LMFDB - Embedded newform 143.4.b.a.12.11

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			12.11
Character	$\chi$	$=$	143.12
Dual form			143.4.b.a.12.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37174i q^{2} -6.00967 q^{3} +2.37485 q^{4} +22.0017i q^{5} +14.2534i q^{6} -21.9243i q^{7} -24.6064i q^{8} +9.11608 q^{9} +O(q^{10})$	\(q-2.37174i q^{2} -6.00967 q^{3} +2.37485 q^{4} +22.0017i q^{5} +14.2534i q^{6} -21.9243i q^{7} -24.6064i q^{8} +9.11608 q^{9} +52.1824 q^{10} -11.0000i q^{11} -14.2720 q^{12} +(-26.6562 - 38.5545i) q^{13} -51.9987 q^{14} -132.223i q^{15} -39.3613 q^{16} +45.0465 q^{17} -21.6210i q^{18} -118.734i q^{19} +52.2507i q^{20} +131.757i q^{21} -26.0891 q^{22} -37.3506 q^{23} +147.877i q^{24} -359.076 q^{25} +(-91.4413 + 63.2215i) q^{26} +107.476 q^{27} -52.0667i q^{28} -137.520 q^{29} -313.599 q^{30} -1.53563i q^{31} -103.497i q^{32} +66.1063i q^{33} -106.839i q^{34} +482.371 q^{35} +21.6493 q^{36} -236.355i q^{37} -281.607 q^{38} +(160.195 + 231.700i) q^{39} +541.384 q^{40} -72.6689i q^{41} +312.495 q^{42} +60.4521 q^{43} -26.1233i q^{44} +200.569i q^{45} +88.5860i q^{46} -397.359i q^{47} +236.549 q^{48} -137.673 q^{49} +851.635i q^{50} -270.714 q^{51} +(-63.3043 - 91.5610i) q^{52} +0.405257 q^{53} -254.906i q^{54} +242.019 q^{55} -539.478 q^{56} +713.555i q^{57} +326.161i q^{58} +37.1386i q^{59} -314.009i q^{60} +308.289 q^{61} -3.64212 q^{62} -199.863i q^{63} -560.358 q^{64} +(848.265 - 586.482i) q^{65} +156.787 q^{66} +427.027i q^{67} +106.978 q^{68} +224.465 q^{69} -1144.06i q^{70} +1013.88i q^{71} -224.314i q^{72} +186.363i q^{73} -560.573 q^{74} +2157.93 q^{75} -281.976i q^{76} -241.167 q^{77} +(549.531 - 379.940i) q^{78} -831.039 q^{79} -866.017i q^{80} -892.031 q^{81} -172.352 q^{82} -1348.22i q^{83} +312.904i q^{84} +991.100i q^{85} -143.377i q^{86} +826.447 q^{87} -270.671 q^{88} +840.976i q^{89} +475.699 q^{90} +(-845.278 + 584.417i) q^{91} -88.7020 q^{92} +9.22864i q^{93} -942.433 q^{94} +2612.36 q^{95} +621.980i q^{96} +1234.39i q^{97} +326.525i q^{98} -100.277i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.37174i		−	0.838537i	−0.907862	−	0.419269i	$-0.862287\pi$
$2$		−	2.37174i		−	0.838537i	0.907862	−	0.419269i	$-0.137713\pi$
$3$	−6.00967			−1.15656			−0.578280	−	0.815838i	$-0.696276\pi$
$3$	−6.00967			−1.15656			−0.578280	+	0.815838i	$0.696276\pi$
$4$	2.37485			0.296856
$5$			22.0017i			1.96789i	0.178461	+	0.983947i	$0.442888\pi$
$5$			22.0017i			1.96789i	−0.178461	+	0.983947i	$0.557112\pi$
$6$			14.2534i			0.969819i
$7$		−	21.9243i		−	1.18380i	−0.806012	−	0.591899i	$-0.798378\pi$
$7$		−	21.9243i		−	1.18380i	0.806012	−	0.591899i	$-0.201622\pi$
$8$		−	24.6064i		−	1.08746i
$9$	9.11608			0.337633
$10$	52.1824			1.65015
$11$		−	11.0000i		−	0.301511i
$11$		−	11.0000i		−	0.301511i
$12$	−14.2720			−0.343332
$13$	−26.6562	−	38.5545i	−0.568699	−	0.822545i
$13$	−26.6562	−	38.5545i	−0.568699	−	0.822545i
$14$	−51.9987			−0.992659
$15$		−	132.223i		−	2.27599i
$16$	−39.3613			−0.615021
$17$	45.0465			0.642669			0.321334	−	0.946966i	$-0.395869\pi$
$17$	45.0465			0.642669			0.321334	+	0.946966i	$0.395869\pi$
$18$		−	21.6210i		−	0.283117i
$19$		−	118.734i		−	1.43366i	−0.697247	−	0.716831i	$-0.745592\pi$
$19$		−	118.734i		−	1.43366i	0.697247	−	0.716831i	$-0.254408\pi$
$20$			52.2507i			0.584181i
$21$			131.757i			1.36913i
$22$	−26.0891			−0.252828
$23$	−37.3506			−0.338615			−0.169308	−	0.985563i	$-0.554153\pi$
$23$	−37.3506			−0.338615			−0.169308	+	0.985563i	$0.554153\pi$
$24$			147.877i			1.25772i
$25$	−359.076			−2.87261
$26$	−91.4413	+	63.2215i	−0.689735	+	0.476875i
$27$	107.476			0.766068
$28$		−	52.0667i		−	0.351417i
$29$	−137.520			−0.880578			−0.440289	−	0.897856i	$-0.645124\pi$
$29$	−137.520			−0.880578			−0.440289	+	0.897856i	$0.645124\pi$
$30$	−313.599			−1.90850
$31$		−	1.53563i		−	0.00889702i	−0.999990	−	0.00444851i	$-0.998584\pi$
$31$		−	1.53563i		−	0.00889702i	0.999990	−	0.00444851i	$-0.00141601\pi$
$32$		−	103.497i		−	0.571744i
$33$			66.1063i			0.348716i
$34$		−	106.839i		−	0.538902i
$35$	482.371			2.32959
$36$	21.6493			0.100228
$37$		−	236.355i		−	1.05018i	−0.851048	−	0.525088i	$-0.824032\pi$
$37$		−	236.355i		−	1.05018i	0.851048	−	0.525088i	$-0.175968\pi$
$38$	−281.607			−1.20218
$39$	160.195	+	231.700i	0.657735	+	0.951324i
$40$	541.384			2.14001
$41$		−	72.6689i		−	0.276804i	−0.990376	−	0.138402i	$-0.955803\pi$
$41$		−	72.6689i		−	0.276804i	0.990376	−	0.138402i	$-0.0441966\pi$
$42$	312.495			1.14807
$43$	60.4521			0.214392			0.107196	−	0.994238i	$-0.465813\pi$
$43$	60.4521			0.214392			0.107196	+	0.994238i	$0.465813\pi$
$44$		−	26.1233i		−	0.0895054i
$45$			200.569i			0.664425i
$46$			88.5860i			0.283941i
$47$		−	397.359i		−	1.23321i	−0.787273	−	0.616604i	$-0.788508\pi$
$47$		−	397.359i		−	1.23321i	0.787273	−	0.616604i	$-0.211492\pi$
$48$	236.549			0.711309
$49$	−137.673			−0.401379
$50$			851.635i			2.40879i
$51$	−270.714			−0.743286
$52$	−63.3043	−	91.5610i	−0.168822	−	0.244177i
$53$	0.405257			0.00105031			0.000525155	−	1.00000i	$-0.499833\pi$
$53$	0.405257			0.00105031			0.000525155		1.00000i	$0.499833\pi$
$54$		−	254.906i		−	0.642376i
$55$	242.019			0.593342
$56$	−539.478			−1.28734
$57$			713.555i			1.65812i
$58$			326.161i			0.738397i
$59$			37.1386i			0.0819496i	0.999160	+	0.0409748i	$0.0130463\pi$
$59$			37.1386i			0.0819496i	−0.999160	+	0.0409748i	$0.986954\pi$
$60$		−	314.009i		−	0.675640i
$61$	308.289			0.647088			0.323544	−	0.946213i	$-0.395126\pi$
$61$	308.289			0.647088			0.323544	+	0.946213i	$0.395126\pi$
$62$	−3.64212			−0.00746048
$63$		−	199.863i		−	0.399689i
$64$	−560.358			−1.09445
$65$	848.265	−	586.482i	1.61868	−	1.11914i
$66$	156.787			0.292411
$67$			427.027i			0.778652i	0.921100	+	0.389326i	$0.127292\pi$
$67$			427.027i			0.778652i	−0.921100	+	0.389326i	$0.872708\pi$
$68$	106.978			0.190780
$69$	224.465			0.391629
$70$		−	1144.06i		−	1.95345i
$71$			1013.88i			1.69472i	0.531016	+	0.847362i	$0.321810\pi$
$71$			1013.88i			1.69472i	−0.531016	+	0.847362i	$0.678190\pi$
$72$		−	224.314i		−	0.367162i
$73$			186.363i			0.298796i	0.988777	+	0.149398i	$0.0477336\pi$
$73$			186.363i			0.298796i	−0.988777	+	0.149398i	$0.952266\pi$
$74$	−560.573			−0.880612
$75$	2157.93			3.32234
$76$		−	281.976i		−	0.425590i
$77$	−241.167			−0.356929
$78$	549.531	−	379.940i	0.797720	−	0.551535i
$79$	−831.039			−1.18353			−0.591767	−	0.806109i	$-0.701569\pi$
