LMFDB - Embedded newform 287.3.d.d.286.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(286,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("287.286");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.d (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:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			286.9
Character	$\chi$	$=$	287.286
Dual form			287.3.d.d.286.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31240 q^{2} -5.31887 q^{3} +1.34721 q^{4} -9.29617i q^{5} +12.2994 q^{6} +(-2.62328 + 6.48987i) q^{7} +6.13432 q^{8} +19.2904 q^{9} +O(q^{10})$	\(q-2.31240 q^{2} -5.31887 q^{3} +1.34721 q^{4} -9.29617i q^{5} +12.2994 q^{6} +(-2.62328 + 6.48987i) q^{7} +6.13432 q^{8} +19.2904 q^{9} +21.4965i q^{10} -4.30172i q^{11} -7.16563 q^{12} +4.06994 q^{13} +(6.06607 - 15.0072i) q^{14} +49.4451i q^{15} -19.5739 q^{16} +19.2739 q^{17} -44.6072 q^{18} +13.2350 q^{19} -12.5239i q^{20} +(13.9529 - 34.5188i) q^{21} +9.94732i q^{22} +23.0589 q^{23} -32.6277 q^{24} -61.4187 q^{25} -9.41134 q^{26} -54.7334 q^{27} +(-3.53410 + 8.74321i) q^{28} -41.6081i q^{29} -114.337i q^{30} -19.3984i q^{31} +20.7254 q^{32} +22.8803i q^{33} -44.5691 q^{34} +(60.3309 + 24.3864i) q^{35} +25.9882 q^{36} +45.0642 q^{37} -30.6047 q^{38} -21.6475 q^{39} -57.0257i q^{40} +(-38.8459 - 13.1148i) q^{41} +(-32.2647 + 79.8214i) q^{42} +23.7089 q^{43} -5.79532i q^{44} -179.327i q^{45} -53.3215 q^{46} -31.6879 q^{47} +104.111 q^{48} +(-35.2368 - 34.0495i) q^{49} +142.025 q^{50} -102.516 q^{51} +5.48306 q^{52} +14.1941i q^{53} +126.566 q^{54} -39.9895 q^{55} +(-16.0920 + 39.8110i) q^{56} -70.3953 q^{57} +96.2146i q^{58} +102.088i q^{59} +66.6129i q^{60} -37.3731i q^{61} +44.8569i q^{62} +(-50.6041 + 125.192i) q^{63} +30.3700 q^{64} -37.8348i q^{65} -52.9085i q^{66} +86.4202i q^{67} +25.9660 q^{68} -122.647 q^{69} +(-139.509 - 56.3912i) q^{70} -20.8304i q^{71} +118.334 q^{72} +36.1452i q^{73} -104.207 q^{74} +326.678 q^{75} +17.8303 q^{76} +(27.9176 + 11.2846i) q^{77} +50.0577 q^{78} -73.3847i q^{79} +181.962i q^{80} +117.506 q^{81} +(89.8273 + 30.3267i) q^{82} -124.813i q^{83} +(18.7974 - 46.5040i) q^{84} -179.174i q^{85} -54.8245 q^{86} +221.308i q^{87} -26.3882i q^{88} -31.9858 q^{89} +414.676i q^{90} +(-10.6766 + 26.4134i) q^{91} +31.0652 q^{92} +103.177i q^{93} +73.2752 q^{94} -123.035i q^{95} -110.236 q^{96} -59.8897 q^{97} +(81.4818 + 78.7361i) q^{98} -82.9820i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 68 q^{4} - 88 q^{8} + 44 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 + 68 * q^4 - 88 * q^8 + 44 * q^9	$ 32 q + 4 q^{2} + 68 q^{4} - 88 q^{8} + 44 q^{9} - 92 q^{16} - 48 q^{18} - 72 q^{21} + 140 q^{23} - 500 q^{25} + 92 q^{32} - 284 q^{36} + 312 q^{37} + 140 q^{39} + 8 q^{42} - 120 q^{43} - 344 q^{46} - 552 q^{49} + 416 q^{50} - 364 q^{51} - 316 q^{57} - 320 q^{64} + 972 q^{72} + 680 q^{74} + 428 q^{77} + 1144 q^{78} - 240 q^{81} + 640 q^{84} + 260 q^{86} - 160 q^{91} + 676 q^{92} + 532 q^{98}+O(q^{100}) $ 32 * q + 4 * q^2 + 68 * q^4 - 88 * q^8 + 44 * q^9 - 92 * q^16 - 48 * q^18 - 72 * q^21 + 140 * q^23 - 500 * q^25 + 92 * q^32 - 284 * q^36 + 312 * q^37 + 140 * q^39 + 8 * q^42 - 120 * q^43 - 344 * q^46 - 552 * q^49 + 416 * q^50 - 364 * q^51 - 316 * q^57 - 320 * q^64 + 972 * q^72 + 680 * q^74 + 428 * q^77 + 1144 * q^78 - 240 * q^81 + 640 * q^84 + 260 * q^86 - 160 * q^91 + 676 * q^92 + 532 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.31240			−1.15620			−0.578101	−	0.815965i	$-0.696206\pi$
$2$	−2.31240			−1.15620			−0.578101	+	0.815965i	$0.696206\pi$
$3$	−5.31887			−1.77296			−0.886479	−	0.462769i	$-0.846856\pi$
$3$	−5.31887			−1.77296			−0.886479	+	0.462769i	$0.846856\pi$
$4$	1.34721			0.336802
$5$		−	9.29617i		−	1.85923i	−0.368528	−	0.929617i	$-0.620138\pi$
$5$		−	9.29617i		−	1.85923i	0.368528	−	0.929617i	$-0.379862\pi$
$6$	12.2994			2.04990
$7$	−2.62328	+	6.48987i	−0.374754	+	0.927124i
$7$	−2.62328	+	6.48987i	−0.374754	+	0.927124i
$8$	6.13432			0.766790
$9$	19.2904			2.14338
$10$			21.4965i			2.14965i
$11$		−	4.30172i		−	0.391066i	−0.980697	−	0.195533i	$-0.937356\pi$
$11$		−	4.30172i		−	0.391066i	0.980697	−	0.195533i	$-0.0626436\pi$
$12$	−7.16563			−0.597136
$13$	4.06994			0.313072			0.156536	−	0.987672i	$-0.449967\pi$
$13$	4.06994			0.313072			0.156536	+	0.987672i	$0.449967\pi$
$14$	6.06607	−	15.0072i	0.433291	−	1.07194i
$15$			49.4451i			3.29634i
$16$	−19.5739			−1.22337
$17$	19.2739			1.13376			0.566881	−	0.823800i	$-0.308150\pi$
$17$	19.2739			1.13376			0.566881	+	0.823800i	$0.308150\pi$
$18$	−44.6072			−2.47818
$19$	13.2350			0.696579			0.348289	−	0.937387i	$-0.386763\pi$
$19$	13.2350			0.696579			0.348289	+	0.937387i	$0.386763\pi$
$20$		−	12.5239i		−	0.626194i
$21$	13.9529	−	34.5188i	0.664423	−	1.64375i
$22$			9.94732i			0.452151i
$23$	23.0589			1.00256			0.501281	−	0.865285i	$-0.332862\pi$
$23$	23.0589			1.00256			0.501281	+	0.865285i	$0.332862\pi$
$24$	−32.6277			−1.35949
$25$	−61.4187			−2.45675
$26$	−9.41134			−0.361975
$27$	−54.7334			−2.02716
$28$	−3.53410	+	8.74321i	−0.126218	+	0.312257i
$29$		−	41.6081i		−	1.43476i	−0.696682	−	0.717381i	$-0.745341\pi$
$29$		−	41.6081i		−	1.43476i	0.696682	−	0.717381i	$-0.254659\pi$
$30$		−	114.337i		−	3.81124i
$31$		−	19.3984i		−	0.625754i	−0.949794	−	0.312877i	$-0.898707\pi$
$31$		−	19.3984i		−	0.625754i	0.949794	−	0.312877i	$-0.101293\pi$
$32$	20.7254			0.647668
$33$			22.8803i			0.693343i
$34$	−44.5691			−1.31086
$35$	60.3309	+	24.3864i	1.72374	+	0.696755i
$36$	25.9882			0.721894
$37$	45.0642			1.21795			0.608975	−	0.793189i	$-0.291581\pi$
$37$	45.0642			1.21795			0.608975	+	0.793189i	$0.291581\pi$
$38$	−30.6047			−0.805386
$39$	−21.6475			−0.555064
$40$		−	57.0257i		−	1.42564i
$41$	−38.8459	−	13.1148i	−0.947460	−	0.319873i
$41$	−38.8459	−	13.1148i	−0.947460	−	0.319873i
$42$	−32.2647	+	79.8214i	−0.768207	+	1.90051i
$43$	23.7089			0.551370			0.275685	−	0.961248i	$-0.411095\pi$
$43$	23.7089			0.551370			0.275685	+	0.961248i	$0.411095\pi$
$44$		−	5.79532i		−	0.131712i
$45$		−	179.327i		−	3.98504i
$46$	−53.3215			−1.15916
$47$	−31.6879			−0.674210			−0.337105	−	0.941467i	$-0.609448\pi$
$47$	−31.6879			−0.674210			−0.337105	+	0.941467i	$0.609448\pi$
$48$	104.111			2.16898
$49$	−35.2368	−	34.0495i	−0.719119	−	0.694887i
$50$	142.025			2.84050
$51$	−102.516			−2.01011
$52$	5.48306			0.105443
$53$			14.1941i			0.267814i	0.990994	+	0.133907i	$0.0427523\pi$
$53$			14.1941i			0.267814i	−0.990994	+	0.133907i	$0.957248\pi$
$54$	126.566			2.34381
$55$	−39.9895			−0.727082
$56$	−16.0920	+	39.8110i	−0.287358	+	0.710910i
$57$	−70.3953			−1.23500
$58$			96.2146i			1.65887i
$59$			102.088i			1.73030i	0.501512	+	0.865151i	$0.332777\pi$
$59$			102.088i			1.73030i	−0.501512	+	0.865151i	$0.667223\pi$
$60$			66.6129i			1.11021i
$61$		−	37.3731i		−	0.612673i	−0.951923	−	0.306337i	$-0.900897\pi$
$61$		−	37.3731i		−	0.612673i	0.951923	−	0.306337i	$-0.0991033\pi$
