LMFDB - Embedded newform 228.2.q.a.25.1

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			25.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	228.25
Dual form			228.2.q.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{3} +(0.233956 + 1.32683i) q^{5} +(-1.20574 + 2.08840i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{3} +(0.233956 + 1.32683i) q^{5} +(-1.20574 + 2.08840i) q^{7} +(0.766044 + 0.642788i) q^{9} +(2.97178 + 5.14728i) q^{11} +(3.47178 - 1.26363i) q^{13} +(0.233956 - 1.32683i) q^{15} +(-0.124485 + 0.104455i) q^{17} +(-4.11721 - 1.43128i) q^{19} +(1.84730 - 1.55007i) q^{21} +(-1.14156 + 6.47410i) q^{23} +(2.99273 - 1.08926i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(1.83022 + 1.53574i) q^{29} +(1.29813 - 2.24843i) q^{31} +(-1.03209 - 5.85327i) q^{33} +(-3.05303 - 1.11121i) q^{35} -6.94356 q^{37} -3.69459 q^{39} +(0.340022 + 0.123758i) q^{41} +(-1.98886 - 11.2794i) q^{43} +(-0.673648 + 1.16679i) q^{45} +(-5.26991 - 4.42198i) q^{47} +(0.592396 + 1.02606i) q^{49} +(0.152704 - 0.0555796i) q^{51} +(0.698463 - 3.96118i) q^{53} +(-6.13429 + 5.14728i) q^{55} +(3.37939 + 2.75314i) q^{57} +(9.23055 - 7.74535i) q^{59} +(1.07398 - 6.09083i) q^{61} +(-2.26604 + 0.824773i) q^{63} +(2.48886 + 4.31082i) q^{65} +(-4.41147 - 3.70167i) q^{67} +(3.28699 - 5.69323i) q^{69} +(2.11721 + 12.0073i) q^{71} +(8.61721 + 3.13641i) q^{73} -3.18479 q^{75} -14.3327 q^{77} +(9.10994 + 3.31575i) q^{79} +(0.173648 + 0.984808i) q^{81} +(-1.01367 + 1.75573i) q^{83} +(-0.167718 - 0.140732i) q^{85} +(-1.19459 - 2.06910i) q^{87} +(-3.24035 + 1.17939i) q^{89} +(-1.54710 + 8.77406i) q^{91} +(-1.98886 + 1.66885i) q^{93} +(0.935822 - 5.79769i) q^{95} +(9.26264 - 7.77228i) q^{97} +(-1.03209 + 5.85327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$	$1$

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
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$4$		0			0
$5$	0.233956	+	1.32683i	0.104628	+	0.593375i	0.991368	+	0.131107i	$0.0418532\pi$
$5$	0.233956	+	1.32683i	0.104628	+	0.593375i	−0.886740	+	0.462268i	$0.847036\pi$
$6$		0			0
$7$	−1.20574	+	2.08840i	−0.455726	+	0.789340i	−0.998730	−	0.0503900i	$-0.983954\pi$
$7$	−1.20574	+	2.08840i	−0.455726	+	0.789340i	0.543004	+	0.839730i	$0.317287\pi$
$8$		0			0
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$		0			0
$11$	2.97178	+	5.14728i	0.896026	+	1.55196i	0.832530	+	0.553980i	$0.186892\pi$
$11$	2.97178	+	5.14728i	0.896026	+	1.55196i	0.0634960	+	0.997982i	$0.479775\pi$
$12$		0			0
$13$	3.47178	−	1.26363i	0.962899	−	0.350467i	0.187730	−	0.982221i	$-0.439887\pi$
$13$	3.47178	−	1.26363i	0.962899	−	0.350467i	0.775169	+	0.631754i	$0.217665\pi$
$14$		0			0
$15$	0.233956	−	1.32683i	0.0604071	−	0.342585i
$16$		0			0
$17$	−0.124485	+	0.104455i	−0.0301921	+	0.0253342i	−0.657759	−	0.753229i	$-0.728495\pi$
$17$	−0.124485	+	0.104455i	−0.0301921	+	0.0253342i	0.627567	+	0.778563i	$0.284051\pi$
$18$		0			0
$19$	−4.11721	−	1.43128i	−0.944553	−	0.328359i
$19$	−4.11721	−	1.43128i	−0.944553	−	0.328359i
$20$		0			0
$21$	1.84730	−	1.55007i	0.403113	−	0.338252i
$22$		0			0
$23$	−1.14156	+	6.47410i	−0.238032	+	1.34994i	0.598103	+	0.801419i	$0.295921\pi$
$23$	−1.14156	+	6.47410i	−0.238032	+	1.34994i	−0.836134	+	0.548525i	$0.815190\pi$
$24$		0			0
$25$	2.99273	−	1.08926i	0.598545	−	0.217853i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	1.83022	+	1.53574i	0.339864	+	0.285180i	0.796705	−	0.604369i	$-0.206575\pi$
$29$	1.83022	+	1.53574i	0.339864	+	0.285180i	−0.456841	+	0.889548i	$0.651019\pi$
$30$		0			0
$31$	1.29813	−	2.24843i	0.233152	−	0.403830i	−0.725582	−	0.688135i	$-0.758429\pi$
$31$	1.29813	−	2.24843i	0.233152	−	0.403830i	0.958734	+	0.284305i	$0.0917628\pi$
$32$		0			0
$33$	−1.03209	−	5.85327i	−0.179664	−	1.01892i
$34$		0			0
$35$	−3.05303	−	1.11121i	−0.516057	−	0.187829i
$36$		0			0
$37$	−6.94356			−1.14151			−0.570757	−	0.821119i	$-0.693350\pi$
$37$	−6.94356			−1.14151			−0.570757	+	0.821119i	$0.693350\pi$
$38$		0			0
$39$	−3.69459			−0.591608
$40$		0			0
$41$	0.340022	+	0.123758i	0.0531026	+	0.0193278i	0.368435	−	0.929654i	$-0.379894\pi$
$41$	0.340022	+	0.123758i	0.0531026	+	0.0193278i	−0.315332	+	0.948981i	$0.602116\pi$
$42$		0			0
$43$	−1.98886	−	11.2794i	−0.303298	−	1.72009i	−0.631411	−	0.775448i	$-0.717524\pi$
$43$	−1.98886	−	11.2794i	−0.303298	−	1.72009i	0.328114	−	0.944638i	$-0.393587\pi$
$44$		0			0
$45$	−0.673648	+	1.16679i	−0.100422	+	0.173935i
$46$		0			0
$47$	−5.26991	−	4.42198i	−0.768696	−	0.645013i	0.171679	−	0.985153i	$-0.445081\pi$
$47$	−5.26991	−	4.42198i	−0.768696	−	0.645013i	−0.940375	+	0.340140i	$0.889525\pi$
$48$		0			0
$49$	0.592396	+	1.02606i	0.0846280	+	0.146580i
$50$		0			0
$51$	0.152704	−	0.0555796i	0.0213828	−	0.00778270i
$52$		0			0
$53$	0.698463	−	3.96118i	0.0959413	−	0.544110i	−0.898514	−	0.438946i	$-0.855352\pi$
$53$	0.698463	−	3.96118i	0.0959413	−	0.544110i	0.994455	−	0.105164i	$-0.0335369\pi$
$54$		0			0
$55$	−6.13429	+	5.14728i	−0.827147	+	0.694059i
$56$		0			0
$57$	3.37939	+	2.75314i	0.447611	+	0.364662i
$58$		0			0
$59$	9.23055	−	7.74535i	1.20172	−	1.00836i	0.202136	−	0.979357i	$-0.435212\pi$
$59$	9.23055	−	7.74535i	1.20172	−	1.00836i	0.999579	−	0.0290016i	$-0.00923279\pi$
$60$		0			0
$61$	1.07398	−	6.09083i	0.137509	−	0.779851i	−0.835571	−	0.549383i	$-0.814863\pi$
$61$	1.07398	−	6.09083i	0.137509	−	0.779851i	0.973080	−	0.230469i	$-0.0740259\pi$
$62$		0			0
$63$	−2.26604	+	0.824773i	−0.285495	+	0.103912i
$64$		0			0
$65$	2.48886	+	4.31082i	0.308705	+	0.534692i
$66$		0			0
$67$	−4.41147	−	3.70167i	−0.538947	−	0.452231i	0.332230	−	0.943198i	$-0.392199\pi$
$67$	−4.41147	−	3.70167i	−0.538947	−	0.452231i	−0.871178	+	0.490968i	$0.836643\pi$
$68$		0			0
$69$	3.28699	−	5.69323i	0.395707	−	0.685385i
$70$		0			0
$71$	2.11721	+	12.0073i	0.251267	+	1.42500i	0.805477	+	0.592628i	$0.201909\pi$
$71$	2.11721	+	12.0073i	0.251267	+	1.42500i	−0.554210	+	0.832377i	$0.686980\pi$
$72$		0			0
$73$	8.61721	+	3.13641i	1.00857	+	0.367089i	0.792883	−	0.609374i	$-0.208579\pi$
$73$	8.61721	+	3.13641i	1.00857	+	0.367089i	0.215685	+	0.976463i	$0.430801\pi$
$74$		0			0
$75$	−3.18479			−0.367748
$76$		0			0
$77$	−14.3327			−1.63337
$78$		0			0
$79$	9.10994	+	3.31575i	1.02495	+	0.373051i	0.799155	−	0.601125i	$-0.205281\pi$
$79$	9.10994	+	3.31575i	1.02495	+	0.373051i	0.225793	+	0.974175i	$0.427503\pi$
$80$		0			0
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$		0			0
$83$	−1.01367	+	1.75573i	−0.111265	+	0.192716i	−0.916280	−	0.400537i	$-0.868824\pi$
$83$	−1.01367	+	1.75573i	−0.111265	+	0.192716i	0.805016	+	0.593254i	$0.202157\pi$
$84$		0			0
$85$	−0.167718	−	0.140732i	−0.0181916	−	0.0152646i
$86$		0			0
