LMFDB - Embedded newform 189.2.u.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(4,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 12]))

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

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

chi := DirichletCharacter("189.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.u (of order $9$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.1
Character	$\chi$	$=$	189.4
Dual form			189.2.u.a.142.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.467294 - 2.65016i) q^{2} +(1.66541 + 0.475808i) q^{3} +(-4.92558 + 1.79277i) q^{4} +(2.75387 - 1.00233i) q^{5} +(0.482727 - 4.63595i) q^{6} +(-0.609446 - 2.57460i) q^{7} +(4.36176 + 7.55480i) q^{8} +(2.54721 + 1.58484i) q^{9} +O(q^{10})$	\(q+(-0.467294 - 2.65016i) q^{2} +(1.66541 + 0.475808i) q^{3} +(-4.92558 + 1.79277i) q^{4} +(2.75387 - 1.00233i) q^{5} +(0.482727 - 4.63595i) q^{6} +(-0.609446 - 2.57460i) q^{7} +(4.36176 + 7.55480i) q^{8} +(2.54721 + 1.58484i) q^{9} +(-3.94319 - 6.82980i) q^{10} +(-2.20625 - 0.803010i) q^{11} +(-9.05615 + 0.642067i) q^{12} +(-1.68408 + 0.612957i) q^{13} +(-6.53831 + 2.81822i) q^{14} +(5.06325 - 0.358977i) q^{15} +(9.95243 - 8.35108i) q^{16} +(-0.185180 - 0.320741i) q^{17} +(3.00976 - 7.49110i) q^{18} +(-0.496899 + 0.860655i) q^{19} +(-11.7675 + 9.87408i) q^{20} +(0.210035 - 4.57776i) q^{21} +(-1.09713 + 6.22215i) q^{22} +(-1.14680 + 6.50383i) q^{23} +(3.66952 + 14.6572i) q^{24} +(2.74891 - 2.30661i) q^{25} +(2.41139 + 4.17666i) q^{26} +(3.48809 + 3.85139i) q^{27} +(7.61753 + 11.5888i) q^{28} +(6.76911 + 2.46375i) q^{29} +(-3.31737 - 13.2507i) q^{30} +(-3.45754 + 1.25844i) q^{31} +(-13.4172 - 11.2583i) q^{32} +(-3.29225 - 2.38710i) q^{33} +(-0.763481 + 0.640637i) q^{34} +(-4.25893 - 6.47925i) q^{35} +(-15.3877 - 3.23968i) q^{36} -1.65927 q^{37} +(2.51307 + 0.914682i) q^{38} +(-3.09635 + 0.219526i) q^{39} +(19.5841 + 16.4330i) q^{40} +(8.90071 - 3.23959i) q^{41} +(-12.2299 + 1.58253i) q^{42} +(-1.36359 - 7.73328i) q^{43} +12.3067 q^{44} +(8.60321 + 1.81129i) q^{45} +17.7721 q^{46} +(-0.234461 - 0.0853368i) q^{47} +(20.5484 - 9.17257i) q^{48} +(-6.25715 + 3.13816i) q^{49} +(-7.39743 - 6.20718i) q^{50} +(-0.155790 - 0.622278i) q^{51} +(7.19621 - 6.03834i) q^{52} +(-4.11638 + 7.12978i) q^{53} +(8.57683 - 11.0437i) q^{54} -6.88060 q^{55} +(16.7923 - 15.8341i) q^{56} +(-1.23705 + 1.19692i) q^{57} +(3.36617 - 19.0905i) q^{58} +(3.89379 + 3.26728i) q^{59} +(-24.2959 + 10.8454i) q^{60} +(0.813935 + 0.296248i) q^{61} +(4.95075 + 8.57495i) q^{62} +(2.52793 - 7.52393i) q^{63} +(-10.5746 + 18.3158i) q^{64} +(-4.02336 + 3.37600i) q^{65} +(-4.78773 + 9.84044i) q^{66} +(0.371283 - 2.10565i) q^{67} +(1.48713 + 1.24785i) q^{68} +(-5.00447 + 10.2859i) q^{69} +(-15.1809 + 14.3145i) q^{70} +(0.743006 - 1.28692i) q^{71} +(-0.862762 + 26.1564i) q^{72} -9.96945 q^{73} +(0.775366 + 4.39732i) q^{74} +(5.67558 - 2.53351i) q^{75} +(0.904566 - 5.13005i) q^{76} +(-0.722839 + 6.16961i) q^{77} +(2.02869 + 8.10323i) q^{78} +(1.60454 + 9.09978i) q^{79} +(19.0372 - 32.9734i) q^{80} +(3.97660 + 8.07383i) q^{81} +(-12.7447 - 22.0744i) q^{82} +(-6.30367 - 2.29435i) q^{83} +(7.17230 + 22.9247i) q^{84} +(-0.831449 - 0.697669i) q^{85} +(-19.8572 + 7.22743i) q^{86} +(10.1011 + 7.32396i) q^{87} +(-3.55657 - 20.1703i) q^{88} +(6.39738 - 11.0806i) q^{89} +(0.779968 - 23.6463i) q^{90} +(2.60448 + 3.96228i) q^{91} +(-6.01118 - 34.0911i) q^{92} +(-6.35701 + 0.450702i) q^{93} +(-0.116594 + 0.661236i) q^{94} +(-0.505738 + 2.86819i) q^{95} +(-16.9883 - 25.1338i) q^{96} +(2.55575 + 14.4944i) q^{97} +(11.2406 + 15.1160i) q^{98} +(-4.34716 - 5.54198i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.467294	−	2.65016i	−0.330427	−	1.87394i	−0.468413	−	0.883510i	$-0.655174\pi$
$2$	−0.467294	−	2.65016i	−0.330427	−	1.87394i	0.137986	−	0.990434i	$-0.455937\pi$
$3$	1.66541	+	0.475808i	0.961528	+	0.274708i
$3$	1.66541	+	0.475808i	0.961528	+	0.274708i
$4$	−4.92558	+	1.79277i	−2.46279	+	0.896383i
$5$	2.75387	−	1.00233i	1.23157	−	0.448254i	0.357433	−	0.933939i	$-0.383652\pi$
$5$	2.75387	−	1.00233i	1.23157	−	0.448254i	0.874134	+	0.485685i	$0.161430\pi$
$6$	0.482727	−	4.63595i	0.197072	−	1.89262i
$7$	−0.609446	−	2.57460i	−0.230349	−	0.973108i
$7$	−0.609446	−	2.57460i	−0.230349	−	0.973108i
$8$	4.36176	+	7.55480i	1.54212	+	2.67102i
$9$	2.54721	+	1.58484i	0.849071	+	0.528278i
$10$	−3.94319	−	6.82980i	−1.24695	−	2.15977i
$11$	−2.20625	−	0.803010i	−0.665210	−	0.242117i	−0.0127258	−	0.999919i	$-0.504051\pi$
$11$	−2.20625	−	0.803010i	−0.665210	−	0.242117i	−0.652484	+	0.757802i	$0.726273\pi$
$12$	−9.05615	+	0.642067i	−2.61429	+	0.185349i
$13$	−1.68408	+	0.612957i	−0.467081	+	0.170004i	−0.564830	−	0.825208i	$-0.691058\pi$
$13$	−1.68408	+	0.612957i	−0.467081	+	0.170004i	0.0977486	+	0.995211i	$0.468836\pi$
$14$	−6.53831	+	2.81822i	−1.74744	+	0.753202i
$15$	5.06325	−	0.358977i	1.30733	−	0.0926874i
$16$	9.95243	−	8.35108i	2.48811	−	2.08777i
$17$	−0.185180	−	0.320741i	−0.0449128	−	0.0777912i	0.842695	−	0.538391i	$-0.180968\pi$
$17$	−0.185180	−	0.320741i	−0.0449128	−	0.0777912i	−0.887608	+	0.460600i	$0.847634\pi$
$18$	3.00976	−	7.49110i	0.709408	−	1.76567i
$19$	−0.496899	+	0.860655i	−0.113997	+	0.197448i	−0.917378	−	0.398017i	$-0.869699\pi$
$19$	−0.496899	+	0.860655i	−0.113997	+	0.197448i	0.803382	+	0.595464i	$0.203032\pi$
$20$	−11.7675	+	9.87408i	−2.63129	+	2.20791i
$21$	0.210035	−	4.57776i	0.0458334	−	0.998949i
$22$	−1.09713	+	6.22215i	−0.233910	+	1.32657i
$23$	−1.14680	+	6.50383i	−0.239124	+	1.35614i	0.594627	+	0.804002i	$0.297300\pi$
$23$	−1.14680	+	6.50383i	−0.239124	+	1.35614i	−0.833751	+	0.552140i	$0.813811\pi$
$24$	3.66952	+	14.6572i	0.749037	+	2.99190i
$25$	2.74891	−	2.30661i	0.549782	−	0.461322i
$26$	2.41139	+	4.17666i	0.472913	+	0.819110i
$27$	3.48809	+	3.85139i	0.671283	+	0.741201i
$28$	7.61753	+	11.5888i	1.43958	+	2.19008i
$29$	6.76911	+	2.46375i	1.25699	+	0.457507i	0.882758	−	0.469827i	$-0.155684\pi$
$29$	6.76911	+	2.46375i	1.25699	+	0.457507i	0.374233	+	0.927335i	$0.377906\pi$
$30$	−3.31737	−	13.2507i	−0.605666	−	2.41923i
$31$	−3.45754	+	1.25844i	−0.620992	+	0.226023i	−0.633306	−	0.773902i	$-0.718302\pi$
$31$	−3.45754	+	1.25844i	−0.620992	+	0.226023i	0.0123140	+	0.999924i	$0.496080\pi$
$32$	−13.4172	−	11.2583i	−2.37184	−	1.99021i
$33$	−3.29225	−	2.38710i	−0.573106	−	0.415540i
$34$	−0.763481	+	0.640637i	−0.130936	+	0.109868i
$35$	−4.25893	−	6.47925i	−0.719890	−	1.09519i
$36$	−15.3877	−	3.23968i	−2.56462	−	0.539947i
$37$	−1.65927			−0.272782			−0.136391	−	0.990655i	$-0.543550\pi$
$37$	−1.65927			−0.272782			−0.136391	+	0.990655i	$0.543550\pi$
$38$	2.51307	+	0.914682i	0.407674	+	0.148381i
$39$	−3.09635	+	0.219526i	−0.495813	+	0.0351524i
$40$	19.5841	+	16.4330i	3.09652	+	2.59829i
$41$	8.90071	−	3.23959i	1.39006	−	0.505939i	0.464845	−	0.885392i	$-0.346110\pi$
$41$	8.90071	−	3.23959i	1.39006	−	0.505939i	0.925211	+	0.379453i	$0.123888\pi$
$42$	−12.2299	+	1.58253i	−1.88712	+	0.244190i
$43$	−1.36359	−	7.73328i	−0.207945	−	1.17931i	−0.892738	−	0.450577i	$-0.851218\pi$
$43$	−1.36359	−	7.73328i	−0.207945	−	1.17931i	0.684793	−	0.728738i	$-0.259893\pi$
$44$	12.3067			1.85530
$45$	8.60321	+	1.81129i	1.28249	+	0.270011i
$46$	17.7721			2.62035
$47$	−0.234461	−	0.0853368i	−0.0341996	−	0.0124477i	0.324864	−	0.945761i	$-0.394682\pi$
$47$	−0.234461	−	0.0853368i	−0.0341996	−	0.0124477i	−0.359063	+	0.933313i	$0.616904\pi$
$48$	20.5484	−	9.17257i	2.96591	−	1.32395i
$49$	−6.25715	+	3.13816i	−0.893879	+	0.448309i
$50$	−7.39743	−	6.20718i	−1.04615	−	0.877828i
$51$	−0.155790	−	0.622278i	−0.0218150	−	0.0871363i
$52$	7.19621	−	6.03834i	0.997935	−	0.837367i
$53$	−4.11638	+	7.12978i	−0.565429	+	0.979351i	0.431581	+	0.902074i	$0.357956\pi$
$53$	−4.11638	+	7.12978i	−0.565429	+	0.979351i	−0.997010	+	0.0772769i	$0.975377\pi$
$54$	8.57683	−	11.0437i	1.16716	−	1.50286i
$55$	−6.88060			−0.927781
$56$	16.7923	−	15.8341i	2.24397	−	2.11591i
$57$	−1.23705	+	1.19692i	−0.163851	+	0.158536i
$58$	3.36617	−	19.0905i	0.442000	−	2.50670i
$59$	3.89379	+	3.26728i	0.506928	+	0.425363i	0.860047	−	0.510215i	$-0.170434\pi$
$59$	3.89379	+	3.26728i	0.506928	+	0.425363i	−0.353119	+	0.935579i	$0.614879\pi$
$60$	−24.2959	+	10.8454i	−3.13659	+	1.40013i
$61$	0.813935	+	0.296248i	0.104214	+	0.0379307i	0.393601	−	0.919281i	$-0.371229\pi$
$61$	0.813935	+	0.296248i	0.104214	+	0.0379307i	−0.289387	+	0.957212i	$0.593451\pi$
$62$	4.95075	+	8.57495i	0.628746	+	1.08902i
$63$	2.52793	−	7.52393i	0.318489	−	0.947926i
$64$	−10.5746	+	18.3158i	−1.32183	+	2.28947i
$65$	−4.02336	+	3.37600i	−0.499037	+	0.418742i
$66$	−4.78773	+	9.84044i	−0.589329	+	1.21127i
$67$	0.371283	−	2.10565i	0.0453595	−	0.257246i	−0.953692	−	0.300784i	$-0.902752\pi$
$67$	0.371283	−	2.10565i	0.0453595	−	0.257246i	0.999052	+	0.0435375i	$0.0138628\pi$
$68$	1.48713	+	1.24785i	0.180341	+	0.151324i
$69$	−5.00447	+	10.2859i	−0.602467	+	1.23828i
$70$	−15.1809	+	14.3145i	−1.81446	+	1.71091i
$71$	0.743006	−	1.28692i	0.0881786	−	0.152730i	−0.818563	−	0.574417i	$-0.805229\pi$
$71$	0.743006	−	1.28692i	0.0881786	−	0.152730i	0.906741	+	0.421687i	$0.138562\pi$
$72$	−0.862762	+	26.1564i	−0.101678	+	3.08256i
