LMFDB - Embedded newform 668.2.e.a.9.5

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			9.5
Character	$\chi$	$=$	668.9
Dual form			668.2.e.a.297.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.178407 - 1.33882i) q^{3} +(-1.62557 - 0.718841i) q^{5} +(-0.315447 + 0.678340i) q^{7} +(1.13471 - 0.307883i) q^{9} +O(q^{10})$	\(q+(-0.178407 - 1.33882i) q^{3} +(-1.62557 - 0.718841i) q^{5} +(-0.315447 + 0.678340i) q^{7} +(1.13471 - 0.307883i) q^{9} +(1.52116 - 1.95037i) q^{11} +(1.00511 - 1.96345i) q^{13} +(-0.672384 + 2.30459i) q^{15} +(-5.09594 - 0.386506i) q^{17} +(1.04555 - 1.57282i) q^{19} +(0.964452 + 0.301306i) q^{21} +(-4.90068 - 1.94890i) q^{23} +(-1.23861 - 1.36174i) q^{25} +(-2.18295 - 5.20038i) q^{27} +(-2.38370 + 0.947953i) q^{29} +(-2.94022 + 0.679454i) q^{31} +(-2.88258 - 1.68859i) q^{33} +(1.00040 - 0.875933i) q^{35} +(-0.619516 - 0.168095i) q^{37} +(-2.80803 - 0.995372i) q^{39} +(-6.16684 + 3.01098i) q^{41} +(0.510488 - 5.37867i) q^{43} +(-2.06587 - 0.315188i) q^{45} +(-0.0873353 - 4.61420i) q^{47} +(4.15014 + 4.92488i) q^{49} +(0.391691 + 6.89149i) q^{51} +(0.991179 + 5.76288i) q^{53} +(-3.87475 + 2.07700i) q^{55} +(-2.29226 - 1.11920i) q^{57} +(5.11457 - 0.387920i) q^{59} +(-3.03294 + 3.09088i) q^{61} +(-0.149091 + 0.866838i) q^{63} +(-3.04530 + 2.46922i) q^{65} +(4.23717 - 1.87371i) q^{67} +(-1.73491 + 6.90882i) q^{69} +(4.23010 - 0.482409i) q^{71} +(10.1577 - 7.61759i) q^{73} +(-1.60214 + 1.90122i) q^{75} +(0.843169 + 1.64710i) q^{77} +(2.69600 - 7.17167i) q^{79} +(-3.52945 + 2.06753i) q^{81} +(4.97769 - 6.90601i) q^{83} +(8.00597 + 4.29146i) q^{85} +(1.69441 + 3.02223i) q^{87} +(-4.27601 - 14.6560i) q^{89} +(1.01483 + 1.30118i) q^{91} +(1.43422 + 3.81520i) q^{93} +(-2.83023 + 1.80515i) q^{95} +(-9.87660 - 2.28238i) q^{97} +(1.12558 - 2.68144i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.178407	−	1.33882i	−0.103004	−	0.772967i	−0.964290	−	0.264848i	$-0.914678\pi$
$3$	−0.178407	−	1.33882i	−0.103004	−	0.772967i	0.861287	−	0.508119i	$-0.169659\pi$
$4$		0			0
$5$	−1.62557	−	0.718841i	−0.726977	−	0.321476i	0.00762730	−	0.999971i	$-0.497572\pi$
$5$	−1.62557	−	0.718841i	−0.726977	−	0.321476i	−0.734605	+	0.678495i	$0.762632\pi$
$6$		0			0
$7$	−0.315447	+	0.678340i	−0.119228	+	0.256388i	−0.957258	−	0.289236i	$-0.906599\pi$
$7$	−0.315447	+	0.678340i	−0.119228	+	0.256388i	0.838030	+	0.545624i	$0.183707\pi$
$8$		0			0
$9$	1.13471	−	0.307883i	0.378236	−	0.102628i
$10$		0			0
$11$	1.52116	−	1.95037i	0.458646	−	0.588059i	−0.502335	−	0.864673i	$-0.667526\pi$
$11$	1.52116	−	1.95037i	0.458646	−	0.588059i	0.960981	+	0.276614i	$0.0892124\pi$
$12$		0			0
$13$	1.00511	−	1.96345i	0.278769	−	0.544564i	−0.708095	−	0.706117i	$-0.750445\pi$
$13$	1.00511	−	1.96345i	0.278769	−	0.544564i	0.986864	+	0.161553i	$0.0516502\pi$
$14$		0			0
$15$	−0.672384	+	2.30459i	−0.173609	+	0.595043i
$16$		0			0
$17$	−5.09594	−	0.386506i	−1.23595	−	0.0937415i	−0.558620	−	0.829424i	$-0.688669\pi$
$17$	−5.09594	−	0.386506i	−1.23595	−	0.0937415i	−0.677327	+	0.735682i	$0.736862\pi$
$18$		0			0
$19$	1.04555	−	1.57282i	0.239866	−	0.360830i	−0.693071	−	0.720869i	$-0.743743\pi$
$19$	1.04555	−	1.57282i	0.239866	−	0.360830i	0.932937	+	0.360039i	$0.117237\pi$
$20$		0			0
$21$	0.964452	+	0.301306i	0.210461	+	0.0657503i
$22$		0			0
$23$	−4.90068	−	1.94890i	−1.02186	−	0.406375i	−0.202275	−	0.979329i	$-0.564833\pi$
$23$	−4.90068	−	1.94890i	−1.02186	−	0.406375i	−0.819587	+	0.572954i	$0.805797\pi$
$24$		0			0
$25$	−1.23861	−	1.36174i	−0.247723	−	0.272347i
$26$		0			0
$27$	−2.18295	−	5.20038i	−0.420109	−	1.00081i
$28$		0			0
$29$	−2.38370	+	0.947953i	−0.442643	+	0.176030i	−0.580218	−	0.814461i	$-0.697033\pi$
$29$	−2.38370	+	0.947953i	−0.442643	+	0.176030i	0.137576	+	0.990491i	$0.456069\pi$
$30$		0			0
$31$	−2.94022	+	0.679454i	−0.528079	+	0.122034i	−0.480770	−	0.876847i	$-0.659643\pi$
$31$	−2.94022	+	0.679454i	−0.528079	+	0.122034i	−0.0473088	+	0.998880i	$0.515064\pi$
$32$		0			0
$33$	−2.88258	−	1.68859i	−0.501792	−	0.293946i
$34$		0			0
$35$	1.00040	−	0.875933i	0.169099	−	0.148060i
$36$		0			0
$37$	−0.619516	−	0.168095i	−0.101848	−	0.0276346i	0.210576	−	0.977578i	$-0.432466\pi$
$37$	−0.619516	−	0.168095i	−0.101848	−	0.0276346i	−0.312424	+	0.949943i	$0.601141\pi$
$38$		0			0
$39$	−2.80803	−	0.995372i	−0.449644	−	0.159387i
$40$		0			0
$41$	−6.16684	+	3.01098i	−0.963098	+	0.470236i	−0.851982	−	0.523571i	$-0.824599\pi$
$41$	−6.16684	+	3.01098i	−0.963098	+	0.470236i	−0.111117	+	0.993807i	$0.535443\pi$
$42$		0			0
$43$	0.510488	−	5.37867i	0.0778487	−	0.820239i	−0.868200	−	0.496215i	$-0.834723\pi$
$43$	0.510488	−	5.37867i	0.0778487	−	0.820239i	0.946049	−	0.324025i	$-0.105036\pi$
$44$		0			0
$45$	−2.06587	−	0.315188i	−0.307961	−	0.0469855i
$46$		0			0
$47$	−0.0873353	−	4.61420i	−0.0127392	−	0.673050i	−0.947854	−	0.318705i	$-0.896752\pi$
$47$	−0.0873353	−	4.61420i	−0.0127392	−	0.673050i	0.935115	−	0.354345i	$-0.115296\pi$
$48$		0			0
$49$	4.15014	+	4.92488i	0.592877	+	0.703554i
$50$		0			0
$51$	0.391691	+	6.89149i	0.0548477	+	0.965002i
$52$		0			0
$53$	0.991179	+	5.76288i	0.136149	+	0.791592i	0.970634	+	0.240561i	$0.0773316\pi$
$53$	0.991179	+	5.76288i	0.136149	+	0.791592i	−0.834485	+	0.551031i	$0.814235\pi$
$54$		0			0
$55$	−3.87475	+	2.07700i	−0.522472	+	0.280062i
$56$		0			0
$57$	−2.29226	−	1.11920i	−0.303617	−	0.148242i
$58$		0			0
$59$	5.11457	−	0.387920i	0.665861	−	0.0505028i	0.261642	−	0.965165i	$-0.415736\pi$
$59$	5.11457	−	0.387920i	0.665861	−	0.0505028i	0.404219	+	0.914662i	$0.367543\pi$
$60$		0			0
$61$	−3.03294	+	3.09088i	−0.388328	+	0.395747i	−0.879954	−	0.475059i	$-0.842427\pi$
$61$	−3.03294	+	3.09088i	−0.388328	+	0.395747i	0.491626	+	0.870806i	$0.336403\pi$
$62$		0			0
$63$	−0.149091	+	0.866838i	−0.0187837	+	0.109211i
$64$		0			0
$65$	−3.04530	+	2.46922i	−0.377723	+	0.306268i
$66$		0			0
$67$	4.23717	−	1.87371i	0.517653	−	0.228911i	−0.129070	−	0.991636i	$-0.541199\pi$
$67$	4.23717	−	1.87371i	0.517653	−	0.228911i	0.646723	+	0.762725i	$0.276139\pi$
$68$		0			0
$69$	−1.73491	+	6.90882i	−0.208859	+	0.831724i
$70$		0			0
$71$	4.23010	−	0.482409i	0.502020	−	0.0572515i	0.141378	−	0.989956i	$-0.454847\pi$
$71$	4.23010	−	0.482409i	0.502020	−	0.0572515i	0.360642	+	0.932704i	$0.382558\pi$
$72$		0			0
$73$	10.1577	−	7.61759i	1.18887	−	0.891571i	0.192893	−	0.981220i	$-0.438213\pi$
$73$	10.1577	−	7.61759i	1.18887	−	0.891571i	0.995973	+	0.0896486i	$0.0285744\pi$
$74$		0			0
$75$	−1.60214	+	1.90122i	−0.184999	+	0.219534i
$76$		0			0
$77$	0.843169	+	1.64710i	0.0960881	+	0.187704i
$78$		0			0
$79$	2.69600	−	7.17167i	0.303323	−	0.806876i	−0.692979	−	0.720958i	$-0.743702\pi$
$79$	2.69600	−	7.17167i	0.303323	−	0.806876i	0.996302	−	0.0859178i	$-0.0273823\pi$
$80$		0			0
$81$	−3.52945	+	2.06753i	−0.392162	+	0.229725i
$82$		0			0
