LMFDB - Embedded newform 143.4.b.a.12.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(12,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("143.12");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.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:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			12.3
Character	$\chi$	$=$	143.12
Dual form			143.4.b.a.12.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.98751i q^{2} -4.47034 q^{3} -16.8752 q^{4} -20.1605i q^{5} +22.2959i q^{6} -23.8481i q^{7} +44.2654i q^{8} -7.01607 q^{9} +O(q^{10})$	\(q-4.98751i q^{2} -4.47034 q^{3} -16.8752 q^{4} -20.1605i q^{5} +22.2959i q^{6} -23.8481i q^{7} +44.2654i q^{8} -7.01607 q^{9} -100.551 q^{10} -11.0000i q^{11} +75.4381 q^{12} +(45.1909 + 12.4411i) q^{13} -118.943 q^{14} +90.1244i q^{15} +85.7719 q^{16} +111.997 q^{17} +34.9927i q^{18} -3.85957i q^{19} +340.214i q^{20} +106.609i q^{21} -54.8626 q^{22} +76.9220 q^{23} -197.881i q^{24} -281.447 q^{25} +(62.0503 - 225.390i) q^{26} +152.063 q^{27} +402.443i q^{28} -85.3018 q^{29} +449.496 q^{30} -244.686i q^{31} -73.6653i q^{32} +49.1737i q^{33} -558.588i q^{34} -480.790 q^{35} +118.398 q^{36} -180.288i q^{37} -19.2496 q^{38} +(-202.019 - 55.6161i) q^{39} +892.413 q^{40} +470.715i q^{41} +531.714 q^{42} +194.463 q^{43} +185.628i q^{44} +141.448i q^{45} -383.649i q^{46} -287.601i q^{47} -383.430 q^{48} -225.732 q^{49} +1403.72i q^{50} -500.666 q^{51} +(-762.608 - 209.947i) q^{52} -564.081 q^{53} -758.417i q^{54} -221.766 q^{55} +1055.65 q^{56} +17.2536i q^{57} +425.444i q^{58} +50.4331i q^{59} -1520.87i q^{60} +334.404 q^{61} -1220.37 q^{62} +167.320i q^{63} +318.769 q^{64} +(250.820 - 911.072i) q^{65} +245.254 q^{66} +199.275i q^{67} -1889.98 q^{68} -343.868 q^{69} +2397.95i q^{70} -152.078i q^{71} -310.569i q^{72} +245.095i q^{73} -899.188 q^{74} +1258.16 q^{75} +65.1311i q^{76} -262.329 q^{77} +(-277.386 + 1007.57i) q^{78} -281.145 q^{79} -1729.21i q^{80} -490.341 q^{81} +2347.69 q^{82} -434.099i q^{83} -1799.06i q^{84} -2257.92i q^{85} -969.884i q^{86} +381.328 q^{87} +486.919 q^{88} +1032.68i q^{89} +705.472 q^{90} +(296.698 - 1077.72i) q^{91} -1298.08 q^{92} +1093.83i q^{93} -1434.41 q^{94} -77.8109 q^{95} +329.309i q^{96} -802.898i q^{97} +1125.84i q^{98} +77.1768i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 152 q^{4} + 360 q^{9}+O(q^{10}) $ 36 * q - 152 * q^4 + 360 * q^9	$ 36 q - 152 q^{4} + 360 q^{9} - 112 q^{10} - 108 q^{12} - 50 q^{13} + 8 q^{14} + 728 q^{16} + 276 q^{17} + 44 q^{22} - 472 q^{23} - 1172 q^{25} + 152 q^{26} - 12 q^{27} - 572 q^{29} + 712 q^{30} + 68 q^{35} - 430 q^{36} - 50 q^{38} + 640 q^{39} - 216 q^{40} + 1126 q^{42} + 920 q^{43} + 1674 q^{48} - 2164 q^{49} - 340 q^{51} - 800 q^{52} + 2432 q^{53} + 440 q^{55} - 2274 q^{56} - 1844 q^{61} + 2796 q^{62} - 2592 q^{64} + 2264 q^{65} + 1078 q^{66} - 4548 q^{68} - 3288 q^{69} - 4036 q^{74} + 820 q^{75} - 616 q^{77} + 2222 q^{78} + 360 q^{79} + 852 q^{81} + 1948 q^{82} - 2480 q^{87} + 264 q^{88} - 496 q^{90} + 4600 q^{91} + 454 q^{92} - 488 q^{94} + 952 q^{95}+O(q^{100}) $ 36 * q - 152 * q^4 + 360 * q^9 - 112 * q^10 - 108 * q^12 - 50 * q^13 + 8 * q^14 + 728 * q^16 + 276 * q^17 + 44 * q^22 - 472 * q^23 - 1172 * q^25 + 152 * q^26 - 12 * q^27 - 572 * q^29 + 712 * q^30 + 68 * q^35 - 430 * q^36 - 50 * q^38 + 640 * q^39 - 216 * q^40 + 1126 * q^42 + 920 * q^43 + 1674 * q^48 - 2164 * q^49 - 340 * q^51 - 800 * q^52 + 2432 * q^53 + 440 * q^55 - 2274 * q^56 - 1844 * q^61 + 2796 * q^62 - 2592 * q^64 + 2264 * q^65 + 1078 * q^66 - 4548 * q^68 - 3288 * q^69 - 4036 * q^74 + 820 * q^75 - 616 * q^77 + 2222 * q^78 + 360 * q^79 + 852 * q^81 + 1948 * q^82 - 2480 * q^87 + 264 * q^88 - 496 * q^90 + 4600 * q^91 + 454 * q^92 - 488 * q^94 + 952 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	4.98751i		−	1.76335i	−0.471857	−	0.881675i	$-0.656416\pi$
$2$		−	4.98751i		−	1.76335i	0.471857	−	0.881675i	$-0.343584\pi$
$3$	−4.47034			−0.860317			−0.430159	−	0.902753i	$-0.641542\pi$
$3$	−4.47034			−0.860317			−0.430159	+	0.902753i	$0.641542\pi$
$4$	−16.8752			−2.10941
$5$		−	20.1605i		−	1.80321i	−0.432558	−	0.901606i	$-0.642389\pi$
$5$		−	20.1605i		−	1.80321i	0.432558	−	0.901606i	$-0.357611\pi$
$6$			22.2959i			1.51704i
$7$		−	23.8481i		−	1.28768i	−0.765161	−	0.643839i	$-0.777341\pi$
$7$		−	23.8481i		−	1.28768i	0.765161	−	0.643839i	$-0.222659\pi$
$8$			44.2654i			1.95627i
$9$	−7.01607			−0.259855
$10$	−100.551			−3.17969
$11$		−	11.0000i		−	0.301511i
$11$		−	11.0000i		−	0.301511i
$12$	75.4381			1.81476
$13$	45.1909	+	12.4411i	0.964131	+	0.265427i
$13$	45.1909	+	12.4411i	0.964131	+	0.265427i
$14$	−118.943			−2.27063
$15$			90.1244i			1.55133i
$16$	85.7719			1.34019
$17$	111.997			1.59784			0.798922	−	0.601435i	$-0.205404\pi$
$17$	111.997			1.59784			0.798922	+	0.601435i	$0.205404\pi$
$18$			34.9927i			0.458215i
$19$		−	3.85957i		−	0.0466024i	−0.999728	−	0.0233012i	$-0.992582\pi$
$19$		−	3.85957i		−	0.0466024i	0.999728	−	0.0233012i	$-0.00741767\pi$
$20$			340.214i			3.80371i
$21$			106.609i			1.10781i
$22$	−54.8626			−0.531670
$23$	76.9220			0.697363			0.348682	−	0.937241i	$-0.386629\pi$
$23$	76.9220			0.697363			0.348682	+	0.937241i	$0.386629\pi$
$24$		−	197.881i		−	1.68301i
$25$	−281.447			−2.25157
$26$	62.0503	−	225.390i	0.468041	−	1.70010i
$27$	152.063			1.08387
$28$			402.443i			2.71623i
$29$	−85.3018			−0.546212			−0.273106	−	0.961984i	$-0.588051\pi$
$29$	−85.3018			−0.546212			−0.273106	+	0.961984i	$0.588051\pi$
$30$	449.496			2.73555
$31$		−	244.686i		−	1.41764i	−0.705388	−	0.708821i	$-0.749227\pi$
$31$		−	244.686i		−	1.41764i	0.705388	−	0.708821i	$-0.250773\pi$
$32$		−	73.6653i		−	0.406947i
$33$			49.1737i			0.259395i
$34$		−	558.588i		−	2.81756i
$35$	−480.790			−2.32195
$36$	118.398			0.548139
$37$		−	180.288i		−	0.801058i	−0.916284	−	0.400529i	$-0.868826\pi$
$37$		−	180.288i		−	0.801058i	0.916284	−	0.400529i	$-0.131174\pi$
$38$	−19.2496			−0.0821763
$39$	−202.019	−	55.6161i	−0.829458	−	0.228351i
$40$	892.413			3.52757
$41$			470.715i			1.79301i	0.443037	+	0.896503i	$0.353901\pi$
$41$			470.715i			1.79301i	−0.443037	+	0.896503i	$0.646099\pi$
$42$	531.714			1.95346
$43$	194.463			0.689658			0.344829	−	0.938666i	$-0.387937\pi$
$43$	194.463			0.689658			0.344829	+	0.938666i	$0.387937\pi$
$44$			185.628i			0.636010i
$45$			141.448i			0.468573i
$46$		−	383.649i		−	1.22970i
$47$		−	287.601i		−	0.892572i	−0.894890	−	0.446286i	$-0.852746\pi$
$47$		−	287.601i		−	0.892572i	0.894890	−	0.446286i	$-0.147254\pi$
$48$	−383.430			−1.15299
$49$	−225.732			−0.658112
$50$			1403.72i			3.97031i
$51$	−500.666			−1.37465
$52$	−762.608	−	209.947i	−2.03374	−	0.559893i
$53$	−564.081			−1.46193			−0.730966	−	0.682414i	$-0.760930\pi$
$53$	−564.081			−1.46193			−0.730966	+	0.682414i	$0.760930\pi$
