LMFDB - Embedded newform 354.3.b.a.119.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,3,Mod(119,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.119");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	354.b (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:	$9.64580135835$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.9
Character	$\chi$	$=$	354.119
Dual form			354.3.b.a.119.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-0.495685 + 2.95877i) q^{3} -2.00000 q^{4} -8.96910i q^{5} +(4.18433 + 0.701004i) q^{6} -9.25455 q^{7} +2.82843i q^{8} +(-8.50859 - 2.93323i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-0.495685 + 2.95877i) q^{3} -2.00000 q^{4} -8.96910i q^{5} +(4.18433 + 0.701004i) q^{6} -9.25455 q^{7} +2.82843i q^{8} +(-8.50859 - 2.93323i) q^{9} -12.6842 q^{10} +17.1827i q^{11} +(0.991370 - 5.91753i) q^{12} +21.0587 q^{13} +13.0879i q^{14} +(26.5375 + 4.44585i) q^{15} +4.00000 q^{16} +15.0740i q^{17} +(-4.14822 + 12.0330i) q^{18} -11.0933 q^{19} +17.9382i q^{20} +(4.58734 - 27.3820i) q^{21} +24.3001 q^{22} +38.9760i q^{23} +(-8.36865 - 1.40201i) q^{24} -55.4448 q^{25} -29.7815i q^{26} +(12.8963 - 23.7210i) q^{27} +18.5091 q^{28} +8.28196i q^{29} +(6.28738 - 37.5297i) q^{30} +31.3061 q^{31} -5.65685i q^{32} +(-50.8397 - 8.51723i) q^{33} +21.3178 q^{34} +83.0050i q^{35} +(17.0172 + 5.86646i) q^{36} -30.2403 q^{37} +15.6882i q^{38} +(-10.4385 + 62.3078i) q^{39} +25.3684 q^{40} +27.3913i q^{41} +(-38.7241 - 6.48748i) q^{42} -61.4214 q^{43} -34.3655i q^{44} +(-26.3085 + 76.3144i) q^{45} +55.1203 q^{46} +11.7552i q^{47} +(-1.98274 + 11.8351i) q^{48} +36.6467 q^{49} +78.4108i q^{50} +(-44.6004 - 7.47195i) q^{51} -42.1175 q^{52} -14.5448i q^{53} +(-33.5465 - 18.2382i) q^{54} +154.114 q^{55} -26.1758i q^{56} +(5.49877 - 32.8224i) q^{57} +11.7125 q^{58} +7.68115i q^{59} +(-53.0749 - 8.89170i) q^{60} -5.82583 q^{61} -44.2735i q^{62} +(78.7432 + 27.1457i) q^{63} -8.00000 q^{64} -188.878i q^{65} +(-12.0452 + 71.8982i) q^{66} -73.2111 q^{67} -30.1480i q^{68} +(-115.321 - 19.3198i) q^{69} +117.387 q^{70} +46.1106i q^{71} +(8.29643 - 24.0659i) q^{72} +85.4930 q^{73} +42.7663i q^{74} +(27.4831 - 164.048i) q^{75} +22.1865 q^{76} -159.019i q^{77} +(88.1166 + 14.7623i) q^{78} -13.7855 q^{79} -35.8764i q^{80} +(63.7923 + 49.9154i) q^{81} +38.7371 q^{82} +32.5823i q^{83} +(-9.17468 + 54.7641i) q^{84} +135.200 q^{85} +86.8630i q^{86} +(-24.5044 - 4.10524i) q^{87} -48.6001 q^{88} -32.8739i q^{89} +(107.925 + 37.2058i) q^{90} -194.889 q^{91} -77.9519i q^{92} +(-15.5180 + 92.6275i) q^{93} +16.6243 q^{94} +99.4966i q^{95} +(16.7373 + 2.80402i) q^{96} -88.8138 q^{97} -51.8262i q^{98} +(50.4010 - 146.201i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9}+O(q^{10}) $ 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9	$ 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9} - 16 q^{10} + 34 q^{15} + 160 q^{16} + 16 q^{18} + 24 q^{19} - 18 q^{21} - 16 q^{22} - 16 q^{24} - 216 q^{25} - 30 q^{27} - 16 q^{28} - 64 q^{30} + 96 q^{31} + 76 q^{33} + 80 q^{34} + 48 q^{36} - 200 q^{37} - 28 q^{39} + 32 q^{40} + 48 q^{42} - 104 q^{43} + 58 q^{45} + 32 q^{46} + 288 q^{49} - 176 q^{51} - 40 q^{54} + 360 q^{55} + 214 q^{57} - 128 q^{58} - 68 q^{60} - 32 q^{61} - 132 q^{63} - 320 q^{64} - 112 q^{66} - 344 q^{67} + 88 q^{69} + 192 q^{70} - 32 q^{72} + 40 q^{73} + 28 q^{75} - 48 q^{76} + 96 q^{78} + 32 q^{79} + 336 q^{81} - 80 q^{82} + 36 q^{84} + 168 q^{85} - 162 q^{87} + 32 q^{88} + 112 q^{90} + 88 q^{91} - 316 q^{93} - 400 q^{94} + 32 q^{96} - 184 q^{97} - 148 q^{99}+O(q^{100}) $ 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9 - 16 * q^10 + 34 * q^15 + 160 * q^16 + 16 * q^18 + 24 * q^19 - 18 * q^21 - 16 * q^22 - 16 * q^24 - 216 * q^25 - 30 * q^27 - 16 * q^28 - 64 * q^30 + 96 * q^31 + 76 * q^33 + 80 * q^34 + 48 * q^36 - 200 * q^37 - 28 * q^39 + 32 * q^40 + 48 * q^42 - 104 * q^43 + 58 * q^45 + 32 * q^46 + 288 * q^49 - 176 * q^51 - 40 * q^54 + 360 * q^55 + 214 * q^57 - 128 * q^58 - 68 * q^60 - 32 * q^61 - 132 * q^63 - 320 * q^64 - 112 * q^66 - 344 * q^67 + 88 * q^69 + 192 * q^70 - 32 * q^72 + 40 * q^73 + 28 * q^75 - 48 * q^76 + 96 * q^78 + 32 * q^79 + 336 * q^81 - 80 * q^82 + 36 * q^84 + 168 * q^85 - 162 * q^87 + 32 * q^88 + 112 * q^90 + 88 * q^91 - 316 * q^93 - 400 * q^94 + 32 * q^96 - 184 * q^97 - 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	−0.495685	+	2.95877i	−0.165228	+	0.986255i
$3$	−0.495685	+	2.95877i	−0.165228	+	0.986255i
$4$	−2.00000			−0.500000
$5$		−	8.96910i		−	1.79382i	−0.442213	−	0.896910i	$-0.645806\pi$
$5$		−	8.96910i		−	1.79382i	0.442213	−	0.896910i	$-0.354194\pi$
$6$	4.18433	+	0.701004i	0.697388	+	0.116834i
$7$	−9.25455			−1.32208			−0.661039	−	0.750351i	$-0.729884\pi$
$7$	−9.25455			−1.32208			−0.661039	+	0.750351i	$0.729884\pi$
$8$			2.82843i			0.353553i
$9$	−8.50859	−	2.93323i	−0.945399	−	0.325915i
$10$	−12.6842			−1.26842
$11$			17.1827i			1.56207i	0.624489	+	0.781034i	$0.285307\pi$
$11$			17.1827i			1.56207i	−0.624489	+	0.781034i	$0.714693\pi$
$12$	0.991370	−	5.91753i	0.0826142	−	0.493128i
$13$	21.0587			1.61990			0.809951	−	0.586498i	$-0.199494\pi$
$13$	21.0587			1.61990			0.809951	+	0.586498i	$0.199494\pi$
$14$			13.0879i			0.934851i
$15$	26.5375	+	4.44585i	1.76916	+	0.296390i
$16$	4.00000			0.250000
$17$			15.0740i			0.886705i	0.896347	+	0.443352i	$0.146211\pi$
$17$			15.0740i			0.886705i	−0.896347	+	0.443352i	$0.853789\pi$
$18$	−4.14822	+	12.0330i	−0.230456	+	0.668498i
$19$	−11.0933			−0.583856			−0.291928	−	0.956440i	$-0.594297\pi$
$19$	−11.0933			−0.583856			−0.291928	+	0.956440i	$0.594297\pi$
$20$			17.9382i			0.896910i
$21$	4.58734	−	27.3820i	0.218445	−	1.30391i
$22$	24.3001			1.10455
$23$			38.9760i			1.69461i	0.531109	+	0.847304i	$0.321776\pi$
$23$			38.9760i			1.69461i	−0.531109	+	0.847304i	$0.678224\pi$
$24$	−8.36865	−	1.40201i	−0.348694	−	0.0584170i
$25$	−55.4448			−2.21779
$26$		−	29.7815i		−	1.14544i
$27$	12.8963	−	23.7210i	0.477642	−	0.878555i
$28$	18.5091			0.661039
$29$			8.28196i			0.285585i	0.989753	+	0.142792i	$0.0456081\pi$
$29$			8.28196i			0.285585i	−0.989753	+	0.142792i	$0.954392\pi$
$30$	6.28738	−	37.5297i	0.209579	−	1.25099i
$31$	31.3061			1.00987			0.504937	−	0.863156i	$-0.331516\pi$
$31$	31.3061			1.00987			0.504937	+	0.863156i	$0.331516\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−50.8397	−	8.51723i	−1.54060	−	0.258098i
$34$	21.3178			0.626995
$35$			83.0050i			2.37157i
$36$	17.0172	+	5.86646i	0.472700	+	0.162957i
$37$	−30.2403			−0.817306			−0.408653	−	0.912690i	$-0.634001\pi$
$37$	−30.2403			−0.817306			−0.408653	+	0.912690i	$0.634001\pi$
$38$			15.6882i			0.412849i
$39$	−10.4385	+	62.3078i	−0.267654	+	1.59764i
$40$	25.3684			0.634211
$41$			27.3913i			0.668080i	0.942559	+	0.334040i	$0.108412\pi$
$41$			27.3913i			0.668080i	−0.942559	+	0.334040i	$0.891588\pi$
$42$	−38.7241	−	6.48748i	−0.922001	−	0.154464i
$43$	−61.4214			−1.42841			−0.714203	−	0.699939i	$-0.753210\pi$
$43$	−61.4214			−1.42841			−0.714203	+	0.699939i	$0.753210\pi$
$44$		−	34.3655i		−	0.781034i
$45$	−26.3085	+	76.3144i	−0.584632	+	1.69588i
$46$	55.1203			1.19827
$47$			11.7552i			0.250110i	0.992150	+	0.125055i	$0.0399107\pi$
$47$			11.7552i			0.250110i	−0.992150	+	0.125055i	$0.960089\pi$
$48$	−1.98274	+	11.8351i	−0.0413071	+	0.246564i
$49$	36.6467			0.747891
$50$			78.4108i			1.56822i
$51$	−44.6004	−	7.47195i	−0.874517	−	0.146509i
$52$	−42.1175			−0.809951
$53$		−	14.5448i		−	0.274431i	−0.990541	−	0.137215i	$-0.956185\pi$