$83$	4.97769	−	6.90601i	0.546372	−	0.758034i	−0.444066	−	0.895994i	$-0.646464\pi$
$83$	4.97769	−	6.90601i	0.546372	−	0.758034i	0.990438	+	0.137961i	$0.0440547\pi$
$84$		0			0
$85$	8.00597	+	4.29146i	0.868370	+	0.465475i
$86$		0			0
$87$	1.69441	+	3.02223i	0.181660	+	0.324017i
$88$		0			0
$89$	−4.27601	−	14.6560i	−0.453256	−	1.55353i	−0.790711	−	0.612190i	$-0.790289\pi$
$89$	−4.27601	−	14.6560i	−0.453256	−	1.55353i	0.337455	−	0.941342i	$-0.390434\pi$
$90$		0			0
$91$	1.01483	+	1.30118i	0.106383	+	0.136400i
$92$		0			0
$93$	1.43422	+	3.81520i	0.148722	+	0.395618i
$94$		0			0
$95$	−2.83023	+	1.80515i	−0.290375	+	0.185204i
$96$		0			0
$97$	−9.87660	−	2.28238i	−1.00282	−	0.231741i	−0.308356	−	0.951271i	$-0.599779\pi$
$97$	−9.87660	−	2.28238i	−1.00282	−	0.231741i	−0.694461	+	0.719530i	$0.744357\pi$
$98$		0			0
$99$	1.12558	−	2.68144i	0.113125	−	0.269495i
$100$		0			0
$101$	0.521352	+	5.49313i	0.0518764	+	0.546587i	0.983217	+	0.182438i	$0.0583990\pi$
$101$	0.521352	+	5.49313i	0.0518764	+	0.546587i	−0.931341	+	0.364149i	$0.881360\pi$
$102$		0			0
$103$	8.67399	−	6.00589i	0.854674	−	0.591778i	−0.0589852	−	0.998259i	$-0.518786\pi$
$103$	8.67399	−	6.00589i	0.854674	−	0.591778i	0.913659	+	0.406481i	$0.133244\pi$
$104$		0			0
$105$	−1.35119	−	1.18308i	−0.131863	−	0.115457i
$106$		0			0
$107$	−0.506253	−	0.350531i	−0.0489413	−	0.0338871i	0.544539	−	0.838735i	$-0.316704\pi$
$107$	−0.506253	−	0.350531i	−0.0489413	−	0.0338871i	−0.593481	+	0.804848i	$0.702247\pi$
$108$		0			0
$109$	7.16033	+	4.56693i	0.685835	+	0.437432i	0.834172	−	0.551505i	$-0.185946\pi$
$109$	7.16033	+	4.56693i	0.685835	+	0.437432i	−0.148337	+	0.988937i	$0.547392\pi$
$110$		0			0
$111$	−0.114523	+	0.859409i	−0.0108700	+	0.0815715i
$112$		0			0
$113$	2.49697	−	4.08335i	0.234895	−	0.384129i	−0.713786	−	0.700364i	$-0.753021\pi$
$113$	2.49697	−	4.08335i	0.234895	−	0.384129i	0.948681	+	0.316235i	$0.102419\pi$
$114$		0			0
$115$	6.56545	+	6.69089i	0.612231	+	0.623929i
$116$		0			0
$117$	0.535997	−	2.53740i	0.0495529	−	0.234583i
$118$		0			0
$119$	1.86968	−	3.33485i	0.171393	−	0.305706i
$120$		0			0
$121$	1.18906	+	4.73513i	0.108097	+	0.430466i
$122$		0			0
$123$	5.13137	+	7.71910i	0.462680	+	0.696008i
$124$		0			0
$125$	3.84475	+	11.5351i	0.343885	+	1.03173i
$126$		0			0
$127$	8.26235	+	0.942255i	0.733165	+	0.0836116i	0.471896	−	0.881654i	$-0.343570\pi$
$127$	8.26235	+	0.942255i	0.733165	+	0.0836116i	0.261269	+	0.965266i	$0.415859\pi$
$128$		0			0
$129$	−7.29214	+	0.276143i	−0.642037	+	0.0243130i
$130$		0			0
$131$	0.488687	−	8.59807i	0.0426968	−	0.751217i	−0.903691	−	0.428185i	$-0.859153\pi$
$131$	0.488687	−	8.59807i	0.0426968	−	0.751217i	0.946388	−	0.323032i	$-0.104702\pi$
$132$		0			0
$133$	0.737091	+	1.20538i	0.0639139	+	0.104520i
$134$		0			0
$135$	−0.189707	+	10.0228i	−0.0163273	+	0.862624i
$136$		0			0
$137$	−8.84862	+	3.13660i	−0.755989	+	0.267978i	−0.684054	−	0.729431i	$-0.739785\pi$
$137$	−8.84862	+	3.13660i	−0.755989	+	0.267978i	−0.0719346	+	0.997409i	$0.522917\pi$
$138$		0			0
$139$	5.75643	+	5.43854i	0.488254	+	0.461291i	0.890989	−	0.454026i	$-0.150013\pi$
$139$	5.75643	+	5.43854i	0.488254	+	0.461291i	−0.402735	+	0.915317i	$0.631940\pi$
$140$		0			0
$141$	−6.16199	+	0.940133i	−0.518934	+	0.0791735i
$142$		0			0
$143$	−2.30053	−	4.94707i	−0.192380	−	0.413694i
$144$		0			0
$145$	4.55631	+	0.172541i	0.378381	+	0.0143288i
$146$		0			0
$147$	5.85310	−	6.43492i	0.482756	−	0.530743i
$148$		0			0
$149$	0.328823	+	0.266619i	0.0269382	+	0.0218423i	0.643185	−	0.765711i	$-0.277613\pi$
$149$	0.328823	+	0.266619i	0.0269382	+	0.0218423i	−0.616247	+	0.787553i	$0.711348\pi$
$150$		0			0
$151$	3.92316	+	2.94211i	0.319262	+	0.239426i	0.747533	−	0.664225i	$-0.231238\pi$
$151$	3.92316	+	2.94211i	0.319262	+	0.239426i	−0.428270	+	0.903651i	$0.640877\pi$
$152$		0			0
$153$	−5.90140	+	1.13038i	−0.477100	+	0.0913860i
$154$		0			0
$155$	5.26795	+	1.00905i	0.423132	+	0.0810488i
$156$		0			0
$157$	1.25035	+	5.91916i	0.0997891	+	0.472401i	0.999365	+	0.0356359i	$0.0113457\pi$
$157$	1.25035	+	5.91916i	0.0997891	+	0.472401i	−0.899576	+	0.436765i	$0.856124\pi$
$158$		0			0
$159$	7.53862	−	2.35515i	0.597851	−	0.186775i
$160$		0			0
$161$	2.86792	−	2.70955i	0.226024	−	0.213542i
$162$		0			0
$163$	0.802028	−	2.40625i	0.0628196	−	0.188472i	−0.912588	−	0.408880i	$-0.865919\pi$
$163$	0.802028	−	2.40625i	0.0628196	−	0.188472i	0.975408	+	0.220408i	$0.0707388\pi$
$164$		0			0
$165$	3.47201	+	4.81704i	0.270295	+	0.375006i
$166$		0			0
$167$	−0.554686	−	12.9109i	−0.0429229	−	0.999078i
$167$	−0.554686	−	12.9109i	−0.0429229	−	0.999078i
$168$		0			0
$169$	4.75645	+	6.59907i	0.365881	+	0.507621i
$170$		0			0
$171$	0.702150	−	2.10660i	0.0536948	−	0.161096i
$172$		0			0
$173$	−18.3727	+	17.3581i	−1.39685	+	1.31971i	−0.508120	+	0.861286i	$0.669659\pi$
$173$	−18.3727	+	17.3581i	−1.39685	+	1.31971i	−0.888732	+	0.458427i	$0.848413\pi$
$174$		0			0
$175$	1.31444	−	0.410645i	0.0993622	−	0.0310419i
$176$		0			0
$177$	−1.43183	−	6.77828i	−0.107623	−	0.509487i
$178$		0			0
$179$	12.0773	+	2.31334i	0.902699	+	0.172907i	0.618433	−	0.785838i	$-0.287768\pi$
$179$	12.0773	+	2.31334i	0.902699	+	0.172907i	0.284267	+	0.958745i	$0.408250\pi$
$180$		0			0
$181$	2.29641	−	0.439865i	0.170691	−	0.0326949i	−0.102068	−	0.994777i	$-0.532546\pi$
$181$	2.29641	−	0.439865i	0.170691	−	0.0326949i	0.272759	+	0.962083i	$0.412064\pi$
$182$		0			0
$183$	4.67923	+	3.50911i	0.345899	+	0.259401i
$184$		0			0
$185$	0.886234	+	0.718584i	0.0651572	+	0.0528313i
$186$		0			0
$187$	−8.50555	+	9.35103i	−0.621987	+	0.683815i
$188$		0			0
$189$	4.21623	+	0.159663i	0.306686	+	0.0116138i
$190$		0			0
$191$	−1.27526	−	2.74233i	−0.0922747	−	0.198428i	0.855170	−	0.518348i	$-0.173453\pi$
$191$	−1.27526	−	2.74233i	−0.0922747	−	0.198428i	−0.947445	+	0.319919i	$0.896344\pi$
$192$		0			0
$193$	15.5268	−	2.36891i	1.11764	−	0.170518i	0.434407	−	0.900717i	$-0.356958\pi$
$193$	15.5268	−	2.36891i	1.11764	−	0.170518i	0.683235	+	0.730199i	$0.260573\pi$
$194$		0			0
$195$	3.84914	+	3.63657i	0.275642	+	0.260421i
$196$		0			0
$197$	−3.87834	+	1.37477i	−0.276320	+	0.0979482i	−0.468655	−	0.883381i	$-0.655261\pi$
$197$	−3.87834	+	1.37477i	−0.276320	+	0.0979482i	0.192335	+	0.981329i	$0.438394\pi$
$198$		0			0
$199$	−0.00538423	+	0.284466i	−0.000381678	+	0.0201653i	−0.999961	−	0.00884054i	$-0.997186\pi$
$199$	−0.00538423	+	0.284466i	−0.000381678	+	0.0201653i	0.999579	+	0.0290058i	$0.00923413\pi$
$200$		0			0
$201$	−3.26451	−	5.33852i	−0.230261	−	0.376551i
$202$		0			0
$203$	0.108899	−	1.91599i	0.00764320	−	0.134476i
$204$		0			0
$205$	12.1891	−	0.461582i	0.851320	−	0.0322383i
$206$		0			0
$207$	−6.16087	−	0.702599i	−0.428210	−	0.0488340i
$208$		0			0
$209$	−1.47714	−	4.43172i	−0.102176	−	0.306549i
$210$		0			0
$211$	12.8567	+	19.3404i	0.885095	+	1.33145i	0.942886	+	0.333117i	$0.108100\pi$
