LMFDB - Embedded newform 560.2.g.f.449.2

Newspace parameters

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.g (of order $2$, degree $1$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.5161984.1
Defining polynomial:	$x^{6} - 4 x^{3} + 25 x^{2} - 20 x + 8$
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.2
Root			$0.432320 - 0.432320i$ of defining polynomial
Character	$\chi$	$=$	560.449
Dual form			560.2.g.f.449.5

$q$-expansion

$f(q)$	$=$	$q-1.76156i q^{3} +(0.432320 + 2.19388i) q^{5} +1.00000i q^{7} -0.103084 q^{9} +O(q^{10})$	$q-1.76156i q^{3} +(0.432320 + 2.19388i) q^{5} +1.00000i q^{7} -0.103084 q^{9} +0.626198 q^{11} +5.49084i q^{13} +(3.86464 - 0.761557i) q^{15} -0.896916i q^{17} +6.38776 q^{19} +1.76156 q^{21} +3.72928i q^{23} +(-4.62620 + 1.89692i) q^{25} -5.10308i q^{27} +7.87859 q^{29} -7.52311 q^{31} -1.10308i q^{33} +(-2.19388 + 0.432320i) q^{35} -6.00000i q^{37} +9.67243 q^{39} +7.72928 q^{41} -1.72928i q^{43} +(-0.0445652 - 0.226153i) q^{45} +5.87859i q^{47} -1.00000 q^{49} -1.57997 q^{51} -6.77551i q^{53} +(0.270718 + 1.37380i) q^{55} -11.2524i q^{57} -0.593923 q^{59} +7.13536 q^{61} -0.103084i q^{63} +(-12.0462 + 2.37380i) q^{65} -5.79383i q^{67} +6.56934 q^{69} -5.52311 q^{71} -3.72928i q^{73} +(3.34153 + 8.14931i) q^{75} +0.626198i q^{77} -5.67243 q^{79} -9.29862 q^{81} +17.4340i q^{83} +(1.96772 - 0.387755i) q^{85} -13.8786i q^{87} -14.2986 q^{89} -5.49084 q^{91} +13.2524i q^{93} +(2.76156 + 14.0140i) q^{95} +10.1493i q^{97} -0.0645508 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6q - 8q^{9} + O(q^{10}) $	$ 6q - 8q^{9} - 14q^{11} + 18q^{15} + 8q^{19} - 2q^{21} - 10q^{25} - 6q^{29} - 20q^{31} + 2q^{35} - 10q^{39} + 36q^{41} - 28q^{45} - 6q^{49} - 42q^{51} + 12q^{55} + 12q^{59} + 48q^{61} - 22q^{65} - 36q^{69} - 8q^{71} + 40q^{75} + 34q^{79} + 30q^{81} + 14q^{85} - 10q^{91} + 4q^{95} + 4q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$-1$	$1$	$1$

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
$3$		−	1.76156i		−	1.01704i	−0.861052	−	0.508518i	$-0.830194\pi$
$3$		−	1.76156i		−	1.01704i	0.861052	−	0.508518i	$-0.169806\pi$
$4$		0			0
$5$	0.432320	+	2.19388i	0.193340	+	0.981132i
$5$	0.432320	+	2.19388i	0.193340	+	0.981132i
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		0			0
$9$	−0.103084			−0.0343612
$10$		0			0
$11$	0.626198			0.188806			0.0944029	−	0.995534i	$-0.469906\pi$
$11$	0.626198			0.188806			0.0944029	+	0.995534i	$0.469906\pi$
$12$		0			0
$13$			5.49084i			1.52288i	0.648233	+	0.761442i	$0.275508\pi$
$13$			5.49084i			1.52288i	−0.648233	+	0.761442i	$0.724492\pi$
$14$		0			0
$15$	3.86464	−	0.761557i	0.997846	−	0.196633i
$16$		0			0
$17$		−	0.896916i		−	0.217534i	−0.994067	−	0.108767i	$-0.965310\pi$
$17$		−	0.896916i		−	0.217534i	0.994067	−	0.108767i	$-0.0346903\pi$
$18$		0			0
$19$	6.38776			1.46545			0.732726	−	0.680524i	$-0.238248\pi$
$19$	6.38776			1.46545			0.732726	+	0.680524i	$0.238248\pi$
$20$		0			0
$21$	1.76156			0.384403
$22$		0			0
$23$			3.72928i			0.777609i	0.921320	+	0.388805i	$0.127112\pi$
$23$			3.72928i			0.777609i	−0.921320	+	0.388805i	$0.872888\pi$
$24$		0			0
$25$	−4.62620	+	1.89692i	−0.925240	+	0.379383i
$26$		0			0
$27$		−	5.10308i		−	0.982089i
$28$		0			0
$29$	7.87859			1.46302			0.731509	−	0.681832i	$-0.238816\pi$
$29$	7.87859			1.46302			0.731509	+	0.681832i	$0.238816\pi$
$30$		0			0
$31$	−7.52311			−1.35119			−0.675596	−	0.737272i	$-0.736113\pi$
$31$	−7.52311			−1.35119			−0.675596	+	0.737272i	$0.736113\pi$
$32$		0			0
$33$		−	1.10308i		−	0.192022i
$34$		0			0
$35$	−2.19388	+	0.432320i	−0.370833	+	0.0730755i
$36$		0			0
$37$		−	6.00000i		−	0.986394i	−0.869918	−	0.493197i	$-0.835828\pi$
$37$		−	6.00000i		−	0.986394i	0.869918	−	0.493197i	$-0.164172\pi$
$38$		0			0
$39$	9.67243			1.54883
$40$		0			0
$41$	7.72928			1.20711			0.603556	−	0.797321i	$-0.293750\pi$
$41$	7.72928			1.20711			0.603556	+	0.797321i	$0.293750\pi$
$42$		0			0
$43$		−	1.72928i		−	0.263713i	−0.991269	−	0.131856i	$-0.957906\pi$
$43$		−	1.72928i		−	0.263713i	0.991269	−	0.131856i	$-0.0420938\pi$
$44$		0			0
$45$	−0.0445652	−	0.226153i	−0.00664339	−	0.0337129i
$46$		0			0
$47$			5.87859i			0.857481i	0.903428	+	0.428741i	$0.141043\pi$
$47$			5.87859i			0.857481i	−0.903428	+	0.428741i	$0.858957\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−1.57997			−0.221240
$52$		0			0
$53$		−	6.77551i		−	0.930688i	−0.885130	−	0.465344i	$-0.845931\pi$
