LMFDB - Embedded newform 668.2.e.a.9.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [668,2,Mod(9,668)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(668, base_ring=CyclotomicField(166))

chi = DirichletCharacter(H, H._module([0, 22]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("668.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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			9.3
Character	$\chi$	$=$	668.9
Dual form			668.2.e.a.297.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$335$
$\chi(n)$	$e\left(\frac{11}{83}\right)$	$1$

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	−0.755648	−	0.654977i	$-0.772678\pi$
$3$	−0.342745	−	2.57205i	−0.197884	−	1.48498i	0.557765	−	0.829999i	$-0.311659\pi$
$4$		0			0
$5$	−0.628586	−	0.277966i	−0.281112	−	0.124310i	0.259069	−	0.965859i	$-0.416584\pi$
$5$	−0.628586	−	0.277966i	−0.281112	−	0.124310i	−0.540181	+	0.841549i	$0.681644\pi$
$6$		0			0
$7$	−1.47454	+	3.17087i	−0.557325	+	1.19848i	0.401861	+	0.915701i	$0.368364\pi$
$7$	−1.47454	+	3.17087i	−0.557325	+	1.19848i	−0.959186	+	0.282775i	$0.908745\pi$
$8$		0			0
$9$	−3.60268	+	0.977525i	−1.20089	+	0.325842i
$10$		0			0
$11$	−0.684433	+	0.877554i	−0.206364	+	0.264593i	−0.880533	−	0.473985i	$-0.842815\pi$
$11$	−0.684433	+	0.877554i	−0.206364	+	0.264593i	0.674169	+	0.738577i	$0.264502\pi$
$12$		0			0
$13$	−1.75582	+	3.42993i	−0.486977	+	0.951291i	0.508922	+	0.860813i	$0.330044\pi$
$13$	−1.75582	+	3.42993i	−0.486977	+	0.951291i	−0.995898	+	0.0904779i	$0.971161\pi$
$14$		0			0
$15$	−0.499499	+	1.71203i	−0.128970	+	0.442044i
$16$		0			0
$17$	0.451009	+	0.0342072i	0.109386	+	0.00829646i	0.130208	−	0.991487i	$-0.458436\pi$
$17$	0.451009	+	0.0342072i	0.109386	+	0.00829646i	−0.0208221	+	0.999783i	$0.506628\pi$
$18$		0			0
$19$	−4.29462	+	6.46039i	−0.985254	+	1.48212i	−0.112681	+	0.993631i	$0.535944\pi$
$19$	−4.29462	+	6.46039i	−0.985254	+	1.48212i	−0.872573	+	0.488484i	$0.837550\pi$
$20$		0			0
$21$	8.66104	+	2.70581i	1.88999	+	0.590456i
$22$		0			0
$23$	1.87555	+	0.745869i	0.391079	+	0.155524i	0.556797	−	0.830649i	$-0.312030\pi$
$23$	1.87555	+	0.745869i	0.391079	+	0.155524i	−0.165718	+	0.986173i	$0.552994\pi$
$24$		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	−0.441293	−	0.897363i	$-0.645480\pi$
$29$	−0.785163	+	0.312244i	−0.145801	+	0.0579823i	0.295492	+	0.955345i	$0.404516\pi$
$30$		0			0
$31$	−1.72875	+	0.399495i	−0.310492	+	0.0717515i	−0.377525	−	0.925999i	$-0.623225\pi$
$31$	−1.72875	+	0.399495i	−0.310492	+	0.0717515i	0.0670335	+	0.997751i	$0.478647\pi$
$32$		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	0.00359603	−	0.999994i	$-0.498855\pi$
$37$	−3.03378	−	0.823165i	−0.498751	−	0.135328i	−0.502347	+	0.864666i	$0.667530\pi$
$38$		0			0
$39$	9.42376	+	3.34047i	1.50901	+	0.534904i
$40$		0			0
$41$	8.80006	−	4.29666i	1.37434	−	0.671025i	0.404447	−	0.914562i	$-0.367464\pi$
$41$	8.80006	−	4.29666i	1.37434	−	0.671025i	0.969892	+	0.243536i	$0.0783075\pi$
$42$		0			0
$43$	0.281863	−	2.96980i	0.0429837	−	0.452890i	−0.947938	−	0.318454i	$-0.896837\pi$
$43$	0.281863	−	2.96980i	0.0429837	−	0.452890i	0.990922	−	0.134437i	$-0.0429225\pi$
$44$		0			0
$45$	2.53631	+	0.386964i	0.378091	+	0.0576852i
$46$		0			0
$47$	0.207333	+	10.9540i	0.0302426	+	1.59781i	0.616279	+	0.787528i	$0.288639\pi$
$47$	0.207333	+	10.9540i	0.0302426	+	1.59781i	−0.586037	+	0.810284i	$0.699313\pi$
$48$		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	0.844388	+	0.535731i	$0.179964\pi$
$53$	1.65631	+	9.63007i	0.227512	+	1.32279i	−0.616877	+	0.787060i	$0.711602\pi$
$54$		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	−0.817303	−	0.576209i	$-0.804532\pi$
$59$	−11.8163	+	0.896218i	−1.53835	+	0.116678i	−0.721047	+	0.692886i	$0.756339\pi$
$60$		0			0
$61$	10.0304	−	10.2220i	1.28426	−	1.30880i	0.357132	−	0.934054i	$-0.383755\pi$
$61$	10.0304	−	10.2220i	1.28426	−	1.30880i	0.927128	−	0.374744i	$-0.122269\pi$
$62$		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	−0.636103	−	0.771604i	$-0.719455\pi$
$67$	−4.03799	+	1.78563i	−0.493319	+	0.218150i	0.142784	+	0.989754i	$0.454395\pi$
$68$		0			0
$69$	1.27558	−	5.07965i	0.153562	−	0.611519i
$70$		0			0
$71$	−8.69542	+	0.991644i	−1.03196	+	0.117686i	−0.612808	−	0.790231i	$-0.709960\pi$
$71$	−8.69542	+	0.991644i	−1.03196	+	0.117686i	−0.419148	+	0.907918i	$0.637671\pi$
$72$		0			0
$73$	−1.19028	+	0.892634i	−0.139312	+	0.104475i	−0.667344	−	0.744750i	$-0.732569\pi$
$73$	−1.19028	+	0.892634i	−0.139312	+	0.104475i	0.528032	+	0.849225i	$0.322930\pi$
$74$		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	0.723106	+	0.690737i	$0.242714\pi$
$79$	−2.45274	+	6.52457i	−0.275955	+	0.734072i	−0.999061	+	0.0433345i	$0.986202\pi$
