LMFDB - Embedded newform 882.2.bb.a.151.20

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			151.20
Character	$\chi$	$=$	882.151
Dual form			882.2.bb.a.625.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.900969 + 0.433884i) q^{2} +(1.03458 + 1.38911i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.385039 + 0.357264i) q^{5} +(-1.53484 - 0.802661i) q^{6} +(-1.74511 + 1.98862i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-0.859279 + 2.87431i) q^{9} +O(q^{10})$	\(q+(-0.900969 + 0.433884i) q^{2} +(1.03458 + 1.38911i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.385039 + 0.357264i) q^{5} +(-1.53484 - 0.802661i) q^{6} +(-1.74511 + 1.98862i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-0.859279 + 2.87431i) q^{9} +(-0.501920 - 0.154822i) q^{10} +(1.08168 + 0.737476i) q^{11} +(1.73111 + 0.0572297i) q^{12} +(4.58158 + 3.12367i) q^{13} +(0.709461 - 2.54886i) q^{14} +(-0.0979261 + 0.904483i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(0.965657 - 0.145549i) q^{17} +(-0.472932 - 2.96249i) q^{18} +(-2.78132 - 4.81739i) q^{19} +(0.519389 - 0.0782852i) q^{20} +(-4.56787 - 0.366770i) q^{21} +(-1.29454 - 0.195120i) q^{22} +(2.70546 + 6.89340i) q^{23} +(-1.58450 + 0.699536i) q^{24} +(-0.353033 - 4.71090i) q^{25} +(-5.48317 - 0.826455i) q^{26} +(-4.88174 + 1.78007i) q^{27} +(0.466704 + 2.60426i) q^{28} +(-6.77769 + 1.02157i) q^{29} +(-0.304212 - 0.857400i) q^{30} -0.724717 q^{31} +(0.623490 + 0.781831i) q^{32} +(0.0946470 + 2.26556i) q^{33} +(-0.806876 + 0.550118i) q^{34} +(-1.38240 + 0.142230i) q^{35} +(1.71147 + 2.46391i) q^{36} +(-0.227425 + 0.579468i) q^{37} +(4.59608 + 3.13355i) q^{38} +(0.400889 + 9.59604i) q^{39} +(-0.433986 + 0.295887i) q^{40} +(-10.7207 + 3.30690i) q^{41} +(4.27465 - 1.65148i) q^{42} +(9.86774 + 3.04379i) q^{43} +(1.25100 - 0.385882i) q^{44} +(-1.35774 + 0.799732i) q^{45} +(-5.42847 - 5.03689i) q^{46} +(-3.22347 + 1.55234i) q^{47} +(1.12407 - 1.31775i) q^{48} +(-0.909186 - 6.94070i) q^{49} +(2.36205 + 4.09120i) q^{50} +(1.20124 + 1.19083i) q^{51} +(5.29875 - 1.63445i) q^{52} +(-1.23656 - 3.15071i) q^{53} +(3.62595 - 3.72189i) q^{54} +(0.153015 + 0.670402i) q^{55} +(-1.55043 - 2.14386i) q^{56} +(3.81440 - 8.84757i) q^{57} +(5.66324 - 3.86113i) q^{58} +(0.968357 + 4.24265i) q^{59} +(0.646097 + 0.640498i) q^{60} +(8.31111 + 10.4218i) q^{61} +(0.652947 - 0.314443i) q^{62} +(-4.21636 - 6.72476i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(0.648114 + 2.83957i) q^{65} +(-1.06826 - 2.00013i) q^{66} -8.10525 q^{67} +(0.488282 - 0.845730i) q^{68} +(-6.77671 + 10.8900i) q^{69} +(1.18379 - 0.727944i) q^{70} +(-0.0628095 + 0.0787607i) q^{71} +(-2.61103 - 1.47733i) q^{72} +(10.5992 - 7.22644i) q^{73} +(-0.0465194 - 0.620759i) q^{74} +(6.17873 - 5.36421i) q^{75} +(-5.50052 - 0.829070i) q^{76} +(-3.35420 + 0.864067i) q^{77} +(-4.52475 - 8.47179i) q^{78} +0.726798 q^{79} +(0.262628 - 0.454884i) q^{80} +(-7.52328 - 4.93966i) q^{81} +(8.22421 - 7.63095i) q^{82} +(-7.53476 + 5.13712i) q^{83} +(-3.13478 + 3.34263i) q^{84} +(0.423816 + 0.288953i) q^{85} +(-10.2112 + 1.53909i) q^{86} +(-8.43115 - 8.35808i) q^{87} +(-0.959682 + 0.890455i) q^{88} +(0.193324 + 2.57973i) q^{89} +(0.876294 - 1.30964i) q^{90} +(-14.2071 + 3.65986i) q^{91} +(7.07631 + 2.18275i) q^{92} +(-0.749779 - 1.00671i) q^{93} +(2.23071 - 2.79722i) q^{94} +(0.650164 - 2.84855i) q^{95} +(-0.441002 + 1.67497i) q^{96} +(0.991276 - 1.71694i) q^{97} +(3.83061 + 5.85888i) q^{98} +(-3.04920 + 2.47538i) 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} - 56 q^{8} - 15 q^{9}+O(q^{10}) $ 336 * q - 56 * q^2 - 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 - 56 * q^8 - 15 * q^9	\( 336 q - 56 q^{2} - 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} - 56 q^{8} - 15 q^{9} + 2 q^{10} + 2 q^{12} - 21 q^{13} - 7 q^{15} - 56 q^{16} + 7 q^{17} + 6 q^{18} - 34 q^{19} + 2 q^{20} + 16 q^{21} - 36 q^{23} + 2 q^{24} + 32 q^{25} + 7 q^{26} + 49 q^{27} - 16 q^{29} - 7 q^{30} + 92 q^{31} - 56 q^{32} + 14 q^{33} + 7 q^{34} + 16 q^{35} - 15 q^{36} - 26 q^{37} + q^{38} + 44 q^{39} + 2 q^{40} + 3 q^{41} - 33 q^{42} - 3 q^{43} + 106 q^{45} - 36 q^{46} + 27 q^{47} + 2 q^{48} - 74 q^{49} - 164 q^{50} - 7 q^{51} + 21 q^{52} - 78 q^{53} - 28 q^{54} - 53 q^{55} - 18 q^{57} + 40 q^{58} - 16 q^{59} - 7 q^{60} - 45 q^{61} - 20 q^{62} - 50 q^{63} - 56 q^{64} - 14 q^{65} + 14 q^{66} + 86 q^{67} - 21 q^{68} - 85 q^{69} - 26 q^{70} + 7 q^{71} + 6 q^{72} + 36 q^{73} + 2 q^{74} - 35 q^{75} + 8 q^{76} - 37 q^{77} - 12 q^{78} - 2 q^{79} - 12 q^{80} + 41 q^{81} + 3 q^{82} + 191 q^{83} - 5 q^{84} + 159 q^{85} - 3 q^{86} + 72 q^{87} + 59 q^{89} + 22 q^{90} - 29 q^{91} + 27 q^{92} + 23 q^{93} + 6 q^{94} + 26 q^{95} + 2 q^{96} - 113 q^{97} - 18 q^{98} - 33 q^{99}+O(q^{100}) \) 336 * q - 56 * q^2 - 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 - 56 * q^8 - 15 * q^9 + 2 * q^10 + 2 * q^12 - 21 * q^13 - 7 * q^15 - 56 * q^16 + 7 * q^17 + 6 * q^18 - 34 * q^19 + 2 * q^20 + 16 * q^21 - 36 * q^23 + 2 * q^24 + 32 * q^25 + 7 * q^26 + 49 * q^27 - 16 * q^29 - 7 * q^30 + 92 * q^31 - 56 * q^32 + 14 * q^33 + 7 * q^34 + 16 * q^35 - 15 * q^36 - 26 * q^37 + q^38 + 44 * q^39 + 2 * q^40 + 3 * q^41 - 33 * q^42 - 3 * q^43 + 106 * q^45 - 36 * q^46 + 27 * q^47 + 2 * q^48 - 74 * q^49 - 164 * q^50 - 7 * q^51 + 21 * q^52 - 78 * q^53 - 28 * q^54 - 53 * q^55 - 18 * q^57 + 40 * q^58 - 16 * q^59 - 7 * q^60 - 45 * q^61 - 20 * q^62 - 50 * q^63 - 56 * q^64 - 14 * q^65 + 14 * q^66 + 86 * q^67 - 21 * q^68 - 85 * q^69 - 26 * q^70 + 7 * q^71 + 6 * q^72 + 36 * q^73 + 2 * q^74 - 35 * q^75 + 8 * q^76 - 37 * q^77 - 12 * q^78 - 2 * q^79 - 12 * q^80 + 41 * q^81 + 3 * q^82 + 191 * q^83 - 5 * q^84 + 159 * q^85 - 3 * q^86 + 72 * q^87 + 59 * q^89 + 22 * q^90 - 29 * q^91 + 27 * q^92 + 23 * q^93 + 6 * q^94 + 26 * q^95 + 2 * q^96 - 113 * q^97 - 18 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{3}\right)$

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
$3$	1.03458	+	1.38911i	0.597316	+	0.802006i
$3$	1.03458	+	1.38911i	0.597316	+	0.802006i
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	0.385039	+	0.357264i	0.172195	+	0.159773i	0.761562	−	0.648091i	$-0.224433\pi$
$5$	0.385039	+	0.357264i	0.172195	+	0.159773i	−0.589368	+	0.807865i	$0.700623\pi$
$6$	−1.53484	−	0.802661i	−0.626596	−	0.327685i
$7$	−1.74511	+	1.98862i	−0.659589	+	0.751626i
$7$	−1.74511	+	1.98862i	−0.659589	+	0.751626i
$8$	−0.222521	+	0.974928i	−0.0786730	+	0.344689i
$9$	−0.859279	+	2.87431i	−0.286426	+	0.958102i
$10$	−0.501920	−	0.154822i	−0.158721	−	0.0489589i
$11$	1.08168	+	0.737476i	0.326138	+	0.222357i	0.715309	−	0.698808i	$-0.246286\pi$
$11$	1.08168	+	0.737476i	0.326138	+	0.222357i	−0.389171	+	0.921166i	$0.627238\pi$
$12$	1.73111	+	0.0572297i	0.499727	+	0.0165208i
$13$	4.58158	+	3.12367i	1.27070	+	0.866350i	0.995475	−	0.0950287i	$-0.0302943\pi$
$13$	4.58158	+	3.12367i	1.27070	+	0.866350i	0.275228	+	0.961379i	$0.411247\pi$
$14$	0.709461	−	2.54886i	0.189612	−	0.681210i
$15$	−0.0979261	+	0.904483i	−0.0252844	+	0.233537i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	0.965657	−	0.145549i	0.234206	−	0.0353009i	−0.0308903	−	0.999523i	$-0.509834\pi$
$17$	0.965657	−	0.145549i	0.234206	−	0.0353009i	0.265097	+	0.964222i	$0.414596\pi$
$18$	−0.472932	−	2.96249i	−0.111471	−	0.698265i
$19$	−2.78132	−	4.81739i	−0.638079	−	1.10519i	−0.985854	−	0.167608i	$-0.946396\pi$
$19$	−2.78132	−	4.81739i	−0.638079	−	1.10519i	0.347774	−	0.937578i	$-0.386938\pi$
$20$	0.519389	−	0.0782852i	0.116139	−	0.0175051i
$21$	−4.56787	−	0.366770i	−0.996792	−	0.0800358i
$22$	−1.29454	−	0.195120i	−0.275996	−	0.0415998i
$23$	2.70546	+	6.89340i	0.564128	+	1.43737i	0.873684	+	0.486493i	$0.161724\pi$
$23$	2.70546	+	6.89340i	0.564128	+	1.43737i	−0.309557	+	0.950881i	$0.600181\pi$
$24$	−1.58450	+	0.699536i	−0.323435	+	0.142792i
$25$	−0.353033	−	4.71090i	−0.0706066	−	0.942179i
$26$	−5.48317	−	0.826455i	−1.07534	−	0.162081i
$27$	−4.88174	+	1.78007i	−0.939491	+	0.342575i
$28$	0.466704	+	2.60426i	0.0881988	+	0.492159i
$29$	−6.77769	+	1.02157i	−1.25858	+	0.189701i	−0.744257	−	0.667893i	$-0.767196\pi$
$29$	−6.77769	+	1.02157i	−1.25858	+	0.189701i	−0.514327	+	0.857594i	$0.671958\pi$
$30$	−0.304212	−	0.857400i	−0.0555413	−	0.156539i
$31$	−0.724717			−0.130163			−0.0650815	−	0.997880i	$-0.520731\pi$
$31$	−0.724717			−0.130163			−0.0650815	+	0.997880i	$0.520731\pi$
$32$	0.623490	+	0.781831i	0.110218	+	0.138210i
$33$	0.0946470	+	2.26556i	0.0164759	+	0.394383i
$34$	−0.806876	+	0.550118i	−0.138378	+	0.0943445i
$35$	−1.38240	+	0.142230i	−0.233668	+	0.0240413i
$36$	1.71147	+	2.46391i	0.285245	+	0.410652i
$37$	−0.227425	+	0.579468i	−0.0373884	+	0.0952640i	−0.948348	−	0.317230i	$-0.897247\pi$
$37$	−0.227425	+	0.579468i	−0.0373884	+	0.0952640i	0.910960	+	0.412494i	$0.135342\pi$
$38$	4.59608	+	3.13355i	0.745582	+	0.508329i
$39$	0.400889	+	9.59604i	0.0641936	+	1.53660i
$40$	−0.433986	+	0.295887i	−0.0686192	+	0.0467838i
$41$	−10.7207	+	3.30690i	−1.67429	+	0.516451i	−0.979274	−	0.202540i	$-0.935080\pi$
$41$	−10.7207	+	3.30690i	−1.67429	+	0.516451i	−0.695019	+	0.718991i	$0.744604\pi$
$42$	4.27465	−	1.65148i	0.659593	−	0.254829i
$43$	9.86774	+	3.04379i	1.50482	+	0.464174i	0.934112	−	0.356981i	$-0.116194\pi$
$43$	9.86774	+	3.04379i	1.50482	+	0.464174i	0.570705	+	0.821155i	$0.306670\pi$
$44$	1.25100	−	0.385882i	0.188595	−	0.0581738i
$45$	−1.35774	+	0.799732i	−0.202400	+	0.119217i
$46$	−5.42847	−	5.03689i	−0.800385	−	0.742648i
$47$	−3.22347	+	1.55234i	−0.470191	+	0.226432i	−0.653948	−	0.756540i	$-0.726888\pi$
$47$	−3.22347	+	1.55234i	−0.470191	+	0.226432i	0.183757	+	0.982972i	$0.441174\pi$
$48$	1.12407	−	1.31775i	0.162246	−	0.190201i
$49$	−0.909186	−	6.94070i	−0.129884	−	0.991529i
$50$	2.36205	+	4.09120i	0.334045	+	0.578583i
$51$	1.20124	+	1.19083i	0.168207	+	0.166749i
$52$	5.29875	−	1.63445i	0.734805	−	0.226657i
$53$	−1.23656	−	3.15071i	−0.169855	−	0.432783i	0.820446	−	0.571724i	$-0.193725\pi$
