	+	0.0406329i
$10$	−2.25900	+	2.09605i	−0.714359	+	0.662828i
$11$	−0.310915	+	4.14887i	−0.0937445	+	1.25093i	0.729792	+	0.683669i	$0.239617\pi$
$11$	−0.310915	+	4.14887i	−0.0937445	+	1.25093i	−0.823536	+	0.567263i	$0.808002\pi$
$12$	1.37584	+	1.05218i	0.397170	+	0.303737i
$13$	0.420253	−	5.60788i	0.116557	−	1.55535i	−0.565932	−	0.824452i	$-0.691484\pi$
$13$	0.420253	−	5.60788i	0.116557	−	1.55535i	0.682490	−	0.730895i	$-0.260897\pi$
$14$	−2.35436	−	1.20707i	−0.629228	−	0.322602i
$15$	−1.67659	−	5.06740i	−0.432894	−	1.30840i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	1.61683	−	4.11961i	0.392138	−	0.999152i	−0.589393	−	0.807847i	$-0.700633\pi$
$17$	1.61683	−	4.11961i	0.392138	−	0.999152i	0.981531	−	0.191305i	$-0.0612719\pi$
$18$	−2.64778	+	1.41040i	−0.624089	+	0.332435i
$19$	3.38128	−	5.85655i	0.775719	−	1.34359i	−0.158670	−	0.987332i	$-0.550721\pi$
$19$	3.38128	−	5.85655i	0.775719	−	1.34359i	0.934389	−	0.356254i	$-0.115946\pi$
$20$	−1.12585	+	2.86862i	−0.251747	+	0.641442i
$21$	3.59600	−	2.84056i	0.784711	−	0.619862i
$22$	1.52000	+	3.87291i	0.324066	+	0.825707i
$23$	−3.76283	−	0.567155i	−0.784604	−	0.118260i	−0.255491	−	0.966811i	$-0.582237\pi$
$23$	−3.76283	−	0.567155i	−0.784604	−	0.118260i	−0.529113	+	0.848551i	$0.677475\pi$
$24$	1.69611	+	0.351024i	0.346217	+	0.0716525i
$25$	3.71518	−	2.53296i	0.743035	−	0.506593i
$26$	−2.05453	−	5.23487i	−0.402927	−	1.02664i
$27$	−0.316593	−	5.18650i	−0.0609284	−	0.998142i
$28$	−2.64493	−	0.0660140i	−0.499844	−	0.0124755i
$29$	1.68907	−	4.30367i	0.313652	−	0.799171i	−0.683922	−	0.729555i	$-0.739727\pi$
$29$	1.68907	−	4.30367i	0.313652	−	0.799171i	0.997574	−	0.0696164i	$-0.0221775\pi$
$30$	−3.70922	−	3.83812i	−0.677207	−	0.700742i
$31$	−0.590748			−0.106101			−0.0530507	−	0.998592i	$-0.516894\pi$
$31$	−0.590748			−0.106101			−0.0530507	+	0.998592i	$0.516894\pi$
$32$	−0.623490	−	0.781831i	−0.110218	−	0.138210i
$33$	−7.19552	−	0.392384i	−1.25258	−	0.0683053i
$34$	−0.330720	−	4.41315i	−0.0567180	−	0.756850i
$35$	6.61984	+	4.75954i	1.11896	+	0.804509i
$36$	−1.77362	+	2.41956i	−0.295603	+	0.403260i
$37$	−6.18068	+	0.931588i	−1.01610	+	0.153152i	−0.635915	−	0.771759i	$-0.719377\pi$
$37$	−6.18068	+	0.931588i	−1.01610	+	0.153152i	−0.380183	+	0.924911i	$0.624139\pi$
$38$	0.505367	−	6.74366i	0.0819814	−	1.09397i
$39$	9.72592	+	0.530371i	1.55739	+	0.0849274i
$40$	0.230291	+	3.07302i	0.0364122	+	0.485887i
$41$	3.83950	+	3.56253i	0.599628	+	0.556374i	0.920497	−	0.390750i	$-0.127784\pi$
$41$	3.83950	+	3.56253i	0.599628	+	0.556374i	−0.320868	+	0.947124i	$0.603975\pi$
$42$	2.00741	−	4.11950i	0.309749	−	0.635653i
$43$	−4.97839	+	4.61927i	−0.759197	+	0.704432i	−0.961474	−	0.274896i	$-0.911356\pi$
$43$	−4.97839	+	4.61927i	−0.759197	+	0.704432i	0.202277	+	0.979328i	$0.435166\pi$
$44$	3.04987	+	2.82986i	0.459785	+	0.426618i
$45$	8.71617	−	3.08169i	1.29933	−	0.459392i
$46$	−3.63627	+	1.12164i	−0.536139	+	0.165377i
$47$	−8.44580	+	4.06728i	−1.23195	+	0.593274i	−0.932614	−	0.360875i	$-0.882478\pi$
$47$	−8.44580	+	4.06728i	−1.23195	+	0.593274i	−0.299332	+	0.954149i	$0.596764\pi$
$48$	1.68044	−	0.419652i	0.242551	−	0.0605715i
$49$	−1.89616	+	6.73829i	−0.270879	+	0.962613i
$50$	2.24825	−	3.89408i	0.317950	−	0.550706i
$51$	7.19080	+	2.65485i	1.00691	+	0.371754i
$52$	−4.12240	−	3.82502i	−0.571674	−	0.530436i
$53$	−5.81961	−	0.877164i	−0.799384	−	0.120488i	−0.263368	−	0.964695i	$-0.584833\pi$
$53$	−5.81961	−	0.877164i	−0.799384	−	0.120488i	−0.536016	+	0.844208i	$0.680071\pi$
$54$	−2.53558	−	4.53551i	−0.345048	−	0.617205i
$55$	−2.85298	−	12.4997i	−0.384696	−	1.68546i
$56$	−2.41164	+	1.08811i	−0.322269	+	0.145405i
$57$	10.2608	+	5.64921i	1.35907	+	0.748257i
$58$	−0.345496	−	4.61033i	−0.0453659	−	0.605366i
$59$	0.383049	+	1.67825i	0.0498688	+	0.218489i	0.993722	−	0.111875i	$-0.0356856\pi$
$59$	0.383049	+	1.67825i	0.0498688	+	0.218489i	−0.943854	+	0.330364i	$0.892828\pi$
$60$	−5.00719	−	1.84866i	−0.646425	−	0.238661i
$61$	−6.86073	−	8.60309i	−0.878427	−	1.10151i	−0.994126	−	0.108228i	$-0.965482\pi$
$61$	−6.86073	−	8.60309i	−0.878427	−	1.10151i	0.115699	−	0.993284i	$-0.463089\pi$
$62$	−0.532245	+	0.256316i	−0.0675952	+	0.0325521i
$63$	5.04555	+	6.12718i	0.635680	+	0.771953i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	3.85627	+	16.8954i	0.478312	+	2.09562i
$66$	−6.65319	+	2.76849i	−0.818951	+	0.340778i
$67$	−8.21095			−1.00313			−0.501564	−	0.865121i	$-0.667242\pi$
$67$	−8.21095			−1.00313			−0.501564	+	0.865121i	$0.667242\pi$
$68$	−2.21276	−	3.83262i	−0.268337	−	0.464773i
$69$	0.849700	−	6.53602i	0.102292	−	0.786845i
$70$	8.02935	+	1.41596i	0.959691	+	0.169240i
$71$	−1.20071	+	1.50565i	−0.142498	+	0.178687i	−0.847959	−	0.530062i	$-0.822169\pi$
$71$	−1.20071	+	1.50565i	−0.142498	+	0.178687i	0.705461	+	0.708749i	$0.250740\pi$
$72$	−0.548169	+	2.94949i	−0.0646023	+	0.347601i
$73$	−0.216525	−	2.88932i	−0.0253423	−	0.338169i	−0.995436	−	0.0954366i	$-0.969575\pi$
$73$	−0.216525	−	2.88932i	−0.0253423	−	0.338169i	0.970093	−	0.242733i	$-0.0780438\pi$
$74$	−5.16440	+	3.52103i	−0.600349	+	0.409311i
$75$	4.51708	+	6.34440i	0.521587	+	0.732588i
$76$	−2.47064	−	6.29509i	−0.283402	−	0.722097i
$77$	9.24685	−	5.97198i	1.05378	−	0.680571i
$78$	8.99287	−	3.74207i	1.01824	−	0.423706i
$79$	11.6922			1.31548			0.657740	−	0.753245i	$-0.271513\pi$
$79$	11.6922			1.31548			0.657740	+	0.753245i	$0.271513\pi$
$80$	1.54082	+	2.66878i	0.172269	+	0.298378i
$81$	8.97028	−	0.730789i	0.996698	−	0.0811988i
$82$	5.00499	+	1.54384i	0.552709	+	0.170488i
$83$	−0.833374	−	11.1206i	−0.0914747	−	1.22064i	−0.834358	−	0.551223i	$-0.814161\pi$
$83$	−0.833374	−	11.1206i	−0.0914747	−	1.22064i	0.742883	−	0.669421i	$-0.233458\pi$
$84$	0.0212240	−	4.58253i	0.00231573	−	0.499995i
$85$	−1.01916	+	13.5997i	−0.110543	+	1.47510i
$86$	−2.48115	+	6.32186i	−0.267549	+	0.681704i
$87$	7.51208	+	2.77347i	0.805380	+	0.297347i
$88$	3.97567	+	1.22633i	0.423808	+	0.130727i
$89$	13.4454	−	9.16694i	1.42521	−	0.971694i	0.427506	−	0.904012i	$-0.359392\pi$
$89$	13.4454	−	9.16694i	1.42521	−	0.971694i	0.997707	−	0.0676813i	$-0.0215601\pi$
$90$	6.51590	−	6.55831i	0.686836	−	0.691307i
$91$	−12.4986	+	8.07211i	−1.31021	+	0.846187i
$92$	−2.78950	+	2.58828i	−0.290826	+	0.269847i
$93$	−0.0207922	−	1.02299i	−0.00215605	−	0.106079i
$94$	−5.84467	+	7.32899i	−0.602832	+	0.755928i
$95$	−4.63729	+	20.3173i	−0.475776	+	2.08451i
$96$	1.33195	−	1.10721i	0.135941	−	0.113004i
$97$	1.51281	+	2.62027i	0.153603	+	0.266048i	0.932549	−	0.361042i	$-0.117579\pi$
$97$	1.51281	+	2.62027i	0.153603	+	0.266048i	−0.778947	+	0.627090i	$0.784246\pi$
$98$	1.21526	+	6.89370i	0.122760	+	0.696369i
$99$	0.426232	−	12.4742i	0.0428380	−	1.25371i
$100$	0.336023	−	4.48392i	0.0336023	−	0.448392i
$101$	−4.01561	−	3.72595i	−0.399569	−	0.370745i	0.454641	−	0.890675i	$-0.349768\pi$
$101$	−4.01561	−	3.72595i	−0.399569	−	0.370745i	−0.854209	+	0.519930i	$0.825958\pi$
$102$	7.63059	−	0.728033i	0.755541	−	0.0720860i
$103$	−10.4336	+	3.21833i	−1.02805	+	0.317112i	−0.762502	−	0.646986i	$-0.776029\pi$
$103$	−10.4336	+	3.21833i	−1.02805	+	0.317112i	−0.265549	+	0.964097i	$0.585553\pi$
$104$	−5.37377	−	1.65759i	−0.526941	−	0.162540i
$105$	−8.00907	+	11.6310i	−0.781605	+	1.13507i
$106$	−5.62387	+	1.73473i	−0.546239	+	0.168492i
$107$	7.14306	−	4.87005i	0.690546	−	0.470806i	−0.166503	−	0.986041i	$-0.553248\pi$
$107$	7.14306	−	4.87005i	0.690546	−	0.470806i	0.857049	+	0.515235i	$0.172295\pi$
$108$	−4.25236	−	2.98621i	−0.409184	−	0.287348i
$109$	−2.36984	−	1.61573i	−0.226989	−	0.154759i	0.444486	−	0.895786i	$-0.353386\pi$
$109$	−2.36984	−	1.61573i	−0.226989	−	0.154759i	−0.671475	+	0.741027i	$0.734339\pi$
$110$	−7.99388	−	10.0240i	−0.762186	−	0.955751i
$111$	−1.83076	−	10.6703i	−0.173768	−	1.01278i
$112$	−1.70070	+	2.02673i	−0.160701	+	0.191508i
$113$	−6.02924	+	4.11066i	−0.567183	+	0.386699i	−0.812690	−	0.582696i	$-0.801998\pi$
$113$	−6.02924	+	4.11066i	−0.567183	+	0.386699i	0.245507	+	0.969395i	$0.421045\pi$
$114$	11.6957	+	0.637788i	1.09541	+	0.0597343i
$115$	11.5957	−	1.74777i	1.08130	−	0.162980i
$116$	−2.31163	−	4.00386i	−0.214629	−	0.371749i
$117$	−0.576123	+	16.8610i	−0.0532626	+	1.55880i
$118$	1.07328	+	1.34585i	0.0988035	+	0.123896i
$119$	−11.2713	+	3.17100i	−1.03324	+	0.290685i
$120$	−5.31342	+	0.506953i	−0.485047	+	0.0462783i
$121$	−6.23935	−	0.940431i	−0.567214	−	0.0854938i
$122$	−9.91405	−	4.77435i	−0.897576	−	0.432250i
$123$	−6.03407	+	6.77422i	−0.544074	+	0.610811i
$124$	−0.368325	+	0.461865i	−0.0330766	+	0.0414767i
$125$	0.967423	−	1.21311i	0.0865290	−	0.108504i
$126$	7.20437	+	3.33122i	0.641816	+	0.296769i
$127$	4.32618	+	5.42486i	0.383886	+	0.481378i	0.935804	−	0.352520i	$-0.114675\pi$
$127$	4.32618	+	5.42486i	0.383886	+	0.481378i	−0.551918	+	0.833898i	$0.686104\pi$
$128$	−1.00000			−0.0883883
$129$	−8.17438	−	8.45846i	−0.719714	−	0.744726i
$130$	10.8050	+	13.5491i	0.947664	+	1.18833i
$131$	−14.8632	+	13.7910i	−1.29860	+	1.20493i	−0.333594	+	0.942717i	$0.608262\pi$
$131$	−14.8632	+	13.7910i	−1.29860	+	1.20493i	−0.965010	+	0.262212i	$0.915548\pi$
$132$	−4.79311	+	5.38104i	−0.417187	+	0.468359i
