LMFDB - Embedded newform 668.2.e.a.9.7

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			9.7
Character	$\chi$	$=$	668.9
Dual form			668.2.e.a.297.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0142693 - 0.107081i) q^{3} +(2.37141 + 1.04866i) q^{5} +(-0.709794 + 1.52635i) q^{7} +(2.88405 - 0.782538i) q^{9} +O(q^{10})$	\(q+(-0.0142693 - 0.107081i) q^{3} +(2.37141 + 1.04866i) q^{5} +(-0.709794 + 1.52635i) q^{7} +(2.88405 - 0.782538i) q^{9} +(-3.35961 + 4.30756i) q^{11} +(-2.66055 + 5.19729i) q^{13} +(0.0784527 - 0.268896i) q^{15} +(-0.517944 - 0.0392840i) q^{17} +(1.49067 - 2.24242i) q^{19} +(0.173570 + 0.0542253i) q^{21} +(-1.78155 - 0.708489i) q^{23} +(1.15954 + 1.27481i) q^{25} +(-0.250384 - 0.596482i) q^{27} +(9.05639 - 3.60155i) q^{29} +(-3.29354 + 0.761104i) q^{31} +(0.509196 + 0.298283i) q^{33} +(-3.28383 + 2.87526i) q^{35} +(6.35944 + 1.72552i) q^{37} +(0.594493 + 0.210732i) q^{39} +(-10.1623 + 4.96177i) q^{41} +(0.0217449 - 0.229112i) q^{43} +(7.65989 + 1.16867i) q^{45} +(0.0934650 + 4.93805i) q^{47} +(2.68486 + 3.18606i) q^{49} +(0.00318414 + 0.0560224i) q^{51} +(-0.741992 - 4.31406i) q^{53} +(-12.4842 + 6.69193i) q^{55} +(-0.261390 - 0.127625i) q^{57} +(11.2284 - 0.851629i) q^{59} +(4.47266 - 4.55812i) q^{61} +(-0.852659 + 4.95750i) q^{63} +(-11.7594 + 9.53490i) q^{65} +(2.01203 - 0.889737i) q^{67} +(-0.0504440 + 0.200880i) q^{69} +(12.5514 - 1.43139i) q^{71} +(5.08275 - 3.81172i) q^{73} +(0.119961 - 0.142355i) q^{75} +(-4.19020 - 8.18540i) q^{77} +(1.89257 - 5.03445i) q^{79} +(7.67518 - 4.49606i) q^{81} +(-2.31465 + 3.21134i) q^{83} +(-1.18706 - 0.636305i) q^{85} +(-0.514884 - 0.918372i) q^{87} +(-1.63105 - 5.59042i) q^{89} +(-6.04441 - 7.74993i) q^{91} +(0.128496 + 0.341814i) q^{93} +(5.88653 - 3.75449i) q^{95} +(-3.78589 - 0.874881i) q^{97} +(-6.31845 + 15.0523i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.0142693	−	0.107081i	−0.00823837	−	0.0618231i	0.986636	−	0.162937i	$-0.0520967\pi$
$3$	−0.0142693	−	0.107081i	−0.00823837	−	0.0618231i	−0.994875	+	0.101114i	$0.967759\pi$
$4$		0			0
$5$	2.37141	+	1.04866i	1.06053	+	0.468974i	0.859778	−	0.510668i	$-0.170602\pi$
$5$	2.37141	+	1.04866i	1.06053	+	0.468974i	0.200750	+	0.979643i	$0.435662\pi$
$6$		0			0
$7$	−0.709794	+	1.52635i	−0.268277	+	0.576904i	−0.993786	−	0.111308i	$-0.964496\pi$
$7$	−0.709794	+	1.52635i	−0.268277	+	0.576904i	0.725509	+	0.688213i	$0.241604\pi$
$8$		0			0
$9$	2.88405	−	0.782538i	0.961350	−	0.260846i
$10$		0			0
$11$	−3.35961	+	4.30756i	−1.01296	+	1.29878i	−0.0591882	+	0.998247i	$0.518851\pi$
$11$	−3.35961	+	4.30756i	−1.01296	+	1.29878i	−0.953771	+	0.300533i	$0.902836\pi$
$12$		0			0
$13$	−2.66055	+	5.19729i	−0.737905	+	1.44147i	0.153447	+	0.988157i	$0.450962\pi$
$13$	−2.66055	+	5.19729i	−0.737905	+	1.44147i	−0.891352	+	0.453312i	$0.850242\pi$
$14$		0			0
$15$	0.0784527	−	0.268896i	0.0202564	−	0.0694286i
$16$		0			0
$17$	−0.517944	−	0.0392840i	−0.125620	−	0.00952777i	0.0126686	−	0.999920i	$-0.495967\pi$
$17$	−0.517944	−	0.0392840i	−0.125620	−	0.00952777i	−0.138289	+	0.990392i	$0.544160\pi$
$18$		0			0
$19$	1.49067	−	2.24242i	0.341984	−	0.514446i	−0.621069	−	0.783756i	$-0.713302\pi$
$19$	1.49067	−	2.24242i	0.341984	−	0.514446i	0.963054	+	0.269310i	$0.0867955\pi$
$20$		0			0
$21$	0.173570	+	0.0542253i	0.0378761	+	0.0118329i
$22$		0			0
$23$	−1.78155	−	0.708489i	−0.371480	−	0.147730i	0.176334	−	0.984330i	$-0.443576\pi$
$23$	−1.78155	−	0.708489i	−0.371480	−	0.147730i	−0.547814	+	0.836600i	$0.684540\pi$
$24$		0			0
$25$	1.15954	+	1.27481i	0.231909	+	0.254961i
$26$		0			0
$27$	−0.250384	−	0.596482i	−0.0481864	−	0.114793i
$28$		0			0
$29$	9.05639	−	3.60155i	1.68173	−	0.668791i	0.683595	−	0.729861i	$-0.260415\pi$
$29$	9.05639	−	3.60155i	1.68173	−	0.668791i	0.998133	+	0.0610708i	$0.0194515\pi$
$30$		0			0
$31$	−3.29354	+	0.761104i	−0.591538	+	0.136698i	−0.510300	−	0.859997i	$-0.670466\pi$
$31$	−3.29354	+	0.761104i	−0.591538	+	0.136698i	−0.0812377	+	0.996695i	$0.525887\pi$
$32$		0			0
$33$	0.509196	+	0.298283i	0.0886397	+	0.0519244i
$34$		0			0
$35$	−3.28383	+	2.87526i	−0.555068	+	0.486008i
$36$		0			0
$37$	6.35944	+	1.72552i	1.04548	+	0.283674i	0.742868	−	0.669438i	$-0.233465\pi$
$37$	6.35944	+	1.72552i	1.04548	+	0.283674i	0.302617	+	0.953112i	$0.402140\pi$
$38$		0			0
$39$	0.594493	+	0.210732i	0.0951951	+	0.0337442i
$40$		0			0
$41$	−10.1623	+	4.96177i	−1.58708	+	0.774898i	−0.999415	−	0.0342055i	$-0.989110\pi$
$41$	−10.1623	+	4.96177i	−1.58708	+	0.774898i	−0.587667	+	0.809103i	$0.699953\pi$
$42$		0			0
$43$	0.0217449	−	0.229112i	0.00331607	−	0.0349392i	−0.993715	−	0.111940i	$-0.964293\pi$
$43$	0.0217449	−	0.229112i	0.00331607	−	0.0349392i	0.997031	+	0.0770010i	$0.0245345\pi$
$44$		0			0
$45$	7.65989	+	1.16867i	1.14187	+	0.174214i
$46$		0			0
$47$	0.0934650	+	4.93805i	0.0136333	+	0.720288i	0.939521	+	0.342490i	$0.111270\pi$
$47$	0.0934650	+	4.93805i	0.0136333	+	0.720288i	−0.925888	+	0.377798i	$0.876681\pi$
$48$		0			0
$49$	2.68486	+	3.18606i	0.383551	+	0.455151i
$50$		0			0
$51$	0.00318414	+	0.0560224i	0.000445868	+	0.00784470i
$52$		0			0
$53$	−0.741992	−	4.31406i	−0.101920	−	0.592582i	−0.990896	−	0.134628i	$-0.957016\pi$
$53$	−0.741992	−	4.31406i	−0.101920	−	0.592582i	0.888976	−	0.457954i	$-0.151418\pi$
$54$		0			0
$55$	−12.4842	+	6.69193i	−1.68337	+	0.902339i
$56$		0			0
$57$	−0.261390	−	0.127625i	−0.0346220	−	0.0169043i
$58$		0			0
$59$	11.2284	−	0.851629i	1.46181	−	0.110873i	0.679462	−	0.733710i	$-0.262213\pi$
$59$	11.2284	−	0.851629i	1.46181	−	0.110873i	0.782351	+	0.622838i	$0.214020\pi$
$60$		0			0
$61$	4.47266	−	4.55812i	0.572665	−	0.583607i	−0.365060	−	0.930984i	$-0.618952\pi$
$61$	4.47266	−	4.55812i	0.572665	−	0.583607i	0.937726	+	0.347377i	$0.112928\pi$
$62$		0			0
$63$	−0.852659	+	4.95750i	−0.107425	+	0.624586i
$64$		0			0
$65$	−11.7594	+	9.53490i	−1.45858	+	1.18266i
$66$		0			0
$67$	2.01203	−	0.889737i	0.245809	−	0.108699i	−0.277857	−	0.960622i	$-0.589624\pi$
$67$	2.01203	−	0.889737i	0.245809	−	0.108699i	0.523666	+	0.851924i	$0.324564\pi$
$68$		0			0
$69$	−0.0504440	+	0.200880i	−0.00607274	+	0.0241831i
$70$		0			0
$71$	12.5514	−	1.43139i	1.48958	−	0.169875i	0.669796	−	0.742545i	$-0.266382\pi$
$71$	12.5514	−	1.43139i	1.48958	−	0.169875i	0.819786	+	0.572670i	$0.194092\pi$
$72$		0			0
$73$	5.08275	−	3.81172i	0.594890	−	0.446128i	−0.259512	−	0.965740i	$-0.583562\pi$
$73$	5.08275	−	3.81172i	0.594890	−	0.446128i	0.854403	+	0.519611i	$0.173923\pi$
$74$		0			0
$75$	0.119961	−	0.142355i	0.0138519	−	0.0164378i
$76$		0			0
$77$	−4.19020	−	8.18540i	−0.477518	−	0.932813i
$78$		0			0
$79$	1.89257	−	5.03445i	0.212930	−	0.566420i	−0.785707	−	0.618598i	$-0.787701\pi$
$79$	1.89257	−	5.03445i	0.212930	−	0.566420i	0.998638	+	0.0521786i	$0.0166165\pi$
$80$		0			0
$81$	7.67518	−	4.49606i	0.852798	−	0.499562i
$82$		0			0
$83$	−2.31465	+	3.21134i	−0.254066	+	0.352490i	−0.918893	−	0.394508i	$-0.870915\pi$