$53$	−1.23656	−	3.15071i	−0.169855	−	0.432783i	−0.990301	+	0.138941i	$0.955630\pi$
$54$	3.62595	−	3.72189i	0.493429	−	0.506486i
$55$	0.153015	+	0.670402i	0.0206325	+	0.0903970i
$56$	−1.55043	−	2.14386i	−0.207185	−	0.286486i
$57$	3.81440	−	8.84757i	0.505230	−	1.17189i
$58$	5.66324	−	3.86113i	0.743620	−	0.506991i
$59$	0.968357	+	4.24265i	0.126069	+	0.552346i	0.998028	+	0.0627668i	$0.0199924\pi$
$59$	0.968357	+	4.24265i	0.126069	+	0.552346i	−0.871959	+	0.489579i	$0.837150\pi$
$60$	0.646097	+	0.640498i	0.0834108	+	0.0826879i
$61$	8.31111	+	10.4218i	1.06413	+	1.33438i	0.939644	+	0.342154i	$0.111156\pi$
$61$	8.31111	+	10.4218i	1.06413	+	1.33438i	0.124485	+	0.992222i	$0.460272\pi$
$62$	0.652947	−	0.314443i	0.0829244	−	0.0399343i
$63$	−4.21636	−	6.72476i	−0.531211	−	0.847240i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	0.648114	+	2.83957i	0.0803886	+	0.352206i
$66$	−1.06826	−	2.00013i	−0.131494	−	0.246199i
$67$	−8.10525			−0.990214			−0.495107	−	0.868832i	$-0.664871\pi$
$67$	−8.10525			−0.990214			−0.495107	+	0.868832i	$0.664871\pi$
$68$	0.488282	−	0.845730i	0.0592129	−	0.102560i
$69$	−6.77671	+	10.8900i	−0.815819	+	1.31100i
$70$	1.18379	−	0.727944i	0.141489	−	0.0870060i
$71$	−0.0628095	+	0.0787607i	−0.00745412	+	0.00934717i	−0.785545	−	0.618805i	$-0.787617\pi$
$71$	−0.0628095	+	0.0787607i	−0.00745412	+	0.00934717i	0.778090	+	0.628152i	$0.216188\pi$
$72$	−2.61103	−	1.47733i	−0.307713	−	0.174105i
$73$	10.5992	−	7.22644i	1.24055	−	0.845791i	0.248133	−	0.968726i	$-0.420183\pi$
$73$	10.5992	−	7.22644i	1.24055	−	0.845791i	0.992415	+	0.122935i	$0.0392306\pi$
$74$	−0.0465194	−	0.620759i	−0.00540778	−	0.0721617i
$75$	6.17873	−	5.36421i	0.713459	−	0.619406i
$76$	−5.50052	−	0.829070i	−0.630953	−	0.0951008i
$77$	−3.35420	+	0.864067i	−0.382247	+	0.0984696i
$78$	−4.52475	−	8.47179i	−0.512327	−	0.959242i
$79$	0.726798			0.0817711			0.0408856	−	0.999164i	$-0.486982\pi$
$79$	0.726798			0.0817711			0.0408856	+	0.999164i	$0.486982\pi$
$80$	0.262628	−	0.454884i	0.0293627	−	0.0508576i
$81$	−7.52328	−	4.93966i	−0.835920	−	0.548851i
$82$	8.22421	−	7.63095i	0.908212	−	0.842698i
$83$	−7.53476	+	5.13712i	−0.827048	+	0.563872i	−0.901214	−	0.433374i	$-0.857323\pi$
$83$	−7.53476	+	5.13712i	−0.827048	+	0.563872i	0.0741662	+	0.997246i	$0.476370\pi$
$84$	−3.13478	+	3.34263i	−0.342032	+	0.364711i
$85$	0.423816	+	0.288953i	0.0459693	+	0.0313413i
$86$	−10.2112	+	1.53909i	−1.10110	+	0.165964i
$87$	−8.43115	−	8.35808i	−0.903915	−	0.896080i
$88$	−0.959682	+	0.890455i	−0.102302	+	0.0949228i
$89$	0.193324	+	2.57973i	0.0204923	+	0.273451i	0.998032	+	0.0627012i	$0.0199715\pi$
$89$	0.193324	+	2.57973i	0.0204923	+	0.273451i	−0.977540	+	0.210750i	$0.932409\pi$
$90$	0.876294	−	1.30964i	0.0923695	−	0.138048i
$91$	−14.2071	+	3.65986i	−1.48931	+	0.383658i
$92$	7.07631	+	2.18275i	0.737756	+	0.227568i
$93$	−0.749779	−	1.00671i	−0.0777485	−	0.104391i
$94$	2.23071	−	2.79722i	0.230080	−	0.288511i
$95$	0.650164	−	2.84855i	0.0667054	−	0.292255i
$96$	−0.441002	+	1.67497i	−0.0450096	+	0.170951i
$97$	0.991276	−	1.71694i	0.100649	−	0.174329i	−0.811303	−	0.584625i	$-0.801241\pi$
$97$	0.991276	−	1.71694i	0.100649	−	0.174329i	0.911952	+	0.410297i	$0.134575\pi$
$98$	3.83061	+	5.85888i	0.386950	+	0.591836i
$99$	−3.04920	+	2.47538i	−0.306456	+	0.248785i
$100$	−3.90324	−	2.66118i	−0.390324	−	0.266118i
$101$	12.2810	−	3.78818i	1.22200	−	0.376938i	0.384375	−	0.923177i	$-0.374417\pi$
$101$	12.2810	−	3.78818i	1.22200	−	0.376938i	0.837629	+	0.546239i	$0.183941\pi$
$102$	−1.59896	−	0.551700i	−0.158320	−	0.0546264i
$103$	−1.21673	−	1.12896i	−0.119888	−	0.111240i	0.617951	−	0.786217i	$-0.287963\pi$
$103$	−1.21673	−	1.12896i	−0.119888	−	0.111240i	−0.737839	+	0.674977i	$0.764154\pi$
$104$	−4.06485	+	3.77163i	−0.398591	+	0.369839i
$105$	−1.62778	−	1.77316i	−0.158855	−	0.173043i
$106$	2.48114	+	2.30216i	0.240990	+	0.223606i
$107$	1.17771	+	15.7154i	0.113853	+	1.51927i	0.702971	+	0.711219i	$0.251856\pi$
$107$	1.17771	+	15.7154i	0.113853	+	1.51927i	−0.589118	+	0.808047i	$0.700525\pi$
$108$	−1.65200	+	4.92655i	−0.158964	+	0.474058i
$109$	0.501258	−	6.68882i	0.0480118	−	0.640673i	−0.920346	−	0.391106i	$-0.872093\pi$
$109$	0.501258	−	6.68882i	0.0480118	−	0.640673i	0.968357	−	0.249567i	$-0.0802884\pi$
$110$	−0.428738	−	0.537621i	−0.0408786	−	0.0512601i
$111$	−1.04024	+	0.283589i	−0.0987350	+	0.0269171i
$112$	2.32708	+	1.25885i	0.219888	+	0.118950i
$113$	0.804410	+	10.7341i	0.0756726	+	1.00978i	0.897779	+	0.440446i	$0.145180\pi$
$113$	0.804410	+	10.7341i	0.0756726	+	1.00978i	−0.822106	+	0.569334i	$0.807201\pi$
$114$	0.402157	+	9.62639i	0.0376655	+	0.901594i
$115$	−1.42106	+	3.62080i	−0.132514	+	0.337641i
$116$	−3.42712	+	5.93595i	−0.318200	+	0.551139i
$117$	−12.9152	+	10.4848i	−1.19401	+	0.969318i
$118$	−2.71328	−	3.40234i	−0.249777	−	0.313211i
$119$	−1.39574	+	2.17432i	−0.127947	+	0.199320i
$120$	−0.860015	−	0.296737i	−0.0785083	−	0.0270883i
$121$	−3.39259	−	8.64419i	−0.308418	−	0.785835i
$122$	−12.0099	−	5.78366i	−1.08733	−	0.523628i
$123$	−15.6851	−	11.4710i	−1.41428	−	1.03431i
$124$	−0.451853	+	0.566606i	−0.0405776	+	0.0508827i
$125$	3.18456	−	3.99331i	0.284836	−	0.357173i
$126$	6.71657	+	4.22939i	0.598359	+	0.376784i
$127$	−9.22512	−	11.5679i	−0.818597	−	1.02649i	−0.999079	−	0.0429096i	$-0.986337\pi$
$127$	−9.22512	−	11.5679i	−0.818597	−	1.02649i	0.180482	−	0.983578i	$-0.442234\pi$
$128$	1.00000			0.0883883
$129$	5.98081	+	16.8565i	0.526581	+	1.48413i
$130$	−1.81597	−	2.27716i	−0.159271	−	0.199720i
$131$	15.7715	+	4.86486i	1.37796	+	0.425044i	0.893222	−	0.449615i	$-0.148439\pi$
$131$	15.7715	+	4.86486i	1.37796	+	0.425044i	0.484738	+	0.874659i	$0.338915\pi$
$132$	1.83029	+	1.33855i	0.159307	+	0.116506i
$133$	14.4337	+	2.87590i	1.25156	+	0.249372i
$134$	7.30258	−	3.51674i	0.630847	−	0.303800i
$135$	−2.51562	−	1.05867i	−0.216510	−	0.0911160i
$136$	−0.0729788	+	0.973834i	−0.00625788	+	0.0835056i
$137$	13.4092	−	12.4420i	1.14563	−	1.06299i	0.148375	−	0.988931i	$-0.452596\pi$
$137$	13.4092	−	12.4420i	1.14563	−	1.06299i	0.997254	−	0.0740568i	$-0.0235946\pi$
$138$	1.38061	−	12.7518i	0.117525	−	1.08551i
$139$	−3.21089	+	0.990427i	−0.272344	+	0.0840069i	−0.427919	−	0.903817i	$-0.640753\pi$
$139$	−3.21089	+	0.990427i	−0.272344	+	0.0840069i	0.155575	+	0.987824i	$0.450277\pi$
$140$	−0.750711	+	1.16948i	−0.0634466	+	0.0988391i
$141$	−5.49133	−	2.87174i	−0.462453	−	0.241844i
$142$	0.0224165	−	0.0982129i	0.00188115	−	0.00824185i
$143$	2.65217	+	6.75761i	0.221785	+	0.565100i
$144$	2.99345	+	0.198141i	0.249454	+	0.0165118i
$145$	−2.97465	−	2.02808i	−0.247031	−	0.168423i
$146$	−6.41415	+	11.1096i	−0.530839	+	0.919440i
$147$	8.70081	−	8.44369i	0.717630	−	0.696424i
$148$	0.311250	+	0.539100i	0.0255846	+	0.0443138i
$149$	1.11809	−	14.9198i	0.0915973	−	1.22228i	−0.742188	−	0.670192i	$-0.766212\pi$
$149$	1.11809	−	14.9198i	0.0915973	−	1.22228i	0.833785	−	0.552089i	$-0.186169\pi$
$150$	−3.23940	+	7.51384i	−0.264496	+	0.613503i
$151$	18.1924	+	2.74207i	1.48048	+	0.223146i	0.839057	−	0.544043i	$-0.183107\pi$
$151$	18.1924	+	2.74207i	1.48048	+	0.223146i	0.641421	+	0.767189i	$0.278345\pi$
$152$	5.31552	−	1.63962i	0.431145	−	0.132991i
$153$	−0.411415	+	2.90066i	−0.0332609	+	0.234505i
$154$	2.64713	−	2.23383i	0.213312	−	0.180007i
$155$	−0.279044	−	0.258915i	−0.0224134	−	0.0207966i
$156$	7.75243	+	5.66960i	0.620692	+	0.453932i
$157$	−3.39542	−	14.8763i	−0.270984	−	1.18726i	−0.908854	−	0.417114i	$-0.863042\pi$
$157$	−3.39542	−	14.8763i	−0.270984	−	1.18726i	0.637870	−	0.770144i	$-0.279816\pi$
$158$	−0.654822	+	0.315346i	−0.0520949	+	0.0250876i
$159$	3.09737	−	4.97739i	0.245637	−	0.394733i
$160$	−0.0392524	+	0.523786i	−0.00310317	+	0.0414090i
$161$	−18.4297	−	6.64962i	−1.45246	−	0.524064i
$162$	8.92148	+	1.18625i	0.700938	+	0.0932007i
$163$	−1.59452	+	1.47950i	−0.124892	+	0.115883i	−0.740146	−	0.672446i	$-0.765244\pi$
$163$	−1.59452	+	1.47950i	−0.124892	+	0.115883i	0.615254	+	0.788329i	$0.289053\pi$
$164$	−4.09881	+	10.4436i	−0.320063	+	0.815508i
$165$	−0.772959	+	0.906142i	−0.0601748	+	0.0705430i
$166$	4.55968	−	7.89759i	0.353900	−	0.612972i
$167$	−5.34780	+	13.6260i	−0.413825	+	1.05441i	0.560278	+	0.828305i	$0.310694\pi$
$167$	−5.34780	+	13.6260i	−0.413825	+	1.05441i	−0.974103	+	0.226104i	$0.927401\pi$
$168$	1.37402	−	4.37173i	0.106008	−	0.337287i
$169$	6.48415	+	16.5213i	0.498781	+	1.27087i
$170$	−0.507216	−	0.0764506i	−0.0389017	−	0.00586349i
$171$	16.2366	−	3.85490i	1.24164	−	0.294791i
$172$	8.53217	−	5.81713i	0.650572	−	0.443552i
$173$	8.95951	−	11.2349i	0.681179	−	0.854171i	−0.314283	−	0.949329i	$-0.601764\pi$
$173$	8.95951	−	11.2349i	0.681179	−	0.854171i	0.995462	+	0.0951581i	$0.0303357\pi$
$174$	11.2226	+	3.87223i	0.850786	+	0.293553i
$175$	9.98425	+	7.51899i	0.754738	+	0.568382i
$176$	0.478290	−	1.21866i	0.0360524	−	0.0918601i
$177$	−4.89168	+	5.73453i	−0.367681	+	0.431034i
$178$	−1.29348	−	2.24038i	−0.0969506	−	0.167923i
$179$	−7.78002	+	1.17265i	−0.581506	+	0.0876479i	−0.433207	−	0.901295i	$-0.642618\pi$
$179$	−7.78002	+	1.17265i	−0.581506	+	0.0876479i	−0.148299	+	0.988943i	$0.547380\pi$
$180$	−0.221284	+	1.56015i	−0.0164935	+	0.116287i
$181$	18.0708	+	8.70242i	1.34319	+	0.646845i	0.960822	−	0.277165i	$-0.0893950\pi$
$181$	18.0708	+	8.70242i	1.34319	+	0.646845i	0.382366	+	0.924011i	$0.375109\pi$
$182$	11.2122	−	9.46167i	0.831107	−	0.701346i
$183$	−5.87855	+	22.3273i	−0.434555	+	1.65048i
$184$	−7.32259	+	1.10370i	−0.539829	+	0.0813661i
$185$	−0.294591	+	0.141867i	−0.0216587	+	0.0104303i
$186$	1.11232	+	0.581701i	0.0815596	+	0.0426524i
$187$	1.15187	+	0.554711i	0.0842331	+	0.0405645i
$188$	−0.796131	+	3.48808i	−0.0580638	+	0.254394i
$189$	4.97929	−	12.8143i	0.362190	−	0.932104i
$190$	0.650164	+	2.84855i	0.0471678	+	0.206656i
$191$	5.32918	−	23.3486i	0.385606	−	1.68945i	−0.293947	−	0.955822i	$-0.594969\pi$
$191$	5.32918	−	23.3486i	0.385606	−	1.68945i	0.679552	−	0.733627i	$-0.262174\pi$
$192$	−0.329412	−	1.70044i	−0.0237733	−	0.122719i
$193$	−1.87522	+	8.21590i	−0.134982	+	0.591393i	0.861513	+	0.507736i	$0.169517\pi$
