LMFDB - Embedded newform 71.2.g.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(2,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(70))

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

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

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

chi := DirichletCharacter("71.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.g (of order $35$, degree $24$, 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:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$5$ over $\Q(\zeta_{35})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	71.19
Dual form			71.2.g.a.15.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.569315 - 1.33198i) q^{2} +(1.33945 - 0.243074i) q^{3} +(-0.0679233 + 0.0710422i) q^{4} +(0.862898 + 2.65573i) q^{5} +(-1.08634 - 1.64573i) q^{6} +(-2.26960 - 1.98289i) q^{7} +(-2.57906 - 0.967939i) q^{8} +(-1.07366 + 0.402953i) q^{9} +O(q^{10})$	\(q+(-0.569315 - 1.33198i) q^{2} +(1.33945 - 0.243074i) q^{3} +(-0.0679233 + 0.0710422i) q^{4} +(0.862898 + 2.65573i) q^{5} +(-1.08634 - 1.64573i) q^{6} +(-2.26960 - 1.98289i) q^{7} +(-2.57906 - 0.967939i) q^{8} +(-1.07366 + 0.402953i) q^{9} +(3.04611 - 2.66131i) q^{10} +(4.37920 + 1.20858i) q^{11} +(-0.0737113 + 0.111668i) q^{12} +(-5.09730 + 1.40677i) q^{13} +(-1.34905 + 4.15196i) q^{14} +(1.80135 + 3.34747i) q^{15} +(0.187845 + 4.18270i) q^{16} +(1.64509 + 1.19523i) q^{17} +(1.14798 + 1.20069i) q^{18} +(1.57897 - 2.93423i) q^{19} +(-0.247280 - 0.119084i) q^{20} +(-3.52201 - 2.10430i) q^{21} +(-0.883339 - 6.52107i) q^{22} +(1.08502 + 4.75376i) q^{23} +(-3.68981 - 0.669601i) q^{24} +(-2.26321 + 1.64432i) q^{25} +(4.77575 + 5.98860i) q^{26} +(-4.84606 + 2.89539i) q^{27} +(0.295028 - 0.0265530i) q^{28} +(1.05301 - 7.77366i) q^{29} +(3.43322 - 4.30512i) q^{30} +(0.0798823 - 1.77872i) q^{31} +(0.500494 - 0.241025i) q^{32} +(6.15950 + 0.554365i) q^{33} +(0.655444 - 2.87169i) q^{34} +(3.30759 - 7.73849i) q^{35} +(0.0443001 - 0.103645i) q^{36} +(1.24145 - 5.43914i) q^{37} +(-4.80726 - 0.432661i) q^{38} +(-6.48563 + 3.12331i) q^{39} +(0.345112 - 7.68452i) q^{40} +(-2.63002 + 3.29794i) q^{41} +(-0.797755 + 5.88926i) q^{42} +(6.75768 - 0.608202i) q^{43} +(-0.383310 + 0.229017i) q^{44} +(-1.99659 - 2.50365i) q^{45} +(5.71420 - 4.15161i) q^{46} +(-9.05378 - 1.64302i) q^{47} +(1.26832 + 5.55686i) q^{48} +(0.279605 + 2.06412i) q^{49} +(3.47868 + 2.07841i) q^{50} +(2.49405 + 1.20107i) q^{51} +(0.246286 - 0.457675i) q^{52} +(0.00506880 + 0.00530155i) q^{53} +(6.61553 + 4.80646i) q^{54} +(0.569138 + 12.6728i) q^{55} +(3.93414 + 7.31085i) q^{56} +(1.40172 - 4.31406i) q^{57} +(-10.9539 + 3.02307i) q^{58} +(-2.15204 + 3.26021i) q^{59} +(-0.360165 - 0.0993992i) q^{60} +(-2.44931 + 2.13990i) q^{61} +(-2.41469 + 0.906249i) q^{62} +(3.23580 + 1.21442i) q^{63} +(5.70011 + 4.98004i) q^{64} +(-8.13443 - 12.3231i) q^{65} +(-2.76829 - 8.51993i) q^{66} +(3.36449 - 3.51898i) q^{67} +(-0.196652 + 0.0356870i) q^{68} +(2.60884 + 6.10369i) q^{69} -12.1906 q^{70} +(4.00722 - 7.41230i) q^{71} +3.15908 q^{72} +(0.0284136 + 0.0664769i) q^{73} +(-7.95159 + 1.44300i) q^{74} +(-2.63176 + 2.75261i) q^{75} +(0.101205 + 0.311476i) q^{76} +(-7.54257 - 11.4265i) q^{77} +(7.85256 + 6.86057i) q^{78} +(11.0228 + 4.13694i) q^{79} +(-10.9460 + 4.10811i) q^{80} +(-3.19642 + 2.79263i) q^{81} +(5.89009 + 1.62556i) q^{82} +(2.61121 - 3.95581i) q^{83} +(0.388721 - 0.107280i) q^{84} +(-1.75466 + 5.40027i) q^{85} +(-4.65736 - 8.65483i) q^{86} +(-0.479118 - 10.6684i) q^{87} +(-10.1244 - 7.35581i) q^{88} +(7.88631 + 8.24844i) q^{89} +(-2.19812 + 4.08479i) q^{90} +(14.3583 + 6.91460i) q^{91} +(-0.411416 - 0.245809i) q^{92} +(-0.325362 - 2.40192i) q^{93} +(2.96599 + 12.9948i) q^{94} +(9.15500 + 1.66139i) q^{95} +(0.611800 - 0.444499i) q^{96} +(-11.5705 - 14.5089i) q^{97} +(2.59019 - 1.54756i) q^{98} +(-5.18879 + 0.467000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) $ 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{8}{35}\right)$

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 $

$2$	−0.569315	−	1.33198i	−0.402567	−	0.941851i	−0.991068	−	0.133355i	$-0.957425\pi$
$2$	−0.569315	−	1.33198i	−0.402567	−	0.941851i	0.588502	−	0.808496i	$-0.299718\pi$
$3$	1.33945	−	0.243074i	0.773332	−	0.140339i	0.222475	−	0.974938i	$-0.428587\pi$
$3$	1.33945	−	0.243074i	0.773332	−	0.140339i	0.550857	+	0.834599i	$0.314301\pi$
$4$	−0.0679233	+	0.0710422i	−0.0339617	+	0.0355211i
$5$	0.862898	+	2.65573i	0.385900	+	1.18768i	0.935825	+	0.352464i	$0.114656\pi$
$5$	0.862898	+	2.65573i	0.385900	+	1.18768i	−0.549926	+	0.835214i	$0.685344\pi$
$6$	−1.08634	−	1.64573i	−0.443496	−	0.671868i
$7$	−2.26960	−	1.98289i	−0.857830	−	0.749464i	0.111880	−	0.993722i	$-0.464313\pi$
$7$	−2.26960	−	1.98289i	−0.857830	−	0.749464i	−0.969710	+	0.244258i	$0.921456\pi$
$8$	−2.57906	−	0.967939i	−0.911837	−	0.342218i
$9$	−1.07366	+	0.402953i	−0.357888	+	0.134318i
$10$	3.04611	−	2.66131i	0.963265	−	0.841579i
$11$	4.37920	+	1.20858i	1.32038	+	0.364401i	0.854041	−	0.520205i	$-0.174145\pi$
$11$	4.37920	+	1.20858i	1.32038	+	0.364401i	0.466338	+	0.884607i	$0.345573\pi$
$12$	−0.0737113	+	0.111668i	−0.0212786	+	0.0322357i
$13$	−5.09730	+	1.40677i	−1.41374	+	0.390166i	−0.887750	−	0.460326i	$-0.847732\pi$
$13$	−5.09730	+	1.40677i	−1.41374	+	0.390166i	−0.525987	+	0.850493i	$0.676304\pi$
$14$	−1.34905	+	4.15196i	−0.360550	+	1.10966i
$15$	1.80135	+	3.34747i	0.465106	+	0.864312i
$16$	0.187845	+	4.18270i	0.0469613	+	1.04567i
$17$	1.64509	+	1.19523i	0.398993	+	0.289886i	0.769131	−	0.639091i	$-0.220689\pi$
$17$	1.64509	+	1.19523i	0.398993	+	0.289886i	−0.370138	+	0.928977i	$0.620689\pi$
$18$	1.14798	+	1.20069i	0.270581	+	0.283005i
$19$	1.57897	−	2.93423i	0.362242	−	0.673158i	−0.632613	−	0.774468i	$-0.718018\pi$
$19$	1.57897	−	2.93423i	0.362242	−	0.673158i	0.994855	+	0.101310i	$0.0323034\pi$
$20$	−0.247280	−	0.119084i	−0.0552934	−	0.0266279i
$21$	−3.52201	−	2.10430i	−0.768566	−	0.459197i
$22$	−0.883339	−	6.52107i	−0.188329	−	1.39030i
$23$	1.08502	+	4.75376i	0.226241	+	0.991228i	0.952675	+	0.303991i	$0.0983193\pi$
$23$	1.08502	+	4.75376i	0.226241	+	0.991228i	−0.726434	+	0.687237i	$0.758824\pi$
$24$	−3.68981	−	0.669601i	−0.753179	−	0.136682i
$25$	−2.26321	+	1.64432i	−0.452642	+	0.328863i
$26$	4.77575	+	5.98860i	0.936602	+	1.17446i
$27$	−4.84606	+	2.89539i	−0.932625	+	0.557217i
$28$	0.295028	−	0.0265530i	0.0557551	−	0.00501805i
$29$	1.05301	−	7.77366i	0.195540	−	1.44353i	−0.581226	−	0.813742i	$-0.697427\pi$
$29$	1.05301	−	7.77366i	0.195540	−	1.44353i	0.776765	−	0.629790i	$-0.216859\pi$
$30$	3.43322	−	4.30512i	0.626817	−	0.786004i
$31$	0.0798823	−	1.77872i	0.0143473	−	0.319467i	−0.978966	−	0.204021i	$-0.934599\pi$
$31$	0.0798823	−	1.77872i	0.0143473	−	0.319467i	0.993314	−	0.115446i	$-0.0368297\pi$
$32$	0.500494	−	0.241025i	0.0884757	−	0.0426076i
$33$	6.15950	+	0.554365i	1.07223	+	0.0965025i
$34$	0.655444	−	2.87169i	0.112408	−	0.492491i
$35$	3.30759	−	7.73849i	0.559084	−	1.30804i
$36$	0.0443001	−	0.103645i	0.00738335	−	0.0172742i
$37$	1.24145	−	5.43914i	0.204093	−	0.894189i	−0.764320	−	0.644837i	$-0.776925\pi$
$37$	1.24145	−	5.43914i	0.204093	−	0.894189i	0.968413	−	0.249352i	$-0.0802176\pi$
$38$	−4.80726	−	0.432661i	−0.779841	−	0.0701870i
$39$	−6.48563	+	3.12331i	−1.03853	+	0.500131i
$40$	0.345112	−	7.68452i	0.0545670	−	1.21503i
$41$	−2.63002	+	3.29794i	−0.410740	+	0.515051i	−0.943571	−	0.331170i	$-0.892557\pi$
$41$	−2.63002	+	3.29794i	−0.410740	+	0.515051i	0.532831	+	0.846221i	$0.321128\pi$
$42$	−0.797755	+	5.88926i	−0.123096	+	0.908733i
$43$	6.75768	−	0.608202i	1.03054	−	0.0927500i	0.438557	−	0.898703i	$-0.355490\pi$
$43$	6.75768	−	0.608202i	1.03054	−	0.0927500i	0.591979	+	0.805953i	$0.298347\pi$
$44$	−0.383310	+	0.229017i	−0.0577862	+	0.0345256i
$45$	−1.99659	−	2.50365i	−0.297635	−	0.373222i
$46$	5.71420	−	4.15161i	0.842512	−	0.612121i
$47$	−9.05378	−	1.64302i	−1.32063	−	0.239659i	−0.527939	−	0.849282i	$-0.677035\pi$
$47$	−9.05378	−	1.64302i	−1.32063	−	0.239659i	−0.792691	+	0.609624i	$0.791321\pi$
$48$	1.26832	+	5.55686i	0.183066	+	0.802063i
$49$	0.279605	+	2.06412i	0.0399435	+	0.294875i
$50$	3.47868	+	2.07841i	0.491959	+	0.293932i
$51$	2.49405	+	1.20107i	0.349236	+	0.168183i
$52$	0.246286	−	0.457675i	0.0341537	−	0.0634682i
$53$	0.00506880	+	0.00530155i	0.000696253	+	0.000728224i	0.723143	−	0.690698i	$-0.242697\pi$
$53$	0.00506880	+	0.00530155i	0.000696253	+	0.000728224i	−0.722447	+	0.691427i	$0.756983\pi$
$54$	6.61553	+	4.80646i	0.900260	+	0.654077i
$55$	0.569138	+	12.6728i	0.0767426	+	1.70881i
$56$	3.93414	+	7.31085i	0.525721	+	0.976953i
$57$	1.40172	−	4.31406i	0.185663	−	0.571411i
$58$	−10.9539	+	3.02307i	−1.43831	+	0.396949i
$59$	−2.15204	+	3.26021i	−0.280172	+	0.424443i	−0.947226	−	0.320567i	$-0.896127\pi$
$59$	−2.15204	+	3.26021i	−0.280172	+	0.424443i	0.667054	+	0.745010i	$0.267555\pi$
$60$	−0.360165	−	0.0993992i	−0.0464971	−	0.0128324i
$61$	−2.44931	+	2.13990i	−0.313602	+	0.273986i	−0.800320	−	0.599574i	$-0.795337\pi$
$61$	−2.44931	+	2.13990i	−0.313602	+	0.273986i	0.486718	+	0.873559i	$0.338194\pi$
$62$	−2.41469	+	0.906249i	−0.306666	+	0.115094i
$63$	3.23580	+	1.21442i	0.407673	+	0.153002i
$64$	5.70011	+	4.98004i	0.712514	+	0.622505i
$65$	−8.13443	−	12.3231i	−1.00895	−	1.52850i
$66$	−2.76829	−	8.51993i	−0.340753	−	1.04873i
$67$	3.36449	−	3.51898i	0.411038	−	0.429912i	−0.484573	−	0.874751i	$-0.661025\pi$
$67$	3.36449	−	3.51898i	0.411038	−	0.429912i	0.895610	+	0.444839i	$0.146739\pi$
