LMFDB - Embedded newform 668.2.e.a.297.3

Newspace parameters

Level:	$ N $	$=$	$ 668 = 2^{2} \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	668.e (of order $83$, degree $82$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.33400685502$
Analytic rank:	$0$
Dimension:	$1148$
Relative dimension:	$14$ over $\Q(\zeta_{83})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label			297.3
Character	$\chi$	$=$	668.297
Dual form			668.2.e.a.9.3

$q$-expansion

$f(q)$	$=$	$q+(-0.342745 + 2.57205i) q^{3} +(-0.628586 + 0.277966i) q^{5} +(-1.47454 - 3.17087i) q^{7} +(-3.60268 - 0.977525i) q^{9} +O(q^{10})$	\(q+(-0.342745 + 2.57205i) q^{3} +(-0.628586 + 0.277966i) q^{5} +(-1.47454 - 3.17087i) q^{7} +(-3.60268 - 0.977525i) q^{9} +(-0.684433 - 0.877554i) q^{11} +(-1.75582 - 3.42993i) q^{13} +(-0.499499 - 1.71203i) q^{15} +(0.451009 - 0.0342072i) q^{17} +(-4.29462 - 6.46039i) q^{19} +(8.66104 - 2.70581i) q^{21} +(1.87555 - 0.745869i) q^{23} +(-3.04651 + 3.34934i) q^{25} +(0.736103 - 1.75360i) q^{27} +(-0.785163 - 0.312244i) q^{29} +(-1.72875 - 0.399495i) q^{31} +(2.49170 - 1.45962i) q^{33} +(1.80827 + 1.58329i) q^{35} +(-3.03378 + 0.823165i) q^{37} +(9.42376 - 3.34047i) q^{39} +(8.80006 + 4.29666i) q^{41} +(0.281863 + 2.96980i) q^{43} +(2.53631 - 0.386964i) q^{45} +(0.207333 - 10.9540i) q^{47} +(-3.36935 + 3.99834i) q^{49} +(-0.0665982 + 1.17174i) q^{51} +(1.65631 - 9.63007i) q^{53} +(0.674155 + 0.361369i) q^{55} +(18.0884 - 8.83174i) q^{57} +(-11.8163 - 0.896218i) q^{59} +(10.0304 + 10.2220i) q^{61} +(2.21270 + 12.8650i) q^{63} +(2.05709 + 1.66795i) q^{65} +(-4.03799 - 1.78563i) q^{67} +(1.27558 + 5.07965i) q^{69} +(-8.69542 - 0.991644i) q^{71} +(-1.19028 - 0.892634i) q^{73} +(-7.57052 - 8.98376i) q^{75} +(-1.77338 + 3.46424i) q^{77} +(-2.45274 - 6.52457i) q^{79} +(-5.40490 - 3.16615i) q^{81} +(-1.50388 - 2.08647i) q^{83} +(-0.273989 + 0.146867i) q^{85} +(1.07222 - 1.91246i) q^{87} +(1.02809 - 3.52376i) q^{89} +(-8.28682 + 10.6251i) q^{91} +(1.62004 - 4.30950i) q^{93} +(4.49531 + 2.86715i) q^{95} +(-2.71211 + 0.626740i) q^{97} +(1.60796 + 3.83060i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1148q - 2q^{5} - 14q^{9} + O(q^{10}) $	$ 1148q - 2q^{5} - 14q^{9} + 2q^{11} + 4q^{13} + 14q^{15} + 2q^{17} + 2q^{19} + 14q^{23} - 6q^{25} + 2q^{29} - 2q^{31} + 16q^{33} - 2q^{35} + 10q^{37} + 6q^{39} + 4q^{41} + 4q^{43} - 2q^{45} + 2q^{47} - 30q^{49} - 2q^{51} - 6q^{55} - 4q^{57} + 6q^{59} + 2q^{61} + 14q^{63} + 22q^{65} + 12q^{67} - 14q^{69} - 8q^{71} - 18q^{73} - 26q^{75} - 2q^{79} - 6q^{81} - 22q^{83} + 34q^{85} + 2q^{87} + 14q^{89} - 6q^{91} + 32q^{93} - 8q^{95} + 44q^{97} + 2q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$.

$n$	$5$	$335$
$\chi(n)$	$e\left(\frac{72}{83}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.342745	+	2.57205i	−0.197884	+	1.48498i	0.557765	+	0.829999i	$0.311659\pi$
$3$	−0.342745	+	2.57205i	−0.197884	+	1.48498i	−0.755648	+	0.654977i	$0.772678\pi$
$4$		0			0
$5$	−0.628586	+	0.277966i	−0.281112	+	0.124310i	−0.540181	−	0.841549i	$-0.681644\pi$
$5$	−0.628586	+	0.277966i	−0.281112	+	0.124310i	0.259069	+	0.965859i	$0.416584\pi$
$6$		0			0
$7$	−1.47454	−	3.17087i	−0.557325	−	1.19848i	−0.959186	−	0.282775i	$-0.908745\pi$
$7$	−1.47454	−	3.17087i	−0.557325	−	1.19848i	0.401861	−	0.915701i	$-0.368364\pi$
$8$		0			0
$9$	−3.60268	−	0.977525i	−1.20089	−	0.325842i
$10$		0			0
$11$	−0.684433	−	0.877554i	−0.206364	−	0.264593i	0.674169	−	0.738577i	$-0.264502\pi$
$11$	−0.684433	−	0.877554i	−0.206364	−	0.264593i	−0.880533	+	0.473985i	$0.842815\pi$
$12$		0			0
$13$	−1.75582	−	3.42993i	−0.486977	−	0.951291i	−0.995898	−	0.0904779i	$-0.971161\pi$
$13$	−1.75582	−	3.42993i	−0.486977	−	0.951291i	0.508922	−	0.860813i	$-0.330044\pi$
$14$		0			0
$15$	−0.499499	−	1.71203i	−0.128970	−	0.442044i
$16$		0			0
$17$	0.451009	−	0.0342072i	0.109386	−	0.00829646i	−0.0208221	−	0.999783i	$-0.506628\pi$
$17$	0.451009	−	0.0342072i	0.109386	−	0.00829646i	0.130208	+	0.991487i	$0.458436\pi$
$18$		0			0
$19$	−4.29462	−	6.46039i	−0.985254	−	1.48212i	−0.872573	−	0.488484i	$-0.837550\pi$
$19$	−4.29462	−	6.46039i	−0.985254	−	1.48212i	−0.112681	−	0.993631i	$-0.535944\pi$
$20$		0			0
$21$	8.66104	−	2.70581i	1.88999	−	0.590456i
$22$		0			0
$23$	1.87555	−	0.745869i	0.391079	−	0.155524i	−0.165718	−	0.986173i	$-0.552994\pi$
$23$	1.87555	−	0.745869i	0.391079	−	0.155524i	0.556797	+	0.830649i	$0.312030\pi$
$24$		0			0
$25$	−3.04651	+	3.34934i	−0.609302	+	0.669868i
$26$		0			0
$27$	0.736103	−	1.75360i	0.141663	−	0.337480i
$28$		0			0
$29$	−0.785163	−	0.312244i	−0.145801	−	0.0579823i	0.295492	−	0.955345i	$-0.404516\pi$
$29$	−0.785163	−	0.312244i	−0.145801	−	0.0579823i	−0.441293	+	0.897363i	$0.645480\pi$
$30$		0			0
$31$	−1.72875	−	0.399495i	−0.310492	−	0.0717515i	0.0670335	−	0.997751i	$-0.478647\pi$
$31$	−1.72875	−	0.399495i	−0.310492	−	0.0717515i	−0.377525	+	0.925999i	$0.623225\pi$
$32$		0			0
$33$	2.49170	−	1.45962i	0.433750	−	0.254087i
$34$		0			0
$35$	1.80827	+	1.58329i	0.305654	+	0.267625i
$36$		0			0
$37$	−3.03378	+	0.823165i	−0.498751	+	0.135328i	−0.502347	−	0.864666i	$-0.667530\pi$
$37$	−3.03378	+	0.823165i	−0.498751	+	0.135328i	0.00359603	+	0.999994i	$0.498855\pi$
$38$		0			0
$39$	9.42376	−	3.34047i	1.50901	−	0.534904i
$40$		0			0
$41$	8.80006	+	4.29666i	1.37434	+	0.671025i	0.969892	−	0.243536i	$-0.0783075\pi$
$41$	8.80006	+	4.29666i	1.37434	+	0.671025i	0.404447	+	0.914562i	$0.367464\pi$
$42$		0			0