$73$	−9.96945			−1.16684			−0.583418	−	0.812172i	$-0.698285\pi$
$73$	−9.96945			−1.16684			−0.583418	+	0.812172i	$0.698285\pi$
$74$	0.775366	+	4.39732i	0.0901345	+	0.511178i
$75$	5.67558	−	2.53351i	0.655360	−	0.292545i
$76$	0.904566	−	5.13005i	0.103761	−	0.588457i
$77$	−0.722839	+	6.16961i	−0.0823752	+	0.703092i
$78$	2.02869	+	8.10323i	0.229703	+	0.917510i
$79$	1.60454	+	9.09978i	0.180525	+	1.02381i	0.931572	+	0.363557i	$0.118438\pi$
$79$	1.60454	+	9.09978i	0.180525	+	1.02381i	−0.751047	+	0.660248i	$0.770451\pi$
$80$	19.0372	−	32.9734i	2.12842	−	3.68653i
$81$	3.97660	+	8.07383i	0.441844	+	0.897092i
$82$	−12.7447	−	22.0744i	−1.40741	−	2.43771i
$83$	−6.30367	−	2.29435i	−0.691918	−	0.251838i	−0.0279619	−	0.999609i	$-0.508902\pi$
$83$	−6.30367	−	2.29435i	−0.691918	−	0.251838i	−0.663956	+	0.747771i	$0.731124\pi$
$84$	7.17230	+	22.9247i	0.782562	+	2.50129i
$85$	−0.831449	−	0.697669i	−0.0901833	−	0.0756728i
$86$	−19.8572	+	7.22743i	−2.14126	+	0.779354i
$87$	10.1011	+	7.32396i	1.08295	+	0.785211i
$88$	−3.55657	−	20.1703i	−0.379132	−	2.15016i
$89$	6.39738	−	11.0806i	0.678121	−	1.17454i	−0.297425	−	0.954745i	$-0.596128\pi$
$89$	6.39738	−	11.0806i	0.678121	−	1.17454i	0.975546	−	0.219795i	$-0.0705389\pi$
$90$	0.779968	−	23.6463i	0.0822158	−	2.49254i
$91$	2.60448	+	3.96228i	0.273024	+	0.415360i
$92$	−6.01118	−	34.0911i	−0.626708	−	3.55424i
$93$	−6.35701	+	0.450702i	−0.659191	+	0.0467356i
$94$	−0.116594	+	0.661236i	−0.0120257	+	0.0682012i
$95$	−0.505738	+	2.86819i	−0.0518877	+	0.294270i
$96$	−16.9883	−	25.1338i	−1.73386	−	2.56521i
$97$	2.55575	+	14.4944i	0.259497	+	1.47168i	0.784261	+	0.620431i	$0.213042\pi$
$97$	2.55575	+	14.4944i	0.259497	+	1.47168i	−0.524764	+	0.851248i	$0.675847\pi$
$98$	11.2406	+	15.1160i	1.13547	+	1.52695i
$99$	−4.34716	−	5.54198i	−0.436906	−	0.556990i
$100$	−9.40478	+	16.2896i	−0.940478	+	1.62896i
$101$	1.48438	+	8.41831i	0.147701	+	0.837653i	0.965159	+	0.261665i	$0.0842716\pi$
$101$	1.48438	+	8.41831i	0.147701	+	0.837653i	−0.817458	+	0.575988i	$0.804617\pi$
$102$	−1.57633	+	0.703656i	−0.156080	+	0.0696723i
$103$	−7.98496	+	2.90629i	−0.786782	+	0.286365i	−0.703998	−	0.710202i	$-0.748603\pi$
$103$	−7.98496	+	2.90629i	−0.786782	+	0.286365i	−0.0827842	+	0.996567i	$0.526381\pi$
$104$	−11.9763	−	10.0493i	−1.17438	−	0.985419i
$105$	−4.01000	−	12.8171i	−0.391336	−	1.25082i
$106$	20.8186	+	7.57735i	2.02208	+	0.735978i
$107$	−7.94622	−	13.7633i	−0.768190	−	1.33054i	−0.938543	−	0.345161i	$-0.887824\pi$
$107$	−7.94622	−	13.7633i	−0.768190	−	1.33054i	0.170353	−	0.985383i	$-0.445509\pi$
$108$	−24.0855	−	12.7170i	−2.31763	−	1.22370i
$109$	2.43123	−	4.21101i	0.232869	−	0.403341i	−0.725782	−	0.687925i	$-0.758522\pi$
$109$	2.43123	−	4.21101i	0.232869	−	0.403341i	0.958651	+	0.284583i	$0.0918552\pi$
$110$	3.21527	+	18.2347i	0.306564	+	1.73861i
$111$	−2.76337	−	0.789493i	−0.262287	−	0.0749353i
$112$	−27.5662	−	20.5340i	−2.60476	−	1.94028i
$113$	1.58605	−	8.99494i	0.149203	−	0.846173i	−0.814693	−	0.579893i	$-0.803094\pi$
$113$	1.58605	−	8.99494i	0.149203	−	0.846173i	0.963896	−	0.266280i	$-0.0857945\pi$
$114$	3.75009	+	2.71906i	0.351228	+	0.254664i
$115$	3.36082	+	19.0602i	0.313398	+	1.77737i
$116$	−37.7587			−3.50581
$117$	−5.26116	−	1.10766i	−0.486394	−	0.102404i
$118$	6.83925	−	11.8459i	0.629604	−	1.09051i
$119$	−0.712924	+	0.672240i	−0.0653536	+	0.0616241i
$120$	24.7967	+	36.6860i	2.26362	+	3.34896i
$121$	−4.20377	−	3.52738i	−0.382161	−	0.320671i
$122$	0.404757	−	2.29549i	0.0366450	−	0.207824i
$123$	16.3648	−	1.16024i	1.47556	−	0.104615i
$124$	14.7743	−	12.3971i	1.32677	−	1.11329i
$125$	−2.06835	+	3.58249i	−0.184999	+	0.320427i
$126$	−21.1209	−	3.18352i	−1.88160	−	0.283611i
$127$	−6.07362	−	10.5198i	−0.538947	−	0.933483i	−0.998961	−	0.0455717i	$-0.985489\pi$
$127$	−6.07362	−	10.5198i	−0.538947	−	0.933483i	0.460014	−	0.887911i	$-0.347844\pi$
$128$	20.5640	+	7.48467i	1.81761	+	0.661558i
$129$	1.40862	−	13.5279i	0.124022	−	1.19107i
$130$	10.8270	+	9.08496i	0.949594	+	0.796804i
$131$	−2.39787	+	13.5990i	−0.209502	+	1.18815i	0.680693	+	0.732569i	$0.261679\pi$
$131$	−2.39787	+	13.5990i	−0.209502	+	1.18815i	−0.890195	+	0.455579i	$0.849432\pi$
$132$	20.4957	+	5.85562i	1.78392	+	0.509666i
$133$	2.51868	+	0.754795i	0.218397	+	0.0654490i
$134$	−5.75381			−0.497053
$135$	13.4661	+	7.11002i	1.15898	+	0.611933i
$136$	1.61542	−	2.79800i	0.138521	−	0.239926i
$137$	8.80875	−	7.39142i	0.752582	−	0.631492i	−0.183602	−	0.983001i	$-0.558776\pi$
$137$	8.80875	−	7.39142i	0.752582	−	0.631492i	0.936184	+	0.351509i	$0.114331\pi$
$138$	29.5978	+	8.45608i	2.51954	+	0.719830i
$139$	−7.48876	−	6.28381i	−0.635188	−	0.532986i	0.267348	−	0.963600i	$-0.413853\pi$
$139$	−7.48876	−	6.28381i	−0.635188	−	0.532986i	−0.902536	+	0.430614i	$0.858297\pi$
$140$	32.5935	+	24.2788i	2.75465	+	2.05194i
$141$	−0.349871	−	0.253680i	−0.0294644	−	0.0213637i
$142$	−3.75775	−	1.36771i	−0.315344	−	0.114776i
$143$	4.20772			0.351868
$144$	38.5860	−	5.49903i	3.21550	−	0.458252i
$145$	21.1107			1.75315
$146$	4.65866	+	26.4206i	0.385554	+	2.18658i
$147$	−11.9139	+	2.24914i	−0.982643	+	0.185506i
$148$	8.17286	−	2.97468i	0.671805	−	0.244517i
$149$	−1.42758	−	1.19789i	−0.116952	−	0.0981346i	0.582436	−	0.812877i	$-0.302100\pi$
$149$	−1.42758	−	1.19789i	−0.116952	−	0.0981346i	−0.699388	+	0.714742i	$0.746544\pi$
$150$	−9.36637	−	13.8573i	−0.764761	−	1.13144i
$151$	−15.4952	−	5.63979i	−1.26098	−	0.458960i	−0.376883	−	0.926261i	$-0.623004\pi$
$151$	−15.4952	−	5.63979i	−1.26098	−	0.458960i	−0.884098	+	0.467301i	$0.845226\pi$
$152$	−8.66943			−0.703184
$153$	0.0366289	−	1.11048i	0.00296127	−	0.0897767i
$154$	16.6882	−	0.967386i	1.34477	−	0.0779542i
$155$	−8.26023	+	6.93116i	−0.663478	+	0.556724i
$156$	14.8578	−	6.63232i	1.18957	−	0.531011i
$157$	−0.979587	−	0.821971i	−0.0781796	−	0.0656005i	0.602860	−	0.797847i	$-0.294028\pi$
$157$	−0.979587	−	0.821971i	−0.0781796	−	0.0656005i	−0.681040	+	0.732246i	$0.738472\pi$
$158$	23.3661	−	8.50455i	1.85890	−	0.676586i
$159$	−10.2479	+	9.91544i	−0.812711	+	0.786346i
$160$	−48.2336	−	17.5556i	−3.81320	−	1.38789i
$161$	17.4437	−	1.01118i	1.37475	−	0.0796921i
$162$	19.5387	−	14.3115i	1.53510	−	1.12441i
$163$	0.824782	+	1.42856i	0.0646019	+	0.111894i	0.896517	−	0.443009i	$-0.146089\pi$
$163$	0.824782	+	1.42856i	0.0646019	+	0.111894i	−0.831915	+	0.554902i	$0.812756\pi$
$164$	−38.0333	+	31.9137i	−2.96990	+	2.49205i
$165$	−11.4591	−	3.27385i	−0.892087	−	0.254869i
$166$	−3.13472	+	17.7779i	−0.243301	+	1.37983i
$167$	2.59321	−	14.7068i	0.200669	−	1.13805i	−0.703443	−	0.710752i	$-0.748355\pi$
$167$	2.59321	−	14.7068i	0.200669	−	1.13805i	0.904111	−	0.427297i	$-0.140534\pi$
$168$	35.5002	−	18.3803i	2.73890	−	1.41807i
$169$	−7.49815	+	6.29170i	−0.576781	+	0.483977i
$170$	−1.46040	+	2.52949i	−0.112008	+	0.194003i
$171$	−2.62970	+	1.40477i	−0.201099	+	0.107425i
$172$	20.5804	+	35.6463i	1.56924	+	2.71801i
$173$	−5.87313	+	4.92815i	−0.446526	+	0.374680i	−0.838145	−	0.545448i	$-0.816360\pi$
$173$	−5.87313	+	4.92815i	−0.446526	+	0.374680i	0.391619	+	0.920128i	$0.371915\pi$
$174$	14.6895	−	30.1919i	1.11361	−	2.28884i
$175$	−7.61392	−	5.67160i	−0.575558	−	0.428733i
$176$	−28.6636	+	10.4327i	−2.16060	+	0.786393i
$177$	4.93018	+	7.29407i	0.370575	+	0.548256i
$178$	−32.3548	−	11.7762i	−2.42509	−	0.882661i
$179$	−11.4119	−	19.7659i	−0.852963	−	1.47737i	−0.878522	−	0.477701i	$-0.841470\pi$
$179$	−11.4119	−	19.7659i	−0.852963	−	1.47737i	0.0255596	−	0.999673i	$-0.491863\pi$
$180$	−45.6230	+	6.50189i	−3.40054	+	0.484622i
$181$	−6.10213	−	10.5692i	−0.453567	−	0.785602i	0.545037	−	0.838412i	$-0.316516\pi$
$181$	−6.10213	−	10.5692i	−0.453567	−	0.785602i	−0.998605	+	0.0528100i	$0.983182\pi$
$182$	9.28361	−	8.75383i	0.688147	−	0.648877i
$183$	1.21458	+	0.880653i	0.0897845	+	0.0650997i
$184$	−54.1372	+	19.7043i	−3.99104	+	1.45262i
$185$	−4.56940	+	1.66313i	−0.335949	+	0.122276i
$186$	4.16502	+	16.6365i	0.305394	+	1.21984i
$187$	0.150995	+	0.856338i	0.0110419	+	0.0626216i
$188$	1.30785			0.0953844
$189$	7.79000	−	11.3277i	0.566639	−	0.823966i
$190$	7.83747			0.568590
$191$	−1.26078	−	7.15023i	−0.0912267	−	0.517372i	−0.995838	−	0.0911358i	$-0.970950\pi$
$191$	−1.26078	−	7.15023i	−0.0912267	−	0.517372i	0.904612	−	0.426236i	$-0.140161\pi$
$192$	−26.3259	+	25.4719i	−1.89991	+	1.83827i
$193$	23.0279	−	8.38149i	1.65759	−	0.603313i	0.667607	−	0.744514i	$-0.267319\pi$
$193$	23.0279	−	8.38149i	1.65759	−	0.603313i	0.989981	+	0.141202i	$0.0450966\pi$
$194$	37.2180	−	13.5463i	2.67210	−	0.972564i
$195$	−8.30690	+	3.70810i	−0.594870	+	0.265542i
$196$	25.1941	−	26.6749i	1.79958	−	1.90535i
$197$	0.145635	+	0.252248i	0.0103761	+	0.0179719i	0.871167	−	0.490987i	$-0.163364\pi$
$197$	0.145635	+	0.252248i	0.0103761	+	0.0179719i	−0.860791	+	0.508959i	$0.830030\pi$
$198$	−12.6557	+	14.1104i	−0.899403	+	1.00278i
$199$	−0.581824	−	1.00775i	−0.0412444	−	0.0714374i	0.844666	−	0.535293i	$-0.179799\pi$
$199$	−0.581824	−	1.00775i	−0.0412444	−	0.0714374i	−0.885911	+	0.463856i	$0.846466\pi$
$200$	29.4161	+	10.7066i	2.08003	+	0.757070i
$201$	1.62023	−	3.33013i	0.114282	−	0.234889i
$202$	21.6162	−	7.86766i	1.52091	−	0.553566i
$203$	2.21778	−	18.9293i	0.155657	−	1.32857i
$204$	1.88296	+	2.78578i	0.131833	+	0.195044i
