LMFDB - Embedded newform 354.3.b.a.119.15

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			119.15
Character	$\chi$	$=$	354.119
Dual form			354.3.b.a.119.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(1.89028 + 2.32956i) q^{3} -2.00000 q^{4} -1.71502i q^{5} +(3.29449 - 2.67326i) q^{6} -3.39354 q^{7} +2.82843i q^{8} +(-1.85367 + 8.80704i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(1.89028 + 2.32956i) q^{3} -2.00000 q^{4} -1.71502i q^{5} +(3.29449 - 2.67326i) q^{6} -3.39354 q^{7} +2.82843i q^{8} +(-1.85367 + 8.80704i) q^{9} -2.42540 q^{10} -20.1481i q^{11} +(-3.78056 - 4.65911i) q^{12} +22.6824 q^{13} +4.79919i q^{14} +(3.99523 - 3.24187i) q^{15} +4.00000 q^{16} -19.8504i q^{17} +(12.4550 + 2.62149i) q^{18} +33.1705 q^{19} +3.43004i q^{20} +(-6.41475 - 7.90545i) q^{21} -28.4937 q^{22} +17.1941i q^{23} +(-6.58898 + 5.34652i) q^{24} +22.0587 q^{25} -32.0778i q^{26} +(-24.0205 + 12.3295i) q^{27} +6.78708 q^{28} +20.0602i q^{29} +(-4.58469 - 5.65011i) q^{30} -5.04155 q^{31} -5.65685i q^{32} +(46.9361 - 38.0855i) q^{33} -28.0727 q^{34} +5.81998i q^{35} +(3.70735 - 17.6141i) q^{36} +23.3446 q^{37} -46.9102i q^{38} +(42.8761 + 52.8400i) q^{39} +4.85080 q^{40} -13.5414i q^{41} +(-11.1800 + 9.07182i) q^{42} -7.24435 q^{43} +40.2962i q^{44} +(15.1042 + 3.17908i) q^{45} +24.3161 q^{46} -64.1532i q^{47} +(7.56113 + 9.31823i) q^{48} -37.4839 q^{49} -31.1957i q^{50} +(46.2427 - 37.5229i) q^{51} -45.3648 q^{52} +51.6584i q^{53} +(17.4366 + 33.9701i) q^{54} -34.5543 q^{55} -9.59838i q^{56} +(62.7016 + 77.2727i) q^{57} +28.3693 q^{58} -7.68115i q^{59} +(-7.99047 + 6.48373i) q^{60} -51.7692 q^{61} +7.12982i q^{62} +(6.29051 - 29.8870i) q^{63} -8.00000 q^{64} -38.9008i q^{65} +(-53.8611 - 66.3777i) q^{66} -11.2496 q^{67} +39.7009i q^{68} +(-40.0545 + 32.5016i) q^{69} +8.23070 q^{70} -128.662i q^{71} +(-24.9101 - 5.24298i) q^{72} -135.333 q^{73} -33.0142i q^{74} +(41.6972 + 51.3870i) q^{75} -66.3411 q^{76} +68.3733i q^{77} +(74.7270 - 60.6360i) q^{78} -10.1741 q^{79} -6.86007i q^{80} +(-74.1278 - 32.6507i) q^{81} -19.1505 q^{82} +12.5108i q^{83} +(12.8295 + 15.8109i) q^{84} -34.0439 q^{85} +10.2451i q^{86} +(-46.7313 + 37.9193i) q^{87} +56.9874 q^{88} -37.5422i q^{89} +(4.49590 - 21.3606i) q^{90} -76.9737 q^{91} -34.3881i q^{92} +(-9.52994 - 11.7446i) q^{93} -90.7264 q^{94} -56.8881i q^{95} +(13.1780 - 10.6930i) q^{96} +62.8295 q^{97} +53.0102i q^{98} +(177.445 + 37.3480i) 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
$3$	1.89028	+	2.32956i	0.630094	+	0.776519i
$3$	1.89028	+	2.32956i	0.630094	+	0.776519i
$4$	−2.00000			−0.500000
$5$		−	1.71502i		−	0.343004i	−0.985184	−	0.171502i	$-0.945138\pi$
$5$		−	1.71502i		−	0.343004i	0.985184	−	0.171502i	$-0.0548619\pi$
$6$	3.29449	−	2.67326i	0.549082	−	0.445544i
$7$	−3.39354			−0.484791			−0.242396	−	0.970177i	$-0.577933\pi$
$7$	−3.39354			−0.484791			−0.242396	+	0.970177i	$0.577933\pi$
$8$			2.82843i			0.353553i
$9$	−1.85367	+	8.80704i	−0.205964	+	0.978560i
$10$	−2.42540			−0.242540
$11$		−	20.1481i		−	1.83164i	−0.401585	−	0.915822i	$-0.631541\pi$
$11$		−	20.1481i		−	1.83164i	0.401585	−	0.915822i	$-0.368459\pi$
$12$	−3.78056	−	4.65911i	−0.315047	−	0.388260i
$13$	22.6824			1.74480			0.872401	−	0.488792i	$-0.162562\pi$
$13$	22.6824			1.74480			0.872401	+	0.488792i	$0.162562\pi$
$14$			4.79919i			0.342799i
$15$	3.99523	−	3.24187i	0.266349	−	0.216124i
$16$	4.00000			0.250000
$17$		−	19.8504i		−	1.16767i	−0.811872	−	0.583836i	$-0.801551\pi$
$17$		−	19.8504i		−	1.16767i	0.811872	−	0.583836i	$-0.198449\pi$
$18$	12.4550	+	2.62149i	0.691946	+	0.145638i
$19$	33.1705			1.74582			0.872909	−	0.487883i	$-0.162231\pi$
$19$	33.1705			1.74582			0.872909	+	0.487883i	$0.162231\pi$
$20$			3.43004i			0.171502i
$21$	−6.41475	−	7.90545i	−0.305464	−	0.376450i
$22$	−28.4937			−1.29517
$23$			17.1941i			0.747568i	0.927516	+	0.373784i	$0.121940\pi$
$23$			17.1941i			0.747568i	−0.927516	+	0.373784i	$0.878060\pi$
$24$	−6.58898	+	5.34652i	−0.274541	+	0.222772i
$25$	22.0587			0.882348
$26$		−	32.0778i		−	1.23376i
$27$	−24.0205	+	12.3295i	−0.889647	+	0.456650i
$28$	6.78708			0.242396
$29$			20.0602i			0.691729i	0.938284	+	0.345865i	$0.112414\pi$
$29$			20.0602i			0.691729i	−0.938284	+	0.345865i	$0.887586\pi$
$30$	−4.58469	−	5.65011i	−0.152823	−	0.188337i
$31$	−5.04155			−0.162630			−0.0813152	−	0.996688i	$-0.525912\pi$
$31$	−5.04155			−0.162630			−0.0813152	+	0.996688i	$0.525912\pi$
$32$		−	5.65685i		−	0.176777i
$33$	46.9361	−	38.0855i	1.42231	−	1.15411i
$34$	−28.0727			−0.825669
$35$			5.81998i			0.166285i
$36$	3.70735	−	17.6141i	0.102982	−	0.489280i
$37$	23.3446			0.630935			0.315467	−	0.948936i	$-0.397839\pi$
$37$	23.3446			0.630935			0.315467	+	0.948936i	$0.397839\pi$
$38$		−	46.9102i		−	1.23448i
$39$	42.8761	+	52.8400i	1.09939	+	1.35487i
$40$	4.85080			0.121270
$41$		−	13.5414i		−	0.330279i	−0.986270	−	0.165139i	$-0.947193\pi$
$41$		−	13.5414i		−	0.330279i	0.986270	−	0.165139i	$-0.0528074\pi$
$42$	−11.1800	+	9.07182i	−0.266190	+	0.215996i
$43$	−7.24435			−0.168473			−0.0842367	−	0.996446i	$-0.526845\pi$
$43$	−7.24435			−0.168473			−0.0842367	+	0.996446i	$0.526845\pi$
$44$			40.2962i			0.915822i
$45$	15.1042	+	3.17908i	0.335650	+	0.0706463i
$46$	24.3161			0.528610
$47$		−	64.1532i		−	1.36496i	−0.730903	−	0.682481i	$-0.760901\pi$
$47$		−	64.1532i		−	1.36496i	0.730903	−	0.682481i	$-0.239099\pi$
$48$	7.56113	+	9.31823i	0.157523	+	0.194130i
$49$	−37.4839			−0.764977
$50$		−	31.1957i		−	0.623915i
$51$	46.2427	−	37.5229i	0.906720	−	0.735743i
$52$	−45.3648			−0.872401
$53$			51.6584i			0.974686i	0.873211	+	0.487343i	$0.162034\pi$
$53$			51.6584i			0.974686i	−0.873211	+	0.487343i	$0.837966\pi$
$54$	17.4366	+	33.9701i	0.322900	+	0.629075i
$55$	−34.5543			−0.628261
$56$		−	9.59838i		−	0.171400i
$57$	62.7016	+	77.2727i	1.10003	+	1.35566i
$58$	28.3693			0.489127
$59$		−	7.68115i		−	0.130189i
$59$		−	7.68115i		−	0.130189i
$60$	−7.99047	+	6.48373i	−0.133174	+	0.108062i
$61$	−51.7692			−0.848676			−0.424338	−	0.905504i	$-0.639493\pi$
$61$	−51.7692			−0.848676			−0.424338	+	0.905504i	$0.639493\pi$
$62$			7.12982i			0.114997i
$63$	6.29051	−	29.8870i	0.0998494	−	0.474397i
$64$	−8.00000			−0.125000
$65$		−	38.9008i		−	0.598473i
$66$	−53.8611	−	66.3777i	−0.816077	−	1.00572i
$67$	−11.2496			−0.167905			−0.0839525	−	0.996470i	$-0.526754\pi$
$67$	−11.2496			−0.167905			−0.0839525	+	0.996470i	$0.526754\pi$
$68$			39.7009i			0.583836i
$69$	−40.0545	+	32.5016i	−0.580500	+	0.471038i
$70$	8.23070			0.117581
$71$		−	128.662i		−	1.81214i	−0.423130	−	0.906069i	$-0.639069\pi$
$71$		−	128.662i		−	1.81214i	0.423130	−	0.906069i	$-0.360931\pi$
$72$	−24.9101	−	5.24298i	−0.345973	−	0.0728192i
$73$	−135.333			−1.85387			−0.926936	−	0.375220i	$-0.877567\pi$
$73$	−135.333			−1.85387			−0.926936	+	0.375220i	$0.877567\pi$
$74$		−	33.0142i		−	0.446138i
$75$	41.6972	+	51.3870i	0.555962	+	0.685160i
$76$	−66.3411			−0.872909
$77$			68.3733i			0.887965i
$78$	74.7270	−	60.6360i	0.958039	−	0.777385i
$79$	−10.1741			−0.128786			−0.0643930	−	0.997925i	$-0.520511\pi$
$79$	−10.1741			−0.128786			−0.0643930	+	0.997925i	$0.520511\pi$
