LMFDB - Embedded newform 349.2.e.a.123.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(123,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("349.123");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.e (of order $6$, degree $2$, 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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			123.11
Character	$\chi$	$=$	349.123
Dual form			349.2.e.a.227.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.941972 + 0.543848i) q^{2} +(-0.443096 + 0.767465i) q^{3} +(-0.408460 + 0.707473i) q^{4} +(-1.75571 + 3.04098i) q^{5} -0.963907i q^{6} +(2.73929 - 1.58153i) q^{7} -3.06395i q^{8} +(1.10733 + 1.91796i) q^{9} +O(q^{10})$	\(q+(-0.941972 + 0.543848i) q^{2} +(-0.443096 + 0.767465i) q^{3} +(-0.408460 + 0.707473i) q^{4} +(-1.75571 + 3.04098i) q^{5} -0.963907i q^{6} +(2.73929 - 1.58153i) q^{7} -3.06395i q^{8} +(1.10733 + 1.91796i) q^{9} -3.81936i q^{10} +6.06346i q^{11} +(-0.361974 - 0.626957i) q^{12} +(-3.50246 + 2.02214i) q^{13} +(-1.72022 + 2.97952i) q^{14} +(-1.55590 - 2.69490i) q^{15} +(0.849402 + 1.47121i) q^{16} -1.94697 q^{17} +(-2.08615 - 1.20444i) q^{18} +(3.67875 - 6.37179i) q^{19} +(-1.43428 - 2.48424i) q^{20} +2.80308i q^{21} +(-3.29760 - 5.71160i) q^{22} +(-4.36037 - 7.55238i) q^{23} +(2.35147 + 1.35762i) q^{24} +(-3.66505 - 6.34806i) q^{25} +(2.19948 - 3.80961i) q^{26} -4.62119 q^{27} +2.58397i q^{28} +(-0.895330 + 1.55076i) q^{29} +(2.93122 + 1.69234i) q^{30} +1.09276 q^{31} +(3.70669 + 2.14006i) q^{32} +(-4.65349 - 2.68669i) q^{33} +(1.83399 - 1.05885i) q^{34} +11.1069i q^{35} -1.80920 q^{36} -7.33548 q^{37} +8.00272i q^{38} -3.58402i q^{39} +(9.31742 + 5.37941i) q^{40} +7.17690 q^{41} +(-1.52445 - 2.64042i) q^{42} +(6.25909 + 3.61368i) q^{43} +(-4.28973 - 2.47668i) q^{44} -7.77663 q^{45} +(8.21469 + 4.74275i) q^{46} +6.94109i q^{47} -1.50547 q^{48} +(1.50249 - 2.60239i) q^{49} +(6.90475 + 3.98646i) q^{50} +(0.862694 - 1.49423i) q^{51} -3.30386i q^{52} +5.58046i q^{53} +(4.35303 - 2.51322i) q^{54} +(-18.4389 - 10.6457i) q^{55} +(-4.84573 - 8.39306i) q^{56} +(3.26008 + 5.64663i) q^{57} -1.94769i q^{58} +(6.20745 + 3.58387i) q^{59} +2.54209 q^{60} +4.62479i q^{61} +(-1.02935 + 0.594293i) q^{62} +(6.06662 + 3.50256i) q^{63} -8.05307 q^{64} -14.2012i q^{65} +5.84461 q^{66} -0.116953 q^{67} +(0.795258 - 1.37743i) q^{68} +7.72825 q^{69} +(-6.04044 - 10.4624i) q^{70} +(-0.617077 + 0.356269i) q^{71} +(5.87652 - 3.39281i) q^{72} +(2.29384 - 3.97305i) q^{73} +(6.90981 - 3.98938i) q^{74} +6.49588 q^{75} +(3.00524 + 5.20524i) q^{76} +(9.58955 + 16.6096i) q^{77} +(1.94916 + 3.37604i) q^{78} +10.1985i q^{79} -5.96523 q^{80} +(-1.27436 + 2.20726i) q^{81} +(-6.76044 + 3.90314i) q^{82} +(-6.45749 - 11.1847i) q^{83} +(-1.98310 - 1.14495i) q^{84} +(3.41832 - 5.92070i) q^{85} -7.86118 q^{86} +(-0.793434 - 1.37427i) q^{87} +18.5781 q^{88} +(-2.81356 - 1.62441i) q^{89} +(7.32536 - 4.22930i) q^{90} +(-6.39617 + 11.0785i) q^{91} +7.12414 q^{92} +(-0.484196 + 0.838653i) q^{93} +(-3.77489 - 6.53831i) q^{94} +(12.9177 + 22.3741i) q^{95} +(-3.28484 + 1.89650i) q^{96} +(3.74416 - 2.16169i) q^{97} +3.26850i q^{98} +(-11.6294 + 6.71426i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) $ 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9	$ 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) $ 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9 - q^12 - 3 * q^13 - 10 * q^14 + q^15 - 29 * q^16 - 10 * q^17 + 15 * q^18 - 9 * q^19 - 3 * q^22 - 17 * q^23 - 48 * q^24 - 29 * q^25 - 4 * q^26 + 18 * q^27 - 2 * q^29 + 9 * q^30 + 32 * q^31 + 9 * q^32 - 12 * q^33 - 63 * q^34 + 24 * q^36 - 16 * q^37 + 54 * q^40 - 10 * q^41 - 15 * q^42 - 45 * q^43 + 18 * q^44 - 2 * q^45 + 27 * q^46 + 6 * q^48 + 35 * q^49 + 6 * q^50 - 14 * q^51 + 27 * q^54 + 24 * q^55 + 11 * q^56 - 29 * q^57 - 18 * q^59 + 116 * q^60 - 9 * q^62 - 21 * q^63 - 132 * q^64 + 130 * q^66 + 58 * q^67 + 42 * q^69 + 40 * q^70 - 24 * q^71 + 72 * q^72 - 6 * q^73 + 30 * q^74 - 58 * q^75 + 37 * q^76 - 4 * q^77 - 33 * q^78 - 40 * q^80 - 81 * q^81 + 21 * q^82 + 12 * q^83 + 18 * q^84 - 11 * q^85 - 126 * q^86 - 42 * q^87 - 50 * q^88 + 3 * q^89 - 12 * q^90 - 28 * q^91 - 120 * q^92 + 31 * q^93 + 29 * q^94 + 60 * q^95 - 120 * q^96 - 15 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.941972	+	0.543848i	−0.666075	+	0.384558i	−0.794588	−	0.607149i	$-0.792313\pi$
$2$	−0.941972	+	0.543848i	−0.666075	+	0.384558i	0.128513	+	0.991708i	$0.458980\pi$
$3$	−0.443096	+	0.767465i	−0.255822	+	0.443096i	−0.965118	−	0.261814i	$-0.915679\pi$
$3$	−0.443096	+	0.767465i	−0.255822	+	0.443096i	0.709297	+	0.704910i	$0.249013\pi$
$4$	−0.408460	+	0.707473i	−0.204230	+	0.353736i
$5$	−1.75571	+	3.04098i	−0.785179	+	1.35997i	0.143714	+	0.989619i	$0.454096\pi$
$5$	−1.75571	+	3.04098i	−0.785179	+	1.35997i	−0.928892	+	0.370350i	$0.879238\pi$
$6$		−	0.963907i		−	0.393513i
$7$	2.73929	−	1.58153i	1.03536	−	0.597763i	0.116841	−	0.993151i	$-0.462723\pi$
$7$	2.73929	−	1.58153i	1.03536	−	0.597763i	0.918514	+	0.395388i	$0.129390\pi$
$8$		−	3.06395i		−	1.08327i
$9$	1.10733	+	1.91796i	0.369111	+	0.639318i
$10$		−	3.81936i		−	1.20779i
$11$			6.06346i			1.82820i	0.405488	+	0.914100i	$0.367102\pi$
$11$			6.06346i			1.82820i	−0.405488	+	0.914100i	$0.632898\pi$
$12$	−0.361974	−	0.626957i	−0.104493	−	0.180987i
$13$	−3.50246	+	2.02214i	−0.971407	+	0.560842i	−0.899665	−	0.436581i	$-0.856189\pi$
$13$	−3.50246	+	2.02214i	−0.971407	+	0.560842i	−0.0717421	+	0.997423i	$0.522856\pi$
$14$	−1.72022	+	2.97952i	−0.459749	+	0.796309i
$15$	−1.55590	−	2.69490i	−0.401731	−	0.695819i
$16$	0.849402	+	1.47121i	0.212351	+	0.367802i
$17$	−1.94697			−0.472209			−0.236105	−	0.971728i	$-0.575871\pi$
$17$	−1.94697			−0.472209			−0.236105	+	0.971728i	$0.575871\pi$
$18$	−2.08615	−	1.20444i	−0.491710	−	0.283889i
$19$	3.67875	−	6.37179i	0.843964	−	1.46179i	−0.0425541	−	0.999094i	$-0.513549\pi$
$19$	3.67875	−	6.37179i	0.843964	−	1.46179i	0.886518	−	0.462694i	$-0.153117\pi$
$20$	−1.43428	−	2.48424i	−0.320714	−	0.555492i
$21$			2.80308i			0.611683i
$22$	−3.29760	−	5.71160i	−0.703050	−	1.21772i
$23$	−4.36037	−	7.55238i	−0.909200	−	1.57478i	−0.815179	−	0.579210i	$-0.803361\pi$
$23$	−4.36037	−	7.55238i	−0.909200	−	1.57478i	−0.0940210	−	0.995570i	$-0.529972\pi$
$24$	2.35147	+	1.35762i	0.479992	+	0.277124i
$25$	−3.66505	−	6.34806i	−0.733011	−	1.26961i
$26$	2.19948	−	3.80961i	0.431353	−	0.747125i
$27$	−4.62119			−0.889349
$28$			2.58397i			0.488324i
$29$	−0.895330	+	1.55076i	−0.166259	+	0.287968i	−0.937102	−	0.349057i	$-0.886502\pi$
$29$	−0.895330	+	1.55076i	−0.166259	+	0.287968i	0.770843	+	0.637025i	$0.219835\pi$
$30$	2.93122	+	1.69234i	0.535166	+	0.308978i
$31$	1.09276			0.196265			0.0981325	−	0.995173i	$-0.468713\pi$
$31$	1.09276			0.196265			0.0981325	+	0.995173i	$0.468713\pi$
$32$	3.70669	+	2.14006i	0.655256	+	0.378312i
$33$	−4.65349	−	2.68669i	−0.810068	−	0.467693i
$34$	1.83399	−	1.05885i	0.314526	−	0.181592i
$35$			11.1069i			1.87740i
$36$	−1.80920			−0.301534
$37$	−7.33548			−1.20594			−0.602972	−	0.797762i	$-0.706017\pi$
$37$	−7.33548			−1.20594			−0.602972	+	0.797762i	$0.706017\pi$
$38$			8.00272i			1.29821i
$39$		−	3.58402i		−	0.573902i
$40$	9.31742	+	5.37941i	1.47321	+	0.850560i
$41$	7.17690			1.12084			0.560422	−	0.828207i	$-0.310639\pi$
$41$	7.17690			1.12084			0.560422	+	0.828207i	$0.310639\pi$
$42$	−1.52445	−	2.64042i	−0.235228	−	0.407426i
$43$	6.25909	+	3.61368i	0.954502	+	0.551082i	0.894476	−	0.447115i	$-0.147549\pi$
$43$	6.25909	+	3.61368i	0.954502	+	0.551082i	0.0600252	+	0.998197i	$0.480882\pi$
$44$	−4.28973	−	2.47668i	−0.646701	−	0.373373i
$45$	−7.77663			−1.15927
$46$	8.21469	+	4.74275i	1.21119	+	0.699281i
$47$			6.94109i			1.01246i	0.862398	+	0.506231i	$0.168962\pi$
$47$			6.94109i			1.01246i	−0.862398	+	0.506231i	$0.831038\pi$
$48$	−1.50547			−0.217295
$49$	1.50249	−	2.60239i	0.214641	−	0.371769i
$50$	6.90475	+	3.98646i	0.976480	+	0.563771i
$51$	0.862694	−	1.49423i	0.120801	−	0.209234i
$52$		−	3.30386i		−	0.458163i
$53$			5.58046i			0.766535i	0.923637	+	0.383268i	$0.125201\pi$
$53$			5.58046i			0.766535i	−0.923637	+	0.383268i	$0.874799\pi$
$54$	4.35303	−	2.51322i	0.592373	−	0.342007i
$55$	−18.4389	−	10.6457i	−2.48630	−	1.43546i
$56$	−4.84573	−	8.39306i	−0.647539	−	1.12157i
$57$	3.26008	+	5.64663i	0.431808	+	0.747914i
$58$		−	1.94769i		−	0.255745i
$59$	6.20745	+	3.58387i	0.808141	+	0.466580i	0.846310	−	0.532691i	$-0.178819\pi$
$59$	6.20745	+	3.58387i	0.808141	+	0.466580i	−0.0381689	+	0.999271i	$0.512152\pi$
$60$	2.54209			0.328182
$61$			4.62479i			0.592143i	0.955166	+	0.296072i	$0.0956767\pi$
