LMFDB - Embedded newform 605.2.s.b.16.11

Newspace parameters

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.s (of order $55$, degree $40$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$880$
Relative dimension:	$22$ over $\Q(\zeta_{55})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{55}]$

Embedding invariants

Embedding label			16.11
Character	$\chi$	$=$	605.16
Dual form			605.2.s.b.416.11

$q$-expansion

$f(q)$	$=$	$q+(0.00892359 + 0.00102389i) q^{2} +(-0.467498 - 0.339657i) q^{3} +(-1.94795 - 0.452975i) q^{4} +(-0.564443 + 0.825472i) q^{5} +(-0.00382399 - 0.00350963i) q^{6} +(1.06012 + 1.09083i) q^{7} +(-0.0338384 - 0.0120735i) q^{8} +(-0.823864 - 2.53559i) q^{9} +O(q^{10})$	\(q+(0.00892359 + 0.00102389i) q^{2} +(-0.467498 - 0.339657i) q^{3} +(-1.94795 - 0.452975i) q^{4} +(-0.564443 + 0.825472i) q^{5} +(-0.00382399 - 0.00350963i) q^{6} +(1.06012 + 1.09083i) q^{7} +(-0.0338384 - 0.0120735i) q^{8} +(-0.823864 - 2.53559i) q^{9} +(-0.00588205 + 0.00678825i) q^{10} +(-0.898752 + 3.19253i) q^{11} +(0.756804 + 0.873399i) q^{12} +(0.398934 - 0.661558i) q^{13} +(0.00834315 + 0.0108196i) q^{14} +(0.544254 - 0.194189i) q^{15} +(3.58916 + 1.76467i) q^{16} +(3.12830 - 2.55800i) q^{17} +(-0.00475566 - 0.0234701i) q^{18} +(5.99164 + 0.342614i) q^{19} +(1.47342 - 1.35230i) q^{20} +(-0.125093 - 0.870039i) q^{21} +(-0.0112889 + 0.0275686i) q^{22} +(0.897887 - 6.24494i) q^{23} +(0.0117185 + 0.0171378i) q^{24} +(-0.362808 - 0.931864i) q^{25} +(0.00423728 - 0.00549501i) q^{26} +(-1.01178 + 3.11395i) q^{27} +(-1.57093 - 2.60509i) q^{28} +(1.00939 - 2.59260i) q^{29} +(0.00505552 - 0.00117561i) q^{30} +(1.31577 + 0.556050i) q^{31} +(0.0906702 + 0.0582702i) q^{32} +(1.50453 - 1.18723i) q^{33} +(0.0305348 - 0.0196235i) q^{34} +(-1.49883 + 0.259383i) q^{35} +(0.456281 + 5.31238i) q^{36} +(-0.326199 + 3.79787i) q^{37} +(0.0531161 + 0.00919210i) q^{38} +(-0.411204 + 0.173776i) q^{39} +(0.0290662 - 0.0211178i) q^{40} +(9.68335 - 5.46844i) q^{41} +(-0.000225455 - 0.00789195i) q^{42} +(6.28029 - 1.84406i) q^{43} +(3.19686 - 5.81176i) q^{44} +(2.55808 + 0.751121i) q^{45} +(0.0144065 - 0.0548079i) q^{46} +(-1.00434 + 4.95663i) q^{47} +(-1.07854 - 2.04406i) q^{48} +(0.133820 - 4.68432i) q^{49} +(-0.00228342 - 0.00868704i) q^{50} +(-2.33132 + 0.133310i) q^{51} +(-1.07677 + 1.10797i) q^{52} +(4.04193 - 1.98728i) q^{53} +(-0.0122171 + 0.0267516i) q^{54} +(-2.12805 - 2.54390i) q^{55} +(-0.0227025 - 0.0497114i) q^{56} +(-2.68471 - 2.19527i) q^{57} +(0.0116619 - 0.0221018i) q^{58} +(6.16460 + 3.48131i) q^{59} +(-1.14814 + 0.131737i) q^{60} +(-4.62829 + 0.531047i) q^{61} +(0.0111721 + 0.00630916i) q^{62} +(1.89252 - 3.58672i) q^{63} +(-6.19163 - 5.06287i) q^{64} +(0.320922 + 0.702721i) q^{65} +(0.0146414 - 0.00905392i) q^{66} +(-2.24379 + 4.91321i) q^{67} +(-7.25248 + 3.56580i) q^{68} +(-2.54090 + 2.61452i) q^{69} +(-0.0136405 + 0.000779992i) q^{70} +(-1.37069 - 5.21465i) q^{71} +(-0.00273528 + 0.0957473i) q^{72} +(7.44974 + 14.1188i) q^{73} +(-0.00679946 + 0.0335567i) q^{74} +(-0.146902 + 0.558875i) q^{75} +(-11.5162 - 3.38146i) q^{76} +(-4.43530 + 2.40406i) q^{77} +(-0.00384734 + 0.00112968i) q^{78} +(-0.193251 - 6.76466i) q^{79} +(-3.48256 + 1.96669i) q^{80} +(-4.94003 + 3.58914i) q^{81} +(0.0920093 - 0.0388834i) q^{82} +(-1.15317 - 0.199564i) q^{83} +(-0.150432 + 1.75145i) q^{84} +(0.345808 + 4.02617i) q^{85} +(0.0579308 - 0.0100253i) q^{86} +(-1.35248 + 0.869189i) q^{87} +(0.0689574 - 0.0971790i) q^{88} +(-9.75946 - 6.27202i) q^{89} +(0.0220582 + 0.00932188i) q^{90} +(1.14457 - 0.266158i) q^{91} +(-4.57784 + 11.7581i) q^{92} +(-0.426254 - 0.706864i) q^{93} +(-0.0140374 + 0.0432026i) q^{94} +(-3.66476 + 4.75254i) q^{95} +(-0.0225962 - 0.0580380i) q^{96} +(2.20585 + 3.22595i) q^{97} +(0.00599037 - 0.0416639i) q^{98} +(8.83540 - 0.351342i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 880q + 4q^{2} - q^{3} + 24q^{4} + 22q^{5} - 13q^{6} + 3q^{7} + 2q^{8} - 217q^{9} + O(q^{10}) $	\( 880q + 4q^{2} - q^{3} + 24q^{4} + 22q^{5} - 13q^{6} + 3q^{7} + 2q^{8} - 217q^{9} - 6q^{10} + 5q^{11} - 5q^{12} - 26q^{13} - 108q^{14} - 12q^{15} + 34q^{16} - q^{17} - 14q^{18} + q^{19} + 19q^{20} - 10q^{21} + 275q^{22} - 51q^{23} + 283q^{24} + 22q^{25} - 16q^{27} - 4q^{28} - 19q^{29} + q^{30} - 34q^{31} - 122q^{32} + 19q^{33} + 52q^{34} + 8q^{35} - 21q^{36} - 109q^{37} - 10q^{38} - 9q^{39} - 64q^{40} + 4q^{41} - 49q^{42} - 97q^{43} + 17q^{44} - 80q^{45} - 91q^{46} + 166q^{47} - 159q^{48} + 175q^{49} + 4q^{50} - 112q^{51} - 128q^{52} - 141q^{53} - 37q^{54} - 5q^{55} + 79q^{56} - 204q^{57} - 190q^{58} + 9q^{59} - 22q^{60} + 2q^{61} - 105q^{62} - q^{63} - 176q^{64} - 14q^{65} - 112q^{66} - 13q^{67} - 35q^{68} - 53q^{69} + 24q^{70} - 50q^{71} + 705q^{72} + q^{73} + 40q^{74} - q^{75} - 148q^{76} - 104q^{77} - 187q^{78} - 83q^{79} - q^{80} - 238q^{81} - 54q^{82} - 151q^{83} + 4q^{84} - 29q^{85} - 39q^{86} - 74q^{87} - 143q^{88} - 52q^{89} - 28q^{90} - 188q^{91} - 253q^{92} + 122q^{93} - 187q^{94} + 122q^{95} - 155q^{96} + 283q^{97} - 92q^{98} + 172q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{2}{55}\right)$

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 $

$2$	0.00892359	+	0.00102389i	0.00630993	+	0.000723997i	0.117146	−	0.993115i	$-0.462626\pi$
$2$	0.00892359	+	0.00102389i	0.00630993	+	0.000723997i	−0.110836	+	0.993839i	$0.535353\pi$
$3$	−0.467498	−	0.339657i	−0.269910	−	0.196101i	0.444594	−	0.895732i	$-0.353348\pi$
$3$	−0.467498	−	0.339657i	−0.269910	−	0.196101i	−0.714505	+	0.699631i	$0.753348\pi$
$4$	−1.94795	−	0.452975i	−0.973973	−	0.226488i
$5$	−0.564443	+	0.825472i	−0.252427	+	0.369162i
$5$	−0.564443	+	0.825472i	−0.252427	+	0.369162i
$6$	−0.00382399	−	0.00350963i	−0.00156114	−	0.00143280i
$7$	1.06012	+	1.09083i	0.400686	+	0.412297i	0.887206	−	0.461373i	$-0.152643\pi$
$7$	1.06012	+	1.09083i	0.400686	+	0.412297i	−0.486520	+	0.873670i	$0.661734\pi$
$8$	−0.0338384	−	0.0120735i	−0.0119637	−	0.00426863i
$9$	−0.823864	−	2.53559i	−0.274621	−	0.845197i
$10$	−0.00588205	+	0.00678825i	−0.00186007	+	0.00214663i
$11$	−0.898752	+	3.19253i	−0.270984	+	0.962584i
$11$	−0.898752	+	3.19253i	−0.270984	+	0.962584i
$12$	0.756804	+	0.873399i	0.218471	+	0.252128i
$13$	0.398934	−	0.661558i	0.110644	−	0.183483i	−0.796098	−	0.605167i	$-0.793106\pi$
$13$	0.398934	−	0.661558i	0.110644	−	0.183483i	0.906743	+	0.421684i	$0.138561\pi$
$14$	0.00834315	+	0.0108196i	0.00222980	+	0.00289166i
$15$	0.544254	−	0.194189i	0.140526	−	0.0501395i
$16$	3.58916	+	1.76467i	0.897290	+	0.441168i
$17$	3.12830	−	2.55800i	0.758725	−	0.620407i	−0.172433	−	0.985021i	$-0.555163\pi$
$17$	3.12830	−	2.55800i	0.758725	−	0.620407i	0.931159	+	0.364615i	$0.118799\pi$
$18$	−0.00475566	−	0.0234701i	−0.00112092	−	0.00553196i
$19$	5.99164	+	0.342614i	1.37458	+	0.0786011i	0.728695	−	0.684838i	$-0.240127\pi$
$19$	5.99164	+	0.342614i	1.37458	+	0.0786011i	0.645880	+	0.763439i	$0.276491\pi$
$20$	1.47342	−	1.35230i	0.329467	−	0.302382i
$21$	−0.125093	−	0.870039i	−0.0272975	−	0.189858i
$22$	−0.0112889	+	0.0275686i	−0.00240680	+	0.00587765i
$23$	0.897887	−	6.24494i	0.187222	−	1.30216i	−0.651937	−	0.758273i	$-0.726043\pi$
$23$	0.897887	−	6.24494i	0.187222	−	1.30216i	0.839159	−	0.543886i	$-0.183048\pi$
$24$	0.0117185	+	0.0171378i	0.00239204	+	0.00349824i
$25$	−0.362808	−	0.931864i	−0.0725615	−	0.186373i
$26$	0.00423728	−	0.00549501i	0.000830999	−	0.00107766i
$27$	−1.01178	+	3.11395i	−0.194718	+	0.599279i
$28$	−1.57093	−	2.60509i	−0.296878	−	0.492316i
$29$	1.00939	−	2.59260i	0.187439	−	0.481434i	−0.806517	−	0.591211i	$-0.798650\pi$
$29$	1.00939	−	2.59260i	0.187439	−	0.481434i	0.993956	+	0.109777i	$0.0350136\pi$
$30$	0.00505552	−	0.00117561i	0.000923008	−	0.000214636i
$31$	1.31577	+	0.556050i	0.236320	+	0.0998695i	0.504214	−	0.863579i	$-0.331782\pi$
$31$	1.31577	+	0.556050i	0.236320	+	0.0998695i	−0.267894	+	0.963448i	$0.586328\pi$
$32$	0.0906702	+	0.0582702i	0.0160284	+	0.0103008i
$33$	1.50453	−	1.18723i	0.261905	−	0.206671i
$34$	0.0305348	−	0.0196235i	0.00523668	−	0.00336541i
$35$	−1.49883	+	0.259383i	−0.253348	+	0.0438436i
$36$	0.456281	+	5.31238i	0.0760468	+	0.885397i
