LMFDB - Embedded newform 756.2.ck.a.605.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5, 15]))

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

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

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ck (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			605.1
Character	$\chi$	$=$	756.605
Dual form			756.2.ck.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70107 + 0.326131i) q^{3} +(-0.752649 - 4.26848i) q^{5} +(-2.02371 + 1.70429i) q^{7} +(2.78728 - 1.10954i) q^{9} +O(q^{10})$	\(q+(-1.70107 + 0.326131i) q^{3} +(-0.752649 - 4.26848i) q^{5} +(-2.02371 + 1.70429i) q^{7} +(2.78728 - 1.10954i) q^{9} +(4.32943 + 0.763395i) q^{11} +(-1.92336 - 2.29217i) q^{13} +(2.67239 + 7.01553i) q^{15} -2.90177 q^{17} -7.24080i q^{19} +(2.88665 - 3.55911i) q^{21} +(0.613310 + 0.730915i) q^{23} +(-12.9550 + 4.71524i) q^{25} +(-4.37950 + 2.79643i) q^{27} +(-1.81160 + 2.15898i) q^{29} +(-3.48739 + 9.58153i) q^{31} +(-7.61363 + 0.113372i) q^{33} +(8.79786 + 7.35545i) q^{35} +(-1.55745 + 2.69759i) q^{37} +(4.01932 + 3.27188i) q^{39} +(-1.60343 + 1.34544i) q^{41} +(-6.51659 + 2.37185i) q^{43} +(-6.83391 - 11.0624i) q^{45} +(-6.33367 + 2.30527i) q^{47} +(1.19081 - 6.89797i) q^{49} +(4.93612 - 0.946358i) q^{51} +(-3.91722 - 2.26161i) q^{53} -19.0547i q^{55} +(2.36145 + 12.3171i) q^{57} +(-2.94386 + 2.47019i) q^{59} +(0.378045 + 1.03867i) q^{61} +(-3.74966 + 6.99571i) q^{63} +(-8.33648 + 9.93503i) q^{65} +(-2.23922 - 12.6992i) q^{67} +(-1.28166 - 1.04332i) q^{69} +(1.85714 - 1.07222i) q^{71} +(3.23289 - 1.86651i) q^{73} +(20.4996 - 12.2460i) q^{75} +(-10.0626 + 5.83370i) q^{77} +(1.72657 - 9.79189i) q^{79} +(6.53783 - 6.18521i) q^{81} +(12.4261 + 10.4268i) q^{83} +(2.18402 + 12.3862i) q^{85} +(2.37755 - 4.26340i) q^{87} +2.59484 q^{89} +(7.79884 + 1.36073i) q^{91} +(2.80746 - 17.4362i) q^{93} +(-30.9073 + 5.44978i) q^{95} +(1.09651 + 3.01263i) q^{97} +(12.9143 - 2.67589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.70107	+	0.326131i	−0.982113	+	0.188292i
$3$	−1.70107	+	0.326131i	−0.982113	+	0.188292i
$4$		0			0
$5$	−0.752649	−	4.26848i	−0.336595	−	1.90892i	−0.410885	−	0.911687i	$-0.634780\pi$
$5$	−0.752649	−	4.26848i	−0.336595	−	1.90892i	0.0742902	−	0.997237i	$-0.476331\pi$
$6$		0			0
$7$	−2.02371	+	1.70429i	−0.764891	+	0.644160i
$7$	−2.02371	+	1.70429i	−0.764891	+	0.644160i
$8$		0			0
$9$	2.78728	−	1.10954i	0.929092	−	0.369848i
$10$		0			0
$11$	4.32943	+	0.763395i	1.30537	+	0.230172i	0.782720	−	0.622374i	$-0.213832\pi$
$11$	4.32943	+	0.763395i	1.30537	+	0.230172i	0.522652	+	0.852546i	$0.324943\pi$
$12$		0			0
$13$	−1.92336	−	2.29217i	−0.533444	−	0.635734i	0.430260	−	0.902705i	$-0.358422\pi$
$13$	−1.92336	−	2.29217i	−0.533444	−	0.635734i	−0.963705	+	0.266971i	$0.913977\pi$
$14$		0			0
$15$	2.67239	+	7.01553i	0.690009	+	1.81140i
$16$		0			0
$17$	−2.90177			−0.703783			−0.351892	−	0.936041i	$-0.614461\pi$
$17$	−2.90177			−0.703783			−0.351892	+	0.936041i	$0.614461\pi$
$18$		0			0
$19$		−	7.24080i		−	1.66115i	−0.556904	−	0.830577i	$-0.688011\pi$
$19$		−	7.24080i		−	1.66115i	0.556904	−	0.830577i	$-0.311989\pi$
$20$		0			0
$21$	2.88665	−	3.55911i	0.629919	−	0.776661i
$22$		0			0
$23$	0.613310	+	0.730915i	0.127884	+	0.152406i	0.826187	−	0.563396i	$-0.190506\pi$
$23$	0.613310	+	0.730915i	0.127884	+	0.152406i	−0.698303	+	0.715802i	$0.746061\pi$
$24$		0			0
$25$	−12.9550	+	4.71524i	−2.59100	+	0.943047i
$26$		0			0
$27$	−4.37950	+	2.79643i	−0.842835	+	0.538173i
$28$		0			0
$29$	−1.81160	+	2.15898i	−0.336406	+	0.400913i	−0.907555	−	0.419933i	$-0.862054\pi$
$29$	−1.81160	+	2.15898i	−0.336406	+	0.400913i	0.571149	+	0.820847i	$0.306498\pi$
$30$		0			0
$31$	−3.48739	+	9.58153i	−0.626354	+	1.72089i	0.0645186	+	0.997917i	$0.479449\pi$
$31$	−3.48739	+	9.58153i	−0.626354	+	1.72089i	−0.690872	+	0.722977i	$0.742773\pi$
$32$		0			0
$33$	−7.61363	+	0.113372i	−1.32536	+	0.0197355i
$34$		0			0
$35$	8.79786	+	7.35545i	1.48711	+	1.24330i
$36$		0			0
$37$	−1.55745	+	2.69759i	−0.256044	+	0.443481i	−0.965178	−	0.261592i	$-0.915752\pi$
$37$	−1.55745	+	2.69759i	−0.256044	+	0.443481i	0.709135	+	0.705073i	$0.249086\pi$
$38$		0			0
$39$	4.01932	+	3.27188i	0.643606	+	0.523920i
$40$		0			0
$41$	−1.60343	+	1.34544i	−0.250414	+	0.210122i	−0.759351	−	0.650682i	$-0.774483\pi$
$41$	−1.60343	+	1.34544i	−0.250414	+	0.210122i	0.508936	+	0.860804i	$0.330039\pi$
$42$		0			0
$43$	−6.51659	+	2.37185i	−0.993771	+	0.361703i	−0.787179	−	0.616724i	$-0.788459\pi$
$43$	−6.51659	+	2.37185i	−0.993771	+	0.361703i	−0.206592	+	0.978427i	$0.566237\pi$
$44$		0			0
$45$	−6.83391	−	11.0624i	−1.01874	−	1.64908i
$46$		0			0
$47$	−6.33367	+	2.30527i	−0.923861	+	0.336258i	−0.759773	−	0.650188i	$-0.774690\pi$
$47$	−6.33367	+	2.30527i	−0.923861	+	0.336258i	−0.164087	+	0.986446i	$0.552468\pi$
$48$		0			0
$49$	1.19081	−	6.89797i	0.170116	−	0.985424i
$50$		0			0
$51$	4.93612	−	0.946358i	0.691195	−	0.132517i
$52$		0			0
$53$	−3.91722	−	2.26161i	−0.538071	−	0.310655i	0.206226	−	0.978504i	$-0.433882\pi$
$53$	−3.91722	−	2.26161i	−0.538071	−	0.310655i	−0.744297	+	0.667849i	$0.767215\pi$
$54$		0			0
$55$		−	19.0547i		−	2.56933i
$56$		0			0
$57$	2.36145	+	12.3171i	0.312782	+	1.63144i
$58$		0			0
$59$	−2.94386	+	2.47019i	−0.383257	+	0.321591i	−0.813980	−	0.580893i	$-0.802703\pi$
$59$	−2.94386	+	2.47019i	−0.383257	+	0.321591i	0.430722	+	0.902485i	$0.358259\pi$
$60$		0			0
$61$	0.378045	+	1.03867i	0.0484037	+	0.132988i	0.961539	−	0.274669i	$-0.0885682\pi$
$61$	0.378045	+	1.03867i	0.0484037	+	0.132988i	−0.913135	+	0.407657i	$0.866346\pi$
$62$		0			0
$63$	−3.74966	+	6.99571i	−0.472413	+	0.881377i
$64$		0			0
$65$	−8.33648	+	9.93503i	−1.03401	+	1.23229i
$66$		0			0
$67$	−2.23922	−	12.6992i	−0.273564	−	1.55146i	−0.743486	−	0.668752i	$-0.766829\pi$
$67$	−2.23922	−	12.6992i	−0.273564	−	1.55146i	0.469921	−	0.882708i	$-0.344282\pi$
$68$		0			0
$69$	−1.28166	−	1.04332i	−0.154293	−	0.125601i
$70$		0			0
$71$	1.85714	−	1.07222i	0.220402	−	0.127249i	−0.385735	−	0.922610i	$-0.626052\pi$
$71$	1.85714	−	1.07222i	0.220402	−	0.127249i	0.606136	+	0.795361i	$0.292719\pi$
$72$		0			0
$73$	3.23289	−	1.86651i	0.378381	−	0.218458i	−0.298733	−	0.954337i	$-0.596564\pi$
$73$	3.23289	−	1.86651i	0.378381	−	0.218458i	0.677113	+	0.735879i	$0.263231\pi$
$74$		0			0
$75$	20.4996	−	12.2460i	2.36709	−	1.41404i
$76$		0			0
$77$	−10.0626	+	5.83370i	−1.14673	+	0.664811i
$78$		0			0
$79$	1.72657	−	9.79189i	0.194255	−	1.10167i	−0.719221	−	0.694781i	$-0.755501\pi$
$79$	1.72657	−	9.79189i	0.194255	−	1.10167i	0.913476	−	0.406893i	$-0.133388\pi$
$80$		0			0
$81$	6.53783	−	6.18521i	0.726425	−	0.687245i
$82$		0			0