$61$			4.62479i			0.592143i	−0.955166	+	0.296072i	$0.904323\pi$
$62$	−1.02935	+	0.594293i	−0.130727	+	0.0754753i
$63$	6.06662	+	3.50256i	0.764322	+	0.441281i
$64$	−8.05307			−1.00663
$65$		−	14.2012i		−	1.76144i
$66$	5.84461			0.719421
$67$	−0.116953			−0.0142880			−0.00714402	−	0.999974i	$-0.502274\pi$
$67$	−0.116953			−0.0142880			−0.00714402	+	0.999974i	$0.502274\pi$
$68$	0.795258	−	1.37743i	0.0964392	−	0.167038i
$69$	7.72825			0.930372
$70$	−6.04044	−	10.4624i	−0.721971	−	1.25049i
$71$	−0.617077	+	0.356269i	−0.0732335	+	0.0422814i	−0.536170	−	0.844110i	$-0.680129\pi$
$71$	−0.617077	+	0.356269i	−0.0732335	+	0.0422814i	0.462936	+	0.886392i	$0.346796\pi$
$72$	5.87652	−	3.39281i	0.692554	−	0.399846i
$73$	2.29384	−	3.97305i	0.268474	−	0.465010i	−0.699994	−	0.714149i	$-0.746814\pi$
$73$	2.29384	−	3.97305i	0.268474	−	0.465010i	0.968468	+	0.249138i	$0.0801474\pi$
$74$	6.90981	−	3.98938i	0.803249	−	0.463756i
$75$	6.49588			0.750080
$76$	3.00524	+	5.20524i	0.344725	+	0.597081i
$77$	9.58955	+	16.6096i	1.09283	+	1.89284i
$78$	1.94916	+	3.37604i	0.220699	+	0.382262i
$79$			10.1985i			1.14742i	0.819057	+	0.573712i	$0.194497\pi$
$79$			10.1985i			1.14742i	−0.819057	+	0.573712i	$0.805503\pi$
$80$	−5.96523			−0.666933
$81$	−1.27436	+	2.20726i	−0.141596	+	0.245251i
$82$	−6.76044	+	3.90314i	−0.746565	+	0.431030i
$83$	−6.45749	−	11.1847i	−0.708802	−	1.22768i	−0.965302	−	0.261136i	$-0.915903\pi$
$83$	−6.45749	−	11.1847i	−0.708802	−	1.22768i	0.256500	−	0.966544i	$-0.417431\pi$
$84$	−1.98310	−	1.14495i	−0.216374	−	0.124924i
$85$	3.41832	−	5.92070i	0.370769	−	0.642190i
$86$	−7.86118			−0.847692
$87$	−0.793434	−	1.37427i	−0.0850651	−	0.147337i
$88$	18.5781			1.98043
$89$	−2.81356	−	1.62441i	−0.298237	−	0.172187i	0.343414	−	0.939184i	$-0.388417\pi$
$89$	−2.81356	−	1.62441i	−0.298237	−	0.172187i	−0.641651	+	0.766997i	$0.721750\pi$
$90$	7.32536	−	4.22930i	0.772161	−	0.445807i
$91$	−6.39617	+	11.0785i	−0.670501	+	1.16134i
$92$	7.12414			0.742743
$93$	−0.484196	+	0.838653i	−0.0502088	+	0.0869642i
$94$	−3.77489	−	6.53831i	−0.389351	−	0.674375i
$95$	12.9177	+	22.3741i	1.32532	+	2.29553i
$96$	−3.28484	+	1.89650i	−0.335258	+	0.193561i
$97$	3.74416	−	2.16169i	0.380162	−	0.219486i	−0.297727	−	0.954651i	$-0.596228\pi$
$97$	3.74416	−	2.16169i	0.380162	−	0.219486i	0.677889	+	0.735165i	$0.262895\pi$
$98$			3.26850i			0.330168i
$99$	−11.6294	+	6.71426i	−1.16880	+	0.674808i
$100$	5.98811			0.598811
$101$			9.24864i			0.920274i	0.887848	+	0.460137i	$0.152200\pi$
$101$			9.24864i			0.920274i	−0.887848	+	0.460137i	$0.847800\pi$
$102$			1.87670i			0.185821i
$103$		−	5.37474i		−	0.529589i	−0.964305	−	0.264794i	$-0.914696\pi$
$103$		−	5.37474i		−	0.529589i	0.964305	−	0.264794i	$-0.0853041\pi$
$104$	6.19575	+	10.7314i	0.607543	+	1.05230i
$105$	−8.52413	−	4.92141i	−0.831870	−	0.480280i
$106$	−3.03492	−	5.25664i	−0.294778	−	0.510570i
$107$	−10.7843	+	6.22630i	−1.04255	+	0.601919i	−0.920556	−	0.390612i	$-0.872264\pi$
$107$	−10.7843	+	6.22630i	−1.04255	+	0.601919i	−0.121998	+	0.992530i	$0.538930\pi$
$108$	1.88757	−	3.26937i	0.181632	−	0.314595i
$109$	2.15229	−	3.72788i	0.206152	−	0.357066i	−0.744347	−	0.667793i	$-0.767239\pi$
$109$	2.15229	−	3.72788i	0.206152	−	0.357066i	0.950499	+	0.310727i	$0.100572\pi$
$110$	23.1585			2.20808
$111$	3.25032	−	5.62972i	0.308507	−	0.534349i
$112$	4.65353	+	2.68671i	0.439717	+	0.253871i
$113$	6.66151	−	3.84602i	0.626662	−	0.361803i	−0.152796	−	0.988258i	$-0.548828\pi$
$113$	6.66151	−	3.84602i	0.626662	−	0.361803i	0.779458	+	0.626454i	$0.215495\pi$
$114$	−6.14181	−	3.54598i	−0.575233	−	0.332111i
$115$	30.6222			2.85554
$116$	−0.731412	−	1.26684i	−0.0679099	−	0.117623i
$117$	−7.75677	−	4.47837i	−0.717113	−	0.414026i
$118$	−7.79632			−0.717709
$119$	−5.33332	+	3.07919i	−0.488904	+	0.282269i
$120$	−8.25702	+	4.76719i	−0.753760	+	0.435183i
$121$	−25.7655			−2.34232
$122$	−2.51518	−	4.35642i	−0.227714	−	0.394412i
$123$	−3.18006	+	5.50802i	−0.286736	+	0.496641i
$124$	−0.446347	+	0.773096i	−0.0400832	+	0.0694261i
$125$	8.18200			0.731821
$126$	−7.61944			−0.678794
$127$			11.6955i			1.03781i	0.854833	+	0.518903i	$0.173659\pi$
$127$			11.6955i			1.03781i	−0.854833	+	0.518903i	$0.826341\pi$
$128$	0.172385	−	0.0995267i	0.0152369	−	0.00879700i
$129$	−5.54675	+	3.20242i	−0.488364	+	0.281957i
$130$	7.72330	+	13.3771i	0.677378	+	1.17325i
$131$		−	4.87865i		−	0.426250i	−0.977025	−	0.213125i	$-0.931636\pi$
$131$		−	4.87865i		−	0.426250i	0.977025	−	0.213125i	$-0.0683641\pi$
$132$	3.80152	−	2.19481i	0.330880	−	0.191034i
$133$		−	23.2723i		−	2.01796i
$134$	0.110166	−	0.0636044i	0.00951690	−	0.00549458i
$135$	8.11349	−	14.0530i	0.698298	−	1.20949i
$136$			5.96541i			0.511530i
$137$	3.85114	+	2.22345i	0.329025	+	0.189963i	0.655408	−	0.755275i	$-0.272497\pi$
$137$	3.85114	+	2.22345i	0.329025	+	0.189963i	−0.326383	+	0.945238i	$0.605830\pi$
$138$	−7.27979	+	4.20299i	−0.619697	+	0.357782i
$139$	12.8106			1.08658			0.543290	−	0.839545i	$-0.317178\pi$
$139$	12.8106			1.08658			0.543290	+	0.839545i	$0.317178\pi$
$140$	−7.85780	−	4.53671i	−0.664106	−	0.383422i
$141$	−5.32704	−	3.07557i	−0.448618	−	0.259010i
$142$	0.387513	−	0.671191i	0.0325193	−	0.0563251i
$143$	−12.2612	−	21.2370i	−1.02533	−	1.77593i
$144$	−1.88114	+	3.25823i	−0.156762	+	0.271519i
$145$	−3.14389	−	5.44537i	−0.261085	−	0.452213i
$146$			4.99000i			0.412975i
$147$	1.33149	+	2.30621i	0.109820	+	0.190213i
$148$	2.99625	−	5.18965i	0.246290	−	0.426587i
$149$	0.435958	−	0.251701i	0.0357151	−	0.0206201i	−0.482036	−	0.876151i	$-0.660103\pi$
$149$	0.435958	−	0.251701i	0.0357151	−	0.0206201i	0.517751	+	0.855531i	$0.326769\pi$
$150$	−6.11894	+	3.53277i	−0.499609	+	0.288450i
$151$	2.87152	−	4.97361i	0.233681	−	0.404747i	−0.725208	−	0.688530i	$-0.758256\pi$
$151$	2.87152	−	4.97361i	0.233681	−	0.404747i	0.958888	+	0.283783i	$0.0915896\pi$
$152$	−19.5228	−	11.2715i	−1.58351	−	0.914241i
$153$	−2.15594	−	3.73420i	−0.174297	−	0.301892i
$154$	−18.0662	−	10.4305i	−1.45581	−	0.840514i
$155$	−1.91857	+	3.32306i	−0.154103	+	0.266914i
$156$	2.53559	+	1.46393i	0.203010	+	0.117208i
$157$	0.00488589	−	0.00846261i	0.000389937	−	0.000675390i	−0.865830	−	0.500338i	$-0.833209\pi$
$157$	0.00488589	−	0.00846261i	0.000389937	−	0.000675390i	0.866220	+	0.499662i	$0.166543\pi$
$158$	−5.54645	−	9.60673i	−0.441252	−	0.764271i
$159$	−4.28281	−	2.47268i	−0.339649	−	0.196096i
$160$	−13.0158	+	7.51466i	−1.02899	+	0.594086i
$161$	−23.8887	−	13.7921i	−1.88269	−	1.08697i
$162$		−	2.77224i		−	0.217808i
$163$			11.6184i			0.910024i	0.890485	+	0.455012i	$0.150365\pi$
$163$			11.6184i			0.910024i	−0.890485	+	0.455012i	$0.849635\pi$
$164$	−2.93147	+	5.07746i	−0.228910	+	0.396483i
$165$	16.3404	−	9.43412i	1.27210	−	0.734445i
$166$	12.1655	+	7.02378i	0.944229	+	0.545151i
$167$			20.3265i			1.57291i	0.617648	+	0.786455i	$0.288086\pi$
$167$			20.3265i			1.57291i	−0.617648	+	0.786455i	$0.711914\pi$
$168$	8.58850			0.662617
$169$	1.67814	−	2.90662i	0.129088	−	0.223586i
$170$			7.43617i			0.570328i
$171$	16.2944			1.24606
$172$	−5.11317	+	2.95209i	−0.389875	+	0.225095i
$173$	11.4716	−	6.62316i	0.872173	−	0.503549i	0.00410338	−	0.999992i	$-0.498694\pi$
$173$	11.4716	−	6.62316i	0.872173	−	0.503549i	0.868070	+	0.496442i	$0.165361\pi$
$174$	1.49479	+	0.863015i	0.113319	+	0.0654250i
$175$	−20.0793	−	11.5928i	−1.51785	−	0.876333i
$176$	−8.92060	+	5.15031i	−0.672416	+	0.388219i
$177$	−5.50099	+	3.17600i	−0.413480	+	0.238723i
$178$	3.53373			0.264864
$179$			16.7016i			1.24834i	0.781290	+	0.624168i	$0.214562\pi$
$179$			16.7016i			1.24834i	−0.781290	+	0.624168i	$0.785438\pi$
$180$	3.17644	−	5.50175i	0.236758	−	0.410076i
$181$	2.43139			0.180724			0.0903620	−	0.995909i	$-0.471198\pi$
$181$	2.43139			0.180724			0.0903620	+	0.995909i	$0.471198\pi$
$182$		−	13.9142i		−	1.03139i
$183$	−3.54936	−	2.04922i	−0.262376	−	0.151483i
$184$	−23.1401	+	13.3599i	−1.70591	+	0.984908i
$185$	12.8790	−	22.3071i	0.946882	−	1.64005i
$186$		−	1.05332i		−	0.0772329i
$187$		−	11.8054i		−	0.863293i
$188$	−4.91063	−	2.83515i	−0.358145	−	0.206775i
$189$	−12.6588	+	7.30857i	−0.920793	+	0.531620i
$190$	−24.3362	−	14.0505i	−1.76553	−	1.01933i
$191$	9.08206	+	15.7306i	0.657155	+	1.13823i	0.981349	+	0.192235i	$0.0615736\pi$
$191$	9.08206	+	15.7306i	0.657155	+	1.13823i	−0.324194	+	0.945991i	$0.605093\pi$
$192$	3.56828	−	6.18045i	0.257519	−	0.446036i
$193$	15.3636	+	8.87020i	1.10590	+	0.638491i	0.937764	−	0.347273i	$-0.112892\pi$
$193$	15.3636	+	8.87020i	1.10590	+	0.638491i	0.168135	+	0.985764i	$0.446226\pi$
$194$	−2.35126	+	4.07250i	−0.168811	+	0.292389i
$195$	10.8989	+	6.29250i	0.780489	+	0.450616i