$43$	0.281863	+	2.96980i	0.0429837	+	0.452890i	0.990922	+	0.134437i	$0.0429225\pi$
$43$	0.281863	+	2.96980i	0.0429837	+	0.452890i	−0.947938	+	0.318454i	$0.896837\pi$
$44$		0			0
$45$	2.53631	−	0.386964i	0.378091	−	0.0576852i
$46$		0			0
$47$	0.207333	−	10.9540i	0.0302426	−	1.59781i	−0.586037	−	0.810284i	$-0.699313\pi$
$47$	0.207333	−	10.9540i	0.0302426	−	1.59781i	0.616279	−	0.787528i	$-0.288639\pi$
$48$		0			0
$49$	−3.36935	+	3.99834i	−0.481336	+	0.571191i
$50$		0			0
$51$	−0.0665982	+	1.17174i	−0.00932561	+	0.164077i
$52$		0			0
$53$	1.65631	−	9.63007i	0.227512	−	1.32279i	−0.616877	−	0.787060i	$-0.711602\pi$
$53$	1.65631	−	9.63007i	0.227512	−	1.32279i	0.844388	−	0.535731i	$-0.179964\pi$
$54$		0			0
$55$	0.674155	+	0.361369i	0.0909030	+	0.0487270i
$56$		0			0
$57$	18.0884	−	8.83174i	2.39587	−	1.16979i
$58$		0			0
$59$	−11.8163	−	0.896218i	−1.53835	−	0.116678i	−0.721047	−	0.692886i	$-0.756339\pi$
$59$	−11.8163	−	0.896218i	−1.53835	−	0.116678i	−0.817303	+	0.576209i	$0.804532\pi$
$60$		0			0
$61$	10.0304	+	10.2220i	1.28426	+	1.30880i	0.927128	+	0.374744i	$0.122269\pi$
$61$	10.0304	+	10.2220i	1.28426	+	1.30880i	0.357132	+	0.934054i	$0.383755\pi$
$62$		0			0
$63$	2.21270	+	12.8650i	0.278775	+	1.62084i
$64$		0			0
$65$	2.05709	+	1.66795i	0.255150	+	0.206883i
$66$		0			0
$67$	−4.03799	−	1.78563i	−0.493319	−	0.218150i	0.142784	−	0.989754i	$-0.454395\pi$
$67$	−4.03799	−	1.78563i	−0.493319	−	0.218150i	−0.636103	+	0.771604i	$0.719455\pi$
$68$		0			0
$69$	1.27558	+	5.07965i	0.153562	+	0.611519i
$70$		0			0
$71$	−8.69542	−	0.991644i	−1.03196	−	0.117686i	−0.419148	−	0.907918i	$-0.637671\pi$
$71$	−8.69542	−	0.991644i	−1.03196	−	0.117686i	−0.612808	+	0.790231i	$0.709960\pi$
$72$		0			0
$73$	−1.19028	−	0.892634i	−0.139312	−	0.104475i	0.528032	−	0.849225i	$-0.322930\pi$
$73$	−1.19028	−	0.892634i	−0.139312	−	0.104475i	−0.667344	+	0.744750i	$0.732569\pi$
$74$		0			0
$75$	−7.57052	−	8.98376i	−0.874168	−	1.03735i
$76$		0			0
$77$	−1.77338	+	3.46424i	−0.202096	+	0.394787i
$78$		0			0
$79$	−2.45274	−	6.52457i	−0.275955	−	0.734072i	−0.999061	−	0.0433345i	$-0.986202\pi$
$79$	−2.45274	−	6.52457i	−0.275955	−	0.734072i	0.723106	−	0.690737i	$-0.242714\pi$
$80$		0			0
$81$	−5.40490	−	3.16615i	−0.600544	−	0.351794i
$82$		0			0
$83$	−1.50388	−	2.08647i	−0.165072	−	0.229020i	0.720578	−	0.693374i	$-0.243877\pi$
$83$	−1.50388	−	2.08647i	−0.165072	−	0.229020i	−0.885649	+	0.464355i	$0.846286\pi$
$84$		0			0
$85$	−0.273989	+	0.146867i	−0.0297183	+	0.0159300i
$86$		0			0
$87$	1.07222	−	1.91246i	0.114954	−	0.205038i
$88$		0			0
$89$	1.02809	−	3.52376i	0.108977	−	0.373517i	−0.887146	−	0.461489i	$-0.847315\pi$
$89$	1.02809	−	3.52376i	0.108977	−	0.373517i	0.996123	+	0.0879713i	$0.0280384\pi$
$90$		0			0
$91$	−8.28682	+	10.6251i	−0.868695	+	1.11381i
$92$		0			0
$93$	1.62004	−	4.30950i	0.167991	−	0.446875i
$94$		0			0
$95$	4.49531	+	2.86715i	0.461209	+	0.294163i
$96$		0			0
$97$	−2.71211	+	0.626740i	−0.275373	+	0.0636358i	−0.360583	−	0.932727i	$-0.617422\pi$
$97$	−2.71211	+	0.626740i	−0.275373	+	0.0636358i	0.0852100	+	0.996363i	$0.472844\pi$
$98$		0			0
$99$	1.60796	+	3.83060i	0.161606	+	0.384989i
$100$		0			0
$101$	−0.783642	+	8.25670i	−0.0779753	+	0.821573i	0.867835	+	0.496853i	$0.165511\pi$
$101$	−0.783642	+	8.25670i	−0.0779753	+	0.821573i	−0.945810	+	0.324720i	$0.894730\pi$
$102$		0			0
$103$	1.29322	+	0.895429i	0.127425	+	0.0882292i	0.631263	−	0.775569i	$-0.282537\pi$
$103$	1.29322	+	0.895429i	0.127425	+	0.0882292i	−0.503838	+	0.863798i	$0.668079\pi$
$104$		0			0
$105$	−4.69208	+	4.10831i	−0.457901	+	0.400930i
$106$		0			0
$107$	−10.2876	+	7.12314i	−0.994539	+	0.688620i	−0.950601	−	0.310414i	$-0.899532\pi$
$107$	−10.2876	+	7.12314i	−0.994539	+	0.688620i	−0.0439371	+	0.999034i	$0.513990\pi$
$108$		0			0
$109$	−13.9444	+	8.89388i	−1.33563	+	0.851880i	−0.996058	−	0.0886995i	$-0.971729\pi$
$109$	−13.9444	+	8.89388i	−1.33563	+	0.851880i	−0.339575	+	0.940579i	$0.610283\pi$
$110$		0			0
$111$	−1.07741	−	8.08520i	−0.102263	−	0.767413i
$112$		0			0
$113$	−0.974842	−	1.59418i	−0.0917055	−	0.149968i	0.803980	−	0.594657i	$-0.202712\pi$
$113$	−0.974842	−	1.59418i	−0.0917055	−	0.149968i	−0.895685	+	0.444689i	$0.853314\pi$
$114$		0			0
$115$	−0.971616	+	0.990181i	−0.0906037	+	0.0923348i
$116$		0			0
$117$	2.97282	+	14.0733i	0.274837	+	1.30108i
$118$		0			0
$119$	−0.773499	−	1.37965i	−0.0709065	−	0.126472i
$120$		0			0
$121$	2.37744	−	9.46751i	0.216131	−	0.860682i
$122$		0			0
$123$	−14.0674	+	21.1616i	−1.26842	+	1.90808i
$124$		0			0
$125$	2.07064	−	6.21236i	0.185204	−	0.555650i
$126$		0			0
$127$	18.8365	−	2.14816i	1.67147	−	0.190618i	0.774459	−	0.632624i	$-0.218022\pi$
$127$	18.8365	−	2.14816i	1.67147	−	0.190618i	0.897012	+	0.442005i	$0.145733\pi$
$128$		0			0
$129$	−7.73510	−	0.292917i	−0.681037	−	0.0257899i
$130$		0			0
$131$	−0.696551	−	12.2553i	−0.0608580	−	1.07075i	−0.873136	−	0.487477i	$-0.837917\pi$
$131$	−0.696551	−	12.2553i	−0.0608580	−	1.07075i	0.812278	−	0.583271i	$-0.198227\pi$
$132$		0			0
$133$	−14.1524	+	23.1438i	−1.22717	+	2.00682i
$134$		0			0
$135$	0.0247363	+	1.30690i	0.00212896	+	0.112480i
$136$		0			0
$137$	−2.87001	−	1.01734i	−0.245201	−	0.0869173i	0.208665	−	0.977987i	$-0.433088\pi$
$137$	−2.87001	−	1.01734i	−0.245201	−	0.0869173i	−0.453866	+	0.891070i	$0.649956\pi$
$138$		0			0
$139$	−13.9728	+	13.2012i	−1.18516	+	1.11971i	−0.194851	+	0.980833i	$0.562422\pi$
$139$	−13.9728	+	13.2012i	−1.18516	+	1.11971i	−0.990309	+	0.138879i	$0.955650\pi$