$79$	−831.039			−1.18353			−0.591767	+	0.806109i	$0.701569\pi$
$80$		−	866.017i		−	1.21030i
$81$	−892.031			−1.22364
$82$	−172.352			−0.232111
$83$		−	1348.22i		−	1.78297i	−0.453052	−	0.891484i	$-0.649665\pi$
$83$		−	1348.22i		−	1.78297i	0.453052	−	0.891484i	$-0.350335\pi$
$84$			312.904i			0.406435i
$85$			991.100i			1.26470i
$86$		−	143.377i		−	0.179776i
$87$	826.447			1.01844
$88$	−270.671			−0.327882
$89$			840.976i			1.00161i	0.865560	+	0.500805i	$0.166963\pi$
$89$			840.976i			1.00161i	−0.865560	+	0.500805i	$0.833037\pi$
$90$	475.699			0.557145
$91$	−845.278	+	584.417i	−0.973728	+	0.673225i
$92$	−88.7020			−0.100520
$93$			9.22864i			0.0102899i
$94$	−942.433			−1.03409
$95$	2612.36			2.82129
$96$			621.980i			0.661256i
$97$			1234.39i			1.29210i	0.763296	+	0.646049i	$0.223580\pi$
$97$			1234.39i			1.29210i	−0.763296	+	0.646049i	$0.776420\pi$
$98$			326.525i			0.336571i
$99$		−	100.277i		−	0.101800i
$100$	−852.750			−0.852750
$101$	−928.816			−0.915056			−0.457528	−	0.889195i	$-0.651265\pi$
$101$	−928.816			−0.915056			−0.457528	+	0.889195i	$0.651265\pi$
$102$			642.064i			0.623272i
$103$	−278.239			−0.266172			−0.133086	−	0.991104i	$-0.542489\pi$
$103$	−278.239			−0.266172			−0.133086	+	0.991104i	$0.542489\pi$
$104$	−948.689	+	655.914i	−0.894487	+	0.618439i
$105$	−2898.89			−2.69431
$106$		−	0.961166i		−	0.000880723i
$107$	1607.66			1.45251			0.726254	−	0.687427i	$-0.241260\pi$
$107$	1607.66			1.45251			0.726254	+	0.687427i	$0.241260\pi$
$108$	255.240			0.227412
$109$		−	678.269i		−	0.596022i	−0.954562	−	0.298011i	$-0.903677\pi$
$109$		−	678.269i		−	0.596022i	0.954562	−	0.298011i	$-0.0963232\pi$
$110$		−	574.006i		−	0.497539i
$111$			1420.41i			1.21459i
$112$			862.968i			0.728061i
$113$	2249.33			1.87256			0.936280	−	0.351254i	$-0.114245\pi$
$113$	2249.33			1.87256			0.936280	+	0.351254i	$0.114245\pi$
$114$	1692.37			1.39039
$115$		−	821.778i		−	0.666358i
$116$	−326.588			−0.261405
$117$	−243.000	−	351.466i	−0.192011	−	0.277718i
$118$	88.0830			0.0687178
$119$		−	987.610i		−	0.760790i
$120$	−3253.54			−2.47505
$121$	−121.000			−0.0909091
$122$		−	731.182i		−	0.542607i
$123$			436.716i			0.320141i
$124$		−	3.64689i		−	0.00264113i
$125$		−	5150.07i		−	3.68509i
$126$	−474.024			−0.335154
$127$	−1052.64			−0.735485			−0.367743	−	0.929928i	$-0.619869\pi$
$127$	−1052.64			−0.735485			−0.367743	+	0.929928i	$0.619869\pi$
$128$			501.051i			0.345993i
$129$	−363.297			−0.247958
$130$	−1390.98	−	2011.87i	−0.938440	−	1.35732i
$131$	142.840			0.0952671			0.0476335	−	0.998865i	$-0.484832\pi$
$131$	142.840			0.0952671			0.0476335	+	0.998865i	$0.484832\pi$
$132$			156.992i			0.103518i
$133$	−2603.17			−1.69717
$134$	1012.80			0.652929
$135$			2364.67i			1.50754i
$136$		−	1108.43i		−	0.698878i
$137$			492.398i			0.307069i	0.988143	+	0.153534i	$0.0490656\pi$
$137$			492.398i			0.307069i	−0.988143	+	0.153534i	$0.950934\pi$
$138$		−	532.372i		−	0.328395i
$139$	−1364.51			−0.832634			−0.416317	−	0.909219i	$-0.636679\pi$
$139$	−1364.51			−0.832634			−0.416317	+	0.909219i	$0.636679\pi$
$140$	1145.56			0.691552
$141$			2388.00i			1.42628i
$142$	2404.66			1.42109
$143$	−424.099	+	293.218i	−0.248007	+	0.171469i
$144$	−358.821			−0.207651
$145$		−	3025.67i		−	1.73288i
$146$	442.004			0.250551
$147$	827.368			0.464219
$148$		−	561.307i		−	0.311751i
$149$		−	2202.56i		−	1.21101i	−0.795841	−	0.605506i	$-0.792971\pi$
$149$		−	2202.56i		−	1.21101i	0.795841	−	0.605506i	$-0.207029\pi$
$150$		−	5118.04i		−	2.78591i
$151$			1690.18i			0.910895i	0.890263	+	0.455447i	$0.150521\pi$
$151$			1690.18i			0.910895i	−0.890263	+	0.455447i	$0.849479\pi$
$152$	−2921.63			−1.55905
$153$	410.647			0.216986
$154$			571.985i			0.299298i
$155$	33.7866			0.0175084
$156$	380.438	+	550.251i	0.195252	+	0.282406i
$157$	1900.04			0.965857			0.482929	−	0.875660i	$-0.339573\pi$
$157$	1900.04			0.965857			0.482929	+	0.875660i	$0.339573\pi$
$158$			1971.01i			0.992437i
$159$	−2.43546			−0.00121475
$160$	2277.10			1.12513
$161$			818.885i			0.400852i
$162$			2115.67i			1.02606i
$163$		−	3356.66i		−	1.61297i	−0.591255	−	0.806485i	$-0.701367\pi$
$163$		−	3356.66i		−	1.61297i	0.591255	−	0.806485i	$-0.298633\pi$
$164$		−	172.577i		−	0.0821709i
$165$	−1454.45			−0.686236
$166$	−3197.63			−1.49509
$167$			1557.33i			0.721615i	0.932640	+	0.360808i	$0.117499\pi$
$167$			1557.33i			0.721615i	−0.932640	+	0.360808i	$0.882501\pi$
$168$	3242.08			1.48888
$169$	−775.897	+	2055.43i	−0.353162	+	0.935562i
$170$	2350.63			1.06050
$171$		−	1082.39i		−	0.484051i
$172$	143.564			0.0636435
$173$	−1991.41			−0.875167			−0.437583	−	0.899178i	$-0.644166\pi$
$173$	−1991.41			−0.875167			−0.437583	+	0.899178i	$0.644166\pi$
$174$		−	1960.12i		−	0.854001i
$175$			7872.47i			3.40059i
$176$			432.975i			0.185436i
$177$		−	223.190i		−	0.0947797i
$178$	1994.58			0.839887
$179$	−1397.48			−0.583533			−0.291767	−	0.956490i	$-0.594243\pi$
$179$	−1397.48			−0.583533			−0.291767	+	0.956490i	$0.594243\pi$
$180$			476.322i			0.197238i
$181$	986.237			0.405008			0.202504	−	0.979281i	$-0.435092\pi$
$181$	986.237			0.405008			0.202504	+	0.979281i	$0.435092\pi$
$182$	1386.08	+	2004.78i	0.564524	+	0.816507i
$183$	−1852.71			−0.748397
$184$			919.066i			0.368231i
$185$	5200.22			2.06664
$186$	21.8879			0.00862850
$187$		−	495.511i		−	0.193772i
$188$		−	943.667i		−	0.366085i
$189$		−	2356.34i		−	0.906870i
$190$		−	6195.85i		−	2.36576i
$191$	308.011			0.116685			0.0583426	−	0.998297i	$-0.481418\pi$
$191$	308.011			0.116685			0.0583426	+	0.998297i	$0.481418\pi$
$192$	3367.56			1.26580
$193$			88.0548i			0.0328411i	0.999865	+	0.0164205i	$0.00522705\pi$
$193$			88.0548i			0.0328411i	−0.999865	+	0.0164205i	$0.994773\pi$
$194$	2927.66			1.08347
$195$	−5097.79	+	3524.56i	−1.87210	+	1.29435i
$196$	−326.952			−0.119152
$197$			1427.37i			0.516222i	0.966115	+	0.258111i	$0.0831000\pi$
$197$			1427.37i			0.516222i	−0.966115	+	0.258111i	$0.916900\pi$
$198$	−237.831			−0.0853631
$199$	3908.62			1.39234			0.696168	−	0.717879i	$-0.254887\pi$
$199$	3908.62			1.39234			0.696168	+	0.717879i	$0.254887\pi$
$200$			8835.58i			3.12385i
$201$		−	2566.29i		−	0.900559i
$202$			2202.91i			0.767308i
$203$			3015.02i			1.04243i
$204$	−642.904			−0.220649
$205$	1598.84			0.544721
$206$			659.912i			0.223195i
$207$	−340.491			−0.114327
$208$	1049.22	+	1517.56i	0.349762	+	0.505883i
$209$	−1306.08			−0.432265
$210$			6875.42i			2.25928i
$211$	−2013.69			−0.657005			−0.328502	−	0.944503i	$-0.606544\pi$