$196$	1.22741	+	2.12594i	0.0876722	+	0.151853i
$197$	−4.82276	−	2.78442i	−0.343608	−	0.198382i	0.318259	−	0.948004i	$-0.396902\pi$
$197$	−4.82276	−	2.78442i	−0.343608	−	0.198382i	−0.661866	+	0.749622i	$0.730235\pi$
$198$	7.30307	−	12.6493i	0.519006	−	0.898945i
$199$	4.69313	−	2.70958i	0.332687	−	0.192077i	−0.324346	−	0.945938i	$-0.605144\pi$
$199$	4.69313	−	2.70958i	0.332687	−	0.192077i	0.657034	+	0.753861i	$0.271811\pi$
$200$	−19.4501	+	11.2295i	−1.37533	+	0.794048i
$201$	0.0518212	−	0.0897570i	0.00365519	−	0.00633097i
$202$	−5.02985	−	8.71195i	−0.353899	−	0.612971i
$203$			5.66397i			0.397533i
$204$	0.704751	+	1.22066i	0.0493424	+	0.0854636i
$205$	−12.6006	+	21.8248i	−0.880062	+	1.52431i
$206$	2.92304	+	5.06285i	0.203658	+	0.352746i
$207$	9.65675	−	16.7260i	0.671190	−	1.16254i
$208$	−5.94999	−	3.43523i	−0.412558	−	0.238190i
$209$	38.6351	+	22.3060i	2.67244	+	1.54294i
$210$	10.7060			0.738783
$211$	−4.95719	+	2.86203i	−0.341267	+	0.197030i	−0.660832	−	0.750534i	$-0.729796\pi$
$211$	−4.95719	+	2.86203i	−0.341267	+	0.197030i	0.319565	+	0.947564i	$0.396463\pi$
$212$	−3.94802	−	2.27939i	−0.271151	−	0.156549i
$213$		−	0.631446i		−	0.0432660i
$214$	6.77231	−	11.7300i	0.462946	−	0.801846i
$215$	−21.9783	+	12.6892i	−1.49891	+	0.865395i
$216$			14.1591i			0.963405i
$217$	2.99338	−	1.72823i	0.203204	−	0.117320i
$218$			4.68208i			0.317111i
$219$	2.03278	+	3.52089i	0.137363	+	0.237919i
$220$	15.0631	−	8.69667i	1.01555	−	0.586329i
$221$	6.81917	−	3.93705i	0.458707	−	0.264835i
$222$			7.07072i			0.474555i
$223$	−8.00222			−0.535868			−0.267934	−	0.963437i	$-0.586341\pi$
$223$	−8.00222			−0.535868			−0.267934	+	0.963437i	$0.586341\pi$
$224$	13.5383			0.904565
$225$	8.11686	−	14.0588i	0.541124	−	0.937255i
$226$	−4.18330	+	7.24569i	−0.278269	+	0.481976i
$227$	12.5556	+	21.7470i	0.833345	+	1.44340i	0.895371	+	0.445322i	$0.146911\pi$
$227$	12.5556	+	21.7470i	0.833345	+	1.44340i	−0.0620253	+	0.998075i	$0.519756\pi$
$228$	−5.32645			−0.352753
$229$	−13.3717	+	7.72018i	−0.883630	+	0.510164i	−0.871854	−	0.489767i	$-0.837082\pi$
$229$	−13.3717	+	7.72018i	−0.883630	+	0.510164i	−0.0117764	+	0.999931i	$0.503749\pi$
$230$	−28.8453	+	16.6538i	−1.90200	+	1.09812i
$231$	−16.9964			−1.11828
$232$	4.75144	+	2.74325i	0.311947	+	0.180103i
$233$	−11.0491	−	19.1376i	−0.723851	−	1.25375i	−0.959445	−	0.281895i	$-0.909037\pi$
$233$	−11.0491	−	19.1376i	−0.723851	−	1.25375i	0.235594	−	0.971852i	$-0.424296\pi$
$234$	9.74221			0.636868
$235$	−21.1077	−	12.1866i	−1.37692	−	0.794963i
$236$	−5.07098	+	2.92773i	−0.330093	+	0.190579i
$237$	−7.82702	−	4.51893i	−0.508419	−	0.293536i
$238$	3.34922	−	5.80102i	0.217098	−	0.376025i
$239$	−6.85688			−0.443535			−0.221767	−	0.975100i	$-0.571183\pi$
$239$	−6.85688			−0.443535			−0.221767	+	0.975100i	$0.571183\pi$
$240$	2.64317	−	4.57810i	0.170616	−	0.295515i
$241$	4.96522	−	8.60002i	0.319838	−	0.553976i	−0.660616	−	0.750724i	$-0.729705\pi$
$241$	4.96522	−	8.60002i	0.319838	−	0.553976i	0.980454	+	0.196748i	$0.0630381\pi$
$242$	24.2704	−	14.0125i	1.56016	−	0.900758i
$243$	−8.06112	−	13.9623i	−0.517121	−	0.895680i
$244$	−3.27191	−	1.88904i	−0.209463	−	0.120933i
$245$	5.27587	+	9.13808i	0.337063	+	0.583811i
$246$		−	6.91786i		−	0.441067i
$247$			29.7559i			1.89332i
$248$		−	3.34815i		−	0.212608i
$249$	11.4452			0.725307
$250$	−7.70721	+	4.44976i	−0.487447	+	0.281428i
$251$		−	9.94849i		−	0.627943i	−0.949432	−	0.313971i	$-0.898340\pi$
$251$		−	9.94849i		−	0.627943i	0.949432	−	0.313971i	$-0.101660\pi$
$252$	−4.95593	+	2.86131i	−0.312195	+	0.180246i
$253$	45.7935	−	26.4389i	2.87901	−	1.66220i
$254$	−6.36055	−	11.0168i	−0.399097	−	0.691256i
$255$	3.02928	+	5.24688i	0.189701	+	0.328572i
$256$	7.94482	−	13.7608i	0.496551	−	0.860052i
$257$	14.6933			0.916541			0.458271	−	0.888813i	$-0.348469\pi$
$257$	14.6933			0.916541			0.458271	+	0.888813i	$0.348469\pi$
$258$	3.48326	−	6.03318i	0.216858	−	0.375609i
$259$	−20.0940	+	11.6013i	−1.24858	+	0.720869i
$260$	10.0470	+	5.80063i	0.623087	+	0.359740i
$261$	−3.96571			−0.245471
$262$	2.65324	+	4.59555i	0.163918	+	0.283914i
$263$	−27.5227			−1.69712			−0.848560	−	0.529099i	$-0.822530\pi$
$263$	−27.5227			−1.69712			−0.848560	+	0.529099i	$0.822530\pi$
$264$	−8.23189	+	14.2581i	−0.506638	+	0.877523i
$265$	−16.9701	−	9.79769i	−1.04246	−	0.601867i
$266$	12.6566	+	21.9218i	0.776024	+	1.34411i
$267$	2.49336	−	1.43954i	0.152591	−	0.0880984i
$268$	0.0477704	−	0.0827408i	0.00291804	−	0.00505420i
$269$	2.72686			0.166260			0.0831298	−	0.996539i	$-0.473508\pi$
$269$	2.72686			0.166260			0.0831298	+	0.996539i	$0.473508\pi$
$270$			17.6500i			1.07414i
$271$	−9.30594	−	16.1184i	−0.565296	−	0.979121i	−0.997022	−	0.0771161i	$-0.975429\pi$
$271$	−9.30594	−	16.1184i	−0.565296	−	0.979121i	0.431727	−	0.902005i	$-0.357905\pi$
$272$	−1.65376	−	2.86440i	−0.100274	−	0.173679i
$273$	−5.66824	−	9.81768i	−0.343057	−	0.594193i
$274$	−4.83688			−0.292207
$275$	38.4912	−	22.2229i	2.32111	−	1.34009i
$276$	−3.15668	+	5.46752i	−0.190010	+	0.329106i
$277$	16.7371	−	9.66319i	1.00564	−	0.580605i	0.0957258	−	0.995408i	$-0.469483\pi$
$277$	16.7371	−	9.66319i	1.00564	−	0.580605i	0.909911	+	0.414803i	$0.136149\pi$
$278$	−12.0672	+	6.96701i	−0.723743	+	0.417853i
$279$	1.21004	+	2.09586i	0.0724435	+	0.125476i
$280$	34.0309			2.03373
$281$	−2.12324	+	3.67756i	−0.126662	+	0.219385i	−0.922381	−	0.386280i	$-0.873760\pi$
$281$	−2.12324	+	3.67756i	−0.126662	+	0.219385i	0.795719	+	0.605665i	$0.207093\pi$
$282$	6.69056			0.398417
$283$	8.27179			0.491707			0.245854	−	0.969307i	$-0.420932\pi$
$283$	8.27179			0.491707			0.245854	+	0.969307i	$0.420932\pi$
$284$		−	0.582087i		−	0.0345405i
$285$	−22.8951			−1.35619
$286$	23.0994	+	13.3364i	1.36589	+	0.788600i
$287$	19.6596	−	11.3505i	1.16047	−	0.669999i
$288$			9.47902i			0.558557i
$289$	−13.2093			−0.777019
$290$	5.92290	+	3.41959i	0.347805	+	0.200805i
$291$			3.83135i			0.224598i
$292$	1.87388	+	3.24566i	0.109661	+	0.189938i
$293$	−5.21552	−	9.03355i	−0.304694	−	0.527746i	0.672499	−	0.740098i	$-0.265221\pi$
$293$	−5.21552	−	9.03355i	−0.304694	−	0.527746i	−0.977193	+	0.212352i	$0.931888\pi$
$294$	−2.50846	−	1.44826i	−0.146296	−	0.0844641i
$295$	−21.7970	+	12.5845i	−1.26907	+	0.732698i
$296$			22.4755i			1.30636i
$297$		−	28.0204i		−	1.62591i
$298$	−0.273774	+	0.474190i	−0.0158593	+	0.0274691i
$299$	30.5440	+	17.6346i	1.76641	+	1.01983i
$300$	−2.65331	+	4.59566i	−0.153189	+	0.265331i
$301$	22.8606			1.31767
$302$			6.24667i			0.359456i
$303$	−7.09800	−	4.09803i	−0.407770	−	0.235426i
$304$	12.4990			0.716865
$305$	−14.0639	−	8.11980i	−0.805297	−	0.464938i
$306$	4.06167	+	2.34501i	0.232190	+	0.134055i
$307$	14.1333	+	24.4796i	0.806631	+	1.39713i	0.915184	+	0.403036i	$0.132045\pi$
$307$	14.1333	+	24.4796i	0.806631	+	1.39713i	−0.108553	+	0.994091i	$0.534622\pi$
$308$	−15.6678			−0.892754
$309$	4.12492	+	2.38153i	0.234659	+	0.135480i
$310$		−	4.17363i		−	0.237046i
$311$			2.99274i			0.169702i	0.996394	+	0.0848512i	$0.0270415\pi$
$311$			2.99274i			0.169702i	−0.996394	+	0.0848512i	$0.972958\pi$
$312$	−10.9812			−0.621691
$313$	−3.11406			−0.176017			−0.0880084	−	0.996120i	$-0.528050\pi$
$313$	−3.11406			−0.176017			−0.0880084	+	0.996120i	$0.528050\pi$
$314$			0.0106287i			0.000599813i
$315$	−21.3025	+	12.2990i	−1.20026	+	0.692969i
$316$	−7.21519	−	4.16569i	−0.405886	−	0.234338i
$317$	−8.71669	−	5.03258i	−0.489578	−	0.282658i	0.234821	−	0.972039i	$-0.424550\pi$
$317$	−8.71669	−	5.03258i	−0.489578	−	0.282658i	−0.724399	+	0.689380i	$0.757883\pi$
$318$	5.37904			0.301642
$319$	−9.40295	−	5.42880i	−0.526464	−	0.303954i
$320$	14.1389	−	24.4893i	0.790387	−	1.36899i
$321$		−	11.0354i		−	0.615935i
$322$	30.0033			1.67202
$323$	−7.16242	+	12.4057i	−0.398527	+	0.690270i
$324$	−1.04105	−	1.80315i	−0.0578362	−	0.100175i
$325$	25.6734	+	14.8225i	1.42410	+	0.822207i
$326$	−6.31864	−	10.9442i	−0.349957	−	0.606144i
$327$	1.90735	+	3.30362i	0.105476	+	0.182691i
$328$		−	21.9897i		−	1.21418i
$329$	10.9776	+	19.0137i	0.605212	+	1.04826i
$330$	−10.2614	+	17.7734i	−0.564874	+	0.978391i
$331$	21.8322	+	12.6048i	1.20001	+	0.692824i	0.960557	−	0.278085i	$-0.0896996\pi$
$331$	21.8322	+	12.6048i	1.20001	+	0.692824i	0.239450	+	0.970909i	$0.423033\pi$
$332$	10.5505			0.579034
$333$	−8.12281	−	14.0691i	−0.445127	−	0.770983i
$334$	−11.0545	−	19.1470i	−0.604875	−	1.04767i
$335$	0.205335	−	0.355651i	0.0112187	−	0.0194313i
$336$	−4.12392	+	2.38094i	−0.224978	+	0.129891i
$337$	1.51932	+	2.63155i	0.0827629	+	0.143350i	0.904436	−	0.426610i	$-0.140292\pi$
$337$	1.51932	+	2.63155i	0.0827629	+	0.143350i	−0.821673	+	0.569959i	$0.806959\pi$
$338$			3.65061i			0.198567i