$53$		−	14.5448i		−	0.274431i	0.990541	−	0.137215i	$-0.0438152\pi$
$54$	−33.5465	−	18.2382i	−0.621232	−	0.337744i
$55$	154.114			2.80207
$56$		−	26.1758i		−	0.467425i
$57$	5.49877	−	32.8224i	0.0964696	−	0.575831i
$58$	11.7125			0.201939
$59$			7.68115i			0.130189i
$59$			7.68115i			0.130189i
$60$	−53.0749	−	8.89170i	−0.884582	−	0.148195i
$61$	−5.82583			−0.0955054			−0.0477527	−	0.998859i	$-0.515206\pi$
$61$	−5.82583			−0.0955054			−0.0477527	+	0.998859i	$0.515206\pi$
$62$		−	44.2735i		−	0.714089i
$63$	78.7432	+	27.1457i	1.24989	+	0.430885i
$64$	−8.00000			−0.125000
$65$		−	188.878i		−	2.90581i
$66$	−12.0452	+	71.8982i	−0.182503	+	1.08937i
$67$	−73.2111			−1.09270			−0.546351	−	0.837556i	$-0.683984\pi$
$67$	−73.2111			−1.09270			−0.546351	+	0.837556i	$0.683984\pi$
$68$		−	30.1480i		−	0.443352i
$69$	−115.321	−	19.3198i	−1.67132	−	0.279997i
$70$	117.387			1.67695
$71$			46.1106i			0.649445i	0.945809	+	0.324723i	$0.105271\pi$
$71$			46.1106i			0.649445i	−0.945809	+	0.324723i	$0.894729\pi$
$72$	8.29643	−	24.0659i	0.115228	−	0.334249i
$73$	85.4930			1.17114			0.585569	−	0.810623i	$-0.300871\pi$
$73$	85.4930			1.17114			0.585569	+	0.810623i	$0.300871\pi$
$74$			42.7663i			0.577923i
$75$	27.4831	−	164.048i	0.366442	−	2.18731i
$76$	22.1865			0.291928
$77$		−	159.019i		−	2.06518i
$78$	88.1166	+	14.7623i	1.12970	+	0.189260i
$79$	−13.7855			−0.174500			−0.0872501	−	0.996186i	$-0.527808\pi$
$79$	−13.7855			−0.174500			−0.0872501	+	0.996186i	$0.527808\pi$
$80$		−	35.8764i		−	0.448455i
$81$	63.7923	+	49.9154i	0.787559	+	0.616239i
$82$	38.7371			0.472404
$83$			32.5823i			0.392558i	0.980548	+	0.196279i	$0.0628858\pi$
$83$			32.5823i			0.392558i	−0.980548	+	0.196279i	$0.937114\pi$
$84$	−9.17468	+	54.7641i	−0.109222	+	0.651953i
$85$	135.200			1.59059
$86$			86.8630i			1.01003i
$87$	−24.5044	−	4.10524i	−0.281660	−	0.0471867i
$88$	−48.6001			−0.552274
$89$		−	32.8739i		−	0.369370i	−0.982798	−	0.184685i	$-0.940874\pi$
$89$		−	32.8739i		−	0.369370i	0.982798	−	0.184685i	$-0.0591265\pi$
$90$	107.925	+	37.2058i	1.19917	+	0.413397i
$91$	−194.889			−2.14164
$92$		−	77.9519i		−	0.847304i
$93$	−15.5180	+	92.6275i	−0.166860	+	0.995994i
$94$	16.6243			0.176855
$95$			99.4966i			1.04733i
$96$	16.7373	+	2.80402i	0.174347	+	0.0292085i
$97$	−88.8138			−0.915607			−0.457803	−	0.889054i	$-0.651364\pi$
$97$	−88.8138			−0.915607			−0.457803	+	0.889054i	$0.651364\pi$
$98$		−	51.8262i		−	0.528839i
$99$	50.4010	−	146.201i	0.509101	−	1.47678i
$100$	110.890			1.10890
$101$			21.6713i			0.214568i	0.994228	+	0.107284i	$0.0342154\pi$
$101$			21.6713i			0.214568i	−0.994228	+	0.107284i	$0.965785\pi$
$102$	−10.5669	+	63.0745i	−0.103597	+	0.618377i
$103$	110.222			1.07011			0.535056	−	0.844816i	$-0.320290\pi$
$103$	110.222			1.07011			0.535056	+	0.844816i	$0.320290\pi$
$104$			59.5631i			0.572722i
$105$	−245.592	−	41.1443i	−2.33897	−	0.391851i
$106$	−20.5695			−0.194052
$107$		−	41.5747i		−	0.388548i	−0.980947	−	0.194274i	$-0.937765\pi$
$107$		−	41.5747i		−	0.388548i	0.980947	−	0.194274i	$-0.0622352\pi$
$108$	−25.7927	+	47.4420i	−0.238821	+	0.439277i
$109$	−111.009			−1.01843			−0.509214	−	0.860640i	$-0.670064\pi$
$109$	−111.009			−1.01843			−0.509214	+	0.860640i	$0.670064\pi$
$110$		−	217.950i		−	1.98136i
$111$	14.9897	−	89.4741i	0.135042	−	0.806073i
$112$	−37.0182			−0.330520
$113$		−	0.847675i		−	0.00750155i	−0.999993	−	0.00375077i	$-0.998806\pi$
$113$		−	0.847675i		−	0.00750155i	0.999993	−	0.00375077i	$-0.00119391\pi$
$114$	−46.4179	−	7.77643i	−0.407174	−	0.0682143i
$115$	349.579			3.03982
$116$		−	16.5639i		−	0.142792i
$117$	−179.180	−	61.7701i	−1.53145	−	0.527950i
$118$	10.8628			0.0920575
$119$		−	139.503i		−	1.17229i
$120$	−12.5748	+	75.0593i	−0.104790	+	0.625494i
$121$	−174.247			−1.44006
$122$			8.23897i			0.0675325i
$123$	−81.0444	−	13.5775i	−0.658898	−	0.110386i
$124$	−62.6122			−0.504937
$125$			273.062i			2.18450i
$126$	38.3899	−	111.360i	0.304681	−	0.883807i
$127$	−209.176			−1.64705			−0.823527	−	0.567278i	$-0.807997\pi$
$127$	−209.176			−1.64705			−0.823527	+	0.567278i	$0.807997\pi$
$128$			11.3137i			0.0883883i
$129$	30.4457	−	181.732i	0.236013	−	1.40877i
$130$	−267.114			−2.05472
$131$			118.745i			0.906449i	0.891396	+	0.453224i	$0.149726\pi$
$131$			118.745i			0.906449i	−0.891396	+	0.453224i	$0.850274\pi$
$132$	101.679	+	17.0345i	0.770299	+	0.129049i
$133$	102.663			0.771903
$134$			103.536i			0.772657i
$135$	−212.756	−	115.668i	−1.57597	−	0.856804i
$136$	−42.6357			−0.313498
$137$			196.396i			1.43355i	0.697307	+	0.716773i	$0.254382\pi$
$137$			196.396i			1.43355i	−0.697307	+	0.716773i	$0.745618\pi$
$138$	−27.3223	+	163.088i	−0.197988	+	1.18180i
$139$	4.55102			0.0327412			0.0163706	−	0.999866i	$-0.494789\pi$
$139$	4.55102			0.0327412			0.0163706	+	0.999866i	$0.494789\pi$
$140$		−	166.010i		−	1.18579i
$141$	−34.7808	−	5.82686i	−0.246672	−	0.0413253i
$142$	65.2103			0.459227
$143$			361.847i			2.53040i
$144$	−34.0344	−	11.7329i	−0.236350	−	0.0814787i
$145$	74.2817			0.512288
$146$		−	120.905i		−	0.828119i
$147$	−18.1652	+	108.429i	−0.123573	+	0.737612i
$148$	60.4807			0.408653
$149$		−	211.704i		−	1.42083i	−0.703782	−	0.710416i	$-0.748507\pi$
$149$		−	211.704i		−	1.42083i	0.703782	−	0.710416i	$-0.251493\pi$
$150$	−231.999	−	38.8670i	−1.54666	−	0.259114i
$151$	−124.876			−0.826992			−0.413496	−	0.910506i	$-0.635693\pi$
$151$	−124.876			−0.826992			−0.413496	+	0.910506i	$0.635693\pi$
$152$		−	31.3765i		−	0.206424i
$153$	44.2155	−	128.258i	0.288990	−	0.838290i
$154$	−224.886			−1.46030
$155$		−	280.788i		−	1.81153i
$156$	20.8770	−	124.616i	0.133827	−	0.798819i
$157$	108.108			0.688586			0.344293	−	0.938862i	$-0.388119\pi$
$157$	108.108			0.688586			0.344293	+	0.938862i	$0.388119\pi$
$158$			19.4957i			0.123390i
$159$	43.0347	+	7.20965i	0.270659	+	0.0453437i
$160$	−50.7369			−0.317106
$161$		−	360.705i		−	2.24040i
$162$	70.5910	−	90.2159i	0.435747	−	0.556889i
$163$	105.196			0.645372			0.322686	−	0.946506i	$-0.395414\pi$
$163$	105.196			0.645372			0.322686	+	0.946506i	$0.395414\pi$
$164$		−	54.7826i		−	0.334040i
$165$	−76.3919	+	455.987i	−0.462981	+	2.76356i
$166$	46.0783			0.277580
$167$		−	34.0871i		−	0.204114i	−0.994779	−	0.102057i	$-0.967458\pi$
$167$		−	34.0871i		−	0.204114i	0.994779	−	0.102057i	$-0.0325425\pi$
$168$	77.4481	+	12.9750i	0.461001	+	0.0772319i
$169$	274.470			1.62408
$170$		−	191.202i		−	1.12472i
$171$	94.3881	+	32.5391i	0.551977	+	0.190287i
$172$	122.843			0.714203
$173$			96.7164i			0.559054i	0.960138	+	0.279527i	$0.0901777\pi$
$173$			96.7164i			0.559054i	−0.960138	+	0.279527i	$0.909822\pi$
$174$	−5.80569	+	34.6544i	−0.0333660	+	0.199163i
$175$	513.116			2.93209
$176$			68.7310i			0.390517i
$177$	−22.7267	−	3.80743i	−0.128400	−	0.0215109i
$178$	−46.4908			−0.261184
$179$		−	34.9485i		−	0.195243i	−0.995224	−	0.0976215i	$-0.968877\pi$
$179$		−	34.9485i		−	0.195243i	0.995224	−	0.0976215i	$-0.0311235\pi$
$180$	52.6169	−	152.629i	0.292316	−	0.847938i
$181$	89.8055			0.496163			0.248081	−	0.968739i	$-0.420200\pi$
$181$	89.8055			0.496163			0.248081	+	0.968739i	$0.420200\pi$
$182$			275.615i			1.51437i
$183$	2.88778	−	17.2373i	0.0157802	−	0.0941927i
$184$	−110.241			−0.599134
$185$			271.229i			1.46610i
$186$	130.995	+	21.9457i	0.704274	+	0.117988i
$187$	−259.012			−1.38509
$188$		−	23.5103i		−	0.125055i
$189$	−119.350	+	219.527i	−0.631480	+	1.16152i
$190$	140.709			0.740576
$191$		−	299.708i		−	1.56915i	−0.620031	−	0.784577i	$-0.712880\pi$
$191$		−	299.708i		−	1.56915i	0.620031	−	0.784577i	$-0.287120\pi$