$68$	−0.196652	+	0.0356870i	−0.0238475	+	0.00432769i
$69$	2.60884	+	6.10369i	0.314068	+	0.734798i
$70$	−12.1906			−1.45705
$71$	4.00722	−	7.41230i	0.475570	−	0.879678i
$71$	4.00722	−	7.41230i	0.475570	−	0.879678i
$72$	3.15908			0.372301
$73$	0.0284136	+	0.0664769i	0.00332556	+	0.00778053i	0.921182	−	0.389131i	$-0.127225\pi$
$73$	0.0284136	+	0.0664769i	0.00332556	+	0.00778053i	−0.917857	+	0.396912i	$0.870082\pi$
$74$	−7.95159	+	1.44300i	−0.924354	+	0.167746i
$75$	−2.63176	+	2.75261i	−0.303890	+	0.317844i
$76$	0.101205	+	0.311476i	0.0116090	+	0.0357288i
$77$	−7.54257	−	11.4265i	−0.859555	−	1.30217i
$78$	7.85256	+	6.86057i	0.889127	+	0.776807i
$79$	11.0228	+	4.13694i	1.24017	+	0.465442i	0.883342	−	0.468729i	$-0.155288\pi$
$79$	11.0228	+	4.13694i	1.24017	+	0.465442i	0.356825	+	0.934171i	$0.383859\pi$
$80$	−10.9460	+	4.10811i	−1.22380	+	0.459301i
$81$	−3.19642	+	2.79263i	−0.355158	+	0.310292i
$82$	5.89009	+	1.62556i	0.650452	+	0.179513i
$83$	2.61121	−	3.95581i	0.286618	−	0.434207i	−0.662532	−	0.749034i	$-0.730518\pi$
$83$	2.61121	−	3.95581i	0.286618	−	0.434207i	0.949149	+	0.314827i	$0.101947\pi$
$84$	0.388721	−	0.107280i	0.0424130	−	0.0117052i
$85$	−1.75466	+	5.40027i	−0.190319	+	0.585742i
$86$	−4.65736	−	8.65483i	−0.502216	−	0.933274i
$87$	−0.479118	−	10.6684i	−0.0513668	−	1.14377i
$88$	−10.1244	−	7.35581i	−1.07927	−	0.784132i
$89$	7.88631	+	8.24844i	0.835948	+	0.874333i	0.993576	−	0.113166i	$-0.0360991\pi$
$89$	7.88631	+	8.24844i	0.835948	+	0.874333i	−0.157629	+	0.987498i	$0.550385\pi$
$90$	−2.19812	+	4.08479i	−0.231702	+	0.430574i
$91$	14.3583	+	6.91460i	1.50516	+	0.724847i
$92$	−0.411416	−	0.245809i	−0.0428930	−	0.0256274i
$93$	−0.325362	−	2.40192i	−0.0337385	−	0.249067i
$94$	2.96599	+	12.9948i	0.305918	+	1.34032i
$95$	9.15500	+	1.66139i	0.939283	+	0.170455i
$96$	0.611800	−	0.444499i	0.0624415	−	0.0453664i
$97$	−11.5705	−	14.5089i	−1.17480	−	1.47316i	−0.849532	−	0.527537i	$-0.823116\pi$
$97$	−11.5705	−	14.5089i	−1.17480	−	1.47316i	−0.325271	−	0.945621i	$-0.605456\pi$
$98$	2.59019	−	1.54756i	0.261648	−	0.156328i
$99$	−5.18879	+	0.467000i	−0.521493	+	0.0469352i
$100$	0.0369087	−	0.272471i	0.00369087	−	0.0272471i
$101$	−8.42712	+	10.5673i	−0.838530	+	1.05148i	0.159403	+	0.987214i	$0.449043\pi$
$101$	−8.42712	+	10.5673i	−0.838530	+	1.05148i	−0.997933	+	0.0642694i	$0.979528\pi$
$102$	0.179901	−	4.00581i	0.0178129	−	0.396634i
$103$	11.6388	−	5.60496i	1.14681	−	0.552273i	0.238734	−	0.971085i	$-0.423268\pi$
$103$	11.6388	−	5.60496i	1.14681	−	0.552273i	0.908073	+	0.418812i	$0.137553\pi$
$104$	14.5079	+	1.30574i	1.42262	+	0.128038i
$105$	2.54932	−	11.1693i	0.248788	−	1.09001i
$106$	0.00417581	−	0.00976979i	0.000405590	−	0.000948926i
$107$	−1.21923	+	2.85254i	−0.117868	+	0.275765i	−0.968065	−	0.250699i	$-0.919340\pi$
$107$	−1.21923	+	2.85254i	−0.117868	+	0.275765i	0.850198	+	0.526464i	$0.176482\pi$
$108$	0.123466	−	0.540939i	0.0118805	−	0.0520519i
$109$	−16.5474	−	1.48929i	−1.58495	−	0.142648i	−0.738181	−	0.674603i	$-0.764315\pi$
$109$	−16.5474	−	1.48929i	−1.58495	−	0.142648i	−0.846773	+	0.531955i	$0.821458\pi$
$110$	16.5560	−	7.97293i	1.57855	−	0.760189i
$111$	0.340742	−	7.58722i	0.0323418	−	0.720147i
$112$	7.86752	−	9.86555i	0.743410	−	0.932207i
$113$	−1.53685	+	11.3455i	−0.144574	+	1.06729i	0.762700	+	0.646752i	$0.223873\pi$
$113$	−1.53685	+	11.3455i	−0.144574	+	1.06729i	−0.907275	+	0.420539i	$0.861841\pi$
$114$	−6.54426	+	0.588994i	−0.612926	+	0.0551643i
$115$	−11.6884	+	6.98352i	−1.08995	+	0.651216i
$116$	0.480734	+	0.602821i	0.0446350	+	0.0559705i
$117$	4.90592	−	3.56436i	0.453553	−	0.329525i
$118$	5.56772	+	1.01039i	0.512550	+	0.0930141i
$119$	−1.36370	−	5.97474i	−0.125010	−	0.547703i
$120$	−1.40565	−	10.3769i	−0.128318	−	0.947279i
$121$	8.27380	+	4.94337i	0.752164	+	0.449397i
$122$	4.24473	+	2.04415i	0.384300	+	0.185069i
$123$	−2.72113	+	5.05671i	−0.245356	+	0.455948i
$124$	0.120938	+	0.126491i	0.0108606	+	0.0113593i
$125$	4.97571	+	3.61506i	0.445041	+	0.323341i
$126$	−0.224614	−	5.00141i	−0.0200102	−	0.445561i
$127$	5.83687	+	10.8467i	0.517938	+	0.962491i	0.996432	+	0.0843996i	$0.0268972\pi$
$127$	5.83687	+	10.8467i	0.517938	+	0.962491i	−0.478494	+	0.878091i	$0.658817\pi$
$128$	3.73147	−	11.4843i	0.329818	−	1.01508i
$129$	8.90374	−	2.45728i	0.783930	−	0.216351i
$130$	−11.7831	+	17.8506i	−1.03345	+	1.56561i
$131$	4.09105	+	1.12906i	0.357436	+	0.0986462i	0.440143	−	0.897928i	$-0.354928\pi$
$131$	4.09105	+	1.12906i	0.357436	+	0.0986462i	−0.0827065	+	0.996574i	$0.526356\pi$
$132$	−0.457757	+	0.399930i	−0.0398426	+	0.0348094i
$133$	−9.40191	+	3.52860i	−0.815249	+	0.305968i
$134$	−6.60266	−	2.47802i	−0.570383	−	0.214068i
$135$	−11.8710	−	10.3714i	−1.02169	−	0.892627i
$136$	−3.08589	−	4.67492i	−0.264613	−	0.400871i
$137$	3.42829	+	10.5512i	0.292899	+	0.901450i	0.983919	+	0.178614i	$0.0571614\pi$
$137$	3.42829	+	10.5512i	0.292899	+	0.901450i	−0.691020	+	0.722835i	$0.742839\pi$
$138$	6.64473	−	6.94984i	0.565637	−	0.591610i
$139$	−6.39189	+	1.15996i	−0.542153	+	0.0983863i	−0.442723	−	0.896658i	$-0.645988\pi$
$139$	−6.39189	+	1.15996i	−0.542153	+	0.0983863i	−0.0994299	+	0.995045i	$0.531702\pi$
$140$	0.325097	+	0.760602i	0.0274757	+	0.0642826i
$141$	−12.5265			−1.05492
$142$	−12.1544	−	1.11760i	−1.01997	−	0.0937869i
$143$	−24.0223			−2.00885
$144$	−1.88711	−	4.41512i	−0.157259	−	0.367927i
$145$	21.5534	−	3.91136i	1.78991	−	0.324821i
$146$	0.0723695	−	0.0756926i	0.00598934	−	0.00626436i
$147$	0.876252	+	2.69683i	0.0722720	+	0.222430i
$148$	0.302085	+	0.457639i	0.0248312	+	0.0376177i
$149$	5.69123	+	4.97227i	0.466243	+	0.407345i	0.858742	−	0.512408i	$-0.171246\pi$
$149$	5.69123	+	4.97227i	0.466243	+	0.407345i	−0.392499	+	0.919753i	$0.628389\pi$
$150$	5.16472	+	1.93835i	0.421698	+	0.158266i
$151$	−17.0199	+	6.38769i	−1.38506	+	0.519823i	−0.928985	−	0.370117i	$-0.879318\pi$
$151$	−17.0199	+	6.38769i	−1.38506	+	0.519823i	−0.456078	+	0.889940i	$0.650746\pi$
$152$	−6.91243	+	6.03921i	−0.560672	+	0.489844i
$153$	−2.24789	−	0.620380i	−0.181732	−	0.0501547i
$154$	−10.9258	+	16.5518i	−0.880423	+	1.33378i
$155$	4.79272	−	1.32271i	0.384960	−	0.106242i
$156$	0.218638	−	0.672899i	0.0175051	−	0.0538751i
$157$	8.86672	+	16.4771i	0.707642	+	1.31502i	0.939594	+	0.342291i	$0.111203\pi$
$157$	8.86672	+	16.4771i	0.707642	+	1.31502i	−0.231952	+	0.972727i	$0.574511\pi$
$158$	−0.765152	−	17.0374i	−0.0608722	−	1.35542i
$159$	0.00807808	+	0.00586907i	0.000640633	+	0.000465447i
$160$	1.07197	+	1.12120i	0.0847469	+	0.0886383i
$161$	6.96365	−	12.9406i	0.548813	−	1.01986i
$162$	5.53949	+	2.66768i	0.435224	+	0.209593i
$163$	2.90971	+	1.73847i	0.227906	+	0.136168i	0.622313	−	0.782768i	$-0.286193\pi$
$163$	2.90971	+	1.73847i	0.227906	+	0.136168i	−0.394407	+	0.918936i	$0.629050\pi$
$164$	−0.0556533	−	0.410849i	−0.00434579	−	0.0320819i
$165$	3.84278	+	16.8363i	0.299160	+	1.31070i
$166$	−6.75566	−	1.22597i	−0.524341	−	0.0951539i
$167$	2.69206	−	1.95590i	0.208318	−	0.151352i	−0.478734	−	0.877960i	$-0.658904\pi$
$167$	2.69206	−	1.95590i	0.208318	−	0.151352i	0.687052	+	0.726608i	$0.258904\pi$
$168$	7.04666	+	8.83623i	0.543661	+	0.681730i
$169$	12.8436	−	7.67371i	0.987972	−	0.590286i
$170$	8.19201	−	0.737294i	0.628298	−	0.0565479i
$171$	−0.512933	+	3.78662i	−0.0392250	+	0.289570i
$172$	−0.415796	+	0.521392i	−0.0317041	+	0.0397557i
$173$	−0.656910	+	14.6272i	−0.0499439	+	1.11209i	0.804969	+	0.593317i	$0.202182\pi$
$173$	−0.656910	+	14.6272i	−0.0499439	+	1.11209i	−0.854913	+	0.518771i	$0.826390\pi$
$174$	−13.9373	+	6.71185i	−1.05658	+	0.508824i
$175$	8.39710	+	0.755752i	0.634761	+	0.0571295i
$176$	−4.23253	+	18.5439i	−0.319039	+	1.39780i
$177$	−2.09008	+	4.88999i	−0.157100	+	0.367554i
$178$	6.49695	−	15.2004i	0.486967	−	1.13932i
$179$	2.69618	−	11.8127i	0.201522	−	0.882926i	−0.768488	−	0.639864i	$-0.778991\pi$
$179$	2.69618	−	11.8127i	0.201522	−	0.882926i	0.970011	−	0.243063i	$-0.0781520\pi$
$180$	0.313480	+	0.0282137i	0.0233654	+	0.00210293i
$181$	−15.8837	+	7.64916i	−1.18062	+	0.568558i	−0.918093	−	0.396366i	$-0.870271\pi$
$181$	−15.8837	+	7.64916i	−1.18062	+	0.568558i	−0.262530	+	0.964924i	$0.584557\pi$
$182$	1.03570	−	23.0616i	0.0767709	−	1.70944i
$183$	−2.76057	+	3.46165i	−0.204067	+	0.255893i
$184$	1.80303	−	13.3105i	0.132921	−	0.981262i
$185$	15.5161	−	1.39648i	1.14077	−	0.102671i
$186$	−3.01407	+	1.80082i	−0.221003	+	0.132043i
$187$	5.75965	+	7.22238i	0.421188	+	0.528153i
$188$	0.731686	−	0.531601i	0.0533637	−	0.0387710i
$189$	16.7399	+	3.03784i	1.21765	+	0.220970i
$190$	−2.99915	−	13.1401i	−0.217581	−	0.953285i
$191$	−1.14284	−	8.43675i	−0.0826927	−	0.610462i	−0.984116	−	0.177524i	$-0.943191\pi$
$191$	−1.14284	−	8.43675i	−0.0826927	−	0.610462i	0.901424	−	0.432938i	$-0.142523\pi$
$192$	8.84554	+	5.28496i	0.638372	+	0.381409i
$193$	−3.38626	−	1.63073i	−0.243748	−	0.117383i	0.308022	−	0.951379i	$-0.400333\pi$
$193$	−3.38626	−	1.63073i	−0.243748	−	0.117383i	−0.551770	+	0.833996i	$0.686047\pi$
$194$	−12.7383	+	23.6718i	−0.914559	+	1.69953i
$195$	−13.8911	−	14.5290i	−0.994763	−	1.04044i
$196$	−0.165632	−	0.120338i	−0.0118308	−	0.00859560i
$197$	−1.15759	−	25.7757i	−0.0824747	−	1.83644i	−0.434757	−	0.900548i	$-0.643166\pi$
$197$	−1.15759	−	25.7757i	−0.0824747	−	1.83644i	0.352283	−	0.935894i	$-0.385406\pi$
$198$	3.57609	+	6.64549i	0.254142	+	0.472274i
$199$	−0.387337	+	1.19210i	−0.0274576	+	0.0845059i	−0.963846	−	0.266459i	$-0.914146\pi$
$199$	−0.387337	+	1.19210i	−0.0274576	+	0.0845059i	0.936389	+	0.350965i	$0.114146\pi$
$200$	7.42856	−	2.05015i	0.525278	−	0.144968i
