LMFDB - Embedded newform 342.4.g.h.235.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,4,Mod(163,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("342.163");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	342.g (of order $3$, degree $2$, 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:	$20.1786532220$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.627014547.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 26x^{4} + 169x^{2} + 147 $ x^6 + 26x^4 + 169x^2 + 147
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.3
Root			$2.99107i$ of defining polynomial
Character	$\chi$	$=$	342.235
Dual form			342.4.g.h.163.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(7.12716 + 12.3446i) q^{5} +13.2543 q^{7} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(7.12716 + 12.3446i) q^{5} +13.2543 q^{7} -8.00000 q^{8} +(-14.2543 + 24.6892i) q^{10} +65.9138 q^{11} +(34.2629 - 59.3451i) q^{13} +(13.2543 + 22.9571i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(49.8470 + 86.3375i) q^{17} +(-80.3556 - 20.0493i) q^{19} -57.0172 q^{20} +(65.9138 + 114.166i) q^{22} +(1.76943 - 3.06475i) q^{23} +(-39.0927 + 67.7105i) q^{25} +137.052 q^{26} +(-26.5086 + 45.9143i) q^{28} +(-40.9504 + 70.9282i) q^{29} -247.190 q^{31} +(16.0000 - 27.7128i) q^{32} +(-99.6940 + 172.675i) q^{34} +(94.4655 + 163.619i) q^{35} +421.065 q^{37} +(-45.6293 - 159.229i) q^{38} +(-57.0172 - 98.7568i) q^{40} +(-172.629 - 299.003i) q^{41} +(183.084 + 317.111i) q^{43} +(-131.828 + 228.332i) q^{44} +7.07773 q^{46} +(-45.4699 + 78.7562i) q^{47} -167.323 q^{49} -156.371 q^{50} +(137.052 + 237.381i) q^{52} +(-344.246 + 596.251i) q^{53} +(469.778 + 813.680i) q^{55} -106.034 q^{56} -163.802 q^{58} +(91.1444 + 157.867i) q^{59} +(0.258685 - 0.448055i) q^{61} +(-247.190 - 428.145i) q^{62} +64.0000 q^{64} +976.789 q^{65} +(79.9310 - 138.445i) q^{67} -398.776 q^{68} +(-188.931 + 327.238i) q^{70} +(-395.942 - 685.792i) q^{71} +(-161.065 - 278.972i) q^{73} +(421.065 + 729.306i) q^{74} +(230.164 - 238.262i) q^{76} +873.642 q^{77} +(-159.185 - 275.717i) q^{79} +(114.034 - 197.514i) q^{80} +(345.259 - 598.005i) q^{82} -684.160 q^{83} +(-710.535 + 1230.68i) q^{85} +(-366.168 + 634.222i) q^{86} -527.311 q^{88} +(360.203 - 623.890i) q^{89} +(454.132 - 786.579i) q^{91} +(7.07773 + 12.2590i) q^{92} -181.880 q^{94} +(-325.207 - 1134.85i) q^{95} +(-207.696 - 359.740i) q^{97} +(-167.323 - 289.812i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 12 q^{4} + 10 q^{5} + 14 q^{7} - 48 q^{8}+O(q^{10}) $ 6 * q + 6 * q^2 - 12 * q^4 + 10 * q^5 + 14 * q^7 - 48 * q^8	$ 6 q + 6 q^{2} - 12 q^{4} + 10 q^{5} + 14 q^{7} - 48 q^{8} - 20 q^{10} + 88 q^{11} + 9 q^{13} + 14 q^{14} - 48 q^{16} - 84 q^{17} + 32 q^{19} - 80 q^{20} + 88 q^{22} - 2 q^{23} + 83 q^{25} + 36 q^{26} - 28 q^{28} + 92 q^{29} - 218 q^{31} + 96 q^{32} + 168 q^{34} + 282 q^{35} + 490 q^{37} + 74 q^{38} - 80 q^{40} - 688 q^{41} + 103 q^{43} - 176 q^{44} - 8 q^{46} + 322 q^{47} - 1508 q^{49} + 332 q^{50} + 36 q^{52} - 1322 q^{53} + 248 q^{55} - 112 q^{56} + 368 q^{58} + 252 q^{59} + 435 q^{61} - 218 q^{62} + 384 q^{64} + 3164 q^{65} + 719 q^{67} + 672 q^{68} - 564 q^{70} - 62 q^{71} + 581 q^{73} + 490 q^{74} + 20 q^{76} + 408 q^{77} + 489 q^{79} + 160 q^{80} + 1376 q^{82} - 4992 q^{83} - 1632 q^{85} - 206 q^{86} - 704 q^{88} + 1584 q^{89} + 1573 q^{91} - 8 q^{92} + 1288 q^{94} - 2362 q^{95} - 974 q^{97} - 1508 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 - 12 * q^4 + 10 * q^5 + 14 * q^7 - 48 * q^8 - 20 * q^10 + 88 * q^11 + 9 * q^13 + 14 * q^14 - 48 * q^16 - 84 * q^17 + 32 * q^19 - 80 * q^20 + 88 * q^22 - 2 * q^23 + 83 * q^25 + 36 * q^26 - 28 * q^28 + 92 * q^29 - 218 * q^31 + 96 * q^32 + 168 * q^34 + 282 * q^35 + 490 * q^37 + 74 * q^38 - 80 * q^40 - 688 * q^41 + 103 * q^43 - 176 * q^44 - 8 * q^46 + 322 * q^47 - 1508 * q^49 + 332 * q^50 + 36 * q^52 - 1322 * q^53 + 248 * q^55 - 112 * q^56 + 368 * q^58 + 252 * q^59 + 435 * q^61 - 218 * q^62 + 384 * q^64 + 3164 * q^65 + 719 * q^67 + 672 * q^68 - 564 * q^70 - 62 * q^71 + 581 * q^73 + 490 * q^74 + 20 * q^76 + 408 * q^77 + 489 * q^79 + 160 * q^80 + 1376 * q^82 - 4992 * q^83 - 1632 * q^85 - 206 * q^86 - 704 * q^88 + 1584 * q^89 + 1573 * q^91 - 8 * q^92 + 1288 * q^94 - 2362 * q^95 - 974 * q^97 - 1508 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	7.12716	+	12.3446i	0.637472	+	1.10413i	0.985986	+	0.166830i	$0.0533532\pi$
$5$	7.12716	+	12.3446i	0.637472	+	1.10413i	−0.348513	+	0.937304i	$0.613313\pi$
$6$		0			0
$7$	13.2543			0.715666			0.357833	−	0.933786i	$-0.383516\pi$
$7$	13.2543			0.715666			0.357833	+	0.933786i	$0.383516\pi$
$8$	−8.00000			−0.353553
$9$		0			0
$10$	−14.2543	+	24.6892i	−0.450761	+	0.780741i
$11$	65.9138			1.80671			0.903353	−	0.428898i	$-0.141098\pi$
$11$	65.9138			1.80671			0.903353	+	0.428898i	$0.141098\pi$
$12$		0			0
$13$	34.2629	−	59.3451i	0.730987	−	1.26611i	−0.225475	−	0.974249i	$-0.572393\pi$
$13$	34.2629	−	59.3451i	0.730987	−	1.26611i	0.956462	−	0.291857i	$-0.0942732\pi$
$14$	13.2543	+	22.9571i	0.253026	+	0.438254i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	49.8470	+	86.3375i	0.711157	+	1.23176i	0.964423	+	0.264364i	$0.0851620\pi$
$17$	49.8470	+	86.3375i	0.711157	+	1.23176i	−0.253266	+	0.967397i	$0.581505\pi$
$18$		0			0
$19$	−80.3556	−	20.0493i	−0.970255	−	0.242085i
$19$	−80.3556	−	20.0493i	−0.970255	−	0.242085i
$20$	−57.0172			−0.637472
$21$		0			0
$22$	65.9138	+	114.166i	0.638767	+	1.10638i
$23$	1.76943	−	3.06475i	0.0160414	−	0.0277845i	−0.857893	−	0.513828i	$-0.828227\pi$
$23$	1.76943	−	3.06475i	0.0160414	−	0.0277845i	0.873935	+	0.486043i	$0.161560\pi$
$24$		0			0
$25$	−39.0927	+	67.7105i	−0.312742	+	0.541684i
$26$	137.052			1.03377
$27$		0			0
$28$	−26.5086	+	45.9143i	−0.178916	+	0.309892i
$29$	−40.9504	+	70.9282i	−0.262217	+	0.454174i	−0.966831	−	0.255418i	$-0.917787\pi$
$29$	−40.9504	+	70.9282i	−0.262217	+	0.454174i	0.704614	+	0.709591i	$0.251120\pi$
$30$		0			0
$31$	−247.190			−1.43215			−0.716074	−	0.698025i	$-0.754063\pi$
$31$	−247.190			−1.43215			−0.716074	+	0.698025i	$0.754063\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$		0			0
$34$	−99.6940	+	172.675i	−0.502864	+	0.870986i
$35$	94.4655	+	163.619i	0.456217	+	0.790191i
$36$		0			0
$37$	421.065			1.87088			0.935441	−	0.353483i	$-0.115003\pi$
$37$	421.065			1.87088			0.935441	+	0.353483i	$0.115003\pi$
$38$	−45.6293	−	159.229i	−0.194791	−	0.679747i
$39$		0			0
$40$	−57.0172	−	98.7568i	−0.225380	−	0.390370i
$41$	−172.629	−	299.003i	−0.657565	−	1.13894i	−0.981244	−	0.192769i	$-0.938253\pi$
$41$	−172.629	−	299.003i	−0.657565	−	1.13894i	0.323679	−	0.946167i	$-0.395080\pi$
$42$		0			0
$43$	183.084	+	317.111i	0.649304	+	1.12463i	0.983289	+	0.182049i	$0.0582730\pi$
$43$	183.084	+	317.111i	0.649304	+	1.12463i	−0.333986	+	0.942578i	$0.608394\pi$
$44$	−131.828	+	228.332i	−0.451677	+	0.782327i
$45$		0			0
$46$	7.07773			0.0226860
$47$	−45.4699	+	78.7562i	−0.141116	+	0.244421i	−0.927917	−	0.372786i	$-0.878403\pi$
$47$	−45.4699	+	78.7562i	−0.141116	+	0.244421i	0.786801	+	0.617207i	$0.211736\pi$
$48$		0			0
$49$	−167.323			−0.487823
$50$	−156.371			−0.442283
$51$		0			0
$52$	137.052	+	237.381i	0.365493	+	0.633053i
$53$	−344.246	+	596.251i	−0.892185	+	1.54531i	−0.0549339	+	0.998490i	$0.517495\pi$
$53$	−344.246	+	596.251i	−0.892185	+	1.54531i	−0.837251	+	0.546819i	$0.815839\pi$