$80$		0			0
$81$	−5.40490	+	3.16615i	−0.600544	+	0.351794i
$82$		0			0
$83$	−1.50388	+	2.08647i	−0.165072	+	0.229020i	−0.885649	−	0.464355i	$-0.846286\pi$
$83$	−1.50388	+	2.08647i	−0.165072	+	0.229020i	0.720578	+	0.693374i	$0.243877\pi$
$84$		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	0.996123	−	0.0879713i	$-0.0280384\pi$
$89$	1.02809	+	3.52376i	0.108977	+	0.373517i	−0.887146	+	0.461489i	$0.847315\pi$
$90$		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	0.0852100	−	0.996363i	$-0.472844\pi$
$97$	−2.71211	−	0.626740i	−0.275373	−	0.0636358i	−0.360583	+	0.932727i	$0.617422\pi$
$98$		0			0
$99$	1.60796	−	3.83060i	0.161606	−	0.384989i
$100$		0			0
$101$	−0.783642	−	8.25670i	−0.0779753	−	0.821573i	−0.945810	−	0.324720i	$-0.894730\pi$
$101$	−0.783642	−	8.25670i	−0.0779753	−	0.821573i	0.867835	−	0.496853i	$-0.165511\pi$
$102$		0			0
$103$	1.29322	−	0.895429i	0.127425	−	0.0882292i	−0.503838	−	0.863798i	$-0.668079\pi$
$103$	1.29322	−	0.895429i	0.127425	−	0.0882292i	0.631263	+	0.775569i	$0.282537\pi$
$104$		0			0
$105$	−4.69208	−	4.10831i	−0.457901	−	0.400930i
$106$		0			0
$107$	−10.2876	−	7.12314i	−0.994539	−	0.688620i	−0.0439371	−	0.999034i	$-0.513990\pi$
$107$	−10.2876	−	7.12314i	−0.994539	−	0.688620i	−0.950601	+	0.310414i	$0.899532\pi$
$108$		0			0
$109$	−13.9444	−	8.89388i	−1.33563	−	0.851880i	−0.339575	−	0.940579i	$-0.610283\pi$
$109$	−13.9444	−	8.89388i	−1.33563	−	0.851880i	−0.996058	+	0.0886995i	$0.971729\pi$
$110$		0			0
$111$	−1.07741	+	8.08520i	−0.102263	+	0.767413i
$112$		0			0
$113$	−0.974842	+	1.59418i	−0.0917055	+	0.149968i	−0.895685	−	0.444689i	$-0.853314\pi$
$113$	−0.974842	+	1.59418i	−0.0917055	+	0.149968i	0.803980	+	0.594657i	$0.202712\pi$
$114$		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	0.897012	−	0.442005i	$-0.145733\pi$
$127$	18.8365	+	2.14816i	1.67147	+	0.190618i	0.774459	+	0.632624i	$0.218022\pi$
$128$		0			0
$129$	−7.73510	+	0.292917i	−0.681037	+	0.0257899i
$130$		0			0
$131$	−0.696551	+	12.2553i	−0.0608580	+	1.07075i	0.812278	+	0.583271i	$0.198227\pi$
$131$	−0.696551	+	12.2553i	−0.0608580	+	1.07075i	−0.873136	+	0.487477i	$0.837917\pi$
$132$		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	−0.453866	−	0.891070i	$-0.649956\pi$
$137$	−2.87001	+	1.01734i	−0.245201	+	0.0869173i	0.208665	+	0.977987i	$0.433088\pi$
$138$		0			0
$139$	−13.9728	−	13.2012i	−1.18516	−	1.11971i	−0.990309	−	0.138879i	$-0.955650\pi$
$139$	−13.9728	−	13.2012i	−1.18516	−	1.11971i	−0.194851	−	0.980833i	$-0.562422\pi$
$140$		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	0.840305	−	0.542114i	$-0.182376\pi$
$149$	5.90270	+	4.78608i	0.483568	+	0.392091i	−0.356737	+	0.934205i	$0.616111\pi$
$150$		0			0
$151$	1.26088	+	0.945573i	0.102609	+	0.0769497i	0.650035	−	0.759904i	$-0.274754\pi$
$151$	1.26088	+	0.945573i	0.102609	+	0.0769497i	−0.547427	+	0.836854i	$0.684393\pi$
$152$		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	0.998621	+	0.0525064i	$0.0167210\pi$
$157$	1.33505	+	6.32011i	0.106548	+	0.504399i	−0.892072	+	0.451893i	$0.850749\pi$
$158$		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	−0.793834	−	0.608135i	$-0.791918\pi$
$163$	2.63149	−	7.89501i	0.206114	−	0.618385i	0.999947	−	0.0102502i	$-0.00326278\pi$
$164$		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	−0.857056	−	0.515223i	$-0.827709\pi$
$173$	−5.14672	+	4.86250i	−0.391298	+	0.369689i	0.465759	+	0.884912i	$0.345781\pi$
$174$		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	−0.0326264	−	0.999468i	$-0.510387\pi$
$179$	−5.78349	−	1.10780i	−0.432279	−	0.0828008i	−0.399652	+	0.916667i	$0.630869\pi$
$180$		0			0
$181$	4.02778	−	0.771500i	0.299382	−	0.0573452i	−0.0362358	−	0.999343i	$-0.511537\pi$
$181$	4.02778	−	0.771500i	0.299382	−	0.0573452i	0.335618	+	0.941998i	$0.391055\pi$
$182$		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	−0.978089	−	0.208188i	$-0.933243\pi$
$191$	−7.00703	−	15.0680i	−0.507011	−	1.09028i	0.471078	−	0.882092i	$-0.343865\pi$
$192$		0			0
$193$	4.06364	−	0.619988i	0.292507	−	0.0446277i	−0.00291102	−	0.999996i	$-0.500927\pi$
$193$	4.06364	−	0.619988i	0.292507	−	0.0446277i	0.295418	+	0.955368i	$0.404541\pi$
$194$		0			0
$195$	−4.99510	−	4.71926i	−0.357707	−	0.337953i
$196$		0			0
$197$	13.1975	−	4.67815i	0.940280	−	0.333304i	0.180567	−	0.983563i	$-0.442207\pi$
$197$	13.1975	−	4.67815i	0.940280	−	0.333304i	0.759713	+	0.650258i	$0.225339\pi$
$198$		0			0
$199$	0.108310	−	5.72234i	0.00767787	−	0.405646i	−0.975194	−	0.221354i	$-0.928952\pi$
$199$	0.108310	−	5.72234i	0.00767787	−	0.405646i	0.982871	−	0.184292i	$-0.0589993\pi$
$200$		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	0.850593	−	0.525825i	$-0.176243\pi$