$37$	−0.326199	+	3.79787i	−0.0536269	+	0.624366i	0.919346	+	0.393449i	$0.128718\pi$
$37$	−0.326199	+	3.79787i	−0.0536269	+	0.624366i	−0.972973	+	0.230917i	$0.925827\pi$
$38$	0.0531161	+	0.00919210i	0.00861657	+	0.00149116i
$39$	−0.411204	+	0.173776i	−0.0658453	+	0.0278264i
$40$	0.0290662	−	0.0211178i	0.00459577	−	0.00333902i
$41$	9.68335	−	5.46844i	1.51229	−	0.854027i	0.512297	−	0.858809i	$-0.328795\pi$
$41$	9.68335	−	5.46844i	1.51229	−	0.854027i	0.999989	+	0.00478191i	$0.00152214\pi$
$42$	−0.000225455	−	0.00789195i	−3.47884e−5	−	0.00121775i
$43$	6.28029	−	1.84406i	0.957735	−	0.281216i	0.234731	−	0.972060i	$-0.424579\pi$
$43$	6.28029	−	1.84406i	0.957735	−	0.281216i	0.723004	+	0.690844i	$0.242761\pi$
$44$	3.19686	−	5.81176i	0.481944	−	0.876156i
$45$	2.55808	+	0.751121i	0.381337	+	0.111971i
$46$	0.0144065	−	0.0548079i	0.00212412	−	0.00808099i
$47$	−1.00434	+	4.95663i	−0.146499	+	0.722999i	0.837728	+	0.546088i	$0.183883\pi$
$47$	−1.00434	+	4.95663i	−0.146499	+	0.722999i	−0.984227	+	0.176912i	$0.943389\pi$
$48$	−1.07854	−	2.04406i	−0.155674	−	0.295035i
$49$	0.133820	−	4.68432i	0.0191172	−	0.669189i
$50$	−0.00228342	−	0.00868704i	−0.000322925	−	0.00122853i
$51$	−2.33132	+	0.133310i	−0.326450	+	0.0186671i
$52$	−1.07677	+	1.10797i	−0.149321	+	0.153648i
$53$	4.04193	−	1.98728i	0.555202	−	0.272975i	−0.141979	−	0.989870i	$-0.545346\pi$
$53$	4.04193	−	1.98728i	0.555202	−	0.272975i	0.697181	+	0.716895i	$0.254437\pi$
$54$	−0.0122171	+	0.0267516i	−0.00166253	+	0.00364043i
$55$	−2.12805	−	2.54390i	−0.286946	−	0.343019i
$56$	−0.0227025	−	0.0497114i	−0.00303374	−	0.00664297i
$57$	−2.68471	−	2.19527i	−0.355598	−	0.290771i
$58$	0.0116619	−	0.0221018i	0.00153129	−	0.00290211i
$59$	6.16460	+	3.48131i	0.802563	+	0.453228i	0.837684	−	0.546155i	$-0.183909\pi$
$59$	6.16460	+	3.48131i	0.802563	+	0.453228i	−0.0351215	+	0.999383i	$0.511182\pi$
$60$	−1.14814	+	0.131737i	−0.148224	+	0.0170071i
$61$	−4.62829	+	0.531047i	−0.592592	+	0.0679936i	−0.405100	−	0.914273i	$-0.632763\pi$
$61$	−4.62829	+	0.531047i	−0.592592	+	0.0679936i	−0.187492	+	0.982266i	$0.560036\pi$
$62$	0.0111721	+	0.00630916i	0.00141885	+	0.000801264i
$63$	1.89252	−	3.58672i	0.238435	−	0.451884i
$64$	−6.19163	−	5.06287i	−0.773954	−	0.632859i
$65$	0.320922	+	0.702721i	0.0398054	+	0.0871618i
$66$	0.0146414	−	0.00905392i	0.00180223	−	0.00111446i
$67$	−2.24379	+	4.91321i	−0.274122	+	0.600244i	−0.995756	−	0.0920307i	$-0.970664\pi$
$67$	−2.24379	+	4.91321i	−0.274122	+	0.600244i	0.721634	+	0.692275i	$0.243391\pi$
$68$	−7.25248	+	3.56580i	−0.879492	+	0.432417i
$69$	−2.54090	+	2.61452i	−0.305888	+	0.314751i
$70$	−0.0136405		0.000779992i	−0.00163035		9.32269e-5i
$71$	−1.37069	−	5.21465i	−0.162671	−	0.618865i	−0.997646	−	0.0685766i	$-0.978154\pi$
$71$	−1.37069	−	5.21465i	−0.162671	−	0.618865i	0.834975	−	0.550288i	$-0.185482\pi$
$72$	−0.00273528	+	0.0957473i	−0.000322356	+	0.0112839i
$73$	7.44974	+	14.1188i	0.871926	+	1.65248i	0.751472	+	0.659766i	$0.229344\pi$
$73$	7.44974	+	14.1188i	0.871926	+	1.65248i	0.120455	+	0.992719i	$0.461565\pi$
$74$	−0.00679946	+	0.0335567i	−0.000790421	+	0.00390088i
$75$	−0.146902	+	0.558875i	−0.0169628	+	0.0645333i
$76$	−11.5162	−	3.38146i	−1.32100	−	0.387880i
$77$	−4.43530	+	2.40406i	−0.505450	+	0.273969i
$78$	−0.00384734	+	0.00112968i	−0.000435625	+	0.000127911i
$79$	−0.193251	−	6.76466i	−0.0217424	−	0.761084i	−0.935194	−	0.354136i	$-0.884775\pi$
$79$	−0.193251	−	6.76466i	−0.0217424	−	0.761084i	0.913451	−	0.406948i	$-0.133407\pi$
$80$	−3.48256	+	1.96669i	−0.389362	+	0.219883i
$81$	−4.94003	+	3.58914i	−0.548892	+	0.398793i
$82$	0.0920093	−	0.0388834i	0.0101607	−	0.00429396i
$83$	−1.15317	−	0.199564i	−0.126577	−	0.0219050i	0.106882	−	0.994272i	$-0.465913\pi$
$83$	−1.15317	−	0.199564i	−0.126577	−	0.0219050i	−0.233459	+	0.972367i	$0.575004\pi$
$84$	−0.150432	+	1.75145i	−0.0164135	+	0.191099i
$85$	0.345808	+	4.02617i	0.0375082	+	0.436700i
$86$	0.0579308	−	0.0100253i	0.00624684	−	0.00108106i
$87$	−1.35248	+	0.869189i	−0.145002	+	0.0931869i
$88$	0.0689574	−	0.0971790i	0.00735088	−	0.0103593i
$89$	−9.75946	−	6.27202i	−1.03450	−	0.664833i	−0.0908799	−	0.995862i	$-0.528968\pi$
$89$	−9.75946	−	6.27202i	−1.03450	−	0.664833i	−0.943621	+	0.331029i	$0.892604\pi$
$90$	0.0220582	+	0.00932188i	0.00232514	+	0.000982613i
$91$	1.14457	−	0.266158i	0.119983	−	0.0279009i
$92$	−4.57784	+	11.7581i	−0.477272	+	1.22586i
$93$	−0.426254	−	0.706864i	−0.0442005	−	0.0732983i
$94$	−0.0140374	+	0.0432026i	−0.00144785	+	0.00445601i
$95$	−3.66476	+	4.75254i	−0.375996	+	0.487600i
$96$	−0.0225962	−	0.0580380i	−0.00230622	−	0.00592347i
$97$	2.20585	+	3.22595i	0.223970	+	0.327546i	0.921048	−	0.389450i	$-0.127335\pi$
$97$	2.20585	+	3.22595i	0.223970	+	0.327546i	−0.697078	+	0.716996i	$0.745517\pi$
$98$	0.00599037	−	0.0416639i	0.000605119	−	0.00420869i
$99$	8.83540	−	0.351342i	0.887991	−	0.0353112i
$100$	0.284618	+	1.97956i	0.0284618	+	0.197956i
$101$	3.33418	−	3.06008i	0.331763	−	0.304490i	−0.492931	−	0.870068i	$-0.664074\pi$
$101$	3.33418	−	3.06008i	0.331763	−	0.304490i	0.824694	+	0.565579i	$0.191347\pi$
$102$	−0.0209402	−	0.00119741i	−0.00207339	−	0.000118561i
$103$	1.19984	+	5.92146i	0.118224	+	0.583459i	0.994770	+	0.102140i	$0.0325691\pi$
$103$	1.19984	+	5.92146i	0.118224	+	0.583459i	−0.876546	+	0.481318i	$0.840158\pi$
$104$	−0.0214866	+	0.0175695i	−0.00210694	+	0.00172283i
$105$	0.788800	+	0.387827i	0.0769790	+	0.0378480i
$106$	0.0381033	−	0.0135952i	0.00370092	−	0.00132049i
$107$	6.70715	+	8.69799i	0.648405	+	0.840867i	0.995280	−	0.0970447i	$-0.0309390\pi$
$107$	6.70715	+	8.69799i	0.648405	+	0.840867i	−0.346875	+	0.937911i	$0.612757\pi$
$108$	3.38144	−	5.60748i	0.325379	−	0.539580i
$109$	−0.0394249	−	0.0454987i	−0.00377622	−	0.00435799i	0.753858	−	0.657037i	$-0.228190\pi$
$109$	−0.0394249	−	0.0454987i	−0.00377622	−	0.00435799i	−0.757635	+	0.652679i	$0.773645\pi$
$110$	−0.0163852	−	0.0248796i	−0.00156227	−	0.00237217i
$111$	1.44247	−	1.66470i	0.136913	−	0.158006i
$112$	1.87996	+	5.78593i	0.177640	+	0.546719i
$113$	−16.9541	−	6.04919i	−1.59490	−	0.569060i	−0.618645	−	0.785671i	$-0.712318\pi$
$113$	−16.9541	−	6.04919i	−1.59490	−	0.569060i	−0.976258	+	0.216611i	$0.930500\pi$
$114$	−0.0217095	−	0.0223385i	−0.00203328	−	0.00209220i
$115$	4.64821	+	4.26609i	0.433448	+	0.397815i
$116$	−3.14063	+	4.59302i	−0.291600	+	0.426451i
$117$	−2.00611	−	0.466500i	−0.185465	−	0.0431280i
$118$	0.0514459	+	0.0373776i	0.00473598	+	0.00344089i
$119$	6.10672	+	0.700681i	0.559802	+	0.0642313i
$120$	−0.0207612			−0.00189523
$121$	−9.38449	−	5.73858i	−0.853136	−	0.521689i
$122$	−0.0418447			−0.00378844
$123$	−6.38434	−	0.732535i	−0.575657	−	0.0660504i
$124$	−2.31117	−	1.67917i	−0.207550	−	0.150794i
$125$	0.974012	+	0.226497i	0.0871183	+	0.0202585i
$126$	0.0205605	−	0.0300687i	0.00183167	−	0.00267873i
$127$	−3.26730	−	2.99870i	−0.289926	−	0.266092i	0.517993	−	0.855385i	$-0.326679\pi$
$127$	−3.26730	−	2.99870i	−0.289926	−	0.266092i	−0.807920	+	0.589293i	$0.799406\pi$
$128$	−0.200299	−	0.206103i	−0.0177041	−	0.0182171i
$129$	−3.56237	−	1.27105i	−0.313649	−	0.111910i
$130$	0.00214427	+	0.00659938i	0.000188065	+	0.000578804i
$131$	−4.32758	+	4.99429i	−0.378102	+	0.436353i	−0.912623	−	0.408802i	$-0.865947\pi$
$131$	−4.32758	+	4.99429i	−0.378102	+	0.436353i	0.534521	+	0.845155i	$0.320492\pi$
$132$	−3.46853	+	1.63115i	−0.301897	+	0.141974i
$133$	5.97810	+	6.89909i	0.518367	+	0.598227i
$134$	−0.0250532	+	0.0415461i	−0.00216427	+	0.00358904i
$135$	−1.99938	−	2.59284i	−0.172079	−	0.223156i
$136$	−0.136741	+	0.0487891i	−0.0117254	+	0.00418363i
$137$	5.94157	+	2.92128i	0.507623	+	0.249581i	0.677017	−	0.735967i	$-0.263272\pi$
$137$	5.94157	+	2.92128i	0.507623	+	0.249581i	−0.169395	+	0.985548i	$0.554181\pi$
$138$	−0.0253509	+	0.0207293i	−0.00215801	+	0.00176460i
$139$	−0.424099	−	2.09301i	−0.0359716	−	0.177527i	0.958069	−	0.286538i	$-0.0925044\pi$
$139$	−0.424099	−	2.09301i	−0.0359716	−	0.177527i	−0.994041	+	0.109011i	$0.965232\pi$
$140$	3.03713	+	0.173669i	0.256684	+	0.0146777i
$141$	2.15308	−	1.97608i	0.181322	−	0.166416i
$142$	−0.00689227	−	0.0479368i	−0.000578386	−	0.00402277i
$143$	1.75350	+	1.86818i	0.146635	+	0.156225i
