LMFDB - Embedded newform 287.3.d.d.286.11

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			286.11
Character	$\chi$	$=$	287.286
Dual form			287.3.d.d.286.12

$q$-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	$-0.153144\pi$
$3$	5.31887			1.77296			0.886479	+	0.462769i	$0.153144\pi$
$4$	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	$0.0626436\pi$
$11$			4.30172i			0.391066i	−0.980697	+	0.195533i	$0.937356\pi$
$12$	7.16563			0.597136
$13$	−4.06994			−0.313072			−0.156536	−	0.987672i	$-0.550033\pi$
$13$	−4.06994			−0.313072			−0.156536	+	0.987672i	$0.550033\pi$
$14$	−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	$-0.691850\pi$
$17$	−19.2739			−1.13376			−0.566881	+	0.823800i	$0.691850\pi$
$18$	−44.6072			−2.47818
$19$	−13.2350			−0.696579			−0.348289	−	0.937387i	$-0.613237\pi$
$19$	−13.2350			−0.696579			−0.348289	+	0.937387i	$0.613237\pi$
$20$		−	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	$0.254659\pi$
$29$			41.6081i			1.43476i	−0.696682	+	0.717381i	$0.745341\pi$
$30$			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	$-0.390552\pi$
$47$	31.6879			0.674210			0.337105	+	0.941467i	$0.390552\pi$
$48$	−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	$-0.957248\pi$
$53$		−	14.1941i		−	0.267814i	0.990994	−	0.133907i	$-0.0427523\pi$
$54$	−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	$-0.776888\pi$
$67$		−	86.4202i		−	1.28985i	0.764244	−	0.644927i	$-0.223112\pi$
$68$	−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	$0.0468630\pi$
$71$			20.8304i			0.293386i	−0.989182	+	0.146693i	$0.953137\pi$
$72$	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	$0.153752\pi$
$79$			73.3847i			0.928920i	−0.885594	+	0.464460i	$0.846248\pi$
$80$			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	$-0.442489\pi$
$89$	31.9858			0.359391			0.179696	+	0.983722i	$0.442489\pi$
$90$			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	$-0.400103\pi$
$97$	59.8897			0.617420			0.308710	+	0.951156i	$0.400103\pi$
$98$	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	$-0.603924\pi$
$101$	−64.7847			−0.641433			−0.320716	+	0.947175i	$0.603924\pi$
$102$	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	$0.125413\pi$
$109$			83.6865i			0.767766i	−0.923382	+	0.383883i	$0.874587\pi$
$110$	−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	$0.258119\pi$
$137$			198.625i			1.44982i	−0.688843	+	0.724910i	$0.741881\pi$
$138$	−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	$0.272866\pi$
$149$			225.298i			1.51207i	−0.654532	+	0.756034i	$0.727134\pi$
$150$	755.412			5.03608
$151$		−	65.2361i		−	0.432027i	−0.976390	−	0.216014i	$-0.930694\pi$
$151$		−	65.2361i		−	0.432027i	0.976390	−	0.216014i	$-0.0693056\pi$
$152$	−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	$-0.260454\pi$
$157$	214.621			1.36701			0.683507	+	0.729944i	$0.260454\pi$
$158$		−	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	$-0.418529\pi$
$167$	84.5567			0.506328			0.253164	+	0.967423i	$0.418529\pi$
$168$	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	$0.124957\pi$
$179$			136.956i			0.765116i	−0.923931	+	0.382558i	$0.875043\pi$
$180$		−	241.591i		−	1.34217i
$181$	−173.228			−0.957059			−0.478529	−	0.878072i	$-0.658830\pi$
$181$	−173.228			−0.957059			−0.478529	+	0.878072i	$0.658830\pi$
$182$	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	$-0.899347\pi$
$191$		−	118.789i		−	0.621934i	0.950421	−	0.310967i	$-0.100653\pi$
$192$	161.534			0.841325
$193$		−	243.094i		−	1.25955i	−0.776776	−	0.629777i	$-0.783146\pi$
$193$		−	243.094i		−	1.25955i	0.776776	−	0.629777i	$-0.216854\pi$
$194$	−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	$-0.140732\pi$
$199$	359.731			1.80769			0.903846	+	0.427858i	$0.140732\pi$
$200$	−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	$0.315733\pi$
$211$			353.243i			1.67414i	−0.547098	+	0.837069i	$0.684267\pi$
$212$		−	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	$-0.625413\pi$
$227$	−174.283			−0.767765			−0.383883	+	0.923382i	$0.625413\pi$
$228$	−94.8371			−0.415952
$229$	−130.242			−0.568744			−0.284372	−	0.958714i	$-0.591785\pi$
$229$	−130.242			−0.568744			−0.284372	+	0.958714i	$0.591785\pi$
$230$			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	$0.112327\pi$
$233$			161.053i			0.691217i	−0.938379	+	0.345608i	$0.887673\pi$
$234$	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	$0.0488188\pi$
