LMFDB - Embedded newform 418.2.m.b.227.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(151,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("418.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.m (of order $10$, degree $4$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			227.10
Character	$\chi$	$=$	418.227
Dual form			418.2.m.b.151.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(2.71373 + 0.881745i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.18335 + 0.859758i) q^{5} +(1.67718 + 2.30844i) q^{6} +(3.23095 - 1.04980i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(4.15981 + 3.02228i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(2.71373 + 0.881745i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.18335 + 0.859758i) q^{5} +(1.67718 + 2.30844i) q^{6} +(3.23095 - 1.04980i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(4.15981 + 3.02228i) q^{9} -1.46271 q^{10} +(-1.63953 - 2.88304i) q^{11} +2.85339i q^{12} +(-3.93112 - 2.85613i) q^{13} +(3.23095 + 1.04980i) q^{14} +(-3.96939 + 1.28973i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.99776 - 2.74968i) q^{17} +(1.58891 + 4.89015i) q^{18} +(-4.35751 - 0.109891i) q^{19} +(-1.18335 - 0.859758i) q^{20} +9.69359 q^{21} +(0.368199 - 3.29612i) q^{22} -1.03359 q^{23} +(-1.67718 + 2.30844i) q^{24} +(-0.883940 + 2.72049i) q^{25} +(-1.50155 - 4.62131i) q^{26} +(3.59219 + 4.94423i) q^{27} +(1.99684 + 2.74841i) q^{28} +(2.76958 + 8.52388i) q^{29} +(-3.96939 - 1.28973i) q^{30} +(-1.42396 + 1.95992i) q^{31} -1.00000 q^{32} +(-1.90715 - 9.26945i) q^{33} -3.39879i q^{34} +(-2.92079 + 4.02012i) q^{35} +(-1.58891 + 4.89015i) q^{36} +(11.3294 - 3.68114i) q^{37} +(-3.46071 - 2.65019i) q^{38} +(-8.14963 - 11.2170i) q^{39} +(-0.452001 - 1.39112i) q^{40} +(-1.50274 + 4.62495i) q^{41} +(7.84228 + 5.69775i) q^{42} -12.3044i q^{43} +(2.23529 - 2.45020i) q^{44} -7.52096 q^{45} +(-0.836194 - 0.607530i) q^{46} +(-1.19758 + 3.68577i) q^{47} +(-2.71373 + 0.881745i) q^{48} +(3.67384 - 2.66920i) q^{49} +(-2.31418 + 1.68135i) q^{50} +(-2.99686 - 9.22339i) q^{51} +(1.50155 - 4.62131i) q^{52} +(1.42191 - 1.95709i) q^{53} +6.11141i q^{54} +(4.41887 + 2.00206i) q^{55} +3.39722i q^{56} +(-11.7282 - 4.14043i) q^{57} +(-2.76958 + 8.52388i) q^{58} +(-6.62279 + 2.15187i) q^{59} +(-2.45322 - 3.37657i) q^{60} +(-3.50666 - 4.82650i) q^{61} +(-2.30402 + 0.748622i) q^{62} +(16.6129 + 5.39787i) q^{63} +(-0.809017 - 0.587785i) q^{64} +7.10749 q^{65} +(3.90553 - 8.62013i) q^{66} +3.43561i q^{67} +(1.99776 - 2.74968i) q^{68} +(-2.80489 - 0.911364i) q^{69} +(-4.72593 + 1.53555i) q^{70} +(5.58258 + 7.68376i) q^{71} +(-4.15981 + 3.02228i) q^{72} +(11.7051 - 3.80323i) q^{73} +(11.3294 + 3.68114i) q^{74} +(-4.79755 + 6.60326i) q^{75} +(-1.24203 - 4.17820i) q^{76} +(-8.32387 - 7.59378i) q^{77} -13.8650i q^{78} +(5.96067 + 4.33068i) q^{79} +(0.452001 - 1.39112i) q^{80} +(0.621980 + 1.91426i) q^{81} +(-3.93422 + 2.85838i) q^{82} +(0.294537 + 0.405395i) q^{83} +(2.99548 + 9.21915i) q^{84} +(4.72811 + 1.53626i) q^{85} +(7.23236 - 9.95450i) q^{86} +25.5736i q^{87} +(3.24858 - 0.668380i) q^{88} +5.68988i q^{89} +(-6.08458 - 4.42071i) q^{90} +(-15.6996 - 5.10112i) q^{91} +(-0.319398 - 0.983005i) q^{92} +(-5.59240 + 4.06312i) q^{93} +(-3.13531 + 2.27793i) q^{94} +(5.25096 - 3.61636i) q^{95} +(-2.71373 - 0.881745i) q^{96} +(0.135020 - 0.185839i) q^{97} +4.54112 q^{98} +(1.89321 - 16.9480i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) $ 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9	$ 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{13} - 5 q^{14} - 30 q^{15} - 10 q^{16} - 15 q^{17} - 13 q^{18} + 11 q^{19} + 2 q^{20} - 4 q^{22} + 6 q^{23} - 5 q^{24} - 36 q^{25} - 2 q^{26} + 45 q^{27} + 2 q^{29} - 30 q^{30} - 40 q^{32} - 27 q^{33} - 5 q^{35} + 13 q^{36} + 14 q^{38} + 30 q^{39} + 3 q^{40} + 8 q^{41} + 20 q^{42} - 6 q^{44} + 18 q^{45} - q^{46} - 8 q^{47} + 31 q^{49} - 9 q^{50} - 41 q^{51} + 2 q^{52} + 40 q^{53} - 31 q^{55} - 10 q^{57} - 2 q^{58} - 35 q^{59} - 20 q^{60} + 5 q^{61} + 30 q^{62} - 25 q^{63} - 10 q^{64} - 8 q^{65} - 48 q^{66} + 15 q^{68} + 60 q^{69} + 10 q^{70} - 50 q^{71} - 8 q^{72} + 10 q^{73} + 35 q^{75} + 11 q^{76} - 64 q^{77} + 42 q^{79} - 3 q^{80} + 11 q^{81} + 7 q^{82} + 25 q^{83} + 20 q^{84} - 45 q^{85} + 40 q^{86} + 6 q^{88} + 22 q^{90} + 70 q^{91} - 4 q^{92} - 18 q^{93} - 7 q^{94} - 5 q^{95} + 15 q^{97} + 74 q^{98} + 50 q^{99}+O(q^{100}) $ 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^13 - 5 * q^14 - 30 * q^15 - 10 * q^16 - 15 * q^17 - 13 * q^18 + 11 * q^19 + 2 * q^20 - 4 * q^22 + 6 * q^23 - 5 * q^24 - 36 * q^25 - 2 * q^26 + 45 * q^27 + 2 * q^29 - 30 * q^30 - 40 * q^32 - 27 * q^33 - 5 * q^35 + 13 * q^36 + 14 * q^38 + 30 * q^39 + 3 * q^40 + 8 * q^41 + 20 * q^42 - 6 * q^44 + 18 * q^45 - q^46 - 8 * q^47 + 31 * q^49 - 9 * q^50 - 41 * q^51 + 2 * q^52 + 40 * q^53 - 31 * q^55 - 10 * q^57 - 2 * q^58 - 35 * q^59 - 20 * q^60 + 5 * q^61 + 30 * q^62 - 25 * q^63 - 10 * q^64 - 8 * q^65 - 48 * q^66 + 15 * q^68 + 60 * q^69 + 10 * q^70 - 50 * q^71 - 8 * q^72 + 10 * q^73 + 35 * q^75 + 11 * q^76 - 64 * q^77 + 42 * q^79 - 3 * q^80 + 11 * q^81 + 7 * q^82 + 25 * q^83 + 20 * q^84 - 45 * q^85 + 40 * q^86 + 6 * q^88 + 22 * q^90 + 70 * q^91 - 4 * q^92 - 18 * q^93 - 7 * q^94 - 5 * q^95 + 15 * q^97 + 74 * q^98 + 50 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	2.71373	+	0.881745i	1.56677	+	0.509075i	0.958607	−	0.284734i	$-0.0919052\pi$
$3$	2.71373	+	0.881745i	1.56677	+	0.509075i	0.608167	+	0.793809i	$0.291905\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.18335	+	0.859758i	−0.529212	+	0.384495i	−0.820063	−	0.572273i	$-0.806062\pi$
$5$	−1.18335	+	0.859758i	−0.529212	+	0.384495i	0.290851	+	0.956768i	$0.406062\pi$
$6$	1.67718	+	2.30844i	0.684705	+	0.942416i
$7$	3.23095	−	1.04980i	1.22118	−	0.396787i	0.373671	−	0.927561i	$-0.378099\pi$
$7$	3.23095	−	1.04980i	1.22118	−	0.396787i	0.847513	+	0.530774i	$0.178099\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	4.15981	+	3.02228i	1.38660	+	1.00743i
$10$	−1.46271			−0.462549
$11$	−1.63953	−	2.88304i	−0.494338	−	0.869270i
$11$	−1.63953	−	2.88304i	−0.494338	−	0.869270i
$12$			2.85339i			0.823701i
$13$	−3.93112	−	2.85613i	−1.09030	−	0.792147i	−0.110848	−	0.993837i	$-0.535357\pi$
$13$	−3.93112	−	2.85613i	−1.09030	−	0.792147i	−0.979449	+	0.201690i	$0.935357\pi$
$14$	3.23095	+	1.04980i	0.863508	+	0.280571i
$15$	−3.96939	+	1.28973i	−1.02489	+	0.333008i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.99776	−	2.74968i	−0.484527	−	0.666894i	0.494840	−	0.868984i	$-0.335227\pi$
$17$	−1.99776	−	2.74968i	−0.484527	−	0.666894i	−0.979367	+	0.202090i	$0.935227\pi$
$18$	1.58891	+	4.89015i	0.374509	+	1.15262i
$19$	−4.35751	−	0.109891i	−0.999682	−	0.0252108i
$19$	−4.35751	−	0.109891i	−0.999682	−	0.0252108i
$20$	−1.18335	−	0.859758i	−0.264606	−	0.192248i
$21$	9.69359			2.11531
$22$	0.368199	−	3.29612i	0.0785003	−	0.702736i
$23$	−1.03359			−0.215519			−0.107759	−	0.994177i	$-0.534368\pi$
$23$	−1.03359			−0.215519			−0.107759	+	0.994177i	$0.534368\pi$
$24$	−1.67718	+	2.30844i	−0.342353	+	0.471208i
$25$	−0.883940	+	2.72049i	−0.176788	+	0.544097i
$26$	−1.50155	−	4.62131i	−0.294479	−	0.906314i
$27$	3.59219	+	4.94423i	0.691318	+	0.951518i
$28$	1.99684	+	2.74841i	0.377367	+	0.519401i
$29$	2.76958	+	8.52388i	0.514298	+	1.58285i	0.784556	+	0.620058i	$0.212891\pi$
$29$	2.76958	+	8.52388i	0.514298	+	1.58285i	−0.270259	+	0.962788i	$0.587109\pi$
$30$	−3.96939	−	1.28973i	−0.724709	−	0.235472i
$31$	−1.42396	+	1.95992i	−0.255751	+	0.352011i	−0.917515	−	0.397701i	$-0.869808\pi$
$31$	−1.42396	+	1.95992i	−0.255751	+	0.352011i	0.661764	+	0.749712i	$0.269808\pi$
$32$	−1.00000			−0.176777
$33$	−1.90715	−	9.26945i	−0.331991	−	1.61360i
$34$		−	3.39879i		−	0.582887i
$35$	−2.92079	+	4.02012i	−0.493703	+	0.679524i
$36$	−1.58891	+	4.89015i	−0.264818	+	0.815025i
$37$	11.3294	−	3.68114i	1.86254	−	0.605176i	0.868566	−	0.495574i	$-0.165042\pi$
$37$	11.3294	−	3.68114i	1.86254	−	0.605176i	0.993975	−	0.109603i	$-0.0349578\pi$
$38$	−3.46071	−	2.65019i	−0.561401	−	0.429917i
$39$	−8.14963	−	11.2170i	−1.30499	−	1.79616i
$40$	−0.452001	−	1.39112i	−0.0714677	−	0.219955i
$41$	−1.50274	+	4.62495i	−0.234688	+	0.722296i	0.762474	+	0.647018i	$0.223984\pi$
$41$	−1.50274	+	4.62495i	−0.234688	+	0.722296i	−0.997163	+	0.0752778i	$0.976016\pi$
$42$	7.84228	+	5.69775i	1.21009	+	0.879181i
$43$		−	12.3044i		−	1.87641i	−0.346082	−	0.938204i	$-0.612488\pi$
$43$		−	12.3044i		−	1.87641i	0.346082	−	0.938204i	$-0.387512\pi$
$44$	2.23529	−	2.45020i	0.336983	−	0.369381i
$45$	−7.52096			−1.12116
$46$	−0.836194	−	0.607530i	−0.123290	−	0.0895755i
$47$	−1.19758	+	3.68577i	−0.174685	+	0.537625i	−0.999619	−	0.0276038i	$-0.991212\pi$
$47$	−1.19758	+	3.68577i	−0.174685	+	0.537625i	0.824934	+	0.565229i	$0.191212\pi$
$48$	−2.71373	+	0.881745i	−0.391693	+	0.127269i
$49$	3.67384	−	2.66920i	0.524835	−	0.381315i
$50$	−2.31418	+	1.68135i	−0.327275	+	0.237779i
$51$	−2.99686	−	9.22339i	−0.419644	−	1.29153i
$52$	1.50155	−	4.62131i	0.208228	−	0.640860i
$53$	1.42191	−	1.95709i	0.195315	−	0.268827i	−0.700115	−	0.714030i	$-0.746868\pi$
$53$	1.42191	−	1.95709i	0.195315	−	0.268827i	0.895430	+	0.445202i	$0.146868\pi$
$54$			6.11141i			0.831657i
$55$	4.41887	+	2.00206i	0.595840	+	0.269958i
$56$			3.39722i			0.453973i
