LMFDB - Embedded newform 201.3.c.a.68.14

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			68.14
Character	$\chi$	$=$	201.68
Dual form			201.3.c.a.68.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.81184i q^{2} +(0.454991 - 2.96530i) q^{3} +0.717236 q^{4} +6.02732i q^{5} +(-5.37264 - 0.824371i) q^{6} +13.4974 q^{7} -8.54688i q^{8} +(-8.58597 - 2.69837i) q^{9} +O(q^{10})$	\(q-1.81184i q^{2} +(0.454991 - 2.96530i) q^{3} +0.717236 q^{4} +6.02732i q^{5} +(-5.37264 - 0.824371i) q^{6} +13.4974 q^{7} -8.54688i q^{8} +(-8.58597 - 2.69837i) q^{9} +10.9205 q^{10} -4.38146i q^{11} +(0.326336 - 2.12682i) q^{12} +11.7213 q^{13} -24.4552i q^{14} +(17.8728 + 2.74238i) q^{15} -12.6166 q^{16} +1.06983i q^{17} +(-4.88901 + 15.5564i) q^{18} -26.2982 q^{19} +4.32301i q^{20} +(6.14120 - 40.0238i) q^{21} -7.93851 q^{22} +15.8281i q^{23} +(-25.3440 - 3.88875i) q^{24} -11.3286 q^{25} -21.2371i q^{26} +(-11.9080 + 24.2322i) q^{27} +9.68084 q^{28} +3.83175i q^{29} +(4.96875 - 32.3826i) q^{30} -59.1179 q^{31} -11.3282i q^{32} +(-12.9923 - 1.99353i) q^{33} +1.93836 q^{34} +81.3532i q^{35} +(-6.15817 - 1.93537i) q^{36} +40.7500 q^{37} +47.6481i q^{38} +(5.33307 - 34.7570i) q^{39} +51.5148 q^{40} -20.7595i q^{41} +(-72.5168 - 11.1269i) q^{42} +2.22180 q^{43} -3.14255i q^{44} +(16.2639 - 51.7504i) q^{45} +28.6779 q^{46} -6.59202i q^{47} +(-5.74045 + 37.4120i) q^{48} +133.180 q^{49} +20.5256i q^{50} +(3.17236 + 0.486762i) q^{51} +8.40692 q^{52} -36.2204i q^{53} +(43.9049 + 21.5754i) q^{54} +26.4085 q^{55} -115.361i q^{56} +(-11.9654 + 77.9819i) q^{57} +6.94252 q^{58} +69.4818i q^{59} +(12.8190 + 1.96693i) q^{60} -75.2142 q^{61} +107.112i q^{62} +(-115.888 - 36.4210i) q^{63} -70.9914 q^{64} +70.6478i q^{65} +(-3.61195 + 23.5400i) q^{66} -8.18535 q^{67} +0.767319i q^{68} +(46.9350 + 7.20164i) q^{69} +147.399 q^{70} +133.217i q^{71} +(-23.0626 + 73.3832i) q^{72} +31.0744 q^{73} -73.8324i q^{74} +(-5.15441 + 33.5927i) q^{75} -18.8620 q^{76} -59.1384i q^{77} +(-62.9742 - 9.66267i) q^{78} +21.0158 q^{79} -76.0445i q^{80} +(66.4376 + 46.3362i) q^{81} -37.6128 q^{82} -30.9402i q^{83} +(4.40469 - 28.7065i) q^{84} -6.44819 q^{85} -4.02554i q^{86} +(11.3623 + 1.74341i) q^{87} -37.4478 q^{88} +148.877i q^{89} +(-93.7634 - 29.4676i) q^{90} +158.207 q^{91} +11.3525i q^{92} +(-26.8981 + 175.302i) q^{93} -11.9437 q^{94} -158.508i q^{95} +(-33.5915 - 5.15423i) q^{96} -50.4272 q^{97} -241.301i q^{98} +(-11.8228 + 37.6191i) 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 $

$2$		−	1.81184i		−	0.905920i	−0.891531	−	0.452960i	$-0.850368\pi$
$2$		−	1.81184i		−	0.905920i	0.891531	−	0.452960i	$-0.149632\pi$
$3$	0.454991	−	2.96530i	0.151664	−	0.988432i
$3$	0.454991	−	2.96530i	0.151664	−	0.988432i
$4$	0.717236			0.179309
$5$			6.02732i			1.20546i	0.797944	+	0.602732i	$0.205921\pi$
$5$			6.02732i			1.20546i	−0.797944	+	0.602732i	$0.794079\pi$
$6$	−5.37264	−	0.824371i	−0.895440	−	0.137395i
$7$	13.4974			1.92820			0.964101	−	0.265536i	$-0.0855489\pi$
$7$	13.4974			1.92820			0.964101	+	0.265536i	$0.0855489\pi$
$8$		−	8.54688i		−	1.06836i
$9$	−8.58597	−	2.69837i	−0.953996	−	0.299819i
$10$	10.9205			1.09205
$11$		−	4.38146i		−	0.398315i	−0.979968	−	0.199157i	$-0.936179\pi$
$11$		−	4.38146i		−	0.398315i	0.979968	−	0.199157i	$-0.0638205\pi$
$12$	0.326336	−	2.12682i	0.0271947	−	0.177235i
$13$	11.7213			0.901636			0.450818	−	0.892616i	$-0.351132\pi$
$13$	11.7213			0.901636			0.450818	+	0.892616i	$0.351132\pi$
$14$		−	24.4552i		−	1.74680i
$15$	17.8728	+	2.74238i	1.19152	+	0.182825i
$16$	−12.6166			−0.788539
$17$			1.06983i			0.0629310i	0.999505	+	0.0314655i	$0.0100174\pi$
$17$			1.06983i			0.0629310i	−0.999505	+	0.0314655i	$0.989983\pi$
$18$	−4.88901	+	15.5564i	−0.271612	+	0.864244i
$19$	−26.2982			−1.38411			−0.692057	−	0.721842i	$-0.743296\pi$
$19$	−26.2982			−1.38411			−0.692057	+	0.721842i	$0.743296\pi$
$20$			4.32301i			0.216151i
$21$	6.14120	−	40.0238i	0.292438	−	1.90590i
$22$	−7.93851			−0.360841
$23$			15.8281i			0.688177i	0.938937	+	0.344089i	$0.111812\pi$
$23$			15.8281i			0.688177i	−0.938937	+	0.344089i	$0.888188\pi$
$24$	−25.3440	−	3.88875i	−1.05600	−	0.162031i
$25$	−11.3286			−0.453144
$26$		−	21.2371i		−	0.816810i
$27$	−11.9080	+	24.2322i	−0.441037	+	0.897489i
$28$	9.68084			0.345744
$29$			3.83175i			0.132129i	0.997815	+	0.0660647i	$0.0210444\pi$
$29$			3.83175i			0.132129i	−0.997815	+	0.0660647i	$0.978956\pi$
$30$	4.96875	−	32.3826i	0.165625	−	1.07942i
$31$	−59.1179			−1.90703			−0.953514	−	0.301347i	$-0.902564\pi$
$31$	−59.1179			−1.90703			−0.953514	+	0.301347i	$0.902564\pi$
$32$		−	11.3282i		−	0.354006i
$33$	−12.9923	−	1.99353i	−0.393707	−	0.0604099i
$34$	1.93836			0.0570105
$35$			81.3532i			2.32438i
$36$	−6.15817	−	1.93537i	−0.171060	−	0.0537602i
$37$	40.7500			1.10135			0.550675	−	0.834720i	$-0.314370\pi$
$37$	40.7500			1.10135			0.550675	+	0.834720i	$0.314370\pi$
$38$			47.6481i			1.25390i
$39$	5.33307	−	34.7570i	0.136745	−	0.891206i
$40$	51.5148			1.28787
$41$		−	20.7595i		−	0.506328i	−0.967423	−	0.253164i	$-0.918529\pi$
$41$		−	20.7595i		−	0.506328i	0.967423	−	0.253164i	$-0.0814713\pi$
$42$	−72.5168	−	11.1269i	−1.72659	−	0.264926i
$43$	2.22180			0.0516697			0.0258349	−	0.999666i	$-0.491776\pi$
$43$	2.22180			0.0516697			0.0258349	+	0.999666i	$0.491776\pi$
$44$		−	3.14255i		−	0.0714215i
$45$	16.2639	−	51.7504i	0.361421	−	1.15001i
$46$	28.6779			0.623434
$47$		−	6.59202i		−	0.140256i	−0.997538	−	0.0701278i	$-0.977659\pi$
$47$		−	6.59202i		−	0.140256i	0.997538	−	0.0701278i	$-0.0223407\pi$
$48$	−5.74045	+	37.4120i	−0.119593	+	0.779417i
$49$	133.180			2.71796
$50$			20.5256i			0.410512i
$51$	3.17236	+	0.486762i	0.0622031	+	0.00954435i
$52$	8.40692			0.161671
$53$		−	36.2204i		−	0.683404i	−0.939808	−	0.341702i	$-0.888997\pi$
$53$		−	36.2204i		−	0.683404i	0.939808	−	0.341702i	$-0.111003\pi$
$54$	43.9049	+	21.5754i	0.813053	+	0.399544i
$55$	26.4085			0.480154
$56$		−	115.361i		−	2.06001i
$57$	−11.9654	+	77.9819i	−0.209920	+	1.36810i
$58$	6.94252			0.119699
$59$			69.4818i			1.17766i	0.808257	+	0.588829i	$0.200411\pi$
$59$			69.4818i			1.17766i	−0.808257	+	0.588829i	$0.799589\pi$
$60$	12.8190	+	1.96693i	0.213650	+	0.0327822i
$61$	−75.2142			−1.23302			−0.616510	−	0.787347i	$-0.711454\pi$
$61$	−75.2142			−1.23302			−0.616510	+	0.787347i	$0.711454\pi$
$62$			107.112i			1.72762i
$63$	−115.888	−	36.4210i	−1.83950	−	0.578111i
$64$	−70.9914			−1.10924
$65$			70.6478i			1.08689i
$66$	−3.61195	+	23.5400i	−0.0547265	+	0.356667i
$67$	−8.18535			−0.122169
$67$	−8.18535			−0.122169
$68$			0.767319i			0.0112841i
$69$	46.9350	+	7.20164i	0.680217	+	0.104372i
$70$	147.399			2.10570
$71$			133.217i			1.87630i	0.346236	+	0.938148i	$0.387460\pi$
$71$			133.217i			1.87630i	−0.346236	+	0.938148i	$0.612540\pi$
$72$	−23.0626	+	73.3832i	−0.320314	+	1.01921i
$73$	31.0744			0.425677			0.212839	−	0.977087i	$-0.431729\pi$
$73$	31.0744			0.425677			0.212839	+	0.977087i	$0.431729\pi$
$74$		−	73.8324i		−	0.997735i
$75$	−5.15441	+	33.5927i	−0.0687255	+	0.447902i
$76$	−18.8620			−0.248184
$77$		−	59.1384i		−	0.768032i
$78$	−62.9742	−	9.66267i	−0.807361	−	0.123880i