$140$		0			0
$141$	28.1033	+	4.28772i	2.36673	+	0.361091i
$142$		0			0
$143$	−1.80821	+	3.88838i	−0.151210	+	0.325163i
$144$		0			0
$145$	0.580335	−	0.0219765i	0.0481942	−	0.00182505i
$146$		0			0
$147$	−9.12911	−	10.0366i	−0.752956	−	0.827803i
$148$		0			0
$149$	5.90270	−	4.78608i	0.483568	−	0.392091i	−0.356737	−	0.934205i	$-0.616111\pi$
$149$	5.90270	−	4.78608i	0.483568	−	0.392091i	0.840305	+	0.542114i	$0.182376\pi$
$150$		0			0
$151$	1.26088	−	0.945573i	0.102609	−	0.0769497i	−0.547427	−	0.836854i	$-0.684393\pi$
$151$	1.26088	−	0.945573i	0.102609	−	0.0769497i	0.650035	+	0.759904i	$0.274754\pi$
$152$		0			0
$153$	−1.65828	−	0.317635i	−0.134064	−	0.0256792i
$154$		0			0
$155$	1.19771	−	0.229415i	0.0962024	−	0.0184271i
$156$		0			0
$157$	1.33505	−	6.32011i	0.106548	−	0.504399i	−0.892072	−	0.451893i	$-0.850749\pi$
$157$	1.33505	−	6.32011i	0.106548	−	0.504399i	0.998621	−	0.0525064i	$-0.0167210\pi$
$158$		0			0
$159$	24.2014	+	7.56078i	1.91929	+	0.599609i
$160$		0			0
$161$	−5.13063	−	4.84730i	−0.404350	−	0.382021i
$162$		0			0
$163$	2.63149	+	7.89501i	0.206114	+	0.618385i	0.999947	+	0.0102502i	$0.00326278\pi$
$163$	2.63149	+	7.89501i	0.206114	+	0.618385i	−0.793834	+	0.608135i	$0.791918\pi$
$164$		0			0
$165$	−1.16052	+	1.61011i	−0.0903467	+	0.125347i
$166$		0			0
$167$	9.42530	−	8.84102i	0.729352	−	0.684139i
$167$	9.42530	−	8.84102i	0.729352	−	0.684139i
$168$		0			0
$169$	−1.08015	+	1.49860i	−0.0830888	+	0.115277i
$170$		0			0
$171$	9.15696	+	27.4728i	0.700250	+	2.10090i
$172$		0			0
$173$	−5.14672	−	4.86250i	−0.391298	−	0.369689i	0.465759	−	0.884912i	$-0.345781\pi$
$173$	−5.14672	−	4.86250i	−0.391298	−	0.369689i	−0.857056	+	0.515223i	$0.827709\pi$
$174$		0			0
$175$	15.1125	+	4.72133i	1.14240	+	0.356899i
$176$		0			0
$177$	6.35509	−	30.0850i	0.477678	−	2.26132i
$178$		0			0
$179$	−5.78349	+	1.10780i	−0.432279	+	0.0828008i	−0.399652	−	0.916667i	$-0.630869\pi$
$179$	−5.78349	+	1.10780i	−0.432279	+	0.0828008i	−0.0326264	+	0.999468i	$0.510387\pi$
$180$		0			0
$181$	4.02778	+	0.771500i	0.299382	+	0.0573452i	0.335618	−	0.941998i	$-0.391055\pi$
$181$	4.02778	+	0.771500i	0.299382	+	0.0573452i	−0.0362358	+	0.999343i	$0.511537\pi$
$182$		0			0
$183$	−29.7295	+	22.2952i	−2.19767	+	1.64811i
$184$		0			0
$185$	1.67818	−	1.36072i	0.123382	−	0.100042i
$186$		0			0
$187$	−0.338704	−	0.372372i	−0.0247685	−	0.0272305i
$188$		0			0
$189$	−6.64585	+	0.251669i	−0.483414	+	0.0183062i
$190$		0			0
$191$	−7.00703	+	15.0680i	−0.507011	+	1.09028i	0.471078	+	0.882092i	$0.343865\pi$
$191$	−7.00703	+	15.0680i	−0.507011	+	1.09028i	−0.978089	+	0.208188i	$0.933243\pi$
$192$		0			0
$193$	4.06364	+	0.619988i	0.292507	+	0.0446277i	0.295418	−	0.955368i	$-0.404541\pi$
$193$	4.06364	+	0.619988i	0.292507	+	0.0446277i	−0.00291102	+	0.999996i	$0.500927\pi$
$194$		0			0
$195$	−4.99510	+	4.71926i	−0.357707	+	0.337953i
$196$		0			0
$197$	13.1975	+	4.67815i	0.940280	+	0.333304i	0.759713	−	0.650258i	$-0.225339\pi$
$197$	13.1975	+	4.67815i	0.940280	+	0.333304i	0.180567	+	0.983563i	$0.442207\pi$
$198$		0			0
$199$	0.108310	+	5.72234i	0.00767787	+	0.405646i	0.982871	+	0.184292i	$0.0589993\pi$
$199$	0.108310	+	5.72234i	0.00767787	+	0.405646i	−0.975194	+	0.221354i	$0.928952\pi$
$200$		0			0
$201$	5.97675	−	9.77392i	0.421568	−	0.689399i
$202$		0			0
$203$	0.167673	+	2.95007i	0.0117683	+	0.207054i
$204$		0			0
$205$	−6.72592	−	0.254701i	−0.469758	−	0.0177891i
$206$		0			0
$207$	−7.48610	+	0.853731i	−0.520320	+	0.0593384i
$208$		0			0
$209$	−2.72996	+	8.19047i	−0.188836	+	0.566547i
$210$		0			0
$211$	0.530613	−	0.798200i	0.0365289	−	0.0549503i	−0.814064	−	0.580776i	$-0.802749\pi$
$211$	0.530613	−	0.798200i	0.0365289	−	0.0549503i	0.850593	+	0.525825i	$0.176243\pi$
$212$		0			0
$213$	5.53087	−	22.0252i	0.378969	−	1.50914i
$214$		0			0
$215$	−1.00268	−	1.78843i	−0.0683821	−	0.121970i
$216$		0			0
$217$	1.28236	+	6.07070i	0.0870525	+	0.412106i
$218$		0			0
$219$	2.70387	−	2.75553i	0.182710	−	0.186201i
$220$		0			0
$221$	−0.909218	−	1.48687i	−0.0611606	−	0.100017i
$222$		0			0
$223$	−1.78496	−	13.3949i	−0.119530	−	0.896986i	−0.943737	−	0.330697i	$-0.892716\pi$
$223$	−1.78496	−	13.3949i	−0.119530	−	0.896986i	0.824207	−	0.566289i	$-0.191621\pi$
$224$		0			0
$225$	14.2497	−	9.08857i	0.949977	−	0.605904i
$226$		0			0
$227$	9.19734	−	6.36826i	0.610449	−	0.422676i	−0.223354	−	0.974737i	$-0.571701\pi$
$227$	9.19734	−	6.36826i	0.610449	−	0.422676i	0.833804	+	0.552061i	$0.186159\pi$
$228$		0			0
$229$	−1.13129	+	0.990539i	−0.0747578	+	0.0654566i	−0.695318	−	0.718702i	$-0.744737\pi$
$229$	−1.13129	+	0.990539i	−0.0747578	+	0.0654566i	0.620560	+	0.784159i	$0.286905\pi$
$230$		0			0
$231$	−8.30240	−	5.74859i	−0.546258	−	0.378230i
$232$		0			0
$233$	−1.32294	+	13.9389i	−0.0866686	+	0.913168i	0.841315	+	0.540546i	$0.181782\pi$
$233$	−1.32294	+	13.9389i	−0.0866686	+	0.913168i	−0.927983	+	0.372622i	$0.878459\pi$
$234$		0			0
$235$	2.91452	+	6.94319i	0.190123	+	0.452924i
$236$		0			0
$237$	17.6222	−	4.07231i	1.14469	−	0.264525i
$238$		0			0
$239$	−3.76269	−	2.39988i	−0.243388	−	0.155235i	0.410418	−	0.911898i	$-0.365383\pi$
$239$	−3.76269	−	2.39988i	−0.243388	−	0.155235i	−0.653806	+	0.756662i	$0.726829\pi$
$240$		0			0
$241$	−1.80058	+	4.78976i	−0.115986	+	0.308536i	−0.981238	−	0.192801i	$-0.938243\pi$
$241$	−1.80058	+	4.78976i	−0.115986	+	0.308536i	0.865252	+	0.501337i	$0.167158\pi$
$242$		0			0
$243$	13.5049	−	17.3154i	0.866338	−	1.11079i
$244$		0			0
