LMFDB - Embedded newform 93.4.c.b.92.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [93,4,Mod(92,93)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("93.92"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(93, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	93.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.48717763053$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			92.1
Character	$\chi$	$=$	93.92
Dual form			93.4.c.b.92.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.24508i q^{2} +(-5.08240 + 1.08131i) q^{3} -19.5109 q^{4} -7.60471i q^{5} +(5.67158 + 26.6576i) q^{6} -11.1491 q^{7} +60.3756i q^{8} +(24.6615 - 10.9913i) q^{9} -39.8873 q^{10} +35.9161 q^{11} +(99.1621 - 21.0974i) q^{12} +45.7305i q^{13} +58.4779i q^{14} +(8.22308 + 38.6502i) q^{15} +160.588 q^{16} -126.000 q^{17} +(-57.6505 - 129.352i) q^{18} -41.2122 q^{19} +148.375i q^{20} +(56.6641 - 12.0557i) q^{21} -188.383i q^{22} -13.0795 q^{23} +(-65.2850 - 306.853i) q^{24} +67.1684 q^{25} +239.860 q^{26} +(-113.455 + 82.5292i) q^{27} +217.529 q^{28} -161.652 q^{29} +(202.723 - 43.1308i) q^{30} +(-136.507 + 105.625i) q^{31} -359.291i q^{32} +(-182.540 + 38.8366i) q^{33} +660.881i q^{34} +84.7856i q^{35} +(-481.168 + 214.451i) q^{36} -135.083i q^{37} +216.161i q^{38} +(-49.4490 - 232.420i) q^{39} +459.139 q^{40} -393.359i q^{41} +(-63.2330 - 297.208i) q^{42} +421.163i q^{43} -700.755 q^{44} +(-83.5860 - 187.544i) q^{45} +68.6029i q^{46} +538.321i q^{47} +(-816.170 + 173.646i) q^{48} -218.698 q^{49} -352.304i q^{50} +(640.382 - 136.246i) q^{51} -892.242i q^{52} -174.894 q^{53} +(432.872 + 595.078i) q^{54} -273.132i q^{55} -673.133i q^{56} +(209.457 - 44.5634i) q^{57} +847.880i q^{58} -506.952i q^{59} +(-160.440 - 754.099i) q^{60} -695.438i q^{61} +(554.014 + 715.992i) q^{62} +(-274.954 + 122.543i) q^{63} -599.810 q^{64} +347.767 q^{65} +(203.701 + 957.437i) q^{66} +273.706 q^{67} +2458.37 q^{68} +(66.4751 - 14.1430i) q^{69} +444.708 q^{70} +188.613i q^{71} +(663.608 + 1488.95i) q^{72} -882.796i q^{73} -708.520 q^{74} +(-341.376 + 72.6301i) q^{75} +804.087 q^{76} -400.432 q^{77} +(-1219.06 + 259.364i) q^{78} -400.853i q^{79} -1221.22i q^{80} +(487.381 - 542.126i) q^{81} -2063.20 q^{82} -805.095 q^{83} +(-1105.57 + 235.217i) q^{84} +958.194i q^{85} +2209.03 q^{86} +(821.581 - 174.797i) q^{87} +2168.45i q^{88} -1244.40 q^{89} +(-983.682 + 438.415i) q^{90} -509.853i q^{91} +255.192 q^{92} +(579.570 - 684.438i) q^{93} +2823.54 q^{94} +313.407i q^{95} +(388.507 + 1826.06i) q^{96} -157.045 q^{97} +1147.09i q^{98} +(885.746 - 394.766i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 144 q^{4} - 64 q^{7} + 20 q^{9} - 8 q^{10} + 248 q^{16} + 88 q^{18} + 308 q^{19} - 840 q^{25} - 420 q^{28} + 328 q^{31} - 180 q^{33} + 540 q^{36} + 1152 q^{39} + 44 q^{40} - 1568 q^{45} - 84 q^{49}+ \cdots - 988 q^{97}+O(q^{100}) $ 28 * q - 144 * q^4 - 64 * q^7 + 20 * q^9 - 8 * q^10 + 248 * q^16 + 88 * q^18 + 308 * q^19 - 840 * q^25 - 420 * q^28 + 328 * q^31 - 180 * q^33 + 540 * q^36 + 1152 * q^39 + 44 * q^40 - 1568 * q^45 - 84 * q^49 + 1620 * q^51 - 200 * q^63 + 148 * q^64 + 2052 * q^66 - 748 * q^67 - 288 * q^69 - 2068 * q^70 - 628 * q^72 + 4560 * q^76 - 3312 * q^78 + 164 * q^81 - 5396 * q^82 + 5688 * q^87 - 1312 * q^90 - 1368 * q^93 - 932 * q^94 - 988 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	5.24508i		−	1.85442i	−0.374546	−	0.927208i	$-0.622201\pi$
$2$		−	5.24508i		−	1.85442i	0.374546	−	0.927208i	$-0.377799\pi$
$3$	−5.08240	+	1.08131i	−0.978108	+	0.208099i
$3$	−5.08240	+	1.08131i	−0.978108	+	0.208099i
$4$	−19.5109			−2.43886
$5$		−	7.60471i		−	0.680186i	−0.940392	−	0.340093i	$-0.889541\pi$
$5$		−	7.60471i		−	0.680186i	0.940392	−	0.340093i	$-0.110459\pi$
$6$	5.67158	+	26.6576i	0.385902	+	1.81382i
$7$	−11.1491			−0.601994			−0.300997	−	0.953625i	$-0.597319\pi$
$7$	−11.1491			−0.601994			−0.300997	+	0.953625i	$0.597319\pi$
$8$			60.3756i			2.66825i
$9$	24.6615	−	10.9913i	0.913390	−	0.407087i
$10$	−39.8873			−1.26135
$11$	35.9161			0.984465			0.492232	−	0.870464i	$-0.336181\pi$
$11$	35.9161			0.984465			0.492232	+	0.870464i	$0.336181\pi$
$12$	99.1621	−	21.0974i	2.38547	−	0.507525i
$13$			45.7305i			0.975642i	0.872944	+	0.487821i	$0.162208\pi$
$13$			45.7305i			0.975642i	−0.872944	+	0.487821i	$0.837792\pi$
$14$			58.4779i			1.11635i
$15$	8.22308	+	38.6502i	0.141546	+	0.665295i
$16$	160.588			2.50918
$17$	−126.000			−1.79762			−0.898809	−	0.438341i	$-0.855566\pi$
$17$	−126.000			−1.79762			−0.898809	+	0.438341i	$0.855566\pi$
$18$	−57.6505	−	129.352i	−0.754908	−	1.69380i
$19$	−41.2122			−0.497617			−0.248809	−	0.968553i	$-0.580039\pi$
$19$	−41.2122			−0.497617			−0.248809	+	0.968553i	$0.580039\pi$
$20$			148.375i			1.65888i
$21$	56.6641	−	12.0557i	0.588815	−	0.125274i
$22$		−	188.383i		−	1.82561i
$23$	−13.0795			−0.118576			−0.0592882	−	0.998241i	$-0.518883\pi$
$23$	−13.0795			−0.118576			−0.0592882	+	0.998241i	$0.518883\pi$
$24$	−65.2850	−	306.853i	−0.555260	−	2.60983i
$25$	67.1684			0.537347
$26$	239.860			1.80925
$27$	−113.455	+	82.5292i	−0.808679	+	0.588250i
$28$	217.529			1.46818
$29$	−161.652			−1.03511			−0.517553	−	0.855651i	$-0.673157\pi$
$29$	−161.652			−1.03511			−0.517553	+	0.855651i	$0.673157\pi$
$30$	202.723	−	43.1308i	1.23373	−	0.262485i
$31$	−136.507	+	105.625i	−0.790886	+	0.611964i
$31$	−136.507	+	105.625i	−0.790886	+	0.611964i
$32$		−	359.291i		−	1.98482i
$33$	−182.540	+	38.8366i	−0.962913	+	0.204866i
$34$			660.881i			3.33353i
$35$			84.7856i			0.409468i
$36$	−481.168	+	214.451i	−2.22763	+	0.992828i
$37$		−	135.083i		−	0.600202i	−0.953907	−	0.300101i	$-0.902980\pi$
$37$		−	135.083i		−	0.600202i	0.953907	−	0.300101i	$-0.0970204\pi$
$38$			216.161i			0.922790i
$39$	−49.4490	−	232.420i	−0.203030	−	0.954283i
$40$	459.139			1.81491
$41$		−	393.359i		−	1.49835i	−0.662372	−	0.749175i	$-0.730450\pi$
$41$		−	393.359i		−	1.49835i	0.662372	−	0.749175i	$-0.269550\pi$
$42$	−63.2330	−	297.208i	−0.232311	−	1.09191i
$43$			421.163i			1.49365i	0.665023	+	0.746823i	$0.268422\pi$
$43$			421.163i			1.49365i	−0.665023	+	0.746823i	$0.731578\pi$
$44$	−700.755			−2.40097
$45$	−83.5860	−	187.544i	−0.276895	−	0.621275i
$46$			68.6029i			0.219890i
$47$			538.321i			1.67069i	0.549730	+	0.835343i	$0.314731\pi$
$47$			538.321i			1.67069i	−0.549730	+	0.835343i	$0.685269\pi$
$48$	−816.170	+	173.646i	−2.45425	+	0.522159i
$49$	−218.698			−0.637603
$50$		−	352.304i		−	0.996465i
$51$	640.382	−	136.246i	1.75826	−	0.374083i
$52$		−	892.242i		−	2.37946i
$53$	−174.894			−0.453273			−0.226637	−	0.973979i	$-0.572773\pi$
$53$	−174.894			−0.453273			−0.226637	+	0.973979i	$0.572773\pi$
$54$	432.872	+	595.078i	1.09086	+	1.49963i
$55$		−	273.132i		−	0.669619i
$56$		−	673.133i		−	1.60627i
$57$	209.457	−	44.5634i	0.486723	−	0.103554i
$58$			847.880i			1.91952i
$59$		−	506.952i		−	1.11864i	−0.828953	−	0.559318i	$-0.811063\pi$
$59$		−	506.952i		−	1.11864i	0.828953	−	0.559318i	$-0.188937\pi$
$60$	−160.440	−	754.099i	−0.345211	−	1.62256i
$61$		−	695.438i		−	1.45970i	−0.683607	−	0.729850i	$-0.739590\pi$
$61$		−	695.438i		−	1.45970i	0.683607	−	0.729850i	$-0.260410\pi$
$62$	554.014	+	715.992i	1.13484	+	1.46663i
$63$	−274.954	+	122.543i	−0.549855	+	0.245064i
$64$	−599.810			−1.17150
$65$	347.767			0.663618
$66$	203.701	+	957.437i	0.379907	+	1.78564i