$54$		−	758.417i		−	1.91125i
$55$	−221.766			−0.543689
$56$	1055.65			2.51905
$57$			17.2536i			0.0400928i
$58$			425.444i			0.963164i
$59$			50.4331i			0.111285i	0.998451	+	0.0556426i	$0.0177207\pi$
$59$			50.4331i			0.111285i	−0.998451	+	0.0556426i	$0.982279\pi$
$60$		−	1520.87i		−	3.27239i
$61$	334.404			0.701902			0.350951	−	0.936394i	$-0.385858\pi$
$61$	334.404			0.701902			0.350951	+	0.936394i	$0.385858\pi$
$62$	−1220.37			−2.49980
$63$			167.320i			0.334609i
$64$	318.769			0.622595
$65$	250.820	−	911.072i	0.478621	−	1.73853i
$66$	245.254			0.457405
$67$			199.275i			0.363363i	0.983357	+	0.181681i	$0.0581540\pi$
$67$			199.275i			0.363363i	−0.983357	+	0.181681i	$0.941846\pi$
$68$	−1889.98			−3.37050
$69$	−343.868			−0.599954
$70$			2397.95i			4.09442i
$71$		−	152.078i		−	0.254202i	−0.991890	−	0.127101i	$-0.959433\pi$
$71$		−	152.078i		−	0.254202i	0.991890	−	0.127101i	$-0.0405673\pi$
$72$		−	310.569i		−	0.508346i
$73$			245.095i			0.392961i	0.980508	+	0.196480i	$0.0629512\pi$
$73$			245.095i			0.392961i	−0.980508	+	0.196480i	$0.937049\pi$
$74$	−899.188			−1.41255
$75$	1258.16			1.93707
$76$			65.1311i			0.0983033i
$77$	−262.329			−0.388249
$78$	−277.386	+	1007.57i	−0.402663	+	1.46263i
$79$	−281.145			−0.400396			−0.200198	−	0.979756i	$-0.564158\pi$
$79$	−281.145			−0.400396			−0.200198	+	0.979756i	$0.564158\pi$
$80$		−	1729.21i		−	2.41664i
$81$	−490.341			−0.672621
$82$	2347.69			3.16170
$83$		−	434.099i		−	0.574080i	−0.957919	−	0.287040i	$-0.907329\pi$
$83$		−	434.099i		−	0.574080i	0.957919	−	0.287040i	$-0.0926712\pi$
$84$		−	1799.06i		−	2.33682i
$85$		−	2257.92i		−	2.88125i
$86$		−	969.884i		−	1.21611i
$87$	381.328			0.469916
$88$	486.919			0.589838
$89$			1032.68i			1.22993i	0.788555	+	0.614964i	$0.210829\pi$
$89$			1032.68i			1.22993i	−0.788555	+	0.614964i	$0.789171\pi$
$90$	705.472			0.826258
$91$	296.698	−	1077.72i	0.341784	−	1.24149i
$92$	−1298.08			−1.47102
$93$			1093.83i			1.21962i
$94$	−1434.41			−1.57392
$95$	−77.8109			−0.0840339
$96$			329.309i			0.350104i
$97$		−	802.898i		−	0.840432i	−0.907424	−	0.420216i	$-0.861954\pi$
$97$		−	802.898i		−	0.840432i	0.907424	−	0.420216i	$-0.138046\pi$
$98$			1125.84i			1.16048i
$99$			77.1768i			0.0783491i
$100$	4749.48			4.74948
$101$	1228.44			1.21024			0.605118	−	0.796136i	$-0.293126\pi$
$101$	1228.44			1.21024			0.605118	+	0.796136i	$0.293126\pi$
$102$			2497.08i			2.42399i
$103$	334.122			0.319632			0.159816	−	0.987147i	$-0.448910\pi$
$103$	334.122			0.319632			0.159816	+	0.987147i	$0.448910\pi$
$104$	−550.711	+	2000.39i	−0.519247	+	1.88610i
$105$	2149.30			1.99762
$106$			2813.36i			2.57790i
$107$	1230.22			1.11149			0.555747	−	0.831351i	$-0.312432\pi$
$107$	1230.22			1.11149			0.555747	+	0.831351i	$0.312432\pi$
$108$	−2566.11			−2.28633
$109$			333.762i			0.293290i	0.989189	+	0.146645i	$0.0468475\pi$
$109$			333.762i			0.293290i	−0.989189	+	0.146645i	$0.953153\pi$
$110$			1106.06i			0.958714i
$111$			805.948i			0.689164i
$112$		−	2045.50i		−	1.72573i
$113$	−1369.00			−1.13969			−0.569843	−	0.821753i	$-0.692996\pi$
$113$	−1369.00			−1.13969			−0.569843	+	0.821753i	$0.692996\pi$
$114$	86.0523			0.0706977
$115$		−	1550.79i		−	1.25749i
$116$	1439.49			1.15218
$117$	−317.063	−	87.2879i	−0.250534	−	0.0689724i
$118$	251.535			0.196235
$119$		−	2670.92i		−	2.05751i
$120$	−3989.39			−3.03483
$121$	−121.000			−0.0909091
$122$		−	1667.84i		−	1.23770i
$123$		−	2104.25i		−	1.54255i
$124$			4129.14i			2.99038i
$125$			3154.05i			2.25685i
$126$	834.510			0.590032
$127$	−500.653			−0.349809			−0.174904	−	0.984585i	$-0.555962\pi$
$127$	−500.653			−0.349809			−0.174904	+	0.984585i	$0.555962\pi$
$128$		−	2179.19i		−	1.50480i
$129$	−869.314			−0.593324
$130$	−4543.98	−	1250.97i	−3.06564	−	0.843977i
$131$	205.190			0.136851			0.0684256	−	0.997656i	$-0.478202\pi$
$131$	205.190			0.136851			0.0684256	+	0.997656i	$0.478202\pi$
$132$		−	829.819i		−	0.547170i
$133$	−92.0433			−0.0600088
$134$	993.886			0.640736
$135$		−	3065.68i		−	1.95446i
$136$			4957.60i			3.12581i
$137$			2302.23i			1.43571i	0.696192	+	0.717856i	$0.254876\pi$
$137$			2302.23i			1.43571i	−0.696192	+	0.717856i	$0.745124\pi$
$138$			1715.04i			1.05793i
$139$	−469.268			−0.286351			−0.143175	−	0.989697i	$-0.545731\pi$
$139$	−469.268			−0.286351			−0.143175	+	0.989697i	$0.545731\pi$
$140$	8113.46			4.89794
$141$			1285.67i			0.767895i
$142$	−758.491			−0.448248
$143$	136.852	−	497.100i	0.0800292	−	0.290696i
$144$	−601.782			−0.348253
$145$			1719.73i			0.984936i
$146$	1222.41			0.692928
$147$	1009.10			0.566185
$148$			3042.40i			1.68976i
$149$			749.151i			0.411898i	0.978563	+	0.205949i	$0.0660281\pi$
$149$			749.151i			0.411898i	−0.978563	+	0.205949i	$0.933972\pi$
$150$		−	6275.09i		−	3.41573i
$151$		−	2358.29i		−	1.27096i	−0.772117	−	0.635480i	$-0.780802\pi$
$151$		−	2358.29i		−	1.27096i	0.772117	−	0.635480i	$-0.219198\pi$
$152$	170.845			0.0911669
$153$	−785.781			−0.415207
$154$			1308.37i			0.684620i
$155$	−4933.00			−2.55631
$156$	3409.11	+	938.535i	1.74966	+	0.481685i
$157$	−1366.74			−0.694764			−0.347382	−	0.937724i	$-0.612929\pi$
$157$	−1366.74			−0.694764			−0.347382	+	0.937724i	$0.612929\pi$
$158$			1402.21i			0.706038i
$159$	2521.63			1.25773
$160$	−1485.13			−0.733812
$161$		−	1834.45i		−	0.897979i
$162$			2445.58i			1.18607i
$163$			2841.66i			1.36550i	0.730653	+	0.682749i	$0.239216\pi$
$163$			2841.66i			1.36550i	−0.730653	+	0.682749i	$0.760784\pi$
$164$		−	7943.42i		−	3.78218i
$165$	991.368			0.467745
$166$	−2165.07			−1.01230
$167$			526.823i			0.244113i	0.992523	+	0.122056i	$0.0389489\pi$
$167$			526.823i			0.244113i	−0.992523	+	0.122056i	$0.961051\pi$
$168$	−4719.09			−2.16718
$169$	1887.44	+	1124.45i	0.859097	+	0.511813i
$170$	−11261.4			−5.08065
$171$			27.0790i			0.0121098i
$172$	−3281.60			−1.45477
$173$	1622.90			0.713219			0.356610	−	0.934254i	$-0.383933\pi$
$173$	1622.90			0.713219			0.356610	+	0.934254i	$0.383933\pi$
$174$		−	1901.88i		−	0.828626i
$175$			6711.97i			2.89930i
$176$		−	943.491i		−	0.404081i
$177$		−	225.453i		−	0.0957406i
$178$	5150.49			2.16879
$179$	3536.08			1.47653			0.738265	−	0.674510i	$-0.235645\pi$
$179$	3536.08			1.47653			0.738265	+	0.674510i	$0.235645\pi$
$180$		−	2386.96i		−	0.988410i
$181$	3338.97			1.37118			0.685590	−	0.727988i	$-0.259544\pi$
$181$	3338.97			1.37118			0.685590	+	0.727988i	$0.259544\pi$
$182$	−5375.13	−	1479.78i	−2.18918	−	0.602685i
$183$	−1494.90			−0.603858
$184$			3404.98i			1.36423i
$185$	−3634.70			−1.44448
$186$	5455.48			2.15062
$187$		−	1231.97i		−	0.481768i
$188$			4853.33i			1.88280i
$189$		−	3626.42i		−	1.39568i
$190$			388.082i			0.148181i
$191$	−1085.16			−0.411096			−0.205548	−	0.978647i	$-0.565898\pi$
$191$	−1085.16			−0.411096			−0.205548	+	0.978647i	$0.565898\pi$