$201$	3.65119	−	5.53132i	0.257535	−	0.390149i
$202$	18.8731	+	5.20864i	1.32790	+	0.366478i
$203$	−17.8043	+	15.5551i	−1.24961	+	1.09176i
$204$	−0.254731	+	0.0956020i	−0.0178347	+	0.00669348i
$205$	−11.0279	−	4.13882i	−0.770219	−	0.289068i
$206$	−14.0918	−	12.3117i	−0.981825	−	0.857795i
$207$	−3.08048	−	4.66673i	−0.214108	−	0.324360i
$208$	−6.84158	−	21.0562i	−0.474378	−	1.45999i
$209$	10.4609	−	10.9412i	0.723596	−	0.756822i
$210$	−16.3287	+	2.96321i	−1.12678	+	0.204481i
$211$	−2.77824	−	6.50003i	−0.191262	−	0.447480i	0.796261	−	0.604953i	$-0.206808\pi$
$211$	−2.77824	−	6.50003i	−0.191262	−	0.447480i	−0.987523	+	0.157473i	$0.949665\pi$
$212$	−0.000720923	0		−4.95132e−5	0
$213$	3.56573	−	10.9025i	0.244320	−	0.747024i
$214$	4.49364			0.307179
$215$	7.44641	+	17.4217i	0.507841	+	1.18815i
$216$	15.3009	−	2.77670i	1.04109	−	0.188930i
$217$	−3.70831	+	3.87859i	−0.251736	+	0.263296i
$218$	7.43698	+	22.8887i	0.503696	+	1.55022i
$219$	0.0542174	+	0.0821358i	0.00366367	+	0.00555022i
$220$	−0.938965	−	0.820349i	−0.0633050	−	0.0553079i
$221$	−10.0669	−	3.77818i	−0.677175	−	0.254148i
$222$	−10.3000	+	3.86566i	−0.691291	+	0.259446i
$223$	14.9680	−	13.0771i	1.00233	−	0.875709i	0.0100772	−	0.999949i	$-0.496792\pi$
$223$	14.9680	−	13.0771i	1.00233	−	0.875709i	0.992252	+	0.124240i	$0.0396494\pi$
$224$	−1.61385	−	0.445395i	−0.107830	−	0.0297592i
$225$	1.76734	−	2.67741i	0.117823	−	0.178494i
$226$	15.9869	−	4.41209i	1.06343	−	0.293488i
$227$	1.50175	−	4.62192i	0.0996749	−	0.306768i	−0.888769	−	0.458356i	$-0.848439\pi$
$227$	1.50175	−	4.62192i	0.0996749	−	0.306768i	0.988444	+	0.151588i	$0.0484386\pi$
$228$	0.211271	+	0.392607i	0.0139917	+	0.0260010i
$229$	0.0385003	+	0.857276i	0.00254417	+	0.0566504i	0.999864	−	0.0165216i	$-0.00525923\pi$
$229$	0.0385003	+	0.857276i	0.00254417	+	0.0566504i	−0.997319	+	0.0731720i	$0.976688\pi$
$230$	15.9563	+	11.5929i	1.05213	+	0.764415i
$231$	−12.8804	−	13.4718i	−0.847467	−	0.886381i
$232$	−10.2402	+	19.0295i	−0.672303	+	1.24935i
$233$	1.76254	+	0.848795i	0.115468	+	0.0556064i	0.490726	−	0.871314i	$-0.336732\pi$
$233$	1.76254	+	0.848795i	0.115468	+	0.0556064i	−0.375258	+	0.926920i	$0.622446\pi$
$234$	−7.54067	−	4.50534i	−0.492949	−	0.294523i
$235$	−3.44908	−	25.4621i	−0.224993	−	1.66097i
$236$	−0.0854384	−	0.374330i	−0.00556156	−	0.0243668i
$237$	15.7701	+	2.86186i	1.02438	+	0.185898i
$238$	−7.18186	+	5.21792i	−0.465531	+	0.338228i
$239$	0.330563	+	0.414512i	0.0213823	+	0.0268126i	0.792408	−	0.609992i	$-0.208827\pi$
$239$	0.330563	+	0.414512i	0.0213823	+	0.0268126i	−0.771025	+	0.636804i	$0.780256\pi$
$240$	−13.6631	+	8.16330i	−0.881947	+	0.526939i
$241$	10.2011	−	0.918120i	0.657113	−	0.0591413i	0.243935	−	0.969792i	$-0.421562\pi$
$241$	10.2011	−	0.918120i	0.657113	−	0.0591413i	0.413178	+	0.910650i	$0.364419\pi$
$242$	1.87406	−	13.8349i	0.120469	−	0.889339i
$243$	6.95642	−	8.72308i	0.446255	−	0.559586i
$244$	0.0143422	−	0.319353i	0.000918163	−	0.0204445i
$245$	−5.24048	+	2.52368i	−0.334802	+	0.161232i
$246$	8.28462	+	0.745629i	0.528208	+	0.0475396i
$247$	−3.92074	+	17.1779i	−0.249471	+	1.09300i
$248$	−1.92771	+	4.51010i	−0.122410	+	0.286392i
$249$	2.53603	−	5.93333i	0.160714	−	0.376010i
$250$	1.98244	−	8.68565i	0.125381	−	0.549328i
$251$	−11.9780	−	1.07804i	−0.756048	−	0.0680455i	−0.295092	−	0.955469i	$-0.595350\pi$
$251$	−11.9780	−	1.07804i	−0.756048	−	0.0680455i	−0.460955	+	0.887423i	$0.652493\pi$
$252$	−0.306061	+	0.147391i	−0.0192801	+	0.00928478i
$253$	−0.993815	+	22.1290i	−0.0624806	+	1.39124i
$254$	11.1246	−	13.9498i	0.698019	−	0.875288i
$255$	−1.03761	+	7.65991i	−0.0649774	+	0.479682i
$256$	−2.34384	+	0.210949i	−0.146490	+	0.0131843i
$257$	−0.171878	+	0.102692i	−0.0107214	+	0.00640576i	−0.518250	−	0.855229i	$-0.673416\pi$
$257$	−0.171878	+	0.102692i	−0.0107214	+	0.00640576i	0.507529	+	0.861635i	$0.330559\pi$
$258$	−8.34207	−	10.4606i	−0.519355	−	0.651250i
$259$	−13.6028	+	9.88304i	−0.845239	+	0.614102i
$260$	1.42798	+	0.259140i	0.0885596	+	0.0160712i
$261$	2.00183	+	8.77061i	0.123910	+	0.542887i
$262$	−0.825214	−	6.09198i	−0.0509819	−	0.376364i
$263$	1.09604	+	0.654852i	0.0675846	+	0.0403799i	0.546294	−	0.837593i	$-0.316038\pi$
$263$	1.09604	+	0.654852i	0.0675846	+	0.0403799i	−0.478709	+	0.877973i	$0.658895\pi$
$264$	−15.3491	−	7.39176i	−0.944675	−	0.454931i
$265$	−0.00970561	+	0.0180360i	−0.000596211	+	0.00110795i
$266$	10.0527	+	10.5143i	0.616368	+	0.644671i
$267$	12.5683	+	9.13141i	0.769168	+	0.558833i
$268$	0.0214689	+	0.478041i	0.00131142	+	0.0292010i
$269$	6.44860	+	11.9835i	0.393178	+	0.730647i	0.997830	−	0.0658427i	$-0.0209736\pi$
$269$	6.44860	+	11.9835i	0.393178	+	0.730647i	−0.604652	+	0.796490i	$0.706688\pi$
$270$	−7.05613	+	21.7165i	−0.429422	+	1.32163i
$271$	−4.63967	+	1.28047i	−0.281840	+	0.0777828i	−0.404099	−	0.914715i	$-0.632415\pi$
$271$	−4.63967	+	1.28047i	−0.281840	+	0.0777828i	0.122259	+	0.992498i	$0.460986\pi$
$272$	−4.69026	+	7.10544i	−0.284389	+	0.430831i
$273$	20.9130	+	5.77163i	1.26571	+	0.349315i
$274$	12.1022	−	10.5734i	0.731120	−	0.638761i
$275$	−11.8983	+	4.46552i	−0.717497	+	0.269281i
$276$	−0.610821	−	0.229245i	−0.0367671	−	0.0137989i
$277$	10.9957	+	9.60666i	0.660668	+	0.577208i	0.921596	−	0.388150i	$-0.126886\pi$
$277$	10.9957	+	9.60666i	0.660668	+	0.577208i	−0.260928	+	0.965358i	$0.584029\pi$
$278$	5.18404	+	7.85349i	0.310918	+	0.471021i
$279$	0.630972	+	1.94193i	0.0377753	+	0.116260i
$280$	−16.0209	+	16.7565i	−0.957430	+	1.00139i
$281$	−19.7974	+	3.59270i	−1.18101	+	0.214322i	−0.733332	−	0.679870i	$-0.762036\pi$
$281$	−19.7974	+	3.59270i	−1.18101	+	0.214322i	−0.447682	+	0.894193i	$0.647750\pi$
$282$	7.13151	+	16.6850i	0.424675	+	0.993577i
$283$	11.5985			0.689459			0.344729	−	0.938702i	$-0.387971\pi$
$283$	11.5985			0.689459			0.344729	+	0.938702i	$0.387971\pi$
$284$	0.254402	+	0.788150i	0.0150960	+	0.0467681i
$285$	12.6665			0.750299
$286$	13.6763	+	31.9972i	0.808694	+	1.89203i
$287$	12.5086	−	2.26997i	0.738357	−	0.133992i
$288$	−0.440240	+	0.460455i	−0.0259414	+	0.0271326i
$289$	−3.97554	−	12.2354i	−0.233855	−	0.719732i
$290$	−17.4805	−	26.4818i	−1.02649	−	1.55507i
$291$	−19.0248	−	16.6215i	−1.11525	−	0.974369i
$292$	−0.00665261	−	0.00249676i	−0.000389314	−	0.000146112i
$293$	−10.1378	+	3.80480i	−0.592259	+	0.222279i	−0.629465	−	0.777029i	$-0.716726\pi$
$293$	−10.1378	+	3.80480i	−0.592259	+	0.222279i	0.0372056	+	0.999308i	$0.488154\pi$
$294$	3.09325	−	2.70249i	0.180402	−	0.157613i
$295$	−10.5152	−	2.90201i	−0.612219	−	0.168962i
$296$	−8.46653	+	12.8262i	−0.492107	+	0.745510i
$297$	−24.7212	+	6.82261i	−1.43447	+	0.395888i
$298$	3.38286	−	10.4114i	0.195964	−	0.603115i
$299$	−12.2181	−	22.7050i	−0.706589	−	1.31306i
$300$	−0.0167933	−	0.373933i	−0.000969563	−	0.0215890i
$301$	−16.5433	−	12.0194i	−0.953538	−	0.692786i
$302$	18.1980	+	19.0336i	1.04718	+	1.09526i
$303$	−8.71907	+	16.2028i	−0.500898	+	0.930824i
$304$	12.5696	+	6.05320i	0.720916	+	0.347175i
$305$	−7.79649	−	4.65818i	−0.446426	−	0.266727i
$306$	0.453428	+	3.34734i	0.0259208	+	0.191355i
$307$	−3.82501	−	16.7585i	−0.218305	−	0.956456i	−0.958730	−	0.284317i	$-0.908233\pi$
$307$	−3.82501	−	16.7585i	−0.218305	−	0.956456i	0.740425	−	0.672139i	$-0.234624\pi$
$308$	1.32408	+	0.240285i	0.0754464	+	0.0136915i
$309$	14.2272	−	10.3367i	0.809357	−	0.588032i
$310$	−4.49038	−	5.63076i	−0.255037	−	0.319806i
$311$	−1.39642	+	0.834320i	−0.0791835	+	0.0473100i	−0.551945	−	0.833880i	$-0.686114\pi$
$311$	−1.39642	+	0.834320i	−0.0791835	+	0.0473100i	0.472762	+	0.881190i	$0.343257\pi$
$312$	19.7500	−	1.77753i	1.11813	−	0.100633i
$313$	3.34474	−	24.6919i	0.189056	−	1.39567i	−0.609042	−	0.793138i	$-0.708446\pi$
$313$	3.34474	−	24.6919i	0.189056	−	1.39567i	0.798098	−	0.602528i	$-0.205840\pi$
$314$	16.8992	−	21.1910i	0.953679	−	1.19588i
$315$	−0.432993	+	9.64133i	−0.0243964	+	0.543227i
$316$	−1.04261	+	0.502092i	−0.0586511	+	0.0282449i
$317$	−33.0196	−	2.97182i	−1.85457	−	0.166914i	−0.894570	−	0.446928i	$-0.852518\pi$
$317$	−33.0196	−	2.97182i	−1.85457	−	0.166914i	−0.959996	+	0.280014i	$0.909661\pi$
$318$	0.00321850	−	0.0141012i	0.000180485	−	0.000790755i
$319$	14.0065	−	32.7698i	0.784212	−	1.83476i
$320$	−8.30701	+	19.4352i	−0.464376	+	1.08646i
$321$	−0.939722	+	4.11719i	−0.0524502	+	0.229799i
$322$	−21.2012	−	1.90814i	−1.18149	−	0.106336i
$323$	6.10463	−	2.93983i	0.339671	−	0.163577i
$324$	0.0187170	−	0.416765i	0.00103983	−	0.0231536i
$325$	9.22308	−	11.5654i	0.511605	−	0.641532i
$326$	0.659065	−	4.86541i	0.0365022	−	0.269470i
$327$	−22.5264	+	2.02742i	−1.24571	+	0.112116i
$328$	9.97518	−	5.95989i	0.550787	−	0.329080i
$329$	17.2906	+	21.6817i	0.953260	+	1.19535i
$330$	20.2379	−	14.7037i	1.11406	−	0.809410i
$331$	17.8467	+	3.23871i	0.980946	+	0.178015i	0.645264	−	0.763960i	$-0.276748\pi$
$331$	17.8467	+	3.23871i	0.980946	+	0.178015i	0.335682	+	0.941975i	$0.391033\pi$
$332$	0.103668	+	0.454198i	0.00568951	+	0.0249274i
$333$	0.858818	+	6.34005i	0.0470629	+	0.347432i
$334$	−4.13784	−	2.47225i	−0.226413	−	0.135275i
$335$	12.2487	+	5.89864i	0.669215	+	0.322277i
$336$	8.14008	−	15.1268i	0.444078	−	0.825235i
$337$	1.62914	+	1.70395i	0.0887449	+	0.0928198i	0.765676	−	0.643227i	$-0.222405\pi$
$337$	1.62914	+	1.70395i	0.0887449	+	0.0928198i	−0.676931	+	0.736047i	$0.736690\pi$
$338$	−17.5333	−	12.7387i	−0.953686	−	0.692893i
$339$	0.699260	+	15.5702i	0.0379786	+	0.845659i
$340$	−0.264465	−	0.491459i	−0.0143427	−	0.0266531i
$341$	2.49955	−	7.69282i	0.135358	−	0.416589i
$342$	5.33572	−	1.47257i	0.288523	−	0.0796273i