$211$	12.8567	+	19.3404i	0.885095	+	1.33145i	−0.0577908	+	0.998329i	$0.518406\pi$
$212$		0			0
$213$	−1.40054	−	5.57727i	−0.0959634	−	0.382148i
$214$		0			0
$215$	−4.69624	+	8.37645i	−0.320281	+	0.571269i
$216$		0			0
$217$	0.466583	−	2.20880i	0.0316737	−	0.149943i
$218$		0			0
$219$	−12.0108	−	12.2403i	−0.811613	−	0.827120i
$220$		0			0
$221$	−5.88089	+	9.61716i	−0.395591	+	0.646920i
$222$		0			0
$223$	−3.89849	+	29.2554i	−0.261062	+	1.95909i	0.0212846	+	0.999773i	$0.493224\pi$
$223$	−3.89849	+	29.2554i	−0.261062	+	1.95909i	−0.282347	+	0.959312i	$0.591113\pi$
$224$		0			0
$225$	−1.82472	−	1.16382i	−0.121648	−	0.0775883i
$226$		0			0
$227$	10.9288	+	7.56710i	0.725368	+	0.502246i	0.873562	−	0.486712i	$-0.161804\pi$
$227$	10.9288	+	7.56710i	0.725368	+	0.502246i	−0.148194	+	0.988958i	$0.547346\pi$
$228$		0			0
$229$	1.26483	+	1.10747i	0.0835826	+	0.0731835i	0.699527	−	0.714606i	$-0.253394\pi$
$229$	1.26483	+	1.10747i	0.0835826	+	0.0731835i	−0.615944	+	0.787790i	$0.711225\pi$
$230$		0			0
$231$	2.05474	−	1.42271i	0.135192	−	0.0936072i
$232$		0			0
$233$	0.0609304	+	0.641982i	0.00399168	+	0.0420577i	0.997300	−	0.0734352i	$-0.0233962\pi$
$233$	0.0609304	+	0.641982i	0.00399168	+	0.0420577i	−0.993308	+	0.115493i	$0.963155\pi$
$234$		0			0
$235$	−3.17491	+	7.56349i	−0.207108	+	0.493387i
$236$		0			0
$237$	−10.0826	−	2.32997i	−0.654932	−	0.151348i
$238$		0			0
$239$	−14.2242	+	9.07232i	−0.920086	+	0.586840i	−0.910678	−	0.413116i	$-0.864440\pi$
$239$	−14.2242	+	9.07232i	−0.920086	+	0.586840i	−0.00940770	+	0.999956i	$0.502995\pi$
$240$		0			0
$241$	−4.90485	−	13.0475i	−0.315949	−	0.840462i	−0.994387	−	0.105804i	$-0.966258\pi$
$241$	−4.90485	−	13.0475i	−0.315949	−	0.840462i	0.678438	−	0.734658i	$-0.262657\pi$
$242$		0			0
$243$	−7.00800	−	8.98539i	−0.449563	−	0.576413i
$244$		0			0
$245$	−3.20614	−	10.9890i	−0.204833	−	0.702063i
$246$		0			0
$247$	−2.03726	−	3.63376i	−0.129628	−	0.231211i
$248$		0			0
$249$	−10.1340	−	5.43213i	−0.642214	−	0.344248i
$250$		0			0
$251$	6.89835	−	9.57074i	0.435420	−	0.604099i	−0.535198	−	0.844727i	$-0.679763\pi$
$251$	6.89835	−	9.57074i	0.435420	−	0.604099i	0.970618	+	0.240627i	$0.0773532\pi$
$252$		0			0
$253$	−11.2558	+	6.59355i	−0.707645	+	0.414533i
$254$		0			0
$255$	4.31717	−	11.4842i	0.270352	−	0.719167i
$256$		0			0
$257$	−7.71616	−	15.0732i	−0.481321	−	0.940242i	−0.996535	−	0.0831802i	$-0.973492\pi$
$257$	−7.71616	−	15.0732i	−0.481321	−	0.940242i	0.515214	−	0.857062i	$-0.327713\pi$
$258$		0			0
$259$	0.309450	−	0.367217i	0.0192283	−	0.0228178i
$260$		0			0
$261$	−2.41295	+	1.80955i	−0.149358	+	0.112008i
$262$		0			0
$263$	13.6299	−	1.55439i	0.840458	−	0.0958476i	0.317555	−	0.948240i	$-0.397138\pi$
$263$	13.6299	−	1.55439i	0.840458	−	0.0958476i	0.522903	+	0.852392i	$0.324849\pi$
$264$		0			0
$265$	2.53136	−	10.0805i	0.155500	−	0.619238i
$266$		0			0
$267$	−18.8588	+	8.33954i	−1.15414	+	0.510372i
$268$		0			0
$269$	19.6986	−	15.9722i	1.20104	−	0.973840i	0.201059	−	0.979579i	$-0.435562\pi$
$269$	19.6986	−	15.9722i	1.20104	−	0.973840i	0.999984	+	0.00573887i	$0.00182675\pi$
$270$		0			0
$271$	0.424924	−	2.47058i	0.0258123	−	0.150077i	−0.969762	−	0.244051i	$-0.921523\pi$
$271$	0.424924	−	2.47058i	0.0258123	−	0.150077i	0.995575	+	0.0939745i	$0.0299572\pi$
$272$		0			0
$273$	1.56098	−	1.59081i	0.0944751	−	0.0962802i
$274$		0			0
$275$	−4.54002	+	0.344342i	−0.273773	+	0.0207646i
$276$		0			0
$277$	−5.97460	−	2.91712i	−0.358979	−	0.175273i	0.250418	−	0.968138i	$-0.419432\pi$
$277$	−5.97460	−	2.91712i	−0.358979	−	0.175273i	−0.609397	+	0.792865i	$0.708588\pi$
$278$		0			0
$279$	−3.12709	+	1.67623i	−0.187214	+	0.100353i
$280$		0			0
$281$	3.32801	+	19.3496i	0.198532	+	1.15430i	0.898119	+	0.439752i	$0.144934\pi$
$281$	3.32801	+	19.3496i	0.198532	+	1.15430i	−0.699587	+	0.714547i	$0.746633\pi$
$282$		0			0
$283$	−0.576932	−	10.1507i	−0.0342950	−	0.603394i	−0.968861	−	0.247605i	$-0.920357\pi$
$283$	−0.576932	−	10.1507i	−0.0342950	−	0.603394i	0.934566	−	0.355790i	$-0.115788\pi$
$284$		0			0
$285$	2.92170	+	3.46711i	0.173066	+	0.205374i
$286$		0			0
$287$	−0.0971552	−	5.13302i	−0.00573489	−	0.302992i
$288$		0			0
$289$	9.01366	+	1.37521i	0.530215	+	0.0808948i
$290$		0			0
$291$	−1.29364	+	13.6302i	−0.0758343	+	0.799015i
$292$		0			0
$293$	1.54535	−	0.754521i	0.0902802	−	0.0440796i	−0.393055	−	0.919515i	$-0.628582\pi$
$293$	1.54535	−	0.754521i	0.0902802	−	0.0440796i	0.483335	+	0.875435i	$0.339425\pi$
$294$		0			0
$295$	−8.59295	−	3.04598i	−0.500301	−	0.177344i
$296$		0			0
$297$	−13.4633	−	3.65303i	−0.781219	−	0.211970i
$298$		0			0
$299$	−8.75233	+	7.66339i	−0.506160	+	0.443185i
$300$		0			0
$301$	3.48753	+	2.04297i	0.201018	+	0.117755i
$302$		0			0
$303$	7.26130	−	1.67801i	0.417150	−	0.0963992i
$304$		0			0
$305$	7.15211	−	2.84425i	0.409529	−	0.162861i
$306$		0			0
$307$	−5.33342	−	12.7056i	−0.304394	−	0.725149i	−0.999978	−	0.00670386i	$-0.997866\pi$
$307$	−5.33342	−	12.7056i	−0.304394	−	0.725149i	0.695583	−	0.718445i	$-0.255146\pi$
$308$		0			0
$309$	−9.58830	−	10.5414i	−0.545459	−	0.599680i
$310$		0			0
$311$	−4.96995	−	1.97645i	−0.281820	−	0.112074i	0.224348	−	0.974509i	$-0.427975\pi$
$311$	−4.96995	−	1.97645i	−0.281820	−	0.112074i	−0.506168	+	0.862435i	$0.668938\pi$
$312$		0			0
$313$	−8.06704	−	2.52023i	−0.455976	−	0.142452i	0.0615787	−	0.998102i	$-0.480386\pi$
$313$	−8.06704	−	2.52023i	−0.455976	−	0.142452i	−0.517555	+	0.855650i	$0.673158\pi$
$314$		0			0
$315$	0.865476	−	1.30193i	0.0487641	−	0.0733557i
$316$		0			0
$317$	3.64542	+	0.276490i	0.204747	+	0.0155292i	0.177603	−	0.984102i	$-0.443166\pi$
$317$	3.64542	+	0.276490i	0.204747	+	0.0155292i	0.0271444	+	0.999632i	$0.491359\pi$
$318$		0			0
$319$	−1.77713	+	6.09109i	−0.0995001	+	0.341036i
$320$		0			0
$321$	−0.378978	+	0.740319i	−0.0211525	+	0.0413205i
$322$		0			0
$323$	−5.93597	+	7.61089i	−0.330286	+	0.423481i
$324$		0			0
$325$	−3.91866	+	1.06326i	−0.217368	+	0.0589791i
$326$		0			0
$327$	4.83683	−	10.4012i	0.267477	−	0.575185i
$328$		0			0
$329$	3.15754	+	1.39629i	0.174081	+	0.0769801i
$330$		0			0
$331$	−2.26456	−	16.9939i	−0.124472	−	0.934071i	−0.936553	−	0.350526i	$-0.886003\pi$
$331$	−2.26456	−	16.9939i	−0.124472	−	0.934071i	0.812081	−	0.583544i	$-0.198335\pi$
$332$		0			0
$333$	−0.754723			−0.0413586
$334$		0			0
$335$	−8.23473			−0.449911
$336$		0			0
$337$	−1.85690	−	13.9347i	−0.101152	−	0.759070i	−0.966275	−	0.257511i	$-0.917098\pi$
$337$	−1.85690	−	13.9347i	−0.101152	−	0.759070i	0.865124	−	0.501559i	$-0.167240\pi$
$338$		0			0
$339$	−5.91234	−	2.61449i	−0.321114	−	0.142000i
$340$		0			0
$341$	−3.14734	+	6.76807i	−0.170438	+	0.366512i
$342$		0			0
$343$	−9.70384	+	2.63297i	−0.523958	+	0.142167i
$344$		0			0
$345$	7.78657	−	9.98365i	0.419215	−	0.537502i
$346$		0			0
$347$	11.0232	−	21.5333i	0.591754	−	1.15597i	−0.381096	−	0.924535i	$-0.624453\pi$
