LMFDB - Embedded newform 261.3.s.a.19.1

Newspace parameters

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	261.s (of order $28$, degree $12$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.11173489980$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	261.19
Dual form			261.3.s.a.55.1

$q$-expansion

$f(q)$	$=$	$q+(-1.42815 - 2.27289i) q^{2} +(-1.39088 + 2.88819i) q^{4} +(6.69994 + 1.52922i) q^{5} +(-4.78081 + 2.30231i) q^{7} +(-2.11889 + 0.238741i) q^{8} +O(q^{10})$	\(q+(-1.42815 - 2.27289i) q^{2} +(-1.39088 + 2.88819i) q^{4} +(6.69994 + 1.52922i) q^{5} +(-4.78081 + 2.30231i) q^{7} +(-2.11889 + 0.238741i) q^{8} +(-6.09279 - 17.4122i) q^{10} +(3.10194 + 0.349505i) q^{11} +(14.9316 - 11.9076i) q^{13} +(12.0606 + 7.57819i) q^{14} +(11.5635 + 14.5002i) q^{16} +(19.1156 - 19.1156i) q^{17} +(3.26204 - 1.14144i) q^{19} +(-13.7355 + 17.2238i) q^{20} +(-3.63566 - 7.54952i) q^{22} +(3.11691 + 13.6561i) q^{23} +(20.0264 + 9.64422i) q^{25} +(-48.3892 - 16.9321i) q^{26} -17.0101i q^{28} +(22.5579 - 18.2247i) q^{29} +(-30.9563 - 49.2666i) q^{31} +(13.6259 - 38.9405i) q^{32} +(-70.7477 - 16.1477i) q^{34} +(-35.5518 + 8.11447i) q^{35} +(23.4414 - 2.64121i) q^{37} +(-7.25305 - 5.78412i) q^{38} +(-14.5615 - 1.64069i) q^{40} +(-29.0869 - 29.0869i) q^{41} +(28.3964 + 17.8426i) q^{43} +(-5.32387 + 8.47289i) q^{44} +(26.5873 - 26.5873i) q^{46} +(-5.42166 + 48.1186i) q^{47} +(-12.9956 + 16.2959i) q^{49} +(-6.68052 - 59.2913i) q^{50} +(13.6233 + 59.6874i) q^{52} +(-2.93760 + 12.8705i) q^{53} +(20.2483 + 7.08520i) q^{55} +(9.58032 - 6.01972i) q^{56} +(-73.6390 - 25.2439i) q^{58} -11.7545 q^{59} +(-18.2928 + 52.2779i) q^{61} +(-67.7674 + 140.721i) q^{62} +(-35.6416 + 8.13496i) q^{64} +(118.250 - 56.9463i) q^{65} +(-6.83210 - 5.44842i) q^{67} +(28.6221 + 81.7971i) q^{68} +(69.2167 + 69.2167i) q^{70} +(49.1193 - 39.1713i) q^{71} +(33.0911 - 52.6641i) q^{73} +(-39.4811 - 49.5078i) q^{74} +(-1.24042 + 11.0090i) q^{76} +(-15.6344 + 5.47073i) q^{77} +(5.05536 + 44.8675i) q^{79} +(55.3008 + 114.833i) q^{80} +(-24.5708 + 107.652i) q^{82} +(123.603 + 59.5242i) q^{83} +(157.305 - 98.8415i) q^{85} -90.0238i q^{86} -6.65610 q^{88} +(-38.7651 - 61.6944i) q^{89} +(-43.9702 + 91.3050i) q^{91} +(-43.7766 - 9.99172i) q^{92} +(117.111 - 56.3978i) q^{94} +(23.6010 - 2.65919i) q^{95} +(16.9565 + 48.4590i) q^{97} +(55.5985 + 6.26444i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) $	$ 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{9}{28}\right)$	$1$

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 $

$2$	−1.42815	−	2.27289i	−0.714076	−	1.13645i	−0.984784	−	0.173784i	$-0.944401\pi$
$2$	−1.42815	−	2.27289i	−0.714076	−	1.13645i	0.270708	−	0.962662i	$-0.412742\pi$
$3$		0			0
$3$		0			0
$4$	−1.39088	+	2.88819i	−0.347720	+	0.722048i
$5$	6.69994	+	1.52922i	1.33999	+	0.305843i	0.831643	−	0.555311i	$-0.187401\pi$
$5$	6.69994	+	1.52922i	1.33999	+	0.305843i	0.508344	+	0.861154i	$0.330258\pi$
$6$		0			0
$7$	−4.78081	+	2.30231i	−0.682972	+	0.328902i	−0.742997	−	0.669295i	$-0.766596\pi$
$7$	−4.78081	+	2.30231i	−0.682972	+	0.328902i	0.0600247	+	0.998197i	$0.480882\pi$
$8$	−2.11889	+	0.238741i	−0.264861	+	0.0298426i
$9$		0			0
$10$	−6.09279	−	17.4122i	−0.609279	−	1.74122i
$11$	3.10194	+	0.349505i	0.281995	+	0.0317732i	0.251829	−	0.967772i	$-0.418968\pi$
$11$	3.10194	+	0.349505i	0.281995	+	0.0317732i	0.0301656	+	0.999545i	$0.490397\pi$
$12$		0			0
$13$	14.9316	−	11.9076i	1.14859	−	0.915967i	0.151220	−	0.988500i	$-0.451680\pi$
$13$	14.9316	−	11.9076i	1.14859	−	0.915967i	0.997366	+	0.0725336i	$0.0231085\pi$
$14$	12.0606	+	7.57819i	0.861473	+	0.541300i
$15$		0			0
$16$	11.5635	+	14.5002i	0.722718	+	0.906260i
$17$	19.1156	−	19.1156i	1.12445	−	1.12445i	0.133383	−	0.991065i	$-0.457416\pi$
$17$	19.1156	−	19.1156i	1.12445	−	1.12445i	0.991065	−	0.133383i	$-0.0425841\pi$
$18$		0			0
$19$	3.26204	−	1.14144i	0.171686	−	0.0600756i	−0.243067	−	0.970009i	$-0.578154\pi$
$19$	3.26204	−	1.14144i	0.171686	−	0.0600756i	0.414753	+	0.909934i	$0.363868\pi$
$20$	−13.7355	+	17.2238i	−0.686774	+	0.861188i
$21$		0			0
$22$	−3.63566	−	7.54952i	−0.165257	−	0.343160i
$23$	3.11691	+	13.6561i	0.135518	+	0.593742i	0.996388	+	0.0849173i	$0.0270626\pi$
$23$	3.11691	+	13.6561i	0.135518	+	0.593742i	−0.860870	+	0.508824i	$0.830080\pi$
$24$		0			0
$25$	20.0264	+	9.64422i	0.801057	+	0.385769i
$26$	−48.3892	−	16.9321i	−1.86112	−	0.651235i
$27$		0			0
$28$		−	17.0101i		−	0.607505i
$29$	22.5579	−	18.2247i	0.777858	−	0.628440i
$29$	22.5579	−	18.2247i	0.777858	−	0.628440i
$30$		0			0
$31$	−30.9563	−	49.2666i	−0.998590	−	1.58925i	−0.791726	−	0.610877i	$-0.790817\pi$
$31$	−30.9563	−	49.2666i	−0.998590	−	1.58925i	−0.206864	−	0.978370i	$-0.566326\pi$
$32$	13.6259	−	38.9405i	0.425808	−	1.21689i
$33$		0			0
$34$	−70.7477	−	16.1477i	−2.08082	−	0.474932i
$35$	−35.5518	+	8.11447i	−1.01577	+	0.231842i
$36$		0			0
$37$	23.4414	−	2.64121i	0.633552	−	0.0713842i	0.210653	−	0.977561i	$-0.432441\pi$
$37$	23.4414	−	2.64121i	0.633552	−	0.0713842i	0.422899	+	0.906177i	$0.361012\pi$
$38$	−7.25305	−	5.78412i	−0.190870	−	0.152214i
$39$		0			0
$40$	−14.5615	−	1.64069i	−0.364037	−	0.0410171i
$41$	−29.0869	−	29.0869i	−0.709436	−	0.709436i	0.256981	−	0.966417i	$-0.417272\pi$
$41$	−29.0869	−	29.0869i	−0.709436	−	0.709436i	−0.966417	+	0.256981i	$0.917272\pi$
$42$		0			0
$43$	28.3964	+	17.8426i	0.660380	+	0.414945i	0.820102	−	0.572218i	$-0.193917\pi$
$43$	28.3964	+	17.8426i	0.660380	+	0.414945i	−0.159721	+	0.987162i	$0.551060\pi$
$44$	−5.32387	+	8.47289i	−0.120997	+	0.192566i
$45$		0			0
$46$	26.5873	−	26.5873i	0.577985	−	0.577985i
$47$	−5.42166	+	48.1186i	−0.115355	+	1.02380i	0.794040	+	0.607865i	$0.207974\pi$
$47$	−5.42166	+	48.1186i	−0.115355	+	1.02380i	−0.909395	+	0.415934i	$0.863455\pi$
$48$		0			0
$49$	−12.9956	+	16.2959i	−0.265215	+	0.332570i
$50$	−6.68052	−	59.2913i	−0.133610	−	1.18583i
$51$		0			0
$52$	13.6233	+	59.6874i	0.261986	+	1.14783i
$53$	−2.93760	+	12.8705i	−0.0554265	+	0.242839i	−0.995051	−	0.0993688i	$-0.968318\pi$
$53$	−2.93760	+	12.8705i	−0.0554265	+	0.242839i	0.939624	+	0.342208i	$0.111175\pi$
