LMFDB - Embedded newform 668.2.e.a.21.4

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			21.4
Character	$\chi$	$=$	668.21
Dual form			668.2.e.a.509.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.77371 - 0.270614i) q^{3} +(-1.21708 - 1.44428i) q^{5} +(-0.212405 + 0.294689i) q^{7} +(0.209294 + 0.0653857i) q^{9} +O(q^{10})$	\(q+(-1.77371 - 0.270614i) q^{3} +(-1.21708 - 1.44428i) q^{5} +(-0.212405 + 0.294689i) q^{7} +(0.209294 + 0.0653857i) q^{9} +(-2.42906 + 2.29492i) q^{11} +(-0.424686 + 3.18696i) q^{13} +(1.76790 + 2.89109i) q^{15} +(2.82992 - 4.25704i) q^{17} +(5.24079 + 1.21109i) q^{19} +(0.456490 - 0.465212i) q^{21} +(0.693178 + 3.28150i) q^{23} +(0.242860 - 1.41202i) q^{25} +(4.48341 + 2.18904i) q^{27} +(-0.511898 + 2.42332i) q^{29} +(0.832857 - 0.159530i) q^{31} +(4.92948 - 3.41318i) q^{33} +(0.684128 - 0.0518884i) q^{35} +(-0.474860 + 0.148352i) q^{37} +(1.61570 - 5.53781i) q^{39} +(-0.439269 + 0.174689i) q^{41} +(11.5486 + 4.09369i) q^{43} +(-0.160292 - 0.381859i) q^{45} +(-2.37229 + 9.44702i) q^{47} +(2.17173 + 6.51564i) q^{49} +(-6.17147 + 6.78493i) q^{51} +(1.38084 + 1.03554i) q^{53} +(6.27088 + 0.715144i) q^{55} +(-8.96789 - 3.56636i) q^{57} +(2.10406 + 3.16513i) q^{59} +(4.62066 + 5.92443i) q^{61} +(-0.0637234 + 0.0477883i) q^{63} +(5.11975 - 3.26542i) q^{65} +(-8.41804 + 9.98949i) q^{67} +(-0.341476 - 6.00800i) q^{69} +(-1.33750 - 14.0923i) q^{71} +(3.57533 - 6.37713i) q^{73} +(-0.812875 + 2.43880i) q^{75} +(-0.160344 - 1.20327i) q^{77} +(7.02518 + 0.266034i) q^{79} +(-7.90070 - 5.47046i) q^{81} +(-7.61971 + 2.06748i) q^{83} +(-9.59262 + 1.09396i) q^{85} +(1.56374 - 4.15974i) q^{87} +(2.52173 - 4.12384i) q^{89} +(-0.848957 - 0.802075i) q^{91} +(-1.52042 + 0.0575760i) q^{93} +(-4.62931 - 9.04319i) q^{95} +(-17.4069 - 3.33420i) q^{97} +(-0.658442 + 0.321486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$.

$n$	$5$	$335$
$\chi(n)$	$e\left(\frac{23}{83}\right)$	$1$

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
$3$	−1.77371	−	0.270614i	−1.02405	−	0.156239i	−0.383008	−	0.923745i	$-0.625112\pi$
$3$	−1.77371	−	0.270614i	−1.02405	−	0.156239i	−0.641042	+	0.767506i	$0.721498\pi$
$4$		0			0
$5$	−1.21708	−	1.44428i	−0.544296	−	0.645903i	0.421001	−	0.907060i	$-0.361679\pi$
$5$	−1.21708	−	1.44428i	−0.544296	−	0.645903i	−0.965296	+	0.261157i	$0.915896\pi$
$6$		0			0
$7$	−0.212405	+	0.294689i	−0.0802814	+	0.111382i	−0.849463	−	0.527648i	$-0.823074\pi$
$7$	−0.212405	+	0.294689i	−0.0802814	+	0.111382i	0.769181	+	0.639030i	$0.220664\pi$
$8$		0			0
$9$	0.209294	+	0.0653857i	0.0697645	+	0.0217952i
$10$		0			0
$11$	−2.42906	+	2.29492i	−0.732389	+	0.691944i	−0.959432	−	0.281940i	$-0.909022\pi$
$11$	−2.42906	+	2.29492i	−0.732389	+	0.691944i	0.227043	+	0.973885i	$0.427094\pi$
$12$		0			0
$13$	−0.424686	+	3.18696i	−0.117787	+	0.883904i	0.828367	+	0.560186i	$0.189270\pi$
$13$	−0.424686	+	3.18696i	−0.117787	+	0.883904i	−0.946154	+	0.323718i	$0.895067\pi$
$14$		0			0
$15$	1.76790	+	2.89109i	0.456471	+	0.746477i
$16$		0			0
$17$	2.82992	−	4.25704i	0.686357	−	1.03248i	−0.310288	−	0.950642i	$-0.600426\pi$
$17$	2.82992	−	4.25704i	0.686357	−	1.03248i	0.996645	−	0.0818423i	$-0.0260804\pi$
$18$		0			0
$19$	5.24079	+	1.21109i	1.20232	+	0.277844i	0.778349	−	0.627832i	$-0.216057\pi$
$19$	5.24079	+	1.21109i	1.20232	+	0.277844i	0.423971	+	0.905676i	$0.360636\pi$
$20$		0			0
$21$	0.456490	−	0.465212i	0.0996144	−	0.101518i
$22$		0			0
$23$	0.693178	+	3.28150i	0.144538	+	0.684240i	0.988914	+	0.148489i	$0.0474411\pi$
$23$	0.693178	+	3.28150i	0.144538	+	0.684240i	−0.844376	+	0.535750i	$0.820029\pi$
$24$		0			0
$25$	0.242860	−	1.41202i	0.0485719	−	0.282405i
$26$		0			0
$27$	4.48341	+	2.18904i	0.862833	+	0.421281i
$28$		0			0
$29$	−0.511898	+	2.42332i	−0.0950571	+	0.450000i	0.904658	+	0.426138i	$0.140126\pi$
$29$	−0.511898	+	2.42332i	−0.0950571	+	0.450000i	−0.999715	+	0.0238616i	$0.992404\pi$
$30$		0			0
$31$	0.832857	−	0.159530i	0.149586	−	0.0286523i	−0.112786	−	0.993619i	$-0.535977\pi$
$31$	0.832857	−	0.159530i	0.149586	−	0.0286523i	0.262371	+	0.964967i	$0.415495\pi$
$32$		0			0
$33$	4.92948	−	3.41318i	0.858112	−	0.594158i
$34$		0			0
$35$	0.684128	−	0.0518884i	0.115639	−	0.00877073i
$36$		0			0
$37$	−0.474860	+	0.148352i	−0.0780665	+	0.0243889i	−0.336982	−	0.941511i	$-0.609406\pi$
$37$	−0.474860	+	0.148352i	−0.0780665	+	0.0243889i	0.258915	+	0.965900i	$0.416635\pi$
$38$		0			0
$39$	1.61570	−	5.53781i	0.258720	−	0.886759i
$40$		0			0
$41$	−0.439269	+	0.174689i	−0.0686022	+	0.0272818i	−0.403581	−	0.914944i	$-0.632235\pi$
$41$	−0.439269	+	0.174689i	−0.0686022	+	0.0272818i	0.334979	+	0.942226i	$0.391271\pi$
$42$		0			0
$43$	11.5486	+	4.09369i	1.76115	+	0.624282i	0.999713	−	0.0239549i	$-0.00762581\pi$
$43$	11.5486	+	4.09369i	1.76115	+	0.624282i	0.761439	+	0.648237i	$0.224493\pi$
$44$		0			0
$45$	−0.160292	−	0.381859i	−0.0238949	−	0.0569242i
$46$		0			0
$47$	−2.37229	+	9.44702i	−0.346035	+	1.37799i	0.509601	+	0.860411i	$0.329793\pi$
$47$	−2.37229	+	9.44702i	−0.346035	+	1.37799i	−0.855635	+	0.517579i	$0.826833\pi$
$48$		0			0
$49$	2.17173	+	6.51564i	0.310247	+	0.930806i
$50$		0			0
$51$	−6.17147	+	6.78493i	−0.864178	+	0.950081i
$52$		0			0
$53$	1.38084	+	1.03554i	0.189672	+	0.142242i	0.690572	−	0.723264i	$-0.257359\pi$
$53$	1.38084	+	1.03554i	0.189672	+	0.142242i	−0.500900	+	0.865505i	$0.666997\pi$
$54$		0			0
$55$	6.27088	+	0.715144i	0.845565	+	0.0964300i
$56$		0			0
$57$	−8.96789	−	3.56636i	−1.18783	−	0.472375i
$58$		0			0
$59$	2.10406	+	3.16513i	0.273925	+	0.412065i	0.943855	−	0.330359i	$-0.107170\pi$
$59$	2.10406	+	3.16513i	0.273925	+	0.412065i	−0.669930	+	0.742424i	$0.733676\pi$
$60$		0			0
$61$	4.62066	+	5.92443i	0.591614	+	0.758546i	0.987131	−	0.159913i	$-0.0511213\pi$
$61$	4.62066	+	5.92443i	0.591614	+	0.758546i	−0.395517	+	0.918459i	$0.629435\pi$
$62$		0			0
$63$	−0.0637234	+	0.0477883i	−0.00802839	+	0.00602076i
$64$		0			0
$65$	5.11975	−	3.26542i	0.635027	−	0.405026i
$66$		0			0
$67$	−8.41804	+	9.98949i	−1.02843	+	1.22041i	−0.0533424	+	0.998576i	$0.516987\pi$
$67$	−8.41804	+	9.98949i	−1.02843	+	1.22041i	−0.975084	+	0.221834i	$0.928796\pi$
$68$		0			0
$69$	−0.341476	−	6.00800i	−0.0411089	−	0.723278i
$70$		0			0
$71$	−1.33750	−	14.0923i	−0.158732	−	1.67245i	−0.619552	−	0.784956i	$-0.712686\pi$
$71$	−1.33750	−	14.0923i	−0.158732	−	1.67245i	0.460820	−	0.887494i	$-0.347555\pi$
$72$		0			0
$73$	3.57533	−	6.37713i	0.418461	−	0.746387i	−0.579168	−	0.815208i	$-0.696623\pi$
$73$	3.57533	−	6.37713i	0.418461	−	0.746387i	0.997629	+	0.0688213i	$0.0219238\pi$
$74$		0			0
$75$	−0.812875	+	2.43880i	−0.0938627	+	0.281608i
$76$		0			0
$77$	−0.160344	−	1.20327i	−0.0182729	−	0.137125i
$78$		0			0
$79$	7.02518	+	0.266034i	0.790395	+	0.0299312i	0.429954	−	0.902851i	$-0.358530\pi$
$79$	7.02518	+	0.266034i	0.790395	+	0.0299312i	0.360441	+	0.932782i	$0.382626\pi$
$80$		0			0