$53$		−	6.77551i		−	0.930688i	0.885130	−	0.465344i	$-0.154069\pi$
$54$		0			0
$55$	0.270718	+	1.37380i	0.0365036	+	0.185243i
$56$		0			0
$57$		−	11.2524i		−	1.49042i
$58$		0			0
$59$	−0.593923			−0.0773221			−0.0386611	−	0.999252i	$-0.512309\pi$
$59$	−0.593923			−0.0773221			−0.0386611	+	0.999252i	$0.512309\pi$
$60$		0			0
$61$	7.13536			0.913589			0.456795	−	0.889572i	$-0.348997\pi$
$61$	7.13536			0.913589			0.456795	+	0.889572i	$0.348997\pi$
$62$		0			0
$63$		−	0.103084i		−	0.0129873i
$64$		0			0
$65$	−12.0462	+	2.37380i	−1.49415	+	0.294434i
$66$		0			0
$67$		−	5.79383i		−	0.707829i	−0.935278	−	0.353915i	$-0.884850\pi$
$67$		−	5.79383i		−	0.707829i	0.935278	−	0.353915i	$-0.115150\pi$
$68$		0			0
$69$	6.56934			0.790856
$70$		0			0
$71$	−5.52311			−0.655473			−0.327737	−	0.944769i	$-0.606286\pi$
$71$	−5.52311			−0.655473			−0.327737	+	0.944769i	$0.606286\pi$
$72$		0			0
$73$		−	3.72928i		−	0.436479i	−0.975895	−	0.218240i	$-0.929969\pi$
$73$		−	3.72928i		−	0.436479i	0.975895	−	0.218240i	$-0.0700315\pi$
$74$		0			0
$75$	3.34153	+	8.14931i	0.385846	+	0.941002i
$76$		0			0
$77$			0.626198i			0.0713619i
$78$		0			0
$79$	−5.67243			−0.638198			−0.319099	−	0.947721i	$-0.603380\pi$
$79$	−5.67243			−0.638198			−0.319099	+	0.947721i	$0.603380\pi$
$80$		0			0
$81$	−9.29862			−1.03318
$82$		0			0
$83$			17.4340i			1.91363i	0.290700	+	0.956814i	$0.406112\pi$
$83$			17.4340i			1.91363i	−0.290700	+	0.956814i	$0.593888\pi$
$84$		0			0
$85$	1.96772	−	0.387755i	0.213430	−	0.0420580i
$86$		0			0
$87$		−	13.8786i		−	1.48794i
$88$		0			0
$89$	−14.2986			−1.51565			−0.757826	−	0.652457i	$-0.773738\pi$
$89$	−14.2986			−1.51565			−0.757826	+	0.652457i	$0.773738\pi$
$90$		0			0
$91$	−5.49084			−0.575596
$92$		0			0
$93$			13.2524i			1.37421i
$94$		0			0
$95$	2.76156	+	14.0140i	0.283330	+	1.43780i
$96$		0			0
$97$			10.1493i			1.03051i	0.857038	+	0.515253i	$0.172302\pi$
$97$			10.1493i			1.03051i	−0.857038	+	0.515253i	$0.827698\pi$
$98$		0			0
$99$	−0.0645508			−0.00648760
$100$		0			0
$101$	9.64015			0.959231			0.479615	−	0.877479i	$-0.340776\pi$
$101$	9.64015			0.959231			0.479615	+	0.877479i	$0.340776\pi$
$102$		0			0
$103$			0.626198i			0.0617011i	0.999524	+	0.0308506i	$0.00982160\pi$
$103$			0.626198i			0.0617011i	−0.999524	+	0.0308506i	$0.990178\pi$
$104$		0			0
$105$	0.761557	+	3.86464i	0.0743204	+	0.377150i
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$	−18.9248			−1.81267			−0.906335	−	0.422561i	$-0.861131\pi$
$109$	−18.9248			−1.81267			−0.906335	+	0.422561i	$0.861131\pi$
$110$		0			0
$111$	−10.5693			−1.00320
$112$		0			0
$113$		−	1.04623i		−	0.0984209i	−0.998788	−	0.0492105i	$-0.984329\pi$
$113$		−	1.04623i		−	0.0984209i	0.998788	−	0.0492105i	$-0.0156705\pi$
$114$		0			0
$115$	−8.18159	+	1.61224i	−0.762937	+	0.150343i
$116$		0			0
$117$		−	0.566016i		−	0.0523282i
$118$		0			0
$119$	0.896916			0.0822202
$120$		0			0
$121$	−10.6079			−0.964352
$122$		0			0
$123$		−	13.6156i		−	1.22767i
$124$		0			0
$125$	−6.16160	−	9.32924i	−0.551110	−	0.834432i
$126$		0			0
$127$		−	21.2803i		−	1.88832i	−0.329485	−	0.944161i	$-0.606875\pi$
$127$		−	21.2803i		−	1.88832i	0.329485	−	0.944161i	$-0.393125\pi$
$128$		0			0
$129$	−3.04623			−0.268205
$130$		0			0
$131$	9.91087			0.865917			0.432958	−	0.901414i	$-0.357470\pi$
$131$	9.91087			0.865917			0.432958	+	0.901414i	$0.357470\pi$
$132$		0			0
$133$			6.38776i			0.553889i
$134$		0			0
$135$	11.1955	−	2.20617i	0.963559	−	0.189877i
$136$		0			0
$137$		−	3.45856i		−	0.295485i	−0.989026	−	0.147743i	$-0.952799\pi$
$137$		−	3.45856i		−	0.295485i	0.989026	−	0.147743i	$-0.0472007\pi$
$138$		0			0
$139$	−20.4157			−1.73163			−0.865817	−	0.500361i	$-0.833201\pi$
$139$	−20.4157			−1.73163			−0.865817	+	0.500361i	$0.833201\pi$
$140$		0			0
$141$	10.3555			0.872089
$142$		0			0
$143$			3.43835i			0.287530i
$144$		0			0
$145$	3.40608	+	17.2847i	0.282859	+	1.43541i
$146$		0			0
$147$			1.76156i			0.145291i
$148$		0			0
$149$	17.0462			1.39648			0.698241	−	0.715863i	$-0.253967\pi$
$149$	17.0462			1.39648			0.698241	+	0.715863i	$0.253967\pi$
$150$		0			0
$151$	−2.89692			−0.235748			−0.117874	−	0.993029i	$-0.537608\pi$
$151$	−2.89692			−0.235748			−0.117874	+	0.993029i	$0.537608\pi$
$152$		0			0
$153$			0.0924575i			0.00747474i
$154$		0			0
$155$	−3.25240	−	16.5048i	−0.261239	−	1.32570i
$156$		0			0
$157$		−	10.1170i		−	0.807427i	−0.914885	−	0.403714i	$-0.867719\pi$
$157$		−	10.1170i		−	0.807427i	0.914885	−	0.403714i	$-0.132281\pi$
$158$		0			0