$57$	−11.7282	−	4.14043i	−1.55344	−	0.548413i
$58$	−2.76958	+	8.52388i	−0.363663	+	1.11924i
$59$	−6.62279	+	2.15187i	−0.862214	+	0.280150i	−0.706553	−	0.707660i	$-0.749751\pi$
$59$	−6.62279	+	2.15187i	−0.862214	+	0.280150i	−0.155661	+	0.987811i	$0.549751\pi$
$60$	−2.45322	−	3.37657i	−0.316709	−	0.435913i
$61$	−3.50666	−	4.82650i	−0.448982	−	0.617971i	0.523197	−	0.852212i	$-0.324739\pi$
$61$	−3.50666	−	4.82650i	−0.448982	−	0.617971i	−0.972178	+	0.234242i	$0.924739\pi$
$62$	−2.30402	+	0.748622i	−0.292611	+	0.0950750i
$63$	16.6129	+	5.39787i	2.09303	+	0.680067i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	7.10749			0.881575
$66$	3.90553	−	8.62013i	0.480738	−	1.06107i
$67$			3.43561i			0.419727i	0.977731	+	0.209863i	$0.0673019\pi$
$67$			3.43561i			0.419727i	−0.977731	+	0.209863i	$0.932698\pi$
$68$	1.99776	−	2.74968i	0.242264	−	0.333447i
$69$	−2.80489	−	0.911364i	−0.337669	−	0.109715i
$70$	−4.72593	+	1.53555i	−0.564857	+	0.183533i
$71$	5.58258	+	7.68376i	0.662530	+	0.911894i	0.999562	−	0.0295989i	$-0.00942300\pi$
$71$	5.58258	+	7.68376i	0.662530	+	0.911894i	−0.337032	+	0.941493i	$0.609423\pi$
$72$	−4.15981	+	3.02228i	−0.490238	+	0.356179i
$73$	11.7051	−	3.80323i	1.36998	−	0.445134i	0.470619	−	0.882337i	$-0.344031\pi$
$73$	11.7051	−	3.80323i	1.36998	−	0.445134i	0.899363	+	0.437203i	$0.144031\pi$
$74$	11.3294	+	3.68114i	1.31702	+	0.427924i
$75$	−4.79755	+	6.60326i	−0.553973	+	0.762479i
$76$	−1.24203	−	4.17820i	−0.142471	−	0.479272i
$77$	−8.32387	−	7.59378i	−0.948593	−	0.865392i
$78$		−	13.8650i		−	1.56990i
$79$	5.96067	+	4.33068i	0.670628	+	0.487240i	0.870235	−	0.492636i	$-0.163967\pi$
$79$	5.96067	+	4.33068i	0.670628	+	0.487240i	−0.199607	+	0.979876i	$0.563967\pi$
$80$	0.452001	−	1.39112i	0.0505353	−	0.155532i
$81$	0.621980	+	1.91426i	0.0691089	+	0.212695i
$82$	−3.93422	+	2.85838i	−0.434462	+	0.315655i
$83$	0.294537	+	0.405395i	0.0323296	+	0.0444979i	0.824876	−	0.565314i	$-0.191245\pi$
$83$	0.294537	+	0.405395i	0.0323296	+	0.0444979i	−0.792546	+	0.609812i	$0.791245\pi$
$84$	2.99548	+	9.21915i	0.326834	+	1.00589i
$85$	4.72811	+	1.53626i	0.512835	+	0.166630i
$86$	7.23236	−	9.95450i	0.779886	−	1.07342i
$87$			25.5736i			2.74178i
$88$	3.24858	−	0.668380i	0.346300	−	0.0712495i
$89$			5.68988i			0.603126i	0.953446	+	0.301563i	$0.0975083\pi$
$89$			5.68988i			0.603126i	−0.953446	+	0.301563i	$0.902492\pi$
$90$	−6.08458	−	4.42071i	−0.641371	−	0.465984i
$91$	−15.6996	−	5.10112i	−1.64577	−	0.534742i
$92$	−0.319398	−	0.983005i	−0.0332995	−	0.102485i
$93$	−5.59240	+	4.06312i	−0.579905	+	0.421325i
$94$	−3.13531	+	2.27793i	−0.323382	+	0.234951i
$95$	5.25096	−	3.61636i	0.538738	−	0.371031i
$96$	−2.71373	−	0.881745i	−0.276969	−	0.0899927i
$97$	0.135020	−	0.185839i	0.0137092	−	0.0188691i	−0.802107	−	0.597180i	$-0.796288\pi$
$97$	0.135020	−	0.185839i	0.0137092	−	0.0188691i	0.815817	+	0.578311i	$0.196288\pi$
$98$	4.54112			0.458722
$99$	1.89321	−	16.9480i	0.190275	−	1.70334i
$100$	−2.86049			−0.286049
$101$	−6.14792	+	8.46188i	−0.611741	+	0.841989i	−0.996719	−	0.0809367i	$-0.974209\pi$
$101$	−6.14792	+	8.46188i	−0.611741	+	0.841989i	0.384979	+	0.922926i	$0.374209\pi$
$102$	2.99686	−	9.22339i	0.296733	−	0.913252i
$103$	−3.25631	+	1.05804i	−0.320854	+	0.104252i	−0.465016	−	0.885302i	$-0.653951\pi$
$103$	−3.25631	+	1.05804i	−0.320854	+	0.104252i	0.144162	+	0.989554i	$0.453951\pi$
$104$	3.93112	−	2.85613i	0.385478	−	0.280066i
$105$	−11.4709	+	8.33413i	−1.11945	+	0.813328i
$106$	2.30070	−	0.747543i	0.223464	−	0.0726078i
$107$	3.67123	−	11.2989i	0.354911	−	1.09231i	−0.601149	−	0.799137i	$-0.705290\pi$
$107$	3.67123	−	11.2989i	0.354911	−	1.09231i	0.956061	−	0.293168i	$-0.0947097\pi$
$108$	−3.59219	+	4.94423i	−0.345659	+	0.475759i
$109$	5.73571			0.549381			0.274691	−	0.961533i	$-0.411425\pi$
$109$	5.73571			0.549381			0.274691	+	0.961533i	$0.411425\pi$
$110$	2.39816	+	4.21705i	0.228655	+	0.402079i
$111$	33.9908			3.22626
$112$	−1.99684	+	2.74841i	−0.188683	+	0.259700i
$113$	−10.4720	−	3.40255i	−0.985121	−	0.320085i	−0.228216	−	0.973610i	$-0.573289\pi$
$113$	−10.4720	−	3.40255i	−0.985121	−	0.320085i	−0.756905	+	0.653525i	$0.773289\pi$
$114$	−7.05465	−	10.2434i	−0.660728	−	0.959378i
$115$	1.22311	−	0.888639i	0.114055	−	0.0828660i
$116$	−7.25085	+	5.26805i	−0.673224	+	0.489126i
$117$	−7.72071	−	23.7619i	−0.713780	−	2.19679i
$118$	−6.62279	−	2.15187i	−0.609677	−	0.198096i
$119$	−9.34126	−	6.78682i	−0.856312	−	0.622147i
$120$		−	4.17367i		−	0.381002i
$121$	−5.62386	+	9.45369i	−0.511260	+	0.859426i
$122$		−	5.96589i		−	0.540126i
$123$	−8.15605	+	11.2258i	−0.735407	+	1.01220i
$124$	−2.30402	−	0.748622i	−0.206907	−	0.0672282i
$125$	−3.55295	−	10.9349i	−0.317786	−	0.978043i
$126$	10.2674	+	14.1318i	0.914689	+	1.25896i
$127$	9.04470	−	6.57136i	0.802588	−	0.583114i	−0.109085	−	0.994032i	$-0.534792\pi$
$127$	9.04470	−	6.57136i	0.802588	−	0.583114i	0.911672	+	0.410919i	$0.134792\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	10.8494	−	33.3909i	0.955234	−	2.93991i
$130$	5.75008	+	4.17768i	0.504315	+	0.366406i
$131$		−	15.2055i		−	1.32851i	−0.747507	−	0.664254i	$-0.768749\pi$
$131$		−	15.2055i		−	1.32851i	0.747507	−	0.664254i	$-0.231251\pi$
$132$	8.22643	−	4.67822i	0.716019	−	0.407187i
$133$	−14.1943	+	4.21946i	−1.23080	+	0.365874i
$134$	−2.01940	+	2.77947i	−0.174450	+	0.240110i
$135$	−8.50168	−	2.76236i	−0.731708	−	0.237746i
$136$	3.23244	−	1.05028i	0.277179	−	0.0900610i
$137$	−14.7274	+	10.7001i	−1.25825	+	0.914172i	−0.998670	−	0.0515503i	$-0.983584\pi$
$137$	−14.7274	+	10.7001i	−1.25825	+	0.914172i	−0.259579	+	0.965722i	$0.583584\pi$
$138$	−1.73352	−	2.38598i	−0.147567	−	0.203108i
$139$	12.2435	−	3.97817i	1.03848	−	0.337424i	0.260345	−	0.965516i	$-0.416164\pi$
$139$	12.2435	−	3.97817i	1.03848	−	0.337424i	0.778139	+	0.628092i	$0.216164\pi$
$140$	−4.72593	−	1.53555i	−0.399414	−	0.129778i
$141$	−6.49982	+	8.94624i	−0.547384	+	0.753409i
$142$			9.49765i			0.797025i
$143$	−1.78913	+	16.0163i	−0.149614	+	1.33935i
$144$	−5.14181			−0.428484
$145$	−10.6059	−	7.70561i	−0.880769	−	0.639916i
$146$	11.7051	+	3.80323i	0.968723	+	0.314757i
$147$	12.3234	−	4.00411i	1.01642	−	0.330253i
$148$	7.00195	+	9.63736i	0.575557	+	0.792186i
$149$	12.9726	+	17.8552i	1.06276	+	1.46276i	0.877200	+	0.480125i	$0.159409\pi$
$149$	12.9726	+	17.8552i	1.06276	+	1.46276i	0.185556	+	0.982634i	$0.440591\pi$
$150$	−7.76260	+	2.52222i	−0.633813	+	0.205938i
$151$	−3.18966	+	9.81677i	−0.259571	+	0.798878i	0.733323	+	0.679880i	$0.237968\pi$
$151$	−3.18966	+	9.81677i	−0.259571	+	0.798878i	−0.992895	+	0.118998i	$0.962032\pi$
$152$	1.45106	−	4.11028i	0.117696	−	0.333388i
$153$		−	17.4759i		−	1.41284i
$154$	−2.27064	−	11.0361i	−0.182973	−	0.889318i
$155$		−	3.54354i		−	0.284624i
$156$	8.14963	−	11.2170i	0.652493	−	0.898079i
$157$	0.294410	−	0.906101i	0.0234965	−	0.0723147i	−0.938621	−	0.344951i	$-0.887896\pi$
$157$	0.294410	−	0.906101i	0.0234965	−	0.0723147i	0.962117	+	0.272636i	$0.0878955\pi$
$158$	2.27677	+	7.00719i	0.181130	+	0.557462i
$159$	5.58434	−	4.05726i	0.442867	−	0.321762i
$160$	1.18335	−	0.859758i	0.0935524	−	0.0679698i
$161$	−3.33949	+	1.08506i	−0.263188	+	0.0855151i
$162$	−0.621980	+	1.91426i	−0.0488674	+	0.150398i
$163$	−2.53058	−	1.83857i	−0.198210	−	0.144008i	0.484253	−	0.874928i	$-0.339091\pi$
$163$	−2.53058	−	1.83857i	−0.198210	−	0.144008i	−0.682463	+	0.730920i	$0.739091\pi$
$164$	−4.86296			−0.379734
$165$	10.2263	+	9.32936i	0.796117	+	0.726290i
$166$			0.501096i			0.0388926i
$167$	0.287877	+	0.209155i	0.0222766	+	0.0161849i	0.598868	−	0.800848i	$-0.295617\pi$
$167$	0.287877	+	0.209155i	0.0222766	+	0.0161849i	−0.576591	+	0.817033i	$0.695617\pi$
$168$	−2.99548	+	9.21915i	−0.231106	+	0.711273i
$169$	3.27903	+	10.0918i	0.252233	+	0.776295i
$170$	2.92213	+	4.02197i	0.224117	+	0.308471i
$171$	−17.7943	−	13.6267i	−1.36076	−	1.04206i
$172$	11.7022	−	3.80228i	0.892285	−	0.289921i
$173$	0.972337	−	2.99254i	0.0739254	−	0.227519i	−0.907266	−	0.420558i	$-0.861834\pi$
$173$	0.972337	−	2.99254i	0.0739254	−	0.227519i	0.981191	+	0.193039i	$0.0618344\pi$
$174$	−15.0318	+	20.6895i	−1.13956	+	1.56846i
$175$			9.71772i			0.734590i
$176$	3.02102	+	1.36874i	0.227718	+	0.103172i
$177$	−19.8699			−1.49351
$178$	−3.34443	+	4.60321i	−0.250675	+	0.345025i
$179$	16.0192	+	5.20496i	1.19733	+	0.389037i	0.838779	−	0.544472i	$-0.183270\pi$
$179$	16.0192	+	5.20496i	1.19733	+	0.389037i	0.358553	+	0.933509i	$0.383270\pi$
$180$	−2.32410	−	7.15286i	−0.173228	−	0.533142i
$181$	6.72865	+	9.26119i	0.500137	+	0.688379i	0.982217	−	0.187748i	$-0.0601188\pi$
$181$	6.72865	+	9.26119i	0.500137	+	0.688379i	−0.482081	+	0.876127i	$0.660119\pi$
$182$	−9.70290	−	13.3549i	−0.719227	−	0.989931i
$183$	−5.26039	−	16.1898i	−0.388859	−	1.19679i
$184$	0.319398	−	0.983005i	0.0235463	−	0.0724681i
$185$	−10.2418	+	14.0966i	−0.752992	+	1.03641i
$186$	−6.91258			−0.506855
$187$	−4.65204	+	10.2678i	−0.340191	+	0.750856i
$188$	−3.87545			−0.282646
$189$	16.7967	+	12.2035i	1.22178	+	0.887673i
$190$	6.37376	+	0.160739i	0.462402	+	0.0116612i
$191$	−0.744392	−	2.29100i	−0.0538623	−	0.165771i	0.920507	−	0.390727i	$-0.127776\pi$
$191$	−0.744392	−	2.29100i	−0.0538623	−	0.165771i	−0.974369	+	0.224956i	$0.927776\pi$
$192$	−1.67718	−	2.30844i	−0.121040	−	0.166597i
$193$	−11.7996	+	8.57294i	−0.849357	+	0.617094i	−0.924969	−	0.380044i	$-0.875909\pi$
