LMFDB - Embedded newform 228.2.q.a.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,2,Mod(25,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("228.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.q (of order $9$, 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:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			85.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	228.85
Dual form			228.2.q.a.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{3} +(0.826352 + 0.300767i) q^{5} +(1.09240 - 1.89209i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{3} +(0.826352 + 0.300767i) q^{5} +(1.09240 - 1.89209i) q^{7} +(0.173648 - 0.984808i) q^{9} +(0.0812519 + 0.140732i) q^{11} +(0.581252 + 0.487728i) q^{13} +(0.826352 - 0.300767i) q^{15} +(0.539363 + 3.05888i) q^{17} +(2.77719 - 3.35965i) q^{19} +(-0.379385 - 2.15160i) q^{21} +(-1.21301 + 0.441500i) q^{23} +(-3.23783 - 2.71686i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(-1.13176 + 6.41852i) q^{29} +(-0.479055 + 0.829748i) q^{31} +(0.152704 + 0.0555796i) q^{33} +(1.47178 - 1.23497i) q^{35} -1.16250 q^{37} +0.758770 q^{39} +(-8.11721 + 6.81115i) q^{41} +(0.166374 + 0.0605553i) q^{43} +(0.439693 - 0.761570i) q^{45} +(-0.602196 + 3.41523i) q^{47} +(1.11334 + 1.92836i) q^{49} +(2.37939 + 1.99654i) q^{51} +(-7.83022 + 2.84997i) q^{53} +(0.0248149 + 0.140732i) q^{55} +(-0.0320889 - 4.35878i) q^{57} +(-0.482926 - 2.73881i) q^{59} +(-6.79086 + 2.47167i) q^{61} +(-1.67365 - 1.40436i) q^{63} +(0.333626 + 0.577857i) q^{65} +(0.184793 - 1.04801i) q^{67} +(-0.645430 + 1.11792i) q^{69} +(-4.77719 - 1.73875i) q^{71} +(1.72281 - 1.44561i) q^{73} -4.22668 q^{75} +0.355037 q^{77} +(-4.01501 + 3.36900i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(8.55690 - 14.8210i) q^{83} +(-0.474308 + 2.68993i) q^{85} +(3.25877 + 5.64436i) q^{87} +(11.9684 + 10.0427i) q^{89} +(1.55778 - 0.566986i) q^{91} +(0.166374 + 0.943555i) q^{93} +(3.30541 - 1.94096i) q^{95} +(-1.63563 - 9.27612i) q^{97} +(0.152704 - 0.0555796i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{5} + 3 q^{7}+O(q^{10}) $ 6 * q + 6 * q^5 + 3 * q^7	$ 6 q + 6 q^{5} + 3 q^{7} + 3 q^{11} + 6 q^{13} + 6 q^{15} + 12 q^{17} + 6 q^{19} + 9 q^{21} - 15 q^{23} - 3 q^{27} - 12 q^{29} - 6 q^{31} + 3 q^{33} - 6 q^{35} - 12 q^{37} - 18 q^{39} - 18 q^{41} - 18 q^{43} - 3 q^{45} - 3 q^{47} + 3 q^{51} - 24 q^{53} - 27 q^{55} + 9 q^{57} + 18 q^{59} - 9 q^{61} - 9 q^{63} + 21 q^{65} - 6 q^{67} + 12 q^{69} - 18 q^{71} + 21 q^{73} - 12 q^{75} - 48 q^{77} + 6 q^{79} + 15 q^{83} + 27 q^{85} - 3 q^{87} + 15 q^{89} + 30 q^{91} - 18 q^{93} + 24 q^{95} + 9 q^{97} + 3 q^{99}+O(q^{100}) $ 6 * q + 6 * q^5 + 3 * q^7 + 3 * q^11 + 6 * q^13 + 6 * q^15 + 12 * q^17 + 6 * q^19 + 9 * q^21 - 15 * q^23 - 3 * q^27 - 12 * q^29 - 6 * q^31 + 3 * q^33 - 6 * q^35 - 12 * q^37 - 18 * q^39 - 18 * q^41 - 18 * q^43 - 3 * q^45 - 3 * q^47 + 3 * q^51 - 24 * q^53 - 27 * q^55 + 9 * q^57 + 18 * q^59 - 9 * q^61 - 9 * q^63 + 21 * q^65 - 6 * q^67 + 12 * q^69 - 18 * q^71 + 21 * q^73 - 12 * q^75 - 48 * q^77 + 6 * q^79 + 15 * q^83 + 27 * q^85 - 3 * q^87 + 15 * q^89 + 30 * q^91 - 18 * q^93 + 24 * q^95 + 9 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$	$1$

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
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$4$		0			0
$5$	0.826352	+	0.300767i	0.369556	+	0.134507i	0.520121	−	0.854093i	$-0.325887\pi$
$5$	0.826352	+	0.300767i	0.369556	+	0.134507i	−0.150565	+	0.988600i	$0.548109\pi$
$6$		0			0
$7$	1.09240	−	1.89209i	0.412887	−	0.715141i	−0.582317	−	0.812962i	$-0.697854\pi$
$7$	1.09240	−	1.89209i	0.412887	−	0.715141i	0.995204	+	0.0978205i	$0.0311871\pi$
$8$		0			0
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$		0			0
$11$	0.0812519	+	0.140732i	0.0244984	+	0.0424324i	0.878015	−	0.478634i	$-0.158868\pi$
$11$	0.0812519	+	0.140732i	0.0244984	+	0.0424324i	−0.853516	+	0.521066i	$0.825534\pi$
$12$		0			0
$13$	0.581252	+	0.487728i	0.161210	+	0.135271i	0.719824	−	0.694156i	$-0.244222\pi$
$13$	0.581252	+	0.487728i	0.161210	+	0.135271i	−0.558614	+	0.829428i	$0.688667\pi$
$14$		0			0
$15$	0.826352	−	0.300767i	0.213363	−	0.0776578i
$16$		0			0
$17$	0.539363	+	3.05888i	0.130815	+	0.741887i	0.977683	+	0.210085i	$0.0673740\pi$
$17$	0.539363	+	3.05888i	0.130815	+	0.741887i	−0.846868	+	0.531802i	$0.821515\pi$
$18$		0			0
$19$	2.77719	−	3.35965i	0.637131	−	0.770756i
$19$	2.77719	−	3.35965i	0.637131	−	0.770756i
$20$		0			0
$21$	−0.379385	−	2.15160i	−0.0827886	−	0.469518i
$22$		0			0
$23$	−1.21301	+	0.441500i	−0.252930	+	0.0920591i	−0.465374	−	0.885114i	$-0.654080\pi$
$23$	−1.21301	+	0.441500i	−0.252930	+	0.0920591i	0.212443	+	0.977173i	$0.431858\pi$
$24$		0			0
$25$	−3.23783	−	2.71686i	−0.647565	−	0.543372i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	−1.13176	+	6.41852i	−0.210162	+	1.19189i	0.678944	+	0.734190i	$0.262438\pi$
$29$	−1.13176	+	6.41852i	−0.210162	+	1.19189i	−0.889107	+	0.457700i	$0.848673\pi$
$30$		0			0
$31$	−0.479055	+	0.829748i	−0.0860409	+	0.149027i	−0.905834	−	0.423632i	$-0.860755\pi$
$31$	−0.479055	+	0.829748i	−0.0860409	+	0.149027i	0.819793	+	0.572659i	$0.194088\pi$
$32$		0			0
$33$	0.152704	+	0.0555796i	0.0265823	+	0.00967516i
$34$		0			0
$35$	1.47178	−	1.23497i	0.248776	−	0.208748i
$36$		0			0
$37$	−1.16250			−0.191114			−0.0955572	−	0.995424i	$-0.530463\pi$
$37$	−1.16250			−0.191114			−0.0955572	+	0.995424i	$0.530463\pi$
$38$		0			0
$39$	0.758770			0.121501
$40$		0			0
$41$	−8.11721	+	6.81115i	−1.26770	+	1.06372i	−0.272878	+	0.962049i	$0.587975\pi$
$41$	−8.11721	+	6.81115i	−1.26770	+	1.06372i	−0.994818	+	0.101674i	$0.967580\pi$
$42$		0			0
$43$	0.166374	+	0.0605553i	0.0253718	+	0.00923459i	0.354675	−	0.934990i	$-0.384592\pi$
$43$	0.166374	+	0.0605553i	0.0253718	+	0.00923459i	−0.329303	+	0.944224i	$0.606814\pi$
$44$		0			0
$45$	0.439693	−	0.761570i	0.0655455	−	0.113528i
$46$		0			0
$47$	−0.602196	+	3.41523i	−0.0878394	+	0.498162i	0.908868	+	0.417083i	$0.136948\pi$
$47$	−0.602196	+	3.41523i	−0.0878394	+	0.498162i	−0.996708	+	0.0810787i	$0.974163\pi$
$48$		0			0
$49$	1.11334	+	1.92836i	0.159049	+	0.275480i
$50$		0			0
$51$	2.37939	+	1.99654i	0.333181	+	0.279572i
$52$		0			0
$53$	−7.83022	+	2.84997i	−1.07556	+	0.391473i	−0.818255	−	0.574856i	$-0.805058\pi$
$53$	−7.83022	+	2.84997i	−1.07556	+	0.391473i	−0.257309	+	0.966329i	$0.582836\pi$
$54$		0			0
$55$	0.0248149	+	0.140732i	0.00334604	+	0.0189764i
$56$		0			0
$57$	−0.0320889	−	4.35878i	−0.00425028	−	0.577335i
$58$		0			0
$59$	−0.482926	−	2.73881i	−0.0628716	−	0.356563i	−0.999972	−	0.00750222i	$-0.997612\pi$
$59$	−0.482926	−	2.73881i	−0.0628716	−	0.356563i	0.937100	−	0.349060i	$-0.113499\pi$
$60$		0			0
$61$	−6.79086	+	2.47167i	−0.869480	+	0.316465i	−0.737957	−	0.674848i	$-0.764209\pi$
$61$	−6.79086	+	2.47167i	−0.869480	+	0.316465i	−0.131524	+	0.991313i	$0.541987\pi$
$62$		0			0
$63$	−1.67365	−	1.40436i	−0.210860	−	0.176932i
$64$		0			0
$65$	0.333626	+	0.577857i	0.0413812	+	0.0716743i
$66$		0			0