$144$	1.51751	−	10.5545i	0.126459	−	0.879541i
$145$	1.57038	+	2.29660i	0.130413	+	0.190722i
$146$	0.0520224	+	0.133618i	0.00430540	+	0.0110583i
$147$	−1.65362	+	2.14446i	−0.136389	+	0.176872i
$148$	2.35576	−	7.25029i	0.193642	−	0.595970i
$149$	−5.19828	−	8.62038i	−0.425860	−	0.706209i	0.567231	−	0.823559i	$-0.308015\pi$
$149$	−5.19828	−	8.62038i	−0.425860	−	0.706209i	−0.993091	+	0.117350i	$0.962560\pi$
$150$	−0.00188312	+	0.00483676i	−0.000153756	+	0.000394920i
$151$	11.7563	−	2.73381i	0.956713	−	0.222474i	0.281057	−	0.959691i	$-0.409315\pi$
$151$	11.7563	−	2.73381i	0.956713	−	0.222474i	0.675656	+	0.737217i	$0.263860\pi$
$152$	−0.198611	−	0.0839337i	−0.0161095	−	0.00680792i
$153$	−9.06334	−	5.82466i	−0.732728	−	0.470896i
$154$	−0.0420403	+	0.0169116i	−0.00338770	+	0.00136278i
$155$	−1.20168	+	0.772274i	−0.0965214	+	0.0620306i
$156$	0.879719	−	0.152241i	0.0704339	−	0.0121891i
$157$	1.19971	+	13.9680i	0.0957476	+	1.11477i	0.873706	+	0.486453i	$0.161710\pi$
$157$	1.19971	+	13.9680i	0.0957476	+	1.11477i	−0.777959	+	0.628315i	$0.783745\pi$
$158$	0.00520176	−	0.0605629i	0.000413829	−	0.00481813i
$159$	−2.56459	−	0.443820i	−0.203385	−	0.0351972i
$160$	−0.0992786	+	0.0419555i	−0.00784866	+	0.00331687i
$161$	7.76406	−	5.64092i	0.611893	−	0.444567i
$162$	−0.0477577	+	0.0269700i	−0.00375220	+	0.00211896i
$163$	−0.284123	−	9.94559i	−0.0222542	−	0.778999i	−0.931711	−	0.363200i	$-0.881684\pi$
$163$	−0.284123	−	9.94559i	−0.0222542	−	0.778999i	0.909457	−	0.415798i	$-0.136498\pi$
$164$	−21.3397	+	6.26590i	−1.66635	+	0.489285i
$165$	0.130806	+	1.91207i	0.0101833	+	0.148855i
$166$	−0.0100861	−	0.00296154i	−0.000782833	−	0.000229860i
$167$	5.98410	−	22.7659i	0.463064	−	1.76168i	−0.167838	−	0.985815i	$-0.553679\pi$
$167$	5.98410	−	22.7659i	0.463064	−	1.76168i	0.630902	−	0.775863i	$-0.282685\pi$
$168$	−0.00627150	+	0.0309511i	−0.000483856	+	0.00238793i
$169$	5.78816	+	10.9698i	0.445243	+	0.843830i
$170$	−0.00103649	+	0.0362820i	−7.94954e−5	+	0.00278270i
$171$	−4.06756	−	15.4746i	−0.311054	−	1.18337i
$172$	−13.0690	+	0.747311i	−0.996500	+	0.0569819i
$173$	−13.7427	+	14.1409i	−1.04483	+	1.07511i	−0.0477461	+	0.998860i	$0.515204\pi$
$173$	−13.7427	+	14.1409i	−1.04483	+	1.07511i	−0.997089	+	0.0762501i	$0.975705\pi$
$174$	−0.0129590	+	0.00637150i	−0.000982417	+	0.000483022i
$175$	0.631891	−	1.38365i	0.0477664	−	0.104594i
$176$	−8.85953	+	9.87250i	−0.667812	+	0.744167i
$177$	−1.69949	−	3.72136i	−0.127741	−	0.279714i
$178$	−0.0806676	−	0.0659615i	−0.00604629	−	0.00494403i
$179$	3.16447	−	5.99734i	0.236524	−	0.448262i	−0.737301	−	0.675565i	$-0.763900\pi$
$179$	3.16447	−	5.99734i	0.236524	−	0.448262i	0.973824	+	0.227303i	$0.0729907\pi$
$180$	−4.64277	−	2.62189i	−0.346051	−	0.195424i
$181$	6.07699	−	0.697270i	0.451699	−	0.0518276i	0.114843	−	0.993384i	$-0.463364\pi$
$181$	6.07699	−	0.697270i	0.451699	−	0.0518276i	0.336856	+	0.941556i	$0.390636\pi$
$182$	0.0104862	−	0.00120317i	0.000777285	−	8.91852e-5i
$183$	2.34409	+	1.32377i	0.173280	+	0.0978558i
$184$	−0.105781	+	0.200478i	−0.00779831	+	0.0147794i
$185$	−2.95092	−	2.41295i	−0.216956	−	0.177404i
$186$	−0.00307997	−	0.00674419i	−0.000225834	−	0.000494508i
$187$	5.35493	+	12.2862i	0.391591	+	0.898457i
$188$	4.20164	−	9.20031i	0.306436	−	0.671001i
$189$	−4.46941	+	2.19746i	−0.325101	+	0.159842i
$190$	−0.0375688	+	0.0386574i	−0.00272553	+	0.00280450i
$191$	12.9505	−	0.740537i	0.937066	−	0.0535833i	0.418121	−	0.908391i	$-0.362689\pi$
$191$	12.9505	−	0.740537i	0.937066	−	0.0535833i	0.518944	+	0.854808i	$0.326325\pi$
$192$	1.17493	+	4.46992i	0.0847936	+	0.322588i
$193$	−0.572950	+	20.0559i	−0.0412418	+	1.44365i	0.670864	+	0.741580i	$0.265923\pi$
$193$	−0.572950	+	20.0559i	−0.0412418	+	1.44365i	−0.712106	+	0.702072i	$0.752259\pi$
$194$	0.0163811	+	0.0310456i	0.00117609	+	0.00222895i
$195$	0.0886538	−	0.437524i	0.00634863	−	0.0313317i
$196$	−2.38256	+	9.06419i	−0.170183	+	0.647442i
$197$	−4.53025	−	1.33020i	−0.322767	−	0.0947729i	0.116335	−	0.993210i	$-0.462885\pi$
$197$	−4.53025	−	1.33020i	−0.322767	−	0.0947729i	−0.439102	+	0.898437i	$0.644703\pi$
$198$	0.0792032	+	0.00591121i	0.00562873	+	0.000420092i
$199$	15.6764	−	4.60299i	1.11127	−	0.326297i	0.325947	−	0.945388i	$-0.394317\pi$
$199$	15.6764	−	4.60299i	1.11127	−	0.326297i	0.785320	+	0.619090i	$0.212499\pi$
$200$	0.00102596	+	0.0359132i	7.25461e−5	+	0.00253944i
$201$	2.71777	−	1.53480i	0.191697	−	0.108256i
$202$	0.0328860	−	0.0238931i	0.00231385	−	0.00168111i
$203$	3.89817	−	1.64738i	0.273598	−	0.115624i
$204$	4.60167	+	0.796350i	0.322181	+	0.0557557i
$205$	−0.951658	+	11.0800i	−0.0664667	+	0.773858i
$206$	0.00464400	+	0.0540691i	0.000323563	+	0.00376718i
$207$	−16.5743	+	2.86830i	−1.15200	+	0.199361i
$208$	2.59927	−	1.67045i	0.180227	−	0.115825i
$209$	−6.47880	+	18.8205i	−0.448148	+	1.30184i
$210$	0.00664184	+	0.00426845i	0.000458330	+	0.000294551i
$211$	4.22331	+	1.78478i	0.290744	+	0.122870i	0.529764	−	0.848145i	$-0.322281\pi$
$211$	4.22331	+	1.78478i	0.290744	+	0.122870i	−0.239020	+	0.971015i	$0.576826\pi$
$212$	−8.77365	+	2.04023i	−0.602577	+	0.140123i
$213$	−1.13040	+	2.90340i	−0.0774535	+	0.198938i
$214$	0.0509461	+	0.0844847i	0.00348261	+	0.00577525i
$215$	−2.02265	+	6.22507i	−0.137943	+	0.424546i
$216$	0.0718334	−	0.0931552i	0.00488764	−	0.00633841i
$217$	0.788313	+	2.02477i	0.0535142	+	0.137450i
$218$	−0.000305226	0	0.000446379i	−2.06725e−5	0	3.02326e-5i
$219$	1.31282	−	9.13088i	0.0887124	−	0.617008i
$220$	2.99300	+	5.91932i	0.201788	+	0.399081i
$221$	−0.444279	−	3.09003i	−0.0298854	−	0.207858i
$222$	0.0145765	−	0.0133782i	0.000978310	−	0.000897885i
$223$	−14.2255	−	0.813445i	−0.952612	−	0.0544723i	−0.426133	−	0.904660i	$-0.640125\pi$
$223$	−14.2255	−	0.813445i	−0.952612	−	0.0544723i	−0.526479	+	0.850188i	$0.676488\pi$
$224$	0.0325578	+	0.160679i	0.00217536	+	0.0107358i
$225$	−2.06392	+	1.68766i	−0.137595	+	0.112511i
$226$	−0.145097	−	0.0713395i	−0.00965173	−	0.00474543i
$227$	3.76659	−	1.34392i	0.249997	−	0.0891988i	−0.208078	−	0.978112i	$-0.566721\pi$
$227$	3.76659	−	1.34392i	0.249997	−	0.0891988i	0.458075	+	0.888913i	$0.348539\pi$
$228$	4.23526	+	5.49238i	0.280487	+	0.363742i
$229$	13.6513	−	22.6382i	0.902104	−	1.49597i	0.0340983	−	0.999418i	$-0.489144\pi$
$229$	13.6513	−	22.6382i	0.902104	−	1.49597i	0.868006	−	0.496554i	$-0.165401\pi$
$230$	0.0371108	+	0.0428281i	0.00244701	+	0.00282400i
$231$	2.89005	+	0.382587i	0.190152	+	0.0251724i
$232$	−0.0654581	+	0.0755427i	−0.00429753	+	0.00495962i
$233$	−5.91411	−	18.2018i	−0.387446	−	1.19244i	−0.934690	−	0.355464i	$-0.884323\pi$
$233$	−5.91411	−	18.2018i	−0.387446	−	1.19244i	0.547244	−	0.836973i	$-0.315677\pi$
$234$	−0.0174240	−	0.00621688i	−0.00113904	−	0.000406410i
$235$	−3.52467	−	3.62680i	−0.229924	−	0.236586i
$236$	−10.4314	−	9.57381i	−0.679023	−	0.623202i
$237$	−2.20732	+	3.22811i	−0.143381	+	0.209688i
$238$	0.0537765	+	0.0125052i	0.00348581	+	0.000810591i
$239$	0.968688	+	0.703793i	0.0626592	+	0.0455246i	0.618674	−	0.785648i	$-0.287670\pi$
$239$	0.968688	+	0.703793i	0.0626592	+	0.0455246i	−0.556015	+	0.831172i	$0.687670\pi$
$240$	2.29609	+	0.263452i	0.148212	+	0.0170058i
$241$	−12.8940			−0.830574			−0.415287	−	0.909690i	$-0.636319\pi$
$241$	−12.8940			−0.830574			−0.415287	+	0.909690i	$0.636319\pi$
$242$	−0.0778677	−	0.0608174i	−0.00500552	−	0.00390949i
$243$	13.3511			0.856475
$244$	9.25621	+	1.06205i	0.592568	+	0.0679908i
$245$	3.79124	+	2.75450i	0.242214	+	0.175978i
$246$	−0.0562212	−	0.0130737i	−0.00358453	−	0.000833547i
$247$	2.61693	−	3.82713i	0.166511	−	0.243515i
$248$	−0.0378102	−	0.0347018i	−0.00240095	−	0.00220357i
$249$	0.471322	+	0.484979i	0.0298688	+	0.0307343i
$250$	0.00845977	+	0.00301844i	0.000535043	+	0.000190903i
$251$	−5.15248	−	15.8577i	−0.325222	−	1.00093i	−0.971341	−	0.237692i	$-0.923609\pi$
$251$	−5.15248	−	15.8577i	−0.325222	−	1.00093i	0.646119	−	0.763237i	$-0.276391\pi$
$252$	−5.31122	+	6.12947i	−0.334575	+	0.386120i
$253$	19.1302	+	8.47918i	1.20270	+	0.533081i
$254$	−0.0260857	−	0.0301045i	−0.00163676	−	0.00188893i
$255$	1.20585	−	1.99968i	0.0755135	−	0.125225i
$256$	9.76643	+	12.6653i	0.610402	+	0.791583i
