LMFDB - Embedded newform 225.2.q.a.106.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			106.8
Character	$\chi$	$=$	225.106
Dual form			225.2.q.a.121.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39627 - 0.296787i) q^{2} +(-0.399711 + 1.68530i) q^{3} +(0.0344061 + 0.0153186i) q^{4} +(-2.10438 - 0.756030i) q^{5} +(1.05828 - 2.23451i) q^{6} +(1.20474 - 2.08666i) q^{7} +(2.26620 + 1.64649i) q^{8} +(-2.68046 - 1.34726i) q^{9} +O(q^{10})$	\(q+(-1.39627 - 0.296787i) q^{2} +(-0.399711 + 1.68530i) q^{3} +(0.0344061 + 0.0153186i) q^{4} +(-2.10438 - 0.756030i) q^{5} +(1.05828 - 2.23451i) q^{6} +(1.20474 - 2.08666i) q^{7} +(2.26620 + 1.64649i) q^{8} +(-2.68046 - 1.34726i) q^{9} +(2.71391 + 1.68018i) q^{10} +(0.0309094 + 0.00656999i) q^{11} +(-0.0395688 + 0.0518615i) q^{12} +(6.17253 - 1.31201i) q^{13} +(-2.30144 + 2.55600i) q^{14} +(2.11528 - 3.24432i) q^{15} +(-2.72598 - 3.02750i) q^{16} +(2.72065 + 1.97667i) q^{17} +(3.34281 + 2.67668i) q^{18} +(1.81267 + 1.31698i) q^{19} +(-0.0608222 - 0.0582481i) q^{20} +(3.03511 + 2.86440i) q^{21} +(-0.0412081 - 0.0183470i) q^{22} +(1.28687 - 1.42922i) q^{23} +(-3.68065 + 3.16110i) q^{24} +(3.85684 + 3.18195i) q^{25} -9.00793 q^{26} +(3.34195 - 3.97886i) q^{27} +(0.0734149 - 0.0533391i) q^{28} +(-0.977408 - 9.29942i) q^{29} +(-3.91638 + 3.90216i) q^{30} +(0.393002 - 3.73917i) q^{31} +(0.106511 + 0.184482i) q^{32} +(-0.0234272 + 0.0494655i) q^{33} +(-3.21212 - 3.56742i) q^{34} +(-4.11281 + 3.48032i) q^{35} +(-0.0715860 - 0.0874149i) q^{36} +(3.22975 - 9.94014i) q^{37} +(-2.14012 - 2.37684i) q^{38} +(-0.256096 + 10.9270i) q^{39} +(-3.52414 - 5.17815i) q^{40} +(-1.58800 + 0.337539i) q^{41} +(-3.38772 - 4.90027i) q^{42} +(-5.58816 + 9.67898i) q^{43} +(0.000962828 + 0.000699535i) q^{44} +(4.62214 + 4.86167i) q^{45} +(-2.22100 + 1.61365i) q^{46} +(0.330264 + 3.14225i) q^{47} +(6.19185 - 3.38396i) q^{48} +(0.597221 + 1.03442i) q^{49} +(-4.44084 - 5.58753i) q^{50} +(-4.41875 + 3.79501i) q^{51} +(0.232471 + 0.0494131i) q^{52} +(1.23376 - 0.896379i) q^{53} +(-5.84716 + 4.56373i) q^{54} +(-0.0600780 - 0.0371942i) q^{55} +(6.16584 - 2.74521i) q^{56} +(-2.94405 + 2.52848i) q^{57} +(-1.39522 + 13.2746i) q^{58} +(12.5447 - 2.66646i) q^{59} +(0.122477 - 0.0792211i) q^{60} +(-10.3888 - 2.20821i) q^{61} +(-1.65848 + 5.10426i) q^{62} +(-6.04054 + 3.97013i) q^{63} +(2.42385 + 7.45983i) q^{64} +(-13.9813 - 1.90565i) q^{65} +(0.0473915 - 0.0621144i) q^{66} +(0.237987 - 2.26429i) q^{67} +(0.0633271 + 0.109686i) q^{68} +(1.89428 + 2.74004i) q^{69} +(6.77551 - 3.63885i) q^{70} +(-3.63556 + 2.64139i) q^{71} +(-3.85620 - 7.46651i) q^{72} +(0.380414 + 1.17080i) q^{73} +(-7.45971 + 12.9206i) q^{74} +(-6.90416 + 5.22806i) q^{75} +(0.0421926 + 0.0730797i) q^{76} +(0.0509470 - 0.0565824i) q^{77} +(3.60057 - 15.1810i) q^{78} +(-0.0961757 - 0.915050i) q^{79} +(3.44761 + 8.43194i) q^{80} +(5.36976 + 7.22258i) q^{81} +2.31745 q^{82} +(5.07918 - 2.26140i) q^{83} +(0.0605475 + 0.145046i) q^{84} +(-4.23086 - 6.21655i) q^{85} +(10.6752 - 11.8560i) q^{86} +(16.0630 + 2.06986i) q^{87} +(0.0592293 + 0.0657808i) q^{88} +(-0.932477 - 2.86987i) q^{89} +(-5.01089 - 8.16001i) q^{90} +(4.69854 - 14.4606i) q^{91} +(0.0661697 - 0.0294607i) q^{92} +(6.14453 + 2.15691i) q^{93} +(0.471441 - 4.48546i) q^{94} +(-2.81887 - 4.14186i) q^{95} +(-0.353480 + 0.105763i) q^{96} +(1.08643 + 10.3367i) q^{97} +(-0.526882 - 1.62158i) q^{98} +(-0.0739999 - 0.0592538i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−1.39627	−	0.296787i	−0.987314	−	0.209860i	−0.314166	−	0.949368i	$-0.601725\pi$
$2$	−1.39627	−	0.296787i	−0.987314	−	0.209860i	−0.673148	+	0.739508i	$0.735058\pi$
$3$	−0.399711	+	1.68530i	−0.230773	+	0.973008i
$3$	−0.399711	+	1.68530i	−0.230773	+	0.973008i
$4$	0.0344061	+	0.0153186i	0.0172030	+	0.00765928i
$5$	−2.10438	−	0.756030i	−0.941108	−	0.338107i
$5$	−2.10438	−	0.756030i	−0.941108	−	0.338107i
$6$	1.05828	−	2.23451i	0.432041	−	0.912234i
$7$	1.20474	−	2.08666i	0.455348	−	0.788685i	−0.543361	−	0.839499i	$-0.682848\pi$
$7$	1.20474	−	2.08666i	0.455348	−	0.788685i	0.998708	+	0.0508144i	$0.0161817\pi$
$8$	2.26620	+	1.64649i	0.801221	+	0.582121i
$9$	−2.68046	−	1.34726i	−0.893487	−	0.449088i
$10$	2.71391	+	1.68018i	0.858214	+	0.531319i
$11$	0.0309094	+	0.00656999i	0.00931953	+	0.00198093i	0.212569	−	0.977146i	$-0.431817\pi$
$11$	0.0309094	+	0.00656999i	0.00931953	+	0.00198093i	−0.203250	+	0.979127i	$0.565150\pi$
$12$	−0.0395688	+	0.0518615i	−0.0114225	+	0.0149711i
$13$	6.17253	−	1.31201i	1.71195	−	0.363886i	0.755358	−	0.655312i	$-0.227463\pi$
$13$	6.17253	−	1.31201i	1.71195	−	0.363886i	0.956593	+	0.291426i	$0.0941297\pi$
$14$	−2.30144	+	2.55600i	−0.615085	+	0.683121i
$15$	2.11528	−	3.24432i	0.546163	−	0.837679i
$16$	−2.72598	−	3.02750i	−0.681494	−	0.756876i
$17$	2.72065	+	1.97667i	0.659854	+	0.479412i	0.866614	−	0.498980i	$-0.166292\pi$
$17$	2.72065	+	1.97667i	0.659854	+	0.479412i	−0.206760	+	0.978392i	$0.566292\pi$
$18$	3.34281	+	2.67668i	0.787907	+	0.630899i
$19$	1.81267	+	1.31698i	0.415855	+	0.302136i	0.775968	−	0.630772i	$-0.217262\pi$
$19$	1.81267	+	1.31698i	0.415855	+	0.302136i	−0.360113	+	0.932909i	$0.617262\pi$
$20$	−0.0608222	−	0.0582481i	−0.0136002	−	0.0130247i
$21$	3.03511	+	2.86440i	0.662314	+	0.625064i
$22$	−0.0412081	−	0.0183470i	−0.00878559	−	0.00391160i
$23$	1.28687	−	1.42922i	0.268331	−	0.298012i	−0.593888	−	0.804548i	$-0.702408\pi$
$23$	1.28687	−	1.42922i	0.268331	−	0.298012i	0.862219	+	0.506536i	$0.169074\pi$
$24$	−3.68065	+	3.16110i	−0.751309	+	0.645256i
$25$	3.85684	+	3.18195i	0.771367	+	0.636390i
$26$	−9.00793			−1.76660
$27$	3.34195	−	3.97886i	0.643159	−	0.765733i
$28$	0.0734149	−	0.0533391i	0.0138741	−	0.0100801i
$29$	−0.977408	−	9.29942i	−0.181500	−	1.72686i	−0.584271	−	0.811558i	$-0.698620\pi$
$29$	−0.977408	−	9.29942i	−0.181500	−	1.72686i	0.402771	−	0.915301i	$-0.368047\pi$
$30$	−3.91638	+	3.90216i	−0.715030	+	0.712435i
$31$	0.393002	−	3.73917i	0.0705853	−	0.671574i	−0.900827	−	0.434177i	$-0.857039\pi$
$31$	0.393002	−	3.73917i	0.0705853	−	0.671574i	0.971413	−	0.237397i	$-0.0762942\pi$
$32$	0.106511	+	0.184482i	0.0188286	+	0.0326121i
$33$	−0.0234272	+	0.0494655i	−0.00407816	+	0.00861083i
$34$	−3.21212	−	3.56742i	−0.550874	−	0.611808i
$35$	−4.11281	+	3.48032i	−0.695191	+	0.588281i
$36$	−0.0715860	−	0.0874149i	−0.0119310	−	0.0145692i
$37$	3.22975	−	9.94014i	0.530967	−	1.63415i	−0.221238	−	0.975220i	$-0.571010\pi$
$37$	3.22975	−	9.94014i	0.530967	−	1.63415i	0.752205	−	0.658929i	$-0.228990\pi$
$38$	−2.14012	−	2.37684i	−0.347173	−	0.385575i
$39$	−0.256096	+	10.9270i	−0.0410082	+	1.74972i
$40$	−3.52414	−	5.17815i	−0.557216	−	0.818737i
$41$	−1.58800	+	0.337539i	−0.248003	+	0.0527147i	−0.330236	−	0.943898i	$-0.607128\pi$
$41$	−1.58800	+	0.337539i	−0.248003	+	0.0527147i	0.0822327	+	0.996613i	$0.473795\pi$
$42$	−3.38772	−	4.90027i	−0.522737	−	0.756128i
$43$	−5.58816	+	9.67898i	−0.852186	+	1.47603i	0.0270444	+	0.999634i	$0.491390\pi$
$43$	−5.58816	+	9.67898i	−0.852186	+	1.47603i	−0.879231	+	0.476396i	$0.841943\pi$
$44$	0.000962828	0	0.000699535i	0.000145152	0	0.000105459i
$45$	4.62214	+	4.86167i	0.689028	+	0.724735i
$46$	−2.22100	+	1.61365i	−0.327468	+	0.237919i
$47$	0.330264	+	3.14225i	0.0481739	+	0.458344i	0.991844	+	0.127457i	$0.0406814\pi$
$47$	0.330264	+	3.14225i	0.0481739	+	0.458344i	−0.943670	+	0.330888i	$0.892652\pi$
$48$	6.19185	−	3.38396i	0.893716	−	0.488432i
$49$	0.597221	+	1.03442i	0.0853173	+	0.147774i
$50$	−4.44084	−	5.58753i	−0.628029	−	0.790197i
$51$	−4.41875	+	3.79501i	−0.618748	+	0.531408i
$52$	0.232471	+	0.0494131i	0.0322379	+	0.00685237i
$53$	1.23376	−	0.896379i	0.169470	−	0.123127i	−0.499817	−	0.866131i	$-0.666600\pi$
$53$	1.23376	−	0.896379i	0.169470	−	0.123127i	0.669287	+	0.743004i	$0.266600\pi$
$54$	−5.84716	+	4.56373i	−0.795697	+	0.621045i
$55$	−0.0600780	−	0.0371942i	−0.00810092	−	0.00501527i
$56$	6.16584	−	2.74521i	0.823945	−	0.366844i
$57$	−2.94405	+	2.52848i	−0.389949	+	0.334905i
$58$	−1.39522	+	13.2746i	−0.183201	+	1.74304i
$59$	12.5447	−	2.66646i	1.63318	−	0.347144i	0.702136	−	0.712043i	$-0.252230\pi$
$59$	12.5447	−	2.66646i	1.63318	−	0.347144i	0.931047	+	0.364899i	$0.118897\pi$
$60$	0.122477	−	0.0792211i	0.0158117	−	0.0102274i
$61$	−10.3888	−	2.20821i	−1.33015	−	0.282732i	−0.512619	−	0.858616i	$-0.671325\pi$
$61$	−10.3888	−	2.20821i	−1.33015	−	0.282732i	−0.817532	+	0.575884i	$0.804658\pi$
$62$	−1.65848	+	5.10426i	−0.210627	+	0.648242i
$63$	−6.04054	+	3.97013i	−0.761036	+	0.500189i
$64$	2.42385	+	7.45983i	0.302981	+	0.932479i
$65$	−13.9813	−	1.90565i	−1.73416	−	0.236366i
$66$	0.0473915	−	0.0621144i	0.00583349	−	0.00764576i
$67$	0.237987	−	2.26429i	0.0290747	−	0.276627i	−0.970320	−	0.241826i	$-0.922254\pi$
$67$	0.237987	−	2.26429i	0.0290747	−	0.276627i	0.999394	−	0.0348011i	$-0.0110798\pi$
$68$	0.0633271	+	0.109686i	0.00767954	+	0.0133014i
$69$	1.89428	+	2.74004i	0.228044	+	0.329861i
$70$	6.77551	−	3.63885i	0.809829	−	0.434926i
$71$	−3.63556	+	2.64139i	−0.431462	+	0.313475i	−0.782233	−	0.622986i	$-0.785919\pi$
$71$	−3.63556	+	2.64139i	−0.431462	+	0.313475i	0.350771	+	0.936461i	$0.385919\pi$
$72$	−3.85620	−	7.46651i	−0.454457	−	0.879937i
$73$	0.380414	+	1.17080i	0.0445241	+	0.137031i	0.970847	−	0.239698i	$-0.0770486\pi$
$73$	0.380414	+	1.17080i	0.0445241	+	0.137031i	−0.926323	+	0.376730i	$0.877049\pi$
$74$	−7.45971	+	12.9206i	−0.867174	+	1.50199i
$75$	−6.90416	+	5.22806i	−0.797223	+	0.603684i
$76$	0.0421926	+	0.0730797i	0.00483982	+	0.00838281i