$54$		0			0
$55$	469.778	+	813.680i	1.15172	+	1.99485i
$56$	−106.034			−0.253026
$57$		0			0
$58$	−163.802			−0.370831
$59$	91.1444	+	157.867i	0.201118	+	0.348347i	0.948889	−	0.315610i	$-0.102209\pi$
$59$	91.1444	+	157.867i	0.201118	+	0.348347i	−0.747771	+	0.663957i	$0.768876\pi$
$60$		0			0
$61$	0.258685	−	0.448055i	0.000542971	−	0.000940453i	−0.865754	−	0.500470i	$-0.833161\pi$
$61$	0.258685	−	0.448055i	0.000542971	−	0.000940453i	0.866297	+	0.499530i	$0.166494\pi$
$62$	−247.190	−	428.145i	−0.506341	−	0.877008i
$63$		0			0
$64$	64.0000			0.125000
$65$	976.789			1.86393
$66$		0			0
$67$	79.9310	−	138.445i	0.145748	−	0.252443i	−0.783904	−	0.620883i	$-0.786774\pi$
$67$	79.9310	−	138.445i	0.145748	−	0.252443i	0.929652	+	0.368439i	$0.120108\pi$
$68$	−398.776			−0.711157
$69$		0			0
$70$	−188.931	+	327.238i	−0.322594	+	0.558749i
$71$	−395.942	−	685.792i	−0.661826	−	1.14632i	−0.980135	−	0.198330i	$-0.936448\pi$
$71$	−395.942	−	685.792i	−0.661826	−	1.14632i	0.318309	−	0.947987i	$-0.396885\pi$
$72$		0			0
$73$	−161.065	−	278.972i	−0.258235	−	0.447277i	0.707534	−	0.706679i	$-0.249808\pi$
$73$	−161.065	−	278.972i	−0.258235	−	0.447277i	−0.965769	+	0.259403i	$0.916474\pi$
$74$	421.065	+	729.306i	0.661457	+	1.14568i
$75$		0			0
$76$	230.164	−	238.262i	0.347390	−	0.359611i
$77$	873.642			1.29300
$78$		0			0
$79$	−159.185	−	275.717i	−0.226706	−	0.392666i	0.730124	−	0.683315i	$-0.239462\pi$
$79$	−159.185	−	275.717i	−0.226706	−	0.392666i	−0.956830	+	0.290649i	$0.906129\pi$
$80$	114.034	−	197.514i	0.159368	−	0.276034i
$81$		0			0
$82$	345.259	−	598.005i	0.464969	−	0.805349i
$83$	−684.160			−0.904774			−0.452387	−	0.891822i	$-0.649427\pi$
$83$	−684.160			−0.904774			−0.452387	+	0.891822i	$0.649427\pi$
$84$		0			0
$85$	−710.535	+	1230.68i	−0.906686	+	1.57043i
$86$	−366.168	+	634.222i	−0.459127	+	0.795232i
$87$		0			0
$88$	−527.311			−0.638767
$89$	360.203	−	623.890i	0.429005	−	0.743058i	−0.567780	−	0.823180i	$-0.692198\pi$
$89$	360.203	−	623.890i	0.429005	−	0.743058i	0.996785	+	0.0801222i	$0.0255310\pi$
$90$		0			0
$91$	454.132	−	786.579i	0.523142	−	0.906109i
$92$	7.07773	+	12.2590i	0.00802070	+	0.0138923i
$93$		0			0
$94$	−181.880			−0.199569
$95$	−325.207	−	1134.85i	−0.351216	−	1.22561i
$96$		0			0
$97$	−207.696	−	359.740i	−0.217406	−	0.376558i	0.736608	−	0.676319i	$-0.236426\pi$
$97$	−207.696	−	359.740i	−0.217406	−	0.376558i	−0.954014	+	0.299762i	$0.903093\pi$
$98$	−167.323	−	289.812i	−0.172471	−	0.298729i
$99$		0			0
$100$	−156.371	−	270.842i	−0.156371	−	0.270842i
$101$	168.670	−	292.146i	0.166172	−	0.287818i	−0.770899	−	0.636957i	$-0.780193\pi$
$101$	168.670	−	292.146i	0.166172	−	0.287818i	0.937071	+	0.349140i	$0.113526\pi$
$102$		0			0
$103$	−1467.05			−1.40342			−0.701711	−	0.712462i	$-0.747580\pi$
$103$	−1467.05			−1.40342			−0.701711	+	0.712462i	$0.747580\pi$
$104$	−274.103	+	474.761i	−0.258443	+	0.447636i
$105$		0			0
$106$	−1376.98			−1.26174
$107$	−382.014			−0.345146			−0.172573	−	0.984997i	$-0.555208\pi$
$107$	−382.014			−0.345146			−0.172573	+	0.984997i	$0.555208\pi$
$108$		0			0
$109$	66.4287	+	115.058i	0.0583736	+	0.101106i	0.893735	−	0.448594i	$-0.148075\pi$
$109$	66.4287	+	115.058i	0.0583736	+	0.101106i	−0.835362	+	0.549700i	$0.814742\pi$
$110$	−939.556	+	1627.36i	−0.814393	+	1.41057i
$111$		0			0
$112$	−106.034	−	183.657i	−0.0894582	−	0.154946i
$113$	1137.94			0.947331			0.473665	−	0.880705i	$-0.342931\pi$
$113$	1137.94			0.947331			0.473665	+	0.880705i	$0.342931\pi$
$114$		0			0
$115$	50.4441			0.0409038
$116$	−163.802	−	283.713i	−0.131109	−	0.227087i
$117$		0			0
$118$	−182.289	+	315.733i	−0.142212	+	0.246319i
$119$	660.688	+	1144.34i	0.508951	+	0.881529i
$120$		0			0
$121$	3013.63			2.26419
$122$	1.03474			0.000767877
$123$		0			0
$124$	494.379	−	856.290i	0.358037	−	0.620138i
$125$	667.310			0.477488
$126$		0			0
$127$	754.987	−	1307.68i	0.527514	−	0.913681i	−0.471971	−	0.881614i	$-0.656457\pi$
$127$	754.987	−	1307.68i	0.527514	−	0.913681i	0.999486	−	0.0320676i	$-0.0102092\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$		0			0
$130$	976.789	+	1691.85i	0.659001	+	1.14142i
$131$	−185.472	−	321.247i	−0.123701	−	0.214256i	0.797524	−	0.603288i	$-0.206143\pi$
$131$	−185.472	−	321.247i	−0.123701	−	0.214256i	−0.921224	+	0.389032i	$0.872810\pi$
$132$		0			0
$133$	−1065.06	−	265.739i	−0.694378	−	0.173252i
$134$	319.724			0.206119
$135$		0			0
$136$	−398.776	−	690.700i	−0.251432	−	0.435493i
$137$	−845.187	+	1463.91i	−0.527075	+	0.912920i	0.472428	+	0.881370i	$0.343378\pi$
$137$	−845.187	+	1463.91i	−0.527075	+	0.912920i	−0.999502	+	0.0315505i	$0.989955\pi$
$138$		0			0
$139$	1355.76	−	2348.25i	0.827296	−	1.43292i	−0.0728556	−	0.997343i	$-0.523211\pi$
$139$	1355.76	−	2348.25i	0.827296	−	1.43292i	0.900152	−	0.435576i	$-0.143455\pi$
$140$	−755.724			−0.456217
$141$		0			0
$142$	791.884	−	1371.58i	0.467982	−	0.810568i
$143$	2258.40	−	3911.67i	1.32068	−	2.28748i
$144$		0			0
$145$	−1167.44			−0.668625
$146$	322.129	−	557.944i	0.182600	−	0.316273i
$147$		0			0
$148$	−842.130	+	1458.61i	−0.467720	+	0.810116i
$149$	1299.45	+	2250.71i	0.714464	+	1.23749i	0.963166	+	0.268908i	$0.0866628\pi$
$149$	1299.45	+	2250.71i	0.714464	+	1.23749i	−0.248702	+	0.968580i	$0.580004\pi$
$150$		0			0
$151$	594.863			0.320591			0.160296	−	0.987069i	$-0.448755\pi$
$151$	594.863			0.320591			0.160296	+	0.987069i	$0.448755\pi$
$152$	642.845	+	160.394i	0.343037	+	0.0855900i
$153$		0			0
$154$	873.642	+	1513.19i	0.457144	+	0.791796i
$155$	−1761.76	−	3051.46i	−0.912954	−	1.58128i
$156$		0			0
$157$	29.1274	+	50.4502i	0.0148065	+	0.0256456i	0.873334	−	0.487122i	$-0.161953\pi$
$157$	29.1274	+	50.4502i	0.0148065	+	0.0256456i	−0.858527	+	0.512768i	$0.828620\pi$
$158$	318.371	−	551.434i	0.160305	−	0.277657i
$159$		0			0
$160$	456.138			0.225380
$161$	23.4526	−	40.6211i	0.0114803	−	0.0198844i
$162$		0			0
$163$	1152.53			0.553825			0.276912	−	0.960895i	$-0.410689\pi$
$163$	1152.53			0.553825			0.276912	+	0.960895i	$0.410689\pi$
$164$	1381.03			0.657565
$165$		0			0
$166$	−684.160	−	1185.00i	−0.319886	−	0.554059i
$167$	629.554	−	1090.42i	0.291715	−	0.505265i	−0.682500	−	0.730885i	$-0.739107\pi$
$167$	629.554	−	1090.42i	0.291715	−	0.505265i	0.974215	+	0.225620i	$0.0724408\pi$
$168$		0			0
$169$	−1249.40	−	2164.02i	−0.568683	−	0.984988i
$170$	−2842.14			−1.28225
$171$		0			0
$172$	−1464.67			−0.649304
$173$	−637.050	−	1103.40i	−0.279965	−	0.484914i	0.691411	−	0.722462i	$-0.256990\pi$
$173$	−637.050	−	1103.40i	−0.279965	−	0.484914i	−0.971376	+	0.237548i	$0.923656\pi$
$174$		0			0
$175$	−518.147	+	897.456i	−0.223818	+	0.387665i
$176$	−527.311	−	913.329i	−0.225838	−	0.391163i
$177$		0			0
$178$	1440.81			0.606704
$179$	−2034.50			−0.849528			−0.424764	−	0.905304i	$-0.639643\pi$
$179$	−2034.50			−0.849528			−0.424764	+	0.905304i	$0.639643\pi$
$180$		0			0
$181$	−516.657	+	894.876i	−0.212170	+	0.367490i	−0.952393	−	0.304872i	$-0.901386\pi$
$181$	−516.657	+	894.876i	−0.212170	+	0.367490i	0.740223	+	0.672361i	$0.234720\pi$
$182$	1816.53			0.739835
$183$		0			0
$184$	−14.1555	+	24.5180i	−0.00567149	+	0.00982331i
$185$	3000.99	+	5197.87i	1.19264	+	2.06570i
$186$		0			0
$187$	3285.61	+	5690.84i	1.28485	+	2.22543i
$188$	−181.880	−	315.025i	−0.0705582	−	0.122210i
$189$		0			0
$190$	1640.41	−	1698.13i	0.626359	−	0.648395i
$191$	1135.46			0.430154			0.215077	−	0.976597i	$-0.431000\pi$
