LMFDB - Embedded newform 1386.2.g.a.881.2

Newspace parameters

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.g (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
Defining polynomial:	$x^{16} - 4 x^{14} + 8 x^{12} + 80 x^{10} + 1189 x^{8} - 2028 x^{6} + 1800 x^{4} + 1080 x^{2} + 324$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			881.2
Root			$2.43348 - 1.00798i$ of defining polynomial
Character	$\chi$	$=$	1386.881
Dual form			1386.2.g.a.881.10

$q$-expansion

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} -2.01596 q^{5} +(1.78450 + 1.95335i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} -2.01596 q^{5} +(1.78450 + 1.95335i) q^{7} +1.00000i q^{8} +2.01596i q^{10} +1.00000i q^{11} +(1.95335 - 1.78450i) q^{14} +1.00000 q^{16} -5.92266 q^{17} -0.657927i q^{19} +2.01596 q^{20} +1.00000 q^{22} -7.87575i q^{23} -0.935886 q^{25} +(-1.78450 - 1.95335i) q^{28} -1.32636i q^{29} -10.6942i q^{31} -1.00000i q^{32} +5.92266i q^{34} +(-3.59749 - 3.93788i) q^{35} +5.87575 q^{37} -0.657927 q^{38} -2.01596i q^{40} -4.56462 q^{41} -1.56900 q^{43} -1.00000i q^{44} -7.87575 q^{46} -0.532690 q^{47} +(-0.631122 + 6.97149i) q^{49} +0.935886i q^{50} -7.44475i q^{53} -2.01596i q^{55} +(-1.95335 + 1.78450i) q^{56} -1.32636 q^{58} -4.03193 q^{59} -0.250475i q^{61} -10.6942 q^{62} -1.00000 q^{64} -7.81164 q^{67} +5.92266 q^{68} +(-3.93788 + 3.59749i) q^{70} +0.609527i q^{71} -0.532690i q^{73} -5.87575i q^{74} +0.657927i q^{76} +(-1.95335 + 1.78450i) q^{77} -12.7711 q^{79} -2.01596 q^{80} +4.56462i q^{82} -13.3681 q^{83} +11.9399 q^{85} +1.56900i q^{86} -1.00000 q^{88} -5.22255 q^{89} +7.87575i q^{92} +0.532690i q^{94} +1.32636i q^{95} +2.71607i q^{97} +(6.97149 + 0.631122i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16q - 16q^{4} - 8q^{7} + O(q^{10}) $	$ 16q - 16q^{4} - 8q^{7} + 16q^{16} + 16q^{22} + 16q^{25} + 8q^{28} - 16q^{37} + 48q^{43} - 16q^{46} + 8q^{49} - 16q^{58} - 16q^{64} + 16q^{67} - 8q^{70} - 16q^{79} + 112q^{85} - 16q^{88} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−2.01596			−0.901567			−0.450783	−	0.892633i	$-0.648855\pi$
$5$	−2.01596			−0.901567			−0.450783	+	0.892633i	$0.648855\pi$
$6$		0			0
$7$	1.78450	+	1.95335i	0.674477	+	0.738295i
$7$	1.78450	+	1.95335i	0.674477	+	0.738295i
$8$			1.00000i			0.353553i
$9$		0			0
$10$			2.01596i			0.637504i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	1.95335	−	1.78450i	0.522054	−	0.476928i
$15$		0			0
$16$	1.00000			0.250000
$17$	−5.92266			−1.43646			−0.718228	−	0.695808i	$-0.755046\pi$
$17$	−5.92266			−1.43646			−0.718228	+	0.695808i	$0.755046\pi$
$18$		0			0
$19$		−	0.657927i		−	0.150939i	−0.997148	−	0.0754695i	$-0.975954\pi$
$19$		−	0.657927i		−	0.150939i	0.997148	−	0.0754695i	$-0.0240455\pi$
$20$	2.01596			0.450783
$21$		0			0
$22$	1.00000			0.213201
$23$		−	7.87575i		−	1.64221i	−0.570778	−	0.821104i	$-0.693358\pi$
$23$		−	7.87575i		−	1.64221i	0.570778	−	0.821104i	$-0.306642\pi$
$24$		0			0
$25$	−0.935886			−0.187177
$26$		0			0
$27$		0			0
$28$	−1.78450	−	1.95335i	−0.337239	−	0.369148i
$29$		−	1.32636i		−	0.246299i	−0.992388	−	0.123149i	$-0.960701\pi$
$29$		−	1.32636i		−	0.246299i	0.992388	−	0.123149i	$-0.0392994\pi$
$30$		0			0
$31$		−	10.6942i		−	1.92074i	−0.278732	−	0.960369i	$-0.589914\pi$
$31$		−	10.6942i		−	1.92074i	0.278732	−	0.960369i	$-0.410086\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$			5.92266i			1.01573i
$35$	−3.59749	−	3.93788i	−0.608087	−	0.665623i
$36$		0			0
$37$	5.87575			0.965968			0.482984	−	0.875629i	$-0.339553\pi$
$37$	5.87575			0.965968			0.482984	+	0.875629i	$0.339553\pi$
$38$	−0.657927			−0.106730
$39$		0			0
$40$		−	2.01596i		−	0.318752i
$41$	−4.56462			−0.712874			−0.356437	−	0.934319i	$-0.616009\pi$
$41$	−4.56462			−0.712874			−0.356437	+	0.934319i	$0.616009\pi$
$42$		0			0
$43$	−1.56900			−0.239270			−0.119635	−	0.992818i	$-0.538172\pi$
$43$	−1.56900			−0.239270			−0.119635	+	0.992818i	$0.538172\pi$
$44$		−	1.00000i		−	0.150756i
$45$		0			0
$46$	−7.87575			−1.16122
$47$	−0.532690			−0.0777008			−0.0388504	−	0.999245i	$-0.512370\pi$
$47$	−0.532690			−0.0777008			−0.0388504	+	0.999245i	$0.512370\pi$
$48$		0			0
$49$	−0.631122	+	6.97149i	−0.0901603	+	0.995927i
$50$			0.935886i			0.132354i
$51$		0			0
$52$		0			0
$53$		−	7.44475i		−	1.02262i	−0.859398	−	0.511308i	$-0.829161\pi$
$53$		−	7.44475i		−	1.02262i	0.859398	−	0.511308i	$-0.170839\pi$
$54$		0			0
$55$		−	2.01596i		−	0.271833i