$67$	0.184793	−	1.04801i	0.0225760	−	0.128035i	−0.971437	−	0.237298i	$-0.923738\pi$
$67$	0.184793	−	1.04801i	0.0225760	−	0.128035i	0.994013	+	0.109263i	$0.0348492\pi$
$68$		0			0
$69$	−0.645430	+	1.11792i	−0.0777006	+	0.134581i
$70$		0			0
$71$	−4.77719	−	1.73875i	−0.566948	−	0.206352i	0.0426126	−	0.999092i	$-0.486432\pi$
$71$	−4.77719	−	1.73875i	−0.566948	−	0.206352i	−0.609561	+	0.792739i	$0.708654\pi$
$72$		0			0
$73$	1.72281	−	1.44561i	0.201640	−	0.169196i	−0.536376	−	0.843979i	$-0.680207\pi$
$73$	1.72281	−	1.44561i	0.201640	−	0.169196i	0.738016	+	0.674783i	$0.235763\pi$
$74$		0			0
$75$	−4.22668			−0.488055
$76$		0			0
$77$	0.355037			0.0404602
$78$		0			0
$79$	−4.01501	+	3.36900i	−0.451724	+	0.379042i	−0.840075	−	0.542470i	$-0.817489\pi$
$79$	−4.01501	+	3.36900i	−0.451724	+	0.379042i	0.388351	+	0.921512i	$0.373045\pi$
$80$		0			0
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$		0			0
$83$	8.55690	−	14.8210i	0.939242	−	1.62682i	0.172353	−	0.985035i	$-0.444863\pi$
$83$	8.55690	−	14.8210i	0.939242	−	1.62682i	0.766889	−	0.641780i	$-0.221804\pi$
$84$		0			0
$85$	−0.474308	+	2.68993i	−0.0514459	+	0.291764i
$86$		0			0
$87$	3.25877	+	5.64436i	0.349377	+	0.605138i
$88$		0			0
$89$	11.9684	+	10.0427i	1.26865	+	1.06452i	0.994705	+	0.102773i	$0.0327717\pi$
$89$	11.9684	+	10.0427i	1.26865	+	1.06452i	0.273941	+	0.961747i	$0.411673\pi$
$90$		0			0
$91$	1.55778	−	0.566986i	0.163300	−	0.0594363i
$92$		0			0
$93$	0.166374	+	0.943555i	0.0172522	+	0.0978421i
$94$		0			0
$95$	3.30541	−	1.94096i	0.339128	−	0.199138i
$96$		0			0
$97$	−1.63563	−	9.27612i	−0.166073	−	0.941847i	−0.947951	−	0.318416i	$-0.896849\pi$
$97$	−1.63563	−	9.27612i	−0.166073	−	0.941847i	0.781878	−	0.623431i	$-0.214262\pi$
$98$		0			0
$99$	0.152704	−	0.0555796i	0.0153473	−	0.00558596i
$100$		0			0
$101$	−4.83022	−	4.05304i	−0.480625	−	0.403292i	0.370027	−	0.929021i	$-0.379348\pi$
$101$	−4.83022	−	4.05304i	−0.480625	−	0.403292i	−0.850652	+	0.525729i	$0.823793\pi$
$102$		0			0
$103$	4.30793	+	7.46156i	0.424473	+	0.735209i	0.996371	−	0.0851156i	$-0.0271259\pi$
$103$	4.30793	+	7.46156i	0.424473	+	0.735209i	−0.571898	+	0.820325i	$0.693793\pi$
$104$		0			0
$105$	0.333626	−	1.89209i	0.0325585	−	0.184649i
$106$		0			0
$107$	6.57398	−	11.3865i	0.635530	−	1.10077i	−0.350872	−	0.936423i	$-0.614115\pi$
$107$	6.57398	−	11.3865i	0.635530	−	1.10077i	0.986402	−	0.164348i	$-0.0525519\pi$
$108$		0			0
$109$	9.44356	+	3.43718i	0.904529	+	0.329222i	0.752066	−	0.659087i	$-0.229057\pi$
$109$	9.44356	+	3.43718i	0.904529	+	0.329222i	0.152463	+	0.988309i	$0.451280\pi$
$110$		0			0
$111$	−0.890530	+	0.747243i	−0.0845253	+	0.0709252i
$112$		0			0
$113$	8.04458			0.756770			0.378385	−	0.925648i	$-0.376480\pi$
$113$	8.04458			0.756770			0.378385	+	0.925648i	$0.376480\pi$
$114$		0			0
$115$	−1.13516			−0.105854
$116$		0			0
$117$	0.581252	−	0.487728i	0.0537368	−	0.0450905i
$118$		0			0
$119$	6.37686	+	2.32099i	0.584566	+	0.212765i
$120$		0			0
$121$	5.48680	−	9.50341i	0.498800	−	0.863946i
$122$		0			0
$123$	−1.84002	+	10.4353i	−0.165909	+	0.940918i
$124$		0			0
$125$	−4.05690	−	7.02676i	−0.362861	−	0.628493i
$126$		0			0
$127$	15.3589	+	12.8877i	1.36288	+	1.14359i	0.975080	+	0.221852i	$0.0712101\pi$
$127$	15.3589	+	12.8877i	1.36288	+	1.14359i	0.387802	+	0.921743i	$0.373234\pi$
$128$		0			0
$129$	0.166374	−	0.0605553i	0.0146484	−	0.00533159i
$130$		0			0
$131$	−2.76264	−	15.6677i	−0.241373	−	1.36889i	−0.828767	−	0.559594i	$-0.810957\pi$
$131$	−2.76264	−	15.6677i	−0.241373	−	1.36889i	0.587394	−	0.809301i	$-0.300154\pi$
$132$		0			0
$133$	−3.32295	−	8.92474i	−0.288136	−	0.773873i
$134$		0			0
$135$	−0.152704	−	0.866025i	−0.0131426	−	0.0745356i
$136$		0			0
$137$	4.74035	−	1.72535i	0.404996	−	0.147406i	−0.131487	−	0.991318i	$-0.541975\pi$
$137$	4.74035	−	1.72535i	0.404996	−	0.147406i	0.536482	+	0.843912i	$0.319753\pi$
$138$		0			0
$139$	−8.08512	−	6.78422i	−0.685771	−	0.575430i	0.231915	−	0.972736i	$-0.425501\pi$
$139$	−8.08512	−	6.78422i	−0.685771	−	0.575430i	−0.917686	+	0.397306i	$0.869945\pi$
$140$		0			0
$141$	1.73396	+	3.00330i	0.146025	+	0.252923i
$142$		0			0
$143$	−0.0214114	+	0.121430i	−0.00179051	+	0.0101545i
$144$		0			0
$145$	−2.86571	+	4.96356i	−0.237985	+	0.412202i
$146$		0			0
$147$	2.09240	+	0.761570i	0.172578	+	0.0628132i
$148$		0			0
$149$	10.5680	−	8.86765i	0.865768	−	0.726466i	−0.0974344	−	0.995242i	$-0.531064\pi$
$149$	10.5680	−	8.86765i	0.865768	−	0.726466i	0.963203	+	0.268776i	$0.0866192\pi$
$150$		0			0
$151$	−20.2841			−1.65069			−0.825346	−	0.564627i	$-0.809020\pi$
$151$	−20.2841			−1.65069			−0.825346	+	0.564627i	$0.809020\pi$
$152$		0			0
$153$	3.10607			0.251111
$154$		0			0
$155$	−0.645430	+	0.541580i	−0.0518422	+	0.0435007i
$156$		0			0
$157$	12.3807	+	4.50622i	0.988090	+	0.359635i	0.784980	−	0.619521i	$-0.212673\pi$
$157$	12.3807	+	4.50622i	0.988090	+	0.359635i	0.203110	+	0.979156i	$0.434895\pi$
$158$		0			0
$159$	−4.16637	+	7.21637i	−0.330415	+	0.572296i
$160$		0			0
$161$	−0.489733	+	2.77741i	−0.0385964	+	0.218891i
$162$		0			0
$163$	8.74510	+	15.1470i	0.684969	+	1.18640i	0.973447	+	0.228915i	$0.0735176\pi$
$163$	8.74510	+	15.1470i	0.684969	+	1.18640i	−0.288477	+	0.957487i	$0.593149\pi$
$164$		0			0
$165$	0.109470	+	0.0918566i	0.00852226	+	0.00715102i
$166$		0			0
$167$	−14.0077	+	5.09840i	−1.08395	+	0.394526i	−0.821377	−	0.570386i	$-0.806794\pi$
$167$	−14.0077	+	5.09840i	−1.08395	+	0.394526i	−0.262574	+	0.964912i	$0.584572\pi$
$168$		0			0
$169$	−2.15745	−	12.2355i	−0.165958	−	0.941193i
$170$		0			0
$171$	−2.82635	−	3.31839i	−0.216137	−	0.253764i
$172$		0			0
$173$	0.311804	+	1.76833i	0.0237060	+	0.134443i	0.994364	−	0.106021i	$-0.0338112\pi$
$173$	0.311804	+	1.76833i	0.0237060	+	0.134443i	−0.970658	+	0.240465i	$0.922700\pi$
$174$		0			0
$175$	−8.67752	+	3.15836i	−0.655959	+	0.238749i
$176$		0			0
$177$	−2.13041	−	1.78763i	−0.160132	−	0.134367i
$178$		0			0
$179$	−3.91740	−	6.78514i	−0.292801	−	0.507145i	0.681670	−	0.731659i	$-0.261254\pi$
$179$	−3.91740	−	6.78514i	−0.292801	−	0.507145i	−0.974471	+	0.224514i	$0.927921\pi$
$180$		0			0
$181$	−0.0727959	+	0.412846i	−0.00541088	+	0.0306866i	−0.987394	−	0.158284i	$-0.949404\pi$
$181$	−0.0727959	+	0.412846i	−0.00541088	+	0.0306866i	0.981983	+	0.188970i	$0.0605150\pi$
$182$		0			0
$183$	−3.61334	+	6.25849i	−0.267106	+	0.462641i
$184$		0			0
$185$	−0.960637	−	0.349643i	−0.0706274	−	0.0257063i
$186$		0			0
$187$	−0.386659	+	0.324446i	−0.0282753	+	0.0237258i
$188$		0			0
$189$	−2.18479			−0.158920
$190$		0			0
$191$	−19.5398			−1.41385			−0.706926	−	0.707287i	$-0.749919\pi$
$191$	−19.5398			−1.41385			−0.706926	+	0.707287i	$0.749919\pi$
$192$		0			0
$193$	−12.7476	+	10.6965i	−0.917594	+	0.769953i	−0.973549	−	0.228480i	$-0.926624\pi$
$193$	−12.7476	+	10.6965i	−0.917594	+	0.769953i	0.0559543	+	0.998433i	$0.482180\pi$
$194$		0			0
$195$	0.627011	+	0.228213i	0.0449012	+	0.0163427i
$196$		0			0
$197$	10.9979	−	19.0490i	0.783571	−	1.35718i	−0.146278	−	0.989243i	$-0.546730\pi$
$197$	10.9979	−	19.0490i	0.783571	−	1.35718i	0.929849	−	0.367941i	$-0.119937\pi$