$159$	−11.9354			−0.946543
$160$		0			0
$161$	−3.72928			−0.293909
$162$		0			0
$163$		−	0.476886i		−	0.0373526i	−0.999826	−	0.0186763i	$-0.994055\pi$
$163$		−	0.476886i		−	0.0373526i	0.999826	−	0.0186763i	$-0.00594519\pi$
$164$		0			0
$165$	2.42003	−	0.476886i	0.188399	−	0.0371255i
$166$		0			0
$167$		−	13.1676i		−	1.01894i	−0.860488	−	0.509471i	$-0.829841\pi$
$167$		−	13.1676i		−	1.01894i	0.860488	−	0.509471i	$-0.170159\pi$
$168$		0			0
$169$	−17.1493			−1.31918
$170$		0			0
$171$	−0.658473			−0.0503547
$172$		0			0
$173$			13.9677i			1.06195i	0.847389	+	0.530973i	$0.178174\pi$
$173$			13.9677i			1.06195i	−0.847389	+	0.530973i	$0.821826\pi$
$174$		0			0
$175$	−1.89692	−	4.62620i	−0.143393	−	0.349708i
$176$		0			0
$177$			1.04623i			0.0786394i
$178$		0			0
$179$	7.45856			0.557479			0.278740	−	0.960367i	$-0.410083\pi$
$179$	7.45856			0.557479			0.278740	+	0.960367i	$0.410083\pi$
$180$		0			0
$181$	−14.1170			−1.04931			−0.524656	−	0.851315i	$-0.675806\pi$
$181$	−14.1170			−1.04931			−0.524656	+	0.851315i	$0.675806\pi$
$182$		0			0
$183$		−	12.5693i		−	0.929153i
$184$		0			0
$185$	13.1633	−	2.59392i	0.967783	−	0.190709i
$186$		0			0
$187$		−	0.561647i		−	0.0410717i
$188$		0			0
$189$	5.10308			0.371195
$190$		0			0
$191$	8.42003			0.609252			0.304626	−	0.952472i	$-0.401469\pi$
$191$	8.42003			0.609252			0.304626	+	0.952472i	$0.401469\pi$
$192$		0			0
$193$		−	22.2986i		−	1.60509i	−0.596591	−	0.802545i	$-0.703479\pi$
$193$		−	22.2986i		−	1.60509i	0.596591	−	0.802545i	$-0.296521\pi$
$194$		0			0
$195$	4.18159	+	21.2201i	0.299450	+	1.51960i
$196$		0			0
$197$		−	26.3632i		−	1.87830i	−0.343509	−	0.939149i	$-0.611616\pi$
$197$		−	26.3632i		−	1.87830i	0.343509	−	0.939149i	$-0.388384\pi$
$198$		0			0
$199$	22.4402			1.59075			0.795373	−	0.606120i	$-0.207275\pi$
$199$	22.4402			1.59075			0.795373	+	0.606120i	$0.207275\pi$
$200$		0			0
$201$	−10.2062			−0.719888
$202$		0			0
$203$			7.87859i			0.552969i
$204$		0			0
$205$	3.34153	+	16.9571i	0.233382	+	1.18434i
$206$		0			0
$207$		−	0.384428i		−	0.0267196i
$208$		0			0
$209$	4.00000			0.276686
$210$		0			0
$211$	15.1955			1.04610			0.523052	−	0.852301i	$-0.324793\pi$
$211$	15.1955			1.04610			0.523052	+	0.852301i	$0.324793\pi$
$212$		0			0
$213$			9.72928i			0.666639i
$214$		0			0
$215$	3.79383	−	0.747604i	0.258737	−	0.0509862i
$216$		0			0
$217$		−	7.52311i		−	0.510702i
$218$		0			0
$219$	−6.56934			−0.443915
$220$		0			0
$221$	4.92482			0.331279
$222$		0			0
$223$			6.89692i			0.461852i	0.972971	+	0.230926i	$0.0741755\pi$
$223$			6.89692i			0.461852i	−0.972971	+	0.230926i	$0.925825\pi$
$224$		0			0
$225$	0.476886	−	0.195541i	0.0317924	−	0.0130361i
$226$		0			0
$227$		−	2.77988i		−	0.184507i	−0.995736	−	0.0922535i	$-0.970593\pi$
$227$		−	2.77988i		−	0.184507i	0.995736	−	0.0922535i	$-0.0294070\pi$
$228$		0			0
$229$	−18.6585			−1.23299			−0.616493	−	0.787360i	$-0.711447\pi$
$229$	−18.6585			−1.23299			−0.616493	+	0.787360i	$0.711447\pi$
$230$		0			0
$231$	1.10308			0.0725776
$232$		0			0
$233$		−	11.0462i		−	0.723663i	−0.932244	−	0.361831i	$-0.882152\pi$
$233$		−	11.0462i		−	0.723663i	0.932244	−	0.361831i	$-0.117848\pi$
$234$		0			0
$235$	−12.8969	+	2.54144i	−0.841302	+	0.165785i
$236$		0			0
$237$			9.99230i			0.649070i
$238$		0			0
$239$	−20.1493			−1.30335			−0.651675	−	0.758498i	$-0.725934\pi$
$239$	−20.1493			−1.30335			−0.651675	+	0.758498i	$0.725934\pi$
$240$		0			0
$241$	3.72928			0.240224			0.120112	−	0.992760i	$-0.461675\pi$
$241$	3.72928			0.240224			0.120112	+	0.992760i	$0.461675\pi$
$242$		0			0
$243$			1.07081i			0.0686924i
$244$		0			0
$245$	−0.432320	−	2.19388i	−0.0276199	−	0.140162i
$246$		0			0
$247$			35.0741i			2.23171i
$248$		0			0
$249$	30.7110			1.94623
$250$		0			0
$251$	21.4985			1.35698			0.678488	−	0.734612i	$-0.262636\pi$
$251$	21.4985			1.35698			0.678488	+	0.734612i	$0.262636\pi$
$252$		0			0
$253$			2.33527i			0.146817i
$254$		0			0
$255$	−0.683053	−	3.46626i	−0.0427744	−	0.217066i
$256$		0			0
$257$		−	4.27072i		−	0.266400i	−0.991089	−	0.133200i	$-0.957475\pi$
$257$		−	4.27072i		−	0.266400i	0.991089	−	0.133200i	$-0.0425253\pi$
$258$		0			0
$259$	6.00000			0.372822
$260$		0			0
$261$	−0.812155			−0.0502711
$262$		0			0
$263$			11.4586i			0.706565i	0.935517	+	0.353283i	$0.114935\pi$
$263$			11.4586i			0.706565i	−0.935517	+	0.353283i	$0.885065\pi$
$264$		0			0
$265$	14.8646	−	2.92919i	0.913128	−	0.179939i
$266$		0			0
$267$			25.1878i			1.54147i