$83$	12.4261	+	10.4268i	1.36395	+	1.14449i	0.974742	+	0.223336i	$0.0716947\pi$
$83$	12.4261	+	10.4268i	1.36395	+	1.14449i	0.389205	+	0.921151i	$0.372750\pi$
$84$		0			0
$85$	2.18402	+	12.3862i	0.236890	+	1.34347i
$86$		0			0
$87$	2.37755	−	4.26340i	0.254900	−	0.457085i
$88$		0			0
$89$	2.59484			0.275052			0.137526	−	0.990498i	$-0.456085\pi$
$89$	2.59484			0.275052			0.137526	+	0.990498i	$0.456085\pi$
$90$		0			0
$91$	7.79884	+	1.36073i	0.817541	+	0.142644i
$92$		0			0
$93$	2.80746	−	17.4362i	0.291120	−	1.80805i
$94$		0			0
$95$	−30.9073	+	5.44978i	−3.17102	+	0.559136i
$96$		0			0
$97$	1.09651	+	3.01263i	0.111334	+	0.305887i	0.982829	−	0.184516i	$-0.0590719\pi$
$97$	1.09651	+	3.01263i	0.111334	+	0.305887i	−0.871496	+	0.490403i	$0.836850\pi$
$98$		0			0
$99$	12.9143	−	2.67589i	1.29794	−	0.268937i
$100$		0			0
$101$	−1.88932	−	1.58532i	−0.187994	−	0.157746i	0.543933	−	0.839128i	$-0.316934\pi$
$101$	−1.88932	−	1.58532i	−0.187994	−	0.157746i	−0.731927	+	0.681383i	$0.761379\pi$
$102$		0			0
$103$	−13.6220	+	2.40193i	−1.34222	+	0.236669i	−0.798194	−	0.602401i	$-0.794211\pi$
$103$	−13.6220	+	2.40193i	−1.34222	+	0.236669i	−0.544023	+	0.839070i	$0.683100\pi$
$104$		0			0
$105$	−17.3646	−	9.64287i	−1.69461	−	0.941048i
$106$		0			0
$107$	−0.786735	+	0.454221i	−0.0760565	+	0.0439112i	−0.537546	−	0.843234i	$-0.680649\pi$
$107$	−0.786735	+	0.454221i	−0.0760565	+	0.0439112i	0.461489	+	0.887146i	$0.347315\pi$
$108$		0			0
$109$	−1.61722	+	2.80111i	−0.154902	+	0.268298i	−0.933023	−	0.359816i	$-0.882839\pi$
$109$	−1.61722	+	2.80111i	−0.154902	+	0.268298i	0.778121	+	0.628114i	$0.216173\pi$
$110$		0			0
$111$	1.76957	−	5.09672i	0.167960	−	0.483759i
$112$		0			0
$113$	4.89305	−	13.4435i	0.460299	−	1.26466i	−0.464962	−	0.885331i	$-0.653932\pi$
$113$	4.89305	−	13.4435i	0.460299	−	1.26466i	0.925261	−	0.379331i	$-0.123846\pi$
$114$		0			0
$115$	2.65829	−	3.16803i	0.247887	−	0.295420i
$116$		0			0
$117$	−7.90420	−	4.25487i	−0.730744	−	0.393363i
$118$		0			0
$119$	5.87235	−	4.94545i	0.538317	−	0.453349i
$120$		0			0
$121$	7.82456	+	2.84791i	0.711324	+	0.258901i
$122$		0			0
$123$	2.28876	−	2.81162i	0.206371	−	0.253515i
$124$		0			0
$125$	19.0417	+	32.9811i	1.70314	+	2.94992i
$126$		0			0
$127$	−0.308792	+	0.534844i	−0.0274009	+	0.0474597i	−0.879401	−	0.476082i	$-0.842056\pi$
$127$	−0.308792	+	0.534844i	−0.0274009	+	0.0474597i	0.852000	+	0.523542i	$0.175390\pi$
$128$		0			0
$129$	10.3116	−	6.15994i	0.907890	−	0.542352i
$130$		0			0
$131$	−2.14776	+	1.80218i	−0.187651	+	0.157458i	−0.731773	−	0.681548i	$-0.761307\pi$
$131$	−2.14776	+	1.80218i	−0.187651	+	0.157458i	0.544123	+	0.839006i	$0.316863\pi$
$132$		0			0
$133$	12.3404	+	14.6533i	1.07005	+	1.27060i
$134$		0			0
$135$	15.2327	+	16.5891i	1.31102	+	1.42776i
$136$		0			0
$137$	−0.761525	−	2.09227i	−0.0650615	−	0.178755i	0.902902	−	0.429847i	$-0.141433\pi$
$137$	−0.761525	−	2.09227i	−0.0650615	−	0.178755i	−0.967963	+	0.251092i	$0.919210\pi$
$138$		0			0
$139$	3.14112	−	0.553864i	0.266426	−	0.0469781i	−0.0388391	−	0.999245i	$-0.512366\pi$
$139$	3.14112	−	0.553864i	0.266426	−	0.0469781i	0.305265	+	0.952267i	$0.401255\pi$
$140$		0			0
$141$	10.0222	−	5.98703i	0.844021	−	0.504199i
$142$		0			0
$143$	−6.57722	−	11.3921i	−0.550015	−	0.952653i
$144$		0			0
$145$	10.5791	+	6.10784i	0.878546	+	0.507229i
$146$		0			0
$147$	0.223986	+	12.1223i	0.0184740	+	0.999829i
$148$		0			0
$149$	−1.48706	+	4.08565i	−0.121824	+	0.334710i	−0.985582	−	0.169197i	$-0.945882\pi$
$149$	−1.48706	+	4.08565i	−0.121824	+	0.334710i	0.863758	+	0.503907i	$0.168105\pi$
$150$		0			0
$151$	−1.64956	+	9.35512i	−0.134239	+	0.761309i	0.841147	+	0.540806i	$0.181881\pi$
$151$	−1.64956	+	9.35512i	−0.134239	+	0.761309i	−0.975386	+	0.220503i	$0.929230\pi$
$152$		0			0
$153$	−8.08805	+	3.21964i	−0.653880	+	0.260293i
$154$		0			0
$155$	43.5234	+	7.67434i	3.49588	+	0.616418i
$156$		0			0
$157$	−7.53512	−	8.98000i	−0.601368	−	0.716682i	0.376380	−	0.926465i	$-0.377169\pi$
$157$	−7.53512	−	8.98000i	−0.601368	−	0.716682i	−0.977748	+	0.209783i	$0.932724\pi$
$158$		0			0
$159$	7.40104	+	2.56962i	0.586940	+	0.203784i
$160$		0			0
$161$	−2.48685	−	0.433903i	−0.195991	−	0.0341964i
$162$		0			0
$163$	5.42078	+	9.38907i	0.424588	+	0.735408i	0.996382	−	0.0849891i	$-0.0270855\pi$
$163$	5.42078	+	9.38907i	0.424588	+	0.735408i	−0.571794	+	0.820397i	$0.693752\pi$
$164$		0			0
$165$	6.21431	+	32.4133i	0.483784	+	2.52337i
$166$		0			0
$167$	8.96909	+	3.26448i	0.694049	+	0.252613i	0.664868	−	0.746961i	$-0.268488\pi$
$167$	8.96909	+	3.26448i	0.694049	+	0.252613i	0.0291811	+	0.999574i	$0.490710\pi$
$168$		0			0
$169$	0.702691	−	3.98516i	0.0540532	−	0.306551i
$170$		0			0
$171$	−8.03398	−	20.1821i	−0.614374	−	1.54337i
$172$		0			0
$173$	−2.14560	−	1.80038i	−0.163127	−	0.136880i	0.557570	−	0.830130i	$-0.311734\pi$
$173$	−2.14560	−	1.80038i	−0.163127	−	0.136880i	−0.720697	+	0.693250i	$0.756178\pi$
$174$		0			0
$175$	18.1811	−	31.6213i	1.37436	−	2.39035i
$176$		0			0
$177$	4.20210	−	5.16205i	0.315849	−	0.388003i
$178$		0			0
$179$			5.74007i			0.429033i	0.976720	+	0.214516i	$0.0688176\pi$
$179$			5.74007i			0.429033i	−0.976720	+	0.214516i	$0.931182\pi$
$180$		0			0
$181$	−12.3552	−	7.13329i	−0.918356	−	0.530213i	−0.0352458	−	0.999379i	$-0.511221\pi$
$181$	−12.3552	−	7.13329i	−0.918356	−	0.530213i	−0.883110	+	0.469166i	$0.844555\pi$
$182$		0			0
$183$	−0.981824	−	1.64356i	−0.0725785	−	0.121495i
$184$		0			0
$185$	12.6868	+	4.61762i	0.932753	+	0.339494i
$186$		0			0
$187$	−12.5630	−	2.21520i	−0.918699	−	0.161991i
$188$		0			0
$189$	4.09692	−	13.1231i	0.298007	−	0.954564i
$190$		0			0
$191$	−12.4959	−	2.20336i	−0.904172	−	0.159430i	−0.297816	−	0.954623i	$-0.596258\pi$
$191$	−12.4959	−	2.20336i	−0.904172	−	0.159430i	−0.606356	+	0.795193i	$0.707369\pi$
$192$		0			0
$193$	−18.1759	−	6.61549i	−1.30833	−	0.476193i	−0.408630	−	0.912700i	$-0.633993\pi$
$193$	−18.1759	−	6.61549i	−1.30833	−	0.476193i	−0.899701	+	0.436507i	$0.856215\pi$
$194$		0			0
$195$	10.9408	−	19.6190i	0.783488	−	1.40494i
$196$		0			0
$197$	−16.8427	−	9.72416i	−1.20000	−	0.692818i	−0.239442	−	0.970911i	$-0.576964\pi$
$197$	−16.8427	−	9.72416i	−1.20000	−	0.692818i	−0.960554	+	0.278093i	$0.910298\pi$
$198$		0			0
$199$			2.05689i			0.145809i	0.997339	+	0.0729045i	$0.0232268\pi$
$199$			2.05689i			0.145809i	−0.997339	+	0.0729045i	$0.976773\pi$
$200$		0			0
$201$	7.95069	+	20.8720i	0.560798	+	1.47220i
$202$		0			0
$203$	−0.0133679	−	7.45665i	−0.000938244	−	0.523354i
$204$		0			0
$205$	6.94981	+	5.83159i	0.485396	+	0.407296i
$206$		0			0
$207$	2.52045	+	1.35677i	0.175183	+	0.0943019i
$208$		0			0
$209$	5.52759	−	31.3485i	0.382352	−	2.16842i
$210$		0			0
$211$	−15.5379	−	5.65535i	−1.06968	−	0.389330i	−0.253620	−	0.967304i	$-0.581621\pi$