$62$			44.8569i			0.723498i
$63$	−50.6041	+	125.192i	−0.803239	+	1.98718i
$64$	30.3700			0.474532
$65$		−	37.8348i		−	0.582074i
$66$		−	52.9085i		−	0.801644i
$67$			86.4202i			1.28985i	0.764244	+	0.644927i	$0.223112\pi$
$67$			86.4202i			1.28985i	−0.764244	+	0.644927i	$0.776888\pi$
$68$	25.9660			0.381853
$69$	−122.647			−1.77750
$70$	−139.509	−	56.3912i	−1.99299	−	0.805589i
$71$		−	20.8304i		−	0.293386i	−0.989182	−	0.146693i	$-0.953137\pi$
$71$		−	20.8304i		−	0.293386i	0.989182	−	0.146693i	$-0.0468630\pi$
$72$	118.334			1.64352
$73$			36.1452i			0.495139i	0.968870	+	0.247570i	$0.0796319\pi$
$73$			36.1452i			0.495139i	−0.968870	+	0.247570i	$0.920368\pi$
$74$	−104.207			−1.40820
$75$	326.678			4.35571
$76$	17.8303			0.234609
$77$	27.9176	+	11.2846i	0.362567	+	0.146553i
$78$	50.0577			0.641766
$79$		−	73.3847i		−	0.928920i	−0.885594	−	0.464460i	$-0.846248\pi$
$79$		−	73.3847i		−	0.928920i	0.885594	−	0.464460i	$-0.153752\pi$
$80$			181.962i			2.27452i
$81$	117.506			1.45069
$82$	89.8273	+	30.3267i	1.09546	+	0.369838i
$83$		−	124.813i		−	1.50377i	−0.659294	−	0.751885i	$-0.729145\pi$
$83$		−	124.813i		−	1.50377i	0.659294	−	0.751885i	$-0.270855\pi$
$84$	18.7974	−	46.5040i	0.223779	−	0.553619i
$85$		−	179.174i		−	2.10793i
$86$	−54.8245			−0.637495
$87$			221.308i			2.54377i
$88$		−	26.3882i		−	0.299865i
$89$	−31.9858			−0.359391			−0.179696	−	0.983722i	$-0.557511\pi$
$89$	−31.9858			−0.359391			−0.179696	+	0.983722i	$0.557511\pi$
$90$			414.676i			4.60751i
$91$	−10.6766	+	26.4134i	−0.117325	+	0.290257i
$92$	31.0652			0.337665
$93$			103.177i			1.10944i
$94$	73.2752			0.779523
$95$		−	123.035i		−	1.29510i
$96$	−110.236			−1.14829
$97$	−59.8897			−0.617420			−0.308710	−	0.951156i	$-0.599897\pi$
$97$	−59.8897			−0.617420			−0.308710	+	0.951156i	$0.599897\pi$
$98$	81.4818	+	78.7361i	0.831447	+	0.803429i
$99$		−	82.9820i		−	0.838202i
$100$	−82.7438			−0.827438
$101$	64.7847			0.641433			0.320716	−	0.947175i	$-0.396076\pi$
$101$	64.7847			0.641433			0.320716	+	0.947175i	$0.396076\pi$
$102$	237.058			2.32409
$103$		−	133.944i		−	1.30043i	−0.759751	−	0.650214i	$-0.774679\pi$
$103$		−	133.944i		−	1.30043i	0.759751	−	0.650214i	$-0.225321\pi$
$104$	24.9663			0.240061
$105$	−320.892	−	129.708i	−3.05612	−	1.23532i
$106$		−	32.8225i		−	0.309647i
$107$	−1.87527			−0.0175259			−0.00876296	−	0.999962i	$-0.502789\pi$
$107$	−1.87527			−0.0175259			−0.00876296	+	0.999962i	$0.502789\pi$
$108$	−73.7373			−0.682752
$109$		−	83.6865i		−	0.767766i	−0.923382	−	0.383883i	$-0.874587\pi$
$109$		−	83.6865i		−	0.767766i	0.923382	−	0.383883i	$-0.125413\pi$
$110$	92.4719			0.840654
$111$	−239.691			−2.15938
$112$	51.3477	−	127.032i	0.458461	−	1.13421i
$113$	103.725			0.917924			0.458962	−	0.888456i	$-0.348221\pi$
$113$	103.725			0.917924			0.458962	+	0.888456i	$0.348221\pi$
$114$	162.782			1.42791
$115$		−	214.359i		−	1.86400i
$116$		−	56.0547i		−	0.483231i
$117$	78.5108			0.671032
$118$		−	236.068i		−	2.00058i
$119$	−50.5609	+	125.085i	−0.424881	+	1.05114i
$120$			303.312i			2.52760i
$121$	102.495			0.847068
$122$			86.4216i			0.708374i
$123$	206.616	+	69.7560i	1.67981	+	0.567122i
$124$		−	26.1337i		−	0.210755i
$125$			338.554i			2.70843i
$126$	117.017	−	289.495i	0.928707	−	2.29758i
$127$	−141.240			−1.11212			−0.556062	−	0.831141i	$-0.687688\pi$
$127$	−141.240			−1.11212			−0.556062	+	0.831141i	$0.687688\pi$
$128$	−153.129			−1.19632
$129$	−126.105			−0.977555
$130$			87.4894i			0.672995i
$131$			83.2585i			0.635561i	0.948164	+	0.317781i	$0.102938\pi$
$131$			83.2585i			0.635561i	−0.948164	+	0.317781i	$0.897062\pi$
$132$			30.8246i			0.233519i
$133$	−34.7191	+	85.8934i	−0.261046	+	0.645815i
$134$		−	199.838i		−	1.49133i
$135$			508.811i			3.76897i
$136$	118.233			0.869357
$137$		−	198.625i		−	1.44982i	−0.688843	−	0.724910i	$-0.741881\pi$
$137$		−	198.625i		−	1.44982i	0.688843	−	0.724910i	$-0.258119\pi$
$138$	283.610			2.05515
$139$		−	139.854i		−	1.00614i	−0.864245	−	0.503072i	$-0.832203\pi$
$139$		−	139.854i		−	1.00614i	0.864245	−	0.503072i	$-0.167797\pi$
$140$	81.2783	+	32.8536i	0.580559	+	0.234668i
$141$	168.544			1.19535
$142$			48.1683i			0.339213i
$143$		−	17.5078i		−	0.122432i
$144$	−377.588			−2.62214
$145$	−386.796			−2.66756
$146$		−	83.5822i		−	0.572481i
$147$	187.420	+	181.105i	1.27497	+	1.23200i
$148$	60.7108			0.410208
$149$		−	225.298i		−	1.51207i	−0.654532	−	0.756034i	$-0.727134\pi$
$149$		−	225.298i		−	1.51207i	0.654532	−	0.756034i	$-0.272866\pi$
$150$	−755.412			−5.03608
$151$			65.2361i			0.432027i	0.976390	+	0.216014i	$0.0693056\pi$
$151$			65.2361i			0.432027i	−0.976390	+	0.216014i	$0.930694\pi$
$152$	81.1878			0.534130
$153$	371.802			2.43008
$154$	−64.5568	−	26.0946i	−0.419200	−	0.169445i
$155$	−180.331			−1.16342
$156$	−29.1637			−0.186947
$157$	−214.621			−1.36701			−0.683507	−	0.729944i	$-0.739546\pi$
$157$	−214.621			−1.36701			−0.683507	+	0.729944i	$0.739546\pi$
$158$			169.695i			1.07402i
$159$		−	75.4968i		−	0.474822i
$160$		−	192.666i		−	1.20417i
$161$	−60.4899	+	149.649i	−0.375714	+	0.929499i
$162$	−271.722			−1.67729
$163$	−112.715			−0.691502			−0.345751	−	0.938326i	$-0.612376\pi$
$163$	−112.715			−0.691502			−0.345751	+	0.938326i	$0.612376\pi$
$164$	−52.3335	−	17.6684i	−0.319107	−	0.107734i
$165$	212.699			1.28909
$166$			288.618i			1.73866i
$167$	−84.5567			−0.506328			−0.253164	−	0.967423i	$-0.581471\pi$
$167$	−84.5567			−0.506328			−0.253164	+	0.967423i	$0.581471\pi$
$168$	85.5915	−	211.749i	0.509473	−	1.26041i
$169$	−152.436			−0.901986
$170$			414.322i			2.43719i
$171$	255.309			1.49303
$172$	31.9408			0.185702
$173$			188.935i			1.09211i	0.837749	+	0.546055i	$0.183871\pi$
$173$			188.935i			1.09211i	−0.837749	+	0.546055i	$0.816129\pi$
$174$		−	511.753i		−	2.94111i
$175$	161.118	−	398.599i	0.920676	−	2.27771i
$176$			84.2013i			0.478417i
$177$		−	542.992i		−	3.06775i
$178$	73.9642			0.415529
$179$		−	136.956i		−	0.765116i	−0.923931	−	0.382558i	$-0.875043\pi$
$179$		−	136.956i		−	0.765116i	0.923931	−	0.382558i	$-0.124957\pi$
$180$		−	241.591i		−	1.34217i
$181$	173.228			0.957059			0.478529	−	0.878072i	$-0.341170\pi$
$181$	173.228			0.957059			0.478529	+	0.878072i	$0.341170\pi$
$182$	24.6886	−	61.0784i	0.135651	−	0.335595i
$183$			198.783i			1.08624i
$184$	141.451			0.768755
$185$		−	418.924i		−	2.26445i
$186$		−	238.588i		−	1.28273i
$187$		−	82.9112i		−	0.443375i
$188$	−42.6902			−0.227075
$189$	143.581	−	355.213i	0.759687	−	1.87943i
$190$			284.506i			1.49740i
$191$			118.789i			0.621934i	0.950421	+	0.310967i	$0.100653\pi$
$191$			118.789i			0.621934i	−0.950421	+	0.310967i	$0.899347\pi$
$192$	−161.534			−0.841325
$193$			243.094i			1.25955i	0.776776	+	0.629777i	$0.216854\pi$
$193$			243.094i			1.25955i	−0.776776	+	0.629777i	$0.783146\pi$
$194$	138.489			0.713862
$195$			201.239i			1.03199i
$196$	−47.4714	−	45.8717i	−0.242201	−	0.234039i