$347$	11.0232	−	21.5333i	0.591754	−	1.15597i	0.972850	−	0.231435i	$-0.0743419\pi$
$348$		0			0
$349$	7.33606	−	25.1443i	0.392690	−	1.34594i	−0.488245	−	0.872707i	$-0.662363\pi$
$349$	7.33606	−	25.1443i	0.392690	−	1.34594i	0.880936	−	0.473236i	$-0.156914\pi$
$350$		0			0
$351$	−12.4048	−	0.940856i	−0.662121	−	0.0502192i
$352$		0			0
$353$	−5.94264	+	8.93950i	−0.316295	+	0.475801i	−0.956225	−	0.292631i	$-0.905469\pi$
$353$	−5.94264	+	8.93950i	−0.316295	+	0.475801i	0.639931	+	0.768433i	$0.278963\pi$
$354$		0			0
$355$	−7.22310	−	2.25658i	−0.383362	−	0.119767i
$356$		0			0
$357$	−4.79833	−	1.90820i	−0.253955	−	0.100993i
$358$		0			0
$359$	−8.46472	−	9.30614i	−0.446751	−	0.491159i	0.474431	−	0.880293i	$-0.342654\pi$
$359$	−8.46472	−	9.30614i	−0.446751	−	0.491159i	−0.921181	+	0.389133i	$0.872774\pi$
$360$		0			0
$361$	5.97337	+	14.2302i	0.314388	+	0.748957i
$362$		0			0
$363$	6.12734	−	2.43672i	0.321602	−	0.127895i
$364$		0			0
$365$	−21.9879	+	5.08117i	−1.15090	+	0.265961i
$366$		0			0
$367$	−9.68957	−	5.67608i	−0.505792	−	0.296289i	0.230360	−	0.973105i	$-0.426010\pi$
$367$	−9.68957	−	5.67608i	−0.505792	−	0.296289i	−0.736152	+	0.676817i	$0.763359\pi$
$368$		0			0
$369$	−6.07053	+	5.31525i	−0.316019	+	0.276701i
$370$		0			0
$371$	−4.22185	−	1.14553i	−0.219188	−	0.0594728i
$372$		0			0
$373$	19.5807	+	6.94083i	1.01385	+	0.359383i	0.788592	−	0.614917i	$-0.210810\pi$
$373$	19.5807	+	6.94083i	1.01385	+	0.359383i	0.225257	+	0.974299i	$0.427678\pi$
$374$		0			0
$375$	14.7574	−	7.20536i	0.762070	−	0.372083i
$376$		0			0
$377$	−0.534636	+	5.63310i	−0.0275351	+	0.290119i
$378$		0			0
$379$	15.2625	+	2.32859i	0.783981	+	0.119612i	0.530451	−	0.847716i	$-0.322023\pi$
$379$	15.2625	+	2.32859i	0.783981	+	0.119612i	0.253530	+	0.967327i	$0.418408\pi$
$380$		0			0
$381$	−0.212554	−	11.2299i	−0.0108895	−	0.575325i
$382$		0			0
$383$	−8.66296	−	10.2801i	−0.442656	−	0.525290i	0.496843	−	0.867840i	$-0.334492\pi$
$383$	−8.66296	−	10.2801i	−0.442656	−	0.525290i	−0.939499	+	0.342550i	$0.888709\pi$
$384$		0			0
$385$	−0.186628	−	3.28358i	−0.00951147	−	0.167347i
$386$		0			0
$387$	−1.07675	−	6.26039i	−0.0547342	−	0.318233i
$388$		0			0
$389$	28.6810	−	15.3740i	1.45418	−	0.779491i	0.460076	−	0.887879i	$-0.347822\pi$
$389$	28.6810	−	15.3740i	1.45418	−	0.779491i	0.994109	+	0.108389i	$0.0345691\pi$
$390$		0			0
$391$	24.2203	+	11.8256i	1.22487	+	0.598048i
$392$		0			0
$393$	−11.5984	+	0.879695i	−0.585064	+	0.0443747i
$394$		0			0
$395$	−9.53783	+	9.72006i	−0.479900	+	0.489069i
$396$		0			0
$397$	1.15923	−	6.73993i	0.0581799	−	0.338267i	−0.941818	−	0.336124i	$-0.890884\pi$
$397$	1.15923	−	6.73993i	0.0581799	−	0.338267i	0.999998	−	0.00214363i	$-0.000682340\pi$
$398$		0			0
$399$	1.48229	−	1.20188i	0.0742071	−	0.0601693i
$400$		0			0
$401$	1.45558	−	0.643669i	0.0726881	−	0.0321433i	−0.367767	−	0.929918i	$-0.619877\pi$
$401$	1.45558	−	0.643669i	0.0726881	−	0.0321433i	0.440455	+	0.897775i	$0.354817\pi$
$402$		0			0
$403$	−1.62118	+	6.45591i	−0.0807567	+	0.321592i
$404$		0			0
$405$	7.22360	−	0.823795i	0.358944	−	0.0409347i
$406$		0			0
$407$	−1.27023	+	0.952587i	−0.0629629	+	0.0472180i
$408$		0			0
$409$	−7.07516	+	8.39593i	−0.349844	+	0.415152i	−0.910901	−	0.412625i	$-0.864612\pi$
$409$	−7.07516	+	8.39593i	−0.349844	+	0.415152i	0.561057	+	0.827777i	$0.310395\pi$
$410$		0			0
$411$	5.77800	+	11.2871i	0.285008	+	0.556752i
$412$		0			0
$413$	−1.35024	+	3.59179i	−0.0664408	+	0.176740i
$414$		0			0
$415$	−13.0559	+	7.64805i	−0.640889	+	0.375428i
$416$		0			0
$417$	6.25423	−	8.67709i	0.306271	−	0.424919i
$418$		0			0
$419$	−14.9602	−	8.01916i	−0.730854	−	0.391762i	0.0644917	−	0.997918i	$-0.479457\pi$
$419$	−14.9602	−	8.01916i	−0.730854	−	0.391762i	−0.795345	+	0.606157i	$0.792710\pi$
$420$		0			0
$421$	15.3593	+	27.3956i	0.748566	+	1.33518i	0.935683	+	0.352841i	$0.114785\pi$
$421$	15.3593	+	27.3956i	0.748566	+	1.33518i	−0.187117	+	0.982338i	$0.559914\pi$
$422$		0			0
$423$	−1.51973	−	5.20888i	−0.0738920	−	0.253264i
$424$		0			0
$425$	5.78558	+	7.41806i	0.280642	+	0.359829i
$426$		0			0
$427$	−1.13994	−	3.03237i	−0.0551655	−	0.146747i
$428$		0			0
$429$	−6.21279	+	3.96258i	−0.299957	+	0.191315i
$430$		0			0
$431$	−21.2836	−	4.91841i	−1.02519	−	0.236912i	−0.321120	−	0.947039i	$-0.604059\pi$
$431$	−21.2836	−	4.91841i	−1.02519	−	0.236912i	−0.704074	+	0.710127i	$0.748638\pi$
$432$		0			0
$433$	15.6620	−	37.3111i	0.752667	−	1.79306i	0.160860	−	0.986977i	$-0.448573\pi$
$433$	15.6620	−	37.3111i	0.752667	−	1.79306i	0.591807	−	0.806080i	$-0.298415\pi$
$434$		0			0
$435$	−0.581878	−	6.13085i	−0.0278989	−	0.293952i
$436$		0			0
$437$	−8.18920	+	5.67021i	−0.391742	+	0.271243i
$438$		0			0
$439$	4.19431	+	3.67246i	0.200183	+	0.175277i	0.752989	−	0.658033i	$-0.228611\pi$
$439$	4.19431	+	3.67246i	0.200183	+	0.175277i	−0.552806	+	0.833310i	$0.686443\pi$
$440$		0			0
$441$	6.22548	+	4.31054i	0.296452	+	0.205264i
$442$		0			0
$443$	−22.9919	−	14.6645i	−1.09238	−	0.696731i	−0.136545	−	0.990634i	$-0.543600\pi$
$443$	−22.9919	−	14.6645i	−1.09238	−	0.696731i	−0.955835	+	0.293903i	$0.905046\pi$
$444$		0			0
$445$	−3.58437	+	26.8981i	−0.169915	+	1.27509i
$446$		0			0
$447$	0.298290	−	0.487801i	0.0141086	−	0.0230722i
$448$		0			0
$449$	4.67534	+	4.76467i	0.220643	+	0.224859i	0.815177	−	0.579212i	$-0.196639\pi$
$449$	4.67534	+	4.76467i	0.220643	+	0.224859i	−0.594534	+	0.804070i	$0.702664\pi$
$450$		0			0
$451$	−3.50820	+	16.6078i	−0.165195	+	0.782030i
$452$		0			0
$453$	3.23903	−	5.77730i	0.152183	−	0.271441i
$454$		0			0
$455$	−0.714337	−	2.84465i	−0.0334886	−	0.133359i
$456$		0			0
$457$	6.50895	+	9.79140i	0.304476	+	0.458022i	0.952912	−	0.303247i	$-0.0980706\pi$
$457$	6.50895	+	9.79140i	0.304476	+	0.458022i	−0.648436	+	0.761269i	$0.724577\pi$
$458$		0			0
$459$	9.11421	+	27.3446i	0.425415	+	1.27633i
$460$		0			0
$461$	6.63987	+	0.757225i	0.309250	+	0.0352675i	0.266552	−	0.963821i	$-0.414116\pi$
$461$	6.63987	+	0.757225i	0.309250	+	0.0352675i	0.0426977	+	0.999088i	$0.486405\pi$
$462$		0			0
$463$	−33.0015	+	1.24972i	−1.53371	+	0.0580795i	−0.791118	−	0.611664i	$-0.790501\pi$
$463$	−33.0015	+	1.24972i	−1.53371	+	0.0580795i	−0.742593	+	0.669743i	$0.766404\pi$
$464$		0			0
$465$	0.411093	−	7.23286i	0.0190640	−	0.335416i
$466$		0			0
$467$	−11.7946	−	19.2879i	−0.545787	−	0.892539i	−0.999999	−	0.00164469i	$-0.999476\pi$
$467$	−11.7946	−	19.2879i	−0.545787	−	0.892539i	0.454211	−	0.890894i	$-0.349921\pi$
$468$		0			0
$469$	−0.0655896	+	3.46530i	−0.00302864	+	0.160013i
$470$		0			0
$471$	7.70161	−	2.73002i	0.354872	−	0.125793i
$472$		0			0
$473$	−9.71386	−	9.17744i	−0.446644	−	0.421979i
$474$		0			0
$475$	−3.43681	+	0.524352i	−0.157691	+	0.0240589i
$476$		0			0
$477$	2.89899	+	6.23401i	0.132736	+	0.285436i
$478$		0			0
$479$	−16.4200	−	0.621804i	−0.750251	−	0.0284110i	−0.340052	−	0.940407i	$-0.610445\pi$
