LMFDB - Embedded newform 189.2.w.a.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(25,189)]

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([10, 12]))

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

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

chi := DirichletCharacter("189.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.w (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			25.3
Character	$\chi$	$=$	189.25
Dual form			189.2.w.a.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.11851 + 0.771075i) q^{2} +(1.70797 + 0.287798i) q^{3} +(2.36145 - 1.98149i) q^{4} +(-1.51793 - 0.552482i) q^{5} +(-3.84028 + 0.707271i) q^{6} +(2.02397 + 1.70398i) q^{7} +(-1.22040 + 2.11380i) q^{8} +(2.83434 + 0.983104i) q^{9} +O(q^{10})$	\(q+(-2.11851 + 0.771075i) q^{2} +(1.70797 + 0.287798i) q^{3} +(2.36145 - 1.98149i) q^{4} +(-1.51793 - 0.552482i) q^{5} +(-3.84028 + 0.707271i) q^{6} +(2.02397 + 1.70398i) q^{7} +(-1.22040 + 2.11380i) q^{8} +(2.83434 + 0.983104i) q^{9} +3.64176 q^{10} +(0.906628 - 0.329986i) q^{11} +(4.60356 - 2.70471i) q^{12} +(-0.0325017 - 0.184326i) q^{13} +(-5.60170 - 2.04928i) q^{14} +(-2.43358 - 1.38048i) q^{15} +(-0.115055 + 0.652508i) q^{16} +4.70815 q^{17} +(-6.76264 + 0.102775i) q^{18} +0.504342 q^{19} +(-4.67925 + 1.70311i) q^{20} +(2.96648 + 3.49285i) q^{21} +(-1.66626 + 1.39816i) q^{22} +(1.36276 + 7.72859i) q^{23} +(-2.69276 + 3.25908i) q^{24} +(-1.83134 - 1.53668i) q^{25} +(0.210985 + 0.365436i) q^{26} +(4.55805 + 2.49484i) q^{27} +(8.15591 + 0.0133961i) q^{28} +(-1.02634 + 5.82066i) q^{29} +(6.22003 + 1.04809i) q^{30} +(-2.85990 + 2.39974i) q^{31} +(-1.10707 - 6.27850i) q^{32} +(1.64347 - 0.302680i) q^{33} +(-9.97427 + 3.63034i) q^{34} +(-2.13082 - 3.70473i) q^{35} +(8.64116 - 3.29467i) q^{36} +(4.84361 - 8.38937i) q^{37} +(-1.06846 + 0.388886i) q^{38} +(-0.00246320 - 0.324178i) q^{39} +(3.02032 - 2.53435i) q^{40} +(-1.93086 - 10.9505i) q^{41} +(-8.97777 - 5.11227i) q^{42} +(-6.60401 - 5.54143i) q^{43} +(1.48709 - 2.57572i) q^{44} +(-3.75919 - 3.05821i) q^{45} +(-8.84634 - 15.3223i) q^{46} +(-1.15853 - 0.972120i) q^{47} +(-0.384301 + 1.08135i) q^{48} +(1.19289 + 6.89761i) q^{49} +(5.06461 + 1.84337i) q^{50} +(8.04140 + 1.35500i) q^{51} +(-0.441991 - 0.370875i) q^{52} +(1.38569 - 2.40009i) q^{53} +(-11.5800 - 1.77074i) q^{54} -1.55851 q^{55} +(-6.07193 + 2.19871i) q^{56} +(0.861403 + 0.145149i) q^{57} +(-2.31386 - 13.1225i) q^{58} +(-0.120799 - 0.685087i) q^{59} +(-8.48218 + 1.56218i) q^{60} +(-6.80963 - 5.71396i) q^{61} +(4.20835 - 7.28908i) q^{62} +(4.06143 + 6.81944i) q^{63} +(6.52397 + 11.2998i) q^{64} +(-0.0525016 + 0.297751i) q^{65} +(-3.24831 + 1.90847i) q^{66} +(2.99646 + 1.09062i) q^{67} +(11.1180 - 9.32915i) q^{68} +(0.103279 + 13.5924i) q^{69} +(7.37080 + 6.20550i) q^{70} +(-1.43937 - 2.49307i) q^{71} +(-5.53712 + 4.79145i) q^{72} +(0.0174169 + 0.0301670i) q^{73} +(-3.79240 + 21.5078i) q^{74} +(-2.68563 - 3.15166i) q^{75} +(1.19098 - 0.999349i) q^{76} +(2.39727 + 0.876998i) q^{77} +(0.255184 + 0.684876i) q^{78} +(-7.85664 + 2.85958i) q^{79} +(0.535144 - 0.926896i) q^{80} +(7.06701 + 5.57291i) q^{81} +(12.5342 + 21.7098i) q^{82} +(2.38942 - 13.5510i) q^{83} +(13.9262 + 2.37014i) q^{84} +(-7.14665 - 2.60117i) q^{85} +(18.2635 + 6.64738i) q^{86} +(-3.42814 + 9.64616i) q^{87} +(-0.408927 + 2.31914i) q^{88} -11.4122 q^{89} +(10.3220 + 3.58023i) q^{90} +(0.248306 - 0.428452i) q^{91} +(18.5322 + 15.5503i) q^{92} +(-5.57528 + 3.27562i) q^{93} +(3.20393 + 1.16614i) q^{94} +(-0.765557 - 0.278640i) q^{95} +(-0.0839014 - 11.0421i) q^{96} +(-7.73226 - 6.48814i) q^{97} +(-7.84572 - 13.6929i) q^{98} +(2.89411 - 0.0439831i) 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} + 3 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 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.11851	+	0.771075i	−1.49801	+	0.545233i	−0.955546	−	0.294844i	$-0.904732\pi$
$2$	−2.11851	+	0.771075i	−1.49801	+	0.545233i	−0.542468	+	0.840076i	$0.682510\pi$
$3$	1.70797	+	0.287798i	0.986099	+	0.166161i
$3$	1.70797	+	0.287798i	0.986099	+	0.166161i
$4$	2.36145	−	1.98149i	1.18072	−	0.990744i
$5$	−1.51793	−	0.552482i	−0.678840	−	0.247077i	−0.0204904	−	0.999790i	$-0.506523\pi$
$5$	−1.51793	−	0.552482i	−0.678840	−	0.247077i	−0.658349	+	0.752713i	$0.728745\pi$
$6$	−3.84028	+	0.707271i	−1.56779	+	0.288742i
$7$	2.02397	+	1.70398i	0.764988	+	0.644045i
$7$	2.02397	+	1.70398i	0.764988	+	0.644045i
$8$	−1.22040	+	2.11380i	−0.431477	+	0.747340i
$9$	2.83434	+	0.983104i	0.944781	+	0.327701i
$10$	3.64176			1.15163
$11$	0.906628	−	0.329986i	0.273359	−	0.0994944i	−0.201704	−	0.979447i	$-0.564648\pi$
$11$	0.906628	−	0.329986i	0.273359	−	0.0994944i	0.475062	+	0.879952i	$0.342426\pi$
$12$	4.60356	−	2.70471i	1.32893	−	0.780782i
$13$	−0.0325017	−	0.184326i	−0.00901434	−	0.0511229i	0.979969	−	0.199151i	$-0.0638185\pi$
$13$	−0.0325017	−	0.184326i	−0.00901434	−	0.0511229i	−0.988983	+	0.148028i	$0.952707\pi$
$14$	−5.60170	−	2.04928i	−1.49712	−	0.547692i
$15$	−2.43358	−	1.38048i	−0.628348	−	0.356439i
$16$	−0.115055	+	0.652508i	−0.0287637	+	0.163127i
$17$	4.70815			1.14189			0.570947	−	0.820987i	$-0.306576\pi$
$17$	4.70815			1.14189			0.570947	+	0.820987i	$0.306576\pi$
$18$	−6.76264	+	0.102775i	−1.59397	+	0.0242243i
$19$	0.504342			0.115704			0.0578520	−	0.998325i	$-0.481575\pi$
$19$	0.504342			0.115704			0.0578520	+	0.998325i	$0.481575\pi$
$20$	−4.67925	+	1.70311i	−1.04631	+	0.380826i
$21$	2.96648	+	3.49285i	0.647338	+	0.762203i
$22$	−1.66626	+	1.39816i	−0.355247	+	0.298088i
$23$	1.36276	+	7.72859i	0.284155	+	1.61152i	0.708289	+	0.705922i	$0.249467\pi$
$23$	1.36276	+	7.72859i	0.284155	+	1.61152i	−0.424135	+	0.905599i	$0.639422\pi$
$24$	−2.69276	+	3.25908i	−0.549657	+	0.665257i
$25$	−1.83134	−	1.53668i	−0.366268	−	0.307336i
$26$	0.210985	+	0.365436i	0.0413775	+	0.0716679i
$27$	4.55805	+	2.49484i	0.877197	+	0.480131i
$28$	8.15591	+	0.0133961i	1.54132	+	0.00253162i
$29$	−1.02634	+	5.82066i	−0.190587	+	1.08087i	0.727978	+	0.685600i	$0.240460\pi$
$29$	−1.02634	+	5.82066i	−0.190587	+	1.08087i	−0.918565	+	0.395270i	$0.870651\pi$
$30$	6.22003	+	1.04809i	1.13562	+	0.191355i
$31$	−2.85990	+	2.39974i	−0.513653	+	0.431006i	−0.862413	−	0.506206i	$-0.831048\pi$
$31$	−2.85990	+	2.39974i	−0.513653	+	0.431006i	0.348759	+	0.937212i	$0.386603\pi$
$32$	−1.10707	−	6.27850i	−0.195704	−	1.10989i
$33$	1.64347	−	0.302680i	0.286091	−	0.0526899i
$34$	−9.97427	+	3.63034i	−1.71057	+	0.622598i
$35$	−2.13082	−	3.70473i	−0.360175	−	0.626214i
$36$	8.64116	−	3.29467i	1.44019	−	0.549112i
$37$	4.84361	−	8.38937i	0.796284	−	1.37920i	−0.125737	−	0.992064i	$-0.540129\pi$
$37$	4.84361	−	8.38937i	0.796284	−	1.37920i	0.922021	−	0.387141i	$-0.126537\pi$
$38$	−1.06846	+	0.388886i	−0.173326	+	0.0630856i
$39$	−0.00246320	−	0.324178i	−0.000394428	−	0.0519100i
$40$	3.02032	−	2.53435i	0.477555	−	0.400716i
$41$	−1.93086	−	10.9505i	−0.301550	−	1.71017i	−0.639316	−	0.768944i	$-0.720783\pi$
$41$	−1.93086	−	10.9505i	−0.301550	−	1.71017i	0.337767	−	0.941230i	$-0.390329\pi$
$42$	−8.97777	−	5.11227i	−1.38530	−	0.788840i
$43$	−6.60401	−	5.54143i	−1.00710	−	0.845060i	−0.0191503	−	0.999817i	$-0.506096\pi$
$43$	−6.60401	−	5.54143i	−1.00710	−	0.845060i	−0.987953	+	0.154757i	$0.950541\pi$
$44$	1.48709	−	2.57572i	0.224187	−	0.388304i
$45$	−3.75919	−	3.05821i	−0.560387	−	0.455891i
$46$	−8.84634	−	15.3223i	−1.30432	−	2.25915i
$47$	−1.15853	−	0.972120i	−0.168989	−	0.141798i	0.554371	−	0.832269i	$-0.312959\pi$
$47$	−1.15853	−	0.972120i	−0.168989	−	0.141798i	−0.723360	+	0.690471i	$0.757403\pi$
$48$	−0.384301	+	1.08135i	−0.0554691	+	0.156080i
$49$	1.19289	+	6.89761i	0.170412	+	0.985373i
$50$	5.06461	+	1.84337i	0.716245	+	0.260692i
$51$	8.04140	+	1.35500i	1.12602	+	0.189738i
$52$	−0.441991	−	0.370875i	−0.0612932	−	0.0514311i
$53$	1.38569	−	2.40009i	0.190340	−	0.329678i	−0.755023	−	0.655698i	$-0.772374\pi$
$53$	1.38569	−	2.40009i	0.190340	−	0.329678i	0.945363	+	0.326020i	$0.105708\pi$
$54$	−11.5800	−	1.77074i	−1.57584	−	0.240967i
$55$	−1.55851			−0.210149
$56$	−6.07193	+	2.19871i	−0.811395	+	0.293815i
$57$	0.861403	+	0.145149i	0.114096	+	0.0192255i
$58$	−2.31386	−	13.1225i	−0.303824	−	1.72307i
$59$	−0.120799	−	0.685087i	−0.0157267	−	0.0891908i	0.975934	−	0.218065i	$-0.0699746\pi$
$59$	−0.120799	−	0.685087i	−0.0157267	−	0.0891908i	−0.991661	+	0.128875i	$0.958864\pi$
$60$	−8.48218	+	1.56218i	−1.09505	+	0.201677i
$61$	−6.80963	−	5.71396i	−0.871884	−	0.731598i	0.0926097	−	0.995702i	$-0.470479\pi$
$61$	−6.80963	−	5.71396i	−0.871884	−	0.731598i	−0.964494	+	0.264105i	$0.914924\pi$
$62$	4.20835	−	7.28908i	0.534461	−	0.925714i
$63$	4.06143	+	6.81944i	0.511692	+	0.859169i
$64$	6.52397	+	11.2998i	0.815496	+	1.41248i
$65$	−0.0525016	+	0.297751i	−0.00651202	+	0.0369315i
$66$	−3.24831	+	1.90847i	−0.399839	+	0.234916i
$67$	2.99646	+	1.09062i	0.366076	+	0.133241i	0.518507	−	0.855073i	$-0.326488\pi$
$67$	2.99646	+	1.09062i	0.366076	+	0.133241i	−0.152431	+	0.988314i	$0.548710\pi$
$68$	11.1180	−	9.32915i	1.34826	−	1.13133i
$69$	0.103279	+	13.5924i	0.0124334	+	1.63633i
$70$	7.37080	+	6.20550i	0.880980	+	0.741699i
$71$	−1.43937	−	2.49307i	−0.170822	−	0.295873i	0.767885	−	0.640587i	$-0.221309\pi$
$71$	−1.43937	−	2.49307i	−0.170822	−	0.295873i	−0.938708	+	0.344714i	$0.887976\pi$
$72$	−5.53712	+	4.79145i	−0.652556	+	0.564677i