$239$			73.0232i			0.305537i	−0.988262	+	0.152768i	$0.951181\pi$
$240$			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	$-0.329658\pi$
$257$	262.122			1.01993			0.509965	+	0.860195i	$0.329658\pi$
$258$	−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	$0.171705\pi$
$263$			270.177i			1.02729i	−0.858003	+	0.513644i	$0.828295\pi$
$264$			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	$-0.691736\pi$
$281$		−	463.089i		−	1.64800i	0.566587	−	0.824002i	$-0.308264\pi$
$282$	−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
$287$	16.7901	−	286.508i	0.0585019	−	0.998287i
$288$	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	$-0.272938\pi$
$293$	383.455			1.30872			0.654360	+	0.756183i	$0.272938\pi$
$294$	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	$-0.580321\pi$
$311$	−155.293			−0.499335			−0.249667	+	0.968332i	$0.580321\pi$
$312$	−132.793			−0.425618
$313$	−375.456			−1.19954			−0.599770	−	0.800173i	$-0.704741\pi$
$313$	−375.456			−1.19954			−0.599770	+	0.800173i	$0.704741\pi$
$314$	−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	$-0.987021\pi$
$317$		−	25.8436i		−	0.0815256i	0.999169	−	0.0407628i	$-0.0129788\pi$
$318$			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	$-0.990926\pi$
$331$		−	18.8685i		−	0.0570045i	0.999594	−	0.0285023i	$-0.00907378\pi$
$332$		−	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	$0.0182295\pi$
$347$			39.7233i			0.114476i	−0.998361	+	0.0572382i	$0.981771\pi$
$348$			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	$-0.519987\pi$
$383$	−48.0656			−0.125498			−0.0627488	+	0.998029i	$0.519987\pi$
$384$	−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	$-0.506371\pi$
$397$	−15.8905			−0.0400265			−0.0200132	+	0.999800i	$0.506371\pi$
$398$	−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	$-0.988395\pi$
$421$		−	30.6910i		−	0.0729003i	0.999335	−	0.0364502i	$-0.0116050\pi$
$422$		−	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	$-0.430362\pi$
$439$	190.556			0.434069			0.217035	+	0.976164i	$0.430362\pi$
$440$	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	$0.211611\pi$
$457$			563.845i			1.23380i	−0.787043	+	0.616898i	$0.788389\pi$
$458$	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	$0.250725\pi$
$463$			656.271i			1.41743i	−0.705494	+	0.708716i	$0.749275\pi$
$464$		−	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	$-0.544284\pi$
$479$	−132.850			−0.277349			−0.138675	+	0.990338i	$0.544284\pi$
$480$		−	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	$0.145344\pi$
$499$			440.027i			0.881818i	−0.897552	+	0.440909i	$0.854656\pi$
$500$			456.103i			0.912206i
$501$	449.746			0.897697
$502$			361.362i			0.719845i
$503$	−62.1914			−0.123641			−0.0618205	−	0.998087i	$-0.519691\pi$
$503$	−62.1914			−0.123641			−0.0618205	+	0.998087i	$0.519691\pi$
$504$	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	$-0.590610\pi$
$509$	−285.887			−0.561664			−0.280832	+	0.959757i	$0.590610\pi$
$510$		−	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	$-0.710122\pi$
$521$	−638.966			−1.22642			−0.613211	+	0.789919i	$0.710122\pi$
$522$		−	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	$-0.863954\pi$
$547$		−	453.471i		−	0.829015i	0.910046	−	0.414508i	$-0.136046\pi$
$548$			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	$0.320492\pi$
$557$			941.504i			1.69031i	−0.534520	+	0.845156i	$0.679508\pi$
$558$			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	$-0.523995\pi$
$563$	−84.8009			−0.150623			−0.0753116	+	0.997160i	$0.523995\pi$
$564$	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	$-0.989286\pi$
$571$		−	38.4302i		−	0.0673033i	0.999434	−	0.0336517i	$-0.0107137\pi$
$572$		−	23.5866i		−	0.0412353i
$573$		−	631.826i		−	1.10266i
$574$	−38.8254	+	662.523i	−0.0676400	+	1.15422i
$575$	−1416.25			−2.46304
$576$	585.851			1.01710
$577$	−999.960			−1.73303			−0.866516	−	0.499149i	$-0.833646\pi$
$577$	−999.960			−1.73303			−0.866516	+	0.499149i	$0.833646\pi$
$578$	−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	$-0.354552\pi$
$587$	517.973			0.882407			0.441204	+	0.897407i	$0.354552\pi$
$588$	−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	$-0.628153\pi$
$593$	−464.694			−0.783633			−0.391816	+	0.920043i	$0.628153\pi$
$594$		−	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	$-0.745243\pi$
$601$	−837.147			−1.39292			−0.696461	+	0.717594i	$0.745243\pi$