$133$	−17.7533	+	2.22441i	−1.53940	+	0.192880i
$134$	−7.39781	+	3.56260i	−0.639074	+	0.307762i
$135$	5.64333	+	14.9853i	0.485700	+	1.28973i
$136$	−3.65654	−	2.49299i	−0.313546	−	0.213772i
$137$	0.817554	+	0.252182i	0.0698484	+	0.0215454i	0.329482	−	0.944162i	$-0.393126\pi$
$137$	0.817554	+	0.252182i	0.0698484	+	0.0215454i	−0.259634	+	0.965707i	$0.583602\pi$
$138$	−2.07032	−	6.25743i	−0.176237	−	0.532667i
$139$	4.30681	+	3.99613i	0.365299	+	0.338948i	0.841371	−	0.540459i	$-0.181749\pi$
$139$	4.30681	+	3.99613i	0.365299	+	0.338948i	−0.476072	+	0.879406i	$0.657940\pi$
$140$	7.84856	−	2.20807i	0.663324	−	0.186616i
$141$	−7.34055	−	14.4824i	−0.618186	−	1.21964i
$142$	−0.428529	+	1.87751i	−0.0359614	+	0.157557i
$143$	23.1357	+	3.48715i	1.93471	+	0.291610i
$144$	0.785854	+	2.89524i	0.0654878	+	0.241270i
$145$	−1.06470	+	14.2074i	−0.0884181	+	1.17986i
$146$	−1.44871	−	2.50924i	−0.119896	−	0.207666i
$147$	−11.7354	−	3.04640i	−0.967919	−	0.251263i
$148$	−3.12525	+	5.41309i	−0.256894	+	0.444953i
$149$	11.3142	+	7.71388i	0.926894	+	0.631946i	0.929806	−	0.368050i	$-0.119974\pi$
$149$	11.3142	+	7.71388i	0.926894	+	0.631946i	−0.00291162	+	0.999996i	$0.500927\pi$
$150$	6.82248	+	3.75622i	0.557053	+	0.306694i
$151$	−3.57561	−	9.11050i	−0.290979	−	0.741402i	−0.999367	−	0.0355786i	$-0.988673\pi$
$151$	−3.57561	−	9.11050i	−0.290979	−	0.741402i	0.708388	−	0.705823i	$-0.249423\pi$
$152$	−4.95731	−	4.59971i	−0.402091	−	0.373086i
$153$	−4.34430	+	12.5457i	−0.351216	+	1.01426i
$154$	5.73998	−	9.39263i	0.462541	−	0.756880i
$155$	1.73959	−	0.536593i	0.139727	−	0.0431002i
$156$	6.47868	−	7.27335i	0.518709	−	0.582334i
$157$	−3.08627	−	13.5218i	−0.246311	−	1.07916i	−0.935152	−	0.354246i	$-0.884737\pi$
$157$	−3.08627	−	13.5218i	−0.246311	−	1.07916i	0.688841	−	0.724912i	$-0.258120\pi$
$158$	10.5343	−	5.07307i	0.838068	−	0.403592i
$159$	1.31415	−	10.1086i	0.104219	−	0.801668i
$160$	2.54617	+	1.73595i	0.201292	+	0.137239i
$161$	4.81486	+	8.84199i	0.379464	+	0.696847i
$162$	7.76487	−	4.55048i	0.610066	−	0.357519i
$163$	18.9523	+	5.84600i	1.48446	+	0.457894i	0.927872	−	0.372898i	$-0.121636\pi$
$163$	18.9523	+	5.84600i	1.48446	+	0.457894i	0.556583	+	0.830792i	$0.312112\pi$
$164$	5.17919	−	0.780637i	0.404426	−	0.0609575i
$165$	21.5453	−	5.38043i	1.67730	−	0.418866i
$166$	−5.57589	−	9.65773i	−0.432773	−	0.749585i
$167$	16.8333	−	2.53721i	1.30260	−	0.196335i	0.539154	−	0.842207i	$-0.318744\pi$
$167$	16.8333	−	2.53721i	1.30260	−	0.196335i	0.763446	+	0.645872i	$0.223506\pi$
$168$	−1.96916	−	4.13792i	−0.151924	−	0.319248i
$169$	−18.4169	−	2.77591i	−1.41669	−	0.213531i
$170$	4.98248	+	12.6951i	0.382138	+	0.973673i
$171$	−9.42156	+	17.9673i	−0.720485	+	1.37400i
$172$	0.507516	+	6.77233i	0.0386977	+	0.516385i
$173$	−12.3269	+	15.4574i	−0.937194	+	1.17520i	0.0471400	+	0.998888i	$0.484989\pi$
$173$	−12.3269	+	15.4574i	−0.937194	+	1.17520i	−0.984334	+	0.176315i	$0.943582\pi$
$174$	7.97152	−	0.760561i	0.604319	−	0.0576580i
$175$	−11.2770	−	3.78914i	−0.852464	−	0.286432i
$176$	4.11404	−	0.620092i	0.310107	−	0.0467412i
$177$	−2.89273	+	0.722392i	−0.217431	+	0.0542983i
$178$	8.13653	−	14.0929i	0.609859	−	1.05631i
$179$	6.82129	−	17.3804i	0.509847	−	1.29907i	−0.411882	−	0.911237i	$-0.635129\pi$
$179$	6.82129	−	17.3804i	0.509847	−	1.29907i	0.921730	−	0.387833i	$-0.126776\pi$
$180$	3.02508	−	8.73598i	0.225476	−	0.651142i
$181$	−5.25635	−	2.53133i	−0.390702	−	0.188152i	0.228211	−	0.973612i	$-0.426712\pi$
$181$	−5.25635	−	2.53133i	−0.390702	−	0.188152i	−0.618913	+	0.785460i	$0.712427\pi$
$182$	−7.75852	+	12.6957i	−0.575100	+	0.941066i
$183$	14.6564	−	12.1835i	1.08343	−	0.900629i
$184$	−1.39024	+	3.54228i	−0.102490	+	0.261140i
$185$	17.3542	−	8.35736i	1.27591	−	0.614445i
$186$	−0.462593	−	0.912664i	−0.0339190	−	0.0669198i
$187$	16.5890	+	7.98886i	1.21311	+	0.584203i
$188$	−2.08594	+	9.13910i	−0.152133	+	0.666537i
$189$	−10.4328	+	8.95300i	−0.758876	+	0.651235i
$190$	4.63729	+	20.3173i	0.336424	+	1.47397i
$191$	1.85010	−	8.10583i	0.133869	−	0.586517i	−0.862842	−	0.505474i	$-0.831318\pi$
$191$	1.85010	−	8.10583i	0.133869	−	0.586517i	0.996711	−	0.0810431i	$-0.0258252\pi$
$192$	0.719643	−	1.57547i	0.0519357	−	0.113700i
$193$	−1.08508	+	4.75405i	−0.0781058	+	0.342204i	−0.998849	−	0.0479653i	$-0.984726\pi$
$193$	−1.08508	+	4.75405i	−0.0781058	+	0.342204i	0.920743	+	0.390169i	$0.127583\pi$
$194$	2.49989	+	1.70439i	0.179481	+	0.122368i
$195$	−29.1220	+	7.27254i	−2.08547	+	0.520797i
$196$	4.08598	+	5.68373i	0.291855	+	0.405981i
$197$	−25.9393			−1.84810			−0.924048	−	0.382277i	$-0.875140\pi$
$197$	−25.9393			−1.84810			−0.924048	+	0.382277i	$0.875140\pi$
$198$	−5.02835	−	11.4238i	−0.357349	−	0.811857i
$199$	10.7745	−	3.32349i	0.763784	−	0.235596i	0.111699	−	0.993742i	$-0.464371\pi$
$199$	10.7745	−	3.32349i	0.763784	−	0.235596i	0.652085	+	0.758146i	$0.273894\pi$
$200$	−1.64275	−	4.18567i	−0.116160	−	0.295971i
$201$	−0.288996	−	14.2189i	−0.0203842	−	1.00292i
$202$	−5.23457	−	1.61465i	−0.368303	−	0.113606i
$203$	−11.7749	+	3.31268i	−0.826434	+	0.232505i
$204$	6.55904	−	3.96672i	0.459225	−	0.277726i
$205$	−14.5422	−	7.00317i	−1.01567	−	0.489122i
$206$	−8.00394	+	7.42657i	−0.557661	+	0.517434i
$207$	11.3483	+	1.24138i	0.788761	+	0.0862816i
$208$	−5.56080	+	0.838155i	−0.385572	+	0.0581156i
$209$	23.2468	+	15.8494i	1.60802	+	1.09633i
$210$	−2.16940	+	13.9542i	−0.149703	+	0.962932i
$211$	17.7881	−	12.1277i	1.22458	−	0.834906i	0.234055	−	0.972223i	$-0.424800\pi$
$211$	17.7881	−	12.1277i	1.22458	−	0.834906i	0.990527	+	0.137317i	$0.0438479\pi$
$212$	−4.31426	+	4.00305i	−0.296305	+	0.274930i
$213$	−2.64958	−	2.02627i	−0.181546	−	0.138838i
$214$	4.32264	−	7.48702i	0.295489	−	0.511802i
$215$	10.4642	−	18.1245i	0.713652	−	1.23608i
$216$	−5.12691	−	0.845449i	−0.348842	−	0.0575255i
$217$	0.943704	+	1.24591i	0.0640628	+	0.0845782i
$218$	−2.83619	−	0.427487i	−0.192091	−	0.0289530i
$219$	4.99579	−	0.476648i	0.337584	−	0.0322089i
$220$	−11.5515	−	5.56290i	−0.778801	−	0.375051i
$221$	−22.4228	−	10.7983i	−1.50832	−	0.726369i
$222$	−6.27911	−	8.81923i	−0.421426	−	0.591908i
$223$	21.5650	+	3.25040i	1.44410	+	0.217663i	0.823879	−	0.566766i	$-0.191806\pi$
$223$	21.5650	+	3.25040i	1.44410	+	0.217663i	0.620219	+	0.784429i	$0.287044\pi$
$224$	−0.652911	+	2.56392i	−0.0436244	+	0.171309i
$225$	−10.8276	+	8.04549i	−0.721837	+	0.536366i
$226$	−3.64860	+	6.31957i	−0.242701	+	0.420371i
$227$	−11.0944	+	19.2161i	−0.736362	+	1.27542i	0.217761	+	0.976002i	$0.430125\pi$
$227$	−11.0944	+	19.2161i	−0.736362	+	1.27542i	−0.954123	+	0.299415i	$0.903209\pi$
$228$	10.8142	−	4.49996i	0.716189	−	0.298017i
$229$	−4.43769	+	4.11757i	−0.293251	+	0.272097i	−0.813053	−	0.582190i	$-0.802196\pi$
$229$	−4.43769	+	4.11757i	−0.293251	+	0.272097i	0.519802	+	0.854287i	$0.326006\pi$
$230$	9.68901	−	6.60586i	0.638875	−	0.435577i
$231$	10.6671	+	15.8025i	0.701844	+	1.03973i
$232$	−3.81991	−	2.60437i	−0.250790	−	0.170986i
$233$	−1.41950	+	0.213956i	−0.0929948	+	0.0140167i	−0.195375	−	0.980729i	$-0.562592\pi$
$233$	−1.41950	+	0.213956i	−0.0929948	+	0.0140167i	0.102380	+	0.994745i	$0.467354\pi$
$234$	6.79664	+	15.4412i	0.444310	+	1.00942i
$235$	21.1762	−	19.6486i	1.38138	−	1.28173i
$236$	1.55093	+	0.746891i	0.100957	+	0.0486185i
$237$	0.411525	+	20.2474i	0.0267314	+	1.31521i
$238$	−8.77923	+	7.74740i	−0.569073	+	0.502189i
$239$	−7.49381	−	2.31153i	−0.484734	−	0.149521i	0.0427495	−	0.999086i	$-0.486388\pi$
$239$	−7.49381	−	2.31153i	−0.484734	−	0.149521i	−0.527484	+	0.849565i	$0.676864\pi$
$240$	−4.56727	+	2.76216i	−0.294816	+	0.178296i
$241$	−11.1847	−	28.4981i	−0.720469	−	1.83573i	−0.515326	−	0.856994i	$-0.672329\pi$
$241$	−11.1847	−	28.4981i	−0.720469	−	1.83573i	−0.205143	−	0.978732i	$-0.565766\pi$
$242$	−6.02950	+	1.85985i	−0.387591	+	0.119556i
$243$	1.58122	+	15.5081i	0.101436	+	0.994842i
$244$	−11.0038			−0.704444
$245$	−0.536917	−	21.5648i	−0.0343024	−	1.37772i
$246$	−2.49729	+	8.72145i	−0.159221	+	0.556059i
$247$	−31.4219	−	21.4231i	−1.99933	−	1.36312i
$248$	−0.131454	+	0.575936i	−0.00834732	+	0.0365720i
$249$	19.2281	−	1.83455i	1.21853	−	0.116260i
$250$	0.345269	−	1.51272i	0.0218368	−	0.0956731i
$251$	4.72387	+	20.6966i	0.298168	+	1.30636i	0.872852	+	0.487984i	$0.162268\pi$
$251$	4.72387	+	20.6966i	0.298168	+	1.30636i	−0.574684	+	0.818375i	$0.694875\pi$
$252$	7.93628	−	0.124535i	0.499938	−	0.00784497i
$253$	3.52298	−	15.4352i	0.221488	−	0.970400i
$254$	6.25151	+	3.01057i	0.392255	+	0.188900i
$255$	−23.5864	−	1.28621i	−1.47704	−	0.0805456i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	1.65484	−	4.21645i	0.103226	−	0.263015i	−0.869925	−	0.493184i	$-0.835833\pi$
$257$	1.65484	−	4.21645i	0.103226	−	0.263015i	0.973151	+	0.230169i	$0.0739280\pi$
$258$	−11.0348	−	4.07408i	−0.687000	−	0.253641i
$259$	11.8382	+	11.5472i	0.735592	+	0.717505i
$260$	15.6137	+	7.51917i	0.968322	+	0.466319i
$261$	−4.53840	+	13.1062i	−0.280920	+	0.811256i
$262$	−7.40758	+	18.8742i	−0.457642	+	1.16605i
$263$	−2.69505	+	4.66796i	−0.166184	+	0.287839i	−0.937075	−	0.349128i	$-0.886478\pi$
$263$	−2.69505	+	4.66796i	−0.166184	+	0.287839i	0.770891	+	0.636967i	$0.219811\pi$