$67$	273.706			0.499082			0.249541	−	0.968364i	$-0.419720\pi$
$67$	273.706			0.499082			0.249541	+	0.968364i	$0.419720\pi$
$68$	2458.37			4.38414
$69$	66.4751	−	14.1430i	0.115981	−	0.0246757i
$70$	444.708			0.759325
$71$			188.613i			0.315270i	0.987497	+	0.157635i	$0.0503870\pi$
$71$			188.613i			0.315270i	−0.987497	+	0.157635i	$0.949613\pi$
$72$	663.608	+	1488.95i	1.08621	+	2.43715i
$73$		−	882.796i		−	1.41539i	−0.706518	−	0.707695i	$-0.749735\pi$
$73$		−	882.796i		−	1.41539i	0.706518	−	0.707695i	$-0.250265\pi$
$74$	−708.520			−1.11302
$75$	−341.376	+	72.6301i	−0.525583	+	0.111821i
$76$	804.087			1.21362
$77$	−400.432			−0.592642
$78$	−1219.06	+	259.364i	−1.76964	+	0.376503i
$79$		−	400.853i		−	0.570879i	−0.958397	−	0.285439i	$-0.907860\pi$
$79$		−	400.853i		−	0.570879i	0.958397	−	0.285439i	$-0.0921395\pi$
$80$		−	1221.22i		−	1.70671i
$81$	487.381	−	542.126i	0.668561	−	0.743657i
$82$	−2063.20			−2.77856
$83$	−805.095			−1.06471			−0.532353	−	0.846522i	$-0.678692\pi$
$83$	−805.095			−1.06471			−0.532353	+	0.846522i	$0.678692\pi$
$84$	−1105.57	+	235.217i	−1.43604	+	0.305527i
$85$			958.194i			1.22271i
$86$	2209.03			2.76984
$87$	821.581	−	174.797i	1.01245	−	0.215405i
$88$			2168.45i			2.62680i
$89$	−1244.40			−1.48209			−0.741045	−	0.671455i	$-0.765670\pi$
$89$	−1244.40			−1.48209			−0.741045	+	0.671455i	$0.765670\pi$
$90$	−983.682	+	438.415i	−1.15210	+	0.513478i
$91$		−	509.853i		−	0.587331i
$92$	255.192			0.289192
$93$	579.570	−	684.438i	0.646222	−	0.763149i
$94$	2823.54			3.09815
$95$			313.407i			0.338472i
$96$	388.507	+	1826.06i	0.413040	+	1.94137i
$97$	−157.045			−0.164386			−0.0821931	−	0.996616i	$-0.526192\pi$
$97$	−157.045			−0.164386			−0.0821931	+	0.996616i	$0.526192\pi$
$98$			1147.09i			1.18238i
$99$	885.746	−	394.766i	0.899200	−	0.400762i
$100$	−1310.51			−1.31051
$101$			1499.34i			1.47713i	0.674182	+	0.738565i	$0.264496\pi$
$101$			1499.34i			1.47713i	−0.674182	+	0.738565i	$0.735504\pi$
$102$	−714.620	−	3358.86i	−0.693705	−	3.26055i
$103$	107.472			0.102811			0.0514054	−	0.998678i	$-0.483630\pi$
$103$	107.472			0.102811			0.0514054	+	0.998678i	$0.483630\pi$
$104$	−2761.00			−2.60325
$105$	−91.6799	−	430.914i	−0.0852099	−	0.400504i
$106$			917.331i			0.840557i
$107$			158.454i			0.143162i	0.997435	+	0.0715811i	$0.0228045\pi$
$107$			158.454i			0.143162i	−0.997435	+	0.0715811i	$0.977196\pi$
$108$	2213.60	−	1610.22i	1.97226	−	1.43466i
$109$	−54.8227			−0.0481749			−0.0240874	−	0.999710i	$-0.507668\pi$
$109$	−54.8227			−0.0481749			−0.0240874	+	0.999710i	$0.507668\pi$
$110$	−1432.60			−1.24175
$111$	146.067	+	686.544i	0.124901	+	0.587062i
$112$	−1790.41			−1.51051
$113$			1215.39i			1.01181i	0.862589	+	0.505905i	$0.168841\pi$
$113$			1215.39i			1.01181i	−0.862589	+	0.505905i	$0.831159\pi$
$114$	−233.739	−	1098.62i	−0.192032	−	0.902588i
$115$			99.4656i			0.0806541i
$116$	3153.98			2.52448
$117$	502.639	+	1127.78i	0.397171	+	0.891141i
$118$	−2659.01			−2.07442
$119$	1404.79			1.08216
$120$	−2333.53	+	496.473i	−1.77517	+	0.377680i
$121$	−41.0335			−0.0308291
$122$	−3647.63			−2.70689
$123$	425.345	+	1999.21i	0.311805	+	1.46555i
$124$	2663.38	−	2060.85i	1.92886	−	1.49250i
$125$		−	1461.38i		−	1.04568i
$126$	642.750	+	1442.15i	0.454450	+	1.01966i
$127$			1068.97i			0.746894i	0.927652	+	0.373447i	$0.121824\pi$
$127$			1068.97i			0.746894i	−0.927652	+	0.373447i	$0.878176\pi$
$128$			271.724i			0.187634i
$129$	−455.410	−	2140.52i	−0.310826	−	1.46095i
$130$		−	1824.07i		−	1.23062i
$131$			144.937i			0.0966660i	0.998831	+	0.0483330i	$0.0153909\pi$
$131$			144.937i			0.0966660i	−0.998831	+	0.0483330i	$0.984609\pi$
$132$	3561.52	−	757.737i	2.34841	−	0.499640i
$133$	459.479			0.299563
$134$		−	1435.61i		−	0.925506i
$135$	627.611	+	862.789i	0.400120	+	0.550052i
$136$		−	7607.32i		−	4.79649i
$137$	−253.316			−0.157972			−0.0789862	−	0.996876i	$-0.525168\pi$
$137$	−253.316			−0.157972			−0.0789862	+	0.996876i	$0.525168\pi$
$138$	−74.1813	−	348.667i	−0.0457589	−	0.215076i
$139$		−	1595.55i		−	0.973619i	−0.873508	−	0.486809i	$-0.838161\pi$
$139$		−	1595.55i		−	0.973619i	0.873508	−	0.486809i	$-0.161839\pi$
$140$		−	1654.24i		−	0.998636i
$141$	−582.094	−	2735.96i	−0.347668	−	1.63411i
$142$	989.289			0.584643
$143$			1642.46i			0.960485i
$144$	3960.34	−	1765.07i	2.29186	−	1.02145i
$145$			1229.32i			0.704065i
$146$	−4630.34			−2.62472
$147$	1111.51	−	236.481i	0.623644	−	0.132685i
$148$			2635.58i			1.46381i
$149$		−	1103.17i		−	0.606542i	−0.952904	−	0.303271i	$-0.901921\pi$
$149$		−	1103.17i		−	0.606542i	0.952904	−	0.303271i	$-0.0980788\pi$
$150$	380.951	+	1790.55i	0.207363	+	0.974650i
$151$		−	134.369i		−	0.0724157i	−0.999344	−	0.0362078i	$-0.988472\pi$
$151$		−	134.369i		−	0.0724157i	0.999344	−	0.0362078i	$-0.0115278\pi$
$152$		−	2488.21i		−	1.32777i
$153$	−3107.35	+	1384.91i	−1.64193	+	0.731786i
$154$			2100.30i			1.09901i
$155$	803.251	+	1038.10i	0.416249	+	0.537949i
$156$	964.794	+	4534.73i	0.495162	+	2.32736i
$157$	−2282.15			−1.16010			−0.580050	−	0.814581i	$-0.696967\pi$
$157$	−2282.15			−1.16010			−0.580050	+	0.814581i	$0.696967\pi$
$158$	−2102.50			−1.05865
$159$	888.879	−	189.115i	0.443350	−	0.0943257i
$160$	−2732.30			−1.35005
$161$	145.824			0.0713824
$162$	−2843.50	−	2556.35i	−1.37905	−	1.23979i
$163$	−2338.66			−1.12379			−0.561895	−	0.827208i	$-0.689928\pi$
$163$	−2338.66			−1.12379			−0.561895	+	0.827208i	$0.689928\pi$
$164$			7674.78i			3.65427i
$165$	295.341	+	1388.16i	0.139347	+	0.654960i
$166$			4222.79i			1.97441i
$167$	3130.72			1.45067			0.725336	−	0.688395i	$-0.241684\pi$
$167$	3130.72			1.45067			0.725336	+	0.688395i	$0.241684\pi$
$168$	727.868	+	3421.13i	0.334263	+	1.57111i
$169$	105.726			0.0481228
$170$	5025.81			2.26742
$171$	−1016.36	+	452.977i	−0.454519	+	0.202573i
$172$		−	8217.26i		−	3.64279i
$173$		−	770.165i		−	0.338466i	−0.985576	−	0.169233i	$-0.945871\pi$
$173$		−	770.165i		−	0.338466i	0.985576	−	0.169233i	$-0.0541290\pi$
$174$	−916.825	−	4309.26i	−0.399450	−	1.87750i
$175$	−748.866			−0.323480
$176$	5767.68			2.47020
$177$	548.175	+	2576.53i	0.232787	+	1.09415i
$178$			6526.97i			2.74841i
$179$	−722.064			−0.301506			−0.150753	−	0.988571i	$-0.548170\pi$
$179$	−722.064			−0.301506			−0.150753	+	0.988571i	$0.548170\pi$
$180$	1630.84	+	3659.14i	0.675308	+	1.51520i
$181$			1334.51i			0.548029i	0.961726	+	0.274014i	$0.0883516\pi$
$181$			1334.51i			0.548029i	−0.961726	+	0.274014i	$0.911648\pi$
$182$	−2674.22			−1.08916
$183$	751.987	+	3534.49i	0.303762	+	1.42774i
$184$		−	789.680i		−	0.316391i
$185$	−1027.27			−0.408249
$186$	−3589.93	−	3039.89i	−1.41520	−	1.19836i
$187$	−4525.43			−1.76969
$188$		−	10503.1i		−	4.07457i
$189$	1264.91	−	920.126i	0.486820	−	0.354123i
$190$	1643.85			0.627669
$191$		−	1378.42i		−	0.522194i	−0.965313	−	0.261097i	$-0.915916\pi$
$191$		−	1378.42i		−	0.522194i	0.965313	−	0.261097i	$-0.0840842\pi$
$192$	3048.47	−	648.583i	1.14586	−	0.243789i
$193$	3959.12			1.47660			0.738299	−	0.674474i	$-0.235629\pi$
$193$	3959.12			1.47660			0.738299	+	0.674474i	$0.235629\pi$
$194$			823.711i			0.304840i
$195$	−1767.49	+	376.045i	−0.649090	+	0.138098i
$196$	4266.99			1.55502
$197$	−521.480			−0.188599			−0.0942993	−	0.995544i	$-0.530061\pi$
$197$	−521.480			−0.188599			−0.0942993	+	0.995544i	$0.530061\pi$
$198$	−2070.58	−	4645.81i	−0.743181	−	1.66749i
$199$			2173.97i			0.774416i	0.921992	+	0.387208i	$0.126560\pi$