$193$	−1.87522	+	8.21590i	−0.134982	+	0.591393i	−0.996495	+	0.0836576i	$0.973340\pi$
$194$	−0.148156	+	1.97701i	−0.0106370	+	0.141941i
$195$	−3.27396	+	3.83808i	−0.234453	+	0.274850i
$196$	−5.99333	−	3.61663i	−0.428095	−	0.258331i
$197$	20.7100			1.47552			0.737762	−	0.675061i	$-0.235883\pi$
$197$	20.7100			1.47552			0.737762	+	0.675061i	$0.235883\pi$
$198$	1.67320	−	3.55324i	0.118909	−	0.252517i
$199$	11.5967	+	10.7602i	0.822070	+	0.762769i	0.974223	−	0.225588i	$-0.0724302\pi$
$199$	11.5967	+	10.7602i	0.822070	+	0.762769i	−0.152153	+	0.988357i	$0.548621\pi$
$200$	4.67134	+	0.704092i	0.330314	+	0.0497868i
$201$	−8.38555	−	11.2591i	−0.591471	−	0.794157i
$202$	−9.42116	+	8.74156i	−0.662870	+	0.615054i
$203$	9.79629	−	15.2610i	0.687565	−	1.07111i
$204$	1.67998	−	0.196697i	0.117622	−	0.0137715i
$205$	−5.30933	−	2.55684i	−0.370820	−	0.178577i
$206$	1.58607	+	0.489238i	0.110507	+	0.0340869i
$207$	−22.1385	+	1.85297i	−1.53873	+	0.128791i
$208$	2.02586	−	5.16180i	0.140468	−	0.357906i
$209$	0.544214	−	7.26203i	0.0376441	−	0.502325i
$210$	2.23592	+	0.891295i	0.154293	+	0.0615052i
$211$	1.14883	+	15.3301i	0.0790890	+	1.05537i	0.885691	+	0.464275i	$0.153685\pi$
$211$	1.14883	+	15.3301i	0.0790890	+	1.05537i	−0.806602	+	0.591095i	$0.798696\pi$
$212$	−3.23430	−	0.997651i	−0.222133	−	0.0685189i
$213$	−0.174389	−	0.00576524i	−0.0119490	−	0.000395028i
$214$	−7.87974	−	13.6481i	−0.538648	−	0.932965i
$215$	2.71203	+	4.69737i	0.184959	+	0.320358i
$216$	−0.649152	−	5.15544i	−0.0441692	−	0.350784i
$217$	1.26471	−	1.44118i	0.0858541	−	0.0978339i
$218$	2.45055	+	6.24391i	0.165972	+	0.422891i
$219$	21.0041	+	7.24721i	1.41933	+	0.489721i
$220$	0.619545	+	0.298357i	0.0417697	+	0.0201152i
$221$	4.87889	+	2.34955i	0.328189	+	0.158048i
$222$	0.814177	−	0.706847i	0.0546440	−	0.0474405i
$223$	0.357943	+	0.912025i	0.0239697	+	0.0610737i	0.942358	−	0.334608i	$-0.108604\pi$
$223$	0.357943	+	0.912025i	0.0239697	+	0.0610737i	−0.918388	+	0.395681i	$0.870509\pi$
$224$	−2.64282	−	0.124500i	−0.176581	−	0.00831850i
$225$	13.8439	+	3.03325i	0.922928	+	0.202217i
$226$	−5.38210	−	9.32208i	−0.358012	−	0.620095i
$227$	−4.57828	−	7.92981i	−0.303871	−	0.526320i	0.673138	−	0.739517i	$-0.264946\pi$
$227$	−4.57828	−	7.92981i	−0.303871	−	0.526320i	−0.977009	+	0.213197i	$0.931612\pi$
$228$	−4.53907	−	8.49859i	−0.300607	−	0.562833i
$229$	7.53591	+	2.32452i	0.497987	+	0.153609i	0.533566	−	0.845758i	$-0.320852\pi$
$229$	7.53591	+	2.32452i	0.497987	+	0.153609i	−0.0355795	+	0.999367i	$0.511328\pi$
$230$	−0.290676	−	3.87880i	−0.0191666	−	0.255760i
$231$	−4.67049	−	3.76543i	−0.307296	−	0.247747i
$232$	0.512218	−	6.83508i	0.0336288	−	0.448745i
$233$	4.81006	−	12.2558i	0.315117	−	0.802906i	−0.682299	−	0.731073i	$-0.739020\pi$
$233$	4.81006	−	12.2558i	0.315117	−	0.802906i	0.997417	−	0.0718331i	$-0.0228849\pi$
$234$	7.08706	−	15.0502i	0.463296	−	0.983860i
$235$	−1.79576	−	0.553918i	−0.117142	−	0.0361336i
$236$	3.92080	+	1.88816i	0.255222	+	0.122909i
$237$	0.751932	+	1.00961i	0.0488432	+	0.0655809i
$238$	0.314112	−	2.56458i	0.0203609	−	0.166237i
$239$	5.17723	−	4.80376i	0.334887	−	0.310730i	−0.494747	−	0.869037i	$-0.664739\pi$
$239$	5.17723	−	4.80376i	0.334887	−	0.310730i	0.829634	+	0.558307i	$0.188549\pi$
$240$	0.903596	−	0.105796i	0.0583269	−	0.00682907i
$241$	−0.104071	−	0.0156862i	−0.00670380	−	0.00101043i	0.145690	−	0.989330i	$-0.453460\pi$
$241$	−0.104071	−	0.0156862i	−0.00670380	−	0.00101043i	−0.152393	+	0.988320i	$0.548698\pi$
$242$	6.80719	+	6.31615i	0.437583	+	0.406018i
$243$	−0.921699	−	15.5612i	−0.0591270	−	0.998250i
$244$	13.3300			0.853365
$245$	2.12959	−	2.99726i	0.136055	−	0.191488i
$246$	19.1089	+	3.52952i	1.21834	+	0.225034i
$247$	2.30509	−	30.7592i	0.146669	−	1.95716i
$248$	0.161265	−	0.706546i	0.0102403	−	0.0448657i
$249$	−14.9314	−	5.15188i	−0.946237	−	0.326487i
$250$	−1.13656	+	4.97958i	−0.0718821	+	0.314936i
$251$	1.01590	+	4.45094i	0.0641229	+	0.280941i	0.996817	−	0.0797286i	$-0.0254054\pi$
$251$	1.01590	+	4.45094i	0.0641229	+	0.280941i	−0.932694	+	0.360670i	$0.882548\pi$
$252$	−7.88648	−	0.896336i	−0.496802	−	0.0564638i
$253$	−2.15728	+	9.45166i	−0.135627	+	0.594221i
$254$	13.3307	+	6.41972i	0.836441	+	0.402809i
$255$	0.0370839	+	0.887674i	0.00232228	+	0.0555883i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	−18.4340	+	2.77848i	−1.14988	+	0.173317i	−0.696201	−	0.717847i	$-0.745128\pi$
$257$	−18.4340	+	2.77848i	−1.14988	+	0.173317i	−0.453681	+	0.891164i	$0.649890\pi$
$258$	−12.7023	−	12.5922i	−0.790809	−	0.783955i
$259$	−0.755459	−	1.46350i	−0.0469420	−	0.0909372i
$260$	2.62416	+	1.26373i	0.162743	+	0.0783731i
$261$	2.88761	−	20.3590i	0.178739	−	1.26019i
$262$	−16.3204	+	2.45990i	−1.00828	+	0.151973i
$263$	11.2727	+	19.5249i	0.695103	+	1.20395i	0.970146	+	0.242522i	$0.0779746\pi$
$263$	11.2727	+	19.5249i	0.695103	+	1.20395i	−0.275043	+	0.961432i	$0.588692\pi$
$264$	−2.22981	−	0.411859i	−0.137236	−	0.0253482i
$265$	0.649510	−	1.65492i	0.0398991	−	0.101661i
$266$	−14.2521	+	3.67144i	−0.873851	+	0.225110i
$267$	−3.38353	+	2.93749i	−0.207069	+	0.179772i
$268$	−5.05354	+	6.33694i	−0.308694	+	0.387090i
$269$	7.38286	−	5.03355i	0.450141	−	0.306901i	−0.316947	−	0.948443i	$-0.602658\pi$
$269$	7.38286	−	5.03355i	0.450141	−	0.306901i	0.767087	+	0.641543i	$0.221705\pi$
$270$	2.72583	−	0.137654i	0.165889	−	0.00837735i
$271$	6.91379	+	1.04209i	0.419983	+	0.0633022i	0.355634	−	0.934625i	$-0.384265\pi$
$271$	6.91379	+	1.04209i	0.419983	+	0.0633022i	0.0643487	+	0.997927i	$0.479503\pi$
$272$	−0.356779	−	0.909058i	−0.0216329	−	0.0551198i
$273$	−19.7824	−	15.9489i	−1.19729	−	0.965273i
$274$	−6.68294	+	17.0279i	−0.403731	+	1.02869i
$275$	3.09231	−	5.35603i	0.186473	−	0.322981i
$276$	4.28893	+	12.0880i	0.258163	+	0.727615i
$277$	1.45126	−	3.69776i	0.0871979	−	0.222177i	−0.880623	−	0.473819i	$-0.842875\pi$
$277$	1.45126	−	3.69776i	0.0871979	−	0.222177i	0.967820	+	0.251642i	$0.0809705\pi$
$278$	2.46318	−	2.28549i	0.147732	−	0.137075i
$279$	0.622733	−	2.08306i	0.0372821	−	0.124709i
$280$	0.168948	−	1.37939i	0.0100966	−	0.0824341i
$281$	0.163271	−	2.17869i	0.00973990	−	0.129970i	−0.990214	−	0.139556i	$-0.955432\pi$
$281$	0.163271	−	2.17869i	0.00973990	−	0.129970i	0.999954	+	0.00958625i	$0.00305145\pi$
$282$	6.19352	+	0.204755i	0.368819	+	0.0121930i
$283$	28.4052	−	13.6792i	1.68852	−	0.813146i	0.692755	−	0.721173i	$-0.256397\pi$
$283$	28.4052	−	13.6792i	1.68852	−	0.813146i	0.995762	−	0.0919730i	$-0.0293173\pi$
$284$	0.0224165	+	0.0982129i	0.00133017	+	0.00582787i
$285$	4.62962	−	2.04391i	0.274235	−	0.121071i
$286$	−5.32154	−	4.93767i	−0.314669	−	0.291970i
$287$	12.1327	−	27.0903i	0.716168	−	1.59909i
$288$	−2.78298	+	1.12029i	−0.163988	+	0.0660137i
$289$	−15.3334	+	4.72974i	−0.901966	+	0.278220i
$290$	3.56001	+	0.536586i	0.209051	+	0.0315094i
$291$	3.41058	−	0.399320i	0.199932	−	0.0234086i
$292$	0.958661	−	12.7924i	0.0561014	−	0.748621i
$293$	5.02420	+	8.70216i	0.293517	+	0.508386i	0.974639	−	0.223784i	$-0.0718410\pi$
$293$	5.02420	+	8.70216i	0.293517	+	0.508386i	−0.681122	+	0.732170i	$0.738508\pi$
$294$	−4.17557	+	11.3826i	−0.243524	+	0.663849i
$295$	−1.14289	+	1.97955i	−0.0665417	+	0.115254i
$296$	−0.514333	−	0.350666i	−0.0298950	−	0.0203821i
$297$	−6.59323	−	1.67470i	−0.382578	−	0.0971759i
$298$	5.46611	+	13.9274i	0.316643	+	0.806794i
$299$	−9.13743	+	40.0337i	−0.528431	+	2.31521i
$300$	−0.341534	−	8.17526i	−0.0197185	−	0.471999i
$301$	−23.2732	+	14.3114i	−1.34145	+	0.824895i
$302$	−17.5805	+	5.42288i	−1.01165	+	0.312052i
$303$	17.9679	+	13.1405i	1.03223	+	0.754903i
$304$	−4.07771	+	3.78356i	−0.233873	+	0.217002i
$305$	−0.523234	+	6.98207i	−0.0299603	+	0.399792i
$306$	−0.887878	−	2.79191i	−0.0507566	−	0.159603i
$307$	18.4224	−	8.87174i	1.05142	−	0.506337i	0.173345	−	0.984861i	$-0.444542\pi$
$307$	18.4224	−	8.87174i	1.05142	−	0.506337i	0.878074	+	0.478524i	$0.158828\pi$
$308$	−1.41576	+	3.16116i	−0.0806703	+	0.180124i
$309$	0.309448	−	2.85818i	0.0176039	−	0.162596i
$310$	0.363749	+	0.112202i	0.0206596	+	0.00637264i
$311$	4.64766	+	5.82798i	0.263544	+	0.330474i	0.895943	−	0.444169i	$-0.146501\pi$
$311$	4.64766	+	5.82798i	0.263544	+	0.330474i	−0.632399	+	0.774643i	$0.717930\pi$
$312$	−9.44465	−	1.74448i	−0.534698	−	0.0987618i
$313$	−5.94178			−0.335850			−0.167925	−	0.985800i	$-0.553707\pi$
$313$	−5.94178			−0.335850			−0.167925	+	0.985800i	$0.553707\pi$
$314$	9.51375	+	11.9299i	0.536892	+	0.673241i
$315$	0.779052	−	4.09565i	0.0438946	−	0.230764i
$316$	0.453151	−	0.568233i	0.0254917	−	0.0319656i
$317$	12.1654	−	15.2549i	0.683275	−	0.856800i	−0.312376	−	0.949958i	$-0.601125\pi$
$317$	12.1654	−	15.2549i	0.683275	−	0.856800i	0.995651	+	0.0931588i	$0.0296964\pi$
$318$	−0.631023	+	5.82837i	−0.0353860	+	0.326839i
$319$	−8.08466	−	3.89337i	−0.452654	−	0.217987i
$320$	−0.191897	−	0.488946i	−0.0107274	−	0.0273329i
$321$	−20.6121	+	17.8949i	−1.15045	+	0.998793i
$322$	19.4897	−	2.00523i	1.08612	−	0.111747i
$323$	−3.38697	−	4.24713i	−0.188456	−	0.236317i
$324$	−8.55267	+	2.80211i	−0.475148	+	0.155673i
$325$	13.0978	−	22.6861i	0.726537	−	1.25840i
$326$	0.794682	−	2.02482i	0.0440134	−	0.112144i
$327$	9.81014	−	6.22384i	0.542502	−	0.344179i
$328$	−0.838407	−	11.1878i	−0.0462933	−	0.617741i
$329$	2.53830	−	9.11925i	0.139941	−	0.502760i
$330$	0.303252	−	1.15178i	0.0166935	−	0.0634034i
$331$	1.49171	+	1.87054i	0.0819915	+	0.102814i	0.821135	−	0.570733i	$-0.193341\pi$
$331$	1.49171	+	1.87054i	0.0819915	+	0.102814i	−0.739144	+	0.673548i	$0.764770\pi$
$332$	−0.681490	+	9.09385i	−0.0374016	+	0.499090i
$333$	−1.47015	−	1.15161i	−0.0805637	−	0.0631080i
$334$	−1.09389	−	14.5969i	−0.0598548	−	0.798707i
$335$	−3.12084	−	2.89572i	−0.170510	−	0.158210i
$336$	0.658873	+	4.53496i	0.0359445	+	0.247402i
$337$	−8.07780	+	7.49510i	−0.440026	+	0.408284i	−0.868828	−	0.495114i	$-0.835126\pi$
$337$	−8.07780	+	7.49510i	−0.440026	+	0.408284i	0.428802	+	0.903398i	$0.358936\pi$
$338$	−13.0104	−	12.0719i	−0.707671	−	0.656622i
$339$	−14.0787	+	12.2227i	−0.764649	+	0.663848i