$192$	−1425.00			−0.535629
$193$			1802.02i			0.672085i	0.941847	+	0.336042i	$0.109089\pi$
$193$			1802.02i			0.672085i	−0.941847	+	0.336042i	$0.890911\pi$
$194$	−4004.46			−1.48198
$195$	−1121.25	+	4072.80i	−0.411766	+	1.49569i
$196$	3809.29			1.38823
$197$		−	2704.82i		−	0.978225i	−0.872221	−	0.489112i	$-0.837321\pi$
$197$		−	2704.82i		−	0.978225i	0.872221	−	0.489112i	$-0.162679\pi$
$198$	384.920			0.138157
$199$	759.103			0.270409			0.135204	−	0.990818i	$-0.456831\pi$
$199$	759.103			0.270409			0.135204	+	0.990818i	$0.456831\pi$
$200$		−	12458.3i		−	4.40469i
$201$		−	890.827i		−	0.312607i
$202$		−	6126.83i		−	2.13407i
$203$			2034.29i			0.703345i
$204$	8448.86			2.89970
$205$	9489.85			3.23317
$206$		−	1666.44i		−	0.563622i
$207$	−539.691			−0.181213
$208$	3876.11	+	1067.10i	1.29212	+	0.355721i
$209$	−42.4552			−0.0140511
$210$		−	10719.6i		−	3.52250i
$211$	−3908.28			−1.27515			−0.637577	−	0.770387i	$-0.720063\pi$
$211$	−3908.28			−1.27515			−0.637577	+	0.770387i	$0.720063\pi$
$212$	9519.00			3.08381
$213$			679.841i			0.218694i
$214$		−	6135.74i		−	1.95995i
$215$		−	3920.47i		−	1.24360i
$216$			6731.14i			2.12035i
$217$	−5835.30			−1.82547
$218$	1664.64			0.517173
$219$		−	1095.66i		−	0.338071i
$220$	3742.35			1.14686
$221$	5061.26	+	1393.37i	1.54053	+	0.424111i
$222$	4019.67			1.21524
$223$		−	4141.64i		−	1.24370i	−0.783138	−	0.621848i	$-0.786382\pi$
$223$		−	4141.64i		−	1.24370i	0.783138	−	0.621848i	$-0.213618\pi$
$224$	−1756.78			−0.524017
$225$	1974.65			0.585081
$226$			6827.89i			2.00967i
$227$			2515.57i			0.735524i	0.929920	+	0.367762i	$0.119876\pi$
$227$			2515.57i			0.735524i	−0.929920	+	0.367762i	$0.880124\pi$
$228$		−	291.158i		−	0.0845720i
$229$		−	2143.71i		−	0.618605i	−0.950964	−	0.309302i	$-0.899905\pi$
$229$		−	2143.71i		−	0.618605i	0.950964	−	0.309302i	$-0.100095\pi$
$230$	−7734.57			−2.21740
$231$	1172.70			0.334017
$232$		−	3775.92i		−	1.06854i
$233$	−1945.07			−0.546893			−0.273447	−	0.961887i	$-0.588164\pi$
$233$	−1945.07			−0.546893			−0.273447	+	0.961887i	$0.588164\pi$
$234$	−435.349	+	1581.35i	−0.121622	+	0.441779i
$235$	−5798.18			−1.60950
$236$		−	851.071i		−	0.234746i
$237$	1256.81			0.344467
$238$	−13321.3			−3.62810
$239$		−	5694.26i		−	1.54114i	−0.637358	−	0.770568i	$-0.719973\pi$
$239$		−	5694.26i		−	1.54114i	0.637358	−	0.770568i	$-0.280027\pi$
$240$			7730.14i			2.07908i
$241$			2009.60i			0.537137i	0.963261	+	0.268568i	$0.0865505\pi$
$241$			2009.60i			0.537137i	−0.963261	+	0.268568i	$0.913449\pi$
$242$			603.489i			0.160305i
$243$	−1913.72			−0.505207
$244$	−5643.15			−1.48060
$245$			4550.88i			1.18672i
$246$	−10495.0			−2.72006
$247$	48.0174	−	174.417i	0.0123695	−	0.0449308i
$248$	10831.1			2.77329
$249$			1940.57i			0.493890i
$250$	15730.8			3.97962
$251$	−5321.13			−1.33812			−0.669058	−	0.743210i	$-0.733302\pi$
$251$	−5321.13			−1.33812			−0.669058	+	0.743210i	$0.733302\pi$
$252$		−	2823.57i		−	0.705825i
$253$		−	846.143i		−	0.210263i
$254$			2497.01i			0.616836i
$255$			10093.7i			2.47879i
$256$	−8318.55			−2.03090
$257$	−3786.94			−0.919156			−0.459578	−	0.888138i	$-0.651999\pi$
$257$	−3786.94			−0.919156			−0.459578	+	0.888138i	$0.651999\pi$
$258$			4335.71i			1.04624i
$259$	−4299.53			−1.03150
$260$	−4232.64	+	15374.6i	−1.00961	+	3.66727i
$261$	598.484			0.141936
$262$		−	1023.39i		−	0.241317i
$263$	−1430.47			−0.335385			−0.167693	−	0.985839i	$-0.553632\pi$
$263$	−1430.47			−0.335385			−0.167693	+	0.985839i	$0.553632\pi$
$264$	−2176.69			−0.507448
$265$			11372.2i			2.63617i
$266$			459.067i			0.105817i
$267$		−	4616.42i		−	1.05813i
$268$		−	3362.81i		−	0.766480i
$269$	−3302.24			−0.748481			−0.374240	−	0.927332i	$-0.622096\pi$
$269$	−3302.24			−0.748481			−0.374240	+	0.927332i	$0.622096\pi$
$270$	−15290.1			−3.44639
$271$		−	8402.73i		−	1.88350i	−0.336308	−	0.941752i	$-0.609178\pi$
$271$		−	8402.73i		−	1.88350i	0.336308	−	0.941752i	$-0.390822\pi$
$272$	9606.22			2.14141
$273$	−1326.34	+	4817.76i	−0.294043	+	1.06807i
$274$	11482.4			2.53166
$275$			3095.91i			0.678875i
$276$	5802.85			1.26555
$277$	5501.14			1.19326			0.596628	−	0.802518i	$-0.296507\pi$
$277$	5501.14			1.19326			0.596628	+	0.802518i	$0.296507\pi$
$278$			2340.48i			0.504937i
$279$			1716.73i			0.368381i
$280$		−	21282.4i		−	4.54237i
$281$		−	3082.87i		−	0.654478i	−0.944942	−	0.327239i	$-0.893882\pi$
$281$		−	3082.87i		−	0.654478i	0.944942	−	0.327239i	$-0.106118\pi$
$282$	6412.31			1.35407
$283$	−6542.77			−1.37430			−0.687151	−	0.726515i	$-0.741139\pi$
$283$	−6542.77			−1.37430			−0.687151	+	0.726515i	$0.741139\pi$
$284$			2566.36i			0.536215i
$285$	347.841			0.0722958
$286$	−2479.29	−	682.553i	−0.512600	−	0.141120i
$287$	11225.7			2.30881
$288$			516.841i			0.105747i
$289$	7630.39			1.55310
$290$	8577.17			1.73679
$291$			3589.22i			0.723038i
$292$		−	4136.03i		−	0.828914i
$293$			5546.77i			1.10596i	0.833195	+	0.552980i	$0.186509\pi$
$293$			5546.77i			1.10596i	−0.833195	+	0.552980i	$0.813491\pi$
$294$		−	5032.90i		−	0.998383i
$295$	1016.76			0.200671
$296$	7980.51			1.56709
$297$		−	1672.70i		−	0.326800i
$298$	3736.40			0.726321
$299$	3476.18	+	956.997i	0.672350	+	0.185099i
$300$	−21231.8			−4.08606
$301$		−	4637.57i		−	0.888056i
$302$	−11762.0			−2.24115
$303$	−5491.52			−1.04119
$304$		−	331.042i		−	0.0624559i
$305$		−	6741.75i		−	1.26568i
$306$			3919.09i			0.732155i
$307$			372.191i			0.0691923i	0.999401	+	0.0345962i	$0.0110145\pi$
$307$			372.191i			0.0691923i	−0.999401	+	0.0345962i	$0.988985\pi$
$308$	4426.87			0.818975
$309$	−1493.64			−0.274984
$310$			24603.4i			4.50767i
$311$	−7890.69			−1.43871			−0.719357	−	0.694640i	$-0.755564\pi$
$311$	−7890.69			−1.43871			−0.719357	+	0.694640i	$0.755564\pi$
$312$	2461.87	−	8942.43i	0.446717	−	1.62265i
$313$	348.406			0.0629171			0.0314586	−	0.999505i	$-0.489985\pi$
$313$	348.406			0.0629171			0.0314586	+	0.999505i	$0.489985\pi$
$314$			6816.64i			1.22511i
$315$	3373.26			0.603370
$316$	4744.39			0.844597
$317$			6274.13i			1.11164i	0.831302	+	0.555820i	$0.187596\pi$
$317$			6274.13i			1.11164i	−0.831302	+	0.555820i	$0.812404\pi$
$318$		−	12576.7i		−	2.21781i
$319$			938.320i			0.164689i
$320$		−	6426.55i		−	1.12267i
$321$	−5499.50			−0.956238
$322$	−9149.31			−1.58345
$323$		−	432.261i		−	0.0744633i
$324$	8274.62			1.41883
$325$	−12718.8	−	3501.52i	−2.17081	−	0.597628i
$326$	14172.8			2.40785
$327$		−	1492.03i		−	0.252322i
$328$	−20836.4			−3.50761
$329$	−6858.74			−1.14934
$330$		−	4944.46i		−	0.824798i
$331$		−	3876.67i		−	0.643749i	−0.946782	−	0.321875i	$-0.895687\pi$
$331$		−	3876.67i		−	0.643749i	0.946782	−	0.321875i	$-0.104313\pi$
$332$			7325.53i			1.21097i
$333$			1264.91i			0.208159i
$334$	2627.54			0.430456
$335$	4017.49			0.655220
$336$			9144.07i			1.48467i