$193$	−11.7996	+	8.57294i	−0.849357	+	0.617094i	0.0756120	+	0.997137i	$0.475909\pi$
$194$	0.218467	−	0.0709841i	0.0156850	−	0.00509636i
$195$	19.2878	+	6.26699i	1.38123	+	0.448788i
$196$	3.67384	+	2.66920i	0.262417	+	0.190657i
$197$			4.42865i			0.315529i	0.987477	+	0.157764i	$0.0504286\pi$
$197$			4.42865i			0.315529i	−0.987477	+	0.157764i	$0.949571\pi$
$198$	11.4934	−	12.5984i	0.816804	−	0.895333i
$199$	25.7836			1.82775			0.913875	−	0.405996i	$-0.133075\pi$
$199$	25.7836			1.82775			0.913875	+	0.405996i	$0.133075\pi$
$200$	−2.31418	−	1.68135i	−0.163638	−	0.118890i
$201$	−3.02933	+	9.32333i	−0.213673	+	0.657617i
$202$	−9.94754	+	3.23215i	−0.699906	+	0.227413i
$203$	17.8967	+	24.6327i	1.25610	+	1.72888i
$204$	7.84588	−	5.70037i	0.549322	−	0.399106i
$205$	−2.19807	−	6.76495i	−0.153520	−	0.472485i
$206$	−3.25631	−	1.05804i	−0.226878	−	0.0737172i
$207$	−4.29955	−	3.12380i	−0.298839	−	0.217119i
$208$	4.85913			0.336920
$209$	6.82747	+	12.7431i	0.472266	+	0.881456i
$210$	−14.1789			−0.978435
$211$	−14.5120	−	10.5436i	−0.999047	−	0.725850i	−0.0371636	−	0.999309i	$-0.511832\pi$
$211$	−14.5120	−	10.5436i	−0.999047	−	0.725850i	−0.961884	+	0.273459i	$0.911832\pi$
$212$	2.30070	+	0.747543i	0.158013	+	0.0513415i
$213$	8.37450	+	25.7741i	0.573811	+	1.76601i
$214$	9.61141	−	6.98310i	0.657023	−	0.477355i
$215$	10.5788	+	14.5605i	0.721470	+	0.993018i
$216$	−5.81229	+	1.88853i	−0.395476	+	0.128498i
$217$	−2.54323	+	7.82727i	−0.172646	+	0.531350i
$218$	4.64028	+	3.37136i	0.314280	+	0.228338i
$219$	35.1180			2.37306
$220$	−0.538567	+	4.82126i	−0.0363102	+	0.325049i
$221$			16.5152i			1.11093i
$222$	27.4991	+	19.9793i	1.84562	+	1.34092i
$223$	−0.318014	−	0.103329i	−0.0212958	−	0.00691941i	0.298350	−	0.954457i	$-0.403564\pi$
$223$	−0.318014	−	0.103329i	−0.0212958	−	0.00691941i	−0.319646	+	0.947537i	$0.603564\pi$
$224$	−3.23095	+	1.04980i	−0.215877	+	0.0701427i
$225$	−11.8991	+	8.64520i	−0.793273	+	0.576346i
$226$	−6.47204	−	8.90800i	−0.430514	−	0.592551i
$227$	0.669053	+	2.05913i	0.0444066	+	0.136670i	0.970802	−	0.239884i	$-0.0771093\pi$
$227$	0.669053	+	2.05913i	0.0444066	+	0.136670i	−0.926395	+	0.376553i	$0.877109\pi$
$228$	0.313562	−	12.4337i	0.0207662	−	0.823440i
$229$	−8.42032	−	6.11772i	−0.556431	−	0.404271i	0.273720	−	0.961809i	$-0.411746\pi$
$229$	−8.42032	−	6.11772i	−0.556431	−	0.404271i	−0.830151	+	0.557539i	$0.811746\pi$
$230$	1.51184			0.0996879
$231$	−15.8930	−	27.9470i	−1.04568	−	1.83878i
$232$	−8.96254			−0.588420
$233$	11.4732	−	15.7915i	0.751634	−	1.03454i	−0.246230	−	0.969211i	$-0.579192\pi$
$233$	11.4732	−	15.7915i	0.751634	−	1.03454i	0.997864	−	0.0653241i	$-0.0208081\pi$
$234$	7.72071	−	23.7619i	0.504718	−	1.55336i
$235$	−1.75171	−	5.39121i	−0.114269	−	0.351684i
$236$	−4.09311	−	5.63368i	−0.266439	−	0.366721i
$237$	12.3571	+	17.0081i	0.802680	+	1.10479i
$238$	−3.56804	−	10.9813i	−0.231282	−	0.711812i
$239$	−24.4255	−	7.93634i	−1.57996	−	0.513359i	−0.617911	−	0.786248i	$-0.712021\pi$
$239$	−24.4255	−	7.93634i	−1.57996	−	0.513359i	−0.962046	+	0.272889i	$0.912021\pi$
$240$	2.45322	−	3.37657i	0.158355	−	0.217956i
$241$	−2.21331			−0.142572			−0.0712860	−	0.997456i	$-0.522710\pi$
$241$	−2.21331			−0.142572			−0.0712860	+	0.997456i	$0.522710\pi$
$242$	−10.1065	+	4.34257i	−0.649673	+	0.279151i
$243$		−	12.5910i		−	0.807714i
$244$	3.50666	−	4.82650i	0.224491	−	0.308985i
$245$	−2.05259	+	6.31723i	−0.131135	+	0.403593i
$246$	−13.1968	+	4.28789i	−0.841395	+	0.273386i
$247$	16.8161	+	12.8776i	1.06998	+	0.819383i
$248$	−1.42396	−	1.95992i	−0.0904217	−	0.124455i
$249$	0.441839	+	1.35984i	0.0280004	+	0.0861764i
$250$	3.55295	−	10.9349i	0.224708	−	0.691581i
$251$	6.32467	+	4.59514i	0.399210	+	0.290043i	0.769219	−	0.638985i	$-0.220646\pi$
$251$	6.32467	+	4.59514i	0.399210	+	0.290043i	−0.370009	+	0.929028i	$0.620646\pi$
$252$			17.4679i			1.10037i
$253$	1.69461	+	2.97989i	0.106539	+	0.187344i
$254$	11.1799			0.701487
$255$	11.4762	+	8.33797i	0.718669	+	0.522144i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−24.5068	+	7.96275i	−1.52869	+	0.496703i	−0.948230	−	0.317583i	$-0.897129\pi$
$257$	−24.5068	+	7.96275i	−1.52869	+	0.496703i	−0.580464	+	0.814286i	$0.697129\pi$
$258$	28.4040	−	20.6367i	1.76836	−	1.28479i
$259$	32.7403	−	23.7872i	2.03438	−	1.47806i
$260$	2.19633	+	6.75962i	0.136211	+	0.419214i
$261$	−14.2406	+	43.8282i	−0.881473	+	2.71290i
$262$	8.93755	−	12.3015i	0.552164	−	0.759988i
$263$			7.12612i			0.439415i	0.975566	+	0.219708i	$0.0705104\pi$
$263$			7.12612i			0.439415i	−0.975566	+	0.219708i	$0.929490\pi$
$264$	9.40511	+	1.05061i	0.578845	+	0.0646608i
$265$			3.53844i			0.217364i
$266$	−13.9635	−	4.92957i	−0.856160	−	0.302251i
$267$	−5.01702	+	15.4408i	−0.307037	+	0.944961i
$268$	−3.26746	+	1.06166i	−0.199592	+	0.0648514i
$269$	−5.99079	−	8.24561i	−0.365265	−	0.502744i	0.586341	−	0.810064i	$-0.300568\pi$
$269$	−5.99079	−	8.24561i	−0.365265	−	0.502744i	−0.951606	+	0.307320i	$0.900568\pi$
$270$	−5.25433	−	7.23196i	−0.319768	−	0.440123i
$271$	−23.6802	+	7.69417i	−1.43847	+	0.467387i	−0.921420	−	0.388568i	$-0.872970\pi$
$271$	−23.6802	+	7.69417i	−1.43847	+	0.467387i	−0.517050	+	0.855955i	$0.672970\pi$
$272$	3.23244	+	1.05028i	0.195995	+	0.0636827i
$273$	−38.1067	−	27.6861i	−2.30632	−	1.67564i
$274$	−18.2041			−1.09975
$275$	9.29252	−	1.91189i	0.560360	−	0.115291i
$276$		−	2.94924i		−	0.177523i
$277$	11.6084	−	15.9776i	0.697482	−	0.960001i	−0.302495	−	0.953151i	$-0.597819\pi$
$277$	11.6084	−	15.9776i	0.697482	−	0.960001i	0.999977	−	0.00685030i	$-0.00218054\pi$
$278$	12.2435	+	3.97817i	0.734319	+	0.238595i
$279$	−11.8468	+	3.84927i	−0.709251	+	0.230450i
$280$	−2.92079	−	4.02012i	−0.174550	−	0.240248i
$281$	−19.7292	+	14.3341i	−1.17694	+	0.855099i	−0.991824	−	0.127617i	$-0.959267\pi$
$281$	−19.7292	+	14.3341i	−1.17694	+	0.855099i	−0.185119	+	0.982716i	$0.559267\pi$
$282$	−10.5169	+	3.41716i	−0.626274	+	0.203489i
$283$	−0.712150	−	0.231391i	−0.0423329	−	0.0137548i	0.287774	−	0.957698i	$-0.407085\pi$
$283$	−0.712150	−	0.231391i	−0.0423329	−	0.0137548i	−0.330107	+	0.943944i	$0.607085\pi$
$284$	−5.58258	+	7.68376i	−0.331265	+	0.455947i
$285$	17.4384	−	5.18383i	1.03296	−	0.307064i
$286$	−10.8616	+	11.9058i	−0.642259	+	0.704007i
$287$			16.5206i			0.975178i
$288$	−4.15981	−	3.02228i	−0.245119	−	0.178090i
$289$	1.68360	−	5.18160i	0.0990355	−	0.304800i
$290$	−4.05108	−	12.4679i	−0.237888	−	0.732143i
$291$	0.530269	−	0.385263i	0.0310849	−	0.0225845i
$292$	7.23417	+	9.95698i	0.423348	+	0.582688i
$293$	−6.73017	−	20.7133i	−0.393181	−	1.21009i	−0.930369	−	0.366624i	$-0.880514\pi$
$293$	−6.73017	−	20.7133i	−0.393181	−	1.21009i	0.537188	−	0.843462i	$-0.319486\pi$
$294$	12.3234	+	4.00411i	0.718714	+	0.233524i
$295$	5.98702	−	8.24042i	0.348578	−	0.479776i
$296$			11.9124i			0.692396i
$297$	8.36490	−	18.4627i	0.485381	−	1.07131i
$298$			22.0703i			1.27850i
$299$	4.06318	+	2.95207i	0.234980	+	0.170723i
$300$	−7.76260	−	2.52222i	−0.448174	−	0.145620i
$301$	−12.9172	−	39.7550i	−0.744534	−	2.29144i
$302$	−8.35065	+	6.06710i	−0.480526	+	0.349122i
$303$	−24.1450	+	17.5424i	−1.38709	+	1.00778i
$304$	3.58989	−	2.47238i	0.205895	−	0.141801i
$305$	8.29925	+	2.69659i	0.475213	+	0.154406i
$306$	10.2721	−	14.1383i	0.587216	−	0.808233i
$307$	−6.84315			−0.390559			−0.195280	−	0.980748i	$-0.562561\pi$
$307$	−6.84315			−0.390559			−0.195280	+	0.980748i	$0.562561\pi$
$308$	4.64990	−	10.2631i	0.264953	−	0.584793i
$309$	−9.76968			−0.555778
$310$	2.08284	−	2.86678i	0.118297	−	0.162822i
$311$	−1.85101	+	5.69681i	−0.104961	+	0.323037i	−0.989721	−	0.143010i	$-0.954322\pi$
$311$	−1.85101	+	5.69681i	−0.104961	+	0.323037i	0.884760	+	0.466046i	$0.154322\pi$
$312$	13.1864	−	4.28451i	0.746532	−	0.242563i
$313$	−7.41633	+	5.38828i	−0.419196	+	0.304564i	−0.777314	−	0.629113i	$-0.783418\pi$
$313$	−7.41633	+	5.38828i	−0.419196	+	0.304564i	0.358118	+	0.933676i	$0.383418\pi$
$314$	0.770775	−	0.560001i	0.0434974	−	0.0316027i
$315$	−24.2998	+	7.89550i	−1.36914	+	0.444861i
$316$	−2.27677	+	7.00719i	−0.128079	+	0.394185i
$317$	−0.332073	+	0.457059i	−0.0186511	+	0.0256710i	−0.818241	−	0.574876i	$-0.805050\pi$
$317$	−0.332073	+	0.457059i	−0.0186511	+	0.0256710i	0.799590	+	0.600547i	$0.205050\pi$
$318$	6.90263			0.387080
$319$	20.0339	−	21.9600i	1.12168	−	1.22952i
$320$	1.46271			0.0817678
$321$	19.9255	−	27.4251i	1.11213	−	1.53072i
$322$	−3.33949	−	1.08506i	−0.186102	−	0.0604683i
$323$	8.40308	+	12.2013i	0.467560	+	0.678898i
$324$	−1.62836	+	1.18308i	−0.0904647	+	0.0657265i
$325$	11.2449	−	8.16992i	0.623756	−	0.453186i
$326$	−0.966594	−	2.97487i	−0.0535347	−	0.164763i
$327$	15.5652	+	5.05743i	0.860756	+	0.279676i
$328$	−3.93422	−	2.85838i	−0.217231	−	0.157828i
$329$			13.1658i			0.725853i
$330$	2.78959	+	13.5585i	0.153562	+	0.746370i
$331$		−	4.39940i		−	0.241813i	−0.992664	−	0.120907i	$-0.961420\pi$
$331$		−	4.39940i		−	0.241813i	0.992664	−	0.120907i	$-0.0385801\pi$
$332$	−0.294537	+	0.405395i	−0.0161648	+	0.0222490i
$333$	58.2536	+	18.9277i	3.19228	+	1.03723i
$334$	0.109959	+	0.338419i	0.00601670	+	0.0185175i
$335$	−2.95379	−	4.06555i	−0.161383	−	0.222125i
$336$	−7.84228	+	5.69775i	−0.427831	+	0.310838i
$337$	0.925214	+	2.84752i	0.0503996	+	0.155114i	0.973089	−	0.230431i	$-0.0740135\pi$
$337$	0.925214	+	2.84752i	0.0503996	+	0.155114i	−0.922689	+	0.385545i	$0.874014\pi$
$338$	−3.27903	+	10.0918i	−0.178356	+	0.548923i