$83$	−2.31465	+	3.21134i	−0.254066	+	0.352490i	0.664827	+	0.746998i	$0.268505\pi$
$84$		0			0
$85$	−1.18706	−	0.636305i	−0.128755	−	0.0690170i
$86$		0			0
$87$	−0.514884	−	0.918372i	−0.0552014	−	0.0984599i
$88$		0			0
$89$	−1.63105	−	5.59042i	−0.172891	−	0.592583i	−0.999553	−	0.0298847i	$-0.990486\pi$
$89$	−1.63105	−	5.59042i	−0.172891	−	0.592583i	0.826662	−	0.562699i	$-0.190237\pi$
$90$		0			0
$91$	−6.04441	−	7.74993i	−0.633627	−	0.812413i
$92$		0			0
$93$	0.128496	+	0.341814i	0.0133244	+	0.0354445i
$94$		0			0
$95$	5.88653	−	3.75449i	0.603945	−	0.385202i
$96$		0			0
$97$	−3.78589	−	0.874881i	−0.384399	−	0.0888307i	0.0285320	−	0.999593i	$-0.490917\pi$
$97$	−3.78589	−	0.874881i	−0.384399	−	0.0888307i	−0.412931	+	0.910762i	$0.635495\pi$
$98$		0			0
$99$	−6.31845	+	15.0523i	−0.635028	+	1.51281i
$100$		0			0
$101$	−0.388847	−	4.09701i	−0.0386917	−	0.407668i	−0.993781	−	0.111351i	$-0.964482\pi$
$101$	−0.388847	−	4.09701i	−0.0386917	−	0.407668i	0.955089	−	0.296318i	$-0.0957587\pi$
$102$		0			0
$103$	1.79910	−	1.24570i	0.177271	−	0.122743i	−0.477309	−	0.878736i	$-0.658388\pi$
$103$	1.79910	−	1.24570i	0.177271	−	0.122743i	0.654580	+	0.755993i	$0.272846\pi$
$104$		0			0
$105$	0.354743	+	0.310606i	0.0346193	+	0.0303121i
$106$		0			0
$107$	−7.59949	−	5.26190i	−0.734670	−	0.508687i	0.141948	−	0.989874i	$-0.454664\pi$
$107$	−7.59949	−	5.26190i	−0.734670	−	0.508687i	−0.876618	+	0.481187i	$0.840206\pi$
$108$		0			0
$109$	−1.24003	−	0.790903i	−0.118773	−	0.0757548i	0.477021	−	0.878892i	$-0.341717\pi$
$109$	−1.24003	−	0.790903i	−0.118773	−	0.0757548i	−0.595794	+	0.803137i	$0.703163\pi$
$110$		0			0
$111$	0.0940256	−	0.705595i	0.00892452	−	0.0669721i
$112$		0			0
$113$	−7.47163	+	12.2185i	−0.702872	+	1.14942i	0.279075	+	0.960269i	$0.409972\pi$
$113$	−7.47163	+	12.2185i	−0.702872	+	1.14942i	−0.981947	+	0.189154i	$0.939425\pi$
$114$		0			0
$115$	−3.48183	−	3.54836i	−0.324683	−	0.330886i
$116$		0			0
$117$	−3.60610	+	17.0712i	−0.333384	+	1.57824i
$118$		0			0
$119$	0.427595	−	0.762678i	0.0391975	−	0.0699146i
$120$		0			0
$121$	−4.58906	−	18.2747i	−0.417187	−	1.66134i
$122$		0			0
$123$	0.676318	+	1.01738i	0.0609815	+	0.0917343i
$124$		0			0
$125$	−2.68660	−	8.06037i	−0.240297	−	0.720941i
$126$		0			0
$127$	−15.4843	−	1.76586i	−1.37401	−	0.156695i	−0.605149	−	0.796112i	$-0.706887\pi$
$127$	−15.4843	−	1.76586i	−1.37401	−	0.156695i	−0.768860	+	0.639417i	$0.779176\pi$
$128$		0			0
$129$	−0.0248437		0.000940797i	−0.00218737		8.28325e-5i
$130$		0			0
$131$	0.230395	−	4.05363i	0.0201297	−	0.354167i	−0.972494	−	0.232929i	$-0.925169\pi$
$131$	0.230395	−	4.05363i	0.0201297	−	0.354167i	0.992623	−	0.121238i	$-0.0386864\pi$
$132$		0			0
$133$	2.36463	+	3.86694i	0.205040	+	0.335306i
$134$		0			0
$135$	0.0317428	−	1.67707i	0.00273199	−	0.144339i
$136$		0			0
$137$	19.1824	−	6.79966i	1.63886	−	0.580934i	0.654343	−	0.756198i	$-0.272945\pi$
$137$	19.1824	−	6.79966i	1.63886	−	0.580934i	0.984522	+	0.175263i	$0.0560777\pi$
$138$		0			0
$139$	−12.9380	−	12.2235i	−1.09738	−	1.03678i	−0.999133	−	0.0416216i	$-0.986748\pi$
$139$	−12.9380	−	12.2235i	−1.09738	−	1.03678i	−0.0982507	−	0.995162i	$-0.531325\pi$
$140$		0			0
$141$	0.527436	−	0.0804707i	0.0444181	−	0.00677685i
$142$		0			0
$143$	−13.4492	−	28.9214i	−1.12468	−	2.41853i
$144$		0			0
$145$	25.2532	+	0.956304i	2.09716	+	0.0794167i
$146$		0			0
$147$	0.302854	−	0.332959i	0.0249790	−	0.0274620i
$148$		0			0
$149$	3.16211	+	2.56393i	0.259050	+	0.210045i	0.750517	−	0.660851i	$-0.229804\pi$
$149$	3.16211	+	2.56393i	0.259050	+	0.210045i	−0.491467	+	0.870896i	$0.663539\pi$
$150$		0			0
$151$	−2.90048	−	2.17517i	−0.236038	−	0.177013i	0.475383	−	0.879779i	$-0.342309\pi$
$151$	−2.90048	−	2.17517i	−0.236038	−	0.177013i	−0.711421	+	0.702766i	$0.751948\pi$
$152$		0			0
$153$	−1.52452	+	0.292014i	−0.123250	+	0.0236079i
$154$		0			0
$155$	−8.60848	−	1.64891i	−0.691450	−	0.132444i
$156$		0			0
$157$	−0.231445	−	1.09566i	−0.0184713	−	0.0874431i	0.968196	−	0.250193i	$-0.0804939\pi$
$157$	−0.231445	−	1.09566i	−0.0184713	−	0.0874431i	−0.986667	+	0.162749i	$0.947964\pi$
$158$		0			0
$159$	−0.451365	+	0.141012i	−0.0357956	+	0.0111829i
$160$		0			0
$161$	2.34593	−	2.21638i	0.184885	−	0.174676i
$162$		0			0
$163$	5.41008	−	16.2314i	0.423751	−	1.27134i	−0.492352	−	0.870396i	$-0.663863\pi$
$163$	5.41008	−	16.2314i	0.423751	−	1.27134i	0.916102	−	0.400945i	$-0.131318\pi$
$164$		0			0
$165$	0.894716	+	1.24132i	0.0696536	+	0.0966370i
$166$		0			0
$167$	7.49551	+	10.5270i	0.580020	+	0.814602i
$167$	7.49551	+	10.5270i	0.580020	+	0.814602i
$168$		0			0
$169$	−12.3319	−	17.1093i	−0.948610	−	1.31610i
$170$		0			0
$171$	2.54441	−	7.63376i	0.194576	−	0.583768i
$172$		0			0
$173$	−1.32033	+	1.24741i	−0.100382	+	0.0948391i	−0.735303	−	0.677738i	$-0.762960\pi$
$173$	−1.32033	+	1.24741i	−0.100382	+	0.0948391i	0.634921	+	0.772577i	$0.281033\pi$
$174$		0			0
$175$	−2.76883	+	0.865015i	−0.209304	+	0.0653890i
$176$		0			0
$177$	−0.251414	−	1.19019i	−0.0188974	−	0.0894603i
$178$		0			0
$179$	−4.50338	−	0.862599i	−0.336598	−	0.0644737i	0.0170431	−	0.999855i	$-0.494575\pi$
$179$	−4.50338	−	0.862599i	−0.336598	−	0.0644737i	−0.353641	+	0.935381i	$0.615057\pi$
$180$		0			0
$181$	2.91010	−	0.557414i	0.216306	−	0.0414323i	−0.0788278	−	0.996888i	$-0.525118\pi$
$181$	2.91010	−	0.557414i	0.216306	−	0.0414323i	0.295134	+	0.955456i	$0.404636\pi$
$182$		0			0
$183$	−0.551908	−	0.413894i	−0.0407982	−	0.0305960i
$184$		0			0
$185$	13.2714	+	10.7608i	0.975729	+	0.791150i
$186$		0			0
$187$	1.90931	−	2.09910i	0.139622	−	0.153501i
$188$		0			0
$189$	1.08816	+	0.0412070i	0.0791519	+	0.00299737i
$190$		0			0
$191$	8.02581	+	17.2587i	0.580727	+	1.24880i	0.947877	+	0.318637i	$0.103225\pi$
$191$	8.02581	+	17.2587i	0.580727	+	1.24880i	−0.367150	+	0.930162i	$0.619666\pi$
$192$		0			0
$193$	−10.2835	+	1.56896i	−0.740226	+	0.112936i	−0.509968	−	0.860194i	$-0.670343\pi$
$193$	−10.2835	+	1.56896i	−0.740226	+	0.112936i	−0.230258	+	0.973130i	$0.573957\pi$
$194$		0			0
$195$	1.18880	+	1.12315i	0.0851319	+	0.0804307i
$196$		0			0
$197$	16.0211	−	5.67905i	1.14145	−	0.404616i	0.304838	−	0.952404i	$-0.401398\pi$
$197$	16.0211	−	5.67905i	1.14145	−	0.404616i	0.836617	+	0.547789i	$0.184530\pi$
$198$		0			0
$199$	−0.0811298	+	4.28634i	−0.00575114	+	0.303851i	0.985335	+	0.170630i	$0.0545802\pi$
$199$	−0.0811298	+	4.28634i	−0.00575114	+	0.303851i	−0.991086	+	0.133221i	$0.957468\pi$
$200$		0			0
$201$	−0.123984	−	0.202754i	−0.00874514	−	0.0143011i
$202$		0			0
$203$	−0.930961	+	16.3795i	−0.0653406	+	1.14962i
$204$		0			0
$205$	−29.3021	+	1.10963i	−2.04655	+	0.0775000i
$206$		0			0
$207$	−5.69251	−	0.649186i	−0.395657	−	0.0451215i
$208$		0			0
$209$	4.65128	+	13.9548i	0.321736	+	0.965275i
$210$		0			0
$211$	6.83736	+	10.2854i	0.470703	+	0.708078i	0.989130	−	0.147044i	$-0.0469760\pi$