$197$	296.058			1.50283			0.751417	−	0.659827i	$-0.229371\pi$
$197$	296.058			1.50283			0.751417	+	0.659827i	$0.229371\pi$
$198$			191.888i			0.969130i
$199$	−359.731			−1.80769			−0.903846	−	0.427858i	$-0.859268\pi$
$199$	−359.731			−1.80769			−0.903846	+	0.427858i	$0.859268\pi$
$200$	−376.762			−1.88381
$201$		−	459.658i		−	2.28686i
$202$	−149.808			−0.741625
$203$	270.031	+	109.149i	1.33020	+	0.537682i
$204$	−138.110			−0.677010
$205$	−121.917	+	361.118i	−0.594719	+	1.76155i
$206$			309.733i			1.50356i
$207$	444.816			2.14887
$208$	−79.6644			−0.383002
$209$		−	56.9333i		−	0.272408i
$210$	742.033	+	299.938i	3.53349	+	1.42828i
$211$		−	353.243i		−	1.67414i	−0.547098	−	0.837069i	$-0.684267\pi$
$211$		−	353.243i		−	1.67414i	0.547098	−	0.837069i	$-0.315733\pi$
$212$			19.1224i			0.0902002i
$213$			110.794i			0.520161i
$214$	4.33639			0.0202635
$215$		−	220.402i		−	1.02512i
$216$	−335.752			−1.55441
$217$	125.893	+	50.8873i	0.580152	+	0.234504i
$218$			193.517i			0.887693i
$219$		−	192.252i		−	0.877861i
$220$	−53.8742			−0.244883
$221$	78.4438			0.354949
$222$	554.261			2.49667
$223$			55.1570i			0.247341i	0.992323	+	0.123670i	$0.0394666\pi$
$223$			55.1570i			0.247341i	−0.992323	+	0.123670i	$0.960533\pi$
$224$	−54.3684	+	134.505i	−0.242716	+	0.600469i
$225$	−1184.79			−5.26574
$226$	−239.855			−1.06131
$227$	174.283			0.767765			0.383883	−	0.923382i	$-0.374587\pi$
$227$	174.283			0.767765			0.383883	+	0.923382i	$0.374587\pi$
$228$	−94.8371			−0.415952
$229$	130.242			0.568744			0.284372	−	0.958714i	$-0.408215\pi$
$229$	130.242			0.568744			0.284372	+	0.958714i	$0.408215\pi$
$230$			495.685i			2.15515i
$231$	−148.490	−	60.0214i	−0.642815	−	0.259833i
$232$		−	255.237i		−	1.10016i
$233$		−	161.053i		−	0.691217i	−0.938379	−	0.345608i	$-0.887673\pi$
$233$		−	161.053i		−	0.691217i	0.938379	−	0.345608i	$-0.112327\pi$
$234$	−181.549			−0.775849
$235$			294.576i			1.25351i
$236$			137.533i			0.582769i
$237$			390.324i			1.64694i
$238$	116.917	−	289.248i	0.491249	−	1.21533i
$239$		−	73.0232i		−	0.305537i	−0.988262	−	0.152768i	$-0.951181\pi$
$239$		−	73.0232i		−	0.305537i	0.988262	−	0.152768i	$-0.0488188\pi$
$240$		−	967.832i		−	4.03263i
$241$			91.0737i			0.377899i	0.981987	+	0.188950i	$0.0605083\pi$
$241$			91.0737i			0.377899i	−0.981987	+	0.188950i	$0.939492\pi$
$242$	−237.010			−0.979381
$243$	−132.400			−0.544857
$244$		−	50.3493i		−	0.206350i
$245$	−316.529	+	327.567i	−1.29196	+	1.33701i
$246$	−477.780	−	161.304i	−1.94220	−	0.655707i
$247$	53.8656			0.218080
$248$		−	118.996i		−	0.479822i
$249$			663.864i			2.66612i
$250$		−	782.874i		−	3.13150i
$251$		−	156.271i		−	0.622594i	−0.950313	−	0.311297i	$-0.899237\pi$
$251$		−	156.271i		−	0.622594i	0.950313	−	0.311297i	$-0.100763\pi$
$252$	−68.1742	+	168.660i	−0.270533	+	0.669286i
$253$		−	99.1930i		−	0.392067i
$254$	326.603			1.28584
$255$			953.003i			3.73726i
$256$	232.616			0.908658
$257$	−262.122			−1.01993			−0.509965	−	0.860195i	$-0.670342\pi$
$257$	−262.122			−1.01993			−0.509965	+	0.860195i	$0.670342\pi$
$258$	291.605			1.13025
$259$	−118.216	+	292.461i	−0.456432	+	1.12919i
$260$		−	50.9714i		−	0.196044i
$261$		−	802.637i		−	3.07524i
$262$		−	192.527i		−	0.734837i
$263$		−	270.177i		−	1.02729i	−0.858003	−	0.513644i	$-0.828295\pi$
$263$		−	270.177i		−	1.02729i	0.858003	−	0.513644i	$-0.171705\pi$
$264$			140.355i			0.531649i
$265$	131.951			0.497928
$266$	80.2845	−	198.620i	0.301821	−	0.746693i
$267$	170.129			0.637186
$268$			116.426i			0.434426i
$269$		−	493.532i		−	1.83469i	−0.398090	−	0.917346i	$-0.630327\pi$
$269$		−	493.532i		−	1.83469i	0.398090	−	0.917346i	$-0.369673\pi$
$270$		−	1176.58i		−	4.35769i
$271$			402.552i			1.48543i	0.669606	+	0.742716i	$0.266463\pi$
$271$			402.552i			1.48543i	−0.669606	+	0.742716i	$0.733537\pi$
$272$	−377.266			−1.38701
$273$	56.7874	−	140.489i	0.208012	−	0.514613i
$274$			459.302i			1.67628i
$275$			264.206i			0.960750i
$276$	−165.232			−0.598665
$277$	−333.806			−1.20508			−0.602538	−	0.798090i	$-0.705844\pi$
$277$	−333.806			−1.20508			−0.602538	+	0.798090i	$0.705844\pi$
$278$			323.399i			1.16330i
$279$		−	374.203i		−	1.34123i
$280$	370.089	+	149.594i	1.32175	+	0.534265i
$281$			463.089i			1.64800i	0.566587	+	0.824002i	$0.308264\pi$
$281$			463.089i			1.64800i	−0.566587	+	0.824002i	$0.691736\pi$
$282$	−389.741			−1.38206
$283$			269.762i			0.953222i	0.879114	+	0.476611i	$0.158135\pi$
$283$			269.762i			0.953222i	−0.879114	+	0.476611i	$0.841865\pi$
$284$		−	28.0629i		−	0.0988130i
$285$			654.406i			2.29616i
$286$			40.4850i			0.141556i
$287$	187.017	−	217.701i	0.651627	−	0.758540i
$288$	399.801			1.38820
$289$	82.4849			0.285415
$290$	894.427			3.08423
$291$	318.546			1.09466
$292$			48.6951i			0.166764i
$293$	−383.455			−1.30872			−0.654360	−	0.756183i	$-0.727062\pi$
$293$	−383.455			−1.30872			−0.654360	+	0.756183i	$0.727062\pi$
$294$	−433.391	−	418.787i	−1.47412	−	1.42445i
$295$	949.025			3.21703
$296$	276.438			0.933913
$297$			235.448i			0.792754i
$298$			520.980i			1.74826i
$299$	93.8484			0.313874
$300$	440.104			1.46701
$301$	−62.1950	+	153.868i	−0.206628	+	0.511188i
$302$		−	150.852i		−	0.499511i
$303$	−344.581			−1.13723
$304$	−259.060			−0.852171
$305$	−347.426			−1.13910
$306$	−859.757			−2.80966
$307$			96.8702i			0.315538i	0.987476	+	0.157769i	$0.0504302\pi$
$307$			96.8702i			0.315538i	−0.987476	+	0.157769i	$0.949570\pi$
$308$	37.6109	+	15.2027i	0.122113	+	0.0493595i
$309$			712.432i			2.30560i
$310$	416.997			1.34515
$311$	155.293			0.499335			0.249667	−	0.968332i	$-0.419679\pi$
$311$	155.293			0.499335			0.249667	+	0.968332i	$0.419679\pi$
$312$	−132.793			−0.425618
$313$	375.456			1.19954			0.599770	−	0.800173i	$-0.295259\pi$
$313$	375.456			1.19954			0.599770	+	0.800173i	$0.295259\pi$
$314$	496.291			1.58054
$315$	1163.81	+	470.424i	3.69463	+	1.49341i
$316$		−	98.8644i		−	0.312862i
$317$			25.8436i			0.0815256i	0.999169	+	0.0407628i	$0.0129788\pi$
$317$			25.8436i			0.0815256i	−0.999169	+	0.0407628i	$0.987021\pi$
$318$			174.579i			0.548990i
$319$	−178.986			−0.561086
$320$		−	282.325i		−	0.882266i
$321$	9.97434			0.0310727
$322$	139.877	−	346.050i	0.434401	−	1.07469i
$323$	255.091			0.789754
$324$	158.305			0.488597
$325$	−249.970			−0.769140
$326$	260.642			0.799515
$327$			445.118i			1.36122i
$328$	−238.293	−	80.4505i	−0.726504	−	0.245276i
$329$	83.1261	−	205.650i	0.252663	−	0.625077i
$330$	−491.846			−1.49044
$331$			18.8685i			0.0570045i	0.999594	+	0.0285023i	$0.00907378\pi$
$331$			18.8685i			0.0570045i	−0.999594	+	0.0285023i	$0.990926\pi$
$332$		−	168.149i		−	0.506473i
$333$	869.306			2.61053
$334$	195.529			0.585417
$335$	803.377			2.39814
$336$	−273.112	+	675.666i	−0.812832	+	2.01091i
$337$	−19.3892			−0.0575346			−0.0287673	−	0.999586i	$-0.509158\pi$
$337$	−19.3892			−0.0575346			−0.0287673	+	0.999586i	$0.509158\pi$
$338$	352.493			1.04288
$339$	−551.702			−1.62744