$192$	3.96548	−	23.6701i	0.0206535	−	0.123282i
$193$	180.455			0.935002			0.467501	−	0.883993i	$-0.345154\pi$
$193$	180.455			0.935002			0.467501	+	0.883993i	$0.345154\pi$
$194$			125.602i			0.647432i
$195$	558.845	+	93.6239i	2.86587	+	0.480123i
$196$	−73.2933			−0.373946
$197$			211.362i			1.07290i	0.843932	+	0.536451i	$0.180235\pi$
$197$			211.362i			1.07290i	−0.843932	+	0.536451i	$0.819765\pi$
$198$	−206.759	−	71.2777i	−1.04424	−	0.359989i
$199$	−373.964			−1.87922			−0.939608	−	0.342254i	$-0.888810\pi$
$199$	−373.964			−1.87922			−0.939608	+	0.342254i	$0.888810\pi$
$200$		−	156.822i		−	0.784108i
$201$	36.2896	−	216.614i	0.180545	−	1.07768i
$202$	30.6479			0.151722
$203$		−	76.6458i		−	0.377566i
$204$	89.2008	+	14.9439i	0.437259	+	0.0732544i
$205$	245.675			1.19842
$206$		−	155.877i		−	0.756684i
$207$	114.326	−	331.631i	0.552297	−	1.60208i
$208$	84.2349			0.404976
$209$		−	190.613i		−	0.912023i
$210$	−58.1869	+	347.320i	−0.277080	+	1.65390i
$211$	163.985			0.777178			0.388589	−	0.921411i	$-0.372963\pi$
$211$	163.985			0.777178			0.388589	+	0.921411i	$0.372963\pi$
$212$			29.0897i			0.137215i
$213$	−136.431	−	22.8563i	−0.640519	−	0.107307i
$214$	−58.7955			−0.274745
$215$			550.895i			2.56230i
$216$	67.0931	+	36.4763i	0.310616	+	0.168872i
$217$	−289.724			−1.33513
$218$			156.990i			0.720137i
$219$	−42.3776	+	252.954i	−0.193505	+	1.15504i
$220$	−308.228			−1.40103
$221$			317.439i			1.43638i
$222$	−126.535	−	21.1986i	−0.569979	−	0.0954892i
$223$	335.950			1.50650			0.753251	−	0.657733i	$-0.228485\pi$
$223$	335.950			1.50650			0.753251	+	0.657733i	$0.228485\pi$
$224$			52.3516i			0.233713i
$225$	471.757	+	162.632i	2.09670	+	0.722811i
$226$	−1.19879			−0.00530440
$227$		−	377.581i		−	1.66335i	−0.555261	−	0.831676i	$-0.687382\pi$
$227$		−	377.581i		−	1.66335i	0.555261	−	0.831676i	$-0.312618\pi$
$228$	−10.9975	+	65.6448i	−0.0482348	+	0.287916i
$229$	−268.973			−1.17456			−0.587278	−	0.809385i	$-0.699800\pi$
$229$	−268.973			−1.17456			−0.587278	+	0.809385i	$0.699800\pi$
$230$		−	494.380i		−	2.14948i
$231$	470.499	+	78.8231i	2.03679	+	0.341226i
$232$	−23.4249			−0.100969
$233$			456.958i			1.96119i	0.196035	+	0.980597i	$0.437193\pi$
$233$			456.958i			1.96119i	−0.196035	+	0.980597i	$0.562807\pi$
$234$	−87.3562	+	253.399i	−0.373317	+	1.08290i
$235$	105.433			0.448653
$236$		−	15.3623i		−	0.0650945i
$237$	6.83327	−	40.7881i	0.0288324	−	0.172102i
$238$	−197.287			−0.828937
$239$			261.649i			1.09477i	0.836882	+	0.547384i	$0.184376\pi$
$239$			261.649i			1.09477i	−0.836882	+	0.547384i	$0.815624\pi$
$240$	106.150	+	17.7834i	0.442291	+	0.0740975i
$241$	−53.9882			−0.224018			−0.112009	−	0.993707i	$-0.535728\pi$
$241$	−53.9882			−0.224018			−0.112009	+	0.993707i	$0.535728\pi$
$242$			246.422i			1.01827i
$243$	−179.309	+	164.004i	−0.737896	+	0.674914i
$244$	11.6517			0.0477527
$245$		−	328.688i		−	1.34158i
$246$	−19.2014	+	114.614i	−0.0780546	+	0.465911i
$247$	−233.610			−0.945790
$248$			88.5470i			0.357045i
$249$	−96.4034	−	16.1506i	−0.387162	−	0.0648617i
$250$	386.168			1.54467
$251$		−	217.016i		−	0.864605i	−0.901729	−	0.432302i	$-0.857701\pi$
$251$		−	217.016i		−	0.864605i	0.901729	−	0.432302i	$-0.142299\pi$
$252$	−157.486	−	54.2915i	−0.624946	−	0.215442i
$253$	−669.714			−2.64709
$254$			295.819i			1.16464i
$255$	−67.0167	+	400.025i	−0.262810	+	1.56873i
$256$	16.0000			0.0625000
$257$			64.8764i			0.252438i	0.992002	+	0.126219i	$0.0402841\pi$
$257$			64.8764i			0.252438i	−0.992002	+	0.126219i	$0.959716\pi$
$258$	−257.007	−	43.0567i	−0.996152	−	0.166886i
$259$	279.861			1.08054
$260$			377.756i			1.45291i
$261$	24.2929	−	70.4678i	0.0930763	−	0.269992i
$262$	167.930			0.640956
$263$		−	105.289i		−	0.400337i	−0.979762	−	0.200168i	$-0.935851\pi$
$263$		−	105.289i		−	0.400337i	0.979762	−	0.200168i	$-0.0641489\pi$
$264$	24.0904	−	143.796i	0.0912514	−	0.544684i
$265$	−130.454			−0.492279
$266$		−	145.188i		−	0.545818i
$267$	97.2663	+	16.2951i	0.364293	+	0.0610304i
$268$	146.422			0.546351
$269$		−	319.428i		−	1.18747i	−0.804662	−	0.593733i	$-0.797654\pi$
$269$		−	319.428i		−	1.18747i	0.804662	−	0.593733i	$-0.202346\pi$
$270$	−163.580	+	300.882i	−0.605852	+	1.11438i
$271$	−137.484			−0.507321			−0.253660	−	0.967293i	$-0.581635\pi$
$271$	−137.484			−0.507321			−0.253660	+	0.967293i	$0.581635\pi$
$272$			60.2959i			0.221676i
$273$	96.6036	−	576.631i	0.353859	−	2.11220i
$274$	277.746			1.01367
$275$		−	952.694i		−	3.46434i
$276$	230.642	+	38.6396i	0.835658	+	0.139999i
$277$	−31.2450			−0.112798			−0.0563989	−	0.998408i	$-0.517962\pi$
$277$	−31.2450			−0.112798			−0.0563989	+	0.998408i	$0.517962\pi$
$278$		−	6.43612i		−	0.0231515i
$279$	−266.371	−	91.8281i	−0.954735	−	0.329133i
$280$	−234.774			−0.838477
$281$			228.749i			0.814054i	0.913416	+	0.407027i	$0.133435\pi$
$281$			228.749i			0.814054i	−0.913416	+	0.407027i	$0.866565\pi$
$282$	−8.24043	+	49.1875i	−0.0292214	+	0.174424i
$283$	52.3256			0.184896			0.0924481	−	0.995718i	$-0.470531\pi$
$283$	52.3256			0.184896			0.0924481	+	0.995718i	$0.470531\pi$
$284$		−	92.2213i		−	0.324723i
$285$	−294.387	−	49.3190i	−1.03294	−	0.173049i
$286$	511.729			1.78926
$287$		−	253.494i		−	0.883255i
$288$	−16.5929	+	48.1319i	−0.0576141	+	0.167125i
$289$	61.7750			0.213754
$290$		−	105.050i		−	0.362242i
$291$	44.0237	−	262.779i	0.151284	−	0.903022i
$292$	−170.986			−0.585569
$293$			189.465i			0.646640i	0.946290	+	0.323320i	$0.104799\pi$
$293$			189.465i			0.646640i	−0.946290	+	0.323320i	$0.895201\pi$
$294$	153.342	+	25.6895i	0.521570	+	0.0873792i
$295$	68.8930			0.233536
$296$		−	85.5326i		−	0.288961i
$297$	407.592	+	221.594i	1.37236	+	0.746109i
$298$	−299.395			−1.00468
$299$			820.784i			2.74510i
$300$	−54.9663	+	328.096i	−0.183221	+	1.09365i
$301$	568.428			1.88846
$302$			176.601i			0.584772i
$303$	−64.1204	−	10.7422i	−0.211619	−	0.0354527i
$304$	−44.3731			−0.145964
$305$			52.2525i			0.171320i
$306$	−181.385	−	62.5301i	−0.592761	−	0.204347i
$307$	−270.280			−0.880391			−0.440196	−	0.897902i	$-0.645091\pi$
$307$	−270.280			−0.880391			−0.440196	+	0.897902i	$0.645091\pi$
$308$			318.037i			1.03259i
$309$	−54.6352	+	326.120i	−0.176813	+	1.05540i
$310$	−397.094			−1.28095
$311$		−	256.254i		−	0.823968i	−0.911191	−	0.411984i	$-0.864836\pi$
$311$		−	256.254i		−	0.823968i	0.911191	−	0.411984i	$-0.135164\pi$
$312$	−176.233	−	29.5245i	−0.564850	−	0.0946299i
$313$	−449.362			−1.43566			−0.717831	−	0.696217i	$-0.754865\pi$
$313$	−449.362			−1.43566			−0.717831	+	0.696217i	$0.754865\pi$
$314$		−	152.888i		−	0.486904i
$315$	243.473	−	706.256i	0.772930	−	2.24208i
$316$	27.5710			0.0872501
$317$			506.823i			1.59881i	0.600792	+	0.799406i	$0.294852\pi$
$317$			506.823i			1.59881i	−0.600792	+	0.799406i	$0.705148\pi$
$318$	10.1960	−	60.8603i	0.0320629	−	0.191385i
$319$	−142.307			−0.446103
$320$			71.7528i			0.224228i
$321$	123.010	+	20.6079i	0.383208	+	0.0641992i
$322$	−510.114			−1.58420
$323$		−	167.220i		−	0.517708i
$324$	−127.585	−	99.8307i	−0.393780	−	0.308119i
$325$	−1167.60			−3.59260
$326$		−	148.769i		−	0.456347i
$327$	55.0253	−	328.449i	0.168273	−	1.00443i
$328$	−77.4743			−0.236202
$329$		−	108.789i		−	0.330665i
$330$	644.863	+	108.034i	1.95413	+	0.327377i
$331$	183.359			0.553955			0.276977	−	0.960876i	$-0.410667\pi$
$331$	183.359			0.553955			0.276977	+	0.960876i	$0.410667\pi$
$332$		−	65.1646i		−	0.196279i
$333$	257.303	+	88.7019i	0.772681	+	0.266372i
$334$	−48.2065			−0.144331
$335$			656.637i			1.96011i
$336$	18.3494	−	109.528i	0.0546112	−	0.325977i
$337$	100.071			0.296946			0.148473	−	0.988916i	$-0.452564\pi$