$339$			6.81663i			0.370228i
$340$	2.79249	+	4.83673i	0.151444	+	0.262309i
$341$			6.62588i			0.358812i
$342$	−15.3489	+	8.86167i	−0.829972	+	0.479184i
$343$			12.6365i			0.682308i
$344$	11.0721	−	19.1775i	0.596970	−	1.03398i
$345$	−13.5686	+	23.5015i	−0.730508	+	1.26528i
$346$	−7.20398	+	12.4777i	−0.387288	+	0.670803i
$347$	18.7577	−	10.8297i	1.00696	−	0.581371i	0.0966626	−	0.995317i	$-0.469183\pi$
$347$	18.7577	−	10.8297i	1.00696	−	0.581371i	0.910301	+	0.413946i	$0.135850\pi$
$348$	1.29634			0.0694913
$349$	−2.88885	+	18.4568i	−0.154636	+	0.987971i
$349$	−2.88885	+	18.4568i	−0.154636	+	0.987971i
$350$	25.2189			1.34801
$351$	16.1855	−	9.34472i	0.863920	−	0.498784i
$352$	−12.9762	+	22.4754i	−0.691631	+	1.19794i
$353$	4.42830	−	7.67005i	0.235695	−	0.408235i	−0.723780	−	0.690031i	$-0.757597\pi$
$353$	4.42830	−	7.67005i	0.235695	−	0.408235i	0.959474	+	0.281796i	$0.0909301\pi$
$354$	3.45452	−	5.98340i	0.183606	−	0.318014i
$355$		−	2.50203i		−	0.132794i
$356$	2.29845	−	1.32701i	0.121818	−	0.0703315i
$357$		−	5.45751i		−	0.288842i
$358$	−9.08312	−	15.7324i	−0.480058	−	0.831485i
$359$		−	23.9863i		−	1.26595i	−0.774172	−	0.632975i	$-0.781834\pi$
$359$		−	23.9863i		−	1.26595i	0.774172	−	0.632975i	$-0.218166\pi$
$360$			23.8272i			1.25580i
$361$	−17.5665	−	30.4260i	−0.924550	−	1.60137i
$362$	−2.29030	+	1.32231i	−0.120376	+	0.0694989i
$363$	11.4166	−	19.7741i	0.599215	−	1.03787i
$364$	−5.22516	−	9.05024i	−0.273873	−	0.474361i
$365$	8.05465	+	13.9511i	0.421600	+	0.730232i
$366$	4.45786			0.233016
$367$	9.15607	+	5.28626i	0.477943	+	0.275941i	0.719559	−	0.694431i	$-0.244344\pi$
$367$	9.15607	+	5.28626i	0.477943	+	0.275941i	−0.241616	+	0.970372i	$0.577677\pi$
$368$	7.40741	−	12.8300i	0.386138	−	0.668811i
$369$	7.94721	+	13.7650i	0.413715	+	0.716576i
$370$			28.0168i			1.45653i
$371$	8.82568	+	15.2865i	0.458206	+	0.793637i
$372$	−0.395549	−	0.685111i	−0.0205083	−	0.0355214i
$373$	11.8531	+	6.84342i	0.613733	+	0.354339i	0.774425	−	0.632666i	$-0.218039\pi$
$373$	11.8531	+	6.84342i	0.613733	+	0.354339i	−0.160692	+	0.987005i	$0.551373\pi$
$374$	6.42031	+	11.1203i	0.331987	+	0.575018i
$375$	−3.62541	+	6.27940i	−0.187215	+	0.324267i
$376$	21.2671			1.09677
$377$		−	7.24195i		−	0.372979i
$378$	7.94949	−	13.7689i	0.408878	−	0.708197i
$379$	−8.48979	−	4.90158i	−0.436091	−	0.251777i	0.265847	−	0.964015i	$-0.414348\pi$
$379$	−8.48979	−	4.90158i	−0.436091	−	0.251777i	−0.701938	+	0.712238i	$0.747682\pi$
$380$	−21.1054			−1.08268
$381$	−8.97586	−	5.18222i	−0.459847	−	0.265493i
$382$	−17.1101	−	9.87852i	−0.875428	−	0.505429i
$383$	14.4502	−	8.34283i	0.738371	−	0.426299i	−0.0831056	−	0.996541i	$-0.526484\pi$
$383$	14.4502	−	8.34283i	0.738371	−	0.426299i	0.821477	+	0.570242i	$0.193151\pi$
$384$			0.176400i			0.00900185i
$385$	−67.3460			−3.43227
$386$	−19.2962			−0.982148
$387$			16.0062i			0.813641i
$388$			3.53185i			0.179303i
$389$	−22.0857	−	12.7512i	−1.11979	−	0.646511i	−0.178443	−	0.983950i	$-0.557106\pi$
$389$	−22.0857	−	12.7512i	−1.11979	−	0.646511i	−0.941347	+	0.337439i	$0.890439\pi$
$390$	−13.6887			−0.693152
$391$	8.48950	+	14.7042i	0.429332	+	0.743625i
$392$	−7.97358	−	4.60355i	−0.402726	−	0.232514i
$393$	3.74419	+	2.16171i	0.188869	+	0.109044i
$394$	6.05721			0.305158
$395$	−31.0136	−	17.9057i	−1.56046	−	0.900933i
$396$		−	10.9700i		−	0.551264i
$397$	25.7430			1.29200			0.646002	−	0.763336i	$-0.276440\pi$
$397$	25.7430			1.29200			0.646002	+	0.763336i	$0.276440\pi$
$398$	−2.94720	+	5.10470i	−0.147730	+	0.255875i
$399$	17.8606	+	10.3118i	0.894151	+	0.516238i
$400$	6.22621	−	10.7841i	0.311311	−	0.539206i
$401$			18.1819i			0.907958i	0.891012	+	0.453979i	$0.149996\pi$
$401$			18.1819i			0.907958i	−0.891012	+	0.453979i	$0.850004\pi$
$402$			0.112731i			0.00562253i
$403$	−3.82734	+	2.20971i	−0.190653	+	0.110074i
$404$	−6.54316	−	3.77769i	−0.325534	−	0.187947i
$405$	−4.47483	−	7.75064i	−0.222356	−	0.385132i
$406$	−3.08034	−	5.33530i	−0.152875	−	0.264787i
$407$		−	44.4783i		−	2.20471i
$408$	−4.57824	−	2.64325i	−0.226657	−	0.130860i
$409$	0.595970			0.0294688			0.0147344	−	0.999891i	$-0.495310\pi$
$409$	0.595970			0.0294688			0.0147344	+	0.999891i	$0.495310\pi$
$410$		−	27.4112i		−	1.35374i
$411$	−3.41285	+	1.97041i	−0.168343	+	0.0971931i
$412$	3.80248	+	2.19536i	0.187335	+	0.108158i
$413$	22.6720			1.11562
$414$			21.0072i			1.03245i
$415$	45.3500			2.22614
$416$	−17.3100			−0.848694
$417$	−5.67632	+	9.83167i	−0.277971	+	0.481459i
$418$	−48.5242			−2.37339
$419$	−15.2644	−	26.4387i	−0.745713	−	1.29161i	−0.949861	−	0.312673i	$-0.898776\pi$
$419$	−15.2644	−	26.4387i	−0.745713	−	1.29161i	0.204148	−	0.978940i	$-0.434558\pi$
$420$	6.96352	−	4.02039i	0.339785	−	0.196175i
$421$	21.0747	−	12.1675i	1.02712	−	0.593008i	0.110962	−	0.993825i	$-0.464607\pi$
$421$	21.0747	−	12.1675i	1.02712	−	0.593008i	0.916158	+	0.400817i	$0.131274\pi$
$422$	3.11302	−	5.39191i	0.151539	−	0.262474i
$423$	−13.3127	+	7.68609i	−0.647285	+	0.373710i
$424$	17.0983			0.830364
$425$	7.13574	+	12.3595i	0.346134	+	0.599522i
$426$	0.343411	+	0.594804i	0.0166383	+	0.0288184i
$427$	7.31425	+	12.6687i	0.353961	+	0.613079i
$428$		−	10.1728i		−	0.491719i
$429$	21.7315			1.04921
$430$	13.8020	−	23.9057i	0.665590	−	1.15284i
$431$	9.94360	−	5.74094i	0.478967	−	0.276531i	−0.241019	−	0.970520i	$-0.577482\pi$
$431$	9.94360	−	5.74094i	0.478967	−	0.276531i	0.719986	+	0.693989i	$0.244148\pi$
$432$	−3.92525	−	6.79874i	−0.188854	−	0.327104i
$433$	23.9338	+	13.8182i	1.15018	+	0.664059i	0.948932	−	0.315481i	$-0.102166\pi$
$433$	23.9338	+	13.8182i	1.15018	+	0.664059i	0.201252	+	0.979540i	$0.435499\pi$
$434$	−1.87979	+	3.25589i	−0.0902327	+	0.156288i
$435$	5.57217			0.267165
$436$	1.75825	+	3.04538i	0.0842049	+	0.145847i
$437$	−64.1629			−3.06933
$438$	−3.82965	−	2.21105i	−0.182988	−	0.105648i
$439$	27.5135	−	15.8849i	1.31315	−	0.758146i	0.330531	−	0.943795i	$-0.392772\pi$
$439$	27.5135	−	15.8849i	1.31315	−	0.758146i	0.982616	+	0.185649i	$0.0594388\pi$
$440$	−32.6178	+	56.4958i	−1.55499	+	2.69333i
$441$	6.65501			0.316905
$442$	−4.28231	+	7.41718i	−0.203689	+	0.352799i
$443$	−18.1410	−	31.4212i	−0.861906	−	1.49287i	−0.870086	−	0.492899i	$-0.835937\pi$
$443$	−18.1410	−	31.4212i	−0.861906	−	1.49287i	0.00818002	−	0.999967i	$-0.497396\pi$
$444$	2.65525	+	4.59903i	0.126013	+	0.218260i
$445$	9.87961	−	5.70400i	0.468339	−	0.270395i
$446$	7.53786	−	4.35199i	0.356928	−	0.206073i
$447$			0.446110i			0.0211003i
$448$	−22.0597	+	12.7362i	−1.04222	+	0.601729i
$449$	−11.5766			−0.546334			−0.273167	−	0.961967i	$-0.588071\pi$
$449$	−11.5766			−0.546334			−0.273167	+	0.961967i	$0.588071\pi$
$450$			17.6573i			0.832375i
$451$			43.5168i			2.04913i
$452$			6.28378i			0.295564i
$453$	2.54472	+	4.40758i	0.119561	+	0.207086i
$454$	−23.6541	−	13.6567i	−1.11014	−	0.640940i
$455$	−22.4597	−	38.9013i	−1.05293	−	1.82372i
$456$	17.3010	−	9.98873i	0.810193	−	0.467765i
$457$	−5.96503	+	10.3317i	−0.279032	+	0.483298i	−0.971144	−	0.238492i	$-0.923347\pi$
$457$	−5.96503	+	10.3317i	−0.279032	+	0.483298i	0.692112	+	0.721790i	$0.256680\pi$
$458$	8.39720	−	14.5444i	0.392376	−	0.679614i
$459$	8.99732			0.419959
$460$	−12.5079	+	21.6644i	−0.583186	+	1.01011i
$461$	−30.7579	−	17.7581i	−1.43254	−	0.827075i	−0.435222	−	0.900323i	$-0.643330\pi$
$461$	−30.7579	−	17.7581i	−1.43254	−	0.827075i	−0.997314	+	0.0732478i	$0.976664\pi$
$462$	16.0101	−	9.24343i	0.744857	−	0.430043i
$463$	22.1811	+	12.8063i	1.03084	+	0.595157i	0.917226	−	0.398367i	$-0.130423\pi$
$463$	22.1811	+	12.8063i	1.03084	+	0.595157i	0.113617	+	0.993525i	$0.463756\pi$
$464$	−3.04198			−0.141220
$465$	−1.70022	−	2.94487i	−0.0788458	−	0.136565i
$466$	20.8159	+	12.0181i	0.964278	+	0.556726i
$467$	2.35532			0.108991			0.0544956	−	0.998514i	$-0.482645\pi$
$467$	2.35532			0.108991			0.0544956	+	0.998514i	$0.482645\pi$
$468$	6.33665	−	3.65847i	0.292912	−	0.169113i
$469$	−0.320368	+	0.184964i	−0.0147932	+	0.00854086i
$470$	26.5105			1.22284
$471$	0.00432984	+	0.00749950i	0.000199508	+	0.000345559i
$472$	10.9808	−	19.0193i	0.505432	−	0.875435i
$473$	−21.9114	+	37.9517i	−1.00749	+	1.74502i
$474$	9.83044			0.451527
$475$	−53.9313			−2.47454
$476$		−	5.03090i		−	0.230591i
$477$	−10.7031	+	6.17942i	−0.490060	+	0.282936i
$478$	6.45899	−	3.72910i	0.295427	−	0.170565i
$479$	11.6267	+	20.1381i	0.531239	+	0.920133i	0.999335	+	0.0364555i	$0.0116067\pi$
$479$	11.6267	+	20.1381i	0.531239	+	0.920133i	−0.468096	+	0.883677i	$0.655060\pi$
$480$		−	13.3189i		−	0.607920i
$481$	25.6922	−	14.8334i	1.17146	−	0.676345i
$482$			10.8013i			0.491986i
$483$	21.1699	−	12.2225i	0.963266	−	0.556142i
$484$	10.5242	−	18.2284i	0.478371	−	0.828563i
