LMFDB - Embedded newform 882.2.bb.b.151.2

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			151.2
Character	$\chi$	$=$	882.151
Dual form			882.2.bb.b.625.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 - 0.433884i) q^{2} +(-1.71205 - 0.262484i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.07432 - 1.92469i) q^{5} +(-1.65639 + 0.506339i) q^{6} +(-0.0394492 - 2.64546i) q^{7} +(0.222521 - 0.974928i) q^{8} +(2.86220 + 0.898770i) q^{9} +O(q^{10})$	\(q+(0.900969 - 0.433884i) q^{2} +(-1.71205 - 0.262484i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.07432 - 1.92469i) q^{5} +(-1.65639 + 0.506339i) q^{6} +(-0.0394492 - 2.64546i) q^{7} +(0.222521 - 0.974928i) q^{8} +(2.86220 + 0.898770i) q^{9} +(-2.70399 - 0.834070i) q^{10} +(-4.40359 - 3.00232i) q^{11} +(-1.27266 + 1.17488i) q^{12} +(2.98387 + 2.03437i) q^{13} +(-1.18336 - 2.36636i) q^{14} +(3.04613 + 3.83963i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-7.16964 + 1.08065i) q^{17} +(2.96872 - 0.432100i) q^{18} +(3.55369 + 6.15517i) q^{19} +(-2.79810 + 0.421745i) q^{20} +(-0.626852 + 4.53950i) q^{21} +(-5.27016 - 0.794349i) q^{22} +(0.0838262 + 0.213586i) q^{23} +(-0.636869 + 1.61071i) q^{24} +(0.224730 + 2.99881i) q^{25} +(3.57105 + 0.538250i) q^{26} +(-4.66431 - 2.29002i) q^{27} +(-2.09290 - 1.61857i) q^{28} +(8.78435 - 1.32403i) q^{29} +(4.41042 + 2.13772i) q^{30} -2.27432 q^{31} +(-0.623490 - 0.781831i) q^{32} +(6.75110 + 6.29599i) q^{33} +(-5.99074 + 4.08442i) q^{34} +(-5.00985 + 5.56345i) q^{35} +(2.48724 - 1.67739i) q^{36} +(0.419744 - 1.06949i) q^{37} +(5.87239 + 4.00373i) q^{38} +(-4.57454 - 4.26615i) q^{39} +(-2.33801 + 1.59403i) q^{40} +(-9.16683 + 2.82759i) q^{41} +(1.40484 + 4.36193i) q^{42} +(-10.7199 - 3.30666i) q^{43} +(-5.09290 + 1.57095i) q^{44} +(-4.20727 - 7.37318i) q^{45} +(0.168196 + 0.156063i) q^{46} +(-4.08753 + 1.96845i) q^{47} +(0.125063 + 1.72753i) q^{48} +(-6.99689 + 0.208722i) q^{49} +(1.50361 + 2.60433i) q^{50} +(12.5584 + 0.0317963i) q^{51} +(3.45095 - 1.06448i) q^{52} +(4.29986 + 10.9559i) q^{53} +(-5.19600 - 0.0394676i) q^{54} +(3.35594 + 14.7033i) q^{55} +(-2.58791 - 0.550210i) q^{56} +(-4.46844 - 11.4707i) q^{57} +(7.33995 - 5.00429i) q^{58} +(-1.59138 - 6.97230i) q^{59} +(4.90117 + 0.0124092i) q^{60} +(-0.377083 - 0.472847i) q^{61} +(-2.04910 + 0.986793i) q^{62} +(2.26475 - 7.60729i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-2.27398 - 9.96295i) q^{65} +(8.81425 + 2.74330i) q^{66} -1.62597 q^{67} +(-3.62531 + 6.27922i) q^{68} +(-0.0874515 - 0.387672i) q^{69} +(-2.09983 + 7.18619i) q^{70} +(-0.944023 + 1.18377i) q^{71} +(1.51314 - 2.59045i) q^{72} +(-3.69693 + 2.52052i) q^{73} +(-0.0858581 - 1.14570i) q^{74} +(0.402393 - 5.19309i) q^{75} +(7.02799 + 1.05930i) q^{76} +(-7.76879 + 11.7680i) q^{77} +(-5.97253 - 1.85885i) q^{78} +5.89897 q^{79} +(-1.41485 + 2.45060i) q^{80} +(7.38442 + 5.14493i) q^{81} +(-7.03218 + 6.52491i) q^{82} +(7.19001 - 4.90207i) q^{83} +(3.15829 + 3.32042i) q^{84} +(16.9520 + 11.5577i) q^{85} +(-11.0930 + 1.67200i) q^{86} +(-15.3867 - 0.0389573i) q^{87} +(-3.90694 + 3.62511i) q^{88} +(-0.552959 - 7.37872i) q^{89} +(-6.98973 - 4.81754i) q^{90} +(5.26412 - 7.97396i) q^{91} +(0.219253 + 0.0676305i) q^{92} +(3.89375 + 0.596975i) q^{93} +(-2.82866 + 3.54702i) q^{94} +(4.47529 - 19.6075i) q^{95} +(0.862225 + 1.50219i) q^{96} +(3.66044 - 6.34007i) q^{97} +(-6.21342 + 3.22389i) q^{98} +(-9.90559 - 12.5511i) 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 $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

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

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
$3$	−1.71205	−	0.262484i	−0.988450	−	0.151545i
$3$	−1.71205	−	0.262484i	−0.988450	−	0.151545i
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	−2.07432	−	1.92469i	−0.927664	−	0.860746i	0.0628691	−	0.998022i	$-0.479975\pi$
$5$	−2.07432	−	1.92469i	−0.927664	−	0.860746i	−0.990533	+	0.137276i	$0.956165\pi$
$6$	−1.65639	+	0.506339i	−0.676218	+	0.206712i
$7$	−0.0394492	−	2.64546i	−0.0149104	−	0.999889i
$7$	−0.0394492	−	2.64546i	−0.0149104	−	0.999889i
$8$	0.222521	−	0.974928i	0.0786730	−	0.344689i
$9$	2.86220	+	0.898770i	0.954068	+	0.299590i
$10$	−2.70399	−	0.834070i	−0.855076	−	0.263756i
$11$	−4.40359	−	3.00232i	−1.32773	−	0.905234i	−0.328505	−	0.944502i	$-0.606545\pi$
$11$	−4.40359	−	3.00232i	−1.32773	−	0.905234i	−0.999229	+	0.0392686i	$0.987497\pi$
$12$	−1.27266	+	1.17488i	−0.367386	+	0.339157i
$13$	2.98387	+	2.03437i	0.827577	+	0.564232i	0.901374	−	0.433041i	$-0.142559\pi$
$13$	2.98387	+	2.03437i	0.827577	+	0.564232i	−0.0737973	+	0.997273i	$0.523512\pi$
$14$	−1.18336	−	2.36636i	−0.316267	−	0.632436i
$15$	3.04613	+	3.83963i	0.786507	+	0.991388i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	−7.16964	+	1.08065i	−1.73889	+	0.262096i	−0.940439	−	0.339961i	$-0.889586\pi$
$17$	−7.16964	+	1.08065i	−1.73889	+	0.262096i	−0.798453	+	0.602057i	$0.794348\pi$
$18$	2.96872	−	0.432100i	0.699734	−	0.101847i
$19$	3.55369	+	6.15517i	0.815272	+	1.41209i	0.909132	+	0.416508i	$0.136746\pi$
$19$	3.55369	+	6.15517i	0.815272	+	1.41209i	−0.0938600	+	0.995585i	$0.529921\pi$
$20$	−2.79810	+	0.421745i	−0.625674	+	0.0943051i
$21$	−0.626852	+	4.53950i	−0.136790	+	0.990600i
$22$	−5.27016	−	0.794349i	−1.12360	−	0.169356i
$23$	0.0838262	+	0.213586i	0.0174790	+	0.0445357i	0.939347	−	0.342969i	$-0.111432\pi$
$23$	0.0838262	+	0.213586i	0.0174790	+	0.0445357i	−0.921868	+	0.387504i	$0.873337\pi$
$24$	−0.636869	+	1.61071i	−0.130000	+	0.328785i
$25$	0.224730	+	2.99881i	0.0449460	+	0.599763i
$26$	3.57105	+	0.538250i	0.700341	+	0.105559i
$27$	−4.66431	−	2.29002i	−0.897647	−	0.440715i
$28$	−2.09290	−	1.61857i	−0.395521	−	0.305882i
$29$	8.78435	−	1.32403i	1.63121	−	0.245866i	0.731338	−	0.682015i	$-0.238896\pi$
$29$	8.78435	−	1.32403i	1.63121	−	0.245866i	0.899874	+	0.436149i	$0.143658\pi$
$30$	4.41042	+	2.13772i	0.805229	+	0.390293i
$31$	−2.27432			−0.408481			−0.204240	−	0.978921i	$-0.565472\pi$
$31$	−2.27432			−0.408481			−0.204240	+	0.978921i	$0.565472\pi$
$32$	−0.623490	−	0.781831i	−0.110218	−	0.138210i
$33$	6.75110	+	6.29599i	1.17521	+	1.09599i
$34$	−5.99074	+	4.08442i	−1.02740	+	0.700472i
$35$	−5.00985	+	5.56345i	−0.846819	+	0.940395i
$36$	2.48724	−	1.67739i	0.414540	−	0.279564i
$37$	0.419744	−	1.06949i	0.0690054	−	0.175823i	−0.892211	−	0.451620i	$-0.850846\pi$
$37$	0.419744	−	1.06949i	0.0690054	−	0.175823i	0.961216	+	0.275797i	$0.0889416\pi$
$38$	5.87239	+	4.00373i	0.952628	+	0.649491i
$39$	−4.57454	−	4.26615i	−0.732512	−	0.683131i
$40$	−2.33801	+	1.59403i	−0.369672	+	0.252038i
$41$	−9.16683	+	2.82759i	−1.43162	+	0.441596i	−0.911075	−	0.412240i	$-0.864746\pi$
$41$	−9.16683	+	2.82759i	−1.43162	+	0.441596i	−0.520543	+	0.853836i	$0.674270\pi$
$42$	1.40484	+	4.36193i	0.216772	+	0.673060i
$43$	−10.7199	−	3.30666i	−1.63477	−	0.504260i	−0.664706	−	0.747105i	$-0.731443\pi$
$43$	−10.7199	−	3.30666i	−1.63477	−	0.504260i	−0.970065	+	0.242845i	$0.921920\pi$
$44$	−5.09290	+	1.57095i	−0.767784	+	0.236830i
$45$	−4.20727	−	7.37318i	−0.627183	−	1.09913i
$46$	0.168196	+	0.156063i	0.0247992	+	0.0230103i
$47$	−4.08753	+	1.96845i	−0.596227	+	0.287128i	−0.707558	−	0.706656i	$-0.750203\pi$
$47$	−4.08753	+	1.96845i	−0.596227	+	0.287128i	0.111331	+	0.993783i	$0.464489\pi$
$48$	0.125063	+	1.72753i	0.0180513	+	0.249347i
$49$	−6.99689	+	0.208722i	−0.999555	+	0.0298174i
$50$	1.50361	+	2.60433i	0.212643	+	0.368308i
$51$	12.5584	+	0.0317963i	1.75853	+	0.00445238i
$52$	3.45095	−	1.06448i	0.478560	−	0.147616i
$53$	4.29986	+	10.9559i	0.590632	+	1.50491i	0.843350	+	0.537365i	$0.180580\pi$
$53$	4.29986	+	10.9559i	0.590632	+	1.50491i	−0.252718	+	0.967540i	$0.581324\pi$
$54$	−5.19600	−	0.0394676i	−0.707086	−	0.00537086i
$55$	3.35594	+	14.7033i	0.452514	+	1.98259i
$56$	−2.58791	−	0.550210i	−0.345824	−	0.0735248i
$57$	−4.46844	−	11.4707i	−0.591860	−	1.51933i
$58$	7.33995	−	5.00429i	0.963783	−	0.657096i
$59$	−1.59138	−	6.97230i	−0.207180	−	0.907717i	−0.966433	−	0.256920i	$-0.917292\pi$
$59$	−1.59138	−	6.97230i	−0.207180	−	0.907717i	0.759252	−	0.650797i	$-0.225565\pi$
$60$	4.90117	+	0.0124092i	0.632739	+	0.00160202i
$61$	−0.377083	−	0.472847i	−0.0482805	−	0.0605418i	0.757105	−	0.653293i	$-0.226613\pi$
$61$	−0.377083	−	0.472847i	−0.0482805	−	0.0605418i	−0.805385	+	0.592751i	$0.798042\pi$
$62$	−2.04910	+	0.986793i	−0.260235	+	0.125323i
$63$	2.26475	−	7.60729i	0.285331	−	0.958429i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	−2.27398	−	9.96295i	−0.282052	−	1.23575i
$66$	8.81425	+	2.74330i	1.08496	+	0.337676i
$67$	−1.62597			−0.198643			−0.0993216	−	0.995055i	$-0.531667\pi$
$67$	−1.62597			−0.198643			−0.0993216	+	0.995055i	$0.531667\pi$
$68$	−3.62531	+	6.27922i	−0.439633	+	0.761468i
$69$	−0.0874515	−	0.387672i	−0.0105279	−	0.0466702i
$70$	−2.09983	+	7.18619i	−0.250977	+	0.858914i
$71$	−0.944023	+	1.18377i	−0.112035	+	0.140487i	−0.834687	−	0.550725i	$-0.814351\pi$
$71$	−0.944023	+	1.18377i	−0.112035	+	0.140487i	0.722652	+	0.691212i	$0.242923\pi$
$72$	1.51314	−	2.59045i	0.178325	−	0.305287i
$73$	−3.69693	+	2.52052i	−0.432693	+	0.295005i	−0.760012	−	0.649909i	$-0.774807\pi$
$73$	−3.69693	+	2.52052i	−0.432693	+	0.295005i	0.327319	+	0.944914i	$0.393855\pi$
$74$	−0.0858581	−	1.14570i	−0.00998080	−	0.133185i
$75$	0.402393	−	5.19309i	0.0464644	−	0.599647i
