LMFDB - Embedded newform 1520.2.d.h.609.3

Newspace parameters

Level:	$ N $	$=$	$ 1520 = 2^{4} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1520.d (of order $2$, degree $1$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$12.1372611072$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.16516096.1
Defining polynomial:	$ x^{6} + 9x^{4} + 13x^{2} + 1 $ x^6 + 9x^4 + 13x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			609.3
Root			$-1.30397i$ of defining polynomial
Character	$\chi$	$=$	1520.609
Dual form			1520.2.d.h.609.4

$q$-expansion

$f(q)$	$=$	$q-0.537080i q^{3} +(-2.07772 - 0.826491i) q^{5} -3.18676i q^{7} +2.71155 q^{9} +O(q^{10})$	$q-0.537080i q^{3} +(-2.07772 - 0.826491i) q^{5} -3.18676i q^{7} +2.71155 q^{9} -4.15544 q^{11} +2.07086i q^{13} +(-0.443892 + 1.11590i) q^{15} -5.79470i q^{17} -1.00000 q^{19} -1.71155 q^{21} +2.60794i q^{23} +(3.63383 + 3.43443i) q^{25} -3.06756i q^{27} -6.00000 q^{29} -2.59933 q^{31} +2.23180i q^{33} +(-2.63383 + 6.62119i) q^{35} -4.30266i q^{37} +1.11222 q^{39} -0.599328 q^{41} -3.18676i q^{43} +(-5.63383 - 2.24107i) q^{45} +11.7086i q^{47} -3.15544 q^{49} -3.11222 q^{51} +11.7503i q^{53} +(8.63383 + 3.43443i) q^{55} +0.537080i q^{57} -1.71155 q^{59} -8.75476 q^{61} -8.64104i q^{63} +(1.71155 - 4.30266i) q^{65} +4.76228i q^{67} +1.40067 q^{69} -13.7115 q^{71} -2.72714i q^{73} +(1.84456 - 1.95166i) q^{75} +13.2424i q^{77} -1.40067 q^{79} +6.48711 q^{81} +7.07154i q^{83} +(-4.78926 + 12.0398i) q^{85} +3.22248i q^{87} -16.5353 q^{89} +6.59933 q^{91} +1.39605i q^{93} +(2.07772 + 0.826491i) q^{95} -2.07086i q^{97} -11.2677 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{5} - 14 q^{9}+O(q^{10}) $ 6 * q - q^5 - 14 * q^9	$ 6 q - q^{5} - 14 q^{9} - 2 q^{11} - 10 q^{15} - 6 q^{19} + 20 q^{21} + 3 q^{25} - 36 q^{29} + 3 q^{35} - 8 q^{39} + 12 q^{41} - 15 q^{45} + 4 q^{49} - 4 q^{51} + 33 q^{55} + 20 q^{59} - 14 q^{61} - 20 q^{65} + 24 q^{69} - 52 q^{71} + 34 q^{75} - 24 q^{79} + 38 q^{81} + 13 q^{85} - 24 q^{89} + 24 q^{91} + q^{95} - 30 q^{99}+O(q^{100}) $ 6 * q - q^5 - 14 * q^9 - 2 * q^11 - 10 * q^15 - 6 * q^19 + 20 * q^21 + 3 * q^25 - 36 * q^29 + 3 * q^35 - 8 * q^39 + 12 * q^41 - 15 * q^45 + 4 * q^49 - 4 * q^51 + 33 * q^55 + 20 * q^59 - 14 * q^61 - 20 * q^65 + 24 * q^69 - 52 * q^71 + 34 * q^75 - 24 * q^79 + 38 * q^81 + 13 * q^85 - 24 * q^89 + 24 * q^91 + q^95 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times$.

$n$	$191$	$401$	$1141$	$1217$
$\chi(n)$	$1$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	0.537080i		−	0.310083i	−0.987908	−	0.155042i	$-0.950449\pi$
$3$		−	0.537080i		−	0.310083i	0.987908	−	0.155042i	$-0.0495512\pi$
$4$		0			0
$5$	−2.07772	−	0.826491i	−0.929184	−	0.369618i
$5$	−2.07772	−	0.826491i	−0.929184	−	0.369618i
$6$		0			0
$7$		−	3.18676i		−	1.20448i	−0.798314	−	0.602241i	$-0.794275\pi$
$7$		−	3.18676i		−	1.20448i	0.798314	−	0.602241i	$-0.205725\pi$
$8$		0			0
$9$	2.71155			0.903848
$10$		0			0
$11$	−4.15544			−1.25291			−0.626456	−	0.779457i	$-0.715495\pi$
$11$	−4.15544			−1.25291			−0.626456	+	0.779457i	$0.715495\pi$
$12$		0			0
$13$			2.07086i			0.574353i	0.957878	+	0.287176i	$0.0927166\pi$
$13$			2.07086i			0.574353i	−0.957878	+	0.287176i	$0.907283\pi$
$14$		0			0
$15$	−0.443892	+	1.11590i	−0.114612	+	0.288124i
$16$		0			0
$17$		−	5.79470i		−	1.40542i	−0.711476	−	0.702710i	$-0.751973\pi$
$17$		−	5.79470i		−	1.40542i	0.711476	−	0.702710i	$-0.248027\pi$
$18$		0			0
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$		0			0
$21$	−1.71155			−0.373490
$22$		0			0
$23$			2.60794i			0.543793i	0.962327	+	0.271896i	$0.0876508\pi$
$23$			2.60794i			0.543793i	−0.962327	+	0.271896i	$0.912349\pi$
$24$		0			0
$25$	3.63383	+	3.43443i	0.726765	+	0.686886i
$26$		0			0
$27$		−	3.06756i		−	0.590352i
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	−2.59933			−0.466853			−0.233427	−	0.972374i	$-0.574994\pi$
$31$	−2.59933			−0.466853			−0.233427	+	0.972374i	$0.574994\pi$
$32$		0			0
$33$			2.23180i			0.388507i
$34$		0			0
$35$	−2.63383	+	6.62119i	−0.445198	+	1.11919i
$36$		0			0
$37$		−	4.30266i		−	0.707353i	−0.935368	−	0.353677i	$-0.884931\pi$
$37$		−	4.30266i		−	0.707353i	0.935368	−	0.353677i	$-0.115069\pi$
$38$		0			0
$39$	1.11222			0.178097
$40$		0			0
$41$	−0.599328			−0.0935993			−0.0467997	−	0.998904i	$-0.514902\pi$
$41$	−0.599328			−0.0935993			−0.0467997	+	0.998904i	$0.514902\pi$
$42$		0			0
$43$		−	3.18676i		−	0.485976i	−0.970029	−	0.242988i	$-0.921872\pi$
$43$		−	3.18676i		−	0.485976i	0.970029	−	0.242988i	$-0.0781276\pi$
$44$		0			0