$205$	21.2642	−	17.8428i	1.48516	−	1.24620i
$206$	11.4334	+	19.8033i	0.796606	+	1.37976i
$207$	−13.2286	+	14.7491i	−0.919454	+	1.02514i
$208$	−11.6419	+	20.1643i	−0.807219	+	1.39814i
$209$	1.78740	−	1.49981i	0.123637	−	0.103744i
$210$	−32.0934	+	16.6165i	−2.21466	+	1.14665i
$211$	0.497448	−	2.82117i	0.0342458	−	0.194217i	−0.962885	−	0.269911i	$-0.913006\pi$
$211$	0.497448	−	2.82117i	0.0342458	−	0.194217i	0.997131	+	0.0756932i	$0.0241170\pi$
$212$	7.49355	−	42.4980i	0.514659	−	2.91878i
$213$	1.84974	−	1.78973i	0.126742	−	0.122631i
$214$	−32.7616	+	27.4902i	−2.23953	+	1.87919i
$215$	−11.5064	−	19.9297i	−0.784730	−	1.35919i
$216$	−13.8823	+	43.1507i	−0.944568	+	2.93603i
$217$	5.34716	+	8.13483i	0.362989	+	0.552228i
$218$	−12.2959	−	4.47535i	−0.832785	−	0.303109i
$219$	−16.6033	−	4.74354i	−1.12194	−	0.320539i
$220$	33.8910	−	12.3353i	2.28493	−	0.831646i
$221$	0.508459	+	0.426648i	0.0342027	+	0.0286995i
$222$	−0.800973	+	7.69229i	−0.0537578	+	0.516272i
$223$	−1.16906	+	0.980960i	−0.0782862	+	0.0656899i	−0.681091	−	0.732199i	$-0.738494\pi$
$223$	−1.16906	+	0.980960i	−0.0782862	+	0.0656899i	0.602805	+	0.797889i	$0.294050\pi$
$224$	−20.8087	+	41.4052i	−1.39034	+	2.76650i
$225$	10.6577	−	1.51886i	0.710511	−	0.101257i
$226$	−24.5791			−1.63498
$227$	16.2298	+	5.90717i	1.07721	+	0.392073i	0.818869	−	0.573980i	$-0.194601\pi$
$227$	16.2298	+	5.90717i	1.07721	+	0.392073i	0.258342	+	0.966053i	$0.416824\pi$
$228$	3.94740	−	8.11326i	0.261423	−	0.537314i
$229$	−6.89707	−	5.78733i	−0.455771	−	0.382438i	0.385801	−	0.922582i	$-0.373925\pi$
$229$	−6.89707	−	5.78733i	−0.455771	−	0.382438i	−0.841572	+	0.540144i	$0.818370\pi$
$230$	48.9419	−	17.8134i	3.22713	−	1.17458i
$231$	−4.13938	+	9.93103i	−0.272351	+	0.653414i
$232$	10.9121	+	61.8855i	0.716414	+	4.06298i
$233$	3.91280			0.256336			0.128168	−	0.991752i	$-0.459090\pi$
$233$	3.91280			0.256336			0.128168	+	0.991752i	$0.459090\pi$
$234$	−0.476977	+	14.4605i	−0.0311809	+	0.945312i
$235$	−0.731210			−0.0476989
$236$	−25.0366	−	9.11259i	−1.62975	−	0.593179i
$237$	−1.65753	+	15.9184i	−0.107668	+	1.03401i
$238$	2.11469	+	1.57523i	0.137075	+	0.102107i
$239$	9.32029	+	7.82065i	0.602879	+	0.505876i	0.892370	−	0.451305i	$-0.149041\pi$
$239$	9.32029	+	7.82065i	0.602879	+	0.505876i	−0.289490	+	0.957181i	$0.593486\pi$
$240$	47.3938	−	45.8563i	3.05926	−	2.96001i
$241$	21.1617	−	17.7568i	1.36315	−	1.14381i	0.388149	−	0.921597i	$-0.373115\pi$
$241$	21.1617	−	17.7568i	1.36315	−	1.14381i	0.974997	−	0.222218i	$-0.0713297\pi$
$242$	−7.38371	+	12.7890i	−0.474643	+	0.822106i
$243$	2.78109	+	15.3384i	0.178407	+	0.983957i
$244$	−4.54021			−0.290657
$245$	−14.0859	+	14.9138i	−0.899916	+	0.952807i
$246$	−10.7220	−	42.8271i	−0.683609	−	2.73056i
$247$	0.309276	−	1.75399i	0.0196788	−	0.111604i
$248$	−24.5882	−	20.6320i	−1.56135	−	1.31013i
$249$	−9.40656	−	6.82038i	−0.596117	−	0.432224i
$250$	10.4607	+	3.80737i	0.661591	+	0.240799i
$251$	3.00566	+	5.20596i	0.189716	+	0.328597i	0.945155	−	0.326621i	$-0.105910\pi$
$251$	3.00566	+	5.20596i	0.189716	+	0.328597i	−0.755440	+	0.655218i	$0.772577\pi$
$252$	1.03712	+	41.5917i	0.0653324	+	2.62003i
$253$	7.75277	−	13.4282i	0.487412	−	0.844223i
$254$	−25.0410	+	21.0119i	−1.57121	+	1.31840i
$255$	−1.05275	−	1.55752i	−0.0659259	−	0.0975356i
$256$	2.88108	−	16.3394i	0.180067	−	1.02121i
$257$	−2.55476	−	2.14370i	−0.159361	−	0.133720i	0.559620	−	0.828749i	$-0.310947\pi$
$257$	−2.55476	−	2.14370i	−0.159361	−	0.133720i	−0.718982	+	0.695029i	$0.755391\pi$
$258$	−36.5094	+	2.58846i	−2.27297	+	0.161150i
$259$	1.01123	+	4.27195i	0.0628350	+	0.265446i
$260$	13.7650	−	23.8417i	0.853671	−	1.47860i
$261$	13.3377	+	17.0036i	0.825584	+	1.05250i
$262$	37.1599			2.29575
$263$	−2.14434	−	12.1611i	−0.132225	−	0.749888i	−0.976752	−	0.214374i	$-0.931229\pi$
$263$	−2.14434	−	12.1611i	−0.132225	−	0.749888i	0.844526	−	0.535514i	$-0.179882\pi$
$264$	3.67403	−	35.2842i	0.226121	−	2.17159i
$265$	−4.18961	+	23.7604i	−0.257366	+	1.45959i
$266$	0.823362	−	7.02760i	0.0504836	−	0.430890i
$267$	15.9265	−	15.4099i	0.974688	−	0.943068i
$268$	1.94615	+	11.0372i	0.118880	+	0.674204i
$269$	−1.34615	+	2.33159i	−0.0820760	+	0.142160i	−0.904141	−	0.427233i	$-0.859488\pi$
$269$	−1.34615	+	2.33159i	−0.0820760	+	0.142160i	0.822066	+	0.569393i	$0.192822\pi$
$270$	12.5501	−	39.0097i	0.763772	−	2.37406i
$271$	11.0044	+	19.0602i	0.668469	+	1.15782i	0.978332	+	0.207041i	$0.0663833\pi$
$271$	11.0044	+	19.0602i	0.668469	+	1.15782i	−0.309864	+	0.950781i	$0.600283\pi$
$272$	−4.52153	−	1.64570i	−0.274158	−	0.0997853i
$273$	2.45225	+	7.83808i	0.148417	+	0.474382i
$274$	−23.7047	−	19.8906i	−1.43205	−	1.20164i
$275$	−7.91702	+	2.88156i	−0.477414	+	0.173765i
$276$	6.20970	−	59.6359i	0.373780	−	3.58966i
$277$	1.69737	+	9.62627i	0.101985	+	0.578387i	0.992382	+	0.123201i	$0.0393160\pi$
$277$	1.69737	+	9.62627i	0.101985	+	0.578387i	−0.890397	+	0.455186i	$0.849573\pi$
$278$	−13.1536	+	22.7828i	−0.788903	+	1.36642i
$279$	−10.8015	−	2.27411i	−0.646669	−	0.136147i
$280$	30.3730	−	60.4363i	1.81513	−	3.61176i
$281$	1.22691	+	6.95814i	0.0731912	+	0.415088i	0.999285	+	0.0377956i	$0.0120336\pi$
$281$	1.22691	+	6.95814i	0.0731912	+	0.415088i	−0.926094	+	0.377292i	$0.876855\pi$
$282$	−0.508798	+	1.04576i	−0.0302985	+	0.0622738i
$283$	−1.58826	+	9.00744i	−0.0944120	+	0.535437i	0.900514	+	0.434827i	$0.143190\pi$
$283$	−1.58826	+	9.00744i	−0.0944120	+	0.535437i	−0.994926	+	0.100610i	$0.967921\pi$
$284$	−1.35258	+	7.67088i	−0.0802611	+	0.455183i
$285$	−2.20697	+	4.53608i	−0.130730	+	0.268694i
$286$	−1.96624	−	11.1511i	−0.116266	−	0.659380i
$287$	−13.7652	−	20.9414i	−0.812532	−	1.23613i
$288$	−16.3338	−	49.9414i	−0.962477	−	2.94282i
$289$	8.43142	−	14.6036i	0.495966	−	0.859038i
$290$	−9.86491	−	55.9467i	−0.579288	−	3.28530i
$291$	−2.64015	+	25.3552i	−0.154768	+	1.48635i
$292$	49.1053	−	17.8729i	2.87367	−	1.04593i
$293$	−15.1908	−	12.7466i	−0.887455	−	0.744663i	0.0802432	−	0.996775i	$-0.474430\pi$
$293$	−15.1908	−	12.7466i	−0.887455	−	0.744663i	−0.967698	+	0.252112i	$0.918875\pi$
$294$	11.5279	+	30.5227i	0.672320	+	1.78012i
$295$	13.9979	+	5.09480i	0.814987	+	0.296631i
$296$	−7.23733	−	12.5354i	−0.420662	−	0.728607i
$297$	−4.60290	−	11.2981i	−0.267087	−	0.655583i
$298$	−2.50748	+	4.34309i	−0.145255	+	0.251588i
$299$	−2.05526	−	11.6559i	−0.118858	−	0.674080i
$300$	−23.4136	+	22.6540i	−1.35178	+	1.30793i
$301$	−19.0791	+	8.22371i	−1.09970	+	0.474007i
$302$	−7.70551	+	43.7001i	−0.443403	+	2.51466i
$303$	−1.53340	+	14.7263i	−0.0880914	+	0.846002i
$304$	2.24204	+	12.7153i	0.128590	+	0.729270i
$305$	2.53841			0.145349
$306$	−2.96005	+	0.421847i	−0.169215	+	0.0241154i
$307$	−12.8118	+	22.1907i	−0.731210	+	1.26649i	0.225157	+	0.974323i	$0.427711\pi$
$307$	−12.8118	+	22.1907i	−0.731210	+	1.26649i	−0.956366	+	0.292170i	$0.905623\pi$
$308$	−7.50026	−	31.6848i	−0.427367	−	1.80541i
$309$	−14.6811	+	1.04087i	−0.835179	+	0.0592129i
$310$	22.2286	+	18.6520i	1.26250	+	1.05936i
$311$	−5.62406	+	31.8956i	−0.318911	+	1.80863i	0.230489	+	0.973075i	$0.425968\pi$
$311$	−5.62406	+	31.8956i	−0.318911	+	1.80863i	−0.549400	+	0.835560i	$0.685144\pi$
$312$	−15.1640	−	22.4348i	−0.858494	−	1.27012i
$313$	−1.51083	+	1.26774i	−0.0853971	+	0.0716567i	−0.684487	−	0.729025i	$-0.739974\pi$
$313$	−1.51083	+	1.26774i	−0.0853971	+	0.0716567i	0.599090	+	0.800682i	$0.295529\pi$
$314$	−1.72060	+	2.98016i	−0.0970989	+	0.168180i
$315$	−0.579849	−	23.2537i	−0.0326708	−	1.31020i
$316$	−24.2170	−	41.9452i	−1.36232	−	2.35960i
$317$	2.19415	+	0.798604i	0.123236	+	0.0448541i	0.402902	−	0.915243i	$-0.368002\pi$
$317$	2.19415	+	0.798604i	0.123236	+	0.0448541i	−0.279666	+	0.960097i	$0.590224\pi$
$318$	31.0663	+	22.5251i	1.74211	+	1.26314i
$319$	−12.9559	−	10.8713i	−0.725393	−	0.608677i
$320$	−10.7627	+	61.0384i	−0.601655	+	3.41215i
$321$	−6.68509	−	26.7024i	−0.373125	−	1.49038i
$322$	−10.8311	−	45.7560i	−0.603594	−	2.54988i
$323$	0.368063			0.0204796
$324$	−34.0615	−	32.6392i	−1.89231	−	1.81329i
$325$	−3.21555	+	5.56949i	−0.178366	+	0.308940i
$326$	3.40050	−	2.85336i	0.188336	−	0.158033i
$327$	6.05263	−	5.85628i	0.334711	−	0.323853i
$328$	63.2972	+	53.1127i	3.49501	+	2.93266i
$329$	−0.0768170	+	0.655652i	−0.00423506	+	0.0361472i
$330$	−3.32145	+	31.8982i	−0.182840	+	1.75594i
$331$	5.76896	+	2.09973i	0.317091	+	0.115412i	0.495662	−	0.868515i	$-0.334925\pi$
$331$	5.76896	+	2.09973i	0.317091	+	0.115412i	−0.178571	+	0.983927i	$0.557148\pi$
$332$	35.1625			1.92979
$333$	−4.22651	−	2.62967i	−0.231611	−	0.144105i
$334$	−40.1872			−2.19895
$335$	−1.08809	−	6.17084i	−0.0594485	−	0.337149i
$336$	−36.1389	−	47.3139i	−1.97154	−	2.58118i
$337$	−18.6292	+	6.78048i	−1.01480	+	0.369356i	−0.795273	−	0.606251i	$-0.792673\pi$
$337$	−18.6292	+	6.78048i	−1.01480	+	0.369356i	−0.219524	+	0.975607i	$0.570450\pi$
$338$	20.1778	+	16.9312i	1.09753	+	0.920936i
$339$	6.92129	−	14.2256i	0.375913	−	0.772631i
$340$	5.34613	+	1.94583i	0.289934	+	0.105528i
$341$	8.63873			0.467814
$342$	4.95170	+	6.31269i	0.267757	+	0.341351i
$343$	11.8929	+	14.1971i	0.642157	+	0.766573i
$344$	52.4757	−	44.0324i	2.82930	−	2.37407i
$345$	−3.47181	+	33.3422i	−0.186916	+	1.79508i
$346$	15.8048	+	13.2618i	0.849673	+	0.712961i