$339$	−25.4180	−	18.4672i	−1.38051	−	1.00300i
$340$			4.97143i			0.269613i
$341$	7.98516	+	0.891996i	0.432421	+	0.0483043i
$342$	−6.38630	−	21.4835i	−0.345331	−	1.16169i
$343$	−4.90998	+	6.75801i	−0.265114	+	0.364898i
$344$	11.7022	+	3.80228i	0.630941	+	0.205005i
$345$	4.10273	−	1.33306i	0.220884	−	0.0717695i
$346$	2.54561	−	1.84949i	0.136853	−	0.0994294i
$347$	16.0114	+	22.0378i	0.859537	+	1.18305i	0.981680	+	0.190538i	$0.0610233\pi$
$347$	16.0114	+	22.0378i	0.859537	+	1.18305i	−0.122143	+	0.992512i	$0.538977\pi$
$348$	−24.3219	+	7.90267i	−1.30379	+	0.423628i
$349$	23.5429	+	7.64956i	1.26022	+	0.409472i	0.861574	−	0.507631i	$-0.169479\pi$
$349$	23.5429	+	7.64956i	1.26022	+	0.409472i	0.398650	+	0.917103i	$0.369479\pi$
$350$	−5.71193	+	7.86180i	−0.305316	+	0.420231i
$351$		−	29.6961i		−	1.58506i
$352$	1.63953	+	2.88304i	0.0873874	+	0.153667i
$353$	17.9698			0.956434			0.478217	−	0.878242i	$-0.341283\pi$
$353$	17.9698			0.956434			0.478217	+	0.878242i	$0.341283\pi$
$354$	−16.0751	−	11.6792i	−0.854380	−	0.620743i
$355$	−13.2123	−	4.29295i	−0.701238	−	0.227846i
$356$	−5.41140	+	1.75827i	−0.286803	+	0.0931881i
$357$	−19.3654	−	26.6542i	−1.02493	−	1.41069i
$358$	9.90042	+	13.6268i	0.523253	+	0.720196i
$359$	−1.03191	+	0.335289i	−0.0544623	+	0.0176959i	−0.336121	−	0.941819i	$-0.609115\pi$
$359$	−1.03191	+	0.335289i	−0.0544623	+	0.0176959i	0.281659	+	0.959515i	$0.409115\pi$
$360$	2.32410	−	7.15286i	0.122491	−	0.376989i
$361$	18.9758	+	0.957705i	0.998729	+	0.0504055i
$362$			11.4475i			0.601665i
$363$	−23.5974	+	20.6960i	−1.23854	+	1.08626i
$364$		−	16.5076i		−	0.865231i
$365$	−10.5815	+	14.5641i	−0.553859	+	0.762322i
$366$	5.26039	−	16.1898i	0.274965	−	0.846255i
$367$	0.276229	+	0.850145i	0.0144190	+	0.0443772i	0.958007	−	0.286744i	$-0.0925730\pi$
$367$	0.276229	+	0.850145i	0.0144190	+	0.0443772i	−0.943588	+	0.331121i	$0.892573\pi$
$368$	0.836194	−	0.607530i	0.0435896	−	0.0316697i
$369$	−20.2290	+	14.6972i	−1.05308	+	0.765107i
$370$	−16.5716	+	5.38443i	−0.861516	+	0.279923i
$371$	2.53957	−	7.81600i	0.131848	−	0.405786i
$372$	−5.59240	−	4.06312i	−0.289952	−	0.210663i
$373$	−27.3964			−1.41853			−0.709267	−	0.704940i	$-0.750974\pi$
$373$	−27.3964			−1.41853			−0.709267	+	0.704940i	$0.750974\pi$
$374$	−9.79884	+	5.57242i	−0.506686	+	0.288143i
$375$		−	32.8071i		−	1.69415i
$376$	−3.13531	−	2.27793i	−0.161691	−	0.117475i
$377$	13.4577	−	41.4187i	0.693109	−	2.13317i
$378$	6.41575	+	19.7456i	0.329991	+	1.01561i
$379$	13.3043	+	18.3118i	0.683395	+	0.940613i	0.999968	−	0.00795545i	$-0.00253233\pi$
$379$	13.3043	+	18.3118i	0.683395	+	0.940613i	−0.316573	+	0.948568i	$0.602532\pi$
$380$	5.06200	+	3.87645i	0.259675	+	0.198857i
$381$	30.3391	−	9.85779i	1.55432	−	0.505030i
$382$	0.744392	−	2.29100i	0.0380864	−	0.117218i
$383$	9.05050	−	12.4569i	0.462459	−	0.636520i	−0.512557	−	0.858653i	$-0.671302\pi$
$383$	9.05050	−	12.4569i	0.462459	−	0.636520i	0.975016	+	0.222133i	$0.0713018\pi$
$384$		−	2.85339i		−	0.145611i
$385$	16.3789	+	1.82963i	0.834746	+	0.0932468i
$386$	−14.5852			−0.742365
$387$	37.1874	−	51.1841i	1.89034	−	2.60183i
$388$	0.218467	+	0.0709841i	0.0110910	+	0.00360367i
$389$	−4.21638	−	12.9767i	−0.213779	−	0.657944i	−0.999238	−	0.0390306i	$-0.987573\pi$
$389$	−4.21638	−	12.9767i	−0.213779	−	0.657944i	0.785459	−	0.618914i	$-0.212427\pi$
$390$	11.9205	+	16.4072i	0.603619	+	0.830810i
$391$	2.06487	+	2.84204i	0.104425	+	0.143728i
$392$	1.40328	+	4.31886i	0.0708765	+	0.218135i
$393$	13.4073	−	41.2636i	0.676311	−	2.08147i
$394$	−2.60310	+	3.58286i	−0.131142	+	0.180502i
$395$	−10.7769			−0.542246
$396$	16.7036	−	3.43668i	0.839386	−	0.172700i
$397$	−3.28583			−0.164911			−0.0824556	−	0.996595i	$-0.526276\pi$
$397$	−3.28583			−0.164911			−0.0824556	+	0.996595i	$0.526276\pi$
$398$	20.8594	+	15.1552i	1.04558	+	0.759662i
$399$	−42.2399	−	1.06524i	−2.11464	−	0.0533287i
$400$	−0.883940	−	2.72049i	−0.0441970	−	0.136024i
$401$	−0.467478	−	0.643429i	−0.0233448	−	0.0321313i	0.797185	−	0.603735i	$-0.206321\pi$
$401$	−0.467478	−	0.643429i	−0.0233448	−	0.0321313i	−0.820530	+	0.571604i	$0.806321\pi$
$402$	−7.93090	+	5.76213i	−0.395557	+	0.287389i
$403$	11.1955	−	3.63765i	0.557690	−	0.181204i
$404$	−9.94754	−	3.23215i	−0.494909	−	0.160806i
$405$	−2.38182	−	1.73049i	−0.118354	−	0.0859889i
$406$			30.4477i			1.51110i
$407$	−29.1878	−	26.6278i	−1.44679	−	1.31989i
$408$	9.69805			0.480125
$409$	−20.3590	−	14.7917i	−1.00669	−	0.731401i	−0.0431750	−	0.999068i	$-0.513747\pi$
$409$	−20.3590	−	14.7917i	−1.00669	−	0.731401i	−0.963511	+	0.267667i	$0.913747\pi$
$410$	2.19807	−	6.76495i	0.108555	−	0.334097i
$411$	−49.4010	+	16.0514i	−2.43677	+	0.791756i
$412$	−2.01251	−	2.76999i	−0.0991494	−	0.136467i
$413$	−19.1389	+	13.9052i	−0.941762	+	0.684230i
$414$	−1.64228	−	5.05442i	−0.0807137	−	0.248411i
$415$	−0.697083	−	0.226496i	−0.0342185	−	0.0111183i
$416$	3.93112	+	2.85613i	0.192739	+	0.140033i
$417$	36.7334			1.79884
$418$	−1.96665	+	14.3224i	−0.0961919	+	0.700533i
$419$	−5.46800			−0.267129			−0.133565	−	0.991040i	$-0.542642\pi$
$419$	−5.46800			−0.267129			−0.133565	+	0.991040i	$0.542642\pi$
$420$	−11.4709	−	8.33413i	−0.559725	−	0.406664i
$421$	−31.6603	−	10.2871i	−1.54303	−	0.501361i	−0.590820	−	0.806803i	$-0.701196\pi$
$421$	−31.6603	−	10.2871i	−1.54303	−	0.501361i	−0.952211	+	0.305443i	$0.901196\pi$
$422$	−5.54309	−	17.0599i	−0.269833	−	0.830462i
$423$	−16.1211	+	11.7127i	−0.783837	+	0.569491i
$424$	1.42191	+	1.95709i	0.0690541	+	0.0950449i
$425$	9.24635	−	3.00432i	0.448514	−	0.145731i
$426$	−8.37450	+	25.7741i	−0.405746	+	1.24876i
$427$	−16.3967	−	11.9129i	−0.793492	−	0.576506i
$428$	11.8804			0.574259
$429$	−18.9775	+	41.8864i	−0.916243	+	2.02229i
$430$			17.9978i			0.867930i
$431$	−4.86594	−	3.53531i	−0.234384	−	0.170290i	0.464394	−	0.885629i	$-0.346272\pi$
$431$	−4.86594	−	3.53531i	−0.234384	−	0.170290i	−0.698778	+	0.715339i	$0.746272\pi$
$432$	−5.81229	−	1.88853i	−0.279644	−	0.0908619i
$433$	−31.1077	+	10.1075i	−1.49494	+	0.485735i	−0.938537	−	0.345178i	$-0.887819\pi$
$433$	−31.1077	+	10.1075i	−1.49494	+	0.485735i	−0.556402	+	0.830913i	$0.687819\pi$
$434$	−6.65827	+	4.83752i	−0.319607	+	0.232208i
$435$	−21.9871	−	30.2626i	−1.05420	−	1.45098i
$436$	1.77243	+	5.45498i	0.0848841	+	0.261246i
$437$	4.50389	+	0.113583i	0.215450	+	0.00543340i
$438$	28.4111	+	20.6419i	1.35753	+	0.986307i
$439$	21.7384			1.03752			0.518759	−	0.854920i	$-0.326394\pi$
$439$	21.7384			1.03752			0.518759	+	0.854920i	$0.326394\pi$
$440$	−3.26958	+	3.58392i	−0.155871	+	0.170857i
$441$	23.3496			1.11188
$442$	−9.70736	+	13.3610i	−0.461732	+	0.635520i
$443$	1.49070	−	4.58790i	0.0708252	−	0.217978i	−0.909378	−	0.415970i	$-0.863442\pi$
$443$	1.49070	−	4.58790i	0.0708252	−	0.217978i	0.980204	+	0.197992i	$0.0634421\pi$
$444$	10.5037	+	32.3271i	0.498485	+	1.53418i
$445$	−4.89192	−	6.73314i	−0.231899	−	0.319182i
$446$	−0.196543	−	0.270518i	−0.00930659	−	0.0128094i
$447$	19.4604	+	59.8928i	0.920444	+	2.83283i
$448$	−3.23095	−	1.04980i	−0.152648	−	0.0495984i
$449$	22.0948	−	30.4109i	1.04272	−	1.43518i	0.147764	−	0.989023i	$-0.452792\pi$
$449$	22.0948	−	30.4109i	1.04272	−	1.43518i	0.894955	−	0.446156i	$-0.147208\pi$
$450$	−14.7081			−0.693346
$451$	15.7977	−	3.25031i	0.743886	−	0.153051i
$452$		−	11.0109i		−	0.517909i
$453$	−17.3118	+	23.8276i	−0.813378	+	1.11952i
$454$	−0.669053	+	2.05913i	−0.0314002	+	0.0966399i
$455$	22.9639	−	7.46144i	1.07657	−	0.349798i
$456$	7.56200	−	9.87474i	0.354123	−	0.462427i
$457$	−19.3659	−	26.6549i	−0.905900	−	1.24686i	−0.968548	−	0.248828i	$-0.919955\pi$
$457$	−19.3659	−	26.6549i	−0.905900	−	1.24686i	0.0626480	−	0.998036i	$-0.480045\pi$
$458$	−3.21628	−	9.89869i	−0.150287	−	0.462535i
$459$	6.41870	−	19.7547i	0.299599	−	0.922072i
$460$	1.22311	+	0.888639i	0.0570276	+	0.0414330i
$461$			21.2923i			0.991681i	0.868414	+	0.495840i	$0.165140\pi$
$461$			21.2923i			0.991681i	−0.868414	+	0.495840i	$0.834860\pi$
$462$	3.56917	−	31.9513i	0.166053	−	1.48651i
$463$	6.94881			0.322939			0.161469	−	0.986878i	$-0.448377\pi$
$463$	6.94881			0.322939			0.161469	+	0.986878i	$0.448377\pi$
$464$	−7.25085	−	5.26805i	−0.336612	−	0.244563i
$465$	3.12450	−	9.61621i	0.144895	−	0.445941i
$466$	18.5640	−	6.03182i	0.859962	−	0.279418i
$467$	4.71910	−	3.42863i	0.218374	−	0.158658i	−0.473220	−	0.880944i	$-0.656909\pi$
$467$	4.71910	−	3.42863i	0.218374	−	0.158658i	0.691594	+	0.722286i	$0.256909\pi$
$468$	20.2131	−	14.6857i	0.934350	−	0.678845i
$469$	3.60670	+	11.1003i	0.166542	+	0.512564i
$470$	1.75171	−	5.39121i	0.0808003	−	0.248678i
$471$	1.59790	−	2.19932i	0.0736273	−	0.101339i
$472$		−	6.96361i		−	0.320526i
$473$	−35.4742	+	20.1735i	−1.63111	+	0.927580i
$474$			21.0232i			0.965626i
$475$	4.15074	−	11.7574i	0.190449	−	0.539467i
$476$	3.56804	−	10.9813i	0.163541	−	0.503327i
$477$	11.8298	−	3.84372i	0.541648	−	0.175992i
$478$	−15.0958	−	20.7776i	−0.690467	−	0.950346i
$479$	2.43783	+	3.35538i	0.111387	+	0.153311i	0.861071	−	0.508485i	$-0.169794\pi$
$479$	2.43783	+	3.35538i	0.111387	+	0.153311i	−0.749684	+	0.661796i	$0.769794\pi$
$480$	3.96939	−	1.28973i	0.181177	−	0.0588680i
$481$	−55.0511	−	17.8872i	−2.51011	−	0.815585i
$482$	−1.79061	−	1.30095i	−0.0815599	−	0.0592567i
$483$	−10.0192			−0.455890
$484$	−10.7289	−	2.42726i	−0.487675	−	0.110330i
$485$			0.335997i			0.0152569i
$486$	7.40081	−	10.1863i	0.335708	−	0.462062i