$211$	6.83736	+	10.2854i	0.470703	+	0.708078i	−0.518426	+	0.855122i	$0.673482\pi$
$212$		0			0
$213$	−0.332374	−	1.32359i	−0.0227739	−	0.0906910i
$214$		0			0
$215$	0.291826	−	0.520515i	0.0199024	−	0.0354988i
$216$		0			0
$217$	1.17603	−	5.56731i	0.0798340	−	0.377933i
$218$		0			0
$219$	−0.480689	−	0.489873i	−0.0324819	−	0.0331026i
$220$		0			0
$221$	1.58219	−	2.58739i	0.106430	−	0.174047i
$222$		0			0
$223$	3.28526	−	24.6535i	0.219997	−	1.65092i	−0.438790	−	0.898590i	$-0.644593\pi$
$223$	3.28526	−	24.6535i	0.219997	−	1.65092i	0.658787	−	0.752330i	$-0.271070\pi$
$224$		0			0
$225$	4.34177	+	2.76922i	0.289451	+	0.184615i
$226$		0			0
$227$	−1.29664	−	0.897798i	−0.0860612	−	0.0595889i	0.525451	−	0.850824i	$-0.323896\pi$
$227$	−1.29664	−	0.897798i	−0.0860612	−	0.0595889i	−0.611513	+	0.791235i	$0.709439\pi$
$228$		0			0
$229$	−9.04161	−	7.91668i	−0.597487	−	0.523149i	0.305851	−	0.952079i	$-0.401059\pi$
$229$	−9.04161	−	7.91668i	−0.597487	−	0.523149i	−0.903337	+	0.428931i	$0.858890\pi$
$230$		0			0
$231$	−0.816707	+	0.565489i	−0.0537354	+	0.0372065i
$232$		0			0
$233$	2.64172	+	27.8340i	0.173065	+	1.82347i	0.486302	+	0.873791i	$0.338346\pi$
$233$	2.64172	+	27.8340i	0.173065	+	1.82347i	−0.313237	+	0.949675i	$0.601413\pi$
$234$		0			0
$235$	−4.95668	+	11.8082i	−0.323338	+	0.770279i
$236$		0			0
$237$	−0.566098	−	0.130819i	−0.0367720	−	0.00849763i
$238$		0			0
$239$	−6.62001	+	4.22231i	−0.428213	+	0.273118i	−0.734221	−	0.678911i	$-0.762452\pi$
$239$	−6.62001	+	4.22231i	−0.428213	+	0.273118i	0.306008	+	0.952029i	$0.401007\pi$
$240$		0			0
$241$	0.141916	+	0.377512i	0.00914158	+	0.0243177i	0.940537	−	0.339692i	$-0.110323\pi$
$241$	0.141916	+	0.377512i	0.00914158	+	0.0243177i	−0.931395	+	0.364010i	$0.881407\pi$
$242$		0			0
$243$	−1.78449	−	2.28801i	−0.114475	−	0.146776i
$244$		0			0
$245$	3.02581	+	10.3709i	0.193312	+	0.662576i
$246$		0			0
$247$	7.68848	+	13.7135i	0.489206	+	0.872572i
$248$		0			0
$249$	0.376900	+	0.202031i	0.0238851	+	0.0128032i
$250$		0			0
$251$	−14.4093	+	19.9914i	−0.909507	+	1.26185i	0.0551879	+	0.998476i	$0.482424\pi$
$251$	−14.4093	+	19.9914i	−0.909507	+	1.26185i	−0.964695	+	0.263370i	$0.915166\pi$
$252$		0			0
$253$	9.03718	−	5.29391i	0.568163	−	0.332825i
$254$		0			0
$255$	−0.0511974	+	0.136191i	−0.00320611	+	0.00852862i
$256$		0			0
$257$	7.63412	+	14.9130i	0.476204	+	0.930246i	0.997062	+	0.0766024i	$0.0244072\pi$
$257$	7.63412	+	14.9130i	0.476204	+	0.930246i	−0.520858	+	0.853643i	$0.674388\pi$
$258$		0			0
$259$	−7.14763	+	8.48193i	−0.444132	+	0.527041i
$260$		0			0
$261$	23.3007	−	17.4740i	1.44228	−	1.08161i
$262$		0			0
$263$	15.7109	−	1.79170i	0.968773	−	0.110481i	0.385457	−	0.922726i	$-0.374044\pi$
$263$	15.7109	−	1.79170i	0.968773	−	0.110481i	0.583316	+	0.812245i	$0.301755\pi$
$264$		0			0
$265$	2.76441	−	11.0085i	0.169816	−	0.676248i
$266$		0			0
$267$	−0.575352	+	0.254426i	−0.0352110	+	0.0155706i
$268$		0			0
$269$	14.3735	−	11.6545i	0.876369	−	0.710585i	−0.0818427	−	0.996645i	$-0.526081\pi$
$269$	14.3735	−	11.6545i	0.876369	−	0.710585i	0.958212	+	0.286060i	$0.0923456\pi$
$270$		0			0
$271$	4.70731	−	27.3691i	0.285949	−	1.66255i	−0.386409	−	0.922328i	$-0.626285\pi$
$271$	4.70731	−	27.3691i	0.285949	−	1.66255i	0.672358	−	0.740226i	$-0.265282\pi$
$272$		0			0
$273$	−0.743618	+	0.757826i	−0.0450058	+	0.0458657i
$274$		0			0
$275$	−9.38693	+	0.711961i	−0.566053	+	0.0429328i
$276$		0			0
$277$	−28.3524	−	13.8432i	−1.70353	−	0.831755i	−0.991575	−	0.129531i	$-0.958653\pi$
$277$	−28.3524	−	13.8432i	−1.70353	−	0.831755i	−0.711956	−	0.702224i	$-0.752191\pi$
$278$		0			0
$279$	−8.90315	+	4.77238i	−0.533018	+	0.285715i
$280$		0			0
$281$	−2.22668	−	12.9463i	−0.132832	−	0.772309i	−0.973143	−	0.230203i	$-0.926061\pi$
$281$	−2.22668	−	12.9463i	−0.132832	−	0.772309i	0.840310	−	0.542106i	$-0.182373\pi$
$282$		0			0
$283$	−1.15895	−	20.3907i	−0.0688922	−	1.21210i	−0.827845	−	0.560957i	$-0.810433\pi$
$283$	−1.15895	−	20.3907i	−0.0688922	−	1.21210i	0.758952	−	0.651146i	$-0.225711\pi$
$284$		0			0
$285$	−0.486029	−	0.576760i	−0.0287899	−	0.0341643i
$286$		0			0
$287$	−0.360247	−	19.0330i	−0.0212647	−	1.12348i
$288$		0			0
$289$	−16.5388	−	2.52332i	−0.972871	−	0.148431i
$290$		0			0
$291$	−0.0396609	+	0.417880i	−0.00232496	+	0.0244966i
$292$		0			0
$293$	−14.3945	+	7.02817i	−0.840937	+	0.410590i	−0.808224	−	0.588875i	$-0.799571\pi$
$293$	−14.3945	+	7.02817i	−0.840937	+	0.410590i	−0.0327126	+	0.999465i	$0.510415\pi$
$294$		0			0
$295$	27.5202	+	9.75519i	1.60229	+	0.567969i
$296$		0			0
$297$	3.41058	+	0.925401i	0.197902	+	0.0536972i
$298$		0			0
$299$	8.42214	−	7.37428i	0.487065	−	0.426465i
$300$		0			0
$301$	0.334269	+	0.195812i	0.0192670	+	0.0112864i
$302$		0			0
$303$	−0.433163	+	0.100099i	−0.0248845	+	0.00575056i
$304$		0			0
$305$	15.3864	−	6.11888i	0.881024	−	0.350366i
$306$		0			0
$307$	12.2452	+	29.1713i	0.698868	+	1.66489i	0.745950	+	0.666002i	$0.231996\pi$
$307$	12.2452	+	29.1713i	0.698868	+	1.66489i	−0.0470814	+	0.998891i	$0.514992\pi$
$308$		0			0
$309$	−0.159062	−	0.174874i	−0.00904875	−	0.00994822i
$310$		0			0
$311$	11.4757	+	4.56366i	0.650728	+	0.258782i	0.671502	−	0.741002i	$-0.265649\pi$
$311$	11.4757	+	4.56366i	0.650728	+	0.258782i	−0.0207745	+	0.999784i	$0.506613\pi$
$312$		0			0
$313$	−9.61498	−	3.00383i	−0.543471	−	0.169786i	0.0141232	−	0.999900i	$-0.495504\pi$
$313$	−9.61498	−	3.00383i	−0.543471	−	0.169786i	−0.557594	+	0.830114i	$0.688275\pi$
$314$		0			0
$315$	−7.22073	+	10.8621i	−0.406842	+	0.612011i
$316$		0			0
$317$	−4.95030	−	0.375460i	−0.278036	−	0.0210879i	−0.0641280	−	0.997942i	$-0.520427\pi$
$317$	−4.95030	−	0.375460i	−0.278036	−	0.0210879i	−0.213908	+	0.976854i	$0.568619\pi$
$318$		0			0
$319$	−14.9120	+	51.1108i	−0.834912	+	2.86165i
$320$		0			0
$321$	−0.455008	+	0.888842i	−0.0253961	+	0.0496103i
$322$		0			0
$323$	−0.860178	+	1.10289i	−0.0478616	+	0.0613663i
$324$		0			0
$325$	−9.71057	+	2.63480i	−0.538646	+	0.146152i
$326$		0			0
$327$	−0.0669961	+	0.144069i	−0.00370489	+	0.00796703i
$328$		0			0
$329$	−7.60351	−	3.36234i	−0.419195	−	0.185372i
$330$		0			0
$331$	−2.37953	−	17.8567i	−0.130791	−	0.981492i	−0.926628	−	0.375981i	$-0.877306\pi$
$331$	−2.37953	−	17.8567i	−0.130791	−	0.981492i	0.795837	−	0.605511i	$-0.207031\pi$
$332$		0			0
$333$	19.6912			1.07907
$334$		0			0
$335$	5.70438			0.311664
$336$		0			0
$337$	4.43306	+	33.2669i	0.241484	+	1.81216i	0.522697	+	0.852518i	$0.324926\pi$
$337$	4.43306	+	33.2669i	0.241484	+	1.81216i	−0.281213	+	0.959645i	$0.590737\pi$
$338$		0			0
$339$	1.41498	+	0.625718i	0.0768514	+	0.0339843i
$340$		0			0
$341$	7.78650	−	16.7442i	0.421663	−	0.906747i
$342$		0			0
$343$	−18.1407	+	4.92217i	−0.979507	+	0.265772i
$344$		0			0
$345$	−0.330277	+	0.423469i	−0.0177815	+	0.0227988i
$346$		0			0
$347$	−5.78234	+	11.2956i	−0.310412	+	0.606378i	−0.992126	−	0.125240i	$-0.960030\pi$