$347$	19.1981	−	6.98752i	1.03061	−	0.375110i	0.229294	−	0.973357i	$-0.426358\pi$
$347$	19.1981	−	6.98752i	1.03061	−	0.375110i	0.801312	+	0.598247i	$0.204136\pi$
$348$	−62.8839	−	17.9659i	−3.37093	−	0.963073i
$349$	33.7947	+	12.3003i	1.80899	+	0.658418i	0.997226	+	0.0744315i	$0.0237142\pi$
$349$	33.7947	+	12.3003i	1.80899	+	0.658418i	0.811763	+	0.583987i	$0.198508\pi$
$350$	−11.4727	+	22.8284i	−0.613241	+	1.22023i
$351$	−8.23498	−	4.34802i	−0.439550	−	0.232080i
$352$	20.5611	+	35.6128i	1.09591	+	1.89817i
$353$	2.22254	−	1.86493i	0.118294	−	0.0992602i	−0.581722	−	0.813388i	$-0.697621\pi$
$353$	2.22254	−	1.86493i	0.118294	−	0.0992602i	0.700016	+	0.714128i	$0.253176\pi$
$354$	17.0266	−	16.4742i	0.904952	−	0.875595i
$355$	0.756223	−	4.28875i	0.0401361	−	0.227623i
$356$	−11.6459	+	66.0474i	−0.617233	+	3.50050i
$357$	−1.50717	+	0.780343i	−0.0797680	+	0.0413001i
$358$	−47.0501	+	39.4797i	−2.48668	+	2.08657i
$359$	5.64377	−	9.77530i	0.297867	−	0.515921i	−0.677781	−	0.735264i	$-0.737058\pi$
$359$	5.64377	−	9.77530i	0.297867	−	0.515921i	0.975648	+	0.219343i	$0.0703915\pi$
$360$	23.8413	+	72.8960i	1.25655	+	3.84195i
$361$	9.00618	+	15.5992i	0.474010	+	0.821009i
$362$	−25.1585	+	21.1105i	−1.32230	+	1.10954i
$363$	−5.32266	−	7.87474i	−0.279367	−	0.413316i
$364$	−19.9320	−	14.8473i	−1.04472	−	0.778212i
$365$	−27.4545	+	9.99264i	−1.43704	+	0.523039i
$366$	1.76630	−	3.63036i	0.0923260	−	0.189762i
$367$	−23.9923	−	8.73249i	−1.25239	−	0.455832i	−0.371181	−	0.928561i	$-0.621047\pi$
$367$	−23.9923	−	8.73249i	−1.25239	−	0.455832i	−0.881208	+	0.472729i	$0.843269\pi$
$368$	42.9005	+	74.3059i	2.23634	+	3.87346i
$369$	27.8062	+	5.85422i	1.44753	+	0.304758i
$370$	6.54280	+	11.3325i	0.340144	+	0.589147i
$371$	20.8651	+	6.25283i	1.08326	+	0.324631i
$372$	30.5040	−	13.6166i	1.58156	−	0.705987i
$373$	25.7924	−	9.38767i	1.33548	−	0.486075i	0.427094	−	0.904207i	$-0.359537\pi$
$373$	25.7924	−	9.38767i	1.33548	−	0.486075i	0.908386	+	0.418132i	$0.137315\pi$
$374$	2.19887	−	0.800323i	0.113701	−	0.0413837i
$375$	−5.14923	+	4.98219i	−0.265905	+	0.257279i
$376$	−0.377961	−	2.14352i	−0.0194919	−	0.110544i
$377$	−12.9099			−0.664895
$378$	−33.6603	−	15.3514i	−1.73130	−	0.789589i
$379$	12.8185			0.658443			0.329221	−	0.944253i	$-0.393214\pi$
$379$	12.8185			0.658443			0.329221	+	0.944253i	$0.393214\pi$
$380$	−2.65093	−	15.0342i	−0.135990	−	0.771236i
$381$	−5.10969	−	20.4097i	−0.261777	−	1.04562i
$382$	−18.3601	+	6.68252i	−0.939383	+	0.341907i
$383$	−17.8169	+	6.48482i	−0.910401	+	0.331359i	−0.754413	−	0.656400i	$-0.772078\pi$
$383$	−17.8169	+	6.48482i	−0.910401	+	0.331359i	−0.155988	+	0.987759i	$0.549856\pi$
$384$	30.6863	+	22.2496i	1.56595	+	1.13542i
$385$	4.19336	+	17.7148i	0.213713	+	0.902831i
$386$	−32.9731	−	57.1110i	−1.67829	−	2.90688i
$387$	8.78263	−	21.8594i	0.446446	−	1.11117i
$388$	−38.5735	−	66.8113i	−1.95827	−	3.39183i
$389$	18.5894	+	6.76599i	0.942520	+	0.343049i	0.767161	−	0.641455i	$-0.221669\pi$
$389$	18.5894	+	6.76599i	0.942520	+	0.343049i	0.175360	+	0.984504i	$0.443891\pi$
$390$	13.7088	+	20.2818i	0.694172	+	1.02701i
$391$	2.29841	−	0.836553i	0.116236	−	0.0423063i
$392$	−51.0004	−	33.5836i	−2.57591	−	1.69623i
$393$	−10.4639	+	21.5070i	−0.527836	+	1.08488i
$394$	0.600442	−	0.503830i	0.0302498	−	0.0253826i
$395$	13.5396	+	23.4513i	0.681253	+	1.17996i
$396$	31.3477	+	19.5041i	1.57528	+	0.980116i
$397$	3.21569	−	5.56973i	0.161391	−	0.279537i	−0.773977	−	0.633214i	$-0.781735\pi$
$397$	3.21569	−	5.56973i	0.161391	−	0.279537i	0.935368	+	0.353677i	$0.115069\pi$
$398$	−2.39881	+	2.01284i	−0.120241	+	0.100895i
$399$	3.83550	+	2.45545i	0.192015	+	0.122926i
$400$	8.09566	−	45.9128i	0.404783	−	2.29564i
$401$	−2.94198	+	16.6848i	−0.146916	+	0.833199i	0.818894	+	0.573945i	$0.194588\pi$
$401$	−2.94198	+	16.6848i	−0.146916	+	0.833199i	−0.965809	+	0.259254i	$0.916523\pi$
$402$	−9.58248	−	2.73771i	−0.477931	−	0.136544i
$403$	5.05141	−	4.23864i	0.251629	−	0.211142i
$404$	−22.4035	−	38.8040i	−1.11461	−	1.93057i
$405$	19.0436	+	18.2484i	0.946286	+	0.906771i
$406$	−51.2019	+	2.96808i	−2.54111	+	0.147303i
$407$	3.66076	+	1.33241i	0.181457	+	0.0660450i
$408$	4.02166	−	3.89119i	0.199102	−	0.192643i
$409$	−20.2490	+	7.37004i	−1.00125	+	0.364425i	−0.790066	−	0.613022i	$-0.789954\pi$
$409$	−20.2490	+	7.37004i	−1.00125	+	0.364425i	−0.211183	+	0.977447i	$0.567732\pi$
$410$	−57.2229	−	48.0157i	−2.82604	−	2.37133i
$411$	18.1871	−	8.11851i	0.897105	−	0.400456i
$412$	34.1203	−	28.6303i	1.68099	−	1.41051i
$413$	6.03888	−	12.0162i	0.297154	−	0.591278i
$414$	45.2692	+	28.1658i	2.22486	+	1.38427i
$415$	−19.6592			−0.965031
$416$	29.4965	+	10.7358i	1.44618	+	0.526368i
$417$	−9.48200	−	14.0284i	−0.464336	−	0.686972i
$418$	−4.80996	−	4.03604i	−0.235263	−	0.197409i
$419$	12.2407	−	4.45526i	0.597998	−	0.217654i	−0.0252454	−	0.999681i	$-0.508037\pi$
$419$	12.2407	−	4.45526i	0.597998	−	0.217654i	0.623244	+	0.782028i	$0.285814\pi$
$420$	42.7296	+	55.9426i	2.08499	+	2.72972i
$421$	−3.24633	−	18.4109i	−0.158216	−	0.897290i	−0.955786	−	0.294063i	$-0.904992\pi$
$421$	−3.24633	−	18.4109i	−0.158216	−	0.897290i	0.797569	−	0.603227i	$-0.206119\pi$
$422$	−7.70900			−0.375268
$423$	−0.461977	−	0.588953i	−0.0224621	−	0.0286359i
$424$	−71.8188			−3.48783
$425$	−1.24887	−	0.454551i	−0.0605791	−	0.0220490i
$426$	−5.60745	−	4.06577i	−0.271682	−	0.196987i
$427$	0.266671	−	2.27611i	0.0129051	−	0.110149i
$428$	63.8140	+	53.5463i	3.08457	+	2.58826i
$429$	7.00761	+	2.00207i	0.338330	+	0.0966608i
$430$	−47.4399	+	39.8068i	−2.28776	+	1.91965i
$431$	0.578897	−	1.00268i	0.0278845	−	0.0482974i	−0.851746	−	0.523954i	$-0.824456\pi$
$431$	0.578897	−	1.00268i	0.0278845	−	0.0482974i	0.879631	+	0.475657i	$0.157790\pi$
$432$	66.8783	+	9.20139i	3.21768	+	0.442702i
$433$	16.9175			0.813004			0.406502	−	0.913650i	$-0.366748\pi$
$433$	16.9175			0.813004			0.406502	+	0.913650i	$0.366748\pi$
$434$	19.0599	−	17.9722i	0.914903	−	0.862692i
$435$	35.1581	+	10.0446i	1.68570	+	0.481604i
$436$	−4.42586	+	25.1003i	−0.211960	+	1.20209i
$437$	−5.02771	−	4.21875i	−0.240508	−	0.201810i
$438$	−4.81252	+	46.2179i	−0.229951	+	2.20838i
$439$	−14.8184	−	5.39346i	−0.707244	−	0.257416i	−0.0367432	−	0.999325i	$-0.511698\pi$
$439$	−14.8184	−	5.39346i	−0.707244	−	0.257416i	−0.670500	+	0.741909i	$0.733921\pi$
$440$	−30.0116	−	51.9816i	−1.43075	−	2.47812i
$441$	−20.9118	−	1.92298i	−0.995799	−	0.0915705i
$442$	0.893084	−	1.54687i	0.0424797	−	0.0735770i
$443$	30.3711	−	25.4843i	1.44297	−	1.21080i	0.505458	−	0.862851i	$-0.331324\pi$
$443$	30.3711	−	25.4843i	1.44297	−	1.21080i	0.937514	−	0.347946i	$-0.113121\pi$
$444$	15.0266	−	1.06536i	0.713130	−	0.0505598i
$445$	6.51118	−	36.9268i	0.308660	−	1.75050i
$446$	3.14599	+	2.63980i	0.148967	+	0.124998i
$447$	−1.80756	−	2.67423i	−0.0854945	−	0.126487i
$448$	53.6005	+	16.0629i	2.53238	+	0.758903i
$449$	−17.1715	+	29.7420i	−0.810375	+	1.40361i	0.102226	+	0.994761i	$0.467403\pi$
$449$	−17.1715	+	29.7420i	−0.810375	+	1.40361i	−0.912602	+	0.408850i	$0.865930\pi$
$450$	−9.00548	−	27.5347i	−0.424522	−	1.29800i
$451$	−22.2386			−1.04718
$452$	8.31359	+	47.1487i	0.391038	+	2.21769i
$453$	−23.1225	−	16.7653i	−1.08639	−	0.787704i
$454$	8.07083	−	45.7720i	0.378783	−	2.14819i
$455$	11.1439	+	8.30107i	0.522434	+	0.389160i
$456$	−14.4382	−	4.12498i	−0.676131	−	0.193170i
$457$	−6.31205	−	35.7974i	−0.295265	−	1.67453i	−0.666122	−	0.745842i	$-0.732047\pi$
$457$	−6.31205	−	35.7974i	−0.295265	−	1.67453i	0.370857	−	0.928690i	$-0.379064\pi$
$458$	−12.1144	+	20.9827i	−0.566067	+	0.980457i
$459$	0.589376	−	1.83198i	0.0275097	−	0.0855093i
$460$	−50.7244	−	87.8572i	−2.36504	−	4.09636i
$461$	23.0683	+	8.39618i	1.07440	+	0.391049i	0.817820	−	0.575474i	$-0.195183\pi$
$461$	23.0683	+	8.39618i	1.07440	+	0.391049i	0.256578	+	0.966523i	$0.417405\pi$
$462$	28.2531	+	6.32929i	1.31445	+	0.294465i
$463$	7.47936	+	6.27593i	0.347595	+	0.291667i	0.799824	−	0.600235i	$-0.204926\pi$
$463$	7.47936	+	6.27593i	0.347595	+	0.291667i	−0.452228	+	0.891902i	$0.649371\pi$
$464$	87.9440	−	32.0090i	4.08270	−	1.48598i
$465$	−17.0546	+	7.61297i	−0.790889	+	0.353043i
$466$	−1.82843	−	10.3695i	−0.0847004	−	0.480360i
$467$	−13.6607	+	23.6610i	−0.632140	+	1.09490i	0.354973	+	0.934876i	$0.384490\pi$
$467$	−13.6607	+	23.6610i	−0.632140	+	1.09490i	−0.987113	+	0.160022i	$0.948843\pi$
$468$	27.9000	−	3.97613i	1.28968	−	0.183797i
$469$	−5.64750	+	0.327375i	−0.260777	+	0.0151168i
$470$	0.341690	+	1.93782i	0.0157610	+	0.0893850i
$471$	−1.24032	−	1.83502i	−0.0571509	−	0.0845532i
$472$	−7.69983	+	43.6679i	−0.354413	+	2.00998i
$473$	−3.20149	+	18.1565i	−0.147205	+	0.834838i
$474$	42.9607	−	3.04585i	1.97325	−	0.139900i
$475$	0.619263	+	3.51202i	0.0284138	+	0.161142i
$476$	2.30640	−	4.58928i	0.105714	−	0.210349i
$477$	−21.7848	+	11.6373i	−0.997459	+	0.532835i
$478$	16.3706	−	28.3548i	0.748775	−	1.29692i
$479$	1.47080	+	8.34133i	0.0672027	+	0.381125i	0.999796	+	0.0201965i	$0.00642917\pi$
$479$	1.47080	+	8.34133i	0.0672027	+	0.381125i	−0.932593	+	0.360929i	$0.882460\pi$
$480$	−71.9759	−	52.1873i	−3.28524	−	2.38201i
$481$	2.79435	−	1.01706i	0.127411	−	0.0463739i
$482$	−56.9470	−	47.7842i	−2.59386	−	2.17651i
$483$	29.5321	+	6.61581i	1.34376	+	0.301030i
