LMFDB - Embedded newform 354.3.b.a.119.28

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			119.28
Character	$\chi$	$=$	354.119
Dual form			354.3.b.a.119.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(-0.865873 + 2.87233i) q^{3} -2.00000 q^{4} -4.52476i q^{5} +(-4.06208 - 1.22453i) q^{6} +8.90636 q^{7} -2.82843i q^{8} +(-7.50053 - 4.97414i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(-0.865873 + 2.87233i) q^{3} -2.00000 q^{4} -4.52476i q^{5} +(-4.06208 - 1.22453i) q^{6} +8.90636 q^{7} -2.82843i q^{8} +(-7.50053 - 4.97414i) q^{9} +6.39898 q^{10} -1.10489i q^{11} +(1.73175 - 5.74465i) q^{12} +23.9421 q^{13} +12.5955i q^{14} +(12.9966 + 3.91787i) q^{15} +4.00000 q^{16} +11.7724i q^{17} +(7.03450 - 10.6073i) q^{18} +5.12651 q^{19} +9.04953i q^{20} +(-7.71177 + 25.5820i) q^{21} +1.56255 q^{22} -14.0933i q^{23} +(8.12417 + 2.44906i) q^{24} +4.52652 q^{25} +33.8593i q^{26} +(20.7819 - 17.2370i) q^{27} -17.8127 q^{28} +22.9443i q^{29} +(-5.54070 + 18.3800i) q^{30} -29.7208 q^{31} +5.65685i q^{32} +(3.17360 + 0.956692i) q^{33} -16.6487 q^{34} -40.2992i q^{35} +(15.0011 + 9.94828i) q^{36} +16.3944 q^{37} +7.24998i q^{38} +(-20.7309 + 68.7697i) q^{39} -12.7980 q^{40} +58.0345i q^{41} +(-36.1784 - 10.9061i) q^{42} +28.7493 q^{43} +2.20977i q^{44} +(-22.5068 + 33.9381i) q^{45} +19.9309 q^{46} -44.5446i q^{47} +(-3.46349 + 11.4893i) q^{48} +30.3232 q^{49} +6.40146i q^{50} +(-33.8143 - 10.1934i) q^{51} -47.8843 q^{52} +39.7777i q^{53} +(24.3768 + 29.3900i) q^{54} -4.99935 q^{55} -25.1910i q^{56} +(-4.43891 + 14.7250i) q^{57} -32.4482 q^{58} -7.68115i q^{59} +(-25.9932 - 7.83574i) q^{60} -45.3879 q^{61} -42.0316i q^{62} +(-66.8024 - 44.3015i) q^{63} -8.00000 q^{64} -108.333i q^{65} +(-1.35297 + 4.48814i) q^{66} +42.1993 q^{67} -23.5449i q^{68} +(40.4805 + 12.2030i) q^{69} +56.9916 q^{70} -30.8163i q^{71} +(-14.0690 + 21.2147i) q^{72} +110.375 q^{73} +23.1852i q^{74} +(-3.91939 + 13.0016i) q^{75} -10.2530 q^{76} -9.84052i q^{77} +(-97.2550 - 29.3179i) q^{78} +97.0474 q^{79} -18.0991i q^{80} +(31.5159 + 74.6174i) q^{81} -82.0731 q^{82} +13.1808i q^{83} +(15.4235 - 51.1639i) q^{84} +53.2675 q^{85} +40.6577i q^{86} +(-65.9037 - 19.8669i) q^{87} -3.12509 q^{88} -7.50619i q^{89} +(-47.9957 - 31.8294i) q^{90} +213.237 q^{91} +28.1865i q^{92} +(25.7345 - 85.3680i) q^{93} +62.9955 q^{94} -23.1962i q^{95} +(-16.2483 - 4.89812i) q^{96} +129.189 q^{97} +42.8834i q^{98} +(-5.49586 + 8.28724i) 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
$3$	−0.865873	+	2.87233i	−0.288624	+	0.957442i
$3$	−0.865873	+	2.87233i	−0.288624	+	0.957442i
$4$	−2.00000			−0.500000
$5$		−	4.52476i		−	0.904953i	−0.891776	−	0.452476i	$-0.850541\pi$
$5$		−	4.52476i		−	0.904953i	0.891776	−	0.452476i	$-0.149459\pi$
$6$	−4.06208	−	1.22453i	−0.677014	−	0.204088i
$7$	8.90636			1.27234			0.636168	−	0.771550i	$-0.280518\pi$
$7$	8.90636			1.27234			0.636168	+	0.771550i	$0.280518\pi$
$8$		−	2.82843i		−	0.353553i
$9$	−7.50053	−	4.97414i	−0.833392	−	0.552682i
$10$	6.39898			0.639898
$11$		−	1.10489i		−	0.100444i	−0.998738	−	0.0502221i	$-0.984007\pi$
$11$		−	1.10489i		−	0.100444i	0.998738	−	0.0502221i	$-0.0159929\pi$
$12$	1.73175	−	5.74465i	0.144312	−	0.478721i
$13$	23.9421			1.84170			0.920852	−	0.389913i	$-0.127495\pi$
$13$	23.9421			1.84170			0.920852	+	0.389913i	$0.127495\pi$
$14$			12.5955i			0.899678i
$15$	12.9966	+	3.91787i	0.866440	+	0.261191i
$16$	4.00000			0.250000
$17$			11.7724i			0.692497i	0.938143	+	0.346248i	$0.112545\pi$
$17$			11.7724i			0.692497i	−0.938143	+	0.346248i	$0.887455\pi$
$18$	7.03450	−	10.6073i	0.390805	−	0.589297i
$19$	5.12651			0.269816			0.134908	−	0.990858i	$-0.456926\pi$
$19$	5.12651			0.269816			0.134908	+	0.990858i	$0.456926\pi$
$20$			9.04953i			0.452476i
$21$	−7.71177	+	25.5820i	−0.367227	+	1.21819i
$22$	1.56255			0.0710248
$23$		−	14.0933i		−	0.612751i	−0.951911	−	0.306375i	$-0.900884\pi$
$23$		−	14.0933i		−	0.612751i	0.951911	−	0.306375i	$-0.0991162\pi$
$24$	8.12417	+	2.44906i	0.338507	+	0.102044i
$25$	4.52652			0.181061
$26$			33.8593i			1.30228i
$27$	20.7819	−	17.2370i	0.769699	−	0.638407i
$28$	−17.8127			−0.636168
$29$			22.9443i			0.791184i	0.918426	+	0.395592i	$0.129461\pi$
$29$			22.9443i			0.791184i	−0.918426	+	0.395592i	$0.870539\pi$
$30$	−5.54070	+	18.3800i	−0.184690	+	0.612666i
$31$	−29.7208			−0.958737			−0.479368	−	0.877614i	$-0.659134\pi$
$31$	−29.7208			−0.958737			−0.479368	+	0.877614i	$0.659134\pi$
$32$			5.65685i			0.176777i
$33$	3.17360	+	0.956692i	0.0961696	+	0.0289907i
$34$	−16.6487			−0.489669
$35$		−	40.2992i		−	1.15140i
$36$	15.0011	+	9.94828i	0.416696	+	0.276341i
$37$	16.3944			0.443092			0.221546	−	0.975150i	$-0.428890\pi$
$37$	16.3944			0.443092			0.221546	+	0.975150i	$0.428890\pi$
$38$			7.24998i			0.190789i
$39$	−20.7309	+	68.7697i	−0.531560	+	1.76332i
$40$	−12.7980			−0.319949
$41$			58.0345i			1.41547i	0.706476	+	0.707737i	$0.250284\pi$
$41$			58.0345i			1.41547i	−0.706476	+	0.707737i	$0.749716\pi$
$42$	−36.1784	−	10.9061i	−0.861390	−	0.259669i
$43$	28.7493			0.668589			0.334295	−	0.942469i	$-0.391502\pi$
$43$	28.7493			0.668589			0.334295	+	0.942469i	$0.391502\pi$
$44$			2.20977i			0.0502221i
$45$	−22.5068	+	33.9381i	−0.500151	+	0.754180i
$46$	19.9309			0.433280
$47$		−	44.5446i		−	0.947757i	−0.880590	−	0.473878i	$-0.842854\pi$
$47$		−	44.5446i		−	0.947757i	0.880590	−	0.473878i	$-0.157146\pi$
$48$	−3.46349	+	11.4893i	−0.0721561	+	0.239361i
$49$	30.3232			0.618840
$50$			6.40146i			0.128029i
$51$	−33.8143	−	10.1934i	−0.663026	−	0.199871i
$52$	−47.8843			−0.920852
$53$			39.7777i			0.750522i	0.926919	+	0.375261i	$0.122447\pi$
$53$			39.7777i			0.750522i	−0.926919	+	0.375261i	$0.877553\pi$
$54$	24.3768	+	29.3900i	0.451422	+	0.544259i
$55$	−4.99935			−0.0908973
$56$		−	25.1910i		−	0.449839i
$57$	−4.43891	+	14.7250i	−0.0778755	+	0.258334i
$58$	−32.4482			−0.559452
$59$		−	7.68115i		−	0.130189i
$59$		−	7.68115i		−	0.130189i
$60$	−25.9932	−	7.83574i	−0.433220	−	0.130596i
$61$	−45.3879			−0.744064			−0.372032	−	0.928220i	$-0.621339\pi$
$61$	−45.3879			−0.744064			−0.372032	+	0.928220i	$0.621339\pi$
$62$		−	42.0316i		−	0.677929i
$63$	−66.8024	−	44.3015i	−1.06036	−	0.703198i
$64$	−8.00000			−0.125000
$65$		−	108.333i		−	1.66665i
$66$	−1.35297	+	4.48814i	−0.0204995	+	0.0680022i
$67$	42.1993			0.629840			0.314920	−	0.949118i	$-0.398022\pi$
$67$	42.1993			0.629840			0.314920	+	0.949118i	$0.398022\pi$
$68$		−	23.5449i		−	0.346248i
$69$	40.4805	+	12.2030i	0.586673	+	0.176855i
$70$	56.9916			0.814166
$71$		−	30.8163i		−	0.434033i	−0.976168	−	0.217016i	$-0.930367\pi$
$71$		−	30.8163i		−	0.434033i	0.976168	−	0.217016i	$-0.0696325\pi$
$72$	−14.0690	+	21.2147i	−0.195403	+	0.294649i
$73$	110.375			1.51198			0.755990	−	0.654583i	$-0.227156\pi$
$73$	110.375			1.51198			0.755990	+	0.654583i	$0.227156\pi$
$74$			23.1852i			0.313313i
$75$	−3.91939	+	13.0016i	−0.0522585	+	0.173355i
$76$	−10.2530			−0.134908
$77$		−	9.84052i		−	0.127799i
$78$	−97.2550	−	29.3179i	−1.24686	−	0.375870i
$79$	97.0474			1.22845			0.614224	−	0.789132i	$-0.289469\pi$
$79$	97.0474			1.22845			0.614224	+	0.789132i	$0.289469\pi$