$79$	21.0158			0.266022			0.133011	−	0.991115i	$-0.457535\pi$
$79$	21.0158			0.266022			0.133011	+	0.991115i	$0.457535\pi$
$80$		−	76.0445i		−	0.950556i
$81$	66.4376	+	46.3362i	0.820218	+	0.572052i
$82$	−37.6128			−0.458693
$83$		−	30.9402i		−	0.372773i	−0.982476	−	0.186387i	$-0.940322\pi$
$83$		−	30.9402i		−	0.372773i	0.982476	−	0.186387i	$-0.0596777\pi$
$84$	4.40469	−	28.7065i	0.0524368	−	0.341745i
$85$	−6.44819			−0.0758611
$86$		−	4.02554i		−	0.0468086i
$87$	11.3623	+	1.74341i	0.130601	+	0.0200392i
$88$	−37.4478			−0.425544
$89$			148.877i			1.67278i	0.548137	+	0.836388i	$0.315337\pi$
$89$			148.877i			1.67278i	−0.548137	+	0.836388i	$0.684663\pi$
$90$	−93.7634	−	29.4676i	−1.04182	−	0.327418i
$91$	158.207			1.73854
$92$			11.3525i			0.123396i
$93$	−26.8981	+	175.302i	−0.289227	+	1.88497i
$94$	−11.9437			−0.127060
$95$		−	158.508i		−	1.66850i
$96$	−33.5915	−	5.15423i	−0.349911	−	0.0536899i
$97$	−50.4272			−0.519869			−0.259934	−	0.965626i	$-0.583701\pi$
$97$	−50.4272			−0.519869			−0.259934	+	0.965626i	$0.583701\pi$
$98$		−	241.301i		−	2.46226i
$99$	−11.8228	+	37.6191i	−0.119422	+	0.379991i
$100$	−8.12528			−0.0812528
$101$		−	162.939i		−	1.61325i	−0.591060	−	0.806627i	$-0.701291\pi$
$101$		−	162.939i		−	1.61325i	0.591060	−	0.806627i	$-0.298709\pi$
$102$	0.881935	−	5.74780i	0.00864642	−	0.0563510i
$103$	−96.7162			−0.938992			−0.469496	−	0.882935i	$-0.655564\pi$
$103$	−96.7162			−0.938992			−0.469496	+	0.882935i	$0.655564\pi$
$104$		−	100.180i		−	0.963271i
$105$	241.236	+	37.0150i	2.29749	+	0.352524i
$106$	−65.6255			−0.619109
$107$			87.2987i			0.815875i	0.913010	+	0.407938i	$0.133752\pi$
$107$			87.2987i			0.815875i	−0.913010	+	0.407938i	$0.866248\pi$
$108$	−8.54085	+	17.3802i	−0.0790819	+	0.160928i
$109$	84.4942			0.775176			0.387588	−	0.921833i	$-0.373308\pi$
$109$	84.4942			0.775176			0.387588	+	0.921833i	$0.373308\pi$
$110$		−	47.8480i		−	0.434981i
$111$	18.5409	−	120.836i	0.167035	−	1.08861i
$112$	−170.292			−1.52046
$113$			175.598i			1.55396i	0.629524	+	0.776981i	$0.283250\pi$
$113$			175.598i			1.55396i	−0.629524	+	0.776981i	$0.716750\pi$
$114$	141.291	+	21.6795i	1.23939	+	0.190171i
$115$	−95.4009			−0.829573
$116$			2.74827i			0.0236920i
$117$	−100.638	−	31.6283i	−0.860157	−	0.270327i
$118$	125.890			1.06686
$119$			14.4399i			0.121344i
$120$	23.4388	−	152.757i	0.195323	−	1.27297i
$121$	101.803			0.841345
$122$			136.276i			1.11702i
$123$	−61.5579	−	9.44537i	−0.500471	−	0.0767916i
$124$	−42.4015			−0.341948
$125$			82.4019i			0.659215i
$126$	−65.9890	+	209.971i	−0.523722	+	1.66644i
$127$	48.9492			0.385427			0.192713	−	0.981255i	$-0.438271\pi$
$127$	48.9492			0.385427			0.192713	+	0.981255i	$0.438271\pi$
$128$			83.3122i			0.650877i
$129$	1.01090	−	6.58829i	0.00783642	−	0.0510720i
$130$	128.003			0.984635
$131$		−	137.259i		−	1.04777i	−0.851788	−	0.523887i	$-0.824481\pi$
$131$		−	137.259i		−	1.04777i	0.851788	−	0.523887i	$-0.175519\pi$
$132$	−9.31858	−	1.42983i	−0.0705953	−	0.0108320i
$133$	−354.957			−2.66885
$134$			14.8305i			0.110676i
$135$	−146.055	−	71.7733i	−1.08189	−	0.531654i
$136$	9.14368			0.0672330
$137$		−	159.427i		−	1.16370i	−0.813297	−	0.581849i	$-0.802329\pi$
$137$		−	159.427i		−	1.16370i	0.813297	−	0.581849i	$-0.197671\pi$
$138$	13.0482	−	85.0386i	0.0945522	−	0.616222i
$139$	−108.731			−0.782237			−0.391118	−	0.920340i	$-0.627912\pi$
$139$	−108.731			−0.782237			−0.391118	+	0.920340i	$0.627912\pi$
$140$			58.3495i			0.416782i
$141$	−19.5473	−	2.99931i	−0.138633	−	0.0212717i
$142$	241.368			1.69977
$143$		−	51.3563i		−	0.359135i
$144$	108.326	+	34.0443i	0.752263	+	0.236419i
$145$	−23.0952			−0.159277
$146$		−	56.3019i		−	0.385629i
$147$	60.5958	−	394.919i	0.412216	−	2.68652i
$148$	29.2273			0.197482
$149$		−	65.0190i		−	0.436369i	−0.975908	−	0.218185i	$-0.929986\pi$
$149$		−	65.0190i		−	0.436369i	0.975908	−	0.218185i	$-0.0700135\pi$
$150$	60.8645	+	9.33897i	0.405763	+	0.0622598i
$151$	−101.300			−0.670859			−0.335429	−	0.942065i	$-0.608881\pi$
$151$	−101.300			−0.670859			−0.335429	+	0.942065i	$0.608881\pi$
$152$			224.767i			1.47873i
$153$	2.88679	−	9.18550i	0.0188679	−	0.0600360i
$154$	−107.149			−0.695775
$155$		−	356.323i		−	2.29886i
$156$	3.82507	−	24.9290i	0.0245197	−	0.159801i
$157$	−64.0595			−0.408023			−0.204011	−	0.978969i	$-0.565398\pi$
$157$	−64.0595			−0.408023			−0.204011	+	0.978969i	$0.565398\pi$
$158$		−	38.0772i		−	0.240995i
$159$	−107.404	−	16.4800i	−0.675498	−	0.103648i
$160$	68.2787			0.426742
$161$			213.638i			1.32694i
$162$	83.9537	−	120.374i	0.518233	−	0.743052i
$163$	−27.5742			−0.169167			−0.0845834	−	0.996416i	$-0.526956\pi$
$163$	−27.5742			−0.169167			−0.0845834	+	0.996416i	$0.526956\pi$
$164$		−	14.8894i		−	0.0907892i
$165$	12.0156	−	78.3090i	0.0728220	−	0.474600i
$166$	−56.0586			−0.337702
$167$		−	147.078i		−	0.880708i	−0.897824	−	0.440354i	$-0.854853\pi$
$167$		−	147.078i		−	0.880708i	0.897824	−	0.440354i	$-0.145147\pi$
$168$	−342.079	−	52.4881i	−2.03618	−	0.312429i
$169$	−31.6120			−0.187053
$170$			11.6831i			0.0687241i
$171$	225.795	+	70.9621i	1.32044	+	0.414983i
$172$	1.59355			0.00926485
$173$			30.0504i			0.173702i	0.996221	+	0.0868509i	$0.0276804\pi$
$173$			30.0504i			0.173702i	−0.996221	+	0.0868509i	$0.972320\pi$
$174$	3.15879	−	20.5866i	0.0181539	−	0.118314i
$175$	−152.907			−0.873753
$176$			55.2793i			0.314087i
$177$	206.034	+	31.6136i	1.16404	+	0.178608i
$178$	269.741			1.51540
$179$			186.554i			1.04220i	0.853496	+	0.521100i	$0.174478\pi$
$179$			186.554i			1.04220i	−0.853496	+	0.521100i	$0.825522\pi$
$180$	11.6651	−	37.1173i	0.0648060	−	0.206207i
$181$	139.720			0.771932			0.385966	−	0.922513i	$-0.373868\pi$
$181$	139.720			0.771932			0.385966	+	0.922513i	$0.373868\pi$
$182$		−	286.645i		−	1.57497i
$183$	−34.2218	+	223.032i	−0.187004	+	1.21876i
$184$	135.281			0.735221
$185$			245.613i			1.32764i
$186$	317.619	+	48.7351i	1.70763	+	0.262017i
$187$	4.68741			0.0250664
$188$		−	4.72803i		−	0.0251491i
$189$	−160.727	+	327.072i	−0.850408	+	1.73054i
$190$	−287.190			−1.51153
$191$			209.659i			1.09769i	0.835924	+	0.548846i	$0.184932\pi$
$191$			209.659i			1.09769i	−0.835924	+	0.548846i	$0.815068\pi$
$192$	−32.3004	+	210.511i	−0.168232	+	1.09641i
$193$	183.474			0.950644			0.475322	−	0.879812i	$-0.342331\pi$
$193$	183.474			0.950644			0.475322	+	0.879812i	$0.342331\pi$
$194$			91.3661i			0.470959i
$195$	209.492	+	32.1441i	1.07432	+	0.164842i
$196$	95.5217			0.487355
$197$		−	263.724i		−	1.33870i	−0.742946	−	0.669351i	$-0.766572\pi$
$197$		−	263.724i		−	1.33870i	0.742946	−	0.669351i	$-0.233428\pi$
$198$	68.1598	+	21.4210i	0.344241	+	0.108187i
$199$	−90.3192			−0.453865			−0.226933	−	0.973910i	$-0.572870\pi$
$199$	−90.3192			−0.453865			−0.226933	+	0.973910i	$0.572870\pi$
$200$			96.8242i			0.484121i
$201$	−3.72426	+	24.2720i	−0.0185287	+	0.120756i
$202$	−295.219			−1.46148
$203$			51.7188i			0.254772i
$204$	2.27533	+	0.349123i	0.0111536	+	0.00171139i
$205$	125.124			0.610360
$206$			175.234i			0.850652i
$207$	42.7100	−	135.899i	0.206328	−	0.656519i
$208$	−147.883			−0.710975
$209$			115.225i			0.551314i