$337$	100.071			0.296946			0.148473	+	0.988916i	$0.452564\pi$
$338$		−	388.159i		−	1.14840i
$339$	2.50807	+	0.420180i	0.00739844	+	0.00123947i
$340$	−270.400			−0.795295
$341$			537.925i			1.57749i
$342$	46.0173	−	133.485i	0.134553	−	0.390307i
$343$	114.325			0.333308
$344$		−	173.726i		−	0.505017i
$345$	−173.281	+	1034.32i	−0.502265	+	2.99804i
$346$	136.778			0.395311
$347$			505.650i			1.45720i	0.684937	+	0.728602i	$0.259830\pi$
$347$			505.650i			1.45720i	−0.684937	+	0.728602i	$0.740170\pi$
$348$	49.0088	+	8.21049i	0.140830	+	0.0235934i
$349$	405.344			1.16144			0.580722	−	0.814102i	$-0.302770\pi$
$349$	405.344			1.16144			0.580722	+	0.814102i	$0.302770\pi$
$350$		−	725.656i		−	2.07330i
$351$	271.580	−	499.534i	0.773733	−	1.42317i
$352$	97.2003			0.276137
$353$			180.248i			0.510617i	0.966860	+	0.255309i	$0.0821771\pi$
$353$			180.248i			0.510617i	−0.966860	+	0.255309i	$0.917823\pi$
$354$	−5.38452	+	32.1404i	−0.0152105	+	0.0907922i
$355$	413.571			1.16499
$356$			65.7479i			0.184685i
$357$	412.756	+	69.1495i	1.15618	+	0.193696i
$358$	−49.4247			−0.138058
$359$			456.649i			1.27200i	0.771688	+	0.636002i	$0.219413\pi$
$359$			456.649i			1.27200i	−0.771688	+	0.636002i	$0.780587\pi$
$360$	−215.850	−	74.4115i	−0.599583	−	0.206699i
$361$	−237.939			−0.659112
$362$		−	127.004i		−	0.350840i
$363$	86.3715	−	515.555i	0.237938	−	1.42026i
$364$	389.778			1.07082
$365$		−	766.796i		−	2.10081i
$366$	−24.3772	−	4.08393i	−0.0666043	−	0.0111583i
$367$	403.812			1.10030			0.550152	−	0.835064i	$-0.314570\pi$
$367$	403.812			1.10030			0.550152	+	0.835064i	$0.314570\pi$
$368$			155.904i			0.423652i
$369$	80.3450	−	233.061i	0.217737	−	0.631603i
$370$	383.575			1.03669
$371$			134.606i			0.362819i
$372$	31.0359	−	185.255i	0.0834299	−	0.497997i
$373$	326.128			0.874337			0.437169	−	0.899380i	$-0.355981\pi$
$373$	326.128			0.874337			0.437169	+	0.899380i	$0.355981\pi$
$374$			366.299i			0.979409i
$375$	−807.927	−	135.353i	−2.15447	−	0.360941i
$376$	−33.2487			−0.0884273
$377$			174.408i			0.462620i
$378$	310.458	+	168.786i	0.821317	+	0.446524i
$379$	−399.946			−1.05527			−0.527633	−	0.849472i	$-0.676920\pi$
$379$	−399.946			−1.05527			−0.527633	+	0.849472i	$0.676920\pi$
$380$		−	198.993i		−	0.523666i
$381$	103.685	−	618.902i	0.272140	−	1.62442i
$382$	−423.852			−1.10956
$383$			480.714i			1.25513i	0.778565	+	0.627563i	$0.215948\pi$
$383$			480.714i			1.25513i	−0.778565	+	0.627563i	$0.784052\pi$
$384$	−33.4746	−	5.60804i	−0.0871735	−	0.0146043i
$385$	−1426.25			−3.70455
$386$		−	255.202i		−	0.661146i
$387$	522.610	+	180.163i	1.35041	+	0.465538i
$388$	177.628			0.457803
$389$		−	548.261i		−	1.40941i	−0.709500	−	0.704705i	$-0.751079\pi$
$389$		−	548.261i		−	1.40941i	0.709500	−	0.704705i	$-0.248921\pi$
$390$	132.404	−	790.327i	0.339498	−	2.02648i
$391$	−587.523			−1.50262
$392$			103.652i			0.264419i
$393$	−351.338	−	58.8600i	−0.893990	−	0.149771i
$394$	298.910			0.758656
$395$			123.644i			0.313022i
$396$	−100.802	+	292.402i	−0.254550	+	0.738389i
$397$	309.135			0.778678			0.389339	−	0.921094i	$-0.372703\pi$
$397$	309.135			0.778678			0.389339	+	0.921094i	$0.372703\pi$
$398$			528.865i			1.32881i
$399$	−50.8886	+	303.756i	−0.127540	+	0.761294i
$400$	−221.779			−0.554448
$401$		−	94.1980i		−	0.234908i	−0.993078	−	0.117454i	$-0.962527\pi$
$401$		−	94.1980i		−	0.234908i	0.993078	−	0.117454i	$-0.0374732\pi$
$402$	−306.339	−	51.3213i	−0.762037	−	0.127665i
$403$	659.267			1.63590
$404$		−	43.3427i		−	0.107284i
$405$	447.696	−	572.160i	1.10542	−	1.41274i
$406$	−108.394			−0.266979
$407$		−	519.612i		−	1.27669i
$408$	21.1339	−	126.149i	0.0517987	−	0.309189i
$409$	−298.046			−0.728719			−0.364360	−	0.931258i	$-0.618712\pi$
$409$	−298.046			−0.728719			−0.364360	+	0.931258i	$0.618712\pi$
$410$		−	347.437i		−	0.847408i
$411$	−581.089	−	97.3504i	−1.41384	−	0.236862i
$412$	−220.443			−0.535056
$413$		−	71.0855i		−	0.172120i
$414$	−468.997	−	161.681i	−1.13284	−	0.390533i
$415$	292.234			0.704178
$416$		−	119.126i		−	0.286361i
$417$	−2.25587	+	13.4654i	−0.00540977	+	0.0322911i
$418$	−269.567			−0.644898
$419$		−	652.807i		−	1.55801i	−0.627016	−	0.779006i	$-0.715724\pi$
$419$		−	652.807i		−	1.55801i	0.627016	−	0.779006i	$-0.284276\pi$
$420$	491.185	+	82.2886i	1.16949	+	0.195925i
$421$	326.387			0.775267			0.387634	−	0.921814i	$-0.373293\pi$
$421$	326.387			0.775267			0.387634	+	0.921814i	$0.373293\pi$
$422$		−	231.909i		−	0.549548i
$423$	34.4806	−	100.020i	0.0815145	−	0.236454i
$424$	41.1390			0.0970259
$425$		−	835.774i		−	1.96653i
$426$	−32.3238	+	192.942i	−0.0758774	+	0.452915i
$427$	53.9154			0.126266
$428$			83.1494i			0.194274i
$429$	−1070.62	−	179.362i	−2.49562	−	0.418093i
$430$	779.083			1.81182
$431$			428.656i			0.994562i	0.867590	+	0.497281i	$0.165668\pi$
$431$			428.656i			0.994562i	−0.867590	+	0.497281i	$0.834332\pi$
$432$	51.5853	−	94.8839i	0.119410	−	0.219639i
$433$	629.092			1.45287			0.726434	−	0.687236i	$-0.241176\pi$
$433$	629.092			1.45287			0.726434	+	0.687236i	$0.241176\pi$
$434$			409.731i			0.944082i
$435$	−36.8203	+	219.782i	−0.0846445	+	0.505247i
$436$	222.017			0.509214
$437$		−	432.371i		−	0.989407i
$438$	357.731	+	59.9310i	0.816737	+	0.136829i
$439$	−82.4724			−0.187864			−0.0939322	−	0.995579i	$-0.529944\pi$
$439$	−82.4724			−0.187864			−0.0939322	+	0.995579i	$0.529944\pi$
$440$			435.900i			0.990681i
$441$	−311.812	−	107.493i	−0.707056	−	0.243749i
$442$	448.926			1.01567
$443$			372.525i			0.840915i	0.907312	+	0.420457i	$0.138130\pi$
$443$			372.525i			0.840915i	−0.907312	+	0.420457i	$0.861870\pi$
$444$	−29.9794	+	178.948i	−0.0675211	+	0.403036i
$445$	−294.850			−0.662583
$446$		−	475.105i		−	1.06526i
$447$	626.383	+	104.939i	1.40130	+	0.234762i
$448$	74.0364			0.165260
$449$		−	404.982i		−	0.901964i	−0.892533	−	0.450982i	$-0.851074\pi$
$449$		−	404.982i		−	0.901964i	0.892533	−	0.450982i	$-0.148926\pi$
$450$	229.997	−	667.165i	0.511104	−	1.48259i
$451$	−470.658			−1.04359
$452$			1.69535i			0.00375077i
$453$	61.8991	−	369.478i	0.136643	−	0.815626i
$454$	−533.980			−1.17617
$455$			1747.98i			3.84171i
$456$	92.8357	+	15.5529i	0.203587	+	0.0341071i
$457$	−439.564			−0.961847			−0.480924	−	0.876762i	$-0.659699\pi$
$457$	−439.564			−0.961847			−0.480924	+	0.876762i	$0.659699\pi$
$458$			380.386i			0.830536i
$459$	357.570	+	194.399i	0.779019	+	0.423527i
$460$	−699.159			−1.51991
$461$			137.965i			0.299272i	0.988741	+	0.149636i	$0.0478102\pi$
$461$			137.965i			0.299272i	−0.988741	+	0.149636i	$0.952190\pi$
$462$	111.473	−	665.386i	0.241283	−	1.44023i
$463$	−469.895			−1.01489			−0.507446	−	0.861684i	$-0.669410\pi$
$463$	−469.895			−1.01489			−0.507446	+	0.861684i	$0.669410\pi$
$464$			33.1278i			0.0713962i
$465$	830.785	+	139.182i	1.78663	+	0.299317i
$466$	646.236			1.38677
$467$		−	290.977i		−	0.623078i	−0.950233	−	0.311539i	$-0.899156\pi$
$467$		−	290.977i		−	0.623078i	0.950233	−	0.311539i	$-0.100844\pi$
$468$	358.360	+	123.540i	0.765727	+	0.263975i
$469$	677.535			1.44464
$470$		−	149.105i		−	0.317245i
$471$	−53.5875	+	319.866i	−0.113774	+	0.679121i
$472$	−21.7256			−0.0460287
$473$		−	1055.39i		−	2.23127i
$474$	−57.6831	−	9.66371i	−0.121694	−	0.0203876i
$475$	615.064			1.29487
$476$			279.006i			0.586147i
$477$	−42.6633	+	123.756i	−0.0894410	+	0.259447i
$478$	370.028			0.774118
$479$		−	152.918i		−	0.319245i	−0.987178	−	0.159623i	$-0.948972\pi$
$479$		−	152.918i		−	0.319245i	0.987178	−	0.159623i	$-0.0510277\pi$
$480$	25.1495	−	150.119i	0.0523948	−	0.312747i
$481$	−636.823			−1.32396