$80$		−	18.0991i		−	0.226238i
$81$	31.5159	+	74.6174i	0.389085	+	0.921202i
$82$	−82.0731			−1.00089
$83$			13.1808i			0.158805i	0.996843	+	0.0794024i	$0.0253012\pi$
$83$			13.1808i			0.158805i	−0.996843	+	0.0794024i	$0.974699\pi$
$84$	15.4235	−	51.1639i	0.183614	−	0.609095i
$85$	53.2675			0.626677
$86$			40.6577i			0.472764i
$87$	−65.9037	−	19.8669i	−0.757513	−	0.228355i
$88$	−3.12509			−0.0355124
$89$		−	7.50619i		−	0.0843392i	−0.999110	−	0.0421696i	$-0.986573\pi$
$89$		−	7.50619i		−	0.0843392i	0.999110	−	0.0421696i	$-0.0134270\pi$
$90$	−47.9957	−	31.8294i	−0.533286	−	0.353660i
$91$	213.237			2.34327
$92$			28.1865i			0.306375i
$93$	25.7345	−	85.3680i	0.276715	−	0.917935i
$94$	62.9955			0.670165
$95$		−	23.1962i		−	0.244171i
$96$	−16.2483	−	4.89812i	−0.169254	−	0.0510220i
$97$	129.189			1.33185			0.665923	−	0.746021i	$-0.268038\pi$
$97$	129.189			1.33185			0.665923	+	0.746021i	$0.268038\pi$
$98$			42.8834i			0.437586i
$99$	−5.49586	+	8.28724i	−0.0555138	+	0.0837095i
$100$	−9.05303			−0.0905303
$101$		−	88.0606i		−	0.871887i	−0.899974	−	0.435943i	$-0.856415\pi$
$101$		−	88.0606i		−	0.871887i	0.899974	−	0.435943i	$-0.143585\pi$
$102$	14.4157	−	47.8207i	0.141330	−	0.468830i
$103$	−145.752			−1.41506			−0.707532	−	0.706681i	$-0.750192\pi$
$103$	−145.752			−1.41506			−0.707532	+	0.706681i	$0.750192\pi$
$104$		−	67.7186i		−	0.651140i
$105$	115.752	+	34.8939i	1.10240	+	0.332323i
$106$	−56.2541			−0.530699
$107$			7.92447i			0.0740605i	0.999314	+	0.0370302i	$0.0117898\pi$
$107$			7.92447i			0.0740605i	−0.999314	+	0.0370302i	$0.988210\pi$
$108$	−41.5637	+	34.4740i	−0.384849	+	0.319204i
$109$	−112.649			−1.03348			−0.516741	−	0.856142i	$-0.672855\pi$
$109$	−112.649			−1.03348			−0.516741	+	0.856142i	$0.672855\pi$
$110$		−	7.07015i		−	0.0642741i
$111$	−14.1955	+	47.0901i	−0.127887	+	0.424235i
$112$	35.6254			0.318084
$113$			45.7251i			0.404647i	0.979319	+	0.202323i	$0.0648492\pi$
$113$			45.7251i			0.404647i	−0.979319	+	0.202323i	$0.935151\pi$
$114$	−20.8243	−	6.27756i	−0.182669	−	0.0550663i
$115$	−63.7687			−0.554510
$116$		−	45.8887i		−	0.395592i
$117$	−179.579	−	119.092i	−1.53486	−	1.01788i
$118$	10.8628			0.0920575
$119$			104.850i			0.881089i
$120$	11.0814	−	36.7599i	0.0923451	−	0.306333i
$121$	119.779			0.989911
$122$		−	64.1882i		−	0.526132i
$123$	−166.694	−	50.2505i	−1.35524	−	0.408540i
$124$	59.4417			0.479368
$125$		−	133.600i		−	1.06880i
$126$	62.6517	−	94.4728i	0.497236	−	0.749784i
$127$	−129.867			−1.02257			−0.511286	−	0.859411i	$-0.670831\pi$
$127$	−129.867			−1.02257			−0.511286	+	0.859411i	$0.670831\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	−24.8933	+	82.5775i	−0.192971	+	0.640136i
$130$	153.205			1.17850
$131$		−	225.703i		−	1.72293i	−0.507821	−	0.861463i	$-0.669549\pi$
$131$		−	225.703i		−	1.72293i	0.507821	−	0.861463i	$-0.330451\pi$
$132$	−6.34719	−	1.91338i	−0.0480848	−	0.0144953i
$133$	45.6585			0.343297
$134$			59.6788i			0.445364i
$135$	−77.9933	−	94.0330i	−0.577728	−	0.696541i
$136$	33.2975			0.244835
$137$		−	180.893i		−	1.32039i	−0.751096	−	0.660193i	$-0.770474\pi$
$137$		−	180.893i		−	1.32039i	0.751096	−	0.660193i	$-0.229526\pi$
$138$	−17.2576	+	57.2480i	−0.125055	+	0.414841i
$139$	−212.098			−1.52589			−0.762943	−	0.646466i	$-0.776246\pi$
$139$	−212.098			−1.52589			−0.762943	+	0.646466i	$0.776246\pi$
$140$			80.5983i			0.575702i
$141$	127.947	+	38.5699i	0.907423	+	0.273546i
$142$	43.5809			0.306908
$143$		−	26.4534i		−	0.184989i
$144$	−30.0021	−	19.8966i	−0.208348	−	0.138171i
$145$	103.818			0.715984
$146$			156.093i			1.06913i
$147$	−26.2560	+	87.0981i	−0.178612	+	0.592504i
$148$	−32.7888			−0.221546
$149$			273.192i			1.83351i	0.399454	+	0.916753i	$0.369200\pi$
$149$			273.192i			1.83351i	−0.399454	+	0.916753i	$0.630800\pi$
$150$	−18.3871	−	5.54285i	−0.122581	−	0.0369523i
$151$	−106.728			−0.706806			−0.353403	−	0.935471i	$-0.614975\pi$
$151$	−106.728			−0.706806			−0.353403	+	0.935471i	$0.614975\pi$
$152$		−	14.5000i		−	0.0953945i
$153$	58.5578	−	88.2995i	0.382731	−	0.577121i
$154$	13.9166			0.0903675
$155$			134.480i			0.867611i
$156$	41.4617	−	137.539i	0.265780	−	0.881662i
$157$	−152.871			−0.973700			−0.486850	−	0.873486i	$-0.661854\pi$
$157$	−152.871			−0.973700			−0.486850	+	0.873486i	$0.661854\pi$
$158$			137.246i			0.868644i
$159$	−114.255	−	34.4424i	−0.718582	−	0.216619i
$160$	25.5959			0.159975
$161$		−	125.520i		−	0.779625i
$162$	−105.525	+	44.5701i	−0.651388	+	0.275124i
$163$	−46.3251			−0.284203			−0.142102	−	0.989852i	$-0.545386\pi$
$163$	−46.3251			−0.284203			−0.142102	+	0.989852i	$0.545386\pi$
$164$		−	116.069i		−	0.707737i
$165$	4.32880	−	14.3598i	0.0262352	−	0.0870289i
$166$	−18.6405			−0.112292
$167$			100.202i			0.600014i	0.953937	+	0.300007i	$0.0969891\pi$
$167$			100.202i			0.600014i	−0.953937	+	0.300007i	$0.903011\pi$
$168$	72.3567	+	21.8122i	0.430695	+	0.129834i
$169$	404.226			2.39187
$170$			75.3317i			0.443127i
$171$	−38.4515	−	25.5000i	−0.224863	−	0.149123i
$172$	−57.4987			−0.334295
$173$		−	46.9258i		−	0.271247i	−0.990760	−	0.135624i	$-0.956696\pi$
$173$		−	46.9258i		−	0.271247i	0.990760	−	0.135624i	$-0.0433038\pi$
$174$	28.0960	−	93.2019i	0.161471	−	0.535643i
$175$	40.3148			0.230370
$176$		−	4.41955i		−	0.0251111i
$177$	22.0628	+	6.65090i	0.124648	+	0.0375757i
$178$	10.6153			0.0596368
$179$			241.495i			1.34914i	0.738213	+	0.674568i	$0.235670\pi$
$179$			241.495i			1.34914i	−0.738213	+	0.674568i	$0.764330\pi$
$180$	45.0136	−	67.8762i	0.250076	−	0.377090i
$181$	−148.250			−0.819061			−0.409530	−	0.912296i	$-0.634307\pi$
$181$	−148.250			−0.819061			−0.409530	+	0.912296i	$0.634307\pi$
$182$			301.563i			1.65694i
$183$	39.3001	−	130.369i	0.214755	−	0.712398i
$184$	−39.8618			−0.216640
$185$		−	74.1807i		−	0.400977i
$186$	120.729	+	36.3940i	0.649078	+	0.195667i
$187$	13.0072			0.0695573
$188$			89.0891i			0.473878i
$189$	185.091	−	153.519i	0.979316	−	0.812269i
$190$	32.8044			0.172655
$191$		−	283.386i		−	1.48370i	−0.670568	−	0.741848i	$-0.733949\pi$
$191$		−	283.386i		−	1.48370i	0.670568	−	0.741848i	$-0.266051\pi$
$192$	6.92698	−	22.9786i	0.0360780	−	0.119680i
$193$	−313.424			−1.62396			−0.811978	−	0.583688i	$-0.801609\pi$
$193$	−313.424			−1.62396			−0.811978	+	0.583688i	$0.801609\pi$
$194$			182.701i			0.941757i
$195$	311.166	+	93.8022i	1.59573	+	0.481037i
$196$	−60.6464			−0.309420
$197$		−	288.670i		−	1.46533i	−0.680590	−	0.732664i	$-0.738277\pi$
$197$		−	288.670i		−	1.46533i	0.680590	−	0.732664i	$-0.261723\pi$
$198$	−11.7199	−	7.77232i	−0.0591915	−	0.0392542i
$199$	−51.6780			−0.259689			−0.129844	−	0.991534i	$-0.541448\pi$
$199$	−51.6780			−0.259689			−0.129844	+	0.991534i	$0.541448\pi$
$200$		−	12.8029i		−	0.0640146i
$201$	−36.5392	+	121.210i	−0.181787	+	0.603035i
$202$	124.536			0.616517
$203$			204.350i			1.00665i
$204$	67.6286	+	20.3869i	0.331513	+	0.0999357i
$205$	262.592			1.28094
$206$		−	206.124i		−	1.00060i
$207$	−70.1019	+	105.707i	−0.338656	+	0.510661i
$208$	95.7686			0.460426
$209$		−	5.66421i		−	0.0271015i
$210$	−49.3475	+	163.699i	−0.234988	+	0.779517i
$211$	−189.571			−0.898440			−0.449220	−	0.893421i	$-0.648298\pi$