$76$	7.02799	+	1.05930i	0.806166	+	0.121510i
$77$	−7.76879	+	11.7680i	−0.885336	+	1.34108i
$78$	−5.97253	−	1.85885i	−0.676256	−	0.210474i
$79$	5.89897			0.663686			0.331843	−	0.943335i	$-0.392330\pi$
$79$	5.89897			0.663686			0.331843	+	0.943335i	$0.392330\pi$
$80$	−1.41485	+	2.45060i	−0.158185	+	0.273985i
$81$	7.38442	+	5.14493i	0.820491	+	0.571659i
$82$	−7.03218	+	6.52491i	−0.776574	+	0.720556i
$83$	7.19001	−	4.90207i	0.789207	−	0.538072i	−0.100320	−	0.994955i	$-0.531987\pi$
$83$	7.19001	−	4.90207i	0.789207	−	0.538072i	0.889527	+	0.456883i	$0.151034\pi$
$84$	3.15829	+	3.32042i	0.344597	+	0.362288i
$85$	16.9520	+	11.5577i	1.83871	+	1.25361i
$86$	−11.0930	+	1.67200i	−1.19619	+	0.180297i
$87$	−15.3867	−	0.0389573i	−1.64963	−	0.00417666i
$88$	−3.90694	+	3.62511i	−0.416481	+	0.386438i
$89$	−0.552959	−	7.37872i	−0.0586135	−	0.782143i	−0.946628	−	0.322328i	$-0.895535\pi$
$89$	−0.552959	−	7.37872i	−0.0586135	−	0.782143i	0.888015	−	0.459815i	$-0.152084\pi$
$90$	−6.98973	−	4.81754i	−0.736782	−	0.507814i
$91$	5.26412	−	7.97396i	0.551830	−	0.835898i
$92$	0.219253	+	0.0676305i	0.0228587	+	0.00705097i
$93$	3.89375	+	0.596975i	0.403763	+	0.0619034i
$94$	−2.82866	+	3.54702i	−0.291754	+	0.365847i
$95$	4.47529	−	19.6075i	0.459155	−	2.01169i
$96$	0.862225	+	1.50219i	0.0880005	+	0.153316i
$97$	3.66044	−	6.34007i	0.371661	−	0.643737i	−0.618160	−	0.786052i	$-0.712122\pi$
$97$	3.66044	−	6.34007i	0.371661	−	0.643737i	0.989821	+	0.142316i	$0.0454549\pi$
$98$	−6.21342	+	3.22389i	−0.627650	+	0.325662i
$99$	−9.90559	−	12.5511i	−0.995549	−	1.26143i
$100$	2.48468	+	1.69403i	0.248468	+	0.169403i
$101$	4.77352	−	1.47244i	0.474983	−	0.146513i	−0.0480150	−	0.998847i	$-0.515290\pi$
$101$	4.77352	−	1.47244i	0.474983	−	0.146513i	0.522998	+	0.852334i	$0.324813\pi$
$102$	11.3285	−	5.42024i	1.12169	−	0.536684i
$103$	−2.31814	−	2.15092i	−0.228414	−	0.211937i	0.557660	−	0.830069i	$-0.311699\pi$
$103$	−2.31814	−	2.15092i	−0.228414	−	0.211937i	−0.786074	+	0.618132i	$0.787890\pi$
$104$	2.64734	−	2.45637i	0.259593	−	0.240867i
$105$	10.0374	−	8.20988i	0.979551	−	0.801202i
$106$	8.62762	+	8.00526i	0.837989	+	0.777540i
$107$	−1.32931	−	17.7384i	−0.128509	−	1.71483i	−0.573424	−	0.819259i	$-0.694385\pi$
$107$	−1.32931	−	17.7384i	−0.128509	−	1.71483i	0.444915	−	0.895573i	$-0.353234\pi$
$108$	−4.69856	+	2.21890i	−0.452119	+	0.213514i
$109$	1.03694	−	13.8371i	0.0993213	−	1.32535i	−0.695508	−	0.718518i	$-0.744821\pi$
$109$	1.03694	−	13.8371i	0.0993213	−	1.32535i	0.794830	−	0.606833i	$-0.207560\pi$
$110$	9.40312	+	11.7911i	0.896552	+	1.12424i
$111$	−0.999345	+	1.72084i	−0.0948536	+	0.163335i
$112$	−2.57035	+	0.627130i	−0.242875	+	0.0592582i
$113$	0.371725	+	4.96033i	0.0349690	+	0.466629i	0.987010	+	0.160658i	$0.0513618\pi$
$113$	0.371725	+	4.96033i	0.0349690	+	0.466629i	−0.952041	+	0.305970i	$0.901019\pi$
$114$	−9.00289	−	8.39598i	−0.843198	−	0.786355i
$115$	0.237203	−	0.604384i	0.0221193	−	0.0563591i
$116$	4.44178	−	7.69340i	0.412409	−	0.714314i
$117$	6.71202	+	8.50459i	0.620526	+	0.786250i
$118$	−4.45896	−	5.59135i	−0.410480	−	0.514726i
$119$	3.14165	+	18.9243i	0.287994	+	1.73479i
$120$	4.42119	−	2.11536i	0.403598	−	0.193105i
$121$	6.35897	+	16.2024i	0.578088	+	1.47294i
$122$	−0.544900	−	0.262410i	−0.0493330	−	0.0237575i
$123$	16.4362	−	2.43482i	1.48200	−	0.219540i
$124$	−1.41802	+	1.77814i	−0.127342	+	0.159682i
$125$	−3.51584	+	4.40873i	−0.314466	+	0.394328i
$126$	−1.26021	−	7.83657i	−0.112269	−	0.698137i
$127$	−11.2417	−	14.0966i	−0.997537	−	1.25087i	−0.967907	−	0.251310i	$-0.919138\pi$
$127$	−11.2417	−	14.0966i	−0.997537	−	1.25087i	−0.0296302	−	0.999561i	$-0.509433\pi$
$128$	−1.00000			−0.0883883
$129$	17.4850	+	8.47496i	1.53947	+	0.746178i
$130$	−6.37155	−	7.98967i	−0.558822	−	0.700740i
$131$	−4.53315	−	1.39829i	−0.396063	−	0.122169i	0.0903248	−	0.995912i	$-0.471209\pi$
$131$	−4.53315	−	1.39829i	−0.396063	−	0.122169i	−0.486388	+	0.873743i	$0.661686\pi$
$132$	9.13164	−	1.35274i	0.794807	−	0.117741i
$133$	16.1430	−	9.64395i	1.39978	−	0.836236i
$134$	−1.46494	+	0.705480i	−0.126552	+	0.0609442i
$135$	5.26770	+	13.7276i	0.453372	+	1.18148i
$136$	−0.541840	+	7.23035i	−0.0464624	+	0.619997i
$137$	−8.47896	+	7.86733i	−0.724407	+	0.672151i	−0.953548	−	0.301242i	$-0.902599\pi$
$137$	−8.47896	+	7.86733i	−0.724407	+	0.672151i	0.229141	+	0.973393i	$0.426408\pi$
$138$	−0.246995	−	0.311336i	−0.0210257	−	0.0265027i
$139$	8.69674	−	2.68259i	0.737648	−	0.227534i	0.0969091	−	0.995293i	$-0.469104\pi$
$139$	8.69674	−	2.68259i	0.737648	−	0.227534i	0.640739	+	0.767759i	$0.278628\pi$
$140$	1.22609	+	7.38561i	0.103624	+	0.624198i
$141$	7.51472	−	2.29716i	0.632854	−	0.193456i
$142$	−0.336918	+	1.47613i	−0.0282735	+	0.123874i
$143$	−7.03193	−	17.9171i	−0.588040	−	1.49830i
$144$	0.239336	−	2.99044i	0.0199447	−	0.249203i
$145$	−20.7699	−	14.1607i	−1.72484	−	1.17598i
$146$	−2.23720	+	3.87495i	−0.185152	+	0.320693i
$147$	12.0338	+	1.47923i	0.992529	+	0.122005i
$148$	−0.574455	−	0.994985i	−0.0472199	−	0.0817872i
$149$	0.322187	−	4.29928i	0.0263945	−	0.352211i	−0.968333	−	0.249661i	$-0.919681\pi$
$149$	0.322187	−	4.29928i	0.0263945	−	0.352211i	0.994728	−	0.102550i	$-0.0327001\pi$
$150$	−1.89066	−	4.85341i	−0.154371	−	0.396279i
$151$	−5.37373	−	0.809959i	−0.437308	−	0.0659135i	−0.0733010	−	0.997310i	$-0.523353\pi$
$151$	−5.37373	−	0.809959i	−0.437308	−	0.0659135i	−0.364007	+	0.931396i	$0.618591\pi$
$152$	6.79162	−	2.09494i	0.550873	−	0.169922i
$153$	−21.4922	−	3.35082i	−1.73754	−	0.270898i
$154$	−1.89351	+	13.9733i	−0.152584	+	1.12600i
$155$	4.71768	+	4.37736i	0.378933	+	0.351598i
$156$	−6.18759	+	0.916613i	−0.495404	+	0.0733878i
$157$	0.517720	+	2.26828i	0.0413185	+	0.181028i	0.991376	−	0.131046i	$-0.0418335\pi$
$157$	0.517720	+	2.26828i	0.0413185	+	0.181028i	−0.950058	+	0.312074i	$0.898976\pi$
$158$	5.31479	−	2.55947i	0.422822	−	0.203620i
$159$	−4.48582	−	19.8856i	−0.355749	−	1.57703i
$160$	−0.211464	+	2.82179i	−0.0167177	+	0.223082i
$161$	0.561725	−	0.230184i	0.0442701	−	0.0181411i
$162$	8.88544	+	1.43144i	0.698106	+	0.112464i
$163$	−9.58397	+	8.89262i	−0.750674	+	0.696524i	−0.959588	−	0.281410i	$-0.909198\pi$
$163$	−9.58397	+	8.89262i	−0.750674	+	0.696524i	0.208913	+	0.977934i	$0.433007\pi$
$164$	−3.50472	+	8.92989i	−0.273673	+	0.697307i
$165$	−1.88613	−	26.0536i	−0.146835	−	2.02827i
$166$	4.35105	−	7.53624i	0.337707	−	0.584926i
$167$	0.836343	−	2.13097i	0.0647182	−	0.164899i	−0.894856	−	0.446355i	$-0.852722\pi$
$167$	0.836343	−	2.13097i	0.0647182	−	0.164899i	0.959574	+	0.281456i	$0.0908172\pi$
$168$	4.28620	+	1.62127i	0.330687	+	0.125084i
$169$	0.0153973	+	0.0392316i	0.00118441	+	0.00301782i
$170$	20.2879	+	3.05792i	1.55601	+	0.234531i
$171$	4.63930	+	20.8113i	0.354776	+	1.59148i
$172$	−9.26900	+	6.31950i	−0.706755	+	0.481857i
$173$	−3.28843	+	4.12356i	−0.250015	+	0.313508i	−0.890963	−	0.454075i	$-0.849970\pi$
$173$	−3.28843	+	4.12356i	−0.250015	+	0.313508i	0.640949	+	0.767584i	$0.278541\pi$
$174$	−13.8799	+	6.64096i	−1.05223	+	0.503450i
$175$	7.92437	−	0.712814i	0.599026	−	0.0538837i
$176$	−1.94715	+	4.96127i	−0.146772	+	0.373970i
$177$	0.894401	+	12.3546i	0.0672273	+	0.928630i
$178$	−3.69971	−	6.40808i	−0.277305	−	0.480306i
$179$	10.6801	−	1.60977i	0.798270	−	0.120320i	0.262774	−	0.964857i	$-0.415363\pi$
$179$	10.6801	−	1.60977i	0.798270	−	0.120320i	0.535496	+	0.844538i	$0.320125\pi$
$180$	−8.38778	−	1.30773i	−0.625188	−	0.0974722i
$181$	−8.94007	−	4.30531i	−0.664510	−	0.320011i	0.0710478	−	0.997473i	$-0.477366\pi$
$181$	−8.94007	−	4.30531i	−0.664510	−	0.320011i	−0.735558	+	0.677462i	$0.763080\pi$
$182$	1.28304	−	9.46831i	0.0951054	−	0.701838i
$183$	0.521468	+	0.908514i	0.0385480	+	0.0671593i
$184$	0.226884	−	0.0341972i	0.0167261	−	0.00252105i
$185$	−2.92912	+	1.41059i	−0.215353	+	0.103708i
$186$	3.76716	−	1.15158i	0.276222	−	0.0844379i
$187$	34.8166	+	16.7668i	2.54604	+	1.22611i
$188$	−1.00954	+	4.42307i	−0.0736280	+	0.322585i
$189$	−5.87415	+	12.4296i	−0.427281	+	0.904119i
$190$	−4.47529	−	19.6075i	−0.324672	−	1.42248i
$191$	3.28391	−	14.3878i	0.237616	−	1.04106i	−0.705529	−	0.708681i	$-0.749291\pi$
$191$	3.28391	−	14.3878i	0.237616	−	1.04106i	0.943145	−	0.332381i	$-0.107852\pi$
$192$	1.42861	+	0.979319i	0.103101	+	0.0706763i
$193$	−2.74917	+	12.0449i	−0.197889	+	0.867010i	0.774301	+	0.632818i	$0.218102\pi$
$193$	−2.74917	+	12.0449i	−0.197889	+	0.867010i	−0.972190	+	0.234193i	$0.924755\pi$
$194$	0.547090	−	7.30041i	0.0392788	−	0.524139i
$195$	1.27804	+	17.6539i	0.0915222	+	1.26422i
$196$	−4.19930	+	5.60052i	−0.299950	+	0.400037i
$197$	−6.88206			−0.490327			−0.245163	−	0.969482i	$-0.578842\pi$
$197$	−6.88206			−0.490327			−0.245163	+	0.969482i	$0.578842\pi$
$198$	−14.3703	−	7.01025i	−1.02126	−	0.498197i
$199$	−8.40399	−	7.79776i	−0.595743	−	0.552769i	0.323616	−	0.946188i	$-0.395101\pi$
$199$	−8.40399	−	7.79776i	−0.595743	−	0.552769i	−0.919359	+	0.393420i	$0.871292\pi$
$200$	2.97363	+	0.448203i	0.210268	+	0.0316927i
$201$	2.78373	+	0.426790i	0.196349	+	0.0301035i
$202$	3.66193	−	3.39778i	0.257653	−	0.239067i
$203$	−3.84919	−	23.1864i	−0.270160	−	1.62737i
$204$	7.85490	−	9.79873i	0.549953	−	0.686048i
$205$	24.4572	+	11.7779i	1.70816	+	0.822607i
$206$	−3.02183	−	0.932110i	−0.210541	−	0.0649432i
$207$	0.0479632	+	0.686666i	0.00333367	+	0.0477266i
$208$	1.31939	−	3.36175i	0.0914832	−	0.233095i
$209$	2.83078	−	37.7742i	0.195809	−	2.61290i