$264$	−1.98370	+	6.92780i	−0.122088	+	0.426377i
$265$	17.9339	−	2.70310i	1.10167	−	0.166050i
$266$	−15.0300	+	9.70697i	−0.921548	+	0.595172i
$267$	16.3476	+	22.9607i	1.00045	+	1.40517i
$268$	−5.11945	+	6.41958i	−0.312720	+	0.392138i
$269$	−0.346621	−	4.62534i	−0.0211339	−	0.282012i	−0.997751	−	0.0670268i	$-0.978649\pi$
$269$	−0.346621	−	4.62534i	−0.0211339	−	0.282012i	0.976617	−	0.214985i	$-0.0689703\pi$
$270$	11.5863	+	11.0527i	0.705121	+	0.672646i
$271$	0.942679	+	2.40191i	0.0572636	+	0.145905i	0.956643	−	0.291265i	$-0.0940760\pi$
$271$	0.942679	+	2.40191i	0.0572636	+	0.145905i	−0.899379	+	0.437170i	$0.855981\pi$
$272$	−4.37610	−	0.659591i	−0.265340	−	0.0399936i
$273$	−14.4183	−	21.3597i	−0.872637	−	1.29275i
$274$	0.846009	−	0.127515i	0.0511093	−	0.00770348i
$275$	9.35385	+	16.2013i	0.564058	+	0.976978i
$276$	−4.58029	−	4.73947i	−0.275701	−	0.285282i
$277$	−1.96277	+	0.295839i	−0.117931	+	0.0177753i	−0.207743	−	0.978184i	$-0.566612\pi$
$277$	−1.96277	+	0.295839i	−0.117931	+	0.0177753i	0.0898114	+	0.995959i	$0.471374\pi$
$278$	5.61416	+	1.73174i	0.336715	+	0.103863i
$279$	1.77078	−	0.0720114i	0.106014	−	0.00431121i
$280$	6.11326	−	5.39476i	0.365337	−	0.322399i
$281$	20.5377	+	14.0024i	1.22518	+	0.835310i	0.990600	−	0.136788i	$-0.0436778\pi$
$281$	20.5377	+	14.0024i	1.22518	+	0.835310i	0.234575	+	0.972098i	$0.424630\pi$
$282$	−12.8973	−	9.86323i	−0.768021	−	0.587347i
$283$	23.9122	−	11.5155i	1.42143	−	0.684525i	0.444047	−	0.896003i	$-0.353542\pi$
$283$	23.9122	−	11.5155i	1.42143	−	0.684525i	0.977383	+	0.211479i	$0.0678279\pi$
$284$	0.428529	+	1.87751i	0.0254285	+	0.111410i
$285$	−35.3465	−	7.31526i	−2.09375	−	0.433319i
$286$	22.3576	−	6.89641i	1.32203	−	0.407793i
$287$	1.38005	−	13.7887i	0.0814619	−	0.813923i
$288$	1.96423	+	2.26755i	0.115743	+	0.133617i
$289$	−1.89516	−	1.75845i	−0.111480	−	0.103438i
$290$	5.20509	+	13.2624i	0.305653	+	0.778792i
$291$	−4.48425	+	2.71195i	−0.262872	+	0.158977i
$292$	−2.39396	−	1.63218i	−0.140096	−	0.0955159i
$293$	5.69749	−	9.86834i	0.332851	−	0.576515i	−0.650219	−	0.759747i	$-0.725323\pi$
$293$	5.69749	−	9.86834i	0.332851	−	0.576515i	0.983070	+	0.183232i	$0.0586561\pi$
$294$	−11.8950	+	2.34709i	−0.693731	+	0.136885i
$295$	−2.65238	−	4.59405i	−0.154427	−	0.267476i
$296$	−0.467100	+	6.23301i	−0.0271496	+	0.362287i
$297$	21.6166	+	0.299055i	1.25432	+	0.0173529i
$298$	13.5407	+	2.04093i	0.784389	+	0.118228i
$299$	−4.76188	+	20.8632i	−0.275387	+	1.20655i
$300$	7.77660	+	0.424071i	0.448982	+	0.0244838i
$301$	17.6951	+	3.12049i	1.01993	+	0.179862i
$302$	−7.17441	−	6.65688i	−0.412841	−	0.383060i
$303$	6.31086	−	7.08495i	0.362549	−	0.407020i
$304$	−6.46212	−	1.99330i	−0.370628	−	0.114324i
$305$	28.0174	+	19.1020i	1.60427	+	1.09378i
$306$	1.52930	+	13.1882i	0.0874242	+	0.753920i
$307$	−9.06499	+	4.36547i	−0.517366	+	0.249150i	−0.674298	−	0.738459i	$-0.735554\pi$
$307$	−9.06499	+	4.36547i	−0.517366	+	0.249150i	0.156932	+	0.987609i	$0.449840\pi$
$308$	1.09623	−	10.9529i	0.0624636	−	0.624102i
$309$	−5.94039	−	17.9545i	−0.337937	−	1.02139i
$310$	1.33450	−	1.23823i	0.0757945	−	0.0703270i
$311$	16.0374	+	20.1103i	0.909400	+	1.14035i	0.989639	+	0.143576i	$0.0458600\pi$
$311$	16.0374	+	20.1103i	0.909400	+	1.14035i	−0.0802396	+	0.996776i	$0.525569\pi$
$312$	2.68130	−	9.36406i	0.151798	−	0.530135i
$313$	−29.0664			−1.64293			−0.821465	−	0.570259i	$-0.806843\pi$
$313$	−29.0664			−1.64293			−0.821465	+	0.570259i	$0.806843\pi$
$314$	−8.64753	−	10.8437i	−0.488008	−	0.611943i
$315$	−20.4233	−	13.4599i	−1.15072	−	0.758378i
$316$	7.28999	−	9.14136i	0.410094	−	0.514242i
$317$	0.0461398	−	0.0578575i	0.00259147	−	0.00324960i	−0.780534	−	0.625113i	$-0.785053\pi$
$317$	0.0461398	−	0.0578575i	0.00259147	−	0.00324960i	0.783126	+	0.621864i	$0.213624\pi$
$318$	−3.20197	−	9.67776i	−0.179557	−	0.542702i
$319$	17.3302	+	8.34580i	0.970307	+	0.467275i
$320$	3.04722	+	0.459294i	0.170345	+	0.0256753i
$321$	8.68485	+	12.1982i	0.484741	+	0.680836i
$322$	8.17444	+	5.87727i	0.455544	+	0.327528i
$323$	−18.6598	−	23.3986i	−1.03826	−	1.30193i
$324$	5.02153	−	7.46889i	0.278974	−	0.414938i
$325$	−12.6433	−	21.8988i	−0.701322	−	1.21472i
$326$	19.6119	−	2.95602i	1.08620	−	0.163719i
$327$	2.71454	−	4.16070i	0.150114	−	0.230087i
$328$	4.32758	−	2.95049i	0.238951	−	0.162914i
$329$	22.0700	+	11.3152i	1.21676	+	0.623828i
$330$	17.0771	−	14.1957i	0.940066	−	0.781450i
$331$	−8.36458	−	10.4888i	−0.459759	−	0.576519i	0.496871	−	0.867824i	$-0.334482\pi$
$331$	−8.36458	−	10.4888i	−0.459759	−	0.576519i	−0.956630	+	0.291305i	$0.905911\pi$
$332$	−9.21404	−	6.28202i	−0.505686	−	0.344771i
$333$	18.4132	−	3.54587i	1.00904	−	0.194313i
$334$	14.0654	−	9.58964i	0.769625	−	0.524722i
$335$	24.1790	−	7.45825i	1.32104	−	0.407487i
$336$	−3.56953	−	2.87375i	−0.194734	−	0.156776i
$337$	10.7882	+	3.32772i	0.587672	+	0.181273i	0.574310	−	0.818638i	$-0.305270\pi$
$337$	10.7882	+	3.32772i	0.587672	+	0.181273i	0.0133618	+	0.999911i	$0.495747\pi$
$338$	−17.7975	+	5.48981i	−0.968057	+	0.298606i
$339$	−7.33061	−	10.2961i	−0.398144	−	0.559208i
$340$	9.99727	+	9.27611i	0.542178	+	0.503068i
$341$	0.183672	−	2.45094i	0.00994642	−	0.132726i
$342$	−0.692806	+	20.2759i	−0.0374626	+	1.09639i
$343$	17.2404	−	6.76516i	0.930896	−	0.365284i
$344$	3.39566	+	5.88145i	0.183082	+	0.317107i
$345$	3.43472	+	20.0186i	0.184919	+	1.07777i
$346$	−4.39940	+	19.2751i	−0.236513	+	1.03623i
$347$	−0.530307	+	0.664984i	−0.0284684	+	0.0356982i	−0.795862	−	0.605478i	$-0.792982\pi$
$347$	−0.530307	+	0.664984i	−0.0284684	+	0.0356982i	0.767394	+	0.641176i	$0.221553\pi$
$348$	6.85209	−	4.14395i	0.367311	−	0.222139i
$349$	9.23516	−	8.56898i	0.494347	−	0.458687i	−0.393167	−	0.919467i	$-0.628621\pi$
$349$	9.23516	−	8.56898i	0.494347	−	0.458687i	0.887514	+	0.460780i	$0.152430\pi$
$350$	−11.8043	+	1.47903i	−0.630967	+	0.0790574i
$351$	−29.2183	−	0.404222i	−1.55956	−	0.0215757i
$352$	3.43757	−	2.34370i	0.183223	−	0.124920i
$353$	−28.1612	−	8.68657i	−1.49887	−	0.462340i	−0.566565	−	0.824017i	$-0.691728\pi$
$353$	−28.1612	−	8.68657i	−1.49887	−	0.462340i	−0.932303	+	0.361677i	$0.882204\pi$
$354$	−2.29283	+	1.90596i	−0.121862	+	0.101301i
$355$	2.16815	−	5.52436i	0.115074	−	0.293203i
$356$	1.21609	−	16.2276i	0.0644525	−	0.860059i
$357$	−5.88791	−	19.4068i	−0.311621	−	1.02712i
$358$	−1.39529	−	18.6188i	−0.0737432	−	0.984035i
$359$	−7.32934	−	2.26080i	−0.386828	−	0.119321i	0.0952402	−	0.995454i	$-0.469638\pi$
$359$	−7.32934	−	2.26080i	−0.386828	−	0.119321i	−0.482068	+	0.876134i	$0.660114\pi$
$360$	−1.06490	−	9.18338i	−0.0561252	−	0.484006i
$361$	−13.3661	−	23.1508i	−0.703481	−	1.21847i
$362$	−5.83411			−0.306634
$363$	1.40894	−	10.8377i	0.0739499	−	0.568834i
$364$	−1.48174	+	14.8047i	−0.0776641	+	0.775977i
$365$	3.26206	+	8.31159i	0.170744	+	0.435048i
$366$	7.91877	−	17.3361i	0.413921	−	0.906174i
$367$	11.7528	−	8.01290i	0.613490	−	0.418270i	−0.216315	−	0.976324i	$-0.569404\pi$
$367$	11.7528	−	8.01290i	0.613490	−	0.418270i	0.829805	+	0.558053i	$0.188452\pi$
$368$	0.284373	+	3.79469i	0.0148240	+	0.197812i
$369$	−11.9432	−	10.2107i	−0.621740	−	0.531550i
$370$	12.0095	−	15.0594i	0.624345	−	0.782903i
$371$	7.44668	+	13.6751i	0.386613	+	0.709974i
$372$	−0.812772	−	0.621570i	−0.0421403	−	0.0322269i
$373$	−6.96996	−	12.0723i	−0.360891	−	0.625082i	0.627217	−	0.778845i	$-0.284194\pi$
$373$	−6.96996	−	12.0723i	−0.360891	−	0.625082i	−0.988108	+	0.153763i	$0.950861\pi$
$374$	18.4124			0.952085
$375$	2.13478	+	1.63258i	0.110240	+	0.0843062i
$376$	2.08594	+	9.13910i	0.107574	+	0.471313i
$377$	−23.4246	−	11.2807i	−1.20643	−	0.580986i
$378$	−5.51508	+	12.5930i	−0.283665	+	0.647714i
$379$	9.78812	−	4.71371i	0.502782	−	0.242127i	−0.165261	−	0.986250i	$-0.552847\pi$
$379$	9.78812	−	4.71371i	0.502782	−	0.242127i	0.668043	+	0.744123i	$0.267132\pi$
$380$	12.9934	+	16.2932i	0.666547	+	0.835823i
$381$	−9.24192	+	7.68255i	−0.473478	+	0.393589i
$382$	−1.85010	−	8.10583i	−0.0946595	−	0.414730i
$383$	0.377568	+	5.03829i	0.0192928	+	0.257445i	0.998507	+	0.0546174i	$0.0173939\pi$
$383$	0.377568	+	5.03829i	0.0192928	+	0.257445i	−0.979215	+	0.202827i	$0.934987\pi$
$384$	−0.0351964	−	1.73169i	−0.00179611	−	0.0883701i
$385$	−21.8049	+	25.9851i	−1.11128	+	1.32432i
$386$	1.08508	+	4.75405i	0.0552291	+	0.241975i
$387$	14.3597	−	14.4532i	0.729947	−	0.734699i
$388$	2.99183	+	0.450946i	0.151887	+	0.0228933i
$389$	−15.2412	−	14.1417i	−0.772758	−	0.717014i	0.191641	−	0.981465i	$-0.438619\pi$
$389$	−15.2412	−	14.1417i	−0.772758	−	0.717014i	−0.964399	+	0.264451i	$0.914809\pi$
$390$	−23.0826	+	19.1879i	−1.16883	+	0.971616i
$391$	−8.42030	+	14.5844i	−0.425833	+	0.737564i
$392$	6.14742	+	3.34803i	0.310491	+	0.169101i
$393$	−24.4050	−	25.2531i	−1.23107	−	1.27385i
$394$	−23.3705	+	11.2546i	−1.17739	+	0.567000i
$395$	−34.4305	+	10.6204i	−1.73239	+	0.534370i
$396$	−9.48701	−	8.11081i	−0.476740	−	0.407583i
$397$	16.3322	+	15.1540i	0.819688	+	0.760560i	0.973779	−	0.227497i	$-0.0730542\pi$
$397$	16.3322	+	15.1540i	0.819688	+	0.760560i	−0.154090	+	0.988057i	$0.549245\pi$
$398$	8.26548	−	7.66925i	0.414311	−	0.384425i
$399$	−4.47684	−	30.6649i	−0.224122	−	1.53517i