$211$	−15.5379	−	5.65535i	−1.06968	−	0.389330i	−0.816055	+	0.577974i	$0.803844\pi$
$212$		0			0
$213$	−2.80944	+	2.42959i	−0.192499	+	0.166473i
$214$		0			0
$215$	15.0289	+	26.0308i	1.02496	+	1.77529i
$216$		0			0
$217$	−9.27220	−	25.3338i	−0.629438	−	1.71977i
$218$		0			0
$219$	−4.89064	+	4.22940i	−0.330479	+	0.285797i
$220$		0			0
$221$	5.58115	+	6.65136i	0.375429	+	0.447419i
$222$		0			0
$223$	−17.4743	−	3.08118i	−1.17016	−	0.206331i	−0.445402	−	0.895331i	$-0.646939\pi$
$223$	−17.4743	−	3.08118i	−1.17016	−	0.206331i	−0.724762	+	0.688999i	$0.758050\pi$
$224$		0			0
$225$	−30.8774	+	27.5168i	−2.05850	+	1.83445i
$226$		0			0
$227$	4.57912	−	25.9695i	0.303927	−	1.72366i	−0.324585	−	0.945856i	$-0.605225\pi$
$227$	4.57912	−	25.9695i	0.303927	−	1.72366i	0.628512	−	0.777800i	$-0.283664\pi$
$228$		0			0
$229$	6.47887	−	17.8006i	0.428136	−	1.17629i	−0.518807	−	0.854891i	$-0.673624\pi$
$229$	6.47887	−	17.8006i	0.428136	−	1.17629i	0.946943	−	0.321402i	$-0.104154\pi$
$230$		0			0
$231$	15.2146	−	13.2052i	1.00104	−	0.868841i
$232$		0			0
$233$	7.05865	+	4.07531i	0.462427	+	0.266983i	0.713064	−	0.701099i	$-0.247307\pi$
$233$	7.05865	+	4.07531i	0.462427	+	0.266983i	−0.250637	+	0.968081i	$0.580640\pi$
$234$		0			0
$235$	14.6070	+	25.3001i	0.952857	+	1.65040i
$236$		0			0
$237$	0.256414	+	17.2198i	0.0166559	+	1.11855i
$238$		0			0
$239$	15.2709	−	2.69267i	0.987792	−	0.174174i	0.343665	−	0.939092i	$-0.388332\pi$
$239$	15.2709	−	2.69267i	0.987792	−	0.174174i	0.644128	+	0.764918i	$0.277221\pi$
$240$		0			0
$241$	−6.27100	−	17.2294i	−0.403951	−	1.10985i	−0.960318	−	0.278909i	$-0.910027\pi$
$241$	−6.27100	−	17.2294i	−0.403951	−	1.10985i	0.556367	−	0.830937i	$-0.312195\pi$
$242$		0			0
$243$	−9.10412	+	12.6537i	−0.584029	+	0.811732i
$244$		0			0
$245$	−30.3401	+	0.108785i	−1.93836	+	0.00695002i
$246$		0			0
$247$	−16.5972	+	13.9267i	−1.05605	+	0.886133i
$248$		0			0
$249$	−24.5382	−	13.6841i	−1.55505	−	0.867196i
$250$		0			0
$251$	2.09345	−	3.62596i	0.132137	−	0.228869i	−0.792363	−	0.610050i	$-0.791149\pi$
$251$	2.09345	−	3.62596i	0.132137	−	0.228869i	0.924500	+	0.381181i	$0.124483\pi$
$252$		0			0
$253$	2.09731	+	3.63264i	0.131856	+	0.228382i
$254$		0			0
$255$	−7.75468	−	20.3575i	−0.485617	−	1.27483i
$256$		0			0
$257$	22.5787	+	8.21799i	1.40842	+	0.512624i	0.930667	−	0.365868i	$-0.119228\pi$
$257$	22.5787	+	8.21799i	1.40842	+	0.512624i	0.477757	+	0.878492i	$0.341450\pi$
$258$		0			0
$259$	−1.44563	−	8.11348i	−0.0898270	−	0.504147i
$260$		0			0
$261$	−2.65395	+	8.02774i	−0.164276	+	0.496905i
$262$		0			0
$263$	10.8318	−	12.9088i	0.667917	−	0.795993i	−0.320582	−	0.947221i	$-0.603878\pi$
$263$	10.8318	−	12.9088i	0.667917	−	0.795993i	0.988499	+	0.151228i	$0.0483229\pi$
$264$		0			0
$265$	−6.70534	+	18.4228i	−0.411906	+	1.13170i
$266$		0			0
$267$	−4.41400	+	0.846257i	−0.270133	+	0.0517901i
$268$		0			0
$269$	13.0831	−	22.6606i	0.797690	−	1.38164i	−0.123427	−	0.992354i	$-0.539389\pi$
$269$	13.0831	−	22.6606i	0.797690	−	1.38164i	0.921117	−	0.389286i	$-0.127278\pi$
$270$		0			0
$271$	−17.1840	+	9.92120i	−1.04385	+	0.602670i	−0.920923	−	0.389745i	$-0.872563\pi$
$271$	−17.1840	+	9.92120i	−1.04385	+	0.602670i	−0.122932	+	0.992415i	$0.539230\pi$
$272$		0			0
$273$	−13.7102	+	0.228738i	−0.829776	+	0.0138439i
$274$		0			0
$275$	−59.6874	+	10.5245i	−3.59928	+	0.634651i
$276$		0			0
$277$	16.7162	+	14.0265i	1.00438	+	0.842773i	0.987585	−	0.157086i	$-0.0502100\pi$
$277$	16.7162	+	14.0265i	1.00438	+	0.842773i	0.0167929	+	0.999859i	$0.494654\pi$
$278$		0			0
$279$	0.910790	+	30.5758i	0.0545276	+	1.83052i
$280$		0			0
$281$	−10.6039	−	29.1339i	−0.632575	−	1.73799i	−0.673882	−	0.738839i	$-0.735374\pi$
$281$	−10.6039	−	29.1339i	−0.632575	−	1.73799i	0.0413070	−	0.999147i	$-0.486848\pi$
$282$		0			0
$283$	−7.29589	+	1.28646i	−0.433695	+	0.0764722i	−0.386234	−	0.922401i	$-0.626224\pi$
$283$	−7.29589	+	1.28646i	−0.433695	+	0.0764722i	−0.0474615	+	0.998873i	$0.515113\pi$
$284$		0			0
$285$	50.7981	−	19.3503i	3.00902	−	1.14621i
$286$		0			0
$287$	0.951869	−	5.45549i	0.0561871	−	0.322028i
$288$		0			0
$289$	−8.57971			−0.504689
$290$		0			0
$291$	−2.84775	−	4.76709i	−0.166938	−	0.279452i
$292$		0			0
$293$	0.184679	+	1.04737i	0.0107891	+	0.0611878i	0.989727	−	0.142970i	$-0.0456654\pi$
$293$	0.184679	+	1.04737i	0.0107891	+	0.0611878i	−0.978938	+	0.204158i	$0.934554\pi$
$294$		0			0
$295$	12.7597	+	10.7066i	0.742896	+	0.623363i
$296$		0			0
$297$	−21.0955	+	8.76364i	−1.22408	+	0.508518i
$298$		0			0
$299$	0.495765	−	2.81162i	0.0286708	−	0.162600i
$300$		0			0
$301$	9.14539	−	15.9061i	0.527132	−	0.916811i
$302$		0			0
$303$	3.73088	+	2.08058i	0.214333	+	0.119526i
$304$		0			0
$305$	4.14901	−	2.39543i	0.237572	−	0.137162i
$306$		0			0
$307$	21.3745	−	12.3406i	1.21991	−	0.704313i	0.255009	−	0.966939i	$-0.417922\pi$
$307$	21.3745	−	12.3406i	1.21991	−	0.704313i	0.964898	+	0.262625i	$0.0845883\pi$
$308$		0			0
$309$	22.3887	−	8.52841i	1.27365	−	0.485164i
$310$		0			0
$311$	3.38324	+	19.1873i	0.191846	+	1.08801i	0.916840	+	0.399256i	$0.130731\pi$
$311$	3.38324	+	19.1873i	0.191846	+	1.08801i	−0.724994	+	0.688755i	$0.758157\pi$
$312$		0			0
$313$	−0.941625	+	1.12219i	−0.0532238	+	0.0634297i	−0.792000	−	0.610522i	$-0.790960\pi$
$313$	−0.941625	+	1.12219i	−0.0532238	+	0.0634297i	0.738776	+	0.673951i	$0.235404\pi$
$314$		0			0
$315$	32.6833	+	10.7401i	1.84149	+	0.605134i
$316$		0			0
$317$	−5.51824	−	15.1612i	−0.309935	−	0.851541i	−0.992668	−	0.120872i	$-0.961431\pi$
$317$	−5.51824	−	15.1612i	−0.309935	−	0.851541i	0.682733	−	0.730668i	$-0.260791\pi$
$318$		0			0
$319$	−9.49136	+	7.96420i	−0.531414	+	0.445910i
$320$		0			0
$321$	1.19016	−	1.02924i	0.0664280	−	0.0574466i
$322$		0			0
$323$			21.0112i			1.16909i
$324$		0			0
$325$	35.7253	+	20.6260i	1.98168	+	1.14412i
$326$		0			0
$327$	1.83748	−	5.29231i	0.101613	−	0.292665i
$328$		0			0
$329$	8.88868	−	15.4596i	0.490049	−	0.852315i
$330$		0			0
$331$	−2.87169	+	1.04521i	−0.157842	+	0.0574500i	−0.419733	−	0.907648i	$-0.637876\pi$
$331$	−2.87169	+	1.04521i	−0.157842	+	0.0574500i	0.261891	+	0.965098i	$0.415654\pi$
$332$		0			0
$333$	−1.34796	+	9.24698i	−0.0738680	+	0.506731i
$334$		0			0
$335$	−52.5212	+	19.1161i	−2.86954	+	1.04443i
$336$		0			0
$337$	2.25773	−	1.89446i	0.122986	−	0.103198i	−0.579220	−	0.815171i	$-0.696643\pi$
$337$	2.25773	−	1.89446i	0.122986	−	0.103198i	0.702206	+	0.711973i	$0.252198\pi$
$338$		0			0
$339$	−3.93906	+	24.4642i	−0.213941	+	1.32871i
$340$		0			0
$341$	−22.4129	+	38.8203i	−1.21373	+	2.10224i
$342$		0			0
$343$	9.34626	+	15.9890i	0.504650	+	0.863324i
$344$		0			0
$345$	−3.48875	+	6.25598i	−0.187828	+	0.336811i
$346$		0			0