$191$	1135.46			0.430154			0.215077	+	0.976597i	$0.431000\pi$
$192$		0			0
$193$	−545.536	−	944.897i	−0.203464	−	0.352410i	0.746178	−	0.665746i	$-0.231887\pi$
$193$	−545.536	−	944.897i	−0.203464	−	0.352410i	−0.949642	+	0.313336i	$0.898553\pi$
$194$	415.392	−	719.480i	0.153729	−	0.266266i
$195$		0			0
$196$	334.646	−	579.625i	0.121956	−	0.211233i
$197$	−4138.08			−1.49658			−0.748289	−	0.663373i	$-0.769124\pi$
$197$	−4138.08			−1.49658			−0.748289	+	0.663373i	$0.769124\pi$
$198$		0			0
$199$	1367.12	−	2367.91i	0.486997	−	0.843503i	−0.512892	−	0.858453i	$-0.671426\pi$
$199$	1367.12	−	2367.91i	0.486997	−	0.843503i	0.999888	+	0.0149506i	$0.00475910\pi$
$200$	312.742	−	541.684i	0.110571	−	0.191514i
$201$		0			0
$202$	674.682			0.235002
$203$	−542.770	+	940.104i	−0.187660	+	0.325036i
$204$		0			0
$205$	2460.71	−	4262.08i	0.838359	−	1.45208i
$206$	−1467.05	−	2541.00i	−0.496185	−	0.859417i
$207$		0			0
$208$	−1096.41			−0.365493
$209$	−5296.55	−	1321.52i	−1.75297	−	0.437377i
$210$		0			0
$211$	−1529.00	−	2648.31i	−0.498867	−	0.864063i	0.501132	−	0.865371i	$-0.332917\pi$
$211$	−1529.00	−	2648.31i	−0.498867	−	0.864063i	−0.999999	+	0.00130803i	$0.999584\pi$
$212$	−1376.98	−	2385.00i	−0.446092	−	0.772655i
$213$		0			0
$214$	−382.014	−	661.667i	−0.122028	−	0.211358i
$215$	−2609.74	+	4520.20i	−0.827826	+	1.43384i
$216$		0			0
$217$	−3276.33			−1.02494
$218$	−132.857	+	230.116i	−0.0412764	+	0.0714927i
$219$		0			0
$220$	−3758.23			−1.15172
$221$	6831.62			2.07939
$222$		0			0
$223$	−809.133	−	1401.46i	−0.242976	−	0.420846i	0.718585	−	0.695439i	$-0.244790\pi$
$223$	−809.133	−	1401.46i	−0.242976	−	0.420846i	−0.961561	+	0.274593i	$0.911457\pi$
$224$	212.069	−	367.314i	0.0632565	−	0.109563i
$225$		0			0
$226$	1137.94	+	1970.97i	0.334932	+	0.580119i
$227$	6065.43			1.77347			0.886733	−	0.462282i	$-0.152969\pi$
$227$	6065.43			1.77347			0.886733	+	0.462282i	$0.152969\pi$
$228$		0			0
$229$	−1916.36			−0.552999			−0.276500	−	0.961014i	$-0.589174\pi$
$229$	−1916.36			−0.552999			−0.276500	+	0.961014i	$0.589174\pi$
$230$	50.4441	+	87.3717i	0.0144617	+	0.0250483i
$231$		0			0
$232$	327.603	−	567.426i	0.0927078	−	0.160575i
$233$	−2004.27	−	3471.50i	−0.563537	−	0.976074i	−0.997184	−	0.0749917i	$-0.976107\pi$
$233$	−2004.27	−	3471.50i	−0.563537	−	0.976074i	0.433647	−	0.901083i	$-0.357226\pi$
$234$		0			0
$235$	−1296.29			−0.359831
$236$	−729.155			−0.201118
$237$		0			0
$238$	−1321.38	+	2288.69i	−0.359883	+	0.623335i
$239$	−530.292			−0.143522			−0.0717610	−	0.997422i	$-0.522862\pi$
$239$	−530.292			−0.143522			−0.0717610	+	0.997422i	$0.522862\pi$
$240$		0			0
$241$	−635.613	+	1100.91i	−0.169890	+	0.294258i	−0.938381	−	0.345603i	$-0.887674\pi$
$241$	−635.613	+	1100.91i	−0.169890	+	0.294258i	0.768491	+	0.639860i	$0.221008\pi$
$242$	3013.63	+	5219.77i	0.800511	+	1.38653i
$243$		0			0
$244$	1.03474	+	1.79222i	0.000271485	+	0.000470226i
$245$	−1192.54	−	2065.54i	−0.310973	−	0.538622i
$246$		0			0
$247$	−3943.05	+	4081.77i	−1.01575	+	1.05148i
$248$	1977.52			0.506341
$249$		0			0
$250$	667.310	+	1155.81i	0.168818	+	0.292401i
$251$	275.994	−	478.036i	0.0694048	−	0.120213i	−0.829235	−	0.558901i	$-0.811223\pi$
$251$	275.994	−	478.036i	0.0694048	−	0.120213i	0.898639	+	0.438688i	$0.144557\pi$
$252$		0			0
$253$	116.630	−	202.009i	0.0289821	−	0.0501984i
$254$	3019.95			0.746018
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−2617.92	+	4534.37i	−0.635414	+	1.10057i	0.351014	+	0.936370i	$0.385837\pi$
$257$	−2617.92	+	4534.37i	−0.635414	+	1.10057i	−0.986427	+	0.164198i	$0.947496\pi$
$258$		0			0
$259$	5580.92			1.33893
$260$	−1953.58	+	3383.70i	−0.465984	+	0.807107i
$261$		0			0
$262$	370.944	−	642.494i	0.0874695	−	0.151502i
$263$	−907.129	−	1571.19i	−0.212684	−	0.368380i	0.739869	−	0.672750i	$-0.234887\pi$
$263$	−907.129	−	1571.19i	−0.212684	−	0.368380i	−0.952554	+	0.304371i	$0.901554\pi$
$264$		0			0
$265$	−9813.97			−2.27497
$266$	−604.785	−	2110.47i	−0.139405	−	0.486472i
$267$		0			0
$268$	319.724	+	553.779i	0.0728741	+	0.126222i
$269$	506.699	+	877.629i	0.114848	+	0.198922i	0.917719	−	0.397231i	$-0.130029\pi$
$269$	506.699	+	877.629i	0.114848	+	0.198922i	−0.802871	+	0.596153i	$0.796695\pi$
$270$		0			0
$271$	959.258	+	1661.48i	0.215021	+	0.372428i	0.953279	−	0.302091i	$-0.0976845\pi$
$271$	959.258	+	1661.48i	0.215021	+	0.372428i	−0.738258	+	0.674519i	$0.764351\pi$
$272$	797.552	−	1381.40i	0.177789	−	0.307940i
$273$		0			0
$274$	−3380.75			−0.745396
$275$	−2576.75	+	4463.06i	−0.565032	+	0.978664i
$276$		0			0
$277$	6283.45			1.36295			0.681473	−	0.731844i	$-0.261340\pi$
$277$	6283.45			1.36295			0.681473	+	0.731844i	$0.261340\pi$
$278$	5423.04			1.16997
$279$		0			0
$280$	−755.724	−	1308.95i	−0.161297	−	0.279375i
$281$	−4028.68	+	6977.88i	−0.855270	+	1.48137i	0.0211241	+	0.999777i	$0.493276\pi$
$281$	−4028.68	+	6977.88i	−0.855270	+	1.48137i	−0.876394	+	0.481594i	$0.840058\pi$
$282$		0			0
$283$	96.7083	+	167.504i	0.0203135	+	0.0351840i	0.876003	−	0.482305i	$-0.160200\pi$
$283$	96.7083	+	167.504i	0.0203135	+	0.0351840i	−0.855690	+	0.517489i	$0.826867\pi$
$284$	3167.54			0.661826
$285$		0			0
$286$	9033.61			1.86772
$287$	−2288.08	−	3963.07i	−0.470597	−	0.815097i
$288$		0			0
$289$	−2512.95	+	4352.55i	−0.511489	+	0.885926i
$290$	−1167.44	−	2022.07i	−0.236395	−	0.409447i
$291$		0			0
$292$	1288.52			0.258235
$293$	4735.47			0.944194			0.472097	−	0.881547i	$-0.343497\pi$
$293$	4735.47			0.944194			0.472097	+	0.881547i	$0.343497\pi$
$294$		0			0
$295$	−1299.20	+	2250.28i	−0.256415	+	0.444124i
$296$	−3368.52			−0.661457
$297$		0			0
$298$	−2598.90	+	4501.43i	−0.505202	+	0.875036i
$299$	−121.252	−	210.014i	−0.0234521	−	0.0406202i
$300$		0			0
$301$	2426.65	+	4203.09i	0.464684	+	0.804857i
$302$	594.863	+	1030.33i	0.113346	+	0.196321i
$303$		0			0
$304$	365.034	+	1273.83i	0.0688689	+	0.240327i
$305$	7.37475			0.00138451
$306$		0			0
$307$	14.3561	+	24.8655i	0.00266888	+	0.00462263i	0.867357	−	0.497687i	$-0.165817\pi$
$307$	14.3561	+	24.8655i	0.00266888	+	0.00462263i	−0.864688	+	0.502310i	$0.832484\pi$
$308$	−1747.28	+	3026.39i	−0.323249	+	0.559884i
$309$		0			0
$310$	3523.52	−	6102.91i	0.645556	−	1.11814i
$311$	1165.69			0.212540			0.106270	−	0.994337i	$-0.466109\pi$
$311$	1165.69			0.212540			0.106270	+	0.994337i	$0.466109\pi$
$312$		0			0
$313$	−1256.38	+	2176.11i	−0.226884	+	0.392974i	−0.956883	−	0.290474i	$-0.906187\pi$
$313$	−1256.38	+	2176.11i	−0.226884	+	0.392974i	0.729999	+	0.683448i	$0.239520\pi$
$314$	−58.2549	+	100.900i	−0.0104698	+	0.0181342i
$315$		0			0
$316$	1273.48			0.226706
$317$	−863.783	+	1496.12i	−0.153044	+	0.265080i	−0.932345	−	0.361570i	$-0.882241\pi$
$317$	−863.783	+	1496.12i	−0.153044	+	0.265080i	0.779301	+	0.626649i	$0.215574\pi$
$318$		0			0
$319$	−2699.20	+	4675.15i	−0.473750	+	0.820558i
$320$	456.138	+	790.054i	0.0796840	+	0.138017i
$321$		0			0
$322$	93.8104			0.0162356
$323$	−2274.48	−	7937.10i	−0.391813	−	1.36728i
$324$		0			0
$325$	2678.86	+	4639.92i	0.457220	+	0.791928i
$326$	1152.53	+	1996.25i	0.195807	+	0.339147i
$327$		0			0
$328$	1381.03	+	2392.02i	0.232484	+	0.402675i
$329$	−602.673	+	1043.86i	−0.100992	+	0.174924i
$330$		0			0
$331$	−6816.13			−1.13187			−0.565934	−	0.824450i	$-0.691484\pi$
$331$	−6816.13			−1.13187			−0.565934	+	0.824450i	$0.691484\pi$
$332$	1368.32	−	2370.00i	0.226194	−	0.391779i
$333$		0			0
$334$	2518.22			0.412547
$335$	2278.72			0.371642