$77$	0.0509470	−	0.0565824i	0.00580595	−	0.00644817i
$78$	3.60057	−	15.1810i	0.407684	−	1.71891i
$79$	−0.0961757	−	0.915050i	−0.0108206	−	0.102951i	0.987779	−	0.155864i	$-0.0498161\pi$
$79$	−0.0961757	−	0.915050i	−0.0108206	−	0.102951i	−0.998599	+	0.0529128i	$0.983149\pi$
$80$	3.44761	+	8.43194i	0.385454	+	0.942719i
$81$	5.36976	+	7.22258i	0.596640	+	0.802509i
$82$	2.31745			0.255920
$83$	5.07918	−	2.26140i	0.557512	−	0.248220i	−0.108583	−	0.994087i	$-0.534631\pi$
$83$	5.07918	−	2.26140i	0.557512	−	0.248220i	0.666095	+	0.745867i	$0.267965\pi$
$84$	0.0605475	+	0.145046i	0.00660628	+	0.0158259i
$85$	−4.23086	−	6.21655i	−0.458901	−	0.674280i
$86$	10.6752	−	11.8560i	1.15114	−	1.27847i
$87$	16.0630	+	2.06986i	1.72213	+	0.221912i
$88$	0.0592293	+	0.0657808i	0.00631387	+	0.00701226i
$89$	−0.932477	−	2.86987i	−0.0988424	−	0.304206i	0.889394	−	0.457142i	$-0.151127\pi$
$89$	−0.932477	−	2.86987i	−0.0988424	−	0.304206i	−0.988236	+	0.152937i	$0.951127\pi$
$90$	−5.01089	−	8.16001i	−0.528194	−	0.860141i
$91$	4.69854	−	14.4606i	0.492541	−	1.51589i
$92$	0.0661697	−	0.0294607i	0.00689867	−	0.00307149i
$93$	6.14453	+	2.15691i	0.637158	+	0.223661i
$94$	0.471441	−	4.48546i	0.0486254	−	0.462640i
$95$	−2.81887	−	4.14186i	−0.289210	−	0.424946i
$96$	−0.353480	+	0.105763i	−0.0360769	+	0.0107944i
$97$	1.08643	+	10.3367i	0.110310	+	1.04953i	0.899959	+	0.435974i	$0.143596\pi$
$97$	1.08643	+	10.3367i	0.110310	+	1.04953i	−0.789649	+	0.613559i	$0.789737\pi$
$98$	−0.526882	−	1.62158i	−0.0532232	−	0.163804i
$99$	−0.0739999	−	0.0592538i	−0.00743727	−	0.00595523i
$100$	0.0839556	+	0.168560i	0.00839556	+	0.0168560i
$101$	2.74091	−	4.74740i	0.272731	−	0.472384i	−0.696829	−	0.717237i	$-0.745406\pi$
$101$	2.74091	−	4.74740i	0.272731	−	0.472384i	0.969560	+	0.244853i	$0.0787398\pi$
$102$	7.29609	−	3.98744i	0.722420	−	0.394816i
$103$	−1.67428	−	0.745436i	−0.164971	−	0.0734500i	0.322590	−	0.946539i	$-0.395447\pi$
$103$	−1.67428	−	0.745436i	−0.164971	−	0.0734500i	−0.487561	+	0.873089i	$0.662113\pi$
$104$	16.1484	+	7.18972i	1.58348	+	0.705010i
$105$	−4.22144	−	8.32243i	−0.411971	−	0.812186i
$106$	−1.98870	+	0.885426i	−0.193160	+	0.0860002i
$107$	18.4750			1.78604			0.893021	−	0.450014i	$-0.148581\pi$
$107$	18.4750			1.78604			0.893021	+	0.450014i	$0.148581\pi$
$108$	0.175934	−	0.0857031i	0.0169293	−	0.00824678i
$109$	1.39665	−	4.29846i	0.133775	−	0.411718i	−0.861622	−	0.507550i	$-0.830551\pi$
$109$	1.39665	−	4.29846i	0.133775	−	0.411718i	0.995397	+	0.0958324i	$0.0305513\pi$
$110$	0.0728466	+	0.0697637i	0.00694565	+	0.00665170i
$111$	15.4611	+	9.41627i	1.46751	+	0.893753i
$112$	−9.60146	+	2.04085i	−0.907253	+	0.192843i
$113$	−3.64667	+	0.775123i	−0.343050	+	0.0729175i	−0.376215	−	0.926532i	$-0.622775\pi$
$113$	−3.64667	+	0.775123i	−0.343050	+	0.0729175i	0.0331652	+	0.999450i	$0.489441\pi$
$114$	4.86112	−	2.65669i	0.455286	−	0.248822i
$115$	−3.78860	+	2.03470i	−0.353288	+	0.189737i
$116$	0.108825	−	0.334929i	0.0101041	−	0.0310974i
$117$	−18.3129	−	4.79923i	−1.69302	−	0.443689i
$118$	−18.3072			−1.68532
$119$	7.40230	−	3.29572i	0.678568	−	0.302118i
$120$	10.1354	−	3.86947i	0.925228	−	0.353233i
$121$	−10.0481	−	4.47370i	−0.913463	−	0.406700i
$122$	13.8503	+	6.16653i	1.25394	+	0.558291i
$123$	0.0658854	−	2.81116i	0.00594069	−	0.253474i
$124$	0.0708003	−	0.122630i	0.00635806	−	0.0110125i
$125$	−5.71060	−	9.61192i	−0.510772	−	0.859716i
$126$	9.61253	−	3.75063i	0.856352	−	0.334133i
$127$	3.06084	+	9.42031i	0.271606	+	0.835917i	0.990098	+	0.140381i	$0.0448329\pi$
$127$	3.06084	+	9.42031i	0.271606	+	0.835917i	−0.718492	+	0.695536i	$0.755167\pi$
$128$	−1.21490	−	11.5590i	−0.107383	−	1.02168i
$129$	−14.0783	−	13.2865i	−1.23953	−	1.16981i
$130$	18.9561	+	6.81026i	1.66256	+	0.597300i
$131$	−0.0925641	+	0.880688i	−0.00808736	+	0.0769461i	−0.997821	−	0.0659772i	$-0.978984\pi$
$131$	−0.0925641	+	0.880688i	−0.00808736	+	0.0769461i	0.989734	+	0.142923i	$0.0456502\pi$
$132$	−0.00156378	+	0.00134304i	−0.000136109	+	0.000116897i
$133$	4.93189	−	2.19582i	0.427649	−	0.190402i
$134$	−1.00431	+	3.09094i	−0.0867590	+	0.267017i
$135$	−10.0409	+	5.84642i	−0.864182	+	0.503180i
$136$	2.91097	+	8.95903i	0.249613	+	0.768230i
$137$	−7.48952	−	8.31795i	−0.639873	−	0.710650i	0.332757	−	0.943013i	$-0.392021\pi$
$137$	−7.48952	−	8.31795i	−0.639873	−	0.710650i	−0.972629	+	0.232362i	$0.925355\pi$
$138$	−1.83172	−	4.38804i	−0.155927	−	0.373534i
$139$	−0.0269569	+	0.0299387i	−0.00228645	+	0.00253936i	−0.744287	−	0.667860i	$-0.767211\pi$
$139$	−0.0269569	+	0.0299387i	−0.00228645	+	0.00253936i	0.742001	+	0.670399i	$0.233877\pi$
$140$	−0.194819	+	0.0567418i	−0.0164652	+	0.00479556i
$141$	−5.42764	−	0.699399i	−0.457090	−	0.0589000i
$142$	5.86017	−	2.60912i	0.491775	−	0.218952i
$143$	0.199409			0.0166754
$144$	3.22803	+	11.7877i	0.269002	+	0.982310i
$145$	−4.97380	+	20.3085i	−0.413052	+	1.68653i
$146$	−0.183686	−	1.74765i	−0.0152019	−	0.144637i
$147$	−1.98202	+	0.593028i	−0.163474	+	0.0489121i
$148$	0.263392	−	0.292526i	0.0216506	−	0.0240455i
$149$	4.04741	+	7.01032i	0.331577	+	0.574308i	0.982821	−	0.184560i	$-0.0590861\pi$
$149$	4.04741	+	7.01032i	0.331577	+	0.574308i	−0.651245	+	0.758868i	$0.725753\pi$
$150$	11.1917	−	5.25074i	0.913799	−	0.428721i
$151$	−4.63305	+	8.02468i	−0.377032	+	0.653039i	−0.990629	−	0.136580i	$-0.956389\pi$
$151$	−4.63305	+	8.02468i	−0.377032	+	0.653039i	0.613597	+	0.789620i	$0.289722\pi$
$152$	1.93947	+	5.96908i	0.157312	+	0.484156i
$153$	−4.62950	−	8.96381i	−0.374273	−	0.724681i
$154$	−0.0879289	+	0.0638841i	−0.00708552	+	0.00514793i
$155$	−3.65395	+	7.57151i	−0.293492	+	0.608158i
$156$	−0.176197	+	0.372031i	−0.0141070	+	0.0297863i
$157$	−5.80545	−	10.0553i	−0.463326	−	0.802503i	0.535799	−	0.844346i	$-0.320011\pi$
$157$	−5.80545	−	10.0553i	−0.463326	−	0.802503i	−0.999124	+	0.0418424i	$0.986677\pi$
$158$	−0.137288	+	1.30620i	−0.0109220	+	0.103916i
$159$	1.01752	+	2.43755i	0.0806945	+	0.193310i
$160$	−0.0846650	−	0.468745i	−0.00669335	−	0.0370575i
$161$	−1.43195	−	4.40710i	−0.112854	−	0.347328i
$162$	−5.35408	−	11.6784i	−0.420656	−	0.917540i
$163$	−1.85642	+	5.71348i	−0.145406	+	0.447515i	−0.997063	−	0.0765854i	$-0.975598\pi$
$163$	−1.85642	+	5.71348i	−0.145406	+	0.447515i	0.851657	+	0.524100i	$0.175598\pi$
$164$	−0.0598073	−	0.0127124i	−0.00467016	−	0.000992674i
$165$	0.0866972	−	0.0863825i	0.00674937	−	0.00672487i
$166$	−7.76307	+	1.65009i	−0.602531	+	0.128072i
$167$	−1.41337	+	13.4473i	−0.109370	+	1.04058i	0.792882	+	0.609375i	$0.208580\pi$
$167$	−1.41337	+	13.4473i	−0.109370	+	1.04058i	−0.902252	+	0.431209i	$0.858087\pi$
$168$	2.16194	+	11.4886i	0.166797	+	0.886362i
$169$	24.5026	−	10.9093i	1.88482	−	0.839175i
$170$	4.06245	+	9.93567i	0.311575	+	0.762031i
$171$	−3.08447	−	5.97227i	−0.235875	−	0.456711i
$172$	−0.340535	+	0.247413i	−0.0259655	+	0.0188651i
$173$	6.61768	+	1.40663i	0.503133	+	0.106944i	0.452484	−	0.891772i	$-0.350538\pi$
$173$	6.61768	+	1.40663i	0.503133	+	0.106944i	0.0506485	+	0.998717i	$0.483871\pi$
$174$	−21.8140	−	7.65737i	−1.65372	−	0.580504i
$175$	11.2861	−	4.21451i	0.853152	−	0.318587i
$176$	−0.0643676	−	0.111488i	−0.00485189	−	0.00840372i
$177$	−0.520476	+	22.2074i	−0.0391214	+	1.66921i
$178$	0.450253	+	4.28387i	0.0337479	+	0.321090i
$179$	5.82355	−	4.23106i	0.435272	−	0.316244i	−0.348481	−	0.937316i	$-0.613302\pi$
$179$	5.82355	−	4.23106i	0.435272	−	0.316244i	0.783754	+	0.621072i	$0.213302\pi$
$180$	0.0845559	+	0.238075i	0.00630242	+	0.0177451i
$181$	−5.56870	−	4.04590i	−0.413918	−	0.300729i	0.361268	−	0.932462i	$-0.382344\pi$
$181$	−5.56870	−	4.04590i	−0.413918	−	0.300729i	−0.775186	+	0.631733i	$0.782344\pi$
$182$	−10.8522	+	18.7965i	−0.804417	+	1.39329i
$183$	7.87402	−	16.6256i	0.582064	−	1.22900i
$184$	5.26949	−	1.12006i	0.388472	−	0.0825722i
$185$	−14.3117	+	18.4760i	−1.05221	+	1.35839i
$186$	−7.93929	−	4.83525i	−0.582137	−	0.354538i
$187$	0.0711069	+	0.0789722i	0.00519985	+	0.00577502i
$188$	−0.0367717	+	0.113172i	−0.00268185	+	0.00825389i
$189$	−4.27638	−	11.7670i	−0.311061	−	0.855924i
$190$	2.70666	+	6.61978i	0.196362	+	0.480249i
$191$	7.55661	+	8.39246i	0.546777	+	0.607257i	0.951676	−	0.307104i	$-0.0993600\pi$
$191$	7.55661	+	8.39246i	0.546777	+	0.607257i	−0.404899	+	0.914361i	$0.632693\pi$
$192$	−13.5409	+	1.10313i	−0.977229	+	0.0796114i
$193$	11.1617	+	19.3326i	0.803434	+	1.39159i	0.917343	+	0.398098i	$0.130330\pi$
$193$	11.1617	+	19.3326i	0.803434	+	1.39159i	−0.113909	+	0.993491i	$0.536337\pi$
$194$	1.55084	−	14.7553i	0.111344	−	1.05937i
$195$	8.80005	−	22.8009i	0.630185	−	1.63281i
$196$	0.00470224	+	0.0447388i	0.000335874	+	0.00319563i
$197$	−21.1964	+	15.4001i	−1.51018	+	1.09721i	−0.544083	+	0.839031i	$0.683122\pi$
$197$	−21.1964	+	15.4001i	−1.51018	+	1.09721i	−0.966097	+	0.258179i	$0.916878\pi$
$198$	0.0857384	+	0.104697i	0.00609316	+	0.00744047i
$199$	−16.6094			−1.17741			−0.588703	−	0.808349i	$-0.700361\pi$
$199$	−16.6094			−1.17741			−0.588703	+	0.808349i	$0.700361\pi$
$200$	3.50130	+	13.5612i	0.247580	+	0.958919i
$201$	3.72088	+	1.30614i	0.262451	+	0.0921281i
$202$	−5.23603	+	5.81520i	−0.368406	+	0.409156i
$203$	−20.5823	−	9.16383i	−1.44459	−	0.643174i
$204$	−0.210166	+	0.0628825i	−0.0147145	+	0.00440265i
$205$	3.59694	+	0.490262i	0.251221	+	0.0342414i
$206$	2.11651	+	1.53774i	0.147464	+	0.107139i
$207$	−5.37494	+	2.09720i	−0.373584	+	0.145766i
$208$	−20.7983	−	15.1108i	−1.44210	−	1.04775i
$209$	0.0473760	+	0.0526163i	0.00327706	+	0.00363955i
$210$	3.42430	+	12.8733i	0.236299	+	0.888339i