$400$	−3.29616	−	3.05839i	−0.164808	−	0.152920i
$401$	0.961020	+	12.8239i	0.0479911	+	0.640396i	0.968394	+	0.249425i	$0.0802417\pi$
$401$	0.961020	+	12.8239i	0.0479911	+	0.640396i	−0.920403	+	0.390971i	$0.872139\pi$
$402$	−6.42971	−	12.6854i	−0.320685	−	0.632688i
$403$	−0.248263	+	3.31284i	−0.0123669	+	0.165025i
$404$	−5.41676	+	0.816445i	−0.269494	+	0.0406196i
$405$	−25.7513	+	10.2999i	−1.27959	+	0.511808i
$406$	−9.17148	+	8.09355i	−0.455173	+	0.401676i
$407$	−1.94337	−	25.9325i	−0.0963294	−	1.28543i
$408$	4.18839	−	6.41975i	0.207356	−	0.317825i
$409$	−17.8532	−	22.3872i	−0.882784	−	1.10698i	−0.993580	−	0.113133i	$-0.963911\pi$
$409$	−17.8532	−	22.3872i	−0.882784	−	1.10698i	0.110796	−	0.993843i	$-0.464660\pi$
$410$	−16.1407			−0.797130
$411$	−0.407927	+	1.42463i	−0.0201216	+	0.0702718i
$412$	−3.98903	+	10.1639i	−0.196526	+	0.500739i
$413$	2.92759	−	3.48883i	0.144057	−	0.171674i
$414$	10.7631	−	3.80540i	0.528976	−	0.187025i
$415$	12.5552	+	31.9902i	0.616312	+	1.57034i
$416$	−4.64644	+	3.16789i	−0.227811	+	0.155319i
$417$	−6.76849	+	7.59872i	−0.331455	+	0.372111i
$418$	27.8215	+	4.19341i	1.36079	+	0.205106i
$419$	−5.52386	−	14.0746i	−0.269858	−	0.687588i	−0.999991	−	0.00428241i	$-0.998637\pi$
$419$	−5.52386	−	14.0746i	−0.269858	−	0.687588i	0.730132	−	0.683306i	$-0.239458\pi$
$420$	4.09994	+	13.5136i	0.200057	+	0.659395i
$421$	−4.71027	+	12.0016i	−0.229565	+	0.584921i	−0.998520	−	0.0543810i	$-0.982681\pi$
$421$	−4.71027	+	12.0016i	−0.229565	+	0.584921i	0.768956	+	0.639302i	$0.220777\pi$
$422$	10.7645	−	18.6447i	0.524008	−	0.907608i
$423$	24.8207	−	13.2213i	1.20682	−	0.642842i
$424$	−2.15016	+	5.47851i	−0.104421	+	0.266060i
$425$	−4.42802	−	19.4004i	−0.214791	−	0.941059i
$426$	−3.26635	−	0.676000i	−0.158255	−	0.0327523i
$427$	−7.18447	+	28.2128i	−0.347681	+	1.36531i
$428$	0.646062	−	8.62110i	0.0312286	−	0.416716i
$429$	−5.22438	+	40.1867i	−0.252236	+	1.94023i
$430$	1.56398	−	20.8699i	0.0754218	−	1.00643i
$431$	−5.69285	+	5.28219i	−0.274215	+	0.254434i	−0.805277	−	0.592899i	$-0.797984\pi$
$431$	−5.69285	+	5.28219i	−0.274215	+	0.254434i	0.531062	+	0.847333i	$0.321793\pi$
$432$	−4.98601	+	1.46276i	−0.239890	+	0.0703771i
$433$	−2.36438	+	10.3590i	−0.113625	+	0.497823i	0.885805	+	0.464058i	$0.153607\pi$
$433$	−2.36438	+	10.3590i	−0.113625	+	0.497823i	−0.999430	+	0.0337650i	$0.989250\pi$
$434$	1.39083	+	0.713072i	0.0667620	+	0.0342286i
$435$	−24.6403	−	1.34368i	−1.18141	−	0.0644244i
$436$	−2.74080	+	0.845424i	−0.131260	+	0.0404885i
$437$	−16.0448	+	20.1195i	−0.767525	+	0.962446i
$438$	4.29425	−	2.59704i	0.205187	−	0.124091i
$439$	12.5048	−	6.02202i	0.596824	−	0.287415i	−0.110982	−	0.993822i	$-0.535400\pi$
$439$	12.5048	−	6.02202i	0.596824	−	0.287415i	0.707806	+	0.706407i	$0.249685\pi$
$440$	−12.8212			−0.611226
$441$	4.86238	−	20.4293i	0.231542	−	0.972825i
$442$	−24.8874			−1.18377
$443$	7.36644	−	3.54749i	0.349990	−	0.168546i	−0.250626	−	0.968084i	$-0.580636\pi$
$443$	7.36644	−	3.54749i	0.349990	−	0.168546i	0.600616	+	0.799538i	$0.294922\pi$
$444$	−9.48380	−	5.22145i	−0.450081	−	0.247799i
$445$	−31.2666	+	39.2070i	−1.48218	+	1.85859i
$446$	20.8397	−	6.42818i	0.986787	−	0.304383i
$447$	−12.9599	+	19.8642i	−0.612980	+	0.939545i
$448$	0.524193	+	2.59330i	0.0247658	+	0.122522i
$449$	−0.878199	+	3.84764i	−0.0414448	+	0.181581i	−0.991414	−	0.130763i	$-0.958257\pi$
$449$	−0.878199	+	3.84764i	−0.0414448	+	0.181581i	0.949969	+	0.312345i	$0.101114\pi$
$450$	−6.26449	+	11.9466i	−0.295311	+	0.563170i
$451$	−15.9743	+	14.8219i	−0.752198	+	0.697938i
$452$	−0.545321	+	7.27680i	−0.0256497	+	0.342272i
$453$	15.6507	−	6.51251i	0.735336	−	0.305984i
$454$	−1.65817	+	22.1268i	−0.0778219	+	1.03846i
$455$	29.4730	−	35.1231i	1.38171	−	1.64659i
$456$	7.79081	−	8.74644i	0.364838	−	0.409589i
$457$	−0.269635	−	1.18135i	−0.0126130	−	0.0552612i	0.968230	−	0.250062i	$-0.0804511\pi$
$457$	−0.269635	−	1.18135i	−0.0126130	−	0.0552612i	−0.980843	+	0.194801i	$0.937594\pi$
$458$	−2.21167	+	5.63524i	−0.103345	+	0.263318i
$459$	−21.8782	−	7.08143i	−1.02119	−	0.330533i
$460$	5.86332	−	10.1556i	0.273379	−	0.473506i
$461$	−1.66456	+	4.24122i	−0.0775262	+	0.197533i	−0.964382	−	0.264512i	$-0.914789\pi$
$461$	−1.66456	+	4.24122i	−0.0775262	+	0.197533i	0.886856	+	0.462046i	$0.152884\pi$
$462$	16.4672	+	9.60929i	0.766122	+	0.447065i
$463$	−13.4179	−	34.1882i	−0.623581	−	1.58886i	−0.796979	−	0.604007i	$-0.793570\pi$
$463$	−13.4179	−	34.1882i	−0.623581	−	1.58886i	0.173397	−	0.984852i	$-0.444525\pi$
$464$	−4.57162	−	0.689061i	−0.212232	−	0.0319888i
$465$	0.990442	+	2.99355i	0.0459306	+	0.138823i
$466$	−1.18610	+	0.808668i	−0.0549449	+	0.0374608i
$467$	−2.25186	−	5.73764i	−0.104204	−	0.265506i	0.869257	−	0.494360i	$-0.164598\pi$
$467$	−2.25186	−	5.73764i	−0.104204	−	0.265506i	−0.973461	+	0.228854i	$0.926502\pi$
$468$	12.8232	+	10.9631i	0.592755	+	0.506769i
$469$	13.1168	+	17.3173i	0.605677	+	0.799638i
$470$	10.5539	−	26.8908i	0.486813	−	1.24038i
$471$	23.3070	−	5.82039i	1.07393	−	0.268189i
$472$	1.72141			0.0792342
$473$	−17.6169	−	22.0909i	−0.810027	−	1.01574i
$474$	9.15578	+	18.0637i	0.420539	+	0.829693i
$475$	−2.27238	−	30.3228i	−0.104264	−	1.39131i
$476$	−4.54834	+	10.7893i	−0.208473	+	0.494528i
$477$	17.5513	+	1.91992i	0.803620	+	0.0879070i
$478$	−7.75463	+	1.16882i	−0.354688	+	0.0534607i
$479$	−0.211982	+	2.82870i	−0.00968569	+	0.129247i	−0.999951	−	0.00994971i	$-0.996833\pi$
$479$	−0.211982	+	2.82870i	−0.00968569	+	0.129247i	0.990265	+	0.139196i	$0.0444519\pi$
$480$	−2.91651	+	4.47028i	−0.133120	+	0.204040i
$481$	2.62679	+	35.0520i	0.119771	+	1.59824i
$482$	−22.4419	−	20.8231i	−1.02220	−	0.948465i
$483$	−15.1422	+	8.64907i	−0.688992	+	0.393546i
$484$	−4.62543	+	4.29177i	−0.210247	+	0.195081i
$485$	−6.83489	−	6.34185i	−0.310356	−	0.287968i
$486$	8.15333	+	13.2862i	0.369842	+	0.602675i
$487$	24.4781	−	7.55049i	1.10921	−	0.342145i	0.314573	−	0.949233i	$-0.398139\pi$
$487$	24.4781	−	7.55049i	1.10921	−	0.342145i	0.794635	+	0.607088i	$0.207662\pi$
$488$	−9.91405	+	4.77435i	−0.448788	+	0.216125i
$489$	−9.45643	+	33.0253i	−0.427634	+	1.49345i
$490$	−9.84035	−	19.1962i	−0.444542	−	0.867198i
$491$	17.7662	−	30.7720i	0.801779	−	1.38872i	−0.116666	−	0.993171i	$-0.537221\pi$
$491$	17.7662	−	30.7720i	0.801779	−	1.38872i	0.918444	−	0.395550i	$-0.129446\pi$
$492$	1.53411	+	8.94128i	0.0691631	+	0.403104i
$493$	−14.9985	−	13.9166i	−0.675499	−	0.626771i
$494$	−37.6053	−	5.66808i	−1.69194	−	0.255019i
$495$	10.0756	+	37.1204i	0.452863	+	1.66844i
$496$	0.131454	+	0.575936i	0.00590245	+	0.0258603i
$497$	5.09359	+	0.127129i	0.228479	+	0.00570253i
$498$	16.5280	−	9.99565i	0.740636	−	0.447916i
$499$	2.95808	+	39.4728i	0.132422	+	1.76704i	0.528601	+	0.848871i	$0.322717\pi$
$499$	2.95808	+	39.4728i	0.132422	+	1.76704i	−0.396179	+	0.918173i	$0.629664\pi$
$500$	−0.345269	−	1.51272i	−0.0154409	−	0.0676511i
$501$	4.98614	+	29.0608i	0.222764	+	1.29834i
$502$	13.2360	+	16.5974i	0.590751	+	0.740778i
$503$	32.8870	−	15.8376i	1.46636	−	0.706162i	0.481012	−	0.876714i	$-0.340269\pi$
$503$	32.8870	−	15.8376i	1.46636	−	0.706162i	0.985349	+	0.170552i	$0.0545549\pi$
$504$	7.09630	−	3.55562i	0.316095	−	0.158380i
$505$	15.2093	+	7.32440i	0.676804	+	0.325932i
$506$	−3.52298	−	15.4352i	−0.156615	−	0.686177i
$507$	4.15881	−	31.9902i	0.184699	−	1.42073i
$508$	6.93865			0.307853
$509$	−4.05065	−	7.01593i	−0.179542	−	0.310975i	0.762182	−	0.647363i	$-0.224128\pi$
$509$	−4.05065	−	7.01593i	−0.179542	−	0.310975i	−0.941724	+	0.336387i	$0.890795\pi$
$510$	−21.8087	+	9.07494i	−0.965706	+	0.401845i
$511$	−5.74782	+	5.07227i	−0.254268	+	0.224384i
$512$	−0.623490	+	0.781831i	−0.0275546	+	0.0345524i
$513$	−31.4455	−	15.6829i	−1.38835	−	0.692416i
$514$	−0.338495	−	4.51690i	−0.0149304	−	0.199232i
$515$	27.8007	−	18.9542i	1.22505	−	0.835223i
$516$	−11.7097	+	1.11722i	−0.515492	+	0.0491830i
$517$	−14.2487	−	36.3051i	−0.626658	−	1.59670i
$518$	15.6760	+	5.26721i	0.688764	+	0.231428i
$519$	−27.2013	−	20.8023i	−1.19401	−	0.913119i
$520$	17.3299			0.759967
$521$	−6.22213	−	10.7770i	−0.272596	−	0.472151i	0.696929	−	0.717140i	$-0.254549\pi$
$521$	−6.22213	−	10.7770i	−0.272596	−	0.472151i	−0.969526	+	0.244989i	$0.921216\pi$
$522$	1.59763	+	13.7775i	0.0699262	+	0.603023i
$523$	−24.7001	−	7.61896i	−1.08006	−	0.333154i	−0.296857	−	0.954922i	$-0.595939\pi$
$523$	−24.7001	−	7.61896i	−1.08006	−	0.333154i	−0.783202	+	0.621768i	$0.786415\pi$
$524$	1.51521	+	20.2191i	0.0661923	+	0.883275i
$525$	6.16471	−	19.6617i	0.269050	−	0.858108i
$526$	−0.402802	+	5.37503i	−0.0175630	+	0.234362i
$527$	−0.955137	+	2.43365i	−0.0416064	+	0.106011i
$528$	1.21861	+	7.10243i	0.0530331	+	0.309094i
$529$	−8.14097	−	2.51116i	−0.353955	−	0.109181i
$530$	14.9851	−	10.2166i	0.650910	−	0.443783i
$531$	−1.35278	−	4.98389i	−0.0587054	−	0.216283i
$532$	−9.32986	+	15.2669i	−0.404501	+	0.661906i
$533$	21.5918	−	20.0343i	0.935246	−	0.867781i
$534$	24.6909	+	13.5940i	1.06848	+	0.588268i
$535$	−16.6108	+	20.8292i	−0.718146	+	0.900527i
$536$	−1.82711	+	8.00509i	−0.0789191	+	0.345767i
$537$	30.3375	+	11.2007i	1.30916	+	0.483344i