$73$	0.0174169	+	0.0301670i	0.00203850	+	0.00353078i	0.867043	−	0.498234i	$-0.166018\pi$
$73$	0.0174169	+	0.0301670i	0.00203850	+	0.00353078i	−0.865004	+	0.501764i	$0.832684\pi$
$74$	−3.79240	+	21.5078i	−0.440858	+	2.50023i
$75$	−2.68563	−	3.15166i	−0.310110	−	0.363923i
$76$	1.19098	−	0.999349i	0.136614	−	0.114633i
$77$	2.39727	+	0.876998i	0.273195	+	0.0999432i
$78$	0.255184	+	0.684876i	0.0288939	+	0.0775469i
$79$	−7.85664	+	2.85958i	−0.883941	+	0.321728i	−0.743799	−	0.668403i	$-0.766978\pi$
$79$	−7.85664	+	2.85958i	−0.883941	+	0.321728i	−0.140142	+	0.990131i	$0.544756\pi$
$80$	0.535144	−	0.926896i	0.0598309	−	0.103630i
$81$	7.06701	+	5.57291i	0.785224	+	0.619212i
$82$	12.5342	+	21.7098i	1.38417	+	2.39745i
$83$	2.38942	−	13.5510i	0.262272	−	1.48742i	−0.514419	−	0.857539i	$-0.671992\pi$
$83$	2.38942	−	13.5510i	0.262272	−	1.48742i	0.776691	−	0.629882i	$-0.216897\pi$
$84$	13.9262	+	2.37014i	1.51948	+	0.258603i
$85$	−7.14665	−	2.60117i	−0.775163	−	0.282136i
$86$	18.2635	+	6.64738i	1.96941	+	0.716806i
$87$	−3.42814	+	9.64616i	−0.367535	+	1.03418i
$88$	−0.408927	+	2.31914i	−0.0435918	+	0.247221i
$89$	−11.4122			−1.20970			−0.604848	−	0.796341i	$-0.706766\pi$
$89$	−11.4122			−1.20970			−0.604848	+	0.796341i	$0.706766\pi$
$90$	10.3220	+	3.58023i	1.08803	+	0.377389i
$91$	0.248306	−	0.428452i	0.0260296	−	0.0449140i
$92$	18.5322	+	15.5503i	1.93211	+	1.62124i
$93$	−5.57528	+	3.27562i	−0.578129	+	0.339666i
$94$	3.20393	+	1.16614i	0.330460	+	0.120278i
$95$	−0.765557	−	0.278640i	−0.0785445	−	0.0285879i
$96$	−0.0839014	−	11.0421i	−0.00856315	−	1.12698i
$97$	−7.73226	−	6.48814i	−0.785092	−	0.658770i	0.159433	−	0.987209i	$-0.449033\pi$
$97$	−7.73226	−	6.48814i	−0.785092	−	0.658770i	−0.944525	+	0.328438i	$0.893478\pi$
$98$	−7.84572	−	13.6929i	−0.792537	−	1.38319i
$99$	2.89411	−	0.0439831i	0.290869	−	0.00442047i
$100$	−7.36953			−0.736953
$101$	−0.358407	+	2.03263i	−0.0356628	+	0.202254i	−0.997433	−	0.0716032i	$-0.977188\pi$
$101$	−0.358407	+	2.03263i	−0.0356628	+	0.202254i	0.961770	+	0.273857i	$0.0882996\pi$
$102$	−18.0806	+	3.32994i	−1.79025	+	0.329713i
$103$	16.6558	+	6.06221i	1.64114	+	0.597328i	0.987239	−	0.159248i	$-0.0509070\pi$
$103$	16.6558	+	6.06221i	1.64114	+	0.597328i	0.653906	+	0.756576i	$0.273129\pi$
$104$	0.429293	+	0.156250i	0.0420957	+	0.0153216i
$105$	−2.57317	−	6.94083i	−0.251116	−	0.677356i
$106$	−1.08496	+	6.15310i	−0.105380	+	0.597642i
$107$	−8.44399	−	14.6254i	−0.816311	−	1.41389i	−0.908383	−	0.418140i	$-0.862682\pi$
$107$	−8.44399	−	14.6254i	−0.816311	−	1.41389i	0.0920719	−	0.995752i	$-0.470651\pi$
$108$	15.7071	−	3.14030i	1.51141	−	0.302176i
$109$	−6.03251	+	10.4486i	−0.577810	+	1.00080i	0.417920	+	0.908484i	$0.362759\pi$
$109$	−6.03251	+	10.4486i	−0.577810	+	1.00080i	−0.995730	+	0.0923121i	$0.970574\pi$
$110$	3.30172	−	1.20173i	0.314807	−	0.114580i
$111$	10.6872	−	12.9348i	1.01438	−	1.22772i
$112$	−1.34473	+	1.12460i	−0.127065	+	0.106265i
$113$	−12.9494	+	10.8658i	−1.21818	+	1.02217i	−0.219258	+	0.975667i	$0.570364\pi$
$113$	−12.9494	+	10.8658i	−1.21818	+	1.02217i	−0.998918	+	0.0465043i	$0.985192\pi$
$114$	−1.93681	+	0.356707i	−0.181399	+	0.0334087i
$115$	2.20133	−	12.4844i	0.205275	−	1.16417i
$116$	9.10993	+	15.7789i	0.845836	+	1.46503i
$117$	0.0890909	−	0.554396i	0.00823646	−	0.0512540i
$118$	0.784169	+	1.35822i	0.0721886	+	0.125034i
$119$	9.52914	+	8.02261i	0.873535	+	0.735431i
$120$	5.88801	−	3.45936i	0.537499	−	0.315795i
$121$	−7.71341	+	6.47232i	−0.701219	+	0.588392i
$122$	18.8322	+	6.85435i	1.70499	+	0.620564i
$123$	−0.146334	−	19.2588i	−0.0131945	−	1.73651i
$124$	−1.99844	+	11.3337i	−0.179465	+	1.01780i
$125$	5.96924	+	10.3390i	0.533905	+	0.924750i
$126$	−13.8625	−	11.3154i	−1.23497	−	1.00806i
$127$	−3.25167	+	5.63206i	−0.288539	+	0.499765i	−0.973461	−	0.228852i	$-0.926503\pi$
$127$	−3.25167	+	5.63206i	−0.288539	+	0.499765i	0.684922	+	0.728616i	$0.259836\pi$
$128$	−12.7665	−	10.7124i	−1.12841	−	0.946849i
$129$	−9.68467	−	11.3652i	−0.852687	−	1.00065i
$130$	−0.118363	−	0.671272i	−0.0103812	−	0.0588744i
$131$	0.392080	+	2.22359i	0.0342562	+	0.194276i	0.997133	−	0.0756632i	$-0.0241074\pi$
$131$	0.392080	+	2.22359i	0.0342562	+	0.194276i	−0.962877	+	0.269940i	$0.912996\pi$
$132$	3.28120	−	3.97127i	0.285592	−	0.345655i
$133$	1.02077	+	0.859391i	0.0885122	+	0.0745186i
$134$	−7.18899			−0.621034
$135$	−5.54045	−	6.30523i	−0.476846	−	0.542668i
$136$	−5.74583	+	9.95208i	−0.492701	+	0.853383i
$137$	8.19370	+	6.87533i	0.700035	+	0.587399i	0.921784	−	0.387705i	$-0.126732\pi$
$137$	8.19370	+	6.87533i	0.700035	+	0.587399i	−0.221749	+	0.975104i	$0.571176\pi$
$138$	−10.6996	−	28.7161i	−0.910808	−	2.44447i
$139$	5.14608	+	1.87302i	0.436485	+	0.158868i	0.550911	−	0.834564i	$-0.314281\pi$
$139$	5.14608	+	1.87302i	0.436485	+	0.158868i	−0.114426	+	0.993432i	$0.536503\pi$
$140$	−12.3727	−	4.52633i	−1.04569	−	0.382545i
$141$	−1.69896	−	1.99378i	−0.143078	−	0.167906i
$142$	4.97168	+	4.17173i	0.417214	+	0.350084i
$143$	−0.0902919	−	0.156390i	−0.00755059	−	0.0130780i
$144$	−0.967588	+	1.73632i	−0.0806323	+	0.144693i
$145$	4.77372	−	8.26833i	0.396436	−	0.686648i
$146$	−0.0601590	−	0.0504794i	−0.00497880	−	0.00417771i
$147$	0.0522941	+	12.1242i	0.00431314	+	0.999991i
$148$	−5.18553	−	29.4086i	−0.426248	−	2.41737i
$149$	−8.99259	+	7.54568i	−0.736702	+	0.618166i	−0.931950	−	0.362588i	$-0.881893\pi$
$149$	−8.99259	+	7.54568i	−0.736702	+	0.618166i	0.195248	+	0.980754i	$0.437449\pi$
$150$	8.11971	+	4.60601i	0.662971	+	0.376079i
$151$	−0.205412	+	0.0747638i	−0.0167162	+	0.00608419i	−0.350365	−	0.936613i	$-0.613942\pi$
$151$	−0.205412	+	0.0747638i	−0.0167162	+	0.00608419i	0.333649	+	0.942698i	$0.391720\pi$
$152$	−0.615500	+	1.06608i	−0.0499237	+	0.0864703i
$153$	13.3445	+	4.62860i	1.07884	+	0.374200i
$154$	−5.75489	−	0.00945238i	−0.463742	−	0.000761695i
$155$	5.66695	−	2.06260i	0.455180	−	0.165672i
$156$	−0.648172	−	0.760648i	−0.0518953	−	0.0609006i
$157$	−3.76555	−	21.3555i	−0.300524	−	1.70435i	−0.643861	−	0.765142i	$-0.722669\pi$
$157$	−3.76555	−	21.3555i	−0.300524	−	1.70435i	0.343338	−	0.939212i	$-0.388442\pi$
$158$	14.4394	−	12.1161i	1.14874	−	0.963907i
$159$	3.05747	−	3.70049i	0.242473	−	0.293468i
$160$	−1.78830	+	10.1420i	−0.141378	+	0.801794i
$161$	−10.4112	+	17.9645i	−0.820517	+	1.41580i
$162$	−19.2687	−	6.35708i	−1.51389	−	0.499459i
$163$	4.59071	+	7.95135i	0.359572	+	0.622798i	0.987889	−	0.155160i	$-0.0495892\pi$
$163$	4.59071	+	7.95135i	0.359572	+	0.622798i	−0.628317	+	0.777957i	$0.716256\pi$
$164$	−26.2578	−	22.0329i	−2.05039	−	1.72048i
$165$	−2.66189	−	0.448537i	−0.207228	−	0.0349185i
$166$	5.38687	+	30.5505i	0.418102	+	2.37118i
$167$	6.56510	−	5.50878i	0.508023	−	0.426282i	−0.352410	−	0.935846i	$-0.614638\pi$
$167$	6.56510	−	5.50878i	0.508023	−	0.426282i	0.860433	+	0.509564i	$0.170193\pi$
$168$	−11.0035	+	2.00785i	−0.848936	+	0.154909i
$169$	12.1831	−	4.43428i	0.937160	−	0.341098i
$170$	17.1460			1.31504
$171$	1.42948	+	0.495821i	0.109315	+	0.0379164i
$172$	−26.5753			−2.02635
$173$	3.39752	−	19.2683i	0.258309	−	1.46494i	−0.529126	−	0.848543i	$-0.677480\pi$
$173$	3.39752	−	19.2683i	0.258309	−	1.46494i	0.787435	−	0.616398i	$-0.211409\pi$
$174$	−0.175360	−	23.0788i	−0.0132940	−	1.74960i
$175$	−1.08810	−	6.23076i	−0.0822528	−	0.471001i
$176$	0.111006	+	0.629548i	0.00836742	+	0.0474540i
$177$	−0.00915501	−	1.20488i	−0.000688133	−	0.0905641i
$178$	24.1770	−	8.79970i	1.81214	−	0.659565i
$179$	5.85235			0.437425			0.218713	−	0.975789i	$-0.429814\pi$
$179$	5.85235			0.437425			0.218713	+	0.975789i	$0.429814\pi$
$180$	−14.9369	+	0.227004i	−1.11333	+	0.0169199i
$181$	−0.331408	+	0.574015i	−0.0246334	+	0.0426662i	−0.878079	−	0.478515i	$-0.841175\pi$
$181$	−0.331408	+	0.574015i	−0.0246334	+	0.0426662i	0.853446	+	0.521181i	$0.174509\pi$
$182$	−0.195671	+	1.09914i	−0.0145041	+	0.0814740i
$183$	−9.98620	−	11.7191i	−0.738201	−	0.866300i
$184$	−17.9998	−	6.55138i	−1.32696	−	0.482974i
$185$	−11.9872	+	10.0585i	−0.881319	+	0.739515i
$186$	9.28554	−	11.2384i	0.680849	−	0.824039i
$187$	4.26854	−	1.55362i	0.312147	−	0.113612i
$188$	−4.66205			−0.340015
$189$	4.97418	+	12.8163i	0.361818	+	0.932249i
$190$	1.83669			0.133248
$191$	−8.29180	+	3.01797i	−0.599974	+	0.218372i	−0.624110	−	0.781336i	$-0.714538\pi$
$191$	−8.29180	+	3.01797i	−0.599974	+	0.218372i	0.0241369	+	0.999709i	$0.492316\pi$
$192$	7.89068	+	21.1774i	0.569461	+	1.52835i
$193$	6.59508	−	5.53393i	0.474725	−	0.398341i	−0.373790	−	0.927513i	$-0.621942\pi$
$193$	6.59508	−	5.53393i	0.474725	−	0.398341i	0.848514	+	0.529172i	$0.177497\pi$
$194$	21.3837	+	7.78304i	1.53526	+	0.558790i
$195$	−0.175364	+	0.493441i	−0.0125580	+	0.0353360i
$196$	16.4845	+	13.9246i	1.17746	+	0.994618i
$197$	−8.50014	+	14.7227i	−0.605610	+	1.04895i	0.386345	+	0.922354i	$0.373737\pi$
$197$	−8.50014	+	14.7227i	−0.605610	+	1.04895i	−0.991955	+	0.126593i	$0.959596\pi$
$198$	−6.09728	+	2.32475i	−0.433315	+	0.165213i
$199$	22.9181			1.62462			0.812309	−	0.583228i	$-0.198210\pi$
$199$	22.9181			1.62462			0.812309	+	0.583228i	$0.198210\pi$
$200$	5.48320	−	1.99572i	0.387721	−	0.141119i
$201$	4.80400	+	2.72513i	0.338848	+	0.192216i
$202$	−0.808019	−	4.58250i	−0.0568520	−	0.322424i
$203$	−11.9956	+	10.0320i	−0.841925	+	0.704106i
$204$	21.6742	−	12.7342i	1.51750	−	0.891571i
$205$	−3.11901	+	17.6888i	−0.217841	+	1.23544i