$56$	−1.95335	+	1.78450i	−0.261027	+	0.238464i
$57$		0			0
$58$	−1.32636			−0.174159
$59$	−4.03193			−0.524913			−0.262456	−	0.964944i	$-0.584533\pi$
$59$	−4.03193			−0.524913			−0.262456	+	0.964944i	$0.584533\pi$
$60$		0			0
$61$		−	0.250475i		−	0.0320700i	−0.999871	−	0.0160350i	$-0.994896\pi$
$61$		−	0.250475i		−	0.0320700i	0.999871	−	0.0160350i	$-0.00510432\pi$
$62$	−10.6942			−1.35817
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	−7.81164			−0.954344			−0.477172	−	0.878810i	$-0.658338\pi$
$67$	−7.81164			−0.954344			−0.477172	+	0.878810i	$0.658338\pi$
$68$	5.92266			0.718228
$69$		0			0
$70$	−3.93788	+	3.59749i	−0.470666	+	0.429982i
$71$			0.609527i			0.0723376i	0.999346	+	0.0361688i	$0.0115154\pi$
$71$			0.609527i			0.0723376i	−0.999346	+	0.0361688i	$0.988485\pi$
$72$		0			0
$73$		−	0.532690i		−	0.0623466i	−0.999514	−	0.0311733i	$-0.990076\pi$
$73$		−	0.532690i		−	0.0623466i	0.999514	−	0.0311733i	$-0.00992438\pi$
$74$		−	5.87575i		−	0.683043i
$75$		0			0
$76$			0.657927i			0.0754695i
$77$	−1.95335	+	1.78450i	−0.222604	+	0.203363i
$78$		0			0
$79$	−12.7711			−1.43686			−0.718431	−	0.695598i	$-0.755139\pi$
$79$	−12.7711			−1.43686			−0.718431	+	0.695598i	$0.755139\pi$
$80$	−2.01596			−0.225392
$81$		0			0
$82$			4.56462i			0.504078i
$83$	−13.3681			−1.46734			−0.733670	−	0.679506i	$-0.762194\pi$
$83$	−13.3681			−1.46734			−0.733670	+	0.679506i	$0.762194\pi$
$84$		0			0
$85$	11.9399			1.29506
$86$			1.56900i			0.169190i
$87$		0			0
$88$	−1.00000			−0.106600
$89$	−5.22255			−0.553589			−0.276794	−	0.960929i	$-0.589272\pi$
$89$	−5.22255			−0.553589			−0.276794	+	0.960929i	$0.589272\pi$
$90$		0			0
$91$		0			0
$92$			7.87575i			0.821104i
$93$		0			0
$94$			0.532690i			0.0549428i
$95$			1.32636i			0.136082i
$96$		0			0
$97$			2.71607i			0.275776i	0.990448	+	0.137888i	$0.0440313\pi$
$97$			2.71607i			0.275776i	−0.990448	+	0.137888i	$0.955969\pi$
$98$	6.97149	+	0.631122i	0.704227	+	0.0637530i
$99$		0			0
$100$	0.935886			0.0935886
$101$	−3.41352			−0.339658			−0.169829	−	0.985474i	$-0.554322\pi$
$101$	−3.41352			−0.339658			−0.169829	+	0.985474i	$0.554322\pi$
$102$		0			0
$103$			13.3681i			1.31720i	0.752494	+	0.658599i	$0.228851\pi$
$103$			13.3681i			1.31720i	−0.752494	+	0.658599i	$0.771149\pi$
$104$		0			0
$105$		0			0
$106$	−7.44475			−0.723098
$107$		−	14.4002i		−	1.39212i	−0.717982	−	0.696062i	$-0.754934\pi$
$107$		−	14.4002i		−	1.39212i	0.717982	−	0.696062i	$-0.245066\pi$
$108$		0			0
$109$	−3.41140			−0.326753			−0.163376	−	0.986564i	$-0.552238\pi$
$109$	−3.41140			−0.326753			−0.163376	+	0.986564i	$0.552238\pi$
$110$	−2.01596			−0.192215
$111$		0			0
$112$	1.78450	+	1.95335i	0.168619	+	0.184574i
$113$		−	4.95947i		−	0.466548i	−0.972411	−	0.233274i	$-0.925056\pi$
$113$		−	4.95947i		−	0.466548i	0.972411	−	0.233274i	$-0.0749439\pi$
$114$		0			0
$115$			15.8772i			1.48056i
$116$			1.32636i			0.123149i
$117$		0			0
$118$			4.03193i			0.371169i
$119$	−10.5690	−	11.5690i	−0.968857	−	1.06053i
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	−0.250475			−0.0226769
$123$		0			0
$124$			10.6942i			0.960369i
$125$	11.9665			1.07032
$126$		0			0
$127$	9.50488			0.843422			0.421711	−	0.906730i	$-0.361430\pi$
$127$	9.50488			0.843422			0.421711	+	0.906730i	$0.361430\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$		0			0
$131$	19.0838			1.66736			0.833681	−	0.552247i	$-0.186229\pi$
$131$	19.0838			1.66736			0.833681	+	0.552247i	$0.186229\pi$
$132$		0			0
$133$	1.28516	−	1.17407i	0.111438	−	0.101805i
$134$			7.81164i			0.674823i
$135$		0			0
$136$		−	5.92266i		−	0.507864i
$137$		−	8.05428i		−	0.688124i	−0.938947	−	0.344062i	$-0.888197\pi$
$137$		−	8.05428i		−	0.688124i	0.938947	−	0.344062i	$-0.111803\pi$
$138$		0			0
$139$		−	19.3725i		−	1.64315i	−0.570099	−	0.821576i	$-0.693095\pi$
$139$		−	19.3725i		−	1.64315i	0.570099	−	0.821576i	$-0.306905\pi$
$140$	3.59749	+	3.93788i	0.304043	+	0.332811i
$141$		0			0
$142$	0.609527			0.0511504
$143$		0			0
$144$		0			0
$145$			2.67389i			0.222055i
$146$	−0.532690			−0.0440857
$147$		0			0
$148$	−5.87575			−0.482984
$149$			3.26224i			0.267253i	0.991032	+	0.133627i	$0.0426623\pi$
$149$			3.26224i			0.267253i	−0.991032	+	0.133627i	$0.957338\pi$
$150$		0			0
$151$	−14.1785			−1.15383			−0.576916	−	0.816803i	$-0.695744\pi$
$151$	−14.1785			−1.15383			−0.576916	+	0.816803i	$0.695744\pi$
$152$	0.657927			0.0533650
$153$		0			0
$154$	1.78450	+	1.95335i	0.143799	+	0.157405i