$54$		0			0
$55$	20.2483	+	7.08520i	0.368152	+	0.128822i
$56$	9.58032	−	6.01972i	0.171077	−	0.107495i
$57$		0			0
$58$	−73.6390	−	25.2439i	−1.26964	−	0.435240i
$59$	−11.7545			−0.199228			−0.0996140	−	0.995026i	$-0.531761\pi$
$59$	−11.7545			−0.199228			−0.0996140	+	0.995026i	$0.531761\pi$
$60$		0			0
$61$	−18.2928	+	52.2779i	−0.299882	+	0.857014i	0.691069	+	0.722789i	$0.257140\pi$
$61$	−18.2928	+	52.2779i	−0.299882	+	0.857014i	−0.990951	+	0.134225i	$0.957145\pi$
$62$	−67.7674	+	140.721i	−1.09302	+	2.26969i
$63$		0			0
$64$	−35.6416	+	8.13496i	−0.556900	+	0.127109i
$65$	118.250	−	56.9463i	1.81923	−	0.876096i
$66$		0			0
$67$	−6.83210	−	5.44842i	−0.101972	−	0.0813196i	0.571177	−	0.820827i	$-0.306487\pi$
$67$	−6.83210	−	5.44842i	−0.101972	−	0.0813196i	−0.673148	+	0.739507i	$0.735058\pi$
$68$	28.6221	+	81.7971i	0.420913	+	1.20290i
$69$		0			0
$70$	69.2167	+	69.2167i	0.988811	+	0.988811i
$71$	49.1193	−	39.1713i	0.691821	−	0.551709i	−0.213235	−	0.977001i	$-0.568400\pi$
$71$	49.1193	−	39.1713i	0.691821	−	0.551709i	0.905056	+	0.425292i	$0.139829\pi$
$72$		0			0
$73$	33.0911	−	52.6641i	0.453302	−	0.721426i	−0.539396	−	0.842052i	$-0.681347\pi$
$73$	33.0911	−	52.6641i	0.453302	−	0.721426i	0.992698	+	0.120626i	$0.0384902\pi$
$74$	−39.4811	−	49.5078i	−0.533529	−	0.669024i
$75$		0			0
$76$	−1.24042	+	11.0090i	−0.0163213	+	0.144855i
$77$	−15.6344	+	5.47073i	−0.203045	+	0.0710484i
$78$		0			0
$79$	5.05536	+	44.8675i	0.0639919	+	0.567943i	0.984269	+	0.176676i	$0.0565346\pi$
$79$	5.05536	+	44.8675i	0.0639919	+	0.567943i	−0.920277	+	0.391267i	$0.872037\pi$
$80$	55.3008	+	114.833i	0.691260	+	1.43542i
$81$		0			0
$82$	−24.5708	+	107.652i	−0.299644	+	1.31283i
$83$	123.603	+	59.5242i	1.48920	+	0.717159i	0.988885	−	0.148686i	$-0.0475042\pi$
$83$	123.603	+	59.5242i	1.48920	+	0.717159i	0.500312	+	0.865845i	$0.333218\pi$
$84$		0			0
$85$	157.305	−	98.8415i	1.85065	−	1.16284i
$86$		−	90.0238i		−	1.04679i
$87$		0			0
$88$	−6.65610			−0.0756375
$89$	−38.7651	−	61.6944i	−0.435563	−	0.693195i	0.554754	−	0.832014i	$-0.312812\pi$
$89$	−38.7651	−	61.6944i	−0.435563	−	0.693195i	−0.990318	+	0.138819i	$0.955669\pi$
$90$		0			0
$91$	−43.9702	+	91.3050i	−0.483189	+	1.00335i
$92$	−43.7766	−	9.99172i	−0.475833	−	0.108606i
$93$		0			0
$94$	117.111	−	56.3978i	1.24586	−	0.599977i
$95$	23.6010	−	2.65919i	0.248431	−	0.0279915i
$96$		0			0
$97$	16.9565	+	48.4590i	0.174810	+	0.499577i	0.997636	−	0.0687153i	$-0.0218900\pi$
$97$	16.9565	+	48.4590i	0.174810	+	0.499577i	−0.822827	+	0.568292i	$0.807604\pi$
$98$	55.5985	+	6.26444i	0.567331	+	0.0639229i
$99$		0			0
$100$	−55.7087	+	44.4262i	−0.557087	+	0.444262i
$101$	−10.9319	−	6.86898i	−0.108237	−	0.0680097i	0.476826	−	0.878998i	$-0.341787\pi$
$101$	−10.9319	−	6.86898i	−0.108237	−	0.0680097i	−0.585063	+	0.810988i	$0.698930\pi$
$102$		0			0
$103$	−21.5998	−	27.0853i	−0.209706	−	0.262964i	0.665843	−	0.746092i	$-0.268072\pi$
$103$	−21.5998	−	27.0853i	−0.209706	−	0.262964i	−0.875550	+	0.483128i	$0.839501\pi$
$104$	−28.7956	+	28.7956i	−0.276880	+	0.276880i
$105$		0			0
$106$	33.4486	−	11.7042i	0.315552	−	0.110417i
$107$	−87.5840	+	109.827i	−0.818542	+	1.02642i	0.180539	+	0.983568i	$0.442216\pi$
$107$	−87.5840	+	109.827i	−0.818542	+	1.02642i	−0.999081	+	0.0428518i	$0.986356\pi$
$108$		0			0
$109$	13.2898	+	27.5965i	0.121925	+	0.253179i	0.952994	−	0.302990i	$-0.0979849\pi$
$109$	13.2898	+	27.5965i	0.121925	+	0.253179i	−0.831069	+	0.556169i	$0.812271\pi$
$110$	−12.8138	−	56.1410i	−0.116489	−	0.510373i
$111$		0			0
$112$	−88.6667	−	42.6996i	−0.791667	−	0.381247i
$113$	−28.9202	−	10.1196i	−0.255931	−	0.0895541i	0.199264	−	0.979946i	$-0.436145\pi$
$113$	−28.9202	−	10.1196i	−0.255931	−	0.0895541i	−0.455195	+	0.890392i	$0.650430\pi$
$114$		0			0
$115$			96.2612i			0.837054i
$116$	21.2613	+	90.5000i	0.183287	+	0.780173i
$117$		0			0
$118$	16.7872	+	26.7166i	0.142264	+	0.226412i
$119$	−47.3779	+	135.398i	−0.398133	+	1.13780i
$120$		0			0
$121$	−108.466	−	24.7567i	−0.896416	−	0.204601i
$122$	144.947	−	33.0832i	1.18809	−	0.271174i
$123$		0			0
$124$	185.348	−	20.8837i	1.49474	−	0.168417i
$125$	−14.8956	−	11.8789i	−0.119165	−	0.0950311i
$126$		0			0
$127$	4.07151	+	0.458749i	0.0320591	+	0.00361220i	0.127979	−	0.991777i	$-0.459151\pi$
$127$	4.07151	+	0.458749i	0.0320591	+	0.00361220i	−0.0959203	+	0.995389i	$0.530579\pi$
$128$	−47.2969	−	47.2969i	−0.369507	−	0.369507i
$129$		0			0
$130$	−298.312	−	187.442i	−2.29471	−	1.44186i
$131$	15.8863	−	25.2830i	0.121270	−	0.193000i	−0.780572	−	0.625065i	$-0.785072\pi$
$131$	15.8863	−	25.2830i	0.121270	−	0.193000i	0.901842	+	0.432066i	$0.142215\pi$
$132$		0			0
$133$	−12.9672	+	12.9672i	−0.0974980	+	0.0974980i
$134$	−2.62638	+	23.3098i	−0.0195999	+	0.173954i
$135$		0			0
$136$	−35.9401	+	45.0675i	−0.264266	+	0.331379i
$137$	13.7929	+	122.415i	0.100678	+	0.893542i	0.937954	+	0.346761i	$0.112718\pi$
$137$	13.7929	+	122.415i	0.100678	+	0.893542i	−0.837276	+	0.546781i	$0.815853\pi$
$138$		0			0
$139$	52.0026	+	227.838i	0.374119	+	1.63912i	0.715077	+	0.699045i	$0.246392\pi$
$139$	52.0026	+	227.838i	0.374119	+	1.63912i	−0.340958	+	0.940079i	$0.610751\pi$
$140$	26.0122	−	113.967i	0.185801	−	0.814049i
$141$		0			0
$142$	−159.182	−	55.7002i	−1.12100	−	0.392255i
$143$	50.4787	−	31.7179i	0.352998	−	0.221803i
$144$		0			0
$145$	179.006	−	87.6087i	1.23452	−	0.604198i
$146$	−166.959			−1.14355
$147$		0			0
$148$	−24.9759	+	71.3770i	−0.168756	+	0.482277i
$149$	−44.8786	+	93.1914i	−0.301199	+	0.625446i	−0.995555	−	0.0941861i	$-0.969975\pi$
$149$	−44.8786	+	93.1914i	−0.301199	+	0.625446i	0.694356	+	0.719632i	$0.255689\pi$
$150$		0			0
$151$	17.1757	−	3.92024i	0.113746	−	0.0259618i	−0.165269	−	0.986249i	$-0.552849\pi$
$151$	17.1757	−	3.92024i	0.113746	−	0.0259618i	0.279015	+	0.960287i	$0.409992\pi$
$152$	−6.63938	+	3.19736i	−0.0436801	+	0.0210352i
$153$		0			0
$154$	34.7627	+	27.7224i	0.225732	+	0.180015i
$155$	−132.066	−	377.422i	−0.852037	−	2.43498i
$156$		0			0
$157$	55.4971	+	55.4971i	0.353485	+	0.353485i	0.861404	−	0.507920i	$-0.169585\pi$
$157$	55.4971	+	55.4971i	0.353485	+	0.353485i	−0.507920	+	0.861404i	$0.669585\pi$