$45$	−5.63383	−	2.24107i	−0.839841	−	0.334078i
$46$		0			0
$47$			11.7086i			1.70787i	0.520376	+	0.853937i	$0.325792\pi$
$47$			11.7086i			1.70787i	−0.520376	+	0.853937i	$0.674208\pi$
$48$		0			0
$49$	−3.15544			−0.450777
$50$		0			0
$51$	−3.11222			−0.435798
$52$		0			0
$53$			11.7503i			1.61403i	0.590529	+	0.807017i	$0.298919\pi$
$53$			11.7503i			1.61403i	−0.590529	+	0.807017i	$0.701081\pi$
$54$		0			0
$55$	8.63383	+	3.43443i	1.16418	+	0.463098i
$56$		0			0
$57$			0.537080i			0.0711380i
$58$		0			0
$59$	−1.71155			−0.222824			−0.111412	−	0.993774i	$-0.535537\pi$
$59$	−1.71155			−0.222824			−0.111412	+	0.993774i	$0.535537\pi$
$60$		0			0
$61$	−8.75476			−1.12093			−0.560466	−	0.828177i	$-0.689378\pi$
$61$	−8.75476			−1.12093			−0.560466	+	0.828177i	$0.689378\pi$
$62$		0			0
$63$		−	8.64104i		−	1.08867i
$64$		0			0
$65$	1.71155	−	4.30266i	0.212291	−	0.533679i
$66$		0			0
$67$			4.76228i			0.581805i	0.956753	+	0.290902i	$0.0939555\pi$
$67$			4.76228i			0.581805i	−0.956753	+	0.290902i	$0.906044\pi$
$68$		0			0
$69$	1.40067			0.168621
$70$		0			0
$71$	−13.7115			−1.62726			−0.813631	−	0.581382i	$-0.802512\pi$
$71$	−13.7115			−1.62726			−0.813631	+	0.581382i	$0.802512\pi$
$72$		0			0
$73$		−	2.72714i		−	0.319188i	−0.987183	−	0.159594i	$-0.948982\pi$
$73$		−	2.72714i		−	0.319188i	0.987183	−	0.159594i	$-0.0510185\pi$
$74$		0			0
$75$	1.84456	−	1.95166i	0.212992	−	0.225358i
$76$		0			0
$77$			13.2424i			1.50911i
$78$		0			0
$79$	−1.40067			−0.157588			−0.0787939	−	0.996891i	$-0.525107\pi$
$79$	−1.40067			−0.157588			−0.0787939	+	0.996891i	$0.525107\pi$
$80$		0			0
$81$	6.48711			0.720790
$82$		0			0
$83$			7.07154i			0.776203i	0.921617	+	0.388101i	$0.126869\pi$
$83$			7.07154i			0.776203i	−0.921617	+	0.388101i	$0.873131\pi$
$84$		0			0
$85$	−4.78926	+	12.0398i	−0.519469	+	1.30589i
$86$		0			0
$87$			3.22248i			0.345486i
$88$		0			0
$89$	−16.5353			−1.75274			−0.876370	−	0.481639i	$-0.840042\pi$
$89$	−16.5353			−1.75274			−0.876370	+	0.481639i	$0.840042\pi$
$90$		0			0
$91$	6.59933			0.691798
$92$		0			0
$93$			1.39605i			0.144763i
$94$		0			0
$95$	2.07772	+	0.826491i	0.213169	+	0.0847961i
$96$		0			0
$97$		−	2.07086i		−	0.210264i	−0.994458	−	0.105132i	$-0.966474\pi$
$97$		−	2.07086i		−	0.210264i	0.994458	−	0.105132i	$-0.0335265\pi$
$98$		0			0
$99$	−11.2677			−1.13244
$100$		0			0
$101$	−1.71155			−0.170305			−0.0851525	−	0.996368i	$-0.527138\pi$
$101$	−1.71155			−0.170305			−0.0851525	+	0.996368i	$0.527138\pi$
$102$		0			0
$103$		−	5.75296i		−	0.566856i	−0.958994	−	0.283428i	$-0.908528\pi$
$103$		−	5.75296i		−	0.566856i	0.958994	−	0.283428i	$-0.0914716\pi$
$104$		0			0
$105$	3.55611	+	1.41458i	0.347041	+	0.138048i
$106$		0			0
$107$		−	15.4324i		−	1.49191i	−0.665996	−	0.745955i	$-0.731993\pi$
$107$		−	15.4324i		−	1.49191i	0.665996	−	0.745955i	$-0.268007\pi$
$108$		0			0
$109$	−11.7115			−1.12176			−0.560881	−	0.827896i	$-0.689538\pi$
$109$	−11.7115			−1.12176			−0.560881	+	0.827896i	$0.689538\pi$
$110$		0			0
$111$	−2.31087			−0.219338
$112$		0			0
$113$		−	10.5927i		−	0.996477i	−0.867040	−	0.498239i	$-0.833980\pi$
$113$		−	10.5927i		−	0.996477i	0.867040	−	0.498239i	$-0.166020\pi$
$114$		0			0
$115$	2.15544	−	5.41856i	0.200996	−	0.505283i
$116$		0			0
$117$			5.61523i			0.519128i
$118$		0			0
$119$	−18.4663			−1.69280
$120$		0			0
$121$	6.26765			0.569787
$122$		0			0
$123$			0.321887i			0.0290236i
$124$		0			0
$125$	−4.71155	−	10.1391i	−0.421413	−	0.906869i
$126$		0			0
$127$		−	6.07484i		−	0.539055i	−0.962993	−	0.269528i	$-0.913132\pi$
$127$		−	6.07484i		−	0.539055i	0.962993	−	0.269528i	$-0.0868676\pi$
$128$		0			0
$129$	−1.71155			−0.150693
$130$		0			0
$131$	13.5785			1.18636			0.593181	−	0.805069i	$-0.297872\pi$
$131$	13.5785			1.18636			0.593181	+	0.805069i	$0.297872\pi$
$132$		0			0
$133$			3.18676i			0.276327i
$134$		0			0
$135$	−2.53531	+	6.37352i	−0.218204	+	0.548545i
$136$		0			0
$137$			7.94302i			0.678618i	0.940675	+	0.339309i	$0.110193\pi$
$137$			7.94302i			0.678618i	−0.940675	+	0.339309i	$0.889807\pi$
$138$		0			0
$139$	3.26765			0.277159			0.138579	−	0.990351i	$-0.455746\pi$
$139$	3.26765			0.277159			0.138579	+	0.990351i	$0.455746\pi$
$140$		0			0
$141$	6.28845			0.529583
$142$		0			0
$143$		−	8.60532i		−	0.719613i
$144$		0			0
$145$	12.4663	+	4.95894i	1.03527	+	0.411818i
$146$		0			0
$147$			1.69472i			0.139778i
$148$		0			0
$149$	−8.44389			−0.691751			−0.345875	−	0.938280i	$-0.612418\pi$
$149$	−8.44389			−0.691751			−0.345875	+	0.938280i	$0.612418\pi$
$150$		0			0
$151$	−0.887783			−0.0722468			−0.0361234	−	0.999347i	$-0.511501\pi$