$155$			21.5592i			1.73167i
$156$		0			0
$157$		−	11.7596i		−	0.938518i	−0.883061	−	0.469259i	$-0.844521\pi$
$157$		−	11.7596i		−	0.938518i	0.883061	−	0.469259i	$-0.155479\pi$
$158$			12.7711i			1.01602i
$159$		0			0
$160$			2.01596i			0.159376i
$161$	15.3841	−	14.0543i	1.21243	−	1.10763i
$162$		0			0
$163$	12.5285			0.981306			0.490653	−	0.871355i	$-0.336758\pi$
$163$	12.5285			0.981306			0.490653	+	0.871355i	$0.336758\pi$
$164$	4.56462			0.356437
$165$		0			0
$166$			13.3681i			1.03757i
$167$	23.0722			1.78538			0.892691	−	0.450669i	$-0.148815\pi$
$167$	23.0722			1.78538			0.892691	+	0.450669i	$0.148815\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		−	11.9399i		−	0.915746i
$171$		0			0
$172$	1.56900			0.119635
$173$	−17.7244			−1.34756			−0.673782	−	0.738930i	$-0.735331\pi$
$173$	−17.7244			−1.34756			−0.673782	+	0.738930i	$0.735331\pi$
$174$		0			0
$175$	−1.67009	−	1.82811i	−0.126247	−	0.138192i
$176$			1.00000i			0.0753778i
$177$		0			0
$178$			5.22255i			0.391446i
$179$		−	3.81164i		−	0.284895i	−0.989802	−	0.142448i	$-0.954503\pi$
$179$		−	3.81164i		−	0.284895i	0.989802	−	0.142448i	$-0.0454973\pi$
$180$		0			0
$181$		−	19.1260i		−	1.42163i	−0.703382	−	0.710813i	$-0.748327\pi$
$181$		−	19.1260i		−	1.42163i	0.703382	−	0.710813i	$-0.251673\pi$
$182$		0			0
$183$		0			0
$184$	7.87575			0.580608
$185$	−11.8453			−0.870885
$186$		0			0
$187$		−	5.92266i		−	0.433108i
$188$	0.532690			0.0388504
$189$		0			0
$190$	1.32636			0.0962242
$191$			21.6665i			1.56773i	0.620931	+	0.783865i	$0.286755\pi$
$191$			21.6665i			1.56773i	−0.620931	+	0.783865i	$0.713245\pi$
$192$		0			0
$193$	−21.6233			−1.55648			−0.778239	−	0.627968i	$-0.783887\pi$
$193$	−21.6233			−1.55648			−0.778239	+	0.627968i	$0.783887\pi$
$194$	2.71607			0.195003
$195$		0			0
$196$	0.631122	−	6.97149i	0.0450802	−	0.497964i
$197$			21.6914i			1.54545i	0.634743	+	0.772723i	$0.281106\pi$
$197$			21.6914i			1.54545i	−0.634743	+	0.772723i	$0.718894\pi$
$198$		0			0
$199$			3.94621i			0.279740i	0.990170	+	0.139870i	$0.0446684\pi$
$199$			3.94621i			0.279740i	−0.990170	+	0.139870i	$0.955332\pi$
$200$		−	0.935886i		−	0.0661771i
$201$		0			0
$202$			3.41352i			0.240175i
$203$	2.59084	−	2.36689i	0.181841	−	0.166123i
$204$		0			0
$205$	9.20211			0.642703
$206$	13.3681			0.931400
$207$		0			0
$208$		0			0
$209$	0.657927			0.0455098
$210$		0			0
$211$	2.30277			0.158529			0.0792647	−	0.996854i	$-0.474743\pi$
$211$	2.30277			0.158529			0.0792647	+	0.996854i	$0.474743\pi$
$212$			7.44475i			0.511308i
$213$		0			0
$214$	−14.4002			−0.984380
$215$	3.16305			0.215718
$216$		0			0
$217$	20.8895	−	19.0838i	1.41807	−	1.29549i
$218$			3.41140i			0.231049i
$219$		0			0
$220$			2.01596i			0.135916i
$221$		0			0
$222$		0			0
$223$			18.2571i			1.22259i	0.791404	+	0.611294i	$0.209351\pi$
$223$			18.2571i			1.22259i	−0.791404	+	0.611294i	$0.790649\pi$
$224$	1.95335	−	1.78450i	0.130513	−	0.119232i
$225$		0			0
$226$	−4.95947			−0.329899
$227$	20.0739			1.33235			0.666177	−	0.745794i	$-0.267930\pi$
$227$	20.0739			1.33235			0.666177	+	0.745794i	$0.267930\pi$
$228$		0			0
$229$		−	14.6840i		−	0.970344i	−0.874419	−	0.485172i	$-0.838757\pi$
$229$		−	14.6840i		−	0.970344i	0.874419	−	0.485172i	$-0.161243\pi$
$230$	15.8772			1.04691
$231$		0			0
$232$	1.32636			0.0870797
$233$			2.48528i			0.162816i	0.996681	+	0.0814081i	$0.0259417\pi$
$233$			2.48528i			0.162816i	−0.996681	+	0.0814081i	$0.974058\pi$
$234$		0			0
$235$	1.07388			0.0700525
$236$	4.03193			0.262456
$237$		0			0
$238$	−11.5690	+	10.5690i	−0.749907	+	0.685085i
$239$			22.3610i			1.44642i	0.690631	+	0.723208i	$0.257333\pi$
$239$			22.3610i			1.44642i	−0.690631	+	0.723208i	$0.742667\pi$
$240$		0			0
$241$			3.45706i			0.222689i	0.993782	+	0.111344i	$0.0355156\pi$
$241$			3.45706i			0.222689i	−0.993782	+	0.111344i	$0.964484\pi$
$242$			1.00000i			0.0642824i
$243$		0			0
$244$			0.250475i			0.0160350i
$245$	1.27232	−	14.0543i	0.0812855	−	0.897895i
$246$		0			0
$247$		0			0
$248$	10.6942			0.679083
$249$		0			0
$250$		−	11.9665i		−	0.756830i
$251$	−3.78145			−0.238683			−0.119342	−	0.992853i	$-0.538078\pi$
$251$	−3.78145			−0.238683			−0.119342	+	0.992853i	$0.538078\pi$
$252$		0			0
$253$	7.87575			0.495144
$254$		−	9.50488i		−	0.596390i
$255$		0			0
$256$	1.00000			0.0625000
$257$	5.22255			0.325774			0.162887	−	0.986645i	$-0.447919\pi$
$257$	5.22255			0.325774			0.162887	+	0.986645i	$0.447919\pi$
$258$		0			0