$336$		0			0
$337$	5204.19	+	9013.93i	0.841218	+	1.45703i	0.888865	+	0.458168i	$0.151494\pi$
$337$	5204.19	+	9013.93i	0.841218	+	1.45703i	−0.0476473	+	0.998864i	$0.515172\pi$
$338$	2498.79	−	4328.04i	0.402120	−	0.696492i
$339$		0			0
$340$	−2842.14	−	4922.73i	−0.453343	−	0.785213i
$341$	−16293.2			−2.58747
$342$		0			0
$343$	−6763.98			−1.06478
$344$	−1464.67	−	2536.89i	−0.229564	−	0.397616i
$345$		0			0
$346$	1274.10	−	2206.80i	0.197965	−	0.342886i
$347$	−2792.02	−	4835.92i	−0.431940	−	0.748143i	0.565100	−	0.825022i	$-0.308838\pi$
$347$	−2792.02	−	4835.92i	−0.431940	−	0.748143i	−0.997040	+	0.0768797i	$0.975504\pi$
$348$		0			0
$349$	5505.82			0.844470			0.422235	−	0.906486i	$-0.361246\pi$
$349$	5505.82			0.844470			0.422235	+	0.906486i	$0.361246\pi$
$350$	−2072.59			−0.316527
$351$		0			0
$352$	1054.62	−	1826.66i	0.159692	−	0.276594i
$353$	5782.46			0.871868			0.435934	−	0.899979i	$-0.356418\pi$
$353$	5782.46			0.871868			0.435934	+	0.899979i	$0.356418\pi$
$354$		0			0
$355$	5643.88	−	9775.49i	0.843792	−	1.46149i
$356$	1440.81	+	2495.56i	0.214502	+	0.371529i
$357$		0			0
$358$	−2034.50	−	3523.85i	−0.300353	−	0.520227i
$359$	−951.820	−	1648.60i	−0.139931	−	0.242367i	0.787539	−	0.616264i	$-0.211355\pi$
$359$	−951.820	−	1648.60i	−0.139931	−	0.242367i	−0.927470	+	0.373897i	$0.878021\pi$
$360$		0			0
$361$	6055.05	+	3222.14i	0.882790	+	0.469769i
$362$	−2066.63			−0.300054
$363$		0			0
$364$	1816.53	+	3146.32i	0.261571	+	0.453054i
$365$	2295.87	−	3976.55i	0.329236	−	0.570253i
$366$		0			0
$367$	6374.02	−	11040.1i	0.906597	−	1.57027i	0.0878374	−	0.996135i	$-0.472004\pi$
$367$	6374.02	−	11040.1i	0.906597	−	1.57027i	0.818759	−	0.574137i	$-0.194662\pi$
$368$	−56.6218			−0.00802070
$369$		0			0
$370$	−6001.99	+	10395.7i	−0.843320	+	1.46067i
$371$	−4562.74	+	7902.90i	−0.638506	+	1.10592i
$372$		0			0
$373$	−736.660			−0.102260			−0.0511298	−	0.998692i	$-0.516282\pi$
$373$	−736.660			−0.102260			−0.0511298	+	0.998692i	$0.516282\pi$
$374$	−6571.21	+	11381.7i	−0.908528	+	1.57362i
$375$		0			0
$376$	363.760	−	630.050i	0.0498922	−	0.0864158i
$377$	2806.16	+	4860.42i	0.383355	+	0.663990i
$378$		0			0
$379$	1543.57			0.209202			0.104601	−	0.994514i	$-0.466643\pi$
$379$	1543.57			0.209202			0.104601	+	0.994514i	$0.466643\pi$
$380$	4581.66	+	1143.15i	0.618511	+	0.154323i
$381$		0			0
$382$	1135.46	+	1966.68i	0.152082	+	0.263414i
$383$	3282.18	+	5684.90i	0.437889	+	0.758446i	0.997527	−	0.0702912i	$-0.0223929\pi$
$383$	3282.18	+	5684.90i	0.437889	+	0.758446i	−0.559637	+	0.828738i	$0.689060\pi$
$384$		0			0
$385$	6226.59	+	10784.8i	0.824250	+	1.42764i
$386$	1091.07	−	1889.79i	0.143871	−	0.249192i
$387$		0			0
$388$	1661.57			0.217406
$389$	−1749.13	+	3029.59i	−0.227981	+	0.394875i	−0.957210	−	0.289395i	$-0.906546\pi$
$389$	−1749.13	+	3029.59i	−0.227981	+	0.394875i	0.729229	+	0.684270i	$0.239879\pi$
$390$		0			0
$391$	352.803			0.0456318
$392$	1338.59			0.172471
$393$		0			0
$394$	−4138.08	−	7167.36i	−0.529120	−	0.916463i
$395$	2269.08	−	3930.16i	0.289037	−	0.500627i
$396$		0			0
$397$	−4305.30	−	7457.00i	−0.544274	−	0.942710i	−0.998652	−	0.0519013i	$-0.983472\pi$
$397$	−4305.30	−	7457.00i	−0.544274	−	0.942710i	0.454378	−	0.890809i	$-0.349861\pi$
$398$	5468.47			0.688717
$399$		0			0
$400$	1250.97			0.156371
$401$	882.872	+	1529.18i	0.109946	+	0.190433i	0.915748	−	0.401752i	$-0.131599\pi$
$401$	882.872	+	1529.18i	0.109946	+	0.190433i	−0.805802	+	0.592185i	$0.798265\pi$
$402$		0			0
$403$	−8469.44	+	14669.5i	−1.04688	+	1.81325i
$404$	674.682	+	1168.58i	0.0830858	+	0.143909i
$405$		0			0
$406$	−2171.08			−0.265391
$407$	27754.0			3.38013
$408$		0			0
$409$	−6697.86	+	11601.0i	−0.809751	+	1.40253i	0.103286	+	0.994652i	$0.467064\pi$
$409$	−6697.86	+	11601.0i	−0.809751	+	1.40253i	−0.913037	+	0.407877i	$0.866269\pi$
$410$	9842.85			1.18562
$411$		0			0
$412$	2934.10	−	5082.00i	0.350856	−	0.607700i
$413$	1208.06	+	2092.41i	0.143934	+	0.249300i
$414$		0			0
$415$	−4876.11	−	8445.67i	−0.576769	−	0.998992i
$416$	−1096.41	−	1899.04i	−0.129221	−	0.223818i
$417$		0			0
$418$	−3007.60	−	10495.4i	−0.351930	−	1.22810i
$419$	−9117.71			−1.06308			−0.531539	−	0.847034i	$-0.678386\pi$
$419$	−9117.71			−1.06308			−0.531539	+	0.847034i	$0.678386\pi$
$420$		0			0
$421$	−4102.23	−	7105.27i	−0.474894	−	0.822540i	0.524693	−	0.851292i	$-0.324180\pi$
$421$	−4102.23	−	7105.27i	−0.474894	−	0.822540i	−0.999587	+	0.0287514i	$0.990847\pi$
$422$	3058.01	−	5296.62i	0.352752	−	0.610985i
$423$		0			0
$424$	2753.97	−	4770.01i	0.315435	−	0.546349i
$425$	−7794.61			−0.889634
$426$		0			0
$427$	3.42869	−	5.93867i	0.000388585	−	0.000673050i
$428$	764.027	−	1323.33i	0.0862865	−	0.149453i
$429$		0			0
$430$	−10439.0			−1.17072
$431$	−635.672	+	1101.02i	−0.0710423	+	0.123049i	−0.899358	−	0.437212i	$-0.855966\pi$
$431$	−635.672	+	1101.02i	−0.0710423	+	0.123049i	0.828316	+	0.560261i	$0.189299\pi$
$432$		0			0
$433$	1983.79	−	3436.03i	0.220173	−	0.381351i	−0.734687	−	0.678406i	$-0.762671\pi$
$433$	1983.79	−	3436.03i	0.220173	−	0.381351i	0.954860	+	0.297055i	$0.0960044\pi$
$434$	−3276.33	−	5674.77i	−0.362370	−	0.627644i
$435$		0			0
$436$	−531.430			−0.0583736
$437$	−203.630	+	210.794i	−0.0222905	+	0.0230747i
$438$		0			0
$439$	−104.519	−	181.032i	−0.0113632	−	0.0196816i	0.860288	−	0.509808i	$-0.170284\pi$
$439$	−104.519	−	181.032i	−0.0113632	−	0.0196816i	−0.871651	+	0.490127i	$0.836950\pi$
$440$	−3758.23	−	6509.44i	−0.407196	−	0.705285i
$441$		0			0
$442$	6831.62	+	11832.7i	0.735174	+	1.27336i
$443$	2867.02	−	4965.83i	0.307486	−	0.532581i	−0.670326	−	0.742067i	$-0.733846\pi$
$443$	2867.02	−	4965.83i	0.307486	−	0.532581i	0.977812	+	0.209486i	$0.0671789\pi$
$444$		0			0
$445$	10268.9			1.09391
$446$	1618.27	−	2802.92i	0.171810	−	0.297583i
$447$		0			0
$448$	848.276			0.0894582
$449$	−9741.13			−1.02386			−0.511929	−	0.859028i	$-0.671069\pi$
$449$	−9741.13			−1.02386			−0.511929	+	0.859028i	$0.671069\pi$
$450$		0			0
$451$	−11378.7	−	19708.4i	−1.18803	−	2.05772i
$452$	−2275.88	+	3941.94i	−0.236833	+	0.410206i
$453$		0			0
$454$	6065.43	+	10505.6i	0.627015	+	1.08602i
$455$	12946.7			1.33395
$456$		0			0
$457$	−17233.8			−1.76403			−0.882016	−	0.471220i	$-0.843814\pi$
$457$	−17233.8			−1.76403			−0.882016	+	0.471220i	$0.843814\pi$
$458$	−1916.36	−	3319.24i	−0.195515	−	0.338641i
$459$		0			0
$460$	−100.888	+	174.743i	−0.0102259	+	0.0177118i
$461$	832.617	+	1442.14i	0.0841190	+	0.145698i	0.905015	−	0.425379i	$-0.139859\pi$
$461$	832.617	+	1442.14i	0.0841190	+	0.145698i	−0.820896	+	0.571077i	$0.806526\pi$
$462$		0			0
$463$	−10694.0			−1.07342			−0.536710	−	0.843767i	$-0.680333\pi$
$463$	−10694.0			−1.07342			−0.536710	+	0.843767i	$0.680333\pi$
$464$	1310.41			0.131109
$465$		0			0
$466$	4008.54	−	6942.99i	0.398481	−	0.690189i
$467$	−13212.7			−1.30923			−0.654614	−	0.755963i	$-0.727169\pi$
$467$	−13212.7			−1.30923			−0.654614	+	0.755963i	$0.727169\pi$
$468$		0			0
$469$	1059.43	−	1834.99i	0.104307	−	0.180665i
$470$	−1296.29	−	2245.23i	−0.127220	−	0.220351i
$471$		0			0
$472$	−729.155	−	1262.93i	−0.0711061	−	0.123159i
$473$	12067.8	+	20902.0i	1.17310	+	2.03187i
$474$		0			0
$475$	4498.86	−	4657.14i	0.434573	−	0.449862i
$476$	−5285.50			−0.508951
$477$		0			0
$478$	−530.292	−	918.493i	−0.0507427	−	0.0878889i
$479$	2704.77	−	4684.79i	0.258004	−	0.446876i	−0.707703	−	0.706510i	$-0.750269\pi$