$87$	−1.19459	−	2.06910i	−0.128074	−	0.221830i
$88$		0			0
$89$	−3.24035	+	1.17939i	−0.343477	+	0.125015i	−0.507998	−	0.861358i	$-0.669614\pi$
$89$	−3.24035	+	1.17939i	−0.343477	+	0.125015i	0.164521	+	0.986374i	$0.447392\pi$
$90$		0			0
$91$	−1.54710	+	8.77406i	−0.162181	+	0.919771i
$92$		0			0
$93$	−1.98886	+	1.66885i	−0.206235	+	0.173051i
$94$		0			0
$95$	0.935822	−	5.79769i	0.0960133	−	0.594830i
$96$		0			0
$97$	9.26264	−	7.77228i	0.940479	−	0.789155i	−0.0371898	−	0.999308i	$-0.511841\pi$
$97$	9.26264	−	7.77228i	0.940479	−	0.789155i	0.977669	+	0.210153i	$0.0673962\pi$
$98$		0			0
$99$	−1.03209	+	5.85327i	−0.103729	+	0.588275i
$100$		0			0
$101$	3.69846	−	1.34613i	0.368011	−	0.133945i	−0.151394	−	0.988474i	$-0.548376\pi$
$101$	3.69846	−	1.34613i	0.368011	−	0.133945i	0.519404	+	0.854529i	$0.326154\pi$
$102$		0			0
$103$	6.15657	+	10.6635i	0.606625	+	1.05071i	0.991792	+	0.127859i	$0.0408105\pi$
$103$	6.15657	+	10.6635i	0.606625	+	1.05071i	−0.385167	+	0.922847i	$0.625856\pi$
$104$		0			0
$105$	2.48886	+	2.08840i	0.242887	+	0.203807i
$106$		0			0
$107$	6.71688	−	11.6340i	0.649345	−	1.12470i	−0.333934	−	0.942596i	$-0.608376\pi$
$107$	6.71688	−	11.6340i	0.649345	−	1.12470i	0.983279	−	0.182103i	$-0.0582904\pi$
$108$		0			0
$109$	0.393933	+	2.23411i	0.0377320	+	0.213989i	0.997844	−	0.0656260i	$-0.0209044\pi$
$109$	0.393933	+	2.23411i	0.0377320	+	0.213989i	−0.960112	+	0.279615i	$0.909793\pi$
$110$		0			0
$111$	6.52481	+	2.37484i	0.619308	+	0.225410i
$112$		0			0
$113$	−12.7101			−1.19566			−0.597832	−	0.801622i	$-0.703971\pi$
$113$	−12.7101			−1.19566			−0.597832	+	0.801622i	$0.703971\pi$
$114$		0			0
$115$	−8.85710			−0.825929
$116$		0			0
$117$	3.47178	+	1.26363i	0.320966	+	0.116822i
$118$		0			0
$119$	−0.0680482	−	0.385920i	−0.00623797	−	0.0353773i
$120$		0			0
$121$	−12.1630	+	21.0669i	−1.10572	+	1.91517i
$122$		0			0
$123$	−0.277189	−	0.232589i	−0.0249933	−	0.0209718i
$124$		0			0
$125$	5.51367	+	9.54996i	0.493158	+	0.854174i
$126$		0			0
$127$	−7.26517	+	2.64430i	−0.644679	+	0.234644i	−0.643608	−	0.765355i	$-0.722563\pi$
$127$	−7.26517	+	2.64430i	−0.644679	+	0.234644i	−0.00107137	+	0.999999i	$0.500341\pi$
$128$		0			0
$129$	−1.98886	+	11.2794i	−0.175109	+	0.993092i
$130$		0			0
$131$	9.62701	−	8.07802i	0.841116	−	0.705780i	−0.116699	−	0.993167i	$-0.537231\pi$
$131$	9.62701	−	8.07802i	0.841116	−	0.705780i	0.957814	+	0.287387i	$0.0927867\pi$
$132$		0			0
$133$	7.95336	−	6.87262i	0.689644	−	0.595932i
$134$		0			0
$135$	1.03209	−	0.866025i	0.0888281	−	0.0745356i
$136$		0			0
$137$	2.72803	−	15.4714i	0.233071	−	1.32181i	−0.613567	−	0.789642i	$-0.710266\pi$
$137$	2.72803	−	15.4714i	0.233071	−	1.32181i	0.846638	−	0.532169i	$-0.178623\pi$
$138$		0			0
$139$	−3.03936	+	1.10624i	−0.257795	+	0.0938298i	−0.467685	−	0.883895i	$-0.654912\pi$
$139$	−3.03936	+	1.10624i	−0.257795	+	0.0938298i	0.209890	+	0.977725i	$0.432690\pi$
$140$		0			0
$141$	3.43969	+	5.95772i	0.289674	+	0.501731i
$142$		0			0
$143$	16.8216	+	14.1150i	1.40669	+	1.18036i
$144$		0			0
$145$	−1.60947	+	2.78768i	−0.133659	+	0.231505i
$146$		0			0
$147$	−0.205737	−	1.16679i	−0.0169689	−	0.0962355i
$148$		0			0
$149$	−4.19119	−	1.52547i	−0.343356	−	0.124971i	0.164586	−	0.986363i	$-0.447371\pi$
$149$	−4.19119	−	1.52547i	−0.343356	−	0.124971i	−0.507942	+	0.861392i	$0.669593\pi$
$150$		0			0
$151$	8.94862			0.728228			0.364114	−	0.931354i	$-0.381372\pi$
$151$	8.94862			0.728228			0.364114	+	0.931354i	$0.381372\pi$
$152$		0			0
$153$	−0.162504			−0.0131377
$154$		0			0
$155$	3.28699	+	1.19637i	0.264017	+	0.0960944i
$156$		0			0
$157$	−2.00047	−	11.3452i	−0.159655	−	0.905446i	−0.954406	−	0.298511i	$-0.903510\pi$
$157$	−2.00047	−	11.3452i	−0.159655	−	0.905446i	0.794751	−	0.606935i	$-0.207601\pi$
$158$		0			0
$159$	−2.01114	+	3.48340i	−0.159494	+	0.276252i
$160$		0			0
$161$	−12.1441	−	10.1901i	−0.957088	−	0.803092i
$162$		0			0
$163$	5.26217	+	9.11435i	0.412165	+	0.713891i	0.995126	−	0.0986089i	$-0.0314393\pi$
$163$	5.26217	+	9.11435i	0.412165	+	0.713891i	−0.582961	+	0.812500i	$0.698106\pi$
$164$		0			0
$165$	7.52481	−	2.73881i	0.585806	−	0.213216i
$166$		0			0
$167$	1.86484	−	10.5760i	0.144305	−	0.818397i	−0.823617	−	0.567147i	$-0.808047\pi$
$167$	1.86484	−	10.5760i	0.144305	−	0.818397i	0.967922	−	0.251250i	$-0.0808417\pi$
$168$		0			0
$169$	0.497941	−	0.417822i	0.0383031	−	0.0321401i
$170$		0			0
$171$	−2.23396	−	3.74292i	−0.170835	−	0.286228i
$172$		0			0
$173$	−5.77584	+	4.84651i	−0.439129	+	0.368473i	−0.835383	−	0.549668i	$-0.814754\pi$
$173$	−5.77584	+	4.84651i	−0.439129	+	0.368473i	0.396254	+	0.918141i	$0.370310\pi$
$174$		0			0
$175$	−1.33363	+	7.56337i	−0.100813	+	0.571737i
$176$		0			0
$177$	−11.3229	+	4.12122i	−0.851085	+	0.309770i
$178$		0			0
$179$	−13.1814	−	22.8308i	−0.985223	−	1.70646i	−0.640940	−	0.767591i	$-0.721455\pi$
$179$	−13.1814	−	22.8308i	−0.985223	−	1.70646i	−0.344283	−	0.938866i	$-0.611878\pi$
$180$		0			0
$181$	16.1570	+	13.5574i	1.20094	+	1.00771i	0.999603	+	0.0281899i	$0.00897431\pi$
$181$	16.1570	+	13.5574i	1.20094	+	1.00771i	0.201341	+	0.979521i	$0.435470\pi$
$182$		0			0
$183$	−3.09240	+	5.35619i	−0.228597	+	0.395941i
$184$		0			0
$185$	−1.62449	−	9.21291i	−0.119435	−	0.677347i
$186$		0			0
$187$	−0.907604	−	0.330341i	−0.0663706	−	0.0241569i
$188$		0			0
$189$	2.41147			0.175409
$190$		0			0
$191$	−0.255777			−0.0185074			−0.00925370	−	0.999957i	$-0.502946\pi$
$191$	−0.255777			−0.0185074			−0.00925370	+	0.999957i	$0.502946\pi$
$192$		0			0
$193$	−13.4829	−	4.90738i	−0.970522	−	0.353241i	−0.192374	−	0.981322i	$-0.561619\pi$
$193$	−13.4829	−	4.90738i	−0.970522	−	0.353241i	−0.778148	+	0.628081i	$0.783841\pi$
$194$		0			0
$195$	−0.864370	−	4.90209i	−0.0618989	−	0.351046i
$196$		0			0
$197$	−11.8405	+	20.5083i	−0.843600	+	1.46116i	0.0432316	+	0.999065i	$0.486235\pi$
$197$	−11.8405	+	20.5083i	−0.843600	+	1.46116i	−0.886832	+	0.462093i	$0.847099\pi$
$198$		0			0
$199$	−9.03596	−	7.58207i	−0.640542	−	0.537479i	0.263642	−	0.964620i	$-0.415076\pi$
$199$	−9.03596	−	7.58207i	−0.640542	−	0.537479i	−0.904185	+	0.427142i	$0.859521\pi$
$200$		0			0
$201$	2.87939	+	4.98724i	0.203096	+	0.351773i
$202$		0			0
$203$	−5.41400	+	1.97053i	−0.379988	+	0.138304i
$204$		0			0
$205$	−0.0846555	+	0.480105i	−0.00591260	+	0.0335320i
$206$		0			0
$207$	−5.03596	+	4.22567i	−0.350023	+	0.293704i
$208$		0			0
$209$	−4.86824	−	25.4459i	−0.336743	−	1.76013i
$210$		0			0
$211$	21.3405	−	17.9068i	1.46914	−	1.23275i	0.552211	−	0.833705i	$-0.313784\pi$
$211$	21.3405	−	17.9068i	1.46914	−	1.23275i	0.916929	−	0.399050i	$-0.130660\pi$
$212$		0			0
$213$	2.11721	−	12.0073i	0.145069	−	0.822727i
$214$		0			0
$215$	14.5005	−	5.27774i	0.988924	−	0.359939i