$347$	−6.74241	+	18.5246i	−0.361952	+	0.994454i	0.616387	+	0.787443i	$0.288596\pi$
$347$	−6.74241	+	18.5246i	−0.361952	+	0.994454i	−0.978339	+	0.207011i	$0.933627\pi$
$348$		0			0
$349$	−10.9431	+	13.0415i	−0.585773	+	0.698097i	−0.974788	−	0.223134i	$-0.928371\pi$
$349$	−10.9431	+	13.0415i	−0.585773	+	0.698097i	0.389014	+	0.921232i	$0.372816\pi$
$350$		0			0
$351$	14.8332	+	4.66002i	0.791740	+	0.248734i
$352$		0			0
$353$	31.5747	−	11.4922i	1.68055	−	0.611670i	0.687166	−	0.726501i	$-0.258855\pi$
$353$	31.5747	−	11.4922i	1.68055	−	0.611670i	0.993385	+	0.114830i	$0.0366325\pi$
$354$		0			0
$355$	−5.97452	−	7.12015i	−0.317094	−	0.377898i
$356$		0			0
$357$	−8.37641	+	10.3277i	−0.443327	+	0.546601i
$358$		0			0
$359$			35.8639i			1.89282i	0.322963	+	0.946412i	$0.395321\pi$
$359$			35.8639i			1.89282i	−0.322963	+	0.946412i	$0.604679\pi$
$360$		0			0
$361$	−33.4292			−1.75943
$362$		0			0
$363$	−14.2389	−	2.29266i	−0.747349	−	0.120333i
$364$		0			0
$365$	−10.4004	−	12.3947i	−0.544381	−	0.648768i
$366$		0			0
$367$	−10.2889	−	1.81421i	−0.537075	−	0.0947008i	−0.101470	−	0.994839i	$-0.532354\pi$
$367$	−10.2889	−	1.81421i	−0.537075	−	0.0947008i	−0.435605	+	0.900138i	$0.643466\pi$
$368$		0			0
$369$	−2.97639	+	5.52919i	−0.154945	+	0.287838i
$370$		0			0
$371$	11.7817	−	2.09922i	0.611677	−	0.108986i
$372$		0			0
$373$	−3.57682	−	20.2851i	−0.185200	−	1.05032i	−0.925698	−	0.378264i	$-0.876521\pi$
$373$	−3.57682	−	20.2851i	−0.185200	−	1.05032i	0.740497	−	0.672060i	$-0.234590\pi$
$374$		0			0
$375$	−43.1473	−	49.8931i	−2.22812	−	2.57647i
$376$		0			0
$377$	8.43313			0.434328
$378$		0			0
$379$	17.6242			0.905295			0.452647	−	0.891690i	$-0.350480\pi$
$379$	17.6242			0.905295			0.452647	+	0.891690i	$0.350480\pi$
$380$		0			0
$381$	0.350848	−	1.01051i	0.0179745	−	0.0517702i
$382$		0			0
$383$	−3.38965	−	19.2237i	−0.173203	−	0.982283i	−0.940198	−	0.340630i	$-0.889360\pi$
$383$	−3.38965	−	19.2237i	−0.173203	−	0.982283i	0.766994	−	0.641654i	$-0.221751\pi$
$384$		0			0
$385$	32.4746	+	38.5611i	1.65506	+	1.96526i
$386$		0			0
$387$	−15.5319	+	13.8414i	−0.789530	+	0.703599i
$388$		0			0
$389$	19.1065	+	3.36900i	0.968739	+	0.170815i	0.635562	−	0.772049i	$-0.280768\pi$
$389$	19.1065	+	3.36900i	0.968739	+	0.170815i	0.333177	+	0.942864i	$0.391879\pi$
$390$		0			0
$391$	−1.77969	−	2.12095i	−0.0900026	−	0.107261i
$392$		0			0
$393$	3.06574	−	3.76609i	0.154646	−	0.189974i
$394$		0			0
$395$	−43.0960			−2.16840
$396$		0			0
$397$			14.2349i			0.714430i	0.934022	+	0.357215i	$0.116274\pi$
$397$			14.2349i			0.714430i	−0.934022	+	0.357215i	$0.883726\pi$
$398$		0			0
$399$	−25.7708	−	20.9017i	−1.29015	−	1.04639i
$400$		0			0
$401$	−5.44418	−	6.48813i	−0.271870	−	0.324002i	0.612784	−	0.790250i	$-0.290050\pi$
$401$	−5.44418	−	6.48813i	−0.271870	−	0.324002i	−0.884654	+	0.466249i	$0.845605\pi$
$402$		0			0
$403$	28.6700	−	10.4350i	1.42815	−	0.519806i
$404$		0			0
$405$	−31.3221	−	23.2513i	−1.55641	−	1.15537i
$406$		0			0
$407$	−8.80220	+	10.4901i	−0.436309	+	0.519973i
$408$		0			0
$409$	−7.95252	+	21.8494i	−0.393227	+	1.08038i	0.572293	+	0.820049i	$0.306054\pi$
$409$	−7.95252	+	21.8494i	−0.393227	+	1.08038i	−0.965519	+	0.260332i	$0.916168\pi$
$410$		0			0
$411$	1.97776	+	3.31075i	0.0975558	+	0.163307i
$412$		0			0
$413$	1.74760	−	10.0161i	0.0859940	−	0.492861i
$414$		0			0
$415$	35.1540	−	60.8885i	1.72564	−	2.98890i
$416$		0			0
$417$	−5.16263	+	1.96658i	−0.252815	+	0.0963037i
$418$		0			0
$419$	22.3451	−	18.7498i	1.09163	−	0.915986i	0.0947953	−	0.995497i	$-0.469780\pi$
$419$	22.3451	−	18.7498i	1.09163	−	0.915986i	0.996834	+	0.0795111i	$0.0253359\pi$
$420$		0			0
$421$	0.0754834	−	0.0274737i	0.00367883	−	0.00133899i	−0.340180	−	0.940360i	$-0.610488\pi$
$421$	0.0754834	−	0.0274737i	0.00367883	−	0.00133899i	0.343859	+	0.939021i	$0.388266\pi$
$422$		0			0
$423$	−15.0959	+	13.4529i	−0.733988	+	0.654102i
$424$		0			0
$425$	37.5925	−	13.6825i	1.82350	−	0.663701i
$426$		0			0
$427$	−2.53525	−	1.45767i	−0.122689	−	0.0705417i
$428$		0			0
$429$	14.9036	+	17.2337i	0.719553	+	0.832050i
$430$		0			0
$431$	−5.28143	−	3.04924i	−0.254398	−	0.146877i	0.367379	−	0.930072i	$-0.380255\pi$
$431$	−5.28143	−	3.04924i	−0.254398	−	0.146877i	−0.621776	+	0.783195i	$0.713589\pi$
$432$		0			0
$433$		−	14.5293i		−	0.698233i	−0.937079	−	0.349117i	$-0.886482\pi$
$433$		−	14.5293i		−	0.698233i	0.937079	−	0.349117i	$-0.113518\pi$
$434$		0			0
$435$	−19.9877	−	6.93970i	−0.958338	−	0.332733i
$436$		0			0
$437$	5.29241	−	4.44086i	0.253170	−	0.212435i
$438$		0			0
$439$	−5.60029	−	15.3867i	−0.267287	−	0.734366i	−0.998629	−	0.0523540i	$-0.983328\pi$
$439$	−5.60029	−	15.3867i	−0.267287	−	0.734366i	0.731341	−	0.682012i	$-0.238895\pi$
$440$		0			0
$441$	−4.33447	−	20.5478i	−0.206403	−	0.978467i
$442$		0			0
$443$	9.21074	−	10.9769i	0.437615	−	0.521530i	−0.501488	−	0.865165i	$-0.667214\pi$
$443$	9.21074	−	10.9769i	0.437615	−	0.521530i	0.939103	+	0.343635i	$0.111658\pi$
$444$		0			0
$445$	−1.95300	−	11.0760i	−0.0925812	−	0.525054i
$446$		0			0
$447$	1.19713	−	7.43496i	0.0566222	−	0.351661i
$448$		0			0
$449$	0.400129	−	0.231014i	0.0188832	−	0.0109022i	−0.490529	−	0.871425i	$-0.663196\pi$
$449$	0.400129	−	0.231014i	0.0188832	−	0.0109022i	0.509412	+	0.860523i	$0.329863\pi$
$450$		0			0
$451$	−7.96905	+	4.60093i	−0.375248	+	0.216650i
$452$		0			0
$453$	−0.244977	−	16.4517i	−0.0115100	−	0.772968i
$454$		0			0
$455$	−0.0615154	−	34.3134i	−0.00288388	−	1.60864i
$456$		0			0
$457$	−3.13328	+	17.7697i	−0.146569	+	0.831233i	0.819525	+	0.573043i	$0.194237\pi$
$457$	−3.13328	+	17.7697i	−0.146569	+	0.831233i	−0.966094	+	0.258190i	$0.916874\pi$
$458$		0			0
$459$	12.7083	−	8.11460i	0.593173	−	0.378757i
$460$		0			0
$461$	−25.2637	−	21.1987i	−1.17665	−	0.987324i	−0.999995	−	0.00305036i	$-0.999029\pi$
$461$	−25.2637	−	21.1987i	−1.17665	−	0.987324i	−0.176651	−	0.984273i	$-0.556527\pi$
$462$		0			0
$463$	−0.520482	−	2.95180i	−0.0241888	−	0.137182i	0.970322	−	0.241817i	$-0.0777435\pi$
$463$	−0.520482	−	2.95180i	−0.0241888	−	0.137182i	−0.994511	+	0.104636i	$0.966632\pi$
$464$		0			0
$465$	−76.5391	+	1.13972i	−3.54942	+	0.0528532i
$466$		0			0
$467$	−12.8978			−0.596837			−0.298419	−	0.954435i	$-0.596459\pi$
$467$	−12.8978			−0.596837			−0.298419	+	0.954435i	$0.596459\pi$
$468$		0			0
$469$	26.1747	+	21.8833i	1.20864	+	1.01048i
$470$		0			0
$471$	15.7464	+	12.8182i	0.725556	+	0.590630i
$472$		0			0
$473$	−30.0238	+	5.29400i	−1.38049	+	0.243418i
$474$		0			0
$475$	34.1421	+	93.8047i	1.56655	+	4.30405i
$476$		0			0
$477$	−13.4277	−	1.95740i	−0.614813	−	0.0896233i
$478$		0			0
$479$	−7.07175	−	5.93390i	−0.323117	−	0.271127i	0.466772	−	0.884378i	$-0.345417\pi$
