LMFDB - Embedded newform 201.3.c.a.68.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(68,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("201.68");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.c (of order $2$, degree $1$, 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:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			68.18
Character	$\chi$	$=$	201.68
Dual form			201.3.c.a.68.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.898014i q^{2} +(1.52814 - 2.58162i) q^{3} +3.19357 q^{4} -1.98358i q^{5} +(-2.31833 - 1.37229i) q^{6} -8.12242 q^{7} -6.45992i q^{8} +(-4.32955 - 7.89018i) q^{9} +O(q^{10})$	\(q-0.898014i q^{2} +(1.52814 - 2.58162i) q^{3} +3.19357 q^{4} -1.98358i q^{5} +(-2.31833 - 1.37229i) q^{6} -8.12242 q^{7} -6.45992i q^{8} +(-4.32955 - 7.89018i) q^{9} -1.78129 q^{10} -4.54213i q^{11} +(4.88024 - 8.24460i) q^{12} +6.47428 q^{13} +7.29404i q^{14} +(-5.12087 - 3.03120i) q^{15} +6.97319 q^{16} +9.96566i q^{17} +(-7.08549 + 3.88800i) q^{18} +5.63221 q^{19} -6.33472i q^{20} +(-12.4122 + 20.9690i) q^{21} -4.07890 q^{22} +3.21970i q^{23} +(-16.6771 - 9.87170i) q^{24} +21.0654 q^{25} -5.81399i q^{26} +(-26.9857 - 0.880067i) q^{27} -25.9395 q^{28} -15.6090i q^{29} +(-2.72206 + 4.59861i) q^{30} +5.13255 q^{31} -32.1017i q^{32} +(-11.7261 - 6.94103i) q^{33} +8.94930 q^{34} +16.1115i q^{35} +(-13.8267 - 25.1979i) q^{36} +9.34778 q^{37} -5.05780i q^{38} +(9.89363 - 16.7141i) q^{39} -12.8138 q^{40} +35.0118i q^{41} +(18.8305 + 11.1464i) q^{42} +25.5344 q^{43} -14.5056i q^{44} +(-15.6508 + 8.58803i) q^{45} +2.89134 q^{46} +12.0529i q^{47} +(10.6560 - 18.0021i) q^{48} +16.9737 q^{49} -18.9170i q^{50} +(25.7276 + 15.2290i) q^{51} +20.6761 q^{52} +67.4529i q^{53} +(-0.790312 + 24.2335i) q^{54} -9.00970 q^{55} +52.4702i q^{56} +(8.60683 - 14.5402i) q^{57} -14.0171 q^{58} -12.5570i q^{59} +(-16.3539 - 9.68037i) q^{60} +101.833 q^{61} -4.60910i q^{62} +(35.1664 + 64.0874i) q^{63} -0.935025 q^{64} -12.8423i q^{65} +(-6.23314 + 10.5302i) q^{66} -8.18535 q^{67} +31.8260i q^{68} +(8.31205 + 4.92017i) q^{69} +14.4684 q^{70} +41.6062i q^{71} +(-50.9700 + 27.9686i) q^{72} -18.0054 q^{73} -8.39443i q^{74} +(32.1910 - 54.3829i) q^{75} +17.9869 q^{76} +36.8931i q^{77} +(-15.0095 - 8.88461i) q^{78} +87.5665 q^{79} -13.8319i q^{80} +(-43.5100 + 68.3219i) q^{81} +31.4410 q^{82} -16.5014i q^{83} +(-39.6393 + 66.9661i) q^{84} +19.7677 q^{85} -22.9302i q^{86} +(-40.2966 - 23.8528i) q^{87} -29.3418 q^{88} -116.399i q^{89} +(7.71217 + 14.0547i) q^{90} -52.5868 q^{91} +10.2823i q^{92} +(7.84327 - 13.2503i) q^{93} +10.8237 q^{94} -11.1720i q^{95} +(-82.8745 - 49.0560i) q^{96} +83.8793 q^{97} -15.2426i q^{98} +(-35.8382 + 19.6654i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	$ 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) $ 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	0.898014i		−	0.449007i	−0.974473	−	0.224503i	$-0.927924\pi$
$2$		−	0.898014i		−	0.449007i	0.974473	−	0.224503i	$-0.0720760\pi$
$3$	1.52814	−	2.58162i	0.509381	−	0.860541i
$3$	1.52814	−	2.58162i	0.509381	−	0.860541i
$4$	3.19357			0.798393
$5$		−	1.98358i		−	0.396717i	−0.980130	−	0.198358i	$-0.936439\pi$
$5$		−	1.98358i		−	0.396717i	0.980130	−	0.198358i	$-0.0635610\pi$
$6$	−2.31833	−	1.37229i	−0.386389	−	0.228716i
$7$	−8.12242			−1.16035			−0.580173	−	0.814493i	$-0.697015\pi$
$7$	−8.12242			−1.16035			−0.580173	+	0.814493i	$0.697015\pi$
$8$		−	6.45992i		−	0.807491i
$9$	−4.32955	−	7.89018i	−0.481061	−	0.876687i
$10$	−1.78129			−0.178129
$11$		−	4.54213i		−	0.412921i	−0.978455	−	0.206461i	$-0.933806\pi$
$11$		−	4.54213i		−	0.412921i	0.978455	−	0.206461i	$-0.0661945\pi$
$12$	4.88024	−	8.24460i	0.406686	−	0.687050i
$13$	6.47428			0.498021			0.249011	−	0.968501i	$-0.419895\pi$
$13$	6.47428			0.498021			0.249011	+	0.968501i	$0.419895\pi$
$14$			7.29404i			0.521003i
$15$	−5.12087	−	3.03120i	−0.341391	−	0.202080i
$16$	6.97319			0.435824
$17$			9.96566i			0.586215i	0.956079	+	0.293108i	$0.0946894\pi$
$17$			9.96566i			0.586215i	−0.956079	+	0.293108i	$0.905311\pi$
$18$	−7.08549	+	3.88800i	−0.393638	+	0.216000i
$19$	5.63221			0.296432			0.148216	−	0.988955i	$-0.452647\pi$
$19$	5.63221			0.296432			0.148216	+	0.988955i	$0.452647\pi$
$20$		−	6.33472i		−	0.316736i
$21$	−12.4122	+	20.9690i	−0.591059	+	0.998525i
$22$	−4.07890			−0.185404
$23$			3.21970i			0.139987i	0.997547	+	0.0699935i	$0.0222979\pi$
$23$			3.21970i			0.139987i	−0.997547	+	0.0699935i	$0.977702\pi$
$24$	−16.6771	−	9.87170i	−0.694879	−	0.411321i
$25$	21.0654			0.842616
$26$		−	5.81399i		−	0.223615i
$27$	−26.9857	−	0.880067i	−0.999469	−	0.0325951i
$28$	−25.9395			−0.926412
$29$		−	15.6090i		−	0.538242i	−0.963106	−	0.269121i	$-0.913267\pi$
$29$		−	15.6090i		−	0.538242i	0.963106	−	0.269121i	$-0.0867332\pi$
$30$	−2.72206	+	4.59861i	−0.0907354	+	0.153287i
$31$	5.13255			0.165566			0.0827830	−	0.996568i	$-0.473619\pi$
$31$	5.13255			0.165566			0.0827830	+	0.996568i	$0.473619\pi$
$32$		−	32.1017i		−	1.00318i
$33$	−11.7261	−	6.94103i	−0.355335	−	0.210334i
$34$	8.94930			0.263215
$35$			16.1115i			0.460329i
$36$	−13.8267	−	25.1979i	−0.384076	−	0.699941i
$37$	9.34778			0.252643			0.126321	−	0.991989i	$-0.459683\pi$
$37$	9.34778			0.252643			0.126321	+	0.991989i	$0.459683\pi$
$38$		−	5.05780i		−	0.133100i
$39$	9.89363	−	16.7141i	0.253683	−	0.428568i
$40$	−12.8138			−0.320345
$41$			35.0118i			0.853946i	0.904264	+	0.426973i	$0.140420\pi$
$41$			35.0118i			0.853946i	−0.904264	+	0.426973i	$0.859580\pi$
$42$	18.8305	+	11.1464i	0.448345	+	0.265389i
$43$	25.5344			0.593824			0.296912	−	0.954905i	$-0.404043\pi$
$43$	25.5344			0.593824			0.296912	+	0.954905i	$0.404043\pi$
$44$		−	14.5056i		−	0.329673i
$45$	−15.6508	+	8.58803i	−0.347797	+	0.190845i
$46$	2.89134			0.0628551
$47$			12.0529i			0.256445i	0.991745	+	0.128222i	$0.0409272\pi$
$47$			12.0529i			0.256445i	−0.991745	+	0.128222i	$0.959073\pi$
$48$	10.6560	−	18.0021i	0.222001	−	0.375045i
$49$	16.9737			0.346403
$50$		−	18.9170i		−	0.378340i
$51$	25.7276	+	15.2290i	0.504462	+	0.298607i
$52$	20.6761			0.397617
$53$			67.4529i			1.27270i	0.771402	+	0.636348i	$0.219556\pi$
$53$			67.4529i			1.27270i	−0.771402	+	0.636348i	$0.780444\pi$
$54$	−0.790312	+	24.2335i	−0.0146354	+	0.448768i
$55$	−9.00970			−0.163813
$56$			52.4702i			0.936968i
$57$	8.60683	−	14.5402i	0.150997	−	0.255092i
$58$	−14.0171			−0.241674
$59$		−	12.5570i		−	0.212830i	−0.994322	−	0.106415i	$-0.966063\pi$
$59$		−	12.5570i		−	0.212830i	0.994322	−	0.106415i	$-0.0339372\pi$
$60$	−16.3539	−	9.68037i	−0.272564	−	0.161339i
$61$	101.833			1.66939			0.834696	−	0.550711i	$-0.185643\pi$
$61$	101.833			1.66939			0.834696	+	0.550711i	$0.185643\pi$
$62$		−	4.60910i		−	0.0743403i
$63$	35.1664	+	64.0874i	0.558198	+	1.01726i
$64$	−0.935025			−0.0146098
$65$		−	12.8423i		−	0.197574i
$66$	−6.23314	+	10.5302i	−0.0944415	+	0.159548i
$67$	−8.18535			−0.122169
$67$	−8.18535			−0.122169
$68$			31.8260i			0.468030i
$69$	8.31205	+	4.92017i	0.120465	+	0.0713068i
$70$	14.4684			0.206691
$71$			41.6062i			0.586003i	0.956112	+	0.293002i	$0.0946542\pi$
$71$			41.6062i			0.586003i	−0.956112	+	0.293002i	$0.905346\pi$
$72$	−50.9700	+	27.9686i	−0.707916	+	0.388452i
$73$	−18.0054			−0.246649			−0.123324	−	0.992366i	$-0.539356\pi$
$73$	−18.0054			−0.246649			−0.123324	+	0.992366i	$0.539356\pi$
$74$		−	8.39443i		−	0.113438i
$75$	32.1910	−	54.3829i	0.429213	−	0.725105i