$81$	−7.90070	−	5.47046i	−0.877855	−	0.607828i
$82$		0			0
$83$	−7.61971	+	2.06748i	−0.836372	+	0.226935i	−0.654190	−	0.756330i	$-0.726990\pi$
$83$	−7.61971	+	2.06748i	−0.836372	+	0.226935i	−0.182181	+	0.983265i	$0.558316\pi$
$84$		0			0
$85$	−9.59262	+	1.09396i	−1.04047	+	0.118657i
$86$		0			0
$87$	1.56374	−	4.15974i	0.167651	−	0.445971i
$88$		0			0
$89$	2.52173	−	4.12384i	0.267302	−	0.437126i	−0.691011	−	0.722844i	$-0.742835\pi$
$89$	2.52173	−	4.12384i	0.267302	−	0.437126i	0.958314	+	0.285718i	$0.0922321\pi$
$90$		0			0
$91$	−0.848957	−	0.802075i	−0.0889948	−	0.0840803i
$92$		0			0
$93$	−1.52042	+	0.0575760i	−0.157660	+	0.00597035i
$94$		0			0
$95$	−4.62931	−	9.04319i	−0.474958	−	0.927812i
$96$		0			0
$97$	−17.4069	−	3.33420i	−1.76740	−	0.338537i	−0.801608	−	0.597850i	$-0.796022\pi$
$97$	−17.4069	−	3.33420i	−1.76740	−	0.338537i	−0.965793	+	0.259314i	$0.916504\pi$
$98$		0			0
$99$	−0.658442	+	0.321486i	−0.0661759	+	0.0323106i
$100$		0			0
$101$	4.53855	−	1.60880i	0.451603	−	0.160081i	−0.0985735	−	0.995130i	$-0.531428\pi$
$101$	4.53855	−	1.60880i	0.451603	−	0.160081i	0.550176	+	0.835048i	$0.314560\pi$
$102$		0			0
$103$	−0.144821	+	7.65135i	−0.0142696	+	0.753910i	0.918903	+	0.394482i	$0.129076\pi$
$103$	−0.144821	+	7.65135i	−0.0142696	+	0.753910i	−0.933173	+	0.359427i	$0.882972\pi$
$104$		0			0
$105$	−1.22748	−	0.0930998i	−0.119790	−	0.00908561i
$106$		0			0
$107$	0.146050	+	7.71627i	0.0141192	+	0.745960i	0.934706	+	0.355422i	$0.115663\pi$
$107$	0.146050	+	7.71627i	0.0141192	+	0.745960i	−0.920587	+	0.390538i	$0.872289\pi$
$108$		0			0
$109$	4.29164	−	8.38356i	0.411065	−	0.803000i	−0.588922	−	0.808190i	$-0.700447\pi$
$109$	4.29164	−	8.38356i	0.411065	−	0.803000i	0.999987	+	0.00519038i	$0.00165216\pi$
$110$		0			0
$111$	0.882409	−	0.134629i	0.0837546	−	0.0127784i
$112$		0			0
$113$	−5.23597	−	4.58452i	−0.492558	−	0.431275i	0.376180	−	0.926547i	$-0.377237\pi$
$113$	−5.23597	−	4.58452i	−0.492558	−	0.431275i	−0.868738	+	0.495271i	$0.835069\pi$
$114$		0			0
$115$	3.89576	−	4.99500i	0.363281	−	0.465786i
$116$		0			0
$117$	−0.297266	+	0.639242i	−0.0274822	+	0.0590979i
$118$		0			0
$119$	0.653416	+	1.73816i	0.0598985	+	0.159337i
$120$		0			0
$121$	0.00947595	−	0.166722i	0.000861450	−	0.0151565i
$122$		0			0
$123$	0.826407	−	0.190974i	0.0745146	−	0.0172196i
$124$		0			0
$125$	−10.4834	+	6.14108i	−0.937661	+	0.549275i
$126$		0			0
$127$	−1.21146	+	12.7643i	−0.107500	+	1.13265i	0.764998	+	0.644033i	$0.222740\pi$
$127$	−1.21146	+	12.7643i	−0.107500	+	1.13265i	−0.872498	+	0.488619i	$0.837501\pi$
$128$		0			0
$129$	−19.3761	−	10.3862i	−1.70597	−	0.914457i
$130$		0			0
$131$	6.08128	+	6.68578i	0.531324	+	0.584139i	0.945322	−	0.326138i	$-0.105748\pi$
$131$	6.08128	+	6.68578i	0.531324	+	0.584139i	−0.413998	+	0.910278i	$0.635868\pi$
$132$		0			0
$133$	−1.47006	+	1.28716i	−0.127471	+	0.111611i
$134$		0			0
$135$	−2.29509	−	9.13956i	−0.197529	−	0.786608i
$136$		0			0
$137$	−3.55524	−	12.1855i	−0.303744	−	1.04108i	−0.958465	−	0.285210i	$-0.907937\pi$
$137$	−3.55524	−	12.1855i	−0.303744	−	1.04108i	0.654721	−	0.755871i	$-0.272786\pi$
$138$		0			0
$139$	4.66463	−	2.06274i	0.395649	−	0.174959i	−0.197031	−	0.980397i	$-0.563130\pi$
$139$	4.66463	−	2.06274i	0.395649	−	0.174959i	0.592680	+	0.805438i	$0.298070\pi$
$140$		0			0
$141$	6.76425	−	16.1143i	0.569653	−	1.35707i
$142$		0			0
$143$	−6.28223	−	8.71594i	−0.525347	−	0.728863i
$144$		0			0
$145$	4.12299	−	2.21006i	0.342395	−	0.183535i
$146$		0			0
$147$	−2.08879	−	12.1445i	−0.172280	−	1.00167i
$148$		0			0
$149$	2.53370	+	1.61602i	0.207568	+	0.132389i	0.637437	−	0.770502i	$-0.279994\pi$
$149$	2.53370	+	1.61602i	0.207568	+	0.132389i	−0.429869	+	0.902891i	$0.641440\pi$
$150$		0			0
$151$	−1.22242	−	2.18036i	−0.0994789	−	0.177435i	0.818002	−	0.575216i	$-0.195082\pi$
$151$	−1.22242	−	2.18036i	−0.0994789	−	0.177435i	−0.917481	+	0.397780i	$0.869781\pi$
$152$		0			0
$153$	0.870634	−	0.705936i	0.0703866	−	0.0570715i
$154$		0			0
$155$	−1.24406	−	1.00872i	−0.0999254	−	0.0810224i
$156$		0			0
$157$	7.76214	+	16.6918i	0.619486	+	1.33215i	0.925003	+	0.379960i	$0.124062\pi$
$157$	7.76214	+	16.6918i	0.619486	+	1.33215i	−0.305517	+	0.952187i	$0.598829\pi$
$158$		0			0
$159$	−2.16897	−	2.21041i	−0.172010	−	0.175297i
$160$		0			0
$161$	−1.11426	−	0.492733i	−0.0878156	−	0.0388328i
$162$		0			0
$163$	−11.2663	−	6.59973i	−0.882447	−	0.516931i	−0.00685176	−	0.999977i	$-0.502181\pi$
$163$	−11.2663	−	6.59973i	−0.882447	−	0.516931i	−0.875595	+	0.483046i	$0.839530\pi$
$164$		0			0
$165$	−10.9292	−	2.96544i	−0.850835	−	0.230859i
$166$		0			0
$167$	5.09867	+	11.8745i	0.394547	+	0.918876i
$167$	5.09867	+	11.8745i	0.394547	+	0.918876i
$168$		0			0
$169$	2.57001	+	0.697327i	0.197693	+	0.0536405i
$170$		0			0
$171$	1.01768	+	0.596147i	0.0778237	+	0.0455885i
$172$		0			0
$173$	−1.94957	−	0.862118i	−0.148223	−	0.0655457i	0.328988	−	0.944334i	$-0.393292\pi$
$173$	−1.94957	−	0.862118i	−0.148223	−	0.0655457i	−0.477212	+	0.878788i	$0.658353\pi$
$174$		0			0
$175$	0.364524	+	0.371488i	0.0275554	+	0.0280819i
$176$		0			0
$177$	−2.87546	−	6.18340i	−0.216133	−	0.464773i
$178$		0			0
$179$	−3.97866	−	3.22601i	−0.297379	−	0.241123i	0.469474	−	0.882946i	$-0.344444\pi$
$179$	−3.97866	−	3.22601i	−0.297379	−	0.241123i	−0.766853	+	0.641823i	$0.778178\pi$
$180$		0			0
$181$	0.435438	−	0.353066i	0.0323658	−	0.0262432i	−0.613491	−	0.789702i	$-0.710235\pi$
$181$	0.435438	−	0.353066i	0.0323658	−	0.0262432i	0.645857	+	0.763459i	$0.276500\pi$
$182$		0			0
$183$	−6.59246	−	11.7586i	−0.487328	−	0.869223i
$184$		0			0
$185$	0.792206	+	0.505276i	0.0582441	+	0.0371487i
$186$		0			0
$187$	2.89553	+	16.8351i	0.211742	+	1.23110i
$188$		0			0
$189$	−1.59738	+	0.856250i	−0.116193	+	0.0622830i
$190$		0			0
$191$	−5.46467	−	7.58166i	−0.395410	−	0.548589i	0.565752	−	0.824575i	$-0.308586\pi$
$191$	−5.46467	−	7.58166i	−0.395410	−	0.548589i	−0.961162	+	0.275986i	$0.910996\pi$
$192$		0			0
$193$	0.604207	−	1.43939i	0.0434918	−	0.103609i	−0.898856	−	0.438244i	$-0.855601\pi$
$193$	0.604207	−	1.43939i	0.0434918	−	0.103609i	0.942348	+	0.334634i	$0.108613\pi$
$194$		0			0
$195$	−9.96461	+	4.40643i	−0.713580	+	0.315551i
$196$		0			0
$197$	3.99468	+	13.6917i	0.284609	+	0.975495i	0.969140	+	0.246511i	$0.0792842\pi$
$197$	3.99468	+	13.6917i	0.284609	+	0.975495i	−0.684531	+	0.728984i	$0.739993\pi$
$198$		0			0
$199$	4.95979	+	19.7510i	0.351590	+	1.40011i	0.847064	+	0.531491i	$0.178368\pi$
$199$	4.95979	+	19.7510i	0.351590	+	1.40011i	−0.495474	+	0.868623i	$0.665006\pi$
$200$		0			0
$201$	17.6344	−	15.4404i	1.24384	−	1.08908i
$202$		0			0
$203$	−0.605397	−	0.665575i	−0.0424905	−	0.0467142i
$204$		0			0
$205$	0.786926	+	0.421818i	0.0549613	+	0.0294611i
$206$		0			0
$207$	−0.0694854	+	0.732121i	−0.00482957	+	0.0508859i
$208$		0			0
$209$	−15.5096	+	9.08538i	−1.07282	+	0.628449i
$210$		0			0
