LMFDB - Embedded newform 230.4.b.a.139.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,4,Mod(139,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("230.139");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.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:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 212 x^{12} + 17560 x^{10} + 728073 x^{8} + 16036416 x^{6} + 183184060 x^{4} + 961600400 x^{2} + 1560250000 $ x^14 + 212x^12 + 17560x^10 + 728073x^8 + 16036416x^6 + 183184060x^4 + 961600400x^2 + 1560250000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.8
Root			$-8.41501i$ of defining polynomial
Character	$\chi$	$=$	230.139
Dual form			230.4.b.a.139.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -7.41501i q^{3} -4.00000 q^{4} +(-9.96609 - 5.06726i) q^{5} +14.8300 q^{6} -26.6333i q^{7} -8.00000i q^{8} -27.9823 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} -7.41501i q^{3} -4.00000 q^{4} +(-9.96609 - 5.06726i) q^{5} +14.8300 q^{6} -26.6333i q^{7} -8.00000i q^{8} -27.9823 q^{9} +(10.1345 - 19.9322i) q^{10} -25.3692 q^{11} +29.6600i q^{12} +60.6466i q^{13} +53.2667 q^{14} +(-37.5738 + 73.8986i) q^{15} +16.0000 q^{16} +36.6195i q^{17} -55.9646i q^{18} +49.1712 q^{19} +(39.8643 + 20.2690i) q^{20} -197.486 q^{21} -50.7384i q^{22} -23.0000i q^{23} -59.3200 q^{24} +(73.6457 + 101.002i) q^{25} -121.293 q^{26} +7.28378i q^{27} +106.533i q^{28} -6.51697 q^{29} +(-147.797 - 75.1476i) q^{30} -145.280 q^{31} +32.0000i q^{32} +188.113i q^{33} -73.2389 q^{34} +(-134.958 + 265.430i) q^{35} +111.929 q^{36} +264.263i q^{37} +98.3424i q^{38} +449.695 q^{39} +(-40.5381 + 79.7287i) q^{40} -440.729 q^{41} -394.973i q^{42} -50.0251i q^{43} +101.477 q^{44} +(278.874 + 141.794i) q^{45} +46.0000 q^{46} -542.030i q^{47} -118.640i q^{48} -366.335 q^{49} +(-202.003 + 147.291i) q^{50} +271.533 q^{51} -242.586i q^{52} +186.225i q^{53} -14.5676 q^{54} +(252.832 + 128.552i) q^{55} -213.067 q^{56} -364.605i q^{57} -13.0339i q^{58} -458.921 q^{59} +(150.295 - 295.594i) q^{60} +104.258 q^{61} -290.561i q^{62} +745.262i q^{63} -64.0000 q^{64} +(307.312 - 604.409i) q^{65} -376.226 q^{66} -634.153i q^{67} -146.478i q^{68} -170.545 q^{69} +(-530.860 - 269.916i) q^{70} -319.766 q^{71} +223.858i q^{72} +731.912i q^{73} -528.526 q^{74} +(748.927 - 546.083i) q^{75} -196.685 q^{76} +675.667i q^{77} +899.390i q^{78} -6.71111 q^{79} +(-159.457 - 81.0762i) q^{80} -701.513 q^{81} -881.459i q^{82} -950.691i q^{83} +789.945 q^{84} +(185.560 - 364.953i) q^{85} +100.050 q^{86} +48.3234i q^{87} +202.954i q^{88} +690.124 q^{89} +(-283.587 + 557.748i) q^{90} +1615.22 q^{91} +92.0000i q^{92} +1077.25i q^{93} +1084.06 q^{94} +(-490.044 - 249.163i) q^{95} +237.280 q^{96} -551.999i q^{97} -732.669i q^{98} +709.889 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 56 q^{4} - 6 q^{5} - 36 q^{6} - 68 q^{9}+O(q^{10}) $ 14 * q - 56 * q^4 - 6 * q^5 - 36 * q^6 - 68 * q^9	$ 14 q - 56 q^{4} - 6 q^{5} - 36 q^{6} - 68 q^{9} - 40 q^{10} - 146 q^{11} + 176 q^{14} - 206 q^{15} + 224 q^{16} + 154 q^{19} + 24 q^{20} - 220 q^{21} + 144 q^{24} - 286 q^{25} - 180 q^{26} + 790 q^{29} - 232 q^{30} - 320 q^{31} - 200 q^{34} - 426 q^{35} + 272 q^{36} + 1616 q^{39} + 160 q^{40} - 1904 q^{41} + 584 q^{44} + 622 q^{45} + 644 q^{46} + 610 q^{49} + 200 q^{50} - 1834 q^{51} + 192 q^{54} + 854 q^{55} - 704 q^{56} + 2814 q^{59} + 824 q^{60} - 3742 q^{61} - 896 q^{64} + 1730 q^{65} - 612 q^{66} + 414 q^{69} + 348 q^{70} - 3808 q^{71} + 268 q^{74} + 2904 q^{75} - 616 q^{76} - 1528 q^{79} - 96 q^{80} - 4618 q^{81} + 880 q^{84} + 2574 q^{85} - 2024 q^{86} + 2336 q^{89} + 2092 q^{90} - 3866 q^{91} + 456 q^{94} + 838 q^{95} - 576 q^{96} + 3342 q^{99}+O(q^{100}) $ 14 * q - 56 * q^4 - 6 * q^5 - 36 * q^6 - 68 * q^9 - 40 * q^10 - 146 * q^11 + 176 * q^14 - 206 * q^15 + 224 * q^16 + 154 * q^19 + 24 * q^20 - 220 * q^21 + 144 * q^24 - 286 * q^25 - 180 * q^26 + 790 * q^29 - 232 * q^30 - 320 * q^31 - 200 * q^34 - 426 * q^35 + 272 * q^36 + 1616 * q^39 + 160 * q^40 - 1904 * q^41 + 584 * q^44 + 622 * q^45 + 644 * q^46 + 610 * q^49 + 200 * q^50 - 1834 * q^51 + 192 * q^54 + 854 * q^55 - 704 * q^56 + 2814 * q^59 + 824 * q^60 - 3742 * q^61 - 896 * q^64 + 1730 * q^65 - 612 * q^66 + 414 * q^69 + 348 * q^70 - 3808 * q^71 + 268 * q^74 + 2904 * q^75 - 616 * q^76 - 1528 * q^79 - 96 * q^80 - 4618 * q^81 + 880 * q^84 + 2574 * q^85 - 2024 * q^86 + 2336 * q^89 + 2092 * q^90 - 3866 * q^91 + 456 * q^94 + 838 * q^95 - 576 * q^96 + 3342 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$		−	7.41501i		−	1.42702i	−0.700646	−	0.713509i	$-0.747105\pi$
$3$		−	7.41501i		−	1.42702i	0.700646	−	0.713509i	$-0.252895\pi$
$4$	−4.00000			−0.500000
$5$	−9.96609	−	5.06726i	−0.891394	−	0.453230i
$5$	−9.96609	−	5.06726i	−0.891394	−	0.453230i
$6$	14.8300			1.00905
$7$		−	26.6333i		−	1.43807i	−0.694976	−	0.719033i	$-0.744585\pi$
$7$		−	26.6333i		−	1.43807i	0.694976	−	0.719033i	$-0.255415\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−27.9823			−1.03638
$10$	10.1345	−	19.9322i	0.320482	−	0.630311i
$11$	−25.3692			−0.695373			−0.347687	−	0.937611i	$-0.613033\pi$
$11$	−25.3692			−0.695373			−0.347687	+	0.937611i	$0.613033\pi$
$12$			29.6600i			0.713509i
$13$			60.6466i			1.29387i	0.762544	+	0.646936i	$0.223950\pi$
$13$			60.6466i			1.29387i	−0.762544	+	0.646936i	$0.776050\pi$
$14$	53.2667			1.01687
$15$	−37.5738	+	73.8986i	−0.646767	+	1.27204i
$16$	16.0000			0.250000
$17$			36.6195i			0.522442i	0.965279	+	0.261221i	$0.0841252\pi$
$17$			36.6195i			0.522442i	−0.965279	+	0.261221i	$0.915875\pi$
$18$		−	55.9646i		−	0.732832i
$19$	49.1712			0.593718			0.296859	−	0.954921i	$-0.404061\pi$
$19$	49.1712			0.593718			0.296859	+	0.954921i	$0.404061\pi$
$20$	39.8643	+	20.2690i	0.445697	+	0.226615i
$21$	−197.486			−2.05215
$22$		−	50.7384i		−	0.491703i
$23$		−	23.0000i		−	0.208514i
$23$		−	23.0000i		−	0.208514i
$24$	−59.3200			−0.504527
$25$	73.6457	+	101.002i	0.589166	+	0.808012i
$26$	−121.293			−0.914906
$27$			7.28378i			0.0519172i
$28$			106.533i			0.719033i
$29$	−6.51697			−0.0417300			−0.0208650	−	0.999782i	$-0.506642\pi$
$29$	−6.51697			−0.0417300			−0.0208650	+	0.999782i	$0.506642\pi$
$30$	−147.797	−	75.1476i	−0.899465	−	0.457333i
$31$	−145.280			−0.841713			−0.420857	−	0.907127i	$-0.638270\pi$
$31$	−145.280			−0.841713			−0.420857	+	0.907127i	$0.638270\pi$
$32$			32.0000i			0.176777i
$33$			188.113i			0.992310i
$34$	−73.2389			−0.369423
$35$	−134.958	+	265.430i	−0.651774	+	1.28188i
$36$	111.929			0.518191
$37$			264.263i			1.17418i	0.809523	+	0.587089i	$0.199726\pi$
$37$			264.263i			1.17418i	−0.809523	+	0.587089i	$0.800274\pi$
$38$			98.3424i			0.419822i
$39$	449.695			1.84638
$40$	−40.5381	+	79.7287i	−0.160241	+	0.315155i
$41$	−440.729			−1.67879			−0.839395	−	0.543522i	$-0.817090\pi$
$41$	−440.729			−1.67879			−0.839395	+	0.543522i	$0.817090\pi$
$42$		−	394.973i		−	1.45109i
$43$		−	50.0251i		−	0.177413i	−0.996058	−	0.0887065i	$-0.971727\pi$
$43$		−	50.0251i		−	0.177413i	0.996058	−	0.0887065i	$-0.0282733\pi$
$44$	101.477			0.347687
$45$	278.874	+	141.794i	0.923824	+	0.469719i
$46$	46.0000			0.147442
$47$		−	542.030i		−	1.68220i	−0.540882	−	0.841098i	$-0.681910\pi$
$47$		−	542.030i		−	1.68220i	0.540882	−	0.841098i	$-0.318090\pi$