$210$	67.0653	−	437.082i	0.319358	−	2.08134i
$211$	−37.0914			−0.175788			−0.0878942	−	0.996130i	$-0.528014\pi$
$211$	−37.0914			−0.175788			−0.0878942	+	0.996130i	$0.528014\pi$
$212$		−	25.9786i		−	0.122540i
$213$	395.028	+	60.6125i	1.85459	+	0.284566i
$214$	158.171			0.739118
$215$			13.3915i			0.0622860i
$216$	207.110	+	101.776i	0.958841	+	0.471186i
$217$	−797.939			−3.67714
$218$		−	153.090i		−	0.702247i
$219$	14.1386	−	92.1449i	0.0645597	−	0.420753i
$220$	18.9411			0.0860960
$221$			12.5397i			0.0567409i
$222$	−218.935	−	33.5931i	−0.986193	−	0.151320i
$223$	256.728			1.15124			0.575622	−	0.817716i	$-0.304760\pi$
$223$	256.728			1.15124			0.575622	+	0.817716i	$0.304760\pi$
$224$		−	152.901i		−	0.682596i
$225$	97.2670	+	30.5687i	0.432298	+	0.135861i
$226$	318.155			1.40777
$227$		−	162.175i		−	0.714429i	−0.934022	−	0.357214i	$-0.883727\pi$
$227$		−	162.175i		−	0.714429i	0.934022	−	0.357214i	$-0.116273\pi$
$228$	−8.58205	+	55.9315i	−0.0376406	+	0.245313i
$229$	−264.578			−1.15536			−0.577681	−	0.816262i	$-0.696042\pi$
$229$	−264.578			−1.15536			−0.577681	+	0.816262i	$0.696042\pi$
$230$			172.851i			0.751527i
$231$	−175.363	−	26.9075i	−0.759147	−	0.116482i
$232$	32.7495			0.141162
$233$		−	265.024i		−	1.13744i	−0.822530	−	0.568721i	$-0.807438\pi$
$233$		−	265.024i		−	1.13744i	0.822530	−	0.568721i	$-0.192562\pi$
$234$	−57.3054	+	182.341i	−0.244895	+	0.779233i
$235$	39.7322			0.169073
$236$			49.8349i			0.211165i
$237$	9.56198	−	62.3179i	0.0403459	−	0.262945i
$238$	26.1628			0.109928
$239$		−	123.526i		−	0.516847i	−0.966032	−	0.258423i	$-0.916797\pi$
$239$		−	123.526i		−	0.516847i	0.966032	−	0.258423i	$-0.0832029\pi$
$240$	−225.494	−	34.5996i	−0.939560	−	0.144165i
$241$	−435.212			−1.80586			−0.902929	−	0.429789i	$-0.858588\pi$
$241$	−435.212			−1.80586			−0.902929	+	0.429789i	$0.858588\pi$
$242$		−	184.450i		−	0.762191i
$243$	167.629	−	175.925i	0.689831	−	0.723970i
$244$	−53.9464			−0.221092
$245$			802.720i			3.27641i
$246$	−17.1135	+	111.533i	−0.0695670	+	0.453387i
$247$	−308.248			−1.24797
$248$			505.273i			2.03739i
$249$	−91.7467	−	14.0775i	−0.368461	−	0.0565361i
$250$	149.299			0.597196
$251$		−	67.7900i		−	0.270080i	−0.990840	−	0.135040i	$-0.956884\pi$
$251$		−	67.7900i		−	0.270080i	0.990840	−	0.135040i	$-0.0431162\pi$
$252$	−83.1193	−	26.1224i	−0.329839	−	0.103660i
$253$	69.3502			0.274111
$254$		−	88.6881i		−	0.349166i
$255$	−2.93387	+	19.1208i	−0.0115054	+	0.0749836i
$256$	−133.017			−0.519598
$257$			332.772i			1.29483i	0.762137	+	0.647416i	$0.224150\pi$
$257$			332.772i			1.29483i	−0.762137	+	0.647416i	$0.775850\pi$
$258$	−11.9369	−	1.83159i	−0.0462672	−	0.00709917i
$259$	550.019			2.12363
$260$			50.6712i			0.194889i
$261$	10.3395	−	32.8993i	0.0396149	−	0.126051i
$262$	−248.690			−0.949200
$263$			150.708i			0.573036i	0.958075	+	0.286518i	$0.0924978\pi$
$263$			150.708i			0.573036i	−0.958075	+	0.286518i	$0.907502\pi$
$264$	−17.0384	+	111.044i	−0.0645395	+	0.420621i
$265$	218.312			0.823819
$266$			643.126i			2.41777i
$267$	441.465	+	67.7378i	1.65343	+	0.253699i
$268$	−5.87083			−0.0219061
$269$		−	378.380i		−	1.40662i	−0.710885	−	0.703308i	$-0.751705\pi$
$269$		−	378.380i		−	1.40662i	0.710885	−	0.703308i	$-0.248295\pi$
$270$	−130.042	+	264.629i	−0.481636	+	0.980106i
$271$	222.999			0.822873			0.411437	−	0.911438i	$-0.365027\pi$
$271$	222.999			0.822873			0.411437	+	0.911438i	$0.365027\pi$
$272$		−	13.4976i		−	0.0496236i
$273$	71.9827	−	469.130i	0.263673	−	1.71842i
$274$	−288.856			−1.05422
$275$			49.6359i			0.180494i
$276$	33.6635	+	5.16527i	0.121969	+	0.0187148i
$277$	13.5065			0.0487599			0.0243800	−	0.999703i	$-0.492239\pi$
$277$	13.5065			0.0487599			0.0243800	+	0.999703i	$0.492239\pi$
$278$			197.003i			0.708644i
$279$	507.584	+	159.522i	1.81930	+	0.571763i
$280$	695.316			2.48327
$281$		−	482.783i		−	1.71809i	−0.511902	−	0.859044i	$-0.671059\pi$
$281$		−	482.783i		−	1.71809i	0.511902	−	0.859044i	$-0.328941\pi$
$282$	−5.43427	+	35.4165i	−0.0192704	+	0.125591i
$283$	−375.818			−1.32798			−0.663989	−	0.747742i	$-0.731138\pi$
$283$	−375.818			−1.32798			−0.663989	+	0.747742i	$0.731138\pi$
$284$			95.5480i			0.336437i
$285$	−470.022	−	72.1195i	−1.64920	−	0.253051i
$286$	−93.0494			−0.325347
$287$		−	280.199i		−	0.976303i
$288$	−30.5676	+	97.2635i	−0.106138	+	0.337721i
$289$	287.855			0.996040
$290$			41.8448i			0.144292i
$291$	−22.9439	+	149.532i	−0.0788452	+	0.513855i
$292$	22.2877			0.0763278
$293$			268.114i			0.915066i	0.889193	+	0.457533i	$0.151267\pi$
$293$			268.114i			0.915066i	−0.889193	+	0.457533i	$0.848733\pi$
$294$	−715.529	−	109.790i	−2.43377	−	0.373435i
$295$	−418.789			−1.41963
$296$		−	348.285i		−	1.17664i
$297$	106.173	+	52.1745i	0.357483	+	0.175672i
$298$	−117.804			−0.395316
$299$			185.525i			0.620485i
$300$	−3.69693	+	24.0939i	−0.0123231	+	0.0803129i
$301$	29.9885			0.0996297
$302$			183.539i			0.607744i
$303$	−483.162	−	74.1357i	−1.59459	−	0.244672i
$304$	331.794			1.09143
$305$		−	453.340i		−	1.48636i
$306$	−16.6427	−	5.23040i	−0.0543878	−	0.0170928i
$307$	39.4785			0.128594			0.0642972	−	0.997931i	$-0.479519\pi$
$307$	39.4785			0.128594			0.0642972	+	0.997931i	$0.479519\pi$
$308$		−	42.4162i		−	0.137715i
$309$	−44.0050	+	286.792i	−0.142411	+	0.928130i
$310$	−645.599			−2.08258
$311$		−	259.877i		−	0.835616i	−0.908535	−	0.417808i	$-0.862799\pi$
$311$		−	259.877i		−	0.835616i	0.908535	−	0.417808i	$-0.137201\pi$
$312$	−297.064	−	45.5811i	−0.952128	−	0.146093i
$313$	116.387			0.371843			0.185921	−	0.982565i	$-0.440473\pi$
$313$	116.387			0.371843			0.185921	+	0.982565i	$0.440473\pi$
$314$			116.066i			0.369636i
$315$	219.521	−	698.496i	0.696892	−	2.21745i
$316$	15.0733			0.0477002
$317$		−	572.632i		−	1.80641i	−0.429208	−	0.903206i	$-0.641207\pi$
$317$		−	572.632i		−	1.80641i	0.429208	−	0.903206i	$-0.358793\pi$
$318$	−29.8590	+	194.599i	−0.0938963	+	0.611947i
$319$	16.7887			0.0526291
$320$		−	427.888i		−	1.33715i
$321$	258.866	+	39.7201i	0.806437	+	0.123739i
$322$	387.078			1.20211
$323$		−	28.1345i		−	0.0871038i
$324$	47.6515	+	33.2340i	0.147072	+	0.102574i
$325$	−132.786			−0.408571
$326$			49.9600i			0.153252i
$327$	38.4441	−	250.550i	0.117566	−	0.766209i
$328$	−177.429			−0.540941
$329$		−	88.9752i		−	0.270441i
$330$	−141.883	−	21.7704i	−0.429950	−	0.0659709i
$331$	466.380			1.40900			0.704501	−	0.709703i	$-0.251171\pi$
$331$	466.380			1.40900			0.704501	+	0.709703i	$0.251171\pi$
$332$		−	22.1914i		−	0.0668416i
$333$	−349.878	−	109.958i	−1.05068	−	0.330205i
$334$	−266.482			−0.797851
$335$		−	49.3358i		−	0.147271i
$336$	−77.4813	+	504.966i	−0.230599	+	1.50287i
$337$	−202.284			−0.600250			−0.300125	−	0.953900i	$-0.597028\pi$
$337$	−202.284			−0.600250			−0.300125	+	0.953900i	$0.597028\pi$
$338$			57.2759i			0.169455i
$339$	520.699	+	79.8954i	1.53599	+	0.235680i
$340$	−4.62488			−0.0136026
$341$			259.023i			0.759598i
$342$	128.572	−	409.105i	0.375942	−	1.19621i
$343$	1136.21			3.31258
$344$		−	18.9894i		−	0.0552018i
$345$	−43.4066	+	282.892i	−0.125816	+	0.819977i
$346$	54.4466			0.157360
$347$		−	586.382i		−	1.68986i	−0.534876	−	0.844931i	$-0.679642\pi$