$479$	−16.4200	−	0.621804i	−0.750251	−	0.0284110i	−0.410200	+	0.911996i	$0.634541\pi$
$480$		0			0
$481$	−0.952732	+	1.04744i	−0.0434408	+	0.0477590i
$482$		0			0
$483$	−4.13925	−	3.35623i	−0.188343	−	0.152714i
$484$		0			0
$485$	14.4145	+	10.8099i	0.654527	+	0.490852i
$486$		0			0
$487$	−3.82656	+	0.732958i	−0.173398	+	0.0332135i	−0.274089	−	0.961704i	$-0.588376\pi$
$487$	−3.82656	+	0.732958i	−0.173398	+	0.0332135i	0.100691	+	0.994918i	$0.467895\pi$
$488$		0			0
$489$	−3.36462	−	0.644476i	−0.152154	−	0.0291442i
$490$		0			0
$491$	6.82817	+	32.3245i	0.308151	+	1.45878i	0.806204	+	0.591638i	$0.201518\pi$
$491$	6.82817	+	32.3245i	0.308151	+	1.45878i	−0.498053	+	0.867147i	$0.665952\pi$
$492$		0			0
$493$	12.5136	−	3.90939i	0.563584	−	0.176070i
$494$		0			0
$495$	−3.75724	+	3.54975i	−0.168875	+	0.159550i
$496$		0			0
$497$	−1.00714	+	3.02162i	−0.0451762	+	0.135538i
$498$		0			0
$499$	−14.2960	−	19.8341i	−0.639975	−	0.887898i	0.358992	−	0.933341i	$-0.383121\pi$
$499$	−14.2960	−	19.8341i	−0.639975	−	0.887898i	−0.998967	+	0.0454426i	$0.985530\pi$
$500$		0			0
$501$	−17.1864	+	3.04603i	−0.767834	+	0.136087i
$502$		0			0
$503$	7.81845	+	10.8473i	0.348608	+	0.483657i	0.948657	−	0.316306i	$-0.102443\pi$
$503$	7.81845	+	10.8473i	0.348608	+	0.483657i	−0.600049	+	0.799963i	$0.704852\pi$
$504$		0			0
$505$	3.10120	−	9.30424i	0.138001	−	0.414033i
$506$		0			0
$507$	7.98638	−	7.54535i	0.354688	−	0.335101i
$508$		0			0
$509$	−20.8205	+	6.50457i	−0.922854	+	0.288310i	−0.722466	−	0.691407i	$-0.756991\pi$
$509$	−20.8205	+	6.50457i	−0.922854	+	0.288310i	−0.200388	+	0.979717i	$0.564220\pi$
$510$		0			0
$511$	1.96310	+	9.29330i	0.0868425	+	0.411112i
$512$		0			0
$513$	−10.4617	−	2.00388i	−0.461894	−	0.0884734i
$514$		0			0
$515$	−18.4175	+	3.52777i	−0.811571	+	0.155452i
$516$		0			0
$517$	−9.13225	−	6.84858i	−0.401636	−	0.301200i
$518$		0			0
$519$	26.5172	+	21.5009i	1.16398	+	0.943786i
$520$		0			0
$521$	−6.29575	+	6.92157i	−0.275822	+	0.303240i	−0.861965	−	0.506968i	$-0.830766\pi$
$521$	−6.29575	+	6.92157i	−0.275822	+	0.303240i	0.586143	+	0.810208i	$0.300646\pi$
$522$		0			0
$523$	26.7865	+	1.01437i	1.17129	+	0.0443552i	0.616308	−	0.787505i	$-0.288628\pi$
$523$	26.7865	+	1.01437i	1.17129	+	0.0443552i	0.554985	+	0.831860i	$0.312724\pi$
$524$		0			0
$525$	−0.784285	−	1.68653i	−0.0342290	−	0.0736063i
$526$		0			0
$527$	15.2458	−	2.32604i	0.664117	−	0.101324i
$528$		0			0
$529$	3.49991	+	3.30663i	0.152170	+	0.143767i
$530$		0			0
$531$	5.68411	−	2.01487i	0.246669	−	0.0874378i
$532$		0			0
$533$	−0.286462	+	15.1347i	−0.0124080	+	0.655556i
$534$		0			0
$535$	0.570975	+	0.933728i	0.0246854	+	0.0403686i
$536$		0			0
$537$	0.942470	−	16.5820i	0.0406706	−	0.715567i
$538$		0			0
$539$	15.9183	−	0.602806i	0.685652	−	0.0259647i
$540$		0			0
$541$	23.2197	+	2.64802i	0.998293	+	0.113847i	0.597117	−	0.802154i	$-0.296313\pi$
$541$	23.2197	+	2.64802i	0.998293	+	0.113847i	0.401175	+	0.916001i	$0.368602\pi$
$542$		0			0
$543$	−0.998596	−	2.99600i	−0.0428539	−	0.128571i
$544$		0			0
$545$	−8.35673	−	12.5710i	−0.357963	−	0.538483i
$546$		0			0
$547$	−0.723280	−	2.88027i	−0.0309252	−	0.123151i	0.952468	−	0.304638i	$-0.0985355\pi$
$547$	−0.723280	−	2.88027i	−0.0309252	−	0.123151i	−0.983393	+	0.181487i	$0.941909\pi$
$548$		0			0
$549$	−2.48986	+	4.44104i	−0.106265	+	0.189539i
$550$		0			0
$551$	−1.00133	+	4.74028i	−0.0426580	+	0.201943i
$552$		0			0
$553$	4.01438	+	4.09108i	0.170709	+	0.173971i
$554$		0			0
$555$	0.803943	−	1.31471i	0.0341255	−	0.0558062i
$556$		0			0
$557$	−0.855637	+	6.42094i	−0.0362545	+	0.272064i	0.963732	+	0.266872i	$0.0859901\pi$
$557$	−0.855637	+	6.42094i	−0.0362545	+	0.272064i	−0.999987	+	0.00519209i	$0.998347\pi$
$558$		0			0
$559$	−10.0477	−	6.40850i	−0.424971	−	0.271051i
$560$		0			0
$561$	14.0368	+	9.71909i	0.592634	+	0.410341i
$562$		0			0
$563$	15.2328	+	13.3376i	0.641986	+	0.562112i	0.916781	−	0.399391i	$-0.130778\pi$
$563$	15.2328	+	13.3376i	0.641986	+	0.562112i	−0.274794	+	0.961503i	$0.588610\pi$
$564$		0			0
$565$	−6.99428	+	4.84285i	−0.294252	+	0.203740i
$566$		0			0
$567$	−0.289130	−	3.04636i	−0.0121423	−	0.127935i
$568$		0			0
$569$	11.3650	−	27.0744i	0.476444	−	1.13502i	−0.488500	−	0.872564i	$-0.662456\pi$
$569$	11.3650	−	27.0744i	0.476444	−	1.13502i	0.964944	−	0.262455i	$-0.0845321\pi$
$570$		0			0
$571$	10.3478	+	2.39127i	0.433042	+	0.100071i	0.436047	−	0.899924i	$-0.356378\pi$
$571$	10.3478	+	2.39127i	0.433042	+	0.100071i	−0.00300504	+	0.999995i	$0.500957\pi$
$572$		0			0
$573$	−3.44397	+	2.19660i	−0.143874	+	0.0917642i
$574$		0			0
$575$	3.41616	+	9.08738i	0.142464	+	0.378970i
$576$		0			0
$577$	12.5334	+	16.0698i	0.521771	+	0.668996i	0.974950	−	0.222424i	$-0.0713968\pi$
$577$	12.5334	+	16.0698i	0.521771	+	0.668996i	−0.453179	+	0.891420i	$0.649710\pi$
$578$		0			0
$579$	−5.94164	−	20.3649i	−0.246926	−	0.846336i
$580$		0			0
$581$	3.11443	+	5.55504i	0.129208	+	0.230462i
$582$		0			0
$583$	12.7475	+	6.83307i	0.527947	+	0.282997i
$584$		0			0
$585$	−2.69529	+	3.73943i	−0.111437	+	0.154607i
$586$		0			0
$587$	−23.6082	+	13.8295i	−0.974417	+	0.570806i	−0.904375	−	0.426738i	$-0.859663\pi$
$587$	−23.6082	+	13.8295i	−0.974417	+	0.570806i	−0.0700414	+	0.997544i	$0.522313\pi$
$588$		0			0
$589$	−2.00549	+	5.33484i	−0.0826349	+	0.219818i
$590$		0			0
$591$	2.53249	+	4.94712i	0.104173	+	0.203497i
$592$		0			0
$593$	15.6462	−	18.5670i	0.642513	−	0.762456i	−0.341629	−	0.939835i	$-0.610979\pi$
$593$	15.6462	−	18.5670i	0.642513	−	0.762456i	0.984143	+	0.177379i	$0.0567619\pi$
$594$		0			0
$595$	−5.43653	+	4.07704i	−0.222876	+	0.167142i
$596$		0			0
$597$	0.381809	−	0.0435423i	0.0156264	−	0.00178207i
$598$		0			0
$599$	4.50942	−	17.9576i	0.184250	−	0.733726i	−0.805702	−	0.592321i	$-0.798212\pi$
$599$	4.50942	−	17.9576i	0.184250	−	0.733726i	0.989952	−	0.141405i	$-0.0451619\pi$
$600$		0			0
$601$	−10.6765	+	4.72122i	−0.435502	+	0.192583i	−0.610551	−	0.791977i	$-0.709052\pi$
$601$	−10.6765	+	4.72122i	−0.435502	+	0.192583i	0.175049	+	0.984560i	$0.443992\pi$
$602$		0			0
$603$	4.23107	−	3.43067i	0.172302	−	0.139708i
$604$		0			0
$605$	1.47090	−	8.55203i	0.0598004	−	0.347689i
$606$		0			0
$607$	−15.0692	+	15.3571i	−0.611639	+	0.623325i	−0.947948	−	0.318426i	$-0.896846\pi$
$607$	−15.0692	+	15.3571i	−0.611639	+	0.623325i	0.336308	+	0.941752i	$0.390822\pi$
$608$		0			0
$609$	−2.58459	+	0.196031i	−0.104733	+	0.00794357i
$610$		0			0
$611$	−9.14755	−	4.46632i	−0.370070	−	0.180688i
$612$		0			0
$613$	18.0928	−	9.69835i	0.730762	−	0.391713i	−0.0645484	−	0.997915i	$-0.520561\pi$
$613$	18.0928	−	9.69835i	0.730762	−	0.391713i	0.795311	+	0.606202i	$0.207308\pi$
$614$		0			0
$615$	−2.79259	−	16.2366i	−0.112608	−	0.654722i
$616$		0			0
$617$	0.687261	+	12.0918i	0.0276681	+	0.486799i	0.982099	+	0.188366i	$0.0603192\pi$
$617$	0.687261	+	12.0918i	0.0276681	+	0.486799i	−0.954431	+	0.298432i	$0.903536\pi$