$485$			15.1812i			0.689344i
$486$	15.1867	+	8.76804i	0.688882	+	0.397726i
$487$	−26.0936	+	15.0651i	−1.18241	+	0.682666i	−0.956571	−	0.291498i	$-0.905846\pi$
$487$	−26.0936	+	15.0651i	−1.18241	+	0.682666i	−0.225841	+	0.974164i	$0.572513\pi$
$488$	14.1701			0.641451
$489$	−8.91672	−	5.14807i	−0.403228	−	0.232804i
$490$	−9.93945	−	5.73854i	−0.449019	−	0.259241i
$491$	20.3805	−	35.3001i	0.919760	−	1.59307i	0.119982	−	0.992776i	$-0.461716\pi$
$491$	20.3805	−	35.3001i	0.919760	−	1.59307i	0.799779	−	0.600295i	$-0.204950\pi$
$492$	−2.59785	−	4.49961i	−0.117120	−	0.202858i
$493$	1.74318	−	3.01928i	0.0785089	−	0.135981i
$494$	−16.1827	−	28.0292i	−0.728093	−	1.26109i
$495$		−	47.1532i		−	2.11938i
$496$	0.928190	+	1.60767i	0.0416770	+	0.0721866i
$497$	−1.12690	+	1.95185i	−0.0505485	+	0.0875526i
$498$	−10.7810	+	6.22442i	−0.483109	+	0.278923i
$499$	6.67205	−	3.85211i	0.298682	−	0.172444i	−0.343169	−	0.939274i	$-0.611500\pi$
$499$	6.67205	−	3.85211i	0.298682	−	0.172444i	0.641851	+	0.766830i	$0.278167\pi$
$500$	−3.34202	+	5.78854i	−0.149460	+	0.258872i
$501$	−15.5998	−	9.00658i	−0.696950	−	0.402384i
$502$	5.41046	+	9.37119i	0.241481	+	0.418257i
$503$	21.4843	+	12.4039i	0.957936	+	0.553064i	0.895537	−	0.444987i	$-0.146792\pi$
$503$	21.4843	+	12.4039i	0.957936	+	0.553064i	0.0623986	+	0.998051i	$0.480125\pi$
$504$	10.7317	−	18.5878i	0.478027	−	0.827967i
$505$	−28.1250	−	16.2380i	−1.25154	−	0.722579i
$506$	−28.7575	+	49.8094i	−1.27843	+	2.21430i
$507$	1.48715	+	2.57583i	0.0660468	+	0.114396i
$508$	−8.27423	−	4.77713i	−0.367109	−	0.211951i
$509$	1.00599	−	0.580807i	0.0445896	−	0.0257438i	−0.477539	−	0.878610i	$-0.658471\pi$
$509$	1.00599	−	0.580807i	0.0445896	−	0.0257438i	0.522129	+	0.852866i	$0.325138\pi$
$510$	−5.70700	−	3.29494i	−0.252710	−	0.145902i
$511$		−	14.5111i		−	0.641935i
$512$			17.6812i			0.781405i
$513$	−17.0002	+	29.4453i	−0.750578	+	1.30004i
$514$	−13.8407	+	7.99090i	−0.610485	+	0.352464i
$515$	16.3445	+	9.43650i	0.720224	+	0.415822i
$516$		−	5.23223i		−	0.230336i
$517$	−42.0870			−1.85098
$518$	12.6187	−	21.8562i	0.554433	−	0.960305i
$519$			11.7388i			0.515275i
$520$	−43.5118			−1.90812
$521$	28.4351	−	16.4170i	1.24576	−	0.719241i	0.275501	−	0.961301i	$-0.411156\pi$
$521$	28.4351	−	16.4170i	1.24576	−	0.719241i	0.970261	+	0.242060i	$0.0778229\pi$
$522$	3.73559	−	2.15674i	0.163502	−	0.0943980i
$523$	−10.3549	−	5.97840i	−0.452788	−	0.261417i	0.256219	−	0.966619i	$-0.417523\pi$
$523$	−10.3549	−	5.97840i	−0.452788	−	0.261417i	−0.709007	+	0.705201i	$0.750857\pi$
$524$	3.45151	+	1.99273i	0.150780	+	0.0870529i
$525$	17.7941	−	10.2734i	0.776600	−	0.448370i
$526$	25.9256	−	14.9681i	1.13041	−	0.652642i
$527$	−2.12756			−0.0926781
$528$		−	9.12833i		−	0.397260i
$529$	−26.5256	+	45.9437i	−1.15329	+	1.99755i
$530$	21.3138			0.925812
$531$			15.8741i			0.688879i
$532$	16.4645	+	9.50578i	0.713826	+	0.412128i
$533$	−25.1368	+	14.5127i	−1.08880	+	0.628616i
$534$	−1.56578	+	2.71201i	−0.0677579	+	0.117360i
$535$		−	43.7264i		−	1.89046i
$536$			0.358337i			0.0154778i
$537$	−12.8179	−	7.40041i	−0.553133	−	0.319351i
$538$	−2.56863	+	1.48300i	−0.110741	+	0.0639365i
$539$	15.7794	+	9.11027i	0.679669	+	0.392407i
$540$	6.62806	+	11.4801i	0.285226	+	0.494027i
$541$	−15.0436	+	26.0563i	−0.646774	+	1.12025i	0.337114	+	0.941464i	$0.390549\pi$
$541$	−15.0436	+	26.0563i	−0.646774	+	1.12025i	−0.983889	+	0.178782i	$0.942784\pi$
$542$	17.5319	+	10.1220i	0.753058	+	0.434778i
$543$	−1.07734	+	1.86601i	−0.0462331	+	0.0800781i
$544$	−7.21681	−	4.16663i	−0.309418	−	0.178643i
$545$	7.55762	+	13.0902i	0.323733	+	0.560722i
$546$	10.6786	+	6.16532i	0.457004	+	0.263851i
$547$	−6.78862	+	11.7582i	−0.290260	+	0.502746i	−0.973871	−	0.227101i	$-0.927075\pi$
$547$	−6.78862	+	11.7582i	−0.290260	+	0.502746i	0.683611	+	0.729847i	$0.260409\pi$
$548$	−3.14607	+	1.81638i	−0.134393	+	0.0775920i
$549$	−8.87013	+	5.12117i	−0.378568	+	0.218566i
$550$	−24.1717	+	41.8667i	−1.03069	+	1.78520i
$551$	6.58740	+	11.4097i	0.280633	+	0.486070i
$552$		−	23.6790i		−	1.00784i
$553$	16.1293	+	27.9368i	0.685888	+	1.18799i
$554$	−10.5106	+	18.2049i	−0.446553	+	0.773452i
$555$	11.4133	+	19.7683i	0.484466	+	0.839119i
$556$	−5.23261	+	9.06314i	−0.221912	+	0.384363i
$557$	−34.4407	−	19.8844i	−1.45930	−	0.842528i	−0.460324	−	0.887751i	$-0.652267\pi$
$557$	−34.4407	−	19.8844i	−1.45930	−	0.842528i	−0.998977	+	0.0452228i	$0.985600\pi$
$558$	−2.27966	−	1.31616i	−0.0965055	−	0.0557175i
$559$	−29.2296			−1.23628
$560$	−16.3405	+	9.43420i	−0.690512	+	0.398668i
$561$	9.06019	+	5.23091i	0.382522	+	0.220849i
$562$		−	4.61888i		−	0.194836i
$563$	18.1306	−	31.4032i	0.764114	−	1.32349i	−0.176599	−	0.984283i	$-0.556510\pi$
$563$	18.1306	−	31.4032i	0.764114	−	1.32349i	0.940714	−	0.339202i	$-0.110157\pi$
$564$	4.35176	−	2.51249i	0.183242	−	0.105795i
$565$			27.0100i			1.13632i
$566$	−7.79180	+	4.49860i	−0.327514	+	0.189090i
$567$			8.06179i			0.338563i
$568$	1.09159	+	1.89069i	0.0458022	+	0.0793317i
$569$	37.3238	−	21.5489i	1.56470	−	0.903378i	0.567926	−	0.823079i	$-0.307746\pi$
$569$	37.3238	−	21.5489i	1.56470	−	0.903378i	0.996771	−	0.0802988i	$-0.0255874\pi$
$570$	21.5665	−	12.4514i	0.903321	−	0.521533i
$571$			30.2488i			1.26587i	0.774204	+	0.632936i	$0.218150\pi$
$571$			30.2488i			1.26587i	−0.774204	+	0.632936i	$0.781850\pi$
$572$	20.0328			0.837613
$573$	−16.0969			−0.672458
$574$	−12.3459	+	21.3837i	−0.515307	+	0.892538i
$575$	−31.9620	+	55.3598i	−1.33291	+	2.30866i
$576$	−8.91742	−	15.4454i	−0.371559	−	0.643560i
$577$	32.0241			1.33318			0.666590	−	0.745424i	$-0.267753\pi$
$577$	32.0241			1.33318			0.666590	+	0.745424i	$0.267753\pi$
$578$	12.4428	−	7.18385i	0.517552	−	0.298809i
$579$	−13.6151	+	7.86070i	−0.565826	+	0.326680i
$580$	5.13660			0.213286
$581$	−35.3779	−	20.4255i	−1.46772	−	0.847391i
$582$	−2.08367	−	3.60902i	−0.0863708	−	0.149599i
$583$	−33.8369			−1.40138
$584$	−12.1732	−	7.02821i	−0.503732	−	0.290830i
$585$	27.2373	−	15.7255i	1.12612	−	0.650168i
$586$	9.82575	+	5.67290i	0.405898	+	0.234345i
$587$	−2.59664	+	4.49751i	−0.107175	+	0.185632i	−0.914625	−	0.404304i	$-0.867514\pi$
$587$	−2.59664	+	4.49751i	−0.107175	+	0.185632i	0.807450	+	0.589936i	$0.200847\pi$
$588$	−2.17544			−0.0897138
$589$	4.01998	−	6.96282i	0.165641	−	0.286898i
$590$	13.6881	−	23.7085i	0.563530	−	0.976063i
$591$	4.27389	−	2.46753i	0.175804	−	0.101501i
$592$	−6.23077	−	10.7920i	−0.256083	−	0.443549i
$593$	−16.1061	−	9.29889i	−0.661400	−	0.381860i	0.131410	−	0.991328i	$-0.458050\pi$
$593$	−16.1061	−	9.29889i	−0.661400	−	0.381860i	−0.792810	+	0.609469i	$0.791383\pi$
$594$	15.2388	+	26.3944i	0.625257	+	1.08298i
$595$		−	21.6247i		−	0.886527i
$596$			0.411238i			0.0168450i
$597$			4.80242i			0.196550i
$598$	−38.3621			−1.56874
$599$	38.1423	−	22.0215i	1.55845	−	0.899772i	0.561046	−	0.827785i	$-0.310399\pi$
$599$	38.1423	−	22.0215i	1.55845	−	0.899772i	0.997406	−	0.0719872i	$-0.0229341\pi$
$600$		−	19.9031i		−	0.812539i
$601$	2.29319	−	1.32397i	0.0935412	−	0.0540060i	−0.452500	−	0.891765i	$-0.649468\pi$
$601$	2.29319	−	1.32397i	0.0935412	−	0.0540060i	0.546041	+	0.837759i	$0.316134\pi$
$602$	−21.5341	+	12.4327i	−0.877663	+	0.506719i
$603$	−0.129505	−	0.224310i	−0.00527387	−	0.00913460i
$604$	2.34580	+	4.06304i	0.0954492	+	0.165323i
$605$	45.2368	−	78.3525i	1.83914	−	3.18548i
$606$	8.91482			0.362140
$607$	5.07052	−	8.78239i	0.205806	−	0.356466i	−0.744583	−	0.667530i	$-0.767352\pi$
$607$	5.07052	−	8.78239i	0.205806	−	0.356466i	0.950389	+	0.311063i	$0.100685\pi$
$608$	27.2720	−	15.7455i	1.10603	−	0.638564i
$609$	−4.34690	−	2.50968i	−0.176145	−	0.101698i
$610$	17.6637			0.715183
$611$	−14.0359	−	24.3109i	−0.567831	−	0.983512i
$612$	3.52246			0.142387
$613$	9.33046	−	16.1608i	0.376854	−	0.652730i	−0.613749	−	0.789501i	$-0.710339\pi$
$613$	9.33046	−	16.1608i	0.376854	−	0.652730i	0.990603	+	0.136772i	$0.0436726\pi$
$614$	−26.6264	−	15.3727i	−1.07455	−	0.620394i
$615$	−11.1665	−	19.3410i	−0.450278	−	0.779904i
$616$	50.8909	−	29.3819i	2.05045	−	1.18383i
$617$	−15.4603	+	26.7780i	−0.622407	+	1.07804i	0.366630	+	0.930367i	$0.380512\pi$
$617$	−15.4603	+	26.7780i	−0.622407	+	1.07804i	−0.989036	+	0.147673i	$0.952822\pi$
$618$	−5.18075			−0.208400
$619$		−	25.6603i		−	1.03137i	−0.856777	−	0.515687i	$-0.827537\pi$
$619$		−	25.6603i		−	1.03137i	0.856777	−	0.515687i	$-0.172463\pi$
$620$	−1.56731	−	2.71467i	−0.0629449	−	0.109024i
$621$	20.1501	+	34.9010i	0.808596	+	1.40053i
$622$	−1.62759	−	2.81907i	−0.0652605	−	0.113035i
$623$	−10.2762			−0.411708
$624$	5.27283	−	3.04427i	0.211082	−	0.121868i
$625$	3.96003	−	6.85897i	0.158401	−	0.274359i