$482$			76.3509i			0.158404i
$483$	1067.24	+	178.796i	2.20961	+	0.370178i
$484$	348.494			0.720028
$485$			796.580i			1.64243i
$486$	231.937	+	253.581i	0.477237	+	0.521771i
$487$	613.133			1.25900			0.629500	−	0.777000i	$-0.283260\pi$
$487$	613.133			1.25900			0.629500	+	0.777000i	$0.283260\pi$
$488$		−	16.4779i		−	0.0337663i
$489$	−52.1439	+	311.249i	−0.106634	+	0.636502i
$490$	−464.835			−0.948642
$491$		−	802.381i		−	1.63418i	−0.576512	−	0.817088i	$-0.695587\pi$
$491$		−	802.381i		−	1.63418i	0.576512	−	0.817088i	$-0.304413\pi$
$492$	162.089	+	27.1549i	0.329449	+	0.0551929i
$493$	−124.842			−0.253229
$494$			330.375i			0.668774i
$495$	−1311.29	−	452.051i	−2.64907	−	0.913235i
$496$	125.224			0.252469
$497$		−	426.733i		−	0.858618i
$498$	−22.8403	+	136.335i	−0.0458641	+	0.273765i
$499$	641.199			1.28497			0.642484	−	0.766299i	$-0.277904\pi$
$499$	641.199			1.28497			0.642484	+	0.766299i	$0.277904\pi$
$500$		−	546.125i		−	1.09225i
$501$	100.856	+	16.8965i	0.201309	+	0.0337255i
$502$	−306.907			−0.611368
$503$		−	759.025i		−	1.50900i	−0.656302	−	0.754498i	$-0.727880\pi$
$503$		−	759.025i		−	1.50900i	0.656302	−	0.754498i	$-0.272120\pi$
$504$	−76.7797	+	222.719i	−0.152341	+	0.441903i
$505$	194.372			0.384896
$506$			947.119i			1.87178i
$507$	−136.051	+	812.092i	−0.268344	+	1.60176i
$508$	418.352			0.823527
$509$		−	847.183i		−	1.66441i	−0.554471	−	0.832203i	$-0.687079\pi$
$509$		−	847.183i		−	1.66441i	0.554471	−	0.832203i	$-0.312921\pi$
$510$	565.721	+	94.7759i	1.10926	+	0.185835i
$511$	−791.199			−1.54834
$512$		−	22.6274i		−	0.0441942i
$513$	−143.062	+	263.143i	−0.278874	+	0.512949i
$514$	91.7491			0.178500
$515$		−	988.589i		−	1.91959i
$516$	−60.8914	+	363.463i	−0.118006	+	0.704386i
$517$	−201.986			−0.390689
$518$		−	395.783i		−	0.764059i
$519$	−286.161	−	47.9409i	−0.551370	−	0.0923716i
$520$	534.227			1.02736
$521$		−	251.175i		−	0.482102i	−0.970512	−	0.241051i	$-0.922508\pi$
$521$		−	251.175i		−	0.482102i	0.970512	−	0.241051i	$-0.0774921\pi$
$522$	−99.6566	−	34.3554i	−0.190913	−	0.0658149i
$523$	−440.254			−0.841786			−0.420893	−	0.907110i	$-0.638283\pi$
$523$	−440.254			−0.841786			−0.420893	+	0.907110i	$0.638283\pi$
$524$		−	237.490i		−	0.453224i
$525$	−254.344	+	1518.19i	−0.484465	+	2.89179i
$526$	−148.900			−0.283081
$527$			471.908i			0.895461i
$528$	−203.359	−	34.0689i	−0.385149	−	0.0645245i
$529$	−990.126			−1.87169
$530$			184.490i			0.348094i
$531$	22.5306	−	65.3557i	0.0424305	−	0.123080i
$532$	−205.326			−0.385952
$533$			576.826i			1.08222i
$534$	23.0448	−	137.555i	0.0431550	−	0.257594i
$535$	−372.888			−0.696986
$536$		−	207.072i		−	0.386329i
$537$	103.404	+	17.3235i	0.192560	+	0.0322597i
$538$	−451.740			−0.839665
$539$			629.690i			1.16826i
$540$	425.512	+	231.337i	0.787985	+	0.428402i
$541$	1000.75			1.84982			0.924909	−	0.380189i	$-0.124141\pi$
$541$	1000.75			1.84982			0.924909	+	0.380189i	$0.124141\pi$
$542$			194.432i			0.358730i
$543$	−44.5152	+	265.713i	−0.0819801	+	0.489343i
$544$	85.2713			0.156749
$545$			995.647i			1.82688i
$546$	−815.479	−	136.618i	−1.49355	−	0.250216i
$547$	−2.15801			−0.00394518			−0.00197259	−	0.999998i	$-0.500628\pi$
$547$	−2.15801			−0.00394518			−0.00197259	+	0.999998i	$0.500628\pi$
$548$		−	392.792i		−	0.716773i
$549$	49.5696	+	17.0885i	0.0902907	+	0.0311266i
$550$	−1347.31			−2.44966
$551$		−	91.8740i		−	0.166740i
$552$	54.6447	−	326.176i	0.0989939	−	0.590899i
$553$	127.579			0.230703
$554$			44.1871i			0.0797600i
$555$	−802.502	−	134.444i	−1.44595	−	0.242241i
$556$	−9.10204			−0.0163706
$557$			797.024i			1.43092i	0.698652	+	0.715461i	$0.253783\pi$
$557$			797.024i			1.43092i	−0.698652	+	0.715461i	$0.746217\pi$
$558$	−129.865	+	376.705i	−0.232732	+	0.675099i
$559$	−1293.46			−2.31388
$560$			332.020i			0.592893i
$561$	128.389	−	766.357i	0.228857	−	1.36606i
$562$	323.500			0.575623
$563$		−	506.411i		−	0.899486i	−0.893158	−	0.449743i	$-0.851516\pi$
$563$		−	506.411i		−	0.899486i	0.893158	−	0.449743i	$-0.148484\pi$
$564$	69.5616	+	11.6537i	0.123336	+	0.0206626i
$565$	−7.60288			−0.0134564
$566$		−	73.9996i		−	0.130741i
$567$	−590.369	−	461.944i	−1.04122	−	0.814716i
$568$	−130.421			−0.229614
$569$		−	531.703i		−	0.934452i	−0.884138	−	0.467226i	$-0.845253\pi$
$569$		−	531.703i		−	0.934452i	0.884138	−	0.467226i	$-0.154747\pi$
$570$	−69.7476	+	416.326i	−0.122364	+	0.730397i
$571$	−275.203			−0.481968			−0.240984	−	0.970529i	$-0.577470\pi$
$571$	−275.203			−0.481968			−0.240984	+	0.970529i	$0.577470\pi$
$572$		−	723.694i		−	1.26520i
$573$	886.767	+	148.561i	1.54759	+	0.259269i
$574$	−358.495			−0.624555
$575$		−	2161.01i		−	3.75829i
$576$	68.0687	+	23.4659i	0.118175	+	0.0407393i
$577$	−329.741			−0.571475			−0.285738	−	0.958308i	$-0.592239\pi$
$577$	−329.741			−0.571475			−0.285738	+	0.958308i	$0.592239\pi$
$578$		−	87.3631i		−	0.151147i
$579$	−89.4490	+	533.925i	−0.154489	+	0.922150i
$580$	−148.563			−0.256144
$581$		−	301.534i		−	0.518992i
$582$	−371.626	−	62.2589i	−0.638533	−	0.106974i
$583$	249.920			0.428679
$584$			241.811i			0.414060i
$585$	−554.023	+	1607.08i	−0.947047	+	2.74715i
$586$	267.945			0.457243
$587$			1074.66i			1.83077i	0.402575	+	0.915387i	$0.368115\pi$
$587$			1074.66i			1.83077i	−0.402575	+	0.915387i	$0.631885\pi$
$588$	36.3304	−	216.858i	0.0617864	−	0.368806i
$589$	−347.287			−0.589621
$590$		−	97.4294i		−	0.165135i
$591$	−625.369	−	104.769i	−1.05815	−	0.177274i
$592$	−120.961			−0.204327
$593$		−	499.939i		−	0.843068i	−0.906813	−	0.421534i	$-0.861492\pi$
$593$		−	499.939i		−	0.843068i	0.906813	−	0.421534i	$-0.138508\pi$
$594$	313.382	−	576.421i	0.527579	−	0.970406i
$595$	−1251.22			−2.10288
$596$			423.408i			0.710416i
$597$	185.368	−	1106.47i	0.310500	−	1.85339i
$598$	1160.76			1.94108
$599$		−	80.6262i		−	0.134601i	−0.997733	−	0.0673007i	$-0.978561\pi$
$599$		−	80.6262i		−	0.134601i	0.997733	−	0.0673007i	$-0.0214387\pi$
$600$	463.998	+	77.7341i	0.773330	+	0.129557i
$601$	−56.3863			−0.0938209			−0.0469104	−	0.998899i	$-0.514938\pi$
$601$	−56.3863			−0.0938209			−0.0469104	+	0.998899i	$0.514938\pi$
$602$		−	803.878i		−	1.33535i
$603$	622.923	+	214.745i	1.03304	+	0.356128i
$604$	249.752			0.413496
$605$			1562.84i			2.58320i
$606$	−15.1917	+	90.6800i	−0.0250688	+	0.149637i
$607$	644.685			1.06208			0.531042	−	0.847345i	$-0.321801\pi$
$607$	644.685			1.06208			0.531042	+	0.847345i	$0.321801\pi$
$608$			62.7530i			0.103212i
$609$	226.777	+	37.9922i	0.372376	+	0.0623845i
$610$	73.8961			0.121141
$611$			247.549i			0.405154i
$612$	−88.4310	+	256.517i	−0.144495	+	0.419145i
$613$	672.062			1.09635			0.548175	−	0.836364i	$-0.315323\pi$
$613$	672.062			1.09635			0.548175	+	0.836364i	$0.315323\pi$
$614$			382.234i			0.622530i
$615$	−121.778	+	726.896i	−0.198012	+	1.18194i
$616$	449.772			0.730150
$617$			152.747i			0.247564i	0.992309	+	0.123782i	$0.0395024\pi$
$617$			152.747i			0.247564i	−0.992309	+	0.123782i	$0.960498\pi$
$618$	461.203	+	77.2658i	0.746284	+	0.125026i
$619$	620.572			1.00254			0.501270	−	0.865291i	$-0.332866\pi$
$619$	620.572			1.00254			0.501270	+	0.865291i	$0.332866\pi$
$620$			561.575i			0.905767i
$621$	924.548	+	502.647i	1.48881	+	0.809415i
$622$	−362.398			−0.582633
$623$			304.233i			0.488336i
$624$	−41.7540	+	249.231i	−0.0669134	+	0.399409i
$625$	1063.00			1.70081
$626$			635.494i			1.01517i
$627$	563.979	+	94.4839i	0.899487	+	0.150692i
$628$	−216.216			−0.344293
$629$		−	455.842i		−	0.724709i
$630$	−998.796	−	344.323i	−1.58539	−	0.546544i
$631$	329.365			0.521973			0.260987	−	0.965342i	$-0.415952\pi$