$538$	−2.31916	−	4.01690i	−0.0999859	−	0.173181i
$539$	−27.3668	−	9.96195i	−1.17877	−	0.429092i
$540$	15.2345	+	4.93103i	0.655589	+	0.212198i
$541$	−0.547697	+	7.30850i	−0.0235473	+	0.314217i	0.972976	+	0.230905i	$0.0741688\pi$
$541$	−0.547697	+	7.30850i	−0.0235473	+	0.314217i	−0.996524	+	0.0833118i	$0.973450\pi$
$542$	1.89147	+	1.75503i	0.0812457	+	0.0753850i
$543$	4.19847	−	9.19148i	0.180174	−	0.394444i
$544$	−4.22891	+	1.30445i	−0.181313	+	0.0559277i
$545$	8.44614	+	2.60529i	0.361793	+	0.111598i
$546$	−22.2581	−	12.9885i	−0.952558	−	0.555858i
$547$	−19.7252	+	6.08442i	−0.843389	+	0.260151i	−0.686196	−	0.727417i	$-0.740721\pi$
$547$	−19.7252	+	6.08442i	−0.843389	+	0.260151i	−0.157193	+	0.987568i	$0.550245\pi$
$548$	0.706901	−	0.481957i	0.0301973	−	0.0205882i
$549$	21.6139	+	24.9516i	0.922459	+	1.06491i
$550$	15.4570	+	10.5384i	0.659090	+	0.449360i
$551$	−19.4935	−	24.4440i	−0.830449	−	1.04135i
$552$	−6.18308	−	2.28280i	−0.263169	−	0.0971624i
$553$	−18.6781	−	24.6595i	−0.794272	−	1.04863i
$554$	−1.64003	+	1.11815i	−0.0696783	+	0.0475058i
$555$	15.0832	+	29.7581i	0.640246	+	1.26316i
$556$	5.80956	−	0.875650i	0.246380	−	0.0371358i
$557$	4.66312	+	8.07676i	0.197583	+	0.342223i	0.947744	−	0.319032i	$-0.103358\pi$
$557$	4.66312	+	8.07676i	0.197583	+	0.342223i	−0.750161	+	0.661255i	$0.770024\pi$
$558$	1.56417	−	0.833192i	0.0662167	−	0.0352718i
$559$	23.8121	+	29.8595i	1.00715	+	1.26292i
$560$	3.16716	−	7.51296i	0.133837	−	0.317480i
$561$	−13.2504	+	29.0083i	−0.559432	+	1.22473i
$562$	24.5792	+	3.70472i	1.03681	+	0.156274i
$563$	−17.6232	−	8.48687i	−0.742728	−	0.357679i	0.0239480	−	0.999713i	$-0.492376\pi$
$563$	−17.6232	−	8.48687i	−0.742728	−	0.357679i	−0.766676	+	0.642034i	$0.778091\pi$
$564$	−15.8995	−	3.29054i	−0.669491	−	0.138557i
$565$	14.0206	−	17.5813i	0.589852	−	0.739652i
$566$	16.5477	−	20.7502i	0.695553	−	0.872196i
$567$	−15.8711	−	17.7513i	−0.666522	−	0.745486i
$568$	1.20071	+	1.50565i	0.0503808	+	0.0631755i
$569$	16.6448			0.697787			0.348893	−	0.937162i	$-0.386558\pi$
$569$	16.6448			0.697787			0.348893	+	0.937162i	$0.386558\pi$
$570$	−35.0201	+	8.74545i	−1.46683	+	0.366307i
$571$	−19.8077	−	24.8381i	−0.828928	−	1.03944i	−0.998545	−	0.0539326i	$-0.982824\pi$
$571$	−19.8077	−	24.8381i	−0.828928	−	1.03944i	0.169617	−	0.985510i	$-0.445747\pi$
$572$	17.1513	−	15.9140i	0.717130	−	0.665400i
$573$	14.1019	+	2.91851i	0.589116	+	0.121923i
$574$	−4.73932	−	13.0220i	−0.197815	−	0.543528i
$575$	−15.4162	+	7.42403i	−0.642898	+	0.309603i
$576$	2.75356	+	1.19075i	0.114732	+	0.0496146i
$577$	21.9071	+	14.9360i	0.912003	+	0.621793i	0.925760	−	0.378112i	$-0.123427\pi$
$577$	21.9071	+	14.9360i	0.912003	+	0.621793i	−0.0137567	+	0.999905i	$0.504379\pi$
$578$	−2.47044	−	0.762030i	−0.102757	−	0.0316963i
$579$	−8.27074	−	1.71170i	−0.343720	−	0.0711359i
$580$	10.4439	+	9.69056i	0.433661	+	0.402379i
$581$	−22.1226	+	19.5225i	−0.917799	+	0.809930i
$582$	−2.86350	+	4.38903i	−0.118696	+	0.181931i
$583$	5.44865	−	23.8721i	0.225660	−	0.988681i
$584$	−2.86506	−	0.431838i	−0.118557	−	0.0178696i
$585$	−13.6188	−	50.1743i	−0.563068	−	2.07445i
$586$	0.851548	−	11.3631i	0.0351771	−	0.469406i
$587$	−6.13879	−	10.6327i	−0.253375	−	0.438858i	0.711078	−	0.703113i	$-0.248207\pi$
$587$	−6.13879	−	10.6327i	−0.253375	−	0.438858i	−0.964453	+	0.264255i	$0.914874\pi$
$588$	−9.69867	+	7.27570i	−0.399966	+	0.300045i
$589$	−1.99748	+	3.45975i	−0.0823049	+	0.142556i
$590$	−4.38299	−	2.98828i	−0.180445	−	0.123025i
$591$	−0.912969	−	44.9188i	−0.0375545	−	1.84771i
$592$	2.28356	+	5.81842i	0.0938538	+	0.239136i
$593$	−33.7833	−	31.3463i	−1.38731	−	1.28724i	−0.913632	−	0.406543i	$-0.866734\pi$
$593$	−33.7833	−	31.3463i	−1.38731	−	1.28724i	−0.473682	−	0.880696i	$-0.657075\pi$
$594$	19.6056	−	9.10964i	0.804428	−	0.373773i
$595$	30.3106	−	19.5758i	1.24261	−	0.802528i
$596$	13.0852	−	4.03626i	0.535992	−	0.165332i
$597$	6.13450	+	18.5412i	0.251068	+	0.758839i
$598$	4.76188	+	20.8632i	0.194728	+	0.853158i
$599$	−23.8409	+	11.4812i	−0.974111	+	0.469107i	−0.852076	−	0.523418i	$-0.824656\pi$
$599$	−23.8409	+	11.4812i	−0.974111	+	0.469107i	−0.122036	+	0.992526i	$0.538942\pi$
$600$	7.19047	−	2.99207i	0.293550	−	0.122151i
$601$	19.5112	+	13.3025i	0.795878	+	0.542621i	0.891619	−	0.452786i	$-0.149570\pi$
$601$	19.5112	+	13.3025i	0.795878	+	0.542621i	−0.0957412	+	0.995406i	$0.530522\pi$
$602$	17.2967	−	4.86615i	0.704959	−	0.198329i
$603$	24.6125	−	1.00091i	1.00230	−	0.0407600i
$604$	−9.35223	−	2.88478i	−0.380537	−	0.117380i
$605$	19.2274	−	2.89807i	0.781706	−	0.117823i
$606$	2.61184	−	9.12150i	0.106099	−	0.370536i
$607$	−10.5317	−	18.2414i	−0.427466	−	0.740394i	0.569181	−	0.822212i	$-0.307260\pi$
$607$	−10.5317	−	18.2414i	−0.427466	−	0.740394i	−0.996647	+	0.0818188i	$0.973927\pi$
$608$	−6.68703	+	1.00791i	−0.271195	+	0.0408761i
$609$	−6.15098	−	20.2739i	−0.249250	−	0.821539i
$610$	33.5309	+	5.05396i	1.35763	+	0.204629i
$611$	19.2595	+	49.0723i	0.779155	+	1.98525i
$612$	7.10000	+	11.2186i	0.287001	+	0.453486i
$613$	0.244888	+	3.26780i	0.00989092	+	0.131985i	0.999963	−	0.00857369i	$-0.00272912\pi$
$613$	0.244888	+	3.26780i	0.00989092	+	0.131985i	−0.990072	+	0.140559i	$0.955110\pi$
$614$	−6.27317	+	7.86630i	−0.253164	+	0.317458i
$615$	11.6155	−	25.4292i	0.468382	−	1.02540i
$616$	−3.76464	−	10.3439i	−0.151681	−	0.416768i
$617$	35.9091	−	5.41242i	1.44564	−	0.217896i	0.621117	−	0.783718i	$-0.286679\pi$
$617$	35.9091	−	5.41242i	1.44564	−	0.217896i	0.824528	+	0.565822i	$0.191441\pi$
$618$	−13.1423	−	13.5990i	−0.528659	−	0.547031i
$619$	19.5707	−	33.8975i	0.786614	−	1.36246i	−0.141416	−	0.989950i	$-0.545166\pi$
$619$	19.5707	−	33.8975i	0.786614	−	1.36246i	0.928030	−	0.372505i	$-0.121501\pi$
$620$	0.665092	−	1.69463i	0.0267108	−	0.0680579i
$621$	−1.75026	+	19.6955i	−0.0702356	+	0.790352i
$622$	23.1748	+	11.1604i	0.929224	+	0.447491i
$623$	−40.8122	−	13.7131i	−1.63511	−	0.549404i
$624$	−1.64715	−	9.60009i	−0.0659387	−	0.384311i
$625$	−9.96066	+	25.3794i	−0.398427	+	1.01517i
$626$	−26.1879	+	12.6114i	−1.04668	+	0.504055i
$627$	−26.6281	+	40.8142i	−1.06342	+	1.62996i
$628$	−12.4960	−	6.01778i	−0.498646	−	0.240135i
$629$	−6.15531	+	26.9682i	−0.245428	+	1.07529i
$630$	−24.2408	−	3.26560i	−0.965775	−	0.130105i
$631$	10.2275	+	44.8095i	0.407149	+	1.78384i	0.597231	+	0.802069i	$0.296268\pi$
$631$	10.2275	+	44.8095i	0.407149	+	1.78384i	−0.190082	+	0.981768i	$0.560875\pi$
$632$	2.60177	−	11.3991i	0.103493	−	0.453432i
$633$	21.6276	+	30.3767i	0.859618	+	1.20736i
$634$	0.0164671	−	0.0721472i	0.000653993	−	0.00286533i
$635$	−17.6670	−	12.0451i	−0.701093	−	0.477997i
$636$	−7.08390	−	7.33008i	−0.280895	−	0.290657i
$637$	36.9907	+	13.4652i	1.46562	+	0.533511i
$638$	19.2351			0.761525
$639$	3.41563	−	4.65957i	0.135120	−	0.184330i
$640$	2.94473	−	0.908329i	0.116401	−	0.0359048i
$641$	−1.22129	−	3.11179i	−0.0482380	−	0.122908i	0.904724	−	0.425998i	$-0.140077\pi$
$641$	−1.22129	−	3.11179i	−0.0482380	−	0.122908i	−0.952962	+	0.303090i	$0.901982\pi$
$642$	13.1174	+	7.22196i	0.517701	+	0.285028i
$643$	2.65099	+	0.817721i	0.104545	+	0.0322478i	0.346586	−	0.938018i	$-0.387341\pi$
$643$	2.65099	+	0.817721i	0.104545	+	0.0322478i	−0.242041	+	0.970266i	$0.577817\pi$
$644$	9.91497	+	1.74848i	0.390704	+	0.0688999i
$645$	31.7544	+	17.4829i	1.25033	+	0.688387i
$646$	−26.9641	−	12.9852i	−1.06089	−	0.510897i
$647$	−3.78805	+	3.51480i	−0.148924	+	0.138181i	−0.751116	−	0.660170i	$-0.770484\pi$
$647$	−3.78805	+	3.51480i	−0.148924	+	0.138181i	0.602193	+	0.798351i	$0.294294\pi$
$648$	1.28361	−	8.90799i	0.0504249	−	0.349939i
$649$	−7.08194	+	1.06743i	−0.277990	+	0.0419003i
$650$	−20.8927	−	14.2444i	−0.819479	−	0.558711i
$651$	−2.12433	+	1.67806i	−0.0832589	+	0.0657682i
$652$	16.3871	−	11.1726i	0.641770	−	0.437551i
$653$	−3.22031	+	2.98801i	−0.126020	+	0.116930i	−0.740666	−	0.671874i	$-0.765490\pi$
$653$	−3.22031	+	2.98801i	−0.126020	+	0.116930i	0.614645	+	0.788804i	$0.289299\pi$
$654$	0.640452	−	4.92645i	0.0250437	−	0.192640i
$655$	31.2413	−	54.1116i	1.22070	−	2.11431i
$656$	2.61884	−	4.53597i	0.102249	−	0.177100i
$657$	1.00124	+	8.63441i	0.0390622	+	0.336860i
$658$	24.7939	+	0.618824i	0.966567	+	0.0241243i
$659$	10.3870	+	1.56558i	0.404619	+	0.0609865i	0.348199	−	0.937421i	$-0.386793\pi$
$659$	10.3870	+	1.56558i	0.404619	+	0.0609865i	0.0564199	+	0.998407i	$0.482031\pi$
$660$	9.22667	−	20.1994i	0.359148	−	0.786261i
$661$	22.5520	+	10.8604i	0.877169	+	0.422422i	0.817590	−	0.575801i	$-0.195310\pi$
$661$	22.5520	+	10.8604i	0.877169	+	0.422422i	0.0595794	+	0.998224i	$0.481024\pi$
$662$	−12.0872	−	5.82087i	−0.469781	−	0.226235i
$663$	17.9101	−	39.2095i	0.695569	−	1.52277i
$664$	−11.0272	−	1.66209i	−0.427940	−	0.0645015i
$665$	50.2580	−	22.6761i	1.94892	−	0.879340i
$666$	15.0512	−	11.1839i	0.583222	−	0.433367i
$667$	−8.79651	+	15.2360i	−0.340602	+	0.589940i
$668$	8.51172	−	14.7427i	0.329328	−	0.570413i
$669$	−4.86968	+	37.4583i	−0.188273	+	1.44822i
$670$	18.5485	−	17.2105i	0.716593	−	0.664901i
$671$	37.8262	−	25.7895i	1.46027	−	0.995592i
$672$	−4.46291	−	1.04040i	−0.172161	−	0.0401343i
$673$	−2.00029	−	1.36378i	−0.0771056	−	0.0525697i	0.524154	−	0.851624i	$-0.324382\pi$