$347$	−5.78234	+	11.2956i	−0.310412	+	0.606378i	0.681714	+	0.731618i	$0.261235\pi$
$348$		0			0
$349$	1.89422	−	6.49242i	0.101395	−	0.347531i	−0.893421	−	0.449220i	$-0.851702\pi$
$349$	1.89422	−	6.49242i	0.101395	−	0.347531i	0.994816	+	0.101689i	$0.0324247\pi$
$350$		0			0
$351$	3.76625	+	0.285655i	0.201028	+	0.0152471i
$352$		0			0
$353$	−18.7865	+	28.2605i	−0.999905	+	1.50415i	−0.142314	+	0.989822i	$0.545454\pi$
$353$	−18.7865	+	28.2605i	−0.999905	+	1.50415i	−0.857591	+	0.514332i	$0.828040\pi$
$354$		0			0
$355$	31.2657	+	9.76775i	1.65941	+	0.518418i
$356$		0			0
$357$	−0.0877696	−	0.0349042i	−0.00464526	−	0.00184733i
$358$		0			0
$359$	5.28041	+	5.80530i	0.278689	+	0.306392i	0.863067	−	0.505090i	$-0.168541\pi$
$359$	5.28041	+	5.80530i	0.278689	+	0.306392i	−0.584377	+	0.811482i	$0.698661\pi$
$360$		0			0
$361$	4.54763	+	10.8337i	0.239349	+	0.570194i
$362$		0			0
$363$	−1.89138	+	0.752166i	−0.0992719	+	0.0394785i
$364$		0			0
$365$	16.0505	−	3.70910i	0.840120	−	0.194143i
$366$		0			0
$367$	−30.8715	−	18.0843i	−1.61148	−	0.943992i	−0.986578	−	0.163289i	$-0.947790\pi$
$367$	−30.8715	−	18.0843i	−1.61148	−	0.943992i	−0.624901	−	0.780704i	$-0.714861\pi$
$368$		0			0
$369$	−25.4258	+	22.2624i	−1.32361	+	1.15893i
$370$		0			0
$371$	7.11141	+	1.92956i	0.369206	+	0.100178i
$372$		0			0
$373$	26.0473	+	9.23309i	1.34868	+	0.478071i	0.907766	−	0.419478i	$-0.137787\pi$
$373$	26.0473	+	9.23309i	1.34868	+	0.478071i	0.440914	+	0.897549i	$0.354654\pi$
$374$		0			0
$375$	−0.824774	+	0.402698i	−0.0425911	+	0.0207953i
$376$		0			0
$377$	−5.37671	+	56.6508i	−0.276915	+	2.91766i
$378$		0			0
$379$	14.0746	+	2.14735i	0.722962	+	0.110302i	0.501860	−	0.864949i	$-0.332649\pi$
$379$	14.0746	+	2.14735i	0.722962	+	0.110302i	0.221102	+	0.975251i	$0.429035\pi$
$380$		0			0
$381$	0.0318600	+	1.68327i	0.00163224	+	0.0862363i
$382$		0			0
$383$	12.0872	+	14.3436i	0.617627	+	0.732924i	0.979975	−	0.199119i	$-0.0638080\pi$
$383$	12.0872	+	14.3436i	0.617627	+	0.732924i	−0.362348	+	0.932043i	$0.618025\pi$
$384$		0			0
$385$	−1.35300	−	23.8050i	−0.0689555	−	1.21322i
$386$		0			0
$387$	−0.116575	−	0.677786i	−0.00592584	−	0.0344538i
$388$		0			0
$389$	−1.38633	+	0.743117i	−0.0702896	+	0.0376775i	−0.507209	−	0.861823i	$-0.669323\pi$
$389$	−1.38633	+	0.743117i	−0.0702896	+	0.0376775i	0.436919	+	0.899501i	$0.356070\pi$
$390$		0			0
$391$	0.894913	+	0.436944i	0.0452577	+	0.0220972i
$392$		0			0
$393$	−0.437353	+	0.0331714i	−0.0220615	+	0.00167328i
$394$		0			0
$395$	9.76747	−	9.95409i	0.491455	−	0.500845i
$396$		0			0
$397$	0.761591	−	4.42801i	0.0382231	−	0.222236i	−0.960134	−	0.279542i	$-0.909817\pi$
$397$	0.761591	−	4.42801i	0.0382231	−	0.222236i	0.998357	+	0.0573063i	$0.0182512\pi$
$398$		0			0
$399$	0.380333	−	0.308385i	0.0190404	−	0.0154386i
$400$		0			0
$401$	20.1681	−	8.91852i	1.00715	−	0.445370i	0.165972	−	0.986130i	$-0.446924\pi$
$401$	20.1681	−	8.91852i	1.00715	−	0.445370i	0.841176	+	0.540761i	$0.181864\pi$
$402$		0			0
$403$	4.80697	−	19.1424i	0.239452	−	0.953553i
$404$		0			0
$405$	22.9158	−	2.61337i	1.13870	−	0.129859i
$406$		0			0
$407$	−28.7980	+	21.5966i	−1.42746	+	1.07050i
$408$		0			0
$409$	−8.92036	+	10.5856i	−0.441083	+	0.523424i	−0.939054	−	0.343771i	$-0.888296\pi$
$409$	−8.92036	+	10.5856i	−0.441083	+	0.523424i	0.497970	+	0.867194i	$0.334079\pi$
$410$		0			0
$411$	−1.00183	−	1.95704i	−0.0494167	−	0.0965337i
$412$		0			0
$413$	−6.66997	+	17.7429i	−0.328208	+	0.873071i
$414$		0			0
$415$	−8.85659	+	5.18812i	−0.434753	+	0.254675i
$416$		0			0
$417$	−1.12428	+	1.55983i	−0.0550565	+	0.0763850i
$418$		0			0
$419$	31.0784	+	16.6591i	1.51828	+	0.813848i	0.999165	−	0.0408563i	$-0.0130086\pi$
$419$	31.0784	+	16.6591i	1.51828	+	0.813848i	0.519115	+	0.854704i	$0.326262\pi$
$420$		0			0
$421$	−11.0293	−	19.6724i	−0.537536	−	0.958775i	−0.997488	−	0.0708318i	$-0.977435\pi$
$421$	−11.0293	−	19.6724i	−0.537536	−	0.958775i	0.459952	−	0.887944i	$-0.347867\pi$
$422$		0			0
$423$	4.13377	+	14.1684i	0.200991	+	0.688893i
$424$		0			0
$425$	−0.550500	−	0.705831i	−0.0267032	−	0.0342378i
$426$		0			0
$427$	3.78259	+	10.0621i	0.183053	+	0.486941i
$428$		0			0
$429$	−2.90501	+	1.85284i	−0.140255	+	0.0894560i
$430$		0			0
$431$	30.1977	+	6.97838i	1.45457	+	0.336137i	0.877114	−	0.480283i	$-0.159466\pi$
$431$	30.1977	+	6.97838i	1.45457	+	0.336137i	0.577459	+	0.816420i	$0.304044\pi$
$432$		0			0
$433$	−4.58216	+	10.9159i	−0.220204	+	0.524587i	−0.994067	−	0.108767i	$-0.965310\pi$
$433$	−4.58216	+	10.9159i	−0.220204	+	0.524587i	0.773863	+	0.633353i	$0.218322\pi$
$434$		0			0
$435$	−0.257943	−	2.71778i	−0.0123674	−	0.130307i
$436$		0			0
$437$	−4.24444	+	2.93886i	−0.203039	+	0.140585i
$438$		0			0
$439$	−24.0198	−	21.0313i	−1.14640	−	1.00377i	−0.999894	−	0.0145598i	$-0.995365\pi$
$439$	−24.0198	−	21.0313i	−1.14640	−	1.00377i	−0.146508	−	0.989210i	$-0.546803\pi$
$440$		0			0
$441$	10.2365	+	7.08775i	0.487451	+	0.337512i
$442$		0			0
$443$	−13.3165	−	8.49338i	−0.632685	−	0.403533i	0.182113	−	0.983278i	$-0.441706\pi$
$443$	−13.3165	−	8.49338i	−0.632685	−	0.403533i	−0.814798	+	0.579745i	$0.803152\pi$
$444$		0			0
$445$	1.99454	−	14.9676i	0.0945504	−	0.709533i
$446$		0			0
$447$	0.229426	−	0.375186i	0.0108515	−	0.0177457i
$448$		0			0
$449$	−13.9611	−	14.2278i	−0.658864	−	0.671452i	0.300449	−	0.953798i	$-0.402863\pi$
$449$	−13.9611	−	14.2278i	−0.658864	−	0.671452i	−0.959313	+	0.282346i	$0.908888\pi$
$450$		0			0
$451$	12.7681	−	60.4443i	0.601228	−	2.84621i
$452$		0			0
$453$	−0.191531	+	0.341623i	−0.00899889	+	0.0160509i
$454$		0			0
$455$	−6.20677	−	24.7168i	−0.290978	−	1.15874i
$456$		0			0
$457$	−12.2063	−	18.3618i	−0.570984	−	0.858930i	0.428010	−	0.903774i	$-0.359215\pi$
$457$	−12.2063	−	18.3618i	−0.570984	−	0.858930i	−0.998994	+	0.0448440i	$0.985721\pi$
$458$		0			0
$459$	0.106253	+	0.318781i	0.00495945	+	0.0148794i
$460$		0			0
$461$	18.4391	+	2.10283i	0.858794	+	0.0979386i	0.531576	−	0.847010i	$-0.321600\pi$
$461$	18.4391	+	2.10283i	0.858794	+	0.0979386i	0.327217	+	0.944949i	$0.393889\pi$
$462$		0			0
$463$	26.9953	−	1.02227i	1.25458	−	0.0475090i	0.597831	−	0.801622i	$-0.296029\pi$
$463$	26.9953	−	1.02227i	1.25458	−	0.0475090i	0.656745	+	0.754113i	$0.271933\pi$
$464$		0			0
$465$	−0.0537296	+	0.945330i	−0.00249165	+	0.0438386i
$466$		0			0
$467$	−2.81174	−	4.59811i	−0.130112	−	0.212775i	0.781419	−	0.624007i	$-0.214496\pi$
$467$	−2.81174	−	4.59811i	−0.130112	−	0.212775i	−0.911531	+	0.411232i	$0.865099\pi$
$468$		0			0
$469$	−0.0700807	+	3.70258i	−0.00323602	+	0.170969i
$470$		0			0
$471$	−0.114021	+	0.0404175i	−0.00525383	+	0.00186234i
$472$		0			0
$473$	0.913859	+	0.863393i	0.0420193	+	0.0396989i
$474$		0			0
$475$	4.58715	−	0.699860i	0.210473	−	0.0321118i
$476$		0			0
$477$	−5.51586	−	11.8613i	−0.252554	−	0.543094i
$478$		0			0
$479$	3.75042	+	0.142023i	0.171361	+	0.00648921i	0.123383	−	0.992359i	$-0.460626\pi$