$80$		−	6.86007i		−	0.0857509i
$81$	−74.1278	−	32.6507i	−0.915158	−	0.403095i
$82$	−19.1505			−0.233542
$83$			12.5108i			0.150733i	0.997156	+	0.0753663i	$0.0240126\pi$
$83$			12.5108i			0.150733i	−0.997156	+	0.0753663i	$0.975987\pi$
$84$	12.8295	+	15.8109i	0.152732	+	0.188225i
$85$	−34.0439			−0.400516
$86$			10.2451i			0.119129i
$87$	−46.7313	+	37.9193i	−0.537141	+	0.435854i
$88$	56.9874			0.647584
$89$		−	37.5422i		−	0.421822i	−0.977505	−	0.210911i	$-0.932357\pi$
$89$		−	37.5422i		−	0.421822i	0.977505	−	0.210911i	$-0.0676430\pi$
$90$	4.49590	−	21.3606i	0.0499545	−	0.237340i
$91$	−76.9737			−0.845865
$92$		−	34.3881i		−	0.373784i
$93$	−9.52994	−	11.7446i	−0.102472	−	0.126286i
$94$	−90.7264			−0.965174
$95$		−	56.8881i		−	0.598822i
$96$	13.1780	−	10.6930i	0.137270	−	0.111386i
$97$	62.8295			0.647727			0.323863	−	0.946104i	$-0.395018\pi$
$97$	62.8295			0.647727			0.323863	+	0.946104i	$0.395018\pi$
$98$			53.0102i			0.540921i
$99$	177.445	+	37.3480i	1.79237	+	0.377252i
$100$	−44.1174			−0.441174
$101$			137.024i			1.35667i	0.734753	+	0.678334i	$0.237298\pi$
$101$			137.024i			1.35667i	−0.734753	+	0.678334i	$0.762702\pi$
$102$	−53.0654	−	65.3971i	−0.520249	−	0.641148i
$103$	156.341			1.51787			0.758935	−	0.651167i	$-0.225720\pi$
$103$	156.341			1.51787			0.758935	+	0.651167i	$0.225720\pi$
$104$			64.1556i			0.616880i
$105$	−13.5580	+	11.0014i	−0.129124	+	0.104775i
$106$	73.0559			0.689207
$107$			52.6468i			0.492026i	0.969267	+	0.246013i	$0.0791206\pi$
$107$			52.6468i			0.492026i	−0.969267	+	0.246013i	$0.920879\pi$
$108$	48.0409	−	24.6591i	0.444823	−	0.228325i
$109$	144.576			1.32639			0.663195	−	0.748447i	$-0.269200\pi$
$109$	144.576			1.32639			0.663195	+	0.748447i	$0.269200\pi$
$110$			48.8672i			0.444247i
$111$	44.1278	+	54.3825i	0.397548	+	0.489933i
$112$	−13.5742			−0.121198
$113$			190.568i			1.68644i	0.537568	+	0.843221i	$0.319343\pi$
$113$			190.568i			1.68644i	−0.537568	+	0.843221i	$0.680657\pi$
$114$	109.280	−	88.6735i	0.958597	−	0.777838i
$115$	29.4881			0.256418
$116$		−	40.1203i		−	0.345865i
$117$	−42.0458	+	199.765i	−0.359366	+	1.70739i
$118$	−10.8628			−0.0920575
$119$			67.3632i			0.566078i
$120$	9.16939	+	11.3002i	0.0764115	+	0.0941686i
$121$	−284.945			−2.35492
$122$			73.2128i			0.600105i
$123$	31.5455	−	25.5971i	0.256468	−	0.208107i
$124$	10.0831			0.0813152
$125$		−	80.7066i		−	0.645652i
$126$	−42.2666	−	8.89613i	−0.335450	−	0.0706042i
$127$	−37.2320			−0.293165			−0.146583	−	0.989198i	$-0.546827\pi$
$127$	−37.2320			−0.293165			−0.146583	+	0.989198i	$0.546827\pi$
$128$			11.3137i			0.0883883i
$129$	−13.6939	−	16.8761i	−0.106154	−	0.130823i
$130$	−55.0140			−0.423184
$131$			229.878i			1.75480i	0.479763	+	0.877398i	$0.340723\pi$
$131$			229.878i			1.75480i	−0.479763	+	0.877398i	$0.659277\pi$
$132$	−93.8722	+	76.1711i	−0.711153	+	0.577054i
$133$	−112.566			−0.846358
$134$			15.9094i			0.118727i
$135$	21.1454	+	41.1955i	0.156633	+	0.305152i
$136$	56.1455			0.412834
$137$			56.1523i			0.409871i	0.978776	+	0.204935i	$0.0656984\pi$
$137$			56.1523i			0.409871i	−0.978776	+	0.204935i	$0.934302\pi$
$138$	45.9642	+	56.6457i	0.333074	+	0.410476i
$139$	−189.725			−1.36493			−0.682464	−	0.730919i	$-0.739092\pi$
$139$	−189.725			−1.36493			−0.682464	+	0.730919i	$0.739092\pi$
$140$		−	11.6400i		−	0.0831426i
$141$	149.449	−	121.268i	1.05992	−	0.860054i
$142$	−181.955			−1.28137
$143$		−	457.007i		−	3.19585i
$144$	−7.41469	+	35.2281i	−0.0514909	+	0.244640i
$145$	34.4035			0.237266
$146$			191.389i			1.31089i
$147$	−70.8551	−	87.3209i	−0.482007	−	0.594019i
$148$	−46.6892			−0.315467
$149$			110.623i			0.742434i	0.928546	+	0.371217i	$0.121059\pi$
$149$			110.623i			0.742434i	−0.928546	+	0.371217i	$0.878941\pi$
$150$	72.6722	−	58.9687i	0.484482	−	0.393125i
$151$	−54.8404			−0.363182			−0.181591	−	0.983374i	$-0.558125\pi$
$151$	−54.8404			−0.363182			−0.181591	+	0.983374i	$0.558125\pi$
$152$			93.8204i			0.617240i
$153$	174.823	+	36.7962i	1.14264	+	0.240498i
$154$	96.6945			0.627886
$155$			8.64634i			0.0557829i
$156$	−85.7523	−	105.680i	−0.549694	−	0.677436i
$157$	280.604			1.78729			0.893644	−	0.448776i	$-0.148140\pi$
$157$	280.604			1.78729			0.893644	+	0.448776i	$0.148140\pi$
$158$			14.3883i			0.0910654i
$159$	−120.341	+	97.6488i	−0.756862	+	0.614143i
$160$	−9.70161			−0.0606351
$161$		−	58.3487i		−	0.362414i
$162$	−46.1751	+	104.833i	−0.285032	+	0.647114i
$163$	−146.607			−0.899428			−0.449714	−	0.893173i	$-0.648474\pi$
$163$	−146.607			−0.899428			−0.449714	+	0.893173i	$0.648474\pi$
$164$			27.0829i			0.165139i
$165$	−65.3174	−	80.4963i	−0.395863	−	0.487856i
$166$	17.6929			0.106584
$167$		−	62.7247i		−	0.375597i	−0.982208	−	0.187798i	$-0.939865\pi$
$167$		−	62.7247i		−	0.375597i	0.982208	−	0.187798i	$-0.0601352\pi$
$168$	22.3600	−	18.1436i	0.133095	−	0.107998i
$169$	345.492			2.04433
$170$			48.1453i			0.283208i
$171$	−61.4873	+	292.134i	−0.359575	+	1.70839i
$172$	14.4887			0.0842367
$173$			220.761i			1.27608i	0.770004	+	0.638039i	$0.220254\pi$
$173$			220.761i			1.27608i	−0.770004	+	0.638039i	$0.779746\pi$
$174$	53.6260	+	66.0880i	0.308196	+	0.379816i
$175$	−74.8571			−0.427755
$176$		−	80.5923i		−	0.457911i
$177$	17.8937	−	14.5195i	0.101094	−	0.0820312i
$178$	−53.0926			−0.298273
$179$		−	155.921i		−	0.871068i	−0.900172	−	0.435534i	$-0.856560\pi$
$179$		−	155.921i		−	0.871068i	0.900172	−	0.435534i	$-0.143440\pi$
$180$	−30.2085	−	6.35817i	−0.167825	−	0.0353231i
$181$	65.7160			0.363072			0.181536	−	0.983384i	$-0.441893\pi$
$181$	65.7160			0.363072			0.181536	+	0.983384i	$0.441893\pi$
$182$			108.857i			0.598117i
$183$	−97.8584	−	120.599i	−0.534746	−	0.659013i
$184$	−48.6321			−0.264305
$185$		−	40.0364i		−	0.216413i
$186$	−16.6093	+	13.4774i	−0.0892975	+	0.0724590i
$187$	−399.948			−2.13876
$188$			128.306i			0.682481i
$189$	81.5144	−	41.8408i	0.431293	−	0.221380i
$190$	−80.4519			−0.423431
$191$			92.6637i			0.485150i	0.970133	+	0.242575i	$0.0779921\pi$
$191$			92.6637i			0.485150i	−0.970133	+	0.242575i	$0.922008\pi$
$192$	−15.1223	−	18.6365i	−0.0787617	−	0.0970649i
$193$	103.605			0.536815			0.268407	−	0.963306i	$-0.413503\pi$
$193$	103.605			0.536815			0.268407	+	0.963306i	$0.413503\pi$
$194$		−	88.8543i		−	0.458012i
$195$	90.6215	−	73.5334i	0.464726	−	0.377094i
$196$	74.9678			0.382489
$197$		−	162.469i		−	0.824716i	−0.911022	−	0.412358i	$-0.864705\pi$
$197$		−	162.469i		−	0.824716i	0.911022	−	0.412358i	$-0.135295\pi$
$198$	52.8180	−	250.945i	0.266757	−	1.26740i
$199$	32.8048			0.164848			0.0824242	−	0.996597i	$-0.473734\pi$
$199$	32.8048			0.164848			0.0824242	+	0.996597i	$0.473734\pi$
$200$			62.3915i			0.311957i
$201$	−21.2650	−	26.2067i	−0.105796	−	0.130382i
$202$	193.781			0.959310
$203$		−	68.0749i		−	0.335345i
$204$	−92.4854	+	75.0458i	−0.453360	+	0.367872i
$205$	−23.2238			−0.113287
$206$		−	221.099i		−	1.07330i
$207$	−151.429	−	31.8722i	−0.731539	−	0.153972i
$208$	90.7297			0.436200
$209$		−	668.323i		−	3.19772i
$210$	15.5583	+	19.1739i	0.0740873	+	0.0913042i
$211$	150.973			0.715512			0.357756	−	0.933815i	$-0.383542\pi$