$259$	10.4853	+	11.4774i	0.651524	+	0.713170i
$260$		0			0
$261$		0			0
$262$		−	19.0838i		−	1.17900i
$263$			13.7306i			0.846664i	0.905975	+	0.423332i	$0.139140\pi$
$263$			13.7306i			0.846664i	−0.905975	+	0.423332i	$0.860860\pi$
$264$		0			0
$265$			15.0084i			0.921956i
$266$	−1.17407	−	1.28516i	−0.0719869	−	0.0787982i
$267$		0			0
$268$	7.81164			0.477172
$269$	−29.6093			−1.80531			−0.902655	−	0.430366i	$-0.858385\pi$
$269$	−29.6093			−1.80531			−0.902655	+	0.430366i	$0.858385\pi$
$270$		0			0
$271$		−	15.5015i		−	0.941651i	−0.882226	−	0.470825i	$-0.843956\pi$
$271$		−	15.5015i		−	0.941651i	0.882226	−	0.470825i	$-0.156044\pi$
$272$	−5.92266			−0.359114
$273$		0			0
$274$	−8.05428			−0.486577
$275$		−	0.935886i		−	0.0564360i
$276$		0			0
$277$	−19.0347			−1.14368			−0.571841	−	0.820364i	$-0.693771\pi$
$277$	−19.0347			−1.14368			−0.571841	+	0.820364i	$0.693771\pi$
$278$	−19.3725			−1.16188
$279$		0			0
$280$	3.93788	−	3.59749i	0.235333	−	0.214991i
$281$			10.9706i			0.654449i	0.944947	+	0.327224i	$0.106113\pi$
$281$			10.9706i			0.654449i	−0.944947	+	0.327224i	$0.893887\pi$
$282$		0			0
$283$		−	19.2091i		−	1.14186i	−0.820999	−	0.570930i	$-0.806583\pi$
$283$		−	19.2091i		−	1.14186i	0.820999	−	0.570930i	$-0.193417\pi$
$284$		−	0.609527i		−	0.0361688i
$285$		0			0
$286$		0			0
$287$	−8.14556	−	8.91628i	−0.480817	−	0.526311i
$288$		0			0
$289$	18.0779			1.06340
$290$	2.67389			0.157016
$291$		0			0
$292$			0.532690i			0.0311733i
$293$	−9.91105			−0.579010			−0.289505	−	0.957177i	$-0.593491\pi$
$293$	−9.91105			−0.579010			−0.289505	+	0.957177i	$0.593491\pi$
$294$		0			0
$295$	8.12823			0.473244
$296$			5.87575i			0.341521i
$297$		0			0
$298$	3.26224			0.188977
$299$		0			0
$300$		0			0
$301$	−2.79988	−	3.06480i	−0.161382	−	0.176652i
$302$			14.1785i			0.815883i
$303$		0			0
$304$		−	0.657927i		−	0.0377347i
$305$			0.504949i			0.0289133i
$306$		0			0
$307$		−	1.64427i		−	0.0938433i	−0.998899	−	0.0469216i	$-0.985059\pi$
$307$		−	1.64427i		−	0.0938433i	0.998899	−	0.0469216i	$-0.0149411\pi$
$308$	1.95335	−	1.78450i	0.111302	−	0.101681i
$309$		0			0
$310$	21.5592			1.22448
$311$	−2.14120			−0.121416			−0.0607082	−	0.998156i	$-0.519336\pi$
$311$	−2.14120			−0.121416			−0.0607082	+	0.998156i	$0.519336\pi$
$312$		0			0
$313$		−	12.7932i		−	0.723116i	−0.932350	−	0.361558i	$-0.882245\pi$
$313$		−	12.7932i		−	0.723116i	0.932350	−	0.361558i	$-0.117755\pi$
$314$	−11.7596			−0.663632
$315$		0			0
$316$	12.7711			0.718431
$317$			6.51604i			0.365977i	0.983115	+	0.182989i	$0.0585771\pi$
$317$			6.51604i			0.365977i	−0.983115	+	0.182989i	$0.941423\pi$
$318$		0			0
$319$	1.32636			0.0742618
$320$	2.01596			0.112696
$321$		0			0
$322$	−14.0543	−	15.3841i	−0.783214	−	0.857321i
$323$			3.89668i			0.216817i
$324$		0			0
$325$		0			0
$326$		−	12.5285i		−	0.693888i
$327$		0			0
$328$		−	4.56462i		−	0.252039i
$329$	−0.950585	−	1.04053i	−0.0524074	−	0.0573662i
$330$		0			0
$331$	−30.2159			−1.66081			−0.830407	−	0.557157i	$-0.811892\pi$
$331$	−30.2159			−1.66081			−0.830407	+	0.557157i	$0.811892\pi$
$332$	13.3681			0.733670
$333$		0			0
$334$		−	23.0722i		−	1.26246i
$335$	15.7480			0.860405
$336$		0			0
$337$	24.8895			1.35582			0.677909	−	0.735146i	$-0.262886\pi$
$337$	24.8895			1.35582			0.677909	+	0.735146i	$0.262886\pi$
$338$		−	13.0000i		−	0.707107i
$339$		0			0
$340$	−11.9399			−0.647530
$341$	10.6942			0.579124
$342$		0			0
$343$	−14.7440	+	11.2078i	−0.796100	+	0.605166i
$344$		−	1.56900i		−	0.0845948i
$345$		0			0
$346$			17.7244i			0.952872i
$347$		−	9.09481i		−	0.488235i	−0.969746	−	0.244117i	$-0.921502\pi$
$347$		−	9.09481i		−	0.488235i	0.969746	−	0.244117i	$-0.0784982\pi$
$348$		0			0
$349$		−	31.8335i		−	1.70401i	−0.523534	−	0.852005i	$-0.675387\pi$
$349$		−	31.8335i		−	1.70401i	0.523534	−	0.852005i	$-0.324613\pi$
$350$	−1.82811	+	1.67009i	−0.0977165	+	0.0892699i
$351$		0			0
$352$	1.00000			0.0533002
$353$	10.9052			0.580424			0.290212	−	0.956962i	$-0.406274\pi$
$353$	10.9052			0.580424			0.290212	+	0.956962i	$0.406274\pi$
$354$		0			0
$355$		−	1.22879i		−	0.0652171i
$356$	5.22255			0.276794
$357$		0			0
$358$	−3.81164			−0.201451
$359$			23.6874i			1.25017i	0.780556	+	0.625086i	$0.214936\pi$
$359$			23.6874i			1.25017i	−0.780556	+	0.625086i	$0.785064\pi$
$360$		0			0
$361$	18.5671			0.977217
$362$	−19.1260			−1.00524
$363$		0			0
$364$		0			0
$365$			1.07388i			0.0562097i
$366$		0			0