$343$	−8.16370	+	12.3675i	−0.440798	+	0.667781i
$344$	−18.0172	−	4.97243i	−0.971422	−	0.268095i
$345$	−13.9586	+	12.1952i	−0.751504	+	0.656569i
$346$	19.8572	−	7.45252i	1.06753	−	0.400650i
$347$	−1.73497	−	0.651144i	−0.0931379	−	0.0349552i	0.304371	−	0.952554i	$-0.401554\pi$
$347$	−1.73497	−	0.651144i	−0.0931379	−	0.0349552i	−0.397509	+	0.917598i	$0.630125\pi$
$348$	0.790449	+	0.690595i	0.0423725	+	0.0370198i
$349$	1.73647	+	2.63064i	0.0929512	+	0.140815i	0.878074	−	0.478526i	$-0.158829\pi$
$349$	1.73647	+	2.63064i	0.0929512	+	0.140815i	−0.785122	+	0.619341i	$0.787400\pi$
$350$	−3.77395	−	11.6150i	−0.201726	−	0.620849i
$351$	20.6287	−	21.5759i	1.10108	−	1.15164i
$352$	2.48306	−	0.450610i	0.132348	−	0.0240176i
$353$	−0.403541	−	0.944130i	−0.0214783	−	0.0502510i	0.908445	−	0.418004i	$-0.137270\pi$
$353$	−0.403541	−	0.944130i	−0.0214783	−	0.0502510i	−0.929924	+	0.367753i	$0.880127\pi$
$354$	7.70328			0.409425
$355$	23.1429	+	4.24603i	1.22830	+	0.225356i
$356$	−1.12165			−0.0594474
$357$	−3.27891	−	7.67139i	−0.173538	−	0.406013i
$358$	−17.2693	+	3.13392i	−0.912711	+	0.165633i
$359$	−10.9202	+	11.4217i	−0.576348	+	0.602813i	−0.945127	−	0.326704i	$-0.894062\pi$
$359$	−10.9202	+	11.4217i	−0.576348	+	0.602813i	0.368778	+	0.929517i	$0.379776\pi$
$360$	2.72596	+	8.38965i	0.143671	+	0.442174i
$361$	4.35052	+	6.59075i	0.228975	+	0.346882i
$362$	19.2313	+	16.8019i	1.01078	+	0.883089i
$363$	12.2840	+	4.61024i	0.644740	+	0.241975i
$364$	−1.46649	+	0.550384i	−0.0768651	+	0.0288480i
$365$	−0.152026	+	0.132821i	−0.00795742	+	0.00695219i
$366$	6.18248	+	1.70626i	0.323163	+	0.0891875i
$367$	6.84489	−	10.3696i	0.357300	−	0.541287i	−0.610821	−	0.791769i	$-0.709160\pi$
$367$	6.84489	−	10.3696i	0.357300	−	0.541287i	0.968121	+	0.250482i	$0.0805891\pi$
$368$	−19.6797	+	5.43126i	−1.02588	+	0.283124i
$369$	1.49484	−	4.60065i	0.0778183	−	0.239500i
$370$	−10.6936	−	19.8721i	−0.555936	−	1.03310i
$371$	−0.000991763	−	0.0220833i	−5.14898e−5	−	0.00114651i
$372$	0.192737	+	0.140032i	0.00999296	+	0.00726031i
$373$	−9.45036	−	9.88430i	−0.489321	−	0.511790i	0.431320	−	0.902199i	$-0.358048\pi$
$373$	−9.45036	−	9.88430i	−0.489321	−	0.511790i	−0.920641	+	0.390409i	$0.872334\pi$
$374$	6.34100	−	11.7835i	0.327885	−	0.609313i
$375$	7.54344	+	3.63273i	0.389541	+	0.187593i
$376$	21.7599	+	13.0010i	1.12218	+	0.670473i
$377$	5.56819	+	41.1060i	0.286776	+	2.11707i
$378$	−5.48393	−	24.0267i	−0.282063	−	1.23580i
$379$	−31.4250	−	5.70280i	−1.61420	−	0.292933i	−0.704970	−	0.709237i	$-0.749040\pi$
$379$	−31.4250	−	5.70280i	−1.61420	−	0.292933i	−0.909226	+	0.416304i	$0.863325\pi$
$380$	−0.739866	+	0.537544i	−0.0379543	+	0.0275754i
$381$	10.4548	+	13.1098i	0.535613	+	0.671638i
$382$	−10.5869	+	6.32541i	−0.541675	+	0.323636i
$383$	3.43510	−	0.309165i	0.175526	−	0.0157976i	−0.00152786	−	0.999999i	$-0.500486\pi$
$383$	3.43510	−	0.309165i	0.175526	−	0.0157976i	0.177053	+	0.984201i	$0.443343\pi$
$384$	2.20658	−	16.2896i	0.112604	−	0.831278i
$385$	23.8372	−	29.8909i	1.21486	−	1.52338i
$386$	−0.244258	+	5.43882i	−0.0124324	+	0.276829i
$387$	−7.01040	+	3.37603i	−0.356358	+	0.171613i
$388$	1.81665	+	0.163501i	0.0922264	+	0.00830053i
$389$	6.90463	−	30.2511i	0.350079	−	1.53379i	−0.426919	−	0.904290i	$-0.640401\pi$
$389$	6.90463	−	30.2511i	0.350079	−	1.53379i	0.776997	−	0.629504i	$-0.216742\pi$
$390$	−11.4439	+	26.7742i	−0.579482	+	1.35577i
$391$	−3.89688	+	9.11721i	−0.197074	+	0.461077i
$392$	1.27683	−	5.59415i	0.0644895	−	0.282547i
$393$	5.75420	+	0.517887i	0.290261	+	0.0261239i
$394$	−33.6736	+	16.2164i	−1.69645	+	0.816969i
$395$	−1.47500	+	32.8434i	−0.0742153	+	1.65253i
$396$	0.319263	−	0.400343i	0.0160436	−	0.0201180i
$397$	−3.59358	+	26.5289i	−0.180356	+	1.33145i	0.643848	+	0.765153i	$0.277337\pi$
$397$	−3.59358	+	26.5289i	−0.180356	+	1.33145i	−0.824205	+	0.566292i	$0.808377\pi$
$398$	1.80837	−	0.162756i	0.0906455	−	0.00815824i
$399$	−11.7357	+	7.01174i	−0.587519	+	0.351026i
$400$	−7.30282	−	9.15745i	−0.365141	−	0.457872i
$401$	18.4516	−	13.4059i	0.921431	−	0.669459i	−0.0224486	−	0.999748i	$-0.507146\pi$
$401$	18.4516	−	13.4059i	0.921431	−	0.669459i	0.943880	+	0.330289i	$0.107146\pi$
$402$	−9.44627	−	1.71425i	−0.471137	−	0.0854988i
$403$	2.09505	+	9.17903i	0.104362	+	0.457240i
$404$	−0.178325	−	1.31645i	−0.00887198	−	0.0654956i
$405$	−10.1746	−	6.07907i	−0.505582	−	0.302071i
$406$	30.8553	+	14.8592i	1.53132	+	0.737447i
$407$	12.0102	−	22.3187i	0.595324	−	1.10630i
$408$	−5.26974	−	5.51172i	−0.260891	−	0.272871i
$409$	−26.1119	−	18.9714i	−1.29115	−	0.938074i	−0.291320	−	0.956626i	$-0.594095\pi$
$409$	−26.1119	−	18.9714i	−1.29115	−	0.938074i	−0.999828	+	0.0185515i	$0.994095\pi$
$410$	0.765500	+	17.0452i	0.0378053	+	0.841801i
$411$	7.15675	+	13.2995i	0.353016	+	0.656015i
$412$	−0.392358	+	1.20755i	−0.0193301	+	0.0594919i
$413$	11.3489	−	3.13211i	0.558445	−	0.154121i
$414$	−4.46222	+	6.75998i	−0.219306	+	0.332235i
$415$	12.7588	+	3.52120i	0.626303	+	0.172849i
$416$	−2.21210	+	1.93266i	−0.108457	+	0.0947562i
$417$	−8.27966	+	3.10741i	−0.405457	+	0.152171i
$418$	−20.5291	−	7.70469i	−1.00411	−	0.376849i
$419$	−12.7399	−	11.1305i	−0.622384	−	0.543761i	0.287944	−	0.957647i	$-0.407028\pi$
$419$	−12.7399	−	11.1305i	−0.622384	−	0.543761i	−0.910328	+	0.413887i	$0.864171\pi$
$420$	0.620334	+	0.939766i	0.0302692	+	0.0458559i
$421$	−1.25545	−	3.86387i	−0.0611868	−	0.188314i	0.915791	−	0.401656i	$-0.131565\pi$
$421$	−1.25545	−	3.86387i	−0.0611868	−	0.188314i	−0.976978	+	0.213342i	$0.931565\pi$
$422$	−7.07620	+	7.40113i	−0.344464	+	0.360281i
$423$	10.3828	−	1.88420i	0.504828	−	0.0916127i
$424$	−0.00794118	−	0.0185793i	−0.000385658	−	0.000902292i
$425$	−5.68852			−0.275934
$426$	−16.5519	+	1.45745i	−0.801941	+	0.0706139i
$427$	9.80215			0.474359
$428$	−0.119836	−	0.280371i	−0.00579250	−	0.0135522i
$429$	−32.1767	+	5.83920i	−1.55350	+	0.281919i
$430$	18.9660	−	19.8369i	0.914624	−	0.956621i
$431$	−2.21461	−	6.81586i	−0.106674	−	0.328309i	0.883446	−	0.468533i	$-0.155217\pi$
$431$	−2.21461	−	6.81586i	−0.106674	−	0.328309i	−0.990120	+	0.140225i	$0.955217\pi$
$432$	−13.0208	−	19.7257i	−0.626465	−	0.949055i
$433$	2.13187	+	1.86256i	0.102451	+	0.0895088i	0.707640	−	0.706573i	$-0.249760\pi$
$433$	2.13187	+	1.86256i	0.102451	+	0.0895088i	−0.605189	+	0.796082i	$0.706903\pi$
$434$	7.27739	+	2.73125i	0.349326	+	0.131104i
$435$	27.9189	−	10.4781i	1.33861	−	0.502388i
$436$	1.22976	−	1.07441i	0.0588947	−	0.0514547i
$437$	15.6618	+	4.32239i	0.749207	+	0.206768i
$438$	0.0785364	−	0.118978i	0.00375262	−	0.00568497i
$439$	24.5404	−	6.77271i	1.17125	−	0.323244i	0.374309	−	0.927304i	$-0.377880\pi$
$439$	24.5404	−	6.77271i	1.17125	−	0.323244i	0.796938	+	0.604060i	$0.206451\pi$
$440$	10.7987	−	33.2350i	0.514808	−	1.58442i
$441$	−1.13195	−	2.10351i	−0.0539022	−	0.100167i
$442$	0.698797	+	15.5599i	0.0332384	+	0.740110i
$443$	−10.5088	−	7.63508i	−0.499287	−	0.362753i	0.309457	−	0.950913i	$-0.399853\pi$
$443$	−10.5088	−	7.63508i	−0.499287	−	0.362753i	−0.808745	+	0.588160i	$0.799853\pi$
$444$	0.515868	+	0.539556i	0.0244820	+	0.0256062i
$445$	−15.1005	+	28.0615i	−0.715833	+	1.33024i
$446$	−25.9399	−	12.4920i	−1.22829	−	0.591514i
$447$	8.83174	+	5.27672i	0.417727	+	0.249580i
$448$	−3.06212	−	22.6054i	−0.144671	−	1.06801i
$449$	8.54871	+	37.4543i	0.403439	+	1.76758i	0.613301	+	0.789849i	$0.289841\pi$
$449$	8.54871	+	37.4543i	0.403439	+	1.76758i	−0.209863	+	0.977731i	$0.567302\pi$
$450$	−4.57243	−	0.829773i	−0.215546	−	0.0391159i
$451$	−15.5032	+	11.2637i	−0.730017	+	0.530389i
$452$	−0.701618	−	0.879802i	−0.0330014	−	0.0413824i
$453$	−21.2447	+	12.6931i	−0.998162	+	0.596374i
$454$	−7.01128	+	0.631026i	−0.329056	+	0.0296155i
$455$	−5.97353	+	44.0984i	−0.280043	+	2.06736i
$456$	−7.79088	+	9.76945i	−0.364841	+	0.457496i
$457$	−0.175418	+	3.90599i	−0.00820571	+	0.182714i	0.990704	+	0.136034i	$0.0434356\pi$
$457$	−0.175418	+	3.90599i	−0.00820571	+	0.182714i	−0.998910	+	0.0466804i	$0.985136\pi$
$458$	1.11995	−	0.539342i	0.0523320	−	0.0252018i
$459$	−11.4329	−	1.02898i	−0.533640	−	0.0480285i
$460$	0.297793	−	1.30472i	0.0138847	−	0.0608327i
$461$	1.48825	−	3.48193i	0.0693146	−	0.162170i	−0.881288	−	0.472579i	$-0.843323\pi$
$461$	1.48825	−	3.48193i	0.0693146	−	0.162170i	0.950603	+	0.310409i	$0.100466\pi$
$462$	−10.6112	+	24.8261i	−0.493677	+	1.15502i
$463$	1.51489	−	6.63715i	0.0704027	−	0.308454i	−0.927450	−	0.373946i	$-0.878004\pi$
$463$	1.51489	−	6.63715i	0.0704027	−	0.308454i	0.997853	+	0.0654918i	$0.0208616\pi$
$464$	32.7127	+	2.94420i	1.51865	+	0.136681i
$465$	6.09809	−	2.93668i	0.282792	−	0.136185i
$466$	0.127136	−	2.83090i	0.00588945	−	0.131139i
$467$	−17.1887	+	21.5540i	−0.795399	+	0.997399i	0.204429	+	0.978881i	$0.434466\pi$
$467$	−17.1887	+	21.5540i	−0.795399	+	0.997399i	−0.999829	+	0.0185179i	$0.994105\pi$
$468$	−0.0800064	+	0.590631i	−0.00369830	+	0.0273019i
$469$	−14.6138	+	1.31527i	−0.674803	+	0.0607334i
$470$	−31.9514	+	19.0901i	−1.47381	+	0.880560i
$471$	15.8817	+	19.9150i	0.731790	+	0.917636i
$472$	8.70594	−	6.32523i	0.400723	−	0.291143i
$473$	30.3283	+	5.50378i	1.39450	+	0.253064i
$474$	−5.16624	−	22.6348i	−0.237293	−	1.03965i
$475$	1.25125	+	9.23710i	0.0574113	+	0.423827i
$476$	0.517085	+	0.308944i	0.0237006	+	0.0141604i
$477$	−0.00757846	−	0.00364959i	−0.000346994	−	0.000167103i
$478$	0.363927	−	0.676291i	0.0166457	−	0.0309328i
$479$	−7.60650	−	7.95578i	−0.347550	−	0.363509i	0.525795	−	0.850611i	$-0.323768\pi$
$479$	−7.60650	−	7.95578i	−0.347550	−	0.363509i	−0.873345	+	0.487103i	$0.838054\pi$