$216$		0			0
$217$	3.13041	+	5.42204i	0.212506	+	0.368072i
$218$		0			0
$219$	−7.02481	−	5.89452i	−0.474693	−	0.398315i
$220$		0			0
$221$	−0.300193	+	0.519949i	−0.0201931	+	0.0349756i
$222$		0			0
$223$	−4.29561	−	24.3616i	−0.287655	−	1.63137i	−0.695644	−	0.718386i	$-0.744881\pi$
$223$	−4.29561	−	24.3616i	−0.287655	−	1.63137i	0.407989	−	0.912987i	$-0.366230\pi$
$224$		0			0
$225$	2.99273	+	1.08926i	0.199515	+	0.0726175i
$226$		0			0
$227$	−22.0155			−1.46122			−0.730609	−	0.682796i	$-0.760764\pi$
$227$	−22.0155			−1.46122			−0.730609	+	0.682796i	$0.760764\pi$
$228$		0			0
$229$	−9.29591			−0.614291			−0.307146	−	0.951663i	$-0.599374\pi$
$229$	−9.29591			−0.614291			−0.307146	+	0.951663i	$0.599374\pi$
$230$		0			0
$231$	13.4684	+	4.90209i	0.886154	+	0.322534i
$232$		0			0
$233$	−1.38713	−	7.86678i	−0.0908736	−	0.515370i	−0.995934	−	0.0900867i	$-0.971286\pi$
$233$	−1.38713	−	7.86678i	−0.0908736	−	0.515370i	0.905060	−	0.425283i	$-0.139826\pi$
$234$		0			0
$235$	4.63429	−	8.02682i	0.302307	−	0.523612i
$236$		0			0
$237$	−7.42649	−	6.23156i	−0.482402	−	0.404784i
$238$		0			0
$239$	13.2246	+	22.9057i	0.855430	+	1.48165i	0.876246	+	0.481864i	$0.160040\pi$
$239$	13.2246	+	22.9057i	0.855430	+	1.48165i	−0.0208161	+	0.999783i	$0.506626\pi$
$240$		0			0
$241$	2.57398	−	0.936851i	0.165804	−	0.0603479i	−0.257784	−	0.966202i	$-0.582992\pi$
$241$	2.57398	−	0.936851i	0.165804	−	0.0603479i	0.423589	+	0.905855i	$0.360770\pi$
$242$		0			0
$243$	0.173648	−	0.984808i	0.0111395	−	0.0631754i
$244$		0			0
$245$	−1.22281	+	1.02606i	−0.0781225	+	0.0655526i
$246$		0			0
$247$	−16.1027	+	0.233508i	−1.02459	+	0.0148578i
$248$		0			0
$249$	1.55303	−	1.30315i	0.0984195	−	0.0825838i
$250$		0			0
$251$	2.64455	−	14.9980i	0.166923	−	0.946665i	−0.780137	−	0.625608i	$-0.784851\pi$
$251$	2.64455	−	14.9980i	0.166923	−	0.946665i	0.947060	−	0.321057i	$-0.104038\pi$
$252$		0			0
$253$	−36.7165	+	13.3637i	−2.30834	+	0.840169i
$254$		0			0
$255$	0.109470	+	0.189608i	0.00685530	+	0.0118737i
$256$		0			0
$257$	9.98545	+	8.37879i	0.622875	+	0.522655i	0.898706	−	0.438552i	$-0.144508\pi$
$257$	9.98545	+	8.37879i	0.622875	+	0.522655i	−0.275831	+	0.961206i	$0.588953\pi$
$258$		0			0
$259$	8.37211	−	14.5009i	0.520218	−	0.901043i
$260$		0			0
$261$	0.414878	+	2.35289i	0.0256803	+	0.145640i
$262$		0			0
$263$	11.2071	+	4.07904i	0.691058	+	0.251525i	0.663588	−	0.748098i	$-0.269033\pi$
$263$	11.2071	+	4.07904i	0.691058	+	0.251525i	0.0274700	+	0.999623i	$0.491255\pi$
$264$		0			0
$265$	5.41921			0.332900
$266$		0			0
$267$	3.44831			0.211033
$268$		0			0
$269$	−24.2986	−	8.84397i	−1.48151	−	0.539226i	−0.530312	−	0.847802i	$-0.677925\pi$
$269$	−24.2986	−	8.84397i	−1.48151	−	0.539226i	−0.951200	+	0.308576i	$0.900148\pi$
$270$		0			0
$271$	2.06165	+	11.6922i	0.125236	+	0.710251i	0.981167	+	0.193161i	$0.0618738\pi$
$271$	2.06165	+	11.6922i	0.125236	+	0.710251i	−0.855931	+	0.517090i	$0.827015\pi$
$272$		0			0
$273$	4.45471	−	7.71578i	0.269611	−	0.466980i
$274$		0			0
$275$	14.5005	+	12.1673i	0.874411	+	0.733718i
$276$		0			0
$277$	−7.20574	−	12.4807i	−0.432951	−	0.749893i	0.564175	−	0.825655i	$-0.309194\pi$
$277$	−7.20574	−	12.4807i	−0.432951	−	0.749893i	−0.997126	+	0.0757624i	$0.975861\pi$
$278$		0			0
$279$	2.43969	−	0.887975i	0.146061	−	0.0531617i
$280$		0			0
$281$	−0.456929	+	2.59137i	−0.0272581	+	0.154588i	−0.995399	−	0.0958183i	$-0.969453\pi$
$281$	−0.456929	+	2.59137i	−0.0272581	+	0.154588i	0.968141	+	0.250407i	$0.0805643\pi$
$282$		0			0
$283$	4.66637	−	3.91555i	0.277387	−	0.232755i	−0.493471	−	0.869762i	$-0.664272\pi$
$283$	4.66637	−	3.91555i	0.277387	−	0.232755i	0.770858	+	0.637007i	$0.219828\pi$
$284$		0			0
$285$	−2.86231	+	5.12797i	−0.169549	+	0.303755i
$286$		0			0
$287$	−0.668434	+	0.560882i	−0.0394564	+	0.0331078i
$288$		0			0
$289$	−2.94743	+	16.7157i	−0.173378	+	0.983278i
$290$		0			0
$291$	−11.3623	+	4.13554i	−0.666070	+	0.242430i
$292$		0			0
$293$	16.3653	+	28.3455i	0.956071	+	1.65596i	0.731897	+	0.681415i	$0.238635\pi$
$293$	16.3653	+	28.3455i	0.956071	+	1.65596i	0.224174	+	0.974549i	$0.428032\pi$
$294$		0			0
$295$	12.4363	+	10.4353i	0.724069	+	0.607566i
$296$		0			0
$297$	2.97178	−	5.14728i	0.172440	−	0.298675i
$298$		0			0
$299$	4.21760	+	23.9192i	0.243910	+	1.38328i
$300$		0			0
$301$	25.9538	+	9.44642i	1.49595	+	0.544483i
$302$		0			0
$303$	−3.93582			−0.226107
$304$		0			0
$305$	8.33275			0.477132
$306$		0			0
$307$	5.83497	+	2.12376i	0.333019	+	0.121209i	0.503118	−	0.864218i	$-0.332186\pi$
$307$	5.83497	+	2.12376i	0.333019	+	0.121209i	−0.170098	+	0.985427i	$0.554408\pi$
$308$		0			0
$309$	−2.13816	−	12.1261i	−0.121635	−	0.689829i
$310$		0			0
$311$	−1.55303	+	2.68993i	−0.0880644	+	0.152532i	−0.906693	−	0.421791i	$-0.861401\pi$
$311$	−1.55303	+	2.68993i	−0.0880644	+	0.152532i	0.818628	+	0.574323i	$0.194735\pi$
$312$		0			0
$313$	−12.9251	−	10.8455i	−0.730572	−	0.613023i	0.199715	−	0.979854i	$-0.435998\pi$
$313$	−12.9251	−	10.8455i	−0.730572	−	0.613023i	−0.930288	+	0.366831i	$0.880443\pi$
$314$		0			0
$315$	−1.62449	−	2.81369i	−0.0915294	−	0.158534i
$316$		0			0
$317$	−13.5560	+	4.93399i	−0.761382	+	0.277120i	−0.693387	−	0.720565i	$-0.743882\pi$
$317$	−13.5560	+	4.93399i	−0.761382	+	0.277120i	−0.0679951	+	0.997686i	$0.521660\pi$
$318$		0			0
$319$	−2.46585	+	13.9845i	−0.138061	+	0.782984i
$320$		0			0
$321$	−10.2909	+	8.63506i	−0.574380	+	0.481962i
$322$		0			0
$323$	0.662037	−	0.251892i	0.0368367	−	0.0140156i
$324$		0			0
$325$	9.01367	−	7.56337i	0.499988	−	0.419540i
$326$		0			0
$327$	0.393933	−	2.23411i	0.0217846	−	0.123546i
$328$		0			0
$329$	15.5890	−	5.67393i	0.859449	−	0.312814i
$330$		0			0
$331$	4.49866	+	7.79190i	0.247268	+	0.428282i	0.962767	−	0.270333i	$-0.0871337\pi$
$331$	4.49866	+	7.79190i	0.247268	+	0.428282i	−0.715498	+	0.698614i	$0.753800\pi$
$332$		0			0
$333$	−5.31908	−	4.46324i	−0.291484	−	0.244584i
$334$		0			0
$335$	3.87939	−	6.71929i	0.211953	−	0.367114i
$336$		0			0
$337$	−0.395582	−	2.24346i	−0.0215487	−	0.122209i	0.972136	−	0.234418i	$-0.0753185\pi$
$337$	−0.395582	−	2.24346i	−0.0215487	−	0.122209i	−0.993685	+	0.112209i	$0.964207\pi$
$338$		0			0
$339$	11.9436	+	4.34710i	0.648685	+	0.236102i
$340$		0			0
$341$	15.4311			0.835640
$342$		0			0
$343$	−19.7374			−1.06572
$344$		0			0
$345$	8.32295	+	3.02931i	0.448092	+	0.163092i
$346$		0			0
$347$	1.30288	+	7.38901i	0.0699423	+	0.396663i	0.999601	+	0.0282410i	$0.00899059\pi$
$347$	1.30288	+	7.38901i	0.0699423	+	0.396663i	−0.929659	+	0.368422i	$0.879898\pi$
$348$		0			0
$349$	14.5175	−	25.1451i	0.777106	−	1.34599i	−0.156497	−	0.987678i	$-0.550020\pi$
$349$	14.5175	−	25.1451i	0.777106	−	1.34599i	0.933603	−	0.358309i	$-0.116647\pi$