$479$	−7.07175	−	5.93390i	−0.323117	−	0.271127i	−0.789888	+	0.613251i	$0.789861\pi$
$480$		0			0
$481$	9.17887	−	1.61848i	0.418521	−	0.0737965i
$482$		0			0
$483$	4.37182	−	0.0729388i	0.198925	−	0.00331883i
$484$		0			0
$485$	12.0341	−	6.94789i	0.546440	−	0.315487i
$486$		0			0
$487$	0.254346	−	0.440540i	0.0115255	−	0.0199628i	−0.860205	−	0.509948i	$-0.829665\pi$
$487$	0.254346	−	0.440540i	0.0115255	−	0.0199628i	0.871731	+	0.489985i	$0.162998\pi$
$488$		0			0
$489$	−12.2832	−	14.2036i	−0.555465	−	0.642308i
$490$		0			0
$491$	−5.98576	+	16.4457i	−0.270134	+	0.742186i	0.728248	+	0.685314i	$0.240335\pi$
$491$	−5.98576	+	16.4457i	−0.270134	+	0.742186i	−0.998381	+	0.0568721i	$0.981887\pi$
$492$		0			0
$493$	5.25686	−	6.26488i	0.236757	−	0.282156i
$494$		0			0
$495$	−21.1420	−	53.1106i	−0.950261	−	2.38715i
$496$		0			0
$497$	−1.93094	+	5.33495i	−0.0866145	+	0.239305i
$498$		0			0
$499$	−3.27700	−	1.19273i	−0.146699	−	0.0533940i	0.267627	−	0.963523i	$-0.413760\pi$
$499$	−3.27700	−	1.19273i	−0.146699	−	0.0533940i	−0.414326	+	0.910129i	$0.635983\pi$
$500$		0			0
$501$	−16.3217	−	2.62801i	−0.729200	−	0.117411i
$502$		0			0
$503$	−17.1485	−	29.7021i	−0.764614	−	1.32435i	−0.940450	−	0.339931i	$-0.889596\pi$
$503$	−17.1485	−	29.7021i	−0.764614	−	1.32435i	0.175836	−	0.984419i	$-0.443737\pi$
$504$		0			0
$505$	−5.34494	+	9.25770i	−0.237847	+	0.411962i
$506$		0			0
$507$	0.104357	+	7.00820i	0.00463465	+	0.311245i
$508$		0			0
$509$	−5.27529	+	4.42649i	−0.233823	+	0.196201i	−0.752169	−	0.658970i	$-0.770992\pi$
$509$	−5.27529	+	4.42649i	−0.233823	+	0.196201i	0.518346	+	0.855171i	$0.326548\pi$
$510$		0			0
$511$	−3.36136	+	9.28704i	−0.148698	+	0.410834i
$512$		0			0
$513$	20.2484	+	31.7111i	0.893988	+	1.40008i
$514$		0			0
$515$	20.5052	+	56.3375i	0.903566	+	2.48253i
$516$		0			0
$517$	−29.1810	+	5.14540i	−1.28338	+	0.226294i
$518$		0			0
$519$	4.23698	+	2.36282i	0.185983	+	0.103716i
$520$		0			0
$521$	14.2509	+	24.6832i	0.624341	+	1.08139i	0.988668	+	0.150120i	$0.0479659\pi$
$521$	14.2509	+	24.6832i	0.624341	+	1.08139i	−0.364326	+	0.931271i	$0.618701\pi$
$522$		0			0
$523$	23.7033	+	13.6851i	1.03647	+	0.598408i	0.918832	−	0.394648i	$-0.129134\pi$
$523$	23.7033	+	13.6851i	1.03647	+	0.598408i	0.117641	+	0.993056i	$0.462467\pi$
$524$		0			0
$525$	−20.6146	+	59.7195i	−0.899694	+	2.60637i
$526$		0			0
$527$	10.1196	−	27.8034i	0.440817	−	1.21114i
$528$		0			0
$529$	3.83582	−	21.7540i	0.166775	−	0.945827i
$530$		0			0
$531$	−5.46456	+	10.1514i	−0.237142	+	0.440535i
$532$		0			0
$533$	6.16796	+	1.08758i	0.267164	+	0.0471082i
$534$		0			0
$535$	2.53097	+	3.01629i	0.109423	+	0.130406i
$536$		0			0
$537$	−1.87201	−	9.76426i	−0.0807834	−	0.421359i
$538$		0			0
$539$	10.4214	−	28.9552i	0.448882	−	1.24719i
$540$		0			0
$541$	5.53654	+	9.58956i	0.238034	+	0.412287i	0.960150	−	0.279485i	$-0.0901636\pi$
$541$	5.53654	+	9.58956i	0.238034	+	0.412287i	−0.722116	+	0.691772i	$0.756830\pi$
$542$		0			0
$543$	23.3435	+	8.10480i	1.00176	+	0.347810i
$544$		0			0
$545$	13.1737	+	4.79483i	0.564299	+	0.205388i
$546$		0			0
$547$	5.69539	−	32.3002i	0.243517	−	1.38105i	−0.580394	−	0.814336i	$-0.697101\pi$
$547$	5.69539	−	32.3002i	0.243517	−	1.38105i	0.823911	−	0.566719i	$-0.191787\pi$
$548$		0			0
$549$	2.20617	+	2.47561i	0.0941569	+	0.105656i
$550$		0			0
$551$	15.6328	+	13.1175i	0.665979	+	0.558823i
$552$		0			0
$553$	13.1941	+	22.7585i	0.561070	+	0.967792i
$554$		0			0
$555$	−23.0871	−	3.71734i	−0.979993	−	0.157792i
$556$		0			0
$557$		−	21.6610i		−	0.917804i	−0.888487	−	0.458902i	$-0.848243\pi$
$557$		−	21.6610i		−	0.917804i	0.888487	−	0.458902i	$-0.151757\pi$
$558$		0			0
$559$	17.9704	+	10.3752i	0.760068	+	0.438825i
$560$		0			0
$561$	22.0930	−	0.328980i	0.932768	−	0.0138895i
$562$		0			0
$563$	−25.3800	−	9.23755i	−1.06964	−	0.389316i	−0.253596	−	0.967310i	$-0.581614\pi$
$563$	−25.3800	−	9.23755i	−1.06964	−	0.389316i	−0.816041	+	0.577994i	$0.803836\pi$
$564$		0			0
$565$	−61.0663	−	10.7676i	−2.56908	−	0.452998i
$566$		0			0
$567$	−2.68931	+	23.6594i	−0.112940	+	0.993602i
$568$		0			0
$569$	2.52733	+	0.445636i	0.105951	+	0.0186820i	0.226372	−	0.974041i	$-0.427313\pi$
$569$	2.52733	+	0.445636i	0.105951	+	0.0186820i	−0.120421	+	0.992723i	$0.538425\pi$
$570$		0			0
$571$	−8.40208	−	3.05811i	−0.351616	−	0.127978i	0.160173	−	0.987089i	$-0.448795\pi$
$571$	−8.40208	−	3.05811i	−0.351616	−	0.127978i	−0.511789	+	0.859111i	$0.671017\pi$
$572$		0			0
$573$	21.9750	−	0.327222i	0.918018	−	0.0136699i
$574$		0			0
$575$	−11.3919	−	6.57710i	−0.475074	−	0.274284i
$576$		0			0
$577$			22.4290i			0.933730i	0.884329	+	0.466865i	$0.154617\pi$
$577$			22.4290i			0.933730i	−0.884329	+	0.466865i	$0.845383\pi$
$578$		0			0
$579$	33.0760	+	5.32569i	1.37459	+	0.221328i
$580$		0			0
$581$	−42.9171	+	0.0769398i	−1.78050	+	0.00319200i
$582$		0			0
$583$	−15.2328	−	12.7818i	−0.630878	−	0.529370i
$584$		0			0
$585$	−12.2127	+	36.9414i	−0.504935	+	1.52734i
$586$		0			0
$587$	−0.0953518	+	0.540767i	−0.00393559	+	0.0223198i	−0.986712	−	0.162477i	$-0.948052\pi$
$587$	−0.0953518	+	0.540767i	−0.00393559	+	0.0223198i	0.982777	+	0.184797i	$0.0591627\pi$
$588$		0			0
$589$	69.3780	+	25.2515i	2.85867	+	1.04047i
$590$		0			0
$591$	31.8220	+	11.0485i	1.30898	+	0.454476i
$592$		0			0
$593$	6.42425	+	11.1271i	0.263812	+	0.456936i	0.967252	−	0.253819i	$-0.0816867\pi$
$593$	6.42425	+	11.1271i	0.263812	+	0.456936i	−0.703439	+	0.710755i	$0.748353\pi$
$594$		0			0
$595$	−25.5294	−	21.3438i	−1.04660	−	0.875012i
$596$		0			0
$597$	−0.670815	−	3.49891i	−0.0274546	−	0.143201i
$598$		0			0
$599$	−15.6455	−	18.6455i	−0.639256	−	0.761836i	0.344997	−	0.938604i	$-0.387880\pi$
$599$	−15.6455	−	18.6455i	−0.639256	−	0.761836i	−0.984252	+	0.176768i	$0.943436\pi$
$600$		0			0
$601$	−11.2471	−	1.98317i	−0.458779	−	0.0808951i	−0.0605177	−	0.998167i	$-0.519275\pi$
$601$	−11.2471	−	1.98317i	−0.458779	−	0.0808951i	−0.398261	+	0.917272i	$0.630386\pi$
$602$		0			0
$603$	−20.3317	−	32.9118i	−0.827970	−	1.34027i
$604$		0			0
$605$	6.26710	−	35.5425i	0.254794	−	1.44501i
$606$		0			0
$607$	−6.58645	+	18.0961i	−0.267336	+	0.734499i	0.731289	+	0.682068i	$0.238919\pi$
$607$	−6.58645	+	18.0961i	−0.267336	+	0.734499i	−0.998625	+	0.0524309i	$0.983303\pi$
$608$		0			0
$609$	2.45458	+	12.6799i	0.0994648	+	0.513817i
$610$		0			0
$611$	17.4660	+	10.0840i	0.706599	+	0.407955i
$612$		0			0
$613$	1.49015	+	2.58101i	0.0601865	+	0.104246i	0.894549	−	0.446971i	$-0.147497\pi$
$613$	1.49015	+	2.58101i	0.0601865	+	0.104246i	−0.834362	+	0.551217i	$0.814164\pi$
$614$		0			0
$615$	−13.7240	−	7.65339i	−0.553404	−	0.308614i
$616$		0			0
$617$	4.17081	−	0.735426i	0.167910	−	0.0296071i	−0.0890608	−	0.996026i	$-0.528387\pi$