$631$	329.365			0.521973			0.260987	+	0.965342i	$0.415952\pi$
$632$		−	38.9913i		−	0.0616951i
$633$	−81.2847	+	485.192i	−0.128412	+	0.766496i
$634$	716.756			1.13053
$635$			1876.12i			2.95452i
$636$	−86.0695	−	14.4193i	−0.135329	−	0.0226719i
$637$	771.732			1.21151
$638$			201.252i			0.315442i
$639$	135.253	−	392.337i	0.211664	−	0.613985i
$640$	101.474			0.158553
$641$		−	1145.71i		−	1.78737i	−0.448692	−	0.893687i	$-0.648110\pi$
$641$		−	1145.71i		−	1.78737i	0.448692	−	0.893687i	$-0.351890\pi$
$642$	29.1440	−	173.962i	0.0453957	−	0.270969i
$643$	−583.222			−0.907032			−0.453516	−	0.891248i	$-0.649831\pi$
$643$	−583.222			−0.907032			−0.453516	+	0.891248i	$0.649831\pi$
$644$			721.410i			1.12020i
$645$	−1629.97	−	273.070i	−2.52708	−	0.423365i
$646$	−236.484			−0.366075
$647$		−	40.0323i		−	0.0618738i	−0.999521	−	0.0309369i	$-0.990151\pi$
$647$		−	40.0323i		−	0.0618738i	0.999521	−	0.0309369i	$-0.00984909\pi$
$648$	−141.182	+	180.432i	−0.217873	+	0.278444i
$649$	−131.983			−0.203364
$650$			1651.23i			2.54035i
$651$	143.612	−	857.225i	0.220602	−	1.31678i
$652$	−210.391			−0.322686
$653$		−	65.5338i		−	0.100358i	−0.998740	−	0.0501790i	$-0.984021\pi$
$653$		−	65.5338i		−	0.100358i	0.998740	−	0.0501790i	$-0.0159792\pi$
$654$	−464.496	−	77.8175i	−0.710239	−	0.118987i
$655$	1065.03			1.62601
$656$			109.565i			0.167020i
$657$	−727.425	−	250.771i	−1.10719	−	0.381691i
$658$	−153.851			−0.233816
$659$			662.001i			1.00455i	0.864707	+	0.502277i	$0.167504\pi$
$659$			662.001i			1.00455i	−0.864707	+	0.502277i	$0.832496\pi$
$660$	152.784	−	911.973i	0.231491	−	1.38178i
$661$	688.413			1.04147			0.520736	−	0.853718i	$-0.325658\pi$
$661$	688.413			1.04147			0.520736	+	0.853718i	$0.325658\pi$
$662$		−	259.309i		−	0.391705i
$663$	−939.227	−	157.350i	−1.41663	−	0.237330i
$664$	−92.1566			−0.138790
$665$		−	920.796i		−	1.38466i
$666$	125.443	−	363.881i	0.188353	−	0.546368i
$667$	−322.797			−0.483954
$668$			68.1742i			0.102057i
$669$	−166.525	+	993.997i	−0.248917	+	1.48580i
$670$	928.626			1.38601
$671$		−	100.104i		−	0.149186i
$672$	−154.896	−	25.9499i	−0.230500	−	0.0386159i
$673$	310.353			0.461149			0.230574	−	0.973055i	$-0.425939\pi$
$673$	310.353			0.461149			0.230574	+	0.973055i	$0.425939\pi$
$674$		−	141.521i		−	0.209972i
$675$	−715.034	+	1315.20i	−1.05931	+	1.94845i
$676$	−548.940			−0.812041
$677$			463.558i			0.684724i	0.939568	+	0.342362i	$0.111227\pi$
$677$			463.558i			0.684724i	−0.939568	+	0.342362i	$0.888773\pi$
$678$	0.594224	−	3.54695i	0.000876436	−	0.00523149i
$679$	821.932			1.21050
$680$			382.404i			0.562358i
$681$	1117.17	+	187.161i	1.64049	+	0.274833i
$682$	760.741			1.11546
$683$			492.981i			0.721788i	0.932607	+	0.360894i	$0.117528\pi$
$683$			492.981i			0.721788i	−0.932607	+	0.360894i	$0.882472\pi$
$684$	−188.776	−	65.0782i	−0.275989	−	0.0951436i
$685$	1761.49			2.57152
$686$		−	161.679i		−	0.235684i
$687$	133.326	−	795.829i	0.194070	−	1.15841i
$688$	−245.686			−0.357101
$689$		−	306.296i		−	0.444551i
$690$	1462.75	+	245.057i	2.11993	+	0.355155i
$691$	−320.567			−0.463917			−0.231959	−	0.972726i	$-0.574513\pi$
$691$	−320.567			−0.463917			−0.231959	+	0.972726i	$0.574513\pi$
$692$		−	193.433i		−	0.279527i
$693$	−466.438	+	1353.02i	−0.673071	+	1.95242i
$694$	715.097			1.03040
$695$		−	40.8186i		−	0.0587318i
$696$	11.6114	−	69.3089i	0.0166830	−	0.0995817i
$697$	−412.896			−0.592390
$698$		−	573.243i		−	0.821265i
$699$	−1352.03	−	226.507i	−1.93424	−	0.324045i
$700$	−1026.23			−1.46605
$701$		−	218.409i		−	0.311568i	−0.987791	−	0.155784i	$-0.950210\pi$
$701$		−	218.409i		−	0.311568i	0.987791	−	0.155784i	$-0.0497904\pi$
$702$	−706.447	−	384.072i	−1.00633	−	0.547112i
$703$	335.464			0.477189
$704$		−	137.462i		−	0.195258i
$705$	−52.2617	+	311.953i	−0.0741301	+	0.442486i
$706$	254.909			0.361061
$707$		−	200.559i		−	0.283675i
$708$	45.4534	+	7.61486i	0.0641998	+	0.0107554i
$709$	1268.22			1.78875			0.894376	−	0.447317i	$-0.147620\pi$
$709$	1268.22			1.78875			0.894376	+	0.447317i	$0.147620\pi$
$710$		−	584.878i		−	0.823771i
$711$	117.295	+	40.4361i	0.164972	+	0.0568722i
$712$	92.9815			0.130592
$713$			1220.19i			1.71134i
$714$	97.7922	−	583.726i	0.136964	−	0.817543i
$715$	3245.44			4.53908
$716$			69.8970i			0.0976215i
$717$	−774.160	−	129.696i	−1.07972	−	0.180887i
$718$	645.799			0.899442
$719$			9.46003i			0.0131572i	0.999978	+	0.00657860i	$0.00209405\pi$
$719$			9.46003i			0.0131572i	−0.999978	+	0.00657860i	$0.997906\pi$
$720$	−105.234	+	305.258i	−0.146158	+	0.423969i
$721$	−1020.05			−1.41477
$722$			336.497i			0.466063i
$723$	26.7612	−	159.739i	0.0370141	−	0.220939i
$724$	−179.611			−0.248081
$725$		−	459.191i		−	0.633368i
$726$	−729.105	−	122.148i	−1.00428	−	0.168248i
$727$	247.572			0.340539			0.170269	−	0.985398i	$-0.445536\pi$
$727$	247.572			0.340539			0.170269	+	0.985398i	$0.445536\pi$
$728$		−	551.229i		−	0.757183i
$729$	−396.369	−	611.827i	−0.543717	−	0.839269i
$730$	−1084.41			−1.48550
$731$		−	925.865i		−	1.26657i
$732$	−5.77555	+	34.4745i	−0.00789010	+	0.0470964i
$733$	−19.4805			−0.0265763			−0.0132882	−	0.999912i	$-0.504230\pi$
$733$	−19.4805			−0.0265763			−0.0132882	+	0.999912i	$0.504230\pi$
$734$		−	571.076i		−	0.778033i
$735$	972.510	+	162.926i	1.32314	+	0.221667i
$736$	220.481			0.299567
$737$		−	1257.97i		−	1.70688i
$738$	−329.599	−	113.625i	−0.446611	−	0.153963i
$739$	−633.173			−0.856798			−0.428399	−	0.903590i	$-0.640922\pi$
$739$	−633.173			−0.856798			−0.428399	+	0.903590i	$0.640922\pi$
$740$		−	542.457i		−	0.733050i
$741$	115.797	−	691.197i	0.156271	−	0.932790i
$742$	190.361			0.256552
$743$		−	872.511i		−	1.17431i	−0.809475	−	0.587154i	$-0.800248\pi$
$743$		−	872.511i		−	1.17431i	0.809475	−	0.587154i	$-0.199752\pi$
$744$	−261.990	−	43.8914i	−0.352137	−	0.0589939i
$745$	−1898.80			−2.54872
$746$		−	461.214i		−	0.618250i
$747$	95.5714	−	277.229i	0.127940	−	0.371124i
$748$	518.025			0.692547
$749$			384.755i			0.513692i
$750$	−191.418	+	1142.58i	−0.255224	+	1.52344i
$751$	−290.059			−0.386231			−0.193115	−	0.981176i	$-0.561859\pi$
$751$	−290.059			−0.386231			−0.193115	+	0.981176i	$0.561859\pi$
$752$			47.0207i			0.0625275i
$753$	642.099	+	107.571i	0.852721	+	0.142857i
$754$	246.650			0.327121
$755$			1120.02i			1.48348i
$756$	238.699	−	439.054i	0.315740	−	0.580759i
$757$	−476.723			−0.629753			−0.314877	−	0.949133i	$-0.601963\pi$
$757$	−476.723			−0.629753			−0.314877	+	0.949133i	$0.601963\pi$
$758$			565.609i			0.746186i
$759$	331.967	−	1981.53i	0.437375	−	2.61071i
$760$	−281.419			−0.370288
$761$			276.469i			0.363297i	0.983364	+	0.181648i	$0.0581433\pi$
$761$			276.469i			0.363297i	−0.983364	+	0.181648i	$0.941857\pi$
$762$	−875.260	−	146.633i	−1.14863	−	0.192432i
$763$	1027.33			1.34644
$764$			599.417i			0.784577i
$765$	−1150.36	−	396.573i	−1.50374	−	0.518396i
$766$	679.832			0.887509
$767$			161.755i			0.210893i
$768$	−7.93096	+	47.3403i	−0.0103268	+	0.0616410i
$769$	1471.81			1.91392			0.956962	−	0.290213i	$-0.0937260\pi$
$769$	1471.81			1.91392			0.956962	+	0.290213i	$0.0937260\pi$
$770$			2017.03i			2.61952i
$771$	−191.954	−	32.1583i	−0.248968	−	0.0417098i
$772$	−360.911			−0.467501
$773$			32.5620i			0.0421241i	0.999778	+	0.0210621i	$0.00670476\pi$
$773$			32.5620i			0.0421241i	−0.999778	+	0.0210621i	$0.993295\pi$
$774$	254.789	−	739.082i	0.329185	−	0.954886i
$775$	−1735.76			−2.23969
$776$		−	251.203i		−	0.323716i
$777$	−138.723	+	828.042i	−0.178536	+	1.06569i
$778$	−775.358			−0.996604
$779$		−	303.859i		−	0.390063i
$780$	−1117.69	−	187.248i	−1.43294	−	0.240061i