$479$	2704.77	−	4684.79i	0.258004	−	0.446876i	0.965707	+	0.259634i	$0.0836019\pi$
$480$		0			0
$481$	14426.9	−	24988.1i	1.36759	−	2.36874i
$482$	−2542.45			−0.240260
$483$		0			0
$484$	−6027.27	+	10439.5i	−0.566047	+	0.980422i
$485$	2960.56	−	5127.85i	0.277180	−	0.480090i
$486$		0			0
$487$	14297.0			1.33031			0.665154	−	0.746706i	$-0.268366\pi$
$487$	14297.0			1.33031			0.665154	+	0.746706i	$0.268366\pi$
$488$	−2.06948	+	3.58444i	−0.000191969	+	0.000332500i
$489$		0			0
$490$	2385.08	−	4131.08i	0.219891	−	0.380863i
$491$	1401.21	+	2426.97i	0.128790	+	0.223070i	0.923208	−	0.384301i	$-0.125557\pi$
$491$	1401.21	+	2426.97i	0.128790	+	0.223070i	−0.794418	+	0.607371i	$0.792224\pi$
$492$		0			0
$493$	−8165.02			−0.745911
$494$	−11012.9	−	2747.79i	−1.00302	−	0.250261i
$495$		0			0
$496$	1977.52	+	3425.16i	0.179018	+	0.310069i
$497$	−5247.94	−	9089.70i	−0.473646	−	0.820380i
$498$		0			0
$499$	−7089.13	−	12278.7i	−0.635978	−	1.10155i	−0.986307	−	0.164919i	$-0.947264\pi$
$499$	−7089.13	−	12278.7i	−0.635978	−	1.10155i	0.350329	−	0.936627i	$-0.386070\pi$
$500$	−1334.62	+	2311.63i	−0.119372	+	0.206758i
$501$		0			0
$502$	1103.98			0.0981533
$503$	−2768.93	+	4795.92i	−0.245448	+	0.425128i	−0.962257	−	0.272141i	$-0.912268\pi$
$503$	−2768.93	+	4795.92i	−0.245448	+	0.425128i	0.716810	+	0.697269i	$0.245602\pi$
$504$		0			0
$505$	4808.56			0.423719
$506$	466.520			0.0409869
$507$		0			0
$508$	3019.95	+	5230.71i	0.263757	+	0.456841i
$509$	4557.55	−	7893.90i	0.396876	−	0.687409i	−0.596463	−	0.802641i	$-0.703428\pi$
$509$	4557.55	−	7893.90i	0.396876	−	0.687409i	0.993339	+	0.115232i	$0.0367611\pi$
$510$		0			0
$511$	−2134.80	−	3697.58i	−0.184810	−	0.320101i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−10471.7			−0.898610
$515$	−10455.9	−	18110.1i	−0.894643	−	1.54957i
$516$		0			0
$517$	−2997.10	+	5191.13i	−0.254956	+	0.441597i
$518$	5580.92	+	9666.44i	0.473382	+	0.819921i
$519$		0			0
$520$	−7814.31			−0.659001
$521$	2705.46			0.227502			0.113751	−	0.993509i	$-0.463713\pi$
$521$	2705.46			0.227502			0.113751	+	0.993509i	$0.463713\pi$
$522$		0			0
$523$	11564.2	−	20029.7i	0.966856	−	1.67464i	0.262311	−	0.964983i	$-0.415515\pi$
$523$	11564.2	−	20029.7i	0.966856	−	1.67464i	0.704544	−	0.709660i	$-0.251151\pi$
$524$	1483.78			0.123701
$525$		0			0
$526$	1814.26	−	3142.39i	0.150390	−	0.260484i
$527$	−12321.7	−	21341.7i	−1.01848	−	1.76406i
$528$		0			0
$529$	6077.24	+	10526.1i	0.499485	+	0.865134i
$530$	−9813.97	−	16998.3i	−0.804324	−	1.39313i
$531$		0			0
$532$	3050.66	−	3157.99i	0.248615	−	0.257362i
$533$	−23659.1			−1.92269
$534$		0			0
$535$	−2722.67	−	4715.80i	−0.220021	−	0.381088i
$536$	−639.448	+	1107.56i	−0.0515298	+	0.0892522i
$537$		0			0
$538$	−1013.40	+	1755.26i	−0.0812095	+	0.140659i
$539$	−11028.9			−0.881353
$540$		0			0
$541$	4820.58	−	8349.50i	0.383093	−	0.663536i	−0.608410	−	0.793623i	$-0.708192\pi$
$541$	4820.58	−	8349.50i	0.383093	−	0.663536i	0.991503	+	0.130087i	$0.0415257\pi$
$542$	−1918.52	+	3322.97i	−0.152043	+	0.263346i
$543$		0			0
$544$	3190.21			0.251432
$545$	−946.896	+	1640.07i	−0.0744231	+	0.128905i
$546$		0			0
$547$	8688.50	−	15048.9i	0.679147	−	1.17632i	−0.296091	−	0.955160i	$-0.595683\pi$
$547$	8688.50	−	15048.9i	0.679147	−	1.17632i	0.975238	−	0.221158i	$-0.0709835\pi$
$548$	−3380.75	−	5855.63i	−0.263537	−	0.456460i
$549$		0			0
$550$	−10307.0			−0.799076
$551$	4712.66	−	4878.45i	0.364366	−	0.377185i
$552$		0			0
$553$	−2109.89	−	3654.44i	−0.162246	−	0.281018i
$554$	6283.45	+	10883.3i	0.481874	+	0.834630i
$555$		0			0
$556$	5423.04	+	9392.99i	0.413648	+	0.716459i
$557$	9372.14	−	16233.0i	0.712945	−	1.23486i	−0.250802	−	0.968038i	$-0.580694\pi$
$557$	9372.14	−	16233.0i	0.712945	−	1.23486i	0.963747	−	0.266819i	$-0.0859725\pi$
$558$		0			0
$559$	25092.0			1.89853
$560$	1511.45	−	2617.91i	0.114054	−	0.197548i
$561$		0			0
$562$	−16114.7			−1.20953
$563$	7618.70			0.570320			0.285160	−	0.958480i	$-0.407953\pi$
$563$	7618.70			0.570320			0.285160	+	0.958480i	$0.407953\pi$
$564$		0			0
$565$	8110.28	+	14047.4i	0.603897	+	1.04598i
$566$	−193.417	+	335.007i	−0.0143638	+	0.0248788i
$567$		0			0
$568$	3167.54	+	5486.33i	0.233991	+	0.405284i
$569$	13081.6			0.963816			0.481908	−	0.876222i	$-0.339944\pi$
$569$	13081.6			0.963816			0.481908	+	0.876222i	$0.339944\pi$
$570$		0			0
$571$	8643.49			0.633483			0.316741	−	0.948512i	$-0.397411\pi$
$571$	8643.49			0.633483			0.316741	+	0.948512i	$0.397411\pi$
$572$	9033.61	+	15646.7i	0.660339	+	1.14374i
$573$		0			0
$574$	4576.16	−	7926.15i	0.332762	−	0.576361i
$575$	138.344	+	239.618i	0.0100336	+	0.0173787i
$576$		0			0
$577$	9841.26			0.710047			0.355024	−	0.934857i	$-0.384473\pi$
$577$	9841.26			0.710047			0.355024	+	0.934857i	$0.384473\pi$
$578$	−10051.8			−0.723355
$579$		0			0
$580$	2334.88	−	4044.13i	0.167156	−	0.289523i
$581$	−9068.06			−0.647516
$582$		0			0
$583$	−22690.6	+	39301.2i	−1.61192	+	2.79192i
$584$	1288.52	+	2231.78i	0.0913000	+	0.158136i
$585$		0			0
$586$	4735.47	+	8202.07i	0.333823	+	0.578198i
$587$	9949.24	+	17232.6i	0.699573	+	1.21170i	0.968615	+	0.248567i	$0.0799596\pi$
$587$	9949.24	+	17232.6i	0.699573	+	1.21170i	−0.269042	+	0.963128i	$0.586707\pi$
$588$		0			0
$589$	19863.1	+	4955.97i	1.38955	+	0.346702i
$590$	−5196.80			−0.362625
$591$		0			0
$592$	−3368.52	−	5834.44i	−0.233860	−	0.405058i
$593$	11097.5	−	19221.4i	0.768497	−	1.33108i	−0.169881	−	0.985465i	$-0.554338\pi$
$593$	11097.5	−	19221.4i	0.768497	−	1.33108i	0.938378	−	0.345611i	$-0.112328\pi$
$594$		0			0
$595$	−9417.65	+	16311.8i	−0.648884	+	1.12390i
$596$	−10395.6			−0.714464
$597$		0			0
$598$	242.504	−	420.029i	0.0165831	−	0.0287228i
$599$	9848.11	−	17057.4i	0.671758	−	1.16352i	−0.305647	−	0.952145i	$-0.598873\pi$
$599$	9848.11	−	17057.4i	0.671758	−	1.16352i	0.977405	−	0.211374i	$-0.0677938\pi$
$600$		0			0
$601$	−14626.5			−0.992724			−0.496362	−	0.868116i	$-0.665331\pi$
$601$	−14626.5			−0.992724			−0.496362	+	0.868116i	$0.665331\pi$
$602$	−4853.31	+	8406.17i	−0.328581	+	0.569120i
$603$		0			0
$604$	−1189.73	+	2060.67i	−0.0801478	+	0.138820i
$605$	21478.6	+	37202.1i	1.44336	+	2.49997i
$606$		0			0
$607$	−16312.0			−1.09075			−0.545375	−	0.838192i	$-0.683613\pi$
$607$	−16312.0			−1.09075			−0.545375	+	0.838192i	$0.683613\pi$
$608$	−1841.31	+	1906.09i	−0.122821	+	0.127142i
$609$		0			0
$610$	7.37475	+	12.7734i	0.000489500	+	0.000847839i
$611$	3115.87	+	5396.84i	0.206308	+	0.357337i
$612$		0			0
$613$	−8874.36	−	15370.8i	−0.584718	−	1.01276i	−0.994911	−	0.100762i	$-0.967872\pi$
$613$	−8874.36	−	15370.8i	−0.584718	−	1.01276i	0.410192	−	0.911999i	$-0.365462\pi$
$614$	−28.7122	+	49.7309i	−0.00188718	+	0.00326869i
$615$		0			0
$616$	−6989.14			−0.457144
$617$	1864.90	−	3230.10i	0.121682	−	0.210760i	−0.798749	−	0.601665i	$-0.794504\pi$
$617$	1864.90	−	3230.10i	0.121682	−	0.210760i	0.920431	+	0.390905i	$0.127838\pi$
$618$		0			0
$619$	−1003.67			−0.0651714			−0.0325857	−	0.999469i	$-0.510374\pi$
$619$	−1003.67			−0.0651714			−0.0325857	+	0.999469i	$0.510374\pi$
$620$	14094.1			0.912954
$621$		0			0
$622$	1165.69	+	2019.03i	0.0751444	+	0.130154i
$623$	4774.24	−	8269.23i	0.307024	−	0.531781i
$624$		0			0
$625$	9642.61	+	16701.5i	0.617127	+	1.06890i
$626$	−5025.51			−0.320862
$627$		0			0
$628$	−233.019			−0.0148065
$629$	20988.8	+	36353.7i	1.33049	+	2.30448i
$630$		0			0
$631$	−8423.38	+	14589.7i	−0.531426	+	0.920456i	0.467902	+	0.883781i	$0.345010\pi$