$340$	0.490157	−	0.151193i	0.0265825	−	0.00819961i
$341$	−0.783910	−	0.534461i	−0.0424511	−	0.0289427i
$342$	−12.9561	+	10.5179i	−0.700585	+	0.568745i
$343$	15.3890	+	10.3043i	0.830929	+	0.556378i
$344$	−5.16326	+	8.94303i	−0.278384	+	0.482176i
$345$	−6.49990	+	1.77200i	−0.349943	+	0.0954013i
$346$	−3.19761	+	14.0096i	−0.171905	+	0.753163i
$347$	−9.06772	+	11.3706i	−0.486781	+	0.610404i	−0.963191	−	0.268820i	$-0.913366\pi$
$347$	−9.06772	+	11.3706i	−0.486781	+	0.610404i	0.476410	+	0.879223i	$0.341938\pi$
$348$	−11.7914	+	1.38056i	−0.632083	+	0.0740060i
$349$	2.47658	+	0.763923i	0.132568	+	0.0408919i	0.360329	−	0.932825i	$-0.382664\pi$
$349$	2.47658	+	0.763923i	0.132568	+	0.0408919i	−0.227761	+	0.973717i	$0.573141\pi$
$350$	−12.2579	−	2.44237i	−0.655210	−	0.130550i
$351$	−27.9264	−	7.09339i	−1.49060	−	0.378617i
$352$	0.0978336	+	1.30550i	0.00521455	+	0.0695833i
$353$	16.5100	−	15.3190i	0.878737	−	0.815349i	−0.105091	−	0.994463i	$-0.533513\pi$
$353$	16.5100	−	15.3190i	0.878737	−	0.815349i	0.983828	+	0.179114i	$0.0573230\pi$
$354$	1.91913	−	7.28905i	0.102001	−	0.387409i
$355$	−0.0523225	+	0.00788635i	−0.00277699	+	0.000418564i
$356$	2.13745	+	1.45729i	0.113285	+	0.0772362i
$357$	−4.46438	+	0.310677i	−0.236280	+	0.0164428i
$358$	6.50076	−	4.43214i	0.343576	−	0.234246i
$359$	2.31286	−	2.14602i	0.122068	−	0.113263i	−0.616777	−	0.787138i	$-0.711562\pi$
$359$	2.31286	−	2.14602i	0.122068	−	0.113263i	0.738845	+	0.673875i	$0.235371\pi$
$360$	−0.477554	−	1.50166i	−0.0251693	−	0.0791444i
$361$	−5.97153	+	10.3430i	−0.314291	+	0.544368i
$362$	−20.0570			−1.05417
$363$	8.49785	−	13.6558i	0.446021	−	0.716745i
$364$	−5.99661	+	13.3895i	−0.314308	+	0.701799i
$365$	6.66288	+	1.00427i	0.348751	+	0.0525657i
$366$	−4.39106	−	22.6668i	−0.229524	−	1.18481i
$367$	2.81889	+	37.6155i	0.147145	+	1.96351i	0.248415	+	0.968654i	$0.420090\pi$
$367$	2.81889	+	37.6155i	0.147145	+	1.96351i	−0.101270	+	0.994859i	$0.532291\pi$
$368$	6.11855	−	4.17156i	0.318952	−	0.217457i
$369$	−0.292972	−	33.6561i	−0.0152515	−	1.75207i
$370$	0.203863	−	0.255636i	0.0105983	−	0.0132899i
$371$	8.42348	+	3.03928i	0.437325	+	0.157792i
$372$	−1.25456	−	0.0414753i	−0.0650459	−	0.00215039i
$373$	−7.17940	+	12.4351i	−0.371735	+	0.643864i	−0.989833	−	0.142237i	$-0.954570\pi$
$373$	−7.17940	+	12.4351i	−0.371735	+	0.643864i	0.618097	+	0.786101i	$0.287904\pi$
$374$	−1.27848			−0.0661086
$375$	8.84186	+	0.292309i	0.456592	+	0.0150947i
$376$	−0.796131	−	3.48808i	−0.0410573	−	0.179884i
$377$	−34.2436	−	16.4908i	−1.76363	−	0.849321i
$378$	1.07374	+	13.7057i	0.0552273	+	0.704947i
$379$	−34.0551	+	16.4001i	−1.74929	+	0.842415i	−0.770533	+	0.637400i	$0.780010\pi$
$379$	−34.0551	+	16.4001i	−1.74929	+	0.842415i	−0.978759	+	0.205014i	$0.934276\pi$
$380$	−1.82172	−	2.28436i	−0.0934522	−	0.117185i
$381$	6.52504	−	24.7827i	0.334288	−	1.26966i
$382$	5.32918	+	23.3486i	0.272664	+	1.19462i
$383$	7.35722	−	5.01606i	0.375936	−	0.256309i	−0.360581	−	0.932728i	$-0.617422\pi$
$383$	7.35722	−	5.01606i	0.375936	−	0.256309i	0.736517	+	0.676419i	$0.236469\pi$
$384$	1.03458	+	1.38911i	0.0527958	+	0.0708880i
$385$	−1.60020	−	0.865638i	−0.0815538	−	0.0441170i
$386$	−1.87522	−	8.21590i	−0.0954464	−	0.418178i
$387$	−17.2279	+	25.7474i	−0.875745	+	1.30882i
$388$	−0.724307	−	1.84550i	−0.0367711	−	0.0936913i
$389$	−15.5729	+	4.80360i	−0.789577	+	0.243552i	−0.663212	−	0.748432i	$-0.730807\pi$
$389$	−15.5729	+	4.80360i	−0.789577	+	0.243552i	−0.126365	+	0.991984i	$0.540331\pi$
$390$	1.28446	−	4.87851i	0.0650412	−	0.247033i
$391$	3.61588	+	6.26289i	0.182863	+	0.316728i
$392$	6.96900	+	0.658062i	0.351988	+	0.0332371i
$393$	9.55905	+	26.9415i	0.482190	+	1.35902i
$394$	−18.6590	+	8.98572i	−0.940029	+	0.452694i
$395$	0.279846	+	0.259659i	0.0140806	+	0.0130649i
$396$	0.0341869	+	3.92733i	0.00171796	+	0.197356i
$397$	13.5955	−	4.19367i	0.682341	−	0.210474i	0.0658421	−	0.997830i	$-0.479027\pi$
$397$	13.5955	−	4.19367i	0.682341	−	0.210474i	0.616499	+	0.787356i	$0.288550\pi$
$398$	−15.1170	−	4.66296i	−0.757745	−	0.233733i
$399$	10.9379	+	23.0254i	0.547578	+	1.15271i
$400$	−4.51423	+	1.39245i	−0.225711	+	0.0696227i
$401$	−25.9130	+	17.6672i	−1.29403	+	0.882258i	−0.997353	−	0.0727184i	$-0.976833\pi$
$401$	−25.9130	+	17.6672i	−1.29403	+	0.882258i	−0.296682	+	0.954976i	$0.595880\pi$
$402$	12.4403	+	6.50576i	0.620464	+	0.324478i
$403$	−3.32035	−	2.26378i	−0.165398	−	0.112767i
$404$	4.69535	−	11.9636i	0.233602	−	0.595209i
$405$	−1.13199	−	4.58976i	−0.0562493	−	0.228067i
$406$	−2.20467	+	18.0001i	−0.109416	+	0.893330i
$407$	−0.673344	+	0.459078i	−0.0333764	+	0.0227557i
$408$	−1.42827	+	0.906136i	−0.0707099	+	0.0448604i
$409$	23.8258	+	29.8766i	1.17811	+	1.47730i	0.845286	+	0.534314i	$0.179430\pi$
$409$	23.8258	+	29.8766i	1.17811	+	1.47730i	0.332824	+	0.942989i	$0.391999\pi$
$410$	5.89291			0.291030
$411$	31.1563	+	5.75474i	1.53683	+	0.283860i
$412$	−1.64127	+	0.247382i	−0.0808598	+	0.0121876i
$413$	−10.1269	−	5.47820i	−0.498312	−	0.269564i
$414$	19.1421	−	11.2750i	0.940784	−	0.554136i
$415$	−4.73649	−	0.713911i	−0.232505	−	0.0350445i
$416$	0.414386	+	5.52960i	0.0203170	+	0.271111i
$417$	−4.69774	−	3.43561i	−0.230049	−	0.168243i
$418$	2.66056	+	6.77899i	0.130132	+	0.331571i
$419$	20.3665	+	3.06975i	0.994967	+	0.149967i	0.626290	−	0.779590i	$-0.284573\pi$
$419$	20.3665	+	3.06975i	0.994967	+	0.149967i	0.368677	+	0.929558i	$0.379811\pi$
$420$	−2.40121	+	0.167101i	−0.117167	+	0.00815369i
$421$	−4.55853	+	0.687088i	−0.222169	+	0.0334866i	−0.259183	−	0.965828i	$-0.583453\pi$
$421$	−4.55853	+	0.687088i	−0.222169	+	0.0334866i	0.0370142	+	0.999315i	$0.488215\pi$
$422$	−7.68656	−	13.3135i	−0.374176	−	0.648092i
$423$	−1.69205	−	10.5991i	−0.0822701	−	0.515348i
$424$	3.34687	−	0.504460i	0.162538	−	0.0244987i
$425$	−1.02658	−	4.49773i	−0.0497963	−	0.218172i
$426$	0.159621	−	0.0704703i	0.00773365	−	0.00341430i
$427$	−35.2288	−	1.65958i	−1.70484	−	0.0803128i
$428$	13.0211	+	8.87763i	0.629398	+	0.429116i
$429$	−6.64321	+	10.6755i	−0.320737	+	0.515417i
$430$	−4.48157	−	3.05548i	−0.216120	−	0.147348i
$431$	−29.9715	−	9.24499i	−1.44368	−	0.445316i	−0.528696	−	0.848811i	$-0.677319\pi$
$431$	−29.9715	−	9.24499i	−1.44368	−	0.445316i	−0.914982	+	0.403495i	$0.867795\pi$
$432$	2.82173	+	4.36324i	0.135761	+	0.209926i
$433$	6.15567	−	26.9698i	0.295823	−	1.29608i	−0.580460	−	0.814288i	$-0.697127\pi$
$433$	6.15567	−	26.9698i	0.295823	−	1.29608i	0.876283	−	0.481796i	$-0.160015\pi$
$434$	−0.514158	+	1.84720i	−0.0246804	+	0.0886683i
$435$	−0.260282	−	6.23034i	−0.0124796	−	0.298722i
$436$	−4.91700	−	4.56231i	−0.235482	−	0.218495i
$437$	25.6835	−	32.2061i	1.22861	−	1.54063i
$438$	−22.0685	+	2.58384i	−1.05448	+	0.123461i
$439$	18.6937	−	9.00242i	0.892203	−	0.429662i	0.0691362	−	0.997607i	$-0.477976\pi$
$439$	18.6937	−	9.00242i	0.892203	−	0.429662i	0.823066	+	0.567945i	$0.192261\pi$
$440$	−0.687643			−0.0327821
$441$	20.7310	+	3.35072i	0.987189	+	0.159558i
$442$	−5.41516			−0.257573
$443$	−12.5318	+	6.03501i	−0.595405	+	0.286732i	−0.707216	−	0.706997i	$-0.750049\pi$
$443$	−12.5318	+	6.03501i	−0.595405	+	0.286732i	0.111811	+	0.993730i	$0.464335\pi$
$444$	−0.426859	+	0.990105i	−0.0202578	+	0.0469883i
$445$	−0.847209	+	1.06237i	−0.0401615	+	0.0503610i
$446$	−0.718209	−	0.666400i	−0.0340082	−	0.0315550i
$447$	21.8821	−	13.8827i	1.03499	−	0.656627i
$448$	2.43512	−	1.03451i	0.115048	−	0.0488758i
$449$	−4.51336	+	19.7743i	−0.212999	+	0.933207i	0.749518	+	0.661984i	$0.230285\pi$
$449$	−4.51336	+	19.7743i	−0.212999	+	0.933207i	−0.962516	+	0.271223i	$0.912572\pi$
$450$	−13.7890	+	3.27379i	−0.650020	+	0.154328i
$451$	−14.0351	−	4.32926i	−0.660888	−	0.203857i
$452$	8.89381	+	6.06369i	0.418329	+	0.285212i
$453$	15.0125	+	28.1083i	0.705350	+	1.32064i
$454$	7.56550	+	5.15807i	0.355067	+	0.242080i
$455$	−6.77785	−	3.66651i	−0.317750	−	0.171889i
$456$	7.77696	+	5.68754i	0.364189	+	0.266343i
$457$	−1.64479	−	7.20630i	−0.0769401	−	0.337097i	0.921778	−	0.387719i	$-0.126737\pi$
$457$	−1.64479	−	7.20630i	−0.0769401	−	0.337097i	−0.998718	+	0.0506220i	$0.983880\pi$
$458$	−7.79819	+	1.17539i	−0.364385	+	0.0549223i
$459$	−4.45500	+	2.42947i	−0.207941	+	0.113398i
$460$	1.94484	+	3.36856i	0.0906785	+	0.157060i
$461$	−39.5338	+	5.95876i	−1.84127	+	0.277527i	−0.975026	−	0.222092i	$-0.928711\pi$
$461$	−39.5338	+	5.95876i	−1.84127	+	0.277527i	−0.866245	+	0.499619i	$0.833473\pi$
$462$	5.84172	+	1.36608i	0.271781	+	0.0635559i
$463$	−29.6405	−	4.46759i	−1.37751	−	0.207626i	−0.581814	−	0.813322i	$-0.697657\pi$
$463$	−29.6405	−	4.46759i	−1.37751	−	0.207626i	−0.795696	+	0.605696i	$0.792895\pi$
$464$	2.50414	+	6.38043i	0.116252	+	0.296204i
$465$	0.0709687	−	0.655494i	0.00329109	−	0.0303978i
$466$	0.983892	+	13.1291i	0.0455779	+	0.608195i
$467$	−13.4737	−	2.03084i	−0.623489	−	0.0939759i	−0.170303	−	0.985392i	$-0.554475\pi$
$467$	−13.4737	−	2.03084i	−0.623489	−	0.0939759i	−0.453186	+	0.891416i	$0.649713\pi$
$468$	0.144803	+	16.6347i	0.00669351	+	0.768939i
$469$	14.1445	−	16.1182i	0.653134	−	0.744271i
$470$	1.85826	−	0.280087i	0.0857151	−	0.0129195i
$471$	17.1520	−	20.1074i	0.790324	−	0.926499i
$472$	−4.35176			−0.200306
$473$	8.42900	+	10.5696i	0.387566	+	0.485992i
$474$	−1.11552	−	0.583372i	−0.0512375	−	0.0267952i
$475$	−21.7124	+	14.8032i	−0.996231	+	0.679219i
$476$	0.829725	+	2.44690i	0.0380304	+	0.112153i
$477$	10.1186	−	0.846922i	0.463301	−	0.0387779i
$478$	−2.58024	+	6.57436i	−0.118018	+	0.300704i
$479$	2.76264	+	1.88353i	0.126228	+	0.0860609i	0.624788	−	0.780794i	$-0.285185\pi$
$479$	2.76264	+	1.88353i	0.126228	+	0.0860609i	−0.498560	+	0.866855i	$0.666138\pi$
$480$	−0.768209	+	0.487374i	−0.0350638	+	0.0222455i
$481$	−2.85203	+	1.94448i	−0.130042	+	0.0886608i
$482$	0.100571	−	0.0310219i	0.00458087	−	0.00141301i
$483$	−9.82992	−	32.4805i	−0.447277	−	1.47791i
$484$	−8.87355	−	2.73713i	−0.403343	−	0.124415i
$485$	0.995081	−	0.306942i	0.0451843	−	0.0139375i
$486$	7.58217	+	13.6202i	0.343934	+	0.617826i
$487$	−20.4371	−	18.9628i	−0.926092	−	0.859288i	0.0642496	−	0.997934i	$-0.479535\pi$