$211$	−189.571			−0.898440			−0.449220	+	0.893421i	$0.648298\pi$
$212$		−	79.5554i		−	0.375261i
$213$	88.5146	+	26.6830i	0.415561	+	0.125272i
$214$	−11.2069			−0.0523687
$215$		−	130.084i		−	0.605042i
$216$	−48.7536	−	58.7800i	−0.225711	−	0.272130i
$217$	−264.704			−1.21984
$218$		−	159.310i		−	0.730781i
$219$	−95.5703	+	317.032i	−0.436394	+	1.44763i
$220$	9.99870			0.0454487
$221$			281.858i			1.27537i
$222$	−66.5954	−	20.0754i	−0.299979	−	0.0904298i
$223$	263.998			1.18385			0.591923	−	0.805994i	$-0.298369\pi$
$223$	263.998			1.18385			0.591923	+	0.805994i	$0.298369\pi$
$224$			50.3820i			0.224919i
$225$	−33.9513	−	22.5155i	−0.150894	−	0.100069i
$226$	−64.6650			−0.286128
$227$			87.2376i			0.384307i	0.981365	+	0.192153i	$0.0615471\pi$
$227$			87.2376i			0.384307i	−0.981365	+	0.192153i	$0.938453\pi$
$228$	8.87781	−	29.4500i	0.0389378	−	0.129167i
$229$	−398.278			−1.73920			−0.869602	−	0.493753i	$-0.835625\pi$
$229$	−398.278			−1.73920			−0.869602	+	0.493753i	$0.835625\pi$
$230$		−	90.1825i		−	0.392098i
$231$	28.2652	+	8.52064i	0.122360	+	0.0368859i
$232$	64.8964			0.279726
$233$			73.7137i			0.316368i	0.987410	+	0.158184i	$0.0505639\pi$
$233$			73.7137i			0.316368i	−0.987410	+	0.158184i	$0.949436\pi$
$234$	168.421	−	253.963i	0.719748	−	1.08531i
$235$	−201.554			−0.857675
$236$			15.3623i			0.0650945i
$237$	−84.0307	+	278.752i	−0.354560	+	1.17617i
$238$	−148.280			−0.623024
$239$			331.596i			1.38743i	0.720248	+	0.693716i	$0.244028\pi$
$239$			331.596i			1.38743i	−0.720248	+	0.693716i	$0.755972\pi$
$240$	51.9864	+	15.6715i	0.216610	+	0.0652978i
$241$	−126.990			−0.526930			−0.263465	−	0.964669i	$-0.584865\pi$
$241$	−126.990			−0.526930			−0.263465	+	0.964669i	$0.584865\pi$
$242$			169.393i			0.699973i
$243$	−241.614	+	25.9147i	−0.994297	+	0.106645i
$244$	90.7758			0.372032
$245$		−	137.205i		−	0.560021i
$246$	71.0649	−	235.741i	0.288882	−	0.958296i
$247$	122.740			0.496922
$248$			84.0632i			0.338965i
$249$	−37.8595	−	11.4129i	−0.152046	−	0.0458349i
$250$	188.940			0.755759
$251$		−	33.1290i		−	0.131988i	−0.997820	−	0.0659940i	$-0.978978\pi$
$251$		−	33.1290i		−	0.131988i	0.997820	−	0.0659940i	$-0.0210218\pi$
$252$	133.605	+	88.6029i	0.530178	+	0.351599i
$253$	−15.5715			−0.0615473
$254$		−	183.659i		−	0.723067i
$255$	−46.1229	+	153.002i	−0.180874	+	0.600007i
$256$	16.0000			0.0625000
$257$			434.332i			1.69001i	0.534761	+	0.845004i	$0.320402\pi$
$257$			434.332i			1.69001i	−0.534761	+	0.845004i	$0.679598\pi$
$258$	−116.782	−	35.2044i	−0.452644	−	0.136451i
$259$	146.014			0.563762
$260$			216.665i			0.833327i
$261$	114.128	−	172.095i	0.437274	−	0.659367i
$262$	319.193			1.21829
$263$		−	18.2159i		−	0.0692621i	−0.999400	−	0.0346311i	$-0.988974\pi$
$263$		−	18.2159i		−	0.0692621i	0.999400	−	0.0346311i	$-0.0110256\pi$
$264$	2.70593	−	8.97629i	0.0102497	−	0.0340011i
$265$	179.985			0.679187
$266$			64.5709i			0.242748i
$267$	21.5602	+	6.49940i	0.0807499	+	0.0243423i
$268$	−84.3985			−0.314920
$269$			212.950i			0.791637i	0.918329	+	0.395818i	$0.129539\pi$
$269$			212.950i			0.791637i	−0.918329	+	0.395818i	$0.870461\pi$
$270$	132.983	−	110.299i	0.492529	−	0.408516i
$271$	121.133			0.446985			0.223493	−	0.974706i	$-0.428254\pi$
$271$	121.133			0.446985			0.223493	+	0.974706i	$0.428254\pi$
$272$			47.0898i			0.173124i
$273$	−184.636	+	612.487i	−0.676324	+	2.24354i
$274$	255.821			0.933654
$275$		−	5.00129i		−	0.0181865i
$276$	−80.9609	−	24.4059i	−0.293337	−	0.0884273i
$277$	−381.641			−1.37776			−0.688882	−	0.724873i	$-0.741898\pi$
$277$	−381.641			−1.37776			−0.688882	+	0.724873i	$0.741898\pi$
$278$		−	299.952i		−	1.07896i
$279$	222.922	+	147.836i	0.799003	+	0.529877i
$280$	−113.983			−0.407083
$281$		−	472.120i		−	1.68014i	−0.542476	−	0.840071i	$-0.682513\pi$
$281$		−	472.120i		−	1.68014i	0.542476	−	0.840071i	$-0.317487\pi$
$282$	−54.5461	+	180.944i	−0.193426	+	0.641645i
$283$	217.931			0.770074			0.385037	−	0.922901i	$-0.374189\pi$
$283$	217.931			0.770074			0.385037	+	0.922901i	$0.374189\pi$
$284$			61.6327i			0.217016i
$285$	66.6272	+	20.0850i	0.233780	+	0.0704737i
$286$	37.4107			0.130807
$287$			516.876i			1.80096i
$288$	28.1380	−	42.4294i	0.0977013	−	0.147324i
$289$	150.410			0.520448
$290$			146.820i			0.506277i
$291$	−111.861	+	371.073i	−0.384403	+	1.27517i
$292$	−220.749			−0.755990
$293$			54.0973i			0.184632i	0.995730	+	0.0923162i	$0.0294271\pi$
$293$			54.0973i			0.184632i	−0.995730	+	0.0923162i	$0.970573\pi$
$294$	−123.175	−	37.1316i	−0.418964	−	0.126298i
$295$	−34.7554			−0.117815
$296$		−	46.3703i		−	0.156657i
$297$	−19.0449	−	22.9616i	−0.0641244	−	0.0773118i
$298$	−386.352			−1.29648
$299$		−	337.423i		−	1.12850i
$300$	7.83877	−	26.0033i	0.0261292	−	0.0866776i
$301$	256.052			0.850671
$302$		−	150.936i		−	0.499787i
$303$	252.939	+	76.2493i	0.834781	+	0.251648i
$304$	20.5060			0.0674541
$305$			205.369i			0.673342i
$306$	124.874	+	82.8132i	0.408086	+	0.270631i
$307$	−232.178			−0.756281			−0.378141	−	0.925748i	$-0.623436\pi$
$307$	−232.178			−0.756281			−0.378141	+	0.925748i	$0.623436\pi$
$308$			19.6810i			0.0638995i
$309$	126.202	−	418.646i	0.408422	−	1.35484i
$310$	−190.183			−0.613494
$311$		−	260.332i		−	0.837080i	−0.908198	−	0.418540i	$-0.862542\pi$
$311$		−	260.332i		−	0.837080i	0.908198	−	0.418540i	$-0.137458\pi$
$312$	194.510	+	58.6357i	0.623429	+	0.187935i
$313$	588.905			1.88149			0.940743	−	0.339119i	$-0.110129\pi$
$313$	588.905			1.88149			0.940743	+	0.339119i	$0.110129\pi$
$314$		−	216.192i		−	0.688510i
$315$	−200.454	+	302.265i	−0.636361	+	0.959571i
$316$	−194.095			−0.614224
$317$		−	452.174i		−	1.42642i	−0.700952	−	0.713209i	$-0.747241\pi$
$317$		−	452.174i		−	1.42642i	0.700952	−	0.713209i	$-0.252759\pi$
$318$	48.7089	−	161.580i	0.153173	−	0.508114i
$319$	25.3509			0.0794699
$320$			36.1981i			0.113119i
$321$	−22.7617	−	6.86158i	−0.0709086	−	0.0213757i
$322$	177.512			0.551278
$323$			60.3516i			0.186847i
$324$	−63.0317	−	149.235i	−0.194542	−	0.460601i
$325$	108.374			0.333460
$326$		−	65.5136i		−	0.200962i
$327$	97.5401	−	323.566i	0.298288	−	0.989499i
$328$	164.146			0.500446
$329$		−	396.730i		−	1.20587i
$330$	20.3078	+	6.12185i	0.0615388	+	0.0185511i
$331$	−331.570			−1.00172			−0.500861	−	0.865528i	$-0.666983\pi$
$331$	−331.570			−1.00172			−0.500861	+	0.865528i	$0.666983\pi$
$332$		−	26.3616i		−	0.0794024i
$333$	−122.967	−	81.5480i	−0.369269	−	0.244889i
$334$	−141.708			−0.424274
$335$		−	190.942i		−	0.569975i
$336$	−30.8471	+	102.328i	−0.0918068	+	0.304547i
$337$	−321.907			−0.955213			−0.477606	−	0.878574i	$-0.658496\pi$
$337$	−321.907			−0.955213			−0.477606	+	0.878574i	$0.658496\pi$
$338$			571.662i			1.69131i
$339$	−131.337	−	39.5921i	−0.387426	−	0.116791i
$340$	−106.535			−0.313338
$341$			32.8382i			0.0962996i
$342$	36.0624	−	54.3787i	0.105446	−	0.159002i
$343$	−166.342			−0.484963
$344$		−	81.3154i		−	0.236382i
$345$	55.2156	−	183.165i	0.160045	−	0.530912i
$346$	66.3631			0.191801
$347$		−	512.957i		−	1.47826i	−0.673562	−	0.739131i	$-0.735237\pi$
$347$		−	512.957i		−	1.47826i	0.673562	−	0.739131i	$-0.264763\pi$