$48$		−	118.640i		−	0.356755i
$49$	−366.335			−1.06803
$50$	−202.003	+	147.291i	−0.571351	+	0.416603i
$51$	271.533			0.745535
$52$		−	242.586i		−	0.646936i
$53$			186.225i			0.482642i	0.970445	+	0.241321i	$0.0775806\pi$
$53$			186.225i			0.482642i	−0.970445	+	0.241321i	$0.922419\pi$
$54$	−14.5676			−0.0367110
$55$	252.832	+	128.552i	0.619851	+	0.315164i
$56$	−213.067			−0.508433
$57$		−	364.605i		−	0.847247i
$58$		−	13.0339i		−	0.0295076i
$59$	−458.921			−1.01265			−0.506325	−	0.862343i	$-0.668997\pi$
$59$	−458.921			−1.01265			−0.506325	+	0.862343i	$0.668997\pi$
$60$	150.295	−	295.594i	0.323384	−	0.636018i
$61$	104.258			0.218834			0.109417	−	0.993996i	$-0.465102\pi$
$61$	104.258			0.218834			0.109417	+	0.993996i	$0.465102\pi$
$62$		−	290.561i		−	0.595181i
$63$			745.262i			1.49038i
$64$	−64.0000			−0.125000
$65$	307.312	−	604.409i	0.586421	−	1.15335i
$66$	−376.226			−0.701669
$67$		−	634.153i		−	1.15633i	−0.815920	−	0.578165i	$-0.803769\pi$
$67$		−	634.153i		−	1.15633i	0.815920	−	0.578165i	$-0.196231\pi$
$68$		−	146.478i		−	0.261221i
$69$	−170.545			−0.297554
$70$	−530.860	−	269.916i	−0.906428	−	0.460874i
$71$	−319.766			−0.534497			−0.267249	−	0.963628i	$-0.586114\pi$
$71$	−319.766			−0.534497			−0.267249	+	0.963628i	$0.586114\pi$
$72$			223.858i			0.366416i
$73$			731.912i			1.17348i	0.809777	+	0.586738i	$0.199588\pi$
$73$			731.912i			1.17348i	−0.809777	+	0.586738i	$0.800412\pi$
$74$	−528.526			−0.830269
$75$	748.927	−	546.083i	1.15305	−	0.840750i
$76$	−196.685			−0.296859
$77$			675.667i			0.999992i
$78$			899.390i			1.30559i
$79$	−6.71111			−0.00955771			−0.00477885	−	0.999989i	$-0.501521\pi$
$79$	−6.71111			−0.00955771			−0.00477885	+	0.999989i	$0.501521\pi$
$80$	−159.457	−	81.0762i	−0.222848	−	0.113307i
$81$	−701.513			−0.962295
$82$		−	881.459i		−	1.18708i
$83$		−	950.691i		−	1.25725i	−0.777708	−	0.628626i	$-0.783618\pi$
$83$		−	950.691i		−	1.25725i	0.777708	−	0.628626i	$-0.216382\pi$
$84$	789.945			1.02607
$85$	185.560	−	364.953i	0.236786	−	0.465702i
$86$	100.050			0.125450
$87$			48.3234i			0.0595495i
$88$			202.954i			0.245852i
$89$	690.124			0.821944			0.410972	−	0.911648i	$-0.365189\pi$
$89$	690.124			0.821944			0.410972	+	0.911648i	$0.365189\pi$
$90$	−283.587	+	557.748i	−0.332141	+	0.653242i
$91$	1615.22			1.86067
$92$			92.0000i			0.104257i
$93$			1077.25i			1.20114i
$94$	1084.06			1.18949
$95$	−490.044	−	249.163i	−0.529237	−	0.269091i
$96$	237.280			0.252264
$97$		−	551.999i		−	0.577804i	−0.957359	−	0.288902i	$-0.906710\pi$
$97$		−	551.999i		−	0.577804i	0.957359	−	0.288902i	$-0.0932902\pi$
$98$		−	732.669i		−	0.755212i
$99$	709.889			0.720672
$100$	−294.583	−	404.006i	−0.294583	−	0.404006i
$101$	992.339			0.977638			0.488819	−	0.872385i	$-0.337428\pi$
$101$	992.339			0.977638			0.488819	+	0.872385i	$0.337428\pi$
$102$			543.067i			0.527173i
$103$			1821.13i			1.74215i	0.491153	+	0.871074i	$0.336576\pi$
$103$			1821.13i			1.74215i	−0.491153	+	0.871074i	$0.663424\pi$
$104$	485.173			0.457453
$105$	1968.17	+	1000.72i	1.82927	+	0.930093i
$106$	−372.450			−0.341279
$107$			1452.42i			1.31225i	0.754653	+	0.656124i	$0.227805\pi$
$107$			1452.42i			1.31225i	−0.754653	+	0.656124i	$0.772195\pi$
$108$		−	29.1351i		−	0.0259586i
$109$	−938.847			−0.825002			−0.412501	−	0.910957i	$-0.635345\pi$
$109$	−938.847			−0.825002			−0.412501	+	0.910957i	$0.635345\pi$
$110$	−257.105	+	505.663i	−0.222854	+	0.438301i
$111$	1959.51			1.67557
$112$		−	426.133i		−	0.359516i
$113$		−	2001.96i		−	1.66662i	−0.552805	−	0.833311i	$-0.686442\pi$
$113$		−	2001.96i		−	1.66662i	0.552805	−	0.833311i	$-0.313558\pi$
$114$	729.210			0.599094
$115$	−116.547	+	229.220i	−0.0945049	+	0.185868i
$116$	26.0679			0.0208650
$117$		−	1697.03i		−	1.34095i
$118$		−	917.841i		−	0.716052i
$119$	975.298			0.751306
$120$	591.189	+	300.590i	0.449732	+	0.228667i
$121$	−687.403			−0.516456
$122$			208.516i			0.154739i
$123$			3268.01i			2.39566i
$124$	581.121			0.420857
$125$	−222.158	−	1379.77i	−0.158963	−	0.987284i
$126$	−1490.52			−1.05386
$127$		−	792.355i		−	0.553623i	−0.960924	−	0.276811i	$-0.910722\pi$
$127$		−	792.355i		−	0.553623i	0.960924	−	0.276811i	$-0.0892777\pi$
$128$		−	128.000i		−	0.0883883i
$129$	−370.936			−0.253172
$130$	1208.82	+	614.624i	0.815541	+	0.414663i
$131$	−1134.13			−0.756407			−0.378203	−	0.925723i	$-0.623458\pi$
$131$	−1134.13			−0.756407			−0.378203	+	0.925723i	$0.623458\pi$
$132$		−	752.451i		−	0.496155i
$133$		−	1309.59i		−	0.853806i
$134$	1268.31			0.817649
$135$	36.9088	−	72.5908i	0.0235304	−	0.0462787i
$136$	292.956			0.184711
$137$			2185.23i			1.36275i	0.731934	+	0.681375i	$0.238618\pi$
$137$			2185.23i			1.36275i	−0.731934	+	0.681375i	$0.761382\pi$
$138$		−	341.090i		−	0.210402i
$139$	842.036			0.513817			0.256908	−	0.966436i	$-0.417296\pi$
$139$	842.036			0.513817			0.256908	+	0.966436i	$0.417296\pi$
$140$	539.832	−	1061.72i	0.325887	−	0.640941i
$141$	−4019.16			−2.40053
$142$		−	639.533i		−	0.377946i
$143$		−	1538.56i		−	0.899724i
$144$	−447.717			−0.259095
$145$	64.9487	+	33.0232i	0.0371979	+	0.0189133i
$146$	−1463.82			−0.829773
$147$			2716.37i			1.52410i
$148$		−	1057.05i		−	0.587089i
$149$	−3198.23			−1.75845			−0.879225	−	0.476407i	$-0.841939\pi$
$149$	−3198.23			−1.75845			−0.879225	+	0.476407i	$0.841939\pi$
$150$	1092.17	+	1497.85i	0.594500	+	0.815328i
$151$	−2273.57			−1.22530			−0.612651	−	0.790354i	$-0.709897\pi$
$151$	−2273.57			−1.22530			−0.612651	+	0.790354i	$0.709897\pi$
$152$		−	393.370i		−	0.209911i
$153$		−	1024.70i		−	0.541450i
$154$	−1351.33			−0.707101
$155$	1447.88	+	736.173i	0.750298	+	0.381490i
$156$	−1798.78			−0.923190
$157$			1465.51i			0.744969i	0.928038	+	0.372485i	$0.121494\pi$
$157$			1465.51i			0.744969i	−0.928038	+	0.372485i	$0.878506\pi$
$158$		−	13.4222i		−	0.00675832i
$159$	1380.86			0.688738
$160$	162.152	−	318.915i	0.0801205	−	0.157578i
$161$	−612.567			−0.299857
$162$		−	1403.03i		−	0.680445i
$163$		−	3096.59i		−	1.48800i	−0.668181	−	0.743999i	$-0.732927\pi$
$163$		−	3096.59i		−	1.48800i	0.668181	−	0.743999i	$-0.267073\pi$
$164$	1762.92			0.839395
$165$	953.217	−	1874.75i	0.449745	−	0.884539i
$166$	1901.38			0.889012
$167$		−	344.415i		−	0.159591i	−0.996811	−	0.0797954i	$-0.974573\pi$
$167$		−	344.415i		−	0.159591i	0.996811	−	0.0797954i	$-0.0254267\pi$
$168$			1579.89i			0.725543i
$169$	−1481.01			−0.674106
$170$	729.905	+	371.121i	0.329301	+	0.167433i
$171$	−1375.92			−0.615319
$172$			200.100i			0.0887065i
$173$		−	3885.58i		−	1.70760i	−0.520599	−	0.853801i	$-0.674291\pi$
$173$		−	3885.58i		−	1.70760i	0.520599	−	0.853801i	$-0.325709\pi$
$174$	−96.6467			−0.0421079
$175$	2690.01	−	1961.43i	1.16197	−	0.847259i
$176$	−405.907			−0.173843
$177$			3402.90i			1.44507i
$178$			1380.25i			0.581202i
$179$	−3531.05			−1.47443			−0.737216	−	0.675657i	$-0.763860\pi$
$179$	−3531.05			−1.47443			−0.737216	+	0.675657i	$0.763860\pi$
$180$	−1115.50	−	567.175i	−0.461912	−	0.234859i
$181$	555.552			0.228143			0.114072	−	0.993473i	$-0.463611\pi$
$181$	555.552			0.228143			0.114072	+	0.993473i	$0.463611\pi$
$182$			3230.44i			1.31569i
$183$		−	773.073i		−	0.312280i
$184$	−184.000			−0.0737210
$185$	1339.09	−	2633.67i	0.532172	−	1.04665i
$186$	−2154.51			−0.849335