$673$	−2.00029	−	1.36378i	−0.0771056	−	0.0525697i	−0.601259	+	0.799054i	$0.705334\pi$
$674$	11.1637	−	1.68266i	0.430009	−	0.0648135i
$675$	−14.3134	−	18.4668i	−0.550924	−	0.710789i
$676$	−13.6531	+	12.6682i	−0.525118	+	0.487238i
$677$	−37.4829	−	18.0508i	−1.44058	−	0.693749i	−0.459652	−	0.888099i	$-0.652026\pi$
$677$	−37.4829	−	18.0508i	−1.44058	−	0.693749i	−0.980932	+	0.194350i	$0.937740\pi$
$678$	−11.0720	−	6.09584i	−0.425216	−	0.234109i
$679$	3.10959	−	7.37640i	0.119335	−	0.283080i
$680$	13.0320	+	4.01983i	0.499754	+	0.154154i
$681$	−33.6669	−	18.5358i	−1.29012	−	0.710293i
$682$	−0.897939	−	2.28791i	−0.0343839	−	0.0876086i
$683$	−34.3634	+	10.5997i	−1.31488	+	0.405587i	−0.871345	−	0.490670i	$-0.836752\pi$
$683$	−34.3634	+	10.5997i	−1.31488	+	0.405587i	−0.443535	+	0.896257i	$0.646276\pi$
$684$	8.17317	+	18.5685i	0.312509	+	0.709985i
$685$	−2.63654			−0.100737
$686$	12.5978	−	13.5755i	0.480986	−	0.518317i
$687$	−7.28656	−	7.53979i	−0.278000	−	0.287661i
$688$	5.61125	+	3.82569i	0.213927	+	0.145853i
$689$	−7.36474	+	32.2670i	−0.280574	+	1.22928i
$690$	11.7803	+	16.5459i	0.448470	+	0.629891i
$691$	−8.88085	+	38.9096i	−0.337844	+	1.48019i	0.465700	+	0.884943i	$0.345803\pi$
$691$	−8.88085	+	38.9096i	−0.337844	+	1.48019i	−0.803543	+	0.595246i	$0.797054\pi$
$692$	4.39940	+	19.2751i	0.167240	+	0.732728i
$693$	−26.9897	+	19.0283i	−1.02525	+	0.722827i
$694$	−0.189264	+	0.829221i	−0.00718437	+	0.0314768i
$695$	−16.3122	−	7.85554i	−0.618757	−	0.297977i
$696$	4.37553	−	6.70659i	0.165854	−	0.254212i
$697$	20.8840	−	10.0572i	0.791039	−	0.380944i
$698$	4.60265	−	11.7274i	0.174213	−	0.443888i
$699$	−0.420467	−	2.45062i	−0.0159035	−	0.0926908i
$700$	−9.99359	+	6.45425i	−0.377722	+	0.243948i
$701$	23.4586	+	11.2971i	0.886020	+	0.426685i	0.820820	−	0.571188i	$-0.193517\pi$
$701$	23.4586	+	11.2971i	0.886020	+	0.426685i	0.0652002	+	0.997872i	$0.479231\pi$
$702$	−26.5002	+	12.3132i	−1.00019	+	0.464731i
$703$	−15.4427	+	39.3474i	−0.582434	+	1.48402i
$704$	2.08025	−	3.60311i	0.0784025	−	0.135797i
$705$	34.7707	+	35.9791i	1.30954	+	1.35505i
$706$	−29.1413	+	4.39235i	−1.09675	+	0.165308i
$707$	−1.44336	+	14.4212i	−0.0542830	+	0.542366i
$708$	−1.23880	+	2.71203i	−0.0465569	+	0.101924i
$709$	21.0554	−	26.4027i	0.790753	−	0.991573i	−0.209153	−	0.977883i	$-0.567071\pi$
$709$	21.0554	−	26.4027i	0.790753	−	0.991573i	0.999906	−	0.0136905i	$-0.00435795\pi$
$710$	−0.443493	−	5.91801i	−0.0166440	−	0.222099i
$711$	−35.0478	+	1.42527i	−1.31439	+	0.0534518i
$712$	−5.94522	−	15.1482i	−0.222806	−	0.567701i
$713$	2.22288	+	0.335045i	0.0832476	+	0.0125476i
$714$	−13.7251	−	14.9303i	−0.513650	−	0.558751i
$715$	−71.2960	+	10.7461i	−2.66632	+	0.401883i
$716$	−9.33551	−	16.1696i	−0.348885	−	0.604286i
$717$	3.73911	−	13.0583i	0.139640	−	0.487673i
$718$	−7.58444	+	1.14317i	−0.283049	+	0.0426627i
$719$	23.3678	+	7.20802i	0.871473	+	0.268814i	0.698064	−	0.716036i	$-0.254045\pi$
$719$	23.3678	+	7.20802i	0.871473	+	0.268814i	0.173410	+	0.984850i	$0.444521\pi$
$720$	−4.94396	−	7.81189i	−0.184251	−	0.291132i
$721$	23.4550	+	16.8637i	0.873509	+	0.628037i
$722$	−22.0873	−	15.0588i	−0.822003	−	0.560432i
$723$	48.9564	−	20.3715i	1.82071	−	0.757624i
$724$	−5.25635	+	2.53133i	−0.195351	+	0.0940760i
$725$	−4.62586	−	20.2672i	−0.171800	−	0.752706i
$726$	−3.43291	−	10.3758i	−0.127407	−	0.385082i
$727$	−14.2670	+	4.40078i	−0.529133	+	0.163216i	−0.547799	−	0.836610i	$-0.684534\pi$
$727$	−14.2670	+	4.40078i	−0.529133	+	0.163216i	0.0186662	+	0.999826i	$0.494058\pi$
$728$	5.08852	+	13.9815i	0.188593	+	0.518188i
$729$	−26.7995	+	3.28402i	−0.992575	+	0.121630i
$730$	6.54528	+	6.07313i	0.242252	+	0.224777i
$731$	10.9804	+	27.9776i	0.406124	+	1.03479i
$732$	−0.387293	−	19.0551i	−0.0143148	−	0.704298i
$733$	25.0706	+	17.0928i	0.926004	+	0.631339i	0.929566	−	0.368655i	$-0.120182\pi$
$733$	25.0706	+	17.0928i	0.926004	+	0.631339i	−0.00356267	+	0.999994i	$0.501134\pi$
$734$	7.11221	−	12.3187i	0.262516	−	0.454692i
$735$	37.3247	−	1.68878i	1.37674	−	0.0622916i
$736$	1.90267	+	3.29551i	0.0701332	+	0.121474i
$737$	2.55291	−	34.0662i	0.0940377	−	1.25485i
$738$	−15.1908	−	4.01758i	−0.559180	−	0.147889i
$739$	34.1456	+	5.14662i	1.25607	+	0.189322i	0.743155	−	0.669120i	$-0.233329\pi$
$739$	34.1456	+	5.14662i	1.25607	+	0.189322i	0.512912	+	0.858441i	$0.328567\pi$
$740$	4.28614	−	18.7788i	0.157562	−	0.690323i
$741$	35.9923	−	55.1671i	1.32221	−	2.02661i
$742$	12.6426	+	9.08981i	0.464125	+	0.333698i
$743$	27.6473	+	25.6530i	1.01428	+	0.941117i	0.998272	−	0.0587553i	$-0.0187132\pi$
$743$	27.6473	+	25.6530i	1.01428	+	0.941117i	0.0160100	+	0.999872i	$0.494904\pi$
$744$	−1.00197	−	0.207367i	−0.0367341	−	0.00760243i
$745$	−40.3240	−	12.4383i	−1.47736	−	0.455704i
$746$	−11.5177	−	7.85264i	−0.421693	−	0.287506i
$747$	3.85365	+	33.2327i	0.140998	+	1.21592i
$748$	16.5890	−	7.98886i	0.606555	−	0.292102i
$749$	−21.6820	−	7.28526i	−0.792244	−	0.266198i
$750$	2.63173	+	0.544658i	0.0960970	+	0.0198881i
$751$	34.5557	−	32.0630i	1.26096	−	1.17000i	0.283475	−	0.958980i	$-0.408513\pi$
$751$	34.5557	−	32.0630i	1.26096	−	1.17000i	0.977482	−	0.211018i	$-0.0676777\pi$
$752$	5.84467	+	7.32899i	0.213133	+	0.267261i
$753$	−35.6739	+	8.90874i	−1.30003	+	0.324653i
$754$	−25.9994			−0.946842
$755$	18.8045	+	23.5801i	0.684367	+	0.858168i
$756$	0.494985	+	13.7388i	0.0180024	+	0.499676i
$757$	4.75075	−	5.95725i	0.172669	−	0.216520i	−0.687965	−	0.725744i	$-0.741496\pi$
$757$	4.75075	−	5.95725i	0.172669	−	0.216520i	0.860634	+	0.509223i	$0.170067\pi$
$758$	6.77359	−	8.49381i	0.246028	−	0.308509i
$759$	26.8530	+	5.55745i	0.974701	+	0.201723i
$760$	18.7760	+	9.04204i	0.681077	+	0.327989i
$761$	−38.8310	−	5.85282i	−1.40762	−	0.212165i	−0.599120	−	0.800659i	$-0.704483\pi$
$761$	−38.8310	−	5.85282i	−1.40762	−	0.212165i	−0.808501	+	0.588495i	$0.799721\pi$
$762$	−4.99335	+	10.9317i	−0.180890	+	0.396012i
$763$	0.378107	+	7.57918i	0.0136884	+	0.274385i
$764$	−5.18387	−	6.50037i	−0.187546	−	0.235175i
$765$	1.39716	−	40.8898i	0.0505145	−	1.47837i
$766$	2.52621	+	4.37552i	0.0912756	+	0.158094i
$767$	9.57240	−	1.44281i	0.345639	−	0.0520967i
$768$	−0.783064	−	1.54493i	−0.0282564	−	0.0557479i
$769$	31.4616	−	21.4502i	1.13454	−	0.773513i	0.157696	−	0.987488i	$-0.449593\pi$
$769$	31.4616	−	21.4502i	1.13454	−	0.773513i	0.976839	+	0.213975i	$0.0686410\pi$
$770$	−8.37109	+	32.8725i	−0.301673	+	1.18464i
$771$	7.35985	+	2.71726i	0.265058	+	0.0978599i
$772$	3.04033	+	3.81245i	0.109424	+	0.137213i
$773$	−26.5930	−	18.1308i	−0.956483	−	0.652119i	−0.0188783	−	0.999822i	$-0.506009\pi$
$773$	−26.5930	−	18.1308i	−0.956483	−	0.652119i	−0.937605	+	0.347703i	$0.886962\pi$
$774$	6.66667	−	19.2524i	0.239628	−	0.692012i
$775$	−2.19473	+	1.49634i	−0.0788371	+	0.0537502i
$776$	2.89120	−	0.891818i	0.103788	−	0.0320144i
$777$	−19.5795	+	20.9066i	−0.702409	+	0.750020i
$778$	−19.8677	−	6.12837i	−0.712291	−	0.219713i
$779$	33.8466	−	10.4403i	1.21268	−	0.374062i
$780$	−12.4714	+	27.3028i	−0.446546	+	0.977598i
$781$	−5.87342	−	5.44974i	−0.210167	−	0.195007i
$782$	−1.25850	+	16.7935i	−0.0450038	+	0.600535i
$783$	−22.8557	−	7.39782i	−0.816797	−	0.264377i
$784$	6.99128	+	0.349205i	0.249689	+	0.0124716i
$785$	21.3705	+	37.0148i	0.762745	+	1.32111i
$786$	−32.9451	−	12.1634i	−1.17511	−	0.433852i
$787$	4.73630	−	20.7511i	0.168831	−	0.739696i	−0.817636	−	0.575735i	$-0.804716\pi$
$787$	4.73630	−	20.7511i	0.168831	−	0.739696i	0.986467	−	0.163960i	$-0.0524269\pi$
$788$	−16.1729	+	20.2801i	−0.576134	+	0.722450i
$789$	−8.17833	−	4.50270i	−0.291156	−	0.160300i
$790$	−26.4128	+	24.5075i	−0.939725	+	0.871937i
$791$	18.3011	+	6.14926i	0.650713	+	0.218643i
$792$	−12.0666	−	3.19133i	−0.428770	−	0.113399i
$793$	−51.1283	+	34.8587i	−1.81562	+	1.23787i
$794$	21.2899	+	6.56706i	0.755549	+	0.233056i
$795$	5.31215	+	30.9609i	0.188403	+	1.09807i
$796$	4.11938	−	10.4960i	0.146008	−	0.372021i
$797$	3.14340	−	41.9458i	0.111345	−	1.48580i	−0.609547	−	0.792750i	$-0.708649\pi$
$797$	3.14340	−	41.9458i	0.111345	−	1.48580i	0.720892	−	0.693047i	$-0.243732\pi$
$798$	−17.3385	−	25.6857i	−0.613776	−	0.909264i
$799$	3.10021	+	41.3695i	0.109678	+	1.46355i
$800$	−4.29673	−	1.32536i	−0.151912	−	0.0468587i
$801$	−39.1855	+	29.1171i	−1.38455	+	1.02880i
$802$	6.42994	+	11.1370i	0.227049	+	0.393261i
$803$	12.0547			0.425403
$804$	−11.2969	−	8.63936i	−0.398412	−	0.304687i
$805$	−22.2099	−	21.6638i	−0.782796	−	0.763549i
$806$	1.21371	+	3.09249i	0.0427512	+	0.108928i
$807$	7.99747	−	0.763037i	0.281524	−	0.0268602i
$808$	−4.52609	+	3.08583i	−0.159227	+	0.108559i
$809$	0.399725	+	5.33395i	0.0140536	+	0.187532i	0.999812	+	0.0193669i	$0.00616506\pi$
$809$	0.399725	+	5.33395i	0.0140536	+	0.187532i	−0.985759	+	0.168165i	$0.946216\pi$
$810$	−18.7321	+	20.4530i	−0.658179	+	0.718644i
$811$	4.76310	−	5.97273i	0.167255	−	0.209731i	−0.691139	−	0.722721i	$-0.742891\pi$
$811$	4.76310	−	5.97273i	0.167255	−	0.209731i	0.858394	+	0.512990i	$0.171462\pi$
$812$	−4.75156	+	11.2714i	−0.166747	+	0.395548i
$813$	−4.12618	+	1.71697i	−0.144712	+	0.0602167i
$814$	−13.0026	−	22.5212i	−0.455741	−	0.789367i