$211$	6.27799	−	1.45078i	0.432195	−	0.0998758i	−0.00345072	−	0.999994i	$-0.501098\pi$
$211$	6.27799	−	1.45078i	0.432195	−	0.0998758i	0.435646	+	0.900118i	$0.356520\pi$
$212$		0			0
$213$	−1.44124	+	25.3576i	−0.0987525	+	1.73747i
$214$		0			0
$215$	−8.14320	−	21.6619i	−0.555362	−	1.47733i
$216$		0			0
$217$	−0.129891	+	0.279319i	−0.00881758	+	0.0189614i
$218$		0			0
$219$	−8.06733	+	10.3436i	−0.545139	+	0.698958i
$220$		0			0
$221$	12.3652	+	10.8268i	0.831773	+	0.728286i
$222$		0			0
$223$	7.72708	−	1.17892i	0.517444	−	0.0789462i	0.113155	−	0.993577i	$-0.463904\pi$
$223$	7.72708	−	1.17892i	0.517444	−	0.0789462i	0.404289	+	0.914631i	$0.367519\pi$
$224$		0			0
$225$	0.143155	−	0.279648i	0.00954368	−	0.0186432i
$226$		0			0
$227$	−0.253262	−	13.3806i	−0.0168096	−	0.888104i	−0.904206	−	0.427097i	$-0.859536\pi$
$227$	−0.253262	−	13.3806i	−0.0168096	−	0.888104i	0.887396	−	0.461007i	$-0.152512\pi$
$228$		0			0
$229$	−3.63069	−	0.275373i	−0.239923	−	0.0181972i	−0.0448819	−	0.998992i	$-0.514291\pi$
$229$	−3.63069	−	0.275373i	−0.239923	−	0.0181972i	−0.195041	+	0.980795i	$0.562484\pi$
$230$		0			0
$231$	−0.0412173	+	2.17764i	−0.00271190	+	0.143278i
$232$		0			0
$233$	8.57804	−	3.04069i	0.561966	−	0.199202i	−0.0379297	−	0.999280i	$-0.512076\pi$
$233$	8.57804	−	3.04069i	0.561966	−	0.199202i	0.599895	+	0.800078i	$0.295209\pi$
$234$		0			0
$235$	16.5315	−	8.07154i	1.07839	−	0.526529i
$236$		0			0
$237$	−12.3886	−	2.37298i	−0.804728	−	0.154142i
$238$		0			0
$239$	0.125755	+	0.245657i	0.00813441	+	0.0158903i	0.894177	−	0.447713i	$-0.147761\pi$
$239$	0.125755	+	0.245657i	0.00813441	+	0.0158903i	−0.886043	+	0.463603i	$0.846556\pi$
$240$		0			0
$241$	21.9426	−	0.830935i	1.41345	−	0.0535253i	0.679970	−	0.733240i	$-0.261993\pi$
$241$	21.9426	−	0.830935i	1.41345	−	0.0535253i	0.733477	+	0.679715i	$0.237896\pi$
$242$		0			0
$243$	1.65314	+	1.56185i	0.106049	+	0.100193i
$244$		0			0
$245$	6.76726	−	11.0667i	0.432345	−	0.707023i
$246$		0			0
$247$	−6.08539	+	16.1879i	−0.387204	+	1.03001i
$248$		0			0
$249$	14.0746	−	1.60510i	0.891943	−	0.101719i
$250$		0			0
$251$	−5.87699	+	1.59462i	−0.370952	+	0.100651i	−0.442459	−	0.896789i	$-0.645894\pi$
$251$	−5.87699	+	1.59462i	−0.370952	+	0.100651i	0.0715071	+	0.997440i	$0.477219\pi$
$252$		0			0
$253$	−9.21455	−	6.38017i	−0.579314	−	0.401118i
$254$		0			0
$255$	17.3105	+	0.655526i	1.08403	+	0.0410506i
$256$		0			0
$257$	2.58702	+	19.4137i	0.161374	+	1.21100i	0.865496	+	0.500916i	$0.167004\pi$
$257$	2.58702	+	19.4137i	0.161374	+	1.21100i	−0.704122	+	0.710079i	$0.748659\pi$
$258$		0			0
$259$	0.0571449	−	0.171447i	0.00355081	−	0.0106532i
$260$		0			0
$261$	−0.265588	+	0.473715i	−0.0164395	+	0.0293222i
$262$		0			0
$263$	−1.36244	−	14.3551i	−0.0840117	−	0.885174i	−0.933740	−	0.357953i	$-0.883475\pi$
$263$	−1.36244	−	14.3551i	−0.0840117	−	0.885174i	0.849728	−	0.527221i	$-0.176766\pi$
$264$		0			0
$265$	−0.184984	−	3.25465i	−0.0113635	−	0.199931i
$266$		0			0
$267$	−5.58877	+	6.63206i	−0.342027	+	0.405876i
$268$		0			0
$269$	5.78769	−	3.69145i	0.352882	−	0.225071i	−0.349395	−	0.936976i	$-0.613613\pi$
$269$	5.78769	−	3.69145i	0.352882	−	0.225071i	0.702277	+	0.711904i	$0.252167\pi$
$270$		0			0
$271$	−14.7388	+	11.0532i	−0.895321	+	0.671431i	−0.944907	−	0.327339i	$-0.893848\pi$
$271$	−14.7388	+	11.0532i	−0.895321	+	0.671431i	0.0495864	+	0.998770i	$0.484210\pi$
$272$		0			0
$273$	1.28875	+	1.65239i	0.0779986	+	0.100007i
$274$		0			0
$275$	2.65056	+	3.98724i	0.159835	+	0.240439i
$276$		0			0
$277$	8.16754	+	3.24807i	0.490740	+	0.195158i	0.601786	−	0.798658i	$-0.294456\pi$
$277$	8.16754	+	3.24807i	0.490740	+	0.195158i	−0.111046	+	0.993815i	$0.535420\pi$
$278$		0			0
$279$	0.184743	+	0.0210684i	0.0110603	+	0.00126133i
$280$		0			0
$281$	10.2142	+	7.66000i	0.609330	+	0.456957i	0.859423	−	0.511265i	$-0.170823\pi$
$281$	10.2142	+	7.66000i	0.609330	+	0.456957i	−0.250093	+	0.968222i	$0.580461\pi$
$282$		0			0
$283$	3.31636	−	3.64602i	0.197137	−	0.216734i	−0.633209	−	0.773981i	$-0.718263\pi$
$283$	3.31636	−	3.64602i	0.197137	−	0.216734i	0.830347	+	0.557247i	$0.188142\pi$
$284$		0			0
$285$	5.76384	+	17.2927i	0.341420	+	1.02433i
$286$		0			0
$287$	0.0418239	−	0.166552i	0.00246879	−	0.00983127i
$288$		0			0
$289$	−3.53411	−	8.41920i	−0.207889	−	0.495247i
$290$		0			0
$291$	29.9724	+	10.6244i	1.75702	+	0.622815i
$292$		0			0
$293$	8.74361	−	3.47716i	0.510807	−	0.203138i	−0.0998956	−	0.994998i	$-0.531851\pi$
$293$	8.74361	−	3.47716i	0.510807	−	0.203138i	0.610703	+	0.791860i	$0.290887\pi$
$294$		0			0
$295$	2.01053	−	6.89108i	0.117058	−	0.401214i
$296$		0			0
$297$	−15.9141	+	4.97176i	−0.923433	+	0.288491i
$298$		0			0
$299$	−10.7524	+	0.815525i	−0.621826	+	0.0471630i
$300$		0			0
$301$	−3.65935	+	2.53374i	−0.210921	+	0.146042i
$302$		0			0
$303$	−8.48543	+	1.62534i	−0.487475	+	0.0933733i
$304$		0			0
$305$	2.93284	−	13.8841i	0.167934	−	0.794999i
$306$		0			0
$307$	−17.0366	−	8.31819i	−0.972332	−	0.474744i	−0.117174	−	0.993111i	$-0.537383\pi$
$307$	−17.0366	−	8.31819i	−0.972332	−	0.474744i	−0.855158	+	0.518367i	$0.826540\pi$
$308$		0			0
$309$	2.32743	−	13.5321i	0.132403	−	0.769812i
$310$		0			0
$311$	−3.54265	−	16.7709i	−0.200885	−	0.950989i	−0.955539	−	0.294866i	$-0.904725\pi$
$311$	−3.54265	−	16.7709i	−0.200885	−	0.950989i	0.754654	−	0.656124i	$-0.227805\pi$
$312$		0			0
$313$	−11.3538	+	11.5708i	−0.641756	+	0.654018i	−0.955328	−	0.295547i	$-0.904498\pi$
$313$	−11.3538	+	11.5708i	−0.641756	+	0.654018i	0.313572	+	0.949564i	$0.398474\pi$
$314$		0			0
$315$	0.146576	+	0.0338723i	0.00825864	+	0.00190849i
$316$		0			0
$317$	−15.7050	+	23.6249i	−0.882078	+	1.32691i	0.0623037	+	0.998057i	$0.480155\pi$
$317$	−15.7050	+	23.6249i	−0.882078	+	1.32691i	−0.944382	+	0.328851i	$0.893339\pi$
$318$		0			0
$319$	−4.31790	−	7.06116i	−0.241756	−	0.395349i
$320$		0			0
$321$	1.82908	−	13.7259i	0.102089	−	0.766107i
$322$		0			0
$323$	19.9867	−	18.8830i	1.11209	−	1.05068i
$324$		0			0
$325$	4.39693	+	1.37365i	0.243898	+	0.0761964i
$326$		0			0
$327$	−9.88083	+	13.7086i	−0.546411	+	0.758088i
$328$		0			0
$329$	−2.28005	−	2.70568i	−0.125703	−	0.149169i
$330$		0			0
$331$	18.7316	+	2.85787i	1.02958	+	0.157083i	0.643551	−	0.765403i	$-0.277460\pi$
$331$	18.7316	+	2.85787i	1.02958	+	0.157083i	0.386030	+	0.922486i	$0.373846\pi$
$332$		0			0
$333$	−0.109085			−0.00597784
$334$		0			0
$335$	24.6731			1.34803
$336$		0			0
$337$	18.6505	+	2.84550i	1.01596	+	0.155004i	0.637368	−	0.770560i	$-0.280023\pi$
$337$	18.6505	+	2.84550i	1.01596	+	0.155004i	0.378591	+	0.925564i	$0.376409\pi$
$338$		0			0
$339$	8.04644	+	9.54852i	0.437023	+	0.518605i
$340$		0			0
$341$	−1.65695	+	2.29885i	−0.0897290	+	0.124490i
$342$		0			0
$343$	−4.80850	−	1.50223i	−0.259635	−	0.0811128i
$344$		0			0
$345$	−8.26165	+	7.80542i	−0.444792	+	0.420230i
$346$		0			0
$347$	1.56815	−	11.7679i	0.0841829	−	0.631732i	−0.897473	−	0.441070i	$-0.854599\pi$