$484$	27.0298	+	9.83803i	1.22863	+	0.447183i
$485$	21.5663	+	37.3539i	0.979273	+	1.69615i
$486$	39.3495	−	14.5379i	1.78493	−	0.659450i
$487$	0.130959	−	0.226827i	0.00593430	−	0.0102785i	−0.863043	−	0.505130i	$-0.831444\pi$
$487$	0.130959	−	0.226827i	0.00593430	−	0.0102785i	0.868977	+	0.494852i	$0.164778\pi$
$488$	1.31210	+	7.44128i	0.0593959	+	0.336851i
$489$	0.693882	+	2.77159i	0.0313784	+	0.125336i
$490$	46.1062	+	30.3607i	2.08286	+	1.37156i
$491$	0.966808	−	5.48304i	0.0436314	−	0.247446i	−0.955189	−	0.295995i	$-0.904349\pi$
$491$	0.966808	−	5.48304i	0.0436314	−	0.247446i	0.998821	+	0.0485493i	$0.0154598\pi$
$492$	−78.5261	+	35.0531i	−3.54023	+	1.58031i
$493$	−0.463276	−	2.62737i	−0.0208649	−	0.118331i
$494$	−4.79288			−0.215642
$495$	−17.5264	−	10.9046i	−0.787752	−	0.490126i
$496$	−23.9015	+	41.3987i	−1.07321	+	1.85886i
$497$	−3.76614	−	1.12863i	−0.168934	−	0.0506261i
$498$	−13.6795	+	28.1160i	−0.612991	+	1.25991i
$499$	25.5742	+	21.4593i	1.14486	+	0.960649i	0.999587	−	0.0287425i	$-0.00915027\pi$
$499$	25.5742	+	21.4593i	1.14486	+	0.960649i	0.145271	+	0.989392i	$0.453595\pi$
$500$	3.76527	−	21.3539i	0.168388	−	0.954975i
$501$	11.3164	−	23.2591i	0.505580	−	1.03914i
$502$	12.3921	−	10.3982i	0.553086	−	0.464094i
$503$	0.241460	−	0.418221i	0.0107662	−	0.0186475i	−0.860592	−	0.509295i	$-0.829906\pi$
$503$	0.241460	−	0.418221i	0.0107662	−	0.0186475i	0.871358	+	0.490647i	$0.163240\pi$
$504$	67.8680	−	13.7196i	3.02308	−	0.611121i
$505$	12.5257	+	21.6951i	0.557385	+	0.965419i
$506$	−39.2096	−	14.2711i	−1.74308	−	0.634429i
$507$	−15.4812	+	6.91061i	−0.687543	+	0.306911i
$508$	48.7757	+	40.9277i	2.16407	+	1.81587i
$509$	−4.08937	+	23.1920i	−0.181258	+	1.02797i	0.749412	+	0.662104i	$0.230336\pi$
$509$	−4.08937	+	23.1920i	−0.181258	+	1.02797i	−0.930670	+	0.365861i	$0.880775\pi$
$510$	−3.63572	+	3.51778i	−0.160992	+	0.155770i
$511$	6.07584	+	25.6674i	0.268779	+	1.13546i
$512$	−0.880867			−0.0389292
$513$	−5.04795	+	1.08829i	−0.222872	+	0.0480491i
$514$	−4.48731	+	7.77225i	−0.197927	+	0.342819i
$515$	−19.0765	+	16.0071i	−0.840611	+	0.705356i
$516$	17.3141	+	69.1582i	0.762212	+	3.04452i
$517$	0.448753	+	0.376549i	0.0197362	+	0.0165606i
$518$	10.8488	−	4.67619i	0.476669	−	0.205460i
$519$	−12.1261	+	5.41292i	−0.532275	+	0.237601i
$520$	−43.0540	−	15.6704i	−1.88804	−	0.687191i
$521$	−12.4066			−0.543544			−0.271772	−	0.962362i	$-0.587610\pi$
$521$	−12.4066			−0.543544			−0.271772	+	0.962362i	$0.587610\pi$
$522$	38.8296	−	43.2927i	1.69953	−	1.89487i
$523$	16.0858			0.703383			0.351692	−	0.936116i	$-0.385607\pi$
$523$	16.0858			0.703383			0.351692	+	0.936116i	$0.385607\pi$
$524$	−12.5689	−	71.2817i	−0.549074	−	3.11395i
$525$	−9.98174	−	13.0683i	−0.435639	−	0.570349i
$526$	−31.2269	+	11.3657i	−1.36156	+	0.495566i
$527$	1.04390	+	0.875937i	0.0454730	+	0.0381564i
$528$	−52.7007	+	3.73640i	−2.29350	+	0.162606i
$529$	−19.3717	−	7.05071i	−0.842247	−	0.306553i
$530$	64.9267			2.82023
$531$	4.74022	+	14.4935i	0.205708	+	0.628963i
$532$	−13.7591	+	0.797592i	−0.596534	+	0.0345800i
$533$	−13.0038	+	10.9115i	−0.563258	+	0.472629i
$534$	−48.2809	−	35.0069i	−2.08932	−	1.51489i
$535$	−35.6781	−	29.9375i	−1.54250	−	1.29431i
$536$	17.5272	−	6.37939i	0.757061	−	0.275548i
$537$	−9.60070	−	38.3483i	−0.414301	−	1.65485i
$538$	6.80814	+	2.47796i	0.293520	+	0.106832i
$539$	16.3248	−	1.89902i	0.703160	−	0.0817967i
$540$	−79.0750	−	10.8795i	−3.40284	−	0.468177i
$541$	−13.1928	−	22.8506i	−0.567204	−	0.982425i	−0.996841	−	0.0794239i	$-0.974692\pi$
$541$	−13.1928	−	22.8506i	−0.567204	−	0.982425i	0.429637	−	0.903002i	$-0.358641\pi$
$542$	45.3701	−	38.0700i	1.94881	−	1.63525i
$543$	−5.13367	−	20.5055i	−0.220307	−	0.879977i
$544$	−1.12642	+	6.38826i	−0.0482950	+	0.273894i
$545$	2.47447	−	14.0334i	0.105995	−	0.601127i
$546$	19.6262	−	10.1615i	0.839924	−	0.434874i
$547$	28.9358	−	24.2800i	1.23721	−	1.03814i	0.239469	−	0.970904i	$-0.423027\pi$
$547$	28.9358	−	24.2800i	1.23721	−	1.03814i	0.997737	−	0.0672347i	$-0.0214176\pi$
$548$	−30.1371	+	52.1991i	−1.28740	+	2.22983i
$549$	1.60376	+	2.04456i	0.0684469	+	0.0872597i
$550$	11.3362	+	19.6348i	0.483376	+	0.837231i
$551$	−5.48400	+	4.60163i	−0.233626	+	0.196036i
$552$	−99.5363	+	7.05697i	−4.23655	+	0.300365i
$553$	22.4504	−	9.67687i	0.954690	−	0.411502i
$554$	24.7180	−	8.99660i	1.05017	−	0.382229i
$555$	−8.40128	+	0.595638i	−0.356615	+	0.0252834i
$556$	48.1519	+	17.5259i	2.04210	+	0.743262i
$557$	−5.24806	−	9.08990i	−0.222367	−	0.385151i	0.733159	−	0.680057i	$-0.238045\pi$
$557$	−5.24806	−	9.08990i	−0.222367	−	0.385151i	−0.955526	+	0.294906i	$0.904712\pi$
$558$	−0.979264	+	29.6884i	−0.0414556	+	1.25681i
$559$	7.03656	+	12.1877i	0.297615	+	0.515484i
$560$	−96.4954	−	28.9177i	−4.07768	−	1.22199i
$561$	−0.155982	+	1.49800i	−0.00658557	+	0.0632457i
$562$	17.8668	−	6.50299i	0.753667	−	0.274312i
$563$	4.98131	−	1.81305i	0.209937	−	0.0764108i	−0.234911	−	0.972017i	$-0.575480\pi$
$563$	4.98131	−	1.81305i	0.209937	−	0.0764108i	0.444848	+	0.895606i	$0.353258\pi$
$564$	2.17810	+	0.622283i	0.0917148	+	0.0262028i
$565$	−4.64809	−	26.3606i	−0.195547	−	1.10900i
$566$	24.6133			1.03457
$567$	18.3634	−	15.1587i	0.771189	−	0.636606i
$568$	12.9633			0.543927
$569$	−1.65775	−	9.40156i	−0.0694965	−	0.394134i	−0.999637	−	0.0269311i	$-0.991427\pi$
$569$	−1.65775	−	9.40156i	−0.0694965	−	0.394134i	0.930141	−	0.367203i	$-0.119685\pi$
$570$	13.0526	+	3.72913i	0.546715	+	0.156196i
$571$	26.6672	−	9.70606i	1.11599	−	0.406186i	0.282801	−	0.959179i	$-0.408737\pi$
$571$	26.6672	−	9.70606i	1.11599	−	0.406186i	0.833186	+	0.552993i	$0.186514\pi$
$572$	−20.7255	+	7.54346i	−0.866576	+	0.315408i
$573$	1.30242	−	12.5080i	0.0544092	−	0.522528i
$574$	−49.0657	+	46.2656i	−2.04796	+	1.93109i
$575$	11.8493	+	20.5237i	0.494152	+	0.855896i
$576$	−55.9633	+	29.8952i	−2.33180	+	1.24563i
$577$	−14.9454	−	25.8862i	−0.622186	−	1.07766i	−0.989078	−	0.147394i	$-0.952912\pi$
$577$	−14.9454	−	25.8862i	−0.622186	−	1.07766i	0.366892	−	0.930263i	$-0.380422\pi$
$578$	−42.6419	−	15.5204i	−1.77367	−	0.645563i
$579$	42.3391	−	3.00177i	1.75955	−	0.124749i
$580$	−103.983	+	37.8465i	−4.31764	+	1.57149i
$581$	−2.06529	+	17.6277i	−0.0856825	+	0.731322i
$582$	68.4289	−	4.85150i	2.83647	−	0.201101i
$583$	14.8071	−	12.4246i	0.613246	−	0.514574i
$584$	−43.4844	−	75.3171i	−1.79940	−	3.11665i
$585$	−15.5988	+	2.22303i	−0.644930	+	0.0919111i
$586$	−26.6819	+	46.2143i	−1.10222	+	1.90910i
$587$	23.2180	−	19.4822i	0.958308	−	0.804116i	−0.0223688	−	0.999750i	$-0.507121\pi$
$587$	23.2180	−	19.4822i	0.958308	−	0.804116i	0.980677	+	0.195634i	$0.0626764\pi$
$588$	54.6508	−	32.4372i	2.25376	−	1.33769i
$589$	0.634965	−	3.60106i	0.0261633	−	0.148379i
$590$	6.96091	−	39.4773i	0.286576	−	1.62525i
$591$	0.122522	+	0.489392i	0.00503987	+	0.0201309i
$592$	−16.5137	+	13.8567i	−0.678711	+	0.569506i
$593$	−6.88951	−	11.9330i	−0.282918	−	0.490029i	0.689184	−	0.724586i	$-0.257969\pi$
$593$	−6.88951	−	11.9330i	−0.282918	−	0.490029i	−0.972102	+	0.234558i	$0.924636\pi$
$594$	−27.7909	+	17.4779i	−1.14027	+	0.717129i
$595$	−1.28950	+	2.56584i	−0.0528642	+	0.105189i
$596$	9.17921	+	3.34096i	0.375995	+	0.136851i
$597$	−0.489484	−	1.95516i	−0.0200332	−	0.0800192i
$598$	−29.9296	+	10.8935i	−1.22391	+	0.445468i
$599$	5.52167	+	4.63323i	0.225609	+	0.189309i	0.748585	−	0.663039i	$-0.230734\pi$
$599$	5.52167	+	4.63323i	0.225609	+	0.189309i	−0.522975	+	0.852348i	$0.675178\pi$
$600$	43.8957	+	31.8273i	1.79204	+	1.29934i
$601$	−34.2145	+	28.7093i	−1.39564	+	1.17108i	−0.432640	+	0.901567i	$0.642418\pi$
$601$	−34.2145	+	28.7093i	−1.39564	+	1.17108i	−0.962997	+	0.269512i	$0.913138\pi$
$602$	30.7097	+	46.7197i	1.25163	+	1.90415i
$603$	4.28285	−	4.77513i	0.174411	−	0.194458i
$604$	86.4337			3.51694
$605$	−15.1122	−	5.50039i	−0.614399	−	0.223623i
$606$	39.7435	−	2.81775i	1.61447	−	0.114463i
$607$	−10.1602	−	8.52543i	−0.412390	−	0.346037i	0.412869	−	0.910790i	$-0.364527\pi$
$607$	−10.1602	−	8.52543i	−0.412390	−	0.346037i	−0.825259	+	0.564754i	$0.808971\pi$
$608$	16.3565	−	5.95329i	0.663344	−	0.241438i
$609$	12.7002	−	30.4699i	0.514639	−	1.23470i
$610$	−1.18618	−	6.72718i	−0.0480271	−	0.272375i
$611$	0.447160			0.0180901
$612$	1.81041	+	5.53541i	0.0731813	+	0.223756i
$613$	−19.4812			−0.786839			−0.393420	−	0.919359i	$-0.628708\pi$
$613$	−19.4812			−0.786839			−0.393420	+	0.919359i	$0.628708\pi$
$614$	64.7958	+	23.5838i	2.61495	+	0.951763i
$615$	43.9035	−	19.5980i	1.77036	−	0.790268i
$616$	−49.7630	+	21.4495i	−2.00501	+	0.864224i
$617$	−26.8526	−	22.5320i	−1.08105	−	0.907105i	−0.0850385	−	0.996378i	$-0.527101\pi$
$617$	−26.8526	−	22.5320i	−1.08105	−	0.907105i	−0.996007	+	0.0892726i	$0.971546\pi$
$618$	9.61886	+	38.4209i	0.386927	+	1.54551i
$619$	33.0617	−	27.7420i	1.32886	−	1.11505i	0.344519	−	0.938779i	$-0.388042\pi$
$619$	33.0617	−	27.7420i	1.32886	−	1.11505i	0.984342	−	0.176267i	$-0.0564024\pi$
$620$	28.2605	−	48.9486i	1.13497	−	1.96582i
$621$	−29.0489	+	18.2692i	−1.16569	+	0.733116i
$622$	87.1565			3.49466
$623$	−32.4270	−	9.71769i	−1.29916	−	0.389331i
$624$	−28.9829	+	28.0427i	−1.16025	+	1.12261i
$625$	−5.22078	+	29.6085i	−0.208831	+	1.18434i
$626$	4.06570	+	3.41153i	0.162498	+	0.136352i