$626$	2.93335	−	1.69357i	0.117240	−	0.0676888i
$627$	−34.2381	+	19.7674i	−1.36734	+	0.789432i
$628$	0.00399138	+	0.00691327i	0.000159273	+	0.000275869i
$629$	14.2819			0.569458
$630$	13.3775	−	23.1706i	0.532974	−	0.923138i
$631$	−14.2050			−0.565491			−0.282746	−	0.959195i	$-0.591245\pi$
$631$	−14.2050			−0.565491			−0.282746	+	0.959195i	$0.591245\pi$
$632$	31.2478			1.24297
$633$		−	5.07262i		−	0.201619i
$634$	10.9478			0.434794
$635$	−35.5657	−	20.5339i	−1.41138	−	0.814862i
$636$	3.49871	−	2.01998i	0.138733	−	0.0800974i
$637$			12.1530i			0.481519i
$638$	11.8097			0.467552
$639$	−1.36662	−	0.789017i	−0.0540626	−	0.0312130i
$640$			0.698961i			0.0276289i
$641$	7.88210	+	13.6522i	0.311324	+	0.539229i	0.978649	−	0.205537i	$-0.0658941\pi$
$641$	7.88210	+	13.6522i	0.311324	+	0.539229i	−0.667325	+	0.744767i	$0.732561\pi$
$642$	6.00157	+	10.3950i	0.236863	+	0.410259i
$643$	−30.2562	−	17.4684i	−1.19319	−	0.688888i	−0.234160	−	0.972198i	$-0.575234\pi$
$643$	−30.2562	−	17.4684i	−1.19319	−	0.688888i	−0.959028	+	0.283310i	$0.908567\pi$
$644$	19.5151	−	11.2671i	0.769003	−	0.443984i
$645$		−	22.4901i		−	0.885547i
$646$		−	15.5810i		−	0.613028i
$647$	15.1391	−	26.2218i	0.595181	−	1.03088i	−0.398340	−	0.917238i	$-0.630414\pi$
$647$	15.1391	−	26.2218i	0.595181	−	1.03088i	0.993521	−	0.113646i	$-0.0362529\pi$
$648$	6.76294	+	3.90458i	0.265673	+	0.153387i
$649$	−21.7306	+	37.6386i	−0.853003	+	1.47744i
$650$	−32.2448			−1.26475
$651$			3.06309i			0.120052i
$652$	−8.21970	−	4.74565i	−0.321908	−	0.185854i
$653$	−4.77070			−0.186692			−0.0933460	−	0.995634i	$-0.529756\pi$
$653$	−4.77070			−0.186692			−0.0933460	+	0.995634i	$0.529756\pi$
$654$	−3.59333	−	2.07461i	−0.140510	−	0.0811237i
$655$	14.8359	+	8.56551i	0.579686	+	0.334682i
$656$	6.09608	+	10.5587i	0.238012	+	0.412248i
$657$	10.1602			0.396386
$658$	−20.6811	−	11.9402i	−0.806233	−	0.465479i
$659$		−	6.18785i		−	0.241044i	−0.992711	−	0.120522i	$-0.961543\pi$
$659$		−	6.18785i		−	0.241044i	0.992711	−	0.120522i	$-0.0384569\pi$
$660$			15.4138i			0.599983i
$661$	−3.41393			−0.132787			−0.0663933	−	0.997794i	$-0.521149\pi$
$661$	−3.41393			−0.132787			−0.0663933	+	0.997794i	$0.521149\pi$
$662$	−27.4204			−1.06572
$663$			6.97797i			0.271002i
$664$	−34.2694	+	19.7854i	−1.32991	+	0.767823i
$665$	70.7706	+	40.8594i	2.74437	+	1.58446i
$666$	15.3029	+	8.83514i	0.592976	+	0.342355i
$667$	15.6159			0.604649
$668$	−14.3804	−	8.30254i	−0.556395	−	0.321235i
$669$	3.54575	−	6.14142i	0.137087	−	0.237441i
$670$			0.446684i			0.0172569i
$671$	−28.0422			−1.08256
$672$	−5.99876	+	10.3902i	−0.231407	+	0.400809i
$673$	7.50295	+	12.9955i	0.289217	+	0.500939i	0.973623	−	0.228162i	$-0.0732716\pi$
$673$	7.50295	+	12.9955i	0.289217	+	0.500939i	−0.684406	+	0.729101i	$0.739938\pi$
$674$	−2.86232	−	1.65256i	−0.110253	−	0.0636543i
$675$	16.9369	+	29.3356i	0.651903	+	1.12913i
$676$	1.37090	+	2.37448i	0.0527271	+	0.0913260i
$677$		−	20.0389i		−	0.770157i	−0.922884	−	0.385078i	$-0.874174\pi$
$677$		−	20.0389i		−	0.770157i	0.922884	−	0.385078i	$-0.125826\pi$
$678$	−3.70721	−	6.42107i	−0.142374	−	0.246600i
$679$	6.83757	−	11.8430i	0.262402	−	0.454493i
$680$	−18.1407	−	10.4735i	−0.695665	−	0.401642i
$681$	−22.2534			−0.852751
$682$	−3.60347	−	6.24140i	−0.137984	−	0.238995i
$683$	24.6272	+	42.6556i	0.942335	+	1.63217i	0.761002	+	0.648750i	$0.224708\pi$
$683$	24.6272	+	42.6556i	0.942335	+	1.63217i	0.181333	+	0.983422i	$0.441959\pi$
$684$	−6.65561	+	11.5278i	−0.254483	+	0.440778i
$685$	−13.5230	+	7.80750i	−0.516687	+	0.298309i
$686$	−6.87234	−	11.9032i	−0.262387	−	0.454468i
$687$		−	13.6831i		−	0.522044i
$688$			12.2779i			0.468090i
$689$	−11.2845	−	19.5453i	−0.429905	−	0.744618i
$690$		−	29.5170i		−	1.12369i
$691$	19.4923	−	11.2539i	0.741523	−	0.428119i	−0.0810995	−	0.996706i	$-0.525843\pi$
$691$	19.4923	−	11.2539i	0.741523	−	0.428119i	0.822623	+	0.568587i	$0.192510\pi$
$692$			10.8212i			0.411359i
$693$	−21.2376	+	36.7847i	−0.806751	+	1.39733i
$694$	−11.7795	+	20.4026i	−0.447142	+	0.774473i
$695$	−22.4917	+	38.9568i	−0.853159	+	1.47772i
$696$	−4.21069	+	2.43104i	−0.159606	+	0.0921485i
$697$	−13.9732			−0.529273
$698$	−7.31649	−	18.9569i	−0.276933	−	0.717529i
$699$	19.5833			0.740707
$700$	16.4032	−	9.47038i	0.619982	−	0.357947i
$701$	−12.7563	+	22.0945i	−0.481798	+	0.834498i	−0.999782	−	0.0208919i	$-0.993349\pi$
$701$	−12.7563	+	22.0945i	−0.481798	+	0.834498i	0.517984	+	0.855390i	$0.326683\pi$
$702$	−10.1642	+	17.6049i	−0.383623	+	0.664455i
$703$	−26.9854	+	46.7401i	−1.01777	+	1.76284i
$704$		−	48.8294i		−	1.84033i
$705$	18.7055	−	10.7996i	0.704490	−	0.406738i
$706$			9.63329i			0.362554i
$707$	14.6270	+	25.3347i	0.550106	+	0.952811i
$708$		−	5.18907i		−	0.195017i
$709$		−	29.9392i		−	1.12439i	−0.827005	−	0.562195i	$-0.809957\pi$
$709$		−	29.9392i		−	1.12439i	0.827005	−	0.562195i	$-0.190043\pi$
$710$	1.36072	+	2.35684i	0.0510670	+	0.0884506i
$711$	−19.5603	+	11.2932i	−0.733570	+	0.423527i
$712$	−4.97711	+	8.62061i	−0.186525	+	0.323071i
$713$	−4.76482	−	8.25292i	−0.178444	−	0.309074i
$714$	2.96805	+	5.14082i	0.111077	+	0.192390i
$715$	86.1085			3.22027
$716$	−11.8159	−	6.82193i	−0.441582	−	0.254947i
$717$	3.03826	−	5.26242i	0.113466	−	0.196528i
$718$	13.0449	+	22.5944i	0.486831	+	0.843217i
$719$			6.14205i			0.229060i	0.993420	+	0.114530i	$0.0365362\pi$
$719$			6.14205i			0.229060i	−0.993420	+	0.114530i	$0.963464\pi$
$720$	−6.60548	−	11.4410i	−0.246172	−	0.426382i
$721$	−8.50032	−	14.7230i	−0.316569	−	0.548313i
$722$	33.0942	+	19.1069i	1.23164	+	0.711087i
$723$	4.40014	+	7.62127i	0.163643	+	0.283438i
$724$	−0.993125	+	1.72014i	−0.0369092	+	0.0639286i
$725$	13.1257			0.487478
$726$			24.8355i			0.921733i
$727$	12.6209	−	21.8601i	0.468084	−	0.810745i	−0.531251	−	0.847215i	$-0.678278\pi$
$727$	12.6209	−	21.8601i	0.468084	−	0.810745i	0.999335	+	0.0364693i	$0.0116111\pi$
$728$	33.9440	+	19.5976i	1.25805	+	0.726334i
$729$	6.64122			0.245971
$730$	−15.1745	−	8.76101i	−0.561634	−	0.324259i
$731$	−12.1862	−	7.03573i	−0.450724	−	0.260226i
$732$	2.89954	−	1.67405i	0.107170	−	0.0618747i
$733$			2.33995i			0.0864280i	0.999066	+	0.0432140i	$0.0137597\pi$
$733$			2.33995i			0.0864280i	−0.999066	+	0.0432140i	$0.986240\pi$
$734$	−11.4997			−0.424461
$735$	−9.35088			−0.344912
$736$		−	37.3258i		−	1.37585i
$737$		−	0.709137i		−	0.0261214i
$738$	−14.9721	−	8.64414i	−0.551130	−	0.318195i
$739$	−15.4369			−0.567854			−0.283927	−	0.958846i	$-0.591637\pi$
$739$	−15.4369			−0.567854			−0.283927	+	0.958846i	$0.591637\pi$
$740$	10.5211	+	18.2231i	0.386763	+	0.669893i
$741$	−22.8366	−	13.1847i	−0.838923	−	0.484353i
$742$	−16.6271	−	9.59965i	−0.610399	−	0.352414i
$743$	26.3773			0.967691			0.483846	−	0.875153i	$-0.339240\pi$
$743$	26.3773			0.967691			0.483846	+	0.875153i	$0.339240\pi$
$744$	2.56959	+	1.48355i	0.0942057	+	0.0543897i
$745$			1.76766i			0.0647619i
$746$	−14.8871			−0.545056
$747$	14.3012	−	24.7704i	0.523252	−	0.906300i
$748$	8.35197	+	4.82201i	0.305378	+	0.176310i
$749$	−19.6942	+	34.1113i	−0.719610	+	1.24640i
$750$		−	7.88669i		−	0.287981i
$751$			21.1875i			0.773142i	0.922260	+	0.386571i	$0.126341\pi$
$751$			21.1875i			0.773142i	−0.922260	+	0.386571i	$0.873659\pi$
$752$	−10.2118	+	5.89578i	−0.372385	+	0.214997i
$753$	7.63511	+	4.40813i	0.278239	+	0.160641i
$754$	3.93852	+	6.82171i	0.143432	+	0.248432i
$755$	10.0831	+	17.4645i	0.366962	+	0.635597i
$756$		−	11.9410i		−	0.434291i
$757$	25.5141	+	14.7306i	0.927325	+	0.535391i	0.885965	−	0.463753i	$-0.153497\pi$
$757$	25.5141	+	14.7306i	0.927325	+	0.535391i	0.0413605	+	0.999144i	$0.486831\pi$
$758$	10.6629			0.387292
$759$			46.8599i			1.70091i
$760$	68.5530	−	39.5791i	2.48668	−	1.43568i
$761$	10.6909	+	6.17239i	0.387544	+	0.223749i	0.681096	−	0.732194i	$-0.261504\pi$
$761$	10.6909	+	6.17239i	0.387544	+	0.223749i	−0.293551	+	0.955943i	$0.594837\pi$
$762$	11.2733			0.408390
$763$		−	13.6157i		−	0.492921i
$764$	−14.8386			−0.536843
$765$	15.1408			0.547418
$766$	−9.07446	+	15.7174i	−0.327873	+	0.567894i
$767$	−28.9884			−1.04671
$768$	7.04063	+	12.1947i	0.254057	+	0.440040i
$769$	−13.3421	+	7.70304i	−0.481127	+	0.277779i	−0.720886	−	0.693054i	$-0.756265\pi$
$769$	−13.3421	+	7.70304i	−0.481127	+	0.277779i	0.239759	+	0.970832i	$0.422932\pi$
$770$	63.4380	−	36.6260i	2.28615	−	1.31991i
$771$	−6.51053	+	11.2766i	−0.234471	+	0.406116i
$772$	−12.5509	+	7.24624i	−0.451715	+	0.260798i
$773$	15.2114			0.547118			0.273559	−	0.961855i	$-0.411799\pi$
$773$	15.2114			0.547118			0.273559	+	0.961855i	$0.411799\pi$
$774$	−8.70493	−	15.0774i	−0.312892	−	0.541945i
$775$	−4.00501	−	6.93689i	−0.143864	−	0.249180i