$211$	−6.43842	+	7.15059i	−0.443239	+	0.492267i	−0.922820	−	0.385231i	$-0.874122\pi$
$211$	−6.43842	+	7.15059i	−0.443239	+	0.492267i	0.479581	+	0.877498i	$0.340789\pi$
$212$	0.0561800	−	0.0119414i	0.00385846	−	0.000820141i
$213$	−2.99836	−	7.18280i	−0.205444	−	0.492158i
$214$	−25.7961	−	5.48313i	−1.76339	−	0.374819i
$215$	19.0772	−	16.1434i	1.30106	−	1.10097i
$216$	14.1247	−	3.51440i	0.961062	−	0.239125i
$217$	−7.32892	−	5.32477i	−0.497520	−	0.361469i
$218$	−3.22584	+	5.58731i	−0.218481	+	0.378421i
$219$	−2.12520	+	0.173132i	−0.143607	+	0.0116992i
$220$	−0.00149729	−	0.00220002i	−0.000100947	−	0.000148325i
$221$	19.3867	+	8.63151i	1.30409	+	0.580618i
$222$	−18.7933	−	17.7363i	−1.26133	−	1.19039i
$223$	25.3493	+	5.38816i	1.69752	+	0.360818i	0.952101	−	0.305783i	$-0.0989181\pi$
$223$	25.3493	+	5.38816i	1.69752	+	0.360818i	0.745415	+	0.666601i	$0.232251\pi$
$224$	0.513268			0.0342942
$225$	−6.05117	−	13.7253i	−0.403412	−	0.915019i
$226$	5.32179			0.354000
$227$	−19.7314	−	4.19403i	−1.30962	−	0.278367i	−0.500357	−	0.865819i	$-0.666798\pi$
$227$	−19.7314	−	4.19403i	−1.30962	−	0.278367i	−0.809259	+	0.587452i	$0.800131\pi$
$228$	−0.140026	+	0.0418963i	−0.00927344	+	0.00277465i
$229$	−6.35755	−	2.83057i	−0.420119	−	0.187049i	0.185779	−	0.982592i	$-0.440519\pi$
$229$	−6.35755	−	2.83057i	−0.420119	−	0.187049i	−0.605898	+	0.795543i	$0.707186\pi$
$230$	5.89379	−	1.71659i	0.388625	−	0.113189i
$231$	0.0749942	+	0.108478i	0.00493426	+	0.00713730i
$232$	13.0964	−	22.6836i	0.859820	−	1.48925i
$233$	−22.8409	−	16.5949i	−1.49636	−	1.08717i	−0.971805	−	0.235787i	$-0.924233\pi$
$233$	−22.8409	−	16.5949i	−1.49636	−	1.08717i	−0.524551	−	0.851379i	$-0.675767\pi$
$234$	24.1454	+	12.1361i	1.57843	+	0.793359i
$235$	1.68064	−	6.86218i	0.109633	−	0.447639i
$236$	0.472461	+	0.100425i	0.0307546	+	0.00653709i
$237$	1.58058	+	0.203671i	0.102669	+	0.0132298i
$238$	−11.3138	+	2.40482i	−0.733363	+	0.155881i
$239$	2.97588	−	3.30505i	0.192494	−	0.213786i	−0.639170	−	0.769065i	$-0.720722\pi$
$239$	2.97588	−	3.30505i	0.192494	−	0.213786i	0.831664	+	0.555279i	$0.187389\pi$
$240$	−15.5884	+	2.43991i	−1.00623	+	0.157495i
$241$	10.1498	+	11.2725i	0.653804	+	0.726123i	0.975324	−	0.220780i	$-0.0708602\pi$
$241$	10.1498	+	11.2725i	0.653804	+	0.726123i	−0.321519	+	0.946903i	$0.604194\pi$
$242$	12.7021	+	9.22865i	0.816525	+	0.593240i
$243$	−14.3186	+	6.16270i	−0.918536	+	0.395337i
$244$	−0.323612	−	0.235118i	−0.0207171	−	0.0150519i
$245$	−0.474730	−	2.62833i	−0.0303294	−	0.167918i
$246$	−0.926311	+	3.90560i	−0.0590594	+	0.249012i
$247$	12.9167	+	5.75086i	0.821867	+	0.365919i
$248$	7.04711	−	7.82661i	0.447492	−	0.496990i
$249$	1.78092	+	9.46384i	0.112861	+	0.599746i
$250$	5.12087	+	15.1157i	0.323872	+	0.956001i
$251$	−14.0348			−0.885869			−0.442935	−	0.896554i	$-0.646063\pi$
$251$	−14.0348			−0.885869			−0.442935	+	0.896554i	$0.646063\pi$
$252$	−0.268648	+	0.0440640i	−0.0169232	+	0.00277577i
$253$	0.0491663	−	0.0357214i	0.00309106	−	0.00224579i
$254$	−1.47795	−	14.0617i	−0.0927347	−	0.882312i
$255$	12.1679	−	4.64544i	0.761981	−	0.290909i
$256$	−0.0944491	+	0.898623i	−0.00590307	+	0.0561639i
$257$	−4.76132	−	8.24684i	−0.297003	−	0.514424i	0.678446	−	0.734650i	$-0.262654\pi$
$257$	−4.76132	−	8.24684i	−0.297003	−	0.514424i	−0.975449	+	0.220226i	$0.929320\pi$
$258$	15.7139	+	22.7299i	0.978306	+	1.41510i
$259$	−16.8507	−	18.7146i	−1.04705	−	1.16287i
$260$	−0.451849	−	0.279739i	−0.0280225	−	0.0173487i
$261$	−9.90887	+	26.2436i	−0.613344	+	1.62444i
$262$	0.390622	−	1.20221i	0.0241327	−	0.0742728i
$263$	16.2416	+	18.0382i	1.00150	+	1.11228i	0.993673	+	0.112312i	$0.0358256\pi$
$263$	16.2416	+	18.0382i	1.00150	+	1.11228i	0.00782953	+	0.999969i	$0.497508\pi$
$264$	−0.134535	+	0.0735258i	−0.00828006	+	0.00452520i
$265$	−3.27399	+	0.953563i	−0.201120	+	0.0585769i
$266$	−7.53795	+	1.60224i	−0.462182	+	0.0982397i
$267$	5.20931	−	0.424384i	0.318804	−	0.0259719i
$268$	0.0428739	−	0.0742598i	0.00261894	−	0.00453614i
$269$	−12.9182	−	9.38564i	−0.787638	−	0.572252i	0.119624	−	0.992819i	$-0.461831\pi$
$269$	−12.9182	−	9.38564i	−0.787638	−	0.572252i	−0.907262	+	0.420567i	$0.861831\pi$
$270$	15.7550	−	5.18320i	0.958816	−	0.315440i
$271$	11.6010	−	8.42860i	0.704709	−	0.512001i	−0.176754	−	0.984255i	$-0.556560\pi$
$271$	11.6010	−	8.42860i	0.704709	−	0.512001i	0.881462	+	0.472254i	$0.156560\pi$
$272$	−1.43206	−	13.6251i	−0.0868312	−	0.826144i
$273$	22.4924	+	13.6985i	1.36130	+	0.829072i
$274$	7.98875	+	13.8369i	0.482618	+	0.835919i
$275$	0.0983071	+	0.123692i	0.00592814	+	0.00745888i
$276$	0.0232012	+	0.123291i	0.00139655	+	0.00742127i
$277$	15.4429	+	3.28249i	0.927874	+	0.197226i	0.646975	−	0.762511i	$-0.276034\pi$
$277$	15.4429	+	3.28249i	0.927874	+	0.197226i	0.280900	+	0.959737i	$0.409367\pi$
$278$	0.0465246	−	0.0338021i	0.00279036	−	0.00202732i
$279$	−6.09107	+	9.49322i	−0.364663	+	0.568344i
$280$	−15.0507	+	1.11540i	−0.899453	+	0.0666580i
$281$	−1.34937	+	0.600776i	−0.0804964	+	0.0358393i	−0.446590	−	0.894739i	$-0.647362\pi$
$281$	−1.34937	+	0.600776i	−0.0804964	+	0.0358393i	0.366094	+	0.930578i	$0.380695\pi$
$282$	7.37090	+	2.58741i	0.438931	+	0.154078i
$283$	1.42383	−	13.5468i	0.0846376	−	0.805273i	−0.867053	−	0.498215i	$-0.833989\pi$
$283$	1.42383	−	13.5468i	0.0846376	−	0.805273i	0.951691	−	0.307058i	$-0.0993445\pi$
$284$	−0.165548	+	0.0351883i	−0.00982345	+	0.00208804i
$285$	8.10701	−	3.09509i	0.480218	−	0.183337i
$286$	−0.278430	−	0.0591820i	−0.0164639	−	0.00349951i
$287$	−1.20879	+	3.72026i	−0.0713523	+	0.219600i
$288$	−0.0369519	−	0.637994i	−0.00217741	−	0.0375941i
$289$	−1.75857	−	5.41233i	−0.103445	−	0.318372i
$290$	12.9721	−	26.8800i	0.761747	−	1.57845i
$291$	−17.8547	−	2.30073i	−1.04666	−	0.134871i
$292$	−0.00484634	+	0.0461099i	−0.000283611	+	0.00269838i
$293$	−8.13530	−	14.0908i	−0.475270	−	0.823191i	0.524329	−	0.851516i	$-0.324316\pi$
$293$	−8.13530	−	14.0908i	−0.475270	−	0.823191i	−0.999599	+	0.0283246i	$0.990983\pi$
$294$	2.94344	−	0.239792i	0.171665	−	0.0139849i
$295$	−28.4148	−	3.87293i	−1.65437	−	0.225491i
$296$	23.6856	−	17.2086i	1.37669	−	1.00023i
$297$	0.129439	−	0.101028i	0.00751080	−	0.00586222i
$298$	−3.57072	−	10.9895i	−0.206846	−	0.636607i
$299$	6.06810	−	10.5103i	0.350927	−	0.607824i
$300$	−0.317631	+	0.0741152i	−0.0183385	+	0.00427904i
$301$	13.4645	+	23.3212i	0.776082	+	1.34421i
$302$	8.85063	−	9.82962i	0.509296	−	0.565631i
$303$	6.90521	+	6.51684i	0.396694	+	0.374383i
$304$	−0.954128	−	9.07792i	−0.0547230	−	0.520654i
$305$	20.1925	+	12.5012i	1.15622	+	0.715815i
$306$	3.80371	+	13.8899i	0.217443	+	0.794033i
$307$	14.3507			0.819040			0.409520	−	0.912301i	$-0.365696\pi$
$307$	14.3507			0.819040			0.409520	+	0.912301i	$0.365696\pi$
$308$	0.00261965	−	0.00116634i	0.000149268	−	6.64586e-5i
$309$	1.92551	−	2.52370i	0.109538	−	0.143568i
$310$	7.34904	−	9.48745i	0.417397	−	0.538851i
$311$	−14.9819	+	16.6391i	−0.849544	+	0.943514i	−0.998975	−	0.0452580i	$-0.985589\pi$
$311$	−14.9819	+	16.6391i	−0.849544	+	0.943514i	0.149431	+	0.988772i	$0.452256\pi$
$312$	−18.5715	+	24.3410i	−1.05140	+	1.37804i
$313$	−16.3521	−	18.1608i	−0.924273	−	1.02651i	−0.999569	−	0.0293476i	$-0.990657\pi$
$313$	−16.3521	−	18.1608i	−0.924273	−	1.02651i	0.0752966	−	0.997161i	$-0.476010\pi$
$314$	5.12170	+	15.7630i	0.289035	+	0.889557i
$315$	15.7131	−	3.78783i	0.885335	−	0.213420i
$316$	0.0107082	−	0.0329566i	0.000602385	−	0.00185395i
$317$	15.8022	−	7.03561i	0.887542	−	0.395159i	0.0882473	−	0.996099i	$-0.471873\pi$
$317$	15.8022	−	7.03561i	0.887542	−	0.395159i	0.799294	+	0.600940i	$0.205207\pi$
$318$	−0.697302	−	3.70547i	−0.0391028	−	0.207792i
$319$	0.0308860	−	0.293861i	0.00172929	−	0.0164531i
$320$	0.539164	−	17.5308i	0.0301402	−	0.980003i
$321$	−7.38465	+	31.1358i	−0.412171	+	1.73783i
$322$	0.691428	+	6.57850i	0.0385318	+	0.366605i
$323$	2.32840	+	7.16609i	0.129556	+	0.398732i
$324$	0.0741126	+	0.330758i	0.00411736	+	0.0183754i
$325$	27.9812	+	14.5805i	1.55212	+	0.808779i
$326$	4.28776	−	7.42662i	0.237477	−	0.411323i
$327$	6.68593	+	4.07192i	0.369733	+	0.225178i
$328$	−4.15446	−	1.84969i	−0.229392	−	0.102132i
$329$	6.95471	+	3.09643i	0.383425	+	0.170712i
$330$	−0.146690	+	0.0948829i	−0.00807503	+	0.00522313i
$331$	−23.9484	+	10.6625i	−1.31632	+	0.586064i	−0.940237	−	0.340522i	$-0.889396\pi$
$331$	−23.9484	+	10.6625i	−1.31632	+	0.586064i	−0.376084	+	0.926585i	$0.622730\pi$
$332$	0.209396			0.0114921
$333$	−22.0492	+	22.2928i	−1.20829	+	1.22164i
$334$	5.96444	−	18.3567i	0.326360	−	1.00443i
$335$	−2.21269	+	4.58501i	−0.120892	+	0.250506i
$336$	0.398362	−	16.9971i	0.0217324	−	0.927267i
$337$	−15.7941	+	3.35713i	−0.860358	+	0.182875i	−0.616905	−	0.787038i	$-0.711614\pi$
$337$	−15.7941	+	3.35713i	−0.860358	+	0.182875i	−0.243453	+	0.969913i	$0.578280\pi$
$338$	−37.4501	+	7.96027i	−2.03702	+	0.432982i
$339$	0.151299	−	6.45555i	0.00821744	−	0.350617i
$340$	−0.0503386	−	0.278698i	−0.00272999	−	0.0151145i
$341$	0.0367138	−	0.112993i	0.00198816	−	0.00611893i
$342$	2.53427	+	9.25435i	0.137038	+	0.500418i
$343$	19.7443			1.06609
$344$	−28.6002	+	12.7336i	−1.54202	+	0.686551i
$345$	−1.91473	−	7.19821i	−0.103086	−	0.387539i
$346$	−8.82262	−	3.92808i	−0.474307	−	0.211175i
$347$	−17.1275	−	7.62567i	−0.919454	−	0.409367i	−0.108246	−	0.994124i	$-0.534523\pi$
$347$	−17.1275	−	7.62567i	−0.919454	−	0.409367i	−0.811209	+	0.584757i	$0.801190\pi$
$348$	0.520957	+	0.317277i	0.0279262	+	0.0170079i
$349$	−0.899591	+	1.55814i	−0.0481540	+	0.0834051i	−0.889098	−	0.457717i	$-0.848667\pi$