$487$	−20.4371	−	18.9628i	−0.926092	−	0.859288i	−0.990342	+	0.138646i	$0.955725\pi$
$488$	−12.0099	+	5.78366i	−0.543663	+	0.261814i
$489$	−3.70485	−	0.684307i	−0.167539	−	0.0309455i
$490$	−0.618234	+	3.62444i	−0.0279289	+	0.163735i
$491$	0.315435	+	0.546350i	0.0142354	+	0.0246564i	0.873055	−	0.487621i	$-0.162135\pi$
$491$	0.315435	+	0.546350i	0.0142354	+	0.0246564i	−0.858820	+	0.512278i	$0.828802\pi$
$492$	−18.7479	+	5.11105i	−0.845222	+	0.230424i
$493$	−6.39623	+	1.97298i	−0.288072	+	0.0888584i
$494$	11.2691	+	28.7132i	0.507022	+	1.29187i
$495$	−2.05842	−	0.136250i	−0.0925193	−	0.00612400i
$496$	0.161265	+	0.706546i	0.00724099	+	0.0317249i
$497$	−0.0470152	−	0.262350i	−0.00210892	−	0.0117680i
$498$	15.6880	−	1.83680i	0.702997	−	0.0823088i
$499$	7.77877	−	5.30348i	0.348226	−	0.237416i	−0.376558	−	0.926393i	$-0.622892\pi$
$499$	7.77877	−	5.30348i	0.348226	−	0.237416i	0.724783	+	0.688977i	$0.241940\pi$
$500$	−1.13656	−	4.97958i	−0.0508283	−	0.222694i
$501$	−24.4608	+	6.66848i	−1.09283	+	0.297926i
$502$	−2.84648	−	3.56938i	−0.127045	−	0.159309i
$503$	−0.521918	+	0.251342i	−0.0232712	+	0.0112068i	−0.445483	−	0.895290i	$-0.646968\pi$
$503$	−0.521918	+	0.251342i	−0.0232712	+	0.0112068i	0.422212	+	0.906497i	$0.361254\pi$
$504$	7.49438	−	2.61425i	0.333826	−	0.116448i
$505$	6.08205	+	2.92896i	0.270647	+	0.130337i
$506$	−2.15728	−	9.45166i	−0.0959028	−	0.420178i
$507$	−16.2417	+	26.0999i	−0.721317	+	1.15914i
$508$	−14.7959			−0.656464
$509$	−1.25922	+	2.18104i	−0.0558140	+	0.0966728i	−0.892582	−	0.450884i	$-0.851109\pi$
$509$	−1.25922	+	2.18104i	−0.0558140	+	0.0966728i	0.836768	+	0.547557i	$0.184442\pi$
$510$	−0.418559	−	0.783676i	−0.0185341	−	0.0347018i
$511$	−4.12622	+	33.6888i	−0.182533	+	1.49030i
$512$	0.623490	−	0.781831i	0.0275546	−	0.0345524i
$513$	22.1530	+	18.5663i	0.978079	+	0.819722i
$514$	15.4029	−	10.5015i	0.679394	−	0.463203i
$515$	−0.0651516	−	0.869387i	−0.00287092	−	0.0383098i
$516$	16.9079	+	5.83386i	0.744329	+	0.256821i
$517$	−4.63157	−	0.698097i	−0.203696	−	0.0307023i
$518$	1.31563	+	0.990783i	0.0578056	+	0.0435325i
$519$	24.8759	+	0.822387i	1.09193	+	0.0360988i
$520$	−2.91260			−0.127726
$521$	12.2359	−	21.1932i	0.536065	−	0.928491i	−0.463046	−	0.886334i	$-0.653244\pi$
$521$	12.2359	−	21.1932i	0.536065	−	0.928491i	0.999111	−	0.0421573i	$-0.0134231\pi$
$522$	6.23178	+	19.5957i	0.272757	+	0.857680i
$523$	−5.02815	+	4.66544i	−0.219866	+	0.204005i	−0.782414	−	0.622759i	$-0.786012\pi$
$523$	−5.02815	+	4.66544i	−0.219866	+	0.204005i	0.562548	+	0.826765i	$0.309821\pi$
$524$	13.6369	−	9.29745i	0.595729	−	0.406161i
$525$	−0.115206	+	21.6483i	−0.00502802	+	0.944808i
$526$	−18.6278	−	12.7003i	−0.812213	−	0.553757i
$527$	−0.699828	+	0.105482i	−0.0304850	+	0.00459487i
$528$	2.18769	−	0.596407i	0.0952071	−	0.0259553i
$529$	−23.3393	+	21.6557i	−1.01475	+	0.941553i
$530$	0.132857	+	1.77285i	0.00577092	+	0.0770076i
$531$	−13.0268	−	0.862262i	−0.565313	−	0.0374190i
$532$	11.2477	−	9.49160i	0.487650	−	0.411513i
$533$	−59.4475	−	18.3371i	−2.57496	−	0.794269i
$534$	1.77393	−	4.11465i	0.0767653	−	0.178058i
$535$	−5.16109	+	6.47180i	−0.223133	+	0.279800i
$536$	1.80359	−	7.90203i	0.0779031	−	0.341316i
$537$	−9.67801	−	9.59413i	−0.417637	−	0.414017i
$538$	−4.46775	+	7.73837i	−0.192618	+	0.333625i
$539$	4.13516	−	8.17811i	0.178114	−	0.352256i
$540$	−2.39616	+	1.30672i	−0.103115	+	0.0562321i
$541$	−22.8255	−	15.5622i	−0.981346	−	0.669071i	−0.0374451	−	0.999299i	$-0.511922\pi$
$541$	−22.8255	−	15.5622i	−0.981346	−	0.669071i	−0.943901	+	0.330228i	$0.892874\pi$
$542$	−6.68126	+	2.06089i	−0.286984	+	0.0885230i
$543$	6.60703	+	34.1057i	0.283535	+	1.46362i
$544$	0.715872	+	0.664233i	0.0306928	+	0.0284787i
$545$	2.58268	−	2.39638i	0.110630	−	0.102650i
$546$	24.7433	+	5.78621i	1.05892	+	0.247627i
$547$	13.7480	+	12.7563i	0.587823	+	0.545420i	0.917020	−	0.398841i	$-0.130588\pi$
$547$	13.7480	+	12.7563i	0.587823	+	0.545420i	−0.329197	+	0.944261i	$0.606778\pi$
$548$	−1.36699	−	18.2412i	−0.0583949	−	0.779225i
$549$	−37.0970	+	14.9335i	−1.58326	+	0.637344i
$550$	−0.462177	+	6.16732i	−0.0197073	+	0.262975i
$551$	23.7723	+	29.8095i	1.01273	+	1.26993i
$552$	−9.10900	−	9.03005i	−0.387705	−	0.384344i
$553$	−1.26834	+	1.44532i	−0.0539354	+	0.0614613i
$554$	0.296854	+	3.96124i	0.0126121	+	0.168297i
$555$	−0.501849	−	0.262447i	−0.0213023	−	0.0111402i
$556$	−1.22761	+	3.12789i	−0.0520621	+	0.132652i
$557$	−1.95215	+	3.38121i	−0.0827150	+	0.143267i	−0.904415	−	0.426653i	$-0.859692\pi$
$557$	−1.95215	+	3.38121i	−0.0827150	+	0.143267i	0.821700	+	0.569920i	$0.193026\pi$
$558$	0.342741	+	2.14696i	0.0145094	+	0.0908882i
$559$	35.7021	+	44.7690i	1.51004	+	1.89353i
$560$	0.446276	+	1.31609i	0.0188586	+	0.0556149i
$561$	0.421147	+	2.17397i	0.0177808	+	0.0917852i
$562$	0.798198	+	2.03378i	0.0336700	+	0.0857897i
$563$	−6.33303	−	3.04983i	−0.266905	−	0.128535i	0.295645	−	0.955298i	$-0.404465\pi$
$563$	−6.33303	−	3.04983i	−0.266905	−	0.128535i	−0.562550	+	0.826763i	$0.690180\pi$
$564$	−5.66901	+	2.50279i	−0.238708	+	0.105386i
$565$	−3.52518	+	4.42044i	−0.148306	+	0.185969i
$566$	−19.6570	+	24.6491i	−0.826247	+	1.03608i
$567$	22.9520	−	6.34067i	0.963895	−	0.266283i
$568$	−0.0628095	−	0.0787607i	−0.00263543	−	0.00330472i
$569$	7.75722			0.325199			0.162600	−	0.986692i	$-0.448012\pi$
$569$	7.75722			0.325199			0.162600	+	0.986692i	$0.448012\pi$
$570$	−3.28432	+	3.85022i	−0.137565	+	0.161268i
$571$	−13.6966	−	17.1750i	−0.573186	−	0.718752i	0.407748	−	0.913095i	$-0.366314\pi$
$571$	−13.6966	−	17.1750i	−0.573186	−	0.718752i	−0.980934	+	0.194342i	$0.937743\pi$
$572$	6.93692	+	2.13976i	0.290047	+	0.0894677i
$573$	37.9474	−	16.7533i	1.58528	−	0.699878i
$574$	0.822884	+	29.6716i	0.0343465	+	1.23847i
$575$	31.5190	−	15.1788i	1.31443	−	0.632998i
$576$	2.02130	−	2.21683i	0.0842208	−	0.0923681i
$577$	2.25014	−	30.0260i	0.0936746	−	1.25000i	−0.730202	−	0.683231i	$-0.760574\pi$
$577$	2.25014	−	30.0260i	0.0936746	−	1.25000i	0.823877	−	0.566769i	$-0.191807\pi$
$578$	11.7628	−	10.9143i	0.489267	−	0.453974i
$579$	−13.3529	+	5.89512i	−0.554927	+	0.244993i
$580$	−3.44028	+	1.06119i	−0.142850	+	0.0440633i
$581$	2.93324	−	23.9486i	0.121691	−	0.993555i
$582$	−2.89957	+	1.83957i	−0.120191	+	0.0762527i
$583$	0.986009	−	4.31999i	0.0408363	−	0.178916i
$584$	4.68671	+	11.9415i	0.193937	+	0.494144i
$585$	−8.71871	−	0.577105i	−0.360474	−	0.0238604i
$586$	−8.30237	−	5.66046i	−0.342968	−	0.233832i
$587$	10.8516	−	18.7955i	0.447892	−	0.775772i	−0.550356	−	0.834930i	$-0.685508\pi$
$587$	10.8516	−	18.7955i	0.447892	−	0.775772i	0.998249	+	0.0591576i	$0.0188415\pi$
$588$	−1.17668	−	12.0671i	−0.0485255	−	0.497640i
$589$	2.01567	+	3.49125i	0.0830543	+	0.143854i
$590$	0.170817	−	2.27939i	0.00703242	−	0.0938411i
$591$	21.4262	+	28.7685i	0.881355	+	1.18338i
$592$	0.615547	+	0.0927787i	0.0252988	+	0.00381318i
$593$	−17.4457	+	5.38129i	−0.716410	+	0.220983i	−0.631467	−	0.775403i	$-0.717547\pi$
$593$	−17.4457	+	5.38129i	−0.716410	+	0.220983i	−0.0849427	+	0.996386i	$0.527071\pi$
$594$	6.66692	−	1.35184i	0.273547	−	0.0554668i
$595$	−1.31422	+	0.338552i	−0.0538778	+	0.0138793i
$596$	−10.9677	−	10.1765i	−0.449254	−	0.416847i
$597$	−2.94937	+	27.2415i	−0.120710	+	1.11492i
$598$	−9.13743	−	40.0337i	−0.373657	−	1.63710i
$599$	40.5726	−	19.5387i	1.65775	−	0.798331i	0.658810	−	0.752309i	$-0.271060\pi$
$599$	40.5726	−	19.5387i	1.65775	−	0.798331i	0.998940	−	0.0460213i	$-0.0146542\pi$
$600$	3.85482	+	7.21747i	0.157373	+	0.294652i
$601$	1.42483	−	19.0130i	0.0581199	−	0.775557i	−0.889658	−	0.456627i	$-0.849057\pi$
$601$	1.42483	−	19.0130i	0.0581199	−	0.775557i	0.947778	−	0.318930i	$-0.103323\pi$
$602$	14.7590	−	22.9920i	0.601531	−	0.937084i
$603$	6.96467	−	23.2970i	0.283623	−	0.948726i
$604$	13.4866	−	12.5138i	0.548763	−	0.509178i
$605$	1.78198	−	4.54040i	0.0724477	−	0.184594i
$606$	−21.8900	−	4.04321i	−0.889220	−	0.164244i
$607$	−6.46901	+	11.2047i	−0.262569	+	0.454783i	−0.966924	−	0.255065i	$-0.917903\pi$
$607$	−6.46901	+	11.2047i	−0.262569	+	0.454783i	0.704355	+	0.709848i	$0.251236\pi$
$608$	2.03226	−	5.17812i	0.0824192	−	0.210001i
$609$	31.3343	−	2.18056i	1.26973	−	0.0883607i
$610$	−2.55799	−	6.51765i	−0.103570	−	0.263892i
$611$	−19.6176	−	2.95688i	−0.793643	−	0.119622i
$612$	2.01132	+	2.13019i	0.0813026	+	0.0861079i
$613$	28.9070	−	19.7085i	1.16754	−	0.796017i	0.185126	−	0.982715i	$-0.440731\pi$
$613$	28.9070	−	19.7085i	1.16754	−	0.796017i	0.982417	+	0.186697i	$0.0597784\pi$
$614$	−12.7487	+	15.9863i	−0.514494	+	0.645156i
$615$	−1.94120	−	10.0205i	−0.0782766	−	0.404067i
$616$	−0.0960222	−	3.46238i	−0.00386885	−	0.139503i
$617$	17.1640	−	43.7331i	0.690995	−	1.76063i	0.0428861	−	0.999080i	$-0.486345\pi$
$617$	17.1640	−	43.7331i	0.690995	−	1.76063i	0.648109	−	0.761547i	$-0.275560\pi$
$618$	0.961314	+	2.70939i	0.0386697	+	0.108988i
$619$	−17.7460	−	30.7370i	−0.713272	−	1.23542i	−0.963622	−	0.267268i	$-0.913879\pi$
$619$	−17.7460	−	30.7370i	−0.713272	−	1.23542i	0.250351	−	0.968155i	$-0.419454\pi$
$620$	−0.376409	+	0.0567346i	−0.0151170	+	0.00227852i
$621$	−25.4781	−	28.8359i	−1.02240	−	1.15714i
$622$	−6.71606	−	3.23428i	−0.269289	−	0.129683i
$623$	−5.46747	−	4.11747i	−0.219049	−	0.164963i
$624$	9.26624	−	2.52616i	0.370946	−	0.101127i
$625$	−20.7039	+	3.12061i	−0.828155	+	0.124824i
$626$	5.35336	−	2.57804i	0.213963	−	0.103039i
$627$	10.6508	−	6.75720i	0.425353	−	0.269856i
$628$	−13.7478	−	6.62057i	−0.548596	−	0.264190i
$629$	−0.135273	+	0.592669i	−0.00539368	+	0.0236313i
$630$	1.07513	+	4.02807i	0.0428344	+	0.160482i
$631$	5.28819	+	23.1691i	0.210519	+	0.922346i	0.964215	+	0.265122i	$0.0854123\pi$
$631$	5.28819	+	23.1691i	0.210519	+	0.922346i	−0.753695	+	0.657224i	$0.771731\pi$
$632$	−0.161728	+	0.708575i	−0.00643318	+	0.0281856i
$633$	−20.1067	+	17.4562i	−0.799172	+	0.693820i
$634$	−4.34177	+	19.0225i	−0.172434	+	0.755481i
$635$	0.580776	−	7.74991i	0.0230474	−	0.307546i
$636$	−1.96030	−	5.52497i	−0.0777311	−	0.219079i