$187$		−	929.007i		−	0.363293i
$188$			2168.12i			0.841098i
$189$	193.991			0.0746603
$190$	498.327	−	980.089i	0.190276	−	0.374227i
$191$	−3820.92			−1.44750			−0.723750	−	0.690063i	$-0.757583\pi$
$191$	−3820.92			−1.44750			−0.723750	+	0.690063i	$0.757583\pi$
$192$			474.560i			0.178377i
$193$		−	3976.53i		−	1.48309i	−0.670902	−	0.741546i	$-0.734093\pi$
$193$		−	3976.53i		−	1.48309i	0.670902	−	0.741546i	$-0.265907\pi$
$194$	1104.00			0.408569
$195$	−4481.70	−	2278.72i	−1.64585	−	0.836834i
$196$	1465.34			0.534016
$197$		−	995.980i		−	0.360206i	−0.983648	−	0.180103i	$-0.942357\pi$
$197$		−	995.980i		−	0.360206i	0.983648	−	0.180103i	$-0.0576431\pi$
$198$			1419.78i			0.509592i
$199$	691.031			0.246160			0.123080	−	0.992397i	$-0.460723\pi$
$199$	691.031			0.246160			0.123080	+	0.992397i	$0.460723\pi$
$200$	808.012	−	589.166i	0.285675	−	0.208302i
$201$	−4702.25			−1.65011
$202$			1984.68i			0.691295i
$203$			173.569i			0.0600105i
$204$	−1086.13			−0.372767
$205$	4392.35	+	2233.29i	1.49646	+	0.760877i
$206$	−3642.26			−1.23188
$207$			643.593i			0.216101i
$208$			970.346i			0.323468i
$209$	−1247.43			−0.412856
$210$	−2001.43	+	3936.33i	−0.657675	+	1.29349i
$211$	4398.05			1.43495			0.717475	−	0.696584i	$-0.245298\pi$
$211$	4398.05			1.43495			0.717475	+	0.696584i	$0.245298\pi$
$212$		−	744.901i		−	0.241321i
$213$			2371.07i			0.762737i
$214$	−2904.84			−0.927900
$215$	−253.490	+	498.554i	−0.0804088	+	0.158145i
$216$	58.2703			0.0183555
$217$			3869.30i			1.21044i
$218$		−	1877.69i		−	0.583365i
$219$	5427.13			1.67457
$220$	−1011.33	−	514.210i	−0.309926	−	0.157582i
$221$	−2220.85			−0.675974
$222$			3919.02i			1.18481i
$223$			5541.43i			1.66404i	0.554743	+	0.832022i	$0.312817\pi$
$223$			5541.43i			1.66404i	−0.554743	+	0.832022i	$0.687183\pi$
$224$	852.267			0.254216
$225$	−2060.78	−	2826.26i	−0.610600	−	0.837409i
$226$	4003.91			1.17848
$227$			3675.12i			1.07457i	0.843402	+	0.537283i	$0.180549\pi$
$227$			3675.12i			1.07457i	−0.843402	+	0.537283i	$0.819451\pi$
$228$			1458.42i			0.423624i
$229$	4710.64			1.35934			0.679668	−	0.733520i	$-0.262124\pi$
$229$	4710.64			1.35934			0.679668	+	0.733520i	$0.262124\pi$
$230$	−458.440	−	233.094i	−0.131429	−	0.0668251i
$231$	5010.07			1.42701
$232$			52.1357i			0.0147538i
$233$		−	1731.69i		−	0.486895i	−0.969914	−	0.243447i	$-0.921722\pi$
$233$		−	1731.69i		−	0.486895i	0.969914	−	0.243447i	$-0.0782783\pi$
$234$	3394.06			0.948192
$235$	−2746.61	+	5401.92i	−0.762421	+	1.49950i
$236$	1835.68			0.506325
$237$			49.7629i			0.0136390i
$238$			1950.60i			0.531254i
$239$	−5150.85			−1.39406			−0.697031	−	0.717041i	$-0.745496\pi$
$239$	−5150.85			−1.39406			−0.697031	+	0.717041i	$0.745496\pi$
$240$	−601.180	+	1182.38i	−0.161692	+	0.318009i
$241$	−1179.54			−0.315272			−0.157636	−	0.987497i	$-0.550387\pi$
$241$	−1179.54			−0.315272			−0.157636	+	0.987497i	$0.550387\pi$
$242$		−	1374.81i		−	0.365190i
$243$			5398.38i			1.42513i
$244$	−417.032			−0.109417
$245$	3650.92	+	1856.31i	0.952036	+	0.484063i
$246$	−6536.02			−1.69399
$247$			2982.07i			0.768196i
$248$			1162.24i			0.297591i
$249$	−7049.38			−1.79412
$250$	2759.54	−	444.316i	0.698116	−	0.112404i
$251$	−1301.86			−0.327381			−0.163691	−	0.986512i	$-0.552340\pi$
$251$	−1301.86			−0.327381			−0.163691	+	0.986512i	$0.552340\pi$
$252$		−	2981.05i		−	0.745192i
$253$			583.492i			0.144995i
$254$	1584.71			0.391470
$255$	−2706.13	−	1375.93i	−0.664565	−	0.337899i
$256$	256.000			0.0625000
$257$		−	5799.91i		−	1.40774i	−0.710330	−	0.703869i	$-0.751454\pi$
$257$		−	5799.91i		−	1.40774i	0.710330	−	0.703869i	$-0.248546\pi$
$258$		−	741.873i		−	0.179019i
$259$	7038.20			1.68854
$260$	−1229.25	+	2417.64i	−0.293211	+	0.576675i
$261$	182.360			0.0432482
$262$		−	2268.26i		−	0.534860i
$263$		−	253.549i		−	0.0594469i	−0.999558	−	0.0297234i	$-0.990537\pi$
$263$		−	253.549i		−	0.0594469i	0.999558	−	0.0297234i	$-0.00946266\pi$
$264$	1504.90			0.350835
$265$	943.652	−	1855.94i	0.218747	−	0.430224i
$266$	2619.19			0.603732
$267$		−	5117.28i		−	1.17293i
$268$			2536.61i			0.578165i
$269$	5379.15			1.21923			0.609614	−	0.792698i	$-0.291324\pi$
$269$	5379.15			1.21923			0.609614	+	0.792698i	$0.291324\pi$
$270$	145.182	+	73.8177i	0.0327240	+	0.0166385i
$271$	−5707.95			−1.27946			−0.639730	−	0.768600i	$-0.720954\pi$
$271$	−5707.95			−1.27946			−0.639730	+	0.768600i	$0.720954\pi$
$272$			585.911i			0.130611i
$273$		−	11976.9i		−	2.65521i
$274$	−4370.46			−0.963610
$275$	−1868.33	−	2562.33i	−0.409690	−	0.561870i
$276$	682.180			0.148777
$277$		−	5086.99i		−	1.10342i	−0.834036	−	0.551710i	$-0.813976\pi$
$277$		−	5086.99i		−	1.10342i	0.834036	−	0.551710i	$-0.186024\pi$
$278$			1684.07i			0.363323i
$279$	4065.28			0.872336
$280$	2123.44	+	1079.66i	0.453214	+	0.230437i
$281$	−4543.03			−0.964464			−0.482232	−	0.876044i	$-0.660174\pi$
$281$	−4543.03			−0.964464			−0.482232	+	0.876044i	$0.660174\pi$
$282$		−	8038.31i		−	1.69743i
$283$		−	746.480i		−	0.156797i	−0.996922	−	0.0783987i	$-0.975019\pi$
$283$		−	746.480i		−	0.156797i	0.996922	−	0.0783987i	$-0.0249807\pi$
$284$	1279.07			0.267249
$285$	−1847.55	+	3633.68i	−0.383998	+	0.755231i
$286$	3077.11			0.636201
$287$			11738.1i			2.41421i
$288$		−	895.434i		−	0.183208i
$289$	3572.02			0.727054
$290$	−66.0464	+	129.897i	−0.0133737	+	0.0263029i
$291$	−4093.07			−0.824537
$292$		−	2927.65i		−	0.586738i
$293$			1621.69i			0.323344i	0.986845	+	0.161672i	$0.0516887\pi$
$293$			1621.69i			0.323344i	−0.986845	+	0.161672i	$0.948311\pi$
$294$	−5432.75			−1.07770
$295$	4573.64	+	2325.47i	0.902671	+	0.458963i
$296$	2114.10			0.415134
$297$		−	184.784i		−	0.0361018i
$298$		−	6396.45i		−	1.24341i
$299$	1394.87			0.269791
$300$	−2995.71	+	2184.33i	−0.576524	+	0.420375i
$301$	−1332.34			−0.255131
$302$		−	4547.14i		−	0.866419i
$303$		−	7358.20i		−	1.39511i
$304$	786.739			0.148430
$305$	−1039.04	−	528.303i	−0.195067	−	0.0991820i
$306$	2049.39			0.382863
$307$		−	9357.68i		−	1.73964i	−0.493365	−	0.869822i	$-0.664233\pi$
$307$		−	9357.68i		−	1.73964i	0.493365	−	0.869822i	$-0.335767\pi$
$308$		−	2702.67i		−	0.499996i
$309$	13503.7			2.48608
$310$	−1472.35	+	2895.75i	−0.269754	+	0.530541i
$311$	−4377.57			−0.798165			−0.399083	−	0.916915i	$-0.630671\pi$
$311$	−4377.57			−0.798165			−0.399083	+	0.916915i	$0.630671\pi$
$312$		−	3597.56i		−	0.652794i
$313$		−	8599.38i		−	1.55292i	−0.630164	−	0.776462i	$-0.717012\pi$
$313$		−	8599.38i		−	1.55292i	0.630164	−	0.776462i	$-0.282988\pi$
$314$	−2931.01			−0.526773
$315$	3776.44	−	7427.35i	0.675486	−	1.32852i
$316$	26.8444			0.00477885
$317$			3733.46i			0.661489i	0.943720	+	0.330745i	$0.107300\pi$
$317$			3733.46i			0.661489i	−0.943720	+	0.330745i	$0.892700\pi$
$318$			2761.72i			0.487012i
$319$	165.330			0.0290179
$320$	637.829	+	324.305i	0.111424	+	0.0566537i
$321$	10769.7			1.87260
$322$		−	1225.13i		−	0.212031i
$323$			1800.62i			0.310184i
$324$	2806.05			0.481147
$325$	−6125.40	+	4466.36i	−1.04546	+	0.762305i
$326$	6193.18			1.05217
$327$			6961.55i			1.17729i
$328$			3525.84i			0.593542i
$329$	−14436.1			−2.41911
$330$	3749.50	+	1906.43i	0.625464	+	0.318017i
$331$	9019.87			1.49782			0.748908	−	0.662674i	$-0.230579\pi$
$331$	9019.87			1.49782			0.748908	+	0.662674i	$0.230579\pi$