$211$	−2013.69			−0.657005			−0.328502	+	0.944503i	$0.606544\pi$
$212$	0.962424			0.000311790
$213$		−	6093.08i		−	1.96005i
$214$		−	3812.95i		−	1.21798i
$215$			1330.05i			0.421901i
$216$		−	2644.61i		−	0.833070i
$217$	−33.6676			−0.0105323
$218$	−1608.68			−0.499786
$219$		−	1119.98i		−	0.345576i
$220$	574.758			0.176137
$221$	−1200.77	−	1736.74i	−0.365485	−	0.528624i
$222$	3368.86			1.01848
$223$		−	3722.68i		−	1.11789i	−0.829206	−	0.558944i	$-0.811207\pi$
$223$		−	3722.68i		−	1.11789i	0.829206	−	0.558944i	$-0.188793\pi$
$224$	−2269.09			−0.676829
$225$	−3273.36			−0.969886
$226$		−	5334.83i		−	1.57021i
$227$			2581.37i			0.754766i	0.926057	+	0.377383i	$0.123176\pi$
$227$			2581.37i			0.754766i	−0.926057	+	0.377383i	$0.876824\pi$
$228$			1694.58i			0.492221i
$229$		−	1773.59i		−	0.511800i	−0.966703	−	0.255900i	$-0.917628\pi$
$229$		−	1773.59i		−	0.511800i	0.966703	−	0.255900i	$-0.0823718\pi$
$230$	−1949.05			−0.558766
$231$	1449.33			0.412810
$232$			3383.87i			0.957594i
$233$	−5633.07			−1.58384			−0.791920	−	0.610625i	$-0.790918\pi$
$233$	−5633.07			−1.58384			−0.791920	+	0.610625i	$0.790918\pi$
$234$	−833.586	+	576.333i	−0.232877	+	0.161009i
$235$	8742.59			2.42682
$236$			88.1983i			0.0243272i
$237$	4994.27			1.36883
$238$	−2342.35			−0.637951
$239$		−	1489.56i		−	0.403145i	−0.979474	−	0.201572i	$-0.935395\pi$
$239$		−	1489.56i		−	0.403145i	0.979474	−	0.201572i	$-0.0646052\pi$
$240$			5204.47i			1.39978i
$241$		−	5808.50i		−	1.55252i	−0.630410	−	0.776262i	$-0.717113\pi$
$241$		−	5808.50i		−	1.55252i	0.630410	−	0.776262i	$-0.282887\pi$
$242$			286.981i			0.0762306i
$243$	2458.95			0.649142
$244$	732.139			0.192092
$245$		−	3029.04i		−	0.789871i
$246$	1035.78			0.268450
$247$	−4577.75	+	3165.01i	−1.17925	+	0.815322i
$248$	−37.7865			−0.00967517
$249$			8102.35i			2.06211i
$250$	−12214.6			−3.09008
$251$	5966.13			1.50031			0.750157	−	0.661259i	$-0.229978\pi$
$251$	5966.13			1.50031			0.750157	+	0.661259i	$0.229978\pi$
$252$		−	474.644i		−	0.118650i
$253$			410.857i			0.102096i
$254$			2496.59i			0.616732i
$255$		−	5956.18i		−	1.46271i
$256$	−3294.50			−0.804322
$257$	−4162.25			−1.01025			−0.505124	−	0.863047i	$-0.668553\pi$
$257$	−4162.25			−1.01025			−0.505124	+	0.863047i	$0.668553\pi$
$258$			861.646i			0.207922i
$259$	−5181.91			−1.24320
$260$	2014.50	−	1392.80i	0.480515	−	0.332223i
$261$	−1253.64			−0.297312
$262$		−	338.779i		−	0.0798850i
$263$	5641.04			1.32259			0.661295	−	0.750126i	$-0.270007\pi$
$263$	5641.04			1.32259			0.661295	+	0.750126i	$0.270007\pi$
$264$	1626.64			0.379215
$265$			8.91636i			0.00206690i
$266$			6174.03i			1.42314i
$267$		−	5053.99i		−	1.15842i
$268$			1014.12i			0.231147i
$269$	7196.93			1.63124			0.815622	−	0.578585i	$-0.196395\pi$
$269$	7196.93			1.63124			0.815622	+	0.578585i	$0.196395\pi$
$270$	5608.37			1.26413
$271$		−	5915.76i		−	1.32604i	−0.748602	−	0.663020i	$-0.769275\pi$
$271$		−	5915.76i		−	1.32604i	0.748602	−	0.663020i	$-0.230725\pi$
$272$	−1773.09			−0.395255
$273$	5079.84	−	3512.15i	1.12618	−	0.778626i
$274$	1167.84			0.257488
$275$			3949.83i			0.866123i
$276$	533.069			0.116257
$277$	1185.15			0.257071			0.128535	−	0.991705i	$-0.458972\pi$
$277$	1185.15			0.257071			0.128535	+	0.991705i	$0.458972\pi$
$278$			3236.26i			0.698195i
$279$		−	13.9989i		−	0.00300393i
$280$		−	11869.4i		−	2.53334i
$281$			3300.30i			0.700639i	0.936630	+	0.350320i	$0.113927\pi$
$281$			3300.30i			0.700639i	−0.936630	+	0.350320i	$0.886073\pi$
$282$	5663.71			1.19599
$283$	1951.54			0.409918			0.204959	−	0.978771i	$-0.434294\pi$
$283$	1951.54			0.409918			0.204959	+	0.978771i	$0.434294\pi$
$284$			2407.81i			0.503088i
$285$	−15699.4			−3.26300
$286$	695.437	+	1005.85i	0.143783	+	0.207963i
$287$	−1593.21			−0.327680
$288$		−	943.484i		−	0.193039i
$289$	−2883.82			−0.586977
$290$	−7176.10			−1.45309
$291$		−	7418.28i		−	1.49439i
$292$			442.583i			0.0886993i
$293$		−	9794.57i		−	1.95292i	−0.215702	−	0.976459i	$-0.569204\pi$
$293$		−	9794.57i		−	1.95292i	0.215702	−	0.976459i	$-0.430796\pi$
$294$		−	1962.30i		−	0.389265i
$295$	−817.112			−0.161268
$296$	−5815.86			−1.14203
$297$		−	1182.24i		−	0.230978i
$298$	−5223.90			−1.01548
$299$	995.625	+	1440.03i	0.192570	+	0.278526i
$300$	5124.74			0.986257
$301$		−	1325.37i		−	0.253797i
$302$	4008.67			0.763819
$303$	5581.88			1.05832
$304$			4673.55i			0.881732i
$305$			6782.89i			1.27340i
$306$		−	973.949i		−	0.181951i
$307$			8789.22i			1.63397i	0.576662	+	0.816983i	$0.304355\pi$
$307$			8789.22i			1.63397i	−0.576662	+	0.816983i	$0.695645\pi$
$308$	−572.734			−0.105956
$309$	1672.13			0.307844
$310$		−	80.1330i		−	0.0146814i
$311$	5140.36			0.937244			0.468622	−	0.883399i	$-0.344751\pi$
$311$	5140.36			0.937244			0.468622	+	0.883399i	$0.344751\pi$
$312$	5701.30	−	3941.82i	1.03453	−	0.715262i
$313$	−3694.65			−0.667202			−0.333601	−	0.942714i	$-0.608264\pi$
$313$	−3694.65			−0.667202			−0.333601	+	0.942714i	$0.608264\pi$
$314$		−	4506.40i		−	0.809907i
$315$	4397.34			0.786546
$316$	−1973.59			−0.351339
$317$		−	1183.73i		−	0.209731i	−0.994486	−	0.104865i	$-0.966559\pi$
$317$		−	1183.73i		−	0.209731i	0.994486	−	0.104865i	$-0.0334412\pi$
$318$			5.77628i			0.00101861i
$319$			1512.72i			0.265504i
$320$		−	12328.8i		−	2.15376i
$321$	−9661.49			−1.67991
$322$	1942.18			0.336129
$323$		−	5348.57i		−	0.921369i
$324$	−2118.44			−0.363244
$325$	9571.59	+	13844.0i	1.63365	+	2.36285i
$326$	−7961.13			−1.35253
$327$			4076.17i			0.689335i
$328$	−1788.12			−0.301014
$329$	−8711.80			−1.45987
$330$			3449.59i			0.575435i
$331$		−	4725.02i		−	0.784624i	−0.919832	−	0.392312i	$-0.871675\pi$
$331$		−	4725.02i		−	0.784624i	0.919832	−	0.392312i	$-0.128325\pi$
$332$		−	3201.81i		−	0.529284i
$333$		−	2154.63i		−	0.354574i
$334$	3693.58			0.605101
$335$	−9395.34			−1.53231
$336$		−	5186.15i		−	0.842047i
$337$	−1623.31			−0.262396			−0.131198	−	0.991356i	$-0.541882\pi$
$337$	−1623.31			−0.262396			−0.131198	+	0.991356i	$0.541882\pi$
$338$	4874.95	+	1840.23i	0.784503	+	0.296140i
$339$	−13517.7			−2.16573
$340$			2353.71i			0.375435i
$341$	−16.8920			−0.00268255
$342$	−2567.16			−0.405894
$343$		−	4501.64i		−	0.708647i
$344$		−	1487.51i		−	0.233143i
$345$			4938.61i			0.770684i
$346$			4723.10i			0.733860i
$347$	−6460.87			−0.999533			−0.499766	−	0.866160i	$-0.666581\pi$
$347$	−6460.87			−0.999533			−0.499766	+	0.866160i	$0.666581\pi$
$348$	1962.68			0.302330