$349$	−0.899591	+	1.55814i	−0.0481540	+	0.0834051i	0.840944	+	0.541123i	$0.182000\pi$
$350$	−17.0093	+	2.53503i	−0.909188	+	0.135503i
$351$	15.4080	−	28.9443i	0.822417	−	1.54493i
$352$	0.00208013	+	0.00640199i	0.000110871	+	0.000341227i
$353$	0.191932	+	1.82612i	0.0102155	+	0.0971943i	0.998442	−	0.0558064i	$-0.0177730\pi$
$353$	0.191932	+	1.82612i	0.0102155	+	0.0971943i	−0.988226	+	0.153001i	$0.951106\pi$
$354$	7.31760	−	30.8531i	0.388926	−	1.63983i
$355$	9.64758	−	2.80990i	0.512040	−	0.149134i
$356$	0.0118794	−	0.113025i	0.000629608	−	0.00599032i
$357$	2.59549	+	13.7924i	0.137368	+	0.729973i
$358$	−9.38699	+	4.17936i	−0.496118	+	0.220886i
$359$	−10.8516	+	33.3977i	−0.572724	+	1.76266i	0.0710775	+	0.997471i	$0.477356\pi$
$359$	−10.8516	+	33.3977i	−0.572724	+	1.76266i	−0.643802	+	0.765192i	$0.722644\pi$
$360$	2.47000	+	18.6278i	0.130180	+	0.981771i
$361$	−4.31999	−	13.2956i	−0.227368	−	0.699767i
$362$	6.57466	+	7.30190i	0.345557	+	0.383779i
$363$	11.5558	−	15.1458i	0.606525	−	0.794951i
$364$	0.383174	−	0.425558i	0.0200838	−	0.0223053i
$365$	0.0846199	−	2.75140i	0.00442921	−	0.144015i
$366$	−15.9285	+	20.8770i	−0.832598	+	1.09126i
$367$	21.9643	−	9.77913i	1.14653	−	0.510466i	0.256576	−	0.966524i	$-0.417406\pi$
$367$	21.9643	−	9.77913i	1.14653	−	0.510466i	0.889950	+	0.456058i	$0.150739\pi$
$368$	−7.83493			−0.408424
$369$	4.71132	+	1.23469i	0.245261	+	0.0642754i
$370$	25.4664	−	21.5501i	1.32394	−	1.12034i
$371$	−0.384087	−	3.65434i	−0.0199408	−	0.189724i
$372$	0.178368	+	0.168336i	0.00924796	+	0.00872782i
$373$	1.34951	−	1.49879i	0.0698751	−	0.0776042i	−0.707194	−	0.707020i	$-0.750039\pi$
$373$	1.34951	−	1.49879i	0.0698751	−	0.0776042i	0.777069	+	0.629416i	$0.216706\pi$
$374$	−0.0758467	−	0.131370i	−0.00392194	−	0.00679300i
$375$	18.4815	−	5.78208i	0.954383	−	0.298585i
$376$	−4.42524	+	7.66473i	−0.228214	+	0.395278i
$377$	−18.2340	−	56.1186i	−0.939100	−	2.89025i
$378$	2.47870	+	17.6991i	0.127490	+	0.910346i
$379$	−15.2526	+	11.0817i	−0.783474	+	0.569227i	−0.906020	−	0.423236i	$-0.860894\pi$
$379$	−15.2526	+	11.0817i	−0.783474	+	0.569227i	0.122546	+	0.992463i	$0.460894\pi$
$380$	−0.0335388	−	0.185686i	−0.00172050	−	0.00952551i
$381$	−17.0995	+	1.39303i	−0.876033	+	0.0713673i
$382$	−8.06032	−	13.9609i	−0.412402	−	0.714301i
$383$	−1.15667	+	11.0050i	−0.0591029	+	0.562327i	0.924399	+	0.381428i	$0.124567\pi$
$383$	−1.15667	+	11.0050i	−0.0591029	+	0.562327i	−0.983502	+	0.180899i	$0.942099\pi$
$384$	19.9660	+	2.57280i	1.01889	+	0.131293i
$385$	−0.149990	+	0.0805535i	−0.00764420	+	0.00410538i
$386$	−9.84708	−	30.3062i	−0.501203	−	1.54254i
$387$	28.0190	−	18.4154i	1.42429	−	0.936108i
$388$	−0.120964	+	0.372288i	−0.00614100	+	0.0189000i
$389$	21.1676	+	4.49931i	1.07324	+	0.228124i	0.710450	−	0.703747i	$-0.248491\pi$
$389$	21.1676	+	4.49931i	1.07324	+	0.228124i	0.362789	+	0.931871i	$0.381825\pi$
$390$	−19.0543	+	29.2246i	−0.964852	+	1.47984i
$391$	6.32621	−	1.34468i	0.319930	−	0.0680032i
$392$	−0.349735	+	3.32751i	−0.0176643	+	0.168065i
$393$	−1.44722	−	0.508019i	−0.0730028	−	0.0256262i
$394$	34.1665	−	15.2119i	1.72128	−	0.766365i
$395$	−0.489416	+	1.99833i	−0.0246252	+	0.100547i
$396$	−0.00163836	−	0.00317226i	−8.23309e−5	−	0.000159412i
$397$	6.42510	−	4.66811i	0.322467	−	0.234286i	−0.414761	−	0.909931i	$-0.636135\pi$
$397$	6.42510	−	4.66811i	0.322467	−	0.234286i	0.737227	+	0.675645i	$0.236135\pi$
$398$	23.1912	+	4.92945i	1.16247	+	0.247091i
$399$	1.72928	+	9.18940i	0.0865722	+	0.460045i
$400$	−0.880276	−	20.3505i	−0.0440138	−	1.01752i
$401$	6.27204	+	10.8635i	0.313211	+	0.542497i	0.979056	−	0.203593i	$-0.0652621\pi$
$401$	6.27204	+	10.8635i	0.313211	+	0.542497i	−0.665845	+	0.746090i	$0.731929\pi$
$402$	−4.80773	−	2.92804i	−0.239788	−	0.146037i
$403$	−2.48001	−	23.5957i	−0.123538	−	1.17539i
$404$	0.167027	−	0.121352i	0.00830992	−	0.00603751i
$405$	−5.83952	−	19.2588i	−0.290168	−	0.956976i
$406$	26.0188	+	18.9038i	1.29129	+	0.938178i
$407$	0.165136	−	0.286024i	0.00818549	−	0.0141777i
$408$	−16.2622	+	1.32482i	−0.805098	+	0.0655885i
$409$	4.34031	−	0.922562i	0.214615	−	0.0456178i	−0.0993494	−	0.995053i	$-0.531676\pi$
$409$	4.34031	−	0.922562i	0.214615	−	0.0456178i	0.313964	+	0.949435i	$0.398343\pi$
$410$	−4.87680	−	1.75206i	−0.240848	−	0.0865283i
$411$	17.0119	−	9.29729i	0.839134	−	0.458602i
$412$	−0.0461862	−	0.0512950i	−0.00227543	−	0.00252712i
$413$	9.54906	−	29.3890i	0.469879	−	1.44614i
$414$	8.12731	−	1.33305i	0.399435	−	0.0655160i
$415$	−12.3982	+	0.918825i	−0.608604	+	0.0451034i
$416$	0.899481	+	0.998975i	0.0441007	+	0.0489788i
$417$	−0.0396806	−	0.0573972i	−0.00194317	−	0.00281075i
$418$	−0.0505340	−	0.0875274i	−0.00247170	−	0.00428110i
$419$	0.767053	−	7.29802i	0.0374730	−	0.356532i	−0.959678	−	0.281101i	$-0.909300\pi$
$419$	0.767053	−	7.29802i	0.0374730	−	0.356532i	0.997151	−	0.0754304i	$-0.0240331\pi$
$420$	−0.0177556	−	0.351008i	−0.000866385	−	0.0171275i
$421$	0.818284	+	7.78545i	0.0398807	+	0.379439i	0.996199	+	0.0871109i	$0.0277634\pi$
$421$	0.818284	+	7.78545i	0.0398807	+	0.379439i	−0.956318	+	0.292329i	$0.905570\pi$
$422$	11.1120	−	8.07334i	0.540924	−	0.393004i
$423$	3.34818	−	8.86764i	0.162794	−	0.431159i
$424$	4.27182			0.207458
$425$	4.20344	+	16.2807i	0.203897	+	0.789728i
$426$	2.05477	+	10.9190i	0.0995537	+	0.529029i
$427$	−17.1236	+	19.0177i	−0.828668	+	0.920329i
$428$	0.635651	+	0.283010i	0.0307254	+	0.0136798i
$429$	−0.0797060	+	0.336064i	−0.00384824	+	0.0162253i
$430$	−31.4282	+	16.8788i	−1.51560	+	0.813967i
$431$	10.2026	+	7.41261i	0.491441	+	0.357053i	0.805738	−	0.592272i	$-0.201769\pi$
$431$	10.2026	+	7.41261i	0.491441	+	0.357053i	−0.314297	+	0.949325i	$0.601769\pi$
$432$	−21.1561	+	0.728511i	−1.01787	+	0.0350505i
$433$	30.3440	+	22.0462i	1.45824	+	1.05947i	0.983817	+	0.179179i	$0.0573441\pi$
$433$	30.3440	+	22.0462i	1.45824	+	1.05947i	0.474425	+	0.880296i	$0.342656\pi$
$434$	8.65286	+	9.60997i	0.415350	+	0.461293i
$435$	−32.2378	−	16.4999i	−1.54568	−	0.791108i
$436$	0.113900	−	0.126498i	0.00545480	−	0.00605817i
$437$	4.21492	−	0.895910i	0.201627	−	0.0428572i
$438$	3.01874	+	0.388991i	0.144241	+	0.0185867i
$439$	−34.1280	−	7.25413i	−1.62884	−	0.346221i	−0.699268	−	0.714860i	$-0.746491\pi$
$439$	−34.1280	−	7.25413i	−1.62884	−	0.346221i	−0.929573	+	0.368639i	$0.879824\pi$
$440$	−0.0749088	−	0.183207i	−0.00357114	−	0.00873406i
$441$	−0.207195	−	3.57733i	−0.00986642	−	0.170349i
$442$	−24.5074	−	17.8057i	−1.16570	−	0.846929i
$443$	−12.2771	+	21.2646i	−0.583304	+	1.01031i	0.411780	+	0.911283i	$0.364907\pi$
$443$	−12.2771	+	21.2646i	−0.583304	+	1.01031i	−0.995085	+	0.0990295i	$0.968426\pi$
$444$	0.387713	+	0.560819i	0.0184000	+	0.0266153i
$445$	−0.207421	+	6.74428i	−0.00983272	+	0.319709i
$446$	−33.7954	−	15.0467i	−1.60026	−	0.712482i
$447$	−13.4323	+	4.01899i	−0.635325	+	0.190092i
$448$	18.4863	+	3.92938i	0.873394	+	0.185646i
$449$	5.69752			0.268882			0.134441	−	0.990922i	$-0.457076\pi$
$449$	5.69752			0.268882			0.134441	+	0.990922i	$0.457076\pi$
$450$	4.37561	+	20.9602i	0.206268	+	0.988071i
$451$	−0.0513016			−0.00241570
$452$	−0.137341	−	0.0291928i	−0.00645999	−	0.00137311i
$453$	−11.6721	−	11.0156i	−0.548403	−	0.517559i
$454$	26.3056	+	11.7120i	1.23458	+	0.549672i
$455$	−20.8202	+	26.8784i	−0.976065	+	1.26008i
$456$	−10.8349	+	0.882682i	−0.507391	+	0.0413354i
$457$	−14.9907	+	25.9647i	−0.701238	+	1.21458i	0.266795	+	0.963753i	$0.414035\pi$
$457$	−14.9907	+	25.9647i	−0.701238	+	1.21458i	−0.968032	+	0.250826i	$0.919298\pi$
$458$	8.03681	+	5.83908i	0.375535	+	0.272842i
$459$	16.9572	−	4.21916i	0.791493	−	0.196933i
$460$	−0.161519	+	0.0119701i	−0.00753088	+	0.000558110i
$461$	4.85788	+	1.03257i	0.226254	+	0.0480917i	0.319643	−	0.947538i	$-0.396437\pi$
$461$	4.85788	+	1.03257i	0.226254	+	0.0480917i	−0.0933896	+	0.995630i	$0.529770\pi$
$462$	−0.0725176	−	0.173722i	−0.00337383	−	0.00808226i
$463$	−11.1874	+	2.37795i	−0.519922	+	0.110513i	−0.460396	−	0.887714i	$-0.652292\pi$
$463$	−11.1874	+	2.37795i	−0.519922	+	0.110513i	−0.0595266	+	0.998227i	$0.518959\pi$
$464$	−25.4896	+	28.3091i	−1.18333	+	1.31422i
$465$	−11.2997	−	9.18441i	−0.524012	−	0.425917i
$466$	26.9670	+	29.9498i	1.24922	+	1.38740i
$467$	21.2823	+	15.4625i	0.984827	+	0.715518i	0.958782	−	0.284142i	$-0.0917088\pi$
$467$	21.2823	+	15.4625i	0.984827	+	0.715518i	0.0260445	+	0.999661i	$0.491709\pi$
$468$	−0.556556	−	0.445649i	−0.0257268	−	0.0206002i
$469$	−4.43811	−	3.22447i	−0.204933	−	0.148892i
$470$	−4.38324	+	9.08269i	−0.202184	+	0.418953i
$471$	19.2668	−	5.76469i	0.887765	−	0.265623i
$472$	32.8191	+	14.6120i	1.51062	+	0.672572i
$473$	−0.236317	+	0.262457i	−0.0108659	+	0.0120678i
$474$	−2.14647	−	0.753475i	−0.0985906	−	0.0346082i
$475$	2.80060	+	10.8472i	0.128500	+	0.497704i
$476$	0.305170			0.0139874
$477$	−4.51470	+	0.740509i	−0.206714	+	0.0339056i
$478$	−5.13604	+	3.73155i	−0.234917	+	0.170677i
$479$	−0.0489279	−	0.465517i	−0.00223557	−	0.0212700i	0.993347	−	0.115158i	$-0.0367373\pi$
$479$	−0.0489279	−	0.465517i	−0.00223557	−	0.0212700i	−0.995583	+	0.0938875i	$0.970071\pi$
$480$	0.823816	+	0.0446767i	0.0376019	+	0.00203920i
$481$	6.89413	−	65.5932i	0.314345	−	2.99079i
$482$	−10.8263	−	18.7518i	−0.493126	−	0.854119i
$483$	7.99964	−	0.651703i	0.363996	−	0.0296535i
$484$	−0.277185	−	0.307845i	−0.0125993	−	0.0139929i
$485$	5.52859	−	22.5737i	0.251041	−	1.02502i
$486$	21.8216	−	4.35525i	0.989849	−	0.197558i
$487$	1.55836	−	4.79614i	0.0706160	−	0.217334i	−0.909520	−	0.415660i	$-0.863551\pi$
$487$	1.55836	−	4.79614i	0.0706160	−	0.217334i	0.980136	+	0.198326i	$0.0635506\pi$