$347$		−	586.382i		−	1.68986i	0.534876	−	0.844931i	$-0.320358\pi$
$348$	8.14944	+	1.25044i	0.0234179	+	0.00359322i
$349$	394.863			1.13141			0.565706	−	0.824607i	$-0.308604\pi$
$349$	394.863			1.13141			0.565706	+	0.824607i	$0.308604\pi$
$350$			277.043i			0.791550i
$351$	−139.577	+	284.032i	−0.397655	+	0.809208i
$352$	−49.6341			−0.141006
$353$			184.674i			0.523156i	0.965182	+	0.261578i	$0.0842429\pi$
$353$			184.674i			0.523156i	−0.965182	+	0.261578i	$0.915757\pi$
$354$	57.2788	−	373.301i	0.161805	−	1.05452i
$355$	−802.941			−2.26181
$356$			106.780i			0.299944i
$357$	42.8186	+	6.57003i	0.119940	+	0.0184034i
$358$	338.005			0.944149
$359$			186.364i			0.519119i	0.965727	+	0.259560i	$0.0835774\pi$
$359$			186.364i			0.519119i	−0.965727	+	0.259560i	$0.916423\pi$
$360$	−442.304	−	139.006i	−1.22862	−	0.386127i
$361$	330.595			0.915774
$362$		−	253.150i		−	0.699308i
$363$	46.3194	−	301.875i	0.127602	−	0.831613i
$364$	113.472			0.311735
$365$			187.296i			0.513138i
$366$	404.099	+	62.0044i	1.10410	+	0.169411i
$367$	−262.726			−0.715874			−0.357937	−	0.933746i	$-0.616520\pi$
$367$	−262.726			−0.715874			−0.357937	+	0.933746i	$0.616520\pi$
$368$		−	199.697i		−	0.542655i
$369$	−56.0166	+	178.240i	−0.151807	+	0.483035i
$370$	445.012			1.20273
$371$		−	488.882i		−	1.31774i
$372$	−19.2923	+	125.733i	−0.0518610	+	0.337992i
$373$	−66.6190			−0.178603			−0.0893016	−	0.996005i	$-0.528464\pi$
$373$	−66.6190			−0.178603			−0.0893016	+	0.996005i	$0.528464\pi$
$374$		−	8.49284i		−	0.0227081i
$375$	244.346	+	37.4921i	0.651590	+	0.0999790i
$376$	−56.3411			−0.149843
$377$			44.9130i			0.119133i
$378$	592.602	+	291.212i	1.56773	+	0.770402i
$379$	−425.343			−1.12228			−0.561138	−	0.827722i	$-0.689636\pi$
$379$	−425.343			−1.12228			−0.561138	+	0.827722i	$0.689636\pi$
$380$		−	113.687i		−	0.299177i
$381$	22.2714	−	145.149i	0.0584552	−	0.380968i
$382$	379.869			0.994420
$383$			238.791i			0.623475i	0.950168	+	0.311737i	$0.100911\pi$
$383$			238.791i			0.623475i	−0.950168	+	0.311737i	$0.899089\pi$
$384$	247.045	+	37.9063i	0.643348	+	0.0987144i
$385$	356.446			0.925835
$386$		−	332.426i		−	0.861208i
$387$	−19.0763	−	5.99523i	−0.0492927	−	0.0154915i
$388$	−36.1683			−0.0932171
$389$		−	431.783i		−	1.10998i	−0.831856	−	0.554991i	$-0.812722\pi$
$389$		−	431.783i		−	1.10998i	0.831856	−	0.554991i	$-0.187278\pi$
$390$	58.2400	−	379.565i	0.149333	−	0.973245i
$391$	−16.9333			−0.0433077
$392$		−	1138.27i		−	2.90376i
$393$	−407.012	−	62.4514i	−1.03565	−	0.158909i
$394$	−477.826			−1.21276
$395$			126.669i			0.320680i
$396$	−8.47974	+	26.9818i	−0.0214135	+	0.0681358i
$397$	339.039			0.854002			0.427001	−	0.904251i	$-0.359570\pi$
$397$	339.039			0.854002			0.427001	+	0.904251i	$0.359570\pi$
$398$			163.644i			0.411165i
$399$	−161.502	+	1052.55i	−0.404768	+	2.63798i
$400$	142.929			0.357322
$401$		−	465.092i		−	1.15983i	−0.814677	−	0.579915i	$-0.803086\pi$
$401$		−	465.092i		−	1.15983i	0.814677	−	0.579915i	$-0.196914\pi$
$402$	43.9770	+	6.74777i	0.109395	+	0.0167855i
$403$	−692.936			−1.71945
$404$		−	116.866i		−	0.289271i
$405$	−279.283	+	400.441i	−0.689588	+	0.988743i
$406$	93.7061			0.230803
$407$		−	178.544i		−	0.438684i
$408$	4.16029	−	27.1137i	0.0101968	−	0.0664552i
$409$	552.222			1.35018			0.675088	−	0.737737i	$-0.264106\pi$
$409$	552.222			1.35018			0.675088	+	0.737737i	$0.264106\pi$
$410$		−	226.704i		−	0.552938i
$411$	−472.747	−	72.5377i	−1.15024	−	0.176491i
$412$	−69.3684			−0.168370
$413$			937.825i			2.27076i
$414$	−246.228	−	77.3836i	−0.594753	−	0.186917i
$415$	186.486			0.449365
$416$		−	132.781i		−	0.319185i
$417$	−49.4716	+	322.419i	−0.118637	+	0.773188i
$418$	208.768			0.499446
$419$			280.238i			0.668827i	0.942426	+	0.334413i	$0.108538\pi$
$419$			280.238i			0.668827i	−0.942426	+	0.334413i	$0.891462\pi$
$420$	173.024	+	26.5485i	0.411961	+	0.0632107i
$421$	116.135			0.275856			0.137928	−	0.990442i	$-0.455956\pi$
$421$	116.135			0.275856			0.137928	+	0.990442i	$0.455956\pi$
$422$			67.2036i			0.159250i
$423$	−17.7877	+	56.5988i	−0.0420512	+	0.133803i
$424$	−309.571			−0.730121
$425$		−	12.1196i		−	0.0285168i
$426$	109.820	−	715.727i	0.257794	−	1.68011i
$427$	−1015.20			−2.37751
$428$			62.6138i			0.146294i
$429$	−152.287	−	23.3667i	−0.354980	−	0.0544677i
$430$	24.2632			0.0564261
$431$		−	436.818i		−	1.01350i	−0.862094	−	0.506749i	$-0.830847\pi$
$431$		−	436.818i		−	1.01350i	0.862094	−	0.506749i	$-0.169153\pi$
$432$	150.239	−	305.729i	0.347775	−	0.707705i
$433$	442.526			1.02200			0.511000	−	0.859581i	$-0.329275\pi$
$433$	442.526			1.02200			0.511000	+	0.859581i	$0.329275\pi$
$434$			1445.74i			3.33119i
$435$	−10.5081	+	68.4841i	−0.0241566	+	0.157435i
$436$	60.6023			0.138996
$437$		−	416.250i		−	0.952517i
$438$	−166.952	−	25.6169i	−0.381168	−	0.0584860i
$439$	−49.8303			−0.113509			−0.0567544	−	0.998388i	$-0.518075\pi$
$439$	−49.8303			−0.113509			−0.0567544	+	0.998388i	$0.518075\pi$
$440$		−	225.710i		−	0.512978i
$441$	−1143.48	−	359.369i	−2.59293	−	0.814896i
$442$	22.7200			0.0514027
$443$		−	302.816i		−	0.683558i	−0.939780	−	0.341779i	$-0.888971\pi$
$443$		−	302.816i		−	0.683558i	0.939780	−	0.341779i	$-0.111029\pi$
$444$	13.2982	−	86.6677i	0.0299509	−	0.195198i
$445$	−897.330			−2.01647
$446$		−	465.149i		−	1.04294i
$447$	−192.801	−	29.5831i	−0.431321	−	0.0661814i
$448$	−958.200			−2.13884
$449$			601.216i			1.33901i	0.742807	+	0.669505i	$0.233494\pi$
$449$			601.216i			1.33901i	−0.742807	+	0.669505i	$0.766506\pi$
$450$	55.3856	−	176.232i	0.123079	−	0.391627i
$451$	−90.9568			−0.201678
$452$			125.945i			0.278640i
$453$	−46.0905	+	300.384i	−0.101745	+	0.663098i
$454$	−293.836			−0.647215
$455$			953.563i			2.09574i
$456$	666.502	+	102.267i	1.46163	+	0.224270i
$457$	777.080			1.70039			0.850197	−	0.526465i	$-0.176483\pi$
$457$	777.080			1.70039			0.850197	+	0.526465i	$0.176483\pi$
$458$			479.373i			1.04667i
$459$	−25.9243	−	12.7395i	−0.0564799	−	0.0277549i
$460$	−68.4250			−0.148750
$461$			124.421i			0.269893i	0.990853	+	0.134946i	$0.0430862\pi$
$461$			124.421i			0.269893i	−0.990853	+	0.134946i	$0.956914\pi$
$462$	−48.7520	+	317.730i	−0.105524	+	0.687726i
$463$	30.5587			0.0660014			0.0330007	−	0.999455i	$-0.489494\pi$
$463$	30.5587			0.0660014			0.0330007	+	0.999455i	$0.489494\pi$
$464$		−	48.3438i		−	0.104189i
$465$	−1056.60	−	162.124i	−2.27226	−	0.348653i
$466$	−480.181			−1.03043
$467$		−	836.932i		−	1.79215i	−0.443907	−	0.896073i	$-0.646408\pi$
$467$		−	836.932i		−	1.79215i	0.443907	−	0.896073i	$-0.353592\pi$
$468$	−72.1815	−	22.6849i	−0.154234	−	0.0484721i
$469$	−110.481			−0.235567
$470$		−	71.9884i		−	0.153167i
$471$	−29.1465	+	189.956i	−0.0618822	+	0.403303i
$472$	593.853			1.25816
$473$		−	9.73473i		−	0.0205808i
$474$	−112.910	−	17.3248i	−0.238207	−	0.0365502i
$475$	297.922			0.627203
$476$			10.3568i			0.0217580i
$477$	−97.7359	+	310.987i	−0.204897	+	0.651964i
$478$	−223.810			−0.468222
$479$		−	646.470i		−	1.34962i	−0.737989	−	0.674812i	$-0.764225\pi$
$479$		−	646.470i		−	1.34962i	0.737989	−	0.674812i	$-0.235775\pi$
$480$	31.0662	−	202.467i	0.0647212	−	0.421805i
$481$	477.641			0.993016
$482$			788.534i			1.63596i