$627$	3.69038	−	1.64734i	0.147380	−	0.0657885i
$628$	6.29864	+	2.29252i	0.251343	+	0.0914814i
$629$	0.307263	+	0.532196i	0.0122514	+	0.0212200i
$630$	−61.3551	+	12.4030i	−2.44444	+	0.494148i
$631$	−20.3466	+	35.2413i	−0.809984	+	1.40293i	0.102890	+	0.994693i	$0.467191\pi$
$631$	−20.3466	+	35.2413i	−0.809984	+	1.40293i	−0.912874	+	0.408241i	$0.866142\pi$
$632$	−61.7484	+	51.8131i	−2.45622	+	2.06101i
$633$	2.17079	−	4.46173i	0.0862813	−	0.177338i
$634$	1.09111	−	6.18802i	0.0433337	−	0.245758i
$635$	−27.2702	−	22.8825i	−1.08219	−	0.908063i
$636$	32.7008	−	67.2114i	1.29667	−	2.66510i
$637$	8.61401	−	9.12029i	0.341300	−	0.361359i
$638$	−22.7565	+	39.4154i	−0.900937	+	1.56047i
$639$	3.93216	−	2.10053i	0.155554	−	0.0830956i
$640$	64.1325			2.53506
$641$	5.24855	+	29.7660i	0.207305	+	1.17569i	0.893771	+	0.448524i	$0.148050\pi$
$641$	5.24855	+	29.7660i	0.207305	+	1.17569i	−0.686466	+	0.727162i	$0.740839\pi$
$642$	−67.6417	+	30.1944i	−2.66960	+	1.19168i
$643$	−2.81411	+	15.9596i	−0.110978	+	0.629387i	0.877685	+	0.479237i	$0.159087\pi$
$643$	−2.81411	+	15.9596i	−0.110978	+	0.629387i	−0.988663	+	0.150150i	$0.952024\pi$
$644$	−84.1075	+	36.2531i	−3.31430	+	1.42857i
$645$	−9.68024	−	38.6660i	−0.381159	−	1.52247i
$646$	−0.171994	−	0.975426i	−0.00676701	−	0.0383776i
$647$	3.51357	−	6.08568i	0.138133	−	0.239253i	−0.788657	−	0.614833i	$-0.789223\pi$
$647$	3.51357	−	6.08568i	0.138133	−	0.239253i	0.926790	+	0.375581i	$0.122557\pi$
$648$	−43.6512	+	65.2585i	−1.71478	+	2.56360i
$649$	−5.96702	−	10.3352i	−0.234226	−	0.405692i
$650$	16.2626	+	5.91911i	0.637873	+	0.232167i
$651$	5.03463	+	16.0921i	0.197323	+	0.630699i
$652$	−6.62361	−	5.55787i	−0.259401	−	0.217663i
$653$	−14.4000	+	5.24117i	−0.563515	+	0.205103i	−0.608041	−	0.793905i	$-0.708044\pi$
$653$	−14.4000	+	5.24117i	−0.563515	+	0.205103i	0.0445260	+	0.999008i	$0.485822\pi$
$654$	−18.3484	−	13.3038i	−0.717480	−	0.520220i
$655$	7.02720	+	39.8532i	0.274575	+	1.55719i
$656$	61.5296	−	106.572i	2.40233	−	4.16095i
$657$	−25.3943	−	15.7999i	−0.990726	−	0.616414i
$658$	1.77348	−	0.102805i	0.0691373	−	0.00400777i
$659$	−0.359040	−	2.03622i	−0.0139862	−	0.0793198i	0.977016	−	0.213167i	$-0.0683779\pi$
$659$	−0.359040	−	2.03622i	−0.0139862	−	0.0793198i	−0.991002	+	0.133847i	$0.957267\pi$
$660$	62.3118	−	4.41781i	2.42548	−	0.171963i
$661$	0.870163	−	4.93494i	0.0338454	−	0.191947i	−0.963197	−	0.268795i	$-0.913375\pi$
$661$	0.870163	−	4.93494i	0.0338454	−	0.191947i	0.997043	+	0.0768482i	$0.0244857\pi$
$662$	2.86881	−	16.2698i	0.111500	−	0.632346i
$663$	0.643793	+	0.952475i	0.0250029	+	0.0369911i
$664$	−10.1618	−	57.6304i	−0.394354	−	2.23649i
$665$	7.69266	−	0.445930i	0.298308	−	0.0172924i
$666$	−4.99400	+	12.4297i	−0.193514	+	0.481643i
$667$	−23.7866	+	41.1997i	−0.921022	+	1.59526i
$668$	13.5928	+	77.0887i	0.525922	+	2.98265i
$669$	−2.41372	+	1.07746i	−0.0933199	+	0.0416568i
$670$	−15.8452	+	5.76719i	−0.612155	+	0.222806i
$671$	−1.55786	−	1.30720i	−0.0601403	−	0.0504637i
$672$	−54.3560	+	59.0559i	−2.09683	+	2.27813i
$673$	−31.9524	−	11.6297i	−1.23168	−	0.448293i	−0.357504	−	0.933911i	$-0.616372\pi$
$673$	−31.9524	−	11.6297i	−1.23168	−	0.448293i	−0.874171	+	0.485618i	$0.838595\pi$
$674$	26.6746	+	46.2018i	1.02747	+	1.77963i
$675$	18.4721	+	2.54147i	0.710992	+	0.0978212i
$676$	25.6532	−	44.4327i	0.986663	−	1.70895i
$677$	5.99400	+	33.9936i	0.230368	+	1.30648i	0.852153	+	0.523293i	$0.175297\pi$
$677$	5.99400	+	33.9936i	0.230368	+	1.30648i	−0.621785	+	0.783188i	$0.713592\pi$
$678$	−40.9345	−	11.6950i	−1.57208	−	0.449142i
$679$	35.7596	−	15.4136i	1.37233	−	0.591518i
$680$	1.64416	−	9.32450i	0.0630507	−	0.357578i
$681$	24.2187	+	17.5602i	0.928063	+	0.672907i
$682$	−4.03683	−	22.8940i	−0.154578	−	0.876657i
$683$	40.3067			1.54229			0.771147	−	0.636657i	$-0.219683\pi$
$683$	40.3067			1.54229			0.771147	+	0.636657i	$0.219683\pi$
$684$	10.4344	−	11.6337i	0.398969	−	0.444827i
$685$	16.8495	−	29.1842i	0.643787	−	1.11507i
$686$	32.0671	−	38.1523i	1.22433	−	1.45666i
$687$	−8.73283	−	12.9200i	−0.333178	−	0.492928i
$688$	−78.1522	−	65.5775i	−2.97953	−	2.50012i
$689$	2.56209	−	14.5303i	0.0976078	−	0.553561i
$690$	89.9843	−	6.37975i	3.42564	−	0.242873i
$691$	−0.421451	+	0.353639i	−0.0160327	+	0.0134531i	−0.650769	−	0.759276i	$-0.725553\pi$
$691$	−0.421451	+	0.353639i	−0.0160327	+	0.0134531i	0.634736	+	0.772729i	$0.281109\pi$
$692$	20.0936	−	34.8031i	0.763844	−	1.32302i
$693$	−11.6190	+	14.5697i	−0.441371	+	0.553459i
$694$	−27.4892	−	47.6126i	−1.04347	−	1.80735i
$695$	−26.9215	−	9.79862i	−1.02119	−	0.371683i
$696$	−11.2725	+	108.257i	−0.427282	+	4.10348i
$697$	−2.68730	−	2.25492i	−0.101789	−	0.0854110i
$698$	16.8056	−	95.3091i	0.636100	−	3.60750i
$699$	6.51644	+	1.86174i	0.246474	+	0.0704176i
$700$	47.6708	+	14.2860i	1.80179	+	0.539958i
$701$	27.6199			1.04319			0.521594	−	0.853194i	$-0.325338\pi$
$701$	27.6199			1.04319			0.521594	+	0.853194i	$0.325338\pi$
$702$	−7.67478	+	23.8558i	−0.289666	+	0.900378i
$703$	0.824489	−	1.42806i	0.0310962	−	0.0538602i
$704$	38.0380	−	31.9177i	1.43361	−	1.20294i
$705$	−1.21777	−	0.347915i	−0.0458638	−	0.0131033i
$706$	−5.98093	−	5.01860i	−0.225095	−	0.188877i
$707$	20.7692	−	8.95219i	0.781105	−	0.336682i
$708$	−37.3605	−	27.0889i	−1.40410	−	1.01806i
$709$	−30.1781	−	10.9839i	−1.13336	−	0.412511i	−0.293852	−	0.955851i	$-0.594937\pi$
$709$	−30.1781	−	10.9839i	−1.13336	−	0.412511i	−0.839513	+	0.543340i	$0.817159\pi$
$710$	−11.7192			−0.439816
$711$	−10.3346	+	25.7220i	−0.387576	+	0.964651i
$712$	111.615			4.18297
$713$	−4.21957	−	23.9304i	−0.158024	−	0.896200i
$714$	2.77232	+	3.62959i	0.103752	+	0.135834i
$715$	11.5875	−	4.21751i	0.433349	−	0.157726i
$716$	91.6457	+	76.8999i	3.42496	+	2.87388i
$717$	11.8010	+	17.4593i	0.440717	+	0.652029i
$718$	−28.5434	−	10.3889i	−1.06523	−	0.387712i
$719$	−15.6211			−0.582570			−0.291285	−	0.956636i	$-0.594083\pi$
$719$	−15.6211			−0.582570			−0.291285	+	0.956636i	$0.594083\pi$
$720$	100.749	−	53.8194i	3.75470	−	2.00573i
$721$	12.3489	+	18.7869i	0.459899	+	0.699660i
$722$	37.1317	−	31.1572i	1.38190	−	1.15955i
$723$	43.6918	−	19.5035i	1.62492	−	0.725343i
$724$	49.0046	+	41.1197i	1.82124	+	1.52820i
$725$	24.2906	−	8.84105i	0.902130	−	0.328348i
$726$	−18.3820	+	17.7857i	−0.682221	+	0.660089i
$727$	−11.7457	−	4.27508i	−0.435623	−	0.158554i	0.114894	−	0.993378i	$-0.463347\pi$
$727$	−11.7457	−	4.27508i	−0.435623	−	0.158554i	−0.550517	+	0.834824i	$0.685569\pi$
$728$	−18.5741	+	36.9589i	−0.688403	+	1.36979i
$729$	−2.66645	+	26.8680i	−0.0987573	+	0.995112i
$730$	39.3114	+	68.0893i	1.45498	+	2.52010i
$731$	−2.22787	+	1.86941i	−0.0824009	+	0.0691426i
$732$	−7.56133	−	2.16027i	−0.279475	−	0.0798457i
$733$	−6.38353	+	36.2028i	−0.235781	+	1.33718i	0.605182	+	0.796087i	$0.293100\pi$
$733$	−6.38353	+	36.2028i	−0.235781	+	1.33718i	−0.840963	+	0.541093i	$0.818011\pi$
$734$	−11.9310	+	67.6640i	−0.440381	+	2.49753i
$735$	−30.5550	+	18.1355i	−1.12704	+	0.668937i
$736$	88.6091	−	74.3518i	3.26617	−	2.74064i
$737$	−2.51001	+	4.34746i	−0.0924572	+	0.160141i
$738$	2.52091	−	76.4265i	0.0927961	−	2.81330i
$739$	−15.6210	−	27.0564i	−0.574628	−	0.995286i	−0.996082	−	0.0884356i	$-0.971813\pi$
$739$	−15.6210	−	27.0564i	−0.574628	−	0.995286i	0.421454	−	0.906850i	$-0.361520\pi$
$740$	19.5254	−	16.3837i	0.717767	−	0.602278i
$741$	1.34964	−	2.77397i	0.0495802	−	0.101904i
$742$	6.82085	−	58.2176i	0.250401	−	2.13724i
$743$	−9.31561	+	3.39060i	−0.341757	+	0.124389i	−0.507196	−	0.861831i	$-0.669318\pi$
$743$	−9.31561	+	3.39060i	−0.341757	+	0.124389i	0.165439	+	0.986220i	$0.447096\pi$
$744$	−31.1327	−	46.0600i	−1.14138	−	1.68864i
$745$	−5.13205	−	1.86791i	−0.188024	−	0.0684351i
$746$	−36.9314	−	63.9671i	−1.35216	−	2.34200i
$747$	−12.4206	−	15.8345i	−0.454447	−	0.579353i
$748$	−2.27895	−	3.94726i	−0.0833268	−	0.144326i
$749$	−30.5921	+	28.8463i	−1.11781	+	1.05402i
$750$	15.6098	+	11.3181i	0.569989	+	0.413280i
$751$	−9.33186	+	3.39652i	−0.340524	+	0.123941i	−0.506621	−	0.862169i	$-0.669106\pi$
$751$	−9.33186	+	3.39652i	−0.340524	+	0.123941i	0.166097	+	0.986109i	$0.446884\pi$
$752$	−3.04611	+	1.10869i	−0.111080	+	0.0404299i
$753$	2.52864	+	10.1002i	0.0921487	+	0.368072i
$754$	6.03273	+	34.2133i	0.219699	+	1.24598i
$755$	−48.3247			−1.75871
$756$	−18.0624	+	69.7610i	−0.656925	+	2.53718i
$757$	−27.0978			−0.984888			−0.492444	−	0.870344i	$-0.663896\pi$
$757$	−27.0978			−0.984888			−0.492444	+	0.870344i	$0.663896\pi$
$758$	−5.99001	−	33.9711i	−0.217567	−	1.23388i
$759$	19.3008	−	18.6747i	0.700575	−	0.677848i
$760$	−23.8745	+	8.68960i	−0.866018	+	0.315205i
$761$	37.5494	−	13.6669i	1.36117	−	0.495424i	0.444751	−	0.895654i	$-0.353292\pi$
$761$	37.5494	−	13.6669i	1.36117	−	0.495424i	0.916415	+	0.400230i	$0.131070\pi$
$762$	−51.7013	+	23.0788i	−1.87294	+	0.836058i
$763$	−12.3234	−	3.69306i	−0.446136	−	0.133698i
$764$	19.0287	+	32.9587i	0.688436	+	1.19241i
$765$	−1.01219	−	3.09482i	−0.0365958	−	0.111893i
$766$	25.5115	+	44.1873i	0.921769	+	1.59655i
$767$	−8.56017	−	3.11565i	−0.309090	−	0.112499i
$768$	12.5726	−	25.8410i	0.453675	−	0.932458i
$769$	0.304754	−	0.110921i	0.0109897	−	0.00399993i	−0.336519	−	0.941677i	$-0.609250\pi$