$348$	131.807	+	39.7338i	0.378757	+	0.114177i
$349$	−47.7009			−0.136679			−0.0683393	−	0.997662i	$-0.521770\pi$
$349$	−47.7009			−0.136679			−0.0683393	+	0.997662i	$0.521770\pi$
$350$			57.0137i			0.162896i
$351$	497.562	−	412.691i	1.41756	−	1.17576i
$352$	6.25018			0.0177562
$353$			577.129i			1.63493i	0.575982	+	0.817463i	$0.304620\pi$
$353$			577.129i			1.63493i	−0.575982	+	0.817463i	$0.695380\pi$
$354$	−9.40579	+	31.2015i	−0.0265700	+	0.0881397i
$355$	−139.437			−0.392779
$356$			15.0124i			0.0421696i
$357$	−301.162	−	90.7864i	−0.843592	−	0.254304i
$358$	−341.526			−0.953983
$359$		−	546.585i		−	1.52252i	−0.648446	−	0.761261i	$-0.724581\pi$
$359$		−	546.585i		−	1.52252i	0.648446	−	0.761261i	$-0.275419\pi$
$360$	95.9915	+	63.6589i	0.266643	+	0.176830i
$361$	−334.719			−0.927199
$362$		−	209.657i		−	0.579164i
$363$	−103.714	+	344.045i	−0.285712	+	0.947783i
$364$	−426.474			−1.17163
$365$		−	499.419i		−	1.36827i
$366$	184.369	+	55.5788i	0.503742	+	0.151855i
$367$	282.425			0.769551			0.384775	−	0.923010i	$-0.374279\pi$
$367$	282.425			0.769551			0.384775	+	0.923010i	$0.374279\pi$
$368$		−	56.3730i		−	0.153188i
$369$	288.672	−	435.289i	0.782308	−	1.17965i
$370$	104.907			0.283534
$371$			354.274i			0.954917i
$372$	−51.4689	+	170.736i	−0.138357	+	0.458968i
$373$	443.457			1.18889			0.594446	−	0.804136i	$-0.297371\pi$
$373$	443.457			1.18889			0.594446	+	0.804136i	$0.297371\pi$
$374$			18.3950i			0.0491845i
$375$	383.744	+	115.681i	1.02332	+	0.308483i
$376$	−125.991			−0.335083
$377$			549.337i			1.45713i
$378$	217.108	+	261.758i	0.574361	+	0.692481i
$379$	−700.938			−1.84944			−0.924721	−	0.380646i	$-0.875702\pi$
$379$	−700.938			−1.84944			−0.924721	+	0.380646i	$0.875702\pi$
$380$			46.3925i			0.122086i
$381$	112.448	−	373.019i	0.295139	−	0.979053i
$382$	400.768			1.04913
$383$			415.184i			1.08403i	0.840368	+	0.542016i	$0.182339\pi$
$383$			415.184i			1.08403i	−0.840368	+	0.542016i	$0.817661\pi$
$384$	32.4967	+	9.79623i	0.0846268	+	0.0255110i
$385$	−44.5260			−0.115652
$386$		−	443.248i		−	1.14831i
$387$	−215.635	−	143.003i	−0.557197	−	0.369518i
$388$	−258.378			−0.665923
$389$		−	80.6708i		−	0.207380i	−0.994610	−	0.103690i	$-0.966935\pi$
$389$		−	80.6708i		−	0.207380i	0.994610	−	0.103690i	$-0.0330650\pi$
$390$	−132.656	+	440.056i	−0.340144	+	1.12835i
$391$	165.912			0.424328
$392$		−	85.7669i		−	0.218793i
$393$	648.294	+	195.430i	1.64960	+	0.497278i
$394$	408.241			1.03614
$395$		−	439.117i		−	1.11169i
$396$	10.9917	−	16.5745i	0.0277569	−	0.0418547i
$397$	192.849			0.485765			0.242882	−	0.970056i	$-0.421907\pi$
$397$	192.849			0.485765			0.242882	+	0.970056i	$0.421907\pi$
$398$		−	73.0837i		−	0.183628i
$399$	−39.5345	+	131.146i	−0.0990839	+	0.328687i
$400$	18.1061			0.0452652
$401$			402.284i			1.00320i	0.865099	+	0.501601i	$0.167256\pi$
$401$			402.284i			1.00320i	−0.865099	+	0.501601i	$0.832744\pi$
$402$	−171.417	−	51.6742i	−0.426410	−	0.128543i
$403$	−711.580			−1.76571
$404$			176.121i			0.435943i
$405$	337.626	−	142.602i	0.833644	−	0.352103i
$406$	−288.995			−0.711811
$407$		−	18.1139i		−	0.0445060i
$408$	−28.8314	+	95.6413i	−0.0706652	+	0.234415i
$409$	428.477			1.04762			0.523811	−	0.851835i	$-0.324510\pi$
$409$	428.477			1.04762			0.523811	+	0.851835i	$0.324510\pi$
$410$			371.362i			0.905760i
$411$	519.584	+	156.630i	1.26419	+	0.381095i
$412$	291.503			0.707532
$413$		−	68.4110i		−	0.165644i
$414$	−149.492	−	99.1390i	−0.361092	−	0.239466i
$415$	59.6400			0.143711
$416$			135.437i			0.325570i
$417$	183.650	−	609.215i	0.440408	−	1.46095i
$418$	8.01041			0.0191637
$419$		−	621.904i		−	1.48426i	−0.670257	−	0.742129i	$-0.733816\pi$
$419$		−	621.904i		−	1.48426i	0.670257	−	0.742129i	$-0.266184\pi$
$420$	−231.505	−	69.7879i	−0.551202	−	0.166162i
$421$	−552.407			−1.31213			−0.656066	−	0.754704i	$-0.727781\pi$
$421$	−552.407			−1.31213			−0.656066	+	0.754704i	$0.727781\pi$
$422$		−	268.094i		−	0.635293i
$423$	−221.571	+	334.108i	−0.523808	+	0.789853i
$424$	112.508			0.265350
$425$			53.2881i			0.125384i
$426$	−37.7355	+	125.179i	−0.0885810	+	0.293846i
$427$	−404.241			−0.946699
$428$		−	15.8489i		−	0.0370302i
$429$	75.9827	+	22.9052i	0.177116	+	0.0533922i
$430$	183.967			0.427829
$431$		−	136.700i		−	0.317169i	−0.987345	−	0.158584i	$-0.949307\pi$
$431$		−	136.700i		−	0.317169i	0.987345	−	0.158584i	$-0.0506930\pi$
$432$	83.1275	−	68.9480i	0.192425	−	0.159602i
$433$	−147.741			−0.341204			−0.170602	−	0.985340i	$-0.554571\pi$
$433$	−147.741			−0.341204			−0.170602	+	0.985340i	$0.554571\pi$
$434$		−	374.348i		−	0.862554i
$435$	−89.8930	+	298.198i	−0.206650	+	0.685514i
$436$	225.299			0.516741
$437$		−	72.2493i		−	0.165330i
$438$	−448.351	−	135.157i	−1.02363	−	0.308577i
$439$	−685.314			−1.56108			−0.780540	−	0.625105i	$-0.785056\pi$
$439$	−685.314			−1.56108			−0.780540	+	0.625105i	$0.785056\pi$
$440$			14.1403i			0.0321371i
$441$	−227.440	−	150.832i	−0.515737	−	0.342022i
$442$	−398.607			−0.901825
$443$			772.287i			1.74331i	0.490118	+	0.871656i	$0.336954\pi$
$443$			772.287i			1.74331i	−0.490118	+	0.871656i	$0.663046\pi$
$444$	28.3909	−	94.1801i	0.0639435	−	0.212117i
$445$	−33.9637			−0.0763230
$446$			373.349i			0.837106i
$447$	−784.698	−	236.550i	−1.75548	−	0.529194i
$448$	−71.2508			−0.159042
$449$			133.231i			0.296729i	0.988933	+	0.148364i	$0.0474008\pi$
$449$			133.231i			0.296729i	−0.988933	+	0.148364i	$0.952599\pi$
$450$	31.8418	−	48.0143i	0.0707595	−	0.106699i
$451$	64.1215			0.142176
$452$		−	91.4501i		−	0.202323i
$453$	92.4126	−	306.557i	0.204001	−	0.676726i
$454$	−123.373			−0.271746
$455$		−	964.848i		−	2.12055i
$456$	41.6486	+	12.5551i	0.0913347	+	0.0275332i
$457$	424.489			0.928860			0.464430	−	0.885610i	$-0.346259\pi$
$457$	424.489			0.928860			0.464430	+	0.885610i	$0.346259\pi$
$458$		−	563.250i		−	1.22980i
$459$	202.922	+	244.653i	0.442095	+	0.533014i
$460$	127.537			0.277255
$461$			47.8529i			0.103802i	0.998652	+	0.0519012i	$0.0165281\pi$
$461$			47.8529i			0.103802i	−0.998652	+	0.0519012i	$0.983472\pi$
$462$	−12.0500	+	39.9730i	−0.0260822	+	0.0865217i
$463$	−440.524			−0.951456			−0.475728	−	0.879592i	$-0.657815\pi$
$463$	−440.524			−0.951456			−0.475728	+	0.879592i	$0.657815\pi$
$464$			91.7774i			0.197796i
$465$	−386.270	−	116.442i	−0.830688	−	0.250414i
$466$	−104.247			−0.223706
$467$		−	807.628i		−	1.72940i	−0.502293	−	0.864698i	$-0.667510\pi$
$467$		−	807.628i		−	1.72940i	0.502293	−	0.864698i	$-0.332490\pi$
$468$	359.157	+	238.183i	0.767430	+	0.508938i
$469$	375.842			0.801368
$470$		−	285.040i		−	0.606468i
$471$	132.367	−	439.095i	0.281033	−	0.932262i
$472$	−21.7256			−0.0460287
$473$		−	31.7648i		−	0.0671560i
$474$	−394.215	−	118.837i	−0.831677	−	0.250712i
$475$	23.2052			0.0488531
$476$		−	209.699i		−	0.440544i
$477$	197.860	−	298.354i	0.414800	−	0.625479i
$478$	−468.948			−0.981063
$479$			211.211i			0.440941i	0.975394	+	0.220471i	$0.0707593\pi$
$479$			211.211i			0.440941i	−0.975394	+	0.220471i	$0.929241\pi$
$480$	−22.1628	+	73.5199i	−0.0461725	+	0.153166i
$481$	392.517			0.816043
$482$		−	179.591i		−	0.372596i
$483$	360.533	+	108.684i	0.746446	+	0.225019i