$479$	3.75042	+	0.142023i	0.171361	+	0.00648921i	0.0479784	+	0.998848i	$0.484722\pi$
$480$		0			0
$481$	−25.8877	+	28.4610i	−1.18038	+	1.29771i
$482$		0			0
$483$	−0.270807	−	0.219578i	−0.0123221	−	0.00999114i
$484$		0			0
$485$	−8.06046	−	6.04481i	−0.366007	−	0.274481i
$486$		0			0
$487$	29.3397	−	5.61986i	1.32951	−	0.254660i	0.526269	−	0.850318i	$-0.323591\pi$
$487$	29.3397	−	5.61986i	1.32951	−	0.254660i	0.803238	+	0.595658i	$0.203109\pi$
$488$		0			0
$489$	−1.81527	−	0.347705i	−0.0820892	−	0.0157238i
$490$		0			0
$491$	−4.36502	−	20.6640i	−0.196991	−	0.932552i	−0.958653	−	0.284578i	$-0.908147\pi$
$491$	−4.36502	−	20.6640i	−0.196991	−	0.932552i	0.761662	−	0.647974i	$-0.224384\pi$
$492$		0			0
$493$	−4.83219	+	1.50963i	−0.217631	+	0.0679903i
$494$		0			0
$495$	−30.7683	+	29.0692i	−1.38293	+	1.30656i
$496$		0			0
$497$	−6.72413	+	20.1738i	−0.301619	+	0.904920i
$498$		0			0
$499$	22.7499	+	31.5631i	1.01843	+	1.41296i	0.907949	+	0.419081i	$0.137648\pi$
$499$	22.7499	+	31.5631i	1.01843	+	1.41296i	0.110478	+	0.993879i	$0.464762\pi$
$500$		0			0
$501$	1.02028	−	0.952837i	0.0455828	−	0.0425696i
$502$		0			0
$503$	−18.8248	−	26.1174i	−0.839356	−	1.16452i	−0.984548	−	0.175114i	$-0.943970\pi$
$503$	−18.8248	−	26.1174i	−0.839356	−	1.16452i	0.145192	−	0.989403i	$-0.453620\pi$
$504$		0			0
$505$	3.37425	−	10.1235i	0.150152	−	0.450489i
$506$		0			0
$507$	−1.65610	+	1.56465i	−0.0735501	+	0.0694885i
$508$		0			0
$509$	−22.6142	+	7.06492i	−1.00235	+	0.313147i	−0.754962	−	0.655768i	$-0.772345\pi$
$509$	−22.6142	+	7.06492i	−1.00235	+	0.313147i	−0.247393	+	0.968915i	$0.579574\pi$
$510$		0			0
$511$	2.21030	+	10.4636i	0.0977781	+	0.462881i
$512$		0			0
$513$	−1.71080	−	0.327696i	−0.0755338	−	0.0144681i
$514$		0			0
$515$	5.57273	−	1.06743i	0.245564	−	0.0470365i
$516$		0			0
$517$	−21.5850	−	16.1873i	−0.949306	−	0.711916i
$518$		0			0
$519$	0.152414	+	0.123582i	0.00669023	+	0.00542463i
$520$		0			0
$521$	−7.17874	+	7.89234i	−0.314506	+	0.345770i	−0.876526	−	0.481354i	$-0.840145\pi$
$521$	−7.17874	+	7.89234i	−0.314506	+	0.345770i	0.562020	+	0.827124i	$0.310025\pi$
$522$		0			0
$523$	26.0869	+	0.987875i	1.14070	+	0.0431968i	0.601423	−	0.798931i	$-0.294601\pi$
$523$	26.0869	+	0.987875i	1.14070	+	0.0431968i	0.539278	+	0.842128i	$0.318697\pi$
$524$		0			0
$525$	0.132136	+	0.284145i	0.00576687	+	0.0124011i
$526$		0			0
$527$	1.73577	−	0.264826i	0.0756113	−	0.0115360i
$528$		0			0
$529$	−14.0466	−	13.2709i	−0.610720	−	0.576994i
$530$		0			0
$531$	31.7169	−	11.2428i	1.37639	−	0.487895i
$532$		0			0
$533$	1.24954	−	66.0174i	0.0541238	−	2.85953i
$534$		0			0
$535$	−12.5036	−	20.4474i	−0.540577	−	0.884018i
$536$		0			0
$537$	−0.0281077	+	0.494533i	−0.00121294	+	0.0213407i
$538$		0			0
$539$	−22.7442	+	0.861291i	−0.979663	+	0.0370985i
$540$		0			0
$541$	−21.3616	−	2.43612i	−0.918407	−	0.104737i	−0.358724	−	0.933444i	$-0.616788\pi$
$541$	−21.3616	−	2.43612i	−0.918407	−	0.104737i	−0.559683	+	0.828707i	$0.689077\pi$
$542$		0			0
$543$	−0.101213	−	0.303661i	−0.00434348	−	0.0130314i
$544$		0			0
$545$	−2.11123	−	3.17592i	−0.0904354	−	0.136042i
$546$		0			0
$547$	7.83601	+	31.2048i	0.335044	+	1.33422i	0.871543	+	0.490320i	$0.163120\pi$
$547$	7.83601	+	31.2048i	0.335044	+	1.33422i	−0.536499	+	0.843901i	$0.680254\pi$
$548$		0			0
$549$	9.33248	−	16.6459i	0.398301	−	0.710428i
$550$		0			0
$551$	5.42395	−	25.6769i	0.231068	−	1.09387i
$552$		0			0
$553$	6.34097	+	6.46213i	0.269646	+	0.274798i
$554$		0			0
$555$	0.962901	−	1.57465i	0.0408729	−	0.0668404i
$556$		0			0
$557$	2.95469	−	22.1728i	0.125194	−	0.939492i	−0.810266	−	0.586062i	$-0.800678\pi$
$557$	2.95469	−	22.1728i	0.125194	−	0.939492i	0.935461	−	0.353431i	$-0.114985\pi$
$558$		0			0
$559$	1.13291	+	0.722579i	0.0479168	+	0.0305618i
$560$		0			0
$561$	−0.252017	−	0.174497i	−0.0106402	−	0.00736728i
$562$		0			0
$563$	8.25236	+	7.22562i	0.347796	+	0.304524i	0.814812	−	0.579725i	$-0.196840\pi$
$563$	8.25236	+	7.22562i	0.347796	+	0.304524i	−0.467017	+	0.884248i	$0.654671\pi$
$564$		0			0
$565$	−30.5314	+	21.1400i	−1.28447	+	0.889366i
$566$		0			0
$567$	1.41475	+	14.9062i	0.0594138	+	0.626004i
$568$		0			0
$569$	−5.75532	+	13.7107i	−0.241276	+	0.574784i	−0.996764	−	0.0803777i	$-0.974387\pi$
$569$	−5.75532	+	13.7107i	−0.241276	+	0.574784i	0.755489	+	0.655161i	$0.227399\pi$
$570$		0			0
$571$	−29.2671	−	6.76333i	−1.22479	−	0.283037i	−0.437273	−	0.899329i	$-0.644056\pi$
$571$	−29.2671	−	6.76333i	−1.22479	−	0.283037i	−0.787518	+	0.616292i	$0.788634\pi$
$572$		0			0
$573$	1.73356	−	1.10568i	0.0724203	−	0.0461904i
$574$		0			0
$575$	−1.16260	−	3.09266i	−0.0484839	−	0.128973i
$576$		0			0
$577$	7.54151	+	9.66945i	0.313957	+	0.402544i	0.919387	−	0.393354i	$-0.128685\pi$
$577$	7.54151	+	9.66945i	0.313957	+	0.402544i	−0.605430	+	0.795899i	$0.706999\pi$
$578$		0			0
$579$	0.314744	+	1.07878i	0.0130803	+	0.0448326i
$580$		0			0
$581$	−3.25868	−	5.81234i	−0.135193	−	0.241137i
$582$		0			0
$583$	21.0759	+	11.2974i	0.872875	+	0.467890i
$584$		0			0
$585$	−26.4534	+	36.7013i	−1.09371	+	1.51741i
$586$		0			0
$587$	7.45606	−	4.36770i	0.307745	−	0.180274i	−0.343479	−	0.939160i	$-0.611605\pi$
$587$	7.45606	−	4.36770i	0.307745	−	0.180274i	0.651224	+	0.758886i	$0.274256\pi$
$588$		0			0
$589$	−3.20289	+	8.52005i	−0.131973	+	0.351063i
$590$		0			0
$591$	−0.836726	−	1.63451i	−0.0344183	−	0.0672348i
$592$		0			0
$593$	−6.31659	+	7.49575i	−0.259391	+	0.307814i	−0.878738	−	0.477304i	$-0.841614\pi$
$593$	−6.31659	+	7.49575i	−0.259391	+	0.307814i	0.619347	+	0.785117i	$0.287397\pi$
$594$		0			0
$595$	1.81379	−	1.36022i	0.0743582	−	0.0557637i
$596$		0			0
$597$	0.460142	−	0.0524756i	0.0188324	−	0.00214768i
$598$		0			0
$599$	7.40875	−	29.5033i	0.302713	−	1.20547i	−0.608505	−	0.793550i	$-0.708230\pi$
$599$	7.40875	−	29.5033i	0.302713	−	1.20547i	0.911218	−	0.411924i	$-0.135143\pi$
$600$		0			0
$601$	−24.9229	+	11.0211i	−1.01662	+	0.449560i	−0.844523	−	0.535519i	$-0.820116\pi$
$601$	−24.9229	+	11.0211i	−1.01662	+	0.449560i	−0.172102	+	0.985079i	$0.555056\pi$
$602$		0			0
$603$	5.10654	−	4.14053i	0.207955	−	0.168616i
$604$		0			0
$605$	8.28136	−	48.1492i	0.336685	−	1.95754i
$606$		0			0
$607$	−0.474909	+	0.483983i	−0.0192760	+	0.0196443i	−0.723337	−	0.690496i	$-0.757392\pi$
$607$	−0.474909	+	0.483983i	−0.0192760	+	0.0196443i	0.704061	+	0.710140i	$0.251368\pi$
$608$		0			0
$609$	1.76721	−	0.134036i	0.0716112	−	0.00543142i
$610$		0			0
$611$	−25.9131	−	12.6522i	−1.04833	−	0.511852i
$612$		0			0
$613$	21.8751	−	11.7258i	0.883526	−	0.473599i	0.0329535	−	0.999457i	$-0.489509\pi$
$613$	21.8751	−	11.7258i	0.883526	−	0.473599i	0.850572	+	0.525858i	$0.176256\pi$
$614$		0			0
$615$	0.536940	+	3.12186i	0.0216515	+	0.125886i
$616$		0			0
$617$	−0.246612	−	4.33894i	−0.00992822	−	0.174679i	−0.999525	−	0.0308119i	$-0.990191\pi$