$211$	0.530613	+	0.798200i	0.0365289	+	0.0549503i	−0.814064	+	0.580776i	$0.802749\pi$
$212$		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	0.824207	+	0.566289i	$0.191621\pi$
$223$	−1.78496	+	13.3949i	−0.119530	+	0.896986i	−0.943737	+	0.330697i	$0.892716\pi$
$224$		0			0
$225$	14.2497	+	9.08857i	0.949977	+	0.605904i
$226$		0			0
$227$	9.19734	+	6.36826i	0.610449	+	0.422676i	0.833804	−	0.552061i	$-0.186159\pi$
$227$	9.19734	+	6.36826i	0.610449	+	0.422676i	−0.223354	+	0.974737i	$0.571701\pi$
$228$		0			0
$229$	−1.13129	−	0.990539i	−0.0747578	−	0.0654566i	0.620560	−	0.784159i	$-0.286905\pi$
$229$	−1.13129	−	0.990539i	−0.0747578	−	0.0654566i	−0.695318	+	0.718702i	$0.744737\pi$
$230$		0			0
$231$	−8.30240	+	5.74859i	−0.546258	+	0.378230i
$232$		0			0
$233$	−1.32294	−	13.9389i	−0.0866686	−	0.913168i	−0.927983	−	0.372622i	$-0.878459\pi$
$233$	−1.32294	−	13.9389i	−0.0866686	−	0.913168i	0.841315	−	0.540546i	$-0.181782\pi$
$234$		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	−0.653806	−	0.756662i	$-0.726829\pi$
$239$	−3.76269	+	2.39988i	−0.243388	+	0.155235i	0.410418	+	0.911898i	$0.365383\pi$
$240$		0			0
$241$	−1.80058	−	4.78976i	−0.115986	−	0.308536i	0.865252	−	0.501337i	$-0.167158\pi$
$241$	−1.80058	−	4.78976i	−0.115986	−	0.308536i	−0.981238	+	0.192801i	$0.938243\pi$
$242$		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	−0.357021	−	0.934096i	$-0.616208\pi$
$251$	10.1718	−	14.1123i	0.642039	−	0.890762i	0.999061	+	0.0433343i	$0.0137980\pi$
$252$		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	0.756508	+	0.653984i	$0.226904\pi$
$257$	13.5416	+	26.4529i	0.844699	+	1.65009i	0.0881912	+	0.996104i	$0.471891\pi$
$258$		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	0.139352	−	0.990243i	$-0.455498\pi$
$263$	8.07758	−	0.921184i	0.498085	−	0.0568027i	0.358733	+	0.933440i	$0.383209\pi$
$264$		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	−0.0699951	−	0.997547i	$-0.522298\pi$
$269$	14.6225	−	11.8563i	0.891548	−	0.722893i	0.961543	+	0.274654i	$0.0885634\pi$
$270$		0			0
$271$	−0.249854	+	1.45269i	−0.0151775	+	0.0882446i	−0.992130	−	0.125213i	$-0.960039\pi$
$271$	−0.249854	+	1.45269i	−0.0151775	+	0.0882446i	0.976952	+	0.213457i	$0.0684724\pi$
$272$		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	−0.130990	−	0.991384i	$-0.541815\pi$
$277$	−16.5315	−	8.07157i	−0.993282	−	0.484973i	−0.862293	+	0.506410i	$0.830972\pi$
$278$		0			0
$279$	5.83760	−	3.12914i	0.349488	−	0.187337i
$280$		0			0
$281$	−0.355865	−	2.06905i	−0.0212291	−	0.123429i	0.972981	−	0.230887i	$-0.0741628\pi$
$281$	−0.355865	−	2.06905i	−0.0212291	−	0.123429i	−0.994210	+	0.107458i	$0.965729\pi$
$282$		0			0
$283$	0.480369	+	8.45171i	0.0285550	+	0.502402i	0.980548	+	0.196281i	$0.0628866\pi$
$283$	0.480369	+	8.45171i	0.0285550	+	0.502402i	−0.951993	+	0.306121i	$0.900969\pi$
$284$		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	−0.678576	+	0.734531i	$0.737402\pi$
$293$	−28.6730	+	13.9997i	−1.67510	+	0.817871i	−0.996521	+	0.0833408i	$0.973441\pi$
$294$		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	0.922460	−	0.386093i	$-0.126176\pi$
$307$	0.0140733	+	0.0335264i	0.000803204	+	0.00191345i	−0.921657	+	0.388007i	$0.873164\pi$
$308$		0			0
$309$	−2.74634	−	3.01933i	−0.156234	−	0.171764i
$310$		0			0
$311$	17.2635	+	6.86536i	0.978924	+	0.389299i	0.803572	−	0.595207i	$-0.202930\pi$
$311$	17.2635	+	6.86536i	0.978924	+	0.389299i	0.175352	+	0.984506i	$0.443894\pi$
$312$		0			0
$313$	19.7941	+	6.18389i	1.11883	+	0.349534i	0.801030	−	0.598624i	$-0.204286\pi$
$313$	19.7941	+	6.18389i	1.11883	+	0.349534i	0.317797	+	0.948159i	$0.397057\pi$
$314$		0			0
$315$	−4.96691	+	7.47171i	−0.279854	+	0.420983i
$316$		0			0
$317$	23.3162	+	1.76844i	1.30957	+	0.0993254i	0.711822	−	0.702360i	$-0.247870\pi$
$317$	23.3162	+	1.76844i	1.30957	+	0.0993254i	0.597746	+	0.801686i	$0.296063\pi$
$318$		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	−0.999086	−	0.0427432i	$-0.986390\pi$
$331$	−0.837922	−	6.28800i	−0.0460564	−	0.345620i	0.953030	−	0.302877i	$-0.0979471\pi$
$332$		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	−0.635255	−	0.772302i	$-0.719105\pi$
$337$	−4.11955	−	30.9142i	−0.224406	−	1.68401i	0.410849	−	0.911703i	$-0.365232\pi$
$338$		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	−0.0451374	+	0.998981i	$0.514373\pi$
$347$	−15.4454	+	30.1721i	−0.829154	+	1.61972i	−0.784016	+	0.620740i	$0.786832\pi$
$348$		0			0
$349$	−5.73871	+	19.6694i	−0.307186	+	1.05288i	0.649163	+	0.760649i	$0.275119\pi$
$349$	−5.73871	+	19.6694i	−0.307186	+	1.05288i	−0.956349	+	0.292227i	$0.905604\pi$
$350$		0			0
$351$	−7.30718	−	0.554220i	−0.390028	−	0.0295821i
$352$		0			0