$257$	23.0021	−	8.20713i	1.43483	−	0.511946i	0.499684	−	0.866208i	$-0.333450\pi$
$257$	23.0021	−	8.20713i	1.43483	−	0.511946i	0.935146	+	0.354261i	$0.115268\pi$
$258$	−0.0304877	−	0.0149898i	−0.00189808	−	0.000933224i
$259$	−4.48866	+	3.67036i	−0.278912	+	0.228065i
$260$	−0.306823	−	1.51423i	−0.0190284	−	0.0939086i
$261$	−7.40538	−	0.423455i	−0.458382	−	0.0262112i
$262$	−0.0437311	+	0.0401360i	−0.00270172	+	0.00247961i
$263$	−0.113962	−	0.792620i	−0.00702717	−	0.0488750i	0.986006	−	0.166709i	$-0.0533140\pi$
$263$	−0.113962	−	0.792620i	−0.00702717	−	0.0488750i	−0.993033	+	0.117834i	$0.962405\pi$
$264$	−0.0652450	+	0.0220091i	−0.00401555	+	0.00135457i
$265$	−0.640994	+	4.45821i	−0.0393759	+	0.273866i
$266$	0.0462822	+	0.0676855i	0.00283774	+	0.00415007i
$267$	2.43219	+	6.24703i	0.148848	+	0.382312i
$268$	6.59634	−	8.55429i	0.402936	−	0.522536i
$269$	8.16831	−	25.1395i	0.498031	−	1.53278i	−0.314149	−	0.949374i	$-0.601719\pi$
$269$	8.16831	−	25.1395i	0.498031	−	1.53278i	0.812180	−	0.583407i	$-0.198281\pi$
$270$	−0.0151869	−	0.0251846i	−0.000924244	−	0.00153269i
$271$	−0.145878	+	0.374684i	−0.00886143	+	0.0227604i	−0.936225	−	0.351400i	$-0.885706\pi$
$271$	−0.145878	+	0.374684i	−0.00886143	+	0.0227604i	0.927364	+	0.374161i	$0.122069\pi$
$272$	15.7420	−	3.66065i	0.954500	−	0.221959i
$273$	−0.625485	−	0.264332i	−0.0378561	−	0.0159981i
$274$	0.0500291	+	0.0321518i	0.00302237	+	0.00194236i
$275$	3.30108	−	0.320760i	0.199062	−	0.0193426i
$276$	6.13384	−	3.94198i	0.369214	−	0.237279i
$277$	−17.3102	+	2.99565i	−1.04007	+	0.179991i	−0.664874	−	0.746955i	$-0.731515\pi$
$277$	−17.3102	+	2.99565i	−1.04007	+	0.179991i	−0.375194	+	0.926946i	$0.622424\pi$
$278$	−0.00164148	−	0.0191114i	−9.84494e−5	−	0.00114623i
$279$	0.325899	−	3.79437i	0.0195110	−	0.227163i
$280$	0.0538496	+	0.00931905i	0.00321813	+	0.000556920i
$281$	−3.54792	+	1.49936i	−0.211651	+	0.0894446i	−0.492518	−	0.870302i	$-0.663924\pi$
$281$	−3.54792	+	1.49936i	−0.211651	+	0.0894446i	0.280867	+	0.959747i	$0.409378\pi$
$282$	0.0212365	−	0.0154292i	0.00126462	−	0.000918798i
$283$	6.36521	−	3.59460i	0.378373	−	0.213677i	−0.290800	−	0.956784i	$-0.593921\pi$
$283$	6.36521	−	3.59460i	0.378373	−	0.213677i	0.669173	+	0.743107i	$0.266649\pi$
$284$	0.307924	+	10.7787i	0.0182719	+	0.639600i
$285$	3.32750	−	0.977042i	0.197104	−	0.0578750i
$286$	0.0137347	+	0.0184663i	0.000812150	+	0.00109193i
$287$	16.2306	+	4.76575i	0.958064	+	0.281313i
$288$	0.0730495	−	0.277909i	0.00430448	−	0.0163760i
$289$	−0.133123	+	0.656986i	−0.00783074	+	0.0386462i
$290$	0.0116619	+	0.0221018i	0.000684812	+	0.00129786i
$291$	0.0644876	−	2.25736i	0.00378033	−	0.132329i
$292$	−8.11621	−	30.8773i	−0.474965	−	1.80696i
$293$	−26.1104	+	1.49305i	−1.52539	+	0.0872248i	−0.799533	−	0.600623i	$-0.794919\pi$
$293$	−26.1104	+	1.49305i	−1.52539	+	0.0872248i	−0.725855	+	0.687847i	$0.758556\pi$
$294$	−0.0169519	+	0.0174431i	−0.000988657	+	0.00101730i
$295$	−6.35329	+	3.12370i	−0.369903	+	0.181869i
$296$	0.0568918	−	0.124576i	0.00330677	−	0.00724081i
$297$	−9.03202	−	6.02881i	−0.524091	−	0.349827i
$298$	−0.0375610	−	0.0822472i	−0.00217585	−	0.00476445i
$299$	−3.77319	−	3.08532i	−0.218209	−	0.178429i
$300$	0.539314	−	1.02211i	0.0311373	−	0.0590118i
$301$	8.66940	+	4.89584i	0.499696	+	0.282191i
$302$	0.107707	−	0.0123583i	0.00619786	−	0.000711139i
$303$	−2.59810	+	0.298104i	−0.149257	+	0.0171256i
$304$	20.9003	+	11.8030i	1.19872	+	0.676946i
$305$	2.17404	−	4.12027i	0.124485	−	0.235926i
$306$	−0.0749138	−	0.0612567i	−0.00428253	−	0.00350181i
$307$	11.2327	+	24.5961i	0.641083	+	1.40378i	0.899147	+	0.437648i	$0.144188\pi$
$307$	11.2327	+	24.5961i	0.641083	+	1.40378i	−0.258064	+	0.966128i	$0.583084\pi$
$308$	9.72871	−	2.67390i	0.554345	−	0.152360i
$309$	1.45034	−	3.17580i	0.0825070	−	0.180665i
$310$	−0.0115140	+	0.00566107i	−0.000653953	+	0.000321527i
$311$	1.68090	−	1.72961i	0.0953153	−	0.0980771i	−0.667796	−	0.744345i	$-0.732762\pi$
$311$	1.68090	−	1.72961i	0.0953153	−	0.0980771i	0.763111	+	0.646268i	$0.223671\pi$
$312$	0.0160126		0.000915632i	0.000906533		5.18374e-5i
$313$	−2.09637	−	7.97541i	−0.118494	−	0.450797i	0.881268	−	0.472616i	$-0.156690\pi$
$313$	−2.09637	−	7.97541i	−0.118494	−	0.450797i	−0.999762	+	0.0218197i	$0.993054\pi$
$314$	−0.00359591	+	0.125873i	−0.000202929	+	0.00710343i
$315$	1.89252	+	3.58672i	0.106631	+	0.202089i
$316$	−2.68778	+	13.2647i	−0.151200	+	0.746200i
$317$	0.782970	−	2.97873i	0.0439760	−	0.167302i	−0.941534	−	0.336917i	$-0.890616\pi$
$317$	0.782970	−	2.97873i	0.0439760	−	0.167302i	0.985510	+	0.169615i	$0.0542523\pi$
$318$	−0.0224309	−	0.00658632i	−0.00125786	−	0.000369342i
$319$	7.36977	+	5.55262i	0.412628	+	0.310887i
$320$	7.67409	−	2.25331i	0.428994	−	0.125964i
$321$	−0.181246	−	6.34443i	−0.0101161	−	0.354111i
$322$	0.0750589	−	0.0423877i	0.00418287	−	0.00236217i
$323$	19.6201	−	14.2548i	1.09169	−	0.793159i
$324$	11.2487	−	4.75374i	0.624928	−	0.264097i
$325$	−0.761218	−	0.131734i	−0.0422248	−	0.00730729i
$326$	0.00764776	−	0.0890412i	0.000423570	−	0.00493154i
$327$	0.00297708	+	0.0346615i	0.000164633	+	0.00191679i
$328$	−0.393693	+	0.0681312i	−0.0217380	+	0.00376191i
$329$	−6.47159	+	4.15904i	−0.356790	+	0.229295i
$330$	−0.000790485		0.0171965i	−4.35148e−5		0.000946635i
$331$	11.7201	+	7.53206i	0.644196	+	0.413999i	0.821541	−	0.570149i	$-0.193115\pi$
$331$	11.7201	+	7.53206i	0.644196	+	0.413999i	−0.177346	+	0.984149i	$0.556751\pi$
$332$	2.15592	+	0.911098i	0.118321	+	0.0500030i
$333$	9.89859	−	2.30182i	0.542440	−	0.126139i
$334$	0.0767093	−	0.197026i	0.00419735	−	0.0107808i
$335$	−2.78923	−	4.62541i	−0.152392	−	0.252713i
$336$	1.08635	−	3.34346i	0.0592655	−	0.182400i
$337$	−15.4296	+	20.0095i	−0.840505	+	1.08999i	0.154283	+	0.988027i	$0.450693\pi$
$337$	−15.4296	+	20.0095i	−0.840505	+	1.08999i	−0.994788	+	0.101960i	$0.967489\pi$
$338$	0.0404194	+	0.103816i	0.00219852	+	0.00564686i
$339$	5.87133	+	8.58655i	0.318887	+	0.466357i
$340$	1.15014	−	7.99941i	0.0623752	−	0.433829i
$341$	−2.95776	+	3.70089i	−0.160172	+	0.200414i
$342$	−0.0204530	−	0.142254i	−0.00110597	−	0.00769220i
$343$	13.0963	−	12.0197i	0.707135	−	0.649002i
$344$	−0.234779	−	0.0134252i	−0.0126585	−	0.000723837i
$345$	−0.724022	−	3.57319i	−0.0389800	−	0.192374i
$346$	−0.137112	+	0.112116i	−0.00737121	+	0.00602741i
$347$	4.54721	+	2.23571i	0.244107	+	0.120019i	0.559175	−	0.829050i	$-0.311118\pi$
$347$	4.54721	+	2.23571i	0.244107	+	0.120019i	−0.315068	+	0.949069i	$0.602027\pi$
$348$	3.02829	−	1.08049i	0.162333	−	0.0579204i
$349$	−1.79388	−	2.32635i	−0.0960242	−	0.124526i	0.741439	−	0.671021i	$-0.234144\pi$
$349$	−1.79388	−	2.32635i	−0.0960242	−	0.124526i	−0.837463	+	0.546494i	$0.815962\pi$
$350$	0.00705543	−	0.0117001i	0.000377129	−	0.000625398i
$351$	1.65642	+	1.91161i	0.0884132	+	0.102034i
$352$	−0.267519	+	0.237097i	−0.0142588	+	0.0126373i
$353$	−15.9440	+	18.4004i	−0.848615	+	0.979353i	−0.999958	−	0.00912775i	$-0.997095\pi$
$353$	−15.9440	+	18.4004i	−0.848615	+	0.979353i	0.151344	+	0.988481i	$0.451640\pi$
$354$	−0.0113553	−	0.0349479i	−0.000603526	−	0.00185746i
$355$	5.07822	+	1.81191i	0.269524	+	0.0961660i
$356$	16.1698	+	16.6384i	0.856999	+	0.881831i
$357$	−2.61689	−	2.40176i	−0.138500	−	0.127115i
$358$	0.0343790	−	0.0502777i	0.00181699	−	0.00265726i
$359$	−32.7118	−	7.60679i	−1.72646	−	0.401471i	−0.758321	−	0.651881i	$-0.773980\pi$
$359$	−32.7118	−	7.60679i	−1.72646	−	0.401471i	−0.968140	+	0.250410i	$0.919435\pi$
$360$	−0.0774928	−	0.0563018i	−0.00408423	−	0.00296737i
$361$	16.9062	+	1.93980i	0.889798	+	0.102095i
$362$	0.0549425			0.00288771
$363$	2.43808	+	5.87029i	0.127966	+	0.308110i
$364$	−2.35012			−0.123180
$365$	−15.8597	−	1.81973i	−0.830132	−	0.0952488i
$366$	0.0195623	+	0.0142128i	0.00102254	+	0.000742917i
$367$	20.9133	+	4.86318i	1.09167	+	0.253856i	0.733423	−	0.679773i	$-0.237922\pi$
$367$	20.9133	+	4.86318i	1.09167	+	0.253856i	0.358242	+	0.933629i	$0.383376\pi$
$368$	14.2429	−	20.8296i	0.742463	−	1.08582i
$369$	−21.8435	−	20.0478i	−1.13713	−	1.04365i
$370$	−0.0238622	−	0.0245536i	−0.00124053	−	0.00127648i
$371$	6.45272	+	2.30233i	0.335008	+	0.119531i
$372$	0.510129	+	1.57001i	0.0264489	+	0.0814014i