$487$	28.4962	+	9.25897i	1.29128	+	0.419564i	0.872541	−	0.488541i	$-0.162471\pi$
$487$	28.4962	+	9.25897i	1.29128	+	0.419564i	0.418744	+	0.908104i	$0.362471\pi$
$488$	5.67390	−	1.84356i	0.256845	−	0.0834541i
$489$	−5.24615	−	7.22071i	−0.237239	−	0.326532i
$490$	−5.37376	+	3.90426i	−0.242762	+	0.176377i
$491$	−10.7240	+	3.48444i	−0.483967	+	0.157250i	−0.540831	−	0.841132i	$-0.681890\pi$
$491$	−10.7240	+	3.48444i	−0.483967	+	0.157250i	0.0568637	+	0.998382i	$0.481890\pi$
$492$	−13.1968	−	4.28789i	−0.594956	−	0.193313i
$493$	17.9050	−	24.6441i	0.806399	−	1.10991i
$494$	6.03520	+	20.3024i	0.271537	+	0.913450i
$495$	12.3309	+	21.6832i	0.554231	+	0.974589i
$496$		−	2.42259i		−	0.108778i
$497$	26.1034	+	18.9653i	1.17090	+	0.850708i
$498$	−0.441839	+	1.35984i	−0.0197993	+	0.0609359i
$499$	1.82174	+	5.60674i	0.0815523	+	0.250992i	0.983516	−	0.180819i	$-0.0578748\pi$
$499$	1.82174	+	5.60674i	0.0815523	+	0.250992i	−0.901964	+	0.431811i	$0.857875\pi$
$500$	9.30175	−	6.75811i	0.415987	−	0.302232i
$501$	0.596799	+	0.821423i	0.0266630	+	0.0366985i
$502$	2.41581	+	7.43509i	0.107823	+	0.331844i
$503$	−22.8221	−	7.41535i	−1.01759	−	0.330634i	−0.247715	−	0.968833i	$-0.579680\pi$
$503$	−22.8221	−	7.41535i	−1.01759	−	0.330634i	−0.769872	+	0.638199i	$0.779680\pi$
$504$	−10.2674	+	14.1318i	−0.457344	+	0.629480i
$505$		−	15.2991i		−	0.680802i
$506$	−0.380568	+	3.40685i	−0.0169183	+	0.151453i
$507$			30.2778i			1.34468i
$508$	9.04470	+	6.57136i	0.401294	+	0.291557i
$509$	−5.54070	−	1.80028i	−0.245587	−	0.0797962i	0.183637	−	0.982994i	$-0.441213\pi$
$509$	−5.54070	−	1.80028i	−0.245587	−	0.0797962i	−0.429224	+	0.903198i	$0.641213\pi$
$510$	4.38353	+	13.4911i	0.194106	+	0.597397i
$511$	33.8261	−	24.5761i	1.49638	−	1.08718i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−15.1097	−	21.9393i	−0.667110	−	0.968644i
$514$	−24.5068	−	7.96275i	−1.08095	−	0.351222i
$515$	2.94372	−	4.05168i	0.129716	−	0.178538i
$516$	35.1093			1.54560
$517$	12.5897	−	2.59027i	0.553695	−	0.113920i
$518$	40.4692			1.77811
$519$	5.27732	−	7.26361i	0.231649	−	0.318837i
$520$	−2.19633	+	6.75962i	−0.0963156	+	0.296429i
$521$	31.7530	−	10.3172i	1.39112	−	0.452003i	0.484813	−	0.874618i	$-0.338888\pi$
$521$	31.7530	−	10.3172i	1.39112	−	0.452003i	0.906310	+	0.422614i	$0.138888\pi$
$522$	−37.2825	+	27.0873i	−1.63181	+	1.18558i
$523$	1.84081	−	1.33743i	0.0804932	−	0.0584817i	−0.546811	−	0.837256i	$-0.684158\pi$
$523$	1.84081	−	1.33743i	0.0804932	−	0.0584817i	0.627304	+	0.778774i	$0.284158\pi$
$524$	14.4613	−	4.69875i	0.631743	−	0.205266i
$525$	−8.56854	+	26.3713i	−0.373962	+	1.15094i
$526$	−4.18863	+	5.76515i	−0.182633	+	0.251373i
$527$	8.23387			0.358673
$528$	6.99136	+	6.37815i	0.304260	+	0.277573i
$529$	−21.9317			−0.953552
$530$	−2.07984	+	2.86265i	−0.0903425	+	0.124346i
$531$	−34.0531	−	11.0645i	−1.47778	−	0.480160i
$532$	−8.39922	−	12.1957i	−0.364152	−	0.528749i
$533$	19.1169	−	13.8892i	0.828045	−	0.601610i
$534$	−13.1347	+	9.54294i	−0.568395	+	0.412963i
$535$	5.36994	+	16.5270i	0.232163	+	0.714523i
$536$	−3.26746	−	1.06166i	−0.141133	−	0.0458568i
$537$	38.8824	+	28.2497i	1.67790	+	1.21906i
$538$		−	10.1921i		−	0.439414i
$539$	−13.7188	−	6.21560i	−0.590911	−	0.267725i
$540$		−	8.93919i		−	0.384682i
$541$	2.34288	−	3.22470i	0.100728	−	0.138641i	−0.755678	−	0.654944i	$-0.772692\pi$
$541$	2.34288	−	3.22470i	0.100728	−	0.138641i	0.856406	+	0.516303i	$0.172692\pi$
$542$	−23.6802	−	7.69417i	−1.01715	−	0.330493i
$543$	10.0937	+	31.0653i	0.433164	+	1.33314i
$544$	1.99776	+	2.74968i	0.0856531	+	0.117891i
$545$	−6.78738	+	4.93132i	−0.290739	+	0.211234i
$546$	−14.5554	−	44.7971i	−0.622916	−	1.91714i
$547$	7.16483	−	22.0511i	0.306346	−	0.942836i	−0.672826	−	0.739801i	$-0.734920\pi$
$547$	7.16483	−	22.0511i	0.306346	−	0.942836i	0.979172	−	0.203035i	$-0.0650804\pi$
$548$	−14.7274	−	10.7001i	−0.629125	−	0.457086i
$549$		−	30.6754i		−	1.30920i
$550$	8.64159	+	3.91525i	0.368479	+	0.166947i
$551$	−11.1318	−	37.4473i	−0.474229	−	1.59531i
$552$	1.73352	−	2.38598i	0.0737834	−	0.101554i
$553$	23.8050	+	7.73471i	1.01229	+	0.328913i
$554$	18.7828	−	6.10290i	0.798005	−	0.259287i
$555$	−40.2231	+	29.2238i	−1.70738	+	1.24048i
$556$	7.56693	+	10.4150i	0.320909	+	0.441694i
$557$	0.574875	−	0.186788i	0.0243582	−	0.00791447i	−0.296813	−	0.954936i	$-0.595924\pi$
$557$	0.574875	−	0.186788i	0.0243582	−	0.00791447i	0.321171	+	0.947021i	$0.395924\pi$
$558$	−11.8468	−	3.84927i	−0.501516	−	0.162953i
$559$	−35.1430	+	48.3702i	−1.48639	+	2.04584i
$560$		−	4.96914i		−	0.209985i
$561$	−21.6780	+	23.7621i	−0.915244	+	1.00324i
$562$	−24.3866			−1.02869
$563$	−8.35532	−	6.07049i	−0.352135	−	0.255841i	0.397629	−	0.917546i	$-0.369833\pi$
$563$	−8.35532	−	6.07049i	−0.352135	−	0.255841i	−0.749764	+	0.661705i	$0.769833\pi$
$564$	−10.5169	−	3.41716i	−0.442843	−	0.143888i
$565$	15.3174	−	4.97694i	0.644409	−	0.209381i
$566$	−0.440133	−	0.605791i	−0.0185002	−	0.0254633i
$567$	4.01917	+	5.53192i	0.168789	+	0.232319i
$568$	−9.03280	+	2.93493i	−0.379008	+	0.123147i
$569$	−3.73079	+	11.4822i	−0.156403	+	0.481358i	−0.998300	−	0.0582791i	$-0.981439\pi$
$569$	−3.73079	+	11.4822i	−0.156403	+	0.481358i	0.841898	+	0.539637i	$0.181439\pi$
$570$	17.1550	+	6.05623i	0.718542	+	0.253668i
$571$		−	27.3220i		−	1.14339i	−0.820467	−	0.571694i	$-0.806286\pi$
$571$		−	27.3220i		−	1.14339i	0.820467	−	0.571694i	$-0.193714\pi$
$572$	−15.7853	+	3.24775i	−0.660016	+	0.135795i
$573$		−	6.87352i		−	0.287146i
$574$	−9.71055	+	13.3654i	−0.405310	+	0.557862i
$575$	0.913633	−	2.81187i	0.0381011	−	0.117263i
$576$	−1.58891	−	4.89015i	−0.0662044	−	0.203756i
$577$	−20.2528	+	14.7145i	−0.843135	+	0.612574i	−0.923245	−	0.384212i	$-0.874473\pi$
$577$	−20.2528	+	14.7145i	−0.843135	+	0.612574i	0.0801095	+	0.996786i	$0.474473\pi$
$578$	4.40773	−	3.20240i	0.183337	−	0.133202i
$579$	−39.5802	+	12.8604i	−1.64490	+	0.534459i
$580$	4.05108	−	12.4679i	0.168212	−	0.517703i
$581$	1.37722	+	1.00061i	0.0571366	+	0.0415122i
$582$	0.655449			0.0271692
$583$	−7.97365	−	0.890711i	−0.330235	−	0.0368895i
$584$			12.3075i			0.509288i
$585$	29.5658	+	21.4808i	1.22240	+	0.888122i
$586$	6.73017	−	20.7133i	0.278021	−	0.855660i
$587$	−12.4065	−	38.1833i	−0.512072	−	1.57599i	−0.788548	−	0.614973i	$-0.789167\pi$
$587$	−12.4065	−	38.1833i	−0.512072	−	1.57599i	0.276476	−	0.961021i	$-0.410833\pi$
$588$	7.61627	+	10.4829i	0.314090	+	0.432307i
$589$	6.42032	−	8.38388i	0.264545	−	0.345452i
$590$	9.68720	−	3.14756i	0.398816	−	0.129583i
$591$	−3.90494	+	12.0182i	−0.160628	+	0.494362i
$592$	−7.00195	+	9.63736i	−0.287778	+	0.396093i
$593$		−	20.9668i		−	0.861004i	−0.902590	−	0.430502i	$-0.858337\pi$
$593$		−	20.9668i		−	0.861004i	0.902590	−	0.430502i	$-0.141663\pi$
$594$	17.6194	−	10.0199i	0.722934	−	0.411120i
$595$	16.8890			0.692383
$596$	−12.9726	+	17.8552i	−0.531378	+	0.731379i
$597$	69.9697	+	22.7345i	2.86367	+	0.930462i
$598$	1.55200	+	4.77655i	0.0634658	+	0.195328i
$599$	2.11527	+	2.91142i	0.0864275	+	0.118957i	0.850041	−	0.526716i	$-0.176577\pi$
$599$	2.11527	+	2.91142i	0.0864275	+	0.118957i	−0.763614	+	0.645673i	$0.776577\pi$
$600$	−4.79755	−	6.60326i	−0.195859	−	0.269577i
$601$	−4.62976	−	14.2489i	−0.188852	−	0.581226i	0.811142	−	0.584850i	$-0.198847\pi$
$601$	−4.62976	−	14.2489i	−0.188852	−	0.581226i	−0.999993	+	0.00362367i	$0.998847\pi$
$602$	12.9172	−	39.7550i	0.526465	−	1.62029i
$603$	−10.3834	+	14.2915i	−0.422844	+	0.581995i
$604$	−10.3220			−0.419995
$605$	−1.47286	−	16.0222i	−0.0598801	−	0.651396i
$606$	−29.8449			−1.21237
$607$	24.3188	+	17.6686i	0.987070	+	0.717148i	0.959277	−	0.282466i	$-0.0911523\pi$
$607$	24.3188	+	17.6686i	0.987070	+	0.717148i	0.0277922	+	0.999614i	$0.491152\pi$
$608$	4.35751	+	0.109891i	0.176721	+	0.00445668i
$609$	26.8471	+	82.6270i	1.08790	+	3.34821i
$610$	5.12922	+	7.05976i	0.207676	+	0.285841i
$611$	15.2349	−	11.0688i	0.616337	−	0.447795i
$612$	16.6206	−	5.40035i	0.671847	−	0.218296i
$613$	6.64971	+	2.16062i	0.268579	+	0.0872667i	0.440211	−	0.897895i	$-0.354904\pi$
$613$	6.64971	+	2.16062i	0.268579	+	0.0872667i	−0.171631	+	0.985161i	$0.554904\pi$
$614$	−5.53623	−	4.02230i	−0.223424	−	0.162327i
$615$		−	20.2964i		−	0.818429i
$616$	9.79433	−	5.56986i	0.394625	−	0.224416i
$617$	46.8710			1.88696			0.943478	−	0.331436i	$-0.107533\pi$
$617$	46.8710			1.88696			0.943478	+	0.331436i	$0.107533\pi$
$618$	−7.90384	−	5.74247i	−0.317939	−	0.230996i
$619$	−3.21718	+	9.90147i	−0.129310	+	0.397974i	−0.994662	−	0.103191i	$-0.967095\pi$
$619$	−3.21718	+	9.90147i	−0.129310	+	0.397974i	0.865352	+	0.501164i	$0.167095\pi$
$620$	3.37011	−	1.09501i	0.135347	−	0.0439768i
$621$	−3.71286	−	5.11032i	−0.148992	−	0.205070i
$622$	−4.84600	+	3.52082i	−0.194307	+	0.141172i
$623$	5.97323	+	18.3837i	0.239312	+	0.736528i
$624$	13.1864	+	4.28451i	0.527878	+	0.171518i
$625$	2.03481	+	1.47837i	0.0813923	+	0.0591350i
$626$	−9.16709			−0.366391
$627$	7.29178	+	40.6013i	0.291206	+	1.62146i
$628$	0.952731			0.0380181
$629$	−32.7553	−	23.7981i	−1.30604	−	0.948894i
$630$	−24.2998	−	7.89550i	−0.968129	−	0.314564i
$631$	−11.9717	−	36.8452i	−0.476587	−	1.46678i	−0.843805	−	0.536649i	$-0.819690\pi$
$631$	−11.9717	−	36.8452i	−0.476587	−	1.46678i	0.367219	−	0.930135i	$-0.380310\pi$
$632$	−5.96067	+	4.33068i	−0.237103	+	0.172265i
$633$	−30.0849	−	41.4083i	−1.19577	−	1.64583i
$634$	−0.537305	+	0.174581i	−0.0213391	+	0.00693350i