$206$	−39.9599			−2.78414
$207$	−3.73548	+	23.2452i	−0.259634	+	1.61565i
$208$	0.124014			0.00859881
$209$	0.457251	−	0.166426i	0.0316287	−	0.0115119i
$210$	10.8032	+	12.7201i	0.745492	+	0.877772i
$211$	12.0864	−	10.1417i	0.832064	−	0.698184i	−0.123700	−	0.992320i	$-0.539476\pi$
$211$	12.0864	−	10.1417i	0.832064	−	0.698184i	0.955764	+	0.294135i	$0.0950316\pi$
$212$	−1.48351	−	8.41343i	−0.101888	−	0.577837i
$213$	−1.74091	−	4.67235i	−0.119285	−	0.320144i
$214$	29.1660	+	24.4732i	1.99375	+	1.67295i
$215$	6.96290	+	12.0601i	0.474866	+	0.822492i
$216$	−10.8362	+	6.59009i	−0.737312	+	0.448399i
$217$	−9.87747	−	0.0162237i	−0.670526	−	0.00110134i
$218$	4.72328	−	26.7870i	0.319901	−	1.81425i
$219$	0.0210656	+	0.0565370i	0.00142348	+	0.00382042i
$220$	−3.68034	+	3.08817i	−0.248128	+	0.208204i
$221$	−0.153023	−	0.867836i	−0.0102934	−	0.0583769i
$222$	−12.6672	+	35.6432i	−0.850168	+	2.39222i
$223$	−9.82253	+	3.57511i	−0.657765	+	0.239407i	−0.649271	−	0.760557i	$-0.724926\pi$
$223$	−9.82253	+	3.57511i	−0.657765	+	0.239407i	−0.00849389	+	0.999964i	$0.502704\pi$
$224$	8.45779	−	14.5939i	0.565110	−	0.975097i
$225$	−3.67994	−	6.15588i	−0.245329	−	0.410392i
$226$	19.0551	−	33.0043i	1.26752	−	2.19542i
$227$	3.25983	−	1.18648i	0.216363	−	0.0787496i	−0.231565	−	0.972820i	$-0.574384\pi$
$227$	3.25983	−	1.18648i	0.216363	−	0.0787496i	0.447928	+	0.894070i	$0.352162\pi$
$228$	2.32177	−	1.36410i	0.153763	−	0.0903397i
$229$	−14.9694	+	12.5608i	−0.989206	+	0.830043i	−0.985453	−	0.169950i	$-0.945639\pi$
$229$	−14.9694	+	12.5608i	−0.989206	+	0.830043i	−0.00375378	+	0.999993i	$0.501195\pi$
$230$	4.96284	+	28.1457i	0.327240	+	1.85587i
$231$	3.84208	+	2.18782i	0.252790	+	0.143948i
$232$	−11.0512	−	9.27302i	−0.725544	−	0.608804i
$233$	−0.00761848	+	0.0131956i	−0.000499103	+	0.000864472i	−0.866275	−	0.499568i	$-0.833492\pi$
$233$	−0.00761848	+	0.0131956i	−0.000499103	+	0.000864472i	0.865776	+	0.500432i	$0.166826\pi$
$234$	0.238741	+	1.24319i	0.0156070	+	0.0812699i
$235$	1.22149	+	2.11568i	0.0796810	+	0.138012i
$236$	−1.64275	−	1.37843i	−0.106934	−	0.0897284i
$237$	−14.2419	+	2.62296i	−0.925112	+	0.170380i
$238$	−26.3736	−	9.64830i	−1.70955	−	0.625407i
$239$	−10.5505	−	3.84008i	−0.682458	−	0.248394i	−0.0225552	−	0.999746i	$-0.507180\pi$
$239$	−10.5505	−	3.84008i	−0.682458	−	0.248394i	−0.659902	+	0.751351i	$0.729402\pi$
$240$	1.18077	−	1.42910i	0.0762184	−	0.0922480i
$241$	−23.1336	−	19.4114i	−1.49016	−	1.25040i	−0.894425	−	0.447218i	$-0.852415\pi$
$241$	−23.1336	−	19.4114i	−1.49016	−	1.25040i	−0.595739	−	0.803178i	$-0.703141\pi$
$242$	11.3503	−	19.6593i	0.729625	−	1.26375i
$243$	10.4664	+	11.5523i	0.671419	+	0.741078i
$244$	−27.4027			−1.75428
$245$	2.00009	−	11.1291i	0.127781	−	0.711015i
$246$	15.1600	+	40.6871i	0.966565	+	2.59412i
$247$	−0.0163920	−	0.0929635i	−0.00104300	−	0.00591513i
$248$	−1.58234	−	8.97390i	−0.100479	−	0.569843i
$249$	7.98103	−	22.4572i	0.505777	−	1.42316i
$250$	−20.6181	−	17.3006i	−1.30400	−	1.09419i
$251$	3.95625	−	6.85242i	0.249716	−	0.432521i	−0.713731	−	0.700420i	$-0.752996\pi$
$251$	3.95625	−	6.85242i	0.249716	−	0.432521i	0.963447	+	0.267899i	$0.0863294\pi$
$252$	23.1035	+	8.05608i	1.45538	+	0.507485i
$253$	3.78584	+	6.55726i	0.238013	+	0.412251i
$254$	2.54596	−	14.4389i	0.159748	−	0.905976i
$255$	−11.4577	−	6.49952i	−0.717507	−	0.407016i
$256$	10.7839	+	3.92503i	0.673996	+	0.245315i
$257$	0.461057	−	0.386873i	0.0287600	−	0.0241325i	−0.628294	−	0.777976i	$-0.716247\pi$
$257$	0.461057	−	0.386873i	0.0287600	−	0.0241325i	0.657054	+	0.753843i	$0.271802\pi$
$258$	29.2805	+	16.6098i	1.82293	+	1.03408i
$259$	24.0986	−	8.72639i	1.49742	−	0.542232i
$260$	0.466011	+	0.807154i	0.0289008	+	0.0500576i
$261$	−8.63132	+	15.4888i	−0.534265	+	0.958730i
$262$	−2.54518	−	4.40839i	−0.157242	−	0.272351i
$263$	−0.0903211	+	0.512236i	−0.00556943	+	0.0315858i	−0.987466	−	0.157833i	$-0.949549\pi$
$263$	−0.0903211	+	0.512236i	−0.00556943	+	0.0315858i	0.981896	+	0.189419i	$0.0606604\pi$
$264$	−1.36588	+	3.84334i	−0.0840643	+	0.236541i
$265$	−3.42940	+	2.87761i	−0.210666	+	0.176770i
$266$	−2.82517	−	1.03354i	−0.173222	−	0.0633702i
$267$	−19.4918	−	3.28443i	−1.19288	−	0.201004i
$268$	9.23704	−	3.36201i	0.564242	−	0.205367i
$269$	−0.0763972	+	0.132324i	−0.00465802	+	0.00806793i	−0.868345	−	0.495961i	$-0.834816\pi$
$269$	−0.0763972	+	0.132324i	−0.00465802	+	0.00806793i	0.863687	+	0.504029i	$0.168149\pi$
$270$	16.5993	+	9.08559i	1.01020	+	0.552932i
$271$	−9.93447	−	17.2070i	−0.603476	−	1.04525i	−0.992290	−	0.123935i	$-0.960449\pi$
$271$	−9.93447	−	17.2070i	−0.603476	−	1.04525i	0.388814	−	0.921316i	$-0.372885\pi$
$272$	−0.541695	+	3.07211i	−0.0328451	+	0.186274i
$273$	0.547408	−	0.660323i	0.0331307	−	0.0399646i
$274$	−22.6598	−	8.24751i	−1.36893	−	0.498250i
$275$	−2.16743	−	0.788879i	−0.130701	−	0.0475712i
$276$	27.1771	+	31.8931i	1.63587	+	1.91974i
$277$	−0.951869	+	5.39832i	−0.0571923	+	0.324353i	−0.999959	−	0.00910069i	$-0.997103\pi$
$277$	−0.951869	+	5.39832i	−0.0571923	+	0.324353i	0.942766	+	0.333454i	$0.108214\pi$
$278$	−12.3463			−0.740480
$279$	−10.4651	+	3.99011i	−0.626532	+	0.238882i
$280$	10.4315	+	0.0171337i	0.623402	+	0.00102394i
$281$	14.9522	+	12.5464i	0.891972	+	0.748454i	0.968605	−	0.248606i	$-0.0799724\pi$
$281$	14.9522	+	12.5464i	0.891972	+	0.748454i	−0.0766325	+	0.997059i	$0.524417\pi$
$282$	5.13662	+	2.91382i	0.305881	+	0.173515i
$283$	21.2428	+	7.73174i	1.26275	+	0.459604i	0.884692	−	0.466177i	$-0.154369\pi$
$283$	21.2428	+	7.73174i	1.26275	+	0.459604i	0.378061	+	0.925781i	$0.376591\pi$
$284$	−8.33899	−	3.03515i	−0.494828	−	0.180103i
$285$	−1.22736	−	0.696236i	−0.0727025	−	0.0412415i
$286$	0.311873	+	0.261693i	0.0184414	+	0.0154742i
$287$	14.7514	−	25.4535i	0.870747	−	1.50247i
$288$	3.03461	−	18.8838i	0.178816	−	1.11274i
$289$	5.16669			0.303923
$290$	−3.73768	+	21.1975i	−0.219484	+	1.24476i
$291$	−11.3392	−	13.3069i	−0.664717	−	0.780064i
$292$	0.100905	+	0.0367263i	0.00590501	+	0.00214925i
$293$	−10.9601	−	3.98916i	−0.640298	−	0.233049i	0.00140924	−	0.999999i	$-0.499551\pi$
$293$	−10.9601	−	3.98916i	−0.640298	−	0.233049i	−0.641707	+	0.766950i	$0.721774\pi$
$294$	−9.45949	−	25.6450i	−0.551689	−	1.49565i
$295$	−0.195133	+	1.10666i	−0.0113611	+	0.0644320i
$296$	11.8223	+	20.4768i	0.687157	+	1.19019i
$297$	4.95571	+	0.757797i	0.287560	+	0.0439719i
$298$	13.2326	−	22.9196i	0.766545	−	1.32769i
$299$	1.38029	−	0.502384i	0.0798242	−	0.0290536i
$300$	−12.5870	−	2.12094i	−0.726708	−	0.122452i
$301$	−3.92381	−	22.4688i	−0.226165	−	1.29508i
$302$	0.377519	−	0.316776i	0.0217238	−	0.0182284i
$303$	−1.19714	+	3.36852i	−0.0687737	+	0.193517i
$304$	−0.0580270	+	0.329087i	−0.00332808	+	0.0188745i
$305$	7.17970	+	12.4356i	0.411108	+	0.712061i
$306$	−31.8395	+	0.483880i	−1.82014	+	0.0276616i
$307$	−4.58756	−	7.94588i	−0.261826	−	0.453495i	0.704901	−	0.709305i	$-0.250991\pi$
$307$	−4.58756	−	7.94588i	−0.261826	−	0.453495i	−0.966727	+	0.255810i	$0.917658\pi$
$308$	7.39880	−	2.67919i	0.421586	−	0.152661i
$309$	26.7030	+	15.1476i	1.51908	+	0.861717i
$310$	−10.4151	+	8.73929i	−0.591537	+	0.496358i
$311$	6.79138	+	2.47186i	0.385104	+	0.140166i	0.527315	−	0.849670i	$-0.323199\pi$
$311$	6.79138	+	2.47186i	0.385104	+	0.140166i	−0.142211	+	0.989836i	$0.545421\pi$
$312$	0.688253	+	0.390421i	0.0389646	+	0.0221032i
$313$	−0.801216	+	4.54392i	−0.0452874	+	0.256838i	−0.999043	−	0.0437467i	$-0.986071\pi$
$313$	−0.801216	+	4.54392i	−0.0452874	+	0.256838i	0.953755	+	0.300584i	$0.0971817\pi$
$314$	24.4441	+	42.3383i	1.37946	+	2.38929i
$315$	−2.39735	−	12.5953i	−0.135075	−	0.709666i
$316$	−12.8868	+	22.3206i	−0.724939	+	1.25563i
$317$	8.07739	+	6.77774i	0.453672	+	0.380676i	0.840796	−	0.541352i	$-0.182087\pi$
$317$	8.07739	+	6.77774i	0.453672	+	0.380676i	−0.387125	+	0.922027i	$0.626532\pi$
$318$	−3.62393	+	10.1971i	−0.203220	+	0.571824i
$319$	0.990226	+	5.61585i	0.0554420	+	0.314427i
$320$	−3.65998	−	20.7568i	−0.204599	−	1.16034i
$321$	−10.2129	−	27.4100i	−0.570030	−	1.52988i
$322$	8.20425	−	46.0859i	0.457205	−	2.56826i
$323$	2.37452			0.132122
$324$	27.7310	−	0.843078i	1.54061	−	0.0468376i
$325$	−0.223728	+	0.387509i	−0.0124102	+	0.0214951i
$326$	−15.8566	−	13.3052i	−0.878214	−	0.736909i
$327$	−13.3105	+	16.1098i	−0.736070	+	0.890874i
$328$	25.5035	+	9.28250i	1.40819	+	0.512540i
$329$	−0.688346	−	3.94165i	−0.0379497	−	0.217310i
$330$	5.98511	−	1.10229i	0.329469	−	0.0606790i
$331$	19.2351	+	16.1402i	1.05726	+	0.887146i	0.993838	−	0.110841i	$-0.0353544\pi$
$331$	19.2351	+	16.1402i	1.05726	+	0.887146i	0.0634211	+	0.997987i	$0.479799\pi$
$332$	−21.2088	−	36.7347i	−1.16398	−	2.01608i
$333$	21.9761	−	19.0166i	1.20428	−	1.04210i
$334$	−9.66057	+	16.7326i	−0.528603	+	0.915567i
$335$	−3.94588	−	3.31098i	−0.215586	−	0.180898i
$336$	−2.62042	+	1.53378i	−0.142956	+	0.0836746i
$337$	1.88012	+	10.6627i	0.102417	+	0.580834i	0.992221	+	0.124491i	$0.0397298\pi$
$337$	1.88012	+	10.6627i	0.102417	+	0.580834i	−0.889804	+	0.456343i	$0.849159\pi$
$338$	−22.3908	+	18.7881i	−1.21790	+	1.02194i
$339$	−25.2444	+	14.8317i	−1.37109	+	0.805549i
$340$	−22.0306	+	8.01849i	−1.19478	+	0.434864i
$341$	−1.80099	+	3.11940i	−0.0975289	+	0.168925i
$342$	−3.41069	+	0.0518338i	−0.184429	+	0.00280285i
$343$	−9.33905	+	15.9932i	−0.504261	+	0.863551i
$344$	19.7730	−	7.19678i	1.06609	−	0.388025i