$353$	−7.38945	+	11.1159i	−0.393301	+	0.591641i	−0.975120	−	0.221677i	$-0.928847\pi$
$353$	−7.38945	+	11.1159i	−0.393301	+	0.591641i	0.581820	+	0.813318i	$0.302341\pi$
$354$		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	0.407754	−	0.913092i	$-0.366312\pi$
$359$	−10.2274	−	11.2440i	−0.539780	−	0.593436i	−0.947534	+	0.319656i	$0.896433\pi$
$360$		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	0.928953	−	0.370197i	$-0.120710\pi$
$367$	20.3131	+	11.8992i	1.06033	+	0.621135i	0.131380	+	0.991332i	$0.458059\pi$
$368$		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	−0.427684	−	0.903928i	$-0.640671\pi$
$373$	−25.6709	−	9.09967i	−1.32919	−	0.471163i	−0.901507	+	0.432765i	$0.857538\pi$
$374$		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	0.163763	−	0.986500i	$-0.447637\pi$
$379$	0.504284	+	0.0769384i	0.0259033	+	0.00395206i	−0.137860	+	0.990452i	$0.544022\pi$
$380$		0			0
$381$	−0.930947	−	49.1849i	−0.0476939	−	2.51982i
$382$		0			0
$383$	16.4205	+	19.4858i	0.839047	+	0.995677i	0.999962	+	0.00870907i	$0.00277222\pi$
$383$	16.4205	+	19.4858i	0.839047	+	0.995677i	−0.160915	+	0.986968i	$0.551445\pi$
$384$		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	0.586915	−	0.809649i	$-0.300342\pi$
$389$	31.2826	−	16.7685i	1.58609	−	0.850198i	0.999178	−	0.0405490i	$-0.0129107\pi$
$390$		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	0.478132	+	0.878288i	$0.341314\pi$
$397$	−5.29930	+	30.8110i	−0.265964	+	1.54636i	−0.744096	+	0.668072i	$0.767120\pi$
$398$		0			0
$399$	−54.6765	+	44.3333i	−2.73725	+	2.21944i
$400$		0			0
$401$	9.75140	−	4.31215i	0.486962	−	0.215339i	−0.146354	−	0.989232i	$-0.546754\pi$
$401$	9.75140	−	4.31215i	0.486962	−	0.215339i	0.633315	+	0.773894i	$0.281694\pi$
$402$		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	−0.798564	−	0.601910i	$-0.794406\pi$
$409$	−1.41572	+	1.68000i	−0.0700028	+	0.0830707i	0.728561	+	0.684981i	$0.240190\pi$
$410$		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	0.329208	−	0.944258i	$-0.393218\pi$
$419$	−5.62711	−	3.01632i	−0.274903	−	0.147357i	−0.604110	+	0.796901i	$0.706471\pi$
$420$		0			0
$421$	−4.64951	−	8.29309i	−0.226603	−	0.404180i	0.735230	−	0.677818i	$-0.237074\pi$
$421$	−4.64951	−	8.29309i	−0.226603	−	0.404180i	−0.961833	+	0.273638i	$0.911773\pi$
$422$		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	0.621565	−	0.783362i	$-0.286497\pi$
$431$	17.3643	+	4.01272i	0.836411	+	0.193286i	0.214845	+	0.976648i	$0.431075\pi$
$432$		0			0
$433$	−5.38277	+	12.8232i	−0.258679	+	0.616244i	−0.998393	−	0.0566781i	$-0.981949\pi$
$433$	−5.38277	+	12.8232i	−0.258679	+	0.616244i	0.739713	+	0.672922i	$0.234961\pi$
$434$		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	0.637836	−	0.770172i	$-0.279830\pi$
$439$	−0.866088	−	0.758332i	−0.0413361	−	0.0361932i	−0.679172	+	0.733979i	$0.737661\pi$
$440$		0			0
$441$	16.0472	+	11.1111i	0.764151	+	0.529100i
$442$		0			0
$443$	27.8462	+	17.7606i	1.32301	+	0.843829i	0.994906	−	0.100812i	$-0.0321440\pi$
$443$	27.8462	+	17.7606i	1.32301	+	0.843829i	0.328106	+	0.944641i	$0.393590\pi$
$444$		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	0.982524	+	0.186138i	$0.0595972\pi$
$449$	24.3688	+	24.8344i	1.15004	+	1.17201i	0.167511	+	0.985870i	$0.446427\pi$
$450$		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	0.944685	−	0.327979i	$-0.106368\pi$
$457$	5.91364	+	8.89587i	0.276628	+	0.416131i	−0.668057	+	0.744110i	$0.732874\pi$
$458$		0			0
$459$	0.272003	+	0.816068i	0.0126960	+	0.0380908i
$460$		0			0
$461$	27.1600	+	3.09738i	1.26497	+	0.144259i	0.719867	−	0.694112i	$-0.244203\pi$
$461$	27.1600	+	3.09738i	1.26497	+	0.144259i	0.545099	+	0.838372i	$0.316492\pi$
$462$		0			0
$463$	20.4800	−	0.775550i	0.951788	−	0.0360429i	0.442619	−	0.896710i	$-0.354049\pi$
$463$	20.4800	−	0.775550i	0.951788	−	0.0360429i	0.509169	+	0.860667i	$0.329953\pi$
$464$		0			0
$465$	0.179559	−	3.15921i	0.00832687	−	0.146505i
$466$		0			0
$467$	−18.6146	−	30.4409i	−0.861380	−	1.40863i	−0.912120	−	0.409923i	$-0.865556\pi$
$467$	−18.6146	−	30.4409i	−0.861380	−	1.40863i	0.0507400	−	0.998712i	$-0.483842\pi$
$468$		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	0.754905	−	0.655834i	$-0.227683\pi$
$479$	31.9110	+	1.20842i	1.45805	+	0.0552143i	0.703143	+	0.711048i	$0.251779\pi$
$480$		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	−0.721070	−	0.692862i	$-0.756349\pi$
$487$	−25.0487	+	4.79796i	−1.13507	+	0.217416i	−0.413997	+	0.910278i	$0.635868\pi$
$488$		0			0
$489$	−21.2083	−	4.06235i	−0.959074	−	0.183706i
$490$		0			0
$491$	1.93532	+	9.16181i	0.0873400	+	0.413467i	0.999989	+	0.00472219i	$0.00150313\pi$
$491$	1.93532	+	9.16181i	0.0873400	+	0.413467i	−0.912649	+	0.408744i	$0.865967\pi$