$268$		0			0
$269$	7.07081			0.431115			0.215557	−	0.976491i	$-0.430843\pi$
$269$	7.07081			0.431115			0.215557	+	0.976491i	$0.430843\pi$
$270$		0			0
$271$	−17.0096			−1.03326			−0.516629	−	0.856209i	$-0.672813\pi$
$271$	−17.0096			−1.03326			−0.516629	+	0.856209i	$0.672813\pi$
$272$		0			0
$273$			9.67243i			0.585402i
$274$		0			0
$275$	−2.89692	+	1.18785i	−0.174691	+	0.0716298i
$276$		0			0
$277$			18.7755i			1.12811i	0.825737	+	0.564056i	$0.190760\pi$
$277$			18.7755i			1.12811i	−0.825737	+	0.564056i	$0.809240\pi$
$278$		0			0
$279$	0.775511			0.0464286
$280$		0			0
$281$	−4.59829			−0.274311			−0.137156	−	0.990550i	$-0.543796\pi$
$281$	−4.59829			−0.274311			−0.137156	+	0.990550i	$0.543796\pi$
$282$		0			0
$283$			13.5833i			0.807443i	0.914882	+	0.403722i	$0.132284\pi$
$283$			13.5833i			0.807443i	−0.914882	+	0.403722i	$0.867716\pi$
$284$		0			0
$285$	24.6864	−	4.86464i	1.46229	−	0.288156i
$286$		0			0
$287$			7.72928i			0.456245i
$288$		0			0
$289$	16.1955			0.952679
$290$		0			0
$291$	17.8786			1.04806
$292$		0			0
$293$			11.8261i			0.690889i	0.938439	+	0.345444i	$0.112272\pi$
$293$			11.8261i			0.690889i	−0.938439	+	0.345444i	$0.887728\pi$
$294$		0			0
$295$	−0.256765	−	1.30299i	−0.0149494	−	0.0758632i
$296$		0			0
$297$		−	3.19554i		−	0.185424i
$298$		0			0
$299$	−20.4769			−1.18421
$300$		0			0
$301$	1.72928			0.0996741
$302$		0			0
$303$		−	16.9817i		−	0.975572i
$304$		0			0
$305$	3.08476	+	15.6541i	0.176633	+	0.896351i
$306$		0			0
$307$		−	20.9860i		−	1.19774i	−0.800847	−	0.598868i	$-0.795617\pi$
$307$		−	20.9860i		−	1.19774i	0.800847	−	0.598868i	$-0.204383\pi$
$308$		0			0
$309$	1.10308			0.0627522
$310$		0			0
$311$	22.5048			1.27613			0.638065	−	0.769983i	$-0.279735\pi$
$311$	22.5048			1.27613			0.638065	+	0.769983i	$0.279735\pi$
$312$		0			0
$313$		−	12.4846i		−	0.705670i	−0.935686	−	0.352835i	$-0.885218\pi$
$313$		−	12.4846i		−	0.705670i	0.935686	−	0.352835i	$-0.114782\pi$
$314$		0			0
$315$	0.226153	−	0.0445652i	0.0127423	−	0.00251096i
$316$		0			0
$317$		−	25.5231i		−	1.43352i	−0.697319	−	0.716760i	$-0.745624\pi$
$317$		−	25.5231i		−	1.43352i	0.697319	−	0.716760i	$-0.254376\pi$
$318$		0			0
$319$	4.93356			0.276226
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	5.72928i		−	0.318786i
$324$		0			0
$325$	−10.4157	−	25.4017i	−0.577757	−	1.40903i
$326$		0			0
$327$			33.3372i			1.84355i
$328$		0			0
$329$	−5.87859			−0.324097
$330$		0			0
$331$	2.68305			0.147474			0.0737370	−	0.997278i	$-0.476507\pi$
$331$	2.68305			0.147474			0.0737370	+	0.997278i	$0.476507\pi$
$332$		0			0
$333$			0.618502i			0.0338937i
$334$		0			0
$335$	12.7110	−	2.50479i	0.694474	−	0.136851i
$336$		0			0
$337$		−	12.5048i		−	0.681179i	−0.940212	−	0.340590i	$-0.889373\pi$
$337$		−	12.5048i		−	0.681179i	0.940212	−	0.340590i	$-0.110627\pi$
$338$		0			0
$339$	−1.84299			−0.100098
$340$		0			0
$341$	−4.71096			−0.255113
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$	2.84006	+	14.4123i	0.152904	+	0.775934i
$346$		0			0
$347$		−	28.9450i		−	1.55385i	−0.629593	−	0.776925i	$-0.716778\pi$
$347$		−	28.9450i		−	1.55385i	0.629593	−	0.776925i	$-0.283222\pi$
$348$		0			0
$349$	−32.1449			−1.72068			−0.860340	−	0.509721i	$-0.829749\pi$
$349$	−32.1449			−1.72068			−0.860340	+	0.509721i	$0.829749\pi$
$350$		0			0
$351$	28.0202			1.49561
$352$		0			0
$353$			8.17722i			0.435229i	0.976035	+	0.217615i	$0.0698276\pi$
$353$			8.17722i			0.435229i	−0.976035	+	0.217615i	$0.930172\pi$
$354$		0			0
$355$	−2.38776	−	12.1170i	−0.126729	−	0.643106i
$356$		0			0
$357$		−	1.57997i		−	0.0836208i
$358$		0			0
$359$	18.5048			0.976646			0.488323	−	0.872663i	$-0.337609\pi$
$359$	18.5048			0.976646			0.488323	+	0.872663i	$0.337609\pi$
$360$		0			0
$361$	21.8034			1.14755
$362$		0			0
$363$			18.6864i			0.980781i
$364$		0			0
$365$	8.18159	−	1.61224i	0.428244	−	0.0843887i
$366$		0			0
$367$		−	27.4942i		−	1.43518i	−0.696464	−	0.717592i	$-0.745244\pi$
$367$		−	27.4942i		−	1.43518i	0.696464	−	0.717592i	$-0.254756\pi$
$368$		0			0
$369$	−0.796763			−0.0414778
$370$		0			0
$371$	6.77551			0.351767
$372$		0			0
$373$			6.06455i			0.314011i	0.987598	+	0.157005i	$0.0501840\pi$
$373$			6.06455i			0.314011i	−0.987598	+	0.157005i	$0.949816\pi$
$374$		0			0
$375$	−16.4340	+	10.8540i	−0.848647	+	0.560499i
$376$		0			0
$377$			43.2601i			2.22801i
$378$		0			0
$379$	−5.72928			−0.294293			−0.147147	−	0.989115i	$-0.547009\pi$
$379$	−5.72928			−0.294293			−0.147147	+	0.989115i	$0.547009\pi$