$349$			1359.73i			0.208552i	0.994548	+	0.104276i	$0.0332525\pi$
$349$			1359.73i			0.208552i	−0.994548	+	0.104276i	$0.966748\pi$
$350$	18671.5			2.85152
$351$	−2864.91	−	4143.70i	−0.435662	−	0.630126i
$352$	−1138.46			−0.172387
$353$			7870.77i			1.18674i	0.804930	+	0.593370i	$0.202203\pi$
$353$			7870.77i			1.18674i	−0.804930	+	0.593370i	$0.797797\pi$
$354$	−529.350			−0.0794763
$355$	−22307.1			−3.33504
$356$			1997.19i			0.297334i
$357$			5935.21i			0.879900i
$358$			3314.46i			0.489314i
$359$		−	2231.50i		−	0.328062i	−0.986455	−	0.164031i	$-0.947550\pi$
$359$		−	2231.50i		−	0.328062i	0.986455	−	0.164031i	$-0.0524496\pi$
$360$	4935.30			0.722537
$361$	−7238.88			−1.05538
$362$		−	2339.10i		−	0.339614i
$363$	727.170			0.105142
$364$	−2007.41	+	1387.90i	−0.289057	+	0.199851i
$365$	−4100.30			−0.587999
$366$			4394.16i			0.627558i
$367$	10457.2			1.48736			0.743678	−	0.668538i	$-0.233080\pi$
$367$	10457.2			1.48736			0.743678	+	0.668538i	$0.233080\pi$
$368$	1470.17			0.208255
$369$		−	662.456i		−	0.0934581i
$370$		−	12333.6i		−	1.73295i
$371$		−	8.88497i		−	0.00124335i
$372$			21.9166i			0.00305463i
$373$	10419.5			1.44638			0.723189	−	0.690651i	$-0.242676\pi$
$373$	10419.5			1.44638			0.723189	+	0.690651i	$0.242676\pi$
$374$	−1175.22			−0.162485
$375$			30950.2i			4.26203i
$376$	−9777.60			−1.34107
$377$	3665.75	+	5302.00i	0.500784	+	0.724315i
$378$	−5588.63			−0.760444
$379$		−	4854.02i		−	0.657874i	−0.944352	−	0.328937i	$-0.893310\pi$
$379$		−	4854.02i		−	0.657874i	0.944352	−	0.328937i	$-0.106690\pi$
$380$	6203.96			0.837517
$381$	6326.01			0.850633
$382$		−	730.522i		−	0.0978449i
$383$			486.117i			0.0648548i	0.999474	+	0.0324274i	$0.0103238\pi$
$383$			486.117i			0.0648548i	−0.999474	+	0.0324274i	$0.989676\pi$
$384$		−	3011.15i		−	0.400161i
$385$		−	5306.09i		−	0.702398i
$386$	208.843			0.0275385
$387$	551.086			0.0723858
$388$			2931.49i			0.383567i
$389$	6956.44			0.906697			0.453349	−	0.891333i	$-0.350229\pi$
$389$	6956.44			0.906697			0.453349	+	0.891333i	$0.350229\pi$
$390$	8359.34	+	12090.6i	1.08536	+	1.56983i
$391$	−1682.51			−0.217617
$392$			3387.64i			0.436484i
$393$	−858.420			−0.110182
$394$	3385.34			0.432871
$395$		−	18284.3i		−	2.32907i
$396$		−	238.142i		−	0.0302199i
$397$		−	13306.4i		−	1.68219i	−0.540887	−	0.841095i	$-0.681911\pi$
$397$		−	13306.4i		−	1.68219i	0.540887	−	0.841095i	$-0.318089\pi$
$398$		−	9270.23i		−	1.16752i
$399$	15644.2			1.96288
$400$	14133.7			1.76671
$401$			10742.2i			1.33775i	0.743373	+	0.668877i	$0.233225\pi$
$401$			10742.2i			1.33775i	−0.743373	+	0.668877i	$0.766775\pi$
$402$	−6086.58			−0.755152
$403$	−59.2055	+	40.9341i	−0.00731821	+	0.00505973i
$404$	−2205.80			−0.271640
$405$		−	19626.2i		−	2.40799i
$406$	7150.84			0.874113
$407$	−2599.91			−0.316640
$408$			6661.31i			0.808294i
$409$			4012.09i			0.485049i	0.970145	+	0.242525i	$0.0779755\pi$
$409$			4012.09i			0.485049i	−0.970145	+	0.242525i	$0.922025\pi$
$410$		−	3792.04i		−	0.456769i
$411$		−	2959.15i		−	0.355143i
$412$	−660.775			−0.0790147
$413$	814.235			0.0970118
$414$			807.557i			0.0958678i
$415$	29663.2			3.50869
$416$	−3990.26	+	2758.82i	−0.470285	+	0.325150i
$417$	8200.25			0.962992
$418$			3097.68i			0.362470i
$419$	12337.6			1.43849			0.719247	−	0.694755i	$-0.244487\pi$
$419$	12337.6			1.43849			0.719247	+	0.694755i	$0.244487\pi$
$420$	−6884.42			−0.799822
$421$			8294.87i			0.960255i	0.877199	+	0.480127i	$0.159410\pi$
$421$			8294.87i			0.960255i	−0.877199	+	0.480127i	$0.840590\pi$
$422$			4775.95i			0.550923i
$423$		−	3622.36i		−	0.416371i
$424$		−	9.97195i		−	0.00114217i
$425$	−16175.1			−1.84613
$426$	−14451.2			−1.64357
$427$		−	6759.01i		−	0.766022i
$428$	3817.94			0.431185
$429$	2548.70	−	1762.14i	0.286835	−	0.198315i
$430$	3154.54			0.353780
$431$		−	4998.83i		−	0.558667i	−0.960194	−	0.279333i	$-0.909887\pi$
$431$		−	4998.83i		−	0.558667i	0.960194	−	0.279333i	$-0.0901134\pi$
$432$	−4230.41			−0.471148
$433$	10834.9			1.20252			0.601261	−	0.799052i	$-0.294665\pi$
$433$	10834.9			1.20252			0.601261	+	0.799052i	$0.294665\pi$
$434$			79.8508i			0.00883171i
$435$			18183.3i			2.00419i
$436$		−	1610.78i		−	0.176932i
$437$			4434.81i			0.485459i
$438$	−2656.30			−0.289778
$439$	11395.3			1.23888			0.619441	−	0.785044i	$-0.287359\pi$
$439$	11395.3			1.23888			0.619441	+	0.785044i	$0.287359\pi$
$440$		−	5955.23i		−	0.645237i
$441$	−1255.04			−0.135519
$442$	−4119.10	+	2847.91i	−0.443271	+	0.306473i
$443$	7028.09			0.753757			0.376879	−	0.926263i	$-0.376997\pi$
$443$	7028.09			0.753757			0.376879	+	0.926263i	$0.376997\pi$
$444$			3373.27i			0.360559i
$445$	−18502.9			−1.97106
$446$	−8829.23			−0.937390
$447$			13236.6i			1.40061i
$448$			12285.4i			1.29561i
$449$			11509.8i			1.20976i	0.796316	+	0.604881i	$0.206779\pi$
$449$			11509.8i			1.20976i	−0.796316	+	0.604881i	$0.793221\pi$
$450$			7763.57i			0.813285i
$451$	−799.358			−0.0834596
$452$	5341.81			0.555880
$453$		−	10157.4i		−	1.05350i
$454$	6122.35			0.632899
$455$	−12858.2	−	18597.6i	−1.32484	−	1.91619i
$456$	17558.0			1.80314
$457$		−	14159.6i		−	1.44936i	−0.689086	−	0.724680i	$-0.741988\pi$
$457$		−	14159.6i		−	1.44936i	0.689086	−	0.724680i	$-0.258012\pi$
$458$	−4206.50			−0.429164
$459$	4841.43			0.492328
$460$		−	1951.60i		−	0.197812i
$461$			8477.39i			0.856467i	0.903668	+	0.428233i	$0.140864\pi$
$461$			8477.39i			0.856467i	−0.903668	+	0.428233i	$0.859136\pi$
$462$		−	3437.44i		−	0.346156i
$463$		−	7760.76i		−	0.778991i	−0.921028	−	0.389496i	$-0.872649\pi$
$463$		−	7760.76i		−	0.778991i	0.921028	−	0.389496i	$-0.127351\pi$
$464$	5412.96			0.541574
$465$	−203.046			−0.0202495
$466$			13360.2i			1.32811i
$467$	8628.05			0.854943			0.427471	−	0.904029i	$-0.359404\pi$
$467$	8628.05			0.854943			0.427471	+	0.904029i	$0.359404\pi$
$468$	−577.087	−	834.677i	−0.0569997	−	0.0824422i
$469$	9362.26			0.921767
$470$		−	20735.1i		−	2.03498i
$471$	−11418.6			−1.11707
$472$	913.848			0.0891171
$473$		−	664.973i		−	0.0646417i
$474$		−	11845.1i		−	1.14781i
$475$			42634.7i			4.11834i
$476$		−	2345.42i		−	0.225845i
$477$	3.69436			0.000354619
$478$	−3532.85			−0.338052
$479$		−	6516.59i		−	0.621609i	−0.950474	−	0.310805i	$-0.899402\pi$
$479$		−	6516.59i		−	0.621609i	0.950474	−	0.310805i	$-0.100598\pi$
$480$	−13684.6			−1.30128
$481$	−9112.55	+	6300.32i	−0.863818	+	0.597235i
$482$	−13776.3			−1.30185
$483$		−	4921.22i		−	0.463610i
$484$	−287.356			−0.0269869