$484$	−239.558			−0.494955
$485$		−	584.550i		−	1.20526i
$486$	−36.6489	−	341.694i	−0.0754093	−	0.703074i
$487$	7.68940			0.0157893			0.00789466	−	0.999969i	$-0.497487\pi$
$487$	7.68940			0.0157893			0.00789466	+	0.999969i	$0.497487\pi$
$488$			128.376i			0.263066i
$489$	40.1116	−	133.061i	0.0820279	−	0.272108i
$490$	194.037			0.395995
$491$		−	526.212i		−	1.07171i	−0.844309	−	0.535857i	$-0.819988\pi$
$491$		−	526.212i		−	1.07171i	0.844309	−	0.535857i	$-0.180012\pi$
$492$	333.388	+	100.501i	0.677618	+	0.204270i
$493$	−270.111			−0.547892
$494$			173.580i			0.351377i
$495$	37.4978	+	24.8675i	0.0757531	+	0.0502373i
$496$	−118.883			−0.239684
$497$		−	274.461i		−	0.552236i
$498$	16.1403	−	53.5415i	0.0324102	−	0.107513i
$499$	717.972			1.43882			0.719410	−	0.694585i	$-0.244412\pi$
$499$	717.972			1.43882			0.719410	+	0.694585i	$0.244412\pi$
$500$			267.201i			0.534402i
$501$	−287.814	−	86.7625i	−0.574479	−	0.173179i
$502$	46.8515			0.0933296
$503$		−	24.6877i		−	0.0490809i	−0.999699	−	0.0245405i	$-0.992188\pi$
$503$		−	24.6877i		−	0.0490809i	0.999699	−	0.0245405i	$-0.00781226\pi$
$504$	−125.303	+	188.946i	−0.248618	+	0.374892i
$505$	−398.453			−0.789016
$506$		−	22.0214i		−	0.0435205i
$507$	−350.008	+	1161.07i	−0.690352	+	2.29008i
$508$	259.733			0.511286
$509$			899.037i			1.76628i	0.469108	+	0.883141i	$0.344575\pi$
$509$			899.037i			1.76628i	−0.469108	+	0.883141i	$0.655425\pi$
$510$	−216.377	−	65.2276i	−0.424269	−	0.127897i
$511$	983.035			1.92375
$512$			22.6274i			0.0441942i
$513$	106.538	−	88.3657i	0.207677	−	0.172253i
$514$	−614.238			−1.19502
$515$			659.492i			1.28057i
$516$	49.7866	−	165.155i	0.0964856	−	0.320068i
$517$	−49.2167			−0.0951967
$518$			206.495i			0.398640i
$519$	134.786	+	40.6317i	0.259704	+	0.0782885i
$520$	−306.411			−0.589251
$521$		−	8.98072i		−	0.0172375i	−0.999963	−	0.00861873i	$-0.997257\pi$
$521$		−	8.98072i		−	0.0172375i	0.999963	−	0.00861873i	$-0.00274346\pi$
$522$	243.379	+	161.402i	0.466243	+	0.309199i
$523$	−822.175			−1.57204			−0.786019	−	0.618203i	$-0.787861\pi$
$523$	−822.175			−1.57204			−0.786019	+	0.618203i	$0.787861\pi$
$524$			451.406i			0.861463i
$525$	−34.9075	+	115.797i	−0.0664904	+	0.220566i
$526$	25.7612			0.0489757
$527$		−	349.887i		−	0.663922i
$528$	12.6944	+	3.82677i	0.0240424	+	0.00724766i
$529$	330.380			0.624537
$530$			254.537i			0.480258i
$531$	−38.2071	+	57.6127i	−0.0719531	+	0.108498i
$532$	−91.3171			−0.171649
$533$			1389.47i			2.60688i
$534$	−9.19154	+	30.4908i	−0.0172126	+	0.0570988i
$535$	35.8564			0.0670212
$536$		−	119.358i		−	0.222682i
$537$	−693.654	−	209.104i	−1.29172	−	0.389393i
$538$	−301.157			−0.559772
$539$		−	33.5037i		−	0.0621590i
$540$	155.987	+	188.066i	0.288864	+	0.348270i
$541$	−716.418			−1.32425			−0.662124	−	0.749394i	$-0.730345\pi$
$541$	−716.418			−1.32425			−0.662124	+	0.749394i	$0.730345\pi$
$542$			171.308i			0.316066i
$543$	128.366	−	425.823i	0.236401	−	0.784204i
$544$	−66.5950			−0.122417
$545$			509.712i			0.935251i
$546$	−866.188	−	261.115i	−1.58642	−	0.478233i
$547$	58.8177			0.107528			0.0537639	−	0.998554i	$-0.482878\pi$
$547$	58.8177			0.107528			0.0537639	+	0.998554i	$0.482878\pi$
$548$			361.786i			0.660193i
$549$	340.433	+	225.766i	0.620097	+	0.411231i
$550$	7.07289			0.0128598
$551$			117.624i			0.213474i
$552$	34.5152	−	114.496i	0.0625276	−	0.207420i
$553$	864.339			1.56300
$554$		−	539.722i		−	0.974227i
$555$	213.071	+	64.2311i	0.383912	+	0.115732i
$556$	424.196			0.762943
$557$			380.139i			0.682477i	0.939977	+	0.341238i	$0.110846\pi$
$557$			380.139i			0.682477i	−0.939977	+	0.341238i	$0.889154\pi$
$558$	−209.071	+	315.259i	−0.374679	+	0.564981i
$559$	688.321			1.23134
$560$		−	161.197i		−	0.287851i
$561$	−11.2626	+	37.3610i	−0.0200759	+	0.0665971i
$562$	667.679			1.18804
$563$			205.772i			0.365493i	0.983160	+	0.182746i	$0.0584987\pi$
$563$			205.772i			0.365493i	−0.983160	+	0.182746i	$0.941501\pi$
$564$	−255.893	−	77.1399i	−0.453711	−	0.136773i
$565$	206.895			0.366186
$566$			308.201i			0.544525i
$567$	280.691	+	664.569i	0.495047	+	1.17208i
$568$	−87.1618			−0.153454
$569$		−	718.339i		−	1.26246i	−0.775596	−	0.631229i	$-0.782551\pi$
$569$		−	718.339i		−	1.26246i	0.775596	−	0.631229i	$-0.217449\pi$
$570$	−28.4045	+	94.2251i	−0.0498324	+	0.165307i
$571$	376.965			0.660184			0.330092	−	0.943949i	$-0.392920\pi$
$571$	376.965			0.660184			0.330092	+	0.943949i	$0.392920\pi$
$572$			52.9067i			0.0924943i
$573$	813.977	+	245.376i	1.42055	+	0.428231i
$574$	−730.973			−1.27347
$575$		−	63.7934i		−	0.110945i
$576$	60.0042	+	39.7931i	0.104174	+	0.0690853i
$577$	−256.286			−0.444171			−0.222085	−	0.975027i	$-0.571286\pi$
$577$	−256.286			−0.444171			−0.222085	+	0.975027i	$0.571286\pi$
$578$			212.711i			0.368013i
$579$	271.385	−	900.255i	0.468713	−	1.55484i
$580$	−207.635			−0.357992
$581$			117.393i			0.202053i
$582$	−524.777	−	158.196i	−0.901678	−	0.271814i
$583$	43.9498			0.0753857
$584$		−	312.186i		−	0.534566i
$585$	−538.861	+	812.551i	−0.921130	+	1.38898i
$586$	−76.5051			−0.130555
$587$		−	234.262i		−	0.399084i	−0.979889	−	0.199542i	$-0.936055\pi$
$587$		−	234.262i		−	0.399084i	0.979889	−	0.199542i	$-0.0639454\pi$
$588$	52.5120	−	174.196i	0.0893062	−	0.296252i
$589$	−152.364			−0.258683
$590$		−	49.1515i		−	0.0833076i
$591$	829.154	+	249.951i	1.40297	+	0.422929i
$592$	65.5776			0.110773
$593$			1064.67i			1.79540i	0.440606	+	0.897701i	$0.354764\pi$
$593$			1064.67i			1.79540i	−0.440606	+	0.897701i	$0.645236\pi$
$594$	32.4726	−	26.9336i	0.0546677	−	0.0453428i
$595$	474.420			0.797344
$596$		−	546.385i		−	0.916753i
$597$	44.7466	−	148.436i	0.0749524	−	0.248637i
$598$	477.188			0.797973
$599$		−	328.712i		−	0.548768i	−0.961620	−	0.274384i	$-0.911526\pi$
$599$		−	328.712i		−	0.548768i	0.961620	−	0.274384i	$-0.0884739\pi$
$600$	36.7742	+	11.0857i	0.0612903	+	0.0184762i
$601$	183.589			0.305473			0.152736	−	0.988267i	$-0.451191\pi$
$601$	183.589			0.305473			0.152736	+	0.988267i	$0.451191\pi$
$602$			362.112i			0.601515i
$603$	−316.517	−	209.905i	−0.524903	−	0.348101i
$604$	213.455			0.353403
$605$		−	541.973i		−	0.895823i
$606$	−107.833	+	357.709i	−0.177942	+	0.590280i
$607$	179.194			0.295213			0.147607	−	0.989046i	$-0.452843\pi$
$607$	179.194			0.295213			0.147607	+	0.989046i	$0.452843\pi$
$608$			28.9999i			0.0476972i
$609$	−586.962	−	176.942i	−0.963812	−	0.290544i
$610$	−290.436			−0.476125
$611$		−	1066.49i		−	1.74549i
$612$	−117.116	+	176.599i	−0.191365	+	0.288561i
$613$	798.315			1.30231			0.651155	−	0.758945i	$-0.274285\pi$
$613$	798.315			1.30231			0.651155	+	0.758945i	$0.274285\pi$
$614$		−	328.350i		−	0.534772i
$615$	−227.371	+	754.251i	−0.369710	+	1.22642i
$616$	−27.8332			−0.0451837
$617$			579.654i			0.939472i	0.882807	+	0.469736i	$0.155651\pi$
$617$			579.654i			0.939472i	−0.882807	+	0.469736i	$0.844349\pi$
$618$	592.055	+	178.477i	0.958018	+	0.288798i
$619$	252.758			0.408332			0.204166	−	0.978936i	$-0.434552\pi$
$619$	252.758			0.408332			0.204166	+	0.978936i	$0.434552\pi$
$620$		−	268.959i		−	0.433806i
$621$	−242.926	−	292.884i	−0.391184	−	0.471633i
$622$	368.165			0.591905