$345$	7.35279	−	20.6894i	0.395861	−	1.11388i
$346$	7.65961	+	43.4398i	0.411783	+	2.33534i
$347$	−1.28400	+	1.07741i	−0.0689289	+	0.0578382i	−0.676601	−	0.736350i	$-0.736548\pi$
$347$	−1.28400	+	1.07741i	−0.0689289	+	0.0578382i	0.607672	+	0.794188i	$0.292103\pi$
$348$	11.0184	+	29.5717i	0.590647	+	1.58521i
$349$	1.60438	−	9.09890i	0.0858806	−	0.487053i	−0.911283	−	0.411782i	$-0.864907\pi$
$349$	1.60438	−	9.09890i	0.0858806	−	0.487053i	0.997163	−	0.0752713i	$-0.0239823\pi$
$350$	7.10954	+	12.3609i	0.380021	+	0.660720i
$351$	0.311719	−	0.921254i	0.0166383	−	0.0491729i
$352$	−3.07552	−	5.32695i	−0.163926	−	0.283927i
$353$	12.7820	+	10.7253i	0.680315	+	0.570852i	0.916098	−	0.400953i	$-0.131321\pi$
$353$	12.7820	+	10.7253i	0.680315	+	0.570852i	−0.235783	+	0.971806i	$0.575766\pi$
$354$	0.948446	+	2.54549i	0.0504093	+	0.135291i
$355$	0.807496	+	4.57954i	0.0428574	+	0.243057i
$356$	−26.9494	+	22.6132i	−1.42832	+	1.19850i
$357$	13.9666	+	16.4449i	0.739192	+	0.870355i
$358$	−12.3983	+	4.51260i	−0.655269	+	0.238498i
$359$	−6.85278			−0.361676			−0.180838	−	0.983513i	$-0.557881\pi$
$359$	−6.85278			−0.361676			−0.180838	+	0.983513i	$0.557881\pi$
$360$	11.0522	−	4.21393i	0.582500	−	0.222094i
$361$	−18.7456			−0.986613
$362$	0.259483	−	1.47160i	0.0136381	−	0.0773455i
$363$	−15.0370	+	8.83463i	−0.789238	+	0.463698i
$364$	−0.262612	−	1.50378i	−0.0137646	−	0.0788197i
$365$	−0.00977099	−	0.0554140i	−0.000511437	−	0.00290050i
$366$	30.1922	+	17.1269i	1.57817	+	0.895239i
$367$	6.75224	−	2.45761i	0.352464	−	0.128286i	−0.159720	−	0.987162i	$-0.551059\pi$
$367$	6.75224	−	2.45761i	0.352464	−	0.128286i	0.512183	+	0.858876i	$0.328837\pi$
$368$	−5.19975			−0.271056
$369$	5.29271	−	32.9356i	0.275528	−	1.71456i
$370$	17.6393	−	30.5521i	0.917021	−	1.58833i
$371$	6.89432	−	2.49651i	0.357935	−	0.129612i
$372$	−6.67511	+	18.7825i	−0.346088	+	0.973830i
$373$	27.5343	+	10.0217i	1.42567	+	0.518902i	0.935688	−	0.352830i	$-0.114780\pi$
$373$	27.5343	+	10.0217i	1.42567	+	0.518902i	0.489984	+	0.871732i	$0.337003\pi$
$374$	−7.84499	+	6.58273i	−0.405655	+	0.340385i
$375$	7.21974	+	19.3767i	0.372826	+	1.00061i
$376$	3.46873	−	1.26252i	0.178886	−	0.0651093i
$377$	1.10626			0.0569752
$378$	−20.4202	−	23.3160i	−1.05030	−	1.19925i
$379$	0.333430			0.0171272			0.00856359	−	0.999963i	$-0.497274\pi$
$379$	0.333430			0.0171272			0.00856359	+	0.999963i	$0.497274\pi$
$380$	−2.35994	+	0.858949i	−0.121063	+	0.0440632i
$381$	−7.17467	+	8.68359i	−0.367569	+	0.444874i
$382$	15.2392	−	12.7872i	0.779705	−	0.654250i
$383$	13.5363	+	4.92681i	0.691672	+	0.251748i	0.663851	−	0.747865i	$-0.268921\pi$
$383$	13.5363	+	4.92681i	0.691672	+	0.251748i	0.0278213	+	0.999613i	$0.491143\pi$
$384$	−18.7218	−	21.9706i	−0.955395	−	1.12118i
$385$	−3.15437	−	2.65567i	−0.160762	−	0.135346i
$386$	−9.70468	+	16.8090i	−0.493955	+	0.855556i
$387$	−13.2703	−	22.1987i	−0.674565	−	1.12843i
$388$	−31.1155			−1.57965
$389$	−21.4697	+	7.81432i	−1.08855	+	0.396202i	−0.823085	−	0.567918i	$-0.807749\pi$
$389$	−21.4697	+	7.81432i	−1.08855	+	0.396202i	−0.265470	+	0.964119i	$0.585527\pi$
$390$	−0.00897039	−	1.18058i	−0.000454233	−	0.0597810i
$391$	6.41607	+	36.3873i	0.324475	+	1.84019i
$392$	−16.0359	−	5.89634i	−0.809938	−	0.297810i
$393$	0.0297145	+	3.91068i	0.00149890	+	0.197268i
$394$	6.65536	−	37.7444i	0.335292	−	1.90154i
$395$	13.5057			0.679546
$396$	6.74712	−	5.83850i	0.339056	−	0.293396i
$397$	22.6020			1.13436			0.567181	−	0.823593i	$-0.308034\pi$
$397$	22.6020			1.13436			0.567181	+	0.823593i	$0.308034\pi$
$398$	−48.5522	+	17.6715i	−2.43370	+	0.885794i
$399$	1.49612	+	1.76159i	0.0748997	+	0.0881900i
$400$	1.21340	−	1.01816i	0.0606700	−	0.0509081i
$401$	−2.29230	−	13.0003i	−0.114472	−	0.649203i	−0.987010	−	0.160657i	$-0.948639\pi$
$401$	−2.29230	−	13.0003i	−0.114472	−	0.649203i	0.872538	−	0.488546i	$-0.162473\pi$
$402$	−12.2786	−	2.06898i	−0.612401	−	0.103191i
$403$	0.535287	+	0.449159i	0.0266645	+	0.0223742i
$404$	3.18127	+	5.51012i	0.158274	+	0.274139i
$405$	−7.64831	−	12.3637i	−0.380048	−	0.614357i
$406$	17.6774	−	30.5023i	0.877314	−	1.51381i
$407$	1.62298	−	9.20436i	0.0804480	−	0.456243i
$408$	−12.6779	+	15.3442i	−0.627651	+	0.759653i
$409$	2.05094	−	1.72095i	0.101413	−	0.0850953i	−0.590672	−	0.806912i	$-0.701137\pi$
$409$	2.05094	−	1.72095i	0.101413	−	0.0850953i	0.692084	+	0.721817i	$0.256693\pi$
$410$	−7.03173	−	39.8789i	−0.347273	−	1.96948i
$411$	12.0159	+	14.1010i	0.592701	+	0.695552i
$412$	51.3440	−	18.6877i	2.52954	−	0.920676i
$413$	0.922883	−	1.59243i	0.0454121	−	0.0783586i
$414$	−10.0101	−	52.1256i	−0.491972	−	2.56183i
$415$	−11.1137	+	19.2495i	−0.545549	+	0.944919i
$416$	−1.12131	+	0.408124i	−0.0549768	+	0.0200099i
$417$	8.25032	+	4.68010i	0.404020	+	0.229186i
$418$	−0.840365	+	0.705150i	−0.0411036	+	0.0344900i
$419$	−4.94281	−	28.0321i	−0.241472	−	1.36946i	−0.828545	−	0.559922i	$-0.810831\pi$
$419$	−4.94281	−	28.0321i	−0.241472	−	1.36946i	0.587073	−	0.809534i	$-0.300280\pi$
$420$	−19.8296	−	11.2917i	−0.967585	−	0.550978i
$421$	−18.7196	−	15.7076i	−0.912339	−	0.765543i	0.0602237	−	0.998185i	$-0.480819\pi$
$421$	−18.7196	−	15.7076i	−0.912339	−	0.765543i	−0.972562	+	0.232642i	$0.925263\pi$
$422$	−17.7852	+	30.8049i	−0.865770	+	1.49956i
$423$	−2.32797	−	3.89428i	−0.113190	−	0.189346i
$424$	3.38221	+	5.85816i	0.164255	+	0.284497i
$425$	−8.62224	−	7.23491i	−0.418240	−	0.350945i
$426$	7.29087	+	8.55604i	0.353244	+	0.414542i
$427$	−4.04598	−	23.1684i	−0.195799	−	1.12120i
$428$	−48.9201	−	17.8055i	−2.36464	−	0.860659i
$429$	−0.109207	−	0.293096i	−0.00527258	−	0.0141508i
$430$	−24.0502	−	20.1806i	−1.15981	−	0.973193i
$431$	11.9105	−	20.6296i	0.573709	−	0.993692i	−0.422472	−	0.906376i	$-0.638838\pi$
$431$	11.9105	−	20.6296i	0.573709	−	0.993692i	0.996181	−	0.0873164i	$-0.0278291\pi$
$432$	−2.15232	+	2.68712i	−0.103554	+	0.129284i
$433$	32.7062			1.57176			0.785880	−	0.618379i	$-0.212210\pi$
$433$	32.7062			1.57176			0.785880	+	0.618379i	$0.212210\pi$
$434$	20.9380	−	7.58190i	1.00506	−	0.363943i
$435$	10.5330	−	12.7482i	0.505019	−	0.611230i
$436$	6.45836	+	36.6272i	0.309299	+	1.75412i
$437$	0.687297	+	3.89785i	0.0328779	+	0.186460i
$438$	−0.0882221	−	0.103531i	−0.00421542	−	0.00494691i
$439$	−18.7534	−	15.7360i	−0.895050	−	0.751036i	0.0741666	−	0.997246i	$-0.476370\pi$
$439$	−18.7534	−	15.7360i	−0.895050	−	0.751036i	−0.969217	+	0.246210i	$0.920815\pi$
$440$	1.90201	−	3.29437i	0.0906747	−	0.157053i
$441$	−3.40002	+	20.7229i	−0.161906	+	0.986806i
$442$	0.993347	+	1.72053i	0.0472487	+	0.0818372i
$443$	−0.643330	+	3.64851i	−0.0305655	+	0.173346i	−0.996269	−	0.0863015i	$-0.972495\pi$
$443$	−0.643330	+	3.64851i	−0.0305655	+	0.173346i	0.965704	+	0.259647i	$0.0836063\pi$
$444$	−0.392995	−	51.7215i	−0.0186507	−	2.45459i
$445$	17.3230	+	6.30506i	0.821189	+	0.298888i
$446$	18.0525	−	15.1478i	0.854809	−	0.717270i
$447$	−17.5307	+	10.2998i	−0.829175	+	0.487162i
$448$	−6.05044	+	33.9872i	−0.285856	+	1.60575i
$449$	−4.45575	−	7.71759i	−0.210280	−	0.364215i	0.741522	−	0.670928i	$-0.234104\pi$
$449$	−4.45575	−	7.71759i	−0.210280	−	0.364215i	−0.951802	+	0.306713i	$0.900771\pi$
$450$	12.5426	+	10.2038i	0.591266	+	0.481011i
$451$	−5.36406	−	9.29083i	−0.252584	−	0.437488i
$452$	−9.04877	+	51.3181i	−0.425618	+	2.41380i
$453$	−0.372355	+	0.0685773i	−0.0174948	+	0.00322204i
$454$	−5.99113	+	5.02716i	−0.281178	+	0.235936i
$455$	−0.613624	+	0.513177i	−0.0287671	+	0.0240581i
$456$	−1.35807	+	1.64369i	−0.0635976	+	0.0769729i
$457$	−6.80857	+	2.47812i	−0.318492	+	0.115921i	−0.496319	−	0.868140i	$-0.665315\pi$
$457$	−6.80857	+	2.47812i	−0.318492	+	0.115921i	0.177827	+	0.984062i	$0.443093\pi$
$458$	22.0275	−	38.1528i	1.02928	−	1.78276i
$459$	21.4600	+	11.7461i	1.00167	+	0.548259i
$460$	−19.5393	−	33.8431i	−0.911025	−	1.57794i
$461$	−0.937013	+	5.31406i	−0.0436410	+	0.247501i	−0.998822	−	0.0485214i	$-0.984549\pi$
$461$	−0.937013	+	5.31406i	−0.0436410	+	0.247501i	0.955181	+	0.296022i	$0.0956602\pi$
$462$	−9.82647	−	1.67239i	−0.457169	−	0.0778067i
$463$	−4.18639	−	1.52372i	−0.194558	−	0.0708133i	0.242904	−	0.970050i	$-0.421900\pi$
$463$	−4.18639	−	1.52372i	−0.194558	−	0.0708133i	−0.437461	+	0.899237i	$0.644122\pi$
$464$	−3.67994	−	1.33939i	−0.170837	−	0.0621796i
$465$	10.2726	−	1.89193i	0.476381	−	0.0877360i
$466$	0.00596504	−	0.0338294i	0.000276325	−	0.00156712i
$467$	−28.6791			−1.32711			−0.663554	−	0.748128i	$-0.730953\pi$
$467$	−28.6791			−1.32711			−0.663554	+	0.748128i	$0.730953\pi$
$468$	−0.888147	−	1.48571i	−0.0410546	−	0.0686770i
$469$	4.20634	+	7.31331i	0.194231	+	0.337697i
$470$	−4.21908	−	3.54023i	−0.194612	−	0.163299i
$471$	−0.285379	−	37.5583i	−0.0131496	−	1.73060i
$472$	1.59556	+	0.580736i	0.0734416	+	0.0267305i
$473$	−7.81597	−	2.84478i	−0.359379	−	0.130803i
$474$	28.1492	−	16.5384i	1.29293	−	0.759632i
$475$	−0.923624	−	0.775012i	−0.0423788	−	0.0355600i
$476$	38.3993	+	0.0630707i	1.76003	+	0.00289084i
$477$	6.28708	−	5.44041i	0.287866	−	0.249099i
$478$	25.3124			1.15776
$479$	−1.94837	+	11.0498i	−0.0890235	+	0.504877i	0.907392	+	0.420285i	$0.138070\pi$
$479$	−1.94837	+	11.0498i	−0.0890235	+	0.504877i	−0.996416	+	0.0845923i	$0.973041\pi$
$480$	−5.97322	+	16.8075i	−0.272639	+	0.767156i
$481$	−1.70381	−	0.620135i	−0.0776869	−	0.0282757i
$482$	63.9764	+	23.2855i	2.91404	+	1.06062i
$483$	−22.9522	+	27.6866i	−1.04436	+	1.25978i