$602$	−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	$-0.739929\pi$
$641$		−	934.734i		−	1.45824i	0.684384	−	0.729122i	$-0.260071\pi$
$642$	23.0647			0.0359263
$643$	456.431			0.709846			0.354923	−	0.934895i	$-0.384507\pi$
$643$	456.431			0.709846			0.354923	+	0.934895i	$0.384507\pi$
$644$	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	$-0.798323\pi$
$653$		−	773.203i		−	1.18408i	0.805909	−	0.592039i	$-0.201677\pi$
$654$		−	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	$0.0235929\pi$
$659$			97.5997i			0.148103i	−0.997254	+	0.0740514i	$0.976407\pi$
$660$	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	$-0.681610\pi$
$673$		−	1132.80i		−	1.68321i	0.540091	−	0.841607i	$-0.318390\pi$
$674$	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	$0.273649\pi$
$683$			1034.94i			1.51528i	−0.652671	+	0.757642i	$0.726351\pi$
$684$	−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	$-0.488441\pi$
$691$	50.1729			0.0726091			0.0363045	+	0.999341i	$0.488441\pi$
$692$			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	$0.0473733\pi$
$709$			210.259i			0.296558i	−0.988946	+	0.148279i	$0.952627\pi$
$710$	−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	$-0.311225\pi$
$719$	803.691			1.11779			0.558895	+	0.829238i	$0.311225\pi$
$720$			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	$-0.451845\pi$
$727$	219.127			0.301412			0.150706	+	0.988579i	$0.451845\pi$
$728$	−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	$-0.817975\pi$
$751$		−	812.865i		−	1.08238i	0.840902	−	0.541188i	$-0.182025\pi$
$752$	−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	$-0.831748\pi$
$757$		−	763.522i		−	1.00862i	0.863524	−	0.504308i	$-0.168252\pi$
$758$	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	$-0.707816\pi$
$773$	−939.152			−1.21494			−0.607472	+	0.794341i	$0.707816\pi$
$774$	−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	$0.344007\pi$
$809$			1427.56i			1.76460i	−0.470684	+	0.882302i	$0.655993\pi$
$810$			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	$-0.945267\pi$
$823$		−	281.637i		−	0.342208i	0.985253	−	0.171104i	$-0.0547334\pi$
$824$		−	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	$-0.991052\pi$
$827$		−	46.4903i		−	0.0562156i	0.999605	−	0.0281078i	$-0.00894817\pi$
$828$	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	$-0.800616\pi$
$839$	−1359.44			−1.62031			−0.810153	+	0.586218i	$0.800616\pi$
$840$	−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
$861$	89.3042	−	1523.90i	0.103721	−	1.76992i
$862$	−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	$0.240541\pi$
$883$			1211.10i			1.37157i	−0.727804	+	0.685786i	$0.759459\pi$
$884$	105.680			0.119548
$885$	5047.74			5.70366
$886$	569.845			0.643165
$887$	143.350			0.161612			0.0808061	−	0.996730i	$-0.474251\pi$
$887$	143.350			0.161612			0.0808061	+	0.996730i	$0.474251\pi$
$888$	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	$-0.917478\pi$
$919$		−	471.184i		−	0.512714i	0.966582	−	0.256357i	$-0.0825223\pi$
$920$		−	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	$-0.355578\pi$
$929$	814.377			0.876617			0.438309	+	0.898825i	$0.355578\pi$
$930$	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	$-0.525470\pi$
$937$	−149.791			−0.159862			−0.0799311	+	0.996800i	$0.525470\pi$
$938$	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	$0.0314135\pi$
$967$			190.554i			0.197057i	−0.995134	+	0.0985283i	$0.968586\pi$
$968$	628.739			0.649523
$969$	1356.79			1.40020
$970$			1287.42i			1.32724i
$971$	−406.258			−0.418392			−0.209196	−	0.977874i	$-0.567085\pi$
$971$	−406.258			−0.418392			−0.209196	+	0.977874i	$0.567085\pi$
$972$	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	$-0.917000\pi$
$977$		−	503.759i		−	0.515618i	0.966196	−	0.257809i	$-0.0830005\pi$
$978$	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	$-0.758486\pi$
$991$		−	1363.63i		−	1.37601i	0.725705	−	0.688006i	$-0.241514\pi$
$992$		−	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	$-0.549433\pi$
$997$	−308.419			−0.309347			−0.154674	+	0.987966i	$0.549433\pi$
$998$		−	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.286.11	yes	32
7.6	odd	2	inner	287.3.d.d.286.10	yes	32
41.40	even	2	inner	287.3.d.d.286.9	✓	32
287.286	odd	2	inner	287.3.d.d.286.12	yes	32

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

Related objects

Downloads

Learn more