$158$	94.7592	−	75.5679i	0.599742	−	0.478278i
$159$		0			0
$160$	150.841	−	240.062i	0.942755	−	1.50039i
$161$	−46.3419	−	58.1109i	−0.287838	−	0.360937i
$162$		0			0
$163$	18.1802	−	161.354i	0.111535	−	0.989899i	−0.805910	−	0.592037i	$-0.798324\pi$
$163$	18.1802	−	161.354i	0.111535	−	0.989899i	0.917445	−	0.397862i	$-0.130248\pi$
$164$	124.465	−	43.5521i	0.758932	−	0.265562i
$165$		0			0
$166$	−41.2323	−	365.947i	−0.248387	−	2.20450i
$167$	−71.6533	−	148.790i	−0.429061	−	0.890955i	−0.997662	−	0.0683416i	$-0.978229\pi$
$167$	−71.6533	−	148.790i	−0.429061	−	0.890955i	0.568600	−	0.822614i	$-0.307485\pi$
$168$		0			0
$169$	43.5570	−	190.836i	0.257734	−	1.12920i
$170$	−449.312	−	216.377i	−2.64301	−	1.27281i
$171$		0			0
$172$	−91.0289	+	57.1972i	−0.529238	+	0.332542i
$173$			41.6753i			0.240898i	0.992720	+	0.120449i	$0.0384334\pi$
$173$			41.6753i			0.240898i	−0.992720	+	0.120449i	$0.961567\pi$
$174$		0			0
$175$	−117.946			−0.673980
$176$	30.8014	+	49.0201i	0.175008	+	0.278523i
$177$		0			0
$178$	−84.8621	+	176.218i	−0.476753	+	0.989988i
$179$	93.6851	+	21.3830i	0.523380	+	0.119458i	0.476045	−	0.879421i	$-0.342070\pi$
$179$	93.6851	+	21.3830i	0.523380	+	0.119458i	0.0473352	+	0.998879i	$0.484927\pi$
$180$		0			0
$181$	−141.858	+	68.3150i	−0.783744	+	0.377431i	−0.782566	−	0.622568i	$-0.786089\pi$
$181$	−141.858	+	68.3150i	−0.783744	+	0.377431i	−0.00117831	+	0.999999i	$0.500375\pi$
$182$	270.323	−	30.4580i	1.48529	−	0.167352i
$183$		0			0
$184$	−9.86463	−	28.1915i	−0.0536121	−	0.153215i
$185$	161.095	+	18.1511i	0.870784	+	0.0981138i
$186$		0			0
$187$	65.9765	−	52.6145i	0.352815	−	0.281361i
$188$	−131.435	−	82.5860i	−0.699122	−	0.439287i
$189$		0			0
$190$	−39.7498	−	49.8447i	−0.209210	−	0.262340i
$191$	−149.268	+	149.268i	−0.781507	+	0.781507i	−0.980085	−	0.198578i	$-0.936368\pi$
$191$	−149.268	+	149.268i	−0.781507	+	0.781507i	0.198578	+	0.980085i	$0.436368\pi$
$192$		0			0
$193$	−7.47034	+	2.61398i	−0.0387064	+	0.0135440i	−0.349563	−	0.936913i	$-0.613670\pi$
$193$	−7.47034	+	2.61398i	−0.0387064	+	0.0135440i	0.310856	+	0.950457i	$0.399384\pi$
$194$	85.9255	−	107.747i	0.442915	−	0.555398i
$195$		0			0
$196$	−28.9905	−	60.1993i	−0.147911	−	0.307139i
$197$	83.3370	+	365.123i	0.423030	+	1.85342i	0.514328	+	0.857594i	$0.328042\pi$
$197$	83.3370	+	365.123i	0.423030	+	1.85342i	−0.0912973	+	0.995824i	$0.529101\pi$
$198$		0			0
$199$	−320.598	−	154.392i	−1.61105	−	0.775840i	−0.611170	−	0.791499i	$-0.709301\pi$
$199$	−320.598	−	154.392i	−1.61105	−	0.775840i	−0.999877	+	0.0156595i	$0.995015\pi$
$200$	−44.7362	−	15.6539i	−0.223681	−	0.0782693i
$201$		0			0
$202$			34.6570i			0.171569i
$203$	−65.8858	+	139.064i	−0.324561	+	0.685046i
$204$		0			0
$205$	−150.400	−	239.360i	−0.733659	−	1.16761i
$206$	−30.7141	+	87.7758i	−0.149097	+	0.426096i
$207$		0			0
$208$	345.323	+	78.8178i	1.66021	+	0.378932i
$209$	10.5176	−	2.40057i	0.0503234	−	0.0114860i
$210$		0			0
$211$	231.167	−	26.0462i	1.09558	−	0.123442i	0.454372	−	0.890812i	$-0.349864\pi$
$211$	231.167	−	26.0462i	1.09558	−	0.123442i	0.641205	+	0.767370i	$0.278435\pi$
$212$	−33.0866	−	26.3857i	−0.156069	−	0.124461i
$213$		0			0
$214$	374.708	+	42.2194i	1.75097	+	0.197287i
$215$	162.969	+	162.969i	0.757993	+	0.757993i
$216$		0			0
$217$	261.423	+	164.263i	1.20472	+	0.756973i
$218$	43.7441	−	69.6183i	0.200661	−	0.319350i
$219$		0			0
$220$	−48.6264	+	48.6264i	−0.221029	+	0.221029i
$221$	57.8066	−	513.047i	0.261568	−	2.32148i
$222$		0			0
$223$	−193.421	+	242.542i	−0.867359	+	1.08763i	0.128036	+	0.991770i	$0.459133\pi$
$223$	−193.421	+	242.542i	−0.867359	+	1.08763i	−0.995394	+	0.0958637i	$0.969439\pi$
$224$	24.5106	+	217.538i	0.109422	+	0.971151i
$225$		0			0
$226$	18.3016	+	80.1848i	0.0809807	+	0.354800i
$227$	−50.9304	+	223.141i	−0.224363	+	0.982999i	0.729788	+	0.683674i	$0.239619\pi$
$227$	−50.9304	+	223.141i	−0.224363	+	0.982999i	−0.954151	+	0.299326i	$0.903238\pi$
$228$		0			0
$229$	17.7179	+	6.19978i	0.0773709	+	0.0270733i	0.368687	−	0.929554i	$-0.379807\pi$
$229$	17.7179	+	6.19978i	0.0773709	+	0.0270733i	−0.291316	+	0.956627i	$0.594093\pi$
$230$	218.791	−	137.476i	0.951266	−	0.597720i
$231$		0			0
$232$	−43.4466	+	44.0017i	−0.187270	+	0.189662i
$233$	−24.0314			−0.103139			−0.0515695	−	0.998669i	$-0.516422\pi$
$233$	−24.0314			−0.103139			−0.0515695	+	0.998669i	$0.516422\pi$
$234$		0			0
$235$	−109.909	+	314.101i	−0.467696	+	1.33660i
$236$	16.3490	−	33.9491i	0.0692756	−	0.143852i
$237$		0			0
$238$	375.408	−	85.6845i	1.57735	−	0.360019i
$239$	247.377	−	119.131i	1.03505	−	0.498454i	0.162362	−	0.986731i	$-0.448089\pi$
$239$	247.377	−	119.131i	1.03505	−	0.498454i	0.872689	+	0.488277i	$0.162374\pi$
$240$		0			0
$241$	−230.544	−	183.853i	−0.956615	−	0.762875i	0.0148913	−	0.999889i	$-0.495260\pi$
$241$	−230.544	−	183.853i	−0.956615	−	0.762875i	−0.971506	+	0.237014i	$0.923831\pi$
$242$	98.6371	+	281.889i	0.407591	+	1.16483i
$243$		0			0
$244$	−125.546	−	125.546i	−0.514531	−	0.514531i
$245$	−111.989	+	89.3085i	−0.457099	+	0.364525i
$246$		0			0
$247$	35.1158	−	55.8864i	0.142169	−	0.226261i
$248$	77.3548	+	96.9998i	0.311914	+	0.391128i
$249$		0			0
$250$	−5.72616	+	50.8210i	−0.0229046	+	0.203284i
$251$	−238.983	+	83.6236i	−0.952122	+	0.333162i	−0.761254	−	0.648454i	$-0.775416\pi$
$251$	−238.983	+	83.6236i	−0.952122	+	0.333162i	−0.190868	+	0.981616i	$0.561130\pi$
$252$		0			0
$253$	4.89560	+	43.4497i	0.0193502	+	0.171738i
$254$	−4.77205	−	9.90926i	−0.0187876	−	0.0390128i
$255$		0			0
$256$	−72.4934	+	317.614i	−0.283177	+	1.24068i
$257$	−177.185	−	85.3278i	−0.689436	−	0.332015i	0.0561518	−	0.998422i	$-0.482117\pi$
$257$	−177.185	−	85.3278i	−0.689436	−	0.332015i	−0.745588	+	0.666407i	$0.767831\pi$
$258$		0			0
$259$	−105.988	+	66.5967i	−0.409220	+	0.257130i
$260$			420.735i			1.61821i
$261$		0			0
$262$	−80.1535			−0.305929
$263$	−244.782	−	389.569i	−0.930731	−	1.48125i	−0.875751	−	0.482763i	$-0.839633\pi$
$263$	−244.782	−	389.569i	−0.930731	−	1.48125i	−0.0549801	−	0.998487i	$-0.517510\pi$
$264$		0			0
$265$	−39.3635	+	81.7392i	−0.148542	+	0.308450i