$769$	0.304754	−	0.110921i	0.0109897	−	0.00399993i	0.347509	+	0.937677i	$0.387028\pi$
$770$	44.9875	−	19.3911i	1.62124	−	0.698806i
$771$	−3.23474	−	4.78572i	−0.116496	−	0.172353i
$772$	−98.4000	+	82.5674i	−3.54149	+	2.97167i
$773$	−2.50904	−	4.34578i	−0.0902439	−	0.156307i	0.817370	−	0.576113i	$-0.195431\pi$
$773$	−2.50904	−	4.34578i	−0.0902439	−	0.156307i	−0.907614	+	0.419806i	$0.862098\pi$
$774$	−62.0348	−	13.0606i	−2.22980	−	0.469453i
$775$	−6.60173	+	11.4345i	−0.237141	+	0.410740i
$776$	−98.3543	+	82.5291i	−3.53072	+	2.96262i
$777$	−0.348504	+	7.59573i	−0.0125025	+	0.272495i
$778$	9.24421	−	52.4265i	0.331421	−	1.87958i
$779$	−1.63458	+	9.27019i	−0.0585650	+	0.332139i
$780$	34.2686	−	33.1569i	1.22701	−	1.18721i
$781$	−2.67267	+	2.24264i	−0.0956357	+	0.0802479i
$782$	−3.29103	−	5.70023i	−0.117687	−	0.203840i
$783$	14.1224	+	34.6643i	0.504693	+	1.23880i
$784$	−36.0668	+	83.4863i	−1.28810	+	2.98165i
$785$	−3.52154	−	1.28173i	−0.125689	−	0.0457471i
$786$	61.8867	+	17.6810i	2.20742	+	0.630660i
$787$	1.94701	−	0.708653i	0.0694033	−	0.0252607i	−0.307085	−	0.951682i	$-0.599354\pi$
$787$	1.94701	−	0.708653i	0.0694033	−	0.0252607i	0.376489	+	0.926421i	$0.377131\pi$
$788$	−1.16956	−	0.981377i	−0.0416638	−	0.0349601i
$789$	2.21515	−	21.2736i	0.0788616	−	0.757361i
$790$	55.8227	−	46.8408i	1.98608	−	1.66652i
$791$	−24.1250	+	1.39848i	−0.857786	+	0.0497243i
$792$	22.9073	−	57.0147i	0.813975	−	2.02593i
$793$	−1.55232			−0.0551246
$794$	−16.2633	−	5.91937i	−0.577164	−	0.210071i
$795$	−18.2828	+	37.5775i	−0.648426	+	1.33274i
$796$	4.67248	+	3.92068i	0.165612	+	0.138965i
$797$	−40.0366	+	14.5721i	−1.41817	+	0.516172i	−0.933516	−	0.358535i	$-0.883276\pi$
$797$	−40.0366	+	14.5721i	−1.41817	+	0.516172i	−0.484653	+	0.874706i	$0.661054\pi$
$798$	4.71503	−	11.3121i	0.166910	−	0.400444i
$799$	0.0160465	+	0.0910040i	0.000567683	+	0.00321949i
$800$	−62.8512			−2.22213
$801$	33.8564	−	18.0858i	1.19626	−	0.639032i
$802$	45.5921			1.60991
$803$	21.9951	+	8.00556i	0.776190	+	0.282510i
$804$	−2.01043	+	19.3075i	−0.0709023	+	0.680923i
$805$	47.0241	−	20.2689i	1.65738	−	0.714385i
$806$	−13.5936	−	11.4063i	−0.478812	−	0.401771i
$807$	−3.35128	+	3.24256i	−0.117971	+	0.114144i
$808$	−57.1242	+	47.9329i	−2.00962	+	1.68627i
$809$	−17.2737	+	29.9189i	−0.607310	+	1.05189i	0.384371	+	0.923179i	$0.374418\pi$
$809$	−17.2737	+	29.9189i	−0.607310	+	1.05189i	−0.991682	+	0.128714i	$0.958915\pi$
$810$	39.4622	−	58.9960i	1.38656	−	2.07291i
$811$	−48.7022			−1.71017			−0.855083	−	0.518491i	$-0.826494\pi$
$811$	−48.7022			−1.71017			−0.855083	+	0.518491i	$0.826494\pi$
$812$	23.0119	+	97.2137i	0.807560	+	3.41153i
$813$	9.25789	+	36.9790i	0.324689	+	1.29691i
$814$	1.82044	−	10.3242i	0.0638063	−	0.361864i
$815$	3.70323	+	3.10738i	0.129718	+	0.108847i
$816$	−6.74718	−	4.89216i	−0.236199	−	0.171260i
$817$	7.33325	+	2.66908i	0.256558	+	0.0933795i
$818$	28.9940	+	50.2191i	1.01375	+	1.75587i
$819$	0.354597	+	14.2205i	0.0123906	+	0.496903i
$820$	−72.7508	+	126.008i	−2.54057	+	4.40039i
$821$	−1.86144	+	1.56193i	−0.0649647	+	0.0545118i	−0.674692	−	0.738100i	$-0.735723\pi$
$821$	−1.86144	+	1.56193i	−0.0649647	+	0.0545118i	0.609727	+	0.792611i	$0.291279\pi$
$822$	−30.0141	−	44.4050i	−1.04686	−	1.54880i
$823$	−2.47662	+	14.0456i	−0.0863297	+	0.489600i	0.910732	+	0.412998i	$0.135518\pi$
$823$	−2.47662	+	14.0456i	−0.0863297	+	0.489600i	−0.997062	+	0.0766022i	$0.975593\pi$
$824$	−56.7850	−	47.6482i	−1.97820	−	1.65990i
$825$	−14.5562	+	1.03201i	−0.506782	+	0.0359301i
$826$	−34.6667	−	10.3889i	−1.20621	−	0.361476i
$827$	−20.4016	+	35.3366i	−0.709433	+	1.22877i	0.255634	+	0.966774i	$0.417716\pi$
$827$	−20.4016	+	35.3366i	−0.709433	+	1.22877i	−0.965068	+	0.262001i	$0.915618\pi$
$828$	38.7170	−	96.3640i	1.34551	−	3.34888i
$829$	51.3055			1.78191			0.890957	−	0.454088i	$-0.150035\pi$
$829$	51.3055			1.78191			0.890957	+	0.454088i	$0.150035\pi$
$830$	9.18662	+	52.0999i	0.318872	+	1.80841i
$831$	−1.75343	+	16.8394i	−0.0608257	+	0.584151i
$832$	6.58177	−	37.3271i	0.228182	−	1.29408i
$833$	2.16524	+	1.42580i	0.0750211	+	0.0494011i
$834$	−32.7465	+	31.6842i	−1.13392	+	1.09713i
$835$	−7.59968	−	43.0999i	−0.262998	−	1.49153i
$836$	−6.11518	+	10.5918i	−0.211498	+	0.366325i
$837$	−16.9069	−	8.92677i	−0.584390	−	0.308554i
$838$	−17.5271	−	30.3579i	−0.605465	−	1.04870i
$839$	52.5210	+	19.1161i	1.81323	+	0.659960i	0.996562	+	0.0828447i	$0.0264005\pi$
$839$	52.5210	+	19.1161i	1.81323	+	0.659960i	0.816663	+	0.577115i	$0.195822\pi$
$840$	79.3397	−	86.1998i	2.73748	−	2.97418i
$841$	17.5354	+	14.7140i	0.604670	+	0.507378i
$842$	−47.2747	+	17.2066i	−1.62919	+	0.592978i
$843$	−1.26743	+	12.1720i	−0.0436525	+	0.419225i
$844$	2.60747	+	14.7877i	0.0897529	+	0.509014i
$845$	−14.3426	+	24.8421i	−0.493400	+	0.854594i
$846$	−1.34494	+	1.49953i	−0.0462399	+	0.0515548i
$847$	−6.51963	+	12.9728i	−0.224017	+	0.445750i
$848$	18.5734	+	105.335i	0.637813	+	3.61722i
$849$	−6.93092	+	14.2454i	−0.237868	+	0.488902i
$850$	−0.621043	+	3.52211i	−0.0213016	+	0.120807i
$851$	1.90285	−	10.7916i	0.0652288	−	0.369931i
$852$	−5.90248	+	12.1316i	−0.202216	+	0.415623i
$853$	−7.21789	−	40.9347i	−0.247136	−	1.40158i	−0.815479	−	0.578786i	$-0.803527\pi$
$853$	−7.21789	−	40.9347i	−0.247136	−	1.40158i	0.568344	−	0.822791i	$-0.307584\pi$
$854$	−6.15665	+	0.356890i	−0.210676	+	0.0122125i
$855$	−5.83382	+	6.50437i	−0.199513	+	0.222445i
$856$	69.3191	−	120.064i	2.36928	−	4.10371i
$857$	1.06702	+	6.05135i	0.0364486	+	0.206710i	0.997593	−	0.0693342i	$-0.0220875\pi$
$857$	1.06702	+	6.05135i	0.0364486	+	0.206710i	−0.961145	+	0.276044i	$0.910976\pi$
$858$	2.03118	−	19.5068i	0.0693434	−	0.665952i
$859$	37.2854	−	13.5708i	1.27216	−	0.463029i	0.384329	−	0.923196i	$-0.374433\pi$
$859$	37.2854	−	13.5708i	1.27216	−	0.463029i	0.887832	+	0.460168i	$0.152211\pi$
$860$	92.4050	+	77.5370i	3.15098	+	2.64399i
$861$	−12.9606	−	41.4257i	−0.441697	−	1.41178i
$862$	−2.92777	−	1.06562i	−0.0997203	−	0.0362952i
$863$	−22.1063	−	38.2892i	−0.752506	−	1.30338i	−0.946605	−	0.322396i	$-0.895512\pi$
$863$	−22.1063	−	38.2892i	−0.752506	−	1.30338i	0.194099	−	0.980982i	$-0.437822\pi$
$864$	−3.44001	−	90.9448i	−0.117031	−	3.09401i
$865$	−11.2342	+	19.4583i	−0.381975	+	0.661601i
$866$	−7.90546	−	44.8341i	−0.268639	−	1.52352i
$867$	20.9903	−	20.3094i	0.712869	−	0.689743i
$868$	−40.9217	−	30.4825i	−1.38897	−	1.03464i
$869$	3.76720	−	21.3649i	0.127794	−	0.724753i
$870$	10.1907	−	97.8683i	0.345497	−	3.31804i
$871$	0.665401	+	3.77368i	0.0225463	+	0.127866i
$872$	42.4178			1.43645
$873$	−16.4611	+	40.9706i	−0.557125	+	1.38665i
$874$	−8.83092	+	15.2956i	−0.298710	+	0.517381i
$875$	10.4840	+	3.14184i	0.354425	+	0.106214i
$876$	90.2848	−	6.40105i	3.05044	−	0.216272i
$877$	21.6178	+	18.1395i	0.729983	+	0.612528i	0.930127	−	0.367238i	$-0.119697\pi$
$877$	21.6178	+	18.1395i	0.729983	+	0.612528i	−0.200144	+	0.979766i	$0.564141\pi$
$878$	−7.36895	+	41.7914i	−0.248690	+	1.41039i
$879$	−19.2340	−	28.4562i	−0.648748	−	0.959805i
$880$	−68.4787	+	57.4605i	−2.30842	+	1.93699i
$881$	22.6545	−	39.2387i	0.763249	−	1.32199i	−0.177918	−	0.984045i	$-0.556936\pi$
$881$	22.6545	−	39.2387i	0.763249	−	1.32199i	0.941167	−	0.337941i	$-0.109730\pi$
$882$	4.67575	+	56.3181i	0.157441	+	1.89633i
$883$	0.386625	+	0.669653i	0.0130110	+	0.0225356i	0.872458	−	0.488690i	$-0.162525\pi$
$883$	0.386625	+	0.669653i	0.0130110	+	0.0225356i	−0.859447	+	0.511225i	$0.829192\pi$
$884$	−3.26934	−	1.18994i	−0.109960	−	0.0400221i
$885$	20.8881	+	15.1453i	0.702146	+	0.509102i
$886$	−81.7297	−	68.5794i	−2.74576	−	2.30397i
$887$	−6.70778	+	38.0417i	−0.225225	+	1.27732i	0.637029	+	0.770840i	$0.280163\pi$
$887$	−6.70778	+	38.0417i	−0.225225	+	1.27732i	−0.862254	+	0.506476i	$0.830948\pi$
$888$	−6.08871	−	24.3203i	−0.204324	−	0.816135i
$889$	−23.3828	+	22.0484i	−0.784234	+	0.739480i
$890$	−100.904			−3.38232
$891$	−2.29001	−	21.0061i	−0.0767181	−	0.703732i
$892$	3.99968	−	6.92765i	0.133919	−	0.231955i
$893$	0.189949	−	0.159386i	0.00635640	−	0.00533365i
$894$	−6.24248	+	6.03996i	−0.208780	+	0.202007i
$895$	−51.2387	−	42.9944i	−1.71272	−	1.43714i
$896$	6.73742	−	57.5055i	0.225081	−	1.92112i
$897$	2.12313	−	20.3899i	0.0708893	−	0.680798i
$898$	86.8451	+	31.6090i	2.89806	+	1.05481i
$899$	−26.5049			−0.883988
$900$	−49.7722	+	26.5880i	−1.65907	+	0.886265i
$901$	3.04909			0.101580
$902$	10.3920	+	58.9358i	0.346015	+	1.96235i
$903$	−35.6875	+	4.61791i	−1.18761	+	0.153674i
$904$	74.8729	−	27.2515i	2.49024	−	0.906372i
$905$	−27.3982	−	22.9898i	−0.910748	−	0.764208i
$906$	−33.6258	+	69.1125i	−1.11714	+	2.29611i
$907$	16.5824	+	6.03548i	0.550608	+	0.200405i	0.602317	−	0.798257i	$-0.294244\pi$
$907$	16.5824	+	6.03548i	0.550608	+	0.200405i	−0.0517085	+	0.998662i	$0.516467\pi$
$908$	−90.5315			−3.00439
$909$	−9.56062	+	23.7957i	−0.317106	+	0.789255i
$910$	16.7917	−	33.4121i	0.556638	−	1.10760i
$911$	31.9509	−	26.8100i	1.05858	−	0.888254i	0.0646099	−	0.997911i	$-0.479420\pi$
$911$	31.9509	−	26.8100i	1.05858	−	0.888254i	0.993969	+	0.109657i	$0.0349753\pi$
$912$	−2.31609	+	22.2430i	−0.0766933	+	0.736538i
$913$	12.0651	+	10.1238i	0.399297	+	0.335050i
$914$	−91.9192	+	33.4558i	−3.04042	+	1.10662i
$915$	4.22750	+	1.20779i	0.139757	+	0.0399285i
