LMFDB - Embedded newform 216.2.t.a.13.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(13,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("216.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			13.19
Character	$\chi$	$=$	216.13
Dual form			216.2.t.a.133.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.201435 + 1.39979i) q^{2} +(1.40283 - 1.01591i) q^{3} +(-1.91885 + 0.563935i) q^{4} +(1.55785 - 1.85658i) q^{5} +(1.70465 + 1.75903i) q^{6} +(0.763942 + 0.278052i) q^{7} +(-1.17592 - 2.57240i) q^{8} +(0.935847 - 2.85030i) q^{9} +O(q^{10})$	\(q+(0.201435 + 1.39979i) q^{2} +(1.40283 - 1.01591i) q^{3} +(-1.91885 + 0.563935i) q^{4} +(1.55785 - 1.85658i) q^{5} +(1.70465 + 1.75903i) q^{6} +(0.763942 + 0.278052i) q^{7} +(-1.17592 - 2.57240i) q^{8} +(0.935847 - 2.85030i) q^{9} +(2.91263 + 1.80670i) q^{10} +(2.23007 + 2.65769i) q^{11} +(-2.11890 + 2.74048i) q^{12} +(-2.83964 - 0.500705i) q^{13} +(-0.235331 + 1.12537i) q^{14} +(0.299281 - 4.18710i) q^{15} +(3.36395 - 2.16421i) q^{16} +(-3.55127 + 6.15099i) q^{17} +(4.17834 + 0.735844i) q^{18} +(5.16371 - 2.98127i) q^{19} +(-1.94230 + 4.44102i) q^{20} +(1.35415 - 0.386038i) q^{21} +(-3.27101 + 3.65699i) q^{22} +(-6.58997 + 2.39855i) q^{23} +(-4.26293 - 2.41400i) q^{24} +(-0.151733 - 0.860521i) q^{25} +(0.128881 - 4.07577i) q^{26} +(-1.58282 - 4.94921i) q^{27} +(-1.62269 - 0.102726i) q^{28} +(-6.59552 + 1.16297i) q^{29} +(5.92137 - 0.424498i) q^{30} +(2.55724 - 0.930757i) q^{31} +(3.70707 + 4.27290i) q^{32} +(5.82838 + 1.46273i) q^{33} +(-9.32547 - 3.73203i) q^{34} +(1.70634 - 0.985154i) q^{35} +(-0.188366 + 5.99704i) q^{36} +(-3.59434 - 2.07519i) q^{37} +(5.21332 + 6.62760i) q^{38} +(-4.49220 + 2.18242i) q^{39} +(-6.60776 - 1.82424i) q^{40} +(-0.742124 + 4.20880i) q^{41} +(0.813149 + 1.81778i) q^{42} +(1.77034 + 2.10981i) q^{43} +(-5.77793 - 3.84209i) q^{44} +(-3.83389 - 6.17782i) q^{45} +(-4.68493 - 8.74145i) q^{46} +(2.80028 + 1.01922i) q^{47} +(2.52040 - 6.45349i) q^{48} +(-4.85602 - 4.07468i) q^{49} +(1.17399 - 0.385734i) q^{50} +(1.26704 + 12.2365i) q^{51} +(5.73120 - 0.640596i) q^{52} -7.38929i q^{53} +(6.60904 - 3.21256i) q^{54} +8.40834 q^{55} +(-0.183072 - 2.29213i) q^{56} +(4.21509 - 9.42808i) q^{57} +(-2.95649 - 8.99811i) q^{58} +(4.72368 - 5.62947i) q^{59} +(1.78698 + 8.20319i) q^{60} +(-0.0900385 + 0.247379i) q^{61} +(1.81799 + 3.39212i) q^{62} +(1.50746 - 1.91725i) q^{63} +(-5.23444 + 6.04985i) q^{64} +(-5.35335 + 4.49199i) q^{65} +(-0.873481 + 8.45318i) q^{66} +(-2.20513 - 0.388825i) q^{67} +(3.34560 - 13.8055i) q^{68} +(-6.80787 + 10.0596i) q^{69} +(1.72273 + 2.19008i) q^{70} +(2.69918 - 4.67512i) q^{71} +(-8.43257 + 0.944340i) q^{72} +(-1.97245 - 3.41639i) q^{73} +(2.18082 - 5.44935i) q^{74} +(-1.08707 - 1.05302i) q^{75} +(-8.22713 + 8.63260i) q^{76} +(0.964666 + 2.65040i) q^{77} +(-3.95983 - 5.84853i) q^{78} +(1.76846 + 10.0295i) q^{79} +(1.22252 - 9.61697i) q^{80} +(-7.24838 - 5.33489i) q^{81} +(-6.04094 - 0.191022i) q^{82} +(-7.86515 + 1.38684i) q^{83} +(-2.38072 + 1.50440i) q^{84} +(5.88742 + 16.1756i) q^{85} +(-2.59669 + 2.90311i) q^{86} +(-8.07090 + 8.33191i) q^{87} +(4.21426 - 8.86184i) q^{88} +(2.14833 + 3.72101i) q^{89} +(7.87540 - 6.61108i) q^{90} +(-2.03010 - 1.17208i) q^{91} +(11.2925 - 8.31878i) q^{92} +(2.64179 - 3.90362i) q^{93} +(-0.862622 + 4.12512i) q^{94} +(2.50935 - 14.2312i) q^{95} +(9.54126 + 2.22808i) q^{96} +(4.28345 - 3.59424i) q^{97} +(4.72554 - 7.61821i) q^{98} +(9.66221 - 3.86916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.201435	+	1.39979i	0.142436	+	0.989804i
$2$	0.201435	+	1.39979i	0.142436	+	0.989804i
$3$	1.40283	−	1.01591i	0.809923	−	0.586537i
$3$	1.40283	−	1.01591i	0.809923	−	0.586537i
$4$	−1.91885	+	0.563935i	−0.959424	+	0.281968i
$5$	1.55785	−	1.85658i	0.696694	−	0.830287i	−0.295454	−	0.955357i	$-0.595471\pi$
$5$	1.55785	−	1.85658i	0.696694	−	0.830287i	0.992148	+	0.125070i	$0.0399154\pi$
$6$	1.70465	+	1.75903i	0.695919	+	0.718121i
$7$	0.763942	+	0.278052i	0.288743	+	0.105094i	0.482331	−	0.875989i	$-0.339790\pi$
$7$	0.763942	+	0.278052i	0.288743	+	0.105094i	−0.193588	+	0.981083i	$0.562012\pi$
$8$	−1.17592	−	2.57240i	−0.415749	−	0.909479i
$9$	0.935847	−	2.85030i	0.311949	−	0.950099i
$10$	2.91263	+	1.80670i	0.921056	+	0.571327i
$11$	2.23007	+	2.65769i	0.672391	+	0.801324i	0.989107	−	0.147196i	$-0.0470248\pi$
$11$	2.23007	+	2.65769i	0.672391	+	0.801324i	−0.316716	+	0.948520i	$0.602580\pi$
$12$	−2.11890	+	2.74048i	−0.611675	+	0.791109i
$13$	−2.83964	−	0.500705i	−0.787574	−	0.138871i	−0.234626	−	0.972086i	$-0.575386\pi$
$13$	−2.83964	−	0.500705i	−0.787574	−	0.138871i	−0.552949	+	0.833215i	$0.686498\pi$
$14$	−0.235331	+	1.12537i	−0.0628949	+	0.300768i
$15$	0.299281	−	4.18710i	0.0772740	−	1.08110i
$16$	3.36395	−	2.16421i	0.840989	−	0.541053i
$17$	−3.55127	+	6.15099i	−0.861310	+	1.49183i	0.00935441	+	0.999956i	$0.497022\pi$
$17$	−3.55127	+	6.15099i	−0.861310	+	1.49183i	−0.870665	+	0.491877i	$0.836311\pi$
$18$	4.17834	+	0.735844i	0.984844	+	0.173440i
$19$	5.16371	−	2.98127i	1.18464	−	0.683950i	0.227554	−	0.973765i	$-0.426927\pi$
$19$	5.16371	−	2.98127i	1.18464	−	0.683950i	0.957083	+	0.289815i	$0.0935939\pi$
$20$	−1.94230	+	4.44102i	−0.434311	+	0.993043i
$21$	1.35415	−	0.386038i	0.295501	−	0.0842405i
$22$	−3.27101	+	3.65699i	−0.697381	+	0.779673i
$23$	−6.58997	+	2.39855i	−1.37410	+	0.500133i	−0.920386	−	0.391012i	$-0.872125\pi$
$23$	−6.58997	+	2.39855i	−1.37410	+	0.500133i	−0.453719	+	0.891145i	$0.649903\pi$
$24$	−4.26293	−	2.41400i	−0.870168	−	0.492756i
$25$	−0.151733	−	0.860521i	−0.0303466	−	0.172104i
$26$	0.128881	−	4.07577i	0.0252757	−	0.799325i
$27$	−1.58282	−	4.94921i	−0.304613	−	0.952476i
$28$	−1.62269	−	0.102726i	−0.306660	−	0.0194134i
$29$	−6.59552	+	1.16297i	−1.22476	+	0.215958i	−0.748372	−	0.663279i	$-0.769164\pi$
$29$	−6.59552	+	1.16297i	−1.22476	+	0.215958i	−0.476385	+	0.879237i	$0.658053\pi$
$30$	5.92137	−	0.424498i	1.08109	−	0.0775023i
$31$	2.55724	−	0.930757i	0.459293	−	0.167169i	−0.102003	−	0.994784i	$-0.532525\pi$
$31$	2.55724	−	0.930757i	0.459293	−	0.167169i	0.561296	+	0.827615i	$0.310303\pi$
$32$	3.70707	+	4.27290i	0.655324	+	0.755348i
$33$	5.82838	+	1.46273i	1.01459	+	0.254629i
$34$	−9.32547	−	3.73203i	−1.59930	−	0.640037i
$35$	1.70634	−	0.985154i	0.288423	−	0.166521i
$36$	−0.188366	+	5.99704i	−0.0313944	+	0.999507i
$37$	−3.59434	−	2.07519i	−0.590905	−	0.341159i	0.174550	−	0.984648i	$-0.444153\pi$
$37$	−3.59434	−	2.07519i	−0.590905	−	0.341159i	−0.765455	+	0.643489i	$0.777486\pi$
$38$	5.21332	+	6.62760i	0.845712	+	1.07514i
$39$	−4.49220	+	2.18242i	−0.719327	+	0.349467i
$40$	−6.60776	−	1.82424i	−1.04478	−	0.288437i
$41$	−0.742124	+	4.20880i	−0.115900	+	0.657304i	0.870400	+	0.492345i	$0.163860\pi$
$41$	−0.742124	+	4.20880i	−0.115900	+	0.657304i	−0.986301	+	0.164959i	$0.947251\pi$
$42$	0.813149	+	1.81778i	0.125472	+	0.280489i
$43$	1.77034	+	2.10981i	0.269975	+	0.321743i	0.883950	−	0.467582i	$-0.154875\pi$
$43$	1.77034	+	2.10981i	0.269975	+	0.321743i	−0.613975	+	0.789326i	$0.710430\pi$
$44$	−5.77793	−	3.84209i	−0.871055	−	0.579217i
$45$	−3.83389	−	6.17782i	−0.571522	−	0.920935i
$46$	−4.68493	−	8.74145i	−0.690756	−	1.28886i
$47$	2.80028	+	1.01922i	0.408463	+	0.148668i	0.538076	−	0.842896i	$-0.319151\pi$
$47$	2.80028	+	1.01922i	0.408463	+	0.148668i	−0.129613	+	0.991565i	$0.541374\pi$
$48$	2.52040	−	6.45349i	0.363788	−	0.931482i
$49$	−4.85602	−	4.07468i	−0.693717	−	0.582097i
$50$	1.17399	−	0.385734i	0.166027	−	0.0545511i
$51$	1.26704	+	12.2365i	0.177420	+	1.71346i
$52$	5.73120	−	0.640596i	0.794775	−	0.0888347i
$53$		−	7.38929i		−	1.01500i	−0.861653	−	0.507498i	$-0.830570\pi$
$53$		−	7.38929i		−	1.01500i	0.861653	−	0.507498i	$-0.169430\pi$
$54$	6.60904	−	3.21256i	0.899377	−	0.437174i
$55$	8.40834			1.13378
$56$	−0.183072	−	2.29213i	−0.0244640	−	0.306298i
$57$	4.21509	−	9.42808i	0.558302	−	1.24878i
$58$	−2.95649	−	8.99811i	−0.388206	−	1.18151i
$59$	4.72368	−	5.62947i	0.614971	−	0.732894i	−0.365226	−	0.930919i	$-0.619008\pi$
$59$	4.72368	−	5.62947i	0.614971	−	0.732894i	0.980197	+	0.198025i	$0.0634526\pi$
$60$	1.78698	+	8.20319i	0.230698	+	1.05903i
$61$	−0.0900385	+	0.247379i	−0.0115283	+	0.0316736i	−0.945323	−	0.326135i	$-0.894254\pi$
$61$	−0.0900385	+	0.247379i	−0.0115283	+	0.0316736i	0.933795	+	0.357808i	$0.116476\pi$
$62$	1.81799	+	3.39212i	0.230884	+	0.430799i
$63$	1.50746	−	1.91725i	0.189923	−	0.241550i
$64$	−5.23444	+	6.04985i	−0.654305	+	0.756231i
$65$	−5.35335	+	4.49199i	−0.664001	+	0.557163i
$66$	−0.873481	+	8.45318i	−0.107518	+	1.04051i
$67$	−2.20513	−	0.388825i	−0.269400	−	0.0475025i	0.0373162	−	0.999304i	$-0.488119\pi$
$67$	−2.20513	−	0.388825i	−0.269400	−	0.0475025i	−0.306716	+	0.951801i	$0.599230\pi$
$68$	3.34560	−	13.8055i	0.405713	−	1.67416i
$69$	−6.80787	+	10.0596i	−0.819572	+	1.21103i
$70$	1.72273	+	2.19008i	0.205905	+	0.261764i
$71$	2.69918	−	4.67512i	0.320334	−	0.554835i	−0.660223	−	0.751070i	$-0.729538\pi$
$71$	2.69918	−	4.67512i	0.320334	−	0.554835i	0.980557	+	0.196235i	$0.0628714\pi$
$72$	−8.43257	+	0.944340i	−0.993788	+	0.111292i
$73$	−1.97245	−	3.41639i	−0.230858	−	0.399858i	0.727203	−	0.686423i	$-0.240820\pi$
$73$	−1.97245	−	3.41639i	−0.230858	−	0.399858i	−0.958061	+	0.286565i	$0.907487\pi$
$74$	2.18082	−	5.44935i	0.253515	−	0.633474i
$75$	−1.08707	−	1.05302i	−0.125524	−	0.121592i