$76$	17.9869			0.236669
$77$			36.8931i			0.479131i
$78$	−15.0095	−	8.88461i	−0.192430	−	0.113905i
$79$	87.5665			1.10844			0.554219	−	0.832371i	$-0.313017\pi$
$79$	87.5665			1.10844			0.554219	+	0.832371i	$0.313017\pi$
$80$		−	13.8319i		−	0.172899i
$81$	−43.5100	+	68.3219i	−0.537160	+	0.843480i
$82$	31.4410			0.383427
$83$		−	16.5014i		−	0.198812i	−0.995047	−	0.0994062i	$-0.968306\pi$
$83$		−	16.5014i		−	0.198812i	0.995047	−	0.0994062i	$-0.0316943\pi$
$84$	−39.6393	+	66.9661i	−0.471897	+	0.797215i
$85$	19.7677			0.232562
$86$		−	22.9302i		−	0.266631i
$87$	−40.2966	−	23.8528i	−0.463179	−	0.274170i
$88$	−29.3418			−0.333430
$89$		−	116.399i		−	1.30785i	−0.756558	−	0.653927i	$-0.773120\pi$
$89$		−	116.399i		−	1.30785i	0.756558	−	0.653927i	$-0.226880\pi$
$90$	7.71217	+	14.0547i	0.0856908	+	0.156163i
$91$	−52.5868			−0.577877
$92$			10.2823i			0.111765i
$93$	7.84327	−	13.2503i	0.0843362	−	0.142476i
$94$	10.8237			0.115146
$95$		−	11.1720i		−	0.117600i
$96$	−82.8745	−	49.0560i	−0.863276	−	0.511000i
$97$	83.8793			0.864736			0.432368	−	0.901697i	$-0.357678\pi$
$97$	83.8793			0.864736			0.432368	+	0.901697i	$0.357678\pi$
$98$		−	15.2426i		−	0.155537i
$99$	−35.8382	+	19.6654i	−0.362002	+	0.198640i
$100$	67.2738			0.672738
$101$			153.986i			1.52461i	0.647216	+	0.762306i	$0.275933\pi$
$101$			153.986i			1.52461i	−0.647216	+	0.762306i	$0.724067\pi$
$102$	13.6758	−	23.1037i	0.134077	−	0.226507i
$103$	−150.895			−1.46500			−0.732501	−	0.680766i	$-0.761647\pi$
$103$	−150.895			−1.46500			−0.732501	+	0.680766i	$0.761647\pi$
$104$		−	41.8234i		−	0.402148i
$105$	41.5938	+	24.6207i	0.396132	+	0.234483i
$106$	60.5736			0.571449
$107$			113.803i			1.06358i	0.846877	+	0.531788i	$0.178480\pi$
$107$			113.803i			1.06358i	−0.846877	+	0.531788i	$0.821520\pi$
$108$	−86.1806	−	2.81056i	−0.797969	−	0.0260237i
$109$	11.0829			0.101678			0.0508391	−	0.998707i	$-0.483810\pi$
$109$	11.0829			0.101678			0.0508391	+	0.998707i	$0.483810\pi$
$110$			8.09083i			0.0735530i
$111$	14.2848	−	24.1324i	0.128692	−	0.217409i
$112$	−56.6392			−0.505707
$113$		−	77.5250i		−	0.686062i	−0.939324	−	0.343031i	$-0.888546\pi$
$113$		−	77.5250i		−	0.686062i	0.939324	−	0.343031i	$-0.111454\pi$
$114$	−13.0573	−	7.72905i	−0.114538	−	0.0677987i
$115$	6.38655			0.0555352
$116$		−	49.8485i		−	0.429729i
$117$	−28.0307	−	51.0832i	−0.239579	−	0.436609i
$118$	−11.2763			−0.0955620
$119$		−	80.9453i		−	0.680212i
$120$	−19.5813	+	33.0804i	−0.163178	+	0.275670i
$121$	100.369			0.829496
$122$		−	91.4474i		−	0.749568i
$123$	90.3872	+	53.5030i	0.734855	+	0.434984i
$124$	16.3912			0.132187
$125$		−	91.3746i		−	0.730997i
$126$	57.5513	−	31.5799i	0.456757	−	0.250634i
$127$	−222.276			−1.75020			−0.875102	−	0.483939i	$-0.839206\pi$
$127$	−222.276			−1.75020			−0.875102	+	0.483939i	$0.839206\pi$
$128$		−	127.567i		−	0.996619i
$129$	39.0203	−	65.9202i	0.302483	−	0.511009i
$130$	−11.5325			−0.0887119
$131$			104.768i			0.799759i	0.916568	+	0.399880i	$0.130948\pi$
$131$			104.768i			0.799759i	−0.916568	+	0.399880i	$0.869052\pi$
$132$	−37.4480	−	22.1667i	−0.283697	−	0.167929i
$133$	−45.7472			−0.343964
$134$			7.35056i			0.0548549i
$135$	−1.74569	+	53.5283i	−0.0129310	+	0.396506i
$136$	64.3774			0.473363
$137$		−	242.098i		−	1.76714i	−0.468302	−	0.883568i	$-0.655134\pi$
$137$		−	242.098i		−	1.76714i	0.468302	−	0.883568i	$-0.344866\pi$
$138$	4.41838	−	7.46434i	0.0320172	−	0.0540894i
$139$	−4.04663			−0.0291124			−0.0145562	−	0.999894i	$-0.504634\pi$
$139$	−4.04663			−0.0291124			−0.0145562	+	0.999894i	$0.504634\pi$
$140$			51.4533i			0.367523i
$141$	31.1161	+	18.4186i	0.220681	+	0.130628i
$142$	37.3630			0.263120
$143$		−	29.4070i		−	0.205644i
$144$	−30.1908	−	55.0197i	−0.209658	−	0.382081i
$145$	−30.9618			−0.213530
$146$			16.1691i			0.110747i
$147$	25.9383	−	43.8198i	0.176451	−	0.298094i
$148$	29.8528			0.201708
$149$			134.063i			0.899754i	0.893090	+	0.449877i	$0.148532\pi$
$149$			134.063i			0.899754i	−0.893090	+	0.449877i	$0.851468\pi$
$150$	−48.8366	−	28.9079i	−0.325577	−	0.192719i
$151$	−206.350			−1.36656			−0.683280	−	0.730157i	$-0.739447\pi$
$151$	−206.350			−1.36656			−0.683280	+	0.730157i	$0.739447\pi$
$152$		−	36.3836i		−	0.239366i
$153$	78.6309	−	43.1468i	0.513927	−	0.282005i
$154$	33.1305			0.215133
$155$		−	10.1808i		−	0.0656828i
$156$	31.5960	−	53.3778i	0.202539	−	0.342166i
$157$	−227.212			−1.44721			−0.723605	−	0.690214i	$-0.757516\pi$
$157$	−227.212			−1.44721			−0.723605	+	0.690214i	$0.757516\pi$
$158$		−	78.6359i		−	0.497696i
$159$	174.138	+	103.078i	1.09521	+	0.648287i
$160$	−63.6765			−0.397978
$161$		−	26.1518i		−	0.162433i
$162$	61.3540	+	39.0725i	0.378728	+	0.241189i
$163$	−227.806			−1.39758			−0.698792	−	0.715325i	$-0.746279\pi$
$163$	−227.806			−1.39758			−0.698792	+	0.715325i	$0.746279\pi$
$164$			111.813i			0.681784i
$165$	−13.7681	+	23.2597i	−0.0834432	+	0.140968i
$166$	−14.8185			−0.0892681
$167$			107.131i			0.641504i	0.947163	+	0.320752i	$0.103936\pi$
$167$			107.131i			0.641504i	−0.947163	+	0.320752i	$0.896064\pi$
$168$	135.458	+	80.1821i	0.806300	+	0.477274i
$169$	−127.084			−0.751975
$170$		−	17.7517i		−	0.104422i
$171$	−24.3849	−	44.4392i	−0.142602	−	0.259878i
$172$	81.5460			0.474105
$173$			320.836i			1.85454i	0.374390	+	0.927271i	$0.377852\pi$
$173$			320.836i			1.85454i	−0.374390	+	0.927271i	$0.622148\pi$
$174$	−21.4202	+	36.1869i	−0.123104	+	0.207971i
$175$	−171.102			−0.977726
$176$		−	31.6731i		−	0.179961i
$177$	−32.4173	−	19.1888i	−0.183149	−	0.108411i
$178$	−104.528			−0.587235
$179$		−	292.120i		−	1.63196i	−0.578083	−	0.815978i	$-0.696199\pi$
$179$		−	292.120i		−	1.63196i	0.578083	−	0.815978i	$-0.303801\pi$
$180$	−49.9821	+	27.4265i	−0.277678	+	0.152369i
$181$	214.430			1.18470			0.592348	−	0.805682i	$-0.298201\pi$
$181$	214.430			1.18470			0.592348	+	0.805682i	$0.298201\pi$
$182$			47.2237i			0.259471i
$183$	155.615	−	262.894i	0.850357	−	1.43658i
$184$	20.7990			0.113038
$185$		−	18.5421i		−	0.100228i
$186$	−11.8989	−	7.04336i	−0.0639728	−	0.0378675i
$187$	45.2653			0.242061
$188$			38.4918i			0.204744i
$189$	219.189	+	7.14827i	1.15973	+	0.0378216i
$190$	−10.0326			−0.0528030
$191$		−	202.965i		−	1.06265i	−0.847169	−	0.531323i	$-0.821695\pi$
$191$		−	202.965i		−	1.06265i	0.847169	−	0.531323i	$-0.178305\pi$
$192$	−1.42885	+	2.41388i	−0.00744194	+	0.0125723i
$193$	−170.939			−0.885693			−0.442846	−	0.896597i	$-0.646031\pi$
$193$	−170.939			−0.885693			−0.442846	+	0.896597i	$0.646031\pi$
$194$		−	75.3248i		−	0.388272i
$195$	−33.1539	−	19.6249i	−0.170020	−	0.100640i
$196$	54.2068			0.276565
$197$			172.592i			0.876104i	0.898950	+	0.438052i	$0.144331\pi$
$197$			172.592i			0.876104i	−0.898950	+	0.438052i	$0.855669\pi$
$198$	17.6598	+	32.1832i	0.0891908	+	0.162542i
$199$	85.4334			0.429314			0.214657	−	0.976690i	$-0.431137\pi$
$199$	85.4334			0.429314			0.214657	+	0.976690i	$0.431137\pi$
$200$		−	136.081i		−	0.680404i
$201$	−12.5084	+	21.1315i	−0.0622308	+	0.105132i
$202$	138.281			0.684561
$203$			126.783i			0.624547i
$204$	82.1628	+	48.6348i	0.402759	+	0.238406i
$205$	69.4488			0.338775
$206$			135.506i			0.657796i
$207$	25.4040	−	13.9399i	0.122725	−	0.0673423i
$208$	45.1464			0.217050
$209$		−	25.5822i		−	0.122403i
$210$	22.1097	−	37.3518i	0.105284	−	0.177866i
$211$	3.47526			0.0164704			0.00823522	−	0.999966i	$-0.497379\pi$
$211$	3.47526			0.0164704			0.00823522	+	0.999966i	$0.497379\pi$