$245$	1.00653	−	3.44986i	0.0643046	−	0.220404i
$246$		0			0
$247$	−14.6181	+	26.0735i	−0.930126	+	1.65902i
$248$		0			0
$249$	5.88196	−	3.15292i	0.372754	−	0.199808i
$250$		0			0
$251$	10.1718	+	14.1123i	0.642039	+	0.890762i	0.999061	−	0.0433343i	$-0.0137980\pi$
$251$	10.1718	+	14.1123i	0.642039	+	0.890762i	−0.357021	+	0.934096i	$0.616208\pi$
$252$		0			0
$253$	−1.93823	−	1.13540i	−0.121855	−	0.0713819i
$254$		0			0
$255$	−0.283842	−	0.755053i	−0.0177749	−	0.0472833i
$256$		0			0
$257$	13.5416	−	26.4529i	0.844699	−	1.65009i	0.0881912	−	0.996104i	$-0.471891\pi$
$257$	13.5416	−	26.4529i	0.844699	−	1.65009i	0.756508	−	0.653984i	$-0.226904\pi$
$258$		0			0
$259$	7.08360	+	8.40594i	0.440153	+	0.522320i
$260$		0			0
$261$	2.52346	+	1.89243i	0.156199	+	0.117139i
$262$		0			0
$263$	8.07758	+	0.921184i	0.498085	+	0.0568027i	0.358733	−	0.933440i	$-0.383209\pi$
$263$	8.07758	+	0.921184i	0.498085	+	0.0568027i	0.139352	+	0.990243i	$0.455498\pi$
$264$		0			0
$265$	1.63570	+	6.51372i	0.100480	+	0.400135i
$266$		0			0
$267$	8.71092	+	3.85204i	0.533100	+	0.235741i
$268$		0			0
$269$	14.6225	+	11.8563i	0.891548	+	0.722893i	0.961543	−	0.274654i	$-0.0885634\pi$
$269$	14.6225	+	11.8563i	0.891548	+	0.722893i	−0.0699951	+	0.997547i	$0.522298\pi$
$270$		0			0
$271$	−0.249854	−	1.45269i	−0.0151775	−	0.0882446i	0.976952	−	0.213457i	$-0.0684724\pi$
$271$	−0.249854	−	1.45269i	−0.0151775	−	0.0882446i	−0.992130	+	0.125213i	$0.960039\pi$
$272$		0			0
$273$	−24.4880	−	24.9558i	−1.48208	−	1.51040i
$274$		0			0
$275$	5.02436	+	0.381077i	0.302980	+	0.0229798i
$276$		0			0
$277$	−16.5315	+	8.07157i	−0.993282	+	0.484973i	−0.862293	−	0.506410i	$-0.830972\pi$
$277$	−16.5315	+	8.07157i	−0.993282	+	0.484973i	−0.130990	+	0.991384i	$0.541815\pi$
$278$		0			0
$279$	5.83760	+	3.12914i	0.349488	+	0.187337i
$280$		0			0
$281$	−0.355865	+	2.06905i	−0.0212291	+	0.123429i	−0.994210	−	0.107458i	$-0.965729\pi$
$281$	−0.355865	+	2.06905i	−0.0212291	+	0.123429i	0.972981	+	0.230887i	$0.0741628\pi$
$282$		0			0
$283$	0.480369	−	8.45171i	0.0285550	−	0.502402i	−0.951993	−	0.306121i	$-0.900969\pi$
$283$	0.480369	−	8.45171i	0.0285550	−	0.502402i	0.980548	−	0.196281i	$-0.0628866\pi$
$284$		0			0
$285$	−8.91521	+	10.5795i	−0.528091	+	0.626674i
$286$		0			0
$287$	0.648068	−	34.2395i	0.0382542	−	2.02109i
$288$		0			0
$289$	−16.6033	+	2.53316i	−0.976664	+	0.149009i
$290$		0			0
$291$	−0.682449	−	7.19050i	−0.0400058	−	0.421515i
$292$		0			0
$293$	−28.6730	−	13.9997i	−1.67510	−	0.817871i	−0.996521	−	0.0833408i	$-0.973441\pi$
$293$	−28.6730	−	13.9997i	−1.67510	−	0.817871i	−0.678576	−	0.734531i	$-0.737402\pi$
$294$		0			0
$295$	7.67667	−	2.72118i	0.446953	−	0.158433i
$296$		0			0
$297$	−2.04269	+	0.554249i	−0.118529	+	0.0321608i
$298$		0			0
$299$	−5.85140	−	5.12338i	−0.338395	−	0.296293i
$300$		0			0
$301$	9.00123	−	5.27285i	0.518822	−	0.303922i
$302$		0			0
$303$	−20.9681	−	4.84551i	−1.20459	−	0.278367i
$304$		0			0
$305$	−9.14634	−	3.63732i	−0.523718	−	0.208272i
$306$		0			0
$307$	0.0140733	−	0.0335264i	0.000803204	−	0.00191345i	−0.921657	−	0.388007i	$-0.873164\pi$
$307$	0.0140733	−	0.0335264i	0.000803204	−	0.00191345i	0.922460	+	0.386093i	$0.126176\pi$
$308$		0			0
$309$	−2.74634	+	3.01933i	−0.156234	+	0.171764i
$310$		0			0
$311$	17.2635	−	6.86536i	0.978924	−	0.389299i	0.175352	−	0.984506i	$-0.443894\pi$
$311$	17.2635	−	6.86536i	0.978924	−	0.389299i	0.803572	+	0.595207i	$0.202930\pi$
$312$		0			0
$313$	19.7941	−	6.18389i	1.11883	−	0.349534i	0.317797	−	0.948159i	$-0.397057\pi$
$313$	19.7941	−	6.18389i	1.11883	−	0.349534i	0.801030	+	0.598624i	$0.204286\pi$
$314$		0			0
$315$	−4.96691	−	7.47171i	−0.279854	−	0.420983i
$316$		0			0
$317$	23.3162	−	1.76844i	1.30957	−	0.0993254i	0.597746	−	0.801686i	$-0.296063\pi$
$317$	23.3162	−	1.76844i	1.30957	−	0.0993254i	0.711822	+	0.702360i	$0.247870\pi$
$318$		0			0
$319$	0.263380	+	0.902733i	0.0147465	+	0.0505434i
$320$		0			0
$321$	−14.7951	−	28.9017i	−0.825782	−	1.61313i
$322$		0			0
$323$	−2.15790	−	2.76678i	−0.120069	−	0.153948i
$324$		0			0
$325$	16.8371	+	4.56846i	0.933955	+	0.253413i
$326$		0			0
$327$	−18.0962	−	38.9141i	−1.00072	−	2.15196i
$328$		0			0
$329$	−35.0396	+	15.4948i	−1.93179	+	0.854256i
$330$		0			0
$331$	−0.837922	+	6.28800i	−0.0460564	+	0.345620i	0.953030	+	0.302877i	$0.0979471\pi$
$331$	−0.837922	+	6.28800i	−0.0460564	+	0.345620i	−0.999086	+	0.0427432i	$0.986390\pi$
$332$		0			0
$333$	11.7344			0.643042
$334$		0			0
$335$	3.03457			0.165796
$336$		0			0
$337$	−4.11955	+	30.9142i	−0.224406	+	1.68401i	0.410849	+	0.911703i	$0.365232\pi$
$337$	−4.11955	+	30.9142i	−0.224406	+	1.68401i	−0.635255	+	0.772302i	$0.719105\pi$
$338$		0			0
$339$	4.43445	−	1.96095i	0.240846	−	0.106504i
$340$		0			0
$341$	0.832631	+	1.79050i	0.0450895	+	0.0969608i
$342$		0			0
$343$	−5.97803	−	1.62204i	−0.322783	−	0.0875817i
$344$		0			0
$345$	−2.21378	−	2.83843i	−0.119186	−	0.152816i
$346$		0			0
$347$	−15.4454	−	30.1721i	−0.829154	−	1.61972i	−0.784016	−	0.620740i	$-0.786832\pi$
$347$	−15.4454	−	30.1721i	−0.829154	−	1.61972i	−0.0451374	−	0.998981i	$-0.514373\pi$
$348$		0			0
$349$	−5.73871	−	19.6694i	−0.307186	−	1.05288i	−0.956349	−	0.292227i	$-0.905604\pi$
$349$	−5.73871	−	19.6694i	−0.307186	−	1.05288i	0.649163	−	0.760649i	$-0.275119\pi$
$350$		0			0
$351$	−7.30718	+	0.554220i	−0.390028	+	0.0295821i
$352$		0			0
$353$	−7.38945	−	11.1159i	−0.393301	−	0.591641i	0.581820	−	0.813318i	$-0.302341\pi$