$76$	−8.22713	+	8.63260i	−0.943717	+	0.990227i
$77$	0.964666	+	2.65040i	0.109934	+	0.302041i
$78$	−3.95983	−	5.84853i	−0.448362	−	0.662216i
$79$	1.76846	+	10.0295i	0.198968	+	1.12840i	0.906654	+	0.421875i	$0.138628\pi$
$79$	1.76846	+	10.0295i	0.198968	+	1.12840i	−0.707686	+	0.706527i	$0.750261\pi$
$80$	1.22252	−	9.61697i	0.136682	−	1.07521i
$81$	−7.24838	−	5.33489i	−0.805375	−	0.592765i
$82$	−6.04094	−	0.191022i	−0.667110	−	0.0210949i
$83$	−7.86515	+	1.38684i	−0.863312	+	0.152225i	−0.587735	−	0.809054i	$-0.699980\pi$
$83$	−7.86515	+	1.38684i	−0.863312	+	0.152225i	−0.275577	+	0.961279i	$0.588869\pi$
$84$	−2.38072	+	1.50440i	−0.259757	+	0.164144i
$85$	5.88742	+	16.1756i	0.638581	+	1.75449i
$86$	−2.59669	+	2.90311i	−0.280009	+	0.313050i
$87$	−8.07090	+	8.33191i	−0.865292	+	0.893274i
$88$	4.21426	−	8.86184i	0.449242	−	0.944676i
$89$	2.14833	+	3.72101i	0.227722	+	0.394426i	0.957133	−	0.289650i	$-0.0935389\pi$
$89$	2.14833	+	3.72101i	0.227722	+	0.394426i	−0.729410	+	0.684076i	$0.760206\pi$
$90$	7.87540	−	6.61108i	0.830140	−	0.696869i
$91$	−2.03010	−	1.17208i	−0.212812	−	0.122867i
$92$	11.2925	−	8.31878i	1.17733	−	0.867292i
$93$	2.64179	−	3.90362i	0.273941	−	0.404786i
$94$	−0.862622	+	4.12512i	−0.0889727	+	0.425474i
$95$	2.50935	−	14.2312i	0.257454	−	1.46009i
$96$	9.54126	+	2.22808i	0.973801	+	0.227402i
$97$	4.28345	−	3.59424i	0.434918	−	0.364940i	−0.398886	−	0.917001i	$-0.630603\pi$
$97$	4.28345	−	3.59424i	0.434918	−	0.364940i	0.833804	+	0.552061i	$0.186159\pi$
$98$	4.72554	−	7.61821i	0.477352	−	0.769555i
$99$	9.66221	−	3.86916i	0.971089	−	0.388865i
$100$	0.776431	+	1.56564i	0.0776431	+	0.156564i
$101$	−5.64914	+	15.5209i	−0.562110	+	1.54438i	0.254427	+	0.967092i	$0.418113\pi$
$101$	−5.64914	+	15.5209i	−0.562110	+	1.54438i	−0.816537	+	0.577293i	$0.804109\pi$
$102$	−16.8734	+	4.23846i	−1.67072	+	0.419670i
$103$	14.0312	+	11.7736i	1.38254	+	1.16009i	0.968262	+	0.249938i	$0.0804101\pi$
$103$	14.0312	+	11.7736i	1.38254	+	1.16009i	0.414278	+	0.910151i	$0.364034\pi$
$104$	2.05117	+	7.89347i	0.201134	+	0.774018i
$105$	1.39287	−	3.11549i	0.135930	−	0.304040i
$106$	10.3435	−	1.48846i	1.00465	−	0.144572i
$107$			17.0660i			1.64983i	0.565254	+	0.824917i	$0.308778\pi$
$107$			17.0660i			1.64983i	−0.565254	+	0.824917i	$0.691222\pi$
$108$	5.82822	+	8.60418i	0.560821	+	0.827937i
$109$		−	18.3759i		−	1.76009i	−0.474890	−	0.880045i	$-0.657512\pi$
$109$		−	18.3759i		−	1.76009i	0.474890	−	0.880045i	$-0.342488\pi$
$110$	1.69373	+	11.7699i	0.161491	+	1.12222i
$111$	−7.15044	+	0.740394i	−0.678690	+	0.0702751i
$112$	3.17163	−	0.717978i	0.299691	−	0.0678425i
$113$	6.55711	+	5.50207i	0.616841	+	0.517591i	0.896809	−	0.442418i	$-0.145879\pi$
$113$	6.55711	+	5.50207i	0.616841	+	0.517591i	−0.279968	+	0.960009i	$0.590324\pi$
$114$	14.0464	+	4.00111i	1.31557	+	0.374738i
$115$	−5.81311	+	15.9714i	−0.542076	+	1.48934i
$116$	12.0000	−	5.95101i	1.11417	−	0.552537i
$117$	−4.08463	+	7.62523i	−0.377624	+	0.704953i
$118$	8.83161	+	5.47821i	0.813016	+	0.504311i
$119$	−4.42326	+	3.71156i	−0.405480	+	0.340238i
$120$	−11.1228	+	4.15381i	−1.01537	+	0.379190i
$121$	−0.179992	+	1.02079i	−0.0163629	+	0.0927987i
$122$	−0.364416	−	0.0762046i	−0.0329927	−	0.00689924i
$123$	3.23469	+	6.65815i	0.291662	+	0.600345i
$124$	−4.38206	+	3.22810i	−0.393520	+	0.289892i
$125$	8.66046	+	5.00012i	0.774615	+	0.447224i
$126$	2.98741	+	1.72394i	0.266139	+	0.153581i
$127$	−2.28240	−	3.95324i	−0.202530	−	0.350793i	0.746813	−	0.665034i	$-0.231583\pi$
$127$	−2.28240	−	3.95324i	−0.202530	−	0.350793i	−0.949343	+	0.314242i	$0.898250\pi$
$128$	−9.52294	−	6.10849i	−0.841717	−	0.539919i
$129$	4.62687	+	1.16119i	0.407373	+	0.102237i
$130$	−7.36621	−	6.58874i	−0.646060	−	0.577871i
$131$	−4.55139	−	12.5048i	−0.397657	−	1.09255i	−0.963422	−	0.267987i	$-0.913641\pi$
$131$	−4.55139	−	12.5048i	−0.397657	−	1.09255i	0.565766	−	0.824566i	$-0.308581\pi$
$132$	−12.0087	+	0.480073i	−1.04522	+	0.0417850i
$133$	4.77372	−	0.841736i	0.413934	−	0.0729878i
$134$	0.100083	−	3.16506i	0.00864587	−	0.273419i
$135$	−11.6544	−	4.77153i	−1.00305	−	0.410668i
$136$	19.9988	+	1.90223i	1.71488	+	0.163115i
$137$	−0.374428	−	2.12348i	−0.0319895	−	0.181422i	0.964626	−	0.263621i	$-0.0849167\pi$
$137$	−0.374428	−	2.12348i	−0.0319895	−	0.181422i	−0.996616	+	0.0821992i	$0.973806\pi$
$138$	−15.4527	−	7.50327i	−1.31542	−	0.638721i
$139$	0.200125	+	0.549839i	0.0169744	+	0.0466367i	0.947890	−	0.318596i	$-0.103211\pi$
$139$	0.200125	+	0.549839i	0.0169744	+	0.0466367i	−0.930916	+	0.365233i	$0.880989\pi$
$140$	−2.71864	+	2.85262i	−0.229767	+	0.241091i
$141$	4.96375	−	1.41505i	0.418023	−	0.119169i
$142$	7.08792	+	2.83657i	0.594805	+	0.238040i
$143$	−5.00187	−	8.66350i	−0.418278	−	0.724478i
$144$	−3.02050	−	11.6136i	−0.251708	−	0.967803i
$145$	−8.11572	+	14.0568i	−0.673974	+	1.16736i
$146$	4.38492	−	3.44921i	0.362899	−	0.285459i
$147$	−10.9517	−	0.782791i	−0.903278	−	0.0645635i
$148$	8.06726	+	1.95500i	0.663125	+	0.160700i
$149$	21.5708	+	3.80351i	1.76715	+	0.311596i	0.960259	−	0.279109i	$-0.0900390\pi$
$149$	21.5708	+	3.80351i	1.76715	+	0.311596i	0.806888	+	0.590705i	$0.201150\pi$
$150$	1.25503	−	1.73379i	0.102473	−	0.141563i
$151$	5.91767	−	4.96552i	0.481573	−	0.404088i	−0.369422	−	0.929262i	$-0.620444\pi$
$151$	5.91767	−	4.96552i	0.481573	−	0.404088i	0.850995	+	0.525174i	$0.176000\pi$
$152$	−13.7411	−	9.77738i	−1.11455	−	0.793051i
$153$	14.2087	+	15.8786i	1.14870	+	1.28371i
$154$	−3.51569	+	1.88422i	−0.283303	+	0.151835i
$155$	2.25578	−	6.19769i	0.181188	−	0.497811i
$156$	7.38910	−	6.72104i	0.591601	−	0.538114i
$157$	0.882254	−	1.05143i	0.0704116	−	0.0839132i	−0.729689	−	0.683779i	$-0.760335\pi$
$157$	0.882254	−	1.05143i	0.0704116	−	0.0839132i	0.800100	+	0.599866i	$0.204780\pi$
$158$	−13.6829	+	4.49577i	−1.08856	+	0.357664i
$159$	−7.50686	−	10.3659i	−0.595333	−	0.822068i
$160$	13.7080	−	0.225917i	1.08372	−	0.0178603i
$161$	−5.70128			−0.449324
$162$	6.00766	−	11.2209i	0.472007	−	0.881595i
$163$		−	13.5989i		−	1.06515i	−0.846383	−	0.532574i	$-0.821225\pi$
$163$		−	13.5989i		−	1.06515i	0.846383	−	0.532574i	$-0.178775\pi$
$164$	−0.949465	−	8.49455i	−0.0741407	−	0.663313i
$165$	11.7954	−	8.54213i	0.918274	−	0.665004i
$166$	−3.52560	−	10.7302i	−0.273640	−	0.832828i
$167$	3.38292	+	2.83861i	0.261778	+	0.219658i	0.764224	−	0.644950i	$-0.223122\pi$
$167$	3.38292	+	2.83861i	0.261778	+	0.219658i	−0.502446	+	0.864609i	$0.667566\pi$
$168$	−2.58542	−	3.02947i	−0.199469	−	0.233729i
$169$	−4.40315	−	1.60262i	−0.338704	−	0.123278i
$170$	−21.4565	+	11.4995i	−1.64564	+	0.881972i
$171$	−3.66506	−	17.5081i	−0.280274	−	1.33888i
$172$	−4.58681	−	3.05005i	−0.349741	−	0.232564i
$173$	−12.4793	−	14.8722i	−0.948781	−	1.13071i	−0.991301	−	0.131617i	$-0.957983\pi$
$173$	−12.4793	−	14.8722i	−0.948781	−	1.13071i	0.0425201	−	0.999096i	$-0.486461\pi$
$174$	−13.2887	−	9.61926i	−1.00742	−	0.729235i
$175$	0.123355	−	0.699578i	0.00932472	−	0.0528831i
$176$	13.2537	+	4.11401i	0.999032	+	0.310105i
$177$	0.907471	−	12.6960i	0.0682097	−	0.954291i
$178$	−4.77590	+	3.75676i	−0.357969	+	0.281581i
$179$	−4.00038	−	2.30962i	−0.299002	−	0.172629i	0.342992	−	0.939338i	$-0.388559\pi$
$179$	−4.00038	−	2.30962i	−0.299002	−	0.172629i	−0.641995	+	0.766709i	$0.721893\pi$
$180$	10.8405	+	9.69224i	0.808006	+	0.722417i
$181$	−5.55052	+	3.20459i	−0.412567	+	0.238195i	−0.691892	−	0.722001i	$-0.743223\pi$
$181$	−5.55052	+	3.20459i	−0.412567	+	0.238195i	0.279325	+	0.960197i	$0.409889\pi$
$182$	1.23173	−	3.07782i	0.0913023	−	0.228143i
$183$	0.125007	+	0.438501i	0.00924075	+	0.0324149i
$184$	13.9193	+	14.1315i	1.02614	+	1.04179i
$185$	−9.45221	+	3.44032i	−0.694940	+	0.252938i
$186$	5.99641	+	2.91164i	0.439678	+	0.213492i
$187$	−24.2670	+	4.27893i	−1.77458	+	0.312906i
$188$	−5.94809	−	0.376549i	−0.433809	−	0.0274626i
$189$	0.166959	−	4.22102i	0.0121444	−	0.307034i
$190$	20.4263	+	0.645905i	1.48188	+	0.0468588i
$191$	−3.51460	−	19.9323i	−0.254307	−	1.44225i	−0.797844	−	0.602864i	$-0.794026\pi$
$191$	−3.51460	−	19.9323i	−0.254307	−	1.44225i	0.543537	−	0.839385i	$-0.317085\pi$
$192$	−1.19691	+	13.8046i	−0.0863793	+	0.996262i
$193$	5.28857	−	1.92488i	0.380680	−	0.138556i	−0.144590	−	0.989492i	$-0.546186\pi$
$193$	5.28857	−	1.92488i	0.380680	−	0.138556i	0.525270	+	0.850935i	$0.323964\pi$
$194$	5.89403	+	5.27194i	0.423167	+	0.378503i
$195$	−2.94635	+	11.7400i	−0.210993	+	0.840720i
$196$	11.6158	+	5.08022i	0.829701	+	0.362873i
$197$	−3.79439	+	2.19069i	−0.270339	+	0.156080i	−0.629042	−	0.777371i	$-0.716553\pi$
$197$	−3.79439	+	2.19069i	−0.270339	+	0.156080i	0.358703	+	0.933452i	$0.383219\pi$
$198$	7.36234	+	12.7457i	0.523219	+	0.905799i
$199$	−6.64564	+	11.5106i	−0.471097	+	0.815963i	−0.999453	−	0.0330592i	$-0.989475\pi$
$199$	−6.64564	+	11.5106i	−0.471097	+	0.815963i	0.528357	+	0.849022i	$0.322808\pi$
$200$	−2.03518	+	1.40222i	−0.143909	+	0.0991519i
$201$	−3.48843	+	1.69477i	−0.246055	+	0.119540i
$202$	−22.8640	−	4.78118i	−1.60870	−	0.336403i
$203$	−5.36196	−	0.945458i	−0.376336	−	0.0663582i
$204$	−9.33187	−	22.7655i	−0.653362	−	1.59391i
$205$	6.65784	+	7.93450i	0.465004	+	0.554170i
$206$	−13.6542	+	22.0125i	−0.951337	+	1.53368i
$207$	0.669380	+	21.0281i	0.0465251	+	1.46155i
$208$	−10.6361	+	4.46123i	−0.737477	+	0.309331i
$209$	19.4387	+	7.07512i	1.34460	+	0.489396i
$210$	4.64161	+	1.32216i	0.320302	+	0.0912375i