$266$	47.9923	+	10.9539i	0.180422	+	0.0411802i
$267$		0			0
$268$	25.2387	−	12.1543i	0.0941743	−	0.0453519i
$269$	−158.746	+	17.8864i	−0.590136	+	0.0664923i	−0.401982	−	0.915647i	$-0.631679\pi$
$269$	−158.746	+	17.8864i	−0.590136	+	0.0664923i	−0.188153	+	0.982140i	$0.560250\pi$
$270$		0			0
$271$	−117.128	−	334.733i	−0.432207	−	1.23518i	−0.929897	−	0.367821i	$-0.880104\pi$
$271$	−117.128	−	334.733i	−0.432207	−	1.23518i	0.497690	−	0.867355i	$-0.334182\pi$
$272$	498.223	+	56.1362i	1.83170	+	0.206383i
$273$		0			0
$274$	258.538	−	206.177i	0.943570	−	0.752472i
$275$	58.7501	+	36.9151i	0.213637	+	0.134237i
$276$		0			0
$277$	317.714	+	398.400i	1.14698	+	1.43827i	0.880259	+	0.474494i	$0.157369\pi$
$277$	317.714	+	398.400i	1.14698	+	1.43827i	0.266721	+	0.963774i	$0.414060\pi$
$278$	443.584	−	443.584i	1.59563	−	1.59563i
$279$		0			0
$280$	73.3930	−	25.6813i	0.262118	−	0.0917190i
$281$	−53.3766	+	66.9321i	−0.189952	+	0.238192i	−0.867683	−	0.497117i	$-0.834392\pi$
$281$	−53.3766	+	66.9321i	−0.189952	+	0.238192i	0.677731	+	0.735310i	$0.262963\pi$
$282$		0			0
$283$	44.3462	+	92.0859i	0.156700	+	0.325392i	0.964508	−	0.264055i	$-0.0850601\pi$
$283$	44.3462	+	92.0859i	0.156700	+	0.325392i	−0.807807	+	0.589447i	$0.799346\pi$
$284$	44.8153	+	196.349i	0.157800	+	0.691369i
$285$		0			0
$286$	−144.183	−	69.4347i	−0.504135	−	0.242779i
$287$	206.026	+	72.0915i	0.717860	+	0.251190i
$288$		0			0
$289$		−	441.813i		−	1.52877i
$290$	−454.773	−	281.743i	−1.56818	−	0.971526i
$291$		0			0
$292$	106.078	+	168.823i	0.363282	+	0.578161i
$293$	−24.9996	+	71.4447i	−0.0853228	+	0.243838i	−0.978638	−	0.205593i	$-0.934088\pi$
$293$	−24.9996	+	71.4447i	−0.0853228	+	0.243838i	0.893315	+	0.449431i	$0.148373\pi$
$294$		0			0
$295$	−78.7541	−	17.9751i	−0.266963	−	0.0609326i
$296$	−49.0391	+	11.1929i	−0.165673	+	0.0378137i
$297$		0			0
$298$	275.907	−	31.0873i	0.925864	−	0.104320i
$299$	209.151	+	166.792i	0.699501	+	0.557834i
$300$		0			0
$301$	−176.837	−	19.9247i	−0.587498	−	0.0661951i
$302$	−33.4398	−	33.4398i	−0.110728	−	0.110728i
$303$		0			0
$304$	54.2716	+	34.1011i	0.178525	+	0.112175i
$305$	−202.505	+	322.285i	−0.663951	+	1.05667i
$306$		0			0
$307$	−36.5877	+	36.5877i	−0.119178	+	0.119178i	−0.764181	−	0.645002i	$-0.776856\pi$
$307$	−36.5877	+	36.5877i	−0.119178	+	0.119178i	0.645002	+	0.764181i	$0.276856\pi$
$308$	5.94512	−	52.7644i	0.0193024	−	0.171313i
$309$		0			0
$310$	−669.230	+	839.187i	−2.15881	+	2.70706i
$311$	−35.9242	−	318.836i	−0.115512	−	1.02520i	−0.909053	−	0.416680i	$-0.863193\pi$
$311$	−35.9242	−	318.836i	−0.115512	−	1.02520i	0.793541	−	0.608516i	$-0.208235\pi$
$312$		0			0
$313$	−32.4462	−	142.156i	−0.103662	−	0.454173i	−0.999943	−	0.0106861i	$-0.996598\pi$
$313$	−32.4462	−	142.156i	−0.103662	−	0.454173i	0.896281	−	0.443487i	$-0.146259\pi$
$314$	46.8806	−	205.397i	0.149301	−	0.654131i
$315$		0			0
$316$	−136.618	−	47.8045i	−0.432334	−	0.151280i
$317$	73.0249	−	45.8846i	0.230362	−	0.144746i	−0.411905	−	0.911227i	$-0.635137\pi$
$317$	73.0249	−	45.8846i	0.230362	−	0.144746i	0.642268	+	0.766480i	$0.277994\pi$
$318$		0			0
$319$	76.3429	−	48.6480i	0.239319	−	0.152502i
$320$	−251.236			−0.785114
$321$		0			0
$322$	−65.8964	+	188.321i	−0.204647	+	0.584848i
$323$	40.5366	−	84.1752i	0.125500	−	0.260604i
$324$		0			0
$325$	413.866	−	94.4622i	1.27343	−	0.290653i
$326$	−392.703	+	189.116i	−1.20461	+	0.580110i
$327$		0			0
$328$	68.5760	+	54.6875i	0.209073	+	0.166730i
$329$	−84.8642	−	242.528i	−0.257946	−	0.737167i
$330$		0			0
$331$	−49.8314	−	49.8314i	−0.150548	−	0.150548i	0.627815	−	0.778363i	$-0.283950\pi$
$331$	−49.8314	−	49.8314i	−0.150548	−	0.150548i	−0.778363	+	0.627815i	$0.783950\pi$
$332$	−343.835	+	274.199i	−1.03565	+	0.825901i
$333$		0			0
$334$	−235.851	+	375.354i	−0.706140	+	1.12381i
$335$	−37.4428	−	46.9518i	−0.111770	−	0.140155i
$336$		0			0
$337$	−34.9489	+	310.180i	−0.103706	+	0.920414i	0.828870	+	0.559441i	$0.188984\pi$
$337$	−34.9489	+	310.180i	−0.103706	+	0.920414i	−0.932576	+	0.360974i	$0.882444\pi$
$338$	−495.954	+	173.542i	−1.46732	+	0.513438i
$339$		0			0
$340$	66.6804	+	591.805i	0.196119	+	1.74060i
$341$	−78.8056	−	163.642i	−0.231102	−	0.479887i
$342$		0			0
$343$	82.4682	−	361.317i	0.240432	−	1.05340i
$344$	−64.4284	−	31.0271i	−0.187292	−	0.0901950i
$345$		0			0
$346$	94.7234	−	59.5187i	0.273767	−	0.172019i
$347$			266.679i			0.768528i	0.923223	+	0.384264i	$0.125545\pi$
$347$			266.679i			0.768528i	−0.923223	+	0.384264i	$0.874455\pi$
$348$		0			0
$349$	−132.806			−0.380532			−0.190266	−	0.981733i	$-0.560935\pi$
$349$	−132.806			−0.380532			−0.190266	+	0.981733i	$0.560935\pi$
$350$	168.445	+	268.079i	0.481273	+	0.765941i
$351$		0			0
$352$	55.8765	−	116.029i	0.158740	−	0.329627i
$353$	325.525	+	74.2990i	0.922168	+	0.210479i	0.657146	−	0.753763i	$-0.271764\pi$
$353$	325.525	+	74.2990i	0.922168	+	0.210479i	0.265022	+	0.964242i	$0.414621\pi$
$354$		0			0
$355$	388.998	−	187.331i	1.09577	−	0.527694i
$356$	232.103	−	26.1517i	0.651975	−	0.0734599i
$357$		0			0
$358$	−85.1953	−	243.474i	−0.237976	−	0.680095i
$359$	−417.651	−	47.0579i	−1.16337	−	0.131081i	−0.490909	−	0.871211i	$-0.663335\pi$
$359$	−417.651	−	47.0579i	−1.16337	−	0.131081i	−0.672464	+	0.740130i	$0.734764\pi$
$360$		0			0
$361$	−272.903	+	217.633i	−0.755964	+	0.602861i
$362$	357.867	+	224.863i	0.988583	+	0.621168i
$363$		0			0
$364$	−202.549	−	253.989i	−0.556454	−	0.697771i
$365$	302.243	−	302.243i	0.828063	−	0.828063i
$366$		0			0
$367$	−658.212	+	230.319i	−1.79349	+	0.627571i	−0.793680	+	0.608336i	$0.791837\pi$
$367$	−658.212	+	230.319i	−1.79349	+	0.627571i	−0.999815	+	0.0192348i	$0.993877\pi$
$368$	−161.973	+	203.107i	−0.440143	+	0.551922i
$369$		0			0
$370$	−188.813	−	392.074i	−0.510305	−	1.05966i
$371$	−15.5878	−	68.2946i	−0.0420156	−	0.184082i
$372$		0			0
$373$	−0.614583	−	0.295968i	−0.00164768	−	0.000793479i	0.433060	−	0.901365i	$-0.357434\pi$
$373$	−0.614583	−	0.295968i	−0.00164768	−	0.000793479i	−0.434707	+	0.900572i	$0.643148\pi$
$374$	−213.812	−	74.8159i	−0.571689	−	0.200042i
$375$		0			0
$376$		−	103.252i		−	0.274607i
$377$	119.813	−	540.735i	0.317807	−	1.43431i