$151$	−0.887783			−0.0722468			−0.0361234	+	0.999347i	$0.511501\pi$
$152$		0			0
$153$		−	15.7126i		−	1.27029i
$154$		0			0
$155$	5.40067	+	2.14832i	0.433792	+	0.172557i
$156$		0			0
$157$		−	4.14172i		−	0.330545i	−0.986248	−	0.165273i	$-0.947150\pi$
$157$		−	4.14172i		−	0.330545i	0.986248	−	0.165273i	$-0.0528504\pi$
$158$		0			0
$159$	6.31087			0.500485
$160$		0			0
$161$	8.31087			0.654989
$162$		0			0
$163$			24.7126i			1.93564i	0.251647	+	0.967819i	$0.419028\pi$
$163$			24.7126i			1.93564i	−0.251647	+	0.967819i	$0.580972\pi$
$164$		0			0
$165$	1.84456	−	4.63706i	0.143599	−	0.360994i
$166$		0			0
$167$		−	3.60464i		−	0.278935i	−0.990227	−	0.139468i	$-0.955461\pi$
$167$		−	3.60464i		−	0.278935i	0.990227	−	0.139468i	$-0.0445391\pi$
$168$		0			0
$169$	8.71155			0.670119
$170$		0			0
$171$	−2.71155			−0.207357
$172$		0			0
$173$		−	22.4205i		−	1.70460i	−0.523054	−	0.852300i	$-0.675207\pi$
$173$		−	22.4205i		−	1.70460i	0.523054	−	0.852300i	$-0.324793\pi$
$174$		0			0
$175$	10.9447	−	11.5801i	0.827342	−	0.875376i
$176$		0			0
$177$			0.919237i			0.0690941i
$178$		0			0
$179$	−5.13464			−0.383781			−0.191890	−	0.981416i	$-0.561462\pi$
$179$	−5.13464			−0.383781			−0.191890	+	0.981416i	$0.561462\pi$
$180$		0			0
$181$	20.8462			1.54948			0.774742	−	0.632277i	$-0.217880\pi$
$181$	20.8462			1.54948			0.774742	+	0.632277i	$0.217880\pi$
$182$		0			0
$183$			4.70201i			0.347583i
$184$		0			0
$185$	−3.55611	+	8.93972i	−0.261450	+	0.657261i
$186$		0			0
$187$			24.0795i			1.76087i
$188$		0			0
$189$	−9.77557			−0.711068
$190$		0			0
$191$	5.26765			0.381154			0.190577	−	0.981672i	$-0.438964\pi$
$191$	5.26765			0.381154			0.190577	+	0.981672i	$0.438964\pi$
$192$		0			0
$193$			2.07086i			0.149064i	0.997219	+	0.0745318i	$0.0237462\pi$
$193$			2.07086i			0.149064i	−0.997219	+	0.0745318i	$0.976254\pi$
$194$		0			0
$195$	−2.31087	−	0.919237i	−0.165485	−	0.0658279i
$196$		0			0
$197$		−	10.4318i		−	0.743232i	−0.928387	−	0.371616i	$-0.878804\pi$
$197$		−	10.4318i		−	0.743232i	0.928387	−	0.371616i	$-0.121196\pi$
$198$		0			0
$199$	−2.73235			−0.193691			−0.0968455	−	0.995299i	$-0.530875\pi$
$199$	−2.73235			−0.193691			−0.0968455	+	0.995299i	$0.530875\pi$
$200$		0			0
$201$	2.55773			0.180408
$202$		0			0
$203$			19.1206i			1.34200i
$204$		0			0
$205$	1.24524	+	0.495339i	0.0869710	+	0.0345960i
$206$		0			0
$207$			7.07154i			0.491506i
$208$		0			0
$209$	4.15544			0.287438
$210$		0			0
$211$	15.7340			1.08317			0.541585	−	0.840646i	$-0.317824\pi$
$211$	15.7340			1.08317			0.541585	+	0.840646i	$0.317824\pi$
$212$		0			0
$213$			7.36420i			0.504586i
$214$		0			0
$215$	−2.63383	+	6.62119i	−0.179625	+	0.451561i
$216$		0			0
$217$			8.28343i			0.562316i
$218$		0			0
$219$	−1.46469			−0.0989748
$220$		0			0
$221$	12.0000			0.807207
$222$		0			0
$223$		−	18.8219i		−	1.26041i	−0.776430	−	0.630203i	$-0.782972\pi$
$223$		−	18.8219i		−	1.26041i	0.776430	−	0.630203i	$-0.217028\pi$
$224$		0			0
$225$	9.85328	+	9.31261i	0.656886	+	0.620841i
$226$		0			0
$227$		−	14.4418i		−	0.958533i	−0.877669	−	0.479267i	$-0.840903\pi$
$227$		−	14.4418i		−	0.958533i	0.877669	−	0.479267i	$-0.159097\pi$
$228$		0			0
$229$	4.17785			0.276080			0.138040	−	0.990427i	$-0.455920\pi$
$229$	4.17785			0.276080			0.138040	+	0.990427i	$0.455920\pi$
$230$		0			0
$231$	7.11222			0.467950
$232$		0			0
$233$			12.0847i			0.791697i	0.918316	+	0.395849i	$0.129550\pi$
$233$			12.0847i			0.791697i	−0.918316	+	0.395849i	$0.870450\pi$
$234$		0			0
$235$	9.67705	−	24.3272i	0.631261	−	1.58693i
$236$		0			0
$237$			0.752273i			0.0488654i
$238$		0			0
$239$	−11.3541			−0.734435			−0.367218	−	0.930135i	$-0.619690\pi$
$239$	−11.3541			−0.734435			−0.367218	+	0.930135i	$0.619690\pi$
$240$		0			0
$241$	−3.40067			−0.219057			−0.109528	−	0.993984i	$-0.534934\pi$
$241$	−3.40067			−0.219057			−0.109528	+	0.993984i	$0.534934\pi$
$242$		0			0
$243$		−	12.6868i		−	0.813857i
$244$		0			0
$245$	6.55611	+	2.60794i	0.418854	+	0.166615i
$246$		0			0
$247$		−	2.07086i		−	0.131766i
$248$		0			0
$249$	3.79798			0.240687
$250$		0			0
$251$	−3.04322			−0.192086			−0.0960432	−	0.995377i	$-0.530619\pi$
$251$	−3.04322			−0.192086			−0.0960432	+	0.995377i	$0.530619\pi$
$252$		0			0
$253$		−	10.8371i		−	0.681324i
$254$		0			0
$255$	6.46631	+	2.57222i	0.404936	+	0.161079i
$256$		0			0
$257$		−	17.2881i		−	1.07840i	−0.842177	−	0.539201i	$-0.818726\pi$
$257$		−	17.2881i		−	1.07840i	0.842177	−	0.539201i	$-0.181274\pi$
$258$		0			0
$259$	−13.7115			−0.851994
$260$		0			0
$261$	−16.2693			−1.00704
$262$		0			0