$212$			215.416i			1.01611i
$213$	107.412	+	63.5803i	0.504280	+	0.298499i
$214$	102.196			0.477553
$215$		−	50.6497i		−	0.235580i
$216$	−5.68517	+	174.325i	−0.0263202	+	0.807062i
$217$	−41.6887			−0.192114
$218$		−	9.95261i		−	0.0456542i
$219$	−27.5148	+	46.4831i	−0.125638	+	0.212251i
$220$	−28.7731			−0.130787
$221$			64.5205i			0.291948i
$222$	−21.6713	−	12.8279i	−0.0976183	−	0.0577834i
$223$	−43.2584			−0.193984			−0.0969920	−	0.995285i	$-0.530922\pi$
$223$	−43.2584			−0.193984			−0.0969920	+	0.995285i	$0.530922\pi$
$224$			260.744i			1.16403i
$225$	−91.2037	−	166.210i	−0.405350	−	0.738710i
$226$	−69.6185			−0.308046
$227$		−	164.736i		−	0.725710i	−0.931846	−	0.362855i	$-0.881802\pi$
$227$		−	164.736i		−	0.725710i	0.931846	−	0.362855i	$-0.118198\pi$
$228$	27.4865	−	46.4353i	0.120555	−	0.203664i
$229$	−84.4500			−0.368777			−0.184389	−	0.982853i	$-0.559031\pi$
$229$	−84.4500			−0.368777			−0.184389	+	0.982853i	$0.559031\pi$
$230$		−	5.73521i		−	0.0249357i
$231$	95.2441	+	56.3780i	0.412312	+	0.244061i
$232$	−100.833			−0.434625
$233$			436.437i			1.87312i	0.350506	+	0.936561i	$0.386010\pi$
$233$			436.437i			1.87312i	−0.350506	+	0.936561i	$0.613990\pi$
$234$	−45.8734	+	25.1720i	−0.196040	+	0.107573i
$235$	23.9080			0.101736
$236$		−	40.1015i		−	0.169922i
$237$	133.814	−	226.064i	0.564617	−	0.953856i
$238$	−72.6900			−0.305420
$239$			211.843i			0.886373i	0.896429	+	0.443187i	$0.146152\pi$
$239$			211.843i			0.886373i	−0.896429	+	0.443187i	$0.853848\pi$
$240$	−35.7088	−	21.1371i	−0.148787	−	0.0880715i
$241$	384.339			1.59477			0.797384	−	0.603472i	$-0.206217\pi$
$241$	384.339			1.59477			0.797384	+	0.603472i	$0.206217\pi$
$242$		−	90.1328i		−	0.372449i
$243$	109.892	+	216.732i	0.452230	+	0.891901i
$244$	325.211			1.33283
$245$		−	33.6688i		−	0.137424i
$246$	48.0465	−	81.1689i	0.195311	−	0.329955i
$247$	36.4645			0.147630
$248$		−	33.1559i		−	0.133693i
$249$	−42.6005	−	25.2166i	−0.171086	−	0.101271i
$250$	−82.0556			−0.328223
$251$		−	262.854i		−	1.04723i	−0.851956	−	0.523613i	$-0.824584\pi$
$251$		−	262.854i		−	1.04723i	0.851956	−	0.523613i	$-0.175416\pi$
$252$	112.307	+	204.668i	0.445661	+	0.812173i
$253$	14.6243			0.0578036
$254$			199.607i			0.785853i
$255$	30.2079	−	51.0328i	0.118462	−	0.200129i
$256$	−118.297			−0.462098
$257$			173.200i			0.673930i	0.941517	+	0.336965i	$0.109400\pi$
$257$			173.200i			0.673930i	−0.941517	+	0.336965i	$0.890600\pi$
$258$	−59.1972	−	35.0407i	−0.229447	−	0.135817i
$259$	−75.9266			−0.293153
$260$		−	41.0127i		−	0.157741i
$261$	−123.158	+	67.5801i	−0.471870	+	0.258927i
$262$	94.0835			0.359097
$263$		−	84.6896i		−	0.322014i	−0.986953	−	0.161007i	$-0.948526\pi$
$263$		−	84.6896i		−	0.322014i	0.986953	−	0.161007i	$-0.0514741\pi$
$264$	−44.8385	+	75.7495i	−0.169843	+	0.286930i
$265$	133.798			0.504900
$266$			41.0816i			0.154442i
$267$	−300.498	−	177.874i	−1.12546	−	0.666197i
$268$	−26.1405			−0.0975392
$269$			345.209i			1.28331i	0.766995	+	0.641653i	$0.221751\pi$
$269$			345.209i			1.28331i	−0.766995	+	0.641653i	$0.778249\pi$
$270$	48.0692	+	1.56765i	0.178034	+	0.00580611i
$271$	−49.7194			−0.183467			−0.0917333	−	0.995784i	$-0.529241\pi$
$271$	−49.7194			−0.183467			−0.0917333	+	0.995784i	$0.529241\pi$
$272$			69.4924i			0.255487i
$273$	−80.3602	+	135.759i	−0.294360	+	0.497287i
$274$	−217.407			−0.793456
$275$		−	95.6818i		−	0.347934i
$276$	26.5451	+	15.7129i	0.0961780	+	0.0569308i
$277$	−351.124			−1.26760			−0.633798	−	0.773498i	$-0.718505\pi$
$277$	−351.124			−1.26760			−0.633798	+	0.773498i	$0.718505\pi$
$278$			3.63393i			0.0130717i
$279$	−22.2216	−	40.4967i	−0.0796474	−	0.145150i
$280$	104.079			0.371711
$281$		−	296.997i		−	1.05693i	−0.848955	−	0.528465i	$-0.822768\pi$
$281$		−	296.997i		−	1.05693i	0.848955	−	0.528465i	$-0.177232\pi$
$282$	16.5401	−	27.9427i	0.0586530	−	0.0990874i
$283$	−60.2250			−0.212809			−0.106405	−	0.994323i	$-0.533934\pi$
$283$	−60.2250			−0.212809			−0.106405	+	0.994323i	$0.533934\pi$
$284$			132.873i			0.467861i
$285$	−28.8418	−	17.0724i	−0.101199	−	0.0599031i
$286$	−26.4079			−0.0923353
$287$		−	284.380i		−	0.990873i
$288$	−253.288	+	138.986i	−0.879474	+	0.482590i
$289$	189.686			0.656352
$290$			27.8041i			0.0958763i
$291$	128.180	−	216.545i	0.440480	−	0.744140i
$292$	−57.5014			−0.196923
$293$			151.044i			0.515507i	0.966211	+	0.257754i	$0.0829823\pi$
$293$			151.044i			0.515507i	−0.966211	+	0.257754i	$0.917018\pi$
$294$	−39.3507	−	23.2930i	−0.133846	−	0.0792277i
$295$	−24.9078			−0.0844332
$296$		−	60.3860i		−	0.204007i
$297$	−3.99738	+	122.572i	−0.0134592	+	0.412702i
$298$	120.391			0.403996
$299$			20.8452i			0.0697165i
$300$	102.804	−	173.676i	0.342680	−	0.578919i
$301$	−207.401			−0.689041
$302$			185.306i			0.613594i
$303$	397.533	+	235.313i	1.31199	+	0.776609i
$304$	39.2744			0.129192
$305$		−	201.994i		−	0.662276i
$306$	−38.7464	−	70.6116i	−0.126622	−	0.230757i
$307$	−475.657			−1.54937			−0.774686	−	0.632347i	$-0.782092\pi$
$307$	−475.657			−1.54937			−0.774686	+	0.632347i	$0.782092\pi$
$308$			117.821i			0.382535i
$309$	−230.590	+	389.555i	−0.746245	+	1.26069i
$310$	−9.14253			−0.0294920
$311$		−	316.203i		−	1.01673i	−0.861141	−	0.508365i	$-0.830250\pi$
$311$		−	316.203i		−	1.01673i	0.861141	−	0.508365i	$-0.169750\pi$
$312$	−107.972	−	63.9121i	−0.346064	−	0.204847i
$313$	30.2723			0.0967165			0.0483582	−	0.998830i	$-0.484601\pi$
$313$	30.2723			0.0967165			0.0483582	+	0.998830i	$0.484601\pi$
$314$			204.039i			0.649807i
$315$	127.123	−	69.7556i	0.403564	−	0.221446i
$316$	279.650			0.884968
$317$		−	533.778i		−	1.68384i	−0.539599	−	0.841922i	$-0.681424\pi$
$317$		−	533.778i		−	1.68384i	0.539599	−	0.841922i	$-0.318576\pi$
$318$	92.5652	−	156.378i	0.291085	−	0.491755i
$319$	−70.8982			−0.222251
$320$			1.85470i			0.00579594i
$321$	293.796	+	173.907i	0.915251	+	0.541766i
$322$	−23.4846			−0.0729337
$323$			56.1287i			0.173773i
$324$	−138.952	+	218.191i	−0.428865	+	0.673429i
$325$	136.383			0.419641
$326$			204.573i			0.627525i
$327$	16.9363	−	28.6119i	0.0517930	−	0.0874982i
$328$	226.173			0.689553
$329$		−	97.8988i		−	0.297565i
$330$	20.8875	+	12.3640i	0.0632954	+	0.0374665i
$331$	−185.129			−0.559302			−0.279651	−	0.960102i	$-0.590219\pi$
$331$	−185.129			−0.559302			−0.279651	+	0.960102i	$0.590219\pi$
$332$		−	52.6985i		−	0.158730i
$333$	−40.4717	−	73.7557i	−0.121537	−	0.221489i
$334$	96.2052			0.288040
$335$			16.2363i			0.0484667i
$336$	−86.5528	+	146.221i	−0.257598	+	0.435181i
$337$	−39.3003			−0.116618			−0.0583090	−	0.998299i	$-0.518571\pi$
$337$	−39.3003			−0.116618			−0.0583090	+	0.998299i	$0.518571\pi$
$338$			114.123i			0.337642i
$339$	−200.140	−	118.469i	−0.590384	−	0.349467i
$340$	63.1297			0.185675
$341$		−	23.3127i		−	0.0683657i
$342$	−39.9070	+	21.8980i	−0.116687	+	0.0640293i
$343$	260.131			0.758399
$344$		−	164.950i		−	0.479507i
$345$	9.75957	−	16.4877i	0.0282886	−	0.0477903i
$346$	288.115			0.832702
$347$		−	529.254i		−	1.52523i	−0.646855	−	0.762613i	$-0.723916\pi$
$347$		−	529.254i		−	1.52523i	0.646855	−	0.762613i	$-0.276084\pi$
$348$	−128.690	−	76.1757i	−0.369799	−	0.218896i
$349$	587.933			1.68462			0.842311	−	0.538991i	$-0.181194\pi$
$349$	587.933			1.68462			0.842311	+	0.538991i	$0.181194\pi$
$350$			153.652i			0.439005i
$351$	−174.713	−	5.69780i	−0.497757	−	0.0162330i
$352$	−145.810			−0.414234
$353$			107.571i			0.304734i	0.988324	+	0.152367i	$0.0486895\pi$