$485$	−27158.7			−2.54271
$486$		−	5831.99i		−	0.544330i
$487$			475.525i			0.0442466i	0.999755	+	0.0221233i	$0.00704263\pi$
$487$			475.525i			0.0442466i	−0.999755	+	0.0221233i	$0.992957\pi$
$488$		−	7585.90i		−	0.703683i
$489$			20172.4i			1.86550i
$490$	−7184.10			−0.662336
$491$	−7161.52			−0.658238			−0.329119	−	0.944288i	$-0.606752\pi$
$491$	−7161.52			−0.658238			−0.329119	+	0.944288i	$0.606752\pi$
$492$			1037.13i			0.0950357i
$493$	−6194.77			−0.565920
$494$	7506.58	+	10857.2i	0.683678	+	0.988846i
$495$	2206.26			0.200332
$496$			60.4446i			0.00547186i
$497$	22228.6			2.00621
$498$	19216.7			1.72916
$499$			5772.30i			0.517843i	0.965898	+	0.258921i	$0.0833670\pi$
$499$			5772.30i			0.517843i	−0.965898	+	0.258921i	$0.916633\pi$
$500$		−	12230.6i		−	1.09394i
$501$		−	9359.03i		−	0.834592i
$502$		−	14150.1i		−	1.25807i
$503$	−8481.30			−0.751814			−0.375907	−	0.926657i	$-0.622669\pi$
$503$	−8481.30			−0.751814			−0.375907	+	0.926657i	$0.622669\pi$
$504$	−4917.92			−0.434646
$505$		−	20435.6i		−	1.80073i
$506$	974.446			0.0856115
$507$	4662.88	−	12352.4i	0.408453	−	1.08203i
$508$	−2499.86			−0.218333
$509$			19532.8i			1.70093i	0.526030	+	0.850466i	$0.323680\pi$
$509$			19532.8i			1.70093i	−0.526030	+	0.850466i	$0.676320\pi$
$510$	−14126.5			−1.22653
$511$	4085.86			0.353714
$512$			11822.1i			1.02045i
$513$		−	12761.2i		−	1.09828i
$514$			9871.77i			0.847131i
$515$		−	6121.74i		−	0.523799i
$516$	−862.774			−0.0736076
$517$	−4370.95			−0.371826
$518$			12290.1i			1.04247i
$519$	11967.7			1.01218
$520$	−14431.2	−	20872.8i	−1.21702	−	1.76025i
$521$	19195.5			1.61414			0.807071	−	0.590454i	$-0.201051\pi$
$521$	19195.5			1.61414			0.807071	+	0.590454i	$0.201051\pi$
$522$			2973.31i			0.249307i
$523$	−8390.29			−0.701495			−0.350747	−	0.936470i	$-0.614072\pi$
$523$	−8390.29			−0.701495			−0.350747	+	0.936470i	$0.614072\pi$
$524$	339.223			0.0282806
$525$		−	47310.9i		−	3.93299i
$526$		−	13379.1i		−	1.10904i
$527$		−	69.1748i		−	0.00571784i
$528$		−	2602.03i		−	0.214468i
$529$	−10771.9			−0.885340
$530$	21.1473			0.00173317
$531$			338.558i			0.0276689i
$532$	−6182.12			−0.503813
$533$	−2801.71	+	1937.07i	−0.227684	+	0.157418i
$534$	−11986.7			−0.971380
$535$			35371.3i			2.85838i
$536$	10507.6			0.846754
$537$	8398.38			0.674892
$538$		−	17069.2i		−	1.36786i
$539$			1514.40i			0.121020i
$540$			5615.71i			0.447522i
$541$		−	13429.4i		−	1.06724i	−0.845725	−	0.533618i	$-0.820832\pi$
$541$		−	13429.4i		−	1.06724i	0.845725	−	0.533618i	$-0.179168\pi$
$542$	−14030.6			−1.11193
$543$	−5926.95			−0.468416
$544$		−	4662.16i		−	0.367442i
$545$	14923.1			1.17291
$546$	−8329.91	−	12048.1i	−0.652907	−	0.944340i
$547$	15701.0			1.22729			0.613643	−	0.789583i	$-0.289703\pi$
$547$	15701.0			1.22729			0.613643	+	0.789583i	$0.289703\pi$
$548$			1169.37i			0.0911551i
$549$	2810.39			0.218478
$550$	9367.98			0.726277
$551$			16328.3i			1.26245i
$552$		−	5523.28i		−	0.425881i
$553$			18219.9i			1.40107i
$554$		−	2810.86i		−	0.215563i
$555$	−31251.6			−2.39019
$556$	−3240.50			−0.247172
$557$			4674.29i			0.355577i	0.984069	+	0.177788i	$0.0568942\pi$
$557$			4674.29i			0.355577i	−0.984069	+	0.177788i	$0.943106\pi$
$558$	−33.2019			−0.00251890
$559$	−1611.42	−	2330.70i	−0.121925	−	0.176347i
$560$	−18986.8			−1.43275
$561$			2977.86i			0.224109i
$562$	7827.46			0.587512
$563$	−5261.19			−0.393841			−0.196921	−	0.980419i	$-0.563094\pi$
$563$	−5261.19			−0.393841			−0.196921	+	0.980419i	$0.563094\pi$
$564$			5671.12i			0.423399i
$565$			49489.2i			3.68500i
$566$		−	4628.54i		−	0.343732i
$567$			19557.1i			1.44854i
$568$	24948.0			1.84295
$569$	−8890.07			−0.654993			−0.327497	−	0.944852i	$-0.606205\pi$
$569$	−8890.07			−0.654993			−0.327497	+	0.944852i	$0.606205\pi$
$570$			37235.0i			2.73614i
$571$	1273.74			0.0933525			0.0466762	−	0.998910i	$-0.485137\pi$
$571$	1273.74			0.0933525			0.0466762	+	0.998910i	$0.485137\pi$
$572$	−1007.17	+	696.347i	−0.0736222	+	0.0509016i
$573$	−1851.04			−0.134954
$574$			3778.68i			0.274772i
$575$	13411.7			0.972708
$576$	−5108.27			−0.369522
$577$			4663.43i			0.336467i	0.985747	+	0.168233i	$0.0538062\pi$
$577$			4663.43i			0.336467i	−0.985747	+	0.168233i	$0.946194\pi$
$578$			6839.67i			0.492202i
$579$		−	529.180i		−	0.0379827i
$580$		−	7185.50i		−	0.514416i
$581$	−29558.7			−2.11068
$582$	−17594.2			−1.25310
$583$		−	4.45783i		−	0.000316680i
$584$	4585.72			0.324929
$585$	7732.85	−	5346.41i	0.546520	−	0.377858i
$586$	−23230.2			−1.63759
$587$		−	20906.5i		−	1.47002i	−0.678055	−	0.735012i	$-0.737177\pi$
$587$		−	20906.5i		−	1.47002i	0.678055	−	0.735012i	$-0.262823\pi$
$588$	1964.87			0.137806
$589$	−182.333			−0.0127553
$590$			1937.98i			0.135229i
$591$		−	8578.00i		−	0.597042i
$592$			9303.25i			0.645881i
$593$			1228.81i			0.0850947i	0.999094	+	0.0425473i	$0.0135473\pi$
$593$			1228.81i			0.0850947i	−0.999094	+	0.0425473i	$0.986453\pi$
$594$	−2803.97			−0.193684
$595$	21729.1			1.49715
$596$		−	5230.74i		−	0.359496i
$597$	−23489.5			−1.61032
$598$	3415.39	−	2361.36i	0.233555	−	0.161477i
$599$	4895.45			0.333927			0.166964	−	0.985963i	$-0.446604\pi$
$599$	4895.45			0.333927			0.166964	+	0.985963i	$0.446604\pi$
$600$		−	53098.9i		−	3.61292i
$601$	1270.91			0.0862590			0.0431295	−	0.999069i	$-0.486267\pi$
$601$	1270.91			0.0862590			0.0431295	+	0.999069i	$0.486267\pi$
$602$	−3143.43			−0.212818
$603$			3892.82i			0.262898i
$604$			4013.92i			0.270404i
$605$		−	2662.21i		−	0.178899i
$606$		−	13238.8i		−	0.887439i
$607$	23014.2			1.53891			0.769453	−	0.638703i	$-0.220529\pi$
$607$	23014.2			1.53891			0.769453	+	0.638703i	$0.220529\pi$
$608$	−12288.6			−0.819687
$609$		−	18119.2i		−	1.20563i
$610$	16087.3			1.06779
$611$	−15320.0	+	10592.1i	−1.01437	+	0.701325i
$612$	975.224			0.0644135
$613$			4986.64i			0.328562i	0.986414	+	0.164281i	$0.0525304\pi$
$613$			4986.64i			0.328562i	−0.986414	+	0.164281i	$0.947470\pi$
$614$	20845.8			1.37014
$615$	−9608.50			−0.630003
$616$			5934.26i			0.388146i
$617$		−	24331.7i		−	1.58761i	−0.608172	−	0.793805i	$-0.708097\pi$
$617$		−	24331.7i		−	1.58761i	0.608172	−	0.793805i	$-0.291903\pi$
$618$		−	3965.85i		−	0.258139i
$619$		−	3492.65i		−	0.226787i	−0.993550	−	0.113394i	$-0.963828\pi$
$619$		−	3492.65i		−	0.226787i	0.993550	−	0.113394i	$-0.0361721\pi$
$620$	80.2379			0.00519747
$621$	−4014.31			−0.259402
$622$		−	12191.6i		−	0.785914i
$623$	18437.8			1.18570
$624$	−6305.48	−	9120.01i	−0.404521	−	0.585084i