$367$			13.1176i			0.684735i	0.939566	+	0.342367i	$0.111229\pi$
$367$			13.1176i			0.684735i	−0.939566	+	0.342367i	$0.888771\pi$
$368$		−	7.87575i		−	0.410552i
$369$		0			0
$370$			11.8453i			0.615809i
$371$	14.5422	−	13.2852i	0.754992	−	0.689731i
$372$		0			0
$373$	3.38649			0.175346			0.0876729	−	0.996149i	$-0.472057\pi$
$373$	3.38649			0.175346			0.0876729	+	0.996149i	$0.472057\pi$
$374$	−5.92266			−0.306253
$375$		0			0
$376$		−	0.532690i		−	0.0274714i
$377$		0			0
$378$		0			0
$379$	8.52847			0.438078			0.219039	−	0.975716i	$-0.429708\pi$
$379$	8.52847			0.438078			0.219039	+	0.975716i	$0.429708\pi$
$380$		−	1.32636i		−	0.0680408i
$381$		0			0
$382$	21.6665			1.10855
$383$	10.1180			0.517005			0.258503	−	0.966011i	$-0.416771\pi$
$383$	10.1180			0.517005			0.258503	+	0.966011i	$0.416771\pi$
$384$		0			0
$385$	3.93788	−	3.59749i	0.200693	−	0.183345i
$386$			21.6233i			1.10060i
$387$		0			0
$388$		−	2.71607i		−	0.137888i
$389$		−	16.7920i		−	0.851390i	−0.904867	−	0.425695i	$-0.860030\pi$
$389$		−	16.7920i		−	0.851390i	0.904867	−	0.425695i	$-0.139970\pi$
$390$		0			0
$391$			46.6454i			2.35896i
$392$	−6.97149	−	0.631122i	−0.352113	−	0.0318765i
$393$		0			0
$394$	21.6914			1.09280
$395$	25.7461			1.29543
$396$		0			0
$397$		−	13.4856i		−	0.676821i	−0.940999	−	0.338411i	$-0.890111\pi$
$397$		−	13.4856i		−	0.676821i	0.940999	−	0.338411i	$-0.109889\pi$
$398$	3.94621			0.197806
$399$		0			0
$400$	−0.935886			−0.0467943
$401$			13.5298i			0.675646i	0.941210	+	0.337823i	$0.109690\pi$
$401$			13.5298i			0.675646i	−0.941210	+	0.337823i	$0.890310\pi$
$402$		0			0
$403$		0			0
$404$	3.41352			0.169829
$405$		0			0
$406$	−2.36689	−	2.59084i	−0.117467	−	0.128581i
$407$			5.87575i			0.291250i
$408$		0			0
$409$			27.0606i			1.33806i	0.743235	+	0.669031i	$0.233291\pi$
$409$			27.0606i			1.33806i	−0.743235	+	0.669031i	$0.766709\pi$
$410$		−	9.20211i		−	0.454460i
$411$		0			0
$412$		−	13.3681i		−	0.658599i
$413$	−7.19498	−	7.87575i	−0.354042	−	0.387541i
$414$		0			0
$415$	26.9496			1.32291
$416$		0			0
$417$		0			0
$418$		−	0.657927i		−	0.0321803i
$419$	10.7799			0.526634			0.263317	−	0.964709i	$-0.415183\pi$
$419$	10.7799			0.526634			0.263317	+	0.964709i	$0.415183\pi$
$420$		0			0
$421$	23.0948			1.12557			0.562786	−	0.826603i	$-0.309729\pi$
$421$	23.0948			1.12557			0.562786	+	0.826603i	$0.309729\pi$
$422$		−	2.30277i		−	0.112097i
$423$		0			0
$424$	7.44475			0.361549
$425$	5.54293			0.268872
$426$		0			0
$427$	0.489264	−	0.446973i	0.0236772	−	0.0216305i
$428$			14.4002i			0.696062i
$429$		0			0
$430$		−	3.16305i		−	0.152536i
$431$			13.8508i			0.667172i	0.942720	+	0.333586i	$0.108259\pi$
$431$			13.8508i			0.667172i	−0.942720	+	0.333586i	$0.891741\pi$
$432$		0			0
$433$		−	36.3968i		−	1.74912i	−0.484919	−	0.874559i	$-0.661151\pi$
$433$		−	36.3968i		−	1.74912i	0.484919	−	0.874559i	$-0.338849\pi$
$434$	−19.0838	−	20.8895i	−0.916053	−	1.00273i
$435$		0			0
$436$	3.41140			0.163376
$437$	−5.18167			−0.247873
$438$		0			0
$439$			24.9603i			1.19129i	0.803248	+	0.595645i	$0.203103\pi$
$439$			24.9603i			1.19129i	−0.803248	+	0.595645i	$0.796897\pi$
$440$	2.01596			0.0961074
$441$		0			0
$442$		0			0
$443$		−	7.20610i		−	0.342372i	−0.985239	−	0.171186i	$-0.945240\pi$
$443$		−	7.20610i		−	0.342372i	0.985239	−	0.171186i	$-0.0547599\pi$
$444$		0			0
$445$	10.5285			0.499097
$446$	18.2571			0.864500
$447$		0			0
$448$	−1.78450	−	1.95335i	−0.0843097	−	0.0922869i
$449$		−	31.8490i		−	1.50305i	−0.659707	−	0.751523i	$-0.729320\pi$
$449$		−	31.8490i		−	1.50305i	0.659707	−	0.751523i	$-0.270680\pi$
$450$		0			0
$451$		−	4.56462i		−	0.214940i
$452$			4.95947i			0.233274i
$453$		0			0
$454$		−	20.0739i		−	0.942116i
$455$		0			0
$456$		0			0
$457$	−10.4853			−0.490481			−0.245240	−	0.969462i	$-0.578867\pi$
$457$	−10.4853			−0.490481			−0.245240	+	0.969462i	$0.578867\pi$
$458$	−14.6840			−0.686137
$459$		0			0
$460$		−	15.8772i		−	0.740280i
$461$	24.3881			1.13587			0.567933	−	0.823075i	$-0.307743\pi$
$461$	24.3881			1.13587			0.567933	+	0.823075i	$0.307743\pi$
$462$		0			0
$463$	−22.6410			−1.05222			−0.526109	−	0.850417i	$-0.676349\pi$
$463$	−22.6410			−1.05222			−0.526109	+	0.850417i	$0.676349\pi$
$464$		−	1.32636i		−	0.0615747i
$465$		0			0
$466$	2.48528			0.115128
$467$	−27.6355			−1.27882			−0.639409	−	0.768867i	$-0.720821\pi$
$467$	−27.6355			−1.27882			−0.639409	+	0.768867i	$0.720821\pi$
$468$		0			0
$469$	−13.9399	−	15.2588i	−0.643683	−	0.704588i