$211$	150.973			0.715512			0.357756	+	0.933815i	$0.383542\pi$
$212$		−	103.317i		−	0.487343i
$213$	299.725	−	243.207i	1.40716	−	1.14182i
$214$	74.4538			0.347915
$215$			12.4242i			0.0577870i
$216$	−34.8732	−	67.9401i	−0.161450	−	0.314538i
$217$	17.1087			0.0788419
$218$		−	204.462i		−	0.937899i
$219$	−255.817	−	315.265i	−1.16811	−	1.43957i
$220$	69.1087			0.314130
$221$		−	450.256i		−	2.03736i
$222$	76.9085	−	62.4062i	0.346435	−	0.281109i
$223$	−62.5403			−0.280450			−0.140225	−	0.990120i	$-0.544783\pi$
$223$	−62.5403			−0.280450			−0.140225	+	0.990120i	$0.544783\pi$
$224$			19.1968i			0.0856998i
$225$	−40.8896	+	194.272i	−0.181732	+	0.863431i
$226$	269.504			1.19249
$227$		−	84.4559i		−	0.372052i	−0.982545	−	0.186026i	$-0.940439\pi$
$227$		−	84.4559i		−	0.372052i	0.982545	−	0.186026i	$-0.0595609\pi$
$228$	−125.403	−	154.545i	−0.550014	−	0.677830i
$229$	−398.468			−1.74004			−0.870018	−	0.493020i	$-0.835893\pi$
$229$	−398.468			−1.74004			−0.870018	+	0.493020i	$0.835893\pi$
$230$		−	41.7025i		−	0.181315i
$231$	−159.280	+	129.245i	−0.689522	+	0.559501i
$232$	−56.7387			−0.244563
$233$			390.973i			1.67800i	0.544134	+	0.838998i	$0.316858\pi$
$233$			390.973i			1.67800i	−0.544134	+	0.838998i	$0.683142\pi$
$234$	282.510	+	59.4617i	1.20731	+	0.254110i
$235$	−110.024			−0.468187
$236$			15.3623i			0.0650945i
$237$	−19.2319	−	23.7011i	−0.0811472	−	0.100005i
$238$	95.2660			0.400277
$239$			94.1042i			0.393741i	0.980429	+	0.196871i	$0.0630779\pi$
$239$			94.1042i			0.393741i	−0.980429	+	0.196871i	$0.936922\pi$
$240$	15.9809	−	12.9675i	0.0665872	−	0.0540311i
$241$	−310.575			−1.28869			−0.644347	−	0.764733i	$-0.722871\pi$
$241$	−310.575			−1.28869			−0.644347	+	0.764733i	$0.722871\pi$
$242$			402.973i			1.66518i
$243$	−64.0606	−	234.404i	−0.263624	−	0.964626i
$244$	103.538			0.424338
$245$			64.2856i			0.262390i
$246$	−36.1998	−	44.6121i	−0.147154	−	0.181350i
$247$	752.388			3.04610
$248$		−	14.2596i		−	0.0574986i
$249$	−29.1446	+	23.6489i	−0.117047	+	0.0949756i
$250$	−114.136			−0.456545
$251$		−	53.9751i		−	0.215040i	−0.994203	−	0.107520i	$-0.965709\pi$
$251$		−	53.9751i		−	0.215040i	0.994203	−	0.107520i	$-0.0342910\pi$
$252$	−12.5810	+	59.7741i	−0.0499247	+	0.237199i
$253$	346.427			1.36928
$254$			52.6540i			0.207299i
$255$	−64.3525	−	79.3071i	−0.252363	−	0.311008i
$256$	16.0000			0.0625000
$257$			364.794i			1.41943i	0.704488	+	0.709716i	$0.251177\pi$
$257$			364.794i			1.41943i	−0.704488	+	0.709716i	$0.748823\pi$
$258$	−23.8665	+	19.3660i	−0.0925056	+	0.0750622i
$259$	−79.2208			−0.305872
$260$			77.8015i			0.299237i
$261$	−176.671	−	37.1850i	−0.676899	−	0.142471i
$262$	325.097			1.24083
$263$		−	10.4959i		−	0.0399083i	−0.999801	−	0.0199542i	$-0.993648\pi$
$263$		−	10.4959i		−	0.0399083i	0.999801	−	0.0199542i	$-0.00635203\pi$
$264$	107.722	+	132.755i	0.408039	+	0.502861i
$265$	88.5950			0.334321
$266$			159.192i			0.598465i
$267$	87.4566	−	70.9653i	0.327553	−	0.265788i
$268$	22.4993			0.0839525
$269$			236.698i			0.879917i	0.898018	+	0.439958i	$0.145007\pi$
$269$			236.698i			0.879917i	−0.898018	+	0.439958i	$0.854993\pi$
$270$	58.2593	−	29.9041i	0.215775	−	0.110756i
$271$	115.153			0.424920			0.212460	−	0.977170i	$-0.431853\pi$
$271$	115.153			0.424920			0.212460	+	0.977170i	$0.431853\pi$
$272$		−	79.4017i		−	0.291918i
$273$	−145.502	−	179.315i	−0.532974	−	0.656830i
$274$	79.4113			0.289822
$275$		−	444.441i		−	1.61615i
$276$	80.1091	−	65.0032i	0.290250	−	0.235519i
$277$	302.609			1.09245			0.546226	−	0.837638i	$-0.316064\pi$
$277$	302.609			1.09245			0.546226	+	0.837638i	$0.316064\pi$
$278$			268.312i			0.965150i
$279$	9.34538	−	44.4011i	0.0334960	−	0.159144i
$280$	−16.4614			−0.0587907
$281$		−	96.8711i		−	0.344737i	−0.985033	−	0.172369i	$-0.944858\pi$
$281$		−	96.8711i		−	0.344737i	0.985033	−	0.172369i	$-0.0551420\pi$
$282$	−171.498	−	211.352i	−0.608150	−	0.749476i
$283$	−401.220			−1.41774			−0.708869	−	0.705340i	$-0.750794\pi$
$283$	−401.220			−1.41774			−0.708869	+	0.705340i	$0.750794\pi$
$284$			257.324i			0.906069i
$285$	132.524	−	107.534i	0.464997	−	0.377314i
$286$	−646.306			−2.25981
$287$			45.9534i			0.160116i
$288$	49.8201	+	10.4860i	0.172987	+	0.0364096i
$289$	−105.040			−0.363459
$290$		−	48.6539i		−	0.167772i
$291$	118.765	+	146.365i	0.408129	+	0.502972i
$292$	270.665			0.926936
$293$		−	508.330i		−	1.73491i	−0.497513	−	0.867457i	$-0.665753\pi$
$293$		−	508.330i		−	1.73491i	0.497513	−	0.867457i	$-0.334247\pi$
$294$	−123.490	+	100.204i	−0.420035	+	0.340831i
$295$	−13.1733			−0.0446553
$296$			66.0285i			0.223069i
$297$	248.417	+	483.966i	0.836419	+	1.62952i
$298$	156.444			0.524980
$299$			390.003i			1.30436i
$300$	−83.3943	−	102.774i	−0.277981	−	0.342580i
$301$	24.5840			0.0816744
$302$			77.5561i			0.256808i
$303$	−319.204	+	259.013i	−1.05348	+	0.854829i
$304$	132.682			0.436454
$305$			88.7852i			0.291099i
$306$	52.0377	−	247.238i	0.170058	−	0.807966i
$307$	−84.2568			−0.274452			−0.137226	−	0.990540i	$-0.543819\pi$
$307$	−84.2568			−0.274452			−0.137226	+	0.990540i	$0.543819\pi$
$308$		−	136.747i		−	0.443983i
$309$	295.528	+	364.204i	0.956400	+	1.17865i
$310$	12.2278			0.0394444
$311$		−	103.180i		−	0.331768i	−0.986145	−	0.165884i	$-0.946952\pi$
$311$		−	103.180i		−	0.331768i	0.986145	−	0.165884i	$-0.0530477\pi$
$312$	−149.454	+	121.272i	−0.479019	+	0.388692i
$313$	−340.212			−1.08694			−0.543469	−	0.839429i	$-0.682890\pi$
$313$	−340.212			−1.08694			−0.543469	+	0.839429i	$0.682890\pi$
$314$		−	396.834i		−	1.26380i
$315$	−51.2568	−	10.7883i	−0.162720	−	0.0342487i
$316$	20.3482			0.0643930
$317$			80.6865i			0.254532i	0.991869	+	0.127266i	$0.0406201\pi$
$317$			80.6865i			0.254532i	−0.991869	+	0.127266i	$0.959380\pi$
$318$	138.096	+	170.188i	0.434265	+	0.535182i
$319$	404.174			1.26700
$320$			13.7201i			0.0428755i
$321$	−122.644	+	99.5172i	−0.382068	+	0.310023i
$322$	−82.5175			−0.256266
$323$		−	658.449i		−	2.03854i
$324$	148.256	+	65.3015i	0.457579	+	0.201548i
$325$	500.345			1.53952
$326$			207.333i			0.635991i
$327$	273.290	+	336.799i	0.835750	+	1.02997i
$328$	38.3010			0.116771
$329$			217.707i			0.661722i
$330$	−113.839	+	92.3728i	−0.344966	+	0.279917i
$331$	−147.412			−0.445354			−0.222677	−	0.974892i	$-0.571479\pi$
$331$	−147.412			−0.445354			−0.222677	+	0.974892i	$0.571479\pi$
$332$		−	25.0216i		−	0.0753663i
$333$	−43.2732	+	205.597i	−0.129950	+	0.617407i
$334$	−88.7061			−0.265587
$335$			19.2933i			0.0575921i
$336$	−25.6590	−	31.6218i	−0.0763660	−	0.0941124i
$337$	−514.554			−1.52687			−0.763433	−	0.645887i	$-0.776488\pi$
$337$	−514.554			−1.52687			−0.763433	+	0.645887i	$0.776488\pi$
$338$		−	488.599i		−	1.44556i
$339$	−443.939	+	360.227i	−1.30955	+	1.06262i
$340$	68.0877			0.200258
$341$			101.577i			0.297881i
$342$	413.140	+	86.9562i	1.20801	+	0.254258i
$343$	293.487			0.855646
$344$		−	20.4901i		−	0.0595643i
$345$	55.7408	+	68.6943i	0.161568	+	0.199114i
$346$	312.204			0.902323
$347$		−	365.011i		−	1.05191i	−0.850514	−	0.525953i	$-0.823709\pi$
$347$		−	365.011i		−	1.05191i	0.850514	−	0.525953i	$-0.176291\pi$
$348$	93.4626	−	75.8387i	0.268571	−	0.217927i