$211$	16.0858	−	19.1703i	1.10739	−	1.31974i	0.164597	−	0.986361i	$-0.447368\pi$
$211$	16.0858	−	19.1703i	1.10739	−	1.31974i	0.942794	−	0.333376i	$-0.108188\pi$
$212$	4.16708	+	14.1789i	0.286196	+	0.973812i
$213$	−0.963024	−	9.30052i	−0.0659853	−	0.637261i
$214$	−23.8889	+	3.43769i	−1.63301	+	0.234996i
$215$	6.67497			0.455229
$216$	−10.8701	+	9.89149i	−0.739615	+	0.673031i
$217$	2.21238			0.150186
$218$	25.7225	−	3.70155i	1.74214	−	0.250700i
$219$	−6.23776	−	2.78877i	−0.421509	−	0.188447i
$220$	−16.1343	+	4.74176i	−1.08778	+	0.319689i
$221$	13.1642	−	15.6884i	0.885518	−	1.05532i
$222$	−2.47675	−	9.86001i	−0.166229	−	0.661761i
$223$	1.52221	+	0.554040i	0.101935	+	0.0371013i	0.392484	−	0.919759i	$-0.371616\pi$
$223$	1.52221	+	0.554040i	0.101935	+	0.0371013i	−0.290549	+	0.956860i	$0.593838\pi$
$224$	1.64390	+	4.29500i	0.109838	+	0.286972i
$225$	−2.59474	−	0.372832i	−0.172983	−	0.0248555i
$226$	−6.38094	+	10.2869i	−0.424454	+	0.684276i
$227$	−4.47903	−	5.33790i	−0.297284	−	0.354289i	0.596639	−	0.802510i	$-0.296502\pi$
$227$	−4.47903	−	5.33790i	−0.297284	−	0.354289i	−0.893923	+	0.448221i	$0.852058\pi$
$228$	−2.77128	+	20.4681i	−0.183533	+	1.35553i
$229$	24.7618	+	4.36618i	1.63631	+	0.288525i	0.914808	−	0.403890i	$-0.132342\pi$
$229$	24.7618	+	4.36618i	1.63631	+	0.288525i	0.721500	+	0.692415i	$0.243453\pi$
$230$	−23.5276	−	4.91996i	−1.55137	−	0.324413i
$231$	4.04583	+	2.73803i	0.266196	+	0.180149i
$232$	10.7474	+	15.5987i	0.705601	+	1.02411i
$233$	7.86096	−	13.6156i	0.514989	−	0.891987i	−0.484860	−	0.874592i	$-0.661129\pi$
$233$	7.86096	−	13.6156i	0.514989	−	0.891987i	0.999849	−	0.0173948i	$-0.00553722\pi$
$234$	−11.4965	−	4.18165i	−0.751553	−	0.273363i
$235$	6.25469	−	3.61115i	0.408011	−	0.235565i
$236$	−5.88938	+	13.4659i	−0.383366	+	0.876558i
$237$	12.6699	+	12.2730i	0.822998	+	0.797216i
$238$	−6.08642	−	5.44402i	−0.394524	−	0.352883i
$239$	14.6050	−	5.31579i	0.944720	−	0.343850i	0.176692	−	0.984266i	$-0.443460\pi$
$239$	14.6050	−	5.31579i	0.944720	−	0.343850i	0.768028	+	0.640416i	$0.221238\pi$
$240$	−8.05501	−	14.7329i	−0.519949	−	0.951006i
$241$	−2.19088	−	12.4251i	−0.141127	−	0.800370i	−0.970396	−	0.241520i	$-0.922354\pi$
$241$	−2.19088	−	12.4251i	−0.141127	−	0.800370i	0.829269	−	0.558850i	$-0.188757\pi$
$242$	−1.46515	−	0.0463299i	−0.0941832	−	0.00297820i
$243$	−15.5880	−	0.120210i	−0.999970	−	0.00771147i
$244$	0.0332646	−	0.525458i	0.00212955	−	0.0336390i
$245$	−15.1299	+	2.66782i	−0.966616	+	0.170441i
$246$	−8.66845	+	5.86909i	−0.552680	+	0.374199i
$247$	−16.1558	+	5.88024i	−1.02797	+	0.374151i
$248$	−5.40137	−	5.48373i	−0.342987	−	0.348217i
$249$	−9.62454	+	9.93579i	−0.609930	+	0.629655i
$250$	−5.25461	+	13.1301i	−0.332331	+	0.830418i
$251$	−4.86765	+	2.81034i	−0.307244	+	0.177387i	−0.645692	−	0.763598i	$-0.723431\pi$
$251$	−4.86765	+	2.81034i	−0.307244	+	0.177387i	0.338449	+	0.940985i	$0.390098\pi$
$252$	−1.81139	+	4.52902i	−0.114107	+	0.285301i
$253$	−21.0707	−	12.1652i	−1.32470	−	0.764818i
$254$	5.07396	−	3.99121i	0.318369	−	0.250431i
$255$	24.6920	+	16.7104i	1.54627	+	1.04645i
$256$	6.63237	−	14.5606i	0.414523	−	0.910039i
$257$	3.35726	−	19.0399i	0.209420	−	1.18768i	−0.680911	−	0.732366i	$-0.738416\pi$
$257$	3.35726	−	19.0399i	0.209420	−	1.18768i	0.890331	−	0.455313i	$-0.150473\pi$
$258$	−0.693414	+	6.71057i	−0.0431701	+	0.417782i
$259$	−2.16885	−	2.58474i	−0.134766	−	0.160608i
$260$	7.73906	−	11.6384i	0.479956	−	0.721782i
$261$	−2.85760	+	19.8876i	−0.176881	+	1.23101i
$262$	16.5874	−	8.88993i	1.02477	−	0.549221i
$263$	10.8424	+	3.94631i	0.668571	+	0.243340i	0.653932	−	0.756553i	$-0.273118\pi$
$263$	10.8424	+	3.94631i	0.668571	+	0.243340i	0.0146383	+	0.999893i	$0.495340\pi$
$264$	−3.09097	−	16.7130i	−0.190236	−	1.02861i
$265$	−13.7188	−	11.5114i	−0.842739	−	0.707142i
$266$	2.13985	+	6.51268i	0.131203	+	0.399318i
$267$	6.79395	+	3.03742i	0.415783	+	0.185887i
$268$	4.45059	−	0.497458i	0.271863	−	0.0303871i
$269$		−	13.3630i		−	0.814758i	−0.913259	−	0.407379i	$-0.866443\pi$
$269$		−	13.3630i		−	0.814758i	0.913259	−	0.407379i	$-0.133557\pi$
$270$	4.33155	−	17.2749i	0.263610	−	1.05132i
$271$	3.26667			0.198436			0.0992182	−	0.995066i	$-0.468366\pi$
$271$	3.26667			0.198436			0.0992182	+	0.995066i	$0.468366\pi$
$272$	1.36572	+	28.3773i	0.0828087	+	1.72063i
$273$	−4.03860	+	0.418178i	−0.244427	+	0.0253093i
$274$	2.89702	−	0.951866i	0.175015	−	0.0575043i
$275$	1.94863	−	2.32228i	0.117507	−	0.140039i
$276$	7.39032	−	23.1420i	0.444845	−	1.39299i
$277$	−0.102104	+	0.280528i	−0.00613482	+	0.0168553i	−0.942722	−	0.333579i	$-0.891744\pi$
$277$	−0.102104	+	0.280528i	−0.00613482	+	0.0168553i	0.936587	+	0.350434i	$0.113966\pi$
$278$	−0.729349	+	0.390891i	−0.0437435	+	0.0234441i
$279$	−0.259753	−	8.15992i	−0.0155510	−	0.488522i
$280$	−4.54071	−	3.23091i	−0.271360	−	0.193084i
$281$	−13.3262	+	11.1820i	−0.794976	+	0.667064i	−0.946972	−	0.321317i	$-0.895874\pi$
$281$	−13.3262	+	11.1820i	−0.794976	+	0.667064i	0.151996	+	0.988381i	$0.451430\pi$
$282$	2.98065	+	6.66318i	0.177495	+	0.396787i
$283$	1.31422	+	0.231732i	0.0781220	+	0.0137750i	0.212573	−	0.977145i	$-0.431816\pi$
$283$	1.31422	+	0.231732i	0.0781220	+	0.0137750i	−0.134451	+	0.990920i	$0.542927\pi$
$284$	−2.54286	+	10.4930i	−0.150891	+	0.622646i
$285$	−10.9375	−	22.5132i	−0.647880	−	1.33357i
$286$	11.1196	−	8.74672i	0.657513	−	0.517205i
$287$	−1.73720	+	3.00893i	−0.102544	+	0.177611i
$288$	15.6483	−	6.56747i	0.922083	−	0.386992i
$289$	−16.7231	−	28.9652i	−0.983711	−	1.70384i
$290$	−21.3115	−	8.52880i	−1.25145	−	0.500828i
$291$	2.35751	−	9.39370i	0.138199	−	0.550668i
$292$	5.71146	+	5.44320i	0.334238	+	0.318539i
$293$	2.77744	+	7.63095i	0.162260	+	0.445805i	0.994003	−	0.109356i	$-0.0348789\pi$
$293$	2.77744	+	7.63095i	0.162260	+	0.445805i	−0.831743	+	0.555161i	$0.812657\pi$
$294$	−1.11030	−	15.4878i	−0.0647543	−	0.903265i
$295$	−3.09274	−	17.5398i	−0.180066	−	1.02121i
$296$	−1.11157	+	11.6863i	−0.0646089	+	0.679253i
$297$	9.62369	−	15.2437i	0.558423	−	0.884530i
$298$	−0.979021	+	30.9608i	−0.0567132	+	1.79351i
$299$	19.9141	−	3.51140i	1.15166	−	0.203069i
$300$	2.67975	+	1.40754i	0.154716	+	0.0812643i
$301$	0.765801	+	2.10402i	0.0441400	+	0.121274i
$302$	8.14273	+	7.28329i	0.468561	+	0.419106i
$303$	7.84307	+	27.5121i	0.450573	+	1.58053i
$304$	10.9184	−	21.2042i	0.626212	−	1.21615i
$305$	0.319011	+	0.552544i	0.0182665	+	0.0316386i
$306$	−19.3646	+	23.0877i	−1.10700	+	1.31984i
$307$	22.1985	+	12.8163i	1.26693	+	0.731464i	0.974406	−	0.224793i	$-0.0721707\pi$
$307$	22.1985	+	12.8163i	1.26693	+	0.731464i	0.292527	+	0.956257i	$0.405504\pi$
$308$	−3.34570	−	4.54170i	−0.190639	−	0.258787i
$309$	31.6444	+	2.26184i	1.80018	+	0.128671i
$310$	9.12989	+	1.90919i	0.518543	+	0.108435i
$311$	−3.08781	+	17.5119i	−0.175094	+	0.993007i	0.762942	+	0.646467i	$0.223754\pi$
$311$	−3.08781	+	17.5119i	−0.175094	+	0.993007i	−0.938035	+	0.346539i	$0.887357\pi$
$312$	10.8965	+	8.98936i	0.616893	+	0.508922i
$313$	−25.2201	+	21.1622i	−1.42553	+	1.19616i	−0.477226	+	0.878781i	$0.658358\pi$
$313$	−25.2201	+	21.1622i	−1.42553	+	1.19616i	−0.948299	+	0.317377i	$0.897198\pi$
$314$	1.64950	+	1.02318i	0.0930868	+	0.0577414i
$315$	−1.21111	−	5.78552i	−0.0682383	−	0.325977i
$316$	−9.04938	−	18.2477i	−0.509067	−	1.02651i
$317$	2.41535	−	6.63611i	0.135659	−	0.372721i	−0.853198	−	0.521587i	$-0.825340\pi$
$317$	2.41535	−	6.63611i	0.135659	−	0.372721i	0.988857	+	0.148866i	$0.0475624\pi$
$318$	12.9980	−	12.5961i	0.728890	−	0.706355i
$319$	−17.7993	−	14.9354i	−0.996568	−	0.836220i
$320$	3.07752	+	19.1429i	0.172038	+	1.07012i
$321$	17.3376	+	23.9407i	0.967688	+	1.33624i
$322$	−1.14844	−	7.98062i	−0.0639999	−	0.444742i
$323$			42.3492i			2.35637i
$324$	16.9171	+	6.14922i	0.939837	+	0.341623i
$325$			2.51954i			0.139759i
$326$	19.0357	−	2.73930i	1.05429	−	0.151716i
$327$	−18.6683	−	25.7782i	−1.03236	−	1.42554i
$328$	11.6994	−	3.04016i	0.645989	−	0.167864i
$329$	1.85586	+	1.55725i	0.102317	+	0.0858539i
$330$	14.3332	+	14.7905i	0.789019	+	0.814191i
$331$	−4.15163	+	11.4065i	−0.228194	+	0.626958i	−0.999960	−	0.00894876i	$-0.997151\pi$
$331$	−4.15163	+	11.4065i	−0.228194	+	0.626958i	0.771766	+	0.635907i	$0.219374\pi$
$332$	14.3099	−	7.09657i	0.785360	−	0.389475i
$333$	−9.27866	+	8.30286i	−0.508468	+	0.454994i
$334$	−3.29203	+	5.30719i	−0.180132	+	0.290396i
$335$	−4.15716	+	3.48827i	−0.227130	+	0.190585i
$336$	3.71985	−	4.22929i	0.202934	−	0.230727i
$337$	−4.48506	+	25.4361i	−0.244317	+	1.38559i	0.577757	+	0.816209i	$0.303928\pi$
$337$	−4.48506	+	25.4361i	−0.244317	+	1.38559i	−0.822074	+	0.569381i	$0.807183\pi$
$338$	1.35638	−	6.48633i	0.0737776	−	0.352810i
$339$	14.7881	+	1.05701i	0.803180	+	0.0574088i
$340$	−20.4190	−	27.7183i	−1.10738	−	1.50324i
$341$	8.17648	+	4.72069i	0.442781	+	0.255640i
$342$	23.7695	−	8.65707i	1.28531	−	0.468121i
$343$	−5.42214	−	9.39142i	−0.292768	−	0.507089i
$344$	3.34550	−	7.03498i	0.180377	−	0.379301i
$345$	8.07074	+	28.3107i	0.434514	+	1.52420i
$346$	18.3043	−	20.4642i	0.984043	−	1.10016i
$347$	−4.43311	−	12.1799i	−0.237982	−	0.653849i	−0.999980	−	0.00627055i	$-0.998004\pi$
$347$	−4.43311	−	12.1799i	−0.237982	−	0.653849i	0.761999	−	0.647578i	$-0.224218\pi$
$348$	10.7882	−	20.5391i	0.578307	−	1.10101i
$349$	−1.00479	+	0.177171i	−0.0537849	+	0.00948374i	−0.200476	−	0.979699i	$-0.564249\pi$