$337$	5219.32			0.843663			0.421831	−	0.906674i	$-0.361387\pi$
$337$	5219.32			0.843663			0.421831	+	0.906674i	$0.361387\pi$
$338$	5608.22	−	9413.61i	0.902505	−	1.51489i
$339$	6119.89			0.980492
$340$			38103.0i			6.07772i
$341$	−2691.55			−0.427435
$342$	135.057			0.0213539
$343$		−	2796.61i		−	0.440241i
$344$			8607.96i			1.34916i
$345$			6932.55i			1.08184i
$346$		−	8094.23i		−	1.25766i
$347$	7654.63			1.18421			0.592107	−	0.805859i	$-0.298296\pi$
$347$	7654.63			1.18421			0.592107	+	0.805859i	$0.298296\pi$
$348$	−6435.00			−0.991243
$349$		−	6159.99i		−	0.944804i	−0.881383	−	0.472402i	$-0.843387\pi$
$349$		−	6159.99i		−	0.944804i	0.881383	−	0.472402i	$-0.156613\pi$
$350$	33476.0			5.11248
$351$	6871.88	+	1891.84i	1.04500	+	0.287689i
$352$	−810.319			−0.122699
$353$		−	11219.6i		−	1.69167i	−0.533445	−	0.845835i	$-0.679103\pi$
$353$		−	11219.6i		−	1.69167i	0.533445	−	0.845835i	$-0.320897\pi$
$354$	−1124.45			−0.168824
$355$	−3065.97			−0.458380
$356$		−	17426.7i		−	2.59442i
$357$			11939.9i			1.77011i
$358$		−	17636.2i		−	2.60364i
$359$		−	7715.95i		−	1.13435i	−0.823597	−	0.567176i	$-0.808036\pi$
$359$		−	7715.95i		−	1.13435i	0.823597	−	0.567176i	$-0.191964\pi$
$360$	−6261.23			−0.916655
$361$	6844.10			0.997828
$362$		−	16653.1i		−	2.41787i
$363$	540.911			0.0782106
$364$	−5006.84	+	18186.8i	−0.720961	+	2.61880i
$365$	4941.23			0.708592
$366$			7455.82i			1.06481i
$367$	5740.64			0.816509			0.408255	−	0.912868i	$-0.366138\pi$
$367$	5740.64			0.816509			0.408255	+	0.912868i	$0.366138\pi$
$368$	6597.75			0.934597
$369$		−	3302.57i		−	0.465921i
$370$			18128.1i			2.54712i
$371$			13452.3i			1.88250i
$372$		−	18458.6i		−	2.57268i
$373$	−1439.07			−0.199764			−0.0998820	−	0.994999i	$-0.531847\pi$
$373$	−1439.07			−0.199764			−0.0998820	+	0.994999i	$0.531847\pi$
$374$	−6144.46			−0.849526
$375$		−	14099.7i		−	1.94161i
$376$	12730.8			1.74611
$377$	−3854.87	−	1061.25i	−0.526620	−	0.144979i
$378$	−18086.8			−2.46107
$379$			5751.71i			0.779540i	0.920912	+	0.389770i	$0.127445\pi$
$379$			5751.71i			0.779540i	−0.920912	+	0.389770i	$0.872555\pi$
$380$	1313.08			0.177262
$381$	2238.09			0.300947
$382$			5412.24i			0.724906i
$383$		−	801.732i		−	0.106962i	−0.998569	−	0.0534812i	$-0.982968\pi$
$383$		−	801.732i		−	0.106962i	0.998569	−	0.0534812i	$-0.0170317\pi$
$384$			9741.70i			1.29461i
$385$			5288.69i			0.700096i
$386$	8987.60			1.18512
$387$	−1364.36			−0.179211
$388$			13549.1i			1.77281i
$389$	12980.3			1.69184			0.845922	−	0.533307i	$-0.179051\pi$
$389$	12980.3			1.69184			0.845922	+	0.533307i	$0.179051\pi$
$390$	20313.1	+	5592.24i	2.63742	+	0.726087i
$391$	8615.06			1.11428
$392$		−	9992.13i		−	1.28745i
$393$	−917.268			−0.117735
$394$	−13490.3			−1.72495
$395$			5668.02i			0.721998i
$396$		−	1302.38i		−	0.165270i
$397$		−	3492.52i		−	0.441523i	−0.975328	−	0.220762i	$-0.929146\pi$
$397$		−	3492.52i		−	0.441523i	0.975328	−	0.220762i	$-0.0708543\pi$
$398$		−	3786.03i		−	0.476826i
$399$	411.465			0.0516266
$400$	−24140.2			−3.01753
$401$			981.877i			0.122276i	0.998129	+	0.0611379i	$0.0194729\pi$
$401$			981.877i			0.122276i	−0.998129	+	0.0611379i	$0.980527\pi$
$402$	−4443.01			−0.551236
$403$	3044.17	−	11057.6i	0.376280	−	1.36679i
$404$	−20730.2			−2.55288
$405$			9885.53i			1.21288i
$406$	10146.0			1.24024
$407$	−1983.17			−0.241528
$408$		−	22162.2i		−	2.68919i
$409$			9119.89i			1.10257i	0.834318	+	0.551283i	$0.185862\pi$
$409$			9119.89i			1.10257i	−0.834318	+	0.551283i	$0.814138\pi$
$410$		−	47330.7i		−	5.70121i
$411$		−	10291.7i		−	1.23517i
$412$	−5638.40			−0.674232
$413$	1202.73			0.143299
$414$			2691.71i			0.319542i
$415$	−8751.67			−1.03519
$416$	916.480	−	3329.00i	0.108015	−	0.392351i
$417$	2097.79			0.246353
$418$			211.746i			0.0247771i
$419$	11055.6			1.28902			0.644512	−	0.764594i	$-0.277061\pi$
$419$	11055.6			1.28902			0.644512	+	0.764594i	$0.277061\pi$
$420$	−36269.9			−4.21378
$421$		−	2544.11i		−	0.294519i	−0.989098	−	0.147259i	$-0.952955\pi$
$421$		−	2544.11i		−	0.294519i	0.989098	−	0.147259i	$-0.0470452\pi$
$422$			19492.6i			2.24854i
$423$			2017.83i			0.231939i
$424$		−	24969.2i		−	2.85994i
$425$	−31521.3			−3.59766
$426$	3390.71			0.385635
$427$		−	7974.90i		−	0.903823i
$428$	−20760.3			−2.34459
$429$	−611.777	+	2222.21i	−0.0688505	+	0.250091i
$430$	−19553.4			−2.19290
$431$			10692.7i			1.19501i	0.801865	+	0.597505i	$0.203841\pi$
$431$			10692.7i			1.19501i	−0.801865	+	0.597505i	$0.796159\pi$
$432$	13042.8			1.45259
$433$	−2822.50			−0.313258			−0.156629	−	0.987658i	$-0.550063\pi$
$433$	−2822.50			−0.313258			−0.156629	+	0.987658i	$0.550063\pi$
$434$			29103.6i			3.21894i
$435$		−	7687.77i		−	0.847357i
$436$		−	5632.31i		−	0.618667i
$437$		−	296.886i		−	0.0324988i
$438$	−5464.59			−0.596138
$439$	−3685.12			−0.400640			−0.200320	−	0.979730i	$-0.564198\pi$
$439$	−3685.12			−0.400640			−0.200320	+	0.979730i	$0.564198\pi$
$440$		−	9816.54i		−	1.06360i
$441$	1583.76			0.171013
$442$	6949.46	−	25243.1i	0.747856	−	2.71649i
$443$	5031.25			0.539598			0.269799	−	0.962917i	$-0.413043\pi$
$443$	5031.25			0.539598			0.269799	+	0.962917i	$0.413043\pi$
$444$		−	13600.6i		−	1.45373i
$445$	20819.3			2.21782
$446$	−20656.4			−2.19307
$447$		−	3348.96i		−	0.354363i
$448$		−	7602.04i		−	0.801702i
$449$			6659.34i			0.699942i	0.936761	+	0.349971i	$0.113809\pi$
$449$			6659.34i			0.699942i	−0.936761	+	0.349971i	$0.886191\pi$
$450$		−	9848.58i		−	1.03170i
$451$	5177.86			0.540612
$452$	23102.2			2.40406
$453$			10542.4i			1.09343i
$454$	12546.4			1.29699
$455$	−21727.4	−	5981.58i	−2.23867	−	0.616309i
$456$	−763.735			−0.0784324
$457$		−	12776.1i		−	1.30775i	−0.756604	−	0.653873i	$-0.773143\pi$
$457$		−	12776.1i		−	1.30775i	0.756604	−	0.653873i	$-0.226857\pi$
$458$	−10691.8			−1.09082
$459$	17030.7			1.73186
$460$			26169.9i			2.65256i
$461$			9355.38i			0.945171i	0.881285	+	0.472585i	$0.156679\pi$
$461$			9355.38i			0.945171i	−0.881285	+	0.472585i	$0.843321\pi$
$462$		−	5848.85i		−	0.588990i
$463$			5632.94i			0.565410i	0.959207	+	0.282705i	$0.0912317\pi$
$463$			5632.94i			0.565410i	−0.959207	+	0.282705i	$0.908768\pi$
$464$	−7316.50			−0.732026
$465$	22052.2			2.19924
$466$			9701.08i			0.964364i
$467$	−7557.42			−0.748856			−0.374428	−	0.927256i	$-0.622161\pi$
$467$	−7557.42			−0.748856			−0.374428	+	0.927256i	$0.622161\pi$
$468$	5350.51	+	1473.00i	0.528477	+	0.145491i
$469$	4752.33			0.467894
$470$			28918.5i			2.83811i
$471$	6109.81			0.597718
$472$	−2232.44			−0.217704
$473$		−	2139.09i		−	0.207940i
$474$		−	6268.36i		−	0.607416i
$475$			1086.26i			0.104929i
$476$			45072.5i			4.34011i
$477$	3957.63			0.379890
$478$	−28400.2			−2.71756
$479$		−	461.346i		−	0.0440072i	−0.999758	−	0.0220036i	$-0.992995\pi$
$479$		−	461.346i		−	0.0440072i	0.999758	−	0.0220036i	$-0.00700452\pi$