$349$	442.436			1.26773			0.633863	−	0.773445i	$-0.281468\pi$
$349$	442.436			1.26773			0.633863	+	0.773445i	$0.281468\pi$
$350$			105.864i			0.302468i
$351$	−544.842	+	279.664i	−1.55226	+	0.796763i
$352$	−113.975			−0.323792
$353$		−	298.573i		−	0.845817i	−0.906173	−	0.422908i	$-0.861009\pi$
$353$		−	298.573i		−	0.845817i	0.906173	−	0.422908i	$-0.138991\pi$
$354$	−20.5337	−	25.3055i	−0.0580048	−	0.0714844i
$355$	−220.657			−0.621570
$356$			75.0843i			0.210911i
$357$	−156.926	+	127.335i	−0.439570	+	0.356682i
$358$	−220.506			−0.615938
$359$		−	305.656i		−	0.851409i	−0.904862	−	0.425704i	$-0.860026\pi$
$359$		−	305.656i		−	0.851409i	0.904862	−	0.425704i	$-0.139974\pi$
$360$	−8.99181	+	42.7212i	−0.0249772	+	0.118670i
$361$	739.285			2.04788
$362$		−	92.9365i		−	0.256731i
$363$	−538.626	−	663.796i	−1.48382	−	1.82864i
$364$	153.947			0.422932
$365$			232.098i			0.635885i
$366$	−170.553	+	138.393i	−0.465993	+	0.378122i
$367$	−437.100			−1.19101			−0.595504	−	0.803352i	$-0.703048\pi$
$367$	−437.100			−1.19101			−0.595504	+	0.803352i	$0.703048\pi$
$368$			68.7762i			0.186892i
$369$	119.260	+	25.1014i	0.323198	+	0.0680254i
$370$	−56.6200			−0.153027
$371$		−	175.305i		−	0.472519i
$372$	19.0599	+	23.4891i	0.0512362	+	0.0631428i
$373$	146.990			0.394075			0.197037	−	0.980396i	$-0.436868\pi$
$373$	146.990			0.394075			0.197037	+	0.980396i	$0.436868\pi$
$374$			565.612i			1.51233i
$375$	188.011	−	152.558i	0.501361	−	0.406822i
$376$	181.453			0.482587
$377$			455.013i			1.20693i
$378$	−59.1718	−	115.279i	−0.156539	−	0.304970i
$379$	20.7213			0.0546737			0.0273368	−	0.999626i	$-0.491297\pi$
$379$	20.7213			0.0546737			0.0273368	+	0.999626i	$0.491297\pi$
$380$			113.776i			0.299411i
$381$	−70.3789	−	86.7340i	−0.184722	−	0.227648i
$382$	131.046			0.343053
$383$			460.021i			1.20110i	0.799588	+	0.600549i	$0.205051\pi$
$383$			460.021i			1.20110i	−0.799588	+	0.600549i	$0.794949\pi$
$384$	−26.3559	+	21.3861i	−0.0686352	+	0.0556929i
$385$	117.261			0.304575
$386$		−	146.520i		−	0.379585i
$387$	13.4287	−	63.8013i	0.0346994	−	0.164861i
$388$	−125.659			−0.323863
$389$			343.867i			0.883978i	0.897021	+	0.441989i	$0.145727\pi$
$389$			343.867i			0.883978i	−0.897021	+	0.441989i	$0.854273\pi$
$390$	−103.992	−	128.158i	−0.266646	−	0.328611i
$391$	341.309			0.872914
$392$		−	106.020i		−	0.270460i
$393$	−535.515	+	434.535i	−1.36263	+	1.10569i
$394$	−229.766			−0.583162
$395$			17.4488i			0.0441741i
$396$	−354.890	−	74.6959i	−0.896186	−	0.188626i
$397$	587.733			1.48044			0.740218	−	0.672367i	$-0.234722\pi$
$397$	587.733			1.48044			0.740218	+	0.672367i	$0.234722\pi$
$398$		−	46.3931i		−	0.116565i
$399$	−212.781	−	262.228i	−0.533285	−	0.657213i
$400$	88.2348			0.220587
$401$			156.631i			0.390601i	0.980743	+	0.195300i	$0.0625682\pi$
$401$			156.631i			0.390601i	−0.980743	+	0.195300i	$0.937432\pi$
$402$	−37.0618	+	30.0732i	−0.0921936	+	0.0748090i
$403$	−114.354			−0.283758
$404$		−	274.047i		−	0.678334i
$405$	−55.9966	+	127.131i	−0.138263	+	0.313903i
$406$	−96.2725			−0.237124
$407$		−	470.349i		−	1.15565i
$408$	106.131	+	130.794i	0.260124	+	0.320574i
$409$	−445.990			−1.09044			−0.545220	−	0.838293i	$-0.683554\pi$
$409$	−445.990			−1.09044			−0.545220	+	0.838293i	$0.683554\pi$
$410$			32.8434i			0.0801059i
$411$	−130.810	+	106.144i	−0.318272	+	0.258257i
$412$	−312.681			−0.758935
$413$			26.0663i			0.0631145i
$414$	−45.0740	+	214.152i	−0.108874	+	0.517277i
$415$	21.4563			0.0517018
$416$		−	128.311i		−	0.308440i
$417$	−358.634	−	441.975i	−0.860033	−	1.05989i
$418$	−945.151			−2.26113
$419$			33.6527i			0.0803166i	0.999193	+	0.0401583i	$0.0127862\pi$
$419$			33.6527i			0.0803166i	−0.999193	+	0.0401583i	$0.987214\pi$
$420$	27.1160	−	22.0028i	0.0645618	−	0.0523876i
$421$	−177.725			−0.422151			−0.211075	−	0.977470i	$-0.567697\pi$
$421$	−177.725			−0.422151			−0.211075	+	0.977470i	$0.567697\pi$
$422$		−	213.508i		−	0.505944i
$423$	565.000	+	118.919i	1.33570	+	0.281133i
$424$	−146.112			−0.344603
$425$		−	437.875i		−	1.03029i
$426$	−343.947	−	423.875i	−0.807386	−	0.995012i
$427$	175.681			0.411431
$428$		−	105.294i		−	0.246013i
$429$	1064.62	−	863.872i	2.48164	−	2.01369i
$430$	17.5705			0.0408616
$431$			182.542i			0.423531i	0.977320	+	0.211766i	$0.0679213\pi$
$431$			182.542i			0.423531i	−0.977320	+	0.211766i	$0.932079\pi$
$432$	−96.0818	+	49.3182i	−0.222412	+	0.114162i
$433$	467.835			1.08045			0.540226	−	0.841520i	$-0.318339\pi$
$433$	467.835			1.08045			0.540226	+	0.841520i	$0.318339\pi$
$434$		−	24.1953i		−	0.0557496i
$435$	65.0324	+	80.1450i	0.149500	+	0.184241i
$436$	−289.153			−0.663195
$437$			570.336i			1.30512i
$438$	−445.852	+	361.779i	−1.01793	+	0.825981i
$439$	−392.114			−0.893198			−0.446599	−	0.894734i	$-0.647365\pi$
$439$	−392.114			−0.893198			−0.446599	+	0.894734i	$0.647365\pi$
$440$		−	97.7344i		−	0.222124i
$441$	69.4829	−	330.122i	0.157558	−	0.748576i
$442$	−636.758			−1.44063
$443$		−	24.2266i		−	0.0546876i	−0.999626	−	0.0273438i	$-0.991295\pi$
$443$		−	24.2266i		−	0.0546876i	0.999626	−	0.0273438i	$-0.00870489\pi$
$444$	−88.2557	−	108.765i	−0.198774	−	0.244966i
$445$	−64.3855			−0.144687
$446$			88.4454i			0.198308i
$447$	−257.702	+	209.108i	−0.576514	+	0.467803i
$448$	27.1483			0.0605989
$449$			398.561i			0.887663i	0.896110	+	0.443831i	$0.146381\pi$
$449$			398.561i			0.887663i	−0.896110	+	0.443831i	$0.853619\pi$
$450$	274.742	+	57.8267i	0.610538	+	0.128504i
$451$	−272.834			−0.604953
$452$		−	381.136i		−	0.843221i
$453$	−103.664	−	127.754i	−0.228839	−	0.282018i
$454$	−119.439			−0.263081
$455$			132.011i			0.290135i
$456$	−218.560	+	177.347i	−0.479298	+	0.388919i
$457$	−523.106			−1.14465			−0.572326	−	0.820026i	$-0.693959\pi$
$457$	−523.106			−1.14465			−0.572326	+	0.820026i	$0.693959\pi$
$458$			563.519i			1.23039i
$459$	244.747	+	476.816i	0.533217	+	1.03882i
$460$	−58.9762			−0.128209
$461$			28.6466i			0.0621402i	0.999517	+	0.0310701i	$0.00989151\pi$
$461$			28.6466i			0.0621402i	−0.999517	+	0.0310701i	$0.990108\pi$
$462$	182.780	+	225.255i	0.395627	+	0.487566i
$463$	−644.832			−1.39273			−0.696363	−	0.717689i	$-0.745200\pi$
$463$	−644.832			−1.39273			−0.696363	+	0.717689i	$0.745200\pi$
$464$			80.2406i			0.172932i
$465$	−20.1421	+	16.3440i	−0.0433164	+	0.0351484i
$466$	552.920			1.18652
$467$			43.3586i			0.0928451i	0.998922	+	0.0464225i	$0.0147821\pi$
$467$			43.3586i			0.0928451i	−0.998922	+	0.0464225i	$0.985218\pi$
$468$	84.0916	−	399.530i	0.179683	−	0.853696i
$469$	38.1761			0.0813990
$470$			155.597i			0.331058i
$471$	530.421	+	653.684i	1.12616	+	1.38786i
$472$	21.7256			0.0460287
$473$			145.960i			0.308583i
$474$	−33.5185	+	27.1980i	−0.0707141	+	0.0573798i
$475$	731.699			1.54042
$476$		−	134.726i		−	0.283039i
$477$	−454.957	−	95.7577i	−0.953788	−	0.200750i
$478$	133.083			0.278417
$479$			753.311i			1.57267i	0.617798	+	0.786337i	$0.288025\pi$
$479$			753.311i			1.57267i	−0.617798	+	0.786337i	$0.711975\pi$
$480$	−18.3388	−	22.6005i	−0.0382058	−	0.0470843i
$481$	529.512			1.10086
$482$			439.220i			0.911244i
$483$	135.927	−	110.295i	0.281422	−	0.228355i
$484$	569.890			1.17746
$485$		−	107.754i		−	0.222173i