$332$			3802.77i			0.628626i
$333$		−	7394.68i		−	1.21690i
$334$	688.831			0.112848
$335$	−3213.42	+	6320.03i	−0.524084	+	1.03075i
$336$	−3159.78			−0.513036
$337$		−	2644.57i		−	0.427474i	−0.976891	−	0.213737i	$-0.931436\pi$
$337$		−	2644.57i		−	0.427474i	0.976891	−	0.213737i	$-0.0685636\pi$
$338$		−	2962.02i		−	0.476665i
$339$	−14844.5			−2.37830
$340$	−742.241	+	1459.81i	−0.118393	+	0.232851i
$341$	3685.65			0.585305
$342$		−	2751.85i		−	0.435096i
$343$			621.481i			0.0978333i
$344$	−400.201			−0.0627249
$345$	1699.67	+	864.197i	0.265238	+	0.134860i
$346$	7771.16			1.20746
$347$			7702.70i			1.19165i	0.803115	+	0.595825i	$0.203175\pi$
$347$			7702.70i			1.19165i	−0.803115	+	0.595825i	$0.796825\pi$
$348$		−	193.293i		−	0.0297748i
$349$	1639.99			0.251538			0.125769	−	0.992060i	$-0.459860\pi$
$349$	1639.99			0.251538			0.125769	+	0.992060i	$0.459860\pi$
$350$	3922.86	+	5380.02i	0.599102	+	0.821640i
$351$	−441.737			−0.0671742
$352$		−	811.815i		−	0.122926i
$353$			9936.57i			1.49822i	0.662448	+	0.749108i	$0.269518\pi$
$353$			9936.57i			1.49822i	−0.662448	+	0.749108i	$0.730482\pi$
$354$	−6805.80			−1.02182
$355$	3186.82	+	1620.34i	0.476447	+	0.242250i
$356$	−2760.50			−0.410972
$357$		−	7231.84i		−	1.07213i
$358$		−	7062.11i		−	1.04258i
$359$	−1639.78			−0.241070			−0.120535	−	0.992709i	$-0.538461\pi$
$359$	−1639.78			−0.241070			−0.120535	+	0.992709i	$0.538461\pi$
$360$	1134.35	−	2230.99i	0.166071	−	0.326621i
$361$	−4441.19			−0.647498
$362$			1111.10i			0.161321i
$363$			5097.10i			0.736992i
$364$	−6460.89			−0.930336
$365$	3708.79	−	7294.29i	0.531854	−	1.04603i
$366$	1546.15			0.220815
$367$			4270.10i			0.607349i	0.952776	+	0.303675i	$0.0982136\pi$
$367$			4270.10i			0.607349i	−0.952776	+	0.303675i	$0.901786\pi$
$368$		−	368.000i		−	0.0521286i
$369$	12332.6			1.73987
$370$	5267.33	+	2678.18i	0.740096	+	0.376302i
$371$	4959.80			0.694070
$372$		−	4309.02i		−	0.600570i
$373$			10457.7i			1.45169i	0.687858	+	0.725845i	$0.258551\pi$
$373$			10457.7i			1.45169i	−0.687858	+	0.725845i	$0.741449\pi$
$374$	1858.01			0.256887
$375$	−10231.0	+	1647.30i	−1.40887	+	0.226844i
$376$	−4336.24			−0.594746
$377$		−	395.232i		−	0.0539933i
$378$			387.983i			0.0527928i
$379$	10804.6			1.46437			0.732184	−	0.681107i	$-0.238501\pi$
$379$	10804.6			1.46437			0.732184	+	0.681107i	$0.238501\pi$
$380$	1960.18	+	996.654i	0.264618	+	0.134545i
$381$	−5875.31			−0.790030
$382$		−	7641.85i		−	1.02354i
$383$		−	6247.24i		−	0.833470i	−0.909028	−	0.416735i	$-0.863174\pi$
$383$		−	6247.24i		−	0.833470i	0.909028	−	0.416735i	$-0.136826\pi$
$384$	−949.121			−0.126132
$385$	3423.78	−	6733.75i	0.453226	−	0.891387i
$386$	7953.06			1.04870
$387$			1399.82i			0.183867i
$388$			2207.99i			0.288902i
$389$	12886.5			1.67962			0.839808	−	0.542884i	$-0.182668\pi$
$389$	12886.5			1.67962			0.839808	+	0.542884i	$0.182668\pi$
$390$	4557.44	−	8963.39i	0.591731	−	1.16379i
$391$	842.247			0.108937
$392$			2930.68i			0.377606i
$393$			8409.57i			1.07941i
$394$	1991.96			0.254704
$395$	66.8835	+	34.0070i	0.00851968	+	0.00433184i
$396$	−2839.56			−0.360336
$397$			3861.28i			0.488141i	0.969757	+	0.244071i	$0.0784829\pi$
$397$			3861.28i			0.488141i	−0.969757	+	0.244071i	$0.921517\pi$
$398$			1382.06i			0.174061i
$399$	−9710.64			−1.21840
$400$	1178.33	+	1616.02i	0.147291	+	0.202003i
$401$	−1100.88			−0.137096			−0.0685478	−	0.997648i	$-0.521837\pi$
$401$	−1100.88			−0.137096			−0.0685478	+	0.997648i	$0.521837\pi$
$402$		−	9404.50i		−	1.16680i
$403$		−	8810.76i		−	1.08907i
$404$	−3969.36			−0.488819
$405$	6991.34	+	3554.75i	0.857784	+	0.436141i
$406$	−347.137			−0.0424338
$407$		−	6704.14i		−	0.816491i
$408$		−	2172.27i		−	0.263586i
$409$	2202.71			0.266301			0.133150	−	0.991096i	$-0.457491\pi$
$409$	2202.71			0.266301			0.133150	+	0.991096i	$0.457491\pi$
$410$	−4466.58	+	8784.69i	−0.538022	+	1.05816i
$411$	16203.5			1.94467
$412$		−	7284.52i		−	0.871074i
$413$			12222.6i			1.45626i
$414$	−1287.19			−0.152806
$415$	−4817.40	+	9474.67i	−0.569824	+	1.12071i
$416$	−1940.69			−0.228726
$417$		−	6243.70i		−	0.733226i
$418$		−	2494.87i		−	0.291933i
$419$	5074.99			0.591717			0.295858	−	0.955232i	$-0.404394\pi$
$419$	5074.99			0.591717			0.295858	+	0.955232i	$0.404394\pi$
$420$	−7872.66	−	4002.86i	−0.914635	−	0.465047i
$421$	510.933			0.0591481			0.0295741	−	0.999563i	$-0.490585\pi$
$421$	510.933			0.0591481			0.0295741	+	0.999563i	$0.490585\pi$
$422$			8796.11i			1.01466i
$423$			15167.3i			1.74340i
$424$	1489.80			0.170640
$425$	−3698.62	+	2696.87i	−0.422140	+	0.307805i
$426$	−4742.14			−0.539337
$427$		−	2776.74i		−	0.314697i
$428$		−	5809.67i		−	0.656124i
$429$	−11408.4			−1.28392
$430$	−997.109	−	506.981i	−0.111825	−	0.0568576i
$431$	−14607.7			−1.63255			−0.816276	−	0.577662i	$-0.803965\pi$
$431$	−14607.7			−1.63255			−0.816276	+	0.577662i	$0.803965\pi$
$432$			116.541i			0.0129793i
$433$		−	17650.2i		−	1.95893i	−0.201625	−	0.979463i	$-0.564622\pi$
$433$		−	17650.2i		−	1.95893i	0.201625	−	0.979463i	$-0.435378\pi$
$434$	−7738.60			−0.855909
$435$	244.867	−	481.595i	0.0269896	−	0.0530821i
$436$	3755.39			0.412501
$437$		−	1130.94i		−	0.123799i
$438$			10854.3i			1.18410i
$439$	5454.72			0.593029			0.296515	−	0.955028i	$-0.404176\pi$
$439$	5454.72			0.593029			0.296515	+	0.955028i	$0.404176\pi$
$440$	1028.42	−	2022.65i	0.111427	−	0.219151i
$441$	10250.9			1.10689
$442$		−	4441.69i		−	0.477986i
$443$		−	2245.81i		−	0.240862i	−0.992722	−	0.120431i	$-0.961572\pi$
$443$		−	2245.81i		−	0.240862i	0.992722	−	0.120431i	$-0.0384276\pi$
$444$	−7838.04			−0.837786
$445$	−6877.84	−	3497.04i	−0.732676	−	0.372530i
$446$	−11082.9			−1.17666
$447$			23714.9i			2.50934i
$448$			1704.53i			0.179758i
$449$	3215.48			0.337969			0.168984	−	0.985619i	$-0.445951\pi$
$449$	3215.48			0.337969			0.168984	+	0.985619i	$0.445951\pi$
$450$	5652.51	−	4121.55i	0.592138	−	0.431760i
$451$	11181.0			1.16739
$452$			8007.83i			0.833311i
$453$			16858.5i			1.74853i
$454$	−7350.24			−0.759832
$455$	−16097.4	−	8184.75i	−1.65859	−	0.843312i
$456$	−2916.84			−0.299547
$457$			4645.03i			0.475461i	0.971331	+	0.237730i	$0.0764034\pi$
$457$			4645.03i			0.475461i	−0.971331	+	0.237730i	$0.923597\pi$
$458$			9421.29i			0.961196i
$459$	−266.728			−0.0271237
$460$	466.188	−	916.880i	0.0472525	−	0.0929342i
$461$	−3513.95			−0.355012			−0.177506	−	0.984120i	$-0.556803\pi$
$461$	−3513.95			−0.355012			−0.177506	+	0.984120i	$0.556803\pi$
$462$			10020.1i			1.00905i
$463$			4584.34i			0.460156i	0.973172	+	0.230078i	$0.0738982\pi$
$463$			4584.34i			0.460156i	−0.973172	+	0.230078i	$0.926102\pi$
$464$	−104.271			−0.0104325
$465$	5458.73	−	10736.0i	0.544393	−	1.07069i
$466$	3463.37			0.344287
$467$		−	5295.74i		−	0.524748i	−0.964966	−	0.262374i	$-0.915495\pi$
$467$		−	5295.74i		−	0.524748i	0.964966	−	0.262374i	$-0.0845055\pi$
$468$			6788.13i			0.670473i
$469$	−16889.6			−1.66288
$470$	−10803.8	−	5493.22i	−1.06031	−	0.539113i
$471$	10866.7			1.06308
$472$			3671.37i			0.358026i
$473$			1269.10i			0.123368i
$474$	−99.5258			−0.00964425
$475$	3621.25	+	4966.37i	0.349798	+	0.479732i
$476$	−3901.19			−0.375653
$477$		−	5211.01i		−	0.500201i
$478$		−	10301.7i		−	0.985751i
$479$	4816.99			0.459486			0.229743	−	0.973251i	$-0.426211\pi$