$198$		0			0
$199$	−3.77584	+	21.4139i	−0.267663	+	1.51799i	0.493682	+	0.869642i	$0.335651\pi$
$199$	−3.77584	+	21.4139i	−0.267663	+	1.51799i	−0.761345	+	0.648347i	$0.775461\pi$
$200$		0			0
$201$	−0.532089	−	0.921605i	−0.0375307	−	0.0650050i
$202$		0			0
$203$	10.9081	+	9.15296i	0.765596	+	0.642412i
$204$		0			0
$205$	−8.75624	+	3.18701i	−0.611563	+	0.222591i
$206$		0			0
$207$	0.224155	+	1.27125i	0.0155799	+	0.0883579i
$208$		0			0
$209$	0.698463	+	0.117863i	0.0483137	+	0.00815275i
$210$		0			0
$211$	−1.49794	−	8.49524i	−0.103122	−	0.584837i	−0.991954	−	0.126602i	$-0.959593\pi$
$211$	−1.49794	−	8.49524i	−0.103122	−	0.584837i	0.888831	−	0.458235i	$-0.151518\pi$
$212$		0			0
$213$	−4.77719	+	1.73875i	−0.327328	+	0.119137i
$214$		0			0
$215$	0.119271	+	0.100080i	0.00813419	+	0.00682539i
$216$		0			0
$217$	1.04664	+	1.81283i	0.0710503	+	0.123063i
$218$		0			0
$219$	0.390530	−	2.21480i	0.0263895	−	0.149663i
$220$		0			0
$221$	−1.17840	+	2.04104i	−0.0792675	+	0.137295i
$222$		0			0
$223$	−14.2442	−	5.18447i	−0.953864	−	0.347178i	−0.182238	−	0.983255i	$-0.558334\pi$
$223$	−14.2442	−	5.18447i	−0.953864	−	0.347178i	−0.771626	+	0.636077i	$0.780556\pi$
$224$		0			0
$225$	−3.23783	+	2.71686i	−0.215855	+	0.181124i
$226$		0			0
$227$	−5.71419			−0.379264			−0.189632	−	0.981855i	$-0.560730\pi$
$227$	−5.71419			−0.379264			−0.189632	+	0.981855i	$0.560730\pi$
$228$		0			0
$229$	22.1634			1.46460			0.732301	−	0.680982i	$-0.238447\pi$
$229$	22.1634			1.46460			0.732301	+	0.680982i	$0.238447\pi$
$230$		0			0
$231$	0.271974	−	0.228213i	0.0178946	−	0.0150153i
$232$		0			0
$233$	10.1750	+	3.70339i	0.666586	+	0.242617i	0.653077	−	0.757291i	$-0.273478\pi$
$233$	10.1750	+	3.70339i	0.666586	+	0.242617i	0.0135087	+	0.999909i	$0.495700\pi$
$234$		0			0
$235$	−1.52481	+	2.64106i	−0.0994680	+	0.172284i
$236$		0			0
$237$	−0.910130	+	5.16160i	−0.0591193	+	0.335282i
$238$		0			0
$239$	4.93107	+	8.54087i	0.318965	+	0.552463i	0.980272	−	0.197652i	$-0.0633315\pi$
$239$	4.93107	+	8.54087i	0.318965	+	0.552463i	−0.661308	+	0.750115i	$0.729998\pi$
$240$		0			0
$241$	−5.29086	−	4.43956i	−0.340814	−	0.285977i	0.456275	−	0.889839i	$-0.349183\pi$
$241$	−5.29086	−	4.43956i	−0.340814	−	0.285977i	−0.797089	+	0.603862i	$0.793628\pi$
$242$		0			0
$243$	−0.939693	+	0.342020i	−0.0602813	+	0.0219406i
$244$		0			0
$245$	0.340022	+	1.92836i	0.0217232	+	0.123199i
$246$		0			0
$247$	3.25284	−	0.598287i	0.206973	−	0.0380681i
$248$		0			0
$249$	−2.97178	−	16.8538i	−0.188329	−	1.06807i
$250$		0			0
$251$	−23.3910	+	8.51363i	−1.47643	+	0.537375i	−0.949837	−	0.312744i	$-0.898752\pi$
$251$	−23.3910	+	8.51363i	−1.47643	+	0.537375i	−0.526589	+	0.850120i	$0.676529\pi$
$252$		0			0
$253$	−0.160693	−	0.134837i	−0.0101027	−	0.00847715i
$254$		0			0
$255$	1.36571	+	2.36549i	0.0855244	+	0.148133i
$256$		0			0
$257$	−2.47565	+	14.0401i	−0.154427	+	0.875799i	0.804881	+	0.593436i	$0.202229\pi$
$257$	−2.47565	+	14.0401i	−0.154427	+	0.875799i	−0.959308	+	0.282362i	$0.908882\pi$
$258$		0			0
$259$	−1.26991	+	2.19956i	−0.0789087	+	0.136674i
$260$		0			0
$261$	6.12449	+	2.22913i	0.379096	+	0.137980i
$262$		0			0
$263$	16.5594	−	13.8950i	1.02110	−	0.856803i	0.0313331	−	0.999509i	$-0.490025\pi$
$263$	16.5594	−	13.8950i	1.02110	−	0.856803i	0.989765	+	0.142706i	$0.0455803\pi$
$264$		0			0
$265$	−7.32770			−0.450137
$266$		0			0
$267$	15.6236			0.956149
$268$		0			0
$269$	−8.14022	+	6.83045i	−0.496318	+	0.416460i	−0.856284	−	0.516505i	$-0.827233\pi$
$269$	−8.14022	+	6.83045i	−0.496318	+	0.416460i	0.359966	+	0.932965i	$0.382788\pi$
$270$		0			0
$271$	11.4179	+	4.15577i	0.693586	+	0.252445i	0.664670	−	0.747137i	$-0.268572\pi$
$271$	11.4179	+	4.15577i	0.693586	+	0.252445i	0.0289163	+	0.999582i	$0.490794\pi$
$272$		0			0
$273$	0.828878	−	1.43566i	0.0501660	−	0.0868900i
$274$		0			0
$275$	0.119271	−	0.676417i	0.00719229	−	0.0407895i
$276$		0			0
$277$	−4.90760	−	8.50022i	−0.294869	−	0.510729i	0.680085	−	0.733133i	$-0.261943\pi$
$277$	−4.90760	−	8.50022i	−0.294869	−	0.510729i	−0.974954	+	0.222404i	$0.928609\pi$
$278$		0			0
$279$	0.733956	+	0.615862i	0.0439408	+	0.0368707i
$280$		0			0
$281$	−26.5133	+	9.65004i	−1.58165	+	0.575673i	−0.975562	−	0.219726i	$-0.929484\pi$
$281$	−26.5133	+	9.65004i	−1.58165	+	0.575673i	−0.606087	+	0.795399i	$0.707262\pi$
$282$		0			0
$283$	−2.67752	−	15.1850i	−0.159162	−	0.902652i	−0.954882	−	0.296987i	$-0.904018\pi$
$283$	−2.67752	−	15.1850i	−0.159162	−	0.902652i	0.795720	−	0.605665i	$-0.207093\pi$
$284$		0			0
$285$	1.28446	−	3.61154i	0.0760850	−	0.213929i
$286$		0			0
$287$	4.02007	+	22.7989i	0.237297	+	1.34578i
$288$		0			0
$289$	6.90895	−	2.51465i	0.406409	−	0.147921i
$290$		0			0
$291$	−7.21554	−	6.05455i	−0.422982	−	0.354924i
$292$		0			0
$293$	−13.8885	−	24.0555i	−0.811373	−	1.40534i	−0.911903	−	0.410405i	$-0.865387\pi$
$293$	−13.8885	−	24.0555i	−0.811373	−	1.40534i	0.100530	−	0.994934i	$-0.467946\pi$
$294$		0			0
$295$	0.424678	−	2.40847i	0.0247257	−	0.140226i
$296$		0			0
$297$	0.0812519	−	0.140732i	0.00471471	−	0.00816612i
$298$		0			0
$299$	−0.920397	−	0.334997i	−0.0532279	−	0.0193734i
$300$		0			0
$301$	0.296322	−	0.248644i	0.0170797	−	0.0143316i
$302$		0			0
$303$	−6.30541			−0.362236
$304$		0			0
$305$	−6.35504			−0.363888
$306$		0			0
$307$	20.8293	−	17.4779i	1.18879	−	0.997516i	0.188914	−	0.981994i	$-0.439503\pi$
$307$	20.8293	−	17.4779i	1.18879	−	0.997516i	0.999880	−	0.0155226i	$-0.00494118\pi$
$308$		0			0
$309$	8.09627	+	2.94680i	0.460581	+	0.167638i
$310$		0			0
$311$	2.97178	−	5.14728i	0.168514	−	0.291875i	−0.769383	−	0.638787i	$-0.779436\pi$
$311$	2.97178	−	5.14728i	0.168514	−	0.291875i	0.937898	+	0.346912i	$0.112770\pi$
$312$		0			0
$313$	1.24170	−	7.04201i	0.0701848	−	0.398038i	−0.929396	−	0.369084i	$-0.879671\pi$
$313$	1.24170	−	7.04201i	0.0701848	−	0.398038i	0.999581	−	0.0289536i	$-0.00921752\pi$
$314$		0			0
$315$	−0.960637	−	1.66387i	−0.0541258	−	0.0937486i
$316$		0			0
$317$	17.0758	+	14.3283i	0.959072	+	0.804757i	0.980802	−	0.195007i	$-0.0624730\pi$
$317$	17.0758	+	14.3283i	0.959072	+	0.804757i	−0.0217300	+	0.999764i	$0.506917\pi$
$318$		0			0
$319$	−0.995252	+	0.362242i	−0.0557234	+	0.0202817i
$320$		0			0
$321$	−2.28312	−	12.9482i	−0.127431	−	0.722699i
$322$		0			0
$323$	11.7747	+	6.68302i	0.655160	+	0.371853i
$324$		0			0
$325$	−0.556904	−	3.15836i	−0.0308915	−	0.175194i
$326$		0			0
$327$	9.44356	−	3.43718i	0.522230	−	0.190076i
$328$		0			0
$329$	5.80406	+	4.87019i	0.319988	+	0.268502i
$330$		0			0
$331$	−3.15183	−	5.45912i	−0.173240	−	0.300061i	0.766311	−	0.642470i	$-0.222090\pi$
$331$	−3.15183	−	5.45912i	−0.173240	−	0.300061i	−0.939551	+	0.342410i	$0.888757\pi$
$332$		0			0
$333$	−0.201867	+	1.14484i	−0.0110622	+	0.0627370i
$334$		0			0
$335$	0.467911	−	0.810446i	0.0255647	−	0.0442794i
$336$		0			0
$337$	24.3123	+	8.84894i	1.32437	+	0.482033i	0.904857	−	0.425715i	$-0.139977\pi$
$337$	24.3123	+	8.84894i	1.32437	+	0.482033i	0.419517	+	0.907748i	$0.362200\pi$
$338$		0			0
$339$	6.16250	−	5.17095i	0.334701	−	0.280848i