$199$			2173.97i			0.774416i	−0.921992	+	0.387208i	$0.873440\pi$
$200$			4055.33i			1.43377i
$201$	−1391.08	+	295.962i	−0.488156	+	0.103859i
$202$	7864.17			2.73921
$203$	1802.28			0.623128
$204$	−12494.4	+	2658.27i	−4.28816	+	0.912335i
$205$	−2991.38			−1.01916
$206$		−	563.699i		−	0.190654i
$207$	−322.560	+	143.761i	−0.108306	+	0.0482709i
$208$			7343.75i			2.44806i
$209$	−1480.18			−0.489887
$210$	−2260.18	+	480.869i	−0.742701	+	0.158015i
$211$	−1122.40			−0.366204			−0.183102	−	0.983094i	$-0.558614\pi$
$211$	−1122.40			−0.366204			−0.183102	+	0.983094i	$0.558614\pi$
$212$	3412.33			1.10547
$213$	−203.950	−	958.604i	−0.0656075	−	0.308368i
$214$	831.106			0.265482
$215$	3202.82			1.01596
$216$	−4982.75	−	6849.88i	−1.56960	−	2.15776i
$217$	1521.93	−	1177.63i	0.476109	−	0.368399i
$218$			287.550i			0.0893363i
$219$	954.580	+	4486.72i	0.294541	+	1.38440i
$220$			5329.04i			1.63311i
$221$		−	5762.04i		−	1.75383i
$222$	3600.98	−	766.133i	1.08866	−	0.231619i
$223$		−	4929.71i		−	1.48035i	−0.672416	−	0.740174i	$-0.734743\pi$
$223$		−	4929.71i		−	1.48035i	0.672416	−	0.740174i	$-0.265257\pi$
$224$			4005.77i			1.19485i
$225$	1656.47	−	738.270i	0.490807	−	0.218747i
$226$	6374.83			1.87632
$227$		−	3138.25i		−	0.917591i	−0.888542	−	0.458795i	$-0.848281\pi$
$227$		−	3138.25i		−	0.917591i	0.888542	−	0.458795i	$-0.151719\pi$
$228$	−4086.69	+	869.471i	−1.18705	+	0.252553i
$229$		−	252.783i		−	0.0729448i	−0.999335	−	0.0364724i	$-0.988388\pi$
$229$		−	252.783i		−	0.0729448i	0.999335	−	0.0364724i	$-0.0116121\pi$
$230$	521.705			0.149566
$231$	2035.15	−	432.993i	0.579668	−	0.123328i
$232$		−	9759.85i		−	2.76192i
$233$			1525.72i			0.428985i	0.976726	+	0.214493i	$0.0688098\pi$
$233$			1525.72i			0.428985i	−0.976726	+	0.214493i	$0.931190\pi$
$234$	5915.31	−	2636.38i	1.65255	−	0.736520i
$235$	4093.78			1.13638
$236$			9891.09i			2.72820i
$237$	433.448	+	2037.29i	0.118799	+	0.558381i
$238$		−	7368.22i		−	2.00677i
$239$	6322.11			1.71106			0.855530	−	0.517753i	$-0.173231\pi$
$239$	6322.11			1.71106			0.855530	+	0.517753i	$0.173231\pi$
$240$	1320.53	+	6206.74i	0.355165	+	1.66935i
$241$		−	1373.49i		−	0.367114i	−0.983009	−	0.183557i	$-0.941239\pi$
$241$		−	1373.49i		−	0.367114i	0.983009	−	0.183557i	$-0.0587612\pi$
$242$			215.224i			0.0571700i
$243$	−1890.85	+	3282.31i	−0.499170	+	0.866504i
$244$			13568.6i			3.56001i
$245$			1663.13i			0.433689i
$246$	10486.0	−	2230.97i	2.71774	−	0.578217i
$247$		−	1884.65i		−	0.485496i
$248$	−6377.19	−	8241.71i	−1.63287	−	2.11028i
$249$	4091.81	−	870.561i	1.04140	−	0.221565i
$250$	−7665.08			−1.93913
$251$	−2038.88			−0.512720			−0.256360	−	0.966581i	$-0.582523\pi$
$251$	−2038.88			−0.512720			−0.256360	+	0.966581i	$0.582523\pi$
$252$	5364.59	−	2390.93i	1.34102	−	0.597677i
$253$	−469.764			−0.116734
$254$	5606.82			1.38505
$255$	−1036.11	−	4869.92i	−0.254446	−	1.19595i
$256$	−3373.27			−0.823551
$257$			2743.56i			0.665908i	0.942943	+	0.332954i	$0.108045\pi$
$257$			2743.56i			0.665908i	−0.942943	+	0.332954i	$0.891955\pi$
$258$	−11227.2	+	2388.66i	−2.70920	+	0.576401i
$259$			1506.05i			0.361318i
$260$	−6785.24			−1.61847
$261$	−3986.59	+	1776.78i	−0.945455	+	0.421378i
$262$	760.209			0.179259
$263$	−3870.45			−0.907461			−0.453731	−	0.891139i	$-0.649907\pi$
$263$	−3870.45			−0.907461			−0.453731	+	0.891139i	$0.649907\pi$
$264$	−2344.78	−	11020.9i	−0.546634	−	2.56929i
$265$			1330.02i			0.308310i
$266$		−	2410.00i		−	0.555514i
$267$	6324.53	−	1345.59i	1.44964	−	0.308422i
$268$	−5340.25			−1.21719
$269$	−65.3717			−0.0148170			−0.00740852	−	0.999973i	$-0.502358\pi$
$269$	−65.3717			−0.0148170			−0.00740852	+	0.999973i	$0.502358\pi$
$270$	4525.40	−	3291.87i	1.02003	−	0.741988i
$271$		−	2737.99i		−	0.613732i	−0.951753	−	0.306866i	$-0.900720\pi$
$271$		−	2737.99i		−	0.613732i	0.951753	−	0.306866i	$-0.0992803\pi$
$272$	−20234.1			−4.51055
$273$	551.311	+	2591.28i	0.122223	+	0.574473i
$274$			1328.66i			0.292947i
$275$	2412.43			0.528999
$276$	−1296.99	+	275.943i	−0.282860	+	0.0601805i
$277$		−	7095.18i		−	1.53902i	−0.638636	−	0.769509i	$-0.720501\pi$
$277$		−	7095.18i		−	1.53902i	0.638636	−	0.769509i	$-0.279499\pi$
$278$	−8368.80			−1.80549
$279$	−2205.51	+	4105.28i	−0.473264	+	0.880921i
$280$	−5118.98			−1.09256
$281$			1010.99i			0.214628i	0.994225	+	0.107314i	$0.0342250\pi$
$281$			1010.99i			0.214628i	−0.994225	+	0.107314i	$0.965775\pi$
$282$	−14350.3	+	3053.13i	−3.03032	+	0.644721i
$283$	−794.678			−0.166921			−0.0834606	−	0.996511i	$-0.526597\pi$
$283$	−794.678			−0.166921			−0.0834606	+	0.996511i	$0.526597\pi$
$284$		−	3680.00i		−	0.768901i
$285$	−338.892	−	1592.86i	−0.0704358	−	0.331063i
$286$	8614.84			1.78114
$287$			4385.59i			0.901998i
$288$	−3949.09	−	8860.66i	−0.807994	−	1.81292i
$289$	10963.0			2.23143
$290$	6447.88			1.30563
$291$	798.163	−	169.815i	0.160787	−	0.0342086i
$292$			17224.1i			3.45194i
$293$		−	8797.40i		−	1.75409i	−0.480404	−	0.877047i	$-0.659510\pi$
$293$		−	8797.40i		−	1.75409i	0.480404	−	0.877047i	$-0.340490\pi$
$294$	−1240.36	−	5829.96i	−0.246052	−	1.15650i
$295$	−3855.23			−0.760881
$296$	8155.70			1.60149
$297$	−4074.84	+	2964.13i	−0.796116	+	0.579112i
$298$	−5786.19			−1.12478
$299$		−	598.130i		−	0.115688i
$300$	6660.55	−	1417.08i	1.28182	−	0.272717i
$301$		−	4695.58i		−	0.899166i
$302$	−704.775			−0.134289
$303$	−1621.26	−	7620.25i	−0.307389	−	1.44479i
$304$	−6618.17			−1.24861
$305$	−5288.61			−0.992868
$306$	7263.96	+	16298.3i	1.35704	+	3.04481i
$307$	−3164.68			−0.588332			−0.294166	−	0.955754i	$-0.595042\pi$
$307$	−3164.68			−0.588332			−0.294166	+	0.955754i	$0.595042\pi$
$308$	7812.78			1.44537
$309$	−546.215	+	116.211i	−0.100560	+	0.0213948i
$310$	5444.92	−	4213.12i	0.997582	−	0.771900i
$311$			4394.69i			0.801285i	0.916234	+	0.400643i	$0.131213\pi$
$311$			4394.69i			0.801285i	−0.916234	+	0.400643i	$0.868787\pi$
$312$	14032.5	−	2985.51i	2.54626	−	0.541735i
$313$			7328.71i			1.32346i	0.749742	+	0.661731i	$0.230178\pi$
$313$			7328.71i			1.32346i	−0.749742	+	0.661731i	$0.769822\pi$
$314$			11970.1i			2.15131i
$315$	931.908	+	2090.94i	0.166689	+	0.374004i
$316$			7820.99i			1.39229i
$317$		−	3968.92i		−	0.703208i	−0.936149	−	0.351604i	$-0.885636\pi$
$317$		−	3968.92i		−	0.703208i	0.936149	−	0.351604i	$-0.114364\pi$
$318$	−991.924	−	4662.24i	−0.174919	−	0.822156i
$319$	−5805.92			−1.01903
$320$			4561.38i			0.796840i
$321$	−171.339	−	805.327i	−0.0297919	−	0.140028i
$322$		−	764.860i		−	0.132373i
$323$	5192.74			0.894526
$324$	−9509.23	+	10577.4i	−1.63053	+	1.81368i
$325$			3071.64i			0.524258i
$326$			12266.5i			2.08398i
$327$	278.631	−	59.2806i	0.0471202	−	0.0100252i
$328$	23749.3			3.99797
$329$		−	6001.79i		−	1.00574i
$330$	7281.03	−	1549.09i	1.21457	−	0.258408i
$331$			6257.48i			1.03910i	0.854440	+	0.519550i	$0.173901\pi$
$331$			6257.48i			1.03910i	−0.854440	+	0.519550i	$0.826099\pi$
$332$	15708.1			2.59667
$333$	−1484.74	−	3331.35i	−0.244334	−	0.548218i
$334$		−	16420.9i		−	2.69015i
$335$		−	2081.45i		−	0.339469i
$336$	9099.56	−	1935.99i	1.47745	−	0.314336i
$337$			903.472i			0.146039i	0.997331	+	0.0730197i	$0.0232636\pi$
$337$			903.472i			0.146039i	−0.997331	+	0.0730197i	$0.976736\pi$
$338$		−	554.540i		−	0.0892396i
$339$	−1314.22	−	6177.10i	−0.210557	−	0.989658i
$340$		−	18695.2i		−	2.98203i
$341$	−4902.81	+	3793.65i	−0.778599	+	0.602457i