$340$		−	241.384i		−	0.709954i
$341$	−83.4464			−0.244711
$342$	−590.376			−1.72625
$343$	313.413	−	139.361i	0.913739	−	0.406301i
$344$	145.438			0.422785
$345$			1140.15i			3.30478i
$346$		−	436.894i		−	1.26270i
$347$		−	39.7233i		−	0.114476i	−0.998361	−	0.0572382i	$-0.981771\pi$
$347$		−	39.7233i		−	0.114476i	0.998361	−	0.0572382i	$-0.0182295\pi$
$348$			298.148i			0.856747i
$349$		−	439.551i		−	1.25946i	−0.776814	−	0.629730i	$-0.783166\pi$
$349$		−	439.551i		−	1.25946i	0.776814	−	0.629730i	$-0.216834\pi$
$350$	−372.570	+	921.723i	−1.06449	+	2.63349i
$351$	−222.762			−0.634648
$352$		−	89.1548i		−	0.253281i
$353$			94.5426i			0.267826i	0.990993	+	0.133913i	$0.0427543\pi$
$353$			94.5426i			0.267826i	−0.990993	+	0.133913i	$0.957246\pi$
$354$			1255.62i			3.54694i
$355$	−193.643			−0.545473
$356$	−43.0916			−0.121044
$357$	268.927	−	665.313i	0.753297	−	1.86362i
$358$			316.697i			0.884628i
$359$	−320.222			−0.891982			−0.445991	−	0.895037i	$-0.647149\pi$
$359$	−320.222			−0.891982			−0.445991	+	0.895037i	$0.647149\pi$
$360$		−	1100.05i		−	3.05569i
$361$	−185.835			−0.514778
$362$	−400.572			−1.10655
$363$	−545.159			−1.50181
$364$	−14.3836	+	35.5843i	−0.0395153	+	0.0977591i
$365$	336.012			0.920580
$366$		−	459.666i		−	1.25592i
$367$		−	340.339i		−	0.927354i	−0.886004	−	0.463677i	$-0.846530\pi$
$367$		−	340.339i		−	0.927354i	0.886004	−	0.463677i	$-0.153470\pi$
$368$	−451.352			−1.22650
$369$	−749.353	−	252.990i	−2.03077	−	0.685610i
$370$			968.721i			2.61817i
$371$	−92.1181	−	37.2351i	−0.248297	−	0.100364i
$372$			139.002i			0.373660i
$373$	−551.937			−1.47972			−0.739862	−	0.672759i	$-0.765109\pi$
$373$	−551.937			−1.47972			−0.739862	+	0.672759i	$0.765109\pi$
$374$			191.724i			0.512631i
$375$		−	1800.73i		−	4.80194i
$376$	−194.384			−0.516978
$377$		−	169.342i		−	0.449184i
$378$	−332.017	+	821.395i	−0.878351	+	2.17300i
$379$	−238.280			−0.628707			−0.314353	−	0.949306i	$-0.601788\pi$
$379$	−238.280			−0.628707			−0.314353	+	0.949306i	$0.601788\pi$
$380$		−	165.753i		−	0.436193i
$381$	751.236			1.97175
$382$		−	274.689i		−	0.719081i
$383$	48.0656			0.125498			0.0627488	−	0.998029i	$-0.480013\pi$
$383$	48.0656			0.125498			0.0627488	+	0.998029i	$0.480013\pi$
$384$	814.475			2.12103
$385$	104.904	−	259.527i	0.272477	−	0.674096i
$386$		−	562.131i		−	1.45630i
$387$	457.354			1.18179
$388$	−80.6839			−0.207948
$389$	546.118			1.40390			0.701952	−	0.712225i	$-0.252312\pi$
$389$	546.118			1.40390			0.701952	+	0.712225i	$0.252312\pi$
$390$		−	465.345i		−	1.19319i
$391$	444.436			1.13667
$392$	−216.154	−	208.870i	−0.551414	−	0.532833i
$393$		−	442.841i		−	1.12682i
$394$	−684.606			−1.73758
$395$	−682.196			−1.72708
$396$		−	111.794i		−	0.282308i
$397$	15.8905			0.0400265			0.0200132	−	0.999800i	$-0.493629\pi$
$397$	15.8905			0.0400265			0.0200132	+	0.999800i	$0.493629\pi$
$398$	831.842			2.09006
$399$	184.666	−	456.856i	0.462823	−	1.14500i
$400$	1202.20			3.00550
$401$	−218.022			−0.543696			−0.271848	−	0.962340i	$-0.587635\pi$
$401$	−218.022			−0.543696			−0.271848	+	0.962340i	$0.587635\pi$
$402$			1062.92i			2.64407i
$403$		−	78.9502i		−	0.195906i
$404$	87.2785			0.216036
$405$		−	1092.36i		−	2.69718i
$406$	−624.421	−	252.398i	−1.53798	−	0.621669i
$407$		−	193.854i		−	0.476299i
$408$	−628.864			−1.54133
$409$			103.600i			0.253300i	0.991947	+	0.126650i	$0.0404224\pi$
$409$			103.600i			0.253300i	−0.991947	+	0.126650i	$0.959578\pi$
$410$	281.922	−	835.050i	0.687615	−	2.03671i
$411$			1056.46i			2.57047i
$412$		−	180.451i		−	0.437987i
$413$	−662.536	−	267.805i	−1.60420	−	0.648437i
$414$	−1028.59			−2.48453
$415$	−1160.28			−2.79586
$416$	84.3510			0.202767
$417$			743.865i			1.78385i
$418$			131.653i			0.314959i
$419$		−	69.5324i		−	0.165948i	−0.996552	−	0.0829742i	$-0.973558\pi$
$419$		−	69.5324i		−	0.165948i	0.996552	−	0.0829742i	$-0.0264419\pi$
$420$	−432.309	−	174.744i	−1.02931	−	0.416057i
$421$			30.6910i			0.0729003i	0.999335	+	0.0364502i	$0.0116050\pi$
$421$			30.6910i			0.0729003i	−0.999335	+	0.0364502i	$0.988395\pi$
$422$			816.840i			1.93564i
$423$	−611.272			−1.44509
$424$			87.0714i			0.205357i
$425$	−1183.78			−2.78537
$426$		−	256.201i		−	0.601411i
$427$	242.546	+	98.0399i	0.568024	+	0.229602i
$428$	−2.52638			−0.00590277
$429$			93.1215i			0.217066i
$430$			509.658i			1.18525i
$431$	163.787			0.380017			0.190009	−	0.981782i	$-0.439148\pi$
$431$	163.787			0.380017			0.190009	+	0.981782i	$0.439148\pi$
$432$	1071.34			2.47996
$433$			378.183i			0.873402i	0.899607	+	0.436701i	$0.143853\pi$
$433$			378.183i			0.873402i	−0.899607	+	0.436701i	$0.856147\pi$
$434$	−291.115	−	117.672i	−0.670772	−	0.271134i
$435$	2057.32			4.72946
$436$		−	112.743i		−	0.258585i
$437$	305.185			0.698363
$438$			444.563i			1.01498i
$439$	−190.556			−0.434069			−0.217035	−	0.976164i	$-0.569638\pi$
$439$	−190.556			−0.434069			−0.217035	+	0.976164i	$0.569638\pi$
$440$	−245.309			−0.557520
$441$	−679.733	−	656.828i	−1.54134	−	1.48941i
$442$	−181.394			−0.410393
$443$	−246.430			−0.556274			−0.278137	−	0.960541i	$-0.589717\pi$
$443$	−246.430			−0.556274			−0.278137	+	0.960541i	$0.589717\pi$
$444$	−322.913			−0.727282
$445$			297.346i			0.668193i
$446$		−	127.545i		−	0.285976i
$447$			1198.33i			2.68083i
$448$	−79.6690	+	197.098i	−0.177833	+	0.439950i
$449$	458.224			1.02054			0.510272	−	0.860013i	$-0.329545\pi$
$449$	458.224			1.02054			0.510272	+	0.860013i	$0.329545\pi$
$450$	2739.72			6.08826
$451$	−56.4163	+	167.104i	−0.125092	+	0.370519i
$452$	139.740			0.309159
$453$		−	346.983i		−	0.765966i
$454$	−403.012			−0.887691
$455$	245.543	+	99.2512i	0.539655	+	0.218135i
$456$	−431.827			−0.946990
$457$		−	563.845i		−	1.23380i	−0.787043	−	0.616898i	$-0.788389\pi$
$457$		−	563.845i		−	1.23380i	0.787043	−	0.616898i	$-0.211611\pi$
$458$	−301.173			−0.657582
$459$	−1054.93			−2.29832
$460$		−	288.787i		−	0.627797i
$461$		−	239.713i		−	0.519985i	−0.965611	−	0.259992i	$-0.916280\pi$
$461$		−	239.713i		−	0.519985i	0.965611	−	0.259992i	$-0.0837201\pi$
$462$	343.369	+	138.794i	0.743224	+	0.300419i
$463$		−	656.271i		−	1.41743i	−0.705494	−	0.708716i	$-0.749275\pi$
$463$		−	656.271i		−	1.41743i	0.705494	−	0.708716i	$-0.250725\pi$
$464$			814.431i			1.75524i
$465$	959.155			2.06270
$466$			372.421i			0.799186i
$467$			203.762i			0.436321i	0.975913	+	0.218161i	$0.0700057\pi$
$467$			203.762i			0.436321i	−0.975913	+	0.218161i	$0.929994\pi$
$468$	105.770			0.226005
$469$	−560.856	−	226.704i	−1.19586	−	0.483378i
$470$		−	681.178i		−	1.44931i
$471$	1141.54			2.42366
$472$			626.239i			1.32678i
$473$		−	101.989i		−	0.215622i
$474$		−	902.586i		−	1.90419i
$475$	−812.876			−1.71132
$476$	−68.1161	+	168.516i	−0.143101	+	0.354025i
$477$			273.811i			0.574026i
$478$			168.859i			0.353262i
$479$	132.850			0.277349			0.138675	−	0.990338i	$-0.455716\pi$
$479$	132.850			0.277349			0.138675	+	0.990338i	$0.455716\pi$
$480$			1024.77i			2.13493i