$349$	−1.00479	+	0.177171i	−0.0537849	+	0.00948374i	0.146691	+	0.989182i	$0.453138\pi$
$350$	1.00411	+	0.0317514i	0.0536721	+	0.00169718i
$351$	2.01653	+	14.8465i	0.107635	+	0.792448i
$352$	−3.08902	+	19.3811i	−0.164645	+	1.03302i
$353$	−2.87234	−	16.2899i	−0.152879	−	0.867022i	−0.960699	−	0.277592i	$-0.910464\pi$
$353$	−2.87234	−	16.2899i	−0.152879	−	0.867022i	0.807820	−	0.589430i	$-0.200648\pi$
$354$	17.9546	−	1.28715i	0.954277	−	0.0684113i
$355$	−4.47480	−	12.2944i	−0.237498	−	0.652520i
$356$	−6.22072	−	5.92854i	−0.329698	−	0.314212i
$357$	−2.43446	+	9.70032i	−0.128845	+	0.513395i
$358$	2.42717	−	6.06494i	0.128280	−	0.320542i
$359$	9.03871	+	15.6555i	0.477045	+	0.826266i	0.999654	−	0.0263063i	$-0.00837453\pi$
$359$	9.03871	+	15.6555i	0.477045	+	0.826266i	−0.522609	+	0.852573i	$0.675041\pi$
$360$	−11.3835	+	17.1269i	−0.599962	+	0.902666i
$361$	8.27594	−	14.3343i	0.435576	−	0.754439i
$362$	−5.60384	−	7.12406i	−0.294531	−	0.374433i
$363$	0.784531	+	1.61484i	0.0411772	+	0.0847573i
$364$	4.55643	+	1.10419i	0.238822	+	0.0578755i
$365$	−9.41559	−	1.66022i	−0.492835	−	0.0869000i
$366$	−0.588630	+	0.263313i	−0.0307682	+	0.0137636i
$367$	−15.6345	+	13.1189i	−0.816112	+	0.684799i	−0.952058	−	0.305917i	$-0.901037\pi$
$367$	−15.6345	+	13.1189i	−0.816112	+	0.684799i	0.135946	+	0.990716i	$0.456593\pi$
$368$	−16.9774	+	22.3307i	−0.885007	+	1.16407i
$369$	11.3018	+	6.05407i	0.588348	+	0.315162i
$370$	−6.71975	−	12.5381i	−0.349343	−	0.651827i
$371$	2.05461	−	5.64499i	0.106670	−	0.293073i
$372$	−2.86781	+	8.98025i	−0.148689	+	0.465604i
$373$	−18.6443	+	22.2194i	−0.965366	+	1.15048i	0.0232061	+	0.999731i	$0.492613\pi$
$373$	−18.6443	+	22.2194i	−0.965366	+	1.15048i	−0.988572	+	0.150748i	$0.951832\pi$
$374$	−10.8778	−	33.1069i	−0.562480	−	1.71192i
$375$	17.2288	−	1.78396i	0.889691	−	0.0921232i
$376$	−0.671062	−	8.40195i	−0.0346074	−	0.433297i
$377$	19.3112			0.994578
$378$	5.94219	−	0.616553i	0.305633	−	0.0317121i
$379$			18.7878i			0.965062i	0.875879	+	0.482531i	$0.160282\pi$
$379$			18.7878i			0.965062i	−0.875879	+	0.482531i	$0.839718\pi$
$380$	3.21043	+	28.7227i	0.164692	+	1.47344i
$381$	−7.21795	−	3.22699i	−0.369787	−	0.165324i
$382$	27.1931	−	8.93478i	1.39132	−	0.457143i
$383$	−11.4097	−	9.57391i	−0.583010	−	0.489204i	0.302924	−	0.953015i	$-0.402037\pi$
$383$	−11.4097	−	9.57391i	−0.583010	−	0.489204i	−0.885934	+	0.463811i	$0.846482\pi$
$384$	−19.5647	+	1.10531i	−0.998408	+	0.0564051i
$385$	6.42348	+	2.33796i	0.327371	+	0.119153i
$386$	3.75974	+	7.01518i	0.191366	+	0.357063i
$387$	7.67036	−	3.07154i	0.389906	−	0.156135i
$388$	−6.19236	+	9.31238i	−0.314370	+	0.472765i
$389$	11.3184	+	13.4888i	0.573866	+	0.683907i	0.972420	−	0.233238i	$-0.0749321\pi$
$389$	11.3184	+	13.4888i	0.573866	+	0.683907i	−0.398553	+	0.917145i	$0.630488\pi$
$390$	−17.0271	−	1.75944i	−0.862201	−	0.0890926i
$391$	8.64932	−	49.0527i	0.437415	−	2.48070i
$392$	−4.77142	+	17.2831i	−0.240993	+	0.872928i
$393$	−19.0886	−	12.9183i	−0.962894	−	0.651643i
$394$	−3.83084	−	4.87009i	−0.192995	−	0.245351i
$395$	21.3755	+	12.3411i	1.07552	+	0.620950i
$396$	−16.3584	+	12.8732i	−0.822039	+	0.646902i
$397$	−13.1290	+	7.58002i	−0.658924	+	0.380430i	−0.791867	−	0.610694i	$-0.790891\pi$
$397$	−13.1290	+	7.58002i	−0.658924	+	0.380430i	0.132943	+	0.991124i	$0.457557\pi$
$398$	−17.4511	−	6.98389i	−0.874745	−	0.350071i
$399$	5.84158	−	6.03049i	0.292445	−	0.301902i
$400$	−2.37277	−	2.56637i	−0.118639	−	0.128319i
$401$	0.563391	−	0.205057i	0.0281344	−	0.0102401i	−0.327915	−	0.944707i	$-0.606346\pi$
$401$	0.563391	−	0.205057i	0.0281344	−	0.0102401i	0.356049	+	0.934467i	$0.384124\pi$
$402$	−3.07502	−	4.54170i	−0.153368	−	0.226520i
$403$	−7.72766	+	1.36260i	−0.384942	+	0.0678757i
$404$	2.08706	−	32.9679i	0.103835	−	1.64022i
$405$	−21.1966	+	5.14621i	−1.05327	+	0.255717i
$406$	0.243360	−	7.69609i	0.0120778	−	0.381951i
$407$	−2.50040	−	14.1805i	−0.123940	−	0.702899i
$408$	29.9873	−	17.6485i	1.48459	−	0.873730i
$409$	26.7235	−	9.72655i	1.32139	−	0.480947i	0.417487	−	0.908683i	$-0.362911\pi$
$409$	26.7235	−	9.72655i	1.32139	−	0.480947i	0.903904	+	0.427736i	$0.140689\pi$
$410$	−9.76555	+	10.9179i	−0.482286	+	0.539196i
$411$	−2.68253	−	2.59850i	−0.132319	−	0.128174i
$412$	−33.5634	−	14.6791i	−1.65355	−	0.723185i
$413$	5.17391	−	2.98716i	0.254591	−	0.146988i
$414$	−29.3001	+	5.17278i	−1.44002	+	0.254228i
$415$	−9.67799	+	16.7628i	−0.475074	+	0.822852i
$416$	−8.38728	−	13.9896i	−0.411220	−	0.685898i
$417$	0.839329	+	0.568020i	0.0411021	+	0.0278160i
$418$	−5.98807	+	28.6354i	−0.292886	+	1.40060i
$419$	−27.5479	−	4.85743i	−1.34580	−	0.237301i	−0.546110	−	0.837713i	$-0.683892\pi$
$419$	−27.5479	−	4.85743i	−1.34580	−	0.237301i	−0.799691	+	0.600412i	$0.795003\pi$
$420$	−0.915764	+	6.76363i	−0.0446847	+	0.330031i
$421$	−21.0378	−	25.0719i	−1.02532	−	1.22193i	−0.974771	−	0.223208i	$-0.928347\pi$
$421$	−21.0378	−	25.0719i	−1.02532	−	1.22193i	−0.0505502	−	0.998722i	$-0.516097\pi$
$422$	30.0747	+	18.6552i	1.46401	+	0.908122i
$423$	5.52571	−	7.02780i	0.268669	−	0.341703i
$424$	−19.0082	+	8.68918i	−0.923118	+	0.421984i
$425$	5.83190	+	2.12264i	0.282889	+	0.102963i
$426$	12.8248	−	3.22149i	0.621365	−	0.156082i
$427$	−0.137568	+	0.163948i	−0.00665740	+	0.00793398i
$428$	−9.62412	−	32.7471i	−0.465200	−	1.58289i
$429$	−15.8181	−	7.07193i	−0.763705	−	0.341436i
$430$	1.34457	+	9.34358i	0.0648410	+	0.450588i
$431$	−9.98011			−0.480725			−0.240363	−	0.970683i	$-0.577266\pi$
$431$	−9.98011			−0.480725			−0.240363	+	0.970683i	$0.577266\pi$
$432$	−16.0357	−	13.2234i	−0.771516	−	0.636210i
$433$	17.4899			0.840513			0.420257	−	0.907405i	$-0.361940\pi$
$433$	17.4899			0.840513			0.420257	+	0.907405i	$0.361940\pi$
$434$	0.445651	+	3.09687i	0.0213919	+	0.148655i
$435$	2.89555	+	27.9642i	0.138831	+	1.34078i
$436$	10.3628	+	35.2605i	0.496289	+	1.68867i
$437$	−26.8780	+	32.0319i	−1.28575	+	1.53229i
$438$	2.64719	−	9.29334i	0.126488	−	0.444053i
$439$	7.21777	+	2.62705i	0.344485	+	0.125382i	0.508468	−	0.861081i	$-0.330212\pi$
$439$	7.21777	+	2.62705i	0.344485	+	0.125382i	−0.163983	+	0.986463i	$0.552434\pi$
$440$	−9.88750	−	21.6296i	−0.471368	−	1.03115i
$441$	−16.1585	+	10.0278i	−0.769454	+	0.477515i
$442$	24.6123	+	15.2669i	1.17069	+	0.726174i
$443$	−3.13735	−	3.73895i	−0.149060	−	0.177643i	0.686348	−	0.727274i	$-0.259213\pi$
$443$	−3.13735	−	3.73895i	−0.149060	−	0.177643i	−0.835408	+	0.549631i	$0.814768\pi$
$444$	13.3031	−	5.45309i	0.631336	−	0.258792i
$445$	10.2551	+	1.80826i	0.486140	+	0.0857196i
$446$	−0.468915	+	2.24239i	−0.0222038	+	0.106180i
$447$	34.1241	−	16.5783i	1.61401	−	0.784129i
$448$	−5.68098	+	3.16628i	−0.268401	+	0.149593i
$449$	−2.49179	+	4.31590i	−0.117595	+	0.203680i	−0.918814	−	0.394691i	$-0.870852\pi$
$449$	−2.49179	+	4.31590i	−0.117595	+	0.203680i	0.801219	+	0.598371i	$0.204185\pi$
$450$	−0.000782996	−	3.70720i	−3.69108e−5	−	0.174759i
$451$	−12.8407	+	7.41357i	−0.604644	+	0.349091i
$452$	−15.6849	−	6.85985i	−0.737756	−	0.322660i
$453$	3.25694	−	12.9776i	0.153025	−	0.609740i
$454$	6.56973	−	7.34496i	0.308333	−	0.344716i
$455$	−5.33865	+	1.94311i	−0.250280	+	0.0910944i
$456$	−29.2093	+	0.243763i	−1.36785	+	0.0114152i
$457$	3.50014	+	19.8503i	0.163729	+	0.928556i	0.950365	+	0.311138i	$0.100710\pi$
$457$	3.50014	+	19.8503i	0.163729	+	0.928556i	−0.786635	+	0.617418i	$0.788179\pi$
$458$	−1.12385	+	35.5410i	−0.0525141	+	1.66072i
$459$	36.0635	+	7.84012i	1.68330	+	0.365945i
$460$	2.14765	−	33.9249i	0.100135	−	1.58176i
$461$	−33.4428	+	5.89687i	−1.55759	+	0.274645i	−0.885077	−	0.465444i	$-0.845895\pi$
$461$	−33.4428	+	5.89687i	−1.55759	+	0.274645i	−0.672510	+	0.740088i	$0.734784\pi$
$462$	−3.01771	+	6.21487i	−0.140397	+	0.289142i
$463$	−35.9891	+	13.0990i	−1.67256	+	0.608760i	−0.992260	−	0.124178i	$-0.960371\pi$
$463$	−35.9891	+	13.0990i	−1.67256	+	0.608760i	−0.680295	+	0.732938i	$0.738148\pi$
$464$	−19.6701	+	18.1863i	−0.913162	+	0.844277i
$465$	−3.13184	−	10.9860i	−0.145236	−	0.509462i
$466$	20.6425	+	8.26107i	0.956245	+	0.382687i
$467$	9.53283	−	5.50378i	0.441127	−	0.254685i	−0.262949	−	0.964810i	$-0.584695\pi$
$467$	9.53283	−	5.50378i	0.441127	−	0.254685i	0.704075	+	0.710125i	$0.251362\pi$
$468$	3.53764	−	16.9351i	0.163528	−	0.782826i
$469$	−1.57648	−	0.910182i	−0.0727951	−	0.0420283i
$470$	6.31478	+	8.02787i	0.291279	+	0.370298i
$471$	0.169491	−	2.37127i	0.00780971	−	0.109262i
$472$	−20.0359	−	5.53140i	−0.922226	−	0.254603i
$473$	−1.65925	+	9.41005i	−0.0762922	+	0.432675i
$474$	−14.6275	+	20.2075i	−0.671863	+	0.928159i
$475$	−3.34895	−	3.99113i	−0.153660	−	0.183125i
$476$	6.39449	−	9.61635i	0.293091	−	0.440765i
$477$	−21.0617	−	6.91524i	−0.964347	−	0.316627i
$478$	10.3830	+	19.3732i	0.474906	+	0.886111i
$479$	21.5794	+	7.85427i	0.985989	+	0.358871i	0.784166	−	0.620551i	$-0.213091\pi$
$479$	21.5794	+	7.85427i	0.985989	+	0.358871i	0.201823	+	0.979422i	$0.435313\pi$
$480$	19.0005	−	14.2431i	0.867250	−	0.650105i
$481$	9.16757	+	7.69250i	0.418005	+	0.350748i
$482$	16.9512	−	5.56963i	0.772108	−	0.253690i
$483$	−7.99791	+	5.79200i	−0.363917	+	0.263545i
$484$	−0.230280	−	2.06024i	−0.0104673	−	0.0936471i
$485$		−	13.5519i		−	0.615358i
$486$	−2.97170	−	21.8442i	−0.134799	−	0.990873i
$487$	8.81274			0.399343			0.199672	−	0.979863i	$-0.436012\pi$
$487$	8.81274			0.399343			0.199672	+	0.979863i	$0.436012\pi$
$488$	0.742234	−	0.0592821i	0.0335994	−	0.00268357i