$480$	1.70839	+	1.24122i	0.0779769	+	0.0566535i
$481$	1.32356	+	29.4713i	0.0603491	+	1.34378i
$482$	−7.03058	−	13.0650i	−0.320234	−	0.595095i
$483$	6.18193	−	19.0260i	0.281287	−	0.865714i
$484$	−0.913172	+	0.252019i	−0.0415078	+	0.0114554i
$485$	28.5476	−	43.2477i	1.29628	−	1.96378i
$486$	−15.5794	−	4.29963i	−0.706694	−	0.195035i
$487$	21.4451	−	18.7360i	0.971770	−	0.849010i	−0.0167870	−	0.999859i	$-0.505344\pi$
$487$	21.4451	−	18.7360i	0.971770	−	0.849010i	0.988557	+	0.150849i	$0.0482009\pi$
$488$	8.38821	−	3.14815i	0.379717	−	0.142510i
$489$	4.31999	+	1.62132i	0.195357	+	0.0733186i
$490$	6.34498	+	5.54344i	0.286637	+	0.250427i
$491$	−10.1512	−	15.3784i	−0.458115	−	0.694015i	0.529954	−	0.848027i	$-0.322209\pi$
$491$	−10.1512	−	15.3784i	−0.458115	−	0.694015i	−0.988069	+	0.154011i	$0.950781\pi$
$492$	−0.174412	−	0.536784i	−0.00786308	−	0.0242001i
$493$	11.0236	−	11.5298i	0.496478	−	0.519276i
$494$	25.1127	−	4.55728i	1.12987	−	0.205042i
$495$	−5.71762	−	13.3770i	−0.256988	−	0.601253i
$496$	7.45484			0.334732
$497$	−23.7926	+	8.87710i	−1.06724	+	0.398192i
$498$	−9.34688			−0.418844
$499$	2.01873	+	4.72305i	0.0903706	+	0.211433i	0.958616	−	0.284703i	$-0.0918949\pi$
$499$	2.01873	+	4.72305i	0.0903706	+	0.211433i	−0.868245	+	0.496135i	$0.834752\pi$
$500$	−0.594788	+	0.107938i	−0.0265997	+	0.00482714i
$501$	3.13045	−	3.27420i	0.139858	−	0.146280i
$502$	5.38335	+	16.5683i	0.240271	+	0.739477i
$503$	12.7448	+	19.3075i	0.568262	+	0.860881i	0.999137	−	0.0415311i	$-0.0132236\pi$
$503$	12.7448	+	19.3075i	0.568262	+	0.860881i	−0.430875	+	0.902412i	$0.641795\pi$
$504$	−7.16986	−	6.26412i	−0.319371	−	0.279026i
$505$	−35.3355	−	13.2617i	−1.57241	−	0.590136i
$506$	30.0412	−	11.2746i	1.33549	−	0.501219i
$507$	15.3381	−	13.4005i	0.681190	−	0.595138i
$508$	−1.16703	−	0.322081i	−0.0517788	−	0.0142900i
$509$	5.20837	−	7.89034i	0.230857	−	0.349733i	−0.700619	−	0.713535i	$-0.747093\pi$
$509$	5.20837	−	7.89034i	0.230857	−	0.349733i	0.931476	+	0.363802i	$0.118521\pi$
$510$	10.7936	−	2.97883i	0.477947	−	0.131905i
$511$	0.0673290	−	0.207217i	0.00297846	−	0.00916675i
$512$	−9.82884	−	18.2650i	−0.434377	−	0.807208i
$513$	0.843913	+	18.7912i	0.0372597	+	0.829651i
$514$	0.234637	+	0.170473i	0.0103494	+	0.00751926i
$515$	24.9284	+	26.0730i	1.09847	+	1.14891i
$516$	−0.430201	+	0.799447i	−0.0189385	+	0.0351937i
$517$	−37.6626	−	18.1374i	−1.65640	−	0.797680i
$518$	20.9083	+	12.4921i	0.918658	+	0.548872i
$519$	2.67561	+	19.7521i	0.117446	+	0.867022i
$520$	9.05118	+	39.6558i	0.396920	+	1.73902i
$521$	−2.75043	−	0.499130i	−0.120499	−	0.0218673i	0.117973	−	0.993017i	$-0.462361\pi$
$521$	−2.75043	−	0.499130i	−0.120499	−	0.0218673i	−0.238471	+	0.971150i	$0.576646\pi$
$522$	10.5426	−	7.65964i	0.461437	−	0.335253i
$523$	−5.91307	−	7.41475i	−0.258560	−	0.324224i	0.635560	−	0.772052i	$-0.280769\pi$
$523$	−5.91307	−	7.41475i	−0.258560	−	0.324224i	−0.894120	+	0.447827i	$0.852198\pi$
$524$	−0.358088	+	0.213948i	−0.0156431	+	0.00934635i
$525$	11.4312	−	1.02883i	0.498898	−	0.0449017i
$526$	0.248258	−	1.83272i	0.0108246	−	0.0799103i
$527$	2.25739	−	2.83067i	0.0983333	−	0.123306i
$528$	−1.16171	+	25.8675i	−0.0505569	+	1.12574i
$529$	−0.698712	+	0.336482i	−0.0303788	+	0.0146297i
$530$	0.0295492	+	0.00265948i	0.00128353	+	0.000115520i
$531$	0.996861	−	4.36754i	0.0432601	−	0.189535i
$532$	0.387930	−	0.907606i	0.0168189	−	0.0393497i
$533$	8.76656	−	20.5104i	0.379722	−	0.888403i
$534$	5.00752	−	21.9394i	0.216697	−	0.949410i
$535$	−8.62763	−	0.776501i	−0.373005	−	0.0335710i
$536$	−12.0834	+	5.81905i	−0.521923	+	0.251345i
$537$	0.740026	−	16.4780i	0.0319345	−	0.711076i
$538$	12.2905	−	15.4118i	0.529881	−	0.664449i
$539$	−1.27022	+	9.37714i	−0.0547123	+	0.403902i
$540$	1.54312	−	0.138884i	0.0664055	−	0.00597660i
$541$	31.3134	−	18.7089i	1.34627	−	0.804357i	0.354828	−	0.934932i	$-0.384539\pi$
$541$	31.3134	−	18.7089i	1.34627	−	0.804357i	0.991438	+	0.130575i	$0.0416822\pi$
$542$	4.34699	+	5.45095i	0.186719	+	0.234138i
$543$	−19.4160	+	14.1066i	−0.833222	+	0.605371i
$544$	1.11144	+	0.201696i	0.0476525	+	0.00864766i
$545$	−10.3236	−	45.2305i	−0.442213	−	1.93746i
$546$	−4.21841	−	31.1416i	−0.180531	−	1.33274i
$547$	−21.7556	−	12.9984i	−0.930202	−	0.555770i	−0.0340029	−	0.999422i	$-0.510826\pi$
$547$	−21.7556	−	12.9984i	−0.930202	−	0.555770i	−0.896199	+	0.443652i	$0.853683\pi$
$548$	−0.982441	−	0.473119i	−0.0419678	−	0.0202106i
$549$	1.76746	−	3.28448i	0.0754332	−	0.140178i
$550$	12.7219	+	13.3061i	0.542463	+	0.567372i
$551$	−21.1470	−	15.3642i	−0.900893	−	0.654537i
$552$	−0.820372	−	18.2670i	−0.0349173	−	0.777495i
$553$	−16.8144	−	31.2464i	−0.715020	−	1.32873i
$554$	6.53585	−	20.1153i	0.277682	−	0.854616i
$555$	20.4436	−	5.64208i	0.867783	−	0.239493i
$556$	0.351753	−	0.532882i	0.0149176	−	0.0225992i
$557$	−6.99601	−	1.93078i	−0.296431	−	0.0818097i	0.114658	−	0.993405i	$-0.463423\pi$
$557$	−6.99601	−	1.93078i	−0.296431	−	0.0818097i	−0.411089	+	0.911595i	$0.634851\pi$
$558$	2.22739	−	1.94601i	0.0942930	−	0.0823813i
$559$	−33.5903	+	12.6067i	−1.42072	+	0.533205i
$560$	32.9891	+	12.3810i	1.39404	+	0.523193i
$561$	9.47034	+	8.27399i	0.399838	+	0.349328i
$562$	16.0564	+	24.3243i	0.677297	+	1.02606i
$563$	0.359079	+	1.10513i	0.0151334	+	0.0465758i	0.958338	−	0.285636i	$-0.0922050\pi$
$563$	0.359079	+	1.10513i	0.0151334	+	0.0465758i	−0.943205	+	0.332212i	$0.892205\pi$
$564$	0.850839	−	0.889908i	0.0358268	−	0.0374719i
$565$	−31.4566	+	5.70853i	−1.32339	+	0.240160i
$566$	−6.60320	−	15.4490i	−0.277553	−	0.649368i
$567$	12.7921			0.537218
$568$	−17.5095	+	15.2380i	−0.734684	+	0.639374i
$569$	21.2762			0.891944			0.445972	−	0.895047i	$-0.352858\pi$
$569$	21.2762			0.891944			0.445972	+	0.895047i	$0.352858\pi$
$570$	−7.21123	−	16.8715i	−0.302045	−	0.706670i
$571$	−23.6107	+	4.28472i	−0.988078	+	0.179310i	−0.648456	−	0.761252i	$-0.724585\pi$
$571$	−23.6107	+	4.28472i	−0.988078	+	0.179310i	−0.339622	+	0.940562i	$0.610299\pi$
$572$	1.63167	−	1.70660i	0.0682237	−	0.0713564i
$573$	−3.58153	−	11.0228i	−0.149621	−	0.460485i
$574$	−10.1449	−	15.3688i	−0.423438	−	0.641482i
$575$	−10.2723	−	8.97465i	−0.428385	−	0.374269i
$576$	−8.12672	−	3.05001i	−0.338613	−	0.127084i
$577$	−22.5100	+	8.44813i	−0.937101	+	0.351700i	−0.772756	−	0.634703i	$-0.781123\pi$
$577$	−22.5100	+	8.44813i	−0.937101	+	0.351700i	−0.164345	+	0.986403i	$0.552551\pi$
$578$	−14.0340	+	12.2612i	−0.583738	+	0.509997i
$579$	−4.93211	−	1.36118i	−0.204971	−	0.0565685i
$580$	−1.18610	+	1.79687i	−0.0492503	+	0.0746110i
$581$	−13.7704	+	3.80038i	−0.571291	+	0.157666i
$582$	−11.3084	+	34.8035i	−0.468746	+	1.44265i
$583$	0.0157899	+	0.0293426i	0.000653952	+	0.00121525i
$584$	−0.00893488	−	0.198951i	−0.000369728	−	0.00823264i
$585$	13.6993	+	9.95311i	0.566396	+	0.411511i
$586$	10.8395	+	11.3373i	0.447777	+	0.468338i
$587$	−17.7804	+	33.0415i	−0.733874	+	1.36377i	0.190273	+	0.981731i	$0.439063\pi$
$587$	−17.7804	+	33.0415i	−0.733874	+	1.36377i	−0.924148	+	0.382036i	$0.875223\pi$
$588$	−0.251106	−	0.120926i	−0.0103555	−	0.00498692i
$589$	−5.09303	−	3.04294i	−0.209854	−	0.125382i
$590$	2.12105	+	15.6582i	0.0873222	+	0.644638i
$591$	−7.81594	−	34.2439i	−0.321505	−	1.40860i
$592$	22.9835	+	4.17089i	0.944615	+	0.171422i
$593$	12.1999	−	8.86374i	0.500989	−	0.363990i	−0.308405	−	0.951255i	$-0.599795\pi$
$593$	12.1999	−	8.86374i	0.500989	−	0.363990i	0.809395	+	0.587265i	$0.199795\pi$
$594$	23.1617	+	29.0439i	0.950337	+	1.19169i
$595$	14.6905	−	8.77719i	0.602254	−	0.359830i
$596$	−0.739808	+	0.0665839i	−0.0303037	+	0.00272738i
$597$	−0.229050	+	1.69091i	−0.00937438	+	0.0692045i
$598$	−23.2866	+	29.2005i	−0.952261	+	1.19410i
$599$	0.887345	−	19.7583i	0.0362559	−	0.807301i	−0.895685	−	0.444690i	$-0.853314\pi$
$599$	0.887345	−	19.7583i	0.0362559	−	0.807301i	0.931941	−	0.362611i	$-0.118115\pi$
$600$	9.45184	−	4.55177i	0.385870	−	0.185825i
$601$	11.8103	+	1.06294i	0.481751	+	0.0433584i	0.327854	−	0.944728i	$-0.393675\pi$
$601$	11.8103	+	1.06294i	0.481751	+	0.0433584i	0.153897	+	0.988087i	$0.450818\pi$
$602$	−6.59124	+	28.8781i	−0.268639	+	1.17698i
$603$	−2.19435	+	5.13393i	−0.0893606	+	0.209070i
$604$	0.702255	−	1.64301i	0.0285743	−	0.0668530i
$605$	−5.98878	+	26.2386i	−0.243479	+	1.06675i
$606$	26.5456	+	2.38915i	1.07834	+	0.0970526i
$607$	37.0825	−	17.8580i	1.50513	−	0.724833i	0.514009	−	0.857785i	$-0.328160\pi$
$607$	37.0825	−	17.8580i	1.50513	−	0.724833i	0.991123	+	0.132952i	$0.0424456\pi$
$608$	0.0830448	−	1.84914i	0.00336791	−	0.0749924i
$609$	−20.0669	+	25.1631i	−0.813151	+	1.01966i
$610$	−1.76595	+	13.0367i	−0.0715010	+	0.527842i
$611$	48.4612	−	4.36158i	1.96053	−	0.176451i
$612$	0.196758	−	0.117557i	0.00795345	−	0.00475197i
$613$	25.1095	+	31.4863i	1.01416	+	1.27172i	0.961991	+	0.273082i	$0.0880431\pi$
$613$	25.1095	+	31.4863i	1.01416	+	1.27172i	0.0521725	+	0.998638i	$0.483385\pi$
$614$	−20.1443	+	14.6357i	−0.812957	+	0.590648i
$615$	−15.7773	−	2.86316i	−0.636202	−	0.115454i
$616$	8.39261	+	36.7704i	0.338148	+	1.48152i
$617$	3.17476	+	23.4370i	0.127811	+	0.943539i	0.935350	+	0.353724i	$0.115085\pi$
$617$	3.17476	+	23.4370i	0.127811	+	0.943539i	−0.807539	+	0.589815i	$0.799201\pi$
$618$	−21.8680	−	13.0655i	−0.879659	−	0.525572i
$619$	5.87006	+	2.82687i	0.235938	+	0.113622i	0.548117	−	0.836402i	$-0.315345\pi$
$619$	5.87006	+	2.82687i	0.235938	+	0.113622i	−0.312180	+	0.950023i	$0.601059\pi$
$620$	−0.231569	+	0.430328i	−0.00930004	+	0.0172824i
$621$	−19.0220	−	19.8955i	−0.763328	−	0.798378i
$622$	1.90630	+	1.38501i	0.0764356	+	0.0555337i
$623$	−1.54304	−	34.3584i	−0.0618205	−	1.37654i