$492$		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	−0.999214	−	0.0396442i	$-0.987378\pi$
$499$	−16.1029	−	22.3411i	−0.720865	−	1.00012i	0.278349	−	0.960480i	$-0.410213\pi$
$500$		0			0
$501$	19.5091	−	27.2726i	0.871603	−	1.21845i
$502$		0			0
$503$	−17.8658	−	24.7869i	−0.796597	−	1.10519i	−0.992218	−	0.124515i	$-0.960263\pi$
$503$	−17.8658	−	24.7869i	−0.796597	−	1.10519i	0.195621	−	0.980680i	$-0.437328\pi$
$504$		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	0.588384	−	0.808582i	$-0.299765\pi$
$509$	34.5730	−	10.8010i	1.53242	−	0.478746i	0.944038	+	0.329836i	$0.106993\pi$
$510$		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	−0.944194	−	0.329388i	$-0.893157\pi$
$521$	−12.0305	+	13.2264i	−0.527067	+	0.579460i	0.417127	+	0.908848i	$0.363037\pi$
$522$		0			0
$523$	29.3291	+	1.11065i	1.28247	+	0.0485654i	0.670258	−	0.742128i	$-0.266183\pi$
$523$	29.3291	+	1.11065i	1.28247	+	0.0485654i	0.612212	+	0.790693i	$0.290280\pi$
$524$		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	−0.310938	−	0.950430i	$-0.600643\pi$
$541$	−19.2562	−	2.19602i	−0.827888	−	0.0944141i	−0.516949	+	0.856016i	$0.672932\pi$
$542$		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	0.490802	+	0.871271i	$0.336704\pi$
$547$	10.9889	+	43.7602i	0.469850	+	1.87105i	−0.0209517	+	0.999780i	$0.506670\pi$
$548$		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	−0.689180	−	0.724590i	$-0.742029\pi$
$557$	3.91055	−	29.3459i	0.165695	−	1.24342i	0.854875	−	0.518834i	$-0.173634\pi$
$558$		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	0.980648	+	0.195779i	$0.0627234\pi$
$563$	30.9466	+	27.0963i	1.30424	+	1.14197i	0.323597	+	0.946195i	$0.395108\pi$
$564$		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	−0.411120	−	0.911581i	$-0.634862\pi$
$569$	12.5823	−	29.9745i	0.527478	−	1.25659i	0.938598	−	0.345013i	$-0.112126\pi$
$570$		0			0
$571$	−16.2231	−	3.74899i	−0.678915	−	0.156890i	−0.128409	−	0.991721i	$-0.540987\pi$
$571$	−16.2231	−	3.74899i	−0.678915	−	0.156890i	−0.550506	+	0.834831i	$0.685565\pi$
$572$		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	−0.999983	−	0.00581146i	$-0.998150\pi$
$577$	−18.3055	−	23.4707i	−0.762070	−	0.977098i	0.237913	−	0.971286i	$-0.423537\pi$
$578$		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	−0.664200	+	0.747555i	$0.731228\pi$
$587$	−39.7603	+	23.2913i	−1.64108	+	0.961334i	−0.976882	+	0.213779i	$0.931423\pi$
$588$		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	−0.876371	−	0.481637i	$-0.840042\pi$
$593$	−6.16470	+	7.31551i	−0.253154	+	0.300412i	0.623217	+	0.782049i	$0.285825\pi$
$594$		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	−0.878396	−	0.477934i	$-0.841386\pi$
$599$	2.97573	−	11.8500i	0.121585	−	0.484179i	0.999980	−	0.00624497i	$-0.00198785\pi$
$600$		0			0
$601$	33.2171	−	14.6889i	1.35495	−	0.599172i	0.405793	−	0.913965i	$-0.366995\pi$
$601$	33.2171	−	14.6889i	1.35495	−	0.599172i	0.949160	+	0.314793i	$0.101935\pi$
$602$		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	−0.975470	−	0.220134i	$-0.929350\pi$
$607$	−18.1556	+	18.5025i	−0.736915	+	0.750995i	0.238555	+	0.971129i	$0.423326\pi$
$608$		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	−0.182195	−	0.983262i	$-0.558320\pi$
$613$	13.2654	−	7.11069i	0.535784	−	0.287198i	0.717979	+	0.696064i	$0.245067\pi$
$614$		0			0
$615$	2.96038	+	17.2121i	0.119374	+	0.694060i
$616$		0			0
$617$	−0.902893	−	15.8857i	−0.0363491	−	0.639534i	−0.963970	−	0.266011i	$-0.914294\pi$
$617$	−0.902893	−	15.8857i	−0.0363491	−	0.639534i	0.927621	−	0.373523i	$-0.121850\pi$
$618$		0			0
$619$	−31.6936	−	37.6101i	−1.27387	−	1.51168i	−0.752959	−	0.658068i	$-0.771374\pi$
$619$	−31.6936	−	37.6101i	−1.27387	−	1.51168i	−0.520915	−	0.853609i	$-0.674409\pi$
$620$		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	−0.476742	−	0.879043i	$-0.658182\pi$
$631$	−33.4699	−	9.08148i	−1.33242	−	0.361528i	−0.855674	+	0.517515i	$0.826857\pi$
$632$		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	0.902450	−	0.430795i	$-0.141767\pi$
$641$	−0.939261	−	2.23757i	−0.0370986	−	0.0883789i	−0.939548	+	0.342416i	$0.888755\pi$
$642$		0			0
$643$	11.8122	+	12.9863i	0.465827	+	0.512131i	0.926940	−	0.375210i	$-0.122429\pi$
$643$	11.8122	+	12.9863i	0.465827	+	0.512131i	−0.461113	+	0.887341i	$0.652550\pi$
$644$		0			0
$645$	4.94359	+	1.96597i	0.194654	+	0.0774100i
$646$		0			0
$647$	−20.7221	−	6.47381i	−0.814669	−	0.254512i	−0.137653	−	0.990480i	$-0.543956\pi$
$647$	−20.7221	−	6.47381i	−0.814669	−	0.254512i	−0.677016	+	0.735969i	$0.736727\pi$
$648$		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	0.581966	+	0.813213i	$0.302284\pi$