$480$	6639.04			0.631311
$481$	2242.99	−	8147.38i	0.212622	−	0.772325i
$482$	10022.9			0.947161
$483$			8200.59i			0.772546i
$484$	2041.90			0.191764
$485$	−16186.8			−1.51548
$486$			9544.70i			0.890857i
$487$		−	8771.88i		−	0.816205i	−0.912936	−	0.408102i	$-0.866191\pi$
$487$		−	8771.88i		−	0.816205i	0.912936	−	0.408102i	$-0.133809\pi$
$488$			14802.5i			1.37311i
$489$		−	12703.2i		−	1.17476i
$490$	22697.6			2.09260
$491$	−6631.14			−0.609489			−0.304745	−	0.952434i	$-0.598571\pi$
$491$	−6631.14			−0.609489			−0.304745	+	0.952434i	$0.598571\pi$
$492$			35509.8i			3.25387i
$493$	−9553.57			−0.872761
$494$	−869.908	−	239.487i	−0.0792287	−	0.0218118i
$495$	1555.92			0.141280
$496$		−	20987.2i		−	1.89990i
$497$	−3626.78			−0.327330
$498$	9678.62			0.870902
$499$		−	419.630i		−	0.0376458i	−0.999823	−	0.0188229i	$-0.994008\pi$
$499$		−	419.630i		−	0.0376458i	0.999823	−	0.0188229i	$-0.00599186\pi$
$500$		−	53225.3i		−	4.76062i
$501$		−	2355.08i		−	0.210014i
$502$			26539.2i			2.35957i
$503$	1162.41			0.103041			0.0515203	−	0.998672i	$-0.483593\pi$
$503$	1162.41			0.103041			0.0515203	+	0.998672i	$0.483593\pi$
$504$	−7406.48			−0.654585
$505$		−	24765.9i		−	2.18231i
$506$	−4220.14			−0.370767
$507$	−8437.48	−	5026.68i	−0.739096	−	0.440321i
$508$	8448.64			0.737889
$509$			9192.32i			0.800476i	0.916411	+	0.400238i	$0.131073\pi$
$509$			9192.32i			0.800476i	−0.916411	+	0.400238i	$0.868927\pi$
$510$	50342.3			4.37097
$511$	5845.04			0.506007
$512$			24055.4i			2.07638i
$513$		−	586.898i		−	0.0505111i
$514$			18887.4i			1.62079i
$515$		−	6736.08i		−	0.576363i
$516$	14669.9			1.25156
$517$	−3163.61			−0.269121
$518$			21443.9i			1.81890i
$519$	−7254.92			−0.613594
$520$	40328.9	+	11102.6i	3.40104	+	0.936312i
$521$	−14292.0			−1.20181			−0.600905	−	0.799320i	$-0.705193\pi$
$521$	−14292.0			−1.20181			−0.600905	+	0.799320i	$0.705193\pi$
$522$		−	2984.94i		−	0.250282i
$523$	19647.2			1.64266			0.821329	−	0.570455i	$-0.193233\pi$
$523$	19647.2			1.64266			0.821329	+	0.570455i	$0.193233\pi$
$524$	−3462.63			−0.288675
$525$		−	30004.8i		−	2.49432i
$526$			7134.46i			0.591402i
$527$		−	27404.2i		−	2.26517i
$528$			4217.73i			0.347638i
$529$	−6250.00			−0.513684
$530$	56718.7			4.64850
$531$		−	353.842i		−	0.0289180i
$532$	1553.25			0.126583
$533$	−5856.22	+	21272.0i	−0.475912	+	1.72869i
$534$	−23024.4			−1.86585
$535$		−	24801.9i		−	2.00426i
$536$	−8820.98			−0.710836
$537$	−15807.5			−1.27028
$538$			16470.0i			1.31983i
$539$			2483.06i			0.198428i
$540$			51734.0i			4.12274i
$541$		−	3805.59i		−	0.302431i	−0.988501	−	0.151216i	$-0.951681\pi$
$541$		−	3805.59i		−	0.302431i	0.988501	−	0.151216i	$-0.0483188\pi$
$542$	−41908.7			−3.32128
$543$	−14926.3			−1.17965
$544$		−	8250.32i		−	0.650238i
$545$	6728.82			0.528864
$546$	24028.6	+	6615.12i	1.88339	+	0.518500i
$547$	4264.30			0.333324			0.166662	−	0.986014i	$-0.446701\pi$
$547$	4264.30			0.333324			0.166662	+	0.986014i	$0.446701\pi$
$548$		−	38850.6i		−	3.02850i
$549$	−2346.20			−0.182392
$550$	15440.9			1.19709
$551$			329.228i			0.0254548i
$552$		−	15221.4i		−	1.17367i
$553$			6704.77i			0.515580i
$554$		−	27437.0i		−	2.10413i
$555$	16248.3			1.24271
$556$	7919.01			0.604030
$557$			21947.0i			1.66952i	0.550612	+	0.834761i	$0.314394\pi$
$557$			21947.0i			1.66952i	−0.550612	+	0.834761i	$0.685606\pi$
$558$	8562.23			0.649584
$559$	8787.94	+	2419.34i	0.664920	+	0.183054i
$560$	−41238.3			−3.11185
$561$			5507.32i			0.414473i
$562$	−15375.8			−1.15408
$563$	24846.0			1.85992			0.929960	−	0.367660i	$-0.119841\pi$
$563$	24846.0			1.85992			0.929960	+	0.367660i	$0.119841\pi$
$564$		−	21696.0i		−	1.61980i
$565$			27599.7i			2.05510i
$566$			32632.1i			2.42338i
$567$			11693.7i			0.866119i
$568$	6731.79			0.497288
$569$	−8838.72			−0.651210			−0.325605	−	0.945506i	$-0.605568\pi$
$569$	−8838.72			−0.651210			−0.325605	+	0.945506i	$0.605568\pi$
$570$		−	1734.86i		−	0.127483i
$571$	−5535.21			−0.405677			−0.202838	−	0.979212i	$-0.565017\pi$
$571$	−5535.21			−0.405677			−0.202838	+	0.979212i	$0.565017\pi$
$572$	−2309.42	+	8388.68i	−0.168814	+	0.613197i
$573$	4851.03			0.353673
$574$		−	55988.0i		−	4.07125i
$575$	−21649.5			−1.57016
$576$	−2236.51			−0.161784
$577$		−	7216.86i		−	0.520696i	−0.965515	−	0.260348i	$-0.916163\pi$
$577$		−	7216.86i		−	0.520696i	0.965515	−	0.260348i	$-0.0838373\pi$
$578$		−	38056.7i		−	2.73866i
$579$		−	8055.65i		−	0.578206i
$580$		−	29020.9i		−	2.07763i
$581$	−10352.5			−0.739229
$582$	17901.3			1.27497
$583$			6204.89i			0.440789i
$584$	−10849.2			−0.768738
$585$	−1759.77	+	6392.15i	−0.124372	+	0.451766i
$586$	27664.6			1.95019
$587$			22137.4i			1.55657i	0.627910	+	0.778286i	$0.283910\pi$
$587$			22137.4i			1.55657i	−0.627910	+	0.778286i	$0.716090\pi$
$588$	−17028.8			−1.19431
$589$	−944.382			−0.0660655
$590$		−	5071.09i		−	0.353853i
$591$			12091.4i			0.841583i
$592$		−	15463.6i		−	1.07357i
$593$			2759.66i			0.191106i	0.995424	+	0.0955529i	$0.0304619\pi$
$593$			2759.66i			0.191106i	−0.995424	+	0.0955529i	$0.969538\pi$
$594$	−8342.59			−0.576264
$595$	−53847.2			−3.71012
$596$		−	12642.1i		−	0.868860i
$597$	−3393.45			−0.232637
$598$	4773.03	−	17337.5i	0.326394	−	1.18559i
$599$	8461.04			0.577143			0.288572	−	0.957458i	$-0.406820\pi$
$599$	8461.04			0.577143			0.288572	+	0.957458i	$0.406820\pi$
$600$			55693.0i			3.78943i
$601$	4257.10			0.288936			0.144468	−	0.989509i	$-0.453853\pi$
$601$	4257.10			0.288936			0.144468	+	0.989509i	$0.453853\pi$
$602$	−23129.9			−1.56595
$603$		−	1398.13i		−	0.0944215i
$604$			39796.7i			2.68097i
$605$			2439.42i			0.163928i
$606$			27389.0i			1.83598i
$607$	−25271.1			−1.68982			−0.844912	−	0.534906i	$-0.820347\pi$
$607$	−25271.1			−1.68982			−0.844912	+	0.534906i	$0.820347\pi$
$608$	−284.316			−0.0189647
$609$		−	9093.95i		−	0.605100i
$610$	−33624.6			−2.23183
$611$	3578.08	−	12996.9i	0.236913	−	0.860556i
$612$	13260.2			0.875839
$613$		−	10020.4i		−	0.660226i	−0.943941	−	0.330113i	$-0.892913\pi$
$613$		−	10020.4i		−	0.660226i	0.943941	−	0.330113i	$-0.107087\pi$
$614$	1856.30			0.122010
$615$	−42422.9			−2.78155
$616$		−	11612.1i		−	0.759521i
$617$		−	3621.59i		−	0.236304i	−0.992996	−	0.118152i	$-0.962303\pi$
$617$		−	3621.59i		−	0.236304i	0.992996	−	0.118152i	$-0.0376971\pi$
$618$			7449.54i			0.484894i
$619$			15993.1i			1.03847i	0.854630	+	0.519237i	$0.173784\pi$
$619$			15993.1i			1.03847i	−0.854630	+	0.519237i	$0.826216\pi$
$620$	83245.5			5.39229
$621$	11697.0			0.755854
$622$			39354.9i			2.53696i
$623$	24627.4			1.58375
$624$	−17327.5	−	4770.30i	−1.11163	−	0.306033i
$625$	28406.4			1.81801
$626$		−	1737.68i		−	0.110945i
$627$	189.789			0.0120884
$628$	23064.1			1.46554
$629$		−	20191.8i		−	1.27997i
$630$		−	16824.2i		−	1.06395i