$624$	−14.2822	−	26.5407i	−0.571745	−	1.06248i
$625$	−9.62943	+	29.6364i	−0.385177	+	1.18545i
$626$	−34.7933	+	9.60233i	−1.39062	+	0.383786i
$627$	11.3523	−	17.1980i	0.453368	−	0.686823i
$628$	−1.77283	−	0.489270i	−0.0707436	−	0.0195240i
$629$	8.54331	−	7.46407i	0.340644	−	0.297612i
$630$	13.0886	−	4.91222i	0.521461	−	0.195707i
$631$	24.6959	+	9.26853i	0.983128	+	0.368974i	0.790611	−	0.612319i	$-0.209763\pi$
$631$	24.6959	+	9.26853i	0.983128	+	0.368974i	0.192518	+	0.981294i	$0.438335\pi$
$632$	−24.4243	−	21.3389i	−0.971547	−	0.848815i
$633$	−5.30131	−	8.03114i	−0.210708	−	0.319209i
$634$	14.8402	+	45.6733i	0.589378	+	1.81392i
$635$	−23.7693	+	24.8607i	−0.943256	+	0.986568i
$636$	−0.000965641	0	0.000175238i	−3.82902e−5	0	6.94864e-6i
$637$	−4.32897	−	10.1281i	−0.171520	−	0.401291i
$638$	−51.6228			−2.04376
$639$	−1.31560	+	9.57303i	−0.0520443	+	0.378703i
$640$	33.7190			1.33286
$641$	−9.24304	−	21.6252i	−0.365078	−	0.854143i	−0.996874	−	0.0790081i	$-0.974825\pi$
$641$	−9.24304	−	21.6252i	−0.365078	−	0.854143i	0.631796	−	0.775135i	$-0.282318\pi$
$642$	6.01901	−	1.09229i	0.237551	−	0.0431092i
$643$	27.1158	−	28.3609i	1.06934	−	1.11844i	0.0767367	−	0.997051i	$-0.475550\pi$
$643$	27.1158	−	28.3609i	1.06934	−	1.11844i	0.992605	−	0.121392i	$-0.0387358\pi$
$644$	0.446337	+	1.37368i	0.0175881	+	0.0541307i
$645$	14.2089	+	21.5255i	0.559474	+	0.847566i
$646$	−7.39126	−	6.45755i	−0.290805	−	0.254069i
$647$	−8.00344	−	3.00374i	−0.314648	−	0.118089i	0.189055	−	0.981967i	$-0.439458\pi$
$647$	−8.00344	−	3.00374i	−0.314648	−	0.118089i	−0.503702	+	0.863877i	$0.668029\pi$
$648$	10.9469	−	4.10843i	0.430034	−	0.161394i
$649$	−13.3645	+	11.6762i	−0.524601	+	0.458330i
$650$	−20.6557	−	5.70061i	−0.810183	−	0.223596i
$651$	−4.02431	+	6.09657i	−0.157725	+	0.238943i
$652$	−0.321142	+	0.0886295i	−0.0125769	+	0.00347100i
$653$	3.66097	−	11.2673i	0.143265	−	0.440924i	−0.853519	−	0.521062i	$-0.825536\pi$
$653$	3.66097	−	11.2673i	0.143265	−	0.440924i	0.996784	+	0.0801377i	$0.0255360\pi$
$654$	15.5251	+	28.8505i	0.607080	+	1.12814i
$655$	0.531688	+	11.8390i	0.0207748	+	0.462587i
$656$	−14.2883	−	10.3811i	−0.557865	−	0.405313i
$657$	−0.0572936	−	0.0599244i	−0.00223524	−	0.00233787i
$658$	19.0358	−	35.3744i	0.742092	−	1.37904i
$659$	23.9819	+	11.5491i	0.934201	+	0.449887i	0.838120	−	0.545486i	$-0.183655\pi$
$659$	23.9819	+	11.5491i	0.934201	+	0.449887i	0.0960811	+	0.995374i	$0.469369\pi$
$660$	−1.45710	−	0.870578i	−0.0567176	−	0.0338872i
$661$	0.435372	+	3.21404i	0.0169340	+	0.125012i	0.997443	−	0.0714601i	$-0.0227658\pi$
$661$	0.435372	+	3.21404i	0.0169340	+	0.125012i	−0.980509	+	0.196472i	$0.937052\pi$
$662$	−5.84653	−	25.6153i	−0.227232	−	0.995568i
$663$	−14.4025	−	2.61367i	−0.559348	−	0.101507i
$664$	−10.5635	+	7.67481i	−0.409942	+	0.297840i
$665$	−17.4839	−	21.9241i	−0.677996	−	0.850180i
$666$	7.95587	−	4.75341i	0.308284	−	0.184191i
$667$	38.0967	−	3.42876i	1.47511	−	0.132762i
$668$	−0.0439024	+	0.324101i	−0.00169864	+	0.0125398i
$669$	16.8701	−	21.1545i	0.652237	−	0.817879i
$670$	0.883522	−	19.6731i	0.0341334	−	0.760040i
$671$	−13.3123	+	6.41085i	−0.513914	+	0.247488i
$672$	−2.26994	−	0.204298i	−0.0875647	−	0.00788097i
$673$	−6.54665	+	28.6827i	−0.252355	+	1.10564i	0.676864	+	0.736108i	$0.263339\pi$
$673$	−6.54665	+	28.6827i	−0.252355	+	1.10564i	−0.929219	+	0.369530i	$0.879519\pi$
$674$	1.34213	−	3.14006i	0.0516968	−	0.120951i
$675$	6.20671	−	14.5213i	0.238896	−	0.558926i
$676$	−0.327224	+	1.43366i	−0.0125856	+	0.0551409i
$677$	−3.96517	−	0.356871i	−0.152394	−	0.0137157i	0.0131798	−	0.999913i	$-0.495805\pi$
$677$	−3.96517	−	0.356871i	−0.152394	−	0.0137157i	−0.165573	+	0.986197i	$0.552947\pi$
$678$	20.3411	−	9.79577i	0.781197	−	0.376204i
$679$	−2.50924	+	55.8725i	−0.0962957	+	2.14419i
$680$	9.75250	−	12.2293i	0.373991	−	0.468970i
$681$	0.888054	−	6.55588i	0.0340303	−	0.251222i
$682$	−11.6697	+	1.05029i	−0.446856	+	0.0402178i
$683$	−19.9161	+	11.8993i	−0.762069	+	0.455315i	−0.840640	−	0.541594i	$-0.817821\pi$
$683$	−19.9161	+	11.8993i	−0.762069	+	0.455315i	0.0785718	+	0.996908i	$0.474964\pi$
$684$	−0.234170	−	0.293640i	−0.00895371	−	0.0112276i
$685$	−25.0628	+	18.2092i	−0.957602	+	0.695738i
$686$	21.1209	+	3.83288i	0.806401	+	0.146340i
$687$	0.259951	+	1.13892i	0.00991775	+	0.0434525i
$688$	3.81333	+	28.1511i	0.145382	+	1.07325i
$689$	−0.0332952	−	0.0198930i	−0.00126845	−	0.000757862i
$690$	24.1906	+	11.6496i	0.920921	+	0.443492i
$691$	−13.0849	+	24.3157i	−0.497771	+	0.925014i	0.500471	+	0.865753i	$0.333160\pi$
$691$	−13.0849	+	24.3157i	−0.497771	+	0.925014i	−0.998243	+	0.0592611i	$0.981126\pi$
$692$	−0.994532	−	1.04020i	−0.0378064	−	0.0395424i
$693$	12.7025	+	9.22892i	0.482529	+	0.350578i
$694$	0.120433	+	2.68165i	0.00457157	+	0.101794i
$695$	−8.59608	−	15.9742i	−0.326068	−	0.605936i
$696$	−9.09067	+	27.9782i	−0.344581	+	1.06051i
$697$	−8.26841	+	2.28194i	−0.313188	+	0.0864345i
$698$	2.51536	−	3.81061i	0.0952078	−	0.144234i
$699$	2.56715	+	0.708490i	0.0970987	+	0.0267975i
$700$	−0.624049	+	0.545215i	−0.0235868	+	0.0206072i
$701$	10.2786	−	3.85763i	0.388218	−	0.145701i	−0.149631	−	0.988742i	$-0.547808\pi$
$701$	10.2786	−	3.85763i	0.388218	−	0.145701i	0.537849	+	0.843041i	$0.319237\pi$
$702$	−40.4829	−	15.1935i	−1.52793	−	0.573441i
$703$	−13.9994	−	12.2310i	−0.527999	−	0.461299i
$704$	18.9432	+	28.6977i	0.713947	+	1.08158i
$705$	−10.8091	−	33.2669i	−0.407093	−	1.25290i
$706$	−1.02782	+	1.07502i	−0.0386825	+	0.0404587i
$707$	40.0800	−	7.27345i	1.50736	−	0.273546i
$708$	−0.205430	−	0.480628i	−0.00772055	−	0.0180631i
$709$	10.1930			0.382807			0.191403	−	0.981511i	$-0.438696\pi$
$709$	10.1930			0.382807			0.191403	+	0.981511i	$0.438696\pi$
$710$	−7.51997	−	33.2431i	−0.282219	−	1.24759i
$711$	−13.5018			−0.506358
$712$	−12.3553	−	28.9067i	−0.463035	−	1.08332i
$713$	8.54227	−	1.55019i	0.319911	−	0.0580552i
$714$	−8.35139	+	8.73487i	−0.312543	+	0.326894i
$715$	−20.7288	−	63.7967i	−0.775213	−	2.38586i
$716$	0.656070	+	0.993904i	0.0245185	+	0.0371439i
$717$	0.543529	+	0.474867i	0.0202985	+	0.0177342i
$718$	21.4305	+	8.04300i	0.799779	+	0.300162i
$719$	−14.5536	+	5.46206i	−0.542758	+	0.203701i	−0.607669	−	0.794191i	$-0.707895\pi$
$719$	−14.5536	+	5.46206i	−0.542758	+	0.203701i	0.0649106	+	0.997891i	$0.479324\pi$
$720$	10.0970	−	8.82145i	0.376292	−	0.328756i
$721$	−37.5296	−	10.3575i	−1.39767	−	0.385733i
$722$	6.30193	−	9.54702i	0.234534	−	0.355303i
$723$	13.4408	−	3.70941i	0.499867	−	0.137955i
$724$	0.535457	−	1.64797i	0.0199001	−	0.0612462i
$725$	10.3992	+	19.3249i	0.386216	+	0.717709i
$726$	−0.852691	−	18.9866i	−0.0316463	−	0.704661i
$727$	13.6595	+	9.92424i	0.506604	+	0.368070i	0.811534	−	0.584305i	$-0.198633\pi$
$727$	13.6595	+	9.92424i	0.506604	+	0.368070i	−0.304930	+	0.952375i	$0.598633\pi$
$728$	−30.3381	−	31.7312i	−1.12441	−	1.17604i
$729$	13.2314	−	24.5882i	0.490054	−	0.910672i
$730$	0.263466	+	0.126879i	0.00975133	+	0.00469599i
$731$	11.8439	+	7.07643i	0.438064	+	0.261731i
$732$	−0.0584160	−	0.431244i	−0.00215912	−	0.0159392i
$733$	−6.22523	−	27.2745i	−0.229934	−	1.00741i	−0.949693	−	0.313183i	$-0.898605\pi$
$733$	−6.22523	−	27.2745i	−0.229934	−	1.00741i	0.719759	−	0.694224i	$-0.244252\pi$
$734$	−17.7089	−	3.21370i	−0.653649	−	0.118620i
$735$	−6.40592	+	4.65417i	−0.236286	+	0.171672i
$736$	1.68882	+	2.11771i	0.0622507	+	0.0780600i
$737$	18.9867	−	11.3441i	0.699386	−	0.417864i
$738$	−6.97900	+	0.628121i	−0.256901	+	0.0231215i
$739$	5.13109	−	37.8792i	0.188750	−	1.39341i	−0.610312	−	0.792161i	$-0.708956\pi$
$739$	5.13109	−	37.8792i	0.188750	−	1.39341i	0.799062	−	0.601248i	$-0.205330\pi$
$740$	−0.954697	+	1.19715i	−0.0350953	+	0.0440082i
$741$	−1.07613	+	23.9619i	−0.0395327	+	0.880264i
$742$	−0.0288499	+	0.0138934i	−0.00105911	+	0.000510042i
$743$	48.4902	+	4.36420i	1.77893	+	0.160107i	0.929798	−	0.368069i	$-0.119981\pi$
$743$	48.4902	+	4.36420i	1.77893	+	0.160107i	0.849135	+	0.528176i	$0.177124\pi$
$744$	−1.48578	+	6.50963i	−0.0544714	+	0.238655i
$745$	−8.29405	+	19.4049i	−0.303871	+	0.710941i
$746$	−7.78545	+	18.2150i	−0.285046	+	0.666897i
$747$	−1.20955	+	5.29941i	−0.0442553	+	0.193895i
$748$	−0.904308	−	0.0813892i	−0.0330648	−	0.00297589i
$749$	8.42345	−	4.05652i	0.307786	−	0.148222i
$750$	0.544124	−	12.1159i	0.0198686	−	0.442409i
$751$	−2.84361	+	3.56578i	−0.103765	+	0.130117i	−0.831002	−	0.556269i	$-0.812232\pi$
$751$	−2.84361	+	3.56578i	−0.103765	+	0.130117i	0.727237	+	0.686386i	$0.240804\pi$
$752$	5.17155	−	38.1779i	0.188587	−	1.39220i
$753$	−16.3060	+	1.46757i	−0.594225	+	0.0534812i
$754$	51.5823	−	30.8190i	1.87852	−	1.12236i
$755$	−31.6504	−	39.6884i	−1.15188	−	1.44441i
$756$	−1.35284	+	0.982898i	−0.0492024	+	0.0357477i
$757$	−24.8467	−	4.50902i	−0.903070	−	0.163883i	−0.292890	−	0.956146i	$-0.594617\pi$
$757$	−24.8467	−	4.50902i	−0.903070	−	0.163883i	−0.610180	+	0.792263i	$0.708903\pi$
$758$	10.2947	+	45.1042i	0.373922	+	1.63826i
$759$	4.04783	+	29.8823i	0.146927	+	1.08466i
$760$	−22.0032	−	13.1463i	−0.798140	−	0.476867i
$761$	−14.3670	−	6.91877i	−0.520803	−	0.250805i	0.154965	−	0.987920i	$-0.450473\pi$
$761$	−14.3670	−	6.91877i	−0.520803	−	0.250805i	−0.675768	+	0.737115i	$0.736188\pi$
$762$	11.5100	−	21.3891i	0.416963	−	0.774847i
$763$	34.6030	+	36.1919i	1.25271	+	1.31023i
$764$	0.676991	+	0.491863i	0.0244927	+	0.0177950i
$765$	−0.292145	−	6.50512i	−0.0105625	−	0.235193i
$766$	−2.36746	−	4.39947i	−0.0855397	−	0.158959i
$767$	6.38326	−	19.6457i	0.230486	−	0.709364i
$768$	−3.08818	+	0.852283i	−0.111435	+	0.0307541i