$353$	−7.38945	−	11.1159i	−0.393301	−	0.591641i	−0.975120	+	0.221677i	$0.928847\pi$
$354$		0			0
$355$	5.74146	−	1.79370i	0.304725	−	0.0951995i
$356$		0			0
$357$	3.81365	−	1.51661i	0.201840	−	0.0802677i
$358$		0			0
$359$	−10.2274	+	11.2440i	−0.539780	+	0.593436i	−0.947534	−	0.319656i	$-0.896433\pi$
$359$	−10.2274	+	11.2440i	−0.539780	+	0.593436i	0.407754	+	0.913092i	$0.366312\pi$
$360$		0			0
$361$	−15.9389	+	37.9708i	−0.838889	+	1.99846i
$362$		0			0
$363$	23.5361	+	9.35984i	1.23532	+	0.491264i
$364$		0			0
$365$	0.996317	+	0.230239i	0.0521496	+	0.0120512i
$366$		0			0
$367$	20.3131	−	11.8992i	1.06033	−	0.621135i	0.131380	−	0.991332i	$-0.458059\pi$
$367$	20.3131	−	11.8992i	1.06033	−	0.621135i	0.928953	+	0.370197i	$0.120710\pi$
$368$		0			0
$369$	−27.5037	−	24.0818i	−1.43179	−	1.25365i
$370$		0			0
$371$	−32.9780	+	8.94801i	−1.71213	+	0.464557i
$372$		0			0
$373$	−25.6709	+	9.09967i	−1.32919	+	0.471163i	−0.901507	−	0.432765i	$-0.857538\pi$
$373$	−25.6709	+	9.09967i	−1.32919	+	0.471163i	−0.427684	+	0.903928i	$0.640671\pi$
$374$		0			0
$375$	15.2688	+	7.45505i	0.788479	+	0.384977i
$376$		0			0
$377$	0.307631	+	3.24130i	0.0158438	+	0.166935i
$378$		0			0
$379$	0.504284	−	0.0769384i	0.0259033	−	0.00395206i	−0.137860	−	0.990452i	$-0.544022\pi$
$379$	0.504284	−	0.0769384i	0.0259033	−	0.00395206i	0.163763	+	0.986500i	$0.447637\pi$
$380$		0			0
$381$	−0.930947	+	49.1849i	−0.0476939	+	2.51982i
$382$		0			0
$383$	16.4205	−	19.4858i	0.839047	−	0.995677i	−0.160915	−	0.986968i	$-0.551445\pi$
$383$	16.4205	−	19.4858i	0.839047	−	0.995677i	0.999962	−	0.00870907i	$-0.00277222\pi$
$384$		0			0
$385$	0.151783	−	2.67051i	0.00773560	−	0.136102i
$386$		0			0
$387$	1.88759	−	10.9748i	0.0959517	−	0.557879i
$388$		0			0
$389$	31.2826	+	16.7685i	1.58609	+	0.850198i	0.999178	+	0.0405490i	$0.0129107\pi$
$389$	31.2826	+	16.7685i	1.58609	+	0.850198i	0.586915	+	0.809649i	$0.300342\pi$
$390$		0			0
$391$	0.820374	−	0.400550i	0.0414881	−	0.0202567i
$392$		0			0
$393$	31.7600	+	2.40887i	1.60208	+	0.121511i
$394$		0			0
$395$	3.35536	+	3.41947i	0.168827	+	0.172052i
$396$		0			0
$397$	−5.29930	−	30.8110i	−0.265964	−	1.54636i	−0.744096	−	0.668072i	$-0.767120\pi$
$397$	−5.29930	−	30.8110i	−0.265964	−	1.54636i	0.478132	−	0.878288i	$-0.341314\pi$
$398$		0			0
$399$	−54.6765	−	44.3333i	−2.73725	−	2.21944i
$400$		0			0
$401$	9.75140	+	4.31215i	0.486962	+	0.215339i	0.633315	−	0.773894i	$-0.281694\pi$
$401$	9.75140	+	4.31215i	0.486962	+	0.215339i	−0.146354	+	0.989232i	$0.546754\pi$
$402$		0			0
$403$	1.66513	+	6.63091i	0.0829458	+	0.330309i
$404$		0			0
$405$	4.27752	+	0.487817i	0.212552	+	0.0242398i
$406$		0			0
$407$	2.79879	+	2.09891i	0.138731	+	0.104039i
$408$		0			0
$409$	−1.41572	−	1.68000i	−0.0700028	−	0.0830707i	0.728561	−	0.684981i	$-0.240190\pi$
$409$	−1.41572	−	1.68000i	−0.0700028	−	0.0830707i	−0.798564	+	0.601910i	$0.794406\pi$
$410$		0			0
$411$	3.60034	−	7.03312i	0.177592	−	0.346918i
$412$		0			0
$413$	14.5818	+	38.7894i	0.717526	+	1.90870i
$414$		0			0
$415$	1.52528	+	0.893498i	0.0748731	+	0.0438601i
$416$		0			0
$417$	−29.1651	−	40.4635i	−1.42822	−	1.98151i
$418$		0			0
$419$	−5.62711	+	3.01632i	−0.274903	+	0.147357i	−0.604110	−	0.796901i	$-0.706471\pi$
$419$	−5.62711	+	3.01632i	−0.274903	+	0.147357i	0.329208	+	0.944258i	$0.393218\pi$
$420$		0			0
$421$	−4.64951	+	8.29309i	−0.226603	+	0.404180i	−0.961833	−	0.273638i	$-0.911773\pi$
$421$	−4.64951	+	8.29309i	−0.226603	+	0.404180i	0.735230	+	0.677818i	$0.237074\pi$
$422$		0			0
$423$	−11.4548	+	39.2612i	−0.556952	+	1.90895i
$424$		0			0
$425$	−1.25943	+	1.61479i	−0.0610913	+	0.0783290i
$426$		0			0
$427$	17.6225	−	46.8779i	0.852812	−	2.26858i
$428$		0			0
$429$	−9.38138	−	5.98353i	−0.452937	−	0.288888i
$430$		0			0
$431$	17.3643	−	4.01272i	0.836411	−	0.193286i	0.214845	−	0.976648i	$-0.431075\pi$
$431$	17.3643	−	4.01272i	0.836411	−	0.193286i	0.621565	+	0.783362i	$0.286497\pi$
$432$		0			0
$433$	−5.38277	−	12.8232i	−0.258679	−	0.616244i	0.739713	−	0.672922i	$-0.234961\pi$
$433$	−5.38277	−	12.8232i	−0.258679	−	0.616244i	−0.998393	+	0.0566781i	$0.981949\pi$
$434$		0			0
$435$	−0.142382	+	1.50019i	−0.00682671	+	0.0719285i
$436$		0			0
$437$	−12.8734	−	8.91355i	−0.615817	−	0.426393i
$438$		0			0
$439$	−0.866088	+	0.758332i	−0.0413361	+	0.0361932i	−0.679172	−	0.733979i	$-0.737661\pi$
$439$	−0.866088	+	0.758332i	−0.0413361	+	0.0361932i	0.637836	+	0.770172i	$0.279830\pi$
$440$		0			0
$441$	16.0472	−	11.1111i	0.764151	−	0.529100i
$442$		0			0
$443$	27.8462	−	17.7606i	1.32301	−	0.843829i	0.328106	−	0.944641i	$-0.393590\pi$
$443$	27.8462	−	17.7606i	1.32301	−	0.843829i	0.994906	+	0.100812i	$0.0321440\pi$
$444$		0			0
$445$	0.333244	+	2.50075i	0.0157973	+	0.118547i
$446$		0			0
$447$	10.2869	+	16.8225i	0.486555	+	0.795675i
$448$		0			0
$449$	24.3688	−	24.8344i	1.15004	−	1.17201i	0.167511	−	0.985870i	$-0.446427\pi$
$449$	24.3688	−	24.8344i	1.15004	−	1.17201i	0.982524	−	0.186138i	$-0.0595972\pi$
$450$		0			0
$451$	−2.25250	−	10.6633i	−0.106066	−	0.502116i
$452$		0			0
$453$	1.99991	+	3.56713i	0.0939639	+	0.167598i
$454$		0			0
$455$	2.25557	−	8.98221i	0.105743	−	0.421092i
$456$		0			0
$457$	5.91364	−	8.89587i	0.276628	−	0.416131i	−0.668057	−	0.744110i	$-0.732874\pi$
$457$	5.91364	−	8.89587i	0.276628	−	0.416131i	0.944685	+	0.327979i	$0.106368\pi$
$458$		0			0
$459$	0.272003	−	0.816068i	0.0126960	−	0.0380908i
$460$		0			0
$461$	27.1600	−	3.09738i	1.26497	−	0.144259i	0.545099	−	0.838372i	$-0.316492\pi$