$340$		0			0
$341$	−0.155697			−0.00843145
$342$		0			0
$343$	20.1584			1.08845
$344$		0			0
$345$	−0.869585	+	0.729669i	−0.0468169	+	0.0392840i
$346$		0			0
$347$	17.4820	+	6.36295i	0.938486	+	0.341581i	0.765568	−	0.643355i	$-0.222458\pi$
$347$	17.4820	+	6.36295i	0.938486	+	0.341581i	0.172918	+	0.984936i	$0.444680\pi$
$348$		0			0
$349$	0.871644	−	1.50973i	0.0466581	−	0.0808141i	−0.841753	−	0.539863i	$-0.818476\pi$
$349$	0.871644	−	1.50973i	0.0466581	−	0.0808141i	0.888411	+	0.459048i	$0.151810\pi$
$350$		0			0
$351$	0.131759	−	0.747243i	0.00703278	−	0.0398849i
$352$		0			0
$353$	5.33615	+	9.24249i	0.284015	+	0.491928i	0.972370	−	0.233446i	$-0.0750002\pi$
$353$	5.33615	+	9.24249i	0.284015	+	0.491928i	−0.688355	+	0.725374i	$0.741667\pi$
$354$		0			0
$355$	−3.42468	−	2.87365i	−0.181763	−	0.152517i
$356$		0			0
$357$	6.37686	−	2.32099i	0.337499	−	0.122840i
$358$		0			0
$359$	−1.18298	−	6.70902i	−0.0624354	−	0.354089i	−0.999981	−	0.00622527i	$-0.998018\pi$
$359$	−1.18298	−	6.70902i	−0.0624354	−	0.354089i	0.937545	−	0.347863i	$-0.113093\pi$
$360$		0			0
$361$	−3.57444	−	18.6607i	−0.188129	−	0.982144i
$362$		0			0
$363$	−1.90554	−	10.8069i	−0.100015	−	0.567214i
$364$		0			0
$365$	1.85844	−	0.676417i	0.0972752	−	0.0354053i
$366$		0			0
$367$	−13.7815	−	11.5641i	−0.719390	−	0.603640i	0.207827	−	0.978166i	$-0.433361\pi$
$367$	−13.7815	−	11.5641i	−0.719390	−	0.603640i	−0.927216	+	0.374526i	$0.877805\pi$
$368$		0			0
$369$	5.29813	+	9.17664i	0.275810	+	0.477717i
$370$		0			0
$371$	−3.16132	+	17.9287i	−0.164128	+	0.930814i
$372$		0			0
$373$	−1.68004	+	2.90992i	−0.0869894	+	0.150670i	−0.906237	−	0.422770i	$-0.861058\pi$
$373$	−1.68004	+	2.90992i	−0.0869894	+	0.150670i	0.819248	+	0.573440i	$0.194391\pi$
$374$		0			0
$375$	−7.62449	−	2.77509i	−0.393727	−	0.143305i
$376$		0			0
$377$	−3.78833	+	3.17879i	−0.195109	+	0.163716i
$378$		0			0
$379$	15.1584			0.778634			0.389317	−	0.921104i	$-0.372711\pi$
$379$	15.1584			0.778634			0.389317	+	0.921104i	$0.372711\pi$
$380$		0			0
$381$	20.0496			1.02717
$382$		0			0
$383$	5.46585	−	4.58639i	0.279292	−	0.234354i	−0.492371	−	0.870385i	$-0.663870\pi$
$383$	5.46585	−	4.58639i	0.279292	−	0.234354i	0.771663	+	0.636032i	$0.219425\pi$
$384$		0			0
$385$	0.293386	+	0.106784i	0.0149523	+	0.00544220i
$386$		0			0
$387$	0.0885259	−	0.153331i	0.00450002	−	0.00779427i
$388$		0			0
$389$	4.33006	−	24.5570i	0.219543	−	1.24509i	−0.653304	−	0.757095i	$-0.726618\pi$
$389$	4.33006	−	24.5570i	0.219543	−	1.24509i	0.872847	−	0.487994i	$-0.162271\pi$
$390$		0			0
$391$	−2.00475	−	3.47232i	−0.101384	−	0.175603i
$392$		0			0
$393$	−12.1873	−	10.2264i	−0.614769	−	0.515852i
$394$		0			0
$395$	−4.33110	+	1.57639i	−0.217921	+	0.0793169i
$396$		0			0
$397$	3.58647	+	20.3399i	0.180000	+	1.02083i	0.932213	+	0.361909i	$0.117875\pi$
$397$	3.58647	+	20.3399i	0.180000	+	1.02083i	−0.752214	+	0.658919i	$0.771014\pi$
$398$		0			0
$399$	−8.28224	−	4.70080i	−0.414631	−	0.235334i
$400$		0			0
$401$	6.30722	+	35.7700i	0.314967	+	1.78627i	0.572402	+	0.819973i	$0.306012\pi$
$401$	6.30722	+	35.7700i	0.314967	+	1.78627i	−0.257434	+	0.966296i	$0.582877\pi$
$402$		0			0
$403$	−0.683144	+	0.248644i	−0.0340298	+	0.0123858i
$404$		0			0
$405$	−0.673648	−	0.565258i	−0.0334738	−	0.0280879i
$406$		0			0
$407$	−0.0944557	−	0.163602i	−0.00468199	−	0.00810945i
$408$		0			0
$409$	0.860662	−	4.88106i	0.0425570	−	0.241353i	−0.956108	−	0.293016i	$-0.905341\pi$
$409$	0.860662	−	4.88106i	0.0425570	−	0.241353i	0.998665	+	0.0516631i	$0.0164522\pi$
$410$		0			0
$411$	2.52229	−	4.36873i	0.124415	−	0.215494i
$412$		0			0
$413$	−5.70961	−	2.07813i	−0.280951	−	0.102258i
$414$		0			0
$415$	11.5287	−	9.67372i	0.565921	−	0.474864i
$416$		0			0
$417$	−10.5544			−0.516850
$418$		0			0
$419$	−35.0966			−1.71458			−0.857290	−	0.514834i	$-0.827854\pi$
$419$	−35.0966			−1.71458			−0.857290	+	0.514834i	$0.827854\pi$
$420$		0			0
$421$	−14.0967	+	11.8286i	−0.687033	+	0.576489i	−0.918052	−	0.396460i	$-0.870238\pi$
$421$	−14.0967	+	11.8286i	−0.687033	+	0.576489i	0.231019	+	0.972949i	$0.425794\pi$
$422$		0			0
$423$	3.25877	+	1.18610i	0.158447	+	0.0576699i
$424$		0			0
$425$	6.56418	−	11.3695i	0.318409	−	0.551501i
$426$		0			0
$427$	−2.74170	+	15.5489i	−0.132680	+	0.752466i
$428$		0			0
$429$	0.0616516	+	0.106784i	0.00297657	+	0.00515556i
$430$		0			0
$431$	6.73648	+	5.65258i	0.324485	+	0.272275i	0.790448	−	0.612529i	$-0.209848\pi$
$431$	6.73648	+	5.65258i	0.324485	+	0.272275i	−0.465963	+	0.884804i	$0.654292\pi$
$432$		0			0
$433$	−16.3614	+	5.95507i	−0.786280	+	0.286183i	−0.703789	−	0.710409i	$-0.748510\pi$
$433$	−16.3614	+	5.95507i	−0.786280	+	0.286183i	−0.0824914	+	0.996592i	$0.526288\pi$
$434$		0			0
$435$	0.995252	+	5.64436i	0.0477187	+	0.270626i
$436$		0			0
$437$	−1.88548	+	5.30142i	−0.0901946	+	0.253601i
$438$		0			0
$439$	−4.94743	−	28.0583i	−0.236128	−	1.33915i	−0.840225	−	0.542238i	$-0.817577\pi$
$439$	−4.94743	−	28.0583i	−0.236128	−	1.33915i	0.604097	−	0.796911i	$-0.293534\pi$
$440$		0			0
$441$	2.09240	−	0.761570i	0.0996379	−	0.0362652i
$442$		0			0
$443$	13.8216	+	11.5977i	0.656684	+	0.551023i	0.909091	−	0.416598i	$-0.136778\pi$
$443$	13.8216	+	11.5977i	0.656684	+	0.551023i	−0.252407	+	0.967621i	$0.581222\pi$
$444$		0			0
$445$	6.86959	+	11.8985i	0.325650	+	0.564042i
$446$		0			0
$447$	2.39558	−	13.5860i	0.113307	−	0.642597i
$448$		0			0
$449$	−4.76739	+	8.25736i	−0.224987	+	0.389689i	−0.956316	−	0.292336i	$-0.905567\pi$
$449$	−4.76739	+	8.25736i	−0.224987	+	0.389689i	0.731329	+	0.682025i	$0.238901\pi$
$450$		0			0
$451$	−1.61809	−	0.588936i	−0.0761928	−	0.0277319i
$452$		0			0
$453$	−15.5385	+	13.0383i	−0.730062	+	0.612595i
$454$		0			0
$455$	1.45781			0.0683430
$456$		0			0
$457$	10.4584			0.489224			0.244612	−	0.969621i	$-0.421339\pi$
$457$	10.4584			0.489224			0.244612	+	0.969621i	$0.421339\pi$
$458$		0			0
$459$	2.37939	−	1.99654i	0.111060	−	0.0931906i
$460$		0			0
$461$	−39.1489	−	14.2490i	−1.82335	−	0.663644i	−0.994571	−	0.104061i	$-0.966816\pi$
$461$	−39.1489	−	14.2490i	−1.82335	−	0.663644i	−0.828775	−	0.559583i	$-0.810961\pi$
$462$		0			0
$463$	−6.90895	+	11.9666i	−0.321086	+	0.556137i	−0.980712	−	0.195456i	$-0.937381\pi$
$463$	−6.90895	+	11.9666i	−0.321086	+	0.556137i	0.659626	+	0.751594i	$0.270715\pi$
$464$		0			0
$465$	−0.146307	+	0.829748i	−0.00678483	+	0.0384787i
$466$		0			0
$467$	3.72668	+	6.45480i	0.172450	+	0.298693i	0.939276	−	0.343163i	$-0.111498\pi$
$467$	3.72668	+	6.45480i	0.172450	+	0.298693i	−0.766826	+	0.641855i	$0.778165\pi$
$468$		0			0
$469$	−1.78106	−	1.49449i	−0.0822417	−	0.0690090i
$470$		0			0
$471$	12.3807	−	4.50622i	0.570474	−	0.207636i
$472$		0			0
$473$	0.00499613	+	0.0283345i	0.000229722	+	0.00130282i
$474$		0			0
$475$	−18.1197	+	3.33272i	−0.831391	+	0.152916i
$476$		0			0
$477$	1.44697	+	8.20616i	0.0662520	+	0.375734i
$478$		0			0
$479$	−22.3525	+	8.13565i	−1.02131	+	0.371727i	−0.797767	−	0.602966i	$-0.793985\pi$
$479$	−22.3525	+	8.13565i	−1.02131	+	0.371727i	−0.223546	+	0.974693i	$0.571763\pi$
$480$		0			0