$347$	1.56815	−	11.7679i	0.0841829	−	0.631732i	0.981656	−	0.190662i	$-0.0610636\pi$
$348$		0			0
$349$	11.6605	+	19.0687i	0.624171	+	1.02072i	0.995730	+	0.0923124i	$0.0294258\pi$
$349$	11.6605	+	19.0687i	0.624171	+	1.02072i	−0.371559	+	0.928409i	$0.621177\pi$
$350$		0			0
$351$	−8.88042	+	13.3588i	−0.474002	+	0.713040i
$352$		0			0
$353$	22.1801	+	5.12559i	1.18053	+	0.272807i	0.769398	−	0.638770i	$-0.220556\pi$
$353$	22.1801	+	5.12559i	1.18053	+	0.272807i	0.411129	+	0.911577i	$0.365135\pi$
$354$		0			0
$355$	−18.7254	+	19.0832i	−0.993843	+	1.01283i
$356$		0			0
$357$	−0.688597	−	3.25981i	−0.0364444	−	0.172528i
$358$		0			0
$359$	5.67172	−	32.9763i	0.299342	−	1.74042i	−0.312929	−	0.949776i	$-0.601310\pi$
$359$	5.67172	−	32.9763i	0.299342	−	1.74042i	0.612271	−	0.790648i	$-0.290256\pi$
$360$		0			0
$361$	8.92558	+	4.35795i	0.469768	+	0.229366i
$362$		0			0
$363$	−0.0619248	+	0.293152i	−0.00325021	+	0.0153865i
$364$		0			0
$365$	−13.5618	+	2.59770i	−0.709860	+	0.135970i
$366$		0			0
$367$	−28.8923	+	20.0051i	−1.50817	+	1.04426i	−0.527275	+	0.849695i	$0.676786\pi$
$367$	−28.8923	+	20.0051i	−1.50817	+	1.04426i	−0.980890	+	0.194562i	$0.937672\pi$
$368$		0			0
$369$	−0.103358	+	0.00783931i	−0.00538062	+	0.000408098i
$370$		0			0
$371$	−0.598457	+	0.186965i	−0.0310703	+	0.00970672i
$372$		0			0
$373$	−2.38330	+	8.16874i	−0.123403	+	0.422961i	−0.998094	−	0.0617200i	$-0.980341\pi$
$373$	−2.38330	+	8.16874i	−0.123403	+	0.422961i	0.874691	+	0.484681i	$0.161064\pi$
$374$		0			0
$375$	20.2563	−	8.05553i	1.04603	−	0.415986i
$376$		0			0
$377$	−7.50563	−	2.66055i	−0.386560	−	0.137025i
$378$		0			0
$379$	3.81816	+	9.09589i	0.196126	+	0.467225i	0.990037	−	0.140809i	$-0.0449705\pi$
$379$	3.81816	+	9.09589i	0.196126	+	0.467225i	−0.793911	+	0.608034i	$0.791958\pi$
$380$		0			0
$381$	5.60298	−	22.3124i	0.287049	−	1.14310i
$382$		0			0
$383$	11.9320	+	35.7986i	0.609697	+	1.82922i	0.556841	+	0.830619i	$0.312013\pi$
$383$	11.9320	+	35.7986i	0.609697	+	1.82922i	0.0528566	+	0.998602i	$0.483167\pi$
$384$		0			0
$385$	−1.54271	+	1.69606i	−0.0786237	+	0.0864392i
$386$		0			0
$387$	2.14939	+	1.61190i	0.109260	+	0.0819375i
$388$		0			0
$389$	−31.6500	−	3.60943i	−1.60472	−	0.183006i	−0.735532	−	0.677490i	$-0.763068\pi$
$389$	−31.6500	−	3.60943i	−1.60472	−	0.183006i	−0.869187	+	0.494484i	$0.835357\pi$
$390$		0			0
$391$	15.9311	+	6.33549i	0.805671	+	0.320400i
$392$		0			0
$393$	−8.97714	−	13.5043i	−0.452837	−	0.681202i
$394$		0			0
$395$	−8.16600	−	10.4701i	−0.410876	−	0.526810i
$396$		0			0
$397$	−22.8412	+	17.1294i	−1.14637	+	0.859701i	−0.991739	−	0.128271i	$-0.959057\pi$
$397$	−22.8412	+	17.1294i	−1.14637	+	0.859701i	−0.154630	+	0.987972i	$0.549419\pi$
$398$		0			0
$399$	2.95579	−	1.88523i	0.147974	−	0.0943795i
$400$		0			0
$401$	23.1470	−	27.4681i	1.15591	−	1.37169i	0.239769	−	0.970830i	$-0.422928\pi$
$401$	23.1470	−	27.4681i	1.15591	−	1.37169i	0.916139	−	0.400860i	$-0.131288\pi$
$402$		0			0
$403$	0.154712	+	2.72203i	0.00770674	+	0.135594i
$404$		0			0
$405$	1.71491	+	18.0688i	0.0852145	+	0.897848i
$406$		0			0
$407$	0.813009	−	1.45012i	0.0402993	−	0.0718799i
$408$		0			0
$409$	−2.45338	+	7.36066i	−0.121312	+	0.363961i	−0.991728	−	0.128355i	$-0.959030\pi$
$409$	−2.45338	+	7.36066i	−0.121312	+	0.363961i	0.870416	+	0.492316i	$0.163850\pi$
$410$		0			0
$411$	3.00837	+	22.5757i	0.148392	+	1.11358i
$412$		0			0
$413$	−1.37964	−	0.0522451i	−0.0678877	−	0.00257081i
$414$		0			0
$415$	12.2598	+	8.48873i	0.601811	+	0.416695i
$416$		0			0
$417$	−8.83190	+	2.39638i	−0.432500	+	0.117351i
$418$		0			0
$419$	−23.4255	+	2.67149i	−1.14441	+	0.130511i	−0.664835	−	0.746990i	$-0.731498\pi$
$419$	−23.4255	+	2.67149i	−1.14441	+	0.130511i	−0.479574	+	0.877501i	$0.659209\pi$
$420$		0			0
$421$	13.1687	−	35.0303i	0.641804	−	1.70727i	−0.0631354	−	0.998005i	$-0.520110\pi$
$421$	13.1687	−	35.0303i	0.641804	−	1.70727i	0.704939	−	0.709268i	$-0.250974\pi$
$422$		0			0
$423$	−1.11421	+	1.82209i	−0.0541746	+	0.0885929i
$424$		0			0
$425$	−5.32378	−	5.02978i	−0.258241	−	0.243980i
$426$		0			0
$427$	−2.72731	+	0.103280i	−0.131984	+	0.00499805i
$428$		0			0
$429$	8.78419	+	17.1596i	0.424105	+	0.828472i
$430$		0			0
$431$	2.47624	+	0.474310i	0.119276	+	0.0228467i	0.247416	−	0.968909i	$-0.420419\pi$
$431$	2.47624	+	0.474310i	0.119276	+	0.0228467i	−0.128140	+	0.991756i	$0.540901\pi$
$432$		0			0
$433$	29.6356	−	14.4697i	1.42419	−	0.695368i	0.444485	−	0.895787i	$-0.353387\pi$
$433$	29.6356	−	14.4697i	1.42419	−	0.695368i	0.979710	+	0.200419i	$0.0642302\pi$
$434$		0			0
$435$	−7.91104	+	2.80426i	−0.379305	+	0.134454i
$436$		0			0
$437$	−0.341399	+	18.0372i	−0.0163313	+	0.862834i
$438$		0			0
$439$	2.90456	+	0.220299i	0.138627	+	0.0105143i	0.144759	−	0.989467i	$-0.453759\pi$
$439$	2.90456	+	0.220299i	0.138627	+	0.0105143i	−0.00613238	+	0.999981i	$0.501952\pi$
$440$		0			0
$441$	0.0284988	+	1.50568i	0.00135709	+	0.0716992i
$442$		0			0
$443$	2.50637	−	4.89610i	0.119081	−	0.232621i	−0.822974	−	0.568080i	$-0.807687\pi$
$443$	2.50637	−	4.89610i	0.119081	−	0.232621i	0.942055	+	0.335459i	$0.108891\pi$
$444$		0			0
$445$	−9.02513	+	1.37696i	−0.427832	+	0.0652742i
$446$		0			0
$447$	−4.05672	−	3.55199i	−0.191876	−	0.168003i
$448$		0			0
$449$	12.1221	−	15.5425i	0.572078	−	0.733497i	−0.412010	−	0.911179i	$-0.635173\pi$
$449$	12.1221	−	15.5425i	0.572078	−	0.733497i	0.984088	+	0.177682i	$0.0568599\pi$
$450$		0			0
$451$	0.666114	−	1.43242i	0.0313661	−	0.0674498i
$452$		0			0
$453$	1.57817	+	4.19813i	0.0741491	+	0.197245i
$454$		0			0
$455$	−0.125173	+	2.20232i	−0.00586821	+	0.103247i
$456$		0			0
$457$	28.7425	−	6.64211i	1.34452	−	0.310705i	0.509285	−	0.860598i	$-0.329910\pi$
$457$	28.7425	−	6.64211i	1.34452	−	0.310705i	0.835235	+	0.549893i	$0.185332\pi$
$458$		0			0
$459$	22.0065	−	12.8913i	1.02718	−	0.601713i
$460$		0			0
$461$	−3.31885	+	34.9684i	−0.154574	+	1.62864i	0.495385	+	0.868673i	$0.335027\pi$
$461$	−3.31885	+	34.9684i	−0.154574	+	1.62864i	−0.649959	+	0.759969i	$0.725214\pi$
$462$		0			0
$463$	−10.5369	−	5.64811i	−0.489690	−	0.262490i	0.208998	−	0.977916i	$-0.432980\pi$
$463$	−10.5369	−	5.64811i	−0.489690	−	0.262490i	−0.698689	+	0.715426i	$0.746233\pi$
$464$		0			0
$465$	1.93363	+	2.12584i	0.0896698	+	0.0985833i
$466$		0			0
$467$	−19.5938	+	17.1560i	−0.906692	+	0.793884i	−0.979076	−	0.203493i	$-0.934771\pi$
$467$	−19.5938	+	17.1560i	−0.906692	+	0.793884i	0.0723843	+	0.997377i	$0.476939\pi$
$468$		0			0
$469$	−1.15576	−	4.60252i	−0.0533682	−	0.212524i
$470$		0			0
$471$	−9.25074	−	31.7068i	−0.426252	−	1.46097i
$472$		0			0
$473$	−37.4470	+	16.5594i	−1.72182	+	0.761402i
$474$		0			0
$475$	2.98287	−	7.10600i	0.136863	−	0.326046i
$476$		0			0
$477$	0.221291	+	0.307018i	0.0101322	+	0.0140574i
$478$		0			0
$479$	28.9066	−	15.4949i	1.32078	−	0.707981i	0.347515	−	0.937674i	$-0.387025\pi$