$342$	2375.90	+	5330.87i	0.375656	+	0.842867i
$343$	6262.42			0.985828
$344$	−25427.9			−3.98542
$345$	−107.554	−	505.524i	−0.0167840	−	0.0788884i
$346$	−4039.58			−0.627657
$347$	−10373.3			−1.60481			−0.802404	−	0.596781i	$-0.796446\pi$
$347$	−10373.3			−1.60481			−0.802404	+	0.596781i	$0.796446\pi$
$348$	−16029.8	+	3410.44i	−2.46921	+	0.525342i
$349$	8913.01			1.36706			0.683528	−	0.729925i	$-0.260445\pi$
$349$	8913.01			1.36706			0.683528	+	0.729925i	$0.260445\pi$
$350$			3927.87i			0.599866i
$351$	−3774.10	−	5188.33i	−0.573922	−	0.788981i
$352$		−	12904.3i		−	1.95399i
$353$	3416.10			0.515072			0.257536	−	0.966269i	$-0.417089\pi$
$353$	3416.10			0.515072			0.257536	+	0.966269i	$0.417089\pi$
$354$	13514.1	−	2875.22i	2.02901	−	0.431685i
$355$	1434.34			0.214443
$356$	24279.3			3.61461
$357$	−7139.68	+	1519.02i	−1.05846	+	0.225196i
$358$			3787.29i			0.559118i
$359$		−	794.525i		−	0.116806i	−0.998293	−	0.0584031i	$-0.981399\pi$
$359$		−	794.525i		−	0.116806i	0.998293	−	0.0584031i	$-0.0186009\pi$
$360$	11323.1	−	5046.55i	1.65772	−	0.738824i
$361$	−5160.55			−0.752377
$362$	6999.61			1.01627
$363$	208.549	−	44.3701i	0.0301542	−	0.00641550i
$364$			9947.68i			1.43242i
$365$	−6713.41			−0.962728
$366$	18538.7	−	3944.23i	2.64763	−	0.563302i
$367$			3189.38i			0.453636i	0.973937	+	0.226818i	$0.0728322\pi$
$367$			3189.38i			0.453636i	−0.973937	+	0.226818i	$0.927168\pi$
$368$	−2100.40			−0.297530
$369$	−4323.54	−	9700.83i	−0.609958	−	1.36858i
$370$			5388.09i			0.757064i
$371$	1949.90			0.272868
$372$	−11307.9	+	13354.0i	−1.57605	+	1.86122i
$373$	887.280			0.123168			0.0615839	−	0.998102i	$-0.480385\pi$
$373$	887.280			0.123168			0.0615839	+	0.998102i	$0.480385\pi$
$374$			23736.3i			3.28175i
$375$	1580.22	+	7427.34i	0.217605	+	1.02279i
$376$	−32501.4			−4.45780
$377$		−	7392.43i		−	1.00989i
$378$	−4826.13	−	6634.58i	−0.656692	−	0.902767i
$379$	1188.78			0.161118			0.0805588	−	0.996750i	$-0.474330\pi$
$379$	1188.78			0.161118			0.0805588	+	0.996750i	$0.474330\pi$
$380$		−	6114.85i		−	0.825487i
$381$	−1155.89	−	5432.91i	−0.155428	−	0.730542i
$382$	−7229.93			−0.968365
$383$	−896.407			−0.119593			−0.0597967	−	0.998211i	$-0.519045\pi$
$383$	−896.407			−0.119593			−0.0597967	+	0.998211i	$0.519045\pi$
$384$	−293.819	−	1381.01i	−0.0390466	−	0.183527i
$385$			3045.17i			0.403107i
$386$		−	20765.9i		−	2.73823i
$387$	4629.14	+	10386.5i	0.608043	+	1.36428i
$388$	3064.08			0.400915
$389$	5726.34			0.746368			0.373184	−	0.927757i	$-0.378266\pi$
$389$	5726.34			0.746368			0.373184	+	0.927757i	$0.378266\pi$
$390$	1972.39	+	9270.63i	0.256092	+	1.20368i
$391$	1648.01			0.213155
$392$		−	13204.0i		−	1.70128i
$393$	−156.723	−	736.629i	−0.0201161	−	0.0945497i
$394$			2735.21i			0.349740i
$395$	−3048.37			−0.388304
$396$	−17281.7	+	7702.24i	−2.19302	+	0.977404i
$397$	−14562.0			−1.84092			−0.920460	−	0.390837i	$-0.872186\pi$
$397$	−14562.0			−1.84092			−0.920460	+	0.390837i	$0.872186\pi$
$398$	11402.7			1.43609
$399$	−2335.25	+	496.841i	−0.293005	+	0.0623388i
$400$	10786.4			1.34830
$401$	8393.97			1.04532			0.522662	−	0.852540i	$-0.324939\pi$
$401$	8393.97			1.04532			0.522662	+	0.852540i	$0.324939\pi$
$402$	1552.35	+	7296.34i	0.192597	+	0.905245i
$403$	−4830.30	−	6242.54i	−0.597058	−	0.771621i
$404$		−	29253.5i		−	3.60251i
$405$	−4122.71	−	3706.39i	−0.505825	−	0.454746i
$406$		−	9453.09i		−	1.15554i
$407$		−	4851.65i		−	0.590878i
$408$	8225.91	+	38663.4i	0.998145	+	4.69148i
$409$		−	6527.83i		−	0.789194i	−0.918854	−	0.394597i	$-0.870884\pi$
$409$		−	6527.83i		−	0.789194i	0.918854	−	0.394597i	$-0.129116\pi$
$410$			15690.0i			1.88994i
$411$	1287.45	−	273.914i	0.154514	−	0.0328739i
$412$	−2096.87			−0.250741
$413$			5652.06i			0.673413i
$414$	754.038	+	1691.85i	0.0895143	+	0.200845i
$415$			6122.52i			0.724199i
$416$	16430.5			1.93648
$417$	1725.29	+	8109.23i	0.202609	+	0.952304i
$418$			7763.68i			0.908454i
$419$			4793.25i			0.558868i	0.960165	+	0.279434i	$0.0901468\pi$
$419$			4793.25i			0.558868i	−0.960165	+	0.279434i	$0.909853\pi$
$420$	1788.76	+	8407.52i	0.207815	+	0.976774i
$421$	−5971.90			−0.691336			−0.345668	−	0.938357i	$-0.612348\pi$
$421$	−5971.90			−0.691336			−0.345668	+	0.938357i	$0.612348\pi$
$422$			5887.06i			0.679094i
$423$	5916.87	+	13275.8i	0.680114	+	1.52599i
$424$		−	10559.3i		−	1.20945i
$425$	−8463.22			−0.965944
$426$	−5027.96	+	1069.73i	−0.571843	+	0.121664i
$427$			7753.50i			0.878731i
$428$		−	3091.58i		−	0.349153i
$429$	−1776.02	−	8347.63i	−0.199876	−	0.939458i
$430$		−	16799.1i		−	1.88401i
$431$			14271.1i			1.59492i	0.603369	+	0.797462i	$0.293825\pi$
$431$			14271.1i			1.59492i	−0.603369	+	0.797462i	$0.706175\pi$
$432$	−18219.4	+	13253.2i	−2.02912	+	1.47603i
$433$			15516.1i			1.72207i	0.508546	+	0.861035i	$0.330183\pi$
$433$			15516.1i			1.72207i	−0.508546	+	0.861035i	$0.669817\pi$
$434$	−6176.75	−	7982.67i	−0.683165	−	0.882904i
$435$	−1329.28	−	6247.89i	−0.146515	−	0.688651i
$436$	1069.64			0.117492
$437$	539.034			0.0590057
$438$	23533.2	−	5006.85i	2.56726	−	0.546202i
$439$	13521.1			1.46999			0.734996	−	0.678071i	$-0.237184\pi$
$439$	13521.1			1.46999			0.734996	+	0.678071i	$0.237184\pi$
$440$	16490.5			1.78671
$441$	−5393.42	+	2403.78i	−0.582380	+	0.259560i
$442$	−30222.4			−3.25233
$443$		−	14964.1i		−	1.60489i	−0.596725	−	0.802446i	$-0.703532\pi$
$443$		−	14964.1i		−	1.60489i	0.596725	−	0.802446i	$-0.296468\pi$
$444$	−2849.90	−	13395.1i	−0.304617	−	1.43176i
$445$			9463.29i			1.00810i
$446$	−25856.7			−2.74518
$447$	1192.87	+	5606.72i	0.126221	+	0.593264i
$448$	6687.34			0.705239
$449$	−6353.80			−0.667827			−0.333913	−	0.942604i	$-0.608369\pi$
$449$	−6353.80			−0.667827			−0.333913	+	0.942604i	$0.608369\pi$
$450$	−3872.29	−	8688.34i	−0.405648	−	0.910161i
$451$		−	14127.9i		−	1.47507i
$452$		−	23713.4i		−	2.46766i
$453$	145.295	+	682.915i	0.0150696	+	0.0708303i
$454$	−16460.4			−1.70160
$455$	−3877.28			−0.399494
$456$	2690.54	+	12646.1i	0.276307	+	1.29870i
$457$		−	10334.0i		−	1.05777i	−0.848693	−	0.528886i	$-0.822610\pi$
$457$		−	10334.0i		−	1.05777i	0.848693	−	0.528886i	$-0.177390\pi$
$458$	−1325.87			−0.135270
$459$	14295.3	−	10398.7i	1.45370	−	1.05745i
$460$		−	1940.66i		−	0.196704i
$461$	13174.9			1.33106			0.665530	−	0.746371i	$-0.268206\pi$
$461$	13174.9			1.33106			0.665530	+	0.746371i	$0.268206\pi$
$462$	−2271.08	−	10674.5i	−0.228702	−	1.07495i
$463$		−	1161.98i		−	0.116635i	−0.998298	−	0.0583174i	$-0.981426\pi$
$463$		−	1161.98i		−	0.116635i	0.998298	−	0.0583174i	$-0.0185735\pi$
$464$	−25959.4			−2.59727
$465$	−5204.95	−	4407.47i	−0.519084	−	0.439551i
$466$	8002.55			0.795517
$467$			4200.45i			0.416218i	0.978106	+	0.208109i	$0.0667308\pi$
$467$			4200.45i			0.416218i	−0.978106	+	0.208109i	$0.933269\pi$
$468$	−9806.93	−	22004.0i	−0.968644	−	2.17337i
$469$	−3051.57			−0.300445
$470$		−	21472.2i		−	2.10732i
$471$	11598.8	−	2467.73i	1.13470	−	0.241416i
$472$	30607.5			2.98480
$473$			15126.5i			1.47044i
$474$	10685.8	−	2273.47i	1.03547	−	0.220304i
$475$	−2768.16			−0.267393
$476$	−27408.6			−2.63923
$477$	−4313.14	+	1922.31i	−0.414015	+	0.184521i
$478$		−	33160.0i		−	3.17302i
$479$			14239.2i			1.35825i	0.734021	+	0.679127i	$0.237641\pi$
$479$			14239.2i			1.35825i	−0.734021	+	0.679127i	$0.762359\pi$
$480$	13886.7	−	2954.48i	1.32049	−	0.280944i
$481$	6177.40			0.585582