$637$	17.5150	−	34.6394i	0.693968	−	1.37246i
$638$	8.97330			0.355256
$639$	−0.172411	−	0.248211i	−0.00682049	−	0.00981908i
$640$	0.385039	+	0.357264i	0.0152200	+	0.0141221i
$641$	6.95880	+	1.04887i	0.274856	+	0.0414279i	0.285024	−	0.958520i	$-0.407998\pi$
$641$	6.95880	+	1.04887i	0.274856	+	0.0414279i	−0.0101678	+	0.999948i	$0.503237\pi$
$642$	10.8065	−	25.0659i	0.426500	−	0.989274i
$643$	7.00115	−	6.49612i	0.276098	−	0.256182i	−0.529953	−	0.848027i	$-0.677791\pi$
$643$	7.00115	−	6.49612i	0.276098	−	0.256182i	0.806052	+	0.591845i	$0.201600\pi$
$644$	−16.6896	+	10.2629i	−0.657662	+	0.404416i
$645$	−3.71937	+	8.62714i	−0.146450	+	0.339693i
$646$	4.89432	+	2.35698i	0.192564	+	0.0927341i
$647$	19.3346	+	5.96395i	0.760123	+	0.234467i	0.650500	−	0.759506i	$-0.274559\pi$
$647$	19.3346	+	5.96395i	0.760123	+	0.234467i	0.109623	+	0.993973i	$0.465036\pi$
$648$	6.48990	−	6.23548i	0.254947	−	0.244953i
$649$	−2.08140	+	5.30332i	−0.0817021	+	0.208174i
$650$	−1.95761	+	26.1224i	−0.0767836	+	1.02461i
$651$	3.31041	+	0.265804i	0.129745	+	0.0104177i
$652$	0.162551	+	2.16910i	0.00636600	+	0.0849484i
$653$	−18.6274	−	5.74578i	−0.728945	−	0.224850i	−0.0920003	−	0.995759i	$-0.529326\pi$
$653$	−18.6274	−	5.74578i	−0.728945	−	0.224850i	−0.636945	+	0.770909i	$0.719802\pi$
$654$	−6.13821	+	9.86394i	−0.240023	+	0.385711i
$655$	4.33460	+	7.50775i	0.169367	+	0.293352i
$656$	5.60957	+	9.71606i	0.219017	+	0.379348i
$657$	11.6633	+	36.6750i	0.455029	+	1.43083i
$658$	1.66977	+	9.31749i	0.0650943	+	0.363233i
$659$	−16.3558	−	41.6739i	−0.637132	−	1.62339i	−0.774286	−	0.632835i	$-0.781891\pi$
$659$	−16.3558	−	41.6739i	−0.637132	−	1.62339i	0.137155	−	0.990550i	$-0.456204\pi$
$660$	0.226518	+	1.16929i	0.00881720	+	0.0455147i
$661$	−33.6298	−	16.1953i	−1.30805	−	0.629922i	−0.355604	−	0.934637i	$-0.615725\pi$
$661$	−33.6298	−	16.1953i	−1.30805	−	0.629922i	−0.952444	+	0.304715i	$0.901439\pi$
$662$	−2.15558	−	1.03807i	−0.0837789	−	0.0403458i
$663$	1.78382	+	9.20813i	0.0692778	+	0.357614i
$664$	−3.33167	−	8.48897i	−0.129294	−	0.329436i
$665$	4.53007	+	6.26396i	0.175669	+	0.242906i
$666$	1.82422	+	0.399694i	0.0706873	+	0.0154878i
$667$	−25.3789	−	43.9575i	−0.982674	−	1.70204i
$668$	7.31891	+	12.6767i	0.283177	+	0.490477i
$669$	−0.896585	+	1.44079i	−0.0346640	+	0.0557041i
$670$	4.06818	+	1.25487i	0.157168	+	0.0484798i
$671$	1.30412	+	17.4023i	0.0503450	+	0.671808i
$672$	−2.56127	−	3.79999i	−0.0988032	−	0.146588i
$673$	1.20026	−	16.0164i	0.0462667	−	0.617386i	−0.925088	−	0.379752i	$-0.876009\pi$
$673$	1.20026	−	16.0164i	0.0462667	−	0.617386i	0.971355	−	0.237634i	$-0.0763718\pi$
$674$	4.02584	−	10.2577i	0.155070	−	0.395111i
$675$	10.1091	+	22.3689i	0.389101	+	0.860981i
$676$	16.9597	+	5.23138i	0.652297	+	0.201207i
$677$	24.8712	+	11.9773i	0.955876	+	0.460326i	0.845743	−	0.533591i	$-0.179158\pi$
$677$	24.8712	+	11.9773i	0.955876	+	0.460326i	0.110134	+	0.993917i	$0.464872\pi$
$678$	7.38120	−	17.1208i	0.283473	−	0.657521i
$679$	1.68445	+	4.96751i	0.0646432	+	0.190636i
$680$	−0.376016	+	0.348892i	−0.0144195	+	0.0133794i
$681$	6.27881	−	14.5638i	0.240604	−	0.558086i
$682$	0.938173	+	0.141407i	0.0359245	+	0.00541475i
$683$	−10.8283	−	10.0472i	−0.414334	−	0.384445i	0.445279	−	0.895392i	$-0.353105\pi$
$683$	−10.8283	−	10.0472i	−0.414334	−	0.384445i	−0.859612	+	0.510947i	$0.829295\pi$
$684$	7.10948	−	15.0978i	0.271838	−	0.577278i
$685$	9.60815			0.367109
$686$	−18.3359	−	2.60678i	−0.700067	−	0.0995273i
$687$	4.56749	+	12.8731i	0.174261	+	0.491141i
$688$	0.771702	−	10.2976i	0.0294209	−	0.392594i
$689$	4.17636	−	18.2978i	0.159107	−	0.697092i
$690$	5.08737	−	4.41672i	0.193673	−	0.168142i
$691$	−9.04328	+	39.6212i	−0.344023	+	1.50726i	0.446474	+	0.894796i	$0.352679\pi$
$691$	−9.04328	+	39.6212i	−0.344023	+	1.50726i	−0.790497	+	0.612466i	$0.790178\pi$
$692$	−3.19761	−	14.0096i	−0.121555	−	0.532567i
$693$	0.398602	−	10.3835i	0.0151417	−	0.394436i
$694$	3.23623	−	14.1789i	0.122846	−	0.538222i
$695$	−1.59016	−	0.765781i	−0.0603183	−	0.0290477i
$696$	10.0246	−	6.35992i	0.379983	−	0.241072i
$697$	−9.87121	+	4.75372i	−0.373899	+	0.180060i
$698$	−2.56277	+	0.386276i	−0.0970024	+	0.0146208i
$699$	22.0012	−	5.99794i	0.832160	−	0.226863i
$700$	12.1037	−	3.11799i	0.457475	−	0.117849i
$701$	−9.95727	−	4.79517i	−0.376081	−	0.181111i	0.236288	−	0.971683i	$-0.424069\pi$
$701$	−9.95727	−	4.79517i	−0.376081	−	0.181111i	−0.612369	+	0.790572i	$0.709783\pi$
$702$	28.2386	−	5.72590i	1.06580	−	0.216110i
$703$	3.42407	−	0.516095i	0.129141	−	0.0194649i
$704$	−0.654580	−	1.13377i	−0.0246704	−	0.0427304i
$705$	−1.08840	−	3.06759i	−0.0409917	−	0.115532i
$706$	−8.22830	+	20.9654i	−0.309676	+	0.789042i
$707$	−13.8984	+	31.0330i	−0.522704	+	1.16711i
$708$	1.43352	+	7.39989i	0.0538751	+	0.278105i
$709$	20.6774	−	25.9286i	0.776555	−	0.973769i	−0.223445	−	0.974717i	$-0.571730\pi$
$709$	20.6774	−	25.9286i	0.776555	−	0.973769i	1.00000		0.000947549i	$0.000301614\pi$
$710$	0.0437192	−	0.0298072i	0.00164075	−	0.00111865i
$711$	−0.624522	+	2.08904i	−0.0234214	+	0.0783451i
$712$	−2.55807	−	0.385567i	−0.0958678	−	0.0144497i
$713$	−1.96069	−	4.99576i	−0.0734285	−	0.187093i
$714$	3.88747	−	2.21693i	0.145485	−	0.0829667i
$715$	−1.39307	+	3.54947i	−0.0520977	+	0.132743i
$716$	−3.93395	+	6.81380i	−0.147019	+	0.254644i
$717$	12.0292	+	2.22187i	0.449240	+	0.0829773i
$718$	−1.15269	+	2.93701i	−0.0430181	+	0.109608i
$719$	10.9966	−	10.2033i	0.410103	−	0.380520i	−0.447969	−	0.894049i	$-0.647853\pi$
$719$	10.9966	−	10.2033i	0.410103	−	0.380520i	0.858072	+	0.513529i	$0.171662\pi$
$720$	1.08181	+	1.14574i	0.0403166	+	0.0426994i
$721$	4.36839	−	0.449448i	0.162687	−	0.0167383i
$722$	0.892505	−	11.9097i	0.0332156	−	0.443232i
$723$	−0.0858800	−	0.160795i	−0.00319391	−	0.00598003i
$724$	18.0708	−	8.70242i	0.671594	−	0.323423i
$725$	7.20527	+	31.5683i	0.267597	+	1.17242i
$726$	−1.73126	+	15.9906i	−0.0642530	+	0.593465i
$727$	20.5044	+	19.0253i	0.760468	+	0.705611i	0.961752	−	0.273922i	$-0.0883210\pi$
$727$	20.5044	+	19.0253i	0.760468	+	0.705611i	−0.201284	+	0.979533i	$0.564511\pi$
$728$	−0.406714	−	14.6653i	−0.0150738	−	0.543534i
$729$	20.6627	−	17.3797i	0.765285	−	0.643692i
$730$	−6.43878	+	1.98610i	−0.238310	+	0.0735089i
$731$	9.97188	+	1.50302i	0.368823	+	0.0555911i
$732$	13.7910	+	18.5169i	0.509729	+	0.684404i
$733$	−0.771052	+	10.2890i	−0.0284795	+	0.380032i	0.964693	+	0.263377i	$0.0848363\pi$
$733$	−0.771052	+	10.2890i	−0.0284795	+	0.380032i	−0.993172	+	0.116655i	$0.962783\pi$
$734$	−18.8605	−	32.6673i	−0.696153	−	1.20577i
$735$	6.36678	−	0.142667i	0.234842	−	0.00526234i
$736$	−3.70265	+	6.41318i	−0.136482	+	0.236393i
$737$	−8.76727	−	5.97743i	−0.322947	−	0.220181i
$738$	14.8668	+	30.1960i	0.547255	+	1.11153i
$739$	−7.77272	−	19.8046i	−0.285924	−	0.728522i	−0.999606	−	0.0280530i	$-0.991069\pi$
$739$	−7.77272	−	19.8046i	−0.285924	−	0.728522i	0.713682	−	0.700469i	$-0.247026\pi$
$740$	−0.0727579	+	0.318773i	−0.00267463	+	0.0117183i
$741$	45.1129	−	28.6209i	1.65726	−	1.05142i
$742$	−8.90799	+	0.916511i	−0.327022	+	0.0336462i
$743$	−3.85846	+	1.19018i	−0.141553	+	0.0436634i	−0.364722	−	0.931116i	$-0.618836\pi$
$743$	−3.85846	+	1.19018i	−0.141553	+	0.0436634i	0.223169	+	0.974780i	$0.428360\pi$
$744$	1.14832	−	0.506965i	0.0420993	−	0.0185863i
$745$	5.76083	−	5.34527i	0.211061	−	0.195836i
$746$	1.07303	−	14.3186i	0.0392866	−	0.524243i
$747$	−8.29118	−	26.0714i	−0.303359	−	0.953904i
$748$	1.15187	−	0.554711i	0.0421165	−	0.0202823i
$749$	−33.3071	−	25.0831i	−1.21702	−	0.916517i
$750$	−8.09307	+	3.57298i	−0.295517	+	0.130467i
$751$	1.86065	+	0.573933i	0.0678960	+	0.0209431i	0.328517	−	0.944498i	$-0.393451\pi$
$751$	1.86065	+	0.573933i	0.0678960	+	0.0209431i	−0.260621	+	0.965441i	$0.583927\pi$
$752$	2.23071	+	2.79722i	0.0813456	+	0.102004i
$753$	−5.13184	+	6.01606i	−0.187015	+	0.219238i
$754$	38.0075			1.38415
$755$	6.02516	+	7.55531i	0.219278	+	0.274966i
$756$	−6.91410	−	11.8826i	−0.251463	−	0.432164i
$757$	−23.8139	+	29.8617i	−0.865532	+	1.08534i	0.130056	+	0.991507i	$0.458484\pi$
$757$	−23.8139	+	29.8617i	−0.865532	+	1.08534i	−0.995588	+	0.0938359i	$0.970087\pi$
$758$	23.5668	−	29.5519i	0.855986	−	1.07337i
$759$	−15.3613	+	6.78181i	−0.557581	+	0.246164i
$760$	2.63246	+	1.26773i	0.0954893	+	0.0459852i
$761$	5.34254	+	13.6126i	0.193667	+	0.493456i	0.994414	−	0.105547i	$-0.0336592\pi$
$761$	5.34254	+	13.6126i	0.193667	+	0.493456i	−0.800747	+	0.599002i	$0.795564\pi$
$762$	4.87396	+	25.1596i	0.176565	+	0.911435i
$763$	12.4268	+	12.6695i	0.449879	+	0.458668i
$764$	−14.9320	−	18.7242i	−0.540222	−	0.677416i
$765$	−1.19471	+	0.969885i	−0.0431950	+	0.0350663i
$766$	−4.45223	+	7.71149i	−0.160866	+	0.278628i
$767$	−8.81603	+	22.4629i	−0.318328	+	0.811087i
$768$	−1.53484	−	0.802661i	−0.0553838	−	0.0289635i
$769$	1.30081	+	17.3581i	0.0469084	+	0.625948i	0.970271	+	0.242020i	$0.0778100\pi$
$769$	1.30081	+	17.3581i	0.0469084	+	0.625948i	−0.923363	+	0.383928i	$0.874571\pi$
$770$	1.81732	+	0.0856115i	0.0654916	+	0.00308522i
$771$	−22.9311	−	22.7324i	−0.825845	−	0.818687i
$772$	5.25426	+	6.58864i	0.189105	+	0.237130i
$773$	−0.635287	+	8.47731i	−0.0228497	+	0.304908i	0.974056	+	0.226306i	$0.0726648\pi$
$773$	−0.635287	+	8.47731i	−0.0228497	+	0.304908i	−0.996906	+	0.0786023i	$0.974954\pi$
$774$	4.35044	−	30.6726i	0.156373	−	1.10250i
$775$	0.255849	+	3.41407i	0.00919036	+	0.122637i
$776$	1.45331	+	1.34848i	0.0521709	+	0.0484075i
$777$	1.25138	−	2.56353i	0.0448930	−	0.0919660i
$778$	11.9465	−	11.0847i	0.428302	−	0.397406i
$779$	45.7484	+	42.4483i	1.63911	+	1.52087i
$780$	0.959445	+	4.95269i	0.0343536	+	0.177335i
$781$	−0.126024	+	0.0388732i	−0.00450949	+	0.00139099i
$782$	−5.97516	−	4.07380i	−0.213671	−	0.145679i
$783$	31.2684	−	17.0518i	1.11744	−	0.609382i
$784$	−6.56437	+	2.43084i	−0.234442	+	0.0868158i
$785$	4.00740	−	6.94102i	0.143030	−	0.247736i
$786$	−20.3019	−	20.1259i	−0.724144	−	0.717868i
$787$	−1.93430	+	8.47471i	−0.0689502	+	0.302091i	−0.997631	−	0.0687887i	$-0.978087\pi$
$787$	−1.93430	+	8.47471i	−0.0689502	+	0.302091i	0.928681	+	0.370879i	$0.120944\pi$