$781$	−792.307			−1.01448
$782$			830.883i			1.06251i
$783$	196.456	+	106.807i	0.250902	+	0.136407i
$784$	146.587			0.186973
$785$		−	969.631i		−	1.23520i
$786$	−83.2406	+	496.867i	−0.105904	+	0.632146i
$787$	393.069			0.499453			0.249726	−	0.968316i	$-0.419659\pi$
$787$	393.069			0.499453			0.249726	+	0.968316i	$0.419659\pi$
$788$		−	422.723i		−	0.536451i
$789$	311.524	+	52.1900i	0.394834	+	0.0661470i
$790$	174.859			0.221340
$791$			7.84485i			0.00991763i
$792$	413.519	+	142.555i	0.522120	+	0.179994i
$793$	−122.685			−0.154709
$794$		−	437.183i		−	0.550609i
$795$	64.6641	−	385.983i	0.0813385	−	0.485513i
$796$	747.928			0.939608
$797$			1038.05i			1.30244i	0.758887	+	0.651222i	$0.225743\pi$
$797$			1038.05i			1.30244i	−0.758887	+	0.651222i	$0.774257\pi$
$798$	429.576	+	71.9673i	0.538316	+	0.0901846i
$799$	−177.197			−0.221774
$800$			313.643i			0.392054i
$801$	−96.4269	+	279.711i	−0.120383	+	0.349202i
$802$	−133.216			−0.166105
$803$			1469.00i			1.82940i
$804$	−72.5793	+	433.229i	−0.0902727	+	0.538842i
$805$	−3235.20			−4.01888
$806$		−	932.344i		−	1.15675i
$807$	945.114	+	158.336i	1.17114	+	0.196203i
$808$	−61.2958			−0.0758612
$809$		−	9.99580i		−	0.0123557i	−0.999981	−	0.00617787i	$-0.998034\pi$
$809$		−	9.99580i		−	0.0123557i	0.999981	−	0.00617787i	$-0.00196649\pi$
$810$	−809.156	−	633.138i	−0.998958	−	0.781651i
$811$	−138.464			−0.170732			−0.0853660	−	0.996350i	$-0.527206\pi$
$811$	−138.464			−0.170732			−0.0853660	+	0.996350i	$0.527206\pi$
$812$			153.292i			0.188783i
$813$	68.1487	−	406.783i	0.0838237	−	0.500348i
$814$	−734.842			−0.902754
$815$		−	943.511i		−	1.15768i
$816$	−178.402	−	29.8878i	−0.218629	−	0.0366272i
$817$	681.364			0.833983
$818$			421.501i			0.515282i
$819$	1658.23	+	571.655i	2.02470	+	0.697991i
$820$	−491.351			−0.599208
$821$		−	468.862i		−	0.571087i	−0.958366	−	0.285543i	$-0.907826\pi$
$821$		−	468.862i		−	0.571087i	0.958366	−	0.285543i	$-0.0921741\pi$
$822$	−137.674	+	821.784i	−0.167487	+	0.999737i
$823$	−1124.68			−1.36656			−0.683281	−	0.730156i	$-0.739448\pi$
$823$	−1124.68			−1.36656			−0.683281	+	0.730156i	$0.739448\pi$
$824$			311.754i			0.378342i
$825$	2818.80	+	472.236i	3.41672	+	0.572407i
$826$	−100.530			−0.121707
$827$			13.5524i			0.0163875i	0.999966	+	0.00819373i	$0.00260817\pi$
$827$			13.5524i			0.0163875i	−0.999966	+	0.00819373i	$0.997392\pi$
$828$	−228.651	+	663.261i	−0.276149	+	0.801040i
$829$	−926.205			−1.11726			−0.558628	−	0.829418i	$-0.688672\pi$
$829$	−926.205			−1.11726			−0.558628	+	0.829418i	$0.688672\pi$
$830$		−	413.281i		−	0.497929i
$831$	15.4877	−	92.4466i	0.0186374	−	0.111247i
$832$	−168.470			−0.202488
$833$			552.411i			0.663159i
$834$	19.0430	+	3.19029i	0.0228333	+	0.00382528i
$835$	−305.731			−0.366145
$836$			381.226i			0.456011i
$837$	403.734	−	742.611i	0.482358	−	0.887230i
$838$	−923.209			−1.10168
$839$			1422.04i			1.69492i	0.530858	+	0.847461i	$0.321870\pi$
$839$			1422.04i			1.69492i	−0.530858	+	0.847461i	$0.678130\pi$
$840$	116.374	−	694.640i	0.138540	−	0.826952i
$841$	772.409			0.918441
$842$		−	461.582i		−	0.548197i
$843$	−676.815	−	113.388i	−0.802865	−	0.134505i
$844$	−327.969			−0.388589
$845$		−	2461.75i		−	2.91331i
$846$	−141.450	−	48.7630i	−0.167198	−	0.0576395i
$847$	1612.58			1.90387
$848$		−	58.1793i		−	0.0686077i
$849$	−25.9370	+	154.819i	−0.0305501	+	0.182355i
$850$	−1181.96			−1.39054
$851$		−	1178.65i		−	1.38501i
$852$	272.861	+	45.7127i	0.320260	+	0.0536534i
$853$	−1583.36			−1.85622			−0.928112	−	0.372302i	$-0.878568\pi$
$853$	−1583.36			−1.85622			−0.928112	+	0.372302i	$0.878568\pi$
$854$		−	76.2479i		−	0.0892833i
$855$	291.847	−	846.576i	0.341341	−	0.990148i
$856$	117.591			0.137373
$857$			828.183i			0.966375i	0.875517	+	0.483187i	$0.160521\pi$
$857$			828.183i			0.966375i	−0.875517	+	0.483187i	$0.839479\pi$
$858$	−253.656	+	1514.09i	−0.295637	+	1.76467i
$859$	1024.09			1.19218			0.596092	−	0.802916i	$-0.296719\pi$
$859$	1024.09			1.19218			0.596092	+	0.802916i	$0.296719\pi$
$860$		−	1101.79i		−	1.28115i
$861$	750.030	+	125.653i	0.871115	+	0.145939i
$862$	606.211			0.703261
$863$			1075.84i			1.24663i	0.781972	+	0.623314i	$0.214214\pi$
$863$			1075.84i			1.24663i	−0.781972	+	0.623314i	$0.785786\pi$
$864$	−134.186	−	72.9526i	−0.155308	−	0.0844359i
$865$	867.459			1.00284
$866$		−	889.671i		−	1.02733i
$867$	−30.6210	+	182.778i	−0.0353183	+	0.210816i
$868$	579.448			0.667567
$869$		−	236.873i		−	0.272581i
$870$	310.819	+	52.0718i	0.357263	+	0.0598527i
$871$	−1541.73			−1.77007
$872$		−	313.980i		−	0.360069i
$873$	755.681	+	260.512i	0.865614	+	0.298410i
$874$	−611.465			−0.699616
$875$		−	2527.07i		−	2.88808i
$876$	84.7552	−	505.908i	0.0967525	−	0.577520i
$877$	886.449			1.01077			0.505387	−	0.862893i	$-0.331350\pi$
$877$	886.449			1.01077			0.505387	+	0.862893i	$0.331350\pi$
$878$			116.634i			0.132840i
$879$	−560.584	−	93.9152i	−0.637752	−	0.106843i
$880$	616.455			0.700517
$881$			617.391i			0.700785i	0.936603	+	0.350392i	$0.113952\pi$
$881$			617.391i			0.700785i	−0.936603	+	0.350392i	$0.886048\pi$
$882$	−152.018	+	440.968i	−0.172356	+	0.499964i
$883$	1190.97			1.34878			0.674391	−	0.738374i	$-0.264406\pi$
$883$	1190.97			1.34878			0.674391	+	0.738374i	$0.264406\pi$
$884$		−	634.878i		−	0.718188i
$885$	−34.1492	+	203.838i	−0.0385867	+	0.230326i
$886$	526.830			0.594617
$887$		−	634.814i		−	0.715686i	−0.933782	−	0.357843i	$-0.883512\pi$
$887$		−	634.814i		−	0.715686i	0.933782	−	0.357843i	$-0.116488\pi$
$888$	253.071	+	42.3972i	0.284990	+	0.0477446i
$889$	1935.83			2.17753
$890$			416.980i			0.468517i
$891$	−857.683	+	1096.13i	−0.962607	+	1.23022i
$892$	−671.900			−0.753251
$893$		−	130.403i		−	0.146028i
$894$	148.405	−	885.839i	0.166002	−	0.990871i
$895$	−313.457			−0.350231
$896$		−	104.703i		−	0.116856i
$897$	−2428.51	−	406.850i	−2.70737	−	0.453568i
$898$	−572.731			−0.637785
$899$			259.276i			0.288405i
$900$	−943.514	−	325.265i	−1.04835	−	0.361405i
$901$	219.248			0.243339
$902$			665.611i			0.737927i
$903$	−281.761	+	1681.84i	−0.312028	+	1.86251i
$904$	2.39759			0.00265220
$905$		−	805.474i		−	0.890027i
$906$	−522.521	−	87.5385i	−0.576734	−	0.0966209i
$907$	1216.61			1.34136			0.670678	−	0.741749i	$-0.266003\pi$
$907$	1216.61			1.34136			0.670678	+	0.741749i	$0.266003\pi$
$908$			755.162i			0.831676i
$909$	63.5671	−	184.393i	0.0699308	−	0.202852i
$910$	2472.02			2.71650
$911$		−	323.799i		−	0.355432i	−0.984082	−	0.177716i	$-0.943129\pi$
$911$		−	323.799i		−	0.355432i	0.984082	−	0.177716i	$-0.0568709\pi$
$912$	21.9951	−	131.290i	0.0241174	−	0.143958i
$913$	−559.853			−0.613202
$914$			621.638i			0.680129i
$915$	−154.603	−	25.9008i	−0.168965	−	0.0283068i
$916$	537.947			0.587278
$917$		−	1098.93i		−	1.19840i
$918$	274.922	−	505.680i	0.299479	−	0.550849i
$919$	−261.983			−0.285074			−0.142537	−	0.989789i	$-0.545526\pi$
$919$	−261.983			−0.285074			−0.142537	+	0.989789i	$0.545526\pi$
$920$			988.760i			1.07474i
$921$	133.974	−	799.695i	0.145466	−	0.868290i
$922$	195.111			0.211617
$923$			971.031i			1.05204i
$924$	−940.997	−	157.646i	−1.01840	−	0.170613i
$925$	1676.67			1.81261
$926$			664.531i			0.717636i
$927$	−937.831	−	323.306i	−1.01168	−	0.348765i
$928$	46.8498			0.0504847
$929$			33.3561i			0.0359054i	0.999839	+	0.0179527i	$0.00571482\pi$
$929$			33.3561i			0.0359054i	−0.999839	+	0.0179527i	$0.994285\pi$
$930$	196.833	−	1174.91i	0.211649	−	1.26334i
$931$	−406.531			−0.436661
$932$		−	913.916i		−	0.980597i
$933$	758.196	+	127.021i	0.812643	+	0.136143i
$934$	−411.504			−0.440583