$489$	−13.8153	−	19.0769i	−0.624749	−	0.862688i
$490$	−6.78209	−	20.6414i	−0.306384	−	0.932484i
$491$	−7.55920	+	9.00870i	−0.341142	+	0.406557i	−0.909152	−	0.416465i	$-0.863269\pi$
$491$	−7.55920	+	9.00870i	−0.341142	+	0.406557i	0.568010	+	0.823022i	$0.307713\pi$
$492$	−9.96165	−	10.9518i	−0.449106	−	0.493746i
$493$	16.2691	−	44.6990i	0.732723	−	2.01314i
$494$	−11.4855	−	21.4303i	−0.516756	−	0.964196i
$495$	7.86892	−	23.9663i	0.353682	−	1.07720i
$496$	6.58807	−	8.66542i	0.295813	−	0.389089i
$497$	3.36195	−	2.82101i	0.150804	−	0.126540i
$498$	−15.8468	−	11.4710i	−0.710111	−	0.514026i
$499$	17.3768	+	3.06399i	0.777891	+	0.137163i	0.548477	−	0.836166i	$-0.315208\pi$
$499$	17.3768	+	3.06399i	0.777891	+	0.137163i	0.229414	+	0.973329i	$0.426319\pi$
$500$	−19.4378	−	4.71053i	−0.869287	−	0.210661i
$501$	7.62943	+	0.545327i	0.340858	+	0.0243634i
$502$	−4.91441	−	6.24761i	−0.219341	−	0.278845i
$503$	−10.0037	+	17.3268i	−0.446041	+	0.772565i	−0.998124	−	0.0612236i	$-0.980500\pi$
$503$	−10.0037	+	17.3268i	−0.446041	+	0.772565i	0.552083	+	0.833789i	$0.313833\pi$
$504$	−6.70457	−	1.62327i	−0.298645	−	0.0723063i
$505$	20.0152	+	34.6673i	0.890664	+	1.54268i
$506$	12.7844	−	31.9451i	0.568334	−	1.42013i
$507$	−7.80498	+	2.22502i	−0.346631	+	0.0988166i
$508$	6.60895	+	6.29853i	0.293225	+	0.279452i
$509$	3.57485	+	9.82182i	0.158452	+	0.435345i	0.993360	−	0.115045i	$-0.0367013\pi$
$509$	3.57485	+	9.82182i	0.158452	+	0.435345i	−0.834908	+	0.550390i	$0.814479\pi$
$510$	−18.4173	+	37.9297i	−0.815532	+	1.67956i
$511$	−0.556906	−	3.15837i	−0.0246361	−	0.139718i
$512$	21.7179	+	6.35094i	0.959803	+	0.280675i
$513$	−22.9281	−	20.8375i	−1.01230	−	0.919998i
$514$	27.3283	+	0.864155i	1.20540	+	0.0381163i
$515$	43.7173	−	7.70853i	1.92641	−	0.339679i
$516$	−9.53309	+	0.381106i	−0.419671	+	0.0167773i
$517$	3.53605	+	9.71521i	0.155515	+	0.427274i
$518$	3.18122	−	3.55661i	0.139775	−	0.156268i
$519$	−32.6151	−	8.18530i	−1.43164	−	0.359295i
$520$	17.8503	+	8.48872i	0.782786	+	0.372255i
$521$	−10.0111	−	17.3397i	−0.438593	−	0.759665i	0.558988	−	0.829175i	$-0.311190\pi$
$521$	−10.0111	−	17.3397i	−0.438593	−	0.759665i	−0.997581	+	0.0695105i	$0.977856\pi$
$522$	−28.4141	+	0.00600132i	−1.24365	+	0.000262671i
$523$	17.8863	+	10.3267i	0.782114	+	0.451554i	0.837179	−	0.546929i	$-0.184203\pi$
$523$	17.8863	+	10.3267i	0.782114	+	0.451554i	−0.0550649	+	0.998483i	$0.517537\pi$
$524$	15.7854	+	21.4282i	0.689586	+	0.936096i
$525$	−0.537664	−	1.10670i	−0.0234656	−	0.0483005i
$526$	−3.33998	+	15.9720i	−0.145630	+	0.696414i
$527$	−3.35636	+	19.0349i	−0.146206	+	0.829173i
$528$	22.7721	−	7.69329i	0.991027	−	0.334808i
$529$	20.0556	−	16.8287i	0.871985	−	0.731682i
$530$	13.3502	−	21.5223i	0.579895	−	0.934869i
$531$	−11.6250	−	18.7322i	−0.504482	−	0.812909i
$532$	−8.68537	+	4.30724i	−0.376558	+	0.186742i
$533$	4.21473	−	11.5799i	0.182560	−	0.501580i
$534$	−2.88323	+	10.1220i	−0.124770	+	0.438021i
$535$	31.6844	+	26.5864i	1.36984	+	1.14943i
$536$	1.59284	+	6.12970i	0.0688003	+	0.264763i
$537$	−7.95820	+	0.824033i	−0.343422	+	0.0355597i
$538$	18.7055	−	2.69178i	0.806451	−	0.116051i
$539$		−	21.9926i		−	0.947289i
$540$	25.0539	+	2.58351i	1.07815	+	0.111176i
$541$			31.7185i			1.36368i	0.731499	+	0.681842i	$0.238821\pi$
$541$			31.7185i			1.36368i	−0.731499	+	0.681842i	$0.761179\pi$
$542$	0.658023	+	4.57267i	0.0282645	+	0.196413i
$543$	−4.53083	+	10.1343i	−0.194437	+	0.434905i
$544$	−39.4473	+	7.62791i	−1.69129	+	0.327044i
$545$	−34.1163	−	28.6270i	−1.46138	−	1.22624i
$546$	−1.39888	−	5.56898i	−0.0598665	−	0.238330i
$547$	2.69951	−	7.41685i	0.115423	−	0.317122i	−0.868507	−	0.495677i	$-0.834920\pi$
$547$	2.69951	−	7.41685i	0.115423	−	0.317122i	0.983930	+	0.178555i	$0.0571423\pi$
$548$	1.91598	+	3.86349i	0.0818465	+	0.165040i
$549$	0.620841	+	0.488145i	0.0264968	+	0.0208335i
$550$	3.64324	+	2.25989i	0.155348	+	0.0963619i
$551$	−30.5902	+	25.6683i	−1.30319	+	1.09350i
$552$	33.8827	+	5.68331i	1.44214	+	0.241898i
$553$	−1.43771	+	8.15365i	−0.0611376	+	0.346728i
$554$	−0.413248	−	0.0864161i	−0.0175572	−	0.00367147i
$555$	−9.76475	+	14.4288i	−0.414491	+	0.612468i
$556$	−0.694083	−	0.942200i	−0.0294357	−	0.0399582i
$557$	−11.9380	−	6.89241i	−0.505829	−	0.292041i	0.225288	−	0.974292i	$-0.427668\pi$
$557$	−11.9380	−	6.89241i	−0.505829	−	0.292041i	−0.731118	+	0.682251i	$0.761001\pi$
$558$	11.3699	−	2.00730i	0.481326	−	0.0849756i
$559$	−3.97074	−	6.87753i	−0.167944	−	0.290888i
$560$	3.60796	−	7.00689i	0.152464	−	0.296095i
$561$	−29.6954	+	30.6557i	−1.25374	+	1.29429i
$562$	−18.3369	−	16.4015i	−0.773496	−	0.691856i
$563$	−4.49431	−	12.3480i	−0.189413	−	0.520407i	0.808242	−	0.588850i	$-0.200419\pi$
$563$	−4.49431	−	12.3480i	−0.189413	−	0.520407i	−0.997655	+	0.0684431i	$0.978197\pi$
$564$	−8.72668	+	5.51450i	−0.367459	+	0.232202i
$565$	20.4301	−	3.60237i	0.859499	−	0.151553i
$566$	−0.0596476	+	1.88631i	−0.00250718	+	0.0792876i
$567$	−4.05396	−	6.09097i	−0.170251	−	0.255797i
$568$	−15.2003	−	1.44581i	−0.637790	−	0.0606650i
$569$	−6.12718	−	34.7490i	−0.256865	−	1.45675i	−0.791241	−	0.611505i	$-0.790564\pi$
$569$	−6.12718	−	34.7490i	−0.256865	−	1.45675i	0.534376	−	0.845247i	$-0.320547\pi$
$570$	29.3107	−	19.8452i	1.22769	−	0.831223i
$571$	−13.0508	−	35.8568i	−0.546159	−	1.50056i	−0.838856	−	0.544354i	$-0.816775\pi$
$571$	−13.0508	−	35.8568i	−0.546159	−	1.50056i	0.292697	−	0.956205i	$-0.405447\pi$
$572$	14.4835	+	13.8032i	0.605585	+	0.577141i
$573$	−25.1798	−	24.3910i	−1.05190	−	1.01895i
$574$	−4.56181	−	1.82563i	−0.190406	−	0.0762001i
$575$	3.06392	+	5.30687i	0.127774	+	0.221312i
$576$	12.3452	+	20.5814i	0.514384	+	0.857560i
$577$	−13.9536	+	24.1683i	−0.580895	+	1.00614i	0.414478	+	0.910059i	$0.363964\pi$
$577$	−13.9536	+	24.1683i	−0.580895	+	1.00614i	−0.995374	+	0.0960807i	$0.969369\pi$
$578$	37.1768	−	29.2435i	1.54635	−	1.21637i
$579$	5.46344	−	8.07300i	0.227053	−	0.335503i
$580$	7.64569	−	31.5497i	0.317470	−	1.31003i
$581$	−6.39413	−	1.12746i	−0.265273	−	0.0467748i
$582$	13.6241	+	1.40780i	0.564738	+	0.0583553i
$583$	19.6384	−	16.4786i	0.813341	−	0.682474i
$584$	−6.46887	+	9.09132i	−0.267684	+	0.376201i
$585$	7.79359	+	19.4624i	0.322225	+	0.804673i
$586$	−10.1223	+	5.42498i	−0.418148	+	0.224104i
$587$	3.04495	−	8.36592i	0.125678	−	0.345299i	−0.860857	−	0.508847i	$-0.830072\pi$
$587$	3.04495	−	8.36592i	0.125678	−	0.345299i	0.986535	+	0.163549i	$0.0522941\pi$
$588$	21.4560	−	4.67398i	0.884832	−	0.192752i
$589$	10.4300	−	12.4300i	0.429760	−	0.512168i
$590$	23.9291	−	7.86232i	0.985146	−	0.323687i
$591$	−3.09733	+	6.92793i	−0.127407	+	0.284977i
$592$	−16.5823	+	0.798058i	−0.681530	+	0.0328000i
$593$	−13.6477			−0.560446			−0.280223	−	0.959935i	$-0.590408\pi$
$593$	−13.6477			−0.560446			−0.280223	+	0.959935i	$0.590408\pi$
$594$	23.2766	+	10.4006i	0.955051	+	0.426740i
$595$			13.9942i			0.573706i
$596$	−43.5360	+	4.86617i	−1.78330	+	0.199326i
$597$	2.37105	+	22.8987i	0.0970407	+	0.937183i
$598$	8.92663	+	27.1683i	0.365037	+	1.11100i
$599$	23.2233	+	19.4867i	0.948878	+	0.796203i	0.979108	−	0.203340i	$-0.0651796\pi$
$599$	23.2233	+	19.4867i	0.948878	+	0.796203i	−0.0302302	+	0.999543i	$0.509624\pi$
$600$	−1.43047	+	4.03463i	−0.0583987	+	0.164713i
$601$	2.85426	+	1.03887i	0.116428	+	0.0423762i	0.399577	−	0.916700i	$-0.369157\pi$
$601$	2.85426	+	1.03887i	0.116428	+	0.0423762i	−0.283149	+	0.959076i	$0.591379\pi$
$602$	−2.79094	+	1.49579i	−0.113750	+	0.0609638i
$603$	−3.17193	+	5.92141i	−0.129171	+	0.241138i
$604$	−8.55488	+	12.8653i	−0.348093	+	0.523480i
$605$	1.61477	+	1.92441i	0.0656497	+	0.0782382i
$606$	−36.9314	+	16.5206i	−1.50024	+	0.671103i
$607$	−4.34423	+	24.6374i	−0.176327	+	0.999999i	0.760274	+	0.649602i	$0.225065\pi$
$607$	−4.34423	+	24.6374i	−0.176327	+	0.999999i	−0.936601	+	0.350397i	$0.886047\pi$
$608$	31.8809	+	11.0122i	1.29294	+	0.446605i
$609$	−8.48241	+	4.12096i	−0.343724	+	0.166990i
$610$	−0.709188	+	0.557852i	−0.0287142	+	0.0225868i
$611$	−7.44146	−	4.29633i	−0.301049	−	0.173811i
$612$	−36.2188	−	22.4558i	−1.46406	−	0.907721i
$613$	11.1629	−	6.44490i	0.450865	−	0.260307i	−0.257331	−	0.966323i	$-0.582843\pi$
$613$	11.1629	−	6.44490i	0.450865	−	0.260307i	0.708195	+	0.706017i	$0.249510\pi$
$614$	−13.4686	+	33.6549i	−0.543549	+	1.35820i
$615$	17.4006	+	4.36696i	0.701658	+	0.176093i
$616$	5.68351	−	5.59815i	0.228995	−	0.225556i
$617$	23.2620	−	8.46669i	0.936495	−	0.340856i	0.171714	−	0.985147i	$-0.445070\pi$
$617$	23.2620	−	8.46669i	0.936495	−	0.340856i	0.764781	+	0.644291i	$0.222847\pi$
$618$	3.20817	+	44.7512i	0.129052	+	1.80016i
$619$	7.07392	−	1.24732i	0.284325	−	0.0501341i	−0.0296670	−	0.999560i	$-0.509445\pi$
$619$	7.07392	−	1.24732i	0.284325	−	0.0501341i	0.313992	+	0.949426i	$0.398334\pi$
$620$	−0.833393	+	13.1645i	−0.0334699	+	0.528701i
$621$	22.3017	+	28.8187i	0.894935	+	1.15645i
$622$	−25.1350	−	0.794801i	−1.00782	−	0.0318686i
$623$	0.606562	+	3.43998i	0.0243014	+	0.137820i
$624$	−10.3883	+	17.0636i	−0.415866	+	0.683092i
$625$	26.8803	−	9.78364i	1.07521	−	0.391346i
$626$	−34.7029	−	31.0402i	−1.38701	−	1.24061i
$627$	34.4569	−	9.82286i	1.37607	−	0.392287i
$628$	−1.09997	+	2.51507i	−0.0438937	+	0.100362i
$629$	25.5289	−	14.7391i	1.01791	−	0.587688i
$630$	7.85458	−	2.86071i	0.312934	−	0.113973i
$631$	19.7806	−	34.2610i	0.787453	−	1.36391i	−0.140070	−	0.990142i	$-0.544733\pi$