$378$		0			0
$379$	56.7788	+	90.3630i	0.149812	+	0.238425i	0.913196	−	0.407520i	$-0.133606\pi$
$379$	56.7788	+	90.3630i	0.149812	+	0.238425i	−0.763384	+	0.645945i	$0.776464\pi$
$380$	−25.1459	+	71.8628i	−0.0661733	+	0.189113i
$381$		0			0
$382$	552.446	+	126.092i	1.44619	+	0.330085i
$383$	427.991	−	97.6862i	1.11747	−	0.255055i	0.376383	−	0.926464i	$-0.377168\pi$
$383$	427.991	−	97.6862i	1.11747	−	0.255055i	0.741087	+	0.671409i	$0.234310\pi$
$384$		0			0
$385$	−113.116	+	12.7451i	−0.293807	+	0.0331041i
$386$	16.6101	+	13.2461i	0.0430313	+	0.0343163i
$387$		0			0
$388$	−163.543	−	18.4269i	−0.421504	−	0.0474920i
$389$	139.368	+	139.368i	0.358272	+	0.358272i	0.863176	−	0.504904i	$-0.168472\pi$
$389$	139.368	+	139.368i	0.358272	+	0.358272i	−0.504904	+	0.863176i	$0.668472\pi$
$390$		0			0
$391$	320.626	+	201.462i	0.820014	+	0.515249i
$392$	23.6456	−	37.6317i	0.0603204	−	0.0959993i
$393$		0			0
$394$	710.867	−	710.867i	1.80423	−	1.80423i
$395$	−34.7416	+	308.340i	−0.0879535	+	0.780609i
$396$		0			0
$397$	91.8303	−	115.152i	0.231311	−	0.290054i	−0.652607	−	0.757696i	$-0.726325\pi$
$397$	91.8303	−	115.152i	0.231311	−	0.290054i	0.883918	+	0.467642i	$0.154896\pi$
$398$	106.947	+	949.181i	0.268711	+	2.38488i
$399$		0			0
$400$	91.7327	+	401.907i	0.229332	+	1.00477i
$401$	62.6107	−	274.315i	0.156136	−	0.684078i	−0.834891	−	0.550416i	$-0.814469\pi$
$401$	62.6107	−	274.315i	0.156136	−	0.684078i	0.991027	−	0.133662i	$-0.0426738\pi$
$402$		0			0
$403$	−1048.87	−	367.017i	−2.60266	−	0.910711i
$404$	35.0439	−	22.0196i	0.0867424	−	0.0545039i
$405$		0			0
$406$	410.173	−	48.8538i	1.01028	−	0.120330i
$407$	73.6370			0.180926
$408$		0			0
$409$	−142.774	+	408.025i	−0.349081	+	0.997615i	0.626775	+	0.779200i	$0.284374\pi$
$409$	−142.774	+	408.025i	−0.349081	+	0.997615i	−0.975856	+	0.218415i	$0.929911\pi$
$410$	−329.246	+	683.686i	−0.803038	+	1.66753i
$411$		0			0
$412$	108.270	−	24.7120i	0.262792	−	0.0599805i
$413$	56.1958	−	27.0625i	0.136067	−	0.0655265i
$414$		0			0
$415$	737.109	+	587.825i	1.77617	+	1.41645i
$416$	−260.230	−	743.695i	−0.625553	−	1.78773i
$417$		0			0
$418$	−20.4770	−	20.4770i	−0.0489879	−	0.0489879i
$419$	−248.060	+	197.821i	−0.592028	+	0.472126i	−0.873087	−	0.487564i	$-0.837886\pi$
$419$	−248.060	+	197.821i	−0.592028	+	0.472126i	0.281060	+	0.959690i	$0.409314\pi$
$420$		0			0
$421$	284.084	−	452.117i	0.674783	−	1.07391i	−0.317299	−	0.948325i	$-0.602776\pi$
$421$	284.084	−	452.117i	0.674783	−	1.07391i	0.992083	−	0.125586i	$-0.0400811\pi$
$422$	−389.342	−	488.219i	−0.922610	−	1.15692i
$423$		0			0
$424$	3.15173	−	27.9724i	0.00743333	−	0.0659727i
$425$	567.172	−	198.462i	1.33452	−	0.466970i
$426$		0			0
$427$	−32.9057	−	292.046i	−0.0770625	−	0.683949i
$428$	−195.382	−	405.716i	−0.456501	−	0.947934i
$429$		0			0
$430$	137.666	−	603.154i	0.320153	−	1.40268i
$431$	−377.110	−	181.607i	−0.874966	−	0.421361i	−0.0581825	−	0.998306i	$-0.518531\pi$
$431$	−377.110	−	181.607i	−0.874966	−	0.421361i	−0.816783	+	0.576945i	$0.804245\pi$
$432$		0			0
$433$	385.889	−	242.470i	0.891198	−	0.559977i	−0.00679946	−	0.999977i	$-0.502164\pi$
$433$	385.889	−	242.470i	0.891198	−	0.559977i	0.897998	+	0.440000i	$0.145021\pi$
$434$		−	828.779i		−	1.90963i
$435$		0			0
$436$	−98.1886			−0.225203
$437$	25.7550	+	40.9889i	0.0589359	+	0.0937960i
$438$		0			0
$439$	−74.7895	+	155.302i	−0.170363	+	0.353763i	−0.968617	−	0.248558i	$-0.920043\pi$
$439$	−74.7895	+	155.302i	−0.170363	+	0.353763i	0.798254	+	0.602321i	$0.205757\pi$
$440$	−44.5954	−	10.1786i	−0.101353	−	0.0231332i
$441$		0			0
$442$	−1248.66	+	601.322i	−2.82502	+	1.36046i
$443$	462.876	−	52.1536i	1.04487	−	0.117728i	0.427191	−	0.904161i	$-0.359503\pi$
$443$	462.876	−	52.1536i	1.04487	−	0.117728i	0.617676	+	0.786433i	$0.288074\pi$
$444$		0			0
$445$	−165.380	−	472.629i	−0.371640	−	1.06209i
$446$	827.507	+	93.2376i	1.85540	+	0.209053i
$447$		0			0
$448$	151.666	−	120.950i	0.338541	−	0.269977i
$449$	74.4790	+	46.7982i	0.165877	+	0.104228i	0.612412	−	0.790539i	$-0.290199\pi$
$449$	74.4790	+	46.7982i	0.165877	+	0.104228i	−0.446535	+	0.894766i	$0.647342\pi$
$450$		0			0
$451$	−80.0597	−	100.392i	−0.177516	−	0.222598i
$452$	69.4519	−	69.4519i	0.153655	−	0.153655i
$453$		0			0
$454$	579.911	−	202.920i	1.27734	−	0.446960i
$455$	−434.223	+	544.498i	−0.954335	+	1.19670i
$456$		0			0
$457$	−152.739	−	317.166i	−0.334221	−	0.694018i	0.664352	−	0.747420i	$-0.268708\pi$
$457$	−152.739	−	317.166i	−0.334221	−	0.694018i	−0.998573	+	0.0534021i	$0.982993\pi$
$458$	−11.2125	−	49.1252i	−0.0244814	−	0.107260i
$459$		0			0
$460$	−278.021	−	133.888i	−0.604393	−	0.291060i
$461$	265.537	+	92.9154i	0.576002	+	0.201552i	0.602530	−	0.798096i	$-0.294159\pi$
$461$	265.537	+	92.9154i	0.576002	+	0.201552i	−0.0265280	+	0.999648i	$0.508445\pi$
$462$		0			0
$463$			683.990i			1.47730i	0.674088	+	0.738651i	$0.264537\pi$
$463$			683.990i			1.47730i	−0.674088	+	0.738651i	$0.735463\pi$
$464$	525.110	+	116.351i	1.13170	+	0.250757i
$465$		0			0
$466$	34.3205	+	54.6207i	0.0736491	+	0.117212i
$467$	128.753	−	367.954i	0.275702	−	0.787911i	−0.719887	−	0.694091i	$-0.755807\pi$
$467$	128.753	−	367.954i	0.275702	−	0.787911i	0.995589	−	0.0938199i	$-0.0299078\pi$
$468$		0			0
$469$	45.2069	+	10.3182i	0.0963900	+	0.0220004i
$470$	870.883	−	198.773i	1.85294	−	0.422922i
$471$		0			0
$472$	24.9063	−	2.80627i	0.0527677	−	0.00594549i
$473$	81.8477	+	65.2714i	0.173040	+	0.137994i
$474$		0			0
$475$	76.3352	+	8.60092i	0.160706	+	0.0181072i
$476$	−325.159	−	325.159i	−0.683108	−	0.683108i
$477$		0			0
$478$	−624.063	−	392.125i	−1.30557	−	0.820345i
$479$	−188.880	+	300.600i	−0.394321	+	0.627558i	−0.983598	−	0.180373i	$-0.942270\pi$
$479$	−188.880	+	300.600i	−0.394321	+	0.627558i	0.589278	+	0.807931i	$0.299412\pi$
$480$		0			0
$481$	318.568	−	318.568i	0.662303	−	0.662303i
$482$	−88.6253	+	786.572i	−0.183870	+	1.63189i
$483$		0			0
$484$	222.366	−	278.838i	0.459434	−	0.576112i
$485$	39.5034	+	350.602i	0.0814503	+	0.722891i
$486$		0			0
$487$	122.134	+	535.104i	0.250788	+	1.09878i	0.930787	+	0.365562i	$0.119123\pi$