$479$	28.9066	−	15.4949i	1.32078	−	0.707981i	0.973263	+	0.229694i	$0.0737724\pi$
$480$		0			0
$481$	−0.271125	−	1.57636i	−0.0123622	−	0.0718760i
$482$		0			0
$483$	1.84302	+	1.17550i	0.0838604	+	0.0534870i
$484$		0			0
$485$	16.3701	+	29.1985i	0.743327	+	1.32583i
$486$		0			0
$487$	7.81750	−	6.33865i	0.354245	−	0.287232i	−0.436095	−	0.899901i	$-0.643639\pi$
$487$	7.81750	−	6.33865i	0.354245	−	0.287232i	0.790340	+	0.612669i	$0.209904\pi$
$488$		0			0
$489$	18.1972	+	14.7548i	0.822905	+	0.667236i
$490$		0			0
$491$	−9.12141	−	19.6148i	−0.411644	−	0.885201i	−0.997215	−	0.0745805i	$-0.976238\pi$
$491$	−9.12141	−	19.6148i	−0.411644	−	0.885201i	0.585571	−	0.810621i	$-0.300870\pi$
$492$		0			0
$493$	8.86756	+	9.03698i	0.399375	+	0.407005i
$494$		0			0
$495$	1.26569	+	0.559701i	0.0568888	+	0.0251567i
$496$		0			0
$497$	4.43694	+	2.59912i	0.199024	+	0.116587i
$498$		0			0
$499$	23.0324	+	6.24944i	1.03107	+	0.279763i	0.736909	−	0.675992i	$-0.236285\pi$
$499$	23.0324	+	6.24944i	1.03107	+	0.279763i	0.294162	+	0.955756i	$0.404959\pi$
$500$		0			0
$501$	−5.83015	−	22.4416i	−0.260472	−	1.00262i
$502$		0			0
$503$	19.8118	+	5.37558i	0.883362	+	0.239685i	0.674513	−	0.738263i	$-0.264354\pi$
$503$	19.8118	+	5.37558i	0.883362	+	0.239685i	0.208849	+	0.977948i	$0.433028\pi$
$504$		0			0
$505$	−7.84735	−	4.59692i	−0.349202	−	0.204560i
$506$		0			0
$507$	−4.36973	−	1.93233i	−0.194067	−	0.0858179i
$508$		0			0
$509$	−19.5449	−	19.9183i	−0.866312	−	0.882864i	0.127736	−	0.991808i	$-0.459229\pi$
$509$	−19.5449	−	19.9183i	−0.866312	−	0.882864i	−0.994048	+	0.108944i	$0.965253\pi$
$510$		0			0
$511$	1.11985	+	2.40814i	0.0495394	+	0.106530i
$512$		0			0
$513$	20.8455	+	16.9021i	0.920351	+	0.746248i
$514$		0			0
$515$	11.2270	−	9.10316i	0.494720	−	0.401133i
$516$		0			0
$517$	−15.9177	−	28.3916i	−0.700061	−	1.24866i
$518$		0			0
$519$	3.22467	+	2.05673i	0.141547	+	0.0902803i
$520$		0			0
$521$	1.40825	+	8.18781i	0.0616966	+	0.358714i	0.999920	+	0.0126829i	$0.00403720\pi$
$521$	1.40825	+	8.18781i	0.0616966	+	0.358714i	−0.938223	+	0.346031i	$0.887529\pi$
$522$		0			0
$523$	−12.1289	+	6.50148i	−0.530359	+	0.284290i	−0.715728	−	0.698379i	$-0.753905\pi$
$523$	−12.1289	+	6.50148i	−0.530359	+	0.284290i	0.185369	+	0.982669i	$0.440652\pi$
$524$		0			0
$525$	−0.546028	−	0.757557i	−0.0238306	−	0.0330625i
$526$		0			0
$527$	1.67780	−	3.99697i	0.0730860	−	0.174111i
$528$		0			0
$529$	10.7474	−	4.75257i	0.467276	−	0.206633i
$530$		0			0
$531$	0.233412	+	0.800017i	0.0101292	+	0.0347178i
$532$		0			0
$533$	−0.370174	−	1.47412i	−0.0160340	−	0.0638512i
$534$		0			0
$535$	10.9667	−	9.60227i	0.474133	−	0.415143i
$536$		0			0
$537$	6.18397	+	6.79868i	0.266858	+	0.293385i
$538$		0			0
$539$	−20.2281	−	10.8429i	−0.871288	−	0.467039i
$540$		0			0
$541$	0.580942	−	6.12100i	0.0249767	−	0.263162i	−0.974304	−	0.225237i	$-0.927684\pi$
$541$	0.580942	−	6.12100i	0.0249767	−	0.263162i	0.999281	−	0.0379250i	$-0.0120748\pi$
$542$		0			0
$543$	−0.867884	+	0.508400i	−0.0372445	+	0.0218175i
$544$		0			0
$545$	−17.3315	+	4.00514i	−0.742401	+	0.171561i
$546$		0			0
$547$	−1.15124	+	20.2553i	−0.0492237	+	0.866052i	0.874982	+	0.484156i	$0.160873\pi$
$547$	−1.15124	+	20.2553i	−0.0492237	+	0.866052i	−0.924205	+	0.381896i	$0.875271\pi$
$548$		0			0
$549$	0.579700	+	1.54207i	0.0247410	+	0.0658140i
$550$		0			0
$551$	−5.61762	+	12.0802i	−0.239319	+	0.514633i
$552$		0			0
$553$	−1.57058	+	2.01374i	−0.0667878	+	0.0856328i
$554$		0			0
$555$	−1.26841	−	1.11059i	−0.0538409	−	0.0471421i
$556$		0			0
$557$	−16.5742	+	2.52872i	−0.702271	+	0.107145i	−0.492125	−	0.870525i	$-0.663780\pi$
$557$	−16.5742	+	2.52872i	−0.702271	+	0.107145i	−0.210146	+	0.977670i	$0.567394\pi$
$558$		0			0
$559$	−17.9510	+	35.0665i	−0.759245	+	1.48316i
$560$		0			0
$561$	−0.580015	−	30.6440i	−0.0244883	−	1.29379i
$562$		0			0
$563$	5.18952	+	0.393604i	0.218712	+	0.0165885i	0.184529	−	0.982827i	$-0.440924\pi$
$563$	5.18952	+	0.393604i	0.218712	+	0.0165885i	0.0341836	+	0.999416i	$0.489117\pi$
$564$		0			0
$565$	−0.248745	+	13.1420i	−0.0104648	+	0.552886i
$566$		0			0
$567$	3.29023	−	1.16630i	0.138177	−	0.0489799i
$568$		0			0
$569$	−31.0648	+	15.1675i	−1.30231	+	0.635855i	−0.953515	−	0.301345i	$-0.902564\pi$
$569$	−31.0648	+	15.1675i	−1.30231	+	0.635855i	−0.348791	+	0.937201i	$0.613408\pi$
$570$		0			0
$571$	9.93218	+	1.90246i	0.415649	+	0.0796154i	0.391689	−	0.920098i	$-0.371891\pi$
$571$	9.93218	+	1.90246i	0.415649	+	0.0796154i	0.0239595	+	0.999713i	$0.492373\pi$
$572$		0			0
$573$	7.64102	+	14.9265i	0.319208	+	0.623562i
$574$		0			0
$575$	4.80190	−	0.181841i	0.200253	−	0.00758331i
$576$		0			0
$577$	−19.0323	−	17.9813i	−0.792325	−	0.748571i	0.179631	−	0.983734i	$-0.442510\pi$
$577$	−19.0323	−	17.9813i	−0.792325	−	0.748571i	−0.971956	+	0.235164i	$0.924437\pi$
$578$		0			0
$579$	−1.46120	+	2.38954i	−0.0607256	+	0.0993059i
$580$		0			0
$581$	1.00920	−	2.68459i	0.0418686	−	0.111375i
$582$		0			0
$583$	−5.73060	+	0.653530i	−0.237337	+	0.0270664i
$584$		0			0
$585$	1.28504	−	0.348674i	0.0531300	−	0.0144159i
$586$		0			0
$587$	−24.3593	−	16.8664i	−1.00542	−	0.696152i	−0.0522608	−	0.998633i	$-0.516643\pi$
$587$	−24.3593	−	16.8664i	−1.00542	−	0.696152i	−0.953155	+	0.302482i	$0.902185\pi$
$588$		0			0
$589$	4.55804	+	0.172606i	0.187811	+	0.00711213i
$590$		0			0
$591$	−3.38022	−	25.3661i	−0.139044	−	1.04342i
$592$		0			0
$593$	2.79622	−	8.38925i	0.114827	−	0.344505i	−0.875508	−	0.483204i	$-0.839473\pi$
$593$	2.79622	−	8.38925i	0.114827	−	0.344505i	0.990335	+	0.138699i	$0.0442921\pi$
$594$		0			0
$595$	1.71514	−	3.05920i	0.0703138	−	0.125415i
$596$		0			0
$597$	−3.45232	−	36.3747i	−0.141294	−	1.48872i
$598$		0			0
$599$	−0.385358	−	6.78008i	−0.0157453	−	0.277027i	−0.996606	−	0.0823168i	$-0.973768\pi$
$599$	−0.385358	−	6.78008i	−0.0157453	−	0.277027i	0.980861	−	0.194710i	$-0.0623765\pi$
$600$		0			0
$601$	7.75934	−	9.20783i	0.316510	−	0.375595i	−0.583017	−	0.812460i	$-0.698128\pi$
$601$	7.75934	−	9.20783i	0.316510	−	0.375595i	0.899527	+	0.436865i	$0.143911\pi$
$602$		0			0
$603$	−2.41501	+	1.54032i	−0.0983469	+	0.0627266i
$604$		0			0
$605$	−0.252327	+	0.189228i	−0.0102585	+	0.00769323i
$606$		0			0
$607$	−28.7825	−	36.9039i	−1.16825	−	1.49788i	−0.830830	−	0.556526i	$-0.812134\pi$
$607$	−28.7825	−	36.9039i	−1.16825	−	1.49788i	−0.337416	−	0.941356i	$-0.609553\pi$
$608$		0			0
$609$	0.893683	+	1.34436i	0.0362139	+	0.0544764i
$610$		0			0
$611$	−29.0998	−	11.5724i	−1.17725	−	0.468170i
$612$		0			0
$613$	−19.1411	−	2.18289i	−0.773102	−	0.0881662i	−0.282170	−	0.959364i	$-0.591054\pi$
$613$	−19.1411	−	2.18289i	−0.773102	−	0.0881662i	−0.490932	+	0.871198i	$0.663344\pi$
$614$		0			0
$615$	−1.28163	−	0.961135i	−0.0516802	−	0.0387567i
$616$		0			0
$617$	−8.25093	+	9.07110i	−0.332170	+	0.365189i	−0.882954	−	0.469459i	$-0.844449\pi$
$617$	−8.25093	+	9.07110i	−0.332170	+	0.365189i	0.550784	+	0.834648i	$0.314329\pi$