$788$	12.9125	−	16.1917i	0.459987	−	0.576806i
$789$	−15.4597	+	35.8591i	−0.550381	+	1.27662i
$790$	−0.364794	−	0.112524i	−0.0129788	−	0.00400343i
$791$	−22.7498	−	17.1325i	−0.808890	−	0.609163i
$792$	−1.73481	−	3.52357i	−0.0616437	−	0.125205i
$793$	5.52377	+	73.7095i	0.196155	+	2.61750i
$794$	−10.4296	+	9.67725i	−0.370133	+	0.343433i
$795$	2.97085	−	0.809912i	0.105365	−	0.0287246i
$796$	15.6431	−	2.35782i	0.554455	−	0.0835706i
$797$	−28.0488	−	19.1233i	−0.993539	−	0.677383i	−0.0466389	−	0.998912i	$-0.514851\pi$
$797$	−28.0488	−	19.1233i	−0.993539	−	0.677383i	−0.946900	+	0.321528i	$0.895803\pi$
$798$	−19.8450	−	15.9994i	−0.702506	−	0.566372i
$799$	−2.88682	+	1.96820i	−0.102129	+	0.0696300i
$800$	3.46302	−	3.21321i	0.122436	−	0.113604i
$801$	−7.58106	−	1.66104i	−0.267864	−	0.0586898i
$802$	15.6813	−	27.1608i	0.553727	−	0.959083i
$803$	16.7943			0.592658
$804$	−14.0310	−	0.463861i	−0.494837	−	0.0163591i
$805$	−4.72047	−	9.14463i	−0.166375	−	0.322306i
$806$	3.97375	+	0.598946i	0.139969	+	0.0210970i
$807$	14.6303	+	5.04802i	0.515013	+	0.177699i
$808$	0.960429	+	12.8160i	0.0337878	+	0.450866i
$809$	−15.9006	+	10.8408i	−0.559035	+	0.381144i	−0.809623	−	0.586950i	$-0.800328\pi$
$809$	−15.9006	+	10.8408i	−0.559035	+	0.381144i	0.250588	+	0.968094i	$0.419376\pi$
$810$	3.01132	+	3.64408i	0.105807	+	0.128040i
$811$	11.0486	−	13.8545i	0.387969	−	0.486498i	−0.549043	−	0.835794i	$-0.685008\pi$
$811$	11.0486	−	13.8545i	0.387969	−	0.486498i	0.937013	+	0.349296i	$0.113579\pi$
$812$	−5.82362	−	17.1741i	−0.204369	−	0.602693i
$813$	5.70531	+	10.6822i	0.200094	+	0.374640i
$814$	0.407476	−	0.705769i	0.0142820	−	0.0247372i
$815$	−1.14252			−0.0400209
$816$	0.893669	−	1.43610i	0.0312847	−	0.0502737i
$817$	−12.7822	−	56.0026i	−0.447193	−	1.95928i
$818$	−34.4293	−	16.5803i	−1.20379	−	0.579715i
$819$	1.68833	−	43.9805i	0.0589950	−	1.53680i
$820$	−5.30933	+	2.55684i	−0.185410	+	0.0892887i
$821$	−5.77404	−	7.24042i	−0.201515	−	0.252692i	0.670797	−	0.741641i	$-0.265952\pi$
$821$	−5.77404	−	7.24042i	−0.201515	−	0.252692i	−0.872313	+	0.488948i	$0.837381\pi$
$822$	−30.5677	+	8.33335i	−1.06617	+	0.290659i
$823$	−7.84233	−	34.3595i	−0.273366	−	1.19770i	−0.906011	−	0.423254i	$-0.860888\pi$
$823$	−7.84233	−	34.3595i	−0.273366	−	1.19770i	0.632645	−	0.774442i	$-0.281969\pi$
$824$	1.37140	−	0.935006i	0.0477750	−	0.0325725i
$825$	10.6394	−	1.24569i	0.370416	−	0.0433693i
$826$	11.5009	+	0.541793i	0.400168	+	0.0188514i
$827$	8.35385	+	36.6006i	0.290492	+	1.27273i	0.883843	+	0.467784i	$0.154948\pi$
$827$	8.35385	+	36.6006i	0.290492	+	1.27273i	−0.593351	+	0.804944i	$0.702195\pi$
$828$	−12.3544	+	18.4639i	−0.429346	+	0.641665i
$829$	4.06381	+	10.3544i	0.141142	+	0.359623i	0.983913	−	0.178649i	$-0.0571725\pi$
$829$	4.06381	+	10.3544i	0.141142	+	0.359623i	−0.842771	+	0.538272i	$0.819077\pi$
$830$	4.57718	−	1.41187i	0.158876	−	0.0490069i
$831$	6.63806	−	1.80966i	0.230272	−	0.0627765i
$832$	−2.77255	−	4.80220i	−0.0961210	−	0.166486i
$833$	−1.88818	−	6.57001i	−0.0654215	−	0.227637i
$834$	5.72317	+	1.05710i	0.198177	+	0.0366045i
$835$	−6.92718	+	3.33596i	−0.239725	+	0.115446i
$836$	−5.33837	−	4.95329i	−0.184632	−	0.171313i
$837$	3.53787	−	1.29005i	0.122287	−	0.0445905i
$838$	−19.6815	+	6.07093i	−0.679885	+	0.209717i
$839$	−36.9940	−	11.4111i	−1.27718	−	0.393957i	−0.419316	−	0.907840i	$-0.637730\pi$
$839$	−36.9940	−	11.4111i	−1.27718	−	0.393957i	−0.857860	+	0.513884i	$0.828206\pi$
$840$	2.09092	−	1.19240i	0.0721435	−	0.0411417i
$841$	17.1818	−	5.29989i	0.592476	−	0.182755i
$842$	3.80898	−	2.59692i	0.131266	−	0.0894957i
$843$	3.19537	−	2.02724i	0.110054	−	0.0698217i
$844$	12.7019	+	8.65999i	0.437216	+	0.298089i
$845$	−3.40583	+	8.67792i	−0.117164	+	0.298530i
$846$	6.12327	+	8.81534i	0.210522	+	0.303078i
$847$	23.1104	+	8.33849i	0.794083	+	0.286514i
$848$	−2.79655	+	1.90666i	−0.0960339	+	0.0654748i
$849$	48.3896	+	25.3058i	1.66073	+	0.868494i
$850$	2.87641	+	3.60690i	0.0986599	+	0.123716i
$851$	−4.60980			−0.158022
$852$	−0.113237	+	0.132748i	−0.00387945	+	0.00454789i
$853$	34.9719	−	5.27117i	1.19742	−	0.180481i	0.480090	−	0.877219i	$-0.340604\pi$
$853$	34.9719	−	5.27117i	1.19742	−	0.180481i	0.717326	+	0.696738i	$0.245366\pi$
$854$	32.4601	−	13.7900i	1.11076	−	0.471883i
$855$	7.62895	+	4.31647i	0.260904	+	0.147620i
$856$	−15.5835	−	2.34883i	−0.532632	−	0.0802813i
$857$	1.39564	+	18.6235i	0.0476741	+	0.636167i	0.968950	+	0.247257i	$0.0795292\pi$
$857$	1.39564	+	18.6235i	0.0476741	+	0.636167i	−0.921276	+	0.388910i	$0.872852\pi$
$858$	1.35341	−	12.5007i	0.0462048	−	0.426765i
$859$	13.2779	+	33.8315i	0.453036	+	1.15432i	0.956870	+	0.290516i	$0.0938270\pi$
$859$	13.2779	+	33.8315i	0.453036	+	1.15432i	−0.503834	+	0.863800i	$0.668078\pi$
$860$	5.36348	+	0.808414i	0.182893	+	0.0275667i
$861$	50.1837	−	11.1735i	1.71026	−	0.380791i
$862$	31.0147	−	4.67471i	1.05636	−	0.159221i
$863$	17.3136	+	29.9880i	0.589362	+	1.02080i	0.994316	+	0.106468i	$0.0339540\pi$
$863$	17.3136	+	29.9880i	0.589362	+	1.02080i	−0.404955	+	0.914337i	$0.632713\pi$
$864$	−4.43543	−	2.70684i	−0.150896	−	0.0920885i
$865$	7.46358	−	1.12495i	0.253769	−	0.0382496i
$866$	6.15567	+	26.9698i	0.209178	+	0.916470i
$867$	−22.4338	−	16.4066i	−0.761893	−	0.557197i
$868$	−0.338228	−	1.88735i	−0.0114802	−	0.0640609i
$869$	0.786162	+	0.535996i	0.0266687	+	0.0181824i
$870$	2.93775	+	5.50041i	0.0995990	+	0.186481i
$871$	−37.1349	−	25.3181i	−1.25827	−	0.857872i
$872$	6.40958	+	1.97709i	0.217056	+	0.0669529i
$873$	4.08323	+	4.32456i	0.138196	+	0.146364i
$874$	−9.16633	+	40.1603i	−0.310056	+	1.35844i
$875$	2.38376	+	13.3016i	0.0805857	+	0.449677i
$876$	18.7620	−	11.9031i	0.633908	−	0.402170i
$877$	4.24710	+	3.94073i	0.143414	+	0.133069i	0.748618	−	0.663002i	$-0.230718\pi$
$877$	4.24710	+	3.94073i	0.143414	+	0.133069i	−0.605204	+	0.796071i	$0.706908\pi$
$878$	−12.9365	+	16.2218i	−0.436584	+	0.547459i
$879$	−6.89036	+	15.9823i	−0.232406	+	0.539069i
$880$	0.619545	−	0.298357i	0.0208849	−	0.0100576i
$881$	26.5178			0.893409			0.446704	−	0.894682i	$-0.352598\pi$
$881$	26.5178			0.893409			0.446704	+	0.894682i	$0.352598\pi$
$882$	−20.1318	+	5.97593i	−0.677872	+	0.201220i
$883$	−35.0945			−1.18102			−0.590511	−	0.807029i	$-0.701074\pi$
$883$	−35.0945			−1.18102			−0.590511	+	0.807029i	$0.701074\pi$
$884$	4.87889	−	2.34955i	0.164095	−	0.0790239i
$885$	−3.93223	+	0.460396i	−0.132181	+	0.0154761i
$886$	8.67229	−	10.8747i	0.291351	−	0.365343i
$887$	−0.216709	−	0.201076i	−0.00727636	−	0.00675148i	0.676526	−	0.736419i	$-0.263485\pi$
$887$	−0.216709	−	0.201076i	−0.00727636	−	0.00675148i	−0.683803	+	0.729667i	$0.739675\pi$
$888$	−0.0450042	−	1.07726i	−0.00151024	−	0.0361505i
$889$	39.1030	+	1.84209i	1.31147	+	0.0617818i
$890$	0.302365	−	1.32475i	0.0101353	−	0.0444057i
$891$	−4.49489	−	10.8914i	−0.150585	−	0.364874i
$892$	0.936224	+	0.288787i	0.0313471	+	0.00966930i
$893$	16.4438	+	11.2112i	0.550269	+	0.375167i
$894$	−13.6917	+	22.0021i	−0.457917	+	0.735861i
$895$	−3.41456	−	2.32801i	−0.114136	−	0.0778167i
$896$	−1.74511	+	1.98862i	−0.0583000	+	0.0664350i
$897$	−65.0648	+	28.7252i	−2.17245	+	0.959107i
$898$	−4.51336	−	19.7743i	−0.150613	−	0.659877i
$899$	4.91190	−	0.740350i	0.163821	−	0.0246921i
$900$	11.0030	−	8.93241i	0.366768	−	0.297747i
$901$	−1.65268	−	2.86252i	−0.0550587	−	0.0953644i
$902$	14.5236	−	2.18908i	0.483583	−	0.0728884i
$903$	−43.9582	−	17.5229i	−1.46284	−	0.583124i
$904$	−10.6440	−	1.60432i	−0.354014	−	0.0533590i
$905$	3.84889	+	9.80681i	0.127941	+	0.325989i
$906$	−25.7215	−	18.8110i	−0.854540	−	0.624953i
$907$	1.63210	+	21.7789i	0.0541930	+	0.723155i	0.956439	+	0.291933i	$0.0942985\pi$
$907$	1.63210	+	21.7789i	0.0541930	+	0.723155i	−0.902246	+	0.431222i	$0.858082\pi$
$908$	−9.05428	−	1.36471i	−0.300477	−	0.0452896i
$909$	0.335611	+	38.5544i	0.0111315	+	1.27877i
$910$	7.69747	+	0.362618i	0.255169	+	0.0120207i
$911$	3.75143	−	0.565437i	0.124290	−	0.0187338i	−0.0866024	−	0.996243i	$-0.527601\pi$
$911$	3.75143	−	0.565437i	0.124290	−	0.0187338i	0.210893	+	0.977509i	$0.432363\pi$
$912$	−9.47453	−	1.75000i	−0.313733	−	0.0579483i
$913$	−11.9387			−0.395113
$914$	4.60860	+	5.77900i	0.152439	+	0.191152i
$915$	−10.2402	+	6.49669i	−0.338531	+	0.214774i
$916$	6.51594	−	4.44249i	0.215293	−	0.146784i
$917$	−37.1973	+	22.8737i	−1.22836	+	0.755356i
$918$	2.95970	−	4.12183i	0.0976848	−	0.136041i
$919$	−9.43310	+	24.0351i	−0.311169	+	0.792846i	0.686659	+	0.726979i	$0.259076\pi$
$919$	−9.43310	+	24.0351i	−0.311169	+	0.792846i	−0.997828	+	0.0658668i	$0.979019\pi$
$920$	−3.21380	−	2.19113i	−0.105956	−	0.0722395i
$921$	31.3833	+	16.4122i	1.03412	+	0.540801i
$922$	33.0333	−	22.5217i	1.08789	−	0.741713i
$923$	−0.533789	+	0.164652i	−0.0175699	+	0.00541959i
$924$	−5.85593	+	1.30383i	−0.192646	+	0.0428929i
$925$	2.81010	+	0.866802i	0.0923957	+	0.0285003i
$926$	28.6436	−	8.83537i	0.941286	−	0.290348i
$927$	4.29048	−	2.52716i	0.140918	−	0.0830029i
$928$	−5.02452	−	4.66207i	−0.164938	−	0.153040i
$929$	−29.3922	+	14.1545i	−0.964325	+	0.464395i	−0.848686	−	0.528897i	$-0.822606\pi$
$929$	−29.3922	+	14.1545i	−0.964325	+	0.464395i	−0.115639	+	0.993291i	$0.536892\pi$
$930$	0.220468	+	0.621372i	0.00722942	+	0.0203756i
$931$	−30.9074	+	23.6843i	−1.01295	+	0.776220i
$932$	−6.58297	−	11.4020i	−0.215632	−	0.373486i
$933$	−3.28734	+	12.4856i	−0.107623	+	0.408762i
$934$	13.0205	−	4.01631i	0.426045	−	0.131418i
$935$	0.245337	+	0.625108i	0.00802337	+	0.0204432i
$936$	−7.34799	−	14.9245i	−0.240176	−	0.487823i
$937$	3.67413	+	16.0974i	0.120029	+	0.525880i	0.998815	+	0.0486646i	$0.0154966\pi$
$937$	3.67413	+	16.0974i	0.120029	+	0.525880i	−0.878787	+	0.477215i	$0.841646\pi$
$938$	−5.75036	+	20.6591i	−0.187756	+	0.674544i
$939$	−6.14727	−	8.25382i	−0.200608	−	0.269353i
$940$	−1.55271	+	1.05862i	−0.0506437	+	0.0345283i
$941$	−9.83376	−	43.0845i	−0.320572	−	1.40452i	−0.836539	−	0.547907i	$-0.815425\pi$
$941$	−9.83376	−	43.0845i	−0.320572	−	1.40452i	0.515967	−	0.856608i	$-0.327433\pi$