$481$	−0.675708	−	0.566986i	−0.0308096	−	0.0258523i
$482$		0			0
$483$	1.41013	+	2.44242i	0.0641631	+	0.111134i
$484$		0			0
$485$	1.43835	−	8.15728i	0.0653120	−	0.370403i
$486$		0			0
$487$	−2.42855	+	4.20637i	−0.110048	+	0.190609i	−0.915789	−	0.401659i	$-0.868434\pi$
$487$	−2.42855	+	4.20637i	−0.110048	+	0.190609i	0.805741	+	0.592268i	$0.201767\pi$
$488$		0			0
$489$	16.4354	+	5.98200i	0.743235	+	0.270515i
$490$		0			0
$491$	−2.29632	+	1.92684i	−0.103632	+	0.0869572i	−0.693131	−	0.720811i	$-0.743769\pi$
$491$	−2.29632	+	1.92684i	−0.103632	+	0.0869572i	0.589500	+	0.807769i	$0.299325\pi$
$492$		0			0
$493$	−20.2439			−0.911740
$494$		0			0
$495$	0.142903			0.00642303
$496$		0			0
$497$	−8.50846	+	7.13944i	−0.381656	+	0.320248i
$498$		0			0
$499$	−2.37211	−	0.863378i	−0.106190	−	0.0386501i	0.288379	−	0.957516i	$-0.406884\pi$
$499$	−2.37211	−	0.863378i	−0.106190	−	0.0386501i	−0.394569	+	0.918866i	$0.629106\pi$
$500$		0			0
$501$	−7.45336	+	12.9096i	−0.332992	+	0.576759i
$502$		0			0
$503$	3.18614	−	18.0695i	0.142063	−	0.805678i	−0.827616	−	0.561295i	$-0.810303\pi$
$503$	3.18614	−	18.0695i	0.142063	−	0.805678i	0.969679	−	0.244383i	$-0.0785855\pi$
$504$		0			0
$505$	−2.77244	−	4.80201i	−0.123372	−	0.213687i
$506$		0			0
$507$	−9.51754	−	7.98617i	−0.422689	−	0.354678i
$508$		0			0
$509$	−15.2922	+	5.56591i	−0.677815	+	0.246704i	−0.657909	−	0.753097i	$-0.728559\pi$
$509$	−15.2922	+	5.56591i	−0.677815	+	0.246704i	−0.0199059	+	0.999802i	$0.506337\pi$
$510$		0			0
$511$	−0.853226	−	4.83889i	−0.0377445	−	0.214060i
$512$		0			0
$513$	−4.29813	−	0.725293i	−0.189767	−	0.0320225i
$514$		0			0
$515$	1.31567	+	7.46156i	0.0579755	+	0.328796i
$516$		0			0
$517$	−0.529563	+	0.192745i	−0.0232901	+	0.00847692i
$518$		0			0
$519$	1.37551	+	1.15419i	0.0603784	+	0.0506635i
$520$		0			0
$521$	−14.1454	−	24.5006i	−0.619723	−	1.07339i	−0.989536	−	0.144285i	$-0.953912\pi$
$521$	−14.1454	−	24.5006i	−0.619723	−	1.07339i	0.369814	−	0.929106i	$-0.379422\pi$
$522$		0			0
$523$	0.841833	−	4.77427i	0.0368108	−	0.208764i	−0.960855	−	0.277052i	$-0.910642\pi$
$523$	0.841833	−	4.77427i	0.0368108	−	0.208764i	0.997666	+	0.0682878i	$0.0217536\pi$
$524$		0			0
$525$	−4.61721	+	7.99724i	−0.201512	+	0.349028i
$526$		0			0
$527$	−2.79648	−	1.01784i	−0.121817	−	0.0443377i
$528$		0			0
$529$	−16.3425	+	13.7130i	−0.710546	+	0.596219i
$530$		0			0
$531$	−2.78106			−0.120688
$532$		0			0
$533$	−8.04013			−0.348257
$534$		0			0
$535$	8.85710	−	7.43199i	0.382926	−	0.321313i
$536$		0			0
$537$	−7.36231	−	2.67966i	−0.317707	−	0.115636i
$538$		0			0
$539$	−0.180922	+	0.313366i	−0.00779287	+	0.0134976i
$540$		0			0
$541$	−4.22193	+	23.9438i	−0.181515	+	1.02942i	0.748837	+	0.662755i	$0.230613\pi$
$541$	−4.22193	+	23.9438i	−0.181515	+	1.02942i	−0.930352	+	0.366669i	$0.880498\pi$
$542$		0			0
$543$	0.209607	+	0.363051i	0.00899512	+	0.0155800i
$544$		0			0
$545$	6.76991	+	5.68063i	0.289991	+	0.243332i
$546$		0			0
$547$	21.3999	−	7.78893i	0.914994	−	0.333031i	0.158749	−	0.987319i	$-0.449254\pi$
$547$	21.3999	−	7.78893i	0.914994	−	0.333031i	0.756245	+	0.654288i	$0.227032\pi$
$548$		0			0
$549$	1.25490	+	7.11689i	0.0535578	+	0.303742i
$550$		0			0
$551$	18.4209	+	21.6278i	0.784755	+	0.921374i
$552$		0			0
$553$	1.98845	+	11.2770i	0.0845573	+	0.479548i
$554$		0			0
$555$	−0.960637	+	0.349643i	−0.0407768	+	0.0148415i
$556$		0			0
$557$	14.6578	+	12.2993i	0.621069	+	0.521139i	0.898139	−	0.439711i	$-0.144919\pi$
$557$	14.6578	+	12.2993i	0.621069	+	0.521139i	−0.277070	+	0.960850i	$0.589364\pi$
$558$		0			0
$559$	0.0671708	+	0.116343i	0.00284102	+	0.00492080i
$560$		0			0
$561$	−0.0876485	+	0.497079i	−0.00370052	+	0.0209867i
$562$		0			0
$563$	10.6741	−	18.4881i	0.449860	−	0.779181i	−0.548516	−	0.836140i	$-0.684807\pi$
$563$	10.6741	−	18.4881i	0.449860	−	0.779181i	0.998377	+	0.0569590i	$0.0181404\pi$
$564$		0			0
$565$	6.64765	+	2.41955i	0.279669	+	0.101791i
$566$		0			0
$567$	−1.67365	+	1.40436i	−0.0702866	+	0.0589775i
$568$		0			0
$569$	39.2121			1.64386			0.821929	−	0.569590i	$-0.192898\pi$
$569$	39.2121			1.64386			0.821929	+	0.569590i	$0.192898\pi$
$570$		0			0
$571$	−7.27900			−0.304617			−0.152308	−	0.988333i	$-0.548671\pi$
$571$	−7.27900			−0.304617			−0.152308	+	0.988333i	$0.548671\pi$
$572$		0			0
$573$	−14.9684	+	12.5600i	−0.625313	+	0.524700i
$574$		0			0
$575$	5.12701	+	1.86608i	0.213811	+	0.0778209i
$576$		0			0
$577$	−7.49613	+	12.9837i	−0.312068	+	0.540518i	−0.978810	−	0.204771i	$-0.934355\pi$
$577$	−7.49613	+	12.9837i	−0.312068	+	0.540518i	0.666742	+	0.745289i	$0.267688\pi$
$578$		0			0
$579$	−2.88965	+	16.3880i	−0.120090	+	0.681063i
$580$		0			0
$581$	−18.6951	−	32.3808i	−0.775602	−	1.34338i
$582$		0			0
$583$	−1.03730	−	0.870401i	−0.0429607	−	0.0360483i
$584$		0			0
$585$	0.627011	−	0.228213i	0.0259237	−	0.00943547i
$586$		0			0
$587$	−2.08559	−	11.8280i	−0.0860815	−	0.488192i	−0.997118	−	0.0758666i	$-0.975828\pi$
$587$	−2.08559	−	11.8280i	−0.0860815	−	0.488192i	0.911037	−	0.412326i	$-0.135283\pi$
$588$		0			0
$589$	1.45723	+	3.91382i	0.0600443	+	0.161266i
$590$		0			0
$591$	−3.81954	−	21.6617i	−0.157115	−	0.891044i
$592$		0			0
$593$	34.1866	−	12.4429i	1.40388	−	0.510969i	0.474549	−	0.880229i	$-0.342611\pi$
$593$	34.1866	−	12.4429i	1.40388	−	0.510969i	0.929326	+	0.369260i	$0.120389\pi$
$594$		0			0
$595$	4.57145	+	3.83590i	0.187411	+	0.157257i
$596$		0			0
$597$	10.8721	+	18.8310i	0.444966	+	0.770704i
$598$		0			0
$599$	2.39739	−	13.5963i	0.0979548	−	0.555529i	−0.895847	−	0.444363i	$-0.853430\pi$
$599$	2.39739	−	13.5963i	0.0979548	−	0.555529i	0.993802	−	0.111167i	$-0.0354587\pi$
$600$		0			0
$601$	0.483803	−	0.837972i	0.0197347	−	0.0341816i	−0.855989	−	0.516993i	$-0.827051\pi$
$601$	0.483803	−	0.837972i	0.0197347	−	0.0341816i	0.875724	+	0.482812i	$0.160384\pi$
$602$		0			0
$603$	−1.00000	−	0.363970i	−0.0407231	−	0.0148220i
$604$		0			0
$605$	7.39234	−	6.20291i	0.300541	−	0.252184i
$606$		0			0
$607$	1.53890			0.0624619			0.0312309	−	0.999512i	$-0.490057\pi$
$607$	1.53890			0.0624619			0.0312309	+	0.999512i	$0.490057\pi$
$608$		0			0
$609$	14.2395			0.577013
$610$		0			0
$611$	−2.01573	+	1.69140i	−0.0815477	+	0.0684266i
$612$		0			0
$613$	−38.6921	−	14.0828i	−1.56276	−	0.568798i	−0.591393	−	0.806383i	$-0.701422\pi$
$613$	−38.6921	−	14.0828i	−1.56276	−	0.568798i	−0.971367	+	0.237585i	$0.923644\pi$
$614$		0			0
$615$	−4.65910	+	8.06980i	−0.187873	+	0.325406i
$616$		0			0
$617$	5.32857	−	30.2198i	0.214520	−	1.21660i	−0.667217	−	0.744864i	$-0.732515\pi$
$617$	5.32857	−	30.2198i	0.214520	−	1.21660i	0.881737	−	0.471741i	$-0.156374\pi$
$618$		0			0
$619$	5.97906	+	10.3560i	0.240319	+	0.416244i	0.960805	−	0.277225i	$-0.0894148\pi$
$619$	5.97906	+	10.3560i	0.240319	+	0.416244i	−0.720486	+	0.693469i	$0.756081\pi$
$620$		0			0
$621$	0.988856	+	0.829748i	0.0396814	+	0.0332967i
$622$		0			0
$623$	32.0758	−	11.6746i	1.28509	−	0.467734i
$624$		0			0
$625$	2.43077	+	13.7856i	0.0972308	+	0.551423i
$626$		0			0
$627$	0.610815	−	0.358675i	0.0243936	−	0.0143241i
$628$		0			0