$618$		0			0
$619$	7.66809	+	9.09954i	0.308206	+	0.365741i	0.896606	−	0.442829i	$-0.146025\pi$
$619$	7.66809	+	9.09954i	0.308206	+	0.365741i	−0.588400	+	0.808570i	$0.700242\pi$
$620$		0			0
$621$	0.562900	+	29.7398i	0.0225884	+	1.19342i
$622$		0			0
$623$	11.2906	+	1.72260i	0.452348	+	0.0690146i
$624$		0			0
$625$	1.17233	−	12.3521i	0.0468933	−	0.494083i
$626$		0			0
$627$	−5.66974	+	2.76827i	−0.226428	+	0.110554i
$628$		0			0
$629$	3.09205	+	1.09605i	0.123288	+	0.0437023i
$630$		0			0
$631$	31.6735	+	8.59406i	1.26090	+	0.342124i	0.828721	−	0.559662i	$-0.189069\pi$
$631$	31.6735	+	8.59406i	1.26090	+	0.342124i	0.432182	+	0.901786i	$0.357744\pi$
$632$		0			0
$633$	23.5995	−	20.6633i	0.937996	−	0.821293i
$634$		0			0
$635$	−12.7537	−	7.47102i	−0.506115	−	0.296478i
$636$		0			0
$637$	13.8411	−	3.19854i	0.548406	−	0.126731i
$638$		0			0
$639$	4.65140	−	1.84977i	0.184006	−	0.0731758i
$640$		0			0
$641$	−2.07015	−	4.93166i	−0.0817661	−	0.194789i	0.876017	−	0.482280i	$-0.160191\pi$
$641$	−2.07015	−	4.93166i	−0.0817661	−	0.194789i	−0.957783	+	0.287491i	$0.907179\pi$
$642$		0			0
$643$	26.2135	+	28.8192i	1.03376	+	1.13652i	0.990508	+	0.137455i	$0.0438922\pi$
$643$	26.2135	+	28.8192i	1.03376	+	1.13652i	0.0432517	+	0.999064i	$0.486228\pi$
$644$		0			0
$645$	12.0524	+	4.79300i	0.474562	+	0.188724i
$646$		0			0
$647$	30.5786	+	9.55310i	1.20217	+	0.375571i	0.832727	−	0.553683i	$-0.186778\pi$
$647$	30.5786	+	9.55310i	1.20217	+	0.375571i	0.369441	+	0.929254i	$0.379549\pi$
$648$		0			0
$649$	7.02348	−	10.5654i	0.275696	−	0.414728i
$650$		0			0
$651$	−3.04042	−	0.230604i	−0.119164	−	0.00903808i
$652$		0			0
$653$	−0.493457	+	1.69132i	−0.0193105	+	0.0661864i	−0.969061	−	0.246822i	$-0.920614\pi$
$653$	−0.493457	+	1.69132i	−0.0193105	+	0.0661864i	0.949750	+	0.313008i	$0.101337\pi$
$654$		0			0
$655$	−6.97504	+	13.6255i	−0.272538	+	0.532392i
$656$		0			0
$657$	9.18067	−	11.7711i	0.358172	−	0.459235i
$658$		0			0
$659$	10.1231	−	2.74673i	0.394340	−	0.106997i	−0.0591712	−	0.998248i	$-0.518846\pi$
$659$	10.1231	−	2.74673i	0.394340	−	0.106997i	0.453512	+	0.891250i	$0.350171\pi$
$660$		0			0
$661$	−8.46552	+	18.2043i	−0.329271	+	0.708066i	−0.999416	−	0.0341638i	$-0.989123\pi$
$661$	−8.46552	+	18.2043i	−0.329271	+	0.708066i	0.670146	+	0.742230i	$0.266232\pi$
$662$		0			0
$663$	13.9248	+	6.15767i	0.540795	+	0.239144i
$664$		0			0
$665$	−0.331715	−	2.48928i	−0.0128634	−	0.0965303i
$666$		0			0
$667$	13.5292			0.523854
$668$		0			0
$669$	39.8632			1.54120
$670$		0			0
$671$	1.41480	+	10.6171i	0.0546178	+	0.409867i
$672$		0			0
$673$	−25.7639	−	11.3930i	−0.993123	−	0.439168i	−0.156934	−	0.987609i	$-0.550161\pi$
$673$	−25.7639	−	11.3930i	−0.993123	−	0.439168i	−0.836189	+	0.548441i	$0.815221\pi$
$674$		0			0
$675$	−4.37772	+	9.41388i	−0.168499	+	0.362340i
$676$		0			0
$677$	−7.80879	+	2.11878i	−0.300116	+	0.0814314i	−0.408738	−	0.912652i	$-0.634031\pi$
$677$	−7.80879	+	2.11878i	−0.300116	+	0.0814314i	0.108622	+	0.994083i	$0.465356\pi$
$678$		0			0
$679$	4.66378	−	5.97972i	0.178979	−	0.229481i
$680$		0			0
$681$	8.18121	−	15.9817i	0.313504	−	0.612419i
$682$		0			0
$683$	−4.86600	+	16.6782i	−0.186192	+	0.638173i	0.812298	+	0.583243i	$0.198216\pi$
$683$	−4.86600	+	16.6782i	−0.186192	+	0.638173i	−0.998490	+	0.0549300i	$0.982506\pi$
$684$		0			0
$685$	16.6388	+	1.26198i	0.635735	+	0.0482179i
$686$		0			0
$687$	1.25704	−	1.89096i	0.0479591	−	0.0721448i
$688$		0			0
$689$	12.3114	+	3.84622i	0.469027	+	0.146529i
$690$		0			0
$691$	−45.3526	−	18.0359i	−1.72530	−	0.686116i	−0.725298	−	0.688435i	$-0.758298\pi$
$691$	−45.3526	−	18.0359i	−1.72530	−	0.686116i	−0.999997	+	0.00231921i	$0.999262\pi$
$692$		0			0
$693$	1.46386	+	1.60938i	0.0556076	+	0.0611352i
$694$		0			0
$695$	−5.44803	−	12.9787i	−0.206656	−	0.492310i
$696$		0			0
$697$	32.5896	−	12.9602i	1.23442	−	0.490904i
$698$		0			0
$699$	0.848627	−	0.196109i	0.0320980	−	0.00741753i
$700$		0			0
$701$	20.4845	+	11.9996i	0.773688	+	0.453220i	0.838652	−	0.544667i	$-0.183344\pi$
$701$	20.4845	+	11.9996i	0.773688	+	0.453220i	−0.0649645	+	0.997888i	$0.520693\pi$
$702$		0			0
$703$	−0.912120	+	0.798636i	−0.0344013	+	0.0301211i
$704$		0			0
$705$	10.6926	+	2.90124i	0.402705	+	0.109267i
$706$		0			0
$707$	−3.89067	−	1.37914i	−0.146324	−	0.0518679i
$708$		0			0
$709$	27.6459	−	13.4982i	1.03826	−	0.506936i	0.161005	−	0.986954i	$-0.448526\pi$
$709$	27.6459	−	13.4982i	1.03826	−	0.506936i	0.877259	+	0.480018i	$0.159370\pi$
$710$		0			0
$711$	0.851131	−	8.96780i	0.0319199	−	0.336319i
$712$		0			0
$713$	15.7333	+	2.40042i	0.589215	+	0.0898963i
$714$		0			0
$715$	0.183512	+	9.69552i	0.00686296	+	0.362592i
$716$		0			0
$717$	14.6839	+	17.4250i	0.548380	+	0.650750i
$718$		0			0
$719$	−1.34456	−	23.6565i	−0.0501436	−	0.882237i	−0.920725	−	0.390213i	$-0.872402\pi$
$719$	−1.34456	−	23.6565i	−0.0501436	−	0.882237i	0.870581	−	0.492025i	$-0.163743\pi$
$720$		0			0
$721$	1.33785	+	7.77845i	0.0498240	+	0.289685i
$722$		0			0
$723$	−16.5931	+	8.89447i	−0.617106	+	0.330789i
$724$		0			0
$725$	4.24335	+	2.07183i	0.157594	+	0.0769459i
$726$		0			0
$727$	4.25995	−	0.323100i	0.157993	−	0.0119831i	0.00360532	−	0.999994i	$-0.498852\pi$
$727$	4.25995	−	0.323100i	0.157993	−	0.0119831i	0.154387	+	0.988010i	$0.450660\pi$
$728$		0			0
$729$	−19.3742	+	19.7444i	−0.717562	+	0.731272i
$730$		0			0
$731$	−4.68030	+	27.2121i	−0.173107	+	1.00647i
$732$		0			0
$733$	−15.1193	+	12.2592i	−0.558444	+	0.452803i	−0.866933	−	0.498425i	$-0.833912\pi$
$733$	−15.1193	+	12.2592i	−0.558444	+	0.452803i	0.308488	+	0.951228i	$0.400177\pi$
$734$		0			0
$735$	−14.1403	+	6.25297i	−0.521574	+	0.230644i
$736$		0			0
$737$	2.79097	−	11.1143i	0.102807	−	0.409400i
$738$		0			0
$739$	−21.0605	+	2.40179i	−0.774724	+	0.0883512i	−0.491704	−	0.870763i	$-0.663626\pi$
$739$	−21.0605	+	2.40179i	−0.774724	+	0.0883512i	−0.283021	+	0.959114i	$0.591337\pi$
$740$		0			0
$741$	−4.50148	+	3.37581i	−0.165366	+	0.124014i
$742$		0			0
$743$	−17.1243	+	20.3211i	−0.628231	+	0.745507i	−0.981803	−	0.189900i	$-0.939184\pi$
$743$	−17.1243	+	20.3211i	−0.628231	+	0.745507i	0.353572	+	0.935407i	$0.384967\pi$
$744$		0			0
$745$	−0.342868	−	0.669780i	−0.0125617	−	0.0245388i
$746$		0			0
$747$	3.52197	−	9.36885i	0.128862	−	0.342788i
$748$		0			0
$749$	0.397475	−	0.232838i	0.0145234	−	0.00850771i
$750$		0			0
$751$	−2.48067	+	3.44167i	−0.0905209	+	0.125588i	−0.854062	−	0.520170i	$-0.825868\pi$
$751$	−2.48067	+	3.44167i	−0.0905209	+	0.125588i	0.763542	+	0.645759i	$0.223459\pi$
$752$		0			0
$753$	−14.0442	−	7.52815i	−0.511799	−	0.274341i
$754$		0			0
$755$	−4.26247	−	7.60274i	−0.155127	−	0.276692i
$756$		0			0
$757$	−10.7517	−	36.8513i	−0.390776	−	1.33938i	−0.883188	−	0.469020i	$-0.844607\pi$
$757$	−10.7517	−	36.8513i	−0.390776	−	1.33938i	0.492411	−	0.870363i	$-0.336116\pi$
$758$		0			0