$484$	−5.38997	+	30.5680i	−0.244999	+	1.38946i
$485$	8.15246	+	14.1205i	0.370184	+	0.641178i
$486$	−31.0808	−	16.4032i	−1.40986	−	0.744065i
$487$	−13.8374	+	23.9671i	−0.627033	+	1.08605i	0.361111	+	0.932523i	$0.382398\pi$
$487$	−13.8374	+	23.9671i	−0.627033	+	1.08605i	−0.988144	+	0.153530i	$0.950936\pi$
$488$	20.3886	−	7.42086i	0.922951	−	0.335927i
$489$	5.55243	+	14.9019i	0.251089	+	0.673887i
$490$	4.34420	+	25.1194i	0.196251	+	1.13478i
$491$	23.0453	−	19.3373i	1.04002	−	0.872682i	0.0480122	−	0.998847i	$-0.484711\pi$
$491$	23.0453	−	19.3373i	1.04002	−	0.872682i	0.992009	+	0.126165i	$0.0402669\pi$
$492$	−38.5066	−	45.1886i	−1.73601	−	2.03726i
$493$	−4.83216	+	27.4046i	−0.217630	+	1.23424i
$494$	0.106408	+	0.184305i	0.00478754	+	0.00829227i
$495$	−4.41735	−	1.53218i	−0.198545	−	0.0688663i
$496$	−1.23681	−	2.14221i	−0.0555342	−	0.0961880i
$497$	1.33490	−	7.49856i	0.0598785	−	0.336356i
$498$	0.408254	+	53.7297i	0.0182943	+	2.40769i
$499$	−9.73355	+	8.16742i	−0.435734	+	0.365624i	−0.834110	−	0.551598i	$-0.814018\pi$
$499$	−9.73355	+	8.16742i	−0.435734	+	0.365624i	0.398376	+	0.917222i	$0.369574\pi$
$500$	34.5827	+	12.5871i	1.54658	+	0.562911i
$501$	12.7984	−	7.51942i	0.571792	−	0.335943i
$502$	−3.09762	+	17.5675i	−0.138254	+	0.784076i
$503$	5.27617	+	9.13860i	0.235253	+	0.407470i	0.959346	−	0.282232i	$-0.0910748\pi$
$503$	5.27617	+	9.13860i	0.235253	+	0.407470i	−0.724093	+	0.689702i	$0.757741\pi$
$504$	−19.3715	+	0.262573i	−0.862875	+	0.0116960i
$505$	1.66703	−	2.88738i	0.0741817	−	0.128487i
$506$	−13.0765	−	10.9725i	−0.581320	−	0.487786i
$507$	22.0846	−	4.06736i	0.980810	−	0.180638i
$508$	3.48122	+	19.7430i	0.154454	+	0.875952i
$509$	0.763789	+	4.33166i	0.0338543	+	0.191998i	0.997045	−	0.0768224i	$-0.0244774\pi$
$509$	0.763789	+	4.33166i	0.0338543	+	0.191998i	−0.963190	+	0.268820i	$0.913366\pi$
$510$	29.2848	+	4.93458i	1.29675	+	0.218507i
$511$	−0.0161528	+	0.0907352i	−0.000714557	+	0.00401389i
$512$	7.45857			0.329625
$513$	2.29882	+	1.25825i	0.101495	+	0.0555531i
$514$	−0.678447	+	1.17511i	−0.0299250	+	0.0518317i
$515$	−21.9331	−	18.4041i	−0.966488	−	0.810979i
$516$	−45.3899	−	7.64833i	−1.99818	−	0.336699i
$517$	−1.37114	−	0.499054i	−0.0603026	−	0.0219484i
$518$	−44.3246	+	37.0688i	−1.94751	+	1.62871i
$519$	11.3483	−	31.9319i	0.498133	−	1.40166i
$520$	−0.565313	−	0.474354i	−0.0247906	−	0.0208018i
$521$	11.1596	+	19.3289i	0.488909	+	0.846816i	0.999919	−	0.0127592i	$-0.00406150\pi$
$521$	11.1596	+	19.3289i	0.488909	+	0.846816i	−0.511009	+	0.859575i	$0.670728\pi$
$522$	6.34255	−	39.4685i	0.277606	−	1.72749i
$523$	−9.08231	+	15.7310i	−0.397142	+	0.687869i	−0.993372	−	0.114944i	$-0.963331\pi$
$523$	−9.08231	+	15.7310i	−0.397142	+	0.687869i	0.596230	+	0.802813i	$0.296664\pi$
$524$	5.33190	+	4.47400i	0.232925	+	0.195447i
$525$	−0.0652457	−	10.9551i	−0.00284756	−	0.478121i
$526$	−0.203626	−	1.15482i	−0.00887853	−	0.0503527i
$527$	−13.4648	+	11.2983i	−0.586538	+	0.492164i
$528$	0.00841282	+	1.10720i	0.000366121	+	0.0481846i
$529$	−36.2610	+	13.1979i	−1.57656	+	0.573823i
$530$	5.04637	−	8.74057i	0.219200	−	0.379666i
$531$	0.331125	−	2.06053i	0.0143696	−	0.0894195i
$532$	4.11337	+	0.00675620i	0.178337	+	0.000292918i
$533$	−1.95570	+	0.711816i	−0.0847107	+	0.0308322i
$534$	43.8262	−	8.07155i	1.89654	−	0.349290i
$535$	4.73712	+	26.8655i	0.204803	+	1.16150i
$536$	−5.96224	+	5.00292i	−0.257530	+	0.216093i
$537$	9.99566	+	1.68430i	0.431344	+	0.0726828i
$538$	0.0598168	−	0.339238i	0.00257888	−	0.0146256i
$539$	3.35761	+	5.85993i	0.144623	+	0.252405i
$540$	−25.5772	−	3.91111i	−1.10067	−	0.168307i
$541$	−14.1984	−	24.5924i	−0.610438	−	1.05731i	−0.991167	−	0.132623i	$-0.957660\pi$
$541$	−14.1984	−	24.5924i	−0.610438	−	1.05731i	0.380729	−	0.924687i	$-0.375673\pi$
$542$	34.3142	+	28.7930i	1.47392	+	1.23677i
$543$	−0.731237	+	0.885024i	−0.0313804	+	0.0379800i
$544$	−5.21225	−	29.5601i	−0.223473	−	1.26738i
$545$	14.9296	−	12.5274i	0.639514	−	0.536616i
$546$	−0.650533	+	1.82100i	−0.0278402	+	0.0779314i
$547$	12.9097	−	4.69873i	0.551977	−	0.200903i	−0.0509474	−	0.998701i	$-0.516224\pi$
$547$	12.9097	−	4.69873i	0.551977	−	0.200903i	0.602925	+	0.797798i	$0.294002\pi$
$548$	32.9724			1.40851
$549$	−13.6834	−	22.8899i	−0.583994	−	0.976918i
$550$	5.20001			0.221729
$551$	−0.517627	+	2.93561i	−0.0220516	+	0.125061i
$552$	−28.8577	−	16.3699i	−1.22826	−	0.696749i
$553$	−20.7743	−	7.59988i	−0.883412	−	0.323180i
$554$	−2.14596	−	12.1704i	−0.0911732	−	0.517069i
$555$	−23.3687	+	13.7297i	−0.991946	+	0.582794i
$556$	15.8636	−	5.77386i	0.672765	−	0.244866i
$557$	10.5881			0.448631			0.224316	−	0.974517i	$-0.427985\pi$
$557$	10.5881			0.448631			0.224316	+	0.974517i	$0.427985\pi$
$558$	19.0938	−	16.5225i	0.808307	−	0.699454i
$559$	−0.806788	+	1.39740i	−0.0341235	+	0.0591037i
$560$	2.66253	−	0.964132i	0.112512	−	0.0407420i
$561$	7.73768	−	1.42506i	0.326685	−	0.0601663i
$562$	−41.3506	−	15.0504i	−1.74427	−	0.634862i
$563$	11.5992	−	9.73288i	0.488848	−	0.410192i	−0.364765	−	0.931100i	$-0.618851\pi$
$563$	11.5992	−	9.73288i	0.488848	−	0.410192i	0.853613	+	0.520907i	$0.174406\pi$
$564$	−7.96265	−	1.34173i	−0.335288	−	0.0564970i
$565$	25.6595	−	9.33928i	1.07950	−	0.392906i
$566$	−50.9648			−2.14221
$567$	4.80726	+	23.3215i	0.201886	+	0.979409i
$568$	7.02646			0.294824
$569$	21.1188	−	7.68663i	0.885348	−	0.322240i	0.140982	−	0.990012i	$-0.454974\pi$
$569$	21.1188	−	7.68663i	0.885348	−	0.322240i	0.744366	+	0.667772i	$0.232752\pi$
$570$	3.13702	+	0.528598i	0.131396	+	0.0221405i
$571$	−7.29087	+	6.11777i	−0.305114	+	0.256021i	−0.782469	−	0.622690i	$-0.786040\pi$
$571$	−7.29087	+	6.11777i	−0.305114	+	0.256021i	0.477355	+	0.878710i	$0.341595\pi$
$572$	−0.523105	−	0.190395i	−0.0218721	−	0.00796080i
$573$	−15.0307	+	2.76824i	−0.627918	+	0.115645i
$574$	−11.6244	+	65.2980i	−0.485194	+	2.72549i
$575$	9.38068	−	16.2478i	0.391201	−	0.677580i
$576$	7.38224	+	38.4414i	0.307594	+	1.60172i
$577$	−42.3017			−1.76104			−0.880521	−	0.474007i	$-0.842807\pi$
$577$	−42.3017			−1.76104			−0.880521	+	0.474007i	$0.842807\pi$
$578$	−10.9457	+	3.98390i	−0.455280	+	0.165709i
$579$	12.8569	−	7.55375i	0.534314	−	0.313923i
$580$	−5.11071	−	28.9843i	−0.212211	−	1.20351i
$581$	27.9269	−	23.3554i	1.15860	−	0.968943i
$582$	34.2829	+	19.4474i	1.42107	+	0.806122i
$583$	0.464313	−	2.63325i	0.0192299	−	0.109058i
$584$	−0.0850226			−0.00351826
$585$	−0.441528	+	0.792315i	−0.0182549	+	0.0327582i
$586$	26.2951			1.08624
$587$	12.4550	−	4.53327i	0.514075	−	0.187108i	−0.0719389	−	0.997409i	$-0.522919\pi$
$587$	12.4550	−	4.53327i	0.514075	−	0.187108i	0.586014	+	0.810301i	$0.300696\pi$
$588$	24.1475	+	28.5271i	0.995828	+	1.17644i
$589$	−1.44237	+	1.21029i	−0.0594318	+	0.0498692i
$590$	−0.439923	−	2.49492i	−0.0181113	−	0.102714i
$591$	−18.7552	+	22.6996i	−0.771485	+	0.933737i
$592$	4.91685	+	4.12573i	0.202081	+	0.169566i
$593$	22.2156	+	38.4786i	0.912287	+	1.58013i	0.810826	+	0.585287i	$0.199018\pi$
$593$	22.2156	+	38.4786i	0.912287	+	1.58013i	0.101460	+	0.994840i	$0.467649\pi$
$594$	−11.0831	+	2.21582i	−0.454743	+	0.0909164i
$595$	−10.0322	−	17.4424i	−0.411282	−	0.715071i
$596$	−6.28384	+	35.6374i	−0.257396	+	1.45977i
$597$	39.1434	+	6.59578i	1.60203	+	0.269947i
$598$	−2.53678	+	2.12861i	−0.103737	+	0.0870455i
$599$	6.77975	+	38.4499i	0.277013	+	1.57102i	0.732494	+	0.680774i	$0.238356\pi$
$599$	6.77975	+	38.4499i	0.277013	+	1.57102i	−0.455480	+	0.890246i	$0.650533\pi$
$600$	9.93952	−	1.83058i	0.405779	−	0.0747332i
$601$	28.8690	−	10.5074i	1.17759	−	0.428608i	0.322240	−	0.946658i	$-0.395564\pi$
$601$	28.8690	−	10.5074i	1.17759	−	0.428608i	0.855350	+	0.518050i	$0.173342\pi$
$602$	25.6378	+	44.5748i	1.04492	+	1.81674i
$603$	7.42081	+	6.03704i	0.302199	+	0.245847i
$604$	−0.336925	+	0.583572i	−0.0137093	+	0.0237452i
$605$	15.2843	−	5.56302i	0.621393	−	0.226169i
$606$	−0.0612372	−	8.05934i	−0.00248759	−	0.327388i
$607$	−5.67351	+	4.76064i	−0.230281	+	0.193228i	−0.750626	−	0.660728i	$-0.770248\pi$
$607$	−5.67351	+	4.76064i	−0.230281	+	0.193228i	0.520345	+	0.853956i	$0.325803\pi$
$608$	−0.558342	−	3.16652i	−0.0226438	−	0.128419i
$609$	−23.3753	+	13.6820i	−0.947216	+	0.554423i
$610$	−24.7991	−	20.8089i	−1.00408	−	0.842527i
$611$	−0.141533	+	0.245143i	−0.00572582	+	0.00991741i
$612$	40.6839	−	15.5118i	1.64455	−	0.627028i
$613$	11.9455	+	20.6902i	0.482475	+	0.835671i	0.999798	−	0.0201196i	$-0.00640471\pi$
$613$	11.9455	+	20.6902i	0.482475	+	0.835671i	−0.517323	+	0.855790i	$0.673071\pi$
$614$	15.8457	+	13.2961i	0.639479	+	0.536587i
$615$	−10.4180	+	29.3144i	−0.420094	+	1.18207i
$616$	−4.77943	+	3.99706i	−0.192569	+	0.161046i
$617$	12.6845	+	4.61680i	0.510661	+	0.185865i	0.584483	−	0.811406i	$-0.301297\pi$
$617$	12.6845	+	4.61680i	0.510661	+	0.185865i	−0.0738220	+	0.997271i	$0.523520\pi$
$618$	−68.2505	−	11.5004i	−2.74544	−	0.462614i
$619$	20.9806	+	17.6048i	0.843280	+	0.707596i	0.958299	−	0.285767i	$-0.0922484\pi$
$619$	20.9806	+	17.6048i	0.843280	+	0.707596i	−0.115019	+	0.993363i	$0.536693\pi$
$620$	9.29517	−	16.0997i	0.373303	−	0.646580i
$621$	−13.0700	+	38.6271i	−0.524482	+	1.55005i
$622$	−16.2936			−0.653314
$623$	−23.0980	−	19.4463i	−0.925402	−	0.779098i
$624$	0.211812	+	0.0356910i	0.00847927	+	0.00142878i
$625$	−1.27311	−	7.22018i	−0.0509245	−	0.288807i
$626$	−1.80632	−	10.2441i	−0.0721951	−	0.409439i