$470$		−	1.07388i		−	0.0495346i
$471$		0			0
$472$		−	4.03193i		−	0.185585i
$473$		−	1.56900i		−	0.0721427i
$474$		0			0
$475$			0.615745i			0.0282523i
$476$	10.5690	+	11.5690i	0.484428	+	0.530264i
$477$		0			0
$478$	22.3610			1.02277
$479$	34.4166			1.57253			0.786267	−	0.617887i	$-0.212011\pi$
$479$	34.4166			1.57253			0.786267	+	0.617887i	$0.212011\pi$
$480$		0			0
$481$		0			0
$482$	3.45706			0.157465
$483$		0			0
$484$	1.00000			0.0454545
$485$		−	5.47551i		−	0.248630i
$486$		0			0
$487$	−15.2662			−0.691779			−0.345889	−	0.938275i	$-0.612423\pi$
$487$	−15.2662			−0.691779			−0.345889	+	0.938275i	$0.612423\pi$
$488$	0.250475			0.0113385
$489$		0			0
$490$	−14.0543	−	1.27232i	−0.634908	−	0.0574776i
$491$			23.6273i			1.06628i	0.846026	+	0.533142i	$0.178989\pi$
$491$			23.6273i			1.06628i	−0.846026	+	0.533142i	$0.821011\pi$
$492$		0			0
$493$			7.85557i			0.353797i
$494$		0			0
$495$		0			0
$496$		−	10.6942i		−	0.480185i
$497$	−1.19062	+	1.08770i	−0.0534065	+	0.0487901i
$498$		0			0
$499$	−36.0484			−1.61375			−0.806875	−	0.590723i	$-0.798843\pi$
$499$	−36.0484			−1.61375			−0.806875	+	0.590723i	$0.798843\pi$
$500$	−11.9665			−0.535160
$501$		0			0
$502$			3.78145i			0.168775i
$503$	−31.1361			−1.38829			−0.694145	−	0.719836i	$-0.744217\pi$
$503$	−31.1361			−1.38829			−0.694145	+	0.719836i	$0.744217\pi$
$504$		0			0
$505$	6.88154			0.306225
$506$		−	7.87575i		−	0.350120i
$507$		0			0
$508$	−9.50488			−0.421711
$509$	−21.5454			−0.954984			−0.477492	−	0.878636i	$-0.658454\pi$
$509$	−21.5454			−0.954984			−0.477492	+	0.878636i	$0.658454\pi$
$510$		0			0
$511$	1.04053	−	0.950585i	0.0460302	−	0.0420514i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$		−	5.22255i		−	0.230357i
$515$		−	26.9496i		−	1.18754i
$516$		0			0
$517$		−	0.532690i		−	0.0234277i
$518$	11.4774	−	10.4853i	0.504287	−	0.460697i
$519$		0			0
$520$		0			0
$521$	24.0663			1.05437			0.527183	−	0.849752i	$-0.323248\pi$
$521$	24.0663			1.05437			0.527183	+	0.849752i	$0.323248\pi$
$522$		0			0
$523$			7.11327i			0.311042i	0.987833	+	0.155521i	$0.0497056\pi$
$523$			7.11327i			0.311042i	−0.987833	+	0.155521i	$0.950294\pi$
$524$	−19.0838			−0.833681
$525$		0			0
$526$	13.7306			0.598682
$527$			63.3382i			2.75905i
$528$		0			0
$529$	−39.0275			−1.69685
$530$	15.0084			0.651922
$531$		0			0
$532$	−1.28516	+	1.17407i	−0.0557188	+	0.0509024i
$533$		0			0
$534$		0			0
$535$			29.0304i			1.25509i
$536$		−	7.81164i		−	0.337411i
$537$		0			0
$538$			29.6093i			1.27655i
$539$	−6.97149	−	0.631122i	−0.300283	−	0.0271844i
$540$		0			0
$541$	4.24849			0.182657			0.0913285	−	0.995821i	$-0.470889\pi$
$541$	4.24849			0.182657			0.0913285	+	0.995821i	$0.470889\pi$
$542$	−15.5015			−0.665848
$543$		0			0
$544$			5.92266i			0.253932i
$545$	6.87726			0.294589
$546$		0			0
$547$	9.69723			0.414624			0.207312	−	0.978275i	$-0.433529\pi$
$547$	9.69723			0.414624			0.207312	+	0.978275i	$0.433529\pi$
$548$			8.05428i			0.344062i
$549$		0			0
$550$	−0.935886			−0.0399063
$551$	−0.872648			−0.0371760
$552$		0			0
$553$	−22.7900	−	24.9464i	−0.969131	−	1.06083i
$554$			19.0347i			0.808706i
$555$		0			0
$556$			19.3725i			0.821576i
$557$			21.6914i			0.919093i	0.888154	+	0.459547i	$0.151988\pi$
$557$			21.6914i			0.919093i	−0.888154	+	0.459547i	$0.848012\pi$
$558$		0			0
$559$		0			0
$560$	−3.59749	−	3.93788i	−0.152022	−	0.166406i
$561$		0			0
$562$	10.9706			0.462765
$563$	1.68243			0.0709062			0.0354531	−	0.999371i	$-0.488713\pi$
$563$	1.68243			0.0709062			0.0354531	+	0.999371i	$0.488713\pi$
$564$		0			0
$565$			9.99812i			0.420624i
$566$	−19.2091			−0.807417
$567$		0			0
$568$	−0.609527			−0.0255752
$569$			14.4853i			0.607255i	0.952791	+	0.303627i	$0.0981978\pi$
$569$			14.4853i			0.607255i	−0.952791	+	0.303627i	$0.901802\pi$
$570$		0			0
$571$	−26.7542			−1.11963			−0.559814	−	0.828619i	$-0.689127\pi$
$571$	−26.7542			−1.11963			−0.559814	+	0.828619i	$0.689127\pi$
$572$		0			0
$573$		0			0
$574$	−8.91628	+	8.14556i	−0.372158	+	0.339989i
$575$			7.37081i			0.307384i
$576$		0			0
$577$		−	42.3630i		−	1.76359i	−0.471629	−	0.881797i	$-0.656334\pi$
$577$		−	42.3630i		−	1.76359i	0.471629	−	0.881797i	$-0.343666\pi$
$578$		−	18.0779i		−	0.751940i
$579$		0			0
$580$		−	2.67389i		−	0.111027i
$581$	−23.8554	−	26.1125i	−0.989688	−	1.08333i
$582$		0			0
$583$	7.44475			0.308330
$584$	0.532690			0.0220429
$585$		0			0
$586$			9.91105i			0.409422i
$587$	2.05172			0.0846835			0.0423418	−	0.999103i	$-0.486518\pi$