$631$	19.7806	−	34.2610i	0.787453	−	1.36391i	0.927523	−	0.373767i	$-0.121934\pi$
$632$	23.7202	−	16.3430i	0.943538	−	0.650089i
$633$	3.09025	−	43.2343i	0.122827	−	1.71841i
$634$	9.77572	+	2.04424i	0.388243	+	0.0811872i
$635$	−10.8951	−	1.92111i	−0.432361	−	0.0762368i
$636$	20.2502	+	15.6572i	0.802973	+	0.620848i
$637$	11.7491	+	14.0021i	0.465517	+	0.554782i
$638$	17.3210	−	27.9238i	0.685747	−	1.10551i
$639$	−10.7995	−	12.0687i	−0.427220	−	0.477430i
$640$	−26.1762	+	8.16395i	−1.03471	+	0.322708i
$641$	20.4795	+	7.45392i	0.808891	+	0.294412i	0.713166	−	0.700995i	$-0.247261\pi$
$641$	20.4795	+	7.45392i	0.808891	+	0.294412i	0.0957255	+	0.995408i	$0.469483\pi$
$642$	−30.0196	+	29.0915i	−1.18478	+	1.14815i
$643$	−24.0829	+	28.7008i	−0.949735	+	1.13185i	0.0414197	+	0.999142i	$0.486812\pi$
$643$	−24.0829	+	28.7008i	−0.949735	+	1.13185i	−0.991155	+	0.132709i	$0.957633\pi$
$644$	10.9399	−	3.21515i	0.431092	−	0.126695i
$645$	9.36383	−	6.78118i	0.368700	−	0.267009i
$646$	−59.2802	+	8.53062i	−2.33235	+	0.335633i
$647$	−13.9531			−0.548554			−0.274277	−	0.961651i	$-0.588439\pi$
$647$	−13.9531			−0.548554			−0.274277	+	0.961651i	$0.588439\pi$
$648$	−5.19995	+	24.9191i	−0.204273	+	0.978914i
$649$	25.4955			1.00079
$650$	−3.52684	+	0.507525i	−0.138334	+	0.0199068i
$651$	3.10358	−	2.24758i	0.121639	−	0.0880896i
$652$	7.66890	+	26.0942i	0.300337	+	1.02193i
$653$	16.3129	−	19.4409i	0.638372	−	0.760782i	−0.345740	−	0.938330i	$-0.612372\pi$
$653$	16.3129	−	19.4409i	0.638372	−	0.760782i	0.984112	+	0.177548i	$0.0568166\pi$
$654$	32.3237	−	31.3244i	1.26396	−	1.22488i
$655$	−30.3066	−	11.0307i	−1.18418	−	0.431006i
$656$	6.61225	+	15.7643i	0.258165	+	0.615493i
$657$	−11.5836	+	2.42486i	−0.451921	+	0.0946027i
$658$	−1.80599	+	2.91150i	−0.0704049	+	0.113502i
$659$	23.0007	+	27.4112i	0.895981	+	1.06779i	0.997336	+	0.0729384i	$0.0232376\pi$
$659$	23.0007	+	27.4112i	0.895981	+	1.06779i	−0.101355	+	0.994850i	$0.532318\pi$
$660$	−17.8165	+	23.0429i	−0.693505	+	0.896944i
$661$	−29.1329	−	5.13692i	−1.13314	−	0.199803i	−0.424536	−	0.905411i	$-0.639563\pi$
$661$	−29.1329	−	5.13692i	−1.13314	−	0.199803i	−0.708603	+	0.705608i	$0.750674\pi$
$662$	−16.8030	−	3.51375i	−0.653069	−	0.136566i
$663$	2.52898	−	35.3818i	0.0982174	−	1.37412i
$664$	12.8163	+	18.6015i	0.497367	+	0.721877i
$665$	5.87402	−	10.1741i	0.227785	−	0.394535i
$666$	−13.4913	−	11.3157i	−0.522779	−	0.438476i
$667$	40.6749	−	23.4836i	1.57494	−	0.909290i
$668$	−8.09210	−	3.53911i	−0.313093	−	0.136932i
$669$	2.69826	−	0.769211i	0.104321	−	0.0297394i
$670$	−5.72026	−	5.11651i	−0.220993	−	0.197668i
$671$	−0.858249	+	0.312377i	−0.0331323	+	0.0120592i
$672$	6.66945	+	4.35509i	0.257280	+	0.168001i
$673$	3.21781	+	18.2491i	0.124038	+	0.703452i	0.981875	+	0.189531i	$0.0606967\pi$
$673$	3.21781	+	18.2491i	0.124038	+	0.703452i	−0.857837	+	0.513922i	$0.828192\pi$
$674$	−36.5087	−	1.15445i	−1.40626	−	0.0444678i
$675$	−4.01874	+	2.11301i	−0.154681	+	0.0813297i
$676$	9.35275	+	0.592084i	0.359721	+	0.0227725i
$677$	31.1495	−	5.49250i	1.19717	−	0.211094i	0.460698	−	0.887557i	$-0.347599\pi$
$677$	31.1495	−	5.49250i	1.19717	−	0.211094i	0.736477	+	0.676463i	$0.236488\pi$
$678$	1.49925	+	20.9132i	0.0575784	+	0.803168i
$679$	4.27169	−	1.55477i	0.163932	−	0.0596665i
$680$	34.6868	−	34.1659i	1.33018	−	1.31020i
$681$	−11.7061	−	2.93785i	−0.448580	−	0.112579i
$682$	−4.96097	+	12.3963i	−0.189965	+	0.474679i
$683$	−29.5187	+	17.0426i	−1.12950	+	0.652117i	−0.943809	−	0.330491i	$-0.892786\pi$
$683$	−29.5187	+	17.0426i	−1.12950	+	0.652117i	−0.185691	+	0.982608i	$0.559452\pi$
$684$	16.9061	+	31.5286i	0.646422	+	1.20552i
$685$	−4.52572	−	2.61293i	−0.172919	−	0.0998348i
$686$	12.0538	−	9.48164i	0.460218	−	0.362011i
$687$	39.1722	−	19.0308i	1.49451	−	0.726072i
$688$	10.5214	+	3.26591i	0.401126	+	0.124512i
$689$	−3.69985	+	20.9829i	−0.140953	+	0.799385i
$690$	−38.0035	+	17.0001i	−1.44677	+	0.647184i
$691$	−5.27112	−	6.28188i	−0.200523	−	0.238974i	0.656407	−	0.754407i	$-0.272075\pi$
$691$	−5.27112	−	6.28188i	−0.200523	−	0.238974i	−0.856930	+	0.515433i	$0.827631\pi$
$692$	32.3328	+	21.5000i	1.22911	+	0.817307i
$693$	8.45720	−	0.269216i	0.321262	−	0.0102267i
$694$	16.1563	−	8.65889i	0.613285	−	0.328687i
$695$	1.33259	+	0.485021i	0.0505478	+	0.0183979i
$696$	30.9237	+	10.9639i	1.17216	+	0.415587i
$697$	−23.2528	−	19.5114i	−0.880761	−	0.739046i
$698$	−0.450402	−	1.37080i	−0.0170480	−	0.0518857i
$699$	−2.80466	−	27.0864i	−0.106082	−	1.02450i
$700$	0.157818	+	1.41195i	0.00596497	+	0.0533666i
$701$			1.97965i			0.0747704i	0.999301	+	0.0373852i	$0.0119029\pi$
$701$			1.97965i			0.0747704i	−0.999301	+	0.0373852i	$0.988097\pi$
$702$	−20.3758	+	5.81334i	−0.769037	+	0.219410i
$703$	−24.7468			−0.933344
$704$	−27.7518	−	0.419962i	−1.04593	−	0.0158279i
$705$	5.10564	−	11.4200i	0.192290	−	0.430103i
$706$	22.2239	−	7.30204i	0.836406	−	0.274816i
$707$	−8.63122	+	10.2863i	−0.324611	+	0.386856i
$708$	5.41843	+	24.8735i	0.203637	+	0.934803i
$709$	−5.97488	+	16.4158i	−0.224391	+	0.616510i	−0.999890	−	0.0148394i	$-0.995276\pi$
$709$	−5.97488	+	16.4158i	−0.224391	+	0.616510i	0.775499	+	0.631349i	$0.217499\pi$
$710$	16.3083	−	8.74033i	0.612038	−	0.328019i
$711$	30.2419	+	4.34540i	1.13416	+	0.162965i
$712$	7.04566	−	9.90194i	0.264047	−	0.371091i
$713$	−14.6196	+	12.2673i	−0.547510	+	0.459415i
$714$	−14.0688	−	1.45376i	−0.526513	−	0.0544054i
$715$	−23.8767	−	4.21010i	−0.892936	−	0.157449i
$716$	8.97859	+	2.17585i	0.335546	+	0.0813154i
$717$	15.0879	−	22.2945i	0.563470	−	0.832605i
$718$	−20.0938	+	15.8059i	−0.749893	+	0.589871i
$719$	17.2073	−	29.8038i	0.641722	−	1.11150i	−0.343326	−	0.939216i	$-0.611554\pi$
$719$	17.2073	−	29.8038i	0.641722	−	1.11150i	0.985048	−	0.172279i	$-0.0551131\pi$
$720$	−26.2671	−	12.4846i	−0.978918	−	0.465272i
$721$	7.44538	+	12.8958i	0.277280	+	0.480264i
$722$	21.7322	+	8.69717i	0.808789	+	0.323675i
$723$	−15.6962	−	15.2045i	−0.583748	−	0.565462i
$724$	8.84342	−	9.27926i	0.328663	−	0.344861i
$725$	2.00152	+	5.49913i	0.0743345	+	0.204232i
$726$	−2.10242	+	1.42347i	−0.0780280	+	0.0528298i
$727$	4.21802	+	23.9216i	0.156438	+	0.887203i	0.957460	+	0.288567i	$0.0931789\pi$
$727$	4.21802	+	23.9216i	0.156438	+	0.887203i	−0.801022	+	0.598635i	$0.795710\pi$
$728$	−0.627822	+	6.60048i	−0.0232686	+	0.244630i
$729$	−21.9894	+	15.6674i	−0.814422	+	0.580274i
$730$	0.427340	−	13.5143i	0.0158166	−	0.500187i
$731$	−19.2644	+	3.39683i	−0.712519	+	0.125636i
$732$	−0.487155	−	0.770921i	−0.0180058	−	0.0284941i
$733$	−7.76866	−	21.3442i	−0.286942	−	0.788366i	−0.996490	−	0.0837095i	$-0.973323\pi$
$733$	−7.76866	−	21.3442i	−0.286942	−	0.788366i	0.709548	−	0.704657i	$-0.248899\pi$
$734$	−21.5130	−	19.2424i	−0.794061	−	0.710251i
$735$	−18.5144	+	19.1132i	−0.682915	+	0.705000i
$736$	−34.6783	−	19.2667i	−1.27826	−	0.710178i
$737$	−3.88422	−	6.72767i	−0.143077	−	0.247817i
$738$	−6.19787	+	17.0397i	−0.228147	+	0.627240i
$739$	−0.214406	−	0.123787i	−0.00788706	−	0.00455360i	0.496051	−	0.868293i	$-0.334783\pi$
$739$	−0.214406	−	0.123787i	−0.00788706	−	0.00455360i	−0.503938	+	0.863740i	$0.668116\pi$
$740$	16.1972	−	11.9319i	0.595422	−	0.438625i
$741$	−16.6900	+	24.6618i	−0.613123	+	0.905975i
$742$	8.31569	+	1.73893i	0.305279	+	0.0638381i
$743$	0.843956	−	4.78631i	0.0309618	−	0.175593i	−0.965406	−	0.260753i	$-0.916029\pi$
$743$	0.843956	−	4.78631i	0.0309618	−	0.175593i	0.996367	+	0.0851603i	$0.0271402\pi$
$744$	−13.1482	−	2.20541i	−0.482035	−	0.0808541i
$745$	40.6657	−	34.1225i	1.48987	−	1.25015i
$746$	−34.8583	−	21.6224i	−1.27625	−	0.791654i
$747$	−3.40768	+	23.7159i	−0.124681	+	0.867719i
$748$	44.1517	−	21.8956i	1.61434	−	0.800584i
$749$	−4.74524	+	13.0374i	−0.173387	+	0.476378i
$750$	5.96766	+	23.7574i	0.217908	+	0.867498i
$751$	23.6852	+	19.8743i	0.864287	+	0.725223i	0.962887	−	0.269905i	$-0.0869921\pi$
$751$	23.6852	+	19.8743i	0.864287	+	0.725223i	−0.0986005	+	0.995127i	$0.531437\pi$
$752$	11.6258	−	2.63180i	0.423950	−	0.0959717i
$753$	−3.97342	+	8.88753i	−0.144799	+	0.323879i
$754$	3.88995	+	27.0317i	0.141664	+	0.984437i
$755$		−	18.7222i		−	0.681370i
$756$	2.06001	+	8.19364i	0.0749219	+	0.298000i
$757$		−	15.9221i		−	0.578697i	−0.957224	−	0.289349i	$-0.906561\pi$
$757$		−	15.9221i		−	0.578697i	0.957224	−	0.289349i	$-0.0934387\pi$
$758$	−26.2990	+	3.78451i	−0.955222	+	0.137460i
$759$	−41.9173	+	4.34033i	−1.52150	+	0.157544i
$760$	−39.5591	+	10.2797i	−1.43496	+	0.372884i
$761$	12.1040	+	10.1564i	0.438768	+	0.368170i	0.835248	−	0.549873i	$-0.185324\pi$
$761$	12.1040	+	10.1564i	0.438768	+	0.368170i	−0.396480	+	0.918043i	$0.629768\pi$
$762$	3.06317	−	10.7537i	0.110967	−	0.389565i
$763$	5.10946	−	14.0381i	0.184975	−	0.508214i
$764$	17.9845	+	36.2650i	0.650656	+	1.31202i
$765$	51.6149	−	1.64304i	1.86614	−	0.0594043i
$766$	11.1032	−	17.8998i	0.401174	−	0.646746i
$767$	−16.2323	+	13.6205i	−0.586113	+	0.491807i
$768$	−5.48823	−	27.1639i	−0.198039	−	0.980194i
$769$	−7.98567	+	45.2890i	−0.287970	+	1.63316i	0.406507	+	0.913648i	$0.366747\pi$
$769$	−7.98567	+	45.2890i	−0.287970	+	1.63316i	−0.694478	+	0.719514i	$0.744365\pi$
$770$	−1.97874	+	9.46250i	−0.0713090	+	0.341005i
$771$	−14.6332	−	30.1204i	−0.527004	−	1.08476i
$772$	−9.06246	+	6.67597i	−0.326165	+	0.240273i
$773$	−35.6666	−	20.5921i	−1.28284	−	0.740647i	−0.305472	−	0.952201i	$-0.598814\pi$
$773$	−35.6666	−	20.5921i	−1.28284	−	0.740647i	−0.977366	+	0.211554i	$0.932147\pi$