$635$	−5.05331	+	15.5525i	−0.200535	+	0.617182i
$636$	5.58434	+	4.05726i	0.221434	+	0.160881i
$637$	−22.0659			−0.874283
$638$	29.1155	−	5.99038i	1.15269	−	0.237162i
$639$			48.8351i			1.93189i
$640$	1.18335	+	0.859758i	0.0467762	+	0.0339849i
$641$	2.54825	+	0.827975i	0.100650	+	0.0327031i	0.358909	−	0.933373i	$-0.383149\pi$
$641$	2.54825	+	0.827975i	0.100650	+	0.0327031i	−0.258259	+	0.966076i	$0.583149\pi$
$642$	32.2401	−	10.4754i	1.27242	−	0.413433i
$643$	−0.428930	+	0.311636i	−0.0169154	+	0.0122897i	−0.596211	−	0.802828i	$-0.703328\pi$
$643$	−0.428930	+	0.311636i	−0.0169154	+	0.0122897i	0.579295	+	0.815118i	$0.303328\pi$
$644$	−2.06392	−	2.84074i	−0.0813297	−	0.111941i
$645$	15.8694	+	48.8411i	0.624859	+	1.92312i
$646$	−0.373497	+	14.8103i	−0.0146950	+	0.582702i
$647$	29.4121	+	21.3692i	1.15631	+	0.840109i	0.989307	−	0.145847i	$-0.0465908\pi$
$647$	29.4121	+	21.3692i	1.15631	+	0.840109i	0.167004	+	0.985956i	$0.446591\pi$
$648$	−2.01277			−0.0790691
$649$	17.0622	+	15.5657i	0.669751	+	0.611007i
$650$	13.8995			0.545183
$651$	−13.8033	+	18.9986i	−0.540994	+	0.744615i
$652$	0.966594	−	2.97487i	0.0378547	−	0.116505i
$653$	12.9484	+	39.8512i	0.506712	+	1.55950i	0.797874	+	0.602825i	$0.205958\pi$
$653$	12.9484	+	39.8512i	0.506712	+	1.55950i	−0.291162	+	0.956674i	$0.594042\pi$
$654$	9.61980	+	13.2405i	0.376164	+	0.517745i
$655$	13.0730	+	17.9935i	0.510805	+	0.703063i
$656$	−1.50274	−	4.62495i	−0.0586721	−	0.180574i
$657$	60.1855	+	19.5555i	2.34806	+	0.762931i
$658$	−7.73865	+	10.6513i	−0.301684	+	0.415232i
$659$	24.3984			0.950428			0.475214	−	0.879870i	$-0.342371\pi$
$659$	24.3984			0.950428			0.475214	+	0.879870i	$0.342371\pi$
$660$	−5.71265	+	12.6087i	−0.222365	+	0.490794i
$661$			26.4297i			1.02800i	0.857791	+	0.513999i	$0.171836\pi$
$661$			26.4297i			1.02800i	−0.857791	+	0.513999i	$0.828164\pi$
$662$	2.58590	−	3.55919i	0.100504	−	0.138332i
$663$	−14.5621	+	44.8177i	−0.565547	+	1.74057i
$664$	−0.476571	+	0.154847i	−0.0184945	+	0.00600924i
$665$	13.1691	−	17.1968i	0.510678	−	0.666862i
$666$	36.0027	+	49.5535i	1.39508	+	1.92016i
$667$	−2.86261	−	8.81022i	−0.110841	−	0.341133i
$668$	−0.109959	+	0.338419i	−0.00425445	+	0.0130938i
$669$	−0.771894	−	0.560813i	−0.0298431	−	0.0216823i
$670$		−	5.02529i		−	0.194144i
$671$	−8.16573	+	18.0231i	−0.315234	+	0.695773i
$672$	−9.69359			−0.373938
$673$	30.8905	+	22.4432i	1.19074	+	0.865123i	0.993342	−	0.115201i	$-0.0367511\pi$
$673$	30.8905	+	22.4432i	1.19074	+	0.865123i	0.197397	+	0.980324i	$0.436751\pi$
$674$	−0.925214	+	2.84752i	−0.0356379	+	0.109682i
$675$	−16.6260	+	5.40211i	−0.639935	+	0.207927i
$676$	−8.58462	+	6.23709i	−0.330178	+	0.239888i
$677$	19.2570	−	13.9910i	0.740105	−	0.537718i	−0.152639	−	0.988282i	$-0.548777\pi$
$677$	19.2570	−	13.9910i	0.740105	−	0.537718i	0.892744	+	0.450564i	$0.148777\pi$
$678$	−9.70879	−	29.8806i	−0.372864	−	1.14756i
$679$	0.241149	−	0.742179i	0.00925444	−	0.0284822i
$680$	−2.92213	+	4.02197i	−0.112059	+	0.154235i
$681$			6.17787i			0.236736i
$682$	5.93583	+	5.41520i	0.227295	+	0.207359i
$683$		−	24.2087i		−	0.926320i	−0.886275	−	0.463160i	$-0.846715\pi$
$683$		−	24.2087i		−	0.926320i	0.886275	−	0.463160i	$-0.153285\pi$
$684$	7.46107	−	21.1343i	0.285281	−	0.808090i
$685$	8.22828	−	25.3240i	0.314386	−	0.967582i
$686$	−7.94452	+	2.58133i	−0.303323	+	0.0985557i
$687$	−17.4562	−	24.0264i	−0.665997	−	0.916666i
$688$	7.23236	+	9.95450i	0.275731	+	0.379512i
$689$	−11.1794	+	3.63241i	−0.425902	+	0.138384i
$690$	4.10273	+	1.33306i	0.156188	+	0.0507487i
$691$	22.9839	+	16.6988i	0.874349	+	0.635252i	0.931750	−	0.363099i	$-0.118281\pi$
$691$	22.9839	+	16.6988i	0.874349	+	0.635252i	−0.0574011	+	0.998351i	$0.518281\pi$
$692$	3.14655			0.119614
$693$	−11.6752	−	56.7458i	−0.443503	−	2.15559i
$694$			27.2402i			1.03402i
$695$	−11.0682	+	15.2341i	−0.419841	+	0.577861i
$696$	−24.3219	−	7.90267i	−0.921920	−	0.299550i
$697$	15.7192	−	5.10748i	0.595408	−	0.193460i
$698$	14.5503	+	20.0268i	0.550738	+	0.758026i
$699$	45.0592	−	32.7374i	1.70430	−	1.23824i
$700$	−9.24210	+	3.00294i	−0.349318	+	0.113500i
$701$	−6.41227	−	2.08347i	−0.242188	−	0.0786917i	0.185408	−	0.982662i	$-0.440639\pi$
$701$	−6.41227	−	2.08347i	−0.242188	−	0.0786917i	−0.427596	+	0.903970i	$0.640639\pi$
$702$	17.4549	−	24.0247i	0.658795	−	0.906753i
$703$	−49.7725	+	14.7956i	−1.87721	+	0.558028i
$704$	−0.368199	+	3.29612i	−0.0138770	+	0.124227i
$705$		−	16.1748i		−	0.609180i
$706$	14.5378	+	10.5624i	0.547139	+	0.397520i
$707$	−10.9803	+	33.7940i	−0.412958	+	1.27095i
$708$	−6.14013	−	18.8974i	−0.230760	−	0.710207i
$709$	−7.21727	+	5.24366i	−0.271050	+	0.196930i	−0.715004	−	0.699120i	$-0.753575\pi$
$709$	−7.21727	+	5.24366i	−0.271050	+	0.196930i	0.443954	+	0.896050i	$0.353575\pi$
$710$	−8.16567	−	11.2391i	−0.306452	−	0.421795i
$711$	11.7067	+	36.0296i	0.439037	+	1.35122i
$712$	−5.41140	−	1.75827i	−0.202801	−	0.0658939i
$713$	1.47180	−	2.02576i	0.0551192	−	0.0758651i
$714$		−	32.9464i		−	1.23299i
$715$	−11.6530	−	20.4912i	−0.435796	−	0.766327i
$716$			16.8436i			0.629475i
$717$	−59.2865	−	43.0742i	−2.21410	−	1.60863i
$718$	−1.03191	−	0.335289i	−0.0385106	−	0.0125129i
$719$	−10.9488	−	33.6969i	−0.408321	−	1.25668i	−0.918090	−	0.396371i	$-0.870269\pi$
$719$	−10.9488	−	33.6969i	−0.408321	−	1.25668i	0.509770	−	0.860311i	$-0.329731\pi$
$720$	6.08458	−	4.42071i	0.226759	−	0.164750i
$721$	−9.41026	+	6.83695i	−0.350456	+	0.254621i
$722$	14.7889	+	11.9285i	0.550384	+	0.443934i
$723$	−6.00633	−	1.95158i	−0.223378	−	0.0725799i
$724$	−6.72865	+	9.26119i	−0.250068	+	0.344189i
$725$	−25.6372			−0.952144
$726$	−31.2555	+	2.87318i	−1.16000	+	0.106634i
$727$	28.3553			1.05164			0.525820	−	0.850596i	$-0.323759\pi$
$727$	28.3553			1.05164			0.525820	+	0.850596i	$0.323759\pi$
$728$	9.70290	−	13.3549i	0.359613	−	0.494965i
$729$	12.9680	−	39.9114i	0.480296	−	1.47820i
$730$	−17.1212	+	5.56301i	−0.633683	+	0.205896i
$731$	−33.8332	+	24.5813i	−1.25137	+	0.909171i
$732$	13.7719	−	10.0059i	0.509023	−	0.369827i
$733$	34.8807	−	11.3334i	1.28835	−	0.418610i	0.416836	−	0.908982i	$-0.363139\pi$
$733$	34.8807	−	11.3334i	1.28835	−	0.418610i	0.871513	+	0.490372i	$0.163139\pi$
$734$	−0.276229	+	0.850145i	−0.0101958	+	0.0313794i
$735$	−11.1404	+	15.3334i	−0.410919	+	0.565581i
$736$	1.03359			0.0380987
$737$	9.90502	−	5.63280i	0.364856	−	0.207487i
$738$	−25.0044			−0.920426
$739$	−20.9771	+	28.8725i	−0.771656	+	1.06209i	0.224498	+	0.974474i	$0.427926\pi$
$739$	−20.9771	+	28.8725i	−0.771656	+	1.06209i	−0.996154	+	0.0876186i	$0.972074\pi$
$740$	−16.5716	−	5.38443i	−0.609184	−	0.197936i
$741$	34.2795	+	49.7738i	1.25929	+	1.82849i
$742$	6.64868	−	4.83055i	0.244081	−	0.177335i
$743$	−4.75573	+	3.45524i	−0.174471	+	0.126760i	−0.671594	−	0.740920i	$-0.734390\pi$
$743$	−4.75573	+	3.45524i	−0.174471	+	0.126760i	0.497123	+	0.867680i	$0.334390\pi$
$744$	−2.13611	−	6.57426i	−0.0783135	−	0.241024i
$745$	−30.7024	−	9.97580i	−1.12485	−	0.365485i
$746$	−22.1642	−	16.1032i	−0.811488	−	0.589581i
$747$			2.57654i			0.0942707i
$748$	−11.2028	−	1.25143i	−0.409616	−	0.0457568i
$749$		−	40.3602i		−	1.47473i
$750$	19.2835	−	26.5415i	0.704134	−	0.969157i
$751$	16.9885	+	5.51991i	0.619920	+	0.201424i	0.602105	−	0.798417i	$-0.294329\pi$
$751$	16.9885	+	5.51991i	0.619920	+	0.201424i	0.0178152	+	0.999841i	$0.494329\pi$
$752$	−1.19758	−	3.68577i	−0.0436713	−	0.134406i
$753$	13.1117	+	18.0467i	0.477817	+	0.657659i
$754$	35.2328	−	25.5982i	1.28310	−	0.932230i
$755$	−4.66554	−	14.3591i	−0.169796	−	0.522580i
$756$	−6.41575	+	19.7456i	−0.233339	+	0.718142i
$757$	−13.9642	−	10.1456i	−0.507538	−	0.368748i	0.304351	−	0.952560i	$-0.401560\pi$
$757$	−13.9642	−	10.1456i	−0.507538	−	0.368748i	−0.811889	+	0.583812i	$0.801560\pi$
$758$			22.6346i			0.822126i
$759$	1.97121	+	9.58083i	0.0715504	+	0.347762i
$760$	1.81673	+	6.11148i	0.0658997	+	0.221687i
$761$	−1.99743	+	2.74923i	−0.0724069	+	0.0996595i	−0.843684	−	0.536839i	$-0.819618\pi$
$761$	−1.99743	+	2.74923i	−0.0724069	+	0.0996595i	0.771278	+	0.636499i	$0.219618\pi$
$762$	30.3391	+	9.85779i	1.09907	+	0.357110i
$763$	18.5318	−	6.02134i	0.670896	−	0.217987i
$764$	1.94884	−	1.41592i	0.0705066	−	0.0512261i
$765$	15.0250	+	20.6802i	0.543231	+	0.747694i
$766$	14.6440	−	4.75813i	0.529110	−	0.171918i
$767$	32.1810	+	10.4562i	1.16199	+	0.377553i
$768$	1.67718	−	2.30844i	0.0605199	−	0.0832986i
$769$		−	0.578614i		−	0.0208653i	−0.999946	−	0.0104327i	$-0.996679\pi$
$769$		−	0.578614i		−	0.0208653i	0.999946	−	0.0104327i	$-0.00332088\pi$
$770$	12.1754	+	11.1075i	0.438770	+	0.400286i
$771$	−73.5261			−2.64798
$772$	−11.7996	−	8.57294i	−0.424678	−	0.308547i
$773$	18.9170	+	6.14651i	0.680398	+	0.221075i	0.628770	−	0.777592i	$-0.283559\pi$
$773$	18.9170	+	6.14651i	0.680398	+	0.221075i	0.0516284	+	0.998666i	$0.483559\pi$
$774$	60.1705	−	19.5506i	2.16279	−	0.702731i
$775$	−4.07323	−	5.60632i	−0.146315	−	0.201385i
$776$	0.135020	+	0.185839i	0.00484693	+	0.00667122i
$777$	109.822	−	35.6835i	3.93986	−	1.28014i
$778$	4.21638	−	12.9767i	0.151165	−	0.465237i
$779$	7.05644	−	19.9882i	0.252823	−	0.716150i
$780$			20.2804i			0.726155i
$781$	12.9998	−	28.6926i	0.465169	−	1.02670i
$782$			3.51296i			0.125623i
$783$	−32.1952	+	44.3129i	−1.15056	+	1.58361i
$784$	−1.40328	+	4.31886i	−0.0501173	+	0.154245i
$785$	0.430635	+	1.32536i	0.0153700	+	0.0473041i
$786$	35.1009	−	25.5023i	1.25201	−	0.909636i