$587$	2.05172			0.0846835			0.0423418	+	0.999103i	$0.486518\pi$
$588$		0			0
$589$	−7.03602			−0.289914
$590$		−	8.12823i		−	0.334634i
$591$		0			0
$592$	5.87575			0.241492
$593$	40.2640			1.65344			0.826721	−	0.562611i	$-0.190203\pi$
$593$	40.2640			1.65344			0.826721	+	0.562611i	$0.190203\pi$
$594$		0			0
$595$	21.3067	+	23.3227i	0.873489	+	0.956137i
$596$		−	3.26224i		−	0.133627i
$597$		0			0
$598$		0			0
$599$		−	35.6273i		−	1.45569i	−0.685741	−	0.727845i	$-0.740522\pi$
$599$		−	35.6273i		−	1.45569i	0.685741	−	0.727845i	$-0.259478\pi$
$600$		0			0
$601$			39.6574i			1.61766i	0.588044	+	0.808829i	$0.299898\pi$
$601$			39.6574i			1.61766i	−0.588044	+	0.808829i	$0.700102\pi$
$602$	−3.06480	+	2.79988i	−0.124912	+	0.114115i
$603$		0			0
$604$	14.1785			0.576916
$605$	2.01596			0.0819606
$606$		0			0
$607$			23.6444i			0.959698i	0.877351	+	0.479849i	$0.159309\pi$
$607$			23.6444i			0.959698i	−0.877351	+	0.479849i	$0.840691\pi$
$608$	−0.657927			−0.0266825
$609$		0			0
$610$	0.504949			0.0204448
$611$		0			0
$612$		0			0
$613$	−36.0654			−1.45667			−0.728333	−	0.685223i	$-0.759705\pi$
$613$	−36.0654			−1.45667			−0.728333	+	0.685223i	$0.759705\pi$
$614$	−1.64427			−0.0663572
$615$		0			0
$616$	−1.78450	−	1.95335i	−0.0718995	−	0.0787026i
$617$			2.45192i			0.0987108i	0.998781	+	0.0493554i	$0.0157167\pi$
$617$			2.45192i			0.0987108i	−0.998781	+	0.0493554i	$0.984283\pi$
$618$		0			0
$619$			12.9107i			0.518925i	0.965753	+	0.259462i	$0.0835453\pi$
$619$			12.9107i			0.518925i	−0.965753	+	0.259462i	$0.916455\pi$
$620$		−	21.5592i		−	0.865837i
$621$		0			0
$622$			2.14120i			0.0858544i
$623$	−9.31963	−	10.2014i	−0.373383	−	0.408712i
$624$		0			0
$625$	−19.4447			−0.777788
$626$	−12.7932			−0.511321
$627$		0			0
$628$			11.7596i			0.469259i
$629$	−34.8001			−1.38757
$630$		0			0
$631$	−6.53245			−0.260053			−0.130026	−	0.991511i	$-0.541506\pi$
$631$	−6.53245			−0.260053			−0.130026	+	0.991511i	$0.541506\pi$
$632$		−	12.7711i		−	0.508008i
$633$		0			0
$634$	6.51604			0.258785
$635$	−19.1615			−0.760401
$636$		0			0
$637$		0			0
$638$		−	1.32636i		−	0.0525110i
$639$		0			0
$640$		−	2.01596i		−	0.0796880i
$641$			6.03336i			0.238303i	0.992876	+	0.119152i	$0.0380175\pi$
$641$			6.03336i			0.238303i	−0.992876	+	0.119152i	$0.961983\pi$
$642$		0			0
$643$			9.21360i			0.363349i	0.983359	+	0.181675i	$0.0581517\pi$
$643$			9.21360i			0.363349i	−0.983359	+	0.181675i	$0.941848\pi$
$644$	−15.3841	+	14.0543i	−0.606217	+	0.553816i
$645$		0			0
$646$	3.89668			0.153313
$647$	−1.72732			−0.0679080			−0.0339540	−	0.999423i	$-0.510810\pi$
$647$	−1.72732			−0.0679080			−0.0339540	+	0.999423i	$0.510810\pi$
$648$		0			0
$649$		−	4.03193i		−	0.158267i
$650$		0			0
$651$		0			0
$652$	−12.5285			−0.490653
$653$		−	41.9575i		−	1.64193i	−0.570982	−	0.820963i	$-0.693437\pi$
$653$		−	41.9575i		−	1.64193i	0.570982	−	0.820963i	$-0.306563\pi$
$654$		0			0
$655$	−38.4723			−1.50324
$656$	−4.56462			−0.178218
$657$		0			0
$658$	−1.04053	+	0.950585i	−0.0405640	+	0.0370577i
$659$			10.3963i			0.404981i	0.979284	+	0.202490i	$0.0649035\pi$
$659$			10.3963i			0.404981i	−0.979284	+	0.202490i	$0.935097\pi$
$660$		0			0
$661$			34.0922i			1.32603i	0.748605	+	0.663016i	$0.230724\pi$
$661$			34.0922i			1.32603i	−0.748605	+	0.663016i	$0.769276\pi$
$662$			30.2159i			1.17437i
$663$		0			0
$664$		−	13.3681i		−	0.518783i
$665$	−2.59084	+	2.36689i	−0.100468	+	0.0917839i
$666$		0			0
$667$	−10.4461			−0.404474
$668$	−23.0722			−0.892691
$669$		0			0
$670$		−	15.7480i		−	0.608398i
$671$	0.250475			0.00966948
$672$		0			0
$673$	9.66513			0.372563			0.186282	−	0.982496i	$-0.440356\pi$
$673$	9.66513			0.372563			0.186282	+	0.982496i	$0.440356\pi$
$674$		−	24.8895i		−	0.958708i
$675$		0			0
$676$	−13.0000			−0.500000
$677$	45.8609			1.76258			0.881288	−	0.472579i	$-0.156677\pi$
$677$	45.8609			1.76258			0.881288	+	0.472579i	$0.156677\pi$
$678$		0			0
$679$	−5.30543	+	4.84683i	−0.203604	+	0.186004i
$680$			11.9399i			0.457873i
$681$		0			0
$682$		−	10.6942i		−	0.409503i
$683$			3.93190i			0.150450i	0.997167	+	0.0752250i	$0.0239675\pi$
$683$			3.93190i			0.150450i	−0.997167	+	0.0752250i	$0.976032\pi$
$684$		0			0
$685$			16.2371i			0.620389i
$686$	11.2078	+	14.7440i	0.427917	+	0.562927i
$687$		0			0
$688$	−1.56900			−0.0598175
$689$		0			0
$690$		0			0
$691$		−	17.6940i		−	0.673113i	−0.941663	−	0.336557i	$-0.890738\pi$