$479$	4816.99			0.459486			0.229743	+	0.973251i	$0.426211\pi$
$480$	−2364.75	−	1202.36i	−0.224866	−	0.114333i
$481$	−16026.6			−1.51924
$482$		−	2359.07i		−	0.222931i
$483$			4542.19i			0.427902i
$484$	2749.61			0.258228
$485$	−2797.12	+	5501.27i	−0.261878	+	0.515051i
$486$	−10796.8			−1.00772
$487$		−	7337.78i		−	0.682765i	−0.939924	−	0.341383i	$-0.889105\pi$
$487$		−	7337.78i		−	0.682765i	0.939924	−	0.341383i	$-0.110895\pi$
$488$		−	834.064i		−	0.0773695i
$489$	−22961.2			−2.12340
$490$	−3712.63	+	7301.85i	−0.342285	+	0.673191i
$491$	16862.1			1.54985			0.774924	−	0.632055i	$-0.217788\pi$
$491$	16862.1			1.54985			0.774924	+	0.632055i	$0.217788\pi$
$492$		−	13072.0i		−	1.19783i
$493$		−	238.648i		−	0.0218015i
$494$	−5964.13			−0.543196
$495$	−7074.81	−	3597.19i	−0.642403	−	0.326630i
$496$	−2324.48			−0.210428
$497$			8516.45i			0.768642i
$498$		−	14098.8i		−	1.26864i
$499$	−4420.50			−0.396571			−0.198285	−	0.980144i	$-0.563537\pi$
$499$	−4420.50			−0.396571			−0.198285	+	0.980144i	$0.563537\pi$
$500$	888.632	+	5519.09i	0.0794817	+	0.493642i
$501$	−2553.84			−0.227739
$502$		−	2603.72i		−	0.231493i
$503$			4286.51i			0.379972i	0.981787	+	0.189986i	$0.0608443\pi$
$503$			4286.51i			0.379972i	−0.981787	+	0.189986i	$0.939156\pi$
$504$	5962.10			0.526930
$505$	−9889.74	−	5028.44i	−0.871461	−	0.443095i
$506$	−1166.98			−0.102527
$507$			10981.7i			0.961961i
$508$			3169.42i			0.276811i
$509$	13227.5			1.15186			0.575932	−	0.817497i	$-0.304639\pi$
$509$	13227.5			1.15186			0.575932	+	0.817497i	$0.304639\pi$
$510$	2751.86	−	5412.25i	0.238930	−	0.469919i
$511$	19493.3			1.68754
$512$			512.000i			0.0441942i
$513$			358.152i			0.0308242i
$514$	11599.8			0.995420
$515$	9228.14	−	18149.5i	0.789593	−	1.55294i
$516$	1483.75			0.126586
$517$			13750.9i			1.16975i
$518$			14076.4i			1.19398i
$519$	−28811.6			−2.43678
$520$	−4835.27	−	2458.50i	−0.407771	−	0.207331i
$521$	16808.0			1.41338			0.706691	−	0.707522i	$-0.250187\pi$
$521$	16808.0			1.41338			0.706691	+	0.707522i	$0.250187\pi$
$522$			364.720i			0.0305811i
$523$		−	5161.90i		−	0.431575i	−0.976440	−	0.215788i	$-0.930768\pi$
$523$		−	5161.90i		−	0.431575i	0.976440	−	0.215788i	$-0.0692319\pi$
$524$	4536.52			0.378203
$525$	−14544.0	−	19946.4i	−1.20905	−	1.65816i
$526$	507.099			0.0420353
$527$		−	5320.09i		−	0.439747i
$528$			3009.81i			0.248078i
$529$	−529.000			−0.0434783
$530$	3711.87	+	1887.30i	0.304214	+	0.154678i
$531$	12841.7			1.04949
$532$			5238.37i			0.426903i
$533$		−	26728.7i		−	2.17214i
$534$	10234.6			0.829386
$535$	7359.78	−	14474.9i	0.594750	−	1.16973i
$536$	−5073.23			−0.408825
$537$			26182.8i			2.10404i
$538$			10758.3i			0.862124i
$539$	9293.62			0.742680
$540$	−147.635	+	290.363i	−0.0117652	+	0.0231393i
$541$	−9051.24			−0.719303			−0.359652	−	0.933087i	$-0.617104\pi$
$541$	−9051.24			−0.719303			−0.359652	+	0.933087i	$0.617104\pi$
$542$		−	11415.9i		−	0.904714i
$543$		−	4119.42i		−	0.325564i
$544$	−1171.82			−0.0923556
$545$	9356.63	+	4757.38i	0.735402	+	0.373915i
$546$	23953.8			1.87752
$547$		−	14780.5i		−	1.15533i	−0.816272	−	0.577667i	$-0.803963\pi$
$547$		−	14780.5i		−	1.15533i	0.816272	−	0.577667i	$-0.196037\pi$
$548$		−	8740.92i		−	0.681375i
$549$	−2917.38			−0.226795
$550$	5124.66	−	3736.67i	0.397302	−	0.289695i
$551$	−320.447			−0.0247759
$552$			1364.36i			0.105201i
$553$			178.739i			0.0137446i
$554$	10174.0			0.780236
$555$	−19528.7	−	9929.36i	−1.49359	−	0.759419i
$556$	−3368.14			−0.256908
$557$			13384.6i			1.01818i	0.860714	+	0.509089i	$0.170018\pi$
$557$			13384.6i			1.01818i	−0.860714	+	0.509089i	$0.829982\pi$
$558$			8130.56i			0.616835i
$559$	3033.85			0.229550
$560$	−2159.33	+	4246.88i	−0.162943	+	0.320471i
$561$	−6888.59			−0.518425
$562$		−	9086.06i		−	0.681979i
$563$			4921.85i			0.368439i	0.982885	+	0.184219i	$0.0589757\pi$
$563$			4921.85i			0.368439i	−0.982885	+	0.184219i	$0.941024\pi$
$564$	16076.6			1.20026
$565$	−10144.4	+	19951.7i	−0.755363	+	1.48562i
$566$	1492.96			0.110872
$567$			18683.6i			1.38384i
$568$			2558.13i			0.188973i
$569$	−4491.21			−0.330899			−0.165449	−	0.986218i	$-0.552907\pi$
$569$	−4491.21			−0.330899			−0.165449	+	0.986218i	$0.552907\pi$
$570$	−7267.36	−	3695.10i	−0.534029	−	0.271527i
$571$	20804.3			1.52475			0.762376	−	0.647134i	$-0.224033\pi$
$571$	20804.3			1.52475			0.762376	+	0.647134i	$0.224033\pi$
$572$			6154.23i			0.449862i
$573$			28332.2i			2.06561i
$574$	−23476.2			−1.70710
$575$	2323.04	−	1693.85i	0.168482	−	0.122850i
$576$	1790.87			0.129548
$577$			9851.32i			0.710773i	0.934720	+	0.355386i	$0.115651\pi$
$577$			9851.32i			0.710773i	−0.934720	+	0.355386i	$0.884349\pi$
$578$			7144.03i			0.514105i
$579$	−29486.0			−2.11640
$580$	−259.795	−	132.093i	−0.0185989	−	0.00945664i
$581$	−25320.1			−1.80801
$582$		−	8186.15i		−	0.583036i
$583$		−	4724.39i		−	0.335616i
$584$	5855.29			0.414887
$585$	−8599.30	+	16912.8i	−0.607756	+	1.19531i
$586$	−3243.37			−0.228639
$587$		−	21285.7i		−	1.49669i	−0.663312	−	0.748343i	$-0.730850\pi$
$587$		−	21285.7i		−	1.49669i	0.663312	−	0.748343i	$-0.269150\pi$
$588$		−	10865.5i		−	0.762050i
$589$	−7143.61			−0.499741
$590$	−4650.94	+	9147.29i	−0.324536	+	0.638284i
$591$	−7385.19			−0.514021
$592$			4228.21i			0.293544i
$593$		−	25025.6i		−	1.73301i	−0.499166	−	0.866507i	$-0.666360\pi$
$593$		−	25025.6i		−	1.73301i	0.499166	−	0.866507i	$-0.333640\pi$
$594$	369.568			0.0255279
$595$	−9719.91	−	4942.09i	−0.669710	−	0.340514i
$596$	12792.9			0.879225
$597$		−	5124.00i		−	0.351275i
$598$			2789.74i			0.190771i
$599$	5675.98			0.387169			0.193584	−	0.981084i	$-0.437989\pi$
$599$	5675.98			0.387169			0.193584	+	0.981084i	$0.437989\pi$
$600$	−4368.67	−	5991.42i	−0.297250	−	0.407664i
$601$	−12140.5			−0.823993			−0.411997	−	0.911185i	$-0.635168\pi$
$601$	−12140.5			−0.823993			−0.411997	+	0.911185i	$0.635168\pi$
$602$		−	2664.67i		−	0.180405i
$603$			17745.1i			1.19840i
$604$	9094.28			0.612651
$605$	6850.72	+	3483.25i	0.460366	+	0.234073i
$606$	14716.4			0.986490
$607$			29118.4i			1.94708i	0.228514	+	0.973541i	$0.426613\pi$
$607$			29118.4i			1.94708i	−0.228514	+	0.973541i	$0.573387\pi$
$608$			1573.48i			0.104956i
$609$	1287.01			0.0856361
$610$	1056.61	−	2078.09i	0.0701323	−	0.137933i
$611$	32872.3			2.17655
$612$			4098.79i			0.270725i
$613$		−	13614.6i		−	0.897047i	−0.893771	−	0.448524i	$-0.851950\pi$
$613$		−	13614.6i		−	0.897047i	0.893771	−	0.448524i	$-0.148050\pi$
$614$	18715.4			1.23011
$615$	16559.9	−	32569.3i	1.08579	−	2.13548i
$616$	5405.33			0.353551
$617$		−	13254.6i		−	0.864848i	−0.901670	−	0.432424i	$-0.857658\pi$
$617$		−	13254.6i		−	0.864848i	0.901670	−	0.432424i	$-0.142342\pi$
$618$			27007.4i			1.75792i
$619$	2828.92			0.183690			0.0918448	−	0.995773i	$-0.470724\pi$
$619$	2828.92			0.183690			0.0918448	+	0.995773i	$0.470724\pi$
$620$	−5791.50	−	2944.69i	−0.375149	−	0.190745i
$621$	167.527			0.0108255
$622$		−	8755.14i		−	0.564388i
$623$		−	18380.3i		−	1.18201i
$624$	7195.12			0.461595
$625$	−4777.62	+	14876.7i	−0.305768	+	0.952106i
$626$	17198.8			1.09808
$627$			9249.74i			0.589153i
$628$		−	5862.03i		−	0.372485i
$629$	−9677.16			−0.613440
$630$	14854.7	+	7552.88i	0.939405	+	0.477641i