$373$	8.08616	−	9.33192i	0.418685	−	0.483189i	−0.506751	−	0.862093i	$-0.669153\pi$
$373$	8.08616	−	9.33192i	0.418685	−	0.483189i	0.925436	+	0.378904i	$0.123699\pi$
$374$	0.0352055	+	0.115120i	0.00182043	+	0.00595271i
$375$	−0.378417	−	0.436717i	−0.0195414	−	0.0225520i
$376$	0.0938294	−	0.155599i	0.00483888	−	0.00802439i
$377$	−1.31248	−	1.70205i	−0.0675959	−	0.0876600i
$378$	−0.0421331	+	0.0150331i	−0.00216709	+	0.000773217i
$379$	32.0030	+	15.7348i	1.64389	+	0.808244i	0.999034	+	0.0439362i	$0.0139898\pi$
$379$	32.0030	+	15.7348i	1.64389	+	0.808244i	0.644851	+	0.764308i	$0.276919\pi$
$380$	9.29153	−	7.59764i	0.476645	−	0.389751i
$381$	0.508926	+	2.51165i	0.0260731	+	0.128676i
$382$	0.116323	+	0.00665160i	0.00595161	+	0.000340326i
$383$	−5.26653	+	4.83358i	−0.269107	+	0.246984i	−0.799356	−	0.600858i	$-0.794826\pi$
$383$	−5.26653	+	4.83358i	−0.269107	+	0.246984i	0.530249	+	0.847842i	$0.322098\pi$
$384$	0.0236351	+	0.164386i	0.00120613	+	0.00838879i
$385$	0.518988	−	5.01818i	0.0264501	−	0.255750i
$386$	−0.0256477	+	0.178384i	−0.00130543	+	0.00907948i
$387$	−9.84988	−	14.4050i	−0.500698	−	0.732247i
$388$	−2.83560	−	7.28317i	−0.143956	−	0.369747i
$389$	−14.4573	+	18.7485i	−0.733013	+	0.950588i	−0.999914	−	0.0131360i	$-0.995819\pi$
$389$	−14.4573	+	18.7485i	−0.733013	+	0.950588i	0.266901	+	0.963724i	$0.414000\pi$
$390$	0.00123908	−	0.00381351i	6.27435e−5	−	0.000193105i
$391$	−13.1657	−	21.8329i	−0.665818	−	1.10414i
$392$	−0.0610845	+	0.156894i	−0.00308523	+	0.00792436i
$393$	3.71948	−	0.864928i	0.187623	−	0.0436298i
$394$	−0.0390641	−	0.0165086i	−0.00196802	−	0.000831693i
$395$	5.69312	+	3.65875i	0.286452	+	0.184091i
$396$	−17.3700	−	3.31782i	−0.872877	−	0.166727i
$397$	30.3994	−	19.5365i	1.52570	−	0.980508i	0.534938	−	0.844891i	$-0.320335\pi$
$397$	30.3994	−	19.5365i	1.52570	−	0.980508i	0.990761	−	0.135617i	$-0.0433016\pi$
$398$	0.144602	−	0.0250244i	0.00724826	−	0.00125436i
$399$	−0.451422	−	5.25581i	−0.0225994	−	0.263120i
$400$	0.342259	−	3.98484i	0.0171129	−	0.199242i
$401$	−29.2994	−	5.07046i	−1.46314	−	0.253207i	−0.617337	−	0.786699i	$-0.711789\pi$
$401$	−29.2994	−	5.07046i	−1.46314	−	0.253207i	−0.845805	+	0.533492i	$0.820879\pi$
$402$	0.0258238	−	0.0109132i	0.00128797	−	0.000544301i
$403$	0.892765	−	0.648632i	0.0444718	−	0.0323107i
$404$	−7.88094	+	4.45057i	−0.392091	+	0.221424i
$405$	−0.174369	−	6.10372i	−0.00866448	−	0.303296i
$406$	0.0364724	−	0.0107093i	0.00181010	−	0.000531492i
$407$	−11.8316	−	4.45474i	−0.586473	−	0.220813i
$408$	0.0804977	+	0.0236363i	0.00398523	+	0.00117017i
$409$	−6.25929	+	23.8128i	−0.309502	+	1.17747i	0.612560	+	0.790424i	$0.290140\pi$
$409$	−6.25929	+	23.8128i	−0.309502	+	1.17747i	−0.922062	+	0.387043i	$0.873497\pi$
$410$	−0.0198368	+	0.0978986i	−0.000979671	+	0.00483487i
$411$	−1.78544	−	3.38379i	−0.0880693	−	0.166910i
$412$	0.345046	−	12.0782i	0.0169992	−	0.595049i
$413$	2.73766	+	10.4152i	0.134712	+	0.512496i
$414$	−0.150839	+	0.00862531i	−0.00741336	+	0.000423911i
$415$	0.815634	−	0.839268i	0.0400379	−	0.0411980i
$416$	0.0747205	−	0.0367376i	0.00366347	−	0.00180121i
$417$	−0.512641	+	1.12253i	−0.0251041	+	0.0549704i
$418$	−0.0770842	+	0.161313i	−0.00377031	+	0.00789009i
$419$	1.57143	+	3.44095i	0.0767693	+	0.168101i	0.944125	−	0.329587i	$-0.106910\pi$
$419$	1.57143	+	3.44095i	0.0767693	+	0.168101i	−0.867356	+	0.497688i	$0.834182\pi$
$420$	−1.36086	−	1.11277i	−0.0664034	−	0.0542978i
$421$	−0.671437	+	1.27251i	−0.0327238	+	0.0620186i	−0.900251	−	0.435371i	$-0.856617\pi$
$421$	−0.671437	+	1.27251i	−0.0327238	+	0.0620186i	0.867527	+	0.497390i	$0.165708\pi$
$422$	0.0358596	+	0.0202509i	0.00174562	+	0.000985796i
$423$	13.3954	−	1.53698i	0.651309	−	0.0747307i
$424$	−0.160766	+	0.0184462i	−0.00780749	+	0.000895826i
$425$	−3.51868	−	1.98709i	−0.170681	−	0.0963881i
$426$	−0.0130600	+	0.0247514i	−0.000632757	+	0.00119921i
$427$	−5.48581	−	4.48573i	−0.265477	−	0.217079i
$428$	−9.12519	−	19.9814i	−0.441083	−	0.965837i
$429$	−0.185215	−	1.46896i	−0.00894229	−	0.0709221i
$430$	−0.0244230	+	0.0534790i	−0.00117778	+	0.00257899i
$431$	29.8025	−	14.6529i	1.43554	−	0.705805i	0.452936	−	0.891543i	$-0.350377\pi$
$431$	29.8025	−	14.6529i	1.43554	−	0.705805i	0.982599	+	0.185738i	$0.0594674\pi$
$432$	−9.12654	+	9.39098i	−0.439101	+	0.451824i
$433$	−20.4808	+	1.17113i	−0.984244	+	0.0562811i	−0.541793	−	0.840512i	$-0.682254\pi$
$433$	−20.4808	+	1.17113i	−0.984244	+	0.0562811i	−0.442450	+	0.896793i	$0.645891\pi$
$434$	0.00496145	+	0.0188753i	0.000238157	+	0.000906045i
$435$	0.0459096	−	1.60705i	0.00220120	−	0.0770520i
$436$	0.0561877	+	0.106488i	0.00269090	+	0.00509983i
$437$	7.51941	−	37.1098i	0.359702	−	1.77520i
$438$	0.0210641	−	0.0801361i	0.00100648	−	0.00382905i
$439$	−9.05164	−	2.65780i	−0.432011	−	0.126850i	0.0584948	−	0.998288i	$-0.481370\pi$
$439$	−9.05164	−	2.65780i	−0.432011	−	0.126850i	−0.490506	+	0.871438i	$0.663188\pi$
$440$	0.0412960	+	0.111774i	0.00196871	+	0.00532864i
$441$	−11.9878	+	3.51993i	−0.570847	+	0.167616i
$442$	−0.000800725	−	0.0280290i	−3.80866e−5	−	0.00133320i
$443$	−31.6345	+	17.8648i	−1.50300	+	0.848784i	−0.999881	−	0.0154323i	$-0.995088\pi$
$443$	−31.6345	+	17.8648i	−1.50300	+	0.848784i	−0.503121	+	0.864216i	$0.667815\pi$
$444$	−3.56392	+	2.58934i	−0.169136	+	0.122885i
$445$	10.6860	−	4.51596i	0.506567	−	0.214077i
$446$	−0.126110	−	0.0218242i	−0.00597148	−	0.00103340i
$447$	−0.497788	+	5.79565i	−0.0235446	+	0.274125i
$448$	−1.04110	−	12.1213i	−0.0491873	−	0.572677i
$449$	0.465192	−	0.0805046i	0.0219538	−	0.00379925i	−0.159535	−	0.987192i	$-0.550999\pi$
$449$	0.465192	−	0.0805046i	0.0219538	−	0.00379925i	0.181488	+	0.983393i	$0.441908\pi$
$450$	−0.0201456	+	0.0129468i	−0.000949671	+	0.000610317i
$451$	8.75523	+	35.8291i	0.412268	+	1.68713i
$452$	30.2854	+	19.4633i	1.42451	+	0.915475i
$453$	−6.42460	−	2.71506i	−0.301854	−	0.127565i
$454$	0.0349875	−	0.00813599i	0.00164204	−	0.000381841i
$455$	−0.426337	+	1.09504i	−0.0199870	+	0.0513362i
$456$	0.0643415	+	0.106698i	0.00301307	+	0.00499661i
$457$	3.91422	−	12.0467i	0.183100	−	0.563523i	−0.816811	−	0.576906i	$-0.804260\pi$
$457$	3.91422	−	12.0467i	0.183100	−	0.563523i	0.999910	+	0.0133829i	$0.00426005\pi$
$458$	0.144998	−	0.188036i	0.00677529	−	0.00878636i
$459$	4.80032	+	12.3295i	0.224060	+	0.575492i
$460$	−7.12203	−	10.4156i	−0.332067	−	0.485632i
$461$	−2.71529	+	18.8852i	−0.126464	+	0.879574i	0.823523	+	0.567283i	$0.192005\pi$
$461$	−2.71529	+	18.8852i	−0.126464	+	0.879574i	−0.949987	+	0.312291i	$0.898904\pi$
$462$	0.0253979	+	0.00637313i	0.00118162	+	0.000296505i
$463$	5.73985	+	39.9216i	0.266754	+	1.85531i	0.478631	+	0.878016i	$0.341133\pi$
$463$	5.73985	+	39.9216i	0.266754	+	1.85531i	−0.211877	+	0.977296i	$0.567958\pi$
$464$	8.19796	−	7.52402i	0.380581	−	0.349294i
$465$	0.824092	+	0.0471233i	0.0382164	+	0.00218529i
$466$	−0.0341386	−	0.168480i	−0.00158144	−	0.00780470i
$467$	−21.8621	+	17.8766i	−1.01166	+	0.827229i	−0.985024	−	0.172416i	$-0.944843\pi$
$467$	−21.8621	+	17.8766i	−1.01166	+	0.827229i	−0.0266348	+	0.999645i	$0.508479\pi$
$468$	3.69647	+	1.81743i	0.170870	+	0.0840109i
$469$	−7.73818	+	2.76098i	−0.357316	+	0.127490i
$470$	−0.0277392	−	0.0359729i	−0.00127952	−	0.00165931i
$471$	4.18347	−	6.93751i	0.192764	−	0.319663i
$472$	−0.166569	−	0.192230i	−0.00766694	−	0.00884812i
$473$	0.242794	+	21.7074i	0.0111637	+	0.998106i
$474$	−0.0230024	+	0.0265462i	−0.00105654	+	0.00121931i
$475$	−1.85454	−	5.70769i	−0.0850922	−	0.261887i
$476$	−11.5782	−	4.13108i	−0.530685	−	0.189348i
$477$	−8.36894	−	8.61144i	−0.383188	−	0.394291i
$478$	0.00792357	+	0.00727218i	0.000362415	+	0.000332622i
$479$	−9.12110	+	13.3392i	−0.416754	+	0.609483i	−0.975538	−	0.219830i	$-0.929450\pi$
$479$	−9.12110	+	13.3392i	−0.416754	+	0.609483i	0.558785	+	0.829313i	$0.311268\pi$
$480$	0.0606630	+	0.0141066i	0.00276887	+	0.000643874i
$481$	2.38238	+	1.73090i	0.108627	+	0.0789222i
$482$	−0.115061	−	0.0132020i	−0.00524087	−	0.000601333i
$483$	−5.54566			−0.252336
$484$	15.6810	+	15.4294i	0.712774	+	0.701336i
$485$	−3.90801			−0.177454
$486$	0.119140	+	0.0136700i	0.00540430	+	0.000620085i
$487$	19.4013	+	14.0959i	0.879157	+	0.638745i	0.933028	−	0.359803i	$-0.117156\pi$