$627$	0.828869	−	0.152655i	0.0331018	−	0.00609643i
$628$	−51.2078	−	42.9685i	−2.04341	−	1.71463i
$629$	22.8044	−	39.4984i	0.909272	−	1.57491i
$630$	14.7907	+	24.8348i	0.589277	+	0.989441i
$631$	14.5897	+	25.2701i	0.580808	+	1.00599i	0.995384	+	0.0959739i	$0.0305965\pi$
$631$	14.5897	+	25.2701i	0.580808	+	1.00599i	−0.414576	+	0.910015i	$0.636070\pi$
$632$	3.54368	−	20.0972i	0.140960	−	0.799423i
$633$	23.5621	−	13.8433i	0.936508	−	0.550223i
$634$	−22.3382	−	8.13044i	−0.887163	−	0.322901i
$635$	8.04743	−	6.75260i	0.319353	−	0.267969i
$636$	−0.112431	−	14.7969i	−0.00445818	−	0.586734i
$637$	1.23264	−	0.444064i	0.0488390	−	0.0175945i
$638$	−6.42805	−	11.1337i	−0.254489	−	0.440788i
$639$	−1.62874	−	8.48127i	−0.0644318	−	0.335514i
$640$	13.4603	+	23.3139i	0.532065	+	0.921563i
$641$	7.93557	−	45.0049i	0.313436	−	1.77759i	−0.267421	−	0.963580i	$-0.586171\pi$
$641$	7.93557	−	45.0049i	0.313436	−	1.77759i	0.580857	−	0.814005i	$-0.302717\pi$
$642$	42.7714	+	50.1934i	1.68805	+	1.98098i
$643$	−1.84788	+	1.55055i	−0.0728732	+	0.0611479i	−0.678497	−	0.734603i	$-0.737368\pi$
$643$	−1.84788	+	1.55055i	−0.0728732	+	0.0611479i	0.605623	+	0.795751i	$0.292924\pi$
$644$	11.0110	+	63.0519i	0.433894	+	2.48459i
$645$	8.42157	+	22.6022i	0.331599	+	0.889963i
$646$	−5.03045	+	1.83093i	−0.197920	+	0.0720371i
$647$	−10.6983	+	18.5300i	−0.420594	+	0.728491i	−0.995998	−	0.0893790i	$-0.971512\pi$
$647$	−10.6983	+	18.5300i	−0.420594	+	0.728491i	0.575403	+	0.817870i	$0.304845\pi$
$648$	−20.4046	+	8.13704i	−0.801568	+	0.319653i
$649$	−0.335589	−	0.581257i	−0.0131730	−	0.0228163i
$650$	0.175173	−	0.993454i	0.00687084	−	0.0389665i
$651$	−16.8658	−	2.87043i	−0.661022	−	0.112501i
$652$	26.5962	+	9.68023i	1.04159	+	0.379107i
$653$	−39.5114	−	14.3810i	−1.54620	−	0.562771i	−0.578678	−	0.815556i	$-0.696431\pi$
$653$	−39.5114	−	14.3810i	−1.54620	−	0.562771i	−0.967522	+	0.252785i	$0.918653\pi$
$654$	15.7765	−	44.3922i	0.616910	−	1.73587i
$655$	0.633345	−	3.59188i	0.0247469	−	0.140346i
$656$	7.36741			0.287649
$657$	0.0197083	+	0.102626i	0.000768893	+	0.00400384i
$658$	4.49758	+	7.81967i	0.175334	+	0.304842i
$659$	18.8582	+	15.8239i	0.734612	+	0.616413i	0.931385	−	0.364036i	$-0.118602\pi$
$659$	18.8582	+	15.8239i	0.734612	+	0.616413i	−0.196772	+	0.980449i	$0.563046\pi$
$660$	−7.17469	+	4.21532i	−0.279274	+	0.164081i
$661$	−18.3545	−	6.68048i	−0.713906	−	0.259841i	−0.0405697	−	0.999177i	$-0.512917\pi$
$661$	−18.3545	−	6.68048i	−0.713906	−	0.259841i	−0.673337	+	0.739336i	$0.735140\pi$
$662$	−53.1952	−	19.3615i	−2.06749	−	0.752505i
$663$	−0.0115971	−	1.52628i	−0.000450395	−	0.0592758i
$664$	25.7281	+	21.5885i	0.998445	+	0.837795i
$665$	−1.07466	−	1.86845i	−0.0416737	−	0.0724556i
$666$	−31.8933	+	57.2321i	−1.23584	+	2.21770i
$667$	−46.3841			−1.79600
$668$	4.58756	−	26.0174i	0.177498	−	1.00664i
$669$	−17.8055	+	3.27928i	−0.688401	+	0.126784i
$670$	10.9124	+	3.97179i	0.421583	+	0.153444i
$671$	−8.05933	−	2.93336i	−0.311127	−	0.113241i
$672$	18.6458	−	22.4919i	0.719277	−	0.867643i
$673$	−3.20923	+	18.2004i	−0.123707	+	0.701575i	0.858361	+	0.513046i	$0.171483\pi$
$673$	−3.20923	+	18.2004i	−0.123707	+	0.701575i	−0.982068	+	0.188529i	$0.939628\pi$
$674$	−12.2048	−	21.1393i	−0.470111	−	0.814256i
$675$	−4.51359	−	11.5732i	−0.173728	−	0.445451i
$676$	19.9832	−	34.6120i	0.768585	−	1.33123i
$677$	−6.42342	+	2.33793i	−0.246872	+	0.0898540i	−0.462492	−	0.886623i	$-0.653045\pi$
$677$	−6.42342	+	2.33793i	−0.246872	+	0.0898540i	0.215621	+	0.976477i	$0.430823\pi$
$678$	42.0441	−	50.8865i	1.61470	−	1.95428i
$679$	−4.59417	−	26.3074i	−0.176308	−	1.00959i
$680$	14.2201	−	11.9321i	0.545317	−	0.457575i
$681$	5.90918	−	1.08831i	0.226440	−	0.0417040i
$682$	1.41012	−	7.99718i	0.0539962	−	0.306228i
$683$	8.17274	+	14.1556i	0.312721	+	0.541649i	0.978950	−	0.204098i	$-0.0654261\pi$
$683$	8.17274	+	14.1556i	0.312721	+	0.541649i	−0.666229	+	0.745747i	$0.732093\pi$
$684$	4.35810	−	1.66164i	0.166636	−	0.0635345i
$685$	−8.63898	−	14.9631i	−0.330078	−	0.571713i
$686$	7.45293	−	41.0829i	0.284554	−	1.56855i
$687$	−29.1823	+	17.1454i	−1.11338	+	0.654137i
$688$	4.37565	−	3.67160i	0.166820	−	0.139979i
$689$	−0.487438	−	0.177413i	−0.0185699	−	0.00675889i
$690$	0.376118	+	49.5003i	0.0143186	+	1.88445i
$691$	−4.69295	+	26.6151i	−0.178528	+	1.01248i	0.755464	+	0.655191i	$0.227412\pi$
$691$	−4.69295	+	26.6151i	−0.178528	+	1.01248i	−0.933992	+	0.357294i	$0.883699\pi$
$692$	−30.1568	−	52.2332i	−1.14639	−	1.98561i
$693$	5.93252	+	4.84249i	0.225358	+	0.183951i
$694$	1.88941	−	3.27256i	0.0717212	−	0.124225i
$695$	−6.77659	−	5.68623i	−0.257051	−	0.215691i
$696$	−16.2063	−	19.0186i	−0.614299	−	0.720897i
$697$	−9.09078	−	51.5564i	−0.344338	−	1.95284i
$698$	3.61704	+	20.5132i	0.136907	+	0.776437i
$699$	−0.0168098	+	0.0203451i	−0.000635806	+	0.000769523i
$700$	−14.9157	−	12.5575i	−0.563760	−	0.474631i
$701$	−10.3899			−0.392422			−0.196211	−	0.980562i	$-0.562864\pi$
$701$	−10.3899			−0.392422			−0.196211	+	0.980562i	$0.562864\pi$
$702$	0.0499751	+	2.19205i	0.00188619	+	0.0827335i
$703$	2.44284	−	4.23112i	0.0921333	−	0.159580i
$704$	9.64359	+	8.09193i	0.363457	+	0.304976i
$705$	1.47738	+	3.96506i	0.0556413	+	0.149333i
$706$	−35.3488	−	12.8659i	−1.33037	−	0.484215i
$707$	−4.18897	+	3.50325i	−0.157542	+	0.131753i
$708$	−2.40907	−	2.82711i	−0.0905383	−	0.106249i
$709$	1.99047	+	1.67020i	0.0747536	+	0.0627257i	0.679399	−	0.733769i	$-0.262241\pi$
$709$	1.99047	+	1.67020i	0.0747536	+	0.0627257i	−0.604645	+	0.796495i	$0.706685\pi$
$710$	−5.24186	−	9.07916i	−0.196723	−	0.340735i
$711$	−25.0797	+	0.381148i	−0.940562	+	0.0142942i
$712$	13.9275	−	24.1232i	0.521956	−	0.904054i
$713$	−22.4440	−	18.8327i	−0.840533	−	0.705291i
$714$	−42.2687	−	24.0693i	−1.58187	−	0.900772i
$715$	0.0506542	+	0.287274i	0.00189436	+	0.0107434i
$716$	13.8200	−	11.5964i	0.516478	−	0.433377i
$717$	−16.9149	−	9.59518i	−0.631697	−	0.358339i
$718$	14.5177	−	5.28401i	0.541795	−	0.197197i
$719$	2.82487	−	4.89282i	0.105350	−	0.182471i	−0.808531	−	0.588453i	$-0.799737\pi$
$719$	2.82487	−	4.89282i	0.105350	−	0.182471i	0.913881	+	0.405982i	$0.133070\pi$
$720$	2.42802	−	2.10104i	0.0904869	−	0.0783012i
$721$	23.3809	+	40.6509i	0.870749	+	1.51392i
$722$	39.7129	−	14.4543i	1.47796	−	0.537933i
$723$	−33.9249	−	39.8119i	−1.26168	−	1.48062i
$724$	0.354803	+	2.01219i	0.0131861	+	0.0747824i
$725$	10.8241	−	9.08247i	0.401996	−	0.337315i
$726$	25.0439	−	30.3109i	0.929467	−	1.12494i
$727$	0.0852680	−	0.483579i	0.00316241	−	0.0179349i	−0.983186	−	0.182608i	$-0.941546\pi$
$727$	0.0852680	−	0.483579i	0.00316241	−	0.0179349i	0.986348	+	0.164674i	$0.0526570\pi$
$728$	0.602628	+	1.04775i	0.0223349	+	0.0388323i
$729$	14.5516	+	22.7432i	0.538948	+	0.842339i
$730$	0.0634283	+	0.109861i	0.00234759	+	0.00406614i
$731$	−31.0927	−	26.0899i	−1.15001	−	0.964969i
$732$	−46.8031	−	7.88646i	−1.72989	−	0.291492i
$733$	−4.35051	−	24.6730i	−0.160690	−	0.911316i	−0.953398	−	0.301715i	$-0.902441\pi$
$733$	−4.35051	−	24.6730i	−0.160690	−	0.911316i	0.792708	−	0.609601i	$-0.208670\pi$
$734$	−12.4097	+	10.4130i	−0.458050	+	0.384350i
$735$	6.61905	−	18.4327i	0.244147	−	0.679899i
$736$	47.0153	−	17.1122i	1.73301	−	0.630763i
$737$	3.07657			0.113327
$738$	14.1831	+	73.8555i	0.522089	+	2.71866i
$739$	−9.83748			−0.361877			−0.180939	−	0.983494i	$-0.557914\pi$
$739$	−9.83748			−0.361877			−0.180939	+	0.983494i	$0.557914\pi$
$740$	−8.37644	+	47.5052i	−0.307924	+	1.74632i
$741$	−0.00124230	−	0.163497i	−4.56369e−5	−	0.00600620i
$742$	−12.6807	+	10.6049i	−0.465523	+	0.389319i
$743$	−1.59945	−	9.07091i	−0.0586780	−	0.332779i	0.941311	−	0.337541i	$-0.109595\pi$
$743$	−1.59945	−	9.07091i	−0.0586780	−	0.332779i	−0.999989	+	0.00476202i	$0.998484\pi$
$744$	−0.119921	−	15.7826i	−0.00439650	−	0.578617i
$745$	17.8190	−	6.48558i	0.652837	−	0.237613i
$746$	−66.0592			−2.41860
$747$	20.0945	−	36.0593i	0.735220	−	1.31934i
$748$	7.00144	−	12.1269i	0.255998	−	0.443402i
$749$	7.83110	−	43.9898i	0.286142	−	1.60735i
$750$	−30.2360	−	35.4828i	−1.10406	−	1.29565i
$751$	37.5722	+	13.6752i	1.37103	+	0.499014i	0.919446	−	0.393215i	$-0.128637\pi$
$751$	37.5722	+	13.6752i	1.37103	+	0.499014i	0.451583	+	0.892229i	$0.350860\pi$
$752$	0.767610	−	0.644101i	0.0279919	−	0.0234880i
$753$	8.72928	−	10.5651i	0.318113	−	0.385015i
$754$	−2.34362	+	0.853008i	−0.0853497	+	0.0310647i
$755$	0.353107			0.0128509
$756$	37.1416	+	20.4087i	1.35083	+	0.742258i
$757$	28.8482			1.04850			0.524252	−	0.851563i	$-0.324345\pi$
$757$	28.8482			1.04850			0.524252	+	0.851563i	$0.324345\pi$
$758$	−0.706376	+	0.257100i	−0.0256567	+	0.00933829i
$759$	4.57894	+	12.2892i	0.166205	+	0.446069i
$760$	1.52328	−	1.27818i	0.0552550	−	0.0463645i
$761$	−17.4626	−	6.35586i	−0.633018	−	0.230400i	0.00552629	−	0.999985i	$-0.498241\pi$
$761$	−17.4626	−	6.35586i	−0.633018	−	0.230400i	−0.638544	+	0.769585i	$0.720463\pi$
$762$	8.50392	−	23.9285i	0.308065	−	0.866838i
$763$	−30.0139	+	10.8684i	−1.08657	+	0.393461i
$764$	−13.6006	+	23.5569i	−0.492051	+	0.852258i
$765$	−17.6988	−	14.3985i	−0.639903	−	0.520579i
$766$	−32.4757			−1.17340
$767$	−0.122353	+	0.0445330i	−0.00441792	+	0.00160799i
$768$	17.2891	+	9.80745i	0.623865	+	0.353896i
$769$	3.72729	+	21.1385i	0.134409	+	0.762274i	0.975269	+	0.221021i	$0.0709389\pi$
$769$	3.72729	+	21.1385i	0.134409	+	0.762274i	−0.840860	+	0.541253i	$0.817950\pi$