$487$	122.134	+	535.104i	0.250788	+	1.09878i	−0.679998	+	0.733214i	$0.738020\pi$
$488$	26.2795	−	115.138i	0.0538515	−	0.235939i
$489$		0			0
$490$	362.926	+	126.993i	0.740666	+	0.259170i
$491$	14.6268	−	9.19065i	0.0297899	−	0.0187182i	−0.517055	−	0.855952i	$-0.672972\pi$
$491$	14.6268	−	9.19065i	0.0297899	−	0.0187182i	0.546845	+	0.837234i	$0.315829\pi$
$492$		0			0
$493$	82.8307	−	779.585i	0.168014	−	1.58131i
$494$	−177.174			−0.358653
$495$		0			0
$496$	356.411	−	1018.57i	0.718571	−	2.05356i
$497$	−144.645	+	300.359i	−0.291036	+	0.604343i
$498$		0			0
$499$	−274.548	+	62.6637i	−0.550196	+	0.125579i	−0.488576	−	0.872521i	$-0.662484\pi$
$499$	−274.548	+	62.6637i	−0.550196	+	0.125579i	−0.0616193	+	0.998100i	$0.519626\pi$
$500$	55.0266	−	26.4994i	0.110053	−	0.0529988i
$501$		0			0
$502$	531.371	+	423.754i	1.05851	+	0.844132i
$503$	13.3525	+	38.1593i	0.0265457	+	0.0758634i	0.956394	−	0.292081i	$-0.0943475\pi$
$503$	13.3525	+	38.1593i	0.0265457	+	0.0758634i	−0.929848	+	0.367944i	$0.880062\pi$
$504$		0			0
$505$	−62.7390	−	62.7390i	−0.124236	−	0.124236i
$506$	91.7647	−	73.1799i	0.181353	−	0.144624i
$507$		0			0
$508$	−6.98794	+	11.1212i	−0.0137558	+	0.0218922i
$509$	53.4784	+	67.0598i	0.105066	+	0.131748i	0.831584	−	0.555399i	$-0.187434\pi$
$509$	53.4784	+	67.0598i	0.105066	+	0.131748i	−0.726519	+	0.687147i	$0.758863\pi$
$510$		0			0
$511$	−36.9525	+	327.963i	−0.0723142	+	0.641806i
$512$	572.897	−	200.465i	1.11894	−	0.391534i
$513$		0			0
$514$	59.1064	+	524.584i	0.114993	+	1.02059i
$515$	−103.298	−	214.500i	−0.200578	−	0.416505i
$516$		0			0
$517$	−33.6354	+	147.366i	−0.0650587	+	0.285041i
$518$	302.734	+	145.789i	0.584429	+	0.281446i
$519$		0			0
$520$	−236.963	+	148.894i	−0.455698	+	0.286334i
$521$		−	299.573i		−	0.574997i	−0.957781	−	0.287498i	$-0.907176\pi$
$521$		−	299.573i		−	0.574997i	0.957781	−	0.287498i	$-0.0928236\pi$
$522$		0			0
$523$	−691.011			−1.32124			−0.660622	−	0.750718i	$-0.729708\pi$
$523$	−691.011			−1.32124			−0.660622	+	0.750718i	$0.729708\pi$
$524$	50.9261	+	81.0484i	0.0971872	+	0.154673i
$525$		0			0
$526$	−535.861	+	1112.73i	−1.01875	+	2.11545i
$527$	−1533.51	−	350.014i	−2.90989	−	0.664163i
$528$		0			0
$529$	299.840	−	144.395i	0.566805	−	0.272959i
$530$	242.001	−	27.2670i	0.456606	−	0.0514472i
$531$		0			0
$532$	−19.4160	−	55.4877i	−0.0364962	−	0.104300i
$533$	−780.668	−	87.9601i	−1.46467	−	0.165028i
$534$		0			0
$535$	−754.757	+	601.898i	−1.41076	+	1.12504i
$536$	15.7772	+	9.91347i	0.0294351	+	0.0184953i
$537$		0			0
$538$	267.368	+	335.269i	0.496967	+	0.623176i
$539$	−46.0069	+	46.0069i	−0.0853561	+	0.0853561i
$540$		0			0
$541$	163.211	−	57.1098i	0.301683	−	0.105563i	−0.175193	−	0.984534i	$-0.556055\pi$
$541$	163.211	−	57.1098i	0.301683	−	0.105563i	0.476876	+	0.878971i	$0.341769\pi$
$542$	−593.534	+	744.268i	−1.09508	+	1.37319i
$543$		0			0
$544$	−483.904	−	1004.84i	−0.889530	−	1.84713i
$545$	46.8396	+	205.218i	0.0859443	+	0.376547i
$546$		0			0
$547$	−608.085	−	292.838i	−1.11167	−	0.535353i	−0.214362	−	0.976754i	$-0.568767\pi$
$547$	−608.085	−	292.838i	−1.11167	−	0.535353i	−0.897310	+	0.441401i	$0.854482\pi$
$548$	−372.743	−	130.428i	−0.680188	−	0.238008i
$549$		0			0
$550$		−	186.253i		−	0.338642i
$551$	52.7823	−	85.1983i	0.0957937	−	0.154625i
$552$		0			0
$553$	−127.468	−	202.864i	−0.230502	−	0.366843i
$554$	451.777	−	1291.10i	0.815482	−	2.33051i
$555$		0			0
$556$	−730.370	−	166.702i	−1.31362	−	0.299824i
$557$	430.440	−	98.2451i	0.772782	−	0.176383i	0.182093	−	0.983281i	$-0.441713\pi$
$557$	430.440	−	98.2451i	0.772782	−	0.176383i	0.590690	+	0.806899i	$0.298856\pi$
$558$		0			0
$559$	636.466	−	71.7124i	1.13858	−	0.128287i
$560$	−528.764	−	421.676i	−0.944222	−	0.752992i
$561$		0			0
$562$	228.359	+	25.7299i	0.406333	+	0.0457827i
$563$	−505.628	−	505.628i	−0.898096	−	0.898096i	0.0971715	−	0.995268i	$-0.469020\pi$
$563$	−505.628	−	505.628i	−0.898096	−	0.898096i	−0.995268	+	0.0971715i	$0.969020\pi$
$564$		0			0
$565$	−178.288	−	112.026i	−0.315554	−	0.198276i
$566$	145.968	−	232.307i	0.257894	−	0.410436i
$567$		0			0
$568$	−94.7263	+	94.7263i	−0.166772	+	0.166772i
$569$	−23.0557	+	204.625i	−0.0405197	+	0.359622i	0.957049	+	0.289927i	$0.0936311\pi$
$569$	−23.0557	+	204.625i	−0.0405197	+	0.359622i	−0.997568	+	0.0696949i	$0.977797\pi$
$570$		0			0
$571$	699.676	−	877.367i	1.22535	−	1.53654i	0.467698	−	0.883888i	$-0.345083\pi$
$571$	699.676	−	877.367i	1.22535	−	1.53654i	0.757655	−	0.652656i	$-0.226345\pi$
$572$	21.3975	+	189.908i	0.0374082	+	0.332007i
$573$		0			0
$574$	−130.380	−	571.232i	−0.227143	−	0.995177i
$575$	−69.2815	+	303.542i	−0.120490	+	0.527899i
$576$		0			0
$577$	648.576	+	226.947i	1.12405	+	0.393322i	0.827371	−	0.561656i	$-0.189836\pi$
$577$	648.576	+	226.947i	1.12405	+	0.393322i	0.296678	+	0.954978i	$0.404121\pi$
$578$	−1004.19	+	630.977i	−1.73736	+	1.09166i
$579$		0			0
$580$	4.05499	+	638.857i	0.00699136	+	1.10148i
$581$	−727.967			−1.25296
$582$		0			0
$583$	−13.6106	+	38.8968i	−0.0233457	+	0.0667183i
$584$	−57.5431	+	119.489i	−0.0985327	+	0.204605i
$585$		0			0
$586$	198.089	−	45.2126i	0.338036	−	0.0771545i
$587$	95.7428	−	46.1073i	0.163105	−	0.0785474i	−0.350550	−	0.936544i	$-0.614005\pi$
$587$	95.7428	−	46.1073i	0.163105	−	0.0785474i	0.513655	+	0.857997i	$0.328291\pi$
$588$		0			0
$589$	−157.215	−	125.375i	−0.266919	−	0.212861i
$590$	71.6174	+	204.671i	0.121385	+	0.346899i
$591$		0			0
$592$	309.363	+	309.363i	0.522572	+	0.522572i
$593$	338.480	−	269.929i	0.570793	−	0.455192i	−0.295069	−	0.955476i	$-0.595343\pi$
$593$	338.480	−	269.929i	0.570793	−	0.455192i	0.865861	+	0.500284i	$0.166771\pi$
$594$		0			0
$595$	−524.482	+	834.708i	−0.881482	+	1.40287i
$596$	−206.734	−	259.236i	−0.346869	−	0.434960i
$597$		0			0
$598$	80.4014	−	713.582i	0.134450	−	1.19328i
$599$	300.963	−	105.311i	0.502442	−	0.175812i	−0.0671447	−	0.997743i	$-0.521389\pi$
$599$	300.963	−	105.311i	0.502442	−	0.175812i	0.569587	+	0.821931i	$0.307103\pi$
$600$		0			0
$601$	90.6856	+	804.857i	0.150891	+	1.33920i	0.809682	+	0.586869i	$0.199640\pi$
$601$	90.6856	+	804.857i	0.150891	+	1.33920i	−0.658791	+	0.752326i	$0.728932\pi$