$653$	−8.84150	+	30.3041i	−0.345994	+	1.18589i	−0.927960	+	0.372680i	$0.878439\pi$
$654$		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	−0.341459	−	0.939897i	$-0.610921\pi$
$659$	−4.13341	+	1.12153i	−0.161015	+	0.0436886i	0.180444	+	0.983585i	$0.442246\pi$
$660$		0			0
$661$	0.0648022	−	0.139351i	0.00252051	−	0.00542013i	−0.905487	−	0.424373i	$-0.860494\pi$
$661$	0.0648022	−	0.139351i	0.00252051	−	0.00542013i	0.908008	+	0.418953i	$0.137603\pi$
$662$		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	0.150451	−	0.988617i	$-0.451927\pi$
$673$	−12.4433	−	5.50251i	−0.479652	−	0.212106i	−0.630104	+	0.776511i	$0.716988\pi$
$674$		0			0
$675$	3.63085	−	7.80781i	0.139752	−	0.300523i
$676$		0			0
$677$	−12.9525	+	3.51444i	−0.497806	+	0.135071i	−0.501909	−	0.864920i	$-0.667369\pi$
$677$	−12.9525	+	3.51444i	−0.497806	+	0.135071i	0.00410280	+	0.999992i	$0.498694\pi$
$678$		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	−0.535486	−	0.844544i	$-0.679872\pi$
$683$	9.67319	−	33.1548i	0.370134	−	1.26863i	0.905621	−	0.424088i	$-0.139405\pi$
$684$		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	0.425192	−	0.905103i	$-0.360207\pi$
$691$	2.96200	+	1.17793i	0.112680	+	0.0448105i	−0.312512	+	0.949914i	$0.601171\pi$
$692$		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	−0.127880	−	0.991790i	$-0.540817\pi$
$701$	−27.9464	−	16.3708i	−1.05552	−	0.618316i	−0.927641	+	0.373473i	$0.878167\pi$
$702$		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	−0.989654	−	0.143475i	$-0.954172\pi$
$709$	−39.5453	+	19.3081i	−1.48516	+	0.725132i	−0.495502	+	0.868607i	$0.665016\pi$
$710$		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	−0.998838	−	0.0481968i	$-0.984653\pi$
$719$	−0.318918	−	5.61111i	−0.0118936	−	0.209259i	0.986944	−	0.161062i	$-0.0514920\pi$
$720$		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	−0.340577	−	0.940217i	$-0.610622\pi$
$727$	−14.4373	+	1.09501i	−0.535451	+	0.0406118i	−0.194874	+	0.980828i	$0.562430\pi$
$728$		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	−0.932310	−	0.361660i	$-0.882210\pi$
$733$	−20.8780	+	16.9285i	−0.771145	+	0.625267i	0.161164	+	0.986928i	$0.448475\pi$
$734$		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	0.737394	−	0.675463i	$-0.236056\pi$
$739$	43.7111	−	4.98491i	1.60794	−	0.183373i	0.870544	+	0.492090i	$0.163767\pi$
$740$		0			0
$741$	−62.0523	+	46.5351i	−2.27955	+	1.70951i
$742$		0			0
$743$	−1.20878	+	1.43443i	−0.0443458	+	0.0526242i	−0.786411	−	0.617703i	$-0.788063\pi$
$743$	−1.20878	+	1.43443i	−0.0443458	+	0.0526242i	0.742065	+	0.670328i	$0.233846\pi$
$744$		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	−0.229381	−	0.973337i	$-0.573670\pi$
$751$	21.0067	−	29.1446i	0.766546	−	1.06350i	0.995927	−	0.0901655i	$-0.0287396\pi$
$752$		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	−0.989807	−	0.142413i	$-0.954514\pi$
$757$	−6.37968	−	21.8663i	−0.231873	−	0.794744i	0.757934	−	0.652331i	$-0.226209\pi$
$758$		0			0
$759$	3.58462	+	4.59607i	0.130114	+	0.166827i
$760$		0			0
$761$	10.5749	+	28.1304i	0.383339	+	1.01973i	0.976666	+	0.214765i	$0.0688984\pi$
$761$	10.5749	+	28.1304i	0.383339	+	1.01973i	−0.593327	+	0.804961i	$0.702186\pi$
$762$		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	0.751524	+	0.659705i	$0.229319\pi$
$769$	3.81369	+	40.1823i	0.137525	+	1.44901i	−0.613999	+	0.789307i	$0.710440\pi$
$770$		0			0
$771$	63.3971	−	43.8962i	2.28319	−	1.58088i
$772$		0			0
$773$	14.5023	+	12.6980i	0.521613	+	0.456715i	0.878712	−	0.477351i	$-0.158403\pi$
$773$	14.5023	+	12.6980i	0.521613	+	0.456715i	−0.357100	+	0.934066i	$0.616234\pi$
$774$		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	−0.377165	−	0.926146i	$-0.623101\pi$
$787$	17.1049	−	30.5092i	0.609725	−	1.08754i	0.986891	−	0.161390i	$-0.0515976\pi$
$788$		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
$797$	−50.7748	+	1.92277i	−1.79854	+	0.0681080i	−0.915770	−	0.401704i	$-0.868418\pi$
$797$	−50.7748	+	1.92277i	−1.79854	+	0.0681080i	−0.882767	+	0.469812i	$0.844322\pi$
$798$		0			0
$799$	−0.281198	+	4.94746i	−0.00994808	+	0.175029i
$800$		0			0
$801$	−7.14842	−	11.6900i	−0.252577	−	0.413045i
$802$		0			0
$803$	0.0313342	−	1.65549i	0.00110576	−	0.0584208i
$804$		0			0
$805$	4.57242	−	1.62080i	0.161157	−	0.0571258i
$806$		0			0
$807$	−35.5069	−	33.5461i	−1.24990	−	1.18088i
$808$		0			0
$809$	23.0736	−	3.52033i	0.811225	−	0.123768i	0.268069	−	0.963400i	$-0.413615\pi$
$809$	23.0736	−	3.52033i	0.811225	−	0.123768i	0.543156	+	0.839632i	$0.317229\pi$
$810$		0			0
$811$	11.3518	+	24.4109i	0.398615	+	0.857184i	0.998374	+	0.0570035i	$0.0181546\pi$
$811$	11.3518	+	24.4109i	0.398615	+	0.857184i	−0.599759	+	0.800181i	$0.704737\pi$