$935$			2323.11i			2.48461i
$936$	174.712	−	506.798i	0.186658	−	0.541451i
$937$	1559.52			1.66437			0.832187	−	0.554495i	$-0.187089\pi$
$937$	1559.52			1.66437			0.832187	+	0.554495i	$0.187089\pi$
$938$		−	958.180i		−	1.02151i
$939$	222.742	−	1329.56i	0.237212	−	1.41593i
$940$	−210.867			−0.224326
$941$			209.615i			0.222757i	0.993778	+	0.111379i	$0.0355266\pi$
$941$			209.615i			0.222757i	−0.993778	+	0.111379i	$0.964473\pi$
$942$	452.359	+	75.7842i	0.480211	+	0.0804503i
$943$	−1067.60			−1.13213
$944$			30.7246i			0.0325472i
$945$	1968.96	+	1070.46i	2.08355	+	1.13276i
$946$	−1492.54			−1.57774
$947$		−	449.642i		−	0.474807i	−0.971411	−	0.237404i	$-0.923704\pi$
$947$		−	449.642i		−	0.474807i	0.971411	−	0.237404i	$-0.0762964\pi$
$948$	−13.6665	+	81.5762i	−0.0144162	+	0.0860509i
$949$	1800.37			1.89713
$950$		−	869.831i		−	0.915612i
$951$	−1499.57	−	251.225i	−1.57684	−	0.264169i
$952$	394.574			0.414468
$953$			792.988i			0.832096i	0.909343	+	0.416048i	$0.136585\pi$
$953$			792.988i			0.832096i	−0.909343	+	0.416048i	$0.863415\pi$
$954$	175.017	+	60.3351i	0.183456	+	0.0632443i
$955$	−2688.12			−2.81478
$956$		−	523.299i		−	0.547384i
$957$	70.5394	−	421.053i	0.0737088	−	0.439971i
$958$	−216.259			−0.225740
$959$		−	1817.55i		−	1.89526i
$960$	−212.300	−	35.5668i	−0.221146	−	0.0370487i
$961$	19.0724			0.0198464
$962$			900.603i			0.936178i
$963$	−121.948	+	353.742i	−0.126634	+	0.367333i
$964$	107.976			0.112009
$965$		−	1618.52i		−	1.67723i
$966$	252.856	−	1509.31i	0.261755	−	1.56243i
$967$	−678.072			−0.701212			−0.350606	−	0.936523i	$-0.614024\pi$
$967$	−678.072			−0.701212			−0.350606	+	0.936523i	$0.614024\pi$
$968$		−	492.844i		−	0.509137i
$969$	494.764	+	82.8883i	0.510592	+	0.0855400i
$970$	1126.53			1.16138
$971$			1536.49i			1.58237i	0.611574	+	0.791187i	$0.290537\pi$
$971$			1536.49i			1.58237i	−0.611574	+	0.791187i	$0.709463\pi$
$972$	358.617	−	328.008i	0.368948	−	0.337457i
$973$	−42.1176			−0.0432864
$974$		−	867.101i		−	0.890248i
$975$	578.760	−	3454.64i	0.593600	−	3.54323i
$976$	−23.3033			−0.0238764
$977$			952.883i			0.975315i	0.873035	+	0.487657i	$0.162148\pi$
$977$			952.883i			0.975315i	−0.873035	+	0.487657i	$0.837852\pi$
$978$	440.173	+	73.7427i	0.450075	+	0.0754015i
$979$	564.864			0.576981
$980$			657.375i			0.670791i
$981$	944.527	+	325.614i	0.962821	+	0.331920i
$982$	−1134.74			−1.15554
$983$			117.064i			0.119088i	0.998226	+	0.0595441i	$0.0189647\pi$
$983$			117.064i			0.119088i	−0.998226	+	0.0595441i	$0.981035\pi$
$984$	38.4028	−	229.228i	0.0390273	−	0.232956i
$985$	1895.72			1.92459
$986$			176.553i			0.179060i
$987$	321.881	+	53.9250i	0.326120	+	0.0546352i
$988$	467.220			0.472895
$989$		−	2393.96i		−	2.42059i
$990$	−639.297	+	1854.45i	−0.645755	+	1.87318i
$991$	−1235.30			−1.24652			−0.623258	−	0.782016i	$-0.714191\pi$
$991$	−1235.30			−1.24652			−0.623258	+	0.782016i	$0.714191\pi$
$992$		−	177.094i		−	0.178522i
$993$	−90.8883	+	542.516i	−0.0915290	+	0.546341i
$994$	−603.492			−0.607134
$995$			3354.12i			3.37097i
$996$	192.807	+	32.3011i	0.193581	+	0.0324308i
$997$	580.760			0.582507			0.291254	−	0.956646i	$-0.405928\pi$
$997$	580.760			0.582507			0.291254	+	0.956646i	$0.405928\pi$
$998$		−	906.792i		−	0.908609i
$999$	−389.989	+	717.330i	−0.390380	+	0.718048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.b.a.119.9	✓	40
3.2	odd	2	inner	354.3.b.a.119.29	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.b.a.119.9	✓	40	1.1	even	1	trivial
354.3.b.a.119.29	yes	40	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	354.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-0.495685 + 2.95877i) q^{3} -2.00000 q^{4} -8.96910i q^{5} +(4.18433 + 0.701004i) q^{6} -9.25455 q^{7} +2.82843i q^{8} +(-8.50859 - 2.93323i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-0.495685 + 2.95877i) q^{3} -2.00000 q^{4} -8.96910i q^{5} +(4.18433 + 0.701004i) q^{6} -9.25455 q^{7} +2.82843i q^{8} +(-8.50859 - 2.93323i) q^{9} -12.6842 q^{10} +17.1827i q^{11} +(0.991370 - 5.91753i) q^{12} +21.0587 q^{13} +13.0879i q^{14} +(26.5375 + 4.44585i) q^{15} +4.00000 q^{16} +15.0740i q^{17} +(-4.14822 + 12.0330i) q^{18} -11.0933 q^{19} +17.9382i q^{20} +(4.58734 - 27.3820i) q^{21} +24.3001 q^{22} +38.9760i q^{23} +(-8.36865 - 1.40201i) q^{24} -55.4448 q^{25} -29.7815i q^{26} +(12.8963 - 23.7210i) q^{27} +18.5091 q^{28} +8.28196i q^{29} +(6.28738 - 37.5297i) q^{30} +31.3061 q^{31} -5.65685i q^{32} +(-50.8397 - 8.51723i) q^{33} +21.3178 q^{34} +83.0050i q^{35} +(17.0172 + 5.86646i) q^{36} -30.2403 q^{37} +15.6882i q^{38} +(-10.4385 + 62.3078i) q^{39} +25.3684 q^{40} +27.3913i q^{41} +(-38.7241 - 6.48748i) q^{42} -61.4214 q^{43} -34.3655i q^{44} +(-26.3085 + 76.3144i) q^{45} +55.1203 q^{46} +11.7552i q^{47} +(-1.98274 + 11.8351i) q^{48} +36.6467 q^{49} +78.4108i q^{50} +(-44.6004 - 7.47195i) q^{51} -42.1175 q^{52} -14.5448i q^{53} +(-33.5465 - 18.2382i) q^{54} +154.114 q^{55} -26.1758i q^{56} +(5.49877 - 32.8224i) q^{57} +11.7125 q^{58} +7.68115i q^{59} +(-53.0749 - 8.89170i) q^{60} -5.82583 q^{61} -44.2735i q^{62} +(78.7432 + 27.1457i) q^{63} -8.00000 q^{64} -188.878i q^{65} +(-12.0452 + 71.8982i) q^{66} -73.2111 q^{67} -30.1480i q^{68} +(-115.321 - 19.3198i) q^{69} +117.387 q^{70} +46.1106i q^{71} +(8.29643 - 24.0659i) q^{72} +85.4930 q^{73} +42.7663i q^{74} +(27.4831 - 164.048i) q^{75} +22.1865 q^{76} -159.019i q^{77} +(88.1166 + 14.7623i) q^{78} -13.7855 q^{79} -35.8764i q^{80} +(63.7923 + 49.9154i) q^{81} +38.7371 q^{82} +32.5823i q^{83} +(-9.17468 + 54.7641i) q^{84} +135.200 q^{85} +86.8630i q^{86} +(-24.5044 - 4.10524i) q^{87} -48.6001 q^{88} -32.8739i q^{89} +(107.925 + 37.2058i) q^{90} -194.889 q^{91} -77.9519i q^{92} +(-15.5180 + 92.6275i) q^{93} +16.6243 q^{94} +99.4966i q^{95} +(16.7373 + 2.80402i) q^{96} -88.8138 q^{97} -51.8262i q^{98} +(50.4010 - 146.201i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9}+O(q^{10}) \) 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9	\( 40 q - 80 q^{4} + 8 q^{6} + 8 q^{7} - 24 q^{9} - 16 q^{10} + 34 q^{15} + 160 q^{16} + 16 q^{18} + 24 q^{19} - 18 q^{21} - 16 q^{22} - 16 q^{24} - 216 q^{25} - 30 q^{27} - 16 q^{28} - 64 q^{30} + 96 q^{31} + 76 q^{33} + 80 q^{34} + 48 q^{36} - 200 q^{37} - 28 q^{39} + 32 q^{40} + 48 q^{42} - 104 q^{43} + 58 q^{45} + 32 q^{46} + 288 q^{49} - 176 q^{51} - 40 q^{54} + 360 q^{55} + 214 q^{57} - 128 q^{58} - 68 q^{60} - 32 q^{61} - 132 q^{63} - 320 q^{64} - 112 q^{66} - 344 q^{67} + 88 q^{69} + 192 q^{70} - 32 q^{72} + 40 q^{73} + 28 q^{75} - 48 q^{76} + 96 q^{78} + 32 q^{79} + 336 q^{81} - 80 q^{82} + 36 q^{84} + 168 q^{85} - 162 q^{87} + 32 q^{88} + 112 q^{90} + 88 q^{91} - 316 q^{93} - 400 q^{94} + 32 q^{96} - 184 q^{97} - 148 q^{99}+O(q^{100}) \) 40 * q - 80 * q^4 + 8 * q^6 + 8 * q^7 - 24 * q^9 - 16 * q^10 + 34 * q^15 + 160 * q^16 + 16 * q^18 + 24 * q^19 - 18 * q^21 - 16 * q^22 - 16 * q^24 - 216 * q^25 - 30 * q^27 - 16 * q^28 - 64 * q^30 + 96 * q^31 + 76 * q^33 + 80 * q^34 + 48 * q^36 - 200 * q^37 - 28 * q^39 + 32 * q^40 + 48 * q^42 - 104 * q^43 + 58 * q^45 + 32 * q^46 + 288 * q^49 - 176 * q^51 - 40 * q^54 + 360 * q^55 + 214 * q^57 - 128 * q^58 - 68 * q^60 - 32 * q^61 - 132 * q^63 - 320 * q^64 - 112 * q^66 - 344 * q^67 + 88 * q^69 + 192 * q^70 - 32 * q^72 + 40 * q^73 + 28 * q^75 - 48 * q^76 + 96 * q^78 + 32 * q^79 + 336 * q^81 - 80 * q^82 + 36 * q^84 + 168 * q^85 - 162 * q^87 + 32 * q^88 + 112 * q^90 + 88 * q^91 - 316 * q^93 - 400 * q^94 + 32 * q^96 - 184 * q^97 - 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more