$488$	−19.9073	−	22.1093i	−0.901161	−	1.00084i
$489$	−8.88689	−	5.41237i	−0.401879	−	0.244756i
$490$	−0.117200	+	3.81075i	−0.00529457	+	0.172152i
$491$	7.35184	−	1.56268i	0.331784	−	0.0705228i	−0.0390079	−	0.999239i	$-0.512420\pi$
$491$	7.35184	−	1.56268i	0.331784	−	0.0705228i	0.370792	+	0.928716i	$0.379086\pi$
$492$	0.0453299	−	0.0957118i	0.00204363	−	0.00431502i
$493$	15.7227	−	27.2325i	0.708113	−	1.22649i
$494$	−16.3284	−	11.8633i	−0.734649	−	0.533754i
$495$	0.110926	+	0.180639i	0.00498577	+	0.00811910i
$496$	−12.3916	+	9.00306i	−0.556401	+	0.404249i
$497$	1.13180	+	10.7684i	0.0507683	+	0.483028i
$498$	0.322088	−	13.7427i	0.0144331	−	0.615823i
$499$	4.05527	+	7.02394i	0.181539	+	0.314435i	0.942405	−	0.334474i	$-0.108559\pi$
$499$	4.05527	+	7.02394i	0.181539	+	0.314435i	−0.760866	+	0.648909i	$0.775225\pi$
$500$	−0.0492384	−	0.418187i	−0.00220201	−	0.0187019i
$501$	−22.0978	−	7.75699i	−0.987257	−	0.346557i
$502$	19.5964	+	4.16535i	0.874631	+	0.185909i
$503$	−16.3455	+	11.8757i	−0.728812	+	0.529513i	−0.889187	−	0.457543i	$-0.848729\pi$
$503$	−16.3455	+	11.8757i	−0.728812	+	0.529513i	0.160376	+	0.987056i	$0.448729\pi$
$504$	−20.2258	−	0.948588i	−0.900929	−	0.0422535i
$505$	−9.35710	+	7.91812i	−0.416385	+	0.352352i
$506$	−0.0792513	+	0.0352850i	−0.00352315	+	0.00156861i
$507$	8.59142	+	45.6548i	0.381558	+	2.02760i
$508$	−0.0389940	+	0.371003i	−0.00173008	+	0.0164606i
$509$	−20.4717	+	4.35139i	−0.907392	+	0.192872i	−0.637890	−	0.770128i	$-0.720193\pi$
$509$	−20.4717	+	4.35139i	−0.907392	+	0.192872i	−0.269502	+	0.963000i	$0.586859\pi$
$510$	−18.3684	+	2.87504i	−0.813365	+	0.127309i
$511$	2.90136	+	0.616702i	0.128348	+	0.0272813i
$512$	−6.78465	+	20.8810i	−0.299842	+	0.922819i
$513$	11.2979	−	2.81107i	0.498817	−	0.124112i
$514$	4.20054	+	12.9279i	0.185278	+	0.570227i
$515$	2.95974	+	2.83448i	0.130422	+	0.124902i
$516$	−0.280849	−	0.672796i	−0.0123637	−	0.0296182i
$517$	−0.0104363	+	0.0992949i	−0.000458989	+	0.00436699i
$518$	17.9740	+	31.1318i	0.789731	+	1.36785i
$519$	−5.01575	+	10.5905i	−0.220167	+	0.464872i
$520$	−28.5467	−	27.3386i	−1.25185	−	1.19888i
$521$	5.09658	−	3.70289i	0.223285	−	0.162226i	−0.470519	−	0.882390i	$-0.655933\pi$
$521$	5.09658	−	3.70289i	0.223285	−	0.162226i	0.693804	+	0.720164i	$0.255933\pi$
$522$	21.6243	−	33.7024i	0.946468	−	1.47511i
$523$	−6.61794	−	20.3679i	−0.289382	−	0.890628i	−0.985051	−	0.172264i	$-0.944892\pi$
$523$	−6.61794	−	20.3679i	−0.289382	−	0.890628i	0.695668	−	0.718363i	$-0.255108\pi$
$524$	−0.0166756	+	0.0288831i	−0.000728479	+	0.00126176i
$525$	2.59152	+	20.7051i	0.113103	+	0.903644i
$526$	−17.3243	−	30.0065i	−0.755374	−	1.30835i
$527$	8.46031	−	9.39612i	0.368537	−	0.409302i
$528$	0.213619	−	0.0639156i	0.00929657	−	0.00278157i
$529$	2.01754	+	19.1956i	0.0877190	+	0.834590i
$530$	4.85439	−	0.359756i	0.210861	−	0.0156268i
$531$	−37.2181	−	9.75370i	−1.61513	−	0.423275i
$532$	0.203324			0.00881520
$533$	−9.35909	+	4.16694i	−0.405387	+	0.180490i
$534$	−7.39957	−	0.953499i	−0.320211	−	0.0412619i
$535$	−38.8784	−	13.9676i	−1.68086	−	0.603874i
$536$	4.26746	−	4.73949i	0.184326	−	0.204715i
$537$	4.80286	+	11.5056i	0.207259	+	0.496504i
$538$	15.2518	+	16.9389i	0.657553	+	0.730287i
$539$	0.0116636	+	0.0358970i	0.000502388	+	0.00154619i
$540$	−0.435026	+	0.0473405i	−0.0187205	+	0.00203721i
$541$	2.06074	−	6.34232i	0.0885983	−	0.272678i	−0.896934	−	0.442164i	$-0.854211\pi$
$541$	2.06074	−	6.34232i	0.0885983	−	0.272678i	0.985533	+	0.169486i	$0.0542109\pi$
$542$	−18.6996	+	8.32561i	−0.803218	+	0.357616i
$543$	9.04442	−	7.76774i	0.388133	−	0.333345i
$544$	−0.0748810	+	0.712445i	−0.00321050	+	0.0305458i
$545$	−6.18886	+	7.98968i	−0.265101	+	0.342240i
$546$	−27.3400	−	25.8023i	−1.17004	−	1.10424i
$547$	3.31270	+	31.5182i	0.141641	+	1.34762i	0.802293	+	0.596930i	$0.203613\pi$
$547$	3.31270	+	31.5182i	0.141641	+	1.34762i	−0.660652	+	0.750692i	$0.729720\pi$
$548$	−0.130266	−	0.400917i	−0.00556467	−	0.0171263i
$549$	24.8718	+	19.9155i	1.06150	+	0.849973i
$550$	−0.100553	−	0.201884i	−0.00428762	−	0.00860834i
$551$	10.4754	−	18.1440i	0.446269	−	0.772961i
$552$	−0.218629	+	9.32836i	−0.00930549	+	0.397041i
$553$	−2.02527	−	0.901708i	−0.0861232	−	0.0383445i
$554$	−20.5883	−	9.16651i	−0.874714	−	0.389448i
$555$	−25.4171	−	31.5045i	−1.07890	−	1.33729i
$556$	−0.00138610		0.000617131i	−5.87836e−5		2.61722e-5i
$557$	−23.0896			−0.978337			−0.489168	−	0.872189i	$-0.662700\pi$
$557$	−23.0896			−0.978337			−0.489168	+	0.872189i	$0.662700\pi$
$558$	11.3223	−	11.4474i	0.479310	−	0.484606i
$559$	−21.7941	+	67.0755i	−0.921794	+	2.83699i
$560$	21.7481	+	2.96426i	0.919024	+	0.125263i
$561$	−0.161514	+	0.0882703i	−0.00681913	+	0.00372678i
$562$	2.06239	−	0.438374i	0.0869965	−	0.0184917i
$563$	35.9249	−	7.63606i	1.51405	−	0.321822i	0.625364	−	0.780333i	$-0.284951\pi$
$563$	35.9249	−	7.63606i	1.51405	−	0.321822i	0.888688	+	0.458511i	$0.151617\pi$
$564$	−0.176030	−	0.107207i	−0.00741220	−	0.00451424i
$565$	8.25999	+	1.12584i	0.347501	+	0.0473643i
$566$	−6.00856	+	18.4925i	−0.252559	+	0.777296i
$567$	21.5402	−	2.50357i	0.904605	−	0.105140i
$568$	−12.5879			−0.528177
$569$	14.5741	−	6.48879i	0.610976	−	0.272024i	−0.0778335	−	0.996966i	$-0.524800\pi$
$569$	14.5741	−	6.48879i	0.610976	−	0.272024i	0.688810	+	0.724942i	$0.258134\pi$
$570$	−12.2382	+	1.91553i	−0.512601	+	0.0802328i
$571$	2.61629	+	1.16485i	0.109488	+	0.0487473i	0.460750	−	0.887530i	$-0.347581\pi$
$571$	2.61629	+	1.16485i	0.109488	+	0.0487473i	−0.351262	+	0.936277i	$0.614247\pi$
$572$	0.00686088	+	0.00305466i	0.000286868	+	0.000127722i
$573$	−17.1643	+	9.38058i	−0.717047	+	0.391879i
$574$	2.79192	−	4.83575i	0.116532	−	0.201840i
$575$	9.51094	−	1.41749i	0.396634	−	0.0591133i
$576$	3.55334	−	23.2614i	0.148056	−	0.969223i
$577$	2.14710	+	6.60811i	0.0893851	+	0.275099i	0.985750	−	0.168218i	$-0.0538014\pi$
$577$	2.14710	+	6.60811i	0.0893851	+	0.275099i	−0.896365	+	0.443318i	$0.853801\pi$
$578$	0.849139	+	8.07902i	0.0353195	+	0.336043i
$579$	−37.0426	+	11.0833i	−1.53944	+	0.460606i
$580$	−0.482226	+	0.622543i	−0.0200233	+	0.0258497i
$581$	1.40030	−	13.3229i	0.0580941	−	0.552728i
$582$	24.2472	+	8.51149i	1.00508	+	0.352813i
$583$	0.0440240	−	0.0196007i	0.00182329	−	0.000811779i
$584$	−1.06561	+	3.27960i	−0.0440951	+	0.135711i
$585$	34.9089	+	23.9445i	1.44330	+	0.989983i
$586$	7.17715	+	22.0890i	0.296485	+	0.912489i
$587$	0.536376	+	0.595706i	0.0221386	+	0.0245874i	0.754112	−	0.656745i	$-0.228067\pi$
$587$	0.536376	+	0.595706i	0.0221386	+	0.0245874i	−0.731974	+	0.681333i	$0.761401\pi$
$588$	−0.0772778	−	0.00995792i	−0.00318688	−	0.000410658i
$589$	5.63680	−	6.26030i	0.232260	−	0.257951i
$590$	38.5254	+	13.8408i	1.58606	+	0.569817i
$591$	−17.4813	−	41.8778i	−0.719085	−	1.72262i
$592$	−38.8980	+	17.3185i	−1.59870	+	0.711786i
$593$	19.9879			0.820804			0.410402	−	0.911905i	$-0.365388\pi$
$593$	19.9879			0.820804			0.410402	+	0.911905i	$0.365388\pi$
$594$	−0.210716	+	0.102646i	−0.00864577	+	0.00421163i
$595$	−18.0689	+	1.33908i	−0.740754	+	0.0548969i
$596$	0.0318674	+	0.303198i	0.00130534	+	0.0124195i
$597$	6.63895	−	27.9917i	0.271714	−	1.14563i
$598$	−11.5920	+	12.8743i	−0.474034	+	0.526468i
$599$	1.80743	+	3.13056i	0.0738495	+	0.127911i	0.900585	−	0.434679i	$-0.143138\pi$
$599$	1.80743	+	3.13056i	0.0738495	+	0.127911i	−0.826736	+	0.562590i	$0.809805\pi$
$600$	−24.2541	+	0.480198i	−0.990170	+	0.0196040i
$601$	18.5936	−	32.2050i	0.758449	−	1.31367i	−0.185193	−	0.982702i	$-0.559291\pi$
$601$	18.5936	−	32.2050i	0.758449	−	1.31367i	0.943642	−	0.330969i	$-0.107376\pi$
$602$	−11.8787	−	36.5589i	−0.484140	−	1.49003i
$603$	−3.68852	+	5.74872i	−0.150208	+	0.234106i
$604$	−0.282332	+	0.205126i	−0.0114879	+	0.00834646i
$605$	17.7628	+	17.0110i	0.722159	+	0.691596i
$606$	−7.70745	−	11.1487i	−0.313094	−	0.452884i
$607$	−16.6597	−	28.8555i	−0.676197	−	1.17121i	−0.976117	−	0.217244i	$-0.930293\pi$
$607$	−16.6597	−	28.8555i	−0.676197	−	1.17121i	0.299920	−	0.953964i	$-0.403040\pi$
$608$	−0.0498905	+	0.474677i	−0.00202333	+	0.0192507i
$609$	23.6707	−	31.0244i	0.959187	−	1.25717i
$610$	−24.4841	−	23.4479i	−0.991333	−	0.949379i
$611$	6.16123	+	18.9623i	0.249257	+	0.767134i
$612$	−0.0219702	−	0.379327i	−0.000888092	−	0.0153334i
$613$	1.94595	−	5.98902i	0.0785962	−	0.241894i	−0.904037	−	0.427455i	$-0.859410\pi$
$613$	1.94595	−	5.98902i	0.0785962	−	0.241894i	0.982633	+	0.185561i	$0.0594102\pi$
$614$	−20.0376	−	4.25911i	−0.808650	−	0.171884i
$615$	−2.26397	+	5.86595i	−0.0912922	+	0.236538i
$616$	0.208618	−	0.0443432i	0.00840547	−	0.00178664i
$617$	−2.76546	+	26.3116i	−0.111333	+	1.05927i	0.786095	+	0.618106i	$0.212100\pi$
$617$	−2.76546	+	26.3116i	−0.111333	+	1.05927i	−0.897428	+	0.441160i	$0.854567\pi$
$618$	−3.43754	+	2.95230i	−0.138278	+	0.118759i
$619$	−14.3187	+	6.37507i	−0.575515	+	0.256236i	−0.673789	−	0.738923i	$-0.735334\pi$
$619$	−14.3187	+	6.37507i	−0.575515	+	0.256236i	0.0982741	+	0.995159i	$0.468668\pi$
$620$	−0.241703	+	0.204533i	−0.00970701	+	0.00821423i
$621$	−1.38599	−	9.89665i	−0.0556178	−	0.397139i
$622$	25.8570	−	18.7862i	1.03677	−	0.753260i
$623$	−7.11184	−	1.51167i	−0.284930	−	0.0605637i
$624$	33.7796	−	29.0113i	1.35226	−	1.16138i
$625$	4.75037	+	24.5445i	0.190015	+	0.981781i
$626$	17.4420	+	30.2105i	0.697124	+	1.20745i
$627$	−0.107611	+	0.0588113i	−0.00429757	+	0.00234870i
$628$	−0.0457094	−	0.434896i	−0.00182400	−	0.0173542i
$629$	28.4353	−	20.6595i	1.13379	−	0.823748i
$630$	−23.0640	+	0.625389i	−0.918892	+	0.0249161i