$776$	−6.62331	−	11.4719i	−0.237763	−	0.411818i
$777$		−	20.5619i		−	0.737656i
$778$	27.7388			0.994485
$779$	26.4020	−	45.7297i	0.945951	−	1.63844i
$780$	−8.90355	+	5.14047i	−0.318798	+	0.184058i
$781$	−2.16022	−	3.74162i	−0.0772989	−	0.133886i
$782$	−15.9937	−	9.23399i	−0.571935	−	0.330207i
$783$	4.13749	−	7.16635i	0.147862	−	0.256104i
$784$	5.10487			0.182317
$785$	0.0171564	+	0.0297158i	0.000612340	+	0.00106060i
$786$	−4.70256			−0.167735
$787$	−8.45682	−	4.88255i	−0.301453	−	0.174044i	0.341642	−	0.939830i	$-0.389017\pi$
$787$	−8.45682	−	4.88255i	−0.301453	−	0.174044i	−0.643095	+	0.765786i	$0.722350\pi$
$788$	3.93981	−	2.27465i	0.140350	−	0.0810310i
$789$	12.1952	−	21.1227i	0.434160	−	0.751987i
$790$	38.9519			1.38585
$791$	12.1652	−	21.0708i	0.432545	−	0.749190i
$792$	20.5721	+	35.6320i	0.730999	+	1.26613i
$793$	−9.35199	−	16.1981i	−0.332099	−	0.575212i
$794$	−24.2492	+	14.0003i	−0.860571	+	0.496851i
$795$	15.0388	−	8.68263i	0.533370	−	0.307941i
$796$			4.42702i			0.156911i
$797$	−25.5117	+	14.7292i	−0.903670	+	0.521734i	−0.878389	−	0.477946i	$-0.841381\pi$
$797$	−25.5117	+	14.7292i	−0.903670	+	0.521734i	−0.0252812	+	0.999680i	$0.508048\pi$
$798$	−22.4323			−0.794095
$799$		−	13.5141i		−	0.478094i
$800$		−	31.3737i		−	1.10923i
$801$		−	7.19505i		−	0.254224i
$802$	−9.88816	−	17.1268i	−0.349163	−	0.604768i
$803$	24.0904	+	13.9086i	0.850132	+	0.490824i
$804$	0.0423338	+	0.0733242i	0.00149300	+	0.00258595i
$805$	83.8832	−	48.4300i	2.95650	−	1.70693i
$806$	2.40349	−	4.16297i	0.0846595	−	0.146635i
$807$	−1.20826	+	2.09277i	−0.0425328	+	0.0736690i
$808$	28.3374			0.996905
$809$	23.9570	−	41.4947i	0.842282	−	1.45888i	−0.0456786	−	0.998956i	$-0.514545\pi$
$809$	23.9570	−	41.4947i	0.842282	−	1.45888i	0.887961	−	0.459919i	$-0.152122\pi$
$810$	8.43033	+	4.86725i	0.296212	+	0.171018i
$811$	26.3791	−	15.2300i	0.926297	−	0.534798i	0.0406584	−	0.999173i	$-0.487054\pi$
$811$	26.3791	−	15.2300i	0.926297	−	0.534798i	0.885639	+	0.464375i	$0.153721\pi$
$812$	−4.00711	−	2.31350i	−0.140622	−	0.0811881i
$813$	16.4937			0.578459
$814$	24.1894	+	41.8973i	0.847839	+	1.46850i
$815$	−35.3314	−	20.3986i	−1.23760	−	0.714531i
$816$	2.93110			0.102609
$817$	46.0513	−	26.5877i	1.61113	−	0.930186i
$818$	−0.561387	+	0.324117i	−0.0196284	+	0.0113325i
$819$	−28.3308			−0.989957
$820$	−10.2937	−	17.8291i	−0.359470	−	0.622620i
$821$	−16.3735	+	28.3598i	−0.571440	+	0.989764i	0.424978	+	0.905204i	$0.360282\pi$
$821$	−16.3735	+	28.3598i	−0.571440	+	0.989764i	−0.996418	+	0.0845600i	$0.973052\pi$
$822$	2.14320	−	3.71214i	0.0747528	−	0.129476i
$823$	−25.1632			−0.877134			−0.438567	−	0.898698i	$-0.644514\pi$
$823$	−25.1632			−0.877134			−0.438567	+	0.898698i	$0.644514\pi$
$824$	−16.4679			−0.573687
$825$			39.3875i			1.37130i
$826$	−21.3564	+	12.3301i	−0.743085	+	0.429020i
$827$	5.35162	−	3.08976i	0.186094	−	0.107441i	−0.404059	−	0.914733i	$-0.632401\pi$
$827$	5.35162	−	3.08976i	0.186094	−	0.107441i	0.590153	+	0.807292i	$0.299068\pi$
$828$	7.88878	+	13.6638i	0.274154	+	0.474849i
$829$		−	25.8736i		−	0.898627i	−0.893374	−	0.449313i	$-0.851669\pi$
$829$		−	25.8736i		−	0.898627i	0.893374	−	0.449313i	$-0.148331\pi$
$830$	−42.7184	+	24.6635i	−1.48278	+	0.856082i
$831$			17.1269i			0.594125i
$832$	28.2055	−	16.2845i	0.977851	−	0.564563i
$833$	−2.92530	+	5.06676i	−0.101356	+	0.175553i
$834$		−	12.3482i		−	0.427584i
$835$	−61.8125	−	35.6874i	−2.13911	−	1.23501i
$836$	−31.5617	+	18.2222i	−1.09158	+	0.630227i
$837$	−5.04984			−0.174548
$838$	28.7572	+	16.6030i	0.993401	+	0.573540i
$839$	8.78988	+	5.07484i	0.303460	+	0.175203i	0.643996	−	0.765029i	$-0.277275\pi$
$839$	8.78988	+	5.07484i	0.303460	+	0.175203i	−0.340536	+	0.940231i	$0.610609\pi$
$840$	−15.0789	+	26.1175i	−0.520273	+	0.901139i
$841$	12.8968	+	22.3379i	0.444716	+	0.770271i
$842$	−13.2345	+	22.9229i	−0.456092	+	0.789975i
$843$	−1.88160	−	3.25903i	−0.0648058	−	0.112247i
$844$		−	4.67610i		−	0.160958i
$845$	5.89266	+	10.2064i	0.202714	+	0.351111i
$846$	8.36012	−	14.4802i	0.287427	−	0.497838i
$847$	−70.5793	+	40.7490i	−2.42513	+	1.40015i
$848$	−8.21002	+	4.74006i	−0.281933	+	0.162774i
$849$	−3.66520	+	6.34831i	−0.125789	+	0.217873i
$850$	−13.4433	−	7.76151i	−0.461103	−	0.266218i
$851$	31.9854	+	55.4003i	1.09644	+	1.89910i
$852$	0.446731	+	0.257920i	0.0153048	+	0.00883620i
$853$	15.3572	−	26.5995i	0.525821	−	0.910749i	−0.473726	−	0.880672i	$-0.657091\pi$
$853$	15.3572	−	26.5995i	0.525821	−	0.910749i	0.999548	−	0.0300771i	$-0.00957527\pi$
$854$	−13.7796	−	7.95567i	−0.471529	−	0.272238i
$855$	−28.6083	+	49.5510i	−0.978383	+	1.69461i
$856$	19.0771	+	33.0424i	0.652040	+	1.12937i
$857$	27.0503	+	15.6175i	0.924019	+	0.533483i	0.884915	−	0.465752i	$-0.154216\pi$
$857$	27.0503	+	15.6175i	0.924019	+	0.533483i	0.0391041	+	0.999235i	$0.487550\pi$
$858$	−20.4705	+	11.8186i	−0.698851	+	0.403482i
$859$	24.1806	+	13.9607i	0.825031	+	0.476332i	0.852148	−	0.523300i	$-0.175299\pi$
$859$	24.1806	+	13.9607i	0.825031	+	0.476332i	−0.0271171	+	0.999632i	$0.508633\pi$
$860$		−	20.7321i		−	0.706958i
$861$			20.1174i			0.685601i
$862$	−6.24440	+	10.8156i	−0.212685	+	0.368381i
$863$	27.5534	−	15.9080i	0.937930	−	0.541514i	0.0486192	−	0.998817i	$-0.484518\pi$
$863$	27.5534	−	15.9080i	0.937930	−	0.541514i	0.889311	+	0.457303i	$0.151185\pi$
$864$	−17.1293	−	9.88962i	−0.582752	−	0.336452i
$865$			46.5135i			1.58150i
$866$	−30.0599			−1.02148
$867$	5.85299	−	10.1377i	0.198778	−	0.344294i
$868$			2.82365i			0.0958409i
$869$	−61.8384			−2.09772
$870$	−5.24883	+	3.03041i	−0.177952	+	0.102741i
$871$	0.409622	−	0.236495i	0.0138795	−	0.00801333i
$872$	−11.4220	−	6.59452i	−0.386799	−	0.223319i
$873$	8.29205	+	4.78742i	0.280643	+	0.162030i
$874$	60.4396	−	34.8948i	2.04440	−	1.18034i
$875$	22.4129	−	12.9401i	0.757695	−	0.437455i
$876$	−3.32124			−0.112214
$877$			47.4611i			1.60265i	0.598231	+	0.801324i	$0.295871\pi$
$877$			47.4611i			1.60265i	−0.598231	+	0.801324i	$0.704129\pi$
$878$	−17.2779	+	29.9263i	−0.583103	+	1.00996i
$879$	9.24391			0.311789
$880$		−	36.1699i		−	1.21929i
$881$	16.1547	+	9.32690i	0.544264	+	0.314231i	0.746805	−	0.665043i	$-0.231587\pi$
$881$	16.1547	+	9.32690i	0.544264	+	0.314231i	−0.202541	+	0.979274i	$0.564920\pi$
$882$	−6.26883	+	3.61931i	−0.211083	+	0.121869i
$883$	−4.41472	+	7.64652i	−0.148567	+	0.257326i	−0.930698	−	0.365788i	$-0.880799\pi$
$883$	−4.41472	+	7.64652i	−0.148567	+	0.257326i	0.782131	+	0.623114i	$0.214133\pi$
$884$			6.43251i			0.216349i
$885$		−	22.3046i		−	0.749760i
$886$	34.1767	+	19.7319i	1.14819	+	0.662907i
$887$	−8.22678	+	4.74973i	−0.276228	+	0.159480i	−0.631715	−	0.775201i	$-0.717649\pi$
$887$	−8.22678	+	4.74973i	−0.276228	+	0.159480i	0.355487	+	0.934681i	$0.384315\pi$
$888$	−17.2492	−	9.95882i	−0.578845	−	0.334196i
$889$	18.4968	+	32.0373i	0.620362	+	1.07450i
$890$	−6.20421	+	10.7460i	−0.207966	+	0.360207i
$891$	−13.3836	−	7.72705i	−0.448369	−	0.258866i
$892$	3.26858	−	5.66135i	0.109440	−	0.189556i
$893$	44.2271	+	25.5346i	1.48000	+	0.854481i
$894$	−0.242616	−	0.420223i	−0.00811429	−	0.0140544i
$895$	−50.7893	−	29.3232i	−1.69770	−	0.980167i
$896$	0.314809	−	0.545266i	0.0105170	−	0.0182161i
$897$	−27.0679	+	15.6276i	−0.903769	+	0.521792i
$898$	10.9048	−	6.29591i	0.363899	−	0.210097i
$899$	−0.978378	+	1.69460i	−0.0326307	+	0.0565181i
$900$	6.63082	+	11.4849i	0.221027	+	0.382831i
$901$		−	10.8650i		−	0.361965i
$902$	−23.6665	−	40.9916i	−0.788009	−	1.36487i
$903$	−10.1295	+	17.5447i	−0.337087	+	0.583852i
$904$	−11.7840	−	20.4105i	−0.391931	−	0.678844i
$905$	−4.26883	+	7.39382i	−0.141901	+	0.245779i
$906$	−4.79410	−	2.76788i	−0.159273	−	0.0919565i
$907$	27.4142	+	15.8276i	0.910273	+	0.525546i	0.880519	−	0.474011i	$-0.157194\pi$
$907$	27.4142	+	15.8276i	0.910273	+	0.525546i	0.0297541	+	0.999557i	$0.490528\pi$
$908$	−20.5138			−0.680776
$909$	−17.7385	+	10.2413i	−0.588348	+	0.339683i
$910$	42.3128	+	24.4293i	1.40266	+	0.809823i
$911$			30.6022i			1.01390i	0.861976	+	0.506949i	$0.169227\pi$
$911$			30.6022i			1.01390i	−0.861976	+	0.506949i	$0.830773\pi$
$912$	−5.53824	+	9.59252i	−0.183390	+	0.317640i
$913$	67.8179	−	39.1547i	2.24445	−	1.29583i
$914$		−	12.9763i		−	0.429216i
$915$	12.4633	−	7.19570i	0.412025	−	0.237882i
$916$		−	12.6135i		−	0.416763i
$917$	−7.71574	−	13.3641i	−0.254796	−	0.441320i
$918$	−8.47522	+	4.89317i	−0.279724	+	0.161499i
$919$	−2.29184	+	1.32319i	−0.0756008	+	0.0436481i	−0.537324	−	0.843376i	$-0.680565\pi$
$919$	−2.29184	+	1.32319i	−0.0756008	+	0.0436481i	0.461723	+	0.887024i	$0.347231\pi$
$920$		−	93.8249i		−	3.09332i
$921$	−25.0497			−0.825415
$922$	38.6307			1.27223
$923$	1.44086	−	2.49564i	0.0474264	−	0.0821449i