$815$	−61.1194			−2.14092
$816$	0.988186	−	7.60128i	0.0345934	−	0.266098i
$817$	10.2197	+	44.7753i	0.357541	+	1.56649i
$818$	−25.7986	−	12.4240i	−0.902028	−	0.434394i
$819$	36.4809	−	25.7199i	1.27475	−	0.898726i
$820$	−14.5422	+	7.00317i	−0.507837	+	0.244561i
$821$	−7.13677	−	8.94922i	−0.249075	−	0.312330i	0.641539	−	0.767091i	$-0.278296\pi$
$821$	−7.13677	−	8.94922i	−0.249075	−	0.312330i	−0.890614	+	0.454760i	$0.849725\pi$
$822$	0.250594	+	1.46054i	0.00874047	+	0.0509422i
$823$	11.8498	+	51.9175i	0.413059	+	1.80973i	0.569438	+	0.822034i	$0.307161\pi$
$823$	11.8498	+	51.9175i	0.413059	+	1.80973i	−0.156379	+	0.987697i	$0.549982\pi$
$824$	0.815952	+	10.8881i	0.0284250	+	0.379306i
$825$	−27.7265	+	16.7682i	−0.965314	+	0.583795i
$826$	1.12393	−	4.41356i	0.0391064	−	0.153567i
$827$	0.0337505	+	0.147870i	0.00117362	+	0.00514196i	0.975511	−	0.219949i	$-0.0705892\pi$
$827$	0.0337505	+	0.147870i	0.00117362	+	0.00514196i	−0.974338	+	0.225091i	$0.927732\pi$
$828$	8.04609	−	8.09847i	0.279621	−	0.281441i
$829$	9.58944	+	1.44538i	0.333055	+	0.0502000i	0.313441	−	0.949608i	$-0.398518\pi$
$829$	9.58944	+	1.44538i	0.333055	+	0.0502000i	0.0196140	+	0.999808i	$0.493756\pi$
$830$	25.1919	+	23.3747i	0.874423	+	0.811346i
$831$	−0.581385	−	3.38850i	−0.0201680	−	0.117546i
$832$	−2.81180	+	4.87019i	−0.0974818	+	0.168843i
$833$	24.6934	+	18.7061i	0.855574	+	0.648127i
$834$	−2.80124	+	9.78295i	−0.0969991	+	0.338756i
$835$	−47.2649	+	22.7616i	−1.63567	+	0.787696i
$836$	26.8857	−	8.29315i	0.929862	−	0.286824i
$837$	0.187027	+	3.06391i	0.00646459	+	0.105904i
$838$	−11.0836	−	10.2840i	−0.382875	−	0.355256i
$839$	−10.8911	+	10.1055i	−0.376003	+	0.348880i	−0.845425	−	0.534094i	$-0.820653\pi$
$839$	−10.8911	+	10.1055i	−0.376003	+	0.348880i	0.469422	+	0.882974i	$0.344462\pi$
$840$	9.55724	+	10.3964i	0.329756	+	0.358710i
$841$	5.58988	+	5.18665i	0.192754	+	0.178850i
$842$	0.963481	+	12.8568i	0.0332037	+	0.443073i
$843$	−23.5249	+	36.0578i	−0.810241	+	1.24190i
$844$	1.60886	−	21.4688i	0.0553794	−	0.738986i
$845$	56.7544	−	8.55434i	1.95241	−	0.294278i
$846$	16.6261	−	22.6813i	0.571619	−	0.779798i
$847$	7.98379	+	14.6614i	0.274326	+	0.503772i
$848$	0.439812	+	5.86888i	0.0151032	+	0.201538i
$849$	20.7829	+	41.0032i	0.713268	+	1.40723i
$850$	−12.4070	−	15.5579i	−0.425558	−	0.533633i
$851$	23.7852			0.815346
$852$	−3.23619	+	0.808163i	−0.110870	+	0.0276872i
$853$	−10.2212	+	26.0433i	−0.349968	+	0.891704i	0.642171	+	0.766562i	$0.278034\pi$
$853$	−10.2212	+	26.0433i	−0.349968	+	0.891704i	−0.992139	+	0.125142i	$0.960061\pi$
$854$	5.76809	+	28.5361i	0.197380	+	0.976485i
$855$	11.4237	−	61.4668i	0.390683	−	2.10212i
$856$	−3.15847	−	8.04766i	−0.107954	−	0.275063i
$857$	−29.8567	+	20.3560i	−1.01989	+	0.695346i	−0.953173	−	0.302426i	$-0.902203\pi$
$857$	−29.8567	+	20.3560i	−1.01989	+	0.695346i	−0.0667127	+	0.997772i	$0.521251\pi$
$858$	12.7294	+	38.4738i	0.434573	+	1.31347i
$859$	−25.5467	−	3.85054i	−0.871642	−	0.131379i	−0.302035	−	0.953297i	$-0.597666\pi$
$859$	−25.5467	−	3.85054i	−0.871642	−	0.131379i	−0.569606	+	0.821918i	$0.692904\pi$
$860$	−7.64600	−	19.4817i	−0.260726	−	0.664320i
$861$	23.9264	+	1.90451i	0.815410	+	0.0649056i
$862$	−2.83722	+	7.22913i	−0.0966362	+	0.246225i
$863$	4.86683	−	8.42960i	0.165669	−	0.286947i	−0.771224	−	0.636564i	$-0.780355\pi$
$863$	4.86683	−	8.42960i	0.165669	−	0.286947i	0.936893	+	0.349617i	$0.113688\pi$
$864$	−3.85758	+	3.48125i	−0.131237	+	0.118435i
$865$	22.2589	−	56.7147i	0.756824	−	1.92836i
$866$	2.36438	+	10.3590i	0.0803448	+	0.352014i
$867$	2.97839	−	3.34372i	0.101151	−	0.113559i
$868$	1.56248	+	0.0389976i	0.0530342	+	0.00132367i
$869$	−3.63530	+	48.5097i	−0.123319	+	1.64558i
$870$	−22.7831	+	9.48040i	−0.772420	+	0.321416i
$871$	−3.45068	+	46.0461i	−0.116922	+	1.56021i
$872$	−2.10256	+	1.95089i	−0.0712016	+	0.0660654i
$873$	−4.85409	−	7.66990i	−0.164286	−	0.259587i
$874$	−5.72631	+	25.0886i	−0.193695	+	0.848634i
$875$	−4.10394	−	0.102429i	−0.138738	−	0.00346274i
$876$	2.74217	−	4.20305i	0.0926493	−	0.142008i
$877$	33.4018	−	10.3031i	1.12790	−	0.347911i	0.325999	−	0.945370i	$-0.394299\pi$
$877$	33.4018	−	10.3031i	1.12790	−	0.347911i	0.801899	+	0.597459i	$0.203823\pi$
$878$	8.65362	−	10.8513i	0.292046	−	0.366214i
$879$	17.2895	+	9.51897i	0.583159	+	0.321067i
$880$	−11.5515	+	5.56290i	−0.389400	+	0.187525i
$881$	31.3035			1.05464			0.527321	−	0.849666i	$-0.323196\pi$
$881$	31.3035			1.05464			0.527321	+	0.849666i	$0.323196\pi$
$882$	−4.48310	−	20.5159i	−0.150954	−	0.690806i
$883$	−21.6823			−0.729667			−0.364834	−	0.931073i	$-0.618874\pi$
$883$	−21.6823			−0.729667			−0.364834	+	0.931073i	$0.618874\pi$
$884$	−22.4228	+	10.7983i	−0.754161	+	0.363185i
$885$	7.86214	−	4.75480i	0.264283	−	0.159831i
$886$	5.09774	−	6.39236i	0.171262	−	0.214756i
$887$	−1.06359	+	0.328073i	−0.0357117	+	0.0110156i	−0.312560	−	0.949898i	$-0.601186\pi$
$887$	−1.06359	+	0.328073i	−0.0357117	+	0.0110156i	0.276848	+	0.960914i	$0.410710\pi$
$888$	−10.8101	−	0.589494i	−0.362764	−	0.0197821i
$889$	4.53032	−	17.7902i	0.151942	−	0.596663i
$890$	−11.1589	+	48.8904i	−0.374047	+	1.63881i
$891$	0.242955	+	37.4438i	0.00813929	+	1.25441i
$892$	15.9868	−	14.8336i	0.535278	−	0.496665i
$893$	−4.73738	+	63.2159i	−0.158530	+	2.11544i
$894$	−3.05768	+	23.5201i	−0.102264	+	0.786630i
$895$	−4.29977	+	57.3765i	−0.143725	+	1.91788i
$896$	1.59747	+	2.10905i	0.0533678	+	0.0704583i
$897$	−36.2962	−	7.51180i	−1.21189	−	0.250812i
$898$	0.878199	+	3.84764i	0.0293059	+	0.128397i
$899$	−0.997812	+	2.54238i	−0.0332789	+	0.0847932i
$900$	−0.460653	+	13.4816i	−0.0153551	+	0.449387i
$901$	−13.0229	+	22.5563i	−0.433855	+	0.751458i
$902$	−7.96131	+	20.2851i	−0.265082	+	0.675419i
$903$	−4.78093	+	30.7523i	−0.159099	+	1.02337i
$904$	2.66597	+	6.79278i	0.0886688	+	0.225924i
$905$	17.7778	+	2.67957i	0.590954	+	0.0890720i
$906$	11.2752	−	12.6582i	0.374592	−	0.420539i
$907$	40.0927	−	27.3347i	1.33126	−	0.907635i	0.331893	−	0.943317i	$-0.392313\pi$
$907$	40.0927	−	27.3347i	1.33126	−	0.907635i	0.999363	+	0.0356821i	$0.0113604\pi$
$908$	8.10649	+	20.6550i	0.269023	+	0.685460i
$909$	12.4911	+	10.6791i	0.414303	+	0.354204i
$910$	11.3149	−	44.4326i	0.375085	−	1.47293i
$911$	2.74790	−	7.00153i	0.0910419	−	0.231971i	−0.878099	−	0.478480i	$-0.841188\pi$
$911$	2.74790	−	7.00153i	0.0910419	−	0.231971i	0.969141	+	0.246509i	$0.0792833\pi$
$912$	3.22434	−	11.2606i	0.106769	−	0.372875i
$913$	46.3971			1.53552
$914$	−0.755501	−	0.947369i	−0.0249898	−	0.0313362i
$915$	−32.0926	+	49.1899i	−1.06095	+	1.62617i
$916$	0.452395	+	6.03679i	0.0149475	+	0.199461i
$917$	52.8295	+	9.31638i	1.74459	+	0.307654i
$918$	−22.7841	+	3.11245i	−0.751988	+	0.102726i
$919$	−51.6637	+	7.78705i	−1.70423	+	0.256871i	−0.927731	−	0.373250i	$-0.878243\pi$
$919$	−51.6637	+	7.78705i	−1.70423	+	0.256871i	−0.776497	+	0.630121i	$0.783005\pi$
$920$	0.876334	−	11.6939i	0.0288919	−	0.385535i
$921$	−7.87871	−	15.5441i	−0.259612	−	0.512196i
$922$	0.340483	+	4.54343i	0.0112132	+	0.149630i
$923$	7.93889	+	7.36621i	0.261312	+	0.242462i
$924$	19.0057	+	1.51283i	0.625243	+	0.0497685i
$925$	−20.6026	+	19.1165i	−0.677411	+	0.628545i
$926$	−26.9228	−	24.9807i	−0.884737	−	0.820916i
$927$	30.8826	−	10.9189i	1.01432	−	0.358622i
$928$	−4.41786	+	1.36273i	−0.145023	+	0.0447338i
$929$	47.8838	−	23.0596i	1.57102	−	0.756561i	0.573001	−	0.819555i	$-0.305779\pi$
$929$	47.8838	−	23.0596i	1.57102	−	0.756561i	0.998014	+	0.0629936i	$0.0200648\pi$
$930$	2.19121	+	2.26736i	0.0718527	+	0.0743497i
$931$	33.0517	+	33.8890i	1.08323	+	1.11067i
$932$	−0.717769	+	1.24321i	−0.0235113	+	0.0407228i
$933$	−34.2604	+	28.4797i	−1.12164	+	0.932385i
$934$	−4.51832	−	4.19239i	−0.147844	−	0.137179i
$935$	−56.1067	−	8.45673i	−1.83489	−	0.276565i
$936$	16.3100	+	4.31360i	0.533110	+	0.140994i
$937$	−1.89045	−	8.28261i	−0.0617584	−	0.270581i	0.934616	−	0.355658i	$-0.115743\pi$
$937$	−1.89045	−	8.28261i	−0.0617584	−	0.270581i	−0.996374	+	0.0850775i	$0.972886\pi$
$938$	19.3315	+	9.91118i	0.631196	+	0.323611i
$939$	−1.02303	−	50.3341i	−0.0333854	−	1.64259i
$940$	−2.15878	−	28.8069i	−0.0704116	−	0.939578i
$941$	−7.83533	−	34.3288i	−0.255425	−	1.11909i	−0.926082	−	0.377321i	$-0.876845\pi$
$941$	−7.83533	−	34.3288i	−0.255425	−	1.11909i	0.670658	−	0.741767i	$-0.266012\pi$
$942$	18.4735	−	15.3565i	0.601900	−	0.500343i
$943$	−12.4269	−	15.5828i	−0.404674	−	0.507445i
$944$	1.55093	−	0.746891i	0.0504786	−	0.0243092i
$945$	22.5896	−	35.8406i	0.734838	−	1.16590i
$946$	−25.4572	−	12.2595i	−0.827684	−	0.398592i
$947$	−0.662039	−	2.90058i	−0.0215134	−	0.0942563i	0.963031	−	0.269389i	$-0.0868217\pi$
$947$	−0.662039	−	2.90058i	−0.0215134	−	0.0942563i	−0.984545	+	0.175133i	$0.943965\pi$
$948$	16.0866	+	12.3023i	0.522469	+	0.399560i
$949$	−16.2940			−0.528924
$950$	−15.2039	−	26.3340i	−0.493280	−	0.854386i
$951$	0.101815	+	0.0778637i	0.00330159	+	0.00252490i
$952$	0.583401	+	11.6943i	0.0189081	+	0.379015i
$953$	20.8503	−	26.1454i	0.675407	−	0.846934i	−0.319515	−	0.947581i	$-0.603520\pi$
$953$	20.8503	−	26.1454i	0.675407	−	0.846934i	0.994922	+	0.100647i	$0.0320914\pi$
$954$	16.6462	−	5.88545i	0.538941	−	0.190548i