$210$	5.48126	−	11.7519i	0.378243	−	0.810959i
$211$	1.34662	+	17.9694i	0.0927050	+	1.23706i	0.828551	+	0.559913i	$0.189166\pi$
$211$	1.34662	+	17.9694i	0.0927050	+	1.23706i	−0.735846	+	0.677149i	$0.763215\pi$
$212$	11.2466	+	3.46911i	0.772418	+	0.238259i
$213$	1.92693	−	1.77887i	0.132031	−	0.121886i
$214$	−8.89405	−	15.4049i	−0.607985	−	1.05306i
$215$	15.8722	+	27.4915i	1.08248	+	1.87491i
$216$	−3.27051	+	4.03779i	−0.222530	+	0.274737i
$217$	0.0897202	+	6.01663i	0.00609060	+	0.408435i
$218$	−5.06942	−	12.9167i	−0.343345	−	0.874828i
$219$	6.99091	−	3.34487i	0.472402	−	0.226025i
$220$	13.5879	+	6.54359i	0.916096	+	0.441169i
$221$	−23.5917	−	11.3612i	−1.58695	−	0.764235i
$222$	−0.153734	+	1.98402i	−0.0103180	+	0.133159i
$223$	−3.87746	−	9.87962i	−0.259654	−	0.661588i	0.740289	−	0.672289i	$-0.234689\pi$
$223$	−3.87746	−	9.87962i	−0.259654	−	0.661588i	−0.999943	+	0.0107012i	$0.996594\pi$
$224$	−2.04371	+	1.68026i	−0.136551	+	0.112267i
$225$	−2.05202	+	8.78519i	−0.136801	+	0.585680i
$226$	2.48712	+	4.30782i	0.165441	+	0.286552i
$227$	−0.907011	−	1.57099i	−0.0602004	−	0.104270i	0.834354	−	0.551228i	$-0.185841\pi$
$227$	−0.907011	−	1.57099i	−0.0602004	−	0.104270i	−0.894555	+	0.446958i	$0.852507\pi$
$228$	−11.7542	−	3.65831i	−0.778441	−	0.242277i
$229$	10.9490	+	3.37732i	0.723530	+	0.223179i	0.634581	−	0.772857i	$-0.281173\pi$
$229$	10.9490	+	3.37732i	0.723530	+	0.223179i	0.0889494	+	0.996036i	$0.471649\pi$
$230$	−0.0485197	−	0.647450i	−0.00319929	−	0.0426916i
$231$	16.3894	−	18.1081i	1.07835	−	1.19143i
$232$	0.663870	−	8.85873i	0.0435852	−	0.581604i
$233$	1.29661	−	3.30370i	0.0849435	−	0.216433i	−0.882090	−	0.471080i	$-0.843864\pi$
$233$	1.29661	−	3.30370i	0.0849435	−	0.216433i	0.967034	+	0.254648i	$0.0819595\pi$
$234$	9.73732	+	4.75014i	0.636549	+	0.310526i
$235$	12.2675	+	3.78402i	0.800242	+	0.246842i
$236$	−6.44338	−	3.10297i	−0.419428	−	0.201986i
$237$	−10.0993	−	1.54839i	−0.656021	−	0.100579i
$238$	11.0415	+	15.6871i	0.715713	+	1.01685i
$239$	−17.6584	+	16.3846i	−1.14223	+	1.05983i	−0.144706	+	0.989475i	$0.546224\pi$
$239$	−17.6584	+	16.3846i	−1.14223	+	1.05983i	−0.997522	+	0.0703577i	$0.977586\pi$
$240$	3.06553	−	3.82416i	0.197879	−	0.246848i
$241$	−17.0958	−	2.57678i	−1.10124	−	0.165985i	−0.426823	−	0.904335i	$-0.640367\pi$
$241$	−17.0958	−	2.57678i	−1.10124	−	0.165985i	−0.674418	+	0.738350i	$0.735605\pi$
$242$	12.7592	+	11.8388i	0.820192	+	0.761027i
$243$	−11.2920	−	10.7467i	−0.724383	−	0.689398i
$244$	−0.604794			−0.0387180
$245$	14.9155	+	13.0339i	0.952917	+	0.832703i
$246$	13.7521	−	9.32511i	0.876802	−	0.594547i
$247$	−1.91814	+	25.5958i	−0.122048	+	1.62862i
$248$	−0.506085	+	2.21730i	−0.0321364	+	0.140799i
$249$	−13.5964	+	6.50530i	−0.861634	+	0.412257i
$250$	−1.25479	+	5.49759i	−0.0793598	+	0.347698i
$251$	−6.07335	−	26.6091i	−0.383346	−	1.67955i	−0.686913	−	0.726739i	$-0.741035\pi$
$251$	−6.07335	−	26.6091i	−0.383346	−	1.67955i	0.303567	−	0.952810i	$-0.401822\pi$
$252$	−4.53558	−	6.51372i	−0.285714	−	0.410326i
$253$	0.272116	−	1.19222i	0.0171078	−	0.0749541i
$254$	−16.2447	−	7.82303i	−1.01928	−	0.490860i
$255$	−25.9889	−	24.2370i	−1.62749	−	1.51778i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	10.9823	−	1.65532i	0.685058	−	0.103256i	0.202714	−	0.979238i	$-0.435024\pi$
$257$	10.9823	−	1.65532i	0.685058	−	0.103256i	0.482344	+	0.875982i	$0.339786\pi$
$258$	19.4306	+	0.0491959i	1.20970	+	0.00306280i
$259$	−2.84585	−	1.06822i	−0.176832	−	0.0663762i
$260$	−9.20715	−	4.43393i	−0.571003	−	0.274981i
$261$	26.3326	+	4.10548i	1.62995	+	0.254123i
$262$	−4.69092	+	0.707042i	−0.289806	+	0.0436812i
$263$	−11.6187	−	20.1242i	−0.716439	−	1.24091i	−0.962402	−	0.271629i	$-0.912437\pi$
$263$	−11.6187	−	20.1242i	−0.716439	−	1.24091i	0.245963	−	0.969279i	$-0.420896\pi$
$264$	7.64039	−	5.18084i	0.470234	−	0.318859i
$265$	12.1673	−	31.0019i	0.747434	−	1.90443i
$266$	10.3600	−	15.6931i	0.635214	−	0.962206i
$267$	−0.990108	+	12.7779i	−0.0605936	+	0.781992i
$268$	−1.01377	+	1.27123i	−0.0619260	+	0.0776528i
$269$	2.83996	−	1.93625i	0.173156	−	0.118055i	−0.473641	−	0.880718i	$-0.657061\pi$
$269$	2.83996	−	1.93625i	0.173156	−	0.118055i	0.646797	+	0.762662i	$0.276108\pi$
$270$	10.7022	+	10.0825i	0.651316	+	0.613604i
$271$	−12.9832	−	1.95691i	−0.788676	−	0.118874i	−0.257660	−	0.966236i	$-0.582951\pi$
$271$	−12.9832	−	1.95691i	−0.788676	−	0.118874i	−0.531016	+	0.847362i	$0.678190\pi$
$272$	2.64895	+	6.74941i	0.160616	+	0.409243i
$273$	−11.1055	+	12.2700i	−0.672133	+	0.742616i
$274$	−4.22578	+	10.7671i	−0.255288	+	0.650464i
$275$	8.01378	−	13.8803i	0.483249	−	0.837012i
$276$	−0.357619	−	0.173337i	−0.0215261	−	0.0104337i
$277$	4.78046	−	12.1804i	0.287230	−	0.731850i	−0.712320	−	0.701855i	$-0.752356\pi$
$277$	4.78046	−	12.1804i	0.287230	−	0.731850i	0.999550	−	0.0299950i	$-0.00954912\pi$
$278$	6.67156	−	6.19030i	0.400134	−	0.371270i
$279$	−6.50958	−	2.04410i	−0.389718	−	0.122377i
$280$	4.30917	+	6.12222i	0.257522	+	0.365873i
$281$	−2.05021	+	27.3581i	−0.122305	+	1.63205i	0.512015	+	0.858977i	$0.328899\pi$
$281$	−2.05021	+	27.3581i	−0.122305	+	1.63205i	−0.634320	+	0.773071i	$0.718720\pi$
$282$	5.77383	−	5.33019i	0.343826	−	0.317408i
$283$	1.03429	−	0.498087i	0.0614821	−	0.0296082i	−0.402890	−	0.915248i	$-0.631994\pi$
$283$	1.03429	−	0.498087i	0.0614821	−	0.0296082i	0.464372	+	0.885640i	$0.346280\pi$
$284$	0.336918	+	1.47613i	0.0199924	+	0.0875924i
$285$	−12.8086	+	32.3943i	−0.758714	+	1.91887i
$286$	−14.1095	−	13.0917i	−0.834311	−	0.774128i
$287$	7.84190	+	24.1389i	0.462892	+	1.42487i
$288$	−1.08187	−	2.79814i	−0.0637497	−	0.164882i
$289$	33.9912	−	10.4849i	1.99948	−	0.616758i
$290$	−24.8571	−	3.74660i	−1.45966	−	0.220008i
$291$	−7.93101	+	9.89368i	−0.464924	+	0.579978i
$292$	−0.334373	+	4.46190i	−0.0195677	+	0.261113i
$293$	−4.86811	−	8.43181i	−0.284398	−	0.492591i	0.688065	−	0.725649i	$-0.258460\pi$
$293$	−4.86811	−	8.43181i	−0.284398	−	0.492591i	−0.972463	+	0.233057i	$0.925127\pi$
$294$	11.4839	−	3.88852i	0.669753	−	0.226783i
$295$	−10.1185	+	17.5257i	−0.589120	+	1.02039i
$296$	−0.949273	−	0.647204i	−0.0551754	−	0.0376179i
$297$	13.6644	+	24.0881i	0.792887	+	1.39773i
$298$	−1.57511	−	4.01331i	−0.0912435	−	0.232485i
$299$	−0.184386	+	0.807846i	−0.0106633	+	0.0467189i
$300$	−3.80924	−	3.55244i	−0.219926	−	0.205100i
$301$	−8.32472	+	28.4895i	−0.479829	+	1.64211i
$302$	−5.19299	+	1.60182i	−0.298823	+	0.0921747i
$303$	−8.55899	+	1.26791i	−0.491701	+	0.0728393i
$304$	5.21008	−	4.83425i	0.298818	−	0.277263i
$305$	−0.127892	+	1.70660i	−0.00732308	+	0.0977197i
$306$	−20.8177	+	6.30614i	−1.19007	+	0.360498i
$307$	13.5927	−	6.54588i	0.775774	−	0.373593i	−0.00372779	−	0.999993i	$-0.501187\pi$
$307$	13.5927	−	6.54588i	0.775774	−	0.373593i	0.779502	+	0.626400i	$0.215472\pi$
$308$	4.35680	+	13.4111i	0.248252	+	0.764168i
$309$	3.40419	+	4.29096i	0.193657	+	0.244104i
$310$	6.14975	+	1.89695i	0.349282	+	0.107739i
$311$	−11.3391	−	14.2187i	−0.642979	−	0.806270i	0.348393	−	0.937348i	$-0.386727\pi$
$311$	−11.3391	−	14.2187i	−0.642979	−	0.806270i	−0.991372	+	0.131079i	$0.958156\pi$
$312$	−5.17712	+	3.51053i	−0.293097	+	0.198745i
$313$	−14.9907			−0.847326			−0.423663	−	0.905820i	$-0.639256\pi$
$313$	−14.9907			−0.847326			−0.423663	+	0.905820i	$0.639256\pi$
$314$	1.45062	+	1.81902i	0.0818631	+	0.102653i
$315$	−19.3395	+	11.4210i	−1.08966	+	0.643502i
$316$	3.67795	−	4.61200i	0.206901	−	0.259445i
$317$	−18.7486	+	23.5100i	−1.05303	+	1.32045i	−0.107753	+	0.994178i	$0.534365\pi$
$317$	−18.7486	+	23.5100i	−1.05303	+	1.32045i	−0.945274	+	0.326277i	$0.894206\pi$
$318$	−12.6696	−	15.9700i	−0.710477	−	0.895553i
$319$	−42.6579	−	20.5429i	−2.38838	−	1.15018i
$320$	1.03381	+	2.63410i	0.0577916	+	0.147250i
$321$	−2.38021	+	30.7178i	−0.132850	+	1.71450i
$322$	0.406223	−	0.451112i	0.0226379	−	0.0251395i
$323$	−32.1302	−	40.2900i	−1.78777	−	2.24180i
$324$	8.62658	−	2.56556i	0.479254	−	0.142531i
$325$	−5.43013	+	9.40525i	−0.301209	+	0.521710i
$326$	−4.77649	+	12.1703i	−0.264545	+	0.674051i
$327$	−5.40731	+	23.4175i	−0.299025	+	1.29499i
$328$	0.716887	+	9.56619i	0.0395835	+	0.528205i
$329$	5.36870	+	10.7357i	0.295986	+	0.591880i
$330$	−13.0036	−	22.6552i	−0.715824	−	1.24712i
$331$	5.03403	+	6.31247i	0.276695	+	0.346965i	0.900689	−	0.434464i	$-0.143062\pi$
$331$	5.03403	+	6.31247i	0.276695	+	0.346965i	−0.623994	+	0.781429i	$0.714491\pi$
$332$	0.650309	−	8.67777i	0.0356903	−	0.476255i
$333$	2.16262	−	2.68384i	0.118511	−	0.147074i
$334$	−0.171073	−	2.28281i	−0.00936070	−	0.124910i
$335$	3.37277	+	3.12947i	0.184274	+	0.170981i
$336$	4.56517	−	0.398998i	0.249051	−	0.0217671i
$337$	−1.85111	+	1.71758i	−0.100836	+	0.0935626i	−0.728980	−	0.684535i	$-0.760005\pi$
$337$	−1.85111	+	1.71758i	−0.100836	+	0.0935626i	0.628144	+	0.778097i	$0.283815\pi$
$338$	0.0308944	+	0.0286658i	0.00168043	+	0.00155922i
$339$	0.665598	−	8.58989i	0.0361503	−	0.466539i
$340$	19.6056	−	6.04752i	1.06326	−	0.327973i
$341$	10.0152	+	6.82825i	0.542354	+	0.369771i
$342$	13.2095	+	16.7374i	0.714291	+	0.905056i
$343$	0.828187	+	18.5017i	0.0447179	+	0.999000i
$344$	−5.60916	+	9.71534i	−0.302425	+	0.523816i
$345$	−0.564744	+	0.972472i	−0.0304048	+	0.0523561i
$346$	−1.17363	+	5.14200i	−0.0630946	+	0.276435i
$347$	2.84444	−	3.56681i	0.152698	−	0.191477i	−0.699599	−	0.714536i	$-0.746638\pi$
$347$	2.84444	−	3.56681i	0.152698	−	0.191477i	0.852296	+	0.523059i	$0.175209\pi$