$623$		−	66.8528i		−	0.107308i
$624$	−82.9234	+	275.079i	−0.132890	+	0.440831i
$625$	−491.348			−0.786156
$626$			832.838i			1.33041i
$627$	16.2695	+	4.90449i	0.0259481	+	0.00782215i
$628$	305.742			0.486850
$629$			193.002i			0.306839i
$630$	−427.467	−	283.484i	−0.678519	−	0.449975i
$631$	−62.2227			−0.0986097			−0.0493048	−	0.998784i	$-0.515701\pi$
$631$	−62.2227			−0.0986097			−0.0493048	+	0.998784i	$0.515701\pi$
$632$		−	274.492i		−	0.434322i
$633$	164.144	−	544.509i	0.259312	−	0.860204i
$634$	639.471			1.00863
$635$			587.616i			0.925379i
$636$	228.509	+	68.8848i	0.359291	+	0.108309i
$637$	726.002			1.13972
$638$			35.8516i			0.0561937i
$639$	−153.285	+	231.139i	−0.239882	+	0.361720i
$640$	−51.1919			−0.0799873
$641$			790.007i			1.23246i	0.787566	+	0.616230i	$0.211341\pi$
$641$			790.007i			1.23246i	−0.787566	+	0.616230i	$0.788659\pi$
$642$	9.70375	−	32.1899i	0.0151149	−	0.0501400i
$643$	595.821			0.926626			0.463313	−	0.886195i	$-0.346661\pi$
$643$	595.821			0.926626			0.463313	+	0.886195i	$0.346661\pi$
$644$			251.039i			0.389812i
$645$	373.644	+	112.636i	0.579293	+	0.174630i
$646$	−85.3500			−0.132121
$647$			654.897i			1.01220i	0.862473	+	0.506102i	$0.168914\pi$
$647$			654.897i			1.01220i	−0.862473	+	0.506102i	$0.831086\pi$
$648$	211.050	−	89.1403i	0.325694	−	0.137562i
$649$	−8.48680			−0.0130767
$650$			153.265i			0.235792i
$651$	229.200	−	760.317i	0.352074	−	1.16792i
$652$	92.6502			0.142102
$653$		−	381.417i		−	0.584099i	−0.956403	−	0.292050i	$-0.905663\pi$
$653$		−	381.417i		−	0.584099i	0.956403	−	0.292050i	$-0.0943372\pi$
$654$	457.592	+	137.943i	0.699681	+	0.210921i
$655$	−1021.25			−1.55917
$656$			232.138i			0.353869i
$657$	−827.868	−	549.019i	−1.26007	−	0.835645i
$658$	561.061			0.852676
$659$			434.878i			0.659906i	0.943997	+	0.329953i	$0.107033\pi$
$659$			434.878i			0.659906i	−0.943997	+	0.329953i	$0.892967\pi$
$660$	−8.65761	+	28.7196i	−0.0131176	+	0.0435145i
$661$	659.194			0.997267			0.498634	−	0.866813i	$-0.333835\pi$
$661$	659.194			0.997267			0.498634	+	0.866813i	$0.333835\pi$
$662$		−	468.911i		−	0.708325i
$663$	−809.587	−	244.053i	−1.22110	−	0.368104i
$664$	37.2809			0.0561459
$665$		−	206.594i		−	0.310668i
$666$	115.326	−	173.901i	0.173163	−	0.261113i
$667$	323.361			0.484799
$668$		−	200.405i		−	0.300007i
$669$	−228.588	+	758.288i	−0.341687	+	1.13346i
$670$	270.032			0.403033
$671$			50.1485i			0.0747369i
$672$	−144.713	−	43.6244i	−0.215347	−	0.0649172i
$673$	843.005			1.25261			0.626304	−	0.779579i	$-0.284567\pi$
$673$	843.005			1.25261			0.626304	+	0.779579i	$0.284567\pi$
$674$		−	455.245i		−	0.675438i
$675$	94.0694	−	78.0235i	0.139362	−	0.115590i
$676$	−808.452			−1.19594
$677$			730.208i			1.07859i	0.842116	+	0.539297i	$0.181310\pi$
$677$			730.208i			1.07859i	−0.842116	+	0.539297i	$0.818690\pi$
$678$	55.9917	−	185.739i	0.0825836	−	0.273951i
$679$	1150.60			1.69456
$680$		−	150.663i		−	0.221564i
$681$	−250.575	−	75.5367i	−0.367952	−	0.110920i
$682$	−46.4402			−0.0680941
$683$			485.133i			0.710297i	0.934810	+	0.355148i	$0.115570\pi$
$683$			485.133i			0.710297i	−0.934810	+	0.355148i	$0.884430\pi$
$684$	76.9031	+	51.0000i	0.112431	+	0.0745614i
$685$	−818.497			−1.19489
$686$		−	235.244i		−	0.342921i
$687$	344.858	−	1143.98i	0.501977	−	1.66519i
$688$	114.997			0.167147
$689$			952.363i			1.38224i
$690$	259.034	+	78.0866i	0.375411	+	0.113169i
$691$	104.608			0.151386			0.0756932	−	0.997131i	$-0.475883\pi$
$691$	104.608			0.151386			0.0756932	+	0.997131i	$0.475883\pi$
$692$			93.8515i			0.135624i
$693$	−48.9481	+	73.8091i	−0.0706322	+	0.106507i
$694$	725.430			1.04529
$695$			959.694i			1.38085i
$696$	−56.1920	+	186.404i	−0.0807357	+	0.267821i
$697$	−683.207			−0.980212
$698$		−	67.4592i		−	0.0966464i
$699$	−211.730	−	63.8267i	−0.302904	−	0.0913114i
$700$	−80.6295			−0.115185
$701$		−	1175.02i		−	1.67620i	−0.545515	−	0.838101i	$-0.683666\pi$
$701$		−	1175.02i		−	1.67620i	0.545515	−	0.838101i	$-0.316334\pi$
$702$	583.633	+	703.659i	0.831386	+	1.00236i
$703$	84.0460			0.119553
$704$			8.83910i			0.0125555i
$705$	174.520	−	578.928i	0.247546	−	0.821175i
$706$	−816.183			−1.15607
$707$		−	784.299i		−	1.10933i
$708$	−44.1255	−	13.3018i	−0.0623242	−	0.0187878i
$709$	500.127			0.705398			0.352699	−	0.935737i	$-0.385264\pi$
$709$	500.127			0.705398			0.352699	+	0.935737i	$0.385264\pi$
$710$		−	197.193i		−	0.277737i
$711$	−727.907	−	482.728i	−1.02378	−	0.678942i
$712$	−21.2307			−0.0298184
$713$			418.863i			0.587466i
$714$	128.391	−	425.908i	0.179820	−	0.596510i
$715$	−119.695			−0.167406
$716$		−	482.991i		−	0.674568i
$717$	−952.454	−	287.120i	−1.32839	−	0.400447i
$718$	772.988			1.07658
$719$			914.060i			1.27129i	0.771980	+	0.635647i	$0.219267\pi$
$719$			914.060i			1.27129i	−0.771980	+	0.635647i	$0.780733\pi$
$720$	−90.0272	+	135.752i	−0.125038	+	0.188545i
$721$	−1298.12			−1.80044
$722$		−	473.364i		−	0.655629i
$723$	109.957	−	364.757i	0.152085	−	0.504505i
$724$	296.500			0.409530
$725$			103.858i			0.143252i
$726$	−486.553	−	146.673i	−0.670184	−	0.202029i
$727$	880.507			1.21115			0.605575	−	0.795788i	$-0.292943\pi$
$727$	880.507			1.21115			0.605575	+	0.795788i	$0.292943\pi$
$728$		−	603.126i		−	0.828470i
$729$	134.772	−	716.434i	0.184872	−	0.982763i
$730$	706.285			0.967514
$731$			338.450i			0.462996i
$732$	−78.6003	+	260.738i	−0.107377	+	0.356199i
$733$	−1430.18			−1.95113			−0.975565	−	0.219710i	$-0.929489\pi$
$733$	−1430.18			−1.95113			−0.975565	+	0.219710i	$0.929489\pi$
$734$			399.409i			0.544154i
$735$	394.098	+	118.802i	0.536188	+	0.161636i
$736$	79.7235			0.108320
$737$		−	46.6254i		−	0.0632638i
$738$	615.592	+	408.243i	0.834135	+	0.553175i
$739$	−697.532			−0.943886			−0.471943	−	0.881629i	$-0.656447\pi$
$739$	−697.532			−0.943886			−0.471943	+	0.881629i	$0.656447\pi$
$740$			148.361i			0.200488i
$741$	−106.277	+	352.548i	−0.143424	+	0.475774i
$742$	−501.019			−0.675228
$743$			850.909i			1.14523i	0.819823	+	0.572617i	$0.194072\pi$
$743$			850.909i			1.14523i	−0.819823	+	0.572617i	$0.805928\pi$
$744$	−241.457	−	72.7881i	−0.324539	−	0.0978334i
$745$	1236.13			1.65924
$746$			627.142i			0.840673i
$747$	65.5631	−	98.8629i	0.0877685	−	0.132347i
$748$	−26.0144			−0.0347787
$749$			70.5782i			0.0942299i
$750$	−163.598	+	542.696i	−0.218130	+	0.723595i
$751$	208.156			0.277172			0.138586	−	0.990350i	$-0.455744\pi$
$751$	208.156			0.277172			0.138586	+	0.990350i	$0.455744\pi$
$752$		−	178.178i		−	0.236939i
$753$	95.1573	+	28.6855i	0.126371	+	0.0380950i
$754$	−776.879			−1.03034
$755$			482.917i			0.639626i
$756$	−370.181	+	307.038i	−0.489658	+	0.406135i
$757$	41.2360			0.0544729			0.0272364	−	0.999629i	$-0.491329\pi$
$757$	41.2360			0.0544729			0.0272364	+	0.999629i	$0.491329\pi$
$758$		−	991.276i		−	1.30775i
$759$	13.4829	−	44.7263i	0.0177640	−	0.0589280i
$760$	−65.6089			−0.0863275
$761$		−	456.393i		−	0.599728i	−0.953982	−	0.299864i	$-0.903059\pi$
$761$		−	456.393i		−	0.599728i	0.953982	−	0.299864i	$-0.0969413\pi$
$762$	527.529	+	159.025i	0.692295	+	0.208695i
$763$	−1003.30			−1.31494
$764$			566.772i			0.741848i
$765$	−399.535	−	264.960i	−0.522267	−	0.346353i