$263$			1.19336i			0.0735859i	0.999323	+	0.0367930i	$0.0117142\pi$
$263$			1.19336i			0.0735859i	−0.999323	+	0.0367930i	$0.988286\pi$
$264$		0			0
$265$	9.71155	−	24.4139i	0.596575	−	1.49973i
$266$		0			0
$267$			8.88078i			0.543495i
$268$		0			0
$269$	−22.1089			−1.34800			−0.674000	−	0.738731i	$-0.735425\pi$
$269$	−22.1089			−1.34800			−0.674000	+	0.738731i	$0.735425\pi$
$270$		0			0
$271$	4.08644			0.248234			0.124117	−	0.992268i	$-0.460390\pi$
$271$	4.08644			0.248234			0.124117	+	0.992268i	$0.460390\pi$
$272$		0			0
$273$		−	3.54437i		−	0.214515i
$274$		0			0
$275$	−15.1001	−	14.2716i	−0.910572	−	0.860607i
$276$		0			0
$277$			10.0199i			0.602037i	0.953618	+	0.301019i	$0.0973266\pi$
$277$			10.0199i			0.602037i	−0.953618	+	0.301019i	$0.902673\pi$
$278$		0			0
$279$	−7.04820			−0.421964
$280$		0			0
$281$	0.599328			0.0357529			0.0178765	−	0.999840i	$-0.494309\pi$
$281$	0.599328			0.0357529			0.0178765	+	0.999840i	$0.494309\pi$
$282$		0			0
$283$		−	5.41856i		−	0.322100i	−0.986946	−	0.161050i	$-0.948512\pi$
$283$		−	5.41856i		−	0.322100i	0.986946	−	0.161050i	$-0.0514880\pi$
$284$		0			0
$285$	0.443892	−	1.11590i	0.0262939	−	0.0661003i
$286$		0			0
$287$			1.90991i			0.112739i
$288$		0			0
$289$	−16.5785			−0.975207
$290$		0			0
$291$	−1.11222			−0.0651993
$292$		0			0
$293$			3.46691i			0.202539i	0.994859	+	0.101269i	$0.0322904\pi$
$293$			3.46691i			0.202539i	−0.994859	+	0.101269i	$0.967710\pi$
$294$		0			0
$295$	3.55611	+	1.41458i	0.207045	+	0.0823598i
$296$		0			0
$297$			12.7470i			0.739658i
$298$		0			0
$299$	−5.40067			−0.312329
$300$		0			0
$301$	−10.1554			−0.585350
$302$		0			0
$303$			0.919237i			0.0528088i
$304$		0			0
$305$	18.1899	+	7.23573i	1.04155	+	0.414317i
$306$		0			0
$307$		−	16.5901i		−	0.946846i	−0.880835	−	0.473423i	$-0.843018\pi$
$307$		−	16.5901i		−	0.946846i	0.880835	−	0.473423i	$-0.156982\pi$
$308$		0			0
$309$	−3.08980			−0.175772
$310$		0			0
$311$	4.15544			0.235633			0.117817	−	0.993035i	$-0.462411\pi$
$311$	4.15544			0.235633			0.117817	+	0.993035i	$0.462411\pi$
$312$		0			0
$313$		−	0.919237i		−	0.0519583i	−0.999662	−	0.0259792i	$-0.991730\pi$
$313$		−	0.919237i		−	0.0519583i	0.999662	−	0.0259792i	$-0.00827036\pi$
$314$		0			0
$315$	−7.14174	+	17.9537i	−0.402391	+	1.01157i
$316$		0			0
$317$			26.7292i			1.50126i	0.660723	+	0.750630i	$0.270250\pi$
$317$			26.7292i			1.50126i	−0.660723	+	0.750630i	$0.729750\pi$
$318$		0			0
$319$	24.9326			1.39596
$320$		0			0
$321$	−8.28845			−0.462616
$322$		0			0
$323$			5.79470i			0.322426i
$324$		0			0
$325$	−7.11222	+	7.52514i	−0.394515	+	0.417420i
$326$		0			0
$327$			6.29004i			0.347840i
$328$		0			0
$329$	37.3125			2.05710
$330$		0			0
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$		0			0
$333$		−	11.6669i		−	0.639340i
$334$		0			0
$335$	3.93598	−	9.89467i	0.215045	−	0.540604i
$336$		0			0
$337$		−	22.5040i		−	1.22587i	−0.790133	−	0.612935i	$-0.789989\pi$
$337$		−	22.5040i		−	1.22587i	0.790133	−	0.612935i	$-0.210011\pi$
$338$		0			0
$339$	−5.68913			−0.308991
$340$		0			0
$341$	10.8013			0.584926
$342$		0			0
$343$		−	12.2517i		−	0.661530i
$344$		0			0
$345$	−2.91020	−	1.15764i	−0.156680	−	0.0623254i
$346$		0			0
$347$		−	14.4543i		−	0.775946i	−0.921671	−	0.387973i	$-0.873175\pi$
$347$		−	14.4543i		−	0.775946i	0.921671	−	0.387973i	$-0.126825\pi$
$348$		0			0
$349$	13.3541			0.714828			0.357414	−	0.933946i	$-0.383658\pi$
$349$	13.3541			0.714828			0.357414	+	0.933946i	$0.383658\pi$
$350$		0			0
$351$	6.35248			0.339070
$352$		0			0
$353$			17.6410i			0.938937i	0.882949	+	0.469469i	$0.155554\pi$
$353$			17.6410i			0.938937i	−0.882949	+	0.469469i	$0.844446\pi$
$354$		0			0
$355$	28.4887	+	11.3325i	1.51202	+	0.601465i
$356$		0			0
$357$			9.91789i			0.524910i
$358$		0			0
$359$	12.4663			0.657947			0.328973	−	0.944339i	$-0.393297\pi$
$359$	12.4663			0.657947			0.328973	+	0.944339i	$0.393297\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$		0			0
$363$		−	3.36623i		−	0.176681i
$364$		0			0
$365$	−2.25396	+	5.66623i	−0.117977	+	0.296584i
$366$		0			0
$367$		−	16.4291i		−	0.857594i	−0.903401	−	0.428797i	$-0.858938\pi$
$367$		−	16.4291i		−	0.857594i	0.903401	−	0.428797i	$-0.141062\pi$
$368$		0			0
$369$	−1.62511			−0.0845996
$370$		0			0
$371$	37.4455			1.94407
$372$		0			0
$373$		−	5.29334i		−	0.274079i	−0.990566	−	0.137039i	$-0.956241\pi$
$373$		−	5.29334i		−	0.274079i	0.990566	−	0.137039i	$-0.0437587\pi$
$374$		0			0
$375$	−5.44551	+	2.53048i	−0.281205	+	0.130673i
$376$		0			0
$377$		−	12.4252i		−	0.639928i
$378$		0			0