$353$			107.571i			0.304734i	−0.988324	+	0.152367i	$0.951310\pi$
$354$	−17.2318	+	29.1112i	−0.0486775	+	0.0822350i
$355$	82.5295			0.232478
$356$		−	371.729i		−	1.04418i
$357$	−208.970	−	123.696i	−0.585351	−	0.346488i
$358$	−262.328			−0.732759
$359$		−	583.066i		−	1.62414i	−0.583561	−	0.812069i	$-0.698341\pi$
$359$		−	583.066i		−	1.62414i	0.583561	−	0.812069i	$-0.301659\pi$
$360$	55.4780	+	101.103i	0.154106	+	0.280842i
$361$	−329.278			−0.912128
$362$		−	192.561i		−	0.531936i
$363$	153.378	−	259.115i	0.422530	−	0.713815i
$364$	−167.940			−0.461373
$365$			35.7152i			0.0978498i
$366$	−236.083	−	139.745i	−0.645034	−	0.381816i
$367$	146.353			0.398783			0.199392	−	0.979920i	$-0.436103\pi$
$367$	146.353			0.398783			0.199392	+	0.979920i	$0.436103\pi$
$368$			22.4516i			0.0610097i
$369$	276.249	−	151.585i	0.748643	−	0.410800i
$370$	−16.6511			−0.0450029
$371$		−	547.881i		−	1.47677i
$372$	25.0480	−	42.3158i	0.0673335	−	0.113752i
$373$	−109.086			−0.292455			−0.146228	−	0.989251i	$-0.546713\pi$
$373$	−109.086			−0.292455			−0.146228	+	0.989251i	$0.546713\pi$
$374$		−	40.6489i		−	0.108687i
$375$	−235.895	−	139.634i	−0.629053	−	0.372356i
$376$	77.8609			0.207077
$377$		−	101.057i		−	0.268056i
$378$	6.41925	−	196.835i	0.0169821	−	0.520726i
$379$	395.551			1.04367			0.521835	−	0.853046i	$-0.325248\pi$
$379$	395.551			1.04367			0.521835	+	0.853046i	$0.325248\pi$
$380$		−	35.6785i		−	0.0938907i
$381$	−339.670	+	573.832i	−0.891521	+	1.50612i
$382$	−182.266			−0.477135
$383$		−	57.8225i		−	0.150973i	−0.997147	−	0.0754863i	$-0.975949\pi$
$383$		−	57.8225i		−	0.150973i	0.997147	−	0.0754863i	$-0.0240509\pi$
$384$	−329.330	−	194.941i	−0.857631	−	0.507659i
$385$	73.1806			0.190079
$386$			153.505i			0.397682i
$387$	−110.553	−	201.471i	−0.285666	−	0.520597i
$388$	267.875			0.690399
$389$			249.329i			0.640947i	0.947257	+	0.320474i	$0.103842\pi$
$389$			249.329i			0.640947i	−0.947257	+	0.320474i	$0.896158\pi$
$390$	−17.6234	+	29.7727i	−0.0451882	+	0.0763402i
$391$	−32.0864			−0.0820625
$392$		−	109.649i		−	0.279717i
$393$	270.473	+	160.101i	0.688226	+	0.407382i
$394$	154.990			0.393377
$395$		−	173.696i		−	0.439736i
$396$	−114.452	+	62.8028i	−0.289020	+	0.158593i
$397$	37.6400			0.0948112			0.0474056	−	0.998876i	$-0.484905\pi$
$397$	37.6400			0.0948112			0.0474056	+	0.998876i	$0.484905\pi$
$398$		−	76.7204i		−	0.192765i
$399$	−69.9083	+	118.102i	−0.175209	+	0.295995i
$400$	146.893			0.367232
$401$			126.781i			0.316162i	0.987426	+	0.158081i	$0.0505306\pi$
$401$			126.781i			0.316162i	−0.987426	+	0.158081i	$0.949469\pi$
$402$	18.9764	+	11.2327i	0.0472049	+	0.0279421i
$403$	33.2295			0.0824554
$404$			491.765i			1.21724i
$405$	135.522	+	86.3057i	0.334623	+	0.213101i
$406$	113.853			0.280426
$407$		−	42.4589i		−	0.104322i
$408$	98.3779	−	166.198i	0.241122	−	0.407348i
$409$	−583.237			−1.42601			−0.713003	−	0.701161i	$-0.752666\pi$
$409$	−583.237			−1.42601			−0.713003	+	0.701161i	$0.752666\pi$
$410$		−	62.3660i		−	0.152112i
$411$	−625.005	−	369.960i	−1.52069	−	0.900146i
$412$	−481.895			−1.16965
$413$			101.993i			0.246956i
$414$	−12.5182	−	22.8132i	−0.0302372	−	0.0551043i
$415$	−32.7320			−0.0788722
$416$		−	207.835i		−	0.499604i
$417$	−6.18383	+	10.4469i	−0.0148293	+	0.0250524i
$418$	−22.9732			−0.0549598
$419$		−	273.483i		−	0.652704i	−0.945248	−	0.326352i	$-0.894180\pi$
$419$		−	273.483i		−	0.652704i	0.945248	−	0.326352i	$-0.105820\pi$
$420$	132.833	+	78.6280i	0.316269	+	0.187210i
$421$	36.9788			0.0878356			0.0439178	−	0.999035i	$-0.486016\pi$
$421$	36.9788			0.0878356			0.0439178	+	0.999035i	$0.486016\pi$
$422$		−	3.12083i		−	0.00739534i
$423$	95.0997	−	52.1837i	0.224822	−	0.123366i
$424$	435.740			1.02769
$425$			209.930i			0.493954i
$426$	57.0960	−	96.4571i	0.134028	−	0.226425i
$427$	−827.130			−1.93707
$428$			363.437i			0.849152i
$429$	−75.9178	−	44.9382i	−0.176965	−	0.104751i
$430$	−45.4841			−0.105777
$431$			593.916i			1.37799i	0.724764	+	0.688997i	$0.241949\pi$
$431$			593.916i			1.37799i	−0.724764	+	0.688997i	$0.758051\pi$
$432$	−188.176	−	6.13687i	−0.435593	−	0.0142057i
$433$	853.464			1.97105			0.985524	−	0.169534i	$-0.0542264\pi$
$433$	853.464			1.97105			0.985524	+	0.169534i	$0.0542264\pi$
$434$			37.4370i			0.0862604i
$435$	−47.3141	+	79.9317i	−0.108768	+	0.183751i
$436$	35.3941			0.0811791
$437$			18.1340i			0.0414966i
$438$	41.7424	+	24.7087i	0.0953023	+	0.0564124i
$439$	109.438			0.249289			0.124645	−	0.992201i	$-0.460221\pi$
$439$	109.438			0.249289			0.124645	+	0.992201i	$0.460221\pi$
$440$			58.2020i			0.132277i
$441$	−73.4886	−	133.926i	−0.166641	−	0.303687i
$442$	57.9402			0.131087
$443$			135.771i			0.306481i	0.988189	+	0.153241i	$0.0489710\pi$
$443$			135.771i			0.306481i	−0.988189	+	0.153241i	$0.951029\pi$
$444$	45.6194	−	77.0687i	0.102746	−	0.173578i
$445$	−230.887			−0.518848
$446$			38.8467i			0.0871001i
$447$	346.101	+	204.868i	0.774275	+	0.458318i
$448$	7.59467			0.0169524
$449$			722.815i			1.60983i	0.593389	+	0.804916i	$0.297790\pi$
$449$			722.815i			1.60983i	−0.593389	+	0.804916i	$0.702210\pi$
$450$	−149.259	+	81.9022i	−0.331686	+	0.182005i
$451$	159.028			0.352612
$452$		−	247.582i		−	0.547747i
$453$	−315.333	+	532.719i	−0.696100	+	1.17598i
$454$	−147.935			−0.325849
$455$			104.310i			0.229254i
$456$	−93.9288	−	55.5994i	−0.205984	−	0.121929i
$457$	84.5485			0.185008			0.0925038	−	0.995712i	$-0.470513\pi$
$457$	84.5485			0.185008			0.0925038	+	0.995712i	$0.470513\pi$
$458$			75.8372i			0.165584i
$459$	8.77045	−	268.930i	0.0191077	−	0.585904i
$460$	20.3959			0.0443389
$461$			719.941i			1.56169i	0.624722	+	0.780847i	$0.285212\pi$
$461$			719.941i			1.56169i	−0.624722	+	0.780847i	$0.714788\pi$
$462$	50.6282	−	85.5305i	0.109585	−	0.185131i
$463$	−75.2164			−0.162454			−0.0812272	−	0.996696i	$-0.525884\pi$
$463$	−75.2164			−0.162454			−0.0812272	+	0.996696i	$0.525884\pi$
$464$		−	108.845i		−	0.234579i
$465$	−26.2831	−	15.5578i	−0.0565228	−	0.0334576i
$466$	391.927			0.841044
$467$			265.404i			0.568318i	0.958777	+	0.284159i	$0.0917144\pi$
$467$			265.404i			0.568318i	−0.958777	+	0.284159i	$0.908286\pi$
$468$	−89.5181	−	163.138i	−0.191278	−	0.348585i
$469$	66.4849			0.141759
$470$		−	21.4697i		−	0.0456802i
$471$	−347.213	+	586.576i	−0.737182	+	1.24538i
$472$	−81.1170			−0.171858
$473$		−	115.981i		−	0.245202i
$474$	−203.008	−	120.167i	−0.428288	−	0.253517i
$475$	118.645			0.249778
$476$		−	258.505i		−	0.543077i
$477$	532.215	−	292.041i	1.11576	−	0.612245i
$478$	190.238			0.397988
$479$			899.530i			1.87793i	0.344009	+	0.938966i	$0.388215\pi$
$479$			899.530i			1.87793i	−0.344009	+	0.938966i	$0.611785\pi$
$480$	−97.3068	+	164.389i	−0.202723	+	0.342476i
$481$	60.5202			0.125822
$482$		−	345.142i		−	0.716061i
$483$	−67.5140	−	39.9637i	−0.139781	−	0.0827405i
$484$	320.536			0.662264
$485$		−	166.382i		−	0.343055i
$486$	194.628	−	98.6844i	0.400470	−	0.203054i
$487$	−53.7974			−0.110467			−0.0552335	−	0.998473i	$-0.517590\pi$
$487$	−53.7974			−0.110467			−0.0552335	+	0.998473i	$0.517590\pi$
$488$		−	657.833i		−	1.34802i
$489$	−348.121	+	588.110i	−0.711904	+	1.20268i
$490$	−30.2351			−0.0617042
$491$			74.7722i			0.152286i	0.997097	+	0.0761428i	$0.0242605\pi$
$491$			74.7722i			0.152286i	−0.997097	+	0.0761428i	$0.975740\pi$
$492$	288.658	+	170.866i	0.586703	+	0.347288i
$493$	155.554			0.315526
$494$		−	32.7456i		−	0.0662867i