$461$	27.1600	−	3.09738i	1.26497	−	0.144259i	0.719867	+	0.694112i	$0.244203\pi$
$462$		0			0
$463$	20.4800	+	0.775550i	0.951788	+	0.0360429i	0.509169	−	0.860667i	$-0.329953\pi$
$463$	20.4800	+	0.775550i	0.951788	+	0.0360429i	0.442619	+	0.896710i	$0.354049\pi$
$464$		0			0
$465$	0.179559	+	3.15921i	0.00832687	+	0.146505i
$466$		0			0
$467$	−18.6146	+	30.4409i	−0.861380	+	1.40863i	0.0507400	+	0.998712i	$0.483842\pi$
$467$	−18.6146	+	30.4409i	−0.861380	+	1.40863i	−0.912120	+	0.409923i	$0.865556\pi$
$468$		0			0
$469$	0.292183	+	15.4369i	0.0134918	+	0.712812i
$470$		0			0
$471$	15.7981	+	5.60000i	0.727937	+	0.258034i
$472$		0			0
$473$	2.41325	−	2.27998i	0.110961	−	0.104834i
$474$		0			0
$475$	34.7217	+	5.29747i	1.59314	+	0.243065i
$476$		0			0
$477$	−15.3808	+	33.0749i	−0.704238	+	1.51440i
$478$		0			0
$479$	31.9110	−	1.20842i	1.45805	−	0.0552143i	0.703143	−	0.711048i	$-0.251779\pi$
$479$	31.9110	−	1.20842i	1.45805	−	0.0552143i	0.754905	+	0.655834i	$0.227683\pi$
$480$		0			0
$481$	8.15018	+	8.96033i	0.371616	+	0.408556i
$482$		0			0
$483$	14.2260	−	11.5349i	0.647306	−	0.524855i
$484$		0			0
$485$	1.53058	−	1.14783i	0.0695000	−	0.0521204i
$486$		0			0
$487$	−25.0487	−	4.79796i	−1.13507	−	0.217416i	−0.413997	−	0.910278i	$-0.635868\pi$
$487$	−25.0487	−	4.79796i	−1.13507	−	0.217416i	−0.721070	+	0.692862i	$0.756349\pi$
$488$		0			0
$489$	−21.2083	+	4.06235i	−0.959074	+	0.183706i
$490$		0			0
$491$	1.93532	−	9.16181i	0.0873400	−	0.413467i	−0.912649	−	0.408744i	$-0.865967\pi$
$491$	1.93532	−	9.16181i	0.0873400	−	0.413467i	0.999989	−	0.00472219i	$-0.00150313\pi$
$492$		0			0
$493$	−0.364796	−	0.113967i	−0.0164296	−	0.00513279i
$494$		0			0
$495$	−2.07552	−	1.96090i	−0.0932875	−	0.0881359i
$496$		0			0
$497$	9.67740	+	29.0343i	0.434091	+	1.30236i
$498$		0			0
$499$	−16.1029	+	22.3411i	−0.720865	+	1.00012i	0.278349	+	0.960480i	$0.410213\pi$
$499$	−16.1029	+	22.3411i	−0.720865	+	1.00012i	−0.999214	+	0.0396442i	$0.987378\pi$
$500$		0			0
$501$	19.5091	+	27.2726i	0.871603	+	1.21845i
$502$		0			0
$503$	−17.8658	+	24.7869i	−0.796597	+	1.10519i	0.195621	+	0.980680i	$0.437328\pi$
$503$	−17.8658	+	24.7869i	−0.796597	+	1.10519i	−0.992218	+	0.124515i	$0.960263\pi$
$504$		0			0
$505$	−1.80250	−	5.40787i	−0.0802100	−	0.240647i
$506$		0			0
$507$	−3.48427	−	3.29186i	−0.154742	−	0.146196i
$508$		0			0
$509$	34.5730	+	10.8010i	1.53242	+	0.478746i	0.944038	−	0.329836i	$-0.106993\pi$
$509$	34.5730	+	10.8010i	1.53242	+	0.478746i	0.588384	+	0.808582i	$0.299765\pi$
$510$		0			0
$511$	−1.07530	+	5.09046i	−0.0475685	+	0.225189i
$512$		0			0
$513$	−14.4902	+	2.77553i	−0.639758	+	0.122542i
$514$		0			0
$515$	−1.06180	−	0.203382i	−0.0467885	−	0.00896209i
$516$		0			0
$517$	−9.75468	+	7.31536i	−0.429010	+	0.321729i
$518$		0			0
$519$	14.2706	−	11.5710i	0.626411	−	0.507912i
$520$		0			0
$521$	−12.0305	−	13.2264i	−0.527067	−	0.579460i	0.417127	−	0.908848i	$-0.363037\pi$
$521$	−12.0305	−	13.2264i	−0.527067	−	0.579460i	−0.944194	+	0.329388i	$0.893157\pi$
$522$		0			0
$523$	29.3291	−	1.11065i	1.28247	−	0.0485654i	0.612212	−	0.790693i	$-0.290280\pi$
$523$	29.3291	−	1.11065i	1.28247	−	0.0485654i	0.670258	+	0.742128i	$0.266183\pi$
$524$		0			0
$525$	−17.3233	+	37.2521i	−0.756049	+	1.62581i
$526$		0			0
$527$	−0.793345	−	0.121040i	−0.0345586	−	0.00527260i
$528$		0			0
$529$	−13.7572	+	12.9975i	−0.598138	+	0.565107i
$530$		0			0
$531$	41.6942	+	14.7795i	1.80937	+	0.641375i
$532$		0			0
$533$	−0.714092	−	37.7277i	−0.0309308	−	1.63417i
$534$		0			0
$535$	4.48664	−	7.33710i	0.193974	−	0.317211i
$536$		0			0
$537$	−0.867055	−	15.2552i	−0.0374162	−	0.658309i
$538$		0			0
$539$	5.81485	+	0.220200i	0.250463	+	0.00948470i
$540$		0			0
$541$	−19.2562	+	2.19602i	−0.827888	+	0.0944141i	−0.516949	−	0.856016i	$-0.672932\pi$
$541$	−19.2562	+	2.19602i	−0.827888	+	0.0944141i	−0.310938	+	0.950430i	$0.600643\pi$
$542$		0			0
$543$	−3.36484	+	10.0952i	−0.144399	+	0.433228i
$544$		0			0
$545$	6.29306	−	9.46664i	0.269565	−	0.405506i
$546$		0			0
$547$	10.9889	−	43.7602i	0.469850	−	1.87105i	−0.0209517	−	0.999780i	$-0.506670\pi$
$547$	10.9889	−	43.7602i	0.469850	−	1.87105i	0.490802	−	0.871271i	$-0.336704\pi$
$548$		0			0
$549$	−26.1440	−	46.6317i	−1.11580	−	1.99019i
$550$		0			0
$551$	1.35476	+	6.41343i	0.0577148	+	0.273221i
$552$		0			0
$553$	−17.0719	+	17.3981i	−0.725971	+	0.739842i
$554$		0			0
$555$	2.92465	+	4.78275i	0.124145	+	0.203017i
$556$		0			0
$557$	3.91055	+	29.3459i	0.165695	+	1.24342i	0.854875	+	0.518834i	$0.173634\pi$
$557$	3.91055	+	29.3459i	0.165695	+	1.24342i	−0.689180	+	0.724590i	$0.742029\pi$
$558$		0			0
$559$	9.69130	−	6.18120i	0.409898	−	0.261437i
$560$		0			0
$561$	1.07385	−	0.743536i	0.0453380	−	0.0313921i
$562$		0			0
$563$	30.9466	−	27.0963i	1.30424	−	1.14197i	0.323597	−	0.946195i	$-0.395108\pi$
$563$	30.9466	−	27.0963i	1.30424	−	1.14197i	0.980648	−	0.195779i	$-0.0627234\pi$
$564$		0			0
$565$	1.05590	+	0.731107i	0.0444221	+	0.0307579i
$566$		0			0
$567$	−2.06968	+	21.8068i	−0.0869184	+	0.915801i
$568$		0			0
$569$	12.5823	+	29.9745i	0.527478	+	1.25659i	0.938598	+	0.345013i	$0.112126\pi$
$569$	12.5823	+	29.9745i	0.527478	+	1.25659i	−0.411120	+	0.911581i	$0.634862\pi$
$570$		0			0
$571$	−16.2231	+	3.74899i	−0.678915	+	0.156890i	−0.550506	−	0.834831i	$-0.685565\pi$
$571$	−16.2231	+	3.74899i	−0.678915	+	0.156890i	−0.128409	+	0.991721i	$0.540987\pi$
$572$		0			0
$573$	−36.3540	−	23.1869i	−1.51871	−	0.968648i
$574$		0			0
$575$	−3.21570	+	8.55414i	−0.134104	+	0.356733i