$774$	5.84460	+	10.1182i	0.210080	+	0.363692i
$775$	−1.18895	−	2.05933i	−0.0427085	−	0.0739733i
$776$	−14.2828	−	6.79219i	−0.512722	−	0.243826i
$777$	−5.66839	−	1.42258i	−0.203352	−	0.0510347i
$778$	−16.6016	+	18.5606i	−0.595195	+	0.665428i
$779$	8.71544	+	23.9455i	0.312263	+	0.857936i
$780$	−0.967002	−	24.1888i	−0.0346242	−	0.866100i
$781$	18.4444	−	3.25225i	0.659993	−	0.116375i
$782$	70.4060	+	2.22633i	2.51771	+	0.0796134i
$783$	16.1953	+	30.8019i	0.578772	+	1.10077i
$784$	−25.1539	−	3.19759i	−0.898353	−	0.114200i
$785$	−0.577638	−	3.27595i	−0.0206168	−	0.116924i
$786$	14.2379	−	29.3224i	0.507848	−	1.04589i
$787$	−6.23669	−	17.1352i	−0.222314	−	0.610803i	0.777523	−	0.628854i	$-0.216476\pi$
$787$	−6.23669	−	17.1352i	−0.222314	−	0.610803i	−0.999837	+	0.0180518i	$0.994254\pi$
$788$	6.04545	−	6.34340i	0.215360	−	0.225974i
$789$	19.2191	−	5.47892i	0.684218	−	0.195055i
$790$	−12.9693	+	32.4072i	−0.461427	+	1.15300i
$791$	3.47939	+	6.02648i	0.123713	+	0.214277i
$792$	−21.3150	−	20.3052i	−0.757395	−	0.721515i
$793$	0.379541	−	0.657384i	0.0134779	−	0.0233444i
$794$	−13.2551	−	16.8510i	−0.470406	−	0.598019i
$795$	−30.9397	−	2.21147i	−1.09732	−	0.0784328i
$796$	6.26074	−	25.8348i	0.221906	−	0.915689i
$797$	40.7976	+	7.19372i	1.44512	+	0.254814i	0.840550	−	0.541734i	$-0.182232\pi$
$797$	40.7976	+	7.19372i	1.44512	+	0.254814i	0.604575	+	0.796548i	$0.293343\pi$
$798$	9.61815	+	6.96226i	0.340479	+	0.246461i
$799$	−16.2138	+	13.6050i	−0.573602	+	0.481309i
$800$	3.11443	−	3.83835i	0.110112	−	0.135706i
$801$	12.6165	−	2.64107i	0.445782	−	0.0933176i
$802$	0.400525	+	0.747325i	0.0141430	+	0.0263890i
$803$	4.68101	−	12.8610i	0.165189	−	0.453853i
$804$	5.73803	−	5.21925i	0.202365	−	0.184069i
$805$	−8.88176	+	10.5849i	−0.313041	+	0.373068i
$806$	−3.46398	−	10.5427i	−0.122013	−	0.371349i
$807$	−13.5757	−	18.7460i	−0.477886	−	0.659891i
$808$	46.5687	−	3.71944i	1.63828	−	0.130849i
$809$	−19.2719			−0.677564			−0.338782	−	0.940865i	$-0.610015\pi$
$809$	−19.2719			−0.677564			−0.338782	+	0.940865i	$0.610015\pi$
$810$	−11.4734	−	28.6342i	−0.403133	−	1.00610i
$811$			15.7750i			0.553935i	0.960879	+	0.276968i	$0.0893295\pi$
$811$			15.7750i			0.553935i	−0.960879	+	0.276968i	$0.910671\pi$
$812$	10.8220	−	1.20961i	0.379777	−	0.0424489i
$813$	4.58258	−	3.31865i	0.160718	−	0.116390i
$814$	19.3461	−	6.35648i	0.678079	−	0.222795i
$815$	−25.2474	−	21.1851i	−0.884380	−	0.742083i
$816$	30.7447	+	38.4211i	1.07628	+	1.34501i
$817$	15.4315	+	5.61659i	0.539878	+	0.196500i
$818$	18.9982	+	35.4481i	0.664257	+	1.23941i
$819$	−5.24063	+	4.68950i	−0.183122	+	0.163864i
$820$	−17.2499	−	11.4705i	−0.602394	−	0.400568i
$821$	6.66717	+	7.94562i	0.232686	+	0.277304i	0.869735	−	0.493519i	$-0.164290\pi$
$821$	6.66717	+	7.94562i	0.232686	+	0.277304i	−0.637049	+	0.770823i	$0.719845\pi$
$822$	3.09700	−	4.27842i	0.108020	−	0.149227i
$823$	9.20557	−	52.2074i	0.320886	−	1.81983i	−0.216249	−	0.976338i	$-0.569382\pi$
$823$	9.20557	−	52.2074i	0.320886	−	1.81983i	0.537135	−	0.843496i	$-0.319507\pi$
$824$	13.7868	−	49.9387i	0.480287	−	1.73970i
$825$	0.374352	−	5.23739i	0.0130333	−	0.182343i
$826$	5.22361	+	6.64069i	0.181753	+	0.231059i
$827$	−23.9359	−	13.8194i	−0.832332	−	0.480547i	0.0223184	−	0.999751i	$-0.492895\pi$
$827$	−23.9359	−	13.8194i	−0.832332	−	0.480547i	−0.854650	+	0.519204i	$0.826229\pi$
$828$	−13.1429	−	39.9721i	−0.456747	−	1.38913i
$829$	−34.2649	+	19.7829i	−1.19007	+	0.687088i	−0.958323	−	0.285688i	$-0.907778\pi$
$829$	−34.2649	+	19.7829i	−1.19007	+	0.687088i	−0.231748	+	0.972776i	$0.574445\pi$
$830$	−25.4139	−	10.1706i	−0.882129	−	0.353026i
$831$	0.141757	+	0.497260i	0.00491751	+	0.0172498i
$832$	17.8931	−	14.5585i	0.620332	−	0.504724i
$833$	42.3084	−	15.3990i	1.46590	−	0.533543i
$834$	−0.626041	+	1.28931i	−0.0216780	+	0.0446450i
$835$	10.5402	−	1.85852i	0.364759	−	0.0643168i
$836$	−41.2899	−	2.61389i	−1.42804	−	0.0904033i
$837$	−8.65415	−	11.1831i	−0.299131	−	0.386544i
$838$	1.25030	−	39.5398i	0.0431909	−	1.36588i
$839$	4.95699	+	28.1125i	0.171134	+	0.970551i	0.942512	+	0.334173i	$0.108457\pi$
$839$	4.95699	+	28.1125i	0.171134	+	0.970551i	−0.771378	+	0.636378i	$0.780432\pi$
$840$	−9.65216	+	0.0805508i	−0.333031	+	0.00277927i
$841$	14.8973	−	5.42218i	0.513700	−	0.186972i
$842$	30.8578	−	34.4990i	1.06343	−	1.18891i
$843$	−7.33444	+	29.2247i	−0.252611	+	1.00655i
$844$	−20.0554	+	45.8562i	−0.690334	+	1.57844i
$845$	−9.83486	+	5.67816i	−0.338329	+	0.195335i
$846$	10.9505	+	6.31921i	0.376487	+	0.217259i
$847$	−0.421335	+	0.729774i	−0.0144773	+	0.0250753i
$848$	−15.9920	−	24.8572i	−0.549167	−	0.853600i
$849$	2.07904	−	1.01005i	0.0713524	−	0.0346647i
$850$	−1.79651	+	8.59103i	−0.0616197	+	0.294670i
$851$	28.6640	+	5.05424i	0.982591	+	0.173257i
$852$	7.09279	+	17.3032i	0.242995	+	0.592798i
$853$	4.41611	+	5.26292i	0.151205	+	0.180199i	0.836330	−	0.548227i	$-0.184697\pi$
$853$	4.41611	+	5.26292i	0.151205	+	0.180199i	−0.685125	+	0.728425i	$0.740252\pi$
$854$	−0.257204	−	0.159543i	−0.00880134	−	0.00545944i
$855$	−38.2148	−	20.4706i	−1.30692	−	0.700081i
$856$	43.9005	−	20.0682i	1.50049	−	0.685917i
$857$	−26.6254	−	9.69084i	−0.909505	−	0.331033i	−0.155450	−	0.987844i	$-0.549683\pi$
$857$	−26.6254	−	9.69084i	−0.909505	−	0.331033i	−0.754055	+	0.656811i	$0.771905\pi$
$858$	6.71292	−	23.5666i	0.229175	−	0.804551i
$859$	14.7282	−	17.5524i	0.502520	−	0.598879i	−0.453836	−	0.891085i	$-0.649945\pi$
$859$	14.7282	−	17.5524i	0.502520	−	0.598879i	0.956355	+	0.292206i	$0.0943892\pi$
$860$	−12.8082	+	3.76425i	−0.436758	+	0.128360i
$861$	0.619806	+	5.98585i	0.0211229	+	0.203997i
$862$	−2.01034	−	13.9701i	−0.0684726	−	0.475824i
$863$	24.0297			0.817980			0.408990	−	0.912539i	$-0.365881\pi$
$863$	24.0297			0.817980			0.408990	+	0.912539i	$0.365881\pi$
$864$	15.2798	−	25.1103i	0.519831	−	0.854269i
$865$	−47.0523			−1.59983
$866$	3.52309	+	24.4823i	0.119719	+	0.831943i
$867$	−52.8857	−	23.6440i	−1.79609	−	0.802994i
$868$	−4.24522	+	1.24764i	−0.144092	+	0.0423476i
$869$	−22.7114	+	27.0664i	−0.770432	+	0.918165i
$870$	−38.5608	+	9.68614i	−1.30733	+	0.328391i
$871$	6.06710	+	2.20824i	0.205576	+	0.0748235i
$872$	−47.2701	+	21.6085i	−1.60077	+	0.731756i
$873$	−6.23599	−	15.5727i	−0.211056	−	0.527058i
$874$	−50.2523	−	31.1713i	−1.69981	−	1.05438i
$875$	5.22579	+	6.22786i	0.176664	+	0.210540i
$876$	13.5420	+	1.83352i	0.457542	+	0.0619490i
$877$	−0.500115	−	0.0881838i	−0.0168877	−	0.00297776i	0.165198	−	0.986260i	$-0.447174\pi$
$877$	−0.500115	−	0.0881838i	−0.0168877	−	0.00297776i	−0.182086	+	0.983283i	$0.558285\pi$
$878$	−2.22342	+	10.6326i	−0.0750369	+	0.358832i
$879$	11.6486	+	7.88327i	0.392899	+	0.265896i
$880$	28.2853	−	18.1974i	0.953496	−	0.613435i
$881$	−11.2219	+	19.4369i	−0.378076	+	0.654847i	−0.990782	−	0.135464i	$-0.956747\pi$
$881$	−11.2219	+	19.4369i	−0.378076	+	0.654847i	0.612706	+	0.790311i	$0.290081\pi$
$882$	−17.2918	−	20.5987i	−0.582244	−	0.693594i
$883$	−45.9402	+	26.5236i	−1.54601	+	0.892589i	−0.547570	+	0.836760i	$0.684447\pi$
$883$	−45.9402	+	26.5236i	−1.54601	+	0.892589i	−0.998440	+	0.0558294i	$0.982220\pi$
$884$	−16.4128	+	37.5275i	−0.552021	+	1.26219i
$885$	−22.1574	−	21.4633i	−0.744814	−	0.721482i
$886$	4.60179	−	5.14480i	0.154600	−	0.172843i
$887$	−26.2975	+	9.57151i	−0.882984	+	0.321380i	−0.743413	−	0.668832i	$-0.766794\pi$
$887$	−26.2975	+	9.57151i	−0.882984	+	0.321380i	−0.139571	+	0.990212i	$0.544572\pi$
$888$	10.3129	+	17.5231i	0.346079	+	0.588038i
$889$	−0.644417	−	3.65467i	−0.0216130	−	0.122574i
$890$	−0.465444	+	14.7193i	−0.0156017	+	0.493393i
$891$	−1.98590	−	31.1611i	−0.0665301	−	1.04394i
$892$	−3.23334	−	0.204689i	−0.108260	−	0.00685351i
$893$	17.4984	−	3.08544i	0.585562	−	0.103250i
$894$	30.0801	+	44.4273i	1.00603	+	1.48587i
$895$	−10.5200	+	3.82896i	−0.351644	+	0.127988i
$896$	−5.57649	−	7.31440i	−0.186298	−	0.244357i
$897$	24.3688	−	25.1569i	0.813650	−	0.839963i
$898$	−6.54330	−	2.61861i	−0.218353	−	0.0873843i
$899$	−15.7839	+	9.11281i	−0.526421	+	0.303929i
$900$	5.18916	−	0.747857i	0.172972	−	0.0249286i
$901$	45.4514	+	26.2414i	1.51421	+	0.874227i
$902$	−12.9640	−	16.4809i	−0.431655	−	0.548756i
$903$	3.21179	+	2.17359i	0.106882	+	0.0723326i
$904$	6.44289	−	23.3375i	0.214287	−	0.776193i
$905$	−2.69732	+	15.2973i	−0.0896620	+	0.508498i
$906$	18.8220	+	1.94491i	0.625320	+	0.0646153i
$907$	17.3874	+	20.7215i	0.577338	+	0.688045i	0.973120	−	0.230300i	$-0.0739707\pi$
$907$	17.3874	+	20.7215i	0.577338	+	0.688045i	−0.395781	+	0.918345i	$0.629526\pi$
$908$	11.6048	+	7.71673i	0.385119	+	0.256089i
$909$	38.9524	+	30.6269i	1.29197	+	1.01583i
$910$	−3.79535	−	7.08160i	−0.125815	−	0.234753i
$911$	9.03367	+	3.28799i	0.299299	+	0.108936i	0.487305	−	0.873232i	$-0.337980\pi$
$911$	9.03367	+	3.28799i	0.299299	+	0.108936i	−0.188006	+	0.982168i	$0.560202\pi$
$912$	−6.22500	−	40.8380i	−0.206130	−	1.35228i
$913$	−21.2256	−	17.8104i	−0.702465	−	0.589438i
$914$	−27.0812	+	8.89801i	−0.895767	+	0.294320i
$915$	1.00885	+	0.451036i	0.0333517	+	0.0149108i
$916$	−49.9764	+	5.58604i	−1.65127	+	0.184568i
$917$		−	10.8185i		−	0.357258i
$918$	−3.71009	+	52.0608i	−0.122451	+	1.71826i
$919$	0.257674			0.00849989			0.00424994	−	0.999991i	$-0.498647\pi$
$919$	0.257674			0.00849989			0.00424994	+	0.999991i	$0.498647\pi$
$920$	47.9205	−	3.82740i	1.57989	−	0.126186i
$921$	44.1608	−	4.57264i	1.45515	−	0.150674i