$379$	14.5353			0.746629			0.373314	−	0.927705i	$-0.378221\pi$
$379$	14.5353			0.746629			0.373314	+	0.927705i	$0.378221\pi$
$380$		0			0
$381$	−3.26268			−0.167152
$382$		0			0
$383$		−	0.453598i		−	0.0231778i	−0.999933	−	0.0115889i	$-0.996311\pi$
$383$		−	0.453598i		−	0.0231778i	0.999933	−	0.0115889i	$-0.00368894\pi$
$384$		0			0
$385$	10.9447	−	27.5139i	0.557794	−	1.40224i
$386$		0			0
$387$		−	8.64104i		−	0.439249i
$388$		0			0
$389$	−16.1554			−0.819113			−0.409557	−	0.912285i	$-0.634317\pi$
$389$	−16.1554			−0.819113			−0.409557	+	0.912285i	$0.634317\pi$
$390$		0			0
$391$	15.1122			0.764258
$392$		0			0
$393$		−	7.29276i		−	0.367871i
$394$		0			0
$395$	2.91020	+	1.15764i	0.146428	+	0.0582473i
$396$		0			0
$397$		−	32.7563i		−	1.64399i	−0.569495	−	0.821995i	$-0.692861\pi$
$397$		−	32.7563i		−	1.64399i	0.569495	−	0.821995i	$-0.307139\pi$
$398$		0			0
$399$	1.71155			0.0856844
$400$		0			0
$401$	12.0864			0.603568			0.301784	−	0.953376i	$-0.402418\pi$
$401$	12.0864			0.603568			0.301784	+	0.953376i	$0.402418\pi$
$402$		0			0
$403$		−	5.38284i		−	0.268138i
$404$		0			0
$405$	−13.4784	−	5.36154i	−0.669747	−	0.266417i
$406$		0			0
$407$			17.8794i			0.886251i
$408$		0			0
$409$	19.1346			0.946147			0.473073	−	0.881023i	$-0.343145\pi$
$409$	19.1346			0.946147			0.473073	+	0.881023i	$0.343145\pi$
$410$		0			0
$411$	4.26604			0.210428
$412$		0			0
$413$			5.45428i			0.268388i
$414$		0			0
$415$	5.84456	−	14.6927i	0.286898	−	0.721235i
$416$		0			0
$417$		−	1.75499i		−	0.0859423i
$418$		0			0
$419$	8.04484			0.393016			0.196508	−	0.980502i	$-0.437040\pi$
$419$	8.04484			0.393016			0.196508	+	0.980502i	$0.437040\pi$
$420$		0			0
$421$	−29.3591			−1.43087			−0.715437	−	0.698678i	$-0.753772\pi$
$421$	−29.3591			−1.43087			−0.715437	+	0.698678i	$0.753772\pi$
$422$		0			0
$423$			31.7484i			1.54366i
$424$		0			0
$425$	19.9015	−	21.0569i	0.965364	−	1.02141i
$426$		0			0
$427$			27.8993i			1.35014i
$428$		0			0
$429$	−4.62175			−0.223140
$430$		0			0
$431$	32.0448			1.54355			0.771773	−	0.635898i	$-0.219370\pi$
$431$	32.0448			1.54355			0.771773	+	0.635898i	$0.219370\pi$
$432$		0			0
$433$			0.482831i			0.0232034i	0.999933	+	0.0116017i	$0.00369301\pi$
$433$			0.482831i			0.0232034i	−0.999933	+	0.0116017i	$0.996307\pi$
$434$		0			0
$435$	2.66335	−	6.69541i	0.127698	−	0.321020i
$436$		0			0
$437$		−	2.60794i		−	0.124755i
$438$		0			0
$439$	−27.3591			−1.30578			−0.652889	−	0.757454i	$-0.726443\pi$
$439$	−27.3591			−1.30578			−0.652889	+	0.757454i	$0.726443\pi$
$440$		0			0
$441$	−8.55611			−0.407434
$442$		0			0
$443$		−	23.3815i		−	1.11089i	−0.831554	−	0.555444i	$-0.812548\pi$
$443$		−	23.3815i		−	1.11089i	0.831554	−	0.555444i	$-0.187452\pi$
$444$		0			0
$445$	34.3557	+	13.6663i	1.62862	+	0.647844i
$446$		0			0
$447$			4.53505i			0.214500i
$448$		0			0
$449$	−23.1346			−1.09179			−0.545895	−	0.837853i	$-0.683810\pi$
$449$	−23.1346			−1.09179			−0.545895	+	0.837853i	$0.683810\pi$
$450$		0			0
$451$	2.49047			0.117272
$452$		0			0
$453$			0.476811i			0.0224025i
$454$		0			0
$455$	−13.7115	−	5.45428i	−0.642807	−	0.255701i
$456$		0			0
$457$		−	21.2503i		−	0.994049i	−0.867736	−	0.497025i	$-0.834426\pi$
$457$		−	21.2503i		−	0.994049i	0.867736	−	0.497025i	$-0.165574\pi$
$458$		0			0
$459$	−17.7756			−0.829692
$460$		0			0
$461$	31.5785			1.47076			0.735379	−	0.677656i	$-0.237004\pi$
$461$	31.5785			1.47076			0.735379	+	0.677656i	$0.237004\pi$
$462$		0			0
$463$			15.6119i			0.725547i	0.931877	+	0.362774i	$0.118170\pi$
$463$			15.6119i			0.725547i	−0.931877	+	0.362774i	$0.881830\pi$
$464$		0			0
$465$	1.15382	−	2.90059i	0.0535071	−	0.134512i
$466$		0			0
$467$		−	29.8264i		−	1.38020i	−0.723713	−	0.690101i	$-0.757566\pi$
$467$		−	29.8264i		−	1.38020i	0.723713	−	0.690101i	$-0.242434\pi$
$468$		0			0
$469$	15.1762			0.700774
$470$		0			0
$471$	−2.22443			−0.102496
$472$		0			0
$473$			13.2424i			0.608885i
$474$		0			0
$475$	−3.63383	−	3.43443i	−0.166731	−	0.157582i
$476$		0			0
$477$			31.8616i			1.45884i
$478$		0			0
$479$	4.53531			0.207223			0.103612	−	0.994618i	$-0.466960\pi$
$479$	4.53531			0.207223			0.103612	+	0.994618i	$0.466960\pi$
$480$		0			0
$481$	8.91020			0.406270
$482$		0			0
$483$		−	4.46360i		−	0.203101i
$484$		0			0
$485$	−1.71155	+	4.30266i	−0.0777173	+	0.195374i
$486$		0			0
$487$			39.2550i			1.77881i	0.457116	+	0.889407i	$0.348882\pi$
$487$			39.2550i			1.77881i	−0.457116	+	0.889407i	$0.651118\pi$
$488$		0			0
$489$	13.2726			0.600209
$490$		0			0
$491$	−38.8910			−1.75513			−0.877564	−	0.479460i	$-0.840832\pi$