$380$		0			0
$381$	−37.4865			−1.92049
$382$		0			0
$383$			1.72928i			0.0883622i	0.999024	+	0.0441811i	$0.0140679\pi$
$383$			1.72928i			0.0883622i	−0.999024	+	0.0441811i	$0.985932\pi$
$384$		0			0
$385$	−1.37380	+	0.270718i	−0.0700154	+	0.0137971i
$386$		0			0
$387$			0.178261i			0.00906150i
$388$		0			0
$389$	36.7187			1.86171			0.930855	−	0.365389i	$-0.119064\pi$
$389$	36.7187			1.86171			0.930855	+	0.365389i	$0.119064\pi$
$390$		0			0
$391$	3.34485			0.169157
$392$		0			0
$393$		−	17.4586i		−	0.880668i
$394$		0			0
$395$	−2.45231	−	12.4446i	−0.123389	−	0.626156i
$396$		0			0
$397$			2.03228i			0.101997i	0.998699	+	0.0509985i	$0.0162404\pi$
$397$			2.03228i			0.101997i	−0.998699	+	0.0509985i	$0.983760\pi$
$398$		0			0
$399$	11.2524			0.563324
$400$		0			0
$401$	−1.64452			−0.0821234			−0.0410617	−	0.999157i	$-0.513074\pi$
$401$	−1.64452			−0.0821234			−0.0410617	+	0.999157i	$0.513074\pi$
$402$		0			0
$403$		−	41.3082i		−	2.05771i
$404$		0			0
$405$	−4.01999	−	20.4000i	−0.199755	−	1.01369i
$406$		0			0
$407$		−	3.75719i		−	0.186237i
$408$		0			0
$409$	4.98168			0.246328			0.123164	−	0.992386i	$-0.460696\pi$
$409$	4.98168			0.246328			0.123164	+	0.992386i	$0.460696\pi$
$410$		0			0
$411$	−6.09246			−0.300519
$412$		0			0
$413$		−	0.593923i		−	0.0292250i
$414$		0			0
$415$	−38.2480	+	7.53707i	−1.87752	+	0.369980i
$416$		0			0
$417$			35.9634i			1.76113i
$418$		0			0
$419$	22.9205			1.11974			0.559869	−	0.828581i	$-0.310852\pi$
$419$	22.9205			1.11974			0.559869	+	0.828581i	$0.310852\pi$
$420$		0			0
$421$	−20.9527			−1.02117			−0.510587	−	0.859826i	$-0.670572\pi$
$421$	−20.9527			−1.02117			−0.510587	+	0.859826i	$0.670572\pi$
$422$		0			0
$423$		−	0.605987i		−	0.0294641i
$424$		0			0
$425$	1.70138	+	4.14931i	0.0825288	+	0.201271i
$426$		0			0
$427$			7.13536i			0.345304i
$428$		0			0
$429$	6.05685			0.292428
$430$		0			0
$431$	−33.1589			−1.59721			−0.798604	−	0.601857i	$-0.794428\pi$
$431$	−33.1589			−1.59721			−0.798604	+	0.601857i	$0.794428\pi$
$432$		0			0
$433$		−	18.5414i		−	0.891045i	−0.895271	−	0.445522i	$-0.853018\pi$
$433$		−	18.5414i		−	0.891045i	0.895271	−	0.445522i	$-0.146982\pi$
$434$		0			0
$435$	30.4479	−	6.00000i	1.45987	−	0.287678i
$436$		0			0
$437$			23.8217i			1.13955i
$438$		0			0
$439$	−20.8401			−0.994642			−0.497321	−	0.867567i	$-0.665683\pi$
$439$	−20.8401			−0.994642			−0.497321	+	0.867567i	$0.665683\pi$
$440$		0			0
$441$	0.103084			0.00490875
$442$		0			0
$443$		−	17.5510i		−	0.833874i	−0.908935	−	0.416937i	$-0.863104\pi$
$443$		−	17.5510i		−	0.833874i	0.908935	−	0.416937i	$-0.136896\pi$
$444$		0			0
$445$	−6.18159	−	31.3694i	−0.293035	−	1.48705i
$446$		0			0
$447$		−	30.0279i		−	1.42027i
$448$		0			0
$449$	13.1955			0.622736			0.311368	−	0.950289i	$-0.399213\pi$
$449$	13.1955			0.622736			0.311368	+	0.950289i	$0.399213\pi$
$450$		0			0
$451$	4.84006			0.227910
$452$		0			0
$453$			5.10308i			0.239764i
$454$		0			0
$455$	−2.37380	−	12.0462i	−0.111286	−	0.564736i
$456$		0			0
$457$			29.1020i			1.36134i	0.732592	+	0.680668i	$0.238310\pi$
$457$			29.1020i			1.36134i	−0.732592	+	0.680668i	$0.761690\pi$
$458$		0			0
$459$	−4.57704			−0.213638
$460$		0			0
$461$	−18.8280			−0.876907			−0.438454	−	0.898754i	$-0.644474\pi$
$461$	−18.8280			−0.876907			−0.438454	+	0.898754i	$0.644474\pi$
$462$		0			0
$463$			14.0925i			0.654932i	0.944863	+	0.327466i	$0.106195\pi$
$463$			14.0925i			0.654932i	−0.944863	+	0.327466i	$0.893805\pi$
$464$		0			0
$465$	−29.0741	+	5.72928i	−1.34828	+	0.265689i
$466$		0			0
$467$		−	12.2663i		−	0.567619i	−0.958881	−	0.283809i	$-0.908402\pi$
$467$		−	12.2663i		−	0.567619i	0.958881	−	0.283809i	$-0.0915983\pi$
$468$		0			0
$469$	5.79383			0.267534
$470$		0			0
$471$	−17.8217			−0.821182
$472$		0			0
$473$		−	1.08287i		−	0.0497905i
$474$		0			0
$475$	−29.5510	+	12.1170i	−1.35589	+	0.555968i
$476$		0			0
$477$			0.698445i			0.0319796i
$478$		0			0
$479$	−14.1570			−0.646850			−0.323425	−	0.946254i	$-0.604834\pi$
$479$	−14.1570			−0.646850			−0.323425	+	0.946254i	$0.604834\pi$
$480$		0			0
$481$	32.9450			1.50216
$482$		0			0
$483$			6.56934i			0.298915i
$484$		0			0
$485$	−22.2663	+	4.38776i	−1.01106	+	0.199238i
$486$		0			0
$487$			30.2341i			1.37004i	0.728526	+	0.685018i	$0.240206\pi$
$487$			30.2341i			1.37004i	−0.728526	+	0.685018i	$0.759794\pi$
$488$		0			0
$489$	−0.840061			−0.0379889
$490$		0			0
$491$	−39.9065			−1.80096			−0.900478	−	0.434902i	$-0.856783\pi$