$350$		0			0
$351$	−2.83022	−	2.37484i	−0.151066	−	0.126759i
$352$		0			0
$353$	11.7096	+	20.2816i	0.623240	+	1.07948i	0.988878	+	0.148726i	$0.0475172\pi$
$353$	11.7096	+	20.2816i	0.623240	+	1.07948i	−0.365639	+	0.930757i	$0.619150\pi$
$354$		0			0
$355$	−15.4363	+	5.61835i	−0.819273	+	0.298191i
$356$		0			0
$357$	−0.0680482	+	0.385920i	−0.00360149	+	0.0204251i
$358$		0			0
$359$	−27.3614	+	22.9590i	−1.44408	+	1.21173i	−0.507321	+	0.861757i	$0.669364\pi$
$359$	−27.3614	+	22.9590i	−1.44408	+	1.21173i	−0.936761	+	0.349971i	$0.886192\pi$
$360$		0			0
$361$	14.9029	+	11.7858i	0.784361	+	0.620305i
$362$		0			0
$363$	18.6348	−	15.6364i	0.978071	−	0.820699i
$364$		0			0
$365$	−2.14543	+	12.1673i	−0.112297	+	0.636867i
$366$		0			0
$367$	19.6694	−	7.15906i	1.02673	−	0.373700i	0.226897	−	0.973919i	$-0.427142\pi$
$367$	19.6694	−	7.15906i	1.02673	−	0.373700i	0.799836	+	0.600219i	$0.204920\pi$
$368$		0			0
$369$	0.180922	+	0.313366i	0.00941843	+	0.0163132i
$370$		0			0
$371$	7.43036	+	6.23481i	0.385765	+	0.323695i
$372$		0			0
$373$	1.44562	−	2.50389i	0.0748515	−	0.129647i	−0.826170	−	0.563421i	$-0.809485\pi$
$373$	1.44562	−	2.50389i	0.0748515	−	0.129647i	0.901022	+	0.433774i	$0.142818\pi$
$374$		0			0
$375$	−1.91488	−	10.8598i	−0.0988839	−	0.560798i
$376$		0			0
$377$	8.29473	+	3.01903i	0.427200	+	0.155488i
$378$		0			0
$379$	−24.7374			−1.27068			−0.635338	−	0.772234i	$-0.719139\pi$
$379$	−24.7374			−1.27068			−0.635338	+	0.772234i	$0.719139\pi$
$380$		0			0
$381$	7.73143			0.396093
$382$		0			0
$383$	−13.9611	−	5.08143i	−0.713379	−	0.259649i	−0.0402667	−	0.999189i	$-0.512821\pi$
$383$	−13.9611	−	5.08143i	−0.713379	−	0.259649i	−0.673112	+	0.739540i	$0.735043\pi$
$384$		0			0
$385$	−3.35323	−	19.0171i	−0.170896	−	0.969201i
$386$		0			0
$387$	5.72668	−	9.91890i	0.291104	−	0.504206i
$388$		0			0
$389$	24.3286	+	20.4141i	1.23351	+	1.03504i	0.998003	+	0.0631656i	$0.0201196\pi$
$389$	24.3286	+	20.4141i	1.23351	+	1.03504i	0.235507	+	0.971873i	$0.424325\pi$
$390$		0			0
$391$	−0.534148	−	0.925172i	−0.0270130	−	0.0467880i
$392$		0			0
$393$	−11.8093	+	4.29823i	−0.595699	+	0.216817i
$394$		0			0
$395$	−2.26810	+	12.8631i	−0.114121	+	0.647211i
$396$		0			0
$397$	−13.6138	+	11.4233i	−0.683257	+	0.573321i	−0.916956	−	0.398988i	$-0.869362\pi$
$397$	−13.6138	+	11.4233i	−0.683257	+	0.573321i	0.233699	+	0.972309i	$0.424917\pi$
$398$		0			0
$399$	−9.82429	+	3.73794i	−0.491830	+	0.187131i
$400$		0			0
$401$	−26.8371	+	22.5190i	−1.34018	+	1.12454i	−0.358600	+	0.933491i	$0.616746\pi$
$401$	−26.8371	+	22.5190i	−1.34018	+	1.12454i	−0.981580	+	0.191053i	$0.938810\pi$
$402$		0			0
$403$	1.66566	−	9.44642i	0.0829724	−	0.470560i
$404$		0			0
$405$	−1.26604	+	0.460802i	−0.0629103	+	0.0228975i
$406$		0			0
$407$	−20.6348	−	35.7404i	−1.02283	−	1.77159i
$408$		0			0
$409$	−8.83203	−	7.41096i	−0.436716	−	0.366448i	0.397763	−	0.917488i	$-0.369787\pi$
$409$	−8.83203	−	7.41096i	−0.436716	−	0.366448i	−0.834479	+	0.551040i	$0.814231\pi$
$410$		0			0
$411$	−7.85504	+	13.6053i	−0.387460	+	0.671101i
$412$		0			0
$413$	5.04576	+	28.6159i	0.248286	+	1.40810i
$414$		0			0
$415$	−2.56670	−	0.934204i	−0.125995	−	0.0458583i
$416$		0			0
$417$	3.23442			0.158390
$418$		0			0
$419$	−34.7692			−1.69859			−0.849293	−	0.527921i	$-0.822972\pi$
$419$	−34.7692			−1.69859			−0.849293	+	0.527921i	$0.822972\pi$
$420$		0			0
$421$	14.7579	+	5.37143i	0.719256	+	0.261788i	0.675610	−	0.737259i	$-0.263880\pi$
$421$	14.7579	+	5.37143i	0.719256	+	0.261788i	0.0436459	+	0.999047i	$0.486103\pi$
$422$		0			0
$423$	−1.19459	−	6.77487i	−0.0580831	−	0.329406i
$424$		0			0
$425$	−0.258770	+	0.448204i	−0.0125522	+	0.0217411i
$426$		0			0
$427$	11.4251	+	9.58683i	0.552902	+	0.463939i
$428$		0			0
$429$	−10.9795	−	19.0171i	−0.530096	−	0.918154i
$430$		0			0
$431$	12.6604	−	4.60802i	0.609832	−	0.221961i	−0.0185977	−	0.999827i	$-0.505920\pi$
$431$	12.6604	−	4.60802i	0.609832	−	0.221961i	0.628430	+	0.777866i	$0.283698\pi$
$432$		0			0
$433$	2.04442	−	11.5945i	0.0982483	−	0.557194i	−0.895455	−	0.445152i	$-0.853150\pi$
$433$	2.04442	−	11.5945i	0.0982483	−	0.557194i	0.993703	−	0.112042i	$-0.0357392\pi$
$434$		0			0
$435$	2.46585	−	2.06910i	0.118229	−	0.0992055i
$436$		0			0
$437$	13.9663	−	25.0214i	0.668100	−	1.19693i
$438$		0			0
$439$	12.0385	−	10.1015i	0.574566	−	0.482118i	−0.308592	−	0.951195i	$-0.599858\pi$
$439$	12.0385	−	10.1015i	0.574566	−	0.482118i	0.883157	+	0.469077i	$0.155413\pi$
$440$		0			0
$441$	−0.205737	+	1.16679i	−0.00979700	+	0.0555616i
$442$		0			0
$443$	14.6998	−	5.35029i	0.698409	−	0.254200i	0.0316775	−	0.999498i	$-0.489915\pi$
$443$	14.6998	−	5.35029i	0.698409	−	0.254200i	0.666731	+	0.745298i	$0.267693\pi$
$444$		0			0
$445$	−2.32295	−	4.02346i	−0.110118	−	0.190731i
$446$		0			0
$447$	3.41669	+	2.86694i	0.161604	+	0.135602i
$448$		0			0
$449$	9.09286	−	15.7493i	0.429119	−	0.743255i	−0.567676	−	0.823252i	$-0.692158\pi$
$449$	9.09286	−	15.7493i	0.429119	−	0.743255i	0.996795	+	0.0799963i	$0.0254909\pi$
$450$		0			0
$451$	0.373455	+	2.11797i	0.0175853	+	0.0997314i
$452$		0			0
$453$	−8.40895	−	3.06061i	−0.395087	−	0.143800i
$454$		0			0
$455$	−12.0036			−0.562738
$456$		0			0
$457$	16.8111			0.786390			0.393195	−	0.919455i	$-0.371370\pi$
$457$	16.8111			0.786390			0.393195	+	0.919455i	$0.371370\pi$
$458$		0			0
$459$	0.152704	+	0.0555796i	0.00712760	+	0.00259423i
$460$		0			0
$461$	−2.19429	−	12.4444i	−0.102198	−	0.579595i	−0.992302	−	0.123838i	$-0.960480\pi$
$461$	−2.19429	−	12.4444i	−0.102198	−	0.579595i	0.890104	−	0.455757i	$-0.150631\pi$
$462$		0			0
$463$	2.94743	−	5.10510i	0.136979	−	0.237254i	−0.789373	−	0.613914i	$-0.789594\pi$
$463$	2.94743	−	5.10510i	0.136979	−	0.237254i	0.926352	+	0.376660i	$0.122927\pi$
$464$		0			0
$465$	−2.67958	−	2.24843i	−0.124262	−	0.104269i
$466$		0			0
$467$	2.68479	+	4.65020i	0.124237	+	0.215185i	0.921435	−	0.388534i	$-0.127018\pi$
$467$	2.68479	+	4.65020i	0.124237	+	0.215185i	−0.797197	+	0.603719i	$0.793685\pi$
$468$		0			0
$469$	13.0496	−	4.74968i	0.602576	−	0.219320i
$470$		0			0
$471$	−2.00047	+	11.3452i	−0.0921766	+	0.522760i
$472$		0			0
$473$	52.1475	−	43.7570i	2.39775	−	2.01195i
$474$		0			0
$475$	−13.8807	+	0.201288i	−0.636892	+	0.00923571i
$476$		0			0
$477$	3.08125	−	2.58548i	0.141081	−	0.118381i
$478$		0			0
$479$	−3.44650	+	19.5461i	−0.157475	+	0.893083i	0.799014	+	0.601313i	$0.205355\pi$
$479$	−3.44650	+	19.5461i	−0.157475	+	0.893083i	−0.956488	+	0.291770i	$0.905756\pi$
$480$		0			0
$481$	−24.1065	+	8.77406i	−1.09916	+	0.400063i
$482$		0			0
$483$	7.92649	+	13.7291i	0.360668	+	0.624695i
$484$		0			0
$485$	12.4795	+	10.4716i	0.566666	+	0.475489i
$486$		0			0