$691$		−	17.6940i		−	0.673113i	0.941663	−	0.336557i	$-0.109262\pi$
$692$	17.7244			0.673782
$693$		0			0
$694$	−9.09481			−0.345234
$695$			39.0542i			1.48141i
$696$		0			0
$697$	27.0347			1.02401
$698$	−31.8335			−1.20492
$699$		0			0
$700$	1.67009	+	1.82811i	0.0631234	+	0.0690960i
$701$		−	27.9189i		−	1.05448i	−0.849715	−	0.527242i	$-0.823226\pi$
$701$		−	27.9189i		−	1.05448i	0.849715	−	0.527242i	$-0.176774\pi$
$702$		0			0
$703$		−	3.86582i		−	0.145802i
$704$		−	1.00000i		−	0.0376889i
$705$		0			0
$706$		−	10.9052i		−	0.410422i
$707$	−6.09143	−	6.66779i	−0.229092	−	0.250768i
$708$		0			0
$709$	−25.4951			−0.957487			−0.478743	−	0.877955i	$-0.658908\pi$
$709$	−25.4951			−0.957487			−0.478743	+	0.877955i	$0.658908\pi$
$710$	−1.22879			−0.0461155
$711$		0			0
$712$		−	5.22255i		−	0.195723i
$713$	−84.2250			−3.15425
$714$		0			0
$715$		0			0
$716$			3.81164i			0.142448i
$717$		0			0
$718$	23.6874			0.884006
$719$	−43.0169			−1.60426			−0.802130	−	0.597150i	$-0.796300\pi$
$719$	−43.0169			−1.60426			−0.802130	+	0.597150i	$0.796300\pi$
$720$		0			0
$721$	−26.1125	+	23.8554i	−0.972482	+	0.888421i
$722$		−	18.5671i		−	0.690997i
$723$		0			0
$724$			19.1260i			0.710813i
$725$			1.24132i			0.0461015i
$726$		0			0
$727$			30.2686i			1.12260i	0.827613	+	0.561299i	$0.189698\pi$
$727$			30.2686i			1.12260i	−0.827613	+	0.561299i	$0.810302\pi$
$728$		0			0
$729$		0			0
$730$	1.07388			0.0397462
$731$	9.29264			0.343701
$732$		0			0
$733$			7.56291i			0.279342i	0.990198	+	0.139671i	$0.0446046\pi$
$733$			7.56291i			0.279342i	−0.990198	+	0.139671i	$0.955395\pi$
$734$	13.1176			0.484181
$735$		0			0
$736$	−7.87575			−0.290304
$737$		−	7.81164i		−	0.287745i
$738$		0			0
$739$	−17.1923			−0.632428			−0.316214	−	0.948688i	$-0.602412\pi$
$739$	−17.1923			−0.632428			−0.316214	+	0.948688i	$0.602412\pi$
$740$	11.8453			0.435442
$741$		0			0
$742$	−13.2852	−	14.5422i	−0.487714	−	0.533860i
$743$			23.9843i			0.879899i	0.898022	+	0.439950i	$0.145004\pi$
$743$			23.9843i			0.879899i	−0.898022	+	0.439950i	$0.854996\pi$
$744$		0			0
$745$		−	6.57657i		−	0.240947i
$746$		−	3.38649i		−	0.123988i
$747$		0			0
$748$			5.92266i			0.216554i
$749$	28.1287	−	25.6972i	1.02780	−	0.938956i
$750$		0			0
$751$	−32.4736			−1.18498			−0.592489	−	0.805579i	$-0.701855\pi$
$751$	−32.4736			−1.18498			−0.592489	+	0.805579i	$0.701855\pi$
$752$	−0.532690			−0.0194252
$753$		0			0
$754$		0			0
$755$	28.5834			1.04026
$756$		0			0
$757$	40.0315			1.45497			0.727485	−	0.686124i	$-0.240689\pi$
$757$	40.0315			1.45497			0.727485	+	0.686124i	$0.240689\pi$
$758$		−	8.52847i		−	0.309768i
$759$		0			0
$760$	−1.32636			−0.0481121
$761$	−20.6923			−0.750097			−0.375048	−	0.927005i	$-0.622374\pi$
$761$	−20.6923			−0.750097			−0.375048	+	0.927005i	$0.622374\pi$
$762$		0			0
$763$	−6.08764	−	6.66364i	−0.220387	−	0.241240i
$764$		−	21.6665i		−	0.783865i
$765$		0			0
$766$		−	10.1180i		−	0.365578i
$767$		0			0
$768$		0			0
$769$			33.6030i			1.21176i	0.795557	+	0.605878i	$0.207178\pi$
$769$			33.6030i			1.21176i	−0.795557	+	0.605878i	$0.792822\pi$
$770$	−3.59749	−	3.93788i	−0.129644	−	0.141911i
$771$		0			0
$772$	21.6233			0.778239
$773$	−13.9825			−0.502916			−0.251458	−	0.967868i	$-0.580910\pi$
$773$	−13.9825			−0.502916			−0.251458	+	0.967868i	$0.580910\pi$
$774$		0			0
$775$			10.0086i			0.359518i
$776$	−2.71607			−0.0975014
$777$		0			0
$778$	−16.7920			−0.602024
$779$			3.00319i			0.107600i
$780$		0			0
$781$	−0.609527			−0.0218106
$782$	46.6454			1.66804
$783$		0			0
$784$	−0.631122	+	6.97149i	−0.0225401	+	0.248982i
$785$			23.7069i			0.846137i
$786$		0			0
$787$		−	20.4800i		−	0.730034i	−0.931001	−	0.365017i	$-0.881063\pi$
$787$		−	20.4800i		−	0.730034i	0.931001	−	0.365017i	$-0.118937\pi$
$788$		−	21.6914i		−	0.772723i
$789$		0			0
$790$		−	25.7461i		−	0.916006i
$791$	9.68757	−	8.85018i	0.344450	−	0.314676i
$792$		0			0
$793$		0			0
$794$	−13.4856			−0.478585
$795$		0			0
$796$		−	3.94621i		−	0.139870i
$797$	38.1741			1.35220			0.676098	−	0.736812i	$-0.263670\pi$
$797$	38.1741			1.35220			0.676098	+	0.736812i	$0.263670\pi$
$798$		0			0
$799$	3.15494			0.111614
$800$			0.935886i			0.0330886i

Overview	Random
Universe	Knowledge

Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ zeros

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.g (of order \(2\), degree \(1\), minimal)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

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