$481$	183.408			0.381307
$482$		−	210.599i		−	0.436928i
$483$	321.738	−	795.966i	0.666125	−	1.64796i
$484$	138.082			0.285294
$485$			556.745i			1.14793i
$486$	306.163			0.629964
$487$	114.750			0.235626			0.117813	−	0.993036i	$-0.462412\pi$
$487$	114.750			0.235626			0.117813	+	0.993036i	$0.462412\pi$
$488$		−	229.259i		−	0.469792i
$489$	599.515			1.22600
$490$	731.944	−	757.468i	1.49376	−	1.54585i
$491$	−327.120			−0.666233			−0.333116	−	0.942886i	$-0.608100\pi$
$491$	−327.120			−0.666233			−0.333116	+	0.942886i	$0.608100\pi$
$492$	278.355	+	93.9759i	0.565762	+	0.191008i
$493$		−	801.952i		−	1.62668i
$494$	−124.559			−0.252144
$495$	−771.414			−1.55841
$496$			379.701i			0.765526i
$497$	135.187	+	54.6439i	0.272005	+	0.109948i
$498$		−	1535.12i		−	3.08257i
$499$		−	440.027i		−	0.881818i	−0.897552	−	0.440909i	$-0.854656\pi$
$499$		−	440.027i		−	0.881818i	0.897552	−	0.440909i	$-0.145344\pi$
$500$			456.103i			0.912206i
$501$	449.746			0.897697
$502$			361.362i			0.719845i
$503$	62.1914			0.123641			0.0618205	−	0.998087i	$-0.480309\pi$
$503$	62.1914			0.123641			0.0618205	+	0.998087i	$0.480309\pi$
$504$	−310.422	+	767.970i	−0.615916	+	1.52375i
$505$		−	602.249i		−	1.19257i
$506$			229.374i			0.453309i
$507$	810.786			1.59918
$508$	−190.279			−0.374565
$509$	285.887			0.561664			0.280832	−	0.959757i	$-0.409390\pi$
$509$	285.887			0.561664			0.280832	+	0.959757i	$0.409390\pi$
$510$		−	2203.73i		−	4.32103i
$511$	−234.577	−	94.8188i	−0.459056	−	0.185555i
$512$	74.6142			0.145731
$513$	−724.396			−1.41208
$514$	606.132			1.17925
$515$	−1245.17			−2.41780
$516$	−169.889			−0.329243
$517$			136.312i			0.263661i
$518$	273.363	−	676.287i	0.527727	−	1.30557i
$519$		−	1004.92i		−	1.93626i
$520$		−	232.091i		−	0.446329i
$521$	638.966			1.22642			0.613211	−	0.789919i	$-0.289878\pi$
$521$	638.966			1.22642			0.613211	+	0.789919i	$0.289878\pi$
$522$			1856.02i			3.55559i
$523$			113.204i			0.216451i	0.994126	+	0.108226i	$0.0345169\pi$
$523$			113.204i			0.216451i	−0.994126	+	0.108226i	$0.965483\pi$
$524$			112.167i			0.214058i
$525$	−856.968	+	2120.10i	−1.63232	+	4.03828i
$526$			624.758i			1.18775i
$527$		−	373.883i		−	0.709456i
$528$		−	447.856i		−	0.848213i
$529$	2.71338			0.00512926
$530$	−305.124			−0.575705
$531$			1969.32i			3.70869i
$532$	−46.7738	+	115.716i	−0.0879207	+	0.217512i
$533$	−158.100	−	53.3765i	−0.296624	−	0.100143i
$534$	−393.406			−0.736715
$535$			17.4328i			0.0325848i
$536$			530.130i			0.989048i
$537$			728.450i			1.35652i
$538$			1141.25i			2.12127i
$539$	−146.471	+	151.579i	−0.271746	+	0.281223i
$540$			685.474i			1.26940i
$541$	86.6503			0.160167			0.0800835	−	0.996788i	$-0.474481\pi$
$541$	86.6503			0.160167			0.0800835	+	0.996788i	$0.474481\pi$
$542$		−	930.863i		−	1.71746i
$543$	−921.376			−1.69682
$544$	399.460			0.734301
$545$	−777.964			−1.42746
$546$	−131.315	+	324.868i	−0.240504	+	0.594997i
$547$			453.471i			0.829015i	0.910046	+	0.414508i	$0.136046\pi$
$547$			453.471i			0.829015i	−0.910046	+	0.414508i	$0.863954\pi$
$548$		−	267.590i		−	0.488303i
$549$		−	720.942i		−	1.31319i
$550$		−	610.951i		−	1.11082i
$551$		−	550.683i		−	0.999424i
$552$	−752.359			−1.36297
$553$	476.257	+	192.508i	0.861224	+	0.348116i
$554$	771.894			1.39331
$555$			2228.20i			4.01478i
$556$		−	188.412i		−	0.338871i
$557$		−	941.504i		−	1.69031i	−0.534520	−	0.845156i	$-0.679508\pi$
$557$		−	941.504i		−	1.69031i	0.534520	−	0.845156i	$-0.320492\pi$
$558$			865.307i			1.55073i
$559$	96.4938			0.172619
$560$	−1180.91	−	477.336i	−2.10877	−	0.852386i
$561$			440.994i			0.786085i
$562$		−	1070.85i		−	1.90542i
$563$	84.8009			0.150623			0.0753116	−	0.997160i	$-0.476005\pi$
$563$	84.8009			0.150623			0.0753116	+	0.997160i	$0.476005\pi$
$564$	227.064			0.402595
$565$		−	964.249i		−	1.70664i
$566$		−	623.798i		−	1.10212i
$567$	−308.251	+	762.600i	−0.543653	+	1.34497i
$568$		−	127.780i		−	0.224966i
$569$	249.784			0.438988			0.219494	−	0.975614i	$-0.429559\pi$
$569$	249.784			0.438988			0.219494	+	0.975614i	$0.429559\pi$
$570$		−	1513.25i		−	2.65483i
$571$			38.4302i			0.0673033i	0.999434	+	0.0336517i	$0.0107137\pi$
$571$			38.4302i			0.0673033i	−0.999434	+	0.0336517i	$0.989286\pi$
$572$		−	23.5866i		−	0.0412353i
$573$		−	631.826i		−	1.10266i
$574$	−432.458	+	503.412i	−0.753412	+	0.877025i
$575$	−1416.25			−2.46304
$576$	585.851			1.01710
$577$	999.960			1.73303			0.866516	−	0.499149i	$-0.166354\pi$
$577$	999.960			1.73303			0.866516	+	0.499149i	$0.166354\pi$
$578$	−190.738			−0.329997
$579$		−	1292.98i		−	2.23313i
$580$	−521.094			−0.898438
$581$	810.020	+	327.419i	1.39418	+	0.563544i
$582$	−736.606			−1.26565
$583$	61.0592			0.104733
$584$			221.726i			0.379668i
$585$		−	729.849i		−	1.24761i
$586$	886.703			1.51314
$587$	−517.973			−0.882407			−0.441204	−	0.897407i	$-0.645448\pi$
$587$	−517.973			−0.882407			−0.441204	+	0.897407i	$0.645448\pi$
$588$	252.494	+	243.986i	0.429412	+	0.414942i
$589$		−	256.737i		−	0.435887i
$590$	−2194.53			−3.71954
$591$	−1574.70			−2.66446
$592$	−882.080			−1.49000
$593$	464.694			0.783633			0.391816	−	0.920043i	$-0.371847\pi$
$593$	464.694			0.783633			0.391816	+	0.920043i	$0.371847\pi$
$594$		−	544.450i		−	0.916583i
$595$	1162.81	+	470.022i	1.95431	+	0.789954i
$596$		−	303.524i		−	0.509268i
$597$	1913.36			3.20496
$598$	−217.015			−0.362902
$599$	−977.373			−1.63167			−0.815837	−	0.578281i	$-0.803724\pi$
$599$	−977.373			−1.63167			−0.815837	+	0.578281i	$0.803724\pi$
$600$	2003.95			3.33992
$601$	837.147			1.39292			0.696461	−	0.717594i	$-0.254757\pi$
$601$	837.147			1.39292			0.696461	+	0.717594i	$0.254757\pi$
$602$	143.820	−	355.804i	0.238904	−	0.591037i
$603$			1667.08i			2.76465i
$604$			87.8867i			0.145508i
$605$		−	952.812i		−	1.57490i
$606$	796.811			1.31487
$607$			851.329i			1.40252i	0.712906	+	0.701260i	$0.247379\pi$
$607$			851.329i			1.40252i	−0.712906	+	0.701260i	$0.752621\pi$
$608$	274.300			0.451152
$609$	−1436.26	−	580.552i	−2.35839	−	0.953288i
$610$	803.390			1.31703
$611$	−128.968			−0.211077
$612$	500.895			0.818456
$613$	140.600			0.229364			0.114682	−	0.993402i	$-0.463415\pi$
$613$	140.600			0.229364			0.114682	+	0.993402i	$0.463415\pi$
$614$		−	224.003i		−	0.364826i
$615$	648.463	−	1920.74i	1.05441	−	3.12315i
$616$	171.256	+	69.2235i	0.278013	+	0.112376i
$617$	−554.757			−0.899120			−0.449560	−	0.893250i	$-0.648419\pi$
$617$	−554.757			−0.899120			−0.449560	+	0.893250i	$0.648419\pi$
$618$		−	1647.43i		−	2.66574i
$619$		−	1048.95i		−	1.69458i	−0.531129	−	0.847291i	$-0.678232\pi$
$619$		−	1048.95i		−	1.69458i	0.531129	−	0.847291i	$-0.321768\pi$
$620$	−242.943			−0.391843
$621$	−1262.09			−2.03235
$622$	−359.100			−0.577332
$623$	83.9077	−	207.584i	0.134683	−	0.333201i
$624$	423.725			0.679046
$625$	1611.79			2.57886
$626$	−868.205			−1.38691
$627$			302.821i			0.482968i
$628$	−289.139			−0.460413
$629$	868.564			1.38087