$617$	4.17081	−	0.735426i	0.167910	−	0.0296071i	0.256971	+	0.966419i	$0.417275\pi$
$618$		0			0
$619$	−5.06792	−	13.9240i	−0.203697	−	0.559652i	0.795213	−	0.606330i	$-0.207359\pi$
$619$	−5.06792	−	13.9240i	−0.203697	−	0.559652i	−0.998910	+	0.0466775i	$0.985137\pi$
$620$		0			0
$621$	−4.72994	−	1.48596i	−0.189806	−	0.0596296i
$622$		0			0
$623$	−5.25121	+	4.42235i	−0.210385	+	0.177178i
$624$		0			0
$625$	73.6426	−	61.7934i	2.94570	−	2.47174i
$626$		0			0
$627$	0.820905	+	55.1288i	0.0327838	+	2.20163i
$628$		0			0
$629$	4.51937	−	7.82778i	0.180199	−	0.312114i
$630$		0			0
$631$	−17.7526	−	30.7485i	−0.706721	−	1.22408i	−0.966067	−	0.258292i	$-0.916840\pi$
$631$	−17.7526	−	30.7485i	−0.706721	−	1.22408i	0.259346	−	0.965785i	$-0.416493\pi$
$632$		0			0
$633$	28.2755	+	4.55274i	1.12385	+	0.180955i
$634$		0			0
$635$	2.51538	+	0.915525i	0.0998200	+	0.0363315i
$636$		0			0
$637$	−18.1017	+	10.5377i	−0.717215	+	0.417520i
$638$		0			0
$639$	3.98668	−	5.04914i	0.157711	−	0.199741i
$640$		0			0
$641$	27.7797	−	33.1065i	1.09723	−	1.30763i	0.149429	−	0.988772i	$-0.452257\pi$
$641$	27.7797	−	33.1065i	1.09723	−	1.30763i	0.947803	−	0.318857i	$-0.103299\pi$
$642$		0			0
$643$	−5.11111	+	14.0427i	−0.201563	+	0.553789i	−0.998752	−	0.0499403i	$-0.984097\pi$
$643$	−5.11111	+	14.0427i	−0.201563	+	0.553789i	0.797190	+	0.603729i	$0.206319\pi$
$644$		0			0
$645$	−34.0546	−	39.3788i	−1.34090	−	1.55054i
$646$		0			0
$647$	−11.6483	+	20.1754i	−0.457942	+	0.793178i	−0.998852	−	0.0479021i	$-0.984746\pi$
$647$	−11.6483	+	20.1754i	−0.457942	+	0.793178i	0.540910	+	0.841080i	$0.318080\pi$
$648$		0			0
$649$	−14.6309	+	8.44718i	−0.574315	+	0.331581i
$650$		0			0
$651$	24.0348	+	40.0705i	0.941997	+	1.57049i
$652$		0			0
$653$	−1.35897	+	0.239623i	−0.0531805	+	0.00937716i	−0.200175	−	0.979760i	$-0.564151\pi$
$653$	−1.35897	+	0.239623i	−0.0531805	+	0.00937716i	0.146995	+	0.989137i	$0.453040\pi$
$654$		0			0
$655$	9.30910	+	7.81126i	0.363737	+	0.305211i
$656$		0			0
$657$	6.93998	−	8.78950i	0.270754	−	0.342911i
$658$		0			0
$659$	7.35876	+	20.2180i	0.286657	+	0.787582i	0.996529	+	0.0832516i	$0.0265305\pi$
$659$	7.35876	+	20.2180i	0.286657	+	0.787582i	−0.709872	+	0.704331i	$0.751247\pi$
$660$		0			0
$661$	−16.8878	+	2.97778i	−0.656860	+	0.115822i	−0.492137	−	0.870518i	$-0.663784\pi$
$661$	−16.8878	+	2.97778i	−0.656860	+	0.115822i	−0.164723	+	0.986340i	$0.552673\pi$
$662$		0			0
$663$	−11.6631	−	9.49424i	−0.452959	−	0.368726i
$664$		0			0
$665$	53.2594	−	63.7036i	2.06531	−	2.47032i
$666$		0			0
$667$	−2.68911			−0.104123
$668$		0			0
$669$	30.7298	−	0.457588i	1.18808	−	0.0176914i
$670$		0			0
$671$	0.843803	+	4.78545i	0.0325747	+	0.184740i
$672$		0			0
$673$	10.0604	+	8.44171i	0.387802	+	0.325404i	0.815756	−	0.578396i	$-0.196321\pi$
$673$	10.0604	+	8.44171i	0.387802	+	0.325404i	−0.427954	+	0.903800i	$0.640766\pi$
$674$		0			0
$675$	43.5506	−	56.8781i	1.67626	−	2.18924i
$676$		0			0
$677$	−5.88291	+	33.3637i	−0.226099	+	1.28227i	0.634475	+	0.772943i	$0.281216\pi$
$677$	−5.88291	+	33.3637i	−0.226099	+	1.28227i	−0.860574	+	0.509326i	$0.829895\pi$
$678$		0			0
$679$	−7.35341	−	4.22793i	−0.282198	−	0.162253i
$680$		0			0
$681$	0.680047	+	45.6693i	0.0260595	+	1.75005i
$682$		0			0
$683$	16.6120	−	9.59095i	0.635641	−	0.366988i	−0.147292	−	0.989093i	$-0.547056\pi$
$683$	16.6120	−	9.59095i	0.635641	−	0.366988i	0.782934	+	0.622105i	$0.213722\pi$
$684$		0			0
$685$	−8.35767	+	4.82531i	−0.319330	+	0.184365i
$686$		0			0
$687$	−5.21570	+	32.3929i	−0.198991	+	1.23587i
$688$		0			0
$689$	2.35023	+	13.3288i	0.0895366	+	0.507787i
$690$		0			0
$691$	−10.2108	+	12.1688i	−0.388437	+	0.462921i	−0.924458	−	0.381283i	$-0.875482\pi$
$691$	−10.2108	+	12.1688i	−0.388437	+	0.462921i	0.536021	+	0.844204i	$0.319927\pi$
$692$		0			0
$693$	−21.5744	+	27.4250i	−0.819544	+	1.04179i
$694$		0			0
$695$	−4.72832	−	12.9909i	−0.179355	−	0.492775i
$696$		0			0
$697$	4.65280	−	3.90416i	0.176237	−	0.147881i
$698$		0			0
$699$	−13.3363	−	4.63035i	−0.504427	−	0.175136i
$700$		0			0
$701$			19.7654i			0.746528i	0.927725	+	0.373264i	$0.121762\pi$
$701$			19.7654i			0.746528i	−0.927725	+	0.373264i	$0.878238\pi$
$702$		0			0
$703$	19.5327	+	11.2772i	0.736690	+	0.425328i
$704$		0			0
$705$	−33.0987	−	38.2735i	−1.24657	−	1.44146i
$706$		0			0
$707$	6.52527	−	0.0116982i	0.245408	−	0.000439956i
$708$		0			0
$709$	6.82226	−	2.48310i	0.256215	−	0.0932547i	−0.210719	−	0.977547i	$-0.567581\pi$
$709$	6.82226	−	2.48310i	0.256215	−	0.0932547i	0.466934	+	0.884292i	$0.345358\pi$
$710$		0			0
$711$	−6.05208	−	29.2084i	−0.226971	−	1.09540i
$712$		0			0
$713$	−9.14213	+	3.32746i	−0.342375	+	0.124614i
$714$		0			0
$715$	−43.6765	+	36.6490i	−1.63341	+	1.37059i
$716$		0			0
$717$	−25.0987	+	9.56073i	−0.937328	+	0.357052i
$718$		0			0
$719$	12.6317	−	21.8787i	0.471082	−	0.815937i	−0.528371	−	0.849013i	$-0.677197\pi$
$719$	12.6317	−	21.8787i	0.471082	−	0.815937i	0.999453	+	0.0330761i	$0.0105304\pi$
$720$		0			0
$721$	23.4734	−	28.0766i	0.874197	−	1.04563i
$722$		0			0
$723$	16.2865	+	27.2633i	0.605700	+	1.01393i
$724$		0			0
$725$	13.2892	−	36.5118i	0.493549	−	1.35601i
$726$		0			0
$727$	−21.7868	+	25.9645i	−0.808028	+	0.962970i	−0.999830	−	0.0184634i	$-0.994123\pi$
$727$	−21.7868	+	25.9645i	−0.808028	+	0.962970i	0.191801	+	0.981434i	$0.438567\pi$
$728$		0			0
$729$	11.3600	−	24.4939i	0.420740	−	0.907181i
$730$		0			0
$731$	18.9097	−	6.88256i	0.699399	−	0.254561i
$732$		0			0
$733$	−6.91575	−	8.24187i	−0.255439	−	0.304420i	0.623051	−	0.782181i	$-0.285893\pi$
$733$	−6.91575	−	8.24187i	−0.255439	−	0.304420i	−0.878490	+	0.477761i	$0.841449\pi$
$734$		0			0
$735$	51.5752	−	10.0799i	1.90238	−	0.371803i
$736$		0			0
$737$		−	56.6899i		−	2.08820i
$738$		0			0
$739$	−30.7257			−1.13026			−0.565131	−	0.825001i	$-0.691174\pi$
$739$	−30.7257			−1.13026			−0.565131	+	0.825001i	$0.691174\pi$
$740$		0			0
$741$	23.6910	−	29.1031i	0.870311	−	1.06913i
$742$		0			0
$743$	−7.95620	−	9.48183i	−0.291885	−	0.347855i	0.600096	−	0.799928i	$-0.295129\pi$
$743$	−7.95620	−	9.48183i	−0.291885	−	0.347855i	−0.891981	+	0.452073i	$0.850685\pi$
$744$		0			0
$745$	18.5588	+	3.27241i	0.679941	+	0.119892i
$746$		0			0
$747$	46.2041	+	15.2750i	1.69052	+	0.558882i
$748$		0			0
$749$	0.818000	−	2.26003i	0.0298891	−	0.0825799i
$750$		0			0
$751$	−6.95023	−	39.4167i	−0.253618	−	1.43834i	−0.799596	−	0.600538i	$-0.794953\pi$
$751$	−6.95023	−	39.4167i	−0.253618	−	1.43834i	0.545979	−	0.837799i	$-0.316158\pi$
$752$		0			0
$753$	−2.37857	+	6.85075i	−0.0866798	+	0.249655i
$754$		0			0
$755$	41.1737			1.49847
$756$		0			0
$757$	37.7607			1.37244			0.686218	−	0.727396i	$-0.259270\pi$
$757$	37.7607			1.37244			0.686218	+	0.727396i	$0.259270\pi$