$348$	−9.62394	+	12.0056i	−0.515897	+	0.643565i
$349$	28.1093	+	8.67056i	1.50465	+	0.464124i	0.934062	−	0.357110i	$-0.116238\pi$
$349$	28.1093	+	8.67056i	1.50465	+	0.464124i	0.570592	+	0.821234i	$0.306714\pi$
$350$	6.83033	−	4.08048i	0.365096	−	0.218111i
$351$	−9.25896	−	16.3221i	−0.494207	−	0.871207i
$352$	0.398288	+	5.31479i	0.0212288	+	0.283279i
$353$	−7.19527	+	6.67624i	−0.382966	+	0.355340i	−0.848041	−	0.529931i	$-0.822218\pi$
$353$	−7.19527	+	6.67624i	−0.382966	+	0.355340i	0.465075	+	0.885271i	$0.346027\pi$
$354$	6.16630	+	10.7431i	0.327735	+	0.570987i
$355$	4.23659	−	0.638562i	0.224855	−	0.0338914i
$356$	−6.11368	−	4.16824i	−0.324025	−	0.220916i
$357$	−0.411303	−	33.2240i	−0.0217684	−	1.75840i
$358$	8.92401	−	6.08428i	0.471648	−	0.321564i
$359$	−5.89939	+	5.47383i	−0.311358	+	0.288898i	−0.820336	−	0.571881i	$-0.806214\pi$
$359$	−5.89939	+	5.47383i	−0.311358	+	0.288898i	0.508979	+	0.860779i	$0.330023\pi$
$360$	−8.12453	+	2.46110i	−0.428200	+	0.129711i
$361$	−15.7574	+	27.2926i	−0.829338	+	1.43645i
$362$	−9.92273			−0.521527
$363$	−6.63398	−	29.4084i	−0.348194	−	1.54354i
$364$	−2.95216	−	9.08734i	−0.154735	−	0.476306i
$365$	12.5198	+	1.88706i	0.655318	+	0.0987733i
$366$	0.864016	+	0.592286i	0.0451628	+	0.0309593i
$367$	−0.788443	−	10.5210i	−0.0411564	−	0.549194i	−0.979229	−	0.202756i	$-0.935010\pi$
$367$	−0.788443	−	10.5210i	−0.0411564	−	0.549194i	0.938073	−	0.346438i	$-0.112609\pi$
$368$	0.189578	−	0.129252i	0.00988242	−	0.00673772i
$369$	−28.7787	−	0.145729i	−1.49816	−	0.00758635i
$370$	−2.02701	+	2.54179i	−0.105379	+	0.132141i
$371$	28.8137	−	11.8073i	1.49593	−	0.613005i
$372$	2.89445	−	2.67205i	0.150070	−	0.138539i
$373$	4.63110	−	8.02131i	0.239790	−	0.415328i	−0.720864	−	0.693076i	$-0.756255\pi$
$373$	4.63110	−	8.02131i	0.239790	−	0.415328i	0.960654	+	0.277749i	$0.0895882\pi$
$374$	38.6435			1.99821
$375$	7.17650	−	6.62509i	0.370593	−	0.342118i
$376$	1.00954	+	4.42307i	0.0520628	+	0.228102i
$377$	28.9049	+	13.9199i	1.48868	+	0.716910i
$378$	0.100568	+	13.7474i	0.00517267	+	0.707088i
$379$	−5.45456	+	2.62678i	−0.280182	+	0.134928i	−0.568698	−	0.822547i	$-0.692553\pi$
$379$	−5.45456	+	2.62678i	−0.280182	+	0.134928i	0.288516	+	0.957475i	$0.406838\pi$
$380$	−12.5395	−	15.7240i	−0.643262	−	0.806625i
$381$	15.5461	+	27.0848i	0.796452	+	1.38760i
$382$	−3.28391	−	14.3878i	−0.168020	−	0.736142i
$383$	−22.0231	+	15.0151i	−1.12533	+	0.767235i	−0.975177	−	0.221428i	$-0.928928\pi$
$383$	−22.0231	+	15.0151i	−1.12533	+	0.767235i	−0.150151	+	0.988663i	$0.547976\pi$
$384$	1.71205	+	0.262484i	0.0873675	+	0.0133948i
$385$	38.7646	−	9.45802i	1.97563	−	0.482025i
$386$	2.74917	+	12.0449i	0.139929	+	0.613069i
$387$	−27.7107	−	19.0991i	−1.40861	−	0.970860i
$388$	−2.67462	−	6.81482i	−0.135783	−	0.345970i
$389$	9.85462	−	3.03975i	0.499649	−	0.154121i	−0.0346791	−	0.999399i	$-0.511041\pi$
$389$	9.85462	−	3.03975i	0.499649	−	0.154121i	0.534328	+	0.845277i	$0.320565\pi$
$390$	8.81122	+	15.3511i	0.446173	+	0.777333i
$391$	−0.831815	−	1.44075i	−0.0420667	−	0.0728616i
$392$	−1.35346	+	6.86791i	−0.0683603	+	0.346882i
$393$	7.39393	+	3.58382i	0.372974	+	0.180780i
$394$	−6.20053	+	2.98602i	−0.312378	+	0.150433i
$395$	−12.2364	−	11.3537i	−0.615678	−	0.571265i
$396$	−15.9889	−	0.0809641i	−0.803470	−	0.00406860i
$397$	31.1343	−	9.60367i	1.56259	−	0.481994i	0.611585	−	0.791179i	$-0.290532\pi$
$397$	31.1343	−	9.60367i	1.56259	−	0.481994i	0.951002	+	0.309185i	$0.100056\pi$
$398$	−10.9551	−	3.37919i	−0.549127	−	0.169383i
$399$	−30.1690	+	12.2736i	−1.51034	+	0.614448i
$400$	2.87362	−	0.886394i	0.143681	−	0.0443197i
$401$	22.2998	−	15.2038i	1.11360	−	0.759240i	0.140606	−	0.990066i	$-0.455095\pi$
$401$	22.2998	−	15.2038i	1.11360	−	0.759240i	0.972995	+	0.230826i	$0.0741427\pi$
$402$	2.69323	−	0.823289i	0.134326	−	0.0410619i
$403$	−6.78629	−	4.62682i	−0.338049	−	0.230478i
$404$	1.82505	−	4.65014i	0.0907994	−	0.231353i
$405$	−5.41527	−	24.8849i	−0.269087	−	1.23654i
$406$	−13.5282	−	19.2201i	−0.671393	−	0.953878i
$407$	−5.05933	+	3.44939i	−0.250782	+	0.170980i
$408$	2.82551	−	12.2365i	0.139883	−	0.605795i
$409$	−1.16089	−	1.45571i	−0.0574021	−	0.0719800i	0.752302	−	0.658819i	$-0.228944\pi$
$409$	−1.16089	−	1.45571i	−0.0574021	−	0.0719800i	−0.809704	+	0.586839i	$0.800372\pi$
$410$	27.1454			1.34062
$411$	16.5814	−	11.2436i	0.817901	−	0.554608i
$412$	−3.12700	+	0.471319i	−0.154056	+	0.0232202i
$413$	−18.3822	+	4.48499i	−0.904527	+	0.220692i
$414$	0.341147	+	0.597855i	0.0167664	+	0.0293830i
$415$	−24.3493	−	3.67007i	−1.19526	−	0.180157i
$416$	−0.269880	−	3.60129i	−0.0132319	−	0.176568i
$417$	−15.5934	+	2.30996i	−0.763610	+	0.113119i
$418$	−13.8392	−	35.2616i	−0.676895	−	1.72470i
$419$	34.7541	+	5.23834i	1.69785	+	0.255910i	0.925353	−	0.379108i	$-0.123769\pi$
$419$	34.7541	+	5.23834i	1.69785	+	0.255910i	0.772498	+	0.635017i	$0.219007\pi$
$420$	−0.160519	−	12.9663i	−0.00783254	−	0.632692i
$421$	14.9891	−	2.25924i	0.730524	−	0.110109i	0.226761	−	0.973950i	$-0.427186\pi$
$421$	14.9891	−	2.25924i	0.730524	−	0.110109i	0.503763	+	0.863842i	$0.331948\pi$
$422$	9.00987	+	15.6056i	0.438594	+	0.759667i
$423$	−13.4685	+	1.96035i	−0.654862	+	0.0953157i
$424$	11.6380	−	1.75415i	0.565191	−	0.0851889i
$425$	−4.85190	−	21.2575i	−0.235352	−	1.03114i
$426$	0.964281	−	2.43877i	0.0467195	−	0.118159i
$427$	−1.23602	+	1.01621i	−0.0598152	+	0.0491778i
$428$	−14.6972	−	10.0204i	−0.710417	−	0.484354i
$429$	7.33604	+	32.5206i	0.354188	+	1.57011i
$430$	26.2285	+	17.8823i	1.26485	+	0.862362i
$431$	16.2217	+	5.00373i	0.781372	+	0.241021i	0.659680	−	0.751547i	$-0.270692\pi$
$431$	16.2217	+	5.00373i	0.781372	+	0.241021i	0.121692	+	0.992568i	$0.461168\pi$
$432$	−1.19470	+	5.05695i	−0.0574799	+	0.243302i
$433$	3.27321	−	14.3409i	0.157300	−	0.689178i	−0.833349	−	0.552747i	$-0.813580\pi$
$433$	3.27321	−	14.3409i	0.157300	−	0.689178i	0.990650	−	0.136431i	$-0.0435631\pi$
$434$	2.69135	+	5.38187i	0.129189	+	0.258338i
$435$	31.8420	+	29.6955i	1.52671	+	1.42379i
$436$	−10.1717	−	9.43799i	−0.487138	−	0.451998i
$437$	−1.01676	+	1.27498i	−0.0486384	+	0.0609907i
$438$	4.84731	−	6.04687i	0.231614	−	0.288930i
$439$	−1.58235	+	0.762020i	−0.0755215	+	0.0363693i	−0.471263	−	0.881993i	$-0.656202\pi$
$439$	−1.58235	+	0.762020i	−0.0755215	+	0.0363693i	0.395742	+	0.918362i	$0.370488\pi$
$440$	15.0814			0.718979
$441$	−20.2141	−	5.69119i	−0.962577	−	0.271009i
$442$	−26.1848			−1.24549
$443$	−0.431247	+	0.207678i	−0.0204892	+	0.00986707i	−0.444100	−	0.895977i	$-0.646477\pi$
$443$	−0.431247	+	0.207678i	−0.0204892	+	0.00986707i	0.423611	+	0.905844i	$0.360762\pi$
$444$	0.722325	+	1.85424i	0.0342800	+	0.0879986i
$445$	−13.0547	+	16.3701i	−0.618853	+	0.776017i
$446$	−7.78008	−	7.21886i	−0.368397	−	0.341823i
$447$	−1.68009	+	7.27600i	−0.0794656	+	0.344143i
$448$	−1.11228	+	2.40059i	−0.0525502	+	0.113417i
$449$	1.91684	−	8.39824i	0.0904614	−	0.396337i	−0.909344	−	0.416044i	$-0.863416\pi$
$449$	1.91684	−	8.39824i	0.0904614	−	0.396337i	0.999806	+	0.0197068i	$0.00627327\pi$
$450$	1.96295	+	8.80553i	0.0925341	+	0.415096i
$451$	48.8563	+	15.0702i	2.30055	+	0.709627i
$452$	4.10991	+	2.80209i	0.193314	+	0.131799i
$453$	8.98747	+	2.79721i	0.422268	+	0.131424i
$454$	−1.49882	−	1.02187i	−0.0703429	−	0.0479590i
$455$	−26.2669	+	6.40874i	−1.23141	+	0.300446i
$456$	−12.1775	+	1.80394i	−0.570261	+	0.0844770i
$457$	−5.35747	−	23.4726i	−0.250612	−	1.09800i	−0.930962	−	0.365116i	$-0.881029\pi$
$457$	−5.35747	−	23.4726i	−0.250612	−	1.09800i	0.680350	−	0.732887i	$-0.261828\pi$
$458$	11.3301	−	1.70773i	0.529419	−	0.0797971i
$459$	35.9161	+	11.3781i	1.67642	+	0.531086i
$460$	−0.324633	−	0.562280i	−0.0151361	−	0.0262165i
$461$	20.4196	−	3.07776i	0.951037	−	0.143346i	0.344841	−	0.938661i	$-0.387933\pi$
$461$	20.4196	−	3.07776i	0.951037	−	0.143346i	0.606196	+	0.795315i	$0.292695\pi$
$462$	6.90956	−	23.4259i	0.321462	−	1.08987i
$463$	−6.16280	−	0.928893i	−0.286410	−	0.0431693i	0.00426615	−	0.999991i	$-0.498642\pi$
$463$	−6.16280	−	0.928893i	−0.286410	−	0.0431693i	−0.290676	+	0.956822i	$0.593880\pi$
$464$	−3.24553	−	8.26948i	−0.150670	−	0.383901i
$465$	−6.92789	−	8.73256i	−0.321273	−	0.404963i
$466$	−0.265219	−	3.53911i	−0.0122861	−	0.163946i
$467$	−34.5685	−	5.21037i	−1.59964	−	0.241107i	−0.712182	−	0.701995i	$-0.752293\pi$
$467$	−34.5685	−	5.21037i	−1.59964	−	0.241107i	−0.887458	+	0.460888i	$0.847531\pi$
$468$	10.8340	+	0.0548612i	0.500803	+	0.00253596i
$469$	0.0641430	+	4.30142i	0.00296185	+	0.198621i
$470$	12.6944	−	1.91338i	0.585551	−	0.0882576i
$471$	−0.290973	−	4.01929i	−0.0134073	−	0.185199i
$472$	−7.15161			−0.329180
$473$	37.2785	+	46.7458i	1.71407	+	2.14937i
$474$	−9.77099	+	2.98688i	−0.448796	+	0.137192i
$475$	−17.6596	+	12.0401i	−0.810277	+	0.552438i
$476$	16.7544	+	9.34289i	0.767938	+	0.428231i
$477$	2.46027	+	35.2225i	0.112648	+	1.61273i
$478$	−8.80066	+	22.4237i	−0.402533	+	1.02564i
$479$	20.9248	+	14.2663i	0.956078	+	0.651843i	0.937500	−	0.347984i	$-0.113134\pi$
$479$	20.9248	+	14.2663i	0.956078	+	0.651843i	0.0185778	+	0.999827i	$0.494086\pi$
$480$	1.10271	−	4.77553i	0.0503317	−	0.217972i
$481$	3.42820	−	2.33731i	0.156312	−	0.106572i
$482$	−16.5209	+	5.09601i	−0.752504	+	0.232117i
$483$	−1.02212	+	0.246642i	−0.0465080	+	0.0112226i
$484$	16.6323	+	5.13038i	0.756013	+	0.233199i
$485$	−19.7956	+	6.10613i	−0.898871	+	0.277265i
$486$	−14.8365	−	4.78298i	−0.672999	−	0.216960i