$631$		−	11906.1i		−	0.751148i	−0.926792	−	0.375574i	$-0.877446\pi$
$631$		−	11906.1i		−	0.751148i	0.926792	−	0.375574i	$-0.122554\pi$
$632$		−	12445.0i		−	0.783282i
$633$	17471.4			1.09704
$634$	31292.3			1.96021
$635$			10093.4i			0.630780i
$636$	−42553.1			−2.65305
$637$	−10201.1	−	2808.37i	−0.634506	−	0.174681i
$638$	4679.88			0.290405
$639$			1066.99i			0.0660556i
$640$	−43933.5			−2.71348
$641$	−5547.76			−0.341846			−0.170923	−	0.985284i	$-0.554675\pi$
$641$	−5547.76			−0.341846			−0.170923	+	0.985284i	$0.554675\pi$
$642$			27428.8i			1.68618i
$643$		−	8383.25i		−	0.514158i	−0.966390	−	0.257079i	$-0.917240\pi$
$643$		−	8383.25i		−	0.514158i	0.966390	−	0.257079i	$-0.0827600\pi$
$644$			30956.7i			1.89420i
$645$			17525.8i			1.06989i
$646$	−2155.90			−0.131305
$647$	−26350.5			−1.60115			−0.800575	−	0.599233i	$-0.795472\pi$
$647$	−26350.5			−1.60115			−0.800575	+	0.599233i	$0.795472\pi$
$648$		−	21705.1i		−	1.31583i
$649$	554.764			0.0335538
$650$	−17463.8	+	63435.3i	−1.05383	+	3.82790i
$651$	26085.8			1.57048
$652$		−	47953.7i		−	2.88039i
$653$	22098.6			1.32433			0.662164	−	0.749359i	$-0.269638\pi$
$653$	22098.6			1.32433			0.662164	+	0.749359i	$0.269638\pi$
$654$	−7441.51			−0.444933
$655$		−	4136.73i		−	0.246772i
$656$			40374.1i			2.40296i
$657$		−	1719.60i		−	0.102113i
$658$			34208.0i			2.02670i
$659$	5272.65			0.311674			0.155837	−	0.987783i	$-0.450192\pi$
$659$	5272.65			0.311674			0.155837	+	0.987783i	$0.450192\pi$
$660$	−16729.6			−0.986663
$661$		−	19249.3i		−	1.13270i	−0.824166	−	0.566348i	$-0.808356\pi$
$661$		−	19249.3i		−	1.13270i	0.824166	−	0.566348i	$-0.191644\pi$
$662$	−19334.9			−1.13516
$663$	−22625.5	−	6228.85i	−1.32534	−	0.364870i
$664$	19215.6			1.12306
$665$			1855.64i			0.108209i
$666$	6308.77			0.367057
$667$	−6561.59			−0.380908
$668$		−	8890.27i		−	0.514933i
$669$			18514.5i			1.06997i
$670$		−	20037.3i		−	1.15538i
$671$		−	3678.44i		−	0.211631i
$672$	7853.40			0.450821
$673$	32955.4			1.88757			0.943787	−	0.330553i	$-0.107235\pi$
$673$	32955.4			1.88757			0.943787	+	0.330553i	$0.107235\pi$
$674$		−	26031.4i		−	1.48767i
$675$	−42797.7			−2.44042
$676$	−31851.0	−	18975.4i	−1.81218	−	1.07962i
$677$	−24793.6			−1.40753			−0.703763	−	0.710435i	$-0.748498\pi$
$677$	−24793.6			−1.40753			−0.703763	+	0.710435i	$0.748498\pi$
$678$		−	30523.0i		−	1.72895i
$679$	−19147.6			−1.08221
$680$	99947.8			5.63651
$681$		−	11245.4i		−	0.632784i
$682$			13424.1i			0.753718i
$683$			20604.3i			1.15432i	0.816630	+	0.577161i	$0.195840\pi$
$683$			20604.3i			1.15432i	−0.816630	+	0.577161i	$0.804160\pi$
$684$		−	456.965i		−	0.0255446i
$685$	46414.1			2.58889
$686$	−13948.1			−0.776300
$687$			9583.12i			0.532196i
$688$	16679.4			0.924270
$689$	−25491.3	−	7017.80i	−1.40949	−	0.388036i
$690$	34576.2			1.90767
$691$		−	1561.14i		−	0.0859458i	−0.999076	−	0.0429729i	$-0.986317\pi$
$691$		−	1561.14i		−	0.0859458i	0.999076	−	0.0429729i	$-0.0136829\pi$
$692$	−27386.9			−1.50447
$693$	1840.52			0.100888
$694$		−	38177.5i		−	2.08818i
$695$			9460.68i			0.516351i
$696$			16879.6i			0.919282i
$697$			52718.8i			2.86494i
$698$	−30723.0			−1.66602
$699$	8695.14			0.470502
$700$		−	113266.i		−	6.11580i
$701$	−30999.8			−1.67025			−0.835125	−	0.550060i	$-0.814605\pi$
$701$	−30999.8			−1.67025			−0.835125	+	0.550060i	$0.814605\pi$
$702$	9435.57	−	34273.6i	0.507297	−	1.84270i
$703$	−695.833			−0.0373312
$704$		−	3506.46i		−	0.187720i
$705$	25919.8			1.38468
$706$	−55957.9			−2.98301
$707$		−	29295.9i		−	1.55839i
$708$			3804.57i			0.201956i
$709$		−	36499.5i		−	1.93338i	−0.255950	−	0.966690i	$-0.582388\pi$
$709$		−	36499.5i		−	1.93338i	0.255950	−	0.966690i	$-0.417612\pi$
$710$			15291.6i			0.808285i
$711$	1972.53			0.104045
$712$	−45711.8			−2.40607
$713$		−	18821.7i		−	0.988612i
$714$	59550.5			3.12132
$715$	−10021.8	−	2759.02i	−0.524187	−	0.144310i
$716$	−59672.2			−3.11460
$717$			25455.3i			1.32586i
$718$	−38483.4			−2.00026
$719$	38007.8			1.97142			0.985710	−	0.168453i	$-0.0538772\pi$
$719$	38007.8			1.97142			0.985710	+	0.168453i	$0.0538772\pi$
$720$			12132.2i			0.627975i
$721$		−	7968.19i		−	0.411582i
$722$		−	34135.0i		−	1.75952i
$723$		−	8983.61i		−	0.462108i
$724$	−56345.9			−2.89237
$725$	24007.9			1.22984
$726$		−	2697.80i		−	0.137913i
$727$	20144.5			1.02768			0.513838	−	0.857887i	$-0.328223\pi$
$727$	20144.5			1.02768			0.513838	+	0.857887i	$0.328223\pi$
$728$	47705.6	+	13133.4i	2.42869	+	0.668622i
$729$	21794.2			1.10726
$730$		−	24644.4i		−	1.24950i
$731$	21779.3			1.10196
$732$	25226.8			1.27378
$733$			13433.0i			0.676889i	0.940986	+	0.338444i	$0.109901\pi$
$733$			13433.0i			0.676889i	−0.940986	+	0.338444i	$0.890099\pi$
$734$		−	28631.5i		−	1.43979i
$735$		−	20344.0i		−	1.02095i
$736$		−	5666.49i		−	0.283790i
$737$	2192.02			0.109558
$738$	−16471.6			−0.821582
$739$			15113.2i			0.752300i	0.926559	+	0.376150i	$0.122752\pi$
$739$			15113.2i			0.752300i	−0.926559	+	0.376150i	$0.877248\pi$
$740$	61336.5			3.04699
$741$	−214.654	+	779.704i	−0.0106417	+	0.0386547i
$742$	67093.2			3.31950
$743$			10764.4i			0.531504i	0.964041	+	0.265752i	$0.0856203\pi$
$743$			10764.4i			0.531504i	−0.964041	+	0.265752i	$0.914380\pi$
$744$	−48418.7			−2.38591
$745$	15103.3			0.742739
$746$			7177.35i			0.352254i
$747$			3045.67i			0.149177i
$748$			20789.8i			1.01624i
$749$		−	29338.4i		−	1.43125i
$750$	−70322.2			−3.42374
$751$	−724.420			−0.0351990			−0.0175995	−	0.999845i	$-0.505602\pi$
$751$	−724.420			−0.0351990			−0.0175995	+	0.999845i	$0.505602\pi$
$752$		−	24668.1i		−	1.19621i
$753$	23787.3			1.15120
$754$	−5293.00	+	19226.2i	−0.255649	+	0.928616i
$755$	−47544.4			−2.29181
$756$			61196.8i			2.94406i
$757$	−2475.45			−0.118853			−0.0594265	−	0.998233i	$-0.518927\pi$
$757$	−2475.45			−0.118853			−0.0594265	+	0.998233i	$0.518927\pi$
$758$	28686.7			1.37460
$759$			3782.54i			0.180893i
$760$		−	3444.33i		−	0.164393i
$761$			12024.6i			0.572786i	0.958112	+	0.286393i	$0.0924563\pi$
$761$			12024.6i			0.572786i	−0.958112	+	0.286393i	$0.907544\pi$
$762$		−	11162.5i		−	0.530674i
$763$	7959.59			0.377663
$764$	18312.3			0.867168
$765$			15841.8i			0.748706i
$766$	−3998.65			−0.188612
$767$	−627.445	+	2279.12i	−0.0295381	+	0.107294i
$768$	37186.8			1.74722
$769$		−	4428.79i		−	0.207681i	−0.994594	−	0.103840i	$-0.966887\pi$
$769$		−	4428.79i		−	0.207681i	0.994594	−	0.103840i	$-0.0331131\pi$
$770$	26377.4			1.23451
$771$	16928.9			0.790765
$772$		−	30409.6i		−	1.41770i
$773$			24842.8i			1.15593i	0.816062	+	0.577964i	$0.196153\pi$
$773$			24842.8i			1.15593i	−0.816062	+	0.577964i	$0.803847\pi$
$774$			6804.78i			0.316011i
$775$			68866.1i			3.19192i
$776$	35540.6			1.64411
$777$	19220.3			0.887421
$778$		−	64739.3i		−	2.98331i
$779$	1816.75			0.0835583
$780$	18921.4	−	68729.5i	0.868581	−	3.15502i