$483$	633.500	+	97.2034i	1.31160	+	0.201249i
$484$	73.0167			0.150861
$485$		−	303.941i		−	0.626683i
$486$	−318.747	−	303.717i	−0.655859	−	0.624932i
$487$	499.195			1.02504			0.512520	−	0.858675i	$-0.328712\pi$
$487$	499.195			1.02504			0.512520	+	0.858675i	$0.328712\pi$
$488$			642.847i			1.31731i
$489$	−12.5460	+	81.7656i	−0.0256565	+	0.167210i
$490$	1454.40			2.96816
$491$			267.529i			0.544865i	0.962175	+	0.272432i	$0.0878281\pi$
$491$			267.529i			0.544865i	−0.962175	+	0.272432i	$0.912172\pi$
$492$	−44.1516	−	6.77456i	−0.0897390	−	0.0137694i
$493$	−4.09932			−0.00831504
$494$			558.496i			1.13056i
$495$	−226.742	−	71.2598i	−0.458065	−	0.143959i
$496$	745.868			1.50377
$497$			1798.08i			3.61788i
$498$	−25.5062	+	166.230i	−0.0512172	+	0.333796i
$499$	−676.217			−1.35514			−0.677572	−	0.735456i	$-0.736968\pi$
$499$	−676.217			−1.35514			−0.677572	+	0.735456i	$0.736968\pi$
$500$			59.1016i			0.118203i
$501$	−436.131	−	66.9193i	−0.870520	−	0.133571i
$502$	−122.825			−0.244670
$503$			700.386i			1.39242i	0.717839	+	0.696209i	$0.245131\pi$
$503$			700.386i			1.39242i	−0.717839	+	0.696209i	$0.754869\pi$
$504$	−311.286	+	990.483i	−0.617630	+	1.96524i
$505$	982.084			1.94472
$506$		−	125.651i		−	0.248323i
$507$	−14.3832	+	93.7389i	−0.0283692	+	0.184889i
$508$	35.1081			0.0691105
$509$			557.290i			1.09487i	0.836847	+	0.547436i	$0.184396\pi$
$509$			557.290i			1.09487i	−0.836847	+	0.547436i	$0.815604\pi$
$510$	34.6438	+	5.31570i	0.0679291	+	0.0104229i
$511$	419.424			0.820791
$512$			574.255i			1.12159i
$513$	313.159	−	637.263i	0.610446	−	1.24223i
$514$	602.929			1.17301
$515$		−	582.940i		−	1.13192i
$516$	0.725053	−	4.72536i	0.00140514	−	0.00915768i
$517$	−28.8827			−0.0558659
$518$		−	996.546i		−	1.92383i
$519$	89.1084	+	13.6727i	0.171693	+	0.0263443i
$520$	603.818			1.16119
$521$			348.064i			0.668069i	0.942561	+	0.334035i	$0.108410\pi$
$521$			348.064i			0.668069i	−0.942561	+	0.334035i	$0.891590\pi$
$522$	−59.6083	−	18.7335i	−0.114192	−	0.0358879i
$523$	−140.823			−0.269259			−0.134630	−	0.990896i	$-0.542984\pi$
$523$	−140.823			−0.269259			−0.134630	+	0.990896i	$0.542984\pi$
$524$		−	98.4468i		−	0.187876i
$525$	−69.5712	+	453.414i	−0.132517	+	0.863646i
$526$	273.060			0.519125
$527$		−	63.2460i		−	0.120011i
$528$	163.919	+	25.1516i	0.310454	+	0.0476356i
$529$	278.472			0.526412
$530$		−	395.546i		−	0.746314i
$531$	187.488	−	596.569i	0.353084	−	1.12348i
$532$	−254.588			−0.478550
$533$		−	243.327i		−	0.456524i
$534$	122.730	−	799.864i	0.229831	−	1.49787i
$535$	−526.177			−0.983509
$536$			69.9592i			0.130521i
$537$	553.187	+	84.8803i	1.03014	+	0.158064i
$538$	−685.564			−1.27428
$539$		−	583.524i		−	1.08261i
$540$	−104.756	−	51.4784i	−0.193993	−	0.0953304i
$541$	−76.2844			−0.141006			−0.0705031	−	0.997512i	$-0.522460\pi$
$541$	−76.2844			−0.141006			−0.0705031	+	0.997512i	$0.522460\pi$
$542$		−	404.038i		−	0.745457i
$543$	63.5712	−	414.310i	0.117074	−	0.763002i
$544$	12.1192			0.0222780
$545$			509.273i			0.934447i
$546$	−849.988	−	130.421i	−1.55675	−	0.238866i
$547$	−354.890			−0.648794			−0.324397	−	0.945921i	$-0.605161\pi$
$547$	−354.890			−0.648794			−0.324397	+	0.945921i	$0.605161\pi$
$548$		−	114.347i		−	0.208662i
$549$	645.787	+	202.956i	1.17630	+	0.369682i
$550$	89.9322			0.163513
$551$		−	100.768i		−	0.182882i
$552$	61.5515	−	401.147i	0.111506	−	0.726716i
$553$	283.658			0.512944
$554$		−	24.4716i		−	0.0441726i
$555$	728.316	+	111.752i	1.31228	+	0.201354i
$556$	−77.9858			−0.140262
$557$			663.807i			1.19175i	0.803076	+	0.595877i	$0.203195\pi$
$557$			663.807i			1.19175i	−0.803076	+	0.595877i	$0.796805\pi$
$558$	289.028	−	919.661i	0.517971	−	1.64814i
$559$	26.0423			0.0465873
$560$		−	1026.40i		−	1.83286i
$561$	2.13273	−	13.8996i	0.00380166	−	0.0247764i
$562$	−874.725			−1.55645
$563$		−	121.948i		−	0.216603i	−0.994118	−	0.108302i	$-0.965459\pi$
$563$		−	121.948i		−	0.216603i	0.994118	−	0.108302i	$-0.0345412\pi$
$564$	−14.0200	−	2.15121i	−0.0248582	−	0.00381421i
$565$	−1058.38			−1.87325
$566$			680.921i			1.20304i
$567$	896.736	+	625.418i	1.58155	+	1.10303i
$568$	1138.59			2.00456
$569$			842.272i			1.48027i	0.672460	+	0.740134i	$0.265238\pi$
$569$			842.272i			1.48027i	−0.672460	+	0.740134i	$0.734762\pi$
$570$	−130.669	+	851.605i	−0.229244	+	1.49404i
$571$	−170.293			−0.298236			−0.149118	−	0.988819i	$-0.547643\pi$
$571$	−170.293			−0.298236			−0.149118	+	0.988819i	$0.547643\pi$
$572$		−	36.8346i		−	0.0643962i
$573$	621.701	+	95.3930i	1.08499	+	0.166480i
$574$	−507.676			−0.884452
$575$		−	179.310i		−	0.311843i
$576$	609.530	+	191.561i	1.05821	+	0.332571i
$577$	−659.431			−1.14286			−0.571431	−	0.820650i	$-0.693612\pi$
$577$	−659.431			−1.14286			−0.571431	+	0.820650i	$0.693612\pi$
$578$		−	521.548i		−	0.902332i
$579$	83.4792	−	544.056i	0.144178	−	0.939648i
$580$	−16.5647			−0.0285599
$581$		−	417.612i		−	0.718782i
$582$	270.928	+	41.5708i	0.465511	+	0.0714274i
$583$	−158.698			−0.272210
$584$		−	265.589i		−	0.454776i
$585$	190.634	−	606.580i	0.325870	−	1.03689i
$586$	485.780			0.828977
$587$			405.791i			0.691297i	0.938364	+	0.345648i	$0.112341\pi$
$587$			405.791i			0.691297i	−0.938364	+	0.345648i	$0.887659\pi$
$588$	43.4615	−	283.250i	0.0739141	−	0.481718i
$589$	1554.69			2.63955
$590$			758.779i			1.28607i
$591$	−782.021	−	119.992i	−1.32322	−	0.203032i
$592$	−514.127			−0.868458
$593$		−	227.273i		−	0.383259i	−0.981467	−	0.191629i	$-0.938623\pi$
$593$		−	227.273i		−	0.383259i	0.981467	−	0.191629i	$-0.0613772\pi$
$594$	94.5318	−	192.368i	0.159144	−	0.323851i
$595$	−87.0339			−0.146276
$596$		−	46.6340i		−	0.0782450i
$597$	−41.0944	+	267.823i	−0.0688349	+	0.448615i
$598$	336.142			0.562110
$599$		−	40.4641i		−	0.0675528i	−0.999429	−	0.0337764i	$-0.989247\pi$
$599$		−	40.4641i		−	0.0675528i	0.999429	−	0.0337764i	$-0.0107534\pi$
$600$	287.112	+	44.0541i	0.478521	+	0.0734235i
$601$	210.219			0.349781			0.174891	−	0.984588i	$-0.444043\pi$
$601$	210.219			0.349781			0.174891	+	0.984588i	$0.444043\pi$
$602$		−	54.3344i		−	0.0902565i
$603$	70.2792	+	22.0871i	0.116549	+	0.0366287i
$604$	−72.6558			−0.120291
$605$			613.598i			1.01421i
$606$	−134.322	+	875.411i	−0.221653	+	1.44457i
$607$	−679.617			−1.11963			−0.559816	−	0.828617i	$-0.689128\pi$
$607$	−679.617			−1.11963			−0.559816	+	0.828617i	$0.689128\pi$
$608$			297.911i			0.489985i
$609$	153.361	+	23.5316i	0.251825	+	0.0386397i
$610$	−821.380			−1.34652
$611$		−	77.2667i		−	0.126459i
$612$	2.07051	−	6.58818i	0.00338318	−	0.0107650i
$613$	−1173.62			−1.91454			−0.957272	−	0.289188i	$-0.906615\pi$
$613$	−1173.62			−1.91454			−0.957272	+	0.289188i	$0.906615\pi$
$614$		−	71.5286i		−	0.116496i
$615$	56.9303	−	371.029i	0.0925695	−	0.603300i
$616$	−505.449			−0.820534
$617$		−	908.584i		−	1.47258i	−0.676664	−	0.736292i	$-0.736575\pi$
$617$		−	908.584i		−	1.47258i	0.676664	−	0.736292i	$-0.263425\pi$
$618$	519.622	+	79.7300i	0.840812	+	0.129013i
$619$	−880.579			−1.42258			−0.711292	−	0.702897i	$-0.751889\pi$
$619$	−880.579			−1.42258			−0.711292	+	0.702897i	$0.751889\pi$
$620$		−	255.567i		−	0.412206i
$621$	−383.549	−	188.481i	−0.617632	−	0.303512i