$602$	207.263	+	430.386i	0.344291	+	0.714927i
$603$		0			0
$604$	−12.5669	+	55.0593i	−0.0208062	+	0.0911577i
$605$	−688.860	−	331.737i	−1.13861	−	0.548326i
$606$		0			0
$607$	114.515	−	71.9543i	0.188657	−	0.118541i	−0.434392	−	0.900724i	$-0.643037\pi$
$607$	114.515	−	71.9543i	0.188657	−	0.118541i	0.623049	+	0.782183i	$0.285894\pi$
$608$		−	142.578i		−	0.234504i
$609$		0			0
$610$	1021.73			1.67496
$611$	492.021	+	783.047i	0.805272	+	1.28158i
$612$		0			0
$613$	335.706	−	697.102i	0.547645	−	1.13720i	−0.425063	−	0.905164i	$-0.639748\pi$
$613$	335.706	−	697.102i	0.547645	−	1.13720i	0.972708	−	0.232033i	$-0.0745377\pi$
$614$	135.413	+	30.9071i	0.220542	+	0.0503372i
$615$		0			0
$616$	31.8215	−	15.3244i	0.0516583	−	0.0248773i
$617$	227.497	−	25.6327i	0.368714	−	0.0415441i	0.0743364	−	0.997233i	$-0.476316\pi$
$617$	227.497	−	25.6327i	0.368714	−	0.0415441i	0.294378	+	0.955689i	$0.404888\pi$
$618$		0			0
$619$	−55.4200	−	158.381i	−0.0895314	−	0.255866i	0.890407	−	0.455164i	$-0.150419\pi$
$619$	−55.4200	−	158.381i	−0.0895314	−	0.255866i	−0.979939	+	0.199298i	$0.936134\pi$
$620$	1273.76	+	143.518i	2.05445	+	0.231480i
$621$		0			0
$622$	−673.375	+	536.998i	−1.08260	+	0.863341i
$623$	327.368	+	205.699i	0.525471	+	0.330175i
$624$		0			0
$625$	−428.102	−	536.823i	−0.684964	−	0.858917i
$626$	−276.767	+	276.767i	−0.442120	+	0.442120i
$627$		0			0
$628$	−237.476	+	83.0965i	−0.378147	+	0.132319i
$629$	397.609	−	498.586i	0.632129	−	0.792664i
$630$		0			0
$631$	366.946	+	761.972i	0.581531	+	1.20756i	0.959491	+	0.281740i	$0.0909116\pi$
$631$	366.946	+	761.972i	0.581531	+	1.20756i	−0.377959	+	0.925822i	$0.623374\pi$
$632$	−21.4234	−	93.8622i	−0.0338979	−	0.148516i
$633$		0			0
$634$	−208.581	−	100.447i	−0.328993	−	0.158435i
$635$	26.5773	+	9.29981i	0.0418541	+	0.0146454i
$636$		0			0
$637$			398.070i			0.624913i
$638$	−219.601	−	104.042i	−0.344202	−	0.163076i
$639$		0			0
$640$	−244.559	−	389.213i	−0.382123	−	0.608146i
$641$	−127.709	+	364.971i	−0.199234	+	0.569377i	−0.999544	−	0.0302093i	$-0.990383\pi$
$641$	−127.709	+	364.971i	−0.199234	+	0.569377i	0.800310	+	0.599587i	$0.204668\pi$
$642$		0			0
$643$	190.043	+	43.3761i	0.295557	+	0.0674589i	0.367728	−	0.929933i	$-0.380136\pi$
$643$	190.043	+	43.3761i	0.295557	+	0.0674589i	−0.0721713	+	0.997392i	$0.522993\pi$
$644$	232.291	−	53.0190i	0.360701	−	0.0823277i
$645$		0			0
$646$	−249.213	+	28.0796i	−0.385779	+	0.0434669i
$647$	420.130	+	335.042i	0.649350	+	0.517839i	0.891861	−	0.452309i	$-0.149400\pi$
$647$	420.130	+	335.042i	0.649350	+	0.517839i	−0.242511	+	0.970149i	$0.577971\pi$
$648$		0			0
$649$	−36.4616	−	4.10824i	−0.0561812	−	0.00633010i
$650$	−805.766	−	805.766i	−1.23964	−	1.23964i
$651$		0			0
$652$	440.734	+	276.931i	0.675972	+	0.424742i
$653$	−346.424	+	551.330i	−0.530511	+	0.844304i	−0.999238	−	0.0390396i	$-0.987570\pi$
$653$	−346.424	+	551.330i	−0.530511	+	0.844304i	0.468726	+	0.883343i	$0.344713\pi$
$654$		0			0
$655$	145.101	−	145.101i	0.221528	−	0.221528i
$656$	85.4185	−	758.110i	0.130211	−	1.15566i
$657$		0			0
$658$	−430.041	+	539.254i	−0.653557	+	0.819535i
$659$	21.4040	+	189.966i	0.0324795	+	0.288264i	0.999444	+	0.0333513i	$0.0106180\pi$
$659$	21.4040	+	189.966i	0.0324795	+	0.288264i	−0.966964	+	0.254912i	$0.917953\pi$
$660$		0			0
$661$	220.074	+	964.209i	0.332942	+	1.45871i	0.813405	+	0.581698i	$0.197611\pi$
$661$	220.074	+	964.209i	0.332942	+	1.45871i	−0.480463	+	0.877015i	$0.659532\pi$
$662$	−42.0946	+	184.428i	−0.0635869	+	0.278593i
$663$		0			0
$664$	−276.112	−	96.6158i	−0.415832	−	0.145506i
$665$	−106.709	+	67.0499i	−0.160465	+	0.100827i
$666$		0			0
$667$	319.189	+	251.247i	0.478544	+	0.376682i
$668$	529.394			0.792506
$669$		0			0
$670$	−53.2423	+	152.158i	−0.0794661	+	0.227101i
$671$	−75.0146	+	155.769i	−0.111795	+	0.232145i
$672$		0			0
$673$	1093.28	−	249.533i	1.62448	−	0.370777i	0.689169	−	0.724600i	$-0.257976\pi$
$673$	1093.28	−	249.533i	1.62448	−	0.370777i	0.935312	+	0.353823i	$0.115118\pi$
$674$	754.917	−	363.549i	1.12005	−	0.539390i
$675$		0			0
$676$	490.587	+	391.230i	0.725721	+	0.578743i
$677$	266.705	+	762.199i	0.393951	+	1.12585i	0.954625	+	0.297811i	$0.0962566\pi$
$677$	266.705	+	762.199i	0.393951	+	1.12585i	−0.560673	+	0.828037i	$0.689458\pi$
$678$		0			0
$679$	−192.634	−	192.634i	−0.283702	−	0.283702i
$680$	−309.714	+	246.989i	−0.455462	+	0.363219i
$681$		0			0
$682$	−259.393	+	412.822i	−0.380342	+	0.605310i
$683$	−172.817	−	216.706i	−0.253027	−	0.317285i	0.639054	−	0.769162i	$-0.279326\pi$
$683$	−172.817	−	216.706i	−0.253027	−	0.317285i	−0.892080	+	0.451877i	$0.850755\pi$
$684$		0			0
$685$	−94.7880	+	841.266i	−0.138377	+	1.22813i
$686$	−939.011	+	328.574i	−1.36882	+	0.478971i
$687$		0			0
$688$	69.6403	+	618.075i	0.101221	+	0.898364i
$689$	109.393	+	227.157i	0.158771	+	0.329691i
$690$		0			0
$691$	−129.908	+	569.165i	−0.188000	+	0.823683i	0.789669	+	0.613533i	$0.210252\pi$
$691$	−129.908	+	569.165i	−0.188000	+	0.823683i	−0.977669	+	0.210150i	$0.932605\pi$
$692$	−120.366	−	57.9654i	−0.173940	−	0.0837650i
$693$		0			0
$694$	606.132	−	380.858i	0.873390	−	0.548787i
$695$			1606.02i			2.31083i
$696$		0			0
$697$	−1112.03			−1.59545
$698$	189.667	+	301.853i	0.271729	+	0.432454i
$699$		0			0
$700$	164.049	−	340.652i	0.234356	−	0.486646i
$701$	1089.11	+	248.581i	1.55365	+	0.354610i	0.911280	−	0.411788i	$-0.135096\pi$
$701$	1089.11	+	248.581i	1.55365	+	0.354610i	0.642366	+	0.766398i	$0.277953\pi$
$702$		0			0
$703$	73.4521	−	35.3727i	0.104484	−	0.0503167i
$704$	−113.401	+	12.7773i	−0.161081	+	0.0181495i
$705$		0			0
$706$	−296.026	−	845.994i	−0.419300	−	1.19829i
$707$	68.0779	+	7.67054i	0.0962913	+	0.0108494i
$708$		0			0
$709$	−36.5193	+	29.1232i	−0.0515082	+	0.0410764i	−0.648906	−	0.760869i	$-0.724773\pi$
$709$	−36.5193	+	29.1232i	−0.0515082	+	0.0410764i	0.597397	+	0.801945i	$0.296202\pi$
$710$	−981.331	−	616.611i	−1.38216	−	0.868467i
$711$		0			0
$712$	96.8679	+	121.468i	0.136050	+	0.170602i
$713$	576.300	−	576.300i	0.808275	−	0.808275i
$714$		0			0
$715$	386.708	−	135.315i	0.540850	−	0.189252i
$716$	−192.063	+	240.839i	−0.268244	+	0.336368i
$717$		0			0