$630$	−2691.19	−	1087.81i	−4.27174	−	1.72668i
$631$	673.783			1.06780			0.533901	−	0.845547i	$-0.320726\pi$
$631$	673.783			1.06780			0.533901	+	0.845547i	$0.320726\pi$
$632$		−	450.165i		−	0.712287i
$633$			1878.85i			2.96817i
$634$		−	59.7608i		−	0.0942600i
$635$			1312.99i			2.06770i
$636$		−	101.710i		−	0.159921i
$637$	−143.412	−	138.579i	−0.225136	−	0.217550i
$638$	413.889			0.648728
$639$		−	401.827i		−	0.628837i
$640$			1423.52i			2.22424i
$641$			934.734i			1.45824i	0.684384	+	0.729122i	$0.260071\pi$
$641$			934.734i			1.45824i	−0.684384	+	0.729122i	$0.739929\pi$
$642$	−23.0647			−0.0359263
$643$	−456.431			−0.709846			−0.354923	−	0.934895i	$-0.615493\pi$
$643$	−456.431			−0.709846			−0.354923	+	0.934895i	$0.615493\pi$
$644$	−81.4925	+	201.609i	−0.126541	+	0.313057i
$645$			1172.29i			1.81750i
$646$	−589.872			−0.913115
$647$			26.2895i			0.0406329i	0.999794	+	0.0203165i	$0.00646737\pi$
$647$			26.2895i			0.0406329i	−0.999794	+	0.0203165i	$0.993533\pi$
$648$	720.821			1.11238
$649$	439.153			0.676662
$650$	578.032			0.889280
$651$	−669.609	−	270.663i	−1.02858	−	0.415765i
$652$	−151.850			−0.232899
$653$			773.203i			1.18408i	0.805909	+	0.592039i	$0.201677\pi$
$653$			773.203i			1.18408i	−0.805909	+	0.592039i	$0.798323\pi$
$654$		−	1029.29i		−	1.57384i
$655$	773.985			1.18166
$656$	760.364	+	256.708i	1.15909	+	0.391322i
$657$			697.255i			1.06127i
$658$	−192.221	+	475.546i	−0.292129	+	0.722715i
$659$		−	97.5997i		−	0.148103i	−0.997254	−	0.0740514i	$-0.976407\pi$
$659$		−	97.5997i		−	0.148103i	0.997254	−	0.0740514i	$-0.0235929\pi$
$660$	286.550			0.434167
$661$		−	275.176i		−	0.416302i	−0.978097	−	0.208151i	$-0.933255\pi$
$661$		−	275.176i		−	0.416302i	0.978097	−	0.208151i	$-0.0667446\pi$
$662$		−	43.6316i		−	0.0659087i
$663$	−417.232			−0.629310
$664$		−	765.643i		−	1.15308i
$665$	798.480	+	322.754i	1.20072	+	0.485345i
$666$	−2010.19			−3.01830
$667$		−	959.437i		−	1.43844i
$668$	−113.915			−0.170532
$669$		−	293.373i		−	0.438525i
$670$	−1857.73			−2.77273
$671$	−160.769			−0.239596
$672$	289.178	−	715.415i	0.430325	−	1.06461i
$673$			1132.80i			1.68321i	0.540091	+	0.841607i	$0.318390\pi$
$673$			1132.80i			1.68321i	−0.540091	+	0.841607i	$0.681610\pi$
$674$	44.8356			0.0665216
$675$	3361.65			4.98023
$676$	−205.362			−0.303791
$677$			127.763i			0.188719i	0.995538	+	0.0943596i	$0.0300803\pi$
$677$			127.763i			0.188719i	−0.995538	+	0.0943596i	$0.969920\pi$
$678$	1275.76			1.88165
$679$	157.107	−	388.677i	0.231380	−	0.572425i
$680$		−	1099.11i		−	1.61634i
$681$	−926.987			−1.36121
$682$	192.962			0.282935
$683$		−	1034.94i		−	1.51528i	−0.652671	−	0.757642i	$-0.726351\pi$
$683$		−	1034.94i		−	1.51528i	0.652671	−	0.757642i	$-0.273649\pi$
$684$	343.954			0.502856
$685$	−1846.45			−2.69555
$686$	−724.736	+	322.260i	−1.05647	+	0.469766i
$687$	−692.742			−1.00836
$688$	−464.075			−0.674527
$689$			57.7692i			0.0838451i
$690$		−	2636.49i		−	3.82100i
$691$	−50.1729			−0.0726091			−0.0363045	−	0.999341i	$-0.511559\pi$
$691$	−50.1729			−0.0726091			−0.0363045	+	0.999341i	$0.511559\pi$
$692$			254.535i			0.367825i
$693$	538.542	+	217.685i	0.777117	+	0.314119i
$694$			91.8564i			0.132358i
$695$	−1300.11			−1.87065
$696$			1357.58i			1.95054i
$697$	−748.713	−	252.774i	−1.07419	−	0.362660i
$698$			1016.42i			1.45619i
$699$			856.623i			1.22550i
$700$	217.060	−	536.996i	0.310086	−	0.767138i
$701$	844.800			1.20514			0.602568	−	0.798068i	$-0.294144\pi$
$701$	844.800			1.20514			0.602568	+	0.798068i	$0.294144\pi$
$702$	515.114			0.733781
$703$	596.424			0.848399
$704$		−	130.644i		−	0.185573i
$705$		−	1566.81i		−	2.22243i
$706$		−	218.621i		−	0.309661i
$707$	−169.948	+	420.444i	−0.240379	+	0.594688i
$708$		−	731.523i		−	1.03322i
$709$		−	210.259i		−	0.296558i	−0.988946	−	0.148279i	$-0.952627\pi$
$709$		−	210.259i		−	0.296558i	0.988946	−	0.148279i	$-0.0473733\pi$
$710$	447.781			0.630677
$711$		−	1415.62i		−	1.99103i
$712$	−196.211			−0.275578
$713$		−	447.305i		−	0.627357i
$714$	−621.868	+	1538.47i	−0.870963	+	2.15472i
$715$	−162.755			−0.227629
$716$		−	184.508i		−	0.257693i
$717$			388.401i			0.541703i
$718$	740.481			1.03131
$719$	−803.691			−1.11779			−0.558895	−	0.829238i	$-0.688775\pi$
$719$	−803.691			−1.11779			−0.558895	+	0.829238i	$0.688775\pi$
$720$			3510.12i			4.87517i
$721$	869.280	+	351.373i	1.20566	+	0.487341i
$722$	429.725			0.595187
$723$		−	484.410i		−	0.669999i
$724$	233.374			0.322339
$725$			2555.51i			3.52485i
$726$	1260.63			1.73640
$727$	−219.127			−0.301412			−0.150706	−	0.988579i	$-0.548155\pi$
$727$	−219.127			−0.301412			−0.150706	+	0.988579i	$0.548155\pi$
$728$	−65.4936	+	162.028i	−0.0899637	+	0.222566i
$729$	−353.336			−0.484686
$730$	−776.994			−1.06438
$731$	456.964			0.625122
$732$			267.802i			0.365849i
$733$		−	9.51585i		−	0.0129821i	−0.999979	−	0.00649103i	$-0.997934\pi$
$733$		−	9.51585i		−	0.0129821i	0.999979	−	0.00649103i	$-0.00206617\pi$
$734$			787.001i			1.07221i
$735$	1683.58	−	1742.29i	2.29058	−	2.37046i
$736$	477.904			0.649327
$737$	371.756			0.504418
$738$	1732.81	+	585.015i	2.34798	+	0.792703i
$739$	554.933			0.750924			0.375462	−	0.926838i	$-0.377484\pi$
$739$	554.933			0.750924			0.375462	+	0.926838i	$0.377484\pi$
$740$		−	564.378i		−	0.762673i
$741$	−286.505			−0.386646
$742$	213.014	+	86.1026i	0.287081	+	0.116041i
$743$	−189.875			−0.255552			−0.127776	−	0.991803i	$-0.540784\pi$
$743$	−189.875			−0.255552			−0.127776	+	0.991803i	$0.540784\pi$
$744$			632.924i			0.850704i
$745$	−2094.41			−2.81129
$746$	1276.30			1.71086
$747$		−	2407.69i		−	3.22315i
$748$		−	111.699i		−	0.149330i
$749$	4.91936	−	12.1703i	0.00656790	−	0.0162487i
$750$			4164.01i			5.55201i
$751$			812.865i			1.08238i	0.840902	+	0.541188i	$0.182025\pi$
$751$			812.865i			1.08238i	−0.840902	+	0.541188i	$0.817975\pi$
$752$	620.254			0.824806
$753$			831.187i			1.10383i
$754$			391.588i			0.519347i
$755$	606.446			0.803240
$756$	193.433	−	478.545i	0.255864	−	0.632996i
$757$			763.522i			1.00862i	0.863524	+	0.504308i	$0.168252\pi$
$757$			763.522i			1.00862i	−0.863524	+	0.504308i	$0.831748\pi$
$758$	550.999			0.726912
$759$			527.595i			0.695119i
$760$		−	754.735i		−	0.993072i
$761$		−	454.030i		−	0.596623i	−0.954469	−	0.298311i	$-0.903577\pi$
$761$		−	454.030i		−	0.596623i	0.954469	−	0.298311i	$-0.0964234\pi$
$762$	−1737.16			−2.27974
$763$	543.115	+	219.533i	0.711815	+	0.287723i
$764$			160.034i			0.209469i
$765$		−	3456.34i		−	4.51809i
$766$	−111.147			−0.145101
$767$			415.491i			0.541709i
$768$	−1237.26			−1.61101
$769$		−	246.896i		−	0.321062i	−0.987031	−	0.160531i	$-0.948679\pi$
$769$		−	246.896i		−	0.321062i	0.987031	−	0.160531i	$-0.0513206\pi$
$770$	−242.579	+	600.131i	−0.315038	+	0.779391i
$771$	1394.19			1.80829
$772$			327.498i			0.424220i
$773$	939.152			1.21494			0.607472	−	0.794341i	$-0.292184\pi$
$773$	939.152			1.21494			0.607472	+	0.794341i	$0.292184\pi$