$922$	−14.9910	−	45.6252i	−0.493701	−	1.50259i
$923$	−10.0056	+	11.9242i	−0.329337	+	0.392489i
$924$	−9.30741	−	2.97229i	−0.306191	−	0.0977810i
$925$	−1.24037	+	3.40788i	−0.0407830	+	0.112050i
$926$	−25.5853	−	47.7387i	−0.840786	−	1.56879i
$927$	46.6894	−	28.9749i	1.53348	−	0.951660i
$928$	−29.4193	−	23.8708i	−0.965736	−	0.783596i
$929$	−27.9758	+	23.4745i	−0.917856	+	0.770173i	−0.973597	−	0.228273i	$-0.926692\pi$
$929$	−27.9758	+	23.4745i	−0.917856	+	0.770173i	0.0557411	+	0.998445i	$0.482248\pi$
$930$	14.7472	−	6.59690i	0.483580	−	0.216321i
$931$	−37.2228	−	6.56338i	−1.21993	−	0.215106i
$932$	−7.40568	+	30.5593i	−0.242581	+	1.00100i
$933$	13.4588	+	27.7031i	0.440622	+	0.906957i
$934$	9.62440	+	12.2353i	0.314920	+	0.400353i
$935$	−29.8603	+	51.7196i	−0.976536	+	1.69141i
$936$	24.4183	+	1.54064i	0.798137	+	0.0503575i
$937$	−4.21635	−	7.30293i	−0.137742	−	0.238576i	0.788899	−	0.614522i	$-0.210651\pi$
$937$	−4.21635	−	7.30293i	−0.137742	−	0.238576i	−0.926642	+	0.375946i	$0.877318\pi$
$938$	0.956509	−	2.39009i	0.0312311	−	0.0780393i
$939$	−13.8806	+	55.3083i	−0.452975	+	1.80492i
$940$	−9.96535	+	10.4565i	−0.325034	+	0.341053i
$941$	6.23285	+	17.1246i	0.203185	+	0.558246i	0.998873	−	0.0474602i	$-0.0151127\pi$
$941$	6.23285	+	17.1246i	0.203185	+	0.558246i	−0.795688	+	0.605707i	$0.792891\pi$
$942$	3.35343	−	0.240404i	0.109261	−	0.00783279i
$943$	−5.20444	−	29.5159i	−0.169480	−	0.961169i
$944$	3.70690	−	29.1603i	0.120649	−	0.949088i
$945$	−7.57655	−	6.88570i	−0.246465	−	0.223992i
$946$	−13.5064	−	0.427089i	−0.439130	−	0.0138859i
$947$	−30.4479	+	5.36879i	−0.989424	+	0.174462i	−0.644860	−	0.764301i	$-0.723084\pi$
$947$	−30.4479	+	5.36879i	−0.989424	+	0.174462i	−0.344564	+	0.938763i	$0.611973\pi$
$948$	−31.2328	−	16.4050i	−1.01439	−	0.532810i
$949$	3.89045	+	10.6889i	0.126289	+	0.346977i
$950$	4.91216	−	5.49180i	0.159371	−	0.178177i
$951$	−3.35339	−	11.7631i	−0.108741	−	0.381444i
$952$	14.7490	+	7.01390i	0.478017	+	0.227322i
$953$	17.3439	+	30.0406i	0.561825	+	0.973109i	0.997337	+	0.0729266i	$0.0232339\pi$
$953$	17.3439	+	30.0406i	0.561825	+	0.973109i	−0.435512	+	0.900183i	$0.643433\pi$
$954$	5.43736	−	30.8750i	0.176041	−	0.999614i
$955$	−42.4811	−	24.5265i	−1.37466	−	0.793658i
$956$	−25.0271	+	18.4365i	−0.809433	+	0.596279i
$957$	−40.1423	−	2.86925i	−1.29762	−	0.0927495i
$958$	−6.64751	+	31.7889i	−0.214771	+	1.02705i
$959$	0.304398	−	1.72633i	0.00982954	−	0.0557461i
$960$	23.7648	+	23.7277i	0.767004	+	0.765809i
$961$	−18.0742	+	15.1661i	−0.583040	+	0.489229i
$962$	−8.92125	+	14.3822i	−0.287633	+	0.463702i
$963$	48.6432	+	15.9712i	1.56750	+	0.514664i
$964$	11.2109	+	22.6063i	0.361079	+	0.728101i
$965$	4.66513	−	12.8173i	0.150176	−	0.412605i
$966$	−9.71866	−	10.0287i	−0.312693	−	0.322669i
$967$	23.6086	+	19.8100i	0.759202	+	0.637046i	0.937919	−	0.346854i	$-0.112750\pi$
$967$	23.6086	+	19.8100i	0.759202	+	0.637046i	−0.178717	+	0.983901i	$0.557195\pi$
$968$	2.83752	−	0.737348i	0.0912014	−	0.0236993i
$969$	43.0231	+	59.4086i	1.38210	+	1.90848i
$970$	18.9698	−	2.72982i	0.609084	−	0.0876492i
$971$		−	43.2999i		−	1.38956i	−0.719223	−	0.694779i	$-0.755502\pi$
$971$		−	43.2999i		−	1.38956i	0.719223	−	0.694779i	$-0.244498\pi$
$972$	29.9788	−	8.55995i	0.961570	−	0.274561i
$973$			0.475690i			0.0152499i
$974$	1.77519	+	12.3360i	0.0568809	+	0.395272i
$975$	2.55963	+	3.53449i	0.0819739	+	0.113194i
$976$	0.232495	+	1.02703i	0.00744197	+	0.0328745i
$977$	4.11710	+	3.45466i	0.131718	+	0.110524i	0.706267	−	0.707946i	$-0.250378\pi$
$977$	4.11710	+	3.45466i	0.131718	+	0.110524i	−0.574549	+	0.818470i	$0.694822\pi$
$978$	23.9209	−	23.1813i	0.764905	−	0.741257i
$979$	−5.09839	+	14.0077i	−0.162945	+	0.447688i
$980$	27.5276	−	13.6514i	0.879336	−	0.436079i
$981$	−52.3767	−	17.1970i	−1.67226	−	0.549059i
$982$	−14.1330	−	8.76665i	−0.451003	−	0.279755i
$983$	0.806129	−	0.676422i	0.0257115	−	0.0215745i	−0.629841	−	0.776724i	$-0.716880\pi$
$983$	0.806129	−	0.676422i	0.0257115	−	0.0215745i	0.655553	+	0.755149i	$0.272436\pi$
$984$	13.3237	−	16.1503i	0.424743	−	0.514854i
$985$	−1.84392	+	10.4574i	−0.0587521	+	0.333200i
$986$	65.8465	+	13.7694i	2.09698	+	0.438509i
$987$	4.18547	+	0.299164i	0.133225	+	0.00952250i
$988$	27.6845	−	20.3941i	0.880761	−	0.648823i
$989$	−16.7270	−	9.65734i	−0.531888	−	0.307086i
$990$	35.1329	+	6.18723i	1.11660	+	0.196643i
$991$	10.7235	+	18.5737i	0.340644	+	0.590013i	0.984553	−	0.175090i	$-0.0560215\pi$
$991$	10.7235	+	18.5737i	0.340644	+	0.590013i	−0.643908	+	0.765103i	$0.722688\pi$
$992$	13.4569	+	7.47642i	0.427256	+	0.237376i
$993$	5.76398	+	20.2190i	0.182914	+	0.641632i
$994$	4.62605	+	4.13779i	0.146729	+	0.131243i
$995$	11.0174	+	30.2700i	0.349274	+	0.959622i
$996$	12.8649	−	24.4929i	0.407639	−	0.776087i
$997$	9.02724	−	1.59175i	0.285896	−	0.0504111i	−0.0288614	−	0.999583i	$-0.509188\pi$
$997$	9.02724	−	1.59175i	0.285896	−	0.0504111i	0.314757	+	0.949172i	$0.398077\pi$
$998$	−0.788669	+	24.9411i	−0.0249649	+	0.789496i
$999$	−4.58138	+	21.0738i	−0.144949	+	0.666745i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.13.19	✓	204
3.2	odd	2		648.2.t.a.253.16		204
4.3	odd	2		864.2.bf.a.337.6		204
8.3	odd	2		864.2.bf.a.337.29		204
8.5	even	2	inner	216.2.t.a.13.20	yes	204
24.5	odd	2		648.2.t.a.253.15		204
27.2	odd	18		648.2.t.a.397.15		204
27.25	even	9	inner	216.2.t.a.133.20	yes	204
108.79	odd	18		864.2.bf.a.241.29		204
216.29	odd	18		648.2.t.a.397.16		204
216.133	even	18	inner	216.2.t.a.133.19	yes	204
216.187	odd	18		864.2.bf.a.241.6		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.19	✓	204	1.1	even	1	trivial
216.2.t.a.13.20	yes	204	8.5	even	2	inner
216.2.t.a.133.19	yes	204	216.133	even	18	inner
216.2.t.a.133.20	yes	204	27.25	even	9	inner
648.2.t.a.253.15		204	24.5	odd	2
648.2.t.a.253.16		204	3.2	odd	2
648.2.t.a.397.15		204	27.2	odd	18
648.2.t.a.397.16		204	216.29	odd	18
864.2.bf.a.241.6		204	216.187	odd	18
864.2.bf.a.241.29		204	108.79	odd	18
864.2.bf.a.337.6		204	4.3	odd	2
864.2.bf.a.337.29		204	8.3	odd	2

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.201435 + 1.39979i) q^{2} +(1.40283 - 1.01591i) q^{3} +(-1.91885 + 0.563935i) q^{4} +(1.55785 - 1.85658i) q^{5} +(1.70465 + 1.75903i) q^{6} +(0.763942 + 0.278052i) q^{7} +(-1.17592 - 2.57240i) q^{8} +(0.935847 - 2.85030i) q^{9} +O(q^{10})\)	\(q+(0.201435 + 1.39979i) q^{2} +(1.40283 - 1.01591i) q^{3} +(-1.91885 + 0.563935i) q^{4} +(1.55785 - 1.85658i) q^{5} +(1.70465 + 1.75903i) q^{6} +(0.763942 + 0.278052i) q^{7} +(-1.17592 - 2.57240i) q^{8} +(0.935847 - 2.85030i) q^{9} +(2.91263 + 1.80670i) q^{10} +(2.23007 + 2.65769i) q^{11} +(-2.11890 + 2.74048i) q^{12} +(-2.83964 - 0.500705i) q^{13} +(-0.235331 + 1.12537i) q^{14} +(0.299281 - 4.18710i) q^{15} +(3.36395 - 2.16421i) q^{16} +(-3.55127 + 6.15099i) q^{17} +(4.17834 + 0.735844i) q^{18} +(5.16371 - 2.98127i) q^{19} +(-1.94230 + 4.44102i) q^{20} +(1.35415 - 0.386038i) q^{21} +(-3.27101 + 3.65699i) q^{22} +(-6.58997 + 2.39855i) q^{23} +(-4.26293 - 2.41400i) q^{24} +(-0.151733 - 0.860521i) q^{25} +(0.128881 - 4.07577i) q^{26} +(-1.58282 - 4.94921i) q^{27} +(-1.62269 - 0.102726i) q^{28} +(-6.59552 + 1.16297i) q^{29} +(5.92137 - 0.424498i) q^{30} +(2.55724 - 0.930757i) q^{31} +(3.70707 + 4.27290i) q^{32} +(5.82838 + 1.46273i) q^{33} +(-9.32547 - 3.73203i) q^{34} +(1.70634 - 0.985154i) q^{35} +(-0.188366 + 5.99704i) q^{36} +(-3.59434 - 2.07519i) q^{37} +(5.21332 + 6.62760i) q^{38} +(-4.49220 + 2.18242i) q^{39} +(-6.60776 - 1.82424i) q^{40} +(-0.742124 + 4.20880i) q^{41} +(0.813149 + 1.81778i) q^{42} +(1.77034 + 2.10981i) q^{43} +(-5.77793 - 3.84209i) q^{44} +(-3.83389 - 6.17782i) q^{45} +(-4.68493 - 8.74145i) q^{46} +(2.80028 + 1.01922i) q^{47} +(2.52040 - 6.45349i) q^{48} +(-4.85602 - 4.07468i) q^{49} +(1.17399 - 0.385734i) q^{50} +(1.26704 + 12.2365i) q^{51} +(5.73120 - 0.640596i) q^{52} -7.38929i q^{53} +(6.60904 - 3.21256i) q^{54} +8.40834 q^{55} +(-0.183072 - 2.29213i) q^{56} +(4.21509 - 9.42808i) q^{57} +(-2.95649 - 8.99811i) q^{58} +(4.72368 - 5.62947i) q^{59} +(1.78698 + 8.20319i) q^{60} +(-0.0900385 + 0.247379i) q^{61} +(1.81799 + 3.39212i) q^{62} +(1.50746 - 1.91725i) q^{63} +(-5.23444 + 6.04985i) q^{64} +(-5.35335 + 4.49199i) q^{65} +(-0.873481 + 8.45318i) q^{66} +(-2.20513 - 0.388825i) q^{67} +(3.34560 - 13.8055i) q^{68} +(-6.80787 + 10.0596i) q^{69} +(1.72273 + 2.19008i) q^{70} +(2.69918 - 4.67512i) q^{71} +(-8.43257 + 0.944340i) q^{72} +(-1.97245 - 3.41639i) q^{73} +(2.18082 - 5.44935i) q^{74} +(-1.08707 - 1.05302i) q^{75} +(-8.22713 + 8.63260i) q^{76} +(0.964666 + 2.65040i) q^{77} +(-3.95983 - 5.84853i) q^{78} +(1.76846 + 10.0295i) q^{79} +(1.22252 - 9.61697i) q^{80} +(-7.24838 - 5.33489i) q^{81} +(-6.04094 - 0.191022i) q^{82} +(-7.86515 + 1.38684i) q^{83} +(-2.38072 + 1.50440i) q^{84} +(5.88742 + 16.1756i) q^{85} +(-2.59669 + 2.90311i) q^{86} +(-8.07090 + 8.33191i) q^{87} +(4.21426 - 8.86184i) q^{88} +(2.14833 + 3.72101i) q^{89} +(7.87540 - 6.61108i) q^{90} +(-2.03010 - 1.17208i) q^{91} +(11.2925 - 8.31878i) q^{92} +(2.64179 - 3.90362i) q^{93} +(-0.862622 + 4.12512i) q^{94} +(2.50935 - 14.2312i) q^{95} +(9.54126 + 2.22808i) q^{96} +(4.28345 - 3.59424i) q^{97} +(4.72554 - 7.61821i) q^{98} +(9.66221 - 3.86916i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

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