$495$	39.0080	+	71.0882i	0.0788040	+	0.143613i
$496$	35.7902			0.0721577
$497$		−	337.943i		−	0.679967i
$498$	−22.6448	+	38.2558i	−0.0454715	+	0.0768189i
$499$	−101.640			−0.203688			−0.101844	−	0.994800i	$-0.532474\pi$
$499$	−101.640			−0.203688			−0.101844	+	0.994800i	$0.532474\pi$
$500$		−	291.811i		−	0.583623i
$501$	276.572	+	163.712i	0.552040	+	0.326770i
$502$	−236.046			−0.470211
$503$			491.387i			0.976913i	0.872588	+	0.488456i	$0.162440\pi$
$503$			491.387i			0.976913i	−0.872588	+	0.488456i	$0.837560\pi$
$504$	414.000	−	227.173i	0.821428	−	0.450739i
$505$	305.444			0.604840
$506$		−	13.1328i		−	0.0259542i
$507$	−194.202	+	328.082i	−0.383042	+	0.647105i
$508$	−709.854			−1.39735
$509$			450.666i			0.885396i	0.896671	+	0.442698i	$0.145979\pi$
$509$			450.666i			0.885396i	−0.896671	+	0.442698i	$0.854021\pi$
$510$	−45.8282	−	27.1271i	−0.0898591	−	0.0531905i
$511$	146.247			0.286198
$512$		−	404.036i		−	0.789133i
$513$	−151.989	−	4.95672i	−0.296275	−	0.00966222i
$514$	155.536			0.302599
$515$			299.314i			0.581191i
$516$	124.614	−	210.521i	0.241500	−	0.407986i
$517$	54.7459			0.105892
$518$			68.1831i			0.131628i
$519$	828.277	+	490.283i	1.59591	+	0.944669i
$520$	−82.9602			−0.159539
$521$		−	88.6877i		−	0.170226i	−0.996371	−	0.0851129i	$-0.972875\pi$
$521$		−	88.6877i		−	0.170226i	0.996371	−	0.0851129i	$-0.0271251\pi$
$522$	60.6878	+	110.598i	0.116260	+	0.211873i
$523$	659.154			1.26033			0.630166	−	0.776460i	$-0.282987\pi$
$523$	659.154			1.26033			0.630166	+	0.776460i	$0.282987\pi$
$524$			334.586i			0.638522i
$525$	−261.468	+	441.721i	−0.498035	+	0.841373i
$526$	−76.0524			−0.144586
$527$			51.1492i			0.0970573i
$528$	−81.7681	−	48.4011i	−0.154864	−	0.0916688i
$529$	518.634			0.980404
$530$		−	120.153i		−	0.226703i
$531$	−99.0767	+	54.3660i	−0.186585	+	0.102384i
$532$	−146.097			−0.274618
$533$			226.676i			0.425283i
$534$	−159.734	+	269.852i	−0.299127	+	0.505340i
$535$	225.737			0.421939
$536$			52.8768i			0.0986507i
$537$	−754.144	−	446.401i	−1.40436	−	0.831288i
$538$	310.002			0.576213
$539$		−	77.0969i		−	0.143037i
$540$	−5.57498	+	170.947i	−0.0103240	+	0.316568i
$541$	608.618			1.12499			0.562494	−	0.826802i	$-0.309842\pi$
$541$	608.618			1.12499			0.562494	+	0.826802i	$0.309842\pi$
$542$			44.6487i			0.0823777i
$543$	327.680	−	553.577i	0.603462	−	1.01948i
$544$	319.915			0.588079
$545$		−	21.9839i		−	0.0403375i
$546$	121.914	+	72.1646i	0.223285	+	0.132170i
$547$	969.251			1.77194			0.885970	−	0.463742i	$-0.153494\pi$
$547$	969.251			1.77194			0.885970	+	0.463742i	$0.153494\pi$
$548$		−	773.156i		−	1.41087i
$549$	−440.891	−	803.480i	−0.803080	−	1.46353i
$550$	−85.9235			−0.156225
$551$		−	87.9133i		−	0.159552i
$552$	31.7839	−	53.6952i	0.0575795	−	0.0972740i
$553$	−711.252			−1.28617
$554$			315.314i			0.569159i
$555$	−47.8688	−	28.3350i	−0.0862500	−	0.0510541i
$556$	−12.9232			−0.0232432
$557$		−	635.920i		−	1.14169i	−0.821059	−	0.570844i	$-0.806616\pi$
$557$		−	635.920i		−	1.14169i	0.821059	−	0.570844i	$-0.193384\pi$
$558$	−36.3666	+	19.9553i	−0.0651731	+	0.0357622i
$559$	165.317			0.295737
$560$			112.349i			0.200622i
$561$	69.1719	−	116.858i	0.123301	−	0.208303i
$562$	−266.707			−0.474568
$563$			817.749i			1.45249i	0.687438	+	0.726243i	$0.258735\pi$
$563$			817.749i			1.45249i	−0.687438	+	0.726243i	$0.741265\pi$
$564$	99.3714	+	58.8211i	0.176190	+	0.104293i
$565$	−153.777			−0.272172
$566$			54.0829i			0.0955528i
$567$	353.406	−	554.939i	0.623292	−	0.978729i
$568$	268.773			0.473192
$569$			101.300i			0.178032i	0.996030	+	0.0890159i	$0.0283722\pi$
$569$			101.300i			0.178032i	−0.996030	+	0.0890159i	$0.971628\pi$
$570$	−15.3312	+	25.9003i	−0.0268969	+	0.0454392i
$571$	−927.714			−1.62472			−0.812359	−	0.583157i	$-0.801817\pi$
$571$	−927.714			−1.62472			−0.812359	+	0.583157i	$0.801817\pi$
$572$		−	93.9134i		−	0.164184i
$573$	−523.980	−	310.161i	−0.914451	−	0.541292i
$574$	−255.377			−0.444908
$575$			67.8243i			0.117955i
$576$	4.04824	+	7.37752i	0.00702819	+	0.0128082i
$577$	275.471			0.477419			0.238710	−	0.971091i	$-0.423276\pi$
$577$	275.471			0.477419			0.238710	+	0.971091i	$0.423276\pi$
$578$		−	170.340i		−	0.294706i
$579$	−261.219	+	441.299i	−0.451155	+	0.762175i
$580$	−98.8788			−0.170481
$581$			134.032i			0.230691i
$582$	−194.460	−	115.107i	−0.334124	−	0.197779i
$583$	306.380			0.525523
$584$			116.313i			0.199167i
$585$	−101.328	+	55.6013i	−0.173210	+	0.0950450i
$586$	135.639			0.231466
$587$		−	362.944i		−	0.618303i	−0.951013	−	0.309151i	$-0.899955\pi$
$587$		−	362.944i		−	0.618303i	0.951013	−	0.309151i	$-0.100045\pi$
$588$	82.8358	−	139.942i	0.140877	−	0.237996i
$589$	28.9076			0.0490791
$590$			22.3675i			0.0379111i
$591$	445.569	+	263.746i	0.753923	+	0.446271i
$592$	65.1838			0.110108
$593$		−	761.661i		−	1.28442i	−0.766529	−	0.642210i	$-0.778018\pi$
$593$		−	761.661i		−	1.28442i	0.766529	−	0.642210i	$-0.221982\pi$
$594$	110.072	+	3.58970i	0.185306	+	0.00604327i
$595$	−160.562			−0.269852
$596$			428.141i			0.718357i
$597$	130.555	−	220.557i	0.218684	−	0.369442i
$598$	18.7193			0.0313032
$599$		−	457.562i		−	0.763877i	−0.924188	−	0.381938i	$-0.875257\pi$
$599$		−	457.562i		−	0.763877i	0.924188	−	0.381938i	$-0.124743\pi$
$600$	−351.309	−	207.951i	−0.585516	−	0.346585i
$601$	544.123			0.905362			0.452681	−	0.891672i	$-0.350468\pi$
$601$	544.123			0.905362			0.452681	+	0.891672i	$0.350468\pi$
$602$			186.249i			0.309384i
$603$	35.4389	+	64.5839i	0.0587710	+	0.107104i
$604$	−658.995			−1.09105
$605$		−	199.091i		−	0.329075i
$606$	211.314	−	356.990i	0.348703	−	0.589093i
$607$	−211.819			−0.348960			−0.174480	−	0.984661i	$-0.555825\pi$
$607$	−211.819			−0.348960			−0.174480	+	0.984661i	$0.555825\pi$
$608$		−	180.804i		−	0.297374i
$609$	327.306	+	193.743i	0.537448	+	0.318133i
$610$	−181.394			−0.297367
$611$			78.0339i			0.127715i
$612$	251.113	−	137.792i	0.410316	−	0.225151i
$613$	−108.242			−0.176578			−0.0882889	−	0.996095i	$-0.528140\pi$
$613$	−108.242			−0.176578			−0.0882889	+	0.996095i	$0.528140\pi$
$614$			427.146i			0.695678i
$615$	106.128	−	179.291i	0.172566	−	0.291530i
$616$	238.327			0.386894
$617$		−	496.364i		−	0.804480i	−0.915534	−	0.402240i	$-0.868232\pi$
$617$		−	496.364i		−	0.804480i	0.915534	−	0.402240i	$-0.131768\pi$
$618$	349.825	+	207.073i	0.566060	+	0.335069i
$619$	−701.800			−1.13376			−0.566882	−	0.823799i	$-0.691850\pi$
$619$	−701.800			−1.13376			−0.566882	+	0.823799i	$0.691850\pi$
$620$		−	32.5132i		−	0.0524407i
$621$	2.83355	−	86.8857i	0.00456289	−	0.139913i
$622$	−283.955			−0.456519
$623$			945.442i			1.51756i
$624$	68.9901	−	116.551i	0.110561	−	0.186780i
$625$	345.385			0.552617
$626$		−	27.1849i		−	0.0434264i
$627$	−66.0437	−	39.0933i	−0.105333	−	0.0623498i
$628$	−725.618			−1.15544
$629$			93.1568i			0.148103i
$630$	−62.6415	−	114.158i	−0.0994309	−	0.181203i
$631$	−764.874			−1.21216			−0.606081	−	0.795403i	$-0.707259\pi$
$631$	−764.874			−1.21216			−0.606081	+	0.795403i	$0.707259\pi$
$632$		−	565.673i		−	0.895053i
$633$	5.31070	−	8.97181i	0.00838973	−	0.0141735i
$634$	−479.340			−0.756057
$635$			440.903i			0.694335i
$636$	556.122	+	329.186i	0.874405	+	0.517588i
$637$	109.893			0.172516
$638$			63.6676i			0.0997924i
$639$	328.281	−	180.136i	0.513742	−	0.281904i
$640$	−253.040			−0.395376
$641$			153.095i			0.238838i	0.992844	+	0.119419i	$0.0381032\pi$
$641$			153.095i			0.238838i	−0.992844	+	0.119419i	$0.961897\pi$