$629$	−0.627011	−	3.55596i	−0.0250006	−	0.141785i
$630$		0			0
$631$	45.2708	−	16.4772i	1.80220	−	0.655949i	0.804094	−	0.594503i	$-0.202651\pi$
$631$	45.2708	−	16.4772i	1.80220	−	0.655949i	0.998110	−	0.0614459i	$-0.0195712\pi$
$632$		0			0
$633$	−6.60813	−	5.54488i	−0.262649	−	0.220389i
$634$		0			0
$635$	8.81567	+	15.2692i	0.349839	+	0.605940i
$636$		0			0
$637$	−0.293386	+	1.66387i	−0.0116244	+	0.0659250i
$638$		0			0
$639$	−2.54189	+	4.40268i	−0.100556	+	0.174167i
$640$		0			0
$641$	−6.32383	−	2.30168i	−0.249776	−	0.0909111i	0.214098	−	0.976812i	$-0.431319\pi$
$641$	−6.32383	−	2.30168i	−0.249776	−	0.0909111i	−0.463874	+	0.885901i	$0.653541\pi$
$642$		0			0
$643$	−19.6819	+	16.5150i	−0.776177	+	0.651290i	−0.942283	−	0.334818i	$-0.891325\pi$
$643$	−19.6819	+	16.5150i	−0.776177	+	0.651290i	0.166106	+	0.986108i	$0.446881\pi$
$644$		0			0
$645$	0.155697			0.00613055
$646$		0			0
$647$	−50.4380			−1.98292			−0.991461	−	0.130403i	$-0.958373\pi$
$647$	−50.4380			−1.98292			−0.991461	+	0.130403i	$0.958373\pi$
$648$		0			0
$649$	0.346201	−	0.290497i	0.0135896	−	0.0114030i
$650$		0			0
$651$	1.96703	+	0.715942i	0.0770941	+	0.0280600i
$652$		0			0
$653$	17.9304	−	31.0563i	0.701669	−	1.21533i	−0.266211	−	0.963915i	$-0.585772\pi$
$653$	17.9304	−	31.0563i	0.701669	−	1.21533i	0.967880	−	0.251412i	$-0.0808949\pi$
$654$		0			0
$655$	2.42943	−	13.7780i	0.0949255	−	0.538349i
$656$		0			0
$657$	−1.12449	−	1.94767i	−0.0438703	−	0.0759857i
$658$		0			0
$659$	−9.66044	−	8.10608i	−0.376317	−	0.315768i	0.434937	−	0.900461i	$-0.356771\pi$
$659$	−9.66044	−	8.10608i	−0.376317	−	0.315768i	−0.811255	+	0.584693i	$0.801215\pi$
$660$		0			0
$661$	41.8820	−	15.2438i	1.62902	−	0.592915i	0.643950	−	0.765068i	$-0.277295\pi$
$661$	41.8820	−	15.2438i	1.62902	−	0.592915i	0.985070	+	0.172153i	$0.0550724\pi$
$662$		0			0
$663$	0.409253	+	2.32099i	0.0158941	+	0.0901397i
$664$		0			0
$665$	−0.0616516	−	8.37441i	−0.00239074	−	0.324746i
$666$		0			0
$667$	−1.46094	−	8.28541i	−0.0565679	−	0.320812i
$668$		0			0
$669$	−14.2442	+	5.18447i	−0.550713	+	0.200443i
$670$		0			0
$671$	−0.899615	−	0.754866i	−0.0347292	−	0.0291413i
$672$		0			0
$673$	6.41013	+	11.1027i	0.247092	+	0.427977i	0.962718	−	0.270508i	$-0.0871916\pi$
$673$	6.41013	+	11.1027i	0.247092	+	0.427977i	−0.715625	+	0.698484i	$0.753858\pi$
$674$		0			0
$675$	−0.733956	+	4.16247i	−0.0282500	+	0.160213i
$676$		0			0
$677$	14.6844	−	25.4341i	0.564367	−	0.977512i	−0.432742	−	0.901518i	$-0.642454\pi$
$677$	14.6844	−	25.4341i	0.564367	−	0.977512i	0.997108	−	0.0759937i	$-0.0242129\pi$
$678$		0			0
$679$	−19.3380	−	7.03844i	−0.742123	−	0.270111i
$680$		0			0
$681$	−4.37733	+	3.67301i	−0.167739	+	0.140750i
$682$		0			0
$683$	38.0033			1.45416			0.727078	−	0.686555i	$-0.240878\pi$
$683$	38.0033			1.45416			0.727078	+	0.686555i	$0.240878\pi$
$684$		0			0
$685$	4.43613			0.169496
$686$		0			0
$687$	16.9782	−	14.2464i	0.647758	−	0.543533i
$688$		0			0
$689$	−5.94134	−	2.16247i	−0.226347	−	0.0823836i
$690$		0			0
$691$	−16.1459	+	27.9655i	−0.614219	+	1.06386i	0.376302	+	0.926497i	$0.377195\pi$
$691$	−16.1459	+	27.9655i	−0.614219	+	1.06386i	−0.990521	+	0.137361i	$0.956138\pi$
$692$		0			0
$693$	0.0616516	−	0.349643i	0.00234195	−	0.0132819i
$694$		0			0
$695$	−4.64068	−	8.03790i	−0.176031	−	0.304895i
$696$		0			0
$697$	−25.2126	−	21.1559i	−0.954995	−	0.801336i
$698$		0			0
$699$	10.1750	−	3.70339i	0.384854	−	0.140075i
$700$		0			0
$701$	4.01367	+	22.7627i	0.151594	+	0.859734i	0.961834	+	0.273635i	$0.0882259\pi$
$701$	4.01367	+	22.7627i	0.151594	+	0.859734i	−0.810239	+	0.586099i	$0.800663\pi$
$702$		0			0
$703$	−3.22849	+	3.90560i	−0.121765	+	0.147303i
$704$		0			0
$705$	0.529563	+	3.00330i	0.0199445	+	0.113111i
$706$		0			0
$707$	−12.9452	+	4.71167i	−0.486855	+	0.177201i
$708$		0			0
$709$	28.1589	+	23.6281i	1.05753	+	0.887371i	0.993865	−	0.110600i	$-0.0352773\pi$
$709$	28.1589	+	23.6281i	1.05753	+	0.887371i	0.0636629	+	0.997971i	$0.479722\pi$
$710$		0			0
$711$	2.62061	+	4.53904i	0.0982807	+	0.170227i
$712$		0			0
$713$	0.214766	−	1.21800i	0.00804304	−	0.0456143i
$714$		0			0
$715$	−0.0542155	+	0.0939039i	−0.00202754	+	0.00351181i
$716$		0			0
$717$	9.26739	+	3.37305i	0.346097	+	0.125969i
$718$		0			0
$719$	25.2414	−	21.1801i	0.941347	−	0.789884i	−0.0364721	−	0.999335i	$-0.511612\pi$
$719$	25.2414	−	21.1801i	0.941347	−	0.789884i	0.977819	+	0.209451i	$0.0671675\pi$
$720$		0			0
$721$	18.8239			0.701038
$722$		0			0
$723$	−6.90673			−0.256864
$724$		0			0
$725$	21.1027	−	17.7072i	0.783733	−	0.657630i
$726$		0			0
$727$	7.44521	+	2.70984i	0.276128	+	0.100502i	0.476372	−	0.879244i	$-0.341951\pi$
$727$	7.44521	+	2.70984i	0.276128	+	0.100502i	−0.200245	+	0.979746i	$0.564174\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	−0.0954951	+	0.541580i	−0.00353202	+	0.0200311i
$732$		0			0
$733$	3.71735	+	6.43864i	0.137303	+	0.237816i	0.926475	−	0.376356i	$-0.122823\pi$
$733$	3.71735	+	6.43864i	0.137303	+	0.237816i	−0.789172	+	0.614173i	$0.789490\pi$
$734$		0			0
$735$	1.50000	+	1.25865i	0.0553283	+	0.0464260i
$736$		0			0
$737$	0.162504	−	0.0591466i	0.00598591	−	0.00217869i
$738$		0			0
$739$	3.36009	+	19.0560i	0.123603	+	0.700987i	0.982128	+	0.188215i	$0.0602702\pi$
$739$	3.36009	+	19.0560i	0.123603	+	0.700987i	−0.858525	+	0.512772i	$0.828619\pi$
$740$		0			0
$741$	2.10725	−	2.54920i	0.0774117	−	0.0936472i
$742$		0			0
$743$	5.44965	+	30.9065i	0.199928	+	1.13385i	0.905223	+	0.424936i	$0.139704\pi$
$743$	5.44965	+	30.9065i	0.199928	+	1.13385i	−0.705295	+	0.708914i	$0.749185\pi$
$744$		0			0
$745$	11.4000	−	4.14927i	0.417665	−	0.152017i
$746$		0			0
$747$	−13.1099	−	11.0005i	−0.479668	−	0.402489i
$748$		0			0
$749$	−14.3628	−	24.8771i	−0.524804	−	0.908988i
$750$		0			0
$751$	0.906889	−	5.14322i	0.0330928	−	0.187679i	−0.963780	−	0.266697i	$-0.914068\pi$
$751$	0.906889	−	5.14322i	0.0330928	−	0.187679i	0.996873	+	0.0790187i	$0.0251787\pi$
$752$		0			0
$753$	−12.4461	+	21.5573i	−0.453561	+	0.785590i
$754$		0			0
$755$	−16.7618	−	6.10078i	−0.610023	−	0.222030i
$756$		0			0
$757$	−22.8063	+	19.1368i	−0.828911	+	0.695539i	−0.955041	−	0.296475i	$-0.904189\pi$
$757$	−22.8063	+	19.1368i	−0.828911	+	0.695539i	0.126130	+	0.992014i	$0.459744\pi$
$758$		0			0
$759$	−0.209770			−0.00761415
$760$		0			0
$761$	−9.35267			−0.339034			−0.169517	−	0.985527i	$-0.554221\pi$
$761$	−9.35267			−0.339034			−0.169517	+	0.985527i	$0.554221\pi$
$762$		0			0
$763$	16.8195	−	14.1133i	0.608908	−	0.510935i
$764$		0			0
$765$	2.56670	+	0.934204i	0.0927994	+	0.0337762i
$766$		0			0
$767$	1.05509	−	1.82747i	0.0380972	−	0.0659863i
$768$		0			0
$769$	6.74335	−	38.2434i	0.243171	−	1.37909i	−0.581530	−	0.813525i	$-0.697546\pi$
$769$	6.74335	−	38.2434i	0.243171	−	1.37909i	0.824702	−	0.565568i	$-0.191343\pi$
$770$		0			0
$771$	7.12836	+	12.3467i	0.256721	+	0.444655i
$772$		0			0
$773$	−18.2069	−	15.2774i	−0.654857	−	0.549491i	0.253683	−	0.967287i	$-0.418358\pi$
$773$	−18.2069	−	15.2774i	−0.654857	−	0.549491i	−0.908540	+	0.417797i	$0.862802\pi$
$774$		0			0
$775$	3.80541	−	1.38505i	0.136694	−	0.0497526i