$622$	−470.855			−0.757001
$623$			2009.46i			3.22545i
$624$	−67.2854	+	438.516i	−0.107829	+	0.702751i
$625$	−779.878			−1.24780
$626$		−	210.874i		−	0.336860i
$627$	341.675	+	52.4261i	0.544936	+	0.0836143i
$628$	−45.9458			−0.0731621
$629$			43.5954i			0.0693091i
$630$	−1265.56	−	397.737i	−2.00883	−	0.631328i
$631$	309.174			0.489975			0.244988	−	0.969526i	$-0.421216\pi$
$631$	309.174			0.489975			0.244988	+	0.969526i	$0.421216\pi$
$632$		−	179.619i		−	0.284207i
$633$	−16.8762	+	109.987i	−0.0266607	+	0.173755i
$634$	−1037.52			−1.63646
$635$			295.032i			0.464618i
$636$	−77.0342	−	11.8200i	−0.121123	−	0.0185849i
$637$	1561.04			2.45061
$638$		−	30.4184i		−	0.0476778i
$639$	359.468	−	1143.80i	0.562548	−	1.78998i
$640$	−502.150			−0.784609
$641$			105.562i			0.164683i	0.996604	+	0.0823413i	$0.0262398\pi$
$641$			105.562i			0.164683i	−0.996604	+	0.0823413i	$0.973760\pi$
$642$	71.9665	−	469.024i	0.112097	−	0.730568i
$643$	766.649			1.19230			0.596150	−	0.802873i	$-0.296696\pi$
$643$	766.649			1.19230			0.596150	+	0.802873i	$0.296696\pi$
$644$			153.229i			0.237933i
$645$	39.7097	+	6.09301i	0.0615655	+	0.00944652i
$646$	−50.9753			−0.0789091
$647$		−	248.443i		−	0.383993i	−0.981396	−	0.191996i	$-0.938504\pi$
$647$		−	248.443i		−	0.383993i	0.981396	−	0.191996i	$-0.0614962\pi$
$648$	396.030	−	567.834i	0.611157	−	0.876287i
$649$	304.432			0.469079
$650$			240.586i			0.370132i
$651$	−363.055	+	2366.12i	−0.557688	+	3.63460i
$652$	−19.7772			−0.0303331
$653$		−	414.448i		−	0.634683i	−0.948311	−	0.317342i	$-0.897210\pi$
$653$		−	414.448i		−	0.634683i	0.948311	−	0.317342i	$-0.102790\pi$
$654$	−453.957	−	69.6545i	−0.694124	−	0.106505i
$655$	827.301			1.26306
$656$			261.914i			0.399260i
$657$	−266.804	−	83.8502i	−0.406094	−	0.127626i
$658$	−161.209			−0.244998
$659$			839.446i			1.27382i	0.770939	+	0.636909i	$0.219787\pi$
$659$			839.446i			1.27382i	−0.770939	+	0.636909i	$0.780213\pi$
$660$	8.61804	−	56.1661i	0.0130576	−	0.0851001i
$661$	−93.2487			−0.141072			−0.0705361	−	0.997509i	$-0.522471\pi$
$661$	−93.2487			−0.141072			−0.0705361	+	0.997509i	$0.522471\pi$
$662$		−	845.005i		−	1.27644i
$663$	37.1840	+	5.70547i	0.0560845	+	0.00860553i
$664$	−264.442			−0.398256
$665$		−	2139.44i		−	3.21721i
$666$	−199.227	+	633.922i	−0.299139	+	0.951835i
$667$	−60.6493			−0.0909285
$668$		−	105.490i		−	0.157919i
$669$	116.809	−	761.273i	0.174602	−	1.13793i
$670$	−89.3885			−0.133416
$671$			329.548i			0.491130i
$672$	−453.398	−	69.5688i	−0.674699	−	0.103525i
$673$	232.385			0.345297			0.172648	−	0.984984i	$-0.444768\pi$
$673$	232.385			0.345297			0.172648	+	0.984984i	$0.444768\pi$
$674$			366.507i			0.543778i
$675$	134.901	−	274.517i	0.199853	−	0.406692i
$676$	−22.6733			−0.0335403
$677$		−	405.987i		−	0.599686i	−0.953989	−	0.299843i	$-0.903066\pi$
$677$		−	405.987i		−	0.599686i	0.953989	−	0.299843i	$-0.0969343\pi$
$678$	144.758	−	943.424i	0.213507	−	1.39148i
$679$	−680.637			−1.00241
$680$			55.1119i			0.0810469i
$681$	−480.898	−	73.7883i	−0.706165	−	0.108353i
$682$	469.308			0.688135
$683$			107.591i			0.157528i	0.996893	+	0.0787638i	$0.0250973\pi$
$683$			107.591i			0.157528i	−0.996893	+	0.0787638i	$0.974903\pi$
$684$	161.949	+	50.8966i	0.236767	+	0.0744103i
$685$	960.916			1.40280
$686$		−	2058.64i		−	3.00093i
$687$	−120.381	+	784.553i	−0.175227	+	1.14200i
$688$	−28.0316			−0.0407436
$689$		−	424.549i		−	0.616181i
$690$	512.555	+	78.6457i	0.742833	+	0.113979i
$691$	−253.472			−0.366819			−0.183410	−	0.983037i	$-0.558713\pi$
$691$	−253.472			−0.366819			−0.183410	+	0.983037i	$0.558713\pi$
$692$			21.5533i			0.0311463i
$693$	−159.577	+	507.761i	−0.230270	+	0.732699i
$694$	−1062.43			−1.53088
$695$		−	655.356i		−	0.942959i
$696$	14.9007	−	97.1121i	0.0214091	−	0.139529i
$697$	22.2090			0.0318638
$698$		−	715.429i		−	1.02497i
$699$	−785.875	−	120.584i	−1.12428	−	0.172509i
$700$	−109.670			−0.156672
$701$		−	628.244i		−	0.896211i	−0.893981	−	0.448105i	$-0.852099\pi$
$701$		−	628.244i		−	0.896211i	0.893981	−	0.448105i	$-0.147901\pi$
$702$	514.621	+	252.891i	0.733078	+	0.360243i
$703$	−1071.65			−1.52440
$704$			311.046i			0.441827i
$705$	18.0778	−	117.818i	0.0256423	−	0.167117i
$706$	334.600			0.473937
$707$		−	2199.25i		−	3.11068i
$708$	147.775	+	22.6744i	0.208722	+	0.0320260i
$709$	−638.826			−0.901024			−0.450512	−	0.892770i	$-0.648758\pi$
$709$	−638.826			−0.901024			−0.450512	+	0.892770i	$0.648758\pi$
$710$			1454.80i			2.04902i
$711$	−180.441	−	56.7082i	−0.253784	−	0.0797584i
$712$	1272.43			1.78713
$713$		−	935.723i		−	1.31237i
$714$	11.9038	−	77.5804i	0.0166720	−	0.108656i
$715$	309.541			0.432924
$716$			133.803i			0.186876i
$717$	−366.292	−	56.2034i	−0.510868	−	0.0783869i
$718$	337.661			0.470281
$719$		−	513.939i		−	0.714797i	−0.933952	−	0.357398i	$-0.883664\pi$
$719$		−	513.939i		−	0.714797i	0.933952	−	0.357398i	$-0.116336\pi$
$720$	−205.196	+	652.915i	−0.284994	+	0.906827i
$721$	−1305.42			−1.81057
$722$		−	598.984i		−	0.829618i
$723$	−198.018	+	1290.53i	−0.273883	+	1.78497i
$724$	100.212			0.138414
$725$		−	43.4084i		−	0.0598737i
$726$	−546.950	−	83.9232i	−0.753375	−	0.115597i
$727$	425.335			0.585054			0.292527	−	0.956257i	$-0.405504\pi$
$727$	425.335			0.585054			0.292527	+	0.956257i	$0.405504\pi$
$728$		−	1352.17i		−	1.85738i
$729$	−445.399	−	577.114i	−0.610973	−	0.791651i
$730$	339.350			0.464862
$731$			2.37694i			0.00325163i
$732$	−24.5451	+	159.967i	−0.0335316	+	0.218534i
$733$	263.158			0.359015			0.179508	−	0.983757i	$-0.442550\pi$
$733$	263.158			0.359015			0.179508	+	0.983757i	$0.442550\pi$
$734$			476.017i			0.648524i
$735$	2380.30	+	365.230i	3.23851	+	0.496912i
$736$	179.304			0.243619
$737$			35.8638i			0.0486619i
$738$	322.942	+	101.493i	0.437591	+	0.137525i
$739$	284.887			0.385503			0.192752	−	0.981248i	$-0.438259\pi$
$739$	284.887			0.385503			0.192752	+	0.981248i	$0.438259\pi$
$740$			176.163i			0.238058i
$741$	−140.250	+	914.047i	−0.189271	+	1.23353i
$742$	−885.775			−1.19377
$743$			777.076i			1.04586i	0.852375	+	0.522931i	$0.175162\pi$
$743$			777.076i			1.04586i	−0.852375	+	0.522931i	$0.824838\pi$
$744$	1498.29	+	229.895i	2.01382	+	0.308998i
$745$	391.891			0.526028
$746$			120.703i			0.161800i
$747$	−83.4879	+	265.651i	−0.111764	+	0.355624i
$748$	3.36198			0.00449463
$749$			1178.31i			1.57317i
$750$	67.9297	−	442.716i	0.0905730	−	0.590288i
$751$	−958.485			−1.27628			−0.638139	−	0.769921i	$-0.720296\pi$
$751$	−958.485			−1.27628			−0.638139	+	0.769921i	$0.720296\pi$
$752$			83.1690i			0.110597i
$753$	−201.017	−	30.8438i	−0.266955	−	0.0409613i
$754$	81.3751			0.107925
$755$		−	610.566i		−	0.808696i
$756$	−115.279	+	234.588i	−0.152486	+	0.310302i
$757$	391.780			0.517543			0.258772	−	0.965939i	$-0.416682\pi$
$757$	391.780			0.517543			0.258772	+	0.965939i	$0.416682\pi$
$758$			770.653i			1.01669i
$759$	31.5537	−	205.644i	0.0415727	−	0.270940i
$760$	−1354.74			−1.78256
$761$		−	317.200i		−	0.416820i	−0.978042	−	0.208410i	$-0.933171\pi$
$761$		−	317.200i		−	0.416820i	0.978042	−	0.208410i	$-0.0668289\pi$
$762$	−262.986	−	40.3523i	−0.345127	−	0.0529558i
$763$	1140.45			1.49470
$764$			150.375i			0.196826i