$781$	−1672.86			−0.0766448
$782$		−	42967.7i		−	1.96486i
$783$	−12971.3			−0.592025
$784$	−19361.5			−0.881993
$785$			27554.3i			1.25281i
$786$			4574.88i			0.207609i
$787$			41041.0i			1.85890i	0.368951	+	0.929449i	$0.379717\pi$
$787$			41041.0i			1.85890i	−0.368951	+	0.929449i	$0.620283\pi$
$788$			45644.5i			2.06347i
$789$	6394.67			0.288538
$790$	28269.3			1.27314
$791$			32648.0i			1.46755i
$792$	−3416.26			−0.153272
$793$	15112.0	+	4160.36i	0.676725	+	0.186304i
$794$	−17419.0			−0.778561
$795$		−	50837.4i		−	2.26795i
$796$	−12810.0			−0.570402
$797$	−30301.7			−1.34673			−0.673364	−	0.739312i	$-0.735151\pi$
$797$	−30301.7			−1.34673			−0.673364	+	0.739312i	$0.735151\pi$
$798$		−	2052.18i		−	0.0910358i
$799$		−	32210.5i		−	1.42619i
$800$			20732.9i			0.916272i
$801$		−	7245.34i		−	0.319602i
$802$	4897.12			0.215615
$803$	2696.04			0.118482
$804$			15032.9i			0.659416i
$805$	−36983.4			−1.61925
$806$	−55149.8	−	15182.8i	−2.41013	−	0.663514i
$807$	14762.1			0.643931
$808$			54377.1i			2.36755i
$809$	182.919			0.00794944			0.00397472	−	0.999992i	$-0.498735\pi$
$809$	182.919			0.00794944			0.00397472	+	0.999992i	$0.498735\pi$
$810$	49304.1			2.13873
$811$			18134.4i			0.785186i	0.919712	+	0.392593i	$0.128422\pi$
$811$			18134.4i			0.785186i	−0.919712	+	0.392593i	$0.871578\pi$
$812$		−	34329.1i		−	1.48364i
$813$			37563.1i			1.62041i
$814$			9891.07i			0.425899i
$815$	57289.4			2.46228
$816$	−42943.1			−1.84229
$817$		−	750.541i		−	0.0321397i
$818$	45485.5			1.94421
$819$	−2081.65	+	7561.35i	−0.0888141	+	0.322607i
$820$	−160144.			−6.82007
$821$			24718.5i			1.05077i	0.850865	+	0.525385i	$0.176079\pi$
$821$			24718.5i			1.05077i	−0.850865	+	0.525385i	$0.823921\pi$
$822$	−51330.1			−2.17803
$823$	13607.1			0.576322			0.288161	−	0.957582i	$-0.406956\pi$
$823$	13607.1			0.576322			0.288161	+	0.957582i	$0.406956\pi$
$824$			14790.0i			0.625286i
$825$		−	13839.8i		−	0.584048i
$826$		−	5998.65i		−	0.252687i
$827$		−	22725.4i		−	0.955549i	−0.878483	−	0.477774i	$-0.841444\pi$
$827$		−	22725.4i		−	0.955549i	0.878483	−	0.477774i	$-0.158556\pi$
$828$	9107.41			0.382252
$829$	−17207.3			−0.720910			−0.360455	−	0.932777i	$-0.617378\pi$
$829$	−17207.3			−0.720910			−0.360455	+	0.932777i	$0.617378\pi$
$830$			43649.0i			1.82540i
$831$	−24592.0			−1.02658
$832$	14405.5	+	3965.85i	0.600264	+	0.165254i
$833$	−25281.4			−1.05156
$834$		−	10462.7i		−	0.434406i
$835$	10621.0			0.440187
$836$	716.442			0.0296396
$837$		−	37207.8i		−	1.53655i
$838$		−	55139.9i		−	2.27300i
$839$			22709.3i			0.934460i	0.884136	+	0.467230i	$0.154748\pi$
$839$			22709.3i			0.934460i	−0.884136	+	0.467230i	$0.845252\pi$
$840$			95139.4i			3.90788i
$841$	−17112.6			−0.701652
$842$	−12688.8			−0.519339
$843$			13781.5i			0.563059i
$844$	65953.2			2.68982
$845$	22669.5	−	38051.7i	0.922907	−	1.54913i
$846$	10063.9			0.408990
$847$			2885.62i			0.117062i
$848$	−48382.3			−1.95926
$849$	29248.4			1.18234
$850$			157213.i			6.34394i
$851$		−	13868.1i		−	0.558629i
$852$		−	11472.5i		−	0.461315i
$853$		−	38029.5i		−	1.52650i	−0.646103	−	0.763250i	$-0.723602\pi$
$853$		−	38029.5i		−	1.52650i	0.646103	−	0.763250i	$-0.276398\pi$
$854$	−39774.9			−1.59376
$855$	545.927			0.0218366
$856$			54456.2i			2.17438i
$857$	4498.91			0.179323			0.0896616	−	0.995972i	$-0.471421\pi$
$857$	4498.91			0.179323			0.0896616	+	0.995972i	$0.471421\pi$
$858$	11083.3	+	3051.24i	0.440998	+	0.121408i
$859$	13450.9			0.534271			0.267135	−	0.963659i	$-0.413923\pi$
$859$	13450.9			0.534271			0.267135	+	0.963659i	$0.413923\pi$
$860$			66158.9i			2.62325i
$861$	−50182.5			−1.98631
$862$	53330.0			2.10722
$863$			4350.45i			0.171600i	0.996312	+	0.0858002i	$0.0273447\pi$
$863$			4350.45i			0.171600i	−0.996312	+	0.0858002i	$0.972655\pi$
$864$		−	11201.8i		−	0.441080i
$865$		−	32718.5i		−	1.28609i
$866$			14077.2i			0.552384i
$867$	−34110.4			−1.33616
$868$	98472.1			3.85065
$869$			3092.59i			0.120724i
$870$	−38342.8			−1.49419
$871$	−2479.21	+	9005.42i	−0.0964463	+	0.350329i
$872$	−14774.1			−0.573754
$873$			5633.19i			0.218390i
$874$	−1480.72			−0.0573067
$875$	75218.0			2.90610
$876$			18489.5i			0.713129i
$877$		−	1982.86i		−	0.0763471i	−0.999271	−	0.0381735i	$-0.987846\pi$
$877$		−	1982.86i		−	0.0763471i	0.999271	−	0.0381735i	$-0.0121540\pi$
$878$			18379.6i			0.706469i
$879$		−	24796.0i		−	0.951475i
$880$	−19021.3			−0.728644
$881$	39887.8			1.52537			0.762687	−	0.646768i	$-0.223880\pi$
$881$	39887.8			1.52537			0.762687	+	0.646768i	$0.223880\pi$
$882$		−	7898.99i		−	0.301557i
$883$	−9886.90			−0.376807			−0.188404	−	0.982092i	$-0.560331\pi$
$883$	−9886.90			−0.376807			−0.188404	+	0.982092i	$0.560331\pi$
$884$	−85410.0	−	23513.5i	−3.24960	−	0.894621i
$885$	−4545.25			−0.172641
$886$		−	25093.4i		−	0.951500i
$887$	25867.4			0.979189			0.489595	−	0.871950i	$-0.337145\pi$
$887$	25867.4			0.979189			0.489595	+	0.871950i	$0.337145\pi$
$888$	−35675.6			−1.34819
$889$			11939.6i			0.450441i
$890$		−	103836.i		−	3.91079i
$891$			5393.75i			0.202803i
$892$			69891.1i			2.62346i
$893$	−1110.01			−0.0415960
$894$	−16703.0			−0.624866
$895$		−	71289.2i		−	2.66250i
$896$	−51969.5			−1.93770
$897$	−15539.7	−	4278.10i	−0.578434	−	0.159244i
$898$	33213.5			1.23424
$899$			20872.2i			0.774333i
$900$	−33322.7			−1.23417
$901$	−63175.5			−2.33594
$902$		−	25824.6i		−	0.953288i
$903$			20731.5i			0.764010i
$904$		−	60599.2i		−	2.22954i
$905$		−	67315.4i		−	2.47253i
$906$	52580.1			1.92810
$907$	−2520.36			−0.0922681			−0.0461340	−	0.998935i	$-0.514690\pi$
$907$	−2520.36			−0.0922681			−0.0461340	+	0.998935i	$0.514690\pi$
$908$		−	42450.8i		−	1.55152i
$909$	−8618.79			−0.314485
$910$	−29833.2	+	108365.i	−1.08677	+	3.94756i
$911$	7964.68			0.289662			0.144831	−	0.989456i	$-0.453736\pi$
$911$	7964.68			0.289662			0.144831	+	0.989456i	$0.453736\pi$
$912$			1479.87i			0.0537318i
$913$	−4775.09			−0.173092
$914$	−63720.8			−2.30601
$915$			30137.9i			1.08888i
$916$			36175.7i			1.30489i
$917$		−	4893.39i		−	0.176220i
$918$		−	84940.7i		−	3.05388i
$919$	−17048.0			−0.611929			−0.305965	−	0.952043i	$-0.598979\pi$
$919$	−17048.0			−0.611929			−0.305965	+	0.952043i	$0.598979\pi$
$920$	68646.2			2.46000
$921$		−	1663.82i		−	0.0595274i
$922$	46660.1			1.66667
$923$	1892.02	−	6872.55i	0.0674721	−	0.245084i
$924$	−19789.6			−0.704578
$925$			50741.5i			1.80364i
$926$	28094.3			0.997016
$927$	−2344.23			−0.0830577
$928$			6283.79i			0.222280i
$929$		−	28183.3i		−	0.995334i	−0.867368	−	0.497667i	$-0.834190\pi$
$929$		−	28183.3i		−	0.995334i	0.867368	−	0.497667i	$-0.165810\pi$
$930$		−	109985.i		−	3.87802i
$931$			871.229i			0.0306696i
$932$	32823.6			1.15362
$933$	35274.1			1.23775
$934$			37692.7i			1.32050i
$935$	−24837.2			−0.868730
$936$	3863.83	−	14034.9i	0.134929	−	0.490112i