$812$		0			0
$813$	3.82203	+	0.144735i	0.134045	+	0.00507608i
$814$		0			0
$815$	−3.84866	+	4.23123i	−0.134813	+	0.148213i
$816$		0			0
$817$	17.9756	+	14.5751i	0.628886	+	0.509919i
$818$		0			0
$819$	40.2410	+	30.1781i	1.40613	+	1.05451i
$820$		0			0
$821$	6.00413	−	1.15006i	0.209546	−	0.0401374i	−0.0822785	−	0.996609i	$-0.526220\pi$
$821$	6.00413	−	1.15006i	0.209546	−	0.0401374i	0.291824	+	0.956472i	$0.405738\pi$
$822$		0			0
$823$	2.87222	+	0.550159i	0.100119	+	0.0191773i	0.237940	−	0.971280i	$-0.423528\pi$
$823$	2.87222	+	0.550159i	0.100119	+	0.0191773i	−0.137821	+	0.990457i	$0.544010\pi$
$824$		0			0
$825$	−2.70223	−	12.7923i	−0.0940794	−	0.445371i
$826$		0			0
$827$	16.7949	−	5.24691i	0.584016	−	0.182453i	0.00810691	−	0.999967i	$-0.497419\pi$
$827$	16.7949	−	5.24691i	0.584016	−	0.182453i	0.575909	+	0.817514i	$0.304648\pi$
$828$		0			0
$829$	−22.0274	+	20.8110i	−0.765043	+	0.722795i	−0.966490	−	0.256705i	$-0.917363\pi$
$829$	−22.0274	+	20.8110i	−0.765043	+	0.722795i	0.201447	+	0.979499i	$0.435436\pi$
$830$		0			0
$831$	−15.0944	+	45.2864i	−0.523619	+	1.57097i
$832$		0			0
$833$	−1.38284	−	1.91854i	−0.0479124	−	0.0664735i
$834$		0			0
$835$	−3.46710	−	8.17725i	−0.119984	−	0.282985i
$836$		0			0
$837$	−1.97309	−	2.73745i	−0.0682000	−	0.0946203i
$838$		0			0
$839$	−3.46458	+	10.3945i	−0.119610	+	0.358857i	−0.991373	−	0.131072i	$-0.958158\pi$
$839$	−3.46458	+	10.3945i	−0.119610	+	0.358857i	0.871762	+	0.489929i	$0.162977\pi$
$840$		0			0
$841$	−20.5609	+	19.4255i	−0.708996	+	0.669844i
$842$		0			0
$843$	−5.19975	+	1.62446i	−0.179089	+	0.0559494i
$844$		0			0
$845$	0.262410	+	1.24225i	0.00902717	+	0.0427345i
$846$		0			0
$847$	−33.5259	−	6.42171i	−1.15196	−	0.220652i
$848$		0			0
$849$	21.5736	−	4.13232i	0.740405	−	0.141821i
$850$		0			0
$851$	−5.07604	−	3.80669i	−0.174004	−	0.130492i
$852$		0			0
$853$	2.63884	+	2.13965i	0.0903520	+	0.0732601i	0.673920	−	0.738804i	$-0.264609\pi$
$853$	2.63884	+	2.13965i	0.0903520	+	0.0732601i	−0.583568	+	0.812064i	$0.698344\pi$
$854$		0			0
$855$	−13.3924	+	14.7237i	−0.458012	+	0.503540i
$856$		0			0
$857$	−3.85404	−	0.145947i	−0.131652	−	0.00498546i	−0.0280665	−	0.999606i	$-0.508935\pi$
$857$	−3.85404	−	0.145947i	−0.131652	−	0.00498546i	−0.103585	+	0.994621i	$0.533031\pi$
$858$		0			0
$859$	1.00803	+	2.16768i	0.0343936	+	0.0739602i	0.923194	−	0.384334i	$-0.125569\pi$
$859$	1.00803	+	2.16768i	0.0343936	+	0.0739602i	−0.888800	+	0.458294i	$0.848461\pi$
$860$		0			0
$861$	87.8436	−	13.4023i	2.99370	−	0.456748i
$862$		0			0
$863$	16.2136	+	15.3182i	0.551916	+	0.521438i	0.911295	−	0.411754i	$-0.135084\pi$
$863$	16.2136	+	15.3182i	0.551916	+	0.521438i	−0.359379	+	0.933192i	$0.617011\pi$
$864$		0			0
$865$	4.58676	−	1.62589i	0.155955	−	0.0552818i
$866$		0			0
$867$	−0.824725	+	43.5728i	−0.0280091	+	1.47981i
$868$		0			0
$869$	−4.04693	−	6.61804i	−0.137283	−	0.224502i
$870$		0			0
$871$	0.965390	−	16.9853i	0.0327110	−	0.575524i
$872$		0			0
$873$	10.3835	−	0.393209i	0.351428	−	0.0133081i
$874$		0			0
$875$	−22.7518	−	2.59467i	−0.769152	−	0.0877157i
$876$		0			0
$877$	8.72694	+	26.1827i	0.294688	+	0.884126i	0.986744	+	0.162283i	$0.0518857\pi$
$877$	8.72694	+	26.1827i	0.294688	+	0.884126i	−0.692056	+	0.721843i	$0.743295\pi$
$878$		0			0
$879$	45.8356	+	68.9503i	1.54599	+	2.32564i
$880$		0			0
$881$	12.8873	+	51.3201i	0.434183	+	1.72902i	0.656757	+	0.754102i	$0.271928\pi$
$881$	12.8873	+	51.3201i	0.434183	+	1.72902i	−0.222574	+	0.974916i	$0.571446\pi$
$882$		0			0
$883$	−6.99341	+	12.4738i	−0.235347	+	0.419776i	−0.964310	−	0.264777i	$-0.914702\pi$
$883$	−6.99341	+	12.4738i	−0.235347	+	0.419776i	0.728963	+	0.684554i	$0.240003\pi$
$884$		0			0
$885$	4.36787	−	20.6775i	0.146824	−	0.695066i
$886$		0			0
$887$	27.6216	+	28.1493i	0.927442	+	0.945162i	0.998631	−	0.0523006i	$-0.0166554\pi$
$887$	27.6216	+	28.1493i	0.927442	+	0.945162i	−0.0711895	+	0.997463i	$0.522680\pi$
$888$		0			0
$889$	−34.5868	+	56.5606i	−1.16000	+	1.89698i
$890$		0			0
$891$	0.920822	−	6.91010i	0.0308487	−	0.231497i
$892$		0			0
$893$	−71.6578	−	45.7040i	−2.39794	−	1.52943i
$894$		0			0
$895$	3.32749	+	2.30396i	0.111226	+	0.0770129i
$896$		0			0
$897$	15.1832	+	13.2941i	0.506951	+	0.443877i
$898$		0			0
$899$	1.23261	−	0.853459i	0.0411098	−	0.0284645i
$900$		0			0
$901$	0.417593	+	4.39990i	0.0139121	+	0.146582i
$902$		0			0
$903$	10.4769	−	24.9589i	0.348651	−	0.830580i
$904$		0			0
$905$	−2.74625	−	0.634631i	−0.0912886	−	0.0210959i
$906$		0			0
$907$	9.75799	−	6.22374i	0.324009	−	0.206656i	−0.365718	−	0.930726i	$-0.619177\pi$
$907$	9.75799	−	6.22374i	0.324009	−	0.206656i	0.689727	+	0.724070i	$0.257731\pi$
$908$		0			0
$909$	10.8943	+	28.9802i	0.361342	+	0.961213i