$776$		0			0
$777$	0.441037	+	2.50124i	0.0158221	+	0.0897316i
$778$		0			0
$779$	0.340022	+	46.1868i	0.0121826	+	1.65481i
$780$		0			0
$781$	−0.143457	−	0.813583i	−0.00513328	−	0.0291123i
$782$		0			0
$783$	6.12449	−	2.22913i	0.218871	−	0.0796626i
$784$		0			0
$785$	8.87551	+	7.44744i	0.316781	+	0.265811i
$786$		0			0
$787$	6.87804	+	11.9131i	0.245176	+	0.424657i	0.962181	−	0.272411i	$-0.0878210\pi$
$787$	6.87804	+	11.9131i	0.245176	+	0.424657i	−0.717005	+	0.697068i	$0.754488\pi$
$788$		0			0
$789$	3.75372	−	21.2884i	0.133636	−	0.757887i
$790$		0			0
$791$	8.78787	−	15.2210i	0.312461	−	0.541198i
$792$		0			0
$793$	−5.15270	−	1.87543i	−0.182978	−	0.0665985i
$794$		0			0
$795$	−5.61334	+	4.71015i	−0.199085	+	0.167052i
$796$		0			0
$797$	−7.77238			−0.275312			−0.137656	−	0.990480i	$-0.543957\pi$
$797$	−7.77238			−0.275312			−0.137656	+	0.990480i	$0.543957\pi$
$798$		0			0
$799$	−10.7716			−0.381071
$800$		0			0
$801$	11.9684	−	10.0427i	0.422882	−	0.354840i
$802$		0			0
$803$	0.343426	+	0.124997i	0.0121192	+	0.00441104i
$804$		0			0
$805$	−1.24005	+	2.14783i	−0.0437059	+	0.0757009i
$806$		0			0
$807$	−1.84524	+	10.4649i	−0.0649554	+	0.368380i
$808$		0			0
$809$	−6.84595	−	11.8575i	−0.240691	−	0.416889i	0.720220	−	0.693745i	$-0.244041\pi$
$809$	−6.84595	−	11.8575i	−0.240691	−	0.416889i	−0.960911	+	0.276857i	$0.910707\pi$
$810$		0			0
$811$	−16.9360	−	14.2110i	−0.594705	−	0.499017i	0.295034	−	0.955487i	$-0.404669\pi$
$811$	−16.9360	−	14.2110i	−0.594705	−	0.499017i	−0.889739	+	0.456470i	$0.849114\pi$
$812$		0			0
$813$	11.4179	−	4.15577i	0.400442	−	0.145749i
$814$		0			0
$815$	2.67082	+	15.1470i	0.0935546	+	0.530575i
$816$		0			0
$817$	0.665497	−	0.390785i	0.0232828	−	0.0136718i
$818$		0			0
$819$	−0.287866	−	1.63257i	−0.0100589	−	0.0570466i
$820$		0			0
$821$	20.2763	−	7.37997i	0.707648	−	0.257563i	0.0369753	−	0.999316i	$-0.488228\pi$
$821$	20.2763	−	7.37997i	0.707648	−	0.257563i	0.670673	+	0.741753i	$0.266005\pi$
$822$		0			0
$823$	−7.16431	−	6.01157i	−0.249732	−	0.209550i	0.509325	−	0.860574i	$-0.329895\pi$
$823$	−7.16431	−	6.01157i	−0.249732	−	0.209550i	−0.759057	+	0.651024i	$0.774340\pi$
$824$		0			0
$825$	−0.343426	−	0.594831i	−0.0119566	−	0.0207094i
$826$		0			0
$827$	−5.83110	+	33.0698i	−0.202767	+	1.14995i	0.698148	+	0.715954i	$0.254008\pi$
$827$	−5.83110	+	33.0698i	−0.202767	+	1.14995i	−0.900915	+	0.433996i	$0.857103\pi$
$828$		0			0
$829$	−0.325170	+	0.563211i	−0.0112936	+	0.0195611i	−0.871617	−	0.490188i	$-0.836928\pi$
$829$	−0.325170	+	0.563211i	−0.0112936	+	0.0195611i	0.860323	+	0.509749i	$0.170262\pi$
$830$		0			0
$831$	−9.22328	−	3.35700i	−0.319952	−	0.116453i
$832$		0			0
$833$	−5.29813	+	4.44566i	−0.183569	+	0.154033i
$834$		0			0
$835$	−13.1088			−0.453647
$836$		0			0
$837$	0.958111			0.0331172
$838$		0			0
$839$	−17.5483	+	14.7248i	−0.605834	+	0.508355i	−0.893315	−	0.449431i	$-0.851627\pi$
$839$	−17.5483	+	14.7248i	−0.605834	+	0.508355i	0.287481	+	0.957786i	$0.407182\pi$
$840$		0			0
$841$	−12.6655	−	4.60986i	−0.436741	−	0.158961i
$842$		0			0
$843$	−14.1074	+	24.4348i	−0.485885	+	0.841578i
$844$		0			0
$845$	1.89723	−	10.7597i	0.0652667	−	0.370146i
$846$		0			0
$847$	−11.9875	−	20.7630i	−0.411896	−	0.713424i
$848$		0			0
$849$	−11.8118	−	9.91128i	−0.405380	−	0.340154i
$850$		0			0
$851$	1.41013	−	0.513245i	0.0483386	−	0.0175938i
$852$		0			0
$853$	5.29901	+	30.0522i	0.181435	+	1.02897i	0.930451	+	0.366416i	$0.119415\pi$
$853$	5.29901	+	30.0522i	0.181435	+	1.02897i	−0.749017	+	0.662551i	$0.769474\pi$
$854$		0			0
$855$	−1.33750	−	3.59224i	−0.0457414	−	0.122852i
$856$		0			0
$857$	3.13387	+	17.7731i	0.107051	+	0.607117i	0.990381	+	0.138366i	$0.0441849\pi$
$857$	3.13387	+	17.7731i	0.107051	+	0.607117i	−0.883330	+	0.468751i	$0.844704\pi$
$858$		0			0
$859$	−34.6612	+	12.6157i	−1.18263	+	0.430440i	−0.857129	−	0.515103i	$-0.827754\pi$
$859$	−34.6612	+	12.6157i	−1.18263	+	0.430440i	−0.325497	+	0.945543i	$0.605532\pi$
$860$		0			0
$861$	17.7344	+	14.8809i	0.604387	+	0.507141i
$862$		0			0
$863$	14.0856	+	24.3970i	0.479479	+	0.830482i	0.999723	−	0.0235356i	$-0.00749232\pi$
$863$	14.0856	+	24.3970i	0.479479	+	0.830482i	−0.520244	+	0.854018i	$0.674159\pi$
$864$		0			0
$865$	−0.274196	+	1.55504i	−0.00932294	+	0.0528730i
$866$		0			0
$867$	3.67617	−	6.36732i	0.124849	−	0.216246i
$868$		0			0
$869$	−0.800355	−	0.291305i	−0.0271502	−	0.00988186i
$870$		0			0
$871$	0.618555	−	0.519030i	0.0209589	−	0.0175866i
$872$		0			0
$873$	−9.41921			−0.318792
$874$		0			0
$875$	−17.7270			−0.599282
$876$		0			0
$877$	9.73758	−	8.17080i	0.328815	−	0.275908i	−0.463402	−	0.886148i	$-0.653371\pi$
$877$	9.73758	−	8.17080i	0.328815	−	0.275908i	0.792217	+	0.610240i	$0.208927\pi$
$878$		0			0
$879$	−26.1018	−	9.50027i	−0.880391	−	0.320436i
$880$		0			0
$881$	−18.4265	+	31.9156i	−0.620804	+	1.07526i	0.368532	+	0.929615i	$0.379860\pi$
$881$	−18.4265	+	31.9156i	−0.620804	+	1.07526i	−0.989336	+	0.145649i	$0.953473\pi$
$882$		0			0
$883$	−6.88073	+	39.0226i	−0.231555	+	1.31321i	0.618194	+	0.786026i	$0.287865\pi$
$883$	−6.88073	+	39.0226i	−0.231555	+	1.31321i	−0.849749	+	0.527188i	$0.823246\pi$
$884$		0			0
$885$	−1.22281	−	2.11797i	−0.0411043	−	0.0711948i
$886$		0			0
$887$	−36.3915	−	30.5361i	−1.22191	−	1.02530i	−0.998723	−	0.0505241i	$-0.983911\pi$
$887$	−36.3915	−	30.5361i	−1.22191	−	1.02530i	−0.223183	−	0.974777i	$-0.571645\pi$
$888$		0			0
$889$	41.1626	−	14.9819i	1.38055	−	0.502478i
$890$		0			0
$891$	−0.0282185	−	0.160035i	−0.000945355	−	0.00536138i
$892$		0			0
$893$	9.80154	+	11.5079i	0.327996	+	0.385097i
$894$		0			0
$895$	−1.19640	−	6.78514i	−0.0399914	−	0.226802i
$896$		0			0
$897$	−0.920397	+	0.334997i	−0.0307312	+	0.0111852i
$898$		0			0
$899$	−4.78359	−	4.01390i	−0.159542	−	0.133871i
$900$		0			0
$901$	−12.9410	−	22.4145i	−0.431128	−	0.746736i
$902$		0			0
$903$	0.0671708	−	0.380945i	0.00223530	−	0.0126770i
$904$		0			0
$905$	−0.184326	+	0.319261i	−0.00612719	+	0.0106126i
$906$		0			0
$907$	−21.6186	−	7.86851i	−0.717832	−	0.261270i	−0.0428271	−	0.999083i	$-0.513636\pi$
$907$	−21.6186	−	7.86851i	−0.717832	−	0.261270i	−0.675005	+	0.737813i	$0.735859\pi$
$908$		0			0
$909$	−4.83022	+	4.05304i	−0.160208	+	0.134431i
$910$		0			0
$911$	13.7888			0.456843			0.228422	−	0.973562i	$-0.426644\pi$
$911$	13.7888			0.456843			0.228422	+	0.973562i	$0.426644\pi$
$912$		0			0
$913$	2.78106			0.0920396
$914$		0			0
$915$	−4.86824	+	4.08494i	−0.160939	+	0.135044i
$916$		0			0
$917$	−32.6626	−	11.8882i	−1.07861	−	0.392583i
$918$		0			0
$919$	−27.3312	+	47.3390i	−0.901572	+	1.56157i	−0.0761174	+	0.997099i	$0.524252\pi$
$919$	−27.3312	+	47.3390i	−0.901572	+	1.56157i	−0.825454	+	0.564469i	$0.809081\pi$
$920$		0			0
$921$	4.72163	−	26.7777i	0.155583	−	0.882355i
$922$		0			0
$923$	−1.92871	−	3.34062i	−0.0634843	−	0.109958i
$924$		0			0
$925$	3.76399	+	3.15836i	0.123759	+	0.103846i
$926$		0			0
$927$	8.09627	−	2.94680i	0.265916	−	0.0967856i
$928$		0			0
$929$	8.12819	+	46.0973i	0.266677	+	1.51240i	0.764216	+	0.644961i	$0.223126\pi$