$576$		0			0
$577$	−18.3055	+	23.4707i	−0.762070	+	0.977098i	0.237913	+	0.971286i	$0.423537\pi$
$577$	−18.3055	+	23.4707i	−0.762070	+	0.977098i	−0.999983	+	0.00581146i	$0.998150\pi$
$578$		0			0
$579$	−2.98743	+	10.2394i	−0.124154	+	0.425535i
$580$		0			0
$581$	−4.39839	+	7.84518i	−0.182476	+	0.325473i
$582$		0			0
$583$	−9.58454	+	5.13763i	−0.396951	+	0.212779i
$584$		0			0
$585$	−5.78056	−	8.01992i	−0.238997	−	0.331583i
$586$		0			0
$587$	−39.7603	−	23.2913i	−1.64108	−	0.961334i	−0.976882	−	0.213779i	$-0.931423\pi$
$587$	−39.7603	−	23.2913i	−1.64108	−	0.961334i	−0.664200	−	0.747555i	$-0.731228\pi$
$588$		0			0
$589$	4.84342	+	12.8841i	0.199569	+	0.530878i
$590$		0			0
$591$	−16.5558	+	32.3412i	−0.681016	+	1.33034i
$592$		0			0
$593$	−6.16470	−	7.31551i	−0.253154	−	0.300412i	0.623217	−	0.782049i	$-0.285825\pi$
$593$	−6.16470	−	7.31551i	−0.253154	−	0.300412i	−0.876371	+	0.481637i	$0.840042\pi$
$594$		0			0
$595$	0.869706	+	0.652222i	0.0356545	+	0.0267385i
$596$		0			0
$597$	−14.7553	−	1.68273i	−0.603894	−	0.0688694i
$598$		0			0
$599$	2.97573	+	11.8500i	0.121585	+	0.484179i	0.999980	+	0.00624497i	$0.00198785\pi$
$599$	2.97573	+	11.8500i	0.121585	+	0.484179i	−0.878396	+	0.477934i	$0.841386\pi$
$600$		0			0
$601$	33.2171	+	14.6889i	1.35495	+	0.599172i	0.949160	−	0.314793i	$-0.101935\pi$
$601$	33.2171	+	14.6889i	1.35495	+	0.599172i	0.405793	+	0.913965i	$0.366995\pi$
$602$		0			0
$603$	12.8021	+	10.3803i	0.521341	+	0.422719i
$604$		0			0
$605$	1.13722	+	6.61199i	0.0462346	+	0.268815i
$606$		0			0
$607$	−18.1556	−	18.5025i	−0.736915	−	0.750995i	0.238555	−	0.971129i	$-0.423326\pi$
$607$	−18.1556	−	18.5025i	−0.736915	−	0.750995i	−0.975470	+	0.220134i	$0.929350\pi$
$608$		0			0
$609$	−7.64520	−	0.579858i	−0.309799	−	0.0234970i
$610$		0			0
$611$	−37.9356	+	18.5222i	−1.53471	+	0.749328i
$612$		0			0
$613$	13.2654	+	7.11069i	0.535784	+	0.287198i	0.717979	−	0.696064i	$-0.245067\pi$
$613$	13.2654	+	7.11069i	0.535784	+	0.287198i	−0.182195	+	0.983262i	$0.558320\pi$
$614$		0			0
$615$	2.96038	−	17.2121i	0.119374	−	0.694060i
$616$		0			0
$617$	−0.902893	+	15.8857i	−0.0363491	+	0.639534i	0.927621	+	0.373523i	$0.121850\pi$
$617$	−0.902893	+	15.8857i	−0.0363491	+	0.639534i	−0.963970	+	0.266011i	$0.914294\pi$
$618$		0			0
$619$	−31.6936	+	37.6101i	−1.27387	+	1.51168i	−0.520915	+	0.853609i	$0.674409\pi$
$619$	−31.6936	+	37.6101i	−1.27387	+	1.51168i	−0.752959	+	0.658068i	$0.771374\pi$
$620$		0			0
$621$	0.0726437	−	3.83799i	0.00291509	−	0.154013i
$622$		0			0
$623$	−12.6893	+	1.93601i	−0.508387	+	0.0775644i
$624$		0			0
$625$	−1.71371	−	18.0562i	−0.0685485	−	0.722249i
$626$		0			0
$627$	−20.1307	−	9.82886i	−0.803941	−	0.392527i
$628$		0			0
$629$	−1.34010	+	0.475032i	−0.0534335	+	0.0189408i
$630$		0			0
$631$	−33.4699	+	9.08148i	−1.33242	+	0.361528i	−0.855674	−	0.517515i	$-0.826857\pi$
$631$	−33.4699	+	9.08148i	−1.33242	+	0.361528i	−0.476742	+	0.879043i	$0.658182\pi$
$632$		0			0
$633$	1.87115	+	1.63834i	0.0743715	+	0.0651184i
$634$		0			0
$635$	−11.2433	+	6.58621i	−0.446175	+	0.261366i
$636$		0			0
$637$	19.6300	+	4.53629i	0.777768	+	0.179734i
$638$		0			0
$639$	30.3574	+	12.0726i	1.20092	+	0.477583i
$640$		0			0
$641$	−0.939261	+	2.23757i	−0.0370986	+	0.0883789i	−0.939548	−	0.342416i	$-0.888755\pi$
$641$	−0.939261	+	2.23757i	−0.0370986	+	0.0883789i	0.902450	+	0.430795i	$0.141767\pi$
$642$		0			0
$643$	11.8122	−	12.9863i	0.465827	−	0.512131i	−0.461113	−	0.887341i	$-0.652550\pi$
$643$	11.8122	−	12.9863i	0.465827	−	0.512131i	0.926940	+	0.375210i	$0.122429\pi$
$644$		0			0
$645$	4.94359	−	1.96597i	0.194654	−	0.0774100i
$646$		0			0
$647$	−20.7221	+	6.47381i	−0.814669	+	0.254512i	−0.677016	−	0.735969i	$-0.736727\pi$
$647$	−20.7221	+	6.47381i	−0.814669	+	0.254512i	−0.137653	+	0.990480i	$0.543956\pi$
$648$		0			0
$649$	7.30097	+	10.9828i	0.286588	+	0.431114i
$650$		0			0
$651$	−16.0537	+	1.21761i	−0.629194	+	0.0477218i
$652$		0			0
$653$	−8.84150	−	30.3041i	−0.345994	−	1.18589i	−0.927960	−	0.372680i	$-0.878439\pi$
$653$	−8.84150	−	30.3041i	−0.345994	−	1.18589i	0.581966	−	0.813213i	$-0.302284\pi$
$654$		0			0
$655$	3.84439	+	7.50987i	0.150213	+	0.293435i
$656$		0			0
$657$	3.41564	+	4.37940i	0.133257	+	0.170857i
$658$		0			0
$659$	−4.13341	−	1.12153i	−0.161015	−	0.0436886i	0.180444	−	0.983585i	$-0.442246\pi$
$659$	−4.13341	−	1.12153i	−0.161015	−	0.0436886i	−0.341459	+	0.939897i	$0.610921\pi$
$660$		0			0
$661$	0.0648022	+	0.139351i	0.00252051	+	0.00542013i	0.908008	−	0.418953i	$-0.137603\pi$
$661$	0.0648022	+	0.139351i	0.00252051	+	0.00542013i	−0.905487	+	0.424373i	$0.860494\pi$
$662$		0			0
$663$	4.13593	−	1.82894i	0.160626	−	0.0710303i
$664$		0			0
$665$	2.46283	−	18.4818i	0.0955044	−	0.716692i
$666$		0			0
$667$	−1.70550			−0.0660374
$668$		0			0
$669$	35.0641			1.35566
$670$		0			0
$671$	2.10527	−	15.7985i	0.0812729	−	0.609895i
$672$		0			0
$673$	−12.4433	+	5.50251i	−0.479652	+	0.212106i	−0.630104	−	0.776511i	$-0.716988\pi$
$673$	−12.4433	+	5.50251i	−0.479652	+	0.212106i	0.150451	+	0.988617i	$0.451927\pi$
$674$		0			0
$675$	3.63085	+	7.80781i	0.139752	+	0.300523i
$676$		0			0
$677$	−12.9525	−	3.51444i	−0.497806	−	0.135071i	0.00410280	−	0.999992i	$-0.498694\pi$
$677$	−12.9525	−	3.51444i	−0.497806	−	0.135071i	−0.501909	+	0.864920i	$0.667369\pi$
$678$		0			0
$679$	5.98643	+	7.67558i	0.229738	+	0.294562i
$680$		0			0
$681$	13.2272	+	25.8388i	0.506866	+	0.990144i
$682$		0			0