$631$	−3884.80			−0.245089			−0.122545	−	0.992463i	$-0.539105\pi$
$631$	−3884.80			−0.245089			−0.122545	+	0.992463i	$0.539105\pi$
$632$			53.6889i			0.00337916i
$633$		−	32611.6i		−	2.04770i
$634$	−7466.92			−0.467743
$635$	−4015.07	+	7896.67i	−0.250918	+	0.493496i
$636$	−5523.44			−0.344369
$637$		−	22217.0i		−	1.38190i
$638$			330.661i			0.0205188i
$639$	8947.80			0.553943
$640$	−648.610	+	1275.66i	−0.0400602	+	0.0787888i
$641$	−21776.9			−1.34186			−0.670932	−	0.741519i	$-0.734106\pi$
$641$	−21776.9			−1.34186			−0.670932	+	0.741519i	$0.734106\pi$
$642$			21539.4i			1.32413i
$643$			9109.57i			0.558704i	0.960189	+	0.279352i	$0.0901196\pi$
$643$			9109.57i			0.558704i	−0.960189	+	0.279352i	$0.909880\pi$
$644$	2450.27			0.149929
$645$	3696.78	+	1879.63i	0.225676	+	0.114745i
$646$	−3601.25			−0.219333
$647$		−	12489.1i		−	0.758885i	−0.925215	−	0.379443i	$-0.876116\pi$
$647$		−	12489.1i		−	0.758885i	0.925215	−	0.379443i	$-0.123884\pi$
$648$			5612.10i			0.340223i
$649$	11642.5			0.704170
$650$	−8932.72	−	12250.8i	−0.539031	−	0.739255i
$651$	28690.9			1.72732
$652$			12386.4i			0.743999i
$653$			166.022i			0.00994937i	0.999988	+	0.00497469i	$0.00158350\pi$
$653$			166.022i			0.00994937i	−0.999988	+	0.00497469i	$0.998417\pi$
$654$	−13923.1			−0.832472
$655$	11302.8	+	5746.93i	0.674256	+	0.342826i
$656$	−7051.67			−0.419697
$657$		−	20480.6i		−	1.21617i
$658$		−	28872.1i		−	1.71057i
$659$	−12635.5			−0.746901			−0.373451	−	0.927650i	$-0.621825\pi$
$659$	−12635.5			−0.746901			−0.373451	+	0.927650i	$0.621825\pi$
$660$	−3812.87	+	7498.99i	−0.224872	+	0.442270i
$661$	2113.97			0.124393			0.0621965	−	0.998064i	$-0.480189\pi$
$661$	2113.97			0.124393			0.0621965	+	0.998064i	$0.480189\pi$
$662$			18039.7i			1.05912i
$663$			16467.6i			0.964627i
$664$	−7605.53			−0.444506
$665$	−6636.05	+	13051.5i	−0.386970	+	0.761077i
$666$	14789.4			0.860475
$667$			149.890i			0.00870131i
$668$			1377.66i			0.0797954i
$669$	41089.8			2.37462
$670$	−12640.1	−	6426.84i	−0.728848	−	0.370583i
$671$	−2644.94			−0.152171
$672$		−	6319.56i		−	0.362771i
$673$		−	10625.1i		−	0.608570i	−0.952581	−	0.304285i	$-0.901582\pi$
$673$		−	10625.1i		−	0.608570i	0.952581	−	0.304285i	$-0.0984176\pi$
$674$	5289.14			0.302270
$675$	−735.673	+	536.419i	−0.0419497	+	0.0305878i
$676$	5924.04			0.337053
$677$			5359.69i			0.304268i	0.988360	+	0.152134i	$0.0486145\pi$
$677$			5359.69i			0.304268i	−0.988360	+	0.152134i	$0.951385\pi$
$678$		−	29689.0i		−	1.68171i
$679$	−14701.6			−0.830920
$680$	−2919.62	−	1484.48i	−0.164650	−	0.0837167i
$681$	27251.0			1.53342
$682$			7371.29i			0.413873i
$683$		−	28827.6i		−	1.61502i	−0.589855	−	0.807509i	$-0.700815\pi$
$683$		−	28827.6i		−	1.61502i	0.589855	−	0.807509i	$-0.299185\pi$
$684$	5503.69			0.307659
$685$	11073.1	−	21778.2i	0.617639	−	1.21475i
$686$	−1242.96			−0.0691786
$687$		−	34929.4i		−	1.93980i
$688$		−	800.402i		−	0.0443532i
$689$	−11293.9			−0.624476
$690$	−1728.39	+	3399.33i	−0.0953606	+	0.187551i
$691$	−1262.44			−0.0695014			−0.0347507	−	0.999396i	$-0.511064\pi$
$691$	−1262.44			−0.0695014			−0.0347507	+	0.999396i	$0.511064\pi$
$692$			15542.3i			0.853801i
$693$		−	18906.7i		−	1.03637i
$694$	−15405.4			−0.842623
$695$	−8391.80	−	4266.82i	−0.458013	−	0.232877i
$696$	386.587			0.0210539
$697$		−	16139.3i		−	0.877071i
$698$			3279.98i			0.177864i
$699$	−12840.5			−0.694808
$700$	−10760.0	+	7845.72i	−0.580987	+	0.423629i
$701$	−26478.5			−1.42665			−0.713323	−	0.700836i	$-0.752811\pi$
$701$	−26478.5			−1.42665			−0.713323	+	0.700836i	$0.752811\pi$
$702$		−	883.473i		−	0.0474994i
$703$			12994.1i			0.697131i
$704$	1623.63			0.0869217
$705$	40055.3	+	20366.1i	2.13981	+	1.08799i
$706$	−19873.1			−1.05940
$707$		−	26429.3i		−	1.40591i
$708$		−	13611.6i		−	0.722536i
$709$	27586.4			1.46125			0.730626	−	0.682778i	$-0.239228\pi$
$709$	27586.4			1.46125			0.730626	+	0.682778i	$0.239228\pi$
$710$	−3240.68	+	6373.64i	−0.171297	+	0.336899i
$711$	187.792			0.00990543
$712$		−	5520.99i		−	0.290601i
$713$			3341.45i			0.175509i
$714$	14463.7			0.758109
$715$	−7796.27	+	15333.4i	−0.407782	+	0.802009i
$716$	14124.2			0.737216
$717$			38193.6i			1.98935i
$718$		−	3279.56i		−	0.170462i
$719$	−6624.27			−0.343593			−0.171797	−	0.985132i	$-0.554957\pi$
$719$	−6624.27			−0.343593			−0.171797	+	0.985132i	$0.554957\pi$
$720$	4461.98	+	2268.70i	0.230956	+	0.117430i
$721$	48502.7			2.50532
$722$		−	8882.38i		−	0.457851i
$723$			8746.26i			0.449899i
$724$	−2222.21			−0.114072
$725$	−479.947	−	658.224i	−0.0245859	−	0.0337184i
$726$	−10194.2			−0.521132
$727$		−	30879.9i		−	1.57534i	−0.616098	−	0.787669i	$-0.711288\pi$
$727$		−	30879.9i		−	1.57534i	0.616098	−	0.787669i	$-0.288712\pi$
$728$		−	12921.8i		−	0.657847i
$729$	21088.2			1.07139
$730$	14588.6	+	7417.58i	0.739655	+	0.376078i
$731$	1831.89			0.0926880
$732$			3092.29i			0.156140i
$733$			13403.4i			0.675396i	0.941254	+	0.337698i	$0.109648\pi$
$733$			13403.4i			0.675396i	−0.941254	+	0.337698i	$0.890352\pi$
$734$	−8540.19			−0.429461
$735$	13764.6	−	27071.6i	0.690768	−	1.35857i
$736$	736.000			0.0368605
$737$			16088.0i			0.804082i
$738$			24665.3i			1.23027i
$739$	−30097.4			−1.49817			−0.749087	−	0.662472i	$-0.769507\pi$
$739$	−30097.4			−1.49817			−0.749087	+	0.662472i	$0.769507\pi$
$740$	−5356.36	+	10534.7i	−0.266086	+	0.523327i
$741$	22112.0			1.09623
$742$			9919.60i			0.490782i
$743$			4990.51i			0.246412i	0.992381	+	0.123206i	$0.0393176\pi$
$743$			4990.51i			0.246412i	−0.992381	+	0.123206i	$0.960682\pi$
$744$	8618.03			0.424667
$745$	31873.8	+	16206.3i	1.56747	+	0.796982i
$746$	−20915.5			−1.02650
$747$			26602.5i			1.30299i
$748$			3716.03i			0.181646i
$749$	38682.7			1.88710
$750$	−3294.61	−	20462.0i	−0.160403	−	0.996224i
$751$	−10747.2			−0.522199			−0.261099	−	0.965312i	$-0.584085\pi$
$751$	−10747.2			−0.522199			−0.261099	+	0.965312i	$0.584085\pi$
$752$		−	8672.48i		−	0.420549i
$753$			9653.29i			0.467179i
$754$	790.464			0.0381790
$755$	22658.6	+	11520.8i	1.09223	+	0.555343i
$756$	−775.966			−0.0373302
$757$			22449.3i			1.07785i	0.842353	+	0.538927i	$0.181170\pi$
$757$			22449.3i			1.07785i	−0.842353	+	0.538927i	$0.818830\pi$
$758$			21609.2i			1.03546i
$759$	4326.60			0.206911
$760$	−1993.31	+	3920.36i	−0.0951380	+	0.187113i
$761$	−38506.2			−1.83423			−0.917114	−	0.398626i	$-0.869487\pi$
$761$	−38506.2			−1.83423			−0.917114	+	0.398626i	$0.869487\pi$
$762$		−	11750.6i		−	0.558636i
$763$			25004.6i			1.18641i
$764$	15283.7			0.723750
$765$	−5192.41	+	10212.2i	−0.245401	+	0.482645i
$766$	12494.5			0.589352
$767$		−	27832.0i		−	1.31024i
$768$		−	1898.24i		−	0.0891887i
$769$	13262.4			0.621916			0.310958	−	0.950424i	$-0.399350\pi$
$769$	13262.4			0.621916			0.310958	+	0.950424i	$0.399350\pi$
$770$	13467.5	+	6847.56i	0.630306	+	0.320479i
$771$	−43006.4			−2.00887
$772$			15906.1i			0.741546i
$773$		−	8103.40i		−	0.377049i	−0.982068	−	0.188525i	$-0.939630\pi$
$773$		−	8103.40i		−	0.377049i	0.982068	−	0.188525i	$-0.0603705\pi$
$774$	−2799.63			−0.130014
$775$	−10699.3	−	14673.5i	−0.495909	−	0.680115i
$776$	−4415.99			−0.204285
$777$		−	52188.3i		−	2.40958i
$778$			25773.0i			1.18767i
$779$	−21671.2			−0.996728
$780$	17926.8	+	9114.89i	0.822926	+	0.418417i
$781$	8112.22			0.371675