$758$		0			0
$759$	−4.75238	−	5.49538i	−0.172500	−	0.199470i
$760$		0			0
$761$	5.84612	+	33.1550i	0.211922	+	1.20187i	0.886169	+	0.463362i	$0.153357\pi$
$761$	5.84612	+	33.1550i	0.211922	+	1.20187i	−0.674248	+	0.738505i	$0.735532\pi$
$762$		0			0
$763$	−1.50111	−	8.42485i	−0.0543437	−	0.305000i
$764$		0			0
$765$	19.8304	+	32.1004i	0.716971	+	1.16059i
$766$		0			0
$767$	11.3242	+	1.99676i	0.408893	+	0.0720988i
$768$		0			0
$769$	5.37628	+	6.40720i	0.193874	+	0.231050i	0.854220	−	0.519911i	$-0.174035\pi$
$769$	5.37628	+	6.40720i	0.193874	+	0.231050i	−0.660347	+	0.750961i	$0.729591\pi$
$770$		0			0
$771$	−41.0882	−	6.61575i	−1.47975	−	0.238260i
$772$		0			0
$773$	47.4818			1.70780			0.853901	−	0.520436i	$-0.174230\pi$
$773$	47.4818			1.70780			0.853901	+	0.520436i	$0.174230\pi$
$774$		0			0
$775$		−	140.573i		−	5.04952i
$776$		0			0
$777$	5.10517	+	13.3301i	0.183147	+	0.478216i
$778$		0			0
$779$	9.74207	+	11.6101i	0.349046	+	0.415977i
$780$		0			0
$781$	8.85886	−	3.22436i	0.316995	−	0.115377i
$782$		0			0
$783$	1.89647	−	14.5213i	0.0677742	−	0.518948i
$784$		0			0
$785$	−32.6597	+	38.9223i	−1.16567	+	1.38920i
$786$		0			0
$787$	1.36013	−	3.73694i	0.0484835	−	0.133207i	−0.913088	−	0.407764i	$-0.866309\pi$
$787$	1.36013	−	3.73694i	0.0484835	−	0.133207i	0.961571	+	0.274556i	$0.0885310\pi$
$788$		0			0
$789$	−14.2157	+	25.4914i	−0.506091	+	0.907518i
$790$		0			0
$791$	13.0095	+	35.5450i	0.462566	+	1.26383i
$792$		0			0
$793$	1.65369	−	2.86428i	0.0587244	−	0.101714i
$794$		0			0
$795$	5.39802	−	33.5252i	0.191448	−	1.18902i
$796$		0			0
$797$	5.48408	−	4.60169i	0.194256	−	0.163000i	−0.540472	−	0.841362i	$-0.681754\pi$
$797$	5.48408	−	4.60169i	0.194256	−	0.163000i	0.734728	+	0.678362i	$0.237310\pi$
$798$		0			0
$799$	18.3789	−	6.68936i	0.650198	−	0.236653i
$800$		0			0
$801$	7.23254	−	2.87909i	0.255549	−	0.101727i
$802$		0			0
$803$	15.4214	−	5.61294i	0.544210	−	0.198076i
$804$		0			0
$805$	0.0196157	+	10.9417i	0.000691362	+	0.385643i
$806$		0			0
$807$	−14.8649	+	42.8140i	−0.523270	+	1.50712i
$808$		0			0
$809$	17.2233	+	9.94386i	0.605538	+	0.349607i	0.771217	−	0.636572i	$-0.219648\pi$
$809$	17.2233	+	9.94386i	0.605538	+	0.349607i	−0.165679	+	0.986180i	$0.552982\pi$
$810$		0			0
$811$		−	33.0263i		−	1.15971i	−0.814719	−	0.579855i	$-0.803109\pi$
$811$		−	33.0263i		−	1.15971i	0.814719	−	0.579855i	$-0.196891\pi$
$812$		0			0
$813$	25.9956	−	22.4809i	0.911706	−	0.788439i
$814$		0			0
$815$	35.9971	−	30.2052i	1.26092	−	1.05804i
$816$		0			0
$817$	17.1741	+	47.1854i	0.600844	+	1.65081i
$818$		0			0
$819$	23.2473	−	4.86040i	0.812327	−	0.169836i
$820$		0			0
$821$	−5.04057	+	6.00712i	−0.175917	+	0.209650i	−0.846797	−	0.531916i	$-0.821472\pi$
$821$	−5.04057	+	6.00712i	−0.175917	+	0.209650i	0.670880	+	0.741566i	$0.265917\pi$
$822$		0			0
$823$	1.65207	+	9.36933i	0.0575874	+	0.326594i	0.999968	−	0.00794719i	$-0.00252970\pi$
$823$	1.65207	+	9.36933i	0.0575874	+	0.326594i	−0.942381	+	0.334541i	$0.891419\pi$
$824$		0			0
$825$	98.1000	−	37.3688i	3.41540	−	1.30101i
$826$		0			0
$827$	−27.9537	+	16.1391i	−0.972047	+	0.561211i	−0.899860	−	0.436180i	$-0.856331\pi$
$827$	−27.9537	+	16.1391i	−0.972047	+	0.561211i	−0.0721871	+	0.997391i	$0.522998\pi$
$828$		0			0
$829$	10.8767	−	6.27969i	0.377765	−	0.218103i	−0.299080	−	0.954228i	$-0.596680\pi$
$829$	10.8767	−	6.27969i	0.377765	−	0.218103i	0.676845	+	0.736125i	$0.263347\pi$
$830$		0			0
$831$	−33.0099	−	18.4085i	−1.14510	−	0.638582i
$832$		0			0
$833$	−3.45547	+	20.0163i	−0.119725	+	0.693525i
$834$		0			0
$835$	7.18381	−	40.7414i	0.248606	−	1.40992i
$836$		0			0
$837$	−11.5210	−	51.7145i	−0.398225	−	1.78751i
$838$		0			0
$839$	16.1502	+	13.5516i	0.557568	+	0.467855i	0.877494	−	0.479588i	$-0.159214\pi$
$839$	16.1502	+	13.5516i	0.557568	+	0.467855i	−0.319926	+	0.947442i	$0.603658\pi$
$840$		0			0
$841$	3.65649	+	20.7370i	0.126086	+	0.715068i
$842$		0			0
$843$	27.5394	+	46.1006i	0.948509	+	1.58779i
$844$		0			0
$845$	−17.5395			−0.603376
$846$		0			0
$847$	−20.6883	+	7.57195i	−0.710858	+	0.260175i
$848$		0			0
$849$	11.9913	−	4.56777i	0.411539	−	0.156766i
$850$		0			0
$851$	−2.92691	+	0.516093i	−0.100333	+	0.0176914i
$852$		0			0
$853$	−13.7175	−	37.6885i	−0.469678	−	1.29043i	−0.918008	−	0.396561i	$-0.870204\pi$
$853$	−13.7175	−	37.6885i	−0.469678	−	1.29043i	0.448331	−	0.893868i	$-0.352019\pi$
$854$		0			0
$855$	−80.1003	+	49.4830i	−2.73937	+	1.69228i
$856$		0			0
$857$	7.15441	+	6.00326i	0.244390	+	0.205067i	0.756752	−	0.653702i	$-0.226785\pi$
$857$	7.15441	+	6.00326i	0.244390	+	0.205067i	−0.512362	+	0.858769i	$0.671229\pi$
$858$		0			0
$859$	−1.90976	+	0.336742i	−0.0651602	+	0.0114895i	−0.206133	−	0.978524i	$-0.566088\pi$
$859$	−1.90976	+	0.336742i	−0.0651602	+	0.0114895i	0.140973	+	0.990013i	$0.454977\pi$
$860$		0			0
$861$	0.160008	+	9.59061i	0.00545307	+	0.326847i
$862$		0			0
$863$	−46.2508	+	26.7029i	−1.57440	+	0.908978i	−0.578775	+	0.815487i	$0.696469\pi$
$863$	−46.2508	+	26.7029i	−1.57440	+	0.908978i	−0.995620	+	0.0934908i	$0.970197\pi$
$864$		0			0
$865$	−6.06999	+	10.5135i	−0.206386	+	0.357471i
$866$		0			0
$867$	14.5947	−	2.79811i	0.495662	−	0.0950288i
$868$		0			0
$869$	14.9502	−	41.0752i	0.507150	−	1.39338i
$870$		0			0
$871$	−24.8020	+	29.5579i	−0.840385	+	1.00153i
$872$		0			0
$873$	6.39892	+	7.18042i	0.216571	+	0.243020i
$874$		0			0
$875$	−94.7441	−	34.2918i	−3.20293	−	1.15927i
$876$		0			0
$877$	35.3703	+	12.8737i	1.19437	+	0.434715i	0.861256	−	0.508172i	$-0.169679\pi$
$877$	35.3703	+	12.8737i	1.19437	+	0.434715i	0.333113	+	0.942887i	$0.391901\pi$
$878$		0			0
$879$	−0.655730	−	1.72141i	−0.0221172	−	0.0580618i
$880$		0			0
$881$	−14.2811	−	24.7356i	−0.481142	−	0.833362i	0.518624	−	0.855002i	$-0.326444\pi$
$881$	−14.2811	−	24.7356i	−0.481142	−	0.833362i	−0.999766	+	0.0216404i	$0.993111\pi$
$882$		0			0
$883$	−20.9709	+	36.3227i	−0.705728	+	1.22236i	0.260700	+	0.965420i	$0.416047\pi$
$883$	−20.9709	+	36.3227i	−0.705728	+	1.22236i	−0.966428	+	0.256937i	$0.917287\pi$
$884$		0			0
$885$	−25.1968	−	14.0514i	−0.846982	−	0.472332i
$886$		0			0
$887$	−39.6599	+	33.2786i	−1.33165	+	1.11739i	−0.347960	+	0.937509i	$0.613126\pi$
$887$	−39.6599	+	33.2786i	−1.33165	+	1.11739i	−0.983689	+	0.179877i	$0.942430\pi$
$888$		0			0
$889$	−0.286621	−	1.60864i	−0.00961296	−	0.0539520i
$890$		0			0
$891$	33.0268	−	21.7875i	1.10644	−	0.729908i
$892$		0			0
$893$	16.6920	+	45.8609i	0.558576	+	1.53468i
$894$		0			0
$895$	24.5014	−	4.32026i	0.818991	−	0.144410i
$896$		0			0
$897$	0.0736262	+	4.94445i	0.00245831	+	0.165090i
$898$		0			0
$899$	−14.3686	−	24.8872i	−0.479220	−	0.830033i
$900$		0			0
$901$	11.3669	+	6.56267i	0.378685	+	0.218634i
$902$		0			0