$482$	−7204.09			−0.680783
$483$	−741.137	+	157.682i	−0.0698196	+	0.0148546i
$484$	800.600			0.0751879
$485$			1194.28i			0.111813i
$486$	17216.0	+	9917.69i	1.60686	+	0.925670i
$487$			10602.4i			0.986532i	0.869878	+	0.493266i	$0.164197\pi$
$487$			10602.4i			0.986532i	−0.869878	+	0.493266i	$0.835803\pi$
$488$	41987.5			3.89484
$489$	11886.0	−	2528.83i	1.09919	−	0.233860i
$490$	8723.27			0.804239
$491$	−13413.3			−1.23286			−0.616432	−	0.787409i	$-0.711422\pi$
$491$	−13413.3			−1.23286			−0.616432	+	0.787409i	$0.711422\pi$
$492$	−8298.85	−	39006.3i	−0.760450	−	3.57427i
$493$	20368.2			1.86073
$494$	−9885.16			−0.900313
$495$	−3002.08	−	6735.84i	−0.272593	−	0.611623i
$496$	−21921.4	+	16962.1i	−1.98448	+	1.53553i
$497$		−	2102.86i		−	0.189791i
$498$	−4566.16	−	21461.9i	−0.410873	−	1.93119i
$499$		−	18982.2i		−	1.70293i	−0.524412	−	0.851464i	$-0.675715\pi$
$499$		−	18982.2i		−	1.70293i	0.524412	−	0.851464i	$-0.324285\pi$
$500$			28512.9i			2.55027i
$501$	−15911.6	+	3385.29i	−1.41891	+	0.301884i
$502$			10694.1i			0.950796i
$503$			10109.7i			0.896161i	0.893993	+	0.448080i	$0.147892\pi$
$503$			10109.7i			0.896161i	−0.893993	+	0.448080i	$0.852108\pi$
$504$	−7398.63	−	16600.5i	−0.653891	−	1.46715i
$505$	11402.1			1.00472
$506$			2463.95i			0.216474i
$507$	−537.340	+	114.323i	−0.0470692	+	0.0100143i
$508$		−	20856.5i		−	1.82157i
$509$	4022.57			0.350289			0.175145	−	0.984543i	$-0.443961\pi$
$509$	4022.57			0.350289			0.175145	+	0.984543i	$0.443961\pi$
$510$	−25543.1	+	5434.48i	−2.21778	+	0.471848i
$511$			9842.37i			0.852056i
$512$			19866.8i			1.71484i
$513$	4675.71	−	3401.21i	0.402413	−	0.292724i
$514$	14390.2			1.23487
$515$		−	817.292i		−	0.0699305i
$516$	8885.45	+	41763.4i	0.758062	+	3.56304i
$517$			19334.4i			1.64473i
$518$	7899.36			0.670034
$519$	832.791	+	3914.29i	0.0704344	+	0.331056i
$520$			20996.6i			1.77070i
$521$			7667.60i			0.644767i	0.946609	+	0.322383i	$0.104484\pi$
$521$			7667.60i			0.644767i	−0.946609	+	0.322383i	$0.895516\pi$
$522$	9319.33	+	20910.0i	0.781410	+	1.75327i
$523$		−	12969.4i		−	1.08434i	−0.840269	−	0.542170i	$-0.817603\pi$
$523$		−	12969.4i		−	1.08434i	0.840269	−	0.542170i	$-0.182397\pi$
$524$		−	2827.86i		−	0.235755i
$525$	3806.04	−	809.760i	0.316398	−	0.0673159i
$526$			20300.8i			1.68281i
$527$	17199.9	−	13308.8i	1.42171	−	1.10008i
$528$	−29313.7	+	6236.68i	−2.41612	+	0.514047i
$529$	−11995.9			−0.985940
$530$	6976.04			0.571735
$531$	−5572.09	−	12502.2i	−0.455382	−	1.02175i
$532$	−8964.84			−0.730592
$533$	17988.5			1.46185
$534$	−7057.71	−	33172.7i	−0.571942	−	2.68824i
$535$	1205.00			0.0973769
$536$			16525.1i			1.33167i
$537$	3669.82	−	780.779i	0.294906	−	0.0627432i
$538$			342.880i			0.0274770i
$539$	−7854.77			−0.627698
$540$	−12245.2	−	16833.8i	−0.975836	−	1.34150i
$541$	21991.8			1.74770			0.873848	−	0.486200i	$-0.161617\pi$
$541$	21991.8			1.74770			0.873848	+	0.486200i	$0.161617\pi$
$542$	−14361.0			−1.13811
$543$	−1443.02	−	6782.50i	−0.114044	−	0.536031i
$544$			45270.7i			3.56795i
$545$			416.911i			0.0327679i
$546$	13591.5	−	2891.67i	1.06531	−	0.226652i
$547$	11207.0			0.876011			0.438006	−	0.898972i	$-0.355685\pi$
$547$	11207.0			0.876011			0.438006	+	0.898972i	$0.355685\pi$
$548$	4942.42			0.385273
$549$	−7643.80	−	17150.6i	−0.594224	−	1.33327i
$550$		−	12653.4i		−	0.980985i
$551$	6662.05			0.515087
$552$	853.893	+	4013.47i	0.0658408	+	0.309465i
$553$			4469.14i			0.343666i
$554$	−37214.8			−2.85398
$555$	5220.97	−	1110.80i	0.399311	−	0.0849562i
$556$			31130.6i			2.37452i
$557$	−1649.84			−0.125505			−0.0627524	−	0.998029i	$-0.519988\pi$
$557$	−1649.84			−0.125505			−0.0627524	+	0.998029i	$0.519988\pi$
$558$	21532.5	+	11568.1i	1.63359	+	0.877629i
$559$	−19260.0			−1.45726
$560$			13615.5i			1.02743i
$561$	23000.0	−	4893.41i	1.73095	−	0.368271i
$562$	5302.70			0.398009
$563$			1282.72i			0.0960218i	0.998847	+	0.0480109i	$0.0152882\pi$
$563$			1282.72i			0.0960218i	−0.998847	+	0.0480109i	$0.984712\pi$
$564$	11357.2	+	53381.0i	0.847914	+	3.98537i
$565$	9242.70			0.688218
$566$			4168.15i			0.309541i
$567$	−5433.85	+	6044.21i	−0.402470	+	0.447678i
$568$	−11387.6			−0.841220
$569$	−12303.1			−0.906456			−0.453228	−	0.891395i	$-0.649728\pi$
$569$	−12303.1			−0.906456			−0.453228	+	0.891395i	$0.649728\pi$
$570$	−8354.68	+	1777.51i	−0.613928	+	0.130617i
$571$		−	11706.4i		−	0.857963i	−0.903313	−	0.428982i	$-0.858873\pi$
$571$		−	11706.4i		−	0.857963i	0.903313	−	0.428982i	$-0.141127\pi$
$572$		−	32045.8i		−	2.34249i
$573$	1490.51	+	7005.68i	0.108668	+	0.510762i
$574$	23002.8			1.67268
$575$	−878.527			−0.0637167
$576$	−14792.2	+	6592.71i	−1.07004	+	0.476904i
$577$	−8416.46			−0.607247			−0.303624	−	0.952792i	$-0.598197\pi$
$577$	−8416.46			−0.607247			−0.303624	+	0.952792i	$0.598197\pi$
$578$		−	57501.9i		−	4.13800i
$579$	−20121.8	+	4281.05i	−1.44427	+	0.307279i
$580$		−	23985.1i		−	1.71712i
$581$	8976.08			0.640947
$582$	−890.691	−	4186.43i	−0.0634370	−	0.298167i
$583$	−6281.50			−0.446232
$584$	53299.3			3.77661
$585$	8576.46	−	3822.42i	0.606142	−	0.270150i
$586$	−46143.1			−3.25282
$587$	−15473.9			−1.08803			−0.544017	−	0.839074i	$-0.683097\pi$
$587$	−15473.9			−1.08803			−0.544017	+	0.839074i	$0.683097\pi$
$588$	−21686.5	+	4613.96i	−1.52098	+	0.323599i
$589$	5625.77	−	4353.06i	0.393558	−	0.304524i
$590$			20221.0i			1.41099i
$591$	2650.37	−	563.884i	0.184470	−	0.0392472i
$592$		−	21692.6i		−	1.50602i
$593$			14279.1i			0.988821i	0.869229	+	0.494410i	$0.164616\pi$
$593$			14279.1i			0.988821i	−0.869229	+	0.494410i	$0.835384\pi$
$594$	15547.1	+	21372.9i	1.07391	+	1.47633i
$595$		−	10683.0i		−	0.736067i
$596$			21523.7i			1.47927i
$597$	−2350.75	−	11049.0i	−0.161155	−	0.757462i
$598$	−3137.24			−0.214534
$599$			1639.56i			0.111837i	0.998435	+	0.0559187i	$0.0178088\pi$
$599$			1639.56i			0.111837i	−0.998435	+	0.0559187i	$0.982191\pi$
$600$	−4385.08	−	20610.8i	−0.298367	−	1.40239i
$601$			22297.5i			1.51337i	0.653779	+	0.756685i	$0.273182\pi$
$601$			22297.5i			1.51337i	−0.653779	+	0.756685i	$0.726818\pi$
$602$	−24628.7			−1.66743
$603$	6750.00	−	3008.39i	0.455856	−	0.203170i
$604$			2621.65i			0.176612i
$605$			312.048i			0.0209695i
$606$	−39968.8	+	8503.64i	−2.67925	+	0.570028i
$607$	−13716.0			−0.917160			−0.458580	−	0.888653i	$-0.651642\pi$
$607$	−13716.0			−0.917160			−0.458580	+	0.888653i	$0.651642\pi$
$608$			14807.2i			0.987682i
$609$	−9159.88	+	1948.83i	−0.609486	+	0.129672i
$610$			27739.2i			1.84119i
$611$	−24617.7			−1.62999
$612$	60627.2	−	27020.8i	4.00443	−	1.78472i
$613$		−	5110.82i		−	0.336744i	−0.985724	−	0.168372i	$-0.946149\pi$
$613$		−	5110.82i		−	0.336744i	0.985724	−	0.168372i	$-0.0538510\pi$
$614$			16599.0i			1.09101i
$615$	15203.4	−	3234.62i	0.996845	−	0.212086i
$616$		−	24176.3i		−	1.58132i
$617$			629.658i			0.0410844i	0.999789	+	0.0205422i	$0.00653925\pi$
$617$			629.658i			0.0410844i	−0.999789	+	0.0205422i	$0.993461\pi$
$618$	609.536	+	2864.94i	0.0396749	+	0.186480i
$619$			16612.4i			1.07869i	0.842086	+	0.539343i	$0.181327\pi$
$619$			16612.4i			1.07869i	−0.842086	+	0.539343i	$0.818673\pi$
$620$	−15672.1	−	20254.2i	−1.01517	−	1.31198i
$621$	1483.93	−	1079.44i	0.0958903	−	0.0697526i
$622$	23050.5			1.48592
$623$	13873.9			0.892210
$624$	−7940.90	−	37323.8i	−0.509440	−	2.39447i
$625$	−2717.36			−0.173911
$626$	38439.7			2.45425