$487$	19.4013	+	14.0959i	0.879157	+	0.638745i	−0.0538715	+	0.998548i	$0.517156\pi$
$488$	0.163026	+	0.0379100i	0.00737982	+	0.00171610i
$489$	−3.24526	+	4.74605i	−0.146756	+	0.214624i
$490$	0.0310112	+	0.0284618i	0.00140094	+	0.00128577i
$491$	8.60228	+	8.85154i	0.388216	+	0.399464i	0.882864	−	0.469629i	$-0.155612\pi$
$491$	8.60228	+	8.85154i	0.388216	+	0.399464i	−0.494648	+	0.869093i	$0.664703\pi$
$492$	12.1045	+	4.31889i	0.545714	+	0.194710i
$493$	−3.47420	−	10.6925i	−0.156470	−	0.481565i
$494$	0.0272709	−	0.0314723i	0.00122698	−	0.00141601i
$495$	−4.69706	+	7.49169i	−0.211117	+	0.336726i
$496$	3.74127	+	4.31766i	0.167988	+	0.193868i
$497$	4.23522	−	7.02333i	0.189976	−	0.315039i
$498$	0.00370932	+	0.00481033i	0.000166219	+	0.000215556i
$499$	−13.3696	+	4.77026i	−0.598505	+	0.213546i	−0.617888	−	0.786266i	$-0.712012\pi$
$499$	−13.3696	+	4.77026i	−0.598505	+	0.213546i	0.0193830	+	0.999812i	$0.493830\pi$
$500$	−1.79472	−	0.882407i	−0.0802625	−	0.0394624i
$501$	−10.5302	+	8.61046i	−0.470452	+	0.384687i
$502$	−0.0297421	−	0.146783i	−0.00132746	−	0.00655125i
$503$	−28.6781	−	1.63987i	−1.27869	−	0.0731183i	−0.595500	−	0.803356i	$-0.703046\pi$
$503$	−28.6781	−	1.63987i	−1.27869	−	0.0731183i	−0.683194	+	0.730237i	$0.739410\pi$
$504$	−0.107344	+	0.0985196i	−0.00478149	+	0.00438841i
$505$	0.644057	+	4.47951i	0.0286602	+	0.199336i
$506$	0.162028	+	0.0952518i	0.00720303	+	0.00423446i
$507$	1.02001	−	7.09435i	0.0453004	−	0.315071i
$508$	5.00619	+	7.32132i	0.222114	+	0.324831i
$509$	−5.21221	−	13.3875i	−0.231027	−	0.593389i	0.767857	−	0.640622i	$-0.221323\pi$
$509$	−5.21221	−	13.3875i	−0.231027	−	0.593389i	−0.998884	+	0.0472330i	$0.984960\pi$
$510$	0.0128080	−	0.0166097i	0.000567148	−	0.000735490i
$511$	−7.50371	+	23.0940i	−0.331945	+	1.02162i
$512$	0.371008	+	0.615248i	0.0163964	+	0.0271904i
$513$	−7.12911	+	18.3110i	−0.314758	+	0.808449i
$514$	0.213664	−	0.0496855i	0.00942433	−	0.00219153i
$515$	−5.56524	−	2.35189i	−0.245234	−	0.103637i
$516$	6.36355	+	4.08960i	0.280140	+	0.180035i
$517$	−14.9215	−	7.66118i	−0.656249	−	0.336938i
$518$	−0.0438130	+	0.0281569i	−0.00192503	+	0.00123714i
$519$	11.2277	−	1.94303i	0.492842	−	0.0852896i
$520$	−0.00237517	−	0.0276536i	−0.000104158	−	0.00121269i
$521$	−0.0461698	+	0.537546i	−0.00202274	+	0.0235503i	−0.997274	−	0.0737939i	$-0.976489\pi$
$521$	−0.0461698	+	0.537546i	−0.00202274	+	0.0235503i	0.995251	+	0.0973442i	$0.0310348\pi$
$522$	−0.0656490	−	0.0113610i	−0.00287338	−	0.000497258i
$523$	−9.03887	+	3.81986i	−0.395242	+	0.167031i	−0.577827	−	0.816159i	$-0.696099\pi$
$523$	−9.03887	+	3.81986i	−0.395242	+	0.167031i	0.182585	+	0.983190i	$0.441554\pi$
$524$	10.6922	−	7.76831i	0.467090	−	0.339360i
$525$	−0.765373	+	0.432226i	−0.0334036	+	0.0188639i
$526$	−0.000205393	−	0.00718970i	−8.95557e−6	−	0.000313486i
$527$	5.53851	−	1.62625i	0.241261	−	0.0708407i
$528$	7.49507	−	1.60617i	0.326181	−	0.0698996i
$529$	−16.1247	−	4.73464i	−0.701074	−	0.205854i
$530$	−0.0102847	+	0.0391269i	−0.000446737	+	0.00169957i
$531$	3.74839	−	18.4990i	0.162666	−	0.802790i
$532$	−8.51989	−	16.1470i	−0.369384	−	0.700061i
$533$	0.245329	−	8.58764i	0.0106264	−	0.371972i
$534$	0.0153076	+	0.0582362i	0.000662425	+	0.00252013i
$535$	−10.9658	+	0.627045i	−0.474091	+	0.0271095i
$536$	0.135246	−	0.139165i	0.00584174	−	0.00601101i
$537$	−3.51642	+	1.72891i	−0.151745	+	0.0746079i
$538$	0.0986306	−	0.215971i	0.00425227	−	0.00931117i
$539$	14.8346	+	4.63727i	0.638970	+	0.199741i
$540$	2.72019	+	5.95639i	0.117058	+	0.256322i
$541$	−31.2280	−	25.5350i	−1.34260	−	1.09784i	−0.986566	−	0.163363i	$-0.947766\pi$
$541$	−31.2280	−	25.5350i	−1.34260	−	1.09784i	−0.356031	−	0.934474i	$-0.615870\pi$
$542$	−0.00168539	+	0.00319416i	−7.23935e−5	+	0.000137201i
$543$	−3.07781	−	1.73812i	−0.132082	−	0.0745899i
$544$	0.432699	−	0.0496476i	0.0185518	−	0.00212862i
$545$	0.0598110	−	0.00686268i	0.00256202	−	0.000293965i
$546$	−0.00531092	−	0.00299922i	−0.000227287	−	0.000128355i
$547$	−3.56911	+	6.76422i	−0.152604	+	0.289217i	−0.948833	−	0.315779i	$-0.897734\pi$
$547$	−3.56911	+	6.76422i	−0.152604	+	0.289217i	0.796229	+	0.604996i	$0.206825\pi$
$548$	−10.2506	−	8.38187i	−0.437884	−	0.358056i
$549$	5.15960	+	11.2979i	0.220206	+	0.482184i
$550$	0.0297859		0.000517598i	0.00127007		2.20704e-5i
$551$	6.93617	−	15.1881i	0.295491	−	0.647035i
$552$	0.117546	−	0.0577937i	0.00500311	−	0.00245986i
$553$	7.17426	−	7.38214i	0.305081	−	0.313920i
$554$	−0.157536	+	0.00900824i	−0.00669307	+	0.000382724i
$555$	0.559971	+	2.13035i	0.0237694	+	0.0904283i
$556$	−0.121961	+	4.26918i	−0.00517228	+	0.181053i
$557$	−7.25760	−	13.7547i	−0.307515	−	0.582805i	0.681291	−	0.732012i	$-0.261419\pi$
$557$	−7.25760	−	13.7547i	−0.307515	−	0.582805i	−0.988806	+	0.149208i	$0.952328\pi$
$558$	0.00679319	−	0.0335257i	0.000287579	−	0.00141926i
$559$	1.28547	−	4.89043i	0.0543696	−	0.206843i
$560$	−5.83726	−	1.71397i	−0.246669	−	0.0724286i
$561$	1.66968	−	7.56262i	0.0704940	−	0.319294i
$562$	−0.0331954	+	0.00974704i	−0.00140026	+	0.000411154i
$563$	1.04564	+	36.6022i	0.0440685	+	1.54260i	0.657865	+	0.753136i	$0.271460\pi$
$563$	1.04564	+	36.6022i	0.0440685	+	1.54260i	−0.613797	+	0.789464i	$0.710359\pi$
$564$	−5.08921	+	2.87401i	−0.214294	+	0.121018i
$565$	14.5630	−	10.5807i	0.612672	−	0.445132i
$566$	0.0604810	−	0.0255595i	0.00254221	−	0.00107435i
$567$	−9.15216	−	1.58384i	−0.384355	−	0.0665152i
$568$	−0.0165772	+	0.193004i	−0.000695562	+	0.00809829i
$569$	1.89259	+	22.0351i	0.0793416	+	0.923758i	0.922476	+	0.386055i	$0.126162\pi$
$569$	1.89259	+	22.0351i	0.0793416	+	0.923758i	−0.843134	+	0.537703i	$0.819292\pi$
$570$	0.0306936	−	0.00531174i	0.00128561	−	0.000222484i
$571$	−2.12235	+	1.36395i	−0.0888178	+	0.0570797i	−0.584296	−	0.811541i	$-0.698629\pi$
$571$	−2.12235	+	1.36395i	−0.0888178	+	0.0570797i	0.495478	+	0.868620i	$0.334993\pi$
$572$	−2.56948	−	4.43341i	−0.107435	−	0.185370i
$573$	−6.30586	−	4.05253i	−0.263431	−	0.169297i
$574$	0.139956	+	0.0591459i	0.00584165	+	0.00246870i
$575$	−6.14519	+	1.42900i	−0.256272	+	0.0595936i
$576$	−7.73632	+	19.8706i	−0.322347	+	0.827940i
$577$	5.49579	+	9.11375i	0.228793	+	0.379410i	0.949469	−	0.313862i	$-0.101623\pi$
$577$	5.49579	+	9.11375i	0.228793	+	0.379410i	−0.720676	+	0.693272i	$0.756168\pi$
$578$	−0.00186061	+	0.00572637i	−7.73911e−5	+	0.000238185i
$579$	7.07997	−	9.18146i	0.294233	−	0.381569i
$580$	−2.01870	−	5.18500i	−0.0838221	−	0.215295i
$581$	−1.00480	−	1.46948i	−0.0416863	−	0.0609643i
$582$	0.00288674	−	0.0200777i	0.000119659	−	0.000832248i
$583$	2.71177	+	14.6901i	0.112310	+	0.608400i
$584$	−0.0816234	−	0.567704i	−0.00337760	−	0.0234917i
$585$	1.51742	−	1.39267i	0.0627375	−	0.0575799i
$586$	−0.234527	−	0.0134108i	−0.00968824	−	0.000553994i
$587$	−6.31600	−	31.1707i	−0.260689	−	1.28655i	−0.869775	−	0.493448i	$-0.835736\pi$
$587$	−6.31600	−	31.1707i	−0.260689	−	1.28655i	0.609086	−	0.793104i	$-0.291536\pi$
$588$	4.19256	−	3.42824i	0.172898	−	0.141378i
$589$	7.69311	+	3.78245i	0.316989	+	0.155853i
$590$	−0.0598925	+	0.0213696i	−0.00246573	+	0.000879772i
$591$	1.66607	+	2.16060i	0.0685330	+	0.0888751i
$592$	−7.87278	+	13.0555i	−0.323569	+	0.536579i
$593$	−5.06916	−	5.85012i	−0.208165	−	0.240236i	0.642060	−	0.766654i	$-0.278080\pi$
$593$	−5.06916	−	5.85012i	−0.208165	−	0.240236i	−0.850226	+	0.526419i	$0.823535\pi$
$594$	−0.0744252	−	0.0630464i	−0.00305370	−	0.00258682i
$595$	−4.02529	+	4.64543i	−0.165021	+	0.190444i
$596$	6.22115	+	19.1467i	0.254828	+	0.784280i
$597$	−8.89210	−	3.17270i	−0.363930	−	0.129850i
$598$	−0.0305114	−	0.0313955i	−0.00124770	−	0.00128386i
$599$	−14.5761	−	13.3778i	−0.595563	−	0.546603i	0.320699	−	0.947181i	$-0.396082\pi$
$599$	−14.5761	−	13.3778i	−0.595563	−	0.546603i	−0.916263	+	0.400578i	$0.868809\pi$
$600$	0.0117185	−	0.0171378i	0.000478407	−	0.000699648i
$601$	−27.3373	−	6.35701i	−1.11511	−	0.259308i	−0.371838	−	0.928298i	$-0.621272\pi$
$601$	−27.3373	−	6.35701i	−1.11511	−	0.259308i	−0.743272	+	0.668990i	$0.766727\pi$
$602$	0.0723494	+	0.0525649i	0.00294874	+	0.00214239i
$603$	14.3065	+	1.64151i	0.582605	+	0.0668476i
$604$	−24.1390			−0.982200
$605$	10.0341	−	4.50753i	0.407942	−	0.183257i