$491$	−38.8910			−1.75513			−0.877564	+	0.479460i	$0.840832\pi$
$492$		0			0
$493$			34.7682i			1.56588i
$494$		0			0
$495$	23.4110	+	9.31261i	1.05225	+	0.418571i
$496$		0			0
$497$			43.6954i			1.96001i
$498$		0			0
$499$	4.73235			0.211849			0.105924	−	0.994374i	$-0.466220\pi$
$499$	4.73235			0.211849			0.105924	+	0.994374i	$0.466220\pi$
$500$		0			0
$501$	−1.93598			−0.0864931
$502$		0			0
$503$		−	1.85567i		−	0.0827400i	−0.999144	−	0.0413700i	$-0.986828\pi$
$503$		−	1.85567i		−	0.0827400i	0.999144	−	0.0413700i	$-0.0131722\pi$
$504$		0			0
$505$	3.55611	+	1.41458i	0.158245	+	0.0629478i
$506$		0			0
$507$		−	4.67880i		−	0.207793i
$508$		0			0
$509$	−22.8878			−1.01448			−0.507242	−	0.861804i	$-0.669335\pi$
$509$	−22.8878			−1.01448			−0.507242	+	0.861804i	$0.669335\pi$
$510$		0			0
$511$	−8.69074			−0.384456
$512$		0			0
$513$			3.06756i			0.135436i
$514$		0			0
$515$	−4.75476	+	11.9530i	−0.209520	+	0.526713i
$516$		0			0
$517$		−	48.6543i		−	2.13982i
$518$		0			0
$519$	−12.0416			−0.528568
$520$		0			0
$521$	−29.7340			−1.30267			−0.651334	−	0.758791i	$-0.725790\pi$
$521$	−29.7340			−1.30267			−0.651334	+	0.758791i	$0.725790\pi$
$522$		0			0
$523$		−	30.6497i		−	1.34022i	−0.742263	−	0.670109i	$-0.766248\pi$
$523$		−	30.6497i		−	1.34022i	0.742263	−	0.670109i	$-0.233752\pi$
$524$		0			0
$525$	−6.21946	−	5.87818i	−0.271439	−	0.256545i
$526$		0			0
$527$			15.0623i			0.656125i
$528$		0			0
$529$	16.1987			0.704289
$530$		0			0
$531$	−4.64093			−0.201399
$532$		0			0
$533$		−	1.24112i		−	0.0537590i
$534$		0			0
$535$	−12.7548	+	32.0643i	−0.551437	+	1.38626i
$536$		0			0
$537$			2.75771i			0.119004i
$538$		0			0
$539$	13.1122			0.564783
$540$		0			0
$541$	2.21946			0.0954220			0.0477110	−	0.998861i	$-0.484807\pi$
$541$	2.21946			0.0954220			0.0477110	+	0.998861i	$0.484807\pi$
$542$		0			0
$543$		−	11.1961i		−	0.480469i
$544$		0			0
$545$	24.3333	+	9.67948i	1.04232	+	0.414623i
$546$		0			0
$547$		−	14.4297i		−	0.616970i	−0.951229	−	0.308485i	$-0.900178\pi$
$547$		−	14.4297i		−	0.616970i	0.951229	−	0.308485i	$-0.0998220\pi$
$548$		0			0
$549$	−23.7389			−1.01315
$550$		0			0
$551$	6.00000			0.255609
$552$		0			0
$553$			4.46360i			0.189812i
$554$		0			0
$555$	4.80134	+	1.90991i	0.203806	+	0.0810714i
$556$		0			0
$557$		−	19.4610i		−	0.824588i	−0.911051	−	0.412294i	$-0.864728\pi$
$557$		−	19.4610i		−	0.824588i	0.911051	−	0.412294i	$-0.135272\pi$
$558$		0			0
$559$	6.59933			0.279122
$560$		0			0
$561$	12.9326			0.546016
$562$		0			0
$563$			12.3649i			0.521118i	0.965458	+	0.260559i	$0.0839068\pi$
$563$			12.3649i			0.521118i	−0.965458	+	0.260559i	$0.916093\pi$
$564$		0			0
$565$	−8.75476	+	22.0086i	−0.368316	+	0.925911i
$566$		0			0
$567$		−	20.6729i		−	0.868179i
$568$		0			0
$569$	−15.0898			−0.632597			−0.316299	−	0.948660i	$-0.602440\pi$
$569$	−15.0898			−0.632597			−0.316299	+	0.948660i	$0.602440\pi$
$570$		0			0
$571$	−17.1571			−0.718000			−0.359000	−	0.933337i	$-0.616882\pi$
$571$	−17.1571			−0.718000			−0.359000	+	0.933337i	$0.616882\pi$
$572$		0			0
$573$		−	2.82915i		−	0.118190i
$574$		0			0
$575$	−8.95678	+	9.47680i	−0.373524	+	0.395210i
$576$		0			0
$577$			22.5165i			0.937374i	0.883364	+	0.468687i	$0.155273\pi$
$577$			22.5165i			0.937374i	−0.883364	+	0.468687i	$0.844727\pi$
$578$		0			0
$579$	1.11222			0.0462222
$580$		0			0
$581$	22.5353			0.934922
$582$		0			0
$583$		−	48.8278i		−	2.02224i
$584$		0			0
$585$	4.64093	−	11.6669i	0.191879	−	0.482365i
$586$		0			0
$587$			7.49544i			0.309370i	0.987964	+	0.154685i	$0.0494363\pi$
$587$			7.49544i			0.309370i	−0.987964	+	0.154685i	$0.950564\pi$
$588$		0			0
$589$	2.59933			0.107103
$590$		0			0
$591$	−5.60269			−0.230464
$592$		0			0
$593$			27.8094i			1.14199i	0.820952	+	0.570997i	$0.193443\pi$
$593$			27.8094i			1.14199i	−0.820952	+	0.570997i	$0.806557\pi$
$594$		0			0
$595$	38.3678	+	15.2622i	1.57293	+	0.625690i
$596$		0			0
$597$			1.46749i			0.0600603i
$598$		0			0
$599$	−45.4903			−1.85869			−0.929343	−	0.369219i	$-0.879625\pi$
$599$	−45.4903			−1.85869			−0.929343	+	0.369219i	$0.879625\pi$
$600$		0			0
$601$	−16.5993			−0.677101			−0.338550	−	0.940948i	$-0.609937\pi$
$601$	−16.5993			−0.677101			−0.338550	+	0.940948i	$0.609937\pi$
$602$		0			0
$603$			12.9131i			0.525863i
$604$		0			0
$605$	−13.0224	−	5.18016i	−0.529437	−	0.210603i
$606$		0			0
$607$		−	5.08417i		−	0.206360i	−0.994663	−	0.103180i	$-0.967098\pi$
$607$		−	5.08417i		−	0.206360i	0.994663	−	0.103180i	$-0.0329018\pi$
$608$		0			0
$609$	10.2693			0.416132
$610$		0			0
$611$	−24.2469			−0.980923
$612$		0			0