$774$	−1057.59			−1.36639
$775$			1191.42i			1.53732i
$776$	−367.383			−0.473432
$777$	628.775	−	1555.56i	0.809234	−	2.00201i
$778$	−1262.85			−1.62319
$779$	−514.125	−	173.575i	−0.659981	−	0.222817i
$780$			271.110i			0.347577i
$781$	−89.6067			−0.114733
$782$	−1027.72			−1.31421
$783$			2277.35i			2.90849i
$784$	689.721	+	666.479i	0.879746	+	0.850101i
$785$			1995.15i			2.54160i
$786$			1024.03i			1.30283i
$787$		−	187.383i		−	0.238098i	−0.992888	−	0.119049i	$-0.962015\pi$
$787$		−	187.383i		−	0.238098i	0.992888	−	0.119049i	$-0.0379846\pi$
$788$	398.852			0.506158
$789$			1437.04i			1.82134i
$790$	1577.51			1.99685
$791$	−272.101	+	673.165i	−0.343996	+	0.851030i
$792$		−	509.038i		−	0.642725i
$793$		−	152.106i		−	0.191811i
$794$	−36.7453			−0.0462787
$795$	−701.831			−0.882806
$796$	−484.632			−0.608834
$797$		−	590.315i		−	0.740671i	−0.928898	−	0.370336i	$-0.879243\pi$
$797$		−	590.315i		−	0.740671i	0.928898	−	0.370336i	$-0.120757\pi$
$798$	−427.023	+	1056.44i	−0.535117	+	1.32385i
$799$	−610.750			−0.764394
$800$	−1272.93			−1.59116
$801$	−617.020			−0.770312
$802$	504.155			0.628622
$803$	155.487			0.193632
$804$		−	619.255i		−	0.770218i
$805$	1391.17	+	562.324i	1.72816	+	0.698539i
$806$			182.565i			0.226507i
$807$			2625.04i			3.25283i
$808$	397.410			0.491844
$809$		−	1427.56i		−	1.76460i	−0.470684	−	0.882302i	$-0.655993\pi$
$809$		−	1427.56i		−	1.76460i	0.470684	−	0.882302i	$-0.344007\pi$
$810$			2525.97i			3.11848i
$811$			171.714i			0.211732i	0.994380	+	0.105866i	$0.0337614\pi$
$811$			171.714i			0.211732i	−0.994380	+	0.105866i	$0.966239\pi$
$812$	363.788	+	147.047i	0.448015	+	0.181092i
$813$		−	2141.12i		−	2.63361i
$814$			448.268i			0.550697i
$815$			1047.82i			1.28566i
$816$	2006.63			2.45910
$817$	313.787			0.384073
$818$		−	239.564i		−	0.292865i
$819$	−205.956	+	509.525i	−0.251472	+	0.622131i
$820$	−164.248	+	486.501i	−0.200303	+	0.593294i
$821$	1093.93			1.33243			0.666216	−	0.745759i	$-0.267913\pi$
$821$	1093.93			1.33243			0.666216	+	0.745759i	$0.267913\pi$
$822$		−	2442.97i		−	2.97198i
$823$			281.637i			0.342208i	0.985253	+	0.171104i	$0.0547334\pi$
$823$			281.637i			0.342208i	−0.985253	+	0.171104i	$0.945267\pi$
$824$		−	821.657i		−	0.997156i
$825$		−	1405.28i		−	1.70337i
$826$	1532.05	+	619.272i	1.85478	+	0.749724i
$827$			46.4903i			0.0562156i	0.999605	+	0.0281078i	$0.00894817\pi$
$827$			46.4903i			0.0562156i	−0.999605	+	0.0281078i	$0.991052\pi$
$828$	599.260			0.723743
$829$			1166.96i			1.40768i	0.710361	+	0.703838i	$0.248532\pi$
$829$			1166.96i			1.40768i	−0.710361	+	0.703838i	$0.751468\pi$
$830$	2683.04			3.23258
$831$	1775.47			2.13655
$832$	123.604			0.148563
$833$	−679.153	−	656.267i	−0.815309	−	0.787836i
$834$		−	1720.12i		−	2.06249i
$835$			786.053i			0.941381i
$836$		−	76.7010i		−	0.0917476i
$837$			1061.74i			1.26850i
$838$			160.787i			0.191870i
$839$	1359.44			1.62031			0.810153	−	0.586218i	$-0.199384\pi$
$839$	1359.44			1.62031			0.810153	+	0.586218i	$0.199384\pi$
$840$	−1968.46	−	795.672i	−2.34340	−	0.947229i
$841$	−890.232			−1.05854
$842$		−	70.9700i		−	0.0842875i
$843$		−	2463.11i		−	2.92184i
$844$		−	475.892i		−	0.563853i
$845$			1417.07i			1.67700i
$846$	1413.51			1.67081
$847$	−268.873	+	665.180i	−0.317442	+	0.785337i
$848$		−	277.834i		−	0.327634i
$849$		−	1434.83i		−	1.69002i
$850$	2737.38			3.22044
$851$	1039.13			1.22107
$852$			149.263i			0.175191i
$853$		−	501.964i		−	0.588469i	−0.955733	−	0.294235i	$-0.904935\pi$
$853$		−	501.964i		−	0.588469i	0.955733	−	0.294235i	$-0.0950647\pi$
$854$	−560.865	−	226.708i	−0.656751	−	0.265466i
$855$		−	2373.39i		−	2.77590i
$856$	−11.5035			−0.0134387
$857$			739.992i			0.863468i	0.902001	+	0.431734i	$0.142098\pi$
$857$			739.992i			0.863468i	−0.902001	+	0.431734i	$0.857902\pi$
$858$		−	215.334i		−	0.250973i
$859$			745.080i			0.867380i	0.901062	+	0.433690i	$0.142789\pi$
$859$			745.080i			0.867380i	−0.901062	+	0.433690i	$0.857211\pi$
$860$		−	296.927i		−	0.345264i
$861$	−994.719	+	1157.92i	−1.15531	+	1.34486i
$862$	−378.743			−0.439377
$863$	630.101			0.730128			0.365064	−	0.930982i	$-0.381047\pi$
$863$	630.101			0.730128			0.365064	+	0.930982i	$0.381047\pi$
$864$	−1134.37			−1.31293
$865$	1756.37			2.03049
$866$		−	874.512i		−	1.00983i
$867$	−438.727			−0.506028
$868$	169.604	+	68.5558i	0.195396	+	0.0789813i
$869$	−315.681			−0.363269
$870$	−4757.34			−5.46821
$871$			351.725i			0.403818i
$872$		−	513.360i		−	0.588716i
$873$	−1155.30			−1.32336
$874$	−705.710			−0.807449
$875$	−2197.17	−	888.122i	−2.51106	−	1.01500i
$876$		−	259.003i		−	0.295665i
$877$	−152.103			−0.173435			−0.0867176	−	0.996233i	$-0.527638\pi$
$877$	−152.103			−0.173435			−0.0867176	+	0.996233i	$0.527638\pi$
$878$	440.643			0.501871
$879$	2039.55			2.32031
$880$	782.750			0.889488
$881$		−	775.851i		−	0.880648i	−0.897839	−	0.440324i	$-0.854864\pi$
$881$		−	775.851i		−	0.880648i	0.897839	−	0.440324i	$-0.145136\pi$
$882$	1571.82	+	1518.85i	1.78211	+	1.72205i
$883$		−	1211.10i		−	1.37157i	−0.727804	−	0.685786i	$-0.759459\pi$
$883$		−	1211.10i		−	1.37157i	0.727804	−	0.685786i	$-0.240541\pi$
$884$	105.680			0.119548
$885$	−5047.74			−5.70366
$886$	569.845			0.643165
$887$	−143.350			−0.161612			−0.0808061	−	0.996730i	$-0.525749\pi$
$887$	−143.350			−0.161612			−0.0808061	+	0.996730i	$0.525749\pi$
$888$	−1470.34			−1.65579
$889$	370.511	−	916.627i	0.416772	−	1.03108i
$890$		−	687.583i		−	0.772565i
$891$		−	505.479i		−	0.567317i
$892$			74.3080i			0.0833050i
$893$	−419.389			−0.469641
$894$		−	2771.03i		−	3.09958i
$895$	−1273.16			−1.42253
$896$	401.700	−	993.789i	0.448326	−	1.10914i
$897$	−499.168			−0.556486
$898$	−1059.60			−1.17995
$899$	−807.129			−0.897808
$900$	−1596.16			−1.77351
$901$			273.577i			0.303637i
$902$	130.457	−	386.412i	0.144631	−	0.428395i
$903$	330.807	−	818.403i	0.366343	−	0.906315i
$904$	636.285			0.703856
$905$		−	1610.35i		−	1.77939i
$906$			802.364i			0.885611i
$907$	−732.660			−0.807784			−0.403892	−	0.914807i	$-0.632343\pi$
$907$	−732.660			−0.807784			−0.403892	+	0.914807i	$0.632343\pi$
$908$	234.795			0.258585
$909$	1249.72			1.37483
$910$	−567.795	−	229.509i	−0.623950	−	0.252208i
$911$	−177.780			−0.195149			−0.0975744	−	0.995228i	$-0.531108\pi$
$911$	−177.780			−0.195149			−0.0975744	+	0.995228i	$0.531108\pi$
$912$	1377.91			1.51086
$913$	−536.911			−0.588073
$914$			1303.84i			1.42652i
$915$	1847.92			2.01958
$916$	175.463			0.191554
$917$	−540.337	−	218.410i	−0.589244	−	0.238179i
$918$	2439.42			2.65732
$919$			471.184i			0.512714i	0.966582	+	0.256357i	$0.0825223\pi$
$919$			471.184i			0.512714i	−0.966582	+	0.256357i	$0.917478\pi$
$920$		−	1314.95i		−	1.42929i
$921$		−	515.240i		−	0.559436i
$922$			554.313i			0.601207i
$923$		−	84.7785i		−	0.0918510i
$924$	−200.047	−	80.8613i	−0.216501	−	0.0875123i
$925$	−2767.78			−2.99220
$926$			1517.56i			1.63884i
$927$		−	2583.84i		−	2.78731i
$928$		−	862.343i		−	0.929248i