$487$	−6.50387	+	11.2650i	−0.294718	+	0.510467i	−0.974919	−	0.222558i	$-0.928559\pi$
$487$	−6.50387	+	11.2650i	−0.294718	+	0.510467i	0.680201	+	0.733026i	$0.261893\pi$
$488$		0			0
$489$	−1.82753	−	10.3645i	−0.0826439	−	0.468697i
$490$		0			0
$491$	−27.9538	−	10.1744i	−1.26154	−	0.459163i	−0.377254	−	0.926110i	$-0.623131\pi$
$491$	−27.9538	−	10.1744i	−1.26154	−	0.459163i	−0.884285	+	0.466947i	$0.845354\pi$
$492$		0			0
$493$	−0.388252			−0.0174860
$494$		0			0
$495$	−8.00774			−0.359921
$496$		0			0
$497$	−27.6288	−	10.0561i	−1.23932	−	0.451076i
$498$		0			0
$499$	2.60220	+	14.7578i	0.116490	+	0.660649i	0.986002	+	0.166736i	$0.0533228\pi$
$499$	2.60220	+	14.7578i	0.116490	+	0.660649i	−0.869511	+	0.493913i	$0.835566\pi$
$500$		0			0
$501$	−5.36959	+	9.30039i	−0.239895	+	0.415511i
$502$		0			0
$503$	−13.5646	−	11.3821i	−0.604818	−	0.507502i	0.288173	−	0.957579i	$-0.406952\pi$
$503$	−13.5646	−	11.3821i	−0.604818	−	0.507502i	−0.892990	+	0.450076i	$0.851397\pi$
$504$		0			0
$505$	2.65136	+	4.59229i	0.117984	+	0.204354i
$506$		0			0
$507$	−0.610815	+	0.222318i	−0.0271272	+	0.00987350i
$508$		0			0
$509$	4.72715	−	26.8090i	0.209527	−	1.18829i	−0.680628	−	0.732629i	$-0.738293\pi$
$509$	4.72715	−	26.8090i	0.209527	−	1.18829i	0.890155	−	0.455658i	$-0.150596\pi$
$510$		0			0
$511$	−16.9402	+	14.2145i	−0.749389	+	0.628812i
$512$		0			0
$513$	0.819078	+	4.28125i	0.0361632	+	0.189022i
$514$		0			0
$515$	−12.7083	+	10.6635i	−0.559993	+	0.469890i
$516$		0			0
$517$	7.10014	−	40.2669i	0.312264	−	1.77094i
$518$		0			0
$519$	7.08512	−	2.57877i	0.311002	−	0.113196i
$520$		0			0
$521$	−10.2130	−	17.6895i	−0.447440	−	0.774989i	0.550778	−	0.834651i	$-0.314331\pi$
$521$	−10.2130	−	17.6895i	−0.447440	−	0.774989i	−0.998219	+	0.0596624i	$0.980998\pi$
$522$		0			0
$523$	−31.4957	−	26.4280i	−1.37721	−	1.15562i	−0.970231	−	0.242181i	$-0.922137\pi$
$523$	−31.4957	−	26.4280i	−1.37721	−	1.15562i	−0.406981	−	0.913437i	$-0.633418\pi$
$524$		0			0
$525$	3.84002	−	6.65111i	0.167592	−	0.290278i
$526$		0			0
$527$	0.0732627	+	0.415494i	0.00319137	+	0.0180992i
$528$		0			0
$529$	−18.9979	−	6.91468i	−0.825997	−	0.300638i
$530$		0			0
$531$	12.0496			0.522909
$532$		0			0
$533$	1.33687			0.0579061
$534$		0			0
$535$	17.0077	+	6.19031i	0.735309	+	0.267630i
$536$		0			0
$537$	4.57785	+	25.9623i	0.197549	+	1.12035i
$538$		0			0
$539$	−3.52094	+	6.09845i	−0.151658	+	0.262679i
$540$		0			0
$541$	−4.65064	−	3.90235i	−0.199947	−	0.167775i	0.537317	−	0.843381i	$-0.319438\pi$
$541$	−4.65064	−	3.90235i	−0.199947	−	0.167775i	−0.737264	+	0.675605i	$0.763882\pi$
$542$		0			0
$543$	−10.5458	−	18.2658i	−0.452562	−	0.783860i
$544$		0			0
$545$	−2.87211	+	1.04536i	−0.123028	+	0.0447784i
$546$		0			0
$547$	−4.13547	+	23.4534i	−0.176820	+	1.00280i	0.759203	+	0.650854i	$0.225589\pi$
$547$	−4.13547	+	23.4534i	−0.176820	+	1.00280i	−0.936022	+	0.351941i	$0.885522\pi$
$548$		0			0
$549$	4.73783	−	3.97551i	0.202205	−	0.169671i
$550$		0			0
$551$	−5.33733	−	8.94253i	−0.227378	−	0.380964i
$552$		0			0
$553$	−17.9088	+	15.0273i	−0.761559	+	0.639024i
$554$		0			0
$555$	−1.62449	+	9.21291i	−0.0689556	+	0.391066i
$556$		0			0
$557$	21.9094	−	7.97437i	0.928332	−	0.337885i	0.166784	−	0.985994i	$-0.446662\pi$
$557$	21.9094	−	7.97437i	0.928332	−	0.337885i	0.761548	+	0.648108i	$0.224440\pi$
$558$		0			0
$559$	−21.1578	−	36.6463i	−0.894878	−	1.54997i
$560$		0			0
$561$	0.739885	+	0.620838i	0.0312380	+	0.0262118i
$562$		0			0
$563$	−7.35369	+	12.7370i	−0.309921	+	0.536799i	−0.978345	−	0.206981i	$-0.933636\pi$
$563$	−7.35369	+	12.7370i	−0.309921	+	0.536799i	0.668424	+	0.743781i	$0.266969\pi$
$564$		0			0
$565$	−2.97359	−	16.8641i	−0.125100	−	0.709477i
$566$		0			0
$567$	−2.26604	−	0.824773i	−0.0951649	−	0.0346372i
$568$		0			0
$569$	32.6750			1.36981			0.684903	−	0.728634i	$-0.259844\pi$
$569$	32.6750			1.36981			0.684903	+	0.728634i	$0.259844\pi$
$570$		0			0
$571$	30.3901			1.27179			0.635893	−	0.771777i	$-0.280632\pi$
$571$	30.3901			1.27179			0.635893	+	0.771777i	$0.280632\pi$
$572$		0			0
$573$	0.240352	+	0.0874810i	0.0100409	+	0.00365457i
$574$		0			0
$575$	3.63563	+	20.6187i	0.151616	+	0.859858i
$576$		0			0
$577$	−15.4324	+	26.7297i	−0.642460	+	1.11277i	0.342422	+	0.939546i	$0.388753\pi$
$577$	−15.4324	+	26.7297i	−0.642460	+	1.11277i	−0.984882	+	0.173227i	$0.944581\pi$
$578$		0			0
$579$	10.9914	+	9.22286i	0.456786	+	0.383289i
$580$		0			0
$581$	−2.44444	−	4.23389i	−0.101412	−	0.175652i
$582$		0			0
$583$	22.4650	−	8.17658i	0.930404	−	0.338639i
$584$		0			0
$585$	−0.864370	+	4.90209i	−0.0357373	+	0.202676i
$586$		0			0
$587$	21.5804	−	18.1081i	0.890717	−	0.747401i	−0.0776365	−	0.996982i	$-0.524737\pi$
$587$	21.5804	−	18.1081i	0.890717	−	0.747401i	0.968354	+	0.249581i	$0.0802929\pi$
$588$		0			0
$589$	−8.56283	+	7.39928i	−0.352825	+	0.304882i
$590$		0			0
$591$	18.1407	−	15.2218i	0.746208	−	0.626143i
$592$		0			0
$593$	−1.18438	+	6.71696i	−0.0486367	+	0.275833i	−0.999421	−	0.0340206i	$-0.989169\pi$
$593$	−1.18438	+	6.71696i	−0.0486367	+	0.275833i	0.950784	+	0.309853i	$0.100280\pi$
$594$		0			0
$595$	0.496130	−	0.180576i	0.0203393	−	0.00740291i
$596$		0			0
$597$	5.89780	+	10.2153i	0.241381	+	0.418084i
$598$		0			0
$599$	−27.3562	−	22.9546i	−1.11774	−	0.937899i	−0.119256	−	0.992863i	$-0.538051\pi$
$599$	−27.3562	−	22.9546i	−1.11774	−	0.937899i	−0.998488	+	0.0549642i	$0.982496\pi$
$600$		0			0
$601$	−2.76399	+	4.78736i	−0.112745	+	0.195281i	−0.916876	−	0.399172i	$-0.869298\pi$
$601$	−2.76399	+	4.78736i	−0.112745	+	0.195281i	0.804131	+	0.594452i	$0.202631\pi$
$602$		0			0
$603$	−1.00000	−	5.67128i	−0.0407231	−	0.230952i
$604$		0			0
$605$	−30.7977	−	11.2095i	−1.25211	−	0.455729i
$606$		0			0
$607$	19.4953			0.791288			0.395644	−	0.918404i	$-0.370521\pi$
$607$	19.4953			0.791288			0.395644	+	0.918404i	$0.370521\pi$
$608$		0			0
$609$	5.76146			0.233466
$610$		0			0
$611$	−23.8837	−	8.69296i	−0.966232	−	0.351680i
$612$		0			0
$613$	6.86262	+	38.9198i	0.277178	+	1.57196i	0.731956	+	0.681352i	$0.238608\pi$
$613$	6.86262	+	38.9198i	0.277178	+	1.57196i	−0.454777	+	0.890605i	$0.650281\pi$
$614$		0			0
$615$	0.243756	−	0.422197i	0.00982918	−	0.0170246i
$616$		0			0
$617$	−0.952648	−	0.799367i	−0.0383522	−	0.0321813i	0.623410	−	0.781895i	$-0.285747\pi$
$617$	−0.952648	−	0.799367i	−0.0383522	−	0.0321813i	−0.661762	+	0.749714i	$0.730191\pi$
$618$		0			0
$619$	4.20187	+	7.27785i	0.168887	+	0.292521i	0.938029	−	0.346557i	$-0.112649\pi$
$619$	4.20187	+	7.27785i	0.168887	+	0.292521i	−0.769142	+	0.639078i	$0.779316\pi$
$620$		0			0
$621$	6.17752	−	2.24843i	0.247895	−	0.0902265i
$622$		0			0
$623$	1.44397	−	8.18918i	0.0578516	−	0.328093i
$624$		0			0