$613$			4.63706i			0.187289i	0.995606	+	0.0936445i	$0.0298517\pi$
$613$			4.63706i			0.187289i	−0.995606	+	0.0936445i	$0.970148\pi$
$614$		0			0
$615$	0.266037	−	0.668791i	0.0107276	−	0.0269683i
$616$		0			0
$617$		−	40.2874i		−	1.62191i	−0.585108	−	0.810955i	$-0.698948\pi$
$617$		−	40.2874i		−	1.62191i	0.585108	−	0.810955i	$-0.301052\pi$
$618$		0			0
$619$	−43.3815			−1.74365			−0.871825	−	0.489818i	$-0.837063\pi$
$619$	−43.3815			−1.74365			−0.871825	+	0.489818i	$0.837063\pi$
$620$		0			0
$621$	8.00000			0.321029
$622$		0			0
$623$			52.6940i			2.11114i
$624$		0			0
$625$	1.40939	+	24.9602i	0.0563757	+	0.998410i
$626$		0			0
$627$		−	2.23180i		−	0.0891296i
$628$		0			0
$629$	−24.9326			−0.994129
$630$		0			0
$631$	−7.53369			−0.299911			−0.149956	−	0.988693i	$-0.547913\pi$
$631$	−7.53369			−0.299911			−0.149956	+	0.988693i	$0.547913\pi$
$632$		0			0
$633$		−	8.45040i		−	0.335873i
$634$		0			0
$635$	−5.02080	+	12.6218i	−0.199244	+	0.500881i
$636$		0			0
$637$		−	6.53446i		−	0.258905i
$638$		0			0
$639$	−37.1795			−1.47080
$640$		0			0
$641$	−23.3075			−0.920591			−0.460296	−	0.887766i	$-0.652257\pi$
$641$	−23.3075			−0.920591			−0.460296	+	0.887766i	$0.652257\pi$
$642$		0			0
$643$		−	1.87419i		−	0.0739110i	−0.999317	−	0.0369555i	$-0.988234\pi$
$643$		−	1.87419i		−	0.0739110i	0.999317	−	0.0369555i	$-0.0117660\pi$
$644$		0			0
$645$	3.55611	+	1.41458i	0.140022	+	0.0556989i
$646$		0			0
$647$		−	47.0371i		−	1.84922i	−0.380917	−	0.924609i	$-0.624392\pi$
$647$		−	47.0371i		−	1.84922i	0.380917	−	0.924609i	$-0.375608\pi$
$648$		0			0
$649$	7.11222			0.279179
$650$		0			0
$651$	4.44887			0.174365
$652$		0			0
$653$			24.1630i			0.945571i	0.881178	+	0.472785i	$0.156751\pi$
$653$			24.1630i			0.945571i	−0.881178	+	0.472785i	$0.843249\pi$
$654$		0			0
$655$	−28.2124	−	11.2225i	−1.10235	−	0.438500i
$656$		0			0
$657$		−	7.39477i		−	0.288497i
$658$		0			0
$659$	10.2885			0.400781			0.200391	−	0.979716i	$-0.435779\pi$
$659$	10.2885			0.400781			0.200391	+	0.979716i	$0.435779\pi$
$660$		0			0
$661$	5.93598			0.230883			0.115441	−	0.993314i	$-0.463172\pi$
$661$	5.93598			0.230883			0.115441	+	0.993314i	$0.463172\pi$
$662$		0			0
$663$		−	6.44496i		−	0.250302i
$664$		0			0
$665$	2.63383	−	6.62119i	0.102135	−	0.256759i
$666$		0			0
$667$		−	15.6476i		−	0.605879i
$668$		0			0
$669$	−10.1089			−0.390831
$670$		0			0
$671$	36.3799			1.40443
$672$		0			0
$673$		−	40.7053i		−	1.56907i	−0.620082	−	0.784537i	$-0.712901\pi$
$673$		−	40.7053i		−	1.56907i	0.620082	−	0.784537i	$-0.287099\pi$
$674$		0			0
$675$	10.5353	−	11.1470i	0.405504	−	0.429047i
$676$		0			0
$677$		−	18.8761i		−	0.725469i	−0.931893	−	0.362734i	$-0.881843\pi$
$677$		−	18.8761i		−	0.725469i	0.931893	−	0.362734i	$-0.118157\pi$
$678$		0			0
$679$	−6.59933			−0.253259
$680$		0			0
$681$	−7.75638			−0.297225
$682$		0			0
$683$			19.6576i			0.752179i	0.926583	+	0.376089i	$0.122731\pi$
$683$			19.6576i			0.752179i	−0.926583	+	0.376089i	$0.877269\pi$
$684$		0			0
$685$	6.56483	−	16.5034i	0.250829	−	0.630561i
$686$		0			0
$687$		−	2.24384i		−	0.0856079i
$688$		0			0
$689$	−24.3333			−0.927025
$690$		0			0
$691$	48.2451			1.83533			0.917665	−	0.397354i	$-0.130072\pi$
$691$	48.2451			1.83533			0.917665	+	0.397354i	$0.130072\pi$
$692$		0			0
$693$			35.9073i			1.36401i
$694$		0			0
$695$	−6.78926	−	2.70068i	−0.257531	−	0.102443i
$696$		0			0
$697$			3.47293i			0.131546i
$698$		0			0
$699$	6.49047			0.245492
$700$		0			0
$701$	0.512889			0.0193715			0.00968577	−	0.999953i	$-0.496917\pi$
$701$	0.512889			0.0193715			0.00968577	+	0.999953i	$0.496917\pi$
$702$		0			0
$703$			4.30266i			0.162278i
$704$		0			0
$705$	−13.0656	−	5.19735i	−0.492080	−	0.195743i
$706$		0			0
$707$			5.45428i			0.205129i
$708$		0			0
$709$	8.84618			0.332225			0.166113	−	0.986107i	$-0.446878\pi$
$709$	8.84618			0.332225			0.166113	+	0.986107i	$0.446878\pi$
$710$		0			0
$711$	−3.79798			−0.142436
$712$		0			0
$713$		−	6.77889i		−	0.253871i
$714$		0			0
$715$	−7.11222	+	17.8794i	−0.265982	+	0.668653i
$716$		0			0
$717$			6.09806i			0.227736i
$718$		0			0
$719$	7.84456			0.292553			0.146276	−	0.989244i	$-0.453271\pi$
$719$	7.84456			0.292553			0.146276	+	0.989244i	$0.453271\pi$
$720$		0			0
$721$	−18.3333			−0.682767
$722$		0			0
$723$			1.82643i			0.0679258i
$724$		0			0
$725$	−21.8030	−	20.6066i	−0.809742	−	0.765309i
$726$		0			0
$727$		−	2.91130i		−	0.107974i	−0.998542	−	0.0539870i	$-0.982807\pi$
$727$		−	2.91130i		−	0.107974i	0.998542	−	0.0539870i	$-0.0171930\pi$
$728$		0			0
$729$	12.6475			0.468427
$730$		0			0
$731$	−18.4663			−0.683001