$759$	10.8357	+	13.8931i	0.393311	+	0.504288i
$760$		0			0
$761$	6.43939	+	17.1295i	0.233428	+	0.620945i	0.999769	−	0.0214886i	$-0.00684055\pi$
$761$	6.43939	+	17.1295i	0.233428	+	0.620945i	−0.766341	+	0.642434i	$0.777925\pi$
$762$		0			0
$763$	−5.35663	+	3.41651i	−0.193923	+	0.123686i
$764$		0			0
$765$	10.4057	+	2.40465i	0.376219	+	0.0869403i
$766$		0			0
$767$	4.37907	−	10.4321i	0.158119	−	0.376682i
$768$		0			0
$769$	−4.09025	−	43.0962i	−0.147498	−	1.55409i	−0.696063	−	0.717981i	$-0.745067\pi$
$769$	−4.09025	−	43.0962i	−0.147498	−	1.55409i	0.548565	−	0.836108i	$-0.315174\pi$
$770$		0			0
$771$	−18.8037	+	13.0197i	−0.677199	+	0.468893i
$772$		0			0
$773$	2.01479	+	1.76411i	0.0724668	+	0.0634507i	0.694222	−	0.719761i	$-0.255749\pi$
$773$	2.01479	+	1.76411i	0.0724668	+	0.0634507i	−0.621755	+	0.783212i	$0.713580\pi$
$774$		0			0
$775$	4.56704	+	3.16222i	0.164053	+	0.113590i
$776$		0			0
$777$	−0.546846	−	0.348783i	−0.0196180	−	0.0125125i
$778$		0			0
$779$	−1.71202	+	12.8475i	−0.0613395	+	0.460308i
$780$		0			0
$781$	5.49376	−	8.98408i	0.196582	−	0.321476i
$782$		0			0
$783$	10.1332	+	10.3268i	0.362132	+	0.369051i
$784$		0			0
$785$	2.22240	−	10.5208i	0.0793209	−	0.375504i
$786$		0			0
$787$	−7.47450	+	13.3319i	−0.266437	+	0.475230i	−0.972495	−	0.232924i	$-0.925171\pi$
$787$	−7.47450	+	13.3319i	−0.266437	+	0.475230i	0.706058	+	0.708154i	$0.250472\pi$
$788$		0			0
$789$	−4.51272	−	17.9707i	−0.160657	−	0.639774i
$790$		0			0
$791$	1.98224	+	2.98187i	0.0704802	+	0.106023i
$792$		0			0
$793$	3.02036	+	9.06172i	0.107256	+	0.321791i
$794$		0			0
$795$	−13.9475	−	1.59061i	−0.494668	−	0.0564130i
$796$		0			0
$797$	−13.7530	+	0.520808i	−0.487158	+	0.0184480i	−0.280279	−	0.959919i	$-0.590427\pi$
$797$	−13.7530	+	0.520808i	−0.487158	+	0.0184480i	−0.206879	+	0.978367i	$0.566331\pi$
$798$		0			0
$799$	−1.33836	+	23.5474i	−0.0473478	+	0.833048i
$800$		0			0
$801$	−9.36435	−	15.3137i	−0.330873	−	0.541085i
$802$		0			0
$803$	0.594301	−	31.3988i	0.0209724	−	1.10804i
$804$		0			0
$805$	−6.60975	+	2.34298i	−0.232963	+	0.0825793i
$806$		0			0
$807$	−24.8982	−	23.5233i	−0.876458	−	0.828058i
$808$		0			0
$809$	−1.40672	+	0.214623i	−0.0494578	+	0.00754575i	−0.175506	−	0.984478i	$-0.556156\pi$
$809$	−1.40672	+	0.214623i	−0.0494578	+	0.00754575i	0.126048	+	0.992024i	$0.459771\pi$
$810$		0			0
$811$	4.27754	+	9.19845i	0.150205	+	0.323001i	0.967356	−	0.253422i	$-0.0815562\pi$
$811$	4.27754	+	9.19845i	0.150205	+	0.323001i	−0.817151	+	0.576424i	$0.804448\pi$
$812$		0			0
$813$	−3.38346	−	0.128127i	−0.118663	−	0.00449361i
$814$		0			0
$815$	−3.03347	+	3.33500i	−0.106258	+	0.116820i
$816$		0			0
$817$	−7.92594	−	6.42659i	−0.277294	−	0.224838i
$818$		0			0
$819$	1.55214	+	1.16400i	0.0542363	+	0.0406736i
$820$		0			0
$821$	16.2063	−	3.10424i	0.565605	−	0.108339i	0.102645	−	0.994718i	$-0.467269\pi$
$821$	16.2063	−	3.10424i	0.565605	−	0.108339i	0.462960	+	0.886379i	$0.346787\pi$
$822$		0			0
$823$	−30.9194	−	5.92245i	−1.07778	−	0.206444i	−0.381613	−	0.924322i	$-0.624631\pi$
$823$	−30.9194	−	5.92245i	−1.07778	−	0.206444i	−0.696168	+	0.717879i	$0.745113\pi$
$824$		0			0
$825$	1.27098	+	6.01683i	0.0442500	+	0.209479i
$826$		0			0
$827$	25.0369	−	7.82180i	0.870617	−	0.271991i	0.169927	−	0.985457i	$-0.445647\pi$
$827$	25.0369	−	7.82180i	0.870617	−	0.271991i	0.700690	+	0.713466i	$0.252876\pi$
$828$		0			0
$829$	−25.7985	+	24.3738i	−0.896019	+	0.846538i	−0.988815	−	0.149147i	$-0.952347\pi$
$829$	−25.7985	+	24.3738i	−0.896019	+	0.846538i	0.0927961	+	0.995685i	$0.470420\pi$
$830$		0			0
$831$	−2.83958	+	8.51934i	−0.0985039	+	0.295533i
$832$		0			0
$833$	−19.2454	−	26.7009i	−0.666812	−	0.925132i
$834$		0			0
$835$	−8.37923	+	21.3864i	−0.289975	+	0.740106i
$836$		0			0
$837$	9.95178	+	13.8070i	0.343984	+	0.477241i
$838$		0			0
$839$	−7.14261	+	21.4293i	−0.246590	+	0.739823i	0.750305	+	0.661091i	$0.229906\pi$
$839$	−7.14261	+	21.4293i	−0.246590	+	0.739823i	−0.996896	+	0.0787320i	$0.974913\pi$
$840$		0			0
$841$	−16.2964	+	15.3965i	−0.561946	+	0.530914i
$842$		0			0
$843$	25.3118	−	7.90770i	0.871786	−	0.272356i
$844$		0			0
$845$	−2.98826	−	14.1464i	−0.102799	−	0.486651i
$846$		0			0
$847$	−3.58711	−	0.687093i	−0.123255	−	0.0236088i
$848$		0			0
$849$	−13.4870	+	2.58336i	−0.462872	+	0.0886607i
$850$		0			0
$851$	2.70845	+	2.03116i	0.0928444	+	0.0696272i
$852$		0			0
$853$	−38.3255	−	31.0754i	−1.31224	−	1.06400i	−0.993220	−	0.116253i	$-0.962912\pi$
$853$	−38.3255	−	31.0754i	−1.31224	−	1.06400i	−0.319019	−	0.947748i	$-0.603353\pi$
$854$		0			0
$855$	−2.65571	+	2.91969i	−0.0908232	+	0.0998514i
$856$		0			0
$857$	−8.15586	−	0.308851i	−0.278599	−	0.0105501i	−0.101827	−	0.994802i	$-0.532469\pi$
$857$	−8.15586	−	0.308851i	−0.278599	−	0.0105501i	−0.176771	+	0.984252i	$0.556565\pi$
$858$		0			0
$859$	−21.5277	−	46.2934i	−0.734516	−	1.57951i	−0.812776	−	0.582576i	$-0.802045\pi$
$859$	−21.5277	−	46.2934i	−0.734516	−	1.57951i	0.0782600	−	0.996933i	$-0.475064\pi$
$860$		0			0
$861$	−6.85485	+	1.04584i	−0.233613	+	0.0356422i
$862$		0			0
$863$	34.0244	+	32.1454i	1.15820	+	1.09424i	0.994174	+	0.107788i	$0.0343768\pi$
$863$	34.0244	+	32.1454i	1.15820	+	1.09424i	0.164029	+	0.986455i	$0.447551\pi$
$864$		0			0
$865$	42.3439	−	15.0098i	1.43974	−	0.510348i
$866$		0			0
$867$	0.233055	−	12.3130i	0.00791495	−	0.418172i
$868$		0			0
$869$	−9.88638	−	16.1674i	−0.335372	−	0.548442i
$870$		0			0
$871$	0.579895	−	10.2028i	0.0196490	−	0.345709i
$872$		0			0
$873$	−11.9098	+	0.451006i	−0.403084	+	0.0152642i
$874$		0			0
$875$	−9.03750	−	1.03066i	−0.305523	−	0.0348425i
$876$		0			0
$877$	−8.78218	−	26.3484i	−0.296553	−	0.889722i	−0.986197	−	0.165574i	$-0.947052\pi$
$877$	−8.78218	−	26.3484i	−0.296553	−	0.889722i	0.689644	−	0.724148i	$-0.257767\pi$
$878$		0			0
$879$	−1.28587	−	1.93433i	−0.0433713	−	0.0652433i
$880$		0			0
$881$	10.0778	+	40.1322i	0.339531	+	1.35209i	0.865211	+	0.501407i	$0.167184\pi$
$881$	10.0778	+	40.1322i	0.339531	+	1.35209i	−0.525681	+	0.850682i	$0.676189\pi$
$882$		0			0
$883$	−25.3350	+	45.1888i	−0.852592	+	1.52072i	0.00113203	+	0.999999i	$0.499640\pi$
$883$	−25.3350	+	45.1888i	−0.852592	+	1.52072i	−0.853724	+	0.520725i	$0.825662\pi$
$884$		0			0
$885$	−2.54496	+	12.0478i	−0.0855480	+	0.404983i
$886$		0			0
$887$	9.91532	+	10.1048i	0.332924	+	0.339285i	0.859775	−	0.510673i	$-0.170604\pi$
$887$	9.91532	+	10.1048i	0.332924	+	0.339285i	−0.526852	+	0.849957i	$0.676628\pi$
$888$		0			0
$889$	−3.24550	+	5.30745i	−0.108851	+	0.178006i
$890$		0			0
$891$	−1.33641	+	10.0288i	−0.0447713	+	0.335977i
$892$		0			0
$893$	−7.34862	−	4.68702i	−0.245912	−	0.156845i
$894$		0			0
$895$	−17.9696	−	12.4422i	−0.600657	−	0.415896i
$896$		0			0
$897$	11.8214	+	10.3506i	0.394704	+	0.345596i
$898$		0			0
$899$	6.36452	−	4.40681i	0.212269	−	0.146975i
$900$		0			0
$901$	−2.82360	−	29.7504i	−0.0940677	−	0.991128i