$683$	9.67319	+	33.1548i	0.370134	+	1.26863i	0.905621	+	0.424088i	$0.139405\pi$
$683$	9.67319	+	33.1548i	0.370134	+	1.26863i	−0.535486	+	0.844544i	$0.679872\pi$
$684$		0			0
$685$	2.08683	−	0.158278i	0.0797337	−	0.00604748i
$686$		0			0
$687$	−2.15998	−	3.24925i	−0.0824082	−	0.123966i
$688$		0			0
$689$	−35.9386	+	11.2276i	−1.36915	+	0.427739i
$690$		0			0
$691$	2.96200	−	1.17793i	0.112680	−	0.0448105i	−0.312512	−	0.949914i	$-0.601171\pi$
$691$	2.96200	−	1.17793i	0.112680	−	0.0448105i	0.425192	+	0.905103i	$0.360207\pi$
$692$		0			0
$693$	9.77531	−	10.7470i	0.371333	−	0.408245i
$694$		0			0
$695$	5.11363	−	12.1821i	0.193971	−	0.462092i
$696$		0			0
$697$	4.11588	+	1.63680i	0.155900	+	0.0619984i
$698$		0			0
$699$	−35.3982	−	8.18016i	−1.33888	−	0.309402i
$700$		0			0
$701$	−27.9464	+	16.3708i	−1.05552	+	0.618316i	−0.927641	−	0.373473i	$-0.878167\pi$
$701$	−27.9464	+	16.3708i	−1.05552	+	0.618316i	−0.127880	+	0.991790i	$0.540817\pi$
$702$		0			0
$703$	18.3469	+	16.0642i	0.691967	+	0.605875i
$704$		0			0
$705$	−18.8572	+	5.11658i	−0.710203	+	0.192701i
$706$		0			0
$707$	27.3364	−	9.69005i	1.02809	−	0.364432i
$708$		0			0
$709$	−39.5453	−	19.3081i	−1.48516	−	0.725132i	−0.495502	−	0.868607i	$-0.665016\pi$
$709$	−39.5453	−	19.3081i	−1.48516	−	0.725132i	−0.989654	+	0.143475i	$0.954172\pi$
$710$		0			0
$711$	2.45850	+	25.9035i	0.0922009	+	0.971459i
$712$		0			0
$713$	−3.54032	+	0.540145i	−0.132586	+	0.0202286i
$714$		0			0
$715$	0.0557756	−	2.94680i	0.00208589	−	0.110204i
$716$		0			0
$717$	7.46227	−	8.85530i	0.278684	−	0.330707i
$718$		0			0
$719$	−0.318918	+	5.61111i	−0.0118936	+	0.209259i	0.986944	+	0.161062i	$0.0514920\pi$
$719$	−0.318918	+	5.61111i	−0.0118936	+	0.209259i	−0.998838	+	0.0481968i	$0.984653\pi$
$720$		0			0
$721$	0.932376	−	5.42099i	0.0347235	−	0.201888i
$722$		0			0
$723$	−11.7024	−	6.27286i	−0.435216	−	0.233290i
$724$		0			0
$725$	3.43782	−	1.67853i	0.127677	−	0.0623389i
$726$		0			0
$727$	−14.4373	−	1.09501i	−0.535451	−	0.0406118i	−0.194874	−	0.980828i	$-0.562430\pi$
$727$	−14.4373	−	1.09501i	−0.535451	−	0.0406118i	−0.340577	+	0.940217i	$0.610622\pi$
$728$		0			0
$729$	26.7460	+	27.2570i	0.990592	+	1.00952i
$730$		0			0
$731$	0.228711	+	1.32976i	0.00845919	+	0.0491831i
$732$		0			0
$733$	−20.8780	−	16.9285i	−0.771145	−	0.625267i	0.161164	−	0.986928i	$-0.448475\pi$
$733$	−20.8780	−	16.9285i	−0.771145	−	0.625267i	−0.932310	+	0.361660i	$0.882210\pi$
$734$		0			0
$735$	8.52825	+	3.77127i	0.314569	+	0.139105i
$736$		0			0
$737$	1.19674	+	4.76571i	0.0440826	+	0.175547i
$738$		0			0
$739$	43.7111	+	4.98491i	1.60794	+	0.183373i	0.870544	−	0.492090i	$-0.163767\pi$
$739$	43.7111	+	4.98491i	1.60794	+	0.183373i	0.737394	+	0.675463i	$0.236056\pi$
$740$		0			0
$741$	−62.0523	−	46.5351i	−2.27955	−	1.70951i
$742$		0			0
$743$	−1.20878	−	1.43443i	−0.0443458	−	0.0526242i	0.742065	−	0.670328i	$-0.233846\pi$
$743$	−1.20878	−	1.43443i	−0.0443458	−	0.0526242i	−0.786411	+	0.617703i	$0.788063\pi$
$744$		0			0
$745$	−2.37998	+	4.64921i	−0.0871958	+	0.170334i
$746$		0			0
$747$	3.37840	+	8.98695i	0.123609	+	0.328815i
$748$		0			0
$749$	37.7561	+	22.1172i	1.37958	+	0.808145i
$750$		0			0
$751$	21.0067	+	29.1446i	0.766546	+	1.06350i	0.995927	+	0.0901655i	$0.0287396\pi$
$751$	21.0067	+	29.1446i	0.766546	+	1.06350i	−0.229381	+	0.973337i	$0.573670\pi$
$752$		0			0
$753$	−39.7840	+	21.3255i	−1.44981	+	0.777146i
$754$		0			0
$755$	−0.529731	+	0.944854i	−0.0192789	+	0.0343868i
$756$		0			0
$757$	−6.37968	+	21.8663i	−0.231873	+	0.794744i	0.757934	+	0.652331i	$0.226209\pi$
$757$	−6.37968	+	21.8663i	−0.231873	+	0.794744i	−0.989807	+	0.142413i	$0.954514\pi$
$758$		0			0
$759$	3.58462	−	4.59607i	0.130114	−	0.166827i
$760$		0			0
$761$	10.5749	−	28.1304i	0.383339	−	1.01973i	−0.593327	−	0.804961i	$-0.702186\pi$
$761$	10.5749	−	28.1304i	0.383339	−	1.01973i	0.976666	−	0.214765i	$-0.0688984\pi$
$762$		0			0
$763$	48.7630	+	31.1015i	1.76534	+	1.12595i
$764$		0			0
$765$	1.13066	−	0.261284i	0.0408791	−	0.00944675i
$766$		0			0
$767$	17.6733	+	42.1026i	0.638146	+	1.52024i
$768$		0			0
$769$	3.81369	−	40.1823i	0.137525	−	1.44901i	−0.613999	−	0.789307i	$-0.710440\pi$
$769$	3.81369	−	40.1823i	0.137525	−	1.44901i	0.751524	−	0.659705i	$-0.229319\pi$
$770$		0			0
$771$	63.3971	+	43.8962i	2.28319	+	1.58088i
$772$		0			0
$773$	14.5023	−	12.6980i	0.521613	−	0.456715i	−0.357100	−	0.934066i	$-0.616234\pi$
$773$	14.5023	−	12.6980i	0.521613	−	0.456715i	0.878712	+	0.477351i	$0.158403\pi$
$774$		0			0
$775$	6.60468	−	4.57309i	0.237247	−	0.164270i
$776$		0			0
$777$	−24.0484	+	15.3383i	−0.862732	+	0.550259i
$778$		0			0
$779$	−10.0349	−	75.3043i	−0.359536	−	2.69806i
$780$		0			0
$781$	5.08121	+	8.30942i	0.181820	+	0.297334i
$782$		0			0
$783$	−1.12551	+	1.14702i	−0.0402225	+	0.0409910i
$784$		0			0
$785$	0.917582	+	4.34383i	0.0327499	+	0.155038i
$786$		0			0
$787$	17.1049	+	30.5092i	0.609725	+	1.08754i	0.986891	+	0.161390i	$0.0515976\pi$
$787$	17.1049	+	30.5092i	0.609725	+	1.08754i	−0.377165	+	0.926146i	$0.623101\pi$
$788$		0			0
$789$	−5.13789	+	20.4603i	−0.182914	+	0.728404i
$790$		0			0
$791$	−3.61750	+	5.44179i	−0.128623	+	0.193488i
$792$		0			0
$793$	17.4493	−	52.3516i	0.619643	−	1.85906i
$794$		0			0
$795$	−17.3143	+	1.97456i	−0.614074	+	0.0700303i
$796$		0			0

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:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.e (of order \(83\), degree \(82\), minimal)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about