$491$	−39.9065			−1.80096			−0.900478	+	0.434902i	$0.856783\pi$
$492$		0			0
$493$		−	7.06644i		−	0.318256i
$494$		0			0
$495$	−0.0279066	−	0.141617i	−0.00125431	−	0.00636519i
$496$		0			0
$497$		−	5.52311i		−	0.247746i
$498$		0			0
$499$	27.3246			1.22322			0.611610	−	0.791160i	$-0.290522\pi$
$499$	27.3246			1.22322			0.611610	+	0.791160i	$0.290522\pi$
$500$		0			0
$501$	−23.1955			−1.03630
$502$		0			0
$503$		−	1.40171i		−	0.0624991i	−0.999512	−	0.0312495i	$-0.990051\pi$
$503$		−	1.40171i		−	0.0624991i	0.999512	−	0.0312495i	$-0.00994866\pi$
$504$		0			0
$505$	4.16763	+	21.1493i	0.185457	+	0.941132i
$506$		0			0
$507$			30.2095i			1.34165i
$508$		0			0
$509$	−18.6585			−0.827022			−0.413511	−	0.910499i	$-0.635698\pi$
$509$	−18.6585			−0.827022			−0.413511	+	0.910499i	$0.635698\pi$
$510$		0			0
$511$	3.72928			0.164974
$512$		0			0
$513$		−	32.5972i		−	1.43920i
$514$		0			0
$515$	−1.37380	+	0.270718i	−0.0605369	+	0.0119293i
$516$		0			0
$517$			3.68116i			0.161897i
$518$		0			0
$519$	24.6049			1.08004
$520$		0			0
$521$	−4.02791			−0.176466			−0.0882329	−	0.996100i	$-0.528122\pi$
$521$	−4.02791			−0.176466			−0.0882329	+	0.996100i	$0.528122\pi$
$522$		0			0
$523$		−	38.4436i		−	1.68102i	−0.541796	−	0.840510i	$-0.682256\pi$
$523$		−	38.4436i		−	1.68102i	0.541796	−	0.840510i	$-0.317744\pi$
$524$		0			0
$525$	−8.14931	+	3.34153i	−0.355665	+	0.145836i
$526$		0			0
$527$			6.74760i			0.293930i
$528$		0			0
$529$	9.09246			0.395324
$530$		0			0
$531$	0.0612237			0.00265688
$532$		0			0
$533$			42.4402i			1.83829i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		−	13.1387i		−	0.566976i
$538$		0			0
$539$	−0.626198			−0.0269723
$540$		0			0
$541$	12.4846			0.536754			0.268377	−	0.963314i	$-0.413513\pi$
$541$	12.4846			0.536754			0.268377	+	0.963314i	$0.413513\pi$
$542$		0			0
$543$			24.8680i			1.06719i
$544$		0			0
$545$	−8.18159	−	41.5187i	−0.350461	−	1.77847i
$546$		0			0
$547$			37.7851i			1.61557i	0.589474	+	0.807787i	$0.299335\pi$
$547$			37.7851i			1.61557i	−0.589474	+	0.807787i	$0.700665\pi$
$548$		0			0
$549$	−0.735539			−0.0313921
$550$		0			0
$551$	50.3265			2.14398
$552$		0			0
$553$		−	5.67243i		−	0.241216i
$554$		0			0
$555$	−4.56934	−	23.1878i	−0.193958	−	0.984269i
$556$		0			0
$557$		−	1.93545i		−	0.0820076i	−0.999159	−	0.0410038i	$-0.986944\pi$
$557$		−	1.93545i		−	0.0820076i	0.999159	−	0.0410038i	$-0.0130556\pi$
$558$		0			0
$559$	9.49521			0.401604
$560$		0			0
$561$	−0.989374			−0.0417714
$562$		0			0
$563$			29.8463i			1.25787i	0.777457	+	0.628936i	$0.216509\pi$
$563$			29.8463i			1.25787i	−0.777457	+	0.628936i	$0.783491\pi$
$564$		0			0
$565$	2.29530	−	0.452306i	0.0965639	−	0.0190287i
$566$		0			0
$567$		−	9.29862i		−	0.390506i
$568$		0			0
$569$	−15.3449			−0.643290			−0.321645	−	0.946860i	$-0.604236\pi$
$569$	−15.3449			−0.643290			−0.321645	+	0.946860i	$0.604236\pi$
$570$		0			0
$571$	−35.8217			−1.49909			−0.749547	−	0.661952i	$-0.769728\pi$
$571$	−35.8217			−1.49909			−0.749547	+	0.661952i	$0.769728\pi$
$572$		0			0
$573$		−	14.8324i		−	0.619631i
$574$		0			0
$575$	−7.07414	−	17.2524i	−0.295012	−	0.719475i
$576$		0			0
$577$		−	2.92482i		−	0.121762i	−0.998145	−	0.0608810i	$-0.980609\pi$
$577$		−	2.92482i		−	0.121762i	0.998145	−	0.0608810i	$-0.0193910\pi$
$578$		0			0
$579$	−39.2803			−1.63243
$580$		0			0
$581$	−17.4340			−0.723284
$582$		0			0
$583$		−	4.24281i		−	0.175719i
$584$		0			0
$585$	1.24177	−	0.244700i	0.0513409	−	0.0101171i
$586$		0			0
$587$			19.5756i			0.807972i	0.914765	+	0.403986i	$0.132375\pi$
$587$			19.5756i			0.807972i	−0.914765	+	0.403986i	$0.867625\pi$
$588$		0			0
$589$	−48.0558			−1.98011
$590$		0			0
$591$	−46.4402			−1.91030
$592$		0			0
$593$			8.00770i			0.328837i	0.986391	+	0.164418i	$0.0525747\pi$
$593$			8.00770i			0.328837i	−0.986391	+	0.164418i	$0.947425\pi$
$594$		0			0
$595$	0.387755	+	1.96772i	0.0158964	+	0.0806688i
$596$		0			0
$597$		−	39.5298i		−	1.61785i
$598$		0			0
$599$	−29.3005			−1.19719			−0.598593	−	0.801053i	$-0.704273\pi$
$599$	−29.3005			−1.19719			−0.598593	+	0.801053i	$0.704273\pi$
$600$		0			0
$601$	21.3449			0.870675			0.435337	−	0.900267i	$-0.356629\pi$
$601$	21.3449			0.870675			0.435337	+	0.900267i	$0.356629\pi$
$602$		0			0
$603$			0.597250i			0.0243219i
$604$		0			0
$605$	−4.58600	−	23.2724i	−0.186447	−	0.946157i
$606$		0			0
$607$			9.53081i			0.386844i	0.981116	+	0.193422i	$0.0619586\pi$
$607$			9.53081i			0.386844i	−0.981116	+	0.193422i	$0.938041\pi$