$769$	10.9012	−	16.5147i	0.393109	−	0.595534i	−0.583091	−	0.812407i	$-0.698157\pi$
$769$	10.9012	−	16.5147i	0.393109	−	0.595534i	0.976200	+	0.216872i	$0.0695856\pi$
$770$	−53.3849	−	14.7333i	−1.92386	−	0.530952i
$771$	−0.205260	+	0.179330i	−0.00739225	+	0.00645842i
$772$	0.345857	−	0.129802i	0.0124477	−	0.00467168i
$773$	38.7108	+	14.5284i	1.39233	+	0.522550i	0.931111	−	0.364736i	$-0.118841\pi$
$773$	38.7108	+	14.5284i	1.39233	+	0.522550i	0.461220	+	0.887286i	$0.347412\pi$
$774$	8.48792	+	7.41568i	0.305092	+	0.266551i
$775$	2.74398	+	4.15696i	0.0985668	+	0.149322i
$776$	15.7972	+	48.6189i	0.567088	+	1.74532i
$777$	−15.8180	+	16.5443i	−0.567468	+	0.593525i
$778$	−44.2248	+	8.02562i	−1.58554	+	0.287732i
$779$	5.52416	+	12.9244i	0.197924	+	0.463066i
$780$	1.97570			0.0707414
$781$	26.5068	−	27.6169i	0.948488	−	0.988210i
$782$	14.3625			0.513602
$783$	17.4048	+	40.7205i	0.621996	+	1.45523i
$784$	−8.58109	+	1.55724i	−0.306467	+	0.0556156i
$785$	−36.1077	+	37.7657i	−1.28874	+	1.34792i
$786$	−2.58614	−	7.95931i	−0.0922444	−	0.283899i
$787$	29.1832	+	44.2106i	1.04027	+	1.57594i	0.795119	+	0.606454i	$0.207408\pi$
$787$	29.1832	+	44.2106i	1.04027	+	1.57594i	0.245149	+	0.969485i	$0.421163\pi$
$788$	1.90979	+	1.66853i	0.0680334	+	0.0594390i
$789$	1.62727	+	0.610723i	0.0579322	+	0.0217423i
$790$	44.5865	−	16.7336i	1.58632	−	0.595355i
$791$	25.9849	−	22.7023i	0.923916	−	0.807201i
$792$	13.8342	+	3.81801i	0.491579	+	0.135667i
$793$	9.47453	−	14.3533i	0.336450	−	0.509701i
$794$	37.3818	−	10.3167i	1.32663	−	0.366126i
$795$	−0.00861608	+	0.0265176i	−0.000305581	+	0.000940481i
$796$	−0.0583803	−	0.108489i	−0.00206924	−	0.00384528i
$797$	0.127477	+	2.83851i	0.00451548	+	0.100545i	0.999985	+	0.00546453i	$0.00173942\pi$
$797$	0.127477	+	2.83851i	0.00451548	+	0.100545i	−0.995470	+	0.0950805i	$0.969689\pi$
$798$	16.0208	+	11.6398i	0.567130	+	0.412044i
$799$	−12.9305	−	13.5243i	−0.457449	−	0.478454i
$800$	−0.736400	+	1.36846i	−0.0260357	+	0.0483824i
$801$	−11.7910	−	5.67823i	−0.416614	−	0.200631i
$802$	−28.3612	−	16.9450i	−1.00147	−	0.598350i
$803$	0.0440860	+	0.325456i	0.00155576	+	0.0114851i
$804$	0.144956	+	0.635094i	0.00511220	+	0.0223980i
$805$	40.3757	+	7.32711i	1.42306	+	0.258247i
$806$	11.0335	−	8.01633i	0.388639	−	0.282363i
$807$	11.5505	+	14.4838i	0.406595	+	0.509854i
$808$	31.9626	−	19.0967i	1.12444	−	0.671821i
$809$	−12.9999	+	1.17002i	−0.457054	+	0.0411356i	−0.315775	−	0.948834i	$-0.602264\pi$
$809$	−12.9999	+	1.17002i	−0.457054	+	0.0411356i	−0.141279	+	0.989970i	$0.545121\pi$
$810$	−2.30461	+	17.0133i	−0.0809758	+	0.597787i
$811$	−32.4440	+	40.6835i	−1.13926	+	1.42859i	−0.251759	+	0.967790i	$0.581009\pi$
$811$	−32.4440	+	40.6835i	−1.13926	+	1.42859i	−0.887504	+	0.460801i	$0.847562\pi$
$812$	0.104255	−	2.32141i	0.00365862	−	0.0814655i
$813$	−5.90335	+	2.84291i	−0.207040	+	0.0997050i
$814$	−36.5656	−	3.29097i	−1.28162	−	0.115348i
$815$	−2.10612	+	9.22752i	−0.0737742	+	0.323226i
$816$	−4.55522	+	10.6575i	−0.159465	+	0.373086i
$817$	8.88560	−	20.7889i	0.310868	−	0.727312i
$818$	−10.4036	+	45.5811i	−0.363753	+	1.59371i
$819$	−18.2023	−	1.63823i	−0.636038	−	0.0572445i
$820$	1.04308	−	0.502321i	0.0364259	−	0.0175418i
$821$	1.16597	−	25.9624i	0.0406927	−	0.906093i	−0.870011	−	0.493032i	$-0.835888\pi$
$821$	1.16597	−	25.9624i	0.0406927	−	0.906093i	0.910704	−	0.413060i	$-0.135540\pi$
$822$	13.6402	−	17.1042i	0.475756	−	0.596579i
$823$	4.22038	−	31.1561i	0.147113	−	1.08603i	−0.755367	−	0.655302i	$-0.772541\pi$
$823$	4.22038	−	31.1561i	0.147113	−	1.08603i	0.902480	−	0.430732i	$-0.141745\pi$
$824$	−35.4425	+	3.18988i	−1.23470	+	0.111125i
$825$	−14.8518	+	8.87353i	−0.517073	+	0.308937i
$826$	−10.6330	−	13.3334i	−0.369970	−	0.463928i
$827$	−14.8778	+	10.8093i	−0.517350	+	0.375877i	−0.815605	−	0.578609i	$-0.803596\pi$
$827$	−14.8778	+	10.8093i	−0.517350	+	0.375877i	0.298254	+	0.954486i	$0.403596\pi$
$828$	0.540771	+	0.0981355i	0.0187931	+	0.00341044i
$829$	8.36076	+	36.6309i	0.290381	+	1.27224i	0.883996	+	0.467494i	$0.154843\pi$
$829$	8.36076	+	36.6309i	0.290381	+	1.27224i	−0.593615	+	0.804749i	$0.702300\pi$
$830$	−2.57360	−	18.9991i	−0.0893310	−	0.659468i
$831$	17.0633	+	10.1949i	0.591921	+	0.353656i
$832$	−36.0609	−	17.3660i	−1.25019	−	0.602059i
$833$	−2.00713	+	3.72986i	−0.0695428	+	0.129232i
$834$	8.85274	+	9.25925i	0.306545	+	0.320621i
$835$	7.51730	+	5.46164i	0.260147	+	0.189008i
$836$	0.0667512	+	1.48633i	0.00230864	+	0.0514059i
$837$	4.76296	+	8.85106i	0.164632	+	0.305937i
$838$	−7.57259	+	23.3060i	−0.261591	+	0.805093i
$839$	−28.6521	+	7.90746i	−0.989179	+	0.272996i	−0.722940	−	0.690911i	$-0.757210\pi$
$839$	−28.6521	+	7.90746i	−0.989179	+	0.272996i	−0.266239	+	0.963907i	$0.585781\pi$
$840$	−17.3861	+	26.3388i	−0.599876	+	0.908774i
$841$	−31.3660	−	8.65648i	−1.08159	−	0.298499i
$842$	−4.43185	+	3.87199i	−0.152732	+	0.133438i
$843$	−25.6443	+	9.62448i	−0.883238	+	0.331485i
$844$	0.650484	+	0.244131i	0.0223906	+	0.00840332i
$845$	31.4620	+	27.4876i	1.08233	+	0.945601i
$846$	−8.42078	−	12.7569i	−0.289512	−	0.438592i
$847$	−8.97609	−	27.6256i	−0.308422	−	0.949226i
$848$	−0.0212226	+	0.0221971i	−0.000728788	+	0.000762253i
$849$	15.5356	−	2.81930i	0.533181	−	0.0967580i
$850$	3.23856	+	7.57699i	0.111082	+	0.259889i
$851$	27.2034			0.932519
$852$	0.532338	+	0.993848i	0.0182376	+	0.0340487i
$853$	−49.1915			−1.68429			−0.842143	−	0.539254i	$-0.818706\pi$
$853$	−49.1915			−1.68429			−0.842143	+	0.539254i	$0.818706\pi$
$854$	−5.58052	−	13.0563i	−0.190961	−	0.446776i
$855$	−10.4988	+	1.90526i	−0.359053	+	0.0651585i
$856$	5.90556	−	6.17673i	0.201848	−	0.211116i
$857$	−1.22916	−	3.78296i	−0.0419872	−	0.129223i	0.927866	−	0.372915i	$-0.121642\pi$
$857$	−1.22916	−	3.78296i	−0.0419872	−	0.129223i	−0.969853	+	0.243691i	$0.921642\pi$
$858$	26.0964	+	39.5343i	0.890915	+	1.34968i
$859$	−11.8567	−	10.3589i	−0.404547	−	0.353442i	0.431488	−	0.902119i	$-0.357989\pi$
$859$	−11.8567	−	10.3589i	−0.404547	−	0.353442i	−0.836034	+	0.548677i	$0.815132\pi$
$860$	−1.74346	−	0.654333i	−0.0594516	−	0.0223126i
$861$	16.2028	−	6.08102i	0.552191	−	0.207241i
$862$	−7.81778	+	6.83019i	−0.266275	+	0.232637i
$863$	−7.64871	−	2.11091i	−0.260365	−	0.0718562i	0.133417	−	0.991060i	$-0.457405\pi$
$863$	−7.64871	−	2.11091i	−0.260365	−	0.0718562i	−0.393782	+	0.919204i	$0.628834\pi$
$864$	−1.72756	+	2.61715i	−0.0587729	+	0.0890371i
$865$	−39.4128	+	10.8772i	−1.34008	+	0.369837i
$866$	1.26718	−	3.89998i	0.0430606	−	0.132527i
$867$	−8.29915	−	15.4224i	−0.281854	−	0.523772i
$868$	−0.0236628	−	0.526893i	−0.000803167	−	0.0178839i
$869$	43.2714	+	31.4385i	1.46788	+	1.06648i
$870$	−29.8513	−	31.2220i	−1.01205	−	1.05853i
$871$	−12.1994	+	22.6703i	−0.413362	+	0.768155i
$872$	41.2353	+	19.8579i	1.39640	+	0.672472i
$873$	18.2692	+	10.9153i	0.618319	+	0.369428i
$874$	−3.15918	−	23.3220i	−0.106861	−	0.788879i
$875$	−4.12460	−	18.0711i	−0.139437	−	0.610913i
$876$	−0.00951773	−	0.00172721i	−0.000321574	−	5.83571e-5i
$877$	37.0096	−	26.8891i	1.24973	−	0.907979i	0.251520	−	0.967852i	$-0.419070\pi$
$877$	37.0096	−	26.8891i	1.24973	−	0.907979i	0.998206	+	0.0598732i	$0.0190696\pi$
$878$	−22.9923	−	28.8314i	−0.775953	−	0.973014i
$879$	−12.6543	+	7.56059i	−0.426819	+	0.255012i
$880$	−52.8998	+	4.76107i	−1.78325	+	0.160496i
$881$	−6.85412	+	50.5991i	−0.230921	+	1.70473i	0.389967	+	0.920829i	$0.372486\pi$
$881$	−6.85412	+	50.5991i	−0.230921	+	1.70473i	−0.620888	+	0.783899i	$0.713228\pi$
$882$	−2.15739	+	2.70529i	−0.0726432	+	0.0910917i
$883$	1.23362	−	27.4688i	0.0415147	−	0.924397i	−0.864883	−	0.501973i	$-0.832608\pi$
$883$	1.23362	−	27.4688i	0.0415147	−	0.924397i	0.906398	−	0.422424i	$-0.138821\pi$
$884$	0.952189	−	0.458550i	0.0320256	−	0.0154227i
$885$	−14.7900	−	1.33112i	−0.497161	−	0.0447453i
$886$	−4.18695	+	18.3442i	−0.140663	+	0.616287i
$887$	−2.43266	+	5.69150i	−0.0816808	+	0.191102i	−0.955390	−	0.295346i	$-0.904565\pi$
$887$	−2.43266	+	5.69150i	−0.0816808	+	0.191102i	0.873709	+	0.486448i	$0.161708\pi$
$888$	−8.22276	+	19.2381i	−0.275938	+	0.645588i
$889$	8.26051	−	36.1917i	0.277049	−	1.21383i
$890$	45.9742	+	4.13776i	1.54106	+	0.138698i
$891$	−17.3729	+	8.36635i	−0.582014	+	0.280283i
$892$	−0.0876464	+	1.95160i	−0.00293462	+	0.0653444i
$893$	−19.1167	+	23.9716i	−0.639715	+	0.802178i
$894$	2.00044	−	14.7678i	0.0669046	−	0.493910i
$895$	33.6980	−	3.03287i	1.12640	−	0.101378i
$896$	−31.2411	+	18.6657i	−1.04369	+	0.623576i
$897$	−21.8845	−	27.4423i	−0.730702	−	0.916272i
$898$	45.0215	−	32.7100i	1.50239	−	1.09155i
$899$	−13.7430	−	2.49399i	−0.458356	−	0.0831793i
$900$	0.0701653	+	0.307414i	0.00233884	+	0.0102471i
$901$	0.00200207	+	0.0147799i	6.66988e−5	+	0.000492390i
$902$	23.8293	+	14.2373i	0.793428	+	0.474051i
$903$	−25.0805	−	12.0781i	−0.834626	−	0.401935i
$904$	14.9453	−	27.7731i	0.497074	−	0.923719i
$905$	−34.0201	−	35.5822i	−1.13087	−	1.18279i
$906$	29.0019	+	21.0711i	0.963522	+	0.700040i
$907$	1.50826	+	33.5840i	0.0500809	+	1.11514i	0.853958	+	0.520343i	$0.174196\pi$
$907$	1.50826	+	33.5840i	0.0500809	+	1.11514i	−0.803877	+	0.594796i	$0.797233\pi$
$908$	0.226348	+	0.420624i	0.00751161	+	0.0139589i
$909$	4.78978	−	14.7414i	0.158867	−	0.488942i
$910$	62.1389	−	17.1493i	2.05989	−	0.568492i
$911$	9.12339	−	13.8214i	0.302272	−	0.457922i	−0.651416	−	0.758721i	$-0.725825\pi$
$911$	9.12339	−	13.8214i	0.302272	−	0.457922i	0.953688	+	0.300799i	$0.0972533\pi$
$912$	18.3077	+	5.05261i	0.606229	+	0.167309i
$913$	16.2159	−	14.1674i	0.536669	−	0.468874i
$914$	5.30256	−	1.99008i	0.175393	−	0.0658262i