$929$	8.12819	+	46.0973i	0.266677	+	1.51240i	−0.497538	+	0.867442i	$0.665763\pi$
$930$		0			0
$931$	9.57057	+	1.61500i	0.313663	+	0.0529294i
$932$		0			0
$933$	−1.03209	−	5.85327i	−0.0337891	−	0.191627i
$934$		0			0
$935$	−0.417099	+	0.151812i	−0.0136406	+	0.00496477i
$936$		0			0
$937$	−29.3555	−	24.6322i	−0.959003	−	0.804699i	0.0217880	−	0.999763i	$-0.493064\pi$
$937$	−29.3555	−	24.6322i	−0.959003	−	0.804699i	−0.980791	+	0.195064i	$0.937509\pi$
$938$		0			0
$939$	−3.57532	−	6.19264i	−0.116676	−	0.202089i
$940$		0			0
$941$	−5.11540	+	29.0109i	−0.166757	+	0.945728i	0.780477	+	0.625185i	$0.214976\pi$
$941$	−5.11540	+	29.0109i	−0.166757	+	0.945728i	−0.947234	+	0.320543i	$0.896135\pi$
$942$		0			0
$943$	6.83915	−	11.8457i	0.222713	−	0.385751i
$944$		0			0
$945$	−1.80541	−	0.657115i	−0.0587299	−	0.0213759i
$946$		0			0
$947$	−29.0540	+	24.3792i	−0.944127	+	0.792217i	−0.978299	−	0.207199i	$-0.933565\pi$
$947$	−29.0540	+	24.3792i	−0.944127	+	0.792217i	0.0341717	+	0.999416i	$0.489121\pi$
$948$		0			0
$949$	1.70645			0.0553938
$950$		0			0
$951$	22.2909			0.722831
$952$		0			0
$953$	−6.30659	+	5.29186i	−0.204290	+	0.171420i	−0.739193	−	0.673494i	$-0.764793\pi$
$953$	−6.30659	+	5.29186i	−0.204290	+	0.171420i	0.534902	+	0.844914i	$0.320348\pi$
$954$		0			0
$955$	−16.1468	−	5.87695i	−0.522497	−	0.190173i
$956$		0			0
$957$	−0.529563	+	0.917229i	−0.0171183	+	0.0296498i
$958$		0			0
$959$	1.91384	−	10.8539i	0.0618011	−	0.350491i
$960$		0			0
$961$	15.0410	+	26.0518i	0.485194	+	0.840381i
$962$		0			0
$963$	−10.0719	−	8.45134i	−0.324563	−	0.272341i
$964$		0			0
$965$	−13.7512	+	5.00502i	−0.442667	+	0.161117i
$966$		0			0
$967$	−2.81820	−	15.9828i	−0.0906272	−	0.513972i	−0.996000	−	0.0893546i	$-0.971520\pi$
$967$	−2.81820	−	15.9828i	−0.0906272	−	0.513972i	0.905373	−	0.424618i	$-0.139592\pi$
$968$		0			0
$969$	13.3157	−	2.44912i	0.427761	−	0.0786771i
$970$		0			0
$971$	5.76445	+	32.6918i	0.184990	+	1.04913i	0.925968	+	0.377602i	$0.123251\pi$
$971$	5.76445	+	32.6918i	0.184990	+	1.04913i	−0.740978	+	0.671529i	$0.765638\pi$
$972$		0			0
$973$	−21.6685	+	7.88669i	−0.694660	+	0.252836i
$974$		0			0
$975$	−2.45677	−	2.06147i	−0.0786795	−	0.0660199i
$976$		0			0
$977$	−11.9966	−	20.7787i	−0.383805	−	0.664770i	0.607798	−	0.794092i	$-0.292053\pi$
$977$	−11.9966	−	20.7787i	−0.383805	−	0.664770i	−0.991603	+	0.129322i	$0.958720\pi$
$978$		0			0
$979$	−0.440875	+	2.50032i	−0.0140904	+	0.0799107i
$980$		0			0
$981$	5.02481	−	8.70323i	0.160430	−	0.277873i
$982$		0			0
$983$	−43.6921	−	15.9026i	−1.39356	−	0.507215i	−0.467301	−	0.884098i	$-0.654774\pi$
$983$	−43.6921	−	15.9026i	−1.39356	−	0.507215i	−0.926261	+	0.376883i	$0.876996\pi$
$984$		0			0
$985$	14.8175	−	12.4333i	0.472124	−	0.396159i
$986$		0			0
$987$	7.57667			0.241168
$988$		0			0
$989$	−0.228549			−0.00726743
$990$		0			0
$991$	27.0041	−	22.6591i	0.857813	−	0.719791i	−0.103683	−	0.994610i	$-0.533063\pi$
$991$	27.0041	−	22.6591i	0.857813	−	0.719791i	0.961496	+	0.274820i	$0.0886182\pi$
$992$		0			0
$993$	−5.92350	−	2.15598i	−0.187976	−	0.0684178i
$994$		0			0
$995$	−9.56077	+	16.5597i	−0.303097	+	0.524979i
$996$		0			0
$997$	9.65270	−	54.7432i	0.305704	−	1.73373i	−0.314467	−	0.949268i	$-0.601826\pi$
$997$	9.65270	−	54.7432i	0.305704	−	1.73373i	0.620171	−	0.784466i	$-0.287063\pi$
$998$		0			0
$999$	0.581252	+	1.00676i	0.0183900	+	0.0318524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.q.a.85.1	✓	6
3.2	odd	2		684.2.bo.a.541.1		6
4.3	odd	2		912.2.bo.e.769.1		6
19.6	even	9		4332.2.a.o.1.1		3
19.13	odd	18		4332.2.a.n.1.1		3
19.17	even	9	inner	228.2.q.a.169.1	yes	6
57.17	odd	18		684.2.bo.a.397.1		6
76.55	odd	18		912.2.bo.e.625.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.q.a.85.1	✓	6	1.1	even	1	trivial
228.2.q.a.169.1	yes	6	19.17	even	9	inner
684.2.bo.a.397.1		6	57.17	odd	18
684.2.bo.a.541.1		6	3.2	odd	2
912.2.bo.e.625.1		6	76.55	odd	18
912.2.bo.e.769.1		6	4.3	odd	2
4332.2.a.n.1.1		3	19.13	odd	18
4332.2.a.o.1.1		3	19.6	even	9

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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{3} +(0.826352 + 0.300767i) q^{5} +(1.09240 - 1.89209i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{3} +(0.826352 + 0.300767i) q^{5} +(1.09240 - 1.89209i) q^{7} +(0.173648 - 0.984808i) q^{9} +(0.0812519 + 0.140732i) q^{11} +(0.581252 + 0.487728i) q^{13} +(0.826352 - 0.300767i) q^{15} +(0.539363 + 3.05888i) q^{17} +(2.77719 - 3.35965i) q^{19} +(-0.379385 - 2.15160i) q^{21} +(-1.21301 + 0.441500i) q^{23} +(-3.23783 - 2.71686i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(-1.13176 + 6.41852i) q^{29} +(-0.479055 + 0.829748i) q^{31} +(0.152704 + 0.0555796i) q^{33} +(1.47178 - 1.23497i) q^{35} -1.16250 q^{37} +0.758770 q^{39} +(-8.11721 + 6.81115i) q^{41} +(0.166374 + 0.0605553i) q^{43} +(0.439693 - 0.761570i) q^{45} +(-0.602196 + 3.41523i) q^{47} +(1.11334 + 1.92836i) q^{49} +(2.37939 + 1.99654i) q^{51} +(-7.83022 + 2.84997i) q^{53} +(0.0248149 + 0.140732i) q^{55} +(-0.0320889 - 4.35878i) q^{57} +(-0.482926 - 2.73881i) q^{59} +(-6.79086 + 2.47167i) q^{61} +(-1.67365 - 1.40436i) q^{63} +(0.333626 + 0.577857i) q^{65} +(0.184793 - 1.04801i) q^{67} +(-0.645430 + 1.11792i) q^{69} +(-4.77719 - 1.73875i) q^{71} +(1.72281 - 1.44561i) q^{73} -4.22668 q^{75} +0.355037 q^{77} +(-4.01501 + 3.36900i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(8.55690 - 14.8210i) q^{83} +(-0.474308 + 2.68993i) q^{85} +(3.25877 + 5.64436i) q^{87} +(11.9684 + 10.0427i) q^{89} +(1.55778 - 0.566986i) q^{91} +(0.166374 + 0.943555i) q^{93} +(3.30541 - 1.94096i) q^{95} +(-1.63563 - 9.27612i) q^{97} +(0.152704 - 0.0555796i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{5} + 3 q^{7}+O(q^{10}) \) 6 * q + 6 * q^5 + 3 * q^7	\( 6 q + 6 q^{5} + 3 q^{7} + 3 q^{11} + 6 q^{13} + 6 q^{15} + 12 q^{17} + 6 q^{19} + 9 q^{21} - 15 q^{23} - 3 q^{27} - 12 q^{29} - 6 q^{31} + 3 q^{33} - 6 q^{35} - 12 q^{37} - 18 q^{39} - 18 q^{41} - 18 q^{43} - 3 q^{45} - 3 q^{47} + 3 q^{51} - 24 q^{53} - 27 q^{55} + 9 q^{57} + 18 q^{59} - 9 q^{61} - 9 q^{63} + 21 q^{65} - 6 q^{67} + 12 q^{69} - 18 q^{71} + 21 q^{73} - 12 q^{75} - 48 q^{77} + 6 q^{79} + 15 q^{83} + 27 q^{85} - 3 q^{87} + 15 q^{89} + 30 q^{91} - 18 q^{93} + 24 q^{95} + 9 q^{97} + 3 q^{99}+O(q^{100}) \) 6 * q + 6 * q^5 + 3 * q^7 + 3 * q^11 + 6 * q^13 + 6 * q^15 + 12 * q^17 + 6 * q^19 + 9 * q^21 - 15 * q^23 - 3 * q^27 - 12 * q^29 - 6 * q^31 + 3 * q^33 - 6 * q^35 - 12 * q^37 - 18 * q^39 - 18 * q^41 - 18 * q^43 - 3 * q^45 - 3 * q^47 + 3 * q^51 - 24 * q^53 - 27 * q^55 + 9 * q^57 + 18 * q^59 - 9 * q^61 - 9 * q^63 + 21 * q^65 - 6 * q^67 + 12 * q^69 - 18 * q^71 + 21 * q^73 - 12 * q^75 - 48 * q^77 + 6 * q^79 + 15 * q^83 + 27 * q^85 - 3 * q^87 + 15 * q^89 + 30 * q^91 - 18 * q^93 + 24 * q^95 + 9 * q^97 + 3 * q^99

Introduction

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Modular forms

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Representations

Groups

Database

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