$486$	−331.497	+	90.5954i	−0.682093	+	0.186410i
$487$	−843.317			−1.73166			−0.865828	−	0.500342i	$-0.833208\pi$
$487$	−843.317			−1.73166			−0.865828	+	0.500342i	$0.833208\pi$
$488$		−	146.426i		−	0.300052i
$489$	−277.128	−	341.529i	−0.566724	−	0.698423i
$490$	90.9135			0.185538
$491$		−	40.2181i		−	0.0819106i	−0.999161	−	0.0409553i	$-0.986960\pi$
$491$		−	40.2181i		−	0.0819106i	0.999161	−	0.0409553i	$-0.0130401\pi$
$492$	−63.0911	+	51.1942i	−0.128234	+	0.104053i
$493$	398.203			0.807713
$494$		−	1064.04i		−	2.15392i
$495$	64.0524	−	304.321i	0.129399	−	0.614790i
$496$	−20.1662			−0.0406576
$497$			436.619i			0.878509i
$498$	33.4446	+	41.2167i	0.0671579	+	0.0827645i
$499$	−5.79919			−0.0116216			−0.00581081	−	0.999983i	$-0.501850\pi$
$499$	−5.79919			−0.0116216			−0.00581081	+	0.999983i	$0.501850\pi$
$500$			161.413i			0.322826i
$501$	146.121	−	118.567i	0.291658	−	0.236661i
$502$	−76.3323			−0.152056
$503$		−	679.391i		−	1.35068i	−0.737507	−	0.675339i	$-0.763997\pi$
$503$		−	679.391i		−	1.35068i	0.737507	−	0.675339i	$-0.236003\pi$
$504$	84.5333	+	17.7923i	0.167725	+	0.0353021i
$505$	234.998			0.465342
$506$		−	489.922i		−	0.968225i
$507$	653.077	+	804.843i	1.28812	+	1.58746i
$508$	74.4640			0.146583
$509$			270.372i			0.531184i	0.964086	+	0.265592i	$0.0855674\pi$
$509$			270.372i			0.531184i	−0.964086	+	0.265592i	$0.914433\pi$
$510$	−112.157	+	91.0081i	−0.219916	+	0.178447i
$511$	459.257			0.898741
$512$		−	22.6274i		−	0.0441942i
$513$	−796.772	+	408.977i	−1.55316	+	0.797227i
$514$	515.897			1.00369
$515$		−	268.127i		−	0.520635i
$516$	27.3877	+	33.7523i	0.0530770	+	0.0654114i
$517$	−1292.56			−2.50012
$518$			112.035i			0.216284i
$519$	−514.276	+	417.301i	−0.990898	+	0.804048i
$520$	110.028			0.211592
$521$			207.731i			0.398716i	0.979927	+	0.199358i	$0.0638857\pi$
$521$			207.731i			0.398716i	−0.979927	+	0.199358i	$0.936114\pi$
$522$	−52.5875	+	249.850i	−0.100742	+	0.478640i
$523$	811.683			1.55198			0.775988	−	0.630748i	$-0.217252\pi$
$523$	811.683			1.55198			0.775988	+	0.630748i	$0.217252\pi$
$524$		−	459.757i		−	0.877398i
$525$	−141.501	−	174.384i	−0.269526	−	0.332160i
$526$	−14.8434			−0.0282194
$527$			100.077i			0.189899i
$528$	187.744	−	152.342i	0.355577	−	0.288527i
$529$	233.365			0.441143
$530$		−	125.292i		−	0.236401i
$531$	67.6481	+	14.2383i	0.127398	+	0.0268142i
$532$	225.131			0.423179
$533$		−	307.152i		−	0.576271i
$534$	−100.360	−	123.682i	−0.187940	−	0.231615i
$535$	90.2902			0.168767
$536$		−	31.8188i		−	0.0593634i
$537$	363.227	−	294.735i	0.676401	−	0.548854i
$538$	334.741			0.622195
$539$			755.228i			1.40117i
$540$	−42.2908	−	82.3911i	−0.0783163	−	0.152576i
$541$	−113.946			−0.210621			−0.105310	−	0.994439i	$-0.533584\pi$
$541$	−113.946			−0.210621			−0.105310	+	0.994439i	$0.533584\pi$
$542$		−	162.851i		−	0.300463i
$543$	124.222	+	153.089i	0.228769	+	0.281932i
$544$	−112.291			−0.206417
$545$		−	247.951i		−	0.454957i
$546$	−253.589	+	205.771i	−0.464449	+	0.376870i
$547$	−256.411			−0.468759			−0.234380	−	0.972145i	$-0.575306\pi$
$547$	−256.411			−0.468759			−0.234380	+	0.972145i	$0.575306\pi$
$548$		−	112.305i		−	0.204935i
$549$	95.9632	−	455.934i	0.174796	−	0.830480i
$550$	−628.534			−1.14279
$551$			665.406i			1.20763i
$552$	−91.9284	−	113.291i	−0.166537	−	0.205238i
$553$	34.5262			0.0624343
$554$		−	427.954i		−	0.772481i
$555$	93.2671	−	75.6800i	0.168049	−	0.136360i
$556$	379.450			0.682464
$557$			215.487i			0.386871i	0.981113	+	0.193436i	$0.0619631\pi$
$557$			215.487i			0.386871i	−0.981113	+	0.193436i	$0.938037\pi$
$558$	−62.7926	−	13.2164i	−0.112532	−	0.0236852i
$559$	−164.319			−0.293952
$560$			23.2799i			0.0415713i
$561$	−756.014	−	931.702i	−1.34762	−	1.66079i
$562$	−136.996			−0.243766
$563$			3.70777i			0.00658574i	0.999995	+	0.00329287i	$0.00104816\pi$
$563$			3.70777i			0.00658574i	−0.999995	+	0.00329287i	$0.998952\pi$
$564$	−298.897	+	242.535i	−0.529960	+	0.430027i
$565$	326.827			0.578456
$566$			567.411i			1.00249i
$567$	251.556	+	110.802i	0.443661	+	0.195417i
$568$	363.910			0.640687
$569$			676.690i			1.18926i	0.803999	+	0.594631i	$0.202702\pi$
$569$			676.690i			1.18926i	−0.803999	+	0.594631i	$0.797298\pi$
$570$	−152.077	−	187.417i	−0.266801	−	0.328802i
$571$	−287.718			−0.503885			−0.251942	−	0.967742i	$-0.581069\pi$
$571$	−287.718			−0.503885			−0.251942	+	0.967742i	$0.581069\pi$
$572$			914.014i			1.59793i
$573$	−215.865	+	175.160i	−0.376728	+	0.305690i
$574$	64.9879			0.113219
$575$			379.279i			0.659615i
$576$	14.8294	−	70.4563i	0.0257455	−	0.122320i
$577$	685.617			1.18824			0.594122	−	0.804375i	$-0.297500\pi$
$577$	685.617			1.18824			0.594122	+	0.804375i	$0.297500\pi$
$578$			148.548i			0.257004i
$579$	195.843	+	241.354i	0.338244	+	0.416847i
$580$	−68.8071			−0.118633
$581$		−	42.4559i		−	0.0730738i
$582$	206.991	−	167.960i	0.355655	−	0.288591i
$583$	1040.82			1.78528
$584$		−	382.778i		−	0.655443i
$585$	342.600	+	72.1093i	0.585642	+	0.123264i
$586$	−718.887			−1.22677
$587$		−	536.521i		−	0.914005i	−0.889466	−	0.457002i	$-0.848923\pi$
$587$		−	536.521i		−	0.914005i	0.889466	−	0.457002i	$-0.151077\pi$
$588$	141.710	+	174.642i	0.241004	+	0.297010i
$589$	−167.231			−0.283923
$590$			18.6299i			0.0315760i
$591$	378.481	−	307.112i	0.640408	−	0.519648i
$592$	93.3783			0.157734
$593$		−	331.254i		−	0.558607i	−0.960203	−	0.279303i	$-0.909897\pi$
$593$		−	331.254i		−	0.558607i	0.960203	−	0.279303i	$-0.0901035\pi$
$594$	684.431	−	351.314i	1.15224	−	0.591438i
$595$	115.529			0.194167
$596$		−	221.245i		−	0.371217i
$597$	62.0104	+	76.4208i	0.103870	+	0.128008i
$598$	551.547			0.922320
$599$		−	190.603i		−	0.318202i	−0.987262	−	0.159101i	$-0.949140\pi$
$599$		−	190.603i		−	0.318202i	0.987262	−	0.159101i	$-0.0508596\pi$
$600$	−145.344	+	117.937i	−0.242241	+	0.196562i
$601$	−410.583			−0.683167			−0.341584	−	0.939851i	$-0.610963\pi$
$601$	−410.583			−0.683167			−0.341584	+	0.939851i	$0.610963\pi$
$602$		−	34.7670i		−	0.0577525i
$603$	20.8532	−	99.0760i	0.0345824	−	0.164305i
$604$	109.681			0.181591
$605$			488.686i			0.807746i
$606$	366.300	+	451.423i	0.604455	+	0.744922i
$607$	−89.2949			−0.147109			−0.0735543	−	0.997291i	$-0.523434\pi$
$607$	−89.2949			−0.147109			−0.0735543	+	0.997291i	$0.523434\pi$
$608$		−	187.641i		−	0.308620i
$609$	158.584	−	128.681i	0.260401	−	0.211298i
$610$	125.561			0.205838
$611$		−	1455.15i		−	2.38159i
$612$	−349.647	−	73.5924i	−0.571318	−	0.120249i
$613$	187.081			0.305190			0.152595	−	0.988289i	$-0.451237\pi$
$613$	187.081			0.305190			0.152595	+	0.988289i	$0.451237\pi$
$614$			119.157i			0.194067i
$615$	−43.8995	−	54.1012i	−0.0713813	−	0.0879694i
$616$	−193.389			−0.313943
$617$			482.825i			0.782537i	0.920277	+	0.391268i	$0.127964\pi$
$617$			482.825i			0.782537i	−0.920277	+	0.391268i	$0.872036\pi$
$618$	515.062	−	417.939i	0.833434	−	0.676277i
$619$	−975.338			−1.57567			−0.787834	−	0.615888i	$-0.788797\pi$
$619$	−975.338			−1.57567			−0.787834	+	0.615888i	$0.788797\pi$
$620$		−	17.2927i		−	0.0278914i
$621$	−211.995	−	413.009i	−0.341376	−	0.665071i
$622$	−145.918			−0.234595
$623$			127.401i			0.204496i