$608$		0			0
$609$	13.8786			0.562389
$610$		0			0
$611$	−32.2784			−1.30584
$612$		0			0
$613$		−	9.75719i		−	0.394089i	−0.980395	−	0.197045i	$-0.936866\pi$
$613$		−	9.75719i		−	0.394089i	0.980395	−	0.197045i	$-0.0631344\pi$
$614$		0			0
$615$	29.8709	−	5.88629i	1.20451	−	0.237358i
$616$		0			0
$617$			37.9267i			1.52687i	0.645884	+	0.763436i	$0.276489\pi$
$617$			37.9267i			1.52687i	−0.645884	+	0.763436i	$0.723511\pi$
$618$		0			0
$619$	41.9109			1.68454			0.842270	−	0.539056i	$-0.181219\pi$
$619$	41.9109			1.68454			0.842270	+	0.539056i	$0.181219\pi$
$620$		0			0
$621$	19.0308			0.763681
$622$		0			0
$623$		−	14.2986i		−	0.572862i
$624$		0			0
$625$	17.8034	−	17.5510i	0.712137	−	0.702041i
$626$		0			0
$627$		−	7.04623i		−	0.281399i
$628$		0			0
$629$	−5.38150			−0.214574
$630$		0			0
$631$	8.42003			0.335196			0.167598	−	0.985855i	$-0.446399\pi$
$631$	8.42003			0.335196			0.167598	+	0.985855i	$0.446399\pi$
$632$		0			0
$633$		−	26.7678i		−	1.06393i
$634$		0			0
$635$	46.6864	−	9.19991i	1.85269	−	0.365087i
$636$		0			0
$637$		−	5.49084i		−	0.217555i
$638$		0			0
$639$	0.569343			0.0225229
$640$		0			0
$641$	−2.07707			−0.0820392			−0.0410196	−	0.999158i	$-0.513061\pi$
$641$	−2.07707			−0.0820392			−0.0410196	+	0.999158i	$0.513061\pi$
$642$		0			0
$643$			27.2480i			1.07456i	0.843405	+	0.537279i	$0.180548\pi$
$643$			27.2480i			1.07456i	−0.843405	+	0.537279i	$0.819452\pi$
$644$		0			0
$645$	−1.31695	−	6.68305i	−0.0518547	−	0.263145i
$646$		0			0
$647$			12.3632i			0.486047i	0.970020	+	0.243023i	$0.0781391\pi$
$647$			12.3632i			0.486047i	−0.970020	+	0.243023i	$0.921861\pi$
$648$		0			0
$649$	−0.371913			−0.0145989
$650$		0			0
$651$	−13.2524			−0.519402
$652$		0			0
$653$			37.3449i			1.46142i	0.682690	+	0.730709i	$0.260810\pi$
$653$			37.3449i			1.46142i	−0.682690	+	0.730709i	$0.739190\pi$
$654$		0			0
$655$	4.28467	+	21.7432i	0.167416	+	0.849578i
$656$		0			0
$657$			0.384428i			0.0149980i
$658$		0			0
$659$	−14.1772			−0.552266			−0.276133	−	0.961119i	$-0.589053\pi$
$659$	−14.1772			−0.552266			−0.276133	+	0.961119i	$0.589053\pi$
$660$		0			0
$661$	−1.76925			−0.0688160			−0.0344080	−	0.999408i	$-0.510955\pi$
$661$	−1.76925			−0.0688160			−0.0344080	+	0.999408i	$0.510955\pi$
$662$		0			0
$663$		−	8.67536i		−	0.336923i
$664$		0			0
$665$	−14.0140	+	2.76156i	−0.543438	+	0.107089i
$666$		0			0
$667$			29.3815i			1.13766i
$668$		0			0
$669$	12.1493			0.469720
$670$		0			0
$671$	4.46815			0.172491
$672$		0			0
$673$			4.05581i			0.156340i	0.996940	+	0.0781701i	$0.0249077\pi$
$673$			4.05581i			0.156340i	−0.996940	+	0.0781701i	$0.975092\pi$
$674$		0			0
$675$	9.68012	+	23.6079i	0.372588	+	0.908668i
$676$		0			0
$677$			9.37713i			0.360392i	0.983631	+	0.180196i	$0.0576733\pi$
$677$			9.37713i			0.360392i	−0.983631	+	0.180196i	$0.942327\pi$
$678$		0			0
$679$	−10.1493			−0.389495
$680$		0			0
$681$	−4.89692			−0.187650
$682$		0			0
$683$			5.49521i			0.210268i	0.994458	+	0.105134i	$0.0335272\pi$
$683$			5.49521i			0.210268i	−0.994458	+	0.105134i	$0.966473\pi$
$684$		0			0
$685$	7.58767	−	1.49521i	0.289910	−	0.0571290i
$686$		0			0
$687$			32.8680i			1.25399i
$688$		0			0
$689$	37.2032			1.41733
$690$		0			0
$691$	3.03416			0.115425			0.0577125	−	0.998333i	$-0.481619\pi$
$691$	3.03416			0.115425			0.0577125	+	0.998333i	$0.481619\pi$
$692$		0			0
$693$		−	0.0645508i		−	0.00245208i
$694$		0			0
$695$	−8.82611	−	44.7895i	−0.334793	−	1.69896i
$696$		0			0
$697$		−	6.93252i		−	0.262588i
$698$		0			0
$699$	−19.4586			−0.735990
$700$		0			0
$701$	35.2234			1.33037			0.665186	−	0.746678i	$-0.268352\pi$
$701$	35.2234			1.33037			0.665186	+	0.746678i	$0.268352\pi$
$702$		0			0
$703$		−	38.3265i		−	1.44551i
$704$		0			0
$705$	4.47689	+	22.7187i	0.168609	+	0.855634i
$706$		0			0
$707$			9.64015i			0.362555i
$708$		0			0
$709$	−28.7187			−1.07855			−0.539276	−	0.842129i	$-0.681302\pi$
$709$	−28.7187			−1.07855			−0.539276	+	0.842129i	$0.681302\pi$
$710$		0			0
$711$	0.584735			0.0219293
$712$		0			0
$713$		−	28.0558i		−	1.05070i
$714$		0			0
$715$	−7.54333	+	1.48647i	−0.282104	+	0.0555908i
$716$		0			0
$717$			35.4942i			1.32555i
$718$		0			0
$719$	−8.60599			−0.320949			−0.160475	−	0.987040i	$-0.551302\pi$
$719$	−8.60599			−0.320949			−0.160475	+	0.987040i	$0.551302\pi$
$720$		0			0
$721$	−0.626198			−0.0233208
$722$		0			0
$723$		−	6.56934i		−	0.244316i
$724$		0			0
$725$	−36.4479	+	14.9450i	−1.35364	+	0.555045i
$726$		0			0