$625$	0.817267	−	0.685768i	0.0326907	−	0.0274307i
$626$		0			0
$627$	−4.12836	+	25.5763i	−0.164871	+	1.02142i
$628$		0			0
$629$	0.864370	−	0.725293i	0.0344647	−	0.0289193i
$630$		0			0
$631$	−1.61159	+	9.13976i	−0.0641562	+	0.363848i	0.935780	+	0.352584i	$0.114697\pi$
$631$	−1.61159	+	9.13976i	−0.0641562	+	0.363848i	−0.999937	+	0.0112645i	$0.996414\pi$
$632$		0			0
$633$	−26.1780	+	9.52801i	−1.04048	+	0.378704i
$634$		0			0
$635$	−5.20826	−	9.02098i	−0.206684	−	0.357987i
$636$		0			0
$637$	3.35323	+	2.81369i	0.132860	+	0.111482i
$638$		0			0
$639$	−6.09627	+	10.5590i	−0.241165	+	0.417709i
$640$		0			0
$641$	−1.51320	−	8.58180i	−0.0597680	−	0.338961i	0.940231	−	0.340538i	$-0.110609\pi$
$641$	−1.51320	−	8.58180i	−0.0597680	−	0.338961i	−0.999999	+	0.00157695i	$0.999498\pi$
$642$		0			0
$643$	14.2185	+	5.17512i	0.560724	+	0.204087i	0.606805	−	0.794851i	$-0.292451\pi$
$643$	14.2185	+	5.17512i	0.560724	+	0.204087i	−0.0460808	+	0.998938i	$0.514673\pi$
$644$		0			0
$645$	−15.4311			−0.607598
$646$		0			0
$647$	7.31282			0.287497			0.143748	−	0.989614i	$-0.454084\pi$
$647$	7.31282			0.287497			0.143748	+	0.989614i	$0.454084\pi$
$648$		0			0
$649$	67.2987	+	24.4947i	2.64170	+	0.961501i
$650$		0			0
$651$	−1.08718	−	6.16571i	−0.0426100	−	0.241653i
$652$		0			0
$653$	−8.76904	+	15.1884i	−0.343159	+	0.594369i	−0.985018	−	0.172454i	$-0.944830\pi$
$653$	−8.76904	+	15.1884i	−0.343159	+	0.594369i	0.641859	+	0.766823i	$0.278164\pi$
$654$		0			0
$655$	12.9704	+	10.8835i	0.506797	+	0.425253i
$656$		0			0
$657$	4.58512	+	7.94166i	0.178883	+	0.309834i
$658$		0			0
$659$	7.39693	−	2.69226i	0.288143	−	0.104876i	−0.193905	−	0.981020i	$-0.562115\pi$
$659$	7.39693	−	2.69226i	0.288143	−	0.104876i	0.482048	+	0.876145i	$0.339893\pi$
$660$		0			0
$661$	0.167414	−	0.949450i	0.00651164	−	0.0369293i	−0.981379	−	0.192082i	$-0.938476\pi$
$661$	0.167414	−	0.949450i	0.00651164	−	0.0369293i	0.987890	+	0.155153i	$0.0495871\pi$
$662$		0			0
$663$	0.459922	−	0.385920i	0.0178619	−	0.0149879i
$664$		0			0
$665$	10.9795	+	8.94486i	0.425768	+	0.346867i
$666$		0			0
$667$	−12.0318	+	10.0959i	−0.465875	+	0.390915i
$668$		0			0
$669$	−4.29561	+	24.3616i	−0.166078	+	0.941874i
$670$		0			0
$671$	34.5428	−	12.5726i	1.33351	−	0.485358i
$672$		0			0
$673$	12.9265	+	22.3893i	0.498280	+	0.863045i	0.999998	−	0.00198549i	$-0.000632002\pi$
$673$	12.9265	+	22.3893i	0.498280	+	0.863045i	−0.501719	+	0.865031i	$0.667299\pi$
$674$		0			0
$675$	−2.43969	−	2.04715i	−0.0939038	−	0.0787947i
$676$		0			0
$677$	−14.9978	+	25.9769i	−0.576411	+	0.998374i	0.419475	+	0.907767i	$0.362214\pi$
$677$	−14.9978	+	25.9769i	−0.576411	+	0.998374i	−0.995887	+	0.0906072i	$0.971119\pi$
$678$		0			0
$679$	5.06330	+	28.7154i	0.194312	+	1.10200i
$680$		0			0
$681$	20.6878	+	7.52974i	0.792758	+	0.288540i
$682$		0			0
$683$	33.5084			1.28216			0.641081	−	0.767473i	$-0.278486\pi$
$683$	33.5084			1.28216			0.641081	+	0.767473i	$0.278486\pi$
$684$		0			0
$685$	21.1661			0.808716
$686$		0			0
$687$	8.73530	+	3.17939i	0.333272	+	0.121301i
$688$		0			0
$689$	−2.58054	−	14.6350i	−0.0983106	−	0.557547i
$690$		0			0
$691$	6.40673	−	11.0968i	0.243723	−	0.422141i	−0.718049	−	0.695993i	$-0.754964\pi$
$691$	6.40673	−	11.0968i	0.243723	−	0.422141i	0.961772	+	0.273852i	$0.0882978\pi$
$692$		0			0
$693$	−10.9795	−	9.21291i	−0.417078	−	0.349970i
$694$		0			0
$695$	−2.17886	−	3.77390i	−0.0826490	−	0.143152i
$696$		0			0
$697$	−0.0552549	+	0.0201112i	−0.00209293	+	0.000761764i
$698$		0			0
$699$	−1.38713	+	7.86678i	−0.0524659	+	0.297549i
$700$		0			0
$701$	3.04323	−	2.55358i	0.114941	−	0.0964472i	−0.583505	−	0.812109i	$-0.698319\pi$
$701$	3.04323	−	2.55358i	0.114941	−	0.0964472i	0.698447	+	0.715662i	$0.253875\pi$
$702$		0			0
$703$	28.5881	+	9.93821i	1.07822	+	0.374827i
$704$		0			0
$705$	−7.10014	+	5.95772i	−0.267407	+	0.224381i
$706$		0			0
$707$	−1.64812	+	9.34694i	−0.0619839	+	0.351528i
$708$		0			0
$709$	−30.3572	+	11.0491i	−1.14009	+	0.414958i	−0.841945	−	0.539564i	$-0.818589\pi$
$709$	−30.3572	+	11.0491i	−1.14009	+	0.414958i	−0.298142	+	0.954521i	$0.596367\pi$
$710$		0			0
$711$	4.84730	+	8.39576i	0.181788	+	0.314866i
$712$		0			0
$713$	13.0747	+	10.9710i	0.489651	+	0.410866i
$714$		0			0
$715$	−14.7927	+	25.6217i	−0.553215	+	0.958196i
$716$		0			0
$717$	−4.59286	−	26.0474i	−0.171524	−	0.972759i
$718$		0			0
$719$	−42.5385	−	15.4828i	−1.58642	−	0.577410i	−0.609832	−	0.792530i	$-0.708763\pi$
$719$	−42.5385	−	15.4828i	−1.58642	−	0.577410i	−0.976587	+	0.215121i	$0.930985\pi$
$720$		0			0
$721$	−29.6928			−1.10582
$722$		0			0
$723$	−2.73917			−0.101871
$724$		0			0
$725$	7.15018	+	2.60245i	0.265551	+	0.0966526i
$726$		0			0
$727$	−3.85188	−	21.8451i	−0.142858	−	0.810190i	−0.969062	−	0.246818i	$-0.920615\pi$
$727$	−3.85188	−	21.8451i	−0.142858	−	0.810190i	0.826203	−	0.563372i	$-0.190496\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	1.42577	+	1.19637i	0.0527341	+	0.0442492i
$732$		0			0
$733$	−22.9106	−	39.6823i	−0.846222	−	1.46570i	−0.884556	−	0.466435i	$-0.845538\pi$
$733$	−22.9106	−	39.6823i	−0.846222	−	1.46570i	0.0383334	−	0.999265i	$-0.487795\pi$
$734$		0			0
$735$	1.50000	−	0.545955i	0.0553283	−	0.0201379i
$736$		0			0
$737$	5.94356	−	33.7076i	0.218934	−	1.24164i
$738$		0			0
$739$	−2.89124	+	2.42604i	−0.106356	+	0.0892434i	−0.694415	−	0.719575i	$-0.744337\pi$
$739$	−2.89124	+	2.42604i	−0.106356	+	0.0892434i	0.588059	+	0.808818i	$0.299892\pi$
$740$		0			0
$741$	15.2114	+	5.28801i	0.558805	+	0.194260i
$742$		0			0
$743$	−17.2251	+	14.4536i	−0.631927	+	0.530250i	−0.901527	−	0.432723i	$-0.857553\pi$
$743$	−17.2251	+	14.4536i	−0.631927	+	0.530250i	0.269600	+	0.962972i	$0.413109\pi$
$744$		0			0
$745$	1.04348	−	5.91788i	0.0382302	−	0.216814i
$746$		0			0
$747$	−1.90508	+	0.693392i	−0.0697031	+	0.0253699i
$748$		0			0
$749$	16.1976	+	28.0550i	0.591847	+	1.02511i
$750$		0			0
$751$	−31.7879	−	26.6732i	−1.15996	−	0.973320i	−0.160053	−	0.987108i	$-0.551166\pi$
$751$	−31.7879	−	26.6732i	−1.15996	−	0.973320i	−0.999905	+	0.0137883i	$0.995611\pi$
$752$		0			0
$753$	−7.61468	+	13.1890i	−0.277495	+	0.480635i
$754$		0			0
$755$	2.09358	+	11.8733i	0.0761931	+	0.432113i
$756$		0			0
$757$	16.8037	+	6.11603i	0.610739	+	0.222291i	0.628827	−	0.777546i	$-0.283536\pi$
$757$	16.8037	+	6.11603i	0.610739	+	0.222291i	−0.0180875	+	0.999836i	$0.505758\pi$
$758$		0			0
$759$	39.0729			1.41825
$760$		0			0
$761$	38.0806			1.38042			0.690210	−	0.723609i	$-0.257518\pi$
$761$	38.0806			1.38042			0.690210	+	0.723609i	$0.257518\pi$
$762$		0			0
$763$	−5.14068	−	1.87106i	−0.186105	−	0.0677367i
$764$		0			0
$765$	−0.0380187	−	0.215615i	−0.00137457	−	0.00779556i
$766$		0			0