$606$	−0.0234896			−0.000954200
$607$	−32.9460	−	3.78020i	−1.33724	−	0.153434i	−0.584306	−	0.811533i	$-0.698633\pi$
$607$	−32.9460	−	3.78020i	−1.33724	−	0.153434i	−0.752931	+	0.658100i	$0.771361\pi$
$608$	0.523298	+	0.380199i	0.0212226	+	0.0154191i
$609$	−2.38193	−	0.553895i	−0.0965208	−	0.0224450i
$610$	0.0236189	−	0.0345416i	0.000956303	−	0.00139855i
$611$	2.87843	+	2.64180i	0.116449	+	0.106876i
$612$	15.0165	+	15.4516i	0.607005	+	0.624593i
$613$	−11.9133	−	4.25064i	−0.481172	−	0.171682i	0.0843146	−	0.996439i	$-0.473130\pi$
$613$	−11.9133	−	4.25064i	−0.481172	−	0.171682i	−0.565487	+	0.824757i	$0.691312\pi$
$614$	0.0750521	+	0.230987i	0.00302886	+	0.00932187i
$615$	4.20828	−	4.85662i	0.169694	−	0.195838i
$616$	0.179109	−	0.0278000i	0.00721651	−	0.00112009i
$617$	−10.7869	−	12.4487i	−0.434263	−	0.501167i	0.495866	−	0.868399i	$-0.334851\pi$
$617$	−10.7869	−	12.4487i	−0.434263	−	0.501167i	−0.930129	+	0.367233i	$0.880305\pi$
$618$	0.0161939	−	0.0268546i	0.000651415	−	0.00108025i
$619$	−17.7133	−	22.9710i	−0.711958	−	0.923283i	0.287447	−	0.957797i	$-0.407194\pi$
$619$	−17.7133	−	22.9710i	−0.711958	−	0.923283i	−0.999404	+	0.0345137i	$0.989012\pi$
$620$	2.69063	−	0.960016i	0.108058	−	0.0385552i
$621$	18.5379	+	9.11449i	0.743902	+	0.365752i
$622$	0.0167706	−	0.0137133i	0.000672440	−	0.000549852i
$623$	−3.50443	−	17.2950i	−0.140402	−	0.692911i
$624$	−1.78253	−	0.101929i	−0.0713584	−	0.00408042i
$625$	−0.736741	+	0.676175i	−0.0294696	+	0.0270470i
$626$	−0.0105412	−	0.0733157i	−0.000421311	−	0.00293029i
$627$	9.42136	−	6.59800i	0.376253	−	0.263499i
$628$	3.99019	−	27.7524i	0.159226	−	1.10744i
$629$	8.69451	+	12.7153i	0.346673	+	0.506993i
$630$	0.0132157	+	0.0339441i	0.000526525	+	0.00135237i
$631$	−13.3760	+	17.3463i	−0.532491	+	0.690546i	−0.978913	−	0.204276i	$-0.934516\pi$
$631$	−13.3760	+	17.3463i	−0.532491	+	0.690546i	0.446423	+	0.894822i	$0.352698\pi$
$632$	−0.0751340	+	0.231239i	−0.00298867	+	0.00919818i
$633$	−1.36817	−	2.26886i	−0.0543800	−	0.0901790i
$634$	0.0100368	−	0.0257793i	0.000398612	−	0.00102383i
$635$	4.31955	−	1.00447i	0.171416	−	0.0398611i
$636$	4.79464	+	2.02623i	0.190120	+	0.0803454i
$637$	−3.04556	−	1.95727i	−0.120670	−	0.0775497i
$638$	0.0600795	+	0.0570951i	0.00237857	+	0.00226042i
$639$	−12.0930	+	7.77167i	−0.478390	+	0.307442i
$640$	0.283190	−	0.0490080i	0.0111941	−	0.00193721i
$641$	2.81500	+	32.7745i	0.111186	+	1.29451i	0.813046	+	0.582199i	$0.197808\pi$
$641$	2.81500	+	32.7745i	0.111186	+	1.29451i	−0.701860	+	0.712315i	$0.747647\pi$
$642$	0.00487861	−	0.0568006i	0.000192543	−	0.00224174i
$643$	34.9885	+	6.05500i	1.37981	+	0.238786i	0.811657	−	0.584135i	$-0.198566\pi$
$643$	34.9885	+	6.05500i	1.37981	+	0.238786i	0.568156	+	0.822921i	$0.307657\pi$
$644$	−17.6792	+	7.47127i	−0.696656	+	0.294409i
$645$	3.05997	−	2.22320i	0.120486	−	0.0875384i
$646$	0.189677	−	0.107115i	0.00746273	−	0.00421440i
$647$	−0.708722	−	24.8085i	−0.0278627	−	0.975323i	−0.886497	−	0.462734i	$-0.846868\pi$
$647$	−0.708722	−	24.8085i	−0.0278627	−	0.975323i	0.858634	−	0.512588i	$-0.171313\pi$
$648$	0.210496	−	0.0618073i	0.00826908	−	0.00242802i
$649$	−16.6546	+	16.5518i	−0.653751	+	0.649716i
$650$	−0.00665792	−	0.00195494i	−0.000261145	−	7.66791e-5i
$651$	0.319192	−	1.21433i	0.0125101	−	0.0475934i
$652$	−3.95165	+	19.5022i	−0.154759	+	0.763764i
$653$	22.1800	+	42.0358i	0.867971	+	1.64499i	0.759140	+	0.650928i	$0.225620\pi$
$653$	22.1800	+	42.0358i	0.867971	+	1.64499i	0.108831	+	0.994060i	$0.465289\pi$
$654$	−8.92321e−6	0	0.000312353i	−3.48925e−7	0	1.22140e-5i
$655$	−1.67997	−	6.39128i	−0.0656420	−	0.249728i
$656$	44.4051	−	2.53917i	1.73373	−	0.0991381i
$657$	29.6620	−	30.5215i	1.15723	−	1.19076i
$658$	−0.0620082	+	0.0304874i	−0.00241733	+	0.00118852i
$659$	−4.28797	+	9.38935i	−0.167036	+	0.365757i	−0.974577	−	0.224054i	$-0.928071\pi$
$659$	−4.28797	+	9.38935i	−0.167036	+	0.365757i	0.807541	+	0.589811i	$0.200798\pi$
$660$	0.611319	−	3.78387i	0.0237955	−	0.147287i
$661$	−16.3752	−	35.8567i	−0.636922	−	1.39466i	−0.902549	−	0.430588i	$-0.858306\pi$
$661$	−16.3752	−	35.8567i	−0.636922	−	1.39466i	0.265627	−	0.964076i	$-0.414421\pi$
$662$	0.0968735	+	0.0792130i	0.00376509	+	0.00307870i
$663$	−0.841851	+	1.59548i	−0.0326948	+	0.0619635i
$664$	0.0366120	+	0.0206758i	0.00142082	+	0.000802376i
$665$	−9.06930	+	1.04061i	−0.351692	+	0.0403530i
$666$	0.0906878	−	0.0104055i	0.00351408	−	0.000403203i
$667$	−15.2843	−	8.63145i	−0.591811	−	0.334211i
$668$	−21.9691	+	41.6360i	−0.850009	+	1.61095i
$669$	6.37412	+	5.21209i	0.246438	+	0.201511i
$670$	−0.0201540	−	0.0441311i	−0.000778617	−	0.00170493i
$671$	2.46430	−	15.2532i	0.0951332	−	0.588844i
$672$	0.0393552	−	0.0861758i	0.00151816	−	0.00332430i
$673$	−28.0811	+	13.8066i	−1.08245	+	0.532204i	−0.893170	−	0.449720i	$-0.851524\pi$
$673$	−28.0811	+	13.8066i	−1.08245	+	0.532204i	−0.189278	+	0.981924i	$0.560615\pi$
$674$	−0.158175	+	0.162758i	−0.00609268	+	0.00626922i
$675$	3.26886	−	0.186920i	0.125818	−	0.00719455i
$676$	−6.30598	−	23.9905i	−0.242538	−	0.922710i
$677$	0.241791	−	8.46379i	0.00929278	−	0.325290i	−0.981625	−	0.190820i	$-0.938885\pi$
$677$	0.241791	−	8.46379i	0.00929278	−	0.325290i	0.990918	−	0.134469i	$-0.0429330\pi$
$678$	0.0436017	+	0.0826344i	0.00167451	+	0.00317356i
$679$	−1.18052	+	5.82610i	−0.0453043	+	0.223585i
$680$	0.0369085	−	0.140414i	0.00141538	−	0.00538465i
$681$	−2.21734	−	0.651071i	−0.0849688	−	0.0249491i
$682$	−0.0301831	+	0.0299968i	−0.00115577	+	0.00114864i
$683$	−1.73348	+	0.508994i	−0.0663296	+	0.0194761i	−0.314729	−	0.949182i	$-0.601914\pi$
$683$	−1.73348	+	0.508994i	−0.0663296	+	0.0194761i	0.248399	+	0.968658i	$0.420095\pi$
$684$	0.913772	+	31.9862i	0.0349389	+	1.22302i
$685$	−5.76511	+	3.25571i	−0.220274	+	0.124394i
$686$	0.129173	−	0.0938496i	0.00493185	−	0.00358320i
$687$	−14.0712	+	5.94653i	−0.536849	+	0.226874i
$688$	25.7951	+	4.46402i	0.983430	+	0.170189i
$689$	0.297761	−	3.46677i	0.0113438	−	0.132073i
$690$	−0.00280233	−	0.0326270i	−0.000106683	−	0.00124209i
$691$	9.25941	−	1.60240i	0.352244	−	0.0609583i	0.00834604	−	0.999965i	$-0.497343\pi$
$691$	9.25941	−	1.60240i	0.352244	−	0.0609583i	0.343898	+	0.939007i	$0.388252\pi$
$692$	33.1754	−	21.3205i	1.26114	−	0.810485i
$693$	9.74981	+	9.26549i	0.370365	+	0.351967i
$694$	0.0382883	+	0.0246064i	0.00145340	+	0.000934046i
$695$	1.96710	+	0.831304i	0.0746164	+	0.0315332i
$696$	0.0562601	−	0.0130827i	0.00213253	−	0.000495900i
$697$	16.3042	−	41.8770i	0.617565	−	1.58620i
$698$	−0.0136259	−	0.0225961i	−0.000515749	−	0.000855274i
$699$	−3.41752	+	10.5181i	−0.129263	+	0.397829i
$700$	−1.85765	+	2.40904i	−0.0702124	+	0.0910531i
$701$	−0.0557500	−	0.143193i	−0.00210565	−	0.00540831i	0.930807	−	0.365510i	$-0.119106\pi$
$701$	−0.0557500	−	0.143193i	−0.00210565	−	0.00540831i	−0.932913	+	0.360102i	$0.882742\pi$
$702$	0.0128239	+	0.0187544i	0.000484008	+	0.000707840i
$703$	−3.25567	+	22.6437i	−0.122790	+	0.854023i
$704$	21.7281	−	15.2167i	0.818909	−	0.573501i
$705$	0.415907	+	2.89270i	0.0156640	+	0.108945i
$706$	−0.161118	+	0.147873i	−0.00606375	+	0.00556526i
$707$	6.87266	+	0.392993i	0.258473	+	0.0147800i
$708$	1.62482	+	8.01882i	0.0610646	+	0.301366i
$709$	−15.3095	+	12.5185i	−0.574961	+	0.470144i	−0.875227	−	0.483712i	$-0.839288\pi$
$709$	−15.3095	+	12.5185i	−0.574961	+	0.470144i	0.300266	+	0.953856i	$0.402925\pi$
$710$	0.0434608	+	0.0213682i	0.00163105	+	0.000801935i
$711$	−16.9932	+	6.06317i	−0.637295	+	0.227387i
$712$	0.254519	+	0.330066i	0.00953851	+	0.0123698i
$713$	4.65391	−	7.71764i	0.174290	−	0.289028i
$714$	−0.0208929	−	0.0241117i	−0.000781898	−	0.000902358i
$715$	−2.53189	+	0.392981i	−0.0946871	+	0.0146967i
$716$	−8.88086	+	10.2491i	−0.331893	+	0.383025i
$717$	−0.213811	−	0.658043i	−0.00798493	−	0.0245751i
$718$	−0.284118	−	0.101373i	−0.0106032	−	0.00378321i
$719$	27.6018	+	28.4016i	1.02937	+	1.05920i	0.998217	+	0.0596846i	$0.0190095\pi$
$719$	27.6018	+	28.4016i	1.02937	+	1.05920i	0.0311551	+	0.999515i	$0.490081\pi$
$720$	7.85589	+	7.21007i	0.292772	+	0.268703i
$721$	−5.18736	+	7.58627i	−0.193187	+	0.282527i
$722$	0.148877	+	0.0346200i	0.00554064	+	0.00128842i