$618$		0			0
$619$	−5.98977	−	17.9706i	−0.240749	−	0.722299i	−0.997634	−	0.0687503i	$-0.978099\pi$
$619$	−5.98977	−	17.9706i	−0.240749	−	0.722299i	0.756885	−	0.653549i	$-0.226720\pi$
$620$		0			0
$621$	−4.07553	+	16.2297i	−0.163545	+	0.651275i
$622$		0			0
$623$	0.679623	+	1.61905i	0.0272285	+	0.0648657i
$624$		0			0
$625$	14.8764	+	5.27331i	0.595058	+	0.210932i
$626$		0			0
$627$	29.9681	−	11.9177i	1.19681	−	0.475947i
$628$		0			0
$629$	−0.712277	+	2.44132i	−0.0284004	+	0.0973420i
$630$		0			0
$631$	−3.95326	+	1.23504i	−0.157377	+	0.0491663i	−0.375871	−	0.926672i	$-0.622657\pi$
$631$	−3.95326	+	1.23504i	−0.157377	+	0.0491663i	0.218494	+	0.975838i	$0.429885\pi$
$632$		0			0
$633$	−11.5279	+	0.874347i	−0.458194	+	0.0347522i
$634$		0			0
$635$	19.9098	−	13.7855i	0.790095	−	0.547063i
$636$		0			0
$637$	−21.6874	+	4.15411i	−0.859286	+	0.164592i
$638$		0			0
$639$	0.641506	−	3.03688i	0.0253776	−	0.120137i
$640$		0			0
$641$	−23.5892	−	11.5175i	−0.931719	−	0.454915i	−0.0906744	−	0.995881i	$-0.528902\pi$
$641$	−23.5892	−	11.5175i	−0.931719	−	0.454915i	−0.841045	+	0.540966i	$0.818059\pi$
$642$		0			0
$643$	6.88750	−	40.0450i	0.271616	−	1.57922i	−0.453923	−	0.891041i	$-0.649976\pi$
$643$	6.88750	−	40.0450i	0.271616	−	1.57922i	0.725539	−	0.688181i	$-0.241590\pi$
$644$		0			0
$645$	8.58165	+	40.6255i	0.337902	+	1.59963i
$646$		0			0
$647$	−23.4348	+	23.8825i	−0.921316	+	0.938919i	−0.998310	−	0.0581127i	$-0.981492\pi$
$647$	−23.4348	+	23.8825i	−0.921316	+	0.938919i	0.0769944	+	0.997032i	$0.475468\pi$
$648$		0			0
$649$	−12.3746	−	2.85964i	−0.485746	−	0.112251i
$650$		0			0
$651$	0.305976	−	0.460279i	0.0119922	−	0.0180398i
$652$		0			0
$653$	−3.95714	−	6.47120i	−0.154855	−	0.253237i	0.766258	−	0.642533i	$-0.222116\pi$
$653$	−3.95714	−	6.47120i	−0.154855	−	0.253237i	−0.921113	+	0.389295i	$0.872719\pi$
$654$		0			0
$655$	2.25474	−	16.9202i	0.0881001	−	0.661128i
$656$		0			0
$657$	1.16527	−	1.10092i	0.0454614	−	0.0429509i
$658$		0			0
$659$	−26.1528	−	8.17044i	−1.01877	−	0.318275i	−0.257200	−	0.966358i	$-0.582800\pi$
$659$	−26.1528	−	8.17044i	−1.01877	−	0.318275i	−0.761570	+	0.648083i	$0.775571\pi$
$660$		0			0
$661$	4.50953	−	6.25650i	0.175401	−	0.243350i	−0.714359	−	0.699779i	$-0.753282\pi$
$661$	4.50953	−	6.25650i	0.175401	−	0.243350i	0.889760	+	0.456430i	$0.150872\pi$
$662$		0			0
$663$	−19.0024	−	22.5497i	−0.737991	−	0.875757i
$664$		0			0
$665$	3.64822	+	0.556607i	0.141472	+	0.0215843i
$666$		0			0
$667$	−8.30696			−0.321647
$668$		0			0
$669$	−14.0246			−0.542223
$670$		0			0
$671$	−24.8200	−	3.78677i	−0.958164	−	0.146187i
$672$		0			0
$673$	−24.4536	−	29.0186i	−0.942619	−	1.11858i	−0.992793	−	0.119843i	$-0.961761\pi$
$673$	−24.4536	−	29.0186i	−0.942619	−	1.11858i	0.0501741	−	0.998740i	$-0.484022\pi$
$674$		0			0
$675$	4.17982	−	5.79906i	0.160881	−	0.223206i
$676$		0			0
$677$	43.0794	+	13.4585i	1.65567	+	0.517251i	0.976278	−	0.216520i	$-0.0694708\pi$
$677$	43.0794	+	13.4585i	1.65567	+	0.517251i	0.679396	+	0.733772i	$0.262242\pi$
$678$		0			0
$679$	4.67985	−	4.42142i	0.179596	−	0.169678i
$680$		0			0
$681$	−3.17177	+	23.8019i	−0.121543	+	0.912090i
$682$		0			0
$683$	−17.7807	−	29.0772i	−0.680360	−	1.11261i	−0.986990	−	0.160780i	$-0.948599\pi$
$683$	−17.7807	−	29.0772i	−0.680360	−	1.11261i	0.306631	−	0.951829i	$-0.400798\pi$
$684$		0			0
$685$	−13.2724	+	19.9656i	−0.507111	+	0.762845i
$686$		0			0
$687$	6.36526	+	1.47095i	0.242850	+	0.0561201i
$688$		0			0
$689$	−3.88663	+	3.96089i	−0.148069	+	0.150898i
$690$		0			0
$691$	0.472048	+	2.23467i	0.0179576	+	0.0850110i	0.986464	−	0.163977i	$-0.0524322\pi$
$691$	0.472048	+	2.23467i	0.0179576	+	0.0850110i	−0.968507	+	0.248988i	$0.919902\pi$
$692$		0			0
$693$	0.0451175	−	0.262321i	0.00171387	−	0.00996474i
$694$		0			0
$695$	−8.65642	−	4.22652i	−0.328357	−	0.160321i
$696$		0			0
$697$	−0.499439	+	2.36434i	−0.0189176	+	0.0895558i
$698$		0			0
$699$	−16.0378	+	3.07195i	−0.606604	+	0.116192i
$700$		0			0
$701$	−2.50911	+	1.73731i	−0.0947679	+	0.0656174i	−0.615700	−	0.787981i	$-0.711127\pi$
$701$	−2.50911	+	1.73731i	−0.0947679	+	0.0656174i	0.520932	+	0.853598i	$0.325584\pi$
$702$		0			0
$703$	−2.66831	+	0.202381i	−0.100637	+	0.00763293i
$704$		0			0
$705$	−31.5062	+	9.84291i	−1.18659	+	0.370705i
$706$		0			0
$707$	−0.489914	+	1.67918i	−0.0184251	+	0.0631520i
$708$		0			0
$709$	7.98345	−	3.17486i	0.299825	−	0.119234i	−0.214779	−	0.976663i	$-0.568903\pi$
$709$	7.98345	−	3.17486i	0.299825	−	0.119234i	0.514603	+	0.857428i	$0.327939\pi$
$710$		0			0
$711$	1.45293	+	0.515026i	0.0544892	+	0.0193150i
$712$		0			0
$713$	1.10081	+	2.62244i	0.0412258	+	0.0982110i
$714$		0			0
$715$	−4.94229	+	19.6813i	−0.184831	+	0.736040i
$716$		0			0
$717$	−0.156574	−	0.469755i	−0.00584737	−	0.0175433i
$718$		0			0
$719$	−27.9022	+	30.6758i	−1.04058	+	1.14402i	−0.0511945	+	0.998689i	$0.516303\pi$
$719$	−27.9022	+	30.6758i	−1.04058	+	1.14402i	−0.989384	+	0.145327i	$0.953577\pi$
$720$		0			0
$721$	−2.22401	−	1.66786i	−0.0828264	−	0.0621143i
$722$		0			0
$723$	−39.1446	−	4.46413i	−1.45580	−	0.166023i
$724$		0			0
$725$	3.29747	+	1.31134i	0.122465	+	0.0487019i
$726$		0			0
$727$	8.84419	+	13.3043i	0.328013	+	0.493429i	0.959404	−	0.282036i	$-0.0910097\pi$
$727$	8.84419	+	13.3043i	0.328013	+	0.493429i	−0.631391	+	0.775465i	$0.717516\pi$
$728$		0			0
$729$	15.2204	+	19.5150i	0.563718	+	0.722778i
$730$		0			0
$731$	50.1088	−	37.5783i	1.85334	−	1.38988i
$732$		0			0
$733$	0.0347219	−	0.0221460i	0.00128248	−	0.000817980i	−0.537102	−	0.843518i	$-0.680481\pi$
$733$	0.0347219	−	0.0221460i	0.00128248	−	0.000817980i	0.538384	+	0.842700i	$0.319035\pi$
$734$		0			0
$735$	−14.9979	+	17.7977i	−0.553207	+	0.656478i
$736$		0			0
$737$	−2.47717	−	43.5838i	−0.0912476	−	1.60543i
$738$		0			0
$739$	−2.21432	−	23.3308i	−0.0814549	−	0.858236i	−0.939021	−	0.343861i	$-0.888265\pi$
$739$	−2.21432	−	23.3308i	−0.0814549	−	0.858236i	0.857566	−	0.514375i	$-0.171976\pi$
$740$		0			0
$741$	15.1744	−	27.0657i	0.557444	−	0.994285i
$742$		0			0
$743$	0.682358	−	2.04722i	0.0250333	−	0.0751052i	−0.935430	−	0.353512i	$-0.884987\pi$
$743$	0.682358	−	2.04722i	0.0250333	−	0.0751052i	0.960463	+	0.278407i	$0.0898065\pi$
$744$		0			0
$745$	−0.749732	−	5.62620i	−0.0274680	−	0.206128i
$746$		0			0
$747$	−1.72994	−	0.0655104i	−0.0632952	−	0.00239690i
$748$		0			0
$749$	−2.30492	−	1.59593i	−0.0842200	−	0.0583141i
$750$		0			0
$751$	11.7698	−	3.19354i	0.429488	−	0.116534i	−0.0405558	−	0.999177i	$-0.512913\pi$
$751$	11.7698	−	3.19354i	0.429488	−	0.116534i	0.470044	+	0.882643i	$0.344238\pi$
$752$		0			0
$753$	10.8556	−	1.23799i	0.395599	−	0.0451150i
$754$		0			0
$755$	−1.66128	+	4.41919i	−0.0604601	+	0.160831i
$756$		0			0
$757$	−13.2136	+	21.6085i	−0.480257	+	0.785375i	−0.997515	−	0.0704546i	$-0.977555\pi$
$757$	−13.2136	+	21.6085i	−0.480257	+	0.785375i	0.517258	+	0.855829i	$0.326953\pi$