$625$	68425.9			4.37926
$626$			8762.76i			0.559474i
$627$	7849.10			0.499941
$628$	4512.30			0.286720
$629$		−	10647.0i		−	0.674916i
$630$		−	10429.3i		−	0.659548i
$631$		−	10327.6i		−	0.651561i	−0.945445	−	0.325781i	$-0.894373\pi$
$631$		−	10327.6i		−	0.651561i	0.945445	−	0.325781i	$-0.105627\pi$
$632$			20448.9i			1.28705i
$633$	12101.6			0.759866
$634$	−2807.49			−0.175867
$635$		−	23159.9i		−	1.44736i
$636$	−5.78385			−0.000360604
$637$	3669.83	+	5307.91i	0.228264	+	0.330152i
$638$	3587.77			0.222635
$639$			9242.61i			0.572194i
$640$	−11024.0			−0.680877
$641$	2071.44			0.127640			0.0638199	−	0.997961i	$-0.479672\pi$
$641$	2071.44			0.127640			0.0638199	+	0.997961i	$0.479672\pi$
$642$			22914.6i			1.40867i
$643$		−	9533.95i		−	0.584731i	−0.956307	−	0.292366i	$-0.905558\pi$
$643$		−	9533.95i		−	0.584731i	0.956307	−	0.292366i	$-0.0944425\pi$
$644$			1944.73i			0.118995i
$645$		−	7993.16i		−	0.487954i
$646$	−12685.4			−0.772602
$647$	−1865.33			−0.113344			−0.0566721	−	0.998393i	$-0.518049\pi$
$647$	−1865.33			−0.113344			−0.0566721	+	0.998393i	$0.518049\pi$
$648$			21949.7i			1.33066i
$649$	408.524			0.0247087
$650$	32834.3	−	22701.3i	1.98134	−	1.36988i
$651$	202.331			0.0121812
$652$		−	7971.55i		−	0.478819i
$653$	−21636.7			−1.29665			−0.648323	−	0.761365i	$-0.724529\pi$
$653$	−21636.7			−1.29665			−0.648323	+	0.761365i	$0.724529\pi$
$654$	9667.61			0.578033
$655$			3142.72i			0.187475i
$656$			2860.35i			0.170240i
$657$			1698.90i			0.100883i
$658$			20662.1i			1.22416i
$659$	14547.6			0.859929			0.429965	−	0.902846i	$-0.358526\pi$
$659$	14547.6			0.859929			0.429965	+	0.902846i	$0.358526\pi$
$660$	−3454.10			−0.203713
$661$		−	12435.0i		−	0.731721i	−0.930670	−	0.365860i	$-0.880775\pi$
$661$		−	12435.0i		−	0.731721i	0.930670	−	0.365860i	$-0.119225\pi$
$662$	−11206.5			−0.657936
$663$	7216.20	+	10437.2i	0.422706	+	0.611386i
$664$	−33174.9			−1.93891
$665$		−	57274.1i		−	3.33984i
$666$	−5110.23			−0.297323
$667$	5136.45			0.298177
$668$			3698.42i			0.214216i
$669$			22372.0i			1.29290i
$670$			22283.3i			1.28489i
$671$		−	3391.18i		−	0.195104i
$672$	13636.5			0.782794
$673$	−11888.8			−0.680951			−0.340476	−	0.940253i	$-0.610588\pi$
$673$	−11888.8			−0.680951			−0.340476	+	0.940253i	$0.610588\pi$
$674$			3850.07i			0.220028i
$675$	−38592.2			−2.20061
$676$	−1842.64	+	4881.33i	−0.104838	+	0.277727i
$677$	363.757			0.0206504			0.0103252	−	0.999947i	$-0.496713\pi$
$677$	363.757			0.0206504			0.0103252	+	0.999947i	$0.496713\pi$
$678$			32060.5i			1.81604i
$679$	27063.1			1.52958
$680$	24387.4			1.37532
$681$		−	15513.2i		−	0.872932i
$682$			40.0633i			0.00224942i
$683$			1987.64i			0.111354i	0.998449	+	0.0556770i	$0.0177317\pi$
$683$			1987.64i			0.111354i	−0.998449	+	0.0556770i	$0.982268\pi$
$684$		−	2570.52i		−	0.143693i
$685$	−10833.6			−0.604278
$686$	−10676.7			−0.594227
$687$			10658.7i			0.591928i
$688$	−2379.48			−0.131856
$689$	−10.8026	−	15.6245i	−0.000597310	−	0.000863927i
$690$	11713.1			0.646247
$691$			12163.3i			0.669631i	0.942284	+	0.334816i	$0.108674\pi$
$691$			12163.3i			0.669631i	−0.942284	+	0.334816i	$0.891326\pi$
$692$	−4729.28			−0.259798
$693$	−2198.50			−0.120511
$694$			15323.5i			0.838145i
$695$		−	30021.6i		−	1.63854i
$696$		−	20335.9i		−	1.10752i
$697$		−	3273.48i		−	0.177893i
$698$	3224.92			0.174878
$699$	33852.9			1.83181
$700$			18695.9i			1.00948i
$701$	−15391.5			−0.829283			−0.414642	−	0.909985i	$-0.636093\pi$
$701$	−15391.5			−0.829283			−0.414642	+	0.909985i	$0.636093\pi$
$702$	−9827.77	+	6794.82i	−0.528384	+	0.365319i
$703$	−28063.5			−1.50560
$704$			6163.94i			0.329989i
$705$	−52540.0			−2.80677
$706$	18667.4			0.995125
$707$			20363.6i			1.08324i
$708$		−	530.042i		−	0.0281359i
$709$		−	4752.39i		−	0.251735i	−0.992047	−	0.125867i	$-0.959829\pi$
$709$		−	4752.39i		−	0.251735i	0.992047	−	0.125867i	$-0.0401714\pi$
$710$			52906.7i			2.79655i
$711$	−7575.82			−0.399600
$712$	20693.4			1.08921
$713$			57.3568i			0.00301267i
$714$	14076.8			0.737829
$715$	−6451.30	−	9330.92i	−0.337433	−	0.488051i
$716$	−3318.80			−0.173225
$717$			8951.76i			0.466262i
$718$	−5292.54			−0.275092
$719$	−19390.1			−1.00574			−0.502870	−	0.864362i	$-0.667723\pi$
$719$	−19390.1			−1.00574			−0.502870	+	0.864362i	$0.667723\pi$
$720$		−	7894.68i		−	0.408635i
$721$			6100.19i			0.315094i
$722$			17168.7i			0.884979i
$723$			34907.1i			1.79559i
$724$	2342.16			0.120229
$725$	49380.0			2.52955
$726$		−	1724.66i		−	0.0881654i
$727$	−34383.4			−1.75407			−0.877035	−	0.480426i	$-0.840482\pi$
$727$	−34383.4			−1.75407			−0.877035	+	0.480426i	$0.840482\pi$
$728$	14380.4	+	20799.3i	0.732107	+	1.05889i
$729$	9307.39			0.472864
$730$			9724.85i			0.493059i
$731$	2723.15			0.137783
$732$	−4399.91			−0.222166
$733$			34050.3i			1.71579i	0.513824	+	0.857896i	$0.328228\pi$
$733$			34050.3i			1.71579i	−0.513824	+	0.857896i	$0.671772\pi$
$734$		−	24801.7i		−	1.24720i
$735$			18203.5i			0.913534i
$736$			3865.67i			0.193601i
$737$	4697.30			0.234772
$738$	−1571.17			−0.0783681
$739$			20299.4i			1.01045i	0.862987	+	0.505227i	$0.168591\pi$
$739$			20299.4i			1.01045i	−0.862987	+	0.505227i	$0.831409\pi$
$740$	12349.7			0.613493
$741$	27510.7	−	19020.6i	1.36388	−	0.942969i
$742$	−21.0728			−0.00104260
$743$			6738.83i			0.332737i	0.986064	+	0.166369i	$0.0532041\pi$
$743$			6738.83i			0.332737i	−0.986064	+	0.166369i	$0.946796\pi$
$744$	227.084			0.0111899
$745$	48460.1			2.38314
$746$		−	24712.2i		−	1.21284i
$747$		−	12290.5i		−	0.601988i
$748$		−	1176.76i		−	0.0575223i
$749$		−	35246.7i		−	1.71948i
$750$	73405.9			3.57387
$751$	5780.71			0.280880			0.140440	−	0.990089i	$-0.455148\pi$
$751$	5780.71			0.280880			0.140440	+	0.990089i	$0.455148\pi$
$752$			15640.6i			0.758449i
$753$	−35854.5			−1.73520
$754$	12575.0	−	8694.20i	0.607365	−	0.419926i
$755$	−37186.9			−1.79254
$756$		−	5595.94i		−	0.269210i
$757$	−11340.0			−0.544464			−0.272232	−	0.962232i	$-0.587762\pi$
$757$	−11340.0			−0.544464			−0.272232	+	0.962232i	$0.587762\pi$
$758$	−11512.5			−0.551652
$759$		−	2469.11i		−	0.118081i
$760$		−	64281.0i		−	3.06805i
$761$			26197.4i			1.24790i	0.781463	+	0.623952i	$0.214474\pi$
$761$			26197.4i			1.24790i	−0.781463	+	0.623952i	$0.785526\pi$
$762$		−	15003.7i		−	0.713287i
$763$	−14870.5			−0.705570
$764$	731.478			0.0346387
$765$			9034.94i			0.427005i
$766$	1152.94			0.0543832
$767$	1431.86	−	989.972i	0.0674073	−	0.0466047i