$766$	−587.159			−0.766526
$767$		−	183.903i		−	0.239769i
$768$	−13.8540	+	45.9572i	−0.0180390	+	0.0598402i
$769$	270.426			0.351659			0.175829	−	0.984421i	$-0.443739\pi$
$769$	270.426			0.351659			0.175829	+	0.984421i	$0.443739\pi$
$770$		−	62.9693i		−	0.0817783i
$771$	−1247.54	−	376.076i	−1.61808	−	0.487777i
$772$	626.847			0.811978
$773$			834.104i			1.07905i	0.841970	+	0.539524i	$0.181396\pi$
$773$			834.104i			1.07905i	−0.841970	+	0.539524i	$0.818604\pi$
$774$	202.237	−	304.954i	0.261288	−	0.393998i
$775$	−134.532			−0.173589
$776$		−	365.402i		−	0.470878i
$777$	−126.430	+	419.401i	−0.162715	+	0.539769i
$778$	114.086			0.146640
$779$			297.514i			0.381918i
$780$	−622.333	−	187.604i	−0.797863	−	0.240518i
$781$	−34.0486			−0.0435961
$782$			234.635i			0.300045i
$783$	395.492	+	476.826i	0.505098	+	0.608973i
$784$	121.293			0.154710
$785$			691.705i			0.881152i
$786$	−276.380	+	916.825i	−0.351629	+	1.16644i
$787$	−346.994			−0.440907			−0.220453	−	0.975398i	$-0.570754\pi$
$787$	−346.994			−0.440907			−0.220453	+	0.975398i	$0.570754\pi$
$788$			577.339i			0.732664i
$789$	52.3221	+	15.7727i	0.0663145	+	0.0199907i
$790$	621.005			0.786082
$791$			407.244i			0.514847i
$792$	23.4398	+	15.5446i	0.0295958	+	0.0196271i
$793$	−1086.68			−1.37034
$794$			272.729i			0.343488i
$795$	−155.844	+	516.975i	−0.196030	+	0.650283i
$796$	103.356			0.129844
$797$		−	37.3483i		−	0.0468611i	−0.999725	−	0.0234306i	$-0.992541\pi$
$797$		−	37.3483i		−	0.0468611i	0.999725	−	0.0234306i	$-0.00745886\pi$
$798$	−185.469	−	55.9102i	−0.232417	−	0.0700629i
$799$	524.398			0.656318
$800$			25.6058i			0.0320073i
$801$	−37.3368	+	56.3004i	−0.0466128	+	0.0702876i
$802$	−568.916			−0.709372
$803$		−	121.951i		−	0.151870i
$804$	73.0784	−	242.420i	0.0908935	−	0.301518i
$805$	−567.947			−0.705524
$806$		−	1006.33i		−	1.24854i
$807$	−611.663	−	184.388i	−0.757946	−	0.228486i
$808$	−249.073			−0.308259
$809$		−	788.500i		−	0.974660i	−0.873218	−	0.487330i	$-0.837971\pi$
$809$		−	788.500i		−	0.974660i	0.873218	−	0.487330i	$-0.162029\pi$
$810$	201.669	+	477.475i	0.248975	+	0.589476i
$811$	−1130.83			−1.39437			−0.697185	−	0.716891i	$-0.745565\pi$
$811$	−1130.83			−1.39437			−0.697185	+	0.716891i	$0.745565\pi$
$812$		−	408.701i		−	0.503326i
$813$	−104.886	+	347.934i	−0.129011	+	0.427963i
$814$	25.6170			0.0314705
$815$			209.610i			0.257190i
$816$	−135.257	−	40.7738i	−0.165756	−	0.0499678i
$817$	147.384			0.180396
$818$			605.958i			0.740780i
$819$	−1599.39	−	1060.67i	−1.95286	−	1.29508i
$820$	−525.184			−0.640469
$821$		−	319.107i		−	0.388681i	−0.980934	−	0.194341i	$-0.937743\pi$
$821$		−	319.107i		−	0.388681i	0.980934	−	0.194341i	$-0.0622567\pi$
$822$	−221.509	+	734.802i	−0.269475	+	0.893920i
$823$	−783.357			−0.951831			−0.475915	−	0.879491i	$-0.657883\pi$
$823$	−783.357			−0.951831			−0.475915	+	0.879491i	$0.657883\pi$
$824$			412.248i			0.500301i
$825$	14.3653	+	4.33048i	0.0174125	+	0.00524907i
$826$	96.7478			0.117128
$827$		−	675.621i		−	0.816954i	−0.912769	−	0.408477i	$-0.866060\pi$
$827$		−	675.621i		−	0.816954i	0.912769	−	0.408477i	$-0.133940\pi$
$828$	140.204	−	211.414i	0.169328	−	0.255331i
$829$	1166.21			1.40677			0.703386	−	0.710808i	$-0.251671\pi$
$829$	1166.21			1.40677			0.703386	+	0.710808i	$0.251671\pi$
$830$			84.3436i			0.101619i
$831$	330.452	−	1096.20i	0.397656	−	1.31913i
$832$	−191.537			−0.230213
$833$			356.978i			0.428545i
$834$	861.561	+	259.720i	1.03305	+	0.311415i
$835$	453.392			0.542985
$836$			11.3284i			0.0135508i
$837$	−617.654	+	512.298i	−0.737938	+	0.612064i
$838$	879.505			1.04953
$839$		−	116.463i		−	0.138812i	−0.997588	−	0.0694061i	$-0.977890\pi$
$839$		−	116.463i		−	0.138812i	0.997588	−	0.0694061i	$-0.0221104\pi$
$840$	98.6950	−	327.397i	0.117494	−	0.389758i
$841$	314.557			0.374027
$842$		−	781.222i		−	0.927817i
$843$	1356.08	+	408.796i	1.60864	+	0.484930i
$844$	379.142			0.449220
$845$		−	1829.03i		−	2.16453i
$846$	−472.500	−	313.349i	−0.558510	−	0.370388i
$847$	1066.80			1.25950
$848$			159.111i			0.187631i
$849$	−188.700	+	625.969i	−0.222262	+	0.737301i
$850$	−75.3608			−0.0886598
$851$		−	231.050i		−	0.271505i
$852$	−177.029	−	53.3661i	−0.207781	−	0.0626362i
$853$	−320.940			−0.376248			−0.188124	−	0.982145i	$-0.560241\pi$
$853$	−320.940			−0.376248			−0.188124	+	0.982145i	$0.560241\pi$
$854$		−	571.683i		−	0.669418i
$855$	−115.381	+	173.984i	−0.134949	+	0.203490i
$856$	22.4138			0.0261843
$857$			604.176i			0.704989i	0.935814	+	0.352495i	$0.114666\pi$
$857$			604.176i			0.704989i	−0.935814	+	0.352495i	$0.885334\pi$
$858$	−32.3929	+	107.456i	−0.0377540	+	0.125240i
$859$	607.998			0.707798			0.353899	−	0.935284i	$-0.384856\pi$
$859$	607.998			0.707798			0.353899	+	0.935284i	$0.384856\pi$
$860$			260.168i			0.302521i
$861$	−1484.64	−	447.549i	−1.72432	−	0.519801i
$862$	193.323			0.224272
$863$		−	1056.06i		−	1.22370i	−0.790972	−	0.611852i	$-0.790425\pi$
$863$		−	1056.06i		−	1.22370i	0.790972	−	0.611852i	$-0.209575\pi$
$864$	97.5072	+	117.560i	0.112856	+	0.136065i
$865$	−212.328			−0.245466
$866$		−	208.938i		−	0.241268i
$867$	−130.236	+	432.026i	−0.150214	+	0.498299i
$868$	529.409			0.609918
$869$		−	107.226i		−	0.123391i
$870$	−421.716	−	127.128i	−0.484731	−	0.146124i
$871$	1010.34			1.15998
$872$			318.621i			0.365391i
$873$	−968.986	−	642.604i	−1.10995	−	0.736087i
$874$	102.176			0.116906
$875$		−	1189.89i		−	1.35988i
$876$	191.141	−	634.064i	0.218197	−	0.723817i
$877$	−165.835			−0.189094			−0.0945470	−	0.995520i	$-0.530140\pi$
$877$	−165.835			−0.189094			−0.0945470	+	0.995520i	$0.530140\pi$
$878$		−	969.181i		−	1.10385i
$879$	−155.385	−	46.8414i	−0.176775	−	0.0532894i
$880$	−19.9974			−0.0227243
$881$		−	638.341i		−	0.724564i	−0.932069	−	0.362282i	$-0.881998\pi$
$881$		−	638.341i		−	0.724564i	0.932069	−	0.362282i	$-0.118002\pi$
$882$	213.308	−	321.649i	0.241846	−	0.364681i
$883$	−1406.73			−1.59313			−0.796563	−	0.604555i	$-0.793351\pi$
$883$	−1406.73			−1.59313			−0.796563	+	0.604555i	$0.793351\pi$
$884$		−	563.715i		−	0.637687i
$885$	30.0937	−	99.8288i	0.0340042	−	0.112801i
$886$	−1092.18			−1.23271
$887$		−	654.494i		−	0.737873i	−0.929455	−	0.368937i	$-0.879722\pi$
$887$		−	654.494i		−	0.737873i	0.929455	−	0.368937i	$-0.120278\pi$
$888$	133.191	+	40.1508i	0.149990	+	0.0452149i
$889$	−1156.64			−1.30106
$890$		−	48.0319i		−	0.0539685i
$891$	82.4437	−	34.8215i	0.0925295	−	0.0390813i
$892$	−527.995			−0.591923
$893$		−	228.358i		−	0.255720i
$894$	334.532	−	1109.73i	0.374197	−	1.24131i
$895$	1092.71			1.22090
$896$		−	100.764i		−	0.112460i
$897$	969.189	+	292.165i	1.08048	+	0.325714i
$898$	−188.417			−0.209819
$899$		−	681.925i		−	0.758537i
$900$	67.9025	+	45.0310i	0.0754472	+	0.0500345i
$901$	−468.281			−0.519734
$902$			90.6815i			0.100534i
$903$	−221.708	+	735.465i	−0.245524	+	0.814468i
$904$	129.330			0.143064
$905$			670.796i			0.741211i
$906$	433.537	+	130.691i	0.478517	+	0.144251i
$907$	715.367			0.788718			0.394359	−	0.918956i	$-0.370967\pi$
$907$	715.367			0.788718			0.394359	+	0.918956i	$0.370967\pi$
$908$		−	174.475i		−	0.192153i
$909$	−438.026	+	660.501i	−0.481876	+	0.726623i