$631$	1.57126	+	1.14159i	0.0625508	+	0.0454458i	0.618621	−	0.785689i	$-0.287692\pi$
$631$	1.57126	+	1.14159i	0.0625508	+	0.0454458i	−0.556070	+	0.831135i	$0.687692\pi$
$632$	1.28867	−	2.23204i	0.0512604	−	0.0887856i
$633$	−9.47737	−	13.7088i	−0.376692	−	0.544877i
$634$	−24.1523	+	5.13373i	−0.959211	+	0.203887i
$635$	0.680858	−	22.1380i	0.0270190	−	0.878520i
$636$	−0.00233089	+	0.0994533i	−9.24259e−5	+	0.00394358i
$637$	5.04353	+	5.60141i	0.199832	+	0.221936i
$638$	−0.130340	+	0.401144i	−0.00516019	+	0.0158814i
$639$	13.3036	−	2.18208i	0.526284	−	0.0863219i
$640$	−6.18236	+	25.2431i	−0.244379	+	0.997822i
$641$	11.1795	+	12.4161i	0.441563	+	0.490405i	0.922308	−	0.386455i	$-0.126301\pi$
$641$	11.1795	+	12.4161i	0.441563	+	0.490405i	−0.480746	+	0.876860i	$0.659634\pi$
$642$	19.5517	−	41.2825i	0.771644	−	1.62929i
$643$	15.9436	+	27.6151i	0.628753	+	1.08903i	0.987802	+	0.155713i	$0.0497676\pi$
$643$	15.9436	+	27.6151i	0.628753	+	1.08903i	−0.359050	+	0.933319i	$0.616899\pi$
$644$	0.0182426	−	0.173566i	0.000718857	−	0.00683947i
$645$	19.5811	+	38.6035i	0.771006	+	1.52001i
$646$	−1.12429	−	10.6969i	−0.0442344	−	0.420862i
$647$	16.4808	−	11.9740i	0.647928	−	0.470747i	−0.214637	−	0.976694i	$-0.568857\pi$
$647$	16.4808	−	11.9740i	0.647928	−	0.470747i	0.862565	+	0.505947i	$0.168857\pi$
$648$	0.277025	+	25.2090i	0.0108826	+	0.990304i
$649$	0.405268			0.0159082
$650$	−34.7421	−	28.6628i	−1.36270	−	1.12425i
$651$	11.9033	−	10.2231i	0.466526	−	0.400673i
$652$	−0.151395	+	0.168141i	−0.00592907	+	0.00658490i
$653$	34.2553	+	15.2514i	1.34051	+	0.596835i	0.946629	−	0.322325i	$-0.104464\pi$
$653$	34.2553	+	15.2514i	1.34051	+	0.596835i	0.393884	+	0.919160i	$0.371131\pi$
$654$	−8.12689	−	7.66981i	−0.317787	−	0.299913i
$655$	0.860617	−	1.78332i	0.0336271	−	0.0696802i
$656$	5.35073	+	3.88754i	0.208911	+	0.151783i
$657$	0.557684	−	3.65079i	0.0217573	−	0.142431i
$658$	−8.79169	−	6.38754i	−0.342736	−	0.249012i
$659$	16.4282	+	18.2453i	0.639951	+	0.710737i	0.972645	−	0.232298i	$-0.0746243\pi$
$659$	16.4282	+	18.2453i	0.639951	+	0.710737i	−0.332694	+	0.943035i	$0.607958\pi$
$660$	0.00430616	−	0.00164400i	0.000167617	−	6.39928e-5i
$661$	−4.46101	+	4.95445i	−0.173513	+	0.192706i	−0.823629	−	0.567130i	$-0.808054\pi$
$661$	−4.46101	+	4.95445i	−0.173513	+	0.192706i	0.650115	+	0.759835i	$0.274721\pi$
$662$	36.6030	−	7.78020i	1.42261	−	0.302386i
$663$	−22.2957	+	29.2222i	−0.865895	+	1.13490i
$664$	15.2338	+	3.23804i	0.591185	+	0.125660i
$665$	−12.0387	+	0.892180i	−0.466840	+	0.0345973i
$666$	37.4029	−	24.5830i	1.44933	−	0.952571i
$667$	−14.5487	−	10.5702i	−0.563327	−	0.409281i
$668$	−0.254622	+	0.441018i	−0.00985162	+	0.0170635i
$669$	−19.2131	+	40.5675i	−0.742820	+	1.56843i
$670$	4.45029	−	5.74523i	0.171930	−	0.221958i
$671$	−0.306604	−	0.136509i	−0.0118363	−	0.00526987i
$672$	−0.205159	+	0.865010i	−0.00791418	+	0.0333685i
$673$	−11.7852	−	2.50502i	−0.454286	−	0.0965614i	−0.0249146	−	0.999690i	$-0.507931\pi$
$673$	−11.7852	−	2.50502i	−0.454286	−	0.0965614i	−0.429371	+	0.903128i	$0.641265\pi$
$674$	23.0492			0.887822
$675$	25.5499	−	4.71189i	0.983417	−	0.181361i
$676$	1.01015			0.0388521
$677$	24.5942	+	5.22765i	0.945231	+	0.200915i	0.654647	−	0.755935i	$-0.272817\pi$
$677$	24.5942	+	5.22765i	0.945231	+	0.200915i	0.290584	+	0.956850i	$0.406151\pi$
$678$	−2.12718	+	8.96881i	−0.0816938	+	0.344445i
$679$	22.8781	+	10.1860i	0.877980	+	0.390902i
$680$	0.647519	−	21.0540i	0.0248312	−	0.807384i
$681$	14.9550	−	31.5768i	0.573078	−	1.21003i
$682$	−0.0847974	+	0.146873i	−0.00324706	+	0.00562408i
$683$	29.2073	+	21.2203i	1.11758	+	0.811973i	0.983841	−	0.179043i	$-0.0573002\pi$
$683$	29.2073	+	21.2203i	1.11758	+	0.811973i	0.133743	+	0.991016i	$0.457300\pi$
$684$	−0.0146379	−	0.252732i	−0.000559696	−	0.00966344i
$685$	9.47217	+	23.1664i	0.361913	+	0.885144i
$686$	−27.5684	−	5.85985i	−1.05257	−	0.223730i
$687$	7.31153	−	9.58297i	0.278952	−	0.365613i
$688$	44.5363	−	9.46648i	1.69793	−	0.360906i
$689$	6.43936	−	7.15163i	0.245320	−	0.272455i
$690$	0.537154	+	10.6189i	0.0204491	+	0.404256i
$691$	5.04645	+	5.60465i	0.191976	+	0.213211i	0.831447	−	0.555604i	$-0.187513\pi$
$691$	5.04645	+	5.60465i	0.191976	+	0.213211i	−0.639471	+	0.768815i	$0.720846\pi$
$692$	0.206141	+	0.149770i	0.00783629	+	0.00569340i
$693$	−0.212793	+	0.0830279i	−0.00808334	+	0.00315397i
$694$	21.6515	+	15.7308i	0.821881	+	0.597131i
$695$	0.0793621	−	0.0426221i	0.00301038	−	0.00161675i
$696$	32.9939	+	31.1382i	1.25063	+	1.18029i
$697$	−4.98758	−	2.22061i	−0.188918	−	0.0841117i
$698$	1.71851	−	1.90860i	0.0650465	−	0.0722415i
$699$	37.0971	−	31.8605i	1.40314	−	1.20508i
$700$	0.452872	+	0.0278827i	0.0171169	+	0.00105387i
$701$	−41.9293			−1.58365			−0.791824	−	0.610749i	$-0.790868\pi$
$701$	−41.9293			−1.58365			−0.791824	+	0.610749i	$0.790868\pi$
$702$	−30.1041	+	35.8413i	−1.13620	+	1.35274i
$703$	18.9454	−	13.7647i	0.714541	−	0.519144i
$704$	0.0259086	+	0.246504i	0.000976466	+	0.00929045i
$705$	10.8931	+	5.57526i	0.410256	+	0.209977i
$706$	0.273977	−	2.60672i	0.0103113	−	0.0981052i
$707$	−6.60415	−	11.4387i	−0.248375	−	0.430197i
$708$	−0.358093	+	0.756096i	−0.0134580	+	0.0284158i
$709$	−0.366008	−	0.406493i	−0.0137457	−	0.0152662i	0.736233	−	0.676728i	$-0.236603\pi$
$709$	−0.366008	−	0.406493i	−0.0137457	−	0.0152662i	−0.749978	+	0.661462i	$0.769936\pi$
$710$	−14.3046	+	1.06011i	−0.536842	+	0.0397851i
$711$	−0.975020	+	2.58233i	−0.0365661	+	0.0968450i
$712$	2.61203	−	8.03900i	0.0978899	−	0.301274i
$713$	−4.83833	−	5.37351i	−0.181197	−	0.201240i
$714$	0.469405	−	20.0283i	0.0175670	−	0.749541i
$715$	−0.419632	−	0.150759i	−0.0156934	−	0.00563808i
$716$	0.265179	−	0.0563656i	0.00991021	−	0.00210648i
$717$	4.38051	+	6.33632i	0.163593	+	0.236634i
$718$	25.0638	−	43.4117i	0.935371	−	1.62011i
$719$	−23.1267	−	16.8026i	−0.862482	−	0.626630i	0.0660771	−	0.997815i	$-0.478952\pi$
$719$	−23.1267	−	16.8026i	−0.862482	−	0.626630i	−0.928559	+	0.371185i	$0.878952\pi$
$720$	2.11887	−	27.2463i	0.0789657	−	1.01541i
$721$	−3.57254	+	2.59560i	−0.133048	+	0.0966651i
$722$	2.08594	+	19.8464i	0.0776305	+	0.738605i
$723$	−23.0544	+	12.5997i	−0.857404	+	0.468587i
$724$	−0.129620	−	0.224508i	−0.00481728	−	0.00834378i
$725$	25.8206	−	38.9764i	0.958953	−	1.44755i
$726$	−20.6302	+	17.7181i	−0.765659	+	0.657581i
$727$	−38.1196	−	8.10257i	−1.41378	−	0.300508i	−0.563184	−	0.826331i	$-0.690424\pi$
$727$	−38.1196	−	8.10257i	−1.41378	−	0.300508i	−0.850594	+	0.525824i	$0.823757\pi$
$728$	34.4571	−	25.0345i	1.27706	−	0.927841i
$729$	−4.66270	−	26.5943i	−0.172693	−	0.984976i
$730$	−0.934734	+	3.81660i	−0.0345960	+	0.141259i
$731$	−34.3355	+	15.2872i	−1.26995	+	0.565416i
$732$	0.525594	−	0.451403i	0.0194265	−	0.0166843i
$733$	−1.05126	+	10.0021i	−0.0388293	+	0.369436i	0.957802	+	0.287428i	$0.0928002\pi$
$733$	−1.05126	+	10.0021i	−0.0388293	+	0.369436i	−0.996632	+	0.0820086i	$0.973867\pi$
$734$	−33.5705	+	7.13562i	−1.23911	+	0.263381i
$735$	4.61927	+	0.250509i	0.170384	+	0.00924016i
$736$	0.400729	+	0.0851776i	0.0147711	+	0.00313969i
$737$	0.0222324	−	0.0684244i	0.000818942	−	0.00252044i
$738$	−6.21184	−	3.12222i	−0.228661	−	0.114931i
$739$	−12.4137	−	38.2054i	−0.456645	−	1.40541i	−0.869193	−	0.494473i	$-0.835361\pi$
$739$	−12.4137	−	38.2054i	−0.456645	−	1.40541i	0.412548	−	0.910936i	$-0.364639\pi$
$740$	−0.775434	+	0.416454i	−0.0285055	+	0.0153092i
$741$	−14.8548	+	19.4697i	−0.545707	+	0.715238i
$742$	−0.548271	+	5.21645i	−0.0201277	+	0.191502i
$743$	6.57831	+	11.3940i	0.241335	+	0.418004i	0.961095	−	0.276219i	$-0.0890815\pi$
$743$	6.57831	+	11.3940i	0.241335	+	0.418004i	−0.719760	+	0.694223i	$0.755748\pi$
$744$	10.3734	+	15.0049i	0.380306	+	0.550105i
$745$	−3.21728	−	17.8123i	−0.117872	−	0.652594i
$746$	−2.32911	+	1.69220i	−0.0852747	+	0.0619557i
$747$	−16.6612	−	0.781410i	−0.609603	−	0.0285903i
$748$	0.00123677	+	0.00380638i	4.52207e−5	+	0.000139175i
$749$	22.2575	−	38.5511i	0.813270	−	1.40863i
$750$	−27.5213	+	2.58827i	−1.00494	+	0.0945104i
$751$	6.07148	+	10.5161i	0.221552	+	0.383738i	0.955279	−	0.295705i	$-0.0955546\pi$
$751$	6.07148	+	10.5161i	0.221552	+	0.383738i	−0.733728	+	0.679444i	$0.762221\pi$
$752$	8.61288	−	9.56557i	0.314079	−	0.348821i
$753$	5.60987	−	23.6528i	0.204435	−	0.861957i
$754$	8.80442	+	83.7685i	0.320638	+	3.05067i
$755$	15.8166	−	13.3843i	0.575625	−	0.487103i
$756$	0.0331204	−	0.470365i	0.00120458	−	0.0171070i
$757$	−10.4368			−0.379330			−0.189665	−	0.981849i	$-0.560740\pi$
$757$	−10.4368			−0.379330			−0.189665	+	0.981849i	$0.560740\pi$
$758$	24.5857	−	10.9463i	0.892993	−	0.397586i
$759$	0.0405490	+	0.0971382i	0.00147183	+	0.00352589i
$760$	0.431419	−	14.0275i	0.0156492	−	0.508831i
$761$	−2.49510	+	2.77109i	−0.0904473	+	0.100452i	−0.786669	−	0.617375i	$-0.788196\pi$
$761$	−2.49510	+	2.77109i	−0.0904473	+	0.100452i	0.696222	+	0.717827i	$0.254863\pi$
$762$	24.2890	+	3.12985i	0.879897	+	0.113382i
$763$	−7.28684	−	8.09286i	−0.263801	−	0.292981i
$764$	0.131433	+	0.404508i	0.00475507	+	0.0146346i
$765$	2.96532	+	22.3633i	0.107211	+	0.808548i
$766$	4.88115	−	15.0226i	0.176363	−	0.542790i
$767$	73.9342	−	32.9176i	2.66961	−	1.18859i
$768$	−1.47670	−	0.518364i	−0.0532856	−	0.0187049i
$769$	3.23379	−	30.7674i	0.116613	−	1.10950i	−0.767117	−	0.641507i	$-0.778310\pi$
$769$	3.23379	−	30.7674i	0.116613	−	1.10950i	0.883731	−	0.467996i	$-0.155024\pi$
$770$	0.233334	−	0.0679596i	0.00840878	−	0.00244909i
$771$	15.8015	−	4.72789i	0.569079	−	0.170271i
$772$	0.0878817	+	0.836139i	0.00316293	+	0.0300933i