$723$	6.02791	+	4.37953i	0.224180	+	0.162877i
$724$	−12.1535	−	1.39448i	−0.451681	−	0.0518256i
$725$	−2.78217			−0.103327
$726$	0.0157459	+	0.0548803i	0.000584386	+	0.00203680i
$727$	−46.8513			−1.73762			−0.868809	−	0.495148i	$-0.835114\pi$
$727$	−46.8513			−1.73762			−0.868809	+	0.495148i	$0.835114\pi$
$728$	−0.0419438	−	0.00481260i	−0.00155454	−	0.000178367i
$729$	8.57847	+	6.23262i	0.317721	+	0.230838i
$730$	−0.139662	−	0.0324770i	−0.00516912	−	0.00120203i
$731$	14.9296	−	21.8338i	0.552189	−	0.807551i
$732$	−3.96652	−	3.64044i	−0.146607	−	0.134555i
$733$	18.9749	+	19.5248i	0.700856	+	0.721163i	0.970314	−	0.241849i	$-0.0777538\pi$
$733$	18.9749	+	19.5248i	0.700856	+	0.721163i	−0.269458	+	0.963012i	$0.586845\pi$
$734$	0.181642	+	0.0648098i	0.00670454	+	0.00239218i
$735$	−0.836813	−	2.57545i	−0.0308663	−	0.0949967i
$736$	0.445305	−	0.513910i	0.0164142	−	0.0189430i
$737$	−13.6690	−	11.5791i	−0.503503	−	0.426522i
$738$	−0.174396	−	0.201263i	−0.00641959	−	0.00740860i
$739$	−4.22536	+	7.00697i	−0.155432	+	0.257755i	−0.924312	−	0.381638i	$-0.875360\pi$
$739$	−4.22536	+	7.00697i	−0.155432	+	0.257755i	0.768880	+	0.639394i	$0.220815\pi$
$740$	4.65521	+	6.03699i	0.171129	+	0.221924i
$741$	−2.52332	+	0.900319i	−0.0926965	+	0.0330740i
$742$	0.0552241	+	0.0271519i	0.00202734	+	0.000996776i
$743$	−20.7555	+	16.9717i	−0.761444	+	0.622630i	−0.931892	−	0.362737i	$-0.881842\pi$
$743$	−20.7555	+	16.9717i	−0.761444	+	0.622630i	0.170447	+	0.985367i	$0.445479\pi$
$744$	0.00588944	+	0.0290655i	0.000215917	+	0.00106559i
$745$	10.0500	+	0.574681i	0.368204	+	0.0210547i
$746$	0.0817124	−	0.0749949i	0.00299170	−	0.00274576i
$747$	0.444043	+	3.08839i	0.0162467	+	0.112998i
$748$	−4.86576	−	26.3585i	−0.177910	−	0.963763i
$749$	−2.37770	+	16.5373i	−0.0868793	+	0.604259i
$750$	−0.00292969	−	0.00428454i	−0.000106977	−	0.000156449i
$751$	−15.8884	−	40.8089i	−0.579774	−	1.48914i	−0.850233	−	0.526407i	$-0.823539\pi$
$751$	−15.8884	−	40.8089i	−0.579774	−	1.48914i	0.270458	−	0.962732i	$-0.412825\pi$
$752$	−12.3516	+	16.0178i	−0.450416	+	0.584109i
$753$	−2.97741	+	9.16352i	−0.108503	+	0.333937i
$754$	−0.00996929	−	0.0165322i	−0.000363060	−	0.000602067i
$755$	−4.37908	+	11.2476i	−0.159371	+	0.409341i
$756$	9.70155	−	2.25600i	0.352842	−	0.0820499i
$757$	−23.5867	−	9.96783i	−0.857274	−	0.362287i	−0.0840819	−	0.996459i	$-0.526796\pi$
$757$	−23.5867	−	9.96783i	−0.857274	−	0.362287i	−0.773192	+	0.634172i	$0.781341\pi$
$758$	0.269471	+	0.173179i	0.00978764	+	0.00629013i
$759$	−6.06330	−	10.4617i	−0.220084	−	0.379736i
$760$	0.181389	−	0.116572i	0.00657969	−	0.00422851i
$761$	7.35893	−	1.27351i	0.266761	−	0.0461648i	−0.0355723	−	0.999367i	$-0.511325\pi$
$761$	7.35893	−	1.27351i	0.266761	−	0.0461648i	0.302333	+	0.953202i	$0.402234\pi$
$762$	0.00196980	+	0.0229340i	7.13585e−5	+	0.000830812i
$763$	0.00783661	−	0.0912400i	0.000283704	−	0.00330311i
$764$	−25.5623	−	4.42373i	−0.924812	−	0.160045i
$765$	9.92383	−	4.19385i	0.358797	−	0.151629i
$766$	−0.0519454	+	0.0377405i	−0.00187686	+	0.00136362i
$767$	4.76236	−	2.68943i	0.171959	−	0.0971095i
$768$	−0.263916	−	9.23825i	−0.00952323	−	0.333357i
$769$	−26.6348	+	7.82067i	−0.960474	+	0.282021i	−0.724141	−	0.689652i	$-0.757764\pi$
$769$	−26.6348	+	7.82067i	−0.960474	+	0.282021i	−0.236332	+	0.971672i	$0.575945\pi$
$770$	0.00976928	−	0.0442487i	0.000352060	−	0.00159461i

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.s (of order \(55\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(0.00892359 + 0.00102389i) q^{2} +(-0.467498 - 0.339657i) q^{3} +(-1.94795 - 0.452975i) q^{4} +(-0.564443 + 0.825472i) q^{5} +(-0.00382399 - 0.00350963i) q^{6} +(1.06012 + 1.09083i) q^{7} +(-0.0338384 - 0.0120735i) q^{8} +(-0.823864 - 2.53559i) q^{9} +O(q^{10})\)	\(q+(0.00892359 + 0.00102389i) q^{2} +(-0.467498 - 0.339657i) q^{3} +(-1.94795 - 0.452975i) q^{4} +(-0.564443 + 0.825472i) q^{5} +(-0.00382399 - 0.00350963i) q^{6} +(1.06012 + 1.09083i) q^{7} +(-0.0338384 - 0.0120735i) q^{8} +(-0.823864 - 2.53559i) q^{9} +(-0.00588205 + 0.00678825i) q^{10} +(-0.898752 + 3.19253i) q^{11} +(0.756804 + 0.873399i) q^{12} +(0.398934 - 0.661558i) q^{13} +(0.00834315 + 0.0108196i) q^{14} +(0.544254 - 0.194189i) q^{15} +(3.58916 + 1.76467i) q^{16} +(3.12830 - 2.55800i) q^{17} +(-0.00475566 - 0.0234701i) q^{18} +(5.99164 + 0.342614i) q^{19} +(1.47342 - 1.35230i) q^{20} +(-0.125093 - 0.870039i) q^{21} +(-0.0112889 + 0.0275686i) q^{22} +(0.897887 - 6.24494i) q^{23} +(0.0117185 + 0.0171378i) q^{24} +(-0.362808 - 0.931864i) q^{25} +(0.00423728 - 0.00549501i) q^{26} +(-1.01178 + 3.11395i) q^{27} +(-1.57093 - 2.60509i) q^{28} +(1.00939 - 2.59260i) q^{29} +(0.00505552 - 0.00117561i) q^{30} +(1.31577 + 0.556050i) q^{31} +(0.0906702 + 0.0582702i) q^{32} +(1.50453 - 1.18723i) q^{33} +(0.0305348 - 0.0196235i) q^{34} +(-1.49883 + 0.259383i) q^{35} +(0.456281 + 5.31238i) q^{36} +(-0.326199 + 3.79787i) q^{37} +(0.0531161 + 0.00919210i) q^{38} +(-0.411204 + 0.173776i) q^{39} +(0.0290662 - 0.0211178i) q^{40} +(9.68335 - 5.46844i) q^{41} +(-0.000225455 - 0.00789195i) q^{42} +(6.28029 - 1.84406i) q^{43} +(3.19686 - 5.81176i) q^{44} +(2.55808 + 0.751121i) q^{45} +(0.0144065 - 0.0548079i) q^{46} +(-1.00434 + 4.95663i) q^{47} +(-1.07854 - 2.04406i) q^{48} +(0.133820 - 4.68432i) q^{49} +(-0.00228342 - 0.00868704i) q^{50} +(-2.33132 + 0.133310i) q^{51} +(-1.07677 + 1.10797i) q^{52} +(4.04193 - 1.98728i) q^{53} +(-0.0122171 + 0.0267516i) q^{54} +(-2.12805 - 2.54390i) q^{55} +(-0.0227025 - 0.0497114i) q^{56} +(-2.68471 - 2.19527i) q^{57} +(0.0116619 - 0.0221018i) q^{58} +(6.16460 + 3.48131i) q^{59} +(-1.14814 + 0.131737i) q^{60} +(-4.62829 + 0.531047i) q^{61} +(0.0111721 + 0.00630916i) q^{62} +(1.89252 - 3.58672i) q^{63} +(-6.19163 - 5.06287i) q^{64} +(0.320922 + 0.702721i) q^{65} +(0.0146414 - 0.00905392i) q^{66} +(-2.24379 + 4.91321i) q^{67} +(-7.25248 + 3.56580i) q^{68} +(-2.54090 + 2.61452i) q^{69} +(-0.0136405 + 0.000779992i) q^{70} +(-1.37069 - 5.21465i) q^{71} +(-0.00273528 + 0.0957473i) q^{72} +(7.44974 + 14.1188i) q^{73} +(-0.00679946 + 0.0335567i) q^{74} +(-0.146902 + 0.558875i) q^{75} +(-11.5162 - 3.38146i) q^{76} +(-4.43530 + 2.40406i) q^{77} +(-0.00384734 + 0.00112968i) q^{78} +(-0.193251 - 6.76466i) q^{79} +(-3.48256 + 1.96669i) q^{80} +(-4.94003 + 3.58914i) q^{81} +(0.0920093 - 0.0388834i) q^{82} +(-1.15317 - 0.199564i) q^{83} +(-0.150432 + 1.75145i) q^{84} +(0.345808 + 4.02617i) q^{85} +(0.0579308 - 0.0100253i) q^{86} +(-1.35248 + 0.869189i) q^{87} +(0.0689574 - 0.0971790i) q^{88} +(-9.75946 - 6.27202i) q^{89} +(0.0220582 + 0.00932188i) q^{90} +(1.14457 - 0.266158i) q^{91} +(-4.57784 + 11.7581i) q^{92} +(-0.426254 - 0.706864i) q^{93} +(-0.0140374 + 0.0432026i) q^{94} +(-3.66476 + 4.75254i) q^{95} +(-0.0225962 - 0.0580380i) q^{96} +(2.20585 + 3.22595i) q^{97} +(0.00599037 - 0.0416639i) q^{98} +(8.83540 - 0.351342i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 880q + 4q^{2} - q^{3} + 24q^{4} + 22q^{5} - 13q^{6} + 3q^{7} + 2q^{8} - 217q^{9} + O(q^{10}) \)	\( 880q + 4q^{2} - q^{3} + 24q^{4} + 22q^{5} - 13q^{6} + 3q^{7} + 2q^{8} - 217q^{9} - 6q^{10} + 5q^{11} - 5q^{12} - 26q^{13} - 108q^{14} - 12q^{15} + 34q^{16} - q^{17} - 14q^{18} + q^{19} + 19q^{20} - 10q^{21} + 275q^{22} - 51q^{23} + 283q^{24} + 22q^{25} - 16q^{27} - 4q^{28} - 19q^{29} + q^{30} - 34q^{31} - 122q^{32} + 19q^{33} + 52q^{34} + 8q^{35} - 21q^{36} - 109q^{37} - 10q^{38} - 9q^{39} - 64q^{40} + 4q^{41} - 49q^{42} - 97q^{43} + 17q^{44} - 80q^{45} - 91q^{46} + 166q^{47} - 159q^{48} + 175q^{49} + 4q^{50} - 112q^{51} - 128q^{52} - 141q^{53} - 37q^{54} - 5q^{55} + 79q^{56} - 204q^{57} - 190q^{58} + 9q^{59} - 22q^{60} + 2q^{61} - 105q^{62} - q^{63} - 176q^{64} - 14q^{65} - 112q^{66} - 13q^{67} - 35q^{68} - 53q^{69} + 24q^{70} - 50q^{71} + 705q^{72} + q^{73} + 40q^{74} - q^{75} - 148q^{76} - 104q^{77} - 187q^{78} - 83q^{79} - q^{80} - 238q^{81} - 54q^{82} - 151q^{83} + 4q^{84} - 29q^{85} - 39q^{86} - 74q^{87} - 143q^{88} - 52q^{89} - 28q^{90} - 188q^{91} - 253q^{92} + 122q^{93} - 187q^{94} + 122q^{95} - 155q^{96} + 283q^{97} - 92q^{98} + 172q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about