$487$	−17.7652	−	16.4837i	−0.805017	−	0.746946i	0.165957	−	0.986133i	$-0.446929\pi$
$487$	−17.7652	−	16.4837i	−0.805017	−	0.746946i	−0.970974	+	0.239187i	$0.923119\pi$
$488$	−0.544900	+	0.262410i	−0.0246665	+	0.0118788i
$489$	18.7424	−	12.7089i	0.847559	−	0.574718i
$490$	19.0936	+	5.27151i	0.862560	+	0.238143i
$491$	14.8821	+	25.7765i	0.671619	+	1.16328i	0.977445	+	0.211190i	$0.0677339\pi$
$491$	14.8821	+	25.7765i	0.671619	+	1.16328i	−0.305826	+	0.952087i	$0.598933\pi$
$492$	8.34420	−	14.3684i	0.376186	−	0.647780i
$493$	−61.5498	+	18.9856i	−2.77206	+	0.855068i
$494$	9.37740	+	23.8932i	0.421909	+	1.07501i
$495$	−3.60953	+	45.1001i	−0.162236	+	2.02710i
$496$	0.506085	+	2.21730i	0.0227239	+	0.0995598i
$497$	3.16885	+	2.45067i	0.142142	+	0.109928i
$498$	−9.42735	+	11.7603i	−0.422449	+	0.526992i
$499$	−16.5223	+	11.2647i	−0.739642	+	0.504279i	−0.873562	−	0.486713i	$-0.838196\pi$
$499$	−16.5223	+	11.2647i	−0.739642	+	0.504279i	0.133920	+	0.990992i	$0.457243\pi$
$500$	1.25479	+	5.49759i	0.0561159	+	0.245860i
$501$	−1.99120	+	3.42879i	−0.0889604	+	0.153187i
$502$	−17.0171	−	21.3388i	−0.759512	−	0.952398i
$503$	6.54671	−	3.15273i	0.291903	−	0.140573i	−0.282201	−	0.959355i	$-0.591065\pi$
$503$	6.54671	−	3.15273i	0.291903	−	0.140573i	0.574105	+	0.818782i	$0.305350\pi$
$504$	−6.91261	−	3.90075i	−0.307912	−	0.173753i
$505$	−12.7358	−	6.13324i	−0.566736	−	0.272925i
$506$	−0.272116	−	1.19222i	−0.0120970	−	0.0530006i
$507$	−0.0160632	−	0.0712079i	−0.000713390	−	0.00316245i
$508$	−18.0302			−0.799962
$509$	−0.700053	+	1.21253i	−0.0310293	+	0.0537443i	−0.881123	−	0.472887i	$-0.843212\pi$
$509$	−0.700053	+	1.21253i	−0.0310293	+	0.0537443i	0.850094	+	0.526631i	$0.176545\pi$
$510$	−33.9312	−	10.5606i	−1.50250	−	0.467630i
$511$	6.81378	+	9.68064i	0.301424	+	0.428246i
$512$	−0.623490	+	0.781831i	−0.0275546	+	0.0345524i
$513$	−2.48005	−	36.8477i	−0.109497	−	1.62686i
$514$	9.17651	−	6.25644i	0.404759	−	0.275960i
$515$	0.668717	+	8.92341i	0.0294672	+	0.393212i
$516$	17.5277	−	8.38631i	0.771615	−	0.369187i
$517$	23.9097	+	3.60381i	1.05155	+	0.158495i
$518$	−3.02750	+	0.272331i	−0.133021	+	0.0119655i
$519$	6.71231	−	6.19656i	0.294638	−	0.271999i
$520$	−10.2192			−0.448140
$521$	1.57835	−	2.73378i	0.0691488	−	0.119769i	−0.829378	−	0.558688i	$-0.811305\pi$
$521$	1.57835	−	2.73378i	0.0691488	−	0.119769i	0.898527	+	0.438919i	$0.144638\pi$
$522$	25.5061	−	7.72638i	1.11637	−	0.338174i
$523$	−15.4742	+	14.3579i	−0.676638	+	0.627829i	−0.941720	−	0.336397i	$-0.890792\pi$
$523$	−15.4742	+	14.3579i	−0.676638	+	0.627829i	0.265082	+	0.964226i	$0.414601\pi$
$524$	−3.91960	+	2.67234i	−0.171228	+	0.116742i
$525$	−13.7540	−	0.859651i	−0.600273	−	0.0375182i
$526$	−19.1996	−	13.0901i	−0.837143	−	0.570755i
$527$	16.3061	−	2.45775i	0.710304	−	0.107061i
$528$	4.63587	−	7.98282i	0.201750	−	0.347408i
$529$	16.8216	−	15.6082i	0.731374	−	0.678616i
$530$	−2.48882	−	33.2109i	−0.108107	−	1.44259i
$531$	1.71164	−	21.3864i	0.0742788	−	0.928093i
$532$	2.52508	−	18.6340i	0.109476	−	0.807888i
$533$	−33.1050	−	10.2115i	−1.43394	−	0.442311i
$534$	4.65205	+	11.9420i	0.201314	+	0.516783i
$535$	−31.3834	+	39.3535i	−1.35682	+	1.70140i
$536$	−0.361811	+	1.58520i	−0.0156279	+	0.0684702i
$537$	−18.7074	−	0.0473648i	−0.807284	−	0.00204394i
$538$	1.71861	−	2.97672i	0.0740945	−	0.128335i
$539$	31.4381	+	20.0878i	1.35414	+	0.865241i
$540$	14.0170	+	4.44055i	0.603196	+	0.191091i
$541$	−9.91579	−	6.76047i	−0.426313	−	0.290655i	0.331095	−	0.943598i	$-0.392582\pi$
$541$	−9.91579	−	6.76047i	−0.426313	−	0.290655i	−0.757408	+	0.652942i	$0.773534\pi$
$542$	−12.5466	+	3.87010i	−0.538921	+	0.166235i
$543$	14.1757	+	9.71752i	0.608339	+	0.417019i
$544$	5.31508	+	4.93167i	0.227882	+	0.211444i
$545$	−28.7830	+	26.7067i	−1.23293	+	1.14399i
$546$	−4.68191	+	15.8734i	−0.200367	+	0.679319i
$547$	−10.8426	−	10.0605i	−0.463596	−	0.430154i	0.413475	−	0.910516i	$-0.364315\pi$
$547$	−10.8426	−	10.0605i	−0.463596	−	0.430154i	−0.877071	+	0.480362i	$0.840505\pi$
$548$	0.864378	+	11.5343i	0.0369244	+	0.492722i
$549$	−0.654307	−	1.69229i	−0.0279251	−	0.0722254i
$550$	1.19774	−	15.9827i	0.0510718	−	0.681506i
$551$	39.3665	+	49.3640i	1.67707	+	2.10298i
$552$	−0.397412	−	0.00100620i	−0.0169150	−	4.28266e-5i
$553$	−0.232709	−	15.6055i	−0.00989581	−	0.663612i
$554$	−0.977837	−	13.0483i	−0.0415443	−	0.554370i
$555$	5.38504	−	1.64614i	0.228582	−	0.0698749i
$556$	3.32500	−	8.47195i	0.141011	−	0.359291i
$557$	15.9945	−	27.7033i	0.677709	−	1.17383i	−0.297960	−	0.954578i	$-0.596306\pi$
$557$	15.9945	−	27.7033i	0.677709	−	1.17383i	0.975669	−	0.219249i	$-0.0703606\pi$
$558$	−6.75183	+	0.982735i	−0.285828	+	0.0416025i
$559$	−25.2599	−	31.6749i	−1.06838	−	1.33971i
$560$	6.53876	+	3.64626i	0.276313	+	0.154082i
$561$	−55.2067	−	37.8444i	−2.33083	−	1.59779i
$562$	10.0231	+	25.5384i	0.422797	+	1.07727i
$563$	−2.27474	−	1.09546i	−0.0958690	−	0.0461681i	0.385335	−	0.922777i	$-0.374086\pi$
$563$	−2.27474	−	1.09546i	−0.0958690	−	0.0461681i	−0.481204	+	0.876609i	$0.659800\pi$
$564$	2.88936	−	7.30750i	0.121664	−	0.307701i
$565$	8.77601	−	11.0048i	0.369209	−	0.462974i
$566$	0.715750	−	0.897522i	0.0300852	−	0.0377257i
$567$	13.3194	−	19.7381i	0.559361	−	0.828924i
$568$	0.944023	+	1.18377i	0.0396103	+	0.0496698i
$569$	1.98915			0.0833895			0.0416947	−	0.999130i	$-0.486724\pi$
$569$	1.98915			0.0833895			0.0416947	+	0.999130i	$0.486724\pi$
$570$	2.51524	+	34.7437i	0.105352	+	1.45525i
$571$	−16.2024	−	20.3172i	−0.678050	−	0.850248i	0.317123	−	0.948384i	$-0.397283\pi$
$571$	−16.2024	−	20.3172i	−0.678050	−	0.850248i	−0.995173	+	0.0981368i	$0.968712\pi$
$572$	−18.3925	−	5.67333i	−0.769028	−	0.237214i
$573$	−9.39877	+	23.7705i	−0.392639	+	0.993029i
$574$	17.5388	+	18.3459i	0.732055	+	0.765744i
$575$	−0.621665	+	0.299378i	−0.0259252	+	0.0124849i
$576$	−2.18879	−	2.05163i	−0.0911998	−	0.0854845i
$577$	−2.12860	+	28.4042i	−0.0886147	+	1.18248i	0.758718	+	0.651419i	$0.225826\pi$
$577$	−2.12860	+	28.4042i	−0.0886147	+	1.18248i	−0.847333	+	0.531062i	$0.821793\pi$
$578$	26.0758	−	24.1948i	1.08461	−	1.00637i
$579$	7.86830	−	19.8998i	0.326995	−	0.827007i
$580$	−24.0211	+	7.40952i	−0.997420	+	0.307663i
$581$	−13.2519	−	18.8275i	−0.549780	−	0.781096i
$582$	−2.85289	+	12.3550i	−0.118256	+	0.512133i
$583$	13.9582	−	61.1548i	0.578089	−	2.53277i
$584$	1.63469	+	4.16511i	0.0676438	+	0.172354i
$585$	2.44582	−	30.5598i	0.101122	−	1.26349i
$586$	−8.04444	−	5.48460i	−0.332313	−	0.226567i
$587$	−15.2293	+	26.3778i	−0.628578	+	1.08873i	0.359259	+	0.933238i	$0.383030\pi$
$587$	−15.2293	+	26.3778i	−0.628578	+	1.08873i	−0.987837	+	0.155492i	$0.950304\pi$
$588$	8.65945	−	8.48610i	0.357110	−	0.349961i
$589$	−8.08224	−	13.9989i	−0.333023	−	0.576813i
$590$	−1.51231	+	20.1803i	−0.0622607	+	0.830812i
$591$	11.7824	+	1.80643i	0.484664	+	0.0743067i
$592$	−1.13608	−	0.171236i	−0.0466925	−	0.00703776i
$593$	−12.4295	+	3.83400i	−0.510420	+	0.157444i	−0.539258	−	0.842141i	$-0.681295\pi$
$593$	−12.4295	+	3.83400i	−0.510420	+	0.157444i	0.0288386	+	0.999584i	$0.490819\pi$
$594$	22.7626	+	15.7739i	0.933961	+	0.647209i
$595$	29.9067	−	45.3018i	1.22605	−	1.85719i
$596$	−3.16043	−	2.93245i	−0.129456	−	0.120118i
$597$	12.3412	+	15.5560i	0.505093	+	0.636666i
$598$	0.184386	+	0.807846i	0.00754009	+	0.0330353i
$599$	20.1738	−	9.71517i	0.824278	−	0.396951i	0.0263117	−	0.999654i	$-0.491624\pi$
$599$	20.1738	−	9.71517i	0.824278	−	0.396951i	0.797966	+	0.602703i	$0.205909\pi$
$600$	−4.97335	−	1.54788i	−0.203036	−	0.0631918i
$601$	0.441377	−	5.88977i	0.0180042	−	0.240249i	−0.980940	−	0.194310i	$-0.937753\pi$
$601$	0.441377	−	5.88977i	0.0180042	−	0.240249i	0.998944	−	0.0459385i	$-0.0146278\pi$
$602$	4.86082	+	29.2801i	0.198112	+	1.19337i
$603$	−4.65384	−	1.46137i	−0.189519	−	0.0595116i
$604$	−3.98371	+	3.69635i	−0.162095	+	0.150402i
$605$	17.9940	−	45.8480i	0.731560	−	1.86398i
$606$	−7.16126	+	4.85595i	−0.290906	+	0.197259i
$607$	11.2276	−	19.4469i	0.455716	−	0.789324i	−0.543013	−	0.839724i	$-0.682717\pi$
$607$	11.2276	−	19.4469i	0.455716	−	0.789324i	0.998729	+	0.0504008i	$0.0160499\pi$
$608$	2.59662	−	6.61607i	0.105307	−	0.268317i
$609$	0.503934	+	40.7065i	0.0204204	+	1.64951i
$610$	0.625240	+	1.59309i	0.0253152	+	0.0645021i
$611$	−16.2012	−	2.44194i	−0.655431	−	0.0987903i
$612$	−16.0200	+	14.7141i	−0.647568	+	0.594782i
$613$	−30.4712	+	20.7749i	−1.23072	+	0.839090i	−0.991274	−	0.131820i	$-0.957918\pi$
$613$	−30.4712	+	20.7749i	−1.23072	+	0.839090i	−0.239445	+	0.970910i	$0.576965\pi$
$614$	9.40641	−	11.7953i	0.379612	−	0.476018i
$615$	−38.7803	−	26.5840i	−1.56377	−	1.07197i
$616$	9.74419	+	10.1926i	0.392605	+	0.410673i
$617$	2.64616	−	6.74231i	0.106530	−	0.271435i	−0.867662	−	0.497155i	$-0.834378\pi$
$617$	2.64616	−	6.74231i	0.106530	−	0.271435i	0.974192	+	0.225720i	$0.0724734\pi$
$618$	4.92884	+	2.38900i	0.198267	+	0.0960996i
$619$	1.23835	+	2.14488i	0.0497734	+	0.0862101i	0.889839	−	0.456275i	$-0.150817\pi$
$619$	1.23835	+	2.14488i	0.0497734	+	0.0862101i	−0.840065	+	0.542485i	$0.817483\pi$
$620$	6.36378	−	0.959186i	0.255576	−	0.0385218i
$621$	0.0981239	−	1.18819i	0.00393758	−	0.0476806i
$622$	−16.3854	−	7.89080i	−0.656995	−	0.316392i
$623$	−19.4983	+	1.75391i	−0.781182	+	0.0702691i
$624$	−3.14126	+	5.40915i	−0.125751	+	0.216539i
$625$	30.6466	−	4.61923i	1.22586	−	0.184769i
$626$	−13.5062	+	6.50423i	−0.539815	+	0.259961i