$642$	156.171	−	263.832i	0.243257	−	0.410954i
$643$	180.252			0.280330			0.140165	−	0.990128i	$-0.455237\pi$
$643$	180.252			0.280330			0.140165	+	0.990128i	$0.455237\pi$
$644$		−	83.5176i		−	0.129686i
$645$	−130.758	−	77.4000i	−0.202726	−	0.120000i
$646$	50.4043			0.0780252
$647$			638.129i			0.986290i	0.869947	+	0.493145i	$0.164153\pi$
$647$			638.129i			0.986290i	−0.869947	+	0.493145i	$0.835847\pi$
$648$	441.354	+	281.071i	0.681102	+	0.433752i
$649$	−57.0353			−0.0878819
$650$		−	122.474i		−	0.188422i
$651$	−63.7063	+	107.625i	−0.0978592	+	0.165322i
$652$	−727.516			−1.11582
$653$			638.070i			0.977137i	0.872526	+	0.488568i	$0.162481\pi$
$653$			638.070i			0.977137i	−0.872526	+	0.488568i	$0.837519\pi$
$654$	−25.6939	−	15.2090i	−0.0392873	−	0.0232554i
$655$	207.817			0.317278
$656$			244.144i			0.372170i
$657$	77.9551	+	142.066i	0.118653	+	0.216234i
$658$	−87.9145			−0.133609
$659$			337.148i			0.511605i	0.966729	+	0.255803i	$0.0823397\pi$
$659$			337.148i			0.511605i	−0.966729	+	0.255803i	$0.917660\pi$
$660$	−43.9695	+	74.2814i	−0.0666204	+	0.112548i
$661$	−362.114			−0.547828			−0.273914	−	0.961754i	$-0.588318\pi$
$661$	−362.114			−0.547828			−0.273914	+	0.961754i	$0.588318\pi$
$662$			166.248i			0.251130i
$663$	166.567	+	98.5965i	0.251233	+	0.148713i
$664$	−106.598			−0.160539
$665$			90.7434i			0.136456i
$666$	−66.2336	+	36.3441i	−0.0994499	+	0.0545708i
$667$	50.2564			0.0753469
$668$			342.131i			0.512172i
$669$	−66.1051	+	111.677i	−0.0988118	+	0.166931i
$670$	14.5805			0.0217619
$671$		−	462.539i		−	0.689327i
$672$	673.142	+	398.454i	1.00170	+	0.592937i
$673$	−290.702			−0.431950			−0.215975	−	0.976399i	$-0.569293\pi$
$673$	−290.702			−0.431950			−0.215975	+	0.976399i	$0.569293\pi$
$674$			35.2922i			0.0523623i
$675$	−568.463	−	18.5390i	−0.842168	−	0.0274651i
$676$	−405.851			−0.600371
$677$		−	1240.26i		−	1.83200i	−0.401182	−	0.915999i	$-0.631400\pi$
$677$		−	1240.26i		−	1.83200i	0.401182	−	0.915999i	$-0.368600\pi$
$678$	−106.387	+	179.729i	−0.156913	+	0.265087i
$679$	−681.303			−1.00339
$680$		−	127.698i		−	0.187791i
$681$	−425.287	−	251.741i	−0.624503	−	0.369663i
$682$	−20.9351			−0.0306967
$683$		−	1104.33i		−	1.61688i	−0.588577	−	0.808442i	$-0.700311\pi$
$683$		−	1104.33i		−	1.61688i	0.588577	−	0.808442i	$-0.299689\pi$
$684$	−77.8751	−	141.920i	−0.113852	−	0.207485i
$685$	−480.221			−0.701053
$686$		−	233.601i		−	0.340526i
$687$	−129.052	+	218.018i	−0.187848	+	0.317348i
$688$	178.056			0.258803
$689$			436.709i			0.633830i
$690$	−14.8061	−	8.76423i	−0.0214582	−	0.0127018i
$691$	206.898			0.299419			0.149709	−	0.988730i	$-0.452166\pi$
$691$	206.898			0.299419			0.149709	+	0.988730i	$0.452166\pi$
$692$			1024.61i			1.48065i
$693$	291.093	−	159.731i	0.420048	−	0.230491i
$694$	−475.277			−0.684837
$695$			8.02683i			0.0115494i
$696$	−154.087	+	260.313i	−0.221390	+	0.374013i
$697$	−348.915			−0.500596
$698$		−	527.972i		−	0.756407i
$699$	1126.72	+	666.939i	1.61190	+	0.954133i
$700$	−546.426			−0.780609
$701$		−	480.530i		−	0.685493i	−0.939428	−	0.342746i	$-0.888643\pi$
$701$		−	480.530i		−	0.685493i	0.939428	−	0.342746i	$-0.111357\pi$
$702$	−5.11670	+	156.894i	−0.00728875	+	0.223496i
$703$	52.6487			0.0748914
$704$			4.24700i			0.00603268i
$705$	36.5348	−	61.7214i	0.0518225	−	0.0875481i
$706$	96.6002			0.136828
$707$		−	1250.74i		−	1.76908i
$708$	−103.527	−	61.2809i	−0.146225	−	0.0865550i
$709$	−443.774			−0.625916			−0.312958	−	0.949767i	$-0.601320\pi$
$709$	−443.774			−0.625916			−0.312958	+	0.949767i	$0.601320\pi$
$710$		−	74.1126i		−	0.104384i
$711$	−379.124	−	690.916i	−0.533226	−	0.971752i
$712$	−751.929			−1.05608
$713$			16.5253i			0.0231771i
$714$	−111.081	+	187.658i	−0.155575	+	0.262826i
$715$	−58.3313			−0.0815823
$716$		−	932.906i		−	1.30294i
$717$	546.899	+	323.727i	0.762760	+	0.451502i
$718$	−523.601			−0.729249
$719$		−	594.295i		−	0.826558i	−0.910605	−	0.413279i	$-0.864383\pi$
$719$		−	594.295i		−	0.826558i	0.910605	−	0.413279i	$-0.135617\pi$
$720$	−109.136	+	59.8860i	−0.151578	+	0.0831749i
$721$	1225.63			1.69991
$722$			295.696i			0.409552i
$723$	587.325	−	992.218i	0.812345	−	1.37236i
$724$	684.797			0.945853
$725$		−	328.810i		−	0.453531i
$726$	−232.689	−	137.736i	−0.320508	−	0.189719i
$727$	−242.642			−0.333758			−0.166879	−	0.985977i	$-0.553369\pi$
$727$	−242.642			−0.333758			−0.166879	+	0.985977i	$0.553369\pi$
$728$			339.707i			0.466630i
$729$	727.451	+	47.4984i	0.997875	+	0.0651555i
$730$	32.0727			0.0439352
$731$			254.467i			0.348108i
$732$	496.969	−	839.572i	0.678919	−	1.14696i
$733$	−606.089			−0.826860			−0.413430	−	0.910536i	$-0.635669\pi$
$733$	−606.089			−0.826860			−0.413430	+	0.910536i	$0.635669\pi$
$734$		−	131.427i		−	0.179056i
$735$	−86.9202	−	51.4508i	−0.118259	−	0.0700011i
$736$	103.358			0.140432
$737$			37.1789i			0.0504463i
$738$	−136.126	−	248.076i	−0.184452	−	0.336146i
$739$	−712.608			−0.964287			−0.482143	−	0.876092i	$-0.660142\pi$
$739$	−712.608			−0.964287			−0.482143	+	0.876092i	$0.660142\pi$
$740$		−	59.2156i		−	0.0800211i
$741$	55.7230	−	94.1376i	0.0751997	−	0.127041i
$742$	−492.004			−0.663078
$743$		−	53.5624i		−	0.0720894i	−0.999350	−	0.0360447i	$-0.988524\pi$
$743$		−	53.5624i		−	0.0720894i	0.999350	−	0.0360447i	$-0.0114759\pi$
$744$	−85.5959	−	50.6669i	−0.115048	−	0.0681007i
$745$	265.926			0.356948
$746$			97.9605i			0.131314i
$747$	−130.199	+	71.4438i	−0.174296	+	0.0956409i
$748$	144.558			0.193259
$749$		−	924.354i		−	1.23412i
$750$	−125.393	+	211.837i	−0.167190	+	0.282449i
$751$	−295.330			−0.393249			−0.196624	−	0.980479i	$-0.562998\pi$
$751$	−295.330			−0.393249			−0.196624	+	0.980479i	$0.562998\pi$
$752$			84.0472i			0.111765i
$753$	−678.589	−	401.678i	−0.901180	−	0.533437i
$754$	−90.7507			−0.120359
$755$			409.314i			0.542137i
$756$	699.995	+	22.8285i	0.925920	+	0.0301965i
$757$	1298.84			1.71577			0.857886	−	0.513840i	$-0.171778\pi$
$757$	1298.84			1.71577			0.857886	+	0.513840i	$0.171778\pi$
$758$		−	355.210i		−	0.468615i
$759$	22.3480	−	37.7544i	0.0294441	−	0.0497423i
$760$	−72.1700			−0.0949606
$761$		−	754.018i		−	0.990825i	−0.868658	−	0.495412i	$-0.835017\pi$
$761$		−	754.018i		−	0.990825i	0.868658	−	0.495412i	$-0.164983\pi$
$762$	515.309	+	305.028i	0.676259	+	0.400299i
$763$	−90.0201			−0.117982
$764$		−	648.185i		−	0.848409i
$765$	−85.5854	−	155.971i	−0.111876	−	0.203884i
$766$	−51.9254			−0.0677877
$767$		−	81.2972i		−	0.105994i
$768$	−180.775	+	305.399i	−0.235384	+	0.397654i
$769$	91.5092			0.118998			0.0594988	−	0.998228i	$-0.481050\pi$
$769$	91.5092			0.118998			0.0594988	+	0.998228i	$0.481050\pi$
$770$		−	65.7172i		−	0.0853470i
$771$	447.137	+	264.675i	0.579945	+	0.343288i
$772$	−545.905			−0.707131
$773$		−	924.099i		−	1.19547i	−0.801693	−	0.597736i	$-0.796067\pi$
$773$		−	924.099i		−	1.19547i	0.801693	−	0.597736i	$-0.203933\pi$
$774$	−180.924	+	99.2777i	−0.233752	+	0.128266i
$775$	108.119			0.139509
$776$		−	541.854i		−	0.698266i
$777$	−116.027	+	196.014i	−0.149327	+	0.252270i
$778$	223.900			0.287790
$779$			197.194i			0.253137i
$780$	−105.879	−	62.6734i	−0.135743	−	0.0803505i
$781$	188.981			0.241973
$782$			28.8141i			0.0368466i
$783$	−13.7370	+	421.220i	−0.0175440	+	0.537956i
$784$	118.361			0.150971
$785$			450.694i			0.574133i
$786$	143.773	−	242.888i	0.182917	−	0.309018i
$787$	868.825			1.10397			0.551985	−	0.833854i	$-0.313870\pi$
$787$	868.825			1.10397			0.551985	+	0.833854i	$0.313870\pi$