$765$	55.3640	+	17.3996i	0.0723712	+	0.0227446i
$766$	432.651			0.564818
$767$			814.415i			1.06182i
$768$	−60.5216	+	394.435i	−0.0788042	+	0.513588i
$769$	−264.898			−0.344471			−0.172235	−	0.985056i	$-0.555099\pi$
$769$	−264.898			−0.344471			−0.172235	+	0.985056i	$0.555099\pi$
$770$		−	645.824i		−	0.838732i
$771$	986.766	+	151.408i	1.27985	+	0.196379i
$772$	131.594			0.170459
$773$			1047.41i			1.35499i	0.735527	+	0.677496i	$0.236935\pi$
$773$			1047.41i			1.35499i	−0.735527	+	0.677496i	$0.763065\pi$
$774$	−10.8624	+	34.5632i	−0.0140341	+	0.0446553i
$775$	669.723			0.864159
$776$			430.995i			0.555407i
$777$	250.254	−	1630.97i	0.322077	−	2.09906i
$778$	−782.322			−1.00556
$779$			545.936i			0.700816i
$780$	150.255	+	23.0549i	0.192635	+	0.0295576i
$781$	583.685			0.747356
$782$			30.6805i			0.0392333i
$783$	−92.8518	−	45.6285i	−0.118585	−	0.0582740i
$784$	−1680.28			−2.14322
$785$		−	386.107i		−	0.491857i
$786$	−113.152	+	737.441i	−0.143959	+	0.938220i
$787$	1326.17			1.68509			0.842545	−	0.538627i	$-0.181057\pi$
$787$	1326.17			1.68509			0.842545	+	0.538627i	$0.181057\pi$
$788$		−	189.153i		−	0.240041i
$789$	446.895	+	68.5710i	0.566407	+	0.0869087i
$790$	229.503			0.290511
$791$			2370.12i			2.99635i
$792$	321.526	+	101.048i	0.405967	+	0.127586i
$793$	−881.606			−1.11173
$794$		−	614.284i		−	0.773657i
$795$	99.3300	−	647.360i	0.124943	−	0.814289i
$796$	−64.7802			−0.0813821
$797$		−	142.297i		−	0.178541i	−0.996007	−	0.0892703i	$-0.971546\pi$
$797$		−	142.297i		−	0.178541i	0.996007	−	0.0892703i	$-0.0284535\pi$
$798$	1907.06	+	292.617i	2.38980	+	0.366688i
$799$	7.05232			0.00882643
$800$			128.333i			0.160416i
$801$	401.725	−	1278.25i	0.501529	−	1.59582i
$802$	−842.671			−1.05071
$803$		−	136.151i		−	0.169554i
$804$	−2.67118	+	17.4088i	−0.00332236	+	0.0216527i
$805$	−1287.67			−1.59958
$806$			1255.49i			1.55768i
$807$	−1122.01	−	172.159i	−1.39034	−	0.213333i
$808$	−1392.62			−1.72354
$809$		−	803.726i		−	0.993480i	−0.867899	−	0.496740i	$-0.834530\pi$
$809$		−	803.726i		−	0.993480i	0.867899	−	0.496740i	$-0.165470\pi$
$810$	725.535	+	506.016i	0.895722	+	0.624711i
$811$	−547.092			−0.674589			−0.337295	−	0.941399i	$-0.609512\pi$
$811$	−547.092			−0.674589			−0.337295	+	0.941399i	$0.609512\pi$
$812$			37.0946i			0.0456830i
$813$	101.462	−	661.257i	0.124800	−	0.813354i
$814$	−323.494			−0.397413
$815$		−	166.198i		−	0.203924i
$816$	−40.0244	−	6.14129i	−0.0490495	−	0.00752610i
$817$	−58.4293			−0.0715168
$818$		−	1000.54i		−	1.22315i
$819$	−1358.36	−	426.900i	−1.65856	−	0.521245i
$820$	89.7434			0.109443
$821$		−	1188.86i		−	1.44806i	−0.689768	−	0.724031i	$-0.742287\pi$
$821$		−	1188.86i		−	1.44806i	0.689768	−	0.724031i	$-0.257713\pi$
$822$	−131.427	+	856.542i	−0.159886	+	1.04202i
$823$	1148.69			1.39574			0.697870	−	0.716225i	$-0.254131\pi$
$823$	1148.69			1.39574			0.697870	+	0.716225i	$0.254131\pi$
$824$			826.621i			1.00318i
$825$	147.185	+	22.5839i	0.178406	+	0.0273744i
$826$	1699.19			2.05713
$827$		−	726.831i		−	0.878877i	−0.898273	−	0.439438i	$-0.855177\pi$
$827$		−	726.831i		−	0.878877i	0.898273	−	0.439438i	$-0.144823\pi$
$828$	30.6331	−	97.4720i	0.0369965	−	0.117720i
$829$	404.547			0.487994			0.243997	−	0.969776i	$-0.421541\pi$
$829$	404.547			0.487994			0.243997	+	0.969776i	$0.421541\pi$
$830$		−	337.883i		−	0.407088i
$831$	6.14534	−	40.0508i	0.00739511	−	0.0481959i
$832$	−832.109			−1.00013
$833$			142.480i			0.171044i
$834$	584.172	+	89.6346i	0.700447	+	0.107476i
$835$	886.488			1.06166
$836$			82.6432i			0.0988555i
$837$	703.976	−	1432.56i	0.841070	−	1.71154i
$838$	507.747			0.605904
$839$		−	312.366i		−	0.372308i	−0.982521	−	0.186154i	$-0.940398\pi$
$839$		−	312.366i		−	0.372308i	0.982521	−	0.186154i	$-0.0596023\pi$
$840$	316.363	−	2061.82i	0.376622	−	2.45455i
$841$	826.318			0.982542
$842$		−	210.418i		−	0.249903i
$843$	−1431.59	−	219.662i	−1.69821	−	0.260572i
$844$	−26.6033			−0.0315205
$845$		−	190.536i		−	0.225486i
$846$	102.548	+	32.2284i	0.121215	+	0.0380951i
$847$	1374.07			1.62228
$848$			456.979i			0.538890i
$849$	−170.994	+	1114.41i	−0.201406	+	1.31262i
$850$	−21.9589			−0.0258340
$851$			644.994i			0.757924i
$852$	283.328	+	43.4735i	0.332545	+	0.0510252i
$853$	−490.123			−0.574587			−0.287294	−	0.957843i	$-0.592756\pi$
$853$	−490.123			−0.574587			−0.287294	+	0.957843i	$0.592756\pi$
$854$			1839.37i			2.15383i
$855$	−427.712	+	1360.94i	−0.500248	+	1.59174i
$856$	746.131			0.871648
$857$			1488.77i			1.73719i	0.495525	+	0.868594i	$0.334976\pi$
$857$			1488.77i			1.73719i	−0.495525	+	0.868594i	$0.665024\pi$
$858$	−42.3366	+	275.919i	−0.0493434	+	0.321584i
$859$	1307.09			1.52165			0.760823	−	0.648959i	$-0.224796\pi$
$859$	1307.09			1.52165			0.760823	+	0.648959i	$0.224796\pi$
$860$			9.60486i			0.0111684i
$861$	−830.873	−	127.488i	−0.965009	−	0.148070i
$862$	−791.444			−0.918148
$863$			49.7227i			0.0576161i	0.999585	+	0.0288080i	$0.00917116\pi$
$863$			49.7227i			0.0576161i	−0.999585	+	0.0288080i	$0.990829\pi$
$864$	274.507	+	134.896i	0.317717	+	0.156130i
$865$	−181.124			−0.209391
$866$		−	801.786i		−	0.925850i
$867$	130.972	−	853.577i	0.151063	−	0.984518i
$868$	−572.311			−0.659344
$869$		−	92.0798i		−	0.105961i
$870$	124.082	+	19.0390i	0.142623	+	0.0218839i
$871$	−95.9427			−0.110152
$872$		−	722.161i		−	0.828167i
$873$	432.967	+	136.071i	0.495953	+	0.155866i
$874$	−754.178			−0.862904
$875$			1112.21i			1.27110i
$876$	10.1407	−	66.0897i	0.0115761	−	0.0754448i
$877$	309.310			0.352691			0.176345	−	0.984328i	$-0.443572\pi$
$877$	309.310			0.352691			0.176345	+	0.984328i	$0.443572\pi$
$878$			90.2846i			0.102830i
$879$	795.039	+	121.990i	0.904481	+	0.138782i
$880$	−333.186			−0.378621
$881$			895.359i			1.01630i	0.861269	+	0.508149i	$0.169670\pi$
$881$			895.359i			1.01630i	−0.861269	+	0.508149i	$0.830330\pi$
$882$	−651.119	+	2071.80i	−0.738230	+	2.34898i
$883$	−1048.53			−1.18746			−0.593729	−	0.804665i	$-0.702345\pi$
$883$	−1048.53			−1.18746			−0.593729	+	0.804665i	$0.702345\pi$
$884$			8.99395i			0.0101742i
$885$	−190.545	+	1241.83i	−0.215306	+	1.40320i
$886$	−548.654			−0.619248
$887$		−	22.2772i		−	0.0251152i	−0.999921	−	0.0125576i	$-0.996003\pi$
$887$		−	22.2772i		−	0.0251152i	0.999921	−	0.0125576i	$-0.00399732\pi$
$888$	−1032.77	−	158.466i	−1.16303	−	0.178453i
$889$	660.687			0.743180
$890$			1625.82i			1.82676i
$891$	203.020	−	291.094i	0.227857	−	0.326705i
$892$	184.134			0.206429
$893$			173.358i			0.194130i
$894$	−53.5998	+	349.324i	−0.0599550	+	0.390743i
$895$	−1124.42			−1.25633
$896$			1124.50i			1.25502i
$897$	550.137	+	84.4123i	0.613308	+	0.0941051i
$898$	1089.31			1.21304
$899$		−	226.525i		−	0.251975i
$900$	69.7634	+	21.9250i	0.0775149	+	0.0243611i
$901$	38.7496			0.0430073
$902$			164.799i			0.182704i
$903$	13.6445	−	88.9249i	0.0151102	−	0.0984772i
$904$	1500.81			1.66019
$905$			842.135i			0.930536i
$906$	544.247	+	83.5085i	0.600714	+	0.0921728i
$907$	−488.011			−0.538050			−0.269025	−	0.963133i	$-0.586701\pi$
$907$	−488.011			−0.538050			−0.269025	+	0.963133i	$0.586701\pi$
$908$		−	116.318i		−	0.128104i
$909$	−439.668	+	1398.99i	−0.483684	+	1.53904i