$627$	−14.7616	+	63.9281i	−0.589520	+	2.55304i
$628$	2.09620	+	1.00948i	0.0836477	+	0.0402826i
$629$	−1.85367	+	8.12145i	−0.0739106	+	0.323823i
$630$	−12.4689	+	18.6811i	−0.496771	+	0.744272i
$631$	6.08600	+	26.6645i	0.242280	+	1.06150i	0.938936	+	0.344092i	$0.111813\pi$
$631$	6.08600	+	26.6645i	0.242280	+	1.06150i	−0.696656	+	0.717405i	$0.745330\pi$
$632$	1.31264	−	5.75107i	0.0522142	−	0.228765i
$633$	2.41120	−	31.1178i	0.0958367	−	1.23682i
$634$	−6.69130	+	29.3165i	−0.265746	+	1.16431i
$635$	−3.81275	+	50.8776i	−0.151304	+	2.01901i
$636$	−18.3441	−	8.89132i	−0.727389	−	0.352564i
$637$	−21.3024	−	13.6115i	−0.844033	−	0.539305i
$638$	−47.3467			−1.87447
$639$	−3.76592	+	2.53972i	−0.148977	+	0.100470i
$640$	2.07432	+	1.92469i	0.0819947	+	0.0760799i
$641$	−41.0855	−	6.19265i	−1.62278	−	0.244595i	−0.726203	−	0.687480i	$-0.758717\pi$
$641$	−41.0855	−	6.19265i	−1.62278	−	0.244595i	−0.896578	+	0.442885i	$0.853955\pi$
$642$	11.1835	+	28.7085i	0.441376	+	1.13303i
$643$	22.0817	−	20.4889i	0.870819	−	0.808002i	−0.111782	−	0.993733i	$-0.535656\pi$
$643$	22.0817	−	20.4889i	0.870819	−	0.808002i	0.982601	+	0.185731i	$0.0594652\pi$
$644$	0.170264	−	0.582692i	0.00670936	−	0.0229613i
$645$	−19.9579	−	51.2330i	−0.785842	−	2.01730i
$646$	−46.4295	−	22.3593i	−1.82675	−	0.879715i
$647$	31.6880	+	9.77446i	1.24578	+	0.384274i	0.846419	−	0.532518i	$-0.178754\pi$
$647$	31.6880	+	9.77446i	1.24578	+	0.384274i	0.399366	+	0.916792i	$0.369230\pi$
$648$	6.65912	−	6.05443i	0.261595	−	0.237840i
$649$	−13.9253	+	35.4810i	−0.546615	+	1.39275i
$650$	−0.811588	+	10.8299i	−0.0318331	+	0.424783i
$651$	1.42567	−	10.3243i	0.0558762	−	0.404641i
$652$	0.977026	+	13.0375i	0.0382633	+	0.510588i
$653$	−16.1859	−	4.99270i	−0.633404	−	0.195379i	−0.0386061	−	0.999255i	$-0.512292\pi$
$653$	−16.1859	−	4.99270i	−0.633404	−	0.195379i	−0.594798	+	0.803875i	$0.702768\pi$
$654$	5.28866	+	23.4446i	0.206803	+	0.916756i
$655$	6.71192	+	11.6254i	0.262256	+	0.454241i
$656$	4.79651	+	8.30780i	0.187272	+	0.324365i
$657$	−12.8467	+	3.89156i	−0.501199	+	0.151824i
$658$	9.49509	+	7.34316i	0.370157	+	0.286266i
$659$	13.2586	+	33.7823i	0.516481	+	1.31597i	0.916709	+	0.399556i	$0.130836\pi$
$659$	13.2586	+	33.7823i	0.516481	+	1.31597i	−0.400228	+	0.916416i	$0.631069\pi$
$660$	−21.5455	−	14.7695i	−0.838659	−	0.574904i
$661$	−18.1063	−	8.71954i	−0.704254	−	0.339151i	0.0472468	−	0.998883i	$-0.484955\pi$
$661$	−18.1063	−	8.71954i	−0.704254	−	0.339151i	−0.751500	+	0.659733i	$0.770670\pi$
$662$	7.27438	+	3.50316i	0.282727	+	0.136154i
$663$	37.4080	+	25.6433i	1.45281	+	0.995903i
$664$	−3.17924	−	8.10056i	−0.123378	−	0.314363i
$665$	−52.0474	−	11.0657i	−2.01831	−	0.429109i
$666$	0.783975	−	3.35638i	0.0303784	−	0.130057i
$667$	1.01915	+	1.76522i	0.0394617	+	0.0683497i
$668$	−1.14461	−	1.98252i	−0.0442861	−	0.0767058i
$669$	4.04515	+	17.9321i	0.156395	+	0.693296i
$670$	4.39659	+	1.35617i	0.169855	+	0.0523934i
$671$	0.240882	+	3.21435i	0.00929915	+	0.124089i
$672$	3.93996	−	2.34024i	0.151987	−	0.0902767i
$673$	2.13782	−	28.5273i	0.0824070	−	1.09965i	−0.790728	−	0.612167i	$-0.790298\pi$
$673$	2.13782	−	28.5273i	0.0824070	−	1.09965i	0.873135	−	0.487478i	$-0.162083\pi$
$674$	−0.922564	+	2.35065i	−0.0355358	+	0.0905438i
$675$	5.81913	−	14.5020i	0.223978	−	0.558184i
$676$	0.0402725	+	0.0124224i	0.00154894	+	0.000477786i
$677$	−6.90575	−	3.32563i	−0.265410	−	0.127815i	0.296447	−	0.955049i	$-0.404198\pi$
$677$	−6.90575	−	3.32563i	−0.265410	−	0.127815i	−0.561856	+	0.827235i	$0.689913\pi$
$678$	−3.12733	−	8.02801i	−0.120104	−	0.308314i
$679$	−16.9168	−	9.43343i	−0.649207	−	0.362022i
$680$	15.0401	−	13.9552i	0.576762	−	0.535157i
$681$	1.14048	+	2.92768i	0.0437035	+	0.112189i
$682$	11.9861	+	1.80661i	0.458970	+	0.0691786i
$683$	7.54794	+	7.00346i	0.288814	+	0.267980i	0.811251	−	0.584697i	$-0.198787\pi$
$683$	7.54794	+	7.00346i	0.288814	+	0.267980i	−0.522438	+	0.852678i	$0.674977\pi$
$684$	19.1635	+	9.34849i	0.732734	+	0.357448i
$685$	32.7302			1.25056
$686$	8.77377	+	16.3101i	0.334984	+	0.622724i
$687$	−17.8587	−	8.65606i	−0.681352	−	0.330249i
$688$	−0.838345	+	11.1869i	−0.0319616	+	0.426498i
$689$	−9.45805	+	41.4384i	−0.360323	+	1.57868i
$690$	−0.0868776	+	1.12120i	−0.00330737	+	0.0426834i
$691$	3.77164	−	16.5246i	0.143480	−	0.628627i	−0.851131	−	0.524953i	$-0.824083\pi$
$691$	3.77164	−	16.5246i	0.143480	−	0.628627i	0.994611	−	0.103674i	$-0.0330600\pi$
$692$	1.17363	+	5.14200i	0.0446146	+	0.195469i
$693$	−32.8126	+	26.6999i	−1.24645	+	1.01425i
$694$	1.01517	−	4.44775i	0.0385353	−	0.168834i
$695$	−23.2030	−	11.1740i	−0.880138	−	0.423852i
$696$	−3.46185	+	14.9923i	−0.131221	+	0.568282i
$697$	62.6672	−	30.1789i	2.37369	−	1.14311i
$698$	29.0876	−	4.38425i	1.10098	−	0.165946i
$699$	−3.08702	+	5.31575i	−0.116762	+	0.201060i
$700$	4.38346	−	6.63995i	0.165679	−	0.250967i
$701$	−29.7621	−	14.3327i	−1.12410	−	0.541338i	−0.222943	−	0.974832i	$-0.571566\pi$
$701$	−29.7621	−	14.3327i	−1.12410	−	0.541338i	−0.901157	+	0.433494i	$0.857281\pi$
$702$	−15.4239	−	10.6884i	−0.582138	−	0.403406i
$703$	8.07453	−	1.21704i	0.304537	−	0.0459015i
$704$	2.66484	+	4.61565i	0.100435	+	0.173959i
$705$	−20.0093	−	9.69844i	−0.753592	−	0.365264i
$706$	−3.58601	+	9.13699i	−0.134961	+	0.343875i
$707$	−4.08358	−	12.5701i	−0.153579	−	0.472746i
$708$	10.2169	+	7.00371i	0.383974	+	0.263216i
$709$	3.74183	−	4.69210i	0.140527	−	0.176216i	−0.706587	−	0.707626i	$-0.749766\pi$
$709$	3.74183	−	4.69210i	0.140527	−	0.176216i	0.847115	+	0.531410i	$0.178338\pi$
$710$	3.53997	−	2.41351i	0.132853	−	0.0905774i
$711$	16.8841	+	5.30182i	0.633202	+	0.198834i
$712$	−7.31677	−	1.10283i	−0.274207	−	0.0413301i
$713$	−0.190648	−	0.485763i	−0.00713983	−	0.0181920i
$714$	−14.7859	−	29.7553i	−0.553349	−	1.11356i
$715$	−19.8983	+	50.7000i	−0.744154	+	1.89607i
$716$	5.40038	−	9.35373i	0.201822	−	0.349565i
$717$	34.5327	−	23.4162i	1.28965	−	0.874492i
$718$	−2.94016	+	7.49140i	−0.109726	+	0.279577i
$719$	29.2149	−	27.1075i	1.08953	−	1.01094i	0.0896435	−	0.995974i	$-0.471427\pi$
$719$	29.2149	−	27.1075i	1.08953	−	1.01094i	0.999888	−	0.0149636i	$-0.00476325\pi$
$720$	−6.25212	+	5.74248i	−0.233003	+	0.214009i
$721$	−5.59873	+	6.21740i	−0.208508	+	0.231548i
$722$	−2.35511	+	31.4267i	−0.0876480	+	1.16958i
$723$	28.5925	+	8.89896i	1.06337	+	0.330956i
$724$	−8.94007	+	4.30531i	−0.332255	+	0.160006i
$725$	5.94462	+	26.0451i	0.220777	+	0.967289i
$726$	−18.7368	−	23.6177i	−0.695389	−	0.876533i
$727$	1.03371	+	0.959139i	0.0383380	+	0.0355725i	0.699109	−	0.715015i	$-0.253580\pi$
$727$	1.03371	+	0.959139i	0.0383380	+	0.0355725i	−0.660771	+	0.750587i	$0.729771\pi$
$728$	−6.60266	−	6.90651i	−0.244711	−	0.255972i
$729$	16.5116	+	21.3627i	0.611541	+	0.791212i
$730$	12.0987	−	3.73197i	0.447795	−	0.138126i
$731$	80.4312	+	12.1231i	2.97486	+	0.448387i
$732$	1.03543	+	0.158749i	0.0382708	+	0.00586753i
$733$	1.51677	−	20.2400i	0.0560233	−	0.747580i	−0.896486	−	0.443071i	$-0.853889\pi$
$733$	1.51677	−	20.2400i	0.0560233	−	0.747580i	0.952510	−	0.304508i	$-0.0984921\pi$
$734$	−5.27527	−	9.13704i	−0.194714	−	0.337254i
$735$	−22.1148	−	26.2297i	−0.815718	−	0.967496i
$736$	0.114723	−	0.198707i	0.00422876	−	0.00732442i
$737$	7.16009	+	4.88167i	0.263745	+	0.179819i
$738$	−25.9919	+	12.3553i	−0.956776	+	0.454805i
$739$	6.03785	+	15.3842i	0.222106	+	0.565916i	0.997879	−	0.0650954i	$-0.0207352\pi$
$739$	6.03785	+	15.3842i	0.222106	+	0.565916i	−0.775773	+	0.631012i	$0.782640\pi$
$740$	−0.723432	+	3.16956i	−0.0265939	+	0.116515i
$741$	10.0024	−	43.3176i	0.367448	−	1.59131i
$742$	20.8372	−	23.1398i	0.764959	−	0.849489i
$743$	−8.89782	+	2.74461i	−0.326429	+	0.100690i	−0.453638	−	0.891186i	$-0.649874\pi$
$743$	−8.89782	+	2.74461i	−0.326429	+	0.100690i	0.127209	+	0.991876i	$0.459398\pi$
$744$	1.44845	−	3.66329i	0.0531027	−	0.134303i
$745$	−8.94309	+	8.29797i	−0.327649	+	0.304014i
$746$	0.692166	−	9.23631i	0.0253420	−	0.338165i
$747$	24.9851	−	7.56855i	0.914158	−	0.276919i
$748$	34.8166	−	16.7668i	1.27302	−	0.613055i
$749$	−46.8736	+	4.21638i	−1.71272	+	0.154063i
$750$	3.59129	−	9.08277i	0.131135	−	0.331656i
$751$	13.9492	+	4.30277i	0.509015	+	0.157010i	0.538616	−	0.842552i	$-0.318947\pi$
$751$	13.9492	+	4.30277i	0.509015	+	0.157010i	−0.0296010	+	0.999562i	$0.509424\pi$
$752$	2.82866	+	3.54702i	0.103150	+	0.129347i
$753$	3.41339	+	47.1501i	0.124391	+	1.71825i
$754$	32.0820			1.16836
$755$	9.58791	+	12.0229i	0.348940	+	0.437556i
$756$	6.05536	+	12.3423i	0.220231	+	0.448885i
$757$	14.8222	−	18.5864i	0.538721	−	0.675535i	−0.435745	−	0.900070i	$-0.643515\pi$
$757$	14.8222	−	18.5864i	0.538721	−	0.675535i	0.974466	+	0.224535i	$0.0720864\pi$
$758$	−3.77467	+	4.73329i	−0.137102	+	0.171921i
$759$	−0.778814	+	1.96971i	−0.0282691	+	0.0714958i
$760$	−18.1201	−	8.72617i	−0.657284	−	0.316532i
$761$	17.2139	+	43.8603i	0.624003	+	1.58993i	0.796308	+	0.604891i	$0.206783\pi$
$761$	17.2139	+	43.8603i	0.624003	+	1.58993i	−0.172305	+	0.985044i	$0.555121\pi$
$762$	25.7582	+	17.6574i	0.933122	+	0.639658i
$763$	−36.6463	−	2.19733i	−1.32668	−	0.0795488i
$764$	−9.20132	−	11.5381i	−0.332892	−	0.417434i
$765$	38.1324	+	48.3165i	1.37868	+	1.74689i
$766$	−13.3273	+	23.0836i	−0.481536	+	0.834044i
$767$	9.43576	−	24.0419i	0.340705	−	0.868103i
$768$	1.65639	−	0.506339i	0.0597698	−	0.0182709i
$769$	2.25907	+	30.1451i	0.0814640	+	1.08706i	0.876788	+	0.480877i	$0.159682\pi$