$758$		0			0
$759$	14.6173	+	13.8101i	0.530576	+	0.501276i
$760$		0			0
$761$	6.68636	−	0.253203i	0.242380	−	0.00917861i	0.0836280	−	0.996497i	$-0.473349\pi$
$761$	6.68636	−	0.253203i	0.242380	−	0.00917861i	0.158752	+	0.987318i	$0.449253\pi$
$762$		0			0
$763$	1.55898	+	3.04541i	0.0564388	+	0.110251i
$764$		0			0
$765$	−2.07920	−	0.398261i	−0.0751738	−	0.0143992i
$766$		0			0
$767$	−10.9807	+	5.36137i	−0.396490	+	0.193588i
$768$		0			0
$769$	−7.87642	+	2.79198i	−0.284031	+	0.100682i	−0.472305	−	0.881435i	$-0.656578\pi$
$769$	−7.87642	+	2.79198i	−0.284031	+	0.100682i	0.188274	+	0.982116i	$0.439711\pi$
$770$		0			0
$771$	0.665007	−	35.1344i	0.0239496	−	1.26533i
$772$		0			0
$773$	46.3099	+	3.51242i	1.66565	+	0.126333i	0.874416	−	0.485178i	$-0.161245\pi$
$773$	46.3099	+	3.51242i	1.66565	+	0.126333i	0.791236	+	0.611511i	$0.209438\pi$
$774$		0			0
$775$	−0.0229924	−	1.21476i	−0.000825910	−	0.0436354i
$776$		0			0
$777$	−0.147754	+	0.288632i	−0.00530065	+	0.0103546i
$778$		0			0
$779$	−2.51368	+	0.383511i	−0.0900620	+	0.0137407i
$780$		0			0
$781$	35.5896	+	31.1616i	1.27350	+	1.11505i
$782$		0			0
$783$	−7.59980	+	9.74418i	−0.271595	+	0.348229i
$784$		0			0
$785$	14.6605	−	31.5260i	0.523254	−	1.12521i
$786$		0			0
$787$	−11.2536	−	29.9360i	−0.401149	−	1.06710i	−0.969666	−	0.244432i	$-0.921399\pi$
$787$	−11.2536	−	29.9360i	−0.401149	−	1.06710i	0.568518	−	0.822671i	$-0.307517\pi$
$788$		0			0
$789$	−1.46812	+	25.8305i	−0.0522666	+	0.919589i
$790$		0			0
$791$	2.46315	−	0.569209i	0.0875796	−	0.0202387i
$792$		0			0
$793$	−20.8433	+	12.2098i	−0.740166	+	0.433583i
$794$		0			0
$795$	−0.552645	+	5.82285i	−0.0196003	+	0.206515i
$796$		0			0
$797$	31.9436	+	17.1228i	1.13150	+	0.606521i	0.928009	−	0.372557i	$-0.121519\pi$
$797$	31.9436	+	17.1228i	1.13150	+	0.606521i	0.203489	+	0.979077i	$0.434772\pi$
$798$		0			0
$799$	33.5030	+	36.8333i	1.18525	+	1.30307i
$800$		0			0
$801$	0.797421	−	0.698208i	0.0281755	−	0.0246700i
$802$		0			0
$803$	5.95032	+	23.6955i	0.209982	+	0.836197i
$804$		0			0
$805$	0.644494	+	2.20900i	0.0227154	+	0.0778569i
$806$		0			0
$807$	−11.2646	+	4.98131i	−0.396534	+	0.175351i
$808$		0			0
$809$	7.69543	−	18.3326i	0.270557	−	0.644540i	−0.728628	−	0.684910i	$-0.759842\pi$
$809$	7.69543	−	18.3326i	0.270557	−	0.644540i	0.999185	+	0.0403698i	$0.0128536\pi$
$810$		0			0
$811$	−15.7978	−	21.9178i	−0.554735	−	0.769637i	0.436788	−	0.899564i	$-0.356116\pi$
$811$	−15.7978	−	21.9178i	−0.554735	−	0.769637i	−0.991523	+	0.129928i	$0.958526\pi$
$812$		0			0
$813$	29.1335	−	15.6165i	1.02176	−	0.547695i
$814$		0			0
$815$	4.18017	+	24.3042i	0.146425	+	0.851338i
$816$		0			0
$817$	55.5662	+	35.4407i	1.94402	+	1.23991i
$818$		0			0
$819$	−0.125237	−	0.223379i	−0.00437614	−	0.00780549i
$820$		0			0
$821$	32.8041	−	26.5985i	1.14487	−	0.928294i	0.146725	−	0.989177i	$-0.453127\pi$
$821$	32.8041	−	26.5985i	1.14487	−	0.928294i	0.998145	+	0.0608833i	$0.0193918\pi$
$822$		0			0
$823$	14.8107	+	12.0090i	0.516269	+	0.418606i	0.852149	−	0.523299i	$-0.175299\pi$
$823$	14.8107	+	12.0090i	0.516269	+	0.418606i	−0.335880	+	0.941905i	$0.609034\pi$
$824$		0			0
$825$	−3.62232	−	7.78947i	−0.126113	−	0.271195i
$826$		0			0
$827$	−0.365419	−	0.372401i	−0.0127069	−	0.0129496i	0.707383	−	0.706830i	$-0.249875\pi$
$827$	−0.365419	−	0.372401i	−0.0127069	−	0.0129496i	−0.720090	+	0.693880i	$0.755900\pi$
$828$		0			0
$829$	−31.4963	−	13.9279i	−1.09391	−	0.483737i	−0.222822	−	0.974859i	$-0.571527\pi$
$829$	−31.4963	−	13.9279i	−1.09391	−	0.483737i	−0.871091	+	0.491122i	$0.836587\pi$
$830$		0			0
$831$	−13.6079	−	7.97137i	−0.472051	−	0.276524i
$832$		0			0
$833$	33.8832	+	9.19362i	1.17398	+	0.318540i
$834$		0			0
$835$	10.9446	−	21.8162i	0.378754	−	0.754979i
$836$		0			0
$837$	4.08326	+	1.10792i	0.141138	+	0.0382954i
$838$		0			0
$839$	24.1111	+	14.1241i	0.832407	+	0.487618i	0.858968	−	0.512029i	$-0.171106\pi$
$839$	24.1111	+	14.1241i	0.832407	+	0.487618i	−0.0265606	+	0.999647i	$0.508456\pi$
$840$		0			0
$841$	20.9120	+	9.24749i	0.721105	+	0.318879i
$842$		0			0
$843$	−16.0442	−	16.3507i	−0.552590	−	0.563148i
$844$		0			0
$845$	−2.12077	−	4.56052i	−0.0729568	−	0.156887i
$846$		0			0
$847$	0.0471184	+	0.0382050i	0.00161901	+	0.00131274i
$848$		0			0
$849$	−6.86892	+	5.56952i	−0.235741	+	0.191146i
$850$		0			0
$851$	−0.815979	−	1.45542i	−0.0279714	−	0.0498911i
$852$		0			0
$853$	8.32868	+	5.31211i	0.285169	+	0.181883i	0.672582	−	0.740023i	$-0.265185\pi$
$853$	8.32868	+	5.31211i	0.285169	+	0.181883i	−0.387413	+	0.921906i	$0.626631\pi$
$854$		0			0
$855$	−0.377591	−	2.19537i	−0.0129133	−	0.0750802i
$856$		0			0
$857$	7.62466	−	4.08707i	0.260453	−	0.139612i	−0.337027	−	0.941495i	$-0.609421\pi$
$857$	7.62466	−	4.08707i	0.260453	−	0.139612i	0.597481	+	0.801883i	$0.296168\pi$
$858$		0			0
$859$	−9.94369	−	13.7958i	−0.339274	−	0.470708i	0.606708	−	0.794925i	$-0.292490\pi$
$859$	−9.94369	−	13.7958i	−0.339274	−	0.470708i	−0.945983	+	0.324217i	$0.894899\pi$
$860$		0			0
$861$	−0.119255	+	0.284097i	−0.00406419	+	0.00968200i
$862$		0			0
$863$	−17.0130	+	7.52330i	−0.579130	+	0.256096i	−0.673189	−	0.739470i	$-0.735076\pi$
$863$	−17.0130	+	7.52330i	−0.579130	+	0.256096i	0.0940591	+	0.995567i	$0.470016\pi$
$864$		0			0
$865$	1.12765	+	3.86501i	0.0383412	+	0.131414i
$866$		0			0
$867$	3.99012	+	15.8896i	0.135512	+	0.539638i
$868$		0			0
$869$	−17.6751	+	15.4760i	−0.599587	+	0.524988i
$870$		0			0
$871$	−28.2611	−	31.0703i	−0.957590	−	1.05278i
$872$		0			0
$873$	−3.42514	−	1.83599i	−0.115923	−	0.0621388i
$874$		0			0
$875$	0.417007	−	4.39373i	0.0140974	−	0.148535i
$876$		0			0
$877$	−18.8937	+	11.0678i	−0.637996	+	0.373733i	−0.788640	−	0.614855i	$-0.789214\pi$
$877$	−18.8937	+	11.0678i	−0.637996	+	0.373733i	0.150645	+	0.988588i	$0.451865\pi$
$878$		0			0
$879$	−16.4496	+	3.80133i	−0.554830	+	0.128216i
$880$		0			0
$881$	−2.55674	+	44.9838i	−0.0861387	+	1.51554i	0.606978	+	0.794718i	$0.292381\pi$
$881$	−2.55674	+	44.9838i	−0.0861387	+	1.51554i	−0.693117	+	0.720825i	$0.743763\pi$
$882$		0			0
$883$	7.21144	+	19.1833i	0.242684	+	0.645569i	0.999972	−	0.00751278i	$-0.00239141\pi$
$883$	7.21144	+	19.1833i	0.242684	+	0.645569i	−0.757287	+	0.653082i	$0.773476\pi$
$884$		0			0
$885$	−5.43092	+	11.6787i	−0.182558	+	0.392575i
$886$		0			0
$887$	−7.97522	+	10.2255i	−0.267782	+	0.343340i	−0.903505	−	0.428577i	$-0.859015\pi$
$887$	−7.97522	+	10.2255i	−0.267782	+	0.343340i	0.635724	+	0.771917i	$0.280702\pi$
$888$		0			0
$889$	−3.50419	−	3.06821i	−0.117527	−	0.102904i
$890$		0			0
$891$	31.7455	−	4.84340i	1.06352	−	0.162260i
$892$		0			0
$893$	−23.8739	+	46.6368i	−0.798911	+	1.56064i
$894$		0			0
$895$	0.183079	+	9.67263i	0.00611965	+	0.323320i
$896$		0			0
$897$	19.2923	+	1.46324i	0.644150	+	0.0488562i
$898$		0			0
$899$	−0.0397467	+	2.09994i	−0.00132563	+	0.0700371i
$900$		0			0