$718$	489.511	+	1016.48i	0.681771	+	1.41571i
$719$	−47.5410	−	208.291i	−0.0661210	−	0.289695i	0.931047	−	0.364899i	$-0.118896\pi$
$719$	−47.5410	−	208.291i	−0.0661210	−	0.289695i	−0.997168	+	0.0752038i	$0.976039\pi$
$720$		0			0
$721$	165.623	+	79.7599i	0.229713	+	0.110624i
$722$	884.403	+	309.466i	1.22494	+	0.428623i
$723$		0			0
$724$		−	504.730i		−	0.697141i
$725$	627.517	−	147.423i	0.865541	−	0.203342i
$726$		0			0
$727$	312.925	+	498.018i	0.430434	+	0.685031i	0.989571	−	0.144044i	$-0.0460105\pi$
$727$	312.925	+	498.018i	0.430434	+	0.685031i	−0.559138	+	0.829075i	$0.688868\pi$
$728$	71.3695	−	203.962i	0.0980351	−	0.280168i
$729$		0			0
$730$	−1118.61	−	255.316i	−1.53235	−	0.349748i
$731$	883.886	−	201.741i	1.20915	−	0.275980i
$732$		0			0
$733$	−208.812	+	23.5275i	−0.284873	+	0.0320975i	−0.253245	−	0.967402i	$-0.581498\pi$
$733$	−208.812	+	23.5275i	−0.284873	+	0.0320975i	−0.0316283	+	0.999500i	$0.510069\pi$
$734$	1463.52	+	1167.12i	1.99389	+	1.59008i
$735$		0			0
$736$	574.244	+	64.7017i	0.780222	+	0.0879100i
$737$	−19.2885	−	19.2885i	−0.0261717	−	0.0261717i
$738$		0			0
$739$	291.025	+	182.863i	0.393810	+	0.247447i	0.714351	−	0.699788i	$-0.246722\pi$
$739$	291.025	+	182.863i	0.393810	+	0.247447i	−0.320541	+	0.947234i	$0.603865\pi$
$740$	−276.488	+	440.028i	−0.373632	+	0.594632i
$741$		0			0
$742$	−132.964	+	132.964i	−0.179197	+	0.179197i
$743$	26.4958	−	235.157i	0.0356605	−	0.316496i	−0.963201	−	0.268784i	$-0.913378\pi$
$743$	26.4958	−	235.157i	0.0356605	−	0.316496i	0.998861	−	0.0477124i	$-0.0151931\pi$
$744$		0			0
$745$	−443.194	+	555.747i	−0.594891	+	0.745970i
$746$	0.205016	+	1.81957i	0.000274820	+	0.00243910i
$747$		0			0
$748$	60.1954	+	263.733i	0.0804752	+	0.352585i
$749$	165.866	−	726.707i	0.221450	−	0.970236i
$750$		0			0
$751$	550.749	+	192.716i	0.733355	+	0.256612i	0.671016	−	0.741443i	$-0.265858\pi$
$751$	550.749	+	192.716i	0.733355	+	0.256612i	0.0623390	+	0.998055i	$0.480144\pi$
$752$	−760.421	+	477.804i	−1.01120	+	0.635378i
$753$		0			0
$754$	−1400.14	+	499.928i	−1.85695	+	0.663035i
$755$	121.071			0.160359
$756$		0			0
$757$	363.807	−	1039.70i	0.480590	−	1.37345i	−0.407259	−	0.913313i	$-0.633515\pi$
$757$	363.807	−	1039.70i	0.480590	−	1.37345i	0.887849	−	0.460135i	$-0.152199\pi$
$758$	124.296	−	258.104i	0.163979	−	0.340507i
$759$		0			0
$760$	−49.3729	+	11.2690i	−0.0649643	+	0.0148277i
$761$	−191.779	+	92.3558i	−0.252009	+	0.121361i	−0.555624	−	0.831434i	$-0.687521\pi$
$761$	−191.779	+	92.3558i	−0.252009	+	0.121361i	0.303615	+	0.952795i	$0.401806\pi$
$762$		0			0
$763$	−127.072	−	101.336i	−0.166542	−	0.132813i
$764$	−223.501	−	638.728i	−0.292540	−	0.836031i
$765$		0			0
$766$	−833.267	−	833.267i	−1.08782	−	1.08782i
$767$	−175.513	+	139.967i	−0.228830	+	0.182486i
$768$		0			0
$769$	−122.480	+	194.927i	−0.159272	+	0.253481i	−0.916821	−	0.399298i	$-0.869254\pi$
$769$	−122.480	+	194.927i	−0.159272	+	0.253481i	0.757549	+	0.652779i	$0.226397\pi$
$770$	190.515	+	238.898i	0.247422	+	0.310257i
$771$		0			0
$772$	2.84066	−	25.2115i	0.00367961	−	0.0326574i
$773$	−889.330	+	311.190i	−1.15049	+	0.402575i	−0.837100	−	0.547049i	$-0.815751\pi$
$773$	−889.330	+	311.190i	−1.15049	+	0.402575i	−0.313392	+	0.949624i	$0.601465\pi$
$774$		0			0
$775$	−144.805	−	1285.18i	−0.186846	−	1.65830i
$776$	−47.4981	−	98.6308i	−0.0612089	−	0.127102i
$777$		0			0
$778$	117.729	−	515.806i	0.151323	−	0.662989i
$779$	−128.083	−	61.6817i	−0.164420	−	0.0791806i
$780$		0			0
$781$	166.056	−	104.340i	0.212619	−	0.133598i
$782$		−	1016.47i		−	1.29983i
$783$		0			0
$784$	−386.567			−0.493070
$785$	286.960	+	456.694i	0.365554	+	0.581776i
$786$		0			0
$787$	493.293	−	1024.33i	0.626801	−	1.30157i	−0.309677	−	0.950842i	$-0.600221\pi$
$787$	493.293	−	1024.33i	0.626801	−	1.30157i	0.936479

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	261.s (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42815 - 2.27289i) q^{2} +(-1.39088 + 2.88819i) q^{4} +(6.69994 + 1.52922i) q^{5} +(-4.78081 + 2.30231i) q^{7} +(-2.11889 + 0.238741i) q^{8} +O(q^{10})\)	\(q+(-1.42815 - 2.27289i) q^{2} +(-1.39088 + 2.88819i) q^{4} +(6.69994 + 1.52922i) q^{5} +(-4.78081 + 2.30231i) q^{7} +(-2.11889 + 0.238741i) q^{8} +(-6.09279 - 17.4122i) q^{10} +(3.10194 + 0.349505i) q^{11} +(14.9316 - 11.9076i) q^{13} +(12.0606 + 7.57819i) q^{14} +(11.5635 + 14.5002i) q^{16} +(19.1156 - 19.1156i) q^{17} +(3.26204 - 1.14144i) q^{19} +(-13.7355 + 17.2238i) q^{20} +(-3.63566 - 7.54952i) q^{22} +(3.11691 + 13.6561i) q^{23} +(20.0264 + 9.64422i) q^{25} +(-48.3892 - 16.9321i) q^{26} -17.0101i q^{28} +(22.5579 - 18.2247i) q^{29} +(-30.9563 - 49.2666i) q^{31} +(13.6259 - 38.9405i) q^{32} +(-70.7477 - 16.1477i) q^{34} +(-35.5518 + 8.11447i) q^{35} +(23.4414 - 2.64121i) q^{37} +(-7.25305 - 5.78412i) q^{38} +(-14.5615 - 1.64069i) q^{40} +(-29.0869 - 29.0869i) q^{41} +(28.3964 + 17.8426i) q^{43} +(-5.32387 + 8.47289i) q^{44} +(26.5873 - 26.5873i) q^{46} +(-5.42166 + 48.1186i) q^{47} +(-12.9956 + 16.2959i) q^{49} +(-6.68052 - 59.2913i) q^{50} +(13.6233 + 59.6874i) q^{52} +(-2.93760 + 12.8705i) q^{53} +(20.2483 + 7.08520i) q^{55} +(9.58032 - 6.01972i) q^{56} +(-73.6390 - 25.2439i) q^{58} -11.7545 q^{59} +(-18.2928 + 52.2779i) q^{61} +(-67.7674 + 140.721i) q^{62} +(-35.6416 + 8.13496i) q^{64} +(118.250 - 56.9463i) q^{65} +(-6.83210 - 5.44842i) q^{67} +(28.6221 + 81.7971i) q^{68} +(69.2167 + 69.2167i) q^{70} +(49.1193 - 39.1713i) q^{71} +(33.0911 - 52.6641i) q^{73} +(-39.4811 - 49.5078i) q^{74} +(-1.24042 + 11.0090i) q^{76} +(-15.6344 + 5.47073i) q^{77} +(5.05536 + 44.8675i) q^{79} +(55.3008 + 114.833i) q^{80} +(-24.5708 + 107.652i) q^{82} +(123.603 + 59.5242i) q^{83} +(157.305 - 98.8415i) q^{85} -90.0238i q^{86} -6.65610 q^{88} +(-38.7651 - 61.6944i) q^{89} +(-43.9702 + 91.3050i) q^{91} +(-43.7766 - 9.99172i) q^{92} +(117.111 - 56.3978i) q^{94} +(23.6010 - 2.65919i) q^{95} +(16.9565 + 48.4590i) q^{97} +(55.5985 + 6.26444i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \)	\( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

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