$937$	−31323.9			−1.09211			−0.546055	−	0.837750i	$-0.683871\pi$
$937$	−31323.9			−1.09211			−0.546055	+	0.837750i	$0.683871\pi$
$938$		−	23702.3i		−	0.825061i
$939$	−1557.49			−0.0541287
$940$	97845.8			3.39508
$941$			36257.9i			1.25608i	0.778181	+	0.628041i	$0.216143\pi$
$941$			36257.9i			1.25608i	−0.778181	+	0.628041i	$0.783857\pi$
$942$		−	30472.7i		−	1.05399i
$943$			36208.3i			1.25038i
$944$			4325.74i			0.149143i
$945$	−73110.6			−2.51671
$946$	−10668.7			−0.366670
$947$			51372.2i			1.76280i	0.472369	+	0.881401i	$0.343399\pi$
$947$			51372.2i			1.76280i	−0.472369	+	0.881401i	$0.656601\pi$
$948$	−21209.0			−0.726621
$949$	−3049.25	+	11076.0i	−0.104302	+	0.378866i
$950$	5417.74			0.185026
$951$		−	28047.5i		−	0.956363i
$952$	118229.			4.02504
$953$	31677.7			1.07675			0.538374	−	0.842706i	$-0.319039\pi$
$953$	31677.7			1.07675			0.538374	+	0.842706i	$0.319039\pi$
$954$		−	19738.7i		−	0.669879i
$955$			21877.4i			0.741293i
$956$			96092.1i			3.25088i
$957$		−	4194.61i		−	0.141685i
$958$	−2300.97			−0.0776001
$959$	54903.7			1.84873
$960$			28728.8i			0.965853i
$961$	−30080.2			−1.00971
$962$	−40635.1	−	11186.9i	−1.36188	−	0.374928i
$963$	−8631.32			−0.288827
$964$		−	33912.6i		−	1.13304i
$965$	36329.7			1.21191
$966$	40900.5			1.36227
$967$		−	5938.19i		−	0.197476i	−0.995113	−	0.0987381i	$-0.968519\pi$
$967$		−	5938.19i		−	0.197476i	0.995113	−	0.0987381i	$-0.0314806\pi$
$968$		−	5356.11i		−	0.177843i
$969$			1932.35i			0.0640620i
$970$			80732.0i			2.67232i
$971$	55548.7			1.83588			0.917941	−	0.396717i	$-0.129851\pi$
$971$	55548.7			1.83588			0.917941	+	0.396717i	$0.129851\pi$
$972$	32294.5			1.06569
$973$			11191.2i			0.368727i
$974$	−43749.8			−1.43926
$975$	56857.5	+	15653.0i	1.86759	+	0.514150i
$976$	28682.5			0.940679
$977$			12029.0i			0.393901i	0.980413	+	0.196951i	$0.0631038\pi$
$977$			12029.0i			0.393901i	−0.980413	+	0.196951i	$0.936896\pi$
$978$	−63357.2			−2.07151
$979$	11359.4			0.370837
$980$		−	76797.3i		−	2.50326i
$981$		−	2341.70i		−	0.0762127i
$982$			33072.9i			1.07474i
$983$			3362.61i			0.109106i	0.998511	+	0.0545528i	$0.0173733\pi$
$983$			3362.61i			0.109106i	−0.998511	+	0.0545528i	$0.982627\pi$
$984$	93145.5			3.01765
$985$	−54530.5			−1.76395
$986$			47648.5i			1.53898i
$987$	30660.9			0.988801
$988$	−810.305	+	2943.33i	−0.0260923	+	0.0947773i
$989$	14958.5			0.480942
$990$		−	7760.19i		−	0.249126i
$991$	52987.7			1.69850			0.849248	−	0.527994i	$-0.177056\pi$
$991$	52987.7			1.69850			0.849248	+	0.527994i	$0.177056\pi$
$992$	−18024.9			−0.576906
$993$			17330.0i			0.553828i
$994$			18088.6i			0.577198i
$995$		−	15303.9i		−	0.487605i
$996$		−	32747.6i		−	1.04182i
$997$	−44929.5			−1.42721			−0.713606	−	0.700547i	$-0.752939\pi$
$997$	−44929.5			−1.42721			−0.713606	+	0.700547i	$0.752939\pi$
$998$	−2092.91			−0.0663827
$999$		−	27415.2i		−	0.868247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.b.a.12.3	✓	36
13.5	odd	4		1859.4.a.k.1.2		18
13.8	odd	4		1859.4.a.j.1.17		18
13.12	even	2	inner	143.4.b.a.12.34	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.b.a.12.3	✓	36	1.1	even	1	trivial
143.4.b.a.12.34	yes	36	13.12	even	2	inner
1859.4.a.j.1.17		18	13.8	odd	4
1859.4.a.k.1.2		18	13.5	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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.98751i q^{2} -4.47034 q^{3} -16.8752 q^{4} -20.1605i q^{5} +22.2959i q^{6} -23.8481i q^{7} +44.2654i q^{8} -7.01607 q^{9} +O(q^{10})\)	\(q-4.98751i q^{2} -4.47034 q^{3} -16.8752 q^{4} -20.1605i q^{5} +22.2959i q^{6} -23.8481i q^{7} +44.2654i q^{8} -7.01607 q^{9} -100.551 q^{10} -11.0000i q^{11} +75.4381 q^{12} +(45.1909 + 12.4411i) q^{13} -118.943 q^{14} +90.1244i q^{15} +85.7719 q^{16} +111.997 q^{17} +34.9927i q^{18} -3.85957i q^{19} +340.214i q^{20} +106.609i q^{21} -54.8626 q^{22} +76.9220 q^{23} -197.881i q^{24} -281.447 q^{25} +(62.0503 - 225.390i) q^{26} +152.063 q^{27} +402.443i q^{28} -85.3018 q^{29} +449.496 q^{30} -244.686i q^{31} -73.6653i q^{32} +49.1737i q^{33} -558.588i q^{34} -480.790 q^{35} +118.398 q^{36} -180.288i q^{37} -19.2496 q^{38} +(-202.019 - 55.6161i) q^{39} +892.413 q^{40} +470.715i q^{41} +531.714 q^{42} +194.463 q^{43} +185.628i q^{44} +141.448i q^{45} -383.649i q^{46} -287.601i q^{47} -383.430 q^{48} -225.732 q^{49} +1403.72i q^{50} -500.666 q^{51} +(-762.608 - 209.947i) q^{52} -564.081 q^{53} -758.417i q^{54} -221.766 q^{55} +1055.65 q^{56} +17.2536i q^{57} +425.444i q^{58} +50.4331i q^{59} -1520.87i q^{60} +334.404 q^{61} -1220.37 q^{62} +167.320i q^{63} +318.769 q^{64} +(250.820 - 911.072i) q^{65} +245.254 q^{66} +199.275i q^{67} -1889.98 q^{68} -343.868 q^{69} +2397.95i q^{70} -152.078i q^{71} -310.569i q^{72} +245.095i q^{73} -899.188 q^{74} +1258.16 q^{75} +65.1311i q^{76} -262.329 q^{77} +(-277.386 + 1007.57i) q^{78} -281.145 q^{79} -1729.21i q^{80} -490.341 q^{81} +2347.69 q^{82} -434.099i q^{83} -1799.06i q^{84} -2257.92i q^{85} -969.884i q^{86} +381.328 q^{87} +486.919 q^{88} +1032.68i q^{89} +705.472 q^{90} +(296.698 - 1077.72i) q^{91} -1298.08 q^{92} +1093.83i q^{93} -1434.41 q^{94} -77.8109 q^{95} +329.309i q^{96} -802.898i q^{97} +1125.84i q^{98} +77.1768i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 152 q^{4} + 360 q^{9}+O(q^{10}) \) 36 * q - 152 * q^4 + 360 * q^9	\( 36 q - 152 q^{4} + 360 q^{9} - 112 q^{10} - 108 q^{12} - 50 q^{13} + 8 q^{14} + 728 q^{16} + 276 q^{17} + 44 q^{22} - 472 q^{23} - 1172 q^{25} + 152 q^{26} - 12 q^{27} - 572 q^{29} + 712 q^{30} + 68 q^{35} - 430 q^{36} - 50 q^{38} + 640 q^{39} - 216 q^{40} + 1126 q^{42} + 920 q^{43} + 1674 q^{48} - 2164 q^{49} - 340 q^{51} - 800 q^{52} + 2432 q^{53} + 440 q^{55} - 2274 q^{56} - 1844 q^{61} + 2796 q^{62} - 2592 q^{64} + 2264 q^{65} + 1078 q^{66} - 4548 q^{68} - 3288 q^{69} - 4036 q^{74} + 820 q^{75} - 616 q^{77} + 2222 q^{78} + 360 q^{79} + 852 q^{81} + 1948 q^{82} - 2480 q^{87} + 264 q^{88} - 496 q^{90} + 4600 q^{91} + 454 q^{92} - 488 q^{94} + 952 q^{95}+O(q^{100}) \) 36 * q - 152 * q^4 + 360 * q^9 - 112 * q^10 - 108 * q^12 - 50 * q^13 + 8 * q^14 + 728 * q^16 + 276 * q^17 + 44 * q^22 - 472 * q^23 - 1172 * q^25 + 152 * q^26 - 12 * q^27 - 572 * q^29 + 712 * q^30 + 68 * q^35 - 430 * q^36 - 50 * q^38 + 640 * q^39 - 216 * q^40 + 1126 * q^42 + 920 * q^43 + 1674 * q^48 - 2164 * q^49 - 340 * q^51 - 800 * q^52 + 2432 * q^53 + 440 * q^55 - 2274 * q^56 - 1844 * q^61 + 2796 * q^62 - 2592 * q^64 + 2264 * q^65 + 1078 * q^66 - 4548 * q^68 - 3288 * q^69 - 4036 * q^74 + 820 * q^75 - 616 * q^77 + 2222 * q^78 + 360 * q^79 + 852 * q^81 + 1948 * q^82 - 2480 * q^87 + 264 * q^88 - 496 * q^90 + 4600 * q^91 + 454 * q^92 - 488 * q^94 + 952 * q^95

Introduction

L-functions

Modular forms

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