$732$		0			0
$733$		−	33.7775i		−	1.24760i	−0.781584	−	0.623800i	$-0.785588\pi$
$733$		−	33.7775i		−	1.24760i	0.781584	−	0.623800i	$-0.214412\pi$
$734$		0			0
$735$	1.40067	−	3.52116i	0.0516646	−	0.129880i
$736$		0			0
$737$		−	19.7893i		−	0.728950i
$738$		0			0
$739$	−35.8030			−1.31703			−0.658517	−	0.752566i	$-0.728816\pi$
$739$	−35.8030			−1.31703			−0.658517	+	0.752566i	$0.728816\pi$
$740$		0			0
$741$	−1.11222			−0.0408583
$742$		0			0
$743$			5.66948i			0.207993i	0.994578	+	0.103996i	$0.0331631\pi$
$743$			5.66948i			0.207993i	−0.994578	+	0.103996i	$0.966837\pi$
$744$		0			0
$745$	17.5440	+	6.97880i	0.642763	+	0.255683i
$746$		0			0
$747$			19.1748i			0.701569i
$748$		0			0
$749$	−49.1795			−1.79698
$750$		0			0
$751$	27.4679			1.00232			0.501159	−	0.865355i	$-0.332907\pi$
$751$	27.4679			1.00232			0.501159	+	0.865355i	$0.332907\pi$
$752$		0			0
$753$			1.63445i			0.0595628i
$754$		0			0
$755$	1.84456	+	0.733744i	0.0671305	+	0.0267037i
$756$		0			0
$757$			41.6370i			1.51332i	0.653806	+	0.756662i	$0.273171\pi$
$757$			41.6370i			1.51332i	−0.653806	+	0.756662i	$0.726829\pi$
$758$		0			0
$759$	−5.82040			−0.211267
$760$		0			0
$761$	−9.46967			−0.343275			−0.171638	−	0.985160i	$-0.554906\pi$
$761$	−9.46967			−0.343275			−0.171638	+	0.985160i	$0.554906\pi$
$762$		0			0
$763$			37.3219i			1.35114i
$764$		0			0
$765$	−12.9863	+	32.6463i	−0.469521	+	1.18033i
$766$		0			0
$767$		−	3.54437i		−	0.127980i
$768$		0			0
$769$	−1.90858			−0.0688253			−0.0344127	−	0.999408i	$-0.510956\pi$
$769$	−1.90858			−0.0688253			−0.0344127	+	0.999408i	$0.510956\pi$
$770$		0			0
$771$	−9.28510			−0.334395
$772$		0			0
$773$		−	28.4007i		−	1.02150i	−0.859729	−	0.510751i	$-0.829367\pi$
$773$		−	28.4007i		−	1.02150i	0.859729	−	0.510751i	$-0.170633\pi$
$774$		0			0
$775$	−9.44551	−	8.92721i	−0.339293	−	0.320675i
$776$		0			0
$777$			7.36420i			0.264189i
$778$		0			0
$779$	0.599328			0.0214732
$780$		0			0
$781$	56.9775			2.03881
$782$		0			0
$783$			18.4053i			0.657753i
$784$		0			0
$785$	−3.42309	+	8.60532i	−0.122175	+	0.307137i
$786$		0			0
$787$			15.6708i			0.558605i	0.960203	+	0.279303i	$0.0901033\pi$
$787$			15.6708i			0.558605i	−0.960203	+	0.279303i	$0.909897\pi$
$788$		0			0
$789$	0.640931			0.0228178
$790$		0			0
$791$	−33.7564			−1.20024
$792$		0			0
$793$		−	18.1299i		−	0.643811i
$794$		0			0
$795$	−13.1122	−	5.21588i	−0.465042	−	0.184988i
$796$		0			0
$797$			36.9225i			1.30786i	0.756554	+	0.653932i	$0.226882\pi$
$797$			36.9225i			1.30786i	−0.756554	+	0.653932i	$0.773118\pi$
$798$		0			0
$799$	67.8478			2.40028
$800$

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:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.537080i q^{3} +(-2.07772 - 0.826491i) q^{5} -3.18676i q^{7} +2.71155 q^{9} +O(q^{10})\)	\(q-0.537080i q^{3} +(-2.07772 - 0.826491i) q^{5} -3.18676i q^{7} +2.71155 q^{9} -4.15544 q^{11} +2.07086i q^{13} +(-0.443892 + 1.11590i) q^{15} -5.79470i q^{17} -1.00000 q^{19} -1.71155 q^{21} +2.60794i q^{23} +(3.63383 + 3.43443i) q^{25} -3.06756i q^{27} -6.00000 q^{29} -2.59933 q^{31} +2.23180i q^{33} +(-2.63383 + 6.62119i) q^{35} -4.30266i q^{37} +1.11222 q^{39} -0.599328 q^{41} -3.18676i q^{43} +(-5.63383 - 2.24107i) q^{45} +11.7086i q^{47} -3.15544 q^{49} -3.11222 q^{51} +11.7503i q^{53} +(8.63383 + 3.43443i) q^{55} +0.537080i q^{57} -1.71155 q^{59} -8.75476 q^{61} -8.64104i q^{63} +(1.71155 - 4.30266i) q^{65} +4.76228i q^{67} +1.40067 q^{69} -13.7115 q^{71} -2.72714i q^{73} +(1.84456 - 1.95166i) q^{75} +13.2424i q^{77} -1.40067 q^{79} +6.48711 q^{81} +7.07154i q^{83} +(-4.78926 + 12.0398i) q^{85} +3.22248i q^{87} -16.5353 q^{89} +6.59933 q^{91} +1.39605i q^{93} +(2.07772 + 0.826491i) q^{95} -2.07086i q^{97} -11.2677 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{5} - 14 q^{9}+O(q^{10}) \) 6 * q - q^5 - 14 * q^9	\( 6 q - q^{5} - 14 q^{9} - 2 q^{11} - 10 q^{15} - 6 q^{19} + 20 q^{21} + 3 q^{25} - 36 q^{29} + 3 q^{35} - 8 q^{39} + 12 q^{41} - 15 q^{45} + 4 q^{49} - 4 q^{51} + 33 q^{55} + 20 q^{59} - 14 q^{61} - 20 q^{65} + 24 q^{69} - 52 q^{71} + 34 q^{75} - 24 q^{79} + 38 q^{81} + 13 q^{85} - 24 q^{89} + 24 q^{91} + q^{95} - 30 q^{99}+O(q^{100}) \) 6 * q - q^5 - 14 * q^9 - 2 * q^11 - 10 * q^15 - 6 * q^19 + 20 * q^21 + 3 * q^25 - 36 * q^29 + 3 * q^35 - 8 * q^39 + 12 * q^41 - 15 * q^45 + 4 * q^49 - 4 * q^51 + 33 * q^55 + 20 * q^59 - 14 * q^61 - 20 * q^65 + 24 * q^69 - 52 * q^71 + 34 * q^75 - 24 * q^79 + 38 * q^81 + 13 * q^85 - 24 * q^89 + 24 * q^91 + q^95 - 30 * q^99

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