$627$	7522.87	−	1600.54i	0.479162	−	0.101945i
$628$	44526.8			2.82932
$629$			17020.4i			1.07893i
$630$	10967.2	−	4887.93i	0.693559	−	0.309111i
$631$		−	5138.45i		−	0.324181i	−0.986776	−	0.162091i	$-0.948176\pi$
$631$		−	5138.45i		−	0.324181i	0.986776	−	0.162091i	$-0.0518237\pi$
$632$	24201.7			1.52325
$633$	5704.46	−	1213.66i	0.358186	−	0.0762066i
$634$	−20817.3			−1.30404
$635$	8129.19			0.508027
$636$	−17342.8	+	3689.80i	−1.08127	+	0.230047i
$637$		−	10001.1i		−	0.622072i
$638$			30452.5i			1.88970i
$639$	2073.10	+	4651.47i	0.128342	+	0.287965i
$640$	2066.38			0.127626
$641$	10368.2			0.638877			0.319439	−	0.947607i	$-0.396506\pi$
$641$	10368.2			0.638877			0.319439	+	0.947607i	$0.396506\pi$
$642$	−4224.01	+	898.686i	−0.259670	+	0.0552466i
$643$		−	2776.45i		−	0.170284i	−0.996369	−	0.0851418i	$-0.972866\pi$
$643$		−	2776.45i		−	0.170284i	0.996369	−	0.0851418i	$-0.0271343\pi$
$644$	−2845.16			−0.174092
$645$	−16278.0	+	3463.26i	−0.993715	+	0.211420i
$646$		−	27236.4i		−	1.65882i
$647$	−7220.00			−0.438713			−0.219357	−	0.975645i	$-0.570396\pi$
$647$	−7220.00			−0.438713			−0.219357	+	0.975645i	$0.570396\pi$
$648$	32731.2	+	29425.9i	1.98426	+	1.78389i
$649$		−	18207.8i		−	1.10126i
$650$	16111.0			0.972193
$651$	−6461.68	+	7630.86i	−0.389022	+	0.459412i
$652$	45629.3			2.74077
$653$		−	4529.92i		−	0.271469i	−0.990745	−	0.135735i	$-0.956661\pi$
$653$		−	4529.92i		−	0.271469i	0.990745	−	0.135735i	$-0.0433395\pi$
$654$	−310.932	−	1461.44i	−0.0185908	−	0.0873805i
$655$	1102.21			0.0657508
$656$		−	63168.6i		−	3.75963i
$657$	−9703.11	−	21771.1i	−0.576186	−	1.29280i
$658$	−31479.9			−1.86507
$659$		−	9335.83i		−	0.551855i	−0.961179	−	0.275927i	$-0.911015\pi$
$659$		−	9335.83i		−	0.551855i	0.961179	−	0.275927i	$-0.0889849\pi$
$660$	−5762.37	−	27084.3i	−0.339848	−	1.59736i
$661$	9047.62			0.532393			0.266197	−	0.963919i	$-0.414233\pi$
$661$	9047.62			0.532393			0.266197	+	0.963919i	$0.414233\pi$
$662$	32821.0			1.92693
$663$	6230.58	+	29285.0i	0.364971	+	1.71544i
$664$		−	48608.1i		−	2.84090i
$665$		−	3494.20i		−	0.203758i
$666$	−17473.2	+	7787.59i	−1.01662	+	0.453097i
$667$	2114.33			0.122739
$668$	−61083.1			−3.53799
$669$	5330.56	+	25054.7i	0.308059	+	1.44794i
$670$	−10917.4			−0.629516
$671$		−	24977.4i		−	1.43702i
$672$	−4331.50	−	20358.9i	−0.248647	−	1.16869i
$673$		−	27863.3i		−	1.59591i	−0.602714	−	0.797957i	$-0.705914\pi$
$673$		−	27863.3i		−	1.59591i	0.602714	−	0.797957i	$-0.294086\pi$
$674$	4738.79			0.270818
$675$	−7620.56	+	5543.35i	−0.434541	+	0.316094i
$676$	−2062.80			−0.117365
$677$	15295.3			0.868310			0.434155	−	0.900838i	$-0.357047\pi$
$677$	15295.3			0.868310			0.434155	+	0.900838i	$0.357047\pi$
$678$	−32399.4	+	6893.19i	−1.83524	+	0.390460i
$679$	1750.90			0.0989595
$680$	−57851.5			−3.26251
$681$	3393.44	+	15949.8i	0.190950	+	0.897503i
$682$	19898.0	+	25715.7i	1.11721	+	1.44385i
$683$			4193.67i			0.234943i	0.993076	+	0.117472i	$0.0374790\pi$
$683$			4193.67i			0.234943i	−0.993076	+	0.117472i	$0.962521\pi$
$684$	19830.0	−	8837.99i	1.10851	−	0.494048i
$685$			1926.39i			0.107451i
$686$		−	32846.9i		−	1.82814i
$687$	273.338	+	1284.74i	0.0151797	+	0.0713478i
$688$			67633.6i			3.74783i
$689$		−	7997.96i		−	0.442232i
$690$	−2651.51	+	564.128i	−0.146292	+	0.0311246i
$691$	−23903.9			−1.31599			−0.657995	−	0.753023i	$-0.728595\pi$
$691$	−23903.9			−1.31599			−0.657995	+	0.753023i	$0.728595\pi$
$692$			15026.6i			0.825471i
$693$	−9875.26	+	4401.28i	−0.541313	+	0.241257i
$694$			54408.9i			2.97598i
$695$	−12133.7			−0.662242
$696$	10553.5	+	49603.4i	0.574753	+	2.70146i
$697$			49563.2i			2.69346i
$698$		−	46749.5i		−	2.53509i
$699$	−1649.79	−	7754.34i	−0.0892714	−	0.419594i
$700$	14611.0			0.788922
$701$			15335.8i			0.826282i	0.910667	+	0.413141i	$0.135568\pi$
$701$			15335.8i			0.826282i	−0.910667	+	0.413141i	$0.864432\pi$
$702$	−27213.2	+	19795.5i	−1.46310	+	1.06429i
$703$			5567.06i			0.298671i
$704$	−21542.8			−1.15330
$705$	−20806.2	+	4426.66i	−1.11150	+	0.236479i
$706$		−	17917.7i		−	0.955159i
$707$		−	16716.3i		−	0.889224i
$708$	−10695.4	−	50270.5i	−0.567736	−	2.66847i
$709$			19801.4i			1.04888i	0.851447	+	0.524440i	$0.175725\pi$
$709$			19801.4i			1.04888i	−0.851447	+	0.524440i	$0.824275\pi$
$710$		−	7523.25i		−	0.397666i
$711$	−4405.91	−	9885.63i	−0.232397	−	0.521435i
$712$		−	75131.3i		−	3.95458i
$713$	1785.44	−	1381.52i	0.0937804	−	0.0725645i
$714$	7967.36	+	37448.2i	0.417606	+	1.96283i
$715$	12490.4			0.653309
$716$	14088.1			0.735332
$717$	−32131.5	+	6836.19i	−1.67360	+	0.356070i
$718$	−4167.35			−0.216607
$719$	−8399.35			−0.435665			−0.217832	−	0.975986i	$-0.569899\pi$
$719$	−8399.35			−0.435665			−0.217832	+	0.975986i	$0.569899\pi$
$720$	−13422.9	−	30117.2i	−0.694779	−	1.55889i
$721$	−1198.21			−0.0618915
$722$			27067.5i			1.39522i
$723$	1485.18	+	6980.64i	0.0763962	+	0.359077i
$724$		−	26037.4i		−	1.33657i
$725$	−10857.9			−0.556211
$726$	−232.725	−	1093.85i	−0.0118970	−	0.0559184i
$727$	−33328.5			−1.70025			−0.850127	−	0.526578i	$-0.823475\pi$
$727$	−33328.5			−1.70025			−0.850127	+	0.526578i	$0.823475\pi$
$728$	30782.7			1.56714
$729$	6060.86	−	18726.6i	0.307924	−	0.951411i
$730$			35212.4i			1.78530i
$731$		−	53066.6i		−	2.68500i
$732$	−14671.9	−	68961.1i	−0.740834	−	3.48207i
$733$	20061.9			1.01092			0.505459	−	0.862851i	$-0.331323\pi$
$733$	20061.9			1.01092			0.505459	+	0.862851i	$0.331323\pi$
$734$	16728.6			0.841230
$735$	−1798.37	−	8452.70i	−0.0902502	−	0.424194i
$736$			4699.34i			0.235353i
$737$	9830.45			0.491329
$738$	−50881.6	+	22677.3i	−2.53791	+	1.13112i
$739$			10383.5i			0.516865i	0.966029	+	0.258433i	$0.0832060\pi$
$739$			10383.5i			0.516865i	−0.966029	+	0.258433i	$0.916794\pi$
$740$	20042.9			0.995662
$741$	2037.90	+	9578.56i	0.101031	+	0.474868i
$742$		−	10227.4i		−	0.506011i
$743$	399.839			0.0197425			0.00987123	−	0.999951i	$-0.496858\pi$
$743$	399.839			0.0197425			0.00987123	+	0.999951i	$0.496858\pi$
$744$	41323.3	+	34991.9i	2.03627	+	1.72428i
$745$	−8389.25			−0.412562
$746$		−	4653.86i		−	0.228405i
$747$	−19854.9	+	8849.07i	−0.972492	+	0.433428i
$748$	88295.2			4.31603
$749$		−	1766.62i		−	0.0861828i
$750$	38957.0	−	8288.37i	1.89668	−	0.403531i
$751$	216.634			0.0105261			0.00526304	−	0.999986i	$-0.498325\pi$
$751$	216.634			0.0105261			0.00526304	+	0.999986i	$0.498325\pi$
$752$			86447.7i			4.19205i
$753$	10362.4	−	2204.67i	0.501495	−	0.106697i
$754$	−38773.9			−1.87276
$755$	−1021.83			−0.0492561
$756$	−24679.6	+	17952.5i	−1.18729	+	0.863657i
$757$			32436.9i			1.55738i	0.627407	+	0.778692i	$0.284116\pi$
$757$			32436.9i			1.55738i	−0.627407	+	0.778692i	$0.715884\pi$
$758$		−	6235.25i		−	0.298779i
$759$	2387.53	−	507.962i	0.114179	−	0.0242923i
$760$	−18922.1			−0.903128
$761$	−2899.07			−0.138096			−0.0690480	−	0.997613i	$-0.521996\pi$
$761$	−2899.07			−0.138096			−0.0690480	+	0.997613i	$0.521996\pi$
$762$	−28496.1	+	6062.74i	−1.35473	+	0.288228i
$763$	611.223			0.0290010
$764$			26894.2i			1.27356i
$765$	10531.8	+	23630.5i	0.497751	+	1.11681i
$766$			4701.73i			0.221776i
$767$	23183.2			1.09139
$768$	17144.3	−	3647.56i	0.805522	−	0.171380i
$769$	11670.8			0.547280			0.273640	−	0.961832i	$-0.411772\pi$
$769$	11670.8			0.547280			0.273640	+	0.961832i	$0.411772\pi$
$770$	15972.2			0.747528
$771$	−2966.65	−	13943.8i	−0.138575	−	0.651330i
$772$	−77245.9			−3.60122