$788$			551.186i			0.699475i
$789$	−218.637	−	129.418i	−0.277106	−	0.164028i
$790$	−155.981			−0.197444
$791$			629.691i			0.796069i
$792$	127.037	+	231.512i	0.160400	+	0.292314i
$793$	659.295			0.831393
$794$		−	33.8013i		−	0.0425708i
$795$	204.463	−	345.417i	0.257187	−	0.434487i
$796$	272.838			0.342761
$797$			1466.12i			1.83955i	0.392448	+	0.919774i	$0.371628\pi$
$797$			1466.12i			1.83955i	−0.392448	+	0.919774i	$0.628372\pi$
$798$	106.057	+	62.7786i	0.132904	+	0.0786699i
$799$	−120.115			−0.150332
$800$		−	676.235i		−	0.845294i
$801$	−918.410	+	503.956i	−1.14658	+	0.629158i
$802$	113.851			0.141959
$803$			81.7827i			0.101846i
$804$	−39.9465	+	67.4849i	−0.0496847	+	0.0839365i
$805$	−51.8743			−0.0644401
$806$		−	29.8406i		−	0.0370230i
$807$	891.200	+	527.529i	1.10434	+	0.653692i
$808$	994.737			1.23111
$809$		−	873.275i		−	1.07945i	−0.841841	−	0.539725i	$-0.818528\pi$
$809$		−	873.275i		−	1.07945i	0.841841	−	0.539725i	$-0.181472\pi$
$810$	77.5037	−	121.701i	0.0956836	−	0.150248i
$811$	−399.638			−0.492772			−0.246386	−	0.969172i	$-0.579243\pi$
$811$	−399.638			−0.492772			−0.246386	+	0.969172i	$0.579243\pi$
$812$			404.891i			0.498634i
$813$	−75.9784	+	128.357i	−0.0934544	+	0.157880i
$814$	−38.1286			−0.0468411
$815$			451.873i			0.554446i
$816$	179.403	+	106.194i	0.219857	+	0.130140i
$817$	143.815			0.176028
$818$			523.755i			0.640287i
$819$	227.677	+	414.920i	0.277994	+	0.506617i
$820$	221.790			0.270475
$821$		−	63.5796i		−	0.0774417i	−0.999250	−	0.0387209i	$-0.987672\pi$
$821$		−	63.5796i		−	0.0774417i	0.999250	−	0.0387209i	$-0.0123283\pi$
$822$	−332.229	+	561.263i	−0.404172	+	0.682802i
$823$	462.625			0.562121			0.281060	−	0.959690i	$-0.409314\pi$
$823$	462.625			0.562121			0.281060	+	0.959690i	$0.409314\pi$
$824$			974.772i			1.18298i
$825$	−247.014	−	146.216i	−0.299411	−	0.177231i
$826$	91.5910			0.110885
$827$		−	309.421i		−	0.374149i	−0.982346	−	0.187074i	$-0.940099\pi$
$827$		−	309.421i		−	0.374149i	0.982346	−	0.187074i	$-0.0599005\pi$
$828$	81.1296	−	44.5180i	0.0979826	−	0.0537656i
$829$	−574.402			−0.692885			−0.346443	−	0.938071i	$-0.612610\pi$
$829$	−574.402			−0.692885			−0.346443	+	0.938071i	$0.612610\pi$
$830$			29.3938i			0.0354142i
$831$	−536.568	+	906.470i	−0.645690	+	1.09082i
$832$	−6.05361			−0.00727597
$833$			169.154i			0.203067i
$834$	9.38143	+	5.55316i	0.0112487	+	0.00665847i
$835$	212.504			0.254496
$836$		−	81.6987i		−	0.0977257i
$837$	−138.505	−	4.51698i	−0.165478	−	0.00539664i
$838$	−245.591			−0.293069
$839$			1396.43i			1.66440i	0.554478	+	0.832198i	$0.312918\pi$
$839$			1396.43i			1.66440i	−0.554478	+	0.832198i	$0.687082\pi$
$840$	159.048	−	268.693i	0.189343	−	0.319873i
$841$	597.358			0.710295
$842$		−	33.2075i		−	0.0394388i
$843$	−766.734	−	453.854i	−0.909531	−	0.538380i
$844$	11.0985			0.0131499
$845$			252.081i			0.298321i
$846$	−46.8617	−	85.4008i	−0.0553921	−	0.100947i
$847$	−815.240			−0.962503
$848$			470.361i			0.554672i
$849$	−92.0325	+	155.478i	−0.108401	+	0.183131i
$850$	188.520			0.221789
$851$			30.0971i			0.0353667i
$852$	343.027	+	203.048i	0.402614	+	0.238320i
$853$	726.057			0.851180			0.425590	−	0.904916i	$-0.360067\pi$
$853$	726.057			0.851180			0.425590	+	0.904916i	$0.360067\pi$
$854$			742.774i			0.869759i
$855$	−88.1488	+	48.3696i	−0.103098	+	0.0565726i
$856$	735.157			0.858828
$857$			988.019i			1.15288i	0.817139	+	0.576441i	$0.195559\pi$
$857$			988.019i			1.15288i	−0.817139	+	0.576441i	$0.804441\pi$
$858$	−40.3551	+	68.1752i	−0.0470339	+	0.0794583i
$859$	−526.902			−0.613390			−0.306695	−	0.951808i	$-0.599223\pi$
$859$	−526.902			−0.613390			−0.306695	+	0.951808i	$0.599223\pi$
$860$		−	161.753i		−	0.188085i
$861$	−734.163	−	434.574i	−0.852686	−	0.504732i
$862$	533.344			0.618729
$863$			393.724i			0.456227i	0.973635	+	0.228113i	$0.0732557\pi$
$863$			393.724i			0.456227i	−0.973635	+	0.228113i	$0.926744\pi$
$864$	−28.2517	+	866.286i	−0.0326987	+	1.00265i
$865$	636.405			0.735729
$866$		−	766.422i		−	0.885014i
$867$	289.867	−	489.697i	0.334333	−	0.564818i
$868$	−133.136			−0.153382
$869$		−	397.739i		−	0.457697i
$870$	71.7798	+	42.4887i	0.0825055	+	0.0488376i
$871$	−52.9943			−0.0608430
$872$		−	71.5948i		−	0.0821042i
$873$	−363.160	−	661.823i	−0.415991	−	0.758102i
$874$	16.2846			0.0186323
$875$			742.183i			0.848209i
$876$	−87.8704	+	148.447i	−0.100309	+	0.169460i
$877$	60.1951			0.0686375			0.0343188	−	0.999411i	$-0.489074\pi$
$877$	60.1951			0.0686375			0.0343188	+	0.999411i	$0.489074\pi$
$878$		−	98.2768i		−	0.111933i
$879$	389.938	+	230.816i	0.443615	+	0.262590i
$880$	−62.8263			−0.0713936
$881$			150.758i			0.171122i	0.996333	+	0.0855609i	$0.0272682\pi$
$881$			150.758i			0.171122i	−0.996333	+	0.0855609i	$0.972732\pi$
$882$	−120.267	+	65.9938i	−0.136357	+	0.0748229i
$883$	−258.162			−0.292370			−0.146185	−	0.989257i	$-0.546699\pi$
$883$	−258.162			−0.292370			−0.146185	+	0.989257i	$0.546699\pi$
$884$			206.051i			0.233089i
$885$	−38.0627	+	64.3025i	−0.0430087	+	0.0726582i
$886$	121.924			0.137612
$887$		−	291.122i		−	0.328210i	−0.986443	−	0.164105i	$-0.947526\pi$
$887$		−	291.122i		−	0.328210i	0.986443	−	0.164105i	$-0.0524736\pi$
$888$	−155.894	−	92.2785i	−0.175556	−	0.103917i
$889$	1805.42			2.03084
$890$			207.340i			0.232966i
$891$	310.327	+	197.628i	0.348291	+	0.221805i
$892$	−138.149			−0.154875
$893$			67.8845i			0.0760185i
$894$	183.974	−	310.803i	0.205788	−	0.347655i
$895$	−579.445			−0.647424
$896$			1036.15i			1.15642i
$897$	53.8146	+	31.8545i	0.0599939	+	0.0355123i
$898$	649.097			0.722825
$899$		−	80.1140i		−	0.0891146i
$900$	−291.266	−	530.803i	−0.323628	−	0.589781i
$901$	−672.212			−0.746073
$902$		−	142.809i		−	0.158325i
$903$	−316.939	+	535.432i	−0.350985	+	0.592948i
$904$	−500.806			−0.553988
$905$		−	425.340i		−	0.469989i
$906$	478.389	+	283.174i	0.528023	+	0.312554i
$907$	−1322.48			−1.45808			−0.729038	−	0.684473i	$-0.760032\pi$
$907$	−1322.48			−1.45808			−0.729038	+	0.684473i	$0.760032\pi$
$908$		−	526.097i		−	0.579402i
$909$	1214.98	−	666.690i	1.33661	−	0.733432i
$910$	93.6722			0.102936
$911$			465.661i			0.511153i	0.966789	+	0.255577i	$0.0822653\pi$
$911$			465.661i			0.511153i	−0.966789	+	0.255577i	$0.917735\pi$
$912$	60.0170	−	101.392i	0.0658081	−	0.111175i
$913$	−74.9517			−0.0820938
$914$		−	75.9257i		−	0.0830697i
$915$	−521.473	−	308.676i	−0.569916	−	0.337351i
$916$	−269.697			−0.294429
$917$		−	850.974i		−	0.927997i
$918$	−241.503	−	7.87598i	−0.263075	−	0.00857950i
$919$	873.292			0.950263			0.475132	−	0.879915i	$-0.342400\pi$
$919$	873.292			0.950263			0.475132	+	0.879915i	$0.342400\pi$
$920$		−	41.2566i		−	0.0448442i
$921$	−726.872	+	1227.97i	−0.789221	+	1.33330i
$922$	646.517			0.701211
$923$			269.370i			0.291842i
$924$	304.169	+	180.047i	0.329187	+	0.194856i
$925$	196.915			0.212881
$926$			67.5454i			0.0729432i
$927$	653.309	+	1190.59i	0.704756	+	1.28435i
$928$	−501.076			−0.539953
$929$		−	942.866i		−	1.01493i	−0.861674	−	0.507463i	$-0.830583\pi$
$929$		−	942.866i		−	1.01493i	0.861674	−	0.507463i	$-0.169417\pi$
$930$	−13.9711	+	23.6026i	−0.0150227	+	0.0253791i
$931$	95.5996			0.102685
$932$			1393.79i			1.49549i
$933$	−816.318	−	483.204i	−0.874938	−	0.517904i
$934$	238.337			0.255179
$935$		−	89.7876i		−	0.0960295i
$936$	−329.994	+	181.076i	−0.352558	+	0.193458i
$937$	−1071.92			−1.14399			−0.571994	−	0.820258i	$-0.693830\pi$