$617$	−0.246612	−	4.33894i	−0.00992822	−	0.174679i	0.989597	−	0.143867i	$-0.0459539\pi$
$618$		0			0
$619$	24.8799	+	29.5244i	1.00001	+	1.18668i	0.982390	+	0.186840i	$0.0598246\pi$
$619$	24.8799	+	29.5244i	1.00001	+	1.18668i	0.0176163	+	0.999845i	$0.494392\pi$
$620$		0			0
$621$	0.0234712	+	1.24006i	0.000941868	+	0.0497619i
$622$		0			0
$623$	9.69062	+	1.47849i	0.388247	+	0.0592346i
$624$		0			0
$625$	2.89566	−	30.5096i	0.115826	−	1.22038i
$626$		0			0
$627$	1.42792	−	0.697187i	0.0570257	−	0.0278430i
$628$		0			0
$629$	−3.22605	−	1.14355i	−0.128631	−	0.0455963i
$630$		0			0
$631$	20.9683	+	5.68938i	0.834734	+	0.226491i	0.653478	−	0.756945i	$-0.273309\pi$
$631$	20.9683	+	5.68938i	0.834734	+	0.226491i	0.181256	+	0.983436i	$0.441984\pi$
$632$		0			0
$633$	1.00381	−	0.878915i	0.0398977	−	0.0349337i
$634$		0			0
$635$	−34.8678	−	20.4253i	−1.38369	−	0.810554i
$636$		0			0
$637$	−23.7021	+	5.47730i	−0.939110	+	0.217019i
$638$		0			0
$639$	35.0789	−	13.9502i	1.38770	−	0.551861i
$640$		0			0
$641$	−10.8152	−	25.7647i	−0.427175	−	1.01765i	−0.982542	−	0.186041i	$-0.940434\pi$
$641$	−10.8152	−	25.7647i	−0.427175	−	1.01765i	0.555367	−	0.831605i	$-0.312578\pi$
$642$		0			0
$643$	−2.57687	−	2.83302i	−0.101622	−	0.111723i	0.686835	−	0.726813i	$-0.258999\pi$
$643$	−2.57687	−	2.83302i	−0.101622	−	0.111723i	−0.788457	+	0.615090i	$0.789120\pi$
$644$		0			0
$645$	−0.0599012	−	0.0238216i	−0.00235861	−	0.000937973i
$646$		0			0
$647$	−29.8244	−	9.31748i	−1.17252	−	0.366308i	−0.350936	−	0.936399i	$-0.614137\pi$
$647$	−29.8244	−	9.31748i	−1.17252	−	0.366308i	−0.821581	+	0.570092i	$0.806908\pi$
$648$		0			0
$649$	−34.0546	+	51.2282i	−1.33676	+	2.01088i
$650$		0			0
$651$	−0.612932	−	0.0464884i	−0.0240227	−	0.00182203i
$652$		0			0
$653$	2.77035	−	9.49534i	0.108412	−	0.371582i	−0.887620	−	0.460577i	$-0.847643\pi$
$653$	2.77035	−	9.49534i	0.108412	−	0.371582i	0.996032	+	0.0889951i	$0.0283655\pi$
$654$		0			0
$655$	4.79723	−	9.37121i	0.187443	−	0.366164i
$656$		0			0
$657$	11.6761	−	14.9706i	0.455527	−	0.584060i
$658$		0			0
$659$	38.7726	−	10.5203i	1.51036	−	0.409811i	0.592128	−	0.805844i	$-0.298288\pi$
$659$	38.7726	−	10.5203i	1.51036	−	0.409811i	0.918237	+	0.396032i	$0.129613\pi$
$660$		0			0
$661$	19.7252	−	42.4172i	0.767221	−	1.64984i	0.00716859	−	0.999974i	$-0.497718\pi$
$661$	19.7252	−	42.4172i	0.767221	−	1.64984i	0.760052	−	0.649862i	$-0.225173\pi$
$662$		0			0
$663$	−0.299636	−	0.132502i	−0.0116369	−	0.00514594i
$664$		0			0
$665$	1.55242	+	11.6498i	0.0602002	+	0.451759i
$666$		0			0
$667$	−18.6861			−0.723528
$668$		0			0
$669$	−2.68679			−0.103877
$670$		0			0
$671$	4.60800	+	34.5798i	0.177890	+	1.33494i
$672$		0			0
$673$	−2.40544	−	1.06371i	−0.0927228	−	0.0410028i	0.357549	−	0.933894i	$-0.383613\pi$
$673$	−2.40544	−	1.06371i	−0.0927228	−	0.0410028i	−0.450272	+	0.892892i	$0.648673\pi$
$674$		0			0
$675$	0.470069	−	1.01084i	0.0180929	−	0.0389072i
$676$		0			0
$677$	−28.1532	+	7.63889i	−1.08202	+	0.293586i	−0.757860	−	0.652417i	$-0.773755\pi$
$677$	−28.1532	+	7.63889i	−1.08202	+	0.293586i	−0.324156	+	0.946004i	$0.605080\pi$
$678$		0			0
$679$	4.02257	−	5.15760i	0.154372	−	0.197930i
$680$		0			0
$681$	−0.0776346	+	0.151656i	−0.00297496	+	0.00581148i
$682$		0			0
$683$	−6.19687	+	21.2397i	−0.237117	+	0.812715i	0.751171	+	0.660108i	$0.229490\pi$
$683$	−6.19687	+	21.2397i	−0.237117	+	0.812715i	−0.988287	+	0.152606i	$0.951233\pi$
$684$		0			0
$685$	52.6199	+	3.99101i	2.01050	+	0.152489i
$686$		0			0
$687$	−0.718706	+	1.08115i	−0.0274203	+	0.0412483i
$688$		0			0
$689$	24.3956	+	7.62145i	0.929397	+	0.290354i
$690$		0			0
$691$	18.0537	+	7.17960i	0.686794	+	0.273125i	0.686769	−	0.726875i	$-0.259028\pi$
$691$	18.0537	+	7.17960i	0.686794	+	0.273125i	2.49947e−5		1.00000i	$0.499992\pi$
$692$		0			0
$693$	−18.4901	−	20.3281i	−0.702382	−	0.772202i
$694$		0			0
$695$	−17.8630	−	42.5544i	−0.677581	−	1.61418i
$696$		0			0
$697$	5.45841	−	2.17070i	0.206752	−	0.0822213i
$698$		0			0
$699$	2.94279	−	0.680048i	0.111306	−	0.0257218i
$700$		0			0
$701$	−15.2442	−	8.92993i	−0.575765	−	0.337279i	0.188609	−	0.982052i	$-0.439602\pi$
$701$	−15.2442	−	8.92993i	−0.575765	−	0.337279i	−0.764374	+	0.644774i	$0.776952\pi$
$702$		0			0
$703$	13.3492	−	11.6883i	0.503474	−	0.440833i
$704$		0			0
$705$	1.33515	+	0.362271i	0.0502848	+	0.0136439i
$706$		0			0
$707$	6.52946	+	2.31452i	0.245566	+	0.0870465i
$708$		0			0
$709$	−1.81034	+	0.883904i	−0.0679887	+	0.0331957i	−0.472429	−	0.881369i	$-0.656623\pi$
$709$	−1.81034	+	0.883904i	−0.0679887	+	0.0331957i	0.404441	+	0.914564i	$0.367466\pi$
$710$		0			0
$711$	1.51861	−	16.0006i	0.0569525	−	0.600070i
$712$		0			0
$713$	6.40685	+	0.977491i	0.239939	+	0.0366073i
$714$		0			0
$715$	−1.56508	−	82.6881i	−0.0585307	−	3.09236i
$716$		0			0
$717$	0.546590	+	0.648626i	0.0204128	+	0.0242234i
$718$		0			0
$719$	1.92751	+	33.9129i	0.0718838	+	1.26474i	0.808528	+	0.588458i	$0.200265\pi$
$719$	1.92751	+	33.9129i	0.0718838	+	1.26474i	−0.736644	+	0.676281i	$0.763591\pi$
$720$		0			0
$721$	0.624379	+	3.63024i	0.0232531	+	0.135197i
$722$		0			0
$723$	0.0383992	−	0.0205832i	0.00142808	−	0.000765499i
$724$		0			0
$725$	15.0926	+	7.36899i	0.560524	+	0.273677i
$726$		0			0
$727$	25.2795	−	1.91735i	0.937564	−	0.0711104i	0.402032	−	0.915626i	$-0.368304\pi$
$727$	25.2795	−	1.91735i	0.937564	−	0.0711104i	0.535532	+	0.844515i	$0.320111\pi$
$728$		0			0
$729$	18.4704	−	18.8233i	0.684090	−	0.697161i
$730$		0			0
$731$	−0.0202631	+	0.117813i	−0.000749457	+	0.00435747i
$732$		0			0
$733$	−29.5945	+	23.9961i	−1.09310	+	0.886316i	−0.994067	−	0.108768i	$-0.965309\pi$
$733$	−29.5945	+	23.9961i	−1.09310	+	0.886316i	−0.0990312	+	0.995084i	$0.531574\pi$
$734$		0			0
$735$	1.06735	−	0.471992i	0.0393699	−	0.0174097i
$736$		0			0
$737$	−2.92703	+	11.6561i	−0.107819	+	0.429358i
$738$		0			0
$739$	−35.2231	+	4.01691i	−1.29570	+	0.147764i	−0.733758	−	0.679411i	$-0.762235\pi$
$739$	−35.2231	+	4.01691i	−1.29570	+	0.147764i	−0.561943	+	0.827176i	$0.689946\pi$
$740$		0			0
$741$	1.35875	−	1.01897i	0.0499148	−	0.0374328i
$742$		0			0
$743$	−9.35988	+	11.1072i	−0.343381	+	0.407482i	−0.908740	−	0.417363i	$-0.862954\pi$
$743$	−9.35988	+	11.1072i	−0.343381	+	0.407482i	0.565359	+	0.824845i	$0.308738\pi$
$744$		0			0
$745$	4.80997	+	9.39610i	0.176224	+	0.344246i
$746$		0			0
$747$	−4.16258	+	11.0730i	−0.152301	+	0.405138i
$748$		0			0
$749$	13.4255	−	7.86458i	0.490559	−	0.287365i
$750$		0			0
$751$	−16.6678	+	23.1248i	−0.608216	+	0.843835i	−0.996993	−	0.0774965i	$-0.975307\pi$
$751$	−16.6678	+	23.1248i	−0.608216	+	0.843835i	0.388777	+	0.921332i	$0.372898\pi$
$752$		0			0
$753$	2.34630	+	1.25769i	0.0855040	+	0.0458330i
$754$		0			0
$755$	−4.59722	−	8.19982i	−0.167310	−	0.298422i
$756$		0			0
$757$	−5.87342	−	20.1311i	−0.213473	−	0.731678i	−0.994271	−	0.106893i	$-0.965910\pi$
$757$	−5.87342	−	20.1311i	−0.213473	−	0.731678i	0.780797	−	0.624784i	$-0.214813\pi$