$773$	−10565.9			−0.491627			−0.245814	−	0.969317i	$-0.579055\pi$
$773$	−10565.9			−0.491627			−0.245814	+	0.969317i	$0.579055\pi$
$774$	54478.1	−	24280.2i	2.52994	−	1.12757i
$775$	−9168.98	+	7094.69i	−0.424980	+	0.328837i
$776$		−	9481.65i		−	0.438623i
$777$	−1628.51	−	7654.34i	−0.0751900	−	0.353408i
$778$		−	30035.1i		−	1.38408i
$779$			16211.2i			0.745605i
$780$	34485.3	−	7336.98i	1.58304	−	0.336803i
$781$			6774.23i			0.310373i
$782$		−	8643.97i		−	0.395278i
$783$	18340.2	−	13341.0i	0.837069	−	0.608901i
$784$	−35120.2			−1.59986
$785$			17355.1i			0.789084i
$786$	−3863.68	+	822.025i	−0.175335	+	0.0373036i
$787$			31547.7i			1.42891i	0.699681	+	0.714455i	$0.253325\pi$
$787$			31547.7i			1.42891i	−0.699681	+	0.714455i	$0.746675\pi$
$788$	10174.5			0.459966
$789$	19671.2	−	4185.18i	0.887595	−	0.188842i
$790$			15988.9i			0.720077i
$791$		−	13550.5i		−	0.609103i
$792$	23834.2	+	53477.4i	1.06933	+	2.39929i
$793$	31802.7			1.42414
$794$			76378.8i			3.41383i
$795$	−1438.16	−	6759.67i	−0.0641591	−	0.301561i
$796$		−	42416.1i		−	1.88869i
$797$	−1610.41			−0.0715731			−0.0357866	−	0.999359i	$-0.511394\pi$
$797$	−1610.41			−0.0715731			−0.0357866	+	0.999359i	$0.511394\pi$
$798$	2605.97	+	12248.6i	0.115602	+	0.543353i
$799$		−	67828.5i		−	3.00325i
$800$		−	24133.0i		−	1.06654i
$801$	−30688.8	+	13677.6i	−1.35373	+	0.603339i
$802$		−	44027.0i		−	1.93847i
$803$		−	31706.6i		−	1.39340i
$804$	27141.2	−	5774.48i	1.19054	−	0.253296i
$805$		−	1108.95i		−	0.0485533i
$806$	−32742.7	+	25335.3i	−1.43091	+	1.10719i
$807$	332.245	−	70.6873i	0.0144927	−	0.00308341i
$808$	−90523.6			−3.94135
$809$	3031.92			0.131763			0.0658817	−	0.997827i	$-0.479014\pi$
$809$	3031.92			0.131763			0.0658817	+	0.997827i	$0.479014\pi$
$810$	−19440.3	+	21624.0i	−0.843288	+	0.938011i
$811$	−13508.0			−0.584872			−0.292436	−	0.956285i	$-0.594466\pi$
$811$	−13508.0			−0.584872			−0.292436	+	0.956285i	$0.594466\pi$
$812$	−35164.0			−1.51972
$813$	2960.63	+	13915.6i	0.127717	+	0.600296i
$814$	−25447.3			−1.09573
$815$			17784.8i			0.764387i
$816$	102837.	−	21879.4i	4.41180	−	0.938641i
$817$		−	17357.1i		−	0.743264i
$818$	−34239.0			−1.46349
$819$	−5603.97	−	12573.7i	−0.239095	−	0.536462i
$820$	58364.5			2.48558
$821$	−1315.83			−0.0559352			−0.0279676	−	0.999609i	$-0.508904\pi$
$821$	−1315.83			−0.0559352			−0.0279676	+	0.999609i	$0.508904\pi$
$822$	−1436.70	−	6752.79i	−0.0609620	−	0.286534i
$823$		−	14084.8i		−	0.596556i	−0.954479	−	0.298278i	$-0.903588\pi$
$823$		−	14084.8i		−	0.596556i	0.954479	−	0.298278i	$-0.0964122\pi$
$824$			6488.67i			0.274325i
$825$	−12260.9	+	2608.59i	−0.517418	+	0.110084i
$826$	29645.5			1.24879
$827$	−41894.6			−1.76157			−0.880784	−	0.473518i	$-0.842984\pi$
$827$	−41894.6			−1.76157			−0.880784	+	0.473518i	$0.842984\pi$
$828$	6293.43	−	2804.90i	0.264144	−	0.117726i
$829$		−	6454.61i		−	0.270420i	−0.990817	−	0.135210i	$-0.956829\pi$
$829$		−	6454.61i		−	0.270420i	0.990817	−	0.135210i	$-0.0431708\pi$
$830$	32113.1			1.34297
$831$	7672.12	+	36060.5i	0.320268	+	1.50533i
$832$		−	27429.6i		−	1.14297i
$833$	27555.9			1.14617
$834$	42533.6	−	9049.31i	1.76597	−	0.375722i
$835$		−	23808.2i		−	0.986727i
$836$	28879.7			1.19477
$837$	6770.20	−	23249.5i	0.279585	−	0.960121i
$838$	25141.0			1.03637
$839$		−	8429.94i		−	0.346882i	−0.984844	−	0.173441i	$-0.944511\pi$
$839$		−	8429.94i		−	0.346882i	0.984844	−	0.173441i	$-0.0554886\pi$
$840$	26016.7	−	5535.23i	1.06864	−	0.227361i
$841$	1742.47			0.0714451
$842$			31323.1i			1.28202i
$843$	−1093.19	−	5138.23i	−0.0446638	−	0.209929i
$844$	21898.9			0.893119
$845$		−	804.013i		−	0.0327324i
$846$	69632.7	−	31034.5i	2.82981	−	1.26121i
$847$	457.486			0.0185589
$848$	−28085.8			−1.13735
$849$	4038.87	−	859.297i	0.163267	−	0.0347361i
$850$			44390.3i			1.79126i
$851$			1766.81i			0.0711698i
$852$	3979.24	+	18703.2i	0.160008	+	0.752068i
$853$	−25744.3			−1.03337			−0.516686	−	0.856175i	$-0.672835\pi$
$853$	−25744.3			−1.03337			−0.516686	+	0.856175i	$0.672835\pi$
$854$	40667.8			1.62953
$855$	3444.76	+	7729.09i	0.137788	+	0.309157i
$856$	−9566.76			−0.381992
$857$		−	8134.36i		−	0.324229i	−0.986772	−	0.162115i	$-0.948169\pi$
$857$		−	8134.36i		−	0.324229i	0.986772	−	0.162115i	$-0.0518314\pi$
$858$	−43784.0	+	9315.35i	−1.74215	+	0.370654i
$859$		−	38757.1i		−	1.53944i	−0.638384	−	0.769718i	$-0.720397\pi$
$859$		−	38757.1i		−	1.53944i	0.638384	−	0.769718i	$-0.279603\pi$
$860$	−62489.9			−2.47778
$861$	−4742.21	−	22289.3i	−0.187705	−	0.882251i
$862$	74852.9			2.95765
$863$	−18864.6			−0.744099			−0.372049	−	0.928213i	$-0.621345\pi$
$863$	−18864.6			−0.744099			−0.372049	+	0.928213i	$0.621345\pi$
$864$	29652.0	+	40763.2i	1.16757	+	1.60508i
$865$	−5856.89			−0.230220
$866$	81383.2			3.19343
$867$	−55718.4	+	11854.5i	−2.18258	+	0.464358i
$868$	−29694.3	+	22976.6i	−1.16116	+	0.898474i
$869$		−	14397.1i		−	0.562010i
$870$	−32770.7	+	6972.19i	−1.27705	+	0.271700i
$871$			12516.7i			0.486925i
$872$		−	3309.95i		−	0.128543i
$873$	−3872.96	+	1726.13i	−0.150149	+	0.0669194i
$874$		−	2827.28i		−	0.109421i
$875$			16293.1i			0.629495i
$876$	−18624.7	−	87539.8i	−0.718345	−	3.37637i
$877$	−16405.4			−0.631664			−0.315832	−	0.948815i	$-0.602284\pi$
$877$	−16405.4			−0.631664			−0.315832	+	0.948815i	$0.602284\pi$
$878$		−	70919.2i		−	2.72598i
$879$	9512.76	+	44711.9i	0.365025	+	1.71569i
$880$		−	43861.6i		−	1.68020i
$881$	13141.6			0.502555			0.251277	−	0.967915i	$-0.419149\pi$
$881$	13141.6			0.502555			0.251277	+	0.967915i	$0.419149\pi$
$882$	12608.0	+	28288.9i	0.481332	+	1.07997i
$883$		−	8215.22i		−	0.313096i	−0.987670	−	0.156548i	$-0.949963\pi$
$883$		−	8215.22i		−	0.313096i	0.987670	−	0.156548i	$-0.0500367\pi$
$884$			112423.i			4.27735i
$885$	19593.8	−	4168.71i	0.744224	−	0.158339i
$886$	−78488.1			−2.97614
$887$			4798.95i			0.181661i	0.995866	+	0.0908304i	$0.0289521\pi$
$887$			4798.95i			0.181661i	−0.995866	+	0.0908304i	$0.971048\pi$
$888$	−41450.5	+	8818.87i	−1.56643	+	0.333268i
$889$		−	11918.0i		−	0.449626i
$890$	49635.8			1.86943
$891$	17504.8	−	19471.1i	0.658175	−	0.732104i
$892$			96182.9i			3.61036i
$893$		−	22185.4i		−	0.831362i
$894$	29407.7	−	6256.69i	1.10016	−	0.234066i
$895$			5491.09i			0.205080i
$896$		−	3029.47i		−	0.112955i
$897$	646.767	+	3039.94i	0.0240746	+	0.113155i
$898$			33326.2i			1.23843i
$899$	22066.7	−	17074.6i	0.818651	−	0.633448i
$900$	−32319.3	+	14404.3i	−1.19701	+	0.533493i
$901$	22036.6			0.814812
$902$	−74102.1			−2.73540
$903$	5077.40	+	23864.8i	0.187116	+	0.879481i
$904$	−73379.9			−2.69976
$905$	10148.6			0.372762
$906$	3581.94	−	762.083i	0.131349	−	0.0279454i
$907$	32681.1			1.19643			0.598214	−	0.801337i	$-0.295877\pi$
$907$	32681.1			1.19643			0.598214	+	0.801337i	$0.295877\pi$
$908$			61230.1i			2.23788i
$909$	16479.8	+	36976.0i	0.601320	+	1.34919i
$910$			20336.7i			0.740829i
$911$	28487.6			1.03604			0.518021	−	0.855368i	$-0.326669\pi$
$911$	28487.6			1.03604			0.518021	+	0.855368i	$0.326669\pi$
$912$	33636.2	−	7156.33i	1.22128	−	0.259835i
$913$	−28915.9			−1.04817
$914$	−54202.4			−1.96155
$915$	26878.8	−	5718.65i	0.971132	−	0.206615i
$916$			4932.02i			0.177902i
$917$		−	1615.92i		−	0.0581924i
$918$	−54542.0	−	74979.9i	−1.96095	−	2.69576i
$919$	42200.8			1.51477			0.757385	−	0.652968i	$-0.226476\pi$
$919$	42200.8			1.51477			0.757385	+	0.652968i	$0.226476\pi$