$901$	8.31597	−	2.94779i	0.277045	−	0.0982052i
$902$		0			0
$903$	7.17628	−	3.50384i	0.238812	−	0.116601i
$904$		0			0
$905$	−1.03989	−	0.199186i	−0.0345671	−	0.00662116i
$906$		0			0
$907$	−2.08914	−	4.08106i	−0.0693687	−	0.135509i	0.852879	−	0.522109i	$-0.174854\pi$
$907$	−2.08914	−	4.08106i	−0.0693687	−	0.135509i	−0.922248	+	0.386599i	$0.873650\pi$
$908$		0			0
$909$	1.05508	−	0.0399545i	0.0349949	−	0.00132521i
$910$		0			0
$911$	6.65918	+	6.29144i	0.220628	+	0.208445i	0.789111	−	0.614251i	$-0.210542\pi$
$911$	6.65918	+	6.29144i	0.220628	+	0.208445i	−0.568483	+	0.822695i	$0.692469\pi$
$912$		0			0
$913$	13.7640	−	22.5086i	0.455523	−	0.744927i
$914$		0			0
$915$	−8.95922	+	23.8326i	−0.296183	+	0.787881i
$916$		0			0
$917$	−3.26192	+	0.371996i	−0.107718	+	0.0122844i
$918$		0			0
$919$	5.62886	−	1.52729i	0.185679	−	0.0503808i	−0.167811	−	0.985819i	$-0.553670\pi$
$919$	5.62886	−	1.52729i	0.185679	−	0.0503808i	0.353490	+	0.935438i	$0.384995\pi$
$920$		0			0
$921$	27.9670	+	19.3644i	0.921543	+	0.638078i
$922$		0			0
$923$	45.4796	+	1.72225i	1.49698	+	0.0566885i
$924$		0			0
$925$	0.0941520	+	0.706543i	0.00309570	+	0.0232310i
$926$		0			0
$927$	−0.530599	+	1.59191i	−0.0174272	+	0.0522852i
$928$		0			0
$929$	6.62084	−	11.8093i	0.217223	−	0.387449i	−0.741869	−	0.670545i	$-0.766060\pi$
$929$	6.62084	−	11.8093i	0.217223	−	0.387449i	0.959092	+	0.283096i	$0.0913615\pi$
$930$		0			0
$931$	3.49052	+	36.7773i	0.114397	+	1.20533i
$932$		0			0
$933$	1.74519	+	30.7053i	0.0571351	+	1.00525i
$934$		0			0
$935$	20.7905	−	24.6716i	0.679922	−	0.806848i
$936$		0			0
$937$	29.9542	−	19.1051i	0.978560	−	0.624135i	0.0513514	−	0.998681i	$-0.483647\pi$
$937$	29.9542	−	19.1051i	0.978560	−	0.624135i	0.927208	+	0.374546i	$0.122201\pi$
$938$		0			0
$939$	23.2696	−	17.4506i	0.759373	−	0.569480i
$940$		0			0
$941$	−5.97591	−	7.66209i	−0.194809	−	0.249777i	0.681171	−	0.732124i	$-0.261471\pi$
$941$	−5.97591	−	7.66209i	−0.194809	−	0.249777i	−0.875980	+	0.482347i	$0.839784\pi$
$942$		0			0
$943$	−0.877731	−	1.32037i	−0.0285829	−	0.0429971i
$944$		0			0
$945$	3.18081	+	1.26495i	0.103472	+	0.0411487i
$946$		0			0
$947$	25.1526	+	2.86845i	0.817349	+	0.0932122i	0.511953	−	0.859013i	$-0.328922\pi$
$947$	25.1526	+	2.86845i	0.817349	+	0.0932122i	0.305396	+	0.952225i	$0.401211\pi$
$948$		0			0
$949$	18.8053	+	14.1027i	0.610445	+	0.457793i
$950$		0			0
$951$	34.2492	−	37.6537i	1.11061	−	1.22101i
$952$		0			0
$953$	−9.55041	−	28.6533i	−0.309368	−	0.928170i	−0.982112	−	0.188295i	$-0.939704\pi$
$953$	−9.55041	−	28.6533i	−0.309368	−	0.928170i	0.672744	−	0.739875i	$-0.265115\pi$
$954$		0			0
$955$	−4.29911	+	17.1200i	−0.139116	+	0.553991i
$956$		0			0
$957$	5.74784	+	13.6929i	0.185801	+	0.442629i
$958$		0			0
$959$	4.34609	+	1.54058i	0.140343	+	0.0497478i
$960$		0			0
$961$	−28.1376	+	11.1898i	−0.907663	+	0.360960i
$962$		0			0
$963$	−0.473967	+	1.62452i	−0.0152734	+	0.0523493i
$964$		0			0
$965$	−2.81425	+	0.879203i	−0.0905939	+	0.0283026i
$966$		0			0
$967$	−6.80864	+	0.516408i	−0.218951	+	0.0166066i	−0.184647	−	0.982805i	$-0.559114\pi$
$967$	−6.80864	+	0.516408i	−0.218951	+	0.0166066i	−0.0343040	+	0.999411i	$0.510921\pi$
$968$		0			0
$969$	−40.5606	+	28.0842i	−1.30299	+	0.902195i
$970$		0			0
$971$	36.3483	−	6.96233i	1.16647	−	0.223432i	0.431874	−	0.901934i	$-0.357853\pi$
$971$	36.3483	−	6.96233i	1.16647	−	0.223432i	0.734598	+	0.678502i	$0.237371\pi$
$972$		0			0
$973$	−0.382922	+	1.81275i	−0.0122759	+	0.0581141i
$974$		0			0
$975$	−7.42713	−	3.62632i	−0.237859	−	0.116135i
$976$		0			0
$977$	−6.15018	+	35.7582i	−0.196762	+	1.14400i	0.704166	+	0.710036i	$0.251321\pi$
$977$	−6.15018	+	35.7582i	−0.196762	+	1.14400i	−0.900928	+	0.433969i	$0.857113\pi$
$978$		0			0
$979$	3.33845	+	15.8042i	0.106697	+	0.505105i
$980$		0			0
$981$	1.44638	−	1.47401i	0.0461793	−	0.0470617i
$982$		0			0
$983$	−0.0960204	−	0.0221893i	−0.00306258	−	0.000707730i	0.223624	−	0.974675i	$-0.428211\pi$
$983$	−0.0960204	−	0.0221893i	−0.00306258	−	0.000707730i	−0.226687	+	0.973968i	$0.572789\pi$
$984$		0			0
$985$	14.9129	−	22.4334i	0.475164	−	0.714788i
$986$		0			0
$987$	3.31194	+	5.41610i	0.105420	+	0.172396i
$988$		0			0
$989$	−5.42817	+	40.7345i	−0.172606	+	1.29528i
$990$		0			0
$991$	−5.00518	+	4.72878i	−0.158995	+	0.150215i	−0.762129	−	0.647425i	$-0.775846\pi$
$991$	−5.00518	+	4.72878i	−0.158995	+	0.150215i	0.603134	+	0.797640i	$0.293918\pi$
$992$		0			0
$993$	−32.4510	−	10.1381i	−1.02980	−	0.321721i
$994$		0			0
$995$	22.4896	−	31.2020i	0.712968	−	0.989169i
$996$		0			0
$997$	−15.7936	−	18.7419i	−0.500188	−	0.593561i	0.454657	−	0.890667i	$-0.349762\pi$
$997$	−15.7936	−	18.7419i	−0.500188	−	0.593561i	−0.954845	+	0.297106i	$0.903979\pi$
$998$		0			0
$999$	−2.45374	−	0.374366i	−0.0776330	−	0.0118444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.e.a.21.4	✓	1148
167.8	even	83	inner	668.2.e.a.509.4	yes	1148

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.e.a.21.4	✓	1148	1.1	even	1	trivial
668.2.e.a.509.4	yes	1148	167.8	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)

\(f(q)\)	\(=\)	\(q+(-1.77371 - 0.270614i) q^{3} +(-1.21708 - 1.44428i) q^{5} +(-0.212405 + 0.294689i) q^{7} +(0.209294 + 0.0653857i) q^{9} +O(q^{10})\)	\(q+(-1.77371 - 0.270614i) q^{3} +(-1.21708 - 1.44428i) q^{5} +(-0.212405 + 0.294689i) q^{7} +(0.209294 + 0.0653857i) q^{9} +(-2.42906 + 2.29492i) q^{11} +(-0.424686 + 3.18696i) q^{13} +(1.76790 + 2.89109i) q^{15} +(2.82992 - 4.25704i) q^{17} +(5.24079 + 1.21109i) q^{19} +(0.456490 - 0.465212i) q^{21} +(0.693178 + 3.28150i) q^{23} +(0.242860 - 1.41202i) q^{25} +(4.48341 + 2.18904i) q^{27} +(-0.511898 + 2.42332i) q^{29} +(0.832857 - 0.159530i) q^{31} +(4.92948 - 3.41318i) q^{33} +(0.684128 - 0.0518884i) q^{35} +(-0.474860 + 0.148352i) q^{37} +(1.61570 - 5.53781i) q^{39} +(-0.439269 + 0.174689i) q^{41} +(11.5486 + 4.09369i) q^{43} +(-0.160292 - 0.381859i) q^{45} +(-2.37229 + 9.44702i) q^{47} +(2.17173 + 6.51564i) q^{49} +(-6.17147 + 6.78493i) q^{51} +(1.38084 + 1.03554i) q^{53} +(6.27088 + 0.715144i) q^{55} +(-8.96789 - 3.56636i) q^{57} +(2.10406 + 3.16513i) q^{59} +(4.62066 + 5.92443i) q^{61} +(-0.0637234 + 0.0477883i) q^{63} +(5.11975 - 3.26542i) q^{65} +(-8.41804 + 9.98949i) q^{67} +(-0.341476 - 6.00800i) q^{69} +(-1.33750 - 14.0923i) q^{71} +(3.57533 - 6.37713i) q^{73} +(-0.812875 + 2.43880i) q^{75} +(-0.160344 - 1.20327i) q^{77} +(7.02518 + 0.266034i) q^{79} +(-7.90070 - 5.47046i) q^{81} +(-7.61971 + 2.06748i) q^{83} +(-9.59262 + 1.09396i) q^{85} +(1.56374 - 4.15974i) q^{87} +(2.52173 - 4.12384i) q^{89} +(-0.848957 - 0.802075i) q^{91} +(-1.52042 + 0.0575760i) q^{93} +(-4.62931 - 9.04319i) q^{95} +(-17.4069 - 3.33420i) q^{97} +(-0.658442 + 0.321486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) \) 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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