$631$	−8423.38	+	14589.7i	−0.531426	+	0.920456i	−0.999327	+	0.0366756i	$0.988323\pi$
$632$	1273.48	+	2205.74i	0.0801526	+	0.138828i
$633$		0			0
$634$	−3455.13			−0.216437
$635$	21523.7			1.34510
$636$		0			0
$637$	−5732.98	+	9929.82i	−0.356592	+	0.617636i
$638$	−10796.8			−0.669983
$639$		0			0
$640$	−912.276	+	1580.11i	−0.0563451	+	0.0975926i
$641$	−80.9977	−	140.292i	−0.00499098	−	0.00864463i	0.863519	−	0.504316i	$-0.168255\pi$
$641$	−80.9977	−	140.292i	−0.00499098	−	0.00864463i	−0.868510	+	0.495671i	$0.834922\pi$
$642$		0			0
$643$	−3145.45	−	5448.09i	−0.192915	−	0.334139i	0.753300	−	0.657677i	$-0.228461\pi$
$643$	−3145.45	−	5448.09i	−0.192915	−	0.334139i	−0.946215	+	0.323538i	$0.895128\pi$
$644$	93.8104	+	162.484i	0.00574014	+	0.00994221i
$645$		0			0
$646$	11473.0	−	11876.6i	0.698759	−	0.723343i
$647$	−28249.8			−1.71656			−0.858280	−	0.513181i	$-0.828467\pi$
$647$	−28249.8			−1.71656			−0.858280	+	0.513181i	$0.828467\pi$
$648$		0			0
$649$	6007.68	+	10405.6i	0.363362	+	0.629361i
$650$	−5357.72	+	9279.85i	−0.323303	+	0.559978i
$651$		0			0
$652$	−2305.07	+	3992.50i	−0.138456	+	0.239813i
$653$	−11423.5			−0.684587			−0.342293	−	0.939593i	$-0.611204\pi$
$653$	−11423.5			−0.684587			−0.342293	+	0.939593i	$0.611204\pi$
$654$		0			0
$655$	2643.78	−	4579.16i	0.157711	−	0.273164i
$656$	−2762.07	+	4784.04i	−0.164391	+	0.284734i
$657$		0			0
$658$	−2410.69			−0.142824
$659$	100.069	−	173.324i	0.00591522	−	0.0102455i	−0.863053	−	0.505114i	$-0.831450\pi$
$659$	100.069	−	173.324i	0.00591522	−	0.0102455i	0.868968	+	0.494869i	$0.164784\pi$
$660$		0			0
$661$	1303.50	−	2257.73i	0.0767026	−	0.132853i	−0.825123	−	0.564953i	$-0.808894\pi$
$661$	1303.50	−	2257.73i	0.0767026	−	0.132853i	0.901825	+	0.432101i	$0.142227\pi$
$662$	−6816.13	−	11805.9i	−0.400176	−	0.693125i
$663$		0			0
$664$	5473.28			0.319886
$665$	−4310.39	−	15041.7i	−0.251353	−	0.877130i
$666$		0			0
$667$	144.918	+	251.005i	0.00841266	+	0.0145712i
$668$	2518.22	+	4361.68i	0.145857	+	0.252632i
$669$		0			0
$670$	2278.72	+	3946.87i	0.131395	+	0.227583i
$671$	17.0509	−	29.5331i	0.000980989	−	0.00169912i
$672$		0			0
$673$	14561.2			0.834015			0.417007	−	0.908903i	$-0.363079\pi$
$673$	14561.2			0.834015			0.417007	+	0.908903i	$0.363079\pi$
$674$	−10408.4	+	18027.9i	−0.594831	+	1.03028i
$675$		0			0
$676$	9995.18			0.568683
$677$	−12684.6			−0.720100			−0.360050	−	0.932933i	$-0.617240\pi$
$677$	−12684.6			−0.720100			−0.360050	+	0.932933i	$0.617240\pi$
$678$		0			0
$679$	−2752.87	−	4768.11i	−0.155590	−	0.269489i
$680$	5684.28	−	9845.46i	0.320562	−	0.555230i
$681$		0			0
$682$	−16293.2	−	28220.7i	−0.914809	−	1.58450i
$683$	−12054.5			−0.675332			−0.337666	−	0.941266i	$-0.609637\pi$
$683$	−12054.5			−0.675332			−0.337666	+	0.941266i	$0.609637\pi$
$684$		0			0
$685$	−24095.1			−1.34398
$686$	−6763.98	−	11715.6i	−0.376458	−	0.652044i
$687$		0			0
$688$	2929.35	−	5073.78i	0.162326	−	0.281157i
$689$	23589.7	+	40858.6i	1.30435	+	2.25920i
$690$		0			0
$691$	3338.42			0.183791			0.0918953	−	0.995769i	$-0.470707\pi$
$691$	3338.42			0.183791			0.0918953	+	0.995769i	$0.470707\pi$
$692$	5096.40			0.279965
$693$		0			0
$694$	5584.03	−	9671.83i	0.305428	−	0.529017i
$695$	38650.9			2.10951
$696$		0			0
$697$	17210.1	−	29808.8i	0.935264	−	1.61993i
$698$	5505.82	+	9536.37i	0.298565	+	0.517130i
$699$		0			0
$700$	−2072.59	−	3589.83i	−0.111909	−	0.193832i
$701$	−11891.4	−	20596.5i	−0.640702	−	1.10973i	−0.985276	−	0.170969i	$-0.945310\pi$
$701$	−11891.4	−	20596.5i	−0.640702	−	1.10973i	0.344575	−	0.938759i	$-0.388023\pi$
$702$		0			0
$703$	−33834.9	−	8442.04i	−1.81523	−	0.452913i
$704$	4218.49			0.225838
$705$		0			0
$706$	5782.46	+	10015.5i	0.308252	+	0.533908i
$707$	2235.61	−	3872.19i	0.118923	−	0.205981i
$708$		0			0
$709$	−16092.6	+	27873.1i	−0.852424	+	1.47644i	0.0265907	+	0.999646i	$0.491535\pi$
$709$	−16092.6	+	27873.1i	−0.852424	+	1.47644i	−0.879015	+	0.476795i	$0.841798\pi$
$710$	22575.5			1.19330
$711$		0			0
$712$	−2881.62	+	4991.12i	−0.151676	+	0.262711i
$713$	−437.385	+	757.573i	−0.0229736	+	0.0397915i
$714$		0			0
$715$	64383.9			3.36758
$716$	4068.99	−	7047.70i	0.212382	−	0.367856i
$717$		0			0
$718$	1903.64	−	3297.20i	0.0989459	−	0.171379i
$719$	−19159.7	−	33185.5i	−0.993791	−	1.72130i	−0.593255	−	0.805015i	$-0.702157\pi$
$719$	−19159.7	−	33185.5i	−0.993791	−	1.72130i	−0.400536	−	0.916281i	$-0.631176\pi$
$720$		0			0
$721$	−19444.7			−1.00438
$722$	474.139	+	13709.8i	0.0244399	+	0.706684i
$723$		0			0
$724$	−2066.63	−	3579.50i	−0.106085	−	0.183745i
$725$	−3201.72	−	5545.55i	−0.164012	−	0.284078i
$726$		0			0
$727$	18271.6	+	31647.3i	0.932125	+	1.61449i	0.779683	+	0.626175i	$0.215380\pi$
$727$	18271.6	+	31647.3i	0.932125	+	1.61449i	0.152442	+	0.988312i	$0.451286\pi$
$728$	−3633.05	+	6292.63i	−0.184959	+	0.320358i
$729$		0			0
$730$	9183.46			0.465610
$731$	−18252.4	+	31614.1i	−0.923514	+	1.59957i
$732$		0			0
$733$	−15689.3			−0.790584			−0.395292	−	0.918555i	$-0.629357\pi$
$733$	−15689.3			−0.790584			−0.395292	+	0.918555i	$0.629357\pi$
$734$	25496.1			1.28212
$735$		0			0
$736$	−56.6218	−	98.0719i	−0.00283574	−	0.00491165i
$737$	5268.56	−	9125.42i	0.263324	−	0.456091i
$738$		0			0
$739$	18222.8	+	31562.9i	0.907088	+	1.57112i	0.818089	+	0.575091i	$0.195033\pi$
$739$	18222.8	+	31562.9i	0.907088	+	1.57112i	0.0889991	+	0.996032i	$0.471633\pi$
$740$	−24008.0			−1.19264
$741$		0			0
$742$	−18251.0			−0.902984
$743$	839.144	+	1453.44i	0.0414337	+	0.0717652i	0.885999	−	0.463688i	$-0.153474\pi$
$743$	839.144	+	1453.44i	0.0414337	+	0.0717652i	−0.844565	+	0.535453i	$0.820141\pi$
$744$		0			0
$745$	−18522.8	+	32082.4i	−0.910902	+	1.57773i
$746$	−736.660	−	1275.93i	−0.0361542	−	0.0626209i
$747$		0			0
$748$	−26284.9			−1.28485
$749$	−5063.33			−0.247009
$750$		0			0
$751$	−4320.84	+	7483.91i	−0.209946	+	0.363637i	−0.951697	−	0.307038i	$-0.900662\pi$
$751$	−4320.84	+	7483.91i	−0.209946	+	0.363637i	0.741751	+	0.670675i	$0.233996\pi$
$752$	1455.04			0.0705582
$753$		0			0
$754$	−5612.33	+	9720.83i	−0.271073	+	0.469512i
$755$	4239.68	+	7343.34i	0.204368	+	0.353976i
$756$		0			0
$757$	−1793.40	−	3106.25i	−0.0861058	−	0.149140i	0.819756	−	0.572713i	$-0.194109\pi$
$757$	−1793.40	−	3106.25i	−0.0861058	−	0.149140i	−0.905862	+	0.423573i	$0.860776\pi$
$758$	1543.57	+	2673.54i	0.0739642	+	0.128110i
$759$		0			0
$760$	2601.66	+	9078.82i	0.124174	+	0.433320i
$761$	11615.4			0.553297			0.276649	−	0.960971i	$-0.410776\pi$
$761$	11615.4			0.553297			0.276649	+	0.960971i	$0.410776\pi$
$762$		0			0
$763$	880.467	+	1525.01i	0.0417760	+	0.0723581i
$764$	−2270.93	+	3933.37i	−0.107538	+	0.186262i
$765$		0			0
$766$	−6564.36	+	11369.8i	−0.309634	+	0.536303i
$767$	12491.5			0.588060
$768$		0			0
$769$	−3010.91	+	5215.06i	−0.141192	+	0.244551i	−0.927946	−	0.372716i	$-0.878427\pi$
$769$	−3010.91	+	5215.06i	−0.141192	+	0.244551i	0.786754	+	0.617267i	$0.211760\pi$
$770$	−12453.2	+	21569.5i	−0.582833	+	1.00950i
$771$		0			0
$772$	4364.29			0.203464
$773$	−754.493	+	1306.82i	−0.0351064	+	0.0608061i	−0.883045	−	0.469289i	$-0.844510\pi$
$773$	−754.493	+	1306.82i	−0.0351064	+	0.0608061i	0.847938	+	0.530095i	$0.177844\pi$
$774$		0			0
$775$	9663.31	−	16737.3i	0.447892	−	0.775772i
$776$	1661.57	+	2877.92i	0.0768645	+	0.133133i
$777$		0			0
$778$	−6996.54			−0.322414
$779$	7876.95	+	27487.6i	0.362286	+	1.26425i
$780$		0			0
$781$	−26098.1	−	45203.2i	−1.19573	−	2.07106i