$920$	−6005.29			−0.215205
$921$	16084.2	−	3422.02i	0.575452	−	0.122431i
$922$		−	69103.7i		−	2.46834i
$923$	−8625.34			−0.307591
$924$	−39707.7	+	8448.08i	−1.41373	+	0.300781i
$925$		−	9073.29i		−	0.322517i
$926$	−6094.69			−0.216289
$927$	2650.42	−	1181.26i	0.0939063	−	0.0418529i
$928$			58080.2i			2.05450i
$929$	−42972.6			−1.51764			−0.758818	−	0.651303i	$-0.774223\pi$
$929$	−42972.6			−1.51764			−0.758818	+	0.651303i	$0.774223\pi$
$930$	−23117.5	+	27300.4i	−0.815111	+	0.962597i
$931$	9013.02			0.317282
$932$		−	29768.2i		−	1.04624i
$933$	−4752.04	−	22335.5i	−0.166747	−	0.783743i
$934$	22031.7			0.771841
$935$			34414.6i			1.20372i
$936$	−68090.5	+	30347.1i	−2.37779	+	1.05975i
$937$	−39920.8			−1.39184			−0.695920	−	0.718119i	$-0.745003\pi$
$937$	−39920.8			−1.39184			−0.695920	+	0.718119i	$0.745003\pi$
$938$			16005.7i			0.557149i
$939$	−7924.64	−	37247.4i	−0.275411	−	1.29449i
$940$	−79873.2			−2.77146
$941$	−33894.3			−1.17420			−0.587100	−	0.809514i	$-0.699731\pi$
$941$	−33894.3			−1.17420			−0.587100	+	0.809514i	$0.699731\pi$
$942$	−12943.4	−	60836.7i	−0.447685	−	2.10421i
$943$			5144.93i			0.177669i
$944$		−	81410.3i		−	2.80686i
$945$	−6997.29	−	9619.31i	−0.240870	−	0.331128i
$946$	79339.9			2.72681
$947$	32476.7			1.11442			0.557208	−	0.830373i	$-0.311873\pi$
$947$	32476.7			1.11442			0.557208	+	0.830373i	$0.311873\pi$
$948$	−8456.95	−	39749.4i	−0.289735	−	1.36181i
$949$	40370.6			1.38091
$950$			14519.2i			0.495858i
$951$	4291.65	+	20171.6i	0.146337	+	0.687813i
$952$			84814.7i			2.88746i
$953$	5064.87			0.172159			0.0860794	−	0.996288i	$-0.472566\pi$
$953$	5064.87			0.172159			0.0860794	+	0.996288i	$0.472566\pi$
$954$	10082.7	+	22622.8i	0.342180	+	0.767756i
$955$	−10482.5			−0.355189
$956$	−123350.			−4.17304
$957$	29508.0	−	6278.03i	0.996717	−	0.212058i
$958$	74685.5			2.51877
$959$	2824.24			0.0950985
$960$	−4932.29	−	23182.7i	−0.165822	−	0.779396i
$961$	7477.53	−	28837.3i	0.251000	−	0.967987i
$962$		−	32401.0i		−	1.08591i
$963$	1741.62	+	3907.72i	0.0582794	+	0.130763i
$964$			26798.1i			0.895341i
$965$		−	30107.9i		−	1.00436i
$966$	827.054	+	3887.32i	0.0275466	+	0.129475i
$967$		−	57244.6i		−	1.90368i	−0.306590	−	0.951842i	$-0.599188\pi$
$967$		−	57244.6i		−	1.90368i	0.306590	−	0.951842i	$-0.400812\pi$
$968$		−	2477.42i		−	0.0822596i
$969$	−26391.6	+	5614.99i	−0.874943	+	0.186150i
$970$	6264.09			0.207348
$971$			1433.79i			0.0473867i	0.999719	+	0.0236934i	$0.00754254\pi$
$971$			1433.79i			0.0473867i	−0.999719	+	0.0236934i	$0.992457\pi$
$972$	36892.2	−	64040.8i	1.21741	−	2.11328i
$973$			17789.0i			0.586113i
$974$	55610.5			1.82944
$975$	−3321.41	−	15611.3i	−0.109098	−	0.512781i
$976$		−	111679.i		−	3.66265i
$977$		−	4303.85i		−	0.140934i	−0.997514	−	0.0704669i	$-0.977551\pi$
$977$		−	4303.85i		−	0.140934i	0.997514	−	0.0704669i	$-0.0224489\pi$
$978$	−13263.9	−	62343.0i	−0.433674	−	2.03835i
$979$	−44694.0			−1.45907
$980$		−	32449.2i		−	1.05771i
$981$	−1352.01	+	602.575i	−0.0440024	+	0.0196114i
$982$			70354.1i			2.28624i
$983$	46474.3			1.50794			0.753968	−	0.656911i	$-0.228137\pi$
$983$	46474.3			1.50794			0.753968	+	0.656911i	$0.228137\pi$
$984$	−120703.	+	25680.4i	−3.91044	+	0.831974i
$985$			3965.71i			0.128282i
$986$		−	106833.i		−	3.45056i
$987$	6489.82	+	30503.5i	0.209294	+	0.983725i
$988$			36771.3i			1.18406i
$989$		−	5508.59i		−	0.177111i
$990$	−35330.0	+	15746.2i	−1.13420	+	0.505501i
$991$			24764.7i			0.793820i	0.917857	+	0.396910i	$0.129918\pi$
$991$			24764.7i			0.793820i	−0.917857	+	0.396910i	$0.870082\pi$
$992$	37950.3	+	49045.9i	1.21464	+	1.56977i
$993$	−6766.31	−	31803.0i	−0.216236	−	1.01635i
$994$	−11029.7			−0.351952
$995$	16532.4			0.526747
$996$	−79834.9	+	16985.4i	−2.53983	+	0.540365i
$997$	4065.55			0.129145			0.0645724	−	0.997913i	$-0.479432\pi$
$997$	4065.55			0.129145			0.0645724	+	0.997913i	$0.479432\pi$
$998$	−99563.4			−3.15794
$999$	11148.3	+	15325.8i	0.353069	+	0.485371i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.4.c.b.92.1	✓	28
3.2	odd	2	inner	93.4.c.b.92.28	yes	28
31.30	odd	2	inner	93.4.c.b.92.2	yes	28
93.92	even	2	inner	93.4.c.b.92.27	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.4.c.b.92.1	✓	28	1.1	even	1	trivial
93.4.c.b.92.2	yes	28	31.30	odd	2	inner
93.4.c.b.92.27	yes	28	93.92	even	2	inner
93.4.c.b.92.28	yes	28	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	93.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.24508i q^{2} +(-5.08240 + 1.08131i) q^{3} -19.5109 q^{4} -7.60471i q^{5} +(5.67158 + 26.6576i) q^{6} -11.1491 q^{7} +60.3756i q^{8} +(24.6615 - 10.9913i) q^{9} -39.8873 q^{10} +35.9161 q^{11} +(99.1621 - 21.0974i) q^{12} +45.7305i q^{13} +58.4779i q^{14} +(8.22308 + 38.6502i) q^{15} +160.588 q^{16} -126.000 q^{17} +(-57.6505 - 129.352i) q^{18} -41.2122 q^{19} +148.375i q^{20} +(56.6641 - 12.0557i) q^{21} -188.383i q^{22} -13.0795 q^{23} +(-65.2850 - 306.853i) q^{24} +67.1684 q^{25} +239.860 q^{26} +(-113.455 + 82.5292i) q^{27} +217.529 q^{28} -161.652 q^{29} +(202.723 - 43.1308i) q^{30} +(-136.507 + 105.625i) q^{31} -359.291i q^{32} +(-182.540 + 38.8366i) q^{33} +660.881i q^{34} +84.7856i q^{35} +(-481.168 + 214.451i) q^{36} -135.083i q^{37} +216.161i q^{38} +(-49.4490 - 232.420i) q^{39} +459.139 q^{40} -393.359i q^{41} +(-63.2330 - 297.208i) q^{42} +421.163i q^{43} -700.755 q^{44} +(-83.5860 - 187.544i) q^{45} +68.6029i q^{46} +538.321i q^{47} +(-816.170 + 173.646i) q^{48} -218.698 q^{49} -352.304i q^{50} +(640.382 - 136.246i) q^{51} -892.242i q^{52} -174.894 q^{53} +(432.872 + 595.078i) q^{54} -273.132i q^{55} -673.133i q^{56} +(209.457 - 44.5634i) q^{57} +847.880i q^{58} -506.952i q^{59} +(-160.440 - 754.099i) q^{60} -695.438i q^{61} +(554.014 + 715.992i) q^{62} +(-274.954 + 122.543i) q^{63} -599.810 q^{64} +347.767 q^{65} +(203.701 + 957.437i) q^{66} +273.706 q^{67} +2458.37 q^{68} +(66.4751 - 14.1430i) q^{69} +444.708 q^{70} +188.613i q^{71} +(663.608 + 1488.95i) q^{72} -882.796i q^{73} -708.520 q^{74} +(-341.376 + 72.6301i) q^{75} +804.087 q^{76} -400.432 q^{77} +(-1219.06 + 259.364i) q^{78} -400.853i q^{79} -1221.22i q^{80} +(487.381 - 542.126i) q^{81} -2063.20 q^{82} -805.095 q^{83} +(-1105.57 + 235.217i) q^{84} +958.194i q^{85} +2209.03 q^{86} +(821.581 - 174.797i) q^{87} +2168.45i q^{88} -1244.40 q^{89} +(-983.682 + 438.415i) q^{90} -509.853i q^{91} +255.192 q^{92} +(579.570 - 684.438i) q^{93} +2823.54 q^{94} +313.407i q^{95} +(388.507 + 1826.06i) q^{96} -157.045 q^{97} +1147.09i q^{98} +(885.746 - 394.766i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 144 q^{4} - 64 q^{7} + 20 q^{9} - 8 q^{10} + 248 q^{16} + 88 q^{18} + 308 q^{19} - 840 q^{25} - 420 q^{28} + 328 q^{31} - 180 q^{33} + 540 q^{36} + 1152 q^{39} + 44 q^{40} - 1568 q^{45} - 84 q^{49}+ \cdots - 988 q^{97}+O(q^{100}) \) 28 * q - 144 * q^4 - 64 * q^7 + 20 * q^9 - 8 * q^10 + 248 * q^16 + 88 * q^18 + 308 * q^19 - 840 * q^25 - 420 * q^28 + 328 * q^31 - 180 * q^33 + 540 * q^36 + 1152 * q^39 + 44 * q^40 - 1568 * q^45 - 84 * q^49 + 1620 * q^51 - 200 * q^63 + 148 * q^64 + 2052 * q^66 - 748 * q^67 - 288 * q^69 - 2068 * q^70 - 628 * q^72 + 4560 * q^76 - 3312 * q^78 + 164 * q^81 - 5396 * q^82 + 5688 * q^87 - 1312 * q^90 - 1368 * q^93 - 932 * q^94 - 988 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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