$767$	22.2592	−	38.5541i	0.803734	−	1.39211i
$768$		0			0
$769$	−9.67096	−	8.11490i	−0.348744	−	0.292631i	0.451542	−	0.892250i	$-0.350874\pi$
$769$	−9.67096	−	8.11490i	−0.348744	−	0.292631i	−0.800285	+	0.599619i	$0.795319\pi$
$770$		0			0
$771$	−6.51754	−	11.2887i	−0.234724	−	0.406553i
$772$		0			0
$773$	−31.7606	+	11.5599i	−1.14235	+	0.415781i	−0.842761	−	0.538288i	$-0.819071\pi$
$773$	−31.7606	+	11.5599i	−1.14235	+	0.415781i	−0.299588	+	0.954069i	$0.596849\pi$
$774$		0			0
$775$	1.43582	−	8.14295i	0.0515763	−	0.292503i
$776$		0			0
$777$	−12.8268	+	10.7630i	−0.460160	+	0.386120i
$778$		0			0
$779$	−1.22281	−	0.996206i	−0.0438118	−	0.0356928i
$780$		0			0
$781$	−55.5130	+	46.5809i	−1.98641	+	1.66680i
$782$		0			0
$783$	0.414878	−	2.35289i	0.0148265	−	0.0840854i
$784$		0			0
$785$	14.5851	−	5.30855i	0.520565	−	0.189470i
$786$		0			0
$787$	16.8059	+	29.1086i	0.599065	+	1.03761i	0.992959	+	0.118455i	$0.0377941\pi$
$787$	16.8059	+	29.1086i	0.599065	+	1.03761i	−0.393895	+	0.919156i	$0.628873\pi$
$788$		0			0
$789$	−9.13610	−	7.66610i	−0.325254	−	0.272920i
$790$		0			0
$791$	15.3250	−	26.5437i	0.544895	−	0.943785i
$792$		0			0
$793$	−3.96791	−	22.5031i	−0.140905	−	0.799110i
$794$		0			0
$795$	−5.09240	−	1.85348i	−0.180609	−	0.0657362i
$796$		0			0
$797$	−46.0547			−1.63134			−0.815670	−	0.578517i	$-0.803632\pi$
$797$	−46.0547			−1.63134			−0.815670	+	0.578517i	$0.803632\pi$
$798$		0			0
$799$	1.11793			0.0395494
$800$		0			0
$801$	−3.24035	−	1.17939i	−0.114492	−	0.0416718i
$802$		0			0
$803$	9.46451	+	53.6759i	0.333995	+	1.89418i
$804$		0			0
$805$	10.6793	−	18.4971i	0.376397	−	0.651939i
$806$		0			0
$807$	19.8084	+	16.6212i	0.697289	+	0.585095i
$808$		0			0
$809$	−20.1853	−	34.9619i	−0.709676	−	1.22919i	−0.964977	−	0.262333i	$-0.915508\pi$
$809$	−20.1853	−	34.9619i	−0.709676	−	1.22919i	0.255301	−	0.966862i	$-0.417825\pi$
$810$		0			0
$811$	48.4744	−	17.6432i	1.70217	−	0.619537i	0.706096	−	0.708116i	$-0.250455\pi$
$811$	48.4744	−	17.6432i	1.70217	−	0.619537i	0.996069	+	0.0885787i	$0.0282325\pi$
$812$		0			0
$813$	2.06165	−	11.6922i	0.0723053	−	0.410064i
$814$		0			0
$815$	−10.8621	+	9.11435i	−0.380481	+	0.319262i
$816$		0			0
$817$	−7.95542	+	49.2861i	−0.278325	+	1.72430i
$818$		0			0
$819$	−6.82501	+	5.72686i	−0.238485	+	0.200113i
$820$		0			0
$821$	6.91622	−	39.2238i	0.241378	−	1.36892i	−0.587379	−	0.809312i	$-0.699840\pi$
$821$	6.91622	−	39.2238i	0.241378	−	1.36892i	0.828757	−	0.559609i	$-0.189049\pi$
$822$		0			0
$823$	17.8293	−	6.48935i	0.621492	−	0.226205i	−0.0120321	−	0.999928i	$-0.503830\pi$
$823$	17.8293	−	6.48935i	0.621492	−	0.226205i	0.633524	+	0.773723i	$0.281608\pi$
$824$		0			0
$825$	−9.46451	−	16.3930i	−0.329512	−	0.570731i
$826$		0			0
$827$	−3.76810	−	3.16181i	−0.131030	−	0.109947i	0.574918	−	0.818211i	$-0.305034\pi$
$827$	−3.76810	−	3.16181i	−0.131030	−	0.109947i	−0.705947	+	0.708264i	$0.749479\pi$
$828$		0			0
$829$	16.6400	−	28.8213i	0.577930	−	1.00100i	−0.417787	−	0.908545i	$-0.637194\pi$
$829$	16.6400	−	28.8213i	0.577930	−	1.00100i	0.995717	−	0.0924588i	$-0.0294726\pi$
$830$		0			0
$831$	2.50253	+	14.1925i	0.0868117	+	0.492333i
$832$		0			0
$833$	−0.180922	−	0.0658503i	−0.00626858	−	0.00228158i
$834$		0			0
$835$	14.4688			0.500715
$836$		0			0
$837$	−2.59627			−0.0897401
$838$		0			0
$839$	−17.3846	−	6.32748i	−0.600183	−	0.218449i	0.0240193	−	0.999711i	$-0.492354\pi$
$839$	−17.3846	−	6.32748i	−0.600183	−	0.218449i	−0.624202	+	0.781263i	$0.714576\pi$
$840$		0			0
$841$	−4.04458	−	22.9379i	−0.139468	−	0.790963i
$842$		0			0
$843$	1.31567	−	2.27881i	0.0453142	−	0.0784865i
$844$		0			0
$845$	0.670874	+	0.562930i	0.0230788	+	0.0193654i
$846$		0			0
$847$	−29.3307	−	50.8022i	−1.00781	−	1.74559i
$848$		0			0
$849$	−5.72416	+	2.08342i	−0.196453	+	0.0715029i
$850$		0			0
$851$	7.92649	−	44.9534i	0.271717	−	1.54098i
$852$		0			0
$853$	6.64749	−	5.57791i	0.227606	−	0.190984i	−0.521852	−	0.853036i	$-0.674759\pi$
$853$	6.64749	−	5.57791i	0.227606	−	0.190984i	0.749458	+	0.662052i	$0.230314\pi$
$854$		0			0
$855$	4.44356	−	3.83975i	0.151967	−	0.131317i
$856$		0			0
$857$	−20.6958	+	17.3658i	−0.706954	+	0.593205i	−0.923743	−	0.383014i	$-0.874886\pi$
$857$	−20.6958	+	17.3658i	−0.706954	+	0.593205i	0.216789	+	0.976219i	$0.430442\pi$
$858$		0			0
$859$	−8.89069	+	50.4216i	−0.303346	+	1.72036i	0.327841	+	0.944733i	$0.393679\pi$
$859$	−8.89069	+	50.4216i	−0.303346	+	1.72036i	−0.631187	+	0.775630i	$0.717432\pi$
$860$		0			0
$861$	0.819955	−	0.298439i	0.0279440	−	0.0101708i
$862$		0			0
$863$	−9.58037	−	16.5937i	−0.326120	−	0.564856i	0.655619	−	0.755092i	$-0.272408\pi$
$863$	−9.58037	−	16.5937i	−0.326120	−	0.564856i	−0.981738	+	0.190236i	$0.939075\pi$
$864$		0			0
$865$	−7.78177	−	6.52968i	−0.264588	−	0.222016i
$866$		0			0
$867$	8.48680	−	14.6996i	0.288227	−	0.499223i
$868$		0			0
$869$	10.0057	+	56.7450i	0.339419	+	1.92494i
$870$		0			0
$871$	−19.9932	−	7.27693i	−0.677443	−	0.246569i
$872$		0			0
$873$	12.0915			0.409236
$874$		0			0
$875$	−26.5921			−0.898979
$876$		0			0
$877$	−50.1061	−	18.2371i	−1.69196	−	0.615824i	−0.697093	−	0.716981i	$-0.745524\pi$
$877$	−50.1061	−	18.2371i	−1.69196	−	0.615824i	−0.994871	+	0.101156i	$0.967746\pi$
$878$		0			0
$879$	−5.68361	−	32.2334i	−0.191703	−	1.08720i
$880$		0			0
$881$	0.336619	−	0.583041i	0.0113410	−	0.0196431i	−0.860299	−	0.509789i	$-0.829723\pi$
$881$	0.336619	−	0.583041i	0.0113410	−	0.0196431i	0.871640	+	0.490146i	$0.163057\pi$
$882$		0			0
$883$	7.50047	+	6.29364i	0.252411	+	0.211798i	0.760210	−	0.649678i	$-0.225096\pi$
$883$	7.50047	+	6.29364i	0.252411	+	0.211798i	−0.507799	+	0.861476i	$0.669541\pi$
$884$		0			0
$885$	−8.11721	−	14.0594i	−0.272857	−	0.472602i
$886$		0			0
$887$	8.26429	−	3.00796i	0.277488	−	0.100997i	−0.199528	−	0.979892i	$-0.563941\pi$
$887$	8.26429	−	3.00796i	0.277488	−	0.100997i	0.477015	+	0.878895i	$0.341719\pi$
$888$		0			0
$889$	3.23752	−	18.3609i	0.108583	−	0.615805i
$890$		0			0
$891$	−4.55303	+	3.82045i	−0.152532	+	0.127990i
$892$		0			0
$893$	15.3682	+	25.7490i	0.514279	+	0.861657i
$894$		0			0
$895$	27.2087	−	22.8308i	0.909488	−	0.763151i
$896$		0			0
$897$	4.21760	−	23.9192i	0.140821	−	0.798638i
$898$		0			0
$899$	5.82888	−	2.12154i	0.194404	−	0.0707573i
$900$		0			0
$901$	0.326819	+	0.566067i	0.0108879	+	0.0188584i
$902$		0			0
$903$	−21.1578	−	17.7535i	−0.704086	−	0.590798i
$904$		0			0
$905$	−14.2083	+	24.6094i	−0.472299	+	0.818045i
$906$		0			0
$907$	−1.00681	−	5.70989i	−0.0334305	−	0.189594i	0.963519	−	0.267639i	$-0.0862433\pi$
$907$	−1.00681	−	5.70989i	−0.0334305	−	0.189594i	−0.996950	+	0.0780450i	$0.975132\pi$
$908$		0			0
$909$	3.69846	+	1.34613i	0.122670	+	0.0446483i
$910$		0			0