$782$	352.803	+	611.074i	0.0161333	+	0.0279437i
$783$		0			0
$784$	1338.59	+	2318.50i	0.0609779	+	0.105617i
$785$	−415.192	+	719.133i	−0.0188775	+	0.0326968i
$786$		0			0
$787$	3255.84			0.147469			0.0737346	−	0.997278i	$-0.476508\pi$
$787$	3255.84			0.147469			0.0737346	+	0.997278i	$0.476508\pi$
$788$	8276.16	−	14334.7i	0.374144	−	0.648037i
$789$		0			0
$790$	9076.31			0.408760
$791$	15082.6			0.677972
$792$		0			0
$793$	−17.7266	−	30.7034i	−0.000793809	−	0.00137492i
$794$	8610.60	−	14914.0i	0.384860	−	0.666597i
$795$		0			0
$796$	5468.47	+	9471.66i	0.243498	+	0.421751i
$797$	−31732.8			−1.41033			−0.705164	−	0.709044i	$-0.749127\pi$
$797$	−31732.8			−1.41033			−0.705164	+	0.709044i	$0.749127\pi$
$798$		0			0
$799$	−9066.16			−0.401424
$800$	1250.97	+	2166.74i	0.0552854	+	0.0957572i
$801$		0			0
$802$	−1765.74	+	3058.36i	−0.0777439	+	0.134656i
$803$	−10616.4	−	18388.1i	−0.466556	−	0.808098i
$804$		0			0
$805$	668.601			0.0292734
$806$	−33877.8			−1.48051
$807$		0			0
$808$	−1349.36	+	2337.17i	−0.0587506	+	0.101759i
$809$	−3853.96			−0.167488			−0.0837441	−	0.996487i	$-0.526688\pi$
$809$	−3853.96			−0.167488			−0.0837441	+	0.996487i	$0.526688\pi$
$810$		0			0
$811$	−15935.9	+	27601.8i	−0.689995	+	1.19511i	0.281844	+	0.959460i	$0.409054\pi$
$811$	−15935.9	+	27601.8i	−0.689995	+	1.19511i	−0.971839	+	0.235646i	$0.924279\pi$
$812$	−2171.08	−	3760.42i	−0.0938299	−	0.162518i
$813$		0			0
$814$	27754.0	+	48071.3i	1.19506	+	2.06990i
$815$	8214.29	+	14227.6i	0.353048	+	0.611497i
$816$		0			0
$817$	−8354.00	−	29152.4i	−0.357735	−	1.24836i
$818$	−26791.4			−1.14516
$819$		0			0
$820$	9842.85	+	17048.3i	0.419179	+	0.726040i
$821$	−19585.0	+	33922.2i	−0.832547	+	1.44201i	0.0634643	+	0.997984i	$0.479785\pi$
$821$	−19585.0	+	33922.2i	−0.832547	+	1.44201i	−0.896012	+	0.444030i	$0.853548\pi$
$822$		0			0
$823$	9419.41	−	16314.9i	0.398955	−	0.691010i	−0.594642	−	0.803990i	$-0.702706\pi$
$823$	9419.41	−	16314.9i	0.398955	−	0.691010i	0.993597	+	0.112980i	$0.0360396\pi$
$824$	11736.4			0.496185
$825$		0			0
$826$	−2416.11	+	4184.83i	−0.101776	+	0.176282i
$827$	443.653	−	768.430i	0.0186546	−	0.0323107i	−0.856547	−	0.516068i	$-0.827395\pi$
$827$	443.653	−	768.430i	0.0186546	−	0.0323107i	0.875202	+	0.483758i	$0.160728\pi$
$828$		0			0
$829$	32877.0			1.37740			0.688700	−	0.725046i	$-0.258182\pi$
$829$	32877.0			1.37740			0.688700	+	0.725046i	$0.258182\pi$
$830$	9752.22	−	16891.3i	0.407837	−	0.706394i
$831$		0			0
$832$	2192.83	−	3798.09i	0.0913733	−	0.158263i
$833$	−8340.56	−	14446.3i	−0.346919	−	0.600881i
$834$		0			0
$835$	17947.7			0.743840
$836$	15171.0	−	15704.7i	0.627631	−	0.649712i
$837$		0			0
$838$	−9117.71	−	15792.3i	−0.375855	−	0.650999i
$839$	−20756.4	−	35951.1i	−0.854099	−	1.47934i	−0.877478	−	0.479616i	$-0.840776\pi$
$839$	−20756.4	−	35951.1i	−0.854099	−	1.47934i	0.0233792	−	0.999727i	$-0.492557\pi$
$840$		0			0
$841$	8840.63	+	15312.4i	0.362484	+	0.627841i
$842$	8204.45	−	14210.5i	0.335801	−	0.581624i
$843$		0			0
$844$	12232.0			0.498867
$845$	17809.3	−	30846.6i	0.725040	−	1.25581i
$846$		0			0
$847$	39943.6			1.62040
$848$	11015.9			0.446092
$849$		0			0
$850$	−7794.61	−	13500.7i	−0.314533	−	0.544787i
$851$	745.045	−	1290.46i	0.0300115	−	0.0519815i
$852$		0			0
$853$	−743.876	−	1288.43i	−0.0298591	−	0.0517175i	0.850710	−	0.525636i	$-0.176173\pi$
$853$	−743.876	−	1288.43i	−0.0298591	−	0.0517175i	−0.880569	+	0.473918i	$0.842839\pi$
$854$	13.7148			0.000549543
$855$		0			0
$856$	3056.11			0.122028
$857$	10138.0	+	17559.6i	0.404094	+	0.699911i	0.994216	−	0.107403i	$-0.0342536\pi$
$857$	10138.0	+	17559.6i	0.404094	+	0.699911i	−0.590122	+	0.807314i	$0.700920\pi$
$858$		0			0
$859$	−3718.43	+	6440.51i	−0.147696	+	0.255818i	−0.930376	−	0.366608i	$-0.880519\pi$
$859$	−3718.43	+	6440.51i	−0.147696	+	0.255818i	0.782679	+	0.622425i	$0.213853\pi$
$860$	−10439.0	−	18080.8i	−0.413913	−	0.716919i
$861$		0			0
$862$	−2542.69			−0.100469
$863$	−35570.4			−1.40305			−0.701524	−	0.712646i	$-0.747497\pi$
$863$	−35570.4			−1.40305			−0.701524	+	0.712646i	$0.747497\pi$
$864$		0			0
$865$	9080.70	−	15728.2i	0.356940	−	0.618238i
$866$	7935.18			0.311372
$867$		0			0
$868$	6552.66	−	11349.5i	0.256235	−	0.443811i
$869$	−10492.5	−	18173.6i	−0.409591	−	0.709432i
$870$		0			0
$871$	−5477.34	−	9487.04i	−0.213080	−	0.369065i
$872$	−531.430	−	920.464i	−0.0206382	−	0.0357464i
$873$		0			0
$874$	−568.735	−	141.903i	−0.0220112	−	0.00549193i
$875$	8844.74			0.341722
$876$		0			0
$877$	−1934.21	−	3350.15i	−0.0744740	−	0.128993i	0.826383	−	0.563108i	$-0.190394\pi$
$877$	−1934.21	−	3350.15i	−0.0744740	−	0.128993i	−0.900857	+	0.434115i	$0.857061\pi$
$878$	209.038	−	362.065i	0.00803496	−	0.0139170i
$879$		0			0
$880$	7516.45	−	13018.9i	0.287931	−	0.498712i
$881$	20877.4			0.798384			0.399192	−	0.916867i	$-0.369291\pi$
$881$	20877.4			0.798384			0.399192	+	0.916867i	$0.369291\pi$
$882$		0			0
$883$	12103.4	−	20963.7i	0.461283	−	0.798965i	−0.537742	−	0.843109i	$-0.680723\pi$
$883$	12103.4	−	20963.7i	0.461283	−	0.798965i	0.999025	+	0.0441440i	$0.0140561\pi$
$884$	−13663.2	+	23665.4i	−0.519847	+	0.900401i
$885$		0			0
$886$	11468.1			0.434851
$887$	−13558.8	+	23484.5i	−0.513256	+	0.888986i	0.486625	+	0.873611i	$0.338228\pi$
$887$	−13558.8	+	23484.5i	−0.513256	+	0.888986i	−0.999882	+	0.0153754i	$0.995106\pi$
$888$		0			0
$889$	10006.8	−	17332.4i	0.377524	−	0.653890i
$890$	10268.9	+	17786.2i	0.386757	+	0.669883i
$891$		0			0
$892$	6473.07			0.242976
$893$	5232.77	−	5416.87i	0.196090	−	0.202988i
$894$		0			0
$895$	−14500.2	−	25115.0i	−0.541550	−	0.937993i
$896$	848.276	+	1469.26i	0.0316282	+	0.0547817i
$897$		0			0
$898$	−9741.13	−	16872.1i	−0.361989	−	0.626983i
$899$	10122.5	−	17532.7i	0.375534	−	0.650444i
$900$		0			0
$901$	−68638.5			−2.53793
$902$	22757.3	−	39416.8i	0.840062	−	1.45503i
$903$		0			0
$904$	−9103.52			−0.334932
$905$	−14729.2			−0.541010
$906$		0			0
$907$	17797.4	+	30826.0i	0.651548	+	1.12851i	0.982747	+	0.184953i	$0.0592134\pi$
$907$	17797.4	+	30826.0i	0.651548	+	1.12851i	−0.331199	+	0.943561i	$0.607453\pi$
$908$	−12130.9	+	21011.3i	−0.443367	+	0.767933i
$909$		0			0
$910$	12946.7	+	22424.3i	0.471624	+	0.816877i
$911$	−27909.5			−1.01502			−0.507510	−	0.861646i	$-0.669434\pi$
$911$	−27909.5			−1.01502			−0.507510	+	0.861646i	$0.669434\pi$
$912$		0			0
$913$	−45095.6			−1.63466
$914$	−17233.8	−	29849.8i	−0.623679	−	1.08024i
$915$		0			0
$916$	3832.73	−	6638.47i	0.138250	−	0.239456i
$917$	−2458.30	−	4257.91i	−0.0885282	−	0.153335i
$918$		0			0
$919$	−48960.0			−1.75739			−0.878696	−	0.477383i	$-0.841586\pi$
$919$	−48960.0			−1.75739			−0.878696	+	0.477383i	$0.841586\pi$
$920$	−403.552			−0.0144617
$921$		0			0
$922$	−1665.23	+	2884.27i	−0.0594811	+	0.103024i
$923$	−54264.5			−1.93515
$924$		0			0
$925$	−16460.6	+	28510.5i	−0.585102	+	1.01343i
$926$	−10694.0	−	18522.6i	−0.379511	−	0.657333i
$927$		0			0
$928$	1310.41	+	2269.70i	0.0463539	+	0.0802873i
$929$	−5985.87	−	10367.8i	−0.211399	−	0.366155i	0.740753	−	0.671777i	$-0.234469\pi$
$929$	−5985.87	−	10367.8i	−0.211399	−	0.366155i	−0.952153	+	0.305623i	$0.901135\pi$
$930$		0			0
$931$	13445.4	+	3354.71i	0.473313	+	0.118095i
$932$	16034.2			0.563537
$933$		0			0
$934$	−13212.7	−	22885.0i	−0.462882	−	0.801736i
$935$	−46834.1	+	81119.0i	−1.63812	+	2.83730i
$936$		0			0
$937$	25217.1	−	43677.3i	0.879197	−	1.52281i	0.0269728	−	0.999636i	$-0.491413\pi$