$916$	44.3474	+	16.1411i	1.46528	+	0.533318i
$917$	36.4733	−	2.11429i	1.20445	−	0.0698201i
$918$	−5.13044	−	0.705867i	−0.169330	−	0.0232971i
$919$	3.81069	+	6.60032i	0.125703	+	0.217724i	0.922008	−	0.387172i	$-0.126548\pi$
$919$	3.81069	+	6.60032i	0.125703	+	0.217724i	−0.796304	+	0.604896i	$0.793215\pi$
$920$	−129.336	+	108.526i	−4.26410	+	3.57800i
$921$	−31.8955	+	30.8608i	−1.05099	+	1.01690i
$922$	11.4715	−	65.0581i	0.377794	−	2.14257i
$923$	−0.462456	+	2.62272i	−0.0152219	+	0.0863278i
$924$	2.58483	−	56.3370i	0.0850348	−	1.85335i
$925$	−4.56118	+	3.82728i	−0.149971	+	0.125840i
$926$	13.1371	−	22.7542i	0.431713	−	0.747749i
$927$	−24.9454	−	5.25191i	−0.819314	−	0.172495i
$928$	−63.0844	−	109.265i	−2.07085	−	3.58681i
$929$	15.6723	−	13.1507i	0.514193	−	0.431459i	−0.348409	−	0.937343i	$-0.613278\pi$
$929$	15.6723	−	13.1507i	0.514193	−	0.431459i	0.862602	+	0.505884i	$0.168834\pi$
$930$	28.1451	+	41.6399i	0.922914	+	1.36543i
$931$	0.408299	−	6.94460i	0.0133814	−	0.227600i
$932$	−19.2728	+	7.01474i	−0.631303	+	0.229775i
$933$	−24.5426	+	50.4435i	−0.803488	+	1.65144i
$934$	69.0888	+	25.1463i	2.26066	+	0.822811i
$935$	1.27415	+	2.20689i	0.0416692	+	0.0721732i
$936$	−14.5798	−	44.5784i	−0.476554	−	1.45709i
$937$	−6.66331	−	11.5412i	−0.217681	−	0.377034i	0.736418	−	0.676527i	$-0.236516\pi$
$937$	−6.66331	−	11.5412i	−0.217681	−	0.377034i	−0.954098	+	0.299493i	$0.903182\pi$
$938$	3.50664	+	14.8138i	0.114496	+	0.483687i
$939$	−3.11935	+	1.39244i	−0.101796	+	0.0454406i
$940$	3.60163	−	1.31089i	0.117472	−	0.0427564i
$941$	10.3944	−	3.78324i	0.338846	−	0.123330i	−0.166992	−	0.985958i	$-0.553405\pi$
$941$	10.3944	−	3.78324i	0.338846	−	0.123330i	0.505838	+	0.862628i	$0.331183\pi$
$942$	−4.28349	+	4.14453i	−0.139564	+	0.135036i
$943$	10.8624	+	61.6038i	0.353729	+	2.00610i
$944$	66.0380			2.14935
$945$	10.0986	−	39.0030i	0.328508	−	1.26877i
$946$	49.6137			1.61308
$947$	−5.46656	−	31.0024i	−0.177639	−	1.00744i	−0.935053	−	0.354508i	$-0.884648\pi$
$947$	−5.46656	−	31.0024i	−0.177639	−	1.00744i	0.757414	−	0.652935i	$-0.226463\pi$
$948$	−20.3736	−	81.3788i	−0.661704	−	2.64306i
$949$	16.7894	−	6.11084i	0.545007	−	0.198366i
$950$	9.01802	−	3.28229i	0.292583	−	0.106492i
$951$	3.27418	+	2.37400i	0.106173	+	0.0769822i
$952$	−8.18824	−	2.45385i	−0.265382	−	0.0795296i
$953$	−5.46062	−	9.45807i	−0.176887	−	0.306377i	0.763926	−	0.645304i	$-0.223269\pi$
$953$	−5.46062	−	9.45807i	−0.176887	−	0.306377i	−0.940813	+	0.338927i	$0.889936\pi$
$954$	41.0206	+	52.2952i	1.32809	+	1.69312i
$955$	−10.6389	−	18.4271i	−0.344266	−	0.596286i
$956$	−59.9284	−	21.8122i	−1.93822	−	0.705456i
$957$	−16.4043	−	24.2698i	−0.530277	−	0.784531i
$958$	21.4185	−	7.79571i	0.692002	−	0.251868i
$959$	−24.3984	−	18.1744i	−0.787866	−	0.586881i
$960$	−46.9670	+	96.5334i	−1.51585	+	3.11560i
$961$	−13.3765	+	11.2242i	−0.431500	+	0.362071i
$962$	−4.00115	−	6.93019i	−0.129002	−	0.223438i
$963$	1.57177	−	47.6514i	0.0506496	−	1.53554i
$964$	−72.4000	+	125.400i	−2.33185	+	4.03888i
$965$	55.0149	−	46.1630i	1.77099	−	1.48604i
$966$	3.73275	−	81.3562i	0.120099	−	2.61759i
$967$	2.20487	−	12.5044i	0.0709038	−	0.402115i	−0.928614	−	0.371048i	$-0.878998\pi$
$967$	2.20487	−	12.5044i	0.0709038	−	0.402115i	0.999517	−	0.0310670i	$-0.00989051\pi$
$968$	8.31280	−	47.1442i	0.267183	−	1.51527i
$969$	0.612978	+	0.175128i	0.0196917	+	0.00562591i
$970$	88.9158	−	74.6092i	2.85491	−	2.39556i
$971$	11.5558	+	20.0153i	0.370844	+	0.642320i	0.989696	−	0.143188i	$-0.0457352\pi$
$971$	11.5558	+	20.0153i	0.370844	+	0.642320i	−0.618852	+	0.785508i	$0.712402\pi$
$972$	−41.1966	−	70.5645i	−1.32138	−	2.26336i
$973$	−11.6143	+	23.1102i	−0.372338	+	0.740880i
$974$	−0.662323	−	0.241066i	−0.0212222	−	0.00772424i
$975$	−8.00523	+	7.74553i	−0.256372	+	0.248056i
$976$	10.5746	−	3.84885i	0.338485	−	0.123199i
$977$	23.1076	+	19.3895i	0.739276	+	0.620326i	0.932643	−	0.360800i	$-0.117496\pi$
$977$	23.1076	+	19.3895i	0.739276	+	0.620326i	−0.193367	+	0.981126i	$0.561941\pi$
$978$	7.02090	−	3.13404i	0.224504	−	0.100216i
$979$	−23.0121	+	19.3094i	−0.735469	+	0.617131i
$980$	42.6444	−	98.7118i	1.36222	−	3.15323i
$981$	12.8666	−	6.87324i	0.410799	−	0.219446i
$982$	−14.9827			−0.478117
$983$	10.0260	+	3.64917i	0.319780	+	0.116390i	0.496923	−	0.867795i	$-0.334463\pi$
$983$	10.0260	+	3.64917i	0.319780	+	0.116390i	−0.177143	+	0.984185i	$0.556685\pi$
$984$	80.1447	+	118.572i	2.55492	+	3.77994i
$985$	0.653895	+	0.548683i	0.0208348	+	0.0174825i
$986$	−6.74646	+	2.45551i	−0.214851	+	0.0781994i
$987$	−0.439896	+	1.05538i	−0.0140021	+	0.0335932i
$988$	1.62113	+	9.19390i	0.0515751	+	0.292497i
$989$	51.8597			1.64904
$990$	−20.7090	+	51.5433i	−0.658175	+	1.63815i
$991$	44.8873			1.42589			0.712946	−	0.701219i	$-0.247361\pi$
$991$	44.8873			1.42589			0.712946	+	0.701219i	$0.247361\pi$
$992$	60.5583	+	22.0414i	1.92273	+	0.699815i
$993$	8.60865	+	6.24184i	0.273187	+	0.198079i
$994$	−1.23116	+	10.5083i	−0.0390500	+	0.333302i
$995$	−2.61236	−	2.19203i	−0.0828174	−	0.0694920i
$996$	58.5601	+	16.7306i	1.85555	+	0.530129i
$997$	−20.8299	+	17.4783i	−0.659688	+	0.553544i	−0.909993	−	0.414623i	$-0.863914\pi$
$997$	−20.8299	+	17.4783i	−0.659688	+	0.553544i	0.250305	+	0.968167i	$0.419469\pi$
$998$	44.9198	−	77.8034i	1.42191	−	2.46282i
$999$	−5.78768	−	6.39049i	−0.183114	−	0.202186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.4.1	✓	132
3.2	odd	2		567.2.u.a.550.22		132
7.2	even	3		189.2.w.a.58.1	yes	132
21.2	odd	6		567.2.w.a.226.22		132
27.7	even	9		189.2.w.a.88.1	yes	132
27.20	odd	18		567.2.w.a.424.22		132
189.128	odd	18		567.2.u.a.100.22		132
189.142	even	9	inner	189.2.u.a.142.1	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.1	✓	132	1.1	even	1	trivial
189.2.u.a.142.1	yes	132	189.142	even	9	inner
189.2.w.a.58.1	yes	132	7.2	even	3
189.2.w.a.88.1	yes	132	27.7	even	9
567.2.u.a.100.22		132	189.128	odd	18
567.2.u.a.550.22		132	3.2	odd	2
567.2.w.a.226.22		132	21.2	odd	6
567.2.w.a.424.22		132	27.20	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.467294 - 2.65016i) q^{2} +(1.66541 + 0.475808i) q^{3} +(-4.92558 + 1.79277i) q^{4} +(2.75387 - 1.00233i) q^{5} +(0.482727 - 4.63595i) q^{6} +(-0.609446 - 2.57460i) q^{7} +(4.36176 + 7.55480i) q^{8} +(2.54721 + 1.58484i) q^{9} +O(q^{10})\)	\(q+(-0.467294 - 2.65016i) q^{2} +(1.66541 + 0.475808i) q^{3} +(-4.92558 + 1.79277i) q^{4} +(2.75387 - 1.00233i) q^{5} +(0.482727 - 4.63595i) q^{6} +(-0.609446 - 2.57460i) q^{7} +(4.36176 + 7.55480i) q^{8} +(2.54721 + 1.58484i) q^{9} +(-3.94319 - 6.82980i) q^{10} +(-2.20625 - 0.803010i) q^{11} +(-9.05615 + 0.642067i) q^{12} +(-1.68408 + 0.612957i) q^{13} +(-6.53831 + 2.81822i) q^{14} +(5.06325 - 0.358977i) q^{15} +(9.95243 - 8.35108i) q^{16} +(-0.185180 - 0.320741i) q^{17} +(3.00976 - 7.49110i) q^{18} +(-0.496899 + 0.860655i) q^{19} +(-11.7675 + 9.87408i) q^{20} +(0.210035 - 4.57776i) q^{21} +(-1.09713 + 6.22215i) q^{22} +(-1.14680 + 6.50383i) q^{23} +(3.66952 + 14.6572i) q^{24} +(2.74891 - 2.30661i) q^{25} +(2.41139 + 4.17666i) q^{26} +(3.48809 + 3.85139i) q^{27} +(7.61753 + 11.5888i) q^{28} +(6.76911 + 2.46375i) q^{29} +(-3.31737 - 13.2507i) q^{30} +(-3.45754 + 1.25844i) q^{31} +(-13.4172 - 11.2583i) q^{32} +(-3.29225 - 2.38710i) q^{33} +(-0.763481 + 0.640637i) q^{34} +(-4.25893 - 6.47925i) q^{35} +(-15.3877 - 3.23968i) q^{36} -1.65927 q^{37} +(2.51307 + 0.914682i) q^{38} +(-3.09635 + 0.219526i) q^{39} +(19.5841 + 16.4330i) q^{40} +(8.90071 - 3.23959i) q^{41} +(-12.2299 + 1.58253i) q^{42} +(-1.36359 - 7.73328i) q^{43} +12.3067 q^{44} +(8.60321 + 1.81129i) q^{45} +17.7721 q^{46} +(-0.234461 - 0.0853368i) q^{47} +(20.5484 - 9.17257i) q^{48} +(-6.25715 + 3.13816i) q^{49} +(-7.39743 - 6.20718i) q^{50} +(-0.155790 - 0.622278i) q^{51} +(7.19621 - 6.03834i) q^{52} +(-4.11638 + 7.12978i) q^{53} +(8.57683 - 11.0437i) q^{54} -6.88060 q^{55} +(16.7923 - 15.8341i) q^{56} +(-1.23705 + 1.19692i) q^{57} +(3.36617 - 19.0905i) q^{58} +(3.89379 + 3.26728i) q^{59} +(-24.2959 + 10.8454i) q^{60} +(0.813935 + 0.296248i) q^{61} +(4.95075 + 8.57495i) q^{62} +(2.52793 - 7.52393i) q^{63} +(-10.5746 + 18.3158i) q^{64} +(-4.02336 + 3.37600i) q^{65} +(-4.78773 + 9.84044i) q^{66} +(0.371283 - 2.10565i) q^{67} +(1.48713 + 1.24785i) q^{68} +(-5.00447 + 10.2859i) q^{69} +(-15.1809 + 14.3145i) q^{70} +(0.743006 - 1.28692i) q^{71} +(-0.862762 + 26.1564i) q^{72} -9.96945 q^{73} +(0.775366 + 4.39732i) q^{74} +(5.67558 - 2.53351i) q^{75} +(0.904566 - 5.13005i) q^{76} +(-0.722839 + 6.16961i) q^{77} +(2.02869 + 8.10323i) q^{78} +(1.60454 + 9.09978i) q^{79} +(19.0372 - 32.9734i) q^{80} +(3.97660 + 8.07383i) q^{81} +(-12.7447 - 22.0744i) q^{82} +(-6.30367 - 2.29435i) q^{83} +(7.17230 + 22.9247i) q^{84} +(-0.831449 - 0.697669i) q^{85} +(-19.8572 + 7.22743i) q^{86} +(10.1011 + 7.32396i) q^{87} +(-3.55657 - 20.1703i) q^{88} +(6.39738 - 11.0806i) q^{89} +(0.779968 - 23.6463i) q^{90} +(2.60448 + 3.96228i) q^{91} +(-6.01118 - 34.0911i) q^{92} +(-6.35701 + 0.450702i) q^{93} +(-0.116594 + 0.661236i) q^{94} +(-0.505738 + 2.86819i) q^{95} +(-16.9883 - 25.1338i) q^{96} +(2.55575 + 14.4944i) q^{97} +(11.2406 + 15.1160i) q^{98} +(-4.34716 - 5.54198i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more