$911$	−16.9145			−0.560401			−0.280201	−	0.959941i	$-0.590401\pi$
$911$	−16.9145			−0.560401			−0.280201	+	0.959941i	$0.590401\pi$
$912$		0			0
$913$	−12.0496			−0.398785
$914$		0			0
$915$	−7.83022	−	2.84997i	−0.258859	−	0.0942170i
$916$		0			0
$917$	5.26248	+	29.8450i	0.173782	+	0.985569i
$918$		0			0
$919$	18.4379	−	31.9354i	0.608211	−	1.05345i	−0.383324	−	0.923614i	$-0.625221\pi$
$919$	18.4379	−	31.9354i	0.608211	−	1.05345i	0.991535	−	0.129839i	$-0.0414461\pi$
$920$		0			0
$921$	−4.75671	−	3.99135i	−0.156739	−	0.131520i
$922$		0			0
$923$	22.5232	+	39.0114i	0.741361	+	1.28407i
$924$		0			0
$925$	−20.7802	+	7.56337i	−0.683248	+	0.248682i
$926$		0			0
$927$	−2.13816	+	12.1261i	−0.0702262	+	0.398273i
$928$		0			0
$929$	23.0096	−	19.3073i	0.754919	−	0.633452i	−0.181880	−	0.983321i	$-0.558218\pi$
$929$	23.0096	−	19.3073i	0.754919	−	0.633452i	0.936799	+	0.349869i	$0.113774\pi$
$930$		0			0
$931$	−0.970437	−	5.07239i	−0.0318048	−	0.166241i
$932$		0			0
$933$	2.37939	−	1.99654i	0.0778976	−	0.0653638i
$934$		0			0
$935$	0.225966	−	1.28152i	0.00738989	−	0.0419102i
$936$		0			0
$937$	3.95249	−	1.43859i	0.129122	−	0.0469966i	−0.276651	−	0.960970i	$-0.589225\pi$
$937$	3.95249	−	1.43859i	0.129122	−	0.0469966i	0.405773	+	0.913974i	$0.367002\pi$
$938$		0			0
$939$	8.43629	+	14.6121i	0.275308	+	0.476847i
$940$		0			0
$941$	−27.4329	−	23.0189i	−0.894287	−	0.750395i	0.0747787	−	0.997200i	$-0.476175\pi$
$941$	−27.4329	−	23.0189i	−0.894287	−	0.750395i	−0.969065	+	0.246805i	$0.920619\pi$
$942$		0			0
$943$	−1.18938	+	2.06006i	−0.0387315	+	0.0670849i
$944$		0			0
$945$	0.564178	+	3.19961i	0.0183527	+	0.104083i
$946$		0			0
$947$	9.82073	+	3.57445i	0.319131	+	0.116154i	0.496619	−	0.867969i	$-0.334575\pi$
$947$	9.82073	+	3.57445i	0.319131	+	0.116154i	−0.177488	+	0.984123i	$0.556797\pi$
$948$		0			0
$949$	33.8803			1.09980
$950$		0			0
$951$	14.4260			0.467796
$952$		0			0
$953$	−20.3097	−	7.39214i	−0.657897	−	0.239455i	−0.00856895	−	0.999963i	$-0.502728\pi$
$953$	−20.3097	−	7.39214i	−0.657897	−	0.239455i	−0.649328	+	0.760508i	$0.724950\pi$
$954$		0			0
$955$	−0.0598406	−	0.339373i	−0.00193639	−	0.0109818i
$956$		0			0
$957$	7.10014	−	12.2978i	0.229515	−	0.397531i
$958$		0			0
$959$	29.0212	+	24.3516i	0.937142	+	0.786356i
$960$		0			0
$961$	12.1297	+	21.0093i	0.391281	+	0.677718i
$962$		0			0
$963$	12.6236	−	4.59462i	0.406790	−	0.148059i
$964$		0			0
$965$	3.35685	−	19.0376i	0.108061	−	0.612843i
$966$		0			0
$967$	6.98751	−	5.86322i	0.224703	−	0.188548i	−0.523485	−	0.852035i	$-0.675368\pi$
$967$	6.98751	−	5.86322i	0.224703	−	0.188548i	0.748188	+	0.663486i	$0.230924\pi$
$968$		0			0
$969$	−0.708263	+	0.0102707i	−0.0227527	+	0.000329942i
$970$		0			0
$971$	−37.3999	+	31.3823i	−1.20022	+	1.00710i	−0.200597	+	0.979674i	$0.564288\pi$
$971$	−37.3999	+	31.3823i	−1.20022	+	1.00710i	−0.999624	+	0.0274307i	$0.991267\pi$
$972$		0			0
$973$	1.35441	−	7.68123i	0.0434203	−	0.246249i
$974$		0			0
$975$	−11.0569	+	4.02438i	−0.354104	+	0.128883i
$976$		0			0
$977$	−1.31268	−	2.27363i	−0.0419964	−	0.0727399i	0.844263	−	0.535929i	$-0.180038\pi$
$977$	−1.31268	−	2.27363i	−0.0419964	−	0.0727399i	−0.886260	+	0.463189i	$0.846705\pi$
$978$		0			0
$979$	−15.7003	−	13.1741i	−0.501783	−	0.421046i
$980$		0			0
$981$	−1.13429	+	1.96464i	−0.0362149	+	0.0627261i
$982$		0			0
$983$	1.86262	+	10.5634i	0.0594082	+	0.336921i	0.999997	−	0.00262836i	$-0.000836635\pi$
$983$	1.86262	+	10.5634i	0.0594082	+	0.336921i	−0.940588	+	0.339549i	$0.889726\pi$
$984$		0			0
$985$	−29.9812	−	10.9123i	−0.955280	−	0.347693i
$986$		0			0
$987$	−16.5895			−0.528048
$988$		0			0
$989$	75.2942			2.39421
$990$		0			0
$991$	−53.1656	−	19.3507i	−1.68886	−	0.614695i	−0.694378	−	0.719610i	$-0.744321\pi$
$991$	−53.1656	−	19.3507i	−1.68886	−	0.614695i	−0.994481	+	0.104916i	$0.966543\pi$
$992$		0			0
$993$	−1.56237	−	8.86062i	−0.0495802	−	0.281183i
$994$		0			0
$995$	7.94609	−	13.7630i	0.251908	−	0.436317i
$996$		0			0
$997$	8.46791	+	7.10542i	0.268181	+	0.225031i	0.766954	−	0.641702i	$-0.221771\pi$
$997$	8.46791	+	7.10542i	0.268181	+	0.225031i	−0.498773	+	0.866733i	$0.666216\pi$
$998$		0			0
$999$	3.47178	+	6.01330i	0.109842	+	0.190252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.q.a.25.1	✓	6
3.2	odd	2		684.2.bo.a.253.1		6
4.3	odd	2		912.2.bo.e.481.1		6
19.4	even	9		4332.2.a.o.1.2		3
19.15	odd	18		4332.2.a.n.1.2		3
19.16	even	9	inner	228.2.q.a.73.1	yes	6
57.35	odd	18		684.2.bo.a.73.1		6
76.35	odd	18		912.2.bo.e.529.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.q.a.25.1	✓	6	1.1	even	1	trivial
228.2.q.a.73.1	yes	6	19.16	even	9	inner
684.2.bo.a.73.1		6	57.35	odd	18
684.2.bo.a.253.1		6	3.2	odd	2
912.2.bo.e.481.1		6	4.3	odd	2
912.2.bo.e.529.1		6	76.35	odd	18
4332.2.a.n.1.2		3	19.15	odd	18
4332.2.a.o.1.2		3	19.4	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)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{3} +(0.233956 + 1.32683i) q^{5} +(-1.20574 + 2.08840i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{3} +(0.233956 + 1.32683i) q^{5} +(-1.20574 + 2.08840i) q^{7} +(0.766044 + 0.642788i) q^{9} +(2.97178 + 5.14728i) q^{11} +(3.47178 - 1.26363i) q^{13} +(0.233956 - 1.32683i) q^{15} +(-0.124485 + 0.104455i) q^{17} +(-4.11721 - 1.43128i) q^{19} +(1.84730 - 1.55007i) q^{21} +(-1.14156 + 6.47410i) q^{23} +(2.99273 - 1.08926i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(1.83022 + 1.53574i) q^{29} +(1.29813 - 2.24843i) q^{31} +(-1.03209 - 5.85327i) q^{33} +(-3.05303 - 1.11121i) q^{35} -6.94356 q^{37} -3.69459 q^{39} +(0.340022 + 0.123758i) q^{41} +(-1.98886 - 11.2794i) q^{43} +(-0.673648 + 1.16679i) q^{45} +(-5.26991 - 4.42198i) q^{47} +(0.592396 + 1.02606i) q^{49} +(0.152704 - 0.0555796i) q^{51} +(0.698463 - 3.96118i) q^{53} +(-6.13429 + 5.14728i) q^{55} +(3.37939 + 2.75314i) q^{57} +(9.23055 - 7.74535i) q^{59} +(1.07398 - 6.09083i) q^{61} +(-2.26604 + 0.824773i) q^{63} +(2.48886 + 4.31082i) q^{65} +(-4.41147 - 3.70167i) q^{67} +(3.28699 - 5.69323i) q^{69} +(2.11721 + 12.0073i) q^{71} +(8.61721 + 3.13641i) q^{73} -3.18479 q^{75} -14.3327 q^{77} +(9.10994 + 3.31575i) q^{79} +(0.173648 + 0.984808i) q^{81} +(-1.01367 + 1.75573i) q^{83} +(-0.167718 - 0.140732i) q^{85} +(-1.19459 - 2.06910i) q^{87} +(-3.24035 + 1.17939i) q^{89} +(-1.54710 + 8.77406i) q^{91} +(-1.98886 + 1.66885i) q^{93} +(0.935822 - 5.79769i) q^{95} +(9.26264 - 7.77228i) q^{97} +(-1.03209 + 5.85327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{5} + 3 q^{7}+O(q^{10}) \) 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

L-functions

Modular forms

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Database

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