$937$	25217.1	−	43677.3i	0.879197	−	1.52281i	0.852224	−	0.523177i	$-0.175253\pi$
$938$	4237.72			0.147512
$939$		0			0
$940$	2592.57	−	4490.46i	0.0899578	−	0.155811i
$941$	6297.13	−	10906.9i	0.218151	−	0.377849i	−0.736091	−	0.676882i	$-0.763331\pi$
$941$	6297.13	−	10906.9i	0.218151	−	0.377849i	0.954243	+	0.299033i	$0.0966640\pi$
$942$		0			0
$943$	−1221.82			−0.0421930
$944$	1458.31	−	2525.87i	0.0502796	−	0.0870869i
$945$		0			0
$946$	−24135.5	+	41804.0i	−0.829508	+	1.43675i
$947$	13816.3	+	23930.5i	0.474096	+	0.821158i	0.999560	−	0.0296574i	$-0.00944162\pi$
$947$	13816.3	+	23930.5i	0.474096	+	0.821158i	−0.525464	+	0.850816i	$0.676108\pi$
$948$		0			0
$949$	−22074.2			−0.755067
$950$	12565.3	+	3135.12i	0.429128	+	0.107070i
$951$		0			0
$952$	−5285.50	−	9154.76i	−0.179941	−	0.311667i
$953$	16010.9	+	27731.6i	0.544221	+	0.942619i	0.998655	+	0.0518388i	$0.0165082\pi$
$953$	16010.9	+	27731.6i	0.544221	+	0.942619i	−0.454434	+	0.890780i	$0.650158\pi$
$954$		0			0
$955$	8092.64	+	14016.9i	0.274211	+	0.474947i
$956$	1060.58	−	1836.99i	0.0358805	−	0.0621468i
$957$		0			0
$958$	10819.1			0.364873
$959$	−11202.4	+	19403.1i	−0.377209	+	0.653345i
$960$		0			0
$961$	31311.7			1.05105
$962$	57707.7			1.93406
$963$		0			0
$964$	−2542.45	−	4403.65i	−0.0849448	−	0.147129i
$965$	7776.24	−	13468.9i	0.259405	−	0.449303i
$966$		0			0
$967$	6438.21	+	11151.3i	0.214104	+	0.370840i	0.952995	−	0.302985i	$-0.0979834\pi$
$967$	6438.21	+	11151.3i	0.214104	+	0.370840i	−0.738891	+	0.673825i	$0.764650\pi$
$968$	−24109.1			−0.800511
$969$		0			0
$970$	11842.3			0.391992
$971$	1207.26	+	2091.03i	0.0398998	+	0.0691085i	0.885286	−	0.465048i	$-0.153963\pi$
$971$	1207.26	+	2091.03i	0.0398998	+	0.0691085i	−0.845386	+	0.534156i	$0.820629\pi$
$972$		0			0
$973$	17969.7	−	31124.4i	0.592067	−	1.02549i
$974$	14297.0	+	24763.2i	0.470335	+	0.814644i
$975$		0			0
$976$	−8.27792			−0.000271485
$977$	14131.4			0.462746			0.231373	−	0.972865i	$-0.425678\pi$
$977$	14131.4			0.462746			0.231373	+	0.972865i	$0.425678\pi$
$978$		0			0
$979$	23742.3	−	41122.9i	0.775085	−	1.34249i
$980$	9540.31			0.310973
$981$		0			0
$982$	−2802.42	+	4853.94i	−0.0910681	+	0.157735i
$983$	−10134.1	−	17552.7i	−0.328817	−	0.569528i	0.653460	−	0.756961i	$-0.273317\pi$
$983$	−10134.1	−	17552.7i	−0.328817	−	0.569528i	−0.982277	+	0.187433i	$0.939983\pi$
$984$		0			0
$985$	−29492.7	−	51082.9i	−0.954027	−	1.65242i
$986$	−8165.02	−	14142.2i	−0.263719	−	0.456775i
$987$		0			0
$988$	−6253.57	−	21822.7i	−0.201369	−	0.702703i
$989$	1295.82			0.0416629
$990$		0			0
$991$	−7775.08	−	13466.8i	−0.249226	−	0.431673i	0.714085	−	0.700059i	$-0.246843\pi$
$991$	−7775.08	−	13466.8i	−0.249226	−	0.431673i	−0.963311	+	0.268386i	$0.913510\pi$
$992$	−3955.03	+	6850.32i	−0.126585	+	0.219252i
$993$		0			0
$994$	10495.9	−	18179.4i	0.334919	−	0.580096i
$995$	38974.6			1.24179
$996$		0			0
$997$	−6357.89	+	11012.2i	−0.201962	+	0.349809i	−0.949161	−	0.314792i	$-0.898065\pi$
$997$	−6357.89	+	11012.2i	−0.201962	+	0.349809i	0.747198	+	0.664601i	$0.231399\pi$
$998$	14178.3	−	24557.5i	0.449704	−	0.778910i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.4.g.h.235.3		6
3.2	odd	2		114.4.e.d.7.1	✓	6
19.11	even	3	inner	342.4.g.h.163.3		6
57.11	odd	6		114.4.e.d.49.1	yes	6
57.26	odd	6		2166.4.a.u.1.3		3
57.50	even	6		2166.4.a.t.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.e.d.7.1	✓	6	3.2	odd	2
114.4.e.d.49.1	yes	6	57.11	odd	6
342.4.g.h.163.3		6	19.11	even	3	inner
342.4.g.h.235.3		6	1.1	even	1	trivial
2166.4.a.t.1.3		3	57.50	even	6
2166.4.a.u.1.3		3	57.26	odd	6

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	342.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(7.12716 + 12.3446i) q^{5} +13.2543 q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(7.12716 + 12.3446i) q^{5} +13.2543 q^{7} -8.00000 q^{8} +(-14.2543 + 24.6892i) q^{10} +65.9138 q^{11} +(34.2629 - 59.3451i) q^{13} +(13.2543 + 22.9571i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(49.8470 + 86.3375i) q^{17} +(-80.3556 - 20.0493i) q^{19} -57.0172 q^{20} +(65.9138 + 114.166i) q^{22} +(1.76943 - 3.06475i) q^{23} +(-39.0927 + 67.7105i) q^{25} +137.052 q^{26} +(-26.5086 + 45.9143i) q^{28} +(-40.9504 + 70.9282i) q^{29} -247.190 q^{31} +(16.0000 - 27.7128i) q^{32} +(-99.6940 + 172.675i) q^{34} +(94.4655 + 163.619i) q^{35} +421.065 q^{37} +(-45.6293 - 159.229i) q^{38} +(-57.0172 - 98.7568i) q^{40} +(-172.629 - 299.003i) q^{41} +(183.084 + 317.111i) q^{43} +(-131.828 + 228.332i) q^{44} +7.07773 q^{46} +(-45.4699 + 78.7562i) q^{47} -167.323 q^{49} -156.371 q^{50} +(137.052 + 237.381i) q^{52} +(-344.246 + 596.251i) q^{53} +(469.778 + 813.680i) q^{55} -106.034 q^{56} -163.802 q^{58} +(91.1444 + 157.867i) q^{59} +(0.258685 - 0.448055i) q^{61} +(-247.190 - 428.145i) q^{62} +64.0000 q^{64} +976.789 q^{65} +(79.9310 - 138.445i) q^{67} -398.776 q^{68} +(-188.931 + 327.238i) q^{70} +(-395.942 - 685.792i) q^{71} +(-161.065 - 278.972i) q^{73} +(421.065 + 729.306i) q^{74} +(230.164 - 238.262i) q^{76} +873.642 q^{77} +(-159.185 - 275.717i) q^{79} +(114.034 - 197.514i) q^{80} +(345.259 - 598.005i) q^{82} -684.160 q^{83} +(-710.535 + 1230.68i) q^{85} +(-366.168 + 634.222i) q^{86} -527.311 q^{88} +(360.203 - 623.890i) q^{89} +(454.132 - 786.579i) q^{91} +(7.07773 + 12.2590i) q^{92} -181.880 q^{94} +(-325.207 - 1134.85i) q^{95} +(-207.696 - 359.740i) q^{97} +(-167.323 - 289.812i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 12 q^{4} + 10 q^{5} + 14 q^{7} - 48 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 - 12 * q^4 + 10 * q^5 + 14 * q^7 - 48 * q^8	\( 6 q + 6 q^{2} - 12 q^{4} + 10 q^{5} + 14 q^{7} - 48 q^{8} - 20 q^{10} + 88 q^{11} + 9 q^{13} + 14 q^{14} - 48 q^{16} - 84 q^{17} + 32 q^{19} - 80 q^{20} + 88 q^{22} - 2 q^{23} + 83 q^{25} + 36 q^{26} - 28 q^{28} + 92 q^{29} - 218 q^{31} + 96 q^{32} + 168 q^{34} + 282 q^{35} + 490 q^{37} + 74 q^{38} - 80 q^{40} - 688 q^{41} + 103 q^{43} - 176 q^{44} - 8 q^{46} + 322 q^{47} - 1508 q^{49} + 332 q^{50} + 36 q^{52} - 1322 q^{53} + 248 q^{55} - 112 q^{56} + 368 q^{58} + 252 q^{59} + 435 q^{61} - 218 q^{62} + 384 q^{64} + 3164 q^{65} + 719 q^{67} + 672 q^{68} - 564 q^{70} - 62 q^{71} + 581 q^{73} + 490 q^{74} + 20 q^{76} + 408 q^{77} + 489 q^{79} + 160 q^{80} + 1376 q^{82} - 4992 q^{83} - 1632 q^{85} - 206 q^{86} - 704 q^{88} + 1584 q^{89} + 1573 q^{91} - 8 q^{92} + 1288 q^{94} - 2362 q^{95} - 974 q^{97} - 1508 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 - 12 * q^4 + 10 * q^5 + 14 * q^7 - 48 * q^8 - 20 * q^10 + 88 * q^11 + 9 * q^13 + 14 * q^14 - 48 * q^16 - 84 * q^17 + 32 * q^19 - 80 * q^20 + 88 * q^22 - 2 * q^23 + 83 * q^25 + 36 * q^26 - 28 * q^28 + 92 * q^29 - 218 * q^31 + 96 * q^32 + 168 * q^34 + 282 * q^35 + 490 * q^37 + 74 * q^38 - 80 * q^40 - 688 * q^41 + 103 * q^43 - 176 * q^44 - 8 * q^46 + 322 * q^47 - 1508 * q^49 + 332 * q^50 + 36 * q^52 - 1322 * q^53 + 248 * q^55 - 112 * q^56 + 368 * q^58 + 252 * q^59 + 435 * q^61 - 218 * q^62 + 384 * q^64 + 3164 * q^65 + 719 * q^67 + 672 * q^68 - 564 * q^70 - 62 * q^71 + 581 * q^73 + 490 * q^74 + 20 * q^76 + 408 * q^77 + 489 * q^79 + 160 * q^80 + 1376 * q^82 - 4992 * q^83 - 1632 * q^85 - 206 * q^86 - 704 * q^88 + 1584 * q^89 + 1573 * q^91 - 8 * q^92 + 1288 * q^94 - 2362 * q^95 - 974 * q^97 - 1508 * q^98

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