$624$	171.505	+	211.360i	0.274847	+	0.338718i
$625$	413.055			0.660887
$626$			481.132i			0.768582i
$627$	1556.90	−	1263.32i	2.48309	−	2.01486i
$628$	−561.209			−0.893644
$629$		−	463.400i		−	0.736725i
$630$	−15.2570	+	72.4881i	−0.0242175	+	0.115060i
$631$	−361.363			−0.572683			−0.286341	−	0.958128i	$-0.592439\pi$
$631$	−361.363			−0.572683			−0.286341	+	0.958128i	$0.592439\pi$
$632$		−	28.7767i		−	0.0455327i
$633$	285.382	+	351.701i	0.450840	+	0.555609i
$634$	114.108			0.179981
$635$			63.8535i			0.100557i
$636$	240.682	−	195.298i	0.378431	−	0.307072i
$637$	−850.225			−1.33473
$638$		−	571.588i		−	0.895906i
$639$	1133.13	+	238.497i	1.77328	+	0.373235i
$640$	19.4032			0.0303175
$641$		−	172.824i		−	0.269616i	−0.990872	−	0.134808i	$-0.956958\pi$
$641$		−	172.824i		−	0.269616i	0.990872	−	0.134808i	$-0.0430418\pi$
$642$	140.739	+	173.444i	0.219219	+	0.270163i
$643$	904.846			1.40723			0.703613	−	0.710583i	$-0.251569\pi$
$643$	904.846			1.40723			0.703613	+	0.710583i	$0.251569\pi$
$644$			116.697i			0.181207i
$645$	−28.9429	+	23.4852i	−0.0448727	+	0.0364112i
$646$	−931.188			−1.44147
$647$		−	698.363i		−	1.07939i	−0.841862	−	0.539693i	$-0.818540\pi$
$647$		−	698.363i		−	1.07939i	0.841862	−	0.539693i	$-0.181460\pi$
$648$	92.3502	−	209.665i	0.142516	−	0.323557i
$649$	−154.760			−0.238460
$650$		−	707.594i		−	1.08861i
$651$	32.3402	+	39.8557i	0.0496778	+	0.0612222i
$652$	293.213			0.449714
$653$		−	703.181i		−	1.07685i	−0.842674	−	0.538424i	$-0.819020\pi$
$653$		−	703.181i		−	1.07685i	0.842674	−	0.538424i	$-0.180980\pi$
$654$	476.306	−	386.491i	0.728297	−	0.590964i
$655$	394.246			0.601902
$656$		−	54.1657i		−	0.0825697i
$657$	250.862	−	1191.88i	0.381830	−	1.81412i
$658$	307.884			0.467908
$659$		−	354.647i		−	0.538160i	−0.963118	−	0.269080i	$-0.913280\pi$
$659$		−	354.647i		−	0.538160i	0.963118	−	0.269080i	$-0.0867195\pi$
$660$	130.635	+	160.993i	0.197932	+	0.243928i
$661$	62.4719			0.0945113			0.0472556	−	0.998883i	$-0.484952\pi$
$661$	62.4719			0.0945113			0.0472556	+	0.998883i	$0.484952\pi$
$662$			208.472i			0.314913i
$663$	1048.90	−	851.110i	1.58205	−	1.28373i
$664$	−35.3859			−0.0532920
$665$			193.052i			0.290304i
$666$	290.758	+	61.1976i	0.436573	+	0.0918883i
$667$	−344.915			−0.517115
$668$			125.449i			0.187798i
$669$	−118.219	−	145.691i	−0.176710	−	0.217775i
$670$	27.2849			0.0407237
$671$			1043.05i			1.55447i
$672$	−44.7200	+	36.2873i	−0.0665475	+	0.0539989i
$673$	388.786			0.577692			0.288846	−	0.957376i	$-0.406728\pi$
$673$	388.786			0.577692			0.288846	+	0.957376i	$0.406728\pi$
$674$			727.689i			1.07966i
$675$	−529.860	+	271.974i	−0.784978	+	0.402924i
$676$	−690.984			−1.02217
$677$		−	556.050i		−	0.821344i	−0.911783	−	0.410672i	$-0.865294\pi$
$677$		−	556.050i		−	0.821344i	0.911783	−	0.410672i	$-0.134706\pi$
$678$	509.438	+	627.824i	0.751383	+	0.925994i
$679$	−213.214			−0.314012
$680$		−	96.2906i		−	0.141604i
$681$	196.745	−	159.645i	0.288906	−	0.234428i
$682$	143.652			0.210634
$683$		−	290.060i		−	0.424686i	−0.977195	−	0.212343i	$-0.931891\pi$
$683$		−	290.060i		−	0.424686i	0.977195	−	0.212343i	$-0.0681094\pi$
$684$	122.975	−	584.268i	0.179788	−	0.854193i
$685$	96.3022			0.140587
$686$		−	415.053i		−	0.605033i
$687$	−753.217	−	928.255i	−1.09639	−	1.35117i
$688$	−28.9774			−0.0421183
$689$			1171.74i			1.70063i
$690$	97.1484	−	78.8295i	0.140795	−	0.114246i
$691$	−885.189			−1.28103			−0.640513	−	0.767947i	$-0.721278\pi$
$691$	−885.189			−1.28103			−0.640513	+	0.767947i	$0.721278\pi$
$692$		−	441.523i		−	0.638039i
$693$	−602.166	−	126.742i	−0.868927	−	0.182889i
$694$	−516.204			−0.743810
$695$			325.382i			0.468176i
$696$	−107.252	−	132.176i	−0.154098	−	0.189908i
$697$	−268.803			−0.385657
$698$		−	625.700i		−	0.896418i
$699$	−910.795	+	739.050i	−1.30300	+	1.05730i
$700$	149.714			0.213877
$701$			1188.15i			1.69494i	0.530845	+	0.847469i	$0.321875\pi$
$701$			1188.15i			1.69494i	−0.530845	+	0.847469i	$0.678125\pi$
$702$	395.504	+	770.523i	0.563396	+	1.09761i
$703$	774.352			1.10150
$704$			161.185i			0.228955i
$705$	−207.976	−	256.307i	−0.295002	−	0.363556i
$706$	−422.246			−0.598083
$707$		−	464.995i		−	0.657701i
$708$	−35.7873	+	29.0391i	−0.0505471	+	0.0410156i
$709$	−457.800			−0.645699			−0.322849	−	0.946450i	$-0.604641\pi$
$709$	−457.800			−0.645699			−0.322849	+	0.946450i	$0.604641\pi$
$710$			312.057i			0.439516i
$711$	18.8594	−	89.6036i	0.0265252	−	0.126025i
$712$	106.185			0.149137
$713$		−	86.6846i		−	0.121577i
$714$	180.080	+	221.928i	0.252212	+	0.310823i
$715$	−783.776			−1.09619
$716$			311.842i			0.435534i
$717$	−219.221	+	177.883i	−0.305748	+	0.248094i
$718$	−432.262			−0.602037
$719$			83.1686i			0.115673i	0.998326	+	0.0578363i	$0.0184201\pi$
$719$			83.1686i			0.115673i	−0.998326	+	0.0578363i	$0.981580\pi$
$720$	60.4169	+	12.7163i	0.0839124	+	0.0176616i
$721$	−530.548			−0.735850
$722$		−	1045.51i		−	1.44807i
$723$	−587.075	−	723.503i	−0.811998	−	1.00070i
$724$	−131.432			−0.181536
$725$			442.501i			0.610346i
$726$	−938.749	+	761.733i	−1.29304	+	1.04922i
$727$	433.992			0.596963			0.298482	−	0.954415i	$-0.403520\pi$
$727$	433.992			0.596963			0.298482	+	0.954415i	$0.403520\pi$
$728$		−	217.714i		−	0.299058i
$729$	424.965	−	592.322i	0.582942	−	0.812514i
$730$	328.236			0.449638
$731$			143.804i			0.196722i
$732$	195.717	+	241.199i	0.267373	+	0.329507i
$733$	−986.511			−1.34585			−0.672927	−	0.739709i	$-0.734963\pi$
$733$	−986.511			−1.34585			−0.672927	+	0.739709i	$0.734963\pi$
$734$			618.153i			0.842170i
$735$	−149.757	+	121.518i	−0.203751	+	0.165330i
$736$	97.2643			0.132153
$737$			226.659i			0.307542i
$738$	35.4987	−	168.659i	0.0481013	−	0.228535i
$739$	799.335			1.08164			0.540822	−	0.841137i	$-0.318113\pi$
$739$	799.335			1.08164			0.540822	+	0.841137i	$0.318113\pi$
$740$			80.0728i			0.108206i
$741$	1422.22	+	1752.73i	1.91933	+	2.36536i
$742$	−247.918			−0.334122
$743$			136.729i			0.184024i	0.995758	+	0.0920118i	$0.0293297\pi$
$743$			136.729i			0.184024i	−0.995758	+	0.0920118i	$0.970670\pi$
$744$	33.2187	−	26.9547i	0.0446487	−	0.0362295i
$745$	189.720			0.254658
$746$		−	207.875i		−	0.278653i
$747$	−110.183	−	23.1909i	−0.147501	−	0.0310454i
$748$	799.896			1.06938
$749$		−	178.659i		−	0.238530i
$750$	−215.750	−	265.887i	−0.287666	−	0.354516i
$751$	98.3212			0.130920			0.0654602	−	0.997855i	$-0.479148\pi$
$751$	98.3212			0.130920			0.0654602	+	0.997855i	$0.479148\pi$
$752$		−	256.613i		−	0.341241i
$753$	125.738	−	102.028i	0.166983	−	0.135495i
$754$	643.485			0.853429
$755$			94.0524i			0.124573i
$756$	−163.029	+	83.6816i	−0.215647	+	0.110690i
$757$	454.872			0.600887			0.300444	−	0.953800i	$-0.402865\pi$
$757$	454.872			0.600887			0.300444	+	0.953800i	$0.402865\pi$
$758$		−	29.3044i		−	0.0386601i
$759$	654.845	+	807.022i	0.862773	+	1.06327i
$760$	160.904			0.211716
$761$		−	639.993i		−	0.840990i	−0.907295	−	0.420495i	$-0.861856\pi$
$761$		−	639.993i		−	0.840990i	0.907295	−	0.420495i	$-0.138144\pi$
$762$	−122.660	+	99.5308i	−0.160972	+	0.130618i
$763$	−490.626			−0.643022
$764$		−	185.327i		−	0.242575i
$765$	63.1062	−	299.825i	0.0824917	−	0.391929i