$787$	4.80790	−	3.49314i	0.171383	−	0.124517i	−0.498787	−	0.866725i	$-0.666221\pi$
$787$	4.80790	−	3.49314i	0.171383	−	0.124517i	0.670170	+	0.742207i	$0.266221\pi$
$788$	−4.21190	+	1.36853i	−0.150043	+	0.0487518i
$789$	−6.28342	+	19.3384i	−0.223696	+	0.688464i
$790$	−8.71871	−	6.33452i	−0.310198	−	0.225372i
$791$	−37.4064			−1.33002
$792$	15.5335	+	7.03778i	0.551959	+	0.250077i
$793$			28.9890i			1.02943i
$794$	−2.65830	−	1.93136i	−0.0943394	−	0.0685416i
$795$	−3.12000	+	9.60236i	−0.110655	+	0.340561i
$796$	7.96756	+	24.5216i	0.282403	+	0.869146i
$797$	−18.3940	−	25.3171i	−0.651548	−	0.896778i	0.347617	−	0.937636i	$-0.386991\pi$
$797$	−18.3940	−	25.3171i	−0.651548	−	0.896778i	−0.999165	+	0.0408582i	$0.986991\pi$
$798$	−33.5467	−	25.6898i	−1.18754	−	0.909409i
$799$	12.5272	−	4.07032i	0.443179	−	0.143998i
$800$	0.883940	−	2.72049i	0.0312520	−	0.0961837i
$801$	−17.1964	+	23.6688i	−0.607605	+	0.836296i
$802$		−	0.795322i		−	0.0280838i
$803$	−30.1558	−	27.5109i	−1.06418	−	0.970837i
$804$	−9.80313			−0.345730
$805$	3.01890	−	4.15516i	0.106402	−	0.146450i
$806$	11.1955	+	3.63765i	0.394346	+	0.128131i
$807$	−8.98686	−	27.6587i	−0.316353	−	0.973633i
$808$	−6.14792	−	8.46188i	−0.216283	−	0.297688i
$809$	−2.70827	−	3.72762i	−0.0952178	−	0.131056i	0.758750	−	0.651382i	$-0.225810\pi$
$809$	−2.70827	−	3.72762i	−0.0952178	−	0.131056i	−0.853968	+	0.520326i	$0.825810\pi$
$810$	−0.909774	−	2.80000i	−0.0319662	−	0.0983819i
$811$	−15.5136	+	47.7460i	−0.544757	+	1.67659i	0.176811	+	0.984245i	$0.443422\pi$
$811$	−15.5136	+	47.7460i	−0.544757	+	1.67659i	−0.721568	+	0.692344i	$0.756578\pi$
$812$	−17.8967	+	24.6327i	−0.628052	+	0.864440i
$813$	−71.0460			−2.49169
$814$	−7.96203	−	38.6985i	−0.279069	−	1.35638i
$815$	4.57529			0.160266
$816$	7.84588	+	5.70037i	0.274661	+	0.199553i
$817$	−1.35215	+	53.6167i	−0.0473057	+	1.87581i
$818$	−7.77644	−	23.9334i	−0.271897	−	0.836812i
$819$	−49.8904	−	68.6683i	−1.74331	−	2.39946i
$820$	5.75461	−	4.18097i	0.200960	−	0.146006i
$821$	39.2570	−	12.7554i	1.37008	−	0.445166i	0.470684	−	0.882302i	$-0.344007\pi$
$821$	39.2570	−	12.7554i	1.37008	−	0.445166i	0.899396	+	0.437136i	$0.144007\pi$
$822$	−49.4010	−	16.0514i	−1.72306	−	0.559856i
$823$	27.1714	+	19.7412i	0.947136	+	0.688135i	0.950128	−	0.311861i	$-0.100952\pi$
$823$	27.1714	+	19.7412i	0.947136	+	0.688135i	−0.00299152	+	0.999996i	$0.500952\pi$
$824$		−	3.42389i		−	0.119277i
$825$	26.9032	+	3.00527i	0.936650	+	0.104630i
$826$	−23.6569			−0.823130
$827$	−14.9013	−	10.8264i	−0.518169	−	0.376472i	0.297745	−	0.954646i	$-0.403766\pi$
$827$	−14.9013	−	10.8264i	−0.518169	−	0.376472i	−0.815914	+	0.578174i	$0.803766\pi$
$828$	1.64228	−	5.05442i	0.0570732	−	0.175653i
$829$	−16.1449	+	5.24581i	−0.560737	+	0.182194i	−0.575653	−	0.817694i	$-0.695252\pi$
$829$	−16.1449	+	5.24581i	−0.560737	+	0.182194i	0.0149159	+	0.999889i	$0.495252\pi$
$830$	−0.430821	−	0.592974i	−0.0149540	−	0.0205824i
$831$	45.5903	−	33.1233i	1.58151	−	1.14903i
$832$	1.50155	+	4.62131i	0.0520570	+	0.160215i
$833$	−14.6789	−	4.76946i	−0.508593	−	0.165252i
$834$	29.7180	+	21.5914i	1.02905	+	0.747648i
$835$	−0.520483			−0.0180120
$836$	−10.0096	+	10.4311i	−0.346188	+	0.360768i
$837$	−14.8054			−0.511751
$838$	−4.42370	−	3.21401i	−0.152814	−	0.111026i
$839$	−6.31265	−	2.05110i	−0.217937	−	0.0708120i	0.198014	−	0.980199i	$-0.436551\pi$
$839$	−6.31265	−	2.05110i	−0.217937	−	0.0708120i	−0.415950	+	0.909387i	$0.636551\pi$
$840$	−4.38151	−	13.4849i	−0.151177	−	0.465274i
$841$	−41.5245	+	30.1693i	−1.43188	+	1.04032i
$842$	−19.5672	−	26.9319i	−0.674329	−	0.928134i
$843$	−66.1786	+	21.5027i	−2.27931	+	0.740594i
$844$	5.54309	−	17.0599i	0.190801	−	0.587225i
$845$	−12.5568	−	9.12304i	−0.431967	−	0.313842i
$846$	−19.9268			−0.685099
$847$	−8.24594	+	36.4483i	−0.283334	+	1.25238i
$848$			2.41910i			0.0830723i
$849$	−1.72855	−	1.25587i	−0.0593238	−	0.0431013i
$850$	9.24635	+	3.00432i	0.317147	+	0.103047i
$851$	−11.7100	+	3.80480i	−0.401413	+	0.130427i
$852$	−21.9247	+	15.9292i	−0.751129	+	0.545727i
$853$	−25.1915	−	34.6732i	−0.862541	−	1.18719i	−0.980958	−	0.194222i	$-0.937782\pi$
$853$	−25.1915	−	34.6732i	−0.862541	−	1.18719i	0.118416	−	0.992964i	$-0.462218\pi$
$854$	−6.26298	−	19.2755i	−0.214315	−	0.659594i
$855$	32.7727	+	0.826488i	1.12080	+	0.0282653i
$856$	9.61141	+	6.98310i	0.328511	+	0.238677i
$857$	−17.8996			−0.611437			−0.305719	−	0.952122i	$-0.598897\pi$
$857$	−17.8996			−0.611437			−0.305719	+	0.952122i	$0.598897\pi$
$858$	−39.9733	+	22.7321i	−1.36467	+	0.776061i
$859$	28.7117			0.979630			0.489815	−	0.871826i	$-0.337064\pi$
$859$	28.7117			0.979630			0.489815	+	0.871826i	$0.337064\pi$
$860$	−10.5788	+	14.5605i	−0.360735	+	0.496509i
$861$	−14.5669	+	44.8324i	−0.496439	+	1.52788i
$862$	−1.85862	−	5.72025i	−0.0633050	−	0.194833i
$863$	−9.85503	−	13.5643i	−0.335469	−	0.461733i	0.607642	−	0.794211i	$-0.292115\pi$
$863$	−9.85503	−	13.5643i	−0.335469	−	0.461733i	−0.943111	+	0.332477i	$0.892115\pi$
$864$	−3.59219	−	4.94423i	−0.122209	−	0.168206i
$865$	1.42224	+	4.37722i	0.0483577	+	0.148830i
$866$	−31.1077	−	10.1075i	−1.05708	−	0.343467i
$867$	9.13770	−	12.5770i	0.310332	−	0.427136i
$868$	−8.23008			−0.279347
$869$	2.71282	−	24.2852i	0.0920260	−	0.823818i
$870$		−	37.4067i		−	1.26820i
$871$	9.81255	−	13.5058i	0.332485	−	0.457627i
$872$	−1.77243	+	5.45498i	−0.0600221	+	0.184729i
$873$	1.12331	−	0.364987i	0.0380184	−	0.0123529i
$874$	3.57696	+	2.73921i	0.120993	+	0.0926552i
$875$	−22.9588	−	31.6001i	−0.776150	−	1.06828i
$876$	10.8521	+	33.3992i	0.366658	+	1.12846i
$877$	9.87747	−	30.3997i	0.333539	−	1.02653i	−0.633899	−	0.773416i	$-0.718546\pi$
$877$	9.87747	−	30.3997i	0.333539	−	1.02653i	0.967437	−	0.253110i	$-0.0814535\pi$
$878$	17.5868	+	12.7775i	0.593524	+	0.431221i
$879$		−	62.1447i		−	2.09609i
$880$	−4.75172	+	0.977644i	−0.160180	+	0.0329564i
$881$	6.32588			0.213124			0.106562	−	0.994306i	$-0.466016\pi$
$881$	6.32588			0.213124			0.106562	+	0.994306i	$0.466016\pi$
$882$	18.8902	+	13.7245i	0.636066	+	0.462129i
$883$	15.1814	−	46.7237i	0.510896	−	1.57238i	−0.279731	−	0.960078i	$-0.590245\pi$
$883$	15.1814	−	46.7237i	0.510896	−	1.57238i	0.790627	−	0.612298i	$-0.209755\pi$
$884$	−15.7068	+	5.10346i	−0.528278	+	0.171648i
$885$	23.5131	−	17.0833i	0.790384	−	0.574248i
$886$	3.90270	−	2.83548i	0.131114	−	0.0952597i
$887$	−13.2329	−	40.7268i	−0.444318	−	1.36747i	−0.883230	−	0.468941i	$-0.844636\pi$
$887$	−13.2329	−	40.7268i	−0.444318	−	1.36747i	0.438911	−	0.898530i	$-0.355364\pi$
$888$	−10.5037	+	32.3271i	−0.352482	+	1.08483i
$889$	22.3244	−	30.7269i	0.748735	−	1.03055i
$890$		−	8.32262i		−	0.278975i
$891$	4.49913	−	4.93168i	0.150726	−	0.165218i
$892$		−	0.334379i		−	0.0111958i
$893$	5.62351	−	15.9292i	0.188184	−	0.533051i
$894$	−19.4604	+	59.8928i	−0.650852	+	2.00312i
$895$	−23.4314	+	7.61333i	−0.783226	+	0.254485i
$896$	−1.99684	−	2.74841i	−0.0667097	−	0.0918180i
$897$	8.42340	+	11.5938i	0.281249	+	0.387106i
$898$	35.7502	−	11.6159i	1.19300	−	0.387629i
$899$	−20.6499	−	6.70955i	−0.688712	−	0.223776i
$900$	−11.8991	−	8.64520i	−0.396636	−	0.288173i
$901$	−8.22201			−0.273915
$902$	14.6911	+	6.65611i	0.489160	+	0.221624i
$903$		−	119.274i		−	3.96919i
$904$	6.47204	−	8.90800i	0.215257	−	0.296276i
$905$	−15.9248	−	5.17427i	−0.529357	−	0.171998i
$906$	−28.0110	+	9.10134i	−0.930605	+	0.302372i
$907$	11.1980	+	15.4127i	0.371823	+	0.511770i	0.953395	−	0.301725i	$-0.0975623\pi$
$907$	11.1980	+	15.4127i	0.371823	+	0.511770i	−0.581572	+	0.813495i	$0.697562\pi$
$908$	−1.75160	+	1.27261i	−0.0581290	+	0.0422332i
$909$	−51.1483	+	16.6191i	−1.69648	+	0.551221i
$910$	22.9639	+	7.46144i	0.761247	+	0.247344i
$911$	−7.57994	+	10.4329i	−0.251135	+	0.345657i	−0.915908	−	0.401388i	$-0.868528\pi$
$911$	−7.57994	+	10.4329i	−0.251135	+	0.345657i	0.664774	+	0.747045i	$0.268528\pi$
$912$	11.9220	−	3.54400i	0.394777	−	0.117354i
$913$	0.685868	−	1.51382i	0.0226989	−	0.0501002i
$914$		−	32.9473i		−	1.08980i
$915$	20.1442	+	14.6356i	0.665947	+	0.483839i
$916$	3.21628	−	9.89869i	0.106269	−	0.327062i
$917$	−15.9627	−	49.1281i	−0.527135	−	1.62235i
$918$	16.8044	−	12.2091i	0.554627	−	0.402960i
$919$	20.5723	+	28.3154i	0.678619	+	0.934038i	0.999916	−	0.0129399i	$-0.00411902\pi$
$919$	20.5723	+	28.3154i	0.678619	+	0.934038i	−0.321298	+	0.946978i	$0.604119\pi$
$920$	0.467185	+	1.43785i	0.0154026	+	0.0474044i
$921$	−18.5705	−	6.03391i	−0.611918	−	0.198824i
$922$	−12.5153	+	17.2258i	−0.412169	+	0.567302i
$923$		−	46.1503i		−	1.51906i
$924$	21.6680	−	23.7512i	0.712825	−	0.781357i
$925$			34.0754i			1.12039i
$926$	5.62170	+	4.08441i	0.184741	+	0.134222i
$927$	−16.7433	−	5.44024i	−0.549924	−	0.178681i
$928$	−2.76958	−	8.52388i	−0.0909158	−	0.279810i
$929$	18.8714	−	13.7109i	0.619151	−	0.449840i	−0.233474	−	0.972363i	$-0.575009\pi$
$929$	18.8714	−	13.7109i	0.619151	−	0.449840i	0.852625	+	0.522524i	$0.175009\pi$
$930$	8.18004	−	5.94315i	0.268234	−	0.194883i
$931$	−16.3021	+	11.2274i	−0.534281	+	0.367962i
$932$	18.5640	+	6.03182i	0.608085	+	0.197579i
$933$	−10.0463	+	13.8275i	−0.328900	+	0.452692i
$934$	5.83313			0.190866
$935$	−3.32280	−	16.1501i	−0.108667	−	0.528164i
$936$	24.9847			0.816652
$937$	−19.4557	+	26.7785i	−0.635591	+	0.874816i	−0.998371	−	0.0570588i	$-0.981828\pi$
$937$	−19.4557	+	26.7785i	−0.635591	+	0.874816i	0.362780	+	0.931875i	$0.381828\pi$