$910$		0			0
$911$	18.0026	+	23.0822i	0.596452	+	0.764749i	0.987839	−	0.155477i	$-0.0496915\pi$
$911$	18.0026	+	23.0822i	0.596452	+	0.764749i	−0.391387	+	0.920226i	$0.628005\pi$
$912$		0			0
$913$	−0.801689	−	2.74778i	−0.0265320	−	0.0909383i
$914$		0			0
$915$	12.4902	+	22.2782i	0.412915	+	0.736495i
$916$		0			0
$917$	−37.8328	−	20.2796i	−1.24935	−	0.669692i
$918$		0			0
$919$	−33.6134	+	46.6351i	−1.10880	+	1.53835i	−0.296576	+	0.955009i	$0.595845\pi$
$919$	−33.6134	+	46.6351i	−1.10880	+	1.53835i	−0.812228	+	0.583340i	$0.801745\pi$
$920$		0			0
$921$	0.0814081	−	0.0476882i	0.00268249	−	0.00157138i
$922$		0			0
$923$	11.8663	−	31.5658i	0.390585	−	1.03900i
$924$		0			0
$925$	6.48539	+	12.6690i	0.213238	+	0.416553i
$926$		0			0
$927$	−3.78376	+	4.49010i	−0.124275	+	0.147474i
$928$		0			0
$929$	−24.4398	+	18.3282i	−0.801842	+	0.601329i	−0.920113	−	0.391653i	$-0.871903\pi$
$929$	−24.4398	+	18.3282i	−0.801842	+	0.601329i	0.118271	+	0.992981i	$0.462265\pi$
$930$		0			0
$931$	40.3009	−	4.59600i	1.32081	−	0.150628i
$932$		0			0
$933$	11.7411	−	46.7558i	0.384386	−	1.53072i
$934$		0			0
$935$	0.316411	−	0.139920i	0.0103477	−	0.00457586i
$936$		0			0
$937$	41.1532	−	33.3682i	1.34441	−	1.09009i	0.356634	−	0.934244i	$-0.383924\pi$
$937$	41.1532	−	33.3682i	1.34441	−	1.09009i	0.987781	−	0.155846i	$-0.0498105\pi$
$938$		0			0
$939$	9.12099	−	53.0309i	0.297652	−	1.73060i
$940$		0			0
$941$	−0.0780944	+	0.0795865i	−0.00254580	+	0.00259445i	−0.715038	−	0.699086i	$-0.753591\pi$
$941$	−0.0780944	+	0.0795865i	−0.00254580	+	0.00259445i	0.712492	+	0.701680i	$0.247566\pi$
$942$		0			0
$943$	19.7097	−	1.49490i	0.641835	−	0.0486806i
$944$		0			0
$945$	4.10753	+	2.00551i	0.133618	+	0.0652394i
$946$		0			0
$947$	−20.3087	+	10.8861i	−0.659945	+	0.353752i	−0.768052	−	0.640387i	$-0.778774\pi$
$947$	−20.3087	+	10.8861i	−0.659945	+	0.353752i	0.108108	+	0.994139i	$0.465521\pi$
$948$		0			0
$949$	−0.971746	−	5.64989i	−0.0315442	−	0.183403i
$950$		0			0
$951$	−3.44299	−	60.5766i	−0.111646	−	1.96433i
$952$		0			0
$953$	13.4520	+	15.9632i	0.435754	+	0.517099i	0.937533	−	0.347897i	$-0.113104\pi$
$953$	13.4520	+	15.9632i	0.435754	+	0.517099i	−0.501779	+	0.864996i	$0.667321\pi$
$954$		0			0
$955$	0.216138	+	11.4192i	0.00699405	+	0.369517i
$956$		0			0
$957$	−2.41215	−	0.368021i	−0.0779738	−	0.0118964i
$958$		0			0
$959$	1.00609	−	10.6005i	0.0324884	−	0.342309i
$960$		0			0
$961$	−25.0279	+	12.2200i	−0.807353	+	0.394193i
$962$		0			0
$963$	44.0259	+	15.6060i	1.41872	+	0.502897i
$964$		0			0
$965$	−2.72668	−	0.739837i	−0.0877749	−	0.0238162i
$966$		0			0
$967$	12.8206	−	11.2255i	0.412281	−	0.360986i	−0.427403	−	0.904061i	$-0.640571\pi$
$967$	12.8206	−	11.2255i	0.412281	−	0.360986i	0.839684	+	0.543075i	$0.182740\pi$
$968$		0			0
$969$	7.85593	+	4.60195i	0.252369	+	0.147836i
$970$		0			0
$971$	10.1594	−	2.34772i	0.326029	−	0.0753420i	−0.0589675	−	0.998260i	$-0.518781\pi$
$971$	10.1594	−	2.34772i	0.326029	−	0.0753420i	0.384997	+	0.922918i	$0.374203\pi$
$972$		0			0
$973$	62.4629	−	24.8403i	2.00247	−	0.796342i
$974$		0			0
$975$	−17.5212	−	41.7402i	−0.561127	−	1.33676i
$976$		0			0
$977$	8.93736	+	9.82577i	0.285932	+	0.314354i	0.865834	−	0.500332i	$-0.166789\pi$
$977$	8.93736	+	9.82577i	0.285932	+	0.314354i	−0.579902	+	0.814686i	$0.696909\pi$
$978$		0			0
$979$	−3.79594	−	1.50957i	−0.121319	−	0.0482461i
$980$		0			0
$981$	58.9313	+	18.4108i	1.88153	+	0.587811i
$982$		0			0
$983$	6.18428	−	9.30300i	0.197248	−	0.296720i	−0.720836	−	0.693106i	$-0.756242\pi$
$983$	6.18428	−	9.30300i	0.197248	−	0.296720i	0.918084	+	0.396386i	$0.129736\pi$
$984$		0			0
$985$	−9.59610	−	0.727825i	−0.305757	−	0.0231904i
$986$		0			0
$987$	−27.8438	+	95.4345i	−0.886279	+	3.03771i
$988$		0			0
$989$	2.74373	−	5.35977i	0.0872455	−	0.170431i
$990$		0			0
$991$	−3.30753	+	4.24079i	−0.105067	+	0.134713i	−0.838180	−	0.545394i	$-0.816380\pi$
$991$	−3.30753	+	4.24079i	−0.105067	+	0.134713i	0.733113	+	0.680107i	$0.238067\pi$
$992$		0			0
$993$	−15.8859	+	4.31036i	−0.504124	+	0.136785i
$994$		0			0
$995$	−1.65870	+	3.56687i	−0.0525842	+	0.113078i
$996$		0			0
$997$	12.4540	+	5.50725i	0.394421	+	0.174416i	0.592126	−	0.805845i	$-0.298289\pi$
$997$	12.4540	+	5.50725i	0.394421	+	0.174416i	−0.197705	+	0.980262i	$0.563349\pi$
$998$		0			0
$999$	−0.789679	−	5.92597i	−0.0249843	−	0.187489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.e.a.9.3	✓	1148
167.130	even	83	inner	668.2.e.a.297.3	yes	1148

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.e.a.9.3	✓	1148	1.1	even	1	trivial
668.2.e.a.297.3	yes	1148	167.130	even	83	inner

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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