$769$	2.25907	+	30.1451i	0.0814640	+	1.08706i	−0.795324	+	0.606185i	$0.792699\pi$
$770$	30.8220	−	25.3407i	1.11075	−	0.913216i
$771$	−19.2367	−	0.0487050i	−0.692794	−	0.00175407i
$772$	7.70300	+	9.65925i	0.277237	+	0.347644i
$773$	3.28298	−	43.8084i	0.118081	−	1.57568i	−0.552291	−	0.833652i	$-0.686246\pi$
$773$	3.28298	−	43.8084i	0.118081	−	1.57568i	0.670372	−	0.742026i	$-0.266135\pi$
$774$	−33.2532	−	5.18446i	−1.19526	−	0.186352i
$775$	−0.511109	−	6.82027i	−0.0183596	−	0.244991i
$776$	−5.36659	−	4.97946i	−0.192649	−	0.178752i
$777$	4.59183	+	2.57584i	0.164731	+	0.0924077i
$778$	7.55981	−	7.01448i	0.271032	−	0.251481i
$779$	−49.9804	−	46.3750i	−1.79073	−	1.66156i
$780$	14.5992	+	10.0078i	0.522736	+	0.358338i
$781$	7.71114	−	2.37857i	0.275926	−	0.0851120i
$782$	−1.37456	−	0.937156i	−0.0491540	−	0.0335126i
$783$	−44.0050	−	13.9407i	−1.57261	−	0.498198i
$784$	1.76044	+	6.77502i	0.0628730	+	0.241965i
$785$	3.29181	−	5.70158i	0.117490	−	0.203498i
$786$	8.21666	+	0.0208036i	0.293078	+	0.000742038i
$787$	4.24786	−	18.6111i	0.151420	−	0.663414i	−0.841053	−	0.540952i	$-0.818064\pi$
$787$	4.24786	−	18.6111i	0.151420	−	0.663414i	0.992473	−	0.122462i	$-0.0390789\pi$
$788$	−4.29090	+	5.38061i	−0.152857	+	0.191676i
$789$	14.6095	+	37.5032i	0.520110	+	1.33515i
$790$	−15.9507	−	4.92015i	−0.567502	−	0.175051i
$791$	13.1077	−	1.17906i	0.466055	−	0.0419227i
$792$	−14.4406	+	6.86436i	−0.513124	+	0.243914i
$793$	−0.163221	−	2.17804i	−0.00579617	−	0.0773444i
$794$	23.8842	−	22.1613i	0.847618	−	0.786474i
$795$	−28.9686	+	49.8829i	−1.02741	+	1.76916i
$796$	−11.3363	+	1.70868i	−0.401806	+	0.0605625i
$797$	7.88283	+	5.37442i	0.279224	+	0.190372i	0.694832	−	0.719172i	$-0.255479\pi$
$797$	7.88283	+	5.37442i	0.279224	+	0.190372i	−0.415608	+	0.909544i	$0.636431\pi$
$798$	−21.8560	+	24.1480i	−0.773696	+	0.854829i
$799$	27.1789	−	18.5302i	0.961520	−	0.655553i
$800$	2.20445	−	2.04543i	0.0779391	−	0.0723169i
$801$	5.04910	−	21.6164i	0.178401	−	0.763778i
$802$	13.4948	−	23.3737i	0.476518	−	0.825353i
$803$	23.8472			0.841550
$804$	2.06930	−	1.91031i	0.0729787	−	0.0673713i
$805$	−1.60823	−	0.603669i	−0.0566827	−	0.0212765i
$806$	−8.12174	−	1.22416i	−0.286076	−	0.0431190i
$807$	−5.37038	+	2.56951i	−0.189046	+	0.0904510i
$808$	−0.373311	−	4.98149i	−0.0131330	−	0.175248i
$809$	−13.9455	+	9.50785i	−0.490296	+	0.334278i	−0.783102	−	0.621894i	$-0.786364\pi$
$809$	−13.9455	+	9.50785i	−0.490296	+	0.334278i	0.292805	+	0.956172i	$0.405411\pi$
$810$	−15.6762	−	20.0709i	−0.550804	−	0.705221i
$811$	12.4019	−	15.5515i	0.435490	−	0.546087i	−0.514858	−	0.857275i	$-0.672155\pi$
$811$	12.4019	−	15.5515i	0.435490	−	0.546087i	0.950348	+	0.311188i	$0.100727\pi$
$812$	−20.5278	−	11.4471i	−0.720384	−	0.401713i
$813$	21.7143	+	6.75822i	0.761552	+	0.237021i
$814$	−3.06166	+	5.30296i	−0.107311	+	0.185869i
$815$	36.9957			1.29590
$816$	−2.76351	−	12.2506i	−0.0967422	−	0.428857i
$817$	−17.7422	−	77.7337i	−0.620722	−	2.71956i
$818$	−1.67753	−	0.807856i	−0.0586534	−	0.0282460i
$819$	22.2338	−	18.0919i	0.776910	−	0.632181i
$820$	24.4572	−	11.7779i	0.854081	−	0.411304i
$821$	7.01708	+	8.79914i	0.244898	+	0.307092i	0.889054	−	0.457801i	$-0.151363\pi$
$821$	7.01708	+	8.79914i	0.244898	+	0.307092i	−0.644157	+	0.764894i	$0.722792\pi$
$822$	10.0609	−	17.3246i	0.350915	−	0.604264i
$823$	11.0942	+	48.6070i	0.386721	+	1.69433i	0.675846	+	0.737043i	$0.263779\pi$
$823$	11.0942	+	48.6070i	0.386721	+	1.69433i	−0.289125	+	0.957291i	$0.593364\pi$
$824$	−2.61283	+	1.78140i	−0.0910223	+	0.0620580i
$825$	−17.3633	+	21.6602i	−0.604513	+	0.754110i
$826$	−14.6158	+	12.0166i	−0.508548	+	0.418109i
$827$	8.93898	+	39.1642i	0.310839	+	1.36187i	0.853137	+	0.521687i	$0.174697\pi$
$827$	8.93898	+	39.1642i	0.310839	+	1.36187i	−0.542298	+	0.840186i	$0.682446\pi$
$828$	0.566762	+	0.390630i	0.0196963	+	0.0135753i
$829$	1.87476	+	4.77681i	0.0651131	+	0.165905i	0.959727	−	0.280935i	$-0.0906445\pi$
$829$	1.87476	+	4.77681i	0.0651131	+	0.165905i	−0.894614	+	0.446840i	$0.852549\pi$
$830$	−23.5304	+	7.25816i	−0.816751	+	0.251934i
$831$	−11.3815	+	19.5986i	−0.394821	+	0.679869i
$832$	−1.80570	−	3.12756i	−0.0626012	−	0.108429i
$833$	49.9396	−	9.05764i	1.73030	−	0.313829i
$834$	−13.0469	+	8.84690i	−0.451776	+	0.306343i
$835$	−5.83629	+	2.81061i	−0.201973	+	0.0972651i
$836$	−27.7681	−	25.7650i	−0.960379	−	0.891102i
$837$	10.6082	+	5.20825i	0.366672	+	0.180023i
$838$	33.5852	−	10.3597i	1.16018	−	0.357869i
$839$	29.1673	+	8.99691i	1.00697	+	0.310608i	0.754005	−	0.656869i	$-0.228119\pi$
$839$	29.1673	+	8.99691i	1.00697	+	0.310608i	0.252961	+	0.967477i	$0.418596\pi$
$840$	−5.77051	−	11.6126i	−0.199101	−	0.400673i
$841$	47.7001	−	14.7135i	1.64483	−	0.507363i
$842$	12.5245	−	8.53904i	0.431622	−	0.294275i
$843$	10.6911	−	46.3002i	0.368222	−	1.59466i
$844$	14.8886	+	10.1509i	0.512487	+	0.349408i
$845$	0.0435697	−	0.111014i	0.00149884	−	0.00381899i
$846$	−11.2842	+	7.60999i	−0.387957	+	0.261637i
$847$	42.6119	−	17.4616i	1.46416	−	0.599986i
$848$	9.72438	−	6.62997i	0.333937	−	0.227674i
$849$	−1.90149	+	0.581264i	−0.0652590	+	0.0199489i
$850$	−13.5947	−	17.0472i	−0.466295	−	0.584715i
$851$	0.263613			0.00903654
$852$	−0.189357	−	2.61564i	−0.00648726	−	0.0896105i
$853$	39.8172	−	6.00148i	1.36332	−	0.205487i	0.573689	−	0.819073i	$-0.305512\pi$
$853$	39.8172	−	6.00148i	1.36332	−	0.205487i	0.789627	+	0.613587i	$0.210274\pi$
$854$	−0.672699	+	1.45186i	−0.0230193	+	0.0496817i
$855$	30.4319	−	52.0985i	1.04075	−	1.78173i
$856$	−17.5894	−	2.65118i	−0.601194	−	0.0906154i
$857$	−3.75950	−	50.1670i	−0.128422	−	1.71367i	−0.574356	−	0.818606i	$-0.694747\pi$
$857$	−3.75950	−	50.1670i	−0.128422	−	1.71367i	0.445934	−	0.895066i	$-0.352872\pi$
$858$	20.7197	+	26.1171i	0.707360	+	0.891623i
$859$	−10.9084	−	27.7941i	−0.372190	−	0.948324i	−0.987154	−	0.159769i	$-0.948925\pi$
$859$	−10.9084	−	27.7941i	−0.372190	−	0.948324i	0.614965	−	0.788555i	$-0.289170\pi$
$860$	31.3899	+	4.73127i	1.07039	+	0.161335i
$861$	−7.08960	−	43.3853i	−0.241613	−	1.47857i
$862$	16.7863	−	2.53013i	0.571743	−	0.0861764i
$863$	−13.7333	−	23.7868i	−0.467488	−	0.809713i	0.531822	−	0.846856i	$-0.321508\pi$
$863$	−13.7333	−	23.7868i	−0.467488	−	0.809713i	−0.999310	+	0.0371432i	$0.988174\pi$
$864$	1.11774	+	5.07451i	0.0380263	+	0.172638i
$865$	14.7578	−	2.22438i	0.501781	−	0.0756313i
$866$	−3.27321	−	14.3409i	−0.111228	−	0.487322i
$867$	−60.9466	+	9.02846i	−2.06985	+	0.306623i
$868$	4.75993	+	3.68116i	0.161563	+	0.124947i
$869$	−25.9767	−	17.7106i	−0.881199	−	0.600791i
$870$	41.5731	+	12.9390i	1.40946	+	0.438672i
$871$	−4.85167	−	3.30781i	−0.164393	−	0.112081i
$872$	−13.2594	−	4.08998i	−0.449020	−	0.138504i
$873$	16.1752	−	14.8567i	0.547447	−	0.502822i
$874$	−0.362879	+	1.58988i	−0.0122746	+	0.0537784i
$875$	11.8018	+	9.12709i	0.398973	+	0.308552i
$876$	1.74364	−	7.55121i	0.0589122	−	0.255132i
$877$	−5.95157	−	5.52225i	−0.200970	−	0.186473i	0.573267	−	0.819369i	$-0.305676\pi$
$877$	−5.95157	−	5.52225i	−0.200970	−	0.186473i	−0.774237	+	0.632895i	$0.781866\pi$
$878$	−1.09502	+	1.37311i	−0.0369552	+	0.0463403i
$879$	6.12121	+	15.7134i	0.206463	+	0.530001i
$880$	13.5879	−	6.54359i	0.458048	−	0.220584i
$881$	29.9296			1.00836			0.504178	−	0.863600i	$-0.331796\pi$
$881$	29.9296			1.00836			0.504178	+	0.863600i	$0.331796\pi$
$882$	−20.6816	+	3.64299i	−0.696386	+	0.122666i
$883$	−11.8783			−0.399735			−0.199868	−	0.979823i	$-0.564051\pi$
$883$	−11.8783			−0.399735			−0.199868	+	0.979823i	$0.564051\pi$
$884$	−23.5917	+	11.3612i	−0.793475	+	0.382118i
$885$	21.9235	−	27.3489i	0.736951	−	0.919322i
$886$	−0.298432	+	0.374222i	−0.0100260	+	0.0125723i
$887$	0.866275	+	0.803786i	0.0290867	+	0.0269885i	0.694582	−	0.719413i	$-0.255589\pi$
$887$	0.866275	+	0.803786i	0.0290867	+	0.0269885i	−0.665496	+	0.746402i	$0.731780\pi$
$888$	1.45532	+	1.35721i	0.0488373	+	0.0455450i
$889$	−36.8485	+	30.2954i	−1.23586	+	1.01608i
$890$	−4.65918	+	20.4132i	−0.156176	+	0.684251i
$891$	−17.0713	−	44.8266i	−0.571910	−	1.50175i
$892$	−10.1418	−	3.12832i	−0.339571	−	0.104744i
$893$	−26.6419	−	18.1642i	−0.891539	−	0.607841i
$894$	1.64323	+	7.28441i	0.0549577	+	0.243627i
$895$	−25.2523	−	17.2167i	−0.844091	−	0.575491i
$896$	0.0394492	+	2.64546i	0.00131790	+	0.0883785i
$897$	0.527723	−	1.33467i	0.0176202	−	0.0445634i
$898$	−1.91684	−	8.39824i	−0.0639659	−	0.280253i
$899$	−19.9785	+	3.01127i	−0.666319	+	0.100431i
$900$	5.58913	+	7.08181i	0.186304	+	0.236060i
$901$	−42.6679	−	73.9030i	−1.42147	−	2.46207i
$902$	50.5567	−	7.62020i	1.68336	−	0.253725i
$903$	21.7304	−	46.5903i	0.723141	−	1.55043i
$904$	4.91868	+	0.741372i	0.163593	+	0.0246577i
$905$	10.2582	+	26.1374i	0.340994	+	0.868838i
$906$	9.31109	−	1.37932i	0.309340	−	0.0458248i
$907$	−0.466190	−	6.22088i	−0.0154796	−	0.206561i	−0.999581	−	0.0289522i	$-0.990783\pi$
$907$	−0.466190	−	6.22088i	−0.0154796	−	0.206561i	0.984101	−	0.177609i	$-0.0568361\pi$
$908$	−1.79376	−	0.270366i	−0.0595280	−	0.00897241i
$909$	14.9862	+	0.0758868i	0.497060	+	0.00251701i
$910$	−20.8850	+	17.1708i	−0.692330	+	0.569208i
$911$	48.1540	−	7.25804i	1.59541	−	0.240470i	0.709631	−	0.704573i	$-0.248862\pi$
$911$	48.1540	−	7.25804i	1.59541	−	0.240470i	0.885781	+	0.464104i	$0.153623\pi$
$912$	−10.1888	+	6.90889i	−0.337385	+	0.228776i
$913$	−46.3795			−1.53494
$914$	−15.0113	−	18.8236i	−0.496530	−	0.622629i
$915$	0.666913	−	2.88821i	0.0220475	−	0.0954813i