$770$	8.73030	+	3.19382i	0.314618	+	0.115097i
$771$	0.898815	−	0.528077i	0.0323700	−	0.0190182i
$772$	4.60851	−	26.1362i	0.165864	−	0.940661i
$773$	−18.6930			−0.672340			−0.336170	−	0.941801i	$-0.609132\pi$
$773$	−18.6930			−0.672340			−0.336170	+	0.941801i	$0.609132\pi$
$774$	45.2301	+	36.7959i	1.62576	+	1.32260i
$775$	8.92509			0.320599
$776$	23.1511	−	8.42630i	0.831075	−	0.302486i
$777$	43.6713	−	7.96889i	1.56670	−	0.285882i
$778$	39.4583	−	33.1094i	1.41465	−	1.18703i
$779$	−0.973815	−	5.52278i	−0.0348905	−	0.197874i
$780$	0.563636	+	1.51272i	0.0201814	+	0.0541639i
$781$	−2.12765	−	1.78531i	−0.0761334	−	0.0638835i
$782$	−41.6499	−	72.1398i	−1.48940	−	2.57971i
$783$	−19.1997	+	23.9703i	−0.686141	+	0.856629i
$784$	−4.63799	−	0.0152358i	−0.165643	−	0.000544136i
$785$	−6.08268	+	34.4966i	−0.217100	+	1.23124i
$786$	−3.07838	−	8.26191i	−0.109802	−	0.294692i
$787$	6.04767	−	5.07460i	0.215576	−	0.180890i	−0.528604	−	0.848868i	$-0.677285\pi$
$787$	6.04767	−	5.07460i	0.215576	−	0.180890i	0.744181	+	0.667978i	$0.232840\pi$
$788$	9.10019	+	51.6097i	0.324181	+	1.83852i
$789$	−0.301687	+	0.848891i	−0.0107403	+	0.0302213i
$790$	−28.6120	+	10.4139i	−1.01797	+	0.370511i
$791$	−44.7243	−	0.0734596i	−1.59021	−	0.00261192i
$792$	−3.43900	+	6.17123i	−0.122200	+	0.219285i
$793$	−0.831908	+	1.44091i	−0.0295419	+	0.0511681i
$794$	−47.8826	+	17.4279i	−1.69929	+	0.618491i
$795$	−6.68549	+	3.92790i	−0.237110	+	0.139308i
$796$	54.1197	−	45.4119i	1.91822	−	1.60958i
$797$	−0.0774178	−	0.439058i	−0.00274228	−	0.0155522i	0.983406	−	0.181419i	$-0.0580690\pi$
$797$	−0.0774178	−	0.439058i	−0.00274228	−	0.0155522i	−0.986148	+	0.165867i	$0.946958\pi$
$798$	−4.52787	−	2.57833i	−0.160285	−	0.0912720i
$799$	−5.45452	−	4.57689i	−0.192967	−	0.161919i
$800$	−7.62062	+	13.1993i	−0.269430	+	0.466666i
$801$	−32.3462	−	11.2194i	−1.14290	−	0.396419i
$802$	14.8805	+	25.7737i	0.525448	+	0.910102i
$803$	0.0257454	+	0.0216029i	0.000908534	+	0.000762351i
$804$	16.7442	−	3.08381i	0.590522	−	0.108758i
$805$	25.7286	−	21.5169i	0.906813	−	0.758371i
$806$	−1.48035	−	0.538802i	−0.0521430	−	0.0189785i
$807$	−0.168567	+	0.204019i	−0.00593384	+	0.00718180i
$808$	−3.85916	−	3.23822i	−0.135765	−	0.113920i
$809$	−23.7254	+	41.0936i	−0.834140	+	1.44477i	0.0605883	+	0.998163i	$0.480702\pi$
$809$	−23.7254	+	41.0936i	−0.834140	+	1.44477i	−0.894729	+	0.446610i	$0.852631\pi$
$810$	25.7364	+	20.2952i	0.904284	+	0.713101i
$811$	−16.8993			−0.593416			−0.296708	−	0.954968i	$-0.595889\pi$
$811$	−16.8993			−0.593416			−0.296708	+	0.954968i	$0.595889\pi$
$812$	−8.44871	+	47.4591i	−0.296492	+	1.66549i
$813$	−12.0157	−	32.2482i	−0.421407	−	1.13099i
$814$	3.65896	+	20.7510i	0.128246	+	0.727321i
$815$	−2.57541	−	14.6059i	−0.0902128	−	0.511622i
$816$	−1.80935	+	5.09117i	−0.0633398	+	0.178227i
$817$	−3.33068	−	2.79478i	−0.116526	−	0.0977769i
$818$	−3.01797	+	5.22728i	−0.105521	+	0.182767i
$819$	1.12500	−	0.970271i	0.0393106	−	0.0339040i
$820$	27.6848	+	47.9515i	0.966795	+	1.67454i
$821$	2.80743	−	15.9217i	0.0979798	−	0.555671i	−0.895814	−	0.444430i	$-0.853406\pi$
$821$	2.80743	−	15.9217i	0.0979798	−	0.555671i	0.993793	−	0.111241i	$-0.0354826\pi$
$822$	−36.3288	−	20.6080i	−1.26711	−	0.718786i
$823$	−21.8344	−	7.94707i	−0.761099	−	0.277017i	−0.0678307	−	0.997697i	$-0.521608\pi$
$823$	−21.8344	−	7.94707i	−0.761099	−	0.277017i	−0.693268	+	0.720679i	$0.743830\pi$
$824$	−33.1410	+	27.8086i	−1.15452	+	0.968760i
$825$	−3.47487	−	1.97117i	−0.120979	−	0.0686272i
$826$	−0.727252	+	4.08520i	−0.0253043	+	0.142142i
$827$	−1.36430	−	2.36304i	−0.0474415	−	0.0821710i	0.841330	−	0.540523i	$-0.181773\pi$
$827$	−1.36430	−	2.36304i	−0.0474415	−	0.0821710i	−0.888771	+	0.458352i	$0.848440\pi$
$828$	37.2390	+	62.2941i	1.29414	+	2.16487i
$829$	−6.01275	−	10.4144i	−0.208831	−	0.361706i	0.742515	−	0.669829i	$-0.233633\pi$
$829$	−6.01275	−	10.4144i	−0.208831	−	0.361706i	−0.951347	+	0.308123i	$0.900299\pi$
$830$	8.70168	−	49.3497i	0.302040	−	1.71295i
$831$	−3.17939	+	8.94623i	−0.110292	+	0.310341i
$832$	1.87082	−	1.56980i	0.0648589	−	0.0544231i
$833$	5.61628	+	32.4750i	0.194593	+	1.12519i
$834$	−21.0871	−	3.55324i	−0.730187	−	0.123039i
$835$	−13.0089	+	4.73484i	−0.450191	+	0.163856i
$836$	0.750003	−	1.29904i	0.0259394	−	0.0449283i
$837$	−19.0225	+	3.80316i	−0.657515	+	0.131456i
$838$	32.0862	+	55.5750i	1.10840	+	1.91981i
$839$	−7.27989	+	41.2863i	−0.251330	+	1.42536i	0.553991	+	0.832522i	$0.313104\pi$
$839$	−7.27989	+	41.2863i	−0.251330	+	1.42536i	−0.805321	+	0.592839i	$0.798007\pi$
$840$	17.8118	+	3.03144i	0.614566	+	0.104595i
$841$	−5.57566	−	2.02937i	−0.192264	−	0.0699784i
$842$	51.7695	+	18.8426i	1.78410	+	0.649358i
$843$	21.9271	+	25.7321i	0.755209	+	0.886260i
$844$	8.44575	−	47.8982i	0.290715	−	1.64872i
$845$	−20.9429			−0.720459
$846$	7.93461	+	6.45503i	0.272798	+	0.221928i
$847$	−26.6404	−	0.0437568i	−0.915375	−	0.00150350i
$848$	1.40665	+	1.18032i	0.0483045	+	0.0405323i
$849$	34.0569	+	19.3192i	1.16883	+	0.663035i
$850$	23.8450	+	8.67886i	0.817876	+	0.297682i
$851$	71.4386	+	26.0015i	2.44889	+	0.891321i
$852$	−13.3693	−	7.58390i	−0.458024	−	0.259820i
$853$	14.2353	+	11.9448i	0.487406	+	0.408982i	0.853096	−	0.521754i	$-0.174722\pi$
$853$	14.2353	+	11.9448i	0.487406	+	0.408982i	−0.365689	+	0.930737i	$0.619167\pi$
$854$	26.4360	+	45.9627i	0.904622	+	1.57281i
$855$	−1.89592	−	1.54238i	−0.0648391	−	0.0527484i
$856$	41.2202			1.40888
$857$	−10.1401	+	57.5074i	−0.346379	+	1.96442i	−0.101675	+	0.994818i	$0.532420\pi$
$857$	−10.1401	+	57.5074i	−0.346379	+	1.96442i	−0.244704	+	0.969598i	$0.578691\pi$
$858$	0.457356	+	0.536720i	0.0156139	+	0.0183233i
$859$	−27.3328	−	9.94833i	−0.932584	−	0.339433i	−0.169351	−	0.985556i	$-0.554167\pi$
$859$	−27.3328	−	9.94833i	−0.932584	−	0.339433i	−0.763233	+	0.646123i	$0.776389\pi$
$860$	40.3395	+	14.6824i	1.37556	+	0.500665i
$861$	32.5205	−	39.2285i	1.10829	−	1.33690i
$862$	−9.32557	+	52.8879i	−0.317630	+	1.80137i
$863$	1.95160	+	3.38027i	0.0664332	+	0.115066i	0.897329	−	0.441363i	$-0.145505\pi$
$863$	1.95160	+	3.38027i	0.0664332	+	0.115066i	−0.830896	+	0.556428i	$0.812171\pi$
$864$	10.6178	−	31.3797i	0.361223	−	1.06756i
$865$	−15.8026	+	27.3709i	−0.537304	+	0.930638i
$866$	−69.2885	+	25.2190i	−2.35452	+	0.856975i
$867$	8.82456	+	1.48696i	0.299698	+	0.0505000i
$868$	−23.3572	+	19.5338i	−0.792797	+	0.663019i
$869$	−6.17943	+	5.18516i	−0.209623	+	0.175894i
$870$	−12.4845	+	35.1290i	−0.423263	+	1.19098i
$871$	0.103640	−	0.587774i	0.00351172	−	0.0199159i
$872$	−14.7242	−	25.5030i	−0.498623	−	0.863641i
$873$	−15.5374	−	25.9912i	−0.525860	−	0.879670i
$874$	−4.46158	−	7.72769i	−0.150915	−	0.261393i
$875$	−5.53598	+	31.0973i	−0.187150	+	1.05128i
$876$	0.161773	+	0.0917678i	0.00546580	+	0.00310055i
$877$	30.9522	−	25.9720i	1.04518	−	0.877013i	0.0526043	−	0.998615i	$-0.483248\pi$
$877$	30.9522	−	25.9720i	1.04518	−	0.877013i	0.992579	+	0.121603i	$0.0388033\pi$
$878$	51.8629	+	18.8765i	1.75029	+	0.637052i
$879$	−17.5715	−	9.96770i	−0.592674	−	0.336202i
$880$	0.179314	−	1.01694i	0.00604467	−	0.0342810i
$881$	−2.36050	−	4.08851i	−0.0795274	−	0.137745i	0.823519	−	0.567289i	$-0.192008\pi$
$881$	−2.36050	−	4.08851i	−0.0795274	−	0.137745i	−0.903046	+	0.429544i	$0.858674\pi$
$882$	−8.77595	−	46.5234i	−0.295502	−	1.56653i
$883$	27.0064	−	46.7765i	0.908838	−	1.57415i	0.0931577	−	0.995651i	$-0.470304\pi$
$883$	27.0064	−	46.7765i	0.908838	−	1.57415i	0.815681	−	0.578503i	$-0.196363\pi$
$884$	−2.08096	−	1.74613i	−0.0699903	−	0.0587288i
$885$	−0.651776	+	1.83398i	−0.0219092	+	0.0616485i
$886$	−1.45037	−	8.22546i	−0.0487261	−	0.276340i
$887$	−6.28643	−	35.6521i	−0.211078	−	1.19708i	−0.887585	−	0.460644i	$-0.847618\pi$
$887$	−6.28643	−	35.6521i	−0.211078	−	1.19708i	0.676507	−	0.736436i	$-0.263493\pi$
$888$	14.2990	+	38.3763i	0.479842	+	1.28782i
$889$	−16.1782	+	5.85831i	−0.542600	+	0.196482i
$890$	−41.5607			−1.39312
$891$	8.24613	+	2.72054i	0.276256	+	0.0911416i
$892$	−16.1113	+	27.9056i	−0.539447	+	0.934350i
$893$	−0.584295	−	0.490281i	−0.0195527	−	0.0164066i
$894$	29.1972	−	35.3377i	0.976500	−	1.18187i
$895$	−8.88347	−	3.23332i	−0.296942	−	0.108078i
$896$	−7.58529	−	43.4354i	−0.253407	−	1.45107i
$897$	2.50208	−	0.460813i	0.0835421	−	0.0153861i
$898$	15.3904	+	12.9141i	0.513584	+	0.430948i
$899$	−11.0329	−	19.1095i	−0.367966	−	0.637337i
$900$	−20.8878	−	7.24501i	−0.696259	−	0.241500i
$901$	6.52406	−	11.3000i	0.217348	−	0.376458i
$902$	18.5278	+	15.5466i	0.616907	+	0.517646i
$903$	−0.235283	−	39.5054i	−0.00782973	−	1.31466i
$904$	−7.16470	−	40.6331i	−0.238295	−	1.35144i
$905$	0.820188	−	0.688219i	0.0272640	−	0.0228772i
$906$	0.735960	−	0.432395i	0.0244506	−	0.0143654i
$907$	47.2375	−	17.1931i	1.56850	−	0.570886i	0.595833	−	0.803108i	$-0.296822\pi$
$907$	47.2375	−	17.1931i	1.56850	−	0.570886i	0.972663	+	0.232222i	$0.0745996\pi$
$908$	5.34692	−	9.26114i	0.177444	−	0.307342i
$909$	−3.01413	+	5.40881i	−0.0999725	+	0.179399i
$910$	0.904272	−	1.56032i	0.0299763	−	0.0517242i
$911$	−10.2931	+	3.74638i	−0.341026	+	0.124123i	−0.506855	−	0.862031i	$-0.669192\pi$
$911$	−10.2931	+	3.74638i	−0.341026	+	0.124123i	0.165829	+	0.986154i	$0.446970\pi$
$912$	−0.193819	+	0.545372i	−0.00641800	+	0.0180591i
$913$	−2.30534	−	13.0742i	−0.0762956	−	0.432694i
$914$	12.5132	−	10.4998i	0.413901	−	0.347304i
$915$	8.68378	+	23.3060i	0.287077	+	0.770472i