$955$	1.91471	+	25.5500i	0.0619584	+	0.826777i
$956$	−6.47955	+	4.41768i	−0.209563	+	0.142878i
$957$	−13.8424	+	30.3044i	−0.447461	+	0.979602i
$958$	1.03634	+	2.64055i	0.0334826	+	0.0853122i
$959$	−0.774158	−	2.12711i	−0.0249989	−	0.0686881i
$960$	−0.688106	+	5.29301i	−0.0222085	+	0.170831i
$961$	−30.6510			−0.988742
$962$	17.5752	+	30.4411i	0.566646	+	0.981459i
$963$	−20.8178	+	15.4688i	−0.670845	+	0.498476i
$964$	−29.2543	−	9.02375i	−0.942217	−	0.290635i
$965$	−1.12297	−	14.9850i	−0.0361497	−	0.482384i
$966$	−9.88992	+	14.3625i	−0.318203	+	0.462105i
$967$	−1.26582	+	16.8912i	−0.0407061	+	0.543184i	0.939154	+	0.343497i	$0.111612\pi$
$967$	−1.26582	+	16.8912i	−0.0407061	+	0.543184i	−0.979860	+	0.199687i	$0.936007\pi$
$968$	−2.30524	+	5.87365i	−0.0740932	+	0.188786i
$969$	39.8624	−	33.1365i	1.28057	−	1.06450i
$970$	−8.90964	−	2.74826i	−0.286071	−	0.0882413i
$971$	−41.0583	+	27.9931i	−1.31762	+	0.898341i	−0.998776	−	0.0494645i	$-0.984249\pi$
$971$	−41.0583	+	27.9931i	−1.31762	+	0.898341i	−0.318849	+	0.947806i	$0.603296\pi$
$972$	13.1106	+	8.43286i	0.420521	+	0.270484i
$973$	1.54802	−	15.4670i	0.0496273	−	0.495849i
$974$	18.7780	−	17.4234i	0.601684	−	0.558282i
$975$	37.4769	−	22.6650i	1.20022	−	0.725861i
$976$	−6.86073	+	8.60309i	−0.219607	+	0.275378i
$977$	−5.56768	+	24.3936i	−0.178126	+	0.780420i	0.804369	+	0.594130i	$0.202504\pi$
$977$	−5.56768	+	24.3936i	−0.178126	+	0.780420i	−0.982495	+	0.186290i	$0.940354\pi$
$978$	5.80918	+	33.8577i	0.185757	+	1.08265i
$979$	33.8521	+	58.6336i	1.08192	+	1.87394i
$980$	−17.1948	−	13.0256i	−0.549267	−	0.416089i
$981$	7.30060	+	4.55430i	0.233090	+	0.145408i
$982$	2.65534	−	35.4331i	0.0847354	−	1.13072i
$983$	−18.5507	−	17.2126i	−0.591677	−	0.548996i	0.326485	−	0.945203i	$-0.394136\pi$
$983$	−18.5507	−	17.2126i	−0.591677	−	0.548996i	−0.918161	+	0.396207i	$0.870326\pi$
$984$	5.26167	+	7.39019i	0.167736	+	0.235591i
$985$	76.3841	−	23.5614i	2.43380	−	0.750728i
$986$	−19.5514	−	6.03080i	−0.622642	−	0.192060i
$987$	−18.8177	+	38.6168i	−0.598974	+	1.22919i
$988$	−36.3405	+	11.2095i	−1.15614	+	0.356623i
$989$	21.3527	−	14.5580i	0.678975	−	0.462917i
$990$	25.1837	+	29.0727i	0.800392	+	0.923992i
$991$	−30.9887	−	21.1278i	−0.984390	−	0.671146i	−0.0397347	−	0.999210i	$-0.512651\pi$
$991$	−30.9887	−	21.1278i	−0.984390	−	0.671146i	−0.944655	+	0.328065i	$0.893604\pi$
$992$	0.368325	+	0.461865i	0.0116943	+	0.0146642i
$993$	17.8691	−	14.8541i	0.567058	−	0.471379i
$994$	4.64432	−	2.09548i	0.147309	−	0.0664647i
$995$	−28.7092	+	19.5736i	−0.910142	+	0.620524i
$996$	10.5542	−	16.1770i	0.334424	−	0.512588i
$997$	60.5842	−	9.13160i	1.91872	−	0.289201i	0.923246	−	0.384210i	$-0.125526\pi$
$997$	60.5842	−	9.13160i	1.91872	−	0.289201i	0.995476	+	0.0950092i	$0.0302880\pi$
$998$	19.7917	+	34.2803i	0.626496	+	1.08512i
$999$	6.78844	+	31.7612i	0.214777	+	1.00488i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bb.b.121.15	yes	336
9.7	even	3		882.2.y.a.709.9	yes	336
49.32	even	21		882.2.y.a.571.9	✓	336
441.277	even	21	inner	882.2.bb.b.277.15	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.y.a.571.9	✓	336	49.32	even	21
882.2.y.a.709.9	yes	336	9.7	even	3
882.2.bb.b.121.15	yes	336	1.1	even	1	trivial
882.2.bb.b.277.15	yes	336	441.277	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bb (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900969 - 0.433884i) q^{2} +(0.0351964 + 1.73169i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.94473 + 0.908329i) q^{5} +(0.783064 + 1.54493i) q^{6} +(-1.59747 - 2.10905i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-2.99752 + 0.121899i) q^{9} +O(q^{10})\)	\(q+(0.900969 - 0.433884i) q^{2} +(0.0351964 + 1.73169i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.94473 + 0.908329i) q^{5} +(0.783064 + 1.54493i) q^{6} +(-1.59747 - 2.10905i) q^{7} +(0.222521 - 0.974928i) q^{8} +(-2.99752 + 0.121899i) q^{9} +(-2.25900 + 2.09605i) q^{10} +(-0.310915 + 4.14887i) q^{11} +(1.37584 + 1.05218i) q^{12} +(0.420253 - 5.60788i) q^{13} +(-2.35436 - 1.20707i) q^{14} +(-1.67659 - 5.06740i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(1.61683 - 4.11961i) q^{17} +(-2.64778 + 1.41040i) q^{18} +(3.38128 - 5.85655i) q^{19} +(-1.12585 + 2.86862i) q^{20} +(3.59600 - 2.84056i) q^{21} +(1.52000 + 3.87291i) q^{22} +(-3.76283 - 0.567155i) q^{23} +(1.69611 + 0.351024i) q^{24} +(3.71518 - 2.53296i) q^{25} +(-2.05453 - 5.23487i) q^{26} +(-0.316593 - 5.18650i) q^{27} +(-2.64493 - 0.0660140i) q^{28} +(1.68907 - 4.30367i) q^{29} +(-3.70922 - 3.83812i) q^{30} -0.590748 q^{31} +(-0.623490 - 0.781831i) q^{32} +(-7.19552 - 0.392384i) q^{33} +(-0.330720 - 4.41315i) q^{34} +(6.61984 + 4.75954i) q^{35} +(-1.77362 + 2.41956i) q^{36} +(-6.18068 + 0.931588i) q^{37} +(0.505367 - 6.74366i) q^{38} +(9.72592 + 0.530371i) q^{39} +(0.230291 + 3.07302i) q^{40} +(3.83950 + 3.56253i) q^{41} +(2.00741 - 4.11950i) q^{42} +(-4.97839 + 4.61927i) q^{43} +(3.04987 + 2.82986i) q^{44} +(8.71617 - 3.08169i) q^{45} +(-3.63627 + 1.12164i) q^{46} +(-8.44580 + 4.06728i) q^{47} +(1.68044 - 0.419652i) q^{48} +(-1.89616 + 6.73829i) q^{49} +(2.24825 - 3.89408i) q^{50} +(7.19080 + 2.65485i) q^{51} +(-4.12240 - 3.82502i) q^{52} +(-5.81961 - 0.877164i) q^{53} +(-2.53558 - 4.53551i) q^{54} +(-2.85298 - 12.4997i) q^{55} +(-2.41164 + 1.08811i) q^{56} +(10.2608 + 5.64921i) q^{57} +(-0.345496 - 4.61033i) q^{58} +(0.383049 + 1.67825i) q^{59} +(-5.00719 - 1.84866i) q^{60} +(-6.86073 - 8.60309i) q^{61} +(-0.532245 + 0.256316i) q^{62} +(5.04555 + 6.12718i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(3.85627 + 16.8954i) q^{65} +(-6.65319 + 2.76849i) q^{66} -8.21095 q^{67} +(-2.21276 - 3.83262i) q^{68} +(0.849700 - 6.53602i) q^{69} +(8.02935 + 1.41596i) q^{70} +(-1.20071 + 1.50565i) q^{71} +(-0.548169 + 2.94949i) q^{72} +(-0.216525 - 2.88932i) q^{73} +(-5.16440 + 3.52103i) q^{74} +(4.51708 + 6.34440i) q^{75} +(-2.47064 - 6.29509i) q^{76} +(9.24685 - 5.97198i) q^{77} +(8.99287 - 3.74207i) q^{78} +11.6922 q^{79} +(1.54082 + 2.66878i) q^{80} +(8.97028 - 0.730789i) q^{81} +(5.00499 + 1.54384i) q^{82} +(-0.833374 - 11.1206i) q^{83} +(0.0212240 - 4.58253i) q^{84} +(-1.01916 + 13.5997i) q^{85} +(-2.48115 + 6.32186i) q^{86} +(7.51208 + 2.77347i) q^{87} +(3.97567 + 1.22633i) q^{88} +(13.4454 - 9.16694i) q^{89} +(6.51590 - 6.55831i) q^{90} +(-12.4986 + 8.07211i) q^{91} +(-2.78950 + 2.58828i) q^{92} +(-0.0207922 - 1.02299i) q^{93} +(-5.84467 + 7.32899i) q^{94} +(-4.63729 + 20.3173i) q^{95} +(1.33195 - 1.10721i) q^{96} +(1.51281 + 2.62027i) q^{97} +(1.21526 + 6.89370i) q^{98} +(0.426232 - 12.4742i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9}+O(q^{10}) \) 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9	\( 336 q + 56 q^{2} + 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} + 2 q^{7} + 56 q^{8} + 5 q^{9} - 2 q^{10} - 2 q^{12} + 19 q^{13} - 2 q^{14} + q^{15} - 56 q^{16} + 7 q^{17} + 2 q^{18} + 38 q^{19} + 2 q^{20} + 4 q^{21} - 42 q^{23} + 2 q^{24} + 24 q^{25} + 9 q^{26} + 35 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 88 q^{31} + 56 q^{32} + 26 q^{33} - 7 q^{34} - 2 q^{35} + 5 q^{36} + 52 q^{37} + 11 q^{38} - 60 q^{39} - 2 q^{40} + 3 q^{41} - 53 q^{42} + q^{43} + 108 q^{45} - 42 q^{46} + 3 q^{47} - 2 q^{48} + 70 q^{49} + 172 q^{50} + 13 q^{51} + 5 q^{52} - 78 q^{53} + 14 q^{54} + 23 q^{55} - 2 q^{56} - 30 q^{57} + 38 q^{58} - 28 q^{59} + q^{60} - 37 q^{61} - 24 q^{62} + 26 q^{63} - 56 q^{64} - 14 q^{65} + 2 q^{66} - 58 q^{67} - 21 q^{68} + 19 q^{69} + 44 q^{70} + 7 q^{71} + 2 q^{72} - 8 q^{73} + 4 q^{74} + q^{75} - 4 q^{76} - 13 q^{77} + 4 q^{78} + 18 q^{79} - 12 q^{80} - 87 q^{81} - 3 q^{82} + 185 q^{83} - 17 q^{84} - 159 q^{85} - q^{86} - 132 q^{87} + 47 q^{89} + 60 q^{90} + 45 q^{91} - 21 q^{92} + 53 q^{93} + 18 q^{94} + 26 q^{95} + 2 q^{96} + 111 q^{97} - 14 q^{98} - 157 q^{99}+O(q^{100}) \) 336 * q + 56 * q^2 + 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 + 2 * q^7 + 56 * q^8 + 5 * q^9 - 2 * q^10 - 2 * q^12 + 19 * q^13 - 2 * q^14 + q^15 - 56 * q^16 + 7 * q^17 + 2 * q^18 + 38 * q^19 + 2 * q^20 + 4 * q^21 - 42 * q^23 + 2 * q^24 + 24 * q^25 + 9 * q^26 + 35 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 88 * q^31 + 56 * q^32 + 26 * q^33 - 7 * q^34 - 2 * q^35 + 5 * q^36 + 52 * q^37 + 11 * q^38 - 60 * q^39 - 2 * q^40 + 3 * q^41 - 53 * q^42 + q^43 + 108 * q^45 - 42 * q^46 + 3 * q^47 - 2 * q^48 + 70 * q^49 + 172 * q^50 + 13 * q^51 + 5 * q^52 - 78 * q^53 + 14 * q^54 + 23 * q^55 - 2 * q^56 - 30 * q^57 + 38 * q^58 - 28 * q^59 + q^60 - 37 * q^61 - 24 * q^62 + 26 * q^63 - 56 * q^64 - 14 * q^65 + 2 * q^66 - 58 * q^67 - 21 * q^68 + 19 * q^69 + 44 * q^70 + 7 * q^71 + 2 * q^72 - 8 * q^73 + 4 * q^74 + q^75 - 4 * q^76 - 13 * q^77 + 4 * q^78 + 18 * q^79 - 12 * q^80 - 87 * q^81 - 3 * q^82 + 185 * q^83 - 17 * q^84 - 159 * q^85 - q^86 - 132 * q^87 + 47 * q^89 + 60 * q^90 + 45 * q^91 - 21 * q^92 + 53 * q^93 + 18 * q^94 + 26 * q^95 + 2 * q^96 + 111 * q^97 - 14 * q^98 - 157 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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