$903$	−10.3695	+	30.0399i	−0.345075	+	0.999666i
$904$		0			0
$905$	−21.1492	+	58.1069i	−0.703023	+	1.93154i
$906$		0			0
$907$	−0.777774	+	4.41097i	−0.0258256	+	0.146464i	−0.994994	−	0.0999354i	$-0.968136\pi$
$907$	−0.777774	+	4.41097i	−0.0258256	+	0.146464i	0.969168	+	0.246399i	$0.0792475\pi$
$908$		0			0
$909$	−7.02503	−	2.32246i	−0.233006	−	0.0770312i
$910$		0			0
$911$	4.38117	+	0.772518i	0.145155	+	0.0255947i	0.245753	−	0.969332i	$-0.420965\pi$
$911$	4.38117	+	0.772518i	0.145155	+	0.0255947i	−0.100599	+	0.994927i	$0.532076\pi$
$912$		0			0
$913$	45.8384	+	54.6280i	1.51703	+	1.80792i
$914$		0			0
$915$	−6.27653	+	5.42792i	−0.207496	+	0.179442i
$916$		0			0
$917$	1.27501	−	7.30750i	0.0421044	−	0.241315i
$918$		0			0
$919$	−0.321644	−	0.557104i	−0.0106101	−	0.0183772i	0.860672	−	0.509160i	$-0.170044\pi$
$919$	−0.321644	−	0.557104i	−0.0106101	−	0.0183772i	−0.871282	+	0.490783i	$0.836711\pi$
$920$		0			0
$921$	−32.3349	+	27.9631i	−1.06547	+	0.921414i
$922$		0			0
$923$	−6.02965	−	2.19461i	−0.198468	−	0.0722366i
$924$		0			0
$925$	7.45705	−	42.2910i	0.245186	−	1.39052i
$926$		0			0
$927$	−35.3033	+	21.8090i	−1.15951	+	0.716303i
$928$		0			0
$929$	−37.5878	−	31.5399i	−1.23322	−	1.03479i	−0.998023	−	0.0628430i	$-0.979983\pi$
$929$	−37.5878	−	31.5399i	−1.23322	−	1.03479i	−0.235193	−	0.971949i	$-0.575572\pi$
$930$		0			0
$931$	−49.9468	−	8.62244i	−1.63694	−	0.282589i
$932$		0			0
$933$	−12.0127	−	31.5355i	−0.393278	−	1.03243i
$934$		0			0
$935$			55.2923i			1.80825i
$936$		0			0
$937$	45.7097	+	26.3905i	1.49327	+	0.862141i	0.999970	−	0.00771681i	$-0.00245636\pi$
$937$	45.7097	+	26.3905i	1.49327	+	0.862141i	0.493302	+	0.869858i	$0.335790\pi$
$938$		0			0
$939$	1.23579	−	2.21601i	0.0403285	−	0.0723167i
$940$		0			0
$941$	16.0346	+	5.83611i	0.522712	+	0.190252i	0.589881	−	0.807490i	$-0.299174\pi$
$941$	16.0346	+	5.83611i	0.522712	+	0.190252i	−0.0671691	+	0.997742i	$0.521397\pi$
$942$		0			0
$943$	−1.96680	−	0.346801i	−0.0640480	−	0.0112934i
$944$		0			0
$945$	−59.0992	−	7.61058i	−1.92250	−	0.247572i
$946$		0			0
$947$	−57.5453	−	10.1468i	−1.86997	−	0.329726i	−0.880453	−	0.474134i	$-0.842761\pi$
$947$	−57.5453	−	10.1468i	−1.86997	−	0.329726i	−0.989518	+	0.144408i	$0.953872\pi$
$948$		0			0
$949$	−10.4964	−	3.82036i	−0.340726	−	0.124014i
$950$		0			0
$951$	14.3315	+	23.9907i	0.464730	+	0.777951i
$952$		0			0
$953$	7.91072	+	4.56726i	0.256253	+	0.147948i	0.622624	−	0.782521i	$-0.286066\pi$
$953$	7.91072	+	4.56726i	0.256253	+	0.147948i	−0.366371	+	0.930469i	$0.619400\pi$
$954$		0			0
$955$			54.9969i			1.77966i
$956$		0			0
$957$	13.5481	−	16.6431i	0.437948	−	0.537995i
$958$		0			0
$959$	5.10694	+	2.93630i	0.164912	+	0.0948181i
$960$		0			0
$961$	−55.8964	−	46.9026i	−1.80311	−	1.51299i
$962$		0			0
$963$	−1.68887	+	2.13896i	−0.0544231	+	0.0689269i
$964$		0			0
$965$	−14.5580	+	82.5627i	−0.468640	+	2.65779i
$966$		0			0
$967$	39.0865	+	14.2263i	1.25694	+	0.457487i	0.882740	−	0.469863i	$-0.155697\pi$
$967$	39.0865	+	14.2263i	1.25694	+	0.457487i	0.374196	+	0.927350i	$0.377919\pi$
$968$		0			0
$969$	−6.85239	−	35.7415i	−0.220131	−	1.14818i
$970$		0			0
$971$	−4.62763	−	8.01530i	−0.148508	−	0.257223i	0.782168	−	0.623067i	$-0.214114\pi$
$971$	−4.62763	−	8.01530i	−0.148508	−	0.257223i	−0.930676	+	0.365844i	$0.880780\pi$
$972$		0			0
$973$	−5.41277	+	6.47423i	−0.173526	+	0.207554i
$974$		0			0
$975$	−67.4980	−	23.4351i	−2.16166	−	0.750525i
$976$		0			0
$977$	−2.64525	−	3.15248i	−0.0846290	−	0.100857i	0.722068	−	0.691822i	$-0.243192\pi$
$977$	−2.64525	−	3.15248i	−0.0846290	−	0.100857i	−0.806697	+	0.590965i	$0.798747\pi$
$978$		0			0
$979$	11.2342	+	1.98089i	0.359046	+	0.0633094i
$980$		0			0
$981$	−1.39969	+	9.60185i	−0.0446888	+	0.306563i
$982$		0			0
$983$	7.53134	−	42.7123i	0.240212	−	1.36231i	−0.591141	−	0.806568i	$-0.701322\pi$
$983$	7.53134	−	42.7123i	0.240212	−	1.36231i	0.831354	−	0.555744i	$-0.187566\pi$
$984$		0			0
$985$	−28.8308	+	79.2118i	−0.918624	+	2.52390i
$986$		0			0
$987$	−10.0784	+	29.1967i	−0.320800	+	0.929342i
$988$		0			0
$989$	−5.73031	−	3.30839i	−0.182213	−	0.105201i
$990$		0			0
$991$	25.2203	+	43.6829i	0.801151	+	1.38763i	0.918859	+	0.394586i	$0.129112\pi$
$991$	25.2203	+	43.6829i	0.801151	+	1.38763i	−0.117708	+	0.993048i	$0.537555\pi$
$992$		0			0
$993$	4.54407	−	2.71452i	0.144202	−	0.0861428i
$994$		0			0
$995$	8.77979	−	1.54811i	0.278338	−	0.0490785i
$996$		0			0
$997$	−7.47341	−	20.5330i	−0.236685	−	0.650287i	−0.999991	−	0.00424979i	$-0.998647\pi$
$997$	−7.47341	−	20.5330i	−0.236685	−	0.650287i	0.763306	−	0.646037i	$-0.223575\pi$
$998$		0			0
$999$	−0.722746	−	16.1694i	−0.0228667	−	0.511576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.605.1	yes	144
7.5	odd	6		756.2.ca.a.173.10	✓	144
27.5	odd	18		756.2.ca.a.437.10	yes	144
189.5	even	18	inner	756.2.ck.a.5.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.10	✓	144	7.5	odd	6
756.2.ca.a.437.10	yes	144	27.5	odd	18
756.2.ck.a.5.1	yes	144	189.5	even	18	inner
756.2.ck.a.605.1	yes	144	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70107 + 0.326131i) q^{3} +(-0.752649 - 4.26848i) q^{5} +(-2.02371 + 1.70429i) q^{7} +(2.78728 - 1.10954i) q^{9} +O(q^{10})\)	\(q+(-1.70107 + 0.326131i) q^{3} +(-0.752649 - 4.26848i) q^{5} +(-2.02371 + 1.70429i) q^{7} +(2.78728 - 1.10954i) q^{9} +(4.32943 + 0.763395i) q^{11} +(-1.92336 - 2.29217i) q^{13} +(2.67239 + 7.01553i) q^{15} -2.90177 q^{17} -7.24080i q^{19} +(2.88665 - 3.55911i) q^{21} +(0.613310 + 0.730915i) q^{23} +(-12.9550 + 4.71524i) q^{25} +(-4.37950 + 2.79643i) q^{27} +(-1.81160 + 2.15898i) q^{29} +(-3.48739 + 9.58153i) q^{31} +(-7.61363 + 0.113372i) q^{33} +(8.79786 + 7.35545i) q^{35} +(-1.55745 + 2.69759i) q^{37} +(4.01932 + 3.27188i) q^{39} +(-1.60343 + 1.34544i) q^{41} +(-6.51659 + 2.37185i) q^{43} +(-6.83391 - 11.0624i) q^{45} +(-6.33367 + 2.30527i) q^{47} +(1.19081 - 6.89797i) q^{49} +(4.93612 - 0.946358i) q^{51} +(-3.91722 - 2.26161i) q^{53} -19.0547i q^{55} +(2.36145 + 12.3171i) q^{57} +(-2.94386 + 2.47019i) q^{59} +(0.378045 + 1.03867i) q^{61} +(-3.74966 + 6.99571i) q^{63} +(-8.33648 + 9.93503i) q^{65} +(-2.23922 - 12.6992i) q^{67} +(-1.28166 - 1.04332i) q^{69} +(1.85714 - 1.07222i) q^{71} +(3.23289 - 1.86651i) q^{73} +(20.4996 - 12.2460i) q^{75} +(-10.0626 + 5.83370i) q^{77} +(1.72657 - 9.79189i) q^{79} +(6.53783 - 6.18521i) q^{81} +(12.4261 + 10.4268i) q^{83} +(2.18402 + 12.3862i) q^{85} +(2.37755 - 4.26340i) q^{87} +2.59484 q^{89} +(7.79884 + 1.36073i) q^{91} +(2.80746 - 17.4362i) q^{93} +(-30.9073 + 5.44978i) q^{95} +(1.09651 + 3.01263i) q^{97} +(12.9143 - 2.67589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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