$929$	−814.377			−0.876617			−0.438309	−	0.898825i	$-0.644422\pi$
$929$	−814.377			−0.876617			−0.438309	+	0.898825i	$0.644422\pi$
$930$	−2217.95			−2.38490
$931$	−466.360	−	450.645i	−0.500923	−	0.484044i
$932$		−	216.973i		−	0.232803i
$933$	−825.984			−0.885299
$934$		−	471.180i		−	0.504475i
$935$	−770.756			−0.824338
$936$	481.611			0.514541
$937$	149.791			0.159862			0.0799311	−	0.996800i	$-0.474530\pi$
$937$	149.791			0.159862			0.0799311	+	0.996800i	$0.474530\pi$
$938$	1296.93	+	524.232i	1.38265	+	0.558882i
$939$	−1997.00			−2.12673
$940$			396.855i			0.422186i
$941$		−	557.961i		−	0.592945i	−0.955041	−	0.296473i	$-0.904190\pi$
$941$		−	557.961i		−	0.592945i	0.955041	−	0.296473i	$-0.0958104\pi$
$942$	−2639.71			−2.80224
$943$	−895.743	−	302.413i	−0.949887	−	0.320693i
$944$		−	1998.25i		−	2.11679i
$945$	−3302.11	−	1334.75i	−3.49430	−	1.41244i
$946$			235.840i			0.249302i
$947$	−143.353			−0.151376			−0.0756882	−	0.997132i	$-0.524115\pi$
$947$	−143.353			−0.151376			−0.0756882	+	0.997132i	$0.524115\pi$
$948$			525.847i			0.554691i
$949$			147.109i			0.155014i
$950$	1879.70			1.97863
$951$		−	137.459i		−	0.144541i
$952$	−310.157	+	767.314i	−0.325795	+	0.806002i
$953$	−363.607			−0.381539			−0.190770	−	0.981635i	$-0.561098\pi$
$953$	−363.607			−0.381539			−0.190770	+	0.981635i	$0.561098\pi$
$954$		−	633.160i		−	0.663690i
$955$	1104.29			1.15632
$956$		−	98.3775i		−	0.102905i
$957$	952.006			0.994782
$958$	−307.204			−0.320672
$959$	1289.05	+	521.049i	1.34416	+	0.543326i
$960$			1501.65i			1.56422i
$961$	584.703			0.608432
$962$	−424.114			−0.440867
$963$	−36.1748			−0.0375647
$964$			122.695i			0.127277i
$965$	2259.84			2.34180
$966$	−743.988	+	1840.59i	−0.770174	+	1.90538i
$967$		−	190.554i		−	0.197057i	−0.995134	−	0.0985283i	$-0.968586\pi$
$967$		−	190.554i		−	0.197057i	0.995134	−	0.0985283i	$-0.0314135\pi$
$968$	628.739			0.649523
$969$	−1356.79			−1.40020
$970$		−	1287.42i		−	1.32724i
$971$	406.258			0.418392			0.209196	−	0.977874i	$-0.432915\pi$
$971$	406.258			0.418392			0.209196	+	0.977874i	$0.432915\pi$
$972$	−178.371			−0.183509
$973$	907.634	+	366.876i	0.932820	+	0.377056i
$974$	−265.348			−0.272431
$975$	1329.56			1.36365
$976$			731.536i			0.749524i
$977$			503.759i			0.515618i	0.966196	+	0.257809i	$0.0830005\pi$
$977$			503.759i			0.515618i	−0.966196	+	0.257809i	$0.917000\pi$
$978$	−1386.32			−1.41751
$979$			137.594i			0.140546i
$980$	−426.431	+	441.302i	−0.435134	+	0.450308i
$981$		−	1614.35i		−	1.64561i
$982$	756.434			0.770299
$983$		−	471.010i		−	0.479156i	−0.970877	−	0.239578i	$-0.922991\pi$
$983$		−	471.010i		−	0.479156i	0.970877	−	0.239578i	$-0.0770090\pi$
$984$	1267.45	+	427.906i	1.28806	+	0.434864i
$985$		−	2752.21i		−	2.79412i
$986$			1854.44i			1.88077i
$987$	−442.137	+	1093.83i	−0.447961	+	1.10823i
$988$	72.5682			0.0734496
$989$	546.701			0.552782
$990$	1783.82			1.80184
$991$			1363.63i			1.37601i	0.725705	+	0.688006i	$0.241514\pi$
$991$			1363.63i			1.37601i	−0.725705	+	0.688006i	$0.758486\pi$
$992$		−	402.038i		−	0.405281i
$993$		−	100.359i		−	0.101067i
$994$	−312.606	−	126.359i	−0.314493	−	0.127122i
$995$			3344.12i			3.36092i
$996$			894.363i			0.897955i
$997$	308.419			0.309347			0.154674	−	0.987966i	$-0.450567\pi$
$997$	308.419			0.309347			0.154674	+	0.987966i	$0.450567\pi$
$998$			1017.52i			1.01956i
$999$	−2466.51			−2.46898

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.d.d.286.9	✓	32
7.6	odd	2	inner	287.3.d.d.286.12	yes	32
41.40	even	2	inner	287.3.d.d.286.11	yes	32
287.286	odd	2	inner	287.3.d.d.286.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.d.d.286.9	✓	32	1.1	even	1	trivial
287.3.d.d.286.10	yes	32	287.286	odd	2	inner
287.3.d.d.286.11	yes	32	41.40	even	2	inner
287.3.d.d.286.12	yes	32	7.6	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.31240 q^{2} -5.31887 q^{3} +1.34721 q^{4} -9.29617i q^{5} +12.2994 q^{6} +(-2.62328 + 6.48987i) q^{7} +6.13432 q^{8} +19.2904 q^{9} +O(q^{10})\)	\(q-2.31240 q^{2} -5.31887 q^{3} +1.34721 q^{4} -9.29617i q^{5} +12.2994 q^{6} +(-2.62328 + 6.48987i) q^{7} +6.13432 q^{8} +19.2904 q^{9} +21.4965i q^{10} -4.30172i q^{11} -7.16563 q^{12} +4.06994 q^{13} +(6.06607 - 15.0072i) q^{14} +49.4451i q^{15} -19.5739 q^{16} +19.2739 q^{17} -44.6072 q^{18} +13.2350 q^{19} -12.5239i q^{20} +(13.9529 - 34.5188i) q^{21} +9.94732i q^{22} +23.0589 q^{23} -32.6277 q^{24} -61.4187 q^{25} -9.41134 q^{26} -54.7334 q^{27} +(-3.53410 + 8.74321i) q^{28} -41.6081i q^{29} -114.337i q^{30} -19.3984i q^{31} +20.7254 q^{32} +22.8803i q^{33} -44.5691 q^{34} +(60.3309 + 24.3864i) q^{35} +25.9882 q^{36} +45.0642 q^{37} -30.6047 q^{38} -21.6475 q^{39} -57.0257i q^{40} +(-38.8459 - 13.1148i) q^{41} +(-32.2647 + 79.8214i) q^{42} +23.7089 q^{43} -5.79532i q^{44} -179.327i q^{45} -53.3215 q^{46} -31.6879 q^{47} +104.111 q^{48} +(-35.2368 - 34.0495i) q^{49} +142.025 q^{50} -102.516 q^{51} +5.48306 q^{52} +14.1941i q^{53} +126.566 q^{54} -39.9895 q^{55} +(-16.0920 + 39.8110i) q^{56} -70.3953 q^{57} +96.2146i q^{58} +102.088i q^{59} +66.6129i q^{60} -37.3731i q^{61} +44.8569i q^{62} +(-50.6041 + 125.192i) q^{63} +30.3700 q^{64} -37.8348i q^{65} -52.9085i q^{66} +86.4202i q^{67} +25.9660 q^{68} -122.647 q^{69} +(-139.509 - 56.3912i) q^{70} -20.8304i q^{71} +118.334 q^{72} +36.1452i q^{73} -104.207 q^{74} +326.678 q^{75} +17.8303 q^{76} +(27.9176 + 11.2846i) q^{77} +50.0577 q^{78} -73.3847i q^{79} +181.962i q^{80} +117.506 q^{81} +(89.8273 + 30.3267i) q^{82} -124.813i q^{83} +(18.7974 - 46.5040i) q^{84} -179.174i q^{85} -54.8245 q^{86} +221.308i q^{87} -26.3882i q^{88} -31.9858 q^{89} +414.676i q^{90} +(-10.6766 + 26.4134i) q^{91} +31.0652 q^{92} +103.177i q^{93} +73.2752 q^{94} -123.035i q^{95} -110.236 q^{96} -59.8897 q^{97} +(81.4818 + 78.7361i) q^{98} -82.9820i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 68 q^{4} - 88 q^{8} + 44 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 + 68 * q^4 - 88 * q^8 + 44 * q^9	\( 32 q + 4 q^{2} + 68 q^{4} - 88 q^{8} + 44 q^{9} - 92 q^{16} - 48 q^{18} - 72 q^{21} + 140 q^{23} - 500 q^{25} + 92 q^{32} - 284 q^{36} + 312 q^{37} + 140 q^{39} + 8 q^{42} - 120 q^{43} - 344 q^{46} - 552 q^{49} + 416 q^{50} - 364 q^{51} - 316 q^{57} - 320 q^{64} + 972 q^{72} + 680 q^{74} + 428 q^{77} + 1144 q^{78} - 240 q^{81} + 640 q^{84} + 260 q^{86} - 160 q^{91} + 676 q^{92} + 532 q^{98}+O(q^{100}) \) 32 * q + 4 * q^2 + 68 * q^4 - 88 * q^8 + 44 * q^9 - 92 * q^16 - 48 * q^18 - 72 * q^21 + 140 * q^23 - 500 * q^25 + 92 * q^32 - 284 * q^36 + 312 * q^37 + 140 * q^39 + 8 * q^42 - 120 * q^43 - 344 * q^46 - 552 * q^49 + 416 * q^50 - 364 * q^51 - 316 * q^57 - 320 * q^64 + 972 * q^72 + 680 * q^74 + 428 * q^77 + 1144 * q^78 - 240 * q^81 + 640 * q^84 + 260 * q^86 - 160 * q^91 + 676 * q^92 + 532 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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