$942$	−6.72919	+	25.5581i	−0.219249	+	0.832728i
$943$	−51.8003	−	64.9555i	−1.68685	−	2.11524i
$944$	3.92080	−	1.88816i	0.127611	−	0.0614543i
$945$	6.49532	−	3.15509i	0.211293	−	0.102635i
$946$	−12.1803	−	5.86570i	−0.396014	−	0.190710i
$947$	−3.70416	−	16.2290i	−0.120369	−	0.527371i	−0.998776	−	0.0494578i	$-0.984251\pi$
$947$	−3.70416	−	16.2290i	−0.120369	−	0.527371i	0.878407	−	0.477913i	$-0.158606\pi$
$948$	1.25816	+	0.0415944i	0.0408632	+	0.00135092i
$949$	71.1343			2.30912
$950$	13.1393	−	22.7579i	0.426294	−	0.738363i
$951$	33.7769	+	1.11665i	1.09529	+	0.0362099i
$952$	−1.80923	−	1.84457i	−0.0586373	−	0.0597830i
$953$	2.49512	−	3.12879i	0.0808250	−	0.101351i	−0.739775	−	0.672854i	$-0.765068\pi$
$953$	2.49512	−	3.12879i	0.0808250	−	0.101351i	0.820600	+	0.571503i	$0.193639\pi$
$954$	−8.74912	+	5.15337i	−0.283263	+	0.166846i
$955$	10.3936	−	7.08622i	0.336328	−	0.229305i
$956$	−0.527786	−	7.04282i	−0.0170698	−	0.227781i
$957$	−2.95591	−	15.2585i	−0.0955512	−	0.493238i
$958$	−3.30628	−	0.498342i	−0.106821	−	0.0161007i
$959$	1.34168	+	48.3784i	0.0433251	+	1.56222i
$960$	0.480669	−	0.772423i	0.0155135	−	0.0249298i
$961$	−30.4748			−0.983058
$962$	1.72591	−	2.98937i	0.0556457	−	0.0963811i
$963$	−46.1829	−	10.1188i	−1.48822	−	0.326074i
$964$	−0.0771511	+	0.0715857i	−0.00248487	+	0.00230562i
$965$	−3.65728	+	2.49349i	−0.117732	+	0.0802684i
$966$	22.9492	+	24.9989i	0.738379	+	0.804325i
$967$	18.6408	+	12.7091i	0.599448	+	0.408697i	0.824673	−	0.565610i	$-0.191359\pi$
$967$	18.6408	+	12.7091i	0.599448	+	0.408697i	−0.225225	+	0.974307i	$0.572312\pi$
$968$	9.18238	−	1.38402i	0.295133	−	0.0444841i
$969$	2.39565	−	9.09890i	0.0769593	−	0.292299i
$970$	−0.763360	+	0.708295i	−0.0245100	+	0.0227420i
$971$	0.747126	+	9.96970i	0.0239764	+	0.319943i	0.996277	+	0.0862092i	$0.0274754\pi$
$971$	0.747126	+	9.96970i	0.0239764	+	0.319943i	−0.972301	+	0.233734i	$0.924906\pi$
$972$	−12.7409	−	8.98163i	−0.408664	−	0.288086i
$973$	3.63377	−	8.11362i	0.116493	−	0.260111i
$974$	26.6408	+	8.21761i	0.853628	+	0.263309i
$975$	45.0644	−	5.27626i	1.44322	−	0.168976i
$976$	8.31111	−	10.4218i	0.266032	−	0.333594i
$977$	7.49346	−	32.8310i	0.239737	−	1.05036i	−0.701516	−	0.712654i	$-0.747493\pi$
$977$	7.49346	−	32.8310i	0.239737	−	1.05036i	0.941253	−	0.337702i	$-0.109650\pi$
$978$	3.63487	−	0.990935i	0.116230	−	0.0316866i
$979$	−1.69338	+	2.93301i	−0.0541205	+	0.0937395i
$980$	−1.01558	−	3.53375i	−0.0324414	−	0.112881i
$981$	18.7950	+	7.18833i	0.600079	+	0.229506i
$982$	−0.521250	−	0.355382i	−0.0166337	−	0.0113407i
$983$	−0.0861289	+	0.0265673i	−0.00274709	+	0.000847364i	−0.296128	−	0.955148i	$-0.595696\pi$
$983$	−0.0861289	+	0.0265673i	−0.00274709	+	0.000847364i	0.293381	+	0.955996i	$0.405219\pi$
$984$	14.6737	−	12.7393i	0.467780	−	0.406114i
$985$	7.97415	+	7.39893i	0.254078	+	0.235750i
$986$	4.90676	−	4.55281i	0.156263	−	0.144991i
$987$	15.2938	−	5.90863i	0.486806	−	0.188074i
$988$	−22.6113	−	20.9803i	−0.719362	−	0.667471i
$989$	5.71469	+	76.2572i	0.181716	+	2.42484i
$990$	1.91369	−	0.770360i	0.0608212	−	0.0244836i
$991$	3.65380	−	48.7566i	0.116067	−	1.54880i	−0.570232	−	0.821484i	$-0.693147\pi$
$991$	3.65380	−	48.7566i	0.116067	−	1.54880i	0.686299	−	0.727320i	$-0.259234\pi$
$992$	−0.451853	−	0.566606i	−0.0143464	−	0.0179898i
$993$	−1.05510	+	4.00738i	−0.0334826	+	0.127170i
$994$	0.156189	+	0.215970i	0.00495400	+	0.00685015i
$995$	0.620964	+	8.28619i	0.0196859	+	0.262690i
$996$	−13.3375	+	8.46167i	−0.422614	+	0.268118i
$997$	−15.8260	+	40.3240i	−0.501214	+	1.27707i	0.426739	+	0.904375i	$0.359662\pi$
$997$	−15.8260	+	40.3240i	−0.501214	+	1.27707i	−0.927953	+	0.372698i	$0.878433\pi$
$998$	−4.70734	+	8.15335i	−0.149008	+	0.258090i
$999$	0.0787320	−	3.23364i	0.00249097	−	0.102308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bb.a.151.20	yes	336
9.4	even	3		882.2.y.b.445.23	yes	336
49.37	even	21		882.2.y.b.331.23	✓	336
441.184	even	21	inner	882.2.bb.a.625.20	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.y.b.331.23	✓	336	49.37	even	21
882.2.y.b.445.23	yes	336	9.4	even	3
882.2.bb.a.151.20	yes	336	1.1	even	1	trivial
882.2.bb.a.625.20	yes	336	441.184	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)

\(f(q)\)	\(=\)	\(q+(-0.900969 + 0.433884i) q^{2} +(1.03458 + 1.38911i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.385039 + 0.357264i) q^{5} +(-1.53484 - 0.802661i) q^{6} +(-1.74511 + 1.98862i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-0.859279 + 2.87431i) q^{9} +O(q^{10})\)	\(q+(-0.900969 + 0.433884i) q^{2} +(1.03458 + 1.38911i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.385039 + 0.357264i) q^{5} +(-1.53484 - 0.802661i) q^{6} +(-1.74511 + 1.98862i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-0.859279 + 2.87431i) q^{9} +(-0.501920 - 0.154822i) q^{10} +(1.08168 + 0.737476i) q^{11} +(1.73111 + 0.0572297i) q^{12} +(4.58158 + 3.12367i) q^{13} +(0.709461 - 2.54886i) q^{14} +(-0.0979261 + 0.904483i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(0.965657 - 0.145549i) q^{17} +(-0.472932 - 2.96249i) q^{18} +(-2.78132 - 4.81739i) q^{19} +(0.519389 - 0.0782852i) q^{20} +(-4.56787 - 0.366770i) q^{21} +(-1.29454 - 0.195120i) q^{22} +(2.70546 + 6.89340i) q^{23} +(-1.58450 + 0.699536i) q^{24} +(-0.353033 - 4.71090i) q^{25} +(-5.48317 - 0.826455i) q^{26} +(-4.88174 + 1.78007i) q^{27} +(0.466704 + 2.60426i) q^{28} +(-6.77769 + 1.02157i) q^{29} +(-0.304212 - 0.857400i) q^{30} -0.724717 q^{31} +(0.623490 + 0.781831i) q^{32} +(0.0946470 + 2.26556i) q^{33} +(-0.806876 + 0.550118i) q^{34} +(-1.38240 + 0.142230i) q^{35} +(1.71147 + 2.46391i) q^{36} +(-0.227425 + 0.579468i) q^{37} +(4.59608 + 3.13355i) q^{38} +(0.400889 + 9.59604i) q^{39} +(-0.433986 + 0.295887i) q^{40} +(-10.7207 + 3.30690i) q^{41} +(4.27465 - 1.65148i) q^{42} +(9.86774 + 3.04379i) q^{43} +(1.25100 - 0.385882i) q^{44} +(-1.35774 + 0.799732i) q^{45} +(-5.42847 - 5.03689i) q^{46} +(-3.22347 + 1.55234i) q^{47} +(1.12407 - 1.31775i) q^{48} +(-0.909186 - 6.94070i) q^{49} +(2.36205 + 4.09120i) q^{50} +(1.20124 + 1.19083i) q^{51} +(5.29875 - 1.63445i) q^{52} +(-1.23656 - 3.15071i) q^{53} +(3.62595 - 3.72189i) q^{54} +(0.153015 + 0.670402i) q^{55} +(-1.55043 - 2.14386i) q^{56} +(3.81440 - 8.84757i) q^{57} +(5.66324 - 3.86113i) q^{58} +(0.968357 + 4.24265i) q^{59} +(0.646097 + 0.640498i) q^{60} +(8.31111 + 10.4218i) q^{61} +(0.652947 - 0.314443i) q^{62} +(-4.21636 - 6.72476i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(0.648114 + 2.83957i) q^{65} +(-1.06826 - 2.00013i) q^{66} -8.10525 q^{67} +(0.488282 - 0.845730i) q^{68} +(-6.77671 + 10.8900i) q^{69} +(1.18379 - 0.727944i) q^{70} +(-0.0628095 + 0.0787607i) q^{71} +(-2.61103 - 1.47733i) q^{72} +(10.5992 - 7.22644i) q^{73} +(-0.0465194 - 0.620759i) q^{74} +(6.17873 - 5.36421i) q^{75} +(-5.50052 - 0.829070i) q^{76} +(-3.35420 + 0.864067i) q^{77} +(-4.52475 - 8.47179i) q^{78} +0.726798 q^{79} +(0.262628 - 0.454884i) q^{80} +(-7.52328 - 4.93966i) q^{81} +(8.22421 - 7.63095i) q^{82} +(-7.53476 + 5.13712i) q^{83} +(-3.13478 + 3.34263i) q^{84} +(0.423816 + 0.288953i) q^{85} +(-10.2112 + 1.53909i) q^{86} +(-8.43115 - 8.35808i) q^{87} +(-0.959682 + 0.890455i) q^{88} +(0.193324 + 2.57973i) q^{89} +(0.876294 - 1.30964i) q^{90} +(-14.2071 + 3.65986i) q^{91} +(7.07631 + 2.18275i) q^{92} +(-0.749779 - 1.00671i) q^{93} +(2.23071 - 2.79722i) q^{94} +(0.650164 - 2.84855i) q^{95} +(-0.441002 + 1.67497i) q^{96} +(0.991276 - 1.71694i) q^{97} +(3.83061 + 5.85888i) q^{98} +(-3.04920 + 2.47538i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 56 q^{2} - 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} - 56 q^{8} - 15 q^{9}+O(q^{10}) \) 336 * q - 56 * q^2 - 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 - 56 * q^8 - 15 * q^9	\( 336 q - 56 q^{2} - 5 q^{3} - 56 q^{4} + 2 q^{5} - 5 q^{6} - 56 q^{8} - 15 q^{9} + 2 q^{10} + 2 q^{12} - 21 q^{13} - 7 q^{15} - 56 q^{16} + 7 q^{17} + 6 q^{18} - 34 q^{19} + 2 q^{20} + 16 q^{21} - 36 q^{23} + 2 q^{24} + 32 q^{25} + 7 q^{26} + 49 q^{27} - 16 q^{29} - 7 q^{30} + 92 q^{31} - 56 q^{32} + 14 q^{33} + 7 q^{34} + 16 q^{35} - 15 q^{36} - 26 q^{37} + q^{38} + 44 q^{39} + 2 q^{40} + 3 q^{41} - 33 q^{42} - 3 q^{43} + 106 q^{45} - 36 q^{46} + 27 q^{47} + 2 q^{48} - 74 q^{49} - 164 q^{50} - 7 q^{51} + 21 q^{52} - 78 q^{53} - 28 q^{54} - 53 q^{55} - 18 q^{57} + 40 q^{58} - 16 q^{59} - 7 q^{60} - 45 q^{61} - 20 q^{62} - 50 q^{63} - 56 q^{64} - 14 q^{65} + 14 q^{66} + 86 q^{67} - 21 q^{68} - 85 q^{69} - 26 q^{70} + 7 q^{71} + 6 q^{72} + 36 q^{73} + 2 q^{74} - 35 q^{75} + 8 q^{76} - 37 q^{77} - 12 q^{78} - 2 q^{79} - 12 q^{80} + 41 q^{81} + 3 q^{82} + 191 q^{83} - 5 q^{84} + 159 q^{85} - 3 q^{86} + 72 q^{87} + 59 q^{89} + 22 q^{90} - 29 q^{91} + 27 q^{92} + 23 q^{93} + 6 q^{94} + 26 q^{95} + 2 q^{96} - 113 q^{97} - 18 q^{98} - 33 q^{99}+O(q^{100}) \) 336 * q - 56 * q^2 - 5 * q^3 - 56 * q^4 + 2 * q^5 - 5 * q^6 - 56 * q^8 - 15 * q^9 + 2 * q^10 + 2 * q^12 - 21 * q^13 - 7 * q^15 - 56 * q^16 + 7 * q^17 + 6 * q^18 - 34 * q^19 + 2 * q^20 + 16 * q^21 - 36 * q^23 + 2 * q^24 + 32 * q^25 + 7 * q^26 + 49 * q^27 - 16 * q^29 - 7 * q^30 + 92 * q^31 - 56 * q^32 + 14 * q^33 + 7 * q^34 + 16 * q^35 - 15 * q^36 - 26 * q^37 + q^38 + 44 * q^39 + 2 * q^40 + 3 * q^41 - 33 * q^42 - 3 * q^43 + 106 * q^45 - 36 * q^46 + 27 * q^47 + 2 * q^48 - 74 * q^49 - 164 * q^50 - 7 * q^51 + 21 * q^52 - 78 * q^53 - 28 * q^54 - 53 * q^55 - 18 * q^57 + 40 * q^58 - 16 * q^59 - 7 * q^60 - 45 * q^61 - 20 * q^62 - 50 * q^63 - 56 * q^64 - 14 * q^65 + 14 * q^66 + 86 * q^67 - 21 * q^68 - 85 * q^69 - 26 * q^70 + 7 * q^71 + 6 * q^72 + 36 * q^73 + 2 * q^74 - 35 * q^75 + 8 * q^76 - 37 * q^77 - 12 * q^78 - 2 * q^79 - 12 * q^80 + 41 * q^81 + 3 * q^82 + 191 * q^83 - 5 * q^84 + 159 * q^85 - 3 * q^86 + 72 * q^87 + 59 * q^89 + 22 * q^90 - 29 * q^91 + 27 * q^92 + 23 * q^93 + 6 * q^94 + 26 * q^95 + 2 * q^96 - 113 * q^97 - 18 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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