$727$		−	15.2803i		−	0.566715i	−0.959014	−	0.283358i	$-0.908552\pi$
$727$		−	15.2803i		−	0.566715i	0.959014	−	0.283358i	$-0.0914483\pi$
$728$		0			0
$729$	−26.0096			−0.963318
$730$		0			0
$731$	−1.55102			−0.0573666
$732$		0			0
$733$		−	46.0235i		−	1.69992i	−0.526849	−	0.849959i	$-0.676627\pi$
$733$		−	46.0235i		−	1.69992i	0.526849	−	0.849959i	$-0.323373\pi$
$734$		0			0
$735$	−3.86464	+	0.761557i	−0.142549	+	0.0280905i
$736$		0			0
$737$		−	3.62809i		−	0.133642i
$738$		0			0
$739$	46.3467			1.70489			0.852446	−	0.522815i	$-0.175118\pi$
$739$	46.3467			1.70489			0.852446	+	0.522815i	$0.175118\pi$
$740$		0			0
$741$	61.7851			2.26973
$742$		0			0
$743$		−	10.7755i		−	0.395315i	−0.980271	−	0.197658i	$-0.936667\pi$
$743$		−	10.7755i		−	0.395315i	0.980271	−	0.197658i	$-0.0633334\pi$
$744$		0			0
$745$	7.36943	+	37.3973i	0.269995	+	1.37013i
$746$		0			0
$747$		−	1.79716i		−	0.0657546i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−2.76781			−0.100999			−0.0504995	−	0.998724i	$-0.516081\pi$
$751$	−2.76781			−0.100999			−0.0504995	+	0.998724i	$0.516081\pi$
$752$		0			0
$753$		−	37.8709i		−	1.38009i
$754$		0			0
$755$	−1.25240	−	6.35548i	−0.0455794	−	0.231300i
$756$		0			0
$757$		−	14.8401i		−	0.539371i	−0.962948	−	0.269686i	$-0.913080\pi$
$757$		−	14.8401i		−	0.539371i	0.962948	−	0.269686i	$-0.0869198\pi$
$758$		0			0
$759$	4.11371			0.149318
$760$		0			0
$761$	31.3169			1.13524			0.567619	−	0.823291i	$-0.307865\pi$
$761$	31.3169			1.13524			0.567619	+	0.823291i	$0.307865\pi$
$762$		0			0
$763$		−	18.9248i		−	0.685125i
$764$		0			0
$765$	−0.202840	+	0.0399712i	−0.00733371	+	0.00144516i
$766$		0			0
$767$		−	3.26113i		−	0.117753i
$768$		0			0
$769$	−8.92586			−0.321875			−0.160937	−	0.986965i	$-0.551452\pi$
$769$	−8.92586			−0.321875			−0.160937	+	0.986965i	$0.551452\pi$
$770$		0			0
$771$	−7.52311			−0.270938
$772$		0			0
$773$			36.7711i			1.32257i	0.750136	+	0.661283i	$0.229988\pi$
$773$			36.7711i			1.32257i	−0.750136	+	0.661283i	$0.770012\pi$
$774$		0			0
$775$	34.8034	−	14.2707i	1.25018	−	0.512619i
$776$		0			0
$777$		−	10.5693i		−	0.379173i
$778$		0			0
$779$	49.3728			1.76896
$780$		0			0
$781$	−3.45856			−0.123757
$782$		0			0
$783$		−	40.2051i		−	1.43681i
$784$		0			0
$785$	22.1955	−	4.37380i	0.792193	−	0.156108i
$786$		0			0
$787$			6.53707i			0.233021i	0.993189	+	0.116511i	$0.0371709\pi$
$787$			6.53707i			0.233021i	−0.993189	+	0.116511i	$0.962829\pi$
$788$		0			0
$789$	20.1849			0.718602
$790$		0			0
$791$	1.04623			0.0371996
$792$		0			0
$793$			39.1791i			1.39129i
$794$		0			0
$795$	−5.15994	−	26.1849i	−0.183004	−	0.928683i
$796$		0			0
$797$		−	7.82611i		−	0.277215i	−0.990347	−	0.138607i	$-0.955737\pi$
$797$		−	7.82611i		−	0.277215i	0.990347	−	0.138607i	$-0.0442626\pi$
$798$		0			0
$799$	5.27261			0.186531
$800$		0			0
$801$	1.47396			0.0520796
$802$		0

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.g (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.76156i q^{3} +(0.432320 + 2.19388i) q^{5} +1.00000i q^{7} -0.103084 q^{9} +O(q^{10})\)	\(q-1.76156i q^{3} +(0.432320 + 2.19388i) q^{5} +1.00000i q^{7} -0.103084 q^{9} +0.626198 q^{11} +5.49084i q^{13} +(3.86464 - 0.761557i) q^{15} -0.896916i q^{17} +6.38776 q^{19} +1.76156 q^{21} +3.72928i q^{23} +(-4.62620 + 1.89692i) q^{25} -5.10308i q^{27} +7.87859 q^{29} -7.52311 q^{31} -1.10308i q^{33} +(-2.19388 + 0.432320i) q^{35} -6.00000i q^{37} +9.67243 q^{39} +7.72928 q^{41} -1.72928i q^{43} +(-0.0445652 - 0.226153i) q^{45} +5.87859i q^{47} -1.00000 q^{49} -1.57997 q^{51} -6.77551i q^{53} +(0.270718 + 1.37380i) q^{55} -11.2524i q^{57} -0.593923 q^{59} +7.13536 q^{61} -0.103084i q^{63} +(-12.0462 + 2.37380i) q^{65} -5.79383i q^{67} +6.56934 q^{69} -5.52311 q^{71} -3.72928i q^{73} +(3.34153 + 8.14931i) q^{75} +0.626198i q^{77} -5.67243 q^{79} -9.29862 q^{81} +17.4340i q^{83} +(1.96772 - 0.387755i) q^{85} -13.8786i q^{87} -14.2986 q^{89} -5.49084 q^{91} +13.2524i q^{93} +(2.76156 + 14.0140i) q^{95} +10.1493i q^{97} -0.0645508 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6q - 8q^{9} + O(q^{10}) \)	\( 6q - 8q^{9} - 14q^{11} + 18q^{15} + 8q^{19} - 2q^{21} - 10q^{25} - 6q^{29} - 20q^{31} + 2q^{35} - 10q^{39} + 36q^{41} - 28q^{45} - 6q^{49} - 42q^{51} + 12q^{55} + 12q^{59} + 48q^{61} - 22q^{65} - 36q^{69} - 8q^{71} + 40q^{75} + 34q^{79} + 30q^{81} + 14q^{85} - 10q^{91} + 4q^{95} + 4q^{99} + O(q^{100}) \)

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