$938$	−3.60670	+	11.1003i	−0.117763	+	0.362437i
$939$	−24.8770	+	8.08303i	−0.811831	+	0.263780i
$940$	4.58604	−	3.33195i	0.149580	−	0.108676i
$941$	−44.1558	+	32.0810i	−1.43944	+	1.04581i	−0.451277	+	0.892384i	$0.649031\pi$
$941$	−44.1558	+	32.0810i	−1.43944	+	1.04581i	−0.988160	+	0.153428i	$0.950969\pi$
$942$	2.58545	−	0.840065i	0.0842387	−	0.0273708i
$943$	1.55322	−	4.78032i	0.0505798	−	0.155668i
$944$	4.09311	−	5.63368i	0.133219	−	0.183361i
$945$	−30.3684			−0.987885
$946$	−40.5569	−	4.53048i	−1.31862	−	0.147299i
$947$	38.3516			1.24626			0.623131	−	0.782118i	$-0.285861\pi$
$947$	38.3516			1.24626			0.623131	+	0.782118i	$0.285861\pi$
$948$	−12.3571	+	17.0081i	−0.401340	+	0.552397i
$949$	−56.8768	−	18.4804i	−1.84630	−	0.599899i
$950$	10.2689	−	7.07221i	0.333166	−	0.229453i
$951$	−1.30417	+	0.947532i	−0.0422905	+	0.0307258i
$952$	9.34126	−	6.78682i	0.302752	−	0.219962i
$953$	10.8042	+	33.2520i	0.349983	+	1.07714i	0.958862	+	0.283873i	$0.0916196\pi$
$953$	10.8042	+	33.2520i	0.349983	+	1.07714i	−0.608879	+	0.793263i	$0.708380\pi$
$954$	11.8298	+	3.84372i	0.383003	+	0.124445i
$955$	2.85058	+	2.07107i	0.0922428	+	0.0670183i
$956$		−	25.6825i		−	0.830633i
$957$	73.7297	−	41.9287i	2.38334	−	1.35536i
$958$			4.14748i			0.133999i
$959$	−36.3506	+	50.0324i	−1.17382	+	1.61563i
$960$	3.96939	+	1.28973i	0.128112	+	0.0416260i
$961$	7.76592	+	23.9011i	0.250514	+	0.771002i
$962$	−34.0234	−	46.8292i	−1.09696	−	1.50983i
$963$	49.4200	−	35.9058i	1.59254	−	1.15705i
$964$	−0.683951	−	2.10498i	−0.0220286	−	0.0677970i
$965$	6.59251	−	20.2897i	0.212220	−	0.653147i
$966$	−8.10571	−	5.88915i	−0.260797	−	0.189480i
$967$			27.9848i			0.899931i	0.893046	+	0.449966i	$0.148564\pi$
$967$			27.9848i			0.899931i	−0.893046	+	0.449966i	$0.851436\pi$
$968$	−7.25312	−	8.26996i	−0.233124	−	0.265807i
$969$	12.0453	+	40.5204i	0.386951	+	1.30170i
$970$	−0.197494	+	0.271828i	−0.00634116	+	0.00872786i
$971$	−7.82165	−	2.54141i	−0.251009	−	0.0815576i	0.180810	−	0.983518i	$-0.442128\pi$
$971$	−7.82165	−	2.54141i	−0.251009	−	0.0815576i	−0.431819	+	0.901960i	$0.642128\pi$
$972$	11.9748	−	3.89084i	0.384091	−	0.124799i
$973$	35.3820	−	25.7065i	1.13430	−	0.824114i
$974$	17.6116	+	24.2403i	0.564312	+	0.776709i
$975$	37.7195	−	12.2558i	1.20799	−	0.392500i
$976$	5.67390	+	1.84356i	0.181617	+	0.0590109i
$977$	33.4189	−	45.9971i	1.06916	−	1.47158i	0.198245	−	0.980153i	$-0.436476\pi$
$977$	33.4189	−	45.9971i	1.06916	−	1.47158i	0.870920	−	0.491426i	$-0.163524\pi$
$978$		−	8.92529i		−	0.285399i
$979$	16.4042	−	9.32874i	0.524279	−	0.298148i
$980$	−6.64233			−0.212181
$981$	23.8595	+	17.3349i	0.761774	+	0.553461i
$982$	−10.7240	−	3.48444i	−0.342216	−	0.111193i
$983$	34.6778	−	11.2675i	1.10605	−	0.359378i	0.301623	−	0.953427i	$-0.402472\pi$
$983$	34.6778	−	11.2675i	1.10605	−	0.359378i	0.804428	+	0.594050i	$0.202472\pi$
$984$	−8.15605	−	11.2258i	−0.260006	−	0.357867i
$985$	−3.80757	−	5.24067i	−0.121319	−	0.166982i
$986$	28.9709	−	9.41320i	0.922620	−	0.299777i
$987$	−11.6089	+	35.7284i	−0.369514	+	1.13725i
$988$	−7.05089	+	19.9724i	−0.224319	+	0.635407i
$989$			12.7178i			0.404401i
$990$	−2.76921	+	24.7900i	−0.0880113	+	0.787878i
$991$			46.1378i			1.46562i	0.680436	+	0.732808i	$0.261791\pi$
$991$			46.1378i			1.46562i	−0.680436	+	0.732808i	$0.738209\pi$
$992$	1.42396	−	1.95992i	0.0452109	−	0.0622274i
$993$	3.87915	−	11.9388i	0.123101	−	0.378866i
$994$	9.97063	+	30.6864i	0.316249	+	0.973314i
$995$	−30.5111	+	22.1676i	−0.967267	+	0.702761i
$996$	−1.15675	+	0.840427i	−0.0366530	+	0.0266300i
$997$	−28.4017	+	9.22826i	−0.899490	+	0.292262i	−0.722027	−	0.691865i	$-0.756789\pi$
$997$	−28.4017	+	9.22826i	−0.899490	+	0.292262i	−0.177463	+	0.984127i	$0.556789\pi$
$998$	−1.82174	+	5.60674i	−0.0576662	+	0.177478i
$999$	58.8978	+	42.7918i	1.86344	+	1.35387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.m.b.227.10	yes	40
11.8	odd	10		418.2.m.a.151.1	✓	40
19.18	odd	2		418.2.m.a.227.1	yes	40
209.151	even	10	inner	418.2.m.b.151.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.m.a.151.1	✓	40	11.8	odd	10
418.2.m.a.227.1	yes	40	19.18	odd	2
418.2.m.b.151.10	yes	40	209.151	even	10	inner
418.2.m.b.227.10	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(2.71373 + 0.881745i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.18335 + 0.859758i) q^{5} +(1.67718 + 2.30844i) q^{6} +(3.23095 - 1.04980i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(4.15981 + 3.02228i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(2.71373 + 0.881745i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.18335 + 0.859758i) q^{5} +(1.67718 + 2.30844i) q^{6} +(3.23095 - 1.04980i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(4.15981 + 3.02228i) q^{9} -1.46271 q^{10} +(-1.63953 - 2.88304i) q^{11} +2.85339i q^{12} +(-3.93112 - 2.85613i) q^{13} +(3.23095 + 1.04980i) q^{14} +(-3.96939 + 1.28973i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.99776 - 2.74968i) q^{17} +(1.58891 + 4.89015i) q^{18} +(-4.35751 - 0.109891i) q^{19} +(-1.18335 - 0.859758i) q^{20} +9.69359 q^{21} +(0.368199 - 3.29612i) q^{22} -1.03359 q^{23} +(-1.67718 + 2.30844i) q^{24} +(-0.883940 + 2.72049i) q^{25} +(-1.50155 - 4.62131i) q^{26} +(3.59219 + 4.94423i) q^{27} +(1.99684 + 2.74841i) q^{28} +(2.76958 + 8.52388i) q^{29} +(-3.96939 - 1.28973i) q^{30} +(-1.42396 + 1.95992i) q^{31} -1.00000 q^{32} +(-1.90715 - 9.26945i) q^{33} -3.39879i q^{34} +(-2.92079 + 4.02012i) q^{35} +(-1.58891 + 4.89015i) q^{36} +(11.3294 - 3.68114i) q^{37} +(-3.46071 - 2.65019i) q^{38} +(-8.14963 - 11.2170i) q^{39} +(-0.452001 - 1.39112i) q^{40} +(-1.50274 + 4.62495i) q^{41} +(7.84228 + 5.69775i) q^{42} -12.3044i q^{43} +(2.23529 - 2.45020i) q^{44} -7.52096 q^{45} +(-0.836194 - 0.607530i) q^{46} +(-1.19758 + 3.68577i) q^{47} +(-2.71373 + 0.881745i) q^{48} +(3.67384 - 2.66920i) q^{49} +(-2.31418 + 1.68135i) q^{50} +(-2.99686 - 9.22339i) q^{51} +(1.50155 - 4.62131i) q^{52} +(1.42191 - 1.95709i) q^{53} +6.11141i q^{54} +(4.41887 + 2.00206i) q^{55} +3.39722i q^{56} +(-11.7282 - 4.14043i) q^{57} +(-2.76958 + 8.52388i) q^{58} +(-6.62279 + 2.15187i) q^{59} +(-2.45322 - 3.37657i) q^{60} +(-3.50666 - 4.82650i) q^{61} +(-2.30402 + 0.748622i) q^{62} +(16.6129 + 5.39787i) q^{63} +(-0.809017 - 0.587785i) q^{64} +7.10749 q^{65} +(3.90553 - 8.62013i) q^{66} +3.43561i q^{67} +(1.99776 - 2.74968i) q^{68} +(-2.80489 - 0.911364i) q^{69} +(-4.72593 + 1.53555i) q^{70} +(5.58258 + 7.68376i) q^{71} +(-4.15981 + 3.02228i) q^{72} +(11.7051 - 3.80323i) q^{73} +(11.3294 + 3.68114i) q^{74} +(-4.79755 + 6.60326i) q^{75} +(-1.24203 - 4.17820i) q^{76} +(-8.32387 - 7.59378i) q^{77} -13.8650i q^{78} +(5.96067 + 4.33068i) q^{79} +(0.452001 - 1.39112i) q^{80} +(0.621980 + 1.91426i) q^{81} +(-3.93422 + 2.85838i) q^{82} +(0.294537 + 0.405395i) q^{83} +(2.99548 + 9.21915i) q^{84} +(4.72811 + 1.53626i) q^{85} +(7.23236 - 9.95450i) q^{86} +25.5736i q^{87} +(3.24858 - 0.668380i) q^{88} +5.68988i q^{89} +(-6.08458 - 4.42071i) q^{90} +(-15.6996 - 5.10112i) q^{91} +(-0.319398 - 0.983005i) q^{92} +(-5.59240 + 4.06312i) q^{93} +(-3.13531 + 2.27793i) q^{94} +(5.25096 - 3.61636i) q^{95} +(-2.71373 - 0.881745i) q^{96} +(0.135020 - 0.185839i) q^{97} +4.54112 q^{98} +(1.89321 - 16.9480i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) \) 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9	\( 40 q + 10 q^{2} - 10 q^{4} + 2 q^{5} + 5 q^{6} - 5 q^{7} + 10 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{13} - 5 q^{14} - 30 q^{15} - 10 q^{16} - 15 q^{17} - 13 q^{18} + 11 q^{19} + 2 q^{20} - 4 q^{22} + 6 q^{23} - 5 q^{24} - 36 q^{25} - 2 q^{26} + 45 q^{27} + 2 q^{29} - 30 q^{30} - 40 q^{32} - 27 q^{33} - 5 q^{35} + 13 q^{36} + 14 q^{38} + 30 q^{39} + 3 q^{40} + 8 q^{41} + 20 q^{42} - 6 q^{44} + 18 q^{45} - q^{46} - 8 q^{47} + 31 q^{49} - 9 q^{50} - 41 q^{51} + 2 q^{52} + 40 q^{53} - 31 q^{55} - 10 q^{57} - 2 q^{58} - 35 q^{59} - 20 q^{60} + 5 q^{61} + 30 q^{62} - 25 q^{63} - 10 q^{64} - 8 q^{65} - 48 q^{66} + 15 q^{68} + 60 q^{69} + 10 q^{70} - 50 q^{71} - 8 q^{72} + 10 q^{73} + 35 q^{75} + 11 q^{76} - 64 q^{77} + 42 q^{79} - 3 q^{80} + 11 q^{81} + 7 q^{82} + 25 q^{83} + 20 q^{84} - 45 q^{85} + 40 q^{86} + 6 q^{88} + 22 q^{90} + 70 q^{91} - 4 q^{92} - 18 q^{93} - 7 q^{94} - 5 q^{95} + 15 q^{97} + 74 q^{98} + 50 q^{99}+O(q^{100}) \) 40 * q + 10 * q^2 - 10 * q^4 + 2 * q^5 + 5 * q^6 - 5 * q^7 + 10 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^13 - 5 * q^14 - 30 * q^15 - 10 * q^16 - 15 * q^17 - 13 * q^18 + 11 * q^19 + 2 * q^20 - 4 * q^22 + 6 * q^23 - 5 * q^24 - 36 * q^25 - 2 * q^26 + 45 * q^27 + 2 * q^29 - 30 * q^30 - 40 * q^32 - 27 * q^33 - 5 * q^35 + 13 * q^36 + 14 * q^38 + 30 * q^39 + 3 * q^40 + 8 * q^41 + 20 * q^42 - 6 * q^44 + 18 * q^45 - q^46 - 8 * q^47 + 31 * q^49 - 9 * q^50 - 41 * q^51 + 2 * q^52 + 40 * q^53 - 31 * q^55 - 10 * q^57 - 2 * q^58 - 35 * q^59 - 20 * q^60 + 5 * q^61 + 30 * q^62 - 25 * q^63 - 10 * q^64 - 8 * q^65 - 48 * q^66 + 15 * q^68 + 60 * q^69 + 10 * q^70 - 50 * q^71 - 8 * q^72 + 10 * q^73 + 35 * q^75 + 11 * q^76 - 64 * q^77 + 42 * q^79 - 3 * q^80 + 11 * q^81 + 7 * q^82 + 25 * q^83 + 20 * q^84 - 45 * q^85 + 40 * q^86 + 6 * q^88 + 22 * q^90 + 70 * q^91 - 4 * q^92 - 18 * q^93 - 7 * q^94 - 5 * q^95 + 15 * q^97 + 74 * q^98 + 50 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more