$773$	−1.07567	−	3.31057i	−0.0386891	−	0.119073i	0.929847	−	0.367947i	$-0.119939\pi$
$773$	−1.07567	−	3.31057i	−0.0386891	−	0.119073i	−0.968536	+	0.248874i	$0.919939\pi$
$774$	−44.5876	+	17.3973i	−1.60267	+	0.625332i
$775$	13.4136	−	13.1708i	0.481830	−	0.473111i
$776$	−14.5572	+	25.2138i	−0.522572	+	0.905122i
$777$	38.2752	−	20.9181i	1.37311	−	0.750432i
$778$	−28.2204	−	12.5645i	−1.01175	−	0.450460i
$779$	−3.32304	−	1.47951i	−0.119060	−	0.0530091i
$780$	0.652052	−	0.649685i	0.0233472	−	0.0232625i
$781$	−0.129727	+	0.0577582i	−0.00464200	+	0.00206675i
$782$	−9.23220			−0.330143
$783$	−40.2676	−	27.1893i	−1.43905	−	0.971665i
$784$	1.50369	−	4.62788i	0.0537032	−	0.165282i
$785$	4.61474	+	25.5494i	0.164707	+	0.911896i
$786$	1.86995	+	1.13885i	0.0666988	+	0.0406214i
$787$	−46.0635	+	9.79110i	−1.64199	+	0.349015i	−0.934017	−	0.357228i	$-0.883722\pi$
$787$	−46.0635	+	9.79110i	−1.64199	+	0.349015i	−0.707969	+	0.706243i	$0.750388\pi$
$788$	−0.965192	+	0.205158i	−0.0343835	+	0.00730844i
$789$	−36.8917	+	20.1620i	−1.31338	+	0.717785i
$790$	1.27644	−	2.64496i	0.0454135	−	0.0941034i
$791$	−2.77585	+	8.54319i	−0.0986979	+	0.303761i
$792$	−0.0701378	−	0.256121i	−0.00249224	−	0.00910085i
$793$	−67.0224			−2.38004
$794$	−10.3566	+	4.61107i	−0.367543	+	0.163641i
$795$	−0.298388	−	5.89880i	−0.0105827	−	0.209209i
$796$	−0.571463	−	0.254432i	−0.0202550	−	0.00901809i
$797$	−28.7663	−	12.8076i	−1.01895	−	0.453668i	−0.171866	−	0.985120i	$-0.554980\pi$
$797$	−28.7663	−	12.8076i	−1.01895	−	0.453668i	−0.847088	+	0.531453i	$0.821646\pi$
$798$	0.312747	−	13.3441i	0.0110711	−	0.472377i
$799$	−5.31265	+	9.20178i	−0.187948	+	0.325536i
$800$	−0.176218	+	1.05043i	−0.00623024	+	0.0371382i
$801$	−1.36700	+	8.94887i	−0.0483007	+	0.316193i
$802$	−5.53334	−	17.0299i	−0.195389	−	0.601345i
$803$	0.00406626	+	0.0386879i	0.000143495	+	0.00136527i
$804$	0.108013	+	0.101938i	0.00380932	+	0.00359507i
$805$	−0.318525	+	10.3568i	−0.0112265	+	0.365029i
$806$	−3.54014	+	33.6821i	−0.124696	+	1.18640i
$807$	20.9812	−	18.0195i	0.738572	−	0.634317i
$808$	14.0280	−	6.24566i	0.493502	−	0.219721i
$809$	−8.49171	+	26.1348i	−0.298553	+	0.918851i	0.683452	+	0.729995i	$0.260478\pi$
$809$	−8.49171	+	26.1348i	−0.298553	+	0.918851i	−0.982005	+	0.188856i	$0.939522\pi$
$810$	2.43781	+	28.6236i	0.0856560	+	1.00573i
$811$	−2.41545	−	7.43400i	−0.0848180	−	0.261043i	0.899649	−	0.436615i	$-0.143823\pi$
$811$	−2.41545	−	7.43400i	−0.0848180	−	0.261043i	−0.984467	+	0.175572i	$0.943823\pi$
$812$	−0.567779	−	0.630582i	−0.0199251	−	0.0221291i
$813$	9.56767	+	22.9201i	0.335553	+	0.803843i
$814$	−0.315464	+	0.350358i	−0.0110570	+	0.0122800i
$815$	8.22619	−	10.6198i	0.288151	−	0.371997i
$816$	23.5348	+	3.03266i	0.823882	+	0.106164i
$817$	−22.8765	+	10.1853i	−0.800348	+	0.356338i
$818$	−6.33407			−0.221466
$819$	−32.0765	+	32.4310i	−1.12085	+	1.13323i
$820$	0.116246	+	0.0719679i	0.00405950	+	0.00251323i
$821$	2.23363	+	21.2516i	0.0779542	+	0.741685i	0.961772	+	0.273853i	$0.0882982\pi$
$821$	2.23363	+	21.2516i	0.0779542	+	0.741685i	−0.883817	+	0.467832i	$0.845035\pi$
$822$	−26.5125	+	7.93266i	−0.924731	+	0.276683i
$823$	−21.1008	+	23.4348i	−0.735528	+	0.816887i	−0.988601	−	0.150560i	$-0.951892\pi$
$823$	−21.1008	+	23.4348i	−0.735528	+	0.816887i	0.253073	+	0.967447i	$0.418559\pi$
$824$	−2.56689	−	4.44598i	−0.0894217	−	0.154883i
$825$	−0.247752	+	0.116236i	−0.00862561	+	0.00404681i
$826$	−22.0554	+	38.2010i	−0.767405	+	1.32918i
$827$	0.0456076	+	0.140366i	0.00158593	+	0.00488099i	0.951846	−	0.306575i	$-0.0991832\pi$
$827$	0.0456076	+	0.140366i	0.00158593	+	0.00488099i	−0.950260	+	0.311456i	$0.899183\pi$
$828$	−0.217057	−	0.0101799i	−0.00754324	−	0.000353777i
$829$	−31.5635	+	22.9322i	−1.09625	+	0.796469i	−0.980443	−	0.196803i	$-0.936944\pi$
$829$	−31.5635	+	22.9322i	−1.09625	+	0.796469i	−0.115802	+	0.993272i	$0.536944\pi$
$830$	17.5840	+	2.39670i	0.610349	+	0.0831906i
$831$	−11.7047	+	24.7139i	−0.406031	+	0.857314i
$832$	24.7486	+	42.8659i	0.858005	+	1.48611i
$833$	−0.419870	+	3.99479i	−0.0145476	+	0.138411i
$834$	0.0383702	+	0.0919189i	0.00132865	+	0.00318289i
$835$	13.1408	−	27.2297i	0.454758	−	0.942323i
$836$	0.000824014		0.00253605i	2.84991e−5		8.77112e-5i
$837$	−13.5642	−	14.0598i	−0.468849	−	0.485979i
$838$	−3.23698	+	9.96239i	−0.111819	+	0.344145i
$839$	−37.5930	−	7.99064i	−1.29786	−	0.275868i	−0.493359	−	0.869826i	$-0.664231\pi$
$839$	−37.5930	−	7.99064i	−1.29786	−	0.275868i	−0.804496	+	0.593958i	$0.797565\pi$
$840$	4.13616	−	25.8108i	0.142711	−	0.890557i
$841$	−57.1576	+	12.1492i	−1.97095	+	0.418939i
$842$	1.16807	−	11.1135i	0.0402544	−	0.382995i
$843$	−0.473131	−	2.51422i	−0.0162955	−	0.0865944i
$844$	−0.331058	+	0.147396i	−0.0113955	+	0.00507359i
$845$	−59.8106	+	4.43254i	−2.05755	+	0.152484i
$846$	−7.30678	+	11.3880i	−0.251212	+	0.391526i
$847$	−21.4404	+	15.5774i	−0.736701	+	0.535244i
$848$	−6.07699	−	1.29170i	−0.208685	−	0.0443573i
$849$	22.2613	+	7.81437i	0.764005	+	0.268189i
$850$	−1.03726	−	23.9798i	−0.0355778	−	0.822499i
$851$	−10.0503	−	17.4077i	−0.344521	−	0.596728i
$852$	0.00686853	−	0.293063i	0.000235312	−	0.0100402i
$853$	3.15866	+	30.0527i	0.108151	+	1.02898i	0.905176	+	0.425038i	$0.139739\pi$
$853$	3.15866	+	30.0527i	0.108151	+	1.02898i	−0.797025	+	0.603946i	$0.793594\pi$
$854$	29.5534	−	21.4718i	1.01130	−	0.734750i
$855$	1.97569	+	14.8999i	0.0675670	+	0.509565i
$856$	41.8679	+	30.4188i	1.43102	+	1.03969i
$857$	−3.63200	+	6.29081i	−0.124067	+	0.214890i	−0.921368	−	0.388692i	$-0.872927\pi$
$857$	−3.63200	+	6.29081i	−0.124067	+	0.214890i	0.797301	+	0.603582i	$0.206260\pi$
$858$	0.211031	−	0.445581i	0.00720447	−	0.0152119i
$859$	30.8112	−	6.54913i	1.05127	−	0.223454i	0.350292	−	0.936640i	$-0.386082\pi$
$859$	30.8112	−	6.54913i	1.05127	−	0.223454i	0.700974	+	0.713187i	$0.252749\pi$
$860$	0.903666	−	0.263196i	0.0308148	−	0.00897492i
$861$	−5.78658	−	3.52419i	−0.197206	−	0.120104i
$862$	−12.0456	−	13.3780i	−0.410276	−	0.455658i
$863$	−14.1918	+	43.6780i	−0.483096	+	1.48682i	0.351623	+	0.936142i	$0.385630\pi$
$863$	−14.1918	+	43.6780i	−0.483096	+	1.48682i	−0.834719	+	0.550675i	$0.814370\pi$
$864$	1.08998	+	0.192738i	0.0370819	+	0.00655709i
$865$	−12.8627	−	7.96325i	−0.437344	−	0.270759i
$866$	−35.8255	−	39.7883i	−1.21740	−	1.35206i
$867$	9.82431	−	0.800352i	0.333651	−	0.0271814i
$868$	−0.170591	−	0.295473i	−0.00579025	−	0.0100290i
$869$	0.00303914	−	0.0289155i	0.000103096	−	0.000980892i
$870$	40.1158	+	32.6061i	1.36005	+	1.10545i
$871$	−1.50180	−	14.2887i	−0.0508865	−	0.484153i
$872$	10.2424	−	7.44158i	0.346853	−	0.252004i
$873$	11.0141	−	29.1708i	0.372772	−	0.987283i
$874$	−6.15108			−0.208063
$875$	−26.9366	+	0.336276i	−0.910624	+	0.0113682i
$876$	−0.0757718	−	0.0265982i	−0.00256009	−	0.000898668i
$877$	10.4883	−	11.6484i	0.354164	−	0.393340i	−0.539566	−	0.841943i	$-0.681412\pi$
$877$	10.4883	−	11.6484i	0.354164	−	0.393340i	0.893731	+	0.448604i	$0.148078\pi$
$878$	45.4991	+	20.2575i	1.53552	+	0.683658i
$879$	26.9989	−	8.07819i	0.910651	−	0.272470i
$880$	0.0511656	+	0.283277i	0.00172479	+	0.00954926i
$881$	36.7061	+	26.6685i	1.23666	+	0.898486i	0.997371	−	0.0724624i	$-0.0230857\pi$
$881$	36.7061	+	26.6685i	1.23666	+	0.898486i	0.239289	+	0.970948i	$0.423086\pi$
$882$	−0.772405	+	5.05643i	−0.0260082	+	0.170259i
$883$	2.12115	+	1.54110i	0.0713823	+	0.0518623i	0.622904	−	0.782298i	$-0.285953\pi$
$883$	2.12115	+	1.54110i	0.0713823	+	0.0518623i	−0.551522	+	0.834160i	$0.685953\pi$
$884$	0.534797	+	0.593953i	0.0179872	+	0.0199768i
$885$	17.8848	−	46.3393i	0.601189	−	1.55768i
$886$	23.4533	−	26.0475i	0.787929	−	0.875084i
$887$	−30.7732	+	6.54104i	−1.03326	+	0.219626i	−0.693176	−	0.720768i	$-0.743789\pi$
$887$	−30.7732	+	6.54104i	−1.03326	+	0.219626i	−0.340085	+	0.940395i	$0.610456\pi$
$888$	19.5342	+	46.7957i	0.655524	+	1.57036i
$889$	23.3445	+	4.96203i	0.782950	+	0.166421i
$890$	2.29123	−	9.35530i	0.0768023	−	0.313590i
$891$	0.118524	+	0.258525i	0.00397069	+	0.00866091i
$892$	0.789632	+	0.573701i	0.0264388	+	0.0192089i
$893$	−3.53963	+	6.13082i	−0.118449	+	0.205160i
$894$	19.9479	−	1.62509i	0.667158	−	0.0543510i
$895$	−15.4538	+	4.50097i	−0.516563	+	0.150451i
$896$	−25.5835	−	11.3905i	−0.854684	−	0.380530i
$897$	15.2874	+	14.4276i	0.510433	+	0.481725i
$898$	−7.95529	−	1.69095i	−0.265471	−	0.0564277i
$899$	−35.1562			−1.17253
$900$	0.00205451	−	0.564928i	6.84838e−5	−	0.0188309i
$901$	5.12847			0.170854
$902$	0.0716311	+	0.0152257i	0.00238505	+	0.000506959i
$903$	−44.6851	+	13.3700i	−1.48703	+	0.444925i
$904$	−9.54030	−	4.24761i	−0.317306	−	0.141274i
$905$	8.65985	+	12.7242i	0.287863	+	0.422967i
$906$	13.0281	+	18.8450i	0.432831	+	0.626082i
$907$	19.4248	−	33.6448i	0.644991	−	1.11716i	−0.339312	−	0.940674i	$-0.610194\pi$
$907$	19.4248	−	33.6448i	0.644991	−	1.11716i	0.984304	−	0.176484i	$-0.0564724\pi$
$908$	−0.614632	−	0.446556i	−0.0203973	−	0.0148195i
$909$	−13.7429	+	9.03249i	−0.455824	+	0.299589i
$910$	37.0478	−	31.3505i	1.22812	−	1.03926i
$911$	23.4837	+	4.99161i	0.778049	+	0.165380i	0.579786	−	0.814769i	$-0.303136\pi$
$911$	23.4837	+	4.99161i	0.778049	+	0.165380i	0.198264	+	0.980149i	$0.436470\pi$
$912$	15.6804	+	2.02055i	0.519229	+	0.0669072i
$913$	0.171852	−	0.0365282i	0.00568746	−	0.00120891i
$914$	28.6372	−	31.8048i	0.947234	−	1.05201i
$915$	−29.1394	+	29.0336i	−0.963318	+	0.959821i
$916$	−0.175378	−	0.194777i	−0.00579466	−	0.00643562i
$917$	1.72619	+	1.25415i	0.0570037	+	0.0414156i
$918$	−24.9290	+	0.858432i	−0.822781	+	0.0283325i