$902$		0			0
$903$	2.11297	−	5.03366i	0.0703151	−	0.167510i
$904$		0			0
$905$	−4.04917	−	0.935721i	−0.134599	−	0.0311044i
$906$		0			0
$907$	−8.11461	+	5.17558i	−0.269441	+	0.171852i	−0.665554	−	0.746350i	$-0.731805\pi$
$907$	−8.11461	+	5.17558i	−0.269441	+	0.171852i	0.396113	+	0.918202i	$0.370359\pi$
$908$		0			0
$909$	2.28282	+	6.07258i	0.0757165	+	0.201415i
$910$		0			0
$911$	−11.3722	−	14.5810i	−0.376778	−	0.483090i	0.562233	−	0.826979i	$-0.309943\pi$
$911$	−11.3722	−	14.5810i	−0.376778	−	0.483090i	−0.939010	+	0.343889i	$0.888256\pi$
$912$		0			0
$913$	−5.89745	−	20.2135i	−0.195177	−	0.668968i
$914$		0			0
$915$	−5.08393	−	9.06794i	−0.168069	−	0.299777i
$916$		0			0
$917$	5.67826	+	3.04373i	0.187513	+	0.100513i
$918$		0			0
$919$	−2.56133	+	3.55357i	−0.0844904	+	0.117222i	−0.851361	−	0.524580i	$-0.824222\pi$
$919$	−2.56133	+	3.55357i	−0.0844904	+	0.117222i	0.766871	+	0.641802i	$0.221813\pi$
$920$		0			0
$921$	−16.0590	+	9.40726i	−0.529163	+	0.309980i
$922$		0			0
$923$	3.30455	−	8.79048i	0.108770	−	0.289342i
$924$		0			0
$925$	0.538440	+	1.05182i	0.0177038	+	0.0345837i
$926$		0			0
$927$	7.99333	−	9.48550i	0.262535	−	0.311545i
$928$		0			0
$929$	−26.6950	+	20.0195i	−0.875833	+	0.656817i	−0.940019	−	0.341121i	$-0.889193\pi$
$929$	−26.6950	+	20.0195i	−0.875833	+	0.656817i	0.0641861	+	0.997938i	$0.479555\pi$
$930$		0			0
$931$	12.0851	−	1.37822i	0.396075	−	0.0451692i
$932$		0			0
$933$	−1.75943	+	7.00647i	−0.0576013	+	0.229382i
$934$		0			0
$935$	20.5483	−	9.08662i	0.672001	−	0.297164i
$936$		0			0
$937$	16.9586	−	13.7505i	0.554013	−	0.449210i	−0.311393	−	0.950281i	$-0.600795\pi$
$937$	16.9586	−	13.7505i	0.554013	−	0.449210i	0.865406	+	0.501071i	$0.167061\pi$
$938$		0			0
$939$	−1.93492	+	11.2499i	−0.0631437	+	0.367128i
$940$		0			0
$941$	−36.0824	+	36.7718i	−1.17625	+	1.19873i	−0.200538	+	0.979686i	$0.564269\pi$
$941$	−36.0824	+	36.7718i	−1.17625	+	1.19873i	−0.975716	+	0.219042i	$0.929707\pi$
$942$		0			0
$943$	36.0898	−	2.73727i	1.17525	−	0.0891377i
$944$		0			0
$945$	−6.73901	−	3.29035i	−0.219220	−	0.107035i
$946$		0			0
$947$	36.3554	−	19.4877i	1.18139	−	0.633265i	0.240064	−	0.970757i	$-0.422832\pi$
$947$	36.3554	−	19.4877i	1.18139	−	0.633265i	0.941328	+	0.337492i	$0.109579\pi$
$948$		0			0
$949$	−4.74715	−	27.6007i	−0.154099	−	0.895956i
$950$		0			0
$951$	−0.280199	−	4.92988i	−0.00908607	−	0.159862i
$952$		0			0
$953$	−10.7434	−	12.7490i	−0.348014	−	0.412980i	0.562277	−	0.826949i	$-0.309925\pi$
$953$	−10.7434	−	12.7490i	−0.348014	−	0.412980i	−0.910291	+	0.413969i	$0.864142\pi$
$954$		0			0
$955$	0.101727	+	5.37457i	0.00329182	+	0.173917i
$956$		0			0
$957$	8.47192	+	1.29256i	0.273858	+	0.0417824i
$958$		0			0
$959$	0.663590	−	6.99180i	0.0214284	−	0.225777i
$960$		0			0
$961$	−19.6737	+	9.60574i	−0.634635	+	0.309862i
$962$		0			0
$963$	−0.682372	−	0.241883i	−0.0219891	−	0.00779456i
$964$		0			0
$965$	−26.9427	−	7.31045i	−0.867317	−	0.235332i
$966$		0			0
$967$	36.7167	−	32.1485i	1.18073	−	1.03383i	0.182007	−	0.983297i	$-0.441741\pi$
$967$	36.7167	−	32.1485i	1.18073	−	1.03383i	0.998723	−	0.0505292i	$-0.0160908\pi$
$968$		0			0
$969$	11.2486	+	6.58936i	0.361358	+	0.211681i
$970$		0			0
$971$	9.78561	−	2.26135i	0.314035	−	0.0725703i	−0.0651954	−	0.997873i	$-0.520767\pi$
$971$	9.78561	−	2.26135i	0.314035	−	0.0725703i	0.379230	+	0.925302i	$0.376189\pi$
$972$		0			0
$973$	−5.50503	+	2.18924i	−0.176483	+	0.0701839i
$974$		0			0
$975$	2.12263	+	5.05668i	0.0679786	+	0.161943i
$976$		0			0
$977$	−28.5056	−	31.3391i	−0.911974	−	1.00263i	−0.999979	−	0.00650780i	$-0.997928\pi$
$977$	−28.5056	−	31.3391i	−0.911974	−	1.00263i	0.0880044	−	0.996120i	$-0.471951\pi$
$978$		0			0
$979$	−35.0891	−	13.9542i	−1.12145	−	0.445979i
$980$		0			0
$981$	9.53096	+	2.97758i	0.304300	+	0.0950668i
$982$		0			0
$983$	−14.9150	+	22.4366i	−0.475716	+	0.715618i	−0.989854	−	0.142090i	$-0.954618\pi$
$983$	−14.9150	+	22.4366i	−0.475716	+	0.715618i	0.514138	+	0.857707i	$0.328112\pi$
$984$		0			0
$985$	7.29276	+	0.553126i	0.232367	+	0.0176241i
$986$		0			0
$987$	1.30605	−	4.47649i	0.0415722	−	0.142488i
$988$		0			0
$989$	−12.9842	+	25.3642i	−0.412875	+	0.806536i
$990$		0			0
$991$	−14.3058	+	18.3423i	−0.454437	+	0.582663i	−0.959955	−	0.280153i	$-0.909615\pi$
$991$	−14.3058	+	18.3423i	−0.454437	+	0.582663i	0.505518	+	0.862816i	$0.331301\pi$
$992$		0			0
$993$	−22.3478	+	6.06368i	−0.709185	+	0.192425i
$994$		0			0
$995$	0.213238	−	0.458549i	0.00676011	−	0.0145370i
$996$		0			0
$997$	−4.52407	−	2.00058i	−0.143279	−	0.0633591i	0.331548	−	0.943438i	$-0.392429\pi$
$997$	−4.52407	−	2.00058i	−0.143279	−	0.0633591i	−0.474827	+	0.880079i	$0.657489\pi$
$998$		0			0
$999$	0.478216	+	3.58866i	0.0151301	+	0.113540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.e.a.9.5	✓	1148
167.130	even	83	inner	668.2.e.a.297.5	yes	1148

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.e.a.9.5	✓	1148	1.1	even	1	trivial
668.2.e.a.297.5	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)

\(f(q)\)	\(=\)	\(q+(-0.178407 - 1.33882i) q^{3} +(-1.62557 - 0.718841i) q^{5} +(-0.315447 + 0.678340i) q^{7} +(1.13471 - 0.307883i) q^{9} +O(q^{10})\)	\(q+(-0.178407 - 1.33882i) q^{3} +(-1.62557 - 0.718841i) q^{5} +(-0.315447 + 0.678340i) q^{7} +(1.13471 - 0.307883i) q^{9} +(1.52116 - 1.95037i) q^{11} +(1.00511 - 1.96345i) q^{13} +(-0.672384 + 2.30459i) q^{15} +(-5.09594 - 0.386506i) q^{17} +(1.04555 - 1.57282i) q^{19} +(0.964452 + 0.301306i) q^{21} +(-4.90068 - 1.94890i) q^{23} +(-1.23861 - 1.36174i) q^{25} +(-2.18295 - 5.20038i) q^{27} +(-2.38370 + 0.947953i) q^{29} +(-2.94022 + 0.679454i) q^{31} +(-2.88258 - 1.68859i) q^{33} +(1.00040 - 0.875933i) q^{35} +(-0.619516 - 0.168095i) q^{37} +(-2.80803 - 0.995372i) q^{39} +(-6.16684 + 3.01098i) q^{41} +(0.510488 - 5.37867i) q^{43} +(-2.06587 - 0.315188i) q^{45} +(-0.0873353 - 4.61420i) q^{47} +(4.15014 + 4.92488i) q^{49} +(0.391691 + 6.89149i) q^{51} +(0.991179 + 5.76288i) q^{53} +(-3.87475 + 2.07700i) q^{55} +(-2.29226 - 1.11920i) q^{57} +(5.11457 - 0.387920i) q^{59} +(-3.03294 + 3.09088i) q^{61} +(-0.149091 + 0.866838i) q^{63} +(-3.04530 + 2.46922i) q^{65} +(4.23717 - 1.87371i) q^{67} +(-1.73491 + 6.90882i) q^{69} +(4.23010 - 0.482409i) q^{71} +(10.1577 - 7.61759i) q^{73} +(-1.60214 + 1.90122i) q^{75} +(0.843169 + 1.64710i) q^{77} +(2.69600 - 7.17167i) q^{79} +(-3.52945 + 2.06753i) q^{81} +(4.97769 - 6.90601i) q^{83} +(8.00597 + 4.29146i) q^{85} +(1.69441 + 3.02223i) q^{87} +(-4.27601 - 14.6560i) q^{89} +(1.01483 + 1.30118i) q^{91} +(1.43422 + 3.81520i) q^{93} +(-2.83023 + 1.80515i) q^{95} +(-9.87660 - 2.28238i) q^{97} +(1.12558 - 2.68144i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1148 q - 2 q^{5} - 14 q^{9}+O(q^{10}) \) 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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