$766$	650.568			0.849305
$767$		−	174.227i		−	0.227154i
$768$	30.2445	+	37.2729i	0.0393809	+	0.0485324i
$769$	−492.049			−0.639856			−0.319928	−	0.947442i	$-0.603659\pi$
$769$	−492.049			−0.639856			−0.319928	+	0.947442i	$0.603659\pi$
$770$		−	165.833i		−	0.215367i
$771$	−849.809	+	689.564i	−1.10222	+	0.894376i
$772$	−207.210			−0.268407
$773$		−	508.042i		−	0.657234i	−0.944463	−	0.328617i	$-0.893417\pi$
$773$		−	508.042i		−	0.657234i	0.944463	−	0.328617i	$-0.106583\pi$
$774$	−90.2286	−	18.9910i	−0.116574	−	0.0245362i
$775$	−111.210			−0.143497
$776$			177.709i			0.229006i
$777$	−149.750	−	184.549i	−0.192728	−	0.237515i
$778$	486.302			0.625067
$779$		−	449.177i		−	0.576607i
$780$	−181.243	+	147.067i	−0.232363	+	0.188547i
$781$	−2592.29			−3.31919
$782$		−	482.684i		−	0.617243i
$783$	−247.332	−	481.854i	−0.315878	−	0.615395i
$784$	−149.936			−0.191244
$785$		−	481.242i		−	0.613047i
$786$	614.525	+	757.332i	0.781838	+	0.963527i
$787$	1423.23			1.80842			0.904212	−	0.427085i	$-0.140459\pi$
$787$	1423.23			1.80842			0.904212	+	0.427085i	$0.140459\pi$
$788$			324.938i			0.412358i
$789$	24.4508	−	19.8402i	0.0309896	−	0.0251460i
$790$	24.6763			0.0312358
$791$		−	646.700i		−	0.817572i
$792$	−105.636	+	501.890i	−0.133379	+	0.633699i
$793$	−1174.25			−1.48077
$794$		−	831.180i		−	1.04683i
$795$	167.470	+	206.387i	0.210653	+	0.259607i
$796$	−65.6097			−0.0824242
$797$		−	1020.86i		−	1.28088i	−0.768008	−	0.640440i	$-0.778752\pi$
$797$		−	1020.86i		−	1.28088i	0.768008	−	0.640440i	$-0.221248\pi$
$798$	−370.846	+	300.917i	−0.464720	+	0.377089i
$799$	−1273.47			−1.59383
$800$		−	124.783i		−	0.155979i
$801$	330.635	+	69.5909i	0.412778	+	0.0868800i
$802$	221.510			0.276196
$803$			2726.69i			3.39563i
$804$	42.5300	+	52.4134i	0.0528980	+	0.0651908i
$805$	−100.069			−0.124309
$806$			161.722i			0.200647i
$807$	−551.401	+	447.425i	−0.683272	+	0.554430i
$808$	−387.561			−0.479655
$809$			178.800i			0.221014i	0.993875	+	0.110507i	$0.0352475\pi$
$809$			178.800i			0.221014i	−0.993875	+	0.110507i	$0.964753\pi$
$810$	179.790	+	79.1912i	0.221963	+	0.0977669i
$811$	1460.75			1.80118			0.900588	−	0.434673i	$-0.143136\pi$
$811$	1460.75			1.80118			0.900588	+	0.434673i	$0.143136\pi$
$812$			136.150i			0.167672i
$813$	217.672	+	268.256i	0.267739	+	0.329958i
$814$	−665.173			−0.817166
$815$			251.433i			0.308507i
$816$	184.971	−	150.092i	0.226680	−	0.183936i
$817$	−240.299			−0.294124
$818$			630.725i			0.771058i
$819$	142.684	−	677.910i	0.174217	−	0.827729i
$820$	46.4476			0.0566434
$821$			856.002i			1.04263i	0.853363	+	0.521317i	$0.174559\pi$
$821$			856.002i			1.04263i	−0.853363	+	0.521317i	$0.825441\pi$
$822$	150.110	+	184.993i	0.182615	+	0.225053i
$823$	222.745			0.270650			0.135325	−	0.990801i	$-0.456792\pi$
$823$	222.745			0.270650			0.135325	+	0.990801i	$0.456792\pi$
$824$			442.198i			0.536648i
$825$	1035.35	−	840.118i	1.25497	−	1.01832i
$826$	36.8633			0.0446287
$827$		−	220.764i		−	0.266946i	−0.991052	−	0.133473i	$-0.957387\pi$
$827$		−	220.764i		−	0.266946i	0.991052	−	0.133473i	$-0.0426129\pi$
$828$	302.857	+	63.7443i	0.365770	+	0.0769859i
$829$	−662.849			−0.799576			−0.399788	−	0.916608i	$-0.630916\pi$
$829$	−662.849			−0.799576			−0.399788	+	0.916608i	$0.630916\pi$
$830$		−	30.3437i		−	0.0365587i
$831$	572.017	+	704.946i	0.688348	+	0.848310i
$832$	−181.459			−0.218100
$833$			744.071i			0.893243i
$834$	−625.048	+	507.185i	−0.749458	+	0.608135i
$835$	−107.574			−0.128831
$836$			1336.65i			1.59886i
$837$	121.100	−	62.1599i	0.144684	−	0.0742651i
$838$	47.5920			0.0567924
$839$			424.742i			0.506247i	0.967434	+	0.253124i	$0.0814580\pi$
$839$			424.742i			0.506247i	−0.967434	+	0.253124i	$0.918542\pi$
$840$	−31.1167	−	38.3478i	−0.0370437	−	0.0456521i
$841$	438.590			0.521510
$842$			251.342i			0.298506i
$843$	225.667	−	183.114i	0.267695	−	0.217217i
$844$	−301.946			−0.357756
$845$		−	592.525i		−	0.701213i
$846$	168.177	−	799.031i	0.198791	−	0.944480i
$847$	966.973			1.14164
$848$			206.633i			0.243671i
$849$	−758.419	−	934.665i	−0.893308	−	1.10090i
$850$	−619.249			−0.728528
$851$			401.388i			0.471666i
$852$	−599.450	+	486.414i	−0.703580	+	0.570908i
$853$	−578.554			−0.678258			−0.339129	−	0.940740i	$-0.610132\pi$
$853$	−578.554			−0.678258			−0.339129	+	0.940740i	$0.610132\pi$
$854$		−	248.450i		−	0.290926i
$855$	501.015	+	105.452i	0.585983	+	0.123336i
$856$	−148.908			−0.173957
$857$		−	966.160i		−	1.12737i	−0.825988	−	0.563687i	$-0.809382\pi$
$857$		−	966.160i		−	1.12737i	0.825988	−	0.563687i	$-0.190618\pi$
$858$	−1221.70	−	1505.61i	−1.42389	−	1.75479i
$859$	−685.599			−0.798136			−0.399068	−	0.916921i	$-0.630666\pi$
$859$	−685.599			−0.798136			−0.399068	+	0.916921i	$0.630666\pi$
$860$		−	24.8484i		−	0.0288935i
$861$	−107.051	+	86.8648i	−0.124333	+	0.100888i
$862$	258.153			0.299482
$863$		−	744.769i		−	0.863000i	−0.902113	−	0.431500i	$-0.857985\pi$
$863$		−	744.769i		−	0.863000i	0.902113	−	0.431500i	$-0.142015\pi$
$864$	69.7464	+	135.880i	0.0807250	+	0.157269i
$865$	378.610			0.437699
$866$		−	661.619i		−	0.763994i
$867$	−198.554	−	244.696i	−0.229013	−	0.282232i
$868$	−34.2174			−0.0394209
$869$			204.988i			0.235890i
$870$	113.342	−	91.9696i	0.130278	−	0.105712i
$871$	−255.169			−0.292961
$872$			408.924i			0.468950i
$873$	−116.465	+	553.342i	−0.133408	+	0.633839i
$874$	806.577			0.922857
$875$			273.881i			0.313007i
$876$	511.633	+	630.530i	0.584056	+	0.719783i
$877$	163.210			0.186100			0.0930499	−	0.995661i	$-0.470338\pi$
$877$	163.210			0.186100			0.0930499	+	0.995661i	$0.470338\pi$
$878$			554.533i			0.631587i
$879$	1184.18	−	960.886i	1.34719	−	1.09316i
$880$	−138.217			−0.157065
$881$			504.751i			0.572929i	0.958091	+	0.286465i	$0.0924801\pi$
$881$			504.751i			0.572929i	−0.958091	+	0.286465i	$0.907520\pi$
$882$	−466.863	−	98.2636i	−0.529323	−	0.111410i
$883$	−484.815			−0.549054			−0.274527	−	0.961579i	$-0.588521\pi$
$883$	−484.815			−0.549054			−0.274527	+	0.961579i	$0.588521\pi$
$884$			900.511i			1.01868i
$885$	−24.9013	−	30.6880i	−0.0281370	−	0.0346757i
$886$	−34.2616			−0.0386700
$887$		−	196.731i		−	0.221794i	−0.993832	−	0.110897i	$-0.964628\pi$
$887$		−	196.731i		−	0.221794i	0.993832	−	0.110897i	$-0.0353723\pi$
$888$	−153.817	+	124.812i	−0.173217	+	0.140554i
$889$	126.348			0.142124
$890$			91.0549i			0.102309i
$891$	−657.850	+	1493.53i	−0.738327	+	1.67624i
$892$	125.081			0.140225
$893$		−	2128.00i		−	2.38298i
$894$	295.723	+	364.445i	0.330787	+	0.407657i
$895$	−267.408			−0.298779
$896$		−	38.3935i		−	0.0428499i
$897$	−908.534	+	737.215i	−1.01286	+	0.821867i
$898$	563.650			0.627672
$899$		−	101.134i		−	0.112496i
$900$	81.7793	−	388.544i	0.0908659	−	0.431715i
$901$	1025.44			1.13811
$902$			385.845i			0.427766i
$903$	46.4707	+	57.2698i	0.0514625	+	0.0634217i
$904$	−539.007			−0.596247
$905$		−	112.704i		−	0.124535i
$906$	−180.671	+	146.603i	−0.199416	+	0.161813i
$907$	−1061.57			−1.17042			−0.585212	−	0.810880i	$-0.698989\pi$
$907$	−1061.57			−1.17042			−0.585212	+	0.810880i	$0.698989\pi$
$908$			168.912i			0.186026i
$909$	−1206.77	−	253.997i	−1.32758	−	0.279424i
$910$	186.692			0.205156