$915$	−11.5753	−	4.34428i	−0.382667	−	0.143617i
$916$	−0.0635178	−	0.0554939i	−0.00209869	−	0.00183357i
$917$	−7.04626	−	10.6746i	−0.232688	−	0.352507i
$918$	5.13833	+	15.8141i	0.169590	+	0.521945i
$919$	−20.1333	+	21.0578i	−0.664136	+	0.694631i	−0.965948	−	0.258736i	$-0.916694\pi$
$919$	−20.1333	+	21.0578i	−0.664136	+	0.694631i	0.301812	+	0.953367i	$0.402408\pi$
$920$	36.9048	−	6.69724i	1.21672	−	0.220802i
$921$	−9.19696	−	21.5174i	−0.303050	−	0.709021i
$922$	−5.48514			−0.180643
$923$	−9.99864	+	43.4199i	−0.329109	+	1.42918i
$924$	1.83195			0.0602666
$925$	6.13401	+	14.3512i	0.201685	+	0.471866i
$926$	−9.70299	+	1.76083i	−0.318860	+	0.0578646i
$927$	−10.2376	+	10.7077i	−0.336248	+	0.351688i
$928$	−1.34662	−	4.14447i	−0.0442050	−	0.136049i
$929$	11.6262	+	17.6129i	0.381442	+	0.577860i	0.973685	−	0.227900i	$-0.0731859\pi$
$929$	11.6262	+	17.6129i	0.381442	+	0.577860i	−0.592243	+	0.805760i	$0.701757\pi$
$930$	−7.38334	−	6.45063i	−0.242109	−	0.211524i
$931$	6.49810	+	2.43878i	0.212966	+	0.0799277i
$932$	−0.180018	+	0.0675618i	−0.00589668	+	0.00221306i
$933$	−1.66763	+	1.45696i	−0.0545957	+	0.0476988i
$934$	38.4953	+	10.6240i	1.25960	+	0.347628i
$935$	−14.2107	+	21.5282i	−0.464739	+	0.704049i
$936$	−16.1028	+	4.44408i	−0.526336	+	0.145259i
$937$	−5.62483	+	17.3114i	−0.183755	+	0.565540i	−0.999925	−	0.0122723i	$-0.996094\pi$
$937$	−5.62483	+	17.3114i	−0.183755	+	0.565540i	0.816170	+	0.577813i	$0.196094\pi$
$938$	10.0718	+	18.7165i	0.328855	+	0.611115i
$939$	−1.52185	−	33.8865i	−0.0496636	−	1.10585i
$940$	2.04316	+	1.48444i	0.0666405	+	0.0484172i
$941$	−20.9473	−	21.9092i	−0.682863	−	0.714218i	0.286984	−	0.957935i	$-0.407347\pi$
$941$	−20.9473	−	21.9092i	−0.682863	−	0.714218i	−0.969846	+	0.243717i	$0.921633\pi$
$942$	17.4847	−	32.4920i	0.569682	−	1.05865i
$943$	−18.5312	−	8.92416i	−0.603459	−	0.290611i
$944$	−14.0407	−	8.38894i	−0.456986	−	0.273037i
$945$	6.37714	+	47.0779i	0.207448	+	1.53144i
$946$	−9.93545	−	43.5301i	−0.323029	−	1.41528i
$947$	26.0528	+	4.72789i	0.846603	+	0.153636i	0.584490	−	0.811401i	$-0.301295\pi$
$947$	26.0528	+	4.72789i	0.846603	+	0.153636i	0.262114	+	0.965037i	$0.415580\pi$
$948$	−1.27447	+	0.925958i	−0.0413929	+	0.0300737i
$949$	−0.238350	−	0.298881i	−0.00773716	−	0.00970209i
$950$	11.5913	−	6.92546i	0.376071	−	0.224692i
$951$	−44.9505	+	4.04562i	−1.45762	+	0.131188i
$952$	−2.26613	+	16.7292i	−0.0734455	+	0.542197i
$953$	−22.9407	+	28.7667i	−0.743122	+	0.931846i	−0.999396	−	0.0347585i	$-0.988934\pi$
$953$	−22.9407	+	28.7667i	−0.743122	+	0.931846i	0.256273	+	0.966604i	$0.417505\pi$
$954$	−0.000546650		0.0121721i	−1.76985e−5		0.000394087i
$955$	21.4196	−	10.3151i	0.693121	−	0.333789i
$956$	−0.0519008	−	0.00467115i	−0.00167859	−	0.000151076i
$957$	10.7955	−	47.2981i	0.348968	−	1.52893i
$958$	−6.26643	+	14.6610i	−0.202459	+	0.473677i
$959$	13.1410	−	30.7450i	0.424346	−	0.992807i
$960$	−6.40262	+	28.0517i	−0.206644	+	0.905365i
$961$	27.7178	+	2.49464i	0.894121	+	0.0804723i
$962$	38.5017	−	18.5414i	1.24134	−	0.597800i
$963$	0.159608	−	3.55395i	0.00514331	−	0.114525i
$964$	−0.627670	+	0.787073i	−0.0202159	+	0.0253499i
$965$	1.40879	−	10.4001i	0.0453506	−	0.334792i
$966$	−28.8617	+	2.59760i	−0.928611	+	0.0835765i
$967$	51.6038	−	30.8318i	1.65947	−	0.991484i	0.698183	−	0.715919i	$-0.253992\pi$
$967$	51.6038	−	30.8318i	1.65947	−	0.991484i	0.961282	−	0.275565i	$-0.0888650\pi$
$968$	−16.5538	−	20.7578i	−0.532059	−	0.667181i
$969$	7.46225	−	5.42164i	0.239722	−	0.174168i
$970$	−73.8577	−	13.4032i	−2.37143	−	0.430350i
$971$	−11.4916	−	50.3481i	−0.368784	−	1.61575i	−0.730125	−	0.683313i	$-0.760538\pi$
$971$	−11.4916	−	50.3481i	−0.368784	−	1.61575i	0.361342	−	0.932433i	$-0.382319\pi$
$972$	0.147204	+	1.08670i	0.00472156	+	0.0348559i
$973$	16.8071	+	10.0418i	0.538812	+	0.321925i
$974$	−37.1650	−	17.8977i	−1.19084	−	0.573480i
$975$	9.54261	−	17.7331i	0.305608	−	0.567915i
$976$	−9.41064	−	9.84276i	−0.301227	−	0.315059i
$977$	8.49605	+	6.17274i	0.271813	+	0.197483i	0.715338	−	0.698778i	$-0.246273\pi$
$977$	8.49605	+	6.17274i	0.271813	+	0.197483i	−0.443526	+	0.896262i	$0.646273\pi$
$978$	−0.299872	−	6.67718i	−0.00958886	−	0.213513i
$979$	24.5668	+	45.6528i	0.785160	+	1.45907i
$980$	0.176663	−	0.543712i	0.00564328	−	0.0173682i
$981$	18.3665	−	5.06882i	0.586396	−	0.161835i
$982$	−14.7044	+	22.2763i	−0.469237	+	0.710864i
$983$	21.2775	+	5.87220i	0.678645	+	0.187294i	0.588332	−	0.808619i	$-0.299785\pi$
$983$	21.2775	+	5.87220i	0.678645	+	0.187294i	0.0903130	+	0.995913i	$0.471213\pi$
$984$	11.9126	−	10.4077i	0.379759	−	0.331785i
$985$	67.4543	−	25.3160i	2.14927	−	0.806636i
$986$	−21.6333	−	8.11913i	−0.688946	−	0.258566i
$987$	28.4301	+	24.8387i	0.904941	+	0.790623i
$988$	−0.954045	−	1.44532i	−0.0303522	−	0.0459816i
$989$	10.2234	+	31.4645i	0.325086	+	1.00051i
$990$	−14.5628	+	15.2315i	−0.462836	+	0.484089i
$991$	−31.5816	+	5.73121i	−1.00322	+	0.182058i	−0.655222	−	0.755437i	$-0.727425\pi$
$991$	−31.5816	+	5.73121i	−1.00322	+	0.182058i	−0.348000	+	0.937495i	$0.613139\pi$
$992$	−0.388735	−	0.909491i	−0.0123423	−	0.0288764i
$993$	24.6921			0.783579
$994$	25.3696	+	26.6374i	0.804675	+	0.844887i
$995$	−3.50013			−0.110962
$996$	0.249262	+	0.583177i	0.00789816	+	0.0184787i
$997$	0.859117	−	0.155907i	0.0272085	−	0.00493762i	−0.164936	−	0.986304i	$-0.552742\pi$
$997$	0.859117	−	0.155907i	0.0272085	−	0.00493762i	0.192144	+	0.981367i	$0.438456\pi$
$998$	5.14171	−	5.37780i	0.162758	−	0.170231i
$999$	9.73227	+	29.9529i	0.307916	+	0.947667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.g.a.19.2	yes	120
3.2	odd	2		639.2.v.a.19.4		120
71.15	even	35	inner	71.2.g.a.15.2	✓	120
71.21	odd	70		5041.2.a.t.1.44		60
71.50	even	35		5041.2.a.s.1.44		60
213.86	odd	70		639.2.v.a.370.4		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.g.a.15.2	✓	120	71.15	even	35	inner
71.2.g.a.19.2	yes	120	1.1	even	1	trivial
639.2.v.a.19.4		120	3.2	odd	2
639.2.v.a.370.4		120	213.86	odd	70
5041.2.a.s.1.44		60	71.50	even	35
5041.2.a.t.1.44		60	71.21	odd	70

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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.g (of order \(35\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.569315 - 1.33198i) q^{2} +(1.33945 - 0.243074i) q^{3} +(-0.0679233 + 0.0710422i) q^{4} +(0.862898 + 2.65573i) q^{5} +(-1.08634 - 1.64573i) q^{6} +(-2.26960 - 1.98289i) q^{7} +(-2.57906 - 0.967939i) q^{8} +(-1.07366 + 0.402953i) q^{9} +O(q^{10})\)	\(q+(-0.569315 - 1.33198i) q^{2} +(1.33945 - 0.243074i) q^{3} +(-0.0679233 + 0.0710422i) q^{4} +(0.862898 + 2.65573i) q^{5} +(-1.08634 - 1.64573i) q^{6} +(-2.26960 - 1.98289i) q^{7} +(-2.57906 - 0.967939i) q^{8} +(-1.07366 + 0.402953i) q^{9} +(3.04611 - 2.66131i) q^{10} +(4.37920 + 1.20858i) q^{11} +(-0.0737113 + 0.111668i) q^{12} +(-5.09730 + 1.40677i) q^{13} +(-1.34905 + 4.15196i) q^{14} +(1.80135 + 3.34747i) q^{15} +(0.187845 + 4.18270i) q^{16} +(1.64509 + 1.19523i) q^{17} +(1.14798 + 1.20069i) q^{18} +(1.57897 - 2.93423i) q^{19} +(-0.247280 - 0.119084i) q^{20} +(-3.52201 - 2.10430i) q^{21} +(-0.883339 - 6.52107i) q^{22} +(1.08502 + 4.75376i) q^{23} +(-3.68981 - 0.669601i) q^{24} +(-2.26321 + 1.64432i) q^{25} +(4.77575 + 5.98860i) q^{26} +(-4.84606 + 2.89539i) q^{27} +(0.295028 - 0.0265530i) q^{28} +(1.05301 - 7.77366i) q^{29} +(3.43322 - 4.30512i) q^{30} +(0.0798823 - 1.77872i) q^{31} +(0.500494 - 0.241025i) q^{32} +(6.15950 + 0.554365i) q^{33} +(0.655444 - 2.87169i) q^{34} +(3.30759 - 7.73849i) q^{35} +(0.0443001 - 0.103645i) q^{36} +(1.24145 - 5.43914i) q^{37} +(-4.80726 - 0.432661i) q^{38} +(-6.48563 + 3.12331i) q^{39} +(0.345112 - 7.68452i) q^{40} +(-2.63002 + 3.29794i) q^{41} +(-0.797755 + 5.88926i) q^{42} +(6.75768 - 0.608202i) q^{43} +(-0.383310 + 0.229017i) q^{44} +(-1.99659 - 2.50365i) q^{45} +(5.71420 - 4.15161i) q^{46} +(-9.05378 - 1.64302i) q^{47} +(1.26832 + 5.55686i) q^{48} +(0.279605 + 2.06412i) q^{49} +(3.47868 + 2.07841i) q^{50} +(2.49405 + 1.20107i) q^{51} +(0.246286 - 0.457675i) q^{52} +(0.00506880 + 0.00530155i) q^{53} +(6.61553 + 4.80646i) q^{54} +(0.569138 + 12.6728i) q^{55} +(3.93414 + 7.31085i) q^{56} +(1.40172 - 4.31406i) q^{57} +(-10.9539 + 3.02307i) q^{58} +(-2.15204 + 3.26021i) q^{59} +(-0.360165 - 0.0993992i) q^{60} +(-2.44931 + 2.13990i) q^{61} +(-2.41469 + 0.906249i) q^{62} +(3.23580 + 1.21442i) q^{63} +(5.70011 + 4.98004i) q^{64} +(-8.13443 - 12.3231i) q^{65} +(-2.76829 - 8.51993i) q^{66} +(3.36449 - 3.51898i) q^{67} +(-0.196652 + 0.0356870i) q^{68} +(2.60884 + 6.10369i) q^{69} -12.1906 q^{70} +(4.00722 - 7.41230i) q^{71} +3.15908 q^{72} +(0.0284136 + 0.0664769i) q^{73} +(-7.95159 + 1.44300i) q^{74} +(-2.63176 + 2.75261i) q^{75} +(0.101205 + 0.311476i) q^{76} +(-7.54257 - 11.4265i) q^{77} +(7.85256 + 6.86057i) q^{78} +(11.0228 + 4.13694i) q^{79} +(-10.9460 + 4.10811i) q^{80} +(-3.19642 + 2.79263i) q^{81} +(5.89009 + 1.62556i) q^{82} +(2.61121 - 3.95581i) q^{83} +(0.388721 - 0.107280i) q^{84} +(-1.75466 + 5.40027i) q^{85} +(-4.65736 - 8.65483i) q^{86} +(-0.479118 - 10.6684i) q^{87} +(-10.1244 - 7.35581i) q^{88} +(7.88631 + 8.24844i) q^{89} +(-2.19812 + 4.08479i) q^{90} +(14.3583 + 6.91460i) q^{91} +(-0.411416 - 0.245809i) q^{92} +(-0.325362 - 2.40192i) q^{93} +(2.96599 + 12.9948i) q^{94} +(9.15500 + 1.66139i) q^{95} +(0.611800 - 0.444499i) q^{96} +(-11.5705 - 14.5089i) q^{97} +(2.59019 - 1.54756i) q^{98} +(-5.18879 + 0.467000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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