$910$	1727.70			1.89857
$911$		−	320.472i		−	0.351781i	−0.984410	−	0.175890i	$-0.943720\pi$
$911$		−	320.472i		−	0.351781i	0.984410	−	0.175890i	$-0.0562804\pi$
$912$	150.963	−	983.869i	0.165530	−	1.07880i
$913$	−135.563			−0.148481
$914$		−	1407.94i		−	1.54042i
$915$	−1344.29	−	206.266i	−1.46917	−	0.225427i
$916$	−189.765			−0.207167
$917$		−	1852.63i		−	2.02032i
$918$	−23.0819	+	46.9706i	−0.0251437	+	0.0511663i
$919$	1043.22			1.13517			0.567585	−	0.823315i	$-0.307878\pi$
$919$	1043.22			1.13517			0.567585	+	0.823315i	$0.307878\pi$
$920$			815.380i			0.886283i
$921$	17.9623	−	117.065i	0.0195031	−	0.127107i
$922$	225.430			0.244501
$923$			1561.47i			1.69173i
$924$	−125.777	−	19.2990i	−0.136122	−	0.0208864i
$925$	−461.640			−0.499070
$926$		−	55.3674i		−	0.0597920i
$927$	830.402	+	260.976i	0.895795	+	0.281527i
$928$	43.4069			0.0467746
$929$		−	201.551i		−	0.216955i	−0.994099	−	0.108478i	$-0.965402\pi$
$929$		−	201.551i		−	0.216955i	0.994099	−	0.108478i	$-0.0345976\pi$
$930$	−293.742	+	1914.39i	−0.315852	+	2.05849i
$931$	−3502.40			−3.76197
$932$		−	190.085i		−	0.203954i
$933$	−770.611	−	118.241i	−0.825950	−	0.126733i
$934$	−1516.39			−1.62354
$935$			28.2525i			0.0302166i
$936$	−270.323	+	860.144i	−0.288807	+	0.918957i
$937$	209.713			0.223813			0.111907	−	0.993719i	$-0.464304\pi$
$937$	209.713			0.223813			0.111907	+	0.993719i	$0.464304\pi$
$938$			200.174i			0.213405i
$939$	52.9549	−	345.121i	0.0563950	−	0.367541i
$940$	28.4974			0.0303164
$941$			213.304i			0.226678i	0.993556	+	0.113339i	$0.0361547\pi$
$941$			213.304i			0.226678i	−0.993556	+	0.113339i	$0.963845\pi$
$942$	344.169	+	52.8088i	0.365360	+	0.0560603i
$943$	328.582			0.348444
$944$		−	876.627i		−	0.928630i
$945$	−1971.37	−	968.754i	−2.08610	−	1.02514i
$946$	−17.6378			−0.0186446
$947$		−	1199.79i		−	1.26694i	−0.773769	−	0.633468i	$-0.781631\pi$
$947$		−	1199.79i		−	1.26694i	0.773769	−	0.633468i	$-0.218369\pi$
$948$	6.85820	−	44.6967i	0.00723439	−	0.0471484i
$949$	364.231			0.383806
$950$		−	539.786i		−	0.568196i
$951$	−1698.03	−	260.543i	−1.78552	−	0.273967i
$952$	123.416			0.129639
$953$			579.041i			0.607598i	0.952736	+	0.303799i	$0.0982551\pi$
$953$			579.041i			0.607598i	−0.952736	+	0.303799i	$0.901745\pi$
$954$	563.459	+	177.082i	0.590628	+	0.185620i
$955$	−1263.68			−1.32323
$956$		−	88.5976i		−	0.0926753i
$957$	7.63870	−	49.7834i	0.00798193	−	0.0520203i
$958$	−1171.30			−1.22265
$959$		−	2151.85i		−	2.24384i
$960$	−1268.81	−	194.685i	−1.32168	−	0.202797i
$961$	2533.93			2.63676
$962$		−	865.409i		−	0.899593i
$963$	235.564	−	749.543i	0.244615	−	0.778342i
$964$	−312.150			−0.323807
$965$			1105.86i			1.14597i
$966$	176.117	−	1147.80i	0.182316	−	1.18820i
$967$	−169.293			−0.175071			−0.0875353	−	0.996161i	$-0.527899\pi$
$967$	−169.293			−0.175071			−0.0875353	+	0.996161i	$0.527899\pi$
$968$		−	870.096i		−	0.898859i
$969$	−83.4272	−	12.8010i	−0.0860962	−	0.0132105i
$970$	−550.693			−0.567725
$971$			343.684i			0.353949i	0.984215	+	0.176974i	$0.0566309\pi$
$971$			343.684i			0.353949i	−0.984215	+	0.176974i	$0.943369\pi$
$972$	120.230	−	126.180i	0.123693	−	0.129814i
$973$	−1467.59			−1.50831
$974$		−	904.461i		−	0.928604i
$975$	−60.4162	+	393.748i	−0.0619654	+	0.403845i
$976$	948.950			0.972284
$977$			633.402i			0.648313i	0.946004	+	0.324156i	$0.105080\pi$
$977$			633.402i			0.648313i	−0.946004	+	0.324156i	$0.894920\pi$
$978$	148.146	+	22.7314i	0.151479	+	0.0232427i
$979$	652.300			0.666292
$980$			575.740i			0.587490i
$981$	−725.464	−	227.996i	−0.739515	−	0.232412i
$982$	484.719			0.493604
$983$			1415.47i			1.43995i	0.694002	+	0.719973i	$0.255846\pi$
$983$			1415.47i			1.43995i	−0.694002	+	0.719973i	$0.744154\pi$
$984$	−80.7284	+	526.128i	−0.0820410	+	0.534683i
$985$	1589.55			1.61376
$986$			7.42730i			0.00753276i
$987$	−263.838	−	40.4829i	−0.267313	−	0.0410161i
$988$	−221.087			−0.223772
$989$			35.1668i			0.0355579i
$990$	−129.111	+	410.821i	−0.130415	+	0.414971i
$991$	−397.898			−0.401511			−0.200756	−	0.979641i	$-0.564340\pi$
$991$	−397.898			−0.401511			−0.200756	+	0.979641i	$0.564340\pi$
$992$			669.699i			0.675100i
$993$	212.199	−	1382.95i	0.213694	−	1.39270i
$994$	3257.84			3.27751
$995$		−	544.383i		−	0.547118i
$996$	−65.8041	−	10.0969i	−0.0660684	−	0.0101374i
$997$	466.022			0.467424			0.233712	−	0.972306i	$-0.424913\pi$
$997$	466.022			0.467424			0.233712	+	0.972306i	$0.424913\pi$
$998$			1225.20i			1.22765i
$999$	−485.250	+	987.461i	−0.485736	+	0.988450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.c.a.68.14	✓	44
3.2	odd	2	inner	201.3.c.a.68.31	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.c.a.68.14	✓	44	1.1	even	1	trivial
201.3.c.a.68.31	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)

\(f(q)\)	\(=\)	\(q-1.81184i q^{2} +(0.454991 - 2.96530i) q^{3} +0.717236 q^{4} +6.02732i q^{5} +(-5.37264 - 0.824371i) q^{6} +13.4974 q^{7} -8.54688i q^{8} +(-8.58597 - 2.69837i) q^{9} +O(q^{10})\)	\(q-1.81184i q^{2} +(0.454991 - 2.96530i) q^{3} +0.717236 q^{4} +6.02732i q^{5} +(-5.37264 - 0.824371i) q^{6} +13.4974 q^{7} -8.54688i q^{8} +(-8.58597 - 2.69837i) q^{9} +10.9205 q^{10} -4.38146i q^{11} +(0.326336 - 2.12682i) q^{12} +11.7213 q^{13} -24.4552i q^{14} +(17.8728 + 2.74238i) q^{15} -12.6166 q^{16} +1.06983i q^{17} +(-4.88901 + 15.5564i) q^{18} -26.2982 q^{19} +4.32301i q^{20} +(6.14120 - 40.0238i) q^{21} -7.93851 q^{22} +15.8281i q^{23} +(-25.3440 - 3.88875i) q^{24} -11.3286 q^{25} -21.2371i q^{26} +(-11.9080 + 24.2322i) q^{27} +9.68084 q^{28} +3.83175i q^{29} +(4.96875 - 32.3826i) q^{30} -59.1179 q^{31} -11.3282i q^{32} +(-12.9923 - 1.99353i) q^{33} +1.93836 q^{34} +81.3532i q^{35} +(-6.15817 - 1.93537i) q^{36} +40.7500 q^{37} +47.6481i q^{38} +(5.33307 - 34.7570i) q^{39} +51.5148 q^{40} -20.7595i q^{41} +(-72.5168 - 11.1269i) q^{42} +2.22180 q^{43} -3.14255i q^{44} +(16.2639 - 51.7504i) q^{45} +28.6779 q^{46} -6.59202i q^{47} +(-5.74045 + 37.4120i) q^{48} +133.180 q^{49} +20.5256i q^{50} +(3.17236 + 0.486762i) q^{51} +8.40692 q^{52} -36.2204i q^{53} +(43.9049 + 21.5754i) q^{54} +26.4085 q^{55} -115.361i q^{56} +(-11.9654 + 77.9819i) q^{57} +6.94252 q^{58} +69.4818i q^{59} +(12.8190 + 1.96693i) q^{60} -75.2142 q^{61} +107.112i q^{62} +(-115.888 - 36.4210i) q^{63} -70.9914 q^{64} +70.6478i q^{65} +(-3.61195 + 23.5400i) q^{66} -8.18535 q^{67} +0.767319i q^{68} +(46.9350 + 7.20164i) q^{69} +147.399 q^{70} +133.217i q^{71} +(-23.0626 + 73.3832i) q^{72} +31.0744 q^{73} -73.8324i q^{74} +(-5.15441 + 33.5927i) q^{75} -18.8620 q^{76} -59.1384i q^{77} +(-62.9742 - 9.66267i) q^{78} +21.0158 q^{79} -76.0445i q^{80} +(66.4376 + 46.3362i) q^{81} -37.6128 q^{82} -30.9402i q^{83} +(4.40469 - 28.7065i) q^{84} -6.44819 q^{85} -4.02554i q^{86} +(11.3623 + 1.74341i) q^{87} -37.4478 q^{88} +148.877i q^{89} +(-93.7634 - 29.4676i) q^{90} +158.207 q^{91} +11.3525i q^{92} +(-26.8981 + 175.302i) q^{93} -11.9437 q^{94} -158.508i q^{95} +(-33.5915 - 5.15423i) q^{96} -50.4272 q^{97} -241.301i q^{98} +(-11.8228 + 37.6191i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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