$919$	34.1266	+	24.7944i	1.12573	+	0.817892i	0.985068	−	0.172165i	$-0.0550762\pi$
$919$	34.1266	+	24.7944i	1.12573	+	0.817892i	0.140664	+	0.990057i	$0.455076\pi$
$920$	−11.9358	−	1.62685i	−0.393512	−	0.0536357i
$921$	−5.73615	+	24.1853i	−0.189013	+	0.796932i
$922$	−6.47647	−	2.88351i	−0.213291	−	0.0949633i
$923$	−18.9751	+	21.0740i	−0.624572	+	0.693658i
$924$	0.000918534		0.00488109i	3.02175e−5		0.000160576i
$925$	44.0856	−	28.0606i	1.44953	−	0.922626i
$926$	16.3264			0.536519
$927$	3.48353	+	4.25380i	0.114414	+	0.139713i
$928$	1.61147	−	1.17080i	0.0528990	−	0.0384334i
$929$	−0.412534	−	3.92500i	−0.0135348	−	0.128775i	0.985668	−	0.168697i	$-0.0539558\pi$
$929$	−0.412534	−	3.92500i	−0.0135348	−	0.128775i	−0.999203	+	0.0399216i	$0.987289\pi$
$930$	13.0517	+	16.1776i	0.427982	+	0.530483i
$931$	−0.279744	+	2.66159i	−0.00916824	+	0.0872300i
$932$	−0.531655	−	0.920854i	−0.0174149	−	0.0301636i
$933$	−22.0534	−	31.8997i	−0.721994	−	1.04435i
$934$	−25.1268	−	27.9062i	−0.822175	−	0.913117i
$935$	−0.0899306	−	0.219947i	−0.00294105	−	0.00719302i
$936$	−33.5986	−	41.0279i	−1.09821	−	1.34104i
$937$	9.87834	−	30.4024i	0.322711	−	0.993204i	−0.649752	−	0.760147i	$-0.725127\pi$
$937$	9.87834	−	30.4024i	0.322711	−	0.993204i	0.972463	−	0.233057i	$-0.0748729\pi$
$938$	5.23983	+	5.81942i	0.171087	+	0.190011i
$939$	37.1425	−	20.2990i	1.21210	−	0.662434i
$940$	0.162943	−	0.210356i	0.00531461	−	0.00686105i
$941$	−14.1248	+	3.00231i	−0.460454	+	0.0978726i	−0.432298	−	0.901731i	$-0.642297\pi$
$941$	−14.1248	+	3.00231i	−0.460454	+	0.0978726i	−0.0281566	+	0.999604i	$0.508964\pi$
$942$	−28.6125	+	2.33096i	−0.932247	+	0.0759469i
$943$	−1.56113	+	2.70396i	−0.0508374	+	0.0880529i
$944$	−42.2693	−	30.7104i	−1.37575	−	0.999540i
$945$	0.102910	+	27.9954i	0.00334767	+	0.910689i
$946$	0.407858	−	0.296326i	0.0132606	−	0.00963439i
$947$	−4.99146	−	47.4906i	−0.162201	−	1.54324i	−0.708538	−	0.705672i	$-0.750645\pi$
$947$	−4.99146	−	47.4906i	−0.162201	−	1.54324i	0.546337	−	0.837565i	$-0.316022\pi$
$948$	0.0512614	+	0.0312197i	0.00166489	+	0.00101397i
$949$	3.88422	+	6.72766i	0.126087	+	0.218389i
$950$	−0.691091	−	15.9769i	−0.0224219	−	0.518358i
$951$	5.54077	+	29.4437i	0.179672	+	0.954777i
$952$	22.2014	+	4.71906i	0.719553	+	0.152946i
$953$	−14.1198	+	10.2587i	−0.457387	+	0.332311i	−0.792505	−	0.609865i	$-0.791224\pi$
$953$	−14.1198	+	10.2587i	−0.457387	+	0.332311i	0.335119	+	0.942176i	$0.391224\pi$
$954$	6.52354	+	0.305953i	0.211207	+	0.00990560i
$955$	−9.55702	−	23.3740i	−0.309258	−	0.756364i
$956$	0.153017	−	0.0681276i	0.00494893	−	0.00220340i
$957$	0.482898	+	0.169512i	0.0156099	+	0.00547953i
$958$	−0.0698429	+	0.664511i	−0.00225652	+	0.0214694i
$959$	−26.3797	+	5.60717i	−0.851844	+	0.181065i
$960$	29.3292	+	7.91592i	0.946595	+	0.255485i
$961$	16.4957	+	3.50626i	0.532118	+	0.113105i
$962$	−29.0933	+	89.5400i	−0.938006	+	2.88689i
$963$	−49.5215	−	24.8907i	−1.59581	−	0.802091i
$964$	0.176536	+	0.543321i	0.00568583	+	0.0174992i
$965$	−8.87238	−	49.1217i	−0.285612	−	1.58128i
$966$	−11.3631	−	1.46423i	−0.365602	−	0.0471110i
$967$	−2.68341	+	25.5309i	−0.0862926	+	0.821019i	0.862699	+	0.505718i	$0.168772\pi$
$967$	−2.68341	+	25.5309i	−0.0862926	+	0.821019i	−0.948992	+	0.315301i	$0.897894\pi$
$968$	−15.4051	−	26.6823i	−0.495137	−	0.857603i
$969$	−13.0077	+	1.05969i	−0.417867	+	0.0340422i
$970$	−14.4190	+	29.8783i	−0.462967	+	0.959334i
$971$	−0.505556	+	0.367308i	−0.0162241	+	0.0117875i	−0.595868	−	0.803083i	$-0.703192\pi$
$971$	−0.505556	+	0.367308i	−0.0162241	+	0.0117875i	0.579644	+	0.814870i	$0.303192\pi$
$972$	−0.587049	−	0.00730568i	−0.0188296	−	0.000234330i
$973$	0.0299960	+	0.0923182i	0.000961627	+	0.00295958i
$974$	−3.59933	+	6.23422i	−0.115330	+	0.199757i
$975$	−35.7568	+	41.3287i	−1.14514	+	1.32358i
$976$	21.6343	+	37.4717i	0.692497	+	1.19944i
$977$	−24.6628	+	27.3909i	−0.789034	+	0.876311i	−0.994754	−	0.102300i	$-0.967380\pi$
$977$	−24.6628	+	27.3909i	−0.789034	+	0.876311i	0.205719	+	0.978611i	$0.434047\pi$
$978$	10.8022	+	10.1947i	0.345417	+	0.325989i
$979$	−0.00996728	−	0.0948323i	−0.000318556	−	0.00303085i
$980$	0.0239286	−	0.0977025i	0.000764371	−	0.00312099i
$981$	−9.53484	+	9.64019i	−0.304424	+	0.307788i
$982$	−10.7290			−0.342375
$983$	−26.0981	+	11.6196i	−0.832399	+	0.370608i	−0.778273	−	0.627926i	$-0.783904\pi$
$983$	−26.0981	+	11.6196i	−0.832399	+	0.370608i	−0.0541258	+	0.998534i	$0.517237\pi$
$984$	4.77786	−	6.26217i	0.152313	−	0.199631i
$985$	56.2482	−	16.3825i	1.79222	−	0.521990i
$986$	−30.0354	+	33.3577i	−0.956522	+	1.06232i
$987$	−7.99829	+	10.4831i	−0.254588	+	0.333680i
$988$	0.356316	+	0.395729i	0.0113359	+	0.0125898i
$989$	6.64210	+	20.4423i	0.211206	+	0.650027i
$990$	−0.101272	−	0.285143i	−0.00321865	−	0.00906242i
$991$	18.1246	−	55.7817i	0.575746	−	1.77196i	−0.0578809	−	0.998323i	$-0.518434\pi$
$991$	18.1246	−	55.7817i	0.575746	−	1.77196i	0.633626	−	0.773639i	$-0.281566\pi$
$992$	0.731666	−	0.325759i	0.0232304	−	0.0103429i
$993$	−8.39707	−	44.6221i	−0.266473	−	1.41604i
$994$	1.61561	−	15.3715i	0.0512441	−	0.487555i
$995$	34.9524	+	12.5572i	1.10807	+	0.398090i
$996$	−0.0836978	+	0.352895i	−0.00265207	+	0.0111819i
$997$	5.21007	+	49.5705i	0.165004	+	1.56991i	0.693172	+	0.720772i	$0.256213\pi$
$997$	5.21007	+	49.5705i	0.165004	+	1.56991i	−0.528168	+	0.849140i	$0.677121\pi$
$998$	−3.57766	−	11.0109i	−0.113249	−	0.348544i
$999$	−28.7568	−	46.0702i	−0.909824	−	1.45760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.106.8	yes	224
3.2	odd	2		675.2.r.a.181.21		224
9.4	even	3	inner	225.2.q.a.31.21	✓	224
9.5	odd	6		675.2.r.a.631.8		224
25.21	even	5	inner	225.2.q.a.196.21	yes	224
75.71	odd	10		675.2.r.a.46.8		224
225.121	even	15	inner	225.2.q.a.121.8	yes	224
225.221	odd	30		675.2.r.a.496.21		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.21	✓	224	9.4	even	3	inner
225.2.q.a.106.8	yes	224	1.1	even	1	trivial
225.2.q.a.121.8	yes	224	225.121	even	15	inner
225.2.q.a.196.21	yes	224	25.21	even	5	inner
675.2.r.a.46.8		224	75.71	odd	10
675.2.r.a.181.21		224	3.2	odd	2
675.2.r.a.496.21		224	225.221	odd	30
675.2.r.a.631.8		224	9.5	odd	6

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39627 - 0.296787i) q^{2} +(-0.399711 + 1.68530i) q^{3} +(0.0344061 + 0.0153186i) q^{4} +(-2.10438 - 0.756030i) q^{5} +(1.05828 - 2.23451i) q^{6} +(1.20474 - 2.08666i) q^{7} +(2.26620 + 1.64649i) q^{8} +(-2.68046 - 1.34726i) q^{9} +O(q^{10})\)	\(q+(-1.39627 - 0.296787i) q^{2} +(-0.399711 + 1.68530i) q^{3} +(0.0344061 + 0.0153186i) q^{4} +(-2.10438 - 0.756030i) q^{5} +(1.05828 - 2.23451i) q^{6} +(1.20474 - 2.08666i) q^{7} +(2.26620 + 1.64649i) q^{8} +(-2.68046 - 1.34726i) q^{9} +(2.71391 + 1.68018i) q^{10} +(0.0309094 + 0.00656999i) q^{11} +(-0.0395688 + 0.0518615i) q^{12} +(6.17253 - 1.31201i) q^{13} +(-2.30144 + 2.55600i) q^{14} +(2.11528 - 3.24432i) q^{15} +(-2.72598 - 3.02750i) q^{16} +(2.72065 + 1.97667i) q^{17} +(3.34281 + 2.67668i) q^{18} +(1.81267 + 1.31698i) q^{19} +(-0.0608222 - 0.0582481i) q^{20} +(3.03511 + 2.86440i) q^{21} +(-0.0412081 - 0.0183470i) q^{22} +(1.28687 - 1.42922i) q^{23} +(-3.68065 + 3.16110i) q^{24} +(3.85684 + 3.18195i) q^{25} -9.00793 q^{26} +(3.34195 - 3.97886i) q^{27} +(0.0734149 - 0.0533391i) q^{28} +(-0.977408 - 9.29942i) q^{29} +(-3.91638 + 3.90216i) q^{30} +(0.393002 - 3.73917i) q^{31} +(0.106511 + 0.184482i) q^{32} +(-0.0234272 + 0.0494655i) q^{33} +(-3.21212 - 3.56742i) q^{34} +(-4.11281 + 3.48032i) q^{35} +(-0.0715860 - 0.0874149i) q^{36} +(3.22975 - 9.94014i) q^{37} +(-2.14012 - 2.37684i) q^{38} +(-0.256096 + 10.9270i) q^{39} +(-3.52414 - 5.17815i) q^{40} +(-1.58800 + 0.337539i) q^{41} +(-3.38772 - 4.90027i) q^{42} +(-5.58816 + 9.67898i) q^{43} +(0.000962828 + 0.000699535i) q^{44} +(4.62214 + 4.86167i) q^{45} +(-2.22100 + 1.61365i) q^{46} +(0.330264 + 3.14225i) q^{47} +(6.19185 - 3.38396i) q^{48} +(0.597221 + 1.03442i) q^{49} +(-4.44084 - 5.58753i) q^{50} +(-4.41875 + 3.79501i) q^{51} +(0.232471 + 0.0494131i) q^{52} +(1.23376 - 0.896379i) q^{53} +(-5.84716 + 4.56373i) q^{54} +(-0.0600780 - 0.0371942i) q^{55} +(6.16584 - 2.74521i) q^{56} +(-2.94405 + 2.52848i) q^{57} +(-1.39522 + 13.2746i) q^{58} +(12.5447 - 2.66646i) q^{59} +(0.122477 - 0.0792211i) q^{60} +(-10.3888 - 2.20821i) q^{61} +(-1.65848 + 5.10426i) q^{62} +(-6.04054 + 3.97013i) q^{63} +(2.42385 + 7.45983i) q^{64} +(-13.9813 - 1.90565i) q^{65} +(0.0473915 - 0.0621144i) q^{66} +(0.237987 - 2.26429i) q^{67} +(0.0633271 + 0.109686i) q^{68} +(1.89428 + 2.74004i) q^{69} +(6.77551 - 3.63885i) q^{70} +(-3.63556 + 2.64139i) q^{71} +(-3.85620 - 7.46651i) q^{72} +(0.380414 + 1.17080i) q^{73} +(-7.45971 + 12.9206i) q^{74} +(-6.90416 + 5.22806i) q^{75} +(0.0421926 + 0.0730797i) q^{76} +(0.0509470 - 0.0565824i) q^{77} +(3.60057 - 15.1810i) q^{78} +(-0.0961757 - 0.915050i) q^{79} +(3.44761 + 8.43194i) q^{80} +(5.36976 + 7.22258i) q^{81} +2.31745 q^{82} +(5.07918 - 2.26140i) q^{83} +(0.0605475 + 0.145046i) q^{84} +(-4.23086 - 6.21655i) q^{85} +(10.6752 - 11.8560i) q^{86} +(16.0630 + 2.06986i) q^{87} +(0.0592293 + 0.0657808i) q^{88} +(-0.932477 - 2.86987i) q^{89} +(-5.01089 - 8.16001i) q^{90} +(4.69854 - 14.4606i) q^{91} +(0.0661697 - 0.0294607i) q^{92} +(6.14453 + 2.15691i) q^{93} +(0.471441 - 4.48546i) q^{94} +(-2.81887 - 4.14186i) q^{95} +(-0.353480 + 0.105763i) q^{96} +(1.08643 + 10.3367i) q^{97} +(-0.526882 - 1.62158i) q^{98} +(-0.0739999 - 0.0592538i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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