$782$			1684.49i			0.0770299i
$783$		−	47.4682i		−	0.00216651i
$784$	−5861.36			−0.267008
$785$	7426.11	−	14605.4i	0.337642	−	0.664061i
$786$	−16819.1			−0.763256
$787$			15331.8i			0.694435i	0.937785	+	0.347217i	$0.112873\pi$
$787$			15331.8i			0.694435i	−0.937785	+	0.347217i	$0.887127\pi$
$788$			3983.92i			0.180103i
$789$	−1880.07			−0.0848318
$790$	−68.0139	+	133.767i	−0.00306307	+	0.00602432i
$791$	−53318.8			−2.39671
$792$		−	5679.11i		−	0.254796i
$793$			6322.89i			0.283143i
$794$	−7722.56			−0.345168
$795$	−13761.8	−	6997.18i	−0.613937	−	0.312157i
$796$	−2764.12			−0.123080
$797$			32664.6i			1.45174i	0.687830	+	0.725872i	$0.258564\pi$
$797$			32664.6i			1.45174i	−0.687830	+	0.725872i	$0.741436\pi$
$798$		−	19421.3i		−	0.861536i
$799$	19848.8			0.878851
$800$	−3232.05	+	2356.66i	−0.142838	+	0.104151i
$801$	−19311.3			−0.851848
$802$		−	2201.76i		−	0.0969412i
$803$		−	18568.0i		−	0.816004i
$804$	18809.0			0.825053
$805$	6104.89	+	3104.04i	0.267291	+	0.135904i
$806$	17621.5			0.770089
$807$		−	39886.4i		−	1.73986i
$808$		−	7938.72i		−	0.345647i
$809$	−13154.7			−0.571685			−0.285843	−	0.958277i	$-0.592274\pi$
$809$	−13154.7			−0.571685			−0.285843	+	0.958277i	$0.592274\pi$
$810$	−7109.50	+	13982.7i	−0.308398	+	0.606545i
$811$	−28576.8			−1.23732			−0.618660	−	0.785659i	$-0.712324\pi$
$811$	−28576.8			−1.23732			−0.618660	+	0.785659i	$0.712324\pi$
$812$		−	694.274i		−	0.0300052i
$813$			42324.5i			1.82581i
$814$	13408.3			0.577347
$815$	−15691.2	+	30860.9i	−0.674405	+	1.32639i
$816$	4344.53			0.186384
$817$		−	2459.79i		−	0.105333i
$818$			4405.42i			0.188303i
$819$	−45197.6			−1.92837
$820$	−17569.4	−	8933.17i	−0.748231	−	0.380439i
$821$	11918.8			0.506660			0.253330	−	0.967380i	$-0.418474\pi$
$821$	11918.8			0.506660			0.253330	+	0.967380i	$0.418474\pi$
$822$			32407.0i			1.37509i
$823$			2861.21i			0.121185i	0.998163	+	0.0605926i	$0.0192990\pi$
$823$			2861.21i			0.121185i	−0.998163	+	0.0605926i	$0.980701\pi$
$824$	14569.0			0.615942
$825$	−18999.7	+	13853.7i	−0.801799	+	0.584635i
$826$	−24445.2			−1.02973
$827$		−	35821.3i		−	1.50620i	−0.657905	−	0.753101i	$-0.728557\pi$
$827$		−	35821.3i		−	1.50620i	0.657905	−	0.753101i	$-0.271443\pi$
$828$		−	2574.37i		−	0.108050i
$829$	−33694.8			−1.41166			−0.705831	−	0.708380i	$-0.749426\pi$
$829$	−33694.8			−1.41166			−0.705831	+	0.708380i	$0.749426\pi$
$830$	−18949.3	−	9634.80i	−0.792459	−	0.402926i
$831$	−37720.0			−1.57460
$832$		−	3881.38i		−	0.161734i
$833$		−	13415.0i		−	0.557985i
$834$	12487.4			0.518469
$835$	−1745.24	+	3432.47i	−0.0723313	+	0.142258i
$836$	4989.74			0.206428
$837$		−	1058.19i		−	0.0436994i
$838$			10150.0i			0.418407i
$839$	42930.4			1.76653			0.883266	−	0.468872i	$-0.155339\pi$
$839$	42930.4			1.76653			0.883266	+	0.468872i	$0.155339\pi$
$840$	8005.72	−	15745.3i	0.328838	−	0.646744i
$841$	−24346.5			−0.998259
$842$			1021.87i			0.0418240i
$843$			33686.6i			1.37631i
$844$	−17592.2			−0.717475
$845$	14759.9	+	7504.67i	0.600894	+	0.305525i
$846$	−30334.5			−1.23277
$847$			18307.8i			0.742697i
$848$			2979.60i			0.120660i
$849$	−5535.16			−0.223753
$850$	−5393.73	−	7397.24i	−0.217651	−	0.298498i
$851$	6078.05			0.244833
$852$		−	9484.28i		−	0.381369i
$853$		−	7660.65i		−	0.307498i	−0.988110	−	0.153749i	$-0.950865\pi$
$853$		−	7660.65i		−	0.307498i	0.988110	−	0.153749i	$-0.0491347\pi$
$854$	5553.48			0.222525
$855$	13712.6	+	6972.17i	0.548491	+	0.278881i
$856$	11619.3			0.463950
$857$			17647.1i			0.703398i	0.936113	+	0.351699i	$0.114396\pi$
$857$			17647.1i			0.703398i	−0.936113	+	0.351699i	$0.885604\pi$
$858$		−	22816.8i		−	0.907871i
$859$	−34871.9			−1.38512			−0.692559	−	0.721362i	$-0.743517\pi$
$859$	−34871.9			−1.38512			−0.692559	+	0.721362i	$0.743517\pi$
$860$	1013.96	−	1994.22i	0.0402044	−	0.0790724i
$861$	87038.0			3.44512
$862$		−	29215.5i		−	1.15439i
$863$		−	3617.71i		−	0.142698i	−0.997451	−	0.0713490i	$-0.977270\pi$
$863$		−	3617.71i		−	0.142698i	0.997451	−	0.0713490i	$-0.0227304\pi$
$864$	−233.081			−0.00917775
$865$	−19689.3	+	38724.0i	−0.773936	+	1.52215i
$866$	35300.4			1.38517
$867$		−	26486.5i		−	1.03752i
$868$		−	15477.2i		−	0.605219i
$869$	170.256			0.00664617
$870$	963.189	+	489.734i	0.0375347	+	0.0190845i
$871$	38459.2			1.49614
$872$			7510.77i			0.291682i
$873$			15446.2i			0.598825i
$874$	2261.88			0.0875390
$875$	−36747.9	+	5916.81i	−1.41978	+	0.228600i
$876$	−21708.5			−0.837286
$877$		−	18951.7i		−	0.729707i	−0.931065	−	0.364854i	$-0.881119\pi$
$877$		−	18951.7i		−	0.729707i	0.931065	−	0.364854i	$-0.118881\pi$
$878$			10909.4i			0.419335i
$879$	12024.8			0.461418
$880$	4045.31	+	2056.84i	0.154963	+	0.0787910i
$881$	49650.1			1.89870			0.949350	−	0.314222i	$-0.101744\pi$
$881$	49650.1			1.89870			0.949350	+	0.314222i	$0.101744\pi$
$882$			20501.8i			0.782688i
$883$		−	23831.2i		−	0.908248i	−0.890938	−	0.454124i	$-0.849952\pi$
$883$		−	23831.2i		−	0.908248i	0.890938	−	0.454124i	$-0.150048\pi$
$884$	8883.38			0.337987
$885$	17243.4	−	33913.6i	0.654949	−	1.28813i
$886$	4491.62			0.170315
$887$			5629.77i			0.213111i	0.994307	+	0.106555i	$0.0339821\pi$
$887$			5629.77i			0.213111i	−0.994307	+	0.106555i	$0.966018\pi$
$888$		−	15676.1i		−	0.592404i
$889$	−21103.0			−0.796146
$890$	6994.08	−	13755.7i	0.263418	−	0.518080i
$891$	17796.8			0.669154
$892$		−	22165.7i		−	0.832022i
$893$		−	26652.3i		−	0.998751i
$894$	−47429.7			−1.77437
$895$	35190.8	+	17892.8i	1.31430	+	0.668257i
$896$	−3409.07			−0.127108
$897$		−	10343.0i		−	0.384997i
$898$			6430.96i			0.238980i
$899$	946.787			0.0351247
$900$	8243.11	+	11305.0i	0.305300	+	0.418705i
$901$	−6819.46			−0.252152
$902$			22361.9i			0.825466i
$903$			9879.27i			0.364077i
$904$	−16015.7			−0.589240
$905$	−5536.68	−	2815.13i	−0.203365	−	0.103401i
$906$	−33717.1			−1.23640
$907$		−	13317.5i		−	0.487542i	−0.969833	−	0.243771i	$-0.921616\pi$
$907$		−	13317.5i		−	0.487542i	0.969833	−	0.243771i	$-0.0783845\pi$
$908$		−	14700.5i		−	0.537283i
$909$	−27767.9			−1.01321
$910$	16369.5	−	32194.9i	0.596312	−	1.17280i
$911$	−24307.2			−0.884009			−0.442005	−	0.897013i	$-0.645733\pi$
$911$	−24307.2			−0.884009			−0.442005	+	0.897013i	$0.645733\pi$
$912$		−	5833.68i		−	0.211812i
$913$			24118.3i			0.874260i
$914$	−9290.07			−0.336201
$915$	−3917.37	+	7704.52i	−0.141535	+	0.278364i
$916$	−18842.6			−0.679668
$917$			30205.6i			1.08776i
$918$		−	533.456i		−	0.0191794i
$919$	14643.9			0.525634			0.262817	−	0.964846i	$-0.415348\pi$
$919$	14643.9			0.525634			0.262817	+	0.964846i	$0.415348\pi$
$920$	1833.76	+	932.376i	0.0657144	+	0.0334125i
$921$	−69387.2			−2.48251
$922$		−	7027.89i		−	0.251032i
$923$		−	19392.7i		−	0.691571i
$924$	−20040.3			−0.713504
$925$	−26691.0	+	19461.8i	−0.948750	+	0.691785i
$926$	−9168.68			−0.325380
$927$		−	50959.4i		−	1.80553i
$928$		−	208.543i		−	0.00737690i
$929$	48078.4			1.69796			0.848978	−	0.528428i	$-0.177219\pi$
$929$	48078.4			1.69796			0.848978	+	0.528428i	$0.177219\pi$
$930$	21472.0	+	10917.5i	0.757092	+	0.384944i
$931$	−18013.1			−0.634110
$932$			6926.74i			0.243447i
$933$			32459.7i			1.13900i
$934$	10591.5			0.371053
$935$	−4707.52	+	9258.56i	−0.164655	+	0.323837i
$936$	−13576.3			−0.474096
$937$		−	15245.2i		−	0.531527i	−0.964038	−	0.265763i	$-0.914376\pi$