$910$	1364.50			1.49945
$911$			1517.39i			1.66563i	0.553550	+	0.832816i	$0.313273\pi$
$911$			1517.39i			1.66563i	−0.553550	+	0.832816i	$0.686727\pi$
$912$	−17.7556	+	58.9001i	−0.0194689	+	0.0645834i
$913$	14.5633			0.0159510
$914$			600.318i			0.656803i
$915$	−589.888	−	177.824i	−0.644687	−	0.194343i
$916$	796.556			0.869602
$917$		−	2010.19i		−	2.19214i
$918$	−345.992	+	286.974i	−0.376898	+	0.312608i
$919$	122.459			0.133253			0.0666265	−	0.997778i	$-0.478776\pi$
$919$	122.459			0.133253			0.0666265	+	0.997778i	$0.478776\pi$
$920$			180.365i			0.196049i
$921$	201.037	−	666.892i	0.218281	−	0.724096i
$922$	−67.6743			−0.0733994
$923$		−	737.809i		−	0.799360i
$924$	−56.5304	−	17.0413i	−0.0611801	−	0.0184429i
$925$	74.2095			0.0802264
$926$		−	622.995i		−	0.672781i
$927$	1093.21	+	724.989i	1.17930	+	0.782081i
$928$	−129.793			−0.139863
$929$		−	370.973i		−	0.399325i	−0.979865	−	0.199662i	$-0.936015\pi$
$929$		−	370.973i		−	0.399325i	0.979865	−	0.199662i	$-0.0639845\pi$
$930$	164.674	−	546.268i	0.177069	−	0.587385i
$931$	155.452			0.166973
$932$		−	147.427i		−	0.158184i
$933$	747.758	+	225.414i	0.801456	+	0.241602i
$934$	1142.16			1.22287
$935$		−	58.8546i		−	0.0629461i
$936$	−336.842	+	507.925i	−0.359874	+	0.542655i
$937$	−446.620			−0.476649			−0.238325	−	0.971186i	$-0.576598\pi$
$937$	−446.620			−0.476649			−0.238325	+	0.971186i	$0.576598\pi$
$938$			531.520i			0.566653i
$939$	−509.917	+	1691.53i	−0.543043	+	1.80142i
$940$	403.107			0.428838
$941$			1182.32i			1.25645i	0.778033	+	0.628223i	$0.216217\pi$
$941$			1182.32i			1.25645i	−0.778033	+	0.628223i	$0.783783\pi$
$942$	620.974	+	187.195i	0.659209	+	0.198721i
$943$	817.895			0.867333
$944$		−	30.7246i		−	0.0325472i
$945$	−694.636	−	837.492i	−0.735065	−	0.886234i
$946$	44.9222			0.0474864
$947$		−	1808.70i		−	1.90993i	−0.296722	−	0.954964i	$-0.595893\pi$
$947$		−	1808.70i		−	1.90993i	0.296722	−	0.954964i	$-0.404107\pi$
$948$	168.061	−	557.504i	0.177280	−	0.588084i
$949$	2642.60			2.78462
$950$			32.8171i			0.0345444i
$951$	1298.79	+	391.525i	1.36571	+	0.411699i
$952$	296.559			0.311512
$953$		−	498.505i		−	0.523090i	−0.965191	−	0.261545i	$-0.915768\pi$
$953$		−	498.505i		−	0.523090i	0.965191	−	0.261545i	$-0.0842319\pi$
$954$	421.936	+	279.816i	0.442281	+	0.293308i
$955$	−1282.25			−1.34267
$956$		−	663.193i		−	0.693716i
$957$	−21.9507	+	72.8161i	−0.0229369	+	0.0760879i
$958$	−298.697			−0.311792
$959$		−	1611.10i		−	1.67998i
$960$	−103.973	−	31.3430i	−0.108305	−	0.0326489i
$961$	−77.6721			−0.0808243
$962$			555.103i			0.577030i
$963$	39.4174	−	59.4377i	0.0409319	−	0.0617214i
$964$	253.980			0.263465
$965$			1418.17i			1.46960i
$966$	−153.702	+	509.871i	−0.159112	+	0.527817i
$967$	−1412.17			−1.46036			−0.730181	−	0.683254i	$-0.760564\pi$
$967$	−1412.17			−1.46036			−0.730181	+	0.683254i	$0.760564\pi$
$968$		−	338.787i		−	0.349986i
$969$	−173.349	−	52.2568i	−0.178895	−	0.0539286i
$970$	826.678			0.852245
$971$		−	578.043i		−	0.595307i	−0.954674	−	0.297654i	$-0.903796\pi$
$971$		−	578.043i		−	0.595307i	0.954674	−	0.297654i	$-0.0962040\pi$
$972$	483.228	−	51.8294i	0.497149	−	0.0533224i
$973$	−1889.02			−1.94144
$974$			10.8744i			0.0111647i
$975$	−93.8385	+	311.287i	−0.0962446	+	0.319269i
$976$	−181.552			−0.186016
$977$			525.869i			0.538248i	0.963105	+	0.269124i	$0.0867342\pi$
$977$			525.869i			0.538248i	−0.963105	+	0.269124i	$0.913266\pi$
$978$	188.176	+	56.7264i	0.192409	+	0.0580025i
$979$	−8.29349			−0.00847139
$980$			274.410i			0.280011i
$981$	844.930	+	560.334i	0.861295	+	0.571187i
$982$	744.176			0.757817
$983$		−	1566.90i		−	1.59400i	−0.603980	−	0.796999i	$-0.706419\pi$
$983$		−	1566.90i		−	1.59400i	0.603980	−	0.796999i	$-0.293581\pi$
$984$	−142.130	+	471.482i	−0.144441	+	0.479148i
$985$	−1306.16			−1.32605
$986$		−	381.995i		−	0.387418i
$987$	1139.54	+	343.518i	1.15455	+	0.348042i
$988$	−245.479			−0.248461
$989$		−	405.172i		−	0.409679i
$990$	−35.1679	+	53.0299i	−0.0355232	+	0.0535655i
$991$	1884.54			1.90166			0.950828	−	0.309719i	$-0.100235\pi$
$991$	1884.54			1.90166			0.950828	+	0.309719i	$0.100235\pi$
$992$		−	168.126i		−	0.169482i
$993$	287.098	−	952.378i	0.289122	−	0.959092i
$994$	388.147			0.390490
$995$			233.831i			0.235006i
$996$	75.7191	+	22.8258i	0.0760232	+	0.0229174i
$997$	−1199.66			−1.20327			−0.601634	−	0.798772i	$-0.705483\pi$
$997$	−1199.66			−1.20327			−0.601634	+	0.798772i	$0.705483\pi$
$998$			1015.37i			1.01740i
$999$	340.706	−	282.590i	0.341047	−	0.282873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.b.a.119.28	yes	40
3.2	odd	2	inner	354.3.b.a.119.8	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.b.a.119.8	✓	40	3.2	odd	2	inner
354.3.b.a.119.28	yes	40	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(-0.865873 + 2.87233i) q^{3} -2.00000 q^{4} -4.52476i q^{5} +(-4.06208 - 1.22453i) q^{6} +8.90636 q^{7} -2.82843i q^{8} +(-7.50053 - 4.97414i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(-0.865873 + 2.87233i) q^{3} -2.00000 q^{4} -4.52476i q^{5} +(-4.06208 - 1.22453i) q^{6} +8.90636 q^{7} -2.82843i q^{8} +(-7.50053 - 4.97414i) q^{9} +6.39898 q^{10} -1.10489i q^{11} +(1.73175 - 5.74465i) q^{12} +23.9421 q^{13} +12.5955i q^{14} +(12.9966 + 3.91787i) q^{15} +4.00000 q^{16} +11.7724i q^{17} +(7.03450 - 10.6073i) q^{18} +5.12651 q^{19} +9.04953i q^{20} +(-7.71177 + 25.5820i) q^{21} +1.56255 q^{22} -14.0933i q^{23} +(8.12417 + 2.44906i) q^{24} +4.52652 q^{25} +33.8593i q^{26} +(20.7819 - 17.2370i) q^{27} -17.8127 q^{28} +22.9443i q^{29} +(-5.54070 + 18.3800i) q^{30} -29.7208 q^{31} +5.65685i q^{32} +(3.17360 + 0.956692i) q^{33} -16.6487 q^{34} -40.2992i q^{35} +(15.0011 + 9.94828i) q^{36} +16.3944 q^{37} +7.24998i q^{38} +(-20.7309 + 68.7697i) q^{39} -12.7980 q^{40} +58.0345i q^{41} +(-36.1784 - 10.9061i) q^{42} +28.7493 q^{43} +2.20977i q^{44} +(-22.5068 + 33.9381i) q^{45} +19.9309 q^{46} -44.5446i q^{47} +(-3.46349 + 11.4893i) q^{48} +30.3232 q^{49} +6.40146i q^{50} +(-33.8143 - 10.1934i) q^{51} -47.8843 q^{52} +39.7777i q^{53} +(24.3768 + 29.3900i) q^{54} -4.99935 q^{55} -25.1910i q^{56} +(-4.43891 + 14.7250i) q^{57} -32.4482 q^{58} -7.68115i q^{59} +(-25.9932 - 7.83574i) q^{60} -45.3879 q^{61} -42.0316i q^{62} +(-66.8024 - 44.3015i) q^{63} -8.00000 q^{64} -108.333i q^{65} +(-1.35297 + 4.48814i) q^{66} +42.1993 q^{67} -23.5449i q^{68} +(40.4805 + 12.2030i) q^{69} +56.9916 q^{70} -30.8163i q^{71} +(-14.0690 + 21.2147i) q^{72} +110.375 q^{73} +23.1852i q^{74} +(-3.91939 + 13.0016i) q^{75} -10.2530 q^{76} -9.84052i q^{77} +(-97.2550 - 29.3179i) q^{78} +97.0474 q^{79} -18.0991i q^{80} +(31.5159 + 74.6174i) q^{81} -82.0731 q^{82} +13.1808i q^{83} +(15.4235 - 51.1639i) q^{84} +53.2675 q^{85} +40.6577i q^{86} +(-65.9037 - 19.8669i) q^{87} -3.12509 q^{88} -7.50619i q^{89} +(-47.9957 - 31.8294i) q^{90} +213.237 q^{91} +28.1865i q^{92} +(25.7345 - 85.3680i) q^{93} +62.9955 q^{94} -23.1962i q^{95} +(-16.2483 - 4.89812i) q^{96} +129.189 q^{97} +42.8834i q^{98} +(-5.49586 + 8.28724i) 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

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