$758$		0			0
$759$	−0.695830	−	0.892167i	−0.0252570	−	0.0323836i
$760$		0			0
$761$	0.988960	+	2.63075i	0.0358498	+	0.0953646i	0.952754	−	0.303742i	$-0.0982360\pi$
$761$	0.988960	+	2.63075i	0.0358498	+	0.0953646i	−0.916905	+	0.399106i	$0.869320\pi$
$762$		0			0
$763$	2.08736	−	1.33134i	0.0755674	−	0.0481976i
$764$		0			0
$765$	−3.92148	−	0.906215i	−0.141782	−	0.0327643i
$766$		0			0
$767$	−25.4476	+	60.6231i	−0.918859	+	2.18897i
$768$		0			0
$769$	−1.61357	−	17.0011i	−0.0581867	−	0.613074i	−0.976251	−	0.216643i	$-0.930489\pi$
$769$	−1.61357	−	17.0011i	−0.0581867	−	0.613074i	0.918064	−	0.396432i	$-0.129752\pi$
$770$		0			0
$771$	1.48796	−	1.03026i	0.0535875	−	0.0371041i
$772$		0			0
$773$	14.2381	+	12.4666i	0.512108	+	0.448393i	0.875482	−	0.483251i	$-0.160544\pi$
$773$	14.2381	+	12.4666i	0.512108	+	0.448393i	−0.363374	+	0.931643i	$0.618375\pi$
$774$		0			0
$775$	−4.78927	−	3.31610i	−0.172036	−	0.119118i
$776$		0			0
$777$	1.01024	+	0.644342i	0.0362422	+	0.0231156i
$778$		0			0
$779$	−4.02230	+	30.1845i	−0.144114	+	1.08147i
$780$		0			0
$781$	−36.0021	+	58.8751i	−1.28826	+	2.10671i
$782$		0			0
$783$	−4.41583	−	4.50020i	−0.157809	−	0.160824i
$784$		0			0
$785$	0.600120	−	2.84096i	0.0214192	−	0.101398i
$786$		0			0
$787$	9.98500	−	17.8097i	0.355927	−	0.634849i	−0.634494	−	0.772928i	$-0.718792\pi$
$787$	9.98500	−	17.8097i	0.355927	−	0.634849i	0.990421	+	0.138079i	$0.0440928\pi$
$788$		0			0
$789$	−0.416039	−	1.65676i	−0.0148114	−	0.0589823i
$790$		0			0
$791$	−13.3464	−	20.0769i	−0.474543	−	0.713854i
$792$		0			0
$793$	11.7901	+	35.3728i	0.418679	+	1.25613i
$794$		0			0
$795$	−1.21825	−	0.138931i	−0.0432067	−	0.00492739i
$796$		0			0
$797$	−4.34458	+	0.164523i	−0.153893	+	0.00582771i	−0.114676	−	0.993403i	$-0.536583\pi$
$797$	−4.34458	+	0.164523i	−0.153893	+	0.00582771i	−0.0392174	+	0.999231i	$0.512486\pi$
$798$		0			0
$799$	0.145577	−	2.56131i	0.00515013	−	0.0906125i
$800$		0			0
$801$	−9.07876	−	14.8467i	−0.320782	−	0.524582i
$802$		0			0
$803$	−0.656788	+	34.7001i	−0.0231775	+	1.22454i
$804$		0			0
$805$	7.88740	−	2.79588i	0.277994	−	0.0985417i
$806$		0			0
$807$	−1.45307	−	1.37283i	−0.0511504	−	0.0483257i
$808$		0			0
$809$	24.5492	−	3.74546i	0.863103	−	0.131683i	0.295858	−	0.955232i	$-0.404395\pi$
$809$	24.5492	−	3.74546i	0.863103	−	0.131683i	0.567246	+	0.823549i	$0.308009\pi$
$810$		0			0
$811$	−12.6621	−	27.2286i	−0.444625	−	0.956125i	−0.992803	−	0.119763i	$-0.961787\pi$
$811$	−12.6621	−	27.2286i	−0.444625	−	0.956125i	0.548178	−	0.836362i	$-0.315322\pi$
$812$		0			0
$813$	−2.99787	−	0.113525i	−0.105140	−	0.00398150i
$814$		0			0
$815$	29.8507	−	32.8180i	1.04563	−	1.14956i
$816$		0			0
$817$	−0.481350	−	0.390292i	−0.0168403	−	0.0136546i
$818$		0			0
$819$	−23.4970	−	17.6212i	−0.821052	−	0.615735i
$820$		0			0
$821$	−12.0299	+	2.30426i	−0.419845	+	0.0804192i	−0.393700	−	0.919239i	$-0.628805\pi$
$821$	−12.0299	+	2.30426i	−0.419845	+	0.0804192i	−0.0261452	+	0.999658i	$0.508323\pi$
$822$		0			0
$823$	−40.5532	−	7.76776i	−1.41360	−	0.270767i	−0.576175	−	0.817326i	$-0.695455\pi$
$823$	−40.5532	−	7.76776i	−1.41360	−	0.270767i	−0.837420	+	0.546559i	$0.815937\pi$
$824$		0			0
$825$	0.210182	+	0.994999i	0.00731759	+	0.0346414i
$826$		0			0
$827$	−43.9834	+	13.7409i	−1.52945	+	0.477818i	−0.943176	−	0.332293i	$-0.892178\pi$
$827$	−43.9834	+	13.7409i	−1.52945	+	0.477818i	−0.586276	+	0.810111i	$0.699407\pi$
$828$		0			0
$829$	−3.75744	+	3.54994i	−0.130501	+	0.123295i	−0.749229	−	0.662311i	$-0.769576\pi$
$829$	−3.75744	+	3.54994i	−0.130501	+	0.123295i	0.618728	+	0.785605i	$0.287648\pi$
$830$		0			0
$831$	−1.07777	+	3.23353i	−0.0373873	+	0.112170i
$832$		0			0
$833$	−1.26545	−	1.75567i	−0.0438451	−	0.0608304i
$834$		0			0
$835$	6.73574	+	32.8240i	0.233100	+	1.13592i
$836$		0			0
$837$	1.27863	+	1.77397i	0.0441961	+	0.0613174i
$838$		0			0
$839$	11.2569	−	33.7730i	0.388630	−	1.16597i	−0.554109	−	0.832444i	$-0.686941\pi$
$839$	11.2569	−	33.7730i	0.388630	−	1.16597i	0.942740	−	0.333529i	$-0.108240\pi$
$840$		0			0
$841$	47.9671	−	45.3182i	1.65404	−	1.56270i
$842$		0			0
$843$	−1.35452	+	0.423168i	−0.0466522	+	0.0145747i
$844$		0			0
$845$	−11.3023	−	53.5051i	−0.388812	−	1.84063i
$846$		0			0
$847$	31.1508	+	5.96677i	1.07035	+	0.205021i
$848$		0			0
$849$	−2.16692	+	0.415062i	−0.0743684	+	0.0142449i
$850$		0			0
$851$	−10.1072	−	7.57970i	−0.346469	−	0.259829i
$852$		0			0
$853$	30.7215	+	24.9099i	1.05189	+	0.852900i	0.989410	−	0.145147i	$-0.0463655\pi$
$853$	30.7215	+	24.9099i	1.05189	+	0.852900i	0.0624757	+	0.998046i	$0.480100\pi$
$854$		0			0
$855$	14.0390	−	15.4346i	0.480125	−	0.527851i
$856$		0			0
$857$	−31.3347	−	1.18660i	−1.07037	−	0.0405335i	−0.503230	−	0.864153i	$-0.667855\pi$
$857$	−31.3347	−	1.18660i	−1.07037	−	0.0405335i	−0.567143	+	0.823619i	$0.691951\pi$
$858$		0			0
$859$	−10.9502	−	23.5473i	−0.373615	−	0.803423i	−0.999719	−	0.0236845i	$-0.992460\pi$
$859$	−10.9502	−	23.5473i	−0.373615	−	0.803423i	0.626105	−	0.779739i	$-0.284648\pi$
$860$		0			0
$861$	−2.03292	+	0.310162i	−0.0692818	+	0.0105703i
$862$		0			0
$863$	3.99055	+	3.77018i	0.135840	+	0.128338i	0.751667	−	0.659543i	$-0.229250\pi$
$863$	3.99055	+	3.77018i	0.135840	+	0.128338i	−0.615827	+	0.787882i	$0.711178\pi$
$864$		0			0
$865$	−4.43915	+	1.57356i	−0.150935	+	0.0535026i
$866$		0			0
$867$	−0.0342019	+	1.80699i	−0.00116156	+	0.0613687i
$868$		0			0
$869$	15.3279	+	25.0661i	0.519964	+	0.850310i
$870$		0			0
$871$	−0.728893	+	12.8243i	−0.0246976	+	0.434535i
$872$		0			0
$873$	−11.6033	+	0.439402i	−0.392714	+	0.0148715i
$874$		0			0
$875$	14.2098	+	1.62052i	0.480380	+	0.0547836i
$876$		0			0
$877$	11.3618	+	34.0877i	0.383660	+	1.15106i	0.946003	+	0.324157i	$0.105081\pi$
$877$	11.3618	+	34.0877i	0.383660	+	1.15106i	−0.562343	+	0.826904i	$0.690100\pi$
$878$		0			0
$879$	0.957981	+	1.44109i	0.0323119	+	0.0486067i
$880$		0			0
$881$	−1.58146	−	6.29775i	−0.0532808	−	0.212176i	0.937427	−	0.348181i	$-0.113200\pi$
$881$	−1.58146	−	6.29775i	−0.0532808	−	0.212176i	−0.990708	+	0.136004i	$0.956574\pi$
$882$		0			0
$883$	7.22474	−	12.8864i	0.243132	−	0.433662i	−0.723319	−	0.690514i	$-0.757384\pi$
$883$	7.22474	−	12.8864i	0.243132	−	0.433662i	0.966451	+	0.256852i	$0.0826854\pi$
$884$		0			0
$885$	0.651899	−	3.08608i	0.0219133	−	0.103738i
$886$		0			0
$887$	31.2482	+	31.8453i	1.04921	+	1.06926i	0.997505	+	0.0705974i	$0.0224906\pi$
$887$	31.2482	+	31.8453i	1.04921	+	1.06926i	0.0517078	+	0.998662i	$0.483534\pi$
$888$		0			0
$889$	13.6860	−	22.3810i	0.459013	−	0.750634i
$890$		0			0
$891$	−6.41851	+	48.1663i	−0.215028	+	1.61363i
$892$		0			0
$893$	11.2125	+	7.15143i	0.375212	+	0.239314i
$894$		0			0
$895$	−9.77479	−	6.76808i	−0.326735	−	0.226232i
$896$		0			0
$897$	−0.909820	−	0.796623i	−0.0303780	−	0.0265985i
$898$		0			0
$899$	−27.0864	+	18.7547i	−0.903383	+	0.625504i
$900$		0			0