$937$		−	15245.2i		−	0.531527i	0.964038	−	0.265763i	$-0.0856240\pi$
$938$		−	33779.2i		−	1.17583i
$939$	−63764.4			−2.21605
$940$	10986.4	−	21607.7i	0.381211	−	0.749750i
$941$	−609.283			−0.0211074			−0.0105537	−	0.999944i	$-0.503359\pi$
$941$	−609.283			−0.0211074			−0.0105537	+	0.999944i	$0.503359\pi$
$942$			21733.5i			0.751715i
$943$			10136.8i			0.350052i
$944$	−7342.73			−0.253163
$945$	−1933.33	−	983.005i	−0.0665517	−	0.0338383i
$946$	−2538.19			−0.0872345
$947$		−	36941.2i		−	1.26761i	−0.773492	−	0.633806i	$-0.781492\pi$
$947$		−	36941.2i		−	1.26761i	0.773492	−	0.633806i	$-0.218508\pi$
$948$		−	199.052i		−	0.00681951i
$949$	−44388.0			−1.51833
$950$	−9932.74	+	7242.50i	−0.339222	+	0.247345i
$951$	27683.6			0.943957
$952$		−	7802.39i		−	0.265627i
$953$			20501.9i			0.696876i	0.937332	+	0.348438i	$0.113288\pi$
$953$			20501.9i			0.696876i	−0.937332	+	0.348438i	$0.886712\pi$
$954$	10422.0			0.353695
$955$	38079.7	+	19361.6i	1.29029	+	0.656050i
$956$	20603.4			0.697031
$957$		−	1225.93i		−	0.0414091i
$958$			9633.97i			0.324906i
$959$	58200.0			1.95972
$960$	2404.72	−	4729.51i	0.0808459	−	0.159004i
$961$	−8684.63			−0.291519
$962$		−	32053.3i		−	1.07426i
$963$		−	40642.0i		−	1.35999i
$964$	4718.14			0.157636
$965$	−20150.1	+	39630.4i	−0.672182	+	1.32202i
$966$	−9084.37			−0.302572
$967$			42017.7i			1.39731i	0.715460	+	0.698654i	$0.246217\pi$
$967$			42017.7i			1.39731i	−0.715460	+	0.698654i	$0.753783\pi$
$968$			5499.22i			0.182595i
$969$	13351.6			0.442638
$970$	−11002.5	−	5594.24i	−0.364196	−	0.185176i
$971$	−33748.7			−1.11540			−0.557698	−	0.830044i	$-0.688315\pi$
$971$	−33748.7			−1.11540			−0.557698	+	0.830044i	$0.688315\pi$
$972$		−	21593.5i		−	0.712565i
$973$		−	22426.2i		−	0.738902i
$974$	14675.6			0.482788
$975$	33118.1	+	45419.9i	1.08782	+	1.49190i
$976$	1668.13			0.0547085
$977$		−	14869.5i		−	0.486917i	−0.969911	−	0.243458i	$-0.921718\pi$
$977$		−	14869.5i		−	0.486917i	0.969911	−	0.243458i	$-0.0782820\pi$
$978$		−	45922.5i		−	1.50147i
$979$	−17507.9			−0.571558
$980$	−14603.7	−	7425.26i	−0.476018	−	0.242032i
$981$	26271.1			0.855017
$982$			33724.2i			1.09591i
$983$			45876.2i			1.48853i	0.667886	+	0.744264i	$0.267199\pi$
$983$			45876.2i			1.48853i	−0.667886	+	0.744264i	$0.732801\pi$
$984$	26144.1			0.846995
$985$	−5046.89	+	9926.02i	−0.163256	+	0.321085i
$986$	477.296			0.0154160
$987$			107044.i			3.45211i
$988$		−	11928.3i		−	0.384098i
$989$	−1150.58			−0.0369932
$990$	7194.39	−	14149.6i	0.230962	−	0.454247i
$991$	−27273.4			−0.874237			−0.437118	−	0.899404i	$-0.644001\pi$
$991$	−27273.4			−0.874237			−0.437118	+	0.899404i	$0.644001\pi$
$992$		−	4648.97i		−	0.148795i
$993$		−	66882.4i		−	2.13741i
$994$	−17032.9			−0.543512
$995$	−6886.87	−	3501.63i	−0.219426	−	0.111567i
$996$	28197.5			0.897061
$997$			12178.4i			0.386855i	0.981115	+	0.193428i	$0.0619604\pi$
$997$			12178.4i			0.386855i	−0.981115	+	0.193428i	$0.938040\pi$
$998$		−	8841.01i		−	0.280418i
$999$	−1924.83			−0.0609600

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.b.a.139.8	yes	14
5.2	odd	4		1150.4.a.y.1.1		7
5.3	odd	4		1150.4.a.z.1.7		7
5.4	even	2	inner	230.4.b.a.139.7	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.b.a.139.7	✓	14	5.4	even	2	inner
230.4.b.a.139.8	yes	14	1.1	even	1	trivial
1150.4.a.y.1.1		7	5.2	odd	4
1150.4.a.z.1.7		7	5.3	odd	4

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -7.41501i q^{3} -4.00000 q^{4} +(-9.96609 - 5.06726i) q^{5} +14.8300 q^{6} -26.6333i q^{7} -8.00000i q^{8} -27.9823 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} -7.41501i q^{3} -4.00000 q^{4} +(-9.96609 - 5.06726i) q^{5} +14.8300 q^{6} -26.6333i q^{7} -8.00000i q^{8} -27.9823 q^{9} +(10.1345 - 19.9322i) q^{10} -25.3692 q^{11} +29.6600i q^{12} +60.6466i q^{13} +53.2667 q^{14} +(-37.5738 + 73.8986i) q^{15} +16.0000 q^{16} +36.6195i q^{17} -55.9646i q^{18} +49.1712 q^{19} +(39.8643 + 20.2690i) q^{20} -197.486 q^{21} -50.7384i q^{22} -23.0000i q^{23} -59.3200 q^{24} +(73.6457 + 101.002i) q^{25} -121.293 q^{26} +7.28378i q^{27} +106.533i q^{28} -6.51697 q^{29} +(-147.797 - 75.1476i) q^{30} -145.280 q^{31} +32.0000i q^{32} +188.113i q^{33} -73.2389 q^{34} +(-134.958 + 265.430i) q^{35} +111.929 q^{36} +264.263i q^{37} +98.3424i q^{38} +449.695 q^{39} +(-40.5381 + 79.7287i) q^{40} -440.729 q^{41} -394.973i q^{42} -50.0251i q^{43} +101.477 q^{44} +(278.874 + 141.794i) q^{45} +46.0000 q^{46} -542.030i q^{47} -118.640i q^{48} -366.335 q^{49} +(-202.003 + 147.291i) q^{50} +271.533 q^{51} -242.586i q^{52} +186.225i q^{53} -14.5676 q^{54} +(252.832 + 128.552i) q^{55} -213.067 q^{56} -364.605i q^{57} -13.0339i q^{58} -458.921 q^{59} +(150.295 - 295.594i) q^{60} +104.258 q^{61} -290.561i q^{62} +745.262i q^{63} -64.0000 q^{64} +(307.312 - 604.409i) q^{65} -376.226 q^{66} -634.153i q^{67} -146.478i q^{68} -170.545 q^{69} +(-530.860 - 269.916i) q^{70} -319.766 q^{71} +223.858i q^{72} +731.912i q^{73} -528.526 q^{74} +(748.927 - 546.083i) q^{75} -196.685 q^{76} +675.667i q^{77} +899.390i q^{78} -6.71111 q^{79} +(-159.457 - 81.0762i) q^{80} -701.513 q^{81} -881.459i q^{82} -950.691i q^{83} +789.945 q^{84} +(185.560 - 364.953i) q^{85} +100.050 q^{86} +48.3234i q^{87} +202.954i q^{88} +690.124 q^{89} +(-283.587 + 557.748i) q^{90} +1615.22 q^{91} +92.0000i q^{92} +1077.25i q^{93} +1084.06 q^{94} +(-490.044 - 249.163i) q^{95} +237.280 q^{96} -551.999i q^{97} -732.669i q^{98} +709.889 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 56 q^{4} - 6 q^{5} - 36 q^{6} - 68 q^{9}+O(q^{10}) \) 14 * q - 56 * q^4 - 6 * q^5 - 36 * q^6 - 68 * q^9	\( 14 q - 56 q^{4} - 6 q^{5} - 36 q^{6} - 68 q^{9} - 40 q^{10} - 146 q^{11} + 176 q^{14} - 206 q^{15} + 224 q^{16} + 154 q^{19} + 24 q^{20} - 220 q^{21} + 144 q^{24} - 286 q^{25} - 180 q^{26} + 790 q^{29} - 232 q^{30} - 320 q^{31} - 200 q^{34} - 426 q^{35} + 272 q^{36} + 1616 q^{39} + 160 q^{40} - 1904 q^{41} + 584 q^{44} + 622 q^{45} + 644 q^{46} + 610 q^{49} + 200 q^{50} - 1834 q^{51} + 192 q^{54} + 854 q^{55} - 704 q^{56} + 2814 q^{59} + 824 q^{60} - 3742 q^{61} - 896 q^{64} + 1730 q^{65} - 612 q^{66} + 414 q^{69} + 348 q^{70} - 3808 q^{71} + 268 q^{74} + 2904 q^{75} - 616 q^{76} - 1528 q^{79} - 96 q^{80} - 4618 q^{81} + 880 q^{84} + 2574 q^{85} - 2024 q^{86} + 2336 q^{89} + 2092 q^{90} - 3866 q^{91} + 456 q^{94} + 838 q^{95} - 576 q^{96} + 3342 q^{99}+O(q^{100}) \) 14 * q - 56 * q^4 - 6 * q^5 - 36 * q^6 - 68 * q^9 - 40 * q^10 - 146 * q^11 + 176 * q^14 - 206 * q^15 + 224 * q^16 + 154 * q^19 + 24 * q^20 - 220 * q^21 + 144 * q^24 - 286 * q^25 - 180 * q^26 + 790 * q^29 - 232 * q^30 - 320 * q^31 - 200 * q^34 - 426 * q^35 + 272 * q^36 + 1616 * q^39 + 160 * q^40 - 1904 * q^41 + 584 * q^44 + 622 * q^45 + 644 * q^46 + 610 * q^49 + 200 * q^50 - 1834 * q^51 + 192 * q^54 + 854 * q^55 - 704 * q^56 + 2814 * q^59 + 824 * q^60 - 3742 * q^61 - 896 * q^64 + 1730 * q^65 - 612 * q^66 + 414 * q^69 + 348 * q^70 - 3808 * q^71 + 268 * q^74 + 2904 * q^75 - 616 * q^76 - 1528 * q^79 - 96 * q^80 - 4618 * q^81 + 880 * q^84 + 2574 * q^85 - 2024 * q^86 + 2336 * q^89 + 2092 * q^90 - 3866 * q^91 + 456 * q^94 + 838 * q^95 - 576 * q^96 + 3342 * q^99

Introduction

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