$916$	9.46708	−	6.45455i	0.312801	−	0.213264i
$917$	−3.52029	+	12.0474i	−0.116250	+	0.397840i
$918$	37.2961	−	5.33209i	1.23095	−	0.175985i
$919$	10.9738	−	27.9608i	0.361993	−	0.922343i	−0.627611	−	0.778527i	$-0.715967\pi$
$919$	10.9738	−	27.9608i	0.361993	−	0.922343i	0.989604	−	0.143816i	$-0.0459375\pi$
$920$	−0.536448	−	0.365744i	−0.0176862	−	0.0120582i
$921$	−24.9895	+	7.63899i	−0.823430	+	0.251713i
$922$	17.0621	−	11.6327i	0.561909	−	0.383103i
$923$	−5.22506	+	1.61172i	−0.171985	+	0.0530503i
$924$	−3.93884	−	24.1040i	−0.129578	−	0.792963i
$925$	3.30153	+	1.01839i	0.108554	+	0.0334843i
$926$	−5.95552	+	1.83704i	−0.195711	+	0.0603688i
$927$	−4.70182	−	8.23986i	−0.154428	−	0.270633i
$928$	−6.51212	−	6.04236i	−0.213771	−	0.198350i
$929$	35.6080	−	17.1479i	1.16826	−	0.562605i	0.253791	−	0.967259i	$-0.418322\pi$
$929$	35.6080	−	17.1479i	1.16826	−	0.562605i	0.914470	+	0.404654i	$0.132608\pi$
$930$	−10.0307	−	4.86187i	−0.328921	−	0.159427i
$931$	−26.1495	−	42.3253i	−0.857015	−	1.38716i
$932$	−1.77452	−	3.07355i	−0.0581262	−	0.100678i
$933$	15.6808	+	27.3194i	0.513366	+	0.894398i
$934$	−33.4059	+	10.3043i	−1.09307	+	0.337168i
$935$	−39.9500	−	101.791i	−1.30650	−	3.32892i
$936$	9.78493	−	4.65128i	0.319830	−	0.152032i
$937$	−0.784162	−	3.43564i	−0.0256174	−	0.112237i	0.960503	−	0.278271i	$-0.0897612\pi$
$937$	−0.784162	−	3.43564i	−0.0256174	−	0.112237i	−0.986120	+	0.166033i	$0.946904\pi$
$938$	1.92411	+	3.84762i	0.0628243	+	0.125629i
$939$	25.6648	+	3.93483i	0.837539	+	0.128408i
$940$	10.6071	−	7.23181i	0.345966	−	0.235876i
$941$	4.65505	+	20.3951i	0.151750	+	0.664861i	0.992376	+	0.123245i	$0.0393302\pi$
$941$	4.65505	+	20.3951i	0.151750	+	0.664861i	−0.840626	+	0.541616i	$0.817813\pi$
$942$	−2.00606	−	3.49501i	−0.0653610	−	0.113873i
$943$	−1.37235	−	1.72088i	−0.0446900	−	0.0560395i
$944$	−6.44338	+	3.10297i	−0.209714	+	0.100993i
$945$	36.1079	−	14.4770i	1.17459	−	0.470937i
$946$	53.8690	+	25.9420i	1.75143	+	0.843446i
$947$	3.23837	+	14.1882i	0.105233	+	0.461055i	0.999898	+	0.0143170i	$0.00455740\pi$
$947$	3.23837	+	14.1882i	0.105233	+	0.461055i	−0.894665	+	0.446738i	$0.852585\pi$
$948$	−7.50740	+	6.93056i	−0.243829	+	0.225094i
$949$	−16.1588			−0.524538
$950$	−10.6867	+	18.5100i	−0.346723	+	0.600542i
$951$	38.2695	−	35.3290i	1.24097	−	1.14562i
$952$	19.1489	+	1.14818i	0.620621	+	0.0372128i
$953$	16.8100	−	21.0790i	0.544528	−	0.682817i	−0.431086	−	0.902311i	$-0.641869\pi$
$953$	16.8100	−	21.0790i	0.544528	−	0.682817i	0.975614	+	0.219494i	$0.0704407\pi$
$954$	17.4991	+	30.6669i	0.566555	+	0.992879i
$955$	−34.5038	+	23.5243i	−1.11652	+	0.761229i
$956$	1.80017	+	24.0215i	0.0582215	+	0.776912i
$957$	67.6400	+	46.3675i	2.18649	+	1.49885i
$958$	25.0425	+	3.77455i	0.809086	+	0.121950i
$959$	21.1472	+	22.1204i	0.682878	+	0.714304i
$960$	−1.07852	−	4.78105i	−0.0348089	−	0.154308i
$961$	−25.8274			−0.833143
$962$	2.07458	−	3.59328i	0.0668872	−	0.115852i
$963$	12.1380	−	51.9655i	0.391140	−	1.67457i
$964$	−12.6737	+	11.7595i	−0.408192	+	0.378747i
$965$	28.8853	−	19.6937i	0.929851	−	0.633961i
$966$	−0.813883	+	0.665698i	−0.0261863	+	0.0214185i
$967$	35.7363	+	24.3646i	1.14920	+	0.783513i	0.979393	−	0.201964i	$-0.0647323\pi$
$967$	35.7363	+	24.3646i	1.14920	+	0.783513i	0.169810	+	0.985477i	$0.445685\pi$
$968$	17.2112	−	2.59417i	0.553188	−	0.0833797i
$969$	44.4330	+	77.4121i	1.42739	+	2.48684i
$970$	−15.1858	+	14.0904i	−0.487588	+	0.452416i
$971$	2.61114	+	34.8433i	0.0837955	+	1.11817i	0.867632	+	0.497207i	$0.165641\pi$
$971$	2.61114	+	34.8433i	0.0837955	+	1.11817i	−0.783837	+	0.620967i	$0.786740\pi$
$972$	−15.4425	+	2.12802i	−0.495319	+	0.0682564i
$973$	−7.43975	−	22.9010i	−0.238508	−	0.734173i
$974$	−23.1579	−	7.14325i	−0.742026	−	0.228885i
$975$	11.7654	−	14.6769i	0.376793	−	0.470037i
$976$	−0.377083	+	0.472847i	−0.0120701	+	0.0151355i
$977$	5.34225	−	23.4059i	0.170914	−	0.748822i	−0.814710	−	0.579868i	$-0.803104\pi$
$977$	5.34225	−	23.4059i	0.170914	−	0.748822i	0.985624	−	0.168954i	$-0.0540388\pi$
$978$	11.3721	−	19.5824i	0.363639	−	0.626175i
$979$	−19.7183	+	34.1531i	−0.630199	+	1.09154i
$980$	19.4899	−	3.53493i	0.622584	−	0.112919i
$981$	15.4043	−	38.6725i	0.491821	−	1.23472i
$982$	24.5923	+	16.7667i	0.784772	+	0.535048i
$983$	−52.6108	+	16.2283i	−1.67802	+	0.517602i	−0.980089	−	0.198558i	$-0.936374\pi$
$983$	−52.6108	+	16.2283i	−1.67802	+	0.517602i	−0.697936	+	0.716160i	$0.745898\pi$
$984$	1.28363	−	16.5659i	0.0409207	−	0.528103i
$985$	14.2756	+	13.2458i	0.454858	+	0.422047i
$986$	−47.2169	+	43.8109i	−1.50369	+	1.39522i
$987$	−6.37350	−	19.7893i	−0.202871	−	0.629899i
$988$	18.8156	+	17.4583i	0.598605	+	0.555424i
$989$	−0.192355	−	2.56681i	−0.00611655	−	0.0816197i
$990$	16.3161	+	42.1999i	0.518560	+	1.34120i
$991$	−2.69944	+	36.0215i	−0.0857505	+	1.14426i	0.773876	+	0.633337i	$0.218315\pi$
$991$	−2.69944	+	36.0215i	−0.0857505	+	1.14426i	−0.859626	+	0.510923i	$0.829304\pi$
$992$	1.41802	+	1.77814i	0.0450221	+	0.0564560i
$993$	−6.96157	−	12.1286i	−0.220919	−	0.384890i
$994$	3.91834	+	0.833069i	0.124282	+	0.0264234i
$995$	2.42430	+	32.3501i	0.0768556	+	1.02557i
$996$	−3.39114	+	14.6860i	−0.107452	+	0.465345i
$997$	−10.4597	+	26.6508i	−0.331261	+	0.844040i	0.664083	+	0.747659i	$0.268822\pi$
$997$	−10.4597	+	26.6508i	−0.331261	+	0.844040i	−0.995344	+	0.0963815i	$0.969273\pi$
$998$	−9.99853	+	17.3180i	−0.316498	+	0.548190i
$999$	−4.40697	+	4.02721i	−0.139430	+	0.127415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bb.b.151.2	yes	336
9.4	even	3		882.2.y.a.445.13	yes	336
49.37	even	21		882.2.y.a.331.13	✓	336
441.184	even	21	inner	882.2.bb.b.625.2	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.y.a.331.13	✓	336	49.37	even	21
882.2.y.a.445.13	yes	336	9.4	even	3
882.2.bb.b.151.2	yes	336	1.1	even	1	trivial
882.2.bb.b.625.2	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)

\(f(q)\)	\(=\)	\(q+(0.900969 - 0.433884i) q^{2} +(-1.71205 - 0.262484i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.07432 - 1.92469i) q^{5} +(-1.65639 + 0.506339i) q^{6} +(-0.0394492 - 2.64546i) q^{7} +(0.222521 - 0.974928i) q^{8} +(2.86220 + 0.898770i) q^{9} +O(q^{10})\)	\(q+(0.900969 - 0.433884i) q^{2} +(-1.71205 - 0.262484i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-2.07432 - 1.92469i) q^{5} +(-1.65639 + 0.506339i) q^{6} +(-0.0394492 - 2.64546i) q^{7} +(0.222521 - 0.974928i) q^{8} +(2.86220 + 0.898770i) q^{9} +(-2.70399 - 0.834070i) q^{10} +(-4.40359 - 3.00232i) q^{11} +(-1.27266 + 1.17488i) q^{12} +(2.98387 + 2.03437i) q^{13} +(-1.18336 - 2.36636i) q^{14} +(3.04613 + 3.83963i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-7.16964 + 1.08065i) q^{17} +(2.96872 - 0.432100i) q^{18} +(3.55369 + 6.15517i) q^{19} +(-2.79810 + 0.421745i) q^{20} +(-0.626852 + 4.53950i) q^{21} +(-5.27016 - 0.794349i) q^{22} +(0.0838262 + 0.213586i) q^{23} +(-0.636869 + 1.61071i) q^{24} +(0.224730 + 2.99881i) q^{25} +(3.57105 + 0.538250i) q^{26} +(-4.66431 - 2.29002i) q^{27} +(-2.09290 - 1.61857i) q^{28} +(8.78435 - 1.32403i) q^{29} +(4.41042 + 2.13772i) q^{30} -2.27432 q^{31} +(-0.623490 - 0.781831i) q^{32} +(6.75110 + 6.29599i) q^{33} +(-5.99074 + 4.08442i) q^{34} +(-5.00985 + 5.56345i) q^{35} +(2.48724 - 1.67739i) q^{36} +(0.419744 - 1.06949i) q^{37} +(5.87239 + 4.00373i) q^{38} +(-4.57454 - 4.26615i) q^{39} +(-2.33801 + 1.59403i) q^{40} +(-9.16683 + 2.82759i) q^{41} +(1.40484 + 4.36193i) q^{42} +(-10.7199 - 3.30666i) q^{43} +(-5.09290 + 1.57095i) q^{44} +(-4.20727 - 7.37318i) q^{45} +(0.168196 + 0.156063i) q^{46} +(-4.08753 + 1.96845i) q^{47} +(0.125063 + 1.72753i) q^{48} +(-6.99689 + 0.208722i) q^{49} +(1.50361 + 2.60433i) q^{50} +(12.5584 + 0.0317963i) q^{51} +(3.45095 - 1.06448i) q^{52} +(4.29986 + 10.9559i) q^{53} +(-5.19600 - 0.0394676i) q^{54} +(3.35594 + 14.7033i) q^{55} +(-2.58791 - 0.550210i) q^{56} +(-4.46844 - 11.4707i) q^{57} +(7.33995 - 5.00429i) q^{58} +(-1.59138 - 6.97230i) q^{59} +(4.90117 + 0.0124092i) q^{60} +(-0.377083 - 0.472847i) q^{61} +(-2.04910 + 0.986793i) q^{62} +(2.26475 - 7.60729i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-2.27398 - 9.96295i) q^{65} +(8.81425 + 2.74330i) q^{66} -1.62597 q^{67} +(-3.62531 + 6.27922i) q^{68} +(-0.0874515 - 0.387672i) q^{69} +(-2.09983 + 7.18619i) q^{70} +(-0.944023 + 1.18377i) q^{71} +(1.51314 - 2.59045i) q^{72} +(-3.69693 + 2.52052i) q^{73} +(-0.0858581 - 1.14570i) q^{74} +(0.402393 - 5.19309i) q^{75} +(7.02799 + 1.05930i) q^{76} +(-7.76879 + 11.7680i) q^{77} +(-5.97253 - 1.85885i) q^{78} +5.89897 q^{79} +(-1.41485 + 2.45060i) q^{80} +(7.38442 + 5.14493i) q^{81} +(-7.03218 + 6.52491i) q^{82} +(7.19001 - 4.90207i) q^{83} +(3.15829 + 3.32042i) q^{84} +(16.9520 + 11.5577i) q^{85} +(-11.0930 + 1.67200i) q^{86} +(-15.3867 - 0.0389573i) q^{87} +(-3.90694 + 3.62511i) q^{88} +(-0.552959 - 7.37872i) q^{89} +(-6.98973 - 4.81754i) q^{90} +(5.26412 - 7.97396i) q^{91} +(0.219253 + 0.0676305i) q^{92} +(3.89375 + 0.596975i) q^{93} +(-2.82866 + 3.54702i) q^{94} +(4.47529 - 19.6075i) q^{95} +(0.862225 + 1.50219i) q^{96} +(3.66044 - 6.34007i) q^{97} +(-6.21342 + 3.22389i) q^{98} +(-9.90559 - 12.5511i) 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

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Representations

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Database

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