$901$	0.214837	+	2.26359i	0.00715726	+	0.0754112i
$902$		0			0
$903$	0.0161979	−	0.0385879i	0.000539033	−	0.00128412i
$904$		0			0
$905$	7.48557	+	1.72984i	0.248829	+	0.0575018i
$906$		0			0
$907$	7.44411	−	4.74792i	0.247178	−	0.157652i	−0.408345	−	0.912828i	$-0.633894\pi$
$907$	7.44411	−	4.74792i	0.247178	−	0.157652i	0.655523	+	0.755175i	$0.272448\pi$
$908$		0			0
$909$	−4.32752	−	11.5117i	−0.143535	−	0.381819i
$910$		0			0
$911$	15.6253	+	20.0341i	0.517688	+	0.663761i	0.974129	−	0.225993i	$-0.0725627\pi$
$911$	15.6253	+	20.0341i	0.517688	+	0.663761i	−0.456441	+	0.889754i	$0.650876\pi$
$912$		0			0
$913$	−6.05672	−	20.7593i	−0.200448	−	0.687034i
$914$		0			0
$915$	−0.874767	−	1.56028i	−0.0289189	−	0.0515811i
$916$		0			0
$917$	6.02370	+	3.22890i	0.198920	+	0.106628i
$918$		0			0
$919$	28.2941	−	39.2551i	0.933337	−	1.29491i	−0.0221137	−	0.999755i	$-0.507040\pi$
$919$	28.2941	−	39.2551i	0.933337	−	1.29491i	0.955451	−	0.295151i	$-0.0953700\pi$
$920$		0			0
$921$	2.94895	−	1.72747i	0.0971713	−	0.0569222i
$922$		0			0
$923$	−25.9544	+	69.0418i	−0.854300	+	2.27254i
$924$		0			0
$925$	5.17434	+	10.1079i	0.170131	+	0.332345i
$926$		0			0
$927$	4.21389	−	5.00053i	0.138402	−	0.164239i
$928$		0			0
$929$	20.0544	−	15.0395i	0.657963	−	0.493429i	−0.217911	−	0.975969i	$-0.569924\pi$
$929$	20.0544	−	15.0395i	0.657963	−	0.493429i	0.875874	+	0.482540i	$0.160286\pi$
$930$		0			0
$931$	11.1467	−	1.27120i	0.365319	−	0.0416617i
$932$		0			0
$933$	0.324930	−	1.29395i	0.0106377	−	0.0423619i
$934$		0			0
$935$	6.72899	−	2.97562i	0.220062	−	0.0973131i
$936$		0			0
$937$	−32.0938	+	26.0226i	−1.04846	+	0.850121i	−0.988971	−	0.148108i	$-0.952682\pi$
$937$	−32.0938	+	26.0226i	−1.04846	+	0.850121i	−0.0594879	+	0.998229i	$0.518947\pi$
$938$		0			0
$939$	−0.184453	+	1.07244i	−0.00601940	+	0.0349978i
$940$		0			0
$941$	−2.21019	+	2.25241i	−0.0720500	+	0.0734266i	−0.748846	−	0.662744i	$-0.769392\pi$
$941$	−2.21019	+	2.25241i	−0.0720500	+	0.0734266i	0.676796	+	0.736170i	$0.263368\pi$
$942$		0			0
$943$	21.6200	−	1.63979i	0.704044	−	0.0533989i
$944$		0			0
$945$	2.53726	+	1.23883i	0.0825370	+	0.0402990i
$946$		0			0
$947$	23.3440	−	12.5131i	0.758577	−	0.406622i	−0.0471665	−	0.998887i	$-0.515019\pi$
$947$	23.3440	−	12.5131i	0.758577	−	0.406622i	0.805743	+	0.592265i	$0.201766\pi$
$948$		0			0
$949$	6.28771	+	36.5578i	0.204108	+	1.18672i
$950$		0			0
$951$	0.0304326	+	0.535438i	0.000986846	+	0.0173628i
$952$		0			0
$953$	−17.0038	−	20.1780i	−0.550806	−	0.653629i	0.415932	−	0.909396i	$-0.363455\pi$
$953$	−17.0038	−	20.1780i	−0.550806	−	0.653629i	−0.966739	+	0.255767i	$0.917672\pi$
$954$		0			0
$955$	0.933958	+	49.3439i	0.0302222	+	1.59673i
$956$		0			0
$957$	5.68576	+	0.867474i	0.183794	+	0.0280414i
$958$		0			0
$959$	−3.23693	+	34.1054i	−0.104526	+	1.10132i
$960$		0			0
$961$	−17.5888	+	8.58777i	−0.567379	+	0.277025i
$962$		0			0
$963$	−26.0349	−	9.22870i	−0.838964	−	0.297391i
$964$		0			0
$965$	−26.0318	−	7.06328i	−0.837994	−	0.227375i
$966$		0			0
$967$	15.2619	−	13.3630i	0.490788	−	0.429725i	−0.377333	−	0.926078i	$-0.623159\pi$
$967$	15.2619	−	13.3630i	0.490788	−	0.429725i	0.868121	+	0.496352i	$0.165328\pi$
$968$		0			0
$969$	0.130372	+	0.0763710i	0.00418815	+	0.00245339i
$970$		0			0
$971$	−18.9278	+	4.37401i	−0.607421	+	0.140369i	−0.517648	−	0.855594i	$-0.673192\pi$
$971$	−18.9278	+	4.37401i	−0.607421	+	0.140369i	−0.0897727	+	0.995962i	$0.528614\pi$
$972$		0			0
$973$	27.8406	−	11.0716i	0.892527	−	0.354941i
$974$		0			0
$975$	0.420699	+	1.00222i	0.0134731	+	0.0320967i
$976$		0			0
$977$	14.3359	+	15.7610i	0.458647	+	0.504238i	0.924793	−	0.380470i	$-0.124238\pi$
$977$	14.3359	+	15.7610i	0.458647	+	0.504238i	−0.466147	+	0.884707i	$0.654358\pi$
$978$		0			0
$979$	29.5608	+	11.7558i	0.944767	+	0.375715i
$980$		0			0
$981$	−4.19522	−	1.31064i	−0.133943	−	0.0418454i
$982$		0			0
$983$	−32.1515	+	48.3654i	−1.02547	+	1.54262i	−0.198716	+	0.980057i	$0.563677\pi$
$983$	−32.1515	+	48.3654i	−1.02547	+	1.54262i	−0.826757	+	0.562559i	$0.809817\pi$
$984$		0			0
$985$	43.9480	+	3.33327i	1.40030	+	0.106207i
$986$		0			0
$987$	−0.251545	+	0.862167i	−0.00800675	+	0.0274431i
$988$		0			0
$989$	−0.201063	+	0.392769i	−0.00639343	+	0.0124893i
$990$		0			0
$991$	12.6100	−	16.1681i	0.400571	−	0.513598i	−0.545255	−	0.838270i	$-0.683567\pi$
$991$	12.6100	−	16.1681i	0.400571	−	0.513598i	0.945827	+	0.324672i	$0.105254\pi$
$992$		0			0
$993$	−1.87815	+	0.509604i	−0.0596013	+	0.0161718i
$994$		0			0
$995$	−4.68730	+	10.0796i	−0.148597	+	0.319545i
$996$		0			0
$997$	12.1843	+	5.38799i	0.385880	+	0.170639i	0.588268	−	0.808666i	$-0.299810\pi$
$997$	12.1843	+	5.38799i	0.385880	+	0.170639i	−0.202388	+	0.979305i	$0.564870\pi$
$998$		0			0
$999$	−0.563056	−	4.22533i	−0.0178143	−	0.133684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.e.a.9.7	✓	1148
167.130	even	83	inner	668.2.e.a.297.7	yes	1148

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.e.a.9.7	✓	1148	1.1	even	1	trivial
668.2.e.a.297.7	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)

\(f(q)\)	\(=\)	\(q+(-0.0142693 - 0.107081i) q^{3} +(2.37141 + 1.04866i) q^{5} +(-0.709794 + 1.52635i) q^{7} +(2.88405 - 0.782538i) q^{9} +O(q^{10})\)	\(q+(-0.0142693 - 0.107081i) q^{3} +(2.37141 + 1.04866i) q^{5} +(-0.709794 + 1.52635i) q^{7} +(2.88405 - 0.782538i) q^{9} +(-3.35961 + 4.30756i) q^{11} +(-2.66055 + 5.19729i) q^{13} +(0.0784527 - 0.268896i) q^{15} +(-0.517944 - 0.0392840i) q^{17} +(1.49067 - 2.24242i) q^{19} +(0.173570 + 0.0542253i) q^{21} +(-1.78155 - 0.708489i) q^{23} +(1.15954 + 1.27481i) q^{25} +(-0.250384 - 0.596482i) q^{27} +(9.05639 - 3.60155i) q^{29} +(-3.29354 + 0.761104i) q^{31} +(0.509196 + 0.298283i) q^{33} +(-3.28383 + 2.87526i) q^{35} +(6.35944 + 1.72552i) q^{37} +(0.594493 + 0.210732i) q^{39} +(-10.1623 + 4.96177i) q^{41} +(0.0217449 - 0.229112i) q^{43} +(7.65989 + 1.16867i) q^{45} +(0.0934650 + 4.93805i) q^{47} +(2.68486 + 3.18606i) q^{49} +(0.00318414 + 0.0560224i) q^{51} +(-0.741992 - 4.31406i) q^{53} +(-12.4842 + 6.69193i) q^{55} +(-0.261390 - 0.127625i) q^{57} +(11.2284 - 0.851629i) q^{59} +(4.47266 - 4.55812i) q^{61} +(-0.852659 + 4.95750i) q^{63} +(-11.7594 + 9.53490i) q^{65} +(2.01203 - 0.889737i) q^{67} +(-0.0504440 + 0.200880i) q^{69} +(12.5514 - 1.43139i) q^{71} +(5.08275 - 3.81172i) q^{73} +(0.119961 - 0.142355i) q^{75} +(-4.19020 - 8.18540i) q^{77} +(1.89257 - 5.03445i) q^{79} +(7.67518 - 4.49606i) q^{81} +(-2.31465 + 3.21134i) q^{83} +(-1.18706 - 0.636305i) q^{85} +(-0.514884 - 0.918372i) q^{87} +(-1.63105 - 5.59042i) q^{89} +(-6.04441 - 7.74993i) q^{91} +(0.128496 + 0.341814i) q^{93} +(5.88653 - 3.75449i) q^{95} +(-3.78589 - 0.874881i) q^{97} +(-6.31845 + 15.0523i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) \) 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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