$937$	−1071.92			−1.14399			−0.571994	+	0.820258i	$0.693830\pi$
$938$		−	59.7043i		−	0.0636507i
$939$	46.2604	−	78.1516i	0.0492656	−	0.0832285i
$940$	76.3518			0.0812254
$941$			808.827i			0.859540i	0.902938	+	0.429770i	$0.141405\pi$
$941$			808.827i			0.859540i	−0.902938	+	0.429770i	$0.858595\pi$
$942$	526.753	+	311.802i	0.559186	+	0.331000i
$943$	−112.727			−0.119541
$944$		−	87.5620i		−	0.0927563i
$945$	14.1792	−	434.780i	0.0150045	−	0.460084i
$946$	−104.152			−0.110097
$947$		−	1098.05i		−	1.15950i	−0.814793	−	0.579752i	$-0.803149\pi$
$947$		−	1098.05i		−	1.15950i	0.814793	−	0.579752i	$-0.196851\pi$
$948$	427.346	−	721.951i	0.450786	−	0.761552i
$949$	−116.572			−0.122836
$950$		−	106.545i		−	0.112152i
$951$	−1378.01	−	815.690i	−1.44902	−	0.857719i
$952$	−522.900			−0.549265
$953$			260.350i			0.273189i	0.990627	+	0.136595i	$0.0436158\pi$
$953$			260.350i			0.273189i	−0.990627	+	0.136595i	$0.956384\pi$
$954$	−262.256	−	477.937i	−0.274902	−	0.500982i
$955$	−402.599			−0.421570
$956$			676.537i			0.707674i
$957$	−108.343	+	183.032i	−0.113211	+	0.191256i
$958$	807.790			0.843204
$959$			1966.42i			2.05049i
$960$	4.78814	+	2.83425i	0.00498764	+	0.00295234i
$961$	−934.657			−0.972588
$962$		−	54.3479i		−	0.0564947i
$963$	897.924	−	492.715i	0.932424	−	0.511646i
$964$	1227.41			1.27325
$965$			339.071i			0.351369i
$966$	−35.8879	+	60.6285i	−0.0371511	+	0.0627624i
$967$	117.991			0.122017			0.0610086	−	0.998137i	$-0.480568\pi$
$967$	117.991			0.122017			0.0610086	+	0.998137i	$0.480568\pi$
$968$		−	648.376i		−	0.669810i
$969$	144.903	+	85.7727i	0.149539	+	0.0885167i
$970$	−149.413			−0.154034
$971$		−	1385.12i		−	1.42649i	−0.700916	−	0.713244i	$-0.747225\pi$
$971$		−	1385.12i		−	1.42649i	0.700916	−	0.713244i	$-0.252775\pi$
$972$	350.948	+	692.149i	0.361057	+	0.712088i
$973$	32.8684			0.0337805
$974$			48.3108i			0.0496004i
$975$	208.413	−	352.090i	0.213757	−	0.361118i
$976$	710.100			0.727562
$977$		−	1723.83i		−	1.76442i	−0.470860	−	0.882208i	$-0.656056\pi$
$977$		−	1723.83i		−	1.76442i	0.470860	−	0.882208i	$-0.343944\pi$
$978$	528.131	+	312.617i	0.540011	+	0.319650i
$979$	−528.700			−0.540040
$980$		−	107.524i		−	0.109718i
$981$	−47.9841	−	87.4463i	−0.0489134	−	0.0891399i
$982$	67.1464			0.0683772
$983$			974.059i			0.990904i	0.868635	+	0.495452i	$0.164998\pi$
$983$			974.059i			0.990904i	−0.868635	+	0.495452i	$0.835002\pi$
$984$	345.626	−	583.894i	0.351246	−	0.593389i
$985$	342.352			0.347565
$986$		−	139.690i		−	0.141673i
$987$	−252.738	−	149.604i	−0.256067	−	0.151574i
$988$	116.452			0.117866
$989$			82.2132i			0.0831276i
$990$	63.8382	−	35.0297i	0.0644830	−	0.0353835i
$991$	369.792			0.373150			0.186575	−	0.982441i	$-0.440261\pi$
$991$	369.792			0.373150			0.186575	+	0.982441i	$0.440261\pi$
$992$		−	164.764i		−	0.166092i
$993$	−282.904	+	477.933i	−0.284898	+	0.481302i
$994$	−303.478			−0.305310
$995$		−	169.464i		−	0.170316i
$996$	−136.048	−	80.5309i	−0.136594	−	0.0808543i
$997$	−94.9153			−0.0952009			−0.0476004	−	0.998866i	$-0.515157\pi$
$997$	−94.9153			−0.0952009			−0.0476004	+	0.998866i	$0.515157\pi$
$998$			91.2742i			0.0914572i
$999$	−252.256	−	8.22667i	−0.252509	−	0.00823491i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.c.a.68.18	✓	44
3.2	odd	2	inner	201.3.c.a.68.27	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.c.a.68.18	✓	44	1.1	even	1	trivial
201.3.c.a.68.27	yes	44	3.2	odd	2	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.898014i q^{2} +(1.52814 - 2.58162i) q^{3} +3.19357 q^{4} -1.98358i q^{5} +(-2.31833 - 1.37229i) q^{6} -8.12242 q^{7} -6.45992i q^{8} +(-4.32955 - 7.89018i) q^{9} +O(q^{10})\)	\(q-0.898014i q^{2} +(1.52814 - 2.58162i) q^{3} +3.19357 q^{4} -1.98358i q^{5} +(-2.31833 - 1.37229i) q^{6} -8.12242 q^{7} -6.45992i q^{8} +(-4.32955 - 7.89018i) q^{9} -1.78129 q^{10} -4.54213i q^{11} +(4.88024 - 8.24460i) q^{12} +6.47428 q^{13} +7.29404i q^{14} +(-5.12087 - 3.03120i) q^{15} +6.97319 q^{16} +9.96566i q^{17} +(-7.08549 + 3.88800i) q^{18} +5.63221 q^{19} -6.33472i q^{20} +(-12.4122 + 20.9690i) q^{21} -4.07890 q^{22} +3.21970i q^{23} +(-16.6771 - 9.87170i) q^{24} +21.0654 q^{25} -5.81399i q^{26} +(-26.9857 - 0.880067i) q^{27} -25.9395 q^{28} -15.6090i q^{29} +(-2.72206 + 4.59861i) q^{30} +5.13255 q^{31} -32.1017i q^{32} +(-11.7261 - 6.94103i) q^{33} +8.94930 q^{34} +16.1115i q^{35} +(-13.8267 - 25.1979i) q^{36} +9.34778 q^{37} -5.05780i q^{38} +(9.89363 - 16.7141i) q^{39} -12.8138 q^{40} +35.0118i q^{41} +(18.8305 + 11.1464i) q^{42} +25.5344 q^{43} -14.5056i q^{44} +(-15.6508 + 8.58803i) q^{45} +2.89134 q^{46} +12.0529i q^{47} +(10.6560 - 18.0021i) q^{48} +16.9737 q^{49} -18.9170i q^{50} +(25.7276 + 15.2290i) q^{51} +20.6761 q^{52} +67.4529i q^{53} +(-0.790312 + 24.2335i) q^{54} -9.00970 q^{55} +52.4702i q^{56} +(8.60683 - 14.5402i) q^{57} -14.0171 q^{58} -12.5570i q^{59} +(-16.3539 - 9.68037i) q^{60} +101.833 q^{61} -4.60910i q^{62} +(35.1664 + 64.0874i) q^{63} -0.935025 q^{64} -12.8423i q^{65} +(-6.23314 + 10.5302i) q^{66} -8.18535 q^{67} +31.8260i q^{68} +(8.31205 + 4.92017i) q^{69} +14.4684 q^{70} +41.6062i q^{71} +(-50.9700 + 27.9686i) q^{72} -18.0054 q^{73} -8.39443i q^{74} +(32.1910 - 54.3829i) q^{75} +17.9869 q^{76} +36.8931i q^{77} +(-15.0095 - 8.88461i) q^{78} +87.5665 q^{79} -13.8319i q^{80} +(-43.5100 + 68.3219i) q^{81} +31.4410 q^{82} -16.5014i q^{83} +(-39.6393 + 66.9661i) q^{84} +19.7677 q^{85} -22.9302i q^{86} +(-40.2966 - 23.8528i) q^{87} -29.3418 q^{88} -116.399i q^{89} +(7.71217 + 14.0547i) q^{90} -52.5868 q^{91} +10.2823i q^{92} +(7.84327 - 13.2503i) q^{93} +10.8237 q^{94} -11.1720i q^{95} +(-82.8745 - 49.0560i) q^{96} +83.8793 q^{97} -15.2426i q^{98} +(-35.8382 + 19.6654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9	\( 44 q - 92 q^{4} + 6 q^{6} + 8 q^{7} + 4 q^{9} + 12 q^{10} - 20 q^{12} - 32 q^{13} - 30 q^{15} + 204 q^{16} + 22 q^{18} - 32 q^{19} + 36 q^{21} - 8 q^{22} - 24 q^{24} - 164 q^{25} + 42 q^{27} - 48 q^{28} + 58 q^{30} + 20 q^{31} + 6 q^{33} - 48 q^{34} - 78 q^{36} + 100 q^{37} + 4 q^{39} + 160 q^{40} - 204 q^{42} - 108 q^{43} - 132 q^{45} - 244 q^{46} + 34 q^{48} + 332 q^{49} + 114 q^{51} - 8 q^{52} + 432 q^{54} + 128 q^{55} - 26 q^{57} - 12 q^{58} + 250 q^{60} - 164 q^{61} - 290 q^{63} - 432 q^{64} - 78 q^{66} + 76 q^{69} + 612 q^{70} - 464 q^{72} + 156 q^{73} - 118 q^{75} - 180 q^{76} - 392 q^{79} + 348 q^{81} + 524 q^{82} - 202 q^{84} - 188 q^{85} - 68 q^{87} - 348 q^{88} + 94 q^{90} - 44 q^{91} + 322 q^{93} - 304 q^{94} + 224 q^{96} + 68 q^{97} + 104 q^{99}+O(q^{100}) \) 44 * q - 92 * q^4 + 6 * q^6 + 8 * q^7 + 4 * q^9 + 12 * q^10 - 20 * q^12 - 32 * q^13 - 30 * q^15 + 204 * q^16 + 22 * q^18 - 32 * q^19 + 36 * q^21 - 8 * q^22 - 24 * q^24 - 164 * q^25 + 42 * q^27 - 48 * q^28 + 58 * q^30 + 20 * q^31 + 6 * q^33 - 48 * q^34 - 78 * q^36 + 100 * q^37 + 4 * q^39 + 160 * q^40 - 204 * q^42 - 108 * q^43 - 132 * q^45 - 244 * q^46 + 34 * q^48 + 332 * q^49 + 114 * q^51 - 8 * q^52 + 432 * q^54 + 128 * q^55 - 26 * q^57 - 12 * q^58 + 250 * q^60 - 164 * q^61 - 290 * q^63 - 432 * q^64 - 78 * q^66 + 76 * q^69 + 612 * q^70 - 464 * q^72 + 156 * q^73 - 118 * q^75 - 180 * q^76 - 392 * q^79 + 348 * q^81 + 524 * q^82 - 202 * q^84 - 188 * q^85 - 68 * q^87 - 348 * q^88 + 94 * q^90 - 44 * q^91 + 322 * q^93 - 304 * q^94 + 224 * q^96 + 68 * q^97 + 104 * q^99

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