$911$			44.8952i			0.0492813i	0.999696	+	0.0246406i	$0.00784415\pi$
$911$			44.8952i			0.0492813i	−0.999696	+	0.0246406i	$0.992156\pi$
$912$	250.807	+	309.091i	0.275007	+	0.338915i
$913$	252.069			0.276088
$914$			739.783i			0.809391i
$915$	−206.830	+	167.829i	−0.226044	+	0.183420i
$916$	796.936			0.870018
$917$		−	780.101i		−	0.850710i
$918$	674.320	−	346.124i	0.734554	−	0.377041i
$919$	1144.17			1.24501			0.622507	−	0.782614i	$-0.286114\pi$
$919$	1144.17			1.24501			0.622507	+	0.782614i	$0.286114\pi$
$920$			83.4050i			0.0906576i
$921$	−159.269	−	196.281i	−0.172931	−	0.213117i
$922$	40.5125			0.0439398
$923$		−	2918.36i		−	3.16182i
$924$	318.559	−	258.490i	0.344761	−	0.279751i
$925$	514.951			0.556704
$926$			911.931i			0.984806i
$927$	−289.804	+	1376.90i	−0.312626	+	1.48533i
$928$	113.477			0.122282
$929$			1551.47i			1.67004i	0.550217	+	0.835022i	$0.314545\pi$
$929$			1551.47i			1.67004i	−0.550217	+	0.835022i	$0.685455\pi$
$930$	23.1139	+	28.4853i	0.0248537	+	0.0306294i
$931$	−1243.36			−1.33551
$932$		−	781.947i		−	0.838998i
$933$	240.363	−	195.039i	0.257624	−	0.209045i
$934$	61.3184			0.0656514
$935$			685.918i			0.733602i
$936$	−565.020	−	118.923i	−0.603654	−	0.127055i
$937$	430.829			0.459796			0.229898	−	0.973215i	$-0.426161\pi$
$937$	430.829			0.459796			0.229898	+	0.973215i	$0.426161\pi$
$938$		−	53.9892i		−	0.0575578i
$939$	−643.096	−	792.543i	−0.684873	−	0.844029i
$940$	220.048			0.234094
$941$			1063.71i			1.13041i	0.824952	+	0.565203i	$0.191202\pi$
$941$			1063.71i			1.13041i	−0.824952	+	0.565203i	$0.808798\pi$
$942$	924.449	−	750.129i	0.981368	−	0.796315i
$943$	232.832			0.246906
$944$		−	30.7246i		−	0.0325472i
$945$	−71.7577	−	139.799i	−0.0759341	−	0.147935i
$946$	206.418			0.218201
$947$			1276.45i			1.34789i	0.738783	+	0.673943i	$0.235401\pi$
$947$			1276.45i			1.34789i	−0.738783	+	0.673943i	$0.764599\pi$
$948$	38.4638	+	47.4023i	0.0405736	+	0.0500024i
$949$	−3069.67			−3.23464
$950$		−	1034.78i		−	1.08924i
$951$	−187.964	+	152.520i	−0.197649	+	0.160379i
$952$	−190.532			−0.200139
$953$		−	935.932i		−	0.982090i	−0.871134	−	0.491045i	$-0.836615\pi$
$953$		−	935.932i		−	0.982090i	0.871134	−	0.491045i	$-0.163385\pi$
$954$	−135.422	+	643.406i	−0.141952	+	0.674430i
$955$	158.920			0.166408
$956$		−	188.208i		−	0.196871i
$957$	764.002	+	941.546i	0.798330	+	0.983851i
$958$	1065.34			1.11205
$959$		−	190.555i		−	0.198702i
$960$	−31.9619	+	25.9349i	−0.0332936	+	0.0270156i
$961$	−935.583			−0.973551
$962$		−	748.842i		−	0.778423i
$963$	−463.662	−	97.5899i	−0.481477	−	0.101339i
$964$	621.150			0.644347
$965$		−	177.685i		−	0.184129i
$966$	−155.981	−	192.229i	−0.161471	−	0.198995i
$967$	−271.777			−0.281052			−0.140526	−	0.990077i	$-0.544879\pi$
$967$	−271.777			−0.281052			−0.140526	+	0.990077i	$0.544879\pi$
$968$		−	805.947i		−	0.832589i
$969$	1533.90	−	1244.65i	1.58297	−	1.28447i
$970$	−152.387			−0.157100
$971$			1791.27i			1.84477i	0.386271	+	0.922386i	$0.373763\pi$
$971$			1791.27i			1.84477i	−0.386271	+	0.922386i	$0.626237\pi$
$972$	128.121	+	468.808i	0.131812	+	0.482313i
$973$	643.840			0.661706
$974$			1192.63i			1.22447i
$975$	945.793	+	1165.58i	0.970044	+	1.19547i
$976$	−207.077			−0.212169
$977$		−	229.761i		−	0.235170i	−0.993063	−	0.117585i	$-0.962485\pi$
$977$		−	229.761i		−	0.235170i	0.993063	−	0.117585i	$-0.0375153\pi$
$978$	−482.995	+	391.918i	−0.493859	+	0.400734i
$979$	−756.403			−0.772628
$980$		−	128.571i		−	0.131195i
$981$	−267.998	+	1273.29i	−0.273188	+	1.29795i
$982$	−56.8770			−0.0579195
$983$		−	467.486i		−	0.475570i	−0.971318	−	0.237785i	$-0.923579\pi$
$983$		−	467.486i		−	0.475570i	0.971318	−	0.237785i	$-0.0764214\pi$
$984$	72.3996	+	89.2243i	0.0735768	+	0.0906751i
$985$	−278.637			−0.282881
$986$		−	563.144i		−	0.571140i
$987$	−507.160	+	411.527i	−0.513840	+	0.416947i
$988$	−1504.78			−1.52305
$989$		−	124.560i		−	0.125945i
$990$	−430.375	−	90.5838i	−0.434722	−	0.0914988i
$991$	1549.34			1.56341			0.781706	−	0.623647i	$-0.214350\pi$
$991$	1549.34			1.56341			0.781706	+	0.623647i	$0.214350\pi$
$992$			28.5193i			0.0287493i
$993$	−278.650	−	343.405i	−0.280615	−	0.345826i
$994$	617.472			0.621200
$995$		−	56.2609i		−	0.0565436i
$996$	58.2893	−	47.2979i	0.0585233	−	0.0474878i
$997$	257.635			0.258410			0.129205	−	0.991618i	$-0.458758\pi$
$997$	257.635			0.258410			0.129205	+	0.991618i	$0.458758\pi$
$998$			8.20130i			0.00821773i
$999$	−560.748	+	287.828i	−0.561309	+	0.288116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.3.b.a.119.15	✓	40
3.2	odd	2	inner	354.3.b.a.119.35	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.3.b.a.119.15	✓	40	1.1	even	1	trivial
354.3.b.a.119.35	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)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(1.89028 + 2.32956i) q^{3} -2.00000 q^{4} -1.71502i q^{5} +(3.29449 - 2.67326i) q^{6} -3.39354 q^{7} +2.82843i q^{8} +(-1.85367 + 8.80704i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(1.89028 + 2.32956i) q^{3} -2.00000 q^{4} -1.71502i q^{5} +(3.29449 - 2.67326i) q^{6} -3.39354 q^{7} +2.82843i q^{8} +(-1.85367 + 8.80704i) q^{9} -2.42540 q^{10} -20.1481i q^{11} +(-3.78056 - 4.65911i) q^{12} +22.6824 q^{13} +4.79919i q^{14} +(3.99523 - 3.24187i) q^{15} +4.00000 q^{16} -19.8504i q^{17} +(12.4550 + 2.62149i) q^{18} +33.1705 q^{19} +3.43004i q^{20} +(-6.41475 - 7.90545i) q^{21} -28.4937 q^{22} +17.1941i q^{23} +(-6.58898 + 5.34652i) q^{24} +22.0587 q^{25} -32.0778i q^{26} +(-24.0205 + 12.3295i) q^{27} +6.78708 q^{28} +20.0602i q^{29} +(-4.58469 - 5.65011i) q^{30} -5.04155 q^{31} -5.65685i q^{32} +(46.9361 - 38.0855i) q^{33} -28.0727 q^{34} +5.81998i q^{35} +(3.70735 - 17.6141i) q^{36} +23.3446 q^{37} -46.9102i q^{38} +(42.8761 + 52.8400i) q^{39} +4.85080 q^{40} -13.5414i q^{41} +(-11.1800 + 9.07182i) q^{42} -7.24435 q^{43} +40.2962i q^{44} +(15.1042 + 3.17908i) q^{45} +24.3161 q^{46} -64.1532i q^{47} +(7.56113 + 9.31823i) q^{48} -37.4839 q^{49} -31.1957i q^{50} +(46.2427 - 37.5229i) q^{51} -45.3648 q^{52} +51.6584i q^{53} +(17.4366 + 33.9701i) q^{54} -34.5543 q^{55} -9.59838i q^{56} +(62.7016 + 77.2727i) q^{57} +28.3693 q^{58} -7.68115i q^{59} +(-7.99047 + 6.48373i) q^{60} -51.7692 q^{61} +7.12982i q^{62} +(6.29051 - 29.8870i) q^{63} -8.00000 q^{64} -38.9008i q^{65} +(-53.8611 - 66.3777i) q^{66} -11.2496 q^{67} +39.7009i q^{68} +(-40.0545 + 32.5016i) q^{69} +8.23070 q^{70} -128.662i q^{71} +(-24.9101 - 5.24298i) q^{72} -135.333 q^{73} -33.0142i q^{74} +(41.6972 + 51.3870i) q^{75} -66.3411 q^{76} +68.3733i q^{77} +(74.7270 - 60.6360i) q^{78} -10.1741 q^{79} -6.86007i q^{80} +(-74.1278 - 32.6507i) q^{81} -19.1505 q^{82} +12.5108i q^{83} +(12.8295 + 15.8109i) q^{84} -34.0439 q^{85} +10.2451i q^{86} +(-46.7313 + 37.9193i) q^{87} +56.9874 q^{88} -37.5422i q^{89} +(4.49590 - 21.3606i) q^{90} -76.9737 q^{91} -34.3881i q^{92} +(-9.52994 - 11.7446i) q^{93} -90.7264 q^{94} -56.8881i q^{95} +(13.1780 - 10.6930i) q^{96} +62.8295 q^{97} +53.0102i q^{98} +(177.445 + 37.3480i) 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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