$768$	19798.9			0.930247
$769$			6468.90i			0.303348i	0.988431	+	0.151674i	$0.0484664\pi$
$769$			6468.90i			0.303348i	−0.988431	+	0.151674i	$0.951534\pi$
$770$	−12584.7			−0.588987
$771$	25013.7			1.16841
$772$			209.117i			0.00974906i
$773$			9461.51i			0.440242i	0.975473	+	0.220121i	$0.0706452\pi$
$773$			9461.51i			0.440242i	−0.975473	+	0.220121i	$0.929355\pi$
$774$		−	1307.03i		−	0.0606982i
$775$			551.408i			0.0255576i
$776$	30374.0			1.40511
$777$	31141.5			1.43783
$778$		−	16498.9i		−	0.760299i
$779$	−8628.30			−0.396843
$780$	−12106.5	+	8370.28i	−0.555745	+	0.384236i
$781$	11152.7			0.510978
$782$			3990.49i			0.182480i
$783$	−14780.1			−0.674582
$784$	5418.99			0.246856
$785$			41804.1i			1.90071i
$786$			2035.95i			0.0923918i
$787$		−	25255.5i		−	1.14391i	−0.820284	−	0.571957i	$-0.806184\pi$
$787$		−	25255.5i		−	1.14391i	0.820284	−	0.571957i	$-0.193816\pi$
$788$			3389.78i			0.153243i
$789$	−33900.7			−1.52966
$790$	−43365.6			−1.95301
$791$		−	49314.9i		−	2.21673i
$792$	−2467.46			−0.110704
$793$	−8217.81	−	11885.9i	−0.367999	−	0.532259i
$794$	−31559.4			−1.41058
$795$		−	53.5844i		−	0.00239049i
$796$	9282.37			0.413323
$797$	26161.2			1.16271			0.581354	−	0.813651i	$-0.302523\pi$
$797$	26161.2			1.16271			0.581354	+	0.813651i	$0.302523\pi$
$798$		−	37103.9i		−	1.64594i
$799$		−	17899.6i		−	0.792545i
$800$			37163.1i			1.64239i
$801$			7666.41i			0.338176i
$802$	25477.7			1.12176
$803$	2049.99			0.0900904
$804$		−	6094.55i		−	0.267336i
$805$	−18016.9			−0.788834
$806$	97.0850	+	140.420i	0.00424277	+	0.00613659i
$807$	−43251.1			−1.88663
$808$			22854.9i			0.995088i
$809$	−9626.27			−0.418346			−0.209173	−	0.977879i	$-0.567077\pi$
$809$	−9626.27			−0.418346			−0.209173	+	0.977879i	$0.567077\pi$
$810$	−46548.3			−2.01919
$811$		−	7220.73i		−	0.312644i	−0.987706	−	0.156322i	$-0.950036\pi$
$811$		−	7220.73i		−	0.312644i	0.987706	−	0.156322i	$-0.0499638\pi$
$812$			7160.20i			0.309450i
$813$			35551.7i			1.53364i
$814$			6166.30i			0.265514i
$815$	73852.3			3.17415
$816$	10655.7			0.457136
$817$		−	7177.75i		−	0.307366i
$818$	9515.64			0.406732
$819$	−7705.63	+	5327.59i	−0.328762	+	0.227303i
$820$	3797.00			0.161704
$821$			924.479i			0.0392991i	0.999807	+	0.0196495i	$0.00625504\pi$
$821$			924.479i			0.0392991i	−0.999807	+	0.0196495i	$0.993745\pi$
$822$	−7018.33			−0.297801
$823$	−12444.7			−0.527088			−0.263544	−	0.964647i	$-0.584891\pi$
$823$	−12444.7			−0.527088			−0.263544	+	0.964647i	$0.584891\pi$
$824$			6846.48i			0.289452i
$825$		−	23737.2i		−	1.00172i
$826$		−	1931.15i		−	0.0813480i
$827$			12999.4i			0.546594i	0.961930	+	0.273297i	$0.0881141\pi$
$827$			12999.4i			0.546594i	−0.961930	+	0.273297i	$0.911886\pi$
$828$	−808.615			−0.0339388
$829$	−17245.1			−0.722492			−0.361246	−	0.932470i	$-0.617649\pi$
$829$	−17245.1			−0.722492			−0.361246	+	0.932470i	$0.617649\pi$
$830$		−	70353.3i		−	2.94217i
$831$	−7122.34			−0.297318
$832$	14937.0	+	21604.3i	0.622413	+	0.900234i
$833$	−6201.68			−0.257954
$834$		−	19448.9i		−	0.807505i
$835$	−34263.9			−1.42006
$836$	−3101.74			−0.128320
$837$		−	165.044i		−	0.00681572i
$838$		−	29261.5i		−	1.20623i
$839$		−	6372.02i		−	0.262201i	−0.991369	−	0.131101i	$-0.958149\pi$
$839$		−	6372.02i		−	0.262201i	0.991369	−	0.131101i	$-0.0418511\pi$
$840$			71331.4i			2.92996i
$841$	−5477.35			−0.224583
$842$	19673.3			0.805209
$843$		−	19833.7i		−	0.810332i
$844$	−4782.20			−0.195036
$845$	−45223.0	−	17071.1i	−1.84109	−	0.694986i
$846$	−8591.30			−0.349143
$847$			2652.83i			0.107618i
$848$	−15.9515			−0.000645962
$849$	−11728.1			−0.474095
$850$			38363.1i			1.54805i
$851$			8828.01i			0.355606i
$852$		−	14470.1i		−	0.581852i
$853$		−	1739.23i		−	0.0698125i	−0.999391	−	0.0349062i	$-0.988887\pi$
$853$		−	1739.23i		−	0.0698125i	0.999391	−	0.0349062i	$-0.0111133\pi$
$854$	−16030.6			−0.642338
$855$	23814.5			0.952561
$856$		−	39558.8i		−	1.57955i
$857$	−12058.4			−0.480637			−0.240318	−	0.970694i	$-0.577252\pi$
$857$	−12058.4			−0.480637			−0.240318	+	0.970694i	$0.577252\pi$
$858$	−4179.34	−	6044.84i	−0.166294	−	0.240522i
$859$	−19004.5			−0.754861			−0.377430	−	0.926038i	$-0.623192\pi$
$859$	−19004.5			−0.754861			−0.377430	+	0.926038i	$0.623192\pi$
$860$			3158.67i			0.125244i
$861$	9574.67			0.378982
$862$	−11855.9			−0.468463
$863$		−	14823.3i		−	0.584694i	−0.956312	−	0.292347i	$-0.905564\pi$
$863$		−	14823.3i		−	0.584694i	0.956312	−	0.292347i	$-0.0944362\pi$
$864$		−	11123.4i		−	0.437995i
$865$		−	43814.4i		−	1.72224i
$866$		−	25697.6i		−	1.00836i
$867$	17330.8			0.678874
$868$	−79.9553			−0.00312657
$869$			9141.43i			0.356849i
$870$	43126.0			1.68058
$871$	16463.8	−	11382.9i	0.640477	−	0.442819i
$872$	−16689.8			−0.648151
$873$			11252.8i			0.436254i
$874$	10518.2			0.407075
$875$	−112911.			−4.36240
$876$		−	2659.77i		−	0.102586i
$877$		−	23377.3i		−	0.900110i	−0.893001	−	0.450055i	$-0.851404\pi$
$877$		−	23377.3i		−	0.900110i	0.893001	−	0.450055i	$-0.148596\pi$
$878$		−	27026.7i		−	1.03885i
$879$			58862.1i			2.25867i
$880$	−9526.19			−0.364918
$881$	28678.5			1.09671			0.548356	−	0.836245i	$-0.315254\pi$
$881$	28678.5			1.09671			0.548356	+	0.836245i	$0.315254\pi$
$882$			2976.62i			0.113637i
$883$	10935.2			0.416759			0.208379	−	0.978048i	$-0.433181\pi$
$883$	10935.2			0.416759			0.208379	+	0.978048i	$0.433181\pi$
$884$	−2851.63	−	4124.50i	−0.108496	−	0.156925i
$885$	4910.57			0.186516
$886$		−	16668.8i		−	0.632053i
$887$	15027.6			0.568858			0.284429	−	0.958697i	$-0.408196\pi$
$887$	15027.6			0.568858			0.284429	+	0.958697i	$0.408196\pi$
$888$	34951.4			1.32082
$889$			23078.3i			0.870666i
$890$			43884.1i			1.65281i
$891$			9812.34i			0.368940i
$892$		−	8840.78i		−	0.331851i
$893$	−47180.2			−1.76800
$894$	31393.9			1.17446
$895$		−	30746.9i		−	1.14833i
$896$	10985.2			0.409585
$897$	−5983.37	−	8654.13i	−0.222719	−	0.322133i
$898$	27298.4			1.01443
$899$			211.180i			0.00783452i
$900$	−7773.73			−0.287916
$901$	18.2554			0.000675001
$902$			1895.87i			0.0699840i
$903$			7965.02i			0.293532i
$904$		−	55348.0i		−	2.03634i
$905$			21698.9i			0.797012i
$906$	−24090.8			−0.883403
$907$	8773.55			0.321192			0.160596	−	0.987020i	$-0.448658\pi$
$907$	8773.55			0.321192			0.160596	+	0.987020i	$0.448658\pi$
$908$			6130.36i			0.224056i
$909$	−8467.16			−0.308953
$910$	−44108.6	+	30496.3i	−1.60680	+	1.11092i
$911$	−8621.39			−0.313545			−0.156772	−	0.987635i	$-0.550109\pi$