$924$	6.94233	−	12.0245i	0.228386	−	0.395576i
$925$	26.8849	+	46.5660i	0.883971	+	1.53108i
$926$	−27.8586			−0.915491
$927$	10.3085	−	5.95162i	0.338576	−	0.195477i
$928$	−6.63742	+	3.83212i	−0.217884	+	0.125795i
$929$	−24.5097			−0.804138			−0.402069	−	0.915609i	$-0.631709\pi$
$929$	−24.5097			−0.804138			−0.402069	+	0.915609i	$0.631709\pi$
$930$	3.20312	+	1.84932i	0.105034	+	0.0606416i
$931$	−11.0546	−	19.1471i	−0.362299	−	0.627520i
$932$	18.0525			0.591328
$933$	−2.29682	−	1.32607i	−0.0751945	−	0.0434136i
$934$	−2.21865	+	1.28094i	−0.0725963	+	0.0419135i
$935$	35.8999	+	20.7268i	1.17405	+	0.677839i
$936$	−13.7215	+	23.7663i	−0.448501	+	0.776827i
$937$	−6.40757			−0.209326			−0.104663	−	0.994508i	$-0.533376\pi$
$937$	−6.40757			−0.209326			−0.104663	+	0.994508i	$0.533376\pi$
$938$	0.201185	−	0.348462i	0.00656892	−	0.0113777i
$939$	1.37983	−	2.38993i	0.0450289	−	0.0779924i
$940$	17.2433	−	9.95543i	0.562415	−	0.324710i
$941$	10.1228	+	17.5332i	0.329993	+	0.571565i	0.982510	−	0.186209i	$-0.0596202\pi$
$941$	10.1228	+	17.5332i	0.329993	+	0.571565i	−0.652517	+	0.757774i	$0.726287\pi$
$942$	−0.00815717	−	0.00470954i	−0.000265775	−	0.000153445i
$943$	−31.2939	−	54.2027i	−1.01907	−	1.76508i
$944$			12.1766i			0.396314i
$945$		−	51.3270i		−	1.66967i
$946$		−	47.6659i		−	1.54975i
$947$	−16.6820			−0.542092			−0.271046	−	0.962566i	$-0.587370\pi$
$947$	−16.6820			−0.542092			−0.271046	+	0.962566i	$0.587370\pi$
$948$	6.39404	−	3.69160i	0.207669	−	0.119898i
$949$			18.5539i			0.602286i
$950$	50.8018	−	29.3304i	1.64823	−	0.951604i
$951$	7.72466	−	4.45984i	0.250489	−	0.144620i
$952$	9.43449	+	16.3410i	0.305774	+	0.529615i
$953$	−14.1074	−	24.4347i	−0.456983	−	0.791517i	0.541817	−	0.840496i	$-0.317736\pi$
$953$	−14.1074	−	24.4347i	−0.456983	−	0.791517i	−0.998800	+	0.0489794i	$0.984403\pi$
$954$	6.72133	−	11.6417i	0.217611	−	0.376913i
$955$	−63.7820			−2.06394
$956$	2.80076	−	4.85106i	0.0905830	−	0.156894i
$957$	8.33282	−	4.81096i	0.269362	−	0.155516i
$958$	−21.9041	−	12.6463i	−0.707690	−	0.408585i
$959$	14.0659			0.454210
$960$	12.5298	+	21.7022i	0.404396	+	0.700435i
$961$	−29.8059			−0.961480
$962$	−16.1342	+	27.9453i	−0.520188	+	0.900992i
$963$	−23.8835	−	13.7892i	−0.769635	−	0.444349i
$964$	4.05619	+	7.02552i	0.130641	+	0.226277i
$965$	−53.9483	+	31.1471i	−1.73666	+	1.00266i
$966$	−13.2943	+	23.0264i	−0.427738	+	0.740864i
$967$	27.4434			0.882520			0.441260	−	0.897379i	$-0.354532\pi$
$967$	27.4434			0.882520			0.441260	+	0.897379i	$0.354532\pi$
$968$			78.9442i			2.53736i
$969$	−6.34728	−	10.9938i	−0.203904	−	0.353172i
$970$	−8.25628	−	14.3003i	−0.265093	−	0.459155i
$971$	−22.8859	−	39.6396i	−0.734445	−	1.27210i	−0.954966	−	0.296714i	$-0.904109\pi$
$971$	−22.8859	−	39.6396i	−0.734445	−	1.27210i	0.220522	−	0.975382i	$-0.429224\pi$
$972$	13.1706			0.422446
$973$	35.0920	−	20.2604i	1.12500	−	0.649517i
$974$	16.3863	−	28.3818i	0.525050	−	0.909413i
$975$	−22.7516	+	13.1356i	−0.728633	+	0.420676i
$976$	−6.80402	+	3.92830i	−0.217791	+	0.125742i
$977$	11.1452	+	19.3041i	0.356567	+	0.617592i	0.987385	−	0.158339i	$-0.0506139\pi$
$977$	11.1452	+	19.3041i	0.356567	+	0.617592i	−0.630818	+	0.775931i	$0.717281\pi$
$978$	11.1991			0.358106
$979$	9.84954	−	17.0599i	0.314793	−	0.545237i
$980$	−8.61993			−0.275353
$981$	9.53322			0.304372
$982$			44.3356i			1.41481i
$983$	−47.8597			−1.52649			−0.763244	−	0.646111i	$-0.776394\pi$
$983$	−47.8597			−1.52649			−0.763244	+	0.646111i	$0.776394\pi$
$984$	16.8763	+	9.74353i	0.537996	+	0.310612i
$985$	16.9348	−	9.77729i	0.539587	−	0.311530i
$986$			3.79210i			0.120765i
$987$	−19.4564			−0.619305
$988$	−21.0515	−	12.1541i	−0.669737	−	0.386673i
$989$		−	63.0280i		−	2.00417i
$990$	25.6442	+	44.4170i	0.815025	+	1.41167i
$991$	14.2102	+	24.6128i	0.451402	+	0.781851i	0.998473	−	0.0552348i	$-0.0175907\pi$
$991$	14.2102	+	24.6128i	0.451402	+	0.781851i	−0.547071	+	0.837086i	$0.684257\pi$
$992$	4.05051	+	2.33856i	0.128604	+	0.0742495i
$993$	−19.3475	+	11.1703i	−0.613975	+	0.354479i
$994$		−	2.45145i		−	0.0777554i
$995$			19.0290i			0.603259i
$996$	−4.67488	+	8.09713i	−0.148129	+	0.256567i
$997$	−34.5140	−	19.9267i	−1.09307	−	0.631084i	−0.158677	−	0.987331i	$-0.550723\pi$
$997$	−34.5140	−	19.9267i	−1.09307	−	0.631084i	−0.934392	+	0.356247i	$0.884056\pi$
$998$	−4.18992	+	7.25716i	−0.132630	+	0.229721i
$999$	33.8987			1.07251

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.e.a.123.11	✓	58
349.227	even	6	inner	349.2.e.a.227.11	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.e.a.123.11	✓	58	1.1	even	1	trivial
349.2.e.a.227.11	yes	58	349.227	even	6	inner

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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.941972 + 0.543848i) q^{2} +(-0.443096 + 0.767465i) q^{3} +(-0.408460 + 0.707473i) q^{4} +(-1.75571 + 3.04098i) q^{5} -0.963907i q^{6} +(2.73929 - 1.58153i) q^{7} -3.06395i q^{8} +(1.10733 + 1.91796i) q^{9} +O(q^{10})\)	\(q+(-0.941972 + 0.543848i) q^{2} +(-0.443096 + 0.767465i) q^{3} +(-0.408460 + 0.707473i) q^{4} +(-1.75571 + 3.04098i) q^{5} -0.963907i q^{6} +(2.73929 - 1.58153i) q^{7} -3.06395i q^{8} +(1.10733 + 1.91796i) q^{9} -3.81936i q^{10} +6.06346i q^{11} +(-0.361974 - 0.626957i) q^{12} +(-3.50246 + 2.02214i) q^{13} +(-1.72022 + 2.97952i) q^{14} +(-1.55590 - 2.69490i) q^{15} +(0.849402 + 1.47121i) q^{16} -1.94697 q^{17} +(-2.08615 - 1.20444i) q^{18} +(3.67875 - 6.37179i) q^{19} +(-1.43428 - 2.48424i) q^{20} +2.80308i q^{21} +(-3.29760 - 5.71160i) q^{22} +(-4.36037 - 7.55238i) q^{23} +(2.35147 + 1.35762i) q^{24} +(-3.66505 - 6.34806i) q^{25} +(2.19948 - 3.80961i) q^{26} -4.62119 q^{27} +2.58397i q^{28} +(-0.895330 + 1.55076i) q^{29} +(2.93122 + 1.69234i) q^{30} +1.09276 q^{31} +(3.70669 + 2.14006i) q^{32} +(-4.65349 - 2.68669i) q^{33} +(1.83399 - 1.05885i) q^{34} +11.1069i q^{35} -1.80920 q^{36} -7.33548 q^{37} +8.00272i q^{38} -3.58402i q^{39} +(9.31742 + 5.37941i) q^{40} +7.17690 q^{41} +(-1.52445 - 2.64042i) q^{42} +(6.25909 + 3.61368i) q^{43} +(-4.28973 - 2.47668i) q^{44} -7.77663 q^{45} +(8.21469 + 4.74275i) q^{46} +6.94109i q^{47} -1.50547 q^{48} +(1.50249 - 2.60239i) q^{49} +(6.90475 + 3.98646i) q^{50} +(0.862694 - 1.49423i) q^{51} -3.30386i q^{52} +5.58046i q^{53} +(4.35303 - 2.51322i) q^{54} +(-18.4389 - 10.6457i) q^{55} +(-4.84573 - 8.39306i) q^{56} +(3.26008 + 5.64663i) q^{57} -1.94769i q^{58} +(6.20745 + 3.58387i) q^{59} +2.54209 q^{60} +4.62479i q^{61} +(-1.02935 + 0.594293i) q^{62} +(6.06662 + 3.50256i) q^{63} -8.05307 q^{64} -14.2012i q^{65} +5.84461 q^{66} -0.116953 q^{67} +(0.795258 - 1.37743i) q^{68} +7.72825 q^{69} +(-6.04044 - 10.4624i) q^{70} +(-0.617077 + 0.356269i) q^{71} +(5.87652 - 3.39281i) q^{72} +(2.29384 - 3.97305i) q^{73} +(6.90981 - 3.98938i) q^{74} +6.49588 q^{75} +(3.00524 + 5.20524i) q^{76} +(9.58955 + 16.6096i) q^{77} +(1.94916 + 3.37604i) q^{78} +10.1985i q^{79} -5.96523 q^{80} +(-1.27436 + 2.20726i) q^{81} +(-6.76044 + 3.90314i) q^{82} +(-6.45749 - 11.1847i) q^{83} +(-1.98310 - 1.14495i) q^{84} +(3.41832 - 5.92070i) q^{85} -7.86118 q^{86} +(-0.793434 - 1.37427i) q^{87} +18.5781 q^{88} +(-2.81356 - 1.62441i) q^{89} +(7.32536 - 4.22930i) q^{90} +(-6.39617 + 11.0785i) q^{91} +7.12414 q^{92} +(-0.484196 + 0.838653i) q^{93} +(-3.77489 - 6.53831i) q^{94} +(12.9177 + 22.3741i) q^{95} +(-3.28484 + 1.89650i) q^{96} +(3.74416 - 2.16169i) q^{97} +3.26850i q^{98} +(-11.6294 + 6.71426i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) \) 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9	\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) \) 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9 - q^12 - 3 * q^13 - 10 * q^14 + q^15 - 29 * q^16 - 10 * q^17 + 15 * q^18 - 9 * q^19 - 3 * q^22 - 17 * q^23 - 48 * q^24 - 29 * q^25 - 4 * q^26 + 18 * q^27 - 2 * q^29 + 9 * q^30 + 32 * q^31 + 9 * q^32 - 12 * q^33 - 63 * q^34 + 24 * q^36 - 16 * q^37 + 54 * q^40 - 10 * q^41 - 15 * q^42 - 45 * q^43 + 18 * q^44 - 2 * q^45 + 27 * q^46 + 6 * q^48 + 35 * q^49 + 6 * q^50 - 14 * q^51 + 27 * q^54 + 24 * q^55 + 11 * q^56 - 29 * q^57 - 18 * q^59 + 116 * q^60 - 9 * q^62 - 21 * q^63 - 132 * q^64 + 130 * q^66 + 58 * q^67 + 42 * q^69 + 40 * q^70 - 24 * q^71 + 72 * q^72 - 6 * q^73 + 30 * q^74 - 58 * q^75 + 37 * q^76 - 4 * q^77 - 33 * q^78 - 40 * q^80 - 81 * q^81 + 21 * q^82 + 12 * q^83 + 18 * q^84 - 11 * q^85 - 126 * q^86 - 42 * q^87 - 50 * q^88 + 3 * q^89 - 12 * q^90 - 28 * q^91 - 120 * q^92 + 31 * q^93 + 29 * q^94 + 60 * q^95 - 120 * q^96 - 15 * q^97 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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