$916$	−10.4603	+	59.3234i	−0.345619	+	1.96010i
$917$	−2.99541	+	5.16858i	−0.0989171	+	0.170681i
$918$	−54.5203	−	8.33691i	−1.79944	−	0.275159i
$919$	6.42767	+	11.1330i	0.212029	+	0.367245i	0.952349	−	0.305009i	$-0.0986595\pi$
$919$	6.42767	+	11.1330i	0.212029	+	0.367245i	−0.740320	+	0.672254i	$0.765326\pi$
$920$	23.7029	+	19.8891i	0.781462	+	0.655724i
$921$	−5.54861	−	14.8916i	−0.182833	−	0.490696i
$922$	−2.11247	−	11.9804i	−0.0695705	−	0.394554i
$923$	−0.412756	+	0.346343i	−0.0135860	+	0.0114000i
$924$	13.4080	−	2.44662i	0.441091	−	0.0804878i
$925$	−21.7621	+	7.92075i	−0.715532	+	0.260433i
$926$	10.0438			0.330060
$927$	41.2485	+	33.5568i	1.35478	+	1.10215i
$928$	37.6813			1.23695
$929$	−4.60291	+	26.1044i	−0.151017	+	0.856457i	0.811321	+	0.584601i	$0.198749\pi$
$929$	−4.60291	+	26.1044i	−0.151017	+	0.856457i	−0.962338	+	0.271857i	$0.912362\pi$
$930$	−20.3038	+	11.9290i	−0.665789	+	0.391168i
$931$	0.601623	+	3.47876i	0.0197174	+	0.114012i
$932$	0.00815629	+	0.0462566i	0.000267168	+	0.00151519i
$933$	10.8881	+	6.17642i	0.356460	+	0.202207i
$934$	60.7569	−	22.1137i	1.98803	−	0.723583i
$935$	−7.33770			−0.239968
$936$	1.06315	+	0.864906i	0.0347503	+	0.0282703i
$937$	−15.7304	+	27.2459i	−0.513890	+	0.890083i	0.485980	+	0.873970i	$0.338463\pi$
$937$	−15.7304	+	27.2459i	−0.513890	+	0.890083i	−0.999870	+	0.0161137i	$0.994871\pi$
$938$	−14.5503	−	12.2499i	−0.475084	−	0.399974i
$939$	−2.67619	+	7.53031i	−0.0873341	+	0.245742i
$940$	7.07667	+	2.57570i	0.230815	+	0.0840099i
$941$	19.6665	−	16.5022i	0.641111	−	0.537956i	−0.263248	−	0.964728i	$-0.584794\pi$
$941$	19.6665	−	16.5022i	0.641111	−	0.537956i	0.904359	+	0.426772i	$0.140349\pi$
$942$	29.5649	+	79.3477i	0.963276	+	2.58529i
$943$	82.0002	−	29.8456i	2.67029	−	0.971908i
$944$	0.460923			0.0150018
$945$	−0.469694	−	22.2024i	−0.0152792	−	0.722244i
$946$	18.7518			0.609673
$947$	24.2480	−	8.82557i	0.787956	−	0.286792i	0.0834696	−	0.996510i	$-0.473400\pi$
$947$	24.2480	−	8.82557i	0.787956	−	0.286792i	0.704486	+	0.709718i	$0.251178\pi$
$948$	−28.4341	+	34.4142i	−0.923498	+	1.11772i
$949$	0.00499449	−	0.00419088i	0.000162128	−	0.000136042i
$950$	2.55430	+	0.929689i	0.0828724	+	0.0301631i
$951$	11.8453	+	13.9009i	0.384112	+	0.450766i
$952$	−28.5875	+	10.3519i	−0.926528	+	0.335506i
$953$	−11.0856	+	19.2009i	−0.359098	+	0.621977i	−0.987810	−	0.155661i	$-0.950249\pi$
$953$	−11.0856	+	19.2009i	−0.359098	+	0.621977i	0.628712	+	0.777638i	$0.283582\pi$
$954$	−9.12428	+	16.3734i	−0.295410	+	0.530108i
$955$	14.2538			0.461241
$956$	−32.5236	+	11.8376i	−1.05189	+	0.382856i
$957$	0.0750462	+	9.87671i	0.00242590	+	0.319269i
$958$	−4.39256	−	24.9114i	−0.141917	−	0.804852i
$959$	4.86833	+	27.8774i	0.157207	+	0.900207i
$960$	−0.277378	−	36.5053i	−0.00895234	−	1.17820i
$961$	−2.96282	+	16.8030i	−0.0955749	+	0.542032i
$962$	4.08770			0.131793
$963$	−9.55486	−	49.7548i	−0.307901	−	1.60332i
$964$	−93.0921			−2.99829
$965$	−13.0683	+	4.75647i	−0.420683	+	0.153116i
$966$	27.2761	−	76.3522i	0.877594	−	2.45659i
$967$	−26.4029	+	22.1546i	−0.849059	+	0.712445i	−0.959582	−	0.281428i	$-0.909192\pi$
$967$	−26.4029	+	22.1546i	−0.849059	+	0.712445i	0.110523	+	0.993874i	$0.464747\pi$
$968$	−4.26771	−	24.2034i	−0.137169	−	0.777927i
$969$	4.05562	+	0.683383i	0.130285	+	0.0219534i
$970$	−28.1590	−	23.6282i	−0.904132	−	0.758657i
$971$	−0.797770	−	1.38178i	−0.0256017	−	0.0443434i	0.852941	−	0.522008i	$-0.174817\pi$
$971$	−0.797770	−	1.38178i	−0.0256017	−	0.0443434i	−0.878542	+	0.477664i	$0.841483\pi$
$972$	47.6065	+	6.54099i	1.52698	+	0.209802i
$973$	7.22390	+	12.5598i	0.231588	+	0.402648i
$974$	10.8343	−	61.4443i	0.347153	−	1.96880i
$975$	−0.493647	+	0.597466i	−0.0158093	+	0.0191342i
$976$	4.51188	−	3.78592i	0.144422	−	0.121184i
$977$	2.95474	+	16.7572i	0.0945306	+	0.536109i	0.994890	+	0.100963i	$0.0321923\pi$
$977$	2.95474	+	16.7572i	0.0945306	+	0.536109i	−0.900360	+	0.435147i	$0.856697\pi$
$978$	−23.2534	−	27.2885i	−0.743560	−	0.872590i
$979$	−10.3467	+	3.76588i	−0.330681	+	0.120358i
$980$	−17.3292	−	30.2440i	−0.553560	−	0.966110i
$981$	−27.3703	+	23.6844i	−0.873866	+	0.756184i
$982$	−33.9113	+	58.7361i	−1.08215	+	1.87434i
$983$	−8.18574	+	2.97936i	−0.261084	+	0.0950270i	−0.469246	−	0.883067i	$-0.655474\pi$
$983$	−8.18574	+	2.97936i	−0.261084	+	0.0950270i	0.208162	+	0.978094i	$0.433252\pi$
$984$	40.8877	+	23.1941i	1.30345	+	0.739402i
$985$	21.0366	−	17.6518i	0.670283	−	0.562434i
$986$	−10.8940	−	61.7828i	−0.346935	−	1.96757i
$987$	−0.0412752	−	6.93034i	−0.00131380	−	0.220595i
$988$	−0.222915	−	0.187048i	−0.00709187	−	0.00595078i
$989$	33.8277	−	58.5913i	1.07566	−	1.86310i
$990$	10.5396	−	0.160176i	0.334972	−	0.00509072i
$991$	−19.5540	−	33.8686i	−0.621154	−	1.07587i	−0.989271	−	0.146091i	$-0.953331\pi$
$991$	−19.5540	−	33.8686i	−0.621154	−	1.07587i	0.368117	−	0.929779i	$-0.380002\pi$
$992$	18.2329	+	15.2992i	0.578895	+	0.485751i
$993$	28.2080	+	33.1029i	0.895153	+	1.05049i
$994$	2.95395	+	16.9151i	0.0936936	+	0.536514i
$995$	−34.7880	−	12.6618i	−1.10285	−	0.401406i
$996$	−25.6518	−	68.8457i	−0.812809	−	2.18146i
$997$	−15.5949	−	13.0857i	−0.493896	−	0.414428i	0.361524	−	0.932363i	$-0.382257\pi$
$997$	−15.5949	−	13.0857i	−0.493896	−	0.414428i	−0.855420	+	0.517935i	$0.826701\pi$
$998$	14.3230	−	24.8081i	0.453385	−	0.785286i
$999$	43.0075	−	26.1552i	1.36070	−	0.827513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.25.3	yes	132
3.2	odd	2		567.2.w.a.235.20		132
7.2	even	3		189.2.u.a.79.20	yes	132
21.2	odd	6		567.2.u.a.478.3		132
27.13	even	9		189.2.u.a.67.20	✓	132
27.14	odd	18		567.2.u.a.172.3		132
189.121	even	9	inner	189.2.w.a.121.3	yes	132
189.149	odd	18		567.2.w.a.415.20		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.20	✓	132	27.13	even	9
189.2.u.a.79.20	yes	132	7.2	even	3
189.2.w.a.25.3	yes	132	1.1	even	1	trivial
189.2.w.a.121.3	yes	132	189.121	even	9	inner
567.2.u.a.172.3		132	27.14	odd	18
567.2.u.a.478.3		132	21.2	odd	6
567.2.w.a.235.20		132	3.2	odd	2
567.2.w.a.415.20		132	189.149	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.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.11851 + 0.771075i) q^{2} +(1.70797 + 0.287798i) q^{3} +(2.36145 - 1.98149i) q^{4} +(-1.51793 - 0.552482i) q^{5} +(-3.84028 + 0.707271i) q^{6} +(2.02397 + 1.70398i) q^{7} +(-1.22040 + 2.11380i) q^{8} +(2.83434 + 0.983104i) q^{9} +O(q^{10})\)	\(q+(-2.11851 + 0.771075i) q^{2} +(1.70797 + 0.287798i) q^{3} +(2.36145 - 1.98149i) q^{4} +(-1.51793 - 0.552482i) q^{5} +(-3.84028 + 0.707271i) q^{6} +(2.02397 + 1.70398i) q^{7} +(-1.22040 + 2.11380i) q^{8} +(2.83434 + 0.983104i) q^{9} +3.64176 q^{10} +(0.906628 - 0.329986i) q^{11} +(4.60356 - 2.70471i) q^{12} +(-0.0325017 - 0.184326i) q^{13} +(-5.60170 - 2.04928i) q^{14} +(-2.43358 - 1.38048i) q^{15} +(-0.115055 + 0.652508i) q^{16} +4.70815 q^{17} +(-6.76264 + 0.102775i) q^{18} +0.504342 q^{19} +(-4.67925 + 1.70311i) q^{20} +(2.96648 + 3.49285i) q^{21} +(-1.66626 + 1.39816i) q^{22} +(1.36276 + 7.72859i) q^{23} +(-2.69276 + 3.25908i) q^{24} +(-1.83134 - 1.53668i) q^{25} +(0.210985 + 0.365436i) q^{26} +(4.55805 + 2.49484i) q^{27} +(8.15591 + 0.0133961i) q^{28} +(-1.02634 + 5.82066i) q^{29} +(6.22003 + 1.04809i) q^{30} +(-2.85990 + 2.39974i) q^{31} +(-1.10707 - 6.27850i) q^{32} +(1.64347 - 0.302680i) q^{33} +(-9.97427 + 3.63034i) q^{34} +(-2.13082 - 3.70473i) q^{35} +(8.64116 - 3.29467i) q^{36} +(4.84361 - 8.38937i) q^{37} +(-1.06846 + 0.388886i) q^{38} +(-0.00246320 - 0.324178i) q^{39} +(3.02032 - 2.53435i) q^{40} +(-1.93086 - 10.9505i) q^{41} +(-8.97777 - 5.11227i) q^{42} +(-6.60401 - 5.54143i) q^{43} +(1.48709 - 2.57572i) q^{44} +(-3.75919 - 3.05821i) q^{45} +(-8.84634 - 15.3223i) q^{46} +(-1.15853 - 0.972120i) q^{47} +(-0.384301 + 1.08135i) q^{48} +(1.19289 + 6.89761i) q^{49} +(5.06461 + 1.84337i) q^{50} +(8.04140 + 1.35500i) q^{51} +(-0.441991 - 0.370875i) q^{52} +(1.38569 - 2.40009i) q^{53} +(-11.5800 - 1.77074i) q^{54} -1.55851 q^{55} +(-6.07193 + 2.19871i) q^{56} +(0.861403 + 0.145149i) q^{57} +(-2.31386 - 13.1225i) q^{58} +(-0.120799 - 0.685087i) q^{59} +(-8.48218 + 1.56218i) q^{60} +(-6.80963 - 5.71396i) q^{61} +(4.20835 - 7.28908i) q^{62} +(4.06143 + 6.81944i) q^{63} +(6.52397 + 11.2998i) q^{64} +(-0.0525016 + 0.297751i) q^{65} +(-3.24831 + 1.90847i) q^{66} +(2.99646 + 1.09062i) q^{67} +(11.1180 - 9.32915i) q^{68} +(0.103279 + 13.5924i) q^{69} +(7.37080 + 6.20550i) q^{70} +(-1.43937 - 2.49307i) q^{71} +(-5.53712 + 4.79145i) q^{72} +(0.0174169 + 0.0301670i) q^{73} +(-3.79240 + 21.5078i) q^{74} +(-2.68563 - 3.15166i) q^{75} +(1.19098 - 0.999349i) q^{76} +(2.39727 + 0.876998i) q^{77} +(0.255184 + 0.684876i) q^{78} +(-7.85664 + 2.85958i) q^{79} +(0.535144 - 0.926896i) q^{80} +(7.06701 + 5.57291i) q^{81} +(12.5342 + 21.7098i) q^{82} +(2.38942 - 13.5510i) q^{83} +(13.9262 + 2.37014i) q^{84} +(-7.14665 - 2.60117i) q^{85} +(18.2635 + 6.64738i) q^{86} +(-3.42814 + 9.64616i) q^{87} +(-0.408927 + 2.31914i) q^{88} -11.4122 q^{89} +(10.3220 + 3.58023i) q^{90} +(0.248306 - 0.428452i) q^{91} +(18.5322 + 15.5503i) q^{92} +(-5.57528 + 3.27562i) q^{93} +(3.20393 + 1.16614i) q^{94} +(-0.765557 - 0.278640i) q^{95} +(-0.0839014 - 11.0421i) q^{96} +(-7.73226 - 6.48814i) q^{97} +(-7.84572 - 13.6929i) q^{98} +(2.89411 - 0.0439831i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more