$911$	−8621.39			−0.313545			−0.156772	+	0.987635i	$0.550109\pi$
$912$		−	28086.5i		−	1.01978i
$913$	−14830.4			−0.537585
$914$	−33582.9			−1.21534
$915$		−	40762.9i		−	1.47277i
$916$		−	4212.01i		−	0.151931i
$917$		−	3131.66i		−	0.112777i
$918$		−	11482.6i		−	0.412835i
$919$	−6088.65			−0.218548			−0.109274	−	0.994012i	$-0.534853\pi$
$919$	−6088.65			−0.218548			−0.109274	+	0.994012i	$0.534853\pi$
$920$	−20221.0			−0.724639
$921$		−	52820.3i		−	1.88978i
$922$	20106.2			0.718179
$923$	39089.6	−	27026.1i	1.39399	−	0.963788i
$924$	3441.94			0.122545
$925$			84869.4i			3.01674i
$926$	−18406.5			−0.653213
$927$	−2536.45			−0.0898684
$928$			14232.8i			0.503465i
$929$			34239.9i			1.20923i	0.796517	+	0.604616i	$0.206673\pi$
$929$			34239.9i			1.20923i	−0.796517	+	0.604616i	$0.793327\pi$
$930$			481.572i			0.0169800i
$931$			16346.5i			0.575441i
$932$	−13377.7			−0.470172
$933$	−30891.8			−1.08398
$934$		−	20463.5i		−	0.716901i
$935$	10902.1			0.381323
$936$	−8648.32	+	5979.36i	−0.302008	+	0.208805i
$937$	39690.3			1.38381			0.691903	−	0.721991i	$-0.256773\pi$
$937$	39690.3			1.38381			0.691903	+	0.721991i	$0.256773\pi$
$938$		−	22204.8i		−	0.772936i
$939$	22203.6			0.771660
$940$	20762.3			0.720416
$941$		−	14078.9i		−	0.487736i	−0.969808	−	0.243868i	$-0.921584\pi$
$941$		−	14078.9i		−	0.487736i	0.969808	−	0.243868i	$-0.0784164\pi$
$942$			27082.0i			0.936707i
$943$			2714.23i			0.0937301i
$944$		−	1461.82i		−	0.0504007i
$945$	51843.5			1.78462
$946$	−1577.14			−0.0542044
$947$		−	20875.9i		−	0.716343i	−0.933656	−	0.358172i	$-0.883400\pi$
$947$		−	20875.9i		−	0.716343i	0.933656	−	0.358172i	$-0.116600\pi$
$948$	11860.6			0.406345
$949$	7185.12	−	4967.72i	0.245773	−	0.169925i
$950$	101118.			3.45338
$951$			7113.80i			0.242566i
$952$	−24301.6			−0.827330
$953$	541.243			0.0183973			0.00919863	−	0.999958i	$-0.497072\pi$
$953$	541.243			0.0183973			0.00919863	+	0.999958i	$0.497072\pi$
$954$		−	8.76206i		−	0.000297361i
$955$			6776.77i			0.229624i
$956$		−	3537.48i		−	0.119676i
$957$		−	9090.92i		−	0.307072i
$958$	−15455.7			−0.521242
$959$	10795.5			0.363507
$960$			74092.2i			2.49095i
$961$	29788.6			0.999921
$962$	14942.7	+	21612.6i	0.500803	+	0.724343i
$963$	14655.5			0.490414
$964$		−	13794.3i		−	0.460876i
$965$	−1937.36			−0.0646277
$966$	−11671.9			−0.388754
$967$		−	33692.4i		−	1.12045i	−0.828340	−	0.560225i	$-0.810715\pi$
$967$		−	33692.4i		−	1.12045i	0.828340	−	0.560225i	$-0.189285\pi$
$968$			2977.38i			0.0988601i
$969$			32143.1i			1.06562i
$970$			64413.5i			2.13216i
$971$	−44807.6			−1.48089			−0.740445	−	0.672117i	$-0.765385\pi$
$971$	−44807.6			−1.48089			−0.740445	+	0.672117i	$0.765385\pi$
$972$	5839.62			0.192702
$973$			29915.9i			0.985671i
$974$	1127.82			0.0371024
$975$	−57522.0	−	83197.7i	−1.88941	−	2.73278i
$976$	−12134.7			−0.397973
$977$			52059.1i			1.70473i	0.522951	+	0.852363i	$0.324831\pi$
$977$			52059.1i			1.70473i	−0.522951	+	0.852363i	$0.675169\pi$
$978$	47843.7			1.56429
$979$	9250.74			0.301997
$980$		−	7193.51i		−	0.234478i
$981$		−	6183.15i		−	0.201236i
$982$			16985.3i			0.551957i
$983$		−	41324.6i		−	1.34085i	−0.741979	−	0.670423i	$-0.766113\pi$
$983$		−	41324.6i		−	1.34085i	0.741979	−	0.670423i	$-0.233887\pi$
$984$	10746.0			0.348141
$985$	−31404.5			−1.01587
$986$			14692.4i			0.474545i
$987$	52355.0			1.68843
$988$	−10871.4	+	7516.40i	−0.350067	+	0.242033i
$989$	−2257.93			−0.0725964
$990$		−	5232.69i		−	0.167986i
$991$	58410.7			1.87233			0.936165	−	0.351562i	$-0.114349\pi$
$991$	58410.7			1.87233			0.936165	+	0.351562i	$0.114349\pi$
$992$	−158.933			−0.00508682
$993$			28395.8i			0.907465i
$994$		−	52720.4i		−	1.68228i
$995$			85996.4i			2.73997i
$996$			19241.8i			0.612150i
$997$	49337.9			1.56725			0.783624	−	0.621235i	$-0.213369\pi$
$997$	49337.9			1.56725			0.783624	+	0.621235i	$0.213369\pi$
$998$	13690.4			0.434230
$999$		−	25402.6i		−	0.804507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.b.a.12.11	✓	36
13.5	odd	4		1859.4.a.k.1.6		18
13.8	odd	4		1859.4.a.j.1.13		18
13.12	even	2	inner	143.4.b.a.12.26	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.b.a.12.11	✓	36	1.1	even	1	trivial
143.4.b.a.12.26	yes	36	13.12	even	2	inner
1859.4.a.j.1.13		18	13.8	odd	4
1859.4.a.k.1.6		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)

\(f(q)\)	\(=\)	\(q-2.37174i q^{2} -6.00967 q^{3} +2.37485 q^{4} +22.0017i q^{5} +14.2534i q^{6} -21.9243i q^{7} -24.6064i q^{8} +9.11608 q^{9} +O(q^{10})\)	\(q-2.37174i q^{2} -6.00967 q^{3} +2.37485 q^{4} +22.0017i q^{5} +14.2534i q^{6} -21.9243i q^{7} -24.6064i q^{8} +9.11608 q^{9} +52.1824 q^{10} -11.0000i q^{11} -14.2720 q^{12} +(-26.6562 - 38.5545i) q^{13} -51.9987 q^{14} -132.223i q^{15} -39.3613 q^{16} +45.0465 q^{17} -21.6210i q^{18} -118.734i q^{19} +52.2507i q^{20} +131.757i q^{21} -26.0891 q^{22} -37.3506 q^{23} +147.877i q^{24} -359.076 q^{25} +(-91.4413 + 63.2215i) q^{26} +107.476 q^{27} -52.0667i q^{28} -137.520 q^{29} -313.599 q^{30} -1.53563i q^{31} -103.497i q^{32} +66.1063i q^{33} -106.839i q^{34} +482.371 q^{35} +21.6493 q^{36} -236.355i q^{37} -281.607 q^{38} +(160.195 + 231.700i) q^{39} +541.384 q^{40} -72.6689i q^{41} +312.495 q^{42} +60.4521 q^{43} -26.1233i q^{44} +200.569i q^{45} +88.5860i q^{46} -397.359i q^{47} +236.549 q^{48} -137.673 q^{49} +851.635i q^{50} -270.714 q^{51} +(-63.3043 - 91.5610i) q^{52} +0.405257 q^{53} -254.906i q^{54} +242.019 q^{55} -539.478 q^{56} +713.555i q^{57} +326.161i q^{58} +37.1386i q^{59} -314.009i q^{60} +308.289 q^{61} -3.64212 q^{62} -199.863i q^{63} -560.358 q^{64} +(848.265 - 586.482i) q^{65} +156.787 q^{66} +427.027i q^{67} +106.978 q^{68} +224.465 q^{69} -1144.06i q^{70} +1013.88i q^{71} -224.314i q^{72} +186.363i q^{73} -560.573 q^{74} +2157.93 q^{75} -281.976i q^{76} -241.167 q^{77} +(549.531 - 379.940i) q^{78} -831.039 q^{79} -866.017i q^{80} -892.031 q^{81} -172.352 q^{82} -1348.22i q^{83} +312.904i q^{84} +991.100i q^{85} -143.377i q^{86} +826.447 q^{87} -270.671 q^{88} +840.976i q^{89} +475.699 q^{90} +(-845.278 + 584.417i) q^{91} -88.7020 q^{92} +9.22864i q^{93} -942.433 q^{94} +2612.36 q^{95} +621.980i q^{96} +1234.39i q^{97} +326.525i q^{98} -100.277i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 152 q^{4} + 360 q^{9}+O(q^{10}) \) 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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Database

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